Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [45,9,Mod(28,45)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("45.28");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 45 = 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 45.g (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: | \(18.3320374528\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 3006 x^{14} + 3660359 x^{12} + 2360769624 x^{10} + 888292333775 x^{8} + 201214811046486 x^{6} + \cdots + 60\!\cdots\!84 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{14}\cdot 3^{12}\cdot 5^{19} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 37.2 | ||
Root | \(-14.3888i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 45.37 |
Dual form | 45.9.g.b.28.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(37\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −15.1900 | − | 15.1900i | −0.949373 | − | 0.949373i | 0.0494054 | − | 0.998779i | \(-0.484267\pi\) |
−0.998779 | + | 0.0494054i | \(0.984267\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 205.471i | 0.802620i | ||||||||
\(5\) | −115.601 | + | 614.216i | −0.184961 | + | 0.982746i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 605.930 | + | 605.930i | 0.252366 | + | 0.252366i | 0.821940 | − | 0.569574i | \(-0.192892\pi\) |
−0.569574 | + | 0.821940i | \(0.692892\pi\) | |||||||
\(8\) | −767.539 | + | 767.539i | −0.187387 | + | 0.187387i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 11085.9 | − | 7573.95i | 1.10859 | − | 0.757395i | ||||
\(11\) | −4284.92 | −0.292666 | −0.146333 | − | 0.989235i | \(-0.546747\pi\) | ||||
−0.146333 | + | 0.989235i | \(0.546747\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 28977.7 | − | 28977.7i | 1.01459 | − | 1.01459i | 0.0146990 | − | 0.999892i | \(-0.495321\pi\) |
0.999892 | − | 0.0146990i | \(-0.00467901\pi\) | |||||||
\(14\) | − | 18408.1i | − | 0.479178i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 75918.3 | 1.15842 | ||||||||
\(17\) | −49977.7 | − | 49977.7i | −0.598385 | − | 0.598385i | 0.341498 | − | 0.939883i | \(-0.389066\pi\) |
−0.939883 | + | 0.341498i | \(0.889066\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 12625.1i | 0.0968771i | 0.998826 | + | 0.0484385i | \(0.0154245\pi\) | ||||
−0.998826 | + | 0.0484385i | \(0.984576\pi\) | |||||||
\(20\) | −126203. | − | 23752.6i | −0.788771 | − | 0.148454i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 65087.8 | + | 65087.8i | 0.277849 | + | 0.277849i | ||||
\(23\) | −104680. | + | 104680.i | −0.374071 | + | 0.374071i | −0.868958 | − | 0.494887i | \(-0.835210\pi\) |
0.494887 | + | 0.868958i | \(0.335210\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −363898. | − | 142008.i | −0.931579 | − | 0.363540i | ||||
\(26\) | −880342. | −1.92645 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −124501. | + | 124501.i | −0.202554 | + | 0.202554i | ||||
\(29\) | − | 640943.i | − | 0.906207i | −0.891458 | − | 0.453103i | \(-0.850317\pi\) | ||
0.891458 | − | 0.453103i | \(-0.149683\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.30632e6 | −1.41450 | −0.707248 | − | 0.706966i | \(-0.750063\pi\) | ||||
−0.707248 | + | 0.706966i | \(0.750063\pi\) | |||||||
\(32\) | −956707. | − | 956707.i | −0.912387 | − | 0.912387i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.51832e6i | 1.13618i | ||||||||
\(35\) | −442218. | + | 302126.i | −0.294689 | + | 0.201333i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 311959. | + | 311959.i | 0.166453 | + | 0.166453i | 0.785418 | − | 0.618965i | \(-0.212448\pi\) |
−0.618965 | + | 0.785418i | \(0.712448\pi\) | |||||||
\(38\) | 191775. | − | 191775.i | 0.0919725 | − | 0.0919725i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −382707. | − | 560163.i | −0.149495 | − | 0.218814i | ||||
\(41\) | −3.20281e6 | −1.13343 | −0.566716 | − | 0.823913i | \(-0.691786\pi\) | ||||
−0.566716 | + | 0.823913i | \(0.691786\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.12468e6 | − | 4.12468e6i | 1.20647 | − | 1.20647i | 0.234308 | − | 0.972162i | \(-0.424717\pi\) |
0.972162 | − | 0.234308i | \(-0.0752825\pi\) | |||||||
\(44\) | − | 880425.i | − | 0.234899i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.18019e6 | 0.710266 | ||||||||
\(47\) | 3.49502e6 | + | 3.49502e6i | 0.716240 | + | 0.716240i | 0.967833 | − | 0.251593i | \(-0.0809545\pi\) |
−0.251593 | + | 0.967833i | \(0.580955\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 5.03050e6i | − | 0.872623i | ||||||
\(50\) | 3.37050e6 | + | 7.68470e6i | 0.539281 | + | 1.22955i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.95407e6 | + | 5.95407e6i | 0.814331 | + | 0.814331i | ||||
\(53\) | 9.08340e6 | − | 9.08340e6i | 1.15118 | − | 1.15118i | 0.164869 | − | 0.986316i | \(-0.447280\pi\) |
0.986316 | − | 0.164869i | \(-0.0527201\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 495340. | − | 2.63186e6i | 0.0541318 | − | 0.287616i | ||||
\(56\) | −930149. | −0.0945803 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −9.73590e6 | + | 9.73590e6i | −0.860329 | + | 0.860329i | ||||
\(59\) | − | 1.10425e7i | − | 0.911295i | −0.890160 | − | 0.455647i | \(-0.849408\pi\) | ||
0.890160 | − | 0.455647i | \(-0.150592\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.13283e7 | −0.818173 | −0.409086 | − | 0.912496i | \(-0.634152\pi\) | ||||
−0.409086 | + | 0.912496i | \(0.634152\pi\) | |||||||
\(62\) | 1.98429e7 | + | 1.98429e7i | 1.34288 | + | 1.34288i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 9.62963e6i | 0.573971i | ||||||||
\(65\) | 1.44487e7 | + | 2.11484e7i | 0.809425 | + | 1.18475i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.93890e7 | − | 1.93890e7i | −0.962178 | − | 0.962178i | 0.0371324 | − | 0.999310i | \(-0.488178\pi\) |
−0.999310 | + | 0.0371324i | \(0.988178\pi\) | |||||||
\(68\) | 1.02689e7 | − | 1.02689e7i | 0.480275 | − | 0.480275i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.13066e7 | + | 2.12800e6i | 0.470911 | + | 0.0886295i | ||||
\(71\) | −2.80078e7 | −1.10216 | −0.551081 | − | 0.834452i | \(-0.685784\pi\) | ||||
−0.551081 | + | 0.834452i | \(0.685784\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.13453e7 | + | 2.13453e7i | −0.751640 | + | 0.751640i | −0.974785 | − | 0.223145i | \(-0.928368\pi\) |
0.223145 | + | 0.974785i | \(0.428368\pi\) | |||||||
\(74\) | − | 9.47731e6i | − | 0.316052i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.59409e6 | −0.0777555 | ||||||||
\(77\) | −2.59636e6 | − | 2.59636e6i | −0.0738587 | − | 0.0738587i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 3.60404e7i | − | 0.925297i | −0.886542 | − | 0.462649i | \(-0.846899\pi\) | ||
0.886542 | − | 0.462649i | \(-0.153101\pi\) | |||||||
\(80\) | −8.77622e6 | + | 4.66302e7i | −0.214263 | + | 1.13843i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.86506e7 | + | 4.86506e7i | 1.07605 | + | 1.07605i | ||||
\(83\) | 4.88658e7 | − | 4.88658e7i | 1.02966 | − | 1.02966i | 0.0301106 | − | 0.999547i | \(-0.490414\pi\) |
0.999547 | − | 0.0301106i | \(-0.00958596\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.64746e7 | − | 2.49196e7i | 0.698738 | − | 0.477382i | ||||
\(86\) | −1.25308e8 | −2.29078 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.28884e6 | − | 3.28884e6i | 0.0548418 | − | 0.0548418i | ||||
\(89\) | − | 9.25997e7i | − | 1.47588i | −0.674869 | − | 0.737938i | \(-0.735800\pi\) | ||
0.674869 | − | 0.737938i | \(-0.264200\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.51169e7 | 0.512096 | ||||||||
\(92\) | −2.15088e7 | − | 2.15088e7i | −0.300237 | − | 0.300237i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 1.06179e8i | − | 1.35996i | ||||||
\(95\) | −7.75455e6 | − | 1.45947e6i | −0.0952055 | − | 0.0179185i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.68733e7 | + | 5.68733e7i | 0.642424 | + | 0.642424i | 0.951151 | − | 0.308727i | \(-0.0999029\pi\) |
−0.308727 | + | 0.951151i | \(0.599903\pi\) | |||||||
\(98\) | −7.64132e7 | + | 7.64132e7i | −0.828445 | + | 0.828445i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.91785e7 | − | 7.47703e7i | 0.291785 | − | 0.747703i | ||||
\(101\) | −5.83352e7 | −0.560590 | −0.280295 | − | 0.959914i | \(-0.590432\pi\) | ||||
−0.280295 | + | 0.959914i | \(0.590432\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.89632e6 | + | 6.89632e6i | −0.0612730 | + | 0.0612730i | −0.737079 | − | 0.675806i | \(-0.763796\pi\) |
0.675806 | + | 0.737079i | \(0.263796\pi\) | |||||||
\(104\) | 4.44831e7i | 0.380243i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.75953e8 | −2.18581 | ||||||||
\(107\) | −4.16325e7 | − | 4.16325e7i | −0.317612 | − | 0.317612i | 0.530237 | − | 0.847849i | \(-0.322103\pi\) |
