Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [115,6,Mod(1,115)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(115, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("115.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 115 = 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 115.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: | \(18.4441392785\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2 x^{9} - 220 x^{8} + 541 x^{7} + 15887 x^{6} - 50180 x^{5} - 417450 x^{4} + 1703213 x^{3} + \cdots + 15136200 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(7.17227\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 115.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.17227 | −1.44467 | −0.722333 | − | 0.691545i | \(-0.756930\pi\) | ||||
−0.722333 | + | 0.691545i | \(0.756930\pi\) | |||||||
\(3\) | 13.4003 | 0.859626 | 0.429813 | − | 0.902918i | \(-0.358579\pi\) | ||||
0.429813 | + | 0.902918i | \(0.358579\pi\) | |||||||
\(4\) | 34.7860 | 1.08706 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | −109.510 | −1.24187 | ||||||||
\(7\) | 85.3046 | 0.658002 | 0.329001 | − | 0.944330i | \(-0.393288\pi\) | ||||
0.329001 | + | 0.944330i | \(0.393288\pi\) | |||||||
\(8\) | −22.7676 | −0.125775 | ||||||||
\(9\) | −63.4333 | −0.261042 | ||||||||
\(10\) | 204.307 | 0.646075 | ||||||||
\(11\) | −551.213 | −1.37353 | −0.686764 | − | 0.726880i | \(-0.740969\pi\) | ||||
−0.686764 | + | 0.726880i | \(0.740969\pi\) | |||||||
\(12\) | 466.141 | 0.934467 | ||||||||
\(13\) | 400.829 | 0.657810 | 0.328905 | − | 0.944363i | \(-0.393320\pi\) | ||||
0.328905 | + | 0.944363i | \(0.393320\pi\) | |||||||
\(14\) | −697.132 | −0.950594 | ||||||||
\(15\) | −335.006 | −0.384437 | ||||||||
\(16\) | −927.088 | −0.905359 | ||||||||
\(17\) | −333.547 | −0.279920 | −0.139960 | − | 0.990157i | \(-0.544697\pi\) | ||||
−0.139960 | + | 0.990157i | \(0.544697\pi\) | |||||||
\(18\) | 518.394 | 0.377119 | ||||||||
\(19\) | 2668.99 | 1.69615 | 0.848073 | − | 0.529879i | \(-0.177763\pi\) | ||||
0.848073 | + | 0.529879i | \(0.177763\pi\) | |||||||
\(20\) | −869.649 | −0.486149 | ||||||||
\(21\) | 1143.10 | 0.565636 | ||||||||
\(22\) | 4504.66 | 1.98429 | ||||||||
\(23\) | −529.000 | −0.208514 | ||||||||
\(24\) | −305.092 | −0.108119 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | −3275.68 | −0.950316 | ||||||||
\(27\) | −4106.28 | −1.08403 | ||||||||
\(28\) | 2967.40 | 0.715289 | ||||||||
\(29\) | −1249.92 | −0.275985 | −0.137993 | − | 0.990433i | \(-0.544065\pi\) | ||||
−0.137993 | + | 0.990433i | \(0.544065\pi\) | |||||||
\(30\) | 2737.76 | 0.555383 | ||||||||
\(31\) | −2604.42 | −0.486750 | −0.243375 | − | 0.969932i | \(-0.578255\pi\) | ||||
−0.243375 | + | 0.969932i | \(0.578255\pi\) | |||||||
\(32\) | 8304.97 | 1.43372 | ||||||||
\(33\) | −7386.39 | −1.18072 | ||||||||
\(34\) | 2725.83 | 0.404391 | ||||||||
\(35\) | −2132.62 | −0.294268 | ||||||||
\(36\) | −2206.59 | −0.283769 | ||||||||
\(37\) | −16493.7 | −1.98068 | −0.990340 | − | 0.138657i | \(-0.955721\pi\) | ||||
−0.990340 | + | 0.138657i | \(0.955721\pi\) | |||||||
\(38\) | −21811.7 | −2.45037 | ||||||||
\(39\) | 5371.21 | 0.565471 | ||||||||
\(40\) | 569.191 | 0.0562481 | ||||||||
\(41\) | −7787.12 | −0.723464 | −0.361732 | − | 0.932282i | \(-0.617815\pi\) | ||||
−0.361732 | + | 0.932282i | \(0.617815\pi\) | |||||||
\(42\) | −9341.75 | −0.817156 | ||||||||
\(43\) | −19679.5 | −1.62310 | −0.811548 | − | 0.584286i | \(-0.801375\pi\) | ||||
−0.811548 | + | 0.584286i | \(0.801375\pi\) | |||||||
\(44\) | −19174.5 | −1.49311 | ||||||||
\(45\) | 1585.83 | 0.116742 | ||||||||
\(46\) | 4323.13 | 0.301234 | ||||||||
\(47\) | 7018.58 | 0.463452 | 0.231726 | − | 0.972781i | \(-0.425563\pi\) | ||||
0.231726 | + | 0.972781i | \(0.425563\pi\) | |||||||
\(48\) | −12423.2 | −0.778270 | ||||||||
\(49\) | −9530.12 | −0.567033 | ||||||||
\(50\) | −5107.67 | −0.288933 | ||||||||
\(51\) | −4469.61 | −0.240627 | ||||||||
\(52\) | 13943.2 | 0.715080 | ||||||||
\(53\) | −23203.4 | −1.13465 | −0.567324 | − | 0.823495i | \(-0.692021\pi\) | ||||
−0.567324 | + | 0.823495i | \(0.692021\pi\) | |||||||
\(54\) | 33557.6 | 1.56606 | ||||||||
\(55\) | 13780.3 | 0.614261 | ||||||||
\(56\) | −1942.19 | −0.0827600 | ||||||||
\(57\) | 35765.2 | 1.45805 | ||||||||
\(58\) | 10214.7 | 0.398707 | ||||||||
\(59\) | −36537.3 | −1.36649 | −0.683245 | − | 0.730190i | \(-0.739432\pi\) | ||||
−0.683245 | + | 0.730190i | \(0.739432\pi\) | |||||||
\(60\) | −11653.5 | −0.417906 | ||||||||
\(61\) | 55063.4 | 1.89469 | 0.947345 | − | 0.320214i | \(-0.103755\pi\) | ||||
0.947345 | + | 0.320214i | \(0.103755\pi\) | |||||||
\(62\) | 21284.0 | 0.703192 | ||||||||
\(63\) | −5411.15 | −0.171766 | ||||||||
\(64\) | −38203.7 | −1.16588 | ||||||||
\(65\) | −10020.7 | −0.294182 | ||||||||
\(66\) | 60363.6 | 1.70575 | ||||||||
\(67\) | 1882.41 | 0.0512304 | 0.0256152 | − | 0.999672i | \(-0.491846\pi\) | ||||
0.0256152 | + | 0.999672i | \(0.491846\pi\) | |||||||
\(68\) | −11602.7 | −0.304290 | ||||||||
\(69\) | −7088.73 | −0.179245 | ||||||||
\(70\) | 17428.3 | 0.425119 | ||||||||
\(71\) | −20720.9 | −0.487823 | −0.243912 | − | 0.969797i | \(-0.578431\pi\) | ||||
−0.243912 | + | 0.969797i | \(0.578431\pi\) | |||||||
\(72\) | 1444.23 | 0.0328325 | ||||||||
\(73\) | 4194.38 | 0.0921214 | 0.0460607 | − | 0.998939i | \(-0.485333\pi\) | ||||
0.0460607 | + | 0.998939i | \(0.485333\pi\) | |||||||
\(74\) | 134791. | 2.86142 | ||||||||
\(75\) | 8375.16 | 0.171925 | ||||||||
\(76\) | 92843.5 | 1.84382 | ||||||||
\(77\) | −47021.0 | −0.903785 | ||||||||
\(78\) | −43894.9 | −0.816917 | ||||||||
\(79\) | −2776.34 | −0.0500501 | −0.0250251 | − | 0.999687i | \(-0.507967\pi\) | ||||
−0.0250251 | + | 0.999687i | \(0.507967\pi\) | |||||||
\(80\) | 23177.2 | 0.404889 | ||||||||
\(81\) | −39610.9 | −0.670815 | ||||||||
\(82\) | 63638.4 | 1.04516 | ||||||||
\(83\) | −30026.9 | −0.478427 | −0.239213 | − | 0.970967i | \(-0.576890\pi\) | ||||
−0.239213 | + | 0.970967i | \(0.576890\pi\) | |||||||
\(84\) | 39763.9 | 0.614881 | ||||||||
\(85\) | 8338.67 | 0.125184 | ||||||||
\(86\) | 160827. | 2.34483 | ||||||||
\(87\) | −16749.2 | −0.237244 | ||||||||
\(88\) | 12549.8 | 0.172755 | ||||||||
\(89\) | −125647. | −1.68142 | −0.840712 | − | 0.541482i | \(-0.817863\pi\) | ||||
−0.840712 | + | 0.541482i | \(0.817863\pi\) | |||||||
\(90\) | −12959.8 | −0.168653 | ||||||||
\(91\) | 34192.5 | 0.432841 | ||||||||
\(92\) | −18401.8 | −0.226668 | ||||||||
\(93\) | −34899.8 | −0.418423 | ||||||||
\(94\) | −57357.7 | −0.669533 | ||||||||
\(95\) | −66724.8 | −0.758540 | ||||||||
\(96\) | 111289. | 1.23246 | ||||||||
\(97\) | 104126. | 1.12365 | 0.561825 | − | 0.827256i | \(-0.310099\pi\) | ||||
0.561825 | + | 0.827256i | \(0.310099\pi\) | |||||||
\(98\) | 77882.7 | 0.819174 | ||||||||
\(99\) | 34965.2 | 0.358549 | ||||||||
\(100\) | 21741.2 | 0.217412 | ||||||||
\(101\) | 110179. | 1.07472 | 0.537358 | − | 0.843354i | \(-0.319422\pi\) | ||||
0.537358 | + | 0.843354i | \(0.319422\pi\) | |||||||
\(102\) | 36526.8 | 0.347626 | ||||||||
\(103\) | −157717. | −1.46482 | −0.732411 | − | 0.680863i | \(-0.761605\pi\) | ||||
−0.732411 | + | 0.680863i | \(0.761605\pi\) | |||||||
\(104\) | −9125.93 | −0.0827358 | ||||||||
\(105\) | −28577.6 | −0.252960 | ||||||||
\(106\) | 189624. | 1.63919 | ||||||||
\(107\) | −3468.74 | −0.0292896 | −0.0146448 | − | 0.999893i | \(-0.504662\pi\) | ||||
