Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,12,Mod(1,177)]
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, 0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
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: | yes |
Analytic conductor: | \(135.996742959\) |
Analytic rank: | \(1\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.23 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 60.5708 | 1.33844 | 0.669219 | − | 0.743065i | \(-0.266629\pi\) | ||||
0.669219 | + | 0.743065i | \(0.266629\pi\) | |||||||
\(3\) | −243.000 | −0.577350 | ||||||||
\(4\) | 1620.82 | 0.791416 | ||||||||
\(5\) | 3733.47 | 0.534291 | 0.267146 | − | 0.963656i | \(-0.413920\pi\) | ||||
0.267146 | + | 0.963656i | \(0.413920\pi\) | |||||||
\(6\) | −14718.7 | −0.772748 | ||||||||
\(7\) | 51542.9 | 1.15912 | 0.579562 | − | 0.814928i | \(-0.303224\pi\) | ||||
0.579562 | + | 0.814928i | \(0.303224\pi\) | |||||||
\(8\) | −25874.6 | −0.279176 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | 226139. | 0.715116 | ||||||||
\(11\) | 8197.47 | 0.0153469 | 0.00767344 | − | 0.999971i | \(-0.497557\pi\) | ||||
0.00767344 | + | 0.999971i | \(0.497557\pi\) | |||||||
\(12\) | −393859. | −0.456924 | ||||||||
\(13\) | −2.10127e6 | −1.56962 | −0.784808 | − | 0.619739i | \(-0.787239\pi\) | ||||
−0.784808 | + | 0.619739i | \(0.787239\pi\) | |||||||
\(14\) | 3.12200e6 | 1.55142 | ||||||||
\(15\) | −907234. | −0.308473 | ||||||||
\(16\) | −4.88669e6 | −1.16508 | ||||||||
\(17\) | 4.38795e6 | 0.749536 | 0.374768 | − | 0.927119i | \(-0.377722\pi\) | ||||
0.374768 | + | 0.927119i | \(0.377722\pi\) | |||||||
\(18\) | 3.57664e6 | 0.446146 | ||||||||
\(19\) | −3.78954e6 | −0.351108 | −0.175554 | − | 0.984470i | \(-0.556172\pi\) | ||||
−0.175554 | + | 0.984470i | \(0.556172\pi\) | |||||||
\(20\) | 6.05129e6 | 0.422847 | ||||||||
\(21\) | −1.25249e7 | −0.669221 | ||||||||
\(22\) | 496527. | 0.0205408 | ||||||||
\(23\) | 2.08704e7 | 0.676125 | 0.338062 | − | 0.941124i | \(-0.390228\pi\) | ||||
0.338062 | + | 0.941124i | \(0.390228\pi\) | |||||||
\(24\) | 6.28753e6 | 0.161183 | ||||||||
\(25\) | −3.48893e7 | −0.714533 | ||||||||
\(26\) | −1.27276e8 | −2.10083 | ||||||||
\(27\) | −1.43489e7 | −0.192450 | ||||||||
\(28\) | 8.35419e7 | 0.917350 | ||||||||
\(29\) | −1.72215e8 | −1.55913 | −0.779566 | − | 0.626320i | \(-0.784561\pi\) | ||||
−0.779566 | + | 0.626320i | \(0.784561\pi\) | |||||||
\(30\) | −5.49519e7 | −0.412872 | ||||||||
\(31\) | 2.05932e8 | 1.29192 | 0.645960 | − | 0.763372i | \(-0.276457\pi\) | ||||
0.645960 | + | 0.763372i | \(0.276457\pi\) | |||||||
\(32\) | −2.42999e8 | −1.28021 | ||||||||
\(33\) | −1.99198e6 | −0.00886052 | ||||||||
\(34\) | 2.65781e8 | 1.00321 | ||||||||
\(35\) | 1.92434e8 | 0.619310 | ||||||||
\(36\) | 9.57078e7 | 0.263805 | ||||||||
\(37\) | −4.55455e7 | −0.107978 | −0.0539891 | − | 0.998542i | \(-0.517194\pi\) | ||||
−0.0539891 | + | 0.998542i | \(0.517194\pi\) | |||||||
\(38\) | −2.29535e8 | −0.469937 | ||||||||
\(39\) | 5.10609e8 | 0.906218 | ||||||||
\(40\) | −9.66021e7 | −0.149161 | ||||||||
\(41\) | −1.14598e9 | −1.54477 | −0.772387 | − | 0.635152i | \(-0.780938\pi\) | ||||
−0.772387 | + | 0.635152i | \(0.780938\pi\) | |||||||
\(42\) | −7.58645e8 | −0.895710 | ||||||||
\(43\) | 6.27327e8 | 0.650755 | 0.325378 | − | 0.945584i | \(-0.394509\pi\) | ||||
0.325378 | + | 0.945584i | \(0.394509\pi\) | |||||||
\(44\) | 1.32866e7 | 0.0121458 | ||||||||
\(45\) | 2.20458e8 | 0.178097 | ||||||||
\(46\) | 1.26413e9 | 0.904951 | ||||||||
\(47\) | −1.39069e9 | −0.884490 | −0.442245 | − | 0.896894i | \(-0.645818\pi\) | ||||
−0.442245 | + | 0.896894i | \(0.645818\pi\) | |||||||
\(48\) | 1.18746e9 | 0.672657 | ||||||||
\(49\) | 6.79348e8 | 0.343569 | ||||||||
\(50\) | −2.11327e9 | −0.956358 | ||||||||
\(51\) | −1.06627e9 | −0.432745 | ||||||||
\(52\) | −3.40578e9 | −1.24222 | ||||||||
\(53\) | 5.76515e9 | 1.89362 | 0.946810 | − | 0.321792i | \(-0.104285\pi\) | ||||
0.946810 | + | 0.321792i | \(0.104285\pi\) | |||||||
\(54\) | −8.69125e8 | −0.257583 | ||||||||
\(55\) | 3.06050e7 | 0.00819970 | ||||||||
\(56\) | −1.33365e9 | −0.323600 | ||||||||
\(57\) | 9.20857e8 | 0.202713 | ||||||||
\(58\) | −1.04312e10 | −2.08680 | ||||||||
\(59\) | 7.14924e8 | 0.130189 | ||||||||
\(60\) | −1.47046e9 | −0.244131 | ||||||||
\(61\) | −9.92538e9 | −1.50464 | −0.752321 | − | 0.658797i | \(-0.771066\pi\) | ||||
−0.752321 | + | 0.658797i | \(0.771066\pi\) | |||||||
\(62\) | 1.24735e10 | 1.72915 | ||||||||
\(63\) | 3.04356e9 | 0.386375 | ||||||||
\(64\) | −4.71072e9 | −0.548400 | ||||||||
\(65\) | −7.84504e9 | −0.838632 | ||||||||
\(66\) | −1.20656e8 | −0.0118593 | ||||||||
\(67\) | 2.96887e9 | 0.268645 | 0.134323 | − | 0.990938i | \(-0.457114\pi\) | ||||
0.134323 | + | 0.990938i | \(0.457114\pi\) | |||||||
\(68\) | 7.11208e9 | 0.593195 | ||||||||
\(69\) | −5.07150e9 | −0.390361 | ||||||||
\(70\) | 1.16559e10 | 0.828908 | ||||||||
\(71\) | −3.75907e9 | −0.247263 | −0.123632 | − | 0.992328i | \(-0.539454\pi\) | ||||
−0.123632 | + | 0.992328i | \(0.539454\pi\) | |||||||
\(72\) | −1.52787e9 | −0.0930588 | ||||||||
\(73\) | −1.30199e10 | −0.735078 | −0.367539 | − | 0.930008i | \(-0.619799\pi\) | ||||
−0.367539 | + | 0.930008i | \(0.619799\pi\) | |||||||
\(74\) | −2.75873e9 | −0.144522 | ||||||||
\(75\) | 8.47810e9 | 0.412536 | ||||||||
\(76\) | −6.14216e9 | −0.277873 | ||||||||
\(77\) | 4.22522e8 | 0.0177889 | ||||||||
\(78\) | 3.09280e10 | 1.21292 | ||||||||
\(79\) | 1.07884e10 | 0.394463 | 0.197232 | − | 0.980357i | \(-0.436805\pi\) | ||||
0.197232 | + | 0.980357i | \(0.436805\pi\) | |||||||
\(80\) | −1.82443e10 | −0.622490 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | −6.94128e10 | −2.06759 | ||||||||
\(83\) | 3.38622e10 | 0.943595 | 0.471798 | − | 0.881707i | \(-0.343605\pi\) | ||||
0.471798 | + | 0.881707i | \(0.343605\pi\) | |||||||
\(84\) | −2.03007e10 | −0.529632 | ||||||||
\(85\) | 1.63823e10 | 0.400470 | ||||||||
\(86\) | 3.79977e10 | 0.870996 | ||||||||
\(87\) | 4.18484e10 | 0.900166 | ||||||||
\(88\) | −2.12106e8 | −0.00428448 | ||||||||
\(89\) | −7.13197e10 | −1.35383 | −0.676915 | − | 0.736061i | \(-0.736684\pi\) | ||||
−0.676915 | + | 0.736061i | \(0.736684\pi\) | |||||||
\(90\) | 1.33533e10 | 0.238372 | ||||||||
\(91\) | −1.08306e11 | −1.81938 | ||||||||
\(92\) | 3.38271e10 | 0.535096 | ||||||||
\(93\) | −5.00416e10 | −0.745890 | ||||||||
\(94\) | −8.42354e10 | −1.18384 | ||||||||
\(95\) | −1.41481e10 | −0.187594 | ||||||||
\(96\) | 5.90488e10 | 0.739128 | ||||||||
\(97\) | −5.74773e10 | −0.679598 | −0.339799 | − | 0.940498i | \(-0.610359\pi\) | ||||
−0.339799 | + | 0.940498i | \(0.610359\pi\) | |||||||
\(98\) | 4.11486e10 | 0.459846 | ||||||||
\(99\) | 4.84052e8 | 0.00511562 | ||||||||
\(100\) | −5.65493e10 | −0.565493 | ||||||||
\(101\) | −9.01764e10 | −0.853740 | −0.426870 | − | 0.904313i | \(-0.640384\pi\) | ||||
−0.426870 | + | 0.904313i | \(0.640384\pi\) | |||||||
\(102\) | −6.45849e10 | −0.579202 | ||||||||
\(103\) | 1.00632e11 | 0.855321 | 0.427661 | − | 0.903939i | \(-0.359338\pi\) | ||||
0.427661 | + | 0.903939i | \(0.359338\pi\) | |||||||
\(104\) | 5.43695e10 | 0.438200 | ||||||||
\(105\) | −4.67615e10 | −0.357559 | ||||||||
\(106\) | 3.49199e11 | 2.53449 | ||||||||
\(107\) | −2.50318e11 | −1.72537 | −0.862684 | − | 0.505743i | \(-0.831218\pi\) | ||||
−0.862684 | + | 0.505743i | \(0.831218\pi\) | |||||||
\(108\) | −2.32570e10 | −0.152308 | ||||||||
\(109\) | −2.34333e11 | −1.45877 | −0.729385 | − | 0.684103i | \(-0.760194\pi\) | ||||
−0.729385 | + | 0.684103i | \(0.760194\pi\) | |||||||
