Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [69,5,Mod(22,69)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(69, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("69.22");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 69 = 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 69.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: | \(7.13252745279\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 5598 x^{14} + 11369517 x^{12} + 11272666128 x^{10} + 5958872960073 x^{8} + \cdots + 13\!\cdots\!52 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{9} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 22.16 | ||
Root | \(19.1905i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 69.22 |
Dual form | 69.5.d.a.22.15 |
$q$-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 \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(47\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 7.44175 | 1.86044 | 0.930219 | − | 0.367006i | \(-0.119617\pi\) | ||||
0.930219 | + | 0.367006i | \(0.119617\pi\) | |||||||
\(3\) | −5.19615 | −0.577350 | ||||||||
\(4\) | 39.3796 | 2.46123 | ||||||||
\(5\) | 49.1084i | 1.96433i | 0.188010 | + | 0.982167i | \(0.439796\pi\) | ||||
−0.188010 | + | 0.982167i | \(0.560204\pi\) | |||||||
\(6\) | −38.6685 | −1.07412 | ||||||||
\(7\) | − | 11.1740i | − | 0.228041i | −0.993478 | − | 0.114021i | \(-0.963627\pi\) | ||
0.993478 | − | 0.114021i | \(-0.0363730\pi\) | |||||||
\(8\) | 173.985 | 2.71852 | ||||||||
\(9\) | 27.0000 | 0.333333 | ||||||||
\(10\) | 365.452i | 3.65452i | ||||||||
\(11\) | − | 158.229i | − | 1.30768i | −0.756633 | − | 0.653840i | \(-0.773157\pi\) | ||
0.756633 | − | 0.653840i | \(-0.226843\pi\) | |||||||
\(12\) | −204.623 | −1.42099 | ||||||||
\(13\) | 3.48595 | 0.0206269 | 0.0103135 | − | 0.999947i | \(-0.496717\pi\) | ||||
0.0103135 | + | 0.999947i | \(0.496717\pi\) | |||||||
\(14\) | − | 83.1543i | − | 0.424257i | ||||||
\(15\) | − | 255.174i | − | 1.13411i | ||||||
\(16\) | 664.681 | 2.59641 | ||||||||
\(17\) | − | 273.535i | − | 0.946487i | −0.880932 | − | 0.473244i | \(-0.843083\pi\) | ||
0.880932 | − | 0.473244i | \(-0.156917\pi\) | |||||||
\(18\) | 200.927 | 0.620146 | ||||||||
\(19\) | 195.603i | 0.541838i | 0.962602 | + | 0.270919i | \(0.0873275\pi\) | ||||
−0.962602 | + | 0.270919i | \(0.912672\pi\) | |||||||
\(20\) | 1933.87i | 4.83467i | ||||||||
\(21\) | 58.0619i | 0.131660i | ||||||||
\(22\) | − | 1177.50i | − | 2.43286i | ||||||
\(23\) | 415.728 | − | 327.126i | 0.785874 | − | 0.618386i | ||||
\(24\) | −904.054 | −1.56954 | ||||||||
\(25\) | −1786.63 | −2.85861 | ||||||||
\(26\) | 25.9416 | 0.0383751 | ||||||||
\(27\) | −140.296 | −0.192450 | ||||||||
\(28\) | − | 440.029i | − | 0.561261i | ||||||
\(29\) | −1097.57 | −1.30508 | −0.652540 | − | 0.757754i | \(-0.726297\pi\) | ||||
−0.652540 | + | 0.757754i | \(0.726297\pi\) | |||||||
\(30\) | − | 1898.94i | − | 2.10994i | ||||||
\(31\) | 362.469 | 0.377179 | 0.188589 | − | 0.982056i | \(-0.439608\pi\) | ||||
0.188589 | + | 0.982056i | \(0.439608\pi\) | |||||||
\(32\) | 2162.62 | 2.11194 | ||||||||
\(33\) | 822.183i | 0.754989i | ||||||||
\(34\) | − | 2035.58i | − | 1.76088i | ||||||
\(35\) | 548.738 | 0.447949 | ||||||||
\(36\) | 1063.25 | 0.820409 | ||||||||
\(37\) | 1385.65i | 1.01217i | 0.862485 | + | 0.506083i | \(0.168907\pi\) | ||||
−0.862485 | + | 0.506083i | \(0.831093\pi\) | |||||||
\(38\) | 1455.63i | 1.00806i | ||||||||
\(39\) | −18.1135 | −0.0119090 | ||||||||
\(40\) | 8544.13i | 5.34008i | ||||||||
\(41\) | 1118.33 | 0.665274 | 0.332637 | − | 0.943055i | \(-0.392062\pi\) | ||||
0.332637 | + | 0.943055i | \(0.392062\pi\) | |||||||
\(42\) | 432.082i | 0.244945i | ||||||||
\(43\) | − | 2501.85i | − | 1.35308i | −0.736404 | − | 0.676542i | \(-0.763478\pi\) | ||
0.736404 | − | 0.676542i | \(-0.236522\pi\) | |||||||
\(44\) | − | 6231.01i | − | 3.21850i | ||||||
\(45\) | 1325.93i | 0.654778i | ||||||||
\(46\) | 3093.74 | − | 2434.39i | 1.46207 | − | 1.15047i | ||||
\(47\) | −420.680 | −0.190439 | −0.0952196 | − | 0.995456i | \(-0.530355\pi\) | ||||
−0.0952196 | + | 0.995456i | \(0.530355\pi\) | |||||||
\(48\) | −3453.78 | −1.49904 | ||||||||
\(49\) | 2276.14 | 0.947997 | ||||||||
\(50\) | −13295.7 | −5.31826 | ||||||||
\(51\) | 1421.33i | 0.546455i | ||||||||
\(52\) | 137.276 | 0.0507676 | ||||||||
\(53\) | − | 2758.71i | − | 0.982097i | −0.871132 | − | 0.491049i | \(-0.836614\pi\) | ||
0.871132 | − | 0.491049i | \(-0.163386\pi\) | |||||||
\(54\) | −1044.05 | −0.358041 | ||||||||
\(55\) | 7770.38 | 2.56872 | ||||||||
\(56\) | − | 1944.12i | − | 0.619935i | ||||||
\(57\) | − | 1016.39i | − | 0.312830i | ||||||
\(58\) | −8167.86 | −2.42802 | ||||||||
\(59\) | −3196.59 | −0.918298 | −0.459149 | − | 0.888359i | \(-0.651846\pi\) | ||||
−0.459149 | + | 0.888359i | \(0.651846\pi\) | |||||||
\(60\) | − | 10048.7i | − | 2.79130i | ||||||
\(61\) | 3444.94i | 0.925809i | 0.886408 | + | 0.462905i | \(0.153193\pi\) | ||||
−0.886408 | + | 0.462905i | \(0.846807\pi\) | |||||||
\(62\) | 2697.40 | 0.701718 | ||||||||
\(63\) | − | 301.699i | − | 0.0760138i | ||||||
\(64\) | 5458.80 | 1.33271 | ||||||||
\(65\) | 171.189i | 0.0405182i | ||||||||
\(66\) | 6118.48i | 1.40461i | ||||||||
\(67\) | 5967.36i | 1.32933i | 0.747141 | + | 0.664665i | \(0.231426\pi\) | ||||
−0.747141 | + | 0.664665i | \(0.768574\pi\) | |||||||
\(68\) | − | 10771.7i | − | 2.32952i | ||||||
\(69\) | −2160.18 | + | 1699.80i | −0.453725 | + | 0.357025i | ||||
\(70\) | 4083.57 | 0.833382 | ||||||||
\(71\) | 3422.34 | 0.678900 | 0.339450 | − | 0.940624i | \(-0.389759\pi\) | ||||
0.339450 | + | 0.940624i | \(0.389759\pi\) | |||||||
\(72\) | 4697.60 | 0.906173 | ||||||||
\(73\) | −4879.75 | −0.915697 | −0.457849 | − | 0.889030i | \(-0.651380\pi\) | ||||
−0.457849 | + | 0.889030i | \(0.651380\pi\) | |||||||
\(74\) | 10311.7i | 1.88307i | ||||||||
\(75\) | 9283.60 | 1.65042 | ||||||||
\(76\) | 7702.79i | 1.33359i | ||||||||
\(77\) | −1768.06 | −0.298205 | ||||||||
\(78\) | −134.796 | −0.0221559 | ||||||||
\(79\) | 968.983i | 0.155261i | 0.996982 | + | 0.0776304i | \(0.0247354\pi\) | ||||
−0.996982 | + | 0.0776304i | \(0.975265\pi\) | |||||||
\(80\) | 32641.4i | 5.10021i | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | 8322.30 | 1.23770 | ||||||||
\(83\) | 6564.33i | 0.952872i | 0.879209 | + | 0.476436i | \(0.158072\pi\) | ||||
−0.879209 | + | 0.476436i | \(0.841928\pi\) | |||||||
\(84\) | 2286.46i | 0.324044i | ||||||||
\(85\) | 13432.8 | 1.85922 | ||||||||
\(86\) | − | 18618.2i | − | 2.51733i | ||||||
\(87\) | 5703.15 | 0.753488 | ||||||||
\(88\) | − | 27529.6i | − | 3.55495i | ||||||
\(89\) | − | 8072.73i | − | 1.01916i | −0.860425 | − | 0.509578i | \(-0.829802\pi\) | ||
0.860425 | − | 0.509578i | \(-0.170198\pi\) | |||||||
\(90\) | 9867.20i | 1.21817i | ||||||||
\(91\) | − | 38.9521i | − | 0.00470380i | ||||||
\(92\) | 16371.2 | − | 12882.1i | 1.93421 | − | 1.52199i | ||||
\(93\) | −1883.44 | −0.217764 | ||||||||
\(94\) | −3130.60 | −0.354300 | ||||||||
\(95\) | −9605.76 | −1.06435 | ||||||||
\(96\) | −11237.3 | −1.21933 | ||||||||
\(97\) | 9573.09i | 1.01744i | 0.860932 | + | 0.508720i | \(0.169881\pi\) | ||||
−0.860932 | + | 0.508720i | \(0.830119\pi\) | |||||||
\(98\) | 16938.5 | 1.76369 | ||||||||
\(99\) | − | 4272.19i | − | 0.435893i | ||||||
\(100\) | −70356.8 | −7.03568 | ||||||||
\(101\) | −7144.87 | −0.700409 | −0.350204 | − | 0.936673i | \(-0.613888\pi\) | ||||
−0.350204 | + | 0.936673i | \(0.613888\pi\) | |||||||
\(102\) | 10577.2i | 1.01664i | ||||||||
\(103\) | − | 7771.56i | − | 0.732544i | −0.930508 | − | 0.366272i | \(-0.880634\pi\) | ||
0.930508 | − | 0.366272i | \(-0.119366\pi\) | |||||||
\(104\) | 606.504 | 0.0560747 | ||||||||