−0.0146448 | + | 0.999893i | \(0.504662\pi\) | |||||||
\(108\) | −142841. | −1.17840 | ||||||||
\(109\) | 101306. | 0.816712 | 0.408356 | − | 0.912823i | \(-0.366102\pi\) | ||||
0.408356 | + | 0.912823i | \(0.366102\pi\) | |||||||
\(110\) | −112616. | −0.887402 | ||||||||
\(111\) | −221020. | −1.70265 | ||||||||
\(112\) | −79084.8 | −0.595728 | ||||||||
\(113\) | 6017.65 | 0.0443334 | 0.0221667 | − | 0.999754i | \(-0.492944\pi\) | ||||
0.0221667 | + | 0.999754i | \(0.492944\pi\) | |||||||
\(114\) | −292283. | −2.10640 | ||||||||
\(115\) | 13225.0 | 0.0932505 | ||||||||
\(116\) | −43479.6 | −0.300013 | ||||||||
\(117\) | −25425.9 | −0.171716 | ||||||||
\(118\) | 298592. | 1.97412 | ||||||||
\(119\) | −28453.1 | −0.184188 | ||||||||
\(120\) | 7627.30 | 0.0483524 | ||||||||
\(121\) | 142785. | 0.886580 | ||||||||
\(122\) | −449993. | −2.73720 | ||||||||
\(123\) | −104349. | −0.621909 | ||||||||
\(124\) | −90597.1 | −0.529127 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 44221.4 | 0.248145 | ||||||||
\(127\) | −27459.5 | −0.151072 | −0.0755359 | − | 0.997143i | \(-0.524067\pi\) | ||||
−0.0755359 | + | 0.997143i | \(0.524067\pi\) | |||||||
\(128\) | 46451.4 | 0.250596 | ||||||||
\(129\) | −263711. | −1.39526 | ||||||||
\(130\) | 81892.0 | 0.424994 | ||||||||
\(131\) | −297127. | −1.51274 | −0.756368 | − | 0.654146i | \(-0.773028\pi\) | ||||
−0.756368 | + | 0.654146i | \(0.773028\pi\) | |||||||
\(132\) | −256943. | −1.28352 | ||||||||
\(133\) | 227677. | 1.11607 | ||||||||
\(134\) | −15383.6 | −0.0740109 | ||||||||
\(135\) | 102657. | 0.484791 | ||||||||
\(136\) | 7594.07 | 0.0352069 | ||||||||
\(137\) | 294915. | 1.34244 | 0.671220 | − | 0.741258i | \(-0.265771\pi\) | ||||
0.671220 | + | 0.741258i | \(0.265771\pi\) | |||||||
\(138\) | 57931.0 | 0.258949 | ||||||||
\(139\) | 335549. | 1.47306 | 0.736528 | − | 0.676407i | \(-0.236464\pi\) | ||||
0.736528 | + | 0.676407i | \(0.236464\pi\) | |||||||
\(140\) | −74185.1 | −0.319887 | ||||||||
\(141\) | 94050.7 | 0.398396 | ||||||||
\(142\) | 169337. | 0.704742 | ||||||||
\(143\) | −220942. | −0.903521 | ||||||||
\(144\) | 58808.2 | 0.236337 | ||||||||
\(145\) | 31247.9 | 0.123424 | ||||||||
\(146\) | −34277.6 | −0.133085 | ||||||||
\(147\) | −127706. | −0.487437 | ||||||||
\(148\) | −573750. | −2.15312 | ||||||||
\(149\) | 488334. | 1.80199 | 0.900993 | − | 0.433834i | \(-0.142839\pi\) | ||||
0.900993 | + | 0.433834i | \(0.142839\pi\) | |||||||
\(150\) | −68444.0 | −0.248375 | ||||||||
\(151\) | 354250. | 1.26435 | 0.632176 | − | 0.774825i | \(-0.282162\pi\) | ||||
0.632176 | + | 0.774825i | \(0.282162\pi\) | |||||||
\(152\) | −60766.7 | −0.213332 | ||||||||
\(153\) | 21158.0 | 0.0730710 | ||||||||
\(154\) | 384268. | 1.30567 | ||||||||
\(155\) | 65110.4 | 0.217681 | ||||||||
\(156\) | 186843. | 0.614702 | ||||||||
\(157\) | −308639. | −0.999314 | −0.499657 | − | 0.866223i | \(-0.666541\pi\) | ||||
−0.499657 | + | 0.866223i | \(0.666541\pi\) | |||||||
\(158\) | 22689.0 | 0.0723057 | ||||||||
\(159\) | −310931. | −0.975374 | ||||||||
\(160\) | −207624. | −0.641177 | ||||||||
\(161\) | −45126.1 | −0.137203 | ||||||||
\(162\) | 323711. | 0.969103 | ||||||||
\(163\) | −299295. | −0.882329 | −0.441165 | − | 0.897426i | \(-0.645435\pi\) | ||||
−0.441165 | + | 0.897426i | \(0.645435\pi\) | |||||||
\(164\) | −270882. | −0.786450 | ||||||||
\(165\) | 184660. | 0.528035 | ||||||||
\(166\) | 245388. | 0.691167 | ||||||||
\(167\) | −116466. | −0.323152 | −0.161576 | − | 0.986860i | \(-0.551658\pi\) | ||||
−0.161576 | + | 0.986860i | \(0.551658\pi\) | |||||||
\(168\) | −26025.8 | −0.0711427 | ||||||||
\(169\) | −210629. | −0.567286 | ||||||||
\(170\) | −68145.8 | −0.180849 | ||||||||
\(171\) | −169303. | −0.442766 | ||||||||
\(172\) | −684572. | −1.76440 | ||||||||
\(173\) | −331800. | −0.842871 | −0.421435 | − | 0.906858i | \(-0.638474\pi\) | ||||
−0.421435 | + | 0.906858i | \(0.638474\pi\) | |||||||
\(174\) | 136879. | 0.342739 | ||||||||
\(175\) | 53315.4 | 0.131600 | ||||||||
\(176\) | 511023. | 1.24354 | ||||||||
\(177\) | −489609. | −1.17467 | ||||||||
\(178\) | 1.02682e6 | 2.42910 | ||||||||
\(179\) | 280820. | 0.655082 | 0.327541 | − | 0.944837i | \(-0.393780\pi\) | ||||
0.327541 | + | 0.944837i | \(0.393780\pi\) | |||||||
\(180\) | 55164.7 | 0.126905 | ||||||||
\(181\) | −220.792 | −0.000500941 0 | −0.000250470 | − | 1.00000i | \(-0.500080\pi\) | ||||
−0.000250470 | 1.00000i | \(0.500080\pi\) | ||||||||
\(182\) | −279431. | −0.625310 | ||||||||
\(183\) | 737863. | 1.62873 | ||||||||
\(184\) | 12044.1 | 0.0262258 | ||||||||
\(185\) | 412343. | 0.885787 | ||||||||
\(186\) | 285211. | 0.604482 | ||||||||
\(187\) | 183855. | 0.384478 | ||||||||
\(188\) | 244148. | 0.503801 | ||||||||
\(189\) | −350285. | −0.713291 | ||||||||
\(190\) | 545293. | 1.09584 | ||||||||
\(191\) | −166609. | −0.330457 | −0.165229 | − | 0.986255i | \(-0.552836\pi\) | ||||
−0.165229 | + | 0.986255i | \(0.552836\pi\) | |||||||
\(192\) | −511939. | −1.00222 | ||||||||
\(193\) | 20214.5 | 0.0390634 | 0.0195317 | − | 0.999809i | \(-0.493782\pi\) | ||||
0.0195317 | + | 0.999809i | \(0.493782\pi\) | |||||||
\(194\) | −850949. | −1.62330 | ||||||||
\(195\) | −134280. | −0.252886 | ||||||||
\(196\) | −331515. | −0.616400 | ||||||||
\(197\) | −588783. | −1.08091 | −0.540456 | − | 0.841373i | \(-0.681748\pi\) | ||||
−0.540456 | + | 0.841373i | \(0.681748\pi\) | |||||||
\(198\) | −285745. | −0.517984 | ||||||||
\(199\) | 740471. | 1.32549 | 0.662743 | − | 0.748847i | \(-0.269392\pi\) | ||||
0.662743 | + | 0.748847i | \(0.269392\pi\) | |||||||
\(200\) | −14229.8 | −0.0251549 | ||||||||
\(201\) | 25224.8 | 0.0440390 | ||||||||
\(202\) | −900409. | −1.55261 | ||||||||
\(203\) | −106624. | −0.181599 | ||||||||
\(204\) | −155480. | −0.261576 | ||||||||
\(205\) | 194678. | 0.323543 | ||||||||
\(206\) | 1.28890e6 | 2.11618 | ||||||||
\(207\) | 33556.2 | 0.0544311 | ||||||||
\(208\) | −371603. | −0.595554 | ||||||||
\(209\) | −1.47118e6 | −2.32971 | ||||||||
\(210\) | 233544. | 0.365443 | ||||||||
\(211\) | −435057. | −0.672729 | −0.336365 | − | 0.941732i | \(-0.609197\pi\) | ||||
−0.336365 | + | 0.941732i | \(0.609197\pi\) | |||||||
\(212\) | −807151. | −1.23343 | ||||||||
\(213\) | −277665. | −0.419346 | ||||||||
\(214\) | 28347.5 | 0.0423136 | ||||||||
\(215\) | 491989. | 0.725870 | ||||||||
\(216\) | 93490.4 | 0.136343 | ||||||||
\(217\) | −222169. | −0.320283 | ||||||||
\(218\) | −827900. | −1.17988 | ||||||||
\(219\) | 56205.7 | 0.0791900 | ||||||||
\(220\) | 479362. | 0.667739 | ||||||||
\(221\) | −133695. | −0.184134 | ||||||||
\(222\) | 1.80624e6 | 2.45976 | ||||||||
\(223\) | 288757. | 0.388839 | 0.194420 | − | 0.980918i | \(-0.437718\pi\) | ||||
0.194420 | + | 0.980918i | \(0.437718\pi\) | |||||||
\(224\) | 708452. | 0.943389 | ||||||||
\(225\) | −39645.8 | −0.0522085 | ||||||||
\(226\) | −49177.9 | −0.0640470 | ||||||||
\(227\) | 533584. | 0.687287 | 0.343644 | − | 0.939100i | \(-0.388339\pi\) | ||||
0.343644 | + | 0.939100i | \(0.388339\pi\) | |||||||
\(228\) | 1.24413e6 | 1.58499 | ||||||||
\(229\) | 209610. | 0.264133 | 0.132067 | − | 0.991241i | \(-0.457839\pi\) | ||||
0.132067 | + | 0.991241i | \(0.457839\pi\) | |||||||
\(230\) | −108078. | −0.134716 | ||||||||
\(231\) | −630093. | −0.776917 | ||||||||
\(232\) | 28457.7 | 0.0347120 | ||||||||
\(233\) | 824744. | 0.995243 | 0.497622 | − | 0.867394i | \(-0.334207\pi\) | ||||
