Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,9,Mod(42,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.42");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.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: | \(17.5172802326\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 42.22 | ||
Character | \(\chi\) | \(=\) | 43.42 |
Dual form | 43.9.b.b.42.7 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 23.0076i | 1.43798i | 0.695022 | + | 0.718988i | \(0.255394\pi\) | ||||
−0.695022 | + | 0.718988i | \(0.744606\pi\) | |||||||
\(3\) | 78.5211i | 0.969397i | 0.874681 | + | 0.484698i | \(0.161071\pi\) | ||||
−0.874681 | + | 0.484698i | \(0.838929\pi\) | |||||||
\(4\) | −273.350 | −1.06778 | ||||||||
\(5\) | 548.269i | 0.877231i | 0.898675 | + | 0.438616i | \(0.144531\pi\) | ||||
−0.898675 | + | 0.438616i | \(0.855469\pi\) | |||||||
\(6\) | −1806.58 | −1.39397 | ||||||||
\(7\) | 2213.93i | 0.922088i | 0.887377 | + | 0.461044i | \(0.152525\pi\) | ||||
−0.887377 | + | 0.461044i | \(0.847475\pi\) | |||||||
\(8\) | − | 399.191i | − | 0.0974589i | ||||||
\(9\) | 395.432 | 0.0602701 | ||||||||
\(10\) | −12614.4 | −1.26144 | ||||||||
\(11\) | −22302.0 | −1.52325 | −0.761627 | − | 0.648016i | \(-0.775599\pi\) | ||||
−0.761627 | + | 0.648016i | \(0.775599\pi\) | |||||||
\(12\) | − | 21463.8i | − | 1.03510i | ||||||
\(13\) | 25711.7 | 0.900237 | 0.450118 | − | 0.892969i | \(-0.351382\pi\) | ||||
0.450118 | + | 0.892969i | \(0.351382\pi\) | |||||||
\(14\) | −50937.3 | −1.32594 | ||||||||
\(15\) | −43050.7 | −0.850385 | ||||||||
\(16\) | −60793.3 | −0.927632 | ||||||||
\(17\) | 94860.8 | 1.13577 | 0.567886 | − | 0.823107i | \(-0.307762\pi\) | ||||
0.567886 | + | 0.823107i | \(0.307762\pi\) | |||||||
\(18\) | 9097.95i | 0.0866670i | ||||||||
\(19\) | 13775.7i | 0.105706i | 0.998602 | + | 0.0528528i | \(0.0168314\pi\) | ||||
−0.998602 | + | 0.0528528i | \(0.983169\pi\) | |||||||
\(20\) | − | 149870.i | − | 0.936685i | ||||||
\(21\) | −173841. | −0.893869 | ||||||||
\(22\) | − | 513115.i | − | 2.19040i | ||||||
\(23\) | 444307. | 1.58771 | 0.793856 | − | 0.608106i | \(-0.208070\pi\) | ||||
0.793856 | + | 0.608106i | \(0.208070\pi\) | |||||||
\(24\) | 31345.0 | 0.0944763 | ||||||||
\(25\) | 90025.7 | 0.230466 | ||||||||
\(26\) | 591564.i | 1.29452i | ||||||||
\(27\) | 546227.i | 1.02782i | ||||||||
\(28\) | − | 605180.i | − | 0.984582i | ||||||
\(29\) | − | 843909.i | − | 1.19317i | −0.802549 | − | 0.596587i | \(-0.796523\pi\) | ||
0.802549 | − | 0.596587i | \(-0.203477\pi\) | |||||||
\(30\) | − | 990495.i | − | 1.22283i | ||||||
\(31\) | 557250. | 0.603398 | 0.301699 | − | 0.953403i | \(-0.402446\pi\) | ||||
0.301699 | + | 0.953403i | \(0.402446\pi\) | |||||||
\(32\) | − | 1.50090e6i | − | 1.43137i | ||||||
\(33\) | − | 1.75117e6i | − | 1.47664i | ||||||
\(34\) | 2.18252e6i | 1.63321i | ||||||||
\(35\) | −1.21383e6 | −0.808884 | ||||||||
\(36\) | −108092. | −0.0643549 | ||||||||
\(37\) | − | 1.34789e6i | − | 0.719194i | −0.933108 | − | 0.359597i | \(-0.882914\pi\) | ||
0.933108 | − | 0.359597i | \(-0.117086\pi\) | |||||||
\(38\) | −316945. | −0.152002 | ||||||||
\(39\) | 2.01891e6i | 0.872687i | ||||||||
\(40\) | 218864. | 0.0854939 | ||||||||
\(41\) | −2.42209e6 | −0.857146 | −0.428573 | − | 0.903507i | \(-0.640984\pi\) | ||||
−0.428573 | + | 0.903507i | \(0.640984\pi\) | |||||||
\(42\) | − | 3.99966e6i | − | 1.28536i | ||||||
\(43\) | −493656. | + | 3.38297e6i | −0.144395 | + | 0.989520i | ||||
\(44\) | 6.09625e6 | 1.62649 | ||||||||
\(45\) | 216803.i | 0.0528708i | ||||||||
\(46\) | 1.02224e7i | 2.28309i | ||||||||
\(47\) | −4.12862e6 | −0.846084 | −0.423042 | − | 0.906110i | \(-0.639038\pi\) | ||||
−0.423042 | + | 0.906110i | \(0.639038\pi\) | |||||||
\(48\) | − | 4.77356e6i | − | 0.899243i | ||||||
\(49\) | 863301. | 0.149754 | ||||||||
\(50\) | 2.07128e6i | 0.331404i | ||||||||
\(51\) | 7.44857e6i | 1.10101i | ||||||||
\(52\) | −7.02829e6 | −0.961250 | ||||||||
\(53\) | 717126. | 0.0908849 | 0.0454425 | − | 0.998967i | \(-0.485530\pi\) | ||||
0.0454425 | + | 0.998967i | \(0.485530\pi\) | |||||||
\(54\) | −1.25674e7 | −1.47798 | ||||||||
\(55\) | − | 1.22275e7i | − | 1.33625i | ||||||
\(56\) | 883783. | 0.0898656 | ||||||||
\(57\) | −1.08168e6 | −0.102471 | ||||||||
\(58\) | 1.94163e7 | 1.71575 | ||||||||
\(59\) | −1.58674e7 | −1.30947 | −0.654737 | − | 0.755856i | \(-0.727221\pi\) | ||||
−0.654737 | + | 0.755856i | \(0.727221\pi\) | |||||||
\(60\) | 1.17679e7 | 0.908020 | ||||||||
\(61\) | 1.76056e7i | 1.27154i | 0.771877 | + | 0.635772i | \(0.219318\pi\) | ||||
−0.771877 | + | 0.635772i | \(0.780682\pi\) | |||||||
\(62\) | 1.28210e7i | 0.867671i | ||||||||
\(63\) | 875460.i | 0.0555743i | ||||||||
\(64\) | 1.89691e7 | 1.13065 | ||||||||
\(65\) | 1.40969e7i | 0.789716i | ||||||||
\(66\) | 4.02904e7 | 2.12337 | ||||||||
\(67\) | 2.33402e7 | 1.15826 | 0.579129 | − | 0.815236i | \(-0.303393\pi\) | ||||
0.579129 | + | 0.815236i | \(0.303393\pi\) | |||||||
\(68\) | −2.59302e7 | −1.21275 | ||||||||
\(69\) | 3.48875e7i | 1.53912i | ||||||||
\(70\) | − | 2.79274e7i | − | 1.16316i | ||||||
\(71\) | − | 1.27010e7i | − | 0.499811i | −0.968270 | − | 0.249905i | \(-0.919600\pi\) | ||
0.968270 | − | 0.249905i | \(-0.0803995\pi\) | |||||||
\(72\) | − | 157853.i | − | 0.00587386i | ||||||
\(73\) | 4.05442e6i | 0.142770i | 0.997449 | + | 0.0713851i | \(0.0227419\pi\) | ||||
−0.997449 | + | 0.0713851i | \(0.977258\pi\) | |||||||
\(74\) | 3.10116e7 | 1.03418 | ||||||||
\(75\) | 7.06892e6i | 0.223413i | ||||||||
\(76\) | − | 3.76559e6i | − | 0.112870i | ||||||
\(77\) | − | 4.93750e7i | − | 1.40457i | ||||||
\(78\) | −4.64503e7 | −1.25490 | ||||||||
\(79\) | −6.41487e7 | −1.64695 | −0.823473 | − | 0.567356i | \(-0.807966\pi\) | ||||
−0.823473 | + | 0.567356i | \(0.807966\pi\) | |||||||
\(80\) | − | 3.33311e7i | − | 0.813747i | ||||||
\(81\) | −4.02959e7 | −0.936097 | ||||||||
\(82\) | − | 5.57265e7i | − | 1.23256i | ||||||
\(83\) | −4.42985e7 | −0.933420 | −0.466710 | − | 0.884410i | \(-0.654561\pi\) | ||||
−0.466710 | + | 0.884410i | \(0.654561\pi\) | |||||||
\(84\) | 4.75194e7 | 0.954451 | ||||||||
\(85\) | 5.20092e7i | 0.996334i | ||||||||
\(86\) | −7.78341e7 | − | 1.13579e7i | −1.42291 | − | 0.207636i | ||||
\(87\) | 6.62647e7 | 1.15666 | ||||||||
\(88\) | 8.90275e6i | 0.148455i | ||||||||
\(89\) | − | 8.42809e7i | − | 1.34329i | −0.740874 | − | 0.671644i | \(-0.765588\pi\) | ||
0.740874 | − | 0.671644i | \(-0.234412\pi\) | |||||||
\(90\) | −4.98813e6 | −0.0760270 | ||||||||
\(91\) | 5.69239e7i | 0.830098i | ||||||||
\(92\) | −1.21451e8 | −1.69532 | ||||||||
\(93\) | 4.37559e7i | 0.584932i | ||||||||
\(94\) | − | 9.49898e7i | − | 1.21665i | ||||||
\(95\) | −7.55278e6 | −0.0927283 | ||||||||
\(96\) | 1.17852e8 | 1.38757 | ||||||||
\(97\) | 6.90318e7 | 0.779762 | 0.389881 | − | 0.920865i | \(-0.372516\pi\) | ||||
0.389881 | + | 0.920865i | \(0.372516\pi\) | |||||||
\(98\) | 1.98625e7i | 0.215342i | ||||||||
\(99\) | −8.81891e6 | −0.0918067 | ||||||||
\(100\) | −2.46086e7 | −0.246086 | ||||||||
\(101\) | 5.71873e6 | 0.0549558 | 0.0274779 | − | 0.999622i | \(-0.491252\pi\) | ||||
0.0274779 | + | 0.999622i | \(0.491252\pi\) | |||||||
\(102\) | −1.71374e8 | −1.58323 | ||||||||
\(103\) | 4.67582e7 | 0.415441 | 0.207720 | − | 0.978188i | \(-0.433396\pi\) | ||||
0.207720 | + | 0.978188i | \(0.433396\pi\) | |||||||
\(104\) | − | 1.02639e7i | − | 0.0877361i | ||||||
\(105\) | − | 9.53114e7i | − | 0.784130i | ||||||
\(106\) | 1.64994e7i | 0.130690i | ||||||||
\(107\) | 1.33766e8 | 1.02050 | 0.510248 | − | 0.860027i | \(-0.329554\pi\) | ||||
0.510248 | + | 0.860027i | \(0.329554\pi\) | |||||||
\(108\) | − | 1.49311e8i | − | 1.09748i | ||||||
\(109\) | 9.33602e7 | 0.661387 | 0.330694 | − | 0.943738i | \(-0.392717\pi\) | ||||
0.330694 | + | 0.943738i | \(0.392717\pi\) | |||||||