−0.847849 | + | 0.530237i | \(0.822103\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.43647e8i | 1.72606i | 0.505153 | + | 0.863030i | \(0.331436\pi\) | ||||
−0.505153 | + | 0.863030i | \(0.668564\pi\) | |||||||
\(110\) | −4.75022e7 | + | 3.24538e7i | −0.324446 | + | 0.221663i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.60012e7 | + | 4.60012e7i | 0.292346 | + | 0.292346i | ||||
\(113\) | 8.19194e7 | − | 8.19194e7i | 0.502427 | − | 0.502427i | −0.409764 | − | 0.912191i | \(-0.634389\pi\) |
0.912191 | + | 0.409764i | \(0.134389\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.21952e7 | − | 7.63975e7i | −0.298428 | − | 0.436805i | ||||
\(116\) | 1.31695e8 | 0.727340 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.67735e8 | + | 1.67735e8i | −0.865159 | + | 0.865159i | ||||
\(119\) | − | 6.05659e7i | − | 0.302023i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.95998e8 | −0.914347 | ||||||||
\(122\) | 1.72076e8 | + | 1.72076e8i | 0.776751 | + | 0.776751i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 2.68410e8i | − | 1.13530i | ||||||
\(125\) | 1.29290e8 | − | 2.07096e8i | 0.529574 | − | 0.848264i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.58603e8 | + | 3.58603e8i | 1.37848 | + | 1.37848i | 0.847197 | + | 0.531278i | \(0.178288\pi\) |
0.531278 | + | 0.847197i | \(0.321712\pi\) | |||||||
\(128\) | −9.86432e7 | + | 9.86432e7i | −0.367474 | + | 0.367474i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.01768e8 | − | 5.40720e8i | 0.356319 | − | 1.89321i | ||||
\(131\) | 5.79706e8 | 1.96844 | 0.984221 | − | 0.176945i | \(-0.0566213\pi\) | ||||
0.984221 | + | 0.176945i | \(0.0566213\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.64993e6 | + | 7.64993e6i | −0.0244484 | + | 0.0244484i | ||||
\(134\) | 5.89036e8i | 1.82693i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.67196e7 | 0.224259 | ||||||||
\(137\) | −1.35867e8 | − | 1.35867e8i | −0.385683 | − | 0.385683i | 0.487462 | − | 0.873144i | \(-0.337923\pi\) |
−0.873144 | + | 0.487462i | \(0.837923\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 3.73739e8i | − | 1.00117i | −0.865686 | − | 0.500587i | \(-0.833118\pi\) | ||
0.865686 | − | 0.500587i | \(-0.166882\pi\) | |||||||
\(140\) | −6.20780e7 | − | 9.08628e7i | −0.161594 | − | 0.236523i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.25438e8 | + | 4.25438e8i | 1.04636 | + | 1.04636i | ||||
\(143\) | −1.24167e8 | + | 1.24167e8i | −0.296936 | + | 0.296936i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.93677e8 | + | 7.40936e7i | 0.890571 | + | 0.167613i | ||||
\(146\) | 6.48468e8 | 1.42718 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.40985e7 | + | 6.40985e7i | −0.133598 | + | 0.133598i | ||||
\(149\) | 3.18508e8i | 0.646212i | 0.946363 | + | 0.323106i | \(0.104727\pi\) | ||||
−0.946363 | + | 0.323106i | \(0.895273\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.55101e8 | −0.298337 | −0.149169 | − | 0.988812i | \(-0.547660\pi\) | ||||
−0.149169 | + | 0.988812i | \(0.547660\pi\) | |||||||
\(152\) | −9.69027e6 | − | 9.69027e6i | −0.0181535 | − | 0.0181535i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.88772e7i | 0.140239i | ||||||||
\(155\) | 1.51011e8 | − | 8.02360e8i | 0.261627 | − | 1.39009i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.35107e8 | − | 2.35107e8i | −0.386961 | − | 0.386961i | 0.486641 | − | 0.873602i | \(-0.338222\pi\) |
−0.873602 | + | 0.486641i | \(0.838222\pi\) | |||||||
\(158\) | −5.47453e8 | + | 5.47453e8i | −0.878452 | + | 0.878452i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 6.98221e8 | − | 4.77029e8i | 1.06540 | − | 0.727888i | ||||
\(161\) | −1.26858e8 | −0.188805 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.62468e8 | + | 6.62468e8i | −0.938457 | + | 0.938457i | −0.998213 | − | 0.0597563i | \(-0.980968\pi\) |
0.0597563 | + | 0.998213i | \(0.480968\pi\) | |||||||
\(164\) | − | 6.58083e8i | − | 0.909715i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.48454e9 | −1.95506 | ||||||||
\(167\) | −5.95302e8 | − | 5.95302e8i | −0.765369 | − | 0.765369i | 0.211918 | − | 0.977287i | \(-0.432029\pi\) |
−0.977287 | + | 0.211918i | \(0.932029\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 8.63687e8i | − | 1.05879i | ||||||
\(170\) | −9.32576e8 | − | 1.75519e8i | −1.11658 | − | 0.210150i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.47502e8 | + | 8.47502e8i | 0.968337 | + | 0.968337i | ||||
\(173\) | 1.36775e8 | − | 1.36775e8i | 0.152694 | − | 0.152694i | −0.626626 | − | 0.779320i | \(-0.715565\pi\) |
0.779320 | + | 0.626626i | \(0.215565\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.34450e8 | − | 3.06543e8i | −0.143353 | − | 0.326843i | ||||
\(176\) | −3.25304e8 | −0.339030 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.40659e9 | + | 1.40659e9i | −1.40116 | + | 1.40116i | ||||
\(179\) | 1.22129e9i | 1.18961i | 0.803869 | + | 0.594807i | \(0.202771\pi\) | ||||
−0.803869 | + | 0.594807i | \(0.797229\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.84242e8 | −0.264834 | −0.132417 | − | 0.991194i | \(-0.542274\pi\) | ||||
−0.132417 | + | 0.991194i | \(0.542274\pi\) | |||||||
\(182\) | −5.33426e8 | − | 5.33426e8i | −0.486170 | − | 0.486170i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 1.60693e8i | − | 0.140192i | ||||||
\(185\) | −2.27673e8 | + | 1.55548e8i | −0.194368 | + | 0.132793i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.14150e8 | + | 2.14150e8i | 0.175127 | + | 0.175127i | ||||
\(188\) | −7.18125e8 | + | 7.18125e8i | −0.574868 | + | 0.574868i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.56220e7 | + | 1.39961e8i | 0.0733742 | + | 0.107397i | ||||
\(191\) | −7.13822e8 | −0.536360 | −0.268180 | − | 0.963369i | \(-0.586422\pi\) | ||||
−0.268180 | + | 0.963369i | \(0.586422\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.56478e8 | − | 5.56478e8i | 0.401069 | − | 0.401069i | −0.477541 | − | 0.878610i | \(-0.658472\pi\) |
0.878610 | + | 0.477541i | \(0.158472\pi\) | |||||||
\(194\) | − | 1.72781e9i | − | 1.21980i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.03362e9 | 0.700385 | ||||||||
\(197\) | −2.96874e7 | − | 2.96874e7i | −0.0197109 | − | 0.0197109i | 0.697183 | − | 0.716894i | \(-0.254437\pi\) |
−0.716894 | + | 0.697183i | \(0.754437\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 6.20227e8i | − | 0.395493i | −0.980253 | − | 0.197746i | \(-0.936638\pi\) | ||
0.980253 | − | 0.197746i | \(-0.0633623\pi\) | |||||||
\(200\) | 3.88302e8 | − | 1.70309e8i | 0.242689 | − | 0.106443i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8.86111e8 | + | 8.86111e8i | 0.532209 | + | 0.532209i | ||||
\(203\) | 3.88366e8 | − | 3.88366e8i | 0.228695 | − | 0.228695i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.70247e8 | − | 1.96722e9i | 0.209641 | − | 1.11388i | ||||
\(206\) | 2.09510e8 | 0.116342 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.19994e9 | − | 2.19994e9i | 1.17532 | − | 1.17532i | ||||
\(209\) | − | 5.40976e7i | − | 0.0283526i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.91245e8 | 0.449642 | 0.224821 | − | 0.974400i | \(-0.427820\pi\) | ||||
0.224821 | + | 0.974400i | \(0.427820\pi\) | |||||||
\(212\) | 1.86637e9 | + | 1.86637e9i | 0.923963 | + | 0.923963i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.26479e9i | 0.603065i | ||||||||
\(215\) | 2.05663e9 | + | 3.01026e9i | 0.962503 | + | 1.40880i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.91536e8 | − | 7.91536e8i | −0.356970 | − | 0.356970i | ||||
\(218\) | 3.70100e9 | − | 3.70100e9i | 1.63867 | − | 1.63867i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.40771e8 | + | 1.01778e8i | 0.230846 | + | 0.0434473i | ||||
\(221\) | −2.89648e9 | −1.21423 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.96849e8 | + | 3.96849e8i | −0.160475 | + | 0.160475i | −0.782777 | − | 0.622302i | \(-0.786197\pi\) |
0.622302 | + | 0.782777i | \(0.286197\pi\) | |||||||
\(224\) | − | 1.15939e9i | − | 0.460510i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.48871e9 | −0.953982 | ||||||||
\(227\) | 1.46131e9 | + | 1.46131e9i | 0.550349 | + | 0.550349i | 0.926541 | − | 0.376193i | \(-0.122767\pi\) |
−0.376193 | + | 0.926541i | \(0.622767\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.82283e9i | 1.02646i | 0.858251 | + | 0.513231i | \(0.171551\pi\) | ||||
−0.858251 | + | 0.513231i | \(0.828449\pi\) | |||||||
\(230\) | −3.67632e8 | + | 1.95332e9i | −0.131372 | + | 0.698011i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.91948e8 | + | 4.91948e8i | 0.169812 | + | 0.169812i | ||||
