Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4,17,Mod(3,4)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 17, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4.3");
S:= CuspForms(chi, 17);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 17 \) |
Character orbit: | \([\chi]\) | \(=\) | 4.b (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: | \(6.49298175427\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 5152x^{4} + 242526x^{3} + 17329473x^{2} + 402444531x + 64957563630 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{30}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.4 | ||
Root | \(11.8147 - 63.8186i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4.3 |
Dual form | 4.17.b.b.3.3 |
$q$-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 \(\left(\mathbb{Z}/4\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 19.2587 | + | 255.275i | 0.0752294 | + | 0.997166i | ||||
\(3\) | 11183.9i | 1.70460i | 0.523055 | + | 0.852299i | \(0.324792\pi\) | ||||
−0.523055 | + | 0.852299i | \(0.675208\pi\) | |||||||
\(4\) | −64794.2 | + | 9832.53i | −0.988681 | + | 0.150032i | ||||
\(5\) | 389860. | 0.998042 | 0.499021 | − | 0.866590i | \(-0.333693\pi\) | ||||
0.499021 | + | 0.866590i | \(0.333693\pi\) | |||||||
\(6\) | −2.85496e6 | + | 215387.i | −1.69977 | + | 0.128236i | ||||
\(7\) | − | 1.06777e6i | − | 0.185223i | −0.995702 | − | 0.0926113i | \(-0.970479\pi\) | ||
0.995702 | − | 0.0926113i | \(-0.0295214\pi\) | |||||||
\(8\) | −3.75785e6 | − | 1.63509e7i | −0.223985 | − | 0.974593i | ||||
\(9\) | −8.20322e7 | −1.90565 | ||||||||
\(10\) | 7.50821e6 | + | 9.95214e7i | 0.0750821 | + | 0.995214i | ||||
\(11\) | 1.26927e8i | 0.592126i | 0.955168 | + | 0.296063i | \(0.0956739\pi\) | ||||
−0.955168 | + | 0.296063i | \(0.904326\pi\) | |||||||
\(12\) | −1.09966e8 | − | 7.24650e8i | −0.255745 | − | 1.68530i | ||||
\(13\) | 1.12108e9 | 1.37433 | 0.687165 | − | 0.726501i | \(-0.258855\pi\) | ||||
0.687165 | + | 0.726501i | \(0.258855\pi\) | |||||||
\(14\) | 2.72575e8 | − | 2.05639e7i | 0.184698 | − | 0.0139342i | ||||
\(15\) | 4.36015e9i | 1.70126i | ||||||||
\(16\) | 4.10161e9 | − | 1.27418e9i | 0.954981 | − | 0.296669i | ||||
\(17\) | −7.43906e9 | −1.06642 | −0.533208 | − | 0.845984i | \(-0.679014\pi\) | ||||
−0.533208 | + | 0.845984i | \(0.679014\pi\) | |||||||
\(18\) | −1.57984e9 | − | 2.09407e10i | −0.143361 | − | 1.90025i | ||||
\(19\) | 1.76792e10i | 1.04096i | 0.853874 | + | 0.520479i | \(0.174247\pi\) | ||||
−0.853874 | + | 0.520479i | \(0.825753\pi\) | |||||||
\(20\) | −2.52607e10 | + | 3.83331e9i | −0.986746 | + | 0.149739i | ||||
\(21\) | 1.19418e10 | 0.315730 | ||||||||
\(22\) | −3.24014e10 | + | 2.44446e9i | −0.590448 | + | 0.0445453i | ||||
\(23\) | 8.72327e9i | 0.111393i | 0.998448 | + | 0.0556963i | \(0.0177379\pi\) | ||||
−0.998448 | + | 0.0556963i | \(0.982262\pi\) | |||||||
\(24\) | 1.82867e11 | − | 4.20273e10i | 1.66129 | − | 0.381805i | ||||
\(25\) | −5.96851e8 | −0.00391153 | ||||||||
\(26\) | 2.15906e10 | + | 2.86184e11i | 0.103390 | + | 1.37044i | ||||
\(27\) | − | 4.36008e11i | − | 1.54378i | ||||||
\(28\) | 1.04989e10 | + | 6.91854e10i | 0.0277894 | + | 0.183126i | ||||
\(29\) | 2.42638e11 | 0.485038 | 0.242519 | − | 0.970147i | \(-0.422026\pi\) | ||||
0.242519 | + | 0.970147i | \(0.422026\pi\) | |||||||
\(30\) | −1.11303e12 | + | 8.39709e10i | −1.69644 | + | 0.127985i | ||||
\(31\) | − | 6.45199e10i | − | 0.0756485i | −0.999284 | − | 0.0378243i | \(-0.987957\pi\) | ||
0.999284 | − | 0.0378243i | \(-0.0120427\pi\) | |||||||
\(32\) | 4.04258e11 | + | 1.02250e12i | 0.367670 | + | 0.929956i | ||||
\(33\) | −1.41954e12 | −1.00934 | ||||||||
\(34\) | −1.43267e11 | − | 1.89900e12i | −0.0802259 | − | 1.06339i | ||||
\(35\) | − | 4.16282e11i | − | 0.184860i | ||||||
\(36\) | 5.31521e12 | − | 8.06584e11i | 1.88408 | − | 0.285910i | ||||
\(37\) | 2.41678e12 | 0.688055 | 0.344028 | − | 0.938960i | \(-0.388209\pi\) | ||||
0.344028 | + | 0.938960i | \(0.388209\pi\) | |||||||
\(38\) | −4.51305e12 | + | 3.40479e11i | −1.03801 | + | 0.0783107i | ||||
\(39\) | 1.25380e13i | 2.34268i | ||||||||
\(40\) | −1.46504e12 | − | 6.37459e12i | −0.223547 | − | 0.972685i | ||||
\(41\) | 5.45949e12 | 0.683725 | 0.341862 | − | 0.939750i | \(-0.388942\pi\) | ||||
0.341862 | + | 0.939750i | \(0.388942\pi\) | |||||||
\(42\) | 2.29984e11 | + | 3.04844e12i | 0.0237522 | + | 0.314835i | ||||
\(43\) | − | 1.67228e13i | − | 1.43075i | −0.698743 | − | 0.715373i | \(-0.746257\pi\) | ||
0.698743 | − | 0.715373i | \(-0.253743\pi\) | |||||||
\(44\) | −1.24802e12 | − | 8.22417e12i | −0.0888381 | − | 0.585424i | ||||
\(45\) | −3.19811e13 | −1.90192 | ||||||||
\(46\) | −2.22683e12 | + | 1.67999e11i | −0.111077 | + | 0.00838001i | ||||
\(47\) | 1.33646e13i | 0.561272i | 0.959814 | + | 0.280636i | \(0.0905454\pi\) | ||||
−0.959814 | + | 0.280636i | \(0.909455\pi\) | |||||||
\(48\) | 1.42503e13 | + | 4.58719e13i | 0.505701 | + | 1.62786i | ||||
\(49\) | 3.20928e13 | 0.965693 | ||||||||
\(50\) | −1.14946e10 | − | 1.52361e11i | −0.000294262 | − | 0.00390044i | ||||
\(51\) | − | 8.31975e13i | − | 1.81781i | ||||||
\(52\) | −7.26397e13 | + | 1.10231e13i | −1.35877 | + | 0.206194i | ||||
\(53\) | 8.96899e13 | 1.44058 | 0.720289 | − | 0.693675i | \(-0.244009\pi\) | ||||
0.720289 | + | 0.693675i | \(0.244009\pi\) | |||||||
\(54\) | 1.11302e14 | − | 8.39696e12i | 1.53940 | − | 0.116137i | ||||
\(55\) | 4.94840e13i | 0.590967i | ||||||||
\(56\) | −1.74591e13 | + | 4.01252e12i | −0.180517 | + | 0.0414871i | ||||
\(57\) | −1.97722e14 | −1.77442 | ||||||||
\(58\) | 4.67291e12 | + | 6.19394e13i | 0.0364891 | + | 0.483663i | ||||
\(59\) | 9.54083e13i | 0.649785i | 0.945751 | + | 0.324893i | \(0.105328\pi\) | ||||
−0.945751 | + | 0.324893i | \(0.894672\pi\) | |||||||
\(60\) | −4.28713e13 | − | 2.82512e14i | −0.255244 | − | 1.68200i | ||||
\(61\) | −7.10026e13 | −0.370370 | −0.185185 | − | 0.982704i | \(-0.559288\pi\) | ||||
−0.185185 | + | 0.982704i | \(0.559288\pi\) | |||||||
\(62\) | 1.64703e13 | − | 1.24257e12i | 0.0754342 | − | 0.00569099i | ||||
\(63\) | 8.75916e13i | 0.352970i | ||||||||
\(64\) | −2.53232e14 | + | 1.22889e14i | −0.899661 | + | 0.436589i | ||||
\(65\) | 4.37066e14 | 1.37164 | ||||||||
\(66\) | −2.73385e13 | − | 3.62373e14i | −0.0759318 | − | 1.00648i | ||||
\(67\) | 3.55095e14i | 0.874473i | 0.899347 | + | 0.437236i | \(0.144043\pi\) | ||||
−0.899347 | + | 0.437236i | \(0.855957\pi\) | |||||||
\(68\) | 4.82008e14 | − | 7.31448e13i | 1.05435 | − | 0.159997i | ||||
\(69\) | −9.75599e13 | −0.189880 | ||||||||
\(70\) | 1.06266e14 | − | 8.01706e12i | 0.184336 | − | 0.0139069i | ||||
\(71\) | − | 8.97021e14i | − | 1.38911i | −0.719441 | − | 0.694553i | \(-0.755602\pi\) | ||
0.719441 | − | 0.694553i | \(-0.244398\pi\) | |||||||
\(72\) | 3.08264e14 | + | 1.34130e15i | 0.426838 | + | 1.85724i | ||||
\(73\) | −5.31684e14 | −0.659281 | −0.329641 | − | 0.944107i | \(-0.606928\pi\) | ||||
−0.329641 | + | 0.944107i | \(0.606928\pi\) | |||||||
\(74\) | 4.65441e13 | + | 6.16943e14i | 0.0517620 | + | 0.686106i | ||||
\(75\) | − | 6.67511e12i | − | 0.00666758i | ||||||
\(76\) | −1.73831e14 | − | 1.14551e15i | −0.156178 | − | 1.02918i | ||||
\(77\) | 1.35530e14 | 0.109675 | ||||||||
\(78\) | −3.20064e15 | + | 2.41467e14i | −2.33604 | + | 0.176238i | ||||
\(79\) | − | 2.18899e15i | − | 1.44287i | −0.692484 | − | 0.721433i | \(-0.743484\pi\) | ||
0.692484 | − | 0.721433i | \(-0.256516\pi\) | |||||||
\(80\) | 1.59905e15 | − | 4.96753e14i | 0.953111 | − | 0.296088i | ||||
\(81\) | 1.34504e15 | 0.725864 | ||||||||
\(82\) | 1.05143e14 | + | 1.39367e15i | 0.0514362 | + | 0.681787i | ||||
\(83\) | 2.86414e15i | 1.27166i | 0.771831 | + | 0.635828i | \(0.219341\pi\) | ||||
−0.771831 | + | 0.635828i | \(0.780659\pi\) | |||||||
\(84\) | −7.73760e14 | + | 1.17418e14i | −0.312156 | + | 0.0473698i | ||||
\(85\) | −2.90019e15 | −1.06433 | ||||||||
\(86\) | 4.26892e15 | − | 3.22061e14i | 1.42669 | − | 0.107634i | ||||
\(87\) | 2.71364e15i | 0.826794i | ||||||||
\(88\) | 2.07538e15 | − | 4.76974e14i | 0.577082 | − | 0.132627i | ||||
\(89\) | 2.96991e15 | 0.754439 | 0.377219 | − | 0.926124i | \(-0.376880\pi\) | ||||
0.377219 | + | 0.926124i | \(0.376880\pi\) | |||||||
\(90\) | −6.15915e14 | − | 8.16396e15i | −0.143081 | − | 1.89653i | ||||
\(91\) | − | 1.19706e15i | − | 0.254557i | ||||||
\(92\) | −8.57718e13 | − | 5.65217e14i | −0.0167125 | − | 0.110132i | ||||
\(93\) | 7.21583e14 | 0.128950 | ||||||||
\(94\) | −3.41165e15 | + | 2.57386e14i | −0.559682 | + | 0.0422242i | ||||
\(95\) | 6.89241e15i | 1.03892i | ||||||||
\(96\) | −1.14355e16 | + | 4.52117e15i | −1.58520 | + | 0.626730i | ||||
\(97\) | −2.04301e15 | −0.260673 | −0.130336 | − | 0.991470i | \(-0.541606\pi\) | ||||
−0.130336 | + | 0.991470i | \(0.541606\pi\) | |||||||
\(98\) | 6.18066e14 | + | 8.19247e15i | 0.0726485 | + | 0.962956i | ||||
\(99\) | − | 1.04121e16i | − | 1.12839i | ||||||
\(100\) | 3.86725e13 | − | 5.86856e12i | 0.00386725 | − | 0.000586856i | ||||
\(101\) | −8.70720e15 | −0.804095 | −0.402048 | − | 0.915619i | \(-0.631701\pi\) | ||||
−0.402048 | + | 0.915619i | \(0.631701\pi\) | |||||||
\(102\) | 2.12382e16 | − | 1.60228e15i | 1.81266 | − | 0.136753i | ||||
\(103\) | − | 6.28728e15i | − | 0.496324i | −0.968719 | − | 0.248162i | \(-0.920174\pi\) | ||
0.968719 | − | 0.248162i | \(-0.0798265\pi\) | |||||||
\(104\) | −4.21286e15 | − | 1.83308e16i | −0.307830 | − | 1.33941i | ||||
\(105\) | 4.65564e15 | 0.315112 | ||||||||
\(106\) | 1.72731e15 | + | 2.28955e16i | 0.108374 | + | 1.43649i | ||||
\(107\) | − | 1.99151e16i | − | 1.15908i | −0.814945 | − | 0.579538i | \(-0.803233\pi\) | ||
0.814945 | − | 0.579538i | \(-0.196767\pi\) | |||||||
