Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [189,6,Mod(17,189)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(189, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("189.17");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 189 = 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 189.s (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: | \(30.3125419447\) |
Analytic rank: | \(0\) |
Dimension: | \(76\) |
Relative dimension: | \(38\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.20 | ||
Character | \(\chi\) | \(=\) | 189.17 |
Dual form | 189.6.s.a.89.20 |
$q$-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 \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(136\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0316775 | − | 0.0182890i | −0.00559984 | − | 0.00323307i | 0.497197 | − | 0.867637i | \(-0.334362\pi\) |
−0.502797 | + | 0.864404i | \(0.667696\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −15.9993 | − | 27.7117i | −0.499979 | − | 0.865989i | ||||
\(5\) | −62.5776 | −1.11942 | −0.559711 | − | 0.828688i | \(-0.689088\pi\) | ||||
−0.559711 | + | 0.828688i | \(0.689088\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 87.2452 | + | 95.8920i | 0.672971 | + | 0.739669i | ||||
\(8\) | 2.34094i | 0.0129320i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.98230 | + | 1.14448i | 0.00626858 | + | 0.00361917i | ||||
\(11\) | 208.840i | 0.520394i | 0.965556 | + | 0.260197i | \(0.0837875\pi\) | ||||
−0.965556 | + | 0.260197i | \(0.916212\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −447.217 | − | 258.201i | −0.733939 | − | 0.423740i | 0.0859226 | − | 0.996302i | \(-0.472616\pi\) |
−0.819861 | + | 0.572562i | \(0.805950\pi\) | |||||||
\(14\) | −1.00994 | − | 4.63325i | −0.00137713 | − | 0.00631779i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −511.936 | + | 886.699i | −0.499937 | + | 0.865917i | ||||
\(17\) | −558.291 | + | 966.988i | −0.468531 | + | 0.811519i | −0.999353 | − | 0.0359638i | \(-0.988550\pi\) |
0.530822 | + | 0.847483i | \(0.321883\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 819.372 | − | 473.065i | 0.520712 | − | 0.300633i | −0.216514 | − | 0.976279i | \(-0.569469\pi\) |
0.737226 | + | 0.675646i | \(0.236135\pi\) | |||||||
\(20\) | 1001.20 | + | 1734.13i | 0.559687 | + | 0.969407i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.81948 | − | 6.61553i | 0.00168247 | − | 0.00291412i | ||||
\(23\) | − | 1022.14i | − | 0.402894i | −0.979499 | − | 0.201447i | \(-0.935436\pi\) | ||
0.979499 | − | 0.201447i | \(-0.0645644\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 790.950 | 0.253104 | ||||||||
\(26\) | 9.44447 | + | 16.3583i | 0.00273996 | + | 0.00474575i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1261.46 | − | 3951.92i | 0.304074 | − | 0.952605i | ||||
\(29\) | 4524.33 | − | 2612.13i | 0.998987 | − | 0.576765i | 0.0910383 | − | 0.995847i | \(-0.470981\pi\) |
0.907948 | + | 0.419082i | \(0.137648\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8025.88 | − | 4633.74i | 1.49999 | − | 0.866020i | 0.499990 | − | 0.866031i | \(-0.333337\pi\) |
1.00000 | 1.13515e-5i | \(3.61330e-6\pi\) | ||||||||
\(32\) | 97.3078 | − | 56.1807i | 0.0167986 | − | 0.00969867i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 35.3705 | − | 20.4212i | 0.00524740 | − | 0.00302959i | ||||
\(35\) | −5459.59 | − | 6000.69i | −0.753338 | − | 0.828001i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1499.33 | + | 2596.91i | 0.180050 | + | 0.311855i | 0.941897 | − | 0.335901i | \(-0.109041\pi\) |
−0.761848 | + | 0.647756i | \(0.775708\pi\) | |||||||
\(38\) | −34.6075 | −0.00388787 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 146.491i | − | 0.0144764i | ||||||
\(41\) | 6210.55 | − | 10757.0i | 0.576993 | − | 0.999381i | −0.418829 | − | 0.908065i | \(-0.637559\pi\) |
0.995822 | − | 0.0913162i | \(-0.0291074\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6478.23 | + | 11220.6i | 0.534300 | + | 0.925434i | 0.999197 | + | 0.0400696i | \(0.0127580\pi\) |
−0.464897 | + | 0.885365i | \(0.653909\pi\) | |||||||
\(44\) | 5787.31 | − | 3341.30i | 0.450656 | − | 0.260186i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −18.6939 | + | 32.3788i | −0.00130259 | + | 0.00225614i | ||||
\(47\) | 9979.25 | − | 17284.6i | 0.658951 | − | 1.14134i | −0.321936 | − | 0.946761i | \(-0.604334\pi\) |
0.980888 | − | 0.194576i | \(-0.0623329\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1583.56 | + | 16732.2i | −0.0942203 | + | 0.995551i | ||||
\(50\) | −25.0553 | − | 14.4657i | −0.00141734 | − | 0.000818303i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 16524.2i | 0.847444i | ||||||||
\(53\) | −21892.1 | − | 12639.4i | −1.07053 | − | 0.618069i | −0.142202 | − | 0.989838i | \(-0.545418\pi\) |
−0.928326 | + | 0.371768i | \(0.878752\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 13068.7i | − | 0.582540i | ||||||
\(56\) | −224.478 | + | 204.236i | −0.00956540 | + | 0.00870287i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −191.093 | −0.00745889 | ||||||||
\(59\) | 16653.4 | + | 28844.5i | 0.622833 | + | 1.07878i | 0.988956 | + | 0.148212i | \(0.0473518\pi\) |
−0.366122 | + | 0.930567i | \(0.619315\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10462.0 | + | 6040.26i | 0.359991 | + | 0.207841i | 0.669077 | − | 0.743193i | \(-0.266690\pi\) |
−0.309086 | + | 0.951034i | \(0.600023\pi\) | |||||||
\(62\) | −338.986 | −0.0111996 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 32759.8 | 0.999749 | ||||||||
\(65\) | 27985.7 | + | 16157.6i | 0.821587 | + | 0.474343i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11858.5 | − | 20539.5i | −0.322732 | − | 0.558988i | 0.658319 | − | 0.752739i | \(-0.271268\pi\) |
−0.981051 | + | 0.193751i | \(0.937935\pi\) | |||||||
\(68\) | 35729.1 | 0.937023 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 63.1994 | + | 289.937i | 0.00154159 | + | 0.00707227i | ||||
\(71\) | − | 53406.7i | − | 1.25733i | −0.777675 | − | 0.628666i | \(-0.783601\pi\) | ||
0.777675 | − | 0.628666i | \(-0.216399\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 67780.6 | + | 39133.2i | 1.48867 | + | 0.859484i | 0.999916 | − | 0.0129379i | \(-0.00411838\pi\) |
0.488754 | + | 0.872422i | \(0.337452\pi\) | |||||||
\(74\) | − | 109.685i | − | 0.00232845i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −26218.8 | − | 15137.4i | −0.520690 | − | 0.300620i | ||||
\(77\) | −20026.1 | + | 18220.3i | −0.384919 | + | 0.350210i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 24665.4 | − | 42721.6i | 0.444651 | − | 0.770159i | −0.553376 | − | 0.832931i | \(-0.686661\pi\) |
0.998028 | + | 0.0627725i | \(0.0199942\pi\) | |||||||
\(80\) | 32035.7 | − | 55487.4i | 0.559640 | − | 0.969326i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −393.469 | + | 227.170i | −0.00646214 | + | 0.00373092i | ||||
\(83\) | −28362.0 | − | 49124.5i | −0.451899 | − | 0.782713i | 0.546605 | − | 0.837391i | \(-0.315920\pi\) |
−0.998504 | + | 0.0546780i | \(0.982587\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 34936.5 | − | 60511.8i | 0.524484 | − | 0.908432i | ||||
\(86\) | − | 473.921i | − | 0.00690971i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −488.883 | −0.00672974 | ||||||||
\(89\) | 57629.5 | + | 99817.2i | 0.771205 | + | 1.33577i | 0.936903 | + | 0.349589i | \(0.113679\pi\) |
−0.165698 | + | 0.986177i | \(0.552988\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14258.1 | − | 65411.3i | −0.180492 | − | 0.828036i | ||||
\(92\) | −28325.2 | + | 16353.6i | −0.348902 | + | 0.201439i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −632.235 | + | 365.021i | −0.00738004 | + | 0.00426087i | ||||
\(95\) | −51274.3 | + | 29603.2i | −0.582896 | + | 0.336535i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17070.5 | − | 9855.67i | 0.184212 | − | 0.106355i | −0.405058 | − | 0.914291i | \(-0.632749\pi\) |
0.589270 | + | 0.807936i | \(0.299415\pi\) | |||||||
\(98\) | 356.179 | − | 501.073i | 0.00374631 | − | 0.00527031i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −12654.7 | − | 21918.5i | −0.126547 | − | 0.219185i | ||||
\(101\) | −90419.0 | −0.881975 | −0.440988 | − | 0.897513i | \(-0.645372\pi\) | ||||
−0.440988 | + | 0.897513i | \(0.645372\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 136880.i | 1.27130i | 0.771978 | + | 0.635649i | \(0.219267\pi\) | ||||
−0.771978 | + | 0.635649i | \(0.780733\pi\) | |||||||
\(104\) | 604.434 | − | 1046.91i | 0.00547981 | − | 0.00949130i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 462.325 | + | 800.770i | 0.00399652 | + | 0.00692218i | ||||
\(107\) | 42006.7 | − | 24252.6i | 0.354698 | − | 0.204785i | −0.312055 | − | 0.950064i | \(-0.601017\pi\) |