\(110\) | 1.85377e9 | 0.0109748 | ||||||||
\(111\) | 1.10676e10 | 0.0623412 | ||||||||
\(112\) | −2.51874e11 | −1.35047 | ||||||||
\(113\) | −3.10993e11 | −1.58789 | −0.793944 | − | 0.607991i | \(-0.791975\pi\) | ||||
−0.793944 | + | 0.607991i | \(0.791975\pi\) | |||||||
\(114\) | 5.57771e10 | 0.271318 | ||||||||
\(115\) | 7.79190e10 | 0.361248 | ||||||||
\(116\) | −2.79130e11 | −1.23392 | ||||||||
\(117\) | −1.24078e11 | −0.523205 | ||||||||
\(118\) | 4.33035e10 | 0.174250 | ||||||||
\(119\) | 2.26168e11 | 0.868805 | ||||||||
\(120\) | 2.34743e10 | 0.0861184 | ||||||||
\(121\) | −2.85244e11 | −0.999764 | ||||||||
\(122\) | −6.01188e11 | −2.01387 | ||||||||
\(123\) | 2.78473e11 | 0.891876 | ||||||||
\(124\) | 3.33779e11 | 1.02245 | ||||||||
\(125\) | −3.12557e11 | −0.916060 | ||||||||
\(126\) | 1.84351e11 | 0.517139 | ||||||||
\(127\) | −2.28256e10 | −0.0613059 | −0.0306530 | − | 0.999530i | \(-0.509759\pi\) | ||||
−0.0306530 | + | 0.999530i | \(0.509759\pi\) | |||||||
\(128\) | 2.12330e11 | 0.546206 | ||||||||
\(129\) | −1.52441e11 | −0.375714 | ||||||||
\(130\) | −4.75180e11 | −1.12246 | ||||||||
\(131\) | −4.71963e11 | −1.06885 | −0.534424 | − | 0.845217i | \(-0.679471\pi\) | ||||
−0.534424 | + | 0.845217i | \(0.679471\pi\) | |||||||
\(132\) | −3.22865e9 | −0.00701236 | ||||||||
\(133\) | −1.95324e11 | −0.406978 | ||||||||
\(134\) | 1.79827e11 | 0.359565 | ||||||||
\(135\) | −5.35713e10 | −0.102824 | ||||||||
\(136\) | −1.13536e11 | −0.209253 | ||||||||
\(137\) | −9.83893e11 | −1.74175 | −0.870873 | − | 0.491508i | \(-0.836446\pi\) | ||||
−0.870873 | + | 0.491508i | \(0.836446\pi\) | |||||||
\(138\) | −3.07185e11 | −0.522474 | ||||||||
\(139\) | −6.09086e11 | −0.995628 | −0.497814 | − | 0.867284i | \(-0.665864\pi\) | ||||
−0.497814 | + | 0.867284i | \(0.665864\pi\) | |||||||
\(140\) | 3.11901e11 | 0.490132 | ||||||||
\(141\) | 3.37938e11 | 0.510661 | ||||||||
\(142\) | −2.27690e11 | −0.330947 | ||||||||
\(143\) | −1.72251e10 | −0.0240887 | ||||||||
\(144\) | −2.88554e11 | −0.388359 | ||||||||
\(145\) | −6.42962e11 | −0.833031 | ||||||||
\(146\) | −7.88628e11 | −0.983856 | ||||||||
\(147\) | −1.65082e11 | −0.198360 | ||||||||
\(148\) | −7.38211e10 | −0.0854557 | ||||||||
\(149\) | 9.98841e11 | 1.11422 | 0.557111 | − | 0.830438i | \(-0.311910\pi\) | ||||
0.557111 | + | 0.830438i | \(0.311910\pi\) | |||||||
\(150\) | 5.13525e11 | 0.552154 | ||||||||
\(151\) | −1.54795e12 | −1.60466 | −0.802332 | − | 0.596878i | \(-0.796408\pi\) | ||||
−0.802332 | + | 0.596878i | \(0.796408\pi\) | |||||||
\(152\) | 9.80527e10 | 0.0980212 | ||||||||
\(153\) | 2.59104e11 | 0.249845 | ||||||||
\(154\) | 2.55925e10 | 0.0238094 | ||||||||
\(155\) | 7.68843e11 | 0.690261 | ||||||||
\(156\) | 8.27605e11 | 0.717196 | ||||||||
\(157\) | 2.09764e12 | 1.75502 | 0.877510 | − | 0.479558i | \(-0.159203\pi\) | ||||
0.877510 | + | 0.479558i | \(0.159203\pi\) | |||||||
\(158\) | 6.53460e11 | 0.527965 | ||||||||
\(159\) | −1.40093e12 | −1.09328 | ||||||||
\(160\) | −9.07231e11 | −0.684003 | ||||||||
\(161\) | 1.07572e12 | 0.783713 | ||||||||
\(162\) | 2.11197e11 | 0.148715 | ||||||||
\(163\) | 2.42348e12 | 1.64971 | 0.824854 | − | 0.565346i | \(-0.191257\pi\) | ||||
0.824854 | + | 0.565346i | \(0.191257\pi\) | |||||||
\(164\) | −1.85743e12 | −1.22256 | ||||||||
\(165\) | −7.43702e9 | −0.00473410 | ||||||||
\(166\) | 2.05106e12 | 1.26294 | ||||||||
\(167\) | 2.21723e12 | 1.32090 | 0.660450 | − | 0.750870i | \(-0.270365\pi\) | ||||
0.660450 | + | 0.750870i | \(0.270365\pi\) | |||||||
\(168\) | 3.24078e11 | 0.186831 | ||||||||
\(169\) | 2.62318e12 | 1.46370 | ||||||||
\(170\) | 9.92288e11 | 0.536005 | ||||||||
\(171\) | −2.23768e11 | −0.117036 | ||||||||
\(172\) | 1.01679e12 | 0.515018 | ||||||||
\(173\) | 3.06408e12 | 1.50330 | 0.751651 | − | 0.659561i | \(-0.229258\pi\) | ||||
0.751651 | + | 0.659561i | \(0.229258\pi\) | |||||||
\(174\) | 2.53479e12 | 1.20482 | ||||||||
\(175\) | −1.79830e12 | −0.828232 | ||||||||
\(176\) | −4.00584e10 | −0.0178803 | ||||||||
\(177\) | −1.73727e11 | −0.0751646 | ||||||||
\(178\) | −4.31989e12 | −1.81202 | ||||||||
\(179\) | −2.18794e12 | −0.889906 | −0.444953 | − | 0.895554i | \(-0.646780\pi\) | ||||
−0.444953 | + | 0.895554i | \(0.646780\pi\) | |||||||
\(180\) | 3.57323e11 | 0.140949 | ||||||||
\(181\) | −2.33641e12 | −0.893959 | −0.446980 | − | 0.894544i | \(-0.647500\pi\) | ||||
−0.446980 | + | 0.894544i | \(0.647500\pi\) | |||||||
\(182\) | −6.56016e12 | −2.43513 | ||||||||
\(183\) | 2.41187e12 | 0.868705 | ||||||||
\(184\) | −5.40012e11 | −0.188758 | ||||||||
\(185\) | −1.70043e11 | −0.0576918 | ||||||||
\(186\) | −3.03106e12 | −0.998327 | ||||||||
\(187\) | 3.59701e10 | 0.0115030 | ||||||||
\(188\) | −2.25406e12 | −0.700000 | ||||||||
\(189\) | −7.39585e11 | −0.223074 | ||||||||
\(190\) | −8.56964e11 | −0.251083 | ||||||||
\(191\) | 3.50468e12 | 0.997618 | 0.498809 | − | 0.866712i | \(-0.333771\pi\) | ||||
0.498809 | + | 0.866712i | \(0.333771\pi\) | |||||||
\(192\) | 1.14471e12 | 0.316619 | ||||||||
\(193\) | 4.71015e12 | 1.26611 | 0.633053 | − | 0.774109i | \(-0.281802\pi\) | ||||
0.633053 | + | 0.774109i | \(0.281802\pi\) | |||||||
\(194\) | −3.48145e12 | −0.909599 | ||||||||
\(195\) | 1.90634e12 | 0.484185 | ||||||||
\(196\) | 1.10110e12 | 0.271906 | ||||||||
\(197\) | −2.38674e12 | −0.573114 | −0.286557 | − | 0.958063i | \(-0.592511\pi\) | ||||
−0.286557 | + | 0.958063i | \(0.592511\pi\) | |||||||
\(198\) | 2.93194e10 | 0.00684695 | ||||||||
\(199\) | −2.18916e12 | −0.497262 | −0.248631 | − | 0.968598i | \(-0.579981\pi\) | ||||
−0.248631 | + | 0.968598i | \(0.579981\pi\) | |||||||
\(200\) | 9.02746e11 | 0.199481 | ||||||||
\(201\) | −7.21434e11 | −0.155102 | ||||||||
\(202\) | −5.46206e12 | −1.14268 | ||||||||
\(203\) | −8.87649e12 | −1.80723 | ||||||||
\(204\) | −1.72823e12 | −0.342481 | ||||||||
\(205\) | −4.27848e12 | −0.825360 | ||||||||
\(206\) | 6.09533e12 | 1.14479 | ||||||||
\(207\) | 1.23237e12 | 0.225375 | ||||||||
\(208\) | 1.02682e13 | 1.82872 | ||||||||
\(209\) | −3.10646e10 | −0.00538842 | ||||||||
\(210\) | −2.83238e12 | −0.478570 | ||||||||
\(211\) | 1.32116e12 | 0.217471 | 0.108735 | − | 0.994071i | \(-0.465320\pi\) | ||||
0.108735 | + | 0.994071i | \(0.465320\pi\) | |||||||
\(212\) | 9.34427e12 | 1.49864 | ||||||||
\(213\) | 9.13455e11 | 0.142758 | ||||||||
\(214\) | −1.51620e13 | −2.30930 | ||||||||
\(215\) | 2.34211e12 | 0.347693 | ||||||||
\(216\) | 3.71272e11 | 0.0537275 | ||||||||
\(217\) | 1.06144e13 | 1.49749 | ||||||||
\(218\) | −1.41937e13 | −1.95247 | ||||||||
\(219\) | 3.16384e12 | 0.424397 | ||||||||
\(220\) | 4.96053e10 | 0.00648938 | ||||||||
\(221\) | −9.22027e12 | −1.17648 | ||||||||
\(222\) | 6.70370e11 | 0.0834399 | ||||||||
\(223\) | 4.97159e12 | 0.603697 | 0.301848 | − | 0.953356i | \(-0.402396\pi\) | ||||
0.301848 | + | 0.953356i | \(0.402396\pi\) | |||||||
\(224\) | −1.25249e13 | −1.48392 | ||||||||
\(225\) | −2.06018e12 | −0.238178 | ||||||||
\(226\) | −1.88371e13 | −2.12529 | ||||||||
\(227\) | 8.10911e12 | 0.892958 | 0.446479 | − | 0.894794i | \(-0.352678\pi\) | ||||
0.446479 | + | 0.894794i | \(0.352678\pi\) | |||||||
\(228\) | 1.49254e12 | 0.160430 | ||||||||
\(229\) | −1.05022e12 | −0.110201 | −0.0551006 | − | 0.998481i | \(-0.517548\pi\) | ||||
−0.0551006 | + | 0.998481i | \(0.517548\pi\) | |||||||
\(230\) | 4.71961e12 | 0.483508 | ||||||||
\(231\) | −1.02673e11 | −0.0102704 | ||||||||
\(232\) | 4.45600e12 | 0.435273 | ||||||||
\(233\) | −9.21077e12 | −0.878696 | −0.439348 | − | 0.898317i | \(-0.644790\pi\) | ||||