\(105\) | −2851.33 | −0.258624 | ||||||||
\(106\) | − | 20529.6i | − | 1.82713i | ||||||
\(107\) | 16682.6i | 1.45713i | 0.684979 | + | 0.728563i | \(0.259811\pi\) | ||||
−0.684979 | + | 0.728563i | \(0.740189\pi\) | |||||||
\(108\) | −5524.81 | −0.473663 | ||||||||
\(109\) | 2073.27i | 0.174503i | 0.996186 | + | 0.0872517i | \(0.0278084\pi\) | ||||
−0.996186 | + | 0.0872517i | \(0.972192\pi\) | |||||||
\(110\) | 57825.2 | 4.77894 | ||||||||
\(111\) | − | 7200.07i | − | 0.584374i | ||||||
\(112\) | − | 7427.16i | − | 0.592089i | ||||||
\(113\) | 10792.9i | 0.845239i | 0.906307 | + | 0.422619i | \(0.138889\pi\) | ||||
−0.906307 | + | 0.422619i | \(0.861111\pi\) | |||||||
\(114\) | − | 7563.68i | − | 0.582001i | ||||||
\(115\) | 16064.6 | + | 20415.7i | 1.21472 | + | 1.54372i | ||||
\(116\) | −43222.0 | −3.21210 | ||||||||
\(117\) | 94.1207 | 0.00687565 | ||||||||
\(118\) | −23788.2 | −1.70843 | ||||||||
\(119\) | −3056.49 | −0.215838 | ||||||||
\(120\) | − | 44396.6i | − | 3.08310i | ||||||
\(121\) | −10395.5 | −0.710027 | ||||||||
\(122\) | 25636.3i | 1.72241i | ||||||||
\(123\) | −5810.99 | −0.384096 | ||||||||
\(124\) | 14273.9 | 0.928323 | ||||||||
\(125\) | − | 57045.7i | − | 3.65093i | ||||||
\(126\) | − | 2245.17i | − | 0.141419i | ||||||
\(127\) | 8526.40 | 0.528638 | 0.264319 | − | 0.964435i | \(-0.414853\pi\) | ||||
0.264319 | + | 0.964435i | \(0.414853\pi\) | |||||||
\(128\) | 6021.06 | 0.367497 | ||||||||
\(129\) | 13000.0i | 0.781204i | ||||||||
\(130\) | 1273.95i | 0.0753816i | ||||||||
\(131\) | −28518.1 | −1.66180 | −0.830900 | − | 0.556422i | \(-0.812174\pi\) | ||||
−0.830900 | + | 0.556422i | \(0.812174\pi\) | |||||||
\(132\) | 32377.3i | 1.85820i | ||||||||
\(133\) | 2185.68 | 0.123561 | ||||||||
\(134\) | 44407.6i | 2.47314i | ||||||||
\(135\) | − | 6889.71i | − | 0.378036i | ||||||
\(136\) | − | 47591.0i | − | 2.57304i | ||||||
\(137\) | − | 6175.76i | − | 0.329041i | −0.986374 | − | 0.164520i | \(-0.947392\pi\) | ||
0.986374 | − | 0.164520i | \(-0.0526076\pi\) | |||||||
\(138\) | −16075.5 | + | 12649.5i | −0.844126 | + | 0.664223i | ||||
\(139\) | 15175.2 | 0.785423 | 0.392711 | − | 0.919662i | \(-0.371537\pi\) | ||||
0.392711 | + | 0.919662i | \(0.371537\pi\) | |||||||
\(140\) | 21609.1 | 1.10250 | ||||||||
\(141\) | 2185.92 | 0.109950 | ||||||||
\(142\) | 25468.2 | 1.26305 | ||||||||
\(143\) | − | 551.580i | − | 0.0269734i | ||||||
\(144\) | 17946.4 | 0.865470 | ||||||||
\(145\) | − | 53900.0i | − | 2.56361i | ||||||
\(146\) | −36313.9 | −1.70360 | ||||||||
\(147\) | −11827.2 | −0.547326 | ||||||||
\(148\) | 54566.6i | 2.49117i | ||||||||
\(149\) | − | 21863.0i | − | 0.984777i | −0.870376 | − | 0.492389i | \(-0.836124\pi\) | ||
0.870376 | − | 0.492389i | \(-0.163876\pi\) | |||||||
\(150\) | 69086.2 | 3.07050 | ||||||||
\(151\) | −7673.52 | −0.336543 | −0.168272 | − | 0.985741i | \(-0.553819\pi\) | ||||
−0.168272 | + | 0.985741i | \(0.553819\pi\) | |||||||
\(152\) | 34032.1i | 1.47300i | ||||||||
\(153\) | − | 7385.44i | − | 0.315496i | ||||||
\(154\) | −13157.4 | −0.554792 | ||||||||
\(155\) | 17800.3i | 0.740905i | ||||||||
\(156\) | −713.304 | −0.0293107 | ||||||||
\(157\) | − | 3908.72i | − | 0.158575i | −0.996852 | − | 0.0792876i | \(-0.974735\pi\) | ||
0.996852 | − | 0.0792876i | \(-0.0252646\pi\) | |||||||
\(158\) | 7210.93i | 0.288853i | ||||||||
\(159\) | 14334.7i | 0.567014i | ||||||||
\(160\) | 106203.i | 4.14855i | ||||||||
\(161\) | −3655.32 | − | 4645.35i | −0.141018 | − | 0.179212i | ||||
\(162\) | 5425.03 | 0.206715 | ||||||||
\(163\) | −91.9597 | −0.00346117 | −0.00173058 | − | 0.999999i | \(-0.500551\pi\) | ||||
−0.00173058 | + | 0.999999i | \(0.500551\pi\) | |||||||
\(164\) | 44039.3 | 1.63739 | ||||||||
\(165\) | −40376.1 | −1.48305 | ||||||||
\(166\) | 48850.1i | 1.77276i | ||||||||
\(167\) | 3823.49 | 0.137097 | 0.0685484 | − | 0.997648i | \(-0.478163\pi\) | ||||
0.0685484 | + | 0.997648i | \(0.478163\pi\) | |||||||
\(168\) | 10101.9i | 0.357920i | ||||||||
\(169\) | −28548.8 | −0.999575 | ||||||||
\(170\) | 99963.8 | 3.45896 | ||||||||
\(171\) | 5281.29i | 0.180613i | ||||||||
\(172\) | − | 98522.0i | − | 3.33025i | ||||||
\(173\) | 9580.01 | 0.320091 | 0.160046 | − | 0.987110i | \(-0.448836\pi\) | ||||
0.160046 | + | 0.987110i | \(0.448836\pi\) | |||||||
\(174\) | 42441.4 | 1.40182 | ||||||||
\(175\) | 19963.9i | 0.651881i | ||||||||
\(176\) | − | 105172.i | − | 3.39527i | ||||||
\(177\) | 16610.0 | 0.530179 | ||||||||
\(178\) | − | 60075.2i | − | 1.89608i | ||||||
\(179\) | −27250.4 | −0.850484 | −0.425242 | − | 0.905080i | \(-0.639811\pi\) | ||||
−0.425242 | + | 0.905080i | \(0.639811\pi\) | |||||||
\(180\) | 52214.4i | 1.61156i | ||||||||
\(181\) | 60533.0i | 1.84772i | 0.382736 | + | 0.923858i | \(0.374982\pi\) | ||||
−0.382736 | + | 0.923858i | \(0.625018\pi\) | |||||||
\(182\) | − | 289.872i | − | 0.00875112i | ||||||
\(183\) | − | 17900.4i | − | 0.534516i | ||||||
\(184\) | 72330.5 | − | 56915.2i | 2.13642 | − | 1.68110i | ||||
\(185\) | −68047.2 | −1.98823 | ||||||||
\(186\) | −14016.1 | −0.405137 | ||||||||
\(187\) | −43281.2 | −1.23770 | ||||||||
\(188\) | −16566.2 | −0.468714 | ||||||||
\(189\) | 1567.67i | 0.0438866i | ||||||||
\(190\) | −71483.7 | −1.98016 | ||||||||
\(191\) | − | 35942.8i | − | 0.985246i | −0.870243 | − | 0.492623i | \(-0.836038\pi\) | ||
0.870243 | − | 0.492623i | \(-0.163962\pi\) | |||||||
\(192\) | −28364.8 | −0.769443 | ||||||||
\(193\) | 8323.05 | 0.223443 | 0.111722 | − | 0.993740i | \(-0.464363\pi\) | ||||
0.111722 | + | 0.993740i | \(0.464363\pi\) | |||||||
\(194\) | 71240.6i | 1.89288i | ||||||||
\(195\) | − | 889.526i | − | 0.0233932i | ||||||
\(196\) | 89633.6 | 2.33324 | ||||||||
\(197\) | 40003.9 | 1.03079 | 0.515395 | − | 0.856953i | \(-0.327645\pi\) | ||||
0.515395 | + | 0.856953i | \(0.327645\pi\) | |||||||
\(198\) | − | 31792.6i | − | 0.810952i | ||||||
\(199\) | − | 22691.3i | − | 0.572998i | −0.958081 | − | 0.286499i | \(-0.907509\pi\) | ||
0.958081 | − | 0.286499i | \(-0.0924914\pi\) | |||||||
\(200\) | −310847. | −7.77118 | ||||||||
\(201\) | − | 31007.3i | − | 0.767489i | ||||||
\(202\) | −53170.3 | −1.30307 | ||||||||
\(203\) | 12264.3i | 0.297612i | ||||||||
\(204\) | 55971.4i | 1.34495i | ||||||||
\(205\) | 54919.2i | 1.30682i | ||||||||
\(206\) | − | 57834.0i | − | 1.36285i | ||||||
\(207\) | 11224.6 | − | 8832.41i | 0.261958 | − | 0.206129i | ||||
\(208\) | 2317.05 | 0.0535560 | ||||||||
\(209\) | 30950.2 | 0.708550 | ||||||||
\(210\) | −21218.9 | −0.481153 | ||||||||
\(211\) | 41396.3 | 0.929816 | 0.464908 | − | 0.885359i | \(-0.346087\pi\) | ||||
0.464908 | + | 0.885359i | \(0.346087\pi\) | |||||||
\(212\) | − | 108637.i | − | 2.41716i | ||||||
\(213\) | −17783.0 | −0.391963 | ||||||||
\(214\) | 124148.i | 2.71089i | ||||||||
\(215\) | 122862. | 2.65791 | ||||||||
\(216\) | −24409.5 | −0.523179 | ||||||||
\(217\) | − | 4050.24i | − | 0.0860124i | ||||||
\(218\) | 15428.8i | 0.324653i | ||||||||
\(219\) | 25355.9 | 0.528678 | ||||||||
\(220\) | 305995. | 6.32220 | ||||||||
\(221\) | − | 953.529i | − | 0.0195231i | ||||||
\(222\) | − | 53581.1i | − | 1.08719i | ||||||
\(223\) | 30876.5 | 0.620895 | 0.310448 | − | 0.950590i | \(-0.399521\pi\) | ||||
0.310448 | + | 0.950590i | \(0.399521\pi\) | |||||||
\(224\) | − | 24165.2i | − | 0.481609i | ||||||
\(225\) | −48239.0 | −0.952869 | ||||||||
\(226\) | 80317.7i | 1.57251i | ||||||||
\(227\) | 17872.9i | 0.346852i | 0.984847 | + | 0.173426i | \(0.0554838\pi\) | ||||
−0.984847 | + | 0.173426i | \(0.944516\pi\) | |||||||
\(228\) | − | 40024.9i | − | 0.769946i | ||||||
\(229\) | − | 22033.5i | − | 0.420158i | −0.977684 | − | 0.210079i | \(-0.932628\pi\) | ||