0.497622 | + | 0.867394i | \(0.334207\pi\) | |||||||
\(234\) | 207787. | 0.248073 | ||||||||
\(235\) | −175465. | −0.207262 | ||||||||
\(236\) | −1.27098e6 | −1.48546 | ||||||||
\(237\) | −37203.7 | −0.0430244 | ||||||||
\(238\) | 232526. | 0.266090 | ||||||||
\(239\) | −670029. | −0.758751 | −0.379375 | − | 0.925243i | \(-0.623861\pi\) | ||||
−0.379375 | + | 0.925243i | \(0.623861\pi\) | |||||||
\(240\) | 310580. | 0.348053 | ||||||||
\(241\) | −157659. | −0.174855 | −0.0874273 | − | 0.996171i | \(-0.527865\pi\) | ||||
−0.0874273 | + | 0.996171i | \(0.527865\pi\) | |||||||
\(242\) | −1.16687e6 | −1.28081 | ||||||||
\(243\) | 467030. | 0.507375 | ||||||||
\(244\) | 1.91543e6 | 2.05964 | ||||||||
\(245\) | 238253. | 0.253585 | ||||||||
\(246\) | 852771. | 0.898451 | ||||||||
\(247\) | 1.06981e6 | 1.11574 | ||||||||
\(248\) | 59296.4 | 0.0612208 | ||||||||
\(249\) | −402368. | −0.411268 | ||||||||
\(250\) | 127692. | 0.129215 | ||||||||
\(251\) | −1.30181e6 | −1.30426 | −0.652128 | − | 0.758109i | \(-0.726123\pi\) | ||||
−0.652128 | + | 0.758109i | \(0.726123\pi\) | |||||||
\(252\) | −188232. | −0.186721 | ||||||||
\(253\) | 291592. | 0.286400 | ||||||||
\(254\) | 224407. | 0.218248 | ||||||||
\(255\) | 111740. | 0.107612 | ||||||||
\(256\) | 842904. | 0.803856 | ||||||||
\(257\) | 1.08611e6 | 1.02575 | 0.512874 | − | 0.858464i | \(-0.328581\pi\) | ||||
0.512874 | + | 0.858464i | \(0.328581\pi\) | |||||||
\(258\) | 2.15512e6 | 2.01568 | ||||||||
\(259\) | −1.40699e6 | −1.30329 | ||||||||
\(260\) | −348580. | −0.319793 | ||||||||
\(261\) | 79286.4 | 0.0720439 | ||||||||
\(262\) | 2.42820e6 | 2.18540 | ||||||||
\(263\) | 1.74183e6 | 1.55281 | 0.776404 | − | 0.630236i | \(-0.217042\pi\) | ||||
0.776404 | + | 0.630236i | \(0.217042\pi\) | |||||||
\(264\) | 168171. | 0.148505 | ||||||||
\(265\) | 580084. | 0.507430 | ||||||||
\(266\) | −1.86064e6 | −1.61235 | ||||||||
\(267\) | −1.68370e6 | −1.44540 | ||||||||
\(268\) | 65481.5 | 0.0556906 | ||||||||
\(269\) | 954865. | 0.804566 | 0.402283 | − | 0.915515i | \(-0.368217\pi\) | ||||
0.402283 | + | 0.915515i | \(0.368217\pi\) | |||||||
\(270\) | −838941. | −0.700361 | ||||||||
\(271\) | 211939. | 0.175302 | 0.0876512 | − | 0.996151i | \(-0.472064\pi\) | ||||
0.0876512 | + | 0.996151i | \(0.472064\pi\) | |||||||
\(272\) | 309227. | 0.253428 | ||||||||
\(273\) | 458189. | 0.372081 | ||||||||
\(274\) | −2.41012e6 | −1.93938 | ||||||||
\(275\) | −344508. | −0.274706 | ||||||||
\(276\) | −246588. | −0.194850 | ||||||||
\(277\) | 1.35738e6 | 1.06293 | 0.531463 | − | 0.847081i | \(-0.321642\pi\) | ||||
0.531463 | + | 0.847081i | \(0.321642\pi\) | |||||||
\(278\) | −2.74220e6 | −2.12807 | ||||||||
\(279\) | 165207. | 0.127062 | ||||||||
\(280\) | 48554.6 | 0.0370114 | ||||||||
\(281\) | 1.68620e6 | 1.27393 | 0.636963 | − | 0.770894i | \(-0.280190\pi\) | ||||
0.636963 | + | 0.770894i | \(0.280190\pi\) | |||||||
\(282\) | −768608. | −0.575549 | ||||||||
\(283\) | 540012. | 0.400809 | 0.200404 | − | 0.979713i | \(-0.435774\pi\) | ||||
0.200404 | + | 0.979713i | \(0.435774\pi\) | |||||||
\(284\) | −720796. | −0.530294 | ||||||||
\(285\) | −894129. | −0.652061 | ||||||||
\(286\) | 1.80560e6 | 1.30529 | ||||||||
\(287\) | −664277. | −0.476041 | ||||||||
\(288\) | −526812. | −0.374261 | ||||||||
\(289\) | −1.30860e6 | −0.921645 | ||||||||
\(290\) | −255366. | −0.178307 | ||||||||
\(291\) | 1.39532e6 | 0.965920 | ||||||||
\(292\) | 145905. | 0.100142 | ||||||||
\(293\) | 59213.8 | 0.0402953 | 0.0201476 | − | 0.999797i | \(-0.493586\pi\) | ||||
0.0201476 | + | 0.999797i | \(0.493586\pi\) | |||||||
\(294\) | 1.04365e6 | 0.704183 | ||||||||
\(295\) | 913432. | 0.611113 | ||||||||
\(296\) | 375523. | 0.249119 | ||||||||
\(297\) | 2.26344e6 | 1.48894 | ||||||||
\(298\) | −3.99080e6 | −2.60327 | ||||||||
\(299\) | −212038. | −0.137163 | ||||||||
\(300\) | 291338. | 0.186893 | ||||||||
\(301\) | −1.67876e6 | −1.06800 | ||||||||
\(302\) | −2.89503e6 | −1.82657 | ||||||||
\(303\) | 1.47642e6 | 0.923854 | ||||||||
\(304\) | −2.47439e6 | −1.53562 | ||||||||
\(305\) | −1.37658e6 | −0.847331 | ||||||||
\(306\) | −172909. | −0.105563 | ||||||||
\(307\) | −25932.8 | −0.0157037 | −0.00785187 | − | 0.999969i | \(-0.502499\pi\) | ||||
−0.00785187 | + | 0.999969i | \(0.502499\pi\) | |||||||
\(308\) | −1.63567e6 | −0.982470 | ||||||||
\(309\) | −2.11344e6 | −1.25920 | ||||||||
\(310\) | −532100. | −0.314477 | ||||||||
\(311\) | −1.61509e6 | −0.946879 | −0.473440 | − | 0.880826i | \(-0.656988\pi\) | ||||
−0.473440 | + | 0.880826i | \(0.656988\pi\) | |||||||
\(312\) | −122290. | −0.0711219 | ||||||||
\(313\) | −2.57528e6 | −1.48581 | −0.742906 | − | 0.669396i | \(-0.766553\pi\) | ||||
−0.742906 | + | 0.669396i | \(0.766553\pi\) | |||||||
\(314\) | 2.52228e6 | 1.44368 | ||||||||
\(315\) | 135279. | 0.0768163 | ||||||||
\(316\) | −96577.7 | −0.0544075 | ||||||||
\(317\) | −1.12868e6 | −0.630847 | −0.315423 | − | 0.948951i | \(-0.602147\pi\) | ||||
−0.315423 | + | 0.948951i | \(0.602147\pi\) | |||||||
\(318\) | 2.54101e6 | 1.40909 | ||||||||
\(319\) | 688970. | 0.379074 | ||||||||
\(320\) | 955091. | 0.521399 | ||||||||
\(321\) | −46482.0 | −0.0251781 | ||||||||
\(322\) | 368783. | 0.198213 | ||||||||
\(323\) | −890234. | −0.474786 | ||||||||
\(324\) | −1.37790e6 | −0.729217 | ||||||||
\(325\) | 250518. | 0.131562 | ||||||||
\(326\) | 2.44592e6 | 1.27467 | ||||||||
\(327\) | 1.35753e6 | 0.702067 | ||||||||
\(328\) | 177294. | 0.0909935 | ||||||||
\(329\) | 598717. | 0.304952 | ||||||||
\(330\) | −1.50909e6 | −0.762834 | ||||||||
\(331\) | 1.59828e6 | 0.801829 | 0.400915 | − | 0.916115i | \(-0.368692\pi\) | ||||
0.400915 | + | 0.916115i | \(0.368692\pi\) | |||||||
\(332\) | −1.04451e6 | −0.520079 | ||||||||
\(333\) | 1.04625e6 | 0.517042 | ||||||||
\(334\) | 951789. | 0.466847 | ||||||||
\(335\) | −47060.3 | −0.0229109 | ||||||||
\(336\) | −1.05976e6 | −0.512104 | ||||||||
\(337\) | 65142.4 | 0.0312456 | 0.0156228 | − | 0.999878i | \(-0.495027\pi\) | ||||
0.0156228 | + | 0.999878i | \(0.495027\pi\) | |||||||
\(338\) | 1.72132e6 | 0.819539 | ||||||||
\(339\) | 80638.1 | 0.0381102 | ||||||||
\(340\) | 290069. | 0.136083 | ||||||||
\(341\) | 1.43559e6 | 0.668565 | ||||||||
\(342\) | 1.38359e6 | 0.639649 | ||||||||
\(343\) | −2.24668e6 | −1.03111 | ||||||||
\(344\) | 448057. | 0.204144 | ||||||||
\(345\) | 177218. | 0.0801606 | ||||||||
\(346\) | 2.71156e6 | 1.21767 | ||||||||
\(347\) | −196819. | −0.0877492 | −0.0438746 | − | 0.999037i | \(-0.513970\pi\) | ||||
−0.0438746 | + | 0.999037i | \(0.513970\pi\) | |||||||
\(348\) | −582637. | −0.257899 | ||||||||
\(349\) | −1.44649e6 | −0.635702 | −0.317851 | − | 0.948141i | \(-0.602961\pi\) | ||||
−0.317851 | + | 0.948141i | \(0.602961\pi\) | |||||||
\(350\) | −435708. | −0.190119 | ||||||||
\(351\) | −1.64592e6 | −0.713083 | ||||||||
\(352\) | −4.57781e6 | −1.96925 | ||||||||
\(353\) | −3.49462e6 | −1.49267 | −0.746334 | − | 0.665572i | \(-0.768188\pi\) | ||||
−0.746334 | + | 0.665572i | \(0.768188\pi\) | |||||||
\(354\) | 4.00121e6 | 1.69701 | ||||||||
\(355\) | 518022. | 0.218161 | ||||||||
\(356\) | −4.37076e6 | −1.82781 | ||||||||
\(357\) | −381278. | −0.158333 | ||||||||
\(358\) | −2.29494e6 | −0.946375 | ||||||||
\(359\) | −1.31793e6 | −0.539704 | −0.269852 | − | 0.962902i | \(-0.586975\pi\) | ||||
−0.269852 | + | 0.962902i | \(0.586975\pi\) | |||||||