\(233\) | −6.82714e8 | + | 6.82714e8i | −0.231641 | + | 0.231641i | −0.813377 | − | 0.581736i | \(-0.802374\pi\) |
0.581736 | + | 0.813377i | \(0.302374\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.55073e9 | + | 1.74267e9i | −0.836358 | + | 0.571405i | ||||
\(236\) | 2.26891e9 | 0.731423 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −9.19995e8 | + | 9.19995e8i | −0.286733 | + | 0.286733i | ||||
\(239\) | 3.33204e9i | 1.02122i | 0.859813 | + | 0.510608i | \(0.170580\pi\) | ||||
−0.859813 | + | 0.510608i | \(0.829420\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.42023e9 | −0.717445 | −0.358722 | − | 0.933444i | \(-0.616788\pi\) | ||||
−0.358722 | + | 0.933444i | \(0.616788\pi\) | |||||||
\(242\) | 2.97721e9 | + | 2.97721e9i | 0.868057 | + | 0.868057i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 2.32763e9i | − | 0.656682i | ||||||
\(245\) | 3.08981e9 | + | 5.81530e8i | 0.857567 | + | 0.161402i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.65847e8 | + | 3.65847e8i | 0.0982906 | + | 0.0982906i | ||||
\(248\) | 1.00265e9 | − | 1.00265e9i | 0.265059 | − | 0.265059i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.10970e9 | + | 1.18186e9i | −1.30808 | + | 0.302556i | ||||
\(251\) | −5.01881e9 | −1.26446 | −0.632231 | − | 0.774780i | \(-0.717861\pi\) | ||||
−0.632231 | + | 0.774780i | \(0.717861\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.48547e8 | − | 4.48547e8i | 0.109478 | − | 0.109478i | ||||
\(254\) | − | 1.08943e10i | − | 2.61738i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.46196e9 | 1.27171 | ||||||||
\(257\) | −1.84074e9 | − | 1.84074e9i | −0.421948 | − | 0.421948i | 0.463926 | − | 0.885874i | \(-0.346440\pi\) |
−0.885874 | + | 0.463926i | \(0.846440\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.78051e8i | 0.0840139i | ||||||||
\(260\) | −4.34539e9 | + | 2.96879e9i | −0.950900 | + | 0.649660i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −8.80572e9 | − | 8.80572e9i | −1.86879 | − | 1.86879i | ||||
\(263\) | 3.72394e9 | − | 3.72394e9i | 0.778358 | − | 0.778358i | −0.201194 | − | 0.979552i | \(-0.564482\pi\) |
0.979552 | + | 0.201194i | \(0.0644820\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.52912e9 | + | 6.62922e9i | 0.918397 | + | 1.34425i | ||||
\(266\) | 2.32405e8 | 0.0464214 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.98386e9 | − | 3.98386e9i | 0.772263 | − | 0.772263i | ||||
\(269\) | 6.73435e9i | 1.28614i | 0.765809 | + | 0.643068i | \(0.222339\pi\) | ||||
−0.765809 | + | 0.643068i | \(0.777661\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.06460e9 | 1.30982 | 0.654908 | − | 0.755708i | \(-0.272707\pi\) | ||||
0.654908 | + | 0.755708i | \(0.272707\pi\) | |||||||
\(272\) | −3.79422e9 | − | 3.79422e9i | −0.693181 | − | 0.693181i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.12762e9i | 0.732314i | ||||||||
\(275\) | 1.55927e9 | + | 6.08492e8i | 0.272641 | + | 0.106396i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.76284e9 | + | 1.76284e9i | 0.299429 | + | 0.299429i | 0.840790 | − | 0.541361i | \(-0.182091\pi\) |
−0.541361 | + | 0.840790i | \(0.682091\pi\) | |||||||
\(278\) | −5.67709e9 | + | 5.67709e9i | −0.950487 | + | 0.950487i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.07526e8 | − | 5.71313e8i | 0.0174937 | − | 0.0929484i | ||||
\(281\) | −8.08318e9 | −1.29645 | −0.648227 | − | 0.761447i | \(-0.724489\pi\) | ||||
−0.648227 | + | 0.761447i | \(0.724489\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.25335e8 | − | 1.25335e8i | 0.0195401 | − | 0.0195401i | −0.697269 | − | 0.716809i | \(-0.745602\pi\) |
0.716809 | + | 0.697269i | \(0.245602\pi\) | |||||||
\(284\) | − | 5.75478e9i | − | 0.884617i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.77219e9 | 0.563806 | ||||||||
\(287\) | −1.94068e9 | − | 1.94068e9i | −0.286039 | − | 0.286039i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 1.98022e9i | − | 0.283872i | ||||||
\(290\) | −4.85447e9 | − | 7.10543e9i | −0.686357 | − | 1.00461i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.38583e9 | − | 4.38583e9i | −0.603282 | − | 0.603282i | ||||
\(293\) | −4.13188e9 | + | 4.13188e9i | −0.560631 | + | 0.560631i | −0.929487 | − | 0.368855i | \(-0.879750\pi\) |
0.368855 | + | 0.929487i | \(0.379750\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.78247e9 | + | 1.27652e9i | 0.895571 | + | 0.168554i | ||||
\(296\) | −4.78882e8 | −0.0623823 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.83813e9 | − | 4.83813e9i | 0.613497 | − | 0.613497i | ||||
\(299\) | 6.06680e9i | 0.759058i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.99854e9 | 0.608943 | ||||||||
\(302\) | 2.35598e9 | + | 2.35598e9i | 0.283234 | + | 0.283234i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 9.58477e8i | 0.112224i | ||||||||
\(305\) | 1.30956e9 | − | 6.95802e9i | 0.151330 | − | 0.804056i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.15844e10 | − | 1.15844e10i | −1.30413 | − | 1.30413i | −0.925580 | − | 0.378553i | \(-0.876422\pi\) |
−0.378553 | − | 0.925580i | \(-0.623578\pi\) | |||||||
\(308\) | 5.33476e8 | − | 5.33476e8i | 0.0592805 | − | 0.0592805i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.44817e10 | + | 9.89398e9i | −1.56810 | + | 1.07133i | ||||
\(311\) | 1.41409e10 | 1.51160 | 0.755799 | − | 0.654804i | \(-0.227249\pi\) | ||||
0.755799 | + | 0.654804i | \(0.227249\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.49310e9 | + | 6.49310e9i | −0.676511 | + | 0.676511i | −0.959209 | − | 0.282698i | \(-0.908771\pi\) |
0.282698 | + | 0.959209i | \(0.408771\pi\) | |||||||
\(314\) | 7.14254e9i | 0.734741i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.40524e9 | 0.742662 | ||||||||
\(317\) | −1.31825e10 | − | 1.31825e10i | −1.30545 | − | 1.30545i | −0.924659 | − | 0.380796i | \(-0.875650\pi\) |
−0.380796 | − | 0.924659i | \(-0.624350\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.74639e9i | 0.265215i | ||||||||
\(320\) | −5.91467e9 | − | 1.11319e9i | −0.564067 | − | 0.106162i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.92697e9 | + | 1.92697e9i | 0.179247 | + | 0.179247i | ||||
\(323\) | 6.30974e8 | − | 6.30974e8i | 0.0579697 | − | 0.0579697i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.46600e10 | + | 6.42987e9i | −1.31402 | + | 0.576327i | ||||
\(326\) | 2.01257e10 | 1.78189 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.45828e9 | − | 2.45828e9i | 0.212391 | − | 0.212391i | ||||
\(329\) | 4.23548e9i | 0.361509i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.04163e10 | −0.867761 | −0.433880 | − | 0.900971i | \(-0.642856\pi\) | ||||
−0.433880 | + | 0.900971i | \(0.642856\pi\) | |||||||
\(332\) | 1.00405e10 | + | 1.00405e10i | 0.826423 | + | 0.826423i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.80852e10i | 1.45324i | ||||||||
\(335\) | 1.41504e10 | − | 9.66763e9i | 1.12354 | − | 0.767610i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.51923e9 | − | 5.51923e9i | −0.427917 | − | 0.427917i | 0.460002 | − | 0.887918i | \(-0.347849\pi\) |
−0.887918 | + | 0.460002i | \(0.847849\pi\) | |||||||
\(338\) | −1.31194e10 | + | 1.31194e10i | −1.00519 | + | 1.00519i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.12025e9 | + | 7.49445e9i | 0.383156 | + | 0.560821i | ||||
\(341\) | 5.59746e9 | 0.413974 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.54119e9 | − | 6.54119e9i | 0.472586 | − | 0.472586i | ||||
\(344\) | 6.33171e9i | 0.452155i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.15523e9 | −0.289928 | ||||||||
\(347\) | 7.83468e9 | + | 7.83468e9i | 0.540385 | + | 0.540385i | 0.923642 | − | 0.383257i | \(-0.125198\pi\) |
−0.383257 | + | 0.923642i | \(0.625198\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 1.11380e10i | − | 0.750765i | −0.926870 | − | 0.375383i | \(-0.877511\pi\) | ||
0.926870 | − | 0.375383i | \(-0.122489\pi\) | |||||||
\(350\) | −2.61410e9 | + | 6.69867e9i | −0.174201 | + | 0.446392i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.09941e9 | + | 4.09941e9i | 0.267024 | + | 0.267024i | ||||
\(353\) | 8.38048e9 | − | 8.38048e9i | 0.539722 | − | 0.539722i | −0.383725 | − | 0.923447i | \(-0.625359\pi\) |
0.923447 | + | 0.383725i | \(0.125359\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.23773e9 | − | 1.72028e10i | 0.203857 | − | 1.08314i | ||||
\(356\) | 1.90265e10 | 1.18457 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.85513e10 | − | 1.85513e10i | 1.12939 | − | 1.12939i | ||||
\(359\) | 1.42412e10i | 0.857372i | 0.903454 | + | 0.428686i | \(0.141023\pi\) | ||||
−0.903454 | + | 0.428686i | \(0.858977\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.68242e10 | 0.990615 | ||||||||
