Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9,6,Mod(4,9)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9.4");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 9.c (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.44345437832\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 40x^{6} + 568x^{4} + 3363x^{2} + 7056 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 7.4 | ||
Root | \(-2.56934i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9.7 |
Dual form | 9.6.c.a.4.4 |
$q$-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 \(\left(\mathbb{Z}/9\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.96163 | − | 8.59380i | 0.877101 | − | 1.51918i | 0.0225929 | − | 0.999745i | \(-0.492808\pi\) |
0.854508 | − | 0.519438i | \(-0.173859\pi\) | |||||||
\(3\) | −3.07760 | + | 15.2816i | −0.197428 | + | 0.980317i | ||||
\(4\) | −33.2356 | − | 57.5657i | −1.03861 | − | 1.79893i | ||||
\(5\) | 23.6560 | + | 40.9735i | 0.423172 | + | 0.732956i | 0.996248 | − | 0.0865467i | \(-0.0275832\pi\) |
−0.573076 | + | 0.819503i | \(0.694250\pi\) | |||||||
\(6\) | 116.057 | + | 102.270i | 1.31612 | + | 1.15977i | ||||
\(7\) | 1.01546 | − | 1.75882i | 0.00783278 | − | 0.0135668i | −0.862082 | − | 0.506768i | \(-0.830840\pi\) |
0.869915 | + | 0.493201i | \(0.164173\pi\) | |||||||
\(8\) | −342.066 | −1.88967 | ||||||||
\(9\) | −224.057 | − | 94.0614i | −0.922044 | − | 0.387084i | ||||
\(10\) | 469.490 | 1.48466 | ||||||||
\(11\) | −91.8836 | + | 159.147i | −0.228958 | + | 0.396567i | −0.957500 | − | 0.288435i | \(-0.906865\pi\) |
0.728541 | + | 0.685002i | \(0.240199\pi\) | |||||||
\(12\) | 981.984 | − | 330.730i | 1.96857 | − | 0.663011i | ||||
\(13\) | −364.672 | − | 631.630i | −0.598472 | − | 1.03658i | −0.993047 | − | 0.117720i | \(-0.962441\pi\) |
0.394574 | − | 0.918864i | \(-0.370892\pi\) | |||||||
\(14\) | −10.0766 | − | 17.4532i | −0.0137403 | − | 0.0237989i | ||||
\(15\) | −698.946 | + | 235.403i | −0.802075 | + | 0.270137i | ||||
\(16\) | −633.668 | + | 1097.55i | −0.618817 | + | 1.07182i | ||||
\(17\) | 1212.88 | 1.01788 | 0.508940 | − | 0.860802i | \(-0.330037\pi\) | ||||
0.508940 | + | 0.860802i | \(0.330037\pi\) | |||||||
\(18\) | −1920.03 | + | 1458.80i | −1.39678 | + | 1.06124i | ||||
\(19\) | −473.092 | −0.300650 | −0.150325 | − | 0.988637i | \(-0.548032\pi\) | ||||
−0.150325 | + | 0.988637i | \(0.548032\pi\) | |||||||
\(20\) | 1572.44 | − | 2723.55i | 0.879023 | − | 1.52251i | ||||
\(21\) | 23.7525 | + | 20.9308i | 0.0117533 | + | 0.0103571i | ||||
\(22\) | 911.785 | + | 1579.26i | 0.401639 | + | 0.695659i | ||||
\(23\) | 1806.42 | + | 3128.81i | 0.712031 | + | 1.23327i | 0.964094 | + | 0.265563i | \(0.0855578\pi\) |
−0.252063 | + | 0.967711i | \(0.581109\pi\) | |||||||
\(24\) | 1052.74 | − | 5227.33i | 0.373073 | − | 1.85247i | ||||
\(25\) | 443.283 | − | 767.788i | 0.141850 | − | 0.245692i | ||||
\(26\) | −7237.47 | −2.09968 | ||||||||
\(27\) | 2126.97 | − | 3134.47i | 0.561502 | − | 0.827475i | ||||
\(28\) | −134.997 | −0.0325409 | ||||||||
\(29\) | 663.121 | − | 1148.56i | 0.146419 | − | 0.253605i | −0.783482 | − | 0.621414i | \(-0.786559\pi\) |
0.929901 | + | 0.367809i | \(0.119892\pi\) | |||||||
\(30\) | −1444.90 | + | 7174.58i | −0.293113 | + | 1.45544i | ||||
\(31\) | 2590.41 | + | 4486.72i | 0.484133 | + | 0.838542i | 0.999834 | − | 0.0182261i | \(-0.00580186\pi\) |
−0.515701 | + | 0.856769i | \(0.672469\pi\) | |||||||
\(32\) | 814.997 | + | 1411.62i | 0.140696 | + | 0.243692i | ||||
\(33\) | −2149.25 | − | 1893.92i | −0.343559 | − | 0.302745i | ||||
\(34\) | 6017.88 | − | 10423.3i | 0.892784 | − | 1.54635i | ||||
\(35\) | 96.0867 | 0.0132585 | ||||||||
\(36\) | 2031.95 | + | 16024.2i | 0.261310 | + | 2.06072i | ||||
\(37\) | −14715.2 | −1.76710 | −0.883552 | − | 0.468334i | \(-0.844854\pi\) | ||||
−0.883552 | + | 0.468334i | \(0.844854\pi\) | |||||||
\(38\) | −2347.31 | + | 4065.65i | −0.263700 | + | 0.456742i | ||||
\(39\) | 10774.7 | − | 3628.88i | 1.13434 | − | 0.382042i | ||||
\(40\) | −8091.94 | − | 14015.6i | −0.799655 | − | 1.38504i | ||||
\(41\) | −3159.83 | − | 5472.98i | −0.293564 | − | 0.508469i | 0.681085 | − | 0.732204i | \(-0.261508\pi\) |
−0.974650 | + | 0.223735i | \(0.928175\pi\) | |||||||
\(42\) | 297.726 | − | 100.273i | 0.0260431 | − | 0.00877128i | ||||
\(43\) | −3067.89 | + | 5313.75i | −0.253028 | + | 0.438258i | −0.964358 | − | 0.264600i | \(-0.914760\pi\) |
0.711330 | + | 0.702858i | \(0.248093\pi\) | |||||||
\(44\) | 12215.2 | 0.951195 | ||||||||
\(45\) | −1446.28 | − | 11405.5i | −0.106468 | − | 0.839621i | ||||
\(46\) | 35851.1 | 2.49809 | ||||||||
\(47\) | −1584.17 | + | 2743.86i | −0.104606 | + | 0.181183i | −0.913577 | − | 0.406665i | \(-0.866692\pi\) |
0.808971 | + | 0.587848i | \(0.200025\pi\) | |||||||
\(48\) | −14822.1 | − | 13061.3i | −0.928554 | − | 0.818244i | ||||
\(49\) | 8401.44 | + | 14551.7i | 0.499877 | + | 0.865813i | ||||
\(50\) | −4398.81 | − | 7618.96i | −0.248834 | − | 0.430994i | ||||
\(51\) | −3732.76 | + | 18534.8i | −0.200958 | + | 0.997846i | ||||
\(52\) | −24240.2 | + | 41985.2i | −1.24316 | + | 2.15322i | ||||
\(53\) | −12265.0 | −0.599763 | −0.299881 | − | 0.953977i | \(-0.596947\pi\) | ||||
−0.299881 | + | 0.953977i | \(0.596947\pi\) | |||||||
\(54\) | −16383.8 | − | 33830.8i | −0.764592 | − | 1.57880i | ||||
\(55\) | −8694.41 | −0.387555 | ||||||||
\(56\) | −347.353 | + | 601.633i | −0.0148013 | + | 0.0256367i | ||||
\(57\) | 1455.98 | − | 7229.61i | 0.0593567 | − | 0.294732i | ||||
\(58\) | −6580.32 | − | 11397.5i | −0.256849 | − | 0.444875i | ||||
\(59\) | 14773.5 | + | 25588.5i | 0.552528 | + | 0.957006i | 0.998091 | + | 0.0617560i | \(0.0196701\pi\) |
−0.445563 | + | 0.895250i | \(0.646997\pi\) | |||||||
\(60\) | 36781.0 | + | 32411.5i | 1.31900 | + | 1.16231i | ||||
\(61\) | 20153.6 | − | 34907.1i | 0.693472 | − | 1.20113i | −0.277221 | − | 0.960806i | \(-0.589413\pi\) |
0.970693 | − | 0.240323i | \(-0.0772534\pi\) | |||||||
\(62\) | 51410.7 | 1.69853 | ||||||||
\(63\) | −392.957 | + | 298.561i | −0.0124737 | + | 0.00947723i | ||||
\(64\) | −24379.9 | −0.744016 | ||||||||
\(65\) | 17253.4 | − | 29883.8i | 0.506514 | − | 0.877308i | ||||
\(66\) | −26939.7 | + | 9073.25i | −0.761261 | + | 0.256391i | ||||
\(67\) | −11748.9 | − | 20349.7i | −0.319750 | − | 0.553823i | 0.660686 | − | 0.750662i | \(-0.270266\pi\) |
−0.980436 | + | 0.196840i | \(0.936932\pi\) | |||||||
\(68\) | −40310.9 | − | 69820.5i | −1.05718 | − | 1.83109i | ||||
\(69\) | −53372.8 | + | 17975.8i | −1.34957 | + | 0.454534i | ||||
\(70\) | 476.747 | − | 825.750i | 0.0116290 | − | 0.0201420i | ||||
\(71\) | −123.786 | −0.00291425 | −0.00145713 | − | 0.999999i | \(-0.500464\pi\) | ||||
−0.00145713 | + | 0.999999i | \(0.500464\pi\) | |||||||
\(72\) | 76642.3 | + | 32175.2i | 1.74236 | + | 0.731460i | ||||
\(73\) | 35217.6 | 0.773486 | 0.386743 | − | 0.922188i | \(-0.373600\pi\) | ||||
0.386743 | + | 0.922188i | \(0.373600\pi\) | |||||||
\(74\) | −73011.4 | + | 126459.i | −1.54993 | + | 2.68455i | ||||
\(75\) | 10368.8 | + | 9137.03i | 0.212851 | + | 0.187565i | ||||
\(76\) | 15723.5 | + | 27233.8i | 0.312259 | + | 0.540848i | ||||
\(77\) | 186.607 | + | 323.214i | 0.00358676 | + | 0.00621245i | ||||
\(78\) | 22274.0 | − | 110600.i | 0.414536 | − | 2.05836i | ||||
\(79\) | 24072.8 | − | 41695.3i | 0.433969 | − | 0.751656i | −0.563242 | − | 0.826292i | \(-0.690446\pi\) |
0.997211 | + | 0.0746359i | \(0.0237794\pi\) | |||||||
\(80\) | −59960.3 | −1.04746 | ||||||||
\(81\) | 41353.9 | + | 42150.2i | 0.700332 | + | 0.713817i | ||||
\(82\) | −62711.6 | −1.02994 | ||||||||
\(83\) | −5167.97 | + | 8951.18i | −0.0823426 | + | 0.142622i | −0.904256 | − | 0.426991i | \(-0.859574\pi\) |
0.821913 | + | 0.569613i | \(0.192907\pi\) | |||||||
\(84\) | 415.466 | − | 2062.98i | 0.00642447 | − | 0.0319004i | ||||
\(85\) | 28692.0 | + | 49696.1i | 0.430739 | + | 0.746062i | ||||
\(86\) | 30443.5 | + | 52729.7i | 0.443863 | + | 0.768793i | ||||
\(87\) | 15511.0 | + | 13668.4i | 0.219706 | + | 0.193606i | ||||
\(88\) | 31430.3 | − | 54438.8i | 0.432655 | − | 0.749380i | ||||
\(89\) | −42585.7 | −0.569887 | −0.284944 | − | 0.958544i | \(-0.591975\pi\) | ||||
−0.284944 | + | 0.958544i | \(0.591975\pi\) | |||||||
\(90\) | −105193. | − | 44160.9i | −1.36892 | − | 0.574688i | ||||
\(91\) | −1481.23 | −0.0187508 | ||||||||
\(92\) | 120075. | − | 207976.i | 1.47905 | − | 2.56178i | ||||
\(93\) | −76536.7 | + | 25777.4i | −0.917619 | + | 0.309052i | ||||
\(94\) | 15720.1 | + | 27228.1i | 0.183500 | + | 0.317832i | ||||
\(95\) | −11191.5 | − | 19384.2i | −0.127227 | − | 0.220363i | ||||
\(96\) | −24080.0 | + | 8110.10i | −0.266673 | + | 0.0898149i | ||||
\(97\) | −49347.3 | + | 85472.1i | −0.532518 | + | 0.922348i | 0.466761 | + | 0.884383i | \(0.345421\pi\) |
−0.999279 | + | 0.0379646i | \(0.987913\pi\) | |||||||
\(98\) | 166739. | 1.75377 | ||||||||
\(99\) | 35556.7 | − | 27015.3i | 0.364614 | − | 0.277027i | ||||
\(100\) | −58931.0 | −0.589310 | ||||||||
\(101\) | 37818.9 | − | 65504.3i | 0.368898 | − | 0.638949i | −0.620496 | − | 0.784210i | \(-0.713069\pi\) |
0.989393 | + | 0.145260i | \(0.0464020\pi\) | |||||||
\(102\) | 140764. | + | 124042.i | 1.33965 | + | 1.18050i | ||||
\(103\) | −73869.1 | − | 127945.i | −0.686072 | − | 1.18831i | −0.973099 | − | 0.230389i | \(-0.926000\pi\) |
0.287026 | − | 0.957923i | \(-0.407333\pi\) | |||||||
\(104\) | 124742. | + | 216059.i | 1.13091 | + | 1.95880i | ||||
\(105\) | −295.716 | + | 1468.36i | −0.00261759 | + | 0.0129975i | ||||
\(106\) | −60854.6 | + | 105403.i | −0.526052 | + | 0.911149i | ||||
\(107\) | −209139. | −1.76594 | −0.882969 | − | 0.469430i | \(-0.844459\pi\) | ||||
−0.882969 | + | 0.469430i | \(0.844459\pi\) | |||||||
\(108\) | −251129. | − | 18264.4i | −2.07175 | − | 0.150677i | ||||
\(109\) | 115605. | 0.931988 | 0.465994 | − | 0.884788i | \(-0.345697\pi\) | ||||
0.465994 | + | 0.884788i | \(0.345697\pi\) | |||||||
\(110\) | −43138.5 | + | 74718.0i | −0.339925 | + | 0.588767i | ||||
\(111\) | 45287.4 | − | 224872.i | 0.348875 | − | 1.73232i | ||||
\(112\) | 1286.92 | + | 2229.02i | 0.00969411 | + | 0.0167907i | ||||
\(113\) | −23415.8 | − | 40557.3i | −0.172509 | − | 0.298795i | 0.766787 | − | 0.641901i | \(-0.221854\pi\) |
