Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,6,Mod(37,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.37");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.e (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: | \(10.1041806482\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{12} + 187x^{10} + 25399x^{8} + 1518438x^{6} + 66232188x^{4} + 1297462320x^{2} + 18380851776 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 37.1 | ||
Root | \(-5.31117 + 9.19921i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 63.37 |
Dual form | 63.6.e.f.46.1 |
$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.31117 | + | 9.19921i | −0.938891 | + | 1.62621i | −0.171346 | + | 0.985211i | \(0.554811\pi\) |
−0.767545 | + | 0.640995i | \(0.778522\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −40.4170 | − | 70.0043i | −1.26303 | − | 2.18763i | ||||
\(5\) | 33.7376 | − | 58.4352i | 0.603516 | − | 1.04532i | −0.388769 | − | 0.921335i | \(-0.627099\pi\) |
0.992284 | − | 0.123984i | \(-0.0395673\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −120.281 | + | 48.3679i | −0.927796 | + | 0.373089i | ||||
\(8\) | 518.731 | 2.86561 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 358.372 | + | 620.718i | 1.13327 | + | 1.96288i | ||||
\(11\) | 261.323 | + | 452.625i | 0.651173 | + | 1.12787i | 0.982839 | + | 0.184468i | \(0.0590562\pi\) |
−0.331665 | + | 0.943397i | \(0.607610\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 76.6331 | 0.125764 | 0.0628822 | − | 0.998021i | \(-0.479971\pi\) | ||||
0.0628822 | + | 0.998021i | \(0.479971\pi\) | |||||||
\(14\) | 193.887 | − | 1363.38i | 0.264379 | − | 1.85908i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1461.72 | + | 2531.78i | −1.42746 | + | 2.47244i | ||||
\(17\) | 634.801 | + | 1099.51i | 0.532740 | + | 0.922733i | 0.999269 | + | 0.0382267i | \(0.0121709\pi\) |
−0.466529 | + | 0.884506i | \(0.654496\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 946.362 | − | 1639.15i | 0.601414 | − | 1.04168i | −0.391193 | − | 0.920309i | \(-0.627938\pi\) |
0.992607 | − | 0.121371i | \(-0.0387290\pi\) | |||||||
\(20\) | −5454.28 | −3.04904 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5551.73 | −2.44552 | ||||||||
\(23\) | −575.022 | + | 995.967i | −0.226655 | + | 0.392578i | −0.956815 | − | 0.290699i | \(-0.906112\pi\) |
0.730160 | + | 0.683276i | \(0.239446\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −713.945 | − | 1236.59i | −0.228462 | − | 0.395708i | ||||
\(26\) | −407.011 | + | 704.964i | −0.118079 | + | 0.204519i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 8247.36 | + | 6465.31i | 1.98802 | + | 1.55845i | ||||
\(29\) | 3850.03 | 0.850099 | 0.425049 | − | 0.905170i | \(-0.360257\pi\) | ||||
0.425049 | + | 0.905170i | \(0.360257\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5206.86 | + | 9018.55i | 0.973132 | + | 1.68551i | 0.685967 | + | 0.727633i | \(0.259379\pi\) |
0.287165 | + | 0.957881i | \(0.407287\pi\) | |||||||
\(32\) | −7227.21 | − | 12517.9i | −1.24766 | − | 2.16101i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −13486.1 | −2.00074 | ||||||||
\(35\) | −1231.60 | + | 8660.46i | −0.169942 | + | 1.19501i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2801.14 | − | 4851.71i | 0.336380 | − | 0.582627i | −0.647369 | − | 0.762177i | \(-0.724131\pi\) |
0.983749 | + | 0.179550i | \(0.0574641\pi\) | |||||||
\(38\) | 10052.6 | + | 17411.6i | 1.12932 | + | 1.95605i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 17500.7 | − | 30312.1i | 1.72944 | − | 2.99548i | ||||
\(41\) | 14232.7 | 1.32229 | 0.661147 | − | 0.750256i | \(-0.270070\pi\) | ||||
0.661147 | + | 0.750256i | \(0.270070\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −14827.9 | −1.22295 | −0.611475 | − | 0.791264i | \(-0.709424\pi\) | ||||
−0.611475 | + | 0.791264i | \(0.709424\pi\) | |||||||
\(44\) | 21123.8 | − | 36587.5i | 1.64490 | − | 2.84906i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6108.08 | − | 10579.5i | −0.425608 | − | 0.737175i | ||||
\(47\) | −5774.88 | + | 10002.4i | −0.381328 | + | 0.660479i | −0.991252 | − | 0.131981i | \(-0.957866\pi\) |
0.609925 | + | 0.792459i | \(0.291200\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12128.1 | − | 11635.5i | 0.721610 | − | 0.692300i | ||||
\(50\) | 15167.5 | 0.858004 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3097.28 | − | 5364.64i | −0.158844 | − | 0.275127i | ||||
\(53\) | −2338.86 | − | 4051.02i | −0.114371 | − | 0.198096i | 0.803157 | − | 0.595767i | \(-0.203152\pi\) |
−0.917528 | + | 0.397671i | \(0.869818\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 35265.6 | 1.57197 | ||||||||
\(56\) | −62393.5 | + | 25089.9i | −2.65870 | + | 1.06913i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −20448.2 | + | 35417.3i | −0.798150 | + | 1.38244i | ||||
\(59\) | 14551.0 | + | 25203.0i | 0.544205 | + | 0.942590i | 0.998656 | + | 0.0518189i | \(0.0165019\pi\) |
−0.454452 | + | 0.890771i | \(0.650165\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5921.45 | + | 10256.2i | −0.203753 | + | 0.352910i | −0.949735 | − | 0.313056i | \(-0.898647\pi\) |
0.745982 | + | 0.665966i | \(0.231980\pi\) | |||||||
\(62\) | −110618. | −3.65466 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 59989.5 | 1.83073 | ||||||||
\(65\) | 2585.41 | − | 4478.06i | 0.0759008 | − | 0.131464i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 18106.3 | + | 31361.0i | 0.492768 | + | 0.853499i | 0.999965 | − | 0.00833093i | \(-0.00265185\pi\) |
−0.507197 | + | 0.861830i | \(0.669319\pi\) | |||||||
\(68\) | 51313.5 | − | 88877.6i | 1.34573 | − | 2.33088i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −73128.1 | − | 57326.9i | −1.78377 | − | 1.39834i | ||||
\(71\) | 13477.6 | 0.317298 | 0.158649 | − | 0.987335i | \(-0.449286\pi\) | ||||
0.158649 | + | 0.987335i | \(0.449286\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1304.23 | − | 2258.98i | −0.0286448 | − | 0.0496142i | 0.851348 | − | 0.524602i | \(-0.175786\pi\) |
−0.879992 | + | 0.474988i | \(0.842452\pi\) | |||||||
\(74\) | 29754.6 | + | 51536.5i | 0.631648 | + | 1.09405i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −152996. | −3.03842 | ||||||||
\(77\) | −53324.8 | − | 41802.6i | −1.02495 | − | 0.803483i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 39160.2 | − | 67827.4i | 0.705955 | − | 1.22275i | −0.260391 | − | 0.965503i | \(-0.583852\pi\) |
0.966346 | − | 0.257246i | \(-0.0828151\pi\) | |||||||
\(80\) | 98629.9 | + | 170832.i | 1.72299 | + | 2.98431i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −75592.3 | + | 130930.i | −1.24149 | + | 2.15032i | ||||
\(83\) | −16746.0 | −0.266819 | −0.133410 | − | 0.991061i | \(-0.542593\pi\) | ||||
