Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,6,Mod(24,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.24");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.00959549532\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{241})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 121x^{2} + 3600 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 24.4 | ||
Root | \(8.26209i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 25.24 |
Dual form | 25.6.b.b.24.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 10.2621i | 1.81410i | 0.421025 | + | 0.907049i | \(0.361670\pi\) | ||||
−0.421025 | + | 0.907049i | \(0.638330\pi\) | |||||||
\(3\) | 5.52417i | 0.354376i | 0.984177 | + | 0.177188i | \(0.0567001\pi\) | ||||
−0.984177 | + | 0.177188i | \(0.943300\pi\) | |||||||
\(4\) | −73.3104 | −2.29095 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −56.6896 | −0.642873 | ||||||||
\(7\) | 68.9517i | 0.531863i | 0.963992 | + | 0.265931i | \(0.0856795\pi\) | ||||
−0.963992 | + | 0.265931i | \(0.914321\pi\) | |||||||
\(8\) | − 423.931i | − 2.34191i | ||||||||
\(9\) | 212.483 | 0.874418 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −486.104 | −1.21129 | −0.605645 | − | 0.795735i | \(-0.707085\pi\) | ||||
−0.605645 | + | 0.795735i | \(0.707085\pi\) | |||||||
\(12\) | − 404.980i | − 0.811858i | ||||||||
\(13\) | 428.387i | 0.703036i | 0.936181 | + | 0.351518i | \(0.114334\pi\) | ||||
−0.936181 | + | 0.351518i | \(0.885666\pi\) | |||||||
\(14\) | −707.588 | −0.964851 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2004.49 | 1.95751 | ||||||||
\(17\) | 1800.64i | 1.51114i | 0.655066 | + | 0.755571i | \(0.272641\pi\) | ||||
−0.655066 | + | 0.755571i | \(0.727359\pi\) | |||||||
\(18\) | 2180.52i | 1.58628i | ||||||||
\(19\) | 1046.65 | 0.665149 | 0.332575 | − | 0.943077i | \(-0.392083\pi\) | ||||
0.332575 | + | 0.943077i | \(0.392083\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −380.901 | −0.188479 | ||||||||
\(22\) | − 4988.45i | − 2.19740i | ||||||||
\(23\) | − 686.855i | − 0.270736i | −0.990795 | − | 0.135368i | \(-0.956778\pi\) | ||||
0.990795 | − | 0.135368i | \(-0.0432216\pi\) | |||||||
\(24\) | 2341.87 | 0.829917 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4396.14 | −1.27538 | ||||||||
\(27\) | 2516.17i | 0.664249i | ||||||||
\(28\) | − 5054.88i | − 1.21847i | ||||||||
\(29\) | 1339.03 | 0.295663 | 0.147831 | − | 0.989013i | \(-0.452771\pi\) | ||||
0.147831 | + | 0.989013i | \(0.452771\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7990.30 | 1.49334 | 0.746670 | − | 0.665195i | \(-0.231651\pi\) | ||||
0.746670 | + | 0.665195i | \(0.231651\pi\) | |||||||
\(32\) | 7004.41i | 1.20920i | ||||||||
\(33\) | − 2685.33i | − 0.429252i | ||||||||
\(34\) | −18478.4 | −2.74136 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −15577.3 | −2.00325 | ||||||||
\(37\) | − 1970.64i | − 0.236648i | −0.992975 | − | 0.118324i | \(-0.962248\pi\) | ||||
0.992975 | − | 0.118324i | \(-0.0377522\pi\) | |||||||
\(38\) | 10740.9i | 1.20665i | ||||||||
\(39\) | −2366.48 | −0.249139 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10772.2 | 1.00079 | 0.500395 | − | 0.865797i | \(-0.333188\pi\) | ||||
0.500395 | + | 0.865797i | \(0.333188\pi\) | |||||||
\(42\) | − 3908.84i | − 0.341920i | ||||||||
\(43\) | − 15017.7i | − 1.23861i | −0.785152 | − | 0.619303i | \(-0.787415\pi\) | ||||
0.785152 | − | 0.619303i | \(-0.212585\pi\) | |||||||
\(44\) | 35636.5 | 2.77500 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7048.57 | 0.491141 | ||||||||
\(47\) | 895.337i | 0.0591210i | 0.999563 | + | 0.0295605i | \(0.00941077\pi\) | ||||
−0.999563 | + | 0.0295605i | \(0.990589\pi\) | |||||||
\(48\) | 11073.1i | 0.693693i | ||||||||
\(49\) | 12052.7 | 0.717122 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9947.07 | −0.535513 | ||||||||
\(52\) | − 31405.2i | − 1.61062i | ||||||||
\(53\) | 19327.1i | 0.945098i | 0.881304 | + | 0.472549i | \(0.156666\pi\) | ||||
−0.881304 | + | 0.472549i | \(0.843334\pi\) | |||||||
\(54\) | −25821.2 | −1.20501 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 29230.8 | 1.24558 | ||||||||
\(57\) | 5781.90i | 0.235713i | ||||||||
\(58\) | 13741.3i | 0.536361i | ||||||||
\(59\) | −21193.7 | −0.792641 | −0.396321 | − | 0.918112i | \(-0.629713\pi\) | ||||
−0.396321 | + | 0.918112i | \(0.629713\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −27722.2 | −0.953900 | −0.476950 | − | 0.878931i | \(-0.658258\pi\) | ||||
−0.476950 | + | 0.878931i | \(0.658258\pi\) | |||||||
\(62\) | 81997.1i | 2.70906i | ||||||||
\(63\) | 14651.1i | 0.465070i | ||||||||
\(64\) | −7736.31 | −0.236093 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 27557.0 | 0.778705 | ||||||||
\(67\) | − 7719.33i | − 0.210084i | −0.994468 | − | 0.105042i | \(-0.966502\pi\) | ||||
0.994468 | − | 0.105042i | \(-0.0334977\pi\) | |||||||
\(68\) | − 132006.i | − 3.46195i | ||||||||
\(69\) | 3794.31 | 0.0959422 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −51410.1 | −1.21033 | −0.605163 | − | 0.796101i | \(-0.706892\pi\) | ||||
−0.605163 | + | 0.796101i | \(0.706892\pi\) | |||||||
\(72\) | − 90078.4i | − 2.04781i | ||||||||
\(73\) | 43776.4i | 0.961465i | 0.876867 | + | 0.480732i | \(0.159629\pi\) | ||||
−0.876867 | + | 0.480732i | \(0.840371\pi\) | |||||||
\(74\) | 20222.9 | 0.429303 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −76730.7 | −1.52382 | ||||||||
\(77\) | − 33517.7i | − 0.644240i | ||||||||
\(78\) | − 24285.1i | − 0.451963i | ||||||||
\(79\) | 6225.68 | 0.112233 | 0.0561163 | − | 0.998424i | \(-0.482128\pi\) | ||||
0.0561163 | + | 0.998424i | \(0.482128\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 37733.7 | 0.639024 | ||||||||
\(82\) | 110545.i | 1.81553i | ||||||||
\(83\) | − 52949.9i | − 0.843664i | −0.906674 | − | 0.421832i | \(-0.861387\pi\) | ||||
0.906674 | − | 0.421832i | \(-0.138613\pi\) | |||||||
\(84\) | 27924.0 | 0.431797 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 154113. | 2.24695 | ||||||||
\(87\) | 7397.05i | 0.104776i | ||||||||
\(88\) | 206075.i | 2.83673i | ||||||||
\(89\) | −44631.2 | −0.597260 | −0.298630 | − | 0.954369i | \(-0.596530\pi\) | ||||
−0.298630 | + | 0.954369i | \(0.596530\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −29538.0 | −0.373919 | ||||||||
\(92\) | 50353.6i | 0.620242i | ||||||||
\(93\) | 44139.8i | 0.529204i | ||||||||
\(94\) | −9188.03 | −0.107251 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −38693.6 | −0.428510 | ||||||||
\(97\) | − 148018.i | − 1.59730i | −0.601797 | − | 0.798649i | \(-0.705548\pi\) | ||||
0.601797 | − | 0.798649i | \(-0.294452\pi\) | |||||||
\(98\) | 123686.i | 1.30093i | ||||||||
\(99\) | −103289. | −1.05917 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 148476. | 1.44828 | 0.724141 | − | 0.689652i | \(-0.242237\pi\) | ||||
0.724141 | + | 0.689652i | \(0.242237\pi\) | |||||||
\(102\) | − 102078.i | − 0.971472i | ||||||||
\(103\) | − 188391.i | − 1.74972i | −0.484378 | − | 0.874859i | \(-0.660954\pi\) | ||||
0.484378 | − | 0.874859i | \(-0.339046\pi\) | |||||||
\(104\) | 181607. | 1.64645 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −198336. | −1.71450 | ||||||||
\(107\) | 67887.7i | 0.573234i | 0.958045 | + | 0.286617i | \(0.0925307\pi\) | ||||
−0.958045 | + | 0.286617i | \(0.907469\pi\) | |||||||