−0.939296 | + | 0.343107i | \(0.888521\pi\) | |||||||
\(114\) | −54905.8 | − | 48383.1i | −0.395691 | − | 0.348684i | ||||
\(115\) | −85465.5 | + | 148031.i | −0.602623 | + | 1.04377i | ||||
\(116\) | −88156.8 | −0.608290 | ||||||||
\(117\) | 22295.2 | + | 175823.i | 0.150573 | + | 1.18744i | ||||
\(118\) | 293203. | 1.93849 | ||||||||
\(119\) | 1231.63 | − | 2133.25i | 0.00797283 | − | 0.0138094i | ||||
\(120\) | 239086. | − | 80523.5i | 1.51566 | − | 0.510469i | ||||
\(121\) | 63640.3 | + | 110228.i | 0.395156 | + | 0.684431i | ||||
\(122\) | −199990. | − | 346393.i | −1.21649 | − | 2.10702i | ||||
\(123\) | 93360.7 | − | 31443.7i | 0.556418 | − | 0.187400i | ||||
\(124\) | 172188. | − | 298238.i | 1.00565 | − | 1.74184i | ||||
\(125\) | 189796. | 1.08645 | ||||||||
\(126\) | 616.062 | + | 4858.34i | 0.00345699 | + | 0.0272622i | ||||
\(127\) | −93444.5 | −0.514096 | −0.257048 | − | 0.966399i | \(-0.582750\pi\) | ||||
−0.257048 | + | 0.966399i | \(0.582750\pi\) | |||||||
\(128\) | −147044. | + | 254688.i | −0.793273 | + | 1.37399i | ||||
\(129\) | −71761.0 | − | 63236.0i | −0.379677 | − | 0.334572i | ||||
\(130\) | −171210. | − | 296544.i | −0.888527 | − | 1.53897i | ||||
\(131\) | 183869. | + | 318470.i | 0.936115 | + | 1.62140i | 0.772634 | + | 0.634852i | \(0.218939\pi\) |
0.163481 | + | 0.986546i | \(0.447728\pi\) | |||||||
\(132\) | −37593.5 | + | 186668.i | −0.187792 | + | 0.932473i | ||||
\(133\) | −480.404 | + | 832.083i | −0.00235493 | + | 0.00407885i | ||||
\(134\) | −233175. | −1.12181 | ||||||||
\(135\) | 178746. | + | 13000.1i | 0.844115 | + | 0.0613919i | ||||
\(136\) | −414887. | −1.92346 | ||||||||
\(137\) | 76809.2 | − | 133037.i | 0.349632 | − | 0.605581i | −0.636552 | − | 0.771234i | \(-0.719640\pi\) |
0.986184 | + | 0.165653i | \(0.0529731\pi\) | |||||||
\(138\) | −110335. | + | 547864.i | −0.493193 | + | 2.44892i | ||||
\(139\) | −122213. | − | 211679.i | −0.536513 | − | 0.929268i | −0.999088 | − | 0.0426878i | \(-0.986408\pi\) |
0.462575 | − | 0.886580i | \(-0.346925\pi\) | |||||||
\(140\) | −3193.50 | − | 5531.30i | −0.0137704 | − | 0.0238510i | ||||
\(141\) | −37055.3 | − | 32653.2i | −0.156965 | − | 0.138318i | ||||
\(142\) | −614.183 | + | 1063.80i | −0.00255609 | + | 0.00442728i | ||||
\(143\) | 134029. | 0.548101 | ||||||||
\(144\) | 245214. | − | 186309.i | 0.985461 | − | 0.748734i | ||||
\(145\) | 62747.3 | 0.247842 | ||||||||
\(146\) | 174737. | − | 302653.i | 0.678425 | − | 1.17507i | ||||
\(147\) | −248230. | + | 83603.4i | −0.947461 | + | 0.319103i | ||||
\(148\) | 489068. | + | 847091.i | 1.83533 | + | 3.17889i | ||||
\(149\) | 4924.61 | + | 8529.67i | 0.0181721 | + | 0.0314751i | 0.874968 | − | 0.484180i | \(-0.160882\pi\) |
−0.856796 | + | 0.515655i | \(0.827549\pi\) | |||||||
\(150\) | 129968. | − | 43772.9i | 0.471637 | − | 0.158846i | ||||
\(151\) | 109892. | − | 190339.i | 0.392216 | − | 0.679338i | −0.600526 | − | 0.799606i | \(-0.705042\pi\) |
0.992741 | + | 0.120268i | \(0.0383753\pi\) | |||||||
\(152\) | 161829. | 0.568128 | ||||||||
\(153\) | −271755. | − | 114086.i | −0.938531 | − | 0.394005i | ||||
\(154\) | 3703.51 | 0.0125838 | ||||||||
\(155\) | −122558. | + | 212276.i | −0.409743 | + | 0.709696i | ||||
\(156\) | −567001. | − | 499643.i | −1.86540 | − | 1.64380i | ||||
\(157\) | −15290.5 | − | 26483.9i | −0.0495077 | − | 0.0857498i | 0.840210 | − | 0.542262i | \(-0.182432\pi\) |
−0.889717 | + | 0.456512i | \(0.849099\pi\) | |||||||
\(158\) | −238881. | − | 413753.i | −0.761269 | − | 1.31856i | ||||
\(159\) | 37746.8 | − | 187430.i | 0.118410 | − | 0.587958i | ||||
\(160\) | −38559.2 | + | 66786.5i | −0.119077 | + | 0.206248i | ||||
\(161\) | 7337.35 | 0.0223087 | ||||||||
\(162\) | 567413. | − | 146253.i | 1.69868 | − | 0.437843i | ||||
\(163\) | −272367. | −0.802945 | −0.401472 | − | 0.915871i | \(-0.631501\pi\) | ||||
−0.401472 | + | 0.915871i | \(0.631501\pi\) | |||||||
\(164\) | −210037. | + | 363795.i | −0.609799 | + | 1.05620i | ||||
\(165\) | 26757.9 | − | 132865.i | 0.0765142 | − | 0.379927i | ||||
\(166\) | 51283.1 | + | 88824.9i | 0.144445 | + | 0.250187i | ||||
\(167\) | 99337.8 | + | 172058.i | 0.275628 | + | 0.477402i | 0.970293 | − | 0.241931i | \(-0.0777809\pi\) |
−0.694665 | + | 0.719333i | \(0.744448\pi\) | |||||||
\(168\) | −8124.93 | − | 7159.71i | −0.0222099 | − | 0.0195714i | ||||
\(169\) | −80324.9 | + | 139127.i | −0.216338 | + | 0.374709i | ||||
\(170\) | 569437. | 1.51121 | ||||||||
\(171\) | 105999. | + | 44499.6i | 0.277213 | + | 0.116377i | ||||
\(172\) | 407853. | 1.05119 | ||||||||
\(173\) | −33895.9 | + | 58709.5i | −0.0861058 | + | 0.149140i | −0.905862 | − | 0.423573i | \(-0.860776\pi\) |
0.819756 | + | 0.572713i | \(0.194109\pi\) | |||||||
\(174\) | 194423. | − | 65481.3i | 0.486828 | − | 0.163962i | ||||
\(175\) | −900.268 | − | 1559.31i | −0.00222217 | − | 0.00384891i | ||||
\(176\) | −116447. | − | 201693.i | −0.283366 | − | 0.490805i | ||||
\(177\) | −436501. | + | 147013.i | −1.04725 | + | 0.352713i | ||||
\(178\) | −211295. | + | 365973.i | −0.499848 | + | 0.865763i | ||||
\(179\) | 21849.0 | 0.0509681 | 0.0254840 | − | 0.999675i | \(-0.491887\pi\) | ||||
0.0254840 | + | 0.999675i | \(0.491887\pi\) | |||||||
\(180\) | −608498. | + | 462325.i | −1.39984 | + | 1.06357i | ||||
\(181\) | 188080. | 0.426722 | 0.213361 | − | 0.976973i | \(-0.431559\pi\) | ||||
0.213361 | + | 0.976973i | \(0.431559\pi\) | |||||||
\(182\) | −7349.33 | + | 12729.4i | −0.0164463 | + | 0.0284859i | ||||
\(183\) | 471414. | + | 415411.i | 1.04058 | + | 0.916959i | ||||
\(184\) | −617915. | − | 1.07026e6i | −1.34550 | − | 2.33048i | ||||
\(185\) | −348104. | − | 602933.i | −0.747789 | − | 1.29521i | ||||
\(186\) | −158221. | + | 785639.i | −0.335338 | + | 1.66510i | ||||
\(187\) | −111444. | + | 193027.i | −0.233052 | + | 0.403658i | ||||
\(188\) | 210603. | 0.434581 | ||||||||
\(189\) | −3353.13 | − | 6923.87i | −0.00682804 | − | 0.0140992i | ||||
\(190\) | −222112. | −0.446363 | ||||||||
\(191\) | 123200. | − | 213389.i | 0.244359 | − | 0.423241i | −0.717592 | − | 0.696463i | \(-0.754756\pi\) |
0.961951 | + | 0.273222i | \(0.0880893\pi\) | |||||||
\(192\) | 75031.5 | − | 372565.i | 0.146889 | − | 0.729372i | ||||
\(193\) | 113565. | + | 196701.i | 0.219459 | + | 0.380114i | 0.954643 | − | 0.297754i | \(-0.0962375\pi\) |
−0.735184 | + | 0.677868i | \(0.762904\pi\) | |||||||
\(194\) | 489686. | + | 848162.i | 0.934144 | + | 1.61798i | ||||
\(195\) | 403574. | + | 355630.i | 0.760040 | + | 0.669749i | ||||
\(196\) | 558453. | − | 967269.i | 1.03836 | − | 1.79849i | ||||
\(197\) | −503086. | −0.923584 | −0.461792 | − | 0.886988i | \(-0.652793\pi\) | ||||
−0.461792 | + | 0.886988i | \(0.652793\pi\) | |||||||
\(198\) | −55744.4 | − | 439607.i | −0.101051 | − | 0.796896i | ||||
\(199\) | 4126.65 | 0.00738694 | 0.00369347 | − | 0.999993i | \(-0.498824\pi\) | ||||
0.00369347 | + | 0.999993i | \(0.498824\pi\) | |||||||
\(200\) | −151632. | + | 262634.i | −0.268050 | + | 0.464276i | ||||
\(201\) | 347135. | − | 116914.i | 0.606050 | − | 0.204116i | ||||
\(202\) | −375287. | − | 650016.i | −0.647121 | − | 1.12085i | ||||
\(203\) | −1346.74 | − | 2332.62i | −0.00229374 | − | 0.00397287i | ||||
\(204\) | 1.19103e6 | − | 401137.i | 2.00377 | − | 0.674866i | ||||
\(205\) | 149498. | − | 258938.i | 0.248457 | − | 0.430340i | ||||
\(206\) | −1.46605e6 | −2.40702 | ||||||||
\(207\) | −110440. | − | 870945.i | −0.179144 | − | 1.41275i | ||||
\(208\) | 924324. | 1.48138 | ||||||||
\(209\) | 43469.3 | − | 75291.1i | 0.0688363 | − | 0.119228i | ||||
\(210\) | 11151.6 | + | 9826.79i | 0.0174497 | + | 0.0153767i | ||||
\(211\) | 494954. | + | 857285.i | 0.765347 | + | 1.32562i | 0.940063 | + | 0.341001i | \(0.110766\pi\) |
−0.174716 | + | 0.984619i | \(0.555901\pi\) | |||||||
\(212\) | 407636. | + | 706046.i | 0.622921 | + | 1.07893i | ||||
\(213\) | 380.965 | − | 1891.66i | 0.000575355 | − | 0.00285689i | ||||
\(214\) | −1.03767e6 | + | 1.79730e6i | −1.54891 | + | 2.68278i | ||||
\(215\) | −290297. | −0.428298 | ||||||||
\(216\) | −727564. | + | 1.07220e6i | −1.06105 | + | 1.56365i | ||||
\(217\) | 10521.8 | 0.0151684 | ||||||||
\(218\) | 573589. | − | 993485.i | 0.817447 | − | 1.41586i | ||||
\(219\) | −108385. | + | 538182.i | −0.152708 | + | 0.758262i | ||||
\(220\) | 288964. | + | 500500.i | 0.402519 | + | 0.697184i | ||||
\(221\) | −442305. | − | 766094.i | −0.609173 | − | 1.05512i | ||||
\(222\) | −1.70781e6 | − | 1.50492e6i | −2.32572 | − | 2.04943i | ||||
\(223\) | 523910. | − | 907438.i | 0.705496 | − | 1.22195i | −0.261017 | − | 0.965334i | \(-0.584058\pi\) |
0.966512 | − | 0.256620i | \(-0.0826089\pi\) | |||||||
\(224\) | 3310.37 | 0.00440816 | ||||||||
\(225\) | −171540. | + | 130332.i | −0.225896 | + | 0.171631i | ||||
\(226\) | −464722. | −0.605232 | ||||||||
\(227\) | −355537. | + | 615808.i | −0.457952 | + | 0.793196i | −0.998853 | − | 0.0478902i | \(-0.984750\pi\) |
0.540900 | + | 0.841087i | \(0.318084\pi\) | |||||||
\(228\) | −464568. | + | 156466.i | −0.591851 | + | 0.199334i | ||||
\(229\) | −147071. | − | 254734.i | −0.185327 | − | 0.320995i | 0.758360 | − | 0.651836i | \(-0.226001\pi\) |
−0.943687 | + | 0.330841i | \(0.892668\pi\) | |||||||
\(230\) | 848096. | + | 1.46895e6i | 1.05712 | + | 1.83099i | ||||
\(231\) | −5513.53 | + | 1856.95i | −0.00679830 | + | 0.00228965i | ||||
\(232\) | −226831. | + | 392883.i | −0.276683 | + | 0.479230i | ||||
\(233\) | 1.56670e6 | 1.89059 | 0.945294 | − | 0.326218i | \(-0.105774\pi\) | ||||
0.945294 | + | 0.326218i | \(0.105774\pi\) | |||||||
\(234\) | 1.62161e6 | + | 680767.i | 1.93600 | + | 0.812753i | ||||
\(235\) | −149901. | −0.177066 | ||||||||
\(236\) | 982013. | − | 1.70090e6i | 1.14772 | − | 1.98792i | ||||
\(237\) | 563086. | + | 496193.i | 0.651184 | + | 0.573825i | ||||
\(238\) | −12221.8 | − | 21168.8i | −0.0139860 | − | 0.0242244i | ||||
\(239\) | −260961. | − | 451998.i | −0.295516 | − | 0.511849i | 0.679589 | − | 0.733593i | \(-0.262158\pi\) |
−0.975105 | + | 0.221744i | \(0.928825\pi\) | |||||||
\(240\) | 184534. | − | 916292.i | 0.206799 | − | 1.02685i | ||||
\(241\) | 213855. | − | 370407.i | 0.237179 | − | 0.410806i | −0.722725 | − | 0.691136i | \(-0.757111\pi\) |