\(108\) | 4.28706e15 | + | 2.82508e16i | 0.231617 | + | 1.52630i | ||||
\(109\) | 1.86420e16 | 0.935579 | 0.467790 | − | 0.883840i | \(-0.345051\pi\) | ||||
0.467790 | + | 0.883840i | \(0.345051\pi\) | |||||||
\(110\) | −1.26320e16 | + | 9.52999e14i | −0.589292 | + | 0.0444581i | ||||
\(111\) | 2.70290e16i | 1.17286i | ||||||||
\(112\) | −1.36053e15 | − | 4.37958e15i | −0.0549497 | − | 0.176884i | ||||
\(113\) | 2.85508e16 | 1.07397 | 0.536983 | − | 0.843593i | \(-0.319564\pi\) | ||||
0.536983 | + | 0.843593i | \(0.319564\pi\) | |||||||
\(114\) | −3.80787e15 | − | 5.04733e16i | −0.133488 | − | 1.76939i | ||||
\(115\) | 3.40086e15i | 0.111175i | ||||||||
\(116\) | −1.57216e16 | + | 2.38575e15i | −0.479548 | + | 0.0727714i | ||||
\(117\) | −9.19649e16 | −2.61900 | ||||||||
\(118\) | −2.43553e16 | + | 1.83744e15i | −0.647944 | + | 0.0488830i | ||||
\(119\) | 7.94322e15i | 0.197524i | ||||||||
\(120\) | 7.12925e16 | − | 1.63848e16i | 1.65804 | − | 0.381057i | ||||
\(121\) | 2.98391e16 | 0.649387 | ||||||||
\(122\) | −1.36742e15 | − | 1.81252e16i | −0.0278627 | − | 0.369320i | ||||
\(123\) | 6.10582e16i | 1.16548i | ||||||||
\(124\) | 6.34394e14 | + | 4.18052e15i | 0.0113497 | + | 0.0747923i | ||||
\(125\) | −5.97206e16 | −1.00195 | ||||||||
\(126\) | −2.23599e16 | + | 1.68690e15i | −0.351970 | + | 0.0265537i | ||||
\(127\) | − | 6.87377e16i | − | 1.01570i | −0.861446 | − | 0.507849i | \(-0.830441\pi\) | ||
0.861446 | − | 0.507849i | \(-0.169559\pi\) | |||||||
\(128\) | −3.62473e16 | − | 6.22770e16i | −0.503032 | − | 0.864268i | ||||
\(129\) | 1.87026e17 | 2.43885 | ||||||||
\(130\) | 8.41733e15 | + | 1.11572e17i | 0.103188 | + | 1.36775i | ||||
\(131\) | 1.10790e17i | 1.27741i | 0.769454 | + | 0.638703i | \(0.220529\pi\) | ||||
−0.769454 | + | 0.638703i | \(0.779471\pi\) | |||||||
\(132\) | 9.19780e16 | − | 1.39577e16i | 0.997912 | − | 0.151433i | ||||
\(133\) | 1.88773e16 | 0.192809 | ||||||||
\(134\) | −9.06468e16 | + | 6.83868e15i | −0.871995 | + | 0.0657861i | ||||
\(135\) | − | 1.69982e17i | − | 1.54075i | ||||||
\(136\) | 2.79549e16 | + | 1.21636e17i | 0.238861 | + | 1.03932i | ||||
\(137\) | −1.61324e17 | −1.29997 | −0.649985 | − | 0.759947i | \(-0.725225\pi\) | ||||
−0.649985 | + | 0.759947i | \(0.725225\pi\) | |||||||
\(138\) | −1.87888e15 | − | 2.49046e16i | −0.0142845 | − | 0.189342i | ||||
\(139\) | − | 2.52370e17i | − | 1.81100i | −0.424342 | − | 0.905502i | \(-0.639495\pi\) | ||
0.424342 | − | 0.905502i | \(-0.360505\pi\) | |||||||
\(140\) | 4.09310e15 | + | 2.69726e16i | 0.0277350 | + | 0.182768i | ||||
\(141\) | −1.49468e17 | −0.956744 | ||||||||
\(142\) | 2.28987e17 | − | 1.72755e16i | 1.38517 | − | 0.104502i | ||||
\(143\) | 1.42296e17i | 0.813777i | ||||||||
\(144\) | −3.36464e17 | + | 1.04524e17i | −1.81986 | + | 0.565348i | ||||
\(145\) | 9.45951e16 | 0.484088 | ||||||||
\(146\) | −1.02396e16 | − | 1.35725e17i | −0.0495973 | − | 0.657413i | ||||
\(147\) | 3.58922e17i | 1.64612i | ||||||||
\(148\) | −1.56593e17 | + | 2.37631e16i | −0.680267 | + | 0.103231i | ||||
\(149\) | 4.48178e16 | 0.184485 | 0.0922424 | − | 0.995737i | \(-0.470597\pi\) | ||||
0.0922424 | + | 0.995737i | \(0.470597\pi\) | |||||||
\(150\) | 1.70399e15 | − | 1.28554e14i | 0.00664868 | − | 0.000501598i | ||||
\(151\) | − | 2.63140e17i | − | 0.973580i | −0.873519 | − | 0.486790i | \(-0.838168\pi\) | ||
0.873519 | − | 0.486790i | \(-0.161832\pi\) | |||||||
\(152\) | 2.89071e17 | − | 6.64357e16i | 1.01451 | − | 0.233159i | ||||
\(153\) | 6.10242e17 | 2.03222 | ||||||||
\(154\) | 2.61013e15 | + | 3.45972e16i | 0.00825080 | + | 0.109364i | ||||
\(155\) | − | 2.51538e16i | − | 0.0755004i | ||||||
\(156\) | −1.23281e17 | − | 8.12393e17i | −0.351478 | − | 2.31616i | ||||
\(157\) | −6.63199e17 | −1.79658 | −0.898291 | − | 0.439402i | \(-0.855190\pi\) | ||||
−0.898291 | + | 0.439402i | \(0.855190\pi\) | |||||||
\(158\) | 5.58792e17 | − | 4.21571e16i | 1.43878 | − | 0.108546i | ||||
\(159\) | 1.00308e18i | 2.45561i | ||||||||
\(160\) | 1.57604e17 | + | 3.98631e17i | 0.366951 | + | 0.928136i | ||||
\(161\) | 9.31446e15 | 0.0206324 | ||||||||
\(162\) | 2.59038e16 | + | 3.43355e17i | 0.0546063 | + | 0.723807i | ||||
\(163\) | − | 4.53009e17i | − | 0.909089i | −0.890724 | − | 0.454545i | \(-0.849802\pi\) | ||
0.890724 | − | 0.454545i | \(-0.150198\pi\) | |||||||
\(164\) | −3.53743e17 | + | 5.36806e16i | −0.675986 | + | 0.102581i | ||||
\(165\) | −5.53422e17 | −1.00736 | ||||||||
\(166\) | −7.31142e17 | + | 5.51597e16i | −1.26805 | + | 0.0956659i | ||||
\(167\) | − | 1.30678e17i | − | 0.216008i | −0.994150 | − | 0.108004i | \(-0.965554\pi\) | ||
0.994150 | − | 0.108004i | \(-0.0344460\pi\) | |||||||
\(168\) | −4.48755e16 | − | 1.95260e17i | −0.0707189 | − | 0.307708i | ||||
\(169\) | 5.91411e17 | 0.888782 | ||||||||
\(170\) | −5.58541e16 | − | 7.40346e17i | −0.0800688 | − | 1.06131i | ||||
\(171\) | − | 1.45026e18i | − | 1.98371i | ||||||
\(172\) | 1.64428e17 | + | 1.08354e18i | 0.214658 | + | 1.41455i | ||||
\(173\) | 8.96392e17 | 1.11720 | 0.558598 | − | 0.829439i | \(-0.311340\pi\) | ||||
0.558598 | + | 0.829439i | \(0.311340\pi\) | |||||||
\(174\) | −6.92722e17 | + | 5.22612e16i | −0.824451 | + | 0.0621993i | ||||
\(175\) | 6.37301e14i | 0.000724503i | ||||||||
\(176\) | 1.61729e17 | + | 5.20607e17i | 0.175665 | + | 0.565469i | ||||
\(177\) | −1.06703e18 | −1.10762 | ||||||||
\(178\) | 5.71968e16 | + | 7.58144e17i | 0.0567560 | + | 0.752301i | ||||
\(179\) | 1.25142e18i | 1.18735i | 0.804706 | + | 0.593673i | \(0.202323\pi\) | ||||
−0.804706 | + | 0.593673i | \(0.797677\pi\) | |||||||
\(180\) | 2.07219e18 | − | 3.14455e17i | 1.88040 | − | 0.285350i | ||||
\(181\) | −1.13448e17 | −0.0984850 | −0.0492425 | − | 0.998787i | \(-0.515681\pi\) | ||||
−0.0492425 | + | 0.998787i | \(0.515681\pi\) | |||||||
\(182\) | 3.05579e17 | − | 2.30539e16i | 0.253836 | − | 0.0191502i | ||||
\(183\) | − | 7.94084e17i | − | 0.631332i | ||||||
\(184\) | 1.42634e17 | − | 3.27807e16i | 0.108562 | − | 0.0249503i | ||||
\(185\) | 9.42207e17 | 0.686708 | ||||||||
\(186\) | 1.38968e16 | + | 1.84202e17i | 0.00970086 | + | 0.128585i | ||||
\(187\) | − | 9.44221e17i | − | 0.631453i | ||||||
\(188\) | −1.31408e17 | − | 8.65950e17i | −0.0842091 | − | 0.554919i | ||||
\(189\) | −4.65557e17 | −0.285942 | ||||||||
\(190\) | −1.75946e18 | + | 1.32739e17i | −1.03598 | + | 0.0781574i | ||||
\(191\) | 1.56832e18i | 0.885456i | 0.896656 | + | 0.442728i | \(0.145989\pi\) | ||||
−0.896656 | + | 0.442728i | \(0.854011\pi\) | |||||||
\(192\) | −1.37437e18 | − | 2.83211e18i | −0.744208 | − | 1.53356i | ||||
\(193\) | −4.81559e16 | −0.0250145 | −0.0125072 | − | 0.999922i | \(-0.503981\pi\) | ||||
−0.0125072 | + | 0.999922i | \(0.503981\pi\) | |||||||
\(194\) | −3.93457e16 | − | 5.21528e17i | −0.0196103 | − | 0.259934i | ||||
\(195\) | 4.88809e18i | 2.33809i | ||||||||
\(196\) | −2.07943e18 | + | 3.15553e17i | −0.954762 | + | 0.144885i | ||||
\(197\) | 7.87391e17 | 0.347105 | 0.173552 | − | 0.984825i | \(-0.444475\pi\) | ||||
0.173552 | + | 0.984825i | \(0.444475\pi\) | |||||||
\(198\) | 2.65795e18 | − | 2.00525e17i | 1.12519 | − | 0.0848879i | ||||
\(199\) | − | 3.27310e18i | − | 1.33087i | −0.746458 | − | 0.665433i | \(-0.768247\pi\) | ||
0.746458 | − | 0.665433i | \(-0.231753\pi\) | |||||||
\(200\) | 2.24288e15 | + | 9.75909e15i | 0.000876124 | + | 0.00381214i | ||||
\(201\) | −3.97134e18 | −1.49062 | ||||||||
\(202\) | −1.67690e17 | − | 2.22273e18i | −0.0604916 | − | 0.801817i | ||||
\(203\) | − | 2.59082e17i | − | 0.0898399i | ||||||
\(204\) | 8.18042e17 | + | 5.39071e18i | 0.272731 | + | 1.79724i | ||||
\(205\) | 2.12844e18 | 0.682386 | ||||||||
\(206\) | 1.60498e18 | − | 1.21085e17i | 0.494917 | − | 0.0373381i | ||||
\(207\) | − | 7.15589e17i | − | 0.212276i | ||||||
\(208\) | 4.59825e18 | − | 1.42846e18i | 1.31246 | − | 0.407720i | ||||
\(209\) | −2.24397e18 | −0.616379 | ||||||||
\(210\) | 8.96617e16 | + | 1.18847e18i | 0.0237057 | + | 0.314219i | ||||
\(211\) | 1.22766e18i | 0.312476i | 0.987719 | + | 0.156238i | \(0.0499367\pi\) | ||||
−0.987719 | + | 0.156238i | \(0.950063\pi\) | |||||||
\(212\) | −5.81138e18 | + | 8.81878e17i | −1.42427 | + | 0.216133i | ||||
\(213\) | 1.00322e19 | 2.36787 | ||||||||
\(214\) | 5.08382e18 | − | 3.83539e17i | 1.15579 | − | 0.0871967i | ||||
\(215\) | − | 6.51957e18i | − | 1.42795i | ||||||
\(216\) | −7.12915e18 | + | 1.63845e18i | −1.50455 | + | 0.345783i | ||||
\(217\) | −6.88926e16 | −0.0140118 | ||||||||
\(218\) | 3.59021e17 | + | 4.75883e18i | 0.0703831 | + | 0.932928i | ||||
\(219\) | − | 5.94628e18i | − | 1.12381i | ||||||
\(220\) | −4.86553e17 | − | 3.20628e18i | −0.0886642 | − | 0.584278i | ||||
\(221\) | −8.33981e18 | −1.46561 | ||||||||
\(222\) | −6.89980e18 | + | 5.20543e17i | −1.16953 | + | 0.0882334i | ||||
\(223\) | 9.94725e18i | 1.62654i | 0.581889 | + | 0.813268i | \(0.302314\pi\) | ||||
−0.581889 | + | 0.813268i | \(0.697686\pi\) | |||||||
\(224\) | 1.09179e18 | − | 4.31655e17i | 0.172249 | − | 0.0681009i | ||||
\(225\) | 4.89610e16 | 0.00745402 | ||||||||
\(226\) | 5.49852e17 | + | 7.28829e18i | 0.0807938 | + | 1.07092i | ||||
\(227\) | − | 3.06798e18i | − | 0.435157i | −0.976043 | − | 0.217578i | \(-0.930184\pi\) | ||
0.976043 | − | 0.217578i | \(-0.0698158\pi\) | |||||||
\(228\) | 1.28112e19 | − | 1.94410e18i | 1.75433 | − | 0.266220i | ||||
\(229\) | −6.70151e18 | −0.886112 | −0.443056 | − | 0.896494i | \(-0.646106\pi\) | ||||
−0.443056 | + | 0.896494i | \(0.646106\pi\) | |||||||
\(230\) | −8.68152e17 | + | 6.54962e16i | −0.110860 | + | 0.00836360i | ||||
\(231\) | 1.51574e18i | 0.186952i | ||||||||
\(232\) | −9.11798e17 | − | 3.96737e18i | −0.108641 | − | 0.472714i | ||||
