Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,11,Mod(58,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.58");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(112.458233723\) |
Analytic rank: | \(0\) |
Dimension: | \(100\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.13 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.11.c.a.58.88 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 50.8928i | − | 1.59040i | −0.606348 | − | 0.795200i | \(-0.707366\pi\) | ||
0.606348 | − | 0.795200i | \(-0.292634\pi\) | |||||||
\(3\) | 140.296 | 0.577350 | ||||||||
\(4\) | −1566.07 | −1.52937 | ||||||||
\(5\) | 2107.07 | 0.674262 | 0.337131 | − | 0.941458i | \(-0.390543\pi\) | ||||
0.337131 | + | 0.941458i | \(0.390543\pi\) | |||||||
\(6\) | − | 7140.06i | − | 0.918217i | ||||||
\(7\) | −26451.4 | −1.57383 | −0.786917 | − | 0.617059i | \(-0.788324\pi\) | ||||
−0.786917 | + | 0.617059i | \(0.788324\pi\) | |||||||
\(8\) | 27587.7i | 0.841910i | ||||||||
\(9\) | 19683.0 | 0.333333 | ||||||||
\(10\) | − | 107235.i | − | 1.07235i | ||||||
\(11\) | − | 141491.i | − | 0.878549i | −0.898353 | − | 0.439274i | \(-0.855236\pi\) | ||
0.898353 | − | 0.439274i | \(-0.144764\pi\) | |||||||
\(12\) | −219714. | −0.882982 | ||||||||
\(13\) | − | 258539.i | − | 0.696320i | −0.937435 | − | 0.348160i | \(-0.886807\pi\) | ||
0.937435 | − | 0.348160i | \(-0.113193\pi\) | |||||||
\(14\) | 1.34619e6i | 2.50303i | ||||||||
\(15\) | 295614. | 0.389286 | ||||||||
\(16\) | −199646. | −0.190398 | ||||||||
\(17\) | 600229. | 0.422739 | 0.211369 | − | 0.977406i | \(-0.432208\pi\) | ||||
0.211369 | + | 0.977406i | \(0.432208\pi\) | |||||||
\(18\) | − | 1.00172e6i | − | 0.530133i | ||||||
\(19\) | −43051.6 | −0.0173869 | −0.00869344 | − | 0.999962i | \(-0.502767\pi\) | ||||
−0.00869344 | + | 0.999962i | \(0.502767\pi\) | |||||||
\(20\) | −3.29983e6 | −1.03120 | ||||||||
\(21\) | −3.71103e6 | −0.908654 | ||||||||
\(22\) | −7.20088e6 | −1.39724 | ||||||||
\(23\) | − | 1.84919e6i | − | 0.287304i | −0.989628 | − | 0.143652i | \(-0.954115\pi\) | ||
0.989628 | − | 0.143652i | \(-0.0458846\pi\) | |||||||
\(24\) | 3.87045e6i | 0.486077i | ||||||||
\(25\) | −5.32588e6 | −0.545370 | ||||||||
\(26\) | −1.31578e7 | −1.10743 | ||||||||
\(27\) | 2.76145e6 | 0.192450 | ||||||||
\(28\) | 4.14249e7 | 2.40698 | ||||||||
\(29\) | 3.28651e6 | 0.160231 | 0.0801153 | − | 0.996786i | \(-0.474471\pi\) | ||||
0.0801153 | + | 0.996786i | \(0.474471\pi\) | |||||||
\(30\) | − | 1.50446e7i | − | 0.619120i | ||||||
\(31\) | − | 6.86797e6i | − | 0.239894i | −0.992780 | − | 0.119947i | \(-0.961728\pi\) | ||
0.992780 | − | 0.119947i | \(-0.0382725\pi\) | |||||||
\(32\) | 3.84104e7i | 1.14472i | ||||||||
\(33\) | − | 1.98507e7i | − | 0.507230i | ||||||
\(34\) | − | 3.05473e7i | − | 0.672323i | ||||||
\(35\) | −5.57350e7 | −1.06118 | ||||||||
\(36\) | −3.08250e7 | −0.509790 | ||||||||
\(37\) | − | 3.37758e7i | − | 0.487077i | −0.969891 | − | 0.243538i | \(-0.921692\pi\) | ||
0.969891 | − | 0.243538i | \(-0.0783082\pi\) | |||||||
\(38\) | 2.19102e6i | 0.0276521i | ||||||||
\(39\) | − | 3.62720e7i | − | 0.402021i | ||||||
\(40\) | 5.81292e7i | 0.567668i | ||||||||
\(41\) | −1.94974e8 | −1.68290 | −0.841448 | − | 0.540338i | \(-0.818297\pi\) | ||||
−0.841448 | + | 0.540338i | \(0.818297\pi\) | |||||||
\(42\) | 1.88865e8i | 1.44512i | ||||||||
\(43\) | − | 7.75843e7i | − | 0.527754i | −0.964556 | − | 0.263877i | \(-0.914999\pi\) | ||
0.964556 | − | 0.263877i | \(-0.0850014\pi\) | |||||||
\(44\) | 2.21586e8i | 1.34363i | ||||||||
\(45\) | 4.14735e7 | 0.224754 | ||||||||
\(46\) | −9.41104e7 | −0.456929 | ||||||||
\(47\) | 1.56607e8i | 0.682846i | 0.939910 | + | 0.341423i | \(0.110909\pi\) | ||||
−0.939910 | + | 0.341423i | \(0.889091\pi\) | |||||||
\(48\) | −2.80096e7 | −0.109926 | ||||||||
\(49\) | 4.17203e8 | 1.47696 | ||||||||
\(50\) | 2.71049e8i | 0.867356i | ||||||||
\(51\) | 8.42097e7 | 0.244068 | ||||||||
\(52\) | 4.04891e8i | 1.06493i | ||||||||
\(53\) | −1.74257e8 | −0.416688 | −0.208344 | − | 0.978056i | \(-0.566807\pi\) | ||||
−0.208344 | + | 0.978056i | \(0.566807\pi\) | |||||||
\(54\) | − | 1.40538e8i | − | 0.306072i | ||||||
\(55\) | − | 2.98132e8i | − | 0.592372i | ||||||
\(56\) | − | 7.29734e8i | − | 1.32503i | ||||||
\(57\) | −6.03998e6 | −0.0100383 | ||||||||
\(58\) | − | 1.67260e8i | − | 0.254831i | ||||||
\(59\) | 6.14004e8 | − | 3.66219e8i | 0.858837 | − | 0.512249i | ||||
\(60\) | −4.62953e8 | −0.595362 | ||||||||
\(61\) | − | 1.60873e8i | − | 0.190473i | −0.995455 | − | 0.0952365i | \(-0.969639\pi\) | ||
0.995455 | − | 0.0952365i | \(-0.0303607\pi\) | |||||||
\(62\) | −3.49530e8 | −0.381528 | ||||||||
\(63\) | −5.20644e8 | −0.524611 | ||||||||
\(64\) | 1.75037e9 | 1.63016 | ||||||||
\(65\) | − | 5.44760e8i | − | 0.469503i | ||||||
\(66\) | −1.01026e9 | −0.806699 | ||||||||
\(67\) | 1.29604e9i | 0.959938i | 0.877285 | + | 0.479969i | \(0.159352\pi\) | ||||
−0.877285 | + | 0.479969i | \(0.840648\pi\) | |||||||
\(68\) | −9.40003e8 | −0.646524 | ||||||||
\(69\) | − | 2.59434e8i | − | 0.165875i | ||||||
\(70\) | 2.83651e9i | 1.68770i | ||||||||
\(71\) | −1.68138e9 | −0.931910 | −0.465955 | − | 0.884808i | \(-0.654289\pi\) | ||||
−0.465955 | + | 0.884808i | \(0.654289\pi\) | |||||||
\(72\) | 5.43009e8i | 0.280637i | ||||||||
\(73\) | 3.06702e9i | 1.47946i | 0.672905 | + | 0.739729i | \(0.265046\pi\) | ||||
−0.672905 | + | 0.739729i | \(0.734954\pi\) | |||||||
\(74\) | −1.71895e9 | −0.774647 | ||||||||
\(75\) | −7.47200e8 | −0.314870 | ||||||||
\(76\) | 6.74221e7 | 0.0265910 | ||||||||
\(77\) | 3.74264e9i | 1.38269i | ||||||||
\(78\) | −1.84598e9 | −0.639374 | ||||||||
\(79\) | 1.15229e9 | 0.374476 | 0.187238 | − | 0.982315i | \(-0.440046\pi\) | ||||
0.187238 | + | 0.982315i | \(0.440046\pi\) | |||||||
\(80\) | −4.20669e8 | −0.128378 | ||||||||
\(81\) | 3.87420e8 | 0.111111 | ||||||||
\(82\) | 9.92277e9i | 2.67648i | ||||||||
\(83\) | 7.52537e9i | 1.91046i | 0.295867 | + | 0.955229i | \(0.404392\pi\) | ||||
−0.295867 | + | 0.955229i | \(0.595608\pi\) | |||||||
\(84\) | 5.81176e9 | 1.38967 | ||||||||
\(85\) | 1.26472e9 | 0.285037 | ||||||||
\(86\) | −3.94848e9 | −0.839340 | ||||||||
\(87\) | 4.61085e8 | 0.0925092 | ||||||||
\(88\) | 3.90341e9 | 0.739658 | ||||||||
\(89\) | 5.42130e9i | 0.970854i | 0.874277 | + | 0.485427i | \(0.161336\pi\) | ||||
−0.874277 | + | 0.485427i | \(0.838664\pi\) | |||||||
\(90\) | − | 2.11070e9i | − | 0.357449i | ||||||
\(91\) | 6.83873e9i | 1.09589i | ||||||||
\(92\) | 2.89597e9i | 0.439395i | ||||||||
\(93\) | − | 9.63549e8i | − | 0.138503i | ||||||
\(94\) | 7.97019e9 | 1.08600 | ||||||||
\(95\) | −9.07128e7 | −0.0117233 | ||||||||
\(96\) | 5.38882e9i | 0.660903i | ||||||||
\(97\) | − | 3.52047e9i | − | 0.409961i | −0.978766 | − | 0.204980i | \(-0.934287\pi\) | ||
0.978766 | − | 0.204980i | \(-0.0657131\pi\) | |||||||
\(98\) | − | 2.12326e10i | − | 2.34895i | ||||||
\(99\) | − | 2.78497e9i | − | 0.292850i | ||||||
\(100\) | 8.34073e9 | 0.834073 | ||||||||
\(101\) | 1.23159e10i | 1.17182i | 0.810377 | + | 0.585909i | \(0.199262\pi\) | ||||
−0.810377 | + | 0.585909i | \(0.800738\pi\) | |||||||
\(102\) | − | 4.28567e9i | − | 0.388166i | ||||||
\(103\) | 4.05209e9i | 0.349537i | 0.984610 | + | 0.174769i | \(0.0559177\pi\) | ||||
−0.984610 | + | 0.174769i | \(0.944082\pi\) | |||||||
\(104\) | 7.13249e9 | 0.586239 | ||||||||
\(105\) | −7.81941e9 | −0.612671 | ||||||||
\(106\) | 8.86843e9i | 0.662701i | ||||||||
\(107\) | −1.04529e10 | −0.745277 | −0.372638 | − | 0.927977i | \(-0.621547\pi\) | ||||
−0.372638 | + | 0.927977i | \(0.621547\pi\) | |||||||
\(108\) | −4.32463e9 | −0.294327 | ||||||||
\(109\) | 1.90603e10i | 1.23879i | 0.785080 | + | 0.619395i | \(0.212622\pi\) | ||||
−0.785080 | + | 0.619395i | \(0.787378\pi\) | |||||||
\(110\) | −1.51728e10 | −0.942109 | ||||||||
\(111\) | − | 4.73862e9i | − | 0.281214i | ||||||