0.959904 | + | 0.280330i | \(0.0904439\pi\) | |||||||
\(242\) | 1.26304e6 | 1.38637 | ||||||||
\(243\) | −771394. | + | 502234.i | −0.838032 | + | 0.545620i | ||||
\(244\) | −2.67927e6 | −2.88099 | ||||||||
\(245\) | −397490. | + | 688472.i | −0.423068 | + | 0.732776i | ||||
\(246\) | 193001. | − | 958335.i | 0.203339 | − | 1.00967i | ||||
\(247\) | 172523. | + | 298819.i | 0.179931 | + | 0.311649i | ||||
\(248\) | −886092. | − | 1.53476e6i | −0.914849 | − | 1.58457i | ||||
\(249\) | −120884. | − | 106523.i | −0.123558 | − | 0.108879i | ||||
\(250\) | 941696. | − | 1.63106e6i | 0.952929 | − | 1.65052i | ||||
\(251\) | −231914. | −0.232350 | −0.116175 | − | 0.993229i | \(-0.537063\pi\) | ||||
−0.116175 | + | 0.993229i | \(0.537063\pi\) | |||||||
\(252\) | 30247.0 | + | 12698.0i | 0.0300041 | + | 0.0125960i | ||||
\(253\) | −663921. | −0.652101 | ||||||||
\(254\) | −463637. | + | 803043.i | −0.450914 | + | 0.781006i | ||||
\(255\) | −847740. | + | 285517.i | −0.816417 | + | 0.274967i | ||||
\(256\) | 1.06908e6 | + | 1.85170e6i | 1.01955 | + | 1.76592i | ||||
\(257\) | 707127. | + | 1.22478e6i | 0.667828 | + | 1.15671i | 0.978510 | + | 0.206199i | \(0.0661093\pi\) |
−0.310682 | + | 0.950514i | \(0.600557\pi\) | |||||||
\(258\) | −899489. | + | 302946.i | −0.841292 | + | 0.283345i | ||||
\(259\) | −14942.6 | + | 25881.4i | −0.0138413 | + | 0.0239739i | ||||
\(260\) | −2.29371e6 | −2.10428 | ||||||||
\(261\) | −256612. | + | 194968.i | −0.233171 | + | 0.177159i | ||||
\(262\) | 3.64915e6 | 3.28427 | ||||||||
\(263\) | 615838. | − | 1.06666e6i | 0.549006 | − | 0.950907i | −0.449336 | − | 0.893363i | \(-0.648340\pi\) |
0.998343 | − | 0.0575445i | \(-0.0183271\pi\) | |||||||
\(264\) | 735185. | + | 647847.i | 0.649212 | + | 0.572087i | ||||
\(265\) | −290143. | − | 502542.i | −0.253803 | − | 0.439600i | ||||
\(266\) | 4767.17 | + | 8256.98i | 0.00413101 | + | 0.00715513i | ||||
\(267\) | 131062. | − | 650779.i | 0.112512 | − | 0.558670i | ||||
\(268\) | −780963. | + | 1.35267e6i | −0.664192 | + | 1.15041i | ||||
\(269\) | 119245. | 0.100475 | 0.0502377 | − | 0.998737i | \(-0.484002\pi\) | ||||
0.0502377 | + | 0.998737i | \(0.484002\pi\) | |||||||
\(270\) | 998591. | − | 1.47160e6i | 0.833639 | − | 1.22852i | ||||
\(271\) | 50141.4 | 0.0414738 | 0.0207369 | − | 0.999785i | \(-0.493399\pi\) | ||||
0.0207369 | + | 0.999785i | \(0.493399\pi\) | |||||||
\(272\) | −768566. | + | 1.33120e6i | −0.629881 | + | 1.09099i | ||||
\(273\) | 4558.64 | − | 22635.7i | 0.00370193 | − | 0.0183817i | ||||
\(274\) | −762198. | − | 1.32017e6i | −0.613326 | − | 1.06231i | ||||
\(275\) | 81460.8 | + | 141094.i | 0.0649557 | + | 0.112506i | ||||
\(276\) | 2.80866e6 | + | 2.47500e6i | 2.21936 | + | 1.95570i | ||||
\(277\) | −235820. | + | 408452.i | −0.184663 | + | 0.319846i | −0.943463 | − | 0.331478i | \(-0.892453\pi\) |
0.758800 | + | 0.651324i | \(0.225786\pi\) | |||||||
\(278\) | −2.42550e6 | −1.88230 | ||||||||
\(279\) | −158372. | − | 1.24894e6i | −0.121806 | − | 0.960573i | ||||
\(280\) | −32868.0 | −0.0250541 | ||||||||
\(281\) | −1.03652e6 | + | 1.79530e6i | −0.783087 | + | 1.35635i | 0.147048 | + | 0.989129i | \(0.453023\pi\) |
−0.930135 | + | 0.367217i | \(0.880311\pi\) | |||||||
\(282\) | −464470. | + | 156432.i | −0.347804 | + | 0.117140i | ||||
\(283\) | −758046. | − | 1.31297e6i | −0.562639 | − | 0.974519i | −0.997265 | − | 0.0739079i | \(-0.976453\pi\) |
0.434626 | − | 0.900611i | \(-0.356880\pi\) | |||||||
\(284\) | 4114.11 | + | 7125.86i | 0.00302678 | + | 0.00524253i | ||||
\(285\) | 330665. | − | 111367.i | 0.241144 | − | 0.0812168i | ||||
\(286\) | 665005. | − | 1.15182e6i | 0.480739 | − | 0.832665i | ||||
\(287\) | −12834.7 | −0.00919770 | ||||||||
\(288\) | −49827.0 | − | 392942.i | −0.0353984 | − | 0.279156i | ||||
\(289\) | 51229.6 | 0.0360808 | ||||||||
\(290\) | 311329. | − | 539237.i | 0.217382 | − | 0.376517i | ||||
\(291\) | −1.15428e6 | − | 1.01716e6i | −0.799060 | − | 0.704134i | ||||
\(292\) | −1.17048e6 | − | 2.02733e6i | −0.803352 | − | 1.39145i | ||||
\(293\) | −385100. | − | 667013.i | −0.262062 | − | 0.453905i | 0.704727 | − | 0.709478i | \(-0.251069\pi\) |
−0.966790 | + | 0.255573i | \(0.917736\pi\) | |||||||
\(294\) | −513156. | + | 2.54805e6i | −0.346243 | + | 1.71925i | ||||
\(295\) | −698967. | + | 1.21065e6i | −0.467629 | + | 0.809957i | ||||
\(296\) | 5.03357e6 | 3.33924 | ||||||||
\(297\) | 303408. | + | 626507.i | 0.199589 | + | 0.412131i | ||||
\(298\) | 97736.4 | 0.0637552 | ||||||||
\(299\) | 1.31750e6 | − | 2.28198e6i | 0.852262 | − | 1.47616i | ||||
\(300\) | 181366. | − | 900562.i | 0.116346 | − | 0.577711i | ||||
\(301\) | 6230.62 | + | 10791.8i | 0.00396383 | + | 0.00686556i | ||||
\(302\) | −1.09049e6 | − | 1.88879e6i | −0.688026 | − | 1.19170i | ||||
\(303\) | 884622. | + | 779531.i | 0.553543 | + | 0.487783i | ||||
\(304\) | 299783. | − | 519240.i | 0.186047 | − | 0.322243i | ||||
\(305\) | 1.90702e6 | 1.17383 | ||||||||
\(306\) | −2.32878e6 | + | 1.76936e6i | −1.42175 | + | 1.08022i | ||||
\(307\) | 2.13559e6 | 1.29322 | 0.646610 | − | 0.762821i | \(-0.276186\pi\) | ||||
0.646610 | + | 0.762821i | \(0.276186\pi\) | |||||||
\(308\) | 12404.0 | − | 21484.4i | 0.00745050 | − | 0.0129046i | ||||
\(309\) | 2.18255e6 | − | 735078.i | 1.30037 | − | 0.437963i | ||||
\(310\) | 1.21617e6 | + | 2.10647e6i | 0.718772 | + | 1.24495i | ||||
\(311\) | 301713. | + | 522582.i | 0.176886 | + | 0.306375i | 0.940812 | − | 0.338928i | \(-0.110064\pi\) |
−0.763927 | + | 0.645303i | \(0.776731\pi\) | |||||||
\(312\) | −3.68565e6 | + | 1.24132e6i | −2.14352 | + | 0.721932i | ||||
\(313\) | −1.08619e6 | + | 1.88133e6i | −0.626677 | + | 1.08544i | 0.361537 | + | 0.932358i | \(0.382252\pi\) |
−0.988214 | + | 0.153079i | \(0.951081\pi\) | |||||||
\(314\) | −303463. | −0.173693 | ||||||||
\(315\) | −21528.9 | − | 9038.05i | −0.0122249 | − | 0.00513214i | ||||
\(316\) | −3.20029e6 | −1.80290 | ||||||||
\(317\) | −1.60049e6 | + | 2.77213e6i | −0.894550 | + | 1.54941i | −0.0601886 | + | 0.998187i | \(0.519170\pi\) |
−0.834361 | + | 0.551218i | \(0.814163\pi\) | |||||||
\(318\) | −1.42345e6 | − | 1.25435e6i | −0.789358 | − | 0.695585i | ||||
\(319\) | 121860. | + | 211067.i | 0.0670477 | + | 0.116130i | ||||
\(320\) | −576732. | − | 998930.i | −0.314847 | − | 0.545331i | ||||
\(321\) | 643645. | − | 3.19599e6i | 0.348646 | − | 1.73118i | ||||
\(322\) | 36405.2 | − | 63055.7i | 0.0195670 | − | 0.0338910i | ||||
\(323\) | −573805. | −0.306026 | ||||||||
\(324\) | 1.05198e6 | − | 3.78145e6i | 0.556733 | − | 2.00123i | ||||
\(325\) | −646611. | −0.339574 | ||||||||
\(326\) | −1.35139e6 | + | 2.34067e6i | −0.704263 | + | 1.21982i | ||||
\(327\) | −355785. | + | 1.76663e6i | −0.184000 | + | 0.913644i | ||||
\(328\) | 1.08087e6 | + | 1.87212e6i | 0.554739 | + | 0.960836i | ||||
\(329\) | 3217.31 | + | 5572.54i | 0.00163871 | + | 0.00283834i | ||||
\(330\) | −1.00905e6 | − | 889178.i | −0.510068 | − | 0.449473i | ||||
\(331\) | −1.30413e6 | + | 2.25883e6i | −0.654263 | + | 1.13322i | 0.327815 | + | 0.944742i | \(0.393688\pi\) |
−0.982078 | + | 0.188475i | \(0.939645\pi\) | |||||||
\(332\) | 687041. | 0.342088 | ||||||||
\(333\) | 3.29704e6 | + | 1.38413e6i | 1.62935 | + | 0.684017i | ||||
\(334\) | 1.97151e6 | 0.967014 | ||||||||
\(335\) | 555865. | − | 962787.i | 0.270618 | − | 0.468725i | ||||
\(336\) | −38023.7 | + | 12806.3i | −0.0183741 | + | 0.00618835i | ||||
\(337\) | 414934. | + | 718687.i | 0.199024 | + | 0.344719i | 0.948212 | − | 0.317638i | \(-0.102890\pi\) |
−0.749189 | + | 0.662357i | \(0.769556\pi\) | |||||||
\(338\) | 797085. | + | 1.38059e6i | 0.379501 | + | 0.657315i | ||||
\(339\) | 691846. | − | 233012.i | 0.326972 | − | 0.110123i | ||||
\(340\) | 1.90719e6 | − | 3.30335e6i | 0.894741 | − | 1.54974i | ||||
\(341\) | −952065. | −0.443385 | ||||||||
\(342\) | 908351. | − | 690146.i | 0.419941 | − | 0.319063i | ||||
\(343\) | 68258.7 | 0.0313273 | ||||||||
\(344\) | 1.04942e6 | − | 1.81765e6i | 0.478139 | − | 0.828161i | ||||
\(345\) | −1.99912e6 | − | 1.76163e6i | −0.904256 | − | 0.796832i | ||||
\(346\) | 336358. | + | 582589.i | 0.151047 | + | 0.261621i | ||||
\(347\) | −1.15930e6 | − | 2.00796e6i | −0.516858 | − | 0.895224i | −0.999808 | − | 0.0195761i | \(-0.993768\pi\) |
0.482951 | − | 0.875648i | \(-0.339565\pi\) | |||||||
\(348\) | 271311. | − | 1.34718e6i | 0.120093 | − | 0.596318i | ||||
\(349\) | 1.56680e6 | − | 2.71377e6i | 0.688572 | − | 1.19264i | −0.283728 | − | 0.958905i | \(-0.591571\pi\) |
0.972300 | − | 0.233737i | \(-0.0750955\pi\) | |||||||
\(350\) | −17867.2 | −0.00779626 | ||||||||
\(351\) | −2.75547e6 | − | 200404.i | −1.19379 | − | 0.0868236i | ||||
\(352\) | −299539. | −0.128854 | ||||||||
\(353\) | 1.33508e6 | − | 2.31243e6i | 0.570259 | − | 0.987717i | −0.426280 | − | 0.904591i | \(-0.640176\pi\) |
0.996539 | − | 0.0831261i | \(-0.0264904\pi\) | |||||||
\(354\) | −902361. | + | 4.48062e6i | −0.382712 | + | 1.90034i | ||||
\(355\) | −2928.30 | − | 5071.96i | −0.00123323 | − | 0.00213602i | ||||
\(356\) | 1.41536e6 | + | 2.45148e6i | 0.591891 | + | 1.02519i | ||||
\(357\) | 28809.0 | + | 25386.6i | 0.0119635 | + | 0.0105423i | ||||
\(358\) | 108407. | − | 187766.i | 0.0447041 | − | 0.0774299i | ||||
\(359\) | −2.05907e6 | −0.843210 | −0.421605 | − | 0.906780i | \(-0.638533\pi\) | ||||
−0.421605 | + | 0.906780i | \(0.638533\pi\) | |||||||
\(360\) | 494722. | + | 3.90144e6i | 0.201190 | + | 1.58660i | ||||
\(361\) | −2.25228e6 | −0.909610 | ||||||||
\(362\) | 933182. | − | 1.61632e6i | 0.374278 | − | 0.648269i | ||||
\(363\) | −1.88033e6 | + | 633290.i | −0.748974 | + | 0.252253i | ||||
\(364\) | 49229.6 | + | 85268.2i | 0.0194748 | + | 0.0337314i | ||||
\(365\) | 833109. | + | 1.44299e6i | 0.327318 | + | 0.566931i | ||||
\(366\) | 5.90894e6 | − | 1.99012e6i | 2.30572 | − | 0.776562i | ||||
\(367\) | 509190. | − | 881943.i | 0.197340 | − | 0.341803i | −0.750325 | − | 0.661069i | \(-0.770103\pi\) |
0.947665 | + | 0.319266i | \(0.103436\pi\) | |||||||
\(368\) | −4.57868e6 | −1.76247 | ||||||||
\(369\) | 193184. | + | 1.52348e6i | 0.0738595 | + | 0.582465i | ||||
\(370\) | −6.90865e6 | −2.62355 | ||||||||
