Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [162,7,Mod(53,162)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(162, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("162.53");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 162 = 2 \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 162.d (of order \(6\), degree \(2\), not 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: | \(37.2687615464\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{12} \) |
Twist minimal: | no (minimal twist has level 54) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 107.1 | ||
Root | \(-0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 162.107 |
Dual form | 162.7.d.e.53.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).
\(n\) | \(83\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.89898 | − | 2.82843i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 16.0000 | + | 27.7128i | 0.250000 | + | 0.433013i | ||||
\(5\) | −43.4287 | + | 25.0736i | −0.347430 | + | 0.200589i | −0.663553 | − | 0.748130i | \(-0.730952\pi\) |
0.316123 | + | 0.948718i | \(0.397619\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −28.1325 | + | 48.7269i | −0.0820189 | + | 0.142061i | −0.904117 | − | 0.427285i | \(-0.859470\pi\) |
0.822098 | + | 0.569346i | \(0.192803\pi\) | |||||||
\(8\) | − | 181.019i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 283.675 | 0.283675 | ||||||||
\(11\) | 1412.94 | + | 815.764i | 1.06157 | + | 0.612896i | 0.925865 | − | 0.377854i | \(-0.123338\pi\) |
0.135701 | + | 0.990750i | \(0.456671\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1735.09 | − | 3005.26i | −0.789752 | − | 1.36789i | −0.926119 | − | 0.377233i | \(-0.876876\pi\) |
0.136366 | − | 0.990658i | \(-0.456458\pi\) | |||||||
\(14\) | 275.641 | − | 159.141i | 0.100452 | − | 0.0579961i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −512.000 | + | 886.810i | −0.125000 | + | 0.216506i | ||||
\(17\) | 599.995i | 0.122124i | 0.998134 | + | 0.0610620i | \(0.0194487\pi\) | ||||
−0.998134 | + | 0.0610620i | \(0.980551\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5353.81 | 0.780553 | 0.390276 | − | 0.920698i | \(-0.372379\pi\) | ||||
0.390276 | + | 0.920698i | \(0.372379\pi\) | |||||||
\(20\) | −1389.72 | − | 802.355i | −0.173715 | − | 0.100294i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4614.66 | − | 7992.82i | −0.433383 | − | 0.750641i | ||||
\(23\) | 817.994 | − | 472.269i | 0.0672306 | − | 0.0388156i | −0.466008 | − | 0.884781i | \(-0.654308\pi\) |
0.533238 | + | 0.845965i | \(0.320975\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6555.13 | + | 11353.8i | −0.419528 | + | 0.726644i | ||||
\(26\) | 19630.3i | 1.11688i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1800.48 | −0.0820189 | ||||||||
\(29\) | 13159.6 | + | 7597.70i | 0.539571 | + | 0.311522i | 0.744905 | − | 0.667170i | \(-0.232495\pi\) |
−0.205334 | + | 0.978692i | \(0.565828\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −21167.0 | − | 36662.3i | −0.710517 | − | 1.23065i | −0.964663 | − | 0.263486i | \(-0.915128\pi\) |
0.254146 | − | 0.967166i | \(-0.418206\pi\) | |||||||
\(32\) | 5016.55 | − | 2896.31i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1697.04 | − | 2939.36i | 0.0431773 | − | 0.0747853i | ||||
\(35\) | − | 2821.53i | − | 0.0658082i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −53825.9 | −1.06264 | −0.531320 | − | 0.847171i | \(-0.678304\pi\) | ||||
−0.531320 | + | 0.847171i | \(0.678304\pi\) | |||||||
\(38\) | −26228.2 | − | 15142.9i | −0.477989 | − | 0.275967i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4538.81 | + | 7861.44i | 0.0709188 | + | 0.122835i | ||||
\(41\) | −97537.2 | + | 56313.1i | −1.41520 | + | 0.817068i | −0.995872 | − | 0.0907662i | \(-0.971068\pi\) |
−0.419330 | + | 0.907834i | \(0.637735\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 38675.4 | − | 66987.7i | 0.486440 | − | 0.842538i | −0.513439 | − | 0.858126i | \(-0.671629\pi\) |
0.999879 | + | 0.0155879i | \(0.00496197\pi\) | |||||||
\(44\) | 52208.9i | 0.612896i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5343.12 | −0.0548935 | ||||||||
\(47\) | 164513. | + | 94981.5i | 1.58455 | + | 0.914840i | 0.994183 | + | 0.107705i | \(0.0343503\pi\) |
0.590367 | + | 0.807135i | \(0.298983\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 57241.6 | + | 99145.4i | 0.486546 | + | 0.842722i | ||||
\(50\) | 64226.9 | − | 37081.4i | 0.513815 | − | 0.296651i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 55522.7 | − | 96168.2i | 0.394876 | − | 0.683946i | ||||
\(53\) | 243552.i | 1.63592i | 0.575272 | + | 0.817962i | \(0.304896\pi\) | ||||
−0.575272 | + | 0.817962i | \(0.695104\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −81816.5 | −0.491760 | ||||||||
\(56\) | 8820.50 | + | 5092.52i | 0.0502261 | + | 0.0289980i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −42979.1 | − | 74442.0i | −0.220279 | − | 0.381535i | ||||
\(59\) | −72989.8 | + | 42140.7i | −0.355391 | + | 0.205185i | −0.667057 | − | 0.745007i | \(-0.732446\pi\) |
0.311666 | + | 0.950192i | \(0.399113\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −49191.3 | + | 85201.9i | −0.216720 | + | 0.375370i | −0.953803 | − | 0.300432i | \(-0.902869\pi\) |
0.737083 | + | 0.675802i | \(0.236203\pi\) | |||||||
\(62\) | 239477.i | 1.00482i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −32768.0 | −0.125000 | ||||||||
\(65\) | 150705. | + | 87009.7i | 0.548767 | + | 0.316831i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 123800. | + | 214427.i | 0.411618 | + | 0.712944i | 0.995067 | − | 0.0992064i | \(-0.0316304\pi\) |
−0.583449 | + | 0.812150i | \(0.698297\pi\) | |||||||
\(68\) | −16627.5 | + | 9599.92i | −0.0528812 | + | 0.0305310i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7980.49 | + | 13822.6i | −0.0232667 | + | 0.0402992i | ||||
\(71\) | 411915.i | 1.15089i | 0.817842 | + | 0.575443i | \(0.195170\pi\) | ||||
−0.817842 | + | 0.575443i | \(0.804830\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 368946. | 0.948406 | 0.474203 | − | 0.880416i | \(-0.342736\pi\) | ||||
0.474203 | + | 0.880416i | \(0.342736\pi\) | |||||||
\(74\) | 263692. | + | 152243.i | 0.650732 | + | 0.375700i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 85661.0 | + | 148369.i | 0.195138 | + | 0.337989i | ||||
\(77\) | −79499.2 | + | 45898.9i | −0.174137 | + | 0.100538i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −421907. | + | 730765.i | −0.855728 | + | 1.48216i | 0.0202403 | + | 0.999795i | \(0.493557\pi\) |
−0.875968 | + | 0.482369i | \(0.839776\pi\) | |||||||
\(80\) | − | 51350.7i | − | 0.100294i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 637110. | 1.15551 | ||||||||
\(83\) | 407498. | + | 235269.i | 0.712675 | + | 0.411463i | 0.812051 | − | 0.583587i | \(-0.198351\pi\) |
−0.0993759 | + | 0.995050i | \(0.531685\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15044.0 | − | 26057.0i | −0.0244967 | − | 0.0424295i | ||||
\(86\) | −378940. | + | 218781.i | −0.595765 | + | 0.343965i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 147669. | − | 255770.i | 0.216691 | − | 0.375320i | ||||
\(89\) | 752753.i | 1.06778i | 0.845553 | + | 0.533891i | \(0.179271\pi\) | ||||
−0.845553 | + | 0.533891i | \(0.820729\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 195249. | 0.259098 | ||||||||
\(92\) | 26175.8 | + | 15112.6i | 0.0336153 | + | 0.0194078i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −537296. | − | 930624.i | −0.646890 | − | 1.12045i | ||||
\(95\) | −232509. | + | 134239.i | −0.271187 | + | 0.156570i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −230930. | + | 399983.i | −0.253026 | + | 0.438254i | −0.964358 | − | 0.264603i | \(-0.914759\pi\) |
0.711331 | + | 0.702857i | \(0.248093\pi\) | |||||||
\(98\) | − | 647615.i | − | 0.688080i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −419528. | −0.419528 | ||||||||
\(101\) | −1.06425e6 | − | 614444.i | −1.03295 | − | 0.596373i | −0.115121 | − | 0.993352i | \(-0.536725\pi\) |
−0.917828 | + | 0.396978i | \(0.870059\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 273863. | + | 474344.i | 0.250623 | + | 0.434092i | 0.963698 | − | 0.266996i | \(-0.0860311\pi\) |
−0.713074 | + | 0.701088i | \(0.752698\pi\) | |||||||
\(104\) | −544010. | + | 314084.i | −0.483623 | + | 0.279220i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 688868. | − | 1.19315e6i | 0.578387 | − | 1.00180i | ||||
\(107\) | 90822.4i | 0.0741381i | 0.999313 | + | 0.0370690i | \(0.0118021\pi\) | ||||
−0.999313 | + | 0.0370690i | \(0.988198\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.08845e6 | −0.840485 | −0.420242 | − | 0.907412i | \(-0.638055\pi\) | ||||