\(112\) | 5.28093e9 | 0.299654 | ||||||||
\(113\) | − | 2.03020e10i | − | 1.10191i | −0.834534 | − | 0.550956i | \(-0.814263\pi\) | ||
0.834534 | − | 0.550956i | \(-0.185737\pi\) | |||||||
\(114\) | 3.07391e8i | 0.0159649i | ||||||||
\(115\) | − | 3.89637e9i | − | 0.193718i | ||||||
\(116\) | −5.14693e9 | −0.245052 | ||||||||
\(117\) | − | 5.08882e9i | − | 0.232107i | ||||||
\(118\) | −1.86379e10 | − | 3.12483e10i | −0.814680 | − | 1.36589i | ||||
\(119\) | −1.58769e10 | −0.665321 | ||||||||
\(120\) | 8.15530e9i | 0.327743i | ||||||||
\(121\) | 5.91768e9 | 0.228152 | ||||||||
\(122\) | −8.18726e9 | −0.302928 | ||||||||
\(123\) | −2.73541e10 | −0.971621 | ||||||||
\(124\) | 1.07558e10i | 0.366887i | ||||||||
\(125\) | −3.17989e10 | −1.04199 | ||||||||
\(126\) | 2.64970e10i | 0.834342i | ||||||||
\(127\) | 4.04217e10 | 1.22348 | 0.611738 | − | 0.791060i | \(-0.290470\pi\) | ||||
0.611738 | + | 0.791060i | \(0.290470\pi\) | |||||||
\(128\) | − | 4.97491e10i | − | 1.44789i | ||||||
\(129\) | − | 1.08848e10i | − | 0.304699i | ||||||
\(130\) | −2.77243e10 | −0.746697 | ||||||||
\(131\) | − | 3.47554e10i | − | 0.900877i | −0.892807 | − | 0.450439i | \(-0.851268\pi\) | ||
0.892807 | − | 0.450439i | \(-0.148732\pi\) | |||||||
\(132\) | 3.10876e10i | 0.775743i | ||||||||
\(133\) | 1.13878e9 | 0.0273641 | ||||||||
\(134\) | 6.59589e10 | 1.52669 | ||||||||
\(135\) | 5.81857e9 | 0.129762 | ||||||||
\(136\) | 1.65589e10i | 0.355908i | ||||||||
\(137\) | 6.12256e10 | 1.26862 | 0.634308 | − | 0.773080i | \(-0.281285\pi\) | ||||
0.634308 | + | 0.773080i | \(0.281285\pi\) | |||||||
\(138\) | −1.32033e10 | −0.263808 | ||||||||
\(139\) | −1.49800e10 | −0.288694 | −0.144347 | − | 0.989527i | \(-0.546108\pi\) | ||||
−0.144347 | + | 0.989527i | \(0.546108\pi\) | |||||||
\(140\) | 8.72852e10 | 1.62293 | ||||||||
\(141\) | 2.19714e10i | 0.394242i | ||||||||
\(142\) | 8.55701e10i | 1.48211i | ||||||||
\(143\) | −3.65810e10 | −0.611751 | ||||||||
\(144\) | −3.92964e9 | −0.0634659 | ||||||||
\(145\) | 6.92491e9 | 0.108037 | ||||||||
\(146\) | 1.56089e11 | 2.35293 | ||||||||
\(147\) | 5.85320e10 | 0.852720 | ||||||||
\(148\) | 5.28955e10i | 0.744921i | ||||||||
\(149\) | − | 1.48074e10i | − | 0.201626i | −0.994905 | − | 0.100813i | \(-0.967856\pi\) | ||
0.994905 | − | 0.100813i | \(-0.0321444\pi\) | |||||||
\(150\) | 3.80271e10i | 0.500768i | ||||||||
\(151\) | − | 5.55513e10i | − | 0.707635i | −0.935314 | − | 0.353818i | \(-0.884883\pi\) | ||
0.935314 | − | 0.353818i | \(-0.115117\pi\) | |||||||
\(152\) | − | 1.18770e9i | − | 0.0146382i | ||||||
\(153\) | 1.18143e10 | 0.140913 | ||||||||
\(154\) | 1.90474e11 | 2.19903 | ||||||||
\(155\) | − | 1.44713e10i | − | 0.161752i | ||||||
\(156\) | 5.68047e10i | 0.614838i | ||||||||
\(157\) | − | 1.11194e11i | − | 1.16570i | −0.812582 | − | 0.582848i | \(-0.801938\pi\) | ||
0.812582 | − | 0.582848i | \(-0.198062\pi\) | |||||||
\(158\) | − | 5.86430e10i | − | 0.595567i | ||||||
\(159\) | −2.44476e10 | −0.240575 | ||||||||
\(160\) | 8.09333e10i | 0.771840i | ||||||||
\(161\) | 4.89137e10i | 0.452169i | ||||||||
\(162\) | − | 1.97169e10i | − | 0.176711i | ||||||
\(163\) | 6.14155e10 | 0.533753 | 0.266876 | − | 0.963731i | \(-0.414008\pi\) | ||||
0.266876 | + | 0.963731i | \(0.414008\pi\) | |||||||
\(164\) | 3.05344e11 | 2.57377 | ||||||||
\(165\) | − | 4.18267e10i | − | 0.342006i | ||||||
\(166\) | 3.82987e11 | 3.03839 | ||||||||
\(167\) | −6.25161e10 | −0.481293 | −0.240646 | − | 0.970613i | \(-0.577359\pi\) | ||||
−0.240646 | + | 0.970613i | \(0.577359\pi\) | |||||||
\(168\) | − | 1.02379e11i | − | 0.765004i | ||||||
\(169\) | 7.10161e10 | 0.515138 | ||||||||
\(170\) | − | 6.43653e10i | − | 0.453322i | ||||||
\(171\) | −8.47385e8 | −0.00579563 | ||||||||
\(172\) | 1.21503e11i | 0.807132i | ||||||||
\(173\) | 1.32957e11i | 0.857987i | 0.903307 | + | 0.428994i | \(0.141132\pi\) | ||||
−0.903307 | + | 0.428994i | \(0.858868\pi\) | |||||||
\(174\) | − | 2.34659e10i | − | 0.147127i | ||||||
\(175\) | 1.40877e11 | 0.858322 | ||||||||
\(176\) | 2.82482e10i | 0.167274i | ||||||||
\(177\) | 8.61423e10 | − | 5.13791e10i | 0.495850 | − | 0.295747i | ||||
\(178\) | 2.75905e11 | 1.54405 | ||||||||
\(179\) | − | 9.63839e9i | − | 0.0524493i | −0.999656 | − | 0.0262246i | \(-0.991651\pi\) | ||
0.999656 | − | 0.0262246i | \(-0.00834852\pi\) | |||||||
\(180\) | −6.49505e10 | −0.343732 | ||||||||
\(181\) | −1.12840e11 | −0.580857 | −0.290429 | − | 0.956897i | \(-0.593798\pi\) | ||||
−0.290429 | + | 0.956897i | \(0.593798\pi\) | |||||||
\(182\) | 3.48042e11 | 1.74291 | ||||||||
\(183\) | − | 2.25698e10i | − | 0.109970i | ||||||
\(184\) | 5.10149e10 | 0.241884 | ||||||||
\(185\) | − | 7.11681e10i | − | 0.328418i | ||||||
\(186\) | −4.90377e10 | −0.220275 | ||||||||
\(187\) | − | 8.49270e10i | − | 0.371397i | ||||||
\(188\) | − | 2.45259e11i | − | 1.04432i | ||||||
\(189\) | −7.30443e10 | −0.302885 | ||||||||
\(190\) | 4.61663e9i | 0.0186448i | ||||||||
\(191\) | 4.37205e11i | 1.71996i | 0.510329 | + | 0.859979i | \(0.329524\pi\) | ||||
−0.510329 | + | 0.859979i | \(0.670476\pi\) | |||||||
\(192\) | 2.45570e11 | 0.941174 | ||||||||
\(193\) | −4.25062e11 | −1.58732 | −0.793662 | − | 0.608359i | \(-0.791828\pi\) | ||||
−0.793662 | + | 0.608359i | \(0.791828\pi\) | |||||||
\(194\) | −1.79167e11 | −0.652001 | ||||||||
\(195\) | − | 7.64277e10i | − | 0.271068i | ||||||
\(196\) | −6.53371e11 | −2.25881 | ||||||||
\(197\) | −8.09420e10 | −0.272799 | −0.136400 | − | 0.990654i | \(-0.543553\pi\) | ||||
−0.136400 | + | 0.990654i | \(0.543553\pi\) | |||||||
\(198\) | −1.41735e11 | −0.465748 | ||||||||
\(199\) | −4.10305e11 | −1.31475 | −0.657373 | − | 0.753566i | \(-0.728332\pi\) | ||||
−0.657373 | + | 0.753566i | \(0.728332\pi\) | |||||||
\(200\) | − | 1.46929e11i | − | 0.459152i | ||||||
\(201\) | 1.81829e11i | 0.554221i | ||||||||
\(202\) | 6.26791e11 | 1.86366 | ||||||||
\(203\) | −8.69330e10 | −0.252176 | ||||||||
\(204\) | −1.31879e11 | −0.373271 | ||||||||
\(205\) | −4.10824e11 | −1.13471 | ||||||||
\(206\) | 2.06222e11 | 0.555904 | ||||||||
\(207\) | − | 3.63976e10i | − | 0.0957681i | ||||||
\(208\) | 5.16164e10i | 0.132578i | ||||||||
\(209\) | 6.09143e9i | 0.0152752i | ||||||||
\(210\) | 3.97951e11i | 0.974392i | ||||||||
\(211\) | 4.72052e10i | 0.112870i | 0.998406 | + | 0.0564348i | \(0.0179733\pi\) | ||||
−0.998406 | + | 0.0564348i | \(0.982027\pi\) | |||||||
\(212\) | 2.72900e11 | 0.637271 | ||||||||
\(213\) | −2.35891e11 | −0.538039 | ||||||||
\(214\) | 5.31977e11i | 1.18529i | ||||||||
\(215\) | − | 1.63476e11i | − | 0.355845i | ||||||
\(216\) | 7.61820e10i | 0.162026i | ||||||||
\(217\) | 1.81668e11i | 0.377554i | ||||||||
\(218\) | 9.70032e11 | 1.97017 | ||||||||
\(219\) | 4.30291e11i | 0.854165i | ||||||||
\(220\) | 4.66897e11i | 0.905957i | ||||||||
\(221\) | − | 1.55182e11i | − | 0.294362i | ||||||
\(222\) | −2.41161e11 | −0.447242 | ||||||||
\(223\) | −3.57720e11 | −0.648663 | −0.324331 | − | 0.945943i | \(-0.605139\pi\) | ||||
−0.324331 | + | 0.945943i | \(0.605139\pi\) | |||||||
\(224\) | − | 1.01601e12i | − | 1.80160i | ||||||
\(225\) | −1.04829e11 | −0.181790 | ||||||||
\(226\) | −1.03323e12 | −1.75248 | ||||||||
\(227\) | − | 2.97110e11i | − | 0.492933i | −0.969151 | − | 0.246466i | \(-0.920731\pi\) | ||
0.969151 | − | 0.246466i | \(-0.0792695\pi\) | |||||||
\(228\) | 9.45906e9 | 0.0153523 | ||||||||
\(229\) | − | 6.05682e11i | − | 0.961761i | −0.876786 | − | 0.480880i | \(-0.840317\pi\) | ||
0.876786 | − | 0.480880i | \(-0.159683\pi\) | |||||||
\(230\) | −1.98297e11 | −0.308090 | ||||||||
\(231\) | 5.25078e11i | 0.798297i | ||||||||
\(232\) | 9.06673e10i | 0.134900i | ||||||||
\(233\) | − | 5.51638e11i | − | 0.803294i | −0.915795 | − | 0.401647i | \(-0.868438\pi\) | ||
0.915795 | − | 0.401647i | \(-0.131562\pi\) | |||||||
\(234\) | −2.58984e11 | −0.369143 | ||||||||
