Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,6,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.a (trivial) |
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: | yes |
Analytic conductor: | \(132.316651346\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 229 x^{7} + 267 x^{6} + 16434 x^{5} - 16568 x^{4} - 405504 x^{3} + 202288 x^{2} + \cdots + 1190400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4}\cdot 5^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-1.92452\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.92452 | 0.340210 | 0.170105 | − | 0.985426i | \(-0.445589\pi\) | ||||
0.170105 | + | 0.985426i | \(0.445589\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | −28.2962 | −0.884257 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 17.3207 | 0.196420 | ||||||||
\(7\) | −59.1120 | −0.455964 | −0.227982 | − | 0.973665i | \(-0.573213\pi\) | ||||
−0.227982 | + | 0.973665i | \(0.573213\pi\) | |||||||
\(8\) | −116.041 | −0.641044 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −121.000 | −0.301511 | ||||||||
\(12\) | −254.666 | −0.510526 | ||||||||
\(13\) | 599.621 | 0.984053 | 0.492027 | − | 0.870580i | \(-0.336256\pi\) | ||||
0.492027 | + | 0.870580i | \(0.336256\pi\) | |||||||
\(14\) | −113.762 | −0.155124 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 682.155 | 0.666167 | ||||||||
\(17\) | −2271.97 | −1.90669 | −0.953346 | − | 0.301880i | \(-0.902386\pi\) | ||||
−0.953346 | + | 0.301880i | \(0.902386\pi\) | |||||||
\(18\) | 155.886 | 0.113403 | ||||||||
\(19\) | −2998.77 | −1.90572 | −0.952861 | − | 0.303408i | \(-0.901875\pi\) | ||||
−0.952861 | + | 0.303408i | \(0.901875\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −532.008 | −0.263251 | ||||||||
\(22\) | −232.867 | −0.102577 | ||||||||
\(23\) | −1571.78 | −0.619544 | −0.309772 | − | 0.950811i | \(-0.600253\pi\) | ||||
−0.309772 | + | 0.950811i | \(0.600253\pi\) | |||||||
\(24\) | −1044.37 | −0.370107 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1153.98 | 0.334785 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 1672.65 | 0.403189 | ||||||||
\(29\) | 9020.65 | 1.99179 | 0.995894 | − | 0.0905310i | \(-0.0288564\pi\) | ||||
0.995894 | + | 0.0905310i | \(0.0288564\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1838.01 | 0.343514 | 0.171757 | − | 0.985139i | \(-0.445056\pi\) | ||||
0.171757 | + | 0.985139i | \(0.445056\pi\) | |||||||
\(32\) | 5026.14 | 0.867681 | ||||||||
\(33\) | −1089.00 | −0.174078 | ||||||||
\(34\) | −4372.45 | −0.648676 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2291.99 | −0.294752 | ||||||||
\(37\) | 3881.95 | 0.466171 | 0.233086 | − | 0.972456i | \(-0.425118\pi\) | ||||
0.233086 | + | 0.972456i | \(0.425118\pi\) | |||||||
\(38\) | −5771.20 | −0.648346 | ||||||||
\(39\) | 5396.59 | 0.568143 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2147.54 | −0.199518 | −0.0997590 | − | 0.995012i | \(-0.531807\pi\) | ||||
−0.0997590 | + | 0.995012i | \(0.531807\pi\) | |||||||
\(42\) | −1023.86 | −0.0895606 | ||||||||
\(43\) | 2613.13 | 0.215521 | 0.107761 | − | 0.994177i | \(-0.465632\pi\) | ||||
0.107761 | + | 0.994177i | \(0.465632\pi\) | |||||||
\(44\) | 3423.84 | 0.266614 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3024.92 | −0.210775 | ||||||||
\(47\) | −8379.51 | −0.553317 | −0.276659 | − | 0.960968i | \(-0.589227\pi\) | ||||
−0.276659 | + | 0.960968i | \(0.589227\pi\) | |||||||
\(48\) | 6139.40 | 0.384612 | ||||||||
\(49\) | −13312.8 | −0.792097 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −20447.7 | −1.10083 | ||||||||
\(52\) | −16967.0 | −0.870156 | ||||||||
\(53\) | 11261.5 | 0.550690 | 0.275345 | − | 0.961345i | \(-0.411208\pi\) | ||||
0.275345 | + | 0.961345i | \(0.411208\pi\) | |||||||
\(54\) | 1402.98 | 0.0654735 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 6859.43 | 0.292293 | ||||||||
\(57\) | −26988.9 | −1.10027 | ||||||||
\(58\) | 17360.4 | 0.677626 | ||||||||
\(59\) | −2505.76 | −0.0937152 | −0.0468576 | − | 0.998902i | \(-0.514921\pi\) | ||||
−0.0468576 | + | 0.998902i | \(0.514921\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −42835.6 | −1.47394 | −0.736970 | − | 0.675925i | \(-0.763744\pi\) | ||||
−0.736970 | + | 0.675925i | \(0.763744\pi\) | |||||||
\(62\) | 3537.29 | 0.116867 | ||||||||
\(63\) | −4788.07 | −0.151988 | ||||||||
\(64\) | −12156.1 | −0.370974 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2095.80 | −0.0592230 | ||||||||
\(67\) | 8325.99 | 0.226594 | 0.113297 | − | 0.993561i | \(-0.463859\pi\) | ||||
0.113297 | + | 0.993561i | \(0.463859\pi\) | |||||||
\(68\) | 64288.2 | 1.68601 | ||||||||
\(69\) | −14146.0 | −0.357694 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13440.4 | 0.316422 | 0.158211 | − | 0.987405i | \(-0.449427\pi\) | ||||
0.158211 | + | 0.987405i | \(0.449427\pi\) | |||||||
\(72\) | −9399.34 | −0.213681 | ||||||||
\(73\) | 19484.1 | 0.427931 | 0.213966 | − | 0.976841i | \(-0.431362\pi\) | ||||
0.213966 | + | 0.976841i | \(0.431362\pi\) | |||||||
\(74\) | 7470.89 | 0.158596 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 84853.9 | 1.68515 | ||||||||
\(77\) | 7152.55 | 0.137478 | ||||||||
\(78\) | 10385.8 | 0.193288 | ||||||||
\(79\) | −20416.2 | −0.368050 | −0.184025 | − | 0.982922i | \(-0.558913\pi\) | ||||
−0.184025 | + | 0.982922i | \(0.558913\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −4132.99 | −0.0678781 | ||||||||
\(83\) | 82162.1 | 1.30911 | 0.654555 | − | 0.756014i | \(-0.272856\pi\) | ||||
0.654555 | + | 0.756014i | \(0.272856\pi\) | |||||||
\(84\) | 15053.8 | 0.232781 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5029.03 | 0.0733226 | ||||||||
\(87\) | 81185.9 | 1.14996 | ||||||||
\(88\) | 14041.0 | 0.193282 | ||||||||
\(89\) | 38458.1 | 0.514651 | 0.257325 | − | 0.966325i | \(-0.417159\pi\) | ||||
0.257325 | + | 0.966325i | \(0.417159\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −35444.8 | −0.448693 | ||||||||
\(92\) | 44475.4 | 0.547836 | ||||||||
\(93\) | 16542.1 | 0.198328 | ||||||||
\(94\) | −16126.5 | −0.188244 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 45235.3 | 0.500956 | ||||||||
\(97\) | 139725. | 1.50780 | 0.753901 | − | 0.656988i | \(-0.228170\pi\) | ||||
0.753901 | + | 0.656988i | \(0.228170\pi\) | |||||||
\(98\) | −25620.7 | −0.269480 | ||||||||
\(99\) | −9801.00 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −129073. | −1.25902 | −0.629511 | − | 0.776991i | \(-0.716745\pi\) | ||||
−0.629511 | + | 0.776991i | \(0.716745\pi\) | |||||||
\(102\) | −39352.1 | −0.374513 | ||||||||
\(103\) | −26675.0 | −0.247749 | −0.123875 | − | 0.992298i | \(-0.539532\pi\) | ||||
−0.123875 | + | 0.992298i | \(0.539532\pi\) | |||||||
\(104\) | −69580.8 | −0.630821 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 21673.0 | 0.187350 | ||||||||
\(107\) | −116793. | −0.986180 | −0.493090 | − | 0.869978i | \(-0.664133\pi\) | ||||
−0.493090 | + | 0.869978i | \(0.664133\pi\) | |||||||
\(108\) | −20627.9 | −0.170175 | ||||||||
\(109\) | 148976. | 1.20102 | 0.600509 | − | 0.799618i | \(-0.294965\pi\) | ||||