−0.420242 | + | 0.907412i | \(0.638055\pi\) | |||||||
\(110\) | 400818. | + | 231412.i | 0.301140 | + | 0.173863i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −28807.6 | − | 49896.3i | −0.0205047 | − | 0.0355152i | ||||
\(113\) | 2.15675e6 | − | 1.24520e6i | 1.49474 | − | 0.862987i | 0.494756 | − | 0.869032i | \(-0.335257\pi\) |
0.999982 | + | 0.00604466i | \(0.00192409\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −23683.0 | + | 41020.1i | −0.0155719 | + | 0.0269714i | ||||
\(116\) | 486253.i | 0.311522i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 476768. | 0.290175 | ||||||||
\(119\) | −29235.9 | − | 16879.3i | −0.0173490 | − | 0.0100165i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 445162. | + | 771042.i | 0.251282 | + | 0.435233i | ||||
\(122\) | 481975. | − | 278268.i | 0.265427 | − | 0.153244i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 677344. | − | 1.17319e6i | 0.355259 | − | 0.615326i | ||||
\(125\) | − | 1.44099e6i | − | 0.737788i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.12962e6 | −1.52785 | −0.763924 | − | 0.645306i | \(-0.776730\pi\) | ||||
−0.763924 | + | 0.645306i | \(0.776730\pi\) | |||||||
\(128\) | 160530. | + | 92681.9i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −492201. | − | 852517.i | −0.224033 | − | 0.388037i | ||||
\(131\) | −973306. | + | 561939.i | −0.432948 | + | 0.249963i | −0.700602 | − | 0.713553i | \(-0.747085\pi\) |
0.267654 | + | 0.963515i | \(0.413752\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −150616. | + | 260875.i | −0.0640201 | + | 0.110886i | ||||
\(134\) | − | 1.40063e6i | − | 0.582116i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 108611. | 0.0431773 | ||||||||
\(137\) | −1.82514e6 | − | 1.05374e6i | −0.709797 | − | 0.409802i | 0.101189 | − | 0.994867i | \(-0.467735\pi\) |
−0.810986 | + | 0.585066i | \(0.801069\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −78992.8 | − | 136820.i | −0.0294133 | − | 0.0509453i | 0.850944 | − | 0.525256i | \(-0.176031\pi\) |
−0.880357 | + | 0.474311i | \(0.842697\pi\) | |||||||
\(140\) | 78192.5 | − | 45144.5i | 0.0284958 | − | 0.0164521i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.16507e6 | − | 2.01796e6i | 0.406900 | − | 0.704771i | ||||
\(143\) | − | 5.66168e6i | − | 1.93614i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −762007. | −0.249951 | ||||||||
\(146\) | −1.80746e6 | − | 1.04354e6i | −0.580777 | − | 0.335312i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −861215. | − | 1.49167e6i | −0.265660 | − | 0.460137i | ||||
\(149\) | −176935. | + | 102154.i | −0.0534879 | + | 0.0308812i | −0.526505 | − | 0.850172i | \(-0.676498\pi\) |
0.473018 | + | 0.881053i | \(0.343165\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.48147e6 | + | 2.56597e6i | −0.430289 | + | 0.745283i | −0.996898 | − | 0.0787039i | \(-0.974922\pi\) |
0.566609 | + | 0.823987i | \(0.308255\pi\) | |||||||
\(152\) | − | 969144.i | − | 0.275967i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 519287. | 0.142182 | ||||||||
\(155\) | 1.83851e6 | + | 1.06147e6i | 0.493710 | + | 0.285043i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.30241e6 | + | 2.25585e6i | 0.336550 | + | 0.582922i | 0.983781 | − | 0.179372i | \(-0.0574065\pi\) |
−0.647231 | + | 0.762294i | \(0.724073\pi\) | |||||||
\(158\) | 4.13383e6 | − | 2.38667e6i | 1.04805 | − | 0.605091i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −145242. | + | 251566.i | −0.0354594 | + | 0.0614175i | ||||
\(161\) | 53144.4i | 0.0127344i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.62696e6 | 1.29930 | 0.649652 | − | 0.760232i | \(-0.274915\pi\) | ||||
0.649652 | + | 0.760232i | \(0.274915\pi\) | |||||||
\(164\) | −3.12119e6 | − | 1.80202e6i | −0.707601 | − | 0.408534i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.33088e6 | − | 2.30516e6i | −0.290948 | − | 0.503937i | ||||
\(167\) | −1.52697e6 | + | 881596.i | −0.327854 | + | 0.189287i | −0.654888 | − | 0.755726i | \(-0.727284\pi\) |
0.327034 | + | 0.945013i | \(0.393951\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.60764e6 | + | 6.24862e6i | −0.747417 | + | 1.29456i | ||||
\(170\) | 170204.i | 0.0346435i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.47522e6 | 0.486440 | ||||||||
\(173\) | −6.95934e6 | − | 4.01798e6i | −1.34409 | − | 0.776013i | −0.356689 | − | 0.934223i | \(-0.616094\pi\) |
−0.987406 | + | 0.158210i | \(0.949428\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −368824. | − | 638822.i | −0.0688185 | − | 0.119197i | ||||
\(176\) | −1.44686e6 | + | 835342.i | −0.265392 | + | 0.153224i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.12911e6 | − | 3.68772e6i | 0.377518 | − | 0.653880i | ||||
\(179\) | − | 9.88186e6i | − | 1.72298i | −0.507776 | − | 0.861489i | \(-0.669532\pi\) | ||
0.507776 | − | 0.861489i | \(-0.330468\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.82714e6 | 0.645414 | 0.322707 | − | 0.946499i | \(-0.395407\pi\) | ||||
0.322707 | + | 0.946499i | \(0.395407\pi\) | |||||||
\(182\) | −956521. | − | 552247.i | −0.158665 | − | 0.0916051i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −85489.9 | − | 148073.i | −0.0137234 | − | 0.0237696i | ||||
\(185\) | 2.33759e6 | − | 1.34961e6i | 0.369193 | − | 0.213154i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −489454. | + | 847760.i | −0.0748492 | + | 0.129643i | ||||
\(188\) | 6.07881e6i | 0.914840i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.51874e6 | 0.221424 | ||||||||
\(191\) | 3.79194e6 | + | 2.18928e6i | 0.544204 | + | 0.314196i | 0.746781 | − | 0.665070i | \(-0.231598\pi\) |
−0.202577 | + | 0.979266i | \(0.564932\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 445928. | + | 772370.i | 0.0620287 | + | 0.107437i | 0.895372 | − | 0.445319i | \(-0.146910\pi\) |
−0.833343 | + | 0.552756i | \(0.813576\pi\) | |||||||
\(194\) | 2.26264e6 | − | 1.30634e6i | 0.309892 | − | 0.178916i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.83173e6 | + | 3.17265e6i | −0.243273 | + | 0.421361i | ||||
\(197\) | 4.90719e6i | 0.641850i | 0.947105 | + | 0.320925i | \(0.103994\pi\) | ||||
−0.947105 | + | 0.320925i | \(0.896006\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.34946e6 | −1.05950 | −0.529748 | − | 0.848155i | \(-0.677713\pi\) | ||||
−0.529748 | + | 0.848155i | \(0.677713\pi\) | |||||||
\(200\) | 2.05526e6 | + | 1.18661e6i | 0.256908 | + | 0.148326i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.47582e6 | + | 6.02029e6i | 0.421699 | + | 0.730405i | ||||
\(203\) | −740424. | + | 427484.i | −0.0885101 | + | 0.0511013i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.82394e6 | − | 4.89121e6i | 0.327789 | − | 0.567747i | ||||
\(206\) | − | 3.09840e6i | − | 0.354435i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.55346e6 | 0.394876 | ||||||||
\(209\) | 7.56464e6 | + | 4.36745e6i | 0.828609 | + | 0.478398i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.48355e6 | + | 1.12298e7i | 0.690185 | + | 1.19544i | 0.971777 | + | 0.235902i | \(0.0758044\pi\) |
−0.281592 | + | 0.959534i | \(0.590862\pi\) | |||||||
\(212\) | −6.74950e6 | + | 3.89682e6i | −0.708376 | + | 0.408981i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 256884. | − | 444937.i | 0.0262118 | − | 0.0454001i | ||||
\(215\) | 3.87892e6i | 0.390297i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.38192e6 | 0.233103 | ||||||||
\(218\) | 5.33230e6 | + | 3.07861e6i | 0.514690 | + | 0.297156i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.30906e6 | − | 2.26737e6i | −0.122940 | − | 0.212938i | ||||
\(221\) | 1.80314e6 | − | 1.04104e6i | 0.167052 | − | 0.0964476i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.88621e6 | + | 3.26702e6i | −0.170089 | + | 0.294603i | −0.938451 | − | 0.345413i | \(-0.887739\pi\) |
0.768362 | + | 0.640016i | \(0.221072\pi\) | |||||||
\(224\) | 325921.i | 0.0289980i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.40878e7 | −1.22045 | ||||||||
\(227\) | 4.35856e6 | + | 2.51641e6i | 0.372619 | + | 0.215132i | 0.674602 | − | 0.738182i | \(-0.264315\pi\) |
−0.301983 | + | 0.953313i | \(0.597649\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.43726e6 | − | 2.48941e6i | −0.119682 | − | 0.207295i | 0.799960 | − | 0.600054i | \(-0.204854\pi\) |
−0.919642 | + | 0.392758i | \(0.871521\pi\) | |||||||
\(230\) | 232045. | − | 133971.i | 0.0190717 | − | 0.0110110i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.37533e6 | − | 2.38214e6i | 0.110140 | − | 0.190767i | ||||
\(233\) | 2.23245e7i | 1.76487i | 0.470431 | + | 0.882437i | \(0.344098\pi\) | ||||
−0.470431 | + | 0.882437i | \(0.655902\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.52611e6 | −0.734027 | ||||||||
