Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,7,Mod(3,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.3");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.d (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: | \(1.84043266896\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.3803625.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 6x^{2} - 16x + 256 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.1 | ||
Root | \(-2.31174 - 3.26433i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.3 |
Dual form | 8.7.d.b.3.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.62348 | − | 6.52867i | −0.577934 | − | 0.816083i | ||||
\(3\) | −32.4939 | −1.20348 | −0.601739 | − | 0.798693i | \(-0.705525\pi\) | ||||
−0.601739 | + | 0.798693i | \(0.705525\pi\) | |||||||
\(4\) | −21.2470 | + | 60.3702i | −0.331984 | + | 0.943285i | ||||
\(5\) | − | 199.084i | − | 1.59268i | −0.604852 | − | 0.796338i | \(-0.706768\pi\) | ||
0.604852 | − | 0.796338i | \(-0.293232\pi\) | |||||||
\(6\) | 150.235 | + | 212.142i | 0.695531 | + | 0.982138i | ||||
\(7\) | 19.6656i | 0.0573342i | 0.999589 | + | 0.0286671i | \(0.00912627\pi\) | ||||
−0.999589 | + | 0.0286671i | \(0.990874\pi\) | |||||||
\(8\) | 492.372 | − | 140.406i | 0.961664 | − | 0.274231i | ||||
\(9\) | 326.854 | 0.448359 | ||||||||
\(10\) | −1299.76 | + | 920.462i | −1.29976 | + | 0.920462i | ||||
\(11\) | −924.152 | −0.694329 | −0.347165 | − | 0.937804i | \(-0.612856\pi\) | ||||
−0.347165 | + | 0.937804i | \(0.612856\pi\) | |||||||
\(12\) | 690.396 | − | 1961.66i | 0.399535 | − | 1.13522i | ||||
\(13\) | − | 1550.92i | − | 0.705925i | −0.935638 | − | 0.352962i | \(-0.885174\pi\) | ||
0.935638 | − | 0.352962i | \(-0.114826\pi\) | |||||||
\(14\) | 128.390 | − | 90.9235i | 0.0467895 | − | 0.0331354i | ||||
\(15\) | 6469.03i | 1.91675i | ||||||||
\(16\) | −3193.13 | − | 2565.37i | −0.779574 | − | 0.626310i | ||||
\(17\) | 5140.78 | 1.04636 | 0.523181 | − | 0.852221i | \(-0.324745\pi\) | ||||
0.523181 | + | 0.852221i | \(0.324745\pi\) | |||||||
\(18\) | −1511.20 | − | 2133.92i | −0.259122 | − | 0.365898i | ||||
\(19\) | −1696.10 | −0.247281 | −0.123641 | − | 0.992327i | \(-0.539457\pi\) | ||||
−0.123641 | + | 0.992327i | \(0.539457\pi\) | |||||||
\(20\) | 12018.8 | + | 4229.94i | 1.50235 | + | 0.528742i | ||||
\(21\) | − | 639.013i | − | 0.0690004i | ||||||
\(22\) | 4272.80 | + | 6033.48i | 0.401277 | + | 0.566631i | ||||
\(23\) | − | 19210.4i | − | 1.57890i | −0.613817 | − | 0.789448i | \(-0.710367\pi\) | ||
0.613817 | − | 0.789448i | \(-0.289633\pi\) | |||||||
\(24\) | −15999.1 | + | 4562.34i | −1.15734 | + | 0.330031i | ||||
\(25\) | −24009.6 | −1.53662 | ||||||||
\(26\) | −10125.4 | + | 7170.62i | −0.576093 | + | 0.407978i | ||||
\(27\) | 13067.3 | 0.663888 | ||||||||
\(28\) | −1187.22 | − | 417.835i | −0.0540825 | − | 0.0190340i | ||||
\(29\) | 16588.1i | 0.680147i | 0.940399 | + | 0.340074i | \(0.110452\pi\) | ||||
−0.940399 | + | 0.340074i | \(0.889548\pi\) | |||||||
\(30\) | 42234.1 | − | 29909.4i | 1.56423 | − | 1.10776i | ||||
\(31\) | − | 7550.64i | − | 0.253454i | −0.991938 | − | 0.126727i | \(-0.959553\pi\) | ||
0.991938 | − | 0.126727i | \(-0.0404472\pi\) | |||||||
\(32\) | −1985.05 | + | 32707.8i | −0.0605789 | + | 0.998163i | ||||
\(33\) | 30029.3 | 0.835610 | ||||||||
\(34\) | −23768.3 | − | 33562.4i | −0.604729 | − | 0.853919i | ||||
\(35\) | 3915.12 | 0.0913148 | ||||||||
\(36\) | −6944.64 | + | 19732.2i | −0.148848 | + | 0.422930i | ||||
\(37\) | 28960.5i | 0.571743i | 0.958268 | + | 0.285871i | \(0.0922830\pi\) | ||||
−0.958268 | + | 0.285871i | \(0.907717\pi\) | |||||||
\(38\) | 7841.89 | + | 11073.3i | 0.142912 | + | 0.201802i | ||||
\(39\) | 50395.3i | 0.849565i | ||||||||
\(40\) | −27952.7 | − | 98023.6i | −0.436761 | − | 1.53162i | ||||
\(41\) | −52111.3 | −0.756101 | −0.378051 | − | 0.925785i | \(-0.623406\pi\) | ||||
−0.378051 | + | 0.925785i | \(0.623406\pi\) | |||||||
\(42\) | −4171.90 | + | 2954.46i | −0.0563101 | + | 0.0398777i | ||||
\(43\) | 5896.43 | 0.0741625 | 0.0370812 | − | 0.999312i | \(-0.488194\pi\) | ||||
0.0370812 | + | 0.999312i | \(0.488194\pi\) | |||||||
\(44\) | 19635.4 | − | 55791.3i | 0.230506 | − | 0.654951i | ||||
\(45\) | − | 65071.5i | − | 0.714090i | ||||||
\(46\) | −125419. | + | 88819.0i | −1.28851 | + | 0.912499i | ||||
\(47\) | − | 64453.4i | − | 0.620801i | −0.950606 | − | 0.310400i | \(-0.899537\pi\) | ||
0.950606 | − | 0.310400i | \(-0.100463\pi\) | |||||||
\(48\) | 103757. | + | 83358.8i | 0.938200 | + | 0.753751i | ||||
\(49\) | 117262. | 0.996713 | ||||||||
\(50\) | 111008. | + | 156751.i | 0.888064 | + | 1.25401i | ||||
\(51\) | −167044. | −1.25927 | ||||||||
\(52\) | 93629.2 | + | 32952.2i | 0.665888 | + | 0.234355i | ||||
\(53\) | − | 197386.i | − | 1.32583i | −0.748694 | − | 0.662916i | \(-0.769319\pi\) | ||
0.748694 | − | 0.662916i | \(-0.230681\pi\) | |||||||
\(54\) | −60416.4 | − | 85312.1i | −0.383684 | − | 0.541788i | ||||
\(55\) | 183984.i | 1.10584i | ||||||||
\(56\) | 2761.17 | + | 9682.80i | 0.0157228 | + | 0.0551362i | ||||
\(57\) | 55113.0 | 0.297598 | ||||||||
\(58\) | 108298. | − | 76694.7i | 0.555057 | − | 0.393080i | ||||
\(59\) | 142210. | 0.692425 | 0.346212 | − | 0.938156i | \(-0.387468\pi\) | ||||
0.346212 | + | 0.938156i | \(0.387468\pi\) | |||||||
\(60\) | −390537. | − | 137447.i | −1.80804 | − | 0.636330i | ||||
\(61\) | 96476.4i | 0.425042i | 0.977157 | + | 0.212521i | \(0.0681673\pi\) | ||||
−0.977157 | + | 0.212521i | \(0.931833\pi\) | |||||||
\(62\) | −49295.6 | + | 34910.2i | −0.206839 | + | 0.146480i | ||||
\(63\) | 6427.78i | 0.0257063i | ||||||||
\(64\) | 222716. | − | 138264.i | 0.849595 | − | 0.527436i | ||||
\(65\) | −308763. | −1.12431 | ||||||||
\(66\) | −138840. | − | 196051.i | −0.482928 | − | 0.681927i | ||||
\(67\) | −75260.9 | −0.250233 | −0.125117 | − | 0.992142i | \(-0.539930\pi\) | ||||
−0.125117 | + | 0.992142i | \(0.539930\pi\) | |||||||
\(68\) | −109226. | + | 310350.i | −0.347375 | + | 0.987018i | ||||
\(69\) | 624222.i | 1.90017i | ||||||||
\(70\) | −18101.5 | − | 25560.5i | −0.0527740 | − | 0.0745205i | ||||
\(71\) | − | 556121.i | − | 1.55380i | −0.629625 | − | 0.776899i | \(-0.716792\pi\) | ||
0.629625 | − | 0.776899i | \(-0.283208\pi\) | |||||||
\(72\) | 160934. | − | 45892.3i | 0.431171 | − | 0.122954i | ||||
\(73\) | 285914. | 0.734965 | 0.367483 | − | 0.930030i | \(-0.380220\pi\) | ||||
0.367483 | + | 0.930030i | \(0.380220\pi\) | |||||||
\(74\) | 189073. | − | 133898.i | 0.466590 | − | 0.330430i | ||||
\(75\) | 780167. | 1.84928 | ||||||||
\(76\) | 36037.0 | − | 102394.i | 0.0820934 | − | 0.233257i | ||||
\(77\) | − | 18174.0i | − | 0.0398088i | ||||||
\(78\) | 329014. | − | 233002.i | 0.693315 | − | 0.490993i | ||||
\(79\) | 342014.i | 0.693686i | 0.937923 | + | 0.346843i | \(0.112746\pi\) | ||||
−0.937923 | + | 0.346843i | \(0.887254\pi\) | |||||||
\(80\) | −510725. | + | 635703.i | −0.997510 | + | 1.24161i | ||||
\(81\) | −662884. | −1.24733 | ||||||||
\(82\) | 240935. | + | 340217.i | 0.436977 | + | 0.617042i | ||||
\(83\) | −929558. | −1.62571 | −0.812853 | − | 0.582469i | \(-0.802087\pi\) | ||||
−0.812853 | + | 0.582469i | \(0.802087\pi\) | |||||||
\(84\) | 38577.4 | + | 13577.1i | 0.0650871 | + | 0.0229070i | ||||
\(85\) | − | 1.02345e6i | − | 1.66652i | ||||||
\(86\) | −27262.0 | − | 38495.9i | −0.0428610 | − | 0.0605227i | ||||
\(87\) | − | 539012.i | − | 0.818542i | ||||||
\(88\) | −455027. | + | 129757.i | −0.667712 | + | 0.190406i | ||||
\(89\) | 434757. | 0.616704 | 0.308352 | − | 0.951272i | \(-0.400223\pi\) | ||||
0.308352 | + | 0.951272i | \(0.400223\pi\) | |||||||
\(90\) | −424830. | + | 300856.i | −0.582757 | + | 0.412697i | ||||
\(91\) | 30499.7 | 0.0404736 | ||||||||
\(92\) | 1.15974e6 | + | 408163.i | 1.48935 | + | 0.524168i | ||||
\(93\) | 245350.i | 0.305026i | ||||||||
\(94\) | −420795. | + | 297999.i | −0.506625 | + | 0.358782i | ||||
\(95\) | 337668.i | 0.393839i | ||||||||
\(96\) | 64502.0 | − | 1.06280e6i | 0.0729054 | − | 1.20127i | ||||
\(97\) | 643314. | 0.704868 | 0.352434 | − | 0.935837i | \(-0.385354\pi\) | ||||
0.352434 | + | 0.935837i | \(0.385354\pi\) | |||||||
\(98\) | −542159. | − | 765566.i | −0.576035 | − | 0.813401i | ||||
\(99\) | −302063. | −0.311309 | ||||||||
\(100\) | 510131. | − | 1.44947e6i | 0.510131 | − | 1.44947i | ||||
\(101\) | 858368.i | 0.833123i | 0.909107 | + | 0.416562i | \(0.136765\pi\) | ||||
−0.909107 | + | 0.416562i | \(0.863235\pi\) | |||||||
\(102\) | 772324. | + | 1.09057e6i | 0.727778 | + | 1.02767i | ||||
\(103\) | 2.13382e6i | 1.95275i | 0.216089 | + | 0.976374i | \(0.430670\pi\) | ||||
−0.216089 | + | 0.976374i | \(0.569330\pi\) | |||||||
\(104\) | −217758. | − | 763628.i | −0.193586 | − | 0.678862i | ||||
\(105\) | −127218. | −0.109895 | ||||||||
\(106\) | −1.28867e6 | + | 912609.i | −1.08199 | + | 0.766244i | ||||
\(107\) | 1.81311e6 | 1.48004 | 0.740019 | − | 0.672585i | \(-0.234816\pi\) | ||||
0.740019 | + | 0.672585i | \(0.234816\pi\) | |||||||
\(108\) | −277640. | + | 788876.i | −0.220400 | + | 0.626236i | ||||
\(109\) | − | 1.43023e6i | − | 1.10440i | −0.833711 | − | 0.552201i | \(-0.813788\pi\) | ||
0.833711 | − | 0.552201i | \(-0.186212\pi\) | |||||||
\(110\) | 1.20117e6 | − | 850647.i | 0.902459 | − | 0.639104i | ||||
\(111\) | − | 941039.i | − | 0.688080i | ||||||
\(112\) | 50449.6 | − | 62795.0i | 0.0359090 | − | 0.0446962i | ||||
\(113\) | 628373. | 0.435494 | 0.217747 | − | 0.976005i | \(-0.430129\pi\) | ||||