0.600509 | + | 0.799618i | \(0.294965\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 34937.5 | 0.269144 | ||||||||
\(112\) | −40323.5 | −0.303748 | ||||||||
\(113\) | 155580. | 1.14619 | 0.573095 | − | 0.819489i | \(-0.305742\pi\) | ||||
0.573095 | + | 0.819489i | \(0.305742\pi\) | |||||||
\(114\) | −51940.8 | −0.374323 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −255250. | −1.76125 | ||||||||
\(117\) | 48569.3 | 0.328018 | ||||||||
\(118\) | −4822.39 | −0.0318829 | ||||||||
\(119\) | 134301. | 0.869382 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | −82437.9 | −0.501450 | ||||||||
\(123\) | −19327.9 | −0.115192 | ||||||||
\(124\) | −52008.8 | −0.303754 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −9214.74 | −0.0517079 | ||||||||
\(127\) | 193163. | 1.06271 | 0.531354 | − | 0.847150i | \(-0.321684\pi\) | ||||
0.531354 | + | 0.847150i | \(0.321684\pi\) | |||||||
\(128\) | −184231. | −0.993890 | ||||||||
\(129\) | 23518.2 | 0.124431 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 337105. | 1.71628 | 0.858138 | − | 0.513419i | \(-0.171621\pi\) | ||||
0.858138 | + | 0.513419i | \(0.171621\pi\) | |||||||
\(132\) | 30814.6 | 0.153929 | ||||||||
\(133\) | 177263. | 0.868940 | ||||||||
\(134\) | 16023.5 | 0.0770897 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 263642. | 1.22227 | ||||||||
\(137\) | −349973. | −1.59306 | −0.796531 | − | 0.604598i | \(-0.793334\pi\) | ||||
−0.796531 | + | 0.604598i | \(0.793334\pi\) | |||||||
\(138\) | −27224.3 | −0.121691 | ||||||||
\(139\) | 343788. | 1.50923 | 0.754613 | − | 0.656171i | \(-0.227825\pi\) | ||||
0.754613 | + | 0.656171i | \(0.227825\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −75415.6 | −0.319458 | ||||||||
\(142\) | 25866.3 | 0.107650 | ||||||||
\(143\) | −72554.2 | −0.296703 | ||||||||
\(144\) | 55254.6 | 0.222056 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 37497.6 | 0.145587 | ||||||||
\(147\) | −119815. | −0.457317 | ||||||||
\(148\) | −109844. | −0.412215 | ||||||||
\(149\) | 447504. | 1.65132 | 0.825661 | − | 0.564167i | \(-0.190803\pi\) | ||||
0.825661 | + | 0.564167i | \(0.190803\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 496536. | 1.77218 | 0.886091 | − | 0.463510i | \(-0.153410\pi\) | ||||
0.886091 | + | 0.463510i | \(0.153410\pi\) | |||||||
\(152\) | 347981. | 1.22165 | ||||||||
\(153\) | −184030. | −0.635564 | ||||||||
\(154\) | 13765.2 | 0.0467715 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −152703. | −0.502385 | ||||||||
\(157\) | −365502. | −1.18342 | −0.591712 | − | 0.806150i | \(-0.701548\pi\) | ||||
−0.591712 | + | 0.806150i | \(0.701548\pi\) | |||||||
\(158\) | −39291.3 | −0.125214 | ||||||||
\(159\) | 101354. | 0.317941 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 92911.0 | 0.282490 | ||||||||
\(162\) | 12626.8 | 0.0378011 | ||||||||
\(163\) | 536870. | 1.58271 | 0.791353 | − | 0.611359i | \(-0.209377\pi\) | ||||
0.791353 | + | 0.611359i | \(0.209377\pi\) | |||||||
\(164\) | 60767.3 | 0.176425 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 158123. | 0.445373 | ||||||||
\(167\) | 158899. | 0.440890 | 0.220445 | − | 0.975399i | \(-0.429249\pi\) | ||||
0.220445 | + | 0.975399i | \(0.429249\pi\) | |||||||
\(168\) | 61734.9 | 0.168755 | ||||||||
\(169\) | −11747.5 | −0.0316395 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −242901. | −0.635240 | ||||||||
\(172\) | −73941.8 | −0.190576 | ||||||||
\(173\) | −19966.6 | −0.0507211 | −0.0253606 | − | 0.999678i | \(-0.508073\pi\) | ||||
−0.0253606 | + | 0.999678i | \(0.508073\pi\) | |||||||
\(174\) | 156244. | 0.391228 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −82540.8 | −0.200857 | ||||||||
\(177\) | −22551.9 | −0.0541065 | ||||||||
\(178\) | 74013.3 | 0.175089 | ||||||||
\(179\) | 153145. | 0.357247 | 0.178624 | − | 0.983917i | \(-0.442836\pi\) | ||||
0.178624 | + | 0.983917i | \(0.442836\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −790865. | −1.79435 | −0.897173 | − | 0.441680i | \(-0.854383\pi\) | ||||
−0.897173 | + | 0.441680i | \(0.854383\pi\) | |||||||
\(182\) | −68214.2 | −0.152650 | ||||||||
\(183\) | −385520. | −0.850980 | ||||||||
\(184\) | 182391. | 0.397155 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 31835.6 | 0.0674731 | ||||||||
\(187\) | 274908. | 0.574889 | ||||||||
\(188\) | 237109. | 0.489274 | ||||||||
\(189\) | −43092.6 | −0.0877503 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 612916. | 1.21568 | 0.607838 | − | 0.794061i | \(-0.292037\pi\) | ||||
0.607838 | + | 0.794061i | \(0.292037\pi\) | |||||||
\(192\) | −109405. | −0.214182 | ||||||||
\(193\) | 884585. | 1.70941 | 0.854705 | − | 0.519114i | \(-0.173738\pi\) | ||||
0.854705 | + | 0.519114i | \(0.173738\pi\) | |||||||
\(194\) | 268903. | 0.512970 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 376701. | 0.700417 | ||||||||
\(197\) | −14105.8 | −0.0258960 | −0.0129480 | − | 0.999916i | \(-0.504122\pi\) | ||||
−0.0129480 | + | 0.999916i | \(0.504122\pi\) | |||||||
\(198\) | −18862.2 | −0.0341924 | ||||||||
\(199\) | −104501. | −0.187063 | −0.0935316 | − | 0.995616i | \(-0.529816\pi\) | ||||
−0.0935316 | + | 0.995616i | \(0.529816\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 74933.9 | 0.130824 | ||||||||
\(202\) | −248404. | −0.428332 | ||||||||
\(203\) | −533229. | −0.908183 | ||||||||
\(204\) | 578594. | 0.973416 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −51336.7 | −0.0842868 | ||||||||
\(207\) | −127314. | −0.206515 | ||||||||
\(208\) | 409035. | 0.655544 | ||||||||
\(209\) | 362851. | 0.574597 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.08804e6 | 1.68244 | 0.841221 | − | 0.540692i | \(-0.181837\pi\) | ||||
0.841221 | + | 0.540692i | \(0.181837\pi\) | |||||||
\(212\) | −318658. | −0.486952 | ||||||||
\(213\) | 120964. | 0.182686 | ||||||||
\(214\) | −224770. | −0.335509 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −84594.1 | −0.123369 | ||||||||
\(217\) | −108648. | −0.156630 | ||||||||
\(218\) | 286707. | 0.408599 | ||||||||
\(219\) | 175357. | 0.247066 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.36232e6 | −1.87629 | ||||||||
\(222\) | 67238.0 | 0.0915656 | ||||||||
\(223\) | −818867. | −1.10268 | −0.551342 | − | 0.834279i | \(-0.685884\pi\) | ||||
−0.551342 | + | 0.834279i | \(0.685884\pi\) | |||||||
\(224\) | −297105. | −0.395631 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 299416. | 0.389946 | ||||||||
\(227\) | −409868. | −0.527934 | −0.263967 | − | 0.964532i | \(-0.585031\pi\) | ||||
−0.263967 | + | 0.964532i | \(0.585031\pi\) | |||||||
\(228\) | 763685. | 0.972920 | ||||||||
\(229\) | −29456.0 | −0.0371180 | −0.0185590 | − | 0.999828i | \(-0.505908\pi\) | ||||
−0.0185590 | + | 0.999828i | \(0.505908\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 64372.9 | 0.0793731 | ||||||||
\(232\) | −1.04677e6 | −1.27682 | ||||||||
\(233\) | −211115. | −0.254758 | −0.127379 | − | 0.991854i | \(-0.540656\pi\) | ||||
−0.127379 | + | 0.991854i | \(0.540656\pi\) | |||||||