\(236\) | −2.33567e6 | − | 1.34850e6i | −0.177695 | − | 0.102593i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 95483.9 | + | 165383.i | 0.00708271 | + | 0.0122676i | ||||
\(239\) | −1.01660e7 | + | 5.86937e6i | −0.744661 | + | 0.429930i | −0.823761 | − | 0.566937i | \(-0.808128\pi\) |
0.0791008 | + | 0.996867i | \(0.474795\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.32692e7 | − | 2.29829e7i | 0.947969 | − | 1.64193i | 0.198273 | − | 0.980147i | \(-0.436467\pi\) |
0.749696 | − | 0.661783i | \(-0.230200\pi\) | |||||||
\(242\) | − | 5.03643e6i | − | 0.355367i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.14825e6 | −0.216720 | ||||||||
\(245\) | −4.97186e6 | − | 2.87051e6i | −0.338081 | − | 0.195191i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.28932e6 | − | 1.60896e7i | −0.616443 | − | 1.06771i | ||||
\(248\) | −6.63659e6 | + | 3.83164e6i | −0.435101 | + | 0.251206i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.07574e6 | + | 7.05939e6i | −0.260847 | + | 0.451801i | ||||
\(251\) | 2.64855e7i | 1.67489i | 0.546521 | + | 0.837446i | \(0.315952\pi\) | ||||
−0.546521 | + | 0.837446i | \(0.684048\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.54104e6 | 0.0951596 | ||||||||
\(254\) | 1.53319e7 | + | 8.85189e6i | 0.935612 | + | 0.540176i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −524288. | − | 908093.i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 1.93078e7 | − | 1.11473e7i | 1.13745 | − | 0.656708i | 0.191653 | − | 0.981463i | \(-0.438615\pi\) |
0.945798 | + | 0.324755i | \(0.105282\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.51426e6 | − | 2.62277e6i | 0.0871565 | − | 0.150960i | ||||
\(260\) | 5.56862e6i | 0.316831i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.35761e6 | 0.353501 | ||||||||
\(263\) | −1.50734e6 | − | 870261.i | −0.0828596 | − | 0.0478390i | 0.457998 | − | 0.888953i | \(-0.348567\pi\) |
−0.540857 | + | 0.841114i | \(0.681900\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.10671e6 | − | 1.05771e7i | −0.328148 | − | 0.568369i | ||||
\(266\) | 1.47573e6 | − | 852013.i | 0.0784082 | − | 0.0452690i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.96158e6 | + | 6.86167e6i | −0.205809 | + | 0.356472i | ||||
\(269\) | 3.21970e6i | 0.165409i | 0.996574 | + | 0.0827044i | \(0.0263557\pi\) | ||||
−0.996574 | + | 0.0827044i | \(0.973644\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.71025e6 | 0.437646 | 0.218823 | − | 0.975765i | \(-0.429778\pi\) | ||||
0.218823 | + | 0.975765i | \(0.429778\pi\) | |||||||
\(272\) | −532081. | − | 307197.i | −0.0264406 | − | 0.0152655i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.96088e6 | + | 1.03245e7i | 0.289774 | + | 0.501903i | ||||
\(275\) | −1.85241e7 | + | 1.06949e7i | −0.890714 | + | 0.514254i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.37163e6 | + | 4.10779e6i | −0.111586 | + | 0.193272i | −0.916410 | − | 0.400241i | \(-0.868926\pi\) |
0.804824 | + | 0.593513i | \(0.202260\pi\) | |||||||
\(278\) | 893702.i | 0.0415967i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −510751. | −0.0232667 | ||||||||
\(281\) | 6.35229e6 | + | 3.66750e6i | 0.286294 | + | 0.165292i | 0.636269 | − | 0.771467i | \(-0.280477\pi\) |
−0.349976 | + | 0.936759i | \(0.613810\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.93466e7 | − | 3.35093e7i | −0.853581 | − | 1.47845i | −0.877955 | − | 0.478743i | \(-0.841093\pi\) |
0.0243739 | − | 0.999703i | \(-0.492241\pi\) | |||||||
\(284\) | −1.14153e7 | + | 6.59064e6i | −0.498348 | + | 0.287722i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.60137e7 | + | 2.77365e7i | −0.684530 | + | 1.18564i | ||||
\(287\) | − | 6.33691e6i | − | 0.268060i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.37776e7 | 0.985086 | ||||||||
\(290\) | 3.73306e6 | + | 2.15528e6i | 0.153063 | + | 0.0883710i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.90313e6 | + | 1.02245e7i | 0.237101 | + | 0.410672i | ||||
\(293\) | −2.03760e7 | + | 1.17641e7i | −0.810058 | + | 0.467687i | −0.846976 | − | 0.531631i | \(-0.821579\pi\) |
0.0369179 | + | 0.999318i | \(0.488246\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.11324e6 | − | 3.66023e6i | 0.0823156 | − | 0.142575i | ||||
\(296\) | 9.74353e6i | 0.375700i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.15574e6 | 0.0436727 | ||||||||
\(299\) | −2.83858e6 | − | 1.63886e6i | −0.106191 | − | 0.0613094i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.17607e6 | + | 3.76906e6i | 0.0797945 | + | 0.138208i | ||||
\(302\) | 1.45153e7 | − | 8.38043e6i | 0.526995 | − | 0.304261i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.74115e6 | + | 4.74781e6i | −0.0975691 | + | 0.168995i | ||||
\(305\) | − | 4.93361e6i | − | 0.173886i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.92808e7 | −0.666360 | −0.333180 | − | 0.942863i | \(-0.608122\pi\) | ||||
−0.333180 | + | 0.942863i | \(0.608122\pi\) | |||||||
\(308\) | −2.54398e6 | − | 1.46877e6i | −0.0870685 | − | 0.0502690i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.00456e6 | − | 1.04002e7i | −0.201556 | − | 0.349105i | ||||
\(311\) | 2.70295e7 | − | 1.56055e7i | 0.898582 | − | 0.518796i | 0.0218419 | − | 0.999761i | \(-0.493047\pi\) |
0.876740 | + | 0.480965i | \(0.159714\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.76015e6 | − | 3.04866e6i | 0.0574005 | − | 0.0994206i | −0.835897 | − | 0.548886i | \(-0.815052\pi\) |
0.893298 | + | 0.449465i | \(0.148385\pi\) | |||||||
\(314\) | − | 1.47351e7i | − | 0.475954i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.70021e7 | −0.855728 | ||||||||
\(317\) | 4.11426e7 | + | 2.37537e7i | 1.29156 | + | 0.745682i | 0.978931 | − | 0.204193i | \(-0.0654570\pi\) |
0.312629 | + | 0.949875i | \(0.398790\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.23959e7 | + | 2.14703e7i | 0.381861 | + | 0.661402i | ||||
\(320\) | 1.42307e6 | − | 821611.i | 0.0434287 | − | 0.0250736i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 150315. | − | 260353.i | 0.00450230 | − | 0.00779822i | ||||
\(323\) | 3.21226e6i | 0.0953242i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.54948e7 | 1.32529 | ||||||||
\(326\) | −2.75664e7 | − | 1.59154e7i | −0.795658 | − | 0.459374i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.01938e7 | + | 1.76561e7i | 0.288877 | + | 0.500350i | ||||
\(329\) | −9.25630e6 | + | 5.34413e6i | −0.259926 | + | 0.150068i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.44968e6 | − | 9.43912e6i | 0.150275 | − | 0.260284i | −0.781053 | − | 0.624464i | \(-0.785317\pi\) |
0.931329 | + | 0.364180i | \(0.118651\pi\) | |||||||
\(332\) | 1.50572e7i | 0.411463i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9.97412e6 | 0.267692 | ||||||||
\(335\) | −1.07529e7 | − | 6.20820e6i | −0.286017 | − | 0.165132i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.38414e7 | + | 4.12946e7i | 0.622935 | + | 1.07895i | 0.988936 | + | 0.148341i | \(0.0473932\pi\) |
−0.366001 | + | 0.930614i | \(0.619273\pi\) | |||||||
\(338\) | 3.53475e7 | − | 2.04079e7i | 0.915395 | − | 0.528504i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 481409. | − | 833825.i | 0.0122483 | − | 0.0212147i | ||||
\(341\) | − | 6.90692e7i | − | 1.74189i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.30609e7 | −0.323661 | ||||||||
\(344\) | −1.21261e7 | − | 7.00099e6i | −0.297882 | − | 0.171982i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.27291e7 | + | 3.93680e7i | 0.548724 | + | 0.950418i | ||||
\(347\) | 2.23319e7 | − | 1.28933e7i | 0.534487 | − | 0.308586i | −0.208355 | − | 0.978053i | \(-0.566811\pi\) |
0.742842 | + | 0.669467i | \(0.233477\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.94007e7 | − | 5.09235e7i | 0.691642 | − | 1.19796i | −0.279658 | − | 0.960100i | \(-0.590221\pi\) |
0.971300 | − | 0.237859i | \(-0.0764457\pi\) | |||||||
\(350\) | 4.17277e6i | 0.0973240i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 9.45082e6 | 0.216691 | ||||||||
\(353\) | −6.54573e7 | − | 3.77918e7i | −1.48811 | − | 0.859159i | −0.488199 | − | 0.872732i | \(-0.662346\pi\) |
−0.999908 | + | 0.0135736i | \(0.995679\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.03282e7 | − | 1.78889e7i | −0.230855 | − | 0.399852i | ||||
\(356\) | −2.08609e7 | + | 1.20441e7i | −0.462363 | + | 0.266946i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.79501e7 | + | 4.84110e7i | −0.609165 | + | 1.05510i | ||||
\(359\) | − | 4.56033e7i | − | 0.985628i | −0.870135 | − | 0.492814i | \(-0.835968\pi\) | ||
0.870135 | − | 0.492814i | \(-0.164032\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.83826e7 | −0.390737 | ||||||||
\(362\) | −1.87491e7 | − | 1.08248e7i | −0.395234 | − | 0.228188i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.12398e6 | + | 5.41090e6i | 0.0647746 | + | 0.112193i | ||||