0.666752 | + | 0.745279i | \(0.267684\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −62765.7 | + | 108713.i | −0.506007 | + | 0.876429i | 0.493969 | + | 0.869479i | \(0.335546\pi\) |
−0.999976 | + | 0.00695000i | \(0.997788\pi\) | |||||||
\(110\) | −239.014 | + | 413.984i | −0.00188339 | + | 0.00326213i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −129691. | + | 28269.6i | −0.976935 | + | 0.212949i | ||||
\(113\) | 31167.2 | + | 17994.4i | 0.229616 | + | 0.132569i | 0.610395 | − | 0.792097i | \(-0.291011\pi\) |
−0.380779 | + | 0.924666i | \(0.624344\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 63963.1i | 0.451008i | ||||||||
\(116\) | −144773. | − | 83584.5i | −0.998945 | − | 0.576741i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 1218.29i | − | 0.00805465i | ||||||
\(119\) | −141435. | + | 30829.4i | −0.915563 | + | 0.199571i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 117437. | 0.729190 | ||||||||
\(122\) | −220.941 | − | 382.681i | −0.00134393 | − | 0.00232775i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −256817. | − | 148274.i | −1.49993 | − | 0.865984i | ||||
\(125\) | 146059. | 0.836091 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −155648. | −0.856315 | −0.428157 | − | 0.903704i | \(-0.640837\pi\) | ||||
−0.428157 | + | 0.903704i | \(0.640837\pi\) | |||||||
\(128\) | −4151.60 | − | 2396.93i | −0.0223970 | − | 0.0129309i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −591.012 | − | 1023.66i | −0.00306717 | − | 0.00531249i | ||||
\(131\) | 239391. | 1.21879 | 0.609395 | − | 0.792866i | \(-0.291412\pi\) | ||||
0.609395 | + | 0.792866i | \(0.291412\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 116849. | + | 37298.6i | 0.572793 | + | 0.182837i | ||||
\(134\) | 867.519i | 0.00417366i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2263.66 | − | 1306.93i | −0.0104946 | − | 0.00605905i | ||||
\(137\) | 47378.4i | 0.215665i | 0.994169 | + | 0.107832i | \(0.0343910\pi\) | ||||
−0.994169 | + | 0.107832i | \(0.965609\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 40845.5 | + | 23582.1i | 0.179311 | + | 0.103525i | 0.586969 | − | 0.809609i | \(-0.300321\pi\) |
−0.407658 | + | 0.913135i | \(0.633654\pi\) | |||||||
\(140\) | −78939.2 | + | 247301.i | −0.340387 | + | 1.06637i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −976.756 | + | 1691.79i | −0.00406504 | + | 0.00704086i | ||||
\(143\) | 53922.7 | − | 93396.9i | 0.220512 | − | 0.381937i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −283122. | + | 163460.i | −1.11829 | + | 0.645643i | ||||
\(146\) | −1431.41 | − | 2479.28i | −0.00555754 | − | 0.00962595i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 47976.5 | − | 83097.7i | 0.180042 | − | 0.311842i | ||||
\(149\) | 385237.i | 1.42155i | 0.703418 | + | 0.710776i | \(0.251656\pi\) | ||||
−0.703418 | + | 0.710776i | \(0.748344\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −115125. | −0.410892 | −0.205446 | − | 0.978668i | \(-0.565864\pi\) | ||||
−0.205446 | + | 0.978668i | \(0.565864\pi\) | |||||||
\(152\) | 1107.42 | + | 1918.10i | 0.00388779 | + | 0.00673385i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 967.608 | − | 210.916i | 0.00328774 | − | 0.000716650i | ||||
\(155\) | −502240. | + | 289968.i | −1.67912 | + | 0.969441i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22976.9 | − | 13265.7i | 0.0743946 | − | 0.0429518i | −0.462341 | − | 0.886702i | \(-0.652990\pi\) |
0.536736 | + | 0.843750i | \(0.319657\pi\) | |||||||
\(158\) | −1562.67 | + | 902.210i | −0.00497995 | + | 0.00287518i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −6089.28 | + | 3515.65i | −0.0188047 | + | 0.0108569i | ||||
\(161\) | 98015.1 | − | 89176.8i | 0.298008 | − | 0.271136i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −224228. | − | 388374.i | −0.661030 | − | 1.14494i | −0.980345 | − | 0.197289i | \(-0.936786\pi\) |
0.319316 | − | 0.947648i | \(-0.396547\pi\) | |||||||
\(164\) | −397459. | −1.15394 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2074.85i | 0.00584409i | ||||||||
\(167\) | 222908. | − | 386089.i | 0.618494 | − | 1.07126i | −0.371267 | − | 0.928526i | \(-0.621077\pi\) |
0.989761 | − | 0.142737i | \(-0.0455902\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −52311.2 | − | 90605.6i | −0.140889 | − | 0.244027i | ||||
\(170\) | −2213.40 | + | 1277.91i | −0.00587405 | + | 0.00339138i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 207295. | − | 359045.i | 0.534277 | − | 0.925396i | ||||
\(173\) | −189463. | + | 328159.i | −0.481292 | + | 0.833623i | −0.999770 | − | 0.0214686i | \(-0.993166\pi\) |
0.518477 | + | 0.855092i | \(0.326499\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 69006.6 | + | 75845.8i | 0.170332 | + | 0.187213i | ||||
\(176\) | −185178. | − | 106913.i | −0.450618 | − | 0.260164i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 4215.94i | − | 0.00997344i | ||||||
\(179\) | 571478. | + | 329943.i | 1.33311 | + | 0.769673i | 0.985775 | − | 0.168068i | \(-0.0537528\pi\) |
0.347337 | + | 0.937740i | \(0.387086\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 551804.i | 1.25195i | 0.779842 | + | 0.625977i | \(0.215299\pi\) | ||||
−0.779842 | + | 0.625977i | \(0.784701\pi\) | |||||||
\(182\) | −744.646 | + | 2332.83i | −0.00166637 | + | 0.00522042i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2392.77 | 0.00521023 | ||||||||
\(185\) | −93824.2 | − | 162508.i | −0.201551 | − | 0.349097i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −201946. | − | 116594.i | −0.422310 | − | 0.243821i | ||||
\(188\) | −638645. | −1.31785 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2165.66 | 0.00435216 | ||||||||
\(191\) | 35637.9 | + | 20575.6i | 0.0706853 | + | 0.0408102i | 0.534926 | − | 0.844899i | \(-0.320339\pi\) |
−0.464241 | + | 0.885709i | \(0.653673\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −162000. | − | 280592.i | −0.313056 | − | 0.542228i | 0.665967 | − | 0.745982i | \(-0.268019\pi\) |
−0.979022 | + | 0.203753i | \(0.934686\pi\) | |||||||
\(194\) | −721.002 | −0.00137541 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 489014. | − | 223821.i | 0.909245 | − | 0.416161i | ||||
\(197\) | − | 898843.i | − | 1.65013i | −0.565038 | − | 0.825065i | \(-0.691138\pi\) | ||
0.565038 | − | 0.825065i | \(-0.308862\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −185743. | − | 107239.i | −0.332491 | − | 0.191964i | 0.324455 | − | 0.945901i | \(-0.394819\pi\) |
−0.656947 | + | 0.753937i | \(0.728152\pi\) | |||||||
\(200\) | 1851.57i | 0.00327314i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2864.25 | + | 1653.67i | 0.00493892 | + | 0.00285149i | ||||
\(203\) | 645208. | + | 205952.i | 1.09890 | + | 0.350773i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −388641. | + | 673146.i | −0.645898 | + | 1.11873i | ||||
\(206\) | 2503.40 | − | 4336.02i | 0.00411019 | − | 0.00711906i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 457893. | − | 264364.i | 0.733847 | − | 0.423687i | ||||
\(209\) | 98794.9 | + | 171118.i | 0.156448 | + | 0.270975i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 77523.0 | − | 134274.i | 0.119874 | − | 0.207628i | −0.799844 | − | 0.600208i | \(-0.795084\pi\) |
0.919718 | + | 0.392581i | \(0.128418\pi\) | |||||||
\(212\) | 808889.i | 1.23609i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1774.22 | −0.00264834 | ||||||||
\(215\) | −405392. | − | 702159.i | −0.598107 | − | 1.03595i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.14456e6 | + | 365346.i | 1.65002 | + | 0.526690i | ||||
\(218\) | 3976.52 | − | 2295.85i | 0.00566712 | − | 0.00327191i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −362155. | + | 209091.i | −0.504473 | + | 0.291258i | ||||
\(221\) | 499354. | − | 288302.i | 0.687746 | − | 0.397070i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 906052. | − | 523109.i | 1.22009 | − | 0.704418i | 0.255151 | − | 0.966901i | \(-0.417875\pi\) |
0.964937 | + | 0.262483i | \(0.0845415\pi\) | |||||||
\(224\) | 13876.9 | + | 4429.55i | 0.0184788 | + | 0.00589847i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −658.200 | − | 1140.04i | −0.000857209 | − | 0.00148473i | ||||
\(227\) | 903374. | 1.16360 | 0.581799 | − | 0.813333i | \(-0.302349\pi\) | ||||
0.581799 | + | 0.813333i | \(0.302349\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 604327.i | 0.761524i | 0.924673 | + | 0.380762i | \(0.124338\pi\) | ||||
−0.924673 | + | 0.380762i | \(0.875662\pi\) | |||||||
\(230\) | 1169.82 | − | 2026.19i | 0.00145814 | − | 0.00252557i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6114.84 | + | 10591.2i | 0.00745873 | + | 0.0129189i | ||||
\(233\) | −238586. | + | 137747.i | −0.287908 | + | 0.166224i | −0.636998 | − | 0.770865i | \(-0.719824\pi\) |
0.349090 | + | 0.937089i | \(0.386491\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −624477. | + | 1.08163e6i | −0.737644 | + | 1.27764i | ||||
