Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [98,10,Mod(67,98)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(98, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("98.67");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 98 = 2 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 98.c (of order \(3\), degree \(2\), not 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: | \(50.4735119441\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4 x^{7} - 4806 x^{6} + 14432 x^{5} + 8678459 x^{4} - 17380976 x^{3} - 6978412850 x^{2} + \cdots + 2108388231292 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4}\cdot 7^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.2 | ||
Root | \(34.4952 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 98.67 |
Dual form | 98.10.c.m.79.2 |
$q$-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 \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.00000 | + | 13.8564i | 0.353553 | + | 0.612372i | ||||
\(3\) | −51.3408 | + | 88.9249i | −0.365946 | + | 0.633838i | −0.988928 | − | 0.148399i | \(-0.952588\pi\) |
0.622981 | + | 0.782237i | \(0.285921\pi\) | |||||||
\(4\) | −128.000 | + | 221.703i | −0.250000 | + | 0.433013i | ||||
\(5\) | 1047.40 | + | 1814.15i | 0.749459 | + | 1.29810i | 0.948082 | + | 0.318025i | \(0.103020\pi\) |
−0.198623 | + | 0.980076i | \(0.563647\pi\) | |||||||
\(6\) | −1642.91 | −0.517526 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −4096.00 | −0.353553 | ||||||||
\(9\) | 4569.74 | + | 7915.01i | 0.232167 | + | 0.402124i | ||||
\(10\) | −16758.4 | + | 29026.4i | −0.529948 | + | 0.917896i | ||||
\(11\) | −28157.2 | + | 48769.7i | −0.579859 | + | 1.00434i | 0.415636 | + | 0.909531i | \(0.363559\pi\) |
−0.995495 | + | 0.0948139i | \(0.969774\pi\) | |||||||
\(12\) | −13143.3 | − | 22764.8i | −0.182973 | − | 0.316919i | ||||
\(13\) | 124915. | 1.21302 | 0.606510 | − | 0.795076i | \(-0.292569\pi\) | ||||
0.606510 | + | 0.795076i | \(0.292569\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −215098. | −1.09705 | ||||||||
\(16\) | −32768.0 | − | 56755.8i | −0.125000 | − | 0.216506i | ||||
\(17\) | −194320. | + | 336573.i | −0.564285 | + | 0.977369i | 0.432831 | + | 0.901475i | \(0.357515\pi\) |
−0.997116 | + | 0.0758946i | \(0.975819\pi\) | |||||||
\(18\) | −73115.8 | + | 126640.i | −0.164167 | + | 0.284345i | ||||
\(19\) | 123329. | + | 213611.i | 0.217106 | + | 0.376039i | 0.953922 | − | 0.300054i | \(-0.0970049\pi\) |
−0.736816 | + | 0.676093i | \(0.763672\pi\) | |||||||
\(20\) | −536269. | −0.749459 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −901030. | −0.820044 | ||||||||
\(23\) | 858886. | + | 1.48763e6i | 0.639971 | + | 1.10846i | 0.985439 | + | 0.170031i | \(0.0543869\pi\) |
−0.345468 | + | 0.938431i | \(0.612280\pi\) | |||||||
\(24\) | 210292. | − | 364237.i | 0.129382 | − | 0.224095i | ||||
\(25\) | −1.21753e6 | + | 2.10883e6i | −0.623378 | + | 1.07972i | ||||
\(26\) | 999317. | + | 1.73087e6i | 0.428868 | + | 0.742821i | ||||
\(27\) | −2.95954e6 | −1.07173 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.75179e6 | 1.51012 | 0.755061 | − | 0.655654i | \(-0.227607\pi\) | ||||
0.755061 | + | 0.655654i | \(0.227607\pi\) | |||||||
\(30\) | −1.72078e6 | − | 2.98048e6i | −0.387865 | − | 0.671801i | ||||
\(31\) | 2.63393e6 | − | 4.56209e6i | 0.512243 | − | 0.887231i | −0.487656 | − | 0.873036i | \(-0.662148\pi\) |
0.999899 | − | 0.0141951i | \(-0.00451861\pi\) | |||||||
\(32\) | 524288. | − | 908093.i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −2.89123e6 | − | 5.00775e6i | −0.424394 | − | 0.735073i | ||||
\(34\) | −6.21825e6 | −0.798019 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.33970e6 | −0.232167 | ||||||||
\(37\) | 6.17074e6 | + | 1.06880e7i | 0.541290 | + | 0.937541i | 0.998830 | + | 0.0483524i | \(0.0153971\pi\) |
−0.457541 | + | 0.889189i | \(0.651270\pi\) | |||||||
\(38\) | −1.97326e6 | + | 3.41778e6i | −0.153517 | + | 0.265900i | ||||
\(39\) | −6.41322e6 | + | 1.11080e7i | −0.443900 | + | 0.768858i | ||||
\(40\) | −4.29015e6 | − | 7.43076e6i | −0.264974 | − | 0.458948i | ||||
\(41\) | −5.54285e6 | −0.306342 | −0.153171 | − | 0.988200i | \(-0.548948\pi\) | ||||
−0.153171 | + | 0.988200i | \(0.548948\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.78833e6 | −0.258193 | −0.129097 | − | 0.991632i | \(-0.541208\pi\) | ||||
−0.129097 | + | 0.991632i | \(0.541208\pi\) | |||||||
\(44\) | −7.20824e6 | − | 1.24850e7i | −0.289929 | − | 0.502172i | ||||
\(45\) | −9.57269e6 | + | 1.65804e7i | −0.347999 | + | 0.602751i | ||||
\(46\) | −1.37422e7 | + | 2.38021e7i | −0.452528 | + | 0.783801i | ||||
\(47\) | −2.55966e7 | − | 4.43346e7i | −0.765142 | − | 1.32526i | −0.940171 | − | 0.340702i | \(-0.889335\pi\) |
0.175029 | − | 0.984563i | \(-0.443998\pi\) | |||||||
\(48\) | 6.72935e6 | 0.182973 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.89611e7 | −0.881589 | ||||||||
\(51\) | −1.99531e7 | − | 3.45599e7i | −0.412996 | − | 0.715329i | ||||
\(52\) | −1.59891e7 | + | 2.76939e7i | −0.303255 | + | 0.525253i | ||||
\(53\) | 4.07186e7 | − | 7.05267e7i | 0.708845 | − | 1.22776i | −0.256441 | − | 0.966560i | \(-0.582550\pi\) |
0.965286 | − | 0.261196i | \(-0.0841168\pi\) | |||||||
\(54\) | −2.36763e7 | − | 4.10086e7i | −0.378915 | − | 0.656301i | ||||
\(55\) | −1.17967e8 | −1.73832 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.53272e7 | −0.317797 | ||||||||
\(58\) | 4.60143e7 | + | 7.96992e7i | 0.533909 | + | 0.924757i | ||||
\(59\) | 3.92926e7 | − | 6.80568e7i | 0.422160 | − | 0.731202i | −0.573991 | − | 0.818862i | \(-0.694606\pi\) |
0.996150 | + | 0.0876598i | \(0.0279388\pi\) | |||||||
\(60\) | 2.75325e7 | − | 4.76877e7i | 0.274262 | − | 0.475035i | ||||
\(61\) | −6.90133e6 | − | 1.19535e7i | −0.0638188 | − | 0.110537i | 0.832351 | − | 0.554249i | \(-0.186995\pi\) |
−0.896169 | + | 0.443712i | \(0.853661\pi\) | |||||||
\(62\) | 8.42856e7 | 0.724421 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.67772e7 | 0.125000 | ||||||||
\(65\) | 1.30836e8 | + | 2.26614e8i | 0.909109 | + | 1.57462i | ||||
\(66\) | 4.62596e7 | − | 8.01241e7i | 0.300092 | − | 0.519775i | ||||
\(67\) | 5.08587e7 | − | 8.80899e7i | 0.308339 | − | 0.534059i | −0.669660 | − | 0.742668i | \(-0.733560\pi\) |
0.977999 | + | 0.208609i | \(0.0668935\pi\) | |||||||
\(68\) | −4.97460e7 | − | 8.61626e7i | −0.282142 | − | 0.488685i | ||||
\(69\) | −1.76384e8 | −0.936780 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.75670e8 | −1.75446 | −0.877232 | − | 0.480067i | \(-0.840612\pi\) | ||||
−0.877232 | + | 0.480067i | \(0.840612\pi\) | |||||||
\(72\) | −1.87176e7 | − | 3.24199e7i | −0.0820833 | − | 0.142172i | ||||
\(73\) | 2.22973e8 | − | 3.86200e8i | 0.918964 | − | 1.59169i | 0.117972 | − | 0.993017i | \(-0.462361\pi\) |
0.800992 | − | 0.598676i | \(-0.204306\pi\) | |||||||
\(74\) | −9.87319e7 | + | 1.71009e8i | −0.382750 | + | 0.662942i | ||||
\(75\) | −1.25018e8 | − | 2.16538e8i | −0.456245 | − | 0.790240i | ||||
\(76\) | −6.31442e7 | −0.217106 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.05223e8 | −0.627770 | ||||||||
\(79\) | 1.13312e8 | + | 1.96262e8i | 0.327306 | + | 0.566911i | 0.981976 | − | 0.189004i | \(-0.0605258\pi\) |
−0.654670 | + | 0.755915i | \(0.727193\pi\) | |||||||
\(80\) | 6.86425e7 | − | 1.18892e8i | 0.187365 | − | 0.324525i | ||||
\(81\) | 6.19992e7 | − | 1.07386e8i | 0.160031 | − | 0.277181i | ||||
\(82\) | −4.43428e7 | − | 7.68040e7i | −0.108308 | − | 0.187595i | ||||
\(83\) | 5.26823e8 | 1.21847 | 0.609233 | − | 0.792992i | \(-0.291478\pi\) | ||||
0.609233 | + | 0.792992i | \(0.291478\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.14125e8 | −1.69163 | ||||||||
\(86\) | −4.63066e7 | − | 8.02054e7i | −0.0912851 | − | 0.158110i | ||||
\(87\) | −2.95302e8 | + | 5.11478e8i | −0.552624 | + | 0.957172i | ||||
\(88\) | 1.15332e8 | − | 1.99761e8i | 0.205011 | − | 0.355090i | ||||
\(89\) | −2.59691e8 | − | 4.49797e8i | −0.438734 | − | 0.759910i | 0.558858 | − | 0.829263i | \(-0.311240\pi\) |
−0.997592 | + | 0.0693536i | \(0.977906\pi\) | |||||||
\(90\) | −3.06326e8 | −0.492145 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.39750e8 | −0.639971 | ||||||||
\(93\) | 2.70456e8 | + | 4.68444e8i | 0.374907 | + | 0.649358i | ||||
\(94\) | 4.09546e8 | − | 7.09354e8i | 0.541037 | − | 0.937104i | ||||
\(95\) | −2.58349e8 | + | 4.47473e8i | −0.325424 | + | 0.563652i | ||||
\(96\) | 5.38348e7 | + | 9.32446e7i | 0.0646908 | + | 0.112048i | ||||
\(97\) | −8.75899e8 | −1.00457 | −0.502286 | − | 0.864701i | \(-0.667508\pi\) | ||||
−0.502286 | + | 0.864701i | \(0.667508\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.14684e8 | −0.538495 | ||||||||
\(100\) | −3.11689e8 | − | 5.39861e8i | −0.311689 | − | 0.539861i | ||||
\(101\) | 4.36810e6 | − | 7.56578e6i | 0.00417683 | − | 0.00723448i | −0.863929 | − | 0.503613i | \(-0.832004\pi\) |
0.868106 | + | 0.496378i | \(0.165337\pi\) | |||||||
\(102\) | 3.19250e8 | − | 5.52958e8i | 0.292032 | − | 0.505814i | ||||
\(103\) | −4.79514e8 | − | 8.30543e8i | −0.419792 | − | 0.727101i | 0.576126 | − | 0.817361i | \(-0.304564\pi\) |
−0.995918 | + | 0.0902597i | \(0.971230\pi\) | |||||||
\(104\) | −5.11650e8 | −0.428868 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.30299e9 | 1.00246 | ||||||||
\(107\) | 7.42353e8 | + | 1.28579e9i | 0.547499 | + | 0.948297i | 0.998445 | + | 0.0557454i | \(0.0177535\pi\) |
−0.450946 | + | 0.892551i | \(0.648913\pi\) | |||||||
\(108\) | 3.78821e8 | − | 6.56137e8i | 0.267934 | − | 0.464075i | ||||