\(110\) | 2.81325e8 | 1.92149 | ||||||||
\(111\) | 1.05837e8 | 0.697184 | ||||||||
\(112\) | − | 1.34592e8i | − | 0.855358i | ||||||
\(113\) | 2.60559e8i | 1.59806i | 0.601294 | + | 0.799028i | \(0.294652\pi\) | ||||
−0.601294 | + | 0.799028i | \(0.705348\pi\) | |||||||
\(114\) | − | 2.48869e7i | − | 0.147350i | ||||||
\(115\) | 2.43600e8i | 1.39279i | ||||||||
\(116\) | 2.30683e8i | 1.27404i | ||||||||
\(117\) | 1.01672e7 | 0.0542574 | ||||||||
\(118\) | − | 3.65071e8i | − | 1.88299i | ||||||
\(119\) | 2.10015e8i | 1.04728i | ||||||||
\(120\) | 1.71855e7i | 0.0828775i | ||||||||
\(121\) | 2.83018e8 | 1.32030 | ||||||||
\(122\) | −4.05063e8 | −1.82845 | ||||||||
\(123\) | − | 1.90185e8i | − | 0.830914i | ||||||
\(124\) | −1.52325e8 | −0.644293 | ||||||||
\(125\) | 2.63526e8i | 1.07940i | ||||||||
\(126\) | −2.01423e7 | −0.0799146 | ||||||||
\(127\) | 2.42053e8 | 0.930457 | 0.465229 | − | 0.885191i | \(-0.345972\pi\) | ||||
0.465229 | + | 0.885191i | \(0.345972\pi\) | |||||||
\(128\) | 5.22027e7i | 0.194470i | ||||||||
\(129\) | −2.65635e8 | − | 3.87624e7i | −0.959238 | − | 0.139976i | ||||
\(130\) | −3.24337e8 | −1.13559 | ||||||||
\(131\) | − | 3.17260e7i | − | 0.107728i | −0.998548 | − | 0.0538642i | \(-0.982846\pi\) | ||
0.998548 | − | 0.0538642i | \(-0.0171538\pi\) | |||||||
\(132\) | 4.78684e8i | 1.57672i | ||||||||
\(133\) | −3.04984e7 | −0.0974700 | ||||||||
\(134\) | 5.37003e8i | 1.66555i | ||||||||
\(135\) | −2.99479e8 | −0.901638 | ||||||||
\(136\) | − | 3.78676e7i | − | 0.110691i | ||||||
\(137\) | 4.48682e7i | 0.127367i | 0.997970 | + | 0.0636834i | \(0.0202848\pi\) | ||||
−0.997970 | + | 0.0636834i | \(0.979715\pi\) | |||||||
\(138\) | −8.02678e8 | −2.21322 | ||||||||
\(139\) | 2.23751e8 | 0.599384 | 0.299692 | − | 0.954036i | \(-0.403116\pi\) | ||||
0.299692 | + | 0.954036i | \(0.403116\pi\) | |||||||
\(140\) | 3.31801e8 | 0.863706 | ||||||||
\(141\) | − | 3.24184e8i | − | 0.820191i | ||||||
\(142\) | 2.92220e8 | 0.718716 | ||||||||
\(143\) | −5.73421e8 | −1.37129 | ||||||||
\(144\) | −2.40396e7 | −0.0559085 | ||||||||
\(145\) | 4.62689e8 | 1.04669 | ||||||||
\(146\) | −9.32826e7 | −0.205300 | ||||||||
\(147\) | 6.77874e7i | 0.145171i | ||||||||
\(148\) | 3.68445e8i | 0.767937i | ||||||||
\(149\) | − | 5.16841e8i | − | 1.04861i | −0.851532 | − | 0.524303i | \(-0.824326\pi\) | ||
0.851532 | − | 0.524303i | \(-0.175674\pi\) | |||||||
\(150\) | −1.62639e8 | −0.321262 | ||||||||
\(151\) | 2.26895e8i | 0.436432i | 0.975900 | + | 0.218216i | \(0.0700238\pi\) | ||||
−0.975900 | + | 0.218216i | \(0.929976\pi\) | |||||||
\(152\) | 5.49913e6 | 0.0103020 | ||||||||
\(153\) | 3.75110e7 | 0.0684531 | ||||||||
\(154\) | 1.13600e9 | 2.01974 | ||||||||
\(155\) | 3.05523e8i | 0.529319i | ||||||||
\(156\) | − | 5.51870e8i | − | 0.931833i | ||||||
\(157\) | − | 1.47899e8i | − | 0.243426i | −0.992565 | − | 0.121713i | \(-0.961161\pi\) | ||
0.992565 | − | 0.121713i | \(-0.0388387\pi\) | |||||||
\(158\) | − | 1.47591e9i | − | 2.36827i | ||||||
\(159\) | 5.63095e7i | 0.0881035i | ||||||||
\(160\) | 8.22898e8 | 1.25564 | ||||||||
\(161\) | 9.83666e8i | 1.46401i | ||||||||
\(162\) | − | 9.27113e8i | − | 1.34609i | ||||||
\(163\) | − | 5.39395e8i | − | 0.764111i | −0.924139 | − | 0.382056i | \(-0.875216\pi\) | ||
0.924139 | − | 0.382056i | \(-0.124784\pi\) | |||||||
\(164\) | 6.62079e8 | 0.915239 | ||||||||
\(165\) | 9.60116e8 | 1.29535 | ||||||||
\(166\) | − | 1.01920e9i | − | 1.34224i | ||||||
\(167\) | −1.17007e9 | −1.50434 | −0.752171 | − | 0.658968i | \(-0.770993\pi\) | ||||
−0.752171 | + | 0.658968i | \(0.770993\pi\) | |||||||
\(168\) | 6.93957e7i | 0.0871155i | ||||||||
\(169\) | −1.54641e8 | −0.189573 | ||||||||
\(170\) | −1.19661e9 | −1.43270 | ||||||||
\(171\) | 5.44734e6i | 0.00637089i | ||||||||
\(172\) | 1.34941e8 | − | 9.24737e8i | 0.154181 | − | 1.05658i | ||||
\(173\) | −7.41901e7 | −0.0828250 | −0.0414125 | − | 0.999142i | \(-0.513186\pi\) | ||||
−0.0414125 | + | 0.999142i | \(0.513186\pi\) | |||||||
\(174\) | 1.52459e9i | 1.66325i | ||||||||
\(175\) | 1.99311e8i | 0.212510i | ||||||||
\(176\) | 1.35581e9 | 1.41302 | ||||||||
\(177\) | − | 1.24592e9i | − | 1.26940i | ||||||
\(178\) | 1.93910e9 | 1.93162 | ||||||||
\(179\) | 1.95172e9i | 1.90110i | 0.310566 | + | 0.950552i | \(0.399481\pi\) | ||||
−0.310566 | + | 0.950552i | \(0.600519\pi\) | |||||||
\(180\) | − | 5.92633e7i | − | 0.0564541i | ||||||
\(181\) | −1.70935e9 | −1.59264 | −0.796319 | − | 0.604877i | \(-0.793222\pi\) | ||||
−0.796319 | + | 0.604877i | \(0.793222\pi\) | |||||||
\(182\) | −1.30968e9 | −1.19366 | ||||||||
\(183\) | −1.38241e9 | −1.23263 | ||||||||
\(184\) | − | 1.77363e8i | − | 0.154737i | ||||||
\(185\) | 7.39004e8 | 0.630899 | ||||||||
\(186\) | −1.00672e9 | −0.841118 | ||||||||
\(187\) | −2.11558e9 | −1.73007 | ||||||||
\(188\) | 1.12856e9 | 0.903428 | ||||||||
\(189\) | −1.20931e9 | −0.947743 | ||||||||
\(190\) | − | 1.73771e8i | − | 0.133341i | ||||||
\(191\) | − | 2.52030e9i | − | 1.89373i | −0.321628 | − | 0.946866i | \(-0.604230\pi\) | ||
0.321628 | − | 0.946866i | \(-0.395770\pi\) | |||||||
\(192\) | 1.48947e9i | 1.09604i | ||||||||
\(193\) | 1.25620e9 | 0.905380 | 0.452690 | − | 0.891668i | \(-0.350464\pi\) | ||||
0.452690 | + | 0.891668i | \(0.350464\pi\) | |||||||
\(194\) | 1.58826e9i | 1.12128i | ||||||||
\(195\) | −1.10691e9 | −0.765548 | ||||||||
\(196\) | −2.35984e8 | −0.159903 | ||||||||
\(197\) | 7.03003e8 | 0.466758 | 0.233379 | − | 0.972386i | \(-0.425022\pi\) | ||||
0.233379 | + | 0.972386i | \(0.425022\pi\) | |||||||
\(198\) | − | 2.02902e8i | − | 0.132016i | ||||||
\(199\) | − | 1.62062e9i | − | 1.03340i | −0.856166 | − | 0.516701i | \(-0.827160\pi\) | ||
0.856166 | − | 0.516701i | \(-0.172840\pi\) | |||||||
\(200\) | − | 3.59375e7i | − | 0.0224609i | ||||||
\(201\) | 1.83270e9i | 1.12281i | ||||||||
\(202\) | 1.31574e8i | 0.0790252i | ||||||||
\(203\) | 1.86836e9 | 1.10021 | ||||||||
\(204\) | − | 2.03607e9i | − | 1.17563i | ||||||
\(205\) | − | 1.32796e9i | − | 0.751915i | ||||||
\(206\) | 1.07579e9i | 0.597394i | ||||||||
\(207\) | 1.75693e8 | 0.0956916 | ||||||||
\(208\) | −1.56310e9 | −0.835088 | ||||||||
\(209\) | − | 3.07224e8i | − | 0.161017i | ||||||
\(210\) | 2.19289e9 | 1.12756 | ||||||||
\(211\) | − | 2.02893e8i | − | 0.102362i | −0.998689 | − | 0.0511808i | \(-0.983702\pi\) | ||
0.998689 | − | 0.0511808i | \(-0.0162985\pi\) | |||||||
\(212\) | −1.96027e8 | −0.0970446 | ||||||||
\(213\) | 9.97299e8 | 0.484515 | ||||||||
\(214\) | 3.07764e9i | 1.46745i | ||||||||
\(215\) | −1.85478e9 | − | 2.70657e8i | −0.868038 | − | 0.126667i | ||||
\(216\) | 2.18049e8 | 0.100170 | ||||||||
\(217\) | 1.23371e9i | 0.556386i | ||||||||
\(218\) | 2.14800e9i | 0.951059i | ||||||||
\(219\) | −3.18358e8 | −0.138401 | ||||||||
\(220\) | 3.34239e9i | 1.42681i | ||||||||
\(221\) | 2.43903e9 | 1.02246 | ||||||||
\(222\) | 2.43507e9i | 1.00253i | ||||||||
\(223\) | 2.20052e9i | 0.889827i | 0.895573 | + | 0.444914i | \(0.146766\pi\) | ||||
−0.895573 | + | 0.444914i | \(0.853234\pi\) | |||||||
\(224\) | 3.32289e9 | 1.31985 | ||||||||
\(225\) | 3.55990e7 | 0.0138902 | ||||||||
\(226\) | −5.99484e9 | −2.29797 | ||||||||
\(227\) | 3.11333e9i | 1.17252i | 0.810122 | + | 0.586262i | \(0.199401\pi\) | ||||
−0.810122 | + | 0.586262i | \(0.800599\pi\) | |||||||
\(228\) | 2.95678e8 | 0.109416 | ||||||||
\(229\) | 4.08434e9 | 1.48518 | 0.742592 | − | 0.669744i | \(-0.233596\pi\) | ||||
0.742592 | + | 0.669744i | \(0.233596\pi\) | |||||||
\(230\) | −5.60465e9 | −2.00280 | ||||||||
\(231\) | 3.87698e9 | 1.36159 | ||||||||
\(232\) | −3.36881e8 | −0.116285 | ||||||||
\(233\) | − | 3.98505e9i | − | 1.35210i | −0.736854 | − | 0.676052i | \(-0.763689\pi\) | ||
0.736854 | − | 0.676052i | \(-0.236311\pi\) | |||||||
\(234\) | 2.33924e8i | 0.0780208i | ||||||||
\(235\) | − | 2.26360e9i | − | 0.742212i | ||||||