\(236\) | 532885. | − | 922984.i | 0.622807 | − | 1.07873i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5044.13 | + | 1610.10i | 0.00577224 | + | 0.00184251i | ||||
\(239\) | 916492. | + | 529137.i | 1.03785 | + | 0.599202i | 0.919223 | − | 0.393737i | \(-0.128818\pi\) |
0.118625 | + | 0.992939i | \(0.462151\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 495513.i | 0.549557i | 0.961508 | + | 0.274778i | \(0.0886045\pi\) | ||||
−0.961508 | + | 0.274778i | \(0.911396\pi\) | |||||||
\(242\) | −3720.10 | − | 2147.80i | −0.00408335 | − | 0.00235752i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 386561.i | − | 0.415665i | ||||||
\(245\) | 99095.3 | − | 1.04706e6i | 0.105472 | − | 1.11444i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −488583. | −0.509561 | ||||||||
\(248\) | 10847.3 | + | 18788.1i | 0.0111994 | + | 0.0193979i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4626.79 | − | 2671.28i | −0.00468198 | − | 0.00270314i | ||||
\(251\) | 773459. | 0.774913 | 0.387456 | − | 0.921888i | \(-0.373354\pi\) | ||||
0.387456 | + | 0.921888i | \(0.373354\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 213464. | 0.209664 | ||||||||
\(254\) | 4930.53 | + | 2846.64i | 0.00479523 | + | 0.00276853i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −524069. | − | 907714.i | −0.499791 | − | 0.865663i | ||||
\(257\) | −1.09138e6 | −1.03073 | −0.515364 | − | 0.856972i | \(-0.672343\pi\) | ||||
−0.515364 | + | 0.856972i | \(0.672343\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −118214. | + | 370341.i | −0.109501 | + | 0.343046i | ||||
\(260\) | − | 1.03404e6i | − | 0.948647i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7583.30 | − | 4378.22i | −0.00682503 | − | 0.00394044i | ||||
\(263\) | − | 363851.i | − | 0.324365i | −0.986761 | − | 0.162183i | \(-0.948147\pi\) | ||
0.986761 | − | 0.162183i | \(-0.0518533\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.36995e6 | + | 790944.i | 1.19837 | + | 0.691880i | ||||
\(266\) | −3019.34 | − | 3318.59i | −0.00261642 | − | 0.00287574i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −379455. | + | 657236.i | −0.322718 | + | 0.558965i | ||||
\(269\) | 189727. | − | 328617.i | 0.159863 | − | 0.276891i | −0.774956 | − | 0.632015i | \(-0.782228\pi\) |
0.934819 | + | 0.355124i | \(0.115561\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.70719e6 | − | 985645.i | 1.41208 | − | 0.815262i | 0.416492 | − | 0.909139i | \(-0.363259\pi\) |
0.995584 | + | 0.0938771i | \(0.0299261\pi\) | |||||||
\(272\) | −571618. | − | 990072.i | −0.468472 | − | 0.811418i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 866.504 | − | 1500.83i | 0.000697259 | − | 0.00120769i | ||||
\(275\) | 165182.i | 0.131714i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.00010e6 | 1.56622 | 0.783109 | − | 0.621884i | \(-0.213633\pi\) | ||||
0.783109 | + | 0.621884i | \(0.213633\pi\) | |||||||
\(278\) | −862.588 | − | 1494.05i | −0.000669408 | − | 0.00115945i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 14047.3 | − | 12780.6i | 0.0107077 | − | 0.00974217i | ||||
\(281\) | −2.15849e6 | + | 1.24620e6i | −1.63074 | + | 0.941506i | −0.646870 | + | 0.762600i | \(0.723922\pi\) |
−0.983866 | + | 0.178906i | \(0.942744\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 362849. | − | 209491.i | 0.269314 | − | 0.155489i | −0.359262 | − | 0.933237i | \(-0.616971\pi\) |
0.628576 | + | 0.777748i | \(0.283638\pi\) | |||||||
\(284\) | −1.47999e6 | + | 854472.i | −1.08884 | + | 0.628640i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3416.27 | + | 1972.38i | −0.00246966 | + | 0.00142586i | ||||
\(287\) | 1.57335e6 | − | 342953.i | 1.12751 | − | 0.245771i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 86550.9 | + | 149911.i | 0.0609575 | + | 0.105581i | ||||
\(290\) | 11958.1 | 0.00834964 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 2.50442e6i | − | 1.71890i | ||||||
\(293\) | 1.04949e6 | − | 1.81777e6i | 0.714182 | − | 1.23700i | −0.249092 | − | 0.968480i | \(-0.580132\pi\) |
0.963274 | − | 0.268520i | \(-0.0865344\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.04213e6 | − | 1.80502e6i | −0.697213 | − | 1.20761i | ||||
\(296\) | −6079.22 | + | 3509.84i | −0.00403291 | + | 0.00232840i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7045.61 | − | 12203.4i | 0.00459598 | − | 0.00796047i | ||||
\(299\) | −263918. | + | 457119.i | −0.170722 | + | 0.295700i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −510774. | + | 1.60015e6i | −0.324947 | + | 1.01800i | ||||
\(302\) | 3646.87 | + | 2105.52i | 0.00230093 | + | 0.00132844i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 968715.i | 0.601191i | ||||||||
\(305\) | −654689. | − | 377985.i | −0.402982 | − | 0.232662i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.64040e6i | − | 0.993356i | −0.867935 | − | 0.496678i | \(-0.834553\pi\) | ||
0.867935 | − | 0.496678i | \(-0.165447\pi\) | |||||||
\(308\) | 825319. | + | 263444.i | 0.495730 | + | 0.158238i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 21212.9 | 0.0125371 | ||||||||
\(311\) | 1.42933e6 | + | 2.47567e6i | 0.837977 | + | 1.45142i | 0.891584 | + | 0.452856i | \(0.149595\pi\) |
−0.0536068 | + | 0.998562i | \(0.517072\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −362882. | − | 209510.i | −0.209365 | − | 0.120877i | 0.391651 | − | 0.920114i | \(-0.371904\pi\) |
−0.601016 | + | 0.799237i | \(0.705237\pi\) | |||||||
\(314\) | −970.465 | −0.000555464 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.57852e6 | −0.889266 | ||||||||
\(317\) | 402273. | + | 232252.i | 0.224839 | + | 0.129811i | 0.608189 | − | 0.793792i | \(-0.291896\pi\) |
−0.383350 | + | 0.923603i | \(0.625230\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 545517. | + | 944863.i | 0.300145 | + | 0.519867i | ||||
\(320\) | −2.05003e6 | −1.11914 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4735.83 | + | 1032.30i | −0.00254540 | + | 0.000554837i | ||||
\(323\) | 1.05643e6i | 0.563424i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −353726. | − | 204224.i | −0.185763 | − | 0.107250i | ||||
\(326\) | 16403.6i | 0.00854862i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 25181.5 | + | 14538.6i | 0.0129240 | + | 0.00746168i | ||||
\(329\) | 2.52809e6 | − | 551065.i | 1.28767 | − | 0.280681i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.71251e6 | + | 2.96615e6i | −0.859138 | + | 1.48807i | 0.0136135 | + | 0.999907i | \(0.495667\pi\) |
−0.872752 | + | 0.488164i | \(0.837667\pi\) | |||||||
\(332\) | −907547. | + | 1.57192e6i | −0.451881 | + | 0.782680i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −14122.4 | + | 8153.55i | −0.00692693 | + | 0.00399927i | ||||
\(335\) | 742075. | + | 1.28531e6i | 0.361273 | + | 0.625743i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.98556e6 | − | 3.43909e6i | 0.952376 | − | 1.64956i | 0.212114 | − | 0.977245i | \(-0.431965\pi\) |
0.740262 | − | 0.672318i | \(-0.234701\pi\) | |||||||
\(338\) | 3826.88i | 0.00182202i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.23584e6 | −1.04892 | ||||||||
\(341\) | 967712. | + | 1.67613e6i | 0.450671 | + | 0.780586i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.74265e6 | + | 1.30796e6i | −0.799786 | + | 0.600285i | ||||
\(344\) | −26266.8 | + | 15165.2i | −0.0119677 | + | 0.00690957i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12003.4 | − | 6930.18i | 0.00539032 | − | 0.00311210i | ||||
\(347\) | −2.72569e6 | + | 1.57368e6i | −1.21521 | + | 0.701603i | −0.963890 | − | 0.266300i | \(-0.914199\pi\) |
−0.251323 | + | 0.967903i | \(0.580865\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.32028e6 | − | 1.33961e6i | 1.01971 | − | 0.588730i | 0.105690 | − | 0.994399i | \(-0.466295\pi\) |
0.914020 | + | 0.405669i | \(0.132962\pi\) | |||||||
\(350\) | −798.810 | − | 3664.67i | −0.000348557 | − | 0.00159906i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 11732.8 | + | 20321.8i | 0.00504713 | + | 0.00874188i | ||||
\(353\) | 1.27492e6 | 0.544559 | 0.272280 | − | 0.962218i | \(-0.412222\pi\) | ||||
0.272280 | + | 0.962218i | \(0.412222\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.34206e6i | 1.40749i | ||||||||
\(356\) | 1.84407e6 | − | 3.19402e6i | 0.771173 | − | 1.33571i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12068.6 | − | 20903.5i | −0.00497681 | − | 0.00862009i | ||||
\(359\) | −1.66089e6 | + | 958913.i | −0.680148 | + | 0.392684i | −0.799911 | − | 0.600119i | \(-0.795120\pi\) |
0.119763 | + | 0.992803i | \(0.461787\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −790469. | + | 1.36913e6i | −0.319240 | + | 0.552939i | ||||
\(362\) | 10091.9 | − | 17479.8i | 0.00404765 | − | 0.00701074i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.58454e6 | + | 1.44165e6i | −0.626828 | + | 0.570305i | ||||