0.217747 | + | 0.976005i | \(0.430129\pi\) | |||||||
\(114\) | −254814. | − | 359815.i | −0.171992 | − | 0.242865i | ||||
\(115\) | −3.82450e6 | −2.51467 | ||||||||
\(116\) | −1.00143e6 | − | 352447.i | −0.641573 | − | 0.225798i | ||||
\(117\) | − | 506923.i | − | 0.316508i | ||||||
\(118\) | −657502. | − | 928438.i | −0.400176 | − | 0.565076i | ||||
\(119\) | 101097.i | 0.0599924i | ||||||||
\(120\) | 908292. | + | 3.18517e6i | 0.525632 | + | 1.84327i | ||||
\(121\) | −917503. | −0.517907 | ||||||||
\(122\) | 629862. | − | 446056.i | 0.346869 | − | 0.245646i | ||||
\(123\) | 1.69330e6 | 0.909951 | ||||||||
\(124\) | 455834. | + | 160428.i | 0.239079 | + | 0.0841425i | ||||
\(125\) | 1.66925e6i | 0.854656i | ||||||||
\(126\) | 41964.8 | − | 29718.7i | 0.0209785 | − | 0.0148566i | ||||
\(127\) | − | 2.43195e6i | − | 1.18725i | −0.804741 | − | 0.593626i | \(-0.797696\pi\) | ||
0.804741 | − | 0.593626i | \(-0.202304\pi\) | |||||||
\(128\) | −1.93240e6 | − | 814779.i | −0.921442 | − | 0.388517i | ||||
\(129\) | −191598. | −0.0892529 | ||||||||
\(130\) | 1.42756e6 | + | 2.01581e6i | 0.649777 | + | 0.917530i | ||||
\(131\) | 2.66985e6 | 1.18761 | 0.593804 | − | 0.804610i | \(-0.297626\pi\) | ||||
0.593804 | + | 0.804610i | \(0.297626\pi\) | |||||||
\(132\) | −638031. | + | 1.81288e6i | −0.277409 | + | 0.788219i | ||||
\(133\) | − | 33354.9i | − | 0.0141777i | ||||||
\(134\) | 347967. | + | 491353.i | 0.144618 | + | 0.204211i | ||||
\(135\) | − | 2.60150e6i | − | 1.05736i | ||||||
\(136\) | 2.53118e6 | − | 721797.i | 1.00625 | − | 0.286945i | ||||
\(137\) | −4.00205e6 | −1.55640 | −0.778199 | − | 0.628018i | \(-0.783867\pi\) | ||||
−0.778199 | + | 0.628018i | \(0.783867\pi\) | |||||||
\(138\) | 4.07534e6 | − | 2.88608e6i | 1.55069 | − | 1.09817i | ||||
\(139\) | 1.89422e6 | 0.705319 | 0.352660 | − | 0.935752i | \(-0.385277\pi\) | ||||
0.352660 | + | 0.935752i | \(0.385277\pi\) | |||||||
\(140\) | −83184.4 | + | 236357.i | −0.0303150 | + | 0.0861359i | ||||
\(141\) | 2.09434e6i | 0.747120i | ||||||||
\(142\) | −3.63073e6 | + | 2.57121e6i | −1.26803 | + | 0.897993i | ||||
\(143\) | 1.43328e6i | 0.490144i | ||||||||
\(144\) | −1.04369e6 | − | 838500.i | −0.349529 | − | 0.280812i | ||||
\(145\) | 3.30243e6 | 1.08325 | ||||||||
\(146\) | −1.32192e6 | − | 1.86664e6i | −0.424762 | − | 0.599793i | ||||
\(147\) | −3.81031e6 | −1.19952 | ||||||||
\(148\) | −1.74835e6 | − | 615322.i | −0.539316 | − | 0.189809i | ||||
\(149\) | 3.06394e6i | 0.926235i | 0.886297 | + | 0.463118i | \(0.153269\pi\) | ||||
−0.886297 | + | 0.463118i | \(0.846731\pi\) | |||||||
\(150\) | −3.60708e6 | − | 5.09345e6i | −1.06876 | − | 1.50917i | ||||
\(151\) | 2.24437e6i | 0.651873i | 0.945392 | + | 0.325936i | \(0.105680\pi\) | ||||
−0.945392 | + | 0.325936i | \(0.894320\pi\) | |||||||
\(152\) | −835114. | + | 238143.i | −0.237802 | + | 0.0678122i | ||||
\(153\) | 1.68028e6 | 0.469146 | ||||||||
\(154\) | −118652. | + | 84027.2i | −0.0324873 | + | 0.0230069i | ||||
\(155\) | −1.50322e6 | −0.403670 | ||||||||
\(156\) | −3.04238e6 | − | 1.07075e6i | −0.801382 | − | 0.282042i | ||||
\(157\) | − | 4.89064e6i | − | 1.26377i | −0.775064 | − | 0.631883i | \(-0.782282\pi\) | ||
0.775064 | − | 0.631883i | \(-0.217718\pi\) | |||||||
\(158\) | 2.23290e6 | − | 1.58129e6i | 0.566105 | − | 0.400905i | ||||
\(159\) | 6.41384e6i | 1.59561i | ||||||||
\(160\) | 6.51162e6 | + | 395193.i | 1.58975 | + | 0.0964825i | ||||
\(161\) | 377785. | 0.0905248 | ||||||||
\(162\) | 3.06483e6 | + | 4.32775e6i | 0.720877 | + | 1.01793i | ||||
\(163\) | 1.82987e6 | 0.422529 | 0.211265 | − | 0.977429i | \(-0.432242\pi\) | ||||
0.211265 | + | 0.977429i | \(0.432242\pi\) | |||||||
\(164\) | 1.10721e6 | − | 3.14597e6i | 0.251013 | − | 0.713219i | ||||
\(165\) | − | 5.97837e6i | − | 1.33086i | ||||||
\(166\) | 4.29779e6 | + | 6.06877e6i | 0.939552 | + | 1.32671i | ||||
\(167\) | − | 3.94279e6i | − | 0.846554i | −0.906000 | − | 0.423277i | \(-0.860880\pi\) | ||
0.906000 | − | 0.423277i | \(-0.139120\pi\) | |||||||
\(168\) | −89721.3 | − | 314632.i | −0.0189220 | − | 0.0663552i | ||||
\(169\) | 2.42147e6 | 0.501670 | ||||||||
\(170\) | −6.68176e6 | + | 4.73189e6i | −1.36002 | + | 0.963137i | ||||
\(171\) | −554378. | −0.110871 | ||||||||
\(172\) | −125281. | + | 355969.i | −0.0246207 | + | 0.0699563i | ||||
\(173\) | 205167.i | 0.0396249i | 0.999804 | + | 0.0198125i | \(0.00630692\pi\) | ||||
−0.999804 | + | 0.0198125i | \(0.993693\pi\) | |||||||
\(174\) | −3.51903e6 | + | 2.49211e6i | −0.667998 | + | 0.473064i | ||||
\(175\) | − | 472164.i | − | 0.0881007i | ||||||
\(176\) | 2.95094e6 | + | 2.37079e6i | 0.541281 | + | 0.434866i | ||||
\(177\) | −4.62094e6 | −0.833318 | ||||||||
\(178\) | −2.01009e6 | − | 2.83838e6i | −0.356415 | − | 0.503282i | ||||
\(179\) | −3.36007e6 | −0.585853 | −0.292927 | − | 0.956135i | \(-0.594629\pi\) | ||||
−0.292927 | + | 0.956135i | \(0.594629\pi\) | |||||||
\(180\) | 3.92838e6 | + | 1.38257e6i | 0.673591 | + | 0.237066i | ||||
\(181\) | 2.39145e6i | 0.403298i | 0.979458 | + | 0.201649i | \(0.0646300\pi\) | ||||
−0.979458 | + | 0.201649i | \(0.935370\pi\) | |||||||
\(182\) | −141015. | − | 199123.i | −0.0233911 | − | 0.0330298i | ||||
\(183\) | − | 3.13489e6i | − | 0.511528i | ||||||
\(184\) | −2.69726e6 | − | 9.45868e6i | −0.432982 | − | 1.51837i | ||||
\(185\) | 5.76558e6 | 0.910601 | ||||||||
\(186\) | 1.60181e6 | − | 1.13437e6i | 0.248927 | − | 0.176285i | ||||
\(187\) | −4.75086e6 | −0.726520 | ||||||||
\(188\) | 3.89107e6 | + | 1.36944e6i | 0.585592 | + | 0.206096i | ||||
\(189\) | 256977.i | 0.0380635i | ||||||||
\(190\) | 2.20452e6 | − | 1.56120e6i | 0.321406 | − | 0.227613i | ||||
\(191\) | − | 2.02441e6i | − | 0.290535i | −0.989392 | − | 0.145268i | \(-0.953596\pi\) | ||
0.989392 | − | 0.145268i | \(-0.0464043\pi\) | |||||||
\(192\) | −7.23692e6 | + | 4.49274e6i | −1.02247 | + | 0.634757i | ||||
\(193\) | −7.92510e6 | −1.10238 | −0.551192 | − | 0.834378i | \(-0.685827\pi\) | ||||
−0.551192 | + | 0.834378i | \(0.685827\pi\) | |||||||
\(194\) | −2.97434e6 | − | 4.19998e6i | −0.407367 | − | 0.575231i | ||||
\(195\) | 1.00329e7 | 1.35308 | ||||||||
\(196\) | −2.49147e6 | + | 7.07915e6i | −0.330892 | + | 0.940184i | ||||
\(197\) | − | 4.12787e6i | − | 0.539917i | −0.962872 | − | 0.269959i | \(-0.912990\pi\) | ||
0.962872 | − | 0.269959i | \(-0.0870100\pi\) | |||||||
\(198\) | 1.39658e6 | + | 1.97207e6i | 0.179916 | + | 0.254054i | ||||
\(199\) | 1.18196e7i | 1.49983i | 0.661532 | + | 0.749917i | \(0.269907\pi\) | ||||
−0.661532 | + | 0.749917i | \(0.730093\pi\) | |||||||
\(200\) | −1.18217e7 | + | 3.37110e6i | −1.47771 | + | 0.421387i | ||||
\(201\) | 2.44552e6 | 0.301150 | ||||||||
\(202\) | 5.60400e6 | − | 3.96864e6i | 0.679898 | − | 0.481491i | ||||
\(203\) | −326215. | −0.0389957 | ||||||||
\(204\) | 3.54918e6 | − | 1.00845e7i | 0.418058 | − | 1.18785i | ||||
\(205\) | 1.03745e7i | 1.20422i | ||||||||
\(206\) | 1.39310e7 | − | 9.86566e6i | 1.59360 | − | 1.12856i | ||||
\(207\) | − | 6.27900e6i | − | 0.707912i | ||||||
\(208\) | −3.97867e6 | + | 4.95228e6i | −0.442128 | + | 0.550320i | ||||
\(209\) | 1.56746e6 | 0.171695 | ||||||||
\(210\) | 588187. | + | 830561.i | 0.0635123 | + | 0.0896837i | ||||
\(211\) | 1.19422e7 | 1.27127 | 0.635635 | − | 0.771989i | \(-0.280738\pi\) | ||||
0.635635 | + | 0.771989i | \(0.280738\pi\) | |||||||
\(212\) | 1.19162e7 | + | 4.19385e6i | 1.25064 | + | 0.440155i | ||||
\(213\) | 1.80706e7i | 1.86996i | ||||||||
\(214\) | −8.38288e6 | − | 1.18372e7i | −0.855365 | − | 1.20783i | ||||
\(215\) | − | 1.17389e6i | − | 0.118117i | ||||||
\(216\) | 6.43397e6 | − | 1.83473e6i | 0.638437 | − | 0.182058i | ||||
\(217\) | 148488. | 0.0145316 | ||||||||
\(218\) | −9.33752e6 | + | 6.61265e6i | −0.901284 | + | 0.638272i | ||||
\(219\) | −9.29046e6 | −0.884514 | ||||||||
\(220\) | −1.11072e7 | − | 3.90911e6i | −1.04312 | − | 0.367121i | ||||
\(221\) | − | 7.97292e6i | − | 0.738653i | ||||||
\(222\) | −6.14373e6 | + | 4.35087e6i | −0.561530 | + | 0.397665i | ||||
\(223\) | − | 2.10926e7i | − | 1.90202i | −0.309153 | − | 0.951012i | \(-0.600045\pi\) | ||
0.309153 | − | 0.951012i | \(-0.399955\pi\) | |||||||
\(224\) | −643220. | − | 39037.2i | −0.0572289 | − | 0.00347324i | ||||
\(225\) | −7.84764e6 | −0.688956 | ||||||||
\(226\) | −2.90526e6 | − | 4.10243e6i | −0.251687 | − | 0.355399i | ||||
\(227\) | 2.73658e6 | 0.233954 | 0.116977 | − | 0.993135i | \(-0.462680\pi\) | ||||
0.116977 | + | 0.993135i | \(0.462680\pi\) | |||||||
\(228\) | −1.17098e6 | + | 3.32719e6i | −0.0987976 | + | 0.280720i | ||||
\(229\) | − | 7.23777e6i | − | 0.602696i | −0.953514 | − | 0.301348i | \(-0.902563\pi\) | ||
0.953514 | − | 0.301348i | \(-0.0974366\pi\) | |||||||
\(230\) | 1.76825e7 | + | 2.49689e7i | 1.45331 | + | 2.05218i | ||||
\(231\) | 590545.i | 0.0479090i | ||||||||
\(232\) | 2.32907e6 | + | 8.16752e6i | 0.186517 | + | 0.654073i | ||||
\(233\) | −1.63958e7 | −1.29618 | −0.648088 | − | 0.761565i | \(-0.724431\pi\) | ||||
−0.648088 | + | 0.761565i | \(0.724431\pi\) | |||||||
\(234\) | −3.30953e6 | + | 2.34374e6i | −0.258297 | + | 0.182921i | ||||
\(235\) | −1.28317e7 | −0.988734 | ||||||||
\(236\) | −3.02152e6 | + | 8.58522e6i | −0.229874 | + | 0.653154i | ||||
\(237\) | − | 1.11134e7i | − | 0.834835i | ||||||
\(238\) | 660026. | − | 467418.i | 0.0489588 | − | 0.0346717i | ||||
\(239\) | 1.73985e7i | 1.27443i | 0.770685 | + | 0.637217i | \(0.219914\pi\) | ||||
−0.770685 | + | 0.637217i | \(0.780086\pi\) | |||||||
