Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,6,Mod(1,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.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: | \(6.89650425196\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 173x^{6} + 462x^{5} + 9118x^{4} - 14192x^{3} - 167688x^{2} + 106368x + 681984 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(7.21373\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 43.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.21373 | 0.921667 | 0.460833 | − | 0.887487i | \(-0.347551\pi\) | ||||
0.460833 | + | 0.887487i | \(0.347551\pi\) | |||||||
\(3\) | −11.2683 | −0.722863 | −0.361431 | − | 0.932399i | \(-0.617712\pi\) | ||||
−0.361431 | + | 0.932399i | \(0.617712\pi\) | |||||||
\(4\) | −4.81697 | −0.150530 | ||||||||
\(5\) | −9.80186 | −0.175341 | −0.0876705 | − | 0.996150i | \(-0.527942\pi\) | ||||
−0.0876705 | + | 0.996150i | \(0.527942\pi\) | |||||||
\(6\) | −58.7500 | −0.666239 | ||||||||
\(7\) | −11.1041 | −0.0856521 | −0.0428260 | − | 0.999083i | \(-0.513636\pi\) | ||||
−0.0428260 | + | 0.999083i | \(0.513636\pi\) | |||||||
\(8\) | −191.954 | −1.06041 | ||||||||
\(9\) | −116.025 | −0.477470 | ||||||||
\(10\) | −51.1043 | −0.161606 | ||||||||
\(11\) | −557.274 | −1.38863 | −0.694316 | − | 0.719670i | \(-0.744293\pi\) | ||||
−0.694316 | + | 0.719670i | \(0.744293\pi\) | |||||||
\(12\) | 54.2791 | 0.108813 | ||||||||
\(13\) | 107.663 | 0.176688 | 0.0883441 | − | 0.996090i | \(-0.471842\pi\) | ||||
0.0883441 | + | 0.996090i | \(0.471842\pi\) | |||||||
\(14\) | −57.8938 | −0.0789427 | ||||||||
\(15\) | 110.450 | 0.126747 | ||||||||
\(16\) | −846.654 | −0.826810 | ||||||||
\(17\) | 329.005 | 0.276109 | 0.138054 | − | 0.990425i | \(-0.455915\pi\) | ||||
0.138054 | + | 0.990425i | \(0.455915\pi\) | |||||||
\(18\) | −604.924 | −0.440068 | ||||||||
\(19\) | 2938.10 | 1.86716 | 0.933582 | − | 0.358365i | \(-0.116666\pi\) | ||||
0.933582 | + | 0.358365i | \(0.116666\pi\) | |||||||
\(20\) | 47.2153 | 0.0263941 | ||||||||
\(21\) | 125.124 | 0.0619147 | ||||||||
\(22\) | −2905.48 | −1.27986 | ||||||||
\(23\) | −385.537 | −0.151966 | −0.0759830 | − | 0.997109i | \(-0.524209\pi\) | ||||
−0.0759830 | + | 0.997109i | \(0.524209\pi\) | |||||||
\(24\) | 2163.00 | 0.766528 | ||||||||
\(25\) | −3028.92 | −0.969256 | ||||||||
\(26\) | 561.326 | 0.162848 | ||||||||
\(27\) | 4045.61 | 1.06801 | ||||||||
\(28\) | 53.4881 | 0.0128932 | ||||||||
\(29\) | −3309.15 | −0.730670 | −0.365335 | − | 0.930876i | \(-0.619046\pi\) | ||||