\(365\) | −4.24155e6 | − | 2.44886e6i | −1.66645 | − | 0.962125i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 2.45946e6i | − | 0.953180i | −0.879126 | − | 0.476590i | \(-0.841873\pi\) | ||
0.879126 | − | 0.476590i | \(-0.158127\pi\) | |||||||
\(368\) | 906331. | + | 523270.i | 0.348873 | + | 0.201422i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6863.81i | 0.00260652i | ||||||||
\(371\) | −697962. | − | 3.20201e6i | −0.263267 | − | 1.20778i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.66049e6 | −0.990123 | −0.495061 | − | 0.868858i | \(-0.664854\pi\) | ||||
−0.495061 | + | 0.868858i | \(0.664854\pi\) | |||||||
\(374\) | 4264.76 | + | 7386.78i | 0.00157658 | + | 0.00273071i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 40462.2 | + | 23360.9i | 0.0147598 | + | 0.00852156i | ||||
\(377\) | −2.69781e6 | −0.977593 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.62518e6 | −0.581172 | −0.290586 | − | 0.956849i | \(-0.593850\pi\) | ||||
−0.290586 | + | 0.956849i | \(0.593850\pi\) | |||||||
\(380\) | 1.64071e6 | + | 947264.i | 0.582871 | + | 0.336521i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −752.614 | − | 1303.57i | −0.000263884 | − | 0.000457061i | ||||
\(383\) | −1.65754e6 | −0.577388 | −0.288694 | − | 0.957421i | \(-0.593221\pi\) | ||||
−0.288694 | + | 0.957421i | \(0.593221\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.25318e6 | − | 1.14018e6i | 0.430887 | − | 0.392033i | ||||
\(386\) | 11851.3i | 0.00404852i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −546234. | − | 315368.i | −0.184204 | − | 0.106350i | ||||
\(389\) | 3.16936e6i | 1.06193i | 0.847393 | + | 0.530966i | \(0.178171\pi\) | ||||
−0.847393 | + | 0.530966i | \(0.821829\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 988398. | + | 570652.i | 0.326956 | + | 0.188768i | ||||
\(392\) | −39169.2 | − | 3707.02i | −0.0128745 | − | 0.00121846i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −16438.9 | + | 28473.1i | −0.00533499 | + | 0.00924047i | ||||
\(395\) | −1.54350e6 | + | 2.67342e6i | −0.497752 | + | 0.862132i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.14283e6 | + | 1.23716e6i | −0.682357 | + | 0.393959i | −0.800742 | − | 0.599009i | \(-0.795561\pi\) |
0.118386 | + | 0.992968i | \(0.462228\pi\) | |||||||
\(398\) | 3922.59 | + | 6794.12i | 0.00124127 | + | 0.00214994i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −404916. | + | 701334.i | −0.126536 | + | 0.219167i | ||||
\(401\) | − | 5.85321e6i | − | 1.81775i | −0.417072 | − | 0.908874i | \(-0.636944\pi\) | ||
0.417072 | − | 0.908874i | \(-0.363056\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.78575e6 | −1.46787 | ||||||||
\(404\) | 1.44664e6 | + | 2.50566e6i | 0.440969 | + | 0.763781i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −16671.9 | − | 18324.3i | −0.00501962 | − | 0.00551711i | ||||
\(407\) | −542339. | + | 313120.i | −0.162287 | + | 0.0936967i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.16694e6 | + | 673731.i | −0.344936 | + | 0.199149i | −0.662453 | − | 0.749104i | \(-0.730484\pi\) |
0.317517 | + | 0.948253i | \(0.397151\pi\) | |||||||
\(410\) | 24622.3 | − | 14215.7i | 0.00723386 | − | 0.00417647i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.79317e6 | − | 2.18999e6i | 1.10093 | − | 0.635622i | ||||
\(413\) | −1.31303e6 | + | 4.11346e6i | −0.378790 | + | 1.18668i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.77483e6 | + | 3.07409e6i | 0.505866 | + | 0.876185i | ||||
\(416\) | −58023.6 | −0.0164388 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 7227.44i | − | 0.00202322i | ||||||
\(419\) | 1.81560e6 | − | 3.14471e6i | 0.505225 | − | 0.875076i | −0.494757 | − | 0.869032i | \(-0.664743\pi\) |
0.999982 | − | 0.00604403i | \(-0.00192389\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.21059e6 | − | 3.82885e6i | −0.607858 | − | 1.05284i | −0.991593 | − | 0.129397i | \(-0.958696\pi\) |
0.383735 | − | 0.923443i | \(-0.374638\pi\) | |||||||
\(422\) | −4911.47 | + | 2835.64i | −0.00134255 | + | 0.000775121i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 29588.2 | − | 51248.2i | 0.00799288 | − | 0.0138441i | ||||
\(425\) | −441580. | + | 764839.i | −0.118587 | + | 0.205399i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 333550. | + | 1.53021e6i | 0.0885301 | + | 0.406145i | ||||
\(428\) | −1.34416e6 | − | 776049.i | −0.354683 | − | 0.204776i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 29656.8i | 0.00773488i | ||||||||
\(431\) | −911427. | − | 526213.i | −0.236335 | − | 0.136448i | 0.377156 | − | 0.926150i | \(-0.376902\pi\) |
−0.613491 | + | 0.789701i | \(0.710235\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 3.23100e6i | − | 0.828166i | −0.910239 | − | 0.414083i | \(-0.864102\pi\) | ||
0.910239 | − | 0.414083i | \(-0.135898\pi\) | |||||||
\(434\) | −29574.9 | − | 32506.1i | −0.00753701 | − | 0.00828400i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.01684e6 | 1.01197 | ||||||||
\(437\) | −483539. | − | 837514.i | −0.121123 | − | 0.209792i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 338800. | + | 195606.i | 0.0839038 | + | 0.0484419i | 0.541365 | − | 0.840788i | \(-0.317908\pi\) |
−0.457461 | + | 0.889230i | \(0.651241\pi\) | |||||||
\(440\) | 30593.1 | 0.00753341 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −21091.1 | −0.00513503 | ||||||||
\(443\) | 5.81377e6 | + | 3.35658e6i | 1.40750 | + | 0.812621i | 0.995147 | − | 0.0984019i | \(-0.0313731\pi\) |
0.412355 | + | 0.911023i | \(0.364706\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.60631e6 | − | 6.24632e6i | −0.863303 | − | 1.49528i | ||||
\(446\) | −38268.6 | −0.00910973 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.85813e6 | + | 3.14140e6i | 0.672802 | + | 0.739483i | ||||
\(449\) | − | 2.96589e6i | − | 0.694288i | −0.937812 | − | 0.347144i | \(-0.887152\pi\) | ||
0.937812 | − | 0.347144i | \(-0.112848\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.24649e6 | + | 1.29701e6i | 0.520072 | + | 0.300264i | ||||
\(452\) | − | 1.15159e6i | − | 0.265127i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −28616.6 | − | 16521.8i | −0.00651596 | − | 0.00376199i | ||||
\(455\) | 892238. | + | 4.09328e6i | 0.202047 | + | 0.926921i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −855264. | + | 1.48136e6i | −0.191562 | + | 0.331795i | −0.945768 | − | 0.324843i | \(-0.894689\pi\) |
0.754206 | + | 0.656638i | \(0.228022\pi\) | |||||||
\(458\) | 11052.5 | − | 19143.6i | 0.00246206 | − | 0.00426441i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.77252e6 | − | 1.02337e6i | 0.390568 | − | 0.225495i | ||||
\(461\) | −242995. | − | 420880.i | −0.0532532 | − | 0.0922372i | 0.838170 | − | 0.545409i | \(-0.183626\pi\) |
−0.891423 | + | 0.453172i | \(0.850292\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.37552e6 | − | 2.38247e6i | 0.298205 | − | 0.516507i | −0.677520 | − | 0.735504i | \(-0.736945\pi\) |
0.975725 | + | 0.218998i | \(0.0702787\pi\) | |||||||
\(464\) | 5.34896e6i | 1.15339i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10077.1 | 0.00214966 | ||||||||
\(467\) | −653915. | − | 1.13261e6i | −0.138749 | − | 0.240320i | 0.788274 | − | 0.615324i | \(-0.210975\pi\) |
−0.927023 | + | 0.375004i | \(0.877641\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 934978. | − | 2.92910e6i | 0.196277 | − | 0.614898i | ||||
\(470\) | 39563.7 | − | 22842.1i | 0.00826138 | − | 0.00476971i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −67523.3 | + | 38984.6i | −0.0139508 | + | 0.00805448i | ||||
\(473\) | −2.34332e6 | + | 1.35291e6i | −0.481590 | + | 0.278046i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 648083. | − | 374171.i | 0.131794 | − | 0.0760914i | ||||
\(476\) | 3.11719e6 | + | 3.42614e6i | 0.630589 | + | 0.693087i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −19354.8 | − | 33523.5i | −0.00387452 | − | 0.00671087i | ||||
\(479\) | 3.83472e6 | 0.763651 | 0.381825 | − | 0.924235i | \(-0.375296\pi\) | ||||
0.381825 | + | 0.924235i | \(0.375296\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 1.54851e6i | − | 0.305177i | ||||||
\(482\) | 9062.44 | − | 15696.6i | 0.00177676 | − | 0.00307743i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.87891e6 | − | 3.25437e6i | −0.364580 | − | 0.631471i | ||||
\(485\) | −1.06823e6 | + | 616744.i | −0.206211 | + | 0.119056i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.09145e6 | − | 7.08661e6i | 0.781727 | − | 1.35399i | −0.149207 | − | 0.988806i | \(-0.547672\pi\) |
0.930935 | − | 0.365186i | \(-0.118994\pi\) | |||||||
\(488\) | −14139.9 | + | 24491.0i | −0.00268780 | + | 0.00465541i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −22288.8 | + | 31355.9i | −0.00419369 | + | 0.00589970i | ||||