\(360\) | −36105.7 | −0.0146831 | ||||||||
\(361\) | 4.64742e6 | 1.87691 | ||||||||
\(362\) | 1804.37 | 0.000723692 0 | ||||||||
\(363\) | 1.91335e6 | 0.762128 | ||||||||
\(364\) | 1.18942e6 | 0.470524 | ||||||||
\(365\) | −104859. | −0.0411979 | ||||||||
\(366\) | −6.03001e6 | −2.35297 | ||||||||
\(367\) | 3.94840e6 | 1.53023 | 0.765114 | − | 0.643895i | \(-0.222683\pi\) | ||||
0.765114 | + | 0.643895i | \(0.222683\pi\) | |||||||
\(368\) | 490429. | 0.188780 | ||||||||
\(369\) | 493963. | 0.188855 | ||||||||
\(370\) | −3.36978e6 | −1.27967 | ||||||||
\(371\) | −1.97935e6 | −0.746601 | ||||||||
\(372\) | −1.21402e6 | −0.454852 | ||||||||
\(373\) | −4.06998e6 | −1.51468 | −0.757339 | − | 0.653022i | \(-0.773501\pi\) | ||||
−0.757339 | + | 0.653022i | \(0.773501\pi\) | |||||||
\(374\) | −1.50251e6 | −0.555443 | ||||||||
\(375\) | −209379. | −0.0768873 | ||||||||
\(376\) | −159797. | −0.0582905 | ||||||||
\(377\) | −501003. | −0.181546 | ||||||||
\(378\) | 2.86262e6 | 1.03047 | ||||||||
\(379\) | −3.08289e6 | −1.10245 | −0.551226 | − | 0.834356i | \(-0.685840\pi\) | ||||
−0.551226 | + | 0.834356i | \(0.685840\pi\) | |||||||
\(380\) | −2.32109e6 | −0.824579 | ||||||||
\(381\) | −367964. | −0.129865 | ||||||||
\(382\) | 1.36157e6 | 0.477400 | ||||||||
\(383\) | −413860. | −0.144164 | −0.0720820 | − | 0.997399i | \(-0.522964\pi\) | ||||
−0.0720820 | + | 0.997399i | \(0.522964\pi\) | |||||||
\(384\) | 622461. | 0.215419 | ||||||||
\(385\) | 1.17552e6 | 0.404185 | ||||||||
\(386\) | −165198. | −0.0564336 | ||||||||
\(387\) | 1.24834e6 | 0.423697 | ||||||||
\(388\) | 3.62214e6 | 1.22148 | ||||||||
\(389\) | 5.93753e6 | 1.98944 | 0.994722 | − | 0.102605i | \(-0.0327178\pi\) | ||||
0.994722 | + | 0.102605i | \(0.0327178\pi\) | |||||||
\(390\) | 1.09737e6 | 0.365336 | ||||||||
\(391\) | 176446. | 0.0583674 | ||||||||
\(392\) | 216978. | 0.0713184 | ||||||||
\(393\) | −3.98157e6 | −1.30039 | ||||||||
\(394\) | 4.81170e6 | 1.56156 | ||||||||
\(395\) | 69408.5 | 0.0223831 | ||||||||
\(396\) | 1.21630e6 | 0.389765 | ||||||||
\(397\) | −3.92824e6 | −1.25090 | −0.625449 | − | 0.780265i | \(-0.715084\pi\) | ||||
−0.625449 | + | 0.780265i | \(0.715084\pi\) | |||||||
\(398\) | −6.05133e6 | −1.91489 | ||||||||
\(399\) | 3.05093e6 | 0.959402 | ||||||||
\(400\) | −579430. | −0.181072 | ||||||||
\(401\) | −4.27894e6 | −1.32885 | −0.664424 | − | 0.747356i | \(-0.731323\pi\) | ||||
−0.664424 | + | 0.747356i | \(0.731323\pi\) | |||||||
\(402\) | −206144. | −0.0636217 | ||||||||
\(403\) | −1.04392e6 | −0.320189 | ||||||||
\(404\) | 3.83267e6 | 1.16828 | ||||||||
\(405\) | 990273. | 0.299997 | ||||||||
\(406\) | 871357. | 0.262350 | ||||||||
\(407\) | 9.09155e6 | 2.72052 | ||||||||
\(408\) | 101762. | 0.0302648 | ||||||||
\(409\) | 4.02846e6 | 1.19078 | 0.595389 | − | 0.803437i | \(-0.296998\pi\) | ||||
0.595389 | + | 0.803437i | \(0.296998\pi\) | |||||||
\(410\) | −1.59096e6 | −0.467412 | ||||||||
\(411\) | 3.95193e6 | 1.15400 | ||||||||
\(412\) | −5.48633e6 | −1.59235 | ||||||||
\(413\) | −3.11680e6 | −0.899153 | ||||||||
\(414\) | −274230. | −0.0786348 | ||||||||
\(415\) | 750673. | 0.213959 | ||||||||
\(416\) | 3.32887e6 | 0.943113 | ||||||||
\(417\) | 4.49644e6 | 1.26628 | ||||||||
\(418\) | 1.20229e7 | 3.36565 | ||||||||
\(419\) | 6.85980e6 | 1.90887 | 0.954435 | − | 0.298419i | \(-0.0964591\pi\) | ||||
0.954435 | + | 0.298419i | \(0.0964591\pi\) | |||||||
\(420\) | −994099. | −0.274983 | ||||||||
\(421\) | −2.74935e6 | −0.756005 | −0.378003 | − | 0.925805i | \(-0.623389\pi\) | ||||
−0.378003 | + | 0.925805i | \(0.623389\pi\) | |||||||
\(422\) | 3.55541e6 | 0.971870 | ||||||||
\(423\) | −445212. | −0.120981 | ||||||||
\(424\) | 528286. | 0.142710 | ||||||||
\(425\) | −208467. | −0.0559840 | ||||||||
\(426\) | 2.26915e6 | 0.605815 | ||||||||
\(427\) | 4.69716e6 | 1.24671 | ||||||||
\(428\) | −120664. | −0.0318395 | ||||||||
\(429\) | −2.96068e6 | −0.776690 | ||||||||
\(430\) | −4.02066e6 | −1.04864 | ||||||||
\(431\) | 1.30645e6 | 0.338765 | 0.169382 | − | 0.985550i | \(-0.445823\pi\) | ||||
0.169382 | + | 0.985550i | \(0.445823\pi\) | |||||||
\(432\) | 3.80688e6 | 0.981432 | ||||||||
\(433\) | −2.98729e6 | −0.765697 | −0.382849 | − | 0.923811i | \(-0.625057\pi\) | ||||
−0.382849 | + | 0.923811i | \(0.625057\pi\) | |||||||
\(434\) | 1.81562e6 | 0.462702 | ||||||||
\(435\) | 418730. | 0.106099 | ||||||||
\(436\) | 3.52403e6 | 0.887816 | ||||||||
\(437\) | −1.41190e6 | −0.353671 | ||||||||
\(438\) | −459328. | −0.114403 | ||||||||
\(439\) | −3.23159e6 | −0.800305 | −0.400153 | − | 0.916449i | \(-0.631043\pi\) | ||||
−0.400153 | + | 0.916449i | \(0.631043\pi\) | |||||||
\(440\) | −313745. | −0.0772584 | ||||||||
\(441\) | 604527. | 0.148020 | ||||||||
\(442\) | 1.09259e6 | 0.266013 | ||||||||
\(443\) | 1.88453e6 | 0.456241 | 0.228121 | − | 0.973633i | \(-0.426742\pi\) | ||||
0.228121 | + | 0.973633i | \(0.426742\pi\) | |||||||
\(444\) | −7.68840e6 | −1.85088 | ||||||||
\(445\) | 3.14118e6 | 0.751956 | ||||||||
\(446\) | −2.35980e6 | −0.561743 | ||||||||
\(447\) | 6.54380e6 | 1.54903 | ||||||||
\(448\) | −3.25895e6 | −0.767154 | ||||||||
\(449\) | 5.28563e6 | 1.23732 | 0.618659 | − | 0.785660i | \(-0.287676\pi\) | ||||
0.618659 | + | 0.785660i | \(0.287676\pi\) | |||||||
\(450\) | 323996. | 0.0754238 | ||||||||
\(451\) | 4.29236e6 | 0.993699 | ||||||||
\(452\) | 209330. | 0.0481931 | ||||||||
\(453\) | 4.74704e6 | 1.08687 | ||||||||
\(454\) | −4.36059e6 | −0.992901 | ||||||||
\(455\) | −854814. | −0.193572 | ||||||||
\(456\) | −814289. | −0.183386 | ||||||||
\(457\) | −6.09884e6 | −1.36602 | −0.683010 | − | 0.730409i | \(-0.739329\pi\) | ||||
−0.683010 | + | 0.730409i | \(0.739329\pi\) | |||||||
\(458\) | −1.71299e6 | −0.381584 | ||||||||
\(459\) | 1.36964e6 | 0.303441 | ||||||||
\(460\) | 460044. | 0.101369 | ||||||||
\(461\) | −5.03999e6 | −1.10453 | −0.552265 | − | 0.833669i | \(-0.686236\pi\) | ||||
−0.552265 | + | 0.833669i | \(0.686236\pi\) | |||||||
\(462\) | 5.14929e6 | 1.12239 | ||||||||
\(463\) | −4.33452e6 | −0.939698 | −0.469849 | − | 0.882747i | \(-0.655692\pi\) | ||||
−0.469849 | + | 0.882747i | \(0.655692\pi\) | |||||||
\(464\) | 1.15878e6 | 0.249866 | ||||||||
\(465\) | 872495. | 0.187125 | ||||||||
\(466\) | −6.74003e6 | −1.43779 | ||||||||
\(467\) | 2.73020e6 | 0.579299 | 0.289649 | − | 0.957133i | \(-0.406461\pi\) | ||||
0.289649 | + | 0.957133i | \(0.406461\pi\) | |||||||
\(468\) | −884464. | −0.186666 | ||||||||
\(469\) | 160579. | 0.0337097 | ||||||||
\(470\) | 1.43394e6 | 0.299424 | ||||||||
\(471\) | −4.13584e6 | −0.859037 | ||||||||
\(472\) | 831868. | 0.171870 | ||||||||
\(473\) | 1.08476e7 | 2.22937 | ||||||||
\(474\) | 304038. | 0.0621559 | ||||||||
\(475\) | 1.66812e6 | 0.339229 | ||||||||
\(476\) | −989767. | −0.200224 | ||||||||
\(477\) | 1.47187e6 | 0.296191 | ||||||||
\(478\) | 5.47566e6 | 1.09614 | ||||||||
\(479\) | 3.85339e6 | 0.767369 | 0.383684 | − | 0.923464i | \(-0.374655\pi\) | ||||
0.383684 | + | 0.923464i | \(0.374655\pi\) | |||||||
\(480\) | −2.78222e6 | −0.551173 | ||||||||
\(481\) | −6.61116e6 | −1.30291 | ||||||||
\(482\) | 1.28843e6 | 0.252607 | ||||||||
\(483\) | −604702. | −0.117943 | ||||||||
\(484\) | 4.96690e6 | 0.963767 | ||||||||
\(485\) | −2.60316e6 | −0.502512 | ||||||||
\(486\) | −3.81670e6 | −0.732988 | ||||||||
\(487\) | −4.77493e6 | −0.912315 | −0.456158 | − | 0.889899i | \(-0.650775\pi\) | ||||
