Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,11,Mod(58,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.58");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(112.458233723\) |
Analytic rank: | \(0\) |
Dimension: | \(100\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.99 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.11.c.a.58.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 63.4607i | 1.98315i | 0.129551 | + | 0.991573i | \(0.458646\pi\) | ||||
−0.129551 | + | 0.991573i | \(0.541354\pi\) | |||||||
\(3\) | −140.296 | −0.577350 | ||||||||
\(4\) | −3003.25 | −2.93287 | ||||||||
\(5\) | 3537.19 | 1.13190 | 0.565951 | − | 0.824439i | \(-0.308509\pi\) | ||||
0.565951 | + | 0.824439i | \(0.308509\pi\) | |||||||
\(6\) | − | 8903.28i | − | 1.14497i | ||||||
\(7\) | −15274.6 | −0.908823 | −0.454411 | − | 0.890792i | \(-0.650150\pi\) | ||||
−0.454411 | + | 0.890792i | \(0.650150\pi\) | |||||||
\(8\) | − | 125605.i | − | 3.83315i | ||||||
\(9\) | 19683.0 | 0.333333 | ||||||||
\(10\) | 224473.i | 2.24473i | ||||||||
\(11\) | 271175.i | 1.68378i | 0.539648 | + | 0.841891i | \(0.318557\pi\) | ||||
−0.539648 | + | 0.841891i | \(0.681443\pi\) | |||||||
\(12\) | 421345. | 1.69329 | ||||||||
\(13\) | 568274.i | 1.53053i | 0.643717 | + | 0.765264i | \(0.277392\pi\) | ||||
−0.643717 | + | 0.765264i | \(0.722608\pi\) | |||||||
\(14\) | − | 969335.i | − | 1.80233i | ||||||
\(15\) | −496254. | −0.653504 | ||||||||
\(16\) | 4.89563e6 | 4.66884 | ||||||||
\(17\) | −787841. | −0.554873 | −0.277437 | − | 0.960744i | \(-0.589485\pi\) | ||||
−0.277437 | + | 0.960744i | \(0.589485\pi\) | |||||||
\(18\) | 1.24910e6i | 0.661048i | ||||||||
\(19\) | −2.77833e6 | −1.12206 | −0.561030 | − | 0.827796i | \(-0.689595\pi\) | ||||
−0.561030 | + | 0.827796i | \(0.689595\pi\) | |||||||
\(20\) | −1.06231e7 | −3.31972 | ||||||||
\(21\) | 2.14297e6 | 0.524709 | ||||||||
\(22\) | −1.72089e7 | −3.33918 | ||||||||
\(23\) | − | 8.00619e6i | − | 1.24390i | −0.783055 | − | 0.621952i | \(-0.786340\pi\) | ||
0.783055 | − | 0.621952i | \(-0.213660\pi\) | |||||||
\(24\) | 1.76219e7i | 2.21307i | ||||||||
\(25\) | 2.74610e6 | 0.281201 | ||||||||
\(26\) | −3.60631e7 | −3.03526 | ||||||||
\(27\) | −2.76145e6 | −0.192450 | ||||||||
\(28\) | 4.58735e7 | 2.66546 | ||||||||
\(29\) | −3.11900e7 | −1.52063 | −0.760317 | − | 0.649552i | \(-0.774957\pi\) | ||||
−0.760317 | + | 0.649552i | \(0.774957\pi\) | |||||||
\(30\) | − | 3.14926e7i | − | 1.29599i | ||||||
\(31\) | 4.29591e7i | 1.50054i | 0.661133 | + | 0.750269i | \(0.270076\pi\) | ||||
−0.661133 | + | 0.750269i | \(0.729924\pi\) | |||||||
\(32\) | 1.82061e8i | 5.42583i | ||||||||
\(33\) | − | 3.80447e7i | − | 0.972131i | ||||||
\(34\) | − | 4.99969e7i | − | 1.10039i | ||||||
\(35\) | −5.40291e7 | −1.02870 | ||||||||
\(36\) | −5.91131e7 | −0.977622 | ||||||||
\(37\) | − | 6.24534e7i | − | 0.900632i | −0.892869 | − | 0.450316i | \(-0.851311\pi\) | ||
0.892869 | − | 0.450316i | \(-0.148689\pi\) | |||||||
\(38\) | − | 1.76315e8i | − | 2.22521i | ||||||
\(39\) | − | 7.97267e7i | − | 0.883651i | ||||||
\(40\) | − | 4.44288e8i | − | 4.33875i | ||||||
\(41\) | 6.93263e7 | 0.598382 | 0.299191 | − | 0.954193i | \(-0.403283\pi\) | ||||
0.299191 | + | 0.954193i | \(0.403283\pi\) | |||||||
\(42\) | 1.35994e8i | 1.04057i | ||||||||
\(43\) | 9.52345e7i | 0.647816i | 0.946089 | + | 0.323908i | \(0.104997\pi\) | ||||
−0.946089 | + | 0.323908i | \(0.895003\pi\) | |||||||
\(44\) | − | 8.14406e8i | − | 4.93830i | ||||||
\(45\) | 6.96226e7 | 0.377300 | ||||||||
\(46\) | 5.08078e8 | 2.46684 | ||||||||
\(47\) | 3.13127e8i | 1.36531i | 0.730741 | + | 0.682654i | \(0.239175\pi\) | ||||
−0.730741 | + | 0.682654i | \(0.760825\pi\) | |||||||
\(48\) | −6.86838e8 | −2.69555 | ||||||||
\(49\) | −4.91622e7 | −0.174041 | ||||||||
\(50\) | 1.74269e8i | 0.557662i | ||||||||
\(51\) | 1.10531e8 | 0.320356 | ||||||||
\(52\) | − | 1.70667e9i | − | 4.48883i | ||||||
\(53\) | −1.32764e8 | −0.317469 | −0.158734 | − | 0.987321i | \(-0.550741\pi\) | ||||
−0.158734 | + | 0.987321i | \(0.550741\pi\) | |||||||
\(54\) | − | 1.75243e8i | − | 0.381657i | ||||||
\(55\) | 9.59197e8i | 1.90587i | ||||||||
\(56\) | 1.91856e9i | 3.48366i | ||||||||
\(57\) | 3.89789e8 | 0.647821 | ||||||||
\(58\) | − | 1.97934e9i | − | 3.01564i | ||||||
\(59\) | −5.75728e8 | + | 4.23855e8i | −0.805300 | + | 0.592868i | ||||
\(60\) | 1.49038e9 | 1.91664 | ||||||||
\(61\) | − | 8.26364e8i | − | 0.978413i | −0.872168 | − | 0.489206i | \(-0.837287\pi\) | ||
0.872168 | − | 0.489206i | \(-0.162713\pi\) | |||||||
\(62\) | −2.72621e9 | −2.97578 | ||||||||
\(63\) | −3.00650e8 | −0.302941 | ||||||||
\(64\) | −6.54056e9 | −6.09137 | ||||||||
\(65\) | 2.01010e9i | 1.73241i | ||||||||
\(66\) | 2.41434e9 | 1.92788 | ||||||||
\(67\) | 1.28334e8i | 0.0950533i | 0.998870 | + | 0.0475266i | \(0.0151339\pi\) | ||||
−0.998870 | + | 0.0475266i | \(0.984866\pi\) | |||||||
\(68\) | 2.36609e9 | 1.62737 | ||||||||
\(69\) | 1.12324e9i | 0.718168i | ||||||||
\(70\) | − | 3.42873e9i | − | 2.04006i | ||||||
\(71\) | 1.24650e9 | 0.690878 | 0.345439 | − | 0.938441i | \(-0.387730\pi\) | ||||
0.345439 | + | 0.938441i | \(0.387730\pi\) | |||||||
\(72\) | − | 2.47228e9i | − | 1.27772i | ||||||
\(73\) | − | 2.30278e9i | − | 1.11081i | −0.831581 | − | 0.555404i | \(-0.812564\pi\) | ||
0.831581 | − | 0.555404i | \(-0.187436\pi\) | |||||||
\(74\) | 3.96333e9 | 1.78608 | ||||||||
\(75\) | −3.85268e8 | −0.162351 | ||||||||
\(76\) | 8.34403e9 | 3.29085 | ||||||||
\(77\) | − | 4.14208e9i | − | 1.53026i | ||||||
\(78\) | 5.05951e9 | 1.75241 | ||||||||
\(79\) | −1.18761e9 | −0.385957 | −0.192979 | − | 0.981203i | \(-0.561815\pi\) | ||||
−0.192979 | + | 0.981203i | \(0.561815\pi\) | |||||||
\(80\) | 1.73168e10 | 5.28466 | ||||||||
\(81\) | 3.87420e8 | 0.111111 | ||||||||
\(82\) | 4.39949e9i | 1.18668i | ||||||||
\(83\) | − | 2.67136e9i | − | 0.678177i | −0.940755 | − | 0.339088i | \(-0.889881\pi\) | ||
0.940755 | − | 0.339088i | \(-0.110119\pi\) | |||||||
\(84\) | −6.43587e9 | −1.53890 | ||||||||
\(85\) | −2.78674e9 | −0.628062 | ||||||||
\(86\) | −6.04364e9 | −1.28471 | ||||||||
\(87\) | 4.37583e9 | 0.877939 | ||||||||
\(88\) | 3.40608e10 | 6.45419 | ||||||||
\(89\) | − | 4.15156e9i | − | 0.743466i | −0.928340 | − | 0.371733i | \(-0.878764\pi\) | ||
0.928340 | − | 0.371733i | \(-0.121236\pi\) | |||||||
\(90\) | 4.41829e9i | 0.748242i | ||||||||
\(91\) | − | 8.68016e9i | − | 1.39098i | ||||||
\(92\) | 2.40446e10i | 3.64820i | ||||||||
\(93\) | − | 6.02700e9i | − | 0.866336i | ||||||
\(94\) | −1.98712e10 | −2.70761 | ||||||||
\(95\) | −9.82749e9 | −1.27006 | ||||||||
\(96\) | − | 2.55424e10i | − | 3.13260i | ||||||
\(97\) | 6.37540e9i | 0.742418i | 0.928549 | + | 0.371209i | \(0.121057\pi\) | ||||
−0.928549 | + | 0.371209i | \(0.878943\pi\) | |||||||
\(98\) | − | 3.11987e9i | − | 0.345148i | ||||||
\(99\) | 5.33753e9i | 0.561260i | ||||||||
\(100\) | −8.24725e9 | −0.824725 | ||||||||
\(101\) | − | 5.60220e9i | − | 0.533030i | −0.963831 | − | 0.266515i | \(-0.914128\pi\) | ||
0.963831 | − | 0.266515i | \(-0.0858722\pi\) | |||||||
\(102\) | 7.01437e9i | 0.635313i | ||||||||
\(103\) | 8.39383e9i | 0.724060i | 0.932167 | + | 0.362030i | \(0.117916\pi\) | ||||
−0.932167 | + | 0.362030i | \(0.882084\pi\) | |||||||
\(104\) | 7.13780e10 | 5.86675 | ||||||||
\(105\) | 7.58008e9 | 0.593919 | ||||||||
\(106\) | − | 8.42529e9i | − | 0.629587i | ||||||
\(107\) | 1.66010e10 | 1.18363 | 0.591814 | − | 0.806075i | \(-0.298412\pi\) | ||||
0.591814 | + | 0.806075i | \(0.298412\pi\) | |||||||
\(108\) | 8.29333e9 | 0.564430 | ||||||||
\(109\) | 1.14611e10i | 0.744892i | 0.928054 | + | 0.372446i | \(0.121481\pi\) | ||||
−0.928054 | + | 0.372446i | \(0.878519\pi\) | |||||||
\(110\) | −6.08713e10 | −3.77963 | ||||||||
\(111\) | 8.76196e9i | 0.519980i | ||||||||