\(491\) | −4.69323e6 | − | 2.70964e6i | −0.878554 | − | 0.507233i | −0.00837272 | − | 0.999965i | \(-0.502665\pi\) |
−0.870181 | + | 0.492731i | \(0.835998\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.83330e6i | 1.08093i | ||||||||
\(494\) | 15477.1 | + | 8935.70i | 0.00285346 | + | 0.00164745i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.48872e6i | 1.73182i | ||||||||
\(497\) | 5.12128e6 | − | 4.65948e6i | 0.930010 | − | 0.846148i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.40906e6 | −1.15224 | −0.576120 | − | 0.817365i | \(-0.695434\pi\) | ||||
−0.576120 | + | 0.817365i | \(0.695434\pi\) | |||||||
\(500\) | −2.33685e6 | − | 4.04754e6i | −0.418028 | − | 0.724046i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −24501.2 | − | 14145.8i | −0.00433939 | − | 0.00250535i | ||||
\(503\) | 350628. | 0.0617912 | 0.0308956 | − | 0.999523i | \(-0.490164\pi\) | ||||
0.0308956 | + | 0.999523i | \(0.490164\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.65820e6 | 0.987302 | ||||||||
\(506\) | −6762.00 | − | 3904.04i | −0.00117408 | − | 0.000677857i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.49026e6 | + | 4.31326e6i | 0.428140 | + | 0.741559i | ||||
\(509\) | 6.08531e6 | 1.04109 | 0.520545 | − | 0.853834i | \(-0.325729\pi\) | ||||
0.520545 | + | 0.853834i | \(0.325729\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.16097e6 | + | 9.91380e6i | 0.366098 | + | 1.67953i | ||||
\(512\) | 191742.i | 0.0323253i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 34572.2 | + | 19960.3i | 0.00577191 | + | 0.00333241i | ||||
\(515\) | − | 8.56562e6i | − | 1.42312i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.60971e6 | + | 2.08407e6i | 0.593945 | + | 0.342914i | ||||
\(518\) | 10517.9 | − | 9569.47i | 0.00172228 | − | 0.00156698i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −37824.0 | + | 65513.0i | −0.00613421 | + | 0.0106248i | ||||
\(521\) | 4.61410e6 | − | 7.99185e6i | 0.744719 | − | 1.28989i | −0.205607 | − | 0.978635i | \(-0.565917\pi\) |
0.950326 | − | 0.311256i | \(-0.100750\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.25767e6 | + | 3.61287e6i | −1.00037 | + | 0.577561i | −0.908356 | − | 0.418197i | \(-0.862662\pi\) |
−0.0920089 | + | 0.995758i | \(0.529329\pi\) | |||||||
\(524\) | −3.83009e6 | − | 6.63391e6i | −0.609370 | − | 1.05546i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6654.47 | + | 11525.9i | −0.00104869 | + | 0.00181639i | ||||
\(527\) | 1.03479e7i | 1.62303i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.39157e6 | 0.837676 | ||||||||
\(530\) | −28931.1 | − | 50110.2i | −0.00447379 | − | 0.00774884i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −835905. | − | 3.83484e6i | −0.128050 | − | 0.587447i | ||||
\(533\) | −5.55493e6 | + | 3.20714e6i | −0.846955 | + | 0.488990i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.62867e6 | + | 1.51767e6i | −0.397056 | + | 0.229241i | ||||
\(536\) | 48081.8 | − | 27760.0i | 0.00722884 | − | 0.00417357i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −12020.1 | + | 6939.83i | −0.00179042 | + | 0.00103370i | ||||
\(539\) | −3.49436e6 | − | 330711.i | −0.518079 | − | 0.0490317i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −649951. | − | 1.12575e6i | −0.0954746 | − | 0.165367i | 0.814332 | − | 0.580399i | \(-0.197104\pi\) |
−0.909807 | + | 0.415033i | \(0.863770\pi\) | |||||||
\(542\) | −72105.9 | −0.0105432 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 125461.i | 0.0181765i | ||||||||
\(545\) | 3.92773e6 | − | 6.80302e6i | 0.566435 | − | 0.981094i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.06154e6 | + | 1.83864e6i | 0.151694 | + | 0.262742i | 0.931850 | − | 0.362843i | \(-0.118194\pi\) |
−0.780156 | + | 0.625585i | \(0.784861\pi\) | |||||||
\(548\) | 1.31293e6 | − | 758023.i | 0.186763 | − | 0.107828i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3021.02 | − | 5232.55i | 0.000425840 | − | 0.000737576i | ||||
\(551\) | 2.47141e6 | − | 4.28061e6i | 0.346789 | − | 0.600657i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.24860e6 | − | 1.36205e6i | 0.868900 | − | 0.189400i | ||||
\(554\) | −63358.1 | − | 36579.8i | −0.00877057 | − | 0.00506369i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 1.50919e6i | − | 0.207042i | ||||||
\(557\) | −616805. | − | 356112.i | −0.0842383 | − | 0.0486350i | 0.457289 | − | 0.889318i | \(-0.348820\pi\) |
−0.541527 | + | 0.840683i | \(0.682154\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 6.69073e6i | − | 0.905616i | ||||||
\(560\) | 8.11576e6 | − | 1.76904e6i | 1.09360 | − | 0.238379i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 91167.3 | 0.0121758 | ||||||||
\(563\) | 1.53945e6 | + | 2.66640e6i | 0.204689 | + | 0.354532i | 0.950034 | − | 0.312148i | \(-0.101048\pi\) |
−0.745345 | + | 0.666679i | \(0.767715\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.95037e6 | − | 1.12605e6i | −0.257037 | − | 0.148400i | ||||
\(566\) | −15325.5 | −0.00201082 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 125022. | 0.0162598 | ||||||||
\(569\) | 257274. | + | 148537.i | 0.0333131 | + | 0.0192333i | 0.516564 | − | 0.856249i | \(-0.327211\pi\) |
−0.483251 | + | 0.875482i | \(0.660544\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 48109.5 | + | 83328.1i | 0.00617505 | + | 0.0106955i | 0.869096 | − | 0.494643i | \(-0.164701\pi\) |
−0.862921 | + | 0.505338i | \(0.831368\pi\) | |||||||
\(572\) | −3.45091e6 | −0.441005 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −56112.1 | − | 17911.1i | −0.00710848 | − | 0.00226904i | ||||
\(575\) | − | 808462.i | − | 0.101974i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 695339. | + | 401454.i | 0.0869475 | + | 0.0501991i | 0.542843 | − | 0.839834i | \(-0.317348\pi\) |
−0.455896 | + | 0.890033i | \(0.650681\pi\) | |||||||
\(578\) | − | 6331.72i | − | 0.000788319i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9.05952e6 | + | 5.23051e6i | 1.11824 | + | 0.645616i | ||||
\(581\) | 2.23619e6 | − | 7.00556e6i | 0.274833 | − | 0.860999i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.63962e6 | − | 4.57195e6i | 0.321640 | − | 0.557096i | ||||
\(584\) | −91608.5 | + | 158671.i | −0.0111149 | + | 0.0192515i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −66490.4 | + | 38388.2i | −0.00799861 | + | 0.00461800i | ||||
\(587\) | 3.17488e6 | + | 5.49905e6i | 0.380305 | + | 0.658707i | 0.991106 | − | 0.133077i | \(-0.0424857\pi\) |
−0.610801 | + | 0.791784i | \(0.709152\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.38412e6 | − | 7.59352e6i | 0.520708 | − | 0.901893i | ||||
\(590\) | 76237.8i | 0.00901655i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.07024e6 | −0.360054 | ||||||||
\(593\) | −6.03938e6 | − | 1.04605e7i | −0.705271 | − | 1.22156i | −0.966594 | − | 0.256313i | \(-0.917492\pi\) |
0.261323 | − | 0.965251i | \(-0.415841\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.85063e6 | − | 1.92923e6i | 1.02490 | − | 0.223404i | ||||
\(596\) | 1.06756e7 | − | 6.16354e6i | 1.23105 | − | 0.710746i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 16720.5 | − | 9653.58i | 0.00191204 | − | 0.00110391i | ||||
\(599\) | −1.65969e6 | + | 958221.i | −0.188999 | + | 0.109119i | −0.591514 | − | 0.806295i | \(-0.701469\pi\) |
0.402515 | + | 0.915413i | \(0.368136\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −198299. | + | 114488.i | −0.0223941 | + | 0.0129292i | −0.511155 | − | 0.859488i | \(-0.670782\pi\) |
0.488761 | + | 0.872418i | \(0.337449\pi\) | |||||||
\(602\) | 45445.3 | − | 41347.3i | 0.00511090 | − | 0.00465004i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.84192e6 | + | 3.19030e6i | 0.205437 | + | 0.355828i | ||||
\(605\) | −7.34891e6 | −0.816271 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 9.39692e6i | − | 1.03518i | −0.855630 | − | 0.517588i | \(-0.826830\pi\) | ||
0.855630 | − | 0.517588i | \(-0.173170\pi\) | |||||||
\(608\) | 53154.2 | − | 92065.8i | 0.00583148 | − | 0.0101004i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 13825.9 | + | 23947.2i | 0.00150442 | + | 0.00260574i | ||||
\(611\) | −8.92578e6 | + | 5.15330e6i | −0.967260 | + | 0.558448i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.24094e6 | + | 3.88142e6i | −0.240868 | + | 0.417195i | −0.960962 | − | 0.276681i | \(-0.910765\pi\) |
0.720094 | + | 0.693877i | \(0.244099\pi\) | |||||||
\(614\) | −30001.4 | + | 51963.9i | −0.00321159 | + | 0.00556264i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −42652.7 | − | 46880.0i | −0.00452892 | − | 0.00497778i | ||||
\(617\) | −2.69919e6 | − | 1.55838e6i | −0.285444 | − | 0.164801i | 0.350441 | − | 0.936585i | \(-0.386032\pi\) |
−0.635885 | + | 0.771783i | \(0.719365\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.07242e6i | 0.846793i | 0.905944 | + | 0.423397i | \(0.139162\pi\) | ||||