\(362\) | 4.31762e9 | + | 4.31762e9i | 0.251426 | + | 0.251426i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7.21550e9i | 0.411018i | ||||||||
\(365\) | −1.06431e10 | − | 1.55781e10i | −0.599647 | − | 0.877696i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.13528e8 | + | 2.13528e8i | 0.0117704 | + | 0.0117704i | 0.712967 | − | 0.701197i | \(-0.247351\pi\) |
−0.701197 | + | 0.712967i | \(0.747351\pi\) | |||||||
\(368\) | −7.94716e9 | + | 7.94716e9i | −0.433332 | + | 0.433332i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5.82112e9 | + | 1.09559e9i | 0.310599 | + | 0.0584574i | ||||
\(371\) | 1.10078e10 | 0.581039 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.79026e9 | − | 9.79026e9i | 0.505777 | − | 0.505777i | −0.407450 | − | 0.913227i | \(-0.633582\pi\) |
0.913227 | + | 0.407450i | \(0.133582\pi\) | |||||||
\(374\) | − | 6.50587e9i | − | 0.332521i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.36513e9 | −0.268429 | ||||||||
\(377\) | −1.85731e10 | − | 1.85731e10i | −0.919429 | − | 0.919429i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.29022e9i | 0.0625326i | 0.999511 | + | 0.0312663i | \(0.00995399\pi\) | ||||
−0.999511 | + | 0.0312663i | \(0.990046\pi\) | |||||||
\(380\) | 2.99879e8 | − | 1.59333e9i | 0.0143818 | − | 0.0764138i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.08429e10 | + | 1.08429e10i | 0.509206 | + | 0.509206i | ||||
\(383\) | 9.77735e9 | − | 9.77735e9i | 0.454387 | − | 0.454387i | −0.442421 | − | 0.896808i | \(-0.645880\pi\) |
0.896808 | + | 0.442421i | \(0.145880\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.89487e9 | − | 1.29458e9i | 0.0862454 | − | 0.0589233i | ||||
\(386\) | −1.69058e10 | −0.761528 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.16858e10 | + | 1.16858e10i | −0.515622 | + | 0.515622i | ||||
\(389\) | − | 8.38723e9i | − | 0.366286i | −0.983086 | − | 0.183143i | \(-0.941373\pi\) | ||
0.983086 | − | 0.183143i | \(-0.0586271\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.04634e10 | 0.447677 | ||||||||
\(392\) | 3.86110e9 | + | 3.86110e9i | 0.163519 | + | 0.163519i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.01902e8i | 0.0374261i | ||||||||
\(395\) | 2.21366e10 | + | 4.16630e9i | 0.909332 | + | 0.171144i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.53135e8 | + | 7.53135e8i | 0.0303187 | + | 0.0303187i | 0.722104 | − | 0.691785i | \(-0.243175\pi\) |
−0.691785 | + | 0.722104i | \(0.743175\pi\) | |||||||
\(398\) | −9.42124e9 | + | 9.42124e9i | −0.375470 | + | 0.375470i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.76265e10 | − | 1.07810e10i | −1.07916 | − | 0.421133i | ||||
\(401\) | −4.56245e10 | −1.76449 | −0.882247 | − | 0.470786i | \(-0.843970\pi\) | ||||
−0.882247 | + | 0.470786i | \(0.843970\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.78541e10 | + | 3.78541e10i | −1.43513 | + | 1.43513i | ||||
\(404\) | − | 1.19862e10i | − | 0.449941i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.17985e10 | −0.434235 | ||||||||
\(407\) | −1.33672e9 | − | 1.33672e9i | −0.0487150 | − | 0.0487150i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 3.94186e10i | − | 1.40866i | −0.709871 | − | 0.704332i | \(-0.751247\pi\) | ||
0.709871 | − | 0.704332i | \(-0.248753\pi\) | |||||||
\(410\) | −3.55060e10 | + | 2.42579e10i | −1.25651 | + | 0.858456i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.41699e9 | − | 1.41699e9i | −0.0491789 | − | 0.0491789i | ||||
\(413\) | 6.69097e9 | − | 6.69097e9i | 0.229979 | − | 0.229979i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.43652e10 | + | 3.56631e10i | 0.821444 | + | 1.20234i | ||||
\(416\) | −5.54464e10 | −1.85140 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8.21741e8 | + | 8.21741e8i | −0.0269172 | + | 0.0269172i | ||||
\(419\) | − | 3.51993e10i | − | 1.14203i | −0.820940 | − | 0.571015i | \(-0.806550\pi\) | ||
0.820940 | − | 0.571015i | \(-0.193450\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.81133e10 | −0.894920 | −0.447460 | − | 0.894304i | \(-0.647671\pi\) | ||||
−0.447460 | + | 0.894304i | \(0.647671\pi\) | |||||||
\(422\) | −1.35380e10 | − | 1.35380e10i | −0.426878 | − | 0.426878i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.39437e10i | 0.431435i | ||||||||
\(425\) | 1.10895e10 | + | 2.52840e10i | 0.339905 | + | 0.774979i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.86415e9 | − | 6.86415e9i | −0.206479 | − | 0.206479i | ||||
\(428\) | 8.55425e9 | − | 8.55425e9i | 0.254922 | − | 0.254922i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.44857e10 | − | 7.69660e10i | 0.423706 | − | 2.25126i | ||||
\(431\) | 2.83437e9 | 0.0821386 | 0.0410693 | − | 0.999156i | \(-0.486924\pi\) | ||||
0.0410693 | + | 0.999156i | \(0.486924\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.45461e10 | + | 3.45461e10i | −0.982759 | + | 0.982759i | −0.999854 | − | 0.0170951i | \(-0.994558\pi\) |
0.0170951 | + | 0.999854i | \(0.494558\pi\) | |||||||
\(434\) | 2.40468e10i | 0.677796i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.00624e10 | −1.38537 | ||||||||
\(437\) | −1.32160e9 | − | 1.32160e9i | −0.0362389 | − | 0.0362389i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.87810e9i | 0.104415i | 0.998636 | + | 0.0522073i | \(0.0166257\pi\) | ||||
−0.998636 | + | 0.0522073i | \(0.983374\pi\) | |||||||
\(440\) | 1.63987e9 | + | 2.40025e9i | 0.0437520 | + | 0.0640392i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.39975e10 | + | 4.39975e10i | 1.15276 | + | 1.15276i | ||||
\(443\) | 1.45277e10 | − | 1.45277e10i | 0.377208 | − | 0.377208i | −0.492886 | − | 0.870094i | \(-0.664058\pi\) |
0.870094 | + | 0.492886i | \(0.164058\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.68762e10 | + | 1.07046e10i | 1.45041 | + | 0.272980i | ||||
\(446\) | 1.20563e10 | 0.304701 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.83488e9 | + | 5.83488e9i | −0.144850 | + | 0.144850i | ||||
\(449\) | − | 4.42731e10i | − | 1.08932i | −0.838658 | − | 0.544659i | \(-0.816659\pi\) | ||
0.838658 | − | 0.544659i | \(-0.183341\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.37238e10 | 0.331716 | ||||||||
\(452\) | 1.68320e10 | + | 1.68320e10i | 0.403258 | + | 0.403258i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 4.43944e10i | − | 1.04497i | ||||||
\(455\) | −4.05955e9 | + | 2.15694e10i | −0.0947180 | + | 0.503260i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.96557e10 | + | 1.96557e10i | 0.450633 | + | 0.450633i | 0.895564 | − | 0.444932i | \(-0.146772\pi\) |
−0.444932 | + | 0.895564i | \(0.646772\pi\) | |||||||
\(458\) | 4.28787e10 | − | 4.28787e10i | 0.974495 | − | 0.974495i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.56975e10 | − | 1.07246e10i | 0.350589 | − | 0.239524i | ||||
\(461\) | −6.79618e10 | −1.50474 | −0.752370 | − | 0.658741i | \(-0.771089\pi\) | ||||
−0.752370 | + | 0.658741i | \(0.771089\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.98171e9 | − | 7.98171e9i | 0.173689 | − | 0.173689i | −0.614909 | − | 0.788598i | \(-0.710807\pi\) |
0.788598 | + | 0.614909i | \(0.210807\pi\) | |||||||
\(464\) | − | 4.86593e10i | − | 1.04977i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.07408e10 | 0.439827 | ||||||||
\(467\) | 5.78480e10 | + | 5.78480e10i | 1.21624 | + | 1.21624i | 0.968937 | + | 0.247307i | \(0.0795456\pi\) |
0.247307 | + | 0.968937i | \(0.420454\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 2.34967e10i | − | 0.485641i | ||||||
\(470\) | 6.52166e10 | + | 1.22743e10i | 1.33649 | + | 0.251540i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.47554e9 | + | 8.47554e9i | 0.170765 | + | 0.170765i | ||||
\(473\) | −1.76739e10 | + | 1.76739e10i | −0.353092 | + | 0.353092i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.79287e9 | − | 4.59425e9i | 0.0352187 | − | 0.0902486i | ||||
\(476\) | 1.24445e10 | 0.242410 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.06135e10 | − | 5.06135e10i | 0.969516 | − | 0.969516i | ||||
\(479\) | 9.03281e10i | 1.71586i | 0.513770 | + | 0.857928i | \(0.328248\pi\) | ||||
−0.513770 | + | 0.857928i | \(0.671752\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.80798e10 | 0.337763 | ||||||||
\(482\) | 3.67632e10 | + | 3.67632e10i | 0.681123 | + | 0.681123i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 4.02719e10i | − | 0.733873i | ||||||
\(485\) | −4.15071e10 | + | 2.83579e10i | −0.750163 | + | 0.512516i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.93536e10 | + | 2.93536e10i | 0.521850 | + | 0.521850i | 0.918130 | − | 0.396280i | \(-0.129699\pi\) |
−0.396280 | + | 0.918130i | \(0.629699\pi\) | |||||||