\(240\) | 1.65954e7 | − | 2.06565e7i | 1.20048 | − | 1.49425i | ||||
\(241\) | 1.34047e7 | 0.957645 | 0.478822 | − | 0.877912i | \(-0.341064\pi\) | ||||
0.478822 | + | 0.877912i | \(0.341064\pi\) | |||||||
\(242\) | 4.24205e6 | + | 5.99007e6i | 0.299316 | + | 0.422655i | ||||
\(243\) | 1.20136e7 | 0.837250 | ||||||||
\(244\) | −5.82430e6 | − | 2.04983e6i | −0.400935 | − | 0.141107i | ||||
\(245\) | − | 2.33451e7i | − | 1.58744i | ||||||
\(246\) | −7.82892e6 | − | 1.10550e7i | −0.525892 | − | 0.742596i | ||||
\(247\) | 2.63051e6i | 0.174562i | ||||||||
\(248\) | −1.06016e6 | − | 3.71772e6i | −0.0695048 | − | 0.243737i | ||||
\(249\) | 3.02050e7 | 1.95650 | ||||||||
\(250\) | 1.08980e7 | − | 7.71774e6i | 0.697471 | − | 0.493935i | ||||
\(251\) | −1.70047e7 | −1.07534 | −0.537672 | − | 0.843154i | \(-0.680696\pi\) | ||||
−0.537672 | + | 0.843154i | \(0.680696\pi\) | |||||||
\(252\) | −388047. | − | 136571.i | −0.0242484 | − | 0.00853407i | ||||
\(253\) | 1.77534e7i | 1.09627i | ||||||||
\(254\) | −1.58774e7 | + | 1.12440e7i | −0.968896 | + | 0.686154i | ||||
\(255\) | 3.32559e7i | 2.00562i | ||||||||
\(256\) | 3.61500e6 | + | 1.63831e7i | 0.215471 | + | 0.976510i | ||||
\(257\) | 1.94325e7 | 1.14480 | 0.572400 | − | 0.819974i | \(-0.306012\pi\) | ||||
0.572400 | + | 0.819974i | \(0.306012\pi\) | |||||||
\(258\) | 885849. | + | 1.25088e6i | 0.0515823 | + | 0.0728378i | ||||
\(259\) | −569526. | −0.0327804 | ||||||||
\(260\) | 6.56028e6 | − | 1.86401e7i | 0.373252 | − | 1.06054i | ||||
\(261\) | 5.42188e6i | 0.304950i | ||||||||
\(262\) | −1.23440e7 | − | 1.74305e7i | −0.686359 | − | 0.969186i | ||||
\(263\) | − | 1.33303e7i | − | 0.732778i | −0.930462 | − | 0.366389i | \(-0.880594\pi\) | ||
0.930462 | − | 0.366389i | \(-0.119406\pi\) | |||||||
\(264\) | 1.47856e7 | − | 4.21630e6i | 0.803576 | − | 0.229150i | ||||
\(265\) | −3.92965e7 | −2.11162 | ||||||||
\(266\) | −217763. | + | 154216.i | −0.0115702 | + | 0.00819377i | ||||
\(267\) | −1.41270e7 | −0.742190 | ||||||||
\(268\) | 1.59906e6 | − | 4.54352e6i | 0.0830733 | − | 0.236041i | ||||
\(269\) | − | 7.13509e6i | − | 0.366558i | −0.983061 | − | 0.183279i | \(-0.941329\pi\) | ||
0.983061 | − | 0.183279i | \(-0.0586712\pi\) | |||||||
\(270\) | −1.69843e7 | + | 1.20280e7i | −0.862892 | + | 0.611084i | ||||
\(271\) | − | 6.93561e6i | − | 0.348479i | −0.984703 | − | 0.174240i | \(-0.944253\pi\) | ||
0.984703 | − | 0.174240i | \(-0.0557467\pi\) | |||||||
\(272\) | −1.64152e7 | − | 1.31880e7i | −0.815717 | − | 0.655348i | ||||
\(273\) | −991056. | −0.0487091 | ||||||||
\(274\) | 1.85034e7 | + | 2.61280e7i | 0.899496 | + | 1.27015i | ||||
\(275\) | 2.21886e7 | 1.06692 | ||||||||
\(276\) | −3.76844e7 | − | 1.32628e7i | −1.79240 | − | 0.630824i | ||||
\(277\) | 1.79332e7i | 0.843757i | 0.906652 | + | 0.421879i | \(0.138629\pi\) | ||||
−0.906652 | + | 0.421879i | \(0.861371\pi\) | |||||||
\(278\) | −8.75787e6 | − | 1.23667e7i | −0.407628 | − | 0.575599i | ||||
\(279\) | − | 2.46795e6i | − | 0.113638i | ||||||
\(280\) | 1.92770e6 | − | 549707.i | 0.0878141 | − | 0.0250413i | ||||
\(281\) | −4.29329e6 | −0.193496 | −0.0967479 | − | 0.995309i | \(-0.530844\pi\) | ||||
−0.0967479 | + | 0.995309i | \(0.530844\pi\) | |||||||
\(282\) | 1.36733e7 | − | 9.68314e6i | 0.609712 | − | 0.431786i | ||||
\(283\) | 3.39377e7 | 1.49735 | 0.748674 | − | 0.662938i | \(-0.230691\pi\) | ||||
0.748674 | + | 0.662938i | \(0.230691\pi\) | |||||||
\(284\) | 3.35732e7 | + | 1.18159e7i | 1.46567 | + | 0.515835i | ||||
\(285\) | − | 1.09721e7i | − | 0.473977i | ||||||
\(286\) | 9.35743e6 | − | 6.62675e6i | 0.399998 | − | 0.283271i | ||||
\(287\) | − | 1.02480e6i | − | 0.0433505i | ||||||
\(288\) | −648821. | + | 1.06907e7i | −0.0271611 | + | 0.447535i | ||||
\(289\) | 2.29005e6 | 0.0948751 | ||||||||
\(290\) | −1.52687e7 | − | 2.15605e7i | −0.626050 | − | 0.884025i | ||||
\(291\) | −2.09038e7 | −0.848293 | ||||||||
\(292\) | −6.07480e6 | + | 1.72607e7i | −0.243996 | + | 0.693282i | ||||
\(293\) | 3.15178e7i | 1.25301i | 0.779419 | + | 0.626504i | \(0.215515\pi\) | ||||
−0.779419 | + | 0.626504i | \(0.784485\pi\) | |||||||
\(294\) | 1.76169e7 | + | 2.48762e7i | 0.693245 | + | 0.978910i | ||||
\(295\) | − | 2.83117e7i | − | 1.10281i | ||||||
\(296\) | 4.06623e6 | + | 1.42593e7i | 0.156789 | + | 0.549824i | ||||
\(297\) | −1.20762e7 | −0.460957 | ||||||||
\(298\) | 2.00034e7 | − | 1.41660e7i | 0.755885 | − | 0.535303i | ||||
\(299\) | −2.97938e7 | −1.11458 | ||||||||
\(300\) | −1.65762e7 | + | 4.70989e7i | −0.613932 | + | 1.74440i | ||||
\(301\) | 115957.i | 0.00425204i | ||||||||
\(302\) | 1.46527e7 | − | 1.03768e7i | 0.531983 | − | 0.376740i | ||||
\(303\) | − | 2.78917e7i | − | 1.00265i | ||||||
\(304\) | 5.41589e6 | + | 4.35113e6i | 0.192774 | + | 0.154875i | ||||
\(305\) | 1.92069e7 | 0.676953 | ||||||||
\(306\) | −7.76875e6 | − | 1.09700e7i | −0.271136 | − | 0.382862i | ||||
\(307\) | 3.45268e7 | 1.19328 | 0.596638 | − | 0.802510i | \(-0.296503\pi\) | ||||
0.596638 | + | 0.802510i | \(0.296503\pi\) | |||||||
\(308\) | 1.09717e6 | + | 386143.i | 0.0375511 | + | 0.0132159i | ||||
\(309\) | − | 6.93361e7i | − | 2.35009i | ||||||
\(310\) | 6.95008e6 | + | 9.81399e6i | 0.233295 | + | 0.329428i | ||||
\(311\) | 1.55896e7i | 0.518268i | 0.965841 | + | 0.259134i | \(0.0834371\pi\) | ||||
−0.965841 | + | 0.259134i | \(0.916563\pi\) | |||||||
\(312\) | 7.07581e6 | + | 2.48132e7i | 0.232977 | + | 0.816996i | ||||
\(313\) | 2.13473e6 | 0.0696160 | 0.0348080 | − | 0.999394i | \(-0.488918\pi\) | ||||
0.0348080 | + | 0.999394i | \(0.488918\pi\) | |||||||
\(314\) | −3.19293e7 | + | 2.26117e7i | −1.03134 | + | 0.730374i | ||||
\(315\) | 1.27967e6 | 0.0409418 | ||||||||
\(316\) | −2.06475e7 | − | 7.26676e6i | −0.654343 | − | 0.230292i | ||||
\(317\) | 4.15440e7i | 1.30416i | 0.758151 | + | 0.652079i | \(0.226103\pi\) | ||||
−0.758151 | + | 0.652079i | \(0.773897\pi\) | |||||||
\(318\) | 4.18738e7 | − | 2.96542e7i | 1.30215 | − | 0.922158i | ||||
\(319\) | − | 1.53299e7i | − | 0.472246i | ||||||
\(320\) | −2.75262e7 | − | 4.43393e7i | −0.840034 | − | 1.35313i | ||||
\(321\) | −5.89151e7 | −1.78119 | ||||||||
\(322\) | −1.74668e6 | − | 2.46643e6i | −0.0523174 | − | 0.0738757i | ||||
\(323\) | −8.71930e6 | −0.258746 | ||||||||
\(324\) | 1.40843e7 | − | 4.00185e7i | 0.414094 | − | 1.17659i | ||||
\(325\) | 3.72369e7i | 1.08474i | ||||||||
\(326\) | −8.46034e6 | − | 1.19466e7i | −0.244194 | − | 0.344819i | ||||
\(327\) | 4.64739e7i | 1.32912i | ||||||||
\(328\) | −2.56581e7 | + | 7.31674e6i | −0.727115 | + | 0.207346i | ||||
\(329\) | 1.26752e6 | 0.0355931 | ||||||||
\(330\) | −3.90308e7 | + | 2.76409e7i | −1.08609 | + | 0.769147i | ||||
\(331\) | 1.78997e7 | 0.493585 | 0.246793 | − | 0.969068i | \(-0.420623\pi\) | ||||
0.246793 | + | 0.969068i | \(0.420623\pi\) | |||||||
\(332\) | 1.97503e7 | − | 5.61176e7i | 0.539708 | − | 1.53350i | ||||
\(333\) | 9.46584e6i | 0.256346i | ||||||||
\(334\) | −2.57412e7 | + | 1.82294e7i | −0.690858 | + | 0.489253i | ||||
\(335\) | 1.49833e7i | 0.398540i | ||||||||
\(336\) | −1.63930e6 | + | 2.04045e6i | −0.0432157 | + | 0.0537909i | ||||
\(337\) | 1.86244e7 | 0.486624 | 0.243312 | − | 0.969948i | \(-0.421766\pi\) | ||||
0.243312 | + | 0.969948i | \(0.421766\pi\) | |||||||
\(338\) | −1.11956e7 | − | 1.58089e7i | −0.289933 | − | 0.409405i | ||||
\(339\) | −2.04183e7 | −0.524107 | ||||||||
\(340\) | 6.17859e7 | + | 2.17452e7i | 1.57200 | + | 0.553256i | ||||
\(341\) | 6.97794e6i | 0.175980i | ||||||||
\(342\) | 2.56315e6 | + | 3.61935e6i | 0.0640761 | + | 0.0904798i | ||||
\(343\) | 4.61968e6i | 0.114480i | ||||||||
\(344\) | 2.90324e6 | − | 827896.i | 0.0713194 | − | 0.0203376i | ||||
\(345\) | 1.24273e8 | 3.02635 | ||||||||
\(346\) | 1.33946e6 | − | 948583.i | 0.0323372 | − | 0.0229006i | ||||
\(347\) | 3.96438e7 | 0.948827 | 0.474414 | − | 0.880302i | \(-0.342660\pi\) | ||||
0.474414 | + | 0.880302i | \(0.342660\pi\) | |||||||
\(348\) | 3.25403e7 | + | 1.14524e7i | 0.772118 | + | 0.271742i | ||||
\(349\) | − | 6.84414e7i | − | 1.61006i | −0.593232 | − | 0.805031i | \(-0.702148\pi\) | ||
0.593232 | − | 0.805031i | \(-0.297852\pi\) | |||||||
\(350\) | −3.08260e6 | + | 2.18304e6i | −0.0718975 | + | 0.0509164i | ||||
\(351\) | − | 2.02663e7i | − | 0.468655i | ||||||
\(352\) | 1.83449e6 | − | 3.02270e7i | 0.0420617 | − | 0.693054i | ||||
\(353\) | −3.01604e7 | −0.685666 | −0.342833 | − | 0.939396i | \(-0.611387\pi\) | ||||
−0.342833 | + | 0.939396i | \(0.611387\pi\) | |||||||
\(354\) | 2.13648e7 | + | 3.01686e7i | 0.481603 | + | 0.680057i | ||||
\(355\) | −1.10715e8 | −2.47470 | ||||||||
\(356\) | −9.23727e6 | + | 2.62464e7i | −0.204736 | + | 0.581728i | ||||
\(357\) | − | 3.28503e6i | − | 0.0721995i | ||||||
\(358\) | 1.55352e7 | + | 2.19368e7i | 0.338585 | + | 0.478105i | ||||
\(359\) | 6.13950e7i | 1.32694i | 0.748205 | + | 0.663468i | \(0.230916\pi\) | ||||
−0.748205 | + | 0.663468i | \(0.769084\pi\) | |||||||
\(360\) | −9.13644e6 | − | 3.20394e7i | −0.195826 | − | 0.686715i | ||||
\(361\) | −4.41691e7 | −0.938852 | ||||||||
\(362\) | 1.56130e7 | − | 1.10568e7i | 0.329125 | − | 0.233080i | ||||
\(363\) | 2.98133e7 | 0.623289 | ||||||||
\(364\) | −648027. | + | 1.84128e6i | −0.0134366 | + | 0.0381782i | ||||
\(365\) | − | 5.69210e7i | − | 1.17056i | ||||||
\(366\) | −2.04667e7 | + | 1.44941e7i | −0.417449 | + | 0.295630i | ||||
\(367\) | 4.17679e7i | 0.844976i | 0.906368 | + | 0.422488i | \(0.138843\pi\) | ||||
−0.906368 | + | 0.422488i | \(0.861157\pi\) | |||||||