−0.365335 | + | 0.930876i | \(0.619046\pi\) | |||||||
\(30\) | 575.859 | 0.116819 | ||||||||
\(31\) | −5471.71 | −1.02263 | −0.511316 | − | 0.859393i | \(-0.670842\pi\) | ||||
−0.511316 | + | 0.859393i | \(0.670842\pi\) | |||||||
\(32\) | 1728.30 | 0.298362 | ||||||||
\(33\) | 6279.54 | 1.00379 | ||||||||
\(34\) | 1715.34 | 0.254480 | ||||||||
\(35\) | 108.841 | 0.0150183 | ||||||||
\(36\) | 558.890 | 0.0718737 | ||||||||
\(37\) | 4832.22 | 0.580286 | 0.290143 | − | 0.956983i | \(-0.406297\pi\) | ||||
0.290143 | + | 0.956983i | \(0.406297\pi\) | |||||||
\(38\) | 15318.5 | 1.72090 | ||||||||
\(39\) | −1213.18 | −0.127721 | ||||||||
\(40\) | 1881.51 | 0.185933 | ||||||||
\(41\) | 1065.16 | 0.0989587 | 0.0494793 | − | 0.998775i | \(-0.484244\pi\) | ||||
0.0494793 | + | 0.998775i | \(0.484244\pi\) | |||||||
\(42\) | 652.365 | 0.0570647 | ||||||||
\(43\) | −1849.00 | −0.152499 | ||||||||
\(44\) | 2684.37 | 0.209031 | ||||||||
\(45\) | 1137.26 | 0.0837200 | ||||||||
\(46\) | −2010.09 | −0.140062 | ||||||||
\(47\) | −8991.95 | −0.593758 | −0.296879 | − | 0.954915i | \(-0.595946\pi\) | ||||
−0.296879 | + | 0.954915i | \(0.595946\pi\) | |||||||
\(48\) | 9540.36 | 0.597670 | ||||||||
\(49\) | −16683.7 | −0.992664 | ||||||||
\(50\) | −15792.0 | −0.893331 | ||||||||
\(51\) | −3707.33 | −0.199589 | ||||||||
\(52\) | −518.609 | −0.0265969 | ||||||||
\(53\) | −10216.7 | −0.499598 | −0.249799 | − | 0.968298i | \(-0.580365\pi\) | ||||
−0.249799 | + | 0.968298i | \(0.580365\pi\) | |||||||
\(54\) | 21092.7 | 0.984347 | ||||||||
\(55\) | 5462.32 | 0.243484 | ||||||||
\(56\) | 2131.47 | 0.0908260 | ||||||||
\(57\) | −33107.4 | −1.34970 | ||||||||
\(58\) | −17253.0 | −0.673434 | ||||||||
\(59\) | −27457.0 | −1.02689 | −0.513444 | − | 0.858123i | \(-0.671631\pi\) | ||||
−0.513444 | + | 0.858123i | \(0.671631\pi\) | |||||||
\(60\) | −532.036 | −0.0190793 | ||||||||
\(61\) | −36692.9 | −1.26258 | −0.631288 | − | 0.775548i | \(-0.717473\pi\) | ||||
−0.631288 | + | 0.775548i | \(0.717473\pi\) | |||||||
\(62\) | −28528.1 | −0.942525 | ||||||||
\(63\) | 1288.35 | 0.0408963 | ||||||||
\(64\) | 36103.8 | 1.10180 | ||||||||
\(65\) | −1055.30 | −0.0309807 | ||||||||
\(66\) | 32739.9 | 0.925160 | ||||||||
\(67\) | −26272.2 | −0.715004 | −0.357502 | − | 0.933912i | \(-0.616372\pi\) | ||||
−0.357502 | + | 0.933912i | \(0.616372\pi\) | |||||||
\(68\) | −1584.81 | −0.0415627 | ||||||||
\(69\) | 4344.35 | 0.109851 | ||||||||
\(70\) | 567.467 | 0.0138419 | ||||||||