\(488\) | 8.69490e9 | − | 8.69490e9i | 0.153315 | − | 0.153315i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.81008e10 | − | 5.57676e10i | −0.660921 | − | 0.967382i | ||||
\(491\) | 1.01085e11 | 1.73924 | 0.869619 | − | 0.493724i | \(-0.164365\pi\) | ||||
0.869619 | + | 0.493724i | \(0.164365\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.20328e10 | + | 3.20328e10i | −0.542260 | + | 0.542260i | ||||
\(494\) | − | 1.11144e10i | − | 0.186629i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9.91733e10 | −1.63858 | ||||||||
\(497\) | −1.69708e10 | − | 1.69708e10i | −0.278148 | − | 0.278148i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.16998e9i | 0.0995134i | 0.998761 | + | 0.0497567i | \(0.0158446\pi\) | ||||
−0.998761 | + | 0.0497567i | \(0.984155\pi\) | |||||||
\(500\) | 4.25521e10 | + | 2.65654e10i | 0.680834 | + | 0.425046i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7.62356e10 | + | 7.62356e10i | 1.20045 | + | 1.20045i | ||||
\(503\) | 1.79791e10 | − | 1.79791e10i | 0.280864 | − | 0.280864i | −0.552590 | − | 0.833453i | \(-0.686360\pi\) |
0.833453 | + | 0.552590i | \(0.186360\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.74360e9 | − | 3.58304e10i | 0.103688 | − | 0.550917i | ||||
\(506\) | −1.36268e10 | −0.207870 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.36824e10 | + | 7.36824e10i | −1.10639 | + | 1.10639i | ||||
\(509\) | − | 6.48919e10i | − | 0.966762i | −0.875410 | − | 0.483381i | \(-0.839409\pi\) | ||
0.875410 | − | 0.483381i | \(-0.160591\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.58675e10 | −0.379376 | ||||||||
\(512\) | −5.77144e10 | − | 5.77144e10i | −0.839855 | − | 0.839855i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.59215e10i | 0.801173i | ||||||||
\(515\) | −3.43861e9 | − | 5.03306e9i | −0.0488826 | − | 0.0715489i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.49759e10 | − | 1.49759e10i | −0.209619 | − | 0.209619i | ||||
\(518\) | 5.74258e9 | − | 5.74258e9i | 0.0797606 | − | 0.0797606i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.73222e10 | − | 5.14228e9i | −0.373682 | − | 0.0703303i | ||||
\(521\) | 1.34163e10 | 0.182089 | 0.0910443 | − | 0.995847i | \(-0.470980\pi\) | ||||
0.0910443 | + | 0.995847i | \(0.470980\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.20405e10 | + | 5.20405e10i | −0.695560 | + | 0.695560i | −0.963450 | − | 0.267890i | \(-0.913674\pi\) |
0.267890 | + | 0.963450i | \(0.413674\pi\) | |||||||
\(524\) | 1.19113e11i | 1.57991i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.13133e11 | −1.47790 | ||||||||
\(527\) | 6.52866e10 | + | 6.52866e10i | 0.846412 | + | 0.846412i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.63950e10i | 0.720142i | ||||||||
\(530\) | 3.19004e10 | − | 1.69495e11i | 0.404290 | − | 2.14809i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.57184e9 | − | 1.57184e9i | −0.0196228 | − | 0.0196228i | ||||
\(533\) | −9.28101e10 | + | 9.28101e10i | −1.14997 | + | 1.14997i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.03841e10 | − | 2.07586e10i | 0.370878 | − | 0.253386i | ||||
\(536\) | 2.97636e10 | 0.360600 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.02295e11 | − | 1.02295e11i | 1.22102 | − | 1.22102i | ||||
\(539\) | 2.15553e10i | 0.255387i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.89152e9 | 0.103797 | 0.0518987 | − | 0.998652i | \(-0.483473\pi\) | ||||
0.0518987 | + | 0.998652i | \(0.483473\pi\) | |||||||
\(542\) | −1.07311e11 | − | 1.07311e11i | −1.24351 | − | 1.24351i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 9.56280e10i | 1.09192i | ||||||||
\(545\) | −1.49652e11 | − | 2.81659e10i | −1.69628 | − | 0.319254i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.56469e10 | − | 8.56469e10i | −0.956671 | − | 0.956671i | 0.0424288 | − | 0.999099i | \(-0.486490\pi\) |
−0.999099 | + | 0.0424288i | \(0.986490\pi\) | |||||||
\(548\) | 2.79166e10 | − | 2.79166e10i | 0.309557 | − | 0.309557i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.44423e10 | − | 3.29283e10i | −0.157829 | − | 0.359847i | ||||
\(551\) | 8.09198e9 | 0.0877906 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.18379e10 | − | 2.18379e10i | 0.233513 | − | 0.233513i | ||||
\(554\) | − | 5.35551e10i | − | 0.568541i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.67924e10 | 0.803562 | ||||||||
\(557\) | −7.17947e10 | − | 7.17947e10i | −0.745884 | − | 0.745884i | 0.227819 | − | 0.973703i | \(-0.426840\pi\) |
−0.973703 | + | 0.227819i | \(0.926840\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2.39048e11i | − | 2.44815i | ||||||
\(560\) | −3.35724e10 | + | 2.29369e10i | −0.341374 | + | 0.233229i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.22783e11 | + | 1.22783e11i | 1.23082 | + | 1.23082i | ||||
\(563\) | −1.14328e11 | + | 1.14328e11i | −1.13794 | + | 1.13794i | −0.149117 | + | 0.988819i | \(0.547643\pi\) |
−0.988819 | + | 0.149117i | \(0.952357\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.08463e10 | + | 5.97862e10i | 0.400828 | + | 0.586688i | ||||
\(566\) | −3.80768e9 | −0.0371018 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.14971e10 | − | 2.14971e10i | 0.206531 | − | 0.206531i | ||||
\(569\) | 1.17871e11i | 1.12449i | 0.826969 | + | 0.562247i | \(0.190063\pi\) | ||||
−0.826969 | + | 0.562247i | \(0.809937\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.31971e11 | 1.24147 | 0.620733 | − | 0.784022i | \(-0.286835\pi\) | ||||
0.620733 | + | 0.784022i | \(0.286835\pi\) | |||||||
\(572\) | −2.55127e10 | − | 2.55127e10i | −0.238327 | − | 0.238327i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.89576e10i | 0.543116i | ||||||||
\(575\) | 5.29584e10 | − | 2.32275e10i | 0.484466 | − | 0.212487i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.04538e11 | − | 1.04538e11i | −0.943130 | − | 0.943130i | 0.0553376 | − | 0.998468i | \(-0.482376\pi\) |
−0.998468 | + | 0.0553376i | \(0.982376\pi\) | |||||||
\(578\) | −3.00795e10 | + | 3.00795e10i | −0.269500 | + | 0.269500i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.52241e10 | + | 8.08892e10i | −0.134530 | + | 0.714790i | ||||
\(581\) | 5.92185e10 | 0.519700 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.89216e10 | + | 3.89216e10i | −0.336912 | + | 0.336912i | ||||
\(584\) | − | 3.27666e10i | − | 0.281696i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.25526e11 | 1.06450 | ||||||||
\(587\) | 2.48950e10 | + | 2.48950e10i | 0.209681 | + | 0.209681i | 0.804132 | − | 0.594451i | \(-0.202630\pi\) |
−0.594451 | + | 0.804132i | \(0.702630\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 1.64924e10i | − | 0.137032i | ||||||
\(590\) | −8.36353e10 | − | 1.22416e11i | −0.690210 | − | 1.01025i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.36834e10 | + | 2.36834e10i | 0.192822 | + | 0.192822i | ||||
\(593\) | −5.00144e10 | + | 5.00144e10i | −0.404461 | + | 0.404461i | −0.879802 | − | 0.475341i | \(-0.842325\pi\) |
0.475341 | + | 0.879802i | \(0.342325\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.72006e10 | + | 7.00148e9i | 0.296812 | + | 0.0558627i | ||||
\(596\) | −6.54440e10 | −0.518663 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9.21546e10 | − | 9.21546e10i | 0.720630 | − | 0.720630i | ||||
\(599\) | − | 1.89666e11i | − | 1.47327i | −0.676292 | − | 0.736634i | \(-0.736414\pi\) | ||
0.676292 | − | 0.736634i | \(-0.263586\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.55111e10 | −0.425483 | −0.212742 | − | 0.977109i | \(-0.568239\pi\) | ||||
−0.212742 | + | 0.977109i | \(0.568239\pi\) | |||||||
\(602\) | −7.59277e10 | − | 7.59277e10i | −0.578115 | − | 0.578115i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 3.18688e10i | − | 0.239451i | ||||||
\(605\) | 2.26576e10 | − | 1.20385e11i | 0.169119 | − | 0.898571i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.12289e9 | + | 8.12289e9i | 0.0598351 | + | 0.0598351i | 0.736391 | − | 0.676556i | \(-0.236528\pi\) |
−0.676556 | + | 0.736391i | \(0.736528\pi\) | |||||||
\(608\) | 1.20785e10 | − | 1.20785e10i | 0.0883894 | − | 0.0883894i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.25584e11 | + | 8.57999e10i | −0.907018 | + | 0.619680i | ||||
\(611\) | 2.02556e11 | 1.45338 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.38370e11 | + | 1.38370e11i | −0.979939 | + | 0.979939i | −0.999803 | − | 0.0198637i | \(-0.993677\pi\) |
0.0198637 | + | 0.999803i | \(0.493677\pi\) | |||||||
\(614\) | 3.51935e11i | 2.47622i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.98561e9 | 0.0276804 | ||||||||
\(617\) | 6.81338e10 | + | 6.81338e10i | 0.470135 | + | 0.470135i | 0.901958 | − | 0.431824i | \(-0.142130\pi\) |
