Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,5,Mod(2,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(14))
chi = DirichletCharacter(H, H._module([9]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.2");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.f (of order \(14\), degree \(6\), 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: | \(4.44490841261\) |
Analytic rank: | \(0\) |
Dimension: | \(78\) |
Relative dimension: | \(13\) over \(\Q(\zeta_{14})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{14}]$ |
Embedding invariants
Embedding label | 2.10 | ||
Character | \(\chi\) | \(=\) | 43.2 |
Dual form | 43.5.f.a.22.10 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{9}{14}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.83585 | + | 3.81219i | 0.458964 | + | 0.953048i | 0.994119 | + | 0.108294i | \(0.0345388\pi\) |
−0.535155 | + | 0.844754i | \(0.679747\pi\) | |||||||
\(3\) | 5.21899 | − | 10.8373i | 0.579888 | − | 1.20415i | −0.380318 | − | 0.924856i | \(-0.624185\pi\) |
0.960206 | − | 0.279294i | \(-0.0901002\pi\) | |||||||
\(4\) | −1.18660 | + | 1.48795i | −0.0741626 | + | 0.0929969i | ||||
\(5\) | −1.25492 | − | 0.286428i | −0.0501969 | − | 0.0114571i | 0.197349 | − | 0.980333i | \(-0.436767\pi\) |
−0.247546 | + | 0.968876i | \(0.579624\pi\) | |||||||
\(6\) | 50.8953 | 1.41376 | ||||||||
\(7\) | − | 55.1541i | − | 1.12559i | −0.826595 | − | 0.562797i | \(-0.809725\pi\) | ||
0.826595 | − | 0.562797i | \(-0.190275\pi\) | |||||||
\(8\) | 58.1513 | + | 13.2726i | 0.908613 | + | 0.207385i | ||||
\(9\) | −39.7075 | − | 49.7916i | −0.490216 | − | 0.614711i | ||||
\(10\) | −1.21194 | − | 5.30985i | −0.0121194 | − | 0.0530985i | ||||
\(11\) | 23.3205 | + | 29.2430i | 0.192732 | + | 0.241678i | 0.868803 | − | 0.495159i | \(-0.164890\pi\) |
−0.676071 | + | 0.736837i | \(0.736319\pi\) | |||||||
\(12\) | 9.93258 | + | 20.6252i | 0.0689762 | + | 0.143231i | ||||
\(13\) | −56.3787 | + | 247.011i | −0.333602 | + | 1.46160i | 0.478499 | + | 0.878088i | \(0.341181\pi\) |
−0.812101 | + | 0.583517i | \(0.801676\pi\) | |||||||
\(14\) | 210.258 | − | 101.255i | 1.07274 | − | 0.516606i | ||||
\(15\) | −9.65355 | + | 12.1052i | −0.0429047 | + | 0.0538008i | ||||
\(16\) | 62.9353 | + | 275.737i | 0.245841 | + | 1.07710i | ||||
\(17\) | 24.6816 | + | 108.137i | 0.0854036 | + | 0.374178i | 0.999510 | − | 0.0312964i | \(-0.00996359\pi\) |
−0.914107 | + | 0.405474i | \(0.867106\pi\) | |||||||
\(18\) | 116.918 | − | 242.783i | 0.360858 | − | 0.749329i | ||||
\(19\) | −71.0668 | − | 56.6739i | −0.196861 | − | 0.156991i | 0.520098 | − | 0.854106i | \(-0.325895\pi\) |
−0.716959 | + | 0.697115i | \(0.754467\pi\) | |||||||
\(20\) | 1.91528 | − | 1.52739i | 0.00478821 | − | 0.00381847i | ||||
\(21\) | −597.724 | − | 287.849i | −1.35538 | − | 0.652718i | ||||
\(22\) | −68.6669 | + | 142.588i | −0.141874 | + | 0.294604i | ||||
\(23\) | −269.161 | − | 337.517i | −0.508810 | − | 0.638028i | 0.459381 | − | 0.888239i | \(-0.348071\pi\) |
−0.968191 | + | 0.250211i | \(0.919500\pi\) | |||||||
\(24\) | 447.331 | − | 560.935i | 0.776616 | − | 0.973846i | ||||
\(25\) | −561.613 | − | 270.458i | −0.898580 | − | 0.432734i | ||||
\(26\) | −1045.16 | + | 238.550i | −1.54609 | + | 0.352885i | ||||
\(27\) | 203.042 | − | 46.3431i | 0.278522 | − | 0.0635707i | ||||
\(28\) | 82.0666 | + | 65.4459i | 0.104677 | + | 0.0834769i | ||||
\(29\) | 387.428 | + | 804.503i | 0.460675 | + | 0.956602i | 0.993864 | + | 0.110606i | \(0.0352792\pi\) |
−0.533189 | + | 0.845996i | \(0.679006\pi\) | |||||||
\(30\) | −63.8697 | − | 14.5779i | −0.0709664 | − | 0.0161976i | ||||
\(31\) | 26.0743 | − | 12.5567i | 0.0271324 | − | 0.0130663i | −0.420268 | − | 0.907400i | \(-0.638064\pi\) |
0.447401 | + | 0.894334i | \(0.352350\pi\) | |||||||
\(32\) | −189.485 | + | 151.109i | −0.185044 | + | 0.147567i | ||||
\(33\) | 438.626 | − | 100.114i | 0.402779 | − | 0.0919317i | ||||
\(34\) | −366.928 | + | 292.616i | −0.317412 | + | 0.253128i | ||||
\(35\) | −15.7977 | + | 69.2141i | −0.0128961 | + | 0.0565013i | ||||
\(36\) | 121.204 | 0.0935220 | ||||||||
\(37\) | 1793.33i | 1.30995i | 0.755649 | + | 0.654977i | \(0.227322\pi\) | ||||
−0.755649 | + | 0.654977i | \(0.772678\pi\) | |||||||
\(38\) | 85.5834 | − | 374.965i | 0.0592683 | − | 0.259671i | ||||
\(39\) | 2382.71 | + | 1900.14i | 1.56654 | + | 1.24927i | ||||
\(40\) | −69.1737 | − | 33.3123i | −0.0432336 | − | 0.0208202i | ||||
\(41\) | −1040.33 | + | 500.997i | −0.618876 | + | 0.298035i | −0.716929 | − | 0.697146i | \(-0.754453\pi\) |
0.0980530 | + | 0.995181i | \(0.468739\pi\) | |||||||
\(42\) | − | 2807.08i | − | 1.59132i | ||||||
\(43\) | −1727.43 | + | 659.381i | −0.934251 | + | 0.356615i | ||||
\(44\) | −71.1844 | −0.0367688 | ||||||||
\(45\) | 35.5681 | + | 73.8580i | 0.0175645 | + | 0.0364731i | ||||
\(46\) | 792.539 | − | 1645.72i | 0.374546 | − | 0.777752i | ||||
\(47\) | 2219.97 | − | 2783.75i | 1.00496 | − | 1.26018i | 0.0396169 | − | 0.999215i | \(-0.487386\pi\) |
0.965347 | − | 0.260970i | \(-0.0840423\pi\) | |||||||
\(48\) | 3316.72 | + | 757.020i | 1.43955 | + | 0.328568i | ||||
\(49\) | −640.972 | −0.266960 | ||||||||
\(50\) | − | 2637.50i | − | 1.05500i | ||||||
\(51\) | 1300.73 | + | 296.884i | 0.500090 | + | 0.114142i | ||||
\(52\) | −300.642 | − | 376.993i | −0.111184 | − | 0.139420i | ||||
\(53\) | −419.195 | − | 1836.61i | −0.149233 | − | 0.653831i | −0.993099 | − | 0.117278i | \(-0.962583\pi\) |
0.843866 | − | 0.536553i | \(-0.180274\pi\) | |||||||
\(54\) | 549.425 | + | 688.957i | 0.188417 | + | 0.236268i | ||||
\(55\) | −20.8895 | − | 43.3774i | −0.00690561 | − | 0.0143396i | ||||
\(56\) | 732.040 | − | 3207.28i | 0.233431 | − | 1.02273i | ||||
\(57\) | −985.092 | + | 474.395i | −0.303198 | + | 0.146013i | ||||
\(58\) | −2355.66 | + | 2953.90i | −0.700255 | + | 0.878091i | ||||
\(59\) | 935.219 | + | 4097.46i | 0.268664 | + | 1.17709i | 0.911569 | + | 0.411148i | \(0.134872\pi\) |
−0.642905 | + | 0.765946i | \(0.722271\pi\) | |||||||
\(60\) | −6.55698 | − | 28.7280i | −0.00182138 | − | 0.00798001i | ||||
\(61\) | −1733.25 | + | 3599.12i | −0.465801 | + | 0.967247i | 0.527266 | + | 0.849700i | \(0.323217\pi\) |
−0.993067 | + | 0.117546i | \(0.962497\pi\) | |||||||
\(62\) | 95.7371 | + | 76.3478i | 0.0249056 | + | 0.0198615i | ||||
\(63\) | −2746.21 | + | 2190.03i | −0.691915 | + | 0.551784i | ||||
\(64\) | 3153.19 | + | 1518.50i | 0.769822 | + | 0.370727i | ||||
\(65\) | 141.502 | − | 293.832i | 0.0334916 | − | 0.0695460i | ||||
\(66\) | 1186.91 | + | 1488.33i | 0.272476 | + | 0.341674i | ||||
\(67\) | 4427.17 | − | 5551.50i | 0.986227 | − | 1.23669i | 0.0146683 | − | 0.999892i | \(-0.495331\pi\) |
0.971559 | − | 0.236798i | \(-0.0760978\pi\) | |||||||
\(68\) | −190.190 | − | 91.5909i | −0.0411311 | − | 0.0198077i | ||||
\(69\) | −5062.53 | + | 1155.49i | −1.06333 | + | 0.242699i | ||||
\(70\) | −292.860 | + | 66.8433i | −0.0597673 | + | 0.0136415i | ||||
\(71\) | −4654.84 | − | 3712.11i | −0.923395 | − | 0.736383i | 0.0414668 | − | 0.999140i | \(-0.486797\pi\) |
−0.964862 | + | 0.262757i | \(0.915368\pi\) | |||||||
\(72\) | −1648.17 | − | 3422.47i | −0.317935 | − | 0.660198i | ||||
\(73\) | 3060.01 | + | 698.427i | 0.574218 | + | 0.131062i | 0.499762 | − | 0.866163i | \(-0.333421\pi\) |
0.0744561 | + | 0.997224i | \(0.476278\pi\) | |||||||
\(74\) | −6836.50 | + | 3292.29i | −1.24845 | + | 0.601221i | ||||
\(75\) | −5862.10 | + | 4674.87i | −1.04215 | + | 0.831088i | ||||
\(76\) | 168.656 | − | 38.4946i | 0.0291995 | − | 0.00666458i | ||||
\(77\) | 1612.87 | − | 1286.22i | 0.272031 | − | 0.216938i | ||||
\(78\) | −2869.41 | + | 12571.7i | −0.471632 | + | 2.06636i | ||||
\(79\) | −3238.19 | −0.518857 | −0.259429 | − | 0.965762i | \(-0.583534\pi\) | ||||
−0.259429 | + | 0.965762i | \(0.583534\pi\) | |||||||
\(80\) | − | 364.056i | − | 0.0568837i | ||||||
\(81\) | 1705.33 | − | 7471.52i | 0.259919 | − | 1.13878i | ||||
\(82\) | −3819.79 | − | 3046.18i | −0.568083 | − | 0.453031i | ||||
\(83\) | −4632.98 | − | 2231.13i | −0.672519 | − | 0.323868i | 0.0662732 | − | 0.997802i | \(-0.478889\pi\) |
−0.738792 | + | 0.673934i | \(0.764603\pi\) | |||||||
\(84\) | 1137.56 | − | 547.822i | 0.161219 | − | 0.0776392i | ||||
\(85\) | − | 142.774i | − | 0.0197611i | ||||||
\(86\) | −5685.00 | − | 5374.77i | −0.768659 | − | 0.726713i | ||||
\(87\) | 10740.7 | 1.41903 | ||||||||
\(88\) | 967.986 | + | 2010.04i | 0.124998 | + | 0.259561i | ||||
\(89\) | 4293.30 | − | 8915.14i | 0.542015 | − | 1.12551i | −0.432593 | − | 0.901589i | \(-0.642401\pi\) |
0.974608 | − | 0.223917i | \(-0.0718845\pi\) | |||||||
\(90\) | −216.263 | + | 271.185i | −0.0266991 | + | 0.0334796i | ||||
\(91\) | 13623.7 | + | 3109.51i | 1.64517 | + | 0.375500i | ||||
\(92\) | 821.595 | 0.0970694 | ||||||||
\(93\) | − | 348.109i | − | 0.0402485i | ||||||
\(94\) | 14687.7 | + | 3352.37i | 1.66226 | + | 0.379400i | ||||
\(95\) | 72.9504 | + | 91.4770i | 0.00808315 | + | 0.0101360i | ||||
\(96\) | 648.702 | + | 2842.15i | 0.0703887 | + | 0.308393i | ||||
\(97\) | −2634.89 | − | 3304.04i | −0.280039 | − | 0.351158i | 0.621842 | − | 0.783143i | \(-0.286385\pi\) |
−0.901881 | + | 0.431985i | \(0.857813\pi\) | |||||||
\(98\) | −1176.73 | − | 2443.51i | −0.122525 | − | 0.254426i | ||||
\(99\) | 530.058 | − | 2322.33i | 0.0540820 | − | 0.236949i | ||||
\(100\) | 1068.84 | − | 514.726i | 0.106884 | − | 0.0514726i | ||||
\(101\) | 1719.84 | − | 2156.61i | 0.168595 | − | 0.211412i | −0.690355 | − | 0.723471i | \(-0.742546\pi\) |
0.858950 | + | 0.512059i | \(0.171117\pi\) | |||||||
\(102\) | 1256.18 | + | 5503.69i | 0.120740 | + | 0.528997i | ||||
\(103\) | 1786.94 | + | 7829.10i | 0.168436 | + | 0.737967i | 0.986623 | + | 0.163016i | \(0.0521221\pi\) |
−0.818187 | + | 0.574952i | \(0.805021\pi\) | |||||||
\(104\) | −6556.98 | + | 13615.7i | −0.606230 | + | 1.25885i | ||||
\(105\) | 667.650 | + | 532.433i | 0.0605578 | + | 0.0482932i | ||||
\(106\) | 6231.93 | − | 4969.80i | 0.554640 | − | 0.442311i | ||||
\(107\) | −12878.6 | − | 6201.98i | −1.12486 | − | 0.541705i | −0.223471 | − | 0.974711i | \(-0.571739\pi\) |
−0.901391 | + | 0.433005i | \(0.857453\pi\) | |||||||
\(108\) | −171.974 | + | 357.108i | −0.0147440 | + | 0.0306162i | ||||