\(234\) | 93472.6 | 0.111595 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 70903.6 | 0.0828683 | ||||||||
\(237\) | −183745. | −0.212494 | ||||||||
\(238\) | 258464. | 0.295773 | ||||||||
\(239\) | 879085. | 0.995488 | 0.497744 | − | 0.867324i | \(-0.334162\pi\) | ||||
0.497744 | + | 0.867324i | \(0.334162\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −830172. | −0.920715 | −0.460358 | − | 0.887734i | \(-0.652279\pi\) | ||||
−0.460358 | + | 0.887734i | \(0.652279\pi\) | |||||||
\(242\) | 28176.9 | 0.0309282 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 1.21208e6 | 1.30334 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −37196.9 | −0.0391894 | ||||||||
\(247\) | −1.79813e6 | −1.87533 | ||||||||
\(248\) | −213285. | −0.220207 | ||||||||
\(249\) | 739458. | 0.755815 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −96982.6 | −0.0971649 | −0.0485825 | − | 0.998819i | \(-0.515470\pi\) | ||||
−0.0485825 | + | 0.998819i | \(0.515470\pi\) | |||||||
\(252\) | 135484. | 0.134396 | ||||||||
\(253\) | 190185. | 0.186800 | ||||||||
\(254\) | 371745. | 0.361544 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 34437.4 | 0.0328421 | ||||||||
\(257\) | −369343. | −0.348817 | −0.174408 | − | 0.984673i | \(-0.555801\pi\) | ||||
−0.174408 | + | 0.984673i | \(0.555801\pi\) | |||||||
\(258\) | 45261.3 | 0.0423328 | ||||||||
\(259\) | −229470. | −0.212557 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 730673. | 0.663929 | ||||||||
\(262\) | 648765. | 0.583895 | ||||||||
\(263\) | 988642. | 0.881353 | 0.440676 | − | 0.897666i | \(-0.354739\pi\) | ||||
0.440676 | + | 0.897666i | \(0.354739\pi\) | |||||||
\(264\) | 126369. | 0.111591 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 341147. | 0.295622 | ||||||||
\(267\) | 346123. | 0.297134 | ||||||||
\(268\) | −235594. | −0.200367 | ||||||||
\(269\) | 1.36005e6 | 1.14598 | 0.572988 | − | 0.819564i | \(-0.305784\pi\) | ||||
0.572988 | + | 0.819564i | \(0.305784\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −219383. | −0.181460 | −0.0907298 | − | 0.995876i | \(-0.528920\pi\) | ||||
−0.0907298 | + | 0.995876i | \(0.528920\pi\) | |||||||
\(272\) | −1.54984e6 | −1.27018 | ||||||||
\(273\) | −319003. | −0.259053 | ||||||||
\(274\) | −673529. | −0.541976 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 400279. | 0.316293 | ||||||||
\(277\) | 1.78416e6 | 1.39713 | 0.698563 | − | 0.715549i | \(-0.253823\pi\) | ||||
0.698563 | + | 0.715549i | \(0.253823\pi\) | |||||||
\(278\) | 661627. | 0.513454 | ||||||||
\(279\) | 148879. | 0.114505 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.01028e6 | −0.763264 | −0.381632 | − | 0.924314i | \(-0.624638\pi\) | ||||
−0.381632 | + | 0.924314i | \(0.624638\pi\) | |||||||
\(282\) | −145139. | −0.108683 | ||||||||
\(283\) | −270967. | −0.201118 | −0.100559 | − | 0.994931i | \(-0.532063\pi\) | ||||
−0.100559 | + | 0.994931i | \(0.532063\pi\) | |||||||
\(284\) | −380313. | −0.279798 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −139632. | −0.100941 | ||||||||
\(287\) | 126945. | 0.0909730 | ||||||||
\(288\) | 407118. | 0.289227 | ||||||||
\(289\) | 3.74199e6 | 2.63547 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.25752e6 | 0.870530 | ||||||||
\(292\) | −551327. | −0.378401 | ||||||||
\(293\) | 874428. | 0.595052 | 0.297526 | − | 0.954714i | \(-0.403838\pi\) | ||||
0.297526 | + | 0.954714i | \(0.403838\pi\) | |||||||
\(294\) | −230586. | −0.155584 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −450466. | −0.298836 | ||||||||
\(297\) | −88209.0 | −0.0580259 | ||||||||
\(298\) | 861231. | 0.561796 | ||||||||
\(299\) | −942472. | −0.609664 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −154467. | −0.0982700 | ||||||||
\(302\) | 955594. | 0.602915 | ||||||||
\(303\) | −1.16166e6 | −0.726897 | ||||||||
\(304\) | −2.04563e6 | −1.26953 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −354169. | −0.216225 | ||||||||
\(307\) | −2.20038e6 | −1.33245 | −0.666225 | − | 0.745750i | \(-0.732091\pi\) | ||||
−0.666225 | + | 0.745750i | \(0.732091\pi\) | |||||||
\(308\) | −202390. | −0.121566 | ||||||||
\(309\) | −240075. | −0.143038 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 420029. | 0.246251 | 0.123126 | − | 0.992391i | \(-0.460708\pi\) | ||||
0.123126 | + | 0.992391i | \(0.460708\pi\) | |||||||
\(312\) | −626227. | −0.364205 | ||||||||
\(313\) | −342934. | −0.197856 | −0.0989282 | − | 0.995095i | \(-0.531541\pi\) | ||||
−0.0989282 | + | 0.995095i | \(0.531541\pi\) | |||||||
\(314\) | −703415. | −0.402613 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 577700. | 0.325450 | ||||||||
\(317\) | −1.83293e6 | −1.02446 | −0.512232 | − | 0.858847i | \(-0.671181\pi\) | ||||
−0.512232 | + | 0.858847i | \(0.671181\pi\) | |||||||
\(318\) | 195057. | 0.108167 | ||||||||
\(319\) | −1.09150e6 | −0.600546 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.05113e6 | −0.569371 | ||||||||
\(322\) | 178809. | 0.0961059 | ||||||||
\(323\) | 6.81312e6 | 3.63362 | ||||||||
\(324\) | −185652. | −0.0982508 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.03322e6 | 0.538453 | ||||||||
\(327\) | 1.34078e6 | 0.693408 | ||||||||
\(328\) | 249204. | 0.127900 | ||||||||
\(329\) | 495329. | 0.252293 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.42543e6 | 0.715114 | 0.357557 | − | 0.933891i | \(-0.383610\pi\) | ||||
0.357557 | + | 0.933891i | \(0.383610\pi\) | |||||||
\(332\) | −2.32488e6 | −1.15759 | ||||||||
\(333\) | 314438. | 0.155390 | ||||||||
\(334\) | 305805. | 0.149995 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −362912. | −0.175369 | ||||||||
\(337\) | −3.93186e6 | −1.88592 | −0.942961 | − | 0.332903i | \(-0.891972\pi\) | ||||
−0.942961 | + | 0.332903i | \(0.891972\pi\) | |||||||
\(338\) | −22608.3 | −0.0107641 | ||||||||
\(339\) | 1.40022e6 | 0.661754 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −222399. | −0.103573 | ||||||||
\(342\) | −467467. | −0.216115 | ||||||||
\(343\) | 1.78044e6 | 0.817131 | ||||||||
\(344\) | −303231. | −0.138159 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −38426.1 | −0.0172558 | ||||||||
\(347\) | −338208. | −0.150786 | −0.0753929 | − | 0.997154i | \(-0.524021\pi\) | ||||
−0.0753929 | + | 0.997154i | \(0.524021\pi\) | |||||||
\(348\) | −2.29725e6 | −1.01686 | ||||||||
\(349\) | −2.82994e6 | −1.24369 | −0.621846 | − | 0.783139i | \(-0.713617\pi\) | ||||
−0.621846 | + | 0.783139i | \(0.713617\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 437124. | 0.189381 | ||||||||
\(352\) | −608163. | −0.261616 | ||||||||
\(353\) | −4.21459e6 | −1.80019 | −0.900096 | − | 0.435691i | \(-0.856504\pi\) | ||||
−0.900096 | + | 0.435691i | \(0.856504\pi\) | |||||||
\(354\) | −43401.5 | −0.0184076 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.08822e6 | −0.455083 | ||||||||
\(357\) | 1.20871e6 | 0.501938 | ||||||||
\(358\) | 294730. | 0.121539 | ||||||||
\(359\) | 1.88776e6 | 0.773057 | 0.386529 | − | 0.922277i | \(-0.373674\pi\) | ||||
0.386529 | + | 0.922277i | \(0.373674\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.51653e6 | 2.63177 | ||||||||