\(233\) | −7.17629e18 | −0.826138 | −0.413069 | − | 0.910700i | \(-0.635543\pi\) | ||||
−0.413069 | + | 0.910700i | \(0.635543\pi\) | |||||||
\(234\) | −1.77113e18 | − | 2.34763e19i | −0.197026 | − | 2.61158i | ||||
\(235\) | 5.21033e18i | 0.560173i | ||||||||
\(236\) | −9.38104e17 | − | 6.18190e18i | −0.0974889 | − | 0.642430i | ||||
\(237\) | 2.44813e19 | 2.45951 | ||||||||
\(238\) | −2.02770e18 | + | 1.52976e17i | −0.196965 | + | 0.0148596i | ||||
\(239\) | 1.01782e19i | 0.956067i | 0.878342 | + | 0.478034i | \(0.158650\pi\) | ||||
−0.878342 | + | 0.478034i | \(0.841350\pi\) | |||||||
\(240\) | 5.55562e18 | + | 1.78836e19i | 0.504711 | + | 1.62467i | ||||
\(241\) | 2.09501e18 | 0.184098 | 0.0920492 | − | 0.995754i | \(-0.470658\pi\) | ||||
0.0920492 | + | 0.995754i | \(0.470658\pi\) | |||||||
\(242\) | 5.74664e17 | + | 7.61717e18i | 0.0488530 | + | 0.647546i | ||||
\(243\) | − | 3.72596e18i | − | 0.306470i | ||||||
\(244\) | 4.60056e18 | − | 6.98135e17i | 0.366178 | − | 0.0555675i | ||||
\(245\) | 1.25117e19 | 0.963802 | ||||||||
\(246\) | −1.55866e19 | + | 1.17590e18i | −1.16217 | + | 0.0876781i | ||||
\(247\) | 1.98198e19i | 1.43062i | ||||||||
\(248\) | −1.05496e18 | + | 2.42456e17i | −0.0737265 | + | 0.0169441i | ||||
\(249\) | −3.20322e19 | −2.16766 | ||||||||
\(250\) | −1.15014e18 | − | 1.52452e19i | −0.0753758 | − | 0.999107i | ||||
\(251\) | − | 1.97213e19i | − | 1.25183i | −0.779890 | − | 0.625916i | \(-0.784725\pi\) | ||
0.779890 | − | 0.625916i | \(-0.215275\pi\) | |||||||
\(252\) | −8.61247e17 | − | 5.67543e18i | −0.0529570 | − | 0.348975i | ||||
\(253\) | −1.10722e18 | −0.0659585 | ||||||||
\(254\) | 1.75470e19 | − | 1.32380e18i | 1.01282 | − | 0.0764104i | ||||
\(255\) | − | 3.24354e19i | − | 1.81425i | ||||||
\(256\) | 1.51997e19 | − | 1.04524e19i | 0.823976 | − | 0.566625i | ||||
\(257\) | −4.81863e18 | −0.253197 | −0.126598 | − | 0.991954i | \(-0.540406\pi\) | ||||
−0.126598 | + | 0.991954i | \(0.540406\pi\) | |||||||
\(258\) | 3.60189e18 | + | 4.77430e19i | 0.183473 | + | 2.43194i | ||||
\(259\) | − | 2.58057e18i | − | 0.127443i | ||||||
\(260\) | −2.83193e19 | + | 4.29746e18i | −1.35611 | + | 0.205790i | ||||
\(261\) | −1.99042e19 | −0.924314 | ||||||||
\(262\) | −2.82818e19 | + | 2.13367e18i | −1.27379 | + | 0.0960984i | ||||
\(263\) | − | 5.80322e18i | − | 0.253526i | −0.991933 | − | 0.126763i | \(-0.959541\pi\) | ||
0.991933 | − | 0.126763i | \(-0.0404588\pi\) | |||||||
\(264\) | 5.33442e18 | + | 2.32108e19i | 0.226077 | + | 0.983692i | ||||
\(265\) | 3.49665e19 | 1.43776 | ||||||||
\(266\) | 3.63553e17 | + | 4.81890e18i | 0.0145049 | + | 0.192263i | ||||
\(267\) | 3.32151e19i | 1.28601i | ||||||||
\(268\) | −3.49148e18 | − | 2.30081e19i | −0.131199 | − | 0.864575i | ||||
\(269\) | 3.64173e19 | 1.32828 | 0.664139 | − | 0.747609i | \(-0.268798\pi\) | ||||
0.664139 | + | 0.747609i | \(0.268798\pi\) | |||||||
\(270\) | 4.33921e19 | − | 3.27364e18i | 1.53639 | − | 0.115910i | ||||
\(271\) | − | 2.22307e19i | − | 0.764184i | −0.924124 | − | 0.382092i | \(-0.875204\pi\) | ||
0.924124 | − | 0.382092i | \(-0.124796\pi\) | |||||||
\(272\) | −3.05121e19 | + | 9.47872e18i | −1.01841 | + | 0.316372i | ||||
\(273\) | 1.33878e19 | 0.433917 | ||||||||
\(274\) | −3.10689e18 | − | 4.11818e19i | −0.0977960 | − | 1.29629i | ||||
\(275\) | − | 7.57569e16i | − | 0.00231612i | ||||||
\(276\) | 6.32132e18 | − | 9.59260e17i | 0.187731 | − | 0.0284881i | ||||
\(277\) | −5.13041e19 | −1.48018 | −0.740089 | − | 0.672509i | \(-0.765217\pi\) | ||||
−0.740089 | + | 0.672509i | \(0.765217\pi\) | |||||||
\(278\) | 6.44237e19 | − | 4.86033e18i | 1.80587 | − | 0.136241i | ||||
\(279\) | 5.29271e18i | 0.144160i | ||||||||
\(280\) | −6.80660e18 | + | 1.56432e18i | −0.180163 | + | 0.0414059i | ||||
\(281\) | 1.48805e19 | 0.382797 | 0.191398 | − | 0.981512i | \(-0.438698\pi\) | ||||
0.191398 | + | 0.981512i | \(0.438698\pi\) | |||||||
\(282\) | −2.87857e18 | − | 3.81554e19i | −0.0719753 | − | 0.954032i | ||||
\(283\) | 7.34321e19i | 1.78482i | 0.451225 | + | 0.892410i | \(0.350987\pi\) | ||||
−0.451225 | + | 0.892410i | \(0.649013\pi\) | |||||||
\(284\) | 8.81998e18 | + | 5.81217e19i | 0.208411 | + | 1.37338i | ||||
\(285\) | −7.70838e19 | −1.77094 | ||||||||
\(286\) | −3.63246e19 | + | 2.74045e18i | −0.811471 | + | 0.0612199i | ||||
\(287\) | − | 5.82949e18i | − | 0.126641i | ||||||
\(288\) | −3.31622e19 | − | 8.38777e19i | −0.700653 | − | 1.77218i | ||||
\(289\) | 6.67845e18 | 0.137244 | ||||||||
\(290\) | 1.82178e18 | + | 2.41477e19i | 0.0364177 | + | 0.482716i | ||||
\(291\) | − | 2.28487e19i | − | 0.444343i | ||||||
\(292\) | 3.44500e19 | − | 5.22780e18i | 0.651819 | − | 0.0989136i | ||||
\(293\) | 4.26888e19 | 0.785911 | 0.392955 | − | 0.919557i | \(-0.371453\pi\) | ||||
0.392955 | + | 0.919557i | \(0.371453\pi\) | |||||||
\(294\) | −9.16235e19 | + | 6.91237e18i | −1.64145 | + | 0.123836i | ||||
\(295\) | 3.71959e19i | 0.648513i | ||||||||
\(296\) | −9.08189e18 | − | 3.95167e19i | −0.154114 | − | 0.670574i | ||||
\(297\) | 5.53414e19 | 0.914110 | ||||||||
\(298\) | 8.63134e17 | + | 1.14409e19i | 0.0138787 | + | 0.183962i | ||||
\(299\) | 9.77951e18i | 0.153090i | ||||||||
\(300\) | 6.56332e16 | + | 4.32508e17i | 0.00100035 | + | 0.00659211i | ||||
\(301\) | −1.78562e19 | −0.265007 | ||||||||
\(302\) | 6.71730e19 | − | 5.06774e18i | 0.970821 | − | 0.0732418i | ||||
\(303\) | − | 9.73802e19i | − | 1.37066i | ||||||
\(304\) | 2.25265e19 | + | 7.25131e19i | 0.308820 | + | 0.994095i | ||||
\(305\) | −2.76811e19 | −0.369645 | ||||||||
\(306\) | 1.17525e19 | + | 1.55779e20i | 0.152883 | + | 2.02646i | ||||
\(307\) | − | 1.27750e20i | − | 1.61903i | −0.587100 | − | 0.809514i | \(-0.699731\pi\) | ||
0.587100 | − | 0.809514i | \(-0.300269\pi\) | |||||||
\(308\) | −8.78153e18 | + | 1.33260e18i | −0.108434 | + | 0.0164548i | ||||
\(309\) | 7.03161e19 | 0.846032 | ||||||||
\(310\) | 6.42112e18 | − | 4.84430e17i | 0.0752865 | − | 0.00567985i | ||||
\(311\) | 6.03449e19i | 0.689537i | 0.938688 | + | 0.344768i | \(0.112043\pi\) | ||||
−0.938688 | + | 0.344768i | \(0.887957\pi\) | |||||||
\(312\) | 2.05009e20 | − | 4.71161e19i | 2.28316 | − | 0.524726i | ||||
\(313\) | −2.85722e19 | −0.310163 | −0.155081 | − | 0.987902i | \(-0.549564\pi\) | ||||
−0.155081 | + | 0.987902i | \(0.549564\pi\) | |||||||
\(314\) | −1.27724e19 | − | 1.69298e20i | −0.135156 | − | 1.79149i | ||||
\(315\) | 3.41485e19i | 0.352279i | ||||||||
\(316\) | 2.15233e19 | + | 1.41834e20i | 0.216477 | + | 1.42653i | ||||
\(317\) | −1.99139e20 | −1.95291 | −0.976457 | − | 0.215712i | \(-0.930793\pi\) | ||||
−0.976457 | + | 0.215712i | \(0.930793\pi\) | |||||||
\(318\) | −2.56061e20 | + | 1.93180e19i | −2.44865 | + | 0.184734i | ||||
\(319\) | 3.07975e19i | 0.287204i | ||||||||
\(320\) | −9.87252e19 | + | 4.79095e19i | −0.897900 | + | 0.435734i | ||||
\(321\) | 2.22728e20 | 1.97576 | ||||||||
\(322\) | 1.79385e17 | + | 2.37774e18i | 0.00155217 | + | 0.0205740i | ||||
\(323\) | − | 1.31517e20i | − | 1.11010i | ||||||
\(324\) | −8.71509e19 | + | 1.32252e19i | −0.717648 | + | 0.108903i | ||||
\(325\) | −6.69120e17 | −0.00537573 | ||||||||
\(326\) | 1.15642e20 | − | 8.72439e18i | 0.906513 | − | 0.0683902i | ||||
\(327\) | 2.08490e20i | 1.59479i | ||||||||
\(328\) | −2.05159e19 | − | 8.92679e19i | −0.153144 | − | 0.666353i | ||||
\(329\) | 1.42704e19 | 0.103960 | ||||||||
\(330\) | −1.06582e19 | − | 1.41275e20i | −0.0757832 | − | 1.00451i | ||||
\(331\) | − | 1.56745e20i | − | 1.08785i | −0.839133 | − | 0.543926i | \(-0.816937\pi\) | ||
0.839133 | − | 0.543926i | \(-0.183063\pi\) | |||||||
\(332\) | −2.81617e19 | − | 1.85580e20i | −0.190790 | − | 1.25726i | ||||
\(333\) | −1.98254e20 | −1.31120 | ||||||||
\(334\) | 3.33588e19 | − | 2.51669e18i | 0.215396 | − | 0.0162502i | ||||
\(335\) | 1.38438e20i | 0.872761i | ||||||||
\(336\) | 4.89807e19 | − | 1.52160e19i | 0.301516 | − | 0.0936672i | ||||
\(337\) | 3.17497e19 | 0.190854 | 0.0954268 | − | 0.995436i | \(-0.469578\pi\) | ||||
0.0954268 | + | 0.995436i | \(0.469578\pi\) | |||||||
\(338\) | 1.13898e19 | + | 1.50972e20i | 0.0668626 | + | 0.886264i | ||||
\(339\) | 3.19308e20i | 1.83068i | ||||||||
\(340\) | 1.87916e20 | − | 2.85162e19i | 1.05228 | − | 0.159684i | ||||
\(341\) | 8.18935e18 | 0.0447935 | ||||||||
\(342\) | 3.70215e20 | − | 2.79302e19i | 1.97809 | − | 0.149233i | ||||
\(343\) | − | 6.97529e19i | − | 0.364091i | ||||||
\(344\) | −2.73434e20 | + | 6.28419e19i | −1.39439 | + | 0.320466i | ||||
\(345\) | −3.80347e19 | −0.189508 | ||||||||
\(346\) | 1.72634e19 | + | 2.28826e20i | 0.0840459 | + | 1.11403i | ||||
\(347\) | 2.06802e20i | 0.983827i | 0.870644 | + | 0.491914i | \(0.163702\pi\) | ||||
−0.870644 | + | 0.491914i | \(0.836298\pi\) | |||||||
\(348\) | −2.66819e19 | − | 1.75828e20i | −0.124046 | − | 0.817436i | ||||
\(349\) | 3.23582e20 | 1.47021 | 0.735107 | − | 0.677951i | \(-0.237132\pi\) | ||||
0.735107 | + | 0.677951i | \(0.237132\pi\) | |||||||
\(350\) | −1.62687e17 | + | 1.22736e16i | −0.000722450 | + | 5.45039e-5i | ||||
\(351\) | − | 4.88801e20i | − | 2.12166i | ||||||
\(352\) | −1.29783e20 | + | 5.13114e19i | −0.550651 | + | 0.217707i | ||||
\(353\) | 4.02153e19 | 0.166799 | 0.0833996 | − | 0.996516i | \(-0.473422\pi\) | ||||
0.0833996 | + | 0.996516i | \(0.473422\pi\) | |||||||
\(354\) | −2.05497e19 | − | 2.72386e20i | −0.0833258 | − | 1.10448i | ||||
\(355\) | − | 3.49713e20i | − | 1.38639i | ||||||
\(356\) | −1.92433e20 | + | 2.92018e19i | −0.745899 | + | 0.113190i | ||||
\(357\) | −8.88359e19 | −0.336700 | ||||||||
\(358\) | −3.19455e20 | + | 2.41007e19i | −1.18398 | + | 0.0893234i | ||||
\(359\) | − | 7.71450e19i | − | 0.279610i | −0.990179 | − | 0.139805i | \(-0.955352\pi\) | ||
0.990179 | − | 0.139805i | \(-0.0446475\pi\) | |||||||
