Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [84,6,Mod(25,84)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(84, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("84.25");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 84 = 2^{2} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 84.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.4722408643\) |
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: | \( x^{8} - 2x^{7} + 703x^{6} + 2770x^{5} + 427565x^{4} + 718170x^{3} + 42175732x^{2} - 40929504x + 3559792896 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{3}\cdot 7 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 37.1 | ||
Root | \(4.59067 + 7.95128i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 84.37 |
Dual form | 84.6.i.c.25.1 |
$q$-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 \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(43\) | \(73\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 4.50000 | + | 7.79423i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −39.3359 | + | 68.1317i | −0.703662 | + | 1.21878i | 0.263511 | + | 0.964656i | \(0.415120\pi\) |
−0.967172 | + | 0.254121i | \(0.918214\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −100.606 | − | 81.7641i | −0.776033 | − | 0.630692i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −40.5000 | + | 70.1481i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −345.759 | − | 598.873i | −0.861574 | − | 1.49229i | −0.870410 | − | 0.492328i | \(-0.836146\pi\) |
0.00883597 | − | 0.999961i | \(-0.497187\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 818.732 | 1.34364 | 0.671821 | − | 0.740714i | \(-0.265512\pi\) | ||||
0.671821 | + | 0.740714i | \(0.265512\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −708.046 | −0.812518 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −554.638 | − | 960.661i | −0.465465 | − | 0.806209i | 0.533757 | − | 0.845638i | \(-0.320780\pi\) |
−0.999222 | + | 0.0394286i | \(0.987446\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 286.523 | − | 496.273i | 0.182086 | − | 0.315382i | −0.760505 | − | 0.649332i | \(-0.775049\pi\) |
0.942591 | + | 0.333951i | \(0.108382\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 184.559 | − | 1152.09i | 0.0913245 | − | 0.570082i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1258.80 | + | 2180.30i | −0.496177 | + | 0.859403i | −0.999990 | − | 0.00440926i | \(-0.998596\pi\) |
0.503814 | + | 0.863812i | \(0.331930\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1532.12 | − | 2653.71i | −0.490279 | − | 0.849189i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3258.19 | −0.719419 | −0.359710 | − | 0.933064i | \(-0.617124\pi\) | ||||
−0.359710 | + | 0.933064i | \(0.617124\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5059.55 | − | 8763.40i | −0.945601 | − | 1.63783i | −0.754544 | − | 0.656249i | \(-0.772142\pi\) |
−0.191056 | − | 0.981579i | \(-0.561191\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3111.84 | − | 5389.86i | 0.497430 | − | 0.861574i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9528.17 | − | 3638.23i | 1.31474 | − | 0.502018i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2434.81 | + | 4217.21i | −0.292389 | + | 0.506432i | −0.974374 | − | 0.224934i | \(-0.927783\pi\) |
0.681985 | + | 0.731366i | \(0.261117\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3684.30 | + | 6381.39i | 0.387876 | + | 0.671821i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −13094.3 | −1.21653 | −0.608265 | − | 0.793734i | \(-0.708134\pi\) | ||||
−0.608265 | + | 0.793734i | \(0.708134\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9303.64 | −0.767329 | −0.383664 | − | 0.923473i | \(-0.625338\pi\) | ||||
−0.383664 | + | 0.923473i | \(0.625338\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3186.21 | − | 5518.67i | −0.234554 | − | 0.406259i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6452.90 | + | 11176.8i | −0.426099 | + | 0.738025i | −0.996522 | − | 0.0833256i | \(-0.973446\pi\) |
0.570423 | + | 0.821351i | \(0.306779\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3436.28 | + | 16452.0i | 0.204455 | + | 0.978876i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4991.74 | − | 8645.95i | 0.268736 | − | 0.465465i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9770.12 | + | 16922.3i | 0.477760 | + | 0.827505i | 0.999675 | − | 0.0254926i | \(-0.00811542\pi\) |
−0.521915 | + | 0.852998i | \(0.674782\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 54403.0 | 2.42503 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5157.42 | 0.210254 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12560.2 | + | 21755.0i | 0.469751 | + | 0.813632i | 0.999402 | − | 0.0345835i | \(-0.0110105\pi\) |
−0.529651 | + | 0.848216i | \(0.677677\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 15681.1 | − | 27160.5i | 0.539575 | − | 0.934571i | −0.459352 | − | 0.888254i | \(-0.651918\pi\) |
0.998927 | − | 0.0463168i | \(-0.0147484\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9810.15 | − | 3745.90i | 0.311404 | − | 0.118906i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −32205.6 | + | 55781.7i | −0.945469 | + | 1.63760i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −27971.9 | − | 48448.8i | −0.761264 | − | 1.31855i | −0.942200 | − | 0.335052i | \(-0.891246\pi\) |
0.180936 | − | 0.983495i | \(-0.442087\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −22658.4 | −0.572935 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 20501.0 | 0.482647 | 0.241323 | − | 0.970445i | \(-0.422419\pi\) | ||||
0.241323 | + | 0.970445i | \(0.422419\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 33825.0 | + | 58586.6i | 0.742900 | + | 1.28674i | 0.951170 | + | 0.308669i | \(0.0998835\pi\) |
−0.208270 | + | 0.978071i | \(0.566783\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 13789.1 | − | 23883.4i | 0.283063 | − | 0.490279i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −14180.7 | + | 88521.1i | −0.272565 | + | 1.70145i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7039.95 | + | 12193.5i | −0.126912 | + | 0.219818i | −0.922479 | − | 0.386048i | \(-0.873840\pi\) |