\(112\) | −7.47787e10 | −4.24314 | ||||||||
\(113\) | 2.70084e10i | 1.46591i | 0.680279 | + | 0.732953i | \(0.261859\pi\) | ||||
−0.680279 | + | 0.732953i | \(0.738141\pi\) | |||||||
\(114\) | 2.47363e10i | 1.28472i | ||||||||
\(115\) | − | 2.83194e10i | − | 1.40798i | ||||||
\(116\) | 9.36714e10 | 4.45982 | ||||||||
\(117\) | 1.11853e10i | 0.510176i | ||||||||
\(118\) | −2.68981e10 | − | 3.65361e10i | −1.17574 | − | 1.59703i | ||||
\(119\) | 1.20339e10 | 0.504282 | ||||||||
\(120\) | 6.23319e10i | 2.50498i | ||||||||
\(121\) | −4.75983e10 | −1.83512 | ||||||||
\(122\) | 5.24416e10 | 1.94033 | ||||||||
\(123\) | −9.72621e9 | −0.345476 | ||||||||
\(124\) | − | 1.29017e11i | − | 4.40088i | ||||||
\(125\) | −2.48294e10 | −0.813610 | ||||||||
\(126\) | − | 1.90794e10i | − | 0.600776i | ||||||
\(127\) | 5.99776e9 | 0.181539 | 0.0907696 | − | 0.995872i | \(-0.471067\pi\) | ||||
0.0907696 | + | 0.995872i | \(0.471067\pi\) | |||||||
\(128\) | − | 2.28638e11i | − | 6.65424i | ||||||
\(129\) | − | 1.33610e10i | − | 0.374017i | ||||||
\(130\) | −1.27562e11 | −3.43561 | ||||||||
\(131\) | 3.52715e10i | 0.914256i | 0.889401 | + | 0.457128i | \(0.151122\pi\) | ||||
−0.889401 | + | 0.457128i | \(0.848878\pi\) | |||||||
\(132\) | 1.14258e11i | 2.85113i | ||||||||
\(133\) | 4.24378e10 | 1.01975 | ||||||||
\(134\) | −8.14415e9 | −0.188504 | ||||||||
\(135\) | −9.76777e9 | −0.217835 | ||||||||
\(136\) | 9.89566e10i | 2.12692i | ||||||||
\(137\) | −4.49614e10 | −0.931617 | −0.465808 | − | 0.884886i | \(-0.654236\pi\) | ||||
−0.465808 | + | 0.884886i | \(0.654236\pi\) | |||||||
\(138\) | −7.12814e10 | −1.42423 | ||||||||
\(139\) | 6.54168e10 | 1.26071 | 0.630355 | − | 0.776307i | \(-0.282909\pi\) | ||||
0.630355 | + | 0.776307i | \(0.282909\pi\) | |||||||
\(140\) | 1.62263e11 | 3.01703 | ||||||||
\(141\) | − | 4.39305e10i | − | 0.788261i | ||||||
\(142\) | 7.91038e10i | 1.37011i | ||||||||
\(143\) | −1.54102e11 | −2.57707 | ||||||||
\(144\) | 9.63607e10 | 1.55628 | ||||||||
\(145\) | −1.10325e11 | −1.72121 | ||||||||
\(146\) | 1.46136e11 | 2.20289 | ||||||||
\(147\) | 6.89727e9 | 0.100483 | ||||||||
\(148\) | 1.87563e11i | 2.64143i | ||||||||
\(149\) | − | 1.17694e10i | − | 0.160259i | −0.996784 | − | 0.0801296i | \(-0.974467\pi\) | ||
0.996784 | − | 0.0801296i | \(-0.0255334\pi\) | |||||||
\(150\) | − | 2.44493e10i | − | 0.321967i | ||||||
\(151\) | − | 1.26674e11i | − | 1.61363i | −0.590806 | − | 0.806814i | \(-0.701190\pi\) | ||
0.590806 | − | 0.806814i | \(-0.298810\pi\) | |||||||
\(152\) | 3.48972e11i | 4.30103i | ||||||||
\(153\) | −1.55071e10 | −0.184958 | ||||||||
\(154\) | 2.62859e11 | 3.03473 | ||||||||
\(155\) | 1.51955e11i | 1.69846i | ||||||||
\(156\) | 2.39440e11i | 2.59163i | ||||||||
\(157\) | 7.42949e9i | 0.0778862i | 0.999241 | + | 0.0389431i | \(0.0123991\pi\) | ||||
−0.999241 | + | 0.0389431i | \(0.987601\pi\) | |||||||
\(158\) | − | 7.53667e10i | − | 0.765410i | ||||||
\(159\) | 1.86263e10 | 0.183291 | ||||||||
\(160\) | 6.43983e11i | 6.14150i | ||||||||
\(161\) | 1.22291e11i | 1.13049i | ||||||||
\(162\) | 2.45860e10i | 0.220349i | ||||||||
\(163\) | 1.39455e11 | 1.21198 | 0.605992 | − | 0.795471i | \(-0.292776\pi\) | ||||
0.605992 | + | 0.795471i | \(0.292776\pi\) | |||||||
\(164\) | −2.08205e11 | −1.75498 | ||||||||
\(165\) | − | 1.34572e11i | − | 1.10036i | ||||||
\(166\) | 1.69527e11 | 1.34492 | ||||||||
\(167\) | 5.22512e10 | 0.402266 | 0.201133 | − | 0.979564i | \(-0.435538\pi\) | ||||
0.201133 | + | 0.979564i | \(0.435538\pi\) | |||||||
\(168\) | − | 2.69167e11i | − | 2.01129i | ||||||
\(169\) | −1.85077e11 | −1.34252 | ||||||||
\(170\) | − | 1.76849e11i | − | 1.24554i | ||||||
\(171\) | −5.46859e10 | −0.374020 | ||||||||
\(172\) | − | 2.86013e11i | − | 1.89996i | ||||||
\(173\) | 7.25153e10i | 0.467950i | 0.972243 | + | 0.233975i | \(0.0751733\pi\) | ||||
−0.972243 | + | 0.233975i | \(0.924827\pi\) | |||||||
\(174\) | 2.77693e11i | 1.74108i | ||||||||
\(175\) | −4.19456e10 | −0.255562 | ||||||||
\(176\) | 1.32757e12i | 7.86130i | ||||||||
\(177\) | 8.07725e10 | − | 5.94653e10i | 0.464940 | − | 0.342292i | ||||
\(178\) | 2.63461e11 | 1.47440 | ||||||||
\(179\) | − | 1.80016e11i | − | 0.979592i | −0.871837 | − | 0.489796i | \(-0.837071\pi\) | ||
0.871837 | − | 0.489796i | \(-0.162929\pi\) | |||||||
\(180\) | −2.09094e11 | −1.10657 | ||||||||
\(181\) | 3.56609e10 | 0.183569 | 0.0917844 | − | 0.995779i | \(-0.470743\pi\) | ||||
0.0917844 | + | 0.995779i | \(0.470743\pi\) | |||||||
\(182\) | 5.50848e11 | 2.75851 | ||||||||
\(183\) | 1.15936e11i | 0.564887i | ||||||||
\(184\) | −1.00562e12 | −4.76808 | ||||||||
\(185\) | − | 2.20910e11i | − | 1.01943i | ||||||
\(186\) | 3.82477e11 | 1.71807 | ||||||||
\(187\) | − | 2.13642e11i | − | 0.934285i | ||||||
\(188\) | − | 9.40399e11i | − | 4.00427i | ||||||
\(189\) | 4.21800e10 | 0.174903 | ||||||||
\(190\) | − | 6.23659e11i | − | 2.51871i | ||||||
\(191\) | 3.85490e10i | 0.151651i | 0.997121 | + | 0.0758257i | \(0.0241593\pi\) | ||||
−0.997121 | + | 0.0758257i | \(0.975841\pi\) | |||||||
\(192\) | 9.17614e11 | 3.51685 | ||||||||
\(193\) | 2.29585e11 | 0.857349 | 0.428674 | − | 0.903459i | \(-0.358981\pi\) | ||||
0.428674 | + | 0.903459i | \(0.358981\pi\) | |||||||
\(194\) | −4.04587e11 | −1.47232 | ||||||||
\(195\) | − | 2.82009e11i | − | 1.00021i | ||||||
\(196\) | 1.47647e11 | 0.510438 | ||||||||
\(197\) | −2.59798e11 | −0.875599 | −0.437799 | − | 0.899073i | \(-0.644242\pi\) | ||||
−0.437799 | + | 0.899073i | \(0.644242\pi\) | |||||||
\(198\) | −3.38723e11 | −1.11306 | ||||||||
\(199\) | 6.07744e11 | 1.94740 | 0.973700 | − | 0.227832i | \(-0.0731639\pi\) | ||||
0.973700 | + | 0.227832i | \(0.0731639\pi\) | |||||||
\(200\) | − | 3.44924e11i | − | 1.07789i | ||||||
\(201\) | − | 1.80047e10i | − | 0.0548790i | ||||||
\(202\) | 3.55519e11 | 1.05708 | ||||||||
\(203\) | 4.76414e11 | 1.38199 | ||||||||
\(204\) | −3.31953e11 | −0.939562 | ||||||||
\(205\) | 2.45221e11 | 0.677310 | ||||||||
\(206\) | −5.32678e11 | −1.43592 | ||||||||
\(207\) | − | 1.57586e11i | − | 0.414635i | ||||||
\(208\) | 2.78206e12i | 7.14578i | ||||||||
\(209\) | − | 7.53413e11i | − | 1.88930i | ||||||
\(210\) | 4.81037e11i | 1.17783i | ||||||||
\(211\) | − | 3.48490e11i | − | 0.833255i | −0.909077 | − | 0.416628i | \(-0.863212\pi\) | ||
0.909077 | − | 0.416628i | \(-0.136788\pi\) | |||||||
\(212\) | 3.98724e11 | 0.931093 | ||||||||
\(213\) | −1.74879e11 | −0.398879 | ||||||||
\(214\) | 1.05351e12i | 2.34730i | ||||||||
\(215\) | 3.36863e11i | 0.733264i | ||||||||
\(216\) | 3.46851e11i | 0.737691i | ||||||||
\(217\) | − | 6.56183e11i | − | 1.36372i | ||||||
\(218\) | −7.27328e11 | −1.47723 | ||||||||
\(219\) | 3.23072e11i | 0.641325i | ||||||||
\(220\) | − | 2.88071e12i | − | 5.58967i | ||||||
\(221\) | − | 4.47710e11i | − | 0.849249i | ||||||
\(222\) | −5.56040e11 | −1.03120 | ||||||||
\(223\) | −9.61110e10 | −0.174281 | −0.0871403 | − | 0.996196i | \(-0.527773\pi\) | ||||
−0.0871403 | + | 0.996196i | \(0.527773\pi\) | |||||||
\(224\) | − | 2.78090e12i | − | 4.93112i | ||||||
\(225\) | 5.40515e10 | 0.0937336 | ||||||||
\(226\) | −1.71397e12 | −2.90711 | ||||||||
\(227\) | − | 1.97002e11i | − | 0.326845i | −0.986556 | − | 0.163423i | \(-0.947747\pi\) | ||
0.986556 | − | 0.163423i | \(-0.0522534\pi\) | |||||||
\(228\) | −1.17064e12 | −1.89997 | ||||||||
\(229\) | − | 1.93983e11i | − | 0.308026i | −0.988069 | − | 0.154013i | \(-0.950780\pi\) | ||
0.988069 | − | 0.154013i | \(-0.0492197\pi\) | |||||||
\(230\) | 1.79717e12 | 2.79222 | ||||||||
\(231\) | 5.81118e11i | 0.883495i | ||||||||
\(232\) | 3.91761e12i | 5.82883i | ||||||||
\(233\) | 4.62830e11i | 0.673972i | 0.941510 | + | 0.336986i | \(0.109408\pi\) | ||||
−0.941510 | + | 0.336986i | \(0.890592\pi\) | |||||||
\(234\) | −7.09829e11 | −1.01175 | ||||||||
\(235\) | 1.10759e12i | 1.54540i | ||||||||