\(365\) | −1.60229e7 | + | 9.25080e6i | −0.329504 | + | 0.190239i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.57052e7 | − | 2.72022e7i | 0.317721 | − | 0.550309i | −0.662291 | − | 0.749247i | \(-0.730416\pi\) |
0.980012 | + | 0.198938i | \(0.0637491\pi\) | |||||||
\(368\) | 967207.i | 0.0194078i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.52691e7 | −0.301445 | ||||||||
\(371\) | −1.18675e7 | − | 6.85171e6i | −0.232401 | − | 0.134177i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.69047e6 | − | 9.85619e6i | −0.109653 | − | 0.189925i | 0.805977 | − | 0.591948i | \(-0.201641\pi\) |
−0.915630 | + | 0.402022i | \(0.868307\pi\) | |||||||
\(374\) | 4.79565e6 | − | 2.76877e6i | 0.0916712 | − | 0.0529264i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.71935e7 | − | 2.97800e7i | 0.323445 | − | 0.560223i | ||||
\(377\) | − | 5.27307e7i | − | 0.984100i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.52964e7 | −0.832044 | −0.416022 | − | 0.909355i | \(-0.636576\pi\) | ||||
−0.416022 | + | 0.909355i | \(0.636576\pi\) | |||||||
\(380\) | −7.44030e6 | − | 4.29566e6i | −0.135594 | − | 0.0782851i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.23844e7 | − | 2.14505e7i | −0.222170 | − | 0.384810i | ||||
\(383\) | 2.83885e7 | − | 1.63901e7i | 0.505297 | − | 0.291733i | −0.225602 | − | 0.974220i | \(-0.572435\pi\) |
0.730898 | + | 0.682486i | \(0.239101\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.30170e6 | − | 3.98666e6i | 0.0403336 | − | 0.0698598i | ||||
\(386\) | − | 5.04510e6i | − | 0.0877219i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.47795e7 | −0.253026 | ||||||||
\(389\) | 2.98843e7 | + | 1.72537e7i | 0.507686 | + | 0.293113i | 0.731882 | − | 0.681432i | \(-0.238642\pi\) |
−0.224196 | + | 0.974544i | \(0.571976\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 283359. | + | 490792.i | 0.00474031 | + | 0.00821046i | ||||
\(392\) | 1.79472e7 | − | 1.03618e7i | 0.297947 | − | 0.172020i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.38796e7 | − | 2.40402e7i | 0.226928 | − | 0.393051i | ||||
\(395\) | − | 4.23149e7i | − | 0.686597i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.72396e7 | 0.914798 | 0.457399 | − | 0.889262i | \(-0.348781\pi\) | ||||
0.457399 | + | 0.889262i | \(0.348781\pi\) | |||||||
\(398\) | 4.09038e7 | + | 2.36158e7i | 0.648806 | + | 0.374588i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.71245e6 | − | 1.16263e7i | −0.104882 | − | 0.181661i | ||||
\(401\) | −6.90479e7 | + | 3.98648e7i | −1.07082 | + | 0.618239i | −0.928406 | − | 0.371568i | \(-0.878820\pi\) |
−0.142416 | + | 0.989807i | \(0.545487\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.34532e7 | + | 1.27225e8i | −1.12226 | + | 1.94382i | ||||
\(404\) | − | 3.93244e7i | − | 0.596373i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.83643e6 | 0.0722682 | ||||||||
\(407\) | −7.60531e7 | − | 4.39092e7i | −1.12806 | − | 0.651288i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.39594e7 | − | 4.14989e7i | −0.350192 | − | 0.606550i | 0.636091 | − | 0.771614i | \(-0.280550\pi\) |
−0.986283 | + | 0.165064i | \(0.947217\pi\) | |||||||
\(410\) | −2.76689e7 | + | 1.59746e7i | −0.401458 | + | 0.231782i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8.76361e6 | + | 1.51790e7i | −0.125312 | + | 0.217046i | ||||
\(413\) | − | 4.74209e6i | − | 0.0673162i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.35962e7 | −0.330139 | ||||||||
\(416\) | −1.74083e7 | − | 1.00507e7i | −0.241811 | − | 0.139610i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.47060e7 | − | 4.27921e7i | −0.338278 | − | 0.585915i | ||||
\(419\) | 9.53262e7 | − | 5.50366e7i | 1.29590 | − | 0.748186i | 0.316204 | − | 0.948691i | \(-0.397592\pi\) |
0.979693 | + | 0.200505i | \(0.0642582\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.87470e7 | − | 3.24708e7i | 0.251238 | − | 0.435158i | −0.712629 | − | 0.701541i | \(-0.752496\pi\) |
0.963867 | + | 0.266384i | \(0.0858289\pi\) | |||||||
\(422\) | − | 7.33530e7i | − | 0.976070i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.40875e7 | 0.578387 | ||||||||
\(425\) | −6.81223e6 | − | 3.93304e6i | −0.0887407 | − | 0.0512344i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.76775e6 | − | 4.79388e6i | −0.0355503 | − | 0.0615749i | ||||
\(428\) | −2.51694e6 | + | 1.45316e6i | −0.0321027 | + | 0.0185345i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.09712e7 | − | 1.90028e7i | 0.137991 | − | 0.239007i | ||||
\(431\) | 1.35605e8i | 1.69373i | 0.531810 | + | 0.846864i | \(0.321512\pi\) | ||||
−0.531810 | + | 0.846864i | \(0.678488\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.18161e8 | 1.45549 | 0.727746 | − | 0.685846i | \(-0.240568\pi\) | ||||
0.727746 | + | 0.685846i | \(0.240568\pi\) | |||||||
\(434\) | −1.16690e7 | − | 6.73709e6i | −0.142746 | − | 0.0824144i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.74152e7 | − | 3.01641e7i | −0.210121 | − | 0.363941i | ||||
\(437\) | 4.37939e6 | − | 2.52844e6i | 0.0524770 | − | 0.0302976i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.59907e7 | + | 7.96582e7i | −0.543596 | + | 0.941535i | 0.455098 | + | 0.890441i | \(0.349604\pi\) |
−0.998694 | + | 0.0510942i | \(0.983729\pi\) | |||||||
\(440\) | 1.48104e7i | 0.173863i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.17781e7 | −0.136398 | ||||||||
\(443\) | 1.70594e7 | + | 9.84924e6i | 0.196224 | + | 0.113290i | 0.594893 | − | 0.803805i | \(-0.297194\pi\) |
−0.398669 | + | 0.917095i | \(0.630528\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.88742e7 | − | 3.26911e7i | −0.214185 | − | 0.370980i | ||||
\(446\) | 1.84811e7 | − | 1.06700e7i | 0.208316 | − | 0.120271i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 921845. | − | 1.59668e6i | 0.0102524 | − | 0.0177576i | ||||
\(449\) | 1.38530e7i | 0.153040i | 0.997068 | + | 0.0765199i | \(0.0243809\pi\) | ||||
−0.997068 | + | 0.0765199i | \(0.975619\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.83753e8 | −2.00311 | ||||||||
\(452\) | 6.90161e7 | + | 3.98465e7i | 0.747369 | + | 0.431494i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.42350e7 | − | 2.46557e7i | −0.152121 | − | 0.263481i | ||||
\(455\) | −8.47942e6 | + | 4.89559e6i | −0.0900185 | + | 0.0519722i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.69186e7 | − | 6.39448e7i | 0.386809 | − | 0.669972i | −0.605210 | − | 0.796066i | \(-0.706911\pi\) |
0.992018 | + | 0.126094i | \(0.0402441\pi\) | |||||||
\(458\) | 1.62607e7i | 0.169256i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.51571e6 | −0.0155719 | ||||||||
\(461\) | 4.60339e7 | + | 2.65777e7i | 0.469867 | + | 0.271278i | 0.716184 | − | 0.697912i | \(-0.245887\pi\) |
−0.246317 | + | 0.969189i | \(0.579220\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.74332e7 | − | 8.21567e7i | −0.477903 | − | 0.827752i | 0.521776 | − | 0.853082i | \(-0.325270\pi\) |
−0.999679 | + | 0.0253305i | \(0.991936\pi\) | |||||||
\(464\) | −1.34754e7 | + | 7.78005e6i | −0.134893 | + | 0.0778804i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.31432e7 | − | 1.09367e8i | 0.623977 | − | 1.08076i | ||||
\(467\) | 1.90459e8i | 1.87004i | 0.354598 | + | 0.935019i | \(0.384618\pi\) | ||||
−0.354598 | + | 0.935019i | \(0.615382\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.39311e7 | −0.135042 | ||||||||
\(470\) | 4.66682e7 | + | 2.69439e7i | 0.449498 | + | 0.259518i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.62828e6 | + | 1.32126e7i | 0.0725439 | + | 0.125650i | ||||
\(473\) | 1.09292e8 | − | 6.30999e7i | 1.03278 | − | 0.596274i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.50949e7 | + | 6.07862e7i | −0.327464 | + | 0.567184i | ||||
\(476\) | − | 1.08028e6i | − | 0.0100165i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.64043e7 | 0.608013 | ||||||||
\(479\) | 2.45490e7 | + | 1.41734e7i | 0.223371 | + | 0.128963i | 0.607510 | − | 0.794312i | \(-0.292168\pi\) |
−0.384139 | + | 0.923275i | \(0.625502\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.33926e7 | + | 1.61761e8i | 0.839223 | + | 1.45358i | ||||
\(482\) | −1.30011e8 | + | 7.50620e7i | −1.16102 | + | 0.670315i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.42452e7 | + | 2.46734e7i | −0.125641 | + | 0.217617i | ||||
\(485\) | − | 2.31610e7i | − | 0.203017i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.06414e7 | −0.525028 | −0.262514 | − | 0.964928i | \(-0.584552\pi\) | ||||
−0.262514 | + | 0.964928i | \(0.584552\pi\) | |||||||
\(488\) | 1.54232e7 | + | 8.90458e6i | 0.132713 | + | 0.0766221i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.62380e7 | + | 2.81251e7i | 0.138021 | + | 0.239059i | ||||