0.795567 | + | 0.605866i | \(0.207173\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3280.50 | − | 5681.99i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −77129.1 | −1.22892 | −0.614459 | − | 0.788949i | \(-0.710626\pi\) | ||||
−0.614459 | + | 0.788949i | \(0.710626\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 87268.6 | 1.31012 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −14661.9 | − | 25395.1i | −0.207678 | − | 0.359710i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −160.396 | + | 277.815i | −0.00214644 | + | 0.00371775i | −0.867097 | − | 0.498140i | \(-0.834017\pi\) |
0.864950 | + | 0.501858i | \(0.167350\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −82369.7 | − | 66942.9i | −1.04271 | − | 0.847424i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 45536.0 | − | 78870.6i | 0.545943 | − | 0.945601i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 22541.3 | + | 39042.6i | 0.256253 | + | 0.443844i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −112009. | −1.20871 | −0.604355 | − | 0.796715i | \(-0.706569\pi\) | ||||
−0.604355 | + | 0.796715i | \(0.706569\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 56013.0 | 0.574382 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −33627.0 | − | 58243.7i | −0.328008 | − | 0.568127i | 0.654108 | − | 0.756401i | \(-0.273044\pi\) |
−0.982117 | + | 0.188274i | \(0.939711\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 58317.6 | − | 101009.i | 0.541635 | − | 0.938140i | −0.457175 | − | 0.889377i | \(-0.651139\pi\) |
0.998810 | − | 0.0487630i | \(-0.0155279\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 71233.9 | + | 57892.7i | 0.630541 | + | 0.512449i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 80322.6 | − | 139123.i | 0.678232 | − | 1.17473i | −0.297281 | − | 0.954790i | \(-0.596080\pi\) |
0.975513 | − | 0.219942i | \(-0.0705869\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −59668.3 | − | 103349.i | −0.481036 | − | 0.833179i | 0.518727 | − | 0.854940i | \(-0.326406\pi\) |
−0.999763 | + | 0.0217610i | \(0.993073\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −43826.6 | −0.337622 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −110893. | −0.816972 | −0.408486 | − | 0.912765i | \(-0.633943\pi\) | ||||
−0.408486 | + | 0.912765i | \(0.633943\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −99031.8 | − | 171528.i | −0.698281 | − | 1.20946i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −33158.7 | + | 57432.5i | −0.223940 | + | 0.387876i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −22747.4 | + | 141998.i | −0.147253 | + | 0.919210i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −158574. | + | 274658.i | −0.984618 | + | 1.70541i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −58924.4 | − | 102060.i | −0.351182 | − | 0.608265i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4779.64 | −0.0273603 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 315184. | 1.73402 | 0.867012 | − | 0.498287i | \(-0.166038\pi\) | ||||
0.867012 | + | 0.498287i | \(0.166038\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −41866.4 | − | 72514.7i | −0.221509 | − | 0.383664i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −42832.3 | + | 74187.6i | −0.218068 | + | 0.377705i | −0.954217 | − | 0.299114i | \(-0.903309\pi\) |
0.736149 | + | 0.676819i | \(0.236642\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −69403.3 | + | 26500.9i | −0.340213 | + | 0.129907i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 28675.9 | − | 49668.0i | 0.135420 | − | 0.234554i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16316.1 | + | 28260.3i | 0.0742703 | + | 0.128640i | 0.900769 | − | 0.434299i | \(-0.143004\pi\) |
−0.826498 | + | 0.562939i | \(0.809671\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 206590. | 0.906925 | 0.453462 | − | 0.891275i | \(-0.350189\pi\) | ||||
0.453462 | + | 0.891275i | \(0.350189\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −116152. | −0.492017 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −283084. | − | 490317.i | −1.15765 | − | 2.00510i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 128164. | − | 221986.i | 0.506228 | − | 0.876812i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −112767. | + | 100817.i | −0.430417 | + | 0.384805i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −241855. | + | 418906.i | −0.892463 | + | 1.54579i | −0.0555495 | + | 0.998456i | \(0.517691\pi\) |
−0.836913 | + | 0.547335i | \(0.815642\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 83610.4 | + | 144818.i | 0.298413 | + | 0.516867i | 0.975773 | − | 0.218785i | \(-0.0702093\pi\) |
−0.677360 | + | 0.735652i | \(0.736876\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 89851.3 | 0.310310 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 796087. | 2.66153 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7054.26 | + | 12218.3i | 0.0228403 | + | 0.0395606i | 0.877220 | − | 0.480089i | \(-0.159396\pi\) |
−0.854379 | + | 0.519650i | \(0.826062\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −87931.0 | + | 152301.i | −0.275835 | + | 0.477760i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 304913. | − | 116428.i | 0.927068 | − | 0.353991i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −327188. | + | 566706.i | −0.964558 | + | 1.67066i | −0.253762 | + | 0.967267i | \(0.581668\pi\) |
−0.710797 | + | 0.703397i | \(0.751665\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 244814. | + | 424030.i | 0.700044 | + | 1.21251i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 182945. | 0.507610 | 0.253805 | − | 0.967255i | \(-0.418318\pi\) | ||||
0.253805 | + | 0.967255i | \(0.418318\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 299030. | 0.805374 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 23208.4 | + | 40198.1i | 0.0606952 | + | 0.105127i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 146004. | − | 252887.i | 0.370894 | − | 0.642407i | −0.618809 | − | 0.785541i | \(-0.712385\pi\) |
0.989703 | + | 0.143134i | \(0.0457180\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −62837.2 | + | 392253.i | −0.155103 | + | 0.968214i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −113042. | + | 195795.i | −0.271211 | + | 0.469751i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −97383.8 | − | 168674.i | −0.227172 | − | 0.393473i | 0.729797 | − | 0.683664i | \(-0.239615\pi\) |