\(360\) | 1.20180e20 | + | 5.22921e20i | 0.426003 | + | 1.85360i | ||||
\(361\) | −2.41121e19 | −0.0835945 | ||||||||
\(362\) | −2.18487e18 | − | 2.89605e19i | −0.00740897 | − | 0.0982059i | ||||
\(363\) | 3.33717e20i | 1.10694i | ||||||||
\(364\) | 1.17701e19 | + | 7.75626e19i | 0.0381918 | + | 0.251676i | ||||
\(365\) | −2.07282e20 | −0.657990 | ||||||||
\(366\) | 2.02709e20 | − | 1.52930e19i | 0.629543 | − | 0.0474947i | ||||
\(367\) | 8.69548e19i | 0.264220i | 0.991235 | + | 0.132110i | \(0.0421752\pi\) | ||||
−0.991235 | + | 0.132110i | \(0.957825\pi\) | |||||||
\(368\) | 1.11150e19 | + | 3.57795e19i | 0.0330467 | + | 0.106378i | ||||
\(369\) | −4.47854e20 | −1.30294 | ||||||||
\(370\) | 1.81457e19 | + | 2.40521e20i | 0.0516607 | + | 0.684762i | ||||
\(371\) | − | 9.57683e19i | − | 0.266827i | ||||||
\(372\) | −4.67544e19 | + | 7.09498e18i | −0.127491 | + | 0.0193467i | ||||
\(373\) | −1.47147e19 | −0.0392717 | −0.0196358 | − | 0.999807i | \(-0.506251\pi\) | ||||
−0.0196358 | + | 0.999807i | \(0.506251\pi\) | |||||||
\(374\) | 2.41036e20 | − | 1.81845e19i | 0.629664 | − | 0.0475038i | ||||
\(375\) | − | 6.67908e20i | − | 1.70792i | ||||||
\(376\) | 2.18524e20 | − | 5.02222e19i | 0.547012 | − | 0.125717i | ||||
\(377\) | 2.72018e20 | 0.666602 | ||||||||
\(378\) | −8.96604e18 | − | 1.18845e20i | −0.0215113 | − | 0.285132i | ||||
\(379\) | − | 1.42139e20i | − | 0.333888i | −0.985966 | − | 0.166944i | \(-0.946610\pi\) | ||
0.985966 | − | 0.166944i | \(-0.0533899\pi\) | |||||||
\(380\) | −6.77698e19 | − | 4.46588e20i | −0.155872 | − | 1.02716i | ||||
\(381\) | 7.68753e20 | 1.73136 | ||||||||
\(382\) | −4.00352e20 | + | 3.02038e19i | −0.882947 | + | 0.0666123i | ||||
\(383\) | 7.65100e20i | 1.65245i | 0.563340 | + | 0.826225i | \(0.309516\pi\) | ||||
−0.563340 | + | 0.826225i | \(0.690484\pi\) | |||||||
\(384\) | 6.96498e20 | − | 4.05385e20i | 1.47323 | − | 0.857468i | ||||
\(385\) | 5.28376e19 | 0.109460 | ||||||||
\(386\) | −9.27422e17 | − | 1.22930e19i | −0.00188182 | − | 0.0249436i | ||||
\(387\) | 1.37181e21i | 2.72651i | ||||||||
\(388\) | 1.32375e20 | − | 2.00879e19i | 0.257722 | − | 0.0391094i | ||||
\(389\) | 6.56368e20 | 1.25184 | 0.625922 | − | 0.779886i | \(-0.284723\pi\) | ||||
0.625922 | + | 0.779886i | \(0.284723\pi\) | |||||||
\(390\) | −1.24780e21 | + | 9.41383e19i | −2.33147 | + | 0.175893i | ||||
\(391\) | − | 6.48929e19i | − | 0.118791i | ||||||
\(392\) | −1.20600e20 | − | 5.24748e20i | −0.216301 | − | 0.941157i | ||||
\(393\) | −1.23906e21 | −2.17746 | ||||||||
\(394\) | 1.51641e19 | + | 2.01001e20i | 0.0261125 | + | 0.346121i | ||||
\(395\) | − | 8.53399e20i | − | 1.44004i | ||||||
\(396\) | 1.02378e20 | + | 6.74646e20i | 0.169295 | + | 1.11562i | ||||
\(397\) | −3.26185e20 | −0.528616 | −0.264308 | − | 0.964438i | \(-0.585143\pi\) | ||||
−0.264308 | + | 0.964438i | \(0.585143\pi\) | |||||||
\(398\) | 8.35539e20 | − | 6.30357e19i | 1.32709 | − | 0.100120i | ||||
\(399\) | 2.11122e20i | 0.328662i | ||||||||
\(400\) | −2.44805e18 | + | 7.60497e17i | −0.00373543 | + | 0.00116043i | ||||
\(401\) | −3.88647e20 | −0.581299 | −0.290650 | − | 0.956830i | \(-0.593871\pi\) | ||||
−0.290650 | + | 0.956830i | \(0.593871\pi\) | |||||||
\(402\) | −7.64829e19 | − | 1.01378e21i | −0.112139 | − | 1.48640i | ||||
\(403\) | − | 7.23322e19i | − | 0.103966i | ||||||
\(404\) | 5.64176e20 | − | 8.56138e19i | 0.794994 | − | 0.120640i | ||||
\(405\) | 5.24378e20 | 0.724443 | ||||||||
\(406\) | 6.61371e19 | − | 4.98960e18i | 0.0895854 | − | 0.00675861i | ||||
\(407\) | 3.06756e20i | 0.407416i | ||||||||
\(408\) | −1.36036e21 | + | 3.12643e20i | −1.77163 | + | 0.407163i | ||||
\(409\) | −1.37019e21 | −1.74983 | −0.874915 | − | 0.484276i | \(-0.839083\pi\) | ||||
−0.874915 | + | 0.484276i | \(0.839083\pi\) | |||||||
\(410\) | 4.09910e19 | + | 5.43336e20i | 0.0513355 | + | 0.680452i | ||||
\(411\) | − | 1.80422e21i | − | 2.21593i | ||||||
\(412\) | 6.18198e19 | + | 4.07379e20i | 0.0744646 | + | 0.490706i | ||||
\(413\) | 1.01874e20 | 0.120355 | ||||||||
\(414\) | 1.82672e20 | − | 1.37813e19i | 0.211674 | − | 0.0159694i | ||||
\(415\) | 1.11661e21i | 1.26917i | ||||||||
\(416\) | 4.53207e20 | + | 1.14630e21i | 0.505300 | + | 1.27807i | ||||
\(417\) | 2.82247e21 | 3.08703 | ||||||||
\(418\) | −4.32161e19 | − | 5.72830e20i | −0.0463698 | − | 0.614632i | ||||
\(419\) | − | 3.51169e20i | − | 0.369661i | −0.982770 | − | 0.184831i | \(-0.940826\pi\) | ||
0.982770 | − | 0.184831i | \(-0.0591736\pi\) | |||||||
\(420\) | −3.01658e20 | + | 4.57767e19i | −0.311545 | + | 0.0472770i | ||||
\(421\) | 5.99942e20 | 0.607928 | 0.303964 | − | 0.952683i | \(-0.401690\pi\) | ||||
0.303964 | + | 0.952683i | \(0.401690\pi\) | |||||||
\(422\) | −3.13389e20 | + | 2.36431e19i | −0.311591 | + | 0.0235074i | ||||
\(423\) | − | 1.09633e21i | − | 1.06959i | ||||||
\(424\) | −3.37041e20 | − | 1.46651e21i | −0.322668 | − | 1.40398i | ||||
\(425\) | 4.44001e18 | 0.00417132 | ||||||||
\(426\) | 1.93207e20 | + | 2.56096e21i | 0.178133 | + | 2.36116i | ||||
\(427\) | 7.58146e19i | 0.0686009i | ||||||||
\(428\) | 1.95816e20 | + | 1.29038e21i | 0.173899 | + | 1.14596i | ||||
\(429\) | −1.59142e21 | −1.38716 | ||||||||
\(430\) | 1.66428e21 | − | 1.25559e20i | 1.42390 | − | 0.107423i | ||||
\(431\) | − | 4.16237e20i | − | 0.349561i | −0.984607 | − | 0.174780i | \(-0.944078\pi\) | ||
0.984607 | − | 0.174780i | \(-0.0559216\pi\) | |||||||
\(432\) | −5.55554e20 | − | 1.78834e21i | −0.457990 | − | 1.47428i | ||||
\(433\) | −2.60242e20 | −0.210607 | −0.105304 | − | 0.994440i | \(-0.533581\pi\) | ||||
−0.105304 | + | 0.994440i | \(0.533581\pi\) | |||||||
\(434\) | −1.32678e18 | − | 1.75865e19i | −0.00105410 | − | 0.0139721i | ||||
\(435\) | 1.05794e21i | 0.825176i | ||||||||
\(436\) | −1.20789e21 | + | 1.83298e20i | −0.924989 | + | 0.140367i | ||||
\(437\) | −1.54220e20 | −0.115955 | ||||||||
\(438\) | 1.51793e21 | − | 1.14518e20i | 1.12062 | − | 0.0845435i | ||||
\(439\) | 9.76131e20i | 0.707607i | 0.935320 | + | 0.353803i | \(0.115112\pi\) | ||||
−0.935320 | + | 0.353803i | \(0.884888\pi\) | |||||||
\(440\) | 8.09110e20 | − | 1.85953e20i | 0.575952 | − | 0.132368i | ||||
\(441\) | −2.63264e21 | −1.84028 | ||||||||
\(442\) | −1.60614e20 | − | 2.12894e21i | −0.110257 | − | 1.46145i | ||||
\(443\) | − | 2.08187e20i | − | 0.140354i | −0.997535 | − | 0.0701770i | \(-0.977644\pi\) | ||
0.997535 | − | 0.0701770i | \(-0.0223564\pi\) | |||||||
\(444\) | −2.65763e20 | − | 1.75132e21i | −0.175967 | − | 1.15958i | ||||
\(445\) | 1.15785e21 | 0.752962 | ||||||||
\(446\) | −2.53928e21 | + | 1.91571e20i | −1.62193 | + | 0.122363i | ||||
\(447\) | 5.01237e20i | 0.314473i | ||||||||
\(448\) | 1.31217e20 | + | 2.70394e20i | 0.0808661 | + | 0.166638i | ||||
\(449\) | −2.37764e20 | −0.143938 | −0.0719690 | − | 0.997407i | \(-0.522928\pi\) | ||||
−0.0719690 | + | 0.997407i | \(0.522928\pi\) | |||||||
\(450\) | 9.42927e17 | + | 1.24985e19i | 0.000560761 | + | 0.00743289i | ||||
\(451\) | 6.92959e20i | 0.404851i | ||||||||
\(452\) | −1.84993e21 | + | 2.80726e20i | −1.06181 | + | 0.161130i | ||||
\(453\) | 2.94292e21 | 1.65956 | ||||||||
\(454\) | 7.83177e20 | − | 5.90854e19i | 0.433924 | − | 0.0327366i | ||||
\(455\) | − | 4.66686e20i | − | 0.254059i | ||||||
\(456\) | 7.43008e20 | + | 3.23294e21i | 0.397443 | + | 1.72933i | ||||
\(457\) | 6.36224e20 | 0.334411 | 0.167206 | − | 0.985922i | \(-0.446526\pi\) | ||||
0.167206 | + | 0.985922i | \(0.446526\pi\) | |||||||
\(458\) | −1.29063e20 | − | 1.71072e21i | −0.0666617 | − | 0.883601i | ||||
\(459\) | 3.24349e21i | 1.64631i | ||||||||
\(460\) | −3.34390e19 | − | 2.20356e20i | −0.0166798 | − | 0.109916i | ||||
\(461\) | −1.40752e21 | −0.689998 | −0.344999 | − | 0.938603i | \(-0.612121\pi\) | ||||
−0.344999 | + | 0.938603i | \(0.612121\pi\) | |||||||
\(462\) | −3.86931e20 | + | 2.91913e19i | −0.186422 | + | 0.0140643i | ||||
\(463\) | 2.63989e20i | 0.125008i | 0.998045 | + | 0.0625040i | \(0.0199086\pi\) | ||||
−0.998045 | + | 0.0625040i | \(0.980091\pi\) | |||||||
\(464\) | 9.95208e20 | − | 3.09165e20i | 0.463202 | − | 0.143895i | ||||
\(465\) | 2.81316e20 | 0.128698 | ||||||||
\(466\) | −1.38206e20 | − | 1.83192e21i | −0.0621499 | − | 0.823797i | ||||
\(467\) | − | 3.55842e20i | − | 0.157298i | −0.996902 | − | 0.0786488i | \(-0.974939\pi\) | ||
0.996902 | − | 0.0786488i | \(-0.0250606\pi\) | |||||||
\(468\) | 5.95879e21 | − | 9.04247e20i | 2.58935 | − | 0.392935i | ||||
\(469\) | 3.79160e20 | 0.161972 | ||||||||
\(470\) | −1.33007e21 | + | 1.00344e20i | −0.558586 | + | 0.0421415i | ||||
\(471\) | − | 7.41713e21i | − | 3.06245i | ||||||
\(472\) | 1.56002e21 | − | 3.58530e20i | 0.633276 | − | 0.145542i | ||||
\(473\) | 2.12259e21 | 0.847182 | ||||||||
\(474\) | 4.71479e20 | + | 6.24946e21i | 0.185027 | + | 2.45254i | ||||
\(475\) | − | 1.05518e19i | − | 0.00407174i | ||||||
\(476\) | −7.81019e19 | − | 5.14674e20i | −0.0296351 | − | 0.195289i | ||||
\(477\) | −7.35746e21 | −2.74524 | ||||||||
\(478\) | −2.59824e21 | + | 1.96020e20i | −0.953358 | + | 0.0719244i | ||||
\(479\) | − | 5.80813e20i | − | 0.209581i | −0.994494 | − | 0.104791i | \(-0.966583\pi\) | ||
0.994494 | − | 0.104791i | \(-0.0334172\pi\) | |||||||
\(480\) | −4.45824e21 | + | 1.76262e21i | −1.58210 | + | 0.625503i | ||||
\(481\) | 2.70941e21 | 0.945615 | ||||||||
\(482\) | 4.03473e19 | + | 5.34803e20i | 0.0138496 | + | 0.183577i | ||||
\(483\) | 1.04172e20i | 0.0351700i | ||||||||
\(484\) | −1.93340e21 | + | 2.93394e20i | −0.642036 | + | 0.0974291i | ||||
\(485\) | −7.96487e20 | −0.260163 | ||||||||
\(486\) | 9.51142e20 | − | 7.17572e19i | 0.305601 | − | 0.0230555i | ||||
\(487\) | 6.05794e21i | 1.91467i | 0.288988 | + | 0.957333i | \(0.406681\pi\) | ||||