\(368\) | −4.92818e7 | + | 6.13415e7i | −0.988880 | + | 1.23087i | ||||
\(369\) | −1.70328e7 | −0.339005 | ||||||||
\(370\) | −2.66570e7 | − | 3.76416e7i | −0.526268 | − | 0.743126i | ||||
\(371\) | 3.88172e6 | 0.0760155 | ||||||||
\(372\) | −1.48118e7 | − | 5.21293e6i | −0.287726 | − | 0.101264i | ||||
\(373\) | − | 5.61502e7i | − | 1.08199i | −0.841025 | − | 0.540997i | \(-0.818047\pi\) | ||
0.841025 | − | 0.540997i | \(-0.181953\pi\) | |||||||
\(374\) | 2.19655e7 | + | 3.10168e7i | 0.419881 | + | 0.592901i | ||||
\(375\) | − | 5.42405e7i | − | 1.02856i | ||||||
\(376\) | −9.04965e6 | − | 3.17350e7i | −0.170243 | − | 0.597001i | ||||
\(377\) | 2.57268e7 | 0.480133 | ||||||||
\(378\) | 1.67772e6 | − | 1.18813e6i | 0.0310630 | − | 0.0219982i | ||||
\(379\) | −1.96484e7 | −0.360919 | −0.180460 | − | 0.983582i | \(-0.557758\pi\) | ||||
−0.180460 | + | 0.983582i | \(0.557758\pi\) | |||||||
\(380\) | −2.03851e7 | − | 7.17441e6i | −0.371503 | − | 0.130748i | ||||
\(381\) | 7.90234e7i | 1.42883i | ||||||||
\(382\) | −1.32167e7 | + | 9.35982e6i | −0.237101 | + | 0.167910i | ||||
\(383\) | − | 3.86630e7i | − | 0.688176i | −0.938937 | − | 0.344088i | \(-0.888188\pi\) | ||
0.938937 | − | 0.344088i | \(-0.111812\pi\) | |||||||
\(384\) | 6.27913e7 | + | 2.64754e7i | 1.10893 | + | 0.467572i | ||||
\(385\) | −3.61817e6 | −0.0634025 | ||||||||
\(386\) | 3.66415e7 | + | 5.17403e7i | 0.637106 | + | 0.899637i | ||||
\(387\) | 1.92727e6 | 0.0332514 | ||||||||
\(388\) | −1.36685e7 | + | 3.88370e7i | −0.234004 | + | 0.664891i | ||||
\(389\) | − | 2.94915e6i | − | 0.0501012i | −0.999686 | − | 0.0250506i | \(-0.992025\pi\) | ||
0.999686 | − | 0.0250506i | \(-0.00797470\pi\) | |||||||
\(390\) | −4.63870e7 | − | 6.55016e7i | −0.781992 | − | 1.10423i | ||||
\(391\) | − | 9.87566e7i | − | 1.65210i | ||||||
\(392\) | 5.77366e7 | − | 1.64643e7i | 0.958503 | − | 0.273329i | ||||
\(393\) | −8.67538e7 | −1.42926 | ||||||||
\(394\) | −2.69495e7 | + | 1.90851e7i | −0.440617 | + | 0.312037i | ||||
\(395\) | 6.80897e7 | 1.10482 | ||||||||
\(396\) | 6.41791e6 | − | 1.82356e7i | 0.103349 | − | 0.293653i | ||||
\(397\) | 6.88167e7i | 1.09982i | 0.835223 | + | 0.549911i | \(0.185338\pi\) | ||||
−0.835223 | + | 0.549911i | \(0.814662\pi\) | |||||||
\(398\) | 7.71662e7 | − | 5.46476e7i | 1.22399 | − | 0.866806i | ||||
\(399\) | 1.08383e6i | 0.0170625i | ||||||||
\(400\) | 7.66660e7 | + | 6.15935e7i | 1.19791 | + | 0.962399i | ||||
\(401\) | 3.42281e7 | 0.530823 | 0.265412 | − | 0.964135i | \(-0.414492\pi\) | ||||
0.265412 | + | 0.964135i | \(0.414492\pi\) | |||||||
\(402\) | −1.13068e7 | − | 1.59660e7i | −0.174045 | − | 0.245764i | ||||
\(403\) | −1.17104e7 | −0.178919 | ||||||||
\(404\) | −5.18199e7 | − | 1.82377e7i | −0.785873 | − | 0.276583i | ||||
\(405\) | 1.31970e8i | 1.98660i | ||||||||
\(406\) | 1.50825e6 | + | 2.12975e6i | 0.0225369 | + | 0.0318237i | ||||
\(407\) | − | 2.67639e7i | − | 0.396978i | ||||||
\(408\) | −8.22478e7 | + | 2.34540e7i | −1.21100 | + | 0.345332i | ||||
\(409\) | 7.43891e7 | 1.08728 | 0.543638 | − | 0.839320i | \(-0.317047\pi\) | ||||
0.543638 | + | 0.839320i | \(0.317047\pi\) | |||||||
\(410\) | 6.77319e7 | − | 4.79665e7i | 0.982747 | − | 0.695963i | ||||
\(411\) | 1.30042e8 | 1.87309 | ||||||||
\(412\) | −1.28819e8 | − | 4.53372e7i | −1.84200 | − | 0.648280i | ||||
\(413\) | 2.79664e6i | 0.0396996i | ||||||||
\(414\) | −4.09935e7 | + | 2.90308e7i | −0.577715 | + | 0.409127i | ||||
\(415\) | 1.85061e8i | 2.58922i | ||||||||
\(416\) | 5.07271e7 | + | 3.07865e6i | 0.704628 | + | 0.0427641i | ||||
\(417\) | −6.15505e7 | −0.848836 | ||||||||
\(418\) | −7.24710e6 | − | 1.02334e7i | −0.0992283 | − | 0.140117i | ||||
\(419\) | −3.78200e7 | −0.514138 | −0.257069 | − | 0.966393i | \(-0.582757\pi\) | ||||
−0.257069 | + | 0.966393i | \(0.582757\pi\) | |||||||
\(420\) | 2.70299e6 | − | 7.68016e6i | 0.0364834 | − | 0.103663i | ||||
\(421\) | − | 6.21731e7i | − | 0.833213i | −0.909087 | − | 0.416607i | \(-0.863219\pi\) | ||
0.909087 | − | 0.416607i | \(-0.136781\pi\) | |||||||
\(422\) | −5.52146e7 | − | 7.79668e7i | −0.734711 | − | 1.03746i | ||||
\(423\) | − | 2.10668e7i | − | 0.278341i | ||||||
\(424\) | −2.77142e7 | − | 9.71873e7i | −0.363584 | − | 1.27501i | ||||
\(425\) | −1.23428e8 | −1.60786 | ||||||||
\(426\) | 1.17977e8 | − | 8.35488e7i | 1.52604 | − | 1.08072i | ||||
\(427\) | −1.89727e6 | −0.0243694 | ||||||||
\(428\) | −3.85231e7 | + | 1.09458e8i | −0.491349 | + | 1.39610i | ||||
\(429\) | − | 4.65730e7i | − | 0.589878i | ||||||
\(430\) | −7.66393e6 | + | 5.42745e6i | −0.0963931 | + | 0.0682637i | ||||
\(431\) | − | 1.00561e8i | − | 1.25603i | −0.778202 | − | 0.628014i | \(-0.783868\pi\) | ||
0.778202 | − | 0.628014i | \(-0.216132\pi\) | |||||||
\(432\) | −4.17257e7 | − | 3.35224e7i | −0.517550 | − | 0.415800i | ||||
\(433\) | 1.07677e8 | 1.32636 | 0.663179 | − | 0.748461i | \(-0.269207\pi\) | ||||
0.663179 | + | 0.748461i | \(0.269207\pi\) | |||||||
\(434\) | −686531. | − | 969429.i | −0.00839829 | − | 0.0118590i | ||||
\(435\) | −1.07309e8 | −1.30367 | ||||||||
\(436\) | 8.63436e7 | + | 3.03881e7i | 1.04177 | + | 0.366644i | ||||
\(437\) | 3.25829e7i | 0.390432i | ||||||||
\(438\) | 4.29542e7 | + | 6.06543e7i | 0.511191 | + | 0.721837i | ||||
\(439\) | 6.85796e7i | 0.810590i | 0.914186 | + | 0.405295i | \(0.132831\pi\) | ||||
−0.914186 | + | 0.405295i | \(0.867169\pi\) | |||||||
\(440\) | 2.58325e7 | + | 9.05888e7i | 0.303256 | + | 1.06345i | ||||
\(441\) | 3.83276e7 | 0.446885 | ||||||||
\(442\) | −5.20525e7 | + | 3.68626e7i | −0.602803 | + | 0.426893i | ||||
\(443\) | −8.84819e7 | −1.01776 | −0.508878 | − | 0.860839i | \(-0.669939\pi\) | ||||
−0.508878 | + | 0.860839i | \(0.669939\pi\) | |||||||
\(444\) | 5.68108e7 | + | 1.99942e7i | 0.649055 | + | 0.228431i | ||||
\(445\) | − | 8.65534e7i | − | 0.982210i | ||||||
\(446\) | −1.37707e8 | + | 9.75213e7i | −1.55221 | + | 1.09925i | ||||
\(447\) | − | 9.95593e7i | − | 1.11470i | ||||||
\(448\) | 2.71905e6 | + | 4.37985e6i | 0.0302401 | + | 0.0487108i | ||||
\(449\) | 4.28752e7 | 0.473661 | 0.236830 | − | 0.971551i | \(-0.423891\pi\) | ||||
0.236830 | + | 0.971551i | \(0.423891\pi\) | |||||||
\(450\) | 3.62834e7 | + | 5.12346e7i | 0.398171 | + | 0.562245i | ||||
\(451\) | 4.81588e7 | 0.524983 | ||||||||
\(452\) | −1.33510e7 | + | 3.79350e7i | −0.144577 | + | 0.410795i | ||||
\(453\) | − | 7.29282e7i | − | 0.784515i | ||||||
\(454\) | −1.26525e7 | − | 1.78662e7i | −0.135210 | − | 0.190926i | ||||
\(455\) | − | 6.07203e6i | − | 0.0644614i | ||||||
\(456\) | 2.71361e7 | − | 7.73821e6i | 0.286189 | − | 0.0816104i | ||||
\(457\) | −7.01681e7 | −0.735176 | −0.367588 | − | 0.929989i | \(-0.619816\pi\) | ||||
−0.367588 | + | 0.929989i | \(0.619816\pi\) | |||||||
\(458\) | −4.72530e7 | + | 3.34637e7i | −0.491850 | + | 0.348319i | ||||
\(459\) | 6.71761e7 | 0.694668 | ||||||||
\(460\) | 8.12590e7 | − | 2.30886e8i | 0.834830 | − | 2.37205i | ||||
\(461\) | 5.37805e7i | 0.548937i | 0.961596 | + | 0.274468i | \(0.0885018\pi\) | ||||
−0.961596 | + | 0.274468i | \(0.911498\pi\) | |||||||
\(462\) | 3.85547e6 | − | 2.73037e6i | 0.0390977 | − | 0.0276883i | ||||
\(463\) | 4.36059e7i | 0.439342i | 0.975574 | + | 0.219671i | \(0.0704984\pi\) | ||||
−0.975574 | + | 0.219671i | \(0.929502\pi\) | |||||||
\(464\) | 4.25546e7 | − | 5.29680e7i | 0.425983 | − | 0.530225i | ||||
\(465\) | 4.88453e7 | 0.485808 | ||||||||
\(466\) | 7.58055e7 | + | 1.07043e8i | 0.749105 | + | 1.05779i | ||||
\(467\) | −3.09469e7 | −0.303855 | −0.151928 | − | 0.988392i | \(-0.548548\pi\) | ||||
−0.151928 | + | 0.988392i | \(0.548548\pi\) | |||||||
\(468\) | 3.06030e7 | + | 1.07706e7i | 0.298557 | + | 0.105075i | ||||
\(469\) | − | 1.48005e6i | − | 0.0143469i | ||||||
\(470\) | 5.93269e7 | + | 8.37737e7i | 0.571423 | + | 0.806889i | ||||
\(471\) | 1.58916e8i | 1.52091i | ||||||||
\(472\) | 7.00200e7 | − | 1.99671e7i | 0.665880 | − | 0.189884i | ||||
\(473\) | −5.44920e6 | −0.0514932 | ||||||||
\(474\) | −7.25555e7 | + | 5.13824e7i | −0.681295 | + | 0.482480i | ||||
\(475\) | 4.07228e7 | 0.379977 | ||||||||
\(476\) | −6.10323e6 | − | 2.14800e6i | −0.0565899 | − | 0.0199165i | ||||
\(477\) | − | 6.45163e7i | − | 0.594449i | ||||||
\(478\) | 1.13589e8 | − | 8.04414e7i | 1.04004 | − | 0.736539i | ||||
\(479\) | − | 9.72219e7i | − | 0.884622i | −0.896862 | − | 0.442311i | \(-0.854159\pi\) | ||
0.896862 | − | 0.442311i | \(-0.145841\pi\) | |||||||
\(480\) | −2.11588e8 | − | 1.28413e7i | −1.91323 | − | 0.116115i | ||||
\(481\) | 4.49153e7 | 0.403607 | ||||||||
\(482\) | −6.19761e7 | − | 8.75145e7i | −0.553456 | − | 0.781518i | ||||
\(483\) | −1.22757e7 | −0.108945 | ||||||||
\(484\) | 1.94941e7 | − | 5.53899e7i | 0.171937 | − | 0.488534i | ||||
\(485\) | − | 1.28074e8i | − | 1.12263i | ||||||
\(486\) | −5.55447e7 | − | 7.84329e7i | −0.483876 | − | 0.683266i | ||||
\(487\) | 9.02434e7i | 0.781320i | 0.920535 | + | 0.390660i | \(0.127753\pi\) | ||||
−0.920535 | + | 0.390660i | \(0.872247\pi\) | |||||||
\(488\) | 1.35459e7 | + | 4.75022e7i | 0.116559 | + | 0.408747i | ||||
\(489\) | −5.94595e7 | −0.508504 | ||||||||
\(490\) | −1.52412e8 | + | 1.07935e8i | −1.29548 | + | 0.917436i | ||||
\(491\) | −1.00966e8 | −0.852962 | −0.426481 | − | 0.904497i | \(-0.640247\pi\) | ||||
−0.426481 | + | 0.904497i | \(0.640247\pi\) | |||||||
\(492\) | −3.59774e7 | + | 1.02225e8i | −0.302089 | + | 0.858344i | ||||
\(493\) | 8.52758e7i | 0.711681i | ||||||||