−0.456158 | + | 0.889899i | \(0.650775\pi\) | |||||||
\(488\) | −1.25366e6 | −0.238304 | ||||||||
\(489\) | −4.01063e6 | −0.758474 | ||||||||
\(490\) | −1.94707e6 | −0.366346 | ||||||||
\(491\) | −501195. | −0.0938216 | −0.0469108 | − | 0.998899i | \(-0.514938\pi\) | ||||
−0.0469108 | + | 0.998899i | \(0.514938\pi\) | |||||||
\(492\) | −3.62989e6 | −0.676053 | ||||||||
\(493\) | 416906. | 0.0772539 | ||||||||
\(494\) | −8.74277e6 | −1.61188 | ||||||||
\(495\) | −874131. | −0.160348 | ||||||||
\(496\) | 2.41452e6 | 0.440684 | ||||||||
\(497\) | −1.76759e6 | −0.320989 | ||||||||
\(498\) | 3.28826e6 | 0.594145 | ||||||||
\(499\) | 2.32923e6 | 0.418757 | 0.209378 | − | 0.977835i | \(-0.432856\pi\) | ||||
0.209378 | + | 0.977835i | \(0.432856\pi\) | |||||||
\(500\) | −543531. | −0.0972297 | ||||||||
\(501\) | −1.56067e6 | −0.277790 | ||||||||
\(502\) | 1.06387e7 | 1.88421 | ||||||||
\(503\) | −9.10450e6 | −1.60449 | −0.802243 | − | 0.596997i | \(-0.796360\pi\) | ||||
−0.802243 | + | 0.596997i | \(0.796360\pi\) | |||||||
\(504\) | 123199. | 0.0216039 | ||||||||
\(505\) | −2.75446e6 | −0.480628 | ||||||||
\(506\) | −2.38296e6 | −0.413753 | ||||||||
\(507\) | −2.82249e6 | −0.487654 | ||||||||
\(508\) | −955206. | −0.164224 | ||||||||
\(509\) | −3.50476e6 | −0.599602 | −0.299801 | − | 0.954002i | \(-0.596920\pi\) | ||||
−0.299801 | + | 0.954002i | \(0.596920\pi\) | |||||||
\(510\) | −913171. | −0.155463 | ||||||||
\(511\) | 357800. | 0.0606161 | ||||||||
\(512\) | −8.37488e6 | −1.41190 | ||||||||
\(513\) | −1.09596e7 | −1.83867 | ||||||||
\(514\) | −8.87598e6 | −1.48186 | ||||||||
\(515\) | 3.94292e6 | 0.655088 | ||||||||
\(516\) | −9.17344e6 | −1.51673 | ||||||||
\(517\) | −3.86873e6 | −0.636564 | ||||||||
\(518\) | 1.14983e7 | 1.88282 | ||||||||
\(519\) | −4.44620e6 | −0.724554 | ||||||||
\(520\) | 228148. | 0.0370006 | ||||||||
\(521\) | 5.26368e6 | 0.849562 | 0.424781 | − | 0.905296i | \(-0.360351\pi\) | ||||
0.424781 | + | 0.905296i | \(0.360351\pi\) | |||||||
\(522\) | −647949. | −0.104079 | ||||||||
\(523\) | −2.84855e6 | −0.455375 | −0.227688 | − | 0.973734i | \(-0.573117\pi\) | ||||
−0.227688 | + | 0.973734i | \(0.573117\pi\) | |||||||
\(524\) | −1.03358e7 | −1.64444 | ||||||||
\(525\) | 714439. | 0.113127 | ||||||||
\(526\) | −1.42347e7 | −2.24329 | ||||||||
\(527\) | 868694. | 0.136251 | ||||||||
\(528\) | 6.84783e6 | 1.06898 | ||||||||
\(529\) | 279841. | 0.0434783 | ||||||||
\(530\) | −4.74060e6 | −0.733067 | ||||||||
\(531\) | 2.31768e6 | 0.356712 | ||||||||
\(532\) | 7.91998e6 | 1.21323 | ||||||||
\(533\) | −3.12130e6 | −0.475902 | ||||||||
\(534\) | 1.37597e7 | 2.08812 | ||||||||
\(535\) | 86718.6 | 0.0130987 | ||||||||
\(536\) | −42858.1 | −0.00644349 | ||||||||
\(537\) | 3.76306e6 | 0.563126 | ||||||||
\(538\) | −7.80342e6 | −1.16233 | ||||||||
\(539\) | 5.25313e6 | 0.778836 | ||||||||
\(540\) | 3.57103e6 | 0.526997 | ||||||||
\(541\) | −8.01867e6 | −1.17790 | −0.588951 | − | 0.808169i | \(-0.700459\pi\) | ||||
−0.588951 | + | 0.808169i | \(0.700459\pi\) | |||||||
\(542\) | −1.73202e6 | −0.253254 | ||||||||
\(543\) | −2958.66 | −0.000430622 0 | ||||||||
\(544\) | −2.77010e6 | −0.401326 | ||||||||
\(545\) | −2.53265e6 | −0.365245 | ||||||||
\(546\) | −3.74444e6 | −0.537533 | ||||||||
\(547\) | 7.93649e6 | 1.13412 | 0.567061 | − | 0.823676i | \(-0.308080\pi\) | ||||
0.567061 | + | 0.823676i | \(0.308080\pi\) | |||||||
\(548\) | 1.02589e7 | 1.45931 | ||||||||
\(549\) | −3.49285e6 | −0.494594 | ||||||||
\(550\) | 2.81541e6 | 0.396858 | ||||||||
\(551\) | −3.33602e6 | −0.468112 | ||||||||
\(552\) | 161394. | 0.0225444 | ||||||||
\(553\) | −236835. | −0.0329331 | ||||||||
\(554\) | −1.10929e7 | −1.53557 | ||||||||
\(555\) | 5.52550e6 | 0.761446 | ||||||||
\(556\) | 1.16724e7 | 1.60130 | ||||||||
\(557\) | 2.43838e6 | 0.333015 | 0.166508 | − | 0.986040i | \(-0.446751\pi\) | ||||
0.166508 | + | 0.986040i | \(0.446751\pi\) | |||||||
\(558\) | −1.35011e6 | −0.183563 | ||||||||
\(559\) | −7.88813e6 | −1.06769 | ||||||||
\(560\) | 1.97712e6 | 0.266418 | ||||||||
\(561\) | 2.46371e6 | 0.330508 | ||||||||
\(562\) | −1.37801e7 | −1.84040 | ||||||||
\(563\) | 1.32223e7 | 1.75807 | 0.879034 | − | 0.476759i | \(-0.158188\pi\) | ||||
0.879034 | + | 0.476759i | \(0.158188\pi\) | |||||||
\(564\) | 3.27165e6 | 0.433080 | ||||||||
\(565\) | −150441. | −0.0198265 | ||||||||
\(566\) | −4.41312e6 | −0.579035 | ||||||||
\(567\) | −3.37899e6 | −0.441397 | ||||||||
\(568\) | 471766. | 0.0613558 | ||||||||
\(569\) | −5.12347e6 | −0.663412 | −0.331706 | − | 0.943383i | \(-0.607624\pi\) | ||||
−0.331706 | + | 0.943383i | \(0.607624\pi\) | |||||||
\(570\) | 7.30706e6 | 0.942011 | ||||||||
\(571\) | 1.28462e7 | 1.64887 | 0.824434 | − | 0.565958i | \(-0.191494\pi\) | ||||
0.824434 | + | 0.565958i | \(0.191494\pi\) | |||||||
\(572\) | −7.68568e6 | −0.982182 | ||||||||
\(573\) | −2.23260e6 | −0.284070 | ||||||||
\(574\) | 5.42865e6 | 0.687721 | ||||||||
\(575\) | −330625. | −0.0417029 | ||||||||
\(576\) | 2.42338e6 | 0.304345 | ||||||||
\(577\) | −7.09107e6 | −0.886691 | −0.443345 | − | 0.896351i | \(-0.646209\pi\) | ||||
−0.443345 | + | 0.896351i | \(0.646209\pi\) | |||||||
\(578\) | 1.06943e7 | 1.33147 | ||||||||
\(579\) | 270879. | 0.0335799 | ||||||||
\(580\) | 1.08699e6 | 0.134170 | ||||||||
\(581\) | −2.56143e6 | −0.314806 | ||||||||
\(582\) | −1.14029e7 | −1.39543 | ||||||||
\(583\) | 1.27900e7 | 1.55847 | ||||||||
\(584\) | −95496.1 | −0.0115865 | ||||||||
\(585\) | 635647. | 0.0767939 | ||||||||
\(586\) | −483911. | −0.0582132 | ||||||||
\(587\) | −6.16460e6 | −0.738431 | −0.369215 | − | 0.929344i | \(-0.620374\pi\) | ||||
−0.369215 | + | 0.929344i | \(0.620374\pi\) | |||||||
\(588\) | −4.44238e6 | −0.529873 | ||||||||
\(589\) | −6.95117e6 | −0.825599 | ||||||||
\(590\) | −7.46481e6 | −0.882854 | ||||||||
\(591\) | −7.88985e6 | −0.929180 | ||||||||
\(592\) | 1.52911e7 | 1.79323 | ||||||||
\(593\) | 458736. | 0.0535706 | 0.0267853 | − | 0.999641i | \(-0.491473\pi\) | ||||
0.0267853 | + | 0.999641i | \(0.491473\pi\) | |||||||
\(594\) | −1.84974e7 | −2.15102 | ||||||||
\(595\) | 711327. | 0.0823714 | ||||||||
\(596\) | 1.69872e7 | 1.95887 | ||||||||
\(597\) | 9.92249e6 | 1.13942 | ||||||||
\(598\) | 1.73283e6 | 0.198155 | ||||||||
\(599\) | 1.12961e7 | 1.28636 | 0.643181 | − | 0.765714i | \(-0.277614\pi\) | ||||
0.643181 | + | 0.765714i | \(0.277614\pi\) | |||||||
\(600\) | −190683. | −0.0216238 | ||||||||
\(601\) | −1.36855e6 | −0.154552 | −0.0772760 | − | 0.997010i | \(-0.524622\pi\) | ||||
−0.0772760 | + | 0.997010i | \(0.524622\pi\) | |||||||
\(602\) | 1.37192e7 | 1.54290 | ||||||||
\(603\) | −119408. | −0.0133733 | ||||||||
\(604\) | 1.23229e7 | 1.37443 | ||||||||
\(605\) | −3.56961e6 | −0.396491 | ||||||||
\(606\) | −1.20657e7 | −1.33466 | ||||||||
\(607\) | −3.18822e6 | −0.351218 | −0.175609 | − | 0.984460i | \(-0.556189\pi\) | ||||
−0.175609 | + | 0.984460i | \(0.556189\pi\) | |||||||
\(608\) | 2.21659e7 | 2.43179 | ||||||||
\(609\) | −1.42878e6 | −0.156107 | ||||||||
\(610\) | 1.12498e7 | 1.22411 | ||||||||
\(611\) | 2.81325e6 | 0.304863 | ||||||||
\(612\) | 736000. | 0.0794327 | ||||||||
\(613\) | −4.67188e6 | −0.502158 | −0.251079 | − | 0.967967i | \(-0.580785\pi\) | ||||
−0.251079 | + | 0.967967i | \(0.580785\pi\) | |||||||
\(614\) | 211930. | 0.0226867 | ||||||||
\(615\) | 2.60873e6 | 0.278126 | ||||||||
