Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [138,6,Mod(137,138)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(138, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("138.137");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 138 = 2 \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 138.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(22.1329671342\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 137.14 | ||
Character | \(\chi\) | \(=\) | 138.137 |
Dual form | 138.6.d.a.137.16 |
$q$-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 \(\left(\mathbb{Z}/138\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(97\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 4.00000i | − | 0.707107i | ||||||
\(3\) | 15.5676 | + | 0.805444i | 0.998664 | + | 0.0516692i | ||||
\(4\) | −16.0000 | −0.500000 | ||||||||
\(5\) | 10.2990 | 0.184234 | 0.0921170 | − | 0.995748i | \(-0.470637\pi\) | ||||
0.0921170 | + | 0.995748i | \(0.470637\pi\) | |||||||
\(6\) | 3.22177 | − | 62.2705i | 0.0365357 | − | 0.706162i | ||||
\(7\) | − | 139.754i | − | 1.07800i | −0.842305 | − | 0.539001i | \(-0.818802\pi\) | ||
0.842305 | − | 0.539001i | \(-0.181198\pi\) | |||||||
\(8\) | 64.0000i | 0.353553i | ||||||||
\(9\) | 241.703 | + | 25.0777i | 0.994661 | + | 0.103200i | ||||
\(10\) | − | 41.1960i | − | 0.130273i | ||||||
\(11\) | 570.013 | 1.42038 | 0.710188 | − | 0.704012i | \(-0.248610\pi\) | ||||
0.710188 | + | 0.704012i | \(0.248610\pi\) | |||||||
\(12\) | −249.082 | − | 12.8871i | −0.499332 | − | 0.0258346i | ||||
\(13\) | −754.278 | −1.23786 | −0.618932 | − | 0.785444i | \(-0.712434\pi\) | ||||
−0.618932 | + | 0.785444i | \(0.712434\pi\) | |||||||
\(14\) | −559.016 | −0.762262 | ||||||||
\(15\) | 160.331 | + | 8.29526i | 0.183988 | + | 0.00951923i | ||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 143.694 | 0.120592 | 0.0602959 | − | 0.998181i | \(-0.480796\pi\) | ||||
0.0602959 | + | 0.998181i | \(0.480796\pi\) | |||||||
\(18\) | 100.311 | − | 966.810i | 0.0729737 | − | 0.703331i | ||||
\(19\) | − | 2086.45i | − | 1.32594i | −0.748645 | − | 0.662971i | \(-0.769295\pi\) | ||
0.748645 | − | 0.662971i | \(-0.230705\pi\) | |||||||
\(20\) | −164.784 | −0.0921170 | ||||||||
\(21\) | 112.564 | − | 2175.64i | 0.0556995 | − | 1.07656i | ||||
\(22\) | − | 2280.05i | − | 1.00436i | ||||||
\(23\) | 2486.09 | + | 505.680i | 0.979934 | + | 0.199323i | ||||
\(24\) | −51.5484 | + | 996.329i | −0.0182678 | + | 0.353081i | ||||
\(25\) | −3018.93 | −0.966058 | ||||||||
\(26\) | 3017.11i | 0.875302i | ||||||||
\(27\) | 3742.54 | + | 585.078i | 0.988000 | + | 0.154456i | ||||
\(28\) | 2236.06i | 0.539001i | ||||||||
\(29\) | − | 5651.76i | − | 1.24793i | −0.781454 | − | 0.623963i | \(-0.785521\pi\) | ||
0.781454 | − | 0.623963i | \(-0.214479\pi\) | |||||||
\(30\) | 33.1810 | − | 641.324i | 0.00673111 | − | 0.130099i | ||||
\(31\) | 2627.23 | 0.491013 | 0.245507 | − | 0.969395i | \(-0.421046\pi\) | ||||
0.245507 | + | 0.969395i | \(0.421046\pi\) | |||||||
\(32\) | − | 1024.00i | − | 0.176777i | ||||||
\(33\) | 8873.76 | + | 459.113i | 1.41848 | + | 0.0733897i | ||||
\(34\) | − | 574.778i | − | 0.0852713i | ||||||
\(35\) | − | 1439.33i | − | 0.198604i | ||||||
\(36\) | −3867.24 | − | 401.243i | −0.497330 | − | 0.0516002i | ||||
\(37\) | − | 7249.40i | − | 0.870558i | −0.900296 | − | 0.435279i | \(-0.856650\pi\) | ||
0.900296 | − | 0.435279i | \(-0.143350\pi\) | |||||||
\(38\) | −8345.81 | −0.937582 | ||||||||
\(39\) | −11742.3 | − | 607.529i | −1.23621 | − | 0.0639595i | ||||
\(40\) | 659.136i | 0.0651366i | ||||||||
\(41\) | − | 965.744i | − | 0.0897227i | −0.998993 | − | 0.0448613i | \(-0.985715\pi\) | ||
0.998993 | − | 0.0448613i | \(-0.0142846\pi\) | |||||||
\(42\) | −8702.56 | − | 450.256i | −0.761244 | − | 0.0393855i | ||||
\(43\) | − | 12064.3i | − | 0.995021i | −0.867458 | − | 0.497510i | \(-0.834248\pi\) | ||
0.867458 | − | 0.497510i | \(-0.165752\pi\) | |||||||
\(44\) | −9120.21 | −0.710188 | ||||||||
\(45\) | 2489.29 | + | 258.275i | 0.183250 | + | 0.0190130i | ||||
\(46\) | 2022.72 | − | 9944.35i | 0.140942 | − | 0.692918i | ||||
\(47\) | 19373.9i | 1.27930i | 0.768665 | + | 0.639651i | \(0.220921\pi\) | ||||
−0.768665 | + | 0.639651i | \(0.779079\pi\) | |||||||
\(48\) | 3985.31 | + | 206.194i | 0.249666 | + | 0.0129173i | ||||
\(49\) | −2724.18 | −0.162086 | ||||||||
\(50\) | 12075.7i | 0.683106i | ||||||||
\(51\) | 2236.98 | + | 115.738i | 0.120431 | + | 0.00623089i | ||||
\(52\) | 12068.4 | 0.618932 | ||||||||
\(53\) | −28893.1 | −1.41288 | −0.706438 | − | 0.707775i | \(-0.749699\pi\) | ||||
−0.706438 | + | 0.707775i | \(0.749699\pi\) | |||||||
\(54\) | 2340.31 | − | 14970.2i | 0.109217 | − | 0.698621i | ||||
\(55\) | 5870.56 | 0.261681 | ||||||||
\(56\) | 8944.26 | 0.381131 | ||||||||
\(57\) | 1680.52 | − | 32481.1i | 0.0685104 | − | 1.32417i | ||||
\(58\) | −22607.1 | −0.882417 | ||||||||
\(59\) | − | 20760.7i | − | 0.776447i | −0.921565 | − | 0.388223i | \(-0.873089\pi\) | ||
0.921565 | − | 0.388223i | \(-0.126911\pi\) | |||||||
\(60\) | −2565.30 | − | 132.724i | −0.0919939 | − | 0.00475961i | ||||
\(61\) | 8371.14i | 0.288045i | 0.989574 | + | 0.144022i | \(0.0460037\pi\) | ||||
−0.989574 | + | 0.144022i | \(0.953996\pi\) | |||||||
\(62\) | − | 10508.9i | − | 0.347199i | ||||||
\(63\) | 3504.71 | − | 33778.9i | 0.111250 | − | 1.07225i | ||||
\(64\) | −4096.00 | −0.125000 | ||||||||
\(65\) | −7768.30 | −0.228057 | ||||||||
\(66\) | 1836.45 | − | 35495.0i | 0.0518944 | − | 1.00302i | ||||
\(67\) | − | 28343.6i | − | 0.771380i | −0.922628 | − | 0.385690i | \(-0.873963\pi\) | ||
0.922628 | − | 0.385690i | \(-0.126037\pi\) | |||||||
\(68\) | −2299.11 | −0.0602959 | ||||||||
\(69\) | 38295.2 | + | 9874.65i | 0.968326 | + | 0.249689i | ||||
\(70\) | −5757.30 | −0.140435 | ||||||||
\(71\) | 49123.7i | 1.15650i | 0.815860 | + | 0.578249i | \(0.196264\pi\) | ||||
−0.815860 | + | 0.578249i | \(0.803736\pi\) | |||||||
\(72\) | −1604.97 | + | 15469.0i | −0.0364869 | + | 0.351666i | ||||
\(73\) | 1894.77 | 0.0416149 | 0.0208075 | − | 0.999784i | \(-0.493376\pi\) | ||||
0.0208075 | + | 0.999784i | \(0.493376\pi\) | |||||||
\(74\) | −28997.6 | −0.615577 | ||||||||
\(75\) | −46997.6 | − | 2431.58i | −0.964767 | − | 0.0499155i | ||||
\(76\) | 33383.2i | 0.662971i | ||||||||
\(77\) | − | 79661.6i | − | 1.53117i | ||||||
\(78\) | −2430.11 | + | 46969.3i | −0.0452262 | + | 0.874133i | ||||
\(79\) | 99145.8i | 1.78734i | 0.448727 | + | 0.893669i | \(0.351877\pi\) | ||||
−0.448727 | + | 0.893669i | \(0.648123\pi\) | |||||||
\(80\) | 2636.54 | 0.0460585 | ||||||||
\(81\) | 57791.2 | + | 12122.7i | 0.978699 | + | 0.205299i | ||||
\(82\) | −3862.98 | −0.0634435 | ||||||||
\(83\) | 86038.4 | 1.37087 | 0.685436 | − | 0.728133i | \(-0.259612\pi\) | ||||
0.685436 | + | 0.728133i | \(0.259612\pi\) | |||||||
\(84\) | −1801.02 | + | 34810.2i | −0.0278497 | + | 0.538281i | ||||
\(85\) | 1479.91 | 0.0222171 | ||||||||
\(86\) | −48257.3 | −0.703586 | ||||||||
\(87\) | 4552.18 | − | 87984.6i | 0.0644794 | − | 1.24626i | ||||
\(88\) | 36480.8i | 0.502179i | ||||||||
\(89\) | 17436.3 | 0.233335 | 0.116667 | − | 0.993171i | \(-0.462779\pi\) | ||||
0.116667 | + | 0.993171i | \(0.462779\pi\) | |||||||
\(90\) | 1033.10 | − | 9957.17i | 0.0134442 | − | 0.129578i | ||||
\(91\) | 105413.i | 1.33442i | ||||||||
\(92\) | −39777.4 | − | 8090.89i | −0.489967 | − | 0.0996613i | ||||
\(93\) | 40899.7 | + | 2116.08i | 0.490357 | + | 0.0253703i | ||||
\(94\) | 77495.8 | 0.904604 | ||||||||
\(95\) | − | 21488.4i | − | 0.244283i | ||||||
\(96\) | 824.774 | − | 15941.3i | 0.00913392 | − | 0.176541i | ||||
\(97\) | 165173.i | 1.78242i | 0.453595 | + | 0.891208i | \(0.350141\pi\) | ||||
−0.453595 | + | 0.891208i | \(0.649859\pi\) | |||||||
\(98\) | 10896.7i | 0.114612i | ||||||||
\(99\) | 137774. | + | 14294.6i | 1.41279 | + | 0.146583i | ||||
\(100\) | 48302.9 | 0.483029 | ||||||||
\(101\) | 176896.i | 1.72550i | 0.505632 | + | 0.862749i | \(0.331259\pi\) | ||||
−0.505632 | + | 0.862749i | \(0.668741\pi\) | |||||||
\(102\) | 462.951 | − | 8947.93i | 0.00440590 | − | 0.0851574i | ||||
\(103\) | − | 1007.58i | − | 0.00935811i | −0.999989 | − | 0.00467906i | \(-0.998511\pi\) | ||
0.999989 | − | 0.00467906i | \(-0.00148940\pi\) | |||||||
\(104\) | − | 48273.8i | − | 0.437651i | ||||||
\(105\) | 1159.30 | − | 22406.9i | 0.0102617 | − | 0.198339i | ||||
\(106\) | 115572.i | 0.999054i | ||||||||
\(107\) | 219789. | 1.85587 | 0.927935 | − | 0.372743i | \(-0.121583\pi\) | ||||
0.927935 | + | 0.372743i | \(0.121583\pi\) | |||||||
\(108\) | −59880.6 | − | 9361.25i | −0.494000 | − | 0.0772280i | ||||
\(109\) | 115327.i | 0.929751i | 0.885376 | + | 0.464875i | \(0.153901\pi\) | ||||
−0.885376 | + | 0.464875i | \(0.846099\pi\) | |||||||
\(110\) | − | 23482.2i | − | 0.185037i | ||||||