\(109\) | 7.67650e8 | − | 1.32961e9i | 0.520888 | − | 0.902204i | −0.478817 | − | 0.877915i | \(-0.658934\pi\) |
0.999705 | − | 0.0242895i | \(-0.00773235\pi\) | |||||||
\(110\) | −9.43740e8 | − | 1.63461e9i | −0.614589 | − | 1.06450i | ||||
\(111\) | −1.26724e9 | −0.792332 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.29034e9 | 1.89840 | 0.949199 | − | 0.314677i | \(-0.101896\pi\) | ||||
0.949199 | + | 0.314677i | \(0.101896\pi\) | |||||||
\(114\) | −2.02617e8 | − | 3.50943e8i | −0.112358 | − | 0.194610i | ||||
\(115\) | −1.79920e9 | + | 3.11630e9i | −0.959264 | + | 1.66149i | ||||
\(116\) | −7.36229e8 | + | 1.27519e9i | −0.377531 | + | 0.653902i | ||||
\(117\) | 5.70827e8 | + | 9.88701e8i | 0.281623 | + | 0.487785i | ||||
\(118\) | 1.25736e9 | 0.597024 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 8.81040e8 | 0.387865 | ||||||||
\(121\) | −4.06681e8 | − | 7.04392e8i | −0.172472 | − | 0.298731i | ||||
\(122\) | 1.10421e8 | − | 1.91255e8i | 0.0451267 | − | 0.0781618i | ||||
\(123\) | 2.84575e8 | − | 4.92898e8i | 0.112105 | − | 0.194171i | ||||
\(124\) | 6.74285e8 | + | 1.16790e9i | 0.256121 | + | 0.443615i | ||||
\(125\) | −1.00958e9 | −0.369866 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.41672e9 | −1.84765 | −0.923826 | − | 0.382814i | \(-0.874955\pi\) | ||||
−0.923826 | + | 0.382814i | \(0.874955\pi\) | |||||||
\(128\) | 1.34218e8 | + | 2.32472e8i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 2.97178e8 | − | 5.14727e8i | 0.0944849 | − | 0.163653i | ||||
\(130\) | −2.09337e9 | + | 3.62583e9i | −0.642837 | + | 1.11343i | ||||
\(131\) | 1.69396e9 | + | 2.93402e9i | 0.502553 | + | 0.870447i | 0.999996 | + | 0.00295048i | \(0.000939169\pi\) |
−0.497443 | + | 0.867497i | \(0.665727\pi\) | |||||||
\(132\) | 1.48031e9 | 0.424394 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.62748e9 | 0.436057 | ||||||||
\(135\) | −3.09982e9 | − | 5.36905e9i | −0.803221 | − | 1.39122i | ||||
\(136\) | 7.95936e8 | − | 1.37860e9i | 0.199505 | − | 0.345552i | ||||
\(137\) | −2.37364e9 | + | 4.11127e9i | −0.575669 | + | 0.997088i | 0.420300 | + | 0.907385i | \(0.361925\pi\) |
−0.995969 | + | 0.0897026i | \(0.971408\pi\) | |||||||
\(138\) | −1.41107e9 | − | 2.44404e9i | −0.331202 | − | 0.573658i | ||||
\(139\) | 2.17838e9 | 0.494958 | 0.247479 | − | 0.968893i | \(-0.420398\pi\) | ||||
0.247479 | + | 0.968893i | \(0.420398\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.25661e9 | 1.12000 | ||||||||
\(142\) | −3.00536e9 | − | 5.20544e9i | −0.620297 | − | 1.07439i | ||||
\(143\) | −3.51725e9 | + | 6.09205e9i | −0.703381 | + | 1.21829i | ||||
\(144\) | 2.99482e8 | − | 5.18718e8i | 0.0580417 | − | 0.100531i | ||||
\(145\) | 6.02443e9 | + | 1.04346e10i | 1.13177 | + | 1.96029i | ||||
\(146\) | 7.13512e9 | 1.29961 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.15942e9 | −0.541290 | ||||||||
\(149\) | 5.90289e9 | + | 1.02241e10i | 0.981129 | + | 1.69937i | 0.658014 | + | 0.753006i | \(0.271397\pi\) |
0.323116 | + | 0.946360i | \(0.395270\pi\) | |||||||
\(150\) | 2.00030e9 | − | 3.46461e9i | 0.322614 | − | 0.558784i | ||||
\(151\) | 3.15801e9 | − | 5.46983e9i | 0.494330 | − | 0.856204i | −0.505649 | − | 0.862739i | \(-0.668747\pi\) |
0.999979 | + | 0.00653506i | \(0.00208019\pi\) | |||||||
\(152\) | −5.05154e8 | − | 8.74952e8i | −0.0767586 | − | 0.132950i | ||||
\(153\) | −3.55197e9 | −0.524032 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.10351e10 | 1.53562 | ||||||||
\(156\) | −1.64179e9 | − | 2.84366e9i | −0.221950 | − | 0.384429i | ||||
\(157\) | 5.15129e8 | − | 8.92229e8i | 0.0676655 | − | 0.117200i | −0.830208 | − | 0.557454i | \(-0.811778\pi\) |
0.897873 | + | 0.440254i | \(0.145112\pi\) | |||||||
\(158\) | −1.81299e9 | + | 3.14019e9i | −0.231440 | + | 0.400866i | ||||
\(159\) | 4.18105e9 | + | 7.24180e9i | 0.518798 | + | 0.898585i | ||||
\(160\) | 2.19656e9 | 0.264974 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.98397e9 | 0.226318 | ||||||||
\(163\) | 1.67465e9 | + | 2.90057e9i | 0.185814 | + | 0.321840i | 0.943851 | − | 0.330373i | \(-0.107174\pi\) |
−0.758036 | + | 0.652212i | \(0.773841\pi\) | |||||||
\(164\) | 7.09485e8 | − | 1.22886e9i | 0.0765854 | − | 0.132650i | ||||
\(165\) | 6.05655e9 | − | 1.04903e10i | 0.636132 | − | 1.10181i | ||||
\(166\) | 4.21458e9 | + | 7.29987e9i | 0.430793 | + | 0.746155i | ||||
\(167\) | 1.63487e10 | 1.62652 | 0.813261 | − | 0.581899i | \(-0.197690\pi\) | ||||
0.813261 | + | 0.581899i | \(0.197690\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.99917e9 | 0.471420 | ||||||||
\(170\) | −6.51300e9 | − | 1.12808e10i | −0.598082 | − | 1.03591i | ||||
\(171\) | −1.12716e9 | + | 1.95229e9i | −0.100810 | + | 0.174607i | ||||
\(172\) | 7.40906e8 | − | 1.28329e9i | 0.0645483 | − | 0.111801i | ||||
\(173\) | 3.73549e9 | + | 6.47006e9i | 0.317059 | + | 0.549163i | 0.979873 | − | 0.199621i | \(-0.0639712\pi\) |
−0.662814 | + | 0.748784i | \(0.730638\pi\) | |||||||
\(174\) | −9.44966e9 | −0.781528 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.69062e9 | 0.289929 | ||||||||
\(177\) | 4.03463e9 | + | 6.98818e9i | 0.308976 | + | 0.535161i | ||||
\(178\) | 4.15505e9 | − | 7.19676e9i | 0.310232 | − | 0.537337i | ||||
\(179\) | 3.11504e9 | − | 5.39540e9i | 0.226790 | − | 0.392812i | −0.730065 | − | 0.683378i | \(-0.760510\pi\) |
0.956855 | + | 0.290566i | \(0.0938434\pi\) | |||||||
\(180\) | −2.45061e9 | − | 4.24458e9i | −0.173999 | − | 0.301376i | ||||
\(181\) | 5.46976e9 | 0.378804 | 0.189402 | − | 0.981900i | \(-0.439345\pi\) | ||||
0.189402 | + | 0.981900i | \(0.439345\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.41728e9 | 0.0934170 | ||||||||
\(184\) | −3.51800e9 | − | 6.09335e9i | −0.226264 | − | 0.391901i | ||||
\(185\) | −1.29265e10 | + | 2.23893e10i | −0.811349 | + | 1.40530i | ||||
\(186\) | −4.32730e9 | + | 7.49510e9i | −0.265099 | + | 0.459165i | ||||
\(187\) | −1.09430e10 | − | 1.89539e10i | −0.654411 | − | 1.13347i | ||||
\(188\) | 1.31055e10 | 0.765142 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.26716e9 | −0.460220 | ||||||||
\(191\) | −3.46742e9 | − | 6.00576e9i | −0.188520 | − | 0.326526i | 0.756237 | − | 0.654298i | \(-0.227036\pi\) |
−0.944757 | + | 0.327772i | \(0.893702\pi\) | |||||||
\(192\) | −8.61356e8 | + | 1.49191e9i | −0.0457433 | + | 0.0792297i | ||||
\(193\) | −2.08666e9 | + | 3.61420e9i | −0.108254 | + | 0.187501i | −0.915063 | − | 0.403311i | \(-0.867859\pi\) |
0.806809 | + | 0.590812i | \(0.201193\pi\) | |||||||
\(194\) | −7.00720e9 | − | 1.21368e10i | −0.355170 | − | 0.615173i | ||||
\(195\) | −2.68689e10 | −1.33074 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.62569e10 | −1.71511 | −0.857556 | − | 0.514391i | \(-0.828018\pi\) | ||||
−0.857556 | + | 0.514391i | \(0.828018\pi\) | |||||||
\(198\) | −4.11747e9 | − | 7.13167e9i | −0.190387 | − | 0.329760i | ||||
\(199\) | −8.97917e9 | + | 1.55524e10i | −0.405880 | + | 0.703004i | −0.994423 | − | 0.105461i | \(-0.966368\pi\) |
0.588544 | + | 0.808465i | \(0.299701\pi\) | |||||||
\(200\) | 4.98702e9 | − | 8.63777e9i | 0.220397 | − | 0.381739i | ||||
\(201\) | 5.22226e9 | + | 9.04522e9i | 0.225671 | + | 0.390874i | ||||
\(202\) | 1.39779e8 | 0.00590693 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.02160e10 | 0.412996 | ||||||||
\(205\) | −5.80559e9 | − | 1.00556e10i | −0.229591 | − | 0.397662i | ||||
\(206\) | 7.67223e9 | − | 1.32887e10i | 0.296838 | − | 0.514138i | ||||
\(207\) | −7.84976e9 | + | 1.35962e10i | −0.297160 | + | 0.514696i | ||||
\(208\) | −4.09320e9 | − | 7.08964e9i | −0.151628 | − | 0.262627i | ||||
\(209\) | −1.38903e10 | −0.503564 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.33838e9 | 0.220144 | 0.110072 | − | 0.993924i | \(-0.464892\pi\) | ||||
0.110072 | + | 0.993924i | \(0.464892\pi\) | |||||||
\(212\) | 1.04240e10 | + | 1.80548e10i | 0.354423 | + | 0.613878i | ||||
\(213\) | 1.92872e10 | − | 3.34065e10i | 0.642040 | − | 1.11205i | ||||
\(214\) | −1.18777e10 | + | 2.05727e10i | −0.387141 | + | 0.670547i | ||||
\(215\) | −6.06270e9 | − | 1.05009e10i | −0.193505 | − | 0.335161i | ||||
\(216\) | 1.21223e10 | 0.378915 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.45648e10 | 0.736647 | ||||||||
\(219\) | 2.28952e10 | + | 3.96556e10i | 0.672583 | + | 1.16495i | ||||
\(220\) | 1.50998e10 | − | 2.61537e10i | 0.434580 | − | 0.752715i | ||||
\(221\) | −2.42735e10 | + | 4.20429e10i | −0.684489 | + | 1.18557i | ||||
\(222\) | −1.01380e10 | − | 1.75595e10i | −0.280132 | − | 0.485202i | ||||
\(223\) | −4.34746e10 | −1.17724 | −0.588619 | − | 0.808411i | \(-0.700328\pi\) | ||||
−0.588619 | + | 0.808411i | \(0.700328\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.22552e10 | −0.578910 | ||||||||
\(226\) | 2.63227e10 | + | 4.55922e10i | 0.671185 | + | 1.16253i | ||||
\(227\) | 9.47436e9 | − | 1.64101e10i | 0.236828 | − | 0.410199i | −0.722974 | − | 0.690875i | \(-0.757225\pi\) |
0.959802 | + | 0.280676i | \(0.0905588\pi\) | |||||||
\(228\) | 3.24188e9 | − | 5.61509e9i | 0.0794492 | − | 0.137610i | ||||
\(229\) | −1.86189e10 | − | 3.22489e10i | −0.447398 | − | 0.774916i | 0.550818 | − | 0.834626i | \(-0.314316\pi\) |
−0.998216 | + | 0.0597093i | \(0.980983\pi\) | |||||||
\(230\) | −5.75743e10 | −1.35660 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.35593e10 | −0.533909 | ||||||||
\(233\) | −9.19187e9 | − | 1.59208e10i | −0.204316 | − | 0.353886i | 0.745599 | − | 0.666395i | \(-0.232164\pi\) |
−0.949915 | + | 0.312510i | \(0.898830\pi\) | |||||||
\(234\) | −9.13323e9 | + | 1.58192e10i | −0.199138 | + | 0.344916i | ||||