−0.439348 | + | 0.898317i | \(0.644790\pi\) | |||||||
\(234\) | −7.51550e12 | −0.700278 | ||||||||
\(235\) | −5.19211e12 | −0.472575 | ||||||||
\(236\) | 1.15876e12 | 0.103034 | ||||||||
\(237\) | −2.62157e12 | −0.227744 | ||||||||
\(238\) | 1.36992e13 | 1.16284 | ||||||||
\(239\) | 4.53953e12 | 0.376550 | 0.188275 | − | 0.982116i | \(-0.439710\pi\) | ||||
0.188275 | + | 0.982116i | \(0.439710\pi\) | |||||||
\(240\) | 4.43337e12 | 0.359395 | ||||||||
\(241\) | −1.03270e13 | −0.818241 | −0.409121 | − | 0.912480i | \(-0.634164\pi\) | ||||
−0.409121 | + | 0.912480i | \(0.634164\pi\) | |||||||
\(242\) | −1.72775e13 | −1.33812 | ||||||||
\(243\) | −8.47289e11 | −0.0641500 | ||||||||
\(244\) | −1.60873e13 | −1.19080 | ||||||||
\(245\) | 2.53633e12 | 0.183566 | ||||||||
\(246\) | 1.68673e13 | 1.19372 | ||||||||
\(247\) | 7.96284e12 | 0.551106 | ||||||||
\(248\) | −5.32842e12 | −0.360673 | ||||||||
\(249\) | −8.22851e12 | −0.544785 | ||||||||
\(250\) | −1.89318e13 | −1.22609 | ||||||||
\(251\) | −2.40666e13 | −1.52479 | −0.762395 | − | 0.647112i | \(-0.775976\pi\) | ||||
−0.762395 | + | 0.647112i | \(0.775976\pi\) | |||||||
\(252\) | 4.93306e12 | 0.305783 | ||||||||
\(253\) | 1.71084e11 | 0.0103764 | ||||||||
\(254\) | −1.38257e12 | −0.0820541 | ||||||||
\(255\) | −3.98090e12 | −0.231212 | ||||||||
\(256\) | 2.25086e13 | 1.27946 | ||||||||
\(257\) | −7.34188e12 | −0.408484 | −0.204242 | − | 0.978920i | \(-0.565473\pi\) | ||||
−0.204242 | + | 0.978920i | \(0.565473\pi\) | |||||||
\(258\) | −9.23344e12 | −0.502870 | ||||||||
\(259\) | −2.34755e12 | −0.125160 | ||||||||
\(260\) | −1.27154e13 | −0.663707 | ||||||||
\(261\) | −1.01692e13 | −0.519711 | ||||||||
\(262\) | −2.85872e13 | −1.43059 | ||||||||
\(263\) | 1.31064e13 | 0.642284 | 0.321142 | − | 0.947031i | \(-0.395933\pi\) | ||||
0.321142 | + | 0.947031i | \(0.395933\pi\) | |||||||
\(264\) | 5.15418e10 | 0.00247365 | ||||||||
\(265\) | 2.15240e13 | 1.01175 | ||||||||
\(266\) | −1.18309e13 | −0.544715 | ||||||||
\(267\) | 1.73307e13 | 0.781635 | ||||||||
\(268\) | 4.81200e12 | 0.212610 | ||||||||
\(269\) | 3.48998e12 | 0.151072 | 0.0755362 | − | 0.997143i | \(-0.475933\pi\) | ||||
0.0755362 | + | 0.997143i | \(0.475933\pi\) | |||||||
\(270\) | −3.24485e12 | −0.137624 | ||||||||
\(271\) | 2.74166e13 | 1.13942 | 0.569709 | − | 0.821847i | \(-0.307056\pi\) | ||||
0.569709 | + | 0.821847i | \(0.307056\pi\) | |||||||
\(272\) | −2.14425e13 | −0.873267 | ||||||||
\(273\) | 2.63183e13 | 1.05042 | ||||||||
\(274\) | −5.95952e13 | −2.33122 | ||||||||
\(275\) | −2.86004e11 | −0.0109658 | ||||||||
\(276\) | −8.21999e12 | −0.308938 | ||||||||
\(277\) | −4.43374e12 | −0.163354 | −0.0816772 | − | 0.996659i | \(-0.526028\pi\) | ||||
−0.0816772 | + | 0.996659i | \(0.526028\pi\) | |||||||
\(278\) | −3.68928e13 | −1.33259 | ||||||||
\(279\) | 1.21601e13 | 0.430640 | ||||||||
\(280\) | −4.97916e12 | −0.172897 | ||||||||
\(281\) | 1.81627e13 | 0.618436 | 0.309218 | − | 0.950991i | \(-0.399933\pi\) | ||||
0.309218 | + | 0.950991i | \(0.399933\pi\) | |||||||
\(282\) | 2.04692e13 | 0.683488 | ||||||||
\(283\) | 2.15554e13 | 0.705881 | 0.352940 | − | 0.935646i | \(-0.385182\pi\) | ||||
0.352940 | + | 0.935646i | \(0.385182\pi\) | |||||||
\(284\) | −6.09278e12 | −0.195688 | ||||||||
\(285\) | 3.43800e12 | 0.108308 | ||||||||
\(286\) | −1.04334e12 | −0.0322412 | ||||||||
\(287\) | −5.90671e13 | −1.79059 | ||||||||
\(288\) | −1.43489e13 | −0.426735 | ||||||||
\(289\) | −1.50178e13 | −0.438196 | ||||||||
\(290\) | −3.89447e13 | −1.11496 | ||||||||
\(291\) | 1.39670e13 | 0.392366 | ||||||||
\(292\) | −2.11030e13 | −0.581752 | ||||||||
\(293\) | 3.18276e13 | 0.861058 | 0.430529 | − | 0.902577i | \(-0.358327\pi\) | ||||
0.430529 | + | 0.902577i | \(0.358327\pi\) | |||||||
\(294\) | −9.99912e12 | −0.265492 | ||||||||
\(295\) | 2.66915e12 | 0.0695588 | ||||||||
\(296\) | 1.17847e12 | 0.0301449 | ||||||||
\(297\) | −1.17625e11 | −0.00295351 | ||||||||
\(298\) | 6.05006e13 | 1.49132 | ||||||||
\(299\) | −4.38543e13 | −1.06126 | ||||||||
\(300\) | 1.37415e13 | 0.326488 | ||||||||
\(301\) | 3.23343e13 | 0.754306 | ||||||||
\(302\) | −9.37607e13 | −2.14774 | ||||||||
\(303\) | 2.19129e13 | 0.492907 | ||||||||
\(304\) | 1.85183e13 | 0.409068 | ||||||||
\(305\) | −3.70561e13 | −0.803917 | ||||||||
\(306\) | 1.56941e13 | 0.334402 | ||||||||
\(307\) | 6.29154e13 | 1.31673 | 0.658364 | − | 0.752700i | \(-0.271249\pi\) | ||||
0.658364 | + | 0.752700i | \(0.271249\pi\) | |||||||
\(308\) | 6.84832e11 | 0.0140785 | ||||||||
\(309\) | −2.44535e13 | −0.493820 | ||||||||
\(310\) | 4.65694e13 | 0.923872 | ||||||||
\(311\) | −2.26249e13 | −0.440966 | −0.220483 | − | 0.975391i | \(-0.570763\pi\) | ||||
−0.220483 | + | 0.975391i | \(0.570763\pi\) | |||||||
\(312\) | −1.32118e13 | −0.252995 | ||||||||
\(313\) | −7.46918e13 | −1.40533 | −0.702666 | − | 0.711520i | \(-0.748007\pi\) | ||||
−0.702666 | + | 0.711520i | \(0.748007\pi\) | |||||||
\(314\) | 1.27055e14 | 2.34899 | ||||||||
\(315\) | 1.13630e13 | 0.206437 | ||||||||
\(316\) | 1.74860e13 | 0.312185 | ||||||||
\(317\) | 5.89358e13 | 1.03408 | 0.517039 | − | 0.855962i | \(-0.327034\pi\) | ||||
0.517039 | + | 0.855962i | \(0.327034\pi\) | |||||||
\(318\) | −8.48555e13 | −1.46329 | ||||||||
\(319\) | −1.41173e12 | −0.0239278 | ||||||||
\(320\) | −1.75874e13 | −0.293006 | ||||||||
\(321\) | 6.08274e13 | 0.996142 | ||||||||
\(322\) | 6.51572e13 | 1.04895 | ||||||||
\(323\) | −1.66283e13 | −0.263168 | ||||||||
\(324\) | 5.65145e12 | 0.0879351 | ||||||||
\(325\) | 7.33119e13 | 1.12154 | ||||||||
\(326\) | 1.46792e14 | 2.20803 | ||||||||
\(327\) | 5.69428e13 | 0.842221 | ||||||||
\(328\) | 2.96517e13 | 0.431265 | ||||||||
\(329\) | −7.16804e13 | −1.02523 | ||||||||
\(330\) | −4.50466e11 | −0.00633630 | ||||||||
\(331\) | 1.27988e14 | 1.77058 | 0.885290 | − | 0.465039i | \(-0.153960\pi\) | ||||
0.885290 | + | 0.465039i | \(0.153960\pi\) | |||||||
\(332\) | 5.48846e13 | 0.746777 | ||||||||
\(333\) | −2.68942e12 | −0.0359927 | ||||||||
\(334\) | 1.34299e14 | 1.76794 | ||||||||
\(335\) | 1.10842e13 | 0.143535 | ||||||||
\(336\) | 6.12054e13 | 0.779693 | ||||||||
\(337\) | 3.81105e13 | 0.477617 | 0.238809 | − | 0.971067i | \(-0.423243\pi\) | ||||
0.238809 | + | 0.971067i | \(0.423243\pi\) | |||||||
\(338\) | 1.58888e14 | 1.95907 | ||||||||
\(339\) | 7.55714e13 | 0.916767 | ||||||||
\(340\) | 2.65528e13 | 0.316939 | ||||||||
\(341\) | 1.68812e12 | 0.0198269 | ||||||||
\(342\) | −1.35538e13 | −0.156646 | ||||||||
\(343\) | −6.69016e13 | −0.760885 | ||||||||
\(344\) | −1.62318e13 | −0.181675 | ||||||||
\(345\) | −1.89343e13 | −0.208566 | ||||||||
\(346\) | 1.85594e14 | 2.01208 | ||||||||
\(347\) | −3.43199e13 | −0.366213 | −0.183106 | − | 0.983093i | \(-0.558615\pi\) | ||||
−0.183106 | + | 0.983093i | \(0.558615\pi\) | |||||||
\(348\) | 6.78287e13 | 0.712406 | ||||||||
\(349\) | 3.07555e13 | 0.317967 | 0.158984 | − | 0.987281i | \(-0.449178\pi\) | ||||
0.158984 | + | 0.987281i | \(0.449178\pi\) | |||||||
\(350\) | −1.08924e14 | −1.10854 | ||||||||
\(351\) | 3.01509e13 | 0.302073 | ||||||||
\(352\) | −1.99198e12 | −0.0196472 | ||||||||
\(353\) | −1.51838e14 | −1.47442 | −0.737208 | − | 0.675666i | \(-0.763856\pi\) | ||||
−0.737208 | + | 0.675666i | \(0.763856\pi\) | |||||||
\(354\) | −1.05228e13 | −0.100603 | ||||||||
\(355\) | −1.40344e13 | −0.132111 | ||||||||
\(356\) | −1.15596e14 | −1.07144 | ||||||||
\(357\) | −5.49588e13 | −0.501605 | ||||||||
\(358\) | −1.32525e14 | −1.19108 | ||||||||
\(359\) | 5.11655e13 | 0.452853 | 0.226427 | − | 0.974028i | \(-0.427296\pi\) | ||||