−0.431824 | + | 0.901958i | \(0.642130\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 1.25414e11i | − | 0.854249i | −0.904193 | − | 0.427125i | \(-0.859527\pi\) | ||
0.904193 | − | 0.427125i | \(-0.140473\pi\) | |||||||
\(620\) | 1.64862e11 | + | 3.10284e10i | 1.11571 | + | 0.209987i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.14800e11 | − | 2.14800e11i | −1.43507 | − | 1.43507i | ||||
\(623\) | 5.61089e10 | − | 5.61089e10i | 0.372460 | − | 0.372460i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.12255e11 | + | 1.03353e11i | 0.735677 | + | 0.677332i | ||||
\(626\) | 1.97260e11 | 1.28452 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.83076e10 | − | 4.83076e10i | 0.310583 | − | 0.310583i | ||||
\(629\) | − | 3.11820e10i | − | 0.199206i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.70795e10 | −0.486207 | −0.243104 | − | 0.970000i | \(-0.578165\pi\) | ||||
−0.243104 | + | 0.970000i | \(0.578165\pi\) | |||||||
\(632\) | 2.76624e10 | + | 2.76624e10i | 0.173389 | + | 0.173389i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.00485e11i | 2.47873i | ||||||||
\(635\) | −2.61715e11 | + | 1.78805e11i | −1.60966 | + | 1.09973i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.45772e11 | − | 1.45772e11i | −0.885356 | − | 0.885356i | ||||
\(638\) | 4.17175e10 | − | 4.17175e10i | 0.251789 | − | 0.251789i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4.91850e10 | − | 7.19915e10i | −0.293165 | − | 0.429103i | ||||
\(641\) | −2.92061e10 | −0.172998 | −0.0864991 | − | 0.996252i | \(-0.527568\pi\) | ||||
−0.0864991 | + | 0.996252i | \(0.527568\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.29504e10 | + | 1.29504e10i | −0.0757597 | + | 0.0757597i | −0.743971 | − | 0.668212i | \(-0.767060\pi\) |
0.668212 | + | 0.743971i | \(0.267060\pi\) | |||||||
\(644\) | − | 2.60656e10i | − | 0.151539i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.91690e10 | −0.110070 | ||||||||
\(647\) | 9.84373e10 | + | 9.84373e10i | 0.561750 | + | 0.561750i | 0.929804 | − | 0.368055i | \(-0.119976\pi\) |
−0.368055 | + | 0.929804i | \(0.619976\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.73161e10i | 0.266705i | ||||||||
\(650\) | 3.20355e11 | + | 1.25016e11i | 1.79464 | + | 0.700343i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.36118e11 | − | 1.36118e11i | −0.753224 | − | 0.753224i | ||||
\(653\) | 3.36757e10 | − | 3.36757e10i | 0.185210 | − | 0.185210i | −0.608412 | − | 0.793622i | \(-0.708193\pi\) |
0.793622 | + | 0.608412i | \(0.208193\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.70145e10 | + | 3.56065e11i | −0.364086 | + | 1.93448i | ||||
\(656\) | −2.43152e11 | −1.31299 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.43368e10 | − | 6.43368e10i | 0.343207 | − | 0.343207i | ||||
\(659\) | − | 5.43312e10i | − | 0.288077i | −0.989572 | − | 0.144038i | \(-0.953991\pi\) | ||
0.989572 | − | 0.144038i | \(-0.0460089\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.69785e11 | 1.41323 | 0.706614 | − | 0.707599i | \(-0.250222\pi\) | ||||
0.706614 | + | 0.707599i | \(0.250222\pi\) | |||||||
\(662\) | 1.58223e11 | + | 1.58223e11i | 0.823829 | + | 0.823829i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7.50128e10i | 0.385890i | ||||||||
\(665\) | −3.81437e9 | − | 5.58305e9i | −0.0195046 | − | 0.0285486i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.70941e10 | + | 6.70941e10i | 0.338986 | + | 0.338986i | ||||
\(668\) | 1.22317e11 | − | 1.22317e11i | 0.614301 | − | 0.614301i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.61795e11 | − | 6.80931e10i | −1.79541 | − | 0.337912i | ||||
\(671\) | 4.85408e10 | 0.239451 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.07886e10 | − | 7.07886e10i | 0.345067 | − | 0.345067i | −0.513202 | − | 0.858268i | \(-0.671541\pi\) |
0.858268 | + | 0.513202i | \(0.171541\pi\) | |||||||
\(674\) | 1.67674e11i | 0.812505i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.77462e11 | 0.849806 | ||||||||
\(677\) | −2.99576e9 | − | 2.99576e9i | −0.0142611 | − | 0.0142611i | 0.699940 | − | 0.714201i | \(-0.253210\pi\) |
−0.714201 | + | 0.699940i | \(0.753210\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.89225e10i | 0.324251i | ||||||||
\(680\) | −8.86886e9 | + | 4.71224e10i | −0.0414794 | + | 0.220390i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8.50252e10 | − | 8.50252e10i | −0.393016 | − | 0.393016i | ||||
\(683\) | 1.50976e11 | − | 1.50976e11i | 0.693786 | − | 0.693786i | −0.269277 | − | 0.963063i | \(-0.586785\pi\) |
0.963063 | + | 0.269277i | \(0.0867846\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.91578e10 | − | 6.77451e10i | 0.450365 | − | 0.307692i | ||||
\(686\) | −1.98721e11 | −0.897321 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.13139e11 | − | 3.13139e11i | 1.39760 | − | 1.39760i | ||||
\(689\) | − | 5.26433e11i | − | 2.33596i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.51850e11 | 1.54328 | 0.771641 | − | 0.636058i | \(-0.219436\pi\) | ||||
0.771641 | + | 0.636058i | \(0.219436\pi\) | |||||||
\(692\) | 2.81033e10 | + | 2.81033e10i | 0.122556 | + | 0.122556i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 2.38017e11i | − | 1.02605i | ||||||
\(695\) | 2.29557e11 | + | 4.32046e10i | 0.983899 | + | 0.185178i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.60069e11 | + | 1.60069e11i | 0.678228 | + | 0.678228i | ||||
\(698\) | −1.69185e11 | + | 1.69185e11i | −0.712756 | + | 0.712756i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 6.29857e10 | − | 2.76255e10i | 0.262331 | − | 0.115058i | ||||
\(701\) | −9.64074e10 | −0.399244 | −0.199622 | − | 0.979873i | \(-0.563971\pi\) | ||||
−0.199622 | + | 0.979873i | \(0.563971\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.93852e9 | + | 3.93852e9i | −0.0161255 | + | 0.0161255i | ||||
\(704\) | − | 4.12622e10i | − | 0.167981i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.54599e11 | −1.02480 | ||||||||
\(707\) | −3.53470e10 | − | 3.53470e10i | −0.141474 | − | 0.141474i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.40677e7i | 0.000332693i | 1.00000 | 0.000166347i | \(5.29498e-5\pi\) | |||||
−1.00000 | 0.000166347i | \(0.999947\pi\) | ||||||||
\(710\) | −3.10492e11 | + | 2.12130e11i | −1.22185 | + | 0.834772i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.10739e10 | + | 7.10739e10i | 0.276560 | + | 0.276560i | ||||
\(713\) | 1.36746e11 | − | 1.36746e11i | 0.529122 | − | 0.529122i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.19116e10 | − | 9.06193e10i | −0.236891 | − | 0.346734i | ||||
\(716\) | −2.50939e11 | −0.954807 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.16324e11 | − | 2.16324e11i | 0.813966 | − | 0.813966i | ||||
\(719\) | − | 1.00149e11i | − | 0.374741i | −0.982289 | − | 0.187371i | \(-0.940003\pi\) | ||
0.982289 | − | 0.187371i | \(-0.0599965\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.35738e9 | −0.0309264 | ||||||||
\(722\) | −2.55559e11 | − | 2.55559e11i | −0.940463 | − | 0.940463i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 5.84033e10i | − | 0.212561i | ||||||
\(725\) | −9.10189e10 | + | 2.33238e11i | −0.329443 | + | 0.844203i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.90847e11 | − | 1.90847e11i | −0.683199 | − | 0.683199i | 0.277520 | − | 0.960720i | \(-0.410487\pi\) |
−0.960720 | + | 0.277520i | \(0.910487\pi\) | |||||||
\(728\) | −2.69536e10 | + | 2.69536e10i | −0.0959603 | + | 0.0959603i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −7.49635e10 | + | 3.98300e11i | −0.263972 | + | 1.40255i | ||||
\(731\) | −4.12284e11 | −1.44387 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.74944e10 | + | 8.74944e10i | −0.303085 | + | 0.303085i | −0.842220 | − | 0.539135i | \(-0.818751\pi\) |
0.539135 | + | 0.842220i | \(0.318751\pi\) | |||||||
\(734\) | − | 6.48698e9i | − | 0.0223490i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.00297e11 | 0.682595 | ||||||||
\(737\) | 8.30801e10 | + | 8.30801e10i | 0.281596 | + | 0.281596i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.50849e11i | 1.84695i | 0.383659 | + | 0.923475i | \(0.374664\pi\) | ||||
−0.383659 | + | 0.923475i | \(0.625336\pi\) | |||||||
\(740\) | −3.19605e10 | − | 4.67802e10i | −0.106583 | − | 0.156004i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.67208e11 | − | 1.67208e11i | −0.551623 | − | 0.551623i | ||||
\(743\) | 1.58679e9 | − | 1.58679e9i | 0.00520673 | − | 0.00520673i | −0.704499 | − | 0.709705i | \(-0.748828\pi\) |
0.709705 | + | 0.704499i | \(0.248828\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.95633e11 | − | 3.68198e10i | −0.635062 | − | 0.119524i | ||||