−0.288988 | + | 0.957333i | \(0.593319\pi\) | |||||||
\(488\) | 2.66817e20 | + | 1.16096e21i | 0.0829574 | + | 0.360960i | ||||
\(489\) | 5.06640e21 | 1.54963 | ||||||||
\(490\) | 2.40960e20 | + | 3.19392e21i | 0.0725063 | + | 0.961071i | ||||
\(491\) | − | 3.77866e21i | − | 1.11863i | −0.828956 | − | 0.559314i | \(-0.811065\pi\) | ||
0.828956 | − | 0.559314i | \(-0.188935\pi\) | |||||||
\(492\) | −6.00357e20 | − | 3.95622e21i | −0.174859 | − | 1.15228i | ||||
\(493\) | −1.80500e21 | −0.517252 | ||||||||
\(494\) | −5.05950e21 | + | 3.81705e20i | −1.42657 | + | 0.107625i | ||||
\(495\) | − | 4.05928e21i | − | 1.12618i | ||||||
\(496\) | −8.22101e19 | − | 2.64636e20i | −0.0224425 | − | 0.0722429i | ||||
\(497\) | −9.57813e20 | −0.257294 | ||||||||
\(498\) | −6.16899e20 | − | 8.17700e21i | −0.163072 | − | 2.16152i | ||||
\(499\) | − | 1.85736e21i | − | 0.483162i | −0.970381 | − | 0.241581i | \(-0.922334\pi\) | ||
0.970381 | − | 0.241581i | \(-0.0776659\pi\) | |||||||
\(500\) | 3.86955e21 | − | 5.87205e20i | 0.990605 | − | 0.150324i | ||||
\(501\) | 1.46148e21 | 0.368207 | ||||||||
\(502\) | 5.03435e21 | − | 3.79808e20i | 1.24828 | − | 0.0941746i | ||||
\(503\) | 5.73319e21i | 1.39911i | 0.714578 | + | 0.699556i | \(0.246619\pi\) | ||||
−0.714578 | + | 0.699556i | \(0.753381\pi\) | |||||||
\(504\) | 1.43221e21 | − | 3.29156e20i | 0.344002 | − | 0.0790601i | ||||
\(505\) | −3.39459e21 | −0.802521 | ||||||||
\(506\) | −2.13237e19 | − | 2.82646e20i | −0.00496202 | − | 0.0657716i | ||||
\(507\) | 6.61426e21i | 1.51502i | ||||||||
\(508\) | 6.75865e20 | + | 4.45380e21i | 0.152388 | + | 1.00420i | ||||
\(509\) | −2.45518e21 | −0.544930 | −0.272465 | − | 0.962166i | \(-0.587839\pi\) | ||||
−0.272465 | + | 0.962166i | \(0.587839\pi\) | |||||||
\(510\) | 8.27993e21 | − | 6.24664e20i | 1.80911 | − | 0.136485i | ||||
\(511\) | 5.67717e20i | 0.122114i | ||||||||
\(512\) | 2.96096e21 | + | 3.67879e21i | 0.627007 | + | 0.779014i | ||||
\(513\) | 7.70827e21 | 1.60701 | ||||||||
\(514\) | −9.28007e19 | − | 1.23007e21i | −0.0190479 | − | 0.252479i | ||||
\(515\) | − | 2.45116e21i | − | 0.495352i | ||||||
\(516\) | −1.21182e22 | + | 1.83894e21i | −2.41124 | + | 0.365906i | ||||
\(517\) | −1.69634e21 | −0.332344 | ||||||||
\(518\) | 6.58754e20 | − | 4.96985e19i | 0.127082 | − | 0.00958749i | ||||
\(519\) | 1.00251e22i | 1.90437i | ||||||||
\(520\) | −1.64243e21 | − | 7.14644e21i | −0.307227 | − | 1.33679i | ||||
\(521\) | −2.93027e21 | −0.539767 | −0.269884 | − | 0.962893i | \(-0.586985\pi\) | ||||
−0.269884 | + | 0.962893i | \(0.586985\pi\) | |||||||
\(522\) | −3.83329e20 | − | 5.08102e21i | −0.0695356 | − | 0.921695i | ||||
\(523\) | − | 4.71391e21i | − | 0.842109i | −0.907035 | − | 0.421054i | \(-0.861660\pi\) | ||
0.907035 | − | 0.421054i | \(-0.138340\pi\) | |||||||
\(524\) | −1.08934e21 | − | 7.17852e21i | −0.191652 | − | 1.26295i | ||||
\(525\) | −7.12749e18 | −0.00123499 | ||||||||
\(526\) | 1.48141e21 | − | 1.11763e20i | 0.252808 | − | 0.0190726i | ||||
\(527\) | 4.79968e20i | 0.0806728i | ||||||||
\(528\) | −5.82240e21 | + | 1.80875e21i | −0.963897 | + | 0.299438i | ||||
\(529\) | 6.05651e21 | 0.987592 | ||||||||
\(530\) | 6.73411e20 | + | 8.92606e21i | 0.108162 | + | 1.43368i | ||||
\(531\) | − | 7.82655e21i | − | 1.23827i | ||||||
\(532\) | −1.22314e21 | + | 1.85612e20i | −0.190627 | + | 0.0289276i | ||||
\(533\) | 6.12054e21 | 0.939663 | ||||||||
\(534\) | −8.47898e21 | + | 6.39681e20i | −1.28237 | + | 0.0967461i | ||||
\(535\) | − | 7.76411e21i | − | 1.15681i | ||||||
\(536\) | 5.80614e21 | − | 1.33439e21i | 0.852255 | − | 0.195869i | ||||
\(537\) | −1.39957e22 | −2.02395 | ||||||||
\(538\) | 7.01350e20 | + | 9.29640e21i | 0.0999256 | + | 1.32451i | ||||
\(539\) | 4.07346e21i | 0.571812i | ||||||||
\(540\) | 1.67136e21 | + | 1.10139e22i | 0.231163 | + | 1.52331i | ||||
\(541\) | −1.23122e22 | −1.67787 | −0.838933 | − | 0.544235i | \(-0.816820\pi\) | ||||
−0.838933 | + | 0.544235i | \(0.816820\pi\) | |||||||
\(542\) | 5.67492e21 | − | 4.28134e20i | 0.762019 | − | 0.0574891i | ||||
\(543\) | − | 1.26879e21i | − | 0.167877i | ||||||
\(544\) | −3.00730e21 | − | 7.60642e21i | −0.392090 | − | 0.991720i | ||||
\(545\) | 7.26778e21 | 0.933748 | ||||||||
\(546\) | 2.57831e20 | + | 3.41756e21i | 0.0326433 | + | 0.432688i | ||||
\(547\) | − | 9.06413e21i | − | 1.13091i | −0.824780 | − | 0.565454i | \(-0.808701\pi\) | ||
0.824780 | − | 0.565454i | \(-0.191299\pi\) | |||||||
\(548\) | 1.04528e22 | − | 1.58622e21i | 1.28526 | − | 0.195038i | ||||
\(549\) | 5.82450e21 | 0.705797 | ||||||||
\(550\) | 1.93388e19 | − | 1.45898e18i | 0.00230955 | − | 0.000174240i | ||||
\(551\) | 4.28965e21i | 0.504904i | ||||||||
\(552\) | 3.66615e20 | + | 1.59520e21i | 0.0425303 | + | 0.185055i | ||||
\(553\) | −2.33734e21 | −0.267251 | ||||||||
\(554\) | −9.88052e20 | − | 1.30966e22i | −0.111353 | − | 1.47598i | ||||
\(555\) | 1.05375e22i | 1.17056i | ||||||||
\(556\) | 2.48144e21 | + | 1.63521e22i | 0.271709 | + | 1.79051i | ||||
\(557\) | 6.93670e21 | 0.748706 | 0.374353 | − | 0.927286i | \(-0.377865\pi\) | ||||
0.374353 | + | 0.927286i | \(0.377865\pi\) | |||||||
\(558\) | −1.35109e21 | + | 1.01931e20i | −0.143751 | + | 0.0108451i | ||||
\(559\) | − | 1.87477e22i | − | 1.96632i | ||||||
\(560\) | −5.30418e20 | − | 1.70743e21i | −0.0548421 | − | 0.176538i | ||||
\(561\) | 1.05600e22 | 1.07637 | ||||||||
\(562\) | 2.86580e20 | + | 3.79862e21i | 0.0287976 | + | 0.381712i | ||||
\(563\) | 9.45591e21i | 0.936777i | 0.883523 | + | 0.468388i | \(0.155165\pi\) | ||||
−0.883523 | + | 0.468388i | \(0.844835\pi\) | |||||||
\(564\) | 9.68467e21 | − | 1.46965e21i | 0.945914 | − | 0.143543i | ||||
\(565\) | 1.11308e22 | 1.07186 | ||||||||
\(566\) | −1.87454e22 | + | 1.41421e21i | −1.77976 | + | 0.134271i | ||||
\(567\) | − | 1.43620e21i | − | 0.134446i | ||||||
\(568\) | −1.46671e22 | + | 3.37087e21i | −1.35381 | + | 0.311139i | ||||
\(569\) | −1.07736e22 | −0.980536 | −0.490268 | − | 0.871572i | \(-0.663101\pi\) | ||||
−0.490268 | + | 0.871572i | \(0.663101\pi\) | |||||||
\(570\) | −1.48454e21 | − | 1.96775e22i | −0.133227 | − | 1.76592i | ||||
\(571\) | 1.49259e22i | 1.32084i | 0.750895 | + | 0.660421i | \(0.229622\pi\) | ||||
−0.750895 | + | 0.660421i | \(0.770378\pi\) | |||||||
\(572\) | −1.39913e21 | − | 9.21997e21i | −0.122093 | − | 0.804565i | ||||
\(573\) | −1.75399e22 | −1.50935 | ||||||||
\(574\) | 1.48812e21 | − | 1.12269e20i | 0.126282 | − | 0.00952715i | ||||
\(575\) | − | 5.20650e18i | − | 0.000435715i | ||||||
\(576\) | 2.07732e22 | − | 1.00808e22i | 1.71444 | − | 0.831987i | ||||
\(577\) | 4.37719e21 | 0.356278 | 0.178139 | − | 0.984005i | \(-0.442992\pi\) | ||||
0.178139 | + | 0.984005i | \(0.442992\pi\) | |||||||
\(578\) | 1.28618e20 | + | 1.70484e21i | 0.0103248 | + | 0.136855i | ||||
\(579\) | − | 5.38570e20i | − | 0.0426396i | ||||||
\(580\) | −6.12921e21 | + | 9.30109e20i | −0.478609 | + | 0.0726289i | ||||
\(581\) | 3.05825e21 | 0.235539 | ||||||||
\(582\) | 5.83270e21 | − | 4.40037e20i | 0.443083 | − | 0.0334276i | ||||
\(583\) | 1.13841e22i | 0.853003i | ||||||||
\(584\) | 1.99799e21 | + | 8.69354e21i | 0.147669 | + | 0.642530i | ||||
\(585\) | −3.58535e22 | −2.61387 | ||||||||
\(586\) | 8.22133e20 | + | 1.08974e22i | 0.0591236 | + | 0.783684i | ||||
\(587\) | 3.64181e21i | 0.258353i | 0.991622 | + | 0.129176i | \(0.0412333\pi\) | ||||
−0.991622 | + | 0.129176i | \(0.958767\pi\) | |||||||
\(588\) | −3.52911e21 | − | 2.32560e22i | −0.246971 | − | 1.62749i | ||||
\(589\) | 1.14066e21 | 0.0787470 | ||||||||
\(590\) | −9.49516e21 | + | 7.16346e20i | −0.646675 | + | 0.0487873i | ||||
\(591\) | 8.80607e21i | 0.591674i | ||||||||
\(592\) | 9.91269e21 | − | 3.07942e21i | 0.657079 | − | 0.204124i | ||||
\(593\) | −2.66186e21 | −0.174080 | −0.0870399 | − | 0.996205i | \(-0.527741\pi\) | ||||
−0.0870399 | + | 0.996205i | \(0.527741\pi\) | |||||||
\(594\) | 1.06581e21 | + | 1.41273e22i | 0.0687680 | + | 0.911520i | ||||
\(595\) | 3.09674e21i | 0.197138i | ||||||||
\(596\) | −2.90394e21 | + | 4.40673e20i | −0.182397 | + | 0.0276787i | ||||
\(597\) | 3.66059e22 | 2.26859 | ||||||||
\(598\) | −2.49646e21 | + | 1.88341e20i | −0.152656 | + | 0.0115169i | ||||
\(599\) | − | 2.49736e22i | − | 1.50684i | −0.657540 | − | 0.753420i | \(-0.728403\pi\) | ||
0.657540 | − | 0.753420i | \(-0.271597\pi\) | |||||||
\(600\) | −1.09144e20 | + | 2.50840e19i | −0.00649817 | + | 0.00149344i | ||||
\(601\) | 2.22580e22 | 1.30765 | 0.653823 | − | 0.756648i | \(-0.273164\pi\) | ||||
0.653823 | + | 0.756648i | \(0.273164\pi\) | |||||||
\(602\) | −3.43887e20 | − | 4.55823e21i | −0.0199363 | − | 0.264256i | ||||
\(603\) | − | 2.91292e22i | − | 1.66644i | ||||||
\(604\) | 2.58733e21 | + | 1.70500e22i | 0.146069 | + | 0.962560i | ||||
\(605\) | 1.16331e22 | 0.648115 | ||||||||
\(606\) | 2.48587e22 | − | 1.87542e21i | 1.36678 | − | 0.103114i | ||||
\(607\) | − | 8.65974e21i | − | 0.469889i | −0.972009 | − | 0.234945i | \(-0.924509\pi\) | ||
0.972009 | − | 0.234945i | \(-0.0754909\pi\) | |||||||
\(608\) | −1.80769e22 | + | 7.14695e21i | −0.968046 | + | 0.382730i | ||||
\(609\) | 2.89754e21 | 0.153141 | ||||||||
\(610\) | −5.33103e20 | − | 7.06628e21i | −0.0278082 | − | 0.368597i | ||||
\(611\) | 1.49828e22i | 0.771373i | ||||||||
\(612\) | −3.95402e22 | + | 6.00023e21i | −2.00922 | + | 0.304899i | ||||
\(613\) | −1.90666e22 | −0.956287 | −0.478144 | − | 0.878282i | \(-0.658690\pi\) | ||||
−0.478144 | + | 0.878282i | \(0.658690\pi\) | |||||||
\(614\) | 3.26114e22 | − | 2.46031e21i | 1.61444 | − | 0.121799i | ||||
\(615\) | 2.38042e22i | 1.16319i | ||||||||
\(616\) | −5.09299e20 | − | 2.21604e21i | −0.0245656 | − | 0.106889i | ||||