\(362\) | −1.52204e6 | −0.610455 | ||||||||
\(363\) | 131769. | 0.0524864 | ||||||||
\(364\) | 1.00295e6 | 0.396760 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −741941. | −0.289512 | ||||||||
\(367\) | −376896. | −0.146068 | −0.0730342 | − | 0.997329i | \(-0.523268\pi\) | ||||
−0.0730342 | + | 0.997329i | \(0.523268\pi\) | |||||||
\(368\) | −1.07220e6 | −0.412720 | ||||||||
\(369\) | −173951. | −0.0665060 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −665691. | −0.251095 | ||||||||
\(372\) | −468079. | −0.175373 | ||||||||
\(373\) | 2.55080e6 | 0.949300 | 0.474650 | − | 0.880175i | \(-0.342575\pi\) | ||||
0.474650 | + | 0.880175i | \(0.342575\pi\) | |||||||
\(374\) | 529067. | 0.195583 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 972369. | 0.354700 | ||||||||
\(377\) | 5.40897e6 | 1.96002 | ||||||||
\(378\) | −82932.6 | −0.0298535 | ||||||||
\(379\) | 3.97187e6 | 1.42035 | 0.710177 | − | 0.704023i | \(-0.248615\pi\) | ||||
0.710177 | + | 0.704023i | \(0.248615\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.73846e6 | 0.613554 | ||||||||
\(382\) | 1.17957e6 | 0.413585 | ||||||||
\(383\) | −1.85461e6 | −0.646035 | −0.323018 | − | 0.946393i | \(-0.604697\pi\) | ||||
−0.323018 | + | 0.946393i | \(0.604697\pi\) | |||||||
\(384\) | −1.65808e6 | −0.573822 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.70240e6 | 0.581559 | ||||||||
\(387\) | 211664. | 0.0718405 | ||||||||
\(388\) | −3.95369e6 | −1.33329 | ||||||||
\(389\) | −992340. | −0.332496 | −0.166248 | − | 0.986084i | \(-0.553165\pi\) | ||||
−0.166248 | + | 0.986084i | \(0.553165\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.57104e6 | 1.18128 | ||||||||
\(392\) | 1.54483e6 | 0.507769 | ||||||||
\(393\) | 3.03395e6 | 0.990892 | ||||||||
\(394\) | −27146.9 | −0.00881009 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 277331. | 0.0888712 | ||||||||
\(397\) | −148359. | −0.0472430 | −0.0236215 | − | 0.999721i | \(-0.507520\pi\) | ||||
−0.0236215 | + | 0.999721i | \(0.507520\pi\) | |||||||
\(398\) | −201115. | −0.0636408 | ||||||||
\(399\) | 1.59537e6 | 0.501683 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.81078e6 | 1.18346 | 0.591729 | − | 0.806137i | \(-0.298445\pi\) | ||||
0.591729 | + | 0.806137i | \(0.298445\pi\) | |||||||
\(402\) | 144212. | 0.0445077 | ||||||||
\(403\) | 1.10211e6 | 0.338036 | ||||||||
\(404\) | 3.65229e6 | 1.11330 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.02621e6 | −0.308973 | ||||||||
\(407\) | −469716. | −0.140556 | ||||||||
\(408\) | 2.37278e6 | 0.705679 | ||||||||
\(409\) | −74545.8 | −0.0220351 | −0.0110175 | − | 0.999939i | \(-0.503507\pi\) | ||||
−0.0110175 | + | 0.999939i | \(0.503507\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.14975e6 | −0.919754 | ||||||||
\(412\) | 754803. | 0.219074 | ||||||||
\(413\) | 148121. | 0.0427307 | ||||||||
\(414\) | −245019. | −0.0702584 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.01378e6 | 0.853844 | ||||||||
\(417\) | 3.09409e6 | 0.871351 | ||||||||
\(418\) | 698315. | 0.195484 | ||||||||
\(419\) | 1.48992e6 | 0.414599 | 0.207299 | − | 0.978278i | \(-0.433533\pi\) | ||||
0.207299 | + | 0.978278i | \(0.433533\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.60498e6 | −0.716307 | −0.358154 | − | 0.933663i | \(-0.616594\pi\) | ||||
−0.358154 | + | 0.933663i | \(0.616594\pi\) | |||||||
\(422\) | 2.09396e6 | 0.572384 | ||||||||
\(423\) | −678740. | −0.184439 | ||||||||
\(424\) | −1.30680e6 | −0.353016 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 232797. | 0.0621517 | ||||||||
\(427\) | 2.53210e6 | 0.672064 | ||||||||
\(428\) | 3.30479e6 | 0.872037 | ||||||||
\(429\) | −652987. | −0.171302 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.30280e6 | −1.63433 | −0.817166 | − | 0.576402i | \(-0.804456\pi\) | ||||
−0.817166 | + | 0.576402i | \(0.804456\pi\) | |||||||
\(432\) | 497291. | 0.128204 | ||||||||
\(433\) | −4.19051e6 | −1.07411 | −0.537053 | − | 0.843549i | \(-0.680462\pi\) | ||||
−0.537053 | + | 0.843549i | \(0.680462\pi\) | |||||||
\(434\) | −209096. | −0.0532871 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.21545e6 | −1.06201 | ||||||||
\(437\) | 4.71341e6 | 1.18068 | ||||||||
\(438\) | 337478. | 0.0840545 | ||||||||
\(439\) | −2.10556e6 | −0.521442 | −0.260721 | − | 0.965414i | \(-0.583960\pi\) | ||||
−0.260721 | + | 0.965414i | \(0.583960\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.07833e6 | −0.264032 | ||||||||
\(442\) | −2.62182e6 | −0.638332 | ||||||||
\(443\) | 5.79037e6 | 1.40184 | 0.700918 | − | 0.713242i | \(-0.252774\pi\) | ||||
0.700918 | + | 0.713242i | \(0.252774\pi\) | |||||||
\(444\) | −988600. | −0.237993 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.57593e6 | −0.375145 | ||||||||
\(447\) | 4.02754e6 | 0.953391 | ||||||||
\(448\) | 718569. | 0.169150 | ||||||||
\(449\) | −2.51876e6 | −0.589618 | −0.294809 | − | 0.955556i | \(-0.595256\pi\) | ||||
−0.294809 | + | 0.955556i | \(0.595256\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 259853. | 0.0601569 | ||||||||
\(452\) | −4.40232e6 | −1.01353 | ||||||||
\(453\) | 4.46883e6 | 1.02317 | ||||||||
\(454\) | −788800. | −0.179609 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.13183e6 | 0.705320 | ||||||||
\(457\) | −6.44679e6 | −1.44395 | −0.721977 | − | 0.691917i | \(-0.756766\pi\) | ||||
−0.721977 | + | 0.691917i | \(0.756766\pi\) | |||||||
\(458\) | −56688.6 | −0.0126279 | ||||||||
\(459\) | −1.65627e6 | −0.366943 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.26707e6 | 0.496836 | 0.248418 | − | 0.968653i | \(-0.420089\pi\) | ||||
0.248418 | + | 0.968653i | \(0.420089\pi\) | |||||||
\(462\) | 123887. | 0.0270035 | ||||||||
\(463\) | −8.82820e6 | −1.91390 | −0.956951 | − | 0.290251i | \(-0.906261\pi\) | ||||
−0.956951 | + | 0.290251i | \(0.906261\pi\) | |||||||
\(464\) | 6.15349e6 | 1.32686 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −406294. | −0.0866714 | ||||||||
\(467\) | 3.46435e6 | 0.735072 | 0.367536 | − | 0.930009i | \(-0.380201\pi\) | ||||
0.367536 | + | 0.930009i | \(0.380201\pi\) | |||||||
\(468\) | −1.37433e6 | −0.290052 | ||||||||
\(469\) | −492165. | −0.103319 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.28951e6 | −0.683250 | ||||||||
\(472\) | 290772. | 0.0600755 | ||||||||
\(473\) | −316189. | −0.0649822 | ||||||||
\(474\) | −353622. | −0.0722925 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.80020e6 | −0.768757 | ||||||||
\(477\) | 912183. | 0.183563 | ||||||||
\(478\) | 1.69182e6 | 0.338675 | ||||||||
\(479\) | −5.50564e6 | −1.09640 | −0.548200 | − | 0.836347i | \(-0.684687\pi\) | ||||
−0.548200 | + | 0.836347i | \(0.684687\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.32770e6 | 0.458737 | ||||||||
\(482\) | −1.59768e6 | −0.313237 | ||||||||
\(483\) | 836199. | 0.163095 | ||||||||
\(484\) | −414285. | −0.0803870 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 113641. | 0.0218245 | ||||||||
\(487\) | −1.34130e6 | −0.256272 | −0.128136 | − | 0.991757i | \(-0.540899\pi\) | ||||
−0.128136 | + | 0.991757i | \(0.540899\pi\) | |||||||