\(109\) | −12631.7 | − | 15839.6i | −1.06318 | − | 1.33319i | −0.940141 | − | 0.340785i | \(-0.889307\pi\) |
−0.123039 | − | 0.992402i | \(-0.539264\pi\) | |||||||
\(110\) | 127.013 | − | 159.269i | 0.0104969 | − | 0.0131627i | ||||
\(111\) | 19434.9 | + | 9359.35i | 1.57738 | + | 0.759626i | ||||
\(112\) | 15208.0 | − | 3471.14i | 1.21238 | − | 0.276717i | ||||
\(113\) | −3263.35 | + | 744.838i | −0.255568 | + | 0.0583318i | −0.348385 | − | 0.937351i | \(-0.613270\pi\) |
0.0928172 | + | 0.995683i | \(0.470413\pi\) | |||||||
\(114\) | −3616.97 | − | 2884.44i | −0.278314 | − | 0.221948i | ||||
\(115\) | 241.102 | + | 500.653i | 0.0182308 | + | 0.0378566i | ||||
\(116\) | −1656.78 | − | 378.150i | −0.123126 | − | 0.0281027i | ||||
\(117\) | 14537.7 | − | 7001.01i | 1.06200 | − | 0.511433i | ||||
\(118\) | −13903.4 | + | 11087.6i | −0.998519 | + | 0.796293i | ||||
\(119\) | 5964.22 | − | 1361.29i | 0.421172 | − | 0.0961297i | ||||
\(120\) | −722.034 | + | 575.803i | −0.0501412 | + | 0.0399863i | ||||
\(121\) | 2946.62 | − | 12910.0i | 0.201258 | − | 0.881770i | ||||
\(122\) | −16902.5 | −1.13562 | ||||||||
\(123\) | 13889.1i | 0.918046i | ||||||||
\(124\) | −12.2560 | + | 53.6970i | −0.000797086 | + | 0.00349226i | ||||
\(125\) | 1256.30 | + | 1001.86i | 0.0804029 | + | 0.0641192i | ||||
\(126\) | −13390.5 | − | 6448.50i | −0.843440 | − | 0.406179i | ||||
\(127\) | 118.686 | − | 57.1564i | 0.00735858 | − | 0.00354370i | −0.430201 | − | 0.902733i | \(-0.641557\pi\) |
0.437559 | + | 0.899190i | \(0.355843\pi\) | |||||||
\(128\) | 18686.1i | 1.14051i | ||||||||
\(129\) | −1869.50 | + | 22162.1i | −0.112343 | + | 1.33177i | ||||
\(130\) | 1379.92 | 0.0816520 | ||||||||
\(131\) | −7786.31 | − | 16168.4i | −0.453721 | − | 0.942161i | −0.994863 | − | 0.101230i | \(-0.967722\pi\) |
0.541142 | − | 0.840931i | \(-0.317992\pi\) | |||||||
\(132\) | −371.511 | + | 771.450i | −0.0213218 | + | 0.0442751i | ||||
\(133\) | −3125.80 | + | 3919.63i | −0.176709 | + | 0.221586i | ||||
\(134\) | 29291.0 | + | 6685.49i | 1.63127 | + | 0.372326i | ||||
\(135\) | −268.076 | −0.0147093 | ||||||||
\(136\) | 6615.91i | 0.357694i | ||||||||
\(137\) | −19118.9 | − | 4363.76i | −1.01864 | − | 0.232498i | −0.319579 | − | 0.947560i | \(-0.603542\pi\) |
−0.699062 | + | 0.715061i | \(0.746399\pi\) | |||||||
\(138\) | −13699.0 | − | 17178.0i | −0.719335 | − | 0.902018i | ||||
\(139\) | 7382.95 | + | 32346.8i | 0.382121 | + | 1.67418i | 0.690825 | + | 0.723022i | \(0.257247\pi\) |
−0.308705 | + | 0.951158i | \(0.599896\pi\) | |||||||
\(140\) | −84.2417 | − | 105.636i | −0.00429805 | − | 0.00538958i | ||||
\(141\) | −18582.5 | − | 38586.9i | −0.934684 | − | 1.94089i | ||||
\(142\) | 5605.66 | − | 24560.0i | 0.278004 | − | 1.21801i | ||||
\(143\) | −8538.14 | + | 4111.75i | −0.417533 | + | 0.201073i | ||||
\(144\) | 11230.4 | − | 14082.5i | 0.541590 | − | 0.679132i | ||||
\(145\) | −255.760 | − | 1120.56i | −0.0121646 | − | 0.0532965i | ||||
\(146\) | 2955.19 | + | 12947.5i | 0.138637 | + | 0.607410i | ||||
\(147\) | −3345.23 | + | 6946.43i | −0.154807 | + | 0.321460i | ||||
\(148\) | −2668.38 | − | 2127.96i | −0.121822 | − | 0.0971496i | ||||
\(149\) | 26010.8 | − | 20742.9i | 1.17161 | − | 0.934324i | 0.172888 | − | 0.984942i | \(-0.444690\pi\) |
0.998718 | + | 0.0506171i | \(0.0161188\pi\) | |||||||
\(150\) | −28583.5 | − | 13765.1i | −1.27038 | − | 0.611781i | ||||
\(151\) | −18847.7 | + | 39137.6i | −0.826615 | + | 1.71648i | −0.139144 | + | 0.990272i | \(0.544435\pi\) |
−0.687471 | + | 0.726212i | \(0.741279\pi\) | |||||||
\(152\) | −3380.41 | − | 4238.90i | −0.146313 | − | 0.183471i | ||||
\(153\) | 4404.29 | − | 5522.80i | 0.188145 | − | 0.235926i | ||||
\(154\) | 7864.32 | + | 3787.26i | 0.331604 | + | 0.159692i | ||||
\(155\) | −36.3178 | + | 8.28930i | −0.00151167 | + | 0.000345028i | ||||
\(156\) | −5654.64 | + | 1290.64i | −0.232357 | + | 0.0530340i | ||||
\(157\) | 20991.5 | + | 16740.2i | 0.851617 | + | 0.679142i | 0.948715 | − | 0.316133i | \(-0.102384\pi\) |
−0.0970976 | + | 0.995275i | \(0.530956\pi\) | |||||||
\(158\) | −5944.84 | − | 12344.6i | −0.238137 | − | 0.494496i | ||||
\(159\) | −22091.8 | − | 5042.30i | −0.873848 | − | 0.199450i | ||||
\(160\) | 281.071 | − | 135.357i | 0.0109793 | − | 0.00528737i | ||||
\(161\) | −18615.4 | + | 14845.3i | −0.718160 | + | 0.572714i | ||||
\(162\) | 31613.6 | − | 7215.60i | 1.20460 | − | 0.274943i | ||||
\(163\) | 8776.06 | − | 6998.68i | 0.330312 | − | 0.263415i | −0.444264 | − | 0.895896i | \(-0.646535\pi\) |
0.774576 | + | 0.632481i | \(0.217963\pi\) | |||||||
\(164\) | 488.999 | − | 2142.44i | 0.0181811 | − | 0.0796566i | ||||
\(165\) | −579.118 | −0.0212715 | ||||||||
\(166\) | − | 21757.8i | − | 0.789586i | ||||||
\(167\) | −9047.35 | + | 39639.0i | −0.324406 | + | 1.42131i | 0.505219 | + | 0.862991i | \(0.331412\pi\) |
−0.829624 | + | 0.558322i | \(0.811445\pi\) | |||||||
\(168\) | −30937.9 | − | 24672.1i | −1.09615 | − | 0.874154i | ||||
\(169\) | −32103.4 | − | 15460.2i | −1.12403 | − | 0.541304i | ||||
\(170\) | 544.280 | − | 262.112i | 0.0188332 | − | 0.00906960i | ||||
\(171\) | 5788.91i | 0.197972i | ||||||||
\(172\) | 1068.65 | − | 3352.76i | 0.0361224 | − | 0.113330i | ||||
\(173\) | 39819.1 | 1.33045 | 0.665227 | − | 0.746641i | \(-0.268335\pi\) | ||||
0.665227 | + | 0.746641i | \(0.268335\pi\) | |||||||
\(174\) | 19718.3 | + | 40945.4i | 0.651284 | + | 1.35241i | ||||
\(175\) | −14916.9 | + | 30975.2i | −0.487082 | + | 1.01144i | ||||
\(176\) | −6595.71 | + | 8270.76i | −0.212930 | + | 0.267006i | ||||
\(177\) | 49286.5 | + | 11249.3i | 1.57319 | + | 0.359071i | ||||
\(178\) | 41868.1 | 1.32143 | ||||||||
\(179\) | − | 49891.9i | − | 1.55713i | −0.627566 | − | 0.778563i | \(-0.715949\pi\) | ||
0.627566 | − | 0.778563i | \(-0.284051\pi\) | |||||||
\(180\) | −152.102 | − | 34.7164i | −0.00469452 | − | 0.00107149i | ||||
\(181\) | −13606.8 | − | 17062.4i | −0.415335 | − | 0.520814i | 0.529522 | − | 0.848296i | \(-0.322371\pi\) |
−0.944857 | + | 0.327482i | \(0.893800\pi\) | |||||||
\(182\) | 13157.0 | + | 57644.7i | 0.397205 | + | 1.74027i | ||||
\(183\) | 29959.1 | + | 37567.6i | 0.894597 | + | 1.12179i | ||||
\(184\) | −11172.3 | − | 23199.5i | −0.329994 | − | 0.685241i | ||||
\(185\) | 513.659 | − | 2250.49i | 0.0150083 | − | 0.0657557i | ||||
\(186\) | 1327.06 | − | 639.078i | 0.0383587 | − | 0.0184726i | ||||
\(187\) | −2586.67 | + | 3243.59i | −0.0739705 | + | 0.0927561i | ||||
\(188\) | 1507.87 | + | 6606.40i | 0.0426626 | + | 0.186917i | ||||
\(189\) | −2556.01 | − | 11198.6i | −0.0715548 | − | 0.313502i | ||||
\(190\) | −214.801 | + | 446.039i | −0.00595017 | + | 0.0123557i | ||||
\(191\) | 21666.3 | + | 17278.3i | 0.593906 | + | 0.473624i | 0.873720 | − | 0.486430i | \(-0.161701\pi\) |
−0.279813 | + | 0.960054i | \(0.590273\pi\) | |||||||
\(192\) | 32913.0 | − | 26247.2i | 0.892821 | − | 0.712001i | ||||
\(193\) | −17539.6 | − | 8446.63i | −0.470874 | − | 0.226761i | 0.183371 | − | 0.983044i | \(-0.441299\pi\) |
−0.654245 | + | 0.756283i | \(0.727013\pi\) | |||||||
\(194\) | 7758.38 | − | 16110.4i | 0.206142 | − | 0.428059i | ||||
\(195\) | −2445.86 | − | 3067.01i | −0.0643224 | − | 0.0806577i | ||||
\(196\) | 760.578 | − | 953.735i | 0.0197985 | − | 0.0248265i | ||||
\(197\) | 57819.6 | + | 27844.4i | 1.48985 | + | 0.717474i | 0.988980 | − | 0.148049i | \(-0.0472994\pi\) |
0.500869 | + | 0.865523i | \(0.333014\pi\) | |||||||
\(198\) | 9826.29 | − | 2242.79i | 0.250645 | − | 0.0572081i | ||||
\(199\) | 10128.2 | − | 2311.69i | 0.255755 | − | 0.0583745i | −0.0927207 | − | 0.995692i | \(-0.529556\pi\) |
0.348476 | + | 0.937318i | \(0.386699\pi\) | |||||||
\(200\) | −29068.8 | − | 23181.6i | −0.726720 | − | 0.579540i | ||||
\(201\) | −37058.1 | − | 76952.0i | −0.917258 | − | 1.90471i | ||||
\(202\) | 11378.8 | + | 2597.13i | 0.278864 | + | 0.0636489i | ||||
\(203\) | 44371.6 | − | 21368.2i | 1.07675 | − | 0.518533i | ||||
\(204\) | −1985.20 | + | 1583.15i | −0.0477029 | + | 0.0380418i | ||||
\(205\) | 1449.03 | − | 330.733i | 0.0344803 | − | 0.00786990i | ||||
\(206\) | −26565.4 | + | 21185.2i | −0.626012 | + | 0.499228i | ||||
\(207\) | −6117.81 | + | 26803.9i | −0.142776 | + | 0.625543i | ||||
\(208\) | −71658.4 | −1.65631 | ||||||||
\(209\) | − | 3399.88i | − | 0.0778342i | ||||||
\(210\) | −804.028 | + | 3522.68i | −0.0182319 | + | 0.0798793i | ||||
\(211\) | −63275.1 | − | 50460.2i | −1.42124 | − | 1.13340i | −0.970600 | − | 0.240698i | \(-0.922624\pi\) |
−0.450642 | − | 0.892705i | \(-0.648805\pi\) | |||||||
\(212\) | 3230.21 | + | 1555.58i | 0.0718718 | + | 0.0346116i | ||||
\(213\) | −64522.9 | + | 31072.6i | −1.42218 | + | 0.684886i | ||||
\(214\) | − | 60481.4i | − | 1.32067i | ||||||
\(215\) | 2356.66 | − | 332.688i | 0.0509823 | − | 0.00719715i | ||||
\(216\) | 12422.3 | 0.266252 | ||||||||
\(217\) | −692.553 | − | 1438.10i | −0.0147073 | − | 0.0305401i | ||||
\(218\) | 37193.7 | − | 77233.4i | 0.782629 | − | 1.62515i | ||||
\(219\) | 23539.2 | − | 29517.3i | 0.490800 | − | 0.615443i | ||||
\(220\) | 89.3309 | + | 20.3892i | 0.00184568 | + | 0.000421265i | ||||
\(221\) | −28102.7 | −0.575391 | ||||||||
\(222\) | 91272.0i | 1.85196i | ||||||||
\(223\) | 25139.4 | + | 5737.90i | 0.505527 | + | 0.115383i | 0.467676 | − | 0.883900i | \(-0.345091\pi\) |
0.0378516 | + | 0.999283i | \(0.487949\pi\) | |||||||
\(224\) | 8334.28 | + | 10450.9i | 0.166101 | + | 0.208284i | ||||
\(225\) | 8833.67 | + | 38702.8i | 0.174492 | + | 0.764500i | ||||
\(226\) | −8830.50 | − | 11073.1i | −0.172889 | − | 0.216796i | ||||
\(227\) | 15369.0 | + | 31914.1i | 0.298260 | + | 0.619343i | 0.995208 | − | 0.0977786i | \(-0.0311737\pi\) |
−0.696949 | + | 0.717121i | \(0.745459\pi\) | |||||||
\(228\) | 463.034 | − | 2028.69i | 0.00890725 | − | 0.0390252i | ||||
\(229\) | −82940.8 | + | 39942.2i | −1.58160 | + | 0.761659i | −0.998704 | − | 0.0508864i | \(-0.983795\pi\) |
−0.582897 | + | 0.812546i | \(0.698081\pi\) | |||||||
\(230\) | −1465.96 | + | 1838.25i | −0.0277119 | + | 0.0347496i | ||||
\(231\) | −5521.67 | − | 24192.0i | −0.103478 | − | 0.453365i | ||||
\(232\) | 11851.6 | + | 51925.0i | 0.220191 | + | 0.964719i | ||||
\(233\) | −331.105 | + | 687.546i | −0.00609892 | + | 0.0126645i | −0.903996 | − | 0.427541i | \(-0.859380\pi\) |