−0.905944 | + | 0.423397i | \(0.860838\pi\) | |||||||
\(620\) | 1.60710e7 | + | 9.27860e6i | 1.67905 | + | 0.969400i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 104564.i | − | 0.0108369i | ||||||
\(623\) | −4.54378e6 | + | 1.42348e7i | −0.469026 | + | 1.46937i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.16117e7 | −1.18904 | ||||||||
\(626\) | 7663.46 | + | 13273.5i | 0.000781608 | + | 0.00135379i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −735229. | − | 424485.i | −0.0743915 | − | 0.0429500i | ||||
\(629\) | −3.34824e6 | −0.337435 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.90946e6 | −0.290897 | −0.145448 | − | 0.989366i | \(-0.546463\pi\) | ||||
−0.145448 | + | 0.989366i | \(0.546463\pi\) | |||||||
\(632\) | 100009. | + | 57740.2i | 0.00995970 | + | 0.00575024i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8495.32 | − | 14714.3i | −0.000839377 | − | 0.00145384i | ||||
\(635\) | 9.74005e6 | 0.958577 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.02847e6 | − | 7.07406e6i | 0.491007 | − | 0.690749i | ||||
\(638\) | − | 39907.8i | − | 0.00388156i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 259797. | + | 149994.i | 0.0250717 | + | 0.0144752i | ||||
\(641\) | 4.28928e6i | 0.412325i | 0.978518 | + | 0.206162i | \(0.0660975\pi\) | ||||
−0.978518 | + | 0.206162i | \(0.933902\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.44581e6 | − | 4.29884e6i | −0.710206 | − | 0.410038i | 0.100931 | − | 0.994893i | \(-0.467818\pi\) |
−0.811137 | + | 0.584856i | \(0.801151\pi\) | |||||||
\(644\) | −4.03941e6 | − | 1.28939e6i | −0.383799 | − | 0.122510i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 19321.1 | − | 33465.1i | 0.00182159 | − | 0.00315508i | ||||
\(647\) | 2.55765e6 | − | 4.42997e6i | 0.240204 | − | 0.416045i | −0.720568 | − | 0.693384i | \(-0.756119\pi\) |
0.960772 | + | 0.277339i | \(0.0894524\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.02388e6 | + | 3.47789e6i | −0.561390 | + | 0.324119i | ||||
\(650\) | 7470.11 | + | 12938.6i | 0.000693495 | + | 0.00120117i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.17500e6 | + | 1.24275e7i | −0.661002 | + | 1.14489i | ||||
\(653\) | 1.65599e7i | 1.51976i | 0.650063 | + | 0.759880i | \(0.274743\pi\) | ||||
−0.650063 | + | 0.759880i | \(0.725257\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.49805e7 | −1.36434 | ||||||||
\(656\) | 6.35881e6 | + | 1.10138e7i | 0.576921 | + | 0.999256i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −90162.1 | − | 28780.0i | −0.00811819 | − | 0.00259135i | ||||
\(659\) | −1.63291e7 | + | 9.42759e6i | −1.46470 | + | 0.845644i | −0.999223 | − | 0.0394175i | \(-0.987450\pi\) |
−0.465475 | + | 0.885061i | \(0.654116\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.60955e6 | + | 2.66132e6i | −0.410350 | + | 0.236916i | −0.690940 | − | 0.722912i | \(-0.742803\pi\) |
0.280590 | + | 0.959828i | \(0.409470\pi\) | |||||||
\(662\) | 108496. | − | 62640.2i | 0.00962208 | − | 0.00555531i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 114998. | − | 66393.9i | 0.0101220 | − | 0.00584397i | ||||
\(665\) | −7.31215e6 | − | 2.33406e6i | −0.641196 | − | 0.204672i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.66996e6 | − | 4.62451e6i | −0.232375 | − | 0.402486i | ||||
\(668\) | −1.42655e7 | −1.23694 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 54287.2i | − | 0.00467208i | ||||||
\(671\) | −1.26145e6 | + | 2.18489e6i | −0.108159 | + | 0.187337i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.88232e6 | − | 6.72437e6i | −0.330410 | − | 0.572287i | 0.652182 | − | 0.758062i | \(-0.273854\pi\) |
−0.982592 | + | 0.185775i | \(0.940520\pi\) | |||||||
\(674\) | −125795. | + | 72627.8i | −0.0106663 | + | 0.00615819i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.67389e6 | + | 2.89926e6i | −0.140883 | + | 0.244017i | ||||
\(677\) | −7.37106e6 | + | 1.27671e7i | −0.618100 | + | 1.07058i | 0.371732 | + | 0.928340i | \(0.378764\pi\) |
−0.989832 | + | 0.142240i | \(0.954569\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.43440e6 | + | 777067.i | 0.202637 | + | 0.0646821i | ||||
\(680\) | 141655. | + | 81784.3i | 0.0117479 | + | 0.00678263i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 70793.9i | − | 0.00582821i | ||||||
\(683\) | −3.30879e6 | − | 1.91033e6i | −0.271404 | − | 0.156695i | 0.358121 | − | 0.933675i | \(-0.383417\pi\) |
−0.629526 | + | 0.776980i | \(0.716751\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 2.96482e6i | − | 0.241420i | ||||||
\(686\) | 79123.8 | − | 9561.50i | 0.00641944 | − | 0.000775739i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.32657e7 | −1.06847 | ||||||||
\(689\) | 6.52701e6 | + | 1.13051e7i | 0.523801 | + | 0.907250i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.71352e6 | + | 2.14400e6i | 0.295863 | + | 0.170817i | 0.640583 | − | 0.767889i | \(-0.278693\pi\) |
−0.344720 | + | 0.938706i | \(0.612026\pi\) | |||||||
\(692\) | 1.21251e7 | 0.962545 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 115124. | 0.00907333 | ||||||||
\(695\) | −2.55601e6 | − | 1.47571e6i | −0.200724 | − | 0.115888i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.93459e6 | + | 1.20111e7i | 0.540678 | + | 0.936482i | ||||
\(698\) | −98000.8 | −0.00761362 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 997754. | − | 3.12577e6i | 0.0769623 | − | 0.241108i | ||||
\(701\) | 3.30925e6i | 0.254351i | 0.991880 | + | 0.127176i | \(0.0405912\pi\) | ||||
−0.991880 | + | 0.127176i | \(0.959409\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.45701e6 | + | 1.41856e6i | 0.187508 | + | 0.108258i | ||||
\(704\) | 6.84156e6i | 0.520263i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −40386.2 | − | 23317.0i | −0.00304945 | − | 0.00176060i | ||||
\(707\) | −7.88862e6 | − | 8.67046e6i | −0.593544 | − | 0.652370i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.05888e7 | − | 1.83403e7i | 0.791099 | − | 1.37022i | −0.134188 | − | 0.990956i | \(-0.542843\pi\) |
0.925287 | − | 0.379267i | \(-0.123824\pi\) | |||||||
\(710\) | 61123.0 | − | 105868.i | 0.00455050 | − | 0.00788169i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −233666. | + | 134907.i | −0.0172741 | + | 0.00997323i | ||||
\(713\) | −4.73634e6 | − | 8.20358e6i | −0.348914 | − | 0.604337i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.37435e6 | + | 5.84455e6i | −0.246845 | + | 0.427549i | ||||
\(716\) | − | 2.11155e7i | − | 1.53928i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 70150.2 | 0.00507830 | ||||||||
\(719\) | −1.36318e7 | − | 2.36110e7i | −0.983401 | − | 1.70330i | −0.648837 | − | 0.760927i | \(-0.724744\pi\) |
−0.334564 | − | 0.942373i | \(-0.608589\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.31257e7 | + | 1.19421e7i | −0.940339 | + | 0.855546i | ||||
\(722\) | 50080.1 | − | 28913.8i | 0.00357538 | − | 0.00206425i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.52914e7 | − | 8.82849e6i | 1.08418 | − | 0.625950i | ||||
\(725\) | 3.57852e6 | − | 2.06606e6i | 0.252848 | − | 0.145982i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.28331e6 | + | 5.35972e6i | −0.651429 | + | 0.376103i | −0.789003 | − | 0.614389i | \(-0.789403\pi\) |
0.137575 | + | 0.990491i | \(0.456069\pi\) | |||||||
\(728\) | 153124. | − | 33377.5i | 0.0107082 | − | 0.00233413i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 89574.3 | + | 155147.i | 0.00622123 | + | 0.0107755i | ||||
\(731\) | −1.44669e7 | −1.00134 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 1.35789e7i | − | 0.933477i | −0.884395 | − | 0.466739i | \(-0.845429\pi\) | ||
0.884395 | − | 0.466739i | \(-0.154571\pi\) | |||||||
\(734\) | −44981.1 | + | 77909.6i | −0.00308170 | + | 0.00533766i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −57424.6 | − | 99462.3i | −0.00390754 | − | 0.00676805i | ||||
\(737\) | 4.28947e6 | − | 2.47653e6i | 0.290894 | − | 0.167948i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.64402e6 | + | 6.31163e6i | −0.245454 | + | 0.425139i | −0.962259 | − | 0.272135i | \(-0.912270\pi\) |
0.716805 | + | 0.697274i | \(0.245604\pi\) | |||||||
\(740\) | −3.00225e6 | + | 5.20005e6i | −0.201543 | + | 0.349083i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −36451.8 | + | 114197.i | −0.00243058 | + | 0.00761453i | ||||
\(743\) | 1.67522e7 | + | 9.67187e6i | 1.11327 | + | 0.642744i | 0.939673 | − | 0.342073i | \(-0.111129\pi\) |
0.173593 | + | 0.984818i | \(0.444462\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 2.41072e7i | − | 1.59132i | ||||||
\(746\) | 84277.5 | + | 48657.7i | 0.00554453 | + | 0.00320114i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 7.46168e6i | 0.487621i | ||||||||
\(749\) | 5.99050e6 | + | 1.91218e6i | 0.390174 | + | 0.124545i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.51858e7 | 0.982512 | 0.491256 | − | 0.871015i | \(-0.336538\pi\) | ||||