\(617\) | −1.95858e22 | −0.932526 | −0.466263 | − | 0.884646i | \(-0.654400\pi\) | ||||
−0.466263 | + | 0.884646i | \(0.654400\pi\) | |||||||
\(618\) | 1.35420e21 | + | 1.79499e22i | 0.0636465 | + | 0.843635i | ||||
\(619\) | − | 1.14734e22i | − | 0.532314i | −0.963930 | − | 0.266157i | \(-0.914246\pi\) | ||
0.963930 | − | 0.266157i | \(-0.0857539\pi\) | |||||||
\(620\) | 2.47325e20 | + | 1.62982e21i | 0.0113275 | + | 0.0746458i | ||||
\(621\) | 3.80342e21 | 0.171965 | ||||||||
\(622\) | −1.54045e22 | + | 1.16217e21i | −0.687583 | + | 0.0518734i | ||||
\(623\) | − | 3.17119e21i | − | 0.139739i | ||||||
\(624\) | 1.59757e22 | + | 5.14262e22i | 0.694999 | + | 2.23721i | ||||
\(625\) | −2.31916e22 | −0.996073 | ||||||||
\(626\) | −5.50265e20 | − | 7.29376e21i | −0.0233334 | − | 0.309284i | ||||
\(627\) | − | 2.50963e22i | − | 1.05068i | ||||||
\(628\) | 4.29715e22 | − | 6.52093e21i | 1.77625 | − | 0.269546i | ||||
\(629\) | −1.79786e22 | −0.733753 | ||||||||
\(630\) | −8.71724e21 | + | 6.57657e20i | −0.351281 | + | 0.0265018i | ||||
\(631\) | − | 2.17142e22i | − | 0.863991i | −0.901876 | − | 0.431995i | \(-0.857810\pi\) | ||
0.901876 | − | 0.431995i | \(-0.142190\pi\) | |||||||
\(632\) | −3.57920e22 | + | 8.22588e21i | −1.40621 | + | 0.323181i | ||||
\(633\) | −1.37299e22 | −0.532646 | ||||||||
\(634\) | −3.83517e21 | − | 5.08352e22i | −0.146917 | − | 1.94738i | ||||
\(635\) | − | 2.67981e22i | − | 1.01371i | ||||||
\(636\) | −9.86281e21 | − | 6.49938e22i | −0.368420 | − | 2.42781i | ||||
\(637\) | 3.59787e22 | 1.32718 | ||||||||
\(638\) | −7.86181e21 | + | 5.93120e20i | −0.286390 | + | 0.0216062i | ||||
\(639\) | 7.35846e22i | 2.64716i | ||||||||
\(640\) | −1.41314e22 | − | 2.42793e22i | −0.502048 | − | 0.862576i | ||||
\(641\) | −1.08805e22 | −0.381753 | −0.190877 | − | 0.981614i | \(-0.561133\pi\) | ||||
−0.190877 | + | 0.981614i | \(0.561133\pi\) | |||||||
\(642\) | 4.28945e21 | + | 5.68567e22i | 0.148635 | + | 1.97016i | ||||
\(643\) | 2.77111e22i | 0.948345i | 0.880432 | + | 0.474172i | \(0.157253\pi\) | ||||
−0.880432 | + | 0.474172i | \(0.842747\pi\) | |||||||
\(644\) | −6.03523e20 | + | 9.15847e19i | −0.0203989 | + | 0.00309554i | ||||
\(645\) | 7.29141e22 | 2.43407 | ||||||||
\(646\) | 3.35728e22 | − | 2.53284e21i | 1.10695 | − | 0.0835118i | ||||
\(647\) | 2.15902e22i | 0.703109i | 0.936167 | + | 0.351555i | \(0.114347\pi\) | ||||
−0.936167 | + | 0.351555i | \(0.885653\pi\) | |||||||
\(648\) | −5.05446e21 | − | 2.19927e22i | −0.162583 | − | 0.707422i | ||||
\(649\) | −1.21099e22 | −0.384755 | ||||||||
\(650\) | −1.28864e19 | − | 1.70809e20i | −0.000404413 | − | 0.00536049i | ||||
\(651\) | − | 7.70485e20i | − | 0.0238845i | ||||||
\(652\) | 4.45423e21 | + | 2.93524e22i | 0.136393 | + | 0.898799i | ||||
\(653\) | −3.41825e22 | −1.03395 | −0.516973 | − | 0.856002i | \(-0.672941\pi\) | ||||
−0.516973 | + | 0.856002i | \(0.672941\pi\) | |||||||
\(654\) | −5.32221e22 | + | 4.01525e21i | −1.59027 | + | 0.119975i | ||||
\(655\) | 4.31925e22i | 1.27490i | ||||||||
\(656\) | 2.23927e22 | − | 6.95638e21i | 0.652944 | − | 0.202840i | ||||
\(657\) | 4.36152e22 | 1.25636 | ||||||||
\(658\) | 2.74829e20 | + | 3.64286e21i | 0.00782087 | + | 0.103666i | ||||
\(659\) | 1.24387e22i | 0.349696i | 0.984595 | + | 0.174848i | \(0.0559434\pi\) | ||||
−0.984595 | + | 0.174848i | \(0.944057\pi\) | |||||||
\(660\) | 3.58586e22 | − | 5.44154e21i | 0.995959 | − | 0.151137i | ||||
\(661\) | −1.37447e22 | −0.377157 | −0.188578 | − | 0.982058i | \(-0.560388\pi\) | ||||
−0.188578 | + | 0.982058i | \(0.560388\pi\) | |||||||
\(662\) | 4.00130e22 | − | 3.01871e21i | 1.08477 | − | 0.0818385i | ||||
\(663\) | − | 9.32713e22i | − | 2.49827i | ||||||
\(664\) | 4.68314e22 | − | 1.07630e22i | 1.23935 | − | 0.284832i | ||||
\(665\) | 7.35952e21 | 0.192432 | ||||||||
\(666\) | −3.81812e21 | − | 5.06091e22i | −0.0986405 | − | 1.30748i | ||||
\(667\) | 2.11660e21i | 0.0540297i | ||||||||
\(668\) | 1.28489e21 | + | 8.46717e21i | 0.0324083 | + | 0.213563i | ||||
\(669\) | −1.11249e23 | −2.77259 | ||||||||
\(670\) | −3.53396e22 | + | 2.66613e21i | −0.870288 | + | 0.0656573i | ||||
\(671\) | − | 9.01219e21i | − | 0.219306i | ||||||
\(672\) | 4.82757e21 | + | 1.22105e22i | 0.116085 | + | 0.293615i | ||||
\(673\) | 1.81248e22 | 0.430679 | 0.215339 | − | 0.976539i | \(-0.430914\pi\) | ||||
0.215339 | + | 0.976539i | \(0.430914\pi\) | |||||||
\(674\) | 6.11459e20 | + | 8.10489e21i | 0.0143578 | + | 0.190313i | ||||
\(675\) | 2.60232e20i | 0.00603852i | ||||||||
\(676\) | −3.83200e22 | + | 5.81506e21i | −0.878722 | + | 0.133346i | ||||
\(677\) | 2.73580e22 | 0.619977 | 0.309988 | − | 0.950740i | \(-0.399675\pi\) | ||||
0.309988 | + | 0.950740i | \(0.399675\pi\) | |||||||
\(678\) | −8.15113e22 | + | 6.14947e21i | −1.82549 | + | 0.137721i | ||||
\(679\) | 2.18146e21i | 0.0482825i | ||||||||
\(680\) | 1.08985e22 | + | 4.74209e22i | 0.238394 | + | 1.03729i | ||||
\(681\) | 3.43119e22 | 0.741767 | ||||||||
\(682\) | 1.57717e20 | + | 2.09053e21i | 0.00336979 | + | 0.0446665i | ||||
\(683\) | 5.92941e21i | 0.125212i | 0.998038 | + | 0.0626060i | \(0.0199411\pi\) | ||||
−0.998038 | + | 0.0626060i | \(0.980059\pi\) | |||||||
\(684\) | 1.42597e22 | + | 9.39686e22i | 0.297620 | + | 1.96125i | ||||
\(685\) | −6.28937e22 | −1.29743 | ||||||||
\(686\) | 1.78062e22 | − | 1.34335e21i | 0.363059 | − | 0.0273903i | ||||
\(687\) | − | 7.49488e22i | − | 1.51046i | ||||||
\(688\) | −2.13079e22 | − | 6.85906e22i | −0.424457 | − | 1.36633i | ||||
\(689\) | 1.00550e23 | 1.97983 | ||||||||
\(690\) | −7.32501e20 | − | 9.70930e21i | −0.0142566 | − | 0.188971i | ||||
\(691\) | 8.61448e22i | 1.65731i | 0.559757 | + | 0.828657i | \(0.310894\pi\) | ||||
−0.559757 | + | 0.828657i | \(0.689106\pi\) | |||||||
\(692\) | −5.80810e22 | + | 8.81380e21i | −1.10455 | + | 0.167616i | ||||
\(693\) | −1.11178e22 | −0.209003 | ||||||||
\(694\) | −5.27913e22 | + | 3.98274e21i | −0.981039 | + | 0.0740127i | ||||
\(695\) | − | 9.83891e22i | − | 1.80746i | ||||||
\(696\) | 4.43705e22 | − | 1.01974e22i | 0.805788 | − | 0.185190i | ||||
\(697\) | −4.06135e22 | −0.729135 | ||||||||
\(698\) | 6.23177e21 | + | 8.26022e22i | 0.110603 | + | 1.46605i | ||||
\(699\) | − | 8.02586e22i | − | 1.40823i | ||||||
\(700\) | −6.26628e18 | − | 4.12934e19i | −0.000108699 | − | 0.000716302i | ||||
\(701\) | 4.35956e22 | 0.747649 | 0.373825 | − | 0.927499i | \(-0.378046\pi\) | ||||
0.373825 | + | 0.927499i | \(0.378046\pi\) | |||||||
\(702\) | 1.24779e23 | − | 9.41369e21i | 2.11565 | − | 0.159611i | ||||
\(703\) | 4.27267e22i | 0.716237i | ||||||||
\(704\) | −1.55980e22 | − | 3.21421e22i | −0.258516 | − | 0.532713i | ||||
\(705\) | −5.82717e22 | −0.954871 | ||||||||
\(706\) | 7.74496e20 | + | 1.02660e22i | 0.0125482 | + | 0.166327i | ||||
\(707\) | 9.29730e21i | 0.148937i | ||||||||
\(708\) | 6.91376e22 | − | 1.04916e22i | 1.09509 | − | 0.166179i | ||||
\(709\) | 8.06491e22 | 1.26308 | 0.631539 | − | 0.775344i | \(-0.282424\pi\) | ||||
0.631539 | + | 0.775344i | \(0.282424\pi\) | |||||||
\(710\) | 8.92728e22 | − | 6.73502e21i | 1.38246 | − | 0.104297i | ||||
\(711\) | 1.79567e23i | 2.74961i | ||||||||
\(712\) | −1.11605e22 | − | 4.85609e22i | −0.168983 | − | 0.735270i | ||||
\(713\) | 5.62825e20 | 0.00842669 | ||||||||
\(714\) | −1.71087e21 | − | 2.26775e22i | −0.0253297 | − | 0.335746i | ||||
\(715\) | 5.54757e22i | 0.812183i | ||||||||
\(716\) | −1.23046e22 | − | 8.10845e22i | −0.178141 | − | 1.17391i | ||||
\(717\) | −1.13832e23 | −1.62971 | ||||||||
\(718\) | 1.96932e22 | − | 1.48571e21i | 0.278817 | − | 0.0210349i | ||||
\(719\) | − | 1.00543e23i | − | 1.40774i | −0.710329 | − | 0.703870i | \(-0.751454\pi\) | ||
0.710329 | − | 0.703870i | \(-0.248546\pi\) | |||||||
\(720\) | −1.31174e23 | + | 4.07497e22i | −1.81630 | + | 0.564241i | ||||
\(721\) | −6.71338e21 | −0.0919303 | ||||||||
\(722\) | −4.64368e20 | − | 6.15521e21i | −0.00628876 | − | 0.0833576i | ||||
\(723\) | 2.34303e22i | 0.313814i | ||||||||
\(724\) | 7.35080e21 | − | 1.11548e21i | 0.0973702 | − | 0.0147759i | ||||
\(725\) | −1.44819e20 | −0.00189724 | ||||||||
\(726\) | −8.51895e22 | + | 6.42697e21i | −1.10381 | + | 0.0832747i | ||||
\(727\) | − | 1.04861e23i | − | 1.34381i | −0.740637 | − | 0.671905i | \(-0.765476\pi\) | ||
0.740637 | − | 0.671905i | \(-0.234524\pi\) | |||||||
\(728\) | −1.95731e22 | + | 4.49837e21i | −0.248089 | + | 0.0570170i | ||||
\(729\) | 9.95702e22 | 1.24827 | ||||||||
\(730\) | −3.99200e21 | − | 5.29139e22i | −0.0495002 | − | 0.656126i | ||||
\(731\) | 1.24402e23i | 1.52577i | ||||||||
\(732\) | 7.80785e21 | + | 5.14520e22i | 0.0947203 | + | 0.624186i | ||||
\(733\) | 9.82469e22 | 1.17893 | 0.589464 | − | 0.807795i | \(-0.299339\pi\) | ||||
0.589464 | + | 0.807795i | \(0.299339\pi\) | |||||||
\(734\) | −2.21974e22 | + | 1.67464e21i | −0.263471 | + | 0.0198771i | ||||
\(735\) | 1.39929e23i | 1.64290i | ||||||||
\(736\) | −8.91952e21 | + | 3.52645e21i | −0.103590 | + | 0.0409558i | ||||
\(737\) | −4.50713e22 | −0.517798 | ||||||||
\(738\) | −8.62510e21 | − | 1.14326e23i | −0.0980196 | − | 1.29925i | ||||
\(739\) | − | 6.82761e22i | − | 0.767561i | −0.923424 | − | 0.383781i | \(-0.874622\pi\) | ||
0.923424 | − | 0.383781i | \(-0.125378\pi\) | |||||||
\(740\) | −6.10495e22 | + | 9.26427e21i | −0.678936 | + | 0.103029i | ||||
\(741\) | −2.21662e23 | −2.43863 | ||||||||
\(742\) | 2.44472e22 | − | 1.84438e21i | 0.266071 | − | 0.0200733i | ||||
\(743\) | 1.19418e23i | 1.28575i | 0.765970 | + | 0.642876i | \(0.222259\pi\) | ||||
−0.765970 | + | 0.642876i | \(0.777741\pi\) | |||||||
\(744\) | −2.71160e21 | − | 1.17986e22i | −0.0288830 | − | 0.125674i | ||||
\(745\) | 1.74727e22 | 0.184124 | ||||||||