\(111\) | 5838.98 | − | 112856.i | 0.0449811 | − | 0.869395i | ||||
\(112\) | − | 35777.0i | − | 0.269500i | ||||||
\(113\) | −125019. | −0.921041 | −0.460520 | − | 0.887649i | \(-0.652337\pi\) | ||||
−0.460520 | + | 0.887649i | \(0.652337\pi\) | |||||||
\(114\) | −129924. | − | 6722.08i | −0.936330 | − | 0.0484442i | ||||
\(115\) | 25604.2 | + | 5208.00i | 0.180537 | + | 0.0367220i | ||||
\(116\) | 90428.2i | 0.623963i | ||||||||
\(117\) | −182311. | − | 18915.6i | −1.23125 | − | 0.127748i | ||||
\(118\) | −83042.7 | −0.549031 | ||||||||
\(119\) | − | 20081.9i | − | 0.129998i | ||||||
\(120\) | −530.897 | + | 10261.2i | −0.00336556 | + | 0.0650495i | ||||
\(121\) | 163864. | 1.01747 | ||||||||
\(122\) | 33484.6 | 0.203678 | ||||||||
\(123\) | 777.852 | − | 15034.3i | 0.00463590 | − | 0.0896028i | ||||
\(124\) | −42035.6 | −0.245507 | ||||||||
\(125\) | −63276.3 | −0.362215 | ||||||||
\(126\) | −135116. | − | 14018.8i | −0.758192 | − | 0.0786658i | ||||
\(127\) | 86118.7 | 0.473792 | 0.236896 | − | 0.971535i | \(-0.423870\pi\) | ||||
0.236896 | + | 0.971535i | \(0.423870\pi\) | |||||||
\(128\) | 16384.0i | 0.0883883i | ||||||||
\(129\) | 9717.14 | − | 187813.i | 0.0514120 | − | 0.993692i | ||||
\(130\) | 31073.2i | 0.161260i | ||||||||
\(131\) | − | 235204.i | − | 1.19747i | −0.800946 | − | 0.598737i | \(-0.795670\pi\) | ||
0.800946 | − | 0.598737i | \(-0.204330\pi\) | |||||||
\(132\) | −141980. | − | 7345.82i | −0.709239 | − | 0.0366949i | ||||
\(133\) | −291590. | −1.42937 | ||||||||
\(134\) | −113374. | −0.545448 | ||||||||
\(135\) | 38544.4 | + | 6025.72i | 0.182023 | + | 0.0284560i | ||||
\(136\) | 9196.45i | 0.0426356i | ||||||||
\(137\) | 134787. | 0.613547 | 0.306774 | − | 0.951783i | \(-0.400751\pi\) | ||||
0.306774 | + | 0.951783i | \(0.400751\pi\) | |||||||
\(138\) | 39498.6 | − | 153181.i | 0.176557 | − | 0.684710i | ||||
\(139\) | 293765. | 1.28962 | 0.644812 | − | 0.764341i | \(-0.276936\pi\) | ||||
0.644812 | + | 0.764341i | \(0.276936\pi\) | |||||||
\(140\) | 23029.2i | 0.0993022i | ||||||||
\(141\) | −15604.6 | + | 301606.i | −0.0661006 | + | 1.27759i | ||||
\(142\) | 196495. | 0.817767 | ||||||||
\(143\) | −429948. | −1.75823 | ||||||||
\(144\) | 61875.8 | + | 6419.89i | 0.248665 | + | 0.0258001i | ||||
\(145\) | − | 58207.5i | − | 0.229910i | ||||||
\(146\) | − | 7579.07i | − | 0.0294262i | ||||||
\(147\) | −42409.1 | − | 2194.18i | −0.161870 | − | 0.00837487i | ||||
\(148\) | 115990.i | 0.435279i | ||||||||
\(149\) | 90268.2 | 0.333096 | 0.166548 | − | 0.986033i | \(-0.446738\pi\) | ||||
0.166548 | + | 0.986033i | \(0.446738\pi\) | |||||||
\(150\) | −9726.32 | + | 187990.i | −0.0352956 | + | 0.682194i | ||||
\(151\) | −21481.7 | −0.0766703 | −0.0383351 | − | 0.999265i | \(-0.512205\pi\) | ||||
−0.0383351 | + | 0.999265i | \(0.512205\pi\) | |||||||
\(152\) | 133533. | 0.468791 | ||||||||
\(153\) | 34731.3 | + | 3603.53i | 0.119948 | + | 0.0124451i | ||||
\(154\) | −318646. | −1.08270 | ||||||||
\(155\) | 27057.8 | 0.0904613 | ||||||||
\(156\) | 187877. | + | 9720.46i | 0.618105 | + | 0.0319798i | ||||
\(157\) | − | 54700.0i | − | 0.177108i | −0.996071 | − | 0.0885540i | \(-0.971775\pi\) | ||
0.996071 | − | 0.0885540i | \(-0.0282246\pi\) | |||||||
\(158\) | 396583. | 1.26384 | ||||||||
\(159\) | −449797. | − | 23271.7i | −1.41099 | − | 0.0730022i | ||||
\(160\) | − | 10546.2i | − | 0.0325683i | ||||||
\(161\) | 70670.9 | − | 347441.i | 0.214870 | − | 1.05637i | ||||
\(162\) | 48490.8 | − | 231165.i | 0.145168 | − | 0.692045i | ||||
\(163\) | −454850. | −1.34091 | −0.670454 | − | 0.741951i | \(-0.733901\pi\) | ||||
−0.670454 | + | 0.741951i | \(0.733901\pi\) | |||||||
\(164\) | 15451.9i | 0.0448613i | ||||||||
\(165\) | 91390.7 | + | 4728.41i | 0.261332 | + | 0.0135209i | ||||
\(166\) | − | 344153.i | − | 0.969353i | ||||||
\(167\) | 296189.i | 0.821822i | 0.911675 | + | 0.410911i | \(0.134789\pi\) | ||||
−0.911675 | + | 0.410911i | \(0.865211\pi\) | |||||||
\(168\) | 139241. | + | 7204.10i | 0.380622 | + | 0.0196927i | ||||
\(169\) | 197642. | 0.532308 | ||||||||
\(170\) | − | 5919.63i | − | 0.0157099i | ||||||
\(171\) | 52323.4 | − | 504301.i | 0.136838 | − | 1.31886i | ||||
\(172\) | 193029.i | 0.497510i | ||||||||
\(173\) | − | 170665.i | − | 0.433541i | −0.976223 | − | 0.216771i | \(-0.930448\pi\) | ||
0.976223 | − | 0.216771i | \(-0.0695524\pi\) | |||||||
\(174\) | −351938. | − | 18208.7i | −0.881239 | − | 0.0455938i | ||||
\(175\) | 421908.i | 1.04141i | ||||||||
\(176\) | 145923. | 0.355094 | ||||||||
\(177\) | 16721.6 | − | 323195.i | 0.0401184 | − | 0.775410i | ||||
\(178\) | − | 69745.2i | − | 0.164993i | ||||||
\(179\) | 690824.i | 1.61152i | 0.592244 | + | 0.805758i | \(0.298242\pi\) | ||||
−0.592244 | + | 0.805758i | \(0.701758\pi\) | |||||||
\(180\) | −39828.7 | − | 4132.40i | −0.0916251 | − | 0.00950651i | ||||
\(181\) | 265516.i | 0.602412i | 0.953559 | + | 0.301206i | \(0.0973892\pi\) | ||||
−0.953559 | + | 0.301206i | \(0.902611\pi\) | |||||||
\(182\) | 421654. | 0.943577 | ||||||||
\(183\) | −6742.48 | + | 130319.i | −0.0148831 | + | 0.287660i | ||||
\(184\) | −32363.5 | + | 159110.i | −0.0704712 | + | 0.346459i | ||||
\(185\) | − | 74661.5i | − | 0.160386i | ||||||
\(186\) | 8464.33 | − | 163599.i | 0.0179395 | − | 0.346735i | ||||
\(187\) | 81907.7 | 0.171286 | ||||||||
\(188\) | − | 309983.i | − | 0.639651i | ||||||
\(189\) | 81767.1 | − | 523035.i | 0.166504 | − | 1.06506i | ||||
\(190\) | −85953.4 | −0.172735 | ||||||||
\(191\) | −614862. | −1.21954 | −0.609768 | − | 0.792580i | \(-0.708737\pi\) | ||||
−0.609768 | + | 0.792580i | \(0.708737\pi\) | |||||||
\(192\) | −63765.0 | − | 3299.10i | −0.124833 | − | 0.00645865i | ||||
\(193\) | 86677.4 | 0.167499 | 0.0837496 | − | 0.996487i | \(-0.473310\pi\) | ||||
0.0837496 | + | 0.996487i | \(0.473310\pi\) | |||||||
\(194\) | 660691. | 1.26036 | ||||||||
\(195\) | −120934. | − | 6256.93i | −0.227752 | − | 0.0117835i | ||||
\(196\) | 43586.9 | 0.0810431 | ||||||||
\(197\) | 735801.i | 1.35081i | 0.737446 | + | 0.675406i | \(0.236031\pi\) | ||||
−0.737446 | + | 0.675406i | \(0.763969\pi\) | |||||||
\(198\) | 57178.5 | − | 551094.i | 0.103650 | − | 0.998994i | ||||
\(199\) | − | 1.01667e6i | − | 1.81991i | −0.414710 | − | 0.909954i | \(-0.636117\pi\) | ||
0.414710 | − | 0.909954i | \(-0.363883\pi\) | |||||||
\(200\) | − | 193212.i | − | 0.341553i | ||||||
\(201\) | 22829.2 | − | 441243.i | 0.0398566 | − | 0.770350i | ||||
\(202\) | 707584. | 1.22011 | ||||||||
\(203\) | −789857. | −1.34527 | ||||||||
\(204\) | −35791.7 | − | 1851.81i | −0.0602154 | − | 0.00311544i | ||||
\(205\) | − | 9946.19i | − | 0.0165300i | ||||||
\(206\) | −4030.34 | −0.00661719 | ||||||||
\(207\) | 588212. | + | 184570.i | 0.954131 | + | 0.299388i | ||||
\(208\) | −193095. | −0.309466 | ||||||||
\(209\) | − | 1.18930e6i | − | 1.88333i | ||||||
\(210\) | −89627.6 | − | 4637.18i | −0.140247 | − | 0.00725615i | ||||
\(211\) | −153148. | −0.236813 | −0.118406 | − | 0.992965i | \(-0.537779\pi\) | ||||
−0.118406 | + | 0.992965i | \(0.537779\pi\) | |||||||
\(212\) | 462289. | 0.706438 | ||||||||
\(213\) | −39566.3 | + | 764739.i | −0.0597554 | + | 1.15495i | ||||
\(214\) | − | 879158.i | − | 1.31230i | ||||||
\(215\) | − | 124250.i | − | 0.183317i | ||||||
\(216\) | −37445.0 | + | 239522.i | −0.0546084 | + | 0.349311i | ||||
\(217\) | − | 367165.i | − | 0.529313i | ||||||
\(218\) | 461310. | 0.657433 | ||||||||
\(219\) | 29497.1 | + | 1526.13i | 0.0415593 | + | 0.00215021i | ||||
\(220\) | −93929.0 | −0.130841 | ||||||||
\(221\) | −108386. | −0.149276 | ||||||||
\(222\) | −451424. | − | 23355.9i | −0.614755 | − | 0.0318064i | ||||
\(223\) | −532364. | −0.716880 | −0.358440 | − | 0.933553i | \(-0.616691\pi\) | ||||
−0.358440 | + | 0.933553i | \(0.616691\pi\) | |||||||
\(224\) | −143108. | −0.190565 | ||||||||
\(225\) | −729683. | − | 75707.9i | −0.960900 | − | 0.0996976i | ||||
\(226\) | 500075.i | 0.651274i | ||||||||
\(227\) | −626086. | −0.806435 | −0.403218 | − | 0.915104i | \(-0.632108\pi\) | ||||
−0.403218 | + | 0.915104i | \(0.632108\pi\) | |||||||
\(228\) | −26888.3 | + | 519698.i | −0.0342552 | + | 0.662085i | ||||
\(229\) | − | 1.15320e6i | − | 1.45317i | −0.687078 | − | 0.726583i | \(-0.741107\pi\) | ||
0.687078 | − | 0.726583i | \(-0.258893\pi\) | |||||||
\(230\) | 20832.0 | − | 102417.i | 0.0259664 | − | 0.127659i | ||||
\(231\) | 64162.9 | − | 1.24014e6i | 0.0791142 | − | 1.52912i | ||||
\(232\) | 361713. | 0.441209 | ||||||||
\(233\) | − | 395664.i | − | 0.477460i | −0.971086 | − | 0.238730i | \(-0.923269\pi\) | ||
0.971086 | − | 0.238730i | \(-0.0767311\pi\) | |||||||
\(234\) | −75662.3 | + | 729244.i | −0.0903316 | + | 0.870629i | ||||
\(235\) | 199532.i | 0.235691i | ||||||||
\(236\) | 332171.i | 0.388223i | ||||||||
\(237\) | −79856.4 | + | 1.54347e6i | −0.0923504 | + | 1.78495i | ||||
\(238\) | −80327.5 | −0.0919225 | ||||||||