\(746\) | −2.97428e11 | −0.960343 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.40016e10 | + | 4.40016e10i | −0.140560 | + | 0.140560i | ||||
\(749\) | − | 5.04527e10i | − | 0.160309i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.67832e11 | −1.47072 | −0.735360 | − | 0.677677i | \(-0.762987\pi\) | ||||
−0.735360 | + | 0.677677i | \(0.762987\pi\) | |||||||
\(752\) | 2.65336e11 | + | 2.65336e11i | 0.829707 | + | 0.829707i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.64249e11i | 1.74576i | ||||||||
\(755\) | 1.79299e10 | − | 9.52657e10i | 0.0551809 | − | 0.293190i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.00150e11 | − | 1.00150e11i | −0.304976 | − | 0.304976i | 0.537981 | − | 0.842957i | \(-0.319187\pi\) |
−0.842957 | + | 0.537981i | \(0.819187\pi\) | |||||||
\(758\) | 1.95984e10 | − | 1.95984e10i | 0.0593668 | − | 0.0593668i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.07212e9 | − | 4.83171e9i | 0.0211980 | − | 0.0144826i | ||||
\(761\) | 1.53260e10 | 0.0456974 | 0.0228487 | − | 0.999739i | \(-0.492726\pi\) | ||||
0.0228487 | + | 0.999739i | \(0.492726\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.47633e11 | + | 1.47633e11i | −0.435598 | + | 0.435598i | ||||
\(764\) | − | 1.46669e11i | − | 0.430493i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.97035e11 | −0.862766 | ||||||||
\(767\) | −3.19986e11 | − | 3.19986e11i | −0.924591 | − | 0.924591i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 6.35796e11i | − | 1.81808i | −0.416710 | − | 0.909039i | \(-0.636817\pi\) | ||
0.416710 | − | 0.909039i | \(-0.363183\pi\) | |||||||
\(770\) | −4.84477e10 | − | 9.11828e9i | −0.137819 | − | 0.0259388i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.14340e11 | + | 1.14340e11i | 0.321906 | + | 0.321906i | ||||
\(773\) | 1.14853e11 | − | 1.14853e11i | 0.321679 | − | 0.321679i | −0.527732 | − | 0.849411i | \(-0.676957\pi\) |
0.849411 | + | 0.527732i | \(0.176957\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.75366e11 | + | 1.85507e11i | 1.31771 | + | 0.514226i | ||||
\(776\) | −8.73050e10 | −0.240764 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.27402e11 | + | 1.27402e11i | −0.347742 | + | 0.347742i | ||||
\(779\) | − | 4.04358e10i | − | 0.109804i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.20011e11 | 0.322565 | ||||||||
\(782\) | −1.58938e11 | − | 1.58938e11i | −0.425012 | − | 0.425012i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 3.81907e11i | − | 1.01087i | ||||||
\(785\) | 1.71585e11 | − | 1.17228e11i | 0.451857 | − | 0.308711i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.70517e11 | − | 2.70517e11i | −0.705173 | − | 0.705173i | 0.260343 | − | 0.965516i | \(-0.416164\pi\) |
−0.965516 | + | 0.260343i | \(0.916164\pi\) | |||||||
\(788\) | 6.09989e9 | − | 6.09989e9i | 0.0158204 | − | 0.0158204i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.72968e11 | − | 3.99540e11i | −0.700816 | − | 1.02578i | ||||
\(791\) | 9.92748e10 | 0.253591 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.28268e11 | + | 3.28268e11i | −0.830111 | + | 0.830111i | ||||
\(794\) | − | 2.28802e10i | − | 0.0575676i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.27439e11 | 0.317430 | ||||||||
\(797\) | 1.54755e11 | + | 1.54755e11i | 0.383540 | + | 0.383540i | 0.872376 | − | 0.488836i | \(-0.162578\pi\) |
−0.488836 | + | 0.872376i | \(0.662578\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 3.49346e11i | − | 0.857174i | ||||||
\(800\) | 2.12284e11 | + | 4.84004e11i | 0.518271 | + | 1.18165i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.93035e11 | + | 6.93035e11i | 1.67516 | + | 1.67516i | ||||
\(803\) | 9.14627e10 | − | 9.14627e10i | 0.219979 | − | 0.219979i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.46649e10 | − | 7.79182e10i | 0.0349217 | − | 0.185548i | ||||
\(806\) | 1.15001e12 | 2.72496 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.47746e10 | − | 4.47746e10i | 0.105048 | − | 0.105048i | ||||
\(809\) | 7.92854e11i | 1.85097i | 0.378786 | + | 0.925484i | \(0.376342\pi\) | ||||
−0.378786 | + | 0.925484i | \(0.623658\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.89034e11 | 1.13046 | 0.565230 | − | 0.824933i | \(-0.308787\pi\) | ||||
0.565230 | + | 0.824933i | \(0.308787\pi\) | |||||||
\(812\) | 7.97979e10 | + | 7.97979e10i | 0.183555 | + | 0.183555i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.06095e10i | 0.0924975i | ||||||||
\(815\) | −3.30316e11 | − | 4.83480e11i | −0.748686 | − | 1.09584i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.20746e10 | + | 5.20746e10i | 0.116879 | + | 0.116879i | ||||
\(818\) | −5.98767e11 | + | 5.98767e11i | −1.33735 | + | 1.33735i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.04205e11 | + | 7.60750e10i | 0.894018 | + | 0.168262i | ||||
\(821\) | 4.29567e11 | 0.945493 | 0.472746 | − | 0.881199i | \(-0.343263\pi\) | ||||
0.472746 | + | 0.881199i | \(0.343263\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.85110e11 | − | 1.85110e11i | 0.403489 | − | 0.403489i | −0.475972 | − | 0.879461i | \(-0.657904\pi\) |
0.879461 | + | 0.475972i | \(0.157904\pi\) | |||||||
\(824\) | − | 1.05864e10i | − | 0.0229636i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.03271e11 | −0.436673 | ||||||||
\(827\) | 1.55069e11 | + | 1.55069e11i | 0.331515 | + | 0.331515i | 0.853162 | − | 0.521646i | \(-0.174682\pi\) |
−0.521646 | + | 0.853162i | \(0.674682\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 3.62675e11i | − | 0.767891i | −0.923356 | − | 0.383945i | \(-0.874565\pi\) | ||
0.923356 | − | 0.383945i | \(-0.125435\pi\) | |||||||
\(830\) | 1.71614e11 | − | 9.11829e11i | 0.361610 | − | 1.92133i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.79045e11 | + | 2.79045e11i | 0.582345 | + | 0.582345i | ||||
\(833\) | −2.51413e11 | + | 2.51413e11i | −0.522164 | + | 0.522164i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.34461e11 | − | 2.96826e11i | 0.893727 | − | 0.610600i | ||||
\(836\) | 1.11155e10 | 0.0227563 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5.34676e11 | + | 5.34676e11i | −1.08421 | + | 1.08421i | ||||
\(839\) | 3.64884e11i | 0.736388i | 0.929749 | + | 0.368194i | \(0.120024\pi\) | ||||
−0.929749 | + | 0.368194i | \(0.879976\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.94388e10 | 0.178789 | ||||||||
\(842\) | 4.27041e11 | + | 4.27041e11i | 0.849613 | + | 0.849613i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.83125e11i | 0.360892i | ||||||||
\(845\) | 5.30491e11 | + | 9.98430e10i | 1.04052 | + | 0.195835i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.18761e11 | − | 1.18761e11i | −0.230750 | − | 0.230750i | ||||
\(848\) | 6.89596e11 | − | 6.89596e11i | 1.33356 | − | 1.33356i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.15613e11 | − | 5.52513e11i | 0.413047 | − | 1.05844i | ||||
\(851\) | −6.53121e10 | −0.124530 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.28836e11 | − | 1.28836e11i | 0.243355 | − | 0.243355i | −0.574881 | − | 0.818237i | \(-0.694952\pi\) |
0.818237 | + | 0.574881i | \(0.194952\pi\) | |||||||
\(854\) | 2.08532e11i | 0.392051i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.39091e10 | 0.119033 | ||||||||
\(857\) | −2.22087e11 | − | 2.22087e11i | −0.411718 | − | 0.411718i | 0.470619 | − | 0.882337i | \(-0.344031\pi\) |
−0.882337 | + | 0.470619i | \(0.844031\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 2.11229e11i | − | 0.387954i | −0.981006 | − | 0.193977i | \(-0.937861\pi\) | ||
0.981006 | − | 0.193977i | \(-0.0621387\pi\) | |||||||
\(860\) | −6.18521e11 | + | 4.22577e11i | −1.13073 | + | 0.772524i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.30540e10 | − | 4.30540e10i | −0.0779802 | − | 0.0779802i | ||||
\(863\) | −4.98279e11 | + | 4.98279e11i | −0.898316 | + | 0.898316i | −0.995287 | − | 0.0969711i | \(-0.969085\pi\) |
0.0969711 | + | 0.995287i | \(0.469085\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.81982e10 | + | 9.98209e10i | 0.121817 | + | 0.178302i | ||||
\(866\) | 1.04951e12 | 1.86601 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.62637e11 | − | 1.62637e11i | 0.286511 | − | 0.286511i | ||||
\(869\) | 1.54430e11i | 0.270803i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.12370e12 | −1.95243 | ||||||||
\(872\) | −1.87009e11 | − | 1.87009e11i | −0.323442 | − | 0.323442i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.01502e10i | 0.0688085i | ||||||||
\(875\) | 2.03826e11 | − | 4.71445e10i | 0.347719 | − | 0.0804264i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.72052e11 | + | 3.72052e11i | 0.628934 | + | 0.628934i | 0.947800 | − | 0.318865i | \(-0.103302\pi\) |