\(236\) | 1.72906e12 | − | 1.27295e12i | 2.36184 | − | 1.73880i | ||||
\(237\) | 1.66617e11 | 0.222833 | ||||||||
\(238\) | 7.63682e11i | 1.00006i | ||||||||
\(239\) | −1.34407e12 | −1.72358 | −0.861789 | − | 0.507267i | \(-0.830656\pi\) | ||||
−0.861789 | + | 0.507267i | \(0.830656\pi\) | |||||||
\(240\) | −2.42948e12 | −3.05110 | ||||||||
\(241\) | 3.68238e11 | 0.452943 | 0.226471 | − | 0.974018i | \(-0.427281\pi\) | ||||
0.226471 | + | 0.974018i | \(0.427281\pi\) | |||||||
\(242\) | − | 3.02062e12i | − | 3.63931i | ||||||
\(243\) | −5.43536e10 | −0.0641500 | ||||||||
\(244\) | 2.48178e12i | 2.86955i | ||||||||
\(245\) | −1.73896e11 | −0.196997 | ||||||||
\(246\) | − | 6.17232e11i | − | 0.685130i | ||||||
\(247\) | − | 1.57885e12i | − | 1.71734i | ||||||
\(248\) | 5.39587e12 | 5.75179 | ||||||||
\(249\) | 3.74782e11i | 0.391545i | ||||||||
\(250\) | − | 1.57569e12i | − | 1.61351i | ||||||
\(251\) | −4.16900e11 | −0.418469 | −0.209234 | − | 0.977866i | \(-0.567097\pi\) | ||||
−0.209234 | + | 0.977866i | \(0.567097\pi\) | |||||||
\(252\) | 9.02928e11 | 0.888485 | ||||||||
\(253\) | 2.17108e12 | 2.09446 | ||||||||
\(254\) | 3.80622e11i | 0.360019i | ||||||||
\(255\) | 3.90969e11 | 0.362612 | ||||||||
\(256\) | 7.81198e12 | 7.10496 | ||||||||
\(257\) | 1.65267e12 | 1.47407 | 0.737037 | − | 0.675852i | \(-0.236224\pi\) | ||||
0.737037 | + | 0.675852i | \(0.236224\pi\) | |||||||
\(258\) | 8.47899e11 | 0.741730 | ||||||||
\(259\) | 9.53949e11i | 0.818515i | ||||||||
\(260\) | − | 6.03683e12i | − | 5.08092i | ||||||
\(261\) | −6.13912e11 | −0.506878 | ||||||||
\(262\) | −2.23835e12 | −1.81310 | ||||||||
\(263\) | 8.88346e11 | 0.705998 | 0.352999 | − | 0.935624i | \(-0.385162\pi\) | ||||
0.352999 | + | 0.935624i | \(0.385162\pi\) | |||||||
\(264\) | −4.77860e12 | −3.72633 | ||||||||
\(265\) | −4.69612e11 | −0.359343 | ||||||||
\(266\) | 2.69313e12i | 2.02232i | ||||||||
\(267\) | 5.82448e11i | 0.429240i | ||||||||
\(268\) | − | 3.85419e11i | − | 0.278778i | ||||||
\(269\) | − | 8.05656e11i | − | 0.571990i | −0.958231 | − | 0.285995i | \(-0.907676\pi\) | ||
0.958231 | − | 0.285995i | \(-0.0923240\pi\) | |||||||
\(270\) | − | 6.19869e11i | − | 0.431998i | ||||||
\(271\) | 1.43475e12 | 0.981587 | 0.490794 | − | 0.871276i | \(-0.336707\pi\) | ||||
0.490794 | + | 0.871276i | \(0.336707\pi\) | |||||||
\(272\) | −3.85698e12 | −2.59061 | ||||||||
\(273\) | 1.21779e12i | 0.803082i | ||||||||
\(274\) | − | 2.85328e12i | − | 1.84753i | ||||||
\(275\) | 7.44673e11i | 0.473481i | ||||||||
\(276\) | − | 3.37337e12i | − | 2.10629i | ||||||
\(277\) | 1.40442e12 | 0.861191 | 0.430596 | − | 0.902545i | \(-0.358304\pi\) | ||||
0.430596 | + | 0.902545i | \(0.358304\pi\) | |||||||
\(278\) | 4.15139e12i | 2.50017i | ||||||||
\(279\) | 8.45564e11i | 0.500179i | ||||||||
\(280\) | 6.78632e12i | 3.94316i | ||||||||
\(281\) | −1.17796e12 | −0.672355 | −0.336177 | − | 0.941799i | \(-0.609134\pi\) | ||||
−0.336177 | + | 0.941799i | \(0.609134\pi\) | |||||||
\(282\) | 2.78786e12 | 1.56324 | ||||||||
\(283\) | 7.49696e11i | 0.413003i | 0.978446 | + | 0.206501i | \(0.0662078\pi\) | ||||
−0.978446 | + | 0.206501i | \(0.933792\pi\) | |||||||
\(284\) | −3.74356e12 | −2.02625 | ||||||||
\(285\) | 1.37876e12 | 0.733270 | ||||||||
\(286\) | − | 9.77939e12i | − | 5.11071i | ||||||
\(287\) | −1.05893e12 | −0.543824 | ||||||||
\(288\) | 3.58350e12i | 1.80861i | ||||||||
\(289\) | −1.39530e12 | −0.692115 | ||||||||
\(290\) | − | 7.00129e12i | − | 3.41341i | ||||||
\(291\) | − | 8.94444e11i | − | 0.428635i | ||||||
\(292\) | 6.91585e12i | 3.25785i | ||||||||
\(293\) | 3.53806e12 | 1.63843 | 0.819213 | − | 0.573490i | \(-0.194411\pi\) | ||||
0.819213 | + | 0.573490i | \(0.194411\pi\) | |||||||
\(294\) | 4.37705e11i | 0.199271i | ||||||||
\(295\) | −2.03646e12 | + | 1.49926e12i | −0.911520 | + | 0.671068i | ||||
\(296\) | −7.84444e12 | −3.45226 | ||||||||
\(297\) | − | 7.48835e11i | − | 0.324044i | ||||||
\(298\) | 7.46894e11 | 0.317817 | ||||||||
\(299\) | 4.54972e12 | 1.90383 | ||||||||
\(300\) | 1.15706e12 | 0.476155 | ||||||||
\(301\) | − | 1.45467e12i | − | 0.588750i | ||||||
\(302\) | 8.03883e12 | 3.20006 | ||||||||
\(303\) | 7.85967e11i | 0.307745i | ||||||||
\(304\) | −1.36017e13 | −5.23871 | ||||||||
\(305\) | − | 2.92301e12i | − | 1.10747i | ||||||
\(306\) | − | 9.84089e11i | − | 0.366798i | ||||||
\(307\) | −2.20403e11 | −0.0808211 | −0.0404106 | − | 0.999183i | \(-0.512867\pi\) | ||||
−0.0404106 | + | 0.999183i | \(0.512867\pi\) | |||||||
\(308\) | 1.24397e13i | 4.48804i | ||||||||
\(309\) | − | 1.17762e12i | − | 0.418036i | ||||||
\(310\) | −9.64314e12 | −3.36830 | ||||||||
\(311\) | 4.06893e12 | 1.39855 | 0.699276 | − | 0.714852i | \(-0.253506\pi\) | ||||
0.699276 | + | 0.714852i | \(0.253506\pi\) | |||||||
\(312\) | −1.00141e13 | −3.38717 | ||||||||
\(313\) | 3.98362e12i | 1.32604i | 0.748602 | + | 0.663020i | \(0.230725\pi\) | ||||
−0.748602 | + | 0.663020i | \(0.769275\pi\) | |||||||
\(314\) | −4.71480e11 | −0.154460 | ||||||||
\(315\) | −1.06346e12 | −0.342899 | ||||||||
\(316\) | 3.56670e12 | 1.13196 | ||||||||
\(317\) | −1.46358e12 | −0.457216 | −0.228608 | − | 0.973519i | \(-0.573417\pi\) | ||||
−0.228608 | + | 0.973519i | \(0.573417\pi\) | |||||||
\(318\) | 1.18204e12i | 0.363492i | ||||||||
\(319\) | − | 8.45793e12i | − | 2.56042i | ||||||
\(320\) | −2.31352e13 | −6.89483 | ||||||||
\(321\) | −2.32905e12 | −0.683367 | ||||||||
\(322\) | −7.76069e12 | −2.24192 | ||||||||
\(323\) | 2.18888e12 | 0.622601 | ||||||||
\(324\) | −1.16352e12 | −0.325874 | ||||||||
\(325\) | 1.56054e12i | 0.430386i | ||||||||
\(326\) | 8.84993e12i | 2.40354i | ||||||||
\(327\) | − | 1.60794e12i | − | 0.430063i | ||||||
\(328\) | − | 8.70772e12i | − | 2.29369i | ||||||
\(329\) | − | 4.78288e12i | − | 1.24082i | ||||||
\(330\) | 8.54000e12 | 2.18217 | ||||||||
\(331\) | 3.84998e12 | 0.968989 | 0.484495 | − | 0.874794i | \(-0.339003\pi\) | ||||
0.484495 | + | 0.874794i | \(0.339003\pi\) | |||||||
\(332\) | 8.02279e12i | 1.98900i | ||||||||
\(333\) | − | 1.22927e12i | − | 0.300211i | ||||||
\(334\) | 3.31589e12i | 0.797753i | ||||||||
\(335\) | 4.53941e11i | 0.107591i | ||||||||
\(336\) | 1.04912e13 | 2.44978 | ||||||||
\(337\) | − | 2.99149e12i | − | 0.688236i | −0.938926 | − | 0.344118i | \(-0.888178\pi\) | ||
0.938926 | − | 0.344118i | \(-0.111822\pi\) | |||||||
\(338\) | − | 1.17451e13i | − | 2.66240i | ||||||
\(339\) | − | 3.78917e12i | − | 0.846342i | ||||||
\(340\) | 8.36930e12 | 1.84202 | ||||||||
\(341\) | −1.16494e13 | −2.52658 | ||||||||
\(342\) | − | 3.47040e12i | − | 0.741736i | ||||||
\(343\) | 5.06563e12 | 1.06700 | ||||||||
\(344\) | 1.19619e13 | 2.48318 | ||||||||
\(345\) | 3.97311e12i | 0.812896i | ||||||||
\(346\) | −4.60187e12 | −0.928012 | ||||||||
\(347\) | 3.80325e12i | 0.755974i | 0.925811 | + | 0.377987i | \(0.123384\pi\) | ||||
−0.925811 | + | 0.377987i | \(0.876616\pi\) | |||||||
\(348\) | −1.31417e13 | −2.57488 | ||||||||
\(349\) | 4.05477e12i | 0.783139i | 0.920148 | + | 0.391570i | \(0.128068\pi\) | ||||
−0.920148 | + | 0.391570i | \(0.871932\pi\) | |||||||
\(350\) | − | 2.66189e12i | − | 0.506816i | ||||||
\(351\) | − | 1.56926e12i | − | 0.294550i | ||||||
\(352\) | −4.93702e13 | −9.13590 | ||||||||
\(353\) | − | 8.59729e12i | − | 1.56851i | −0.620437 | − | 0.784257i | \(-0.713045\pi\) | ||
0.620437 | − | 0.784257i | \(-0.286955\pi\) | |||||||
\(354\) | 3.77371e12 | + | 5.12587e12i | 0.678815 | + | 0.922044i | ||||
\(355\) | 4.40912e12 | 0.782006 | ||||||||
\(356\) | 1.24682e13i | 2.18049i | ||||||||
\(357\) | −1.68832e12 | −0.291147 | ||||||||
\(358\) | 1.14239e13 | 1.94267 | ||||||||
\(359\) | −4.33032e12 | −0.726186 | −0.363093 | − | 0.931753i | \(-0.618279\pi\) | ||||
−0.363093 | + | 0.931753i | \(0.618279\pi\) | |||||||
\(360\) | − | 8.74493e12i | − | 1.44625i | ||||||