0.897897 | + | 0.440205i | \(0.145094\pi\) | |||||||
\(234\) | 53378.4 | + | 42567.8i | 0.974840 | + | 0.777409i | ||||
\(235\) | −3583.23 | + | 2857.53i | −0.0648842 | + | 0.0517434i | ||||
\(236\) | −7206.56 | − | 3470.49i | −0.129391 | − | 0.0623114i | ||||
\(237\) | −16900.1 | + | 35093.3i | −0.300879 | + | 0.624781i | ||||
\(238\) | 16138.9 | + | 20237.6i | 0.284919 | + | 0.357277i | ||||
\(239\) | −27424.2 | + | 34388.8i | −0.480107 | + | 0.602035i | −0.961613 | − | 0.274408i | \(-0.911518\pi\) |
0.481507 | + | 0.876442i | \(0.340090\pi\) | |||||||
\(240\) | −3945.40 | − | 1900.00i | −0.0684965 | − | 0.0329862i | ||||
\(241\) | −104925. | + | 23948.4i | −1.80653 | + | 0.412328i | −0.987001 | − | 0.160712i | \(-0.948621\pi\) |
−0.819527 | + | 0.573040i | \(0.805764\pi\) | |||||||
\(242\) | 54624.9 | − | 12467.8i | 0.932739 | − | 0.212892i | ||||
\(243\) | −58882.4 | − | 46957.1i | −0.997178 | − | 0.795223i | ||||
\(244\) | −3298.65 | − | 6849.71i | −0.0554059 | − | 0.115052i | ||||
\(245\) | 804.371 | + | 183.592i | 0.0134006 | + | 0.00305860i | ||||
\(246\) | −52948.0 | + | 25498.4i | −0.874942 | + | 0.421350i | ||||
\(247\) | 18005.7 | − | 14359.1i | 0.295133 | − | 0.235360i | ||||
\(248\) | 1682.91 | − | 384.114i | 0.0273626 | − | 0.00624534i | ||||
\(249\) | −48359.0 | + | 38565.0i | −0.779971 | + | 0.622006i | ||||
\(250\) | −1512.91 | + | 6628.51i | −0.0242066 | + | 0.106056i | ||||
\(251\) | 67988.0 | 1.07916 | 0.539579 | − | 0.841935i | \(-0.318584\pi\) | ||||
0.539579 | + | 0.841935i | \(0.318584\pi\) | |||||||
\(252\) | − | 6684.92i | − | 0.105268i | ||||||
\(253\) | 3593.04 | − | 15742.1i | 0.0561334 | − | 0.245937i | ||||
\(254\) | 435.782 | + | 347.525i | 0.00675464 | + | 0.00538664i | ||||
\(255\) | −1547.29 | − | 745.134i | −0.0237953 | − | 0.0114592i | ||||
\(256\) | −20783.8 | + | 10009.0i | −0.317136 | + | 0.152725i | ||||
\(257\) | − | 39236.5i | − | 0.594051i | −0.954870 | − | 0.297025i | \(-0.904005\pi\) | ||
0.954870 | − | 0.297025i | \(-0.0959946\pi\) | |||||||
\(258\) | −87918.2 | + | 33559.4i | −1.32081 | + | 0.504168i | ||||
\(259\) | 98909.3 | 1.47448 | ||||||||
\(260\) | 269.301 | + | 559.209i | 0.00398374 | + | 0.00827232i | ||||
\(261\) | 24673.7 | − | 51235.4i | 0.362204 | − | 0.752124i | ||||
\(262\) | 47342.6 | − | 59365.8i | 0.689683 | − | 0.864836i | ||||
\(263\) | 122034. | + | 27853.6i | 1.76429 | + | 0.402688i | 0.976889 | − | 0.213748i | \(-0.0685673\pi\) |
0.787404 | + | 0.616437i | \(0.211424\pi\) | |||||||
\(264\) | 26835.4 | 0.385036 | ||||||||
\(265\) | 2424.88i | 0.0345301i | ||||||||
\(266\) | −20680.9 | − | 4720.27i | −0.292284 | − | 0.0667120i | ||||
\(267\) | −74209.7 | − | 93056.0i | −1.04097 | − | 1.30534i | ||||
\(268\) | 3007.07 | + | 13174.8i | 0.0418672 | + | 0.183432i | ||||
\(269\) | 23347.2 | + | 29276.5i | 0.322649 | + | 0.404589i | 0.916531 | − | 0.399963i | \(-0.130977\pi\) |
−0.593882 | + | 0.804552i | \(0.702406\pi\) | |||||||
\(270\) | −492.149 | − | 1021.96i | −0.00675102 | − | 0.0140186i | ||||
\(271\) | 1089.06 | − | 4771.50i | 0.0148291 | − | 0.0649705i | −0.966972 | − | 0.254883i | \(-0.917963\pi\) |
0.981801 | + | 0.189912i | \(0.0608203\pi\) | |||||||
\(272\) | −28264.2 | + | 13611.3i | −0.382031 | + | 0.183976i | ||||
\(273\) | 104801. | − | 131416.i | 1.40617 | − | 1.76329i | ||||
\(274\) | −18464.0 | − | 80896.0i | −0.245937 | − | 1.07752i | ||||
\(275\) | −5188.09 | − | 22730.5i | −0.0686028 | − | 0.300569i | ||||
\(276\) | 4287.90 | − | 8903.91i | 0.0562893 | − | 0.116886i | ||||
\(277\) | 32861.0 | + | 26205.7i | 0.428273 | + | 0.341536i | 0.813785 | − | 0.581167i | \(-0.197404\pi\) |
−0.385512 | + | 0.922703i | \(0.625975\pi\) | |||||||
\(278\) | −109758. | + | 87529.3i | −1.42019 | + | 1.13257i | ||||
\(279\) | −1660.56 | − | 799.685i | −0.0213327 | − | 0.0102733i | ||||
\(280\) | −1837.31 | + | 3815.21i | −0.0234351 | + | 0.0486634i | ||||
\(281\) | 24196.3 | + | 30341.2i | 0.306433 | + | 0.384255i | 0.911074 | − | 0.412243i | \(-0.135255\pi\) |
−0.604640 | + | 0.796499i | \(0.706683\pi\) | |||||||
\(282\) | 112986. | − | 141680.i | 1.42078 | − | 1.78160i | ||||
\(283\) | −13109.8 | − | 6313.32i | −0.163690 | − | 0.0788289i | 0.350245 | − | 0.936658i | \(-0.386098\pi\) |
−0.513935 | + | 0.857829i | \(0.671813\pi\) | |||||||
\(284\) | 11046.9 | − | 2521.38i | 0.136963 | − | 0.0312609i | ||||
\(285\) | 1372.09 | − | 313.172i | 0.0168925 | − | 0.00385561i | ||||
\(286\) | −31349.6 | − | 25000.4i | −0.383265 | − | 0.305644i | ||||
\(287\) | 27632.0 | + | 57378.5i | 0.335466 | + | 0.696603i | ||||
\(288\) | 15047.9 | + | 3434.59i | 0.181423 | + | 0.0414086i | ||||
\(289\) | 64165.3 | − | 30900.4i | 0.768254 | − | 0.369971i | ||||
\(290\) | 3802.25 | − | 3032.19i | 0.0452110 | − | 0.0360546i | ||||
\(291\) | −49558.5 | + | 11311.4i | −0.585238 | + | 0.133577i | ||||
\(292\) | −4670.24 | + | 3724.39i | −0.0547738 | + | 0.0436807i | ||||
\(293\) | −1953.83 | + | 8560.31i | −0.0227590 | + | 0.0997136i | −0.985032 | − | 0.172373i | \(-0.944857\pi\) |
0.962273 | + | 0.272087i | \(0.0877137\pi\) | |||||||
\(294\) | −32622.5 | −0.377418 | ||||||||
\(295\) | − | 5409.87i | − | 0.0621646i | ||||||
\(296\) | −23802.2 | + | 104284.i | −0.271665 | + | 1.19024i | ||||
\(297\) | 6090.27 | + | 4856.82i | 0.0690436 | + | 0.0550604i | ||||
\(298\) | 126828. | + | 61077.2i | 1.42818 | + | 0.687775i | ||||
\(299\) | 98545.4 | − | 47457.0i | 1.10228 | − | 0.530832i | ||||
\(300\) | − | 14269.7i | − | 0.158553i | ||||||
\(301\) | 36367.6 | + | 95274.9i | 0.401403 | + | 1.05159i | ||||
\(302\) | −183801. | −2.01528 | ||||||||
\(303\) | −14396.1 | − | 29893.8i | −0.156805 | − | 0.325609i | ||||
\(304\) | 11154.5 | − | 23162.6i | 0.120699 | − | 0.250634i | ||||
\(305\) | 3205.98 | − | 4020.17i | 0.0344637 | − | 0.0432161i | ||||
\(306\) | 29139.6 | + | 6650.92i | 0.311201 | + | 0.0710296i | ||||
\(307\) | 44674.7 | 0.474007 | 0.237003 | − | 0.971509i | \(-0.423835\pi\) | ||||
0.237003 | + | 0.971509i | \(0.423835\pi\) | |||||||
\(308\) | 3926.11i | 0.0413867i | ||||||||
\(309\) | 94172.6 | + | 21494.3i | 0.986297 | + | 0.225116i | ||||
\(310\) | −98.2746 | − | 123.232i | −0.00102263 | − | 0.00128234i | ||||
\(311\) | −11477.6 | − | 50286.8i | −0.118668 | − | 0.519916i | −0.998965 | − | 0.0454935i | \(-0.985514\pi\) |
0.880297 | − | 0.474423i | \(-0.157343\pi\) | |||||||
\(312\) | 113337. | + | 142121.i | 1.16430 | + | 1.45998i | ||||
\(313\) | 50907.4 | + | 105710.i | 0.519628 | + | 1.07902i | 0.981392 | + | 0.192015i | \(0.0615023\pi\) |
−0.461764 | + | 0.887003i | \(0.652783\pi\) | |||||||
\(314\) | −25279.4 | + | 110756.i | −0.256394 | + | 1.12333i | ||||
\(315\) | 4073.57 | − | 1961.73i | 0.0410539 | − | 0.0197705i | ||||
\(316\) | 3842.44 | − | 4818.26i | 0.0384798 | − | 0.0482521i | ||||
\(317\) | 10737.5 | + | 47043.9i | 0.106852 | + | 0.468149i | 0.999837 | + | 0.0180626i | \(0.00574981\pi\) |
−0.892985 | + | 0.450087i | \(0.851393\pi\) | |||||||
\(318\) | −21335.0 | − | 93474.9i | −0.210979 | − | 0.924360i | ||||
\(319\) | −14491.1 | + | 30091.0i | −0.142403 | + | 0.295703i | ||||
\(320\) | −3522.07 | − | 2808.76i | −0.0343953 | − | 0.0274293i | ||||
\(321\) | −134426. | + | 107201.i | −1.30459 | + | 1.04037i | ||||
\(322\) | −90768.4 | − | 43711.7i | −0.875433 | − | 0.421586i | ||||
\(323\) | 4374.52 | − | 9083.79i | 0.0419301 | − | 0.0870687i | ||||
\(324\) | 9093.72 | + | 11403.2i | 0.0866266 | + | 0.108626i | ||||
\(325\) | 98469.3 | − | 123477.i | 0.932253 | − | 1.16901i | ||||
\(326\) | 42791.9 | + | 20607.5i | 0.402649 | + | 0.193905i | ||||
\(327\) | −237584. | + | 54226.9i | −2.22188 | + | 0.507130i | ||||
\(328\) | −67146.1 | + | 15325.7i | −0.624127 | + | 0.142453i | ||||
\(329\) | −153535. | − | 122440.i | −1.41846 | − | 1.13118i | ||||
\(330\) | −1063.18 | − | 2207.71i | −0.00976287 | − | 0.0202728i | ||||
\(331\) | −144924. | − | 33077.9i | −1.32277 | − | 0.301913i | −0.497898 | − | 0.867236i | \(-0.665895\pi\) |
−0.824870 | + | 0.565322i | \(0.808752\pi\) | |||||||
\(332\) | 8817.31 | − | 4246.19i | 0.0799945 | − | 0.0385233i | ||||
\(333\) | 89292.6 | − | 71208.5i | 0.805244 | − | 0.642160i | ||||
\(334\) | −167721. | + | 38281.3i | −1.50347 | + | 0.343157i | ||||
\(335\) | −7145.87 | + | 5698.64i | −0.0636745 | + | 0.0507787i | ||||
\(336\) | 41752.7 | − | 182931.i | 0.369833 | − | 1.62035i | ||||
\(337\) | 8670.64 | 0.0763469 | 0.0381734 | − | 0.999271i | \(-0.487846\pi\) | ||||
0.0381734 | + | 0.999271i | \(0.487846\pi\) | |||||||
\(338\) | − | 150767.i | − | 1.31969i | ||||||
\(339\) | −8959.32 | + | 39253.3i | −0.0779607 | + | 0.341568i | ||||
\(340\) | 212.440 | + | 169.415i | 0.00183772 | + | 0.00146553i | ||||
\(341\) | 975.262 | + | 469.661i | 0.00838711 | + | 0.00403902i | ||||
\(342\) | −22068.4 | + | 10627.6i | −0.188677 | + | 0.0908621i | ||||
\(343\) | − | 97072.7i | − | 0.825104i | ||||||
\(344\) | −109204. | + | 15416.3i | −0.922830 | + | 0.130275i | ||||
\(345\) | 6684.06 | 0.0561567 | ||||||||
\(346\) | 73102.2 | + | 151798.i | 0.610630 | + | 1.26799i | ||||
\(347\) | −13739.3 | + | 28530.0i | −0.114106 | + | 0.236943i | −0.950199 | − | 0.311645i | \(-0.899120\pi\) |
0.836093 | + | 0.548588i | \(0.184834\pi\) | |||||||
\(348\) | −12744.9 | + | 15981.6i | −0.105239 | + | 0.131966i | ||||
\(349\) | −10230.9 | − | 2335.15i | −0.0839972 | − | 0.0191718i | 0.180316 | − | 0.983609i | \(-0.442288\pi\) |
−0.264313 | + | 0.964437i | \(0.585145\pi\) | |||||||
\(350\) | −145469. | −1.18750 | ||||||||
\(351\) | 52766.5i | 0.428296i | ||||||||
\(352\) | −8837.78 | − | 2017.16i | −0.0713276 | − | 0.0162801i | ||||
\(353\) | 107208. | + | 134434.i | 0.860354 | + | 1.07885i | 0.996111 | + | 0.0881078i | \(0.0280820\pi\) |
−0.135757 | + | 0.990742i | \(0.543347\pi\) | |||||||
\(354\) | 47598.3 | + | 208542.i | 0.379826 | + | 1.66413i | ||||
\(355\) | 4778.21 | + | 5991.69i | 0.0379148 | + | 0.0475436i | ||||
\(356\) | 8170.85 | + | 16966.9i | 0.0644714 | + | 0.133876i | ||||
\(357\) | 16374.4 | − | 71740.8i | 0.128478 | − | 0.562898i | ||||
\(358\) | 190197. | − | 91594.3i | 1.48402 | − | 0.714664i | ||||
\(359\) | 152738. | − | 191528.i | 1.18511 | − | 1.48608i | 0.349344 | − | 0.936995i | \(-0.386404\pi\) |
0.835766 | − | 0.549086i | \(-0.185024\pi\) | |||||||