0.226427 | + | 0.974028i | \(0.427296\pi\) | |||||||
\(360\) | −5.70426e12 | −0.0497205 | ||||||||
\(361\) | −1.02130e14 | −0.876723 | ||||||||
\(362\) | −1.41518e14 | −1.19651 | ||||||||
\(363\) | 6.93144e13 | 0.577214 | ||||||||
\(364\) | −1.75544e14 | −1.43989 | ||||||||
\(365\) | −4.86096e13 | −0.392745 | ||||||||
\(366\) | 1.46089e14 | 1.16271 | ||||||||
\(367\) | 1.12307e14 | 0.880530 | 0.440265 | − | 0.897868i | \(-0.354884\pi\) | ||||
0.440265 | + | 0.897868i | \(0.354884\pi\) | |||||||
\(368\) | −1.01987e14 | −0.787737 | ||||||||
\(369\) | −6.76689e13 | −0.514925 | ||||||||
\(370\) | −1.02996e13 | −0.0772169 | ||||||||
\(371\) | 2.97153e14 | 2.19494 | ||||||||
\(372\) | −8.11084e13 | −0.590309 | ||||||||
\(373\) | −1.89088e14 | −1.35602 | −0.678008 | − | 0.735055i | \(-0.737156\pi\) | ||||
−0.678008 | + | 0.735055i | \(0.737156\pi\) | |||||||
\(374\) | 2.17874e12 | 0.0153961 | ||||||||
\(375\) | 7.59513e13 | 0.528887 | ||||||||
\(376\) | 3.59836e13 | 0.246929 | ||||||||
\(377\) | 3.61871e14 | 2.44724 | ||||||||
\(378\) | −4.47972e13 | −0.298570 | ||||||||
\(379\) | −2.69273e14 | −1.76879 | −0.884397 | − | 0.466735i | \(-0.845430\pi\) | ||||
−0.884397 | + | 0.466735i | \(0.845430\pi\) | |||||||
\(380\) | −2.29316e13 | −0.148465 | ||||||||
\(381\) | 5.54663e12 | 0.0353950 | ||||||||
\(382\) | 2.12281e14 | 1.33525 | ||||||||
\(383\) | 1.65685e14 | 1.02728 | 0.513641 | − | 0.858005i | \(-0.328297\pi\) | ||||
0.513641 | + | 0.858005i | \(0.328297\pi\) | |||||||
\(384\) | −5.15962e13 | −0.315352 | ||||||||
\(385\) | 1.57747e12 | 0.00950447 | ||||||||
\(386\) | 2.85298e14 | 1.69460 | ||||||||
\(387\) | 3.70431e13 | 0.216918 | ||||||||
\(388\) | −9.31604e13 | −0.537845 | ||||||||
\(389\) | 2.95800e14 | 1.68374 | 0.841870 | − | 0.539680i | \(-0.181455\pi\) | ||||
0.841870 | + | 0.539680i | \(0.181455\pi\) | |||||||
\(390\) | 1.15469e14 | 0.648051 | ||||||||
\(391\) | 9.15781e13 | 0.506780 | ||||||||
\(392\) | −1.75779e13 | −0.0959163 | ||||||||
\(393\) | 1.14687e14 | 0.617100 | ||||||||
\(394\) | −1.44567e14 | −0.767077 | ||||||||
\(395\) | 4.02781e13 | 0.210758 | ||||||||
\(396\) | 7.84562e11 | 0.00404859 | ||||||||
\(397\) | 2.47790e13 | 0.126106 | 0.0630530 | − | 0.998010i | \(-0.479916\pi\) | ||||
0.0630530 | + | 0.998010i | \(0.479916\pi\) | |||||||
\(398\) | −1.32599e14 | −0.665555 | ||||||||
\(399\) | 4.74637e13 | 0.234969 | ||||||||
\(400\) | 1.70493e14 | 0.832485 | ||||||||
\(401\) | −1.21810e14 | −0.586664 | −0.293332 | − | 0.956011i | \(-0.594764\pi\) | ||||
−0.293332 | + | 0.956011i | \(0.594764\pi\) | |||||||
\(402\) | −4.36978e13 | −0.207595 | ||||||||
\(403\) | −4.32720e14 | −2.02782 | ||||||||
\(404\) | −1.46160e14 | −0.675664 | ||||||||
\(405\) | 1.30178e13 | 0.0593657 | ||||||||
\(406\) | −5.37656e14 | −2.41886 | ||||||||
\(407\) | −3.73358e11 | −0.00165713 | ||||||||
\(408\) | 2.75893e13 | 0.120812 | ||||||||
\(409\) | 6.26630e13 | 0.270728 | 0.135364 | − | 0.990796i | \(-0.456780\pi\) | ||||
0.135364 | + | 0.990796i | \(0.456780\pi\) | |||||||
\(410\) | −2.59151e14 | −1.10469 | ||||||||
\(411\) | 2.39086e14 | 1.00560 | ||||||||
\(412\) | 1.63106e14 | 0.676915 | ||||||||
\(413\) | 3.68493e13 | 0.150905 | ||||||||
\(414\) | 7.46459e13 | 0.301650 | ||||||||
\(415\) | 1.26424e14 | 0.504155 | ||||||||
\(416\) | 5.10607e14 | 2.00943 | ||||||||
\(417\) | 1.48008e14 | 0.574826 | ||||||||
\(418\) | −1.88161e12 | −0.00721206 | ||||||||
\(419\) | 3.19512e14 | 1.20868 | 0.604338 | − | 0.796728i | \(-0.293438\pi\) | ||||
0.604338 | + | 0.796728i | \(0.293438\pi\) | |||||||
\(420\) | −7.57920e13 | −0.282978 | ||||||||
\(421\) | 4.81196e14 | 1.77325 | 0.886627 | − | 0.462486i | \(-0.153042\pi\) | ||||
0.886627 | + | 0.462486i | \(0.153042\pi\) | |||||||
\(422\) | 8.00235e13 | 0.291071 | ||||||||
\(423\) | −8.21190e13 | −0.294830 | ||||||||
\(424\) | −1.49171e14 | −0.528654 | ||||||||
\(425\) | −1.53092e14 | −0.535568 | ||||||||
\(426\) | 5.53287e13 | 0.191072 | ||||||||
\(427\) | −5.11583e14 | −1.74407 | ||||||||
\(428\) | −4.05721e14 | −1.36548 | ||||||||
\(429\) | 4.18570e12 | 0.0139076 | ||||||||
\(430\) | 1.41863e14 | 0.465365 | ||||||||
\(431\) | −3.69293e14 | −1.19604 | −0.598020 | − | 0.801481i | \(-0.704046\pi\) | ||||
−0.598020 | + | 0.801481i | \(0.704046\pi\) | |||||||
\(432\) | 7.01186e13 | 0.224219 | ||||||||
\(433\) | 3.30299e14 | 1.04286 | 0.521428 | − | 0.853295i | \(-0.325400\pi\) | ||||
0.521428 | + | 0.853295i | \(0.325400\pi\) | |||||||
\(434\) | 6.42920e14 | 2.00430 | ||||||||
\(435\) | 1.56240e14 | 0.480951 | ||||||||
\(436\) | −3.79811e14 | −1.15449 | ||||||||
\(437\) | −7.90890e13 | −0.237393 | ||||||||
\(438\) | 1.91637e14 | 0.568029 | ||||||||
\(439\) | 8.70926e13 | 0.254933 | 0.127467 | − | 0.991843i | \(-0.459315\pi\) | ||||
0.127467 | + | 0.991843i | \(0.459315\pi\) | |||||||
\(440\) | −7.91893e11 | −0.00228916 | ||||||||
\(441\) | 4.01148e13 | 0.114523 | ||||||||
\(442\) | −5.58479e14 | −1.57465 | ||||||||
\(443\) | 3.65477e14 | 1.01775 | 0.508873 | − | 0.860842i | \(-0.330062\pi\) | ||||
0.508873 | + | 0.860842i | \(0.330062\pi\) | |||||||
\(444\) | 1.79385e13 | 0.0493379 | ||||||||
\(445\) | −2.66270e14 | −0.723340 | ||||||||
\(446\) | 3.01133e14 | 0.808011 | ||||||||
\(447\) | −2.42718e14 | −0.643297 | ||||||||
\(448\) | −2.42805e14 | −0.635664 | ||||||||
\(449\) | −1.67608e14 | −0.433452 | −0.216726 | − | 0.976232i | \(-0.569538\pi\) | ||||
−0.216726 | + | 0.976232i | \(0.569538\pi\) | |||||||
\(450\) | −1.24787e14 | −0.318786 | ||||||||
\(451\) | −9.39412e12 | −0.0237075 | ||||||||
\(452\) | −5.04064e14 | −1.25668 | ||||||||
\(453\) | 3.76152e14 | 0.926454 | ||||||||
\(454\) | 4.91175e14 | 1.19517 | ||||||||
\(455\) | −4.04356e14 | −0.972079 | ||||||||
\(456\) | −2.38268e13 | −0.0565926 | ||||||||
\(457\) | −1.34461e14 | −0.315543 | −0.157772 | − | 0.987476i | \(-0.550431\pi\) | ||||
−0.157772 | + | 0.987476i | \(0.550431\pi\) | |||||||
\(458\) | −6.36128e13 | −0.147497 | ||||||||
\(459\) | −6.29623e13 | −0.144248 | ||||||||
\(460\) | 1.26293e14 | 0.285897 | ||||||||
\(461\) | 5.77377e14 | 1.29153 | 0.645765 | − | 0.763537i | \(-0.276539\pi\) | ||||
0.645765 | + | 0.763537i | \(0.276539\pi\) | |||||||
\(462\) | −6.21897e12 | −0.0137464 | ||||||||
\(463\) | −4.97910e14 | −1.08757 | −0.543783 | − | 0.839226i | \(-0.683008\pi\) | ||||
−0.543783 | + | 0.839226i | \(0.683008\pi\) | |||||||
\(464\) | 8.41563e14 | 1.81651 | ||||||||
\(465\) | −1.86829e14 | −0.398522 | ||||||||
\(466\) | −5.57904e14 | −1.17608 | ||||||||
\(467\) | 1.38512e14 | 0.288566 | 0.144283 | − | 0.989536i | \(-0.453912\pi\) | ||||
0.144283 | + | 0.989536i | \(0.453912\pi\) | |||||||
\(468\) | −2.01108e14 | −0.414073 | ||||||||
\(469\) | 1.53024e14 | 0.311393 | ||||||||
\(470\) | −3.14491e14 | −0.632513 | ||||||||
\(471\) | −5.09726e14 | −1.01326 | ||||||||
\(472\) | −1.84984e13 | −0.0363457 | ||||||||
\(473\) | 5.14250e12 | 0.00998706 | ||||||||
\(474\) | −1.58791e14 | −0.304821 | ||||||||
\(475\) | 1.32214e14 | 0.250879 | ||||||||
\(476\) | 3.66577e14 | 0.687587 | ||||||||
\(477\) | 3.40426e14 | 0.631207 | ||||||||
\(478\) | 2.74963e14 | 0.503989 | ||||||||
\(479\) | −5.67127e14 | −1.02763 | −0.513813 | − | 0.857902i | \(-0.671767\pi\) | ||||
−0.513813 | + | 0.857902i | \(0.671767\pi\) | |||||||
\(480\) | 2.20457e14 | 0.394909 | ||||||||
\(481\) | 9.57034e13 | 0.169484 | ||||||||
\(482\) | −6.25516e14 | −1.09516 | ||||||||
\(483\) | −2.61400e14 | −0.452477 | ||||||||
\(484\) | −4.62330e14 | −0.791230 | ||||||||
\(485\) | −2.14590e14 | −0.363103 | ||||||||
