Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,6,Mod(193,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("336.193");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(53.8889634572\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{7081})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 1771x^{2} + 1770x + 3132900 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 289.2 | ||
Root | \(21.2872 - 36.8705i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.289 |
Dual form | 336.6.q.g.193.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(5\) | 9.28717 | − | 16.0858i | 0.166134 | − | 0.287752i | −0.770923 | − | 0.636928i | \(-0.780205\pi\) |
0.937057 | + | 0.349175i | \(0.113538\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 127.649 | − | 22.6454i | 0.984626 | − | 0.174677i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −40.5000 | + | 70.1481i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −80.7128 | − | 139.799i | −0.201123 | − | 0.348355i | 0.747768 | − | 0.663960i | \(-0.231126\pi\) |
−0.948890 | + | 0.315606i | \(0.897792\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 14.1283 | 0.0231863 | 0.0115932 | − | 0.999933i | \(-0.496310\pi\) | ||||
0.0115932 | + | 0.999933i | \(0.496310\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 167.169 | 0.191835 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 382.851 | + | 663.118i | 0.321298 | + | 0.556504i | 0.980756 | − | 0.195237i | \(-0.0625476\pi\) |
−0.659458 | + | 0.751741i | \(0.729214\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 707.146 | − | 1224.81i | 0.449392 | − | 0.778369i | −0.548955 | − | 0.835852i | \(-0.684974\pi\) |
0.998346 | + | 0.0574830i | \(0.0183075\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 750.923 | + | 893.019i | 0.371575 | + | 0.441888i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2092.72 | − | 3624.69i | 0.824880 | − | 1.42873i | −0.0771305 | − | 0.997021i | \(-0.524576\pi\) |
0.902011 | − | 0.431713i | \(-0.142091\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1390.00 | + | 2407.55i | 0.444799 | + | 0.770415i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4202.60 | −0.927947 | −0.463974 | − | 0.885849i | \(-0.653577\pi\) | ||||
−0.463974 | + | 0.885849i | \(0.653577\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1193.68 | − | 2067.51i | −0.223091 | − | 0.386405i | 0.732654 | − | 0.680601i | \(-0.238281\pi\) |
−0.955745 | + | 0.294196i | \(0.904948\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 726.415 | − | 1258.19i | 0.116118 | − | 0.201123i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 821.224 | − | 2263.65i | 0.113316 | − | 0.312348i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 336.469 | − | 582.782i | 0.0404056 | − | 0.0699845i | −0.845115 | − | 0.534584i | \(-0.820468\pi\) |
0.885521 | + | 0.464599i | \(0.153802\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 63.5774 | + | 110.119i | 0.00669331 | + | 0.0115932i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4173.45 | −0.387735 | −0.193868 | − | 0.981028i | \(-0.562103\pi\) | ||||
−0.193868 | + | 0.981028i | \(0.562103\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5430.94 | 0.447923 | 0.223962 | − | 0.974598i | \(-0.428101\pi\) | ||||
0.223962 | + | 0.974598i | \(0.428101\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 752.261 | + | 1302.95i | 0.0553780 | + | 0.0959175i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3151.34 | − | 5458.28i | 0.208090 | − | 0.360422i | −0.743023 | − | 0.669266i | \(-0.766609\pi\) |
0.951113 | + | 0.308844i | \(0.0999421\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15781.4 | − | 5781.32i | 0.938976 | − | 0.343983i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3445.66 | + | 5968.06i | −0.185501 | + | 0.321298i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8208.34 | − | 14217.3i | −0.401389 | − | 0.695226i | 0.592505 | − | 0.805567i | \(-0.298139\pi\) |
−0.993894 | + | 0.110341i | \(0.964806\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2998.37 | −0.133653 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12728.6 | 0.518913 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1983.24 | + | 3435.08i | 0.0741731 | + | 0.128472i | 0.900726 | − | 0.434387i | \(-0.143035\pi\) |
−0.826553 | + | 0.562858i | \(0.809702\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 25169.4 | − | 43594.6i | 0.866059 | − | 1.50006i | 6.72450e−5 | − | 1.00000i | \(-0.499979\pi\) |
0.865992 | − | 0.500058i | \(-0.166688\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3581.24 | + | 9871.45i | −0.113679 | + | 0.313350i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 131.212 | − | 227.266i | 0.00385203 | − | 0.00667192i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6822.63 | + | 11817.1i | 0.185680 | + | 0.321607i | 0.943805 | − | 0.330502i | \(-0.107218\pi\) |
−0.758126 | + | 0.652109i | \(0.773885\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 37668.9 | 0.952490 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 83957.2 | 1.97657 | 0.988284 | − | 0.152624i | \(-0.0487723\pi\) | ||||
0.988284 | + | 0.152624i | \(0.0487723\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14289.2 | + | 24749.6i | 0.313834 | + | 0.543576i | 0.979189 | − | 0.202951i | \(-0.0650532\pi\) |
−0.665355 | + | 0.746527i | \(0.731720\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −12510.0 | + | 21667.9i | −0.256805 | + | 0.444799i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −13468.7 | − | 16017.3i | −0.258880 | − | 0.307867i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −29977.7 | + | 51923.0i | −0.540420 | + | 0.936034i | 0.458460 | + | 0.888715i | \(0.348401\pi\) |
−0.998880 | + | 0.0473193i | \(0.984932\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3280.50 | − | 5681.99i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 61583.0 | 0.981219 | 0.490610 | − | 0.871380i | \(-0.336774\pi\) | ||||
0.490610 | + | 0.871380i | \(0.336774\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14222.4 | 0.213514 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −18911.7 | − | 32756.0i | −0.267875 | − | 0.463974i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −21149.2 | + | 36631.4i | −0.283021 | + | 0.490206i | −0.972127 | − | 0.234454i | \(-0.924670\pi\) |