\(108\) | − 184462.i | − 1.52176i | ||||||||
\(109\) | 219292. | 1.76790 | 0.883949 | − | 0.467582i | \(-0.154875\pi\) | ||||
0.883949 | + | 0.467582i | \(0.154875\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10886.2 | 0.0838625 | ||||||||
\(112\) | 138213.i | 1.04112i | ||||||||
\(113\) | 80783.9i | 0.595153i | 0.954698 | + | 0.297577i | \(0.0961784\pi\) | ||||
−0.954698 | + | 0.297577i | \(0.903822\pi\) | |||||||
\(114\) | −59334.4 | −0.427606 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −98165.1 | −0.677348 | ||||||||
\(117\) | 91025.1i | 0.614747i | ||||||||
\(118\) | − 217492.i | − 1.43793i | ||||||||
\(119\) | −124157. | −0.803721 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 75246.5 | 0.467221 | ||||||||
\(122\) | − 284487.i | − 1.73047i | ||||||||
\(123\) | 59507.3i | 0.354656i | ||||||||
\(124\) | −585772. | −3.42117 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −150351. | −0.843683 | ||||||||
\(127\) | 161301.i | 0.887417i | 0.896171 | + | 0.443708i | \(0.146337\pi\) | ||||
−0.896171 | + | 0.443708i | \(0.853663\pi\) | |||||||
\(128\) | 144750.i | 0.780899i | ||||||||
\(129\) | 82960.5 | 0.438932 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −193006. | −0.982636 | −0.491318 | − | 0.870980i | \(-0.663485\pi\) | ||||
−0.491318 | + | 0.870980i | \(0.663485\pi\) | |||||||
\(132\) | 196862.i | 0.983395i | ||||||||
\(133\) | 72168.5i | 0.353768i | ||||||||
\(134\) | 79216.4 | 0.381113 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 763349. | 3.53896 | ||||||||
\(137\) | 250340.i | 1.13954i | 0.821806 | + | 0.569768i | \(0.192967\pi\) | ||||
−0.821806 | + | 0.569768i | \(0.807033\pi\) | |||||||
\(138\) | 38937.5i | 0.174049i | ||||||||
\(139\) | 218650. | 0.959871 | 0.479935 | − | 0.877304i | \(-0.340660\pi\) | ||||
0.479935 | + | 0.877304i | \(0.340660\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4946.00 | −0.0209511 | ||||||||
\(142\) | − 527575.i | − 2.19565i | ||||||||
\(143\) | − 208241.i | − 0.851580i | ||||||||
\(144\) | 425920. | 1.71168 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −449238. | −1.74419 | ||||||||
\(147\) | 66581.1i | 0.254131i | ||||||||
\(148\) | 144469.i | 0.542150i | ||||||||
\(149\) | 38740.0 | 0.142953 | 0.0714766 | − | 0.997442i | \(-0.477229\pi\) | ||||
0.0714766 | + | 0.997442i | \(0.477229\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −154945. | −0.553013 | −0.276507 | − | 0.961012i | \(-0.589177\pi\) | ||||
−0.276507 | + | 0.961012i | \(0.589177\pi\) | |||||||
\(152\) | − 443709.i | − 1.55772i | ||||||||
\(153\) | 382607.i | 1.32137i | ||||||||
\(154\) | 343962. | 1.16871 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 173488. | 0.570766 | ||||||||
\(157\) | − 344442.i | − 1.11523i | −0.830098 | − | 0.557617i | \(-0.811716\pi\) | ||||
0.830098 | − | 0.557617i | \(-0.188284\pi\) | |||||||
\(158\) | 63888.5i | 0.203601i | ||||||||
\(159\) | −106766. | −0.334920 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 47359.8 | 0.143994 | ||||||||
\(162\) | 387227.i | 1.15925i | ||||||||
\(163\) | − 366203.i | − 1.07957i | −0.841801 | − | 0.539787i | \(-0.818505\pi\) | ||||
0.841801 | − | 0.539787i | \(-0.181495\pi\) | |||||||
\(164\) | −789712. | −2.29276 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 543376. | 1.53049 | ||||||||
\(167\) | 249272.i | 0.691644i | 0.938300 | + | 0.345822i | \(0.112400\pi\) | ||||
−0.938300 | + | 0.345822i | \(0.887600\pi\) | |||||||
\(168\) | 161476.i | 0.441402i | ||||||||
\(169\) | 187778. | 0.505740 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 222397. | 0.581618 | ||||||||
\(172\) | 1.10096e6i | 2.83758i | ||||||||
\(173\) | 61460.1i | 0.156127i | 0.996948 | + | 0.0780635i | \(0.0248737\pi\) | ||||
−0.996948 | + | 0.0780635i | \(0.975126\pi\) | |||||||
\(174\) | −75909.2 | −0.190073 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −974389. | −2.37111 | ||||||||
\(177\) | − 117078.i | − 0.280893i | ||||||||
\(178\) | − 458009.i | − 1.08349i | ||||||||
\(179\) | −606803. | −1.41552 | −0.707759 | − | 0.706454i | \(-0.750294\pi\) | ||||
−0.707759 | + | 0.706454i | \(0.750294\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 153684. | 0.348685 | 0.174343 | − | 0.984685i | \(-0.444220\pi\) | ||||
0.174343 | + | 0.984685i | \(0.444220\pi\) | |||||||
\(182\) | − 303121.i | − 0.678325i | ||||||||
\(183\) | − 153142.i | − 0.338039i | ||||||||
\(184\) | −291179. | −0.634039 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −452966. | −0.960027 | ||||||||
\(187\) | − 875301.i | − 1.83043i | ||||||||
\(188\) | − 65637.6i | − 0.135443i | ||||||||
\(189\) | −173494. | −0.353289 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 182315. | 0.361608 | 0.180804 | − | 0.983519i | \(-0.442130\pi\) | ||||
0.180804 | + | 0.983519i | \(0.442130\pi\) | |||||||
\(192\) | − 42736.7i | − 0.0836659i | ||||||||
\(193\) | 102080.i | 0.197265i | 0.995124 | + | 0.0986323i | \(0.0314468\pi\) | ||||
−0.995124 | + | 0.0986323i | \(0.968553\pi\) | |||||||
\(194\) | 1.51898e6 | 2.89766 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −883586. | −1.64289 | ||||||||
\(197\) | − 404656.i | − 0.742882i | −0.928456 | − | 0.371441i | \(-0.878864\pi\) | ||||
0.928456 | − | 0.371441i | \(-0.121136\pi\) | |||||||
\(198\) | − 1.05996e6i | − 1.92144i | ||||||||
\(199\) | 167297. | 0.299472 | 0.149736 | − | 0.988726i | \(-0.452158\pi\) | ||||
0.149736 | + | 0.988726i | \(0.452158\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 42642.9 | 0.0744487 | ||||||||
\(202\) | 1.52367e6i | 2.62732i | ||||||||
\(203\) | 92328.5i | 0.157252i | ||||||||
\(204\) | 729224. | 1.22683 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.93329e6 | 3.17416 | ||||||||
\(207\) | − 145945.i | − 0.236736i | ||||||||
\(208\) | 858695.i | 1.37620i | ||||||||
\(209\) | −508783. | −0.805688 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −460778. | −0.712502 | −0.356251 | − | 0.934390i | \(-0.615945\pi\) | ||||
−0.356251 | + | 0.934390i | \(0.615945\pi\) | |||||||
\(212\) | − 1.41688e6i | − 2.16517i | ||||||||
\(213\) | − 283998.i | − 0.428911i | ||||||||
\(214\) | −696670. | −1.03990 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.06668e6 | 1.55561 | ||||||||
\(217\) | 550944.i | 0.794252i | ||||||||
\(218\) | 2.25040e6i | 3.20714i | ||||||||
\(219\) | −241829. | −0.340720 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −771372. | −1.06239 | ||||||||
\(222\) | 111715.i | 0.152135i | ||||||||
\(223\) | 1.08298e6i | 1.45834i | 0.684330 | + | 0.729172i | \(0.260095\pi\) | ||||
−0.684330 | + | 0.729172i | \(0.739905\pi\) | |||||||
\(224\) | −482966. | −0.643126 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −829012. | −1.07967 | ||||||||
\(227\) | 412201.i | 0.530938i | 0.964119 | + | 0.265469i | \(0.0855269\pi\) | ||||
−0.964119 | + | 0.265469i | \(0.914473\pi\) | |||||||
\(228\) | − 423874.i | − 0.540007i | ||||||||
\(229\) | 433163. | 0.545836 | 0.272918 | − | 0.962037i | \(-0.412011\pi\) | ||||
0.272918 | + | 0.962037i | \(0.412011\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 185158. | 0.228303 | ||||||||
\(232\) | − 567658.i | − 0.692416i | ||||||||
\(233\) | − 760097.i | − 0.917232i | −0.888635 | − | 0.458616i | \(-0.848345\pi\) | ||||
0.888635 | − | 0.458616i | \(-0.151655\pi\) | |||||||
\(234\) | −934108. | −1.11521 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.55372e6 | 1.81590 | ||||||||