\(360\) | 1088.04 | + | 4767.02i | 0.00839538 | + | 0.0367826i | ||||
\(361\) | −27160.6 | − | 118998.i | −0.208413 | − | 0.913117i | ||||
\(362\) | 40064.9 | − | 83195.7i | 0.305737 | − | 0.634869i | ||||
\(363\) | −124532. | − | 99310.7i | −0.945075 | − | 0.753673i | ||||
\(364\) | −20792.7 | + | 16581.6i | −0.156931 | + | 0.125148i | ||||
\(365\) | −3640.03 | − | 1752.94i | −0.0273224 | − | 0.0131578i | ||||
\(366\) | −88214.2 | + | 183179.i | −0.658531 | + | 1.36745i | ||||
\(367\) | −249.174 | − | 312.454i | −0.00185000 | − | 0.00231982i | 0.780906 | − | 0.624649i | \(-0.214758\pi\) |
−0.782756 | + | 0.622329i | \(0.786187\pi\) | |||||||
\(368\) | 76126.3 | − | 95459.4i | 0.562133 | − | 0.704893i | ||||
\(369\) | 66254.3 | + | 31906.4i | 0.486588 | + | 0.234329i | ||||
\(370\) | 9522.29 | − | 2173.40i | 0.0695566 | − | 0.0158758i | ||||
\(371\) | −101297. | + | 23120.3i | −0.735948 | + | 0.167975i | ||||
\(372\) | 517.969 | + | 413.067i | 0.00374299 | + | 0.00298493i | ||||
\(373\) | 75279.4 | + | 156319.i | 0.541076 | + | 1.12356i | 0.974917 | + | 0.222567i | \(0.0714435\pi\) |
−0.433841 | + | 0.900989i | \(0.642842\pi\) | |||||||
\(374\) | −17113.9 | − | 3906.14i | −0.122351 | − | 0.0279258i | ||||
\(375\) | 17414.1 | − | 8386.20i | 0.123834 | − | 0.0596352i | ||||
\(376\) | 166041. | − | 132414.i | 1.17447 | − | 0.936606i | ||||
\(377\) | −220564. | + | 50342.3i | −1.55186 | + | 0.354201i | ||||
\(378\) | 37998.8 | − | 30303.0i | 0.265941 | − | 0.212081i | ||||
\(379\) | −14925.5 | + | 65393.0i | −0.103909 | + | 0.455253i | 0.896028 | + | 0.443997i | \(0.146440\pi\) |
−0.999937 | + | 0.0112557i | \(0.996417\pi\) | |||||||
\(380\) | −222.676 | −0.00154208 | ||||||||
\(381\) | − | 1584.54i | − | 0.0109158i | ||||||
\(382\) | −26092.0 | + | 114316.i | −0.178805 | + | 0.783397i | ||||
\(383\) | −105246. | − | 83931.1i | −0.717479 | − | 0.572171i | 0.195241 | − | 0.980755i | \(-0.437451\pi\) |
−0.912720 | + | 0.408585i | \(0.866022\pi\) | |||||||
\(384\) | 202507. | + | 97522.4i | 1.37334 | + | 0.661366i | ||||
\(385\) | −2392.44 | + | 1152.14i | −0.0161406 | + | 0.00777291i | ||||
\(386\) | − | 82371.1i | − | 0.552841i | ||||||
\(387\) | 101424. | + | 59829.2i | 0.677200 | + | 0.399477i | ||||
\(388\) | 8042.82 | 0.0534250 | ||||||||
\(389\) | 11463.2 | + | 23803.7i | 0.0757545 | + | 0.157306i | 0.935406 | − | 0.353574i | \(-0.115034\pi\) |
−0.859652 | + | 0.510880i | \(0.829320\pi\) | |||||||
\(390\) | 7201.78 | − | 14954.7i | 0.0473490 | − | 0.0983212i | ||||
\(391\) | 29854.9 | − | 37436.8i | 0.195282 | − | 0.244875i | ||||
\(392\) | −37273.3 | − | 8507.40i | −0.242564 | − | 0.0553636i | ||||
\(393\) | −215860. | −1.39761 | ||||||||
\(394\) | 271538.i | 1.74919i | ||||||||
\(395\) | 4063.68 | + | 927.508i | 0.0260450 | + | 0.00594461i | ||||
\(396\) | 2826.55 | + | 3544.39i | 0.0180246 | + | 0.0226022i | ||||
\(397\) | −24730.2 | − | 108350.i | −0.156908 | − | 0.687460i | −0.990778 | − | 0.135498i | \(-0.956736\pi\) |
0.833869 | − | 0.551962i | \(-0.186121\pi\) | |||||||
\(398\) | 27406.4 | + | 34366.6i | 0.173016 | + | 0.216955i | ||||
\(399\) | 26164.8 | + | 54331.8i | 0.164351 | + | 0.341278i | ||||
\(400\) | 39230.3 | − | 171879.i | 0.245189 | − | 1.07424i | ||||
\(401\) | −131315. | + | 63238.0i | −0.816631 | + | 0.393269i | −0.795084 | − | 0.606499i | \(-0.792573\pi\) |
−0.0215471 | + | 0.999768i | \(0.506859\pi\) | |||||||
\(402\) | 225323. | − | 282545.i | 1.39429 | − | 1.74838i | ||||
\(403\) | 1631.61 | + | 7148.57i | 0.0100463 | + | 0.0440158i | ||||
\(404\) | 1168.17 | + | 5118.07i | 0.00715718 | + | 0.0313577i | ||||
\(405\) | −4280.11 | + | 8887.73i | −0.0260942 | + | 0.0541852i | ||||
\(406\) | 162920. | + | 129924.i | 0.988374 | + | 0.788202i | ||||
\(407\) | −52442.3 | + | 41821.3i | −0.316587 | + | 0.252470i | ||||
\(408\) | 71698.9 | + | 34528.4i | 0.430717 | + | 0.207423i | ||||
\(409\) | 54755.6 | − | 113701.i | 0.327327 | − | 0.679702i | −0.670750 | − | 0.741684i | \(-0.734028\pi\) |
0.998077 | + | 0.0619814i | \(0.0197419\pi\) | |||||||
\(410\) | 3921.03 | + | 4916.82i | 0.0233256 | + | 0.0292494i | ||||
\(411\) | −147073. | + | 184423.i | −0.870660 | + | 1.09177i | ||||
\(412\) | −13769.7 | − | 6631.14i | −0.0811204 | − | 0.0390655i | ||||
\(413\) | 225992. | − | 51581.1i | 1.32493 | − | 0.302406i | ||||
\(414\) | −113413. | + | 25885.8i | −0.661701 | + | 0.151029i | ||||
\(415\) | 5174.98 | + | 4126.91i | 0.0300478 | + | 0.0239623i | ||||
\(416\) | −26642.7 | − | 55324.2i | −0.153954 | − | 0.319690i | ||||
\(417\) | 389085. | + | 88806.2i | 2.23755 | + | 0.510706i | ||||
\(418\) | 12961.0 | − | 6241.68i | 0.0741797 | − | 0.0357231i | ||||
\(419\) | 62172.5 | − | 49580.9i | 0.354136 | − | 0.282414i | −0.430221 | − | 0.902724i | \(-0.641564\pi\) |
0.784357 | + | 0.620309i | \(0.212993\pi\) | |||||||
\(420\) | −1584.47 | + | 361.644i | −0.00898224 | + | 0.00205014i | ||||
\(421\) | −204638. | + | 163193.i | −1.15458 | + | 0.920743i | −0.997761 | − | 0.0668852i | \(-0.978694\pi\) |
−0.156814 | + | 0.987628i | \(0.550122\pi\) | |||||||
\(422\) | 76200.1 | − | 333854.i | 0.427888 | − | 1.87470i | ||||
\(423\) | −226757. | −1.26730 | ||||||||
\(424\) | − | 112365.i | − | 0.625028i | ||||||
\(425\) | 15385.1 | − | 67406.7i | 0.0851772 | − | 0.373186i | ||||
\(426\) | −236909. | − | 188929.i | −1.30546 | − | 1.04107i | ||||
\(427\) | 198506. | + | 95595.6i | 1.08873 | + | 0.524303i | ||||
\(428\) | 24510.0 | − | 11803.4i | 0.133800 | − | 0.0644345i | ||||
\(429\) | 113990.i | 0.619372i | ||||||||
\(430\) | 5594.75 | + | 8373.27i | 0.0302583 | + | 0.0452854i | ||||
\(431\) | −51750.1 | −0.278584 | −0.139292 | − | 0.990251i | \(-0.544483\pi\) | ||||
−0.139292 | + | 0.990251i | \(0.544483\pi\) | |||||||
\(432\) | 25557.0 | + | 53069.7i | 0.136944 | + | 0.284367i | ||||
\(433\) | −51826.2 | + | 107618.i | −0.276423 | + | 0.573998i | −0.992247 | − | 0.124283i | \(-0.960337\pi\) |
0.715824 | + | 0.698281i | \(0.246051\pi\) | |||||||
\(434\) | 4210.89 | − | 5280.29i | 0.0223560 | − | 0.0280336i | ||||
\(435\) | −13478.7 | − | 3076.43i | −0.0712311 | − | 0.0162580i | ||||
\(436\) | 38557.3 | 0.202831 | ||||||||
\(437\) | 39240.7i | 0.205482i | ||||||||
\(438\) | 155740. | + | 35546.7i | 0.811806 | + | 0.185289i | ||||
\(439\) | −4677.69 | − | 5865.64i | −0.0242718 | − | 0.0304359i | 0.769547 | − | 0.638590i | \(-0.220482\pi\) |
−0.793819 | + | 0.608154i | \(0.791910\pi\) | |||||||
\(440\) | −639.015 | − | 2799.71i | −0.00330070 | − | 0.0144613i | ||||
\(441\) | 25451.4 | + | 31915.0i | 0.130868 | + | 0.164104i | ||||
\(442\) | −51592.4 | − | 107133.i | −0.264083 | − | 0.548375i | ||||
\(443\) | −29196.5 | + | 127918.i | −0.148773 | + | 0.651816i | 0.844454 | + | 0.535628i | \(0.179925\pi\) |
−0.993227 | + | 0.116189i | \(0.962932\pi\) | |||||||
\(444\) | −36987.7 | + | 17812.4i | −0.187626 | + | 0.0903557i | ||||
\(445\) | −7941.31 | + | 9958.09i | −0.0401026 | + | 0.0502871i | ||||
\(446\) | 24278.3 | + | 106370.i | 0.122053 | + | 0.534749i | ||||
\(447\) | −89048.1 | − | 390145.i | −0.445666 | − | 1.95259i | ||||
\(448\) | 83751.3 | − | 173911.i | 0.417288 | − | 0.866507i | ||||
\(449\) | 118534. | + | 94527.6i | 0.587962 | + | 0.468884i | 0.871715 | − | 0.490013i | \(-0.163008\pi\) |
−0.283753 | + | 0.958898i | \(0.591579\pi\) | |||||||
\(450\) | −131325. | + | 104728.i | −0.648520 | + | 0.517177i | ||||
\(451\) | −38911.7 | − | 18738.9i | −0.191305 | − | 0.0921279i | ||||
\(452\) | 2764.01 | − | 5739.53i | 0.0135289 | − | 0.0280931i | ||||
\(453\) | 325781. | + | 408517.i | 1.58756 | + | 1.99074i | ||||
\(454\) | −93447.4 | + | 117179.i | −0.453373 | + | 0.568511i | ||||
\(455\) | −16206.0 | − | 7804.41i | −0.0782805 | − | 0.0376979i | ||||
\(456\) | −63580.8 | + | 14511.9i | −0.305771 | + | 0.0697902i | ||||
\(457\) | 138942. | − | 31712.6i | 0.665275 | − | 0.151845i | 0.123469 | − | 0.992348i | \(-0.460598\pi\) |
0.541806 | + | 0.840504i | \(0.317741\pi\) | |||||||
\(458\) | −304534. | − | 242858.i | −1.45180 | − | 1.15777i | ||||
\(459\) | 10022.8 | + | 20812.6i | 0.0475735 | + | 0.0987874i | ||||
\(460\) | −1031.04 | − | 235.328i | −0.00487259 | − | 0.00111214i | ||||
\(461\) | 264425. | − | 127340.i | 1.24423 | − | 0.599189i | 0.308271 | − | 0.951299i | \(-0.400250\pi\) |
0.935959 | + | 0.352109i | \(0.114535\pi\) | |||||||
\(462\) | 82087.7 | − | 65462.7i | 0.384586 | − | 0.306697i | ||||
\(463\) | −99056.4 | + | 22609.0i | −0.462084 | + | 0.105468i | −0.447224 | − | 0.894422i | \(-0.647587\pi\) |
−0.0148597 | + | 0.999890i | \(0.504730\pi\) | |||||||
\(464\) | −197449. | + | 157460.i | −0.917103 | + | 0.731365i | ||||
\(465\) | −99.7082 | + | 436.850i | −0.000461132 | + | 0.00202035i | ||||
\(466\) | −3228.92 | −0.0148691 | ||||||||
\(467\) | − | 95657.0i | − | 0.438614i | −0.975656 | − | 0.219307i | \(-0.929620\pi\) | ||
0.975656 | − | 0.219307i | \(-0.0703797\pi\) | |||||||
\(468\) | −6833.35 | + | 29938.9i | −0.0311991 | + | 0.136692i | ||||
\(469\) | −306188. | − | 244177.i | −1.39201 | − | 1.11009i | ||||
\(470\) | −17471.7 | − | 8413.95i | −0.0790934 | − | 0.0380894i | ||||
\(471\) | 290974. | − | 140125.i | 1.31163 | − | 0.631648i | ||||
\(472\) | 250685.i | 1.12524i | ||||||||
\(473\) | −59566.9 | − | 35138.2i | −0.266246 | − | 0.157057i | ||||
\(474\) | −164809. | −0.733539 | ||||||||
\(475\) | 24584.1 | + | 51049.4i | 0.108960 | + | 0.226258i | ||||
\(476\) | −5051.61 | + | 10489.8i | −0.0222954 | + | 0.0462969i | ||||
\(477\) | −74802.7 | + | 93799.6i | −0.328761 | + | 0.412253i | ||||
\(478\) | −181444. | − | 41413.3i | −0.794119 | − | 0.181253i | ||||
\(479\) | 335880. | 1.46391 | 0.731953 | − | 0.681355i | \(-0.238609\pi\) | ||||
0.731953 | + | 0.681355i | \(0.238609\pi\) | |||||||
\(480\) | − | 3752.49i | − | 0.0162868i | ||||||
\(481\) | −442972. | − | 101105.i | −1.91463 | − | 0.437003i | ||||
\(482\) | −283923. | − | 356028.i | −1.22210 | − | 1.53246i | ||||
\(483\) | 63730.0 | + | 279219.i | 0.273180 | + | 1.19688i | ||||
\(484\) | 15713.0 | + | 19703.4i | 0.0670761 | + | 0.0841107i | ||||
\(485\) | 2360.21 | + | 4901.03i | 0.0100338 | + | 0.0208355i | ||||
\(486\) | 70910.1 | − | 310677.i | 0.300217 | − | 1.31534i | ||||
\(487\) | −129440. | + | 62335.0i | −0.545771 | + | 0.262830i | −0.686389 | − | 0.727234i | \(-0.740805\pi\) |