\(236\) | 4.33735e9 | 1.39822 | ||||||||
\(237\) | − | 5.03702e9i | − | 1.59654i | ||||||
\(238\) | −4.83195e9 | −1.50596 | ||||||||
\(239\) | 3.61698e9 | 1.10855 | 0.554274 | − | 0.832334i | \(-0.312996\pi\) | ||||
0.554274 | + | 0.832334i | \(0.312996\pi\) | |||||||
\(240\) | 2.61719e9 | 0.788844 | ||||||||
\(241\) | − | 5.13891e9i | − | 1.52336i | −0.647953 | − | 0.761680i | \(-0.724375\pi\) | ||
0.647953 | − | 0.761680i | \(-0.275625\pi\) | |||||||
\(242\) | 6.51158e9i | 1.89856i | ||||||||
\(243\) | 4.19713e8i | 0.120373i | ||||||||
\(244\) | − | 4.81250e9i | − | 1.35772i | ||||||
\(245\) | 4.73321e8i | 0.131369i | ||||||||
\(246\) | 4.37571e9 | 1.19483 | ||||||||
\(247\) | 3.54195e8i | 0.0951602i | ||||||||
\(248\) | − | 2.22450e8i | − | 0.0588064i | ||||||
\(249\) | − | 3.47837e9i | − | 0.904854i | ||||||
\(250\) | −6.06311e9 | −1.55216 | ||||||||
\(251\) | 3.59876e9 | 0.906688 | 0.453344 | − | 0.891336i | \(-0.350231\pi\) | ||||
0.453344 | + | 0.891336i | \(0.350231\pi\) | |||||||
\(252\) | − | 2.39307e8i | − | 0.0593409i | ||||||
\(253\) | −9.90891e9 | −2.41849 | ||||||||
\(254\) | 5.56907e9i | 1.33798i | ||||||||
\(255\) | −4.08382e9 | −0.965843 | ||||||||
\(256\) | 3.65503e9 | 0.851002 | ||||||||
\(257\) | 3.58551e9i | 0.821898i | 0.911658 | + | 0.410949i | \(0.134803\pi\) | ||||
−0.911658 | + | 0.410949i | \(0.865197\pi\) | |||||||
\(258\) | 8.91832e8 | − | 6.11162e9i | 0.201282 | − | 1.37936i | ||||
\(259\) | 2.98413e9 | 0.663160 | ||||||||
\(260\) | − | 3.85340e9i | − | 0.843239i | ||||||
\(261\) | − | 3.33709e8i | − | 0.0719127i | ||||||
\(262\) | 7.29939e8 | 0.154911 | ||||||||
\(263\) | 2.72133e9i | 0.568799i | 0.958706 | + | 0.284400i | \(0.0917942\pi\) | ||||
−0.958706 | + | 0.284400i | \(0.908206\pi\) | |||||||
\(264\) | −6.99054e8 | −0.143911 | ||||||||
\(265\) | 3.93178e8i | 0.0797271i | ||||||||
\(266\) | − | 7.01696e8i | − | 0.140159i | ||||||
\(267\) | 6.61783e9 | 1.30218 | ||||||||
\(268\) | −6.38006e9 | −1.23676 | ||||||||
\(269\) | −5.51586e9 | −1.05343 | −0.526713 | − | 0.850043i | \(-0.676576\pi\) | ||||
−0.526713 | + | 0.850043i | \(0.676576\pi\) | |||||||
\(270\) | − | 6.89031e9i | − | 1.29653i | ||||||
\(271\) | −2.83300e9 | −0.525255 | −0.262627 | − | 0.964897i | \(-0.584589\pi\) | ||||
−0.262627 | + | 0.964897i | \(0.584589\pi\) | |||||||
\(272\) | −5.76689e9 | −1.05358 | ||||||||
\(273\) | −4.46973e9 | −0.804694 | ||||||||
\(274\) | −1.03231e9 | −0.183150 | ||||||||
\(275\) | −2.00775e9 | −0.351058 | ||||||||
\(276\) | − | 9.53650e9i | − | 1.64344i | ||||||
\(277\) | 9.20304e9i | 1.56319i | 0.623785 | + | 0.781596i | \(0.285594\pi\) | ||||
−0.623785 | + | 0.781596i | \(0.714406\pi\) | |||||||
\(278\) | 5.14797e9i | 0.861900i | ||||||||
\(279\) | 2.20355e8 | 0.0363668 | ||||||||
\(280\) | 4.84551e8i | 0.0788329i | ||||||||
\(281\) | 4.72092e9 | 0.757184 | 0.378592 | − | 0.925564i | \(-0.376408\pi\) | ||||
0.378592 | + | 0.925564i | \(0.376408\pi\) | |||||||
\(282\) | 7.45870e9 | 1.17942 | ||||||||
\(283\) | 1.11248e9 | 0.173439 | 0.0867194 | − | 0.996233i | \(-0.472362\pi\) | ||||
0.0867194 | + | 0.996233i | \(0.472362\pi\) | |||||||
\(284\) | 3.47183e9i | 0.533685i | ||||||||
\(285\) | − | 5.93053e8i | − | 0.0898905i | ||||||
\(286\) | − | 1.31930e10i | − | 1.97188i | ||||||
\(287\) | − | 5.36234e9i | − | 0.790364i | ||||||
\(288\) | − | 5.93505e8i | − | 0.0862689i | ||||||
\(289\) | 2.02281e9 | 0.289976 | ||||||||
\(290\) | 1.06454e10i | 1.50511i | ||||||||
\(291\) | 5.42045e9i | 0.755899i | ||||||||
\(292\) | − | 1.10828e9i | − | 0.152446i | ||||||
\(293\) | −6.59517e9 | −0.894860 | −0.447430 | − | 0.894319i | \(-0.647661\pi\) | ||||
−0.447430 | + | 0.894319i | \(0.647661\pi\) | |||||||
\(294\) | −1.55963e9 | −0.208752 | ||||||||
\(295\) | − | 8.69960e9i | − | 1.14871i | ||||||
\(296\) | −5.38064e8 | −0.0700918 | ||||||||
\(297\) | − | 1.21819e10i | − | 1.56563i | ||||||
\(298\) | 1.18913e10 | 1.50787 | ||||||||
\(299\) | 1.14239e10 | 1.42932 | ||||||||
\(300\) | − | 1.93229e9i | − | 0.238555i | ||||||
\(301\) | −7.48968e9 | − | 1.09292e9i | −0.912425 | − | 0.133144i | ||||
\(302\) | −5.22031e9 | −0.627579 | ||||||||
\(303\) | 4.49041e8i | 0.0532740i | ||||||||
\(304\) | − | 8.37468e8i | − | 0.0980559i | ||||||
\(305\) | −9.65261e9 | −1.11544 | ||||||||
\(306\) | 8.63039e8i | 0.0984339i | ||||||||
\(307\) | 2.40305e9 | 0.270526 | 0.135263 | − | 0.990810i | \(-0.456812\pi\) | ||||
0.135263 | + | 0.990810i | \(0.456812\pi\) | |||||||
\(308\) | 1.34967e10i | 1.49977i | ||||||||
\(309\) | 3.67151e9i | 0.402727i | ||||||||
\(310\) | −7.02936e9 | −0.761148 | ||||||||
\(311\) | 1.25145e10 | 1.33774 | 0.668870 | − | 0.743380i | \(-0.266778\pi\) | ||||
0.668870 | + | 0.743380i | \(0.266778\pi\) | |||||||
\(312\) | 8.05931e8 | 0.0850510 | ||||||||
\(313\) | − | 2.72482e9i | − | 0.283897i | −0.989874 | − | 0.141948i | \(-0.954663\pi\) | ||
0.989874 | − | 0.141948i | \(-0.0453367\pi\) | |||||||
\(314\) | 3.40280e9 | 0.350040 | ||||||||
\(315\) | −4.79988e8 | −0.0487515 | ||||||||
\(316\) | 1.75351e10 | 1.75857 | ||||||||
\(317\) | 2.40399e9 | 0.238065 | 0.119033 | − | 0.992890i | \(-0.462021\pi\) | ||||
0.119033 | + | 0.992890i | \(0.462021\pi\) | |||||||
\(318\) | −1.29555e9 | −0.126691 | ||||||||
\(319\) | 1.88208e10i | 1.81751i | ||||||||
\(320\) | 1.04002e10i | 0.991837i | ||||||||
\(321\) | 1.05035e10i | 0.989265i | ||||||||
\(322\) | −2.26318e10 | −2.10521 | ||||||||
\(323\) | 1.30677e9i | 0.120057i | ||||||||
\(324\) | 1.10149e10 | 0.999541 | ||||||||
\(325\) | 2.31471e9 | 0.207474 | ||||||||
\(326\) | 1.24102e10 | 1.09877 | ||||||||
\(327\) | 7.33075e9i | 0.641147i | ||||||||
\(328\) | 9.66878e8i | 0.0835365i | ||||||||
\(329\) | − | 9.14049e9i | − | 0.780164i | ||||||
\(330\) | 2.20900e10i | 1.86268i | ||||||||
\(331\) | − | 1.85040e10i | − | 1.54153i | −0.637118 | − | 0.770766i | \(-0.719874\pi\) | ||
0.637118 | − | 0.770766i | \(-0.280126\pi\) | |||||||
\(332\) | 1.21090e10 | 0.996683 | ||||||||
\(333\) | − | 5.32997e8i | − | 0.0433459i | ||||||
\(334\) | − | 2.69206e10i | − | 2.16321i | ||||||
\(335\) | 1.27967e10i | 1.01606i | ||||||||
\(336\) | 1.05683e10 | 0.829181 | ||||||||
\(337\) | 1.84917e10 | 1.43370 | 0.716849 | − | 0.697229i | \(-0.245584\pi\) | ||||
0.716849 | + | 0.697229i | \(0.245584\pi\) | |||||||
\(338\) | − | 3.55792e9i | − | 0.272602i | ||||||
\(339\) | −2.04594e10 | −1.54915 | ||||||||
\(340\) | − | 1.42167e10i | − | 1.06386i | ||||||
\(341\) | −1.24278e10 | −0.919128 | ||||||||
\(342\) | −1.25330e8 | −0.00916119 | ||||||||
\(343\) | 1.46742e10i | 1.06017i | ||||||||
\(344\) | 1.35045e9 | + | 1.97063e8i | 0.0964375 | + | 0.0140725i | ||||
\(345\) | −1.91277e10 | −1.35017 | ||||||||
\(346\) | − | 1.70694e9i | − | 0.119100i | ||||||
\(347\) | − | 2.21431e9i | − | 0.152729i | −0.997080 | − | 0.0763643i | \(-0.975669\pi\) | ||
0.997080 | − | 0.0763643i | \(-0.0243312\pi\) | |||||||
\(348\) | −1.81135e10 | −1.23505 | ||||||||
\(349\) | 1.01146e10i | 0.681787i | 0.940102 | + | 0.340893i | \(0.110730\pi\) | ||||
−0.940102 | + | 0.340893i | \(0.889270\pi\) | |||||||
\(350\) | −4.58567e9 | −0.305584 | ||||||||
\(351\) | 1.40444e10i | 0.925284i | ||||||||
\(352\) | 3.34730e10i | 2.18034i | ||||||||
\(353\) | −1.17769e10 | −0.758461 | −0.379230 | − | 0.925302i | \(-0.623811\pi\) | ||||
−0.379230 | + | 0.925302i | \(0.623811\pi\) | |||||||
\(354\) | 2.86658e10 | 1.82537 | ||||||||
\(355\) | 6.96359e9 | 0.438449 | ||||||||
\(356\) | 2.30382e10i | 1.43433i | ||||||||
\(357\) | −1.64906e10 | −1.01523 | ||||||||
\(358\) | −4.49045e10 | −2.73374 | ||||||||
\(359\) | −2.45068e9 | −0.147540 | −0.0737700 | − | 0.997275i | \(-0.523503\pi\) | ||||
−0.0737700 | + | 0.997275i | \(0.523503\pi\) | |||||||
\(360\) | 8.65461e7 | 0.00515273 | ||||||||
\(361\) | 1.67938e10 | 0.988826 | ||||||||