\(237\) | 34391.7i | 0.0397725i | ||||||||
\(238\) | − 1.27411e6i | − 1.45803i | ||||||||
\(239\) | 988624. | 1.11953 | 0.559766 | − | 0.828651i | \(-0.310891\pi\) | ||||
0.559766 | + | 0.828651i | \(0.310891\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −358878. | −0.398020 | −0.199010 | − | 0.979997i | \(-0.563773\pi\) | ||||
−0.199010 | + | 0.979997i | \(0.563773\pi\) | |||||||
\(242\) | 772186.i | 0.847585i | ||||||||
\(243\) | 819877.i | 0.890703i | ||||||||
\(244\) | 2.03232e6 | 2.18534 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −610669. | −0.643381 | ||||||||
\(247\) | 448373.i | 0.467624i | ||||||||
\(248\) | − 3.38734e6i | − 3.49727i | ||||||||
\(249\) | 292504. | 0.298974 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −851049. | −0.852649 | −0.426324 | − | 0.904570i | \(-0.640192\pi\) | ||||
−0.426324 | + | 0.904570i | \(0.640192\pi\) | |||||||
\(252\) | − 1.07408e6i | − 1.06545i | ||||||||
\(253\) | 333883.i | 0.327939i | ||||||||
\(254\) | −1.65528e6 | −1.60986 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.73300e6 | −1.65272 | ||||||||
\(257\) | − 76358.4i | − 0.0721147i | −0.999350 | − | 0.0360574i | \(-0.988520\pi\) | ||||
0.999350 | − | 0.0360574i | \(-0.0114799\pi\) | |||||||
\(258\) | 851348.i | 0.796266i | ||||||||
\(259\) | 135879. | 0.125864 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 284522. | 0.258533 | ||||||||
\(262\) | − 1.98064e6i | − 1.78260i | ||||||||
\(263\) | − 1.19420e6i | − 1.06460i | −0.846555 | − | 0.532301i | \(-0.821327\pi\) | ||||
0.846555 | − | 0.532301i | \(-0.178673\pi\) | |||||||
\(264\) | −1.13839e6 | −1.00527 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −740600. | −0.641770 | ||||||||
\(267\) | − 246551.i | − 0.211655i | ||||||||
\(268\) | 565907.i | 0.481292i | ||||||||
\(269\) | −1.02930e6 | −0.867286 | −0.433643 | − | 0.901085i | \(-0.642772\pi\) | ||||
−0.433643 | + | 0.901085i | \(0.642772\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.12144e6 | 1.75472 | 0.877359 | − | 0.479834i | \(-0.159303\pi\) | ||||
0.877359 | + | 0.479834i | \(0.159303\pi\) | |||||||
\(272\) | 3.60937e6i | 2.95807i | ||||||||
\(273\) | − 163173.i | − 0.132508i | ||||||||
\(274\) | −2.56901e6 | −2.06723 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −278162. | −0.219799 | ||||||||
\(277\) | 1.85145e6i | 1.44982i | 0.688845 | + | 0.724908i | \(0.258118\pi\) | ||||
−0.688845 | + | 0.724908i | \(0.741882\pi\) | |||||||
\(278\) | 2.24381e6i | 1.74130i | ||||||||
\(279\) | 1.69781e6 | 1.30580 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 90653.2 | 0.0684884 | 0.0342442 | − | 0.999413i | \(-0.489098\pi\) | ||||
0.0342442 | + | 0.999413i | \(0.489098\pi\) | |||||||
\(282\) | − 50756.3i | − 0.0380073i | ||||||||
\(283\) | 929308.i | 0.689753i | 0.938648 | + | 0.344877i | \(0.112079\pi\) | ||||
−0.938648 | + | 0.344877i | \(0.887921\pi\) | |||||||
\(284\) | 3.76890e6 | 2.77280 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.13698e6 | 1.54485 | ||||||||
\(287\) | 742759.i | 0.532283i | ||||||||
\(288\) | 1.48832e6i | 1.05734i | ||||||||
\(289\) | −1.82246e6 | −1.28355 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 817679. | 0.566044 | ||||||||
\(292\) | − 3.20927e6i | − 2.20267i | ||||||||
\(293\) | − 2.72733e6i | − 1.85596i | −0.372632 | − | 0.927979i | \(-0.621545\pi\) | ||||
0.372632 | − | 0.927979i | \(-0.378455\pi\) | |||||||
\(294\) | −683261. | −0.461018 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −835417. | −0.554209 | ||||||||
\(297\) | − 1.22312e6i | − 0.804597i | ||||||||
\(298\) | 397553.i | 0.259331i | ||||||||
\(299\) | 294240. | 0.190337 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.03550e6 | 0.658768 | ||||||||
\(302\) | − 1.59006e6i | − 1.00322i | ||||||||
\(303\) | 820208.i | 0.513236i | ||||||||
\(304\) | 2.09800e6 | 1.30203 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.92635e6 | −2.39709 | ||||||||
\(307\) | − 2.29648e6i | − 1.39064i | −0.718698 | − | 0.695322i | \(-0.755262\pi\) | ||||
0.718698 | − | 0.695322i | \(-0.244738\pi\) | |||||||
\(308\) | 2.45720e6i | 1.47592i | ||||||||
\(309\) | 1.04071e6 | 0.620058 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 984847. | 0.577388 | 0.288694 | − | 0.957421i | \(-0.406779\pi\) | ||||
0.288694 | + | 0.957421i | \(0.406779\pi\) | |||||||
\(312\) | 1.00323e6i | 0.583462i | ||||||||
\(313\) | − 2.06650e6i | − 1.19227i | −0.802884 | − | 0.596135i | \(-0.796702\pi\) | ||||
0.802884 | − | 0.596135i | \(-0.203298\pi\) | |||||||
\(314\) | 3.53469e6 | 2.02315 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −456407. | −0.257119 | ||||||||
\(317\) | 1.14349e6i | 0.639125i | 0.947565 | + | 0.319563i | \(0.103536\pi\) | ||||
−0.947565 | + | 0.319563i | \(0.896464\pi\) | |||||||
\(318\) | − 1.09564e6i | − 0.607578i | ||||||||
\(319\) | −650910. | −0.358133 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −375024. | −0.203140 | ||||||||
\(322\) | 486010.i | 0.261220i | ||||||||
\(323\) | 1.88465e6i | 1.00514i | ||||||||
\(324\) | −2.76628e6 | −1.46397 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.75801e6 | 1.95845 | ||||||||
\(327\) | 1.21141e6i | 0.626501i | ||||||||
\(328\) | − 4.56666e6i | − 2.34376i | ||||||||
\(329\) | −61735.0 | −0.0314443 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 205230. | 0.102961 | 0.0514804 | − | 0.998674i | \(-0.483606\pi\) | ||||
0.0514804 | + | 0.998674i | \(0.483606\pi\) | |||||||
\(332\) | 3.88178e6i | 1.93279i | ||||||||
\(333\) | − 418729.i | − 0.206929i | ||||||||
\(334\) | −2.55805e6 | −1.25471 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −763511. | −0.368950 | ||||||||
\(337\) | 488213.i | 0.234172i | 0.993122 | + | 0.117086i | \(0.0373553\pi\) | ||||
−0.993122 | + | 0.117086i | \(0.962645\pi\) | |||||||
\(338\) | 1.92699e6i | 0.917462i | ||||||||
\(339\) | −446265. | −0.210908 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.88412e6 | −1.80887 | ||||||||
\(342\) | 2.28225e6i | 1.05511i | ||||||||
\(343\) | 1.98992e6i | 0.913273i | ||||||||
\(344\) | −6.36648e6 | −2.90070 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −630709. | −0.283230 | ||||||||
\(347\) | − 3.82809e6i | − 1.70670i | −0.521336 | − | 0.853351i | \(-0.674566\pi\) | ||||
0.521336 | − | 0.853351i | \(-0.325434\pi\) | |||||||
\(348\) | − 542281.i | − 0.240036i | ||||||||
\(349\) | −1.45476e6 | −0.639333 | −0.319667 | − | 0.947530i | \(-0.603571\pi\) | ||||
−0.319667 | + | 0.947530i | \(0.603571\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.07789e6 | −0.466991 | ||||||||
\(352\) | − 3.40487e6i | − 1.46469i | ||||||||
\(353\) | 778492.i | 0.332520i | 0.986082 | + | 0.166260i | \(0.0531690\pi\) | ||||
−0.986082 | + | 0.166260i | \(0.946831\pi\) | |||||||
\(354\) | 1.20146e6 | 0.509567 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.27193e6 | 1.36829 | ||||||||
\(357\) | − 685867.i | − 0.284819i | ||||||||
\(358\) | − 6.22707e6i | − 2.56789i | ||||||||
\(359\) | 2.12510e6 | 0.870247 | 0.435124 | − | 0.900371i | \(-0.356705\pi\) | ||||
0.435124 | + | 0.900371i | \(0.356705\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.38061e6 | −0.557577 | ||||||||
\(362\) | 1.57712e6i | 0.632549i | ||||||||
\(363\) | 415675.i | 0.165572i | ||||||||
\(364\) | 2.16544e6 | 0.856630 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.57156e6 | 0.613236 | ||||||||