0.140618 | + | 0.990064i | \(0.455091\pi\) | |||||||
\(488\) | −148560. | + | 186289.i | −0.623826 | + | 0.782253i | ||||
\(489\) | −30044.9 | − | 131635.i | −0.125647 | − | 0.550496i | ||||
\(490\) | 776.819 | + | 3403.46i | 0.00323540 | + | 0.0141752i | ||||
\(491\) | 89073.9 | − | 184964.i | 0.369477 | − | 0.767227i | −0.630483 | − | 0.776203i | \(-0.717143\pi\) |
0.999960 | + | 0.00897625i | \(0.00285727\pi\) | |||||||
\(492\) | −20666.3 | − | 16480.8i | −0.0853755 | − | 0.0680847i | ||||
\(493\) | −77434.4 | + | 61751.9i | −0.318596 | + | 0.254072i | ||||
\(494\) | 87795.6 | + | 42280.1i | 0.359765 | + | 0.173254i | ||||
\(495\) | −1330.36 | + | 2762.53i | −0.00542950 | + | 0.0112745i | ||||
\(496\) | 5103.34 | + | 6399.39i | 0.0207440 | + | 0.0260121i | ||||
\(497\) | −204738. | + | 256733.i | −0.828868 | + | 1.03937i | ||||
\(498\) | −235797. | − | 113554.i | −0.950780 | − | 0.457871i | ||||
\(499\) | −62000.3 | + | 14151.2i | −0.248996 | + | 0.0568317i | −0.345197 | − | 0.938530i | \(-0.612188\pi\) |
0.0962011 | + | 0.995362i | \(0.469331\pi\) | |||||||
\(500\) | −2981.44 | + | 680.495i | −0.0119258 | + | 0.00272198i | ||||
\(501\) | 382364. | + | 304925.i | 1.52336 | + | 1.21484i | ||||
\(502\) | 124816. | + | 259183.i | 0.495294 | + | 1.02849i | ||||
\(503\) | −92921.2 | − | 21208.6i | −0.367264 | − | 0.0838257i | 0.0349059 | − | 0.999391i | \(-0.488887\pi\) |
−0.402170 | + | 0.915565i | \(0.631744\pi\) | |||||||
\(504\) | −188763. | + | 90903.5i | −0.743115 | + | 0.357865i | ||||
\(505\) | −2775.98 | + | 2213.77i | −0.0108851 | + | 0.00868060i | ||||
\(506\) | 66608.4 | − | 15202.9i | 0.260152 | − | 0.0593781i | ||||
\(507\) | −335095. | + | 267229.i | −1.30362 | + | 1.03960i | ||||
\(508\) | −55.7876 | + | 244.422i | −0.000216177 | + | 0.000947135i | ||||
\(509\) | −272684. | −1.05250 | −0.526252 | − | 0.850329i | \(-0.676403\pi\) | ||||
−0.526252 | + | 0.850329i | \(0.676403\pi\) | |||||||
\(510\) | − | 7266.51i | − | 0.0279374i | ||||||
\(511\) | 38521.1 | − | 168772.i | 0.147522 | − | 0.646336i | ||||
\(512\) | 157438. | + | 125552.i | 0.600577 | + | 0.478944i | ||||
\(513\) | −17056.0 | − | 8213.74i | −0.0648101 | − | 0.0312109i | ||||
\(514\) | 149577. | − | 72032.4i | 0.566159 | − | 0.272648i | ||||
\(515\) | − | 10336.7i | − | 0.0389735i | ||||||
\(516\) | −30757.7 | − | 29079.3i | −0.115519 | − | 0.109215i | ||||
\(517\) | 133176. | 0.498247 | ||||||||
\(518\) | 181583. | + | 377061.i | 0.676731 | + | 1.40525i | ||||
\(519\) | 207816. | − | 431534.i | 0.771514 | − | 1.60206i | ||||
\(520\) | 12128.4 | − | 15208.6i | 0.0448537 | − | 0.0562447i | ||||
\(521\) | −168704. | − | 38505.5i | −0.621511 | − | 0.141856i | −0.0998413 | − | 0.995003i | \(-0.531834\pi\) |
−0.521670 | + | 0.853148i | \(0.674691\pi\) | |||||||
\(522\) | 240617. | 0.883049 | ||||||||
\(523\) | 3836.13i | 0.0140246i | 0.999975 | + | 0.00701229i | \(0.00223210\pi\) | ||||
−0.999975 | + | 0.00701229i | \(0.997768\pi\) | |||||||
\(524\) | 33297.1 | + | 7599.84i | 0.121267 | + | 0.0276785i | ||||
\(525\) | 257838. | + | 323319.i | 0.935467 | + | 1.17304i | ||||
\(526\) | 117854. | + | 516353.i | 0.425965 | + | 1.86627i | ||||
\(527\) | 2001.40 | + | 2509.68i | 0.00720632 | + | 0.00903644i | ||||
\(528\) | 55210.1 | + | 114645.i | 0.198039 | + | 0.411233i | ||||
\(529\) | 20800.3 | − | 91132.2i | 0.0743291 | − | 0.325657i | ||||
\(530\) | −9244.09 | + | 4451.72i | −0.0329088 | + | 0.0158481i | ||||
\(531\) | 166884. | − | 209266.i | 0.591869 | − | 0.742181i | ||||
\(532\) | −2123.14 | − | 9302.07i | −0.00750161 | − | 0.0328667i | ||||
\(533\) | −65099.3 | − | 285219.i | −0.229151 | − | 1.00398i | ||||
\(534\) | 218509. | − | 453739.i | 0.766279 | − | 1.59120i | ||||
\(535\) | 14385.2 | + | 11471.8i | 0.0502583 | + | 0.0400796i | ||||
\(536\) | 331129. | − | 264066.i | 1.15257 | − | 0.919144i | ||||
\(537\) | −540696. | − | 260385.i | −1.87501 | − | 0.902959i | ||||
\(538\) | −68745.4 | + | 142751.i | −0.237508 | + | 0.493191i | ||||
\(539\) | −14947.8 | − | 18744.0i | −0.0514517 | − | 0.0645185i | ||||
\(540\) | 318.100 | − | 398.885i | 0.00109088 | − | 0.00136792i | ||||
\(541\) | 514395. | + | 247720.i | 1.75753 | + | 0.846381i | 0.974498 | + | 0.224397i | \(0.0720413\pi\) |
0.783030 | + | 0.621984i | \(0.213673\pi\) | |||||||
\(542\) | 20189.2 | − | 4608.06i | 0.0687260 | − | 0.0156863i | ||||
\(543\) | −255925. | + | 58413.1i | −0.867985 | + | 0.198112i | ||||
\(544\) | −21017.3 | − | 16760.8i | −0.0710199 | − | 0.0566365i | ||||
\(545\) | 11314.9 | + | 23495.5i | 0.0380939 | + | 0.0791029i | ||||
\(546\) | 693381. | + | 158260.i | 2.32588 | + | 0.530866i | ||||
\(547\) | −65811.8 | + | 31693.3i | −0.219953 | + | 0.105924i | −0.540616 | − | 0.841270i | \(-0.681809\pi\) |
0.320663 | + | 0.947193i | \(0.396094\pi\) | |||||||
\(548\) | 29179.5 | − | 23269.9i | 0.0971667 | − | 0.0774878i | ||||
\(549\) | 248029. | − | 56611.0i | 0.822921 | − | 0.187826i | ||||
\(550\) | 77128.4 | − | 61507.9i | 0.254970 | − | 0.203332i | ||||
\(551\) | 18061.0 | − | 79130.5i | 0.0594894 | − | 0.260640i | ||||
\(552\) | −309729. | −1.01649 | ||||||||
\(553\) | 178599.i | 0.584022i | ||||||||
\(554\) | −39573.4 | + | 173382.i | −0.128939 | + | 0.564917i | ||||
\(555\) | −21708.5 | − | 17312.0i | −0.0704765 | − | 0.0562031i | ||||
\(556\) | −56891.1 | − | 27397.3i | −0.184033 | − | 0.0886254i | ||||
\(557\) | 232232. | − | 111837.i | 0.748536 | − | 0.360476i | −0.0204085 | − | 0.999792i | \(-0.506497\pi\) |
0.768944 | + | 0.639316i | \(0.220782\pi\) | |||||||
\(558\) | − | 7798.48i | − | 0.0250462i | ||||||
\(559\) | −65484.2 | − | 463870.i | −0.209562 | − | 1.48447i | ||||
\(560\) | −20079.2 | −0.0640279 | ||||||||
\(561\) | 21652.0 | + | 44960.9i | 0.0687976 | + | 0.142860i | ||||
\(562\) | −71245.5 | + | 147943.i | −0.225572 | + | 0.468405i | ||||
\(563\) | 199228. | − | 249824.i | 0.628541 | − | 0.788165i | −0.360977 | − | 0.932575i | \(-0.617557\pi\) |
0.989518 | + | 0.144409i | \(0.0461282\pi\) | |||||||
\(564\) | 79465.4 | + | 18137.5i | 0.249816 | + | 0.0570188i | ||||
\(565\) | 4308.60 | 0.0134971 | ||||||||
\(566\) | − | 61567.2i | − | 0.192184i | ||||||
\(567\) | −412085. | − | 94055.7i | −1.28180 | − | 0.292563i | ||||
\(568\) | −221415. | − | 277646.i | −0.686295 | − | 0.860586i | ||||
\(569\) | −82205.5 | − | 360166.i | −0.253908 | − | 1.11244i | −0.927642 | − | 0.373470i | \(-0.878168\pi\) |
0.673734 | − | 0.738974i | \(-0.264689\pi\) | |||||||
\(570\) | 3712.84 | + | 4655.75i | 0.0114276 | + | 0.0143298i | ||||
\(571\) | −111720. | − | 231989.i | −0.342657 | − | 0.711534i | 0.656425 | − | 0.754392i | \(-0.272068\pi\) |
−0.999081 | + | 0.0428579i | \(0.986354\pi\) | |||||||
\(572\) | 4013.28 | − | 17583.3i | 0.0122661 | − | 0.0537414i | ||||
\(573\) | 300327. | − | 144630.i | 0.914713 | − | 0.440503i | ||||
\(574\) | −168009. | + | 210677.i | −0.509929 | + | 0.639431i | ||||
\(575\) | 59879.8 | + | 262351.i | 0.181111 | + | 0.793499i | ||||
\(576\) | −49596.9 | − | 217298.i | −0.149489 | − | 0.654955i | ||||
\(577\) | 86100.7 | − | 178790.i | 0.258616 | − | 0.537021i | −0.730720 | − | 0.682678i | \(-0.760815\pi\) |
0.989335 | + | 0.145657i | \(0.0465295\pi\) | |||||||
\(578\) | 235596. | + | 187882.i | 0.705201 | + | 0.562379i | ||||
\(579\) | −183078. | + | 146000.i | −0.546109 | + | 0.435507i | ||||
\(580\) | 1970.82 | + | 949.099i | 0.00585857 | + | 0.00282134i | ||||
\(581\) | −123056. | + | 255528.i | −0.364544 | + | 0.756983i | ||||
\(582\) | −134103. | − | 168160.i | −0.395908 | − | 0.496453i | ||||
\(583\) | 43932.2 | − | 55089.3i | 0.129255 | − | 0.162080i | ||||
\(584\) | 168673. | + | 81228.8i | 0.494562 | + | 0.238169i | ||||
\(585\) | −20249.0 | + | 4621.71i | −0.0591688 | + | 0.0135049i | ||||
\(586\) | −36220.5 | + | 8267.09i | −0.105477 | + | 0.0240745i | ||||
\(587\) | 455985. | + | 363636.i | 1.32335 | + | 1.05534i | 0.993798 | + | 0.111199i | \(0.0354690\pi\) |
0.329552 | + | 0.944138i | \(0.393102\pi\) | |||||||
\(588\) | −6366.51 | − | 13220.2i | −0.0184139 | − | 0.0382369i | ||||
\(589\) | −2564.65 | − | 585.365i | −0.00739261 | − | 0.00168732i | ||||
\(590\) | 20623.5 | − | 9931.74i | 0.0592458 | − | 0.0285313i | ||||
\(591\) | 603519. | − | 481291.i | 1.72789 | − | 1.37795i | ||||
\(592\) | −494487. | + | 112864.i | −1.41095 | + | 0.322040i | ||||
\(593\) | −422877. | + | 337233.i | −1.20255 | + | 0.959004i | −0.999795 | − | 0.0202247i | \(-0.993562\pi\) |
−0.202758 | + | 0.979229i | \(0.564990\pi\) | |||||||
\(594\) | −7334.30 | + | 32133.7i | −0.0207867 | + | 0.0910726i | ||||
\(595\) | −7874.55 | −0.0222429 | ||||||||
\(596\) | 63316.4i | 0.178248i | ||||||||
\(597\) | 27806.2 | − | 121827.i | 0.0780178 | − | 0.341818i | ||||
\(598\) | 361830. | + | 288550.i | 1.01182 | + | 0.806897i | ||||
\(599\) | −151928. | − | 73164.9i | −0.423434 | − | 0.203915i | 0.210017 | − | 0.977698i | \(-0.432648\pi\) |
−0.633451 | + | 0.773783i | \(0.718362\pi\) | |||||||
\(600\) | −402937. | + | 194044.i | −1.11927 | + | 0.539011i | ||||
\(601\) | − | 409845.i | − | 1.13467i | −0.823486 | − | 0.567336i | \(-0.807974\pi\) | ||
0.823486 | − | 0.567336i | \(-0.192026\pi\) | |||||||
\(602\) | −296440. | + | 313551.i | −0.817983 | + | 0.865197i | ||||
\(603\) | −452210. | −1.24367 | ||||||||
\(604\) | −35870.1 | − | 74485.1i | −0.0983239 | − | 0.204172i | ||||
\(605\) | −7395.57 | + | 15357.1i | −0.0202051 | + | 0.0419563i | ||||
\(606\) | 87531.7 | − | 109761.i | 0.238353 | − | 0.298885i | ||||
\(607\) | 504987. | + | 115260.i | 1.37057 | + | 0.312825i | 0.843562 | − | 0.537032i | \(-0.180455\pi\) |
0.527013 | + | 0.849857i | \(0.323312\pi\) | |||||||
\(608\) | 22030.0 | 0.0595947 | ||||||||
\(609\) | − | 592391.i | − | 1.59725i | ||||||
\(610\) | 21211.4 | + | 4841.36i | 0.0570045 | + | 0.0130109i | ||||
\(611\) | 562458. | + | 705300.i | 1.50663 | + | 1.88926i | ||||
\(612\) | 2991.53 | + | 13106.7i | 0.00798711 | + | 0.0349938i | ||||
\(613\) | −353935. | − | 443820.i | −0.941894 | − | 1.18110i | −0.983307 | − | 0.181956i | \(-0.941757\pi\) |
0.0414123 | − | 0.999142i | \(-0.486814\pi\) | |||||||
\(614\) | 82016.2 | + | 170308.i | 0.217552 | + | 0.451751i | ||||
\(615\) | 3978.23 | − | 17429.8i | 0.0105182 | − | 0.0460831i | ||||