\(362\) | − | 3.93281e10i | − | 2.29017i | ||||||
\(363\) | 2.22229e10i | 1.27990i | ||||||||
\(364\) | − | 1.55602e10i | − | 0.886358i | ||||||
\(365\) | −2.22291e9 | −0.125242 | ||||||||
\(366\) | − | 3.18060e10i | − | 1.77249i | ||||||
\(367\) | 1.88958e10 | 1.04160 | 0.520800 | − | 0.853678i | \(-0.325634\pi\) | ||||
0.520800 | + | 0.853678i | \(0.325634\pi\) | |||||||
\(368\) | −2.70109e10 | −1.47281 | ||||||||
\(369\) | −9.57772e8 | −0.0516603 | ||||||||
\(370\) | 1.70027e10i | 0.907218i | ||||||||
\(371\) | 1.58767e9i | 0.0838039i | ||||||||
\(372\) | − | 1.19607e10i | − | 0.624575i | ||||||
\(373\) | − | 6.77386e9i | − | 0.349946i | −0.984573 | − | 0.174973i | \(-0.944016\pi\) | ||
0.984573 | − | 0.174973i | \(-0.0559838\pi\) | |||||||
\(374\) | − | 4.86745e10i | − | 2.48780i | ||||||
\(375\) | −2.06924e10 | −1.04637 | ||||||||
\(376\) | 1.64811e9i | 0.0824584i | ||||||||
\(377\) | − | 2.16983e10i | − | 1.07414i | ||||||
\(378\) | − | 2.78233e10i | − | 1.36283i | ||||||
\(379\) | −3.86135e10 | −1.87147 | −0.935735 | − | 0.352704i | \(-0.885262\pi\) | ||||
−0.935735 | + | 0.352704i | \(0.885262\pi\) | |||||||
\(380\) | 2.06456e9 | 0.0990130 | ||||||||
\(381\) | 1.90063e10i | 0.901982i | ||||||||
\(382\) | 5.79861e10 | 2.72314 | ||||||||
\(383\) | 3.90536e10i | 1.81495i | 0.420101 | + | 0.907477i | \(0.361995\pi\) | ||||
−0.420101 | + | 0.907477i | \(0.638005\pi\) | |||||||
\(384\) | −4.09901e9 | −0.188519 | ||||||||
\(385\) | 2.70708e10 | 1.23214 | ||||||||
\(386\) | 2.89023e10i | 1.30192i | ||||||||
\(387\) | −1.95208e8 | + | 1.33774e9i | −0.00870268 | + | 0.0596385i | ||||
\(388\) | −1.88699e10 | −0.832610 | ||||||||
\(389\) | − | 2.51473e10i | − | 1.09823i | −0.835747 | − | 0.549115i | \(-0.814965\pi\) | ||
0.835747 | − | 0.549115i | \(-0.185035\pi\) | |||||||
\(390\) | − | 2.54673e10i | − | 1.10084i | ||||||
\(391\) | 4.21473e10 | 1.80328 | ||||||||
\(392\) | − | 3.44622e8i | − | 0.0145948i | ||||||
\(393\) | 2.49116e9 | 0.104432 | ||||||||
\(394\) | 1.61744e10i | 0.671187i | ||||||||
\(395\) | − | 3.51707e10i | − | 1.44475i | ||||||
\(396\) | 2.41065e9 | 0.0980289 | ||||||||
\(397\) | 3.45068e10 | 1.38913 | 0.694565 | − | 0.719430i | \(-0.255597\pi\) | ||||
0.694565 | + | 0.719430i | \(0.255597\pi\) | |||||||
\(398\) | 3.72866e10 | 1.48601 | ||||||||
\(399\) | − | 2.39477e9i | − | 0.0944870i | ||||||
\(400\) | −5.47295e9 | −0.213787 | ||||||||
\(401\) | 2.43097e10 | 0.940162 | 0.470081 | − | 0.882623i | \(-0.344225\pi\) | ||||
0.470081 | + | 0.882623i | \(0.344225\pi\) | |||||||
\(402\) | −4.21661e10 | −1.61458 | ||||||||
\(403\) | 1.43278e10 | 0.543201 | ||||||||
\(404\) | −1.56322e9 | −0.0586805 | ||||||||
\(405\) | − | 2.20930e10i | − | 0.821174i | ||||||
\(406\) | 4.29865e10i | 1.58208i | ||||||||
\(407\) | 3.00605e10i | 1.09552i | ||||||||
\(408\) | 2.97341e9 | 0.107303 | ||||||||
\(409\) | − | 2.52284e10i | − | 0.901564i | −0.892634 | − | 0.450782i | \(-0.851145\pi\) | ||
0.892634 | − | 0.450782i | \(-0.148855\pi\) | |||||||
\(410\) | 3.05531e10 | 1.08124 | ||||||||
\(411\) | −3.52310e9 | −0.123469 | ||||||||
\(412\) | −1.27814e10 | −0.443597 | ||||||||
\(413\) | − | 3.51293e10i | − | 1.20745i | ||||||
\(414\) | 4.04228e9i | 0.137602i | ||||||||
\(415\) | − | 2.42875e10i | − | 0.818825i | ||||||
\(416\) | − | 3.85907e10i | − | 1.28857i | ||||||
\(417\) | 1.75692e10i | 0.581041i | ||||||||
\(418\) | 7.06850e9 | 0.231538 | ||||||||
\(419\) | 4.21693e10i | 1.36817i | 0.729402 | + | 0.684085i | \(0.239798\pi\) | ||||
−0.729402 | + | 0.684085i | \(0.760202\pi\) | |||||||
\(420\) | 2.60534e10i | 0.837274i | ||||||||
\(421\) | − | 2.56731e10i | − | 0.817239i | −0.912705 | − | 0.408620i | \(-0.866010\pi\) | ||
0.912705 | − | 0.408620i | \(-0.133990\pi\) | |||||||
\(422\) | 4.66808e9 | 0.147194 | ||||||||
\(423\) | −1.63259e9 | −0.0509936 | ||||||||
\(424\) | − | 2.86270e8i | − | 0.00885754i | ||||||
\(425\) | 8.53990e9 | 0.261756 | ||||||||
\(426\) | 2.29455e10i | 0.696721i | ||||||||
\(427\) | −3.89776e10 | −1.17248 | ||||||||
\(428\) | −3.65650e10 | −1.08966 | ||||||||
\(429\) | − | 4.50256e10i | − | 1.32932i | ||||||
\(430\) | 6.22716e9 | − | 4.26741e10i | 0.182145 | − | 1.24822i | ||||
\(431\) | −4.50399e10 | −1.30523 | −0.652617 | − | 0.757688i | \(-0.726329\pi\) | ||||
−0.652617 | + | 0.757688i | \(0.726329\pi\) | |||||||
\(432\) | − | 3.32069e10i | − | 0.953440i | ||||||
\(433\) | 3.23102e10i | 0.919153i | 0.888138 | + | 0.459577i | \(0.151999\pi\) | ||||
−0.888138 | + | 0.459577i | \(0.848001\pi\) | |||||||
\(434\) | −2.83848e10 | −0.800069 | ||||||||
\(435\) | 3.63309e10i | 1.01466i | ||||||||
\(436\) | −2.55201e10 | −0.706213 | ||||||||
\(437\) | 6.12062e9i | 0.167830i | ||||||||
\(438\) | − | 7.32465e9i | − | 0.199017i | ||||||
\(439\) | 2.51931e10 | 0.678303 | 0.339151 | − | 0.940732i | \(-0.389860\pi\) | ||||
0.339151 | + | 0.940732i | \(0.389860\pi\) | |||||||
\(440\) | −4.88111e9 | −0.130229 | ||||||||
\(441\) | 3.41377e8 | 0.00902568 | ||||||||
\(442\) | 5.61162e10i | 1.47028i | ||||||||
\(443\) | −5.96388e10 | −1.54851 | −0.774255 | − | 0.632874i | \(-0.781875\pi\) | ||||
−0.774255 | + | 0.632874i | \(0.781875\pi\) | |||||||
\(444\) | −2.89307e10 | −0.744436 | ||||||||
\(445\) | 4.62086e10 | 1.17837 | ||||||||
\(446\) | −5.06287e10 | −1.27955 | ||||||||
\(447\) | 4.05830e10 | 1.01651 | ||||||||
\(448\) | 4.19963e10i | 1.04255i | ||||||||
\(449\) | 4.63343e10i | 1.14003i | 0.821633 | + | 0.570016i | \(0.193063\pi\) | ||||
−0.821633 | + | 0.570016i | \(0.806937\pi\) | |||||||
\(450\) | 8.19049e8i | 0.0199738i | ||||||||
\(451\) | 5.40173e10 | 1.30565 | ||||||||
\(452\) | − | 7.12239e10i | − | 1.70636i | ||||||
\(453\) | −1.78160e10 | −0.423076 | ||||||||
\(454\) | −7.16303e10 | −1.68606 | ||||||||
\(455\) | −3.12096e10 | −0.728187 | ||||||||
\(456\) | 4.31798e8i | 0.00998668i | ||||||||
\(457\) | − | 2.64600e10i | − | 0.606631i | −0.952890 | − | 0.303316i | \(-0.901906\pi\) | ||
0.952890 | − | 0.303316i | \(-0.0980937\pi\) | |||||||
\(458\) | 9.39710e10i | 2.13566i | ||||||||
\(459\) | 5.18155e10i | 1.16737i | ||||||||
\(460\) | − | 6.65881e10i | − | 1.48719i | ||||||
\(461\) | −4.70971e10 | −1.04278 | −0.521388 | − | 0.853320i | \(-0.674585\pi\) | ||||
−0.521388 | + | 0.853320i | \(0.674585\pi\) | |||||||
\(462\) | 8.92002e10i | 1.95793i | ||||||||
\(463\) | − | 4.28757e10i | − | 0.933013i | −0.884518 | − | 0.466507i | \(-0.845512\pi\) | ||
0.884518 | − | 0.466507i | \(-0.154488\pi\) | |||||||
\(464\) | 5.13040e10i | 1.10683i | ||||||||
\(465\) | −2.39900e10 | −0.513120 | ||||||||
\(466\) | 9.16865e10 | 1.94429 | ||||||||
\(467\) | 5.17139e10i | 1.08727i | 0.839320 | + | 0.543637i | \(0.182953\pi\) | ||||
−0.839320 | + | 0.543637i | \(0.817047\pi\) | |||||||
\(468\) | −2.77921e9 | −0.0579347 | ||||||||
\(469\) | 5.16737e10i | 1.06802i | ||||||||
\(470\) | 5.20800e10 | 1.06728 | ||||||||
\(471\) | 1.16132e10 | 0.235976 | ||||||||
\(472\) | 6.33412e9i | 0.127620i | ||||||||
\(473\) | 1.10095e10 | − | 7.54469e10i | 0.219950 | − | 1.50729i | ||||
\(474\) | 1.15890e11 | 2.29579 | ||||||||
\(475\) | 1.24016e9i | 0.0243615i | ||||||||
\(476\) | − | 5.74078e10i | − | 1.11826i | ||||||
\(477\) | 2.83575e8 | 0.00547764 | ||||||||
\(478\) | 8.32181e10i | 1.59407i | ||||||||
\(479\) | 5.36737e10 | 1.01958 | 0.509788 | − | 0.860300i | \(-0.329724\pi\) | ||||
0.509788 | + | 0.860300i | \(0.329724\pi\) | |||||||
\(480\) | 6.46149e10i | 1.21722i | ||||||||
\(481\) | − | 3.46564e10i | − | 0.647445i | ||||||
\(482\) | 1.18234e11 | 2.19055 | ||||||||
\(483\) | −7.72385e10 | −1.41921 | ||||||||
\(484\) | −7.73632e10 | −1.40979 | ||||||||
\(485\) | 3.78480e10i | 0.684031i | ||||||||
\(486\) | −9.65660e9 | −0.173093 | ||||||||
\(487\) | 3.86141e10 | 0.686483 | 0.343242 | − | 0.939247i | \(-0.388475\pi\) | ||||
0.343242 | + | 0.939247i | \(0.388475\pi\) | |||||||