\(488\) | 4.97069e6 | 0.944860 | ||||||||
\(489\) | 4.83183e6 | 0.913776 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.76450e6 | 1.26629 | 0.633144 | − | 0.774034i | \(-0.281764\pi\) | ||||
0.633144 | + | 0.774034i | \(0.281764\pi\) | |||||||
\(492\) | 546906. | 0.101859 | ||||||||
\(493\) | −2.04947e7 | −3.79772 | ||||||||
\(494\) | −3.46053e6 | −0.638007 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.25381e6 | 0.228838 | ||||||||
\(497\) | −794489. | −0.144277 | ||||||||
\(498\) | 1.42310e6 | 0.257136 | ||||||||
\(499\) | 6.79946e6 | 1.22243 | 0.611214 | − | 0.791466i | \(-0.290682\pi\) | ||||
0.611214 | + | 0.791466i | \(0.290682\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.43009e6 | 0.254548 | ||||||||
\(502\) | −186645. | −0.0330565 | ||||||||
\(503\) | −5.08998e6 | −0.897007 | −0.448503 | − | 0.893781i | \(-0.648043\pi\) | ||||
−0.448503 | + | 0.893781i | \(0.648043\pi\) | |||||||
\(504\) | 555614. | 0.0974309 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 366016. | 0.0635511 | ||||||||
\(507\) | −105728. | −0.0182670 | ||||||||
\(508\) | −5.46577e6 | −0.939706 | ||||||||
\(509\) | −3.53565e6 | −0.604889 | −0.302444 | − | 0.953167i | \(-0.597803\pi\) | ||||
−0.302444 | + | 0.953167i | \(0.597803\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.15175e6 | −0.195121 | ||||||||
\(512\) | 5.96167e6 | 1.00506 | ||||||||
\(513\) | −2.18610e6 | −0.366756 | ||||||||
\(514\) | −710808. | −0.118671 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −665476. | −0.110029 | ||||||||
\(517\) | 1.01392e6 | 0.166831 | ||||||||
\(518\) | −441619. | −0.0723141 | ||||||||
\(519\) | −179699. | −0.0292839 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.72572e6 | −0.601334 | −0.300667 | − | 0.953729i | \(-0.597209\pi\) | ||||
−0.300667 | + | 0.953729i | \(0.597209\pi\) | |||||||
\(522\) | 1.40619e6 | 0.225875 | ||||||||
\(523\) | −1.46844e6 | −0.234748 | −0.117374 | − | 0.993088i | \(-0.537448\pi\) | ||||
−0.117374 | + | 0.993088i | \(0.537448\pi\) | |||||||
\(524\) | −9.53880e6 | −1.51763 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.90266e6 | 0.299845 | ||||||||
\(527\) | −4.17591e6 | −0.654975 | ||||||||
\(528\) | −742867. | −0.115965 | ||||||||
\(529\) | −3.96585e6 | −0.616165 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −202967. | −0.0312384 | ||||||||
\(532\) | −5.01588e6 | −0.768366 | ||||||||
\(533\) | −1.28771e6 | −0.196336 | ||||||||
\(534\) | 666120. | 0.101088 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −966158. | −0.145257 | ||||||||
\(537\) | 1.37830e6 | 0.206257 | ||||||||
\(538\) | 2.61745e6 | 0.389873 | ||||||||
\(539\) | 1.61085e6 | 0.238826 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −158155. | −0.0232322 | −0.0116161 | − | 0.999933i | \(-0.503698\pi\) | ||||
−0.0116161 | + | 0.999933i | \(0.503698\pi\) | |||||||
\(542\) | −422207. | −0.0617344 | ||||||||
\(543\) | −7.11779e6 | −1.03597 | ||||||||
\(544\) | −1.14193e7 | −1.65440 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −613928. | −0.0881324 | ||||||||
\(547\) | 7.82586e6 | 1.11831 | 0.559157 | − | 0.829062i | \(-0.311125\pi\) | ||||
0.559157 | + | 0.829062i | \(0.311125\pi\) | |||||||
\(548\) | 9.90290e6 | 1.40868 | ||||||||
\(549\) | −3.46968e6 | −0.491314 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.70509e7 | −3.79579 | ||||||||
\(552\) | 1.64152e6 | 0.229297 | ||||||||
\(553\) | 1.20684e6 | 0.167817 | ||||||||
\(554\) | 3.43366e6 | 0.475316 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.72791e6 | −1.33454 | ||||||||
\(557\) | 71452.4 | 0.00975841 | 0.00487920 | − | 0.999988i | \(-0.498447\pi\) | ||||
0.00487920 | + | 0.999988i | \(0.498447\pi\) | |||||||
\(558\) | 286520. | 0.0389556 | ||||||||
\(559\) | 1.56689e6 | 0.212085 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.47418e6 | 0.331912 | ||||||||
\(562\) | −1.94430e6 | −0.259670 | ||||||||
\(563\) | −3.87924e6 | −0.515793 | −0.257897 | − | 0.966173i | \(-0.583029\pi\) | ||||
−0.257897 | + | 0.966173i | \(0.583029\pi\) | |||||||
\(564\) | 2.13398e6 | 0.282483 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −521481. | −0.0684223 | ||||||||
\(567\) | −387834. | −0.0506626 | ||||||||
\(568\) | −1.55964e6 | −0.202840 | ||||||||
\(569\) | 8.73077e6 | 1.13050 | 0.565252 | − | 0.824918i | \(-0.308779\pi\) | ||||
0.565252 | + | 0.824918i | \(0.308779\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 441497. | 0.0566680 | 0.0283340 | − | 0.999599i | \(-0.490980\pi\) | ||||
0.0283340 | + | 0.999599i | \(0.490980\pi\) | |||||||
\(572\) | 2.05301e6 | 0.262362 | ||||||||
\(573\) | 5.51625e6 | 0.701871 | ||||||||
\(574\) | 244309. | 0.0309499 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −984641. | −0.123658 | ||||||||
\(577\) | −1.12074e7 | −1.40141 | −0.700703 | − | 0.713453i | \(-0.747130\pi\) | ||||
−0.700703 | + | 0.713453i | \(0.747130\pi\) | |||||||
\(578\) | 7.20154e6 | 0.896615 | ||||||||
\(579\) | 7.96126e6 | 0.986928 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.85676e6 | −0.596907 | ||||||||
\(582\) | 2.42013e6 | 0.296163 | ||||||||
\(583\) | −1.36264e6 | −0.166039 | ||||||||
\(584\) | −2.26096e6 | −0.274323 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.68285e6 | 0.202443 | ||||||||
\(587\) | 9.06478e6 | 1.08583 | 0.542915 | − | 0.839788i | \(-0.317321\pi\) | ||||
0.542915 | + | 0.839788i | \(0.317321\pi\) | |||||||
\(588\) | 3.39031e6 | 0.404386 | ||||||||
\(589\) | −5.51178e6 | −0.654641 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −126952. | −0.0149511 | ||||||||
\(592\) | 2.64809e6 | 0.310548 | ||||||||
\(593\) | 3789.68 | 0.000442554 0 | 0.000221277 | − | 1.00000i | \(-0.499930\pi\) | ||||
0.000221277 | 1.00000i | \(0.499930\pi\) | ||||||||
\(594\) | −169760. | −0.0197410 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.26627e7 | −1.46019 | ||||||||
\(597\) | −940510. | −0.108001 | ||||||||
\(598\) | −1.81381e6 | −0.207414 | ||||||||
\(599\) | −6.84765e6 | −0.779785 | −0.389892 | − | 0.920860i | \(-0.627488\pi\) | ||||
−0.389892 | + | 0.920860i | \(0.627488\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.82312e6 | −0.996405 | −0.498203 | − | 0.867061i | \(-0.666006\pi\) | ||||
−0.498203 | + | 0.867061i | \(0.666006\pi\) | |||||||
\(602\) | −297276. | −0.0334325 | ||||||||
\(603\) | 674405. | 0.0755314 | ||||||||
\(604\) | −1.40501e7 | −1.56707 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.23564e6 | −0.247298 | ||||||||
\(607\) | 1.19124e7 | 1.31228 | 0.656142 | − | 0.754638i | \(-0.272187\pi\) | ||||
0.656142 | + | 0.754638i | \(0.272187\pi\) | |||||||
\(608\) | −1.50723e7 | −1.65356 | ||||||||
\(609\) | −4.79906e6 | −0.524340 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.02453e6 | −0.544493 | ||||||||
\(612\) | 5.20734e6 | 0.562002 | ||||||||
\(613\) | −5.84838e6 | −0.628615 | −0.314307 | − | 0.949321i | \(-0.601772\pi\) | ||||
−0.314307 | + | 0.949321i | \(0.601772\pi\) | |||||||
\(614\) | −4.23467e6 | −0.453313 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −829991. | −0.0881295 | ||||||||