−0.956969 | + | 0.290191i | \(0.906281\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −256634. | −0.582261 | −0.291130 | − | 0.956683i | \(-0.594031\pi\) | ||||
−0.291130 | + | 0.956683i | \(0.594031\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 282260. | 0.623047 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −191551. | − | 331776.i | −0.411486 | − | 0.712714i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −383542. | + | 664315.i | −0.802065 | + | 1.38922i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 73342.0 | + | 59606.0i | 0.149348 | + | 0.121377i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 146975. | − | 254567.i | 0.291513 | − | 0.504916i | −0.682654 | − | 0.730741i | \(-0.739175\pi\) |
0.974168 | + | 0.225825i | \(0.0725079\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 34565.0 | + | 59868.4i | 0.0667950 | + | 0.115692i | 0.897489 | − | 0.441037i | \(-0.145389\pi\) |
−0.830694 | + | 0.556730i | \(0.812056\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −579700. | −1.09173 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 331748. | 0.609037 | 0.304518 | − | 0.952506i | \(-0.401505\pi\) | ||||
0.304518 | + | 0.952506i | \(0.401505\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −287214. | − | 497470.i | −0.514130 | − | 0.890500i | −0.999866 | − | 0.0163939i | \(-0.994781\pi\) |
0.485735 | − | 0.874106i | \(-0.338552\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 251747. | − | 436039.i | 0.439516 | − | 0.761264i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 327795. | + | 266403.i | 0.558293 | + | 0.453732i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 515076. | − | 892138.i | 0.856025 | − | 1.48268i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −101963. | − | 176604.i | −0.165392 | − | 0.286468i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −396272. | −0.627521 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −383999. | −0.593777 | −0.296889 | − | 0.954912i | \(-0.595949\pi\) | ||||
−0.296889 | + | 0.954912i | \(0.595949\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 92254.5 | + | 159790.i | 0.139328 | + | 0.241323i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 365967. | − | 633873.i | 0.539940 | − | 0.935203i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −207508. | + | 1.29534e6i | −0.299148 | + | 1.86739i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −304425. | + | 527279.i | −0.428913 | + | 0.742900i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −454100. | − | 786524.i | −0.625418 | − | 1.08326i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −347165. | −0.467492 | −0.233746 | − | 0.972298i | \(-0.575098\pi\) | ||||
−0.233746 | + | 0.972298i | \(0.575098\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 248204. | 0.326853 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −180641. | − | 312879.i | −0.232676 | − | 0.403006i | 0.725919 | − | 0.687780i | \(-0.241415\pi\) |
−0.958595 | + | 0.284774i | \(0.908081\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 376492. | − | 652102.i | 0.474424 | − | 0.821726i | −0.525147 | − | 0.851011i | \(-0.675990\pi\) |
0.999571 | + | 0.0292852i | \(0.00932309\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −753767. | + | 287818.i | −0.929410 | + | 0.354885i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −357199. | + | 618686.i | −0.431042 | + | 0.746587i | −0.996963 | − | 0.0778721i | \(-0.975187\pi\) |
0.565921 | + | 0.824460i | \(0.308521\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −507661. | − | 879295.i | −0.599659 | − | 1.03864i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −126719. | −0.146545 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 343587. | 0.389083 | 0.194541 | − | 0.980894i | \(-0.437678\pi\) | ||||
0.194541 | + | 0.980894i | \(0.437678\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 38152.5 | + | 66082.0i | 0.0423136 | + | 0.0732893i | 0.886407 | − | 0.462908i | \(-0.153194\pi\) |
−0.844093 | + | 0.536197i | \(0.819860\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 29524.5 | − | 51137.9i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.25607e6 | − | 413033.i | −1.33690 | − | 0.439612i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 234586. | − | 406314.i | 0.244658 | − | 0.423760i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −347081. | − | 601162.i | −0.354758 | − | 0.614459i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 196249. | 0.196618 | 0.0983090 | − | 0.995156i | \(-0.468657\pi\) | ||||
0.0983090 | + | 0.995156i | \(0.468657\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.74096e6 | 1.70997 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 392709. | + | 680192.i | 0.378199 | + | 0.655060i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 854554. | − | 1.48013e6i | 0.807062 | − | 1.39787i | −0.107828 | − | 0.994170i | \(-0.534390\pi\) |
0.914890 | − | 0.403703i | \(-0.132277\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 589774. | − | 225199.i | 0.546306 | − | 0.208601i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 131957. | − | 228556.i | 0.119903 | − | 0.207678i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 395762. | + | 685481.i | 0.352814 | + | 0.611091i | 0.986741 | − | 0.162301i | \(-0.0518917\pi\) |
−0.633928 | + | 0.773392i | \(0.718558\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.53726e6 | −1.34473 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2887.13 | −0.00247850 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −579502. | − | 1.00373e6i | −0.488286 | − | 0.845736i | 0.511623 | − | 0.859210i | \(-0.329044\pi\) |
−0.999909 | + | 0.0134740i | \(0.995711\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −111567. | + | 193240.i | −0.0922811 | + | 0.159836i | −0.908471 | − | 0.417949i | \(-0.862749\pi\) |
0.816190 | + | 0.577784i | \(0.196083\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 151105. | − | 943251.i | 0.122707 | − | 0.765986i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.05949e6 | + | 1.83509e6i | −0.844823 | + | 1.46328i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 234523. | + | 406205.i | 0.183648 | + | 0.318087i | 0.943120 | − | 0.332452i | \(-0.107876\pi\) |