\(367\) | 4.10801e6i | 1.59208i | 0.605242 | + | 0.796042i | \(0.293077\pi\) | ||||
−0.605242 | + | 0.796042i | \(0.706923\pi\) | |||||||
\(368\) | − 1.37679e6i | − 0.529967i | ||||||||
\(369\) | 2.28891e6 | 0.875109 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.33263e6 | −0.502662 | ||||||||
\(372\) | − 3.23591e6i | − 1.21238i | ||||||||
\(373\) | 4.54570e6i | 1.69172i | 0.533405 | + | 0.845860i | \(0.320912\pi\) | ||||
−0.533405 | + | 0.845860i | \(0.679088\pi\) | |||||||
\(374\) | 8.98241e6 | 3.32058 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 379561. | 0.138456 | ||||||||
\(377\) | 573624.i | 0.207861i | ||||||||
\(378\) | − 1.78041e6i | − 0.640901i | ||||||||
\(379\) | −1.40554e6 | −0.502626 | −0.251313 | − | 0.967906i | \(-0.580862\pi\) | ||||
−0.251313 | + | 0.967906i | \(0.580862\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −891054. | −0.314479 | ||||||||
\(382\) | 1.87093e6i | 0.655993i | ||||||||
\(383\) | − 4.64417e6i | − 1.61775i | −0.587982 | − | 0.808874i | \(-0.700078\pi\) | ||||
0.587982 | − | 0.808874i | \(-0.299922\pi\) | |||||||
\(384\) | −799627. | −0.276732 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.04756e6 | −0.357857 | ||||||||
\(387\) | − 3.19102e6i | − 1.08306i | ||||||||
\(388\) | 1.08513e7i | 3.65933i | ||||||||
\(389\) | −3.53606e6 | −1.18480 | −0.592400 | − | 0.805644i | \(-0.701819\pi\) | ||||
−0.592400 | + | 0.805644i | \(0.701819\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.23678e6 | 0.409120 | ||||||||
\(392\) | − 5.10950e6i | − 1.67944i | ||||||||
\(393\) | − 1.06620e6i | − 0.348223i | ||||||||
\(394\) | 4.15261e6 | 1.34766 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 7.57217e6 | 2.42651 | ||||||||
\(397\) | − 2.95611e6i | − 0.941336i | −0.882310 | − | 0.470668i | \(-0.844013\pi\) | ||||
0.882310 | − | 0.470668i | \(-0.155987\pi\) | |||||||
\(398\) | 1.71682e6i | 0.543272i | ||||||||
\(399\) | −398671. | −0.125367 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −799254. | −0.248213 | −0.124106 | − | 0.992269i | \(-0.539606\pi\) | ||||
−0.124106 | + | 0.992269i | \(0.539606\pi\) | |||||||
\(402\) | 437605.i | 0.135057i | ||||||||
\(403\) | 3.42294e6i | 1.04987i | ||||||||
\(404\) | −1.08848e7 | −3.31794 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −947484. | −0.285270 | ||||||||
\(407\) | 957937.i | 0.286649i | ||||||||
\(408\) | 4.21687e6i | 1.25412i | ||||||||
\(409\) | −898422. | −0.265566 | −0.132783 | − | 0.991145i | \(-0.542391\pi\) | ||||
−0.132783 | + | 0.991145i | \(0.542391\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.38292e6 | −0.403824 | ||||||||
\(412\) | 1.38111e7i | 4.00852i | ||||||||
\(413\) | − 1.46134e6i | − 0.421576i | ||||||||
\(414\) | 1.49770e6 | 0.429462 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.00060e6 | −0.850108 | ||||||||
\(417\) | 1.20786e6i | 0.340155i | ||||||||
\(418\) | − 5.22118e6i | − 1.46160i | ||||||||
\(419\) | −2.31259e6 | −0.643523 | −0.321761 | − | 0.946821i | \(-0.604275\pi\) | ||||
−0.321761 | + | 0.946821i | \(0.604275\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.43296e6 | 1.21896 | 0.609478 | − | 0.792803i | \(-0.291379\pi\) | ||||
0.609478 | + | 0.792803i | \(0.291379\pi\) | |||||||
\(422\) | − 4.72855e6i | − 1.29255i | ||||||||
\(423\) | 190244.i | 0.0516965i | ||||||||
\(424\) | 8.19336e6 | 2.21334 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.91442e6 | 0.778086 | ||||||||
\(427\) | − 1.91149e6i | − 0.507344i | ||||||||
\(428\) | − 4.97688e6i | − 1.31325i | ||||||||
\(429\) | 1.15036e6 | 0.301780 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.97999e6 | 1.55063 | 0.775314 | − | 0.631576i | \(-0.217592\pi\) | ||||
0.775314 | + | 0.631576i | \(0.217592\pi\) | |||||||
\(432\) | 5.04363e6i | 1.30027i | ||||||||
\(433\) | − 2.06419e6i | − 0.529089i | −0.964373 | − | 0.264545i | \(-0.914778\pi\) | ||||
0.964373 | − | 0.264545i | \(-0.0852217\pi\) | |||||||
\(434\) | −5.65384e6 | −1.44085 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.60764e7 | −4.05017 | ||||||||
\(437\) | − 718899.i | − 0.180080i | ||||||||
\(438\) | − 2.48167e6i | − 0.618099i | ||||||||
\(439\) | 4.09148e6 | 1.01326 | 0.506628 | − | 0.862165i | \(-0.330892\pi\) | ||||
0.506628 | + | 0.862165i | \(0.330892\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.56099e6 | 0.627064 | ||||||||
\(442\) | − 7.91589e6i | − 1.92728i | ||||||||
\(443\) | − 2.75822e6i | − 0.667759i | −0.942616 | − | 0.333879i | \(-0.891642\pi\) | ||||
0.942616 | − | 0.333879i | \(-0.108358\pi\) | |||||||
\(444\) | −798070. | −0.192125 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.11137e7 | −2.64558 | ||||||||
\(447\) | 214006.i | 0.0506592i | ||||||||
\(448\) | − 533431.i | − 0.125569i | ||||||||
\(449\) | 3.76648e6 | 0.881698 | 0.440849 | − | 0.897581i | \(-0.354677\pi\) | ||||
0.440849 | + | 0.897581i | \(0.354677\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.23640e6 | −1.21225 | ||||||||
\(452\) | − 5.92231e6i | − 1.36347i | ||||||||
\(453\) | − 855944.i | − 0.195975i | ||||||||
\(454\) | −4.23004e6 | −0.963174 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.45113e6 | 0.552019 | ||||||||
\(457\) | 480604.i | 0.107646i | 0.998550 | + | 0.0538229i | \(0.0171407\pi\) | ||||
−0.998550 | + | 0.0538229i | \(0.982859\pi\) | |||||||
\(458\) | 4.44515e6i | 0.990200i | ||||||||
\(459\) | −4.53073e6 | −1.00377 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.52514e6 | 0.991699 | 0.495849 | − | 0.868409i | \(-0.334857\pi\) | ||||
0.495849 | + | 0.868409i | \(0.334857\pi\) | |||||||
\(462\) | 1.90010e6i | 0.414164i | ||||||||
\(463\) | − 7.39975e6i | − 1.60422i | −0.597175 | − | 0.802111i | \(-0.703710\pi\) | ||||
0.597175 | − | 0.802111i | \(-0.296290\pi\) | |||||||
\(464\) | 2.68407e6 | 0.578761 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.80018e6 | 1.66395 | ||||||||
\(467\) | 1.84711e6i | 0.391923i | 0.980612 | + | 0.195962i | \(0.0627828\pi\) | ||||
−0.980612 | + | 0.195962i | \(0.937217\pi\) | |||||||
\(468\) | − 6.67309e6i | − 1.40836i | ||||||||
\(469\) | 532261. | 0.111736 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.90276e6 | 0.395212 | ||||||||
\(472\) | 8.98467e6i | 1.85630i | ||||||||
\(473\) | 7.30018e6i | 1.50031i | ||||||||
\(474\) | −352931. | −0.0721513 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 9.10203e6 | 1.84128 | ||||||||
\(477\) | 4.10669e6i | 0.826410i | ||||||||
\(478\) | 1.01453e7i | 2.03094i | ||||||||
\(479\) | 3.05088e6 | 0.607555 | 0.303778 | − | 0.952743i | \(-0.401752\pi\) | ||||
0.303778 | + | 0.952743i | \(0.401752\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 844197. | 0.166372 | ||||||||
\(482\) | − 3.68284e6i | − 0.722047i | ||||||||
\(483\) | 261624.i | 0.0510281i | ||||||||
\(484\) | −5.51635e6 | −1.07038 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −8.41365e6 | −1.61582 | ||||||||
\(487\) | 7.28136e6i | 1.39120i | 0.718429 | + | 0.695601i | \(0.244862\pi\) | ||||
−0.718429 | + | 0.695601i | \(0.755138\pi\) | |||||||
\(488\) | 1.17523e7i | 2.23395i | ||||||||
\(489\) | 2.02297e6 | 0.382575 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.60475e6 | −1.23638 | −0.618191 | − | 0.786028i | \(-0.712134\pi\) | ||||
−0.618191 | + | 0.786028i | \(0.712134\pi\) | |||||||
\(492\) | − 4.36251e6i | − 0.812500i | ||||||||