\(235\) | 3.29983e11i | 0.460418i | ||||||||
\(236\) | −9.61576e11 | + | 5.73526e11i | −1.31348 | + | 0.783418i | ||||
\(237\) | 1.61661e11 | 0.216204 | ||||||||
\(238\) | 8.08020e11i | 1.05813i | ||||||||
\(239\) | 9.48583e11 | 1.21643 | 0.608213 | − | 0.793774i | \(-0.291887\pi\) | ||||
0.608213 | + | 0.793774i | \(0.291887\pi\) | |||||||
\(240\) | −5.90182e10 | −0.0741190 | ||||||||
\(241\) | −4.19889e11 | −0.516475 | −0.258238 | − | 0.966081i | \(-0.583142\pi\) | ||||
−0.258238 | + | 0.966081i | \(0.583142\pi\) | |||||||
\(242\) | − | 3.01167e11i | − | 0.362853i | ||||||
\(243\) | 5.43536e10 | 0.0641500 | ||||||||
\(244\) | 2.51939e11i | 0.291304i | ||||||||
\(245\) | 8.79077e11 | 0.995855 | ||||||||
\(246\) | 1.39213e12i | 1.54526i | ||||||||
\(247\) | 1.11305e10i | 0.0121068i | ||||||||
\(248\) | 1.89471e11 | 0.201969 | ||||||||
\(249\) | 1.05578e12i | 1.10300i | ||||||||
\(250\) | 1.61833e12i | 1.65717i | ||||||||
\(251\) | 1.00757e12 | 1.01136 | 0.505680 | − | 0.862721i | \(-0.331242\pi\) | ||||
0.505680 | + | 0.862721i | \(0.331242\pi\) | |||||||
\(252\) | 8.15367e11 | 0.802325 | ||||||||
\(253\) | −2.61644e11 | −0.252411 | ||||||||
\(254\) | − | 2.05717e12i | − | 1.94582i | ||||||
\(255\) | 1.77436e11 | 0.164566 | ||||||||
\(256\) | −7.39488e11 | −0.672560 | ||||||||
\(257\) | −9.37522e11 | −0.836211 | −0.418105 | − | 0.908399i | \(-0.637306\pi\) | ||||
−0.418105 | + | 0.908399i | \(0.637306\pi\) | |||||||
\(258\) | −5.53957e11 | −0.484593 | ||||||||
\(259\) | 8.93419e11i | 0.766578i | ||||||||
\(260\) | 8.53134e11i | 0.718043i | ||||||||
\(261\) | 6.46884e10 | 0.0534102 | ||||||||
\(262\) | −1.76880e12 | −1.43275 | ||||||||
\(263\) | 5.91121e11 | 0.469784 | 0.234892 | − | 0.972022i | \(-0.424526\pi\) | ||||
0.234892 | + | 0.972022i | \(0.424526\pi\) | |||||||
\(264\) | 5.47634e11 | 0.427042 | ||||||||
\(265\) | −3.67172e11 | −0.280957 | ||||||||
\(266\) | − | 5.79556e10i | − | 0.0435198i | ||||||
\(267\) | 7.60588e11i | 0.560523i | ||||||||
\(268\) | − | 2.02969e12i | − | 1.46810i | ||||||
\(269\) | 6.67313e11i | 0.473771i | 0.971538 | + | 0.236885i | \(0.0761266\pi\) | ||||
−0.971538 | + | 0.236885i | \(0.923873\pi\) | |||||||
\(270\) | − | 2.96123e11i | − | 0.206373i | ||||||
\(271\) | −1.30064e12 | −0.889837 | −0.444918 | − | 0.895571i | \(-0.646767\pi\) | ||||
−0.444918 | + | 0.895571i | \(0.646767\pi\) | |||||||
\(272\) | −1.19833e11 | −0.0804884 | ||||||||
\(273\) | 9.59447e11i | 0.632714i | ||||||||
\(274\) | − | 3.11594e12i | − | 2.01761i | ||||||
\(275\) | 7.53565e11i | 0.479134i | ||||||||
\(276\) | 4.06293e11i | 0.253685i | ||||||||
\(277\) | 1.95780e11 | 0.120052 | 0.0600261 | − | 0.998197i | \(-0.480882\pi\) | ||||
0.0600261 | + | 0.998197i | \(0.480882\pi\) | |||||||
\(278\) | 7.62375e11i | 0.459140i | ||||||||
\(279\) | − | 1.35182e11i | − | 0.0799647i | ||||||
\(280\) | − | 1.53760e12i | − | 0.893415i | ||||||
\(281\) | −2.19824e12 | −1.25471 | −0.627354 | − | 0.778734i | \(-0.715862\pi\) | ||||
−0.627354 | + | 0.778734i | \(0.715862\pi\) | |||||||
\(282\) | 1.11819e12 | 0.627001 | ||||||||
\(283\) | 6.67958e11i | 0.367974i | 0.982929 | + | 0.183987i | \(0.0589004\pi\) | ||||
−0.982929 | + | 0.183987i | \(0.941100\pi\) | |||||||
\(284\) | 2.63317e12 | 1.42524 | ||||||||
\(285\) | −1.27267e10 | −0.00676846 | ||||||||
\(286\) | 1.86171e12i | 0.972929i | ||||||||
\(287\) | 5.15734e12 | 2.64860 | ||||||||
\(288\) | 7.56031e11i | 0.381573i | ||||||||
\(289\) | −1.65572e12 | −0.821292 | ||||||||
\(290\) | − | 3.52428e11i | − | 0.171823i | ||||||
\(291\) | − | 4.93909e11i | − | 0.236691i | ||||||
\(292\) | − | 4.80318e12i | − | 2.26264i | ||||||
\(293\) | 1.38989e12 | 0.643639 | 0.321820 | − | 0.946801i | \(-0.395706\pi\) | ||||
0.321820 | + | 0.946801i | \(0.395706\pi\) | |||||||
\(294\) | − | 2.97886e12i | − | 1.35617i | ||||||
\(295\) | 1.29375e12 | − | 7.71649e11i | 0.579082 | − | 0.345390i | ||||
\(296\) | 9.31797e11 | 0.410075 | ||||||||
\(297\) | − | 3.90720e11i | − | 0.169077i | ||||||
\(298\) | −7.53588e11 | −0.320666 | ||||||||
\(299\) | −4.78087e11 | −0.200056 | ||||||||
\(300\) | 1.17017e12 | 0.481552 | ||||||||
\(301\) | 2.05222e12i | 0.830598i | ||||||||
\(302\) | −2.82716e12 | −1.12542 | ||||||||
\(303\) | 1.72788e12i | 0.676549i | ||||||||
\(304\) | 8.59510e9 | 0.00331042 | ||||||||
\(305\) | − | 3.38970e11i | − | 0.128429i | ||||||
\(306\) | − | 6.01262e11i | − | 0.224108i | ||||||
\(307\) | −9.19052e11 | −0.337014 | −0.168507 | − | 0.985700i | \(-0.553895\pi\) | ||||
−0.168507 | + | 0.985700i | \(0.553895\pi\) | |||||||
\(308\) | − | 5.86126e12i | − | 2.11464i | ||||||
\(309\) | 5.68493e11i | 0.201805i | ||||||||
\(310\) | −7.36484e11 | −0.257250 | ||||||||
\(311\) | −2.50050e12 | −0.859458 | −0.429729 | − | 0.902958i | \(-0.641391\pi\) | ||||
−0.429729 | + | 0.902958i | \(0.641391\pi\) | |||||||
\(312\) | 1.00066e12 | 0.338465 | ||||||||
\(313\) | 2.73877e12i | 0.911664i | 0.890066 | + | 0.455832i | \(0.150658\pi\) | ||||
−0.890066 | + | 0.455832i | \(0.849342\pi\) | |||||||
\(314\) | −5.65900e12 | −1.85392 | ||||||||
\(315\) | −1.09703e12 | −0.353726 | ||||||||
\(316\) | −1.80456e12 | −0.572713 | ||||||||
\(317\) | −5.65807e12 | −1.76755 | −0.883776 | − | 0.467911i | \(-0.845007\pi\) | ||||
−0.883776 | + | 0.467911i | \(0.845007\pi\) | |||||||
\(318\) | 1.24421e12i | 0.382611i | ||||||||
\(319\) | − | 4.65012e11i | − | 0.140770i | ||||||
\(320\) | 3.68816e12 | 1.09916 | ||||||||
\(321\) | −1.46650e12 | −0.430286 | ||||||||
\(322\) | 2.48935e12 | 0.719130 | ||||||||
\(323\) | −2.58408e10 | −0.00735011 | ||||||||
\(324\) | −6.06729e11 | −0.169930 | ||||||||
\(325\) | 1.37695e12i | 0.379752i | ||||||||
\(326\) | − | 3.12561e12i | − | 0.848880i | ||||||
\(327\) | 2.67409e12i | 0.715215i | ||||||||
\(328\) | − | 5.37888e12i | − | 1.41685i | ||||||
\(329\) | − | 4.14249e12i | − | 1.07469i | ||||||
\(330\) | −2.12868e12 | −0.543927 | ||||||||
\(331\) | −5.78557e12 | −1.45615 | −0.728075 | − | 0.685498i | \(-0.759585\pi\) | ||||
−0.728075 | + | 0.685498i | \(0.759585\pi\) | |||||||
\(332\) | − | 1.17853e13i | − | 2.92180i | ||||||
\(333\) | − | 6.64810e11i | − | 0.162359i | ||||||
\(334\) | 3.18162e12i | 0.765448i | ||||||||
\(335\) | 2.73084e12i | 0.647250i | ||||||||
\(336\) | 7.40894e11 | 0.173006 | ||||||||
\(337\) | − | 3.77177e12i | − | 0.867752i | −0.900973 | − | 0.433876i | \(-0.857146\pi\) | ||
0.900973 | − | 0.433876i | \(-0.142854\pi\) | |||||||
\(338\) | − | 3.61421e12i | − | 0.819275i | ||||||
\(339\) | − | 2.84830e12i | − | 0.636190i | ||||||
\(340\) | −1.98065e12 | −0.435927 | ||||||||
\(341\) | −9.71757e11 | −0.210759 | ||||||||
\(342\) | 4.31258e10i | 0.00921736i | ||||||||
\(343\) | −3.56375e12 | −0.750648 | ||||||||
\(344\) | 2.14037e12 | 0.444321 | ||||||||
\(345\) | − | 5.46646e11i | − | 0.111843i | ||||||
\(346\) | 6.76655e12 | 1.36454 | ||||||||
\(347\) | − | 1.54001e12i | − | 0.306109i | −0.988218 | − | 0.153054i | \(-0.951089\pi\) | ||
0.988218 | − | 0.153054i | \(-0.0489109\pi\) | |||||||
\(348\) | −7.22094e11 | −0.141481 | ||||||||
\(349\) | − | 4.66261e10i | − | 0.00900538i | −0.999990 | − | 0.00450269i | \(-0.998567\pi\) | ||
0.999990 | − | 0.00450269i | \(-0.00143326\pi\) | |||||||
\(350\) | − | 7.16963e12i | − | 1.36508i | ||||||
\(351\) | − | 7.13942e11i | − | 0.134007i | ||||||
\(352\) | 5.43472e12 | 1.00569 | ||||||||
\(353\) | − | 1.25736e12i | − | 0.229396i | −0.993400 | − | 0.114698i | \(-0.963410\pi\) | ||
0.993400 | − | 0.114698i | \(-0.0365900\pi\) | |||||||
\(354\) | −2.61483e12 | − | 4.38402e12i | −0.470356 | − | 0.788599i | ||||
\(355\) | −3.54278e12 | −0.628352 | ||||||||
\(356\) | − | 8.49017e12i | − | 1.48479i | ||||||
\(357\) | −2.22747e12 | −0.384123 | ||||||||
\(358\) | −4.90525e11 | −0.0834153 | ||||||||
\(359\) | 2.11731e12 | 0.355068 | 0.177534 | − | 0.984115i | \(-0.443188\pi\) | ||||
0.177534 | + | 0.984115i | \(0.443188\pi\) | |||||||