\(239\) | 1.37069e6i | 1.55218i | 0.630619 | + | 0.776092i | \(0.282801\pi\) | ||||
−0.630619 | + | 0.776092i | \(0.717199\pi\) | |||||||
\(240\) | 41044.7 | + | 2123.59i | 0.0459970 | + | 0.00237981i | ||||
\(241\) | 715572.i | 0.793616i | 0.917902 | + | 0.396808i | \(0.129882\pi\) | ||||
−0.917902 | + | 0.396808i | \(0.870118\pi\) | |||||||
\(242\) | − | 655456.i | − | 0.719457i | ||||||
\(243\) | 889908. | + | 235269.i | 0.966784 | + | 0.255593i | ||||
\(244\) | − | 133938.i | − | 0.144022i | ||||||
\(245\) | −28056.3 | −0.0298618 | ||||||||
\(246\) | −60137.4 | − | 3111.41i | −0.0633588 | − | 0.00327808i | ||||
\(247\) | 1.57376e6i | 1.64134i | ||||||||
\(248\) | 168142.i | 0.173599i | ||||||||
\(249\) | 1.33941e6 | + | 69299.1i | 1.36904 | + | 0.0708319i | ||||
\(250\) | 253105.i | 0.256124i | ||||||||
\(251\) | −679196. | −0.680473 | −0.340236 | − | 0.940340i | \(-0.610507\pi\) | ||||
−0.340236 | + | 0.940340i | \(0.610507\pi\) | |||||||
\(252\) | −56075.4 | + | 540462.i | −0.0556251 | + | 0.536123i | ||||
\(253\) | 1.41710e6 | + | 288244.i | 1.39187 | + | 0.283113i | ||||
\(254\) | − | 344475.i | − | 0.335022i | ||||||
\(255\) | 23038.7 | + | 1191.98i | 0.0221874 | + | 0.00114794i | ||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 1.38868e6i | 1.31150i | 0.754977 | + | 0.655751i | \(0.227648\pi\) | ||||
−0.754977 | + | 0.655751i | \(0.772352\pi\) | |||||||
\(258\) | −751253. | − | 38868.6i | −0.702646 | − | 0.0363538i | ||||
\(259\) | −1.01313e6 | −0.938462 | ||||||||
\(260\) | 124293. | 0.114028 | ||||||||
\(261\) | 141733. | − | 1.36605e6i | 0.128787 | − | 1.24126i | ||||
\(262\) | −940815. | −0.846742 | ||||||||
\(263\) | −1.06490e6 | −0.949333 | −0.474666 | − | 0.880166i | \(-0.657431\pi\) | ||||
−0.474666 | + | 0.880166i | \(0.657431\pi\) | |||||||
\(264\) | −29383.3 | + | 567920.i | −0.0259472 | + | 0.501508i | ||||
\(265\) | −297570. | −0.260300 | ||||||||
\(266\) | 1.16636e6i | 1.01071i | ||||||||
\(267\) | 271442. | + | 14044.0i | 0.233023 | + | 0.0120562i | ||||
\(268\) | 453498.i | 0.385690i | ||||||||
\(269\) | − | 102901.i | − | 0.0867041i | −0.999060 | − | 0.0433520i | \(-0.986196\pi\) | ||
0.999060 | − | 0.0433520i | \(-0.0138037\pi\) | |||||||
\(270\) | 24102.9 | − | 154177.i | 0.0201215 | − | 0.128710i | ||||
\(271\) | 1.82316e6 | 1.50800 | 0.753999 | − | 0.656876i | \(-0.228122\pi\) | ||||
0.753999 | + | 0.656876i | \(0.228122\pi\) | |||||||
\(272\) | 36785.8 | 0.0301480 | ||||||||
\(273\) | −84904.5 | + | 1.64104e6i | −0.0689484 | + | 1.33264i | ||||
\(274\) | − | 539150.i | − | 0.433843i | ||||||
\(275\) | −1.72083e6 | −1.37216 | ||||||||
\(276\) | −612723. | − | 157994.i | −0.484163 | − | 0.124844i | ||||
\(277\) | 559043. | 0.437769 | 0.218885 | − | 0.975751i | \(-0.429758\pi\) | ||||
0.218885 | + | 0.975751i | \(0.429758\pi\) | |||||||
\(278\) | − | 1.17506e6i | − | 0.911901i | ||||||
\(279\) | 635007. | + | 65884.8i | 0.488391 | + | 0.0506728i | ||||
\(280\) | 92116.8 | 0.0702173 | ||||||||
\(281\) | 1.09166e6 | 0.824746 | 0.412373 | − | 0.911015i | \(-0.364700\pi\) | ||||
0.412373 | + | 0.911015i | \(0.364700\pi\) | |||||||
\(282\) | 1.20643e6 | + | 62418.5i | 0.903395 | + | 0.0467402i | ||||
\(283\) | 75110.5i | 0.0557487i | 0.999611 | + | 0.0278743i | \(0.00887383\pi\) | ||||
−0.999611 | + | 0.0278743i | \(0.991126\pi\) | |||||||
\(284\) | − | 785978.i | − | 0.578249i | ||||||
\(285\) | 17307.7 | − | 334523.i | 0.0126219 | − | 0.243957i | ||||
\(286\) | 1.71979e6i | 1.24326i | ||||||||
\(287\) | −134967. | −0.0967212 | ||||||||
\(288\) | 25679.6 | − | 247503.i | 0.0182434 | − | 0.175833i | ||||
\(289\) | −1.39921e6 | −0.985458 | ||||||||
\(290\) | −232830. | −0.162571 | ||||||||
\(291\) | −133037. | + | 2.57135e6i | −0.0920961 | + | 1.78003i | ||||
\(292\) | −30316.3 | −0.0208075 | ||||||||
\(293\) | 1.69883e6 | 1.15606 | 0.578030 | − | 0.816015i | \(-0.303822\pi\) | ||||
0.578030 | + | 0.816015i | \(0.303822\pi\) | |||||||
\(294\) | −8776.71 | + | 169636.i | −0.00592193 | + | 0.114459i | ||||
\(295\) | − | 213814.i | − | 0.143048i | ||||||
\(296\) | 463961. | 0.307789 | ||||||||
\(297\) | 2.13330e6 | + | 333502.i | 1.40333 | + | 0.219385i | ||||
\(298\) | − | 361073.i | − | 0.235534i | ||||||
\(299\) | −1.87520e6 | − | 381424.i | −1.21303 | − | 0.246734i | ||||
\(300\) | 751962. | + | 38905.3i | 0.482384 | + | 0.0249577i | ||||
\(301\) | −1.68604e6 | −1.07263 | ||||||||
\(302\) | 85926.9i | 0.0542141i | ||||||||
\(303\) | −142480. | + | 2.75385e6i | −0.0891552 | + | 1.72319i | ||||
\(304\) | − | 534132.i | − | 0.331485i | ||||||
\(305\) | 86214.3i | 0.0530677i | ||||||||
\(306\) | 14414.1 | − | 138925.i | 0.00880003 | − | 0.0848160i | ||||
\(307\) | −1.38489e6 | −0.838627 | −0.419313 | − | 0.907842i | \(-0.637729\pi\) | ||||
−0.419313 | + | 0.907842i | \(0.637729\pi\) | |||||||
\(308\) | 1.27459e6i | 0.765583i | ||||||||
\(309\) | 811.553 | − | 15685.7i | 0.000483527 | − | 0.00934561i | ||||
\(310\) | − | 108231.i | − | 0.0639658i | ||||||
\(311\) | − | 1.77927e6i | − | 1.04314i | −0.853210 | − | 0.521568i | \(-0.825347\pi\) | ||
0.853210 | − | 0.521568i | \(-0.174653\pi\) | |||||||
\(312\) | 38881.8 | − | 751509.i | 0.0226131 | − | 0.437067i | ||||
\(313\) | − | 95522.0i | − | 0.0551116i | −0.999620 | − | 0.0275558i | \(-0.991228\pi\) | ||
0.999620 | − | 0.0275558i | \(-0.00877239\pi\) | |||||||
\(314\) | −218800. | −0.125234 | ||||||||
\(315\) | 36095.0 | − | 347889.i | 0.0204961 | − | 0.197544i | ||||
\(316\) | − | 1.58633e6i | − | 0.893669i | ||||||
\(317\) | 320032.i | 0.178873i | 0.995993 | + | 0.0894366i | \(0.0285066\pi\) | ||||
−0.995993 | + | 0.0894366i | \(0.971493\pi\) | |||||||
\(318\) | −93087.0 | + | 1.79919e6i | −0.0516204 | + | 0.997720i | ||||
\(319\) | − | 3.22158e6i | − | 1.77252i | ||||||
\(320\) | −42184.7 | −0.0230292 | ||||||||
\(321\) | 3.42160e6 | + | 177028.i | 1.85339 | + | 0.0958913i | ||||
\(322\) | −1.38976e6 | − | 282683.i | −0.746966 | − | 0.151936i | ||||
\(323\) | − | 299812.i | − | 0.159898i | ||||||
\(324\) | −924659. | − | 193963.i | −0.489350 | − | 0.102649i | ||||
\(325\) | 2.27711e6 | 1.19585 | ||||||||
\(326\) | 1.81940e6i | 0.948166i | ||||||||
\(327\) | −92889.8 | + | 1.79538e6i | −0.0480395 | + | 0.928509i | ||||
\(328\) | 61807.6 | 0.0317218 | ||||||||
\(329\) | 2.70759e6 | 1.37909 | ||||||||
\(330\) | 18913.6 | − | 365563.i | 0.00956071 | − | 0.184790i | ||||
\(331\) | 476574. | 0.239089 | 0.119545 | − | 0.992829i | \(-0.461857\pi\) | ||||
0.119545 | + | 0.992829i | \(0.461857\pi\) | |||||||
\(332\) | −1.37661e6 | −0.685436 | ||||||||
\(333\) | 181798. | − | 1.75220e6i | 0.0898419 | − | 0.865909i | ||||
\(334\) | 1.18476e6 | 0.581116 | ||||||||
\(335\) | − | 291911.i | − | 0.142114i | ||||||
\(336\) | 28816.4 | − | 556964.i | 0.0139249 | − | 0.269140i | ||||
\(337\) | − | 3.64337e6i | − | 1.74755i | −0.486333 | − | 0.873774i | \(-0.661666\pi\) | ||
0.486333 | − | 0.873774i | \(-0.338334\pi\) | |||||||
\(338\) | − | 790570.i | − | 0.376399i | ||||||
\(339\) | −1.94624e6 | − | 100695.i | −0.919810 | − | 0.0475895i | ||||
\(340\) | −23678.5 | −0.0111086 | ||||||||
\(341\) | 1.49755e6 | 0.697423 | ||||||||
\(342\) | −2.01720e6 | − | 209294.i | −0.932576 | − | 0.0967589i | ||||
\(343\) | − | 1.96813e6i | − | 0.903272i | ||||||
\(344\) | 772117. | 0.351793 | ||||||||
\(345\) | 394402. | + | 101699.i | 0.178399 | + | 0.0460012i | ||||
\(346\) | −682662. | −0.306560 | ||||||||
\(347\) | − | 2.43354e6i | − | 1.08496i | −0.840067 | − | 0.542482i | \(-0.817485\pi\) | ||
0.840067 | − | 0.542482i | \(-0.182515\pi\) | |||||||
\(348\) | −72834.8 | + | 1.40775e6i | −0.0322397 | + | 0.623130i | ||||
\(349\) | 1.08698e6 | 0.477702 | 0.238851 | − | 0.971056i | \(-0.423229\pi\) | ||||
0.238851 | + | 0.971056i | \(0.423229\pi\) | |||||||
\(350\) | 1.68763e6 | 0.736389 | ||||||||
\(351\) | −2.82291e6 | − | 441312.i | −1.22301 | − | 0.191196i | ||||
\(352\) | − | 583693.i | − | 0.251089i | ||||||
\(353\) | − | 1.83446e6i | − | 0.783559i | −0.920059 | − | 0.391779i | \(-0.871860\pi\) | ||
0.920059 | − | 0.391779i | \(-0.128140\pi\) | |||||||
\(354\) | −1.29278e6 | − | 66886.3i | −0.548297 | − | 0.0283680i | ||||
\(355\) | 505924.i | 0.213066i | ||||||||
\(356\) | −278981. | −0.116667 | ||||||||
\(357\) | 16174.8 | − | 312627.i | 0.00671690 | − | 0.129824i | ||||
\(358\) | 2.76330e6 | 1.13951 | ||||||||
\(359\) | −3.97038e6 | −1.62591 | −0.812953 | − | 0.582329i | \(-0.802141\pi\) | ||||
−0.812953 | + | 0.582329i | \(0.802141\pi\) | |||||||
\(360\) | −16529.6 | + | 159315.i | −0.00672212 | + | 0.0647888i | ||||
\(361\) | −1.87718e6 | −0.758121 | ||||||||
\(362\) | 1.06206e6 | 0.425970 | ||||||||
\(363\) | 2.55097e6 | + | 131983.i | 1.01611 | + | 0.0525717i | ||||
\(364\) | − | 1.68661e6i | − | 0.667210i | ||||||
\(365\) | 19514.2 | 0.00766688 | ||||||||
\(366\) | 521276. | + | 26969.9i | 0.203406 | + | 0.0105239i | ||||