0.977684 | − | 0.210079i | \(-0.0673721\pi\) | |||||||
\(230\) | 119549. | + | 151928.i | 2.25990 | + | 2.87199i | ||||
\(231\) | 9187.10 | 0.172169 | ||||||||
\(232\) | −190961. | −3.54789 | ||||||||
\(233\) | −38266.3 | −0.704862 | −0.352431 | − | 0.935838i | \(-0.614645\pi\) | ||||
−0.352431 | + | 0.935838i | \(0.614645\pi\) | |||||||
\(234\) | 700.423 | 0.0127917 | ||||||||
\(235\) | − | 20658.9i | − | 0.374086i | ||||||
\(236\) | −125881. | −2.26014 | ||||||||
\(237\) | − | 5034.98i | − | 0.0896399i | ||||||
\(238\) | −22745.6 | −0.401553 | ||||||||
\(239\) | 82469.8 | 1.44377 | 0.721887 | − | 0.692011i | \(-0.243275\pi\) | ||||
0.721887 | + | 0.692011i | \(0.243275\pi\) | |||||||
\(240\) | − | 169610.i | − | 2.94461i | ||||||
\(241\) | 43509.5i | 0.749117i | 0.927203 | + | 0.374558i | \(0.122206\pi\) | ||||
−0.927203 | + | 0.374558i | \(0.877794\pi\) | |||||||
\(242\) | −77360.7 | −1.32096 | ||||||||
\(243\) | −3788.00 | −0.0641500 | ||||||||
\(244\) | 135660.i | 2.27863i | ||||||||
\(245\) | 111778.i | 1.86218i | ||||||||
\(246\) | −43243.9 | −0.714587 | ||||||||
\(247\) | 681.864i | 0.0111765i | ||||||||
\(248\) | 63064.3 | 1.02537 | ||||||||
\(249\) | − | 34109.3i | − | 0.550141i | ||||||
\(250\) | − | 424520.i | − | 6.79232i | ||||||
\(251\) | − | 9819.06i | − | 0.155856i | −0.996959 | − | 0.0779278i | \(-0.975170\pi\) | ||
0.996959 | − | 0.0779278i | \(-0.0248304\pi\) | |||||||
\(252\) | − | 11880.8i | − | 0.187087i | ||||||
\(253\) | −51761.0 | − | 65780.3i | −0.808651 | − | 1.02767i | ||||
\(254\) | 63451.3 | 0.983497 | ||||||||
\(255\) | −69799.1 | −1.07342 | ||||||||
\(256\) | −42533.6 | −0.649011 | ||||||||
\(257\) | 25987.7 | 0.393461 | 0.196731 | − | 0.980458i | \(-0.436968\pi\) | ||||
0.196731 | + | 0.980458i | \(0.436968\pi\) | |||||||
\(258\) | 96742.8i | 1.45338i | ||||||||
\(259\) | 15483.3 | 0.230816 | ||||||||
\(260\) | 6741.37i | 0.0997245i | ||||||||
\(261\) | −29634.5 | −0.435027 | ||||||||
\(262\) | −212225. | −3.09167 | ||||||||
\(263\) | − | 61615.4i | − | 0.890795i | −0.895333 | − | 0.445398i | \(-0.853062\pi\) | ||
0.895333 | − | 0.445398i | \(-0.146938\pi\) | |||||||
\(264\) | 143048.i | 2.05245i | ||||||||
\(265\) | 135476. | 1.92917 | ||||||||
\(266\) | 16265.3 | 0.229878 | ||||||||
\(267\) | 41947.1i | 0.588410i | ||||||||
\(268\) | 234993.i | 3.27178i | ||||||||
\(269\) | −37018.9 | −0.511587 | −0.255793 | − | 0.966731i | \(-0.582337\pi\) | ||||
−0.255793 | + | 0.966731i | \(0.582337\pi\) | |||||||
\(270\) | − | 51271.5i | − | 0.703313i | ||||||
\(271\) | 52584.0 | 0.716003 | 0.358002 | − | 0.933721i | \(-0.383458\pi\) | ||||
0.358002 | + | 0.933721i | \(0.383458\pi\) | |||||||
\(272\) | − | 181813.i | − | 2.45747i | ||||||
\(273\) | 202.401i | 0.00271574i | ||||||||
\(274\) | − | 45958.5i | − | 0.612159i | ||||||
\(275\) | 282697.i | 3.73814i | ||||||||
\(276\) | −85067.2 | + | 66937.4i | −1.11672 | + | 0.878720i | ||||
\(277\) | −79595.0 | −1.03735 | −0.518676 | − | 0.854971i | \(-0.673575\pi\) | ||||
−0.518676 | + | 0.854971i | \(0.673575\pi\) | |||||||
\(278\) | 112930. | 1.46123 | ||||||||
\(279\) | 9786.66 | 0.125726 | ||||||||
\(280\) | 95472.3 | 1.21776 | ||||||||
\(281\) | − | 49952.4i | − | 0.632621i | −0.948656 | − | 0.316310i | \(-0.897556\pi\) | ||
0.948656 | − | 0.316310i | \(-0.102444\pi\) | |||||||
\(282\) | 16267.1 | 0.204555 | ||||||||
\(283\) | 37069.8i | 0.462858i | 0.972852 | + | 0.231429i | \(0.0743400\pi\) | ||||
−0.972852 | + | 0.231429i | \(0.925660\pi\) | |||||||
\(284\) | 134770. | 1.67093 | ||||||||
\(285\) | 49913.0 | 0.614503 | ||||||||
\(286\) | − | 4104.72i | − | 0.0501824i | ||||||
\(287\) | − | 12496.2i | − | 0.151710i | ||||||
\(288\) | 58390.8 | 0.703979 | ||||||||
\(289\) | 8699.71 | 0.104162 | ||||||||
\(290\) | − | 401110.i | − | 4.76944i | ||||||
\(291\) | − | 49743.3i | − | 0.587419i | ||||||
\(292\) | −192163. | −2.25374 | ||||||||
\(293\) | 40120.2i | 0.467334i | 0.972317 | + | 0.233667i | \(0.0750726\pi\) | ||||
−0.972317 | + | 0.233667i | \(0.924927\pi\) | |||||||
\(294\) | −88014.9 | −1.01827 | ||||||||
\(295\) | − | 156979.i | − | 1.80384i | ||||||
\(296\) | 241084.i | 2.75159i | ||||||||
\(297\) | 22199.0i | 0.251663i | ||||||||
\(298\) | − | 162699.i | − | 1.83212i | ||||||
\(299\) | 1449.21 | − | 1140.35i | 0.0162102 | − | 0.0127554i | ||||
\(300\) | 365585. | 4.06205 | ||||||||
\(301\) | −27955.8 | −0.308559 | ||||||||
\(302\) | −57104.4 | −0.626117 | ||||||||
\(303\) | 37125.8 | 0.404381 | ||||||||
\(304\) | 130014.i | 1.40683i | ||||||||
\(305\) | −169175. | −1.81860 | ||||||||
\(306\) | − | 54960.6i | − | 0.586960i | ||||||
\(307\) | 57405.8 | 0.609087 | 0.304543 | − | 0.952499i | \(-0.401496\pi\) | ||||
0.304543 | + | 0.952499i | \(0.401496\pi\) | |||||||
\(308\) | −69625.5 | −0.733950 | ||||||||
\(309\) | 40382.2i | 0.422934i | ||||||||
\(310\) | 132465.i | 1.37841i | ||||||||
\(311\) | 84357.4 | 0.872173 | 0.436086 | − | 0.899905i | \(-0.356364\pi\) | ||||
0.436086 | + | 0.899905i | \(0.356364\pi\) | |||||||
\(312\) | −3151.49 | −0.0323748 | ||||||||
\(313\) | 48772.2i | 0.497833i | 0.968525 | + | 0.248916i | \(0.0800744\pi\) | ||||
−0.968525 | + | 0.248916i | \(0.919926\pi\) | |||||||
\(314\) | − | 29087.7i | − | 0.295019i | ||||||
\(315\) | 14815.9 | 0.149316 | ||||||||
\(316\) | 38158.2i | 0.382132i | ||||||||
\(317\) | 175587. | 1.74733 | 0.873664 | − | 0.486531i | \(-0.161738\pi\) | ||||
0.873664 | + | 0.486531i | \(0.161738\pi\) | |||||||
\(318\) | 106675.i | 1.05489i | ||||||||
\(319\) | 173668.i | 1.70663i | ||||||||
\(320\) | 268073.i | 2.61790i | ||||||||
\(321\) | − | 86685.5i | − | 0.841272i | ||||||
\(322\) | −27202.0 | − | 34569.5i | −0.262354 | − | 0.333412i | ||||
\(323\) | 53504.3 | 0.512842 | ||||||||
\(324\) | 28707.7 | 0.273470 | ||||||||
\(325\) | −6228.11 | −0.0589643 | ||||||||
\(326\) | −684.341 | −0.00643928 | ||||||||
\(327\) | − | 10773.1i | − | 0.100750i | ||||||
\(328\) | 194572. | 1.80856 | ||||||||
\(329\) | 4700.69i | 0.0434280i | ||||||||
\(330\) | −300469. | −2.75912 | ||||||||
\(331\) | −86667.7 | −0.791045 | −0.395523 | − | 0.918456i | \(-0.629436\pi\) | ||||
−0.395523 | + | 0.918456i | \(0.629436\pi\) | |||||||
\(332\) | 258501.i | 2.34523i | ||||||||
\(333\) | 37412.7i | 0.337389i | ||||||||
\(334\) | 28453.5 | 0.255060 | ||||||||
\(335\) | −293047. | −2.61125 | ||||||||
\(336\) | 38592.7i | 0.341843i | ||||||||
\(337\) | − | 146348.i | − | 1.28862i | −0.764762 | − | 0.644312i | \(-0.777144\pi\) | ||
0.764762 | − | 0.644312i | \(-0.222856\pi\) | |||||||
\(338\) | −212453. | −1.85965 | ||||||||
\(339\) | − | 56081.3i | − | 0.487999i | ||||||
\(340\) | 528980. | 4.57595 | ||||||||
\(341\) | − | 57353.2i | − | 0.493229i | ||||||
\(342\) | 39302.0i | 0.336018i | ||||||||
\(343\) | − | 52262.5i | − | 0.444224i | ||||||
\(344\) | − | 435286.i | − | 3.67839i | ||||||
\(345\) | −83474.3 | − | 106083.i | −0.701317 | − | 0.891267i | ||||
\(346\) | 71292.0 | 0.595510 | ||||||||
\(347\) | 172085. | 1.42917 | 0.714586 | − | 0.699548i | \(-0.246615\pi\) | ||||
0.714586 | + | 0.699548i | \(0.246615\pi\) | |||||||
\(348\) | 224588. | 1.85451 | ||||||||
\(349\) | −68489.2 | −0.562304 | −0.281152 | − | 0.959663i | \(-0.590717\pi\) | ||||
−0.281152 | + | 0.959663i | \(0.590717\pi\) | |||||||
\(350\) | 148566.i | 1.21278i | ||||||||
\(351\) | −489.066 | −0.00396966 | ||||||||
\(352\) | − | 342190.i | − | 2.76174i | ||||||
\(353\) | −156170. | −1.25328 | −0.626641 | − | 0.779308i | \(-0.715571\pi\) | ||||
−0.626641 | + | 0.779308i | \(0.715571\pi\) | |||||||
\(354\) | 123607. | 0.986365 | ||||||||
\(355\) | 168065.i | 1.33359i | ||||||||
\(356\) | − | 317901.i | − | 2.50837i | ||||||
\(357\) | 15882.0 | 0.124614 | ||||||||