\(360\) | 1.14416e12i | 0.189223i | ||||||||
\(361\) | −6.12921e12 | −0.999698 | ||||||||
\(362\) | 5.74273e12i | 0.923795i | ||||||||
\(363\) | 8.30228e11 | 0.131724 | ||||||||
\(364\) | − | 1.07100e13i | − | 1.67603i | ||||||
\(365\) | 6.46243e12i | 0.997542i | ||||||||
\(366\) | −1.14864e12 | −0.174896 | ||||||||
\(367\) | 3.76611e12i | 0.565669i | 0.959169 | + | 0.282834i | \(0.0912747\pi\) | ||||
−0.959169 | + | 0.282834i | \(0.908725\pi\) | |||||||
\(368\) | 3.69184e11i | 0.0547020i | ||||||||
\(369\) | −3.83767e12 | −0.560966 | ||||||||
\(370\) | −3.62194e12 | −0.522315 | ||||||||
\(371\) | 4.60935e12 | 0.655799 | ||||||||
\(372\) | 1.50899e12i | 0.211822i | ||||||||
\(373\) | −7.08756e12 | −0.981641 | −0.490821 | − | 0.871261i | \(-0.663303\pi\) | ||||
−0.490821 | + | 0.871261i | \(0.663303\pi\) | |||||||
\(374\) | −4.32217e12 | −0.590669 | ||||||||
\(375\) | −4.46126e12 | −0.601590 | ||||||||
\(376\) | −4.32044e12 | −0.574895 | ||||||||
\(377\) | − | 8.49691e11i | − | 0.111572i | ||||||
\(378\) | 3.71743e12i | 0.481707i | ||||||||
\(379\) | 1.17226e13 | 1.49910 | 0.749548 | − | 0.661950i | \(-0.230271\pi\) | ||||
0.749548 | + | 0.661950i | \(0.230271\pi\) | |||||||
\(380\) | 1.42063e11 | 0.0179293 | ||||||||
\(381\) | 5.67100e12 | 0.706375 | ||||||||
\(382\) | 2.22506e13 | 2.73542 | ||||||||
\(383\) | 9.52031e12 | 1.15520 | 0.577600 | − | 0.816320i | \(-0.303989\pi\) | ||||
0.577600 | + | 0.816320i | \(0.303989\pi\) | |||||||
\(384\) | − | 6.97960e12i | − | 0.835939i | ||||||
\(385\) | 7.88601e12i | 0.932296i | ||||||||
\(386\) | 2.16326e13i | 2.52448i | ||||||||
\(387\) | − | 1.52709e12i | − | 0.175918i | ||||||
\(388\) | 5.51332e12i | 0.626982i | ||||||||
\(389\) | −7.50109e12 | −0.842125 | −0.421063 | − | 0.907032i | \(-0.638343\pi\) | ||||
−0.421063 | + | 0.907032i | \(0.638343\pi\) | |||||||
\(390\) | −3.88962e12 | −0.431106 | ||||||||
\(391\) | − | 1.10994e12i | − | 0.121455i | ||||||
\(392\) | 1.15097e13i | 1.24346i | ||||||||
\(393\) | − | 4.87605e12i | − | 0.520122i | ||||||
\(394\) | 4.11936e12i | 0.433859i | ||||||||
\(395\) | 2.42795e12 | 0.252495 | ||||||||
\(396\) | 4.36147e12i | 0.447875i | ||||||||
\(397\) | 6.39193e12i | 0.648156i | 0.946030 | + | 0.324078i | \(0.105054\pi\) | ||||
−0.946030 | + | 0.324078i | \(0.894946\pi\) | |||||||
\(398\) | 2.08816e13i | 2.09097i | ||||||||
\(399\) | 1.59766e11 | 0.0157987 | ||||||||
\(400\) | 1.06329e12 | 0.103837 | ||||||||
\(401\) | 3.14324e12i | 0.303148i | 0.988446 | + | 0.151574i | \(0.0484342\pi\) | ||||
−0.988446 | + | 0.151574i | \(0.951566\pi\) | |||||||
\(402\) | 9.25378e12 | 0.881432 | ||||||||
\(403\) | −1.77564e12 | −0.167043 | ||||||||
\(404\) | − | 1.92876e13i | − | 1.79214i | ||||||
\(405\) | 8.16322e11 | 0.0749181 | ||||||||
\(406\) | 4.42426e12i | 0.401061i | ||||||||
\(407\) | −4.77898e12 | −0.427921 | ||||||||
\(408\) | 2.32315e12i | 0.205483i | ||||||||
\(409\) | − | 2.02712e13i | − | 1.77118i | −0.464471 | − | 0.885588i | \(-0.653756\pi\) | ||
0.464471 | − | 0.885588i | \(-0.346244\pi\) | |||||||
\(410\) | 2.09080e13i | 1.80465i | ||||||||
\(411\) | 8.58972e12 | 0.732436 | ||||||||
\(412\) | − | 6.34588e12i | − | 0.534572i | ||||||
\(413\) | −1.62413e13 | + | 9.68702e12i | −1.35167 | + | 0.806195i | ||||
\(414\) | −1.85237e12 | −0.152310 | ||||||||
\(415\) | 1.58565e13i | 1.28815i | ||||||||
\(416\) | 9.93057e12 | 0.797090 | ||||||||
\(417\) | −2.10164e12 | −0.166678 | ||||||||
\(418\) | 3.10010e11 | 0.0242937 | ||||||||
\(419\) | 1.62123e13i | 1.25538i | 0.778465 | + | 0.627688i | \(0.215999\pi\) | ||||
−0.778465 | + | 0.627688i | \(0.784001\pi\) | |||||||
\(420\) | 1.22458e13 | 0.937001 | ||||||||
\(421\) | − | 2.28667e13i | − | 1.72899i | −0.502642 | − | 0.864495i | \(-0.667639\pi\) | ||
0.502642 | − | 0.864495i | \(-0.332361\pi\) | |||||||
\(422\) | 2.40240e12 | 0.179508 | ||||||||
\(423\) | 3.08250e12i | 0.227615i | ||||||||
\(424\) | − | 4.80735e12i | − | 0.350814i | ||||||
\(425\) | −3.19675e12 | −0.230549 | ||||||||
\(426\) | 1.20051e13i | 0.855696i | ||||||||
\(427\) | 4.25532e12i | 0.299773i | ||||||||
\(428\) | 1.63700e13 | 1.13980 | ||||||||
\(429\) | −5.13217e12 | −0.353195 | ||||||||
\(430\) | −8.31973e12 | −0.565936 | ||||||||
\(431\) | 3.91398e12i | 0.263167i | 0.991305 | + | 0.131584i | \(0.0420062\pi\) | ||||
−0.991305 | + | 0.131584i | \(0.957994\pi\) | |||||||
\(432\) | −5.51313e11 | −0.0366420 | ||||||||
\(433\) | −2.66348e13 | −1.74988 | −0.874942 | − | 0.484227i | \(-0.839101\pi\) | ||||
−0.874942 | + | 0.484227i | \(0.839101\pi\) | |||||||
\(434\) | 9.24557e12 | 0.600461 | ||||||||
\(435\) | 9.71538e11 | 0.0623755 | ||||||||
\(436\) | − | 2.98499e13i | − | 1.89457i | ||||||
\(437\) | 7.96106e10i | 0.00499533i | ||||||||
\(438\) | 2.18987e13 | 1.35846 | ||||||||
\(439\) | 1.22436e13 | 0.750910 | 0.375455 | − | 0.926841i | \(-0.377486\pi\) | ||||
0.375455 | + | 0.926841i | \(0.377486\pi\) | |||||||
\(440\) | 8.22477e12 | 0.498724 | ||||||||
\(441\) | 8.21181e12 | 0.492318 | ||||||||
\(442\) | −7.89766e12 | −0.468152 | ||||||||
\(443\) | 8.44368e12i | 0.494895i | 0.968901 | + | 0.247447i | \(0.0795918\pi\) | ||||
−0.968901 | + | 0.247447i | \(0.920408\pi\) | |||||||
\(444\) | 7.42103e12i | 0.430080i | ||||||||
\(445\) | 1.14231e13i | 0.654610i | ||||||||
\(446\) | 1.82054e13i | 1.03163i | ||||||||
\(447\) | − | 2.07742e12i | − | 0.116409i | ||||||
\(448\) | −4.62998e13 | −2.56560 | ||||||||
\(449\) | −2.90029e12 | −0.158931 | −0.0794657 | − | 0.996838i | \(-0.525321\pi\) | ||||
−0.0794657 | + | 0.996838i | \(0.525321\pi\) | |||||||
\(450\) | 5.33505e12i | 0.289119i | ||||||||
\(451\) | 2.75871e13i | 1.47851i | ||||||||
\(452\) | 3.17945e13i | 1.68523i | ||||||||
\(453\) | − | 7.79363e12i | − | 0.408553i | ||||||
\(454\) | −1.51207e13 | −0.783960 | ||||||||
\(455\) | 1.44097e13i | 0.738920i | ||||||||
\(456\) | − | 1.66629e11i | − | 0.00845136i | ||||||
\(457\) | − | 4.37141e12i | − | 0.219301i | −0.993970 | − | 0.109650i | \(-0.965027\pi\) | ||
0.993970 | − | 0.109650i | \(-0.0349731\pi\) | |||||||
\(458\) | −3.08248e13 | −1.52958 | ||||||||
\(459\) | 1.65750e12 | 0.0813561 | ||||||||
\(460\) | 6.10201e12i | 0.296267i | ||||||||
\(461\) | 2.45776e12 | 0.118042 | 0.0590208 | − | 0.998257i | \(-0.481202\pi\) | ||||
0.0590208 | + | 0.998257i | \(0.481202\pi\) | |||||||
\(462\) | 2.67227e13 | 1.26961 | ||||||||
\(463\) | 6.09401e12i | 0.286417i | 0.989693 | + | 0.143208i | \(0.0457419\pi\) | ||||
−0.989693 | + | 0.143208i | \(0.954258\pi\) | |||||||
\(464\) | −6.56140e11 | −0.0305075 | ||||||||
\(465\) | − | 2.03027e12i | − | 0.0933874i | ||||||
\(466\) | −2.80744e13 | −1.27756 | ||||||||
\(467\) | − | 6.90328e12i | − | 0.310793i | −0.987852 | − | 0.155396i | \(-0.950335\pi\) | ||
0.987852 | − | 0.155396i | \(-0.0496655\pi\) | |||||||
\(468\) | 7.96947e12i | 0.354977i | ||||||||
\(469\) | − | 3.42820e13i | − | 1.51078i | ||||||
\(470\) | 1.67937e13 | 0.732248 | ||||||||
\(471\) | − | 1.56002e13i | − | 0.673014i | ||||||
\(472\) | 1.01031e13 | + | 1.69389e13i | 0.431267 | + | 0.723063i | ||||
\(473\) | −1.09775e13 | −0.463658 | ||||||||
\(474\) | − | 8.22738e12i | − | 0.343851i | ||||||
\(475\) | 2.29288e11 | 0.00948229 | ||||||||
\(476\) | 2.48644e13 | 1.01752 | ||||||||
\(477\) | −3.42991e12 | −0.138896 | ||||||||
\(478\) | − | 4.82760e13i | − | 1.93460i | ||||||
\(479\) | −1.35835e13 | −0.538686 | −0.269343 | − | 0.963044i | \(-0.586806\pi\) | ||||
−0.269343 | + | 0.963044i | \(0.586806\pi\) | |||||||
\(480\) | 1.13546e13i | 0.445622i | ||||||||
\(481\) | −8.73237e12 | −0.339162 | ||||||||
\(482\) | 2.13693e13i | 0.821402i | ||||||||
\(483\) | 6.86240e12i | 0.261060i | ||||||||
\(484\) | −9.26753e12 | −0.348929 | ||||||||
\(485\) | − | 7.41789e12i | − | 0.276421i | ||||||
\(486\) | − | 2.76621e12i | − | 0.102024i | ||||||
