Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,6,Mod(107,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.107");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.3214525398\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 30x^{14} + 619x^{12} + 5604x^{10} + 40971x^{8} - 4866x^{6} + 568069x^{4} - 7909632x^{2} + 20340100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{30}\cdot 3^{32}\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 107.2 | ||
Root | \(-1.73205 - 3.53958i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.107 |
Dual form | 108.6.b.b.107.1 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.65395 | + | 0.181119i | −0.999487 | + | 0.0320176i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 31.9344 | − | 2.04808i | 0.997950 | − | 0.0640025i | ||||
\(5\) | − | 69.1814i | − | 1.23755i | −0.785567 | − | 0.618777i | \(-0.787628\pi\) | ||
0.785567 | − | 0.618777i | \(-0.212372\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 238.886i | − | 1.84266i | −0.388779 | − | 0.921331i | \(-0.627103\pi\) | ||
0.388779 | − | 0.921331i | \(-0.372897\pi\) | |||||||
\(8\) | −180.185 | + | 17.3637i | −0.995389 | + | 0.0959216i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 12.5301 | + | 391.148i | 0.0396236 | + | 1.23692i | ||||
\(11\) | −350.956 | −0.874521 | −0.437261 | − | 0.899335i | \(-0.644051\pi\) | ||||
−0.437261 | + | 0.899335i | \(0.644051\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 669.928 | 1.09944 | 0.549718 | − | 0.835350i | \(-0.314735\pi\) | ||||
0.549718 | + | 0.835350i | \(0.314735\pi\) | |||||||
\(14\) | 43.2668 | + | 1350.65i | 0.0589977 | + | 1.84172i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1015.61 | − | 130.808i | 0.991807 | − | 0.127742i | ||||
\(17\) | − | 1396.15i | − | 1.17168i | −0.810425 | − | 0.585842i | \(-0.800764\pi\) | ||
0.810425 | − | 0.585842i | \(-0.199236\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1789.28i | 1.13709i | 0.822652 | + | 0.568545i | \(0.192493\pi\) | ||||
−0.822652 | + | 0.568545i | \(0.807507\pi\) | |||||||
\(20\) | −141.689 | − | 2209.26i | −0.0792065 | − | 1.23502i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1984.29 | − | 63.5648i | 0.874073 | − | 0.0280001i | ||||
\(23\) | −1322.78 | −0.521397 | −0.260698 | − | 0.965420i | \(-0.583953\pi\) | ||||
−0.260698 | + | 0.965420i | \(0.583953\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1661.06 | −0.531540 | ||||||||
\(26\) | −3787.74 | + | 121.337i | −1.09887 | + | 0.0352014i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −489.257 | − | 7628.68i | −0.117935 | − | 1.83888i | ||||
\(29\) | 6894.21i | 1.52226i | 0.648598 | + | 0.761131i | \(0.275356\pi\) | ||||
−0.648598 | + | 0.761131i | \(0.724644\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2334.13i | − | 0.436236i | −0.975922 | − | 0.218118i | \(-0.930008\pi\) | ||
0.975922 | − | 0.218118i | \(-0.0699918\pi\) | |||||||
\(32\) | −5718.52 | + | 923.531i | −0.987209 | + | 0.159432i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 252.870 | + | 7893.79i | 0.0375146 | + | 1.17108i | ||||
\(35\) | −16526.5 | −2.28039 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −12929.6 | −1.55268 | −0.776341 | − | 0.630314i | \(-0.782926\pi\) | ||||
−0.776341 | + | 0.630314i | \(0.782926\pi\) | |||||||
\(38\) | −324.073 | − | 10116.5i | −0.0364069 | − | 1.13651i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1201.24 | + | 12465.4i | 0.118708 | + | 1.23185i | ||||
\(41\) | − | 8719.02i | − | 0.810043i | −0.914307 | − | 0.405021i | \(-0.867264\pi\) | ||
0.914307 | − | 0.405021i | \(-0.132736\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 10647.8i | − | 0.878189i | −0.898441 | − | 0.439095i | \(-0.855299\pi\) | ||
0.898441 | − | 0.439095i | \(-0.144701\pi\) | |||||||
\(44\) | −11207.6 | + | 718.785i | −0.872728 | + | 0.0559715i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7478.94 | − | 239.581i | 0.521130 | − | 0.0166939i | ||||
\(47\) | 3988.75 | 0.263386 | 0.131693 | − | 0.991291i | \(-0.457959\pi\) | ||||
0.131693 | + | 0.991291i | \(0.457959\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −40259.6 | −2.39540 | ||||||||
\(50\) | 9391.56 | − | 300.850i | 0.531267 | − | 0.0170186i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 21393.8 | − | 1372.07i | 1.09718 | − | 0.0703666i | ||||
\(53\) | 4057.38i | 0.198406i | 0.995067 | + | 0.0992032i | \(0.0316294\pi\) | ||||
−0.995067 | + | 0.0992032i | \(0.968371\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 24279.6i | 1.08227i | ||||||||
\(56\) | 4147.94 | + | 43043.6i | 0.176751 | + | 1.83417i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1248.67 | − | 38979.5i | −0.0487393 | − | 1.52148i | ||||
\(59\) | 25135.6 | 0.940068 | 0.470034 | − | 0.882648i | \(-0.344242\pi\) | ||||
0.470034 | + | 0.882648i | \(0.344242\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8968.91 | 0.308614 | 0.154307 | − | 0.988023i | \(-0.450686\pi\) | ||||
0.154307 | + | 0.988023i | \(0.450686\pi\) | |||||||
\(62\) | 422.756 | + | 13197.1i | 0.0139673 | + | 0.436012i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 32165.0 | − | 6257.33i | 0.981598 | − | 0.190959i | ||||
\(65\) | − | 46346.6i | − | 1.36061i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 12405.9i | − | 0.337631i | −0.985648 | − | 0.168815i | \(-0.946006\pi\) | ||
0.985648 | − | 0.168815i | \(-0.0539942\pi\) | |||||||
\(68\) | −2859.43 | − | 44585.3i | −0.0749907 | − | 1.16928i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 93439.9 | − | 2993.26i | 2.27922 | − | 0.0730128i | ||||
\(71\) | −6503.43 | −0.153108 | −0.0765538 | − | 0.997065i | \(-0.524392\pi\) | ||||
−0.0765538 | + | 0.997065i | \(0.524392\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −45851.0 | −1.00703 | −0.503515 | − | 0.863987i | \(-0.667960\pi\) | ||||
−0.503515 | + | 0.863987i | \(0.667960\pi\) | |||||||
\(74\) | 73103.6 | − | 2341.81i | 1.55189 | − | 0.0497132i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3664.59 | + | 57139.6i | 0.0727766 | + | 1.13476i | ||||
\(77\) | 83838.4i | 1.61145i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 37453.2i | 0.675182i | 0.941293 | + | 0.337591i | \(0.109612\pi\) | ||||
−0.941293 | + | 0.337591i | \(0.890388\pi\) | |||||||
\(80\) | −9049.50 | − | 70261.3i | −0.158088 | − | 1.22742i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1579.18 | + | 49296.9i | 0.0259357 | + | 0.809628i | ||||
\(83\) | 48693.7 | 0.775849 | 0.387925 | − | 0.921691i | \(-0.373192\pi\) | ||||
0.387925 | + | 0.921691i | \(0.373192\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −96587.8 | −1.45002 | ||||||||
\(86\) | 1928.52 | + | 60202.1i | 0.0281175 | + | 0.877739i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 63236.8 | − | 6093.88i | 0.870489 | − | 0.0838855i | ||||
\(89\) | 7935.52i | 0.106194i | 0.998589 | + | 0.0530971i | \(0.0169093\pi\) | ||||
−0.998589 | + | 0.0530971i | \(0.983091\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 160037.i | − | 2.02589i | ||||||
\(92\) | −42242.2 | + | 2709.16i | −0.520328 | + | 0.0333707i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −22552.2 | + | 722.439i | −0.263251 | + | 0.00843299i | ||||
\(95\) | 123785. | 1.40721 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 56596.2 | 0.610742 | 0.305371 | − | 0.952233i | \(-0.401219\pi\) | ||||
0.305371 | + | 0.952233i | \(0.401219\pi\) | |||||||
\(98\) | 227626. | − | 7291.78i | 2.39418 | − | 0.0766952i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −53045.0 | + | 3401.98i | −0.530450 | + | 0.0340198i | ||||
\(101\) | 72884.7i | 0.710940i | 0.934688 | + | 0.355470i | \(0.115679\pi\) | ||||
−0.934688 | + | 0.355470i | \(0.884321\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 97537.9i | 0.905900i | 0.891536 | + | 0.452950i | \(0.149628\pi\) | ||||
−0.891536 | + | 0.452950i | \(0.850372\pi\) | |||||||
\(104\) | −120711. | + | 11632.4i | −1.09437 | + | 0.105460i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −734.869 | − | 22940.2i | −0.00635251 | − | 0.198305i | ||||
\(107\) | 16437.8 | 0.138798 | 0.0693990 | − | 0.997589i | \(-0.477892\pi\) | ||||
0.0693990 | + | 0.997589i | \(0.477892\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −173939. | −1.40226 | −0.701132 | − | 0.713032i | \(-0.747322\pi\) | ||||