\(358\) | −202790. | −1.58227 | ||||||||
\(359\) | 60879.0i | 0.472366i | 0.971709 | + | 0.236183i | \(0.0758965\pi\) | ||||
−0.971709 | + | 0.236183i | \(0.924103\pi\) | |||||||
\(360\) | 230692.i | 1.78003i | ||||||||
\(361\) | 92060.3 | 0.706412 | ||||||||
\(362\) | 450471.i | 3.43756i | ||||||||
\(363\) | 54016.6 | 0.409934 | ||||||||
\(364\) | − | 1533.92i | − | 0.0115771i | ||||||
\(365\) | − | 239636.i | − | 1.79874i | ||||||
\(366\) | − | 133210.i | − | 0.994434i | ||||||
\(367\) | 189642.i | 1.40800i | 0.710201 | + | 0.703999i | \(0.248604\pi\) | ||||
−0.710201 | + | 0.703999i | \(0.751396\pi\) | |||||||
\(368\) | 276326. | − | 217435.i | 2.04045 | − | 1.60558i | ||||
\(369\) | 30194.8 | 0.221758 | ||||||||
\(370\) | −506390. | −3.69898 | ||||||||
\(371\) | −30825.9 | −0.223959 | ||||||||
\(372\) | −74169.3 | −0.535967 | ||||||||
\(373\) | 27864.3i | 0.200277i | 0.994974 | + | 0.100138i | \(0.0319285\pi\) | ||||
−0.994974 | + | 0.100138i | \(0.968071\pi\) | |||||||
\(374\) | −322088. | −2.30267 | ||||||||
\(375\) | 296418.i | 2.10786i | ||||||||
\(376\) | −73192.2 | −0.517713 | ||||||||
\(377\) | −3826.09 | −0.0269198 | ||||||||
\(378\) | 11666.2i | 0.0816482i | ||||||||
\(379\) | − | 43587.9i | − | 0.303450i | −0.988423 | − | 0.151725i | \(-0.951517\pi\) | ||
0.988423 | − | 0.151725i | \(-0.0484829\pi\) | |||||||
\(380\) | −378271. | −2.61961 | ||||||||
\(381\) | −44304.5 | −0.305209 | ||||||||
\(382\) | − | 267477.i | − | 1.83299i | ||||||
\(383\) | − | 240133.i | − | 1.63702i | −0.574490 | − | 0.818512i | \(-0.694800\pi\) | ||
0.574490 | − | 0.818512i | \(-0.305200\pi\) | |||||||
\(384\) | −31286.4 | −0.212174 | ||||||||
\(385\) | − | 86826.4i | − | 0.585774i | ||||||
\(386\) | 61938.0 | 0.415703 | ||||||||
\(387\) | − | 67550.0i | − | 0.451028i | ||||||
\(388\) | 376985.i | 2.50415i | ||||||||
\(389\) | − | 187297.i | − | 1.23775i | −0.785491 | − | 0.618873i | \(-0.787590\pi\) | ||
0.785491 | − | 0.618873i | \(-0.212410\pi\) | |||||||
\(390\) | − | 6619.63i | − | 0.0435216i | ||||||
\(391\) | −89480.4 | − | 113716.i | −0.585295 | − | 0.743820i | ||||
\(392\) | 396015. | 2.57715 | ||||||||
\(393\) | 148185. | 0.959441 | ||||||||
\(394\) | 297699. | 1.91772 | ||||||||
\(395\) | −47585.1 | −0.304984 | ||||||||
\(396\) | − | 168237.i | − | 1.07283i | ||||||
\(397\) | 145407. | 0.922580 | 0.461290 | − | 0.887249i | \(-0.347387\pi\) | ||||
0.461290 | + | 0.887249i | \(0.347387\pi\) | |||||||
\(398\) | − | 168863.i | − | 1.06603i | ||||||
\(399\) | −11357.1 | −0.0713382 | ||||||||
\(400\) | −1.18754e6 | −7.42212 | ||||||||
\(401\) | − | 159568.i | − | 0.992330i | −0.868228 | − | 0.496165i | \(-0.834741\pi\) | ||
0.868228 | − | 0.496165i | \(-0.165259\pi\) | |||||||
\(402\) | − | 230749.i | − | 1.42787i | ||||||
\(403\) | 1263.55 | 0.00778005 | ||||||||
\(404\) | −281362. | −1.72386 | ||||||||
\(405\) | 35800.0i | 0.218259i | ||||||||
\(406\) | 91267.9i | 0.553689i | ||||||||
\(407\) | 219251. | 1.32359 | ||||||||
\(408\) | 247290.i | 1.48555i | ||||||||
\(409\) | −150045. | −0.896963 | −0.448482 | − | 0.893792i | \(-0.648035\pi\) | ||||
−0.448482 | + | 0.893792i | \(0.648035\pi\) | |||||||
\(410\) | 408695.i | 2.43126i | ||||||||
\(411\) | 32090.2i | 0.189972i | ||||||||
\(412\) | − | 306041.i | − | 1.80296i | ||||||
\(413\) | 35718.8i | 0.209410i | ||||||||
\(414\) | 83531.0 | − | 65728.6i | 0.487357 | − | 0.383490i | ||||
\(415\) | −322364. | −1.87176 | ||||||||
\(416\) | 7538.80 | 0.0435628 | ||||||||
\(417\) | −78852.4 | −0.453464 | ||||||||
\(418\) | 230324. | 1.31821 | ||||||||
\(419\) | − | 242660.i | − | 1.38220i | −0.722759 | − | 0.691100i | \(-0.757127\pi\) | ||
0.722759 | − | 0.691100i | \(-0.242873\pi\) | |||||||
\(420\) | −112284. | −0.636531 | ||||||||
\(421\) | − | 132304.i | − | 0.746465i | −0.927738 | − | 0.373232i | \(-0.878249\pi\) | ||
0.927738 | − | 0.373232i | \(-0.121751\pi\) | |||||||
\(422\) | 308061. | 1.72986 | ||||||||
\(423\) | −11358.4 | −0.0634798 | ||||||||
\(424\) | − | 479975.i | − | 2.66985i | ||||||
\(425\) | 488706.i | 2.70564i | ||||||||
\(426\) | −132336. | −0.729223 | ||||||||
\(427\) | 38493.8 | 0.211123 | ||||||||
\(428\) | 656956.i | 3.58631i | ||||||||
\(429\) | 2866.09i | 0.0155731i | ||||||||
\(430\) | 914307. | 4.94487 | ||||||||
\(431\) | 283741.i | 1.52745i | 0.645540 | + | 0.763726i | \(0.276632\pi\) | ||||
−0.645540 | + | 0.763726i | \(0.723368\pi\) | |||||||
\(432\) | −93252.1 | −0.499679 | ||||||||
\(433\) | 74552.8i | 0.397638i | 0.980036 | + | 0.198819i | \(0.0637106\pi\) | ||||
−0.980036 | + | 0.198819i | \(0.936289\pi\) | |||||||
\(434\) | − | 30140.9i | − | 0.160021i | ||||||
\(435\) | 280072.i | 1.48010i | ||||||||
\(436\) | 81644.8i | 0.429492i | ||||||||
\(437\) | 63987.0 | + | 81317.7i | 0.335065 | + | 0.425816i | ||||
\(438\) | 188692. | 0.983572 | ||||||||
\(439\) | −252584. | −1.31062 | −0.655310 | − | 0.755360i | \(-0.727462\pi\) | ||||
−0.655310 | + | 0.755360i | \(0.727462\pi\) | |||||||
\(440\) | 1.35193e6 | 6.98312 | ||||||||
\(441\) | 61455.8 | 0.315999 | ||||||||
\(442\) | − | 7095.93i | − | 0.0363216i | ||||||
\(443\) | 292478. | 1.49034 | 0.745172 | − | 0.666872i | \(-0.232367\pi\) | ||||
0.745172 | + | 0.666872i | \(0.232367\pi\) | |||||||
\(444\) | − | 283536.i | − | 1.43828i | ||||||
\(445\) | 396439. | 2.00196 | ||||||||
\(446\) | 229775. | 1.15514 | ||||||||
\(447\) | 113604.i | 0.568561i | ||||||||
\(448\) | − | 60996.8i | − | 0.303914i | ||||||
\(449\) | −144789. | −0.718195 | −0.359097 | − | 0.933300i | \(-0.616915\pi\) | ||||
−0.359097 | + | 0.933300i | \(0.616915\pi\) | |||||||
\(450\) | −358983. | −1.77275 | ||||||||
\(451\) | − | 176952.i | − | 0.869966i | ||||||
\(452\) | 425019.i | 2.08032i | ||||||||
\(453\) | 39872.8 | 0.194303 | ||||||||
\(454\) | 133006.i | 0.645297i | ||||||||
\(455\) | 1912.87 | 0.00923983 | ||||||||
\(456\) | − | 176836.i | − | 0.850435i | ||||||
\(457\) | 298954.i | 1.43144i | 0.698388 | + | 0.715719i | \(0.253901\pi\) | ||||
−0.698388 | + | 0.715719i | \(0.746099\pi\) | |||||||
\(458\) | − | 163968.i | − | 0.781677i | ||||||
\(459\) | 38375.9i | 0.182152i | ||||||||
\(460\) | 632619. | + | 803962.i | 2.98969 | + | 3.79944i | ||||
\(461\) | −156956. | −0.738543 | −0.369271 | − | 0.929322i | \(-0.620393\pi\) | ||||
−0.369271 | + | 0.929322i | \(0.620393\pi\) | |||||||
\(462\) | 68368.1 | 0.320309 | ||||||||
\(463\) | 197172. | 0.919776 | 0.459888 | − | 0.887977i | \(-0.347890\pi\) | ||||
0.459888 | + | 0.887977i | \(0.347890\pi\) | |||||||
\(464\) | −729535. | −3.38852 | ||||||||
\(465\) | − | 92492.8i | − | 0.427762i | ||||||
\(466\) | −284768. | −1.31135 | ||||||||
\(467\) | − | 83794.7i | − | 0.384223i | −0.981373 | − | 0.192111i | \(-0.938467\pi\) | ||
0.981373 | − | 0.192111i | \(-0.0615335\pi\) | |||||||
\(468\) | 3706.44 | 0.0169225 | ||||||||
\(469\) | 66679.5 | 0.303142 | ||||||||
\(470\) | − | 153738.i | − | 0.695964i | ||||||
\(471\) | 20310.3i | 0.0915535i | ||||||||
\(472\) | −556160. | −2.49641 | ||||||||
\(473\) | −395866. | −1.76940 | ||||||||
\(474\) | − | 37469.1i | − | 0.166769i | ||||||
\(475\) | − | 349471.i | − | 1.54890i | ||||||
\(476\) | −120363. | −0.531227 | ||||||||
\(477\) | − | 74485.2i | − | 0.327366i | ||||||
\(478\) | 613719. | 2.68605 | ||||||||
\(479\) | − | 28862.5i | − | 0.125795i | −0.998020 | − | 0.0628975i | \(-0.979966\pi\) | ||
0.998020 | − | 0.0628975i | \(-0.0200341\pi\) | |||||||
\(480\) | − | 551846.i | − | 2.39517i | ||||||
\(481\) | 4830.33i | 0.0208779i | ||||||||
\(482\) | 323786.i | 1.39368i | ||||||||
\(483\) | 18993.6 | + | 24137.9i | 0.0814166 | + | 0.103468i | ||||
\(484\) | −409371. | −1.74754 | ||||||||
\(485\) | −470119. | −1.99859 | ||||||||