\(617\) | −1.65932e6 | −0.175476 | −0.0877381 | − | 0.996144i | \(-0.527964\pi\) | ||||
−0.0877381 | + | 0.996144i | \(0.527964\pi\) | |||||||
\(618\) | −462030. | −0.0486630 | ||||||||
\(619\) | −6.13215e6 | −0.643259 | −0.321630 | − | 0.946866i | \(-0.604231\pi\) | ||||
−0.321630 | + | 0.946866i | \(0.604231\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.14583e6 | −0.119231 | ||||||||
\(622\) | 808355. | 0.0837772 | ||||||||
\(623\) | −2.27333e6 | −0.234662 | ||||||||
\(624\) | 3.68131e6 | 0.378479 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −659984. | −0.0673128 | ||||||||
\(627\) | 3.26566e6 | 0.331744 | ||||||||
\(628\) | 1.03423e7 | 1.04645 | ||||||||
\(629\) | −8.81967e6 | −0.888845 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.82127e7 | 1.82097 | 0.910483 | − | 0.413547i | \(-0.135710\pi\) | ||||
0.910483 | + | 0.413547i | \(0.135710\pi\) | |||||||
\(632\) | 2.36912e6 | 0.235936 | ||||||||
\(633\) | 9.79239e6 | 0.971358 | ||||||||
\(634\) | −3.52750e6 | −0.348533 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.86793e6 | −0.281142 | ||||||||
\(637\) | −7.98262e6 | −0.779466 | ||||||||
\(638\) | −2.10061e6 | −0.204312 | ||||||||
\(639\) | 1.08867e6 | 0.105474 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.32331e7 | 1.27209 | 0.636044 | − | 0.771653i | \(-0.280570\pi\) | ||||
0.636044 | + | 0.771653i | \(0.280570\pi\) | |||||||
\(642\) | −2.02293e6 | −0.193706 | ||||||||
\(643\) | 9.98593e6 | 0.952491 | 0.476246 | − | 0.879312i | \(-0.341997\pi\) | ||||
0.476246 | + | 0.879312i | \(0.341997\pi\) | |||||||
\(644\) | −2.62903e6 | −0.249793 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.31120e7 | 1.23620 | ||||||||
\(647\) | 1.83105e7 | 1.71965 | 0.859823 | − | 0.510593i | \(-0.170574\pi\) | ||||
0.859823 | + | 0.510593i | \(0.170574\pi\) | |||||||
\(648\) | −761347. | −0.0712271 | ||||||||
\(649\) | 303197. | 0.0282562 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −977836. | −0.0904302 | ||||||||
\(652\) | −1.51914e7 | −1.39952 | ||||||||
\(653\) | −1.10272e7 | −1.01201 | −0.506004 | − | 0.862531i | \(-0.668878\pi\) | ||||
−0.506004 | + | 0.862531i | \(0.668878\pi\) | |||||||
\(654\) | 2.58036e6 | 0.235905 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.46496e6 | −0.132912 | ||||||||
\(657\) | 1.57821e6 | 0.142644 | ||||||||
\(658\) | 953271. | 0.0858325 | ||||||||
\(659\) | 8.75231e6 | 0.785072 | 0.392536 | − | 0.919737i | \(-0.371598\pi\) | ||||
0.392536 | + | 0.919737i | \(0.371598\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.04678e6 | −0.0931866 | −0.0465933 | − | 0.998914i | \(-0.514836\pi\) | ||||
−0.0465933 | + | 0.998914i | \(0.514836\pi\) | |||||||
\(662\) | 2.74326e6 | 0.243289 | ||||||||
\(663\) | −1.22609e7 | −1.08327 | ||||||||
\(664\) | −9.53419e6 | −0.839196 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 605142. | 0.0528654 | ||||||||
\(667\) | −1.41785e7 | −1.23400 | ||||||||
\(668\) | −4.49625e6 | −0.389860 | ||||||||
\(669\) | −7.36980e6 | −0.636635 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.18310e6 | 0.444410 | ||||||||
\(672\) | −2.67395e6 | −0.228418 | ||||||||
\(673\) | 5.21480e6 | 0.443813 | 0.221906 | − | 0.975068i | \(-0.428772\pi\) | ||||
0.221906 | + | 0.975068i | \(0.428772\pi\) | |||||||
\(674\) | −7.56695e6 | −0.641610 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 332410. | 0.0279774 | ||||||||
\(677\) | 1.81772e7 | 1.52425 | 0.762125 | − | 0.647430i | \(-0.224156\pi\) | ||||
0.762125 | + | 0.647430i | \(0.224156\pi\) | |||||||
\(678\) | 2.69475e6 | 0.225135 | ||||||||
\(679\) | −8.25942e6 | −0.687503 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.68881e6 | −0.304803 | ||||||||
\(682\) | −428012. | −0.0352367 | ||||||||
\(683\) | −7.22749e6 | −0.592837 | −0.296419 | − | 0.955058i | \(-0.595792\pi\) | ||||
−0.296419 | + | 0.955058i | \(0.595792\pi\) | |||||||
\(684\) | 6.87317e6 | 0.561716 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.42649e6 | 0.277996 | ||||||||
\(687\) | −265104. | −0.0214301 | ||||||||
\(688\) | 1.78256e6 | 0.143573 | ||||||||
\(689\) | 6.75264e6 | 0.541908 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.05510e7 | 0.840619 | 0.420309 | − | 0.907381i | \(-0.361922\pi\) | ||||
0.420309 | + | 0.907381i | \(0.361922\pi\) | |||||||
\(692\) | 564979. | 0.0448505 | ||||||||
\(693\) | 579356. | 0.0458261 | ||||||||
\(694\) | −650888. | −0.0512989 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −9.42091e6 | −0.737174 | ||||||||
\(697\) | 4.87915e6 | 0.380419 | ||||||||
\(698\) | −5.44627e6 | −0.423117 | ||||||||
\(699\) | −1.90003e6 | −0.147085 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.26639e7 | 1.74197 | 0.870985 | − | 0.491310i | \(-0.163482\pi\) | ||||
0.870985 | + | 0.491310i | \(0.163482\pi\) | |||||||
\(702\) | 841253. | 0.0644294 | ||||||||
\(703\) | −1.16411e7 | −0.888392 | ||||||||
\(704\) | 1.47088e6 | 0.111853 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.11107e6 | −0.612444 | ||||||||
\(707\) | 7.62978e6 | 0.574069 | ||||||||
\(708\) | 638132. | 0.0478440 | ||||||||
\(709\) | −1.63112e7 | −1.21863 | −0.609313 | − | 0.792930i | \(-0.708555\pi\) | ||||
−0.609313 | + | 0.792930i | \(0.708555\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.65371e6 | −0.122683 | ||||||||
\(712\) | −4.46272e6 | −0.329913 | ||||||||
\(713\) | −2.88895e6 | −0.212822 | ||||||||
\(714\) | 2.32618e6 | 0.170765 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.33341e6 | −0.315898 | ||||||||
\(717\) | 7.91176e6 | 0.574745 | ||||||||
\(718\) | 3.63304e6 | 0.263002 | ||||||||
\(719\) | 9.77281e6 | 0.705013 | 0.352507 | − | 0.935809i | \(-0.385329\pi\) | ||||
0.352507 | + | 0.935809i | \(0.385329\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.57681e6 | 0.112965 | ||||||||
\(722\) | 1.25412e7 | 0.895357 | ||||||||
\(723\) | −7.47155e6 | −0.531575 | ||||||||
\(724\) | 2.23785e7 | 1.58666 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 253592. | 0.0178564 | ||||||||
\(727\) | −1.05257e7 | −0.738611 | −0.369306 | − | 0.929308i | \(-0.620404\pi\) | ||||
−0.369306 | + | 0.929308i | \(0.620404\pi\) | |||||||
\(728\) | 4.11306e6 | 0.287631 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.93696e6 | −0.410933 | ||||||||
\(732\) | 1.09088e7 | 0.752485 | ||||||||
\(733\) | −1.34590e6 | −0.0925238 | −0.0462619 | − | 0.998929i | \(-0.514731\pi\) | ||||
−0.0462619 | + | 0.998929i | \(0.514731\pi\) | |||||||
\(734\) | −725343. | −0.0496939 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.89999e6 | −0.537566 | ||||||||
\(737\) | −1.00744e6 | −0.0683207 | ||||||||
\(738\) | −334772. | −0.0226260 | ||||||||
\(739\) | −1.89035e7 | −1.27330 | −0.636651 | − | 0.771152i | \(-0.719681\pi\) | ||||
−0.636651 | + | 0.771152i | \(0.719681\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.61831e7 | −1.08272 | ||||||||
\(742\) | −1.28113e6 | −0.0854250 | ||||||||
\(743\) | 1.35078e7 | 0.897659 | 0.448830 | − | 0.893617i | \(-0.351841\pi\) | ||||
0.448830 | + | 0.893617i | \(0.351841\pi\) | |||||||