\(371\) | −12454.6 | + | 21572.0i | −0.00469781 | + | 0.00813685i | ||||
\(372\) | 4.02764e6 | + | 3.54916e6i | 1.50901 | + | 1.32975i | ||||
\(373\) | −2.61768e6 | − | 4.53395e6i | −0.974191 | − | 1.68735i | −0.682579 | − | 0.730812i | \(-0.739142\pi\) |
−0.291612 | − | 0.956537i | \(-0.594192\pi\) | |||||||
\(374\) | 1.10589e6 | + | 1.91546e6i | 0.408820 | + | 0.708098i | ||||
\(375\) | −584114. | + | 2.90039e6i | −0.214496 | + | 1.06507i | ||||
\(376\) | 541891. | − | 938583.i | 0.197671 | − | 0.342376i | ||||
\(377\) | −967286. | −0.350511 | ||||||||
\(378\) | −76139.4 | − | 5537.57i | −0.0274082 | − | 0.00199338i | ||||
\(379\) | 2.73883e6 | 0.979417 | 0.489708 | − | 0.871886i | \(-0.337103\pi\) | ||||
0.489708 | + | 0.871886i | \(0.337103\pi\) | |||||||
\(380\) | −743910. | + | 1.28849e6i | −0.264278 | + | 0.457743i | ||||
\(381\) | 287584. | − | 1.42799e6i | 0.101497 | − | 0.503978i | ||||
\(382\) | −1.22255e6 | − | 2.11751e6i | −0.428654 | − | 0.742451i | ||||
\(383\) | 2.17454e6 | + | 3.76641e6i | 0.757478 | + | 1.31199i | 0.944133 | + | 0.329564i | \(0.106902\pi\) |
−0.186655 | + | 0.982425i | \(0.559765\pi\) | |||||||
\(384\) | −3.43950e6 | − | 3.03090e6i | −1.19033 | − | 1.04892i | ||||
\(385\) | −8828.79 | + | 15291.9i | −0.00303563 | + | 0.00525787i | ||||
\(386\) | 2.25388e6 | 0.769950 | ||||||||
\(387\) | 1.18720e6 | − | 902011.i | 0.402946 | − | 0.306150i | ||||
\(388\) | 6.56035e6 | 2.21232 | ||||||||
\(389\) | −1.50378e6 | + | 2.60462e6i | −0.503860 | + | 0.872712i | 0.496130 | + | 0.868248i | \(0.334754\pi\) |
−0.999990 | + | 0.00446327i | \(0.998579\pi\) | |||||||
\(390\) | 5.05860e6 | − | 1.70373e6i | 1.68410 | − | 0.567202i | ||||
\(391\) | 2.19098e6 | + | 3.79488e6i | 0.724762 | + | 1.25533i | ||||
\(392\) | −2.87385e6 | − | 4.97765e6i | −0.944602 | − | 1.63610i | ||||
\(393\) | −5.43261e6 | + | 1.82969e6i | −1.77430 | + | 0.597581i | ||||
\(394\) | −2.49613e6 | + | 4.32342e6i | −0.810077 | + | 1.40309i | ||||
\(395\) | 2.27787e6 | 0.734574 | ||||||||
\(396\) | −2.73690e6 | − | 1.14898e6i | −0.877044 | − | 0.368192i | ||||
\(397\) | 2.16602e6 | 0.689740 | 0.344870 | − | 0.938650i | \(-0.387923\pi\) | ||||
0.344870 | + | 0.938650i | \(0.387923\pi\) | |||||||
\(398\) | 20474.9 | − | 35463.6i | 0.00647910 | − | 0.0112221i | ||||
\(399\) | −11237.1 | − | 9902.17i | −0.00353364 | − | 0.00311385i | ||||
\(400\) | 561788. | + | 973046.i | 0.175559 | + | 0.304077i | ||||
\(401\) | −1.76996e6 | − | 3.06566e6i | −0.549670 | − | 0.952057i | −0.998297 | − | 0.0583377i | \(-0.981420\pi\) |
0.448626 | − | 0.893719i | \(-0.351913\pi\) | |||||||
\(402\) | 717618. | − | 3.56329e6i | 0.221477 | − | 1.09973i | ||||
\(403\) | 1.88930e6 | − | 3.27236e6i | 0.579480 | − | 1.00369i | ||||
\(404\) | −5.02774e6 | −1.53257 | ||||||||
\(405\) | −748770. | + | 2.69152e6i | −0.226835 | + | 0.815380i | ||||
\(406\) | −26728.1 | −0.00804735 | ||||||||
\(407\) | 1.35209e6 | − | 2.34188e6i | 0.404593 | − | 0.700775i | ||||
\(408\) | 1.27685e6 | − | 6.34014e6i | 0.379744 | − | 1.88560i | ||||
\(409\) | 783644. | + | 1.35731e6i | 0.231638 | + | 0.401210i | 0.958290 | − | 0.285796i | \(-0.0922580\pi\) |
−0.726652 | + | 0.687006i | \(0.758925\pi\) | |||||||
\(410\) | −1.48351e6 | − | 2.56951e6i | −0.435843 | − | 0.754902i | ||||
\(411\) | 1.79664e6 | + | 1.58321e6i | 0.524635 | + | 0.462309i | ||||
\(412\) | −4.91016e6 | + | 8.50465e6i | −1.42513 | + | 2.46839i | ||||
\(413\) | 60007.5 | 0.0173113 | ||||||||
\(414\) | −8.03269e6 | − | 3.37221e6i | −2.30335 | − | 0.966971i | ||||
\(415\) | −489015. | −0.139380 | ||||||||
\(416\) | 594413. | − | 1.02955e6i | 0.168405 | − | 0.291686i | ||||
\(417\) | 3.61092e6 | − | 1.21615e6i | 1.01690 | − | 0.342490i | ||||
\(418\) | −431358. | − | 747133.i | −0.120753 | − | 0.209150i | ||||
\(419\) | 1.18321e6 | + | 2.04937e6i | 0.329250 | + | 0.570277i | 0.982363 | − | 0.186983i | \(-0.0598709\pi\) |
−0.653114 | + | 0.757260i | \(0.726538\pi\) | |||||||
\(420\) | 94355.6 | − | 31778.8i | 0.0261002 | − | 0.00879050i | ||||
\(421\) | 1.84288e6 | − | 3.19196e6i | 0.506747 | − | 0.877712i | −0.493222 | − | 0.869903i | \(-0.664181\pi\) |
0.999970 | − | 0.00780885i | \(-0.00248566\pi\) | |||||||
\(422\) | 9.82311e6 | 2.68515 | ||||||||
\(423\) | 613036. | − | 465772.i | 0.166585 | − | 0.126568i | ||||
\(424\) | 4.19546e6 | 1.13335 | ||||||||
\(425\) | 537650. | − | 931238.i | 0.144387 | − | 0.250085i | ||||
\(426\) | −14366.3 | − | 12659.7i | −0.00383550 | − | 0.00337985i | ||||
\(427\) | −40930.3 | − | 70893.3i | −0.0108636 | − | 0.0188164i | ||||
\(428\) | 6.95086e6 | + | 1.20392e7i | 1.83412 | + | 3.17680i | ||||
\(429\) | −412489. | + | 2.04819e6i | −0.108210 | + | 0.537313i | ||||
\(430\) | −1.44035e6 | + | 2.49475e6i | −0.375661 | + | 0.650664i | ||||
\(431\) | −6.78152e6 | −1.75847 | −0.879233 | − | 0.476391i | \(-0.841945\pi\) | ||||
−0.879233 | + | 0.476391i | \(0.841945\pi\) | |||||||
\(432\) | 2.09243e6 | + | 4.32066e6i | 0.539439 | + | 1.11389i | ||||
\(433\) | −3.20434e6 | −0.821332 | −0.410666 | − | 0.911786i | \(-0.634704\pi\) | ||||
−0.410666 | + | 0.911786i | \(0.634704\pi\) | |||||||
\(434\) | 52205.2 | − | 90422.1i | 0.0133042 | − | 0.0230436i | ||||
\(435\) | −193111. | + | 958881.i | −0.0489309 | + | 0.242964i | ||||
\(436\) | −3.84220e6 | − | 6.65488e6i | −0.967973 | − | 1.67658i | ||||
\(437\) | −854601. | − | 1.48021e6i | −0.214072 | − | 0.370784i | ||||
\(438\) | 4.08726e6 | + | 3.60171e6i | 1.01800 | + | 0.897063i | ||||
\(439\) | −698435. | + | 1.20972e6i | −0.172967 | + | 0.299588i | −0.939456 | − | 0.342670i | \(-0.888669\pi\) |
0.766489 | + | 0.642258i | \(0.222002\pi\) | |||||||
\(440\) | 2.97406e6 | 0.732350 | ||||||||
\(441\) | −513645. | − | 4.05066e6i | −0.125767 | − | 0.991812i | ||||
\(442\) | −8.77821e6 | −2.13723 | ||||||||
\(443\) | 2.48597e6 | − | 4.30583e6i | 0.601847 | − | 1.04243i | −0.390694 | − | 0.920521i | \(-0.627765\pi\) |
0.992541 | − | 0.121910i | \(-0.0389018\pi\) | |||||||
\(444\) | −1.44501e7 | + | 4.86676e6i | −3.47867 | + | 1.17161i | ||||
\(445\) | −1.00741e6 | − | 1.74488e6i | −0.241160 | − | 0.417702i | ||||
\(446\) | −5.19889e6 | − | 9.00475e6i | −1.23758 | − | 2.14355i | ||||
\(447\) | −145503. | + | 49005.2i | −0.0344432 | + | 0.0116004i | ||||
\(448\) | −24756.7 | + | 42879.9i | −0.00582771 | + | 0.0100939i | ||||
\(449\) | 4.85114e6 | 1.13561 | 0.567804 | − | 0.823164i | \(-0.307793\pi\) | ||||
0.567804 | + | 0.823164i | \(0.307793\pi\) | |||||||
\(450\) | 268933. | + | 2.12084e6i | 0.0626056 | + | 0.493715i | ||||
\(451\) | 1.16134e6 | 0.268856 | ||||||||
\(452\) | −1.55647e6 | + | 2.69589e6i | −0.358340 | + | 0.620663i | ||||
\(453\) | 2.57049e6 | + | 2.26512e6i | 0.588532 | + | 0.518616i | ||||
\(454\) | 3.52809e6 | + | 6.11083e6i | 0.803340 | + | 1.39143i | ||||
\(455\) | −35040.1 | − | 60691.3i | −0.00793482 | − | 0.0137435i | ||||
\(456\) | −498043. | + | 2.47301e6i | −0.112164 | + | 0.556946i | ||||
\(457\) | −2.14244e6 | + | 3.71081e6i | −0.479864 | + | 0.831149i | −0.999733 | − | 0.0230972i | \(-0.992647\pi\) |
0.519869 | + | 0.854246i | \(0.325981\pi\) | |||||||
\(458\) | −2.91885e6 | −0.650201 | ||||||||
\(459\) | 2.57976e6 | − | 3.80175e6i | 0.571542 | − | 0.842271i | ||||
\(460\) | 1.13620e7 | 2.50357 | ||||||||
\(461\) | −11973.0 | + | 20737.8i | −0.00262392 | + | 0.00454476i | −0.867334 | − | 0.497726i | \(-0.834169\pi\) |
0.864710 | + | 0.502271i | \(0.167502\pi\) | |||||||
\(462\) | −11397.9 | + | 56595.7i | −0.00248439 | + | 0.0123361i | ||||
\(463\) | 1.76420e6 | + | 3.05569e6i | 0.382469 | + | 0.662456i | 0.991415 | − | 0.130756i | \(-0.0417405\pi\) |
−0.608945 | + | 0.793212i | \(0.708407\pi\) | |||||||
\(464\) | 840397. | + | 1.45561e6i | 0.181213 | + | 0.313870i | ||||
\(465\) | −2.86675e6 | − | 2.52618e6i | −0.614832 | − | 0.541792i | ||||
\(466\) | 7.77341e6 | − | 1.34639e7i | 1.65824 | − | 2.87215i | ||||
\(467\) | −4.66263e6 | −0.989324 | −0.494662 | − | 0.869086i | \(-0.664708\pi\) | ||||
−0.494662 | + | 0.869086i | \(0.664708\pi\) | |||||||
\(468\) | 9.38036e6 | − | 7.12701e6i | 1.97973 | − | 1.50415i | ||||
\(469\) | −47722.0 | −0.0100181 | ||||||||
\(470\) | −743753. | + | 1.28822e6i | −0.155304 | + | 0.268995i | ||||
\(471\) | 451776. | − | 152157.i | 0.0938362 | − | 0.0316038i | ||||
\(472\) | −5.05353e6 | − | 8.75296e6i | −1.04409 | − | 1.80842i | ||||
\(473\) | −563778. | − | 976492.i | −0.115866 | − | 0.200686i | ||||
\(474\) | 7.05800e6 | − | 2.37712e6i | 1.44290 | − | 0.485965i | ||||
\(475\) | −209713. | + | 363234.i | −0.0426473 | + | 0.0738673i | ||||
\(476\) | −163736. | −0.0331227 | ||||||||
\(477\) | 2.74807e6 | + | 1.15367e6i | 0.553008 | + | 0.232158i | ||||
\(478\) | −5.17917e6 | −1.03679 | ||||||||
\(479\) | −3.27492e6 | + | 5.67232e6i | −0.652171 | + | 1.12959i | 0.330424 | + | 0.943832i | \(0.392808\pi\) |
−0.982595 | + | 0.185760i | \(0.940525\pi\) | |||||||
\(480\) | −901938. | − | 794790.i | −0.178679 | − | 0.157452i | ||||
\(481\) | 5.36622e6 | + | 9.29457e6i | 1.05756 | + | 1.83175i | ||||
\(482\) | −2.12214e6 | − | 3.67565e6i | −0.416060 | − | 0.720637i | ||||
\(483\) | −22581.4 | + | 112127.i | −0.00440436 | + | 0.0218696i | ||||
\(484\) | 4.23024e6 | − | 7.32700e6i | 0.820828 | − | 1.42172i | ||||
\(485\) | −4.66945e6 | −0.901387 | ||||||||
\(486\) | 488724. | + | 9.12111e6i | 0.0938584 | + | 1.75169i | ||||
\(487\) | −9.23457e6 | −1.76439 | −0.882194 | − | 0.470886i | \(-0.843934\pi\) | ||||
−0.882194 | + | 0.470886i | \(0.843934\pi\) | |||||||
\(488\) | −6.89388e6 | + | 1.19406e7i | −1.31043 | + | 2.26973i | ||||
\(489\) | 838236. | − | 4.16221e6i | 0.158524 | − | 0.787141i | ||||
\(490\) | 3.94439e6 | + | 6.83189e6i | 0.742147 | + | 1.28544i | ||||
\(491\) | 2.62130e6 | + | 4.54023e6i | 0.490697 | + | 0.849912i | 0.999943 | − | 0.0107089i | \(-0.00340882\pi\) |
−0.509246 | + | 0.860621i | \(0.670075\pi\) | |||||||
\(492\) | −4.91298e6 | − | 4.32933e6i | −0.915023 | − | 0.806320i | ||||
\(493\) | 804288. | − | 1.39307e6i | 0.149037 | − | 0.258140i | ||||
\(494\) | 3.42399e6 | 0.631269 | ||||||||
\(495\) | 1.94804e6 | + | 817808.i | 0.357343 | + | 0.150016i | ||||
\(496\) | −6.56584e6 | −1.19836 | ||||||||