−0.701132 | + | 0.713032i | \(0.747322\pi\) | |||||||
\(110\) | −4397.50 | − | 137276.i | −0.0346517 | − | 1.08171i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −31248.3 | − | 242615.i | −0.235386 | − | 1.82757i | ||||
\(113\) | − | 228039.i | − | 1.68002i | −0.542573 | − | 0.840009i | \(-0.682550\pi\) | ||
0.542573 | − | 0.840009i | \(-0.317450\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 91511.8i | 0.645257i | ||||||||
\(116\) | 14119.9 | + | 220162.i | 0.0974285 | + | 1.51914i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −142116. | + | 4552.54i | −0.939586 | + | 0.0300988i | ||||
\(119\) | −333522. | −2.15902 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −37881.2 | −0.235212 | ||||||||
\(122\) | −50709.8 | + | 1624.44i | −0.308455 | + | 0.00988108i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4780.49 | − | 74539.2i | −0.0279202 | − | 0.435342i | ||||
\(125\) | − | 101277.i | − | 0.579745i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 170464.i | 0.937827i | 0.883244 | + | 0.468913i | \(0.155354\pi\) | ||||
−0.883244 | + | 0.468913i | \(0.844646\pi\) | |||||||
\(128\) | −180726. | + | 41204.4i | −0.974981 | + | 0.222289i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8394.25 | + | 262041.i | 0.0435636 | + | 1.35991i | ||||
\(131\) | 29943.1 | 0.152447 | 0.0762234 | − | 0.997091i | \(-0.475714\pi\) | ||||
0.0762234 | + | 0.997091i | \(0.475714\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 427435. | 2.09527 | ||||||||
\(134\) | 2246.95 | + | 70142.5i | 0.0108101 | + | 0.337458i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 24242.4 | + | 251565.i | 0.112390 | + | 1.16628i | ||||
\(137\) | 171047.i | 0.778600i | 0.921111 | + | 0.389300i | \(0.127283\pi\) | ||||
−0.921111 | + | 0.389300i | \(0.872717\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 263941.i | − | 1.15870i | −0.815080 | − | 0.579348i | \(-0.803307\pi\) | ||
0.815080 | − | 0.579348i | \(-0.196693\pi\) | |||||||
\(140\) | −527763. | + | 33847.5i | −2.27572 | + | 0.145951i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 36770.1 | − | 1177.90i | 0.153029 | − | 0.00490215i | ||||
\(143\) | −235115. | −0.961480 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 476951. | 1.88388 | ||||||||
\(146\) | 259240. | − | 8304.50i | 1.00651 | − | 0.0322427i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −412900. | + | 26480.9i | −1.54950 | + | 0.0993754i | ||||
\(149\) | 47653.0i | 0.175843i | 0.996127 | + | 0.0879215i | \(0.0280225\pi\) | ||||
−0.996127 | + | 0.0879215i | \(0.971978\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 351084.i | − | 1.25305i | −0.779402 | − | 0.626525i | \(-0.784477\pi\) | ||
0.779402 | − | 0.626525i | \(-0.215523\pi\) | |||||||
\(152\) | −31068.5 | − | 322401.i | −0.109072 | − | 1.13185i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −15184.7 | − | 474018.i | −0.0515948 | − | 1.61062i | ||||
\(155\) | −161479. | −0.539866 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 285818. | 0.925424 | 0.462712 | − | 0.886509i | \(-0.346876\pi\) | ||||
0.462712 | + | 0.886509i | \(0.346876\pi\) | |||||||
\(158\) | −6783.49 | − | 211759.i | −0.0216177 | − | 0.674836i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 63891.1 | + | 395615.i | 0.197306 | + | 1.22172i | ||||
\(161\) | 315994.i | 0.960758i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 128969.i | 0.380203i | 0.981764 | + | 0.190101i | \(0.0608816\pi\) | ||||
−0.981764 | + | 0.190101i | \(0.939118\pi\) | |||||||
\(164\) | −17857.2 | − | 278437.i | −0.0518447 | − | 0.808382i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −275312. | + | 8819.36i | −0.775452 | + | 0.0248409i | ||||
\(167\) | 559823. | 1.55331 | 0.776657 | − | 0.629924i | \(-0.216914\pi\) | ||||
0.776657 | + | 0.629924i | \(0.216914\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 77511.0 | 0.208760 | ||||||||
\(170\) | 546103. | − | 17493.9i | 1.44928 | − | 0.0464263i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −21807.5 | − | 340030.i | −0.0562063 | − | 0.876389i | ||||
\(173\) | − | 523424.i | − | 1.32965i | −0.746997 | − | 0.664827i | \(-0.768505\pi\) | ||
0.746997 | − | 0.664827i | \(-0.231495\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 396804.i | 0.979448i | ||||||||
\(176\) | −356434. | + | 45907.9i | −0.867357 | + | 0.111714i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1437.28 | − | 44867.1i | −0.00340009 | − | 0.106140i | ||||
\(179\) | −715299. | −1.66861 | −0.834305 | − | 0.551303i | \(-0.814131\pi\) | ||||
−0.834305 | + | 0.551303i | \(0.814131\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 286861. | 0.650841 | 0.325420 | − | 0.945569i | \(-0.394494\pi\) | ||||
0.325420 | + | 0.945569i | \(0.394494\pi\) | |||||||
\(182\) | 28985.7 | + | 904839.i | 0.0648642 | + | 2.02485i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 238345. | − | 22968.3i | 0.518993 | − | 0.0500132i | ||||
\(185\) | 894490.i | 1.92153i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 489988.i | 1.02466i | ||||||||
\(188\) | 127378. | − | 8169.28i | 0.262846 | − | 0.0168573i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −699875. | + | 22419.8i | −1.40649 | + | 0.0450556i | ||||
\(191\) | 121929. | 0.241838 | 0.120919 | − | 0.992662i | \(-0.461416\pi\) | ||||
0.120919 | + | 0.992662i | \(0.461416\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 237611. | 0.459170 | 0.229585 | − | 0.973289i | \(-0.426263\pi\) | ||||
0.229585 | + | 0.973289i | \(0.426263\pi\) | |||||||
\(194\) | −319992. | + | 10250.7i | −0.610429 | + | 0.0195545i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.28566e6 | + | 82454.7i | −2.39049 | + | 0.153312i | ||||
\(197\) | − | 667755.i | − | 1.22589i | −0.790126 | − | 0.612945i | \(-0.789985\pi\) | ||
0.790126 | − | 0.612945i | \(-0.210015\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 230496.i | 0.412602i | 0.978489 | + | 0.206301i | \(0.0661425\pi\) | ||||
−0.978489 | + | 0.206301i | \(0.933857\pi\) | |||||||
\(200\) | 299298. | − | 28842.1i | 0.529089 | − | 0.0509862i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −13200.8 | − | 412087.i | −0.0227626 | − | 0.710576i | ||||
\(203\) | 1.64693e6 | 2.80502 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −603194. | −1.00247 | ||||||||
\(206\) | −17666.0 | − | 551475.i | −0.0290048 | − | 0.905436i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 680386. | − | 87632.2i | 1.09043 | − | 0.140445i | ||||
\(209\) | − | 627959.i | − | 0.994410i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 788636.i | − | 1.21947i | −0.792606 | − | 0.609734i | \(-0.791276\pi\) | ||
0.792606 | − | 0.609734i | \(-0.208724\pi\) | |||||||
\(212\) | 8309.83 | + | 129570.i | 0.0126985 | + | 0.198000i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −92938.3 | + | 2977.19i | −0.138727 | + | 0.00444398i | ||||
\(215\) | −736628. | −1.08681 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −557592. | −0.803836 | ||||||||
\(218\) | 983441. | − | 31503.6i | 1.40154 | − | 0.0448972i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 49726.5 | + | 775354.i | 0.0692678 | + | 1.08005i | ||||
\(221\) | − | 935323.i | − | 1.28819i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.42387e6i | − | 1.91738i | −0.284450 | − | 0.958691i | \(-0.591811\pi\) | ||
0.284450 | − | 0.958691i | \(-0.408189\pi\) | |||||||
\(224\) | 220619. | + | 1.36608e6i | 0.293780 | + | 1.81909i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 41302.3 | + | 1.28932e6i | 0.0537902 | + | 1.67916i | ||||
\(227\) | 714849. | 0.920767 | 0.460383 | − | 0.887720i | \(-0.347712\pi\) | ||||
0.460383 | + | 0.887720i | \(0.347712\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 640469. | 0.807066 | 0.403533 | − | 0.914965i | \(-0.367782\pi\) | ||||
0.403533 | + | 0.914965i | \(0.367782\pi\) | |||||||
\(230\) | −16574.5 | − | 517404.i | −0.0206596 | − | 0.644926i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −119709. | − | 1.24223e6i | −0.146018 | − | 1.51524i | ||||
\(233\) | 965359.i | 1.16493i | 0.812857 | + | 0.582464i | \(0.197911\pi\) | ||||