\(491\) | −1.34714e8 | + | 7.77769e7i | −1.13806 | + | 0.657062i | −0.945951 | − | 0.324311i | \(-0.894868\pi\) |
−0.192114 | + | 0.981373i | \(0.561534\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.55858e6 | + | 7.89570e6i | −0.0380443 | + | 0.0658946i | ||||
\(494\) | 1.05097e8i | 0.871783i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.33500e7 | 0.355259 | ||||||||
\(497\) | −2.00713e7 | − | 1.15882e7i | −0.163496 | − | 0.0943944i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.46864e7 | + | 1.12040e8i | 0.520609 | + | 0.901721i | 0.999713 | + | 0.0239626i | \(0.00762826\pi\) |
−0.479104 | + | 0.877758i | \(0.659038\pi\) | |||||||
\(500\) | 3.99340e7 | − | 2.30559e7i | 0.319472 | − | 0.184447i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7.49122e7 | − | 1.29752e8i | 0.592163 | − | 1.02566i | ||||
\(503\) | − | 1.43279e8i | − | 1.12585i | −0.826509 | − | 0.562923i | \(-0.809677\pi\) | ||
0.826509 | − | 0.562923i | \(-0.190323\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.16253e7 | 0.478503 | ||||||||
\(506\) | −7.54953e6 | − | 4.35872e6i | −0.0582731 | − | 0.0336440i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.00739e7 | − | 8.67305e7i | −0.381962 | − | 0.661577i | ||||
\(509\) | −1.37466e8 | + | 7.93661e7i | −1.04242 | + | 0.601841i | −0.920517 | − | 0.390702i | \(-0.872232\pi\) |
−0.121901 | + | 0.992542i | \(0.538899\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.03794e7 | + | 1.79776e7i | −0.0777871 | + | 0.134731i | ||||
\(512\) | 5.93164e6i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.26118e8 | −0.928725 | ||||||||
\(515\) | −2.37870e7 | − | 1.37335e7i | −0.174148 | − | 0.100544i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.54965e8 | + | 2.68407e8i | 1.12140 | + | 1.94233i | ||||
\(518\) | −1.48366e7 | + | 8.56592e6i | −0.106745 | + | 0.0616290i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.57504e7 | − | 2.72805e7i | 0.112017 | − | 0.194018i | ||||
\(521\) | 2.21508e8i | 1.56630i | 0.621831 | + | 0.783152i | \(0.286389\pi\) | ||||
−0.621831 | + | 0.783152i | \(0.713611\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.17660e7 | 0.361859 | 0.180930 | − | 0.983496i | \(-0.442089\pi\) | ||||
0.180930 | + | 0.983496i | \(0.442089\pi\) | |||||||
\(524\) | −3.11458e7 | − | 1.79820e7i | −0.216474 | − | 0.124981i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.92294e6 | + | 8.52678e6i | 0.0338273 | + | 0.0585906i | ||||
\(527\) | 2.19972e7 | − | 1.27001e7i | 0.150292 | − | 0.0867711i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.35719e7 | + | 1.27430e8i | −0.496987 | + | 0.860806i | ||||
\(530\) | 6.90896e7i | 0.464071i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −9.63942e6 | −0.0640201 | ||||||||
\(533\) | 3.38471e8 | + | 1.95416e8i | 2.23532 | + | 1.29056i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.27724e6 | − | 3.94430e6i | −0.0148713 | − | 0.0257578i | ||||
\(536\) | 3.88154e7 | − | 2.24101e7i | 0.252064 | − | 0.145529i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9.10669e6 | − | 1.57733e7i | 0.0584809 | − | 0.101292i | ||||
\(539\) | 1.86783e8i | 1.19281i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.49689e7 | 0.0945361 | 0.0472681 | − | 0.998882i | \(-0.484949\pi\) | ||||
0.0472681 | + | 0.998882i | \(0.484949\pi\) | |||||||
\(542\) | −4.26713e7 | − | 2.46363e7i | −0.268002 | − | 0.154731i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.73777e6 | + | 3.00991e6i | 0.0107943 | + | 0.0186963i | ||||
\(545\) | 4.72701e7 | − | 2.72914e7i | 0.292009 | − | 0.168592i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.60003e7 | − | 7.96749e7i | 0.281060 | − | 0.486810i | −0.690586 | − | 0.723250i | \(-0.742647\pi\) |
0.971646 | + | 0.236440i | \(0.0759807\pi\) | |||||||
\(548\) | − | 6.74397e7i | − | 0.409802i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.20999e8 | 0.727265 | ||||||||
\(551\) | 7.04541e7 | + | 4.06767e7i | 0.421164 | + | 0.243159i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.37386e7 | − | 4.11164e7i | −0.140372 | − | 0.243131i | ||||
\(554\) | 2.32372e7 | − | 1.34160e7i | 0.136664 | − | 0.0789030i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.52777e6 | − | 4.37823e6i | 0.0147066 | − | 0.0254726i | ||||
\(557\) | − | 1.53984e8i | − | 0.891066i | −0.895266 | − | 0.445533i | \(-0.853014\pi\) | ||
0.895266 | − | 0.445533i | \(-0.146986\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.68420e8 | −1.53667 | ||||||||
\(560\) | 2.50216e6 | + | 1.44462e6i | 0.0142479 | + | 0.00822603i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.07465e7 | − | 3.59340e7i | −0.116879 | − | 0.202440i | ||||
\(563\) | −9.62471e7 | + | 5.55683e7i | −0.539340 | + | 0.311388i | −0.744811 | − | 0.667275i | \(-0.767461\pi\) |
0.205471 | + | 0.978663i | \(0.434127\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.24434e7 | + | 1.08155e8i | −0.346211 | + | 0.599655i | ||||
\(566\) | 2.18882e8i | 1.20715i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.45646e7 | 0.406900 | ||||||||
\(569\) | −2.79773e8 | − | 1.61527e8i | −1.51869 | − | 0.876817i | −0.999758 | − | 0.0220026i | \(-0.992996\pi\) |
−0.518934 | − | 0.854814i | \(-0.673671\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.71860e7 | − | 4.70875e7i | −0.146028 | − | 0.252928i | 0.783728 | − | 0.621104i | \(-0.213316\pi\) |
−0.929756 | + | 0.368176i | \(0.879982\pi\) | |||||||
\(572\) | 1.56901e8 | − | 9.05869e7i | 0.838374 | − | 0.484036i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.79235e7 | + | 3.10444e7i | −0.0947734 | + | 0.164152i | ||||
\(575\) | 1.23831e7i | 0.0651370i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.74190e8 | 1.42733 | 0.713665 | − | 0.700487i | \(-0.247034\pi\) | ||||
0.713665 | + | 0.700487i | \(0.247034\pi\) | |||||||
\(578\) | −1.16486e8 | − | 6.72531e7i | −0.603239 | − | 0.348280i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.21921e7 | − | 2.11174e7i | −0.0624877 | − | 0.108232i | ||||
\(581\) | −2.29279e7 | + | 1.32374e7i | −0.116906 | + | 0.0674954i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.98681e8 | + | 3.44125e8i | −1.00265 | + | 1.73664i | ||||
\(584\) | − | 6.67863e7i | − | 0.335312i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.33096e8 | 0.661410 | ||||||||
\(587\) | 2.14847e8 | + | 1.24042e8i | 1.06222 | + | 0.613274i | 0.926046 | − | 0.377411i | \(-0.123186\pi\) |
0.136176 | + | 0.990685i | \(0.456519\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.13324e8 | − | 1.96283e8i | −0.554596 | − | 0.960589i | ||||
\(590\) | −2.07054e7 | + | 1.19543e7i | −0.100816 | + | 0.0582059i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.75589e7 | − | 4.77334e7i | 0.132830 | − | 0.230068i | ||||
\(593\) | 2.27716e8i | 1.09202i | 0.837779 | + | 0.546009i | \(0.183854\pi\) | ||||
−0.837779 | + | 0.546009i | \(0.816146\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.69290e6 | 0.00803676 | ||||||||
\(596\) | −5.66192e6 | − | 3.26891e6i | −0.0267439 | − | 0.0154406i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9.27077e6 | + | 1.60574e7i | 0.0433523 | + | 0.0750884i | ||||
\(599\) | −7.43379e7 | + | 4.29190e7i | −0.345884 | + | 0.199696i | −0.662871 | − | 0.748734i | \(-0.730662\pi\) |
0.316987 | + | 0.948430i | \(0.397329\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.73833e8 | − | 3.01088e8i | 0.800774 | − | 1.38698i | −0.118334 | − | 0.992974i | \(-0.537755\pi\) |
0.919108 | − | 0.394007i | \(-0.128911\pi\) | |||||||
\(602\) | − | 2.46194e7i | − | 0.112846i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −9.48138e7 | −0.430289 | ||||||||
\(605\) | −3.86656e7 | − | 2.23236e7i | −0.174606 | − | 0.100809i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.35211e7 | − | 7.53807e7i | −0.194596 | − | 0.337050i | 0.752172 | − | 0.658967i | \(-0.229006\pi\) |
−0.946768 | + | 0.321917i | \(0.895673\pi\) | |||||||
\(608\) | 2.68577e7 | − | 1.55063e7i | 0.119497 | − | 0.0689918i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.39544e7 | + | 2.41697e7i | −0.0614781 | + | 0.106483i | ||||
\(611\) | − | 6.59204e8i | − | 2.88999i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.18298e8 | 1.38182 | 0.690912 | − | 0.722939i | \(-0.257209\pi\) | ||||
0.690912 | + | 0.722939i | \(0.257209\pi\) | |||||||
\(614\) | 9.44560e7 | + | 5.45342e7i | 0.408061 | + | 0.235594i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.30859e6 | + | 1.43909e7i | 0.0355455 | + | 0.0615667i | ||||
\(617\) | 1.18589e8 | − | 6.84674e7i | 0.504881 | − | 0.291493i | −0.225846 | − | 0.974163i | \(-0.572515\pi\) |
0.730727 | + | 0.682670i | \(0.239181\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.03059e7 | + | 1.39094e8i | −0.338591 | + | 0.586457i | −0.984168 | − | 0.177238i | \(-0.943284\pi\) |