−0.133410 | + | 0.991061i | \(0.542593\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 85666.5 | 1.28607 | ||||||||
\(86\) | 78753.5 | − | 136405.i | 1.14822 | − | 1.98877i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 135557. | + | 234791.i | 1.86601 | + | 3.23202i | ||||
\(89\) | 18384.2 | − | 31842.4i | 0.246020 | − | 0.426119i | −0.716398 | − | 0.697692i | \(-0.754210\pi\) |
0.962418 | + | 0.271573i | \(0.0875437\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9217.51 | + | 3706.58i | −0.116684 | + | 0.0469213i | ||||
\(92\) | 92962.7 | 1.14509 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −61342.7 | − | 106249.i | −0.716050 | − | 1.24023i | ||||
\(95\) | −63855.9 | − | 110602.i | −0.725925 | − | 1.25734i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 36133.4 | 0.389924 | 0.194962 | − | 0.980811i | \(-0.437542\pi\) | ||||
0.194962 | + | 0.980811i | \(0.437542\pi\) | |||||||
\(98\) | 42623.0 | + | 173367.i | 0.448310 | + | 1.82348i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −57711.0 | + | 99958.4i | −0.577110 | + | 0.999584i | ||||
\(101\) | −49337.6 | − | 85455.2i | −0.481254 | − | 0.833557i | 0.518514 | − | 0.855069i | \(-0.326485\pi\) |
−0.999769 | + | 0.0215120i | \(0.993152\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3636.75 | + | 6299.03i | −0.0337769 | + | 0.0585034i | −0.882420 | − | 0.470463i | \(-0.844087\pi\) |
0.848643 | + | 0.528966i | \(0.177420\pi\) | |||||||
\(104\) | 39751.9 | 0.360392 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 49688.3 | 0.429526 | ||||||||
\(107\) | −15476.8 | + | 26806.5i | −0.130683 | + | 0.226350i | −0.923940 | − | 0.382537i | \(-0.875050\pi\) |
0.793257 | + | 0.608887i | \(0.208384\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −56915.6 | − | 98580.8i | −0.458844 | − | 0.794742i | 0.540056 | − | 0.841629i | \(-0.318403\pi\) |
−0.998900 | + | 0.0468875i | \(0.985070\pi\) | |||||||
\(110\) | −187302. | + | 324416.i | −1.47591 | + | 2.55635i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 53360.9 | − | 375226.i | 0.401955 | − | 2.82649i | ||||
\(113\) | 894.559 | 0.00659041 | 0.00329521 | − | 0.999995i | \(-0.498951\pi\) | ||||
0.00329521 | + | 0.999995i | \(0.498951\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 38799.7 | + | 67203.0i | 0.273579 | + | 0.473854i | ||||
\(116\) | −155607. | − | 269519.i | −1.07370 | − | 1.85970i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −309131. | −2.04379 | ||||||||
\(119\) | −129535. | − | 101546.i | −0.838535 | − | 0.657348i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −56054.3 | + | 97088.9i | −0.348053 | + | 0.602846i | ||||
\(122\) | −62899.6 | − | 108945.i | −0.382603 | − | 0.662687i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 420891. | − | 729005.i | 2.45819 | − | 4.25771i | ||||
\(125\) | 114513. | 0.655509 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 72325.9 | 0.397910 | 0.198955 | − | 0.980009i | \(-0.436245\pi\) | ||||
0.198955 | + | 0.980009i | \(0.436245\pi\) | |||||||
\(128\) | −87343.4 | + | 151283.i | −0.471200 | + | 0.816142i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 27463.1 | + | 47567.5i | 0.142525 | + | 0.246861i | ||||
\(131\) | −35084.0 | + | 60767.3i | −0.178620 | + | 0.309380i | −0.941408 | − | 0.337269i | \(-0.890497\pi\) |
0.762788 | + | 0.646649i | \(0.223830\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −34547.4 | + | 242932.i | −0.169350 | + | 1.19085i | ||||
\(134\) | −384662. | −1.85062 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 329291. | + | 570348.i | 1.52662 | + | 2.64419i | ||||
\(137\) | 186004. | + | 322169.i | 0.846685 | + | 1.46650i | 0.884150 | + | 0.467203i | \(0.154738\pi\) |
−0.0374656 | + | 0.999298i | \(0.511928\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5566.26 | 0.0244358 | 0.0122179 | − | 0.999925i | \(-0.496111\pi\) | ||||
0.0122179 | + | 0.999925i | \(0.496111\pi\) | |||||||
\(140\) | 656047. | − | 263812.i | 2.82888 | − | 1.13756i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −71581.9 | + | 123984.i | −0.297908 | + | 0.515992i | ||||
\(143\) | 20026.0 | + | 34686.1i | 0.0818944 | + | 0.141845i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 129891. | − | 224977.i | 0.513048 | − | 0.888625i | ||||
\(146\) | 27707.8 | 0.107577 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −452854. | −1.69943 | ||||||||
\(149\) | −166957. | + | 289178.i | −0.616083 | + | 1.06709i | 0.374110 | + | 0.927384i | \(0.377948\pi\) |
−0.990193 | + | 0.139703i | \(0.955385\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −37578.6 | − | 65088.1i | −0.134122 | − | 0.232305i | 0.791140 | − | 0.611635i | \(-0.209488\pi\) |
−0.925262 | + | 0.379330i | \(0.876155\pi\) | |||||||
\(152\) | 490907. | − | 850277.i | 1.72342 | − | 2.98505i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 667768. | − | 268525.i | 2.26894 | − | 0.912396i | ||||
\(155\) | 702667. | 2.34920 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −237792. | − | 411868.i | −0.769926 | − | 1.33355i | −0.937603 | − | 0.347708i | \(-0.886960\pi\) |
0.167677 | − | 0.985842i | \(-0.446373\pi\) | |||||||
\(158\) | 415972. | + | 720485.i | 1.32563 | + | 2.29606i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −975314. | −3.01193 | ||||||||
\(161\) | 20991.4 | − | 147609.i | 0.0638231 | − | 0.448794i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −119611. | + | 207173.i | −0.352617 | + | 0.610751i | −0.986707 | − | 0.162508i | \(-0.948042\pi\) |
0.634090 | + | 0.773259i | \(0.281375\pi\) | |||||||
\(164\) | −575243. | − | 996351.i | −1.67010 | − | 2.89270i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 88941.0 | − | 154050.i | 0.250514 | − | 0.433903i | ||||
\(167\) | 111308. | 0.308842 | 0.154421 | − | 0.988005i | \(-0.450649\pi\) | ||||
0.154421 | + | 0.988005i | \(0.450649\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −365420. | −0.984183 | ||||||||
\(170\) | −454989. | + | 788064.i | −1.20748 | + | 2.09141i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 599299. | + | 1.03802e6i | 1.54462 | + | 2.67537i | ||||
\(173\) | −349497. | + | 605346.i | −0.887826 | + | 1.53776i | −0.0453864 | + | 0.998970i | \(0.514452\pi\) |
−0.842440 | + | 0.538791i | \(0.818881\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 145685. | + | 114206.i | 0.359601 | + | 0.281900i | ||||
\(176\) | −1.52793e6 | −3.71810 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 195284. | + | 338241.i | 0.461972 | + | 0.800159i | ||||
\(179\) | 51954.4 | + | 89987.7i | 0.121196 | + | 0.209918i | 0.920240 | − | 0.391355i | \(-0.127994\pi\) |
−0.799043 | + | 0.601273i | \(0.794660\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −415260. | −0.942159 | −0.471079 | − | 0.882091i | \(-0.656135\pi\) | ||||