\(71\) | 55130.3 | 1.29791 | 0.648955 | − | 0.760827i | \(-0.275206\pi\) | ||||
0.648955 | + | 0.760827i | \(0.275206\pi\) | |||||||
\(72\) | 22271.5 | 0.506311 | ||||||||
\(73\) | −9315.14 | −0.204589 | −0.102294 | − | 0.994754i | \(-0.532618\pi\) | ||||
−0.102294 | + | 0.994754i | \(0.532618\pi\) | |||||||
\(74\) | 25193.9 | 0.534830 | ||||||||
\(75\) | 34130.9 | 0.700639 | ||||||||
\(76\) | −14152.7 | −0.281065 | ||||||||
\(77\) | 6188.02 | 0.118939 | ||||||||
\(78\) | −6325.20 | −0.117717 | ||||||||
\(79\) | 56826.5 | 1.02443 | 0.512216 | − | 0.858856i | \(-0.328825\pi\) | ||||
0.512216 | + | 0.858856i | \(0.328825\pi\) | |||||||
\(80\) | 8298.78 | 0.144974 | ||||||||
\(81\) | −17393.1 | −0.294553 | ||||||||
\(82\) | 5553.44 | 0.0912069 | ||||||||
\(83\) | −5858.19 | −0.0933401 | −0.0466700 | − | 0.998910i | \(-0.514861\pi\) | ||||
−0.0466700 | + | 0.998910i | \(0.514861\pi\) | |||||||
\(84\) | −602.721 | −0.00932004 | ||||||||
\(85\) | −3224.86 | −0.0484132 | ||||||||
\(86\) | −9640.20 | −0.140553 | ||||||||
\(87\) | 37288.5 | 0.528174 | ||||||||
\(88\) | 106971. | 1.47251 | ||||||||
\(89\) | −42815.7 | −0.572965 | −0.286483 | − | 0.958085i | \(-0.592486\pi\) | ||||
−0.286483 | + | 0.958085i | \(0.592486\pi\) | |||||||
\(90\) | 5929.38 | 0.0771619 | ||||||||
\(91\) | −1195.50 | −0.0151337 | ||||||||
\(92\) | 1857.12 | 0.0228755 | ||||||||
\(93\) | 61657.0 | 0.739222 | ||||||||
\(94\) | −46881.7 | −0.547247 | ||||||||
\(95\) | −28798.8 | −0.327390 | ||||||||
\(96\) | −19475.0 | −0.215675 | ||||||||
\(97\) | −231.671 | −0.00250002 | −0.00125001 | − | 0.999999i | \(-0.500398\pi\) | ||||
−0.00125001 | + | 0.999999i | \(0.500398\pi\) | |||||||
\(98\) | −86984.4 | −0.914905 | ||||||||
\(99\) | 64657.8 | 0.663029 | ||||||||
\(100\) | 14590.2 | 0.145902 | ||||||||
\(101\) | −65329.5 | −0.637245 | −0.318622 | − | 0.947882i | \(-0.603220\pi\) | ||||
−0.318622 | + | 0.947882i | \(0.603220\pi\) | |||||||
\(102\) | −19329.0 | −0.183954 | ||||||||
\(103\) | 210856. | 1.95837 | 0.979183 | − | 0.202980i | \(-0.0650628\pi\) | ||||
0.979183 | + | 0.202980i | \(0.0650628\pi\) | |||||||
\(104\) | −20666.3 | −0.187361 | ||||||||
\(105\) | −1226.45 | −0.0108562 | ||||||||
\(106\) | −53267.2 | −0.460463 | ||||||||
\(107\) | −158342. | −1.33702 | −0.668508 | − | 0.743705i | \(-0.733067\pi\) | ||||
−0.668508 | + | 0.743705i | \(0.733067\pi\) | |||||||
\(108\) | −19487.6 | −0.160768 | ||||||||
\(109\) | −85822.7 | −0.691888 | −0.345944 | − | 0.938255i | \(-0.612441\pi\) | ||||
−0.345944 | + | 0.938255i | \(0.612441\pi\) | |||||||