−0.812857 | + | 0.582464i | \(0.802089\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 275947.i | − | 0.325954i | ||||||
\(236\) | 802690. | − | 51479.7i | 0.938141 | − | 0.0601667i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.88572e6 | − | 60407.2i | 2.15791 | − | 0.0691267i | ||||
\(239\) | 657323. | 0.744361 | 0.372181 | − | 0.928160i | \(-0.378610\pi\) | ||||
0.372181 | + | 0.928160i | \(0.378610\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.08719e6 | −1.20577 | −0.602885 | − | 0.797828i | \(-0.705982\pi\) | ||||
−0.602885 | + | 0.797828i | \(0.705982\pi\) | |||||||
\(242\) | 214178. | − | 6861.00i | 0.235092 | − | 0.00753094i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 286417. | − | 18369.0i | 0.307981 | − | 0.0197520i | ||||
\(245\) | 2.78521e6i | 2.96444i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.19869e6i | 1.25016i | ||||||||
\(248\) | 40529.1 | + | 420575.i | 0.0418445 | + | 0.434225i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 18343.3 | + | 572617.i | 0.0185621 | + | 0.579448i | ||||
\(251\) | 51518.6 | 0.0516155 | 0.0258077 | − | 0.999667i | \(-0.491784\pi\) | ||||
0.0258077 | + | 0.999667i | \(0.491784\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 464237. | 0.455973 | ||||||||
\(254\) | −30874.2 | − | 963794.i | −0.0300270 | − | 0.937346i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.01435e6 | − | 265701.i | 0.967364 | − | 0.253392i | ||||
\(257\) | − | 1.05873e6i | − | 0.999888i | −0.866058 | − | 0.499944i | \(-0.833354\pi\) | ||
0.866058 | − | 0.499944i | \(-0.166646\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.08871e6i | 2.86107i | ||||||||
\(260\) | −94921.4 | − | 1.48005e6i | −0.0870825 | − | 1.35782i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −169297. | + | 5423.26i | −0.152369 | + | 0.00488098i | ||||
\(263\) | −1.68934e6 | −1.50601 | −0.753004 | − | 0.658016i | \(-0.771396\pi\) | ||||
−0.753004 | + | 0.658016i | \(0.771396\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 280695. | 0.245539 | ||||||||
\(266\) | −2.41670e6 | + | 77416.6i | −2.09420 | + | 0.0670857i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −25408.3 | − | 396176.i | −0.0216092 | − | 0.336939i | ||||
\(269\) | − | 930054.i | − | 0.783660i | −0.920038 | − | 0.391830i | \(-0.871842\pi\) | ||
0.920038 | − | 0.391830i | \(-0.128158\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 2.01579e6i | − | 1.66733i | −0.552272 | − | 0.833664i | \(-0.686239\pi\) | ||
0.552272 | − | 0.833664i | \(-0.313761\pi\) | |||||||
\(272\) | −182628. | − | 1.41795e6i | −0.149674 | − | 1.16209i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −30979.9 | − | 967093.i | −0.0249289 | − | 0.778201i | ||||
\(275\) | 582959. | 0.464843 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.46037e6 | −1.92664 | −0.963320 | − | 0.268354i | \(-0.913520\pi\) | ||||
−0.963320 | + | 0.268354i | \(0.913520\pi\) | |||||||
\(278\) | 47804.8 | + | 1.49231e6i | 0.0370987 | + | 1.15810i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.97782e6 | − | 286960.i | 2.26988 | − | 0.218739i | ||||
\(281\) | − | 1.20772e6i | − | 0.912433i | −0.889869 | − | 0.456217i | \(-0.849204\pi\) | ||
0.889869 | − | 0.456217i | \(-0.150796\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 516965.i | 0.383703i | 0.981424 | + | 0.191852i | \(0.0614492\pi\) | ||||
−0.981424 | + | 0.191852i | \(0.938551\pi\) | |||||||
\(284\) | −207683. | + | 13319.5i | −0.152794 | + | 0.00979927i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.32933e6 | − | 42583.9i | 0.960988 | − | 0.0307843i | ||||
\(287\) | −2.08285e6 | −1.49264 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −529388. | −0.372846 | ||||||||
\(290\) | −2.69666e6 | + | 86384.9i | −1.88292 | + | 0.0603175i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.46423e6 | + | 93906.5i | −1.00496 | + | 0.0644523i | ||||
\(293\) | 2.06534e6i | 1.40547i | 0.711451 | + | 0.702736i | \(0.248038\pi\) | ||||
−0.711451 | + | 0.702736i | \(0.751962\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 1.73892e6i | − | 1.16338i | ||||||
\(296\) | 2.32972e6 | − | 224506.i | 1.54552 | − | 0.148936i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8630.88 | − | 269428.i | −0.00563008 | − | 0.175753i | ||||
\(299\) | −886169. | −0.573243 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.54361e6 | −1.61821 | ||||||||
\(302\) | 63588.0 | + | 1.98501e6i | 0.0401197 | + | 1.25241i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 234053. | + | 1.81721e6i | 0.145255 | + | 1.12777i | ||||
\(305\) | − | 620481.i | − | 0.381926i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 443153.i | 0.268354i | 0.990957 | + | 0.134177i | \(0.0428390\pi\) | ||||
−0.990957 | + | 0.134177i | \(0.957161\pi\) | |||||||
\(308\) | 171708. | + | 2.67733e6i | 0.103137 | + | 1.60814i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 912993. | − | 29246.9i | 0.539589 | − | 0.0172852i | ||||
\(311\) | −1.59260e6 | −0.933696 | −0.466848 | − | 0.884338i | \(-0.654610\pi\) | ||||
−0.466848 | + | 0.884338i | \(0.654610\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −230766. | −0.133141 | −0.0665703 | − | 0.997782i | \(-0.521206\pi\) | ||||
−0.0665703 | + | 0.997782i | \(0.521206\pi\) | |||||||
\(314\) | −1.61600e6 | + | 51767.2i | −0.924950 | + | 0.0296299i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 76707.0 | + | 1.19604e6i | 0.0432133 | + | 0.673798i | ||||
\(317\) | − | 1.84281e6i | − | 1.02999i | −0.857193 | − | 0.514995i | \(-0.827794\pi\) | ||
0.857193 | − | 0.514995i | \(-0.172206\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 2.41956e6i | − | 1.33125i | ||||||
\(320\) | −432891. | − | 2.22522e6i | −0.236322 | − | 1.21478i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −57232.6 | − | 1.78662e6i | −0.0307612 | − | 0.960266i | ||||
\(323\) | 2.49811e6 | 1.33231 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.11279e6 | −0.584394 | ||||||||
\(326\) | −23358.7 | − | 729183.i | −0.0121732 | − | 0.380008i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 151394. | + | 1.57103e6i | 0.0777007 | + | 0.806308i | ||||
\(329\) | − | 952857.i | − | 0.485331i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 2.00465e6i | − | 1.00570i | −0.864374 | − | 0.502850i | \(-0.832285\pi\) | ||
0.864374 | − | 0.502850i | \(-0.167715\pi\) | |||||||
\(332\) | 1.55500e6 | − | 99728.5i | 0.774259 | − | 0.0496563i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.16521e6 | + | 101395.i | −1.55252 | + | 0.0497335i | ||||
\(335\) | −858259. | −0.417836 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.11878e6 | −0.536623 | −0.268311 | − | 0.963332i | \(-0.586466\pi\) | ||||
−0.268311 | + | 0.963332i | \(0.586466\pi\) | |||||||
\(338\) | −438244. | + | 14038.7i | −0.208653 | + | 0.00668400i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.08447e6 | + | 197819.i | −1.44705 | + | 0.0928051i | ||||
\(341\) | 819178.i | 0.381498i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.60249e6i | 2.57126i | ||||||||
\(344\) | 184885. | + | 1.91857e6i | 0.0842373 | + | 0.874140i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 94802.2 | + | 2.95942e6i | 0.0425724 | + | 1.32897i | ||||
\(347\) | −351285. | −0.156616 | −0.0783080 | − | 0.996929i | \(-0.524952\pi\) | ||||
−0.0783080 | + | 0.996929i | \(0.524952\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.58849e6 | 0.698105 | 0.349053 | − | 0.937103i | \(-0.386503\pi\) | ||||
0.349053 | + | 0.937103i | \(0.386503\pi\) | |||||||
\(350\) | −71868.9 | − | 2.24351e6i | −0.0313596 | − | 0.978946i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.00695e6 | − | 324118.i | 0.863335 | − | 0.139427i | ||||
\(353\) | − | 1.88702e6i | − | 0.806010i | −0.915198 | − | 0.403005i | \(-0.867966\pi\) | ||
0.915198 | − | 0.403005i | \(-0.132034\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 449916.i | 0.189479i | ||||||||
\(356\) | 16252.6 | + | 253416.i | 0.00679669 | + | 0.105976i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.04427e6 | − | 129554.i | 1.66775 | − | 0.0534250i | ||||
\(359\) | 2.13280e6 | 0.873400 | 0.436700 | − | 0.899607i | \(-0.356147\pi\) | ||||
0.436700 | + | 0.899607i | \(0.356147\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −725432. | −0.292974 | ||||||||