0.689107 | + | 0.724660i | \(0.258003\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1803.46 | − | 319.941i | 0.0228298 | − | 0.00405011i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10743.1 | − | 18607.6i | 0.128802 | − | 0.223091i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −13134.8 | − | 22750.1i | −0.149318 | − | 0.258627i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 44638.1 | 0.481700 | 0.240850 | − | 0.970562i | \(-0.422574\pi\) | ||||
0.240850 | + | 0.970562i | \(0.422574\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13075.5 | 0.134082 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 55962.2 | + | 96929.4i | 0.545873 | + | 0.945480i | 0.998551 | + | 0.0538058i | \(0.0171352\pi\) |
−0.452678 | + | 0.891674i | \(0.649531\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 83474.6 | − | 144582.i | 0.775285 | − | 1.34283i | −0.159350 | − | 0.987222i | \(-0.550940\pi\) |
0.934634 | − | 0.355610i | \(-0.115727\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 21338.9 | − | 3785.61i | 0.188886 | − | 0.0335091i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 51492.8 | − | 89188.2i | 0.434798 | − | 0.753092i | −0.562481 | − | 0.826810i | \(-0.690153\pi\) |
0.997279 | + | 0.0737182i | \(0.0234865\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 68910.6 | + | 119357.i | 0.555546 | + | 0.962233i | 0.997861 | + | 0.0653736i | \(0.0208239\pi\) |
−0.442315 | + | 0.896860i | \(0.645843\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6056.45 | 0.0466563 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −129967. | −0.957495 | −0.478748 | − | 0.877953i | \(-0.658909\pi\) | ||||
−0.478748 | + | 0.877953i | \(0.658909\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −38870.8 | − | 67326.3i | −0.274081 | − | 0.474723i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −572.196 | + | 991.073i | −0.00386439 | + | 0.00669331i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 63887.0 | + | 75976.3i | 0.413567 | + | 0.491825i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 67496.4 | − | 116907.i | 0.419099 | − | 0.725901i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −18780.5 | − | 32528.8i | −0.111929 | − | 0.193868i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 109681. | 0.627853 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 243265. | 1.33835 | 0.669177 | − | 0.743103i | \(-0.266647\pi\) | ||||
0.669177 | + | 0.743103i | \(0.266647\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 24439.2 | + | 42330.0i | 0.129304 | + | 0.223962i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 97167.8 | − | 168300.i | 0.494703 | − | 0.856850i | −0.505279 | − | 0.862956i | \(-0.668610\pi\) |
0.999981 | + | 0.00610601i | \(0.00194361\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 62529.8 | − | 172359.i | 0.306519 | − | 0.844900i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6770.35 | + | 11726.6i | −0.0319725 | + | 0.0553780i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1546.85 | + | 2679.22i | 0.00704121 | + | 0.0121957i | 0.869525 | − | 0.493890i | \(-0.164425\pi\) |
−0.862483 | + | 0.506085i | \(0.831092\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −22600.4 | −0.0992155 | −0.0496078 | − | 0.998769i | \(-0.515797\pi\) | ||||
−0.0496078 | + | 0.998769i | \(0.515797\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 56724.1 | 0.240281 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1140.34 | − | 1975.12i | −0.00466329 | − | 0.00807706i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −39030.3 | + | 67602.4i | −0.154164 | + | 0.267019i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 116077. | + | 96987.7i | 0.443050 | + | 0.370189i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 176397. | − | 305529.i | 0.650917 | − | 1.12742i | −0.331983 | − | 0.943285i | \(-0.607718\pi\) |
0.982901 | − | 0.184137i | \(-0.0589489\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 72548.2 | + | 125657.i | 0.258931 | + | 0.448482i | 0.965956 | − | 0.258707i | \(-0.0832963\pi\) |
−0.707025 | + | 0.707189i | \(0.749963\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −62021.9 | −0.214199 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −44343.5 | −0.148252 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 108948. | + | 188703.i | 0.352751 | + | 0.610983i | 0.986730 | − | 0.162367i | \(-0.0519128\pi\) |
−0.633979 | + | 0.773350i | \(0.718579\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 73875.0 | − | 127955.i | 0.231742 | − | 0.401389i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 185050. | − | 510078.i | 0.562632 | − | 1.55086i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −161055. | + | 278956.i | −0.474795 | + | 0.822370i | −0.999583 | − | 0.0288633i | \(-0.990811\pi\) |
0.524788 | + | 0.851233i | \(0.324145\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −13492.7 | − | 23370.0i | −0.0385823 | − | 0.0668266i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −707392. | −1.96277 | −0.981384 | − | 0.192056i | \(-0.938485\pi\) | ||||
−0.981384 | + | 0.192056i | \(0.938485\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −371093. | −0.999462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 57278.8 | + | 99209.8i | 0.149797 | + | 0.259456i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 85253.7 | − | 147664.i | 0.216570 | − | 0.375110i | −0.737187 | − | 0.675689i | \(-0.763846\pi\) |
0.953757 | + | 0.300579i | \(0.0971798\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 231951. | + | 275843.i | 0.572534 | + | 0.680874i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −17849.2 | + | 30915.7i | −0.0428238 | + | 0.0741731i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −207703. | − | 359752.i | −0.484519 | − | 0.839211i | 0.515323 | − | 0.856996i | \(-0.327672\pi\) |
−0.999842 | + | 0.0177851i | \(0.994339\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1162.38 | −0.00263726 | −0.00131863 | − | 0.999999i | \(-0.500420\pi\) | ||||