−0.759472 | + | 0.650540i | \(0.774543\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 819647. | 0.630400 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.51447e6 | −1.14418 | −0.572090 | − | 0.820191i | \(-0.693867\pi\) | ||||
−0.572090 | + | 0.820191i | \(0.693867\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 535303. | + | 927171.i | 0.397314 | + | 0.688167i | 0.993393 | − | 0.114758i | \(-0.0366092\pi\) |
−0.596080 | + | 0.802925i | \(0.703276\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −202871. | + | 351384.i | −0.147948 | + | 0.256253i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.31737e6 | + | 1.07064e6i | 0.944068 | + | 0.767256i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 94682.6 | − | 163995.i | 0.0666846 | − | 0.115501i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −504039. | − | 873021.i | −0.348925 | − | 0.604355i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.45450e6 | 0.989794 | 0.494897 | − | 0.868952i | \(-0.335206\pi\) | ||||
0.494897 | + | 0.868952i | \(0.335206\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.97627e6 | −1.32218 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 252059. | + | 436578.i | 0.165810 | + | 0.287191i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.03062e6 | + | 1.78508e6i | −0.666684 | + | 1.15473i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 936005. | + | 760703.i | 0.595473 | + | 0.483948i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 302643. | − | 524193.i | 0.189376 | − | 0.328008i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.23366e6 | + | 2.13676e6i | 0.759356 | + | 1.31524i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.23869e6 | −1.35565 | −0.677824 | − | 0.735224i | \(-0.737077\pi\) | ||||
−0.677824 | + | 0.735224i | \(0.737077\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.04972e6 | 0.625426 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 750695. | + | 1.30024e6i | 0.440111 | + | 0.762295i | 0.997697 | − | 0.0678240i | \(-0.0216056\pi\) |
−0.557586 | + | 0.830119i | \(0.688272\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 890067. | − | 1.54164e6i | 0.513525 | − | 0.889452i | −0.486352 | − | 0.873763i | \(-0.661673\pi\) |
0.999877 | − | 0.0156888i | \(-0.00499410\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −130676. | + | 815731.i | −0.0742028 | + | 0.463202i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −735500. | + | 1.27392e6i | −0.411088 | + | 0.712025i | −0.995009 | − | 0.0997854i | \(-0.968184\pi\) |
0.583921 | + | 0.811810i | \(0.301518\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.12655e6 | + | 1.95124e6i | 0.619832 | + | 1.07358i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.44581e6 | 0.783155 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −635666. | −0.339018 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.25440e6 | − | 2.17268e6i | −0.658760 | − | 1.14101i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 537015. | − | 930137.i | 0.277726 | − | 0.481036i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.56306e6 | − | 596837.i | 0.796134 | − | 0.303995i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 914873. | − | 1.58461e6i | 0.458977 | − | 0.794971i | −0.539930 | − | 0.841710i | \(-0.681549\pi\) |
0.998907 | + | 0.0467386i | \(0.0148828\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −197220. | − | 341594.i | −0.0974629 | − | 0.168811i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.40120e6 | 2.14269 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.18627e6 | 1.52830 | 0.764148 | − | 0.645041i | \(-0.223160\pi\) | ||||
0.764148 | + | 0.645041i | \(0.223160\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −499018. | − | 864324.i | −0.235840 | − | 0.408486i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.49878e6 | + | 6.06006e6i | −1.62941 | + | 2.82222i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 999468. | − | 1.93614e6i | 0.458705 | − | 0.888589i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 891286. | − | 1.54375e6i | 0.403153 | − | 0.698281i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.23895e6 | − | 2.14592e6i | −0.552370 | − | 0.956732i | −0.998103 | − | 0.0615664i | \(-0.980390\pi\) |
0.445733 | − | 0.895166i | \(-0.352943\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.81720e6 | 0.798618 | 0.399309 | − | 0.916816i | \(-0.369250\pi\) | ||||
0.399309 | + | 0.916816i | \(0.369250\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −596856. | −0.258584 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.57678e6 | − | 2.73106e6i | −0.673493 | − | 1.16652i | −0.976907 | − | 0.213666i | \(-0.931460\pi\) |
0.303413 | − | 0.952859i | \(-0.401874\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −806425. | + | 1.39677e6i | −0.339620 | + | 0.588239i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.20913e6 | + | 461692.i | −0.502113 | + | 0.191726i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.35105e6 | + | 2.34008e6i | −0.553266 | + | 0.958285i | 0.444770 | + | 0.895645i | \(0.353285\pi\) |
−0.998036 | + | 0.0626404i | \(0.980048\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.07386e6 | + | 1.85998e6i | 0.433690 | + | 0.751173i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.85433e6 | −1.13694 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.32214e6 | −2.09100 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.80573e6 | + | 3.12762e6i | 0.699824 | + | 1.21213i | 0.968527 | + | 0.248908i | \(0.0800716\pi\) |
−0.268703 | + | 0.963223i | \(0.586595\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 530319. | − | 918540.i | 0.202755 | − | 0.351182i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 400703. | − | 2.50134e6i | 0.151143 | − | 0.943491i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 216759. | − | 375438.i | 0.0806688 | − | 0.139722i | −0.822869 | − | 0.568232i | \(-0.807628\pi\) |
0.903537 | + | 0.428509i | \(0.140961\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −21508.4 | − | 37253.6i | −0.00789823 | − | 0.0136801i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.66759e6 | −0.966642 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.12163e6 | −0.758704 | −0.379352 | − | 0.925252i | \(-0.623853\pi\) | ||||