\(486\) | −5.13209e13 | −0.0858608 | ||||||||
\(487\) | 9.12154e10 | 0.000150889 0 | 7.54447e−5 | − | 1.00000i | \(-0.499976\pi\) | ||||
7.54447e−5 | 1.00000i | \(0.499976\pi\) | ||||||||
\(488\) | 2.56815e14 | 0.420060 | ||||||||
\(489\) | −5.88905e14 | −0.952460 | ||||||||
\(490\) | 1.53627e14 | 0.245692 | ||||||||
\(491\) | 1.20600e14 | 0.190722 | 0.0953608 | − | 0.995443i | \(-0.469600\pi\) | ||||
0.0953608 | + | 0.995443i | \(0.469600\pi\) | |||||||
\(492\) | 4.51354e14 | 0.705845 | ||||||||
\(493\) | −7.55672e14 | −1.16863 | ||||||||
\(494\) | 4.82316e14 | 0.737621 | ||||||||
\(495\) | 1.80720e12 | 0.00273323 | ||||||||
\(496\) | −1.00633e15 | −1.50518 | ||||||||
\(497\) | −1.93754e14 | −0.286609 | ||||||||
\(498\) | −4.98408e14 | −0.729161 | ||||||||
\(499\) | 6.81501e14 | 0.986082 | 0.493041 | − | 0.870006i | \(-0.335885\pi\) | ||||
0.493041 | + | 0.870006i | \(0.335885\pi\) | |||||||
\(500\) | −5.06599e14 | −0.724985 | ||||||||
\(501\) | −5.38787e14 | −0.762622 | ||||||||
\(502\) | −1.45774e15 | −2.04084 | ||||||||
\(503\) | −3.20766e14 | −0.444186 | −0.222093 | − | 0.975025i | \(-0.571289\pi\) | ||||
−0.222093 | + | 0.975025i | \(0.571289\pi\) | |||||||
\(504\) | −7.87508e13 | −0.107867 | ||||||||
\(505\) | −3.36671e14 | −0.456146 | ||||||||
\(506\) | 1.03627e13 | 0.0138882 | ||||||||
\(507\) | −6.37432e14 | −0.845065 | ||||||||
\(508\) | −3.69962e13 | −0.0485185 | ||||||||
\(509\) | −9.98074e14 | −1.29484 | −0.647418 | − | 0.762135i | \(-0.724151\pi\) | ||||
−0.647418 | + | 0.762135i | \(0.724151\pi\) | |||||||
\(510\) | −2.41126e14 | −0.309463 | ||||||||
\(511\) | −6.71086e14 | −0.852046 | ||||||||
\(512\) | 9.28510e14 | 1.16628 | ||||||||
\(513\) | 5.43757e13 | 0.0675709 | ||||||||
\(514\) | −4.44704e14 | −0.546731 | ||||||||
\(515\) | 3.75705e14 | 0.456991 | ||||||||
\(516\) | −2.47079e14 | −0.297346 | ||||||||
\(517\) | −1.14002e13 | −0.0135742 | ||||||||
\(518\) | −1.42193e14 | −0.167519 | ||||||||
\(519\) | −7.44571e14 | −0.867932 | ||||||||
\(520\) | 2.02987e14 | 0.234126 | ||||||||
\(521\) | −1.66176e15 | −1.89653 | −0.948266 | − | 0.317477i | \(-0.897164\pi\) | ||||
−0.948266 | + | 0.317477i | \(0.897164\pi\) | |||||||
\(522\) | −6.15953e14 | −0.695601 | ||||||||
\(523\) | −4.06295e14 | −0.454027 | −0.227014 | − | 0.973892i | \(-0.572896\pi\) | ||||
−0.227014 | + | 0.973892i | \(0.572896\pi\) | |||||||
\(524\) | −7.64968e14 | −0.845904 | ||||||||
\(525\) | 4.36986e14 | 0.478180 | ||||||||
\(526\) | 7.93866e14 | 0.859658 | ||||||||
\(527\) | 9.03621e14 | 0.968340 | ||||||||
\(528\) | 9.73420e12 | 0.0103232 | ||||||||
\(529\) | −5.17238e14 | −0.542855 | ||||||||
\(530\) | 1.30373e15 | 1.35416 | ||||||||
\(531\) | 4.22156e13 | 0.0433963 | ||||||||
\(532\) | −3.16585e14 | −0.322089 | ||||||||
\(533\) | 2.40801e15 | 2.42470 | ||||||||
\(534\) | 1.04973e15 | 1.04617 | ||||||||
\(535\) | −9.34557e14 | −0.921849 | ||||||||
\(536\) | −7.68182e13 | −0.0749994 | ||||||||
\(537\) | 5.31670e14 | 0.513787 | ||||||||
\(538\) | 2.11391e14 | 0.202201 | ||||||||
\(539\) | 5.56893e12 | 0.00527271 | ||||||||
\(540\) | −8.68294e13 | −0.0813769 | ||||||||
\(541\) | −6.01417e13 | −0.0557944 | −0.0278972 | − | 0.999611i | \(-0.508881\pi\) | ||||
−0.0278972 | + | 0.999611i | \(0.508881\pi\) | |||||||
\(542\) | 1.66065e15 | 1.52504 | ||||||||
\(543\) | 5.67749e14 | 0.516128 | ||||||||
\(544\) | −1.06627e15 | −0.959561 | ||||||||
\(545\) | −8.74874e14 | −0.779408 | ||||||||
\(546\) | 1.59412e15 | 1.40592 | ||||||||
\(547\) | 1.27342e15 | 1.11184 | 0.555919 | − | 0.831236i | \(-0.312366\pi\) | ||||
0.555919 | + | 0.831236i | \(0.312366\pi\) | |||||||
\(548\) | −1.59471e15 | −1.37845 | ||||||||
\(549\) | −5.86084e14 | −0.501547 | ||||||||
\(550\) | −1.73235e13 | −0.0146771 | ||||||||
\(551\) | 6.52617e14 | 0.547425 | ||||||||
\(552\) | 1.31223e14 | 0.108980 | ||||||||
\(553\) | 5.56064e14 | 0.457232 | ||||||||
\(554\) | −2.68555e14 | −0.218640 | ||||||||
\(555\) | 4.13204e13 | 0.0333084 | ||||||||
\(556\) | −9.87218e14 | −0.787956 | ||||||||
\(557\) | −1.28386e14 | −0.101464 | −0.0507322 | − | 0.998712i | \(-0.516155\pi\) | ||||
−0.0507322 | + | 0.998712i | \(0.516155\pi\) | |||||||
\(558\) | 7.36547e14 | 0.576385 | ||||||||
\(559\) | −1.31818e15 | −1.02144 | ||||||||
\(560\) | −9.40365e14 | −0.721543 | ||||||||
\(561\) | −8.74072e12 | −0.00664128 | ||||||||
\(562\) | 1.10013e15 | 0.827738 | ||||||||
\(563\) | 1.70059e15 | 1.26708 | 0.633539 | − | 0.773711i | \(-0.281602\pi\) | ||||
0.633539 | + | 0.773711i | \(0.281602\pi\) | |||||||
\(564\) | 5.47737e14 | 0.404145 | ||||||||
\(565\) | −1.16109e15 | −0.848394 | ||||||||
\(566\) | 1.30563e15 | 0.944777 | ||||||||
\(567\) | 1.79719e14 | 0.128792 | ||||||||
\(568\) | 9.72645e13 | 0.0690301 | ||||||||
\(569\) | 1.15025e15 | 0.808487 | 0.404244 | − | 0.914651i | \(-0.367535\pi\) | ||||
0.404244 | + | 0.914651i | \(0.367535\pi\) | |||||||
\(570\) | 2.08242e14 | 0.144963 | ||||||||
\(571\) | 1.20109e15 | 0.828092 | 0.414046 | − | 0.910256i | \(-0.364115\pi\) | ||||
0.414046 | + | 0.910256i | \(0.364115\pi\) | |||||||
\(572\) | −2.79188e13 | −0.0190642 | ||||||||
\(573\) | −8.51636e14 | −0.575975 | ||||||||
\(574\) | −3.57774e15 | −2.39659 | ||||||||
\(575\) | −7.28152e14 | −0.483114 | ||||||||
\(576\) | −2.78164e14 | −0.182800 | ||||||||
\(577\) | 2.48103e15 | 1.61497 | 0.807487 | − | 0.589885i | \(-0.200827\pi\) | ||||
0.807487 | + | 0.589885i | \(0.200827\pi\) | |||||||
\(578\) | −9.09640e14 | −0.586498 | ||||||||
\(579\) | −1.14457e15 | −0.730986 | ||||||||
\(580\) | −1.04213e15 | −0.659274 | ||||||||
\(581\) | 1.74536e15 | 1.09374 | ||||||||
\(582\) | 8.45991e14 | 0.525157 | ||||||||
\(583\) | 4.72596e13 | 0.0290612 | ||||||||
\(584\) | 3.36886e14 | 0.205216 | ||||||||
\(585\) | −4.63242e14 | −0.279544 | ||||||||
\(586\) | 1.92783e15 | 1.15247 | ||||||||
\(587\) | 7.42648e14 | 0.439818 | 0.219909 | − | 0.975520i | \(-0.429424\pi\) | ||||
0.219909 | + | 0.975520i | \(0.429424\pi\) | |||||||
\(588\) | −2.67568e14 | −0.156985 | ||||||||
\(589\) | −7.80388e14 | −0.453604 | ||||||||
\(590\) | 1.61673e14 | 0.0931001 | ||||||||
\(591\) | 5.79978e14 | 0.330887 | ||||||||
\(592\) | 2.22566e14 | 0.125803 | ||||||||
\(593\) | 1.20478e15 | 0.674696 | 0.337348 | − | 0.941380i | \(-0.390470\pi\) | ||||
0.337348 | + | 0.941380i | \(0.390470\pi\) | |||||||
\(594\) | −7.12462e12 | −0.00395309 | ||||||||
\(595\) | 8.44391e14 | 0.464195 | ||||||||
\(596\) | 1.61894e15 | 0.881814 | ||||||||
\(597\) | 5.31966e14 | 0.287095 | ||||||||
\(598\) | −2.65629e15 | −1.42043 | ||||||||
\(599\) | −3.55760e13 | −0.0188499 | −0.00942497 | − | 0.999956i | \(-0.503000\pi\) | ||||
−0.00942497 | + | 0.999956i | \(0.503000\pi\) | |||||||
\(600\) | −2.19367e14 | −0.115170 | ||||||||
\(601\) | −2.68678e15 | −1.39773 | −0.698864 | − | 0.715255i | \(-0.746311\pi\) | ||||
−0.698864 | + | 0.715255i | \(0.746311\pi\) | |||||||
\(602\) | 1.95851e15 | 1.00959 | ||||||||
\(603\) | 1.75309e14 | 0.0895484 | ||||||||
\(604\) | −2.50895e15 | −1.26996 | ||||||||
\(605\) | −1.06495e15 | −0.534165 | ||||||||
\(606\) | 1.32728e15 | 0.659725 | ||||||||
\(607\) | −3.06560e15 | −1.51000 | −0.755001 | − | 0.655724i | \(-0.772364\pi\) | ||||
−0.755001 | + | 0.655724i | \(0.772364\pi\) | |||||||
\(608\) | 9.20854e14 | 0.449491 | ||||||||
\(609\) | 2.15699e15 | 1.04340 | ||||||||
\(610\) | −2.24452e15 | −1.07599 | ||||||||
\(611\) | 2.92222e15 | 1.38831 | ||||||||
\(612\) | 4.19961e14 | 0.197732 | ||||||||
\(613\) | 3.78497e15 | 1.76616 | 0.883080 | − | 0.469223i | \(-0.155466\pi\) | ||||