−0.00131863 | + | 0.999999i | \(0.500420\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 453048. | 1.00004 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6249.70 | − | 10824.8i | −0.0134255 | − | 0.0232536i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 61802.0 | − | 107044.i | 0.129241 | − | 0.223851i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −93055.9 | + | 16508.5i | −0.189491 | + | 0.0336166i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −372807. | + | 645721.i | −0.739436 | + | 1.28074i | 0.213313 | + | 0.976984i | \(0.431575\pi\) |
−0.952749 | + | 0.303757i | \(0.901759\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 99186.5 | + | 171796.i | 0.191672 | + | 0.331986i | 0.945805 | − | 0.324737i | \(-0.105276\pi\) |
−0.754132 | + | 0.656722i | \(0.771942\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2361.82 | 0.00444795 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −469368. | −0.861684 | −0.430842 | − | 0.902427i | \(-0.641783\pi\) | ||||
−0.430842 | + | 0.902427i | \(0.641783\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −96796.7 | − | 167657.i | −0.173272 | − | 0.300116i | 0.766290 | − | 0.642495i | \(-0.222101\pi\) |
−0.939562 | + | 0.342379i | \(0.888767\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −61403.7 | + | 106354.i | −0.107202 | + | 0.185680i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −536457. | + | 95169.7i | −0.913681 | + | 0.162091i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −38759.5 | + | 67133.4i | −0.0644160 | + | 0.111572i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 169510. | + | 293600.i | 0.274960 | + | 0.476245i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −228303. | −0.361531 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 298066. | 0.460900 | 0.230450 | − | 0.973084i | \(-0.425980\pi\) | ||||
0.230450 | + | 0.973084i | \(0.425980\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 377807. | + | 654381.i | 0.570586 | + | 0.988284i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 50438.0 | − | 87361.3i | 0.0744153 | − | 0.128891i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −199191. | − | 236883.i | −0.287157 | − | 0.341495i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −128602. | + | 222746.i | −0.181192 | + | 0.313834i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5409.04 | + | 9368.73i | 0.00744971 | + | 0.0129033i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 187215. | 0.252103 | 0.126051 | − | 0.992024i | \(-0.459770\pi\) | ||||
0.126051 | + | 0.992024i | \(0.459770\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −225180. | −0.296533 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −669482. | − | 1.15958e6i | −0.862332 | − | 1.49360i | −0.869672 | − | 0.493630i | \(-0.835670\pi\) |
0.00734045 | − | 0.999973i | \(-0.497663\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −475828. | + | 824158.i | −0.599600 | + | 1.03854i | 0.393280 | + | 0.919419i | \(0.371340\pi\) |
−0.992880 | + | 0.119119i | \(0.961993\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 64233.8 | − | 177056.i | 0.0792015 | − | 0.218314i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −371709. | + | 643820.i | −0.448553 | + | 0.776917i | −0.998292 | − | 0.0584197i | \(-0.981394\pi\) |
0.549739 | + | 0.835336i | \(0.314727\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −58534.0 | − | 101384.i | −0.0691415 | − | 0.119757i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −539599. | −0.624023 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 625847. | 0.708718 | 0.354359 | − | 0.935110i | \(-0.384699\pi\) | ||||
0.354359 | + | 0.935110i | \(0.384699\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 666411. | + | 1.15426e6i | 0.739094 | + | 1.28015i | 0.952904 | + | 0.303273i | \(0.0980793\pi\) |
−0.213810 | + | 0.976875i | \(0.568587\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 29524.5 | − | 51137.9i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 53566.9 | − | 307549.i | 0.0570140 | − | 0.327340i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9990.77 | − | 17304.5i | 0.0104197 | − | 0.0180475i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 277124. | + | 479992.i | 0.283254 | + | 0.490610i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.78809e6 | −1.79145 | −0.895726 | − | 0.444606i | \(-0.853344\pi\) | ||||
−0.895726 | + | 0.444606i | \(0.853344\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −675636. | −0.663608 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 64000.9 | + | 110853.i | 0.0616362 | + | 0.106757i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −254462. | + | 440741.i | −0.240320 | + | 0.416247i | −0.960805 | − | 0.277224i | \(-0.910586\pi\) |
0.720485 | + | 0.693470i | \(0.243919\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 29752.5 | − | 82010.9i | 0.0275597 | − | 0.0759665i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 170205. | − | 294804.i | 0.154658 | − | 0.267875i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −168247. | − | 291412.i | −0.149988 | − | 0.259787i | 0.781235 | − | 0.624237i | \(-0.214590\pi\) |
−0.931223 | + | 0.364450i | \(0.881257\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −304929. | −0.266737 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −380685. | −0.326804 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −747765. | − | 1.29517e6i | −0.630064 | − | 1.09130i | −0.987538 | − | 0.157379i | \(-0.949695\pi\) |
0.357475 | − | 0.933923i | \(-0.383638\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −888484. | + | 1.53890e6i | −0.734897 | + | 1.27288i | 0.219871 | + | 0.975529i | \(0.429436\pi\) |
−0.954768 | + | 0.297350i | \(0.903897\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10609.3 | + | 12616.8i | 0.00861546 | + | 0.0102458i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 224381. | − | 388640.i | 0.178918 | − | 0.309896i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −440632. | − | 763198.i | −0.345046 | − | 0.597637i | 0.640316 | − | 0.768112i | \(-0.278803\pi\) |
−0.985362 | + | 0.170474i | \(0.945470\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 193375. | 0.148727 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.13932e6 | −0.860756 | −0.430378 | − | 0.902649i | \(-0.641620\pi\) | ||||