\(362\) | −1.62190e6 | + | 51956.0i | −0.650507 | + | 0.0208384i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −327767. | − | 5.11067e6i | −0.129662 | − | 2.02174i | ||||
\(365\) | 3.17204e6i | 1.24625i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.63065e6i | 0.631970i | 0.948764 | + | 0.315985i | \(0.102335\pi\) | ||||
−0.948764 | + | 0.315985i | \(0.897665\pi\) | |||||||
\(368\) | −1.34343e6 | + | 173031.i | −0.517125 | + | 0.0666045i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −162009. | − | 5.05741e6i | −0.0615228 | − | 1.92054i | ||||
\(371\) | 969251. | 0.365596 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.06922e6 | 1.14224 | 0.571118 | − | 0.820868i | \(-0.306510\pi\) | ||||
0.571118 | + | 0.820868i | \(0.306510\pi\) | |||||||
\(374\) | −88746.2 | − | 2.77037e6i | −0.0328073 | − | 1.02414i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −718712. | + | 69259.4i | −0.262171 | + | 0.0252644i | ||||
\(377\) | 4.61863e6i | 1.67363i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 2.56651e6i | − | 0.917792i | −0.888490 | − | 0.458896i | \(-0.848245\pi\) | ||
0.888490 | − | 0.458896i | \(-0.151755\pi\) | |||||||
\(380\) | 3.95300e6 | − | 253521.i | 1.40433 | − | 0.0900649i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −689382. | + | 22083.7i | −0.241714 | + | 0.00774307i | ||||
\(383\) | −3.73053e6 | −1.29949 | −0.649745 | − | 0.760152i | \(-0.725124\pi\) | ||||
−0.649745 | + | 0.760152i | \(0.725124\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.80006e6 | 1.99425 | ||||||||
\(386\) | −1.34344e6 | + | 43035.9i | −0.458934 | + | 0.0147015i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.80737e6 | − | 115913.i | 0.609490 | − | 0.0390890i | ||||
\(389\) | 3.32039e6i | 1.11254i | 0.831002 | + | 0.556270i | \(0.187768\pi\) | ||||
−0.831002 | + | 0.556270i | \(0.812232\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.84681e6i | 0.610913i | ||||||||
\(392\) | 7.25415e6 | − | 699054.i | 2.38436 | − | 0.229771i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 120943. | + | 3.77545e6i | 0.0392501 | + | 1.22526i | ||||
\(395\) | 2.59106e6 | 0.835574 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.24589e6 | 0.715173 | 0.357587 | − | 0.933880i | \(-0.383600\pi\) | ||||
0.357587 | + | 0.933880i | \(0.383600\pi\) | |||||||
\(398\) | −41747.3 | − | 1.30321e6i | −0.0132105 | − | 0.412390i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.68699e6 | + | 217281.i | −0.527185 | + | 0.0679002i | ||||
\(401\) | − | 4.54280e6i | − | 1.41079i | −0.708814 | − | 0.705395i | \(-0.750770\pi\) | ||
0.708814 | − | 0.705395i | \(-0.249230\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 1.56370e6i | − | 0.479614i | ||||||
\(404\) | 149274. | + | 2.32753e6i | 0.0455019 | + | 0.709483i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.31167e6 | + | 298291.i | −2.80358 | + | 0.0898100i | ||||
\(407\) | 4.53773e6 | 1.35785 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.14681e6 | 0.338986 | 0.169493 | − | 0.985531i | \(-0.445787\pi\) | ||||
0.169493 | + | 0.985531i | \(0.445787\pi\) | |||||||
\(410\) | 3.41043e6 | − | 109250.i | 1.00196 | − | 0.0320968i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 199765. | + | 3.11481e6i | 0.0579798 | + | 0.904043i | ||||
\(413\) | − | 6.00455e6i | − | 1.73223i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 3.36870e6i | − | 0.960155i | ||||||
\(416\) | −3.83100e6 | + | 618699.i | −1.08537 | + | 0.175286i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 113735. | + | 3.55045e6i | 0.0318387 | + | 0.993900i | ||||
\(419\) | 6.30867e6 | 1.75551 | 0.877754 | − | 0.479112i | \(-0.159041\pi\) | ||||
0.877754 | + | 0.479112i | \(0.159041\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.98399e6 | 1.09550 | 0.547750 | − | 0.836642i | \(-0.315484\pi\) | ||||
0.547750 | + | 0.836642i | \(0.315484\pi\) | |||||||
\(422\) | 142837. | + | 4.45891e6i | 0.0390445 | + | 1.21884i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −70451.0 | − | 731077.i | −0.0190315 | − | 0.197492i | ||||
\(425\) | 2.31910e6i | 0.622797i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 2.14255e6i | − | 0.568671i | ||||||
\(428\) | 524930. | − | 33665.8i | 0.138513 | − | 0.00888341i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.16486e6 | − | 133417.i | 1.08625 | − | 0.0347970i | ||||
\(431\) | −2.55041e6 | −0.661327 | −0.330663 | − | 0.943749i | \(-0.607272\pi\) | ||||
−0.330663 | + | 0.943749i | \(0.607272\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.49831e6 | 0.640365 | 0.320182 | − | 0.947356i | \(-0.396256\pi\) | ||||
0.320182 | + | 0.947356i | \(0.396256\pi\) | |||||||
\(434\) | 3.15260e6 | − | 100991.i | 0.803424 | − | 0.0257369i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.55462e6 | + | 356240.i | −1.39939 | + | 0.0897483i | ||||
\(437\) | − | 2.36683e6i | − | 0.592875i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.48279e6i | 0.862514i | 0.902229 | + | 0.431257i | \(0.141930\pi\) | ||||
−0.902229 | + | 0.431257i | \(0.858070\pi\) | |||||||
\(440\) | −421583. | − | 4.37481e6i | −0.103813 | − | 1.07728i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 169405. | + | 5.28827e6i | 0.0412449 | + | 1.28753i | ||||
\(443\) | 5.85754e6 | 1.41810 | 0.709049 | − | 0.705160i | \(-0.249125\pi\) | ||||
0.709049 | + | 0.705160i | \(0.249125\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 548990. | 0.131421 | ||||||||
\(446\) | 257890. | + | 8.05050e6i | 0.0613901 | + | 1.91640i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.49479e6 | − | 7.68377e6i | −0.351872 | − | 1.80875i | ||||
\(449\) | − | 208069.i | − | 0.0487071i | −0.999703 | − | 0.0243535i | \(-0.992247\pi\) | ||
0.999703 | − | 0.0243535i | \(-0.00775274\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.05999e6i | 0.708400i | ||||||||
\(452\) | −467043. | − | 7.28230e6i | −0.107525 | − | 1.67657i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.04172e6 | + | 129473.i | −0.920295 | + | 0.0294808i | ||||
\(455\) | −1.10715e7 | −2.50715 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15198.4 | −0.00340415 | −0.00170207 | − | 0.999999i | \(-0.500542\pi\) | ||||
−0.00170207 | + | 0.999999i | \(0.500542\pi\) | |||||||
\(458\) | −3.62118e6 | + | 116001.i | −0.806652 | + | 0.0258404i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 187423. | + | 2.92237e6i | 0.0412980 | + | 0.643934i | ||||
\(461\) | 344817.i | 0.0755678i | 0.999286 | + | 0.0377839i | \(0.0120299\pi\) | ||||
−0.999286 | + | 0.0377839i | \(0.987970\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 60401.9i | − | 0.0130948i | −0.999979 | − | 0.00654739i | \(-0.997916\pi\) | ||
0.999979 | − | 0.00654739i | \(-0.00208411\pi\) | |||||||
\(464\) | 901820. | + | 7.00183e6i | 0.194458 | + | 1.50979i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −174845. | − | 5.45810e6i | −0.0372982 | − | 1.16433i | ||||
\(467\) | 3.80574e6 | 0.807509 | 0.403754 | − | 0.914867i | \(-0.367705\pi\) | ||||
0.403754 | + | 0.914867i | \(0.367705\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.96360e6 | −0.622140 | ||||||||
\(470\) | 49979.3 | + | 1.56019e6i | 0.0104363 | + | 0.325787i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.52905e6 | + | 436446.i | −0.935733 | + | 0.0901729i | ||||
\(473\) | 3.73690e6i | 0.767995i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 2.97211e6i | − | 0.604408i | ||||||
\(476\) | −1.06508e7 | + | 683079.i | −2.15459 | + | 0.138183i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.71647e6 | + | 119054.i | −0.743980 | + | 0.0238327i | ||||
\(479\) | −4.93357e6 | −0.982476 | −0.491238 | − | 0.871025i | \(-0.663456\pi\) | ||||
−0.491238 | + | 0.871025i | \(0.663456\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.66194e6 | −1.70707 | ||||||||
\(482\) | 6.14694e6 | − | 196912.i | 1.20515 | − | 0.0386059i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.20971e6 | + | 77583.6i | −0.234730 | + | 0.0150542i | ||||
\(485\) | − | 3.91540e6i | − | 0.755827i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 1.40275e6i | − | 0.268013i | −0.990980 | − | 0.134007i | \(-0.957216\pi\) | ||
0.990980 | − | 0.134007i | \(-0.0427844\pi\) | |||||||