\(488\) | 7.02800e9 | 0.123923 | ||||||||
\(489\) | 4.23539e10 | 0.740727 | ||||||||
\(490\) | −1.08900e10 | −0.188905 | ||||||||
\(491\) | − | 8.61031e10i | − | 1.48147i | −0.671797 | − | 0.740735i | \(-0.734477\pi\) | ||
0.671797 | − | 0.740735i | \(-0.265523\pi\) | |||||||
\(492\) | 5.19872e10i | 0.887230i | ||||||||
\(493\) | − | 8.00538e10i | − | 1.35517i | ||||||
\(494\) | −8.14919e9 | −0.136838 | ||||||||
\(495\) | − | 4.83514e9i | − | 0.0805357i | ||||||
\(496\) | −3.38771e10 | −0.559731 | ||||||||
\(497\) | 2.81192e10 | 0.460869 | ||||||||
\(498\) | 8.00290e10 | 1.30116 | ||||||||
\(499\) | 7.90191e10i | 1.27447i | 0.770669 | + | 0.637235i | \(0.219922\pi\) | ||||
−0.770669 | + | 0.637235i | \(0.780078\pi\) | |||||||
\(500\) | − | 7.20350e10i | − | 1.15256i | ||||||
\(501\) | − | 9.18753e10i | − | 1.45830i | ||||||
\(502\) | 8.27988e10i | 1.30380i | ||||||||
\(503\) | − | 9.92805e10i | − | 1.55093i | −0.631391 | − | 0.775464i | \(-0.717516\pi\) | ||
0.631391 | − | 0.775464i | \(-0.282484\pi\) | |||||||
\(504\) | 3.49476e8 | 0.00541621 | ||||||||
\(505\) | 3.13540e9i | 0.0482090i | ||||||||
\(506\) | − | 2.27980e11i | − | 3.47773i | ||||||
\(507\) | − | 1.21426e10i | − | 0.183772i | ||||||
\(508\) | −6.61654e10 | −0.993519 | ||||||||
\(509\) | −8.82552e10 | −1.31483 | −0.657414 | − | 0.753529i | \(-0.728350\pi\) | ||||
−0.657414 | + | 0.753529i | \(0.728350\pi\) | |||||||
\(510\) | − | 9.39591e10i | − | 1.38886i | ||||||
\(511\) | −8.97622e9 | −0.131647 | ||||||||
\(512\) | 9.74573e10i | 1.41819i | ||||||||
\(513\) | −7.52464e9 | −0.108647 | ||||||||
\(514\) | −8.24940e10 | −1.18187 | ||||||||
\(515\) | 2.56361e10i | 0.364437i | ||||||||
\(516\) | 7.26114e10 | + | 1.05957e10i | 1.02425 | + | 0.149462i | ||||
\(517\) | 9.20764e10 | 1.28880 | ||||||||
\(518\) | 6.86577e10i | 0.953608i | ||||||||
\(519\) | − | 5.82549e9i | − | 0.0802903i | ||||||
\(520\) | 5.62737e9 | 0.0769648 | ||||||||
\(521\) | − | 3.93047e10i | − | 0.533450i | −0.963773 | − | 0.266725i | \(-0.914059\pi\) | ||
0.963773 | − | 0.266725i | \(-0.0859415\pi\) | |||||||
\(522\) | 7.67784e9 | 0.103409 | ||||||||
\(523\) | 1.06896e11i | 1.42875i | 0.699763 | + | 0.714375i | \(0.253289\pi\) | ||||
−0.699763 | + | 0.714375i | \(0.746711\pi\) | |||||||
\(524\) | 8.67231e9i | 0.115030i | ||||||||
\(525\) | −1.56501e10 | −0.206006 | ||||||||
\(526\) | −6.26114e10 | −0.817920 | ||||||||
\(527\) | 5.28612e10 | 0.685322 | ||||||||
\(528\) | 1.06460e11i | 1.36978i | ||||||||
\(529\) | 1.19098e11 | 1.52083 | ||||||||
\(530\) | −9.04609e9 | −0.114646 | ||||||||
\(531\) | −6.27447e9 | −0.0789222 | ||||||||
\(532\) | 8.33675e9 | 0.104076 | ||||||||
\(533\) | −6.22760e10 | −0.771634 | ||||||||
\(534\) | 1.52261e11i | 1.87250i | ||||||||
\(535\) | 7.33399e10i | 0.895211i | ||||||||
\(536\) | − | 9.31721e9i | − | 0.112883i | ||||||
\(537\) | −1.53251e11 | −1.84292 | ||||||||
\(538\) | − | 1.26907e11i | − | 1.51480i | ||||||
\(539\) | −1.92533e10 | −0.228113 | ||||||||
\(540\) | 8.18628e10 | 0.962746 | ||||||||
\(541\) | −1.27179e11 | −1.48466 | −0.742331 | − | 0.670034i | \(-0.766280\pi\) | ||||
−0.742331 | + | 0.670034i | \(0.766280\pi\) | |||||||
\(542\) | − | 6.51807e10i | − | 0.755304i | ||||||
\(543\) | − | 1.34220e11i | − | 1.54390i | ||||||
\(544\) | − | 1.42377e11i | − | 1.62571i | ||||||
\(545\) | 5.11866e10i | 0.580190i | ||||||||
\(546\) | − | 1.02838e11i | − | 1.15713i | ||||||
\(547\) | −1.10966e11 | −1.23949 | −0.619744 | − | 0.784804i | \(-0.712763\pi\) | ||||
−0.619744 | + | 0.784804i | \(0.712763\pi\) | |||||||
\(548\) | − | 1.22647e10i | − | 0.135999i | ||||||
\(549\) | 6.96182e9i | 0.0766361i | ||||||||
\(550\) | − | 4.61935e10i | − | 0.504813i | ||||||
\(551\) | 1.16254e10 | 0.126125 | ||||||||
\(552\) | 1.39268e10 | 0.150001 | ||||||||
\(553\) | − | 1.42021e11i | − | 1.51863i | ||||||
\(554\) | −2.11740e11 | −2.24783 | ||||||||
\(555\) | 5.80275e10i | 0.611592i | ||||||||
\(556\) | −6.11624e10 | −0.640007 | ||||||||
\(557\) | 1.70704e10 | 0.177347 | 0.0886734 | − | 0.996061i | \(-0.471737\pi\) | ||||
0.0886734 | + | 0.996061i | \(0.471737\pi\) | |||||||
\(558\) | 5.06984e9i | 0.0522946i | ||||||||
\(559\) | −1.26927e10 | + | 8.69819e10i | −0.129989 | + | 0.890803i | ||||
\(560\) | 7.37928e10 | 0.750346 | ||||||||
\(561\) | − | 1.66118e11i | − | 1.67712i | ||||||
\(562\) | 1.08617e11i | 1.08881i | ||||||||
\(563\) | 6.49015e10 | 0.645983 | 0.322992 | − | 0.946402i | \(-0.395311\pi\) | ||||
0.322992 | + | 0.946402i | \(0.395311\pi\) | |||||||
\(564\) | 8.86159e10i | 0.875780i | ||||||||
\(565\) | −1.42856e11 | −1.40186 | ||||||||
\(566\) | 2.55955e10i | 0.249401i | ||||||||
\(567\) | − | 8.92125e10i | − | 0.863164i | ||||||
\(568\) | −5.07014e9 | −0.0487110 | ||||||||
\(569\) | −9.81338e10 | −0.936202 | −0.468101 | − | 0.883675i | \(-0.655062\pi\) | ||||
−0.468101 | + | 0.883675i | \(0.655062\pi\) | |||||||
\(570\) | 1.36447e10 | 0.129260 | ||||||||
\(571\) | − | 1.38488e10i | − | 0.130277i | −0.997876 | − | 0.0651385i | \(-0.979251\pi\) | ||
0.997876 | − | 0.0651385i | \(-0.0207489\pi\) | |||||||
\(572\) | 1.56745e11 | 1.46423 | ||||||||
\(573\) | 1.97897e11 | 1.83578 | ||||||||
\(574\) | 1.23375e11 | 1.13652 | ||||||||
\(575\) | 3.99990e10 | 0.365913 | ||||||||
\(576\) | 7.50098e9 | 0.0681441 | ||||||||
\(577\) | 1.02819e11i | 0.927621i | 0.885934 | + | 0.463811i | \(0.153518\pi\) | ||||
−0.885934 | + | 0.463811i | \(0.846482\pi\) | |||||||
\(578\) | 4.65399e10i | 0.416979i | ||||||||
\(579\) | 9.86386e10i | 0.877673i | ||||||||
\(580\) | −1.26476e11 | −1.11763 | ||||||||
\(581\) | − | 9.80740e10i | − | 0.860695i | ||||||
\(582\) | −1.24712e11 | −1.08696 | ||||||||
\(583\) | −1.59933e10 | −0.138441 | ||||||||
\(584\) | 1.61849e9 | 0.0139142 | ||||||||
\(585\) | 5.57438e9i | 0.0475963i | ||||||||
\(586\) | − | 1.51739e11i | − | 1.28679i | ||||||
\(587\) | − | 2.83893e10i | − | 0.239113i | −0.992827 | − | 0.119556i | \(-0.961853\pi\) | ||
0.992827 | − | 0.119556i | \(-0.0381472\pi\) | |||||||
\(588\) | − | 1.85297e10i | − | 0.155010i | ||||||
\(589\) | 7.67650e9i | 0.0637826i | ||||||||
\(590\) | 2.00157e11 | 1.65182 | ||||||||
\(591\) | 5.52006e10i | 0.452474i | ||||||||
\(592\) | 8.19424e10i | 0.667147i | ||||||||
\(593\) | − | 1.97060e11i | − | 1.59360i | −0.604242 | − | 0.796801i | \(-0.706524\pi\) | ||
0.604242 | − | 0.796801i | \(-0.293476\pi\) | |||||||
\(594\) | 2.80277e11 | 2.25134 | ||||||||
\(595\) | −1.15145e11 | −0.918707 | ||||||||
\(596\) | 1.41279e11i | 1.11968i | ||||||||
\(597\) | 1.27253e11 | 1.00178 | ||||||||
\(598\) | 2.62836e11i | 2.05532i | ||||||||
\(599\) | 1.92220e11 | 1.49311 | 0.746553 | − | 0.665326i | \(-0.231708\pi\) | ||||
0.746553 | + | 0.665326i | \(0.231708\pi\) | |||||||
\(600\) | 2.82185e9 | 0.0217735 | ||||||||
\(601\) | 7.87414e10i | 0.603539i | 0.953381 | + | 0.301769i | \(0.0975772\pi\) | ||||
−0.953381 | + | 0.301769i | \(0.902423\pi\) | |||||||
\(602\) | 2.51455e10 | − | 1.72320e11i | 0.191459 | − | 1.31204i | ||||
\(603\) | 9.22947e9 | 0.0698084 | ||||||||
\(604\) | − | 6.20218e10i | − | 0.466012i | ||||||
\(605\) | 1.55170e11i | 1.15821i | ||||||||
\(606\) | −1.03314e10 | −0.0766067 | ||||||||
\(607\) | 1.66376e11i | 1.22556i | 0.790252 | + | 0.612781i | \(0.209949\pi\) | ||||
−0.790252 | + | 0.612781i | \(0.790051\pi\) | |||||||
\(608\) | 2.06759e10 | 0.151304 | ||||||||
\(609\) | 1.46706e11i | 1.06654i | ||||||||
\(610\) | − | 2.22084e11i | − | 1.60397i | ||||||
\(611\) | −1.06154e11 | −0.761676 | ||||||||
\(612\) | −1.02536e10 | −0.0730925 | ||||||||
\(613\) | 1.70299e11 | 1.20606 | 0.603031 | − | 0.797718i | \(-0.293960\pi\) | ||||
0.603031 | + | 0.797718i | \(0.293960\pi\) | |||||||
\(614\) | 5.52885e10i | 0.389011i | ||||||||
\(615\) | 1.04273e11 | 0.728904 | ||||||||
\(616\) | −1.97101e10 | −0.136888 | ||||||||