−0.430378 | + | 0.902649i | \(0.641620\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −448733. | − | 777228.i | −0.333059 | − | 0.576876i | 0.650051 | − | 0.759891i | \(-0.274748\pi\) |
−0.983110 | + | 0.183015i | \(0.941414\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 118213. | − | 204751.i | 0.0862090 | − | 0.149318i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −532735. | + | 94509.4i | −0.381774 | + | 0.0677283i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 416778. | − | 721881.i | 0.293535 | − | 0.508418i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 200872. | + | 347920.i | 0.139055 | + | 0.240850i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.84614e6 | −1.25631 | −0.628153 | − | 0.778090i | \(-0.716189\pi\) | ||||
−0.628153 | + | 0.778090i | \(0.716189\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 73674.9 | 0.0492907 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 58839.7 | + | 101913.i | 0.0387061 | + | 0.0670409i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 29566.5 | − | 51210.8i | 0.0191259 | − | 0.0331271i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 693252. | − | 122986.i | 0.441037 | − | 0.0782418i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −503660. | + | 872365.i | −0.315160 | + | 0.545873i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −467504. | − | 809741.i | −0.287764 | − | 0.498421i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.38565e6 | −0.839089 | −0.419544 | − | 0.907735i | \(-0.637810\pi\) | ||||
−0.419544 | + | 0.907735i | \(0.637810\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.50254e6 | 0.895221 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.15624e6 | + | 2.00267e6i | 0.677871 | + | 1.17411i | 0.975621 | + | 0.219463i | \(0.0704305\pi\) |
−0.297750 | + | 0.954644i | \(0.596236\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 584400. | − | 1.01221e6i | 0.337171 | − | 0.583996i | −0.646729 | − | 0.762720i | \(-0.723863\pi\) |
0.983899 | + | 0.178724i | \(0.0571968\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 125531. | + | 149285.i | 0.0712811 | + | 0.0847696i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −717166. | + | 1.24217e6i | −0.400840 | + | 0.694276i | −0.993828 | − | 0.110936i | \(-0.964615\pi\) |
0.592987 | + | 0.805212i | \(0.297948\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 339204. | + | 587519.i | 0.186631 | + | 0.323255i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 926871. | 0.502061 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.08293e6 | 0.577554 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19638.3 | + | 34014.5i | 0.0103132 | + | 0.0178631i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −620195. | + | 1.07421e6i | −0.320744 | + | 0.555546i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 278659. | − | 768105.i | 0.141933 | − | 0.391229i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.11709e6 | + | 1.93486e6i | −0.560426 | + | 0.970686i | 0.437033 | + | 0.899445i | \(0.356029\pi\) |
−0.997459 | + | 0.0712406i | \(0.977304\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 27254.0 | + | 47205.4i | 0.0134685 | + | 0.0233282i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 253452. | 0.123391 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.08787e6 | 1.48110 | 0.740549 | − | 0.672002i | \(-0.234565\pi\) | ||||
0.740549 | + | 0.672002i | \(0.234565\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −584851. | − | 1.01299e6i | −0.276405 | − | 0.478748i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −192690. | + | 333749.i | −0.0897373 | + | 0.155429i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.88355e6 | − | 1.09535e6i | 0.864454 | − | 0.502711i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 349838. | − | 605936.i | 0.158241 | − | 0.274081i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.55877e6 | − | 2.69987e6i | −0.694959 | − | 1.20370i | −0.970195 | − | 0.242327i | \(-0.922089\pi\) |
0.275236 | − | 0.961377i | \(-0.411244\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 613026. | 0.269411 | 0.134706 | − | 0.990886i | \(-0.456991\pi\) | ||||
0.134706 | + | 0.990886i | \(0.456991\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10299.5 | −0.00446221 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.89185e6 | − | 3.27678e6i | −0.808071 | − | 1.39962i | −0.914198 | − | 0.405268i | \(-0.867178\pi\) |
0.106127 | − | 0.994353i | \(-0.466155\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 779724. | − | 1.35052e6i | 0.328375 | − | 0.568762i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −304685. | + | 839844.i | −0.126526 | + | 0.348761i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.86107e6 | − | 3.22346e6i | 0.762125 | − | 1.32004i | −0.179629 | − | 0.983734i | \(-0.557490\pi\) |
0.941753 | − | 0.336304i | \(-0.109177\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 237940. | + | 412123.i | 0.0960945 | + | 0.166441i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.21493e6 | 0.483934 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 530824. | 0.208554 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.06898e6 | + | 3.58357e6i | 0.801845 | + | 1.38884i | 0.918400 | + | 0.395652i | \(0.129481\pi\) |
−0.116555 | + | 0.993184i | \(0.537185\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 169025. | − | 292759.i | 0.0646225 | − | 0.111929i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.36974e6 | − | 1.62893e6i | −0.516658 | − | 0.614424i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.47209e6 | + | 2.54973e6i | −0.547851 | + | 0.948905i | 0.450571 | + | 0.892741i | \(0.351220\pi\) |
−0.998422 | + | 0.0561644i | \(0.982113\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 493566. | + | 854882.i | 0.181245 | + | 0.313926i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −59375.7 | −0.0215157 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.97504e6 | −1.06388 | −0.531942 | − | 0.846781i | \(-0.678538\pi\) | ||||
−0.531942 | + | 0.846781i | \(0.678538\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.09469e6 | + | 1.89606e6i | 0.386349 | + | 0.669177i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.03052e6 | − | 1.78491e6i | 0.358971 | − | 0.621756i | −0.628818 | − | 0.777552i | \(-0.716461\pi\) |