\(488\) | −1.61606e6 | + | 155733.i | −0.307191 | + | 0.0296027i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −504455. | − | 1.57475e7i | −0.0949144 | − | 2.96292i | ||||
\(491\) | −9.21228e6 | −1.72450 | −0.862250 | − | 0.506483i | \(-0.830945\pi\) | ||||
−0.862250 | + | 0.506483i | \(0.830945\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.62537e6 | 1.78361 | ||||||||
\(494\) | −217106. | − | 6.77734e6i | −0.0400271 | − | 1.24952i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −305324. | − | 2.37057e6i | −0.0557259 | − | 0.432662i | ||||
\(497\) | 1.55358e6i | 0.282126i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.76154e6i | 0.676260i | 0.941099 | + | 0.338130i | \(0.109794\pi\) | ||||
−0.941099 | + | 0.338130i | \(0.890206\pi\) | |||||||
\(500\) | −207424. | − | 3.23423e6i | −0.0371051 | − | 0.578556i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −291284. | + | 9331.01i | −0.0515890 | + | 0.00165261i | ||||
\(503\) | −5.84609e6 | −1.03026 | −0.515128 | − | 0.857113i | \(-0.672256\pi\) | ||||
−0.515128 | + | 0.857113i | \(0.672256\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.04227e6 | 0.879827 | ||||||||
\(506\) | −2.62478e6 | + | 84082.3i | −0.455739 | + | 0.0145992i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 349123. | + | 5.44366e6i | 0.0600232 | + | 0.935904i | ||||
\(509\) | − | 2.06029e6i | − | 0.352480i | −0.984347 | − | 0.176240i | \(-0.943607\pi\) | ||
0.984347 | − | 0.176240i | \(-0.0563934\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.09532e7i | 1.85561i | ||||||||
\(512\) | −5.68699e6 | + | 1.68598e6i | −0.958755 | + | 0.284235i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 191756. | + | 5.98599e6i | 0.0320140 | + | 0.999375i | ||||
\(515\) | 6.74780e6 | 1.12110 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.39987e6 | −0.230337 | ||||||||
\(518\) | −559425. | − | 1.74634e7i | −0.0916046 | − | 2.85960i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 804746. | + | 8.35094e6i | 0.130512 | + | 1.35434i | ||||
\(521\) | 9.31147e6i | 1.50288i | 0.659802 | + | 0.751439i | \(0.270640\pi\) | ||||
−0.659802 | + | 0.751439i | \(0.729360\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 6.91429e6i | − | 1.10533i | −0.833402 | − | 0.552667i | \(-0.813610\pi\) | ||
0.833402 | − | 0.552667i | \(-0.186390\pi\) | |||||||
\(524\) | 956214. | − | 61325.8i | 0.152134 | − | 0.00975696i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.55144e6 | − | 305971.i | 1.50524 | − | 0.0482188i | ||||
\(527\) | −3.25881e6 | −0.511131 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.68659e6 | −0.728145 | ||||||||
\(530\) | −1.58704e6 | + | 50839.2i | −0.245413 | + | 0.00786157i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.36499e7 | − | 875420.i | 2.09098 | − | 0.134103i | ||||
\(533\) | − | 5.84112e6i | − | 0.890591i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 1.13719e6i | − | 0.171770i | ||||||
\(536\) | 215412. | + | 2.23536e6i | 0.0323861 | + | 0.336074i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 168451. | + | 5.25848e6i | 0.0250909 | + | 0.783258i | ||||
\(539\) | 1.41293e7 | 2.09483 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.91946e6 | −1.01643 | −0.508217 | − | 0.861229i | \(-0.669695\pi\) | ||||
−0.508217 | + | 0.861229i | \(0.669695\pi\) | |||||||
\(542\) | 365097. | + | 1.13972e7i | 0.0533839 | + | 1.66647i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.28939e6 | + | 7.98394e6i | 0.186804 | + | 1.15670i | ||||
\(545\) | 1.20333e7i | 1.73538i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 8.94295e6i | − | 1.27795i | −0.769229 | − | 0.638973i | \(-0.779360\pi\) | ||
0.769229 | − | 0.638973i | \(-0.220640\pi\) | |||||||
\(548\) | 350318. | + | 5.46229e6i | 0.0498323 | + | 0.777004i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.29602e6 | + | 105585.i | −0.464604 | + | 0.0148832i | ||||
\(551\) | −1.23357e7 | −1.73095 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.94704e6 | 1.24413 | ||||||||
\(554\) | 1.39108e7 | − | 445620.i | 1.92565 | − | 0.0616865i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −540572. | − | 8.42879e6i | −0.0741594 | − | 1.15632i | ||||
\(557\) | 3.85092e6i | 0.525928i | 0.964806 | + | 0.262964i | \(0.0847000\pi\) | ||||
−0.964806 | + | 0.262964i | \(0.915300\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 7.13325e6i | − | 0.965513i | ||||||
\(560\) | −1.67845e7 | + | 2.16180e6i | −2.26171 | + | 0.291303i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 218742. | + | 6.82841e6i | 0.0292140 | + | 0.911966i | ||||
\(563\) | −6.40391e6 | −0.851480 | −0.425740 | − | 0.904846i | \(-0.639986\pi\) | ||||
−0.425740 | + | 0.904846i | \(0.639986\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.57761e7 | −2.07911 | ||||||||
\(566\) | −93632.3 | − | 2.92290e6i | −0.0122853 | − | 0.383506i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.17182e6 | − | 112924.i | 0.152402 | − | 0.0146863i | ||||
\(569\) | − | 1.05210e7i | − | 1.36231i | −0.732137 | − | 0.681157i | \(-0.761477\pi\) | ||
0.732137 | − | 0.681157i | \(-0.238523\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.25121e6i | 0.160598i | 0.996771 | + | 0.0802990i | \(0.0255875\pi\) | ||||
−0.996771 | + | 0.0802990i | \(0.974412\pi\) | |||||||
\(572\) | −7.50826e6 | + | 481534.i | −0.959509 | + | 0.0615371i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.17764e7 | − | 377244.i | 1.49187 | − | 0.0477907i | ||||
\(575\) | 2.19722e6 | 0.277143 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 578609. | 0.0723511 | 0.0361756 | − | 0.999345i | \(-0.488482\pi\) | ||||
0.0361756 | + | 0.999345i | \(0.488482\pi\) | |||||||
\(578\) | 2.99313e6 | − | 95882.2i | 0.372655 | − | 0.0119376i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.52311e7 | − | 976833.i | 1.88002 | − | 0.120573i | ||||
\(581\) | − | 1.16322e7i | − | 1.42963i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1.42396e6i | − | 0.173511i | ||||||
\(584\) | 8.26165e6 | − | 796142.i | 1.00239 | − | 0.0965959i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −374072. | − | 1.16773e7i | −0.0449999 | − | 1.40475i | ||||
\(587\) | 6.35138e6 | 0.760804 | 0.380402 | − | 0.924821i | \(-0.375786\pi\) | ||||
0.380402 | + | 0.924821i | \(0.375786\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.17643e6 | 0.496040 | ||||||||
\(590\) | 314951. | + | 9.83175e6i | 0.0372488 | + | 1.16279i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.31315e7 | + | 1.69130e6i | −1.53996 | + | 0.198343i | ||||
\(593\) | − | 1.12494e7i | − | 1.31369i | −0.754026 | − | 0.656845i | \(-0.771891\pi\) | ||
0.754026 | − | 0.656845i | \(-0.228109\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.30735e7i | 2.67190i | ||||||||
\(596\) | 97597.2 | + | 1.52177e6i | 0.0112544 | + | 0.175482i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.01036e6 | − | 160502.i | 0.572949 | − | 0.0183539i | ||||
\(599\) | −3.98685e6 | −0.454007 | −0.227004 | − | 0.973894i | \(-0.572893\pi\) | ||||
−0.227004 | + | 0.973894i | \(0.572893\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.93772e6 | −0.670553 | −0.335277 | − | 0.942120i | \(-0.608830\pi\) | ||||
−0.335277 | + | 0.942120i | \(0.608830\pi\) | |||||||
\(602\) | 1.43814e7 | − | 460696.i | 1.61738 | − | 0.0518111i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −719047. | − | 1.12116e7i | −0.0801982 | − | 1.25048i | ||||
\(605\) | 2.62067e6i | 0.291088i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 7.86463e6i | − | 0.866376i | −0.901304 | − | 0.433188i | \(-0.857389\pi\) | ||
0.901304 | − | 0.433188i | \(-0.142611\pi\) | |||||||
\(608\) | −1.65246e6 | − | 1.02321e7i | −0.181289 | − | 1.12255i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 112381. | + | 3.50817e6i | 0.0122284 | + | 0.381730i | ||||
\(611\) | 2.67218e6 | 0.289576 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.66739e6 | −0.716646 | −0.358323 | − | 0.933598i | \(-0.616651\pi\) | ||||
−0.358323 | + | 0.933598i | \(0.616651\pi\) | |||||||
\(614\) | −80263.4 | − | 2.50556e6i | −0.00859205 | − | 0.268216i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.45574e6 | − | 1.51064e7i | −0.154573 | − | 1.60402i | ||||