−0.379352 | + | 0.925252i | \(0.623853\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.41833e6 | + | 2.45662e6i | 0.500570 | + | 0.867012i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.12339e6 | − | 3.67782e6i | 0.739662 | − | 1.28113i | −0.212985 | − | 0.977055i | \(-0.568319\pi\) |
0.952647 | − | 0.304077i | \(-0.0983480\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.47329e6 | − | 4.44821e6i | −1.88190 | − | 1.52944i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 376797. | − | 652632.i | 0.127888 | − | 0.221509i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.76088e6 | + | 3.04994e6i | 0.590006 | + | 1.02192i | 0.994231 | + | 0.107261i | \(0.0342081\pi\) |
−0.404224 | + | 0.914660i | \(0.632459\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.79271e6 | 0.923811 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −770981. | −0.251804 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −553845. | − | 959288.i | −0.178606 | − | 0.309354i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 367025. | − | 635706.i | 0.116874 | − | 0.202432i | −0.801653 | − | 0.597790i | \(-0.796046\pi\) |
0.918527 | + | 0.395357i | \(0.129379\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −518869. | − | 421691.i | −0.163164 | − | 0.132606i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 111135. | − | 192492.i | 0.0345136 | − | 0.0597793i | −0.848253 | − | 0.529592i | \(-0.822345\pi\) |
0.882766 | + | 0.469812i | \(0.155678\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.14242e6 | − | 7.17488e6i | −1.27055 | − | 2.20065i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 516165. | 0.156369 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.36743e6 | 1.00766 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.75379e6 | + | 3.03765e6i | 0.518405 | + | 0.897904i | 0.999771 | + | 0.0213846i | \(0.00680745\pi\) |
−0.481366 | + | 0.876520i | \(0.659859\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −146845. | + | 254343.i | −0.0428800 | + | 0.0742703i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 515134. | − | 3.21566e6i | 0.148609 | − | 0.927674i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.03394e6 | − | 5.25494e6i | 0.864742 | − | 1.49778i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 929653. | + | 1.61021e6i | 0.261807 | + | 0.453462i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.97040e6 | −0.548302 | −0.274151 | − | 0.961687i | \(-0.588397\pi\) | ||||
−0.274151 | + | 0.961687i | \(0.588397\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.19318e6 | −1.97795 | −0.988976 | − | 0.148079i | \(-0.952691\pi\) | ||||
−0.988976 | + | 0.148079i | \(0.952691\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −522685. | − | 905317.i | −0.142033 | − | 0.246008i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.69955e6 | + | 2.94370e6i | −0.456416 | + | 0.790535i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.79837e6 | + | 1.45036e6i | −1.00815 | + | 0.384953i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.54776e6 | − | 4.41285e6i | 0.668367 | − | 1.15765i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −262091. | − | 453955.i | −0.0679608 | − | 0.117712i | 0.830043 | − | 0.557700i | \(-0.188316\pi\) |
−0.898004 | + | 0.439988i | \(0.854983\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.49326e6 | 0.382750 | 0.191375 | − | 0.981517i | \(-0.438705\pi\) | ||||
0.191375 | + | 0.981517i | \(0.438705\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.30695e6 | 0.584541 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 721349. | + | 1.24941e6i | 0.180693 | + | 0.312970i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.32835e6 | + | 2.30077e6i | −0.328966 | + | 0.569786i | −0.982307 | − | 0.187278i | \(-0.940034\pi\) |
0.653341 | + | 0.757064i | \(0.273367\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.29324e6 | − | 425256.i | −0.316653 | − | 0.104125i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.34399e6 | − | 4.05991e6i | 0.567474 | − | 0.982895i | −0.429340 | − | 0.903143i | \(-0.641254\pi\) |
0.996815 | − | 0.0797518i | \(-0.0254128\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12618.7 | − | 21856.2i | −0.00302074 | − | 0.00523207i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.35340e6 | −1.03053 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.45899e6 | −0.809716 | −0.404858 | − | 0.914379i | \(-0.632679\pi\) | ||||
−0.404858 | + | 0.914379i | \(0.632679\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.52748e6 | + | 7.84182e6i | 1.04813 | + | 1.81541i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −752494. | + | 1.30336e6i | −0.172289 | + | 0.298413i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.80102e6 | − | 2.97873e6i | 1.76654 | − | 0.674533i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −359140. | + | 622048.i | −0.0804401 | + | 0.139326i | −0.903439 | − | 0.428717i | \(-0.858966\pi\) |
0.822999 | + | 0.568043i | \(0.192299\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 404331. | + | 700322.i | 0.0895788 | + | 0.155155i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.07998e6 | 1.11329 | 0.556647 | − | 0.830749i | \(-0.312088\pi\) | ||||
0.556647 | + | 0.830749i | \(0.312088\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.40607e6 | 0.738416 | 0.369208 | − | 0.929347i | \(-0.379629\pi\) | ||||
0.369208 | + | 0.929347i | \(0.379629\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.58239e6 | + | 6.20489e6i | 0.768318 | + | 1.33077i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −921342. | + | 1.59581e6i | −0.195492 | + | 0.338602i | −0.947062 | − | 0.321052i | \(-0.895964\pi\) |
0.751570 | + | 0.659654i | \(0.229297\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.14722e6 | + | 7.16135e6i | −0.240831 | + | 1.50336i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −63488.3 | + | 109965.i | −0.0131869 | + | 0.0228403i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.21682e6 | + | 5.57170e6i | 0.661110 | + | 1.14508i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.75595e6 | −0.357091 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.58276e6 | −0.318507 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.55714e6 | − | 7.89319e6i | −0.907514 | − | 1.57186i | −0.817507 | − | 0.575919i | \(-0.804644\pi\) |