\(487\) | 4.23136e12 | 0.154467 | 0.0772334 | − | 0.997013i | \(-0.475391\pi\) | ||||
0.0772334 | + | 0.997013i | \(0.475391\pi\) | |||||||
\(488\) | 4.43811e12 | 0.160361 | ||||||||
\(489\) | 8.61636e12 | 0.308162 | ||||||||
\(490\) | − | 4.47386e13i | − | 1.58381i | ||||||
\(491\) | 6.30143e12 | 0.220816 | 0.110408 | − | 0.993886i | \(-0.464784\pi\) | ||||
0.110408 | + | 0.993886i | \(0.464784\pi\) | |||||||
\(492\) | 4.28386e13 | 1.48597 | ||||||||
\(493\) | 1.97266e12 | 0.0677357 | ||||||||
\(494\) | 5.66463e11 | 0.0192547 | ||||||||
\(495\) | − | 5.86813e12i | − | 0.197457i | ||||||
\(496\) | 1.37116e12i | 0.0456753i | ||||||||
\(497\) | 4.44749e13 | 1.46667 | ||||||||
\(498\) | 5.37316e13 | 1.75422 | ||||||||
\(499\) | 6.90808e12 | 0.223282 | 0.111641 | − | 0.993749i | \(-0.464389\pi\) | ||||
0.111641 | + | 0.993749i | \(0.464389\pi\) | |||||||
\(500\) | 4.97994e13 | 1.59358 | ||||||||
\(501\) | −8.77077e12 | −0.277875 | ||||||||
\(502\) | − | 5.12779e13i | − | 1.60847i | ||||||
\(503\) | − | 5.01804e12i | − | 0.155846i | −0.996959 | − | 0.0779228i | \(-0.975171\pi\) | ||
0.996959 | − | 0.0779228i | \(-0.0248288\pi\) | |||||||
\(504\) | − | 1.43634e13i | − | 0.441675i | ||||||
\(505\) | 2.59505e13i | 0.790112i | ||||||||
\(506\) | 1.33158e13i | 0.401434i | ||||||||
\(507\) | 9.96329e12 | 0.297415 | ||||||||
\(508\) | −6.33034e13 | −1.87115 | ||||||||
\(509\) | 3.38091e12i | 0.0989565i | 0.998775 | + | 0.0494783i | \(0.0157559\pi\) | ||||
−0.998775 | + | 0.0494783i | \(0.984244\pi\) | |||||||
\(510\) | − | 9.03020e12i | − | 0.261726i | ||||||
\(511\) | − | 8.11271e13i | − | 2.32842i | ||||||
\(512\) | − | 1.33085e13i | − | 0.378249i | ||||||
\(513\) | −1.18885e11 | −0.00334611 | ||||||||
\(514\) | 4.77131e13i | 1.32991i | ||||||||
\(515\) | 8.53805e12i | 0.235680i | ||||||||
\(516\) | 1.70464e13i | 0.465998i | ||||||||
\(517\) | 2.21586e13 | 0.599914 | ||||||||
\(518\) | 4.54686e13 | 1.21917 | ||||||||
\(519\) | 1.86534e13i | 0.495359i | ||||||||
\(520\) | 1.50287e13 | 0.395279 | ||||||||
\(521\) | 1.96892e13 | 0.512908 | 0.256454 | − | 0.966556i | \(-0.417446\pi\) | ||||
0.256454 | + | 0.966556i | \(0.417446\pi\) | |||||||
\(522\) | − | 3.29217e12i | − | 0.0849435i | ||||||
\(523\) | −1.74191e13 | −0.445162 | −0.222581 | − | 0.974914i | \(-0.571448\pi\) | ||||
−0.222581 | + | 0.974914i | \(0.571448\pi\) | |||||||
\(524\) | 5.44295e13i | 1.37777i | ||||||||
\(525\) | 1.97645e13 | 0.495553 | ||||||||
\(526\) | − | 3.00838e13i | − | 0.747143i | ||||||
\(527\) | − | 4.12235e12i | − | 0.101413i | ||||||
\(528\) | 3.96311e12i | 0.0965754i | ||||||||
\(529\) | 3.80070e13 | 0.917456 | ||||||||
\(530\) | 1.86864e13i | 0.446834i | ||||||||
\(531\) | 1.20854e13 | − | 7.20829e12i | 0.286279 | − | 0.170750i | ||||
\(532\) | −1.78341e12 | −0.0418498 | ||||||||
\(533\) | 5.04084e13i | 1.17184i | ||||||||
\(534\) | 3.87084e13 | 0.891455 | ||||||||
\(535\) | −2.20250e13 | −0.502512 | ||||||||
\(536\) | −3.57547e13 | −0.808181 | ||||||||
\(537\) | − | 1.35223e12i | − | 0.0302816i | ||||||
\(538\) | 3.39614e13 | 0.753485 | ||||||||
\(539\) | − | 5.90306e13i | − | 1.29758i | ||||||
\(540\) | −9.11231e12 | −0.198454 | ||||||||
\(541\) | − | 3.09098e13i | − | 0.666976i | −0.942754 | − | 0.333488i | \(-0.891774\pi\) | ||
0.942754 | − | 0.333488i | \(-0.108226\pi\) | |||||||
\(542\) | 6.61931e13i | 1.41520i | ||||||||
\(543\) | −1.58310e13 | −0.335358 | ||||||||
\(544\) | 2.30550e13i | 0.483917i | ||||||||
\(545\) | 4.01614e13i | 0.835269i | ||||||||
\(546\) | 4.88289e13 | 1.00627 | ||||||||
\(547\) | 9.65358e13 | 1.97130 | 0.985648 | − | 0.168813i | \(-0.0539936\pi\) | ||||
0.985648 | + | 0.168813i | \(0.0539936\pi\) | |||||||
\(548\) | −9.58839e13 | −1.94018 | ||||||||
\(549\) | − | 3.16646e12i | − | 0.0634910i | ||||||
\(550\) | 3.83510e13 | 0.762015 | ||||||||
\(551\) | −1.41490e11 | −0.00278591 | ||||||||
\(552\) | 7.15719e12 | 0.139652 | ||||||||
\(553\) | −3.04796e13 | −0.589364 | ||||||||
\(554\) | − | 9.96381e12i | − | 0.190931i | ||||||
\(555\) | − | 9.98460e12i | − | 0.189612i | ||||||
\(556\) | 2.34598e13 | 0.441521 | ||||||||
\(557\) | −8.42715e13 | −1.57183 | −0.785914 | − | 0.618336i | \(-0.787807\pi\) | ||||
−0.785914 | + | 0.618336i | \(0.787807\pi\) | |||||||
\(558\) | −6.87980e12 | −0.127176 | ||||||||
\(559\) | −2.00586e13 | −0.367486 | ||||||||
\(560\) | 1.11273e13 | 0.202046 | ||||||||
\(561\) | − | 1.19149e13i | − | 0.214426i | ||||||
\(562\) | 1.11874e14i | 1.99549i | ||||||||
\(563\) | 2.46985e13i | 0.436644i | 0.975877 | + | 0.218322i | \(0.0700584\pi\) | ||||
−0.975877 | + | 0.218322i | \(0.929942\pi\) | |||||||
\(564\) | − | 3.44089e13i | − | 0.602941i | ||||||
\(565\) | − | 4.27778e13i | − | 0.742978i | ||||||
\(566\) | 3.39942e13 | 0.585225 | ||||||||
\(567\) | −1.02478e13 | −0.174870 | ||||||||
\(568\) | − | 4.63854e13i | − | 0.784584i | ||||||
\(569\) | − | 5.13881e13i | − | 0.861591i | −0.902450 | − | 0.430796i | \(-0.858233\pi\) | ||
0.902450 | − | 0.430796i | \(-0.141767\pi\) | |||||||
\(570\) | 6.47695e11i | 0.0107646i | ||||||||
\(571\) | 4.30960e13i | 0.709997i | 0.934867 | + | 0.354999i | \(0.115519\pi\) | ||||
−0.934867 | + | 0.354999i | \(0.884481\pi\) | |||||||
\(572\) | 5.72885e13 | 0.935594 | ||||||||
\(573\) | 6.13381e13i | 0.993019i | ||||||||
\(574\) | − | 2.62471e14i | − | 4.21233i | ||||||
\(575\) | 9.84856e12i | 0.156687i | ||||||||
\(576\) | 3.44526e13 | 0.543387 | ||||||||
\(577\) | −3.50752e13 | −0.548430 | −0.274215 | − | 0.961668i | \(-0.588418\pi\) | ||||
−0.274215 | + | 0.961668i | \(0.588418\pi\) | |||||||
\(578\) | 8.42642e13i | 1.30618i | ||||||||
\(579\) | −5.96345e13 | −0.916442 | ||||||||
\(580\) | −1.08449e13 | −0.165229 | ||||||||
\(581\) | − | 1.99057e14i | − | 3.00675i | ||||||
\(582\) | −2.51364e13 | −0.376433 | ||||||||
\(583\) | 2.46559e13i | 0.366081i | ||||||||
\(584\) | −8.46120e13 | −1.24557 | ||||||||
\(585\) | − | 1.07225e13i | − | 0.156501i | ||||||
\(586\) | − | 7.07354e13i | − | 1.02364i | ||||||
\(587\) | − | 8.69944e13i | − | 1.24825i | −0.781326 | − | 0.624124i | \(-0.785456\pi\) | ||
0.781326 | − | 0.624124i | \(-0.214544\pi\) | |||||||
\(588\) | −9.16655e13 | −1.30412 | ||||||||
\(589\) | 2.95677e11i | 0.00417101i | ||||||||
\(590\) | −3.92714e13 | − | 6.58425e13i | −0.549308 | − | 0.920971i | ||||
\(591\) | −1.13559e13 | −0.157501 | ||||||||
\(592\) | 6.74322e12i | 0.0927383i | ||||||||
\(593\) | 9.80223e13 | 1.33675 | 0.668377 | − | 0.743823i | \(-0.266989\pi\) | ||||
0.668377 | + | 0.743823i | \(0.266989\pi\) | |||||||
\(594\) | −1.98849e13 | −0.268900 | ||||||||
\(595\) | −3.34538e13 | −0.448601 | ||||||||
\(596\) | 2.31894e13i | 0.308361i | ||||||||
\(597\) | −5.75642e13 | −0.759069 | ||||||||
\(598\) | 2.43312e13i | 0.318169i | ||||||||
\(599\) | −6.56015e13 | −0.850706 | −0.425353 | − | 0.905028i | \(-0.639850\pi\) | ||||
−0.425353 | + | 0.905028i | \(0.639850\pi\) | |||||||
\(600\) | − | 2.06135e13i | − | 0.265092i | ||||||
\(601\) | − | 7.31596e13i | − | 0.933038i | −0.884511 | − | 0.466519i | \(-0.845508\pi\) | ||
0.884511 | − | 0.466519i | \(-0.154492\pi\) | |||||||
\(602\) | 1.04443e14 | 1.32098 | ||||||||
\(603\) | 2.55099e13i | 0.319979i | ||||||||
\(604\) | 8.69975e13i | 1.08224i | ||||||||
\(605\) | 1.24690e13 | 0.153834 | ||||||||
\(606\) | 8.79364e13 | 1.07598 | ||||||||
\(607\) | −5.58822e13 | −0.678156 | −0.339078 | − | 0.940758i | \(-0.610115\pi\) | ||||
−0.339078 | + | 0.940758i | \(0.610115\pi\) | |||||||
\(608\) | − | 1.65363e12i | − | 0.0199031i | ||||||
\(609\) | −1.21964e13 | −0.145594 | ||||||||
\(610\) | −1.72511e13 | −0.204253 | ||||||||
\(611\) | 4.04891e13 | 0.475480 | ||||||||
\(612\) | −1.85021e13 | −0.215508 | ||||||||
\(613\) | 4.28268e13i | 0.494781i | 0.968916 | + | 0.247391i | \(0.0795731\pi\) | ||||
−0.968916 | + | 0.247391i | \(0.920427\pi\) | |||||||
\(614\) | 4.67731e13i | 0.535987i | ||||||||
\(615\) | −5.76370e13 | −0.655127 | ||||||||