\(616\) | 110862. | − | 53388.4i | 0.292161 | − | 0.140697i | ||||
\(617\) | −262838. | + | 329588.i | −0.690427 | + | 0.865768i | −0.996268 | − | 0.0863147i | \(-0.972491\pi\) |
0.305841 | + | 0.952083i | \(0.401062\pi\) | |||||||
\(618\) | 90946.9 | + | 398464.i | 0.238128 | + | 1.04331i | ||||
\(619\) | 27009.9 | + | 118338.i | 0.0704924 | + | 0.308847i | 0.997866 | − | 0.0652882i | \(-0.0207967\pi\) |
−0.927374 | + | 0.374135i | \(0.877940\pi\) | |||||||
\(620\) | 30.7607 | − | 63.8752i | 8.00226e−5 | − | 0.000166169i | ||||
\(621\) | −70292.6 | − | 56056.4i | −0.182275 | − | 0.145359i | ||||
\(622\) | 170632. | − | 136074.i | 0.441041 | − | 0.351718i | ||||
\(623\) | −491706. | − | 236793.i | −1.26686 | − | 0.610089i | ||||
\(624\) | −373985. | + | 776587.i | −0.960472 | + | 1.99444i | ||||
\(625\) | 241615. | + | 302976.i | 0.618536 | + | 0.775619i | ||||
\(626\) | −309529. | + | 388137.i | −0.789865 | + | 0.990460i | ||||
\(627\) | −36845.6 | − | 17743.9i | −0.0937240 | − | 0.0451351i | ||||
\(628\) | −49817.1 | + | 11370.4i | −0.126316 | + | 0.0288309i | ||||
\(629\) | −193926. | + | 44262.3i | −0.490156 | + | 0.111875i | ||||
\(630\) | 14957.0 | + | 11927.8i | 0.0376845 | + | 0.0300524i | ||||
\(631\) | 89763.5 | + | 186396.i | 0.225445 | + | 0.468142i | 0.982755 | − | 0.184914i | \(-0.0592008\pi\) |
−0.757309 | + | 0.653056i | \(0.773487\pi\) | |||||||
\(632\) | −188305. | − | 42979.3i | −0.471440 | − | 0.107603i | ||||
\(633\) | −877087. | + | 422383.i | −2.18895 | + | 1.05414i | ||||
\(634\) | −159628. | + | 127299.i | −0.397127 | + | 0.316699i | ||||
\(635\) | −165.314 | + | 37.7318i | −0.000409979 | + | 9.35750e-5i | ||||
\(636\) | 33716.8 | − | 26888.3i | 0.0833551 | − | 0.0664735i | ||||
\(637\) | 36137.2 | − | 158327.i | 0.0890585 | − | 0.390191i | ||||
\(638\) | −141316. | −0.347177 | ||||||||
\(639\) | 379170.i | 0.928608i | ||||||||
\(640\) | 5352.22 | − | 23449.6i | 0.0130669 | − | 0.0572500i | ||||
\(641\) | 48188.8 | + | 38429.3i | 0.117282 | + | 0.0935291i | 0.680374 | − | 0.732865i | \(-0.261817\pi\) |
−0.563093 | + | 0.826394i | \(0.690389\pi\) | |||||||
\(642\) | −655458. | − | 315652.i | −1.59028 | − | 0.765841i | ||||
\(643\) | 543860. | − | 261909.i | 1.31542 | − | 0.633473i | 0.361176 | − | 0.932498i | \(-0.382375\pi\) |
0.954245 | + | 0.299024i | \(0.0966612\pi\) | |||||||
\(644\) | − | 45314.3i | − | 0.109261i | ||||||
\(645\) | 8693.92 | − | 27276.2i | 0.0208976 | − | 0.0655639i | ||||
\(646\) | 42660.1 | 0.102225 | ||||||||
\(647\) | 60784.9 | + | 126221.i | 0.145207 | + | 0.301525i | 0.960869 | − | 0.277003i | \(-0.0893413\pi\) |
−0.815662 | + | 0.578529i | \(0.803627\pi\) | |||||||
\(648\) | 198334. | − | 411844.i | 0.472331 | − | 0.980806i | ||||
\(649\) | −98012.4 | + | 122904.i | −0.232697 | + | 0.291793i | ||||
\(650\) | 651491. | + | 148699.i | 1.54199 | + | 0.351949i | ||||
\(651\) | −19199.6 | −0.0453034 | ||||||||
\(652\) | 21363.0i | 0.0502536i | ||||||||
\(653\) | 713686. | + | 162894.i | 1.67371 | + | 0.382014i | 0.951013 | − | 0.309150i | \(-0.100045\pi\) |
0.722698 | + | 0.691164i | \(0.242902\pi\) | |||||||
\(654\) | −642892. | − | 806161.i | −1.50308 | − | 1.88480i | ||||
\(655\) | 5140.13 | + | 22520.4i | 0.0119809 | + | 0.0524920i | ||||
\(656\) | −203617. | − | 255328.i | −0.473158 | − | 0.593322i | ||||
\(657\) | −86729.4 | − | 180096.i | −0.200926 | − | 0.417227i | ||||
\(658\) | 184897. | − | 810087.i | 0.427050 | − | 1.87103i | ||||
\(659\) | 439530. | − | 211667.i | 1.01209 | − | 0.487396i | 0.147064 | − | 0.989127i | \(-0.453018\pi\) |
0.865024 | + | 0.501731i | \(0.167303\pi\) | |||||||
\(660\) | 687.182 | − | 861.699i | 0.00157755 | − | 0.00197819i | ||||
\(661\) | 23986.4 | + | 105091.i | 0.0548988 | + | 0.240527i | 0.994931 | − | 0.100558i | \(-0.0320627\pi\) |
−0.940032 | + | 0.341085i | \(0.889206\pi\) | |||||||
\(662\) | −139960. | − | 613203.i | −0.319365 | − | 1.39923i | ||||
\(663\) | −146667. | + | 304558.i | −0.333662 | + | 0.692856i | ||||
\(664\) | −239801. | − | 191235.i | −0.543894 | − | 0.433741i | ||||
\(665\) | 5045.33 | − | 4023.51i | 0.0114090 | − | 0.00909834i | ||||
\(666\) | 435389. | + | 209672.i | 0.981587 | + | 0.472707i | ||||
\(667\) | 167253. | − | 347304.i | 0.375943 | − | 0.780653i | ||||
\(668\) | −48245.3 | − | 60497.7i | −0.108119 | − | 0.135577i | ||||
\(669\) | 193386. | − | 242498.i | 0.432088 | − | 0.541821i | ||||
\(670\) | −34843.1 | − | 16779.5i | −0.0776188 | − | 0.0373793i | ||||
\(671\) | −145670. | + | 33248.1i | −0.323537 | + | 0.0738452i | ||||
\(672\) | 156756. | − | 35778.6i | 0.347125 | − | 0.0792290i | ||||
\(673\) | −332382. | − | 265066.i | −0.733850 | − | 0.585226i | 0.183636 | − | 0.982994i | \(-0.441213\pi\) |
−0.917486 | + | 0.397769i | \(0.869785\pi\) | |||||||
\(674\) | 15918.0 | + | 33054.1i | 0.0350404 | + | 0.0727622i | ||||
\(675\) | −126565. | − | 28887.6i | −0.277783 | − | 0.0634022i | ||||
\(676\) | 61097.9 | − | 29423.2i | 0.133701 | − | 0.0643868i | ||||
\(677\) | −520941. | + | 415437.i | −1.13661 | + | 0.906416i | −0.996489 | − | 0.0837186i | \(-0.973320\pi\) |
−0.140120 | + | 0.990135i | \(0.544749\pi\) | |||||||
\(678\) | −166089. | + | 37908.8i | −0.361312 | + | 0.0824671i | ||||
\(679\) | −182232. | + | 145325.i | −0.395261 | + | 0.315210i | ||||
\(680\) | 1894.98 | − | 8302.46i | 0.00409815 | − | 0.0179552i | ||||
\(681\) | 426075. | 0.918738 | ||||||||
\(682\) | 4580.11i | 0.00984708i | ||||||||
\(683\) | 150038. | − | 657359.i | 0.321632 | − | 1.40916i | −0.513016 | − | 0.858379i | \(-0.671472\pi\) |
0.834648 | − | 0.550783i | \(-0.185671\pi\) | |||||||
\(684\) | −8613.62 | − | 6869.13i | −0.0184108 | − | 0.0146821i | ||||
\(685\) | 22742.8 | + | 10952.4i | 0.0484689 | + | 0.0233414i | ||||
\(686\) | 370060. | − | 178211.i | 0.786364 | − | 0.378693i | ||||
\(687\) | 1.10732e6i | 2.34616i | ||||||||
\(688\) | −290532. | − | 434819.i | −0.613787 | − | 0.918611i | ||||
\(689\) | 477297. | 1.00543 | ||||||||
\(690\) | 12271.0 | + | 25480.9i | 0.0257739 | + | 0.0535201i | ||||
\(691\) | −240642. | + | 499698.i | −0.503982 | + | 1.04653i | 0.481452 | + | 0.876473i | \(0.340110\pi\) |
−0.985434 | + | 0.170058i | \(0.945605\pi\) | |||||||
\(692\) | −47249.5 | + | 59248.9i | −0.0986699 | + | 0.123728i | ||||
\(693\) | −128086. | − | 29234.8i | −0.266708 | − | 0.0608743i | ||||
\(694\) | −133985. | −0.278188 | ||||||||
\(695\) | − | 42707.5i | − | 0.0884167i | ||||||
\(696\) | 624583. | + | 142557.i | 1.28935 | + | 0.294286i | ||||
\(697\) | −79853.5 | − | 100133.i | −0.164372 | − | 0.206116i | ||||
\(698\) | −9880.50 | − | 43289.3i | −0.0202800 | − | 0.0888525i | ||||
\(699\) | 5723.14 | + | 7176.59i | 0.0117133 | + | 0.0146880i | ||||
\(700\) | −28389.2 | − | 58950.9i | −0.0579372 | − | 0.120308i | ||||
\(701\) | 63660.5 | − | 278915.i | 0.129549 | − | 0.567591i | −0.867934 | − | 0.496680i | \(-0.834552\pi\) |
0.997483 | − | 0.0709109i | \(-0.0225906\pi\) | |||||||
\(702\) | −201156. | + | 96871.5i | −0.408186 | + | 0.196572i | ||||
\(703\) | 101635. | − | 127446.i | 0.205652 | − | 0.257879i | ||||
\(704\) | 29128.7 | + | 127621.i | 0.0587727 | + | 0.257500i | ||||
\(705\) | 12267.2 | + | 53746.1i | 0.0246813 | + | 0.108136i | ||||
\(706\) | −315672. | + | 655499.i | −0.633324 | + | 1.31511i | ||||
\(707\) | −118946. | − | 94856.1i | −0.237963 | − | 0.189769i | ||||
\(708\) | −75221.9 | + | 59987.5i | −0.150064 | + | 0.119672i | ||||
\(709\) | −275023. | − | 132444.i | −0.547112 | − | 0.263475i | 0.139845 | − | 0.990173i | \(-0.455340\pi\) |
−0.686957 | + | 0.726698i | \(0.741054\pi\) | |||||||
\(710\) | −14069.4 | + | 29215.3i | −0.0279098 | + | 0.0579554i | ||||
\(711\) | 128580. | + | 161235.i | 0.254352 | + | 0.318947i | ||||
\(712\) | 367989. | − | 461443.i | 0.725896 | − | 0.910245i | ||||
\(713\) | −11256.3 | − | 5420.73i | −0.0221419 | − | 0.0106630i | ||||
\(714\) | 303551. | − | 69283.5i | 0.595436 | − | 0.135904i | ||||
\(715\) | 11892.4 | − | 2714.37i | 0.0232626 | − | 0.00530954i | ||||
\(716\) | 74236.7 | + | 59201.8i | 0.144808 | + | 0.115481i | ||||
\(717\) | 229557. | + | 476680.i | 0.446532 | + | 0.927233i | ||||
\(718\) | 1.01054e6 | + | 230650.i | 1.96023 | + | 0.447409i | ||||
\(719\) | 164280. | − | 79113.2i | 0.317781 | − | 0.153035i | −0.268193 | − | 0.963365i | \(-0.586426\pi\) |
0.585974 | + | 0.810330i | \(0.300712\pi\) | |||||||
\(720\) | −18126.9 | + | 14455.7i | −0.0349671 | + | 0.0278853i | ||||
\(721\) | 431807. | − | 98557.0i | 0.830651 | − | 0.189591i | ||||
\(722\) | 403781. | − | 322005.i | 0.774590 | − | 0.617715i | ||||
\(723\) | −288065. | + | 1.26209e6i | −0.551079 | + | 2.41443i | ||||
\(724\) | 41533.8 | 0.0792364 | ||||||||
\(725\) | − | 556602.i | − | 1.05893i | ||||||
\(726\) | 149969. | − | 657058.i | 0.284531 | − | 1.24661i | ||||
\(727\) | 261073. | + | 208198.i | 0.493961 | + | 0.393921i | 0.838543 | − | 0.544836i | \(-0.183408\pi\) |
−0.344582 | + | 0.938756i | \(0.611979\pi\) | |||||||
\(728\) | 750962. | + | 361644.i | 1.41695 | + | 0.682368i | ||||
\(729\) | −256914. | + | 123723.i | −0.483429 | + | 0.232807i | ||||
\(730\) | − | 17094.6i | − | 0.0320785i | ||||||
\(731\) | −113940. | − | 170525.i | −0.213226 | − | 0.319120i | ||||
\(732\) | −91448.3 | −0.170669 | ||||||||
\(733\) | 120619. | + | 250469.i | 0.224496 | + | 0.466172i | 0.982545 | − | 0.186027i | \(-0.0595611\pi\) |
−0.758048 | + | 0.652199i | \(0.773847\pi\) | |||||||
\(734\) | 733.688 | − | 1523.52i | 0.00136182 | − | 0.00282785i | ||||
\(735\) | 6187.66 | − | 7759.08i | 0.0114539 | − | 0.0143627i | ||||
\(736\) | 102004. | + | 23281.7i | 0.188304 | + | 0.0429793i | ||||
\(737\) | 265587. | 0.488958 | ||||||||
\(738\) | 311150.i | 0.571290i | ||||||||
\(739\) | −56238.6 | − | 12836.1i | −0.102978 | − | 0.0235041i | 0.170721 | − | 0.985319i | \(-0.445390\pi\) |
−0.273700 | + | 0.961815i | \(0.588247\pi\) | |||||||
\(740\) | 2739.11 | + | 3434.73i | 0.00500202 | + | 0.00627234i | ||||
\(741\) | −61642.7 | − | 270074.i | −0.112265 | − | 0.491866i | ||||
\(742\) | −274105. | − | 343717.i | −0.497862 | − | 0.624299i | ||||
\(743\) | 88689.8 | + | 184166.i | 0.160656 | + | 0.333605i | 0.965721 | − | 0.259581i | \(-0.0835844\pi\) |
−0.805066 | + | 0.593185i | \(0.797870\pi\) | |||||||