−0.471079 | + | 0.882091i | \(0.656135\pi\) | |||||||
\(182\) | 14858.1 | − | 104480.i | 0.0332495 | − | 0.233806i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −298282. | + | 516639.i | −0.649504 | + | 1.12497i | ||||
\(185\) | −189007. | − | 327370.i | −0.406021 | − | 0.703249i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −331777. | + | 574654.i | −0.693812 | + | 1.20172i | ||||
\(188\) | 933613. | 1.92651 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.35660e6 | 2.72626 | ||||||||
\(191\) | 285058. | − | 493735.i | 0.565392 | − | 0.979287i | −0.431621 | − | 0.902055i | \(-0.642058\pi\) |
0.997013 | − | 0.0772324i | \(-0.0246083\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −148854. | − | 257823.i | −0.287653 | − | 0.498229i | 0.685596 | − | 0.727982i | \(-0.259542\pi\) |
−0.973249 | + | 0.229753i | \(0.926208\pi\) | |||||||
\(194\) | −191911. | + | 332399.i | −0.366096 | + | 0.634097i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.30472e6 | − | 378747.i | −2.42591 | − | 0.704221i | ||||
\(197\) | −410678. | −0.753938 | −0.376969 | − | 0.926226i | \(-0.623034\pi\) | ||||
−0.376969 | + | 0.926226i | \(0.623034\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 349672. | + | 605650.i | 0.625934 | + | 1.08415i | 0.988359 | + | 0.152137i | \(0.0486155\pi\) |
−0.362425 | + | 0.932013i | \(0.618051\pi\) | |||||||
\(200\) | −370345. | − | 641457.i | −0.654684 | − | 1.13395i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.04816e6 | 1.80738 | ||||||||
\(203\) | −463086. | + | 186218.i | −0.788718 | + | 0.317162i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 480177. | − | 831691.i | 0.798025 | − | 1.38222i | ||||
\(206\) | −38630.8 | − | 66910.4i | −0.0634257 | − | 0.109857i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −112016. | + | 194018.i | −0.179524 | + | 0.310945i | ||||
\(209\) | 989226. | 1.56650 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −58292.9 | −0.0901384 | −0.0450692 | − | 0.998984i | \(-0.514351\pi\) | ||||
−0.0450692 | + | 0.998984i | \(0.514351\pi\) | |||||||
\(212\) | −189059. | + | 327460.i | −0.288907 | + | 0.500402i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −164399. | − | 284748.i | −0.245395 | − | 0.425036i | ||||
\(215\) | −500257. | + | 866471.i | −0.738069 | + | 1.27837i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.06250e6 | − | 832916.i | −1.53171 | − | 1.20075i | ||||
\(218\) | 1.20915e6 | 1.72322 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.42533e6 | − | 2.46875e6i | −1.98545 | − | 3.43890i | ||||
\(221\) | 48646.7 | + | 84258.6i | 0.0669997 | + | 0.116047i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25758.5 | 0.0346864 | 0.0173432 | − | 0.999850i | \(-0.494479\pi\) | ||||
0.0173432 | + | 0.999850i | \(0.494479\pi\) | |||||||
\(224\) | 1.47476e6 | + | 1.15610e6i | 1.96382 | + | 1.53949i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4751.15 | + | 8229.23i | −0.00618768 | + | 0.0107174i | ||||
\(227\) | −491123. | − | 850649.i | −0.632594 | − | 1.09569i | −0.987019 | − | 0.160601i | \(-0.948657\pi\) |
0.354425 | − | 0.935084i | \(-0.384677\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −259982. | + | 450301.i | −0.327607 | + | 0.567433i | −0.982037 | − | 0.188691i | \(-0.939576\pi\) |
0.654429 | + | 0.756123i | \(0.272909\pi\) | |||||||
\(230\) | −824286. | −1.02744 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.99713e6 | 2.43605 | ||||||||
\(233\) | 609703. | − | 1.05604e6i | 0.735747 | − | 1.27435i | −0.218648 | − | 0.975804i | \(-0.570165\pi\) |
0.954395 | − | 0.298547i | \(-0.0965020\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 389660. | + | 674912.i | 0.460274 | + | 0.797218i | ||||
\(236\) | 1.17621e6 | − | 2.03726e6i | 1.37469 | − | 2.38104i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.62213e6 | − | 652296.i | 1.85628 | − | 0.746453i | ||||
\(239\) | 909357. | 1.02977 | 0.514884 | − | 0.857260i | \(-0.327835\pi\) | ||||
0.514884 | + | 0.857260i | \(0.327835\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 320798. | + | 555638.i | 0.355786 | + | 0.616240i | 0.987252 | − | 0.159164i | \(-0.0508798\pi\) |
−0.631466 | + | 0.775404i | \(0.717546\pi\) | |||||||
\(242\) | −595428. | − | 1.03131e6i | −0.653568 | − | 1.13201i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 957308. | 1.02938 | ||||||||
\(245\) | −270749. | − | 1.10126e6i | −0.288172 | − | 1.17213i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 72522.6 | − | 125613.i | 0.0756365 | − | 0.131006i | ||||
\(248\) | 2.70096e6 | + | 4.67820e6i | 2.78862 | + | 4.83003i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −608196. | + | 1.05343e6i | −0.615451 | + | 1.06599i | ||||
\(251\) | −1.92052e6 | −1.92413 | −0.962066 | − | 0.272816i | \(-0.912045\pi\) | ||||
−0.962066 | + | 0.272816i | \(0.912045\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −601067. | −0.590366 | ||||||||
\(254\) | −384135. | + | 665342.i | −0.373594 | + | 0.647084i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 32041.3 | + | 55497.2i | 0.0305570 | + | 0.0529263i | ||||
\(257\) | −493184. | + | 854221.i | −0.465775 | + | 0.806747i | −0.999236 | − | 0.0390781i | \(-0.987558\pi\) |
0.533461 | + | 0.845825i | \(0.320891\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −102257. | + | 719054.i | −0.0947202 | + | 0.666058i | ||||
\(260\) | −417978. | −0.383460 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −372674. | − | 645491.i | −0.335410 | − | 0.580948i | ||||
\(263\) | 424509. | + | 735272.i | 0.378441 | + | 0.655479i | 0.990836 | − | 0.135073i | \(-0.0431270\pi\) |
−0.612395 | + | 0.790552i | \(0.709794\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −315630. | −0.276098 | ||||||||
\(266\) | −2.05130e6 | − | 1.60806e6i | −1.77756 | − | 1.39347i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.46360e6 | − | 2.53504e6i | 1.24476 | − | 2.15599i | ||||
\(269\) | −866792. | − | 1.50133e6i | −0.730355 | − | 1.26501i | −0.956732 | − | 0.290972i | \(-0.906021\pi\) |
0.226377 | − | 0.974040i | \(-0.427312\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 527825. | − | 914221.i | 0.436583 | − | 0.756184i | −0.560840 | − | 0.827924i | \(-0.689522\pi\) |
0.997423 | + | 0.0717397i | \(0.0228551\pi\) | |||||||
\(272\) | −3.71161e6 | −3.04187 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.95160e6 | −3.17978 | ||||||||
\(275\) | 373141. | − | 646299.i | 0.297537 | − | 0.515349i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −812463. | − | 1.40723e6i | −0.636216 | − | 1.10196i | −0.986256 | − | 0.165223i | \(-0.947166\pi\) |
0.350041 | − | 0.936735i | \(-0.386168\pi\) | |||||||