\(235\) | 5.36198e10 | − | 9.28722e10i | 1.14689 | − | 1.98646i | ||||
\(236\) | 1.00589e10 | + | 1.74225e10i | 0.211080 | + | 0.365601i | ||||
\(237\) | −2.32701e10 | −0.479106 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.65476e10 | −0.724550 | −0.362275 | − | 0.932071i | \(-0.618000\pi\) | ||||
−0.362275 | + | 0.932071i | \(0.618000\pi\) | |||||||
\(240\) | 7.04832e9 | + | 1.22081e10i | 0.137131 | + | 0.237518i | ||||
\(241\) | −1.42953e10 | + | 2.47601e10i | −0.272970 | + | 0.472799i | −0.969621 | − | 0.244612i | \(-0.921339\pi\) |
0.696651 | + | 0.717411i | \(0.254673\pi\) | |||||||
\(242\) | 6.50690e9 | − | 1.12703e10i | 0.121956 | − | 0.211235i | ||||
\(243\) | −2.27601e10 | − | 3.94217e10i | −0.418742 | − | 0.725283i | ||||
\(244\) | 3.53348e9 | 0.0638188 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.10639e9 | 0.158540 | ||||||||
\(247\) | 1.54055e10 | + | 2.66832e10i | 0.263354 | + | 0.456143i | ||||
\(248\) | −1.07886e10 | + | 1.86863e10i | −0.181105 | + | 0.313683i | ||||
\(249\) | −2.70475e10 | + | 4.68477e10i | −0.445893 | + | 0.772309i | ||||
\(250\) | −8.07661e9 | − | 1.39891e10i | −0.130767 | − | 0.226496i | ||||
\(251\) | −1.00172e10 | −0.159300 | −0.0796499 | − | 0.996823i | \(-0.525380\pi\) | ||||
−0.0796499 | + | 0.996823i | \(0.525380\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.67353e10 | −1.48437 | ||||||||
\(254\) | −4.33338e10 | − | 7.50563e10i | −0.653243 | − | 1.13145i | ||||
\(255\) | 4.17979e10 | − | 7.23960e10i | 0.619047 | − | 1.07222i | ||||
\(256\) | −2.14748e9 | + | 3.71955e9i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 8.48406e9 | + | 1.46948e10i | 0.121312 | + | 0.210119i | 0.920285 | − | 0.391248i | \(-0.127956\pi\) |
−0.798973 | + | 0.601367i | \(0.794623\pi\) | |||||||
\(258\) | 9.50968e9 | 0.133622 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −6.69879e10 | −0.909109 | ||||||||
\(261\) | 2.62842e10 | + | 4.55255e10i | 0.350600 | + | 0.607257i | ||||
\(262\) | −2.71033e10 | + | 4.69443e10i | −0.355359 | + | 0.615499i | ||||
\(263\) | −3.53596e9 | + | 6.12447e9i | −0.0455729 | + | 0.0789346i | −0.887912 | − | 0.460013i | \(-0.847845\pi\) |
0.842339 | + | 0.538948i | \(0.181178\pi\) | |||||||
\(264\) | 1.18425e10 | + | 2.05118e10i | 0.150046 | + | 0.259887i | ||||
\(265\) | 1.70595e11 | 2.12500 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.33310e10 | 0.642212 | ||||||||
\(268\) | 1.30198e10 | + | 2.25510e10i | 0.154170 | + | 0.267030i | ||||
\(269\) | 1.84977e8 | − | 3.20389e8i | 0.00215393 | − | 0.00373072i | −0.864946 | − | 0.501864i | \(-0.832648\pi\) |
0.867100 | + | 0.498133i | \(0.165981\pi\) | |||||||
\(270\) | 4.95972e10 | − | 8.59049e10i | 0.567963 | − | 0.983741i | ||||
\(271\) | −6.21441e10 | − | 1.07637e11i | −0.699904 | − | 1.21227i | −0.968499 | − | 0.249016i | \(-0.919893\pi\) |
0.268595 | − | 0.963253i | \(-0.413441\pi\) | |||||||
\(272\) | 2.54700e10 | 0.282142 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.59566e10 | −0.814119 | ||||||||
\(275\) | −6.85647e10 | − | 1.18758e11i | −0.722942 | − | 1.25217i | ||||
\(276\) | 2.25771e10 | − | 3.91047e10i | 0.234195 | − | 0.405638i | ||||
\(277\) | −8.48065e9 | + | 1.46889e10i | −0.0865506 | + | 0.149910i | −0.906051 | − | 0.423169i | \(-0.860918\pi\) |
0.819500 | + | 0.573079i | \(0.194251\pi\) | |||||||
\(278\) | 1.74271e10 | + | 3.01846e10i | 0.174994 | + | 0.303098i | ||||
\(279\) | 4.81454e10 | 0.475703 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.16441e11 | 1.11411 | 0.557053 | − | 0.830477i | \(-0.311932\pi\) | ||||
0.557053 | + | 0.830477i | \(0.311932\pi\) | |||||||
\(282\) | 4.20528e10 | + | 7.28377e10i | 0.395981 | + | 0.685859i | ||||
\(283\) | 1.32766e10 | − | 2.29958e10i | 0.123041 | − | 0.213113i | −0.797925 | − | 0.602757i | \(-0.794069\pi\) |
0.920965 | + | 0.389644i | \(0.127402\pi\) | |||||||
\(284\) | 4.80858e10 | − | 8.32871e10i | 0.438616 | − | 0.759705i | ||||
\(285\) | −2.65277e10 | − | 4.59473e10i | −0.238176 | − | 0.412532i | ||||
\(286\) | −1.12552e11 | −0.994731 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 9.58343e9 | 0.0820833 | ||||||||
\(289\) | −1.62269e10 | − | 2.81058e10i | −0.136834 | − | 0.237004i | ||||
\(290\) | −9.63909e10 | + | 1.66954e11i | −0.800286 | + | 1.38614i | ||||
\(291\) | 4.49694e10 | − | 7.78893e10i | 0.367620 | − | 0.636736i | ||||
\(292\) | 5.70810e10 | + | 9.88671e10i | 0.459482 | + | 0.795846i | ||||
\(293\) | −9.43424e8 | −0.00747829 | −0.00373915 | − | 0.999993i | \(-0.501190\pi\) | ||||
−0.00373915 | + | 0.999993i | \(0.501190\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.64620e11 | 1.26557 | ||||||||
\(296\) | −2.52754e10 | − | 4.37782e10i | −0.191375 | − | 0.331471i | ||||
\(297\) | 8.33323e10 | − | 1.44336e11i | 0.621455 | − | 1.07639i | ||||
\(298\) | −9.44462e10 | + | 1.63586e11i | −0.693763 | + | 1.20163i | ||||
\(299\) | 1.07287e11 | + | 1.85827e11i | 0.776298 | + | 1.34459i | ||||
\(300\) | 6.40095e10 | 0.456245 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.01056e11 | 0.699088 | ||||||||
\(303\) | 4.48524e8 | + | 7.76867e8i | 0.00305699 | + | 0.00529486i | ||||
\(304\) | 8.08246e9 | − | 1.39992e10i | 0.0542766 | − | 0.0940098i | ||||
\(305\) | 1.44569e10 | − | 2.50401e10i | 0.0956592 | − | 0.165687i | ||||
\(306\) | −2.84158e10 | − | 4.92175e10i | −0.185273 | − | 0.320903i | ||||
\(307\) | 2.20668e10 | 0.141780 | 0.0708902 | − | 0.997484i | \(-0.477416\pi\) | ||||
0.0708902 | + | 0.997484i | \(0.477416\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.84747e10 | 0.614485 | ||||||||
\(310\) | 8.82809e10 | + | 1.52907e11i | 0.542924 | + | 0.940372i | ||||
\(311\) | 1.15121e11 | − | 1.99396e11i | 0.697805 | − | 1.20863i | −0.271421 | − | 0.962461i | \(-0.587494\pi\) |
0.969226 | − | 0.246173i | \(-0.0791731\pi\) | |||||||
\(312\) | 2.62686e10 | − | 4.54985e10i | 0.156943 | − | 0.271832i | ||||
\(313\) | 7.87940e10 | + | 1.36475e11i | 0.464027 | + | 0.803719i | 0.999157 | − | 0.0410510i | \(-0.0130706\pi\) |
−0.535130 | + | 0.844770i | \(0.679737\pi\) | |||||||
\(314\) | 1.64841e10 | 0.0956935 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.80158e10 | −0.327306 | ||||||||
\(317\) | −1.20750e11 | − | 2.09145e11i | −0.671614 | − | 1.16327i | −0.977446 | − | 0.211184i | \(-0.932268\pi\) |
0.305832 | − | 0.952085i | \(-0.401065\pi\) | |||||||
\(318\) | −6.68969e10 | + | 1.15869e11i | −0.366846 | + | 0.635396i | ||||
\(319\) | −1.61954e11 | + | 2.80513e11i | −0.875658 | + | 1.51668i | ||||
\(320\) | 1.75725e10 | + | 3.04364e10i | 0.0936824 | + | 0.162263i | ||||
\(321\) | −1.52452e11 | −0.801422 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.58610e10 | −0.490039 | ||||||||
\(324\) | 1.58718e10 | + | 2.74907e10i | 0.0800153 | + | 0.138591i | ||||
\(325\) | −1.52088e11 | + | 2.63424e11i | −0.756170 | + | 1.30972i | ||||
\(326\) | −2.67944e10 | + | 4.64092e10i | −0.131391 | + | 0.227575i | ||||
\(327\) | 7.88236e10 | + | 1.36527e11i | 0.381234 | + | 0.660317i | ||||
\(328\) | 2.27035e10 | 0.108308 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.93810e11 | 0.899627 | ||||||||
\(331\) | −7.17683e10 | − | 1.24306e11i | −0.328630 | − | 0.569203i | 0.653611 | − | 0.756831i | \(-0.273253\pi\) |
−0.982240 | + | 0.187628i | \(0.939920\pi\) | |||||||
\(332\) | −6.74333e10 | + | 1.16798e11i | −0.304616 | + | 0.527611i | ||||
\(333\) | −5.63973e10 | + | 9.76830e10i | −0.251339 | + | 0.435332i | ||||
\(334\) | 1.30790e11 | + | 2.26535e11i | 0.575062 | + | 0.996037i | ||||
\(335\) | 2.13078e11 | 0.924350 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.35343e11 | 0.571612 | 0.285806 | − | 0.958288i | \(-0.407739\pi\) | ||||
0.285806 | + | 0.958288i | \(0.407739\pi\) | |||||||
\(338\) | 3.99934e10 | + | 6.92705e10i | 0.166672 | + | 0.288684i | ||||
\(339\) | −1.68929e11 | + | 2.92593e11i | −0.694712 | + | 1.20328i | ||||
\(340\) | 1.04208e11 | − | 1.80494e11i | 0.422908 | − | 0.732498i | ||||
\(341\) | 1.48328e11 | + | 2.56912e11i | 0.594057 | + | 1.02894i | ||||
\(342\) | −3.60690e10 | −0.142566 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.37090e10 | 0.0912851 | ||||||||
\(345\) | −1.84744e11 | − | 3.19987e11i | −0.702078 | − | 1.21603i | ||||
\(346\) | −5.97679e10 | + | 1.03521e11i | −0.224195 | + | 0.388317i | ||||
\(347\) | −1.93747e11 | + | 3.35579e11i | −0.717383 | + | 1.24254i | 0.244650 | + | 0.969612i | \(0.421327\pi\) |
−0.962033 | + | 0.272933i | \(0.912006\pi\) | |||||||
\(348\) | −7.55973e10 | − | 1.30938e11i | −0.276312 | − | 0.478586i | ||||
\(349\) | −1.02561e11 | −0.370056 | −0.185028 | − | 0.982733i | \(-0.559238\pi\) | ||||
−0.185028 | + | 0.982733i | \(0.559238\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.69690e11 | −1.30004 | ||||||||
\(352\) | 2.95250e10 | + | 5.11387e10i | 0.102506 | + | 0.177545i | ||||
\(353\) | 6.50080e9 | − | 1.12597e10i | 0.0222834 | − | 0.0385959i | −0.854669 | − | 0.519174i | \(-0.826240\pi\) |
0.876952 | + | 0.480578i | \(0.159573\pi\) | |||||||
\(354\) | −6.45541e10 | + | 1.11811e11i | −0.218479 | + | 0.378416i | ||||
\(355\) | −3.93477e11 | − | 6.81523e11i | −1.31490 | − | 2.27747i | ||||
\(356\) | 1.32962e11 | 0.438734 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.96812e10 | 0.320730 | ||||||||
\(359\) | 4.27763e10 | + | 7.40907e10i | 0.135918 | + | 0.235418i | 0.925948 | − | 0.377651i | \(-0.123268\pi\) |
−0.790030 | + | 0.613069i | \(0.789935\pi\) | |||||||
\(360\) | 3.92097e10 | − | 6.79133e10i | 0.123036 | − | 0.213105i | ||||
\(361\) | 1.30924e11 | − | 2.26767e11i | 0.405730 | − | 0.702745i | ||||
