Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [17,10,Mod(4,17)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(17, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("17.4");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 17 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 17.c (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.75560921479\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 13.2 | ||
Character | \(\chi\) | \(=\) | 17.13 |
Dual form | 17.10.c.a.4.11 |
$q$-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 \(\left(\mathbb{Z}/17\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 35.4517i | − | 1.56676i | −0.621543 | − | 0.783380i | \(-0.713494\pi\) | ||
0.621543 | − | 0.783380i | \(-0.286506\pi\) | |||||||
\(3\) | 137.825 | + | 137.825i | 0.982384 | + | 0.982384i | 0.999848 | − | 0.0174636i | \(-0.00555910\pi\) |
−0.0174636 | + | 0.999848i | \(0.505559\pi\) | |||||||
\(4\) | −744.825 | −1.45474 | ||||||||
\(5\) | 178.043 | + | 178.043i | 0.127397 | + | 0.127397i | 0.767930 | − | 0.640533i | \(-0.221287\pi\) |
−0.640533 | + | 0.767930i | \(0.721287\pi\) | |||||||
\(6\) | 4886.12 | − | 4886.12i | 1.53916 | − | 1.53916i | ||||
\(7\) | 7491.11 | − | 7491.11i | 1.17925 | − | 1.17925i | 0.199312 | − | 0.979936i | \(-0.436129\pi\) |
0.979936 | − | 0.199312i | \(-0.0638707\pi\) | |||||||
\(8\) | 8254.04i | 0.712462i | ||||||||
\(9\) | 18308.3i | 0.930156i | ||||||||
\(10\) | 6311.91 | − | 6311.91i | 0.199600 | − | 0.199600i | ||||
\(11\) | 27737.0 | − | 27737.0i | 0.571206 | − | 0.571206i | −0.361259 | − | 0.932465i | \(-0.617653\pi\) |
0.932465 | + | 0.361259i | \(0.117653\pi\) | |||||||
\(12\) | −102655. | − | 102655.i | −1.42911 | − | 1.42911i | ||||
\(13\) | −20877.3 | −0.202735 | −0.101368 | − | 0.994849i | \(-0.532322\pi\) | ||||
−0.101368 | + | 0.994849i | \(0.532322\pi\) | |||||||
\(14\) | −265573. | − | 265573.i | −1.84760 | − | 1.84760i | ||||
\(15\) | 49077.3i | 0.250305i | ||||||||
\(16\) | −88730.4 | −0.338479 | ||||||||
\(17\) | 286460. | − | 191125.i | 0.831847 | − | 0.555005i | ||||
\(18\) | 649060. | 1.45733 | ||||||||
\(19\) | 888282.i | 1.56372i | 0.623453 | + | 0.781861i | \(0.285729\pi\) | ||||
−0.623453 | + | 0.781861i | \(0.714271\pi\) | |||||||
\(20\) | −132610. | − | 132610.i | −0.185329 | − | 0.185329i | ||||
\(21\) | 2.06492e6 | 2.31695 | ||||||||
\(22\) | −983326. | − | 983326.i | −0.894943 | − | 0.894943i | ||||
\(23\) | −839804. | + | 839804.i | −0.625752 | + | 0.625752i | −0.946996 | − | 0.321244i | \(-0.895899\pi\) |
0.321244 | + | 0.946996i | \(0.395899\pi\) | |||||||
\(24\) | −1.13761e6 | + | 1.13761e6i | −0.699911 | + | 0.699911i | ||||
\(25\) | − | 1.88973e6i | − | 0.967540i | ||||||
\(26\) | 740136.i | 0.317637i | ||||||||
\(27\) | 189472. | − | 189472.i | 0.0686132 | − | 0.0686132i | ||||
\(28\) | −5.57957e6 | + | 5.57957e6i | −1.71549 | + | 1.71549i | ||||
\(29\) | 1.43731e6 | + | 1.43731e6i | 0.377363 | + | 0.377363i | 0.870150 | − | 0.492787i | \(-0.164022\pi\) |
−0.492787 | + | 0.870150i | \(0.664022\pi\) | |||||||
\(30\) | 1.73987e6 | 0.392168 | ||||||||
\(31\) | 710945. | + | 710945.i | 0.138264 | + | 0.138264i | 0.772851 | − | 0.634587i | \(-0.218830\pi\) |
−0.634587 | + | 0.772851i | \(0.718830\pi\) | |||||||
\(32\) | 7.37171e6i | 1.24278i | ||||||||
\(33\) | 7.64570e6 | 1.12229 | ||||||||
\(34\) | −6.77571e6 | − | 1.01555e7i | −0.869560 | − | 1.30330i | ||||
\(35\) | 2.66747e6 | 0.300465 | ||||||||
\(36\) | − | 1.36365e7i | − | 1.35313i | ||||||
\(37\) | −8.16382e6 | − | 8.16382e6i | −0.716120 | − | 0.716120i | 0.251689 | − | 0.967808i | \(-0.419014\pi\) |
−0.967808 | + | 0.251689i | \(0.919014\pi\) | |||||||
\(38\) | 3.14911e7 | 2.44998 | ||||||||
\(39\) | −2.87741e6 | − | 2.87741e6i | −0.199164 | − | 0.199164i | ||||
\(40\) | −1.46957e6 | + | 1.46957e6i | −0.0907654 | + | 0.0907654i | ||||
\(41\) | −1.89573e7 | + | 1.89573e7i | −1.04773 | + | 1.04773i | −0.0489266 | + | 0.998802i | \(0.515580\pi\) |
−0.998802 | + | 0.0489266i | \(0.984420\pi\) | |||||||
\(42\) | − | 7.32050e7i | − | 3.63010i | ||||||
\(43\) | 3.58732e7i | 1.60016i | 0.599896 | + | 0.800078i | \(0.295209\pi\) | ||||
−0.599896 | + | 0.800078i | \(0.704791\pi\) | |||||||
\(44\) | −2.06592e7 | + | 2.06592e7i | −0.830954 | + | 0.830954i | ||||
\(45\) | −3.25965e6 | + | 3.25965e6i | −0.118499 | + | 0.118499i | ||||
\(46\) | 2.97725e7 | + | 2.97725e7i | 0.980403 | + | 0.980403i | ||||
\(47\) | −1.67650e7 | −0.501143 | −0.250572 | − | 0.968098i | \(-0.580619\pi\) | ||||
−0.250572 | + | 0.968098i | \(0.580619\pi\) | |||||||
\(48\) | −1.22292e7 | − | 1.22292e7i | −0.332517 | − | 0.332517i | ||||
\(49\) | − | 7.18799e7i | − | 1.78125i | ||||||
\(50\) | −6.69941e7 | −1.51590 | ||||||||
\(51\) | 6.58229e7 | + | 1.31395e7i | 1.36242 | + | 0.271964i | ||||
\(52\) | 1.55499e7 | 0.294926 | ||||||||
\(53\) | 8.53149e7i | 1.48519i | 0.669738 | + | 0.742597i | \(0.266406\pi\) | ||||
−0.669738 | + | 0.742597i | \(0.733594\pi\) | |||||||
\(54\) | −6.71710e6 | − | 6.71710e6i | −0.107500 | − | 0.107500i | ||||
\(55\) | 9.87674e6 | 0.145540 | ||||||||
\(56\) | 6.18319e7 | + | 6.18319e7i | 0.840169 | + | 0.840169i | ||||
\(57\) | −1.22427e8 | + | 1.22427e8i | −1.53618 | + | 1.53618i | ||||
\(58\) | 5.09551e7 | − | 5.09551e7i | 0.591237 | − | 0.591237i | ||||
\(59\) | − | 495397.i | − | 0.00532255i | −0.999996 | − | 0.00266127i | \(-0.999153\pi\) | ||
0.999996 | − | 0.00266127i | \(-0.000847111\pi\) | |||||||
\(60\) | − | 3.65540e7i | − | 0.364128i | ||||||
\(61\) | 5.17968e7 | − | 5.17968e7i | 0.478981 | − | 0.478981i | −0.425825 | − | 0.904806i | \(-0.640016\pi\) |
0.904806 | + | 0.425825i | \(0.140016\pi\) | |||||||
\(62\) | 2.52042e7 | − | 2.52042e7i | 0.216626 | − | 0.216626i | ||||
\(63\) | 1.37149e8 | + | 1.37149e8i | 1.09689 | + | 1.09689i | ||||
\(64\) | 2.15910e8 | 1.60865 | ||||||||
\(65\) | −3.71705e6 | − | 3.71705e6i | −0.0258278 | − | 0.0258278i | ||||
\(66\) | − | 2.71053e8i | − | 1.75836i | ||||||
\(67\) | −2.90055e8 | −1.75851 | −0.879254 | − | 0.476353i | \(-0.841958\pi\) | ||||
−0.879254 | + | 0.476353i | \(0.841958\pi\) | |||||||
\(68\) | −2.13362e8 | + | 1.42355e8i | −1.21012 | + | 0.807386i | ||||
\(69\) | −2.31491e8 | −1.22946 | ||||||||
\(70\) | − | 9.45665e7i | − | 0.470756i | ||||||
\(71\) | 2.15692e8 | + | 2.15692e8i | 1.00733 | + | 1.00733i | 0.999973 | + | 0.00735485i | \(0.00234114\pi\) |
0.00735485 | + | 0.999973i | \(0.497659\pi\) | |||||||
\(72\) | −1.51117e8 | −0.662701 | ||||||||
\(73\) | −7.17563e7 | − | 7.17563e7i | −0.295738 | − | 0.295738i | 0.543604 | − | 0.839342i | \(-0.317059\pi\) |
−0.839342 | + | 0.543604i | \(0.817059\pi\) | |||||||
\(74\) | −2.89421e8 | + | 2.89421e8i | −1.12199 | + | 1.12199i | ||||
\(75\) | 2.60451e8 | − | 2.60451e8i | 0.950496 | − | 0.950496i | ||||
\(76\) | − | 6.61614e8i | − | 2.27480i | ||||||
\(77\) | − | 4.15563e8i | − | 1.34719i | ||||||
\(78\) | −1.02009e8 | + | 1.02009e8i | −0.312042 | + | 0.312042i | ||||
\(79\) | 2.24060e8 | − | 2.24060e8i | 0.647205 | − | 0.647205i | −0.305112 | − | 0.952316i | \(-0.598694\pi\) |
0.952316 | + | 0.305112i | \(0.0986939\pi\) | |||||||
\(80\) | −1.57978e7 | − | 1.57978e7i | −0.0431212 | − | 0.0431212i | ||||
\(81\) | 4.12589e8 | 1.06497 | ||||||||
\(82\) | 6.72069e8 | + | 6.72069e8i | 1.64154 | + | 1.64154i | ||||
\(83\) | 4.86233e7i | 0.112459i | 0.998418 | + | 0.0562293i | \(0.0179078\pi\) | ||||
−0.998418 | + | 0.0562293i | \(0.982092\pi\) | |||||||
\(84\) | −1.53800e9 | −3.37055 | ||||||||
\(85\) | 8.50304e7 | + | 1.69736e7i | 0.176681 | + | 0.0352687i | ||||
\(86\) | 1.27177e9 | 2.50706 | ||||||||
\(87\) | 3.96193e8i | 0.741431i | ||||||||
\(88\) | 2.28943e8 | + | 2.28943e8i | 0.406963 | + | 0.406963i | ||||
\(89\) | 6.13841e7 | 0.103705 | 0.0518526 | − | 0.998655i | \(-0.483487\pi\) | ||||
0.0518526 | + | 0.998655i | \(0.483487\pi\) | |||||||
\(90\) | 1.15560e8 | + | 1.15560e8i | 0.185659 | + | 0.185659i | ||||
\(91\) | −1.56394e8 | + | 1.56394e8i | −0.239075 | + | 0.239075i | ||||
\(92\) | 6.25506e8 | − | 6.25506e8i | 0.910304 | − | 0.910304i | ||||
\(93\) | 1.95971e8i | 0.271656i | ||||||||
\(94\) | 5.94346e8i | 0.785171i | ||||||||
\(95\) | −1.58152e8 | + | 1.58152e8i | −0.199213 | + | 0.199213i | ||||
\(96\) | −1.01600e9 | + | 1.01600e9i | −1.22088 | + | 1.22088i | ||||
\(97\) | −8.46864e8 | − | 8.46864e8i | −0.971272 | − | 0.971272i | 0.0283265 | − | 0.999599i | \(-0.490982\pi\) |
−0.999599 | + | 0.0283265i | \(0.990982\pi\) | |||||||
\(98\) | −2.54827e9 | −2.79079 | ||||||||
\(99\) | 5.07817e8 | + | 5.07817e8i | 0.531311 | + | 0.531311i | ||||
\(100\) | 1.40752e9i | 1.40752i | ||||||||
\(101\) | −6.82815e8 | −0.652916 | −0.326458 | − | 0.945212i | \(-0.605855\pi\) | ||||
−0.326458 | + | 0.945212i | \(0.605855\pi\) | |||||||
\(102\) | 4.65817e8 | − | 2.33354e9i | 0.426103 | − | 2.13459i | ||||
\(103\) | −1.41375e8 | −0.123767 | −0.0618836 | − | 0.998083i | \(-0.519711\pi\) | ||||
−0.0618836 | + | 0.998083i | \(0.519711\pi\) | |||||||
\(104\) | − | 1.72322e8i | − | 0.144441i | ||||||
\(105\) | 3.67644e8 | + | 3.67644e8i | 0.295172 | + | 0.295172i | ||||
\(106\) | 3.02456e9 | 2.32694 | ||||||||
\(107\) | −4.87536e7 | − | 4.87536e7i | −0.0359567 | − | 0.0359567i | 0.688900 | − | 0.724857i | \(-0.258094\pi\) |
−0.724857 | + | 0.688900i | \(0.758094\pi\) | |||||||
\(108\) | −1.41123e8 | + | 1.41123e8i | −0.0998141 | + | 0.0998141i | ||||
\(109\) | 1.63837e9 | − | 1.63837e9i | 1.11172 | − | 1.11172i | 0.118797 | − | 0.992919i | \(-0.462096\pi\) |
0.992919 | − | 0.118797i | \(-0.0379038\pi\) | |||||||
\(110\) | − | 3.50148e8i | − | 0.228026i | ||||||
\(111\) | − | 2.25035e9i | − | 1.40701i | ||||||