\(617\) | − | 1.13568e7i | − | 1.20100i | −0.799627 | − | 0.600498i | \(-0.794969\pi\) | ||
0.799627 | − | 0.600498i | \(-0.205031\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 5.72429e6i | − | 0.600475i | −0.953864 | − | 0.300237i | \(-0.902934\pi\) | ||
0.953864 | − | 0.300237i | \(-0.0970659\pi\) | |||||||
\(620\) | −5.15672e6 | + | 330721.i | −0.538759 | + | 0.0345527i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 9.00448e6 | − | 288450.i | 0.933217 | − | 0.0298947i | ||||
\(623\) | 1.89569e6 | 0.195680 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.21973e7 | −1.24901 | ||||||||
\(626\) | 1.30474e6 | − | 41796.1i | 0.133072 | − | 0.00426285i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.12743e6 | − | 585378.i | 0.923527 | − | 0.0592294i | ||||
\(629\) | 1.80518e7i | 1.81925i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.24837e7i | 1.24816i | 0.781360 | + | 0.624080i | \(0.214526\pi\) | ||||
−0.781360 | + | 0.624080i | \(0.785474\pi\) | |||||||
\(632\) | −650325. | − | 6.74849e6i | −0.0647646 | − | 0.672069i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 333769. | + | 1.04192e7i | 0.0329779 | + | 1.02946i | ||||
\(635\) | 1.17929e7 | 1.16061 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.69710e7 | −2.63359 | ||||||||
\(638\) | 438229. | + | 1.36801e7i | 0.0426235 | + | 1.33057i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.85058e6 | + | 1.25029e7i | 0.275095 | + | 1.20659i | ||||
\(641\) | 1.81736e7i | 1.74702i | 0.486810 | + | 0.873508i | \(0.338160\pi\) | ||||
−0.486810 | + | 0.873508i | \(0.661840\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.93003e6i | 0.565626i | 0.959175 | + | 0.282813i | \(0.0912676\pi\) | ||||
−0.959175 | + | 0.282813i | \(0.908732\pi\) | |||||||
\(644\) | 647181. | + | 1.00911e7i | 0.0614909 | + | 0.958789i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.41242e7 | + | 452456.i | −1.33163 | + | 0.0426575i | ||||
\(647\) | 1.54374e7 | 1.44982 | 0.724909 | − | 0.688844i | \(-0.241882\pi\) | ||||
0.724909 | + | 0.688844i | \(0.241882\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.82148e6 | −0.822110 | ||||||||
\(650\) | 6.29168e6 | − | 201548.i | 0.584094 | − | 0.0187109i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 264138. | + | 4.11854e6i | 0.0243339 | + | 0.379423i | ||||
\(653\) | 1.88052e7i | 1.72582i | 0.505357 | + | 0.862910i | \(0.331361\pi\) | ||||
−0.505357 | + | 0.862910i | \(0.668639\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 2.07150e6i | − | 0.188661i | ||||||
\(656\) | −1.14052e6 | − | 8.85513e6i | −0.103477 | − | 0.803407i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 172581. | + | 5.38741e6i | 0.0155392 | + | 0.485082i | ||||
\(659\) | 1.30752e7 | 1.17283 | 0.586416 | − | 0.810010i | \(-0.300539\pi\) | ||||
0.586416 | + | 0.810010i | \(0.300539\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.29277e7 | 1.15085 | 0.575424 | − | 0.817855i | \(-0.304837\pi\) | ||||
0.575424 | + | 0.817855i | \(0.304837\pi\) | |||||||
\(662\) | 363080. | + | 1.13342e7i | 0.0322001 | + | 1.00518i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.77385e6 | + | 845501.i | −0.772272 | + | 0.0744208i | ||||
\(665\) | − | 2.95705e7i | − | 2.59301i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 9.11953e6i | − | 0.793703i | ||||||
\(668\) | 1.78776e7 | − | 1.14656e6i | 1.55013 | − | 0.0994159i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.85256e6 | − | 155447.i | 0.417622 | − | 0.0133781i | ||||
\(671\) | −3.14769e6 | −0.269889 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.11203e6 | −0.179748 | −0.0898738 | − | 0.995953i | \(-0.528646\pi\) | ||||
−0.0898738 | + | 0.995953i | \(0.528646\pi\) | |||||||
\(674\) | 6.32552e6 | − | 202632.i | 0.536348 | − | 0.0171814i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.47527e6 | − | 158749.i | 0.208332 | − | 0.0133611i | ||||
\(677\) | 1.57270e6i | 0.131878i | 0.997824 | + | 0.0659391i | \(0.0210043\pi\) | ||||
−0.997824 | + | 0.0659391i | \(0.978996\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 1.35200e7i | − | 1.12539i | ||||||
\(680\) | 1.74036e7 | − | 1.67712e6i | 1.44334 | − | 0.139089i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −148369. | − | 4.63159e6i | −0.0122147 | − | 0.381302i | ||||
\(683\) | −990320. | −0.0812314 | −0.0406157 | − | 0.999175i | \(-0.512932\pi\) | ||||
−0.0406157 | + | 0.999175i | \(0.512932\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.18333e7 | 0.963559 | ||||||||
\(686\) | −1.01472e6 | − | 3.16762e7i | −0.0823256 | − | 2.56994i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.39282e6 | − | 1.08140e7i | −0.112182 | − | 0.870994i | ||||
\(689\) | 2.71815e6i | 0.218135i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 3.19912e6i | − | 0.254880i | −0.991846 | − | 0.127440i | \(-0.959324\pi\) | ||
0.991846 | − | 0.127440i | \(-0.0406760\pi\) | |||||||
\(692\) | −1.07201e6 | − | 1.67152e7i | −0.0851011 | − | 1.32693i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.98615e6 | − | 63624.4i | 0.156536 | − | 0.00501447i | ||||
\(695\) | −1.82598e7 | −1.43395 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.21731e7 | −0.949115 | ||||||||
\(698\) | −8.98125e6 | + | 287706.i | −0.697747 | + | 0.0223517i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 812687. | + | 1.26717e7i | 0.0626871 | + | 0.977440i | ||||
\(701\) | 1.09808e7i | 0.843993i | 0.906597 | + | 0.421996i | \(0.138671\pi\) | ||||
−0.906597 | + | 0.421996i | \(0.861329\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 2.31348e7i | − | 1.76554i | ||||||
\(704\) | −1.12885e7 | + | 2.19605e6i | −0.858429 | + | 0.166997i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 341776. | + | 1.06691e7i | 0.0258066 | + | 0.805597i | ||||
\(707\) | 1.74111e7 | 1.31002 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.37875e7 | 1.77719 | 0.888594 | − | 0.458694i | \(-0.151683\pi\) | ||||
0.888594 | + | 0.458694i | \(0.151683\pi\) | |||||||
\(710\) | −81488.5 | − | 2.54381e6i | −0.00606667 | − | 0.189382i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −137790. | − | 1.42986e6i | −0.0101863 | − | 0.105704i | ||||
\(713\) | 3.08755e6i | 0.227452i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.62656e7i | 1.18988i | ||||||||
\(716\) | −2.28426e7 | + | 1.46499e6i | −1.66519 | + | 0.106795i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.20587e7 | + | 386290.i | −0.872952 | + | 0.0279642i | ||||
\(719\) | −1.91638e7 | −1.38248 | −0.691239 | − | 0.722626i | \(-0.742935\pi\) | ||||
−0.691239 | + | 0.722626i | \(0.742935\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.33004e7 | 1.66927 | ||||||||
\(722\) | 4.10156e6 | − | 131390.i | 0.292824 | − | 0.00938033i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.16073e6 | − | 587513.i | 0.649506 | − | 0.0416554i | ||||
\(725\) | − | 1.14517e7i | − | 0.809143i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 977419.i | 0.0685874i | 0.999412 | + | 0.0342937i | \(0.0109182\pi\) | ||||
−0.999412 | + | 0.0342937i | \(0.989082\pi\) | |||||||
\(728\) | 2.77882e6 | + | 2.88361e7i | 0.194327 | + | 2.01655i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −574517. | − | 1.79346e7i | −0.0399021 | − | 1.24561i | ||||
\(731\) | −1.48659e7 | −1.02896 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.68872e6 | 0.116091 | 0.0580455 | − | 0.998314i | \(-0.481513\pi\) | ||||
0.0580455 | + | 0.998314i | \(0.481513\pi\) | |||||||
\(734\) | −295343. | − | 9.21964e6i | −0.0202342 | − | 0.631646i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.56436e6 | − | 1.22163e6i | 0.514728 | − | 0.0831275i | ||||
\(737\) | 4.35393e6i | 0.295265i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.82227e6i | 0.392176i | 0.980586 | + | 0.196088i | \(0.0628238\pi\) | ||||
−0.980586 | + | 0.196088i | \(0.937176\pi\) | |||||||
\(740\) | 1.83199e6 | + | 2.85650e7i | 0.122982 | + | 1.91759i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.48010e6 | + | 175550.i | −0.365409 | + | 0.0117055i | ||||
\(743\) | 4.95294e6 | 0.329148 | 0.164574 | − | 0.986365i | \(-0.447375\pi\) | ||||
0.164574 | + | 0.986365i | \(0.447375\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.29670e6 | 0.217615 | ||||||||