\(497\) | −125.700 | + | 217.718i | −2.28267e−5 | + | 3.95370e-5i | ||||
\(498\) | −1.51522e6 | + | 510322.i | −0.273780 | + | 0.0922086i | ||||
\(499\) | −3.23974e6 | − | 5.61140e6i | −0.582451 | − | 1.00883i | −0.995188 | − | 0.0979844i | \(-0.968760\pi\) |
0.412737 | − | 0.910850i | \(-0.364573\pi\) | |||||||
\(500\) | −6.30796e6 | − | 1.09257e7i | −1.12840 | − | 1.95445i | ||||
\(501\) | −2.93505e6 | + | 988519.i | −0.522422 | + | 0.175951i | ||||
\(502\) | −1.15067e6 | + | 1.99302e6i | −0.203794 | + | 0.352982i | ||||
\(503\) | 4.42908e6 | 0.780538 | 0.390269 | − | 0.920701i | \(-0.372382\pi\) | ||||
0.390269 | + | 0.920701i | \(0.372382\pi\) | |||||||
\(504\) | 134417. | − | 102128.i | 0.0235710 | − | 0.0179088i | ||||
\(505\) | 3.57859e6 | 0.624429 | ||||||||
\(506\) | −3.29413e6 | + | 5.70560e6i | −0.571959 | + | 0.990661i | ||||
\(507\) | −1.87888e6 | − | 1.65567e6i | −0.324622 | − | 0.286058i | ||||
\(508\) | 3.10568e6 | + | 5.37920e6i | 0.533946 | + | 0.924822i | ||||
\(509\) | −2.14026e6 | − | 3.70704e6i | −0.366162 | − | 0.634210i | 0.622800 | − | 0.782381i | \(-0.285995\pi\) |
−0.988962 | + | 0.148170i | \(0.952662\pi\) | |||||||
\(510\) | −1.75250e6 | + | 8.70193e6i | −0.298354 | + | 1.48146i | ||||
\(511\) | 35761.9 | − | 61941.4i | 0.00605855 | − | 0.0104937i | ||||
\(512\) | 1.18067e7 | 1.99046 | ||||||||
\(513\) | −1.00625e6 | + | 1.48289e6i | −0.168816 | + | 0.248780i | ||||
\(514\) | 1.40340e7 | 2.34301 | ||||||||
\(515\) | 3.49490e6 | − | 6.05335e6i | 0.580653 | − | 1.00572i | ||||
\(516\) | −1.25521e6 | + | 6.23266e6i | −0.207535 | + | 1.03050i | ||||
\(517\) | −291118. | − | 504232.i | −0.0479009 | − | 0.0829667i | ||||
\(518\) | 148280. | + | 256828.i | 0.0242805 | + | 0.0420550i | ||||
\(519\) | −792859. | − | 698669.i | −0.129204 | − | 0.113855i | ||||
\(520\) | −5.90181e6 | + | 1.02222e7i | −0.957142 | + | 1.65782i | ||||
\(521\) | 8.64335e6 | 1.39504 | 0.697522 | − | 0.716564i | \(-0.254286\pi\) | ||||
0.697522 | + | 0.716564i | \(0.254286\pi\) | |||||||
\(522\) | 402306. | + | 3.17263e6i | 0.0646220 | + | 0.509616i | ||||
\(523\) | −9.11201e6 | −1.45667 | −0.728333 | − | 0.685224i | \(-0.759704\pi\) | ||||
−0.728333 | + | 0.685224i | \(0.759704\pi\) | |||||||
\(524\) | 1.22220e7 | − | 2.11690e7i | 1.94452 | − | 3.36801i | ||||
\(525\) | 26599.5 | − | 8958.64i | 0.00421187 | − | 0.00141855i | ||||
\(526\) | −6.11113e6 | − | 1.05848e7i | −0.963068 | − | 1.66808i | ||||
\(527\) | 3.14187e6 | + | 5.44187e6i | 0.492789 | + | 0.853536i | ||||
\(528\) | 3.44057e6 | − | 1.15878e6i | 0.537089 | − | 0.180890i | ||||
\(529\) | −3.30813e6 | + | 5.72984e6i | −0.513976 | + | 0.890233i | ||||
\(530\) | −5.75832e6 | −0.890443 | ||||||||
\(531\) | −903220. | − | 7.12290e6i | −0.139014 | − | 1.09628i | ||||
\(532\) | 63865.9 | 0.00978341 | ||||||||
\(533\) | −2.30460e6 | + | 3.99168e6i | −0.351380 | + | 0.608609i | ||||
\(534\) | −4.94239e6 | − | 4.35524e6i | −0.750038 | − | 0.660936i | ||||
\(535\) | −4.94740e6 | − | 8.56915e6i | −0.747296 | − | 1.29436i | ||||
\(536\) | 4.01890e6 | + | 6.96094e6i | 0.604221 | + | 1.04654i | ||||
\(537\) | −67242.3 | + | 333888.i | −0.0100625 | + | 0.0499649i | ||||
\(538\) | 591650. | − | 1.02477e6i | 0.0881271 | − | 0.152641i | ||||
\(539\) | −3.08782e6 | −0.457804 | ||||||||
\(540\) | −5.19236e6 | − | 1.07217e7i | −0.766268 | − | 1.58226i | ||||
\(541\) | 5.76360e6 | 0.846643 | 0.423322 | − | 0.905979i | \(-0.360864\pi\) | ||||
0.423322 | + | 0.905979i | \(0.360864\pi\) | |||||||
\(542\) | 248783. | − | 430905.i | 0.0363767 | − | 0.0630062i | ||||
\(543\) | −578833. | + | 2.87416e6i | −0.0842468 | + | 0.418323i | ||||
\(544\) | 988496. | + | 1.71213e6i | 0.143211 | + | 0.248050i | ||||
\(545\) | 2.73476e6 | + | 4.73674e6i | 0.394391 | + | 0.683106i | ||||
\(546\) | −171908. | − | 151486.i | −0.0246783 | − | 0.0217466i | ||||
\(547\) | 2.80744e6 | − | 4.86263e6i | 0.401183 | − | 0.694869i | −0.592686 | − | 0.805434i | \(-0.701933\pi\) |
0.993869 | + | 0.110564i | \(0.0352659\pi\) | |||||||
\(548\) | −1.02112e7 | −1.45253 | ||||||||
\(549\) | −7.79898e6 | + | 5.92550e6i | −1.10435 | + | 0.839063i | ||||
\(550\) | 1.61671e6 | 0.227891 | ||||||||
\(551\) | −313717. | + | 543374.i | −0.0440209 | + | 0.0762464i | ||||
\(552\) | 1.82570e7 | − | 6.14892e6i | 2.55025 | − | 0.858917i | ||||
\(553\) | −48889.7 | − | 84679.4i | −0.00679837 | − | 0.0117751i | ||||
\(554\) | 2.34010e6 | + | 4.05317e6i | 0.323937 | + | 0.561075i | ||||
\(555\) | 1.02851e7 | − | 3.46401e6i | 1.41735 | − | 0.477360i | ||||
\(556\) | −8.12364e6 | + | 1.40705e7i | −1.11446 | + | 1.93030i | ||||
\(557\) | 2.18422e6 | 0.298303 | 0.149152 | − | 0.988814i | \(-0.452346\pi\) | ||||
0.149152 | + | 0.988814i | \(0.452346\pi\) | |||||||
\(558\) | −1.15189e7 | − | 4.83576e6i | −1.56612 | − | 0.657475i | ||||
\(559\) | 4.47510e6 | 0.605722 | ||||||||
\(560\) | −60887.1 | + | 105460.i | −0.00820456 | + | 0.0142107i | ||||
\(561\) | −2.60679e6 | − | 2.29711e6i | −0.349702 | − | 0.308158i | ||||
\(562\) | 1.02856e7 | + | 1.78152e7i | 1.37369 | + | 2.37931i | ||||
\(563\) | −339673. | − | 588330.i | −0.0451637 | − | 0.0782258i | 0.842560 | − | 0.538603i | \(-0.181048\pi\) |
−0.887724 | + | 0.460377i | \(0.847714\pi\) | |||||||
\(564\) | −648152. | + | 3.21836e6i | −0.0857983 | + | 0.426027i | ||||
\(565\) | 1.10785e6 | − | 1.91885e6i | 0.146002 | − | 0.252883i | ||||
\(566\) | −1.50446e7 | −1.97396 | ||||||||
\(567\) | 116128. | − | 29932.5i | 0.0151697 | − | 0.00391007i | ||||
\(568\) | 42343.2 | 0.00550697 | ||||||||
\(569\) | 3.28195e6 | − | 5.68451e6i | 0.424964 | − | 0.736059i | −0.571453 | − | 0.820635i | \(-0.693620\pi\) |
0.996417 | + | 0.0845759i | \(0.0269536\pi\) | |||||||
\(570\) | 683571. | − | 3.39423e6i | 0.0881244 | − | 0.437577i | ||||
\(571\) | 952119. | + | 1.64912e6i | 0.122208 | + | 0.211671i | 0.920638 | − | 0.390417i | \(-0.127669\pi\) |
−0.798430 | + | 0.602088i | \(0.794336\pi\) | |||||||
\(572\) | −4.45455e6 | − | 7.71550e6i | −0.569264 | − | 0.985994i | ||||
\(573\) | 2.88177e6 | + | 2.53942e6i | 0.366668 | + | 0.323109i | ||||
\(574\) | −63680.8 | + | 110298.i | −0.00806731 | + | 0.0139730i | ||||
\(575\) | 3.20302e6 | 0.404008 | ||||||||
\(576\) | 5.46249e6 | + | 2.29321e6i | 0.686016 | + | 0.287997i | ||||
\(577\) | 1.13367e7 | 1.41758 | 0.708792 | − | 0.705417i | \(-0.249240\pi\) | ||||
0.708792 | + | 0.705417i | \(0.249240\pi\) | |||||||
\(578\) | 254182. | − | 440257.i | 0.0316465 | − | 0.0548133i | ||||
\(579\) | −3.35542e6 | + | 1.13010e6i | −0.415959 | + | 0.140094i | ||||
\(580\) | −2.08544e6 | − | 3.61209e6i | −0.257412 | − | 0.445850i | ||||
\(581\) | 10495.7 | + | 18179.1i | 0.00128994 | + | 0.00223425i | ||||
\(582\) | −1.44684e7 | + | 4.87291e6i | −1.77056 | + | 0.596322i | ||||
\(583\) | 1.12696e6 | − | 1.95195e6i | 0.137321 | − | 0.237846i | ||||
\(584\) | −1.20467e7 | −1.46163 | ||||||||
\(585\) | −6.67665e6 | + | 5.07278e6i | −0.806620 | + | 0.612853i | ||||
\(586\) | −7.64290e6 | −0.919420 | ||||||||
\(587\) | −6.88666e6 | + | 1.19280e7i | −0.824923 | + | 1.42881i | 0.0770557 | + | 0.997027i | \(0.475448\pi\) |
−0.901978 | + | 0.431781i | \(0.857885\pi\) | |||||||
\(588\) | 1.30628e7 | + | 1.15109e7i | 1.55809 | + | 1.37299i | ||||
\(589\) | −1.22550e6 | − | 2.12263e6i | −0.145554 | − | 0.252108i | ||||
\(590\) | 6.93603e6 | + | 1.20136e7i | 0.820315 | + | 1.42083i | ||||
\(591\) | 1.54830e6 | − | 7.68798e6i | 0.182341 | − | 0.905406i | ||||
\(592\) | 9.32456e6 | − | 1.61506e7i | 1.09351 | − | 1.89402i | ||||
\(593\) | 9.94674e6 | 1.16157 | 0.580783 | − | 0.814058i | \(-0.302746\pi\) | ||||
0.580783 | + | 0.814058i | \(0.302746\pi\) | |||||||
\(594\) | 6.88948e6 | + | 501067.i | 0.801162 | + | 0.0582679i | ||||
\(595\) | 116542. | 0.0134955 | ||||||||
\(596\) | 327344. | − | 566977.i | 0.0377476 | − | 0.0653807i | ||||
\(597\) | −12700.2 | + | 63062.0i | −0.00145839 | + | 0.00724155i | ||||
\(598\) | −1.30739e7 | − | 2.26447e7i | −1.49504 | − | 2.58948i | ||||
\(599\) | −2.77125e6 | − | 4.79995e6i | −0.315579 | − | 0.546600i | 0.663981 | − | 0.747749i | \(-0.268866\pi\) |
−0.979561 | + | 0.201150i | \(0.935532\pi\) | |||||||
\(600\) | −3.54682e6 | − | 3.12547e6i | −0.402218 | − | 0.354435i | ||||
\(601\) | −6.63325e6 | + | 1.14891e7i | −0.749101 | + | 1.29748i | 0.199153 | + | 0.979968i | \(0.436181\pi\) |
−0.948254 | + | 0.317513i | \(0.897152\pi\) | |||||||
\(602\) | 123656. | 0.0139067 | ||||||||
\(603\) | 718301. | + | 5.66461e6i | 0.0804476 | + | 0.634419i | ||||
\(604\) | −1.46093e7 | −1.62944 | ||||||||
\(605\) | −3.01096e6 | + | 5.21513e6i | −0.334438 | + | 0.579264i | ||||
\(606\) | 1.10883e7 | − | 3.73451e6i | 1.22654 | − | 0.413098i | ||||
\(607\) | −3.04326e6 | − | 5.27108e6i | −0.335249 | − | 0.580668i | 0.648284 | − | 0.761399i | \(-0.275487\pi\) |
−0.983533 | + | 0.180731i | \(0.942154\pi\) | |||||||
\(608\) | −385568. | − | 667824.i | −0.0423002 | − | 0.0732660i | ||||
\(609\) | 39791.0 | − | 13401.5i | 0.00434752 | − | 0.00146424i | ||||
\(610\) | 9.46194e6 | − | 1.63886e7i | 1.02957 | − | 1.78327i | ||||
\(611\) | 2.31081e6 | 0.250416 | ||||||||
\(612\) | 2.46451e6 | + | 1.94355e7i | 0.265982 | + | 2.09757i | ||||
\(613\) | −4.59806e6 | −0.494223 | −0.247112 | − | 0.968987i | \(-0.579481\pi\) | ||||
−0.247112 | + | 0.968987i | \(0.579481\pi\) | |||||||
\(614\) | 1.05960e7 | − | 1.83528e7i | 1.13428 | − | 1.96464i | ||||
\(615\) | 3.49690e6 | + | 3.08148e6i | 0.372817 | + | 0.328527i | ||||
\(616\) | −63832.1 | − | 110560.i | −0.00677778 | − | 0.0117395i | ||||
\(617\) | −8.01311e6 | − | 1.38791e7i | −0.847399 | − | 1.46774i | −0.883521 | − | 0.468391i | \(-0.844834\pi\) |
0.0361221 | − | 0.999347i | \(-0.488499\pi\) | |||||||
\(618\) | 4.51189e6 | − | 2.24036e7i | 0.475212 | − | 2.35964i | ||||
\(619\) | −1.19878e6 | + | 2.07634e6i | −0.125751 | + | 0.217807i | −0.922026 | − | 0.387127i | \(-0.873467\pi\) |
0.796275 | + | 0.604934i | \(0.206801\pi\) | |||||||
\(620\) | 1.62931e7 | 1.70226 | ||||||||
\(621\) | 1.36494e7 | + | 992709.i | 1.42031 | + | 0.103298i | ||||
\(622\) | 5.98795e6 | 0.620587 | ||||||||
\(623\) | −43243.9 | + | 74900.6i | −0.00446380 | + | 0.00773153i | ||||
\(624\) | −2.84470e6 | + | 1.41252e7i | −0.292465 | + | 1.45222i | ||||