\(112\) | −6.64689e8 | + | 6.64689e8i | −0.399151 | + | 0.399151i | ||||
\(113\) | −1.27796e9 | + | 1.27796e9i | −0.737335 | + | 0.737335i | −0.972061 | − | 0.234727i | \(-0.924581\pi\) |
0.234727 | + | 0.972061i | \(0.424581\pi\) | |||||||
\(114\) | 4.34025e9 | + | 4.34025e9i | 2.40682 | + | 2.40682i | ||||
\(115\) | −2.99041e8 | −0.159438 | ||||||||
\(116\) | −1.07054e9 | − | 1.07054e9i | −0.548963 | − | 0.548963i | ||||
\(117\) | − | 3.82227e8i | − | 0.188575i | ||||||
\(118\) | −1.75627e7 | −0.00833916 | ||||||||
\(119\) | 7.14163e8 | − | 3.57764e9i | 0.326464 | − | 1.63544i | ||||
\(120\) | −4.05086e8 | −0.178333 | ||||||||
\(121\) | 8.19261e8i | 0.347447i | ||||||||
\(122\) | −1.83628e9 | − | 1.83628e9i | −0.750448 | − | 0.750448i | ||||
\(123\) | −5.22556e9 | −2.05854 | ||||||||
\(124\) | −5.29529e8 | − | 5.29529e8i | −0.201137 | − | 0.201137i | ||||
\(125\) | 6.84191e8 | − | 6.84191e8i | 0.250658 | − | 0.250658i | ||||
\(126\) | 4.86218e9 | − | 4.86218e9i | 1.71856 | − | 1.71856i | ||||
\(127\) | − | 1.52729e9i | − | 0.520962i | −0.965479 | − | 0.260481i | \(-0.916119\pi\) | ||
0.965479 | − | 0.260481i | \(-0.0838811\pi\) | |||||||
\(128\) | − | 3.88006e9i | − | 1.27760i | ||||||
\(129\) | −4.94421e9 | + | 4.94421e9i | −1.57197 | + | 1.57197i | ||||
\(130\) | −1.31776e8 | + | 1.31776e8i | −0.0404660 | + | 0.0404660i | ||||
\(131\) | −2.35621e9 | − | 2.35621e9i | −0.699027 | − | 0.699027i | 0.265174 | − | 0.964201i | \(-0.414571\pi\) |
−0.964201 | + | 0.265174i | \(0.914571\pi\) | |||||||
\(132\) | −5.69470e9 | −1.63263 | ||||||||
\(133\) | 6.65422e9 | + | 6.65422e9i | 1.84402 | + | 1.84402i | ||||
\(134\) | 1.02830e10i | 2.75516i | ||||||||
\(135\) | 6.74681e7 | 0.0174822 | ||||||||
\(136\) | 1.57755e9 | + | 2.36445e9i | 0.395420 | + | 0.592659i | ||||
\(137\) | 3.58940e8 | 0.0870521 | 0.0435261 | − | 0.999052i | \(-0.486141\pi\) | ||||
0.0435261 | + | 0.999052i | \(0.486141\pi\) | |||||||
\(138\) | 8.20676e9i | 1.92627i | ||||||||
\(139\) | 2.71208e9 | + | 2.71208e9i | 0.616221 | + | 0.616221i | 0.944560 | − | 0.328339i | \(-0.106489\pi\) |
−0.328339 | + | 0.944560i | \(0.606489\pi\) | |||||||
\(140\) | −1.98680e9 | −0.437097 | ||||||||
\(141\) | −2.31062e9 | − | 2.31062e9i | −0.492315 | − | 0.492315i | ||||
\(142\) | 7.64664e9 | − | 7.64664e9i | 1.57824 | − | 1.57824i | ||||
\(143\) | −5.79074e8 | + | 5.79074e8i | −0.115804 | + | 0.115804i | ||||
\(144\) | − | 1.62450e9i | − | 0.314839i | ||||||
\(145\) | 5.11804e8i | 0.0961497i | ||||||||
\(146\) | −2.54389e9 | + | 2.54389e9i | −0.463351 | + | 0.463351i | ||||
\(147\) | 9.90683e9 | − | 9.90683e9i | 1.74987 | − | 1.74987i | ||||
\(148\) | 6.08061e9 | + | 6.08061e9i | 1.04176 | + | 1.04176i | ||||
\(149\) | 9.74736e9 | 1.62013 | 0.810063 | − | 0.586342i | \(-0.199433\pi\) | ||||
0.810063 | + | 0.586342i | \(0.199433\pi\) | |||||||
\(150\) | −9.23343e9 | − | 9.23343e9i | −1.48920 | − | 1.48920i | ||||
\(151\) | − | 1.70584e9i | − | 0.267019i | −0.991048 | − | 0.133509i | \(-0.957375\pi\) | ||
0.991048 | − | 0.133509i | \(-0.0426247\pi\) | |||||||
\(152\) | −7.33191e9 | −1.11409 | ||||||||
\(153\) | 3.49917e9 | + | 5.24458e9i | 0.516242 | + | 0.773748i | ||||
\(154\) | −1.47324e10 | −2.11072 | ||||||||
\(155\) | 2.53157e8i | 0.0352287i | ||||||||
\(156\) | 2.14316e9 | + | 2.14316e9i | 0.289731 | + | 0.289731i | ||||
\(157\) | 5.43318e9 | 0.713683 | 0.356842 | − | 0.934165i | \(-0.383854\pi\) | ||||
0.356842 | + | 0.934165i | \(0.383854\pi\) | |||||||
\(158\) | −7.94330e9 | − | 7.94330e9i | −1.01401 | − | 1.01401i | ||||
\(159\) | −1.17585e10 | + | 1.17585e10i | −1.45903 | + | 1.45903i | ||||
\(160\) | −1.31248e9 | + | 1.31248e9i | −0.158326 | + | 0.158326i | ||||
\(161\) | 1.25821e10i | 1.47583i | ||||||||
\(162\) | − | 1.46270e10i | − | 1.66854i | ||||||
\(163\) | 5.40333e9 | − | 5.40333e9i | 0.599539 | − | 0.599539i | −0.340651 | − | 0.940190i | \(-0.610647\pi\) |
0.940190 | + | 0.340651i | \(0.110647\pi\) | |||||||
\(164\) | 1.41199e10 | − | 1.41199e10i | 1.52417 | − | 1.52417i | ||||
\(165\) | 1.36126e9 | + | 1.36126e9i | 0.142976 | + | 0.142976i | ||||
\(166\) | 1.72378e9 | 0.176196 | ||||||||
\(167\) | 3.33317e9 | + | 3.33317e9i | 0.331614 | + | 0.331614i | 0.853199 | − | 0.521585i | \(-0.174659\pi\) |
−0.521585 | + | 0.853199i | \(0.674659\pi\) | |||||||
\(168\) | 1.70439e10i | 1.65074i | ||||||||
\(169\) | −1.01686e10 | −0.958898 | ||||||||
\(170\) | 6.01744e8 | − | 3.01447e9i | 0.0552576 | − | 0.276816i | ||||
\(171\) | −1.62629e10 | −1.45451 | ||||||||
\(172\) | − | 2.67193e10i | − | 2.32780i | ||||||
\(173\) | 2.19655e9 | + | 2.19655e9i | 0.186437 | + | 0.186437i | 0.794154 | − | 0.607717i | \(-0.207914\pi\) |
−0.607717 | + | 0.794154i | \(0.707914\pi\) | |||||||
\(174\) | 1.40457e10 | 1.16164 | ||||||||
\(175\) | −1.41562e10 | − | 1.41562e10i | −1.14097 | − | 1.14097i | ||||
\(176\) | −2.46112e9 | + | 2.46112e9i | −0.193342 | + | 0.193342i | ||||
\(177\) | 6.82780e7 | − | 6.82780e7i | 0.00522879 | − | 0.00522879i | ||||
\(178\) | − | 2.17617e9i | − | 0.162481i | ||||||
\(179\) | 1.41139e10i | 1.02756i | 0.857922 | + | 0.513780i | \(0.171755\pi\) | ||||
−0.857922 | + | 0.513780i | \(0.828245\pi\) | |||||||
\(180\) | 2.42787e9 | − | 2.42787e9i | 0.172385 | − | 0.172385i | ||||
\(181\) | −5.83032e9 | + | 5.83032e9i | −0.403774 | + | 0.403774i | −0.879561 | − | 0.475787i | \(-0.842163\pi\) |
0.475787 | + | 0.879561i | \(0.342163\pi\) | |||||||
\(182\) | 5.54444e9 | + | 5.54444e9i | 0.374573 | + | 0.374573i | ||||
\(183\) | 1.42777e10 | 0.941086 | ||||||||
\(184\) | −6.93177e9 | − | 6.93177e9i | −0.445825 | − | 0.445825i | ||||
\(185\) | − | 2.90701e9i | − | 0.182463i | ||||||
\(186\) | 6.94752e9 | 0.425620 | ||||||||
\(187\) | 2.64430e9 | − | 1.32468e10i | 0.158133 | − | 0.792179i | ||||
\(188\) | 1.24870e10 | 0.729031 | ||||||||
\(189\) | − | 2.83871e9i | − | 0.161824i | ||||||
\(190\) | 5.60676e9 | + | 5.60676e9i | 0.312119 | + | 0.312119i | ||||
\(191\) | 7.61281e9 | 0.413899 | 0.206950 | − | 0.978352i | \(-0.433646\pi\) | ||||
0.206950 | + | 0.978352i | \(0.433646\pi\) | |||||||
\(192\) | 2.97577e10 | + | 2.97577e10i | 1.58032 | + | 1.58032i | ||||
\(193\) | 9.45202e9 | − | 9.45202e9i | 0.490362 | − | 0.490362i | −0.418058 | − | 0.908420i | \(-0.637289\pi\) |
0.908420 | + | 0.418058i | \(0.137289\pi\) | |||||||
\(194\) | −3.00228e10 | + | 3.00228e10i | −1.52175 | + | 1.52175i | ||||
\(195\) | − | 1.02460e9i | − | 0.0507457i | ||||||
\(196\) | 5.35380e10i | 2.59125i | ||||||||
\(197\) | −2.57548e10 | + | 2.57548e10i | −1.21831 | + | 1.21831i | −0.250093 | + | 0.968222i | \(0.580461\pi\) |
−0.968222 | + | 0.250093i | \(0.919539\pi\) | |||||||
\(198\) | 1.80030e10 | − | 1.80030e10i | 0.832437 | − | 0.832437i | ||||
\(199\) | −1.14612e10 | − | 1.14612e10i | −0.518075 | − | 0.518075i | 0.398913 | − | 0.916989i | \(-0.369387\pi\) |
−0.916989 | + | 0.398913i | \(0.869387\pi\) | |||||||
\(200\) | 1.55979e10 | 0.689335 | ||||||||
\(201\) | −3.99768e10 | − | 3.99768e10i | −1.72753 | − | 1.72753i | ||||
\(202\) | 2.42070e10i | 1.02296i | ||||||||
\(203\) | 2.15341e10 | 0.890009 | ||||||||
\(204\) | −4.90265e10 | − | 9.78660e9i | −1.98196 | − | 0.395636i | ||||
\(205\) | −6.75041e9 | −0.266955 | ||||||||
\(206\) | 5.01199e9i | 0.193913i | ||||||||
\(207\) | −1.53753e10 | − | 1.53753e10i | −0.582048 | − | 0.582048i | ||||
\(208\) | 1.85245e9 | 0.0686217 | ||||||||
\(209\) | 2.46383e10 | + | 2.46383e10i | 0.893208 | + | 0.893208i | ||||
\(210\) | 1.30336e10 | − | 1.30336e10i | 0.462464 | − | 0.462464i | ||||
\(211\) | 1.70125e10 | − | 1.70125e10i | 0.590876 | − | 0.590876i | −0.346992 | − | 0.937868i | \(-0.612797\pi\) |
0.937868 | + | 0.346992i | \(0.112797\pi\) | |||||||
\(212\) | − | 6.35446e10i | − | 2.16057i | ||||||
\(213\) | 5.94553e10i | 1.97917i | ||||||||
\(214\) | −1.72840e9 | + | 1.72840e9i | −0.0563355 | + | 0.0563355i | ||||
\(215\) | −6.38696e9 | + | 6.38696e9i | −0.203855 | + | 0.203855i | ||||
\(216\) | 1.56391e9 | + | 1.56391e9i | 0.0488843 | + | 0.0488843i | ||||
\(217\) | 1.06515e10 | 0.326094 | ||||||||
\(218\) | −5.80832e10 | − | 5.80832e10i | −1.74179 | − | 1.74179i | ||||
\(219\) | − | 1.97796e10i | − | 0.581057i | ||||||
\(220\) | −7.35644e9 | −0.211722 | ||||||||
\(221\) | −5.98050e9 | + | 3.99017e9i | −0.168645 | + | 0.112519i | ||||
\(222\) | −7.97788e10 | −2.20444 | ||||||||
\(223\) | − | 1.28505e10i | − | 0.347974i | −0.984748 | − | 0.173987i | \(-0.944335\pi\) | ||
0.984748 | − | 0.173987i | \(-0.0556651\pi\) | |||||||
\(224\) | 5.52223e10 | + | 5.52223e10i | 1.46554 | + | 1.46554i | ||||
\(225\) | 3.45976e10 | 0.899964 | ||||||||
\(226\) | 4.53059e10 | + | 4.53059e10i | 1.15523 | + | 1.15523i | ||||
\(227\) | 1.28875e10 | − | 1.28875e10i | 0.322144 | − | 0.322144i | −0.527445 | − | 0.849589i | \(-0.676850\pi\) |
0.849589 | + | 0.527445i | \(0.176850\pi\) | |||||||
\(228\) | 9.11867e10 | − | 9.11867e10i | 2.23473 | − | 2.23473i | ||||
\(229\) | 3.34994e10i | 0.804965i | 0.915428 | + | 0.402482i | \(0.131853\pi\) | ||||
−0.915428 | + | 0.402482i | \(0.868147\pi\) | |||||||
\(230\) | 1.06015e10i | 0.249801i | ||||||||
\(231\) | 5.72748e10 | − | 5.72748e10i | 1.32346 | − | 1.32346i | ||||
\(232\) | −1.18636e10 | + | 1.18636e10i | −0.268857 | + | 0.268857i | ||||
\(233\) | −3.74162e10 | − | 3.74162e10i | −0.831683 | − | 0.831683i | 0.156064 | − | 0.987747i | \(-0.450119\pi\) |
−0.987747 | + | 0.156064i | \(0.950119\pi\) | |||||||
\(234\) | −1.35506e10 | −0.295452 | ||||||||
\(235\) | −2.98487e9 | − | 2.98487e9i | −0.0638441 | − | 0.0638441i | ||||
\(236\) | 3.68984e8i | 0.00774290i | ||||||||
\(237\) | 6.17619e10 | 1.27161 | ||||||||
\(238\) | −1.26834e11 | − | 2.53183e10i | −2.56235 | − | 0.511491i | ||||