0.645577 | + | 0.763695i | \(0.276617\pi\) | |||||||
\(620\) | 6.79338e7i | 0.285043i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.76556e8 | −0.733689 | ||||||||
\(623\) | −3.66793e7 | − | 2.11768e7i | −0.151690 | − | 0.0875783i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.62930e7 | − | 1.14823e8i | −0.271536 | − | 0.470315i | ||||
\(626\) | −1.72458e7 | + | 9.95689e6i | −0.0703010 | + | 0.0405883i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.16772e7 | + | 7.21870e7i | −0.168275 | + | 0.291461i | ||||
\(629\) | − | 3.22953e7i | − | 0.129774i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.09279e8 | −1.62904 | −0.814519 | − | 0.580136i | \(-0.802999\pi\) | ||||
−0.814519 | + | 0.580136i | \(0.802999\pi\) | |||||||
\(632\) | 1.32283e8 | + | 7.63734e7i | 0.524024 | + | 0.302545i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.34371e8 | − | 2.32738e8i | −0.527277 | − | 0.913271i | ||||
\(635\) | 1.35915e8 | − | 7.84708e7i | 0.530820 | − | 0.306469i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.98638e8 | − | 3.44052e8i | 0.768501 | − | 1.33108i | ||||
\(638\) | − | 1.40243e8i | − | 0.540032i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −9.29547e6 | −0.0354594 | ||||||||
\(641\) | −6.47552e7 | − | 3.73865e7i | −0.245867 | − | 0.141952i | 0.372003 | − | 0.928231i | \(-0.378671\pi\) |
−0.617870 | + | 0.786280i | \(0.712004\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.35130e8 | − | 2.34052e8i | −0.508298 | − | 0.880399i | −0.999954 | − | 0.00960888i | \(-0.996941\pi\) |
0.491655 | − | 0.870790i | \(-0.336392\pi\) | |||||||
\(644\) | −1.47278e6 | + | 850310.i | −0.00551417 | + | 0.00318361i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.08564e6 | − | 1.57368e7i | 0.0337022 | − | 0.0583739i | ||||
\(647\) | − | 2.04687e8i | − | 0.755749i | −0.925857 | − | 0.377874i | \(-0.876655\pi\) | ||
0.925857 | − | 0.377874i | \(-0.123345\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.37507e8 | −0.503028 | ||||||||
\(650\) | −2.22878e8 | − | 1.28679e8i | −0.811573 | − | 0.468562i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.00313e7 | + | 1.55939e8i | 0.324826 | + | 0.562615i | ||||
\(653\) | −1.10498e8 | + | 6.37963e7i | −0.396841 | + | 0.229116i | −0.685120 | − | 0.728430i | \(-0.740250\pi\) |
0.288279 | + | 0.957546i | \(0.406917\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.81796e7 | − | 4.88086e7i | 0.100279 | − | 0.173689i | ||||
\(656\) | − | 1.15329e8i | − | 0.408534i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.04619e7 | 0.212229 | ||||||||
\(659\) | −2.79267e8 | − | 1.61235e8i | −0.975807 | − | 0.563383i | −0.0748056 | − | 0.997198i | \(-0.523834\pi\) |
−0.901002 | + | 0.433816i | \(0.857167\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.17389e8 | + | 3.76529e8i | 0.752721 | + | 1.30375i | 0.946500 | + | 0.322705i | \(0.104592\pi\) |
−0.193779 | + | 0.981045i | \(0.562074\pi\) | |||||||
\(662\) | −5.33957e7 | + | 3.08280e7i | −0.184049 | + | 0.106260i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.25883e7 | − | 7.37650e7i | 0.145474 | − | 0.251969i | ||||
\(665\) | − | 1.51059e7i | − | 0.0513668i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.43526e7 | 0.0483676 | ||||||||
\(668\) | −4.88630e7 | − | 2.82111e7i | −0.163927 | − | 0.0946434i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.51189e7 | + | 6.08277e7i | 0.116766 | + | 0.202245i | ||||
\(671\) | −1.39009e8 | + | 8.02570e7i | −0.460125 | + | 0.265654i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.31783e7 | − | 7.47869e7i | 0.141651 | − | 0.245347i | −0.786467 | − | 0.617632i | \(-0.788092\pi\) |
0.928119 | + | 0.372285i | \(0.121426\pi\) | |||||||
\(674\) | − | 2.69735e8i | − | 0.880963i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.30889e8 | −0.747417 | ||||||||
\(677\) | −4.92732e8 | − | 2.84479e8i | −1.58798 | − | 0.916820i | −0.993640 | − | 0.112606i | \(-0.964080\pi\) |
−0.594340 | − | 0.804214i | \(-0.702587\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.29933e7 | − | 2.25050e7i | −0.0415058 | − | 0.0718902i | ||||
\(680\) | −4.71682e6 | + | 2.72326e6i | −0.0150011 | + | 0.00866089i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.95357e8 | + | 3.38368e8i | −0.615852 | + | 1.06669i | ||||
\(683\) | 1.34652e8i | 0.422622i | 0.977419 | + | 0.211311i | \(0.0677733\pi\) | ||||
−0.977419 | + | 0.211311i | \(0.932227\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.05685e8 | 0.328806 | ||||||||
\(686\) | 6.39851e7 | + | 3.69418e7i | 0.198201 | + | 0.114432i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.96036e7 | + | 6.85954e7i | 0.121610 | + | 0.210635i | ||||
\(689\) | 7.31935e8 | − | 4.22583e8i | 2.23777 | − | 1.29198i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.35612e7 | − | 9.27707e7i | 0.162336 | − | 0.281175i | −0.773370 | − | 0.633955i | \(-0.781430\pi\) |
0.935706 | + | 0.352780i | \(0.114764\pi\) | |||||||
\(692\) | − | 2.57151e8i | − | 0.776013i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.45871e8 | −0.436407 | ||||||||
\(695\) | 6.86112e6 | + | 3.96127e6i | 0.0204381 | + | 0.0117999i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.37876e7 | − | 5.85218e7i | −0.0997835 | − | 0.172830i | ||||
\(698\) | −2.88067e8 | + | 1.66315e8i | −0.847085 | + | 0.489065i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.18024e7 | − | 2.04423e7i | 0.0344092 | − | 0.0595985i | ||||
\(701\) | − | 2.39134e8i | − | 0.694204i | −0.937827 | − | 0.347102i | \(-0.887166\pi\) | ||
0.937827 | − | 0.347102i | \(-0.112834\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.88174e8 | −0.829447 | ||||||||
\(704\) | −4.62994e7 | − | 2.67310e7i | −0.132696 | − | 0.0766120i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.13783e8 | + | 3.70282e8i | 0.607517 | + | 1.05225i | ||||
\(707\) | 5.98798e7 | − | 3.45716e7i | 0.169443 | − | 0.0978277i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.85010e8 | − | 3.20446e8i | 0.519106 | − | 0.899118i | −0.480648 | − | 0.876914i | \(-0.659598\pi\) |
0.999753 | − | 0.0222038i | \(-0.00706826\pi\) | |||||||
\(710\) | 1.16850e8i | 0.326478i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.36263e8 | 0.377518 | ||||||||
\(713\) | −3.46290e7 | − | 1.99931e7i | −0.0955369 | − | 0.0551583i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.41959e8 | + | 2.45880e8i | 0.388368 | + | 0.672674i | ||||
\(716\) | 2.73854e8 | − | 1.58110e8i | 0.746071 | − | 0.430744i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.28986e8 | + | 2.23410e8i | −0.348472 | + | 0.603571i | ||||
\(719\) | − | 1.59561e8i | − | 0.429279i | −0.976693 | − | 0.214639i | \(-0.931142\pi\) | ||
0.976693 | − | 0.214639i | \(-0.0688576\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.08177e7 | −0.0822233 | ||||||||
\(722\) | 9.00558e7 | + | 5.19938e7i | 0.239277 | + | 0.138146i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.12342e7 | + | 1.06061e8i | 0.161354 | + | 0.279473i | ||||
\(725\) | −1.72526e8 | + | 9.96079e7i | −0.452731 | + | 0.261384i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.24125e8 | − | 2.14991e8i | 0.323040 | − | 0.559522i | −0.658073 | − | 0.752954i | \(-0.728628\pi\) |
0.981114 | + | 0.193432i | \(0.0619617\pi\) | |||||||
\(728\) | − | 3.53438e7i | − | 0.0916051i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.04661e8 | 0.269039 | ||||||||
\(731\) | 4.01923e7 | + | 2.32050e7i | 0.102894 | + | 0.0594059i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.13730e8 | − | 3.70190e8i | −0.542691 | − | 0.939968i | −0.998748 | − | 0.0500180i | \(-0.984072\pi\) |
0.456057 | − | 0.889950i | \(-0.349261\pi\) | |||||||
\(734\) | −1.53879e8 | + | 8.88422e7i | −0.389127 | + | 0.224663i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.73568e6 | − | 4.73833e6i | 0.00686169 | − | 0.0118848i | ||||
\(737\) | 4.03965e8i | 1.00912i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.68169e8 | 0.664469 | 0.332234 | − | 0.943197i | \(-0.392197\pi\) | ||||
0.332234 | + | 0.943197i | \(0.392197\pi\) | |||||||
\(740\) | 7.48029e7 | + | 4.31875e7i | 0.184596 | + | 0.106577i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.87591e7 | + | 6.71327e7i | 0.0948772 | + | 0.164332i | ||||
\(743\) | 1.46273e8 | − | 8.44510e7i | 0.356614 | − | 0.205891i | −0.310980 | − | 0.950416i | \(-0.600657\pi\) |
0.667595 | + | 0.744525i | \(0.267324\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.12271e6 | − | 8.87280e6i | 0.0123889 | − | 0.0214581i | ||||
\(746\) | 6.43803e7i | 0.155073i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.13251e7 | −0.0748492 | ||||||||