\(110\) | 28479.1 | 0.224411 | ||||||||
\(111\) | −54450.9 | −0.419467 | ||||||||
\(112\) | 9401.32 | 0.0708180 | ||||||||
\(113\) | 101903. | 0.750745 | 0.375372 | − | 0.926874i | \(-0.377515\pi\) | ||||
0.375372 | + | 0.926874i | \(0.377515\pi\) | |||||||
\(114\) | −172613. | −1.24398 | ||||||||
\(115\) | 3778.98 | 0.0266459 | ||||||||
\(116\) | 15940.1 | 0.109988 | ||||||||
\(117\) | −12491.6 | −0.0843633 | ||||||||
\(118\) | −143153. | −0.946448 | ||||||||
\(119\) | −3653.30 | −0.0236493 | ||||||||
\(120\) | −21201.4 | −0.134404 | ||||||||
\(121\) | 149503. | 0.928299 | ||||||||
\(122\) | −191307. | −1.16367 | ||||||||
\(123\) | −12002.5 | −0.0715335 | ||||||||
\(124\) | 26357.1 | 0.153937 | ||||||||
\(125\) | 60319.9 | 0.345291 | ||||||||
\(126\) | 6717.13 | 0.0376927 | ||||||||
\(127\) | 109901. | 0.604635 | 0.302318 | − | 0.953207i | \(-0.402240\pi\) | ||||
0.302318 | + | 0.953207i | \(0.402240\pi\) | |||||||
\(128\) | 132930. | 0.717131 | ||||||||
\(129\) | 20835.1 | 0.110236 | ||||||||
\(130\) | −5502.04 | −0.0285539 | ||||||||
\(131\) | −79310.4 | −0.403787 | −0.201893 | − | 0.979408i | \(-0.564709\pi\) | ||||
−0.201893 | + | 0.979408i | \(0.564709\pi\) | |||||||
\(132\) | −30248.4 | −0.151101 | ||||||||
\(133\) | −32624.9 | −0.159926 | ||||||||
\(134\) | −136976. | −0.658996 | ||||||||
\(135\) | −39654.5 | −0.187266 | ||||||||
\(136\) | −63153.8 | −0.292787 | ||||||||
\(137\) | −360169. | −1.63948 | −0.819738 | − | 0.572738i | \(-0.805881\pi\) | ||||
−0.819738 | + | 0.572738i | \(0.805881\pi\) | |||||||
\(138\) | 22650.3 | 0.101246 | ||||||||
\(139\) | 330826. | 1.45232 | 0.726160 | − | 0.687525i | \(-0.241303\pi\) | ||||
0.726160 | + | 0.687525i | \(0.241303\pi\) | |||||||
\(140\) | −524.283 | −0.00226071 | ||||||||
\(141\) | 101324. | 0.429205 | ||||||||
\(142\) | 287435. | 1.19624 | ||||||||
\(143\) | −59997.8 | −0.245355 | ||||||||
\(144\) | 98233.1 | 0.394777 | ||||||||
\(145\) | 32435.8 | 0.128116 | ||||||||
\(146\) | −48566.7 | −0.188563 | ||||||||
\(147\) | 187997. | 0.717560 | ||||||||
\(148\) | −23276.6 | −0.0873506 | ||||||||
\(149\) | 24179.7 | 0.0892249 | 0.0446125 | − | 0.999004i | \(-0.485795\pi\) | ||||
0.0446125 | + | 0.999004i | \(0.485795\pi\) | |||||||
\(150\) | 177949. | 0.645755 | ||||||||
\(151\) | 278667. | 0.994589 | 0.497295 | − | 0.867582i | \(-0.334327\pi\) | ||||
0.497295 | + | 0.867582i | \(0.334327\pi\) | |||||||
\(152\) | −563979. | −1.97995 | ||||||||
\(153\) | −38172.8 | −0.131833 | ||||||||
\(154\) | 32262.7 | 0.109622 | ||||||||