\(239\) | 3.33753e10 | 0.661659 | 0.330829 | − | 0.943691i | \(-0.392672\pi\) | ||||
0.330829 | + | 0.943691i | \(0.392672\pi\) | |||||||
\(240\) | − | 4.35465e9i | − | 0.0847232i | ||||||
\(241\) | −5.92853e10 | − | 5.92853e10i | −1.13206 | − | 1.13206i | −0.989834 | − | 0.142228i | \(-0.954573\pi\) |
−0.142228 | − | 0.989834i | \(-0.545427\pi\) | |||||||
\(242\) | 2.90442e10 | 0.544365 | ||||||||
\(243\) | 5.31356e10 | + | 5.31356e10i | 0.977592 | + | 0.977592i | ||||
\(244\) | −3.85795e10 | + | 3.85795e10i | −0.696791 | + | 0.696791i | ||||
\(245\) | 1.27977e10 | − | 1.27977e10i | 0.226926 | − | 0.226926i | ||||
\(246\) | 1.85255e11i | 3.22524i | ||||||||
\(247\) | − | 1.85449e10i | − | 0.317021i | ||||||
\(248\) | −5.86816e9 | + | 5.86816e9i | −0.0985076 | + | 0.0985076i | ||||
\(249\) | −6.70149e9 | + | 6.70149e9i | −0.110478 | + | 0.110478i | ||||
\(250\) | −2.42558e10 | − | 2.42558e10i | −0.392721 | − | 0.392721i | ||||
\(251\) | −5.60110e10 | −0.890721 | −0.445360 | − | 0.895351i | \(-0.646924\pi\) | ||||
−0.445360 | + | 0.895351i | \(0.646924\pi\) | |||||||
\(252\) | −1.02152e11 | − | 1.02152e11i | −1.59568 | − | 1.59568i | ||||
\(253\) | 4.65873e10i | 0.714867i | ||||||||
\(254\) | −5.41452e10 | −0.816222 | ||||||||
\(255\) | 9.37990e9 | + | 1.40587e10i | 0.138921 | + | 0.208216i | ||||
\(256\) | −2.70091e10 | −0.393034 | ||||||||
\(257\) | − | 5.71990e10i | − | 0.817880i | −0.912561 | − | 0.408940i | \(-0.865899\pi\) | ||
0.912561 | − | 0.408940i | \(-0.134101\pi\) | |||||||
\(258\) | 1.75281e11 | + | 1.75281e11i | 2.46290 | + | 2.46290i | ||||
\(259\) | −1.22312e11 | −1.68897 | ||||||||
\(260\) | 2.76855e9 | + | 2.76855e9i | 0.0375727 | + | 0.0375727i | ||||
\(261\) | −2.63146e10 | + | 2.63146e10i | −0.351007 | + | 0.351007i | ||||
\(262\) | −8.35318e10 | + | 8.35318e10i | −1.09521 | + | 1.09521i | ||||
\(263\) | − | 7.34514e10i | − | 0.946671i | −0.880882 | − | 0.473335i | \(-0.843050\pi\) | ||
0.880882 | − | 0.473335i | \(-0.156950\pi\) | |||||||
\(264\) | 6.31079e10i | 0.799587i | ||||||||
\(265\) | −1.51897e10 | + | 1.51897e10i | −0.189209 | + | 0.189209i | ||||
\(266\) | 2.35903e11 | − | 2.35903e11i | 2.88913 | − | 2.88913i | ||||
\(267\) | 8.46024e9 | + | 8.46024e9i | 0.101878 | + | 0.101878i | ||||
\(268\) | 2.16040e11 | 2.55816 | ||||||||
\(269\) | 8.83230e10 | + | 8.83230e10i | 1.02846 | + | 1.02846i | 0.999583 | + | 0.0288794i | \(0.00919386\pi\) |
0.0288794 | + | 0.999583i | \(0.490806\pi\) | |||||||
\(270\) | − | 2.39186e9i | − | 0.0273904i | ||||||
\(271\) | −1.21335e11 | −1.36655 | −0.683274 | − | 0.730162i | \(-0.739444\pi\) | ||||
−0.683274 | + | 0.730162i | \(0.739444\pi\) | |||||||
\(272\) | −2.54177e10 | + | 1.69586e10i | −0.281563 | + | 0.187858i | ||||
\(273\) | −4.31099e10 | −0.469727 | ||||||||
\(274\) | − | 1.27250e10i | − | 0.136390i | ||||||
\(275\) | −5.24154e10 | − | 5.24154e10i | −0.552665 | − | 0.552665i | ||||
\(276\) | 1.72420e11 | 1.78854 | ||||||||
\(277\) | 6.44252e10 | + | 6.44252e10i | 0.657501 | + | 0.657501i | 0.954788 | − | 0.297287i | \(-0.0960817\pi\) |
−0.297287 | + | 0.954788i | \(0.596082\pi\) | |||||||
\(278\) | 9.61481e10 | − | 9.61481e10i | 0.965470 | − | 0.965470i | ||||
\(279\) | −1.30162e10 | + | 1.30162e10i | −0.128607 | + | 0.128607i | ||||
\(280\) | 2.20174e10i | 0.214070i | ||||||||
\(281\) | 1.42723e11i | 1.36558i | 0.730616 | + | 0.682788i | \(0.239233\pi\) | ||||
−0.730616 | + | 0.682788i | \(0.760767\pi\) | |||||||
\(282\) | −8.19156e10 | + | 8.19156e10i | −0.771340 | + | 0.771340i | ||||
\(283\) | 6.69221e10 | − | 6.69221e10i | 0.620198 | − | 0.620198i | −0.325384 | − | 0.945582i | \(-0.605494\pi\) |
0.945582 | + | 0.325384i | \(0.105494\pi\) | |||||||
\(284\) | −1.60653e11 | − | 1.60653e11i | −1.46540 | − | 1.46540i | ||||
\(285\) | −4.35945e10 | −0.391408 | ||||||||
\(286\) | 2.05292e10 | + | 2.05292e10i | 0.181436 | + | 0.181436i | ||||
\(287\) | 2.84022e11i | 2.47106i | ||||||||
\(288\) | −1.34963e11 | −1.15598 | ||||||||
\(289\) | 4.55304e10 | − | 1.09499e11i | 0.383938 | − | 0.923359i | ||||
\(290\) | 1.81443e10 | 0.150643 | ||||||||
\(291\) | − | 2.33438e11i | − | 1.90832i | ||||||
\(292\) | 5.34459e10 | + | 5.34459e10i | 0.430221 | + | 0.430221i | ||||
\(293\) | −7.89311e10 | −0.625668 | −0.312834 | − | 0.949808i | \(-0.601278\pi\) | ||||
−0.312834 | + | 0.949808i | \(0.601278\pi\) | |||||||
\(294\) | −3.51214e11 | − | 3.51214e11i | −2.74163 | − | 2.74163i | ||||
\(295\) | 8.82018e7 | − | 8.82018e7i | 0.000678076 | − | 0.000678076i | ||||
\(296\) | 6.73845e10 | − | 6.73845e10i | 0.510208 | − | 0.510208i | ||||
\(297\) | − | 1.05108e10i | − | 0.0783846i | ||||||
\(298\) | − | 3.45561e11i | − | 2.53835i | ||||||
\(299\) | 1.75328e10 | − | 1.75328e10i | 0.126862 | − | 0.126862i | ||||
\(300\) | −1.93990e11 | + | 1.93990e11i | −1.38272 | + | 1.38272i | ||||
\(301\) | 2.68730e11 | + | 2.68730e11i | 1.88698 | + | 1.88698i | ||||
\(302\) | −6.04750e10 | −0.418355 | ||||||||
\(303\) | −9.41088e10 | − | 9.41088e10i | −0.641414 | − | 0.641414i | ||||
\(304\) | − | 7.88175e10i | − | 0.529288i | ||||||
\(305\) | 1.84440e10 | 0.122041 | ||||||||
\(306\) | 1.85929e11 | − | 1.24052e11i | 1.21228 | − | 0.808827i | ||||
\(307\) | −1.58427e11 | −1.01790 | −0.508952 | − | 0.860795i | \(-0.669967\pi\) | ||||
−0.508952 | + | 0.860795i | \(0.669967\pi\) | |||||||
\(308\) | 3.09521e11i | 1.95980i | ||||||||
\(309\) | −1.94850e10 | − | 1.94850e10i | −0.121587 | − | 0.121587i | ||||
\(310\) | 8.97484e9 | 0.0551949 | ||||||||
\(311\) | 2.39841e10 | + | 2.39841e10i | 0.145379 | + | 0.145379i | 0.776050 | − | 0.630671i | \(-0.217220\pi\) |
−0.630671 | + | 0.776050i | \(0.717220\pi\) | |||||||
\(312\) | 2.37502e10 | − | 2.37502e10i | 0.141897 | − | 0.141897i | ||||
\(313\) | −1.06428e10 | + | 1.06428e10i | −0.0626766 | + | 0.0626766i | −0.737750 | − | 0.675074i | \(-0.764112\pi\) |
0.675074 | + | 0.737750i | \(0.264112\pi\) | |||||||
\(314\) | − | 1.92616e11i | − | 1.11817i | ||||||
\(315\) | 4.88368e10i | 0.279479i | ||||||||
\(316\) | −1.66885e11 | + | 1.66885e11i | −0.941512 | + | 0.941512i | ||||
\(317\) | −6.29985e10 | + | 6.29985e10i | −0.350399 | + | 0.350399i | −0.860258 | − | 0.509859i | \(-0.829698\pi\) |
0.509859 | + | 0.860258i | \(0.329698\pi\) | |||||||
\(318\) | 4.16859e11 | + | 4.16859e11i | 2.28595 | + | 2.28595i | ||||
\(319\) | 7.97334e10 | 0.431104 | ||||||||
\(320\) | 3.84412e10 | + | 3.84412e10i | 0.204938 | + | 0.204938i | ||||
\(321\) | − | 1.34389e10i | − | 0.0706465i | ||||||
\(322\) | 4.46058e11 | 2.31228 | ||||||||
\(323\) | 1.69773e11 | + | 2.54457e11i | 0.867874 | + | 1.30078i | ||||
\(324\) | −3.07307e11 | −1.54924 | ||||||||
\(325\) | 3.94524e10i | 0.196154i | ||||||||
\(326\) | −1.91557e11 | − | 1.91557e11i | −0.939333 | − | 0.939333i | ||||
\(327\) | 4.51617e11 | 2.18426 | ||||||||
\(328\) | −1.56474e11 | − | 1.56474e11i | −0.746467 | − | 0.746467i | ||||
\(329\) | −1.25588e11 | + | 1.25588e11i | −0.590972 | + | 0.590972i | ||||
\(330\) | 4.82590e10 | − | 4.82590e10i | 0.224009 | − | 0.224009i | ||||
\(331\) | − | 1.07644e11i | − | 0.492905i | −0.969155 | − | 0.246453i | \(-0.920735\pi\) | ||
0.969155 | − | 0.246453i | \(-0.0792649\pi\) | |||||||
\(332\) | − | 3.62158e10i | − | 0.163598i | ||||||
\(333\) | 1.49465e11 | − | 1.49465e11i | 0.666103 | − | 0.666103i | ||||
\(334\) | 1.18167e11 | − | 1.18167e11i | 0.519560 | − | 0.519560i | ||||
\(335\) | −5.16422e10 | − | 5.16422e10i | −0.224028 | − | 0.224028i | ||||
\(336\) | −1.83221e11 | −0.784239 | ||||||||
\(337\) | 1.68618e10 | + | 1.68618e10i | 0.0712146 | + | 0.0712146i | 0.741817 | − | 0.670602i | \(-0.233964\pi\) |
−0.670602 | + | 0.741817i | \(0.733964\pi\) | |||||||
\(338\) | 3.60496e11i | 1.50236i | ||||||||
\(339\) | −3.52269e11 | −1.44869 | ||||||||
\(340\) | −6.33327e10 | − | 1.26424e10i | −0.257024 | − | 0.0513066i | ||||
\(341\) | 3.94390e10 | 0.157954 | ||||||||
\(342\) | 5.76548e11i | 2.27886i | ||||||||
\(343\) | −2.36167e11 | − | 2.36167e11i | −0.921290 | − | 0.921290i | ||||
\(344\) | −2.96099e11 | −1.14005 | ||||||||
\(345\) | −4.12153e10 | − | 4.12153e10i | −0.156629 | − | 0.156629i | ||||
\(346\) | 7.78714e10 | − | 7.78714e10i | 0.292103 | − | 0.292103i | ||||
\(347\) | 1.71997e11 | − | 1.71997e11i | 0.636853 | − | 0.636853i | −0.312925 | − | 0.949778i | \(-0.601309\pi\) |
0.949778 | + | 0.312925i | \(0.101309\pi\) | |||||||
\(348\) | − | 2.95095e11i | − | 1.07859i | ||||||
\(349\) | − | 1.16043e11i | − | 0.418703i | −0.977840 | − | 0.209351i | \(-0.932865\pi\) | ||
0.977840 | − | 0.209351i | \(-0.0671352\pi\) | |||||||
\(350\) | −5.01860e11 | + | 5.01860e11i | −1.78763 | + | 1.78763i | ||||
\(351\) | −3.95566e9 | + | 3.95566e9i | −0.0139103 | + | 0.0139103i | ||||
\(352\) | 2.04469e11 | + | 2.04469e11i | 0.709882 | + | 0.709882i | ||||
\(353\) | −1.46033e11 | −0.500570 | −0.250285 | − | 0.968172i | \(-0.580524\pi\) | ||||
−0.250285 | + | 0.968172i | \(0.580524\pi\) | |||||||
\(354\) | −2.42057e9 | − | 2.42057e9i | −0.00819225 | − | 0.00819225i | ||||
\(355\) | 7.68046e10i | 0.256661i | ||||||||
\(356\) | −4.57204e10 | −0.150864 | ||||||||
\(357\) | 5.91516e11 | − | 3.94658e11i | 1.92735 | − | 1.28592i | ||||
\(358\) | 5.00360e11 | 1.60994 | ||||||||
\(359\) | − | 3.10843e10i | − | 0.0987680i | −0.998780 | − | 0.0493840i | \(-0.984274\pi\) | ||
0.998780 | − | 0.0493840i | \(-0.0157258\pi\) | |||||||
\(360\) | −2.69053e10 | − | 2.69053e10i | −0.0844260 | − | 0.0844260i | ||||
\(361\) | −4.66356e11 | −1.44523 | ||||||||
\(362\) | 2.06695e11 | + | 2.06695e11i | 0.632617 | + | 0.632617i | ||||
\(363\) | −1.12914e11 | + | 1.12914e11i | −0.341326 | + | 0.341326i | ||||