\(625\) | 3.10456e6 | + | 5.37725e6i | 0.317906 | + | 0.550630i | ||||
\(626\) | 1.07785e7 | + | 1.86689e7i | 1.09932 | + | 1.90407i | ||||
\(627\) | 1.01679e6 | + | 895998.i | 0.103291 | + | 0.0910203i | ||||
\(628\) | −1.01638e6 | + | 1.76042e6i | −0.102839 | + | 0.178122i | ||||
\(629\) | −1.78478e7 | −1.79870 | ||||||||
\(630\) | −184490. | + | 140171.i | −0.0185191 | + | 0.0140704i | ||||
\(631\) | 6.25228e6 | 0.625122 | 0.312561 | − | 0.949898i | \(-0.398813\pi\) | ||||
0.312561 | + | 0.949898i | \(0.398813\pi\) | |||||||
\(632\) | −8.23449e6 | + | 1.42625e7i | −0.820057 | + | 1.42038i | ||||
\(633\) | −1.46240e7 | + | 4.92533e6i | −1.45063 | + | 0.488569i | ||||
\(634\) | 1.58821e7 | + | 2.75086e7i | 1.56922 | + | 2.71797i | ||||
\(635\) | −2.21053e6 | − | 3.82875e6i | −0.217551 | − | 0.376810i | ||||
\(636\) | −1.20441e7 | + | 4.05642e6i | −1.18068 | + | 0.397649i | ||||
\(637\) | 6.12754e6 | − | 1.06132e7i | 0.598325 | − | 1.03633i | ||||
\(638\) | 2.41849e6 | 0.235230 | ||||||||
\(639\) | 27735.2 | + | 11643.5i | 0.00268707 | + | 0.00112806i | ||||
\(640\) | −1.39139e7 | −1.34276 | ||||||||
\(641\) | 9.48142e6 | − | 1.64223e7i | 0.911440 | − | 1.57866i | 0.0994090 | − | 0.995047i | \(-0.468305\pi\) |
0.812031 | − | 0.583614i | \(-0.198362\pi\) | |||||||
\(642\) | −2.42721e7 | − | 2.13887e7i | −2.32418 | − | 2.04808i | ||||
\(643\) | 1.64962e6 | + | 2.85722e6i | 0.157346 | + | 0.272532i | 0.933911 | − | 0.357506i | \(-0.116373\pi\) |
−0.776565 | + | 0.630038i | \(0.783039\pi\) | |||||||
\(644\) | −243861. | − | 422380.i | −0.0231701 | − | 0.0401318i | ||||
\(645\) | 893417. | − | 4.43621e6i | 0.0845580 | − | 0.419868i | ||||
\(646\) | −2.84701e6 | + | 4.93116e6i | −0.268415 | + | 0.464909i | ||||
\(647\) | −1.56481e7 | −1.46961 | −0.734805 | − | 0.678278i | \(-0.762726\pi\) | ||||
−0.734805 | + | 0.678278i | \(0.762726\pi\) | |||||||
\(648\) | −1.41458e7 | − | 1.44182e7i | −1.32339 | − | 1.34888i | ||||
\(649\) | −5.42978e6 | −0.506023 | ||||||||
\(650\) | −3.20825e6 | + | 5.55685e6i | −0.297841 | + | 0.515876i | ||||
\(651\) | −32381.8 | + | 160790.i | −0.00299467 | + | 0.0148699i | ||||
\(652\) | 9.05228e6 | + | 1.56790e7i | 0.833948 | + | 1.44444i | ||||
\(653\) | −7.78514e6 | − | 1.34843e7i | −0.714469 | − | 1.23750i | −0.963164 | − | 0.268915i | \(-0.913335\pi\) |
0.248695 | − | 0.968582i | \(-0.419998\pi\) | |||||||
\(654\) | 1.34168e7 | + | 1.18229e7i | 1.22661 | + | 1.08089i | ||||
\(655\) | −8.69921e6 | + | 1.50675e7i | −0.792276 | + | 1.37226i | ||||
\(656\) | 8.00912e6 | 0.726650 | ||||||||
\(657\) | −7.89074e6 | − | 3.31262e6i | −0.713189 | − | 0.299404i | ||||
\(658\) | 63852.4 | 0.00574927 | ||||||||
\(659\) | −6.40513e6 | + | 1.10940e7i | −0.574532 | + | 0.995119i | 0.421560 | + | 0.906800i | \(0.361483\pi\) |
−0.996092 | + | 0.0883184i | \(0.971851\pi\) | |||||||
\(660\) | −8.53777e6 | + | 2.87550e6i | −0.762930 | + | 0.256953i | ||||
\(661\) | −230248. | − | 398801.i | −0.0204971 | − | 0.0355020i | 0.855595 | − | 0.517646i | \(-0.173192\pi\) |
−0.876092 | + | 0.482144i | \(0.839858\pi\) | |||||||
\(662\) | 1.29413e7 | + | 2.24149e7i | 1.14771 | + | 1.98789i | ||||
\(663\) | 1.30684e7 | − | 4.40141e6i | 1.15462 | − | 0.388873i | ||||
\(664\) | 1.76779e6 | − | 3.06190e6i | 0.155600 | − | 0.269507i | ||||
\(665\) | −45457.8 | −0.00398616 | ||||||||
\(666\) | 2.82537e7 | − | 2.14665e7i | 2.46825 | − | 1.87533i | ||||
\(667\) | 4.79150e6 | 0.417020 | ||||||||
\(668\) | 6.60310e6 | − | 1.14369e7i | 0.572541 | − | 0.991670i | ||||
\(669\) | 1.22548e7 | + | 1.07989e7i | 1.05862 | + | 0.932857i | ||||
\(670\) | −5.51600e6 | − | 9.55399e6i | −0.474719 | − | 0.822238i | ||||
\(671\) | 3.70358e6 | + | 6.41479e6i | 0.317552 | + | 0.550017i | ||||
\(672\) | −10188.0 | + | 50587.9i | −0.000870293 | + | 0.00432139i | ||||
\(673\) | 4.03608e6 | − | 6.99069e6i | 0.343496 | − | 0.594952i | −0.641583 | − | 0.767053i | \(-0.721722\pi\) |
0.985079 | + | 0.172101i | \(0.0550555\pi\) | |||||||
\(674\) | 8.23500e6 | 0.698255 | ||||||||
\(675\) | −1.46376e6 | − | 3.02252e6i | −0.123655 | − | 0.255334i | ||||
\(676\) | 1.06786e7 | 0.898766 | ||||||||
\(677\) | −1.82149e6 | + | 3.15491e6i | −0.152741 | + | 0.264554i | −0.932234 | − | 0.361856i | \(-0.882143\pi\) |
0.779493 | + | 0.626410i | \(0.215477\pi\) | |||||||
\(678\) | 1.43023e6 | − | 7.10171e6i | 0.119490 | − | 0.593319i | ||||
\(679\) | 100220. | + | 173586.i | 0.00834219 | + | 0.0144491i | ||||
\(680\) | −9.81458e6 | − | 1.69993e7i | −0.813953 | − | 1.40981i | ||||
\(681\) | −8.31636e6 | − | 7.32839e6i | −0.687172 | − | 0.605538i | ||||
\(682\) | −4.72380e6 | + | 8.18185e6i | −0.388893 | + | 0.673582i | ||||
\(683\) | 9.57475e6 | 0.785373 | 0.392686 | − | 0.919672i | \(-0.371546\pi\) | ||||
0.392686 | + | 0.919672i | \(0.371546\pi\) | |||||||
\(684\) | −961297. | − | 7.58090e6i | −0.0785628 | − | 0.619556i | ||||
\(685\) | 7.26801e6 | 0.591819 | ||||||||
\(686\) | 338674. | − | 586601.i | 0.0274772 | − | 0.0475919i | ||||
\(687\) | 4.34538e6 | − | 1.46351e6i | 0.351266 | − | 0.118306i | ||||
\(688\) | −3.88805e6 | − | 6.73431e6i | −0.313156 | − | 0.542403i | ||||
\(689\) | 4.47272e6 | + | 7.74698e6i | 0.358941 | + | 0.621705i | ||||
\(690\) | −2.50580e7 | + | 8.43948e6i | −2.00366 | + | 0.674828i | ||||
\(691\) | −3.01871e6 | + | 5.22857e6i | −0.240506 | + | 0.416569i | −0.960859 | − | 0.277039i | \(-0.910647\pi\) |
0.720352 | + | 0.693608i | \(0.243980\pi\) | |||||||
\(692\) | 4.50620e6 | 0.357722 | ||||||||
\(693\) | −11408.8 | − | 89970.8i | −0.000902412 | − | 0.00711653i | ||||
\(694\) | −2.30080e7 | −1.81334 | ||||||||
\(695\) | 5.78215e6 | − | 1.00150e7i | 0.454075 | − | 0.786481i | ||||
\(696\) | −5.30580e6 | − | 4.67549e6i | −0.415172 | − | 0.365851i | ||||
\(697\) | −3.83250e6 | − | 6.63809e6i | −0.298814 | − | 0.517560i | ||||
\(698\) | −1.55478e7 | − | 2.69295e7i | −1.20789 | − | 2.09213i | ||||
\(699\) | −4.82168e6 | + | 2.39418e7i | −0.373255 | + | 1.85338i | ||||
\(700\) | −59841.8 | + | 103649.i | −0.00461594 | + | 0.00799504i | ||||
\(701\) | 1.37603e7 | 1.05763 | 0.528813 | − | 0.848739i | \(-0.322637\pi\) | ||||
0.528813 | + | 0.848739i | \(0.322637\pi\) | |||||||
\(702\) | −1.53939e7 | + | 2.26857e7i | −1.17898 | + | 1.73743i | ||||
\(703\) | 6.96164e6 | 0.531279 | ||||||||
\(704\) | 2.24011e6 | − | 3.87999e6i | 0.170349 | − | 0.295052i | ||||
\(705\) | 461334. | − | 2.29073e6i | 0.0349577 | − | 0.173581i | ||||
\(706\) | −1.32484e7 | − | 2.29469e7i | −1.00035 | − | 1.73266i | ||||
\(707\) | −76806.9 | − | 133033.i | −0.00577899 | − | 0.0100095i | ||||
\(708\) | 2.29702e7 | + | 2.02414e7i | 1.72220 | + | 1.51760i | ||||
\(709\) | 809892. | − | 1.40277e6i | 0.0605078 | − | 0.104803i | −0.834185 | − | 0.551485i | \(-0.814061\pi\) |
0.894693 | + | 0.446683i | \(0.147395\pi\) | |||||||
\(710\) | −58116.6 | −0.00432667 | ||||||||
\(711\) | −9.31559e6 | + | 7.07779e6i | −0.691093 | + | 0.525078i | ||||
\(712\) | 1.45671e7 | 1.07690 | ||||||||
\(713\) | −9.35873e6 | + | 1.62098e7i | −0.689435 | + | 1.19414i | ||||
\(714\) | 361107. | − | 121620.i | 0.0265088 | − | 0.00892811i | ||||
\(715\) | 3.17061e6 | + | 5.49165e6i | 0.231941 | + | 0.401734i | ||||
\(716\) | −726163. | − | 1.25775e6i | −0.0529360 | − | 0.0916879i | ||||
\(717\) | 7.71040e6 | − | 2.59685e6i | 0.560118 | − | 0.188646i | ||||
\(718\) | −1.02164e7 | + | 1.76953e7i | −0.739580 | + | 1.28099i | ||||
\(719\) | 1.42931e7 | 1.03111 | 0.515555 | − | 0.856856i | \(-0.327586\pi\) | ||||
0.515555 | + | 0.856856i | \(0.327586\pi\) | |||||||
\(720\) | 1.34345e7 | + | 5.63995e6i | 0.965809 | + | 0.405457i | ||||
\(721\) | −300043. | −0.0214954 | ||||||||
\(722\) | −1.11750e7 | + | 1.93557e7i | −0.797819 | + | 1.38186i | ||||
\(723\) | 5.00227e6 | + | 4.40802e6i | 0.355895 | + | 0.313615i | ||||
\(724\) | −6.25093e6 | − | 1.08269e7i | −0.443199 | − | 0.767643i | ||||
\(725\) | −587900. | − | 1.01827e6i | −0.0415392 | − | 0.0719481i | ||||
\(726\) | −3.88712e6 | + | 1.93013e7i | −0.273708 | + | 1.35908i | ||||
\(727\) | 1.37208e7 | − | 2.37652e7i | 0.962818 | − | 1.66765i | 0.247450 | − | 0.968901i | \(-0.420407\pi\) |
0.715367 | − | 0.698749i | \(-0.246259\pi\) | |||||||
\(728\) | 506680. | 0.0354328 | ||||||||
\(729\) | −5.30092e6 | − | 1.33338e7i | −0.369430 | − | 0.929258i | ||||
\(730\) | 1.65343e7 | 1.14836 | ||||||||
\(731\) | −3.72100e6 | + | 6.44496e6i | −0.257553 | + | 0.446094i | ||||
\(732\) | 8.24572e6 | − | 4.09437e7i | 0.568788 | − | 2.82429i | ||||
\(733\) | 2.55310e6 | + | 4.42209e6i | 0.175512 | + | 0.303996i | 0.940338 | − | 0.340241i | \(-0.110509\pi\) |
−0.764826 | + | 0.644237i | \(0.777175\pi\) | |||||||
\(734\) | −5.05283e6 | − | 8.75175e6i | −0.346174 | − | 0.599591i | ||||
\(735\) | −9.29767e6 | − | 8.19313e6i | −0.634828 | − | 0.559412i | ||||
\(736\) | −2.94445e6 | + | 5.09994e6i | −0.200359 | + | 0.347033i | ||||
\(737\) | 4.31812e6 | 0.292837 | ||||||||
\(738\) | 1.40510e7 | + | 5.89874e6i | 0.949653 | + | 0.398674i | ||||
\(739\) | −1.34356e7 | −0.904997 | −0.452498 | − | 0.891765i | \(-0.649467\pi\) | ||||
−0.452498 | + | 0.891765i | \(0.649467\pi\) | |||||||
\(740\) | −2.31388e7 | + | 4.00776e7i | −1.55332 | + | 2.69044i | ||||
\(741\) | −5.09740e6 | + | 1.71679e6i | −0.341038 | + | 0.114861i | ||||
\(742\) | 123590. | + | 214065.i | 0.00824091 | + | 0.0142737i | ||||
\(743\) | 343246. | + | 594519.i | 0.0228104 | + | 0.0395088i | 0.877205 | − | 0.480116i | \(-0.159405\pi\) |
−0.854395 | + | 0.519624i | \(0.826072\pi\) | |||||||
\(744\) | 2.61806e7 | − | 8.81758e6i | 1.73399 | − | 0.584005i | ||||
\(745\) | −232994. | + | 403557.i | −0.0153799 | + | 0.0266387i | ||||
\(746\) | −5.19518e7 | −3.41786 | ||||||||
\(747\) | 1.99988e6 | − | 1.51947e6i | 0.131130 | − | 0.0996299i | ||||
\(748\) | 1.48156e7 | 0.968203 | ||||||||
\(749\) | −212371. | + | 367838.i | −0.0138322 | + | 0.0239581i | ||||
\(750\) | 2.20272e7 | + | 1.94104e7i | 1.42990 | + | 1.26003i | ||||
\(751\) | −5.46542e6 | − | 9.46639e6i | −0.353610 | − | 0.612470i | 0.633269 | − | 0.773931i | \(-0.281712\pi\) |
−0.986879 | + | 0.161462i | \(0.948379\pi\) | |||||||
\(752\) | −2.00768e6 | − | 3.47740e6i | −0.129464 | − | 0.224238i | ||||