\(493\) | 2.41112e6i | 0.446788i | ||||||||
\(494\) | −4.60124e6 | −0.848316 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.60164e7 | 2.92322 | ||||||||
\(497\) | − 3.54481e6i | − 0.643727i | ||||||||
\(498\) | 3.00171e6i | 0.542369i | ||||||||
\(499\) | −4.87006e6 | −0.875555 | −0.437777 | − | 0.899083i | \(-0.644234\pi\) | ||||
−0.437777 | + | 0.899083i | \(0.644234\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.37702e6 | −0.245102 | ||||||||
\(502\) | − 8.73354e6i | − 1.54679i | ||||||||
\(503\) | 1.16752e6i | 0.205753i | 0.994694 | + | 0.102876i | \(0.0328046\pi\) | ||||
−0.994694 | + | 0.102876i | \(0.967195\pi\) | |||||||
\(504\) | 6.21105e6 | 1.08915 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.42634e6 | −0.594914 | ||||||||
\(507\) | 1.03732e6i | 0.179222i | ||||||||
\(508\) | − 1.18250e7i | − 2.03303i | ||||||||
\(509\) | 7.41468e6 | 1.26852 | 0.634261 | − | 0.773119i | \(-0.281305\pi\) | ||||
0.634261 | + | 0.773119i | \(0.281305\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.01846e6 | −0.511367 | ||||||||
\(512\) | − 1.31522e7i | − 2.21730i | ||||||||
\(513\) | 2.63356e6i | 0.441824i | ||||||||
\(514\) | 783596. | 0.130823 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −6.08187e6 | −1.00557 | ||||||||
\(517\) | − 435227.i | − 0.0716127i | ||||||||
\(518\) | 1.39440e6i | 0.228330i | ||||||||
\(519\) | −339516. | −0.0553277 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −811897. | −0.131041 | −0.0655204 | − | 0.997851i | \(-0.520871\pi\) | ||||
−0.0655204 | + | 0.997851i | \(0.520871\pi\) | |||||||
\(522\) | 2.91979e6i | 0.469003i | ||||||||
\(523\) | − 5.06828e6i | − 0.810226i | −0.914267 | − | 0.405113i | \(-0.867232\pi\) | ||||
0.914267 | − | 0.405113i | \(-0.132768\pi\) | |||||||
\(524\) | 1.41494e7 | 2.25117 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.22550e7 | 1.93129 | ||||||||
\(527\) | 1.43877e7i | 2.25665i | ||||||||
\(528\) | − 5.38270e6i | − 0.840263i | ||||||||
\(529\) | 5.96457e6 | 0.926702 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.50331e6 | −0.693099 | ||||||||
\(532\) | − 5.29071e6i | − 0.810465i | ||||||||
\(533\) | 4.61465e6i | 0.703592i | ||||||||
\(534\) | 2.53012e6 | 0.383962 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.27247e6 | −0.491998 | ||||||||
\(537\) | − 3.35209e6i | − 0.501626i | ||||||||
\(538\) | − 1.05628e7i | − 1.57334i | ||||||||
\(539\) | −5.85886e6 | −0.868642 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.52830e6 | 0.224499 | 0.112250 | − | 0.993680i | \(-0.464194\pi\) | ||||
0.112250 | + | 0.993680i | \(0.464194\pi\) | |||||||
\(542\) | 2.17704e7i | 3.18323i | ||||||||
\(543\) | 848980.i | 0.123566i | ||||||||
\(544\) | −1.26124e7 | −1.82727 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.67449e6 | 0.240382 | ||||||||
\(547\) | − 1.23234e7i | − 1.76101i | −0.474036 | − | 0.880506i | \(-0.657203\pi\) | ||||
0.474036 | − | 0.880506i | \(-0.342797\pi\) | |||||||
\(548\) | − 1.83525e7i | − 2.61062i | ||||||||
\(549\) | −5.89050e6 | −0.834107 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.40150e6 | 0.196660 | ||||||||
\(552\) | − 1.60853e6i | − 0.224688i | ||||||||
\(553\) | 429271.i | 0.0596923i | ||||||||
\(554\) | −1.89998e7 | −2.63011 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.60293e7 | −2.19902 | ||||||||
\(557\) | − 4.08606e6i | − 0.558042i | −0.960285 | − | 0.279021i | \(-0.909990\pi\) | ||||
0.960285 | − | 0.279021i | \(-0.0900099\pi\) | |||||||
\(558\) | 1.74230e7i | 2.36885i | ||||||||
\(559\) | 6.43339e6 | 0.870784 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.83531e6 | 0.648661 | ||||||||
\(562\) | 930291.i | 0.124245i | ||||||||
\(563\) | − 24160.3i | − 0.00321241i | −0.999999 | − | 0.00160621i | \(-0.999489\pi\) | ||||
0.999999 | − | 0.00160621i | \(-0.000511272\pi\) | |||||||
\(564\) | 362593. | 0.0479979 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −9.53664e6 | −1.25128 | ||||||||
\(567\) | 2.60180e6i | 0.339873i | ||||||||
\(568\) | 2.17943e7i | 2.83448i | ||||||||
\(569\) | −1.42000e7 | −1.83869 | −0.919344 | − | 0.393454i | \(-0.871280\pi\) | ||||
−0.919344 | + | 0.393454i | \(0.871280\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −767642. | −0.0985300 | −0.0492650 | − | 0.998786i | \(-0.515688\pi\) | ||||
−0.0492650 | + | 0.998786i | \(0.515688\pi\) | |||||||
\(572\) | 1.52662e7i | 1.95093i | ||||||||
\(573\) | 1.00714e6i | 0.128145i | ||||||||
\(574\) | −7.62225e6 | −0.965614 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.64384e6 | −0.206444 | ||||||||
\(577\) | − 1.51488e6i | − 0.189426i | −0.995505 | − | 0.0947129i | \(-0.969807\pi\) | ||||
0.995505 | − | 0.0947129i | \(-0.0301933\pi\) | |||||||
\(578\) | − 1.87023e7i | − 2.32849i | ||||||||
\(579\) | −563910. | −0.0699059 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.65098e6 | 0.448714 | ||||||||
\(582\) | 8.39109e6i | 1.02686i | ||||||||
\(583\) | − 9.39498e6i | − 1.14479i | ||||||||
\(584\) | 1.85582e7 | 2.25167 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.79881e7 | 3.36689 | ||||||||
\(587\) | − 1.28973e7i | − 1.54491i | −0.635070 | − | 0.772455i | \(-0.719029\pi\) | ||||
0.635070 | − | 0.772455i | \(-0.280971\pi\) | |||||||
\(588\) | − 4.88109e6i | − 0.582201i | ||||||||
\(589\) | 8.36307e6 | 0.993294 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.23539e6 | 0.263260 | ||||||||
\(592\) | − 3.95012e6i | − 0.463240i | ||||||||
\(593\) | 5.43125e6i | 0.634254i | 0.948383 | + | 0.317127i | \(0.102718\pi\) | ||||
−0.948383 | + | 0.317127i | \(0.897282\pi\) | |||||||
\(594\) | 1.25518e7 | 1.45962 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.84004e6 | −0.327499 | ||||||||
\(597\) | 924180.i | 0.106126i | ||||||||
\(598\) | 3.01951e6i | 0.345290i | ||||||||
\(599\) | −3.92217e6 | −0.446642 | −0.223321 | − | 0.974745i | \(-0.571690\pi\) | ||||
−0.223321 | + | 0.974745i | \(0.571690\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.64824e6 | −0.637863 | −0.318931 | − | 0.947778i | \(-0.603324\pi\) | ||||
−0.318931 | + | 0.947778i | \(0.603324\pi\) | |||||||
\(602\) | 1.06264e7i | 1.19507i | ||||||||
\(603\) | − 1.64023e6i | − 0.183701i | ||||||||
\(604\) | 1.13591e7 | 1.26693 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −8.41704e6 | −0.931061 | ||||||||
\(607\) | − 1.07148e7i | − 1.18035i | −0.807274 | − | 0.590177i | \(-0.799058\pi\) | ||||
0.807274 | − | 0.590177i | \(-0.200942\pi\) | |||||||
\(608\) | 7.33119e6i | 0.804296i | ||||||||
\(609\) | −510039. | −0.0557263 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −383551. | −0.0415642 | ||||||||
\(612\) | − 2.80491e7i | − 3.02719i | ||||||||
\(613\) | − 4.08748e6i | − 0.439344i | −0.975574 | − | 0.219672i | \(-0.929501\pi\) | ||||
0.975574 | − | 0.219672i | \(-0.0704987\pi\) | |||||||
\(614\) | 2.35666e7 | 2.52276 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.42092e7 | −1.50875 | ||||||||
\(617\) | − 7.83395e6i | − 0.828453i | −0.910174 | − | 0.414227i | \(-0.864052\pi\) | ||||
0.910174 | − | 0.414227i | \(-0.135948\pi\) | |||||||
\(618\) | 1.06798e7i | 1.12485i | ||||||||
\(619\) | −1.23423e7 | −1.29470 | −0.647352 | − | 0.762191i | \(-0.724124\pi\) | ||||
−0.647352 | + | 0.762191i | \(0.724124\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.72824e6 | 0.179836 | ||||||||
\(622\) | 1.01066e7i | 1.04744i | ||||||||