\(361\) | 1.58805e12 | 0.259017 | ||||||||
\(362\) | 2.26306e12i | 0.364044i | ||||||||
\(363\) | 6.67785e12 | 1.05951 | ||||||||
\(364\) | 2.60687e13i | 4.07955i | ||||||||
\(365\) | − | 8.14539e12i | − | 1.25733i | ||||||
\(366\) | −7.35735e12 | −1.12025 | ||||||||
\(367\) | 3.71511e12i | 0.558009i | 0.960290 | + | 0.279004i | \(0.0900044\pi\) | ||||
−0.960290 | + | 0.279004i | \(0.909996\pi\) | |||||||
\(368\) | − | 3.91954e13i | − | 5.80758i | ||||||
\(369\) | 1.36455e12 | 0.199461 | ||||||||
\(370\) | 1.40191e13 | 2.02167 | ||||||||
\(371\) | 2.02792e12 | 0.288523 | ||||||||
\(372\) | 1.81006e13i | 2.54085i | ||||||||
\(373\) | −5.40807e12 | −0.749028 | −0.374514 | − | 0.927221i | \(-0.622190\pi\) | ||||
−0.374514 | + | 0.927221i | \(0.622190\pi\) | |||||||
\(374\) | 1.35579e13 | 1.85282 | ||||||||
\(375\) | 3.48347e12 | 0.469738 | ||||||||
\(376\) | 3.93302e13 | 5.23344 | ||||||||
\(377\) | − | 1.77245e13i | − | 2.32737i | ||||||
\(378\) | 2.67677e12i | 0.346858i | ||||||||
\(379\) | −5.39111e12 | −0.689418 | −0.344709 | − | 0.938710i | \(-0.612022\pi\) | ||||
−0.344709 | + | 0.938710i | \(0.612022\pi\) | |||||||
\(380\) | 2.95144e13 | 3.72492 | ||||||||
\(381\) | −8.41462e11 | −0.104812 | ||||||||
\(382\) | −2.44635e12 | −0.300747 | ||||||||
\(383\) | 2.79998e12 | 0.339752 | 0.169876 | − | 0.985465i | \(-0.445663\pi\) | ||||
0.169876 | + | 0.985465i | \(0.445663\pi\) | |||||||
\(384\) | 3.20770e13i | 3.84183i | ||||||||
\(385\) | − | 1.46513e13i | − | 1.73210i | ||||||
\(386\) | 1.45696e13i | 1.70025i | ||||||||
\(387\) | 1.87450e12i | 0.215939i | ||||||||
\(388\) | − | 1.91469e13i | − | 2.17741i | ||||||
\(389\) | −6.90292e12 | −0.774970 | −0.387485 | − | 0.921876i | \(-0.626656\pi\) | ||||
−0.387485 | + | 0.921876i | \(0.626656\pi\) | |||||||
\(390\) | 1.78964e13 | 1.98355 | ||||||||
\(391\) | 6.30761e12i | 0.690209i | ||||||||
\(392\) | 6.17501e12i | 0.667125i | ||||||||
\(393\) | − | 4.94846e12i | − | 0.527846i | ||||||
\(394\) | − | 1.64870e13i | − | 1.73644i | ||||||
\(395\) | −4.20081e12 | −0.436866 | ||||||||
\(396\) | − | 1.60300e13i | − | 1.64610i | ||||||
\(397\) | − | 5.45035e12i | − | 0.552678i | −0.961060 | − | 0.276339i | \(-0.910879\pi\) | ||
0.961060 | − | 0.276339i | \(-0.0891212\pi\) | |||||||
\(398\) | 3.85678e13i | 3.86198i | ||||||||
\(399\) | −5.95386e12 | −0.588755 | ||||||||
\(400\) | 1.34439e13 | 1.31288 | ||||||||
\(401\) | − | 1.49009e12i | − | 0.143711i | −0.997415 | − | 0.0718557i | \(-0.977108\pi\) | ||
0.997415 | − | 0.0718557i | \(-0.0228921\pi\) | |||||||
\(402\) | 1.14259e12 | 0.108833 | ||||||||
\(403\) | −2.44126e13 | −2.29662 | ||||||||
\(404\) | 1.68248e13i | 1.56331i | ||||||||
\(405\) | 1.37038e12 | 0.125767 | ||||||||
\(406\) | 3.02335e13i | 2.74068i | ||||||||
\(407\) | 1.69358e13 | 1.51647 | ||||||||
\(408\) | − | 1.38832e13i | − | 1.22798i | ||||||
\(409\) | 8.65719e12i | 0.756415i | 0.925721 | + | 0.378208i | \(0.123459\pi\) | ||||
−0.925721 | + | 0.378208i | \(0.876541\pi\) | |||||||
\(410\) | 1.55619e13i | 1.34320i | ||||||||
\(411\) | 6.30792e12 | 0.537869 | ||||||||
\(412\) | − | 2.52088e13i | − | 2.12357i | ||||||
\(413\) | 8.79401e12 | − | 6.47422e12i | 0.731875 | − | 0.538812i | ||||
\(414\) | 1.00005e13 | 0.822281 | ||||||||
\(415\) | − | 9.44913e12i | − | 0.767629i | ||||||
\(416\) | −1.03460e14 | −8.30438 | ||||||||
\(417\) | −9.17773e12 | −0.727872 | ||||||||
\(418\) | 4.78121e13 | 3.74676 | ||||||||
\(419\) | 1.38750e13i | 1.07439i | 0.843458 | + | 0.537196i | \(0.180516\pi\) | ||||
−0.843458 | + | 0.537196i | \(0.819484\pi\) | |||||||
\(420\) | −2.27649e13 | −1.74188 | ||||||||
\(421\) | − | 1.17891e13i | − | 0.891397i | −0.895183 | − | 0.445699i | \(-0.852955\pi\) | ||
0.895183 | − | 0.445699i | \(-0.147045\pi\) | |||||||
\(422\) | 2.21154e13 | 1.65247 | ||||||||
\(423\) | 6.16327e12i | 0.455103i | ||||||||
\(424\) | 1.66758e13i | 1.21691i | ||||||||
\(425\) | −2.16349e12 | −0.156031 | ||||||||
\(426\) | − | 1.10980e13i | − | 0.791034i | ||||||
\(427\) | 1.26224e13i | 0.889204i | ||||||||
\(428\) | −4.98570e13 | −3.47142 | ||||||||
\(429\) | 2.16199e13 | 1.48787 | ||||||||
\(430\) | −2.13775e13 | −1.45417 | ||||||||
\(431\) | − | 8.12118e12i | − | 0.546051i | −0.962007 | − | 0.273025i | \(-0.911976\pi\) | ||
0.962007 | − | 0.273025i | \(-0.0880243\pi\) | |||||||
\(432\) | −1.35190e13 | −0.898518 | ||||||||
\(433\) | −1.62737e13 | −1.06917 | −0.534585 | − | 0.845114i | \(-0.679532\pi\) | ||||
−0.534585 | + | 0.845114i | \(0.679532\pi\) | |||||||
\(434\) | 4.16418e13 | 2.70446 | ||||||||
\(435\) | 1.54782e13 | 0.993740 | ||||||||
\(436\) | − | 3.44205e13i | − | 2.18467i | ||||||
\(437\) | 2.22438e13i | 1.39573i | ||||||||
\(438\) | −2.05023e13 | −1.27184 | ||||||||
\(439\) | 2.87183e11 | 0.0176131 | 0.00880655 | − | 0.999961i | \(-0.497197\pi\) | ||||
0.00880655 | + | 0.999961i | \(0.497197\pi\) | |||||||
\(440\) | 1.20480e14 | 7.30551 | ||||||||
\(441\) | −9.67660e11 | −0.0580136 | ||||||||
\(442\) | 2.84120e13 | 1.68418 | ||||||||
\(443\) | − | 2.13237e13i | − | 1.24981i | −0.780700 | − | 0.624906i | \(-0.785137\pi\) | ||
0.780700 | − | 0.624906i | \(-0.214863\pi\) | |||||||
\(444\) | − | 2.63144e13i | − | 1.52503i | ||||||
\(445\) | − | 1.46849e13i | − | 0.841530i | ||||||
\(446\) | − | 6.09927e12i | − | 0.345624i | ||||||
\(447\) | 1.65120e12i | 0.0925257i | ||||||||
\(448\) | 9.99043e13 | 5.53597 | ||||||||
\(449\) | −6.85125e12 | −0.375438 | −0.187719 | − | 0.982223i | \(-0.560109\pi\) | ||||
−0.187719 | + | 0.982223i | \(0.560109\pi\) | |||||||
\(450\) | 3.43015e12i | 0.185887i | ||||||||
\(451\) | 1.87995e13i | 1.00755i | ||||||||
\(452\) | − | 8.11130e13i | − | 4.29931i | ||||||
\(453\) | 1.77719e13i | 0.931629i | ||||||||
\(454\) | 1.25019e13 | 0.648181 | ||||||||
\(455\) | − | 3.07034e13i | − | 1.57445i | ||||||
\(456\) | − | 4.89593e13i | − | 2.48320i | ||||||
\(457\) | − | 2.16366e13i | − | 1.08544i | −0.839912 | − | 0.542722i | \(-0.817394\pi\) | ||
0.839912 | − | 0.542722i | \(-0.182606\pi\) | |||||||
\(458\) | 1.23103e13 | 0.610860 | ||||||||
\(459\) | 2.17558e12 | 0.106785 | ||||||||
\(460\) | 8.50505e13i | 4.12941i | ||||||||
\(461\) | −2.85231e13 | −1.36991 | −0.684954 | − | 0.728586i | \(-0.740178\pi\) | ||||
−0.684954 | + | 0.728586i | \(0.740178\pi\) | |||||||
\(462\) | −3.68781e13 | −1.75210 | ||||||||
\(463\) | − | 2.28437e13i | − | 1.07365i | −0.843695 | − | 0.536823i | \(-0.819624\pi\) | ||
0.843695 | − | 0.536823i | \(-0.180376\pi\) | |||||||
\(464\) | −1.52695e14 | −7.09959 | ||||||||
\(465\) | − | 2.13187e13i | − | 0.980607i | ||||||
\(466\) | −2.93715e13 | −1.33658 | ||||||||
\(467\) | − | 2.57417e13i | − | 1.15892i | −0.815001 | − | 0.579460i | \(-0.803264\pi\) | ||
0.815001 | − | 0.579460i | \(-0.196736\pi\) | |||||||
\(468\) | − | 3.35924e13i | − | 1.49628i | ||||||
\(469\) | − | 1.96025e12i | − | 0.0863866i | ||||||
\(470\) | −7.02884e13 | −3.06474 | ||||||||
\(471\) | − | 1.04233e12i | − | 0.0449676i | ||||||
\(472\) | 5.32383e13 | + | 7.23143e13i | 2.27255 | + | 3.08684i | ||||
\(473\) | −2.58252e13 | −1.09078 | ||||||||
\(474\) | 1.05737e13i | 0.441910i | ||||||||
\(475\) | −7.62958e12 | −0.315524 | ||||||||
\(476\) | −3.61410e13 | −1.47899 | ||||||||
\(477\) | −2.61319e12 | −0.105823 | ||||||||
\(478\) | − | 8.52953e13i | − | 3.41811i | ||||||
\(479\) | 2.39832e13 | 0.951109 | 0.475554 | − | 0.879686i | \(-0.342247\pi\) | ||||
0.475554 | + | 0.879686i | \(0.342247\pi\) | |||||||
\(480\) | − | 9.03483e13i | − | 3.54580i | ||||||
\(481\) | 3.54906e13 | 1.37844 | ||||||||
\(482\) | 2.33686e13i | 0.898252i | ||||||||
\(483\) | − | 1.71570e13i | − | 0.652688i | ||||||
\(484\) | 1.42950e14 | 5.38216 | ||||||||
\(485\) | 2.25510e13i | 0.840344i | ||||||||
\(486\) | − | 3.44931e12i | − | 0.127219i | ||||||