0.883080 | + | 0.469223i | \(0.155466\pi\) | |||||||
\(614\) | 3.81084e15 | 1.76236 | ||||||||
\(615\) | 1.03967e15 | 0.476522 | ||||||||
\(616\) | −1.09326e13 | −0.00496625 | ||||||||
\(617\) | −4.24211e15 | −1.90991 | −0.954957 | − | 0.296744i | \(-0.904099\pi\) | ||||
−0.954957 | + | 0.296744i | \(0.904099\pi\) | |||||||
\(618\) | −1.48117e15 | −0.660948 | ||||||||
\(619\) | −1.01866e15 | −0.450535 | −0.225268 | − | 0.974297i | \(-0.572326\pi\) | ||||
−0.225268 | + | 0.974297i | \(0.572326\pi\) | |||||||
\(620\) | 1.24616e15 | 0.546284 | ||||||||
\(621\) | −2.99467e14 | −0.130120 | ||||||||
\(622\) | −1.37041e15 | −0.590206 | ||||||||
\(623\) | −3.67603e15 | −1.56926 | ||||||||
\(624\) | −2.49518e15 | −1.05581 | ||||||||
\(625\) | 5.36657e14 | 0.225090 | ||||||||
\(626\) | −4.52414e15 | −1.88095 | ||||||||
\(627\) | 7.54870e12 | 0.00311100 | ||||||||
\(628\) | 3.39989e15 | 1.38895 | ||||||||
\(629\) | −1.99851e14 | −0.0809335 | ||||||||
\(630\) | 6.88269e14 | 0.276303 | ||||||||
\(631\) | 1.06023e15 | 0.421928 | 0.210964 | − | 0.977494i | \(-0.432340\pi\) | ||||
0.210964 | + | 0.977494i | \(0.432340\pi\) | |||||||
\(632\) | −2.79145e14 | −0.110125 | ||||||||
\(633\) | −3.21041e14 | −0.125557 | ||||||||
\(634\) | 3.56979e15 | 1.38405 | ||||||||
\(635\) | −8.52189e13 | −0.0327552 | ||||||||
\(636\) | −2.27066e15 | −0.865242 | ||||||||
\(637\) | −1.42749e15 | −0.539271 | ||||||||
\(638\) | −8.55096e13 | −0.0320259 | ||||||||
\(639\) | −2.21970e14 | −0.0824211 | ||||||||
\(640\) | 7.92729e14 | 0.291833 | ||||||||
\(641\) | −1.60975e15 | −0.587543 | −0.293772 | − | 0.955876i | \(-0.594911\pi\) | ||||
−0.293772 | + | 0.955876i | \(0.594911\pi\) | |||||||
\(642\) | 3.68436e15 | 1.33327 | ||||||||
\(643\) | −4.78205e15 | −1.71575 | −0.857875 | − | 0.513858i | \(-0.828216\pi\) | ||||
−0.857875 | + | 0.513858i | \(0.828216\pi\) | |||||||
\(644\) | 1.74355e15 | 0.620243 | ||||||||
\(645\) | −5.69133e14 | −0.200741 | ||||||||
\(646\) | −1.00719e15 | −0.352235 | ||||||||
\(647\) | −1.07304e15 | −0.372084 | −0.186042 | − | 0.982542i | \(-0.559566\pi\) | ||||
−0.186042 | + | 0.982542i | \(0.559566\pi\) | |||||||
\(648\) | −9.02191e13 | −0.0310196 | ||||||||
\(649\) | 5.86057e12 | 0.00199799 | ||||||||
\(650\) | 4.44056e15 | 1.50112 | ||||||||
\(651\) | −2.57929e15 | −0.864579 | ||||||||
\(652\) | 3.92802e15 | 1.30561 | ||||||||
\(653\) | 2.59599e15 | 0.855620 | 0.427810 | − | 0.903869i | \(-0.359285\pi\) | ||||
0.427810 | + | 0.903869i | \(0.359285\pi\) | |||||||
\(654\) | 3.44907e15 | 1.12726 | ||||||||
\(655\) | −1.76206e15 | −0.571076 | ||||||||
\(656\) | 5.60003e15 | 1.79978 | ||||||||
\(657\) | −7.68814e14 | −0.245026 | ||||||||
\(658\) | −4.34174e15 | −1.37221 | ||||||||
\(659\) | 1.47229e15 | 0.461450 | 0.230725 | − | 0.973019i | \(-0.425890\pi\) | ||||
0.230725 | + | 0.973019i | \(0.425890\pi\) | |||||||
\(660\) | −1.20541e13 | −0.00374664 | ||||||||
\(661\) | 3.18725e14 | 0.0982446 | 0.0491223 | − | 0.998793i | \(-0.484358\pi\) | ||||
0.0491223 | + | 0.998793i | \(0.484358\pi\) | |||||||
\(662\) | 7.75234e15 | 2.36981 | ||||||||
\(663\) | 2.24052e15 | 0.679243 | ||||||||
\(664\) | −8.76171e14 | −0.263429 | ||||||||
\(665\) | −7.29237e14 | −0.217445 | ||||||||
\(666\) | −1.62900e14 | −0.0481740 | ||||||||
\(667\) | −3.59420e15 | −1.05417 | ||||||||
\(668\) | 3.59373e15 | 1.04538 | ||||||||
\(669\) | −1.20810e15 | −0.348545 | ||||||||
\(670\) | 6.71378e14 | 0.192112 | ||||||||
\(671\) | −8.13630e13 | −0.0230915 | ||||||||
\(672\) | 3.04355e15 | 0.856741 | ||||||||
\(673\) | 1.03994e15 | 0.290353 | 0.145177 | − | 0.989406i | \(-0.453625\pi\) | ||||
0.145177 | + | 0.989406i | \(0.453625\pi\) | |||||||
\(674\) | 2.30838e15 | 0.639261 | ||||||||
\(675\) | 5.00623e14 | 0.137512 | ||||||||
\(676\) | 4.25170e15 | 1.15839 | ||||||||
\(677\) | −4.99687e15 | −1.35039 | −0.675197 | − | 0.737637i | \(-0.735942\pi\) | ||||
−0.675197 | + | 0.737637i | \(0.735942\pi\) | |||||||
\(678\) | 4.57742e15 | 1.22704 | ||||||||
\(679\) | −2.96255e15 | −0.787738 | ||||||||
\(680\) | −4.23885e14 | −0.111802 | ||||||||
\(681\) | −1.97051e15 | −0.515550 | ||||||||
\(682\) | 1.02251e14 | 0.0265371 | ||||||||
\(683\) | −4.94894e13 | −0.0127409 | −0.00637043 | − | 0.999980i | \(-0.502028\pi\) | ||||
−0.00637043 | + | 0.999980i | \(0.502028\pi\) | |||||||
\(684\) | −3.62688e14 | −0.0926243 | ||||||||
\(685\) | −3.67334e15 | −0.930599 | ||||||||
\(686\) | −4.05229e15 | −1.01840 | ||||||||
\(687\) | 2.55204e14 | 0.0636247 | ||||||||
\(688\) | −3.06555e15 | −0.758180 | ||||||||
\(689\) | −1.21141e16 | −2.97226 | ||||||||
\(690\) | −1.14687e15 | −0.279153 | ||||||||
\(691\) | 3.02572e15 | 0.730634 | 0.365317 | − | 0.930883i | \(-0.380961\pi\) | ||||
0.365317 | + | 0.930883i | \(0.380961\pi\) | |||||||
\(692\) | 4.96632e15 | 1.18974 | ||||||||
\(693\) | 2.49495e13 | 0.00592964 | ||||||||
\(694\) | −2.07878e15 | −0.490153 | ||||||||
\(695\) | −2.27400e15 | −0.531955 | ||||||||
\(696\) | −1.08281e15 | −0.251305 | ||||||||
\(697\) | −5.02849e15 | −1.15786 | ||||||||
\(698\) | 1.86288e15 | 0.425579 | ||||||||
\(699\) | 2.23822e15 | 0.507315 | ||||||||
\(700\) | −2.91472e15 | −0.655477 | ||||||||
\(701\) | 4.61337e15 | 1.02936 | 0.514682 | − | 0.857381i | \(-0.327910\pi\) | ||||
0.514682 | + | 0.857381i | \(0.327910\pi\) | |||||||
\(702\) | 1.82627e15 | 0.404306 | ||||||||
\(703\) | 1.72596e14 | 0.0379120 | ||||||||
\(704\) | −3.86160e13 | −0.00841623 | ||||||||
\(705\) | 1.26168e15 | 0.272841 | ||||||||
\(706\) | −9.19695e15 | −1.97341 | ||||||||
\(707\) | −4.64796e15 | −0.989590 | ||||||||
\(708\) | −2.81580e14 | −0.0594865 | ||||||||
\(709\) | 1.54686e15 | 0.324263 | 0.162131 | − | 0.986769i | \(-0.448163\pi\) | ||||
0.162131 | + | 0.986769i | \(0.448163\pi\) | |||||||
\(710\) | −8.50075e14 | −0.176822 | ||||||||
\(711\) | 6.37042e14 | 0.131488 | ||||||||
\(712\) | 1.84537e15 | 0.377957 | ||||||||
\(713\) | 4.29788e15 | 0.873499 | ||||||||
\(714\) | −3.32890e15 | −0.671367 | ||||||||
\(715\) | −6.43094e13 | −0.0128704 | ||||||||
\(716\) | −3.54626e15 | −0.704286 | ||||||||
\(717\) | −1.10311e15 | −0.217401 | ||||||||
\(718\) | 3.09913e15 | 0.606116 | ||||||||
\(719\) | 5.57795e15 | 1.08259 | 0.541297 | − | 0.840831i | \(-0.317933\pi\) | ||||
0.541297 | + | 0.840831i | \(0.317933\pi\) | |||||||
\(720\) | −1.07731e15 | −0.207497 | ||||||||
\(721\) | 5.18685e15 | 0.991424 | ||||||||
\(722\) | −6.18607e15 | −1.17344 | ||||||||
\(723\) | 2.50947e15 | 0.472412 | ||||||||
\(724\) | −3.78691e15 | −0.707494 | ||||||||
\(725\) | 6.00848e15 | 1.11405 | ||||||||
\(726\) | 4.19843e15 | 0.772566 | ||||||||
\(727\) | 8.15436e15 | 1.48919 | 0.744596 | − | 0.667516i | \(-0.232642\pi\) | ||||
0.744596 | + | 0.667516i | \(0.232642\pi\) | |||||||
\(728\) | 2.80236e15 | 0.507928 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | −2.94432e15 | −0.525665 | ||||||||
\(731\) | 2.75268e15 | 0.487764 | ||||||||
\(732\) | 3.90920e15 | 0.687507 | ||||||||
\(733\) | −3.90202e15 | −0.681111 | −0.340555 | − | 0.940224i | \(-0.610615\pi\) | ||||
−0.340555 | + | 0.940224i | \(0.610615\pi\) | |||||||
\(734\) | 6.80253e15 | 1.17853 | ||||||||
\(735\) | −6.16328e14 | −0.105982 | ||||||||
\(736\) | −5.07148e15 | −0.865579 | ||||||||
\(737\) | 2.43372e13 | 0.00412286 | ||||||||
\(738\) | −4.09876e15 | −0.689195 | ||||||||
\(739\) | −1.56435e15 | −0.261090 | −0.130545 | − | 0.991442i | \(-0.541673\pi\) | ||||
−0.130545 | + | 0.991442i | \(0.541673\pi\) | |||||||
\(740\) | −2.75609e14 | −0.0456582 | ||||||||
\(741\) | −1.93497e15 | −0.318181 | ||||||||