\(494\) | 1.71738e7 | − | 1.21621e7i | 0.142457 | − | 0.100885i | ||||
\(495\) | 6.01360e7i | 0.495814i | ||||||||
\(496\) | −1.93702e7 | + | 2.41102e7i | −0.158741 | + | 0.197586i | ||||
\(497\) | 1.09365e7 | 0.0890857 | ||||||||
\(498\) | −1.39652e8 | − | 1.97198e8i | −1.13073 | − | 1.59667i | ||||
\(499\) | −1.47819e8 | −1.18968 | −0.594839 | − | 0.803845i | \(-0.702784\pi\) | ||||
−0.594839 | + | 0.803845i | \(0.702784\pi\) | |||||||
\(500\) | −1.00773e8 | − | 3.54665e7i | −0.806185 | − | 0.283732i | ||||
\(501\) | 1.28117e8i | 1.01881i | ||||||||
\(502\) | 7.86207e7 | + | 1.11018e8i | 0.621478 | + | 0.877570i | ||||
\(503\) | − | 3.38774e7i | − | 0.266199i | −0.991103 | − | 0.133099i | \(-0.957507\pi\) | ||
0.991103 | − | 0.133099i | \(-0.0424929\pi\) | |||||||
\(504\) | 902500. | + | 3.16486e6i | 0.00704946 | + | 0.0247208i | ||||
\(505\) | 1.70888e8 | 1.32690 | ||||||||
\(506\) | 1.15906e8 | − | 8.20823e7i | 0.894651 | − | 0.633575i | ||||
\(507\) | −7.86829e7 | −0.603749 | ||||||||
\(508\) | 1.46817e8 | + | 5.16714e7i | 1.11992 | + | 0.394148i | ||||
\(509\) | 5.16056e7i | 0.391331i | 0.980671 | + | 0.195665i | \(0.0626866\pi\) | ||||
−0.980671 | + | 0.195665i | \(0.937313\pi\) | |||||||
\(510\) | 2.17116e8 | − | 1.53758e8i | 1.63675 | − | 1.15911i | ||||
\(511\) | 5.62268e6i | 0.0421386i | ||||||||
\(512\) | 9.02461e7 | − | 9.93481e7i | 0.672386 | − | 0.740201i | ||||
\(513\) | −2.21635e7 | −0.164167 | ||||||||
\(514\) | −8.98458e7 | − | 1.26868e8i | −0.661620 | − | 0.934253i | ||||
\(515\) | 4.24810e8 | 3.11009 | ||||||||
\(516\) | 4.07088e6 | − | 1.15668e7i | 0.0296305 | − | 0.0841909i | ||||
\(517\) | 5.95647e7i | 0.431040i | ||||||||
\(518\) | 2.63319e6 | + | 3.71825e6i | 0.0189449 | + | 0.0267515i | ||||
\(519\) | − | 6.66667e6i | − | 0.0476877i | ||||||
\(520\) | −1.52026e8 | + | 4.33523e7i | −1.08121 | + | 0.308320i | ||||
\(521\) | −1.06575e8 | −0.753602 | −0.376801 | − | 0.926294i | \(-0.622976\pi\) | ||||
−0.376801 | + | 0.926294i | \(0.622976\pi\) | |||||||
\(522\) | 3.53977e7 | − | 2.50679e7i | 0.248865 | − | 0.176241i | ||||
\(523\) | 1.10885e8 | 0.775117 | 0.387558 | − | 0.921845i | \(-0.373319\pi\) | ||||
0.387558 | + | 0.921845i | \(0.373319\pi\) | |||||||
\(524\) | −5.67261e7 | + | 1.61179e8i | −0.394266 | + | 1.12025i | ||||
\(525\) | 1.53425e7i | 0.106027i | ||||||||
\(526\) | −8.70290e7 | + | 6.16323e7i | −0.598008 | + | 0.423498i | ||||
\(527\) | − | 3.88162e7i | − | 0.265205i | ||||||
\(528\) | −9.58876e7 | − | 7.70362e7i | −0.651420 | − | 0.523351i | ||||
\(529\) | −2.21005e8 | −1.49292 | ||||||||
\(530\) | 1.81686e8 | + | 2.56554e8i | 1.22038 | + | 1.72326i | ||||
\(531\) | 4.64817e7 | 0.310455 | ||||||||
\(532\) | 2.01365e6 | + | 708691.i | 0.0133736 | + | 0.00470676i | ||||
\(533\) | 8.08202e7i | 0.533751i | ||||||||
\(534\) | 6.53156e7 | + | 9.22302e7i | 0.428937 | + | 0.605689i | ||||
\(535\) | − | 3.60962e8i | − | 2.35722i | ||||||
\(536\) | −3.70563e7 | + | 1.05671e7i | −0.240640 | + | 0.0686216i | ||||
\(537\) | 1.09182e8 | 0.705062 | ||||||||
\(538\) | −4.65826e7 | + | 3.29889e7i | −0.299142 | + | 0.211846i | ||||
\(539\) | −1.08368e8 | −0.692047 | ||||||||
\(540\) | 1.57053e8 | + | 5.52739e7i | 0.997390 | + | 0.351026i | ||||
\(541\) | − | 8.74191e7i | − | 0.552096i | −0.961144 | − | 0.276048i | \(-0.910975\pi\) | ||
0.961144 | − | 0.276048i | \(-0.0890248\pi\) | |||||||
\(542\) | −4.52803e7 | + | 3.20666e7i | −0.284388 | + | 0.201398i | ||||
\(543\) | − | 7.77076e7i | − | 0.485360i | ||||||
\(544\) | −1.02047e7 | + | 1.68144e8i | −0.0633875 | + | 1.04444i | ||||
\(545\) | −2.84737e8 | −1.75896 | ||||||||
\(546\) | 4.58212e6 | + | 6.47027e6i | 0.0281507 | + | 0.0397507i | ||||
\(547\) | −1.11073e7 | −0.0678653 | −0.0339326 | − | 0.999424i | \(-0.510803\pi\) | ||||
−0.0339326 | + | 0.999424i | \(0.510803\pi\) | |||||||
\(548\) | 8.50313e7 | − | 2.41605e8i | 0.516699 | − | 1.46813i | ||||
\(549\) | 3.15336e7i | 0.190571i | ||||||||
\(550\) | −1.02588e8 | − | 1.44862e8i | −0.616609 | − | 0.870694i | ||||
\(551\) | − | 2.81351e7i | − | 0.168188i | ||||||
\(552\) | 8.76446e7 | + | 3.07349e8i | 0.521084 | + | 1.82732i | ||||
\(553\) | −6.72592e6 | −0.0397719 | ||||||||
\(554\) | 1.17080e8 | − | 8.29135e7i | 0.688576 | − | 0.487636i | ||||
\(555\) | −1.87346e8 | −1.09589 | ||||||||
\(556\) | −4.02464e7 | + | 1.14354e8i | −0.234154 | + | 0.665317i | ||||
\(557\) | − | 4.54249e7i | − | 0.262862i | −0.991325 | − | 0.131431i | \(-0.958043\pi\) | ||
0.991325 | − | 0.131431i | \(-0.0419573\pi\) | |||||||
\(558\) | −1.61125e7 | + | 1.14105e7i | −0.0927383 | + | 0.0656755i | ||||
\(559\) | − | 9.14488e6i | − | 0.0523531i | ||||||
\(560\) | −1.25015e7 | − | 1.00437e7i | −0.0711866 | − | 0.0571914i | ||||
\(561\) | 1.54374e8 | 0.874351 | ||||||||
\(562\) | 1.98499e7 | + | 2.80295e7i | 0.111828 | + | 0.157909i | ||||
\(563\) | 5.57201e7 | 0.312239 | 0.156119 | − | 0.987738i | \(-0.450102\pi\) | ||||
0.156119 | + | 0.987738i | \(0.450102\pi\) | |||||||
\(564\) | −1.26436e8 | − | 4.44984e7i | −0.704747 | − | 0.248031i | ||||
\(565\) | − | 1.25099e8i | − | 0.693600i | ||||||
\(566\) | −1.56910e8 | − | 2.21568e8i | −0.865369 | − | 1.22196i | ||||
\(567\) | − | 1.30360e7i | − | 0.0715148i | ||||||
\(568\) | −7.80828e7 | − | 2.73819e8i | −0.426099 | − | 1.49423i | ||||
\(569\) | 3.43539e8 | 1.86483 | 0.932416 | − | 0.361387i | \(-0.117697\pi\) | ||||
0.932416 | + | 0.361387i | \(0.117697\pi\) | |||||||
\(570\) | −7.16335e7 | + | 5.07295e7i | −0.386805 | + | 0.273928i | ||||
\(571\) | −2.25486e8 | −1.21119 | −0.605593 | − | 0.795775i | \(-0.707064\pi\) | ||||
−0.605593 | + | 0.795775i | \(0.707064\pi\) | |||||||
\(572\) | −8.65277e7 | − | 3.04529e7i | −0.462346 | − | 0.162720i | ||||
\(573\) | 6.57811e7i | 0.349653i | ||||||||
\(574\) | −6.69058e6 | + | 4.73814e6i | −0.0353776 | + | 0.0250537i | ||||
\(575\) | 4.61236e8i | 2.42616i | ||||||||
\(576\) | 7.27956e7 | − | 4.51921e7i | 0.380923 | − | 0.236480i | ||||
\(577\) | −8.79050e7 | −0.457600 | −0.228800 | − | 0.973473i | \(-0.573480\pi\) | ||||
−0.228800 | + | 0.973473i | \(0.573480\pi\) | |||||||
\(578\) | −1.05880e7 | − | 1.49510e7i | −0.0548316 | − | 0.0774259i | ||||
\(579\) | 2.57518e8 | 1.32669 | ||||||||
\(580\) | −7.01667e7 | + | 1.99369e8i | −0.359622 | + | 1.02182i | ||||
\(581\) | − | 1.82803e7i | − | 0.0932085i | ||||||
\(582\) | 9.66481e7 | + | 1.36474e8i | 0.490257 | + | 0.692277i | ||||
\(583\) | 1.82415e8i | 0.920564i | ||||||||
\(584\) | 1.40776e8 | − | 4.01441e7i | 0.706789 | − | 0.201550i | ||||
\(585\) | −1.00920e8 | −0.504094 | ||||||||
\(586\) | 2.05769e8 | − | 1.45722e8i | 1.02256 | − | 0.724156i | ||||
\(587\) | −3.94523e7 | −0.195056 | −0.0975278 | − | 0.995233i | \(-0.531093\pi\) | ||||
−0.0975278 | + | 0.995233i | \(0.531093\pi\) | |||||||
\(588\) | 8.09574e7 | − | 2.30029e8i | 0.398222 | − | 1.13149i | ||||
\(589\) | 1.28067e7i | 0.0626744i | ||||||||
\(590\) | −1.84838e8 | + | 1.30898e8i | −0.899983 | + | 0.637351i | ||||
\(591\) | 1.34131e8i | 0.649778i | ||||||||
\(592\) | 7.42943e7 | − | 9.24747e7i | 0.358088 | − | 0.445716i | ||||
\(593\) | 2.30474e8 | 1.10524 | 0.552622 | − | 0.833432i | \(-0.313627\pi\) | ||||
0.552622 | + | 0.833432i | \(0.313627\pi\) | |||||||
\(594\) | 5.58339e7 | + | 7.88413e7i | 0.266403 | + | 0.376179i | ||||
\(595\) | 2.01268e7 | 0.0955484 | ||||||||
\(596\) | −1.84971e8 | − | 6.50994e7i | −0.873704 | − | 0.307495i | ||||
\(597\) | − | 3.84065e8i | − | 1.80502i | ||||||
\(598\) | 1.37751e8 | + | 1.94514e8i | 0.644155 | + | 0.909592i | ||||
\(599\) | 1.85523e8i | 0.863212i | 0.902062 | + | 0.431606i | \(0.142053\pi\) | ||||
−0.902062 | + | 0.431606i | \(0.857947\pi\) | |||||||
\(600\) | 3.84132e8 | − | 1.09540e8i | 1.77839 | − | 0.507130i | ||||
\(601\) | −4.38545e7 | −0.202018 | −0.101009 | − | 0.994885i | \(-0.532207\pi\) | ||||
−0.101009 | + | 0.994885i | \(0.532207\pi\) | |||||||
\(602\) | 757045. | − | 536125.i | 0.00347002 | − | 0.00245740i | ||||
\(603\) | −2.45993e7 | −0.112194 | ||||||||
\(604\) | −1.35493e8 | − | 4.76859e7i | −0.614902 | − | 0.216411i | ||||
\(605\) | 1.82661e8i | 0.824858i | ||||||||
\(606\) | −1.82096e8 | + | 1.28957e8i | −0.818242 | + | 0.579463i | ||||
\(607\) | − | 2.43622e8i | − | 1.08931i | −0.838661 | − | 0.544654i | \(-0.816661\pi\) | ||
0.838661 | − | 0.544654i | \(-0.183339\pi\) | |||||||
\(608\) | 3.36685e6 | − | 5.54758e7i | 0.0149800 | − | 0.246827i | ||||
\(609\) | 1.06000e7 | 0.0469304 | ||||||||
\(610\) | −8.88028e7 | − | 1.25396e8i | −0.391235 | − | 0.552450i | ||||
\(611\) | −9.99618e7 | −0.438238 | ||||||||
\(612\) | −3.57009e7 | + | 1.01439e8i | −0.155749 | + | 0.442539i | ||||
\(613\) | 3.31194e8i | 1.43781i | 0.695109 | + | 0.718905i | \(0.255356\pi\) | ||||
−0.695109 | + | 0.718905i | \(0.744644\pi\) | |||||||
\(614\) | −1.59634e8 | − | 2.25414e8i | −0.689635 | − | 0.973813i | ||||
\(615\) | − | 3.37109e8i | − | 1.44926i | ||||||
\(616\) | −2.55175e6 | − | 8.94839e6i | −0.0109168 | − | 0.0382827i | ||||
\(617\) | 1.49869e8 | 0.638054 | 0.319027 | − | 0.947746i | \(-0.396644\pi\) | ||||
0.319027 | + | 0.947746i | \(0.396644\pi\) | |||||||
\(618\) | −4.52672e8 | + | 3.20574e8i | −1.91787 | + | 1.35820i | ||||
\(619\) | 8.10701e7 | 0.341813 | 0.170907 | − | 0.985287i | \(-0.445330\pi\) | ||||
0.170907 | + | 0.985287i | \(0.445330\pi\) | |||||||
\(620\) | 3.19387e7 | − | 9.07495e7i | 0.134012 | − | 0.380776i | ||||
\(621\) | − | 2.51029e8i | − | 1.04821i | ||||||
\(622\) | 1.01779e8 | − | 7.20782e7i | 0.422949 | − | 0.299525i | ||||