−0.0900071 | − | 0.995941i | \(-0.528689\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.99346e6 | + | 3.45277e6i | −0.392866 | + | 0.680464i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.27957e6 | + | 1.85264e6i | 0.444617 | + | 0.361346i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.40596e6 | − | 7.63134e6i | 0.850523 | − | 1.47315i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.19220e6 | − | 3.79701e6i | −0.418850 | − | 0.725469i | 0.576974 | − | 0.816762i | \(-0.304233\pi\) |
−0.995824 | + | 0.0912933i | \(0.970900\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.88939e6 | −1.11378 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.50592e6 | −1.77947 | −0.889735 | − | 0.456478i | \(-0.849111\pi\) | ||||
−0.889735 | + | 0.456478i | \(0.849111\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.80712e6 | + | 3.13002e6i | 0.334864 | + | 0.580002i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.20332e6 | + | 3.81627e6i | −0.404171 | + | 0.700044i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.06253e6 | − | 1.67625e6i | −0.374550 | − | 0.304401i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.68783e6 | + | 2.92341e6i | −0.303444 | + | 0.525580i | −0.976914 | − | 0.213635i | \(-0.931470\pi\) |
0.673470 | + | 0.739215i | \(0.264803\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 823255. | + | 1.42592e6i | 0.146535 | + | 0.253805i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.82645e6 | 1.37926 | 0.689628 | − | 0.724164i | \(-0.257774\pi\) | ||||
0.689628 | + | 0.724164i | \(0.257774\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.29099e6 | 0.923227 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.34563e6 | + | 2.33070e6i | 0.232491 | + | 0.402687i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.71219e6 | − | 6.42969e6i | 0.635090 | − | 1.10001i | −0.351406 | − | 0.936223i | \(-0.614296\pi\) |
0.986496 | − | 0.163785i | \(-0.0523703\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.38727e6 | − | 8.65985e6i | 0.235022 | − | 1.46709i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −208875. | + | 361783.i | −0.0350424 | + | 0.0606952i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.58795e6 | + | 7.94656e6i | 0.762256 | + | 1.32027i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.92461e6 | 1.46846 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.62807e6 | 0.428272 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 530710. | + | 919217.i | 0.0856570 | + | 0.148362i | 0.905671 | − | 0.423981i | \(-0.139368\pi\) |
−0.820014 | + | 0.572344i | \(0.806034\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 956760. | − | 1.65716e6i | 0.152950 | − | 0.264917i | −0.779361 | − | 0.626575i | \(-0.784456\pi\) |
0.932311 | + | 0.361659i | \(0.117789\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.34008e6 | + | 1.27537e6i | −0.528881 | + | 0.201948i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.61243e6 | + | 9.72102e6i | −0.880288 | + | 1.52470i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 49029.1 | + | 84921.0i | 0.00761755 | + | 0.0131940i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.03476e6 | −0.313167 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.07207e7 | −1.63458 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.31912e6 | + | 1.09450e7i | 0.954492 | + | 1.65323i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 876454. | − | 1.51806e6i | 0.131158 | − | 0.227172i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.66451e6 | − | 7.74632e6i | 1.28461 | − | 1.14848i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.83140e6 | + | 1.01003e7i | −0.856603 | + | 1.48368i | 0.0185472 | + | 0.999828i | \(0.494096\pi\) |
−0.875150 | + | 0.483852i | \(0.839237\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.15485e6 | − | 2.00026e6i | −0.168084 | − | 0.291130i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.38842e6 | 1.35395 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.36659e6 | −0.909785 | −0.454893 | − | 0.890546i | \(-0.650322\pi\) | ||||
−0.454893 | + | 0.890546i | \(0.650322\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.27017e6 | + | 2.20000e6i | 0.179858 | + | 0.311524i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −933548. | + | 1.61695e6i | −0.130996 | + | 0.226891i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.70526e6 | − | 651134.i | 0.237125 | − | 0.0905435i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.72396e6 | − | 2.98598e6i | 0.237571 | − | 0.411486i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.86221e6 | − | 8.42159e6i | −0.664042 | − | 1.15015i | −0.979544 | − | 0.201230i | \(-0.935506\pi\) |
0.315502 | − | 0.948925i | \(-0.397827\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.61719e6 | −1.03102 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.90376e6 | −0.926145 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.15133e6 | − | 5.45826e6i | −0.419008 | − | 0.725744i | 0.576832 | − | 0.816863i | \(-0.304289\pi\) |
−0.995840 | + | 0.0911193i | \(0.970956\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.36207e6 | − | 7.55532e6i | 0.574872 | − | 0.995708i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −134544. | + | 839872.i | −0.0175754 | + | 0.109712i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.08244e6 | + | 7.07099e6i | −0.528614 | + | 0.915586i | 0.470829 | + | 0.882224i | \(0.343955\pi\) |
−0.999443 | + | 0.0333620i | \(0.989379\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.43857e6 | + | 1.11519e7i | 0.826416 | + | 1.43139i | 0.900832 | + | 0.434168i | \(0.142957\pi\) |
−0.0744158 | + | 0.997227i | \(0.523709\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.64554e6 | 0.336611 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.71453e6 | 0.973061 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.70887e6 | − | 9.88805e6i | −0.713856 | − | 1.23643i | −0.963399 | − | 0.268071i | \(-0.913614\pi\) |