\(364\) | 1.16486e11 | − | 1.16486e11i | 0.347791 | − | 0.347791i | ||||
\(365\) | − | 2.55514e10i | − | 0.0753522i | ||||||
\(366\) | − | 5.06170e11i | − | 1.47446i | ||||||
\(367\) | −8.70676e10 | + | 8.70676e10i | −0.250530 | + | 0.250530i | −0.821188 | − | 0.570658i | \(-0.806688\pi\) |
0.570658 | + | 0.821188i | \(0.306688\pi\) | |||||||
\(368\) | 7.45161e10 | − | 7.45161e10i | 0.211804 | − | 0.211804i | ||||
\(369\) | −3.47075e11 | − | 3.47075e11i | −0.974552 | − | 0.974552i | ||||
\(370\) | −1.03059e11 | −0.285875 | ||||||||
\(371\) | 6.39103e11 | + | 6.39103e11i | 1.75141 | + | 1.75141i | ||||
\(372\) | − | 1.45964e11i | − | 0.395188i | ||||||
\(373\) | −2.86421e11 | −0.766153 | −0.383077 | − | 0.923717i | \(-0.625135\pi\) | ||||
−0.383077 | + | 0.923717i | \(0.625135\pi\) | |||||||
\(374\) | −4.69621e11 | − | 9.37450e10i | −1.24115 | − | 0.247757i | ||||
\(375\) | 1.88597e11 | 0.492486 | ||||||||
\(376\) | − | 1.38379e11i | − | 0.357045i | ||||||
\(377\) | −3.00071e10 | − | 3.00071e10i | −0.0765048 | − | 0.0765048i | ||||
\(378\) | −1.00637e11 | −0.253539 | ||||||||
\(379\) | 1.10915e11 | + | 1.10915e11i | 0.276129 | + | 0.276129i | 0.831562 | − | 0.555432i | \(-0.187447\pi\) |
−0.555432 | + | 0.831562i | \(0.687447\pi\) | |||||||
\(380\) | 1.17795e11 | − | 1.17795e11i | 0.289803 | − | 0.289803i | ||||
\(381\) | 2.10499e11 | − | 2.10499e11i | 0.511784 | − | 0.511784i | ||||
\(382\) | − | 2.69887e11i | − | 0.648481i | ||||||
\(383\) | − | 5.08058e11i | − | 1.20648i | −0.797561 | − | 0.603238i | \(-0.793877\pi\) | ||
0.797561 | − | 0.603238i | \(-0.206123\pi\) | |||||||
\(384\) | 5.34768e11 | − | 5.34768e11i | 1.25509 | − | 1.25509i | ||||
\(385\) | 7.39878e10 | − | 7.39878e10i | 0.171627 | − | 0.171627i | ||||
\(386\) | −3.35090e11 | − | 3.35090e11i | −0.768279 | − | 0.768279i | ||||
\(387\) | −6.56777e11 | −1.48840 | ||||||||
\(388\) | 6.30765e11 | + | 6.30765e11i | 1.41294 | + | 1.41294i | ||||
\(389\) | − | 6.40697e11i | − | 1.41866i | −0.704875 | − | 0.709332i | \(-0.748997\pi\) | ||
0.704875 | − | 0.709332i | \(-0.251003\pi\) | |||||||
\(390\) | −3.63239e10 | −0.0795063 | ||||||||
\(391\) | −8.00624e10 | + | 4.01077e11i | −0.173234 | + | 0.867826i | ||||
\(392\) | 5.93300e11 | 1.26907 | ||||||||
\(393\) | − | 6.49489e11i | − | 1.37343i | ||||||
\(394\) | 9.13051e11 | + | 9.13051e11i | 1.90881 | + | 1.90881i | ||||
\(395\) | 7.97843e10 | 0.164904 | ||||||||
\(396\) | −3.78235e11 | − | 3.78235e11i | −0.772918 | − | 0.772918i | ||||
\(397\) | −3.16257e8 | + | 3.16257e8i | −0.000638974 | + | 0.000638974i | −0.707426 | − | 0.706787i | \(-0.750144\pi\) |
0.706787 | + | 0.707426i | \(0.250144\pi\) | |||||||
\(398\) | −4.06321e11 | + | 4.06321e11i | −0.811700 | + | 0.811700i | ||||
\(399\) | 1.83423e12i | 3.62306i | ||||||||
\(400\) | 1.67676e11i | 0.327492i | ||||||||
\(401\) | 1.18020e11 | − | 1.18020e11i | 0.227932 | − | 0.227932i | −0.583896 | − | 0.811828i | \(-0.698472\pi\) |
0.811828 | + | 0.583896i | \(0.198472\pi\) | |||||||
\(402\) | −1.41725e12 | + | 1.41725e12i | −2.70662 | + | 2.70662i | ||||
\(403\) | −1.48426e10 | − | 1.48426e10i | −0.0280309 | − | 0.0280309i | ||||
\(404\) | 5.08578e11 | 0.949820 | ||||||||
\(405\) | 7.34585e10 | + | 7.34585e10i | 0.135673 | + | 0.135673i | ||||
\(406\) | − | 7.63421e11i | − | 1.39443i | ||||||
\(407\) | −4.52880e11 | −0.818104 | ||||||||
\(408\) | −1.08454e11 | + | 5.43305e11i | −0.193764 | + | 0.970673i | ||||
\(409\) | −7.90370e11 | −1.39661 | −0.698306 | − | 0.715800i | \(-0.746062\pi\) | ||||
−0.698306 | + | 0.715800i | \(0.746062\pi\) | |||||||
\(410\) | 2.39314e11i | 0.418254i | ||||||||
\(411\) | 4.94708e10 | + | 4.94708e10i | 0.0855186 | + | 0.0855186i | ||||
\(412\) | 1.05300e11 | 0.180049 | ||||||||
\(413\) | −3.71108e9 | − | 3.71108e9i | −0.00627661 | − | 0.00627661i | ||||
\(414\) | −5.45083e11 | + | 5.45083e11i | −0.911929 | + | 0.911929i | ||||
\(415\) | −8.65701e9 | + | 8.65701e9i | −0.0143269 | + | 0.0143269i | ||||
\(416\) | − | 1.53901e11i | − | 0.251955i | ||||||
\(417\) | 7.47584e11i | 1.21073i | ||||||||
\(418\) | 8.73470e11 | − | 8.73470e11i | 1.39944 | − | 1.39944i | ||||
\(419\) | 6.57921e11 | − | 6.57921e11i | 1.04282 | − | 1.04282i | 0.0437823 | − | 0.999041i | \(-0.486059\pi\) |
0.999041 | − | 0.0437823i | \(-0.0139408\pi\) | |||||||
\(420\) | −2.73830e11 | − | 2.73830e11i | −0.429397 | − | 0.429397i | ||||
\(421\) | 5.05324e11 | 0.783973 | 0.391986 | − | 0.919971i | \(-0.371788\pi\) | ||||
0.391986 | + | 0.919971i | \(0.371788\pi\) | |||||||
\(422\) | −6.03122e11 | − | 6.03122e11i | −0.925761 | − | 0.925761i | ||||
\(423\) | − | 3.06937e11i | − | 0.466142i | ||||||
\(424\) | −7.04192e11 | −1.05814 | ||||||||
\(425\) | −3.61174e11 | − | 5.41330e11i | −0.536990 | − | 0.804845i | ||||
\(426\) | 2.10779e12 | 3.10088 | ||||||||
\(427\) | − | 7.76031e11i | − | 1.12967i | ||||||
\(428\) | 3.63129e10 | + | 3.63129e10i | 0.0523075 | + | 0.0523075i | ||||
\(429\) | −1.59621e11 | −0.227527 | ||||||||
\(430\) | 2.26429e11 | + | 2.26429e11i | 0.319392 | + | 0.319392i | ||||
\(431\) | −4.23744e11 | + | 4.23744e11i | −0.591502 | + | 0.591502i | −0.938037 | − | 0.346535i | \(-0.887358\pi\) |
0.346535 | + | 0.938037i | \(0.387358\pi\) | |||||||
\(432\) | −1.68119e10 | + | 1.68119e10i | −0.0232242 | + | 0.0232242i | ||||
\(433\) | 1.27100e11i | 0.173760i | 0.996219 | + | 0.0868801i | \(0.0276897\pi\) | ||||
−0.996219 | + | 0.0868801i | \(0.972310\pi\) | |||||||
\(434\) | − | 3.77615e11i | − | 0.510911i | ||||||
\(435\) | −7.05393e10 | + | 7.05393e10i | −0.0944559 | + | 0.0944559i | ||||
\(436\) | −1.22030e12 | + | 1.22030e12i | −1.61725 | + | 1.61725i | ||||
\(437\) | −7.45982e11 | − | 7.45982e11i | −0.978502 | − | 0.978502i | ||||
\(438\) | −7.01220e11 | −0.910377 | ||||||||
\(439\) | 2.83275e11 | + | 2.83275e11i | 0.364013 | + | 0.364013i | 0.865288 | − | 0.501275i | \(-0.167135\pi\) |
−0.501275 | + | 0.865288i | \(0.667135\pi\) | |||||||
\(440\) | 8.15230e10i | 0.103692i | ||||||||
\(441\) | 1.31600e12 | 1.65684 | ||||||||
\(442\) | 1.41458e11 | + | 2.12019e11i | 0.176290 | + | 0.264226i | ||||
\(443\) | 7.13038e11 | 0.879622 | 0.439811 | − | 0.898090i | \(-0.355045\pi\) | ||||
0.439811 | + | 0.898090i | \(0.355045\pi\) | |||||||
\(444\) | 1.67612e12i | 2.04683i | ||||||||
\(445\) | 1.09290e10 | + | 1.09290e10i | 0.0132117 | + | 0.0132117i | ||||
\(446\) | −4.55571e11 | −0.545192 | ||||||||
\(447\) | 1.34343e12 | + | 1.34343e12i | 1.59159 | + | 1.59159i | ||||
\(448\) | 1.61741e12 | − | 1.61741e12i | 1.89700 | − | 1.89700i | ||||
\(449\) | −1.43681e11 | + | 1.43681e11i | −0.166836 | + | 0.166836i | −0.785587 | − | 0.618751i | \(-0.787639\pi\) |
0.618751 | + | 0.785587i | \(0.287639\pi\) | |||||||
\(450\) | − | 1.22655e12i | − | 1.41003i | ||||||
\(451\) | 1.05164e12i | 1.19694i | ||||||||
\(452\) | 9.51857e11 | − | 9.51857e11i | 1.07263 | − | 1.07263i | ||||
\(453\) | 2.35107e11 | − | 2.35107e11i | 0.262315 | − | 0.262315i | ||||
\(454\) | −4.56882e11 | − | 4.56882e11i | −0.504723 | − | 0.504723i | ||||
\(455\) | −5.56896e10 | −0.0609148 | ||||||||
\(456\) | −1.01052e12 | − | 1.01052e12i | −1.09447 | − | 1.09447i | ||||
\(457\) | − | 1.60912e12i | − | 1.72570i | −0.505457 | − | 0.862852i | \(-0.668676\pi\) | ||
0.505457 | − | 0.862852i | \(-0.331324\pi\) | |||||||
\(458\) | 1.18761e12 | 1.26119 | ||||||||
\(459\) | 1.80632e10 | − | 9.04888e10i | 0.0189950 | − | 0.0951563i | ||||
\(460\) | 2.22733e11 | 0.231940 | ||||||||
\(461\) | 4.13437e10i | 0.0426339i | 0.999773 | + | 0.0213170i | \(0.00678591\pi\) | ||||
−0.999773 | + | 0.0213170i | \(0.993214\pi\) | |||||||
\(462\) | −2.03049e12 | − | 2.03049e12i | −2.07354 | − | 2.07354i | ||||
\(463\) | −6.72372e11 | −0.679978 | −0.339989 | − | 0.940429i | \(-0.610423\pi\) | ||||
−0.339989 | + | 0.940429i | \(0.610423\pi\) | |||||||
\(464\) | −1.27533e11 | − | 1.27533e11i | −0.127730 | − | 0.127730i | ||||
\(465\) | −3.48912e10 | + | 3.48912e10i | −0.0346081 | + | 0.0346081i | ||||
\(466\) | −1.32647e12 | + | 1.32647e12i | −1.30305 | + | 1.30305i | ||||
\(467\) | − | 1.62022e12i | − | 1.57633i | −0.615463 | − | 0.788166i | \(-0.711031\pi\) | ||
0.615463 | − | 0.788166i | \(-0.288969\pi\) | |||||||
\(468\) | 2.84692e11i | 0.274327i | ||||||||
\(469\) | −2.17284e12 | + | 2.17284e12i | −2.07372 | + | 2.07372i | ||||
\(470\) | −1.05819e11 | + | 1.05819e11i | −0.100028 | + | 0.100028i | ||||
\(471\) | 7.48826e11 | + | 7.48826e11i | 0.701111 | + | 0.701111i | ||||
\(472\) | 4.08903e9 | 0.00379211 | ||||||||
\(473\) | 9.95017e11 | + | 9.95017e11i | 0.914019 | + | 0.914019i | ||||
\(474\) | − | 2.18956e12i | − | 1.99230i | ||||||
\(475\) | 1.67861e12 | 1.51296 | ||||||||
\(476\) | −5.31926e11 | + | 2.66471e12i | −0.474920 | + | 2.37914i | ||||
\(477\) | −1.56197e12 | −1.38146 | ||||||||
\(478\) | − | 1.18321e12i | − | 1.03666i | ||||||
\(479\) | −1.42190e12 | − | 1.42190e12i | −1.23412 | − | 1.23412i | −0.962365 | − | 0.271759i | \(-0.912395\pi\) |
−0.271759 | − | 0.962365i | \(-0.587605\pi\) | |||||||
\(480\) | −3.61784e11 | −0.311074 | ||||||||
\(481\) | 1.70438e11 | + | 1.70438e11i | 0.145183 | + | 0.145183i | ||||
\(482\) | −2.10177e12 | + | 2.10177e12i | −1.77367 | + | 1.77367i | ||||
\(483\) | −1.73413e12 | + | 1.73413e12i | −1.44984 | + | 1.44984i | ||||
\(484\) | − | 6.10206e11i | − | 0.505443i | ||||||
\(485\) | − | 3.01556e11i | − | 0.247474i | ||||||
\(486\) | 1.88375e12 | − | 1.88375e12i | 1.53165 | − | 1.53165i | ||||
\(487\) | 4.08238e11 | − | 4.08238e11i | 0.328877 | − | 0.328877i | −0.523283 | − | 0.852159i | \(-0.675293\pi\) |
0.852159 | + | 0.523283i | \(0.175293\pi\) | |||||||
\(488\) | 4.27532e11 | + | 4.27532e11i | 0.341256 | + | 0.341256i | ||||