\(623\) | 8.54977e6i | 0.0353582i | ||||||||
\(624\) | 1.29283e8 | − | 1.60919e8i | 0.532091 | − | 0.662298i | ||||
\(625\) | −4.28287e7 | −0.175426 | ||||||||
\(626\) | −9.86985e6 | − | 1.39369e7i | −0.0402335 | − | 0.0568125i | ||||
\(627\) | −5.09328e7 | −0.206631 | ||||||||
\(628\) | 2.95249e8 | + | 1.03911e8i | 1.19209 | + | 0.419550i | ||||
\(629\) | 1.48879e8i | 0.598250i | ||||||||
\(630\) | −5.91653e6 | − | 8.35455e6i | −0.0236617 | − | 0.0334119i | ||||
\(631\) | 2.70423e8i | 1.07635i | 0.842832 | + | 0.538177i | \(0.180887\pi\) | ||||
−0.842832 | + | 0.538177i | \(0.819113\pi\) | |||||||
\(632\) | 4.80209e7 | + | 1.68398e8i | 0.190230 | + | 0.667092i | ||||
\(633\) | −3.88050e8 | −1.52995 | ||||||||
\(634\) | 2.71227e8 | − | 1.92078e8i | 1.06430 | − | 0.753718i | ||||
\(635\) | −4.84163e8 | −1.89091 | ||||||||
\(636\) | −3.87205e8 | − | 1.36275e8i | −1.50512 | − | 0.529716i | ||||
\(637\) | − | 1.81864e8i | − | 0.703604i | ||||||
\(638\) | −1.00084e8 | + | 7.08776e7i | −0.385392 | + | 0.272927i | ||||
\(639\) | − | 1.81770e8i | − | 0.696659i | ||||||
\(640\) | −1.62210e8 | + | 3.84711e8i | −0.618782 | + | 1.46756i | ||||
\(641\) | 7.98693e7 | 0.303254 | 0.151627 | − | 0.988438i | \(-0.451549\pi\) | ||||
0.151627 | + | 0.988438i | \(0.451549\pi\) | |||||||
\(642\) | 2.72392e8 | + | 3.84637e8i | 1.02941 | + | 1.45360i | ||||
\(643\) | 3.07378e8 | 1.15622 | 0.578110 | − | 0.815959i | \(-0.303791\pi\) | ||||
0.578110 | + | 0.815959i | \(0.303791\pi\) | |||||||
\(644\) | −8.02679e6 | + | 2.28070e7i | −0.0300527 | + | 0.0853907i | ||||
\(645\) | 3.81442e7i | 0.142151i | ||||||||
\(646\) | 4.03135e7 | + | 5.69254e7i | 0.149538 | + | 0.211158i | ||||
\(647\) | 3.33867e7i | 0.123271i | 0.998099 | + | 0.0616354i | \(0.0196316\pi\) | ||||
−0.998099 | + | 0.0616354i | \(0.980368\pi\) | |||||||
\(648\) | −3.26385e8 | + | 9.30730e7i | −1.19952 | + | 0.342057i | ||||
\(649\) | −1.31423e8 | −0.480771 | ||||||||
\(650\) | 2.43107e8 | − | 1.72164e8i | 0.885234 | − | 0.626906i | ||||
\(651\) | −4.82496e6 | −0.0174884 | ||||||||
\(652\) | −3.88791e7 | + | 1.10469e8i | −0.140273 | + | 0.398565i | ||||
\(653\) | − | 3.92550e8i | − | 1.40979i | −0.709309 | − | 0.704897i | \(-0.750993\pi\) | ||
0.709309 | − | 0.704897i | \(-0.249007\pi\) | |||||||
\(654\) | 3.03412e8 | − | 2.14871e8i | 1.08468 | − | 0.768147i | ||||
\(655\) | − | 5.31525e8i | − | 1.89147i | ||||||
\(656\) | 1.66398e8 | + | 1.33685e8i | 0.589437 | + | 0.473554i | ||||
\(657\) | 9.34520e7 | 0.329528 | ||||||||
\(658\) | −5.86033e6 | − | 8.27519e6i | −0.0205705 | − | 0.0290469i | ||||
\(659\) | 4.88173e8 | 1.70576 | 0.852879 | − | 0.522109i | \(-0.174855\pi\) | ||||
0.852879 | + | 0.522109i | \(0.174855\pi\) | |||||||
\(660\) | 3.60916e8 | + | 1.27022e8i | 1.25538 | + | 0.441822i | ||||
\(661\) | − | 2.56127e8i | − | 0.886853i | −0.896311 | − | 0.443427i | \(-0.853763\pi\) | ||
0.896311 | − | 0.443427i | \(-0.146237\pi\) | |||||||
\(662\) | −8.27589e7 | − | 1.16861e8i | −0.285260 | − | 0.402807i | ||||
\(663\) | 2.59071e8i | 0.888953i | ||||||||
\(664\) | −4.57688e8 | + | 1.30516e8i | −1.56338 | + | 0.445819i | ||||
\(665\) | −6.64045e6 | −0.0225805 | ||||||||
\(666\) | 6.17993e7 | − | 4.37651e7i | 0.209200 | − | 0.148151i | ||||
\(667\) | 3.18665e8 | 1.07388 | ||||||||
\(668\) | 2.38027e8 | + | 8.37723e7i | 0.798542 | + | 0.281042i | ||||
\(669\) | 6.85382e8i | 2.28904i | ||||||||
\(670\) | 9.78208e7 | − | 6.92748e7i | 0.325242 | − | 0.230330i | ||||
\(671\) | − | 8.91589e7i | − | 0.295119i | ||||||
\(672\) | 2.09007e7 | + | 1.26847e6i | 0.0688737 | + | 0.00417997i | ||||
\(673\) | 2.16653e8 | 0.710754 | 0.355377 | − | 0.934723i | \(-0.384352\pi\) | ||||
0.355377 | + | 0.934723i | \(0.384352\pi\) | |||||||
\(674\) | −8.61096e7 | − | 1.21593e8i | −0.281237 | − | 0.397126i | ||||
\(675\) | −3.13741e8 | −1.02014 | ||||||||
\(676\) | −5.14488e7 | + | 1.46185e8i | −0.166546 | + | 0.473218i | ||||
\(677\) | 1.50931e8i | 0.486420i | 0.969974 | + | 0.243210i | \(0.0782005\pi\) | ||||
−0.969974 | + | 0.243210i | \(0.921800\pi\) | |||||||
\(678\) | 9.44034e7 | + | 1.33304e8i | 0.302899 | + | 0.427715i | ||||
\(679\) | 1.26512e7i | 0.0404130i | ||||||||
\(680\) | −1.43699e8 | − | 5.03918e8i | −0.457010 | − | 1.60263i | ||||
\(681\) | −8.89223e7 | −0.281559 | ||||||||
\(682\) | 4.55567e7 | − | 3.22623e7i | 0.143615 | − | 0.101705i | ||||
\(683\) | −3.69947e8 | −1.16112 | −0.580561 | − | 0.814217i | \(-0.697167\pi\) | ||||
−0.580561 | + | 0.814217i | \(0.697167\pi\) | |||||||
\(684\) | 1.17788e7 | − | 3.34679e7i | 0.0368073 | − | 0.104583i | ||||
\(685\) | 7.96746e8i | 2.47884i | ||||||||
\(686\) | 3.01603e7 | − | 2.13590e7i | 0.0934251 | − | 0.0661619i | ||||
\(687\) | 2.35183e8i | 0.725332i | ||||||||
\(688\) | −1.88281e7 | − | 1.51265e7i | −0.0578151 | − | 0.0464487i | ||||
\(689\) | −3.06129e8 | −0.935938 | ||||||||
\(690\) | −5.74573e8 | − | 8.11336e8i | −1.74903 | − | 2.46975i | ||||
\(691\) | −2.15167e7 | −0.0652141 | −0.0326070 | − | 0.999468i | \(-0.510381\pi\) | ||||
−0.0326070 | + | 0.999468i | \(0.510381\pi\) | |||||||
\(692\) | −1.23860e7 | − | 4.35917e6i | −0.0373776 | − | 0.0131548i | ||||
\(693\) | − | 5.94025e6i | − | 0.0178486i | ||||||
\(694\) | −1.83292e8 | − | 2.58821e8i | −0.548360 | − | 0.774322i | ||||
\(695\) | − | 3.77109e8i | − | 1.12334i | ||||||
\(696\) | −7.56806e7 | − | 2.65395e8i | −0.224469 | − | 0.787162i | ||||
\(697\) | −2.67893e8 | −0.791156 | ||||||||
\(698\) | −4.46831e8 | + | 3.16437e8i | −1.31394 | + | 0.930511i | ||||
\(699\) | 5.32763e8 | 1.55992 | ||||||||
\(700\) | 2.85047e7 | + | 1.00321e7i | 0.0831040 | + | 0.0292480i | ||||
\(701\) | − | 2.95578e8i | − | 0.858060i | −0.903290 | − | 0.429030i | \(-0.858855\pi\) | ||
0.903290 | − | 0.429030i | \(-0.141145\pi\) | |||||||
\(702\) | −1.32312e8 | + | 9.37007e7i | −0.382461 | + | 0.270852i | ||||
\(703\) | − | 4.91200e7i | − | 0.141381i | ||||||
\(704\) | −2.05824e8 | + | 1.27777e8i | −0.589899 | + | 0.366214i | ||||
\(705\) | 4.16951e8 | 1.18992 | ||||||||
\(706\) | 1.39446e8 | + | 1.96907e8i | 0.396270 | + | 0.559561i | ||||
\(707\) | −1.68803e7 | −0.0477665 | ||||||||
\(708\) | 9.81809e7 | − | 2.78967e8i | 0.276648 | − | 0.786056i | ||||
\(709\) | 3.43066e8i | 0.962584i | 0.876560 | + | 0.481292i | \(0.159832\pi\) | ||||
−0.876560 | + | 0.481292i | \(0.840168\pi\) | |||||||
\(710\) | 5.11889e8 | + | 7.22822e8i | 1.43021 | + | 2.01956i | ||||
\(711\) | 1.11789e8i | 0.311020i | ||||||||
\(712\) | 2.14062e8 | − | 6.10426e7i | 0.593062 | − | 0.169119i | ||||
\(713\) | −1.45051e8 | −0.400177 | ||||||||
\(714\) | −2.14468e7 | + | 1.51882e7i | −0.0589208 | + | 0.0417266i | ||||
\(715\) | 2.85344e8 | 0.780641 | ||||||||
\(716\) | 7.13912e7 | − | 2.02848e8i | 0.194494 | − | 0.552627i | ||||
\(717\) | − | 5.65344e8i | − | 1.53375i | ||||||
\(718\) | 4.00828e8 | − | 2.83858e8i | 1.08289 | − | 0.766882i | ||||
\(719\) | 2.69203e8i | 0.724257i | 0.932128 | + | 0.362129i | \(0.117950\pi\) | ||||
−0.932128 | + | 0.362129i | \(0.882050\pi\) | |||||||
\(720\) | −1.66932e8 | + | 2.07782e8i | −0.447242 | + | 0.556686i | ||||
\(721\) | −4.19629e7 | −0.111959 | ||||||||
\(722\) | 2.04215e8 | + | 2.88365e8i | 0.542595 | + | 0.766181i | ||||
\(723\) | −4.35569e8 | −1.15250 | ||||||||
\(724\) | −1.44373e8 | − | 5.08111e7i | −0.380425 | − | 0.133888i | ||||
\(725\) | − | 3.98274e8i | − | 1.04513i | ||||||
\(726\) | −1.37841e8 | − | 1.94641e8i | −0.360220 | − | 0.508656i | ||||
\(727\) | − | 1.90694e8i | − | 0.496287i | −0.968723 | − | 0.248144i | \(-0.920180\pi\) | ||
0.968723 | − | 0.248144i | \(-0.0798205\pi\) | |||||||
\(728\) | 1.50172e7 | − | 4.28235e6i | 0.0389220 | − | 0.0110991i | ||||
\(729\) | 9.28730e7 | 0.239721 | ||||||||
\(730\) | −3.71618e8 | + | 2.63173e8i | −0.955275 | + | 0.676508i | ||||
\(731\) | 3.03123e7 | 0.0776008 | ||||||||
\(732\) | 1.89254e8 | + | 6.66069e7i | 0.482517 | + | 0.169819i | ||||
\(733\) | − | 4.68798e8i | − | 1.19035i | −0.803597 | − | 0.595174i | \(-0.797083\pi\) | ||
0.803597 | − | 0.595174i | \(-0.202917\pi\) | |||||||
\(734\) | 2.72689e8 | − | 1.93113e8i | 0.689571 | − | 0.488341i | ||||
\(735\) | 7.58573e8i | 1.91045i | ||||||||
\(736\) | 6.28332e8 | + | 3.81337e7i | 1.57600 | + | 0.0956478i | ||||
\(737\) | 6.95525e7 | 0.173744 | ||||||||
\(738\) | 7.87505e7 | + | 1.11201e8i | 0.195923 | + | 0.276656i | ||||
\(739\) | −6.73855e8 | −1.66968 | −0.834840 | − | 0.550493i | \(-0.814440\pi\) | ||||
−0.834840 | + | 0.550493i | \(0.814440\pi\) | |||||||
\(740\) | −1.22501e8 | + | 3.48070e8i | −0.302305 | + | 0.858956i | ||||
\(741\) | − | 8.54757e7i | − | 0.210082i | ||||||
\(742\) | −1.79470e7 | − | 2.53424e7i | −0.0439320 | − | 0.0620350i | ||||
\(743\) | 7.42053e7i | 0.180913i | 0.995900 | + | 0.0904563i | \(0.0288325\pi\) | ||||
−0.995900 | + | 0.0904563i | \(0.971167\pi\) | |||||||
\(744\) | 3.44486e7 | + | 1.20803e8i | 0.0836475 | + | 0.293332i | ||||
\(745\) | 6.09983e8 | 1.47519 | ||||||||
\(746\) | −3.66586e8 | + | 2.59609e8i | −0.882997 | + | 0.625321i | ||||
\(747\) | −3.03829e8 | −0.728900 | ||||||||
\(748\) | 1.00941e8 | − | 2.86811e8i | 0.241193 | − | 0.685316i | ||||
\(749\) | 3.56560e7i | 0.0848568i | ||||||||
\(750\) | −3.54118e8 | + | 2.50779e8i | −0.839390 | + | 0.594440i | ||||
\(751\) | 9.05182e7i | 0.213706i | 0.994275 | + | 0.106853i | \(0.0340774\pi\) | ||||
−0.994275 | + | 0.106853i | \(0.965923\pi\) | |||||||
\(752\) | −1.65347e8 | + | 2.05808e8i | −0.388814 | + | 0.483960i | ||||