\(487\) | −4.35984e13 | −1.59157 | −0.795785 | − | 0.605579i | \(-0.792942\pi\) | ||||
−0.795785 | + | 0.605579i | \(0.792942\pi\) | |||||||
\(488\) | −1.03795e14 | −3.75041 | ||||||||
\(489\) | −1.95650e13 | −0.699740 | ||||||||
\(490\) | − | 1.10356e13i | − | 0.390674i | ||||||
\(491\) | 1.82138e13 | 0.638253 | 0.319126 | − | 0.947712i | \(-0.396611\pi\) | ||||
0.319126 | + | 0.947712i | \(0.396611\pi\) | |||||||
\(492\) | 2.92103e13 | 1.01324 | ||||||||
\(493\) | 2.45727e13 | 0.843760 | ||||||||
\(494\) | 1.00195e14 | 3.40574 | ||||||||
\(495\) | 1.88799e13i | 0.635291i | ||||||||
\(496\) | 2.10312e14i | 7.00576i | ||||||||
\(497\) | −1.90398e13 | −0.627886 | ||||||||
\(498\) | −2.37839e13 | −0.776491 | ||||||||
\(499\) | −1.37633e13 | −0.444858 | −0.222429 | − | 0.974949i | \(-0.571399\pi\) | ||||
−0.222429 | + | 0.974949i | \(0.571399\pi\) | |||||||
\(500\) | 7.45690e13 | 2.38621 | ||||||||
\(501\) | −7.33064e12 | −0.232249 | ||||||||
\(502\) | − | 2.64567e13i | − | 0.829884i | ||||||
\(503\) | 5.90065e13i | 1.83257i | 0.400529 | + | 0.916284i | \(0.368827\pi\) | ||||
−0.400529 | + | 0.916284i | \(0.631173\pi\) | |||||||
\(504\) | 3.77630e13i | 1.16122i | ||||||||
\(505\) | − | 1.98161e13i | − | 0.603337i | ||||||
\(506\) | 1.37778e14i | 4.15362i | ||||||||
\(507\) | 2.59656e13 | 0.775102 | ||||||||
\(508\) | −1.80128e13 | −0.532430 | ||||||||
\(509\) | − | 2.78998e13i | − | 0.816606i | −0.912846 | − | 0.408303i | \(-0.866121\pi\) | ||
0.912846 | − | 0.408303i | \(-0.133879\pi\) | |||||||
\(510\) | 2.48112e13i | 0.719112i | ||||||||
\(511\) | 3.51741e13i | 1.00953i | ||||||||
\(512\) | 2.61628e14i | 7.43593i | ||||||||
\(513\) | 7.67221e12 | 0.215940 | ||||||||
\(514\) | 1.04879e14i | 2.92330i | ||||||||
\(515\) | 2.96906e13i | 0.819564i | ||||||||
\(516\) | 4.01266e13i | 1.09694i | ||||||||
\(517\) | −8.49120e13 | −2.29888 | ||||||||
\(518\) | −6.05382e13 | −1.62323 | ||||||||
\(519\) | − | 1.01736e13i | − | 0.270171i | ||||||
\(520\) | 2.52478e14 | 6.64058 | ||||||||
\(521\) | −2.12484e12 | −0.0553526 | −0.0276763 | − | 0.999617i | \(-0.508811\pi\) | ||||
−0.0276763 | + | 0.999617i | \(0.508811\pi\) | |||||||
\(522\) | − | 3.89593e13i | − | 1.00521i | ||||||
\(523\) | 6.37536e12 | 0.162928 | 0.0814641 | − | 0.996676i | \(-0.474040\pi\) | ||||
0.0814641 | + | 0.996676i | \(0.474040\pi\) | |||||||
\(524\) | − | 1.05929e14i | − | 2.68139i | ||||||
\(525\) | 5.88480e12 | 0.147549 | ||||||||
\(526\) | 5.63750e13i | 1.40010i | ||||||||
\(527\) | − | 3.38450e13i | − | 0.832609i | ||||||
\(528\) | − | 1.86253e14i | − | 4.53872i | ||||||
\(529\) | −2.26726e13 | −0.547298 | ||||||||
\(530\) | − | 2.98019e13i | − | 0.712630i | ||||||
\(531\) | −1.13321e13 | + | 8.34275e12i | −0.268433 | + | 0.197623i | ||||
\(532\) | −1.27452e14 | −2.99080 | ||||||||
\(533\) | 3.93964e13i | 0.915841i | ||||||||
\(534\) | −3.69625e13 | −0.851246 | ||||||||
\(535\) | 5.87209e13 | 1.33975 | ||||||||
\(536\) | 1.61193e13 | 0.364354 | ||||||||
\(537\) | 2.52555e13i | 0.565567i | ||||||||
\(538\) | 5.11274e13 | 1.13434 | ||||||||
\(539\) | − | 1.33315e13i | − | 0.293047i | ||||||
\(540\) | 2.93351e13 | 0.638879 | ||||||||
\(541\) | − | 2.78098e13i | − | 0.600084i | −0.953926 | − | 0.300042i | \(-0.902999\pi\) | ||
0.953926 | − | 0.300042i | \(-0.0970007\pi\) | |||||||
\(542\) | 9.10500e13i | 1.94663i | ||||||||
\(543\) | −5.00308e12 | −0.105984 | ||||||||
\(544\) | − | 1.43435e14i | − | 3.01065i | ||||||
\(545\) | 4.05400e13i | 0.843144i | ||||||||
\(546\) | −7.72819e13 | −1.59263 | ||||||||
\(547\) | 2.91420e13 | 0.595090 | 0.297545 | − | 0.954708i | \(-0.403832\pi\) | ||||
0.297545 | + | 0.954708i | \(0.403832\pi\) | |||||||
\(548\) | 1.35031e14 | 2.73231 | ||||||||
\(549\) | − | 1.62653e13i | − | 0.326138i | ||||||
\(550\) | −4.72575e13 | −0.938981 | ||||||||
\(551\) | 8.66560e13 | 1.70624 | ||||||||
\(552\) | 1.41084e14 | 2.75285 | ||||||||
\(553\) | 1.81403e13 | 0.350767 | ||||||||
\(554\) | 8.91257e13i | 1.70787i | ||||||||
\(555\) | 3.09927e13i | 0.588566i | ||||||||
\(556\) | −1.96463e14 | −3.69750 | ||||||||
\(557\) | −1.00678e14 | −1.87784 | −0.938918 | − | 0.344141i | \(-0.888170\pi\) | ||||
−0.938918 | + | 0.344141i | \(0.888170\pi\) | |||||||
\(558\) | −5.36601e13 | −0.991928 | ||||||||
\(559\) | −5.41193e13 | −0.991501 | ||||||||
\(560\) | −2.64507e14 | −4.80282 | ||||||||
\(561\) | 2.99732e13i | 0.539410i | ||||||||
\(562\) | − | 7.47540e13i | − | 1.33338i | ||||||
\(563\) | − | 8.71239e13i | − | 1.54027i | −0.637884 | − | 0.770133i | \(-0.720190\pi\) | ||
0.637884 | − | 0.770133i | \(-0.279810\pi\) | |||||||
\(564\) | 1.31934e14i | 2.31186i | ||||||||
\(565\) | 9.55338e13i | 1.65926i | ||||||||
\(566\) | −4.75762e13 | −0.819044 | ||||||||
\(567\) | −5.91769e12 | −0.100980 | ||||||||
\(568\) | − | 1.56567e14i | − | 2.64824i | ||||||
\(569\) | 3.85604e13i | 0.646517i | 0.946311 | + | 0.323258i | \(0.104778\pi\) | ||||
−0.946311 | + | 0.323258i | \(0.895222\pi\) | |||||||
\(570\) | 8.74969e13i | 1.45418i | ||||||||
\(571\) | 2.61452e13i | 0.430736i | 0.976533 | + | 0.215368i | \(0.0690952\pi\) | ||||
−0.976533 | + | 0.215368i | \(0.930905\pi\) | |||||||
\(572\) | 4.62806e14 | 7.55821 | ||||||||
\(573\) | − | 5.40828e12i | − | 0.0875560i | ||||||
\(574\) | − | 6.72004e13i | − | 1.07848i | ||||||
\(575\) | − | 2.19858e13i | − | 0.349787i | ||||||
\(576\) | −1.28738e14 | −2.03046 | ||||||||
\(577\) | 3.06953e13 | 0.479947 | 0.239973 | − | 0.970779i | \(-0.422861\pi\) | ||||
0.239973 | + | 0.970779i | \(0.422861\pi\) | |||||||
\(578\) | − | 8.85467e13i | − | 1.37257i | ||||||
\(579\) | −3.22099e13 | −0.494991 | ||||||||
\(580\) | 3.31334e14 | 5.04807 | ||||||||
\(581\) | 4.08040e13i | 0.616342i | ||||||||
\(582\) | 5.67620e13 | 0.850046 | ||||||||
\(583\) | − | 3.60022e13i | − | 0.534548i | ||||||
\(584\) | −2.89241e14 | −4.25790 | ||||||||
\(585\) | 3.95647e13i | 0.577469i | ||||||||
\(586\) | 2.24527e14i | 3.24924i | ||||||||
\(587\) | − | 2.54401e13i | − | 0.365029i | −0.983203 | − | 0.182515i | \(-0.941576\pi\) | ||
0.983203 | − | 0.182515i | \(-0.0584237\pi\) | |||||||
\(588\) | −2.07143e13 | −0.294702 | ||||||||
\(589\) | − | 1.19355e14i | − | 1.68369i | ||||||
\(590\) | −9.51439e13 | − | 1.29235e14i | −1.33082 | − | 1.80768i | ||||
\(591\) | 3.64487e13 | 0.505527 | ||||||||
\(592\) | − | 3.05748e14i | − | 4.20490i | ||||||
\(593\) | 1.36225e13 | 0.185773 | 0.0928864 | − | 0.995677i | \(-0.470391\pi\) | ||||
0.0928864 | + | 0.995677i | \(0.470391\pi\) | |||||||
\(594\) | 4.75215e13 | 0.642626 | ||||||||
\(595\) | 4.25664e13 | 0.570797 | ||||||||
\(596\) | 3.53465e13i | 0.470019i | ||||||||
\(597\) | −8.52641e13 | −1.12433 | ||||||||
\(598\) | 2.88728e14i | 3.77557i | ||||||||
\(599\) | 1.16474e14 | 1.51041 | 0.755205 | − | 0.655489i | \(-0.227537\pi\) | ||||
0.755205 | + | 0.655489i | \(0.227537\pi\) | |||||||
\(600\) | 4.83915e13i | 0.622318i | ||||||||
\(601\) | − | 1.07353e14i | − | 1.36912i | −0.728956 | − | 0.684560i | \(-0.759994\pi\) | ||
0.728956 | − | 0.684560i | \(-0.240006\pi\) | |||||||
\(602\) | 9.23141e13 | 1.16758 | ||||||||
\(603\) | 2.52599e12i | 0.0316844i | ||||||||
\(604\) | 3.80435e14i | 4.73255i | ||||||||
\(605\) | −1.68364e14 | −2.07717 | ||||||||
\(606\) | −4.98780e13 | −0.610303 | ||||||||
\(607\) | −8.44133e13 | −1.02440 | −0.512198 | − | 0.858868i | \(-0.671168\pi\) | ||||
−0.512198 | + | 0.858868i | \(0.671168\pi\) | |||||||
\(608\) | − | 5.05824e14i | − | 6.08810i | ||||||
\(609\) | −6.68390e13 | −0.797891 | ||||||||
\(610\) | 1.85496e14 | 2.19627 | ||||||||
\(611\) | −1.77942e14 | −2.08964 | ||||||||
\(612\) | 4.65717e13 | 0.542456 | ||||||||
\(613\) | 9.06076e13i | 1.04680i | 0.852088 | + | 0.523398i | \(0.175336\pi\) | ||||
−0.852088 | + | 0.523398i | \(0.824664\pi\) | |||||||
\(614\) | − | 1.39869e13i | − | 0.160280i | ||||||
\(615\) | −3.44035e13 | −0.391045 | ||||||||