\(489\) | 1.48942e12 | 1.17795 | ||||||||
\(490\) | −4.53700e11 | − | 4.53700e11i | −0.355538 | − | 0.355538i | ||||
\(491\) | 1.26185e12i | 0.979812i | 0.871775 | + | 0.489906i | \(0.162969\pi\) | ||||
−0.871775 | + | 0.489906i | \(0.837031\pi\) | |||||||
\(492\) | 3.89213e12 | 2.99464 | ||||||||
\(493\) | 6.86437e11 | + | 1.37025e11i | 0.523347 | + | 0.104470i | ||||
\(494\) | −6.57449e11 | −0.496696 | ||||||||
\(495\) | 1.80826e11i | 0.135375i | ||||||||
\(496\) | −6.30824e10 | − | 6.30824e10i | −0.0467994 | − | 0.0467994i | ||||
\(497\) | 3.23154e12 | 2.37578 | ||||||||
\(498\) | 2.37579e11 | + | 2.37579e11i | 0.173092 | + | 0.173092i | ||||
\(499\) | −8.84504e11 | + | 8.84504e11i | −0.638627 | + | 0.638627i | −0.950217 | − | 0.311590i | \(-0.899139\pi\) |
0.311590 | + | 0.950217i | \(0.399139\pi\) | |||||||
\(500\) | −5.09602e11 | + | 5.09602e11i | −0.364642 | + | 0.364642i | ||||
\(501\) | 9.18786e11i | 0.651545i | ||||||||
\(502\) | 1.98569e12i | 1.39555i | ||||||||
\(503\) | 1.01707e12 | − | 1.01707e12i | 0.708425 | − | 0.708425i | −0.257779 | − | 0.966204i | \(-0.582991\pi\) |
0.966204 | + | 0.257779i | \(0.0829906\pi\) | |||||||
\(504\) | −1.13204e12 | + | 1.13204e12i | −0.781489 | + | 0.781489i | ||||
\(505\) | −1.21570e11 | − | 1.21570e11i | −0.0831794 | − | 0.0831794i | ||||
\(506\) | 1.65160e12 | 1.12003 | ||||||||
\(507\) | −1.40149e12 | − | 1.40149e12i | −0.942006 | − | 0.942006i | ||||
\(508\) | 1.13757e12i | 0.757862i | ||||||||
\(509\) | 8.60532e11 | 0.568247 | 0.284124 | − | 0.958788i | \(-0.408297\pi\) | ||||
0.284124 | + | 0.958788i | \(0.408297\pi\) | |||||||
\(510\) | 4.98404e11 | − | 3.32533e11i | 0.326224 | − | 0.217655i | ||||
\(511\) | −1.07507e12 | −0.697497 | ||||||||
\(512\) | − | 1.02908e12i | − | 0.661808i | ||||||
\(513\) | 1.68304e11 | + | 1.68304e11i | 0.107292 | + | 0.107292i | ||||
\(514\) | −2.02780e12 | −1.28142 | ||||||||
\(515\) | −2.51708e10 | − | 2.51708e10i | −0.0157676 | − | 0.0157676i | ||||
\(516\) | 3.68257e12 | − | 3.68257e12i | 2.28680 | − | 2.28680i | ||||
\(517\) | −4.65010e11 | + | 4.65010e11i | −0.286256 | + | 0.286256i | ||||
\(518\) | 4.33618e12i | 2.64620i | ||||||||
\(519\) | 6.05477e11i | 0.366306i | ||||||||
\(520\) | 3.06806e10 | − | 3.06806e10i | 0.0184013 | − | 0.0184013i | ||||
\(521\) | −3.77471e11 | + | 3.77471e11i | −0.224447 | + | 0.224447i | −0.810368 | − | 0.585921i | \(-0.800733\pi\) |
0.585921 | + | 0.810368i | \(0.300733\pi\) | |||||||
\(522\) | 9.32900e11 | + | 9.32900e11i | 0.549943 | + | 0.549943i | ||||
\(523\) | −2.80630e12 | −1.64013 | −0.820063 | − | 0.572274i | \(-0.806062\pi\) | ||||
−0.820063 | + | 0.572274i | \(0.806062\pi\) | |||||||
\(524\) | 1.75497e12 | + | 1.75497e12i | 1.01690 | + | 1.01690i | ||||
\(525\) | − | 3.90213e12i | − | 2.24174i | ||||||
\(526\) | −2.60398e12 | −1.48321 | ||||||||
\(527\) | 3.39536e11 | + | 6.77777e10i | 0.191751 | + | 0.0382771i | ||||
\(528\) | −6.78405e11 | −0.379871 | ||||||||
\(529\) | 3.90613e11i | 0.216868i | ||||||||
\(530\) | 5.38500e11 | + | 5.38500e11i | 0.296445 | + | 0.296445i | ||||
\(531\) | 9.06987e9 | 0.00495080 | ||||||||
\(532\) | −4.95623e12 | − | 4.95623e12i | −2.68256 | − | 2.68256i | ||||
\(533\) | 3.95777e11 | − | 3.95777e11i | 0.212412 | − | 0.212412i | ||||
\(534\) | 2.99930e11 | − | 2.99930e11i | 0.159619 | − | 0.159619i | ||||
\(535\) | − | 1.73604e10i | − | 0.00916154i | ||||||
\(536\) | − | 2.39413e12i | − | 1.25287i | ||||||
\(537\) | −1.94524e12 | + | 1.94524e12i | −1.00946 | + | 1.00946i | ||||
\(538\) | 3.13120e12 | − | 3.13120e12i | 1.61135 | − | 1.61135i | ||||
\(539\) | −1.99374e12 | − | 1.99374e12i | −1.01746 | − | 1.01746i | ||||
\(540\) | −5.02519e10 | −0.0254320 | ||||||||
\(541\) | −1.28357e12 | − | 1.28357e12i | −0.644216 | − | 0.644216i | 0.307373 | − | 0.951589i | \(-0.400550\pi\) |
−0.951589 | + | 0.307373i | \(0.900550\pi\) | |||||||
\(542\) | 4.30154e12i | 2.14105i | ||||||||
\(543\) | −1.60712e12 | −0.793323 | ||||||||
\(544\) | 1.40892e12 | + | 2.11170e12i | 0.689748 | + | 1.03380i | ||||
\(545\) | 5.83400e11 | 0.283258 | ||||||||
\(546\) | 1.52832e12i | 0.735949i | ||||||||
\(547\) | 1.09744e12 | + | 1.09744e12i | 0.524127 | + | 0.524127i | 0.918815 | − | 0.394688i | \(-0.129147\pi\) |
−0.394688 | + | 0.918815i | \(0.629147\pi\) | |||||||
\(548\) | −2.67347e11 | −0.126638 | ||||||||
\(549\) | 9.48309e11 | + | 9.48309e11i | 0.445527 | + | 0.445527i | ||||
\(550\) | −1.85822e12 | + | 1.85822e12i | −0.865893 | + | 0.865893i | ||||
\(551\) | −1.27674e12 | + | 1.27674e12i | −0.590091 | + | 0.590091i | ||||
\(552\) | − | 1.91074e12i | − | 0.875942i | ||||||
\(553\) | − | 3.35691e12i | − | 1.52643i | ||||||
\(554\) | 2.28398e12 | − | 2.28398e12i | 1.03015 | − | 1.03015i | ||||
\(555\) | 4.00658e11 | − | 4.00658e11i | 0.179248 | − | 0.179248i | ||||
\(556\) | −2.02003e12 | − | 2.02003e12i | −0.896439 | − | 0.896439i | ||||
\(557\) | −1.71558e12 | −0.755202 | −0.377601 | − | 0.925968i | \(-0.623251\pi\) | ||||
−0.377601 | + | 0.925968i | \(0.623251\pi\) | |||||||
\(558\) | 4.61445e11 | + | 4.61445e11i | 0.201496 | + | 0.201496i | ||||
\(559\) | − | 7.48936e11i | − | 0.324408i | ||||||
\(560\) | −2.36686e11 | −0.101701 | ||||||||
\(561\) | 2.19018e12 | − | 1.46128e12i | 0.933571 | − | 0.622876i | ||||
\(562\) | 5.05978e12 | 2.13953 | ||||||||
\(563\) | − | 1.79733e12i | − | 0.753945i | −0.926224 | − | 0.376972i | \(-0.876965\pi\) | ||
0.926224 | − | 0.376972i | \(-0.123035\pi\) | |||||||
\(564\) | 1.72101e12 | + | 1.72101e12i | 0.716189 | + | 0.716189i | ||||
\(565\) | −4.55063e11 | −0.187868 | ||||||||
\(566\) | −2.37250e12 | − | 2.37250e12i | −0.971701 | − | 0.971701i | ||||
\(567\) | 3.09075e12 | − | 3.09075e12i | 1.25586 | − | 1.25586i | ||||
\(568\) | −1.78033e12 | + | 1.78033e12i | −0.717683 | + | 0.717683i | ||||
\(569\) | 3.85698e12i | 1.54256i | 0.636497 | + | 0.771279i | \(0.280383\pi\) | ||||
−0.636497 | + | 0.771279i | \(0.719617\pi\) | |||||||
\(570\) | 1.54550e12i | 0.613242i | ||||||||
\(571\) | 2.46389e12 | − | 2.46389e12i | 0.969970 | − | 0.969970i | −0.0295917 | − | 0.999562i | \(-0.509421\pi\) |
0.999562 | + | 0.0295917i | \(0.00942070\pi\) | |||||||
\(572\) | 4.31309e11 | − | 4.31309e11i | 0.168464 | − | 0.168464i | ||||
\(573\) | 1.04923e12 | + | 1.04923e12i | 0.406608 | + | 0.406608i | ||||
\(574\) | 1.00691e13 | 3.87156 | ||||||||
\(575\) | 1.58700e12 | + | 1.58700e12i | 0.605440 | + | 0.605440i | ||||
\(576\) | 3.95294e12i | 1.49630i | ||||||||
\(577\) | −1.43479e12 | −0.538885 | −0.269442 | − | 0.963017i | \(-0.586839\pi\) | ||||
−0.269442 | + | 0.963017i | \(0.586839\pi\) | |||||||
\(578\) | −3.88193e12 | − | 1.61413e12i | −1.44668 | − | 0.601538i | ||||
\(579\) | 2.60544e12 | 0.963447 | ||||||||
\(580\) | − | 3.81205e11i | − | 0.139872i | ||||||
\(581\) | 3.64243e11 | + | 3.64243e11i | 0.132617 | + | 0.132617i | ||||
\(582\) | −8.27576e12 | −2.98989 | ||||||||
\(583\) | 2.36638e12 | + | 2.36638e12i | 0.848352 | + | 0.848352i | ||||
\(584\) | 5.92280e11 | − | 5.92280e11i | 0.210702 | − | 0.210702i | ||||
\(585\) | 6.80527e10 | − | 6.80527e10i | 0.0240239 | − | 0.0240239i | ||||
\(586\) | 2.79824e12i | 0.980271i | ||||||||
\(587\) | − | 4.09270e12i | − | 1.42278i | −0.702797 | − | 0.711391i | \(-0.748066\pi\) | ||
0.702797 | − | 0.711391i | \(-0.251934\pi\) | |||||||
\(588\) | −7.37885e12 | + | 7.37885e12i | −2.54560 | + | 2.54560i | ||||
\(589\) | −6.31519e11 | + | 6.31519e11i | −0.216206 | + | 0.216206i | ||||
\(590\) | −3.12691e9 | − | 3.12691e9i | −0.00106238 | − | 0.00106238i | ||||
\(591\) | −7.09928e12 | −2.39371 | ||||||||
\(592\) | 7.24378e11 | + | 7.24378e11i | 0.242392 | + | 0.242392i | ||||
\(593\) | 2.09962e12i | 0.697258i | 0.937261 | + | 0.348629i | \(0.113353\pi\) | ||||
−0.937261 | + | 0.348629i | \(0.886647\pi\) | |||||||
\(594\) | −3.72625e11 | −0.122810 | ||||||||
\(595\) | 7.64123e11 | − | 5.09821e11i | 0.249941 | − | 0.166760i | ||||
\(596\) | −7.26008e12 | −2.35686 | ||||||||
\(597\) | − | 3.15928e12i | − | 1.01790i | ||||||
\(598\) | −6.21569e11 | − | 6.21569e11i | −0.198762 | − | 0.198762i | ||||
\(599\) | 5.11389e12 | 1.62304 | 0.811522 | − | 0.584322i | \(-0.198639\pi\) | ||||
0.811522 | + | 0.584322i | \(0.198639\pi\) | |||||||
\(600\) | 2.14977e12 | + | 2.14977e12i | 0.677192 | + | 0.677192i | ||||
\(601\) | −2.66709e12 | + | 2.66709e12i | −0.833879 | + | 0.833879i | −0.988045 | − | 0.154166i | \(-0.950731\pi\) |
0.154166 | + | 0.988045i | \(0.450731\pi\) | |||||||
\(602\) | 9.52695e12 | − | 9.52695e12i | 2.95645 | − | 2.95645i | ||||
\(603\) | − | 5.31041e12i | − | 1.63569i | ||||||
\(604\) | 1.27055e12i | 0.388442i | ||||||||
\(605\) | −1.45863e11 | + | 1.45863e11i | −0.0442636 | + | 0.0442636i | ||||
\(606\) | −3.33632e12 | + | 3.33632e12i | −1.00494 | + | 1.00494i | ||||
\(607\) | 4.44942e12 | + | 4.44942e12i | 1.33031 | + | 1.33031i | 0.905086 | + | 0.425228i | \(0.139806\pi\) |
0.425228 | + | 0.905086i | \(0.360194\pi\) | |||||||
\(608\) | −6.54816e12 | −1.94336 | ||||||||
\(609\) | 2.96793e12 | + | 2.96793e12i | 0.874331 | + | 0.874331i | ||||
\(610\) | − | 6.53873e11i | − | 0.191209i | ||||||
\(611\) | 3.50007e11 | 0.101599 | ||||||||
\(612\) | −2.60627e12 | − | 3.90629e12i | −0.750996 | − | 1.12560i | ||||
\(613\) | −3.31541e12 | −0.948342 | −0.474171 | − | 0.880433i | \(-0.657252\pi\) | ||||
−0.474171 | + | 0.880433i | \(0.657252\pi\) | |||||||
\(614\) | 5.61652e12i | 1.59481i | ||||||||
\(615\) | −9.30373e11 | − | 9.30373e11i | −0.262252 | − | 0.262252i | ||||
\(616\) | 3.43007e12 | 0.959820 | ||||||||
\(617\) | 1.13051e12 | + | 1.13051e12i | 0.314046 | + | 0.314046i | 0.846475 | − | 0.532429i | \(-0.178721\pi\) |
−0.532429 | + | 0.846475i | \(0.678721\pi\) | |||||||