\(155\) | 53633.0 | 0.179309 | ||||||||
\(156\) | 5843.85 | 0.0192259 | ||||||||
\(157\) | −102228. | −0.330995 | −0.165497 | − | 0.986210i | \(-0.552923\pi\) | ||||
−0.165497 | + | 0.986210i | \(0.552923\pi\) | |||||||
\(158\) | 296279. | 0.944186 | ||||||||
\(159\) | 115125. | 0.361141 | ||||||||
\(160\) | −16940.5 | −0.0523151 | ||||||||
\(161\) | 4281.04 | 0.0130162 | ||||||||
\(162\) | −90682.9 | −0.271480 | ||||||||
\(163\) | 444216. | 1.30956 | 0.654780 | − | 0.755819i | \(-0.272761\pi\) | ||||
0.654780 | + | 0.755819i | \(0.272761\pi\) | |||||||
\(164\) | −5130.83 | −0.0148963 | ||||||||
\(165\) | −61551.2 | −0.176006 | ||||||||
\(166\) | −30543.0 | −0.0860285 | ||||||||
\(167\) | −467231. | −1.29640 | −0.648202 | − | 0.761469i | \(-0.724479\pi\) | ||||
−0.648202 | + | 0.761469i | \(0.724479\pi\) | |||||||
\(168\) | −24018.1 | −0.0656547 | ||||||||
\(169\) | −359702. | −0.968781 | ||||||||
\(170\) | −16813.6 | −0.0446208 | ||||||||
\(171\) | −340893. | −0.891514 | ||||||||
\(172\) | 8906.58 | 0.0229557 | ||||||||
\(173\) | 296435. | 0.753033 | 0.376516 | − | 0.926410i | \(-0.377122\pi\) | ||||
0.376516 | + | 0.926410i | \(0.377122\pi\) | |||||||
\(174\) | 194412. | 0.486801 | ||||||||
\(175\) | 33633.5 | 0.0830188 | ||||||||
\(176\) | 471818. | 1.14814 | ||||||||
\(177\) | 309394. | 0.742299 | ||||||||
\(178\) | −223230. | −0.528083 | ||||||||
\(179\) | 211576. | 0.493553 | 0.246777 | − | 0.969072i | \(-0.420629\pi\) | ||||
0.246777 | + | 0.969072i | \(0.420629\pi\) | |||||||
\(180\) | −5478.16 | −0.0126024 | ||||||||
\(181\) | −187769. | −0.426018 | −0.213009 | − | 0.977050i | \(-0.568326\pi\) | ||||
−0.213009 | + | 0.977050i | \(0.568326\pi\) | |||||||
\(182\) | −6233.01 | −0.0139482 | ||||||||
\(183\) | 413467. | 0.912669 | ||||||||
\(184\) | 74005.3 | 0.161146 | ||||||||
\(185\) | −47364.7 | −0.101748 | ||||||||
\(186\) | 321463. | 0.681316 | ||||||||
\(187\) | −183346. | −0.383413 | ||||||||
\(188\) | 43314.0 | 0.0893786 | ||||||||
\(189\) | −44922.8 | −0.0914771 | ||||||||
\(190\) | −150149. | −0.301745 | ||||||||
\(191\) | −655959. | −1.30105 | −0.650524 | − | 0.759486i | \(-0.725450\pi\) | ||||
−0.650524 | + | 0.759486i | \(0.725450\pi\) | |||||||
\(192\) | −406829. | −0.796451 | ||||||||
\(193\) | 450394. | 0.870361 | 0.435180 | − | 0.900343i | \(-0.356685\pi\) | ||||
0.435180 | + | 0.900343i | \(0.356685\pi\) | |||||||
\(194\) | −1207.87 | −0.00230418 | ||||||||
\(195\) | 11891.4 | 0.0223948 | ||||||||
\(196\) | 80364.9 | 0.149426 | ||||||||