\(367\) | 2.68260e6i | 1.03966i | 0.854270 | + | 0.519830i | \(0.174005\pi\) | ||||
−0.854270 | + | 0.519830i | \(0.825995\pi\) | |||||||
\(368\) | 636438. | + | 129454.i | 0.244983 | + | 0.0498306i | ||||
\(369\) | 24218.6 | − | 233423.i | 0.00925942 | − | 0.0892436i | ||||
\(370\) | −298646. | −0.113410 | ||||||||
\(371\) | 4.03792e6i | 1.52308i | ||||||||
\(372\) | −654395. | − | 33857.3i | −0.245179 | − | 0.0126851i | ||||
\(373\) | 1.09025e6i | 0.405747i | 0.979205 | + | 0.202873i | \(0.0650280\pi\) | ||||
−0.979205 | + | 0.202873i | \(0.934972\pi\) | |||||||
\(374\) | − | 327631.i | − | 0.121117i | ||||||
\(375\) | −985062. | − | 50965.5i | −0.361731 | − | 0.0187154i | ||||
\(376\) | −1.23993e6 | −0.452302 | ||||||||
\(377\) | 4.26300e6i | 1.54476i | ||||||||
\(378\) | −2.09214e6 | − | 327068.i | −0.753114 | − | 0.117736i | ||||
\(379\) | − | 3.15942e6i | − | 1.12982i | −0.825153 | − | 0.564909i | \(-0.808911\pi\) | ||
0.825153 | − | 0.564909i | \(-0.191089\pi\) | |||||||
\(380\) | 343814.i | 0.122142i | ||||||||
\(381\) | 1.34066e6 | + | 69363.8i | 0.473160 | + | 0.0244805i | ||||
\(382\) | 2.45945e6i | 0.862342i | ||||||||
\(383\) | −177620. | −0.0618721 | −0.0309361 | − | 0.999521i | \(-0.509849\pi\) | ||||
−0.0309361 | + | 0.999521i | \(0.509849\pi\) | |||||||
\(384\) | −13196.4 | + | 255060.i | −0.00456696 | + | 0.0882703i | ||||
\(385\) | − | 820434.i | − | 0.282093i | ||||||
\(386\) | − | 346710.i | − | 0.118440i | ||||||
\(387\) | 302546. | − | 2.91598e6i | 0.102687 | − | 0.989708i | ||||
\(388\) | − | 2.64276e6i | − | 0.891208i | ||||||
\(389\) | 2.29354e6 | 0.768480 | 0.384240 | − | 0.923233i | \(-0.374464\pi\) | ||||
0.384240 | + | 0.923233i | \(0.374464\pi\) | |||||||
\(390\) | −25027.7 | + | 483737.i | −0.00833220 | + | 0.161045i | ||||
\(391\) | 357237. | + | 72663.5i | 0.118172 | + | 0.0240367i | ||||
\(392\) | − | 174348.i | − | 0.0573061i | ||||||
\(393\) | 189443. | − | 3.66157e6i | 0.0618725 | − | 1.19587i | ||||
\(394\) | 2.94320e6 | 0.955168 | ||||||||
\(395\) | 1.02110e6i | 0.329288i | ||||||||
\(396\) | −2.20438e6 | − | 228714.i | −0.706396 | − | 0.0732917i | ||||
\(397\) | −4.47721e6 | −1.42571 | −0.712856 | − | 0.701311i | \(-0.752599\pi\) | ||||
−0.712856 | + | 0.701311i | \(0.752599\pi\) | |||||||
\(398\) | −4.06670e6 | −1.28687 | ||||||||
\(399\) | −4.53937e6 | − | 234859.i | −1.42746 | − | 0.0738543i | ||||
\(400\) | −772846. | −0.241514 | ||||||||
\(401\) | 3.59903e6 | 1.11770 | 0.558849 | − | 0.829269i | \(-0.311243\pi\) | ||||
0.558849 | + | 0.829269i | \(0.311243\pi\) | |||||||
\(402\) | −1.76497e6 | − | 91316.8i | −0.544719 | − | 0.0281829i | ||||
\(403\) | −1.98166e6 | −0.607808 | ||||||||
\(404\) | − | 2.83034e6i | − | 0.862749i | ||||||
\(405\) | 595191. | + | 124852.i | 0.180310 | + | 0.0378230i | ||||
\(406\) | 3.15943e6i | 0.951247i | ||||||||
\(407\) | − | 4.13225e6i | − | 1.23652i | ||||||
\(408\) | −7407.22 | + | 143167.i | −0.00220295 | + | 0.0425787i | ||||
\(409\) | 884663. | 0.261499 | 0.130749 | − | 0.991415i | \(-0.458262\pi\) | ||||
0.130749 | + | 0.991415i | \(0.458262\pi\) | |||||||
\(410\) | −39784.8 | −0.0116885 | ||||||||
\(411\) | 2.09832e6 | + | 108564.i | 0.612728 | + | 0.0317015i | ||||
\(412\) | 16121.3i | 0.00467906i | ||||||||
\(413\) | −2.90139e6 | −0.837010 | ||||||||
\(414\) | 738278. | − | 2.35285e6i | 0.211699 | − | 0.674673i | ||||
\(415\) | 886108. | 0.252561 | ||||||||
\(416\) | 772381.i | 0.218826i | ||||||||
\(417\) | 4.57322e6 | + | 236611.i | 1.28790 | + | 0.0666339i | ||||
\(418\) | −4.75722e6 | −1.33172 | ||||||||
\(419\) | 3.89660e6 | 1.08430 | 0.542151 | − | 0.840281i | \(-0.317610\pi\) | ||||
0.542151 | + | 0.840281i | \(0.317610\pi\) | |||||||
\(420\) | −18548.7 | + | 358510.i | −0.00513087 | + | 0.0991696i | ||||
\(421\) | − | 1.39428e6i | − | 0.383393i | −0.981454 | − | 0.191696i | \(-0.938601\pi\) | ||
0.981454 | − | 0.191696i | \(-0.0613988\pi\) | |||||||
\(422\) | 612591.i | 0.167452i | ||||||||
\(423\) | −485854. | + | 4.68273e6i | −0.132025 | + | 1.27247i | ||||
\(424\) | − | 1.84916e6i | − | 0.499527i | ||||||
\(425\) | −433804. | −0.116499 | ||||||||
\(426\) | 3.05896e6 | + | 158265.i | 0.816675 | + | 0.0422534i | ||||
\(427\) | 1.16990e6 | 0.310513 | ||||||||
\(428\) | −3.51663e6 | −0.927935 | ||||||||
\(429\) | −6.69328e6 | − | 346299.i | −1.75588 | − | 0.0908465i | ||||
\(430\) | −497002. | −0.129624 | ||||||||
\(431\) | 3.67150e6 | 0.952029 | 0.476014 | − | 0.879437i | \(-0.342081\pi\) | ||||
0.476014 | + | 0.879437i | \(0.342081\pi\) | |||||||
\(432\) | 958090. | + | 149780.i | 0.247000 | + | 0.0386140i | ||||
\(433\) | − | 3.33060e6i | − | 0.853695i | −0.904324 | − | 0.426847i | \(-0.859624\pi\) | ||
0.904324 | − | 0.426847i | \(-0.140376\pi\) | |||||||
\(434\) | −1.46866e6 | −0.374281 | ||||||||
\(435\) | 46882.8 | − | 906153.i | 0.0118793 | − | 0.229603i | ||||
\(436\) | − | 1.84524e6i | − | 0.464875i | ||||||
\(437\) | 1.05508e6 | − | 5.18710e6i | 0.264290 | − | 1.29934i | ||||
\(438\) | 6104.52 | − | 117988.i | 0.00152043 | − | 0.0293869i | ||||
\(439\) | 6.64997e6 | 1.64687 | 0.823434 | − | 0.567413i | \(-0.192056\pi\) | ||||
0.823434 | + | 0.567413i | \(0.192056\pi\) | |||||||
\(440\) | 375716.i | 0.0925183i | ||||||||
\(441\) | −658442. | − | 68316.3i | −0.161221 | − | 0.0167274i | ||||
\(442\) | 433542.i | 0.105554i | ||||||||
\(443\) | 4.09635e6i | 0.991717i | 0.868403 | + | 0.495859i | \(0.165147\pi\) | ||||
−0.868403 | + | 0.495859i | \(0.834853\pi\) | |||||||
\(444\) | −93423.7 | + | 1.80570e6i | −0.0224905 | + | 0.434697i | ||||
\(445\) | 179576. | 0.0429882 | ||||||||
\(446\) | 2.12946e6i | 0.506911i | ||||||||
\(447\) | 1.40526e6 | + | 72705.9i | 0.332651 | + | 0.0172108i | ||||
\(448\) | 572432.i | 0.134750i | ||||||||
\(449\) | 3.04276e6i | 0.712282i | 0.934432 | + | 0.356141i | \(0.115908\pi\) | ||||
−0.934432 | + | 0.356141i | \(0.884092\pi\) | |||||||
\(450\) | −302831. | + | 2.91873e6i | −0.0704968 | + | 0.679459i | ||||
\(451\) | − | 550487.i | − | 0.127440i | ||||||
\(452\) | 2.00030e6 | 0.460520 | ||||||||
\(453\) | −334420. | − | 17302.3i | −0.0765679 | − | 0.00396149i | ||||
\(454\) | 2.50435e6i | 0.570236i | ||||||||
\(455\) | 1.08565e6i | 0.245845i | ||||||||
\(456\) | 2.07879e6 | + | 107553.i | 0.468165 | + | 0.0242221i | ||||
\(457\) | 3.83305e6i | 0.858526i | 0.903179 | + | 0.429263i | \(0.141227\pi\) | ||||
−0.903179 | + | 0.429263i | \(0.858773\pi\) | |||||||
\(458\) | −4.61280e6 | −1.02754 | ||||||||
\(459\) | 537782. | + | 84072.5i | 0.119145 | + | 0.0186261i | ||||
\(460\) | −409667. | − | 83328.0i | −0.0902686 | − | 0.0183610i | ||||
\(461\) | − | 2.62615e6i | − | 0.575530i | −0.957701 | − | 0.287765i | \(-0.907088\pi\) | ||
0.957701 | − | 0.287765i | \(-0.0929121\pi\) | |||||||
\(462\) | −4.96057e6 | − | 256652.i | −1.08125 | − | 0.0559422i | ||||
\(463\) | −3.08478e6 | −0.668762 | −0.334381 | − | 0.942438i | \(-0.608527\pi\) | ||||
−0.334381 | + | 0.942438i | \(0.608527\pi\) | |||||||
\(464\) | − | 1.44685e6i | − | 0.311982i | ||||||
\(465\) | 421226. | + | 21793.5i | 0.0903405 | + | 0.00467407i | ||||
\(466\) | −1.58266e6 | −0.337615 | ||||||||
\(467\) | −1.08071e6 | −0.229307 | −0.114654 | − | 0.993406i | \(-0.536576\pi\) | ||||
−0.114654 | + | 0.993406i | \(0.536576\pi\) | |||||||
\(468\) | 2.91697e6 | + | 302649.i | 0.615627 | + | 0.0638741i | ||||
\(469\) | −3.96113e6 | −0.831548 | ||||||||
\(470\) | 798128. | 0.166659 | ||||||||
\(471\) | 44057.8 | − | 851550.i | 0.00915104 | − | 0.176871i | ||||
\(472\) | 1.32868e6 | 0.274515 | ||||||||
\(473\) | − | 6.87683e6i | − | 1.41330i | ||||||
\(474\) | 6.17386e6 | + | 319425.i | 1.26215 | + | 0.0653016i | ||||
\(475\) | 6.29885e6i | 1.28094i | ||||||||
\(476\) | 321310.i | 0.0649990i | ||||||||
\(477\) | −6.98353e6 | − | 724572.i | −1.40533 | − | 0.145809i | ||||
\(478\) | 5.48275e6 | 1.09756 | ||||||||
\(479\) | −4.99012e6 | −0.993738 | −0.496869 | − | 0.867826i | \(-0.665517\pi\) | ||||
−0.496869 | + | 0.867826i | \(0.665517\pi\) | |||||||
\(480\) | 8494.35 | − | 164179.i | 0.00168278 | − | 0.0325248i | ||||
\(481\) | 5.46806e6i | 1.07763i | ||||||||
\(482\) | 2.86229e6 | 0.561171 | ||||||||
\(483\) | 1.38002e6 | − | 5.35191e6i | 0.269165 | − | 1.04386i | ||||
\(484\) | −2.62182e6 | −0.508733 | ||||||||
\(485\) | 1.70111e6i | 0.328382i | ||||||||
\(486\) | 941077. | − | 3.55963e6i | 0.180732 | − | 0.683620i | ||||
\(487\) | 7.59571e6 | 1.45126 | 0.725631 | − | 0.688084i | \(-0.241548\pi\) | ||||
0.725631 | + | 0.688084i | \(0.241548\pi\) | |||||||
\(488\) | −535753. | −0.101839 | ||||||||
\(489\) | −7.08094e6 | − | 366356.i | −1.33912 | − | 0.0692837i | ||||
\(490\) | 112225.i | 0.0211155i | ||||||||
\(491\) | 1.51703e6i | 0.283981i | 0.989868 | + | 0.141990i | \(0.0453502\pi\) | ||||
−0.989868 | + | 0.141990i | \(0.954650\pi\) | |||||||