\(618\) | −6.90776e11 | + | 6.90776e11i | −0.190497 | + | 0.190497i | ||||
\(619\) | 3.89551e12 | − | 3.89551e12i | 1.06649 | − | 1.06649i | 0.0688618 | − | 0.997626i | \(-0.478063\pi\) |
0.997626 | − | 0.0688618i | \(-0.0219367\pi\) | |||||||
\(620\) | − | 1.88557e11i | − | 0.0512485i | ||||||
\(621\) | 3.18238e11i | 0.0858697i | ||||||||
\(622\) | 8.50276e11 | − | 8.50276e11i | 0.227774 | − | 0.227774i | ||||
\(623\) | 4.59835e11 | − | 4.59835e11i | 0.122294 | − | 0.122294i | ||||
\(624\) | 2.55313e11 | + | 2.55313e11i | 0.0674128 | + | 0.0674128i | ||||
\(625\) | −3.44724e12 | −0.903674 | ||||||||
\(626\) | 3.77305e11 | + | 3.77305e11i | 0.0981992 | + | 0.0981992i | ||||
\(627\) | 6.79153e12i | 1.75495i | ||||||||
\(628\) | −4.04677e12 | −1.03822 | ||||||||
\(629\) | −3.89891e12 | − | 7.78295e11i | −0.993152 | − | 0.198251i | ||||
\(630\) | 1.73135e12 | 0.437877 | ||||||||
\(631\) | 3.91651e12i | 0.983482i | 0.870741 | + | 0.491741i | \(0.163639\pi\) | ||||
−0.870741 | + | 0.491741i | \(0.836361\pi\) | |||||||
\(632\) | 1.84940e12 | + | 1.84940e12i | 0.461109 | + | 0.461109i | ||||
\(633\) | 4.68948e12 | 1.16093 | ||||||||
\(634\) | 2.23341e12 | + | 2.23341e12i | 0.548992 | + | 0.548992i | ||||
\(635\) | 2.71923e11 | − | 2.71923e11i | 0.0663689 | − | 0.0663689i | ||||
\(636\) | 8.75802e12 | − | 8.75802e12i | 2.12250 | − | 2.12250i | ||||
\(637\) | 1.50066e12i | 0.361122i | ||||||||
\(638\) | − | 2.82669e12i | − | 0.675437i | ||||||
\(639\) | −3.94894e12 | + | 3.94894e12i | −0.936972 | + | 0.936972i | ||||
\(640\) | 6.90816e11 | − | 6.90816e11i | 0.162762 | − | 0.162762i | ||||
\(641\) | −8.33887e11 | − | 8.33887e11i | −0.195095 | − | 0.195095i | 0.602799 | − | 0.797893i | \(-0.294052\pi\) |
−0.797893 | + | 0.602799i | \(0.794052\pi\) | |||||||
\(642\) | −4.76432e11 | −0.110686 | ||||||||
\(643\) | −5.78323e12 | − | 5.78323e12i | −1.33420 | − | 1.33420i | −0.901573 | − | 0.432627i | \(-0.857587\pi\) |
−0.432627 | − | 0.901573i | \(-0.642413\pi\) | |||||||
\(644\) | − | 9.37148e12i | − | 2.14695i | ||||||
\(645\) | −1.76056e12 | −0.400527 | ||||||||
\(646\) | 9.02093e12 | − | 6.01874e12i | 2.03800 | − | 1.35975i | ||||
\(647\) | 4.11649e11 | 0.0923544 | 0.0461772 | − | 0.998933i | \(-0.485296\pi\) | ||||
0.0461772 | + | 0.998933i | \(0.485296\pi\) | |||||||
\(648\) | 3.40553e12i | 0.758747i | ||||||||
\(649\) | −1.37409e10 | − | 1.37409e10i | −0.00304027 | − | 0.00304027i | ||||
\(650\) | 1.39865e12 | 0.307327 | ||||||||
\(651\) | 1.46804e12 | + | 1.46804e12i | 0.320350 | + | 0.320350i | ||||
\(652\) | −4.02453e12 | + | 4.02453e12i | −0.872171 | + | 0.872171i | ||||
\(653\) | −1.15152e12 | + | 1.15152e12i | −0.247835 | + | 0.247835i | −0.820082 | − | 0.572246i | \(-0.806072\pi\) |
0.572246 | + | 0.820082i | \(0.306072\pi\) | |||||||
\(654\) | − | 1.60106e13i | − | 3.42222i | ||||||
\(655\) | − | 8.39012e11i | − | 0.178108i | ||||||
\(656\) | 1.68209e12 | − | 1.68209e12i | 0.354635 | − | 0.354635i | ||||
\(657\) | 1.31373e12 | − | 1.31373e12i | 0.275083 | − | 0.275083i | ||||
\(658\) | 4.45232e12 | + | 4.45232e12i | 0.925912 | + | 0.925912i | ||||
\(659\) | −1.03788e12 | −0.214369 | −0.107184 | − | 0.994239i | \(-0.534184\pi\) | ||||
−0.107184 | + | 0.994239i | \(0.534184\pi\) | |||||||
\(660\) | −1.01390e12 | − | 1.01390e12i | −0.207992 | − | 0.207992i | ||||
\(661\) | − | 3.57716e12i | − | 0.728840i | −0.931235 | − | 0.364420i | \(-0.881267\pi\) | ||
0.931235 | − | 0.364420i | \(-0.118733\pi\) | |||||||
\(662\) | −3.81616e12 | −0.772264 | ||||||||
\(663\) | −1.37420e12 | − | 2.74317e11i | −0.276211 | − | 0.0551367i | ||||
\(664\) | −4.01339e11 | −0.0801225 | ||||||||
\(665\) | 2.36947e12i | 0.469844i | ||||||||
\(666\) | −5.29881e12 | − | 5.29881e12i | −1.04362 | − | 1.04362i | ||||
\(667\) | −2.41412e12 | −0.472271 | ||||||||
\(668\) | −2.48263e12 | − | 2.48263e12i | −0.482411 | − | 0.482411i | ||||
\(669\) | 1.77111e12 | − | 1.77111e12i | 0.341844 | − | 0.341844i | ||||
\(670\) | −1.83080e12 | + | 1.83080e12i | −0.350999 | + | 0.350999i | ||||
\(671\) | − | 2.87338e12i | − | 0.547194i | ||||||
\(672\) | 1.52220e13i | 2.87945i | ||||||||
\(673\) | −1.86013e12 | + | 1.86013e12i | −0.349524 | + | 0.349524i | −0.859932 | − | 0.510408i | \(-0.829494\pi\) |
0.510408 | + | 0.859932i | \(0.329494\pi\) | |||||||
\(674\) | 5.97779e11 | − | 5.97779e11i | 0.111576 | − | 0.111576i | ||||
\(675\) | −3.58050e11 | − | 3.58050e11i | −0.0663860 | − | 0.0663860i | ||||
\(676\) | 7.57385e12 | 1.39494 | ||||||||
\(677\) | 1.25400e12 | + | 1.25400e12i | 0.229430 | + | 0.229430i | 0.812454 | − | 0.583025i | \(-0.198131\pi\) |
−0.583025 | + | 0.812454i | \(0.698131\pi\) | |||||||
\(678\) | 1.24886e13i | 2.26975i | ||||||||
\(679\) | −1.26879e13 | −2.29074 | ||||||||
\(680\) | −1.40101e11 | + | 7.01844e11i | −0.0251276 | + | 0.125878i | ||||
\(681\) | 3.55242e12 | 0.632939 | ||||||||
\(682\) | − | 1.39818e12i | − | 0.247476i | ||||||
\(683\) | 3.50606e12 | + | 3.50606e12i | 0.616490 | + | 0.616490i | 0.944629 | − | 0.328139i | \(-0.106421\pi\) |
−0.328139 | + | 0.944629i | \(0.606421\pi\) | |||||||
\(684\) | 1.21130e13 | 2.11592 | ||||||||
\(685\) | 6.39066e10 | + | 6.39066e10i | 0.0110902 | + | 0.0110902i | ||||
\(686\) | −8.37254e12 | + | 8.37254e12i | −1.44344 | + | 1.44344i | ||||
\(687\) | −4.61704e12 | + | 4.61704e12i | −0.790784 | + | 0.790784i | ||||
\(688\) | − | 3.18304e12i | − | 0.541620i | ||||||
\(689\) | − | 1.78114e12i | − | 0.301101i | ||||||
\(690\) | −1.46115e12 | + | 1.46115e12i | −0.245400 | + | 0.245400i | ||||
\(691\) | −7.68434e10 | + | 7.68434e10i | −0.0128220 | + | 0.0128220i | −0.713489 | − | 0.700667i | \(-0.752886\pi\) |
0.700667 | + | 0.713489i | \(0.252886\pi\) | |||||||
\(692\) | −1.63604e12 | − | 1.63604e12i | −0.271217 | − | 0.271217i | ||||
\(693\) | 7.60823e12 | 1.25310 | ||||||||
\(694\) | −6.09760e12 | − | 6.09760e12i | −0.997795 | − | 0.997795i | ||||
\(695\) | 9.65733e11i | 0.157009i | ||||||||
\(696\) | −3.27020e12 | −0.528241 | ||||||||
\(697\) | −1.80729e12 | + | 9.05371e12i | −0.290055 | + | 1.45305i | ||||
\(698\) | −4.11394e12 | −0.656007 | ||||||||
\(699\) | − | 1.03137e13i | − | 1.63406i | ||||||
\(700\) | 1.05439e13 | + | 1.05439e13i | 1.65981 | + | 1.65981i | ||||
\(701\) | −8.17857e12 | −1.27922 | −0.639611 | − | 0.768698i | \(-0.720905\pi\) | ||||
−0.639611 | + | 0.768698i | \(0.720905\pi\) | |||||||
\(702\) | 1.40235e11 | + | 1.40235e11i | 0.0217941 | + | 0.0217941i | ||||
\(703\) | 7.25177e12 | − | 7.25177e12i | 1.11981 | − | 1.11981i | ||||
\(704\) | 5.98870e12 | − | 5.98870e12i | 0.918874 | − | 0.918874i | ||||
\(705\) | − | 8.22778e11i | − | 0.125439i | ||||||
\(706\) | 5.17712e12i | 0.784273i | ||||||||
\(707\) | −5.11505e12 | + | 5.11505e12i | −0.769950 | + | 0.769950i | ||||
\(708\) | −5.08551e10 | + | 5.08551e10i | −0.00760650 | + | 0.00760650i | ||||
\(709\) | 6.78334e12 | + | 6.78334e12i | 1.00817 | + | 1.00817i | 0.999966 | + | 0.00820759i | \(0.00261259\pi\) |
0.00820759 | + | 0.999966i | \(0.497387\pi\) | |||||||
\(710\) | 2.72285e12 | 0.402126 | ||||||||
\(711\) | 4.10214e12 | + | 4.10214e12i | 0.602001 | + | 0.602001i | ||||
\(712\) | 5.06666e11i | 0.0738860i | ||||||||
\(713\) | −1.19411e12 | −0.173038 | ||||||||
\(714\) | −1.39913e13 | − | 2.09703e13i | −2.01473 | − | 3.01969i | ||||
\(715\) | −2.06200e11 | −0.0295060 | ||||||||
\(716\) | − | 1.05123e13i | − | 1.49483i | ||||||
\(717\) | 4.59993e12 | + | 4.59993e12i | 0.650003 | + | 0.650003i | ||||
\(718\) | −1.10199e12 | −0.154746 | ||||||||
\(719\) | 2.10444e12 | + | 2.10444e12i | 0.293668 | + | 0.293668i | 0.838527 | − | 0.544859i | \(-0.183417\pi\) |
−0.544859 | + | 0.838527i | \(0.683417\pi\) | |||||||
\(720\) | 2.89230e11 | − | 2.89230e11i | 0.0401095 | − | 0.0401095i | ||||
\(721\) | −1.05906e12 | + | 1.05906e12i | −0.145952 | + | 0.145952i | ||||
\(722\) | 1.65331e13i | 2.26432i | ||||||||
\(723\) | − | 1.63420e13i | − | 2.22424i | ||||||
\(724\) | 4.34256e12 | − | 4.34256e12i | 0.587385 | − | 0.587385i | ||||
\(725\) | 2.71612e12 | − | 2.71612e12i | 0.365114 | − | 0.365114i | ||||
\(726\) | 4.00301e12 | + | 4.00301e12i | 0.534776 | + | 0.534776i | ||||
\(727\) | 1.39200e13 | 1.84814 | 0.924071 | − | 0.382220i | \(-0.124840\pi\) | ||||
0.924071 | + | 0.382220i | \(0.124840\pi\) | |||||||
\(728\) | −1.29088e12 | − | 1.29088e12i | −0.170332 | − | 0.170332i | ||||
\(729\) | 6.52580e12i | 0.855775i | ||||||||
\(730\) | −9.05840e11 | −0.118059 | ||||||||
\(731\) | 6.85627e12 | + | 1.02762e13i | 0.888095 | + | 1.33108i | ||||
\(732\) | −1.06344e13 | −1.36903 | ||||||||
\(733\) | 2.97939e12i | 0.381206i | 0.981667 | + | 0.190603i | \(0.0610443\pi\) | ||||
−0.981667 | + | 0.190603i | \(0.938956\pi\) | |||||||
\(734\) | 3.08670e12 | + | 3.08670e12i | 0.392520 | + | 0.392520i | ||||
\(735\) | 3.52767e12 | 0.445857 | ||||||||
\(736\) | −6.19079e12 | − | 6.19079e12i | −0.777671 | − | 0.777671i | ||||
\(737\) | −8.04528e12 | + | 8.04528e12i | −1.00447 | + | 1.00447i | ||||
\(738\) | −1.23044e13 | + | 1.23044e13i | −1.52689 | + | 1.52689i | ||||
\(739\) | − | 1.74914e12i | − | 0.215737i | −0.994165 | − | 0.107868i | \(-0.965598\pi\) | ||
0.994165 | − | 0.107868i | \(-0.0344025\pi\) | |||||||
\(740\) | 2.16522e12i | 0.265435i | ||||||||
\(741\) | 2.55595e12 | − | 2.55595e12i | 0.311437 | − | 0.311437i | ||||
\(742\) | 2.26573e13 | − | 2.26573e13i | 2.74404 | − | 2.74404i | ||||
\(743\) | −3.63529e12 | − | 3.63529e12i | −0.437612 | − | 0.437612i | 0.453595 | − | 0.891208i | \(-0.350141\pi\) |
−0.891208 | + | 0.453595i | \(0.850141\pi\) | |||||||
\(744\) | −1.61756e12 | −0.193545 | ||||||||
\(745\) | 1.73545e12 | + | 1.73545e12i | 0.206399 | + | 0.206399i | ||||