\(753\) | 5.52548e8 | 1.29415 | ||||||||
\(754\) | −1.18947e8 | − | 1.67961e8i | −0.277485 | − | 0.391828i | ||||
\(755\) | 4.46819e8 | 1.03822 | ||||||||
\(756\) | −1.55137e7 | − | 5.45997e6i | −0.0359047 | − | 0.0126364i | ||||
\(757\) | 2.19809e8i | 0.506709i | 0.967374 | + | 0.253354i | \(0.0815339\pi\) | ||||
−0.967374 | + | 0.253354i | \(0.918466\pi\) | |||||||
\(758\) | 9.08439e7 | + | 1.28278e8i | 0.208588 | + | 0.294540i | ||||
\(759\) | − | 5.76876e8i | − | 1.31934i | ||||||
\(760\) | 4.74106e7 | + | 1.66258e8i | 0.108003 | + | 0.378741i | ||||
\(761\) | 8.05220e7 | 0.182709 | 0.0913547 | − | 0.995818i | \(-0.470880\pi\) | ||||
0.0913547 | + | 0.995818i | \(0.470880\pi\) | |||||||
\(762\) | 5.15918e8 | − | 3.65363e8i | 1.16605 | − | 0.825771i | ||||
\(763\) | 2.81264e7 | 0.0633200 | ||||||||
\(764\) | 1.22214e8 | + | 4.30126e7i | 0.274058 | + | 0.0964530i | ||||
\(765\) | − | 3.34518e8i | − | 0.747198i | ||||||
\(766\) | −2.52418e8 | + | 1.78758e8i | −0.561609 | + | 0.397721i | ||||
\(767\) | − | 2.20555e8i | − | 0.488800i | ||||||
\(768\) | −1.17465e8 | − | 5.32352e8i | −0.259314 | − | 1.17521i | ||||
\(769\) | −8.94416e8 | −1.96680 | −0.983400 | − | 0.181449i | \(-0.941921\pi\) | ||||
−0.983400 | + | 0.181449i | \(0.941921\pi\) | |||||||
\(770\) | 1.67285e7 | + | 2.36218e7i | 0.0366425 | + | 0.0517417i | ||||
\(771\) | −6.31439e8 | −1.37774 | ||||||||
\(772\) | 1.68384e8 | − | 4.78440e8i | 0.365973 | − | 1.03986i | ||||
\(773\) | − | 7.83108e8i | − | 1.69544i | −0.530442 | − | 0.847721i | \(-0.677974\pi\) | ||
0.530442 | − | 0.847721i | \(-0.322026\pi\) | |||||||
\(774\) | −8.91069e6 | − | 1.25825e7i | −0.0192171 | − | 0.0271359i | ||||
\(775\) | 1.81288e8i | 0.389461i | ||||||||
\(776\) | 3.16750e8 | − | 9.03252e7i | 0.677846 | − | 0.193296i | ||||
\(777\) | 1.85061e7 | 0.0394505 | ||||||||
\(778\) | −1.92540e7 | + | 1.36353e7i | −0.0408868 | + | 0.0289552i | ||||
\(779\) | 8.83861e7 | 0.186970 | ||||||||
\(780\) | −2.13169e8 | + | 6.05690e8i | −0.449201 | + | 1.27634i | ||||
\(781\) | 5.13941e8i | 1.07885i | ||||||||
\(782\) | −6.44749e8 | + | 4.56599e8i | −1.34825 | + | 0.954805i | ||||
\(783\) | 2.16762e8i | 0.451541i | ||||||||
\(784\) | −3.74434e8 | − | 3.00821e8i | −0.777011 | − | 0.624252i | ||||
\(785\) | −9.73650e8 | −2.01277 | ||||||||
\(786\) | 4.01104e8 | + | 5.66387e8i | 0.826018 | + | 1.16639i | ||||
\(787\) | 4.40033e7 | 0.0902737 | 0.0451368 | − | 0.998981i | \(-0.485628\pi\) | ||||
0.0451368 | + | 0.998981i | \(0.485628\pi\) | |||||||
\(788\) | 2.49200e8 | + | 8.77046e7i | 0.509296 | + | 0.179244i | ||||
\(789\) | 4.33153e8i | 0.881882i | ||||||||
\(790\) | −3.14811e8 | − | 4.44535e8i | −0.638511 | − | 0.901622i | ||||
\(791\) | 1.23573e7i | 0.0249687i | ||||||||
\(792\) | −1.48727e8 | + | 4.24114e7i | −0.299374 | + | 0.0853704i | ||||
\(793\) | 1.49627e8 | 0.300047 | ||||||||
\(794\) | 4.49281e8 | − | 3.18172e8i | 0.897546 | − | 0.635625i | ||||
\(795\) | 1.27690e9 | 2.54129 | ||||||||
\(796\) | −7.13552e8 | − | 2.51130e8i | −1.41477 | − | 0.497920i | ||||
\(797\) | 9.71867e8i | 1.91969i | 0.280526 | + | 0.959846i | \(0.409491\pi\) | ||||
−0.280526 | + | 0.959846i | \(0.590509\pi\) | |||||||
\(798\) | 7.07598e6 | − | 5.01107e6i | 0.0139244 | − | 0.00986102i | ||||
\(799\) | − | 3.31341e8i | − | 0.649583i | ||||||
\(800\) | 4.76603e7 | − | 7.85303e8i | 0.0930865 | − | 1.53379i | ||||
\(801\) | 1.42102e8 | 0.276505 | ||||||||
\(802\) | −1.58253e8 | − | 2.23464e8i | −0.306781 | − | 0.433196i | ||||
\(803\) | −2.64228e8 | −0.510308 | ||||||||
\(804\) | −5.19598e7 | + | 1.47637e8i | −0.0999769 | + | 0.284070i | ||||
\(805\) | − | 7.52112e7i | − | 0.144177i | ||||||
\(806\) | 5.41428e7 | + | 7.64534e7i | 0.103404 | + | 0.146013i | ||||
\(807\) | 2.31847e8i | 0.441144i | ||||||||
\(808\) | 1.20520e8 | + | 4.22636e8i | 0.228468 | + | 0.801185i | ||||
\(809\) | 9.68480e8 | 1.82913 | 0.914566 | − | 0.404436i | \(-0.132532\pi\) | ||||
0.914566 | + | 0.404436i | \(0.132532\pi\) | |||||||
\(810\) | 8.61587e8 | − | 6.10160e8i | 1.62123 | − | 1.14812i | ||||
\(811\) | 6.66747e8 | 1.24997 | 0.624984 | − | 0.780638i | \(-0.285106\pi\) | ||||
0.624984 | + | 0.780638i | \(0.285106\pi\) | |||||||
\(812\) | 6.93108e6 | − | 1.96937e7i | 0.0129459 | − | 0.0367840i | ||||
\(813\) | 2.25365e8i | 0.419387i | ||||||||
\(814\) | −1.74733e8 | + | 1.23742e8i | −0.323967 | + | 0.229427i | ||||
\(815\) | − | 3.64298e8i | − | 0.672952i | ||||||
\(816\) | 5.33394e8 | + | 4.28529e8i | 0.981697 | + | 0.788697i | ||||
\(817\) | −1.00010e7 | −0.0183390 | ||||||||
\(818\) | −3.43936e8 | − | 4.85662e8i | −0.628374 | − | 0.887307i | ||||
\(819\) | 9.96895e6 | 0.0181467 | ||||||||
\(820\) | −6.26314e8 | − | 2.20427e8i | −1.13593 | − | 0.399783i | ||||
\(821\) | 1.01581e9i | 1.83563i | 0.397009 | + | 0.917815i | \(0.370048\pi\) | ||||
−0.397009 | + | 0.917815i | \(0.629952\pi\) | |||||||
\(822\) | −6.01247e8 | − | 8.49002e8i | −1.08252 | − | 1.52860i | ||||
\(823\) | 9.24417e8i | 1.65832i | 0.559011 | + | 0.829160i | \(0.311181\pi\) | ||||
−0.559011 | + | 0.829160i | \(0.688819\pi\) | |||||||
\(824\) | 2.99601e8 | + | 1.05063e9i | 0.535503 | + | 1.87789i | ||||
\(825\) | −7.20993e8 | −1.28401 | ||||||||
\(826\) | 1.82583e7 | − | 1.29302e7i | 0.0323982 | − | 0.0229438i | ||||
\(827\) | −5.14562e8 | −0.909748 | −0.454874 | − | 0.890556i | \(-0.650316\pi\) | ||||
−0.454874 | + | 0.890556i | \(0.650316\pi\) | |||||||
\(828\) | 3.79065e8 | + | 1.33410e8i | 0.667763 | + | 0.235015i | ||||
\(829\) | − | 7.43047e8i | − | 1.30423i | −0.758122 | − | 0.652113i | \(-0.773883\pi\) | ||
0.758122 | − | 0.652113i | \(-0.226117\pi\) | |||||||
\(830\) | 1.20820e9 | − | 8.55623e8i | 2.11302 | − | 1.49640i | ||||
\(831\) | − | 5.82718e8i | − | 1.01544i | ||||||
\(832\) | −2.14436e8 | − | 3.45414e8i | −0.372330 | − | 0.599750i | ||||
\(833\) | 6.02820e8 | 1.04292 | ||||||||
\(834\) | 2.84577e8 | + | 4.01843e8i | 0.490571 | + | 0.692721i | ||||
\(835\) | −7.84949e8 | −1.34829 | ||||||||
\(836\) | −3.33037e7 | + | 9.46278e7i | −0.0569999 | + | 0.161957i | ||||
\(837\) | − | 9.86665e7i | − | 0.168265i | ||||||
\(838\) | 1.74860e8 | + | 2.46914e8i | 0.297138 | + | 0.419579i | ||||
\(839\) | − | 9.70115e8i | − | 1.64262i | −0.570482 | − | 0.821310i | \(-0.693244\pi\) | ||
0.570482 | − | 0.821310i | \(-0.306756\pi\) | |||||||
\(840\) | −6.26384e7 | + | 1.78621e7i | −0.105682 | + | 0.0301367i | ||||
\(841\) | 3.19658e8 | 0.537400 | ||||||||
\(842\) | −4.05907e8 | + | 2.87456e8i | −0.679971 | + | 0.481543i | ||||
\(843\) | 1.39506e8 | 0.232868 | ||||||||
\(844\) | −2.53736e8 | + | 7.20956e8i | −0.422041 | + | 1.19917i | ||||
\(845\) | − | 4.82077e8i | − | 0.798998i | ||||||
\(846\) | −1.37538e8 | + | 9.74019e7i | −0.227150 | + | 0.160863i | ||||
\(847\) | − | 1.80433e7i | − | 0.0296938i | ||||||
\(848\) | −5.06368e8 | + | 6.30280e8i | −0.830383 | + | 1.03358i | ||||
\(849\) | −1.10277e9 | −1.80203 | ||||||||
\(850\) | 5.70667e8 | + | 8.05822e8i | 0.929237 | + | 1.31215i | ||||
\(851\) | 5.56344e8 | 0.902723 | ||||||||
\(852\) | −1.09092e9 | − | 3.83944e8i | −1.76391 | − | 0.620797i | ||||
\(853\) | − | 4.99318e8i | − | 0.804507i | −0.915528 | − | 0.402254i | \(-0.868227\pi\) | ||
0.915528 | − | 0.402254i | \(-0.131773\pi\) | |||||||
\(854\) | 8.77197e6 | + | 1.23866e7i | 0.0140839 | + | 0.0198875i | ||||
\(855\) | 1.10368e8i | 0.176581i | ||||||||
\(856\) | 8.92725e8 | − | 2.54572e8i | 1.42330 | − | 0.405872i | ||||
\(857\) | −9.80356e8 | −1.55755 | −0.778774 | − | 0.627305i | \(-0.784158\pi\) | ||||
−0.778774 | + | 0.627305i | \(0.784158\pi\) | |||||||
\(858\) | −3.04059e8 | + | 2.15329e8i | −0.481389 | + | 0.340911i | ||||
\(859\) | 1.39198e8 | 0.219610 | 0.109805 | − | 0.993953i | \(-0.464977\pi\) | ||||
0.109805 | + | 0.993953i | \(0.464977\pi\) | |||||||
\(860\) | 7.08680e7 | + | 2.49416e7i | 0.111418 | + | 0.0392128i | ||||
\(861\) | 3.32998e7i | 0.0521713i | ||||||||
\(862\) | −6.56531e8 | + | 4.64943e8i | −1.02502 | + | 0.725902i | ||||
\(863\) | 4.80087e7i | 0.0746943i | 0.999302 | + | 0.0373471i | \(0.0118907\pi\) | ||||
−0.999302 | + | 0.0373471i | \(0.988109\pi\) | |||||||
\(864\) | −2.59392e7 | + | 4.27403e8i | −0.0402176 | + | 0.662669i | ||||
\(865\) | 4.08455e7 | 0.0631097 | ||||||||
\(866\) | −4.97844e8 | − | 7.02990e8i | −0.766548 | − | 1.08242i | ||||
\(867\) | −7.44128e7 | −0.114180 | ||||||||
\(868\) | −3.15492e6 | + | 8.96426e6i | −0.00482424 | + | 0.0137074i | ||||
\(869\) | − | 3.16073e8i | − | 0.481646i | ||||||
\(870\) | 4.96140e8 | + | 7.00584e8i | 0.753437 | + | 1.06390i | ||||
\(871\) | 1.16723e8i | 0.176646i | ||||||||
\(872\) | −2.00814e8 | − | 7.04207e8i | −0.302861 | − | 1.06206i | ||||
\(873\) | 2.10269e8 | 0.316034 | ||||||||
\(874\) | 2.12723e8 | − | 1.50646e8i | 0.318625 | − | 0.225644i | ||||
\(875\) | −3.28269e7 | −0.0490010 | ||||||||
\(876\) | 1.97394e8 | − | 5.60867e8i | 0.293644 | − | 0.834349i | ||||
\(877\) | 1.09245e8i | 0.161959i | 0.996716 | + | 0.0809793i | \(0.0258048\pi\) | ||||
−0.996716 | + | 0.0809793i | \(0.974195\pi\) | |||||||
\(878\) | 4.47733e8 | − | 3.17076e8i | 0.661509 | − | 0.468468i | ||||
\(879\) | − | 1.02414e9i | − | 1.50797i | ||||||
\(880\) | 4.71988e8 | − | 5.87487e8i | 0.692600 | − | 0.862085i | ||||
\(881\) | 5.54386e8 | 0.810746 | 0.405373 | − | 0.914151i | \(-0.367142\pi\) | ||||
0.405373 | + | 0.914151i | \(0.367142\pi\) | |||||||
\(882\) | −1.77207e8 | − | 2.50228e8i | −0.258270 | − | 0.364695i | ||||
\(883\) | −8.44750e8 | −1.22700 | −0.613502 | − | 0.789693i | \(-0.710240\pi\) | ||||