\(616\) | −1.03251e14 | −1.16410 | ||||||||
\(617\) | −1.09740e14 | −1.22727 | −0.613634 | − | 0.789590i | \(-0.710293\pi\) | ||||
−0.613634 | + | 0.789590i | \(0.710293\pi\) | |||||||
\(618\) | 2.89322e13 | 0.320951 | ||||||||
\(619\) | −7.95094e13 | −0.874914 | −0.437457 | − | 0.899239i | \(-0.644121\pi\) | ||||
−0.437457 | + | 0.899239i | \(0.644121\pi\) | |||||||
\(620\) | 2.26631e13i | 0.247378i | ||||||||
\(621\) | − | 5.10644e12i | − | 0.0552917i | ||||||
\(622\) | 1.27257e14i | 1.36688i | ||||||||
\(623\) | − | 1.43401e14i | − | 1.52796i | ||||||
\(624\) | 7.24157e12i | 0.0765438i | ||||||||
\(625\) | −1.49919e13 | −0.157201 | ||||||||
\(626\) | 1.39384e14 | 1.44991 | ||||||||
\(627\) | 8.54603e11i | 0.00881915i | ||||||||
\(628\) | 1.74139e14i | 1.78278i | ||||||||
\(629\) | − | 2.02732e13i | − | 0.205906i | ||||||
\(630\) | 5.58310e13i | 0.562565i | ||||||||
\(631\) | −1.06133e14 | −1.06097 | −0.530485 | − | 0.847694i | \(-0.677990\pi\) | ||||
−0.530485 | + | 0.847694i | \(0.677990\pi\) | |||||||
\(632\) | 3.17889e13i | 0.315275i | ||||||||
\(633\) | 6.62270e12i | 0.0651653i | ||||||||
\(634\) | 2.87955e14i | 2.81111i | ||||||||
\(635\) | 8.51713e13 | 0.824945 | ||||||||
\(636\) | 3.82868e13 | 0.367928 | ||||||||
\(637\) | − | 1.07863e14i | − | 1.02843i | ||||||
\(638\) | −2.36658e13 | −0.223881 | ||||||||
\(639\) | −3.30946e13 | −0.310637 | ||||||||
\(640\) | − | 1.04825e14i | − | 0.976257i | ||||||
\(641\) | −9.16379e13 | −0.846808 | −0.423404 | − | 0.905941i | \(-0.639165\pi\) | ||||
−0.423404 | + | 0.905941i | \(0.639165\pi\) | |||||||
\(642\) | 7.46343e13i | 0.684326i | ||||||||
\(643\) | 2.54312e13 | 0.231373 | 0.115686 | − | 0.993286i | \(-0.463093\pi\) | ||||
0.115686 | + | 0.993286i | \(0.463093\pi\) | |||||||
\(644\) | − | 7.66025e13i | − | 0.691534i | ||||||
\(645\) | − | 2.29350e13i | − | 0.205447i | ||||||
\(646\) | 1.31511e12i | 0.0116896i | ||||||||
\(647\) | −7.95829e13 | −0.701937 | −0.350969 | − | 0.936387i | \(-0.614148\pi\) | ||||
−0.350969 | + | 0.936387i | \(0.614148\pi\) | |||||||
\(648\) | 1.06880e13i | 0.0935455i | ||||||||
\(649\) | −5.18167e13 | − | 8.68761e13i | −0.450035 | − | 0.754530i | ||||
\(650\) | 7.00767e13 | 0.603958 | ||||||||
\(651\) | 2.54873e13i | 0.217981i | ||||||||
\(652\) | −9.61813e13 | −0.816305 | ||||||||
\(653\) | 1.46937e13 | 0.123756 | 0.0618780 | − | 0.998084i | \(-0.480291\pi\) | ||||
0.0618780 | + | 0.998084i | \(0.480291\pi\) | |||||||
\(654\) | 1.36092e14 | 1.13748 | ||||||||
\(655\) | − | 7.32320e13i | − | 0.607428i | ||||||
\(656\) | 3.89258e13 | 0.320419 | ||||||||
\(657\) | 6.03682e13i | 0.493152i | ||||||||
\(658\) | −2.10823e14 | −1.70918 | ||||||||
\(659\) | − | 3.70636e13i | − | 0.298209i | −0.988821 | − | 0.149105i | \(-0.952361\pi\) | ||
0.988821 | − | 0.149105i | \(-0.0476391\pi\) | |||||||
\(660\) | 6.55038e13i | 0.523054i | ||||||||
\(661\) | 1.96867e14 | 1.56015 | 0.780076 | − | 0.625685i | \(-0.215181\pi\) | ||||
0.780076 | + | 0.625685i | \(0.215181\pi\) | |||||||
\(662\) | 2.94444e14i | 2.31586i | ||||||||
\(663\) | − | 2.17715e13i | − | 0.169950i | ||||||
\(664\) | −2.07608e14 | −1.60843 | ||||||||
\(665\) | 2.39948e12 | 0.0184506 | ||||||||
\(666\) | −3.38340e13 | −0.258216 | ||||||||
\(667\) | − | 6.07738e12i | − | 0.0460349i | ||||||
\(668\) | 9.79049e13 | 0.736075 | ||||||||
\(669\) | −5.01867e13 | −0.374506 | ||||||||
\(670\) | 1.38980e14 | 1.02939 | ||||||||
\(671\) | −2.27621e13 | −0.167340 | ||||||||
\(672\) | − | 1.42542e14i | − | 1.04015i | ||||||
\(673\) | 1.56435e14i | 1.13307i | 0.824037 | + | 0.566536i | \(0.191717\pi\) | ||||
−0.824037 | + | 0.566536i | \(0.808283\pi\) | |||||||
\(674\) | −1.91956e14 | −1.38007 | ||||||||
\(675\) | −1.47071e13 | −0.104957 | ||||||||
\(676\) | −1.11217e14 | −0.787836 | ||||||||
\(677\) | −8.64965e13 | −0.608212 | −0.304106 | − | 0.952638i | \(-0.598358\pi\) | ||||
−0.304106 | + | 0.952638i | \(0.598358\pi\) | |||||||
\(678\) | −1.44958e14 | −1.01180 | ||||||||
\(679\) | 9.31216e13i | 0.645211i | ||||||||
\(680\) | 3.48908e13i | 0.239975i | ||||||||
\(681\) | − | 4.16833e13i | − | 0.284595i | ||||||
\(682\) | 4.94554e13i | 0.335191i | ||||||||
\(683\) | − | 2.51796e14i | − | 1.69412i | −0.531496 | − | 0.847061i | \(-0.678370\pi\) | ||
0.531496 | − | 0.847061i | \(-0.321630\pi\) | |||||||
\(684\) | 1.32707e12 | 0.00886366 | ||||||||
\(685\) | 1.29007e14 | 0.855381 | ||||||||
\(686\) | 1.81369e14i | 1.19383i | ||||||||
\(687\) | − | 8.49748e13i | − | 0.555273i | ||||||
\(688\) | 1.54894e13i | 0.100483i | ||||||||
\(689\) | 4.50523e13i | 0.290149i | ||||||||
\(690\) | −2.78203e13 | −0.177876 | ||||||||
\(691\) | 8.92973e13i | 0.566824i | 0.958998 | + | 0.283412i | \(0.0914663\pi\) | ||||
−0.958998 | + | 0.283412i | \(0.908534\pi\) | |||||||
\(692\) | − | 2.08221e14i | − | 1.31218i | ||||||
\(693\) | 7.36665e13i | 0.460897i | ||||||||
\(694\) | −7.83753e13 | −0.486835 | ||||||||
\(695\) | −3.15640e13 | −0.194656 | ||||||||
\(696\) | 1.27203e13i | 0.0778843i | ||||||||
\(697\) | −1.17029e14 | −0.711426 | ||||||||
\(698\) | −2.37293e12 | −0.0143221 | ||||||||
\(699\) | − | 7.73926e13i | − | 0.463782i | ||||||
\(700\) | −2.20624e14 | −1.31269 | ||||||||
\(701\) | 2.17405e14i | 1.28434i | 0.766563 | + | 0.642169i | \(0.221965\pi\) | ||||
−0.766563 | + | 0.642169i | \(0.778035\pi\) | |||||||
\(702\) | −3.63345e13 | −0.213125 | ||||||||
\(703\) | 1.45411e12i | 0.00846875i | ||||||||
\(704\) | − | 2.47662e14i | − | 1.43218i | ||||||
\(705\) | 4.62953e13i | 0.265822i | ||||||||
\(706\) | −6.39905e13 | −0.364831 | ||||||||
\(707\) | − | 3.25774e14i | − | 1.84425i | ||||||
\(708\) | −1.34905e14 | + | 8.04635e13i | −0.758338 | + | 0.452306i | ||||
\(709\) | 4.37689e13 | 0.244306 | 0.122153 | − | 0.992511i | \(-0.461020\pi\) | ||||
0.122153 | + | 0.992511i | \(0.461020\pi\) | |||||||
\(710\) | 1.80302e14i | 0.999331i | ||||||||
\(711\) | 2.26804e13 | 0.124825 | ||||||||
\(712\) | −1.49561e14 | −0.817371 | ||||||||
\(713\) | −1.27002e13 | −0.0689226 | ||||||||
\(714\) | 1.13362e14i | 0.610909i | ||||||||
\(715\) | −7.70787e13 | −0.412481 | ||||||||
\(716\) | 1.50944e13i | 0.0802143i | ||||||||
\(717\) | 1.33082e14 | 0.702304 | ||||||||
\(718\) | − | 1.07756e14i | − | 0.564700i | ||||||
\(719\) | − | 2.73736e14i | − | 1.42458i | −0.701885 | − | 0.712290i | \(-0.747658\pi\) | ||
0.701885 | − | 0.712290i | \(-0.252342\pi\) | |||||||
\(720\) | −8.28003e12 | −0.0427927 | ||||||||
\(721\) | − | 1.07184e14i | − | 0.550114i | ||||||
\(722\) | 3.11933e14i | 1.58992i | ||||||||
\(723\) | −5.89089e13 | −0.298187 | ||||||||
\(724\) | 1.76716e14 | 0.888345 | ||||||||
\(725\) | −1.75036e13 | −0.0873850 | ||||||||
\(726\) | − | 4.22526e13i | − | 0.209493i | ||||||
\(727\) | −6.53955e13 | −0.322015 | −0.161007 | − | 0.986953i | \(-0.551474\pi\) | ||||
−0.161007 | + | 0.986953i | \(0.551474\pi\) | |||||||
\(728\) | −1.88665e14 | −0.922643 | ||||||||
\(729\) | 7.62560e12 | 0.0370370 | ||||||||
\(730\) | 3.28891e14 | 1.58649 | ||||||||
\(731\) | − | 4.65683e13i | − | 0.223102i | ||||||
\(732\) | 3.53460e13i | 0.168184i | ||||||||
\(733\) | −6.74238e13 | −0.318635 | −0.159318 | − | 0.987227i | \(-0.550929\pi\) | ||||
−0.159318 | + | 0.987227i | \(0.550929\pi\) | |||||||
\(734\) | 1.91668e14 | 0.899639 | ||||||||
\(735\) | 1.23331e14 | 0.574957 | ||||||||
\(736\) | 7.10280e13 | 0.328882 | ||||||||
\(737\) | 1.83378e14 | 0.843353 | ||||||||
\(738\) | 1.95310e14i | 0.892159i | ||||||||
\(739\) | 1.38269e13i | 0.0627341i | 0.999508 | + | 0.0313671i | \(0.00998608\pi\) | ||||
−0.999508 | + | 0.0313671i | \(0.990014\pi\) | |||||||
\(740\) | 1.11455e14i | 0.502272i | ||||||||
\(741\) | 1.56157e12i | 0.00698989i | ||||||||
\(742\) | − | 2.34583e14i | − | 1.04298i | ||||||
\(743\) | −3.62484e13 | −0.160083 | −0.0800414 | − | 0.996792i | \(-0.525505\pi\) | ||||
−0.0800414 | + | 0.996792i | \(0.525505\pi\) | |||||||