\(492\) | −12445.6 | + | 240550.i | −0.00231795 | + | 0.0448014i | ||||
\(493\) | − | 812127.i | − | 0.150490i | ||||||
\(494\) | 6.29506e6 | 1.16060 | ||||||||
\(495\) | 1.41893e6 | + | 147220.i | 0.260284 | + | 0.0270056i | ||||
\(496\) | 672570. | 0.122753 | ||||||||
\(497\) | 6.86523e6 | 1.24671 | ||||||||
\(498\) | 277196. | − | 5.35765e6i | 0.0500857 | − | 0.968058i | ||||
\(499\) | −7.32400e6 | −1.31673 | −0.658365 | − | 0.752698i | \(-0.728752\pi\) | ||||
−0.658365 | + | 0.752698i | \(0.728752\pi\) | |||||||
\(500\) | 1.01242e6 | 0.181107 | ||||||||
\(501\) | −238564. | + | 4.61096e6i | −0.0424629 | + | 0.820725i | ||||
\(502\) | 2.71678e6i | 0.481167i | ||||||||
\(503\) | −2.32651e6 | −0.410001 | −0.205000 | − | 0.978762i | \(-0.565720\pi\) | ||||
−0.205000 | + | 0.978762i | \(0.565720\pi\) | |||||||
\(504\) | 2.16185e6 | + | 224301.i | 0.379096 | + | 0.0393329i | ||||
\(505\) | 1.82185e6i | 0.317895i | ||||||||
\(506\) | 1.15298e6 | − | 5.66841e6i | 0.200191 | − | 0.984204i | ||||
\(507\) | 3.07682e6 | + | 159190.i | 0.531597 | + | 0.0275040i | ||||
\(508\) | −1.37790e6 | −0.236896 | ||||||||
\(509\) | 4.52964e6i | 0.774943i | 0.921882 | + | 0.387471i | \(0.126651\pi\) | ||||
−0.921882 | + | 0.387471i | \(0.873349\pi\) | |||||||
\(510\) | 4767.93 | − | 92154.7i | 0.000811717 | − | 0.0156889i | ||||
\(511\) | − | 264802.i | − | 0.0448609i | ||||||
\(512\) | − | 262144.i | − | 0.0441942i | ||||||
\(513\) | 1.22074e6 | − | 7.80863e6i | 0.204800 | − | 1.31003i | ||||
\(514\) | 5.55472e6 | 0.927372 | ||||||||
\(515\) | − | 10377.1i | − | 0.00172408i | ||||||
\(516\) | −155474. | + | 3.00501e6i | −0.0257060 | + | 0.496846i | ||||
\(517\) | 1.10434e7i | 1.81709i | ||||||||
\(518\) | 4.05253e6i | 0.663593i | ||||||||
\(519\) | 137461. | − | 2.65686e6i | 0.0224007 | − | 0.432962i | ||||
\(520\) | − | 497171.i | − | 0.0806302i | ||||||
\(521\) | 7.46633e6 | 1.20507 | 0.602535 | − | 0.798092i | \(-0.294157\pi\) | ||||
0.602535 | + | 0.798092i | \(0.294157\pi\) | |||||||
\(522\) | −5.46418e6 | − | 566933.i | −0.877706 | − | 0.0910659i | ||||
\(523\) | 672885.i | 0.107569i | 0.998553 | + | 0.0537844i | \(0.0171284\pi\) | ||||
−0.998553 | + | 0.0537844i | \(0.982872\pi\) | |||||||
\(524\) | 3.76326e6i | 0.598737i | ||||||||
\(525\) | −339823. | + | 6.56810e6i | −0.0538089 | + | 1.04002i | ||||
\(526\) | 4.25959e6i | 0.671279i | ||||||||
\(527\) | 377518. | 0.0592122 | ||||||||
\(528\) | 2.27168e6 | + | 117533.i | 0.354620 | + | 0.0183474i | ||||
\(529\) | 5.92492e6 | + | 2.51433e6i | 0.920541 | + | 0.390646i | ||||
\(530\) | 1.19028e6i | 0.184060i | ||||||||
\(531\) | 520630. | − | 5.01791e6i | 0.0801296 | − | 0.772301i | ||||
\(532\) | 4.66544e6 | 0.714683 | ||||||||
\(533\) | 728439.i | 0.111065i | ||||||||
\(534\) | 56175.9 | − | 1.08577e6i | 0.00852504 | − | 0.164772i | ||||
\(535\) | 2.26361e6 | 0.341914 | ||||||||
\(536\) | 1.81399e6 | 0.272724 | ||||||||
\(537\) | −556420. | + | 1.07545e7i | −0.0832659 | + | 1.60936i | ||||
\(538\) | −411605. | −0.0613091 | ||||||||
\(539\) | −1.55282e6 | −0.230223 | ||||||||
\(540\) | −616710. | − | 96411.5i | −0.0910116 | − | 0.0142280i | ||||
\(541\) | 481127. | 0.0706752 | 0.0353376 | − | 0.999375i | \(-0.488749\pi\) | ||||
0.0353376 | + | 0.999375i | \(0.488749\pi\) | |||||||
\(542\) | − | 7.29263e6i | − | 1.06632i | ||||||
\(543\) | −213858. | + | 4.13345e6i | −0.0311262 | + | 0.601608i | ||||
\(544\) | − | 147143.i | − | 0.0213178i | ||||||
\(545\) | 1.18776e6i | 0.171292i | ||||||||
\(546\) | 6.56415e6 | + | 339618.i | 0.942316 | + | 0.0487539i | ||||
\(547\) | 2.76810e6 | 0.395561 | 0.197780 | − | 0.980246i | \(-0.436627\pi\) | ||||
0.197780 | + | 0.980246i | \(0.436627\pi\) | |||||||
\(548\) | −2.15660e6 | −0.306774 | ||||||||
\(549\) | −209929. | + | 2.02333e6i | −0.0297264 | + | 0.286507i | ||||
\(550\) | 6.88332e6i | 0.970267i | ||||||||
\(551\) | −1.17921e7 | −1.65468 | ||||||||
\(552\) | −631978. | + | 2.45089e6i | −0.0882783 | + | 0.342355i | ||||
\(553\) | 1.38560e7 | 1.92675 | ||||||||
\(554\) | − | 2.23617e6i | − | 0.309550i | ||||||
\(555\) | 60135.6 | − | 1.16230e6i | 0.00828704 | − | 0.160172i | ||||
\(556\) | −4.70024e6 | −0.644812 | ||||||||
\(557\) | −1.35648e7 | −1.85258 | −0.926289 | − | 0.376815i | \(-0.877019\pi\) | ||||
−0.926289 | + | 0.376815i | \(0.877019\pi\) | |||||||
\(558\) | 263539. | − | 2.54003e6i | 0.0358311 | − | 0.345345i | ||||
\(559\) | 9.09986e6i | 1.23170i | ||||||||
\(560\) | − | 368467.i | − | 0.0496511i | ||||||
\(561\) | 1.27511e6 | + | 65972.1i | 0.171057 | + | 0.00885020i | ||||
\(562\) | − | 4.36663e6i | − | 0.583184i | ||||||
\(563\) | 3.99287e6 | 0.530902 | 0.265451 | − | 0.964124i | \(-0.414479\pi\) | ||||
0.265451 | + | 0.964124i | \(0.414479\pi\) | |||||||
\(564\) | 249674. | − | 4.82570e6i | 0.0330503 | − | 0.638797i | ||||
\(565\) | −1.28757e6 | −0.169687 | ||||||||
\(566\) | 300442. | 0.0394203 | ||||||||
\(567\) | 1.69419e6 | − | 8.07655e6i | 0.221312 | − | 1.05504i | ||||
\(568\) | −3.14391e6 | −0.408884 | ||||||||
\(569\) | −5.99029e6 | −0.775653 | −0.387826 | − | 0.921732i | \(-0.626774\pi\) | ||||
−0.387826 | + | 0.921732i | \(0.626774\pi\) | |||||||
\(570\) | −1.33809e6 | − | 69230.6i | −0.172504 | − | 0.00892506i | ||||
\(571\) | 1.11294e7i | 1.42850i | 0.699889 | + | 0.714251i | \(0.253233\pi\) | ||||
−0.699889 | + | 0.714251i | \(0.746767\pi\) | |||||||
\(572\) | 6.87917e6 | 0.879116 | ||||||||
\(573\) | −9.57195e6 | − | 495237.i | −1.21791 | − | 0.0630125i | ||||
\(574\) | 539866.i | 0.0683922i | ||||||||
\(575\) | −7.50533e6 | − | 1.52661e6i | −0.946673 | − | 0.192557i | ||||
\(576\) | −990014. | − | 102718.i | −0.124333 | − | 0.0129001i | ||||
\(577\) | −9.78949e6 | −1.22411 | −0.612055 | − | 0.790815i | \(-0.709657\pi\) | ||||
−0.612055 | + | 0.790815i | \(0.709657\pi\) | |||||||
\(578\) | 5.59684e6i | 0.696824i | ||||||||
\(579\) | 1.34936e6 | + | 69813.8i | 0.167276 | + | 0.00865456i | ||||
\(580\) | 931320.i | 0.114955i | ||||||||
\(581\) | − | 1.20242e7i | − | 1.47780i | ||||||
\(582\) | 1.02854e7 | + | 532149.i | 1.25867 | + | 0.0651217i | ||||
\(583\) | −1.64694e7 | −2.00681 | ||||||||
\(584\) | 121265.i | 0.0147131i | ||||||||
\(585\) | −1.87762e6 | − | 194811.i | −0.226839 | − | 0.0235356i | ||||
\(586\) | − | 6.79531e6i | − | 0.817458i | ||||||
\(587\) | 1.27469e7i | 1.52690i | 0.645869 | + | 0.763448i | \(0.276495\pi\) | ||||
−0.645869 | + | 0.763448i | \(0.723505\pi\) | |||||||
\(588\) | 678546. | + | 35106.8i | 0.0809349 | + | 0.00418744i | ||||
\(589\) | − | 5.48158e6i | − | 0.651055i | ||||||
\(590\) | −855257. | −0.101150 | ||||||||
\(591\) | −592646. | + | 1.14547e7i | −0.0697954 | + | 1.34901i | ||||
\(592\) | − | 1.85585e6i | − | 0.217639i | ||||||
\(593\) | 3.33570e6i | 0.389538i | 0.980849 | + | 0.194769i | \(0.0623958\pi\) | ||||
−0.980849 | + | 0.194769i | \(0.937604\pi\) | |||||||
\(594\) | 1.33401e6 | − | 8.53318e6i | 0.155129 | − | 0.992304i | ||||
\(595\) | − | 206823.i | − | 0.0239501i | ||||||
\(596\) | −1.44429e6 | −0.166548 | ||||||||
\(597\) | 818874. | − | 1.58272e7i | 0.0940332 | − | 1.81748i | ||||
\(598\) | −1.52569e6 | + | 7.50080e6i | −0.174468 | + | 0.857738i | ||||
\(599\) | 2.57446e6i | 0.293169i | 0.989198 | + | 0.146585i | \(0.0468281\pi\) | ||||
−0.989198 | + | 0.146585i | \(0.953172\pi\) | |||||||
\(600\) | 155621. | − | 3.00785e6i | 0.0176478 | − | 0.341097i | ||||
\(601\) | 6.52370e6 | 0.736729 | 0.368365 | − | 0.929681i | \(-0.379918\pi\) | ||||
0.368365 | + | 0.929681i | \(0.379918\pi\) | |||||||
\(602\) | 6.74416e6i | 0.758467i | ||||||||
\(603\) | 710793. | − | 6.85072e6i | 0.0796067 | − | 0.767261i | ||||
\(604\) | 343708. | 0.0383351 | ||||||||
\(605\) | 1.68763e6 | 0.187452 | ||||||||
\(606\) | 1.10154e7 | + | 569919.i | 1.21848 | + | 0.0630422i | ||||
\(607\) | −8.25756e6 | −0.909662 | −0.454831 | − | 0.890578i | \(-0.650300\pi\) | ||||
−0.454831 | + | 0.890578i | \(0.650300\pi\) | |||||||
\(608\) | −2.13653e6 | −0.234396 | ||||||||
\(609\) | −1.22962e7 | − | 636185.i | −1.34347 | − | 0.0695089i | ||||
\(610\) | 344857. | 0.0375245 | ||||||||
\(611\) | − | 1.46133e7i | − | 1.58360i | ||||||
\(612\) | −555701. | − | 57656.5i | −0.0599740 | − | 0.00622256i | ||||
\(613\) | 2.72531e6i | 0.292930i | 0.989216 | + | 0.146465i | \(0.0467896\pi\) | ||||
−0.989216 | + | 0.146465i | \(0.953210\pi\) | |||||||
\(614\) | 5.53955e6i | 0.592999i | ||||||||
\(615\) | 8011.10 | − | 154839.i | 0.000854091 | − | 0.0165079i | ||||
\(616\) | 5.09834e6 | 0.541349 | ||||||||
\(617\) | 167441. | 0.0177072 | 0.00885358 | − | 0.999961i | \(-0.497182\pi\) | ||||
0.00885358 | + | 0.999961i | \(0.497182\pi\) | |||||||
\(618\) | −62742.8 | − | 3246.21i | −0.00660835 | − | 0.000341905i | ||||
\(619\) | − | 4.02548e6i | − | 0.422271i | −0.977457 | − | 0.211135i | \(-0.932284\pi\) | ||
0.977457 | − | 0.211135i | \(-0.0677161\pi\) | |||||||