\(746\) | −1.73532e7 | + | 555895.i | −1.14165 | + | 0.0365717i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.00353e6 | + | 1.56475e7i | 0.0655810 | + | 1.02256i | ||||
\(749\) | − | 3.92675e6i | − | 0.255758i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.06174e7i | 0.686940i | 0.939164 | + | 0.343470i | \(0.111602\pi\) | ||||
−0.939164 | + | 0.343470i | \(0.888398\pi\) | |||||||
\(752\) | 4.05102e6 | − | 521762.i | 0.261228 | − | 0.0336456i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −836522. | − | 2.61135e7i | −0.0535857 | − | 1.67277i | ||||
\(755\) | −2.42884e7 | −1.55072 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.59623e6 | −0.291516 | −0.145758 | − | 0.989320i | \(-0.546562\pi\) | ||||
−0.145758 | + | 0.989320i | \(0.546562\pi\) | |||||||
\(758\) | 464843. | + | 1.45109e7i | 0.0293855 | + | 0.917322i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.23042e7 | + | 2.14936e6i | −1.40072 | + | 0.134982i | ||||
\(761\) | − | 2.15027e7i | − | 1.34596i | −0.739661 | − | 0.672979i | \(-0.765014\pi\) | ||
0.739661 | − | 0.672979i | \(-0.234986\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.15515e7i | 2.58390i | ||||||||
\(764\) | 3.89373e6 | − | 249720.i | 0.241342 | − | 0.0154782i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.10922e7 | − | 675670.i | 1.29882 | − | 0.0416066i | ||||
\(767\) | 1.68391e7 | 1.03354 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.82987e7 | 1.72564 | 0.862821 | − | 0.505510i | \(-0.168696\pi\) | ||||
0.862821 | + | 0.505510i | \(0.168696\pi\) | |||||||
\(770\) | −3.27932e7 | + | 1.05050e6i | −1.99323 | + | 0.0638513i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.58796e6 | − | 486646.i | 0.458228 | − | 0.0293880i | ||||
\(773\) | 1.93324e6i | 0.116369i | 0.998306 | + | 0.0581845i | \(0.0185312\pi\) | ||||
−0.998306 | + | 0.0581845i | \(0.981469\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.87714e6i | 0.231877i | ||||||||
\(776\) | −1.01978e7 | + | 982718.i | −0.607926 | + | 0.0585834i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −601387. | − | 1.87733e7i | −0.0356209 | − | 1.11197i | ||||
\(779\) | 1.56008e7 | 0.921092 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.28242e6 | 0.133896 | ||||||||
\(782\) | −334492. | − | 1.04418e7i | −0.0195600 | − | 0.610600i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.08880e7 | + | 5.26628e6i | −2.37578 | + | 0.305995i | ||||
\(785\) | − | 1.97733e7i | − | 1.14526i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 7.01512e6i | − | 0.403737i | −0.979413 | − | 0.201868i | \(-0.935299\pi\) | ||
0.979413 | − | 0.201868i | \(-0.0647013\pi\) | |||||||
\(788\) | −1.36761e6 | − | 2.13243e7i | −0.0784600 | − | 1.22338i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.46497e7 | + | 469291.i | −0.835146 | + | 0.0267531i | ||||
\(791\) | −5.44754e7 | −3.09570 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.00853e6 | 0.339301 | ||||||||
\(794\) | −1.26981e7 | + | 406773.i | −0.714807 | + | 0.0228982i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 472074. | + | 7.36075e6i | 0.0264075 | + | 0.411756i | ||||
\(797\) | 1.01331e7i | 0.565060i | 0.959258 | + | 0.282530i | \(0.0911737\pi\) | ||||
−0.959258 | + | 0.282530i | \(0.908826\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 5.56891e6i | − | 0.308605i | ||||||
\(800\) | 9.49882e6 | − | 1.53404e6i | 0.524741 | − | 0.0847446i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 822787. | + | 2.56848e7i | 0.0451702 | + | 1.41007i | ||||
\(803\) | 1.60917e7 | 0.880669 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.18609e7 | 1.18899 | ||||||||
\(806\) | 283217. | + | 8.84110e6i | 0.0153561 | + | 0.479368i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.26555e6 | − | 1.31327e7i | −0.0681946 | − | 0.707662i | ||||
\(809\) | 5.65648e6i | 0.303861i | 0.988391 | + | 0.151930i | \(0.0485490\pi\) | ||||
−0.988391 | + | 0.151930i | \(0.951451\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 2.13565e7i | − | 1.14019i | −0.821579 | − | 0.570095i | \(-0.806907\pi\) | ||
0.821579 | − | 0.570095i | \(-0.193093\pi\) | |||||||
\(812\) | 5.25937e7 | − | 3.37304e6i | 2.79926 | − | 0.179528i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.56561e7 | + | 821870.i | −1.35716 | + | 0.0434753i | ||||
\(815\) | 8.92223e6 | 0.470521 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.90519e7 | 0.998580 | ||||||||
\(818\) | −6.48400e6 | + | 207709.i | −0.338813 | + | 0.0108535i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.92626e7 | + | 1.23539e6i | −1.00042 | + | 0.0641607i | ||||
\(821\) | − | 2.63136e7i | − | 1.36246i | −0.732071 | − | 0.681229i | \(-0.761446\pi\) | ||
0.732071 | − | 0.681229i | \(-0.238554\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1.75614e7i | − | 0.903772i | −0.892076 | − | 0.451886i | \(-0.850751\pi\) | ||
0.892076 | − | 0.451886i | \(-0.149249\pi\) | |||||||
\(824\) | −1.69362e6 | − | 1.75748e7i | −0.0868954 | − | 0.901723i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.08754e6 | + | 3.39494e7i | 0.0554619 | + | 1.73134i | ||||
\(827\) | 5.50797e6 | 0.280045 | 0.140022 | − | 0.990148i | \(-0.455283\pi\) | ||||
0.140022 | + | 0.990148i | \(0.455283\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.81244e6 | 0.394821 | 0.197411 | − | 0.980321i | \(-0.436747\pi\) | ||||
0.197411 | + | 0.980321i | \(0.436747\pi\) | |||||||
\(830\) | 610135. | + | 1.90465e7i | 0.0307419 | + | 0.959663i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.15483e7 | − | 4.19197e6i | 1.07920 | − | 0.209947i | ||||
\(833\) | 5.62085e7i | 2.80666i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 3.87293e7i | − | 1.92231i | ||||||
\(836\) | −1.28611e6 | − | 2.00535e7i | −0.0636447 | − | 0.992371i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3.56689e7 | + | 1.14262e6i | −1.75461 | + | 0.0562072i | ||||
\(839\) | −3.55868e7 | −1.74535 | −0.872677 | − | 0.488298i | \(-0.837618\pi\) | ||||
−0.872677 | + | 0.488298i | \(0.837618\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.70190e7 | −1.31728 | ||||||||
\(842\) | −2.25253e7 | + | 721576.i | −1.09494 | + | 0.0350754i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.61519e6 | − | 2.51846e7i | −0.0780489 | − | 1.21697i | ||||
\(845\) | − | 5.36232e6i | − | 0.258351i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.04928e6i | 0.433417i | ||||||||
\(848\) | 530739. | + | 4.12072e6i | 0.0253449 | + | 0.196781i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −420033. | − | 1.31121e7i | −0.0199405 | − | 0.622478i | ||||
\(851\) | 1.71031e7 | 0.809563 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.84336e6 | −0.133801 | −0.0669006 | − | 0.997760i | \(-0.521311\pi\) | ||||
−0.0669006 | + | 0.997760i | \(0.521311\pi\) | |||||||
\(854\) | 388056. | + | 1.21139e7i | 0.0182075 | + | 0.568379i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.96183e6 | + | 285420.i | −0.138158 | + | 0.0133137i | ||||
\(857\) | 2.74865e7i | 1.27840i | 0.769039 | + | 0.639202i | \(0.220735\pi\) | ||||
−0.769039 | + | 0.639202i | \(0.779265\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.08862e6i | 0.281537i | 0.990043 | + | 0.140769i | \(0.0449574\pi\) | ||||
−0.990043 | + | 0.140769i | \(0.955043\pi\) | |||||||
\(860\) | −2.35238e7 | + | 1.50867e6i | −1.08458 | + | 0.0695583i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.44199e7 | − | 461927.i | 0.660988 | − | 0.0211741i | ||||
\(863\) | 4.93253e6 | 0.225446 | 0.112723 | − | 0.993626i | \(-0.464043\pi\) | ||||
0.112723 | + | 0.993626i | \(0.464043\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.62112e7 | −1.64552 | ||||||||
\(866\) | −1.41254e7 | + | 452493.i | −0.640036 | + | 0.0205030i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.78064e7 | + | 1.14199e6i | −0.802188 | + | 0.0514475i | ||||
\(869\) | − | 1.31444e7i | − | 0.590461i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 8.31108e6i | − | 0.371204i | ||||||
\(872\) | 3.13411e7 | − | 3.02021e6i | 1.39580 | − | 0.134507i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 428678. | + | 1.33819e7i | 0.0189825 | + | 0.592571i | ||||
\(875\) | −2.41937e7 | −1.06827 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.46817e6 | −0.152266 | −0.0761328 | − | 0.997098i | \(-0.524257\pi\) | ||||