\(742\) | 1.79988e16 | 2.93779 | ||||||||
\(743\) | −1.35429e15 | −0.219419 | −0.109710 | − | 0.993964i | \(-0.534992\pi\) | ||||
−0.109710 | + | 0.993964i | \(0.534992\pi\) | |||||||
\(744\) | 1.29481e15 | 0.208235 | ||||||||
\(745\) | 3.72915e15 | 0.595319 | ||||||||
\(746\) | −1.14532e16 | −1.81494 | ||||||||
\(747\) | 1.99953e15 | 0.314532 | ||||||||
\(748\) | 5.83010e13 | 0.00910369 | ||||||||
\(749\) | −1.29021e16 | −1.99992 | ||||||||
\(750\) | 4.60043e15 | 0.707883 | ||||||||
\(751\) | −1.24477e16 | −1.90139 | −0.950694 | − | 0.310131i | \(-0.899627\pi\) | ||||
−0.950694 | + | 0.310131i | \(0.899627\pi\) | |||||||
\(752\) | 6.79588e15 | 1.03050 | ||||||||
\(753\) | 5.84819e15 | 0.880338 | ||||||||
\(754\) | 2.19188e16 | 3.27548 | ||||||||
\(755\) | −5.77924e15 | −0.857358 | ||||||||
\(756\) | −1.19873e15 | −0.176544 | ||||||||
\(757\) | −8.01462e15 | −1.17181 | −0.585903 | − | 0.810381i | \(-0.699260\pi\) | ||||
−0.585903 | + | 0.810381i | \(0.699260\pi\) | |||||||
\(758\) | −1.63101e16 | −2.36742 | ||||||||
\(759\) | −4.15734e13 | −0.00599082 | ||||||||
\(760\) | 3.66077e14 | 0.0523719 | ||||||||
\(761\) | 6.72624e15 | 0.955338 | 0.477669 | − | 0.878540i | \(-0.341482\pi\) | ||||
0.477669 | + | 0.878540i | \(0.341482\pi\) | |||||||
\(762\) | 3.35964e14 | 0.0473740 | ||||||||
\(763\) | −1.20782e16 | −1.69090 | ||||||||
\(764\) | 5.68045e15 | 0.789531 | ||||||||
\(765\) | 9.67358e14 | 0.133490 | ||||||||
\(766\) | 1.00357e16 | 1.37495 | ||||||||
\(767\) | −1.50225e15 | −0.204347 | ||||||||
\(768\) | −5.46958e15 | −0.738699 | ||||||||
\(769\) | −7.80657e15 | −1.04680 | −0.523402 | − | 0.852086i | \(-0.675337\pi\) | ||||
−0.523402 | + | 0.852086i | \(0.675337\pi\) | |||||||
\(770\) | 9.55488e13 | 0.0127211 | ||||||||
\(771\) | 1.78408e15 | 0.235838 | ||||||||
\(772\) | 7.63431e15 | 1.00202 | ||||||||
\(773\) | 1.77765e15 | 0.231664 | 0.115832 | − | 0.993269i | \(-0.463047\pi\) | ||||
0.115832 | + | 0.993269i | \(0.463047\pi\) | |||||||
\(774\) | 2.24373e15 | 0.290332 | ||||||||
\(775\) | −7.18484e15 | −0.923119 | ||||||||
\(776\) | 1.48720e15 | 0.189728 | ||||||||
\(777\) | 5.70454e14 | 0.0722612 | ||||||||
\(778\) | 1.79168e16 | 2.25358 | ||||||||
\(779\) | 4.34273e15 | 0.542384 | ||||||||
\(780\) | 3.08984e15 | 0.383192 | ||||||||
\(781\) | −3.08149e13 | −0.00379472 | ||||||||
\(782\) | 5.54696e15 | 0.678293 | ||||||||
\(783\) | 2.47110e15 | 0.300055 | ||||||||
\(784\) | −3.31976e15 | −0.400284 | ||||||||
\(785\) | 7.83147e15 | 0.937692 | ||||||||
\(786\) | 6.94668e15 | 0.825950 | ||||||||
\(787\) | 1.99708e15 | 0.235795 | 0.117898 | − | 0.993026i | \(-0.462385\pi\) | ||||
0.117898 | + | 0.993026i | \(0.462385\pi\) | |||||||
\(788\) | −3.86848e15 | −0.453571 | ||||||||
\(789\) | −3.18486e15 | −0.370823 | ||||||||
\(790\) | 2.43968e15 | 0.282087 | ||||||||
\(791\) | −1.60295e16 | −1.84056 | ||||||||
\(792\) | −1.25247e13 | −0.00142816 | ||||||||
\(793\) | 2.08559e16 | 2.36171 | ||||||||
\(794\) | 1.50088e15 | 0.168785 | ||||||||
\(795\) | −5.23034e15 | −0.584131 | ||||||||
\(796\) | −3.54824e15 | −0.393542 | ||||||||
\(797\) | 2.09836e15 | 0.231132 | 0.115566 | − | 0.993300i | \(-0.463132\pi\) | ||||
0.115566 | + | 0.993300i | \(0.463132\pi\) | |||||||
\(798\) | 2.87491e15 | 0.314492 | ||||||||
\(799\) | −6.10229e15 | −0.662957 | ||||||||
\(800\) | 8.47807e15 | 0.914750 | ||||||||
\(801\) | −4.21136e15 | −0.451277 | ||||||||
\(802\) | −7.37814e15 | −0.785213 | ||||||||
\(803\) | −1.06731e14 | −0.0112811 | ||||||||
\(804\) | −1.16932e15 | −0.122751 | ||||||||
\(805\) | 4.01617e15 | 0.418731 | ||||||||
\(806\) | −2.62102e16 | −2.71411 | ||||||||
\(807\) | −8.48064e14 | −0.0872217 | ||||||||
\(808\) | 2.33328e15 | 0.238344 | ||||||||
\(809\) | −3.11783e15 | −0.316327 | −0.158163 | − | 0.987413i | \(-0.550557\pi\) | ||||
−0.158163 | + | 0.987413i | \(0.550557\pi\) | |||||||
\(810\) | 7.88499e14 | 0.0794573 | ||||||||
\(811\) | 4.39769e15 | 0.440159 | 0.220079 | − | 0.975482i | \(-0.429368\pi\) | ||||
0.220079 | + | 0.975482i | \(0.429368\pi\) | |||||||
\(812\) | −1.43872e16 | −1.43027 | ||||||||
\(813\) | −6.66224e15 | −0.657843 | ||||||||
\(814\) | −2.26146e13 | −0.00221796 | ||||||||
\(815\) | 9.04799e15 | 0.881425 | ||||||||
\(816\) | 5.21053e15 | 0.504181 | ||||||||
\(817\) | −2.37728e15 | −0.228486 | ||||||||
\(818\) | 3.79555e15 | 0.362353 | ||||||||
\(819\) | −6.39534e15 | −0.606460 | ||||||||
\(820\) | −6.93465e15 | −0.653203 | ||||||||
\(821\) | 3.55120e15 | 0.332267 | 0.166134 | − | 0.986103i | \(-0.446872\pi\) | ||||
0.166134 | + | 0.986103i | \(0.446872\pi\) | |||||||
\(822\) | 1.44816e16 | 1.34593 | ||||||||
\(823\) | −1.04761e16 | −0.967169 | −0.483584 | − | 0.875298i | \(-0.660665\pi\) | ||||
−0.483584 | + | 0.875298i | \(0.660665\pi\) | |||||||
\(824\) | −2.60380e15 | −0.238785 | ||||||||
\(825\) | 6.94989e13 | 0.00633113 | ||||||||
\(826\) | 2.23199e15 | 0.201977 | ||||||||
\(827\) | 1.66969e16 | 1.50091 | 0.750454 | − | 0.660922i | \(-0.229835\pi\) | ||||
0.750454 | + | 0.660922i | \(0.229835\pi\) | |||||||
\(828\) | 1.99746e15 | 0.178365 | ||||||||
\(829\) | −1.74540e16 | −1.54826 | −0.774132 | − | 0.633024i | \(-0.781813\pi\) | ||||
−0.774132 | + | 0.633024i | \(0.781813\pi\) | |||||||
\(830\) | 7.65758e15 | 0.674780 | ||||||||
\(831\) | 1.07740e15 | 0.0943128 | ||||||||
\(832\) | 9.89850e15 | 0.860778 | ||||||||
\(833\) | 2.98094e15 | 0.257517 | ||||||||
\(834\) | 8.96495e15 | 0.769369 | ||||||||
\(835\) | 8.27797e15 | 0.705745 | ||||||||
\(836\) | −5.03502e13 | −0.00426448 | ||||||||
\(837\) | −2.95490e15 | −0.248630 | ||||||||
\(838\) | 1.93531e16 | 1.61774 | ||||||||
\(839\) | −7.19255e15 | −0.597299 | −0.298650 | − | 0.954363i | \(-0.596536\pi\) | ||||
−0.298650 | + | 0.954363i | \(0.596536\pi\) | |||||||
\(840\) | 1.20993e15 | 0.0998219 | ||||||||
\(841\) | 1.74577e16 | 1.43090 | ||||||||
\(842\) | 2.91464e16 | 2.37339 | ||||||||
\(843\) | −4.41353e15 | −0.357054 | ||||||||
\(844\) | 2.14136e15 | 0.172110 | ||||||||
\(845\) | 9.79356e15 | 0.782040 | ||||||||
\(846\) | −4.97401e15 | −0.394612 | ||||||||
\(847\) | −1.47023e16 | −1.15885 | ||||||||
\(848\) | −2.81725e16 | −2.20621 | ||||||||
\(849\) | −5.23797e15 | −0.407540 | ||||||||
\(850\) | −9.27293e15 | −0.716825 | ||||||||
\(851\) | −9.50551e14 | −0.0730067 | ||||||||
\(852\) | 1.48055e15 | 0.112981 | ||||||||
\(853\) | 1.57811e16 | 1.19651 | 0.598256 | − | 0.801305i | \(-0.295861\pi\) | ||||
0.598256 | + | 0.801305i | \(0.295861\pi\) | |||||||
\(854\) | −3.09870e16 | −2.33432 | ||||||||
\(855\) | −8.35433e14 | −0.0625314 | ||||||||
\(856\) | 6.47688e15 | 0.481682 | ||||||||
\(857\) | −1.65746e16 | −1.22475 | −0.612377 | − | 0.790566i | \(-0.709786\pi\) | ||||
−0.612377 | + | 0.790566i | \(0.709786\pi\) | |||||||
\(858\) | 2.53531e14 | 0.0186145 | ||||||||
\(859\) | −2.23815e16 | −1.63278 | −0.816388 | − | 0.577504i | \(-0.804027\pi\) | ||||
−0.816388 | + | 0.577504i | \(0.804027\pi\) | |||||||
\(860\) | 3.79614e15 | 0.275170 | ||||||||
\(861\) | 1.43533e16 | 1.03380 | ||||||||
\(862\) | −2.23684e16 | −1.60083 | ||||||||
\(863\) | 1.71069e16 | 1.21650 | 0.608251 | − | 0.793745i | \(-0.291872\pi\) | ||||
0.608251 | + | 0.793745i | \(0.291872\pi\) | |||||||
\(864\) | 3.48677e15 | 0.246376 | ||||||||
\(865\) | 1.14397e16 | 0.803201 | ||||||||
\(866\) | 2.00065e16 | 1.39580 | ||||||||
\(867\) | 3.64933e15 | 0.252993 | ||||||||
\(868\) | 1.72040e16 | 1.18514 | ||||||||
\(869\) | 8.84373e13 | 0.00605378 | ||||||||
\(870\) | 9.46356e15 | 0.643723 | ||||||||
\(871\) | −6.23839e15 | −0.421670 | ||||||||