\(362\) | 4.37581e10 | + | 7.57912e10i | 0.133927 | + | 0.231969i | ||||
\(363\) | 8.35174e10 | 0.252463 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.34166e11 | 2.75490 | ||||||||
\(366\) | 1.13383e10 | + | 1.96384e10i | 0.0330279 | + | 0.0572060i | ||||
\(367\) | 5.65584e10 | − | 9.79621e10i | 0.162742 | − | 0.281878i | −0.773109 | − | 0.634273i | \(-0.781299\pi\) |
0.935851 | + | 0.352395i | \(0.114633\pi\) | |||||||
\(368\) | 5.62879e10 | − | 9.74936e10i | 0.159993 | − | 0.277116i | ||||
\(369\) | −2.53294e10 | − | 4.38718e10i | −0.0711223 | − | 0.123187i | ||||
\(370\) | −4.13647e11 | −1.14742 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.38473e11 | −0.374907 | ||||||||
\(373\) | 9.73594e10 | + | 1.68631e11i | 0.260428 | + | 0.451075i | 0.966356 | − | 0.257209i | \(-0.0828029\pi\) |
−0.705927 | + | 0.708284i | \(0.749470\pi\) | |||||||
\(374\) | 1.75088e11 | − | 3.03262e11i | 0.462738 | − | 0.801486i | ||||
\(375\) | 5.18325e10 | − | 8.97765e10i | 0.135351 | − | 0.234435i | ||||
\(376\) | 1.04844e11 | + | 1.81595e11i | 0.270519 | + | 0.468552i | ||||
\(377\) | 7.18483e11 | 1.83181 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.22727e11 | −0.554493 | −0.277247 | − | 0.960799i | \(-0.589422\pi\) | ||||
−0.277247 | + | 0.960799i | \(0.589422\pi\) | |||||||
\(380\) | −6.61373e10 | − | 1.14553e11i | −0.162712 | − | 0.281826i | ||||
\(381\) | 2.78099e11 | − | 4.81682e11i | 0.676141 | − | 1.17111i | ||||
\(382\) | 5.54788e10 | − | 9.60921e10i | 0.133304 | − | 0.230889i | ||||
\(383\) | 1.68297e11 | + | 2.91499e11i | 0.399652 | + | 0.692218i | 0.993683 | − | 0.112224i | \(-0.0357975\pi\) |
−0.594031 | + | 0.804443i | \(0.702464\pi\) | |||||||
\(384\) | −2.75634e10 | −0.0646908 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.67730e10 | −0.153094 | ||||||||
\(387\) | −2.64511e10 | − | 4.58147e10i | −0.0599439 | − | 0.103826i | ||||
\(388\) | 1.12115e11 | − | 1.94189e11i | 0.251143 | − | 0.434993i | ||||
\(389\) | 1.73950e11 | − | 3.01290e11i | 0.385169 | − | 0.667132i | −0.606624 | − | 0.794989i | \(-0.707476\pi\) |
0.991793 | + | 0.127857i | \(0.0408098\pi\) | |||||||
\(390\) | −2.14951e11 | − | 3.72306e11i | −0.470488 | − | 0.814909i | ||||
\(391\) | −6.67596e11 | −1.44450 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.47877e11 | −0.735630 | ||||||||
\(394\) | −2.90055e11 | − | 5.02390e11i | −0.606384 | − | 1.05029i | ||||
\(395\) | −2.37366e11 | + | 4.11130e11i | −0.490605 | + | 0.849753i | ||||
\(396\) | 6.58795e10 | − | 1.14107e11i | 0.134624 | − | 0.233175i | ||||
\(397\) | −1.37755e10 | − | 2.38598e10i | −0.0278323 | − | 0.0482069i | 0.851774 | − | 0.523910i | \(-0.175527\pi\) |
−0.879606 | + | 0.475703i | \(0.842194\pi\) | |||||||
\(398\) | −2.87333e11 | −0.574001 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.59585e11 | 0.311689 | ||||||||
\(401\) | 3.10585e11 | + | 5.37949e11i | 0.599834 | + | 1.03894i | 0.992845 | + | 0.119409i | \(0.0381001\pi\) |
−0.393011 | + | 0.919534i | \(0.628567\pi\) | |||||||
\(402\) | −8.35561e10 | + | 1.44723e11i | −0.159574 | + | 0.276390i | ||||
\(403\) | 3.29016e11 | − | 5.69872e11i | 0.621361 | − | 1.07623i | ||||
\(404\) | 1.11823e9 | + | 1.93684e9i | 0.00208842 | + | 0.00361724i | ||||
\(405\) | 2.59752e11 | 0.479746 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.95003e11 | −1.25549 | ||||||||
\(408\) | 8.17281e10 | + | 1.41557e11i | 0.146016 | + | 0.252907i | ||||
\(409\) | −7.31977e9 | + | 1.26782e10i | −0.0129343 | + | 0.0224029i | −0.872420 | − | 0.488757i | \(-0.837451\pi\) |
0.859486 | + | 0.511160i | \(0.170784\pi\) | |||||||
\(410\) | 9.28894e10 | − | 1.60889e11i | 0.162345 | − | 0.281190i | ||||
\(411\) | −2.43730e11 | − | 4.22152e11i | −0.421328 | − | 0.729761i | ||||
\(412\) | 2.45511e11 | 0.419792 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.51192e11 | −0.420247 | ||||||||
\(415\) | 5.51795e11 | + | 9.55736e11i | 0.913190 | + | 1.58169i | ||||
\(416\) | 6.54913e10 | − | 1.13434e11i | 0.107217 | − | 0.185705i | ||||
\(417\) | −1.11840e11 | + | 1.93713e11i | −0.181128 | + | 0.313723i | ||||
\(418\) | −1.11123e11 | − | 1.92470e11i | −0.178037 | − | 0.308369i | ||||
\(419\) | 1.21505e11 | 0.192589 | 0.0962946 | − | 0.995353i | \(-0.469301\pi\) | ||||
0.0962946 | + | 0.995353i | \(0.469301\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.61016e11 | −0.870373 | −0.435187 | − | 0.900340i | \(-0.643318\pi\) | ||||
−0.435187 | + | 0.900340i | \(0.643318\pi\) | |||||||
\(422\) | 5.07071e10 | + | 8.78272e10i | 0.0778328 | + | 0.134810i | ||||
\(423\) | 2.33939e11 | − | 4.05195e11i | 0.355281 | − | 0.615365i | ||||
\(424\) | −1.66783e11 | + | 2.88877e11i | −0.250615 | + | 0.434077i | ||||
\(425\) | −4.73183e11 | − | 8.19578e11i | −0.703525 | − | 1.21854i | ||||
\(426\) | 6.17192e11 | 0.907981 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.80085e11 | −0.547499 | ||||||||
\(429\) | −3.61157e11 | − | 6.25542e11i | −0.514799 | − | 0.891658i | ||||
\(430\) | 9.70032e10 | − | 1.68014e11i | 0.136829 | − | 0.236995i | ||||
\(431\) | −5.22159e11 | + | 9.04405e11i | −0.728878 | + | 1.26245i | 0.228480 | + | 0.973549i | \(0.426624\pi\) |
−0.957358 | + | 0.288905i | \(0.906709\pi\) | |||||||
\(432\) | 9.69782e10 | + | 1.67971e11i | 0.133967 | + | 0.232037i | ||||
\(433\) | −1.05446e12 | −1.44156 | −0.720781 | − | 0.693163i | \(-0.756216\pi\) | ||||
−0.720781 | + | 0.693163i | \(0.756216\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.23720e12 | −1.65668 | ||||||||
\(436\) | 1.96518e11 | + | 3.40380e11i | 0.260444 | + | 0.451102i | ||||
\(437\) | −2.11850e11 | + | 3.66935e11i | −0.277883 | + | 0.481308i | ||||
\(438\) | −3.66323e11 | + | 6.34490e11i | −0.475588 | + | 0.823743i | ||||
\(439\) | 5.85184e11 | + | 1.01357e12i | 0.751973 | + | 1.30245i | 0.946865 | + | 0.321630i | \(0.104231\pi\) |
−0.194893 | + | 0.980825i | \(0.562436\pi\) | |||||||
\(440\) | 4.83195e11 | 0.614589 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7.76751e11 | −0.968014 | ||||||||
\(443\) | 3.55330e11 | + | 6.15449e11i | 0.438344 | + | 0.759234i | 0.997562 | − | 0.0697869i | \(-0.0222319\pi\) |
−0.559218 | + | 0.829021i | \(0.688899\pi\) | |||||||
\(444\) | 1.62207e11 | − | 2.80951e11i | 0.198083 | − | 0.343090i | ||||
\(445\) | 5.44000e11 | − | 9.42236e11i | 0.657626 | − | 1.13904i | ||||
\(446\) | −3.47797e11 | − | 6.02402e11i | −0.416216 | − | 0.720908i | ||||
\(447\) | −1.21224e12 | −1.43616 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.40485e11 | 1.09205 | 0.546026 | − | 0.837768i | \(-0.316140\pi\) | ||||
0.546026 | + | 0.837768i | \(0.316140\pi\) | |||||||
\(450\) | −1.78042e11 | − | 3.08378e11i | −0.204676 | − | 0.354508i | ||||
\(451\) | 1.56071e11 | − | 2.70323e11i | 0.177635 | − | 0.307673i | ||||
\(452\) | −4.21163e11 | + | 7.29476e11i | −0.474599 | + | 0.822030i | ||||
\(453\) | 3.24269e11 | + | 5.61651e11i | 0.361796 | + | 0.626650i | ||||
\(454\) | 3.03180e11 | 0.334926 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.03740e11 | 0.112358 | ||||||||
\(457\) | 5.75413e11 | + | 9.96644e11i | 0.617102 | + | 1.06885i | 0.990012 | + | 0.140984i | \(0.0450266\pi\) |
−0.372910 | + | 0.927867i | \(0.621640\pi\) | |||||||
\(458\) | 2.97902e11 | − | 5.15982e11i | 0.316358 | − | 0.547949i | ||||
\(459\) | 5.75099e11 | − | 9.96100e11i | 0.604763 | − | 1.04748i | ||||
\(460\) | −4.60594e11 | − | 7.97772e11i | −0.479632 | − | 0.830747i | ||||
\(461\) | −2.66471e11 | −0.274786 | −0.137393 | − | 0.990517i | \(-0.543872\pi\) | ||||
−0.137393 | + | 0.990517i | \(0.543872\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.48766e11 | −0.453843 | −0.226921 | − | 0.973913i | \(-0.572866\pi\) | ||||
−0.226921 | + | 0.973913i | \(0.572866\pi\) | |||||||
\(464\) | −1.88475e11 | − | 3.26448e11i | −0.188765 | − | 0.326951i | ||||
\(465\) | −5.66552e11 | + | 9.81296e11i | −0.561955 | + | 0.973334i | ||||
\(466\) | 1.47070e11 | − | 2.54733e11i | 0.144473 | − | 0.250235i | ||||
\(467\) | −8.89076e11 | − | 1.53992e12i | −0.864993 | − | 1.49821i | −0.867054 | − | 0.498214i | \(-0.833989\pi\) |
0.00206063 | − | 0.999998i | \(-0.499344\pi\) | |||||||
\(468\) | −2.92263e11 | −0.281623 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.71583e12 | 1.62194 | ||||||||
\(471\) | 5.28943e10 | + | 9.16156e10i | 0.0495239 | + | 0.0857779i | ||||
\(472\) | −1.60942e11 | + | 2.78761e11i | −0.149256 | + | 0.258519i | ||||
\(473\) | 1.62983e11 | − | 2.82295e11i | 0.149716 | − | 0.259315i | ||||
\(474\) | −1.86161e11 | − | 3.22441e11i | −0.169389 | − | 0.293391i | ||||
\(475\) | −6.00627e11 | −0.541357 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.44293e11 | 0.658281 | ||||||||
\(478\) | −2.92381e11 | − | 5.06418e11i | −0.256167 | − | 0.443694i | ||||
\(479\) | 9.94531e11 | − | 1.72258e12i | 0.863194 | − | 1.49510i | −0.00563474 | − | 0.999984i | \(-0.501794\pi\) |
0.868829 | − | 0.495112i | \(-0.164873\pi\) | |||||||
\(480\) | −1.12773e11 | + | 1.95329e11i | −0.0969662 | + | 0.167950i | ||||
\(481\) | 7.70816e11 | + | 1.33509e12i | 0.656596 | + | 1.13726i | ||||
\(482\) | −4.57448e11 | −0.386038 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.08221e11 | 0.172472 | ||||||||
\(485\) | −9.17418e11 | − | 1.58901e12i | −0.752886 | − | 1.30404i | ||||
\(486\) | 3.64162e11 | − | 6.30747e11i | 0.296095 | − | 0.512852i | ||||
\(487\) | −3.44296e11 | + | 5.96338e11i | −0.277365 | + | 0.480410i | −0.970729 | − | 0.240177i | \(-0.922794\pi\) |
0.693364 | + | 0.720588i | \(0.256128\pi\) | |||||||
\(488\) | 2.82679e10 | + | 4.89614e10i | 0.0225634 | + | 0.0390809i | ||||