\(278\) | −29563.3 | + | 51205.2i | −0.0229425 | + | 0.0397377i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −638872. | + | 4.49245e6i | −0.486988 | + | 3.42443i | ||||
\(281\) | 1.56484e6 | 1.18224 | 0.591118 | − | 0.806585i | \(-0.298687\pi\) | ||||
0.591118 | + | 0.806585i | \(0.298687\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 347107. | + | 601206.i | 0.257630 | + | 0.446229i | 0.965607 | − | 0.260007i | \(-0.0837250\pi\) |
−0.707976 | + | 0.706236i | \(0.750392\pi\) | |||||||
\(284\) | −544725. | − | 943491.i | −0.400757 | − | 0.694132i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −425446. | −0.307560 | ||||||||
\(287\) | −1.71193e6 | + | 688406.i | −1.22682 | + | 0.493333i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −96015.8 | + | 166304.i | −0.0676236 | + | 0.117127i | ||||
\(290\) | 1.37974e6 | + | 2.38978e6i | 0.963392 | + | 1.66864i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −105426. | + | 182603.i | −0.0723585 | + | 0.125329i | ||||
\(293\) | −999262. | −0.680002 | −0.340001 | − | 0.940425i | \(-0.610427\pi\) | ||||
−0.340001 | + | 0.940425i | \(0.610427\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.96366e6 | 1.31374 | ||||||||
\(296\) | 1.45304e6 | − | 2.51673e6i | 0.963934 | − | 1.66958i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.77347e6 | − | 3.07175e6i | −1.15687 | − | 2.00376i | ||||
\(299\) | −44065.7 | + | 76324.0i | −0.0285051 | + | 0.0493723i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.78352e6 | − | 717195.i | 1.13465 | − | 0.456269i | ||||
\(302\) | 798346. | 0.503702 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.76664e6 | + | 4.79196e6i | 1.71699 | + | 2.97392i | ||||
\(305\) | 399550. | + | 692041.i | 0.245936 | + | 0.425973i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 800764. | 0.484907 | 0.242453 | − | 0.970163i | \(-0.422048\pi\) | ||||
0.242453 | + | 0.970163i | \(0.422048\pi\) | |||||||
\(308\) | −771134. | + | 5.42250e6i | −0.463184 | + | 3.25704i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.73198e6 | + | 6.46398e6i | −2.20564 | + | 3.82029i | ||||
\(311\) | −291472. | − | 504844.i | −0.170882 | − | 0.295976i | 0.767847 | − | 0.640634i | \(-0.221328\pi\) |
−0.938728 | + | 0.344658i | \(0.887995\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 999546. | − | 1.73126e6i | 0.576689 | − | 0.998855i | −0.419166 | − | 0.907909i | \(-0.637678\pi\) |
0.995856 | − | 0.0909459i | \(-0.0289890\pi\) | |||||||
\(314\) | 5.05182e6 | 2.89150 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.33095e6 | −3.56657 | ||||||||
\(317\) | 901038. | − | 1.56064e6i | 0.503610 | − | 0.872279i | −0.496381 | − | 0.868105i | \(-0.665338\pi\) |
0.999991 | − | 0.00417407i | \(-0.00132865\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.00610e6 | + | 1.74262e6i | 0.553561 | + | 0.958797i | ||||
\(320\) | 2.02390e6 | − | 3.50549e6i | 1.10488 | − | 1.91370i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.24639e6 | + | 977079.i | 0.669909 | + | 0.525158i | ||||
\(323\) | 2.40301e6 | 1.28159 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −54711.8 | − | 94763.6i | −0.0287324 | − | 0.0497660i | ||||
\(326\) | −1.27055e6 | − | 2.20066e6i | −0.662138 | − | 1.14686i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.38295e6 | 3.78918 | ||||||||
\(329\) | 210815. | − | 1.48242e6i | 0.107377 | − | 0.755058i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −51885.5 | + | 89868.4i | −0.0260301 | + | 0.0450855i | −0.878747 | − | 0.477288i | \(-0.841620\pi\) |
0.852717 | + | 0.522373i | \(0.174953\pi\) | |||||||
\(332\) | 676824. | + | 1.17229e6i | 0.337001 | + | 0.583702i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −591176. | + | 1.02395e6i | −0.289969 | + | 0.502240i | ||||
\(335\) | 2.44345e6 | 1.18957 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 961978. | 0.461414 | 0.230707 | − | 0.973023i | \(-0.425896\pi\) | ||||
0.230707 | + | 0.973023i | \(0.425896\pi\) | |||||||
\(338\) | 1.94081e6 | − | 3.36158e6i | 0.924040 | − | 1.60048i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.46238e6 | − | 5.99702e6i | −1.62434 | − | 2.81344i | ||||
\(341\) | −2.72135e6 | + | 4.71351e6i | −1.26735 | + | 2.19512i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −895997. | + | 1.98614e6i | −0.411217 | + | 0.911537i | ||||
\(344\) | −7.69169e6 | −3.50450 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.71247e6 | − | 6.43019e6i | −1.66714 | − | 2.88758i | ||||
\(347\) | 1.21674e6 | + | 2.10746e6i | 0.542468 | + | 0.939582i | 0.998762 | + | 0.0497528i | \(0.0158433\pi\) |
−0.456294 | + | 0.889829i | \(0.650823\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.42269e6 | −1.50419 | −0.752096 | − | 0.659053i | \(-0.770957\pi\) | ||||
−0.752096 | + | 0.659053i | \(0.770957\pi\) | |||||||
\(350\) | −1.82437e6 | + | 733621.i | −0.796053 | + | 0.320112i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.77728e6 | − | 6.54244e6i | 1.62488 | − | 2.81438i | ||||
\(353\) | 1.92748e6 | + | 3.33850e6i | 0.823292 | + | 1.42598i | 0.903218 | + | 0.429183i | \(0.141198\pi\) |
−0.0799253 | + | 0.996801i | \(0.525468\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 454702. | − | 787567.i | 0.191494 | − | 0.331678i | ||||
\(356\) | −2.97214e6 | −1.24292 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.10375e6 | −0.455161 | ||||||||
\(359\) | −1.24184e6 | + | 2.15094e6i | −0.508547 | + | 0.880829i | 0.491404 | + | 0.870932i | \(0.336484\pi\) |
−0.999951 | + | 0.00989749i | \(0.996849\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −553154. | − | 958091.i | −0.223397 | − | 0.386936i | ||||
\(362\) | 2.20552e6 | − | 3.82007e6i | 0.884584 | − | 1.53214i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 632020. | + | 495456.i | 0.250022 | + | 0.195998i | ||||
\(365\) | −176005. | −0.0691503 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.03612e6 | + | 3.52666e6i | 0.789111 | + | 1.36678i | 0.926512 | + | 0.376265i | \(0.122792\pi\) |
−0.137401 | + | 0.990516i | \(0.543875\pi\) | |||||||
\(368\) | −1.68105e6 | − | 2.91166e6i | −0.647083 | − | 1.12078i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.01539e6 | 1.52484 | ||||||||
\(371\) | 477260. | + | 374136.i | 0.180020 | + | 0.141122i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.34636e6 | − | 4.06402e6i | 0.873218 | − | 1.51246i | 0.0145699 | − | 0.999894i | \(-0.495362\pi\) |
0.858649 | − | 0.512565i | \(-0.171305\pi\) | |||||||
\(374\) | −3.52424e6 | − | 6.10417e6i | −1.30283 | − | 2.25656i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.99561e6 | + | 5.18854e6i | −1.09274 | + | 1.89267i | ||||
\(377\) | 295040. | 0.106912 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.04599e6 | 1.80446 | 0.902232 | − | 0.431251i | \(-0.141928\pi\) | ||||