\(616\) | 1.07056e6 | 0.113673 | ||||||||
\(617\) | −4.58446e6 | −0.484815 | −0.242407 | − | 0.970175i | \(-0.577937\pi\) | ||||
−0.242407 | + | 0.970175i | \(0.577937\pi\) | |||||||
\(618\) | 1.72716e7 | 1.81912 | ||||||||
\(619\) | −6.87650e6 | −0.721341 | −0.360670 | − | 0.932693i | \(-0.617452\pi\) | ||||
−0.360670 | + | 0.932693i | \(0.617452\pi\) | |||||||
\(620\) | 2.26493e6 | 0.236633 | ||||||||
\(621\) | 2.17222e6 | 0.226035 | ||||||||
\(622\) | 1.31989e7 | 1.36792 | ||||||||
\(623\) | −1.07183e7 | −1.10638 | ||||||||
\(624\) | −4.97958e6 | −0.511954 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 2.10459e7 | 2.14650 | ||||||||
\(627\) | −1.97142e7 | −2.00268 | ||||||||
\(628\) | −1.07363e7 | −1.08632 | ||||||||
\(629\) | 5.50143e6 | 0.554433 | ||||||||
\(630\) | −1.10553e6 | −0.110974 | ||||||||
\(631\) | −582950. | −0.0582851 | −0.0291426 | − | 0.999575i | \(-0.509278\pi\) | ||||
−0.0291426 | + | 0.999575i | \(0.509278\pi\) | |||||||
\(632\) | 63210.7 | 0.00629503 | ||||||||
\(633\) | −5.82988e6 | −0.578296 | ||||||||
\(634\) | 9.22390e6 | 0.911363 | ||||||||
\(635\) | 686488. | 0.0675614 | ||||||||
\(636\) | −1.08160e7 | −1.06029 | ||||||||
\(637\) | −3.81995e6 | −0.373000 | ||||||||
\(638\) | −5.63045e6 | −0.547635 | ||||||||
\(639\) | 1.31439e6 | 0.127343 | ||||||||
\(640\) | −1.16129e6 | −0.112070 | ||||||||
\(641\) | −2.49002e6 | −0.239363 | −0.119682 | − | 0.992812i | \(-0.538187\pi\) | ||||
−0.119682 | + | 0.992812i | \(0.538187\pi\) | |||||||
\(642\) | 379864. | 0.0363739 | ||||||||
\(643\) | 4.28616e6 | 0.408828 | 0.204414 | − | 0.978885i | \(-0.434471\pi\) | ||||
0.204414 | + | 0.978885i | \(0.434471\pi\) | |||||||
\(644\) | −1.56976e6 | −0.149148 | ||||||||
\(645\) | 6.59277e6 | 0.623977 | ||||||||
\(646\) | 7.27523e6 | 0.685907 | ||||||||
\(647\) | −4.08917e6 | −0.384038 | −0.192019 | − | 0.981391i | \(-0.561504\pi\) | ||||
−0.192019 | + | 0.981391i | \(0.561504\pi\) | |||||||
\(648\) | 901847. | 0.0843715 | ||||||||
\(649\) | 2.01398e7 | 1.87691 | ||||||||
\(650\) | −2.04730e6 | −0.190063 | ||||||||
\(651\) | −2.97712e6 | −0.275323 | ||||||||
\(652\) | −1.04113e7 | −0.959146 | ||||||||
\(653\) | −1.72639e7 | −1.58437 | −0.792185 | − | 0.610281i | \(-0.791056\pi\) | ||||
−0.792185 | + | 0.610281i | \(0.791056\pi\) | |||||||
\(654\) | −1.10941e7 | −1.01425 | ||||||||
\(655\) | 7.42817e6 | 0.676517 | ||||||||
\(656\) | 7.21934e6 | 0.654995 | ||||||||
\(657\) | −266063. | −0.0240476 | ||||||||
\(658\) | −4.89288e6 | −0.440555 | ||||||||
\(659\) | 5.70243e6 | 0.511501 | 0.255751 | − | 0.966743i | \(-0.417677\pi\) | ||||
0.255751 | + | 0.966743i | \(0.417677\pi\) | |||||||
\(660\) | 6.42357e6 | 0.574006 | ||||||||
\(661\) | −1.27038e7 | −1.13091 | −0.565457 | − | 0.824778i | \(-0.691300\pi\) | ||||
−0.565457 | + | 0.824778i | \(0.691300\pi\) | |||||||
\(662\) | −1.30615e7 | −1.15838 | ||||||||
\(663\) | −1.79155e6 | −0.158287 | ||||||||
\(664\) | 683642. | 0.0601739 | ||||||||
\(665\) | −5.69193e6 | −0.499121 | ||||||||
\(666\) | −8.55025e6 | −0.746953 | ||||||||
\(667\) | 661206. | 0.0575470 | ||||||||
\(668\) | −4.05137e6 | −0.351286 | ||||||||
\(669\) | 3.86942e6 | 0.334257 | ||||||||
\(670\) | 384590. | 0.0330987 | ||||||||
\(671\) | −3.03516e7 | −2.60241 | ||||||||
\(672\) | 9.49344e6 | 0.810962 | ||||||||
\(673\) | 4.04898e6 | 0.344594 | 0.172297 | − | 0.985045i | \(-0.444881\pi\) | ||||
0.172297 | + | 0.985045i | \(0.444881\pi\) | |||||||
\(674\) | −532361. | −0.0451395 | ||||||||
\(675\) | −2.56643e6 | −0.216805 | ||||||||
\(676\) | −7.32694e6 | −0.616675 | ||||||||
\(677\) | −1.53240e7 | −1.28500 | −0.642498 | − | 0.766287i | \(-0.722102\pi\) | ||||
−0.642498 | + | 0.766287i | \(0.722102\pi\) | |||||||
\(678\) | −658996. | −0.0550565 | ||||||||
\(679\) | 8.88246e6 | 0.739365 | ||||||||
\(680\) | −189852. | −0.0157450 | ||||||||
\(681\) | 7.15016e6 | 0.590811 | ||||||||
\(682\) | −1.17320e7 | −0.965853 | ||||||||
\(683\) | 9.07115e6 | 0.744065 | 0.372032 | − | 0.928220i | \(-0.378661\pi\) | ||||
0.372032 | + | 0.928220i | \(0.378661\pi\) | |||||||
\(684\) | −5.88937e6 | −0.481314 | ||||||||
\(685\) | −7.37286e6 | −0.600357 | ||||||||
\(686\) | 1.83605e7 | 1.48961 | ||||||||
\(687\) | 2.80882e6 | 0.227056 | ||||||||
\(688\) | 1.82447e7 | 1.46948 | ||||||||
\(689\) | −9.30058e6 | −0.746383 | ||||||||
\(690\) | −1.44828e6 | −0.115805 | ||||||||
\(691\) | 5.99487e6 | 0.477623 | 0.238811 | − | 0.971066i | \(-0.423242\pi\) | ||||
0.238811 | + | 0.971066i | \(0.423242\pi\) | |||||||
\(692\) | −1.15420e7 | −0.916252 | ||||||||
\(693\) | 2.98270e6 | 0.235926 | ||||||||
\(694\) | 1.60846e6 | 0.126768 | ||||||||
\(695\) | −8.38873e6 | −0.658770 | ||||||||
\(696\) | 381340. | 0.0298393 | ||||||||
\(697\) | 2.59737e6 | 0.202512 | ||||||||
\(698\) | 1.18211e7 | 0.918377 | ||||||||
\(699\) | 1.10518e7 | 0.855538 | ||||||||
\(700\) | 1.85463e6 | 0.143058 | ||||||||
\(701\) | 4.32960e6 | 0.332776 | 0.166388 | − | 0.986060i | \(-0.446790\pi\) | ||||
0.166388 | + | 0.986060i | \(0.446790\pi\) | |||||||
\(702\) | 1.34509e7 | 1.03017 | ||||||||
\(703\) | −4.40216e7 | −3.35953 | ||||||||
\(704\) | 2.10583e7 | 1.60137 | ||||||||
\(705\) | −2.35127e6 | −0.178168 | ||||||||
\(706\) | 2.85590e7 | 2.15641 | ||||||||
\(707\) | 9.39874e6 | 0.707165 | ||||||||
\(708\) | −1.70315e7 | −1.27694 | ||||||||
\(709\) | 5.08191e6 | 0.379674 | 0.189837 | − | 0.981816i | \(-0.439204\pi\) | ||||
0.189837 | + | 0.981816i | \(0.439204\pi\) | |||||||
\(710\) | −4.23342e6 | −0.315170 | ||||||||
\(711\) | 176112. | 0.0130652 | ||||||||
\(712\) | 2.86069e6 | 0.211481 | ||||||||
\(713\) | 1.37774e6 | 0.101494 | ||||||||
\(714\) | 3.11591e6 | 0.228738 | ||||||||
\(715\) | 5.52355e6 | 0.404067 | ||||||||
\(716\) | 9.76860e6 | 0.712114 | ||||||||
\(717\) | −8.97856e6 | −0.652242 | ||||||||
\(718\) | 1.07705e7 | 0.779693 | ||||||||
\(719\) | 2.03791e7 | 1.47015 | 0.735075 | − | 0.677986i | \(-0.237147\pi\) | ||||
0.735075 | + | 0.677986i | \(0.237147\pi\) | |||||||
\(720\) | −1.47021e6 | −0.105693 | ||||||||
\(721\) | −1.34540e7 | −0.963856 | ||||||||
\(722\) | −3.79800e7 | −2.71151 | ||||||||
\(723\) | −2.11267e6 | −0.150310 | ||||||||
\(724\) | −7680.45 | −0.000544553 0 | ||||||||
\(725\) | −781198. | −0.0551971 | ||||||||
\(726\) | −1.56364e7 | −1.10102 | ||||||||
\(727\) | 2.60136e7 | 1.82543 | 0.912713 | − | 0.408601i | \(-0.133983\pi\) | ||||
0.912713 | + | 0.408601i | \(0.133983\pi\) | |||||||
\(728\) | −778484. | −0.0544404 | ||||||||
\(729\) | 1.58838e7 | 1.10697 | ||||||||
\(730\) | 856939. | 0.0595173 | ||||||||
\(731\) | 6.56405e6 | 0.454337 | ||||||||
\(732\) | 2.56673e7 | 1.77052 | ||||||||
\(733\) | 1.74641e6 | 0.120057 | 0.0600283 | − | 0.998197i | \(-0.480881\pi\) | ||||
0.0600283 | + | 0.998197i | \(0.480881\pi\) | |||||||
\(734\) | −3.22674e7 | −2.21067 | ||||||||
\(735\) | 3.19265e6 | 0.217988 | ||||||||
\(736\) | −4.39333e6 | −0.298951 | ||||||||
\(737\) | −1.03761e6 | −0.0703664 | ||||||||
\(738\) | −4.03680e6 | −0.272832 | ||||||||
\(739\) | −2.22491e7 | −1.49865 | −0.749326 | − | 0.662201i | \(-0.769622\pi\) | ||||
−0.749326 | + | 0.662201i | \(0.769622\pi\) | |||||||
\(740\) | 1.43438e7 | 0.962905 | ||||||||
\(741\) | 1.43357e7 | 0.959122 | ||||||||
\(742\) | 1.61758e7 | 1.07859 | ||||||||
\(743\) | −1.10893e7 | −0.736938 | −0.368469 | − | 0.929640i | \(-0.620118\pi\) | ||||
−0.368469 | + | 0.929640i | \(0.620118\pi\) | |||||||