\(486\) | −28189.3 | −0.119347 | ||||||||
\(487\) | 35373.9 | 0.149150 | 0.0745752 | − | 0.997215i | \(-0.476240\pi\) | ||||
0.0745752 | + | 0.997215i | \(0.476240\pi\) | |||||||
\(488\) | 599368.i | 2.51683i | ||||||||
\(489\) | 477.837 | 0.00199831 | ||||||||
\(490\) | 831820.i | 3.46447i | ||||||||
\(491\) | −224491. | −0.931183 | −0.465592 | − | 0.885000i | \(-0.654158\pi\) | ||||
−0.465592 | + | 0.885000i | \(0.654158\pi\) | |||||||
\(492\) | −228835. | −0.945348 | ||||||||
\(493\) | 300224.i | 1.23524i | ||||||||
\(494\) | 5074.26i | 0.0207931i | ||||||||
\(495\) | 209800. | 0.856240 | ||||||||
\(496\) | 240926. | 0.979311 | ||||||||
\(497\) | − | 38241.3i | − | 0.154817i | ||||||
\(498\) | − | 253833.i | − | 1.02350i | ||||||
\(499\) | −59361.4 | −0.238398 | −0.119199 | − | 0.992870i | \(-0.538033\pi\) | ||||
−0.119199 | + | 0.992870i | \(0.538033\pi\) | |||||||
\(500\) | − | 2.24644e6i | − | 8.98576i | ||||||
\(501\) | −19867.4 | −0.0791528 | ||||||||
\(502\) | − | 73071.0i | − | 0.289960i | ||||||
\(503\) | − | 267762.i | − | 1.05831i | −0.848526 | − | 0.529154i | \(-0.822509\pi\) | ||
0.848526 | − | 0.529154i | \(-0.177491\pi\) | |||||||
\(504\) | − | 52491.1i | − | 0.206645i | ||||||
\(505\) | − | 350873.i | − | 1.37584i | ||||||
\(506\) | −385192. | − | 489520.i | −1.50444 | − | 1.91192i | ||||
\(507\) | 148344. | 0.577105 | ||||||||
\(508\) | 335766. | 1.30110 | ||||||||
\(509\) | 462239. | 1.78415 | 0.892075 | − | 0.451887i | \(-0.149249\pi\) | ||||
0.892075 | + | 0.451887i | \(0.149249\pi\) | |||||||
\(510\) | −519427. | −1.99703 | ||||||||
\(511\) | 54526.5i | 0.208817i | ||||||||
\(512\) | −412861. | −1.57494 | ||||||||
\(513\) | − | 27442.4i | − | 0.104277i | ||||||
\(514\) | 193394. | 0.732010 | ||||||||
\(515\) | 381648. | 1.43896 | ||||||||
\(516\) | 511935.i | 1.92272i | ||||||||
\(517\) | 66563.9i | 0.249034i | ||||||||
\(518\) | 115223. | 0.429418 | ||||||||
\(519\) | −49779.2 | −0.184805 | ||||||||
\(520\) | 29784.4i | 0.110150i | ||||||||
\(521\) | 467093.i | 1.72079i | 0.509629 | + | 0.860394i | \(0.329783\pi\) | ||||
−0.509629 | + | 0.860394i | \(0.670217\pi\) | |||||||
\(522\) | −220532. | −0.809340 | ||||||||
\(523\) | − | 133920.i | − | 0.489600i | −0.969574 | − | 0.244800i | \(-0.921278\pi\) | ||
0.969574 | − | 0.244800i | \(-0.0787223\pi\) | |||||||
\(524\) | −1.12303e6 | −4.09007 | ||||||||
\(525\) | − | 103735.i | − | 0.376364i | ||||||
\(526\) | − | 458527.i | − | 1.65727i | ||||||
\(527\) | − | 99147.9i | − | 0.356995i | ||||||
\(528\) | 546489.i | 1.96026i | ||||||||
\(529\) | 65817.8 | − | 271991.i | 0.235197 | − | 0.971948i | ||||
\(530\) | 1.00818e6 | 3.58909 | ||||||||
\(531\) | −86308.0 | −0.306099 | ||||||||
\(532\) | 86071.2 | 0.304113 | ||||||||
\(533\) | 3898.43 | 0.0137226 | ||||||||
\(534\) | 312160.i | 1.09470i | ||||||||
\(535\) | −819256. | −2.86228 | ||||||||
\(536\) | 1.03823e6i | 3.61381i | ||||||||
\(537\) | 141597. | 0.491027 | ||||||||
\(538\) | −275486. | −0.951775 | ||||||||
\(539\) | − | 360152.i | − | 1.23968i | ||||||
\(540\) | − | 271314.i | − | 0.930433i | ||||||
\(541\) | 273776. | 0.935406 | 0.467703 | − | 0.883886i | \(-0.345082\pi\) | ||||
0.467703 | + | 0.883886i | \(0.345082\pi\) | |||||||
\(542\) | 391317. | 1.33208 | ||||||||
\(543\) | − | 314539.i | − | 1.06678i | ||||||
\(544\) | − | 591552.i | − | 1.99892i | ||||||
\(545\) | −101815. | −0.342783 | ||||||||
\(546\) | 1506.22i | 0.00505246i | ||||||||
\(547\) | 217018. | 0.725305 | 0.362652 | − | 0.931925i | \(-0.381871\pi\) | ||||
0.362652 | + | 0.931925i | \(0.381871\pi\) | |||||||
\(548\) | − | 243199.i | − | 0.809843i | ||||||
\(549\) | 93013.3i | 0.308603i | ||||||||
\(550\) | 2.10376e6i | 6.95458i | ||||||||
\(551\) | − | 214689.i | − | 0.707142i | ||||||
\(552\) | −375840. | + | 295740.i | −1.23346 | + | 0.970581i | ||||
\(553\) | 10827.4 | 0.0354059 | ||||||||
\(554\) | −592326. | −1.92993 | ||||||||
\(555\) | 353584. | 1.14791 | ||||||||
\(556\) | 597592. | 1.93310 | ||||||||
\(557\) | − | 65560.8i | − | 0.211317i | −0.994402 | − | 0.105658i | \(-0.966305\pi\) | ||
0.994402 | − | 0.105658i | \(-0.0336950\pi\) | |||||||
\(558\) | 72829.9 | 0.233906 | ||||||||
\(559\) | − | 8721.34i | − | 0.0279100i | ||||||
\(560\) | 364736. | 1.16306 | ||||||||
\(561\) | 224896. | 0.714588 | ||||||||
\(562\) | − | 371733.i | − | 1.17695i | ||||||
\(563\) | − | 56808.8i | − | 0.179225i | −0.995977 | − | 0.0896126i | \(-0.971437\pi\) | ||
0.995977 | − | 0.0896126i | \(-0.0285629\pi\) | |||||||
\(564\) | 86080.7 | 0.270612 | ||||||||
\(565\) | −530019. | −1.66033 | ||||||||
\(566\) | 275864.i | 0.861118i | ||||||||
\(567\) | − | 8145.86i | − | 0.0253379i | ||||||
\(568\) | 595436. | 1.84560 | ||||||||
\(569\) | 227173.i | 0.701668i | 0.936438 | + | 0.350834i | \(0.114102\pi\) | ||||
−0.936438 | + | 0.350834i | \(0.885898\pi\) | |||||||
\(570\) | 371440. | 1.14324 | ||||||||
\(571\) | 314063.i | 0.963261i | 0.876374 | + | 0.481631i | \(0.159955\pi\) | ||||
−0.876374 | + | 0.481631i | \(0.840045\pi\) | |||||||
\(572\) | − | 21721.0i | − | 0.0663877i | ||||||
\(573\) | 186764.i | 0.568832i | ||||||||
\(574\) | − | 92993.6i | − | 0.282247i | ||||||
\(575\) | −742751. | + | 584454.i | −2.24651 | + | 1.76772i | ||||
\(576\) | 147388. | 0.444238 | ||||||||
\(577\) | −75780.9 | −0.227619 | −0.113809 | − | 0.993503i | \(-0.536305\pi\) | ||||
−0.113809 | + | 0.993503i | \(0.536305\pi\) | |||||||
\(578\) | 64741.0 | 0.193787 | ||||||||
\(579\) | −43247.8 | −0.129005 | ||||||||
\(580\) | − | 2.12256e6i | − | 6.30963i | ||||||
\(581\) | 73350.0 | 0.217294 | ||||||||
\(582\) | − | 370177.i | − | 1.09286i | ||||||
\(583\) | −436509. | −1.28427 | ||||||||
\(584\) | −849005. | −2.48934 | ||||||||
\(585\) | 4622.11i | 0.0135061i | ||||||||
\(586\) | 298564.i | 0.869446i | ||||||||
\(587\) | 467136. | 1.35571 | 0.677856 | − | 0.735195i | \(-0.262909\pi\) | ||||
0.677856 | + | 0.735195i | \(0.262909\pi\) | |||||||
\(588\) | −465750. | −1.34709 | ||||||||
\(589\) | 70900.2i | 0.204370i | ||||||||
\(590\) | − | 1.16820e6i | − | 3.35594i | ||||||
\(591\) | −207866. | −0.595126 | ||||||||
\(592\) | 921018.i | 2.62800i | ||||||||
\(593\) | 523323. | 1.48820 | 0.744098 | − | 0.668070i | \(-0.232879\pi\) | ||||
0.744098 | + | 0.668070i | \(0.232879\pi\) | |||||||
\(594\) | 165199.i | 0.468203i | ||||||||
\(595\) | − | 150099.i | − | 0.423978i | ||||||
\(596\) | − | 860958.i | − | 2.42376i | ||||||
\(597\) | 117907.i | 0.330820i | ||||||||
\(598\) | 10784.6 | − | 8486.17i | 0.0301580 | − | 0.0237306i | ||||
\(599\) | −597662. | −1.66572 | −0.832860 | − | 0.553484i | \(-0.813298\pi\) | ||||
−0.832860 | + | 0.553484i | \(0.813298\pi\) | |||||||
\(600\) | 1.61521e6 | 4.48669 | ||||||||
\(601\) | −699830. | −1.93751 | −0.968754 | − | 0.248025i | \(-0.920218\pi\) | ||||
−0.968754 | + | 0.248025i | \(0.920218\pi\) | |||||||
\(602\) | −208040. | −0.574055 | ||||||||
\(603\) | 161119.i | 0.443110i | ||||||||
\(604\) | −302180. | −0.828309 | ||||||||
\(605\) | − | 510506.i | − | 1.39473i | ||||||
\(606\) | 276281. | 0.752326 | ||||||||
\(607\) | −19307.5 | −0.0524021 | −0.0262010 | − | 0.999657i | \(-0.508341\pi\) | ||||
−0.0262010 | + | 0.999657i | \(0.508341\pi\) | |||||||
\(608\) | 423016.i | 1.14433i | ||||||||
\(609\) | − | 63727.2i | − | 0.171827i | ||||||
\(610\) | −1.25896e6 | −3.38339 | ||||||||
\(611\) | −1466.47 | −0.00392818 | ||||||||
\(612\) | − | 290836.i | − | 0.776506i | ||||||
\(613\) | 664451.i | 1.76824i | 0.467256 | + | 0.884122i | \(0.345243\pi\) | ||||
−0.467256 | + | 0.884122i | \(0.654757\pi\) | |||||||
\(614\) | 427199. | 1.13317 | ||||||||
\(615\) | − | 285368.i | − | 0.754493i | ||||||
\(616\) | −307616. | −0.810676 | ||||||||