\(744\) | 2.65821e13 | 0.116607 | ||||||||
\(745\) | − | 3.12002e13i | − | 0.135949i | ||||||
\(746\) | 3.60706e14i | 1.56120i | ||||||||
\(747\) | 1.48122e14i | 0.636819i | ||||||||
\(748\) | 1.33002e14i | 0.568003i | ||||||||
\(749\) | 2.76494e14 | 1.17294 | ||||||||
\(750\) | 2.27046e14i | 0.956769i | ||||||||
\(751\) | − | 1.53369e14i | − | 0.642004i | −0.947079 | − | 0.321002i | \(-0.895980\pi\) | ||
0.947079 | − | 0.321002i | \(-0.104020\pi\) | |||||||
\(752\) | − | 3.12661e13i | − | 0.130012i | ||||||
\(753\) | 1.41358e14 | 0.583909 | ||||||||
\(754\) | −4.32432e13 | −0.177444 | ||||||||
\(755\) | − | 1.17050e14i | − | 0.477132i | ||||||
\(756\) | 1.14393e14 | 0.463223 | ||||||||
\(757\) | −1.02440e14 | −0.412088 | −0.206044 | − | 0.978543i | \(-0.566059\pi\) | ||||
−0.206044 | + | 0.978543i | \(0.566059\pi\) | |||||||
\(758\) | − | 5.96598e14i | − | 2.38416i | ||||||
\(759\) | −3.67076e13 | −0.145729 | ||||||||
\(760\) | − | 2.50256e12i | − | 0.00986998i | ||||||
\(761\) | 4.48293e13 | 0.175646 | 0.0878230 | − | 0.996136i | \(-0.472009\pi\) | ||||
0.0878230 | + | 0.996136i | \(0.472009\pi\) | |||||||
\(762\) | − | 2.88613e14i | − | 1.12342i | ||||||
\(763\) | − | 5.04172e14i | − | 1.94965i | ||||||
\(764\) | − | 6.84695e14i | − | 2.63045i | ||||||
\(765\) | 2.48936e13 | 0.0950123 | ||||||||
\(766\) | − | 4.84515e14i | − | 1.83723i | ||||||
\(767\) | −9.46819e13 | − | 1.58744e14i | −0.356689 | − | 0.598026i | ||||
\(768\) | −1.03747e14 | −0.388303 | ||||||||
\(769\) | 7.98791e13i | 0.297031i | 0.988910 | + | 0.148515i | \(0.0474494\pi\) | ||||
−0.988910 | + | 0.148515i | \(0.952551\pi\) | |||||||
\(770\) | 4.01341e14 | 1.48272 | ||||||||
\(771\) | −1.31531e14 | −0.482787 | ||||||||
\(772\) | 6.65679e14 | 2.42761 | ||||||||
\(773\) | − | 4.49751e14i | − | 1.62958i | −0.579760 | − | 0.814788i | \(-0.696854\pi\) | ||
0.579760 | − | 0.814788i | \(-0.303146\pi\) | |||||||
\(774\) | −7.77180e13 | −0.279780 | ||||||||
\(775\) | 3.65780e13i | 0.130831i | ||||||||
\(776\) | 9.71217e13 | 0.345150 | ||||||||
\(777\) | 1.25343e14i | 0.442584i | ||||||||
\(778\) | 3.81752e14i | 1.33932i | ||||||||
\(779\) | 8.39395e12 | 0.0292603 | ||||||||
\(780\) | 1.19691e14i | 0.414563i | ||||||||
\(781\) | 2.37900e14i | 0.818728i | ||||||||
\(782\) | −5.64877e13 | −0.193161 | ||||||||
\(783\) | 9.07554e12 | 0.0308364 | ||||||||
\(784\) | −8.32931e13 | −0.281209 | ||||||||
\(785\) | − | 2.34295e14i | − | 0.785984i | ||||||
\(786\) | −2.48155e14 | −0.827201 | ||||||||
\(787\) | −1.28414e14 | −0.425344 | −0.212672 | − | 0.977124i | \(-0.568217\pi\) | ||||
−0.212672 | + | 0.977124i | \(0.568217\pi\) | |||||||
\(788\) | 1.26761e14 | 0.417211 | ||||||||
\(789\) | 8.29320e13 | 0.271230 | ||||||||
\(790\) | − | 1.23565e14i | − | 0.401569i | ||||||
\(791\) | 5.37018e14i | 1.73423i | ||||||||
\(792\) | 7.68309e13 | 0.246553 | ||||||||
\(793\) | −4.15919e13 | −0.132630 | ||||||||
\(794\) | 3.25303e14 | 1.03083 | ||||||||
\(795\) | −5.15128e13 | −0.162211 | ||||||||
\(796\) | 6.42569e14 | 2.01073 | ||||||||
\(797\) | − | 4.67600e14i | − | 1.45406i | −0.686605 | − | 0.727031i | \(-0.740900\pi\) | ||
0.686605 | − | 0.727031i | \(-0.259100\pi\) | |||||||
\(798\) | − | 8.13094e12i | − | 0.0251262i | ||||||
\(799\) | 9.40002e13i | 0.288666i | ||||||||
\(800\) | − | 2.04569e14i | − | 0.624295i | ||||||
\(801\) | 1.06708e14i | 0.323618i | ||||||||
\(802\) | 1.59968e14 | 0.482127 | ||||||||
\(803\) | 4.33956e14 | 1.29978 | ||||||||
\(804\) | − | 2.84758e14i | − | 0.847608i | ||||||
\(805\) | 1.03065e14i | 0.304881i | ||||||||
\(806\) | 9.03671e13i | 0.265665i | ||||||||
\(807\) | 9.36214e13i | 0.273532i | ||||||||
\(808\) | −3.39768e14 | −0.986564 | ||||||||
\(809\) | 5.35501e14i | 1.54532i | 0.634822 | + | 0.772659i | \(0.281074\pi\) | ||||
−0.634822 | + | 0.772659i | \(0.718926\pi\) | |||||||
\(810\) | − | 4.15449e13i | − | 0.119150i | ||||||
\(811\) | 6.40192e14i | 1.82476i | 0.409344 | + | 0.912380i | \(0.365758\pi\) | ||||
−0.409344 | + | 0.912380i | \(0.634242\pi\) | |||||||
\(812\) | 1.36144e14 | 0.385671 | ||||||||
\(813\) | −1.82475e14 | −0.513748 | ||||||||
\(814\) | 2.43216e14i | 0.680565i | ||||||||
\(815\) | 1.29407e14 | 0.359889 | ||||||||
\(816\) | −1.68122e13 | −0.0464700 | ||||||||
\(817\) | 3.34013e12i | 0.00917600i | ||||||||
\(818\) | −1.03166e15 | −2.81688 | ||||||||
\(819\) | 1.34607e14i | 0.365298i | ||||||||
\(820\) | 6.43381e14 | 1.73540 | ||||||||
\(821\) | 4.27084e13i | 0.114498i | 0.998360 | + | 0.0572490i | \(0.0182329\pi\) | ||||
−0.998360 | + | 0.0572490i | \(0.981767\pi\) | |||||||
\(822\) | − | 4.37155e14i | − | 1.16487i | ||||||
\(823\) | 5.55121e14i | 1.47024i | 0.677937 | + | 0.735120i | \(0.262874\pi\) | ||||
−0.677937 | + | 0.735120i | \(0.737126\pi\) | |||||||
\(824\) | −1.11788e14 | −0.294279 | ||||||||
\(825\) | 1.05722e14i | 0.276628i | ||||||||
\(826\) | 4.92999e14 | + | 8.26564e14i | 1.28217 | + | 2.14969i | ||||
\(827\) | −5.66330e14 | −1.46400 | −0.732002 | − | 0.681303i | \(-0.761414\pi\) | ||||
−0.732002 | + | 0.681303i | \(0.761414\pi\) | |||||||
\(828\) | 5.70013e13i | 0.146465i | ||||||||
\(829\) | −6.99218e14 | −1.78583 | −0.892914 | − | 0.450227i | \(-0.851343\pi\) | ||||
−0.892914 | + | 0.450227i | \(0.851343\pi\) | |||||||
\(830\) | 8.06981e14 | 2.04867 | ||||||||
\(831\) | 2.74672e13 | 0.0693122 | ||||||||
\(832\) | − | 4.52539e14i | − | 1.13511i | ||||||
\(833\) | 2.50417e14 | 0.624366 | ||||||||
\(834\) | 1.06958e14i | 0.265084i | ||||||||
\(835\) | −1.31726e14 | −0.324518 | ||||||||
\(836\) | − | 9.53963e12i | − | 0.0233615i | ||||||
\(837\) | − | 1.89655e13i | − | 0.0461677i | ||||||
\(838\) | 8.25087e14 | 1.99655 | ||||||||
\(839\) | − | 3.20522e14i | − | 0.770989i | −0.922710 | − | 0.385495i | \(-0.874031\pi\) | ||
0.922710 | − | 0.385495i | \(-0.125969\pi\) | |||||||
\(840\) | − | 2.15719e14i | − | 0.515814i | ||||||
\(841\) | −4.09906e14 | −0.974326 | ||||||||
\(842\) | −1.16375e15 | −2.74978 | ||||||||
\(843\) | −3.08404e14 | −0.724406 | ||||||||
\(844\) | − | 7.39268e13i | − | 0.172619i | ||||||
\(845\) | 1.49636e14 | 0.347338 | ||||||||
\(846\) | 1.56877e14 | 0.361999 | ||||||||
\(847\) | −1.56531e14 | −0.359074 | ||||||||
\(848\) | 3.47898e13 | 0.0793365 | ||||||||
\(849\) | 9.37119e13i | 0.212450i | ||||||||
\(850\) | 1.62691e14i | 0.366665i | ||||||||
\(851\) | −6.24579e13 | −0.139939 | ||||||||
\(852\) | 3.69423e14 | 0.822860 | ||||||||
\(853\) | −2.49877e14 | −0.553325 | −0.276663 | − | 0.960967i | \(-0.589228\pi\) | ||||
−0.276663 | + | 0.960967i | \(0.589228\pi\) | |||||||
\(854\) | 2.16565e14 | 0.476759 | ||||||||
\(855\) | −1.78550e12 | −0.00390777 | ||||||||
\(856\) | − | 2.88371e14i | − | 0.627456i | ||||||
\(857\) | − | 3.33483e13i | − | 0.0721390i | −0.999349 | − | 0.0360695i | \(-0.988516\pi\) | ||
0.999349 | − | 0.0360695i | \(-0.0114838\pi\) | |||||||
\(858\) | 2.61190e14i | 0.561721i | ||||||||
\(859\) | − | 8.66469e14i | − | 1.85262i | −0.376758 | − | 0.926312i | \(-0.622961\pi\) | ||
0.376758 | − | 0.926312i | \(-0.377039\pi\) | |||||||
\(860\) | 2.56015e14i | 0.544219i | ||||||||
\(861\) | 7.23555e14 | 1.52917 | ||||||||
\(862\) | 1.99193e14 | 0.418541 | ||||||||
\(863\) | − | 1.68794e14i | − | 0.352617i | −0.984335 | − | 0.176309i | \(-0.943584\pi\) | ||
0.984335 | − | 0.176309i | \(-0.0564157\pi\) | |||||||
\(864\) | 1.06068e14i | 0.220301i | ||||||||
\(865\) | 2.80150e14i | 0.578509i | ||||||||
\(866\) | 1.35552e15i | 2.78302i | ||||||||
\(867\) | −2.32291e14 | −0.474173 | ||||||||
\(868\) | − | 2.84505e14i | − | 0.577419i | ||||||
\(869\) | − | 1.63038e14i | − | 0.328996i | ||||||
\(870\) | − | 4.94443e13i | − | 0.0992019i | ||||||
\(871\) | 3.35076e14 | 0.668425 | ||||||||
\(872\) | −5.25830e14 | −1.04295 | ||||||||
\(873\) | − | 6.92935e13i | − | 0.136654i | ||||||
\(874\) | 4.05161e12 | 0.00794456 | ||||||||