\(623\) | − 3.07739e6i | − 0.317660i | ||||||||
\(624\) | −4.74358e6 | −0.487691 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.12066e7 | 2.16290 | ||||||||
\(627\) | − 2.81061e6i | − 0.285516i | ||||||||
\(628\) | 2.52512e7i | 2.55495i | ||||||||
\(629\) | 3.54842e6 | 0.357609 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.31578e6 | −0.131556 | −0.0657780 | − | 0.997834i | \(-0.520953\pi\) | ||||
−0.0657780 | + | 0.997834i | \(0.520953\pi\) | |||||||
\(632\) | − 2.63926e6i | − 0.262839i | ||||||||
\(633\) | − 2.54542e6i | − 0.252494i | ||||||||
\(634\) | −1.17346e7 | −1.15944 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 7.82708e6 | 0.767285 | ||||||||
\(637\) | 5.16320e6i | 0.504163i | ||||||||
\(638\) | − 6.67969e6i | − 0.649688i | ||||||||
\(639\) | −1.09238e7 | −1.05833 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.55744e6 | 0.630360 | 0.315180 | − | 0.949032i | \(-0.397935\pi\) | ||||
0.315180 | + | 0.949032i | \(0.397935\pi\) | |||||||
\(642\) | − 3.84852e6i | − 0.368516i | ||||||||
\(643\) | 4.69954e6i | 0.448258i | 0.974559 | + | 0.224129i | \(0.0719537\pi\) | ||||
−0.974559 | + | 0.224129i | \(0.928046\pi\) | |||||||
\(644\) | −3.47197e6 | −0.329884 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.93405e7 | −1.82341 | ||||||||
\(647\) | 2.05827e7i | 1.93305i | 0.256580 | + | 0.966523i | \(0.417404\pi\) | ||||
−0.256580 | + | 0.966523i | \(0.582596\pi\) | |||||||
\(648\) | − 1.59965e7i | − 1.49654i | ||||||||
\(649\) | 1.03023e7 | 0.960117 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.04351e6 | −0.281464 | ||||||||
\(652\) | 2.68465e7i | 2.47325i | ||||||||
\(653\) | 1.42466e7i | 1.30746i | 0.756727 | + | 0.653731i | \(0.226797\pi\) | ||||
−0.756727 | + | 0.653731i | \(0.773203\pi\) | |||||||
\(654\) | −1.24316e7 | −1.13653 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.15927e7 | 1.95905 | ||||||||
\(657\) | 9.30177e6i | 0.840722i | ||||||||
\(658\) | − 633530.i | − 0.0570430i | ||||||||
\(659\) | 1.35369e7 | 1.21425 | 0.607123 | − | 0.794608i | \(-0.292324\pi\) | ||||
0.607123 | + | 0.794608i | \(0.292324\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.30443e7 | −1.16122 | −0.580612 | − | 0.814180i | \(-0.697187\pi\) | ||||
−0.580612 | + | 0.814180i | \(0.697187\pi\) | |||||||
\(662\) | 2.10609e6i | 0.186781i | ||||||||
\(663\) | − 4.26119e6i | − 0.376485i | ||||||||
\(664\) | −2.24471e7 | −1.97579 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.29703e6 | 0.375390 | ||||||||
\(667\) | − 919721.i | − 0.0800464i | ||||||||
\(668\) | − 1.82743e7i | − 1.58452i | ||||||||
\(669\) | −5.98260e6 | −0.516802 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.34759e7 | 1.15545 | ||||||||
\(672\) | − 2.66799e6i | − 0.227908i | ||||||||
\(673\) | − 4.75951e6i | − 0.405065i | −0.979276 | − | 0.202532i | \(-0.935083\pi\) | ||||
0.979276 | − | 0.202532i | \(-0.0649171\pi\) | |||||||
\(674\) | −5.01008e6 | −0.424810 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.37661e7 | −1.15863 | ||||||||
\(677\) | − 1.51397e7i | − 1.26954i | −0.772701 | − | 0.634770i | \(-0.781095\pi\) | ||||
0.772701 | − | 0.634770i | \(-0.218905\pi\) | |||||||
\(678\) | − 4.57961e6i | − 0.382608i | ||||||||
\(679\) | 1.02061e7 | 0.849543 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.27707e6 | −0.188152 | ||||||||
\(682\) | − 3.98592e7i | − 3.28146i | ||||||||
\(683\) | 2.34145e7i | 1.92058i | 0.278998 | + | 0.960292i | \(0.409998\pi\) | ||||
−0.278998 | + | 0.960292i | \(0.590002\pi\) | |||||||
\(684\) | −1.63040e7 | −1.33246 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.04208e7 | −1.65677 | ||||||||
\(687\) | 2.39287e6i | 0.193431i | ||||||||
\(688\) | − 3.01028e7i | − 2.42458i | ||||||||
\(689\) | −8.27947e6 | −0.664438 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.62194e7 | −1.29223 | −0.646113 | − | 0.763242i | \(-0.723606\pi\) | ||||
−0.646113 | + | 0.763242i | \(0.723606\pi\) | |||||||
\(692\) | − 4.50567e6i | − 0.357679i | ||||||||
\(693\) | − 7.12196e6i | − 0.563334i | ||||||||
\(694\) | 3.92841e7 | 3.09613 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.13584e6 | 0.245375 | ||||||||
\(697\) | 1.93968e7i | 1.51234i | ||||||||
\(698\) | − 1.49289e7i | − 1.15981i | ||||||||
\(699\) | 4.19891e6 | 0.325045 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.89605e7 | −1.45732 | −0.728659 | − | 0.684876i | \(-0.759856\pi\) | ||||
−0.728659 | + | 0.684876i | \(0.759856\pi\) | |||||||
\(702\) | − 1.10614e7i | − 0.847167i | ||||||||
\(703\) | − 2.06258e6i | − 0.157406i | ||||||||
\(704\) | 3.76065e6 | 0.285977 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.98895e6 | −0.603223 | ||||||||
\(707\) | 1.02377e7i | 0.770287i | ||||||||
\(708\) | 8.58301e6i | 0.643512i | ||||||||
\(709\) | −128325. | −0.00958732 | −0.00479366 | − | 0.999989i | \(-0.501526\pi\) | ||||
−0.00479366 | + | 0.999989i | \(0.501526\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.32285e6 | 0.0981382 | ||||||||
\(712\) | 1.89206e7i | 1.39873i | ||||||||
\(713\) | − 5.48817e6i | − 0.404300i | ||||||||
\(714\) | 7.03843e6 | 0.516690 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.44850e7 | 3.24288 | ||||||||
\(717\) | 5.46133e6i | 0.396735i | ||||||||
\(718\) | 2.18079e7i | 1.57871i | ||||||||
\(719\) | 2.41874e7 | 1.74489 | 0.872444 | − | 0.488714i | \(-0.162534\pi\) | ||||
0.872444 | + | 0.488714i | \(0.162534\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.29899e7 | 0.930610 | ||||||||
\(722\) | − 1.41680e7i | − 1.01150i | ||||||||
\(723\) | − 1.98251e6i | − 0.141049i | ||||||||
\(724\) | −1.12667e7 | −0.798821 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −4.26569e6 | −0.300364 | ||||||||
\(727\) | − 513307.i | − 0.0360198i | −0.999838 | − | 0.0180099i | \(-0.994267\pi\) | ||||
0.999838 | − | 0.0180099i | \(-0.00573303\pi\) | |||||||
\(728\) | 1.25221e7i | 0.875685i | ||||||||
\(729\) | 4.64015e6 | 0.323380 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.70416e7 | 1.87171 | ||||||||
\(732\) | 1.12269e7i | 0.774431i | ||||||||
\(733\) | − 1.64153e7i | − 1.12847i | −0.825615 | − | 0.564234i | \(-0.809172\pi\) | ||||
0.825615 | − | 0.564234i | \(-0.190828\pi\) | |||||||
\(734\) | −4.21567e7 | −2.88820 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.81101e6 | 0.327372 | ||||||||
\(737\) | 3.75240e6i | 0.254472i | ||||||||
\(738\) | 2.34890e7i | 1.58753i | ||||||||
\(739\) | −1.16112e7 | −0.782109 | −0.391054 | − | 0.920368i | \(-0.627890\pi\) | ||||
−0.391054 | + | 0.920368i | \(0.627890\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.47689e6 | −0.165715 | ||||||||
\(742\) | − 1.36756e7i | − 0.911879i | ||||||||
\(743\) | 5.72590e6i | 0.380515i | 0.981734 | + | 0.190257i | \(0.0609323\pi\) | ||||
−0.981734 | + | 0.190257i | \(0.939068\pi\) | |||||||
\(744\) | 1.87122e7 | 1.23935 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4.66483e7 | −3.06894 | ||||||||
\(747\) | − 1.12510e7i | − 0.737715i | ||||||||
\(748\) | 6.41687e7i | 4.19343i | ||||||||
\(749\) | −4.68097e6 | −0.304882 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.15324e7 | 0.746137 | 0.373069 | − | 0.927804i | \(-0.378306\pi\) | ||||
0.373069 | + | 0.927804i | \(0.378306\pi\) | |||||||
\(752\) | 1.79469e6i | 0.115730i | ||||||||
\(753\) | − 4.70134e6i | − 0.302158i | ||||||||