0.987789 | + | 0.155796i | \(0.0497944\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −382739. | + | 67899.5i | −0.131598 | + | 0.0233461i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −219953. | + | 380970.i | −0.0746539 | + | 0.129304i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.04542e6 | − | 1.81072e6i | −0.350281 | − | 0.606705i | 0.636018 | − | 0.771675i | \(-0.280581\pi\) |
−0.986299 | + | 0.164970i | \(0.947247\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.20480e6 | 1.06013 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.74902e6 | 0.571233 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 556817. | + | 964435.i | 0.179564 | + | 0.311014i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −585647. | + | 1.01437e6i | −0.186492 | + | 0.323013i | −0.944078 | − | 0.329722i | \(-0.893045\pi\) |
0.757586 | + | 0.652735i | \(0.226378\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.62479e6 | − | 288245.i | 0.510935 | − | 0.0906420i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.54574e6 | + | 2.67731e6i | −0.480039 | + | 0.831452i | −0.999738 | − | 0.0228979i | \(-0.992711\pi\) |
0.519699 | + | 0.854349i | \(0.326044\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16864.6 | − | 29210.4i | −0.00517266 | − | 0.00895930i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −121866. | −0.0369187 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −108630. | −0.0325059 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.17426e6 | + | 3.76593e6i | 0.642693 | + | 1.11318i | 0.984829 | + | 0.173527i | \(0.0555163\pi\) |
−0.342136 | + | 0.939650i | \(0.611150\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13921.7 | + | 24113.0i | −0.00406524 | + | 0.00704121i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 330947. | + | 393572.i | 0.0954737 | + | 0.113540i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 571932. | − | 990616.i | 0.163014 | − | 0.282348i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −101702. | − | 176153.i | −0.0286411 | − | 0.0496078i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.13660e6 | −0.872818 | −0.436409 | − | 0.899748i | \(-0.643750\pi\) | ||||
−0.436409 | + | 0.899748i | \(0.643750\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.02560e6 | 1.65690 | 0.828448 | − | 0.560066i | \(-0.189224\pi\) | ||||
0.828448 | + | 0.560066i | \(0.189224\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 255258. | + | 442120.i | 0.0693632 | + | 0.120141i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.06432e6 | + | 1.84346e6i | −0.285826 | + | 0.495065i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.22562e6 | − | 6.13476e6i | 0.590719 | − | 1.62828i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10263.0 | − | 17776.1i | 0.00269235 | − | 0.00466329i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.14931e6 | − | 1.99067e6i | −0.298020 | − | 0.516186i | 0.677663 | − | 0.735373i | \(-0.262993\pi\) |
−0.975683 | + | 0.219187i | \(0.929660\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.62982e6 | −1.44303 | −0.721515 | − | 0.692399i | \(-0.756554\pi\) | ||||
−0.721515 | + | 0.692399i | \(0.756554\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −702545. | −0.178013 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.95971e6 | − | 5.12637e6i | −0.741388 | − | 1.28412i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.72482e6 | + | 4.71952e6i | −0.674801 | + | 1.16879i | 0.301725 | + | 0.953395i | \(0.402437\pi\) |
−0.976527 | + | 0.215396i | \(0.930896\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −233597. | + | 1.34118e6i | −0.0571968 | + | 0.328389i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.85467e6 | − | 4.94443e6i | 0.691108 | − | 1.19703i | −0.280367 | − | 0.959893i | \(-0.590456\pi\) |
0.971475 | − | 0.237142i | \(-0.0762105\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 392832. | + | 680405.i | 0.0940387 | + | 0.162880i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.17515e6 | 0.751615 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.38234e6 | 1.25996 | 0.629978 | − | 0.776613i | \(-0.283064\pi\) | ||||
0.629978 | + | 0.776613i | \(0.283064\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 336851. | + | 583442.i | 0.0779823 | + | 0.135069i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −652934. | + | 1.13092e6i | −0.149494 | + | 0.258931i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11602.5 | − | 31981.5i | 0.00262738 | − | 0.00724220i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.19525e6 | − | 5.53434e6i | 0.715673 | − | 1.23958i | −0.247026 | − | 0.969009i | \(-0.579453\pi\) |
0.962699 | − | 0.270573i | \(-0.0872133\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −279099. | − | 483413.i | −0.0618338 | − | 0.107099i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.34511e6 | 1.60970 | 0.804851 | − | 0.593476i | \(-0.202245\pi\) | ||||
0.804851 | + | 0.593476i | \(0.202245\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.63416e6 | 1.00466 | 0.502329 | − | 0.864677i | \(-0.332477\pi\) | ||||
0.502329 | + | 0.864677i | \(0.332477\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −199546. | − | 345623.i | −0.0427966 | − | 0.0741259i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.81598e6 | + | 6.60946e6i | −0.809680 | + | 1.40241i | 0.103406 | + | 0.994639i | \(0.467026\pi\) |
−0.913086 | + | 0.407768i | \(0.866307\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.13850e6 | + | 1.35394e6i | 0.239002 | + | 0.284229i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −980529. | + | 1.69833e6i | −0.203661 | + | 0.352751i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −438346. | − | 759238.i | −0.0900875 | − | 0.156036i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.93172e6 | 0.799556 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.32975e6 | 0.267593 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.80631e6 | + | 8.32477e6i | 0.957135 | + | 1.65781i | 0.729406 | + | 0.684081i | \(0.239796\pi\) |