\(875\) | 8.41126e14 | 1.63991 | ||||||||
\(876\) | − | 6.73868e14i | − | 1.30633i | ||||||
\(877\) | 5.35503e14 | 1.03220 | 0.516100 | − | 0.856528i | \(-0.327383\pi\) | ||||
0.516100 | + | 0.856528i | \(0.327383\pi\) | |||||||
\(878\) | − | 6.23113e14i | − | 1.19425i | ||||||
\(879\) | 1.94996e14 | 0.371605 | ||||||||
\(880\) | 5.95209e13i | 0.112786i | ||||||||
\(881\) | 2.99832e12i | 0.00564935i | 0.999996 | + | 0.00282468i | \(0.000899124\pi\) | ||||
−0.999996 | + | 0.00282468i | \(0.999101\pi\) | |||||||
\(882\) | − | 4.17922e14i | − | 0.782983i | ||||||
\(883\) | −1.14025e14 | −0.212420 | −0.106210 | − | 0.994344i | \(-0.533872\pi\) | ||||
−0.106210 | + | 0.994344i | \(0.533872\pi\) | |||||||
\(884\) | 2.43027e14i | 0.450188i | ||||||||
\(885\) | 1.81508e14 | − | 1.08259e14i | 0.334333 | − | 0.199411i | ||||
\(886\) | 4.29722e14 | 0.787081 | ||||||||
\(887\) | − | 5.14714e14i | − | 0.937449i | −0.883344 | − | 0.468725i | \(-0.844714\pi\) | ||
0.883344 | − | 0.468725i | \(-0.155286\pi\) | |||||||
\(888\) | 1.30728e14 | 0.236757 | ||||||||
\(889\) | −1.06921e15 | −1.92555 | ||||||||
\(890\) | 5.81352e14 | 1.04109 | ||||||||
\(891\) | − | 5.48166e13i | − | 0.0976165i | ||||||
\(892\) | 5.60217e14 | 0.992046 | ||||||||
\(893\) | − | 6.74221e12i | − | 0.0118726i | ||||||
\(894\) | −1.05725e14 | −0.185136 | ||||||||
\(895\) | − | 2.03088e13i | − | 0.0353646i | ||||||
\(896\) | 1.31593e15i | 2.27874i | ||||||||
\(897\) | −6.70738e13 | −0.115502 | ||||||||
\(898\) | 1.47604e14i | 0.252764i | ||||||||
\(899\) | − | 2.25717e13i | − | 0.0384384i | ||||||
\(900\) | 1.64171e14 | 0.278024 | ||||||||
\(901\) | −1.04594e14 | −0.176150 | ||||||||
\(902\) | 1.40398e15 | 2.35142 | ||||||||
\(903\) | 2.87918e14i | 0.479546i | ||||||||
\(904\) | 5.60086e14 | 0.927711 | ||||||||
\(905\) | −2.37761e14 | −0.391650 | ||||||||
\(906\) | −3.96640e14 | −0.649763 | ||||||||
\(907\) | −6.33701e14 | −1.03240 | −0.516200 | − | 0.856468i | \(-0.672654\pi\) | ||||
−0.516200 | + | 0.856468i | \(0.672654\pi\) | |||||||
\(908\) | 4.65296e14i | 0.753876i | ||||||||
\(909\) | 2.42414e14i | 0.390606i | ||||||||
\(910\) | 7.33348e14 | 1.17518 | ||||||||
\(911\) | −7.63257e14 | −1.21641 | −0.608203 | − | 0.793781i | \(-0.708109\pi\) | ||||
−0.608203 | + | 0.793781i | \(0.708109\pi\) | |||||||
\(912\) | 1.20586e12 | 0.00191127 | ||||||||
\(913\) | 1.06477e15 | 1.67843 | ||||||||
\(914\) | −2.22473e14 | −0.348776 | ||||||||
\(915\) | − | 4.75562e13i | − | 0.0741484i | ||||||
\(916\) | 9.48543e14i | 1.47089i | ||||||||
\(917\) | 9.19330e14i | 1.41783i | ||||||||
\(918\) | − | 8.43548e13i | − | 0.129389i | ||||||
\(919\) | 7.53959e14i | 1.15019i | 0.818086 | + | 0.575096i | \(0.195035\pi\) | ||||
−0.818086 | + | 0.575096i | \(0.804965\pi\) | |||||||
\(920\) | 1.07492e14 | 0.163093 | ||||||||
\(921\) | −1.28939e14 | −0.194575 | ||||||||
\(922\) | − | 1.25082e14i | − | 0.187733i | ||||||
\(923\) | 4.34702e14i | 0.648908i | ||||||||
\(924\) | − | 8.22312e14i | − | 1.22089i | ||||||
\(925\) | 1.79886e14i | 0.265637i | ||||||||
\(926\) | 3.10141e14 | 0.455517 | ||||||||
\(927\) | 7.97574e13i | 0.116512i | ||||||||
\(928\) | 1.26236e14i | 0.183419i | ||||||||
\(929\) | 1.13752e15i | 1.64392i | 0.569548 | + | 0.821958i | \(0.307118\pi\) | ||||
−0.569548 | + | 0.821958i | \(0.692882\pi\) | |||||||
\(930\) | −1.03326e14 | −0.148523 | ||||||||
\(931\) | −1.79613e13 | −0.0256796 | ||||||||
\(932\) | 8.63906e14i | 1.22853i | ||||||||
\(933\) | −3.50810e14 | −0.496208 | ||||||||
\(934\) | −3.51327e14 | −0.494285 | ||||||||
\(935\) | − | 1.78947e14i | − | 0.250419i | ||||||
\(936\) | 1.40389e14 | 0.195413 | ||||||||
\(937\) | − | 6.68677e14i | − | 0.925803i | −0.886410 | − | 0.462901i | \(-0.846808\pi\) | ||
0.886410 | − | 0.462901i | \(-0.153192\pi\) | |||||||
\(938\) | −1.74471e15 | −2.40275 | ||||||||
\(939\) | 3.84239e14i | 0.526349i | ||||||||
\(940\) | − | 5.16778e14i | − | 0.704149i | ||||||
\(941\) | 6.55700e13i | 0.0888703i | 0.999012 | + | 0.0444352i | \(0.0141488\pi\) | ||||
−0.999012 | + | 0.0444352i | \(0.985851\pi\) | |||||||
\(942\) | −7.93935e14 | −1.07036 | ||||||||
\(943\) | 3.60544e14i | 0.483503i | ||||||||
\(944\) | −1.22584e14 | + | 7.31143e13i | −0.163521 | + | 0.0975309i | ||||
\(945\) | −1.53909e14 | −0.204224 | ||||||||
\(946\) | 5.58675e14i | 0.737401i | ||||||||
\(947\) | 4.02311e14 | 0.528216 | 0.264108 | − | 0.964493i | \(-0.414922\pi\) | ||||
0.264108 | + | 0.964493i | \(0.414922\pi\) | |||||||
\(948\) | −2.53173e14 | −0.330656 | ||||||||
\(949\) | 7.92944e14 | 1.03018 | ||||||||
\(950\) | − | 1.16691e13i | − | 0.0150806i | ||||||
\(951\) | −7.93805e14 | −1.02050 | ||||||||
\(952\) | − | 4.38007e14i | − | 0.560140i | ||||||
\(953\) | 8.91998e14 | 1.13475 | 0.567374 | − | 0.823460i | \(-0.307959\pi\) | ||||
0.567374 | + | 0.823460i | \(0.307959\pi\) | |||||||
\(954\) | 1.74557e14i | 0.220900i | ||||||||
\(955\) | 9.21221e14i | 1.15970i | ||||||||
\(956\) | −1.48555e15 | −1.86037 | ||||||||
\(957\) | − | 6.52394e13i | − | 0.0812738i | ||||||
\(958\) | 6.91304e14i | 0.856725i | ||||||||
\(959\) | −1.61951e15 | −1.99659 | ||||||||
\(960\) | 5.17434e14 | 0.634598 | ||||||||
\(961\) | 7.72459e14 | 0.942451 | ||||||||
\(962\) | 4.44414e14i | 0.539402i | ||||||||
\(963\) | −2.05744e14 | −0.248426 | ||||||||
\(964\) | 6.57578e14 | 0.789882 | ||||||||
\(965\) | −8.95635e14 | −1.07027 | ||||||||
\(966\) | 3.49247e14 | 0.415190 | ||||||||
\(967\) | 3.18395e14i | 0.376560i | 0.982115 | + | 0.188280i | \(0.0602912\pi\) | ||||
−0.982115 | + | 0.188280i | \(0.939709\pi\) | |||||||
\(968\) | 1.63255e14i | 0.192084i | ||||||||
\(969\) | −3.62537e12 | −0.00424359 | ||||||||
\(970\) | −3.77517e14 | −0.439620 | ||||||||
\(971\) | −1.19147e14 | −0.138034 | −0.0690172 | − | 0.997615i | \(-0.521986\pi\) | ||||
−0.0690172 | + | 0.997615i | \(0.521986\pi\) | |||||||
\(972\) | −8.51218e13 | −0.0981091 | ||||||||
\(973\) | 3.96243e14 | 0.454357 | ||||||||
\(974\) | − | 2.15346e14i | − | 0.245664i | ||||||
\(975\) | 1.93180e14i | 0.219250i | ||||||||
\(976\) | 3.21177e13i | 0.0362656i | ||||||||
\(977\) | 4.28514e14i | 0.481385i | 0.970601 | + | 0.240692i | \(0.0773745\pi\) | ||||
−0.970601 | + | 0.240692i | \(0.922626\pi\) | |||||||
\(978\) | − | 4.38510e14i | − | 0.490101i | ||||||
\(979\) | 7.67067e14 | 0.852942 | ||||||||
\(980\) | −1.37670e15 | −1.52303 | ||||||||
\(981\) | 3.75164e14i | 0.412930i | ||||||||
\(982\) | − | 3.20697e14i | − | 0.351186i | ||||||
\(983\) | − | 6.67690e14i | − | 0.727456i | −0.931505 | − | 0.363728i | \(-0.881504\pi\) | ||
0.931505 | − | 0.363728i | \(-0.118496\pi\) | |||||||
\(984\) | − | 7.54636e14i | − | 0.818017i | ||||||
\(985\) | −1.70551e14 | −0.183938 | ||||||||
\(986\) | − | 1.00394e14i | − | 0.107727i | ||||||
\(987\) | − | 5.81175e14i | − | 0.620471i | ||||||
\(988\) | − | 1.74312e13i | − | 0.0185158i | ||||||
\(989\) | −1.43468e14 | −0.151626 | ||||||||
\(990\) | −2.98645e14 | −0.314036 | ||||||||
\(991\) | 7.41790e14i | 0.776091i | 0.921640 | + | 0.388045i | \(0.126850\pi\) | ||||
−0.921640 | + | 0.388045i | \(0.873150\pi\) | |||||||
\(992\) | 2.63801e14 | 0.274611 | ||||||||
\(993\) | −8.11693e14 | −0.840708 | ||||||||
\(994\) | − | 2.26345e15i | − | 2.33259i | ||||||
\(995\) | −8.64542e14 | −0.886483 | ||||||||
\(996\) | − | 1.65343e15i | − | 1.68690i | ||||||
\(997\) | −6.46805e14 | −0.656595 | −0.328298 | − | 0.944574i | \(-0.606475\pi\) | ||||
−0.328298 | + | 0.944574i | \(0.606475\pi\) | |||||||
\(998\) | − | 3.51571e14i | − | 0.355108i | ||||||
\(999\) | − | 9.32702e13i | − | 0.0937380i |
(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 | 177.11.c.a.58.13 | ✓ | 100 | |
59.58 | odd | 2 | inner | 177.11.c.a.58.88 | yes | 100 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.11.c.a.58.13 | ✓ | 100 | 1.1 | even | 1 | trivial | |
177.11.c.a.58.88 | yes | 100 | 59.58 | odd | 2 | inner |