\(744\) | 794587. | 0.0526270 | ||||||||
\(745\) | −1.22084e7 | −0.805873 | ||||||||
\(746\) | 3.32610e7 | 2.18821 | ||||||||
\(747\) | 1.90471e6 | 0.124890 | ||||||||
\(748\) | 6.39558e6 | 0.417952 | ||||||||
\(749\) | −295900. | −0.0192726 | ||||||||
\(750\) | 1.71110e6 | 0.111077 | ||||||||
\(751\) | 2.22405e7 | 1.43895 | 0.719474 | − | 0.694519i | \(-0.244383\pi\) | ||||
0.719474 | + | 0.694519i | \(0.244383\pi\) | |||||||
\(752\) | −6.50684e6 | −0.419590 | ||||||||
\(753\) | −1.74445e7 | −1.12117 | ||||||||
\(754\) | 4.09433e6 | 0.262273 | ||||||||
\(755\) | −8.85626e6 | −0.565435 | ||||||||
\(756\) | −1.21850e7 | −0.775391 | ||||||||
\(757\) | 8.33656e6 | 0.528746 | 0.264373 | − | 0.964421i | \(-0.414835\pi\) | ||||
0.264373 | + | 0.964421i | \(0.414835\pi\) | |||||||
\(758\) | 2.51942e7 | 1.59267 | ||||||||
\(759\) | 3.90740e6 | 0.246197 | ||||||||
\(760\) | 1.51917e6 | 0.0954051 | ||||||||
\(761\) | 1.85004e7 | 1.15803 | 0.579014 | − | 0.815317i | \(-0.303438\pi\) | ||||
0.579014 | + | 0.815317i | \(0.303438\pi\) | |||||||
\(762\) | 3.00710e6 | 0.187612 | ||||||||
\(763\) | 8.64187e6 | 0.537398 | ||||||||
\(764\) | −5.79566e6 | −0.359227 | ||||||||
\(765\) | −528949. | −0.0326784 | ||||||||
\(766\) | 3.38218e6 | 0.208269 | ||||||||
\(767\) | −1.46452e7 | −0.898890 | ||||||||
\(768\) | 1.12951e7 | 0.691015 | ||||||||
\(769\) | −2.80478e6 | −0.171034 | −0.0855172 | − | 0.996337i | \(-0.527254\pi\) | ||||
−0.0855172 | + | 0.996337i | \(0.527254\pi\) | |||||||
\(770\) | −9.60671e6 | −0.583912 | ||||||||
\(771\) | 1.45541e7 | 0.881760 | ||||||||
\(772\) | 703181. | 0.0424643 | ||||||||
\(773\) | −8.78805e6 | −0.528986 | −0.264493 | − | 0.964388i | \(-0.585205\pi\) | ||||
−0.264493 | + | 0.964388i | \(0.585205\pi\) | |||||||
\(774\) | −1.02018e7 | −0.612100 | ||||||||
\(775\) | −1.62776e6 | −0.0973500 | ||||||||
\(776\) | −2.37071e6 | −0.141327 | ||||||||
\(777\) | −1.88540e7 | −1.12034 | ||||||||
\(778\) | −4.85231e7 | −2.87408 | ||||||||
\(779\) | −2.07838e7 | −1.22710 | ||||||||
\(780\) | −4.67106e6 | −0.274903 | ||||||||
\(781\) | 1.14216e7 | 0.670039 | ||||||||
\(782\) | −1.44197e6 | −0.0843214 | ||||||||
\(783\) | 5.13251e6 | 0.299175 | ||||||||
\(784\) | 8.83526e6 | 0.513368 | ||||||||
\(785\) | 7.71598e6 | 0.446907 | ||||||||
\(786\) | 3.25385e7 | 1.87863 | ||||||||
\(787\) | −2.68037e7 | −1.54262 | −0.771309 | − | 0.636461i | \(-0.780398\pi\) | ||||
−0.771309 | + | 0.636461i | \(0.780398\pi\) | |||||||
\(788\) | −2.04814e7 | −1.17502 | ||||||||
\(789\) | 2.33410e7 | 1.33483 | ||||||||
\(790\) | −567225. | −0.0323361 | ||||||||
\(791\) | 513334. | 0.0291715 | ||||||||
\(792\) | −796076. | −0.0450964 | ||||||||
\(793\) | 2.20710e7 | 1.24635 | ||||||||
\(794\) | 3.21026e7 | 1.80713 | ||||||||
\(795\) | 7.77327e6 | 0.436200 | ||||||||
\(796\) | 2.57580e7 | 1.44089 | ||||||||
\(797\) | −2.76614e7 | −1.54251 | −0.771257 | − | 0.636524i | \(-0.780372\pi\) | ||||
−0.771257 | + | 0.636524i | \(0.780372\pi\) | |||||||
\(798\) | −2.49331e7 | −1.38602 | ||||||||
\(799\) | −2.34102e6 | −0.129730 | ||||||||
\(800\) | 5.19061e6 | 0.286743 | ||||||||
\(801\) | 7.97021e6 | 0.438923 | ||||||||
\(802\) | 3.49687e7 | 1.91974 | ||||||||
\(803\) | −2.31199e6 | −0.126531 | ||||||||
\(804\) | 877469. | 0.0478731 | ||||||||
\(805\) | 1.12815e6 | 0.0613590 | ||||||||
\(806\) | 8.53123e6 | 0.462566 | ||||||||
\(807\) | 1.27954e7 | 0.691626 | ||||||||
\(808\) | −2.50851e6 | −0.135172 | ||||||||
\(809\) | 2.90367e7 | 1.55983 | 0.779913 | − | 0.625888i | \(-0.215263\pi\) | ||||
0.779913 | + | 0.625888i | \(0.215263\pi\) | |||||||
\(810\) | −8.09278e6 | −0.433396 | ||||||||
\(811\) | −1.48264e7 | −0.791561 | −0.395781 | − | 0.918345i | \(-0.629526\pi\) | ||||
−0.395781 | + | 0.918345i | \(0.629526\pi\) | |||||||
\(812\) | −3.70901e6 | −0.197409 | ||||||||
\(813\) | 2.84004e6 | 0.150695 | ||||||||
\(814\) | −7.42986e7 | −3.93025 | ||||||||
\(815\) | 7.48238e6 | 0.394590 | ||||||||
\(816\) | 4.14372e6 | 0.217854 | ||||||||
\(817\) | −5.25246e7 | −2.75301 | ||||||||
\(818\) | −3.29217e7 | −1.72028 | ||||||||
\(819\) | −2.16895e6 | −0.112990 | ||||||||
\(820\) | 6.77206e6 | 0.351711 | ||||||||
\(821\) | −1.57559e7 | −0.815804 | −0.407902 | − | 0.913026i | \(-0.633740\pi\) | ||||
−0.407902 | + | 0.913026i | \(0.633740\pi\) | |||||||
\(822\) | −3.22962e7 | −1.66714 | ||||||||
\(823\) | −184301. | −0.00948481 | −0.00474241 | − | 0.999989i | \(-0.501510\pi\) | ||||
−0.00474241 | + | 0.999989i | \(0.501510\pi\) | |||||||
\(824\) | 3.59084e6 | 0.184237 | ||||||||
\(825\) | −4.61649e6 | −0.236144 | ||||||||
\(826\) | 2.54713e7 | 1.29898 | ||||||||
\(827\) | 3.34618e7 | 1.70132 | 0.850659 | − | 0.525718i | \(-0.176203\pi\) | ||||
0.850659 | + | 0.525718i | \(0.176203\pi\) | |||||||
\(828\) | 1.16729e6 | 0.0591699 | ||||||||
\(829\) | 4.68688e6 | 0.236863 | 0.118432 | − | 0.992962i | \(-0.462213\pi\) | ||||
0.118432 | + | 0.992962i | \(0.462213\pi\) | |||||||
\(830\) | −6.13470e6 | −0.309099 | ||||||||
\(831\) | 1.81893e7 | 0.913720 | ||||||||
\(832\) | −1.53131e7 | −0.766930 | ||||||||
\(833\) | 3.17874e6 | 0.158724 | ||||||||
\(834\) | −3.67461e7 | −1.82935 | ||||||||
\(835\) | 2.91164e6 | 0.144518 | ||||||||
\(836\) | −5.11765e7 | −2.53253 | ||||||||
\(837\) | 1.06945e7 | 0.527649 | ||||||||
\(838\) | −5.60601e7 | −2.75768 | ||||||||
\(839\) | 1.02280e6 | 0.0501631 | 0.0250816 | − | 0.999685i | \(-0.492015\pi\) | ||||
0.0250816 | + | 0.999685i | \(0.492015\pi\) | |||||||
\(840\) | 650644. | 0.0318160 | ||||||||
\(841\) | −1.89489e7 | −0.923832 | ||||||||
\(842\) | 2.24684e7 | 1.09218 | ||||||||
\(843\) | 2.25956e7 | 1.09510 | ||||||||
\(844\) | −1.51339e7 | −0.731298 | ||||||||
\(845\) | 5.26573e6 | 0.253698 | ||||||||
\(846\) | 3.63839e6 | 0.174777 | ||||||||
\(847\) | 1.21802e7 | 0.583372 | ||||||||
\(848\) | 2.15116e7 | 1.02726 | ||||||||
\(849\) | 7.23630e6 | 0.344546 | ||||||||
\(850\) | 1.70365e6 | 0.0808783 | ||||||||
\(851\) | 8.72518e6 | 0.413001 | ||||||||
\(852\) | −9.65885e6 | −0.455854 | ||||||||
\(853\) | 5.30980e6 | 0.249865 | 0.124932 | − | 0.992165i | \(-0.460129\pi\) | ||||
0.124932 | + | 0.992165i | \(0.460129\pi\) | |||||||
\(854\) | −3.83864e7 | −1.80108 | ||||||||
\(855\) | 4.23258e6 | 0.198011 | ||||||||
\(856\) | 78975.1 | 0.00368388 | ||||||||
\(857\) | 1.95248e7 | 0.908099 | 0.454050 | − | 0.890976i | \(-0.349979\pi\) | ||||
0.454050 | + | 0.890976i | \(0.349979\pi\) | |||||||
\(858\) | 2.41955e7 | 1.12206 | ||||||||
\(859\) | 1.11237e6 | 0.0514358 | 0.0257179 | − | 0.999669i | \(-0.491813\pi\) | ||||
0.0257179 | + | 0.999669i | \(0.491813\pi\) | |||||||
\(860\) | 1.71143e7 | 0.789065 | ||||||||
\(861\) | −8.90148e6 | −0.409218 | ||||||||
\(862\) | −1.06766e7 | −0.489402 | ||||||||
\(863\) | 3.79774e7 | 1.73579 | 0.867896 | − | 0.496746i | \(-0.165472\pi\) | ||||
0.867896 | + | 0.496746i | \(0.165472\pi\) | |||||||
\(864\) | −3.41026e7 | −1.55418 | ||||||||
\(865\) | 8.29500e6 | 0.376943 | ||||||||
\(866\) | 2.44129e7 | 1.10618 | ||||||||
\(867\) | −1.75356e7 | −0.792270 | ||||||||
\(868\) | −7.72835e6 | −0.348167 | ||||||||
\(869\) | 1.53035e6 | 0.0687452 | ||||||||
\(870\) | −3.42197e6 | −0.153278 | ||||||||
\(871\) | 754525. | 0.0336999 | ||||||||
\(872\) | −2.30650e6 | −0.102722 | ||||||||
\(873\) | −6.60508e6 | −0.293320 | ||||||||
\(874\) | 1.15384e7 | 0.510937 | ||||||||
\(875\) | −1.33288e6 | −0.0588535 | ||||||||