\(620\) | −432924. | −0.0452306 | ||||||||
\(621\) | 9.00841e6 | + | 3.34708e6i | 0.937388 | + | 0.348287i | ||||
\(622\) | −7.11708e6 | −0.737609 | ||||||||
\(623\) | − | 2.43679e6i | − | 0.251535i | ||||||
\(624\) | −3.00604e6 | − | 155527.i | −0.309053 | − | 0.0159899i | ||||
\(625\) | 8.78248e6 | 0.899326 | ||||||||
\(626\) | −382088. | −0.0389698 | ||||||||
\(627\) | 957918. | − | 1.85147e7i | 0.0973105 | − | 1.88082i | ||||
\(628\) | 875200.i | 0.0885540i | ||||||||
\(629\) | − | 1.04170e6i | − | 0.104982i | ||||||
\(630\) | −1.39155e6 | − | 144380.i | −0.139685 | − | 0.0144929i | ||||
\(631\) | − | 5.31227e6i | − | 0.531137i | −0.964092 | − | 0.265569i | \(-0.914440\pi\) | ||
0.964092 | − | 0.265569i | \(-0.0855597\pi\) | |||||||
\(632\) | −6.34533e6 | −0.631919 | ||||||||
\(633\) | −2.38415e6 | − | 123352.i | −0.236496 | − | 0.0122359i | ||||
\(634\) | 1.28013e6 | 0.126482 | ||||||||
\(635\) | 886936. | 0.0872887 | ||||||||
\(636\) | 7.19675e6 | + | 372348.i | 0.705494 | + | 0.0365011i | ||||
\(637\) | 2.05479e6 | 0.200641 | ||||||||
\(638\) | −1.28863e7 | −1.25336 | ||||||||
\(639\) | −1.23191e6 | + | 1.18733e7i | −0.119351 | + | 1.15032i | ||||
\(640\) | 168739.i | 0.0162841i | ||||||||
\(641\) | 8.94382e6 | 0.859761 | 0.429881 | − | 0.902886i | \(-0.358556\pi\) | ||||
0.429881 | + | 0.902886i | \(0.358556\pi\) | |||||||
\(642\) | 708112. | − | 1.36864e7i | 0.0678054 | − | 1.31054i | ||||
\(643\) | − | 1.57124e6i | − | 0.149870i | −0.997188 | − | 0.0749350i | \(-0.976125\pi\) | ||
0.997188 | − | 0.0749350i | \(-0.0238749\pi\) | |||||||
\(644\) | −1.13073e6 | + | 5.55905e6i | −0.107435 | + | 0.528185i | ||||
\(645\) | 100077. | − | 1.93429e6i | 0.00947183 | − | 0.183072i | ||||
\(646\) | −1.19925e6 | −0.113065 | ||||||||
\(647\) | − | 1.02267e7i | − | 0.960450i | −0.877145 | − | 0.480225i | \(-0.840555\pi\) | ||
0.877145 | − | 0.480225i | \(-0.159445\pi\) | |||||||
\(648\) | −775852. | + | 3.69864e6i | −0.0725841 | + | 0.346022i | ||||
\(649\) | − | 1.18339e7i | − | 1.10285i | ||||||
\(650\) | − | 9.10845e6i | − | 0.845593i | ||||||
\(651\) | 295731. | − | 5.71589e6i | 0.0273492 | − | 0.528606i | ||||
\(652\) | 7.27760e6 | 0.670454 | ||||||||
\(653\) | 1.09647e7i | 1.00627i | 0.864209 | + | 0.503133i | \(0.167819\pi\) | ||||
−0.864209 | + | 0.503133i | \(0.832181\pi\) | |||||||
\(654\) | 7.18151e6 | + | 371559.i | 0.656555 | + | 0.0339691i | ||||
\(655\) | − | 2.42236e6i | − | 0.220615i | ||||||
\(656\) | − | 247230.i | − | 0.0224307i | ||||||
\(657\) | 457970. | + | 47516.5i | 0.0413927 | + | 0.00429468i | ||||
\(658\) | − | 1.08303e7i | − | 0.975164i | ||||||
\(659\) | 1.26624e7 | 1.13581 | 0.567903 | − | 0.823096i | \(-0.307755\pi\) | ||||
0.567903 | + | 0.823096i | \(0.307755\pi\) | |||||||
\(660\) | −1.46225e6 | − | 75654.5i | −0.130666 | − | 0.00676044i | ||||
\(661\) | − | 5.76883e6i | − | 0.513552i | −0.966471 | − | 0.256776i | \(-0.917340\pi\) | ||
0.966471 | − | 0.256776i | \(-0.0826602\pi\) | |||||||
\(662\) | − | 1.90629e6i | − | 0.169062i | ||||||
\(663\) | −1.68731e6 | − | 87298.5i | −0.149077 | − | 0.00771299i | ||||
\(664\) | 5.50645e6i | 0.484676i | ||||||||
\(665\) | −3.00308e6 | −0.263338 | ||||||||
\(666\) | −7.00879e6 | − | 727193.i | −0.612290 | − | 0.0635278i | ||||
\(667\) | 2.85799e6 | − | 1.40508e7i | 0.248740 | − | 1.22289i | ||||
\(668\) | − | 4.73903e6i | − | 0.410911i | ||||||
\(669\) | −8.28765e6 | − | 428789.i | −0.715922 | − | 0.0370406i | ||||
\(670\) | −1.16764e6 | −0.100490 | ||||||||
\(671\) | 4.77166e6i | 0.409132i | ||||||||
\(672\) | −2.22785e6 | − | 115266.i | −0.190311 | − | 0.00984637i | ||||
\(673\) | −2.25262e7 | −1.91713 | −0.958564 | − | 0.284878i | \(-0.908047\pi\) | ||||
−0.958564 | + | 0.284878i | \(0.908047\pi\) | |||||||
\(674\) | −1.45735e7 | −1.23570 | ||||||||
\(675\) | −1.12985e7 | − | 1.76631e6i | −0.954465 | − | 0.149213i | ||||
\(676\) | −3.16228e6 | −0.266154 | ||||||||
\(677\) | 2.32505e6 | 0.194967 | 0.0974833 | − | 0.995237i | \(-0.468921\pi\) | ||||
0.0974833 | + | 0.995237i | \(0.468921\pi\) | |||||||
\(678\) | −402782. | + | 7.78498e6i | −0.0336508 | + | 0.650404i | ||||
\(679\) | 2.30835e7 | 1.92145 | ||||||||
\(680\) | 94714.1i | 0.00785493i | ||||||||
\(681\) | −9.74668e6 | − | 504277.i | −0.805358 | − | 0.0416679i | ||||
\(682\) | − | 5.99021e6i | − | 0.493152i | ||||||
\(683\) | 2.41065e7i | 1.97735i | 0.150077 | + | 0.988674i | \(0.452048\pi\) | ||||
−0.150077 | + | 0.988674i | \(0.547952\pi\) | |||||||
\(684\) | −837175. | + | 8.06881e6i | −0.0684189 | + | 0.659431i | ||||
\(685\) | 1.38817e6 | 0.113036 | ||||||||
\(686\) | −7.87252e6 | −0.638710 | ||||||||
\(687\) | 928837. | − | 1.79526e7i | 0.0750840 | − | 1.45123i | ||||
\(688\) | − | 3.08847e6i | − | 0.248755i | ||||||
\(689\) | 2.17934e7 | 1.74895 | ||||||||
\(690\) | 406796. | − | 1.57761e6i | 0.0325277 | − | 0.126147i | ||||
\(691\) | 1.69825e7 | 1.35302 | 0.676512 | − | 0.736431i | \(-0.263491\pi\) | ||||
0.676512 | + | 0.736431i | \(0.263491\pi\) | |||||||
\(692\) | 2.73065e6i | 0.216771i | ||||||||
\(693\) | 1.99773e6 | − | 1.92544e7i | 0.158017 | − | 1.52299i | ||||
\(694\) | −9.73417e6 | −0.767185 | ||||||||
\(695\) | 3.02548e6 | 0.237592 | ||||||||
\(696\) | 5.63101e6 | + | 291339.i | 0.440619 | + | 0.0227969i | ||||
\(697\) | − | 138772.i | − | 0.0108198i | ||||||
\(698\) | − | 4.34791e6i | − | 0.337787i | ||||||
\(699\) | 318685. | − | 6.15956e6i | 0.0246700 | − | 0.476822i | ||||
\(700\) | − | 6.75052e6i | − | 0.520706i | ||||||
\(701\) | 3.19831e6 | 0.245825 | 0.122912 | − | 0.992418i | \(-0.460777\pi\) | ||||
0.122912 | + | 0.992418i | \(0.460777\pi\) | |||||||
\(702\) | −1.76525e6 | + | 1.12917e7i | −0.135196 | + | 0.864798i | ||||
\(703\) | −1.51255e7 | −1.15431 | ||||||||
\(704\) | −2.33477e6 | −0.177547 | ||||||||
\(705\) | −160712. | + | 3.10624e6i | −0.0121780 | + | 0.235376i | ||||
\(706\) | −7.33784e6 | −0.554060 | ||||||||
\(707\) | 2.47219e7 | 1.86009 | ||||||||
\(708\) | −267545. | + | 5.17112e6i | −0.0200592 | + | 0.387705i | ||||
\(709\) | − | 331472.i | − | 0.0247646i | −0.999923 | − | 0.0123823i | \(-0.996058\pi\) | ||
0.999923 | − | 0.0123823i | \(-0.00394151\pi\) | |||||||
\(710\) | 2.02370e6 | 0.150661 | ||||||||
\(711\) | −2.48635e6 | + | 2.39638e7i | −0.184454 | + | 1.77779i | ||||
\(712\) | 1.11592e6i | 0.0824963i | ||||||||
\(713\) | 6.53151e6 | + | 1.32854e6i | 0.481160 | + | 0.0978700i | ||||
\(714\) | −1.25051e6 | − | 64699.3i | −0.0917997 | − | 0.00474957i | ||||
\(715\) | −4.42804e6 | −0.323926 | ||||||||
\(716\) | − | 1.10532e7i | − | 0.805758i | ||||||
\(717\) | −1.10401e6 | + | 2.13383e7i | −0.0802002 | + | 1.55011i | ||||
\(718\) | 1.58815e7i | 1.14969i | ||||||||
\(719\) | − | 2.48340e7i | − | 1.79153i | −0.444530 | − | 0.895764i | \(-0.646629\pi\) | ||
0.444530 | − | 0.895764i | \(-0.353371\pi\) | |||||||
\(720\) | 637259. | + | 66118.4i | 0.0458126 | + | 0.00475326i | ||||
\(721\) | −140814. | −0.0100881 | ||||||||
\(722\) | 7.50873e6i | 0.536072i | ||||||||
\(723\) | −576353. | + | 1.11398e7i | −0.0410055 | + | 0.792556i | ||||
\(724\) | − | 4.24825e6i | − | 0.301206i | ||||||
\(725\) | 1.70623e7i | 1.20557i | ||||||||
\(726\) | 527933. | − | 1.02039e7i | 0.0371738 | − | 0.718496i | ||||
\(727\) | − | 4.76809e6i | − | 0.334586i | −0.985907 | − | 0.167293i | \(-0.946497\pi\) | ||
0.985907 | − | 0.167293i | \(-0.0535027\pi\) | |||||||
\(728\) | −6.74646e6 | −0.471788 | ||||||||
\(729\) | 1.36643e7 | + | 4.37936e6i | 0.952287 | + | 0.305205i | ||||
\(730\) | − | 78056.8i | − | 0.00542130i | ||||||
\(731\) | − | 1.73358e6i | − | 0.119991i | ||||||
\(732\) | 107880. | − | 2.08510e6i | 0.00744153 | − | 0.143830i | ||||
\(733\) | − | 2.36493e6i | − | 0.162577i | −0.996691 | − | 0.0812883i | \(-0.974097\pi\) | ||
0.996691 | − | 0.0812883i | \(-0.0259034\pi\) | |||||||
\(734\) | 1.07304e7 | 0.735151 | ||||||||
\(735\) | −436771. | − | 22597.8i | −0.0298219 | − | 0.00154294i | ||||
\(736\) | 517817. | − | 2.54575e6i | 0.0352356 | − | 0.173229i | ||||
\(737\) | − | 1.61562e7i | − | 1.09565i | ||||||
\(738\) | −933691. | − | 96874.6i | −0.0631048 | − | 0.00654740i | ||||
\(739\) | −1.64314e7 | −1.10678 | −0.553391 | − | 0.832921i | \(-0.686667\pi\) | ||||
−0.553391 | + | 0.832921i | \(0.686667\pi\) | |||||||
\(740\) | 1.19458e6i | 0.0801932i | ||||||||
\(741\) | −1.26758e6 | + | 2.44998e7i | −0.0848066 | + | 1.63914i | ||||
\(742\) | 1.61517e7 | 1.07698 | ||||||||
\(743\) | −880922. | −0.0585417 | −0.0292708 | − | 0.999572i | \(-0.509319\pi\) | ||||
−0.0292708 | + | 0.999572i | \(0.509319\pi\) | |||||||
\(744\) | −135429. | + | 2.61758e6i | −0.00896975 | + | 0.173367i | ||||
\(745\) | 929671. | 0.0613675 | ||||||||
\(746\) | 4.36101e6 | 0.286906 | ||||||||
\(747\) | 2.07957e7 | + | 2.15764e6i | 1.36355 | + | 0.141475i | ||||
\(748\) | −1.31052e6 | −0.0856428 | ||||||||