\(746\) | 1.01541e13i | 1.20038i | ||||||||
\(747\) | −8.90208e11 | −0.104604 | ||||||||
\(748\) | −1.96954e12 | + | 9.86653e12i | −0.230042 | + | 1.15241i | ||||
\(749\) | −7.30437e11 | −0.0848037 | ||||||||
\(750\) | − | 6.68608e12i | − | 0.771607i | ||||||
\(751\) | −6.61319e12 | − | 6.61319e12i | −0.758632 | − | 0.758632i | 0.217441 | − | 0.976073i | \(-0.430229\pi\) |
−0.976073 | + | 0.217441i | \(0.930229\pi\) | |||||||
\(752\) | 1.48756e12 | 0.169627 | ||||||||
\(753\) | −7.71969e12 | − | 7.71969e12i | −0.875030 | − | 0.875030i | ||||
\(754\) | −1.06380e12 | + | 1.06380e12i | −0.119865 | + | 0.119865i | ||||
\(755\) | 3.03712e11 | − | 3.03712e11i | 0.0340174 | − | 0.0340174i | ||||
\(756\) | 2.11434e12i | 0.235411i | ||||||||
\(757\) | − | 4.90172e12i | − | 0.542521i | −0.962506 | − | 0.271261i | \(-0.912560\pi\) | ||
0.962506 | − | 0.271261i | \(-0.0874405\pi\) | |||||||
\(758\) | 3.93212e12 | − | 3.93212e12i | 0.432628 | − | 0.432628i | ||||
\(759\) | −6.42088e12 | + | 6.42088e12i | −0.702274 | + | 0.702274i | ||||
\(760\) | −1.30539e12 | − | 1.30539e12i | −0.141932 | − | 0.141932i | ||||
\(761\) | 9.45949e12 | 1.02244 | 0.511219 | − | 0.859451i | \(-0.329194\pi\) | ||||
0.511219 | + | 0.859451i | \(0.329194\pi\) | |||||||
\(762\) | −7.46254e12 | − | 7.46254e12i | −0.801843 | − | 0.801843i | ||||
\(763\) | − | 2.45465e13i | − | 2.62198i | ||||||
\(764\) | −5.67021e12 | −0.602114 | ||||||||
\(765\) | −3.10758e11 | + | 1.55676e12i | −0.0328054 | + | 0.164341i | ||||
\(766\) | −1.80115e13 | −1.89026 | ||||||||
\(767\) | 1.03426e10i | 0.00107907i | ||||||||
\(768\) | −3.72251e12 | − | 3.72251e12i | −0.386110 | − | 0.386110i | ||||
\(769\) | 1.62983e13 | 1.68064 | 0.840318 | − | 0.542093i | \(-0.182368\pi\) | ||||
0.840318 | + | 0.542093i | \(0.182368\pi\) | |||||||
\(770\) | −2.62300e12 | − | 2.62300e12i | −0.268899 | − | 0.268899i | ||||
\(771\) | 7.88344e12 | − | 7.88344e12i | 0.803472 | − | 0.803472i | ||||
\(772\) | −7.04010e12 | + | 7.04010e12i | −0.713347 | + | 0.713347i | ||||
\(773\) | 1.21072e13i | 1.21965i | 0.792535 | + | 0.609827i | \(0.208761\pi\) | ||||
−0.792535 | + | 0.609827i | \(0.791239\pi\) | |||||||
\(774\) | 2.32839e13i | 2.33196i | ||||||||
\(775\) | 1.34349e12 | − | 1.34349e12i | 0.133776 | − | 0.133776i | ||||
\(776\) | 6.99005e12 | − | 6.99005e12i | 0.691994 | − | 0.691994i | ||||
\(777\) | −1.68576e13 | − | 1.68576e13i | −1.65921 | − | 1.65921i | ||||
\(778\) | −2.27138e13 | −2.22270 | ||||||||
\(779\) | −1.68394e13 | − | 1.68394e13i | −1.63836 | − | 1.63836i | ||||
\(780\) | 7.63148e11i | 0.0738216i | ||||||||
\(781\) | 1.19653e13 | 1.15078 | ||||||||
\(782\) | 1.42189e13 | + | 2.83835e12i | 1.35967 | + | 0.271416i | ||||
\(783\) | 5.44659e11 | 0.0517842 | ||||||||
\(784\) | 6.37793e12i | 0.602917i | ||||||||
\(785\) | 9.67337e11 | + | 9.67337e11i | 0.0909210 | + | 0.0909210i | ||||
\(786\) | −2.30255e13 | −2.15183 | ||||||||
\(787\) | 3.37207e12 | + | 3.37207e12i | 0.313336 | + | 0.313336i | 0.846201 | − | 0.532864i | \(-0.178884\pi\) |
−0.532864 | + | 0.846201i | \(0.678884\pi\) | |||||||
\(788\) | 1.91828e13 | − | 1.91828e13i | 1.77233 | − | 1.77233i | ||||
\(789\) | 1.01234e13 | − | 1.01234e13i | 0.929994 | − | 0.929994i | ||||
\(790\) | − | 2.82849e12i | − | 0.258364i | ||||||
\(791\) | 1.91467e13i | 1.73900i | ||||||||
\(792\) | −4.19154e12 | + | 4.19154e12i | −0.378539 | + | 0.378539i | ||||
\(793\) | −1.08138e12 | + | 1.08138e12i | −0.0971063 | + | 0.0971063i | ||||
\(794\) | 1.12119e10 | + | 1.12119e10i | 0.00100112 | + | 0.00100112i | ||||
\(795\) | −4.18702e12 | −0.371752 | ||||||||
\(796\) | 8.53662e12 | + | 8.53662e12i | 0.753663 | + | 0.753663i | ||||
\(797\) | 8.30651e12i | 0.729216i | 0.931161 | + | 0.364608i | \(0.118797\pi\) | ||||
−0.931161 | + | 0.364608i | \(0.881203\pi\) | |||||||
\(798\) | 6.50266e13 | 5.67647 | ||||||||
\(799\) | −4.80248e12 | + | 3.20420e12i | −0.416874 | + | 0.278137i | ||||
\(800\) | 1.39305e13 | 1.20244 | ||||||||
\(801\) | 1.12384e12i | 0.0964621i | ||||||||
\(802\) | −4.18401e12 | − | 4.18401e12i | −0.357115 | − | 0.357115i | ||||
\(803\) | −3.98062e12 | −0.337855 | ||||||||
\(804\) | 2.97757e13 | + | 2.97757e13i | 2.51310 | + | 2.51310i | ||||
\(805\) | −2.24015e12 | + | 2.24015e12i | −0.188017 | + | 0.188017i | ||||
\(806\) | −5.26196e11 | + | 5.26196e11i | −0.0439177 | + | 0.0439177i | ||||
\(807\) | 2.43462e13i | 2.02069i | ||||||||
\(808\) | − | 5.63599e12i | − | 0.465178i | ||||||
\(809\) | 5.44748e12 | − | 5.44748e12i | 0.447124 | − | 0.447124i | −0.447274 | − | 0.894397i | \(-0.647605\pi\) |
0.894397 | + | 0.447274i | \(0.147605\pi\) | |||||||
\(810\) | 2.60423e12 | − | 2.60423e12i | 0.212567 | − | 0.212567i | ||||
\(811\) | −9.61807e12 | − | 9.61807e12i | −0.780718 | − | 0.780718i | 0.199234 | − | 0.979952i | \(-0.436155\pi\) |
−0.979952 | + | 0.199234i | \(0.936155\pi\) | |||||||
\(812\) | −1.60391e13 | −1.29473 | ||||||||
\(813\) | −1.67230e13 | − | 1.67230e13i | −1.34247 | − | 1.34247i | ||||
\(814\) | 1.60554e13i | 1.28177i | ||||||||
\(815\) | 1.92405e12 | 0.152759 | ||||||||
\(816\) | −5.84049e12 | − | 1.16587e12i | −0.461152 | − | 0.0920543i | ||||
\(817\) | −3.18655e13 | −2.50220 | ||||||||
\(818\) | 2.80200e13i | 2.18815i | ||||||||
\(819\) | −2.86331e12 | − | 2.86331e12i | −0.222377 | − | 0.222377i | ||||
\(820\) | 5.02787e12 | 0.388349 | ||||||||
\(821\) | 8.40128e12 | + | 8.40128e12i | 0.645359 | + | 0.645359i | 0.951868 | − | 0.306509i | \(-0.0991609\pi\) |
−0.306509 | + | 0.951868i | \(0.599161\pi\) | |||||||
\(822\) | 1.75382e12 | − | 1.75382e12i | 0.133987 | − | 0.133987i | ||||
\(823\) | −5.70064e12 | + | 5.70064e12i | −0.433136 | + | 0.433136i | −0.889694 | − | 0.456558i | \(-0.849082\pi\) |
0.456558 | + | 0.889694i | \(0.349082\pi\) | |||||||
\(824\) | − | 1.16692e12i | − | 0.0881794i | ||||||
\(825\) | − | 1.44483e13i | − | 1.08586i | ||||||
\(826\) | −1.31564e11 | + | 1.31564e11i | −0.00983393 | + | 0.00983393i | ||||
\(827\) | −2.57189e12 | + | 2.57189e12i | −0.191195 | + | 0.191195i | −0.796213 | − | 0.605017i | \(-0.793166\pi\) |
0.605017 | + | 0.796213i | \(0.293166\pi\) | |||||||
\(828\) | 1.14519e13 | + | 1.14519e13i | 0.846725 | + | 0.846725i | ||||
\(829\) | 1.25002e13 | 0.919223 | 0.459612 | − | 0.888120i | \(-0.347989\pi\) | ||||
0.459612 | + | 0.888120i | \(0.347989\pi\) | |||||||
\(830\) | 3.06906e11 | + | 3.06906e11i | 0.0224468 | + | 0.0224468i | ||||
\(831\) | 1.77588e13i | 1.29184i | ||||||||
\(832\) | −4.50762e12 | −0.326131 | ||||||||
\(833\) | −1.37380e13 | − | 2.05907e13i | −0.988604 | − | 1.48173i | ||||
\(834\) | 2.65031e13 | 1.89693 | ||||||||
\(835\) | 1.18689e12i | 0.0844932i | ||||||||
\(836\) | −1.83512e13 | − | 1.83512e13i | −1.29938 | − | 1.29938i | ||||
\(837\) | 2.69408e11 | 0.0189734 | ||||||||
\(838\) | −2.33244e13 | − | 2.33244e13i | −1.63385 | − | 1.63385i | ||||
\(839\) | 7.22630e12 | − | 7.22630e12i | 0.503486 | − | 0.503486i | −0.409034 | − | 0.912519i | \(-0.634134\pi\) |
0.912519 | + | 0.409034i | \(0.134134\pi\) | |||||||
\(840\) | −3.03454e12 | + | 3.03454e12i | −0.210299 | + | 0.210299i | ||||
\(841\) | − | 1.03754e13i | − | 0.715194i | ||||||
\(842\) | − | 1.79146e13i | − | 1.22830i | ||||||
\(843\) | −1.96708e13 | + | 1.96708e13i | −1.34152 | + | 1.34152i | ||||
\(844\) | −1.26713e13 | + | 1.26713e13i | −0.859569 | + | 0.859569i | ||||
\(845\) | −1.81045e12 | − | 1.81045e12i | −0.122161 | − | 0.122161i | ||||
\(846\) | −1.08815e13 | −0.730332 | ||||||||
\(847\) | 6.13718e12 | + | 6.13718e12i | 0.409726 | + | 0.409726i | ||||
\(848\) | − | 7.57002e12i | − | 0.502708i | ||||||
\(849\) | 1.84470e13 | 1.21855 | ||||||||
\(850\) | −1.91911e13 | + | 1.28042e13i | −1.26100 | + | 0.841334i | ||||
\(851\) | 1.37120e13 | 0.896227 | ||||||||
\(852\) | − | 4.42838e13i | − | 2.87916i | ||||||
\(853\) | 3.04023e12 | + | 3.04023e12i | 0.196624 | + | 0.196624i | 0.798551 | − | 0.601927i | \(-0.205600\pi\) |
−0.601927 | + | 0.798551i | \(0.705600\pi\) | |||||||
\(854\) | −2.75116e13 | −1.76993 | ||||||||
\(855\) | −2.89549e12 | − | 2.89549e12i | −0.185299 | − | 0.185299i | ||||
\(856\) | 4.02414e11 | − | 4.02414e11i | 0.0256178 | − | 0.0256178i | ||||
\(857\) | 7.28572e12 | − | 7.28572e12i | 0.461380 | − | 0.461380i | −0.437727 | − | 0.899108i | \(-0.644217\pi\) |
0.899108 | + | 0.437727i | \(0.144217\pi\) | |||||||
\(858\) | 5.65885e12i | 0.356480i | ||||||||
\(859\) | 2.08459e13i | 1.30633i | 0.757218 | + | 0.653163i | \(0.226558\pi\) | ||||
−0.757218 | + | 0.653163i | \(0.773442\pi\) | |||||||
\(860\) | 4.75716e12 | − | 4.75716e12i | 0.296555 | − | 0.296555i | ||||
\(861\) | −3.91453e13 | + | 3.91453e13i | −2.42753 | + | 2.42753i | ||||
\(862\) | 1.50225e13 | + | 1.50225e13i | 0.926741 | + | 0.926741i | ||||
\(863\) | 2.55853e13 | 1.57015 | 0.785076 | − | 0.619400i | \(-0.212624\pi\) | ||||
0.785076 | + | 0.619400i | \(0.212624\pi\) | |||||||
\(864\) | 1.39673e12 | + | 1.39673e12i | 0.0852709 | + | 0.0852709i | ||||
\(865\) | 7.82158e11i | 0.0475031i | ||||||||
\(866\) | 4.50592e12 | 0.272240 | ||||||||
\(867\) | 2.13669e13 | − | 8.81648e12i | 1.28427 | − | 0.529919i | ||||
\(868\) | −7.93352e12 | −0.474381 | ||||||||
\(869\) | − | 1.24295e13i | − | 0.739375i | ||||||
\(870\) | 2.50074e12 | + | 2.50074e12i | 0.147990 | + | 0.147990i | ||||
\(871\) | 6.05557e12 | 0.356511 | ||||||||
\(872\) | 1.35232e13 | + | 1.35232e13i | 0.792055 | + | 0.792055i | ||||
\(873\) | 1.55046e13 | − | 1.55046e13i | 0.903435 | − | 0.903435i | ||||
\(874\) | −2.64463e13 | + | 2.64463e13i | −1.53308 | + | 1.53308i | ||||
\(875\) | − | 1.02507e13i | − | 0.591177i | ||||||
\(876\) | 1.47323e13i | 0.845284i | ||||||||