\(872\) | 6.06326e15 | 0.407254 | ||||||||
\(873\) | −3.39398e15 | −0.226533 | ||||||||
\(874\) | −4.79048e15 | −0.317736 | ||||||||
\(875\) | −1.61101e16 | −1.06183 | ||||||||
\(876\) | 5.12802e15 | 0.335875 | ||||||||
\(877\) | 7.48315e15 | 0.487065 | 0.243533 | − | 0.969893i | \(-0.421694\pi\) | ||||
0.243533 | + | 0.969893i | \(0.421694\pi\) | |||||||
\(878\) | 5.27527e15 | 0.341212 | ||||||||
\(879\) | −7.73412e15 | −0.497132 | ||||||||
\(880\) | −1.49557e14 | −0.00955328 | ||||||||
\(881\) | 1.91607e16 | 1.21631 | 0.608154 | − | 0.793819i | \(-0.291910\pi\) | ||||
0.608154 | + | 0.793819i | \(0.291910\pi\) | |||||||
\(882\) | 2.42979e15 | 0.153282 | ||||||||
\(883\) | −2.56429e16 | −1.60762 | −0.803810 | − | 0.594886i | \(-0.797197\pi\) | ||||
−0.803810 | + | 0.594886i | \(0.797197\pi\) | |||||||
\(884\) | −1.49444e16 | −0.931088 | ||||||||
\(885\) | −6.48604e14 | −0.0401598 | ||||||||
\(886\) | 2.21372e16 | 1.36219 | ||||||||
\(887\) | −3.22334e16 | −1.97118 | −0.985590 | − | 0.169153i | \(-0.945897\pi\) | ||||
−0.985590 | + | 0.169153i | \(0.945897\pi\) | |||||||
\(888\) | −2.86368e14 | −0.0174042 | ||||||||
\(889\) | −1.17650e15 | −0.0710612 | ||||||||
\(890\) | −1.61282e16 | −0.968146 | ||||||||
\(891\) | 2.85828e13 | 0.00170521 | ||||||||
\(892\) | 8.05806e15 | 0.477776 | ||||||||
\(893\) | 5.27008e15 | 0.310552 | ||||||||
\(894\) | −1.47016e16 | −0.861013 | ||||||||
\(895\) | −8.16862e15 | −0.475469 | ||||||||
\(896\) | 1.09441e16 | 0.633121 | ||||||||
\(897\) | 1.06566e16 | 0.612717 | ||||||||
\(898\) | −1.01522e16 | −0.580149 | ||||||||
\(899\) | −3.54647e16 | −2.01427 | ||||||||
\(900\) | −3.33918e15 | −0.188498 | ||||||||
\(901\) | 2.52972e16 | 1.41934 | ||||||||
\(902\) | −5.69009e14 | −0.0317310 | ||||||||
\(903\) | −7.85723e15 | −0.435499 | ||||||||
\(904\) | 8.04683e15 | 0.443300 | ||||||||
\(905\) | −8.72294e15 | −0.477635 | ||||||||
\(906\) | 2.27838e16 | 1.24000 | ||||||||
\(907\) | 2.41652e15 | 0.130722 | 0.0653612 | − | 0.997862i | \(-0.479180\pi\) | ||||
0.0653612 | + | 0.997862i | \(0.479180\pi\) | |||||||
\(908\) | 1.31434e16 | 0.706702 | ||||||||
\(909\) | −5.32483e15 | −0.284580 | ||||||||
\(910\) | −2.44922e16 | −1.30107 | ||||||||
\(911\) | 9.85203e15 | 0.520205 | 0.260103 | − | 0.965581i | \(-0.416244\pi\) | ||||
0.260103 | + | 0.965581i | \(0.416244\pi\) | |||||||
\(912\) | −4.49994e15 | −0.236176 | ||||||||
\(913\) | 2.77584e14 | 0.0144812 | ||||||||
\(914\) | −8.14444e15 | −0.422335 | ||||||||
\(915\) | 9.00464e15 | 0.464141 | ||||||||
\(916\) | −1.70222e15 | −0.0872150 | ||||||||
\(917\) | −2.43264e16 | −1.23893 | ||||||||
\(918\) | −3.81367e15 | −0.193067 | ||||||||
\(919\) | −2.49680e16 | −1.25646 | −0.628230 | − | 0.778028i | \(-0.716220\pi\) | ||||
−0.628230 | + | 0.778028i | \(0.716220\pi\) | |||||||
\(920\) | −2.01612e15 | −0.100852 | ||||||||
\(921\) | −1.52885e16 | −0.760213 | ||||||||
\(922\) | 3.49722e16 | 1.72863 | ||||||||
\(923\) | 7.89883e15 | 0.388109 | ||||||||
\(924\) | −1.66414e14 | −0.00812820 | ||||||||
\(925\) | 1.58905e15 | 0.0771539 | ||||||||
\(926\) | −3.01588e16 | −1.45564 | ||||||||
\(927\) | 5.94219e15 | 0.285107 | ||||||||
\(928\) | 4.18482e16 | 1.99601 | ||||||||
\(929\) | −1.59336e16 | −0.755488 | −0.377744 | − | 0.925910i | \(-0.623300\pi\) | ||||
−0.377744 | + | 0.925910i | \(0.623300\pi\) | |||||||
\(930\) | −1.13164e16 | −0.533398 | ||||||||
\(931\) | −2.57441e15 | −0.120630 | ||||||||
\(932\) | −1.49290e16 | −0.695414 | ||||||||
\(933\) | 5.49786e15 | 0.254592 | ||||||||
\(934\) | 8.38979e15 | 0.386227 | ||||||||
\(935\) | 1.34293e14 | 0.00614597 | ||||||||
\(936\) | 3.21047e15 | 0.146067 | ||||||||
\(937\) | 2.77710e16 | 1.25610 | 0.628050 | − | 0.778173i | \(-0.283853\pi\) | ||||
0.628050 | + | 0.778173i | \(0.283853\pi\) | |||||||
\(938\) | 9.26879e15 | 0.416780 | ||||||||
\(939\) | 1.81501e16 | 0.811369 | ||||||||
\(940\) | −8.41549e15 | −0.374004 | ||||||||
\(941\) | 8.94751e15 | 0.395329 | 0.197665 | − | 0.980270i | \(-0.436664\pi\) | ||||
0.197665 | + | 0.980270i | \(0.436664\pi\) | |||||||
\(942\) | −3.08745e16 | −1.35619 | ||||||||
\(943\) | −2.39170e16 | −1.04446 | ||||||||
\(944\) | −3.49361e15 | −0.151680 | ||||||||
\(945\) | −2.76122e15 | −0.119186 | ||||||||
\(946\) | 3.11485e14 | 0.0133671 | ||||||||
\(947\) | 1.99952e16 | 0.853100 | 0.426550 | − | 0.904464i | \(-0.359729\pi\) | ||||
0.426550 | + | 0.904464i | \(0.359729\pi\) | |||||||
\(948\) | −4.24910e15 | −0.180240 | ||||||||
\(949\) | 2.73584e16 | 1.15379 | ||||||||
\(950\) | 8.00832e15 | 0.335785 | ||||||||
\(951\) | −1.43214e16 | −0.597025 | ||||||||
\(952\) | −5.85200e15 | −0.242550 | ||||||||
\(953\) | −4.43727e16 | −1.82854 | −0.914272 | − | 0.405101i | \(-0.867236\pi\) | ||||
−0.914272 | + | 0.405101i | \(0.867236\pi\) | |||||||
\(954\) | 2.06199e16 | 0.844831 | ||||||||
\(955\) | 1.30846e16 | 0.533019 | ||||||||
\(956\) | 7.35776e15 | 0.298008 | ||||||||
\(957\) | 3.43051e14 | 0.0138147 | ||||||||
\(958\) | −3.43513e16 | −1.37541 | ||||||||
\(959\) | −5.07127e16 | −2.01890 | ||||||||
\(960\) | 4.27373e15 | 0.169167 | ||||||||
\(961\) | 1.69997e16 | 0.669055 | ||||||||
\(962\) | 5.79683e15 | 0.226844 | ||||||||
\(963\) | −1.47810e16 | −0.575123 | ||||||||
\(964\) | −1.67382e16 | −0.647569 | ||||||||
\(965\) | 1.75852e16 | 0.676469 | ||||||||
\(966\) | −1.58332e16 | −0.605612 | ||||||||
\(967\) | −1.35151e15 | −0.0514012 | −0.0257006 | − | 0.999670i | \(-0.508182\pi\) | ||||
−0.0257006 | + | 0.999670i | \(0.508182\pi\) | |||||||
\(968\) | 7.38058e15 | 0.279111 | ||||||||
\(969\) | 4.04067e15 | 0.151940 | ||||||||
\(970\) | −1.29979e16 | −0.485991 | ||||||||
\(971\) | 2.35458e16 | 0.875403 | 0.437701 | − | 0.899120i | \(-0.355793\pi\) | ||||
0.437701 | + | 0.899120i | \(0.355793\pi\) | |||||||
\(972\) | −1.37330e15 | −0.0507694 | ||||||||
\(973\) | −3.13941e16 | −1.15406 | ||||||||
\(974\) | 5.52499e12 | 0.000201956 0 | ||||||||
\(975\) | −1.78148e16 | −0.647523 | ||||||||
\(976\) | 4.85022e16 | 1.75302 | ||||||||
\(977\) | 1.95540e16 | 0.702775 | 0.351388 | − | 0.936230i | \(-0.385710\pi\) | ||||
0.351388 | + | 0.936230i | \(0.385710\pi\) | |||||||
\(978\) | −3.56704e16 | −1.27481 | ||||||||
\(979\) | −5.84641e14 | −0.0207771 | ||||||||
\(980\) | 4.11093e15 | 0.145277 | ||||||||
\(981\) | −1.38371e16 | −0.486257 | ||||||||
\(982\) | 7.30485e15 | 0.255269 | ||||||||
\(983\) | 3.28169e16 | 1.14039 | 0.570194 | − | 0.821510i | \(-0.306868\pi\) | ||||
0.570194 | + | 0.821510i | \(0.306868\pi\) | |||||||
\(984\) | −7.20537e15 | −0.248991 | ||||||||
\(985\) | −8.91083e15 | −0.306210 | ||||||||
\(986\) | −4.57717e16 | −1.56413 | ||||||||
\(987\) | 1.74183e16 | 0.591919 | ||||||||
\(988\) | 1.29063e16 | 0.436154 | ||||||||
\(989\) | 1.30926e16 | 0.439992 | ||||||||
\(990\) | 1.09463e14 | 0.00365826 | ||||||||
\(991\) | 3.26920e16 | 1.08652 | 0.543258 | − | 0.839566i | \(-0.317191\pi\) | ||||
0.543258 | + | 0.839566i | \(0.317191\pi\) | |||||||
\(992\) | −5.00414e16 | −1.65392 | ||||||||
\(993\) | −3.11011e16 | −1.02225 | ||||||||
\(994\) | −1.17358e16 | −0.383608 | ||||||||
\(995\) | −8.17317e15 | −0.265683 | ||||||||
\(996\) | −1.33369e16 | −0.431152 | ||||||||
\(997\) | −4.28863e16 | −1.37878 | −0.689390 | − | 0.724391i | \(-0.742121\pi\) | ||||
−0.689390 | + | 0.724391i | \(0.742121\pi\) | |||||||
\(998\) | 4.12790e16 | 1.31981 | ||||||||
\(999\) | 6.53528e14 | 0.0207804 |
(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 | 177.12.a.a.1.23 | ✓ | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.12.a.a.1.23 | ✓ | 26 | 1.1 | even | 1 | trivial |