0.902232 | + | 0.431251i | \(0.141928\pi\) | |||||||
\(380\) | −5.16173e6 | + | 8.94037e6i | −1.83373 | + | 3.17612i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.02798e6 | + | 5.24461e6i | 1.06168 | + | 1.83889i | ||||
\(383\) | 826418. | − | 1.43140e6i | 0.287874 | − | 0.498613i | −0.685428 | − | 0.728141i | \(-0.740385\pi\) |
0.973302 | + | 0.229528i | \(0.0737181\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.24179e6 | + | 1.70572e6i | −1.45847 | + | 0.586485i | ||||
\(386\) | 3.16236e6 | 1.08030 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.46040e6 | − | 2.52950e6i | −0.492486 | − | 0.853011i | ||||
\(389\) | 1.45727e6 | + | 2.52407e6i | 0.488278 | + | 0.845722i | 0.999909 | − | 0.0134832i | \(-0.00429195\pi\) |
−0.511631 | + | 0.859205i | \(0.670959\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.46010e6 | −0.482992 | ||||||||
\(392\) | 6.29122e6 | − | 6.03569e6i | 2.06785 | − | 1.98386i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.18118e6 | − | 3.77791e6i | 0.707865 | − | 1.22606i | ||||
\(395\) | −2.64234e6 | − | 4.57666e6i | −0.852109 | − | 1.47590i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 237471. | − | 411312.i | 0.0756197 | − | 0.130977i | −0.825736 | − | 0.564057i | \(-0.809240\pi\) |
0.901356 | + | 0.433080i | \(0.142573\pi\) | |||||||
\(398\) | −7.42867e6 | −2.35073 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.17436e6 | 1.30449 | ||||||||
\(401\) | 24440.9 | − | 42332.8i | 0.00759025 | − | 0.0131467i | −0.862205 | − | 0.506559i | \(-0.830917\pi\) |
0.869796 | + | 0.493412i | \(0.164251\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 399018. | + | 691119.i | 0.122385 | + | 0.211978i | ||||
\(404\) | −3.98816e6 | + | 6.90769e6i | −1.21568 | + | 2.10562i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 746470. | − | 5.24906e6i | 0.224749 | − | 1.58040i | ||||
\(407\) | 2.92801e6 | 0.876166 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.86947e6 | − | 3.23802e6i | −0.552599 | − | 0.957130i | −0.998086 | − | 0.0618416i | \(-0.980303\pi\) |
0.445487 | − | 0.895289i | \(-0.353031\pi\) | |||||||
\(410\) | 5.10060e6 | + | 8.83450e6i | 1.49852 | + | 2.59551i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 587946. | 0.170645 | ||||||||
\(413\) | −2.96923e6 | − | 2.32765e6i | −0.856581 | − | 0.671495i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −564970. | + | 978557.i | −0.161029 | + | 0.278911i | ||||
\(416\) | −553843. | − | 959285.i | −0.156911 | − | 0.271778i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5.25395e6 | + | 9.10010e6i | −1.47077 | + | 2.54745i | ||||
\(419\) | 681425. | 0.189619 | 0.0948097 | − | 0.995495i | \(-0.469776\pi\) | ||||
0.0948097 | + | 0.995495i | \(0.469776\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.54803e6 | 0.425670 | 0.212835 | − | 0.977088i | \(-0.431730\pi\) | ||||
0.212835 | + | 0.977088i | \(0.431730\pi\) | |||||||
\(422\) | 309604. | − | 536249.i | 0.0846301 | − | 0.146584i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.21324e6 | − | 2.10139e6i | −0.327742 | − | 0.567665i | ||||
\(425\) | 906425. | − | 1.56997e6i | 0.243422 | − | 0.421619i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 216165. | − | 1.52004e6i | 0.0573741 | − | 0.403446i | ||||
\(428\) | 2.50210e6 | 0.660229 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.31390e6 | − | 9.20394e6i | −1.38593 | − | 2.40051i | ||||
\(431\) | −3.18855e6 | − | 5.52273e6i | −0.826799 | − | 1.43206i | −0.900536 | − | 0.434781i | \(-0.856826\pi\) |
0.0737367 | − | 0.997278i | \(-0.476508\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.32669e6 | 0.340056 | 0.170028 | − | 0.985439i | \(-0.445614\pi\) | ||||
0.170028 | + | 0.985439i | \(0.445614\pi\) | |||||||
\(434\) | 1.33053e7 | − | 5.35036e6i | 3.39078 | − | 1.36351i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.60072e6 | + | 7.96868e6i | −1.15907 | + | 2.00757i | ||||
\(437\) | 1.08836e6 | + | 1.88509e6i | 0.272627 | + | 0.472203i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.92664e6 | + | 3.33704e6i | −0.477133 | + | 0.826419i | −0.999657 | − | 0.0262059i | \(-0.991657\pi\) |
0.522523 | + | 0.852625i | \(0.324991\pi\) | |||||||
\(440\) | 1.82934e7 | 4.50466 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.03348e6 | −0.251622 | ||||||||
\(443\) | −645522. | + | 1.11808e6i | −0.156279 | + | 0.270684i | −0.933524 | − | 0.358515i | \(-0.883283\pi\) |
0.777245 | + | 0.629198i | \(0.216617\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.24048e6 | − | 2.14857e6i | −0.296954 | − | 0.514339i | ||||
\(446\) | −136808. | + | 236958.i | −0.0325667 | + | 0.0564072i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7.21560e6 | + | 2.90156e6i | −1.69855 | + | 0.683026i | ||||
\(449\) | −7.49006e6 | −1.75335 | −0.876677 | − | 0.481080i | \(-0.840245\pi\) | ||||
−0.876677 | + | 0.481080i | \(0.840245\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.71934e6 | + | 6.44209e6i | 0.861042 | + | 1.49137i | ||||
\(452\) | −36155.4 | − | 62622.9i | −0.00832390 | − | 0.0144174i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.04337e7 | 2.37575 | ||||||||
\(455\) | −94381.7 | + | 663678.i | −0.0213727 | + | 0.150289i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −249662. | + | 432427.i | −0.0559193 | + | 0.0968550i | −0.892630 | − | 0.450790i | \(-0.851142\pi\) |
0.836711 | + | 0.547645i | \(0.184476\pi\) | |||||||
\(458\) | −2.76161e6 | − | 4.78325e6i | −0.615175 | − | 1.06551i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.13633e6 | − | 5.43229e6i | 0.691079 | − | 1.19698i | ||||
\(461\) | 5.34926e6 | 1.17231 | 0.586153 | − | 0.810200i | \(-0.300642\pi\) | ||||
0.586153 | + | 0.810200i | \(0.300642\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.52516e6 | −1.41462 | −0.707308 | − | 0.706906i | \(-0.750091\pi\) | ||||
−0.707308 | + | 0.706906i | \(0.750091\pi\) | |||||||
\(464\) | −5.62768e6 | + | 9.74743e6i | −1.21348 | + | 2.10182i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.47647e6 | + | 1.12176e7i | 1.38157 | + | 2.39295i | ||||
\(467\) | −1.60324e6 | + | 2.77690e6i | −0.340179 | + | 0.589207i | −0.984466 | − | 0.175577i | \(-0.943821\pi\) |
0.644287 | + | 0.764784i | \(0.277154\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.69471e6 | − | 2.89637e6i | −0.775619 | − | 0.608027i | ||||
\(470\) | −8.27821e6 | −1.72859 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.54804e6 | + | 1.30736e7i | 1.55948 | + | 2.70110i | ||||
\(473\) | −3.87488e6 | − | 6.71149e6i | −0.796352 | − | 1.37932i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.70260e6 | −0.549602 | ||||||||