\(617\) | −2.65299e11 | −1.83060 | −0.915302 | − | 0.402767i | \(-0.868048\pi\) | ||||
−0.915302 | + | 0.402767i | \(0.868048\pi\) | |||||||
\(618\) | −8.44726e10 | −0.579111 | ||||||||
\(619\) | −1.78200e11 | −1.21379 | −0.606896 | − | 0.794781i | \(-0.707586\pi\) | ||||
−0.606896 | + | 0.794781i | \(0.707586\pi\) | |||||||
\(620\) | − | 8.35149e10i | − | 0.565194i | ||||||
\(621\) | 2.42692e11i | 1.63189i | ||||||||
\(622\) | 2.87929e11i | 1.92364i | ||||||||
\(623\) | 1.86592e11 | 1.23863 | ||||||||
\(624\) | − | 1.22736e11i | − | 0.809532i | ||||||
\(625\) | −1.09317e11 | −0.716420 | ||||||||
\(626\) | 6.26916e10 | 0.408236 | ||||||||
\(627\) | 2.41236e10 | 0.156089 | ||||||||
\(628\) | 4.04282e10i | 0.259924i | ||||||||
\(629\) | − | 1.27861e11i | − | 0.816840i | ||||||
\(630\) | − | 1.10434e10i | − | 0.0701035i | ||||||
\(631\) | 1.59654e11i | 1.00708i | 0.863973 | + | 0.503538i | \(0.167969\pi\) | ||||
−0.863973 | + | 0.503538i | \(0.832031\pi\) | |||||||
\(632\) | 2.56076e10i | 0.160509i | ||||||||
\(633\) | 1.59314e10 | 0.0992290 | ||||||||
\(634\) | 5.53101e10i | 0.342332i | ||||||||
\(635\) | 1.32711e11i | 0.816226i | ||||||||
\(636\) | − | 1.53922e10i | − | 0.0940747i | ||||||
\(637\) | 2.21969e10 | 0.134814 | ||||||||
\(638\) | −4.33022e11 | −2.61353 | ||||||||
\(639\) | − | 5.02240e9i | − | 0.0301236i | ||||||
\(640\) | −2.86211e10 | −0.170595 | ||||||||
\(641\) | − | 2.14549e10i | − | 0.127085i | −0.997979 | − | 0.0635425i | \(-0.979760\pi\) | ||
0.997979 | − | 0.0635425i | \(-0.0202398\pi\) | |||||||
\(642\) | −2.41660e11 | −1.42254 | ||||||||
\(643\) | 1.26797e11 | 0.741763 | 0.370882 | − | 0.928680i | \(-0.379056\pi\) | ||||
0.370882 | + | 0.928680i | \(0.379056\pi\) | |||||||
\(644\) | − | 2.68885e11i | − | 1.56323i | ||||||
\(645\) | 2.12523e10 | − | 1.45639e11i | 0.122791 | − | 0.841473i | ||||
\(646\) | −3.00657e10 | −0.172640 | ||||||||
\(647\) | − | 2.05924e11i | − | 1.17514i | −0.809173 | − | 0.587570i | \(-0.800084\pi\) | ||
0.809173 | − | 0.587570i | \(-0.199916\pi\) | |||||||
\(648\) | 1.60858e10i | 0.0912310i | ||||||||
\(649\) | 3.53874e11 | 1.99466 | ||||||||
\(650\) | 5.32560e10i | 0.298342i | ||||||||
\(651\) | −9.68727e10 | −0.539358 | ||||||||
\(652\) | 1.47444e11i | 0.815899i | ||||||||
\(653\) | 9.69391e10i | 0.533146i | 0.963815 | + | 0.266573i | \(0.0858913\pi\) | ||||
−0.963815 | + | 0.266573i | \(0.914109\pi\) | |||||||
\(654\) | −1.68663e11 | −0.921954 | ||||||||
\(655\) | 1.73944e10 | 0.0945026 | ||||||||
\(656\) | 1.47247e11 | 0.795116 | ||||||||
\(657\) | 1.60325e9i | 0.00860477i | ||||||||
\(658\) | 2.10301e11 | 1.12186 | ||||||||
\(659\) | −2.33344e11 | −1.23725 | −0.618623 | − | 0.785688i | \(-0.712309\pi\) | ||||
−0.618623 | + | 0.785688i | \(0.712309\pi\) | |||||||
\(660\) | −2.62448e11 | −1.38314 | ||||||||
\(661\) | 9.21767e10 | 0.482854 | 0.241427 | − | 0.970419i | \(-0.422385\pi\) | ||||
0.241427 | + | 0.970419i | \(0.422385\pi\) | |||||||
\(662\) | 4.25732e11 | 2.21669 | ||||||||
\(663\) | 1.91515e11i | 0.991172i | ||||||||
\(664\) | 1.76836e10i | 0.0909700i | ||||||||
\(665\) | − | 1.67213e10i | − | 0.0855037i | ||||||
\(666\) | 1.22630e10 | 0.0623304 | ||||||||
\(667\) | − | 3.74954e11i | − | 1.89442i | ||||||
\(668\) | 3.19839e11 | 1.60630 | ||||||||
\(669\) | −1.72787e11 | −0.862596 | ||||||||
\(670\) | −2.94422e11 | −1.46107 | ||||||||
\(671\) | − | 3.92639e11i | − | 1.93688i | ||||||
\(672\) | 2.60917e11i | 1.27946i | ||||||||
\(673\) | − | 8.74582e10i | − | 0.426324i | −0.977017 | − | 0.213162i | \(-0.931624\pi\) | ||
0.977017 | − | 0.213162i | \(-0.0683763\pi\) | |||||||
\(674\) | 4.25450e11i | 2.06162i | ||||||||
\(675\) | 4.91744e10i | 0.236878i | ||||||||
\(676\) | 4.22712e10 | 0.202422 | ||||||||
\(677\) | 1.78736e11i | 0.850861i | 0.904991 | + | 0.425430i | \(0.139877\pi\) | ||||
−0.904991 | + | 0.425430i | \(0.860123\pi\) | |||||||
\(678\) | − | 4.70721e11i | − | 2.22764i | ||||||
\(679\) | 1.52832e11i | 0.719009i | ||||||||
\(680\) | 2.07616e10 | 0.0971016 | ||||||||
\(681\) | −2.44462e11 | −1.13664 | ||||||||
\(682\) | − | 2.85933e11i | − | 1.32168i | ||||||
\(683\) | 5.16028e10 | 0.237132 | 0.118566 | − | 0.992946i | \(-0.462170\pi\) | ||||
0.118566 | + | 0.992946i | \(0.462170\pi\) | |||||||
\(684\) | − | 1.48903e9i | − | 0.00680268i | ||||||
\(685\) | −2.45998e10 | −0.111730 | ||||||||
\(686\) | −3.37618e11 | −1.52450 | ||||||||
\(687\) | 3.20707e11i | 1.43973i | ||||||||
\(688\) | 3.00110e10 | − | 2.05662e11i | 0.133945 | − | 0.917910i | ||||
\(689\) | 1.84385e10 | 0.0818180 | ||||||||
\(690\) | − | 4.40084e11i | − | 1.94151i | ||||||
\(691\) | − | 1.07652e11i | − | 0.472183i | −0.971731 | − | 0.236091i | \(-0.924134\pi\) | ||
0.971731 | − | 0.236091i | \(-0.0758665\pi\) | |||||||
\(692\) | 2.02799e10 | 0.0884385 | ||||||||
\(693\) | − | 1.95245e10i | − | 0.0846538i | ||||||
\(694\) | 5.09460e10 | 0.219620 | ||||||||
\(695\) | 1.22676e11i | 0.525798i | ||||||||
\(696\) | − | 2.64523e10i | − | 0.112727i | ||||||
\(697\) | −2.29761e11 | −0.973522 | ||||||||
\(698\) | −2.32714e11 | −0.980393 | ||||||||
\(699\) | 3.12911e11 | 1.31073 | ||||||||
\(700\) | − | 5.44817e10i | − | 0.226913i | ||||||
\(701\) | 2.84901e11 | 1.17984 | 0.589918 | − | 0.807463i | \(-0.299160\pi\) | ||||
0.589918 | + | 0.807463i | \(0.299160\pi\) | |||||||
\(702\) | −3.23128e11 | −1.33054 | ||||||||
\(703\) | 1.85680e10 | 0.0760229 | ||||||||
\(704\) | −4.23048e11 | −1.72226 | ||||||||
\(705\) | 1.77740e11 | 0.719497 | ||||||||
\(706\) | − | 2.70959e11i | − | 1.09065i | ||||||
\(707\) | 1.26609e10i | 0.0506741i | ||||||||
\(708\) | 3.40574e11i | 1.35543i | ||||||||
\(709\) | 1.31805e11 | 0.521611 | 0.260805 | − | 0.965391i | \(-0.416012\pi\) | ||||
0.260805 | + | 0.965391i | \(0.416012\pi\) | |||||||
\(710\) | 1.60216e11i | 0.630480i | ||||||||
\(711\) | −2.53664e10 | −0.0992616 | ||||||||
\(712\) | −3.36442e10 | −0.130915 | ||||||||
\(713\) | 2.47590e11 | 0.958021 | ||||||||
\(714\) | − | 3.79410e11i | − | 1.45988i | ||||||
\(715\) | − | 3.14389e11i | − | 1.20294i | ||||||
\(716\) | − | 5.33504e11i | − | 2.02995i | ||||||
\(717\) | 2.84010e11i | 1.07462i | ||||||||
\(718\) | − | 5.63844e10i | − | 0.212159i | ||||||
\(719\) | 4.05208e11 | 1.51622 | 0.758110 | − | 0.652127i | \(-0.226123\pi\) | ||||
0.758110 | + | 0.652127i | \(0.226123\pi\) | |||||||
\(720\) | − | 1.31802e10i | − | 0.0490446i | ||||||
\(721\) | 1.03520e11i | 0.383073i | ||||||||
\(722\) | 3.86385e11i | 1.42191i | ||||||||
\(723\) | 4.03513e11 | 1.47674 | ||||||||
\(724\) | 4.67252e11 | 1.70058 | ||||||||
\(725\) | − | 7.59735e10i | − | 0.274986i | ||||||
\(726\) | −5.11297e11 | −1.84046 | ||||||||
\(727\) | 5.30950e10i | 0.190071i | 0.995474 | + | 0.0950355i | \(0.0302965\pi\) | ||||
−0.995474 | + | 0.0950355i | \(0.969704\pi\) | |||||||
\(728\) | 2.27235e10 | 0.0809004 | ||||||||
\(729\) | −2.97338e11 | −1.05279 | ||||||||
\(730\) | − | 5.11440e10i | − | 0.180096i | ||||||
\(731\) | −4.68286e10 | + | 3.20911e11i | −0.163999 | + | 1.12387i | ||||
\(732\) | 3.77883e11 | 1.31617 | ||||||||
\(733\) | 2.64810e11i | 0.917314i | 0.888613 | + | 0.458657i | \(0.151669\pi\) | ||||
−0.888613 | + | 0.458657i | \(0.848331\pi\) | |||||||
\(734\) | 4.34748e11i | 1.49780i | ||||||||
\(735\) | −3.71657e10 | −0.127348 | ||||||||
\(736\) | − | 6.66861e11i | − | 2.27260i | ||||||
\(737\) | −5.20532e11 | −1.76432 | ||||||||
\(738\) | − | 2.20361e10i | − | 0.0742862i | ||||||
\(739\) | − | 3.49177e11i | − | 1.17076i | −0.810759 | − | 0.585381i | \(-0.800945\pi\) | ||
0.810759 | − | 0.585381i | \(-0.199055\pi\) | |||||||
\(740\) | −2.02007e11 | −0.673659 | ||||||||
\(741\) | −2.78118e10 | −0.0922480 | ||||||||
\(742\) | −3.65285e10 | −0.120508 | ||||||||
\(743\) | 3.40681e11i | 1.11787i | 0.829210 | + | 0.558937i | \(0.188791\pi\) | ||||
−0.829210 | + | 0.558937i | \(0.811209\pi\) | |||||||