\(749\) | − | 3.07165e7i | − | 2.00063i | ||||||
\(750\) | −203862. | + | 3.94025e6i | −0.0132338 | + | 0.255782i | ||||
\(751\) | 1.49362e7i | 0.966360i | 0.875521 | + | 0.483180i | \(0.160518\pi\) | ||||
−0.875521 | + | 0.483180i | \(0.839482\pi\) | |||||||
\(752\) | 4.95973e6i | 0.319826i | ||||||||
\(753\) | −1.05735e7 | − | 547054.i | −0.679564 | − | 0.0351595i | ||||
\(754\) | 1.70520e7 | 1.09231 | ||||||||
\(755\) | −221240. | −0.0141253 | ||||||||
\(756\) | −1.30827e6 | + | 8.36856e6i | −0.0832518 | + | 0.532532i | ||||
\(757\) | − | 2.64695e7i | − | 1.67883i | −0.543495 | − | 0.839413i | \(-0.682899\pi\) | ||
0.543495 | − | 0.839413i | \(-0.317101\pi\) | |||||||
\(758\) | −1.26377e7 | −0.798903 | ||||||||
\(759\) | 2.18288e7 | + | 5.62868e6i | 1.37539 | + | 0.354652i | ||||
\(760\) | 1.37525e6 | 0.0863673 | ||||||||
\(761\) | − | 5.98030e6i | − | 0.374336i | −0.982328 | − | 0.187168i | \(-0.940069\pi\) | ||
0.982328 | − | 0.187168i | \(-0.0599308\pi\) | |||||||
\(762\) | 277455. | − | 5.36266e6i | 0.0173103 | − | 0.334574i | ||||
\(763\) | 1.61175e7 | 1.00227 | ||||||||
\(764\) | 9.83780e6 | 0.609768 | ||||||||
\(765\) | 357698. | + | 37112.7i | 0.0220985 | + | 0.00229282i | ||||
\(766\) | 710480.i | 0.0437502i | ||||||||
\(767\) | 1.56593e7i | 0.961136i | ||||||||
\(768\) | 1.02024e6 | + | 52785.6i | 0.0624165 | + | 0.00322933i | ||||
\(769\) | 1.63013e7i | 0.994046i | 0.867737 | + | 0.497023i | \(0.165573\pi\) | ||||
−0.867737 | + | 0.497023i | \(0.834427\pi\) | |||||||
\(770\) | −3.28174e6 | −0.199470 | ||||||||
\(771\) | −1.11850e6 | + | 2.16185e7i | −0.0677643 | + | 1.30975i | ||||
\(772\) | −1.38684e6 | −0.0837496 | ||||||||
\(773\) | 1.75987e7 | 1.05933 | 0.529667 | − | 0.848206i | \(-0.322317\pi\) | ||||
0.529667 | + | 0.848206i | \(0.322317\pi\) | |||||||
\(774\) | −1.16639e7 | − | 1.21018e6i | −0.699829 | − | 0.0726104i | ||||
\(775\) | −7.93141e6 | −0.474347 | ||||||||
\(776\) | −1.05711e7 | −0.630179 | ||||||||
\(777\) | −1.57721e7 | − | 816021.i | −0.937209 | − | 0.0484896i | ||||
\(778\) | − | 9.17416e6i | − | 0.543397i | ||||||
\(779\) | −2.01498e6 | −0.118967 | ||||||||
\(780\) | 1.93495e6 | + | 100111.i | 0.113876 | + | 0.00589176i | ||||
\(781\) | 2.80011e7i | 1.64266i | ||||||||
\(782\) | 290654. | − | 1.42895e6i | 0.0169965 | − | 0.0835602i | ||||
\(783\) | 3.30672e6 | − | 2.11519e7i | 0.192750 | − | 1.23295i | ||||
\(784\) | −697391. | −0.0405216 | ||||||||
\(785\) | − | 563355.i | − | 0.0326293i | ||||||
\(786\) | −1.46463e7 | − | 757773.i | −0.845611 | − | 0.0437505i | ||||
\(787\) | − | 2.02421e7i | − | 1.16498i | −0.812838 | − | 0.582490i | \(-0.802078\pi\) | ||
0.812838 | − | 0.582490i | \(-0.197922\pi\) | |||||||
\(788\) | − | 1.17728e7i | − | 0.675406i | ||||||
\(789\) | −1.65779e7 | − | 857715.i | −0.948064 | − | 0.0490513i | ||||
\(790\) | 4.08441e6 | 0.232842 | ||||||||
\(791\) | 1.74719e7i | 0.992883i | ||||||||
\(792\) | −914856. | + | 8.81751e6i | −0.0518250 | + | 0.499497i | ||||
\(793\) | − | 6.31417e6i | − | 0.356561i | ||||||
\(794\) | 1.79089e7i | 1.00813i | ||||||||
\(795\) | −4.63245e6 | − | 239676.i | −0.259952 | − | 0.0134495i | ||||
\(796\) | 1.62668e7i | 0.909954i | ||||||||
\(797\) | −3.03091e7 | −1.69016 | −0.845080 | − | 0.534640i | \(-0.820447\pi\) | ||||
−0.845080 | + | 0.534640i | \(0.820447\pi\) | |||||||
\(798\) | −939437. | + | 1.81575e7i | −0.0522229 | + | 1.00936i | ||||
\(799\) | 2.78393e6i | 0.154273i | ||||||||
\(800\) | 3.09139e6i | 0.170777i | ||||||||
\(801\) | 4.21440e6 | + | 437263.i | 0.232089 | + | 0.0240803i | ||||
\(802\) | − | 1.43961e7i | − | 0.790332i | ||||||
\(803\) | 1.08004e6 | 0.0591088 | ||||||||
\(804\) | −365267. | + | 7.05989e6i | −0.0199283 | + | 0.385175i | ||||
\(805\) | 727839. | − | 3.57829e6i | 0.0395863 | − | 0.194619i | ||||
\(806\) | 7.92663e6i | 0.429785i | ||||||||
\(807\) | 82881.1 | − | 1.60193e6i | 0.00447993 | − | 0.0865883i | ||||
\(808\) | −1.13213e7 | −0.610056 | ||||||||
\(809\) | − | 1.30668e7i | − | 0.701938i | −0.936387 | − | 0.350969i | \(-0.885852\pi\) | ||
0.936387 | − | 0.350969i | \(-0.114148\pi\) | |||||||
\(810\) | 499406. | − | 2.38077e6i | 0.0267449 | − | 0.127498i | ||||
\(811\) | 1.74183e7 | 0.929935 | 0.464968 | − | 0.885328i | \(-0.346066\pi\) | ||||
0.464968 | + | 0.885328i | \(0.346066\pi\) | |||||||
\(812\) | 1.26377e7 | 0.672633 | ||||||||
\(813\) | 2.83822e7 | + | 1.46845e6i | 1.50598 | + | 0.0779171i | ||||
\(814\) | −1.65290e7 | −0.874351 | ||||||||
\(815\) | −4.68450e6 | −0.247041 | ||||||||
\(816\) | 572668. | + | 29628.9i | 0.0301077 | + | 0.00155772i | ||||
\(817\) | −2.51717e7 | −1.31934 | ||||||||
\(818\) | − | 3.53865e6i | − | 0.184907i | ||||||
\(819\) | −2.64353e6 | + | 2.54787e7i | −0.137713 | + | 1.32729i | ||||
\(820\) | 159139.i | 0.00826498i | ||||||||
\(821\) | 1.35544e7i | 0.701816i | 0.936410 | + | 0.350908i | \(0.114127\pi\) | ||||
−0.936410 | + | 0.350908i | \(0.885873\pi\) | |||||||
\(822\) | 434255. | − | 8.39329e6i | 0.0224164 | − | 0.433264i | ||||
\(823\) | −1.27411e7 | −0.655705 | −0.327852 | − | 0.944729i | \(-0.606325\pi\) | ||||
−0.327852 | + | 0.944729i | \(0.606325\pi\) | |||||||
\(824\) | 64485.4 | 0.00330859 | ||||||||
\(825\) | −2.67893e7 | − | 1.38603e6i | −1.37033 | − | 0.0708987i | ||||
\(826\) | 1.16056e7i | 0.591856i | ||||||||
\(827\) | 6.73222e6 | 0.342290 | 0.171145 | − | 0.985246i | \(-0.445253\pi\) | ||||
0.171145 | + | 0.985246i | \(0.445253\pi\) | |||||||
\(828\) | −9.41140e6 | − | 2.95311e6i | −0.477066 | − | 0.149694i | ||||
\(829\) | −8.06147e6 | −0.407406 | −0.203703 | − | 0.979033i | \(-0.565298\pi\) | ||||
−0.203703 | + | 0.979033i | \(0.565298\pi\) | |||||||
\(830\) | − | 3.54443e6i | − | 0.178588i | ||||||
\(831\) | 8.70297e6 | + | 450277.i | 0.437185 | + | 0.0226192i | ||||
\(832\) | 3.08952e6 | 0.154733 | ||||||||
\(833\) | −391450. | −0.0195463 | ||||||||
\(834\) | 946444. | − | 1.82929e7i | 0.0471173 | − | 0.910683i | ||||
\(835\) | 3.05045e6i | 0.151408i | ||||||||
\(836\) | 1.90289e7i | 0.941667i | ||||||||
\(837\) | 9.83249e6 | + | 1.53713e6i | 0.485121 | + | 0.0758399i | ||||
\(838\) | − | 1.55864e7i | − | 0.766718i | ||||||
\(839\) | −5.25374e6 | −0.257670 | −0.128835 | − | 0.991666i | \(-0.541124\pi\) | ||||
−0.128835 | + | 0.991666i | \(0.541124\pi\) | |||||||
\(840\) | 1.43404e6 | + | 74194.9i | 0.0701235 | + | 0.00362807i | ||||
\(841\) | −1.14313e7 | −0.557321 | ||||||||
\(842\) | −5.57711e6 | −0.271099 | ||||||||
\(843\) | 1.69945e7 | + | 879268.i | 0.823645 | + | 0.0426140i | ||||
\(844\) | 2.45036e6 | 0.118406 | ||||||||
\(845\) | 2.03552e6 | 0.0980693 | ||||||||
\(846\) | 1.87309e7 | + | 1.94342e6i | 0.899774 | + | 0.0933555i | ||||
\(847\) | − | 2.29006e7i | − | 1.09683i | ||||||
\(848\) | −7.39663e6 | −0.353219 | ||||||||
\(849\) | −60497.3 | + | 1.16929e6i | −0.00288049 | + | 0.0556742i | ||||
\(850\) | 1.73521e6i | 0.0823770i | ||||||||
\(851\) | 3.66588e6 | − | 1.80226e7i | 0.173522 | − | 0.853089i | ||||
\(852\) | 633061. | − | 1.22358e7i | 0.0298777 | − | 0.577476i | ||||
\(853\) | 1.51042e7 | 0.710764 | 0.355382 | − | 0.934721i | \(-0.384351\pi\) | ||||
0.355382 | + | 0.934721i | \(0.384351\pi\) | |||||||
\(854\) | − | 4.67960e6i | − | 0.219566i | ||||||
\(855\) | 538879. | − | 5.19379e6i | 0.0252102 | − | 0.242979i | ||||
\(856\) | 1.40665e7i | 0.656149i | ||||||||
\(857\) | − | 3.62300e7i | − | 1.68506i | −0.538648 | − | 0.842531i | \(-0.681065\pi\) | ||
0.538648 | − | 0.842531i | \(-0.318935\pi\) | |||||||
\(858\) | −1.38520e6 | + | 2.67731e7i | −0.0642382 | + | 1.24160i | ||||
\(859\) | −1.86346e7 | −0.861660 | −0.430830 | − | 0.902433i | \(-0.641779\pi\) | ||||
−0.430830 | + | 0.902433i | \(0.641779\pi\) | |||||||
\(860\) | 1.98801e6i | 0.0916583i | ||||||||
\(861\) | −2.10111e6 | − | 108708.i | −0.0965920 | − | 0.00499751i | ||||
\(862\) | − | 1.46860e7i | − | 0.673186i | ||||||
\(863\) | 3.58311e7i | 1.63770i | 0.574011 | + | 0.818848i | \(0.305387\pi\) | ||||
−0.574011 | + | 0.818848i | \(0.694613\pi\) | |||||||
\(864\) | 599120. | − | 3.83236e6i | 0.0273042 | − | 0.174655i | ||||
\(865\) | − | 1.75768e6i | − | 0.0798730i | ||||||
\(866\) | −1.33224e7 | −0.603653 | ||||||||
\(867\) | −2.17824e7 | − | 1.12698e6i | −0.984141 | − | 0.0509178i | ||||
\(868\) | 5.87464e6i | 0.264656i | ||||||||
\(869\) | 5.65144e7i | 2.53869i | ||||||||
\(870\) | −3.62461e6 | − | 187531.i | −0.162354 | − | 0.00839993i | ||||
\(871\) | 2.13790e7i | 0.954864i | ||||||||
\(872\) | −7.38096e6 | −0.328717 | ||||||||
\(873\) | −4.14215e6 | + | 3.99227e7i | −0.183946 | + | 1.77290i | ||||
\(874\) | −2.07484e7 | − | 4.22031e6i | −0.918769 | − | 0.186881i | ||||
\(875\) | 8.84312e6i | 0.390468i | ||||||||
\(876\) | −471953. | − | 24418.1i | −0.0207797 | − | 0.00107511i | ||||
\(877\) | 2.02561e7 | 0.889317 | 0.444658 | − | 0.895700i | \(-0.353325\pi\) | ||||
0.444658 | + | 0.895700i | \(0.353325\pi\) | |||||||