\(749\) | −4.42549e6 | − | 2.55506e6i | −0.0105321 | − | 0.00608072i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.90204e8 | − | 3.29444e8i | −0.449056 | − | 0.777788i | 0.549269 | − | 0.835646i | \(-0.314906\pi\) |
−0.998325 | + | 0.0578577i | \(0.981573\pi\) | |||||||
\(752\) | −1.68461e8 | + | 9.72610e7i | −0.396137 | + | 0.228710i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.49145e8 | + | 2.58326e8i | −0.347932 | + | 0.602636i | ||||
\(755\) | − | 1.48583e8i | − | 0.345245i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.93762e8 | 1.36875 | 0.684376 | − | 0.729129i | \(-0.260075\pi\) | ||||
0.684376 | + | 0.729129i | \(0.260075\pi\) | |||||||
\(758\) | 2.21906e8 | + | 1.28118e8i | 0.509521 | + | 0.294172i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.42999e7 | + | 4.20887e7i | 0.0553559 | + | 0.0958792i | ||||
\(761\) | 2.02904e8 | − | 1.17147e8i | 0.460401 | − | 0.265813i | −0.251812 | − | 0.967776i | \(-0.581026\pi\) |
0.712213 | + | 0.701964i | \(0.247693\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.06208e7 | − | 5.30368e7i | 0.0689356 | − | 0.119400i | ||||
\(764\) | 1.40114e8i | 0.314196i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.85433e8 | −0.412573 | ||||||||
\(767\) | 2.53287e8 | + | 1.46235e8i | 0.561342 | + | 0.324091i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.58571e8 | + | 2.74653e8i | 0.348694 | + | 0.603956i | 0.986018 | − | 0.166640i | \(-0.0532919\pi\) |
−0.637324 | + | 0.770596i | \(0.719959\pi\) | |||||||
\(770\) | −2.25520e7 | + | 1.30204e7i | −0.0493983 | + | 0.0285201i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.42697e7 | + | 2.47158e7i | −0.0310144 | + | 0.0537184i | ||||
\(773\) | − | 3.31391e8i | − | 0.717468i | −0.933440 | − | 0.358734i | \(-0.883209\pi\) | ||
0.933440 | − | 0.358734i | \(-0.116791\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.55010e8 | 1.19233 | ||||||||
\(776\) | 7.24046e7 | + | 4.18028e7i | 0.154946 | + | 0.0894582i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.76019e7 | − | 1.69051e8i | −0.207262 | − | 0.358988i | ||||
\(779\) | −5.22196e8 | + | 3.01490e8i | −1.10464 | + | 0.637765i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.36025e8 | + | 5.82013e8i | −0.705373 | + | 1.22174i | ||||
\(782\) | − | 3.20584e6i | − | 0.00670381i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.17231e8 | −0.243273 | ||||||||
\(785\) | −1.13124e8 | − | 6.53123e7i | −0.233855 | − | 0.135016i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.60758e7 | + | 1.66408e8i | 0.197101 | + | 0.341390i | 0.947587 | − | 0.319497i | \(-0.103514\pi\) |
−0.750486 | + | 0.660886i | \(0.770181\pi\) | |||||||
\(788\) | −1.35992e8 | + | 7.85150e7i | −0.277929 | + | 0.160463i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.19685e8 | + | 2.07300e8i | −0.242749 | + | 0.420453i | ||||
\(791\) | 1.40122e8i | 0.283125i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.41405e8 | 0.684621 | ||||||||
\(794\) | −2.80416e8 | − | 1.61898e8i | −0.560197 | − | 0.323430i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.33591e8 | − | 2.31387e8i | −0.264874 | − | 0.458775i | ||||
\(797\) | −1.18277e8 | + | 6.82872e7i | −0.233628 | + | 0.134885i | −0.612245 | − | 0.790668i | \(-0.709733\pi\) |
0.378617 | + | 0.925554i | \(0.376400\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.69884e7 | + | 9.87068e7i | −0.111724 | + | 0.193511i | ||||
\(800\) | 7.59427e7i | 0.148326i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4.51019e8 | 0.874322 | ||||||||
\(803\) | 5.21300e8 | + | 3.00973e8i | 1.00680 | + | 0.581274i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.33252e6 | − | 2.30799e6i | −0.00255439 | − | 0.00442433i | ||||
\(806\) | 7.19691e8 | − | 4.15514e8i | 1.37449 | − | 0.793561i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.11226e8 | + | 1.92649e8i | −0.210850 | + | 0.365202i | ||||
\(809\) | 6.82631e8i | 1.28926i | 0.764495 | + | 0.644630i | \(0.222989\pi\) | ||||
−0.764495 | + | 0.644630i | \(0.777011\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.02342e7 | −0.150417 | −0.0752085 | − | 0.997168i | \(-0.523962\pi\) | ||||
−0.0752085 | + | 0.997168i | \(0.523962\pi\) | |||||||
\(812\) | −2.36936e7 | − | 1.36795e7i | −0.0442550 | − | 0.0255507i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.48388e8 | + | 4.30221e8i | 0.460530 | + | 0.797661i | ||||
\(815\) | −2.44372e8 | + | 1.41088e8i | −0.451417 | + | 0.260626i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.07061e8 | − | 3.58640e8i | 0.379692 | − | 0.657646i | ||||
\(818\) | 2.71070e8i | 0.495246i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.80732e8 | 0.327789 | ||||||||
\(821\) | 7.33039e8 | + | 4.23220e8i | 1.32464 | + | 0.764781i | 0.984465 | − | 0.175582i | \(-0.0561806\pi\) |
0.340174 | + | 0.940362i | \(0.389514\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.00433e8 | − | 5.20365e8i | −0.538949 | − | 0.933487i | −0.998961 | − | 0.0455745i | \(-0.985488\pi\) |
0.460012 | − | 0.887913i | \(-0.347845\pi\) | |||||||
\(824\) | 8.58655e7 | − | 4.95745e7i | 0.153475 | − | 0.0886087i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.34126e7 | + | 2.32314e7i | −0.0237999 | + | 0.0412226i | ||||
\(827\) | 8.30480e8i | 1.46829i | 0.678991 | + | 0.734146i | \(0.262417\pi\) | ||||
−0.678991 | + | 0.734146i | \(0.737583\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.87908e8 | −1.73402 | −0.867008 | − | 0.498294i | \(-0.833960\pi\) | ||||
−0.867008 | + | 0.498294i | \(0.833960\pi\) | |||||||
\(830\) | 1.15597e8 | + | 6.67401e7i | 0.202168 | + | 0.116722i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.68553e7 | + | 9.84762e7i | 0.0987190 | + | 0.170986i | ||||
\(833\) | −5.94867e7 | + | 3.43447e7i | −0.102917 | + | 0.0594189i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.42096e7 | − | 7.65732e7i | 0.0759376 | − | 0.131528i | ||||
\(836\) | 2.79517e8i | 0.478398i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.22668e8 | −1.05810 | ||||||||
\(839\) | −3.20618e8 | − | 1.85109e8i | −0.542878 | − | 0.313431i | 0.203367 | − | 0.979103i | \(-0.434812\pi\) |
−0.746245 | + | 0.665672i | \(0.768145\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.81961e8 | − | 3.15167e8i | −0.305908 | − | 0.529849i | ||||
\(842\) | −1.83683e8 | + | 1.06049e8i | −0.307703 | + | 0.177652i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.07474e8 | + | 3.59355e8i | −0.345093 | + | 0.597718i | ||||
\(845\) | − | 3.61826e8i | − | 0.599694i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.00940e7 | −0.0824395 | ||||||||
\(848\) | −2.15984e8 | − | 1.24698e8i | −0.354188 | − | 0.204491i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.22487e7 | + | 3.85358e7i | 0.0362282 | + | 0.0627491i | ||||
\(851\) | −4.40293e7 | + | 2.54203e7i | −0.0714419 | + | 0.0412470i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.82273e7 | + | 3.15707e7i | −0.0293681 | + | 0.0508671i | −0.880336 | − | 0.474351i | \(-0.842683\pi\) |
0.850968 | + | 0.525218i | \(0.176016\pi\) | |||||||
\(854\) | 3.13135e7i | 0.0502757i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.64406e7 | 0.0262118 | ||||||||
\(857\) | −2.18436e8 | − | 1.26114e8i | −0.347042 | − | 0.200365i | 0.316339 | − | 0.948646i | \(-0.397546\pi\) |
−0.663382 | + | 0.748281i | \(0.730879\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.74242e7 | − | 1.34103e8i | −0.122151 | − | 0.211572i | 0.798465 | − | 0.602042i | \(-0.205646\pi\) |
−0.920616 | + | 0.390470i | \(0.872313\pi\) | |||||||
\(860\) | −1.07496e8 | + | 6.20627e7i | −0.169004 | + | 0.0975743i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.83549e8 | − | 6.64326e8i | 0.598823 | − | 1.03719i | ||||
\(863\) | 8.16338e8i | 1.27010i | 0.772472 | + | 0.635049i | \(0.219020\pi\) | ||||
−0.772472 | + | 0.635049i | \(0.780980\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.02981e8 | 0.622638 | ||||||||
\(866\) | −5.78868e8 | − | 3.34209e8i | −0.891304 | − | 0.514594i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.81107e7 | + | 6.60097e7i | 0.0582758 | + | 0.100937i | ||||
\(869\) | −1.19226e9 | + | 6.88353e8i | −1.81682 | + | 1.04894i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.29606e8 | − | 7.44099e8i | 0.650153 | − | 1.12610i | ||||
\(872\) | 1.97031e8i | 0.297156i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.86060e7 | −0.0428473 | ||||||||
\(875\) | 7.02150e7 | + | 4.05387e7i | 0.104811 | + | 0.0605125i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.75984e7 | + | 3.04813e7i | 0.0260900 | + | 0.0451892i | 0.878776 | − | 0.477235i | \(-0.158361\pi\) |
−0.852686 | + | 0.522424i | \(0.825028\pi\) | |||||||
\(878\) | 4.50615e8 | − | 2.60162e8i | 0.665766 | − | 0.384380i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.18901e7 | − | 7.25557e7i | 0.0614700 | − | 0.106469i | ||||