\(476\) | −1.87322e6 | + | 1.31722e7i | −0.378941 | + | 2.66466i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.82975e6 | + | 8.36536e6i | −0.966840 | + | 1.67462i | ||||
\(479\) | −4.43405e6 | − | 7.68001e6i | −0.883003 | − | 1.52941i | −0.847985 | − | 0.530019i | \(-0.822185\pi\) |
−0.0350175 | − | 0.999387i | \(-0.511149\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 214660. | − | 371801.i | 0.0423046 | − | 0.0732737i | ||||
\(482\) | −6.81525e6 | −1.33618 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.06218e6 | 1.75841 | ||||||||
\(485\) | 1.21905e6 | − | 2.11146e6i | 0.235325 | − | 0.407595i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.92361e6 | − | 5.06384e6i | −0.558595 | − | 0.967515i | −0.997614 | − | 0.0690371i | \(-0.978007\pi\) |
0.439019 | − | 0.898478i | \(-0.355326\pi\) | |||||||
\(488\) | −3.07164e6 | + | 5.32023e6i | −0.583876 | + | 1.01130i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.15687e7 | + | 3.35829e6i | 2.17668 | + | 0.631871i | ||||
\(491\) | 114241. | 0.0213854 | 0.0106927 | − | 0.999943i | \(-0.496596\pi\) | ||||
0.0106927 | + | 0.999943i | \(0.496596\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.44400e6 | + | 4.23314e6i | 0.452881 | + | 0.784414i | ||||
\(494\) | 770360. | + | 1.33430e6i | 0.142029 | + | 0.246001i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.04439e7 | −5.55644 | ||||||||
\(497\) | −1.62110e6 | + | 651884.i | −0.294388 | + | 0.118380i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.67241e6 | − | 8.09285e6i | 0.840020 | − | 1.45496i | −0.0498573 | − | 0.998756i | \(-0.515877\pi\) |
0.889877 | − | 0.456200i | \(-0.150790\pi\) | |||||||
\(500\) | −4.62826e6 | − | 8.01638e6i | −0.827928 | − | 1.43401i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.02002e7 | − | 1.76673e7i | 1.80655 | − | 3.12904i | ||||
\(503\) | 892118. | 0.157218 | 0.0786091 | − | 0.996906i | \(-0.474952\pi\) | ||||
0.0786091 | + | 0.996906i | \(0.474952\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.65812e6 | −1.16178 | ||||||||
\(506\) | 3.19237e6 | − | 5.52934e6i | 0.554289 | − | 0.960057i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.92320e6 | − | 5.06313e6i | −0.502573 | − | 0.870481i | ||||
\(509\) | 3.42011e6 | − | 5.92381e6i | 0.585122 | − | 1.01346i | −0.409739 | − | 0.912203i | \(-0.634380\pi\) |
0.994860 | − | 0.101257i | \(-0.0322865\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 266136. | + | 208631.i | 0.0450870 | + | 0.0353448i | ||||
\(512\) | −6.27068e6 | −1.05716 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.23877e6 | − | 9.07382e6i | −0.874624 | − | 1.51489i | ||||
\(515\) | 245390. | + | 425028.i | 0.0407698 | + | 0.0706154i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.03644e6 | −0.993241 | ||||||||
\(518\) | −6.07163e6 | − | 4.75970e6i | −0.994216 | − | 0.779391i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.34113e6 | − | 2.32291e6i | 0.217502 | − | 0.376725i | ||||
\(521\) | 4.45943e6 | + | 7.72397e6i | 0.719756 | + | 1.24665i | 0.961096 | + | 0.276214i | \(0.0890798\pi\) |
−0.241340 | + | 0.970441i | \(0.577587\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −305911. | + | 529854.i | −0.0489037 | + | 0.0847036i | −0.889441 | − | 0.457050i | \(-0.848906\pi\) |
0.840537 | + | 0.541754i | \(0.182239\pi\) | |||||||
\(524\) | 5.67196e6 | 0.902413 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.01856e6 | −1.42126 | ||||||||
\(527\) | −6.61064e6 | + | 1.14500e7i | −1.03685 | + | 1.79588i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.55687e6 | + | 4.42863e6i | 0.397255 | + | 0.688066i | ||||
\(530\) | 1.67636e6 | − | 2.90354e6i | 0.259226 | − | 0.448992i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.84026e7 | − | 7.40012e6i | 2.81903 | − | 1.13360i | ||||
\(533\) | 1.09070e6 | 0.166298 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.04430e6 | + | 1.80877e6i | 0.157739 | + | 0.273212i | ||||
\(536\) | 9.39229e6 | + | 1.62679e7i | 1.41208 | + | 2.44580i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.84147e7 | 2.74289 | ||||||||
\(539\) | 8.43587e6 | + | 2.44886e6i | 1.25071 | + | 0.363071i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 122172. | − | 211607.i | 0.0179464 | − | 0.0310840i | −0.856913 | − | 0.515461i | \(-0.827621\pi\) |
0.874859 | + | 0.484377i | \(0.160954\pi\) | |||||||
\(542\) | 5.60674e6 | + | 9.71116e6i | 0.819808 | + | 1.41995i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 9.17568e6 | − | 1.58927e7i | 1.32936 | − | 2.30251i | ||||
\(545\) | −7.68078e6 | −1.10768 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.55551e6 | −1.07968 | −0.539840 | − | 0.841767i | \(-0.681515\pi\) | ||||
−0.539840 | + | 0.841767i | \(0.681515\pi\) | |||||||
\(548\) | 1.50355e7 | − | 2.60422e7i | 2.13878 | − | 3.70447i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.96363e6 | + | 6.86520e6i | 0.558709 | + | 0.967713i | ||||
\(551\) | 3.64353e6 | − | 6.31077e6i | 0.511261 | − | 0.885530i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.42956e6 | + | 1.00525e7i | −0.198788 | + | 1.39785i | ||||
\(554\) | 1.72605e7 | 2.38935 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −224972. | − | 389662.i | −0.0308632 | − | 0.0534566i | ||||
\(557\) | 1.28638e6 | + | 2.22808e6i | 0.175684 | + | 0.304293i | 0.940398 | − | 0.340077i | \(-0.110453\pi\) |
−0.764714 | + | 0.644370i | \(0.777120\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.13631e6 | −0.153804 | ||||||||
\(560\) | −2.01261e7 | − | 1.57773e7i | −2.71200 | − | 2.12600i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8.31113e6 | + | 1.43953e7i | −1.10999 | + | 1.92256i | ||||
\(563\) | 5.53466e6 | + | 9.58632e6i | 0.735903 | + | 1.27462i | 0.954326 | + | 0.298767i | \(0.0965752\pi\) |
−0.218424 | + | 0.975854i | \(0.570091\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 30180.2 | − | 52273.7i | 0.00397742 | − | 0.00688909i | ||||
\(566\) | −7.37416e6 | −0.967546 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.99126e6 | 0.909253 | ||||||||
\(569\) | 1.55605e6 | − | 2.69515e6i | 0.201485 | − | 0.348982i | −0.747522 | − | 0.664237i | \(-0.768757\pi\) |
0.949007 | + | 0.315255i | \(0.102090\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.86862e6 | − | 4.96859e6i | −0.368199 | − | 0.637739i | 0.621085 | − | 0.783743i | \(-0.286692\pi\) |
−0.989284 | + | 0.146004i | \(0.953359\pi\) | |||||||
\(572\) | 1.61878e6 | − | 2.80381e6i | 0.206870 | − | 0.358310i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.75953e6 | − | 1.94046e7i | 0.349587 | − | 2.45825i | ||||
\(575\) | 1.64214e6 | 0.207128 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.56528e6 | + | 9.63935e6i | 0.695901 | + | 1.20534i | 0.969876 | + | 0.243599i | \(0.0783282\pi\) |
−0.273975 | + | 0.961737i | \(0.588338\pi\) | |||||||