\(744\) | 4620.33 | − | 20243.0i | 0.00834693 | − | 0.0365703i | ||||
\(745\) | −38582.9 | + | 18580.6i | −0.0695157 | + | 0.0334770i | ||||
\(746\) | −457717. | + | 573959.i | −0.822468 | + | 1.03134i | ||||
\(747\) | 72872.7 | + | 319276.i | 0.130594 | + | 0.572170i | ||||
\(748\) | −1756.95 | − | 7697.69i | −0.00314019 | − | 0.0137581i | ||||
\(749\) | −342065. | + | 710305.i | −0.609740 | + | 1.26614i | ||||
\(750\) | 63939.6 | + | 50990.1i | 0.113670 | + | 0.0906491i | ||||
\(751\) | −345411. | + | 275456.i | −0.612431 | + | 0.488397i | −0.879893 | − | 0.475171i | \(-0.842386\pi\) |
0.267463 | + | 0.963568i | \(0.413815\pi\) | |||||||
\(752\) | 907298. | + | 436932.i | 1.60441 | + | 0.772641i | ||||
\(753\) | 354829. | − | 736809.i | 0.625790 | − | 1.29947i | ||||
\(754\) | −596837. | − | 748410.i | −1.04982 | − | 1.31643i | ||||
\(755\) | 34862.5 | − | 43716.1i | 0.0611595 | − | 0.0766916i | ||||
\(756\) | 19695.9 | + | 9485.07i | 0.0344614 | + | 0.0165957i | ||||
\(757\) | 405337. | − | 92515.6i | 0.707335 | − | 0.161444i | 0.146304 | − | 0.989240i | \(-0.453262\pi\) |
0.561030 | + | 0.827795i | \(0.310405\pi\) | |||||||
\(758\) | −276692. | + | 63153.1i | −0.481568 | + | 0.109915i | ||||
\(759\) | −151851. | − | 121097.i | −0.263593 | − | 0.210209i | ||||
\(760\) | 3028.02 | + | 6287.75i | 0.00524241 | + | 0.0108860i | ||||
\(761\) | −731145. | − | 166879.i | −1.26251 | − | 0.288159i | −0.461677 | − | 0.887048i | \(-0.652752\pi\) |
−0.800832 | + | 0.598889i | \(0.795609\pi\) | |||||||
\(762\) | 6040.59 | − | 2908.99i | 0.0104033 | − | 0.00500994i | ||||
\(763\) | −873618. | + | 696687.i | −1.50063 | + | 1.19671i | ||||
\(764\) | −51418.5 | + | 11735.9i | −0.0880913 | + | 0.0201063i | ||||
\(765\) | −7108.93 | + | 5669.18i | −0.0121473 | + | 0.00968718i | ||||
\(766\) | 126745. | − | 555304.i | 0.216009 | − | 0.946397i | ||||
\(767\) | −1.06485e6 | −1.81007 | ||||||||
\(768\) | 277478.i | 0.470442i | ||||||||
\(769\) | −77415.2 | + | 339178.i | −0.130910 | + | 0.573555i | 0.866341 | + | 0.499454i | \(0.166466\pi\) |
−0.997251 | + | 0.0741012i | \(0.976391\pi\) | |||||||
\(770\) | −8784.35 | − | 7005.28i | −0.0148159 | − | 0.0118153i | ||||
\(771\) | −425219. | − | 204775.i | −0.715326 | − | 0.344483i | ||||
\(772\) | 33380.7 | − | 16075.3i | 0.0560094 | − | 0.0269727i | ||||
\(773\) | − | 875235.i | − | 1.46476i | −0.680898 | − | 0.732378i | \(-0.738410\pi\) | ||
0.680898 | − | 0.732378i | \(-0.261590\pi\) | |||||||
\(774\) | −41881.4 | + | 496484.i | −0.0699100 | + | 0.828749i | ||||
\(775\) | −18039.7 | −0.0300349 | ||||||||
\(776\) | −109369. | − | 227106.i | −0.181622 | − | 0.377143i | ||||
\(777\) | 516207. | − | 1.07191e6i | 0.855030 | − | 1.77549i | ||||
\(778\) | −69699.3 | + | 87400.2i | −0.115151 | + | 0.144395i | ||||
\(779\) | 102326. | + | 23355.3i | 0.168622 | + | 0.0384868i | ||||
\(780\) | 7465.82 | 0.0122712 | ||||||||
\(781\) | − | 222690.i | − | 0.365089i | ||||||
\(782\) | 197525. | + | 45083.9i | 0.323005 | + | 0.0737238i | ||||
\(783\) | 115947. | + | 145393.i | 0.189120 | + | 0.237149i | ||||
\(784\) | −40339.8 | − | 176740.i | −0.0656298 | − | 0.287543i | ||||
\(785\) | −21547.9 | − | 27020.2i | −0.0349676 | − | 0.0438479i | ||||
\(786\) | −396287. | − | 822898.i | −0.641452 | − | 1.33199i | ||||
\(787\) | −148439. | + | 650353.i | −0.239662 | + | 1.05003i | 0.701659 | + | 0.712513i | \(0.252443\pi\) |
−0.941321 | + | 0.337513i | \(0.890414\pi\) | |||||||
\(788\) | −110040. | + | 52992.4i | −0.177214 | + | 0.0853417i | ||||
\(789\) | 938755. | − | 1.17716e6i | 1.50799 | − | 1.89096i | ||||
\(790\) | 3924.48 | + | 17194.3i | 0.00628823 | + | 0.0275505i | ||||
\(791\) | 41080.9 | + | 179987.i | 0.0656578 | + | 0.287666i | ||||
\(792\) | 61647.0 | − | 128011.i | 0.0982793 | − | 0.204079i | ||||
\(793\) | −791306. | − | 631045.i | −1.25834 | − | 1.00349i | ||||
\(794\) | 367650. | − | 293191.i | 0.583167 | − | 0.465060i | ||||
\(795\) | 26279.2 | + | 12655.4i | 0.0415794 | + | 0.0200236i | ||||
\(796\) | −8578.42 | + | 17813.3i | −0.0135388 | + | 0.0281137i | ||||
\(797\) | 71589.3 | + | 89770.1i | 0.112702 | + | 0.141324i | 0.834983 | − | 0.550276i | \(-0.185478\pi\) |
−0.722281 | + | 0.691600i | \(0.756906\pi\) | |||||||
\(798\) | −159088. | + | 199491.i | −0.249823 | + | 0.313269i | ||||
\(799\) | 355820. | + | 171354.i | 0.557361 | + | 0.268411i | ||||
\(800\) | 147286. | − | 33617.0i | 0.230134 | − | 0.0525266i | ||||
\(801\) | −614375. | + | 140227.i | −0.957566 | + | 0.218558i | ||||
\(802\) | −482151. | − | 384503.i | −0.749608 | − | 0.597793i | ||||
\(803\) | 50936.9 | + | 105772.i | 0.0789954 | + | 0.164036i | ||||
\(804\) | 158474. | + | 36170.7i | 0.245158 | + | 0.0559557i | ||||
\(805\) | 27613.1 | − | 13297.7i | 0.0426111 | − | 0.0205204i | ||||
\(806\) | −24256.3 | + | 19343.7i | −0.0373383 | + | 0.0297763i | ||||
\(807\) | 439128. | − | 100228.i | 0.674286 | − | 0.153901i | ||||
\(808\) | 128635. | − | 102583.i | 0.197031 | − | 0.157127i | ||||
\(809\) | −74805.9 | + | 327746.i | −0.114298 | + | 0.500773i | 0.885078 | + | 0.465443i | \(0.154105\pi\) |
−0.999376 | + | 0.0353292i | \(0.988752\pi\) | |||||||
\(810\) | −41739.4 | −0.0636174 | ||||||||
\(811\) | 919015.i | 1.39727i | 0.715477 | + | 0.698636i | \(0.246209\pi\) | ||||
−0.715477 | + | 0.698636i | \(0.753791\pi\) | |||||||
\(812\) | −20856.5 | + | 91378.4i | −0.0316322 | + | 0.138590i | ||||
\(813\) | −46026.6 | − | 36705.0i | −0.0696350 | − | 0.0555321i | ||||
\(814\) | −255707. | − | 123142.i | −0.385918 | − | 0.185848i | ||||
\(815\) | −13017.9 | + | 6269.09i | −0.0195986 | + | 0.00943821i | ||||
\(816\) | 377346.i | 0.566708i | ||||||||
\(817\) | 160133. | + | 51040.1i | 0.239903 | + | 0.0764659i | ||||
\(818\) | 533974. | 0.798020 | ||||||||
\(819\) | −386134. | − | 801816.i | −0.575666 | − | 1.19538i | ||||
\(820\) | −1227.31 | + | 2548.54i | −0.00182527 | + | 0.00379022i | ||||
\(821\) | −232366. | + | 291378.i | −0.344735 | + | 0.432285i | −0.923728 | − | 0.383048i | \(-0.874874\pi\) |
0.578993 | + | 0.815332i | \(0.303446\pi\) | |||||||
\(822\) | −973061. | − | 222095.i | −1.44011 | − | 0.328696i | ||||
\(823\) | −664874. | −0.981612 | −0.490806 | − | 0.871269i | \(-0.663298\pi\) | ||||
−0.490806 | + | 0.871269i | \(0.663298\pi\) | |||||||
\(824\) | 478989.i | 0.705458i | ||||||||
\(825\) | −273415. | − | 62405.1i | −0.401711 | − | 0.0916880i | ||||
\(826\) | 611525. | + | 766828.i | 0.896302 | + | 1.12393i | ||||
\(827\) | 6943.95 | + | 30423.5i | 0.0101530 | + | 0.0444834i | 0.979751 | − | 0.200221i | \(-0.0641661\pi\) |
−0.969598 | + | 0.244705i | \(0.921309\pi\) | |||||||
\(828\) | −32623.5 | − | 40908.5i | −0.0475849 | − | 0.0596696i | ||||
\(829\) | 344668. | + | 715710.i | 0.501524 | + | 1.04142i | 0.986019 | + | 0.166631i | \(0.0532889\pi\) |
−0.484496 | + | 0.874794i | \(0.660997\pi\) | |||||||
\(830\) | −6232.06 | + | 27304.4i | −0.00904639 | + | 0.0396348i | ||||
\(831\) | 455502. | − | 219358.i | 0.659611 | − | 0.317652i | ||||
\(832\) | −552859. | + | 693263.i | −0.798670 | + | 1.00150i | ||||
\(833\) | −15820.2 | − | 69313.0i | −0.0227994 | − | 0.0998907i | ||||
\(834\) | 375758. | + | 1.64630e6i | 0.540226 | + | 2.36689i | ||||
\(835\) | 22707.5 | − | 47152.5i | 0.0325683 | − | 0.0676288i | ||||
\(836\) | 5058.85 | + | 4034.30i | 0.00723834 | + | 0.00577239i | ||||
\(837\) | 4712.26 | − | 3757.90i | 0.00672633 | − | 0.00536407i | ||||
\(838\) | 303152. | + | 145990.i | 0.431690 | + | 0.207891i | ||||
\(839\) | −57595.7 | + | 119599.i | −0.0818212 | + | 0.169904i | −0.937866 | − | 0.346999i | \(-0.887201\pi\) |
0.856044 | + | 0.516902i | \(0.172915\pi\) | |||||||
\(840\) | 31757.9 | + | 39823.1i | 0.0450083 | + | 0.0564386i | ||||
\(841\) | −56141.5 | + | 70399.3i | −0.0793766 | + | 0.0995351i | ||||
\(842\) | −997810. | − | 480520.i | −1.40742 | − | 0.677778i | ||||
\(843\) | 455098. | − | 103873.i | 0.640398 | − | 0.146167i | ||||
\(844\) | 150165. | − | 34274.1i | 0.210806 | − | 0.0481151i | ||||
\(845\) | 35859.1 | + | 28596.7i | 0.0502210 | + | 0.0400499i | ||||
\(846\) | −416292. | − | 864439.i | −0.581644 | − | 1.20780i | ||||
\(847\) | −712039. | − | 162518.i | −0.992514 | − | 0.226535i | ||||
\(848\) | 480040. | − | 231175.i | 0.667554 | − | 0.321477i | ||||
\(849\) | −136839. | + | 109126.i | −0.189843 | + | 0.151395i | ||||
\(850\) | 285212. | − | 65097.8i | 0.394757 | − | 0.0901007i | ||||
\(851\) | 605278. | − | 482693.i | 0.835787 | − | 0.666518i | ||||
\(852\) | 30328.5 | − | 132878.i | 0.0417803 | − | 0.183051i | ||||
\(853\) | 317662. | 0.436583 | 0.218292 | − | 0.975884i | \(-0.429952\pi\) | ||||
0.218292 | + | 0.975884i | \(0.429952\pi\) | |||||||
\(854\) | 932244.i | 1.27824i | ||||||||
\(855\) | 1658.11 | − | 7264.64i | 0.00226819 | − | 0.00993761i | ||||
\(856\) | −666587. | − | 531586.i | −0.909724 | − | 0.725480i | ||||
\(857\) | 114687. | + | 55230.4i | 0.156154 | + | 0.0751998i | 0.510328 | − | 0.859980i | \(-0.329524\pi\) |
−0.354175 | + | 0.935179i | \(0.615238\pi\) | |||||||
\(858\) | −434551. | + | 209269.i | −0.590291 | + | 0.284269i | ||||
\(859\) | − | 105532.i | − | 0.143020i | −0.997440 | − | 0.0715102i | \(-0.977218\pi\) | ||
0.997440 | − | 0.0715102i | \(-0.0227819\pi\) | |||||||
\(860\) | −2301.39 | + | 3901.36i | −0.00311167 | + | 0.00527496i | ||||
\(861\) | 766041. | 1.03335 | ||||||||
\(862\) | −95005.6 | − | 197281.i | −0.127860 | − | 0.265504i | ||||
\(863\) | −35203.4 | + | 73100.7i | −0.0472676 | + | 0.0981522i | −0.923265 | − | 0.384163i | \(-0.874490\pi\) |
0.875997 | + | 0.482316i | \(0.160204\pi\) | |||||||
\(864\) | −31470.6 | + | 39462.8i | −0.0421577 | + | 0.0528641i | ||||
\(865\) | −49970.0 | − | 11405.3i | −0.0667847 | − | 0.0152432i | ||||
\(866\) | −505407. | −0.673915 | ||||||||
\(867\) | − | 856650.i | − | 1.13963i | ||||||
\(868\) | 2961.61 | + | 675.968i | 0.00393087 | + | 0.000897195i | ||||
\(869\) | −75516.3 | − | 94694.4i | −0.100000 | − | 0.125396i | ||||
\(870\) | −13017.0 | − | 57031.2i | −0.0171978 | − | 0.0753485i | ||||
\(871\) | 1.12168e6 | + | 1.40655e6i | 1.47854 | + | 1.85404i | ||||
\(872\) | −524313. | − | 1.08875e6i | −0.689537 | − | 1.43184i | ||||
\(873\) | −59888.9 | + | 262391.i | −0.0785811 | + | 0.344286i | ||||
\(874\) | −149593. | + | 72040.1i | −0.195834 | + | 0.0943087i | ||||