\(744\) | −1.91957e6 | −0.127137 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 4.90906e6 | 0.322962 | ||||||||
\(747\) | 6.65513e6 | 0.436370 | ||||||||
\(748\) | −7.77887e6 | −0.508350 | ||||||||
\(749\) | 6.90385e6 | 0.449662 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.35210e6 | 0.410977 | 0.205488 | − | 0.978660i | \(-0.434122\pi\) | ||||
0.205488 | + | 0.978660i | \(0.434122\pi\) | |||||||
\(752\) | −5.71613e6 | −0.368602 | ||||||||
\(753\) | −872843. | −0.0560982 | ||||||||
\(754\) | 1.04097e7 | 0.666820 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.21936e6 | 0.0775938 | ||||||||
\(757\) | 8.58261e6 | 0.544352 | 0.272176 | − | 0.962248i | \(-0.412257\pi\) | ||||
0.272176 | + | 0.962248i | \(0.412257\pi\) | |||||||
\(758\) | 7.64394e6 | 0.483219 | ||||||||
\(759\) | 1.71167e6 | 0.107849 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.15085e7 | 0.720372 | 0.360186 | − | 0.932880i | \(-0.382713\pi\) | ||||
0.360186 | + | 0.932880i | \(0.382713\pi\) | |||||||
\(762\) | 3.34571e6 | 0.208737 | ||||||||
\(763\) | −8.80626e6 | −0.547621 | ||||||||
\(764\) | −1.73432e7 | −1.07497 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.56924e6 | −0.219788 | ||||||||
\(767\) | −1.50251e6 | −0.0922207 | ||||||||
\(768\) | 309937. | 0.0189614 | ||||||||
\(769\) | −2.72489e7 | −1.66162 | −0.830812 | − | 0.556554i | \(-0.812123\pi\) | ||||
−0.830812 | + | 0.556554i | \(0.812123\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.32409e6 | −0.201389 | ||||||||
\(772\) | −2.50304e7 | −1.51156 | ||||||||
\(773\) | −1.35064e7 | −0.813003 | −0.406502 | − | 0.913650i | \(-0.633251\pi\) | ||||
−0.406502 | + | 0.913650i | \(0.633251\pi\) | |||||||
\(774\) | 407351. | 0.0244409 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.62139e7 | −0.966567 | ||||||||
\(777\) | −2.06523e6 | −0.122720 | ||||||||
\(778\) | −1.90978e6 | −0.113119 | ||||||||
\(779\) | 6.43999e6 | 0.380226 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.62629e6 | −0.0954047 | ||||||||
\(782\) | 6.87253e6 | 0.401883 | ||||||||
\(783\) | 6.57606e6 | 0.383320 | ||||||||
\(784\) | −9.08138e6 | −0.527669 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 5.83889e6 | 0.337112 | ||||||||
\(787\) | −7.81643e6 | −0.449854 | −0.224927 | − | 0.974376i | \(-0.572214\pi\) | ||||
−0.224927 | + | 0.974376i | \(0.572214\pi\) | |||||||
\(788\) | 399141. | 0.0228987 | ||||||||
\(789\) | 8.89778e6 | 0.508849 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.19662e6 | −0.522621 | ||||||||
\(792\) | 1.13732e6 | 0.0644273 | ||||||||
\(793\) | −2.56851e7 | −1.45044 | ||||||||
\(794\) | −285520. | −0.0160726 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.95699e6 | 0.165412 | ||||||||
\(797\) | 2.29316e7 | 1.27876 | 0.639379 | − | 0.768891i | \(-0.279191\pi\) | ||||
0.639379 | + | 0.768891i | \(0.279191\pi\) | |||||||
\(798\) | 3.07032e6 | 0.170678 | ||||||||
\(799\) | 1.90380e7 | 1.05501 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.11510e6 | 0.171550 | ||||||||
\(802\) | 7.33393e6 | 0.402625 | ||||||||
\(803\) | −2.35758e6 | −0.129026 | ||||||||
\(804\) | −2.12035e6 | −0.115682 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.12103e6 | 0.115003 | ||||||||
\(807\) | 1.22405e7 | 0.661629 | ||||||||
\(808\) | 1.49778e7 | 0.807088 | ||||||||
\(809\) | −1.38109e7 | −0.741908 | −0.370954 | − | 0.928651i | \(-0.620969\pi\) | ||||
−0.370954 | + | 0.928651i | \(0.620969\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.89793e7 | 1.01328 | 0.506638 | − | 0.862159i | \(-0.330888\pi\) | ||||
0.506638 | + | 0.862159i | \(0.330888\pi\) | |||||||
\(812\) | 1.50884e7 | 0.803067 | ||||||||
\(813\) | −1.97445e6 | −0.104766 | ||||||||
\(814\) | −903977. | −0.0478186 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.39485e7 | −0.733336 | ||||||||
\(817\) | −7.83619e6 | −0.410724 | ||||||||
\(818\) | −143465. | −0.00749656 | ||||||||
\(819\) | −2.87103e6 | −0.149564 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.65447e6 | −0.189220 | −0.0946098 | − | 0.995514i | \(-0.530160\pi\) | ||||
−0.0946098 | + | 0.995514i | \(0.530160\pi\) | |||||||
\(822\) | −6.06176e6 | −0.312910 | ||||||||
\(823\) | −1.37132e7 | −0.705731 | −0.352865 | − | 0.935674i | \(-0.614793\pi\) | ||||
−0.352865 | + | 0.935674i | \(0.614793\pi\) | |||||||
\(824\) | 3.09541e6 | 0.158818 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 285061. | 0.0145374 | ||||||||
\(827\) | −1.96311e7 | −0.998116 | −0.499058 | − | 0.866569i | \(-0.666321\pi\) | ||||
−0.499058 | + | 0.866569i | \(0.666321\pi\) | |||||||
\(828\) | 3.60251e6 | 0.182612 | ||||||||
\(829\) | −1.78813e7 | −0.903676 | −0.451838 | − | 0.892100i | \(-0.649232\pi\) | ||||
−0.451838 | + | 0.892100i | \(0.649232\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.60575e7 | 0.806631 | ||||||||
\(832\) | −7.28903e6 | −0.365058 | ||||||||
\(833\) | 3.02462e7 | 1.51028 | ||||||||
\(834\) | 5.95465e6 | 0.296443 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.02673e7 | −0.508091 | ||||||||
\(837\) | 1.33991e6 | 0.0661092 | ||||||||
\(838\) | 2.86738e6 | 0.141051 | ||||||||
\(839\) | 2.96975e6 | 0.145651 | 0.0728257 | − | 0.997345i | \(-0.476798\pi\) | ||||
0.0728257 | + | 0.997345i | \(0.476798\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.08610e7 | 2.96722 | ||||||||
\(842\) | −5.01334e6 | −0.243695 | ||||||||
\(843\) | −9.09249e6 | −0.440670 | ||||||||
\(844\) | −3.07875e7 | −1.48771 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.30625e6 | −0.0627481 | ||||||||
\(847\) | −865458. | −0.0414513 | ||||||||
\(848\) | 7.68211e6 | 0.366852 | ||||||||
\(849\) | −2.43870e6 | −0.116115 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.10157e6 | −0.288814 | ||||||||
\(852\) | −3.42281e6 | −0.161542 | ||||||||
\(853\) | 7.98055e6 | 0.375544 | 0.187772 | − | 0.982213i | \(-0.439873\pi\) | ||||
0.187772 | + | 0.982213i | \(0.439873\pi\) | |||||||
\(854\) | 4.87307e6 | 0.228643 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.35528e7 | 0.632184 | ||||||||
\(857\) | −1.41979e7 | −0.660347 | −0.330173 | − | 0.943920i | \(-0.607107\pi\) | ||||
−0.330173 | + | 0.943920i | \(0.607107\pi\) | |||||||
\(858\) | −1.25669e6 | −0.0582786 | ||||||||
\(859\) | −1.26770e7 | −0.586182 | −0.293091 | − | 0.956084i | \(-0.594684\pi\) | ||||
−0.293091 | + | 0.956084i | \(0.594684\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.14251e6 | 0.0525233 | ||||||||
\(862\) | −1.21299e7 | −0.556017 | ||||||||
\(863\) | −3.18697e7 | −1.45664 | −0.728318 | − | 0.685239i | \(-0.759698\pi\) | ||||
−0.728318 | + | 0.685239i | \(0.759698\pi\) | |||||||
\(864\) | 3.66406e6 | 0.166985 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −8.06472e6 | −0.365422 | ||||||||
\(867\) | 3.36780e7 | 1.52159 | ||||||||
\(868\) | 3.07434e6 | 0.138501 | ||||||||
\(869\) | 2.47036e6 | 0.110971 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.99244e6 | 0.222981 | ||||||||
\(872\) | −1.72873e7 | −0.769905 | ||||||||
\(873\) | 1.13177e7 | 0.502601 | ||||||||
\(874\) | 9.07105e6 | 0.401679 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.96195e6 | −0.218470 | ||||||||