\(744\) | 1.74670e10 | 0.0570068 | ||||||||
\(745\) | 2.83368e11 | 0.919869 | ||||||||
\(746\) | 1.55850e11 | 0.503214 | ||||||||
\(747\) | −1.75171e10 | −0.0562573 | ||||||||
\(748\) | 5.78295e11 | 1.84732 | ||||||||
\(749\) | 2.96149e11i | 0.940987i | ||||||||
\(750\) | − | 4.76082e11i | − | 1.50465i | ||||||
\(751\) | 1.73741e11i | 0.546188i | 0.961987 | + | 0.273094i | \(0.0880470\pi\) | ||||
−0.961987 | + | 0.273094i | \(0.911953\pi\) | |||||||
\(752\) | 2.50992e11 | 0.784855 | ||||||||
\(753\) | 2.82579e11i | 0.878940i | ||||||||
\(754\) | 4.99226e11 | 1.54459 | ||||||||
\(755\) | −1.24400e11 | −0.382852 | ||||||||
\(756\) | 3.30565e11 | 1.01198 | ||||||||
\(757\) | − | 5.97510e11i | − | 1.81954i | −0.415114 | − | 0.909769i | \(-0.636258\pi\) | ||
0.415114 | − | 0.909769i | \(-0.363742\pi\) | |||||||
\(758\) | − | 8.88406e11i | − | 2.69113i | ||||||
\(759\) | − | 7.78059e11i | − | 2.34447i | ||||||
\(760\) | 3.01501e9i | 0.00903720i | ||||||||
\(761\) | − | 3.40017e11i | − | 1.01382i | −0.861998 | − | 0.506912i | \(-0.830787\pi\) | ||
0.861998 | − | 0.506912i | \(-0.169213\pi\) | |||||||
\(762\) | −4.37290e11 | −1.29703 | ||||||||
\(763\) | 2.06693e11i | 0.609857i | ||||||||
\(764\) | 6.88925e11i | 2.02208i | ||||||||
\(765\) | 2.05661e10i | 0.0600491i | ||||||||
\(766\) | −8.98530e11 | −2.60986 | ||||||||
\(767\) | −4.07977e11 | −1.17884 | ||||||||
\(768\) | 2.86997e11i | 0.824959i | ||||||||
\(769\) | 3.42285e11 | 0.978774 | 0.489387 | − | 0.872067i | \(-0.337221\pi\) | ||||
0.489387 | + | 0.872067i | \(0.337221\pi\) | |||||||
\(770\) | 6.22835e11i | 1.77178i | ||||||||
\(771\) | −2.81538e11 | −0.796746 | ||||||||
\(772\) | −3.43384e11 | −0.966742 | ||||||||
\(773\) | − | 3.41450e10i | − | 0.0956332i | −0.998856 | − | 0.0478166i | \(-0.984774\pi\) | ||
0.998856 | − | 0.0478166i | \(-0.0152263\pi\) | |||||||
\(774\) | −3.07781e10 | − | 4.49126e9i | −0.0857587 | − | 0.0125142i | ||||
\(775\) | 5.01668e10 | 0.139062 | ||||||||
\(776\) | − | 2.75569e10i | − | 0.0759947i | ||||||
\(777\) | 2.34317e11i | 0.642865i | ||||||||
\(778\) | 5.78580e11 | 1.57923 | ||||||||
\(779\) | − | 3.33659e10i | − | 0.0906052i | ||||||
\(780\) | 3.02573e11 | 0.817433 | ||||||||
\(781\) | 2.83258e11i | 0.761339i | ||||||||
\(782\) | 9.69708e11i | 2.59307i | ||||||||
\(783\) | 4.60966e11 | 1.22637 | ||||||||
\(784\) | −5.24829e10 | −0.138916 | ||||||||
\(785\) | 8.10884e10 | 0.213540 | ||||||||
\(786\) | 5.73157e10i | 0.150170i | ||||||||
\(787\) | −5.26327e11 | −1.37201 | −0.686004 | − | 0.727598i | \(-0.740637\pi\) | ||||
−0.686004 | + | 0.727598i | \(0.740637\pi\) | |||||||
\(788\) | −1.92166e11 | −0.498393 | ||||||||
\(789\) | −2.13682e11 | −0.551392 | ||||||||
\(790\) | 8.09195e11 | 2.07752 | ||||||||
\(791\) | −5.76860e11 | −1.47355 | ||||||||
\(792\) | 3.52043e9i | 0.00894737i | ||||||||
\(793\) | 4.52669e11i | 1.14469i | ||||||||
\(794\) | 7.93919e11i | 1.99754i | ||||||||
\(795\) | −3.08728e10 | −0.0772871 | ||||||||
\(796\) | 4.42997e11i | 1.10344i | ||||||||
\(797\) | −2.80203e11 | −0.694449 | −0.347224 | − | 0.937782i | \(-0.612876\pi\) | ||||
−0.347224 | + | 0.937782i | \(0.612876\pi\) | |||||||
\(798\) | 5.50980e10 | 0.135870 | ||||||||
\(799\) | −3.91644e11 | −0.960958 | ||||||||
\(800\) | − | 1.35120e11i | − | 0.329882i | ||||||
\(801\) | − | 3.33274e10i | − | 0.0809601i | ||||||
\(802\) | 5.59309e11i | 1.35193i | ||||||||
\(803\) | − | 9.04215e10i | − | 0.217475i | ||||||
\(804\) | − | 5.00969e11i | − | 1.19891i | ||||||
\(805\) | −5.39314e11 | −1.28427 | ||||||||
\(806\) | 3.29649e11i | 0.781110i | ||||||||
\(807\) | − | 4.33111e11i | − | 1.02119i | ||||||
\(808\) | − | 2.28287e9i | − | 0.00535593i | ||||||
\(809\) | −4.95228e11 | −1.15614 | −0.578071 | − | 0.815986i | \(-0.696195\pi\) | ||||
−0.578071 | + | 0.815986i | \(0.696195\pi\) | |||||||
\(810\) | 5.08308e11 | 1.18083 | ||||||||
\(811\) | 2.66342e11i | 0.615683i | 0.951438 | + | 0.307841i | \(0.0996066\pi\) | ||||
−0.951438 | + | 0.307841i | \(0.900393\pi\) | |||||||
\(812\) | −5.10716e11 | −1.17478 | ||||||||
\(813\) | − | 2.22451e11i | − | 0.509180i | ||||||
\(814\) | −6.91620e11 | −1.57532 | ||||||||
\(815\) | 2.95734e11 | 0.670302 | ||||||||
\(816\) | − | 4.52823e11i | − | 1.02133i | ||||||
\(817\) | −4.66027e10 | − | 6.80045e9i | −0.104598 | − | 0.0152633i | ||||
\(818\) | 5.80446e11 | 1.29643 | ||||||||
\(819\) | 2.25095e10i | 0.0500301i | ||||||||
\(820\) | 3.62998e11i | 0.802876i | ||||||||
\(821\) | −5.99275e11 | −1.31903 | −0.659513 | − | 0.751693i | \(-0.729237\pi\) | ||||
−0.659513 | + | 0.751693i | \(0.729237\pi\) | |||||||
\(822\) | − | 8.10581e10i | − | 0.177545i | ||||||
\(823\) | 3.34555e11 | 0.729237 | 0.364619 | − | 0.931157i | \(-0.381199\pi\) | ||||
0.364619 | + | 0.931157i | \(0.381199\pi\) | |||||||
\(824\) | − | 1.86655e10i | − | 0.0404884i | ||||||
\(825\) | − | 1.57651e11i | − | 0.340314i | ||||||
\(826\) | 8.08242e11 | 1.73629 | ||||||||
\(827\) | 6.97838e11 | 1.49187 | 0.745937 | − | 0.666016i | \(-0.232002\pi\) | ||||
0.745937 | + | 0.666016i | \(0.232002\pi\) | |||||||
\(828\) | −4.80258e10 | −0.102177 | ||||||||
\(829\) | − | 3.06723e11i | − | 0.649423i | −0.945813 | − | 0.324712i | \(-0.894733\pi\) | ||
0.945813 | − | 0.324712i | \(-0.105267\pi\) | |||||||
\(830\) | 5.58798e11 | 1.17745 | ||||||||
\(831\) | −7.22633e11 | −1.51535 | ||||||||
\(832\) | 4.87727e11 | 1.01785 | ||||||||
\(833\) | 8.18934e10 | 0.170086 | ||||||||
\(834\) | −4.04224e11 | −0.835523 | ||||||||
\(835\) | − | 6.41514e11i | − | 1.31966i | ||||||
\(836\) | 8.39799e10i | 0.171930i | ||||||||
\(837\) | 3.04385e11i | 0.620185i | ||||||||
\(838\) | −9.70215e11 | −1.96740 | ||||||||
\(839\) | − | 5.67989e11i | − | 1.14628i | −0.819456 | − | 0.573142i | \(-0.805724\pi\) | ||
0.819456 | − | 0.573142i | \(-0.194276\pi\) | |||||||
\(840\) | −3.80475e10 | −0.0764204 | ||||||||
\(841\) | −2.11936e11 | −0.423663 | ||||||||
\(842\) | 5.90676e11 | 1.17517 | ||||||||
\(843\) | 3.70692e11i | 0.734012i | ||||||||
\(844\) | 5.54609e10i | 0.109299i | ||||||||
\(845\) | − | 8.47849e10i | − | 0.166300i | ||||||
\(846\) | − | 3.75620e10i | − | 0.0733276i | ||||||
\(847\) | 6.26584e11i | 1.21743i | ||||||||
\(848\) | −4.35964e10 | −0.0843077 | ||||||||
\(849\) | 8.73531e10i | 0.168131i | ||||||||
\(850\) | 1.96483e11i | 0.376399i | ||||||||
\(851\) | − | 5.98875e11i | − | 1.14187i | ||||||
\(852\) | −2.72612e11 | −0.517353 | ||||||||
\(853\) | 5.54160e11 | 1.04674 | 0.523370 | − | 0.852106i | \(-0.324675\pi\) | ||||
0.523370 | + | 0.852106i | \(0.324675\pi\) | |||||||
\(854\) | − | 8.96782e11i | − | 1.68599i | ||||||
\(855\) | −2.98661e9 | −0.00558875 | ||||||||
\(856\) | − | 5.33983e10i | − | 0.0994564i | ||||||
\(857\) | 6.57798e10 | 0.121946 | 0.0609732 | − | 0.998139i | \(-0.480580\pi\) | ||||
0.0609732 | + | 0.998139i | \(0.480580\pi\) | |||||||
\(858\) | 1.03593e12 | 1.91153 | ||||||||
\(859\) | − | 5.78007e11i | − | 1.06160i | −0.847497 | − | 0.530800i | \(-0.821892\pi\) | ||
0.847497 | − | 0.530800i | \(-0.178108\pi\) | |||||||
\(860\) | 5.07005e11 | + | 7.39841e10i | 0.926869 | + | 0.135252i | ||||
\(861\) | 4.21057e11 | 0.766176 | ||||||||
\(862\) | − | 1.03626e12i | − | 1.87690i | ||||||
\(863\) | 2.50288e11i | 0.451228i | 0.974217 | + | 0.225614i | \(0.0724388\pi\) | ||||
−0.974217 | + | 0.225614i | \(0.927561\pi\) | |||||||
\(864\) | 8.19833e11 | 1.47119 | ||||||||
\(865\) | − | 4.06762e10i | − | 0.0726567i | ||||||
\(866\) | −7.43380e11 | −1.32172 | ||||||||
\(867\) | 1.58833e11i | 0.281102i | ||||||||
\(868\) | − | 3.37236e11i | − | 0.594095i | ||||||
\(869\) | 1.43064e12 | 2.50872 | ||||||||
\(870\) | −8.35887e11 | −1.45905 | ||||||||
\(871\) | 6.00116e11 | 1.04271 | ||||||||
\(872\) | − | 3.72686e10i | − | 0.0644581i | ||||||
\(873\) | 2.72974e10 | 0.0469963 | ||||||||
\(874\) | −1.40821e11 | −0.241336 | ||||||||