\(753\) | 713738. | − | 3.54403e6i | 0.0458724 | − | 0.227777i | ||||
\(754\) | −4.79932e6 | + | 8.31266e6i | −0.307434 | + | 0.532491i | ||||
\(755\) | 1.03985e7 | 0.663900 | ||||||||
\(756\) | −287134. | + | 423144.i | −0.0182718 | + | 0.0269268i | ||||
\(757\) | −2.31128e7 | −1.46593 | −0.732966 | − | 0.680265i | \(-0.761865\pi\) | ||||
−0.732966 | + | 0.680265i | \(0.761865\pi\) | |||||||
\(758\) | 1.35891e7 | − | 2.35370e7i | 0.859047 | − | 1.48791i | ||||
\(759\) | 2.04328e6 | − | 1.01458e7i | 0.128743 | − | 0.639266i | ||||
\(760\) | 3.82823e6 | + | 6.63068e6i | 0.240416 | + | 0.416413i | ||||
\(761\) | 5.94528e6 | + | 1.02975e7i | 0.372144 | + | 0.644572i | 0.989895 | − | 0.141801i | \(-0.0452894\pi\) |
−0.617751 | + | 0.786374i | \(0.711956\pi\) | |||||||
\(762\) | −1.08449e7 | − | 9.55658e6i | −0.676611 | − | 0.596232i | ||||
\(763\) | 117392. | − | 203328.i | 0.00730005 | − | 0.0126441i | ||||
\(764\) | −1.63785e7 | −1.01517 | ||||||||
\(765\) | −1.75417e6 | − | 1.38336e7i | −0.108372 | − | 0.854634i | ||||
\(766\) | 4.31570e7 | 2.65754 | ||||||||
\(767\) | 1.07750e7 | − | 1.86628e7i | 0.661345 | − | 1.14548i | ||||
\(768\) | −3.15872e7 | + | 1.06385e7i | −1.93245 | + | 0.650844i | ||||
\(769\) | −1.32545e6 | − | 2.29575e6i | −0.0808253 | − | 0.139994i | 0.822779 | − | 0.568361i | \(-0.192422\pi\) |
−0.903605 | + | 0.428367i | \(0.859089\pi\) | |||||||
\(770\) | 87610.4 | + | 151746.i | 0.00532511 | + | 0.00922337i | ||||
\(771\) | −2.08929e7 | + | 7.03668e6i | −1.26579 | + | 0.426316i | ||||
\(772\) | 7.54883e6 | − | 1.30750e7i | 0.455865 | − | 0.789581i | ||||
\(773\) | −2.12893e7 | −1.28148 | −0.640742 | − | 0.767757i | \(-0.721373\pi\) | ||||
−0.640742 | + | 0.767757i | \(0.721373\pi\) | |||||||
\(774\) | −1.86125e6 | − | 1.46780e7i | −0.111674 | − | 0.880673i | ||||
\(775\) | 4.59314e6 | 0.274698 | ||||||||
\(776\) | 1.68801e7 | − | 2.92371e7i | 1.00628 | − | 1.74293i | ||||
\(777\) | −349523. | − | 308000.i | −0.0207694 | − | 0.0183020i | ||||
\(778\) | 1.49224e7 | + | 2.58464e7i | 0.883873 | + | 1.53091i | ||||
\(779\) | 1.49489e6 | + | 2.58922e6i | 0.0882601 | + | 0.152871i | ||||
\(780\) | 7.05910e6 | − | 3.50516e7i | 0.415444 | − | 2.06287i | ||||
\(781\) | 11373.9 | − | 19700.3i | 0.000667242 | − | 0.00115570i | ||||
\(782\) | 4.34833e7 | 2.54276 | ||||||||
\(783\) | −2.18969e6 | − | 4.52148e6i | −0.127637 | − | 0.263558i | ||||
\(784\) | −2.12949e7 | −1.23733 | ||||||||
\(785\) | 723426. | − | 1.25301e6i | 0.0419006 | − | 0.0725739i | ||||
\(786\) | −1.12306e7 | + | 5.57650e7i | −0.648406 | + | 3.21963i | ||||
\(787\) | 1.14439e7 | + | 1.98214e7i | 0.658623 | + | 1.14077i | 0.980972 | + | 0.194148i | \(0.0621942\pi\) |
−0.322349 | + | 0.946621i | \(0.604472\pi\) | |||||||
\(788\) | 1.67203e7 | + | 2.89605e7i | 0.959246 | + | 1.66146i | ||||
\(789\) | 1.44051e7 | + | 1.26938e7i | 0.823802 | + | 0.725936i | ||||
\(790\) | 1.13019e7 | − | 1.95755e7i | 0.644296 | − | 1.11595i | ||||
\(791\) | −95110.7 | −0.00540491 | ||||||||
\(792\) | −1.21628e7 | + | 9.24102e6i | −0.689000 | + | 0.523488i | ||||
\(793\) | −2.93979e7 | −1.66010 | ||||||||
\(794\) | 1.07470e7 | − | 1.86143e7i | 0.604972 | − | 1.04784i | ||||
\(795\) | 8.57260e6 | − | 2.88723e6i | 0.481055 | − | 0.162018i | ||||
\(796\) | −137152. | − | 237553.i | −0.00767217 | − | 0.0132886i | ||||
\(797\) | 1.28424e7 | + | 2.22437e7i | 0.716146 | + | 1.24040i | 0.962516 | + | 0.271225i | \(0.0874287\pi\) |
−0.246370 | + | 0.969176i | \(0.579238\pi\) | |||||||
\(798\) | −140852. | + | 47438.5i | −0.00782987 | + | 0.00263708i | ||||
\(799\) | −1.92141e6 | + | 3.32799e6i | −0.106477 | + | 0.184423i | ||||
\(800\) | 1.44510e6 | 0.0798310 | ||||||||
\(801\) | 9.54162e6 | + | 4.00567e6i | 0.525461 | + | 0.220594i | ||||
\(802\) | −3.51275e7 | −1.92847 | ||||||||
\(803\) | −3.23592e6 | + | 5.60478e6i | −0.177096 | + | 0.306739i | ||||
\(804\) | −1.82675e7 | − | 1.60974e7i | −0.996641 | − | 0.878242i | ||||
\(805\) | 173573. | + | 300637.i | 0.00944043 | + | 0.0163513i | ||||
\(806\) | −1.87480e7 | − | 3.24725e7i | −1.01652 | − | 1.76067i | ||||
\(807\) | −366988. | + | 1.82226e6i | −0.0198366 | + | 0.0984978i | ||||
\(808\) | −1.29366e7 | + | 2.24068e7i | −0.697094 | + | 1.20740i | ||||
\(809\) | −5.88061e6 | −0.315901 | −0.157951 | − | 0.987447i | \(-0.550489\pi\) | ||||
−0.157951 | + | 0.987447i | \(0.550489\pi\) | |||||||
\(810\) | 1.94153e7 | + | 1.97891e7i | 1.03975 | + | 1.05978i | ||||
\(811\) | −2.04938e7 | −1.09414 | −0.547068 | − | 0.837088i | \(-0.684256\pi\) | ||||
−0.547068 | + | 0.837088i | \(0.684256\pi\) | |||||||
\(812\) | −89519.3 | + | 155052.i | −0.00476460 | + | 0.00825254i | ||||
\(813\) | −154315. | + | 766243.i | −0.00818808 | + | 0.0406575i | ||||
\(814\) | −1.34171e7 | − | 2.32391e7i | −0.709737 | − | 1.22930i | ||||
\(815\) | −6.44313e6 | − | 1.11598e7i | −0.339784 | − | 0.588523i | ||||
\(816\) | −1.79775e7 | − | 1.58418e7i | −0.945157 | − | 0.832875i | ||||
\(817\) | 1.45139e6 | − | 2.51389e6i | 0.0760730 | − | 0.131762i | ||||
\(818\) | 1.55526e7 | 0.812681 | ||||||||
\(819\) | 331880. | + | 139327.i | 0.0172891 | + | 0.00725814i | ||||
\(820\) | −1.98746e7 | −1.03220 | ||||||||
\(821\) | 1.81711e6 | − | 3.14732e6i | 0.0940855 | − | 0.162961i | −0.815141 | − | 0.579263i | \(-0.803341\pi\) |
0.909227 | + | 0.416302i | \(0.136674\pi\) | |||||||
\(822\) | 2.25200e7 | − | 7.58470e6i | 1.16249 | − | 0.391524i | ||||
\(823\) | 7.90337e6 | + | 1.36890e7i | 0.406736 | + | 0.704488i | 0.994522 | − | 0.104529i | \(-0.0333335\pi\) |
−0.587786 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(824\) | 2.52681e7 | + | 4.37657e7i | 1.29645 | + | 2.24551i | ||||
\(825\) | −2.40685e6 | + | 810623.i | −0.123116 | + | 0.0414652i | ||||
\(826\) | 297735. | − | 515692.i | 0.0151838 | − | 0.0262991i | ||||
\(827\) | −1.98096e6 | −0.100719 | −0.0503597 | − | 0.998731i | \(-0.516037\pi\) | ||||
−0.0503597 | + | 0.998731i | \(0.516037\pi\) | |||||||
\(828\) | −4.64660e7 | + | 3.53039e7i | −2.35537 | + | 1.78956i | ||||
\(829\) | 2.56811e7 | 1.29786 | 0.648929 | − | 0.760849i | \(-0.275217\pi\) | ||||
0.648929 | + | 0.760849i | \(0.275217\pi\) | |||||||
\(830\) | −2.42631e6 | + | 4.20249e6i | −0.122251 | + | 0.211744i | ||||
\(831\) | −5.51605e6 | − | 4.86076e6i | −0.277093 | − | 0.244175i | ||||
\(832\) | 8.89067e6 | + | 1.53991e7i | 0.445273 | + | 0.771235i | ||||
\(833\) | 1.01900e7 | + | 1.76495e7i | 0.508815 | + | 0.881294i | ||||
\(834\) | 7.46472e6 | − | 3.70656e7i | 0.371619 | − | 1.84526i | ||||
\(835\) | −4.69988e6 | + | 8.14043e6i | −0.233276 | + | 0.404046i | ||||
\(836\) | −5.77891e6 | −0.285977 | ||||||||
\(837\) | 1.95732e7 | + | 1.42355e6i | 0.965715 | + | 0.0702358i | ||||
\(838\) | 2.34825e7 | 1.15514 | ||||||||
\(839\) | −2.27342e6 | + | 3.93767e6i | −0.111500 | + | 0.193123i | −0.916375 | − | 0.400321i | \(-0.868899\pi\) |
0.804875 | + | 0.593444i | \(0.202232\pi\) | |||||||
\(840\) | 101154. | − | 502277.i | 0.00494637 | − | 0.0245609i | ||||
\(841\) | 9.37612e6 | + | 1.62399e7i | 0.457123 | + | 0.791760i | ||||
\(842\) | −1.82874e7 | − | 3.16747e7i | −0.888937 | − | 1.53968i | ||||
\(843\) | −2.42451e7 | − | 2.13649e7i | −1.17505 | − | 1.03545i | ||||
\(844\) | 3.29001e7 | − | 5.69847e7i | 1.58980 | − | 2.75361i | ||||
\(845\) | −7.60068e6 | −0.366193 | ||||||||
\(846\) | −961093. | − | 7.57929e6i | −0.0461678 | − | 0.364085i | ||||
\(847\) | 258496. | 0.0123807 | ||||||||
\(848\) | 7.77197e6 | − | 1.34614e7i | 0.371143 | − | 0.642839i | ||||
\(849\) | 2.23974e7 | − | 7.54338e6i | 1.06642 | − | 0.359167i | ||||
\(850\) | −5.33525e6 | − | 9.24092e6i | −0.253284 | − | 0.438700i | ||||
\(851\) | −2.65818e7 | − | 4.60411e7i | −1.25823 | − | 2.17932i | ||||
\(852\) | −121556. | + | 40939.9i | −0.00573692 | + | 0.00193218i | ||||
\(853\) | −708511. | + | 1.22718e6i | −0.0333407 | + | 0.0577477i | −0.882214 | − | 0.470848i | \(-0.843948\pi\) |
0.848874 | + | 0.528596i | \(0.177281\pi\) | |||||||
\(854\) | −812324. | −0.0381140 | ||||||||
\(855\) | 684221. | + | 5.39585e6i | 0.0320097 | + | 0.252432i | ||||
\(856\) | 7.15394e7 | 3.33704 | ||||||||
\(857\) | 4.07200e6 | − | 7.05290e6i | 0.189389 | − | 0.328032i | −0.755658 | − | 0.654967i | \(-0.772683\pi\) |
0.945047 | + | 0.326935i | \(0.106016\pi\) | |||||||
\(858\) | 1.55551e7 | + | 1.37072e7i | 0.721365 | + | 0.635669i | ||||
\(859\) | −5.33500e6 | − | 9.24050e6i | −0.246690 | − | 0.427280i | 0.715915 | − | 0.698187i | \(-0.246010\pi\) |
−0.962605 | + | 0.270907i | \(0.912676\pi\) | |||||||
\(860\) | 9.64819e6 | + | 1.67111e7i | 0.444836 | + | 0.770478i | ||||
\(861\) | 39499.9 | − | 196134.i | 0.00181588 | − | 0.00901667i | ||||
\(862\) | −3.36474e7 | + | 5.82791e7i | −1.54235 | + | 2.67143i | ||||
\(863\) | −1.21144e7 | −0.553701 | −0.276851 | − | 0.960913i | \(-0.589291\pi\) | ||||
−0.276851 | + | 0.960913i | \(0.589291\pi\) | |||||||
\(864\) | 6.15814e6 | + | 447878.i | 0.280650 | + | 0.0204115i | ||||
\(865\) | −3.20737e6 | −0.145750 | ||||||||
\(866\) | −1.58987e7 | + | 2.75374e7i | −0.720391 | + | 1.24775i | ||||
\(867\) | −157664. | + | 782872.i | −0.00712335 | + | 0.0353706i | ||||
\(868\) | −349698. | − | 605694.i | −0.0157541 | − | 0.0272869i | ||||
\(869\) | 4.42379e6 | + | 7.66222e6i | 0.198721 | + | 0.344196i | ||||
\(870\) | 7.28229e6 | + | 6.41717e6i | 0.326189 | + | 0.287439i | ||||
\(871\) | −8.56899e6 | + | 1.48419e7i | −0.382723 | + | 0.662895i | ||||
\(872\) | −3.95445e7 | −1.76115 | ||||||||
\(873\) | 1.90962e7 | − | 1.45089e7i | 0.848031 | − | 0.644317i | ||||
\(874\) | −1.69609e7 | −0.751051 | ||||||||
\(875\) | 192729. | − | 333816.i | 0.00850995 | − | 0.0147397i | ||||
\(876\) | 3.45831e7 | − | 1.16475e7i | 1.52266 | − | 0.512829i | ||||
\(877\) | −1.65673e7 | − | 2.86954e7i | −0.727366 | − | 1.25983i | −0.957993 | − | 0.286792i | \(-0.907411\pi\) |
0.230627 | − | 0.973042i | \(-0.425922\pi\) | |||||||
\(878\) | 6.93075e6 | + | 1.20044e7i | 0.303420 | + | 0.525538i | ||||
\(879\) | 1.13782e7 | − | 3.83216e6i | 0.496710 | − | 0.167291i | ||||
\(880\) | 5.50937e6 | − | 9.54251e6i | 0.239826 | − | 0.415390i | ||||
\(881\) | 49573.7 | 0.00215185 | 0.00107592 | − | 0.999999i | \(-0.499658\pi\) | ||||
0.00107592 | + | 0.999999i | \(0.499658\pi\) | |||||||