\(877\) | 452817. | 0.0198804 | 0.00994018 | − | 0.999951i | \(-0.496836\pi\) | ||||
0.00994018 | + | 0.999951i | \(0.496836\pi\) | |||||||
\(878\) | −4.05219e6 | −0.177400 | ||||||||
\(879\) | 7.86985e6 | 0.343554 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.26083e7 | 1.41543 | 0.707715 | − | 0.706498i | \(-0.249726\pi\) | ||||
0.707715 | + | 0.706498i | \(0.249726\pi\) | |||||||
\(882\) | −2.07528e6 | −0.0898265 | ||||||||
\(883\) | 2.36123e7 | 1.01915 | 0.509573 | − | 0.860427i | \(-0.329803\pi\) | ||||
0.509573 | + | 0.860427i | \(0.329803\pi\) | |||||||
\(884\) | 3.85486e7 | 1.65912 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.11437e7 | 0.476919 | ||||||||
\(887\) | −3.31071e7 | −1.41290 | −0.706451 | − | 0.707762i | \(-0.749705\pi\) | ||||
−0.706451 | + | 0.707762i | \(0.749705\pi\) | |||||||
\(888\) | −4.05420e6 | −0.172533 | ||||||||
\(889\) | −1.14182e7 | −0.484556 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −793881. | −0.0335013 | ||||||||
\(892\) | 2.31708e7 | 0.975056 | ||||||||
\(893\) | 2.51282e7 | 1.05447 | ||||||||
\(894\) | 7.75108e6 | 0.324353 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.08903e7 | 0.453178 | ||||||||
\(897\) | −8.48225e6 | −0.351990 | ||||||||
\(898\) | −4.84740e6 | −0.200594 | ||||||||
\(899\) | 1.65801e7 | 0.684206 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.55858e7 | −1.05000 | ||||||||
\(902\) | 500091. | 0.0204660 | ||||||||
\(903\) | −1.39021e6 | −0.0567362 | ||||||||
\(904\) | −1.80537e7 | −0.734758 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 8.60034e6 | 0.348093 | ||||||||
\(907\) | −8.76937e6 | −0.353957 | −0.176978 | − | 0.984215i | \(-0.556632\pi\) | ||||
−0.176978 | + | 0.984215i | \(0.556632\pi\) | |||||||
\(908\) | 1.15977e7 | 0.466829 | ||||||||
\(909\) | −1.04549e7 | −0.419674 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.15460e7 | 0.460932 | 0.230466 | − | 0.973080i | \(-0.425975\pi\) | ||||
0.230466 | + | 0.973080i | \(0.425975\pi\) | |||||||
\(912\) | −1.84107e7 | −0.732963 | ||||||||
\(913\) | −9.94161e6 | −0.394711 | ||||||||
\(914\) | −1.24070e7 | −0.491248 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 833493. | 0.0328219 | ||||||||
\(917\) | −1.99269e7 | −0.782560 | ||||||||
\(918\) | −3.18752e6 | −0.124838 | ||||||||
\(919\) | −2.95602e7 | −1.15456 | −0.577282 | − | 0.816545i | \(-0.695887\pi\) | ||||
−0.577282 | + | 0.816545i | \(0.695887\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.98034e7 | −0.769291 | ||||||||
\(922\) | 4.36302e6 | 0.169029 | ||||||||
\(923\) | 8.05915e6 | 0.311376 | ||||||||
\(924\) | −1.82151e6 | −0.0701862 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.69900e7 | −0.651129 | ||||||||
\(927\) | −2.16068e6 | −0.0825830 | ||||||||
\(928\) | 4.53391e7 | 1.72824 | ||||||||
\(929\) | 4.03347e7 | 1.53334 | 0.766672 | − | 0.642039i | \(-0.221911\pi\) | ||||
0.766672 | + | 0.642039i | \(0.221911\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.99220e7 | 1.50952 | ||||||||
\(932\) | 5.97374e6 | 0.225272 | ||||||||
\(933\) | 3.78026e6 | 0.142173 | ||||||||
\(934\) | 6.66722e6 | 0.250079 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.63605e6 | −0.210274 | ||||||||
\(937\) | −2.52134e6 | −0.0938172 | −0.0469086 | − | 0.998899i | \(-0.514937\pi\) | ||||
−0.0469086 | + | 0.998899i | \(0.514937\pi\) | |||||||
\(938\) | −947182. | −0.0351501 | ||||||||
\(939\) | −3.08641e6 | −0.114232 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.52049e7 | 1.29607 | 0.648036 | − | 0.761609i | \(-0.275590\pi\) | ||||
0.648036 | + | 0.761609i | \(0.275590\pi\) | |||||||
\(942\) | −6.33074e6 | −0.232449 | ||||||||
\(943\) | 3.37546e6 | 0.123610 | ||||||||
\(944\) | −1.70932e6 | −0.0624300 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −608512. | −0.0221076 | ||||||||
\(947\) | 3.15673e7 | 1.14383 | 0.571917 | − | 0.820312i | \(-0.306200\pi\) | ||||
0.571917 | + | 0.820312i | \(0.306200\pi\) | |||||||
\(948\) | 5.19930e6 | 0.187899 | ||||||||
\(949\) | 1.16831e7 | 0.421107 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.64963e7 | −0.591475 | ||||||||
\(952\) | −1.55844e7 | −0.557312 | ||||||||
\(953\) | −2.68995e7 | −0.959427 | −0.479713 | − | 0.877425i | \(-0.659259\pi\) | ||||
−0.479713 | + | 0.877425i | \(0.659259\pi\) | |||||||
\(954\) | 1.75551e6 | 0.0624501 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.48748e7 | −0.880267 | ||||||||
\(957\) | −9.82349e6 | −0.346726 | ||||||||
\(958\) | −1.05957e7 | −0.373007 | ||||||||
\(959\) | 2.06876e7 | 0.726378 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.52509e7 | −0.881998 | ||||||||
\(962\) | 4.47970e6 | 0.156067 | ||||||||
\(963\) | −9.46021e6 | −0.328727 | ||||||||
\(964\) | 2.34907e7 | 0.814149 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.60928e6 | 0.0554867 | ||||||||
\(967\) | −2.96256e7 | −1.01883 | −0.509414 | − | 0.860522i | \(-0.670138\pi\) | ||||
−0.509414 | + | 0.860522i | \(0.670138\pi\) | |||||||
\(968\) | −1.69896e6 | −0.0582767 | ||||||||
\(969\) | 6.13181e7 | 2.09787 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.86746e7 | −1.31637 | −0.658184 | − | 0.752857i | \(-0.728675\pi\) | ||||
−0.658184 | + | 0.752857i | \(0.728675\pi\) | |||||||
\(972\) | −1.67086e6 | −0.0567251 | ||||||||
\(973\) | −2.03220e7 | −0.688152 | ||||||||
\(974\) | −2.58135e6 | −0.0871865 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.92205e7 | −0.981891 | ||||||||
\(977\) | −9.61017e6 | −0.322103 | −0.161051 | − | 0.986946i | \(-0.551489\pi\) | ||||
−0.161051 | + | 0.986946i | \(0.551489\pi\) | |||||||
\(978\) | 9.29896e6 | 0.310876 | ||||||||
\(979\) | −4.65343e6 | −0.155173 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.20670e7 | 0.400339 | ||||||||
\(982\) | 1.30184e7 | 0.430804 | ||||||||
\(983\) | −2.35665e7 | −0.777877 | −0.388939 | − | 0.921264i | \(-0.627158\pi\) | ||||
−0.388939 | + | 0.921264i | \(0.627158\pi\) | |||||||
\(984\) | 2.24283e6 | 0.0738429 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.94424e7 | −1.29202 | ||||||||
\(987\) | 4.45797e6 | 0.145661 | ||||||||
\(988\) | 5.08802e7 | 1.65827 | ||||||||
\(989\) | −4.10727e6 | −0.133525 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.88338e7 | −0.932649 | −0.466325 | − | 0.884614i | \(-0.654422\pi\) | ||||
−0.466325 | + | 0.884614i | \(0.654422\pi\) | |||||||
\(992\) | 9.23811e6 | 0.298060 | ||||||||
\(993\) | 1.28289e7 | 0.412871 | ||||||||
\(994\) | −1.52901e6 | −0.0490845 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.09239e7 | −0.668335 | ||||||||
\(997\) | −4.93391e7 | −1.57200 | −0.786002 | − | 0.618225i | \(-0.787852\pi\) | ||||
−0.786002 | + | 0.618225i | \(0.787852\pi\) | |||||||
\(998\) | 1.30857e7 | 0.415882 | ||||||||
\(999\) | 2.82994e6 | 0.0897147 |
(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 | 825.6.a.r.1.6 | ✓ | 9 | |
5.4 | even | 2 | 825.6.a.s.1.4 | yes | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.6.a.r.1.6 | ✓ | 9 | 1.1 | even | 1 | trivial | |
825.6.a.s.1.4 | yes | 9 | 5.4 | even | 2 |