\(578\) | −1.01991e6 | − | 1.76654e6i | −0.126982 | − | 0.219940i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.09992e7 | −2.59198 | ||||||||
\(581\) | 2.01423e6 | − | 809970.i | 0.247554 | − | 0.0995472i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.22240e6 | − | 2.11725e6i | 0.148950 | − | 0.257989i | ||||
\(584\) | −676542. | − | 1.17180e6i | −0.0820848 | − | 0.142175i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.30725e6 | − | 9.19242e6i | 0.638448 | − | 1.10582i | ||||
\(587\) | −7.71211e6 | −0.923800 | −0.461900 | − | 0.886932i | \(-0.652832\pi\) | ||||
−0.461900 | + | 0.886932i | \(0.652832\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.97103e7 | 2.34102 | ||||||||
\(590\) | −1.04293e7 | + | 1.80641e7i | −1.23346 | + | 2.13642i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.18897e6 | + | 1.41837e7i | 0.960340 | + | 1.66336i | ||||
\(593\) | 4.16650e6 | − | 7.21660e6i | 0.486558 | − | 0.842744i | −0.513322 | − | 0.858196i | \(-0.671585\pi\) |
0.999881 | + | 0.0154520i | \(0.00491872\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.03041e7 | + | 4.14351e6i | −1.19321 | + | 0.479817i | ||||
\(596\) | 2.69916e7 | 3.11253 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −468081. | − | 810739.i | −0.0535264 | − | 0.0927104i | ||||
\(599\) | 2.66790e6 | + | 4.62094e6i | 0.303811 | + | 0.526216i | 0.976996 | − | 0.213258i | \(-0.0684076\pi\) |
−0.673185 | + | 0.739474i | \(0.735074\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.53972e6 | −0.851470 | −0.425735 | − | 0.904848i | \(-0.639984\pi\) | ||||
−0.425735 | + | 0.904848i | \(0.639984\pi\) | |||||||
\(602\) | −2.87493e6 | + | 2.02161e7i | −0.323323 | + | 2.27356i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.03763e6 | + | 5.26133e6i | −0.338799 | + | 0.586818i | ||||
\(605\) | 3.78227e6 | + | 6.55108e6i | 0.420111 | + | 0.727654i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.84283e6 | − | 8.38802e6i | 0.533491 | − | 0.924034i | −0.465744 | − | 0.884920i | \(-0.654213\pi\) |
0.999235 | − | 0.0391140i | \(-0.0124536\pi\) | |||||||
\(608\) | −2.73582e7 | −3.00144 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.48831e6 | −0.923627 | ||||||||
\(611\) | −442547. | + | 766513.i | −0.0479574 | + | 0.0830647i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.83805e6 | − | 1.18438e7i | −0.734989 | − | 1.27304i | −0.954728 | − | 0.297480i | \(-0.903854\pi\) |
0.219739 | − | 0.975559i | \(-0.429479\pi\) | |||||||
\(614\) | −4.25299e6 | + | 7.36639e6i | −0.455275 | + | 0.788559i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.76612e7 | − | 2.16843e7i | −2.93711 | − | 2.30247i | ||||
\(617\) | −1.53796e7 | −1.62642 | −0.813211 | − | 0.581969i | \(-0.802283\pi\) | ||||
−0.813211 | + | 0.581969i | \(0.802283\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.70804e6 | − | 4.69046e6i | −0.284072 | − | 0.492027i | 0.688312 | − | 0.725415i | \(-0.258352\pi\) |
−0.972384 | + | 0.233388i | \(0.925019\pi\) | |||||||
\(620\) | −2.83997e7 | − | 4.91897e7i | −2.96711 | − | 5.13919i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.19223e6 | 0.641757 | ||||||||
\(623\) | −671125. | + | 4.71925e6i | −0.0692761 | + | 0.487139i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.09446e6 | − | 1.05559e7i | 0.624072 | − | 1.08092i | ||||
\(626\) | 1.06175e7 | + | 1.83901e7i | 1.08290 | + | 1.87563i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.92217e7 | + | 3.32930e7i | −1.94488 | + | 3.36863i | ||||
\(629\) | 7.11266e6 | 0.716812 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.44178e7 | 1.44154 | 0.720770 | − | 0.693174i | \(-0.243788\pi\) | ||||
0.720770 | + | 0.693174i | \(0.243788\pi\) | |||||||
\(632\) | 2.03136e7 | − | 3.51842e7i | 2.02299 | − | 3.50392i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.57112e6 | + | 1.65777e7i | 0.945670 | + | 1.63795i | ||||
\(635\) | 2.44010e6 | − | 4.22638e6i | 0.240145 | − | 0.415943i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 929413. | − | 891663.i | 0.0907528 | − | 0.0870667i | ||||
\(638\) | −2.13743e7 | −2.07893 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 5.89350e6 | + | 1.02078e7i | 0.568753 | + | 0.985109i | ||||
\(641\) | 3.06909e6 | + | 5.31582e6i | 0.295029 | + | 0.511005i | 0.974992 | − | 0.222242i | \(-0.0713375\pi\) |
−0.679963 | + | 0.733247i | \(0.738004\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −402177. | −0.0383610 | −0.0191805 | − | 0.999816i | \(-0.506106\pi\) | ||||
−0.0191805 | + | 0.999816i | \(0.506106\pi\) | |||||||
\(644\) | −1.11817e7 | + | 4.49641e6i | −1.06241 | + | 0.427219i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.27628e7 | + | 2.21058e7i | −1.20327 | + | 2.08413i | ||||
\(647\) | 6.64081e6 | + | 1.15022e7i | 0.623678 | + | 1.08024i | 0.988795 | + | 0.149280i | \(0.0476955\pi\) |
−0.365117 | + | 0.930961i | \(0.618971\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.60502e6 | + | 1.31723e7i | −0.708743 | + | 1.22758i | ||||
\(650\) | 1.16233e6 | 0.107906 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.93373e7 | 1.78147 | ||||||||
\(653\) | 5.63657e6 | − | 9.76282e6i | 0.517287 | − | 0.895968i | −0.482511 | − | 0.875890i | \(-0.660275\pi\) |
0.999798 | − | 0.0200780i | \(-0.00639144\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.36730e6 | + | 4.10028e6i | 0.215601 | + | 0.373431i | ||||
\(656\) | −2.08043e7 | + | 3.60341e7i | −1.88753 | + | 3.26929i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.25174e7 | + | 9.81269e6i | 1.12707 | + | 0.883534i | ||||
\(659\) | −9.29624e6 | −0.833861 | −0.416930 | − | 0.908938i | \(-0.636894\pi\) | ||||
−0.416930 | + | 0.908938i | \(0.636894\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 314386. | + | 544533.i | 0.0279872 | + | 0.0484753i | 0.879680 | − | 0.475566i | \(-0.157757\pi\) |
−0.851693 | + | 0.524042i | \(0.824424\pi\) | |||||||
\(662\) | −551146. | − | 954612.i | −0.0488789 | − | 0.0846607i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.68669e6 | −0.764599 | ||||||||
\(665\) | 1.30302e7 | + | 1.02147e7i | 1.14261 | + | 0.895720i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.21385e6 | + | 3.83451e6i | −0.192679 | + | 0.333730i | ||||
\(668\) | −4.49874e6 | − | 7.79205e6i | −0.390077 | − | 0.675633i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.29776e7 | + | 2.24778e7i | −1.11688 | + | 1.93449i | ||||
\(671\) | −6.18965e6 | −0.530713 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.15635e6 | 0.438838 | 0.219419 | − | 0.975631i | \(-0.429584\pi\) | ||||
0.219419 | + | 0.975631i | \(0.429584\pi\) | |||||||
\(674\) | −5.10923e6 | + | 8.84944e6i | −0.433217 | + | 0.750354i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.47692e7 | + | 2.55810e7i | 1.24305 | + | 2.15303i | ||||