\(875\) | −5.83429e11 | −0.995304 | ||||||||
\(876\) | 8.70232e10 | 0.147781 | ||||||||
\(877\) | 3.47482e11 | 0.587400 | 0.293700 | − | 0.955898i | \(-0.405113\pi\) | ||||
0.293700 | + | 0.955898i | \(0.405113\pi\) | |||||||
\(878\) | 5.79633e11i | 0.975383i | ||||||||
\(879\) | − | 5.17860e11i | − | 0.867475i | ||||||
\(880\) | 7.43348e11i | 1.23954i | ||||||||
\(881\) | −7.52008e11 | −1.24830 | −0.624150 | − | 0.781305i | \(-0.714554\pi\) | ||||
−0.624150 | + | 0.781305i | \(0.714554\pi\) | |||||||
\(882\) | 7.85427e9i | 0.0129787i | ||||||||
\(883\) | −1.91526e11 | −0.315054 | −0.157527 | − | 0.987515i | \(-0.550352\pi\) | ||||
−0.157527 | + | 0.987515i | \(0.550352\pi\) | |||||||
\(884\) | −6.66709e11 | −1.09176 | ||||||||
\(885\) | 6.83102e11 | 1.11356 | ||||||||
\(886\) | − | 1.37215e12i | − | 2.22672i | ||||||
\(887\) | 7.30905e11i | 1.18077i | 0.807121 | + | 0.590387i | \(0.201025\pi\) | ||||
−0.807121 | + | 0.590387i | \(0.798975\pi\) | |||||||
\(888\) | − | 4.22494e10i | − | 0.0679468i | ||||||
\(889\) | 5.35890e11i | 0.857963i | ||||||||
\(890\) | 1.06315e12i | 1.69447i | ||||||||
\(891\) | 8.98678e11 | 1.42591 | ||||||||
\(892\) | − | 6.01513e11i | − | 0.950136i | ||||||
\(893\) | − | 5.68745e10i | − | 0.0894359i | ||||||
\(894\) | 9.33717e11i | 1.46172i | ||||||||
\(895\) | −1.07007e12 | −1.66771 | ||||||||
\(896\) | −1.15573e11 | −0.179318 | ||||||||
\(897\) | 8.97015e11i | 1.38557i | ||||||||
\(898\) | −1.06604e12 | −1.63934 | ||||||||
\(899\) | − | 4.70268e11i | − | 0.719958i | ||||||
\(900\) | −9.73101e9 | −0.0148316 | ||||||||
\(901\) | 6.80271e10 | 0.103224 | ||||||||
\(902\) | 1.24281e12i | 1.87749i | ||||||||
\(903\) | 8.58175e10 | − | 5.88098e11i | 0.129070 | − | 0.884501i | ||||
\(904\) | 1.04013e11 | 0.155745 | ||||||||
\(905\) | − | 9.37185e11i | − | 1.39711i | ||||||
\(906\) | − | 4.09905e11i | − | 0.608373i | ||||||
\(907\) | −5.37136e11 | −0.793698 | −0.396849 | − | 0.917884i | \(-0.629896\pi\) | ||||
−0.396849 | + | 0.917884i | \(0.629896\pi\) | |||||||
\(908\) | − | 8.51030e11i | − | 1.25199i | ||||||
\(909\) | 2.26137e9 | 0.00331219 | ||||||||
\(910\) | − | 7.18059e11i | − | 1.04712i | ||||||
\(911\) | − | 1.02946e12i | − | 1.49464i | −0.664465 | − | 0.747319i | \(-0.731341\pi\) | ||
0.664465 | − | 0.747319i | \(-0.268659\pi\) | |||||||
\(912\) | 6.57589e10 | 0.0950551 | ||||||||
\(913\) | 9.87944e11 | 1.42184 | ||||||||
\(914\) | 6.08781e11 | 0.872321 | ||||||||
\(915\) | − | 7.57934e11i | − | 1.08130i | ||||||
\(916\) | −1.11646e12 | −1.58584 | ||||||||
\(917\) | 7.02392e10 | 0.0993350 | ||||||||
\(918\) | −1.19215e12 | −1.67865 | ||||||||
\(919\) | 4.12836e11 | 0.578782 | 0.289391 | − | 0.957211i | \(-0.406547\pi\) | ||||
0.289391 | + | 0.957211i | \(0.406547\pi\) | |||||||
\(920\) | 9.72430e10 | 0.135740 | ||||||||
\(921\) | 1.88690e11i | 0.262247i | ||||||||
\(922\) | − | 1.08359e12i | − | 1.49949i | ||||||
\(923\) | − | 3.26565e11i | − | 0.449948i | ||||||
\(924\) | −1.05978e12 | −1.45387 | ||||||||
\(925\) | − | 1.21344e11i | − | 0.165750i | ||||||
\(926\) | 9.86469e11 | 1.34165 | ||||||||
\(927\) | 1.84897e10 | 0.0250386 | ||||||||
\(928\) | −1.26662e12 | −1.70787 | ||||||||
\(929\) | 5.80653e11i | 0.779568i | 0.920906 | + | 0.389784i | \(0.127450\pi\) | ||||
−0.920906 | + | 0.389784i | \(0.872550\pi\) | |||||||
\(930\) | − | 5.51953e11i | − | 0.737854i | ||||||
\(931\) | 1.18925e10i | 0.0158298i | ||||||||
\(932\) | 1.08932e12i | 1.44374i | ||||||||
\(933\) | 9.82652e11i | 1.29680i | ||||||||
\(934\) | −1.18981e12 | −1.56348 | ||||||||
\(935\) | − | 1.15991e12i | − | 1.51767i | ||||||
\(936\) | − | 4.05867e9i | − | 0.00528786i | ||||||
\(937\) | − | 4.56529e10i | − | 0.0592257i | −0.999561 | − | 0.0296128i | \(-0.990573\pi\) | ||
0.999561 | − | 0.0296128i | \(-0.00942744\pi\) | |||||||
\(938\) | −1.18889e12 | −1.53578 | ||||||||
\(939\) | 2.13956e11 | 0.275208 | ||||||||
\(940\) | 6.18755e11i | 0.792515i | ||||||||
\(941\) | 1.00537e12 | 1.28224 | 0.641119 | − | 0.767441i | \(-0.278470\pi\) | ||||
0.641119 | + | 0.767441i | \(0.278470\pi\) | |||||||
\(942\) | 2.67192e11i | 0.339328i | ||||||||
\(943\) | −1.07615e12 | −1.36090 | ||||||||
\(944\) | 9.64630e11 | 1.21471 | ||||||||
\(945\) | − | 6.63028e11i | − | 0.831389i | ||||||
\(946\) | 1.73585e12 | + | 2.53302e11i | 2.16745 | + | 0.316282i | ||||
\(947\) | −9.74784e11 | −1.21202 | −0.606008 | − | 0.795458i | \(-0.707230\pi\) | ||||
−0.606008 | + | 0.795458i | \(0.707230\pi\) | |||||||
\(948\) | 1.37687e12i | 1.70475i | ||||||||
\(949\) | 1.04246e11i | 0.128527i | ||||||||
\(950\) | −2.85332e10 | −0.0350313 | ||||||||
\(951\) | 1.88764e11i | 0.230780i | ||||||||
\(952\) | 8.38363e10 | 0.102067 | ||||||||
\(953\) | − | 4.92276e11i | − | 0.596812i | −0.954439 | − | 0.298406i | \(-0.903545\pi\) | ||
0.954439 | − | 0.298406i | \(-0.0964549\pi\) | |||||||
\(954\) | 6.52437e9i | 0.00787672i | ||||||||
\(955\) | 1.38180e12 | 1.66124 | ||||||||
\(956\) | −9.88703e11 | −1.18368 | ||||||||
\(957\) | −1.47783e12 | −1.76188 | ||||||||
\(958\) | 1.23490e12i | 1.46613i | ||||||||
\(959\) | −9.93351e10 | −0.117443 | ||||||||
\(960\) | −8.16633e11 | −0.961484 | ||||||||
\(961\) | −5.42363e11 | −0.635911 | ||||||||
\(962\) | 7.97361e11 | 0.931010 | ||||||||
\(963\) | 5.28955e10 | 0.0615054 | ||||||||
\(964\) | 1.40472e12i | 1.62661i | ||||||||
\(965\) | 6.88738e11i | 0.794228i | ||||||||
\(966\) | − | 1.77707e12i | − | 2.04078i | ||||||
\(967\) | −1.72742e11 | −0.197557 | −0.0987785 | − | 0.995109i | \(-0.531494\pi\) | ||||
−0.0987785 | + | 0.995109i | \(0.531494\pi\) | |||||||
\(968\) | − | 1.12979e11i | − | 0.128675i | ||||||
\(969\) | −1.02609e11 | −0.116383 | ||||||||
\(970\) | −8.70792e11 | −0.983621 | ||||||||
\(971\) | 2.24845e10 | 0.0252934 | 0.0126467 | − | 0.999920i | \(-0.495974\pi\) | ||||
0.0126467 | + | 0.999920i | \(0.495974\pi\) | |||||||
\(972\) | − | 1.14729e11i | − | 0.128531i | ||||||
\(973\) | 4.95369e11i | 0.552685i | ||||||||
\(974\) | 8.88418e11i | 0.987146i | ||||||||
\(975\) | 1.81754e11i | 0.201124i | ||||||||
\(976\) | − | 1.07030e12i | − | 1.17952i | ||||||
\(977\) | 1.68860e12 | 1.85331 | 0.926653 | − | 0.375917i | \(-0.122672\pi\) | ||||
0.926653 | + | 0.375917i | \(0.122672\pi\) | |||||||
\(978\) | 9.74463e11i | 1.06515i | ||||||||
\(979\) | 1.87963e12i | 2.04617i | ||||||||
\(980\) | − | 1.29383e11i | − | 0.140272i | ||||||
\(981\) | 3.69176e10 | 0.0398619 | ||||||||
\(982\) | 1.98103e12 | 2.13032 | ||||||||
\(983\) | − | 1.80594e12i | − | 1.93415i | −0.254493 | − | 0.967075i | \(-0.581909\pi\) | ||
0.254493 | − | 0.967075i | \(-0.418091\pi\) | |||||||
\(984\) | −7.59203e10 | −0.0809800 | ||||||||
\(985\) | 3.85435e11i | 0.409455i | ||||||||
\(986\) | 1.84185e12 | 1.94870 | ||||||||
\(987\) | 7.17722e11 | 0.756289 | ||||||||
\(988\) | − | 9.68195e10i | − | 0.101610i | ||||||
\(989\) | −2.19335e11 | + | 1.50308e12i | −0.229257 | + | 1.57107i | ||||
\(990\) | 1.11245e11 | 0.115808 | ||||||||
\(991\) | 4.93967e11i | 0.512157i | 0.966656 | + | 0.256078i | \(0.0824305\pi\) | ||||
−0.966656 | + | 0.256078i | \(0.917569\pi\) | |||||||
\(992\) | − | 8.36377e11i | − | 0.863686i | ||||||
\(993\) | 1.45295e12 | 1.49436 | ||||||||
\(994\) | 6.46957e11i | 0.662719i | ||||||||
\(995\) | 8.88536e11 | 0.906532 | ||||||||
\(996\) | 9.50814e11i | 0.966181i | ||||||||
\(997\) | 3.45858e11i | 0.350040i | 0.984565 | + | 0.175020i | \(0.0559990\pi\) | ||||
−0.984565 | + | 0.175020i | \(0.944001\pi\) | |||||||
\(998\) | −1.81804e12 | −1.83266 | ||||||||
\(999\) | 7.36251e11 | 0.739204 |
(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 | 43.9.b.b.42.22 | yes | 28 | |
43.42 | odd | 2 | inner | 43.9.b.b.42.7 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.9.b.b.42.7 | ✓ | 28 | 43.42 | odd | 2 | inner | |
43.9.b.b.42.22 | yes | 28 | 1.1 | even | 1 | trivial |