0.491256 | + | 0.871015i | \(0.336538\pi\) | |||||||
\(752\) | 1.02175e7 | + | 1.76972e7i | 0.658868 | + | 1.14119i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 85459.9 | + | 49340.3i | 0.00547437 | + | 0.00316063i | ||||
\(755\) | 7.20424e6 | 0.459961 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.74980e7 | −1.10981 | −0.554906 | − | 0.831913i | \(-0.687246\pi\) | ||||
−0.554906 | + | 0.831913i | \(0.687246\pi\) | |||||||
\(758\) | 51481.8 | + | 29723.0i | 0.00325447 | + | 0.00187897i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −69299.5 | − | 120030.i | −0.00435207 | − | 0.00753801i | ||||
\(761\) | 1.07783e7 | 0.674666 | 0.337333 | − | 0.941385i | \(-0.390475\pi\) | ||||
0.337333 | + | 0.941385i | \(0.390475\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.59008e7 | + | 3.46599e6i | −0.988796 | + | 0.215534i | ||||
\(764\) | − | 1.31678e6i | − | 0.0816170i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 52506.8 | + | 30314.8i | 0.00323328 | + | 0.00186674i | ||||
\(767\) | − | 1.71996e7i | − | 1.05568i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.07648e6 | + | 4.66296e6i | 0.492500 | + | 0.284345i | 0.725611 | − | 0.688105i | \(-0.241557\pi\) |
−0.233111 | + | 0.972450i | \(0.574891\pi\) | |||||||
\(770\) | −60550.5 | + | 13198.6i | −0.00368037 | + | 0.000802233i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.18378e6 | + | 8.97857e6i | −0.313043 | + | 0.542206i | ||||
\(773\) | 5.87761e6 | − | 1.01803e7i | 0.353795 | − | 0.612792i | −0.633116 | − | 0.774057i | \(-0.718224\pi\) |
0.986911 | + | 0.161266i | \(0.0515576\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.34807e6 | − | 3.66506e6i | 0.379654 | − | 0.219193i | ||||
\(776\) | 23071.6 | + | 39961.1i | 0.00137538 | + | 0.00238223i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 57964.4 | − | 100397.i | 0.00343330 | − | 0.00594665i | ||||
\(779\) | − | 1.17520e7i | − | 0.693853i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.11535e7 | 0.654308 | ||||||||
\(782\) | −20873.3 | − | 36153.6i | −0.00122060 | − | 0.00211415i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.40258e7 | − | 9.96997e6i | −0.814960 | − | 0.579300i | ||||
\(785\) | −1.43784e6 | + | 830135.i | −0.0832789 | + | 0.0480811i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.84640e6 | + | 4.53012e6i | −0.451579 | + | 0.260719i | −0.708497 | − | 0.705714i | \(-0.750626\pi\) |
0.256918 | + | 0.966433i | \(0.417293\pi\) | |||||||
\(788\) | −2.49084e7 | + | 1.43809e7i | −1.42899 | + | 0.825030i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 97788.2 | − | 56458.1i | 0.00557467 | − | 0.00321854i | ||||
\(791\) | 993670. | + | 4.55861e6i | 0.0564678 | + | 0.259055i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.11920e6 | − | 5.40262e6i | −0.176141 | − | 0.305085i | ||||
\(794\) | 90506.0 | 0.00509479 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.86300e6i | 0.383912i | ||||||||
\(797\) | −588634. | + | 1.01954e6i | −0.0328246 | + | 0.0568538i | −0.881971 | − | 0.471304i | \(-0.843784\pi\) |
0.849146 | + | 0.528157i | \(0.177117\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.11426e7 | + | 1.92996e7i | 0.617478 | + | 1.06950i | ||||
\(800\) | 76965.6 | − | 44436.1i | 0.00425179 | − | 0.00245477i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −107049. | + | 185415.i | −0.00587690 | + | 0.0101791i | ||||
\(803\) | −8.17258e6 | + | 1.41553e7i | −0.447270 | + | 0.774695i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.13355e6 | + | 5.58047e6i | −0.333597 | + | 0.303516i | ||||
\(806\) | 151600. | + | 87526.5i | 0.00821983 | + | 0.00474572i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 211666.i | − | 0.0114057i | ||||||
\(809\) | −2.15920e6 | − | 1.24662e6i | −0.115990 | − | 0.0669671i | 0.440882 | − | 0.897565i | \(-0.354666\pi\) |
−0.556873 | + | 0.830598i | \(0.687999\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 2.14197e7i | − | 1.14357i | −0.820405 | − | 0.571783i | \(-0.806252\pi\) | ||
0.820405 | − | 0.571783i | \(-0.193748\pi\) | |||||||
\(812\) | −4.61563e6 | − | 2.11749e7i | −0.245663 | − | 1.12702i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 22906.6 | 0.00121171 | ||||||||
\(815\) | 1.40316e7 | + | 2.43035e7i | 0.739971 | + | 1.28167i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.06162e7 | + | 6.12924e6i | 0.556432 | + | 0.321256i | ||||
\(818\) | 49287.5 | 0.00257545 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.48720e7 | 1.29174 | ||||||||
\(821\) | −1.12322e7 | − | 6.48492e6i | −0.581577 | − | 0.335774i | 0.180183 | − | 0.983633i | \(-0.442331\pi\) |
−0.761760 | + | 0.647859i | \(0.775664\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.07468e6 | + | 5.32550e6i | 0.158234 | + | 0.274070i | 0.934232 | − | 0.356666i | \(-0.116087\pi\) |
−0.775998 | + | 0.630736i | \(0.782753\pi\) | |||||||
\(824\) | −320429. | −0.0164404 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 116825. | − | 106290.i | 0.00595778 | − | 0.00542055i | ||||
\(827\) | 8.96370e6i | 0.455747i | 0.973691 | + | 0.227873i | \(0.0731772\pi\) | ||||
−0.973691 | + | 0.227873i | \(0.926823\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.22718e6 | + | 5.32732e6i | 0.466319 | + | 0.269229i | 0.714697 | − | 0.699434i | \(-0.246564\pi\) |
−0.248379 | + | 0.968663i | \(0.579898\pi\) | |||||||
\(830\) | − | 129839.i | − | 0.00654200i | ||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.46507e7 | − | 8.45860e6i | −0.733755 | − | 0.423633i | ||||
\(833\) | −1.52958e7 | − | 1.08727e7i | −0.763764 | − | 0.542908i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.39491e7 | + | 2.41605e7i | −0.692355 | + | 1.19919i | ||||
\(836\) | 3.16131e6 | − | 5.47554e6i | 0.156441 | − | 0.270964i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −115027. | + | 66411.0i | −0.00565836 | + | 0.00326686i | ||||
\(839\) | 1.54509e7 | + | 2.67618e7i | 0.757791 | + | 1.31253i | 0.943975 | + | 0.330017i | \(0.107054\pi\) |
−0.186184 | + | 0.982515i | \(0.559612\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.39083e6 | − | 5.87308e6i | 0.165316 | − | 0.286336i | ||||
\(842\) | 161718.i | 0.00786099i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.96127e6 | −0.239738 | ||||||||
\(845\) | 3.27351e6 | + | 5.66988e6i | 0.157714 | + | 0.273169i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.02458e7 | + | 1.12613e7i | 0.490724 | + | 0.539359i | ||||
\(848\) | 2.24147e7 | − | 1.29411e7i | 1.07039 | − | 0.617992i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 27976.3 | − | 16152.1i | 0.00132814 | − | 0.000766800i | ||||
\(851\) | 2.65441e6 | − | 1.53252e6i | 0.125645 | − | 0.0725409i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.38828e7 | + | 8.01527e6i | −0.653290 | + | 0.377177i | −0.789716 | − | 0.613473i | \(-0.789772\pi\) |
0.136426 | + | 0.990650i | \(0.456439\pi\) | |||||||
\(854\) | 17420.0 | − | 54573.5i | 0.000817342 | − | 0.00256057i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 56773.9 | + | 98335.2i | 0.00264828 | + | 0.00458696i | ||||
\(857\) | −1.99838e7 | −0.929450 | −0.464725 | − | 0.885455i | \(-0.653847\pi\) | ||||
−0.464725 | + | 0.885455i | \(0.653847\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.65184e7i | 0.763808i | 0.924202 | + | 0.381904i | \(0.124732\pi\) | ||||
−0.924202 | + | 0.381904i | \(0.875268\pi\) | |||||||
\(860\) | −1.29720e7 | + | 2.24681e7i | −0.598082 | + | 1.03591i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 19247.8 | + | 33338.2i | 0.000882294 | + | 0.00152818i | ||||
\(863\) | 2.59300e7 | − | 1.49707e7i | 1.18516 | − | 0.684251i | 0.227956 | − | 0.973672i | \(-0.426796\pi\) |
0.957202 | + | 0.289420i | \(0.0934625\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.18561e7 | − | 2.05354e7i | 0.538769 | − | 0.933175i | ||||
\(866\) | −59091.8 | + | 102350.i | −0.00267752 | + | 0.00463760i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −8.18782e6 | − | 3.75629e7i | −0.368866 | − | 1.69223i | ||||
\(869\) | 8.92200e6 | + | 5.15112e6i | 0.400786 | + | 0.231394i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.22475e7i | 0.547017i | ||||||||
\(872\) | −254492. | − | 146931.i | −0.0113340 | − | 0.00654368i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 35373.8i | 0.00156640i | ||||||||
\(875\) | 1.27430e7 | + | 1.40059e7i | 0.562665 | + | 0.618431i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.23314e7 | 1.85850 | 0.929252 | − | 0.369447i | \(-0.120453\pi\) | ||||
0.929252 | + | 0.369447i | \(0.120453\pi\) | |||||||
\(878\) | −7154.88 | − | 12392.6i | −0.000313232 | − | 0.000542534i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.15880e7 | + | 6.69034e6i | 0.504431 | + | 0.291234i | ||||