\(617\) | 480320.i | 1.26171i | 0.775900 | + | 0.630856i | \(0.217296\pi\) | ||||
−0.775900 | + | 0.630856i | \(0.782704\pi\) | |||||||
\(618\) | 300514.i | 0.786843i | ||||||||
\(619\) | − | 677097.i | − | 1.76713i | −0.468304 | − | 0.883567i | \(-0.655135\pi\) | ||
0.468304 | − | 0.883567i | \(-0.344865\pi\) | |||||||
\(620\) | 700967.i | 1.82354i | ||||||||
\(621\) | −58325.0 | + | 45894.5i | −0.151242 | + | 0.119008i | ||||
\(622\) | 627767. | 1.62262 | ||||||||
\(623\) | −90204.9 | −0.232410 | ||||||||
\(624\) | −12039.7 | −0.0309206 | ||||||||
\(625\) | 1.68478e6 | 4.31303 | ||||||||
\(626\) | 362950.i | 0.926186i | ||||||||
\(627\) | −160822. | −0.409082 | ||||||||
\(628\) | − | 153924.i | − | 0.390290i | ||||||
\(629\) | 379025. | 0.958002 | ||||||||
\(630\) | 110256. | 0.277794 | ||||||||
\(631\) | − | 483637.i | − | 1.21468i | −0.794443 | − | 0.607338i | \(-0.792237\pi\) | ||
0.794443 | − | 0.607338i | \(-0.207763\pi\) | |||||||
\(632\) | 168589.i | 0.422080i | ||||||||
\(633\) | −215102. | −0.536830 | ||||||||
\(634\) | 1.30668e6 | 3.25079 | ||||||||
\(635\) | 418717.i | 1.03842i | ||||||||
\(636\) | 564494.i | 1.39555i | ||||||||
\(637\) | 7934.52 | 0.0195543 | ||||||||
\(638\) | 1.29239e6i | 3.17507i | ||||||||
\(639\) | 92403.1 | 0.226300 | ||||||||
\(640\) | 295684.i | 0.721886i | ||||||||
\(641\) | − | 607233.i | − | 1.47788i | −0.673771 | − | 0.738940i | \(-0.735327\pi\) | ||
0.673771 | − | 0.738940i | \(-0.264673\pi\) | |||||||
\(642\) | − | 645091.i | − | 1.56513i | ||||||
\(643\) | 20493.9i | 0.0495681i | 0.999693 | + | 0.0247840i | \(0.00788982\pi\) | ||||
−0.999693 | + | 0.0247840i | \(0.992110\pi\) | |||||||
\(644\) | −143945. | − | 182932.i | −0.347076 | − | 0.441081i | ||||
\(645\) | −638409. | −1.53454 | ||||||||
\(646\) | 398166. | 0.954111 | ||||||||
\(647\) | −254027. | −0.606836 | −0.303418 | − | 0.952858i | \(-0.598128\pi\) | ||||
−0.303418 | + | 0.952858i | \(0.598128\pi\) | |||||||
\(648\) | 126835. | 0.302058 | ||||||||
\(649\) | 505795.i | 1.20084i | ||||||||
\(650\) | −46348.0 | −0.109699 | ||||||||
\(651\) | 21045.7i | 0.0496593i | ||||||||
\(652\) | −3621.34 | −0.00851871 | ||||||||
\(653\) | −69362.6 | −0.162667 | −0.0813334 | − | 0.996687i | \(-0.525918\pi\) | ||||
−0.0813334 | + | 0.996687i | \(0.525918\pi\) | |||||||
\(654\) | − | 80170.3i | − | 0.187438i | ||||||
\(655\) | − | 1.40048e6i | − | 3.26433i | ||||||
\(656\) | 743330. | 1.72732 | ||||||||
\(657\) | −131753. | −0.305232 | ||||||||
\(658\) | 34981.4i | 0.0807951i | ||||||||
\(659\) | 438121.i | 1.00884i | 0.863458 | + | 0.504421i | \(0.168294\pi\) | ||||
−0.863458 | + | 0.504421i | \(0.831706\pi\) | |||||||
\(660\) | −1.58999e6 | −3.65013 | ||||||||
\(661\) | 182990.i | 0.418817i | 0.977828 | + | 0.209409i | \(0.0671539\pi\) | ||||
−0.977828 | + | 0.209409i | \(0.932846\pi\) | |||||||
\(662\) | −644959. | −1.47169 | ||||||||
\(663\) | 4954.68i | 0.0112717i | ||||||||
\(664\) | 1.14210e6i | 2.59040i | ||||||||
\(665\) | 107335.i | 0.242716i | ||||||||
\(666\) | 278416.i | 0.627690i | ||||||||
\(667\) | −456291. | + | 359045.i | −1.02563 | + | 0.807044i | ||||
\(668\) | 150568. | 0.337426 | ||||||||
\(669\) | −160439. | −0.358474 | ||||||||
\(670\) | −2.18079e6 | −4.85806 | ||||||||
\(671\) | 545090. | 1.21066 | ||||||||
\(672\) | 125566.i | 0.278057i | ||||||||
\(673\) | 205678. | 0.454108 | 0.227054 | − | 0.973882i | \(-0.427091\pi\) | ||||
0.227054 | + | 0.973882i | \(0.427091\pi\) | |||||||
\(674\) | − | 1.08908e6i | − | 2.39741i | ||||||
\(675\) | 250657. | 0.550139 | ||||||||
\(676\) | −1.12424e6 | −2.46018 | ||||||||
\(677\) | 252173.i | 0.550200i | 0.961416 | + | 0.275100i | \(0.0887110\pi\) | ||||
−0.961416 | + | 0.275100i | \(0.911289\pi\) | |||||||
\(678\) | − | 417343.i | − | 0.907891i | ||||||
\(679\) | 106970. | 0.232018 | ||||||||
\(680\) | 2.33712e6 | 5.05432 | ||||||||
\(681\) | − | 92870.5i | − | 0.200255i | ||||||
\(682\) | − | 426808.i | − | 0.917622i | ||||||
\(683\) | 645549. | 1.38385 | 0.691923 | − | 0.721971i | \(-0.256764\pi\) | ||||
0.691923 | + | 0.721971i | \(0.256764\pi\) | |||||||
\(684\) | 207975.i | 0.444528i | ||||||||
\(685\) | 303281. | 0.646345 | ||||||||
\(686\) | − | 388924.i | − | 0.826451i | ||||||
\(687\) | 114489.i | 0.242578i | ||||||||
\(688\) | − | 1.66293e6i | − | 3.51316i | ||||||
\(689\) | − | 9616.74i | − | 0.0202577i | ||||||
\(690\) | −621195. | − | 789443.i | −1.30476 | − | 1.65815i | ||||
\(691\) | −403276. | −0.844591 | −0.422295 | − | 0.906458i | \(-0.638775\pi\) | ||||
−0.422295 | + | 0.906458i | \(0.638775\pi\) | |||||||
\(692\) | 377257. | 0.787817 | ||||||||
\(693\) | −47737.6 | −0.0994017 | ||||||||
\(694\) | 1.28061e6 | 2.65888 | ||||||||
\(695\) | 745227.i | 1.54283i | ||||||||
\(696\) | 992265. | 2.04837 | ||||||||
\(697\) | − | 305901.i | − | 0.629674i | ||||||
\(698\) | −509680. | −1.04613 | ||||||||
\(699\) | 198837. | 0.406953 | ||||||||
\(700\) | 786169.i | 1.60443i | ||||||||
\(701\) | − | 594481.i | − | 1.20977i | −0.796314 | − | 0.604883i | \(-0.793220\pi\) | ||
0.796314 | − | 0.604883i | \(-0.206780\pi\) | |||||||
\(702\) | −3639.50 | −0.00738530 | ||||||||
\(703\) | −271039. | −0.548429 | ||||||||
\(704\) | − | 863742.i | − | 1.74276i | ||||||
\(705\) | 107347.i | 0.215979i | ||||||||
\(706\) | −1.16218e6 | −2.33165 | ||||||||
\(707\) | 79837.0i | 0.159722i | ||||||||
\(708\) | 654095. | 1.30489 | ||||||||
\(709\) | 931797.i | 1.85365i | 0.375489 | + | 0.926827i | \(0.377475\pi\) | ||||
−0.375489 | + | 0.926827i | \(0.622525\pi\) | |||||||
\(710\) | 1.25070e6i | 2.48105i | ||||||||
\(711\) | 26162.5i | 0.0517536i | ||||||||
\(712\) | − | 1.40454e6i | − | 2.77060i | ||||||
\(713\) | 150688. | − | 118573.i | 0.296415 | − | 0.233242i | ||||
\(714\) | 118190. | 0.231837 | ||||||||
\(715\) | 27087.2 | 0.0529848 | ||||||||
\(716\) | −1.07311e6 | −2.09323 | ||||||||
\(717\) | −428526. | −0.833563 | ||||||||
\(718\) | 453046.i | 0.878808i | ||||||||
\(719\) | −125813. | −0.243371 | −0.121686 | − | 0.992569i | \(-0.538830\pi\) | ||||
−0.121686 | + | 0.992569i | \(0.538830\pi\) | |||||||
\(720\) | 881317.i | 1.70007i | ||||||||
\(721\) | −86839.6 | −0.167050 | ||||||||
\(722\) | 685090. | 1.31423 | ||||||||
\(723\) | − | 226082.i | − | 0.432503i | ||||||
\(724\) | 2.38377e6i | 4.54765i | ||||||||
\(725\) | 1.96096e6 | 3.73071 | ||||||||
\(726\) | 401978. | 0.762657 | ||||||||
\(727\) | 390925.i | 0.739648i | 0.929102 | + | 0.369824i | \(0.120582\pi\) | ||||
−0.929102 | + | 0.369824i | \(0.879418\pi\) | |||||||
\(728\) | − | 6777.10i | − | 0.0127874i | ||||||
\(729\) | 19683.0 | 0.0370370 | ||||||||
\(730\) | − | 1.78331e6i | − | 3.34643i | ||||||
\(731\) | −684344. | −1.28068 | ||||||||
\(732\) | − | 704911.i | − | 1.31557i | ||||||
\(733\) | 483475.i | 0.899842i | 0.893068 | + | 0.449921i | \(0.148548\pi\) | ||||
−0.893068 | + | 0.449921i | \(0.851452\pi\) | |||||||
\(734\) | 1.41127e6i | 2.61949i | ||||||||
\(735\) | − | 580813.i | − | 1.07513i | ||||||
\(736\) | 899062. | − | 707451.i | 1.65972 | − | 1.30599i | ||||
\(737\) | 944212. | 1.73834 | ||||||||
\(738\) | 224702. | 0.412567 | ||||||||
\(739\) | 721370. | 1.32090 | 0.660449 | − | 0.750871i | \(-0.270366\pi\) | ||||
0.660449 | + | 0.750871i | \(0.270366\pi\) | |||||||
\(740\) | −2.67967e6 | −4.89349 | ||||||||
\(741\) | − | 3543.07i | − | 0.00645273i | ||||||
\(742\) | −229399. | −0.416661 | ||||||||
\(743\) | 859654.i | 1.55721i | 0.627517 | + | 0.778603i | \(0.284071\pi\) | ||||
−0.627517 | + | 0.778603i | \(0.715929\pi\) | |||||||
\(744\) | −327692. | −0.591997 | ||||||||
\(745\) | 1.07366e6 | 1.93443 | ||||||||
\(746\) | 207359.i | 0.372602i | ||||||||
\(747\) | 177237.i | 0.317624i | ||||||||