0.227728 | + | 0.973725i | \(0.426870\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4753.74 | − | 8233.72i | 0.000936856 | − | 0.00162268i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.80839e6 | − | 853028.i | 0.937846 | − | 0.166378i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 414562. | − | 718042.i | 0.0800267 | − | 0.138610i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.40112e6 | + | 2.42680e6i | 0.267702 | + | 0.463673i | 0.968268 | − | 0.249914i | \(-0.0804024\pi\) |
−0.700566 | + | 0.713588i | \(0.747069\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.89900e6 | −0.548246 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.82008e6 | −0.902299 | −0.451149 | − | 0.892448i | \(-0.648986\pi\) | ||||
−0.451149 | + | 0.892448i | \(0.648986\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.60897e6 | − | 2.78682e6i | −0.298148 | − | 0.516407i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 121434. | − | 210330.i | 0.0222755 | − | 0.0385823i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.07170e7 | − | 1.90125e6i | 1.94618 | − | 0.345261i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.29829e6 | − | 3.98076e6i | 0.413194 | − | 0.715673i | −0.582043 | − | 0.813158i | \(-0.697747\pi\) |
0.995237 | + | 0.0974853i | \(0.0310799\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.18326e6 | − | 5.51358e6i | −0.566602 | − | 0.981384i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.80055e6 | −0.317311 | −0.158656 | − | 0.987334i | \(-0.550716\pi\) | ||||
−0.158656 | + | 0.987334i | \(0.550716\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.07892e6 | 0.362752 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.66992e6 | − | 2.89239e6i | −0.288520 | − | 0.499731i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.41602e6 | − | 4.18467e6i | 0.413339 | − | 0.715924i | −0.581913 | − | 0.813251i | \(-0.697696\pi\) |
0.995253 | + | 0.0973263i | \(0.0310291\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.38446e6 | + | 2.83566e6i | 0.403959 | + | 0.480400i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −515509. | + | 892888.i | −0.0864854 | + | 0.149797i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.55048e6 | − | 2.68552e6i | −0.257602 | − | 0.446180i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.01741e6 | −0.167406 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.53457e6 | 0.250073 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.40562e6 | − | 2.43461e6i | −0.226869 | − | 0.392948i | 0.730010 | − | 0.683437i | \(-0.239516\pi\) |
−0.956878 | + | 0.290489i | \(0.906182\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.22715e6 | + | 2.12548e6i | −0.196174 | + | 0.339784i | −0.947285 | − | 0.320392i | \(-0.896185\pi\) |
0.751110 | + | 0.660177i | \(0.229519\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.10620e6 | + | 3.04917e6i | −0.175161 | + | 0.482818i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 914000. | − | 1.58309e6i | 0.143357 | − | 0.248302i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.54076e6 | − | 9.59687e6i | −0.860855 | − | 1.49104i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −321286. | −0.0494487 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −58963.7 | −0.00899015 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −956445. | − | 1.65661e6i | −0.144469 | − | 0.250228i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.86933e6 | − | 3.23777e6i | 0.279737 | − | 0.484519i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.08198e6 | − | 1.73959e6i | −0.308677 | − | 0.257914i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 579232. | − | 1.00326e6i | 0.0850862 | − | 0.147374i | −0.820342 | − | 0.571874i | \(-0.806217\pi\) |
0.905428 | + | 0.424500i | \(0.139550\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5230.72 | − | 9059.87i | −0.000761310 | − | 0.00131863i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.55994e6 | 0.369180 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.63638e6 | −0.662538 | −0.331269 | − | 0.943536i | \(-0.607477\pi\) | ||||
−0.331269 | + | 0.943536i | \(0.607477\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.03872e6 | + | 3.53116e6i | 0.288686 | + | 0.500019i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.97185e6 | + | 5.14740e6i | −0.417012 | + | 0.722285i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.65080e6 | + | 7.30676e6i | −0.368608 | + | 1.01604i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 56247.3 | − | 97423.1i | 0.00775120 | − | 0.0134255i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −135916. | − | 235414.i | −0.0185624 | − | 0.0321510i | 0.856595 | − | 0.515989i | \(-0.172576\pi\) |
−0.875157 | + | 0.483838i | \(0.839242\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 76730.0 | 0.0103857 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.11244e6 | 0.149234 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.69122e6 | + | 2.92928e6i | 0.224869 | + | 0.389485i | 0.956280 | − | 0.292452i | \(-0.0944712\pi\) |
−0.731411 | + | 0.681937i | \(0.761138\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.20702e6 | + | 2.09063e6i | −0.159072 | + | 0.275522i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −547423. | − | 651011.i | −0.0715097 | − | 0.0850414i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.56130e6 | + | 1.13645e7i | −0.849590 | + | 1.47153i | 0.0319843 | + | 0.999488i | \(0.489817\pi\) |
−0.881574 | + | 0.472045i | \(0.843516\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.35811e6 | − | 1.27446e7i | −0.944443 | − | 1.63582i | −0.756862 | − | 0.653575i | \(-0.773269\pi\) |
−0.187581 | − | 0.982249i | \(-0.560065\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.71053e6 | −0.853828 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.16355e7 | 1.46762 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.94148e6 | + | 3.36273e6i | 0.242769 | + | 0.420487i | 0.961502 | − | 0.274798i | \(-0.0886111\pi\) |