\(616\) | −5.20265e14 | −5.86572 | ||||||||
\(617\) | −1.24220e14 | −1.38920 | −0.694599 | − | 0.719397i | \(-0.744418\pi\) | ||||
−0.694599 | + | 0.719397i | \(0.744418\pi\) | |||||||
\(618\) | 7.47327e13 | 0.829026 | ||||||||
\(619\) | −2.99465e13 | −0.329528 | −0.164764 | − | 0.986333i | \(-0.552686\pi\) | ||||
−0.164764 | + | 0.986333i | \(0.552686\pi\) | |||||||
\(620\) | − | 4.56359e14i | − | 4.98136i | ||||||
\(621\) | 2.21087e13i | 0.239389i | ||||||||
\(622\) | 2.58217e14i | 2.77353i | ||||||||
\(623\) | 6.34133e13i | 0.675679i | ||||||||
\(624\) | − | 3.90312e14i | − | 4.12562i | ||||||
\(625\) | −1.14644e14 | −1.20213 | ||||||||
\(626\) | −2.52803e14 | −2.62973 | ||||||||
\(627\) | 1.05701e14i | 1.09079i | ||||||||
\(628\) | − | 2.23126e13i | − | 0.228430i | ||||||
\(629\) | 4.92033e13i | 0.499737i | ||||||||
\(630\) | − | 6.74876e13i | − | 0.680019i | ||||||
\(631\) | 7.50471e13 | 0.750218 | 0.375109 | − | 0.926981i | \(-0.377605\pi\) | ||||
0.375109 | + | 0.926981i | \(0.377605\pi\) | |||||||
\(632\) | 1.49170e14i | 1.47943i | ||||||||
\(633\) | 4.88918e13i | 0.481080i | ||||||||
\(634\) | − | 9.28800e13i | − | 0.906726i | ||||||
\(635\) | 2.12152e13 | 0.205484 | ||||||||
\(636\) | −5.59394e13 | −0.537567 | ||||||||
\(637\) | − | 2.79376e13i | − | 0.266374i | ||||||
\(638\) | 5.36746e14 | 5.07768 | ||||||||
\(639\) | 2.45349e13 | 0.230293 | ||||||||
\(640\) | − | 8.08736e14i | − | 7.53194i | ||||||
\(641\) | 1.27671e14 | 1.17978 | 0.589890 | − | 0.807484i | \(-0.299171\pi\) | ||||
0.589890 | + | 0.807484i | \(0.299171\pi\) | |||||||
\(642\) | − | 1.47803e14i | − | 1.35522i | ||||||
\(643\) | −1.71159e14 | −1.55720 | −0.778599 | − | 0.627522i | \(-0.784069\pi\) | ||||
−0.778599 | + | 0.627522i | \(0.784069\pi\) | |||||||
\(644\) | − | 3.67272e14i | − | 3.31557i | ||||||
\(645\) | − | 4.72605e13i | − | 0.423350i | ||||||
\(646\) | 1.38908e14i | 1.23471i | ||||||||
\(647\) | −2.06196e14 | −1.81869 | −0.909346 | − | 0.416041i | \(-0.863417\pi\) | ||||
−0.909346 | + | 0.416041i | \(0.863417\pi\) | |||||||
\(648\) | − | 4.86619e13i | − | 0.425906i | ||||||
\(649\) | −1.14939e14 | − | 1.56123e14i | −0.998259 | − | 1.35595i | ||||
\(650\) | −9.90329e13 | −0.853518 | ||||||||
\(651\) | 9.20599e13i | 0.787346i | ||||||||
\(652\) | −4.18820e14 | −3.55459 | ||||||||
\(653\) | 6.59315e13 | 0.555299 | 0.277650 | − | 0.960682i | \(-0.410445\pi\) | ||||
0.277650 | + | 0.960682i | \(0.410445\pi\) | |||||||
\(654\) | 1.02041e14 | 0.852878 | ||||||||
\(655\) | 1.24762e14i | 1.03485i | ||||||||
\(656\) | 3.39396e14 | 2.79375 | ||||||||
\(657\) | − | 4.53257e13i | − | 0.370269i | ||||||
\(658\) | 3.03525e14 | 2.46073 | ||||||||
\(659\) | − | 4.23653e13i | − | 0.340866i | −0.985369 | − | 0.170433i | \(-0.945483\pi\) | ||
0.985369 | − | 0.170433i | \(-0.0545166\pi\) | |||||||
\(660\) | 4.04153e14i | 3.22720i | ||||||||
\(661\) | 5.82687e13 | 0.461772 | 0.230886 | − | 0.972981i | \(-0.425837\pi\) | ||||
0.230886 | + | 0.972981i | \(0.425837\pi\) | |||||||
\(662\) | 2.44323e14i | 1.92165i | ||||||||
\(663\) | 6.28119e13i | 0.490314i | ||||||||
\(664\) | −3.35536e14 | −2.59955 | ||||||||
\(665\) | 1.50111e14 | 1.15426 | ||||||||
\(666\) | 7.80102e13 | 0.595361 | ||||||||
\(667\) | 2.49713e14i | 1.89152i | ||||||||
\(668\) | −1.56924e14 | −1.17979 | ||||||||
\(669\) | 1.34840e13 | 0.100621 | ||||||||
\(670\) | −2.88074e13 | −0.213368 | ||||||||
\(671\) | 2.24089e14 | 1.64743 | ||||||||
\(672\) | 3.90149e14i | 2.84698i | ||||||||
\(673\) | 2.60802e13i | 0.188901i | 0.995530 | + | 0.0944507i | \(0.0301095\pi\) | ||||
−0.995530 | + | 0.0944507i | \(0.969891\pi\) | |||||||
\(674\) | 1.89842e14 | 1.36487 | ||||||||
\(675\) | −7.58322e12 | −0.0541171 | ||||||||
\(676\) | 5.55834e14 | 3.93742 | ||||||||
\(677\) | 3.97353e13 | 0.279405 | 0.139702 | − | 0.990194i | \(-0.455385\pi\) | ||||
0.139702 | + | 0.990194i | \(0.455385\pi\) | |||||||
\(678\) | 2.40463e14 | 1.67842 | ||||||||
\(679\) | − | 9.73816e13i | − | 0.674727i | ||||||
\(680\) | 3.50028e14i | 2.40746i | ||||||||
\(681\) | 2.76387e13i | 0.188704i | ||||||||
\(682\) | − | 7.39280e14i | − | 5.01057i | ||||||
\(683\) | 9.13519e13i | 0.614630i | 0.951608 | + | 0.307315i | \(0.0994306\pi\) | ||||
−0.951608 | + | 0.307315i | \(0.900569\pi\) | |||||||
\(684\) | 1.64236e14 | 1.09695 | ||||||||
\(685\) | −1.59037e14 | −1.05450 | ||||||||
\(686\) | 3.21468e14i | 2.11601i | ||||||||
\(687\) | 2.72151e13i | 0.177839i | ||||||||
\(688\) | 4.66233e14i | 3.02455i | ||||||||
\(689\) | − | 7.54464e13i | − | 0.485895i | ||||||
\(690\) | −2.52136e14 | −1.61209 | ||||||||
\(691\) | − | 1.66013e13i | − | 0.105378i | −0.998611 | − | 0.0526892i | \(-0.983221\pi\) | ||
0.998611 | − | 0.0526892i | \(-0.0167793\pi\) | |||||||
\(692\) | − | 2.17782e14i | − | 1.37243i | ||||||
\(693\) | − | 8.15286e13i | − | 0.510086i | ||||||
\(694\) | −2.41356e14 | −1.49921 | ||||||||
\(695\) | 2.31392e14 | 1.42700 | ||||||||
\(696\) | − | 5.49625e14i | − | 3.36528i | ||||||
\(697\) | −5.46181e13 | −0.332027 | ||||||||
\(698\) | −2.57318e14 | −1.55308 | ||||||||
\(699\) | − | 6.49333e13i | − | 0.389118i | ||||||
\(700\) | 1.25973e14 | 0.749529 | ||||||||
\(701\) | − | 7.36214e13i | − | 0.434924i | −0.976069 | − | 0.217462i | \(-0.930222\pi\) | ||
0.976069 | − | 0.217462i | \(-0.0697779\pi\) | |||||||
\(702\) | 9.95863e13 | 0.584136 | ||||||||
\(703\) | 1.73516e14i | 1.01056i | ||||||||
\(704\) | − | 1.77363e15i | − | 10.2565i | ||||||
\(705\) | − | 1.55391e14i | − | 0.892234i | ||||||
\(706\) | 5.45590e14 | 3.11059 | ||||||||
\(707\) | 8.55713e13i | 0.484430i | ||||||||
\(708\) | −2.42580e14 | + | 1.78589e14i | −1.36361 | + | 1.00390i | ||||
\(709\) | −7.87948e13 | −0.439811 | −0.219906 | − | 0.975521i | \(-0.570575\pi\) | ||||
−0.219906 | + | 0.975521i | \(0.570575\pi\) | |||||||
\(710\) | 2.79806e14i | 1.55083i | ||||||||
\(711\) | −2.33758e13 | −0.128652 | ||||||||
\(712\) | −5.21456e14 | −2.84982 | ||||||||
\(713\) | 3.43939e14 | 1.86653 | ||||||||
\(714\) | − | 1.07142e14i | − | 0.577387i | ||||||
\(715\) | −5.45087e14 | −2.91699 | ||||||||
\(716\) | 5.40633e14i | 2.87301i | ||||||||
\(717\) | 1.88567e14 | 0.995108 | ||||||||
\(718\) | − | 2.74805e14i | − | 1.44013i | ||||||
\(719\) | 7.23964e12i | 0.0376767i | 0.999823 | + | 0.0188383i | \(0.00599678\pi\) | ||||
−0.999823 | + | 0.0188383i | \(0.994003\pi\) | |||||||
\(720\) | 3.40846e14 | 1.76155 | ||||||||
\(721\) | − | 1.28212e14i | − | 0.658042i | ||||||
\(722\) | 1.00779e14i | 0.513669i | ||||||||
\(723\) | −5.16624e13 | −0.261507 | ||||||||
\(724\) | −1.07099e14 | −0.538383 | ||||||||
\(725\) | −8.56509e13 | −0.427604 | ||||||||
\(726\) | 4.23781e14i | 2.10116i | ||||||||
\(727\) | −1.20450e14 | −0.593111 | −0.296555 | − | 0.955016i | \(-0.595838\pi\) | ||||
−0.296555 | + | 0.955016i | \(0.595838\pi\) | |||||||
\(728\) | −1.09027e15 | −5.33184 | ||||||||
\(729\) | 7.62560e12 | 0.0370370 | ||||||||
\(730\) | 5.16912e14 | 2.49346 | ||||||||
\(731\) | − | 7.50296e13i | − | 0.359456i | ||||||
\(732\) | − | 3.48184e14i | − | 1.65674i | ||||||
\(733\) | 2.09581e14 | 0.990449 | 0.495224 | − | 0.868765i | \(-0.335086\pi\) | ||||
0.495224 | + | 0.868765i | \(0.335086\pi\) | |||||||
\(734\) | −2.35763e14 | −1.10661 | ||||||||
\(735\) | 2.43970e13 | 0.113736 | ||||||||
\(736\) | 1.45761e15 | 6.74921 | ||||||||
\(737\) | −3.48009e13 | −0.160049 | ||||||||
\(738\) | 8.65952e13i | 0.395560i | ||||||||
\(739\) | 1.83607e14i | 0.833041i | 0.909126 | + | 0.416521i | \(0.136751\pi\) | ||||
−0.909126 | + | 0.416521i | \(0.863249\pi\) | |||||||
\(740\) | 6.63448e14i | 2.98984i | ||||||||
\(741\) | 2.21507e14i | 0.991509i | ||||||||
\(742\) | 1.28693e14i | 0.572183i | ||||||||
\(743\) | 1.11239e14 | 0.491261 | 0.245631 | − | 0.969364i | \(-0.421005\pi\) | ||||
0.245631 | + | 0.969364i | \(0.421005\pi\) | |||||||