\(748\) | −1.70440e6 | −3.04627 | ||||||||
\(749\) | 186412. | 0.332285 | ||||||||
\(750\) | 2.20587e6i | 3.92155i | ||||||||
\(751\) | − | 528747.i | − | 0.937492i | −0.883333 | − | 0.468746i | \(-0.844706\pi\) | ||
0.883333 | − | 0.468746i | \(-0.155294\pi\) | |||||||
\(752\) | −279618. | −0.494458 | ||||||||
\(753\) | 51021.4i | 0.0899833i | ||||||||
\(754\) | −28472.8 | −0.0500826 | ||||||||
\(755\) | − | 376834.i | − | 0.661083i | ||||||
\(756\) | 61734.3i | 0.108015i | ||||||||
\(757\) | 273108.i | 0.476588i | 0.971193 | + | 0.238294i | \(0.0765881\pi\) | ||||
−0.971193 | + | 0.238294i | \(0.923412\pi\) | |||||||
\(758\) | − | 324370.i | − | 0.564550i | ||||||
\(759\) | 268958. | + | 341804.i | 0.466875 | + | 0.593327i | ||||
\(760\) | −1.67126e6 | −2.89346 | ||||||||
\(761\) | −265044. | −0.457666 | −0.228833 | − | 0.973466i | \(-0.573491\pi\) | ||||
−0.228833 | + | 0.973466i | \(0.573491\pi\) | |||||||
\(762\) | −329703. | −0.567822 | ||||||||
\(763\) | 23166.8 | 0.0397940 | ||||||||
\(764\) | − | 1.41541e6i | − | 2.42491i | ||||||
\(765\) | 362687. | 0.619739 | ||||||||
\(766\) | − | 1.78701e6i | − | 3.04558i | ||||||
\(767\) | −11143.2 | −0.0189417 | ||||||||
\(768\) | 221011. | 0.374707 | ||||||||
\(769\) | 771637.i | 1.30485i | 0.757853 | + | 0.652425i | \(0.226248\pi\) | ||||
−0.757853 | + | 0.652425i | \(0.773752\pi\) | |||||||
\(770\) | − | 646140.i | − | 1.08980i | ||||||
\(771\) | −135036. | −0.227165 | ||||||||
\(772\) | 327758. | 0.549945 | ||||||||
\(773\) | − | 1.09414e6i | − | 1.83111i | −0.402192 | − | 0.915555i | \(-0.631752\pi\) | ||
0.402192 | − | 0.915555i | \(-0.368248\pi\) | |||||||
\(774\) | − | 502690.i | − | 0.839109i | ||||||
\(775\) | −647598. | −1.07821 | ||||||||
\(776\) | 1.66558e6i | 2.76593i | ||||||||
\(777\) | −80453.8 | −0.133261 | ||||||||
\(778\) | − | 1.39382e6i | − | 2.30275i | ||||||
\(779\) | 218748.i | 0.360471i | ||||||||
\(780\) | − | 35029.2i | − | 0.0575759i | ||||||
\(781\) | − | 541514.i | − | 0.887784i | ||||||
\(782\) | −665891. | − | 846246.i | −1.08890 | − | 1.38383i | ||||
\(783\) | 153985. | 0.251163 | ||||||||
\(784\) | 1.51291e6 | 2.46139 | ||||||||
\(785\) | 191951. | 0.311495 | ||||||||
\(786\) | 1.10275e6 | 1.78498 | ||||||||
\(787\) | 820354.i | 1.32450i | 0.749283 | + | 0.662250i | \(0.230398\pi\) | ||||
−0.749283 | + | 0.662250i | \(0.769602\pi\) | |||||||
\(788\) | 1.57534e6 | 2.53701 | ||||||||
\(789\) | 320163.i | 0.514301i | ||||||||
\(790\) | −354117. | −0.567404 | ||||||||
\(791\) | 120600. | 0.192749 | ||||||||
\(792\) | − | 743298.i | − | 1.18498i | ||||||
\(793\) | 12008.9i | 0.0190966i | ||||||||
\(794\) | 1.08208e6 | 1.71640 | ||||||||
\(795\) | −703953. | −1.11380 | ||||||||
\(796\) | − | 893574.i | − | 1.41028i | ||||||
\(797\) | 1.05531e6i | 1.66135i | 0.556755 | + | 0.830676i | \(0.312046\pi\) | ||||
−0.556755 | + | 0.830676i | \(0.687954\pi\) | |||||||
\(798\) | −84516.8 | −0.132720 | ||||||||
\(799\) | 115071.i | 0.180248i | ||||||||
\(800\) | −3.86381e6 | −6.03720 | ||||||||
\(801\) | − | 217964.i | − | 0.339719i | ||||||
\(802\) | − | 1.18746e6i | − | 1.84617i | ||||||
\(803\) | 772119.i | 1.19744i | ||||||||
\(804\) | − | 1.22106e6i | − | 1.88896i | ||||||
\(805\) | 228126. | − | 179507.i | 0.352032 | − | 0.277006i | ||||
\(806\) | 9403.02 | 0.0144743 | ||||||||
\(807\) | 192356. | 0.295365 | ||||||||
\(808\) | −1.24310e6 | −1.90408 | ||||||||
\(809\) | −134570. | −0.205613 | −0.102806 | − | 0.994701i | \(-0.532782\pi\) | ||||
−0.102806 | + | 0.994701i | \(0.532782\pi\) | |||||||
\(810\) | 266415.i | 0.406058i | ||||||||
\(811\) | −966167. | −1.46896 | −0.734481 | − | 0.678629i | \(-0.762574\pi\) | ||||
−0.734481 | + | 0.678629i | \(0.762574\pi\) | |||||||
\(812\) | 482964.i | 0.732491i | ||||||||
\(813\) | −273234. | −0.413385 | ||||||||
\(814\) | 1.63161e6 | 2.46245 | ||||||||
\(815\) | − | 4515.99i | − | 0.00679889i | ||||||
\(816\) | 944730.i | 1.41882i | ||||||||
\(817\) | 489371. | 0.733152 | ||||||||
\(818\) | −1.11660e6 | −1.66874 | ||||||||
\(819\) | − | 1051.71i | − | 0.00156793i | ||||||
\(820\) | 2.16270e6i | 3.21638i | ||||||||
\(821\) | −1.06373e6 | −1.57814 | −0.789068 | − | 0.614305i | \(-0.789436\pi\) | ||||
−0.789068 | + | 0.614305i | \(0.789436\pi\) | |||||||
\(822\) | 238807.i | 0.353430i | ||||||||
\(823\) | −133222. | −0.196687 | −0.0983434 | − | 0.995153i | \(-0.531354\pi\) | ||||
−0.0983434 | + | 0.995153i | \(0.531354\pi\) | |||||||
\(824\) | − | 1.35214e6i | − | 1.99144i | ||||||
\(825\) | − | 1.46894e6i | − | 2.15822i | ||||||
\(826\) | 265810.i | 0.389594i | ||||||||
\(827\) | − | 543898.i | − | 0.795256i | −0.917547 | − | 0.397628i | \(-0.869834\pi\) | ||
0.917547 | − | 0.397628i | \(-0.130166\pi\) | |||||||
\(828\) | 442022. | − | 347817.i | 0.644738 | − | 0.507329i | ||||
\(829\) | −1.17996e6 | −1.71695 | −0.858473 | − | 0.512859i | \(-0.828586\pi\) | ||||
−0.858473 | + | 0.512859i | \(0.828586\pi\) | |||||||
\(830\) | −2.39895e6 | −3.48229 | ||||||||
\(831\) | 413588. | 0.598915 | ||||||||
\(832\) | 19029.1 | 0.0274898 | ||||||||
\(833\) | − | 622604.i | − | 0.897267i | ||||||
\(834\) | −586800. | −0.843641 | ||||||||
\(835\) | 187765.i | 0.269304i | ||||||||
\(836\) | 1.21881e6 | 1.74390 | ||||||||
\(837\) | −50853.0 | −0.0725881 | ||||||||
\(838\) | − | 1.80582e6i | − | 2.57150i | ||||||
\(839\) | − | 429976.i | − | 0.610829i | −0.952219 | − | 0.305415i | \(-0.901205\pi\) | ||
0.952219 | − | 0.305415i | \(-0.0987951\pi\) | |||||||
\(840\) | −496089. | −0.703074 | ||||||||
\(841\) | 497384. | 0.703234 | ||||||||
\(842\) | − | 984575.i | − | 1.38875i | ||||||
\(843\) | 259560.i | 0.365244i | ||||||||
\(844\) | 1.63017e6 | 2.28849 | ||||||||
\(845\) | − | 1.40199e6i | − | 1.96350i | ||||||
\(846\) | −84526.1 | −0.118100 | ||||||||
\(847\) | 116160.i | 0.161915i | ||||||||
\(848\) | − | 1.83366e6i | − | 2.54993i | ||||||
\(849\) | − | 192620.i | − | 0.267231i | ||||||
\(850\) | 3.63682e6i | 5.03367i | ||||||||
\(851\) | 453284. | + | 576055.i | 0.625909 | + | 0.795435i | ||||
\(852\) | −700287. | −0.964710 | ||||||||
\(853\) | −767502. | −1.05483 | −0.527414 | − | 0.849609i | \(-0.676838\pi\) | ||||
−0.527414 | + | 0.849609i | \(0.676838\pi\) | |||||||
\(854\) | 286461. | 0.392781 | ||||||||
\(855\) | −259356. | −0.354783 | ||||||||
\(856\) | 2.90253e6i | 3.96122i | ||||||||
\(857\) | −1.18822e6 | −1.61784 | −0.808920 | − | 0.587918i | \(-0.799948\pi\) | ||||
−0.808920 | + | 0.587918i | \(0.799948\pi\) | |||||||
\(858\) | 21328.7i | 0.0289728i | ||||||||
\(859\) | 703322. | 0.953165 | 0.476582 | − | 0.879130i | \(-0.341875\pi\) | ||||
0.476582 | + | 0.879130i | \(0.341875\pi\) | |||||||
\(860\) | 4.83825e6 | 6.54172 | ||||||||
\(861\) | 64932.2i | 0.0875898i | ||||||||
\(862\) | 2.11153e6i | 2.84173i | ||||||||
\(863\) | −708330. | −0.951073 | −0.475536 | − | 0.879696i | \(-0.657746\pi\) | ||||
−0.475536 | + | 0.879696i | \(0.657746\pi\) | |||||||
\(864\) | −303408. | −0.406442 | ||||||||
\(865\) | 470459.i | 0.628766i | ||||||||
\(866\) | 554803.i | 0.739781i | ||||||||
\(867\) | −45205.0 | −0.0601379 | ||||||||
\(868\) | − | 159497.i | − | 0.211696i | ||||||
\(869\) | 153321. | 0.203031 | ||||||||
\(870\) | 2.08423e6i | 2.75364i | ||||||||
\(871\) | 20802.0i | 0.0274200i | ||||||||
\(872\) | 360719.i | 0.474391i | ||||||||
\(873\) | 258474.i | 0.339147i | ||||||||
\(874\) | 476175. | + | 605146.i | 0.623367 | + | 0.792205i | ||||
\(875\) | −637431. | −0.832562 | ||||||||
\(876\) | 998507. | 1.30120 | ||||||||
\(877\) | 718291. | 0.933901 | 0.466951 | − | 0.884283i | \(-0.345353\pi\) | ||||
0.466951 | + | 0.884283i | \(0.345353\pi\) | |||||||
\(878\) | −1.87967e6 | −2.43833 | ||||||||
\(879\) | − | 208470.i | − | 0.269815i | ||||||