0.249543 | − | 0.968364i | \(-0.419720\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −311085. | + | 538816.i | −0.0385641 | + | 0.0667950i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.75968e6 | + | 6.30639e6i | 0.953681 | + | 0.775069i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.75622e6 | − | 1.17021e7i | 0.823251 | − | 1.42591i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.60865e6 | − | 4.51831e6i | −0.315156 | − | 0.545867i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.12781e6 | 0.254882 | 0.127441 | − | 0.991846i | \(-0.459324\pi\) | ||||
0.127441 | + | 0.991846i | \(0.459324\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.79871e6 | −0.688721 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.49287e6 | + | 2.58572e6i | 0.175814 | + | 0.304518i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.28689e6 | − | 7.42511e6i | 0.500617 | − | 0.867094i | −0.499383 | − | 0.866382i | \(-0.666440\pi\) |
1.00000 | 0.000712836i | \(-0.000226903\pi\) | ||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.77978e6 | − | 7.13544e6i | −1.01670 | − | 0.826282i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.58493e6 | − | 4.47723e6i | 0.296833 | − | 0.514130i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.64372e6 | − | 9.77521e6i | −0.642686 | − | 1.11316i | −0.984831 | − | 0.173517i | \(-0.944487\pi\) |
0.342145 | − | 0.939647i | \(-0.388846\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.58260e7 | −1.78725 | −0.893625 | − | 0.448814i | \(-0.851847\pi\) | ||||
−0.893625 | + | 0.448814i | \(0.851847\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.53145e6 | 0.507509 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.24753e7 | − | 2.16078e7i | −1.38568 | − | 2.40006i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.87183e6 | + | 8.43826e6i | −0.536686 | + | 0.929568i | 0.462393 | + | 0.886675i | \(0.346991\pi\) |
−0.999080 | + | 0.0428932i | \(0.986342\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −601329. | + | 3.75372e6i | −0.0657006 | + | 0.410128i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.28320e6 | + | 9.15077e6i | −0.572525 | + | 0.991642i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.07524e6 | − | 5.32647e6i | −0.330543 | − | 0.572517i | 0.652075 | − | 0.758154i | \(-0.273899\pi\) |
−0.982618 | + | 0.185637i | \(0.940565\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.27137e6 | 0.988453 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.36084e6 | −0.355414 | −0.177707 | − | 0.984083i | \(-0.556868\pi\) | ||||
−0.177707 | + | 0.984083i | \(0.556868\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.44329e6 | − | 5.96396e6i | −0.361200 | − | 0.625616i | 0.626959 | − | 0.779052i | \(-0.284299\pi\) |
−0.988159 | + | 0.153436i | \(0.950966\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 917663. | − | 1.58944e6i | 0.0954892 | − | 0.165392i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 38852.1 | − | 14835.3i | 0.00401046 | − | 0.00153135i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.97590e6 | − | 8.61850e6i | 0.509532 | − | 0.882535i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.78323e6 | − | 3.08864e6i | −0.181150 | − | 0.313760i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.40175e6 | 0.544387 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.59545e6 | 0.359484 | 0.179742 | − | 0.983714i | \(-0.442474\pi\) | ||||
0.179742 | + | 0.983714i | \(0.442474\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.72799e6 | − | 2.99297e6i | −0.171409 | − | 0.296889i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.23980e7 | + | 2.14740e7i | −1.22017 | + | 2.11339i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.81339e6 | + | 1.34698e7i | 0.274715 | + | 1.31526i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −830291. | + | 1.43811e6i | −0.0804411 | + | 0.139328i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.91433e6 | + | 1.71721e7i | 0.953056 | + | 1.65074i | 0.738756 | + | 0.673973i | \(0.235413\pi\) |
0.214299 | + | 0.976768i | \(0.431253\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.10851e6 | −0.773417 | −0.386708 | − | 0.922202i | \(-0.626388\pi\) | ||||
−0.386708 | + | 0.922202i | \(0.626388\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.58740e6 | 0.623469 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.01373e6 | − | 1.75583e6i | −0.0952053 | − | 0.164900i | 0.814489 | − | 0.580179i | \(-0.197017\pi\) |
−0.909694 | + | 0.415279i | \(0.863684\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.68564e6 | − | 1.50440e7i | 0.809450 | − | 1.40201i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.10300e7 | + | 4.21168e6i | −1.02005 | + | 0.389496i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −757133. | + | 1.31139e6i | −0.0694847 | + | 0.120351i | −0.898675 | − | 0.438616i | \(-0.855469\pi\) |
0.829190 | + | 0.558967i | \(0.188802\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.36969e6 | − | 5.83647e6i | −0.306893 | − | 0.531554i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.47965e6 | −0.495267 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.22358e6 | −0.289151 | −0.144576 | − | 0.989494i | \(-0.546182\pi\) | ||||
−0.144576 | + | 0.989494i | \(0.546182\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.19538e6 | + | 1.24628e7i | 0.640546 | + | 1.10946i | 0.985311 | + | 0.170769i | \(0.0546253\pi\) |
−0.344765 | + | 0.938689i | \(0.612041\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.08690e6 | − | 7.07872e6i | 0.361085 | − | 0.625418i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 924488. | − | 5.77100e6i | 0.0810676 | − | 0.506054i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.10141e6 | − | 7.10384e6i | 0.356959 | − | 0.618271i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.56224e6 | − | 2.70589e6i | −0.134953 | − | 0.233746i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.16875e7 | −1.85953 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.33478e6 | 0.624237 | 0.312118 | − | 0.950043i | \(-0.398961\pi\) | ||||
0.312118 | + | 0.950043i | \(0.398961\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.11692e6 | + | 1.93456e6i | 0.0943543 | + | 0.163426i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.52642e6 | − | 2.64384e6i | 0.127998 | − | 0.221699i | −0.794903 | − | 0.606737i | \(-0.792478\pi\) |