−0.718733 | + | 0.695286i | \(0.755278\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −892678. | + | 1.54616e6i | −0.110662 | + | 0.191672i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.86099e6 | − | 1.39457e6i | 0.966134 | − | 0.171396i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.32504e6 | + | 2.29503e6i | −0.161457 | + | 0.279651i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10628.2 | + | 18408.5i | 0.00128401 | + | 0.00222397i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.97913e6 | −0.596428 | −0.298214 | − | 0.954499i | \(-0.596391\pi\) | ||||
−0.298214 | + | 0.954499i | \(0.596391\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.37641e6 | −0.401021 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.11216e6 | − | 3.65836e6i | −0.248747 | − | 0.430842i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.66344e6 | + | 1.32735e7i | −0.894926 | + | 1.55006i | −0.0610292 | + | 0.998136i | \(0.519438\pi\) |
−0.833896 | + | 0.551921i | \(0.813895\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.81547e6 | − | 322073.i | 0.210231 | − | 0.0372959i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 871171. | − | 1.50891e6i | 0.100039 | − | 0.173272i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.31480e6 | − | 5.74141e6i | −0.377477 | − | 0.653810i | 0.613217 | − | 0.789914i | \(-0.289875\pi\) |
−0.990694 | + | 0.136104i | \(0.956542\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.45010e6 | −0.163762 | −0.0818808 | − | 0.996642i | \(-0.526093\pi\) | ||||
−0.0818808 | + | 0.996642i | \(0.526093\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.10527e6 | −0.123787 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.25370e6 | − | 2.17147e6i | −0.139253 | − | 0.241194i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.95555e6 | − | 3.38711e6i | 0.215425 | − | 0.373128i | −0.737979 | − | 0.674824i | \(-0.764220\pi\) |
0.953404 | + | 0.301696i | \(0.0975528\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.15583e6 | − | 3.75300e6i | −0.344802 | − | 0.410049i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 44523.1 | − | 77116.2i | 0.00482483 | − | 0.00835685i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.88765e6 | − | 1.01977e7i | −0.632835 | − | 1.09610i | −0.986969 | − | 0.160908i | \(-0.948558\pi\) |
0.354134 | − | 0.935195i | \(-0.384776\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −697671. | −0.0743812 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.61462e6 | −0.488004 | −0.244002 | − | 0.969775i | \(-0.578460\pi\) | ||||
−0.244002 | + | 0.969775i | \(0.578460\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.83733e6 | − | 4.91440e6i | −0.297634 | − | 0.515518i | 0.677960 | − | 0.735099i | \(-0.262864\pi\) |
−0.975594 | + | 0.219581i | \(0.929531\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.52559e6 | + | 2.64240e6i | −0.158748 | + | 0.274960i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.87013e6 | + | 5.15489e6i | −0.193042 | + | 0.532107i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.32511e6 | + | 5.75926e6i | −0.340491 | + | 0.589748i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.02736e6 | − | 1.77945e6i | −0.104365 | − | 0.180766i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 515271. | 0.0519289 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.67894e6 | −0.567798 | −0.283899 | − | 0.958854i | \(-0.591628\pi\) | ||||
−0.283899 | + | 0.958854i | \(0.591628\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.34130e6 | + | 2.32320e6i | 0.133050 | + | 0.230450i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.25925e6 | − | 3.91313e6i | 0.222346 | − | 0.385114i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 222964. | − | 81680.2i | 0.0217714 | − | 0.00797569i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.40027e6 | + | 5.88943e6i | −0.329428 | + | 0.570586i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.05369e6 | + | 1.82504e6i | 0.101290 | + | 0.175439i | 0.912216 | − | 0.409709i | \(-0.134370\pi\) |
−0.810926 | + | 0.585148i | \(0.801036\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.30987e6 | 0.220323 | 0.110162 | − | 0.993914i | \(-0.464863\pi\) | ||||
0.110162 | + | 0.993914i | \(0.464863\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 907885. | 0.0859274 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.93033e6 | + | 8.53958e6i | 0.463036 | + | 0.802003i | 0.999111 | − | 0.0421683i | \(-0.0134266\pi\) |
−0.536074 | + | 0.844171i | \(0.680093\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 320147. | − | 554510.i | 0.0298358 | − | 0.0516771i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 949964. | − | 2.61851e6i | 0.0878526 | − | 0.242160i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.01545e6 | + | 8.68701e6i | −0.460285 | + | 0.797237i | −0.998975 | − | 0.0452673i | \(-0.985586\pi\) |
0.538690 | + | 0.842504i | \(0.318919\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.80483e6 | − | 3.12605e6i | −0.164374 | − | 0.284704i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.31484e6 | −0.209223 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.42828e7 | 1.28115 | 0.640575 | − | 0.767895i | \(-0.278696\pi\) | ||||
0.640575 | + | 0.767895i | \(0.278696\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.82097e6 | + | 1.70104e7i | 0.874280 | + | 1.51430i | 0.857527 | + | 0.514438i | \(0.172000\pi\) |
0.0167532 | + | 0.999860i | \(0.494667\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −48681.4 | + | 84318.6i | −0.00430109 | + | 0.00744971i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.19182e6 | − | 2.60657e6i | −0.192199 | − | 0.228568i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.79486e6 | + | 1.52331e7i | −0.765445 | + | 1.32579i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 842466. | + | 1.45919e6i | 0.0727758 | + | 0.126051i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.12596e6 | −0.696736 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.00150e6 | −0.766086 | −0.383043 | − | 0.923731i | \(-0.625124\pi\) | ||||
−0.383043 | + | 0.923731i | \(0.625124\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.01331e6 | − | 1.75510e6i | −0.0856016 | − | 0.148266i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.71181e6 | + | 1.16252e7i | −0.562818 | + | 0.974830i | 0.434431 | + | 0.900705i | \(0.356950\pi\) |