\(877\) | 1.31732e13 | − | 1.31732e13i | 0.751955 | − | 0.751955i | −0.222889 | − | 0.974844i | \(-0.571549\pi\) |
0.974844 | + | 0.222889i | \(0.0715488\pi\) | |||||||
\(878\) | 1.00426e13 | − | 1.00426e13i | 0.570322 | − | 0.570322i | ||||
\(879\) | −1.08787e13 | − | 1.08787e13i | −0.614646 | − | 0.614646i | ||||
\(880\) | −8.76367e11 | −0.0492622 | ||||||||
\(881\) | 7.53673e12 | + | 7.53673e12i | 0.421494 | + | 0.421494i | 0.885718 | − | 0.464224i | \(-0.153667\pi\) |
−0.464224 | + | 0.885718i | \(0.653667\pi\) | |||||||
\(882\) | − | 4.66544e13i | − | 2.59587i | ||||||
\(883\) | 7.80893e12 | 0.432283 | 0.216142 | − | 0.976362i | \(-0.430653\pi\) | ||||
0.216142 | + | 0.976362i | \(0.430653\pi\) | |||||||
\(884\) | 4.45443e12 | − | 2.97198e12i | 0.245333 | − | 0.163686i | ||||
\(885\) | 2.43128e10 | 0.00133226 | ||||||||
\(886\) | − | 2.52784e13i | − | 1.37816i | ||||||
\(887\) | 1.17336e13 | + | 1.17336e13i | 0.636465 | + | 0.636465i | 0.949682 | − | 0.313217i | \(-0.101407\pi\) |
−0.313217 | + | 0.949682i | \(0.601407\pi\) | |||||||
\(888\) | 1.85745e13 | 1.00244 | ||||||||
\(889\) | −1.14411e13 | − | 1.14411e13i | −0.614343 | − | 0.614343i | ||||
\(890\) | 3.87451e11 | − | 3.87451e11i | 0.0206996 | − | 0.0206996i | ||||
\(891\) | 1.14440e13 | − | 1.14440e13i | 0.608315 | − | 0.608315i | ||||
\(892\) | 9.57134e12i | 0.506210i | ||||||||
\(893\) | − | 1.48920e13i | − | 0.783649i | ||||||
\(894\) | 4.76268e13 | − | 4.76268e13i | 2.49363 | − | 2.49363i | ||||
\(895\) | −2.51287e12 | + | 2.51287e12i | −0.130908 | + | 0.130908i | ||||
\(896\) | −2.90660e13 | − | 2.90660e13i | −1.50660 | − | 1.50660i | ||||
\(897\) | 4.83291e12 | 0.249254 | ||||||||
\(898\) | 5.09373e12 | + | 5.09373e12i | 0.261392 | + | 0.261392i | ||||
\(899\) | 2.04369e12i | 0.104351i | ||||||||
\(900\) | −2.57692e13 | −1.30921 | ||||||||
\(901\) | 1.63058e13 | + | 2.44393e13i | 0.824291 | + | 1.23545i | ||||
\(902\) | 3.72824e13 | 1.87532 | ||||||||
\(903\) | 7.40753e13i | 3.70748i | ||||||||
\(904\) | −1.05483e13 | − | 1.05483e13i | −0.525323 | − | 0.525323i | ||||
\(905\) | −2.07609e12 | −0.102879 | ||||||||
\(906\) | −8.33494e12 | − | 8.33494e12i | −0.410985 | − | 0.410985i | ||||
\(907\) | −2.28101e13 | + | 2.28101e13i | −1.11916 | + | 1.11916i | −0.127299 | + | 0.991864i | \(0.540631\pi\) |
−0.991864 | + | 0.127299i | \(0.959369\pi\) | |||||||
\(908\) | −9.59889e12 | + | 9.59889e12i | −0.468635 | + | 0.468635i | ||||
\(909\) | − | 1.25012e13i | − | 0.607314i | ||||||
\(910\) | 1.97429e12i | 0.0954389i | ||||||||
\(911\) | −2.25384e13 | + | 2.25384e13i | −1.08415 | + | 1.08415i | −0.0880334 | + | 0.996118i | \(0.528058\pi\) |
−0.996118 | + | 0.0880334i | \(0.971942\pi\) | |||||||
\(912\) | 1.08630e13 | − | 1.08630e13i | 0.519964 | − | 0.519964i | ||||
\(913\) | 1.34867e12 | + | 1.34867e12i | 0.0642371 | + | 0.0642371i | ||||
\(914\) | −5.70462e13 | −2.70376 | ||||||||
\(915\) | 2.54204e12 | + | 2.54204e12i | 0.119891 | + | 0.119891i | ||||
\(916\) | − | 2.49512e13i | − | 1.17101i | ||||||
\(917\) | −3.53013e13 | −1.64865 | ||||||||
\(918\) | −3.20798e12 | − | 6.40373e11i | −0.149087 | − | 0.0297605i | ||||
\(919\) | 2.75490e13 | 1.27405 | 0.637023 | − | 0.770845i | \(-0.280166\pi\) | ||||
0.637023 | + | 0.770845i | \(0.280166\pi\) | |||||||
\(920\) | − | 2.46830e12i | − | 0.113593i | ||||||
\(921\) | −2.18352e13 | − | 2.18352e13i | −0.999973 | − | 0.999973i | ||||
\(922\) | 1.46571e12 | 0.0667971 | ||||||||
\(923\) | −4.50306e12 | − | 4.50306e12i | −0.204221 | − | 0.204221i | ||||
\(924\) | −4.26597e13 | + | 4.26597e13i | −1.92528 | + | 1.92528i | ||||
\(925\) | −1.54274e13 | + | 1.54274e13i | −0.692874 | + | 0.692874i | ||||
\(926\) | 2.38367e13i | 1.06536i | ||||||||
\(927\) | − | 2.58833e12i | − | 0.115123i | ||||||
\(928\) | −1.05954e13 | + | 1.05954e13i | −0.468978 | + | 0.468978i | ||||
\(929\) | −2.47616e13 | + | 2.47616e13i | −1.09071 | + | 1.09071i | −0.0952519 | + | 0.995453i | \(0.530366\pi\) |
−0.995453 | + | 0.0952519i | \(0.969634\pi\) | |||||||
\(930\) | 1.23695e12 | + | 1.23695e12i | 0.0542226 | + | 0.0542226i | ||||
\(931\) | 6.38496e13 | 2.78538 | ||||||||
\(932\) | 2.78685e13 | + | 2.78685e13i | 1.20988 | + | 1.20988i | ||||
\(933\) | 6.61119e12i | 0.285635i | ||||||||
\(934\) | −5.74395e13 | −2.46973 | ||||||||
\(935\) | 2.82929e12 | − | 1.88769e12i | 0.121067 | − | 0.0807754i | ||||
\(936\) | 3.15492e12 | 0.134353 | ||||||||
\(937\) | − | 3.69015e13i | − | 1.56392i | −0.623326 | − | 0.781962i | \(-0.714219\pi\) | ||
0.623326 | − | 0.781962i | \(-0.285781\pi\) | |||||||
\(938\) | 7.70308e13 | + | 7.70308e13i | 3.24902 | + | 3.24902i | ||||
\(939\) | −2.93367e12 | −0.123145 | ||||||||
\(940\) | 2.22321e12 | + | 2.22321e12i | 0.0928763 | + | 0.0928763i | ||||
\(941\) | 2.56997e13 | − | 2.56997e13i | 1.06850 | − | 1.06850i | 0.0710264 | − | 0.997474i | \(-0.477373\pi\) |
0.997474 | − | 0.0710264i | \(-0.0226275\pi\) | |||||||
\(942\) | 2.65472e13 | − | 2.65472e13i | 1.09847 | − | 1.09847i | ||||
\(943\) | − | 3.18408e13i | − | 1.31124i | ||||||
\(944\) | 4.39568e10i | 0.00180157i | ||||||||
\(945\) | 5.05411e11 | − | 5.05411e11i | 0.0206159 | − | 0.0206159i | ||||
\(946\) | 3.52751e13 | − | 3.52751e13i | 1.43205 | − | 1.43205i | ||||
\(947\) | −1.97657e13 | − | 1.97657e13i | −0.798616 | − | 0.798616i | 0.184261 | − | 0.982877i | \(-0.441011\pi\) |
−0.982877 | + | 0.184261i | \(0.941011\pi\) | |||||||
\(948\) | −4.60018e13 | −1.84985 | ||||||||
\(949\) | 1.49808e12 | + | 1.49808e12i | 0.0599565 | + | 0.0599565i | ||||
\(950\) | − | 5.95096e13i | − | 2.37045i | ||||||
\(951\) | −1.73655e13 | −0.688454 | ||||||||
\(952\) | 2.95300e13 | + | 5.89473e12i | 1.16519 | + | 0.232593i | ||||
\(953\) | 3.85787e12 | 0.151506 | 0.0757529 | − | 0.997127i | \(-0.475864\pi\) | ||||
0.0757529 | + | 0.997127i | \(0.475864\pi\) | |||||||
\(954\) | 5.53744e13i | 2.16442i | ||||||||
\(955\) | 1.35540e12 | + | 1.35540e12i | 0.0527295 | + | 0.0527295i | ||||
\(956\) | −2.48587e13 | −0.962539 | ||||||||
\(957\) | 1.09892e13 | + | 1.09892e13i | 0.423510 | + | 0.423510i | ||||
\(958\) | −5.04088e13 | + | 5.04088e13i | −1.93358 | + | 1.93358i | ||||
\(959\) | 2.68886e12 | − | 2.68886e12i | 0.102656 | − | 0.102656i | ||||
\(960\) | 1.05963e13i | 0.402655i | ||||||||
\(961\) | − | 2.54287e13i | − | 0.961766i | ||||||
\(962\) | 6.04234e12 | − | 6.04234e12i | 0.227466 | − | 0.227466i | ||||
\(963\) | 8.92594e11 | − | 8.92594e11i | 0.0334453 | − | 0.0334453i | ||||
\(964\) | 4.41572e13 | + | 4.41572e13i | 1.64685 | + | 1.64685i | ||||
\(965\) | 3.36572e12 | 0.124941 | ||||||||
\(966\) | 6.14778e13 | + | 6.14778e13i | 2.27154 | + | 2.27154i | ||||
\(967\) | 1.57206e13i | 0.578164i | 0.957304 | + | 0.289082i | \(0.0933500\pi\) | ||||
−0.957304 | + | 0.289082i | \(0.906650\pi\) | |||||||
\(968\) | −6.76221e12 | −0.247542 | ||||||||
\(969\) | −1.16715e13 | + | 5.84693e13i | −0.425277 | + | 2.13045i | ||||
\(970\) | −1.06907e13 | −0.387732 | ||||||||
\(971\) | − | 2.52084e13i | − | 0.910036i | −0.890482 | − | 0.455018i | \(-0.849633\pi\) | ||
0.890482 | − | 0.455018i | \(-0.150367\pi\) | |||||||
\(972\) | −3.95767e13 | − | 3.95767e13i | −1.42214 | − | 1.42214i | ||||
\(973\) | 4.06331e13 | 1.45335 | ||||||||
\(974\) | −1.44727e13 | − | 1.44727e13i | −0.515271 | − | 0.515271i | ||||
\(975\) | −5.43751e12 | + | 5.43751e12i | −0.192699 | + | 0.192699i | ||||
\(976\) | −4.59594e12 | + | 4.59594e12i | −0.162125 | + | 0.162125i | ||||
\(977\) | − | 3.60657e13i | − | 1.26639i | −0.773991 | − | 0.633197i | \(-0.781742\pi\) | ||
0.773991 | − | 0.633197i | \(-0.218258\pi\) | |||||||
\(978\) | − | 5.28027e13i | − | 1.84557i | ||||||
\(979\) | 1.70261e12 | − | 1.70261e12i | 0.0592371 | − | 0.0592371i | ||||
\(980\) | −9.53203e12 | + | 9.53203e12i | −0.330117 | + | 0.330117i | ||||
\(981\) | 2.99958e13 | + | 2.99958e13i | 1.03407 | + | 1.03407i | ||||
\(982\) | 4.47349e13 | 1.53513 | ||||||||
\(983\) | 1.57108e13 | + | 1.57108e13i | 0.536670 | + | 0.536670i | 0.922549 | − | 0.385879i | \(-0.126102\pi\) |
−0.385879 | + | 0.922549i | \(0.626102\pi\) | |||||||
\(984\) | − | 4.31320e13i | − | 1.46663i | ||||||
\(985\) | −9.17088e12 | −0.310419 | ||||||||
\(986\) | 4.85779e12 | − | 2.43354e13i | 0.163679 | − | 0.819958i | ||||
\(987\) | −3.46183e13 | −1.16112 | ||||||||
\(988\) | 1.38127e13i | 0.461182i | ||||||||
\(989\) | −3.01265e13 | − | 3.01265e13i | −1.00130 | − | 1.00130i | ||||
\(990\) | 6.41060e12 | 0.212100 | ||||||||
\(991\) | −7.41356e12 | − | 7.41356e12i | −0.244172 | − | 0.244172i | 0.574402 | − | 0.818574i | \(-0.305235\pi\) |
−0.818574 | + | 0.574402i | \(0.805235\pi\) | |||||||
\(992\) | −5.24088e12 | + | 5.24088e12i | −0.171831 | + | 0.171831i | ||||
\(993\) | 1.48360e13 | − | 1.48360e13i | 0.484222 | − | 0.484222i | ||||
\(994\) | − | 1.14564e14i | − | 3.72227i | ||||||
\(995\) | − | 4.08118e12i | − | 0.132002i | ||||||
\(996\) | 4.99143e12 | − | 4.99143e12i | 0.160716 | − | 0.160716i | ||||
\(997\) | −1.63998e13 | + | 1.63998e13i | −0.525667 | + | 0.525667i | −0.919277 | − | 0.393611i | \(-0.871226\pi\) |
0.393611 | + | 0.919277i | \(0.371226\pi\) | |||||||
\(998\) | 3.13572e13 | + | 3.13572e13i | 1.00058 | + | 1.00058i | ||||
\(999\) | −3.09363e12 | −0.0982705 |
(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 | 17.10.c.a.13.2 | yes | 24 | |
17.2 | even | 8 | 289.10.a.f.1.22 | 24 | |||
17.4 | even | 4 | inner | 17.10.c.a.4.11 | ✓ | 24 | |
17.15 | even | 8 | 289.10.a.f.1.21 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.10.c.a.4.11 | ✓ | 24 | 17.4 | even | 4 | inner | |
17.10.c.a.13.2 | yes | 24 | 1.1 | even | 1 | trivial | |
289.10.a.f.1.21 | 24 | 17.15 | even | 8 | |||
289.10.a.f.1.22 | 24 | 17.2 | even | 8 |