\(880\) | 5.16482e6 | 6.66945 | ||||||||
\(881\) | 425210.i | 0.547837i | 0.961753 | + | 0.273919i | \(0.0883199\pi\) | ||||
−0.961753 | + | 0.273919i | \(0.911680\pi\) | |||||||
\(882\) | 457339. | 0.587896 | ||||||||
\(883\) | 326938. | 0.419318 | 0.209659 | − | 0.977775i | \(-0.432765\pi\) | ||||
0.209659 | + | 0.977775i | \(0.432765\pi\) | |||||||
\(884\) | − | 37549.6i | − | 0.0480509i | ||||||
\(885\) | 815689.i | 1.04145i | ||||||||
\(886\) | 2.17655e6 | 2.77269 | ||||||||
\(887\) | −612556. | −0.778572 | −0.389286 | − | 0.921117i | \(-0.627278\pi\) | ||||
−0.389286 | + | 0.921117i | \(0.627278\pi\) | |||||||
\(888\) | − | 1.25271e6i | − | 1.58863i | ||||||
\(889\) | − | 95274.2i | − | 0.120551i | ||||||
\(890\) | 2.95020e6 | 3.72452 | ||||||||
\(891\) | − | 115349.i | − | 0.145298i | ||||||
\(892\) | 1.21591e6 | 1.52816 | ||||||||
\(893\) | − | 82286.5i | − | 0.103187i | ||||||
\(894\) | 845410.i | 1.05777i | ||||||||
\(895\) | − | 1.33822e6i | − | 1.67063i | ||||||
\(896\) | − | 67279.5i | − | 0.0838044i | ||||||
\(897\) | −7530.30 | + | 5925.42i | −0.00935895 | + | 0.00736434i | ||||
\(898\) | −1.07748e6 | −1.33616 | ||||||||
\(899\) | −397836. | −0.492249 | ||||||||
\(900\) | −1.89963e6 | −2.34523 | ||||||||
\(901\) | −754603. | −0.929542 | ||||||||
\(902\) | − | 1.31683e6i | − | 1.61852i | ||||||
\(903\) | 145262. | 0.178147 | ||||||||
\(904\) | 1.87780e6i | 2.29780i | ||||||||
\(905\) | −2.97268e6 | −3.62953 | ||||||||
\(906\) | 296723. | 0.361489 | ||||||||
\(907\) | − | 913097.i | − | 1.10995i | −0.831868 | − | 0.554974i | \(-0.812728\pi\) | ||
0.831868 | − | 0.554974i | \(-0.187272\pi\) | |||||||
\(908\) | 703830.i | 0.853682i | ||||||||
\(909\) | −192912. | −0.233470 | ||||||||
\(910\) | 14235.1 | 0.0171901 | ||||||||
\(911\) | − | 936548.i | − | 1.12848i | −0.825611 | − | 0.564239i | \(-0.809170\pi\) | ||
0.825611 | − | 0.564239i | \(-0.190830\pi\) | |||||||
\(912\) | − | 675572.i | − | 0.812235i | ||||||
\(913\) | 1.03867e6 | 1.24605 | ||||||||
\(914\) | 2.22474e6i | 2.66310i | ||||||||
\(915\) | 879060. | 1.04997 | ||||||||
\(916\) | − | 867671.i | − | 1.03410i | ||||||
\(917\) | 318663.i | 0.378959i | ||||||||
\(918\) | 285584.i | 0.338882i | ||||||||
\(919\) | − | 794529.i | − | 0.940760i | −0.882464 | − | 0.470380i | \(-0.844117\pi\) | ||
0.882464 | − | 0.470380i | \(-0.155883\pi\) | |||||||
\(920\) | 2.79501e6 | + | 3.55203e6i | 3.30223 | + | 4.19663i | ||||
\(921\) | −298289. | −0.351656 | ||||||||
\(922\) | −1.16803e6 | −1.37401 | ||||||||
\(923\) | 11930.1 | 0.0140036 | ||||||||
\(924\) | 361784. | 0.423746 | ||||||||
\(925\) | − | 2.47565e6i | − | 2.89338i | ||||||
\(926\) | 1.46730e6 | 1.71119 | ||||||||
\(927\) | − | 209832.i | − | 0.244181i | ||||||
\(928\) | −2.37363e6 | −2.75625 | ||||||||
\(929\) | 100991. | 0.117017 | 0.0585086 | − | 0.998287i | \(-0.481366\pi\) | ||||
0.0585086 | + | 0.998287i | \(0.481366\pi\) | |||||||
\(930\) | − | 688308.i | − | 0.795824i | ||||||
\(931\) | 445221.i | 0.513661i | ||||||||
\(932\) | −1.50691e6 | −1.73483 | ||||||||
\(933\) | −438334. | −0.503549 | ||||||||
\(934\) | − | 623579.i | − | 0.714822i | ||||||
\(935\) | − | 2.12547e6i | − | 2.43126i | ||||||
\(936\) | 16375.6 | 0.0186916 | ||||||||
\(937\) | 808400.i | 0.920761i | 0.887722 | + | 0.460381i | \(0.152287\pi\) | ||||
−0.887722 | + | 0.460381i | \(0.847713\pi\) | |||||||
\(938\) | 496212. | 0.563977 | ||||||||
\(939\) | − | 253428.i | − | 0.287424i | ||||||
\(940\) | − | 813540.i | − | 0.920711i | ||||||
\(941\) | − | 25875.4i | − | 0.0292219i | −0.999893 | − | 0.0146110i | \(-0.995349\pi\) | ||
0.999893 | − | 0.0146110i | \(-0.00465098\pi\) | |||||||
\(942\) | 151144.i | 0.170329i | ||||||||
\(943\) | 464919. | − | 365834.i | 0.522822 | − | 0.411396i | ||||
\(944\) | −2.12471e6 | −2.38428 | ||||||||
\(945\) | −76985.8 | −0.0862079 | ||||||||
\(946\) | −2.94594e6 | −3.29186 | ||||||||
\(947\) | 1.27426e6 | 1.42089 | 0.710444 | − | 0.703754i | \(-0.248494\pi\) | ||||
0.710444 | + | 0.703754i | \(0.248494\pi\) | |||||||
\(948\) | − | 198276.i | − | 0.220624i | ||||||
\(949\) | −17010.6 | −0.0188880 | ||||||||
\(950\) | − | 2.60068e6i | − | 2.88163i | ||||||
\(951\) | −912378. | −1.00882 | ||||||||
\(952\) | −531783. | −0.586760 | ||||||||
\(953\) | 1.57859e6i | 1.73813i | 0.494696 | + | 0.869066i | \(0.335279\pi\) | ||||
−0.494696 | + | 0.869066i | \(0.664721\pi\) | |||||||
\(954\) | − | 554300.i | − | 0.609043i | ||||||
\(955\) | 1.76509e6 | 1.93535 | ||||||||
\(956\) | 3.24763e6 | 3.55345 | ||||||||
\(957\) | − | 902406.i | − | 0.985322i | ||||||
\(958\) | − | 214788.i | − | 0.234034i | ||||||
\(959\) | −69008.1 | −0.0750348 | ||||||||
\(960\) | − | 1.39295e6i | − | 1.51144i | ||||||
\(961\) | −792137. | −0.857736 | ||||||||
\(962\) | 35946.1i | 0.0388420i | ||||||||
\(963\) | 450431.i | 0.485708i | ||||||||
\(964\) | 1.71339e6i | 1.84375i | ||||||||
\(965\) | 408731.i | 0.438918i | ||||||||
\(966\) | 141346. | + | 179629.i | 0.151470 | + | 0.192496i | ||||
\(967\) | 68383.2 | 0.0731301 | 0.0365651 | − | 0.999331i | \(-0.488358\pi\) | ||||
0.0365651 | + | 0.999331i | \(0.488358\pi\) | |||||||
\(968\) | −1.80866e6 | −1.93022 | ||||||||
\(969\) | −278017. | −0.296090 | ||||||||
\(970\) | −3.49851e6 | −3.71826 | ||||||||
\(971\) | 902024.i | 0.956709i | 0.878167 | + | 0.478354i | \(0.158767\pi\) | ||||
−0.878167 | + | 0.478354i | \(0.841233\pi\) | |||||||
\(972\) | −149170. | −0.157888 | ||||||||
\(973\) | − | 169568.i | − | 0.179109i | ||||||
\(974\) | 263243. | 0.277485 | ||||||||
\(975\) | 32362.2 | 0.0340431 | ||||||||
\(976\) | 2.28978e6i | 2.40378i | ||||||||
\(977\) | 917308.i | 0.961006i | 0.876993 | + | 0.480503i | \(0.159546\pi\) | ||||
−0.876993 | + | 0.480503i | \(0.840454\pi\) | |||||||
\(978\) | 3555.94 | 0.00371772 | ||||||||
\(979\) | −1.27734e6 | −1.33273 | ||||||||
\(980\) | 4.40176e6i | 4.58325i | ||||||||
\(981\) | 55978.4i | 0.0581678i | ||||||||
\(982\) | −1.67060e6 | −1.73241 | ||||||||
\(983\) | − | 1.81657e6i | − | 1.87994i | −0.341257 | − | 0.939970i | \(-0.610853\pi\) | ||
0.341257 | − | 0.939970i | \(-0.389147\pi\) | |||||||
\(984\) | −1.01103e6 | −1.04417 | ||||||||
\(985\) | 1.96453e6i | 2.02481i | ||||||||
\(986\) | 2.23419e6i | 2.29809i | ||||||||
\(987\) | − | 24425.5i | − | 0.0250732i | ||||||
\(988\) | 26851.6i | 0.0275078i | ||||||||
\(989\) | −818422. | − | 1.04009e6i | −0.836729 | − | 1.06335i | ||||
\(990\) | 1.56128e6 | 1.59298 | ||||||||
\(991\) | −242.686 | −0.000247114 | −0.000123557 | − | 1.00000i | \(-0.500039\pi\) | ||||
−0.000123557 | 1.00000i | \(0.500039\pi\) | ||||||||
\(992\) | 783884. | 0.796578 | ||||||||
\(993\) | 450338. | 0.456710 | ||||||||
\(994\) | − | 284582.i | − | 0.288028i | ||||||
\(995\) | 1.11433e6 | 1.12556 | ||||||||
\(996\) | − | 1.34321e6i | − | 1.35402i | ||||||
\(997\) | 1.34734e6 | 1.35546 | 0.677731 | − | 0.735310i | \(-0.262963\pi\) | ||||
0.677731 | + | 0.735310i | \(0.262963\pi\) | |||||||
\(998\) | −441753. | −0.443525 | ||||||||
\(999\) | − | 194402.i | − | 0.194791i |
(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 | 69.5.d.a.22.16 | yes | 16 | |
3.2 | odd | 2 | 207.5.d.c.91.1 | 16 | |||
4.3 | odd | 2 | 1104.5.c.c.1057.16 | 16 | |||
23.22 | odd | 2 | inner | 69.5.d.a.22.15 | ✓ | 16 | |
69.68 | even | 2 | 207.5.d.c.91.2 | 16 | |||
92.91 | even | 2 | 1104.5.c.c.1057.9 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.5.d.a.22.15 | ✓ | 16 | 23.22 | odd | 2 | inner | |
69.5.d.a.22.16 | yes | 16 | 1.1 | even | 1 | trivial | |
207.5.d.c.91.1 | 16 | 3.2 | odd | 2 | |||
207.5.d.c.91.2 | 16 | 69.68 | even | 2 | |||
1104.5.c.c.1057.9 | 16 | 92.91 | even | 2 | |||
1104.5.c.c.1057.16 | 16 | 4.3 | odd | 2 |