\(878\) | − | 2.65999e7i | − | 1.16451i | ||||||
\(879\) | 2.64467e7 | + | 1.36831e6i | 1.15452 | + | 0.0597327i | ||||
\(880\) | 1.50286e6 | 0.0654204 | ||||||||
\(881\) | 1.08688e7 | 0.471782 | 0.235891 | − | 0.971779i | \(-0.424199\pi\) | ||||
0.235891 | + | 0.971779i | \(0.424199\pi\) | |||||||
\(882\) | −273265. | + | 2.63377e6i | −0.0118280 | + | 0.114000i | ||||
\(883\) | 2.48720e7 | 1.07351 | 0.536757 | − | 0.843737i | \(-0.319649\pi\) | ||||
0.536757 | + | 0.843737i | \(0.319649\pi\) | |||||||
\(884\) | 1.73417e6 | 0.0746382 | ||||||||
\(885\) | 172215. | − | 3.32858e6i | 0.00739118 | − | 0.142857i | ||||
\(886\) | 1.63854e7 | 0.701250 | ||||||||
\(887\) | − | 3.71436e7i | − | 1.58517i | −0.609765 | − | 0.792583i | \(-0.708736\pi\) | ||
0.609765 | − | 0.792583i | \(-0.291264\pi\) | |||||||
\(888\) | 7.22278e6 | + | 373695.i | 0.307378 | + | 0.0159032i | ||||
\(889\) | − | 1.20354e7i | − | 0.510749i | ||||||
\(890\) | − | 718306.i | − | 0.0303972i | ||||||
\(891\) | 3.29418e7 | + | 6.91009e6i | 1.39012 | + | 0.291601i | ||||
\(892\) | 8.51782e6 | 0.358440 | ||||||||
\(893\) | 4.04228e7 | 1.69628 | ||||||||
\(894\) | 290824. | − | 5.62105e6i | 0.0121699 | − | 0.235220i | ||||
\(895\) | 7.11479e6i | 0.296896i | ||||||||
\(896\) | 2.28973e6 | 0.0952827 | ||||||||
\(897\) | −2.88852e7 | − | 7.44823e6i | −1.19866 | − | 0.309081i | ||||
\(898\) | 1.21710e7 | 0.503659 | ||||||||
\(899\) | − | 1.48485e7i | − | 0.612748i | ||||||
\(900\) | 1.16749e7 | + | 1.21133e6i | 0.480450 | + | 0.0498488i | ||||
\(901\) | −4.15178e6 | −0.170381 | ||||||||
\(902\) | −2.20195e6 | −0.0901136 | ||||||||
\(903\) | −2.62476e7 | − | 1.35801e6i | −1.07120 | − | 0.0554222i | ||||
\(904\) | − | 8.00119e6i | − | 0.325637i | ||||||
\(905\) | 2.73454e6i | 0.110985i | ||||||||
\(906\) | −69209.3 | + | 1.33768e6i | −0.00280120 | + | 0.0541417i | ||||
\(907\) | 1.30765e7i | 0.527803i | 0.964550 | + | 0.263902i | \(0.0850094\pi\) | ||||
−0.964550 | + | 0.263902i | \(0.914991\pi\) | |||||||
\(908\) | 1.00174e7 | 0.403218 | ||||||||
\(909\) | −4.43615e6 | + | 4.27562e7i | −0.178072 | + | 1.71629i | ||||
\(910\) | 4.34261e6 | 0.173839 | ||||||||
\(911\) | −1.76520e7 | −0.704690 | −0.352345 | − | 0.935870i | \(-0.614616\pi\) | ||||
−0.352345 | + | 0.935870i | \(0.614616\pi\) | |||||||
\(912\) | 430213. | − | 8.31517e6i | 0.0171276 | − | 0.331043i | ||||
\(913\) | 4.90430e7 | 1.94715 | ||||||||
\(914\) | 1.53322e7 | 0.607070 | ||||||||
\(915\) | −69440.8 | + | 1.34215e6i | −0.00274197 | + | 0.0529968i | ||||
\(916\) | 1.84512e7i | 0.726583i | ||||||||
\(917\) | −3.28707e7 | −1.29088 | ||||||||
\(918\) | 336290. | − | 2.15113e6i | 0.0131707 | − | 0.0842480i | ||||
\(919\) | − | 2.87633e7i | − | 1.12344i | −0.827327 | − | 0.561721i | \(-0.810140\pi\) | ||
0.827327 | − | 0.561721i | \(-0.189860\pi\) | |||||||
\(920\) | −333312. | + | 1.63867e6i | −0.0129832 | + | 0.0638295i | ||||
\(921\) | −2.15594e7 | − | 1.11545e6i | −0.837507 | − | 0.0433312i | ||||
\(922\) | −1.05046e7 | −0.406961 | ||||||||
\(923\) | − | 3.70529e7i | − | 1.43159i | ||||||
\(924\) | −1.02661e6 | + | 1.98423e7i | −0.0395571 | + | 0.764560i | ||||
\(925\) | 2.18854e7i | 0.841009i | ||||||||
\(926\) | 1.23391e7i | 0.472886i | ||||||||
\(927\) | 25267.9 | − | 243536.i | 0.000965762 | − | 0.00930815i | ||||
\(928\) | −5.78741e6 | −0.220604 | ||||||||
\(929\) | 3.89993e7i | 1.48258i | 0.671186 | + | 0.741289i | \(0.265785\pi\) | ||||
−0.671186 | + | 0.741289i | \(0.734215\pi\) | |||||||
\(930\) | 87174.1 | − | 1.68490e6i | 0.00330506 | − | 0.0638804i | ||||
\(931\) | 5.68388e6i | 0.214917i | ||||||||
\(932\) | 6.33063e6i | 0.238730i | ||||||||
\(933\) | 1.43310e6 | − | 2.76990e7i | 0.0538981 | − | 1.04174i | ||||
\(934\) | 4.32285e6i | 0.162145i | ||||||||
\(935\) | 843567. | 0.0315566 | ||||||||
\(936\) | 1.21060e6 | − | 1.16679e7i | 0.0451658 | − | 0.435314i | ||||
\(937\) | − | 1.09436e7i | − | 0.407204i | −0.979054 | − | 0.203602i | \(-0.934735\pi\) | ||
0.979054 | − | 0.203602i | \(-0.0652648\pi\) | |||||||
\(938\) | 1.58445e7i | 0.587993i | ||||||||
\(939\) | 76937.6 | − | 1.48705e6i | 0.00284757 | − | 0.0550380i | ||||
\(940\) | − | 3.19251e6i | − | 0.117846i | ||||||
\(941\) | 3.22825e7 | 1.18848 | 0.594242 | − | 0.804287i | \(-0.297452\pi\) | ||||
0.594242 | + | 0.804287i | \(0.297452\pi\) | |||||||
\(942\) | −3.40620e6 | − | 176231.i | −0.125067 | − | 0.00647076i | ||||
\(943\) | 488358. | − | 2.40092e6i | 0.0178838 | − | 0.0879223i | ||||
\(944\) | − | 5.31474e6i | − | 0.194112i | ||||||
\(945\) | 842118. | − | 5.38673e6i | 0.0306756 | − | 0.196221i | ||||
\(946\) | −2.75073e7 | −0.999356 | ||||||||
\(947\) | − | 1.93494e7i | − | 0.701120i | −0.936540 | − | 0.350560i | \(-0.885991\pi\) | ||
0.936540 | − | 0.350560i | \(-0.114009\pi\) | |||||||
\(948\) | 1.27770e6 | − | 2.46954e7i | 0.0461752 | − | 0.892475i | ||||
\(949\) | −1.42918e6 | −0.0515136 | ||||||||
\(950\) | 2.51954e7 | 0.905759 | ||||||||
\(951\) | −257768. | + | 4.98214e6i | −0.00924224 | + | 0.178634i | ||||
\(952\) | 1.28524e6 | 0.0459613 | ||||||||
\(953\) | −4.27930e7 | −1.52630 | −0.763151 | − | 0.646221i | \(-0.776349\pi\) | ||||
−0.763151 | + | 0.646221i | \(0.776349\pi\) | |||||||
\(954\) | −2.89829e6 | + | 2.79341e7i | −0.103103 | + | 0.993720i | ||||
\(955\) | −6.33246e6 | −0.224680 | ||||||||
\(956\) | − | 2.19310e7i | − | 0.776092i | ||||||
\(957\) | 2.59480e6 | − | 5.01524e7i | 0.0915850 | − | 1.77016i | ||||
\(958\) | 1.99605e7i | 0.702679i | ||||||||
\(959\) | − | 1.88371e7i | − | 0.661404i | ||||||
\(960\) | −656716. | − | 33977.4i | −0.0229985 | − | 0.00118990i | ||||
\(961\) | −2.17268e7 | −0.758906 | ||||||||
\(962\) | 2.18722e7 | 0.762001 | ||||||||
\(963\) | 5.31237e7 | + | 5.51181e6i | 1.84596 | + | 0.191527i | ||||
\(964\) | − | 1.14491e7i | − | 0.396808i | ||||||
\(965\) | 892690. | 0.0308591 | ||||||||
\(966\) | −2.14076e7 | − | 5.52009e6i | −0.738118 | − | 0.190328i | ||||
\(967\) | −5.40541e7 | −1.85893 | −0.929465 | − | 0.368911i | \(-0.879731\pi\) | ||||
−0.929465 | + | 0.368911i | \(0.879731\pi\) | |||||||
\(968\) | 1.04873e7i | 0.359729i | ||||||||
\(969\) | 241481. | − | 4.66736e6i | 0.00826179 | − | 0.159684i | ||||
\(970\) | 6.80445e6 | 0.232201 | ||||||||
\(971\) | 3.80597e6 | 0.129544 | 0.0647721 | − | 0.997900i | \(-0.479368\pi\) | ||||
0.0647721 | + | 0.997900i | \(0.479368\pi\) | |||||||
\(972\) | −1.42385e7 | − | 3.76431e6i | −0.483392 | − | 0.127797i | ||||
\(973\) | − | 4.10548e7i | − | 1.39022i | ||||||
\(974\) | − | 3.03828e7i | − | 1.02620i | ||||||
\(975\) | 3.54493e7 | + | 1.83409e6i | 1.19425 | + | 0.0617886i | ||||
\(976\) | 2.14301e6i | 0.0720112i | ||||||||
\(977\) | −4.53725e7 | −1.52075 | −0.760373 | − | 0.649487i | \(-0.774984\pi\) | ||||
−0.760373 | + | 0.649487i | \(0.774984\pi\) | |||||||
\(978\) | −1.46542e6 | + | 2.83238e7i | −0.0489910 | + | 0.946899i | ||||
\(979\) | 9.93892e6 | 0.331423 | ||||||||
\(980\) | 448902. | 0.0149309 | ||||||||
\(981\) | −2.89215e6 | + | 2.78749e7i | −0.0959507 | + | 0.924787i | ||||
\(982\) | 6.06810e6 | 0.200805 | ||||||||
\(983\) | −4.31706e7 | −1.42497 | −0.712483 | − | 0.701690i | \(-0.752429\pi\) | ||||
−0.712483 | + | 0.701690i | \(0.752429\pi\) | |||||||
\(984\) | 962198. | + | 49782.5i | 0.0316794 | + | 0.00163904i | ||||
\(985\) | 7.57801e6i | 0.248865i | ||||||||
\(986\) | −3.24851e6 | −0.106412 | ||||||||
\(987\) | 4.21507e7 | + | 2.18081e6i | 1.37725 | + | 0.0712565i | ||||
\(988\) | − | 2.51802e7i | − | 0.820668i | ||||||
\(989\) | 6.10070e6 | − | 2.99930e7i | 0.198330 | − | 0.975055i | ||||
\(990\) | 588881. | − | 5.67572e6i | 0.0190959 | − | 0.184049i | ||||
\(991\) | 6.02354e7 | 1.94835 | 0.974176 | − | 0.225790i | \(-0.0724963\pi\) | ||||
0.974176 | + | 0.225790i | \(0.0724963\pi\) | |||||||
\(992\) | − | 2.69028e6i | − | 0.0867997i | ||||||
\(993\) | 7.41912e6 | + | 383853.i | 0.238770 | + | 0.0123536i | ||||
\(994\) | − | 2.74609e7i | − | 0.881554i | ||||||
\(995\) | − | 1.04707e7i | − | 0.335289i | ||||||
\(996\) | −2.14306e7 | − | 1.10878e6i | −0.684520 | − | 0.0354160i | ||||
\(997\) | −2.68093e7 | −0.854176 | −0.427088 | − | 0.904210i | \(-0.640461\pi\) | ||||
−0.427088 | + | 0.904210i | \(0.640461\pi\) | |||||||
\(998\) | 2.92960e7i | 0.931069i | ||||||||
\(999\) | 4.24147e6 | − | 2.71311e7i | 0.134463 | − | 0.860111i |
(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 | 138.6.d.a.137.14 | yes | 40 | |
3.2 | odd | 2 | inner | 138.6.d.a.137.15 | yes | 40 | |
23.22 | odd | 2 | inner | 138.6.d.a.137.13 | ✓ | 40 | |
69.68 | even | 2 | inner | 138.6.d.a.137.16 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
138.6.d.a.137.13 | ✓ | 40 | 23.22 | odd | 2 | inner | |
138.6.d.a.137.14 | yes | 40 | 1.1 | even | 1 | trivial | |
138.6.d.a.137.15 | yes | 40 | 3.2 | odd | 2 | inner | |
138.6.d.a.137.16 | yes | 40 | 69.68 | even | 2 | inner |