\(489\) | −3.43911e11 | −0.271992 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.86881e12 | 1.45111 | 0.725553 | − | 0.688166i | \(-0.241584\pi\) | ||||
0.725553 | + | 0.688166i | \(0.241584\pi\) | |||||||
\(492\) | 7.28512e10 | + | 1.26182e11i | 0.0560523 | + | 0.0970854i | ||||
\(493\) | −1.11769e12 | + | 1.93590e12i | −0.852139 | + | 1.47595i | ||||
\(494\) | −2.46489e11 | + | 4.26931e11i | −0.186220 | + | 0.322542i | ||||
\(495\) | −5.39080e11 | − | 9.33714e11i | −0.403580 | − | 0.699022i | ||||
\(496\) | −3.45234e11 | −0.256121 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −8.65521e11 | −0.630588 | ||||||||
\(499\) | 4.38705e11 | + | 7.59860e11i | 0.316753 | + | 0.548632i | 0.979809 | − | 0.199938i | \(-0.0640741\pi\) |
−0.663056 | + | 0.748570i | \(0.730741\pi\) | |||||||
\(500\) | 1.29226e11 | − | 2.23826e11i | 0.0924664 | − | 0.160157i | ||||
\(501\) | −8.39358e11 | + | 1.45381e12i | −0.595220 | + | 1.03095i | ||||
\(502\) | −8.01377e10 | − | 1.38803e11i | −0.0563210 | − | 0.0975508i | ||||
\(503\) | −2.12177e11 | −0.147789 | −0.0738945 | − | 0.997266i | \(-0.523543\pi\) | ||||
−0.0738945 | + | 0.997266i | \(0.523543\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.83006e10 | 0.0125215 | ||||||||
\(506\) | −7.73882e11 | − | 1.34040e12i | −0.524804 | − | 0.908988i | ||||
\(507\) | −2.56662e11 | + | 4.44551e11i | −0.172514 | + | 0.298804i | ||||
\(508\) | 6.93341e11 | − | 1.20090e12i | 0.461913 | − | 0.800056i | ||||
\(509\) | 9.14357e11 | + | 1.58371e12i | 0.603790 | + | 1.04579i | 0.992242 | + | 0.124325i | \(0.0396766\pi\) |
−0.388452 | + | 0.921469i | \(0.626990\pi\) | |||||||
\(510\) | 1.33753e12 | 0.875464 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −6.87195e10 | −0.0441942 | ||||||||
\(513\) | −3.64996e11 | − | 6.32191e11i | −0.232680 | − | 0.403014i | ||||
\(514\) | −1.35745e11 | + | 2.35117e11i | −0.0857807 | + | 0.148577i | ||||
\(515\) | 1.00449e12 | − | 1.73982e12i | 0.629234 | − | 1.08986i | ||||
\(516\) | 7.60775e10 | + | 1.31770e11i | 0.0472424 | + | 0.0818263i | ||||
\(517\) | 2.88291e12 | 1.77470 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.67134e11 | −0.464107 | ||||||||
\(520\) | −5.35903e11 | − | 9.28211e11i | −0.321419 | − | 0.556714i | ||||
\(521\) | −1.34178e12 | + | 2.32404e12i | −0.797834 | + | 1.38189i | 0.123190 | + | 0.992383i | \(0.460688\pi\) |
−0.921024 | + | 0.389506i | \(0.872646\pi\) | |||||||
\(522\) | −4.20547e11 | + | 7.28408e11i | −0.247912 | + | 0.429396i | ||||
\(523\) | −4.53722e11 | − | 7.85869e11i | −0.265175 | − | 0.459296i | 0.702435 | − | 0.711748i | \(-0.252096\pi\) |
−0.967609 | + | 0.252452i | \(0.918763\pi\) | |||||||
\(524\) | −8.67307e11 | −0.502553 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.13151e11 | −0.0644498 | ||||||||
\(527\) | 1.02365e12 | + | 1.77302e12i | 0.578102 | + | 1.00130i | ||||
\(528\) | −1.89480e11 | + | 3.28188e11i | −0.106099 | + | 0.183768i | ||||
\(529\) | −5.74794e11 | + | 9.95572e11i | −0.319125 | + | 0.552741i | ||||
\(530\) | 1.36476e12 | + | 2.36383e12i | 0.751301 | + | 1.30129i | ||||
\(531\) | 7.18227e11 | 0.392046 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.92384e11 | −0.371599 | ||||||||
\(534\) | 4.26648e11 | + | 7.38975e11i | 0.227056 | + | 0.393273i | ||||
\(535\) | −1.55508e12 | + | 2.69348e12i | −0.820657 | + | 1.42142i | ||||
\(536\) | −2.08317e11 | + | 3.60816e11i | −0.109014 | + | 0.188818i | ||||
\(537\) | 3.19857e11 | + | 5.54009e11i | 0.165986 | + | 0.287497i | ||||
\(538\) | 5.91926e9 | 0.00304612 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.58711e12 | 0.803221 | ||||||||
\(541\) | 2.41567e11 | + | 4.18407e11i | 0.121241 | + | 0.209996i | 0.920257 | − | 0.391314i | \(-0.127979\pi\) |
−0.799016 | + | 0.601310i | \(0.794646\pi\) | |||||||
\(542\) | 9.94306e11 | − | 1.72219e12i | 0.494907 | − | 0.857204i | ||||
\(543\) | −2.80822e11 | + | 4.86398e11i | −0.138622 | + | 0.240100i | ||||
\(544\) | 2.03760e11 | + | 3.52922e11i | 0.0997524 | + | 0.172776i | ||||
\(545\) | 3.21615e12 | 1.56154 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.24340e12 | 1.07143 | 0.535716 | − | 0.844398i | \(-0.320042\pi\) | ||||
0.535716 | + | 0.844398i | \(0.320042\pi\) | |||||||
\(548\) | −6.07653e11 | − | 1.05249e12i | −0.287835 | − | 0.498544i | ||||
\(549\) | 6.30745e10 | − | 1.09248e11i | 0.0296332 | − | 0.0513262i | ||||
\(550\) | 1.09704e12 | − | 1.90012e12i | 0.511197 | − | 0.885419i | ||||
\(551\) | 7.09360e11 | + | 1.22865e12i | 0.327857 | + | 0.567865i | ||||
\(552\) | 7.22468e11 | 0.331202 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2.71381e11 | −0.122401 | ||||||||
\(555\) | −1.32731e12 | − | 2.29897e12i | −0.593820 | − | 1.02853i | ||||
\(556\) | −2.78833e11 | + | 4.82953e11i | −0.123739 | + | 0.214323i | ||||
\(557\) | −3.62305e11 | + | 6.27530e11i | −0.159487 | + | 0.276240i | −0.934684 | − | 0.355480i | \(-0.884317\pi\) |
0.775197 | + | 0.631720i | \(0.217651\pi\) | |||||||
\(558\) | 3.85163e11 | + | 6.67122e11i | 0.168186 | + | 0.291307i | ||||
\(559\) | −7.23047e11 | −0.313194 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.24730e12 | 0.957917 | ||||||||
\(562\) | 9.31526e11 | + | 1.61345e12i | 0.393896 | + | 0.682248i | ||||
\(563\) | 2.10927e12 | − | 3.65336e12i | 0.884799 | − | 1.53252i | 0.0388545 | − | 0.999245i | \(-0.487629\pi\) |
0.845944 | − | 0.533271i | \(-0.179038\pi\) | |||||||
\(564\) | −6.72846e11 | + | 1.16540e12i | −0.280001 | + | 0.484976i | ||||
\(565\) | 3.44630e12 | + | 5.96917e12i | 1.42277 | + | 2.46431i | ||||
\(566\) | 4.24852e11 | 0.174006 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.53875e12 | 0.620297 | ||||||||
\(569\) | −2.17405e12 | − | 3.76556e12i | −0.869488 | − | 1.50600i | −0.862521 | − | 0.506022i | \(-0.831116\pi\) |
−0.00696716 | − | 0.999976i | \(-0.502218\pi\) | |||||||
\(570\) | 4.24443e11 | − | 7.35157e11i | 0.168416 | − | 0.291704i | ||||
\(571\) | 1.12302e12 | − | 1.94512e12i | 0.442103 | − | 0.765745i | −0.555743 | − | 0.831354i | \(-0.687566\pi\) |
0.997845 | + | 0.0656099i | \(0.0208993\pi\) | |||||||
\(572\) | −9.00415e11 | − | 1.55956e12i | −0.351690 | − | 0.609146i | ||||
\(573\) | 7.12082e11 | 0.275952 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.18289e12 | −1.59577 | ||||||||
\(576\) | 7.66674e10 | + | 1.32792e11i | 0.0290208 | + | 0.0502655i | ||||
\(577\) | 1.32414e12 | − | 2.29348e12i | 0.497328 | − | 0.861397i | −0.502668 | − | 0.864480i | \(-0.667648\pi\) |
0.999995 | + | 0.00308304i | \(0.000981362\pi\) | |||||||
\(578\) | 2.59630e11 | − | 4.49692e11i | 0.0967563 | − | 0.167587i | ||||
\(579\) | −2.14261e11 | − | 3.71112e11i | −0.0792302 | − | 0.137231i | ||||
\(580\) | −3.08451e12 | −1.13177 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.43902e12 | 0.519893 | ||||||||
\(583\) | 2.29304e12 | + | 3.97167e12i | 0.822060 | + | 1.42385i | ||||
\(584\) | −9.13296e11 | + | 1.58187e12i | −0.324903 | + | 0.562748i | ||||
\(585\) | −1.19577e12 | + | 2.07113e12i | −0.422130 | + | 0.731150i | ||||
\(586\) | −7.54739e9 | − | 1.30725e10i | −0.00264398 | − | 0.00457950i | ||||
\(587\) | −2.72201e12 | −0.946276 | −0.473138 | − | 0.880988i | \(-0.656879\pi\) | ||||
−0.473138 | + | 0.880988i | \(0.656879\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.29935e12 | 0.444845 | ||||||||
\(590\) | 1.31696e12 | + | 2.28105e12i | 0.447445 | + | 0.774997i | ||||
\(591\) | 1.86146e12 | − | 3.22414e12i | 0.627639 | − | 1.08710i | ||||
\(592\) | 4.04406e11 | − | 7.00451e11i | 0.135322 | − | 0.234385i | ||||
\(593\) | −1.07809e11 | − | 1.86731e11i | −0.0358023 | − | 0.0620114i | 0.847569 | − | 0.530685i | \(-0.178065\pi\) |
−0.883371 | + | 0.468674i | \(0.844732\pi\) | |||||||
\(594\) | 2.66663e12 | 0.878870 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.02228e12 | −0.981129 | ||||||||
\(597\) | −9.21996e11 | − | 1.59694e12i | −0.297060 | − | 0.514524i | ||||
\(598\) | −1.71660e12 | + | 2.97324e12i | −0.548926 | + | 0.950767i | ||||
\(599\) | 5.59513e11 | − | 9.69105e11i | 0.177578 | − | 0.307574i | −0.763472 | − | 0.645841i | \(-0.776507\pi\) |
0.941050 | + | 0.338266i | \(0.109840\pi\) | |||||||
\(600\) | 5.12076e11 | + | 8.86941e11i | 0.161307 | + | 0.279392i | ||||
\(601\) | 2.89926e12 | 0.906467 | 0.453234 | − | 0.891392i | \(-0.350270\pi\) | ||||
0.453234 | + | 0.891392i | \(0.350270\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.29643e11 | 0.286344 | ||||||||
\(604\) | 8.08450e11 | + | 1.40028e12i | 0.247165 | + | 0.428102i | ||||
\(605\) | 8.51916e11 | − | 1.47556e12i | 0.258522 | − | 0.447773i | ||||
\(606\) | −7.17639e9 | + | 1.24299e10i | −0.00216162 | + | 0.00374403i | ||||
\(607\) | −8.83626e11 | − | 1.53049e12i | −0.264192 | − | 0.457594i | 0.703160 | − | 0.711032i | \(-0.251772\pi\) |
−0.967352 | + | 0.253438i | \(0.918439\pi\) | |||||||
\(608\) | 2.58639e11 | 0.0767586 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.62622e11 | 0.135283 | ||||||||
\(611\) | −3.19739e12 | − | 5.53804e12i | −0.928133 | − | 1.60757i | ||||
\(612\) | 4.54652e11 | − | 7.87481e11i | 0.131008 | − | 0.226913i | ||||
\(613\) | 3.97147e11 | − | 6.87878e11i | 0.113600 | − | 0.196761i | −0.803619 | − | 0.595144i | \(-0.797095\pi\) |
0.917219 | + | 0.398383i | \(0.130428\pi\) | |||||||
\(614\) | 1.76534e11 | + | 3.05766e11i | 0.0501269 | + | 0.0868224i | ||||
\(615\) | 1.19226e12 | 0.336071 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.17799e12 | 0.882815 | 0.441407 | − | 0.897307i | \(-0.354479\pi\) | ||||
0.441407 | + | 0.897307i | \(0.354479\pi\) | |||||||
\(618\) | 7.87797e11 | + | 1.36451e12i | 0.217253 | + | 0.376294i | ||||