−0.318865 | + | 0.947800i | \(0.603302\pi\) | |||||||
\(878\) | 5.89083e10 | − | 5.89083e10i | 0.0991284 | − | 0.0991284i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.76054e10 | − | 1.99807e11i | 0.0627075 | − | 0.333180i | ||||
\(881\) | 5.29284e11 | 0.878588 | 0.439294 | − | 0.898343i | \(-0.355229\pi\) | ||||
0.439294 | + | 0.898343i | \(0.355229\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.05100e10 | − | 4.05100e10i | 0.0666376 | − | 0.0666376i | −0.673003 | − | 0.739640i | \(-0.734996\pi\) |
0.739640 | + | 0.673003i | \(0.234996\pi\) | |||||||
\(884\) | − | 5.95142e11i | − | 0.974566i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.41350e11 | −0.716223 | ||||||||
\(887\) | −6.41779e11 | − | 6.41779e11i | −1.03679 | − | 1.03679i | −0.999297 | − | 0.0374934i | \(-0.988063\pi\) |
−0.0374934 | − | 0.999297i | \(-0.511937\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.34577e11i | 0.695760i | ||||||||
\(890\) | −7.01346e11 | − | 1.02655e12i | −1.11782 | − | 1.63614i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.15409e10 | − | 8.15409e10i | −0.128800 | − | 0.128800i | ||||
\(893\) | −4.41251e10 | + | 4.41251e10i | −0.0693872 | + | 0.0693872i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.50135e11 | − | 1.41182e11i | −1.16909 | − | 0.220033i | ||||
\(896\) | −1.19542e11 | −0.185476 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.72507e11 | + | 6.72507e11i | −1.03417 | + | 1.03417i | ||||
\(899\) | 8.37274e11i | 1.28183i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.07934e11 | −1.37770 | ||||||||
\(902\) | −2.08464e11 | − | 2.08464e11i | −0.314923 | − | 0.314923i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.25753e11i | 0.188297i | ||||||||
\(905\) | 3.28586e10 | − | 1.74586e11i | 0.0489841 | − | 0.260264i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.63662e11 | + | 6.63662e11i | 0.980658 | + | 0.980658i | 0.999816 | − | 0.0191584i | \(-0.00609868\pi\) |
−0.0191584 | + | 0.999816i | \(0.506099\pi\) | |||||||
\(908\) | −3.00256e11 | + | 3.00256e11i | −0.441721 | + | 0.441721i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.89303e11 | − | 2.65974e11i | 0.567704 | − | 0.387859i | ||||
\(911\) | −6.46227e11 | −0.938235 | −0.469118 | − | 0.883136i | \(-0.655428\pi\) | ||||
−0.469118 | + | 0.883136i | \(0.655428\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.09386e11 | + | 2.09386e11i | −0.301345 | + | 0.301345i | ||||
\(914\) | − | 5.97138e11i | − | 0.855637i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.80008e11 | −0.823858 | ||||||||
\(917\) | 3.51261e11 | + | 3.51261e11i | 0.496767 | + | 0.496767i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1.63185e11i | − | 0.228780i | −0.993436 | − | 0.114390i | \(-0.963509\pi\) | ||
0.993436 | − | 0.114390i | \(-0.0364914\pi\) | |||||||
\(920\) | 9.87000e10 | + | 1.85762e10i | 0.137773 | + | 0.0259302i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.03234e12 | + | 1.03234e12i | 1.42856 | + | 1.42856i | ||||
\(923\) | −8.11602e11 | + | 8.11602e11i | −1.11824 | + | 1.11824i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.92207e10 | − | 1.57822e11i | −0.0945516 | − | 0.215576i | ||||
\(926\) | −2.42484e11 | −0.329791 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.13194e11 | + | 6.13194e11i | −0.826811 | + | 0.826811i | ||||
\(929\) | 7.83337e11i | 1.05169i | 0.850582 | + | 0.525843i | \(0.176250\pi\) | ||||
−0.850582 | + | 0.525843i | \(0.823750\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.35106e10 | 0.0845372 | ||||||||
\(932\) | −1.40278e11 | − | 1.40278e11i | −0.185920 | − | 0.185920i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 1.75742e12i | − | 2.30934i | ||||||
\(935\) | −1.56290e11 | + | 1.06779e11i | −0.204497 | + | 0.139713i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.59654e8 | + | 4.59654e8i | 0.000596311 | + | 0.000596311i | 0.707405 | − | 0.706809i | \(-0.249866\pi\) |
−0.706809 | + | 0.707405i | \(0.749866\pi\) | |||||||
\(938\) | −3.56914e11 | + | 3.56914e11i | −0.461055 | + | 0.461055i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.58068e11 | − | 5.24100e11i | −0.458621 | − | 0.671278i | ||||
\(941\) | −5.93683e11 | −0.757175 | −0.378587 | − | 0.925566i | \(-0.623590\pi\) | ||||
−0.378587 | + | 0.925566i | \(0.623590\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.35271e11 | − | 3.35271e11i | 0.423984 | − | 0.423984i | ||||
\(944\) | − | 8.38327e11i | − | 1.05566i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.36933e11 | 0.670433 | ||||||||
\(947\) | −7.81898e11 | − | 7.81898e11i | −0.972187 | − | 0.972187i | 0.0274361 | − | 0.999624i | \(-0.491266\pi\) |
−0.999624 | + | 0.0274361i | \(0.991266\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.23707e12i | 1.52522i | ||||||||
\(950\) | −9.70202e10 | + | 4.25530e10i | −0.119115 | + | 0.0522439i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.64867e10 | + | 4.64867e10i | 0.0565954 | + | 0.0565954i | ||||
\(953\) | 9.89132e11 | − | 9.89132e11i | 1.19917 | − | 1.19917i | 0.224761 | − | 0.974414i | \(-0.427840\pi\) |
0.974414 | − | 0.224761i | \(-0.0721601\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.25184e10 | − | 4.38441e11i | 0.0992059 | − | 0.527105i | ||||
\(956\) | −6.84636e11 | −0.819649 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.37208e12 | − | 1.37208e12i | 1.62899 | − | 1.62899i | ||||
\(959\) | − | 1.64651e11i | − | 0.194666i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.53571e11 | 1.00080 | ||||||||
\(962\) | −2.74631e11 | − | 2.74631e11i | −0.320663 | − | 0.320663i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 4.97286e11i | − | 0.575835i | ||||||
\(965\) | 2.77469e11 | + | 4.06127e11i | 0.319966 | + | 0.468331i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.58888e11 | + | 2.58888e11i | 0.296078 | + | 0.296078i | 0.839475 | − | 0.543398i | \(-0.182862\pi\) |
−0.543398 | + | 0.839475i | \(0.682862\pi\) | |||||||
\(968\) | 1.50436e11 | − | 1.50436e11i | 0.171337 | − | 0.171337i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.06125e12 | + | 1.99736e11i | 1.19875 | + | 0.225616i | ||||
\(971\) | −1.02230e12 | −1.15001 | −0.575005 | − | 0.818150i | \(-0.695000\pi\) | ||||
−0.575005 | + | 0.818150i | \(0.695000\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.26460e11 | − | 2.26460e11i | 0.252662 | − | 0.252662i | ||||
\(974\) | − | 8.91761e11i | − | 0.990861i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.60024e11 | −0.947788 | ||||||||
\(977\) | 4.00291e11 | + | 4.00291e11i | 0.439337 | + | 0.439337i | 0.891789 | − | 0.452452i | \(-0.149451\pi\) |
−0.452452 | + | 0.891789i | \(0.649451\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.96782e11i | 0.431938i | ||||||||
\(980\) | −1.19487e11 | + | 6.34866e11i | −0.129544 | + | 0.688300i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.53547e12 | − | 1.53547e12i | −1.65119 | − | 1.65119i | ||||
\(983\) | 8.42757e11 | − | 8.42757e11i | 0.902586 | − | 0.902586i | −0.0930734 | − | 0.995659i | \(-0.529669\pi\) |
0.995659 | + | 0.0930734i | \(0.0296691\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.16664e10 | − | 1.48026e10i | 0.0230166 | − | 0.0157251i | ||||
\(986\) | 9.73156e11 | 1.02961 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.51709e10 | + | 7.51709e10i | −0.0788900 | + | 0.0788900i | ||||
\(989\) | 8.63547e11i | 0.902611i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.85378e12 | 1.92205 | 0.961023 | − | 0.276468i | \(-0.0891641\pi\) | ||||
0.961023 | + | 0.276468i | \(0.0891641\pi\) | |||||||
\(992\) | 1.24976e12 | + | 1.24976e12i | 1.29057 | + | 1.29057i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.15571e11i | 0.528132i | ||||||||
\(995\) | 3.80954e11 | + | 7.16988e10i | 0.388669 | + | 0.0731509i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.39430e11 | + | 9.39430e11i | 0.950788 | + | 0.950788i | 0.998845 | − | 0.0480567i | \(-0.0153028\pi\) |
−0.0480567 | + | 0.998845i | \(0.515303\pi\) | |||||||
\(998\) | 9.37219e10 | − | 9.37219e10i | 0.0944754 | − | 0.0944754i | ||||
\(999\) | 0 | 0 |
(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 | 45.9.g.b.37.2 | yes | 16 | |
3.2 | odd | 2 | inner | 45.9.g.b.37.7 | yes | 16 | |
5.3 | odd | 4 | inner | 45.9.g.b.28.2 | ✓ | 16 | |
15.8 | even | 4 | inner | 45.9.g.b.28.7 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.9.g.b.28.2 | ✓ | 16 | 5.3 | odd | 4 | inner | |
45.9.g.b.28.7 | yes | 16 | 15.8 | even | 4 | inner | |
45.9.g.b.37.2 | yes | 16 | 1.1 | even | 1 | trivial | |
45.9.g.b.37.7 | yes | 16 | 3.2 | odd | 2 | inner |