−0.997249 | + | 0.0741247i | \(0.976384\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.69800e6 | − | 1.01085e6i | 0.474294 | − | 0.0841418i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.02534e6 | − | 1.04362e7i | 0.497868 | − | 0.862332i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.00840e6 | − | 6.94276e6i | −0.328791 | − | 0.569483i | 0.653481 | − | 0.756943i | \(-0.273308\pi\) |
−0.982272 | + | 0.187460i | \(0.939974\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 57463.5 | 0.00467913 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.56491e6 | −0.692358 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −115970. | − | 200866.i | −0.00930673 | − | 0.0161197i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.20987e7 | + | 2.09555e7i | −0.963923 | + | 1.66956i | −0.251442 | + | 0.967872i | \(0.580905\pi\) |
−0.712481 | + | 0.701691i | \(0.752428\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.66907e6 | − | 296100.i | 0.132020 | − | 0.0234210i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −209894. | + | 363547.i | −0.0164831 | + | 0.0285495i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.59781e6 | − | 2.76749e6i | −0.124578 | − | 0.215776i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.69077e6 | −0.517944 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.56268e6 | −0.120109 | −0.0600543 | − | 0.998195i | \(-0.519127\pi\) | ||||
−0.0600543 | + | 0.998195i | \(0.519127\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −475866. | − | 824224.i | −0.0363158 | − | 0.0629009i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 526806. | − | 912455.i | 0.0399189 | − | 0.0691415i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.33851e6 | + | 1.11056e7i | 0.702634 | + | 0.835592i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.76950e6 | − | 1.69213e7i | 0.729889 | − | 1.26420i | −0.227041 | − | 0.973885i | \(-0.572905\pi\) |
0.956930 | − | 0.290320i | \(-0.0937616\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.42820e6 | − | 4.20576e6i | −0.180140 | − | 0.312011i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.99210e6 | −0.736093 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −42362.0 | −0.00309892 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.81631e6 | + | 4.87799e6i | 0.204589 | + | 0.354359i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.05095e6 | + | 7.01645e6i | −0.292237 | + | 0.506169i | −0.974338 | − | 0.225089i | \(-0.927733\pi\) |
0.682102 | + | 0.731257i | \(0.261066\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.38129e6 | − | 2.03460e7i | 0.528804 | − | 1.45761i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.99770e6 | + | 1.03883e7i | −0.426716 | + | 0.739094i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.84161e6 | − | 1.01180e7i | −0.412750 | − | 0.714904i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.52759e7 | −1.77366 | −0.886829 | − | 0.462098i | \(-0.847097\pi\) | ||||
−0.886829 | + | 0.462098i | \(0.847097\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.07924e6 | + | 3.60135e6i | 0.143917 | + | 0.249271i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.37207e7 | + | 2.37650e7i | −0.943228 | + | 1.63372i | −0.183969 | + | 0.982932i | \(0.558894\pi\) |
−0.759260 | + | 0.650787i | \(0.774439\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.63816e6 | − | 966457.i | 0.180128 | − | 0.0659879i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.10135e6 | − | 1.90759e6i | 0.0746888 | − | 0.129365i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.26785e6 | − | 5.66008e6i | −0.220115 | − | 0.381251i | 0.734727 | − | 0.678362i | \(-0.237310\pi\) |
−0.954843 | + | 0.297111i | \(0.903977\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 179834. | 0.0120317 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.46784e7 | 1.64000 | 0.820001 | − | 0.572362i | \(-0.193973\pi\) | ||||
0.820001 | + | 0.572362i | \(0.193973\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.27646e6 | − | 5.67499e6i | −0.216279 | − | 0.374606i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.49411e6 | + | 4.31993e6i | −0.163537 | + | 0.283254i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.55329e6 | − | 1.25508e7i | 0.296565 | − | 0.817463i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.63911e6 | + | 2.83902e6i | −0.106049 | + | 0.183683i | −0.914166 | − | 0.405339i | \(-0.867153\pi\) |
0.808117 | + | 0.589022i | \(0.200487\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.04641e6 | − | 1.39368e7i | −0.517148 | − | 0.895726i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.69507e6 | 0.172069 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.68090e6 | 0.233461 | 0.116731 | − | 0.993164i | \(-0.462759\pi\) | ||||
0.116731 | + | 0.993164i | \(0.462759\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.04036e6 | − | 5.26606e6i | −0.191567 | − | 0.331804i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.05099e7 | + | 1.82037e7i | −0.657866 | + | 1.13946i | 0.323301 | + | 0.946296i | \(0.395208\pi\) |
−0.981167 | + | 0.193162i | \(0.938126\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.14992e7 | + | 1.36752e7i | 0.715084 | + | 0.850399i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −576008. | + | 997675.i | −0.0355857 | + | 0.0616362i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28019.9 | + | 48531.9i | 0.00171980 | + | 0.00297878i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.15418e6 | −0.253320 | −0.126660 | − | 0.991946i | \(-0.540426\pi\) | ||||
−0.126660 | + | 0.991946i | \(0.540426\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.58032e6 | −0.277498 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −731741. | − | 1.26741e6i | −0.0440462 | − | 0.0762903i | 0.843162 | − | 0.537660i | \(-0.180692\pi\) |
−0.887208 | + | 0.461370i | \(0.847358\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.31841e6 | − | 5.74765e6i | 0.198461 | − | 0.343745i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 773098. | − | 137151.i | 0.0459390 | − | 0.00814978i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.95123e6 | + | 5.11169e6i | −0.174245 | + | 0.301801i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.77642e6 | − | 1.17371e7i | −0.397533 | − | 0.688547i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.06370e6 | 0.178584 |