\(619\) | −3.29763e12 | + | 5.71166e12i | −0.902804 | + | 1.56370i | −0.0789670 | + | 0.996877i | \(0.525162\pi\) |
−0.823838 | + | 0.566826i | \(0.808171\pi\) | |||||||
\(620\) | −1.41249e12 | + | 2.44651e12i | −0.383905 | + | 0.664943i | ||||
\(621\) | −2.54191e12 | − | 4.40271e12i | −0.685879 | − | 1.18798i | ||||
\(622\) | 3.68388e12 | 0.986845 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 8.40594e11 | 0.221950 | ||||||||
\(625\) | 1.32057e12 | + | 2.28729e12i | 0.346178 | + | 0.599598i | ||||
\(626\) | −1.26070e12 | + | 2.18360e12i | −0.328117 | + | 0.568315i | ||||
\(627\) | 7.13142e11 | − | 1.23520e12i | 0.184277 | − | 0.319178i | ||||
\(628\) | 1.31873e11 | + | 2.28411e11i | 0.0338328 | + | 0.0586000i | ||||
\(629\) | −4.79640e12 | −1.22177 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.22143e12 | −1.31117 | −0.655583 | − | 0.755123i | \(-0.727577\pi\) | ||||
−0.655583 | + | 0.755123i | \(0.727577\pi\) | |||||||
\(632\) | −4.64126e11 | − | 8.03890e11i | −0.115720 | − | 0.200433i | ||||
\(633\) | −3.25418e11 | + | 5.63640e11i | −0.0805610 | + | 0.139536i | ||||
\(634\) | 1.93200e12 | − | 3.34632e12i | 0.474903 | − | 0.822556i | ||||
\(635\) | −5.67348e12 | − | 9.82676e12i | −1.38474 | − | 2.39844i | ||||
\(636\) | −2.14070e12 | −0.518798 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.18254e12 | −1.23837 | ||||||||
\(639\) | −1.71671e12 | − | 2.97344e12i | −0.407328 | − | 0.705513i | ||||
\(640\) | −2.81160e11 | + | 4.86983e11i | −0.0662434 | + | 0.114737i | ||||
\(641\) | −1.84863e12 | + | 3.20193e12i | −0.432504 | + | 0.749119i | −0.997088 | − | 0.0762567i | \(-0.975703\pi\) |
0.564584 | + | 0.825375i | \(0.309036\pi\) | |||||||
\(642\) | −1.21962e12 | − | 2.11244e12i | −0.283345 | − | 0.490768i | ||||
\(643\) | −5.23082e12 | −1.20676 | −0.603379 | − | 0.797455i | \(-0.706179\pi\) | ||||
−0.603379 | + | 0.797455i | \(0.706179\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.24506e12 | 0.283250 | ||||||||
\(646\) | −7.66888e11 | − | 1.32829e12i | −0.173255 | − | 0.300086i | ||||
\(647\) | 1.46236e12 | − | 2.53289e12i | 0.328085 | − | 0.568260i | −0.654047 | − | 0.756454i | \(-0.726930\pi\) |
0.982132 | + | 0.188194i | \(0.0602635\pi\) | |||||||
\(648\) | −2.53949e11 | + | 4.39852e11i | −0.0565794 | + | 0.0979984i | ||||
\(649\) | 2.21274e12 | + | 3.83258e12i | 0.489586 | + | 0.847988i | ||||
\(650\) | −4.86681e12 | −1.06939 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.57420e11 | −0.185814 | ||||||||
\(653\) | 2.16021e11 | + | 3.74160e11i | 0.0464930 | + | 0.0805282i | 0.888335 | − | 0.459195i | \(-0.151862\pi\) |
−0.841842 | + | 0.539723i | \(0.818529\pi\) | |||||||
\(654\) | −1.26118e12 | + | 2.18442e12i | −0.269573 | + | 0.466914i | ||||
\(655\) | −3.54851e12 | + | 6.14619e12i | −0.753286 | + | 1.30473i | ||||
\(656\) | 1.81628e11 | + | 3.14589e11i | 0.0382927 | + | 0.0663249i | ||||
\(657\) | 4.07570e12 | 0.853411 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.16777e12 | −1.27393 | −0.636963 | − | 0.770894i | \(-0.719810\pi\) | ||||
−0.636963 | + | 0.770894i | \(0.719810\pi\) | |||||||
\(660\) | 1.55048e12 | + | 2.68550e12i | 0.318066 | + | 0.550907i | ||||
\(661\) | 1.12686e12 | − | 1.95179e12i | 0.229596 | − | 0.397672i | −0.728092 | − | 0.685479i | \(-0.759593\pi\) |
0.957689 | + | 0.287807i | \(0.0929261\pi\) | |||||||
\(662\) | 1.14829e12 | − | 1.98890e12i | 0.232376 | − | 0.402487i | ||||
\(663\) | −2.49244e12 | − | 4.31703e12i | −0.500972 | − | 0.867710i | ||||
\(664\) | −2.15787e12 | −0.430793 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.80471e12 | −0.355447 | ||||||||
\(667\) | 4.94013e12 | + | 8.55656e12i | 0.966434 | + | 1.67391i | ||||
\(668\) | −2.09264e12 | + | 3.62456e12i | −0.406631 | + | 0.704305i | ||||
\(669\) | 2.23202e12 | − | 3.86598e12i | 0.430806 | − | 0.746177i | ||||
\(670\) | 1.70462e12 | + | 2.95249e12i | 0.326807 | + | 0.566047i | ||||
\(671\) | 7.77289e11 | 0.148024 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.91498e12 | 0.923536 | 0.461768 | − | 0.887001i | \(-0.347215\pi\) | ||||
0.461768 | + | 0.887001i | \(0.347215\pi\) | |||||||
\(674\) | 1.08274e12 | + | 1.87537e12i | 0.202095 | + | 0.350039i | ||||
\(675\) | 3.60334e12 | − | 6.24117e12i | 0.668095 | − | 1.15718i | ||||
\(676\) | −6.39894e11 | + | 1.10833e12i | −0.117855 | + | 0.204131i | ||||
\(677\) | −5.04615e11 | − | 8.74019e11i | −0.0923233 | − | 0.159909i | 0.816165 | − | 0.577819i | \(-0.196096\pi\) |
−0.908488 | + | 0.417910i | \(0.862763\pi\) | |||||||
\(678\) | −5.40571e12 | −0.982470 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3.33466e12 | 0.598082 | ||||||||
\(681\) | 9.72844e11 | + | 1.68501e12i | 0.173333 | + | 0.300221i | ||||
\(682\) | −2.37325e12 | + | 4.11058e12i | −0.420062 | + | 0.727569i | ||||
\(683\) | 1.16806e12 | − | 2.02313e12i | 0.205386 | − | 0.355739i | −0.744870 | − | 0.667210i | \(-0.767488\pi\) |
0.950256 | + | 0.311471i | \(0.100822\pi\) | |||||||
\(684\) | −2.88552e11 | − | 4.99787e11i | −0.0504048 | − | 0.0873037i | ||||
\(685\) | −9.94462e12 | −1.72576 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.82364e12 | 0.654895 | ||||||||
\(688\) | 1.89672e11 | + | 3.28521e11i | 0.0322742 | + | 0.0559005i | ||||
\(689\) | 5.08635e12 | − | 8.80981e12i | 0.859844 | − | 1.48929i | ||||
\(690\) | 2.95591e12 | − | 5.11979e12i | 0.496444 | − | 0.859867i | ||||
\(691\) | −5.53942e12 | − | 9.59456e12i | −0.924300 | − | 1.60094i | −0.792683 | − | 0.609635i | \(-0.791316\pi\) |
−0.131618 | − | 0.991301i | \(-0.542017\pi\) | |||||||
\(692\) | −1.91257e12 | −0.317059 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.19989e12 | −1.01453 | ||||||||
\(695\) | 2.28164e12 | + | 3.95192e12i | 0.370950 | + | 0.642505i | ||||
\(696\) | 1.20956e12 | − | 2.09501e12i | 0.195382 | − | 0.338412i | ||||
\(697\) | 1.07709e12 | − | 1.86557e12i | 0.172864 | − | 0.299409i | ||||
\(698\) | −8.20488e11 | − | 1.42113e12i | −0.130835 | − | 0.226612i | ||||
\(699\) | 1.88767e12 | 0.299075 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.11682e11 | 0.126956 | 0.0634782 | − | 0.997983i | \(-0.479781\pi\) | ||||
0.0634782 | + | 0.997983i | \(0.479781\pi\) | |||||||
\(702\) | −2.95752e12 | − | 5.12257e12i | −0.459632 | − | 0.796107i | ||||
\(703\) | −1.52206e12 | + | 2.63628e12i | −0.235035 | + | 0.407092i | ||||
\(704\) | −4.72399e11 | + | 8.18220e11i | −0.0724823 | + | 0.125543i | ||||
\(705\) | 5.50577e12 | + | 9.53628e12i | 0.839397 | + | 1.45388i | ||||
\(706\) | 2.08026e11 | 0.0315134 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.06573e12 | −0.308976 | ||||||||
\(709\) | −4.48490e12 | − | 7.76807e12i | −0.666568 | − | 1.15453i | −0.978858 | − | 0.204543i | \(-0.934429\pi\) |
0.312289 | − | 0.949987i | \(-0.398904\pi\) | |||||||
\(710\) | 6.29564e12 | − | 1.09044e13i | 0.929774 | − | 1.61042i | ||||
\(711\) | −1.03561e12 | + | 1.79373e12i | −0.151979 | + | 0.263236i | ||||
\(712\) | 1.06369e12 | + | 1.84237e12i | 0.155116 | + | 0.268669i | ||||
\(713\) | 9.04897e12 | 1.31128 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.47359e13 | −2.10862 | ||||||||
\(716\) | 7.97450e11 | + | 1.38122e12i | 0.113395 | + | 0.196406i | ||||
\(717\) | 1.87638e12 | − | 3.24999e12i | 0.265146 | − | 0.459247i | ||||
\(718\) | −6.84421e11 | + | 1.18545e12i | −0.0961088 | + | 0.166465i | ||||
\(719\) | −5.27879e12 | − | 9.14313e12i | −0.736638 | − | 1.27590i | −0.954001 | − | 0.299804i | \(-0.903079\pi\) |
0.217362 | − | 0.976091i | \(-0.430255\pi\) | |||||||
\(720\) | 1.25471e12 | 0.173999 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 4.18957e12 | 0.573789 | ||||||||
\(723\) | −1.46786e12 | − | 2.54241e12i | −0.199785 | − | 0.346038i | ||||
\(724\) | −7.00129e11 | + | 1.21266e12i | −0.0947010 | + | 0.164027i | ||||
\(725\) | −7.00300e12 | + | 1.21296e13i | −0.941377 | + | 1.63051i | ||||
\(726\) | 6.68139e11 | + | 1.15725e12i | 0.0892590 | + | 0.154601i | ||||
\(727\) | 2.48043e12 | 0.329323 | 0.164661 | − | 0.986350i | \(-0.447347\pi\) | ||||
0.164661 | + | 0.986350i | \(0.447347\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.11476e12 | 0.933010 | ||||||||
\(730\) | 7.47333e12 | + | 1.29442e13i | 0.974005 | + | 1.68703i | ||||
\(731\) | 1.12479e12 | − | 1.94819e12i | 0.145695 | − | 0.252350i | ||||
\(732\) | −1.81412e11 | + | 3.14215e11i | −0.0233543 | + | 0.0404508i | ||||
\(733\) | 4.97539e12 | + | 8.61763e12i | 0.636589 | + | 1.10260i | 0.986176 | + | 0.165701i | \(0.0529886\pi\) |
−0.349587 | + | 0.936904i | \(0.613678\pi\) | |||||||
\(734\) | 1.80987e12 | 0.230152 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.80121e12 | 0.226264 | ||||||||
\(737\) | 2.86408e12 | + | 4.96073e12i | 0.357586 | + | 0.619358i | ||||
\(738\) | 4.05270e11 | − | 7.01948e11i | 0.0502911 | − | 0.0871067i | ||||
\(739\) | 1.76100e12 | − | 3.05015e12i | 0.217200 | − | 0.376202i | −0.736751 | − | 0.676164i | \(-0.763641\pi\) |
0.953951 | + | 0.299963i | \(0.0969742\pi\) | |||||||
\(740\) | −3.30918e12 | − | 5.73167e12i | −0.405674 | − | 0.702649i | ||||
\(741\) | −3.16373e12 | −0.385494 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.25259e13 | −1.50786 | −0.753930 | − | 0.656955i | \(-0.771844\pi\) | ||||
−0.753930 | + | 0.656955i | \(0.771844\pi\) | |||||||
\(744\) | −1.10779e12 | − | 1.91874e12i | −0.132550 | − | 0.229583i | ||||
\(745\) | −1.23654e13 | + | 2.14175e13i | −1.47063 | + | 2.54721i | ||||
\(746\) | −1.55775e12 | + | 2.69810e12i | −0.184151 | + | 0.318958i | ||||
\(747\) | 2.40744e12 | + | 4.16981e12i | 0.282887 | + | 0.489975i | ||||