\(197\) | −973133. | −1.78652 | −0.893258 | − | 0.449545i | \(-0.851586\pi\) | ||||
−0.893258 | + | 0.449545i | \(0.851586\pi\) | |||||||
\(198\) | 337109. | 0.611092 | ||||||||
\(199\) | 259840. | 0.465129 | 0.232564 | − | 0.972581i | \(-0.425288\pi\) | ||||
0.232564 | + | 0.972581i | \(0.425288\pi\) | |||||||
\(200\) | 581414. | 1.02780 | ||||||||
\(201\) | 296043. | 0.516850 | ||||||||
\(202\) | −340611. | −0.587327 | ||||||||
\(203\) | 36745.1 | 0.0625834 | ||||||||
\(204\) | 17858.1 | 0.0300441 | ||||||||
\(205\) | −10440.5 | −0.0173515 | ||||||||
\(206\) | 1.09935e6 | 1.80496 | ||||||||
\(207\) | 44732.0 | 0.0725591 | ||||||||
\(208\) | −91153.2 | −0.146088 | ||||||||
\(209\) | −1.63733e6 | −2.59280 | ||||||||
\(210\) | −6394.39 | −0.0100058 | ||||||||
\(211\) | −621161. | −0.960502 | −0.480251 | − | 0.877131i | \(-0.659454\pi\) | ||||
−0.480251 | + | 0.877131i | \(0.659454\pi\) | |||||||
\(212\) | 49213.5 | 0.0752047 | ||||||||
\(213\) | −621226. | −0.938211 | ||||||||
\(214\) | −825553. | −1.23228 | ||||||||
\(215\) | 18123.6 | 0.0267392 | ||||||||
\(216\) | −776570. | −1.13252 | ||||||||
\(217\) | 60758.4 | 0.0875905 | ||||||||
\(218\) | −447457. | −0.637690 | ||||||||
\(219\) | 104966. | 0.147890 | ||||||||
\(220\) | −26311.8 | −0.0366517 | ||||||||
\(221\) | 35421.6 | 0.0487852 | ||||||||
\(222\) | −283893. | −0.386609 | ||||||||
\(223\) | −779614. | −1.04983 | −0.524913 | − | 0.851156i | \(-0.675902\pi\) | ||||
−0.524913 | + | 0.851156i | \(0.675902\pi\) | |||||||
\(224\) | −19191.2 | −0.0255553 | ||||||||
\(225\) | 351431. | 0.462790 | ||||||||
\(226\) | 531297. | 0.691937 | ||||||||
\(227\) | 795424. | 1.02455 | 0.512276 | − | 0.858821i | \(-0.328803\pi\) | ||||
0.512276 | + | 0.858821i | \(0.328803\pi\) | |||||||
\(228\) | 159477. | 0.203171 | ||||||||
\(229\) | −702980. | −0.885838 | −0.442919 | − | 0.896562i | \(-0.646057\pi\) | ||||
−0.442919 | + | 0.896562i | \(0.646057\pi\) | |||||||
\(230\) | 19702.6 | 0.0245586 | ||||||||
\(231\) | −69728.6 | −0.0859767 | ||||||||
\(232\) | 635204. | 0.774807 | ||||||||
\(233\) | −219327. | −0.264669 | −0.132334 | − | 0.991205i | \(-0.542247\pi\) | ||||
−0.132334 | + | 0.991205i | \(0.542247\pi\) | |||||||
\(234\) | −65127.9 | −0.0777548 | ||||||||
\(235\) | 88137.9 | 0.104110 | ||||||||
\(236\) | 132260. | 0.154578 | ||||||||
\(237\) | −640339. | −0.740524 | ||||||||
\(238\) | −19047.3 | −0.0217968 | ||||||||
\(239\) | 1.75148e6 | 1.98340 | 0.991701 | − | 0.128565i | \(-0.0410372\pi\) | ||||