\(876\) | 1.95517e6 | 0.0860843 | ||||||||
\(877\) | 2.95488e6 | 0.129730 | 0.0648650 | − | 0.997894i | \(-0.479338\pi\) | ||||
0.0648650 | + | 0.997894i | \(0.479338\pi\) | |||||||
\(878\) | 2.64095e7 | 1.15617 | ||||||||
\(879\) | 793480. | 0.0346389 | ||||||||
\(880\) | −1.27756e7 | −0.556126 | ||||||||
\(881\) | 2.35223e7 | 1.02103 | 0.510516 | − | 0.859868i | \(-0.329454\pi\) | ||||
0.510516 | + | 0.859868i | \(0.329454\pi\) | |||||||
\(882\) | −4.94036e6 | −0.213839 | ||||||||
\(883\) | −2.63551e7 | −1.13753 | −0.568766 | − | 0.822499i | \(-0.692579\pi\) | ||||
−0.568766 | + | 0.822499i | \(0.692579\pi\) | |||||||
\(884\) | −4.65071e6 | −0.200165 | ||||||||
\(885\) | 1.22402e7 | 0.525329 | ||||||||
\(886\) | −1.54009e7 | −0.659116 | ||||||||
\(887\) | −2.54991e7 | −1.08822 | −0.544108 | − | 0.839015i | \(-0.683132\pi\) | ||||
−0.544108 | + | 0.839015i | \(0.683132\pi\) | |||||||
\(888\) | 5.03211e6 | 0.214150 | ||||||||
\(889\) | −2.34242e6 | −0.0994056 | ||||||||
\(890\) | −2.56705e7 | −1.08633 | ||||||||
\(891\) | 2.18341e7 | 0.921383 | ||||||||
\(892\) | 1.00447e7 | 0.422692 | ||||||||
\(893\) | 1.87325e7 | 0.786082 | ||||||||
\(894\) | −5.34777e7 | −2.23784 | ||||||||
\(895\) | −7.02050e6 | −0.292962 | ||||||||
\(896\) | 3.96252e6 | 0.164893 | ||||||||
\(897\) | −2.84137e6 | −0.117909 | ||||||||
\(898\) | −4.31956e7 | −1.78751 | ||||||||
\(899\) | 3.25530e6 | 0.134336 | ||||||||
\(900\) | −1.37912e6 | −0.0567538 | ||||||||
\(901\) | 7.73941e6 | 0.317611 | ||||||||
\(902\) | −3.50783e7 | −1.43556 | ||||||||
\(903\) | −2.24958e7 | −0.918081 | ||||||||
\(904\) | −137008. | −0.00557602 | ||||||||
\(905\) | 5519.79 | 0.000224027 0 | ||||||||
\(906\) | −3.87941e7 | −1.57017 | ||||||||
\(907\) | 2.91884e7 | 1.17813 | 0.589063 | − | 0.808087i | \(-0.299497\pi\) | ||||
0.589063 | + | 0.808087i | \(0.299497\pi\) | |||||||
\(908\) | 1.85612e7 | 0.747124 | ||||||||
\(909\) | −6.98899e6 | −0.280546 | ||||||||
\(910\) | 6.98577e6 | 0.279647 | ||||||||
\(911\) | 2.24208e7 | 0.895064 | 0.447532 | − | 0.894268i | \(-0.352303\pi\) | ||||
0.447532 | + | 0.894268i | \(0.352303\pi\) | |||||||
\(912\) | −3.31574e7 | −1.32006 | ||||||||
\(913\) | 1.65512e7 | 0.657133 | ||||||||
\(914\) | 4.98414e7 | 1.97344 | ||||||||
\(915\) | −1.84466e7 | −0.728388 | ||||||||
\(916\) | 7.29148e6 | 0.287129 | ||||||||
\(917\) | −2.53463e7 | −0.995384 | ||||||||
\(918\) | −1.11930e7 | −0.438371 | ||||||||
\(919\) | −9.78554e6 | −0.382205 | −0.191102 | − | 0.981570i | \(-0.561206\pi\) | ||||
−0.191102 | + | 0.981570i | \(0.561206\pi\) | |||||||
\(920\) | −301102. | −0.0117285 | ||||||||
\(921\) | −347506. | −0.0134994 | ||||||||
\(922\) | 4.11881e7 | 1.59568 | ||||||||
\(923\) | −8.30553e6 | −0.320895 | ||||||||
\(924\) | −2.19184e7 | −0.844557 | ||||||||
\(925\) | −1.03086e7 | −0.396136 | ||||||||
\(926\) | 3.54228e7 | 1.35755 | ||||||||
\(927\) | 1.00045e7 | 0.382380 | ||||||||
\(928\) | −1.03805e7 | −0.395685 | ||||||||
\(929\) | 8.39431e6 | 0.319114 | 0.159557 | − | 0.987189i | \(-0.448993\pi\) | ||||
0.159557 | + | 0.987189i | \(0.448993\pi\) | |||||||
\(930\) | −7.13027e6 | −0.270333 | ||||||||
\(931\) | −2.54358e7 | −0.961771 | ||||||||
\(932\) | 2.86895e7 | 1.08189 | ||||||||
\(933\) | −2.16426e7 | −0.813963 | ||||||||
\(934\) | −2.23119e7 | −0.836894 | ||||||||
\(935\) | −4.59638e6 | −0.171944 | ||||||||
\(936\) | 578888. | 0.0215976 | ||||||||
\(937\) | 2.34833e7 | 0.873795 | 0.436897 | − | 0.899511i | \(-0.356077\pi\) | ||||
0.436897 | + | 0.899511i | \(0.356077\pi\) | |||||||
\(938\) | −1.31229e6 | −0.0486993 | ||||||||
\(939\) | −3.45094e7 | −1.27724 | ||||||||
\(940\) | −6.10370e6 | −0.225307 | ||||||||
\(941\) | 3.37480e7 | 1.24244 | 0.621218 | − | 0.783638i | \(-0.286638\pi\) | ||||
0.621218 | + | 0.783638i | \(0.286638\pi\) | |||||||
\(942\) | 3.37992e7 | 1.24102 | ||||||||
\(943\) | 4.11939e6 | 0.150853 | ||||||||
\(944\) | 3.38733e7 | 1.23716 | ||||||||
\(945\) | 8.75712e6 | 0.318994 | ||||||||
\(946\) | −8.86497e7 | −3.22069 | ||||||||
\(947\) | 2.58607e7 | 0.937056 | 0.468528 | − | 0.883449i | \(-0.344784\pi\) | ||||
0.468528 | + | 0.883449i | \(0.344784\pi\) | |||||||
\(948\) | −1.29417e6 | −0.0467702 | ||||||||
\(949\) | 1.68123e6 | 0.0605984 | ||||||||
\(950\) | −1.36323e7 | −0.490073 | ||||||||
\(951\) | −1.51246e7 | −0.542293 | ||||||||
\(952\) | 647809. | 0.0231662 | ||||||||
\(953\) | 1.58198e7 | 0.564245 | 0.282122 | − | 0.959378i | \(-0.408962\pi\) | ||||
0.282122 | + | 0.959378i | \(0.408962\pi\) | |||||||
\(954\) | −1.20285e7 | −0.427898 | ||||||||
\(955\) | 4.16523e6 | 0.147785 | ||||||||
\(956\) | −2.33076e7 | −0.824808 | ||||||||
\(957\) | 9.23238e6 | 0.325862 | ||||||||
\(958\) | −3.14909e7 | −1.10859 | ||||||||
\(959\) | 2.51576e7 | 0.883328 | ||||||||
\(960\) | 1.27985e7 | 0.448208 | ||||||||
\(961\) | −2.18462e7 | −0.763074 | ||||||||
\(962\) | 5.40282e7 | 1.88227 | ||||||||
\(963\) | 220034. | 0.00764582 | ||||||||
\(964\) | −5.48433e6 | −0.190078 | ||||||||
\(965\) | −505363. | −0.0174697 | ||||||||
\(966\) | 4.94178e6 | 0.170389 | ||||||||
\(967\) | 4.67474e7 | 1.60765 | 0.803825 | − | 0.594865i | \(-0.202795\pi\) | ||||
0.803825 | + | 0.594865i | \(0.202795\pi\) | |||||||
\(968\) | −3.25087e6 | −0.111509 | ||||||||
\(969\) | −1.19294e7 | −0.408138 | ||||||||
\(970\) | 2.12737e7 | 0.725962 | ||||||||
\(971\) | 2.86862e7 | 0.976393 | 0.488196 | − | 0.872734i | \(-0.337655\pi\) | ||||
0.488196 | + | 0.872734i | \(0.337655\pi\) | |||||||
\(972\) | 1.62461e7 | 0.551548 | ||||||||
\(973\) | 2.86239e7 | 0.969274 | ||||||||
\(974\) | 3.90220e7 | 1.31799 | ||||||||
\(975\) | 3.35700e6 | 0.113094 | ||||||||
\(976\) | −5.10486e7 | −1.71537 | ||||||||
\(977\) | −4.19859e6 | −0.140724 | −0.0703618 | − | 0.997522i | \(-0.522415\pi\) | ||||
−0.0703618 | + | 0.997522i | \(0.522415\pi\) | |||||||
\(978\) | 3.27759e7 | 1.09574 | ||||||||
\(979\) | 6.92583e7 | 2.30948 | ||||||||
\(980\) | 8.28786e6 | 0.275662 | ||||||||
\(981\) | −6.42617e6 | −0.213196 | ||||||||
\(982\) | 4.09590e6 | 0.135541 | ||||||||
\(983\) | −5.60414e7 | −1.84980 | −0.924900 | − | 0.380209i | \(-0.875852\pi\) | ||||
−0.924900 | + | 0.380209i | \(0.875852\pi\) | |||||||
\(984\) | 2.37579e6 | 0.0782204 | ||||||||
\(985\) | 1.47196e7 | 0.483398 | ||||||||
\(986\) | −3.40707e6 | −0.111606 | ||||||||
\(987\) | 8.02296e6 | 0.262145 | ||||||||
\(988\) | 3.72143e7 | 1.21288 | ||||||||
\(989\) | 1.04105e7 | 0.338439 | ||||||||
\(990\) | 7.14363e6 | 0.231649 | ||||||||
\(991\) | −4.50808e7 | −1.45817 | −0.729083 | − | 0.684425i | \(-0.760053\pi\) | ||||
−0.729083 | + | 0.684425i | \(0.760053\pi\) | |||||||
\(992\) | −2.16296e7 | −0.697862 | ||||||||
\(993\) | 2.14173e7 | 0.689274 | ||||||||
\(994\) | 1.44452e7 | 0.463722 | ||||||||
\(995\) | −1.85118e7 | −0.592776 | ||||||||
\(996\) | −1.39968e7 | −0.447074 | ||||||||
\(997\) | 1.84395e7 | 0.587503 | 0.293752 | − | 0.955882i | \(-0.405096\pi\) | ||||
0.293752 | + | 0.955882i | \(0.405096\pi\) | |||||||
\(998\) | −1.90351e7 | −0.604964 | ||||||||
\(999\) | 6.77279e7 | 2.14711 |
(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 | 115.6.a.d.1.2 | ✓ | 10 | |
3.2 | odd | 2 | 1035.6.a.j.1.9 | 10 | |||
5.4 | even | 2 | 575.6.a.f.1.9 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
115.6.a.d.1.2 | ✓ | 10 | 1.1 | even | 1 | trivial | |
575.6.a.f.1.9 | 10 | 5.4 | even | 2 | |||
1035.6.a.j.1.9 | 10 | 3.2 | odd | 2 |