\(748\) | 5.60283e12 | 0.654411 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.65864e12 | 0.191415 | ||||||||
\(751\) | −3.45930e12 | − | 5.99168e12i | −0.396833 | − | 0.687335i | 0.596500 | − | 0.802613i | \(-0.296558\pi\) |
−0.993333 | + | 0.115278i | \(0.963224\pi\) | |||||||
\(752\) | −1.67750e12 | + | 2.90551e12i | −0.191286 | + | 0.331316i | ||||
\(753\) | 5.14292e11 | − | 8.90780e11i | 0.0582951 | − | 0.100970i | ||||
\(754\) | 5.74786e12 | + | 9.95559e12i | 0.647643 | + | 1.12175i | ||||
\(755\) | 1.32308e13 | 1.48192 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.68669e12 | −0.297362 | −0.148681 | − | 0.988885i | \(-0.547503\pi\) | ||||
−0.148681 | + | 0.988885i | \(0.547503\pi\) | |||||||
\(758\) | −1.78182e12 | − | 3.08620e12i | −0.196043 | − | 0.339556i | ||||
\(759\) | 4.96647e12 | − | 8.60218e12i | 0.543200 | − | 0.940850i | ||||
\(760\) | 1.05820e12 | − | 1.83285e12i | 0.115055 | − | 0.199281i | ||||
\(761\) | −2.27106e12 | − | 3.93360e12i | −0.245470 | − | 0.425166i | 0.716794 | − | 0.697285i | \(-0.245609\pi\) |
−0.962264 | + | 0.272119i | \(0.912276\pi\) | |||||||
\(762\) | 8.89917e12 | 0.956208 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.77532e12 | 0.188520 | ||||||||
\(765\) | −3.72034e12 | − | 6.44381e12i | −0.392741 | − | 0.680247i | ||||
\(766\) | −2.69276e12 | + | 4.66399e12i | −0.282597 | + | 0.489472i | ||||
\(767\) | 4.90822e12 | − | 8.50129e12i | 0.512088 | − | 0.886963i | ||||
\(768\) | −2.20507e11 | − | 3.81930e11i | −0.0228716 | − | 0.0396148i | ||||
\(769\) | −2.34852e12 | −0.242173 | −0.121087 | − | 0.992642i | \(-0.538638\pi\) | ||||
−0.121087 | + | 0.992642i | \(0.538638\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.74232e12 | −0.177575 | ||||||||
\(772\) | −5.34184e11 | − | 9.25234e11i | −0.0541269 | − | 0.0937506i | ||||
\(773\) | −1.89097e11 | + | 3.27525e11i | −0.0190492 | + | 0.0329941i | −0.875393 | − | 0.483412i | \(-0.839397\pi\) |
0.856344 | + | 0.516406i | \(0.172731\pi\) | |||||||
\(774\) | 4.23218e11 | − | 7.33035e11i | 0.0423867 | − | 0.0734160i | ||||
\(775\) | 6.41379e12 | + | 1.11090e13i | 0.638642 | + | 1.10616i | ||||
\(776\) | 3.58768e12 | 0.355170 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.56640e12 | 0.544711 | ||||||||
\(779\) | −6.83592e11 | − | 1.18402e12i | −0.0665087 | − | 0.115196i | ||||
\(780\) | 3.43921e12 | − | 5.95689e12i | 0.332685 | − | 0.576228i | ||||
\(781\) | 1.05778e13 | − | 1.83213e13i | 1.01734 | − | 1.76209i | ||||
\(782\) | −5.34077e12 | − | 9.25048e12i | −0.510709 | − | 0.884574i | ||||
\(783\) | −1.70227e13 | −1.61845 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.15818e12 | 0.202850 | ||||||||
\(786\) | −2.78302e12 | − | 4.82032e12i | −0.260084 | − | 0.450479i | ||||
\(787\) | −6.05426e12 | + | 1.04863e13i | −0.562568 | + | 0.974396i | 0.434704 | + | 0.900573i | \(0.356853\pi\) |
−0.997271 | + | 0.0738222i | \(0.976480\pi\) | |||||||
\(788\) | 4.64088e12 | − | 8.03824e12i | 0.428778 | − | 0.742665i | ||||
\(789\) | −3.63079e11 | − | 6.28870e11i | −0.0333545 | − | 0.0577716i | ||||
\(790\) | −7.59572e12 | −0.693820 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2.10814e12 | 0.190387 | ||||||||
\(793\) | −8.62078e11 | − | 1.49316e12i | −0.0774136 | − | 0.134084i | ||||
\(794\) | 2.20407e11 | − | 3.81757e11i | 0.0196804 | − | 0.0340874i | ||||
\(795\) | −8.75848e12 | + | 1.51701e13i | −0.777636 | + | 1.34691i | ||||
\(796\) | −2.29867e12 | − | 3.98141e12i | −0.202940 | − | 0.351502i | ||||
\(797\) | 2.16394e13 | 1.89969 | 0.949846 | − | 0.312719i | \(-0.101240\pi\) | ||||
0.949846 | + | 0.312719i | \(0.101240\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.98958e13 | 1.72703 | ||||||||
\(800\) | 1.27668e12 | + | 2.21127e12i | 0.110199 | + | 0.190870i | ||||
\(801\) | 2.37344e12 | − | 4.11091e12i | 0.203719 | − | 0.352851i | ||||
\(802\) | −4.96936e12 | + | 8.60719e12i | −0.424147 | + | 0.734644i | ||||
\(803\) | 1.25566e13 | + | 2.17486e13i | 1.06574 | + | 1.84591i | ||||
\(804\) | −2.67380e12 | −0.225671 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.05285e13 | 0.878738 | ||||||||
\(807\) | 1.89937e10 | + | 3.28981e10i | 0.00157645 | + | 0.00273049i | ||||
\(808\) | −1.78918e10 | + | 3.09894e10i | −0.00147673 | + | 0.00255778i | ||||
\(809\) | 2.18435e12 | − | 3.78340e12i | 0.179289 | − | 0.310537i | −0.762348 | − | 0.647167i | \(-0.775954\pi\) |
0.941637 | + | 0.336630i | \(0.109287\pi\) | |||||||
\(810\) | 2.07802e12 | + | 3.59923e12i | 0.169616 | + | 0.293783i | ||||
\(811\) | −1.39017e13 | −1.12843 | −0.564215 | − | 0.825628i | \(-0.690821\pi\) | ||||
−0.564215 | + | 0.825628i | \(0.690821\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.27621e13 | 1.02451 | ||||||||
\(814\) | −5.56003e12 | − | 9.63025e12i | −0.443881 | − | 0.768825i | ||||
\(815\) | −3.50805e12 | + | 6.07613e12i | −0.278520 | + | 0.482412i | ||||
\(816\) | −1.30765e12 | + | 2.26491e12i | −0.103249 | + | 0.178832i | ||||
\(817\) | −7.13866e11 | − | 1.23645e12i | −0.0560554 | − | 0.0970908i | ||||
\(818\) | −2.34233e11 | −0.0182919 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.97246e12 | 0.229591 | ||||||||
\(821\) | −4.01964e12 | − | 6.96221e12i | −0.308775 | − | 0.534814i | 0.669319 | − | 0.742975i | \(-0.266586\pi\) |
−0.978095 | + | 0.208160i | \(0.933252\pi\) | |||||||
\(822\) | 3.89968e12 | − | 6.75444e12i | 0.297924 | − | 0.516019i | ||||
\(823\) | 9.77693e12 | − | 1.69341e13i | 0.742854 | − | 1.28666i | −0.208337 | − | 0.978057i | \(-0.566805\pi\) |
0.951191 | − | 0.308603i | \(-0.0998615\pi\) | |||||||
\(824\) | 1.96409e12 | + | 3.40190e12i | 0.148419 | + | 0.257069i | ||||
\(825\) | 1.40807e13 | 1.05823 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.31390e13 | 0.976760 | 0.488380 | − | 0.872631i | \(-0.337588\pi\) | ||||
0.488380 | + | 0.872631i | \(0.337588\pi\) | |||||||
\(828\) | −2.00954e12 | − | 3.48062e12i | −0.148580 | − | 0.257348i | ||||
\(829\) | −1.09174e13 | + | 1.89094e13i | −0.802827 | + | 1.39054i | 0.114920 | + | 0.993375i | \(0.463339\pi\) |
−0.917748 | + | 0.397163i | \(0.869995\pi\) | |||||||
\(830\) | −8.82871e12 | + | 1.52918e13i | −0.645723 | + | 1.11842i | ||||
\(831\) | −8.70807e11 | − | 1.50828e12i | −0.0633458 | − | 0.109718i | ||||
\(832\) | 2.09572e12 | 0.151628 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −3.57888e12 | −0.256154 | ||||||||
\(835\) | 1.71237e13 | + | 2.96591e13i | 1.21901 | + | 2.11139i | ||||
\(836\) | 1.77796e12 | − | 3.07952e12i | 0.125891 | − | 0.218050i | ||||
\(837\) | −7.79521e12 | + | 1.35017e13i | −0.548989 | + | 0.950876i | ||||
\(838\) | 9.72042e11 | + | 1.68363e12i | 0.0680906 | + | 0.117936i | ||||
\(839\) | −1.23225e13 | −0.858561 | −0.429281 | − | 0.903171i | \(-0.641233\pi\) | ||||
−0.429281 | + | 0.903171i | \(0.641233\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.85760e13 | 1.28047 | ||||||||
\(842\) | −4.48812e12 | − | 7.77366e12i | −0.307723 | − | 0.532993i | ||||
\(843\) | −5.97817e12 | + | 1.03545e13i | −0.407703 | + | 0.706162i | ||||
\(844\) | −8.11313e11 | + | 1.40524e12i | −0.0550361 | + | 0.0953253i | ||||
\(845\) | 5.23613e12 | + | 9.06925e12i | 0.353310 | + | 0.611950i | ||||
\(846\) | 7.48606e12 | 0.502443 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.33707e12 | −0.354423 | ||||||||
\(849\) | 1.36327e12 | + | 2.36125e12i | 0.0900527 | + | 0.155976i | ||||
\(850\) | 7.57093e12 | − | 1.31132e13i | 0.497467 | − | 0.861638i | ||||
\(851\) | −1.05999e13 | + | 1.83596e13i | −0.692819 | + | 1.20000i | ||||
\(852\) | 4.93753e12 | + | 8.55206e12i | 0.321020 | + | 0.556023i | ||||
\(853\) | −9.07085e12 | −0.586647 | −0.293324 | − | 0.956013i | \(-0.594761\pi\) | ||||
−0.293324 | + | 0.956013i | \(0.594761\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.72234e12 | −0.302211 | ||||||||
\(856\) | −3.04068e12 | − | 5.26661e12i | −0.193570 | − | 0.335274i | ||||
\(857\) | 8.32198e11 | − | 1.44141e12i | 0.0527003 | − | 0.0912795i | −0.838472 | − | 0.544945i | \(-0.816551\pi\) |
0.891172 | + | 0.453665i | \(0.149884\pi\) | |||||||
\(858\) | 5.77851e12 | − | 1.00087e13i | 0.364018 | − | 0.630498i | ||||
\(859\) | −7.01160e11 | − | 1.21444e12i | −0.0439388 | − | 0.0761042i | 0.843220 | − | 0.537569i | \(-0.180657\pi\) |
−0.887158 | + | 0.461465i | \(0.847324\pi\) | |||||||
\(860\) | 3.10410e12 | 0.193505 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.67091e13 | −1.03079 | ||||||||
\(863\) | 1.02991e12 | + | 1.78386e12i | 0.0632049 | + | 0.109474i | 0.895896 | − | 0.444263i | \(-0.146535\pi\) |
−0.832691 | + | 0.553737i | \(0.813201\pi\) | |||||||
\(864\) | −1.55165e12 | + | 2.68754e12i | −0.0947289 | + | 0.164075i | ||||
\(865\) | −7.82512e12 | + | 1.35535e13i | −0.475246 | + | 0.823150i | ||||
\(866\) | −8.43565e12 | − | 1.46110e13i | −0.509669 | − | 0.882772i | ||||
\(867\) | 3.33240e12 | 0.200296 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.27622e13 | −0.759165 | ||||||||
\(870\) | −9.89758e12 | − | 1.71431e13i | −0.585723 | − | 1.01450i | ||||
\(871\) | 6.35300e12 | − | 1.10037e13i | 0.374022 | − | 0.647825i | ||||
\(872\) | −3.14430e12 | + | 5.44608e12i | −0.184162 | + | 0.318977i | ||||
\(873\) | −4.00263e12 | − | 6.93276e12i | −0.233228 | − | 0.403963i | ||||
\(874\) | −6.77921e12 | −0.392986 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.17223e13 | −0.672583 | ||||||||
\(877\) | −8.71424e12 | − | 1.50935e13i | −0.497429 | − | 0.861573i | 0.502566 | − | 0.864539i | \(-0.332389\pi\) |
−0.999996 | + | 0.00296566i | \(0.999056\pi\) | |||||||