\(754\) | −5.88658e6 | −0.377081 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.27189e7 | 0.809368 | ||||||||
\(757\) | 8.63293e6i | 0.547544i | 0.961795 | + | 0.273772i | \(0.0882713\pi\) | ||||
−0.961795 | + | 0.273772i | \(0.911729\pi\) | |||||||
\(758\) | − 1.44238e7i | − 0.911812i | ||||||||
\(759\) | −1.84443e6 | −0.116214 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.52622e6 | −0.220723 | −0.110361 | − | 0.993892i | \(-0.535201\pi\) | ||||
−0.110361 | + | 0.993892i | \(0.535201\pi\) | |||||||
\(762\) | − 9.14408e6i | − 0.570496i | ||||||||
\(763\) | 1.51206e7i | 0.940280i | ||||||||
\(764\) | −1.33656e7 | −0.828427 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.76588e7 | 2.93475 | ||||||||
\(767\) | − 9.07910e6i | − 0.557255i | ||||||||
\(768\) | − 9.57341e6i | − 0.585685i | ||||||||
\(769\) | −1.40471e7 | −0.856585 | −0.428293 | − | 0.903640i | \(-0.640885\pi\) | ||||
−0.428293 | + | 0.903640i | \(0.640885\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 421817. | 0.0255557 | ||||||||
\(772\) | − 7.48356e6i | − 0.451924i | ||||||||
\(773\) | − 2.44760e7i | − 1.47330i | −0.676274 | − | 0.736651i | \(-0.736406\pi\) | ||||
0.676274 | − | 0.736651i | \(-0.263594\pi\) | |||||||
\(774\) | 3.27465e7 | 1.96477 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.27496e7 | −3.74073 | ||||||||
\(777\) | 750619.i | 0.0446033i | ||||||||
\(778\) | − 3.62873e7i | − 2.14934i | ||||||||
\(779\) | 1.12747e7 | 0.665675 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.49907e7 | 1.46606 | ||||||||
\(782\) | 1.26920e7i | 0.742184i | ||||||||
\(783\) | 3.36924e6i | 0.196393i | ||||||||
\(784\) | 2.41594e7 | 1.40377 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.09414e7 | 0.631710 | ||||||||
\(787\) | − 4.35977e6i | − 0.250915i | −0.992099 | − | 0.125458i | \(-0.959960\pi\) | ||||
0.992099 | − | 0.125458i | \(-0.0400399\pi\) | |||||||
\(788\) | 2.96655e7i | 1.70191i | ||||||||
\(789\) | 6.59697e6 | 0.377270 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.57019e6 | −0.316540 | ||||||||
\(792\) | 4.37875e7i | 2.48049i | ||||||||
\(793\) | − 1.18758e7i | − 0.670626i | ||||||||
\(794\) | 3.03359e7 | 1.70768 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.22647e7 | −0.686076 | ||||||||
\(797\) | − 1.06887e7i | − 0.596044i | −0.954559 | − | 0.298022i | \(-0.903673\pi\) | ||||
0.954559 | − | 0.298022i | \(-0.0963269\pi\) | |||||||
\(798\) | − 4.09120e6i | − 0.227428i | ||||||||
\(799\) | −1.61218e6 | −0.0893403 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.48339e6 | −0.522255 | ||||||||
\(802\) | − 8.20202e6i | − 0.450282i | ||||||||
\(803\) | − 2.12799e7i | − 1.16461i | ||||||||
\(804\) | −3.12617e6 | −0.170558 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.51265e7 | −1.90457 | ||||||||
\(807\) | − 5.68605e6i | − 0.307345i | ||||||||
\(808\) | − 6.29436e7i | − 3.39175i | ||||||||
\(809\) | −9.12014e6 | −0.489926 | −0.244963 | − | 0.969532i | \(-0.578776\pi\) | ||||
−0.244963 | + | 0.969532i | \(0.578776\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.22575e6 | 0.278995 | 0.139497 | − | 0.990222i | \(-0.455451\pi\) | ||||
0.139497 | + | 0.990222i | \(0.455451\pi\) | |||||||
\(812\) | − 6.76865e6i | − 0.360256i | ||||||||
\(813\) | 1.17192e7i | 0.621830i | ||||||||
\(814\) | −9.83044e6 | −0.520010 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.99388e7 | −1.04827 | ||||||||
\(817\) | − 1.57184e7i | − 0.823857i | ||||||||
\(818\) | − 9.21968e6i | − 0.481762i | ||||||||
\(819\) | −6.27633e6 | −0.326961 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.00437e6 | 0.466225 | 0.233112 | − | 0.972450i | \(-0.425109\pi\) | ||||
0.233112 | + | 0.972450i | \(0.425109\pi\) | |||||||
\(822\) | − 1.41916e7i | − 0.732576i | ||||||||
\(823\) | 2.78867e7i | 1.43515i | 0.696482 | + | 0.717574i | \(0.254748\pi\) | ||||
−0.696482 | + | 0.717574i | \(0.745252\pi\) | |||||||
\(824\) | −7.98650e7 | −4.09768 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.49964e7 | 0.764781 | ||||||||
\(827\) | − 6.64309e6i | − 0.337758i | −0.985637 | − | 0.168879i | \(-0.945985\pi\) | ||||
0.985637 | − | 0.168879i | \(-0.0540148\pi\) | |||||||
\(828\) | 1.06993e7i | 0.542351i | ||||||||
\(829\) | −2.17030e7 | −1.09682 | −0.548408 | − | 0.836211i | \(-0.684766\pi\) | ||||
−0.548408 | + | 0.836211i | \(0.684766\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.02277e7 | −0.513780 | ||||||||
\(832\) | − 3.31413e6i | − 0.165982i | ||||||||
\(833\) | 2.17026e7i | 1.08367i | ||||||||
\(834\) | −1.23952e7 | −0.617075 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.72991e7 | 1.84579 | ||||||||
\(837\) | 2.01049e7i | 0.991949i | ||||||||
\(838\) | − 2.37320e7i | − 1.16741i | ||||||||
\(839\) | 1.01238e7 | 0.496520 | 0.248260 | − | 0.968693i | \(-0.420141\pi\) | ||||
0.248260 | + | 0.968693i | \(0.420141\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.87181e7 | −0.912584 | ||||||||
\(842\) | 4.54914e7i | 2.21131i | ||||||||
\(843\) | 500784.i | 0.0242707i | ||||||||
\(844\) | 3.37799e7 | 1.63231 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.95230e6 | −0.0937825 | ||||||||
\(847\) | 5.18837e6i | 0.248498i | ||||||||
\(848\) | 3.87409e7i | 1.85003i | ||||||||
\(849\) | −5.13366e6 | −0.244432 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.35354e6 | −0.0640691 | ||||||||
\(852\) | 2.08200e7i | 0.982613i | ||||||||
\(853\) | − 1.46326e7i | − 0.688573i | −0.938865 | − | 0.344286i | \(-0.888121\pi\) | ||||
0.938865 | − | 0.344286i | \(-0.111879\pi\) | |||||||
\(854\) | 1.96159e7 | 0.920371 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.87797e7 | 1.34246 | ||||||||
\(857\) | − 5.52218e6i | − 0.256838i | −0.991720 | − | 0.128419i | \(-0.959010\pi\) | ||||
0.991720 | − | 0.128419i | \(-0.0409902\pi\) | |||||||
\(858\) | 1.18051e7i | 0.547458i | ||||||||
\(859\) | 3.02260e6 | 0.139765 | 0.0698824 | − | 0.997555i | \(-0.477738\pi\) | ||||
0.0698824 | + | 0.997555i | \(0.477738\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.10313e6 | −0.188628 | ||||||||
\(862\) | 6.13672e7i | 2.81299i | ||||||||
\(863\) | 3.06818e7i | 1.40234i | 0.712992 | + | 0.701172i | \(0.247339\pi\) | ||||
−0.712992 | + | 0.701172i | \(0.752661\pi\) | |||||||
\(864\) | −1.76243e7 | −0.803207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.11829e7 | 0.959820 | ||||||||
\(867\) | − 1.00676e7i | − 0.454860i | ||||||||
\(868\) | − 4.03900e7i | − 1.81959i | ||||||||
\(869\) | −3.02633e6 | −0.135946 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.30686e6 | 0.147697 | ||||||||
\(872\) | − 9.29649e7i | − 4.14026i | ||||||||
\(873\) | − 3.14514e7i | − 1.39671i | ||||||||
\(874\) | 7.37741e6 | 0.326682 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.77286e7 | 0.780573 | ||||||||
\(877\) | − 5.17607e6i | − 0.227249i | −0.993524 | − | 0.113624i | \(-0.963754\pi\) | ||||
0.993524 | − | 0.113624i | \(-0.0362460\pi\) | |||||||
\(878\) | 4.19871e7i | 1.83815i | ||||||||
\(879\) | 1.50662e7 | 0.657707 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.25937e7 | −1.84887 | −0.924433 | − | 0.381345i | \(-0.875461\pi\) | ||||
−0.924433 | + | 0.381345i | \(0.875461\pi\) | |||||||
\(882\) | 2.62811e7i | 1.13756i | ||||||||
\(883\) | 1.72076e7i | 0.742709i | 0.928491 | + | 0.371354i | \(0.121107\pi\) | ||||
−0.928491 | + | 0.371354i | \(0.878893\pi\) | |||||||