\(746\) | −2.83386e20 | − | 3.75628e21i | −0.00295439 | − | 0.0391604i | ||||
\(747\) | − | 2.34952e23i | − | 2.42334i | ||||||
\(748\) | 9.28408e21 | + | 6.11801e22i | 0.0947384 | + | 0.624306i | ||||
\(749\) | −2.12648e22 | −0.214687 | ||||||||
\(750\) | 1.70500e23 | − | 1.28631e22i | 1.70308 | − | 0.128485i | ||||
\(751\) | − | 4.88585e22i | − | 0.482859i | −0.970418 | − | 0.241430i | \(-0.922384\pi\) | ||
0.970418 | − | 0.241430i | \(-0.0776163\pi\) | |||||||
\(752\) | 1.70289e22 | + | 5.48164e22i | 0.166512 | + | 0.536004i | ||||
\(753\) | 2.20561e23 | 2.13387 | ||||||||
\(754\) | 5.23872e21 | + | 6.94392e22i | 0.0501481 | + | 0.664713i | ||||
\(755\) | − | 1.02588e23i | − | 0.971674i | ||||||
\(756\) | 3.01654e22 | − | 4.57760e21i | 0.282706 | − | 0.0429006i | ||||
\(757\) | −1.86534e23 | −1.72978 | −0.864892 | − | 0.501958i | \(-0.832613\pi\) | ||||
−0.864892 | + | 0.501958i | \(0.832613\pi\) | |||||||
\(758\) | 3.62846e22 | − | 2.73742e21i | 0.332942 | − | 0.0251182i | ||||
\(759\) | − | 1.23830e22i | − | 0.112433i | ||||||
\(760\) | 1.12697e23 | − | 2.59006e22i | 1.01252 | − | 0.232703i | ||||
\(761\) | −1.86105e22 | −0.165456 | −0.0827279 | − | 0.996572i | \(-0.526363\pi\) | ||||
−0.0827279 | + | 0.996572i | \(0.526363\pi\) | |||||||
\(762\) | 1.48052e22 | + | 1.96243e23i | 0.130249 | + | 1.72645i | ||||
\(763\) | − | 1.99054e22i | − | 0.173290i | ||||||
\(764\) | −1.54205e22 | − | 1.01618e23i | −0.132847 | − | 0.875434i | ||||
\(765\) | 2.37909e23 | 2.02824 | ||||||||
\(766\) | −1.95311e23 | + | 1.47349e22i | −1.64777 | + | 0.124313i | ||||
\(767\) | 1.06961e23i | 0.893019i | ||||||||
\(768\) | 1.16898e23 | + | 1.69991e23i | 0.965868 | + | 1.40455i | ||||
\(769\) | 7.64403e21 | 0.0625046 | 0.0312523 | − | 0.999512i | \(-0.490050\pi\) | ||||
0.0312523 | + | 0.999512i | \(0.490050\pi\) | |||||||
\(770\) | 1.01758e21 | + | 1.34881e22i | 0.00823464 | + | 0.109150i | ||||
\(771\) | − | 5.38909e22i | − | 0.431599i | ||||||
\(772\) | 3.12023e21 | − | 4.73495e20i | 0.0247313 | − | 0.00375298i | ||||
\(773\) | −2.77389e22 | −0.217597 | −0.108799 | − | 0.994064i | \(-0.534700\pi\) | ||||
−0.108799 | + | 0.994064i | \(0.534700\pi\) | |||||||
\(774\) | −3.50189e23 | + | 2.64194e22i | −2.71878 | + | 0.205114i | ||||
\(775\) | 3.85088e19i | 0.000295901i | ||||||||
\(776\) | 7.67731e21 | + | 3.34051e22i | 0.0583869 | + | 0.254050i | ||||
\(777\) | 2.88607e22 | 0.217240 | ||||||||
\(778\) | 1.26408e22 | + | 1.67554e23i | 0.0941755 | + | 1.24830i | ||||
\(779\) | 9.65193e22i | 0.711729i | ||||||||
\(780\) | −4.80622e22 | − | 3.16720e23i | −0.350790 | − | 2.31163i | ||||
\(781\) | 1.13857e23 | 0.822526 | ||||||||
\(782\) | 1.65655e22 | − | 1.24976e21i | 0.118454 | − | 0.00893658i | ||||
\(783\) | − | 1.05792e23i | − | 0.748790i | ||||||
\(784\) | 1.31632e23 | − | 4.08920e22i | 0.922218 | − | 0.286491i | ||||
\(785\) | −2.58555e23 | −1.79306 | ||||||||
\(786\) | −2.38626e22 | − | 3.16300e23i | −0.163809 | − | 2.17129i | ||||
\(787\) | − | 1.33486e23i | − | 0.907063i | −0.891240 | − | 0.453531i | \(-0.850164\pi\) | ||
0.891240 | − | 0.453531i | \(-0.149836\pi\) | |||||||
\(788\) | −5.10183e22 | + | 7.74204e21i | −0.343176 | + | 0.0520770i | ||||
\(789\) | 6.49024e22 | 0.432160 | ||||||||
\(790\) | 2.17851e23 | − | 1.64354e22i | 1.43596 | − | 0.108334i | ||||
\(791\) | − | 3.04857e22i | − | 0.198923i | ||||||
\(792\) | −1.70248e23 | + | 3.91272e22i | −1.09972 | + | 0.252742i | ||||
\(793\) | −7.95998e22 | −0.509010 | ||||||||
\(794\) | −6.28191e21 | − | 8.32668e22i | −0.0397674 | − | 0.527118i | ||||
\(795\) | 3.91061e23i | 2.45080i | ||||||||
\(796\) | 3.21828e22 | + | 2.12078e23i | 0.199673 | + | 1.31580i | ||||
\(797\) | −1.00556e23 | −0.617647 | −0.308824 | − | 0.951119i | \(-0.599935\pi\) | ||||
−0.308824 | + | 0.951119i | \(0.599935\pi\) | |||||||
\(798\) | −5.38940e22 | + | 4.06593e21i | −0.327731 | + | 0.0247250i | ||||
\(799\) | − | 9.94202e22i | − | 0.598550i | ||||||
\(800\) | −2.41282e20 | − | 6.10279e20i | −0.00143815 | − | 0.00363755i | ||||
\(801\) | −2.43629e23 | −1.43770 | ||||||||
\(802\) | −7.48484e21 | − | 9.92116e22i | −0.0437308 | − | 0.579652i | ||||
\(803\) | − | 6.74853e22i | − | 0.390378i | ||||||
\(804\) | 2.57320e23 | − | 3.90483e22i | 1.47375 | − | 0.223642i | ||||
\(805\) | 3.63134e21 | 0.0205920 | ||||||||
\(806\) | 1.84646e22 | − | 1.39303e21i | 0.103671 | − | 0.00782130i | ||||
\(807\) | 4.07286e23i | 2.26418i | ||||||||
\(808\) | 3.27203e22 | + | 1.42371e23i | 0.180105 | + | 0.783665i | ||||
\(809\) | 3.21093e22 | 0.175002 | 0.0875010 | − | 0.996164i | \(-0.472112\pi\) | ||||
0.0875010 | + | 0.996164i | \(0.472112\pi\) | |||||||
\(810\) | 1.00989e22 | + | 1.33860e23i | 0.0544994 | + | 0.722390i | ||||
\(811\) | 1.74376e23i | 0.931792i | 0.884839 | + | 0.465896i | \(0.154268\pi\) | ||||
−0.884839 | + | 0.465896i | \(0.845732\pi\) | |||||||
\(812\) | 2.54743e21 | + | 1.67870e22i | 0.0134789 | + | 0.0888231i | ||||
\(813\) | 2.48625e23 | 1.30263 | ||||||||
\(814\) | −7.83070e22 | + | 5.90773e21i | −0.406261 | + | 0.0306496i | ||||
\(815\) | − | 1.76610e23i | − | 0.907309i | ||||||
\(816\) | −1.06009e23 | − | 3.41244e23i | −0.539287 | − | 1.73597i | ||||
\(817\) | 2.95646e23 | 1.48935 | ||||||||
\(818\) | −2.63882e22 | − | 3.49776e23i | −0.131639 | − | 1.74487i | ||||
\(819\) | 9.81975e22i | 0.485098i | ||||||||
\(820\) | −1.37910e23 | + | 2.09279e22i | −0.674662 | + | 0.102380i | ||||
\(821\) | 2.77373e23 | 1.34375 | 0.671875 | − | 0.740664i | \(-0.265489\pi\) | ||||
0.671875 | + | 0.740664i | \(0.265489\pi\) | |||||||
\(822\) | 4.60572e23 | − | 3.47470e22i | 2.20965 | − | 0.166703i | ||||
\(823\) | − | 1.57320e23i | − | 0.747456i | −0.927538 | − | 0.373728i | \(-0.878079\pi\) | ||
0.927538 | − | 0.373728i | \(-0.121921\pi\) | |||||||
\(824\) | −1.02803e23 | + | 2.36266e22i | −0.483713 | + | 0.111169i | ||||
\(825\) | 8.47255e20 | 0.00394805 | ||||||||
\(826\) | 1.96197e21 | + | 2.60059e22i | 0.00905423 | + | 0.120014i | ||||
\(827\) | − | 8.52321e22i | − | 0.389546i | −0.980848 | − | 0.194773i | \(-0.937603\pi\) | ||
0.980848 | − | 0.194773i | \(-0.0623970\pi\) | |||||||
\(828\) | 7.03605e21 | + | 4.63660e22i | 0.0318483 | + | 0.209873i | ||||
\(829\) | −1.30428e23 | −0.584704 | −0.292352 | − | 0.956311i | \(-0.594438\pi\) | ||||
−0.292352 | + | 0.956311i | \(0.594438\pi\) | |||||||
\(830\) | −2.85043e23 | + | 2.15046e22i | −1.26557 | + | 0.0954786i | ||||
\(831\) | − | 5.73778e23i | − | 2.52311i | ||||||
\(832\) | −2.83894e23 | + | 1.37769e23i | −1.23643 | + | 0.600017i | ||||
\(833\) | −2.38740e23 | −1.02983 | ||||||||
\(834\) | 5.43572e22 | + | 7.20506e23i | 0.232236 | + | 3.07829i | ||||
\(835\) | − | 5.09461e22i | − | 0.215585i | ||||||
\(836\) | 1.45397e23 | − | 2.20639e22i | 0.609402 | − | 0.0924768i | ||||
\(837\) | −2.81312e22 | −0.116784 | ||||||||
\(838\) | 8.96445e22 | − | 6.76307e21i | 0.368614 | − | 0.0278094i | ||||
\(839\) | 3.04979e23i | 1.24215i | 0.783751 | + | 0.621075i | \(0.213304\pi\) | ||||
−0.783751 | + | 0.621075i | \(0.786696\pi\) | |||||||
\(840\) | −1.74952e22 | − | 7.61241e22i | −0.0705804 | − | 0.307106i | ||||
\(841\) | −1.91373e23 | −0.764738 | ||||||||
\(842\) | 1.15541e22 | + | 1.53150e23i | 0.0457341 | + | 0.606206i | ||||
\(843\) | 1.66422e23i | 0.652514i | ||||||||
\(844\) | −1.20710e22 | − | 7.95450e22i | −0.0468816 | − | 0.308939i | ||||
\(845\) | 2.30568e23 | 0.887043 | ||||||||
\(846\) | 2.79865e23 | − | 2.11139e22i | 1.06656 | − | 0.0804647i | ||||
\(847\) | − | 3.18614e22i | − | 0.120281i | ||||||
\(848\) | 3.67873e23 | − | 1.14281e23i | 1.37572 | − | 0.427374i | ||||
\(849\) | −8.21255e23 | −3.04240 | ||||||||
\(850\) | 8.55090e19 | + | 1.13342e21i | 0.000313806 | + | 0.00415949i | ||||
\(851\) | 2.10822e22i | 0.0766443i | ||||||||
\(852\) | −6.50026e23 | + | 9.86415e22i | −2.34107 | + | 0.355257i | ||||
\(853\) | −6.07340e22 | −0.216691 | −0.108345 | − | 0.994113i | \(-0.534555\pi\) | ||||
−0.108345 | + | 0.994113i | \(0.534555\pi\) | |||||||
\(854\) | −1.93535e22 | + | 1.46009e21i | −0.0684065 | + | 0.00516080i | ||||
\(855\) | − | 5.65399e23i | − | 1.97982i | ||||||
\(856\) | −3.25631e23 | + | 7.48379e22i | −1.12963 | + | 0.259616i | ||||
\(857\) | 4.13905e23 | 1.42251 | 0.711254 | − | 0.702935i | \(-0.248128\pi\) | ||||
0.711254 | + | 0.702935i | \(0.248128\pi\) | |||||||
\(858\) | −3.06488e22 | − | 4.06250e23i | −0.104355 | − | 1.38323i | ||||
\(859\) | − | 4.51382e23i | − | 1.52264i | −0.648374 | − | 0.761322i | \(-0.724551\pi\) | ||
0.648374 | − | 0.761322i | \(-0.275449\pi\) | |||||||
\(860\) | 6.41039e22 | + | 4.22431e23i | 0.214238 | + | 1.41178i | ||||
\(861\) | 6.51962e22 | 0.215872 | ||||||||
\(862\) | 1.06255e23 | − | 8.01620e21i | 0.348570 | − | 0.0262973i | ||||
\(863\) | 4.39182e23i | 1.42744i | 0.700430 | + | 0.713721i | \(0.252991\pi\) | ||||
−0.700430 | + | 0.713721i | \(0.747009\pi\) | |||||||
\(864\) | 4.45817e23 | − | 1.76260e23i | 1.43564 | − | 0.567601i | ||||
\(865\) | 3.49468e23 | 1.11501 | ||||||||
\(866\) | −5.01192e21 | − | 6.64331e22i | −0.0158439 | − | 0.210011i | ||||
\(867\) | 7.46909e22i | 0.233946i | ||||||||
\(868\) | 4.46384e21 | − | 6.77388e20i | 0.0138532 | − | 0.00210223i | ||||
\(869\) | 2.77842e23 | 0.854359 | ||||||||
\(870\) | −2.70065e23 | + | 2.03746e22i | −0.822837 | + | 0.0620775i | ||||
\(871\) | 3.98091e23i | 1.20181i | ||||||||
\(872\) | −7.00538e22 | − | 3.04814e23i | −0.209556 | − | 0.911808i | ||||
\(873\) | 1.67592e23 | 0.496753 | ||||||||
\(874\) | −2.97009e21 | − | 3.93685e22i | −0.00872324 | − | 0.115627i | ||||
\(875\) | 6.37680e22i | 0.185583i | ||||||||
\(876\) | 5.84670e22 | + | 3.85285e23i | 0.168608 | + | 1.11109i | ||||
\(877\) | 1.92199e23 | 0.549230 | 0.274615 | − | 0.961554i | \(-0.411450\pi\) | ||||