\(881\) | −3.17552e7 | −1.37840 | −0.689201 | − | 0.724571i | \(-0.742038\pi\) | ||||
−0.689201 | + | 0.724571i | \(0.742038\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.71883e7 | 0.741874 | 0.370937 | − | 0.928658i | \(-0.379037\pi\) | ||||
0.370937 | + | 0.928658i | \(0.379037\pi\) | |||||||
\(884\) | −1.59787e7 | − | 9.22529e6i | −0.687717 | − | 0.397054i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −122777. | − | 212656.i | −0.00525452 | − | 0.00910110i | ||||
\(887\) | 2.36859e7 | 1.01084 | 0.505419 | − | 0.862874i | \(-0.331338\pi\) | ||||
0.505419 | + | 0.862874i | \(0.331338\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.35795e7 | − | 1.49254e7i | −0.576275 | − | 0.633390i | ||||
\(890\) | 263823.i | 0.0111645i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.89925e7 | − | 1.67388e7i | −1.22004 | − | 0.704388i | ||||
\(893\) | − | 1.88833e7i | − | 0.792410i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.57617e7 | − | 2.06470e7i | −1.49231 | − | 0.861588i | ||||
\(896\) | −132361. | − | 607225.i | −0.00550794 | − | 0.0252685i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −54243.2 | + | 93952.0i | −0.00224468 | + | 0.00388790i | ||||
\(899\) | 2.42078e7 | − | 4.19292e7i | 0.998980 | − | 1.73028i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.44443e7 | − | 1.41129e7i | 1.00315 | − | 0.579169i | ||||
\(902\) | −47442.1 | − | 82172.2i | −0.00194155 | − | 0.00336286i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −42123.9 | + | 72960.7i | −0.00171438 | + | 0.00296940i | ||||
\(905\) | − | 3.45305e7i | − | 1.40146i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.91466e7 | 1.98370 | 0.991849 | − | 0.127420i | \(-0.0406697\pi\) | ||||
0.991849 | + | 0.127420i | \(0.0406697\pi\) | |||||||
\(908\) | −1.44534e7 | − | 2.50340e7i | −0.581775 | − | 1.00766i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 46598.1 | − | 145983.i | 0.00186537 | − | 0.00584384i | ||||
\(911\) | 3.73255e7 | − | 2.15499e7i | 1.49008 | − | 0.860298i | 0.490145 | − | 0.871641i | \(-0.336944\pi\) |
0.999936 | + | 0.0113430i | \(0.00361066\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.02592e7 | − | 5.92313e6i | 0.407319 | − | 0.235166i | ||||
\(914\) | 54185.2 | − | 31283.9i | 0.00214543 | − | 0.00123867i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.67469e7 | − | 9.66883e6i | 0.659472 | − | 0.380746i | ||||
\(917\) | 2.08857e7 | + | 2.29557e7i | 0.820211 | + | 0.901502i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.93863e7 | + | 3.35781e7i | 0.757193 | + | 1.31150i | 0.944277 | + | 0.329152i | \(0.106763\pi\) |
−0.187084 | + | 0.982344i | \(0.559904\pi\) | |||||||
\(920\) | −149734. | −0.00583244 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 17776.6i | 0.000688685i | ||||||||
\(923\) | −1.37897e7 | + | 2.38844e7i | −0.532782 | + | 0.922805i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.18589e6 | + | 2.05403e6i | 0.0455713 | + | 0.0789317i | ||||
\(926\) | −87146.2 | + | 50313.9i | −0.00333980 | + | 0.00192824i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 293502. | − | 508360.i | 0.0111877 | − | 0.0193777i | ||||
\(929\) | −68816.6 | + | 119194.i | −0.00261610 | + | 0.00453121i | −0.867330 | − | 0.497733i | \(-0.834166\pi\) |
0.864714 | + | 0.502264i | \(0.167499\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.61791e6 | + | 1.44591e7i | 0.250234 | + | 0.546721i | ||||
\(932\) | 7.63442e6 | + | 4.40773e6i | 0.287896 | + | 0.166217i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 47837.8i | 0.00179434i | ||||||||
\(935\) | 1.26373e7 | + | 7.29614e6i | 0.472743 | + | 0.272938i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.30702e7i | 1.23052i | 0.788325 | + | 0.615259i | \(0.210948\pi\) | ||||
−0.788325 | + | 0.615259i | \(0.789052\pi\) | |||||||
\(938\) | −83188.2 | + | 75686.9i | −0.00308713 | + | 0.00280875i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.99649e7 | 1.47523 | ||||||||
\(941\) | −3.37537e6 | − | 5.84631e6i | −0.124265 | − | 0.215233i | 0.797181 | − | 0.603741i | \(-0.206324\pi\) |
−0.921445 | + | 0.388508i | \(0.872990\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.09952e7 | − | 6.34806e6i | −0.402645 | − | 0.232467i | ||||
\(944\) | −3.41018e7 | −1.24551 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 98973.8 | 0.00359577 | ||||||||
\(947\) | −184943. | − | 106777.i | −0.00670137 | − | 0.00386904i | 0.496646 | − | 0.867953i | \(-0.334565\pi\) |
−0.503347 | + | 0.864084i | \(0.667898\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.02084e7 | − | 3.50020e7i | −0.728395 | − | 1.26162i | ||||
\(950\) | −27372.8 | −0.000984036 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −72169.9 | − | 331091.i | −0.00258086 | − | 0.0118401i | ||||
\(953\) | − | 5.03164e6i | − | 0.179464i | −0.995966 | − | 0.0897320i | \(-0.971399\pi\) | ||
0.995966 | − | 0.0897320i | \(-0.0286011\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.23014e6 | − | 1.28757e6i | −0.0791267 | − | 0.0456838i | ||||
\(956\) | − | 3.38634e7i | − | 1.19835i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −121474. | − | 70133.2i | −0.00427632 | − | 0.00246894i | ||||
\(959\) | −4.54321e6 | + | 4.13354e6i | −0.159520 | + | 0.145136i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.86286e7 | − | 4.95862e7i | 0.999980 | − | 1.73202i | ||||
\(962\) | −28320.7 | + | 49052.9i | −0.000986657 | + | 0.00170894i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.37315e7 | − | 7.92788e6i | 0.475910 | − | 0.274767i | ||||
\(965\) | 1.01376e7 | + | 1.75588e7i | 0.350441 | + | 0.606982i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.93524e7 | + | 3.35193e7i | −0.665531 | + | 1.15273i | 0.313610 | + | 0.949552i | \(0.398462\pi\) |
−0.979141 | + | 0.203182i | \(0.934872\pi\) | |||||||
\(968\) | 274913.i | 0.00942989i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 45118.5 | 0.00153966 | ||||||||
\(971\) | 2.76587e6 | + | 4.79062e6i | 0.0941419 | + | 0.163059i | 0.909250 | − | 0.416250i | \(-0.136656\pi\) |
−0.815108 | + | 0.579309i | \(0.803323\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.30223e6 | + | 5.97418e6i | 0.0440967 | + | 0.202300i | ||||
\(974\) | −259214. | + | 149657.i | −0.00875510 | + | 0.00505476i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.07118e7 | + | 6.18445e6i | −0.359946 | + | 0.207815i | ||||
\(977\) | 3.58671e7 | − | 2.07079e7i | 1.20215 | − | 0.694064i | 0.241120 | − | 0.970495i | \(-0.422485\pi\) |
0.961034 | + | 0.276431i | \(0.0891519\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.08458e7 | + | 1.20354e7i | −0.695125 | + | 0.401330i | ||||
\(980\) | −3.06013e7 | + | 1.40062e7i | −1.01783 | + | 0.465860i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 99113.2 | + | 171669.i | 0.00327984 | + | 0.00568085i | ||||
\(983\) | 7.15134e6 | 0.236050 | 0.118025 | − | 0.993011i | \(-0.462344\pi\) | ||||
0.118025 | + | 0.993011i | \(0.462344\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.62474e7i | 1.84719i | ||||||||
\(986\) | 106685. | − | 184784.i | 0.00349472 | − | 0.00605303i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.81700e6 | + | 1.35394e7i | 0.254770 | + | 0.441274i | ||||
\(989\) | 1.14690e7 | − | 6.62166e6i | 0.372852 | − | 0.215266i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.45962e6 | − | 1.11884e7i | 0.208941 | − | 0.361896i | −0.742440 | − | 0.669912i | \(-0.766332\pi\) |
0.951381 | + | 0.308016i | \(0.0996651\pi\) | |||||||
\(992\) | 520654. | − | 901799.i | 0.0167985 | − | 0.0290958i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −247447. | + | 53937.5i | −0.00794357 | + | 0.00173151i | ||||
\(995\) | 1.16234e7 | + | 6.71075e6i | 0.372198 | + | 0.214889i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.20160e6i | 0.229452i | 0.993397 | + | 0.114726i | \(0.0365990\pi\) | ||||
−0.993397 | + | 0.114726i | \(0.963401\pi\) | |||||||
\(998\) | 203023. | + | 117215.i | 0.00645236 | + | 0.00372527i | ||||
\(999\) | 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 | 189.6.s.a.17.20 | 76 | ||
3.2 | odd | 2 | 63.6.s.a.59.19 | yes | 76 | ||
7.5 | odd | 6 | 189.6.i.a.152.19 | 76 | |||
9.2 | odd | 6 | 189.6.i.a.143.20 | 76 | |||
9.7 | even | 3 | 63.6.i.a.38.19 | yes | 76 | ||
21.5 | even | 6 | 63.6.i.a.5.20 | ✓ | 76 | ||
63.47 | even | 6 | inner | 189.6.s.a.89.20 | 76 | ||
63.61 | odd | 6 | 63.6.s.a.47.19 | yes | 76 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.6.i.a.5.20 | ✓ | 76 | 21.5 | even | 6 | ||
63.6.i.a.38.19 | yes | 76 | 9.7 | even | 3 | ||
63.6.s.a.47.19 | yes | 76 | 63.61 | odd | 6 | ||
63.6.s.a.59.19 | yes | 76 | 3.2 | odd | 2 | ||
189.6.i.a.143.20 | 76 | 9.2 | odd | 6 | |||
189.6.i.a.152.19 | 76 | 7.5 | odd | 6 | |||
189.6.s.a.17.20 | 76 | 1.1 | even | 1 | trivial | ||
189.6.s.a.89.20 | 76 | 63.47 | even | 6 | inner |