0.922901 | + | 0.385038i | \(0.125812\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.12688e7 | + | 9.15828e6i | 0.937999 | + | 0.762324i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.62577e6 | − | 2.81591e6i | 0.134335 | − | 0.232676i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.98793e6 | − | 1.38355e7i | −0.655213 | − | 1.13486i | −0.981840 | − | 0.189709i | \(-0.939245\pi\) |
0.326627 | − | 0.945153i | \(-0.394088\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.56724e6 | −0.209045 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.77685e6 | 0.547817 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.99911e6 | + | 1.38549e7i | 0.641939 | + | 1.11187i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.23267e6 | − | 2.13504e6i | 0.0982087 | − | 0.170103i | −0.812735 | − | 0.582634i | \(-0.802022\pi\) |
0.910943 | + | 0.412532i | \(0.135355\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.63527e6 | − | 4.57985e6i | −0.445740 | − | 0.362258i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.12638e6 | + | 1.40753e7i | −0.638168 | + | 1.10534i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.26259e6 | + | 1.25792e7i | 0.566252 | + | 0.980777i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.42958e6 | −0.497725 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.74893e7 | 1.34424 | 0.672122 | − | 0.740440i | \(-0.265383\pi\) | ||||
0.672122 | + | 0.740440i | \(0.265383\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.39526e6 | + | 2.41666e6i | 0.106480 | + | 0.184428i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.56895e6 | − | 7.91366e6i | 0.346213 | − | 0.599659i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.37915e6 | + | 8.60916e6i | −0.103768 | + | 0.647757i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.09216e7 | − | 1.89167e7i | 0.815961 | − | 1.41329i | −0.0926752 | − | 0.995696i | \(-0.529542\pi\) |
0.908636 | − | 0.417589i | \(-0.137125\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −570236. | − | 987677.i | −0.0423039 | − | 0.0732725i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.54758e7 | 1.87674 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.45415e7 | 3.25837 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.54614e6 | + | 2.67800e6i | 0.112319 | + | 0.194541i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.55868e6 | + | 1.65561e7i | −0.689566 | + | 1.19436i | 0.282413 | + | 0.959293i | \(0.408865\pi\) |
−0.971978 | + | 0.235070i | \(0.924468\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.41260e7 | + | 5.39387e6i | −1.01200 | + | 0.386423i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −343372. | + | 594738.i | −0.0244298 | + | 0.0423136i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.99195e6 | + | 8.64632e6i | 0.352716 | + | 0.610923i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.08900e6 | −0.286933 | −0.143467 | − | 0.989655i | \(-0.545825\pi\) | ||||
−0.143467 | + | 0.989655i | \(0.545825\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.16015e6 | + | 8.93764e6i | 0.357165 | + | 0.618628i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.81634e6 | − | 3.14599e6i | 0.124864 | − | 0.216271i | −0.796816 | − | 0.604222i | \(-0.793484\pi\) |
0.921680 | + | 0.387952i | \(0.126817\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.43304e6 | − | 1.16487e7i | −0.166124 | − | 0.795355i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.93431e7 | + | 3.35032e7i | −1.31177 | + | 2.27205i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.08978e6 | − | 1.88756e6i | −0.0734056 | − | 0.127142i | 0.826986 | − | 0.562222i | \(-0.190053\pi\) |
−0.900392 | + | 0.435080i | \(0.856720\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.22254e6 | 0.282507 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.21595e7 | 0.808060 | 0.404030 | − | 0.914746i | \(-0.367609\pi\) | ||||
0.404030 | + | 0.914746i | \(0.367609\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.90272e7 | − | 3.29561e7i | −1.25598 | − | 2.17543i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.12373e6 | − | 5.41045e6i | 0.204820 | − | 0.354758i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.94562e7 | + | 7.42914e6i | −1.26722 | + | 0.483876i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.16248e7 | + | 2.01347e7i | −0.752115 | + | 1.30270i | 0.194681 | + | 0.980867i | \(0.437633\pi\) |
−0.946796 | + | 0.321835i | \(0.895701\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 883121. | + | 1.52961e6i | 0.0567587 | + | 0.0983090i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.31556e7 | −0.839928 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.49939e7 | −0.950985 | −0.475492 | − | 0.879720i | \(-0.657730\pi\) | ||||
−0.475492 | + | 0.879720i | \(0.657730\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.83434e6 | + | 1.35695e7i | 0.493626 | + | 0.854985i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.36596e6 | − | 1.10262e7i | 0.398476 | − | 0.690181i | −0.595062 | − | 0.803680i | \(-0.702873\pi\) |
0.993538 | + | 0.113499i | \(0.0362058\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.44719e6 | + | 1.52762e7i | −0.152179 | + | 0.949960i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.53438e6 | + | 6.12173e6i | −0.218353 | + | 0.378199i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.02835e7 | + | 1.78115e7i | 0.631177 | + | 1.09323i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.34653e6 | 0.143090 | 0.0715451 | − | 0.997437i | \(-0.477207\pi\) | ||||
0.0715451 | + | 0.997437i | \(0.477207\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.53820e7 | 0.931915 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.35931e7 | − | 2.35440e7i | −0.818222 | − | 1.41720i | −0.906991 | − | 0.421150i | \(-0.861627\pi\) |
0.0887694 | − | 0.996052i | \(-0.471707\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.55037e7 | + | 2.68532e7i | −0.927217 | + | 1.60599i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.40923e6 | + | 3.58344e6i | 0.262006 | + | 0.212935i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.75182e6 | + | 6.49834e6i | −0.221513 | + | 0.383671i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.08842e6 | − | 1.22775e7i | −0.415836 | − | 0.720249i | ||||
\(782\) | 0 | 0 |