−0.0761328 | + | 0.997098i | \(0.524257\pi\) | |||||||
\(878\) | −630800. | − | 1.96915e7i | −0.0276157 | − | 0.862072i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.17597e6 | + | 2.46586e7i | 0.138252 | + | 1.07340i | ||||
\(881\) | 2.97742e6i | 0.129241i | 0.997910 | + | 0.0646204i | \(0.0205837\pi\) | ||||
−0.997910 | + | 0.0646204i | \(0.979416\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1.81106e6i | − | 0.0781682i | −0.999236 | − | 0.0390841i | \(-0.987556\pi\) | ||
0.999236 | − | 0.0390841i | \(-0.0124440\pi\) | |||||||
\(884\) | −1.91561e6 | − | 2.98690e7i | −0.0824475 | − | 1.28555i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.31183e7 | + | 1.06091e6i | −1.41737 | + | 0.0454041i | ||||
\(887\) | 3.34260e7 | 1.42651 | 0.713256 | − | 0.700903i | \(-0.247220\pi\) | ||||
0.713256 | + | 0.700903i | \(0.247220\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.07214e7 | 1.72810 | ||||||||
\(890\) | −3.10397e6 | + | 99432.7i | −0.131354 | + | 0.00420779i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.91620e6 | − | 4.54705e7i | −0.122717 | − | 1.91345i | ||||
\(893\) | 7.13700e6i | 0.299493i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.94853e7i | 2.06500i | ||||||||
\(896\) | 9.84315e6 | + | 4.31730e7i | 0.409604 | + | 1.79656i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 37685.3 | + | 1.17641e6i | 0.00155949 | + | 0.0486821i | ||||
\(899\) | 1.60920e7 | 0.664066 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.66472e6 | 0.232470 | ||||||||
\(902\) | −554223. | − | 1.73010e7i | −0.0226813 | − | 0.708037i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.95960e6 | + | 4.10892e7i | 0.161150 | + | 1.67227i | ||||
\(905\) | − | 1.98454e7i | − | 0.805451i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.39164e7i | 1.36896i | 0.729031 | + | 0.684481i | \(0.239971\pi\) | ||||
−0.729031 | + | 0.684481i | \(0.760029\pi\) | |||||||
\(908\) | 2.28283e7 | − | 1.46407e6i | 0.918879 | − | 0.0589313i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 6.25980e7 | − | 2.00527e6i | 2.50586 | − | 0.0802730i | ||||
\(911\) | 2.31991e7 | 0.926136 | 0.463068 | − | 0.886323i | \(-0.346749\pi\) | ||||
0.463068 | + | 0.886323i | \(0.346749\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.70893e7 | −0.678497 | ||||||||
\(914\) | 85931.3 | − | 2752.73i | 0.00340240 | − | 0.000108993i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.04530e7 | − | 1.31173e6i | 0.805411 | − | 0.0516542i | ||||
\(917\) | − | 7.15298e6i | − | 0.280908i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.47623e7i | 1.74833i | 0.485628 | + | 0.874165i | \(0.338591\pi\) | ||||
−0.485628 | + | 0.874165i | \(0.661409\pi\) | |||||||
\(920\) | −1.58898e6 | − | 1.64890e7i | −0.0618941 | − | 0.642281i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −62453.0 | − | 1.94958e6i | −0.00241950 | − | 0.0755290i | ||||
\(923\) | −4.35684e6 | −0.168332 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.14769e7 | 0.825312 | ||||||||
\(926\) | 10939.9 | + | 341509.i | 0.000419264 | + | 0.0130881i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.36701e6 | − | 3.94247e7i | −0.242698 | − | 1.50279i | ||||
\(929\) | 1.75173e7i | 0.665927i | 0.942940 | + | 0.332964i | \(0.108049\pi\) | ||||
−0.942940 | + | 0.332964i | \(0.891951\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 7.20357e7i | − | 2.72379i | ||||||
\(932\) | 1.97713e6 | + | 3.08282e7i | 0.0745582 | + | 1.16254i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.15175e7 | + | 689293.i | −0.807095 | + | 0.0258545i | ||||
\(935\) | 3.38980e7 | 1.26808 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.08368e7 | 1.14742 | 0.573708 | − | 0.819060i | \(-0.305505\pi\) | ||||
0.573708 | + | 0.819060i | \(0.305505\pi\) | |||||||
\(938\) | 1.67561e7 | − | 536765.i | 0.621821 | − | 0.0199194i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −565162. | − | 8.81221e6i | −0.0208619 | − | 0.325286i | ||||
\(941\) | − | 1.99825e7i | − | 0.735658i | −0.929894 | − | 0.367829i | \(-0.880101\pi\) | ||
0.929894 | − | 0.367829i | \(-0.119899\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.15334e7i | 0.422354i | ||||||||
\(944\) | 2.55280e7 | − | 3.28795e6i | 0.932366 | − | 0.120087i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −676824. | − | 2.11283e7i | −0.0245894 | − | 0.767601i | ||||
\(947\) | −3.21068e7 | −1.16338 | −0.581690 | − | 0.813410i | \(-0.697608\pi\) | ||||
−0.581690 | + | 0.813410i | \(0.697608\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.07169e7 | −1.10716 | ||||||||
\(950\) | 538306. | + | 1.68042e7i | 0.0193517 | + | 0.604099i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.00955e7 | − | 5.79116e6i | 2.14906 | − | 0.207097i | ||||
\(953\) | − | 2.79150e7i | − | 0.995648i | −0.867278 | − | 0.497824i | \(-0.834133\pi\) | ||
0.867278 | − | 0.497824i | \(-0.165867\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 8.43522e6i | − | 0.299287i | ||||||
\(956\) | 2.09912e7 | − | 1.34625e6i | 0.742835 | − | 0.0476410i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.78942e7 | − | 893563.i | 0.981973 | − | 0.0314566i | ||||
\(959\) | 4.08608e7 | 1.43470 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.31810e7 | 0.809698 | ||||||||
\(962\) | 4.89742e7 | − | 1.56884e6i | 1.70620 | − | 0.0546565i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.47189e7 | + | 2.22666e6i | −1.20330 | + | 0.0771722i | ||||
\(965\) | − | 1.64382e7i | − | 0.568247i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.25000e7i | 0.429878i | 0.976628 | + | 0.214939i | \(0.0689552\pi\) | ||||
−0.976628 | + | 0.214939i | \(0.931045\pi\) | |||||||
\(968\) | 6.82560e6 | − | 657756.i | 0.234128 | − | 0.0225619i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 709154. | + | 2.21375e7i | 0.0241998 | + | 0.755439i | ||||
\(971\) | −2.43379e7 | −0.828390 | −0.414195 | − | 0.910188i | \(-0.635937\pi\) | ||||
−0.414195 | + | 0.910188i | \(0.635937\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.30518e7 | −2.13509 | ||||||||
\(974\) | 254064. | + | 7.93106e6i | 0.00858116 | + | 0.267876i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.10892e6 | − | 1.17321e6i | 0.306085 | − | 0.0394231i | ||||
\(977\) | − | 1.85003e7i | − | 0.620073i | −0.950725 | − | 0.310037i | \(-0.899659\pi\) | ||
0.950725 | − | 0.310037i | \(-0.100341\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 2.78502e6i | − | 0.0928691i | ||||||
\(980\) | 5.70433e6 | + | 8.89440e7i | 0.189732 | + | 2.95836i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5.20858e7 | − | 1.66852e6i | 1.72362 | − | 0.0552144i | ||||
\(983\) | 5.11354e7 | 1.68787 | 0.843933 | − | 0.536449i | \(-0.180235\pi\) | ||||
0.843933 | + | 0.536449i | \(0.180235\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.61962e7 | −1.51710 | ||||||||
\(986\) | −5.44214e7 | + | 1.74334e6i | −1.78270 | + | 0.0571070i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.45501e6 | + | 3.82795e7i | 0.0800132 | + | 1.24759i | ||||
\(989\) | 1.40847e7i | 0.457885i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 9.59641e6i | − | 0.310402i | −0.987883 | − | 0.155201i | \(-0.950397\pi\) | ||
0.987883 | − | 0.155201i | \(-0.0496025\pi\) | |||||||
\(992\) | 2.15564e6 | + | 1.33478e7i | 0.0695501 | + | 0.430656i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −281383. | − | 8.78387e6i | −0.00903300 | − | 0.281981i | ||||
\(995\) | 1.59460e7 | 0.510617 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.14442e7 | −1.32046 | −0.660232 | − | 0.751062i | \(-0.729542\pi\) | ||||
−0.660232 | + | 0.751062i | \(0.729542\pi\) | |||||||
\(998\) | −681286. | − | 2.12676e7i | −0.0216523 | − | 0.675914i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 108.6.b.b.107.2 | yes | 16 | |
3.2 | odd | 2 | inner | 108.6.b.b.107.15 | yes | 16 | |
4.3 | odd | 2 | inner | 108.6.b.b.107.16 | yes | 16 | |
12.11 | even | 2 | inner | 108.6.b.b.107.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.6.b.b.107.1 | ✓ | 16 | 12.11 | even | 2 | inner | |
108.6.b.b.107.2 | yes | 16 | 1.1 | even | 1 | trivial | |
108.6.b.b.107.15 | yes | 16 | 3.2 | odd | 2 | inner | |
108.6.b.b.107.16 | yes | 16 | 4.3 | odd | 2 | inner |