\(744\) | −7.57020e14 | −3.32080 | ||||||||
\(745\) | − | 4.16306e13i | − | 0.181398i | ||||||
\(746\) | − | 3.43200e14i | − | 1.48543i | ||||||
\(747\) | − | 5.25805e13i | − | 0.226059i | ||||||
\(748\) | 6.41623e14i | 2.74013i | ||||||||
\(749\) | −2.53573e14 | −1.07571 | ||||||||
\(750\) | 2.21063e14i | 0.931558i | ||||||||
\(751\) | − | 2.25353e12i | − | 0.00943331i | −0.999989 | − | 0.00471665i | \(-0.998499\pi\) | ||
0.999989 | − | 0.00471665i | \(-0.00150136\pi\) | |||||||
\(752\) | 1.53295e15i | 6.37440i | ||||||||
\(753\) | 5.84894e13 | 0.241603 | ||||||||
\(754\) | 1.12481e15 | 4.61552 | ||||||||
\(755\) | − | 4.48071e14i | − | 1.82647i | ||||||
\(756\) | −1.26677e14 | −0.512967 | ||||||||
\(757\) | −2.44932e14 | −0.985294 | −0.492647 | − | 0.870229i | \(-0.663971\pi\) | ||||
−0.492647 | + | 0.870229i | \(0.663971\pi\) | |||||||
\(758\) | − | 3.42124e14i | − | 1.36722i | ||||||
\(759\) | −3.04594e14 | −1.20924 | ||||||||
\(760\) | 1.23438e15i | 4.86834i | ||||||||
\(761\) | −1.44245e14 | −0.565167 | −0.282584 | − | 0.959243i | \(-0.591191\pi\) | ||||
−0.282584 | + | 0.959243i | \(0.591191\pi\) | |||||||
\(762\) | − | 5.33997e13i | − | 0.207857i | ||||||
\(763\) | − | 1.75063e14i | − | 0.676975i | ||||||
\(764\) | − | 1.15773e14i | − | 0.444773i | ||||||
\(765\) | −5.48515e13 | −0.209354 | ||||||||
\(766\) | 1.77689e14i | 0.673777i | ||||||||
\(767\) | −2.40866e14 | − | 3.27172e14i | −0.907401 | − | 1.23253i | ||||
\(768\) | −1.09599e15 | −4.10205 | ||||||||
\(769\) | − | 3.66398e14i | − | 1.36245i | −0.732073 | − | 0.681227i | \(-0.761447\pi\) | ||
0.732073 | − | 0.681227i | \(-0.238553\pi\) | |||||||
\(770\) | 9.29783e14 | 3.43501 | ||||||||
\(771\) | −2.31863e14 | −0.851057 | ||||||||
\(772\) | −6.89503e14 | −2.51449 | ||||||||
\(773\) | 8.64869e13i | 0.313367i | 0.987649 | + | 0.156683i | \(0.0500802\pi\) | ||||
−0.987649 | + | 0.156683i | \(0.949920\pi\) | |||||||
\(774\) | −1.18957e14 | −0.428238 | ||||||||
\(775\) | 1.17970e14i | 0.421953i | ||||||||
\(776\) | 8.00780e14 | 2.84580 | ||||||||
\(777\) | − | 1.33835e14i | − | 0.472570i | ||||||
\(778\) | − | 4.38064e14i | − | 1.53688i | ||||||
\(779\) | −1.92611e14 | −0.671421 | ||||||||
\(780\) | 8.46944e14i | 2.93347i | ||||||||
\(781\) | 3.38020e14i | 1.16329i | ||||||||
\(782\) | −4.00285e14 | −1.36879 | ||||||||
\(783\) | 8.61295e13 | 0.292646 | ||||||||
\(784\) | −2.40680e14 | −0.812568 | ||||||||
\(785\) | 2.62795e13i | 0.0881595i | ||||||||
\(786\) | 3.14032e14 | 1.04679 | ||||||||
\(787\) | −2.41866e14 | −0.801128 | −0.400564 | − | 0.916269i | \(-0.631186\pi\) | ||||
−0.400564 | + | 0.916269i | \(0.631186\pi\) | |||||||
\(788\) | 7.80241e14 | 2.56801 | ||||||||
\(789\) | −1.24632e14 | −0.407608 | ||||||||
\(790\) | − | 2.66586e14i | − | 0.866368i | ||||||
\(791\) | − | 4.12542e14i | − | 1.33225i | ||||||
\(792\) | 6.70419e14 | 2.15140 | ||||||||
\(793\) | 4.69601e14 | 1.49749 | ||||||||
\(794\) | 3.45883e14 | 1.09604 | ||||||||
\(795\) | 6.58847e13 | 0.207467 | ||||||||
\(796\) | −1.82521e15 | −5.71146 | ||||||||
\(797\) | − | 1.49789e14i | − | 0.465788i | −0.972502 | − | 0.232894i | \(-0.925181\pi\) | ||
0.972502 | − | 0.232894i | \(-0.0748195\pi\) | |||||||
\(798\) | − | 3.77836e14i | − | 1.16759i | ||||||
\(799\) | − | 2.46694e14i | − | 0.757574i | ||||||
\(800\) | 4.99957e14i | 1.52575i | ||||||||
\(801\) | − | 8.17151e13i | − | 0.247822i | ||||||
\(802\) | 9.45622e13 | 0.285001 | ||||||||
\(803\) | 6.24457e14 | 1.87036 | ||||||||
\(804\) | 5.40728e13i | 0.160953i | ||||||||
\(805\) | 4.32568e14i | 1.27960i | ||||||||
\(806\) | − | 1.54924e15i | − | 4.55452i | ||||||
\(807\) | 1.13030e14i | 0.330238i | ||||||||
\(808\) | −7.03663e14 | −2.04319 | ||||||||
\(809\) | − | 5.91611e13i | − | 0.170724i | −0.996350 | − | 0.0853618i | \(-0.972795\pi\) | ||
0.996350 | − | 0.0853618i | \(-0.0272046\pi\) | |||||||
\(810\) | 8.69653e13i | 0.249414i | ||||||||
\(811\) | 5.27501e14i | 1.50356i | 0.659417 | + | 0.751778i | \(0.270803\pi\) | ||||
−0.659417 | + | 0.751778i | \(0.729197\pi\) | |||||||
\(812\) | −1.43079e15 | −4.05319 | ||||||||
\(813\) | −2.01289e14 | −0.566720 | ||||||||
\(814\) | 1.07475e15i | 3.00737i | ||||||||
\(815\) | 4.93280e14 | 1.37185 | ||||||||
\(816\) | 5.41119e14 | 1.49569 | ||||||||
\(817\) | − | 2.64593e14i | − | 0.726888i | ||||||
\(818\) | −5.49391e14 | −1.50008 | ||||||||
\(819\) | − | 1.70852e14i | − | 0.463660i | ||||||
\(820\) | −7.36460e14 | −1.98646 | ||||||||
\(821\) | − | 2.45054e14i | − | 0.656971i | −0.944509 | − | 0.328485i | \(-0.893462\pi\) | ||
0.944509 | − | 0.328485i | \(-0.106538\pi\) | |||||||
\(822\) | 4.00304e14i | 1.06667i | ||||||||
\(823\) | 2.80071e14i | 0.741770i | 0.928679 | + | 0.370885i | \(0.120946\pi\) | ||||
−0.928679 | + | 0.370885i | \(0.879054\pi\) | |||||||
\(824\) | 1.05431e15 | 2.77543 | ||||||||
\(825\) | − | 1.04475e14i | − | 0.273364i | ||||||
\(826\) | 4.10858e14 | + | 5.58074e14i | 1.06854 | + | 1.45141i | ||||
\(827\) | 9.63150e13 | 0.248981 | 0.124491 | − | 0.992221i | \(-0.460270\pi\) | ||||
0.124491 | + | 0.992221i | \(0.460270\pi\) | |||||||
\(828\) | 4.73271e14i | 1.21607i | ||||||||
\(829\) | 2.75833e14 | 0.704488 | 0.352244 | − | 0.935908i | \(-0.385419\pi\) | ||||
0.352244 | + | 0.935908i | \(0.385419\pi\) | |||||||
\(830\) | 5.99648e14 | 1.52232 | ||||||||
\(831\) | −1.97035e14 | −0.497209 | ||||||||
\(832\) | − | 3.71683e15i | − | 9.32301i | ||||||
\(833\) | 3.87320e13 | 0.0965706 | ||||||||
\(834\) | − | 5.82424e14i | − | 1.44348i | ||||||
\(835\) | 1.84823e14 | 0.455326 | ||||||||
\(836\) | 2.26269e15i | 5.54107i | ||||||||
\(837\) | − | 1.18629e14i | − | 0.288779i | ||||||
\(838\) | −8.80516e14 | −2.13068 | ||||||||
\(839\) | − | 3.50659e13i | − | 0.0843482i | −0.999110 | − | 0.0421741i | \(-0.986572\pi\) | ||
0.999110 | − | 0.0421741i | \(-0.0134284\pi\) | |||||||
\(840\) | − | 9.52094e14i | − | 2.27658i | ||||||
\(841\) | 5.52107e14 | 1.31233 | ||||||||
\(842\) | 7.48146e14 | 1.76777 | ||||||||
\(843\) | 1.65263e14 | 0.388184 | ||||||||
\(844\) | 1.04660e15i | 2.44383i | ||||||||
\(845\) | −6.54654e14 | −1.51960 | ||||||||
\(846\) | −3.91125e14 | −0.902535 | ||||||||
\(847\) | 7.27044e14 | 1.66780 | ||||||||
\(848\) | −6.49963e14 | −1.48221 | ||||||||
\(849\) | − | 1.05179e14i | − | 0.238447i | ||||||
\(850\) | − | 1.37297e14i | − | 0.309432i | ||||||
\(851\) | −5.00014e14 | −1.12030 | ||||||||
\(852\) | 5.25207e14 | 1.16986 | ||||||||
\(853\) | −6.23367e14 | −1.38038 | −0.690190 | − | 0.723628i | \(-0.742473\pi\) | ||||
−0.690190 | + | 0.723628i | \(0.742473\pi\) | |||||||
\(854\) | −8.01024e14 | −1.76342 | ||||||||
\(855\) | −1.93434e14 | −0.423354 | ||||||||
\(856\) | − | 2.08516e15i | − | 4.53703i | ||||||
\(857\) | − | 1.22523e14i | − | 0.265041i | −0.991180 | − | 0.132520i | \(-0.957693\pi\) | ||
0.991180 | − | 0.132520i | \(-0.0423070\pi\) | |||||||
\(858\) | 1.37201e15i | 2.95067i | ||||||||
\(859\) | 5.99314e14i | 1.28141i | 0.767787 | + | 0.640705i | \(0.221358\pi\) | ||||
−0.767787 | + | 0.640705i | \(0.778642\pi\) | |||||||
\(860\) | − | 1.01168e15i | − | 2.15057i | ||||||
\(861\) | 1.48564e14 | 0.313977 | ||||||||
\(862\) | 5.15376e14 | 1.08290 | ||||||||
\(863\) | 3.52693e14i | 0.736789i | 0.929670 | + | 0.368395i | \(0.120092\pi\) | ||||
−0.929670 | + | 0.368395i | \(0.879908\pi\) | |||||||
\(864\) | − | 5.02751e14i | − | 1.04420i | ||||||
\(865\) | 2.56501e14i | 0.529673i | ||||||||
\(866\) | − | 1.03274e15i | − | 2.12032i | ||||||
\(867\) | 1.95755e14 | 0.399593 | ||||||||
\(868\) | 1.97068e15i | 3.99962i | ||||||||
\(869\) | − | 3.22050e14i | − | 0.649868i | ||||||
\(870\) | 9.82254e14i | 1.97073i | ||||||||
\(871\) | −7.29288e13 | −0.145482 | ||||||||
\(872\) | 1.43957e15 | 2.85528 | ||||||||
\(873\) | 1.25487e14i | 0.247473i | ||||||||
\(874\) | −1.41161e15 | −2.76794 | ||||||||