\(875\) | 55256.8 | − | 69289.8i | 0.0721721 | − | 0.0905010i | ||||
\(876\) | 15988.6 | + | 70050.5i | 0.0208354 | + | 0.0912857i | ||||
\(877\) | 159704. | + | 699710.i | 0.207643 | + | 0.909744i | 0.966130 | + | 0.258056i | \(0.0830818\pi\) |
−0.758487 | + | 0.651688i | \(0.774061\pi\) | |||||||
\(878\) | 13773.4 | − | 28600.7i | 0.0178670 | − | 0.0371012i | ||||
\(879\) | 82574.0 | + | 65850.5i | 0.106872 | + | 0.0852279i | ||||
\(880\) | 10646.1 | − | 8489.98i | 0.0137475 | − | 0.0109633i | ||||
\(881\) | −441703. | − | 212713.i | −0.569087 | − | 0.274058i | 0.127134 | − | 0.991886i | \(-0.459422\pi\) |
−0.696221 | + | 0.717828i | \(0.745136\pi\) | |||||||
\(882\) | −74941.2 | + | 155617.i | −0.0963348 | + | 0.200041i | ||||
\(883\) | −423929. | − | 531591.i | −0.543716 | − | 0.681798i | 0.431739 | − | 0.901999i | \(-0.357900\pi\) |
−0.975455 | + | 0.220200i | \(0.929329\pi\) | |||||||
\(884\) | 33346.7 | − | 41815.4i | 0.0426725 | − | 0.0535096i | ||||
\(885\) | −58628.7 | − | 28234.1i | −0.0748555 | − | 0.0360485i | ||||
\(886\) | −541250. | + | 123537.i | −0.689494 | + | 0.157372i | ||||
\(887\) | 580796. | − | 132563.i | 0.738204 | − | 0.168490i | 0.163145 | − | 0.986602i | \(-0.447836\pi\) |
0.575059 | + | 0.818112i | \(0.304979\pi\) | |||||||
\(888\) | 1.00594e6 | + | 802211.i | 1.27569 | + | 1.01733i | ||||
\(889\) | −3152.41 | − | 6546.04i | −0.00398877 | − | 0.00828277i | ||||
\(890\) | −52541.3 | − | 11992.2i | −0.0663316 | − | 0.0151398i | ||||
\(891\) | 258259. | − | 124371.i | 0.325312 | − | 0.156662i | ||||
\(892\) | −38368.1 | + | 30597.6i | −0.0482215 | + | 0.0384554i | ||||
\(893\) | −315532. | + | 72018.1i | −0.395676 | + | 0.0903106i | ||||
\(894\) | 1.32383e6 | − | 1.05572e6i | 1.65637 | − | 1.32091i | ||||
\(895\) | −14290.4 | + | 62610.5i | −0.0178402 | + | 0.0781630i | ||||
\(896\) | 1.03061e6 | 1.28375 | ||||||||
\(897\) | − | 1.31565e6i | − | 1.63514i | ||||||
\(898\) | −142746. | + | 625412.i | −0.177016 | + | 0.775557i | ||||
\(899\) | 20203.8 | + | 16112.0i | 0.0249985 | + | 0.0199356i | ||||
\(900\) | −68070.0 | − | 32780.8i | −0.0840370 | − | 0.0404701i | ||||
\(901\) | 188260. | − | 90661.2i | 0.231904 | − | 0.111679i | ||||
\(902\) | − | 182741.i | − | 0.224607i | ||||||
\(903\) | 1.22233e6 | + | 103111.i | 1.49904 | + | 0.126453i | ||||
\(904\) | −199654. | −0.244310 | ||||||||
\(905\) | 12188.3 | + | 25309.3i | 0.0148815 | + | 0.0309018i | ||||
\(906\) | −959257. | + | 1.99192e6i | −1.16863 | + | 2.42669i | ||||
\(907\) | 626215. | − | 785249.i | 0.761218 | − | 0.954537i | −0.238645 | − | 0.971107i | \(-0.576703\pi\) |
0.999863 | + | 0.0165702i | \(0.00527469\pi\) | |||||||
\(908\) | −65723.5 | − | 15001.0i | −0.0797167 | − | 0.0181948i | ||||
\(909\) | −175671. | −0.212605 | ||||||||
\(910\) | − | 76108.2i | − | 0.0919070i | ||||||
\(911\) | −799382. | − | 182454.i | −0.963202 | − | 0.219845i | −0.288126 | − | 0.957592i | \(-0.593032\pi\) |
−0.675076 | + | 0.737748i | \(0.735889\pi\) | |||||||
\(912\) | −192806. | − | 241771.i | −0.231809 | − | 0.290679i | ||||
\(913\) | −42798.7 | − | 187513.i | −0.0513440 | − | 0.224953i | ||||
\(914\) | 375972. | + | 471454.i | 0.450052 | + | 0.564348i | ||||
\(915\) | −26836.0 | − | 55725.6i | −0.0320535 | − | 0.0665599i | ||||
\(916\) | 38985.6 | − | 170807.i | 0.0464637 | − | 0.203571i | ||||
\(917\) | −891755. | + | 429447.i | −1.06049 | + | 0.510705i | ||||
\(918\) | −60941.2 | + | 76417.9i | −0.0723146 | + | 0.0906796i | ||||
\(919\) | −51085.9 | − | 223822.i | −0.0604881 | − | 0.265015i | 0.935637 | − | 0.352964i | \(-0.114826\pi\) |
−0.996125 | + | 0.0879483i | \(0.971969\pi\) | |||||||
\(920\) | 7375.38 | + | 32313.7i | 0.00871383 | + | 0.0381778i | ||||
\(921\) | 233157. | − | 484155.i | 0.274871 | − | 0.570775i | ||||
\(922\) | 970891. | + | 774260.i | 1.14211 | + | 0.910804i | ||||
\(923\) | 1.17937e6 | − | 940513.i | 1.38435 | − | 1.10398i | ||||
\(924\) | 42548.6 | + | 20490.3i | 0.0498358 | + | 0.0239996i | ||||
\(925\) | 485020. | − | 1.00716e6i | 0.566861 | − | 1.17710i | ||||
\(926\) | −268043. | − | 336115.i | −0.312595 | − | 0.391982i | ||||
\(927\) | 318868. | − | 399848.i | 0.371067 | − | 0.465303i | ||||
\(928\) | −194979. | − | 93897.1i | −0.226409 | − | 0.109033i | ||||
\(929\) | −655577. | + | 149631.i | −0.759613 | + | 0.173377i | −0.584747 | − | 0.811216i | \(-0.698806\pi\) |
−0.174866 | + | 0.984592i | \(0.555949\pi\) | |||||||
\(930\) | −1848.41 | + | 421.887i | −0.00213713 | + | 0.000487787i | ||||
\(931\) | 45551.9 | + | 36326.4i | 0.0525541 | + | 0.0419105i | ||||
\(932\) | −630.145 | − | 1308.51i | −0.000725452 | − | 0.00150642i | ||||
\(933\) | −604877. | − | 138059.i | −0.694871 | − | 0.158600i | ||||
\(934\) | 364663. | − | 175612.i | 0.418020 | − | 0.201308i | ||||
\(935\) | 4175.13 | − | 3329.56i | 0.00477581 | − | 0.00380858i | ||||
\(936\) | 938310. | − | 214163.i | 1.07101 | − | 0.244452i | ||||
\(937\) | −302367. | + | 241129.i | −0.344393 | + | 0.274645i | −0.780376 | − | 0.625311i | \(-0.784972\pi\) |
0.435983 | + | 0.899955i | \(0.356401\pi\) | |||||||
\(938\) | 368732. | − | 1.61552e6i | 0.419088 | − | 1.83614i | ||||
\(939\) | 1.41130e6 | 1.60062 | ||||||||
\(940\) | − | 8722.42i | − | 0.00987146i | ||||||
\(941\) | −204267. | + | 894954.i | −0.230685 | + | 1.01070i | 0.718388 | + | 0.695642i | \(0.244880\pi\) |
−0.949073 | + | 0.315055i | \(0.897977\pi\) | |||||||
\(942\) | 1.06837e6 | + | 851997.i | 1.20398 | + | 0.960144i | ||||
\(943\) | 449111. | + | 216280.i | 0.505045 | + | 0.243217i | ||||
\(944\) | −1.07097e6 | + | 515750.i | −1.20180 | + | 0.578755i | ||||
\(945\) | 14785.5i | 0.0165567i | ||||||||
\(946\) | 24597.3 | − | 291589.i | 0.0274856 | − | 0.325828i | ||||
\(947\) | −896567. | −0.999731 | −0.499865 | − | 0.866103i | \(-0.666617\pi\) | ||||
−0.499865 | + | 0.866103i | \(0.666617\pi\) | |||||||
\(948\) | −32163.5 | − | 66788.3i | −0.0357888 | − | 0.0743162i | ||||
\(949\) | −345039. | + | 716480.i | −0.383120 | + | 0.795557i | ||||
\(950\) | −149477. | + | 187439.i | −0.165626 | + | 0.207688i | ||||
\(951\) | 565869. | + | 129156.i | 0.625684 | + | 0.142808i | ||||
\(952\) | 364895. | 0.402618 | ||||||||
\(953\) | − | 490682.i | − | 0.540275i | −0.962822 | − | 0.270137i | \(-0.912931\pi\) | ||
0.962822 | − | 0.270137i | \(-0.0870691\pi\) | |||||||
\(954\) | −494909. | − | 112960.i | −0.543787 | − | 0.124116i | ||||
\(955\) | −22240.6 | − | 27888.8i | −0.0243859 | − | 0.0305790i | ||||
\(956\) | −18627.3 | − | 81611.7i | −0.0203814 | − | 0.0892969i | ||||
\(957\) | 250478. | + | 314089.i | 0.273493 | + | 0.342949i | ||||
\(958\) | 616627. | + | 1.28044e6i | 0.671879 | + | 1.39517i | ||||
\(959\) | −240679. | + | 1.05448e6i | −0.261698 | + | 1.14658i | ||||
\(960\) | −48821.2 | + | 23511.0i | −0.0529744 | + | 0.0255111i | ||||
\(961\) | −575284. | + | 721383.i | −0.622924 | + | 0.781122i | ||||
\(962\) | −427799. | − | 1.87431e6i | −0.462263 | − | 2.02531i | ||||
\(963\) | 202568. | + | 887509.i | 0.218433 | + | 0.957018i | ||||
\(964\) | 88870.0 | − | 184540.i | 0.0956316 | − | 0.198581i | ||||
\(965\) | 19591.5 | + | 15623.7i | 0.0210384 | + | 0.0167776i | ||||
\(966\) | −947438. | + | 755557.i | −1.01531 | + | 0.809679i | ||||
\(967\) | −206840. | − | 99608.8i | −0.221198 | − | 0.106523i | 0.320003 | − | 0.947416i | \(-0.396316\pi\) |
−0.541201 | + | 0.840893i | \(0.682030\pi\) | |||||||
\(968\) | 342700. | − | 711623.i | 0.365732 | − | 0.759450i | ||||
\(969\) | −75613.5 | − | 94816.4i | −0.0805289 | − | 0.100980i | ||||
\(970\) | −14350.7 | + | 17995.2i | −0.0152520 | + | 0.0191255i | ||||
\(971\) | −287305. | − | 138359.i | −0.304722 | − | 0.146747i | 0.275274 | − | 0.961366i | \(-0.411232\pi\) |
−0.579996 | + | 0.814619i | \(0.696946\pi\) | |||||||
\(972\) | 139740. | − | 31894.7i | 0.147907 | − | 0.0337587i | ||||
\(973\) | 1.78406e6 | − | 407200.i | 1.88445 | − | 0.430112i | ||||
\(974\) | −475266. | − | 379012.i | −0.500978 | − | 0.399517i | ||||
\(975\) | −824248. | − | 1.71157e6i | −0.867059 | − | 1.80047i | ||||
\(976\) | −1.10150e6 | − | 251409.i | −1.15633 | − | 0.263926i | ||||
\(977\) | 287267. | − | 138340.i | 0.300952 | − | 0.144931i | −0.277314 | − | 0.960779i | \(-0.589444\pi\) |
0.578265 | + | 0.815849i | \(0.303730\pi\) | |||||||
\(978\) | 446661. | − | 356200.i | 0.466982 | − | 0.372406i | ||||
\(979\) | 360828. | − | 82356.6i | 0.376474 | − | 0.0859277i | ||||
\(980\) | −1227.64 | + | 979.014i | −0.00127826 | + | 0.00101938i | ||||
\(981\) | −287108. | + | 1.25790e6i | −0.298337 | + | 1.30710i | ||||
\(982\) | 868644. | 0.900781 | ||||||||
\(983\) | − | 1.43895e6i | − | 1.48915i | −0.667537 | − | 0.744577i | \(-0.732651\pi\) | ||
0.667537 | − | 0.744577i | \(-0.267349\pi\) | |||||||
\(984\) | −184345. | + | 807670.i | −0.190389 | + | 0.834149i | ||||
\(985\) | −64583.7 | − | 51503.8i | −0.0665657 | − | 0.0530844i | ||||
\(986\) | −377568. | − | 181827.i | −0.388366 | − | 0.187027i | ||||
\(987\) | −2.12822e6 | + | 1.02490e6i | −2.18466 | + | 1.05207i | ||||
\(988\) | 43830.2i | 0.0449014i | ||||||||
\(989\) | 687509. | + | 405558.i | 0.702887 | + | 0.414629i | ||||
\(990\) | −12973.6 | −0.0132371 | ||||||||
\(991\) | −297628. | − | 618030.i | −0.303058 | − | 0.629307i | 0.692709 | − | 0.721217i | \(-0.256417\pi\) |
−0.995767 | + | 0.0919102i | \(0.970703\pi\) | |||||||
\(992\) | −3043.25 | + | 6319.36i | −0.00309253 | + | 0.00642170i | ||||
\(993\) | −1.11483e6 | + | 1.39796e6i | −1.13061 | + | 1.41773i | ||||
\(994\) | −1.35458e6 | − | 309175.i | −1.37099 | − | 0.312919i | ||||
\(995\) | −13372.2 | −0.0135069 | ||||||||
\(996\) | − | 117717.i | − | 0.118664i | ||||||
\(997\) | −543846. | − | 124129.i | −0.547123 | − | 0.124877i | −0.0599804 | − | 0.998200i | \(-0.519104\pi\) |
−0.487143 | + | 0.873322i | \(0.661961\pi\) | |||||||
\(998\) | −167770. | − | 210377.i | −0.168443 | − | 0.211221i | ||||
\(999\) | 83108.3 | + | 364121.i | 0.0832747 | + | 0.364850i |
(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 | 43.5.f.a.2.10 | ✓ | 78 | |
43.22 | odd | 14 | inner | 43.5.f.a.22.10 | yes | 78 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.5.f.a.2.10 | ✓ | 78 | 1.1 | even | 1 | trivial | |
43.5.f.a.22.10 | yes | 78 | 43.22 | odd | 14 | inner |