\(884\) | 5.65496e7 | 2.43388 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.83051e7 | 1.21138 | ||||||||
\(887\) | 2.53773e6i | 0.108302i | 0.998533 | + | 0.0541510i | \(0.0172452\pi\) | ||||
−0.998533 | + | 0.0541510i | \(0.982755\pi\) | |||||||
\(888\) | − 4.61499e6i | − 0.196398i | ||||||||
\(889\) | −1.11220e7 | −0.471984 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.83425e7 | −0.774043 | ||||||||
\(892\) | − 7.93941e7i | − 3.34100i | ||||||||
\(893\) | 937108.i | 0.0393243i | ||||||||
\(894\) | −2.19615e6 | −0.0919007 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −9.98078e6 | −0.415331 | ||||||||
\(897\) | 1.62543e6i | 0.0674508i | ||||||||
\(898\) | 3.86519e7i | 1.59949i | ||||||||
\(899\) | 1.06993e7 | 0.441525 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.48012e7 | −1.42818 | ||||||||
\(902\) | − 5.37364e7i | − 2.19913i | ||||||||
\(903\) | 5.72026e6i | 0.233452i | ||||||||
\(904\) | 3.42468e7 | 1.39380 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 8.78377e6 | 0.355517 | ||||||||
\(907\) | 2.60899e7i | 1.05306i | 0.850156 | + | 0.526531i | \(0.176508\pi\) | ||||
−0.850156 | + | 0.526531i | \(0.823492\pi\) | |||||||
\(908\) | − 3.02186e7i | − 1.21635i | ||||||||
\(909\) | 3.15487e7 | 1.26640 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.44818e7 | 0.578130 | 0.289065 | − | 0.957309i | \(-0.406656\pi\) | ||||
0.289065 | + | 0.957309i | \(0.406656\pi\) | |||||||
\(912\) | 1.15897e7i | 0.461409i | ||||||||
\(913\) | 2.57392e7i | 1.02192i | ||||||||
\(914\) | −4.93200e6 | −0.195280 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.17553e7 | −1.25048 | ||||||||
\(917\) | − 1.33081e7i | − 0.522627i | ||||||||
\(918\) | − 4.64947e7i | − 1.82095i | ||||||||
\(919\) | −4.61041e7 | −1.80074 | −0.900369 | − | 0.435127i | \(-0.856704\pi\) | ||||
−0.900369 | + | 0.435127i | \(0.856704\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.26861e7 | 0.492811 | ||||||||
\(922\) | 4.64374e7i | 1.79904i | ||||||||
\(923\) | − 2.20234e7i | − 0.850903i | ||||||||
\(924\) | −1.35740e7 | −0.523031 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 7.59369e7 | 2.91022 | ||||||||
\(927\) | − 4.00301e7i | − 1.52998i | ||||||||
\(928\) | 9.37914e6i | 0.357514i | ||||||||
\(929\) | 1.81557e7 | 0.690197 | 0.345098 | − | 0.938567i | \(-0.387846\pi\) | ||||
0.345098 | + | 0.938567i | \(0.387846\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.26150e7 | 0.476993 | ||||||||
\(932\) | 5.57230e7i | 2.10133i | ||||||||
\(933\) | 5.44047e6i | 0.204612i | ||||||||
\(934\) | −1.89552e7 | −0.710987 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.85884e7 | 1.43968 | ||||||||
\(937\) | 1.78946e7i | 0.665844i | 0.942954 | + | 0.332922i | \(0.108035\pi\) | ||||
−0.942954 | + | 0.332922i | \(0.891965\pi\) | |||||||
\(938\) | 5.46210e6i | 0.202700i | ||||||||
\(939\) | 1.14157e7 | 0.422512 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.04463e6 | −0.112088 | −0.0560441 | − | 0.998428i | \(-0.517849\pi\) | ||||
−0.0560441 | + | 0.998428i | \(0.517849\pi\) | |||||||
\(942\) | 1.95262e7i | 0.716954i | ||||||||
\(943\) | − 7.39891e6i | − 0.270950i | ||||||||
\(944\) | −4.24825e7 | −1.55160 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.49151e7 | −2.72171 | ||||||||
\(947\) | 3.17110e7i | 1.14904i | 0.818491 | + | 0.574519i | \(0.194811\pi\) | ||||
−0.818491 | + | 0.574519i | \(0.805189\pi\) | |||||||
\(948\) | − 2.52127e6i | − 0.0911169i | ||||||||
\(949\) | −1.87532e7 | −0.675944 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.31686e6 | −0.226491 | ||||||||
\(952\) | 5.26342e7i | 1.88224i | ||||||||
\(953\) | − 1.01913e7i | − 0.363494i | −0.983345 | − | 0.181747i | \(-0.941825\pi\) | ||||
0.983345 | − | 0.181747i | \(-0.0581752\pi\) | |||||||
\(954\) | −4.21432e7 | −1.49919 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −7.24764e7 | −2.56479 | ||||||||
\(957\) | − 3.59574e6i | − 0.126914i | ||||||||
\(958\) | 3.13084e7i | 1.10216i | ||||||||
\(959\) | −1.72613e7 | −0.606077 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.52157e7 | 1.23006 | ||||||||
\(962\) | 8.66322e6i | 0.301816i | ||||||||
\(963\) | 1.44250e7i | 0.501246i | ||||||||
\(964\) | 2.63095e7 | 0.911844 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.68481e6 | −0.0925699 | ||||||||
\(967\) | − 3.21125e7i | − 1.10435i | −0.833727 | − | 0.552177i | \(-0.813797\pi\) | ||||
0.833727 | − | 0.552177i | \(-0.186203\pi\) | |||||||
\(968\) | − 3.18993e7i | − 1.09419i | ||||||||
\(969\) | −1.04111e7 | −0.356196 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.29867e7 | 0.782399 | 0.391200 | − | 0.920306i | \(-0.372060\pi\) | ||||
0.391200 | + | 0.920306i | \(0.372060\pi\) | |||||||
\(972\) | − 6.01055e7i | − 2.04056i | ||||||||
\(973\) | 1.50763e7i | 0.510519i | ||||||||
\(974\) | −7.47219e7 | −2.52378 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.55687e7 | −1.86726 | ||||||||
\(977\) | − 2.47331e7i | − 0.828978i | −0.910054 | − | 0.414489i | \(-0.863960\pi\) | ||||
0.910054 | − | 0.414489i | \(-0.136040\pi\) | |||||||
\(978\) | 2.07599e7i | 0.694029i | ||||||||
\(979\) | 2.16954e7 | 0.723455 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.65960e7 | 1.54588 | ||||||||
\(982\) | − 6.77785e7i | − 2.24292i | ||||||||
\(983\) | − 5.57031e7i | − 1.83863i | −0.393518 | − | 0.919317i | \(-0.628742\pi\) | ||||
0.393518 | − | 0.919317i | \(-0.371258\pi\) | |||||||
\(984\) | 2.52270e7 | 0.830574 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.47431e7 | −0.810518 | ||||||||
\(987\) | − 341035.i | − 0.0111431i | ||||||||
\(988\) | − 3.28704e7i | − 1.07130i | ||||||||
\(989\) | −1.03150e7 | −0.335335 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.86029e6 | −0.221901 | −0.110950 | − | 0.993826i | \(-0.535389\pi\) | ||||
−0.110950 | + | 0.993826i | \(0.535389\pi\) | |||||||
\(992\) | 5.59673e7i | 1.80574i | ||||||||
\(993\) | 1.13373e6i | 0.0364868i | ||||||||
\(994\) | 3.63772e7 | 1.16778 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.14436e7 | −0.684936 | ||||||||
\(997\) | 6.03725e7i | 1.92354i | 0.273856 | + | 0.961771i | \(0.411701\pi\) | ||||
−0.273856 | + | 0.961771i | \(0.588299\pi\) | |||||||
\(998\) | − 4.99770e7i | − 1.58834i | ||||||||
\(999\) | 4.95847e6 | 0.157193 |
(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 | 25.6.b.b.24.4 | 4 | ||
3.2 | odd | 2 | 225.6.b.i.199.1 | 4 | |||
4.3 | odd | 2 | 400.6.c.n.49.2 | 4 | |||
5.2 | odd | 4 | 25.6.a.b.1.1 | ✓ | 2 | ||
5.3 | odd | 4 | 25.6.a.d.1.2 | yes | 2 | ||
5.4 | even | 2 | inner | 25.6.b.b.24.1 | 4 | ||
15.2 | even | 4 | 225.6.a.s.1.2 | 2 | |||
15.8 | even | 4 | 225.6.a.l.1.1 | 2 | |||
15.14 | odd | 2 | 225.6.b.i.199.4 | 4 | |||
20.3 | even | 4 | 400.6.a.o.1.2 | 2 | |||
20.7 | even | 4 | 400.6.a.w.1.1 | 2 | |||
20.19 | odd | 2 | 400.6.c.n.49.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.6.a.b.1.1 | ✓ | 2 | 5.2 | odd | 4 | ||
25.6.a.d.1.2 | yes | 2 | 5.3 | odd | 4 | ||
25.6.b.b.24.1 | 4 | 5.4 | even | 2 | inner | ||
25.6.b.b.24.4 | 4 | 1.1 | even | 1 | trivial | ||
225.6.a.l.1.1 | 2 | 15.8 | even | 4 | |||
225.6.a.s.1.2 | 2 | 15.2 | even | 4 | |||
225.6.b.i.199.1 | 4 | 3.2 | odd | 2 | |||
225.6.b.i.199.4 | 4 | 15.14 | odd | 2 | |||
400.6.a.o.1.2 | 2 | 20.3 | even | 4 | |||
400.6.a.w.1.1 | 2 | 20.7 | even | 4 | |||
400.6.c.n.49.2 | 4 | 4.3 | odd | 2 | |||
400.6.c.n.49.3 | 4 | 20.19 | odd | 2 |