−0.613502 | + | 0.789693i | \(0.710240\pi\) | |||||||
\(884\) | 4.81327e8 | + | 1.69400e8i | 0.696761 | + | 0.245221i | ||||
\(885\) | 9.19958e8i | 1.32721i | ||||||||
\(886\) | 4.09094e8 | + | 5.77669e8i | 0.588196 | + | 0.830573i | ||||
\(887\) | 7.33580e8i | 1.05118i | 0.850738 | + | 0.525589i | \(0.176155\pi\) | ||||
−0.850738 | + | 0.525589i | \(0.823845\pi\) | |||||||
\(888\) | −1.32128e8 | − | 4.63341e8i | −0.188693 | − | 0.661701i | ||||
\(889\) | 4.78257e7 | 0.0680701 | ||||||||
\(890\) | −5.65078e8 | + | 4.00178e8i | −0.801565 | + | 0.567653i | ||||
\(891\) | 6.12606e8 | 0.866060 | ||||||||
\(892\) | 1.27337e9 | + | 4.48154e8i | 1.79415 | + | 0.631441i | ||||
\(893\) | 1.09320e8i | 0.153512i | ||||||||
\(894\) | −6.49990e8 | + | 4.60310e8i | −0.909691 | + | 0.644226i | ||||
\(895\) | 6.68937e8i | 0.933075i | ||||||||
\(896\) | 1.60231e7 | − | 3.80019e7i | 0.0222753 | − | 0.0528301i | ||||
\(897\) | 9.68116e8 | 1.34138 | ||||||||
\(898\) | −1.98233e8 | − | 2.79918e8i | −0.273745 | − | 0.386547i | ||||
\(899\) | 1.25251e8 | 0.172386 | ||||||||
\(900\) | 1.66738e8 | − | 4.73764e8i | 0.228722 | − | 0.649882i | ||||
\(901\) | − | 1.01472e9i | − | 1.38730i | ||||||
\(902\) | −2.22661e8 | − | 3.14412e8i | −0.303406 | − | 0.428430i | ||||
\(903\) | − | 3.76790e6i | − | 0.00511724i | ||||||
\(904\) | 3.09393e8 | − | 8.82274e7i | 0.418799 | − | 0.119426i | ||||
\(905\) | 4.76101e8 | 0.642323 | ||||||||
\(906\) | −4.76124e8 | + | 3.37182e8i | −0.640229 | + | 0.453398i | ||||
\(907\) | 1.71358e8 | 0.229658 | 0.114829 | − | 0.993385i | \(-0.463368\pi\) | ||||
0.114829 | + | 0.993385i | \(0.463368\pi\) | |||||||
\(908\) | −5.81440e7 | + | 1.65208e8i | −0.0776690 | + | 0.220686i | ||||
\(909\) | 2.80561e8i | 0.373538i | ||||||||
\(910\) | −3.96422e7 | + | 2.80739e7i | −0.0526058 | + | 0.0372544i | ||||
\(911\) | 7.97986e8i | 1.05546i | 0.849413 | + | 0.527728i | \(0.176956\pi\) | ||||
−0.849413 | + | 0.527728i | \(0.823044\pi\) | |||||||
\(912\) | −1.75983e8 | − | 1.41385e8i | −0.231999 | − | 0.186389i | ||||
\(913\) | 8.59053e8 | 1.12878 | ||||||||
\(914\) | 3.24420e8 | + | 4.58104e8i | 0.424883 | + | 0.599965i | ||||
\(915\) | −6.24109e8 | −0.814698 | ||||||||
\(916\) | 4.36946e8 | + | 1.53781e8i | 0.568514 | + | 0.200085i | ||||
\(917\) | 5.25042e7i | 0.0680905i | ||||||||
\(918\) | −3.10587e8 | − | 4.38571e8i | −0.401472 | − | 0.566906i | ||||
\(919\) | − | 7.66471e7i | − | 0.0987527i | −0.998780 | − | 0.0493764i | \(-0.984277\pi\) | ||
0.998780 | − | 0.0493764i | \(-0.0157234\pi\) | |||||||
\(920\) | −1.88308e9 | + | 5.36983e8i | −2.41827 | + | 0.689600i | ||||
\(921\) | −1.12191e9 | −1.43608 | ||||||||
\(922\) | 3.51115e8 | − | 2.48653e8i | 0.447978 | − | 0.317249i | ||||
\(923\) | −8.62498e8 | −1.09686 | ||||||||
\(924\) | −3.56514e7 | − | 1.25473e7i | −0.0451919 | − | 0.0159050i | ||||
\(925\) | − | 6.95331e8i | − | 0.878549i | ||||||
\(926\) | 2.84689e8 | − | 2.01611e8i | 0.358539 | − | 0.253911i | ||||
\(927\) | 6.97447e8i | 0.875532i | ||||||||
\(928\) | −5.42561e8 | − | 3.29282e7i | −0.678898 | − | 0.0412026i | ||||
\(929\) | −5.09008e8 | −0.634860 | −0.317430 | − | 0.948282i | \(-0.602820\pi\) | ||||
−0.317430 | + | 0.948282i | \(0.602820\pi\) | |||||||
\(930\) | −2.25835e8 | − | 3.18895e8i | −0.280765 | − | 0.396459i | ||||
\(931\) | −1.98889e8 | −0.246469 | ||||||||
\(932\) | 3.48360e8 | − | 9.89817e8i | 0.430310 | − | 1.22266i | ||||
\(933\) | − | 5.06567e8i | − | 0.623723i | ||||||
\(934\) | 1.43082e8 | + | 2.02042e8i | 0.175608 | + | 0.247971i | ||||
\(935\) | 9.45823e8i | 1.15711i | ||||||||
\(936\) | −7.11750e7 | − | 2.49594e8i | −0.0867961 | − | 0.304374i | ||||
\(937\) | 8.59374e8 | 1.04463 | 0.522316 | − | 0.852752i | \(-0.325068\pi\) | ||||
0.522316 | + | 0.852752i | \(0.325068\pi\) | |||||||
\(938\) | −9.66277e6 | + | 6.84299e6i | −0.0117083 | + | 0.00829158i | ||||
\(939\) | −6.93656e7 | −0.0837813 | ||||||||
\(940\) | 2.72634e8 | − | 7.74651e8i | 0.328243 | − | 0.932658i | ||||
\(941\) | 1.07856e8i | 0.129442i | 0.997903 | + | 0.0647208i | \(0.0206157\pi\) | ||||
−0.997903 | + | 0.0647208i | \(0.979384\pi\) | |||||||
\(942\) | 1.03751e9 | − | 7.34744e8i | 1.24119 | − | 0.878989i | ||||
\(943\) | 1.00108e9i | 1.19381i | ||||||||
\(944\) | −4.54094e8 | − | 3.64820e8i | −0.539796 | − | 0.433673i | ||||
\(945\) | 5.11601e7 | 0.0606228 | ||||||||
\(946\) | 2.51943e7 | + | 3.55760e7i | 0.0297597 | + | 0.0420227i | ||||
\(947\) | 1.41217e9 | 1.66279 | 0.831396 | − | 0.555680i | \(-0.187542\pi\) | ||||
0.831396 | + | 0.555680i | \(0.187542\pi\) | |||||||
\(948\) | 6.70917e8 | + | 2.36125e8i | 0.787488 | + | 0.277152i | ||||
\(949\) | − | 4.43429e8i | − | 0.518830i | ||||||
\(950\) | −1.88281e8 | − | 2.65866e8i | −0.219602 | − | 0.310093i | ||||
\(951\) | − | 1.34993e9i | − | 1.56953i | ||||||
\(952\) | 1.41946e7 | + | 4.97772e7i | 0.0164517 | + | 0.0576925i | ||||
\(953\) | −1.38550e9 | −1.60077 | −0.800385 | − | 0.599486i | \(-0.795372\pi\) | ||||
−0.800385 | + | 0.599486i | \(0.795372\pi\) | |||||||
\(954\) | −4.21205e8 | + | 2.98290e8i | −0.485120 | + | 0.343552i | ||||
\(955\) | −4.03029e8 | −0.462729 | ||||||||
\(956\) | −1.05035e9 | − | 3.69664e8i | −1.20215 | − | 0.423091i | ||||
\(957\) | 4.98129e8i | 0.568338i | ||||||||
\(958\) | −6.34729e8 | + | 4.49503e8i | −0.721925 | + | 0.511253i | ||||
\(959\) | − | 7.87028e7i | − | 0.0892348i | ||||||
\(960\) | 8.94435e8 | + | 1.44076e9i | 1.01096 | + | 1.62846i | ||||
\(961\) | 8.30491e8 | 0.935761 | ||||||||
\(962\) | −2.07665e8 | − | 2.93237e8i | −0.233259 | − | 0.329377i | ||||
\(963\) | 5.92622e8 | 0.663589 | ||||||||
\(964\) | −2.84808e8 | + | 8.09242e8i | −0.317922 | + | 0.903332i | ||||
\(965\) | 1.57777e9i | 1.75574i | ||||||||
\(966\) | 5.67565e7 | + | 8.01441e7i | 0.0629628 | + | 0.0889078i | ||||
\(967\) | − | 1.22400e9i | − | 1.35364i | −0.736148 | − | 0.676821i | \(-0.763357\pi\) | ||
0.736148 | − | 0.676821i | \(-0.236643\pi\) | |||||||
\(968\) | −4.51753e8 | + | 1.28823e8i | −0.498052 | + | 0.142026i | ||||
\(969\) | 2.83324e8 | 0.311395 | ||||||||
\(970\) | −8.36151e8 | + | 5.92146e8i | −0.916156 | + | 0.648804i | ||||
\(971\) | −8.21087e8 | −0.896874 | −0.448437 | − | 0.893814i | \(-0.648019\pi\) | ||||
−0.448437 | + | 0.893814i | \(0.648019\pi\) | |||||||
\(972\) | −2.55253e8 | + | 7.25265e8i | −0.277953 | + | 0.789766i | ||||
\(973\) | 3.72510e7i | 0.0404389i | ||||||||
\(974\) | 5.89169e8 | − | 4.17238e8i | 0.637622 | − | 0.451552i | ||||
\(975\) | − | 1.20997e9i | − | 1.30546i | ||||||
\(976\) | 2.47497e8 | − | 3.08062e8i | 0.266208 | − | 0.331351i | ||||
\(977\) | −3.89473e8 | −0.417632 | −0.208816 | − | 0.977955i | \(-0.566961\pi\) | ||||
−0.208816 | + | 0.977955i | \(0.566961\pi\) | |||||||
\(978\) | 2.74910e8 | + | 3.88191e8i | 0.293882 | + | 0.414982i | ||||
\(979\) | −4.01782e8 | −0.428196 | ||||||||
\(980\) | 1.40935e9 | + | 4.96012e8i | 1.49741 | + | 0.527004i | ||||
\(981\) | − | 4.67477e8i | − | 0.495169i | ||||||
\(982\) | 4.66813e8 | + | 6.59172e8i | 0.492956 | + | 0.696088i | ||||
\(983\) | − | 1.66072e9i | − | 1.74838i | −0.485584 | − | 0.874190i | \(-0.661393\pi\) | ||
0.485584 | − | 0.874190i | \(-0.338607\pi\) | |||||||
\(984\) | 8.33733e8 | − | 2.37749e8i | 0.875067 | − | 0.249537i | ||||
\(985\) | −8.21794e8 | −0.859913 | ||||||||
\(986\) | 5.56737e8 | − | 3.94271e8i | 0.580791 | − | 0.411305i | ||||
\(987\) | −4.11865e7 | −0.0428355 | ||||||||
\(988\) | −1.58805e8 | − | 5.58904e7i | −0.164662 | − | 0.0579517i | ||||
\(989\) | − | 1.13273e8i | − | 0.117095i | ||||||
\(990\) | 3.92608e8 | − | 2.78037e8i | 0.404625 | − | 0.286548i | ||||
\(991\) | − | 3.03432e8i | − | 0.311775i | −0.987775 | − | 0.155887i | \(-0.950176\pi\) | ||
0.987775 | − | 0.155887i | \(-0.0498237\pi\) | |||||||
\(992\) | 2.46965e8 | + | 1.49884e7i | 0.252988 | + | 0.0153539i | ||||
\(993\) | −5.81632e8 | −0.594019 | ||||||||
\(994\) | −5.05645e7 | − | 7.14006e7i | −0.0514857 | − | 0.0727014i | ||||
\(995\) | 2.35310e9 | 2.38875 | ||||||||
\(996\) | −6.41763e8 | + | 1.82348e9i | −0.649526 | + | 1.84554i | ||||
\(997\) | 1.20614e9i | 1.21706i | 0.793532 | + | 0.608528i | \(0.208240\pi\) | ||||
−0.793532 | + | 0.608528i | \(0.791760\pi\) | |||||||
\(998\) | 6.83438e8 | + | 9.65062e8i | 0.687555 | + | 0.970876i | ||||
\(999\) | 3.78435e8i | 0.379573i |
(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 | 8.7.d.b.3.1 | ✓ | 4 | |
3.2 | odd | 2 | 72.7.b.b.19.4 | 4 | |||
4.3 | odd | 2 | 32.7.d.b.15.3 | 4 | |||
8.3 | odd | 2 | inner | 8.7.d.b.3.2 | yes | 4 | |
8.5 | even | 2 | 32.7.d.b.15.4 | 4 | |||
12.11 | even | 2 | 288.7.b.b.271.4 | 4 | |||
16.3 | odd | 4 | 256.7.c.l.255.7 | 8 | |||
16.5 | even | 4 | 256.7.c.l.255.8 | 8 | |||
16.11 | odd | 4 | 256.7.c.l.255.2 | 8 | |||
16.13 | even | 4 | 256.7.c.l.255.1 | 8 | |||
24.5 | odd | 2 | 288.7.b.b.271.1 | 4 | |||
24.11 | even | 2 | 72.7.b.b.19.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.7.d.b.3.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
8.7.d.b.3.2 | yes | 4 | 8.3 | odd | 2 | inner | |
32.7.d.b.15.3 | 4 | 4.3 | odd | 2 | |||
32.7.d.b.15.4 | 4 | 8.5 | even | 2 | |||
72.7.b.b.19.3 | 4 | 24.11 | even | 2 | |||
72.7.b.b.19.4 | 4 | 3.2 | odd | 2 | |||
256.7.c.l.255.1 | 8 | 16.13 | even | 4 | |||
256.7.c.l.255.2 | 8 | 16.11 | odd | 4 | |||
256.7.c.l.255.7 | 8 | 16.3 | odd | 4 | |||
256.7.c.l.255.8 | 8 | 16.5 | even | 4 | |||
288.7.b.b.271.1 | 4 | 24.5 | odd | 2 | |||
288.7.b.b.271.4 | 4 | 12.11 | even | 2 |