\(882\) | −3.73591e7 | − | 1.56837e7i | −1.61706 | − | 0.678857i | ||||
\(883\) | 4.21109e7 | 1.81758 | 0.908788 | − | 0.417259i | \(-0.137009\pi\) | ||||
0.908788 | + | 0.417259i | \(0.137009\pi\) | |||||||
\(884\) | −2.94005e7 | + | 5.09232e7i | −1.26539 | + | 2.19172i | ||||
\(885\) | −1.63495e7 | − | 1.44072e7i | −0.701692 | − | 0.618333i | ||||
\(886\) | −2.46689e7 | − | 4.27278e7i | −1.05576 | − | 1.82863i | ||||
\(887\) | −550680. | − | 953806.i | −0.0235012 | − | 0.0407053i | 0.854036 | − | 0.520215i | \(-0.174148\pi\) |
−0.877537 | + | 0.479509i | \(0.840815\pi\) | |||||||
\(888\) | −1.54913e7 | + | 7.69212e7i | −0.659258 | + | 3.27351i | ||||
\(889\) | −94888.8 | + | 164352.i | −0.00402680 | + | 0.00697463i | ||||
\(890\) | −1.99936e7 | −0.846088 | ||||||||
\(891\) | −1.05078e7 | + | 2.70844e6i | −0.443423 | + | 0.114294i | ||||
\(892\) | −6.96498e7 | −2.93094 | ||||||||
\(893\) | 749458. | − | 1.29810e6i | 0.0314498 | − | 0.0544727i | ||||
\(894\) | −300793. | + | 1.49357e6i | −0.0125870 | + | 0.0625003i | ||||
\(895\) | 516860. | + | 895228.i | 0.0215683 | + | 0.0373574i | ||||
\(896\) | 298633. | + | 517248.i | 0.0124271 | + | 0.0215243i | ||||
\(897\) | 3.08176e7 | + | 2.71566e7i | 1.27885 | + | 1.12692i | ||||
\(898\) | 2.40696e7 | − | 4.16898e7i | 0.996042 | − | 1.72520i | ||||
\(899\) | 6.87102e6 | 0.283545 | ||||||||
\(900\) | 1.32039e7 | + | 5.54313e6i | 0.543370 | + | 0.228112i | ||||
\(901\) | −1.48761e7 | −0.610487 | ||||||||
\(902\) | 5.76216e6 | − | 9.98036e6i | 0.235814 | − | 0.408441i | ||||
\(903\) | −184091. | + | 62001.4i | −0.00751299 | + | 0.00253036i | ||||
\(904\) | 8.00974e6 | + | 1.38733e7i | 0.325985 | + | 0.564622i | ||||
\(905\) | 4.44922e6 | + | 7.70627e6i | 0.180577 | + | 0.312769i | ||||
\(906\) | 3.22198e7 | − | 1.08516e7i | 1.30408 | − | 0.439210i | ||||
\(907\) | 3.72157e6 | − | 6.44595e6i | 0.150213 | − | 0.260177i | −0.781093 | − | 0.624415i | \(-0.785337\pi\) |
0.931306 | + | 0.364238i | \(0.118671\pi\) | |||||||
\(908\) | 4.72659e7 | 1.90254 | ||||||||
\(909\) | −1.46350e7 | + | 1.11194e7i | −0.587467 | + | 0.446345i | ||||
\(910\) | −695425. | −0.0278386 | ||||||||
\(911\) | 1.61672e7 | − | 2.80024e7i | 0.645414 | − | 1.11789i | −0.338792 | − | 0.940861i | \(-0.610018\pi\) |
0.984206 | − | 0.177028i | \(-0.0566483\pi\) | |||||||
\(912\) | 7.01222e6 | + | 6.17918e6i | 0.279170 | + | 0.246005i | ||||
\(913\) | −949703. | − | 1.64493e6i | −0.0377060 | − | 0.0653087i | ||||
\(914\) | 2.12600e7 | + | 3.68234e7i | 0.841778 | + | 1.45800i | ||||
\(915\) | −5.86905e6 | + | 2.91424e7i | −0.231747 | + | 1.15073i | ||||
\(916\) | −9.77597e6 | + | 1.69325e7i | −0.384965 | + | 0.666779i | ||||
\(917\) | 746841. | 0.0293295 | ||||||||
\(918\) | −1.98716e7 | − | 4.10329e7i | −0.778263 | − | 1.60703i | ||||
\(919\) | 3.18905e7 | 1.24558 | 0.622792 | − | 0.782388i | \(-0.285998\pi\) | ||||
0.622792 | + | 0.782388i | \(0.285998\pi\) | |||||||
\(920\) | 2.92348e7 | − | 5.06362e7i | 1.13876 | − | 1.97239i | ||||
\(921\) | −6.57249e6 | + | 3.26353e7i | −0.255318 | + | 1.26777i | ||||
\(922\) | 118811. | + | 205787.i | 0.00460288 | + | 0.00797243i | ||||
\(923\) | 45141.5 | + | 78187.3i | 0.00174410 | + | 0.00302087i | ||||
\(924\) | 290142. | + | 255674.i | 0.0111797 | + | 0.00985159i | ||||
\(925\) | −6.52299e6 | + | 1.12982e7i | −0.250664 | + | 0.434163i | ||||
\(926\) | 3.50133e7 | 1.34186 | ||||||||
\(927\) | 4.51619e6 | + | 3.56152e7i | 0.172613 | + | 1.36124i | ||||
\(928\) | 2.16177e6 | 0.0824022 | ||||||||
\(929\) | 7.20450e6 | − | 1.24786e7i | 0.273883 | − | 0.474379i | −0.695970 | − | 0.718071i | \(-0.745025\pi\) |
0.969853 | + | 0.243692i | \(0.0783586\pi\) | |||||||
\(930\) | −3.59332e7 | + | 1.21022e7i | −1.36235 | + | 0.458837i | ||||
\(931\) | −3.97465e6 | − | 6.88429e6i | −0.150288 | − | 0.260307i | ||||
\(932\) | −5.20703e7 | − | 9.01884e7i | −1.96359 | − | 3.40103i | ||||
\(933\) | −8.91446e6 | + | 3.00237e6i | −0.335267 | + | 0.112917i | ||||
\(934\) | −2.31342e7 | + | 4.00697e7i | −0.867737 | + | 1.50296i | ||||
\(935\) | −1.05453e7 | −0.394485 | ||||||||
\(936\) | −7.62644e6 | − | 6.01430e7i | −0.284533 | − | 2.24386i | ||||
\(937\) | 2.33199e7 | 0.867718 | 0.433859 | − | 0.900981i | \(-0.357152\pi\) | ||||
0.433859 | + | 0.900981i | \(0.357152\pi\) | |||||||
\(938\) | −236779. | + | 410113.i | −0.00878690 | + | 0.0152194i | ||||
\(939\) | −2.54070e7 | − | 2.23887e7i | −0.940349 | − | 0.828638i | ||||
\(940\) | 4.98204e6 | + | 8.62915e6i | 0.183902 | + | 0.318528i | ||||
\(941\) | 2.35788e7 | + | 4.08396e7i | 0.868054 | + | 1.50351i | 0.863982 | + | 0.503522i | \(0.167963\pi\) |
0.00407185 | + | 0.999992i | \(0.498704\pi\) | |||||||
\(942\) | 933937. | − | 4.63742e6i | 0.0342918 | − | 0.170274i | ||||
\(943\) | 1.14159e7 | − | 1.97730e7i | 0.418054 | − | 0.724091i | ||||
\(944\) | −3.74461e7 | −1.36765 | ||||||||
\(945\) | 204373. | − | 301181.i | 0.00744466 | − | 0.0109710i | ||||
\(946\) | −1.11890e7 | −0.406504 | ||||||||
\(947\) | −1.21868e7 | + | 2.11081e7i | −0.441585 | + | 0.764847i | −0.997807 | − | 0.0661864i | \(-0.978917\pi\) |
0.556223 | + | 0.831033i | \(0.312250\pi\) | |||||||
\(948\) | 9.84920e6 | − | 4.89057e7i | 0.355943 | − | 1.76741i | ||||
\(949\) | −1.28429e7 | − | 2.22445e7i | −0.462910 | − | 0.801784i | ||||
\(950\) | 2.08104e6 | + | 3.60447e6i | 0.0748120 | + | 0.129578i | ||||
\(951\) | −3.74370e7 | − | 3.29896e7i | −1.34230 | − | 1.18284i | ||||
\(952\) | −421299. | + | 729711.i | −0.0150660 | + | 0.0260951i | ||||
\(953\) | −4.33987e7 | −1.54790 | −0.773952 | − | 0.633244i | \(-0.781723\pi\) | ||||
−0.773952 | + | 0.633244i | \(0.781723\pi\) | |||||||
\(954\) | 2.35493e7 | − | 1.78923e7i | 0.837735 | − | 0.636494i | ||||
\(955\) | 1.16577e7 | 0.413623 | ||||||||
\(956\) | −1.73464e7 | + | 3.00448e7i | −0.613853 | + | 1.06322i | ||||
\(957\) | −3.60049e6 | + | 1.21264e6i | −0.127081 | + | 0.0428007i | ||||
\(958\) | 3.24978e7 | + | 5.62879e7i | 1.14404 | + | 1.98153i | ||||
\(959\) | −155993. | − | 270187.i | −0.00547719 | − | 0.00948677i | ||||
\(960\) | 1.70402e7 | − | 5.73911e6i | 0.596757 | − | 0.200986i | ||||
\(961\) | 894119. | − | 1.54866e6i | 0.0312311 | − | 0.0540938i | ||||
\(962\) | 1.06501e8 | 3.71035 | ||||||||
\(963\) | 4.68590e7 | + | 1.96719e7i | 1.62827 | + | 0.683567i | ||||
\(964\) | −2.84303e7 | −0.985348 | ||||||||
\(965\) | −5.37302e6 | + | 9.30634e6i | −0.185738 | + | 0.321707i | ||||
\(966\) | 851554. | + | 750392.i | 0.0293609 | + | 0.0258729i | ||||
\(967\) | −137300. | − | 237810.i | −0.00472176 | − | 0.00817832i | 0.863655 | − | 0.504084i | \(-0.168170\pi\) |
−0.868377 | + | 0.495905i | \(0.834836\pi\) | |||||||
\(968\) | −2.17692e7 | − | 3.77054e7i | −0.746714 | − | 1.29335i | ||||
\(969\) | 1.76594e6 | − | 8.76868e6i | 0.0604180 | − | 0.300002i | ||||
\(970\) | −2.31681e7 | + | 4.01283e7i | −0.790607 | + | 1.36937i | ||||
\(971\) | 3.36920e7 | 1.14678 | 0.573388 | − | 0.819284i | \(-0.305629\pi\) | ||||
0.573388 | + | 0.819284i | \(0.305629\pi\) | |||||||
\(972\) | 5.45492e7 | + | 2.77138e7i | 1.85192 | + | 0.940872i | ||||
\(973\) | −496407. | −0.0168096 | ||||||||
\(974\) | −4.58185e7 | + | 7.93600e7i | −1.54755 | + | 2.68043i | ||||
\(975\) | 1.99001e6 | − | 9.88128e6i | 0.0670414 | − | 0.332891i | ||||
\(976\) | 2.55415e7 | + | 4.42391e7i | 0.858264 | + | 1.48656i | ||||
\(977\) | −6.93084e6 | − | 1.20046e7i | −0.232300 | − | 0.402356i | 0.726184 | − | 0.687500i | \(-0.241292\pi\) |
−0.958485 | + | 0.285144i | \(0.907959\pi\) | |||||||
\(978\) | −3.16102e7 | − | 2.78550e7i | −1.05677 | − | 0.931228i | ||||
\(979\) | 3.91293e6 | − | 6.77739e6i | 0.130480 | − | 0.225999i | ||||
\(980\) | 5.28432e7 | 1.75762 | ||||||||
\(981\) | −2.59021e7 | − | 1.08740e7i | −0.859334 | − | 0.360757i | ||||
\(982\) | 5.20238e7 | 1.72156 | ||||||||
\(983\) | 4.34952e6 | − | 7.53359e6i | 0.143568 | − | 0.248667i | −0.785270 | − | 0.619154i | \(-0.787476\pi\) |
0.928838 | + | 0.370487i | \(0.120809\pi\) | |||||||
\(984\) | −3.19356e7 | + | 1.07558e7i | −1.05145 | + | 0.354125i | ||||
\(985\) | −1.19010e7 | − | 2.06132e7i | −0.390835 | − | 0.676947i | ||||
\(986\) | −7.98116e6 | − | 1.38238e7i | −0.261441 | − | 0.452829i | ||||
\(987\) | −95059.2 | + | 32015.7i | −0.00310600 | + | 0.00104609i | ||||
\(988\) | 1.14678e7 | − | 1.98628e7i | 0.373756 | − | 0.647365i | ||||
\(989\) | −2.21676e7 | −0.720656 | ||||||||
\(990\) | 1.66935e7 | − | 1.26834e7i | 0.541328 | − | 0.411290i | ||||
\(991\) | −4.44501e7 | −1.43777 | −0.718884 | − | 0.695130i | \(-0.755347\pi\) | ||||
−0.718884 | + | 0.695130i | \(0.755347\pi\) | |||||||
\(992\) | −4.22235e6 | + | 7.31333e6i | −0.136231 | + | 0.235959i | ||||
\(993\) | −3.05050e7 | − | 2.68811e7i | −0.981743 | − | 0.865114i | ||||
\(994\) | 1247.35 | + | 2160.48i | 4.00426e−5 | + | 6.93559e-5i | ||||
\(995\) | 97620.2 | + | 169083.i | 0.00312595 | + | 0.00541430i | ||||
\(996\) | −2.11444e6 | + | 1.04991e7i | −0.0675377 | + | 0.335355i | ||||
\(997\) | 8.21072e6 | − | 1.42214e7i | 0.261603 | − | 0.453110i | −0.705065 | − | 0.709143i | \(-0.749082\pi\) |
0.966668 | + | 0.256033i | \(0.0824154\pi\) | |||||||
\(998\) | −6.42977e7 | −2.04347 | ||||||||
\(999\) | −3.12988e7 | + | 4.61244e7i | −0.992232 | + | 1.46223i |
(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 | 9.6.c.a.7.4 | yes | 8 | |
3.2 | odd | 2 | 27.6.c.a.19.1 | 8 | |||
4.3 | odd | 2 | 144.6.i.c.97.3 | 8 | |||
9.2 | odd | 6 | 81.6.a.d.1.4 | 4 | |||
9.4 | even | 3 | inner | 9.6.c.a.4.4 | ✓ | 8 | |
9.5 | odd | 6 | 27.6.c.a.10.1 | 8 | |||
9.7 | even | 3 | 81.6.a.c.1.1 | 4 | |||
12.11 | even | 2 | 432.6.i.c.289.2 | 8 | |||
36.23 | even | 6 | 432.6.i.c.145.2 | 8 | |||
36.31 | odd | 6 | 144.6.i.c.49.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9.6.c.a.4.4 | ✓ | 8 | 9.4 | even | 3 | inner | |
9.6.c.a.7.4 | yes | 8 | 1.1 | even | 1 | trivial | |
27.6.c.a.10.1 | 8 | 9.5 | odd | 6 | |||
27.6.c.a.19.1 | 8 | 3.2 | odd | 2 | |||
81.6.a.c.1.1 | 4 | 9.7 | even | 3 | |||
81.6.a.d.1.4 | 4 | 9.2 | odd | 6 | |||
144.6.i.c.49.3 | 8 | 36.31 | odd | 6 | |||
144.6.i.c.97.3 | 8 | 4.3 | odd | 2 | |||
432.6.i.c.145.2 | 8 | 36.23 | even | 6 | |||
432.6.i.c.289.2 | 8 | 12.11 | even | 2 |