\(878\) | −9.36294e12 | + | 1.62171e13i | −0.531725 | + | 0.920975i | ||||
\(879\) | 4.84362e10 | − | 8.38939e10i | 0.00273665 | − | 0.00474002i | ||||
\(880\) | 3.86556e12 | + | 6.69534e12i | 0.217290 | + | 0.376358i | ||||
\(881\) | 1.33834e11 | 0.00748471 | 0.00374235 | − | 0.999993i | \(-0.498809\pi\) | ||||
0.00374235 | + | 0.999993i | \(0.498809\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.44009e12 | 0.135077 | 0.0675386 | − | 0.997717i | \(-0.478485\pi\) | ||||
0.0675386 | + | 0.997717i | \(0.478485\pi\) | |||||||
\(884\) | −6.21401e12 | − | 1.07630e13i | −0.342244 | − | 0.592785i | ||||
\(885\) | −8.45175e12 | + | 1.46389e13i | −0.463129 | + | 0.802163i | ||||
\(886\) | −5.68528e12 | + | 9.84719e12i | −0.309956 | + | 0.536859i | ||||
\(887\) | −6.80159e12 | − | 1.17807e13i | −0.368939 | − | 0.639021i | 0.620461 | − | 0.784237i | \(-0.286945\pi\) |
−0.989400 | + | 0.145217i | \(0.953612\pi\) | |||||||
\(888\) | 5.19063e12 | 0.280132 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.74080e13 | 0.930024 | ||||||||
\(891\) | 3.49144e12 | + | 6.04736e12i | 0.185590 | + | 0.321452i | ||||
\(892\) | 5.56475e12 | − | 9.63844e12i | 0.294309 | − | 0.509759i | ||||
\(893\) | 6.31358e12 | − | 1.09354e13i | 0.332234 | − | 0.575447i | ||||
\(894\) | −9.69789e12 | − | 1.67972e13i | −0.507760 | − | 0.879466i | ||||
\(895\) | 1.30508e13 | 0.679880 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.20329e13 | −1.13633 | ||||||||
\(898\) | 7.52388e12 | + | 1.30317e13i | 0.386099 | + | 0.668742i | ||||
\(899\) | 1.51498e13 | − | 2.62402e13i | 0.773550 | − | 1.33983i | ||||
\(900\) | 2.84867e12 | − | 4.93404e12i | 0.144727 | − | 0.250675i | ||||
\(901\) | 1.58249e13 | + | 2.74095e13i | 0.799981 | + | 1.38561i | ||||
\(902\) | 4.99428e12 | 0.251214 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.34772e13 | −0.671185 | ||||||||
\(905\) | 5.72903e12 | + | 9.92297e12i | 0.283898 | + | 0.491726i | ||||
\(906\) | −5.18831e12 | + | 8.98642e12i | −0.255829 | + | 0.443108i | ||||
\(907\) | 3.36775e12 | − | 5.83311e12i | 0.165237 | − | 0.286198i | −0.771503 | − | 0.636226i | \(-0.780495\pi\) |
0.936739 | + | 0.350028i | \(0.113828\pi\) | |||||||
\(908\) | 2.42544e12 | + | 4.20098e12i | 0.118414 | + | 0.205099i | ||||
\(909\) | 7.98443e10 | 0.00387888 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.74134e12 | 0.324275 | 0.162137 | − | 0.986768i | \(-0.448161\pi\) | ||||
0.162137 | + | 0.986768i | \(0.448161\pi\) | |||||||
\(912\) | 8.29920e11 | + | 1.43746e12i | 0.0397246 | + | 0.0688050i | ||||
\(913\) | −1.48339e13 | + | 2.56930e13i | −0.706538 | + | 1.22376i | ||||
\(914\) | −9.20661e12 | + | 1.59463e13i | −0.436357 | + | 0.755792i | ||||
\(915\) | 1.48446e12 | + | 2.57116e12i | 0.0700122 | + | 0.121265i | ||||
\(916\) | 9.53287e12 | 0.447398 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.84032e13 | 0.855264 | ||||||||
\(919\) | 1.39722e13 | + | 2.42006e13i | 0.646167 | + | 1.11919i | 0.984031 | + | 0.177999i | \(0.0569625\pi\) |
−0.337863 | + | 0.941195i | \(0.609704\pi\) | |||||||
\(920\) | 7.36951e12 | − | 1.27644e13i | 0.339151 | − | 0.587427i | ||||
\(921\) | −1.13293e12 | + | 1.96229e12i | −0.0518840 | + | 0.0898657i | ||||
\(922\) | −2.13177e12 | − | 3.69233e12i | −0.0971517 | − | 0.168272i | ||||
\(923\) | −4.69267e13 | −2.12820 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.00524e13 | −1.34971 | ||||||||
\(926\) | −3.59013e12 | − | 6.21828e12i | −0.160458 | − | 0.277921i | ||||
\(927\) | 4.38251e12 | − | 7.59073e12i | 0.194923 | − | 0.337617i | ||||
\(928\) | 3.01560e12 | − | 5.22316e12i | 0.133477 | − | 0.231189i | ||||
\(929\) | −5.15477e12 | − | 8.92833e12i | −0.227059 | − | 0.393278i | 0.729876 | − | 0.683579i | \(-0.239578\pi\) |
−0.956935 | + | 0.290302i | \(0.906244\pi\) | |||||||
\(930\) | −1.81297e13 | −0.794724 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 4.70624e12 | 0.204316 | ||||||||
\(933\) | 1.18209e13 | + | 2.04743e13i | 0.510718 | + | 0.884590i | ||||
\(934\) | 1.42252e13 | − | 2.46388e13i | 0.611643 | − | 1.05940i | ||||
\(935\) | 2.29235e13 | − | 3.97046e13i | 0.980908 | − | 1.69898i | ||||
\(936\) | −2.33811e12 | − | 4.04972e12i | −0.0995688 | − | 0.172458i | ||||
\(937\) | −2.54975e13 | −1.08061 | −0.540306 | − | 0.841468i | \(-0.681692\pi\) | ||||
−0.540306 | + | 0.841468i | \(0.681692\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.61814e13 | −0.679236 | ||||||||
\(940\) | 1.37267e13 | + | 2.37753e13i | 0.573443 | + | 0.993232i | ||||
\(941\) | 8.29195e12 | − | 1.43621e13i | 0.344749 | − | 0.597123i | −0.640559 | − | 0.767909i | \(-0.721297\pi\) |
0.985308 | + | 0.170786i | \(0.0546307\pi\) | |||||||
\(942\) | −8.46309e11 | + | 1.46585e12i | −0.0350187 | + | 0.0606541i | ||||
\(943\) | −4.76068e12 | − | 8.24574e12i | −0.196050 | − | 0.339568i | ||||
\(944\) | −5.15016e12 | −0.211080 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.21546e12 | 0.211730 | ||||||||
\(947\) | −1.13116e13 | − | 1.95922e13i | −0.457034 | − | 0.791606i | 0.541769 | − | 0.840527i | \(-0.317755\pi\) |
−0.998803 | + | 0.0489219i | \(0.984421\pi\) | |||||||
\(948\) | 2.97858e12 | − | 5.15905e12i | 0.119776 | − | 0.207459i | ||||
\(949\) | 2.78525e13 | − | 4.82420e13i | 1.11472 | − | 1.93076i | ||||
\(950\) | −4.80501e12 | − | 8.32253e12i | −0.191398 | − | 0.331512i | ||||
\(951\) | 2.47976e13 | 0.983099 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.02695e11 | −0.0118874 | −0.00594370 | − | 0.999982i | \(-0.501892\pi\) | ||||
−0.00594370 | + | 0.999982i | \(0.501892\pi\) | |||||||
\(954\) | 5.95434e12 | + | 1.03132e13i | 0.232737 | + | 0.403113i | ||||
\(955\) | 7.26357e12 | − | 1.25809e13i | 0.282576 | − | 0.489435i | ||||
\(956\) | 4.67809e12 | − | 8.10269e12i | 0.181137 | − | 0.313739i | ||||
\(957\) | −1.66297e13 | − | 2.88036e13i | −0.640887 | − | 1.11005i | ||||
\(958\) | 3.18250e13 | 1.22074 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.60874e12 | −0.137131 | ||||||||
\(961\) | −6.55326e11 | − | 1.13506e12i | −0.0247857 | − | 0.0429302i | ||||
\(962\) | −1.23331e13 | + | 2.13615e13i | −0.464283 | + | 0.804162i | ||||
\(963\) | −6.78472e12 | + | 1.17515e13i | −0.254222 | + | 0.440326i | ||||
\(964\) | −3.65959e12 | − | 6.33859e12i | −0.136485 | − | 0.236399i | ||||
\(965\) | −8.74227e12 | −0.324527 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.03988e12 | 0.111799 | 0.0558994 | − | 0.998436i | \(-0.482197\pi\) | ||||
0.0558994 | + | 0.998436i | \(0.482197\pi\) | |||||||
\(968\) | 1.66577e12 | + | 2.88519e12i | 0.0609782 | + | 0.105617i | ||||
\(969\) | 4.92158e12 | − | 8.52443e12i | 0.179328 | − | 0.310605i | ||||
\(970\) | 1.46787e13 | − | 2.54242e13i | 0.532371 | − | 0.922093i | ||||
\(971\) | 1.07603e13 | + | 1.86374e13i | 0.388453 | + | 0.672821i | 0.992242 | − | 0.124324i | \(-0.0396762\pi\) |
−0.603788 | + | 0.797145i | \(0.706343\pi\) | |||||||
\(972\) | 1.16532e13 | 0.418742 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.10175e13 | −0.392254 | ||||||||
\(975\) | −1.56166e13 | − | 2.70488e13i | −0.553435 | − | 0.958578i | ||||
\(976\) | −4.52286e11 | + | 7.83382e11i | −0.0159547 | + | 0.0276344i | ||||
\(977\) | 7.82269e12 | − | 1.35493e13i | 0.274682 | − | 0.475763i | −0.695373 | − | 0.718649i | \(-0.744761\pi\) |
0.970055 | + | 0.242886i | \(0.0780940\pi\) | |||||||
\(978\) | −2.75129e12 | − | 4.76537e12i | −0.0961638 | − | 0.166561i | ||||
\(979\) | 2.92486e13 | 1.01762 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.40318e13 | 0.483731 | ||||||||
\(982\) | 1.49505e13 | + | 2.58950e13i | 0.513043 | + | 0.888617i | ||||
\(983\) | −1.14381e13 | + | 1.98114e13i | −0.390719 | + | 0.676745i | −0.992545 | − | 0.121883i | \(-0.961107\pi\) |
0.601826 | + | 0.798627i | \(0.294440\pi\) | |||||||
\(984\) | −1.16562e12 | + | 2.01891e12i | −0.0396350 | + | 0.0686498i | ||||
\(985\) | −3.79755e13 | − | 6.57755e13i | −1.28541 | − | 2.22639i | ||||
\(986\) | −3.57661e13 | −1.20511 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.88763e12 | −0.263354 | ||||||||
\(989\) | −4.97151e12 | − | 8.61091e12i | −0.165236 | − | 0.286198i | ||||
\(990\) | 8.62528e12 | − | 1.49394e13i | 0.285374 | − | 0.494283i | ||||
\(991\) | −2.23678e13 | + | 3.87421e13i | −0.736701 | + | 1.27600i | 0.217272 | + | 0.976111i | \(0.430284\pi\) |
−0.953973 | + | 0.299893i | \(0.903049\pi\) | |||||||
\(992\) | −2.76187e12 | − | 4.78370e12i | −0.0905526 | − | 0.156842i | ||||
\(993\) | 1.47386e13 | 0.481043 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.76192e13 | −1.21676 | ||||||||
\(996\) | −6.92417e12 | − | 1.19930e13i | −0.222946 | − | 0.386155i | ||||
\(997\) | 1.62282e13 | − | 2.81081e13i | 0.520166 | − | 0.900954i | −0.479559 | − | 0.877510i | \(-0.659203\pi\) |
0.999725 | − | 0.0234445i | \(-0.00746329\pi\) | |||||||
\(998\) | −7.01928e12 | + | 1.21578e13i | −0.223978 | + | 0.387941i | ||||
\(999\) | −1.82626e13 | − | 3.16317e13i | −0.580119 | − | 1.00480i |
(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 | 98.10.c.m.67.2 | 8 | ||
7.2 | even | 3 | inner | 98.10.c.m.79.2 | 8 | ||
7.3 | odd | 6 | 98.10.a.k.1.2 | ✓ | 4 | ||
7.4 | even | 3 | 98.10.a.k.1.3 | yes | 4 | ||
7.5 | odd | 6 | inner | 98.10.c.m.79.3 | 8 | ||
7.6 | odd | 2 | inner | 98.10.c.m.67.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
98.10.a.k.1.2 | ✓ | 4 | 7.3 | odd | 6 | ||
98.10.a.k.1.3 | yes | 4 | 7.4 | even | 3 | ||
98.10.c.m.67.2 | 8 | 1.1 | even | 1 | trivial | ||
98.10.c.m.67.3 | 8 | 7.6 | odd | 2 | inner | ||
98.10.c.m.79.2 | 8 | 7.2 | even | 3 | inner | ||
98.10.c.m.79.3 | 8 | 7.5 | odd | 6 | inner |