\(875\) | 3.79259e14 | 0.739427 | ||||||||
\(876\) | − | 9.70267e14i | − | 1.88092i | ||||||
\(877\) | −6.80335e14 | −1.31137 | −0.655684 | − | 0.755035i | \(-0.727620\pi\) | ||||
−0.655684 | + | 0.755035i | \(0.727620\pi\) | |||||||
\(878\) | 1.82248e13i | 0.0349293i | ||||||||
\(879\) | −4.96376e14 | −0.945945 | ||||||||
\(880\) | 4.69587e15i | 8.89821i | ||||||||
\(881\) | 8.57109e13i | 0.161494i | 0.996735 | + | 0.0807470i | \(0.0257306\pi\) | ||||
−0.996735 | + | 0.0807470i | \(0.974269\pi\) | |||||||
\(882\) | − | 6.14083e13i | − | 0.115049i | ||||||
\(883\) | −4.71583e14 | −0.878525 | −0.439263 | − | 0.898359i | \(-0.644760\pi\) | ||||
−0.439263 | + | 0.898359i | \(0.644760\pi\) | |||||||
\(884\) | 1.34459e15i | 2.49073i | ||||||||
\(885\) | 2.85708e14 | − | 2.10340e14i | 0.526266 | − | 0.387441i | ||||
\(886\) | 1.35322e15 | 2.47856 | ||||||||
\(887\) | − | 3.52580e14i | − | 0.642154i | −0.947053 | − | 0.321077i | \(-0.895955\pi\) | ||
0.947053 | − | 0.321077i | \(-0.104045\pi\) | |||||||
\(888\) | 1.10054e15 | 1.99316 | ||||||||
\(889\) | −9.16133e13 | −0.164987 | ||||||||
\(890\) | 9.31911e14 | 1.66888 | ||||||||
\(891\) | 1.05059e14i | 0.187087i | ||||||||
\(892\) | 2.88646e14 | 0.511141 | ||||||||
\(893\) | − | 8.69969e14i | − | 1.53196i | ||||||
\(894\) | −1.04786e14 | −0.183492 | ||||||||
\(895\) | − | 6.36750e14i | − | 1.10880i | ||||||
\(896\) | 3.49235e15i | 6.04753i | ||||||||
\(897\) | −6.38307e14 | −1.09918 | ||||||||
\(898\) | − | 4.34785e14i | − | 0.744548i | ||||||
\(899\) | − | 1.33989e15i | − | 2.28177i | ||||||
\(900\) | −1.62331e14 | −0.274908 | ||||||||
\(901\) | 1.04597e14 | 0.176155 | ||||||||
\(902\) | −1.19303e15 | −1.99811 | ||||||||
\(903\) | 2.04084e14i | 0.339915i | ||||||||
\(904\) | 3.39238e15 | 5.61905 | ||||||||
\(905\) | 1.26139e14 | 0.207782 | ||||||||
\(906\) | −1.12782e15 | −1.84755 | ||||||||
\(907\) | −1.17675e15 | −1.91712 | −0.958560 | − | 0.284890i | \(-0.908043\pi\) | ||||
−0.958560 | + | 0.284890i | \(0.908043\pi\) | |||||||
\(908\) | 5.91648e14i | 0.958593i | ||||||||
\(909\) | − | 1.10268e14i | − | 0.177677i | ||||||
\(910\) | 1.94846e15 | 3.12237 | ||||||||
\(911\) | −3.77793e14 | −0.602091 | −0.301045 | − | 0.953610i | \(-0.597336\pi\) | ||||
−0.301045 | + | 0.953610i | \(0.597336\pi\) | |||||||
\(912\) | 1.90826e15 | 3.02457 | ||||||||
\(913\) | 7.24406e14 | 1.14190 | ||||||||
\(914\) | 1.37307e15 | 2.15259 | ||||||||
\(915\) | 4.10087e14i | 0.639396i | ||||||||
\(916\) | 5.82581e14i | 0.903398i | ||||||||
\(917\) | − | 5.38758e14i | − | 0.830897i | ||||||
\(918\) | 1.38064e14i | 0.211771i | ||||||||
\(919\) | 1.02406e15i | 1.56225i | 0.624377 | + | 0.781123i | \(0.285353\pi\) | ||||
−0.624377 | + | 0.781123i | \(0.714647\pi\) | |||||||
\(920\) | −3.55706e15 | −5.39699 | ||||||||
\(921\) | 3.09216e13 | 0.0466621 | ||||||||
\(922\) | − | 1.81009e15i | − | 2.71673i | ||||||
\(923\) | 7.08355e14i | 1.05741i | ||||||||
\(924\) | − | 1.74524e15i | − | 2.59117i | ||||||
\(925\) | − | 1.71503e14i | − | 0.253258i | ||||||
\(926\) | 1.44967e15 | 2.12919 | ||||||||
\(927\) | 1.65216e14i | 0.241353i | ||||||||
\(928\) | − | 5.67846e15i | − | 8.25070i | ||||||
\(929\) | 5.61053e14i | 0.810822i | 0.914135 | + | 0.405411i | \(0.132872\pi\) | ||||
−0.914135 | + | 0.405411i | \(0.867128\pi\) | |||||||
\(930\) | 1.35290e15 | 1.94469 | ||||||||
\(931\) | 1.36589e14 | 0.195284 | ||||||||
\(932\) | − | 1.39000e15i | − | 1.97667i | ||||||
\(933\) | −5.70855e14 | −0.807454 | ||||||||
\(934\) | 1.63359e15 | 2.29831 | ||||||||
\(935\) | − | 7.55694e14i | − | 1.05752i | ||||||
\(936\) | 1.40493e15 | 1.95558 | ||||||||
\(937\) | − | 1.45287e14i | − | 0.201154i | −0.994929 | − | 0.100577i | \(-0.967931\pi\) | ||
0.994929 | − | 0.100577i | \(-0.0320689\pi\) | |||||||
\(938\) | 1.24398e14 | 0.171317 | ||||||||
\(939\) | − | 5.58887e14i | − | 0.765589i | ||||||
\(940\) | − | 3.32637e15i | − | 4.53244i | ||||||
\(941\) | 9.26253e14i | 1.25540i | 0.778456 | + | 0.627699i | \(0.216003\pi\) | ||||
−0.778456 | + | 0.627699i | \(0.783997\pi\) | |||||||
\(942\) | 6.61468e13 | 0.0891773 | ||||||||
\(943\) | − | 5.55040e14i | − | 0.744330i | ||||||
\(944\) | −2.81855e15 | + | 2.07504e15i | −3.75981 | + | 2.76800i | ||||
\(945\) | 1.49199e14 | 0.197973 | ||||||||
\(946\) | − | 1.63888e15i | − | 2.16318i | ||||||
\(947\) | 1.28749e15 | 1.69041 | 0.845206 | − | 0.534440i | \(-0.179477\pi\) | ||||
0.845206 | + | 0.534440i | \(0.179477\pi\) | |||||||
\(948\) | −5.00395e14 | −0.653538 | ||||||||
\(949\) | 1.30861e15 | 1.70012 | ||||||||
\(950\) | − | 4.84178e14i | − | 0.625730i | ||||||
\(951\) | 2.05335e14 | 0.263974 | ||||||||
\(952\) | − | 1.51152e15i | − | 1.93299i | ||||||
\(953\) | −1.38865e15 | −1.76656 | −0.883278 | − | 0.468849i | \(-0.844669\pi\) | ||||
−0.883278 | + | 0.468849i | \(0.844669\pi\) | |||||||
\(954\) | − | 1.65835e14i | − | 0.209862i | ||||||
\(955\) | 1.36355e14i | 0.171655i | ||||||||
\(956\) | 4.03657e15 | 5.05502 | ||||||||
\(957\) | 1.18661e15i | 1.47826i | ||||||||
\(958\) | 1.52199e15i | 1.88619i | ||||||||
\(959\) | 6.86767e14 | 0.846675 | ||||||||
\(960\) | 3.24578e15 | 3.98073 | ||||||||
\(961\) | −1.02586e15 | −1.25161 | ||||||||
\(962\) | 2.25226e15i | 2.73365i | ||||||||
\(963\) | 3.26757e14 | 0.394542 | ||||||||
\(964\) | −1.10591e15 | −1.32842 | ||||||||
\(965\) | 8.12087e14 | 0.970434 | ||||||||
\(966\) | 1.08879e15 | 1.29438 | ||||||||
\(967\) | − | 1.54240e15i | − | 1.82417i | −0.410005 | − | 0.912083i | \(-0.634473\pi\) | ||
0.410005 | − | 0.912083i | \(-0.365527\pi\) | |||||||
\(968\) | 5.97857e15i | 7.03429i | ||||||||
\(969\) | −3.07092e14 | −0.359459 | ||||||||
\(970\) | −1.43110e15 | −1.66652 | ||||||||
\(971\) | −1.47299e15 | −1.70649 | −0.853246 | − | 0.521508i | \(-0.825370\pi\) | ||||
−0.853246 | + | 0.521508i | \(0.825370\pi\) | |||||||
\(972\) | 1.63238e14 | 0.188143 | ||||||||
\(973\) | −9.99215e14 | −1.14576 | ||||||||
\(974\) | − | 2.76678e15i | − | 3.15632i | ||||||
\(975\) | − | 2.18938e14i | − | 0.248483i | ||||||
\(976\) | − | 4.04557e15i | − | 4.56805i | ||||||
\(977\) | − | 1.92591e14i | − | 0.216354i | −0.994132 | − | 0.108177i | \(-0.965499\pi\) | ||
0.994132 | − | 0.108177i | \(-0.0345013\pi\) | |||||||
\(978\) | − | 1.24161e15i | − | 1.38769i | ||||||
\(979\) | 1.12580e15 | 1.25183 | ||||||||
\(980\) | 5.22255e14 | 0.577766 | ||||||||
\(981\) | 2.25588e14i | 0.248297i | ||||||||
\(982\) | 1.15586e15i | 1.26575i | ||||||||
\(983\) | − | 1.33915e15i | − | 1.45902i | −0.683970 | − | 0.729510i | \(-0.739748\pi\) | ||
0.683970 | − | 0.729510i | \(-0.260252\pi\) | |||||||
\(984\) | 1.22166e15i | 1.32426i | ||||||||
\(985\) | −9.18957e14 | −0.991092 | ||||||||
\(986\) | 1.55940e15i | 1.67330i | ||||||||
\(987\) | 6.71020e14i | 0.716390i | ||||||||
\(988\) | 4.74170e15i | 5.03674i | ||||||||
\(989\) | 7.62466e14 | 0.805821 | ||||||||
\(990\) | −1.19813e15 | −1.25988 | ||||||||
\(991\) | − | 1.70616e15i | − | 1.78506i | −0.450992 | − | 0.892528i | \(-0.648930\pi\) | ||
0.450992 | − | 0.892528i | \(-0.351070\pi\) | |||||||
\(992\) | −7.82116e15 | −8.14166 | ||||||||
\(993\) | −5.40138e14 | −0.559446 | ||||||||
\(994\) | − | 1.20828e15i | − | 1.24519i | ||||||
\(995\) | 2.14971e15 | 2.20427 | ||||||||
\(996\) | − | 1.12557e15i | − | 1.14835i | ||||||
\(997\) | 1.52311e14 | 0.154616 | 0.0773080 | − | 0.997007i | \(-0.475368\pi\) | ||||
0.0773080 | + | 0.997007i | \(0.475368\pi\) | |||||||
\(998\) | − | 8.73431e14i | − | 0.882218i | ||||||
\(999\) | 1.72462e14i | 0.173327i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 177.11.c.a.58.99 | yes | 100 | |
59.58 | odd | 2 | inner | 177.11.c.a.58.2 | ✓ | 100 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.11.c.a.58.2 | ✓ | 100 | 59.58 | odd | 2 | inner | |
177.11.c.a.58.99 | yes | 100 | 1.1 | even | 1 | trivial |