\(881\) | 1.48112e8i | 0.216602i | 0.994118 | + | 0.108301i | \(0.0345410\pi\) | ||||
−0.994118 | + | 0.108301i | \(0.965459\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.03227e9 | −1.49937 | −0.749686 | − | 0.661794i | \(-0.769795\pi\) | ||||
−0.749686 | + | 0.661794i | \(0.769795\pi\) | |||||||
\(884\) | 5.77004e7 | + | 3.33134e7i | 0.0835261 | + | 0.0482238i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.57157e7 | − | 9.65025e7i | −0.0801081 | − | 0.138751i | ||||
\(887\) | 2.13506e8 | − | 1.23268e8i | 0.305943 | − | 0.176636i | −0.339167 | − | 0.940726i | \(-0.610145\pi\) |
0.645109 | + | 0.764090i | \(0.276812\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.80439e7 | − | 1.52496e8i | 0.125312 | − | 0.217047i | ||||
\(890\) | 2.13538e8i | 0.302904i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.20718e8 | −0.170089 | ||||||||
\(893\) | 8.80770e8 | + | 5.08513e8i | 1.23683 | + | 0.714081i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.47774e8 | + | 4.29157e8i | 0.345610 | + | 0.598614i | ||||
\(896\) | −9.03220e6 | + | 5.21474e6i | −0.0125565 | + | 0.00724951i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.91822e7 | − | 6.78655e7i | 0.0541078 | − | 0.0937174i | ||||
\(899\) | − | 6.43283e8i | − | 0.885366i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.46130e8 | −0.199786 | ||||||||
\(902\) | 9.00201e8 | + | 5.19732e8i | 1.22665 | + | 0.708206i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.25406e8 | − | 3.90414e8i | −0.305112 | − | 0.528470i | ||||
\(905\) | −1.66208e8 | + | 9.59601e7i | −0.224236 | + | 0.129463i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.47798e8 | + | 6.02404e8i | −0.466128 | + | 0.807357i | −0.999252 | − | 0.0386800i | \(-0.987685\pi\) |
0.533124 | + | 0.846037i | \(0.321018\pi\) | |||||||
\(908\) | 1.61050e8i | 0.215132i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5.53873e7 | 0.0734998 | ||||||||
\(911\) | 8.66691e8 | + | 5.00385e8i | 1.14633 | + | 0.661833i | 0.947990 | − | 0.318300i | \(-0.103112\pi\) |
0.198339 | + | 0.980133i | \(0.436445\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.83848e8 | + | 6.64845e8i | 0.504368 | + | 0.873590i | ||||
\(914\) | −3.61726e8 | + | 2.08843e8i | −0.473742 | + | 0.273515i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.59923e7 | − | 7.96610e7i | 0.0598410 | − | 0.103648i | ||||
\(917\) | − | 6.32349e7i | − | 0.0820066i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.63664e8 | 0.468548 | 0.234274 | − | 0.972171i | \(-0.424729\pi\) | ||||
0.234274 | + | 0.972171i | \(0.424729\pi\) | |||||||
\(920\) | 7.42543e6 | + | 4.28708e6i | 0.00953583 | + | 0.00550551i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.50346e8 | − | 2.60407e8i | −0.191822 | − | 0.332246i | ||||
\(923\) | 1.23791e9 | − | 7.14708e8i | 1.57429 | − | 0.908915i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.52836e8 | − | 6.11130e8i | 0.445808 | − | 0.772162i | ||||
\(926\) | 5.36645e8i | 0.675856i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8.80212e7 | 0.110140 | ||||||||
\(929\) | −3.37250e8 | − | 1.94711e8i | −0.420634 | − | 0.242853i | 0.274715 | − | 0.961526i | \(-0.411417\pi\) |
−0.695349 | + | 0.718673i | \(0.744750\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.06461e8 | + | 5.30806e8i | 0.379775 | + | 0.657789i | ||||
\(932\) | −6.18674e8 | + | 3.57192e8i | −0.764213 | + | 0.441218i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.38699e8 | − | 9.33054e8i | 0.661158 | − | 1.14516i | ||||
\(935\) | − | 4.90895e7i | − | 0.0600556i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.33744e8 | −0.891920 | −0.445960 | − | 0.895053i | \(-0.647138\pi\) | ||||
−0.445960 | + | 0.895053i | \(0.647138\pi\) | |||||||
\(938\) | 6.82484e7 | + | 3.94032e7i | 0.0826959 | + | 0.0477445i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.52418e8 | − | 2.63995e8i | −0.183507 | − | 0.317843i | ||||
\(941\) | −2.41096e8 | + | 1.39197e8i | −0.289348 | + | 0.167055i | −0.637648 | − | 0.770328i | \(-0.720092\pi\) |
0.348300 | + | 0.937383i | \(0.386759\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.31899e7 | + | 9.21276e7i | −0.0634299 | + | 0.109864i | ||||
\(944\) | − | 8.63042e7i | − | 0.102593i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.13894e8 | −0.843258 | ||||||||
\(947\) | −7.22272e8 | − | 4.17004e8i | −0.850454 | − | 0.491010i | 0.0103502 | − | 0.999946i | \(-0.496705\pi\) |
−0.860804 | + | 0.508937i | \(0.830039\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.40153e8 | − | 1.10878e9i | −0.749006 | − | 1.29732i | ||||
\(950\) | 3.43859e8 | − | 1.98527e8i | 0.401060 | − | 0.231552i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.05549e6 | + | 5.29226e6i | −0.00354135 | + | 0.00613381i | ||||
\(953\) | 1.27101e8i | 0.146849i | 0.997301 | + | 0.0734245i | \(0.0233928\pi\) | ||||
−0.997301 | + | 0.0734245i | \(0.976607\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.19572e8 | −0.252097 | ||||||||
\(956\) | −3.25313e8 | − | 1.87820e8i | −0.372330 | − | 0.214965i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.01766e7 | − | 1.38870e8i | −0.0911908 | − | 0.157947i | ||||
\(959\) | 1.02691e8 | − | 5.92889e7i | 0.116434 | − | 0.0672229i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.52333e8 | + | 7.83464e8i | −0.509669 | + | 0.882772i | ||||
\(962\) | − | 1.05662e9i | − | 1.18684i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8.49229e8 | 0.947969 | ||||||||
\(965\) | −3.87322e7 | − | 2.23620e7i | −0.0431013 | − | 0.0248845i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.78470e8 | + | 3.09120e8i | 0.197373 | + | 0.341859i | 0.947676 | − | 0.319235i | \(-0.103426\pi\) |
−0.750303 | + | 0.661094i | \(0.770092\pi\) | |||||||
\(968\) | 1.39574e8 | − | 8.05828e7i | 0.153878 | − | 0.0888416i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −6.55092e7 | + | 1.13465e8i | −0.0717773 | + | 0.124322i | ||||
\(971\) | − | 2.79662e8i | − | 0.305476i | −0.988267 | − | 0.152738i | \(-0.951191\pi\) | ||
0.988267 | − | 0.152738i | \(-0.0488090\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.88905e6 | 0.00964977 | ||||||||
\(974\) | 2.97081e8 | + | 1.71520e8i | 0.321513 | + | 0.185625i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.03719e7 | − | 8.72467e7i | −0.0541800 | − | 0.0938425i | ||||
\(977\) | 7.08671e7 | − | 4.09152e7i | 0.0759908 | − | 0.0438733i | −0.461523 | − | 0.887128i | \(-0.652697\pi\) |
0.537514 | + | 0.843255i | \(0.319364\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.14069e8 | + | 1.06360e9i | −0.654439 | + | 1.13352i | ||||
\(980\) | − | 1.83712e8i | − | 0.195191i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 8.79946e8 | 0.929226 | ||||||||
\(983\) | −7.65774e8 | − | 4.42120e8i | −0.806195 | − | 0.465457i | 0.0394375 | − | 0.999222i | \(-0.487443\pi\) |
−0.845633 | + | 0.533765i | \(0.820777\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.23041e8 | − | 2.13113e8i | −0.128748 | − | 0.222998i | ||||
\(986\) | 4.46648e7 | − | 2.57872e7i | 0.0465945 | − | 0.0269013i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.97258e8 | − | 5.14867e8i | 0.308222 | − | 0.533856i | ||||
\(989\) | − | 7.30607e7i | − | 0.0755258i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.35522e9 | 1.39248 | 0.696239 | − | 0.717810i | \(-0.254855\pi\) | ||||
0.696239 | + | 0.717810i | \(0.254855\pi\) | |||||||
\(992\) | −2.12371e8 | − | 1.22612e8i | −0.217551 | − | 0.125603i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.55527e7 | + | 1.13541e8i | 0.0667469 | + | 0.115609i | ||||
\(995\) | 3.62606e8 | − | 2.09351e8i | 0.368100 | − | 0.212523i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.59348e8 | + | 7.95613e8i | −0.463507 | + | 0.802817i | −0.999133 | − | 0.0416381i | \(-0.986742\pi\) |
0.535626 | + | 0.844455i | \(0.320076\pi\) | |||||||
\(998\) | − | 7.31843e8i | − | 0.736252i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 162.7.d.e.107.1 | 8 | ||
3.2 | odd | 2 | inner | 162.7.d.e.107.4 | 8 | ||
9.2 | odd | 6 | 54.7.b.c.53.2 | ✓ | 4 | ||
9.4 | even | 3 | inner | 162.7.d.e.53.4 | 8 | ||
9.5 | odd | 6 | inner | 162.7.d.e.53.1 | 8 | ||
9.7 | even | 3 | 54.7.b.c.53.3 | yes | 4 | ||
36.7 | odd | 6 | 432.7.e.h.161.2 | 4 | |||
36.11 | even | 6 | 432.7.e.h.161.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
54.7.b.c.53.2 | ✓ | 4 | 9.2 | odd | 6 | ||
54.7.b.c.53.3 | yes | 4 | 9.7 | even | 3 | ||
162.7.d.e.53.1 | 8 | 9.5 | odd | 6 | inner | ||
162.7.d.e.53.4 | 8 | 9.4 | even | 3 | inner | ||
162.7.d.e.107.1 | 8 | 1.1 | even | 1 | trivial | ||
162.7.d.e.107.4 | 8 | 3.2 | odd | 2 | inner | ||
432.7.e.h.161.2 | 4 | 36.7 | odd | 6 | |||
432.7.e.h.161.3 | 4 | 36.11 | even | 6 |