0.274615 | + | 0.961554i | \(0.411450\pi\) | |||||||
\(878\) | −2.49181e23 | + | 1.87990e22i | −0.705601 | + | 0.0532328i | ||||
\(879\) | 4.77426e23i | 1.33966i | ||||||||
\(880\) | 6.30516e22 | + | 2.02964e23i | 0.175321 | + | 0.564362i | ||||
\(881\) | −8.58923e22 | −0.236672 | −0.118336 | − | 0.992974i | \(-0.537756\pi\) | ||||
−0.118336 | + | 0.992974i | \(0.537756\pi\) | |||||||
\(882\) | −5.07013e22 | − | 6.72046e23i | −0.138443 | − | 1.83506i | ||||
\(883\) | − | 1.84130e23i | − | 0.498240i | −0.968473 | − | 0.249120i | \(-0.919859\pi\) | ||
0.968473 | − | 0.249120i | \(-0.0801414\pi\) | |||||||
\(884\) | 5.40371e23 | − | 8.20014e22i | 1.44902 | − | 0.219889i | ||||
\(885\) | −4.15994e23 | −1.10545 | ||||||||
\(886\) | 5.31449e22 | − | 4.00942e21i | 0.139956 | − | 0.0105587i | ||||
\(887\) | − | 3.79305e22i | − | 0.0989920i | −0.998774 | − | 0.0494960i | \(-0.984238\pi\) | ||
0.998774 | − | 0.0494960i | \(-0.0157615\pi\) | |||||||
\(888\) | 4.41949e23 | − | 1.01571e23i | 1.14306 | − | 0.262703i | ||||
\(889\) | −7.33961e22 | −0.188130 | ||||||||
\(890\) | 2.22988e22 | + | 2.95570e23i | 0.0566449 | + | 0.750828i | ||||
\(891\) | 1.70723e23i | 0.429803i | ||||||||
\(892\) | −9.78066e22 | − | 6.44524e23i | −0.244033 | − | 1.60813i | ||||
\(893\) | −2.36275e23 | −0.584261 | ||||||||
\(894\) | −1.27953e23 | + | 9.65318e21i | −0.313581 | + | 0.0236576i | ||||
\(895\) | 4.87878e23i | 1.18502i | ||||||||
\(896\) | −6.64976e22 | + | 3.87038e22i | −0.160082 | + | 0.0931730i | ||||
\(897\) | −1.09373e23 | −0.260957 | ||||||||
\(898\) | −4.57903e21 | − | 6.06951e22i | −0.0108284 | − | 0.143530i | ||||
\(899\) | − | 1.56550e22i | − | 0.0366924i | ||||||
\(900\) | −3.17239e21 | + | 4.81411e20i | −0.00736964 | + | 0.00111834i | ||||
\(901\) | −6.67209e23 | −1.53626 | ||||||||
\(902\) | −1.76895e23 | + | 1.33455e22i | −0.403704 | + | 0.0304567i | ||||
\(903\) | − | 1.99701e23i | − | 0.451730i | ||||||
\(904\) | −1.07290e23 | − | 4.66833e23i | −0.240553 | − | 1.04668i | ||||
\(905\) | −4.42290e22 | −0.0982922 | ||||||||
\(906\) | 5.66770e22 | + | 7.51254e23i | 0.124848 | + | 1.65486i | ||||
\(907\) | − | 1.13073e23i | − | 0.246887i | −0.992352 | − | 0.123444i | \(-0.960606\pi\) | ||
0.992352 | − | 0.123444i | \(-0.0393938\pi\) | |||||||
\(908\) | 3.01660e22 | + | 1.98787e23i | 0.0652876 | + | 0.430231i | ||||
\(909\) | 7.14271e23 | 1.53233 | ||||||||
\(910\) | 1.19133e23 | − | 8.98779e21i | 0.253339 | − | 0.0191127i | ||||
\(911\) | − | 6.25689e23i | − | 1.31890i | −0.751749 | − | 0.659449i | \(-0.770789\pi\) | ||
0.751749 | − | 0.659449i | \(-0.229211\pi\) | |||||||
\(912\) | −8.10977e23 | + | 2.51933e23i | −1.69453 | + | 0.526413i | ||||
\(913\) | −3.63538e23 | −0.752981 | ||||||||
\(914\) | 1.22529e22 | + | 1.62412e23i | 0.0251575 | + | 0.333463i | ||||
\(915\) | − | 3.09582e23i | − | 0.630096i | ||||||
\(916\) | 4.34219e23 | − | 6.58927e22i | 0.876082 | − | 0.132946i | ||||
\(917\) | 1.18298e23 | 0.236604 | ||||||||
\(918\) | −8.27981e23 | + | 6.24655e22i | −1.64164 | + | 0.123851i | ||||
\(919\) | 3.64131e23i | 0.715705i | 0.933778 | + | 0.357852i | \(0.116491\pi\) | ||||
−0.933778 | + | 0.357852i | \(0.883509\pi\) | |||||||
\(920\) | 5.56072e22 | − | 1.27799e22i | 0.108350 | − | 0.0249015i | ||||
\(921\) | 1.42874e24 | 2.75979 | ||||||||
\(922\) | −2.71071e22 | − | 3.59305e23i | −0.0519082 | − | 0.688043i | ||||
\(923\) | − | 1.00563e24i | − | 1.90909i | ||||||
\(924\) | −1.49036e22 | − | 9.82115e22i | −0.0280489 | − | 0.184836i | ||||
\(925\) | −1.44246e21 | −0.00269135 | ||||||||
\(926\) | −6.73896e22 | + | 5.08409e21i | −0.124654 | + | 0.00940427i | ||||
\(927\) | 5.15759e23i | 0.945821i | ||||||||
\(928\) | 9.80885e22 | + | 2.48097e23i | 0.178334 | + | 0.451064i | ||||
\(929\) | −7.59572e23 | −1.36913 | −0.684563 | − | 0.728954i | \(-0.740007\pi\) | ||||
−0.684563 | + | 0.728954i | \(0.740007\pi\) | |||||||
\(930\) | 5.41780e21 | + | 7.18129e22i | 0.00968187 | + | 0.128333i | ||||
\(931\) | 5.67374e23i | 1.00525i | ||||||||
\(932\) | 4.64982e23 | − | 7.05610e22i | 0.816787 | − | 0.123947i | ||||
\(933\) | −6.74889e23 | −1.17538 | ||||||||
\(934\) | 9.08374e22 | − | 6.85306e21i | 0.156852 | − | 0.0118334i | ||||
\(935\) | − | 3.68114e23i | − | 0.630217i | ||||||
\(936\) | 3.45590e23 | + | 1.50371e24i | 0.586617 | + | 2.55246i | ||||
\(937\) | 6.78799e23 | 1.14242 | 0.571208 | − | 0.820805i | \(-0.306475\pi\) | ||||
0.571208 | + | 0.820805i | \(0.306475\pi\) | |||||||
\(938\) | 7.30215e21 | + | 9.67900e22i | 0.0121851 | + | 0.161513i | ||||
\(939\) | − | 3.19548e23i | − | 0.528703i | ||||||
\(940\) | −5.12307e22 | − | 3.37599e23i | −0.0840442 | − | 0.553833i | ||||
\(941\) | 6.36693e23 | 1.03565 | 0.517825 | − | 0.855487i | \(-0.326742\pi\) | ||||
0.517825 | + | 0.855487i | \(0.326742\pi\) | |||||||
\(942\) | 1.89341e24 | − | 1.42845e23i | 3.05377 | − | 0.230386i | ||||
\(943\) | 4.76246e22i | 0.0761619i | ||||||||
\(944\) | 1.21567e23 | + | 3.91327e23i | 0.192771 | + | 0.620532i | ||||
\(945\) | −1.81502e23 | −0.285383 | ||||||||
\(946\) | 4.08784e22 | + | 5.41843e23i | 0.0637330 | + | 0.844782i | ||||
\(947\) | 6.94373e23i | 1.07348i | 0.843749 | + | 0.536738i | \(0.180344\pi\) | ||||
−0.843749 | + | 0.536738i | \(0.819656\pi\) | |||||||
\(948\) | −1.58625e24 | + | 2.40713e23i | −2.43167 | + | 0.369006i | ||||
\(949\) | −5.96062e23 | −0.906070 | ||||||||
\(950\) | 2.69362e21 | − | 2.03215e20i | 0.00406020 | − | 0.000306314i | ||||
\(951\) | − | 2.22715e24i | − | 3.32893i | ||||||
\(952\) | 1.29879e23 | − | 2.98494e22i | 0.192506 | − | 0.0442425i | ||||
\(953\) | −7.36518e23 | −1.08253 | −0.541265 | − | 0.840852i | \(-0.682054\pi\) | ||||
−0.541265 | + | 0.840852i | \(0.682054\pi\) | |||||||
\(954\) | −1.41695e23 | − | 1.87817e24i | −0.206523 | − | 2.73746i | ||||
\(955\) | 6.11425e23i | 0.883723i | ||||||||
\(956\) | −1.00078e23 | − | 6.59489e23i | −0.143441 | − | 0.945246i | ||||
\(957\) | −3.44435e23 | −0.489567 | ||||||||
\(958\) | 1.48267e23 | − | 1.11857e22i | 0.208987 | − | 0.0157667i | ||||
\(959\) | 1.72257e23i | 0.240784i | ||||||||
\(960\) | −5.35813e23 | − | 1.10413e24i | −0.742751 | − | 1.53056i | ||||
\(961\) | 7.23260e23 | 0.994277 | ||||||||
\(962\) | 5.21798e22 | + | 6.91644e23i | 0.0711381 | + | 0.942935i | ||||
\(963\) | 1.63368e24i | 2.20880i | ||||||||
\(964\) | −1.35745e23 | + | 2.05993e22i | −0.182015 | + | 0.0276207i | ||||
\(965\) | −1.87741e22 | −0.0249655 | ||||||||
\(966\) | −2.65924e22 | + | 2.00621e21i | −0.0350704 | + | 0.00264582i | ||||
\(967\) | 7.91831e23i | 1.03567i | 0.855481 | + | 0.517834i | \(0.173261\pi\) | ||||
−0.855481 | + | 0.517834i | \(0.826739\pi\) | |||||||
\(968\) | −1.12131e23 | − | 4.87898e23i | −0.145453 | − | 0.632887i | ||||
\(969\) | 1.47086e24 | 1.89227 | ||||||||
\(970\) | −1.53393e22 | − | 2.03323e23i | −0.0195719 | − | 0.259425i | ||||
\(971\) | − | 2.22361e23i | − | 0.281387i | −0.990053 | − | 0.140694i | \(-0.955067\pi\) | ||
0.990053 | − | 0.140694i | \(-0.0449333\pi\) | |||||||
\(972\) | 3.66356e22 | + | 2.41420e23i | 0.0459804 | + | 0.303001i | ||||
\(973\) | −2.69474e23 | −0.335439 | ||||||||
\(974\) | −1.54644e24 | + | 1.16668e23i | −1.90924 | + | 0.144039i | ||||
\(975\) | − | 7.48335e21i | − | 0.00916345i | ||||||
\(976\) | −2.91225e23 | + | 9.04702e22i | −0.353696 | + | 0.109877i | ||||
\(977\) | −7.83431e23 | −0.943722 | −0.471861 | − | 0.881673i | \(-0.656418\pi\) | ||||
−0.471861 | + | 0.881673i | \(0.656418\pi\) | |||||||
\(978\) | 9.75724e22 | + | 1.29332e24i | 0.116578 | + | 1.54524i | ||||
\(979\) | 3.76964e23i | 0.446723i | ||||||||
\(980\) | −8.10686e23 | + | 1.23022e23i | −0.952893 | + | 0.144602i | ||||
\(981\) | −1.52924e24 | −1.78289 | ||||||||
\(982\) | 9.64595e23 | − | 7.27721e22i | 1.11546 | − | 0.0841537i | ||||
\(983\) | 8.24241e23i | 0.945423i | 0.881217 | + | 0.472712i | \(0.156725\pi\) | ||||
−0.881217 | + | 0.472712i | \(0.843275\pi\) | |||||||
\(984\) | 9.98360e23 | − | 2.29448e23i | 1.13586 | − | 0.261049i | ||||
\(985\) | 3.06972e23 | 0.346425 | ||||||||
\(986\) | −3.47620e22 | − | 4.60771e23i | −0.0389126 | − | 0.515786i | ||||
\(987\) | 1.59598e23i | 0.177211i | ||||||||
\(988\) | −1.94879e23 | − | 1.28421e24i | −0.214639 | − | 1.41443i | ||||
\(989\) | 1.45878e23 | 0.159375 | ||||||||
\(990\) | 1.03623e24 | − | 7.81766e22i | 1.12299 | − | 0.0847218i | ||||
\(991\) | − | 7.40279e23i | − | 0.795804i | −0.917428 | − | 0.397902i | \(-0.869738\pi\) | ||
0.917428 | − | 0.397902i | \(-0.130262\pi\) | |||||||
\(992\) | 6.59715e22 | − | 2.60827e22i | 0.0703498 | − | 0.0278137i | ||||
\(993\) | 1.75302e24 | 1.85435 | ||||||||
\(994\) | −1.84463e22 | − | 2.44505e23i | −0.0193561 | − | 0.256565i | ||||
\(995\) | − | 1.27605e24i | − | 1.32826i | ||||||
\(996\) | 2.07550e24 | − | 3.14957e23i | 2.14313 | − | 0.325220i | ||||
\(997\) | −5.94670e23 | −0.609137 | −0.304569 | − | 0.952490i | \(-0.598512\pi\) | ||||
−0.304569 | + | 0.952490i | \(0.598512\pi\) | |||||||
\(998\) | 4.74137e23 | − | 3.57704e22i | 0.481792 | − | 0.0363480i | ||||
\(999\) | − | 1.05374e24i | − | 1.06220i |
(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 | 4.17.b.b.3.4 | yes | 6 | |
3.2 | odd | 2 | 36.17.d.b.19.3 | 6 | |||
4.3 | odd | 2 | inner | 4.17.b.b.3.3 | ✓ | 6 | |
8.3 | odd | 2 | 64.17.c.d.63.6 | 6 | |||
8.5 | even | 2 | 64.17.c.d.63.1 | 6 | |||
12.11 | even | 2 | 36.17.d.b.19.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.17.b.b.3.3 | ✓ | 6 | 4.3 | odd | 2 | inner | |
4.17.b.b.3.4 | yes | 6 | 1.1 | even | 1 | trivial | |
36.17.d.b.19.3 | 6 | 3.2 | odd | 2 | |||
36.17.d.b.19.4 | 6 | 12.11 | even | 2 | |||
64.17.c.d.63.1 | 6 | 8.5 | even | 2 | |||
64.17.c.d.63.6 | 6 | 8.3 | odd | 2 |