\(677\) | −3.28149e6 | + | 5.68370e6i | −0.275169 | + | 0.476606i | −0.970178 | − | 0.242395i | \(-0.922067\pi\) |
0.695009 | + | 0.719001i | \(0.255400\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.34617e6 | + | 1.74770e6i | −0.361770 | + | 0.145476i | ||||
\(680\) | 4.44379e7 | 3.68537 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.89071e7 | − | 5.00685e7i | −2.37982 | − | 4.12196i | ||||
\(683\) | −1.00766e7 | − | 1.74532e7i | −0.826540 | − | 1.43161i | −0.900737 | − | 0.434365i | \(-0.856973\pi\) |
0.0741975 | − | 0.997244i | \(-0.476360\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.51013e7 | 2.04395 | ||||||||
\(686\) | −1.35121e7 | − | 1.87912e7i | −1.09626 | − | 1.52456i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.16743e7 | − | 3.75410e7i | 1.74572 | − | 3.02367i | ||||
\(689\) | −179234. | − | 310442.i | −0.0143838 | − | 0.0249134i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.05979e6 | − | 8.76382e6i | 0.403123 | − | 0.698229i | −0.590978 | − | 0.806688i | \(-0.701258\pi\) |
0.994101 | + | 0.108458i | \(0.0345914\pi\) | |||||||
\(692\) | 5.65024e7 | 4.48541 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.58492e7 | −2.03727 | ||||||||
\(695\) | 187792. | − | 325265.i | 0.0147474 | − | 0.0255432i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.03494e6 | + | 1.56490e7i | 0.704439 | + | 1.22012i | ||||
\(698\) | 1.81785e7 | − | 3.14860e7i | 1.41227 | − | 2.44613i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.10677e6 | − | 1.48145e7i | 0.162507 | − | 1.14272i | ||||
\(701\) | 3.27446e6 | 0.251678 | 0.125839 | − | 0.992051i | \(-0.459838\pi\) | ||||
0.125839 | + | 0.992051i | \(0.459838\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.30178e6 | − | 9.18295e6i | −0.404607 | − | 0.700800i | ||||
\(704\) | 1.56767e7 | + | 2.71528e7i | 1.19212 | + | 2.06482i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.09488e7 | −3.09193 | ||||||||
\(707\) | 1.00677e7 | + | 7.89230e6i | 0.757496 | + | 0.593820i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.99723e6 | + | 5.19136e6i | −0.223926 | + | 0.387851i | −0.955997 | − | 0.293377i | \(-0.905221\pi\) |
0.732071 | + | 0.681229i | \(0.238554\pi\) | |||||||
\(710\) | 4.83000e6 | + | 8.36580e6i | 0.359585 | + | 0.622819i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.53647e6 | − | 1.65177e7i | 0.704998 | − | 1.22109i | ||||
\(713\) | −1.19762e7 | −0.882260 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.70251e6 | 0.197698 | ||||||||
\(716\) | 4.19968e6 | − | 7.27406e6i | 0.306150 | − | 0.530267i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.31913e7 | − | 2.28480e7i | −0.954940 | − | 1.65400i | ||||
\(719\) | 1.23868e7 | − | 2.14546e7i | 0.893590 | − | 1.54774i | 0.0580490 | − | 0.998314i | \(-0.481512\pi\) |
0.835541 | − | 0.549429i | \(-0.185155\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 132761. | − | 933557.i | 0.00951115 | − | 0.0668810i | ||||
\(722\) | 1.17516e7 | 0.838983 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.67836e7 | + | 2.90700e7i | 1.18998 | + | 2.06110i | ||||
\(725\) | −2.74871e6 | − | 4.76091e6i | −0.194215 | − | 0.336391i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.16194e7 | −0.815357 | −0.407678 | − | 0.913126i | \(-0.633662\pi\) | ||||
−0.407678 | + | 0.913126i | \(0.633662\pi\) | |||||||
\(728\) | −4.78141e6 | + | 1.92272e6i | −0.334370 | + | 0.134458i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 934794. | − | 1.61911e6i | 0.0649245 | − | 0.112453i | ||||
\(731\) | −9.41277e6 | − | 1.63034e7i | −0.651514 | − | 1.12846i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.37168e6 | − | 1.10361e7i | 0.438020 | − | 0.758674i | −0.559516 | − | 0.828819i | \(-0.689013\pi\) |
0.997537 | + | 0.0701457i | \(0.0223464\pi\) | |||||||
\(734\) | −4.32567e7 | −2.96356 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.66232e7 | 1.13115 | ||||||||
\(737\) | −9.46319e6 | + | 1.63907e7i | −0.641754 | + | 1.11155i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.04589e6 | − | 1.04718e7i | −0.407238 | − | 0.705358i | 0.587341 | − | 0.809340i | \(-0.300175\pi\) |
−0.994579 | + | 0.103982i | \(0.966842\pi\) | |||||||
\(740\) | −1.52782e7 | + | 2.64626e7i | −1.02563 | + | 1.77645i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.97656e6 | + | 2.40332e6i | −0.398512 | + | 0.160251i | ||||
\(743\) | −9.79136e6 | −0.650685 | −0.325343 | − | 0.945596i | \(-0.605480\pi\) | ||||
−0.325343 | + | 0.945596i | \(0.605480\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.12654e7 | + | 1.95123e7i | 0.743632 | + | 1.28801i | ||||
\(746\) | 2.49238e7 | + | 4.31694e7i | 1.63971 | + | 2.84007i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5.36376e7 | 3.50522 | ||||||||
\(749\) | 564986. | − | 3.97290e6i | 0.0367988 | − | 0.258763i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.76513e6 | − | 1.51816e7i | 0.567098 | − | 0.982243i | −0.429753 | − | 0.902947i | \(-0.641399\pi\) |
0.996851 | − | 0.0792967i | \(-0.0252674\pi\) | |||||||
\(752\) | −1.68825e7 | − | 2.92414e7i | −1.08866 | − | 1.88562i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.56701e6 | + | 2.71413e6i | −0.100379 | + | 0.173861i | ||||
\(755\) | −5.07125e6 | −0.323778 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.01558e6 | 0.381538 | 0.190769 | − | 0.981635i | \(-0.438902\pi\) | ||||
0.190769 | + | 0.981635i | \(0.438902\pi\) | |||||||
\(758\) | −2.68001e7 | + | 4.64191e7i | −1.69419 | + | 2.93443i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.31240e7 | − | 5.73725e7i | −2.08022 | − | 3.60305i | ||||
\(761\) | 6.38402e6 | − | 1.10575e7i | 0.399607 | − | 0.692139i | −0.594071 | − | 0.804413i | \(-0.702480\pi\) |
0.993677 | + | 0.112274i | \(0.0358133\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.16140e7 | + | 9.10452e6i | 0.722223 | + | 0.566168i | ||||
\(764\) | −4.60847e7 | −2.85643 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.77849e6 | + | 1.52048e7i | 0.540565 | + | 0.936286i | ||||
\(767\) | 1.11509e6 | + | 1.93139e6i | 0.0684416 | + | 0.118544i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.32718e6 | −0.385829 | −0.192914 | − | 0.981216i | \(-0.561794\pi\) | ||||
−0.192914 | + | 0.981216i | \(0.561794\pi\) | |||||||
\(770\) | 6.83754e6 | − | 4.80805e7i | 0.415597 | − | 2.92242i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.20325e7 | + | 2.08409e7i | −0.726628 | + | 1.25856i | ||||
\(773\) | −8.10085e6 | − | 1.40311e7i | −0.487620 | − | 0.844583i | 0.512279 | − | 0.858819i | \(-0.328802\pi\) |
−0.999899 | + | 0.0142365i | \(0.995468\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.43482e6 | − | 1.28775e7i | 0.444648 |