0.991701 | + | 0.128565i | \(0.0410372\pi\) | |||||||
\(240\) | −93513.3 | −0.104796 | ||||||||
\(241\) | 985600. | 1.09310 | 0.546548 | − | 0.837428i | \(-0.315942\pi\) | ||||
0.546548 | + | 0.837428i | \(0.315942\pi\) | |||||||
\(242\) | 779471. | 0.855582 | ||||||||
\(243\) | −787092. | −0.855086 | ||||||||
\(244\) | 176749. | 0.190056 | ||||||||
\(245\) | 163531. | 0.174055 | ||||||||
\(246\) | −62578.0 | −0.0659301 | ||||||||
\(247\) | 316324. | 0.329906 | ||||||||
\(248\) | 1.05032e6 | 1.08440 | ||||||||
\(249\) | 66011.9 | 0.0674721 | ||||||||
\(250\) | 314492. | 0.318243 | ||||||||
\(251\) | 126142. | 0.126379 | 0.0631894 | − | 0.998002i | \(-0.479873\pi\) | ||||
0.0631894 | + | 0.998002i | \(0.479873\pi\) | |||||||
\(252\) | −6205.96 | −0.00615613 | ||||||||
\(253\) | 214850. | 0.211025 | ||||||||
\(254\) | 572996. | 0.557272 | ||||||||
\(255\) | 36338.7 | 0.0349961 | ||||||||
\(256\) | −462259. | −0.440845 | ||||||||
\(257\) | 1.55933e6 | 1.47267 | 0.736335 | − | 0.676617i | \(-0.236555\pi\) | ||||
0.736335 | + | 0.676617i | \(0.236555\pi\) | |||||||
\(258\) | 108629. | 0.101600 | ||||||||
\(259\) | −53657.4 | −0.0497027 | ||||||||
\(260\) | 5083.33 | 0.00466353 | ||||||||
\(261\) | 383944. | 0.348873 | ||||||||
\(262\) | −413503. | −0.372157 | ||||||||
\(263\) | −107289. | −0.0956460 | −0.0478230 | − | 0.998856i | \(-0.515228\pi\) | ||||
−0.0478230 | + | 0.998856i | \(0.515228\pi\) | |||||||
\(264\) | −1.20538e6 | −1.06442 | ||||||||
\(265\) | 100143. | 0.0876001 | ||||||||
\(266\) | −170098. | −0.147399 | ||||||||
\(267\) | 482461. | 0.414175 | ||||||||
\(268\) | 126552. | 0.107630 | ||||||||
\(269\) | 829468. | 0.698906 | 0.349453 | − | 0.936954i | \(-0.386367\pi\) | ||||
0.349453 | + | 0.936954i | \(0.386367\pi\) | |||||||
\(270\) | −206748. | −0.172596 | ||||||||
\(271\) | 2.22835e6 | 1.84315 | 0.921575 | − | 0.388200i | \(-0.126903\pi\) | ||||
0.921575 | + | 0.388200i | \(0.126903\pi\) | |||||||
\(272\) | −278553. | −0.228289 | ||||||||
\(273\) | 13471.3 | 0.0109396 | ||||||||
\(274\) | −1.87783e6 | −1.51105 | ||||||||
\(275\) | 1.68794e6 | 1.34594 | ||||||||
\(276\) | −20926.6 | −0.0165358 | ||||||||
\(277\) | −1.57467e6 | −1.23308 | −0.616538 | − | 0.787325i | \(-0.711465\pi\) | ||||
−0.616538 | + | 0.787325i | \(0.711465\pi\) | |||||||
\(278\) | 1.72484e6 | 1.33856 | ||||||||
\(279\) | 634856. | 0.488275 | ||||||||
\(280\) | −20892.4 | −0.0159255 | ||||||||
\(281\) | −2.26025e6 | −1.70762 | −0.853809 | − | 0.520586i | \(-0.825713\pi\) | ||||
−0.853809 | + | 0.520586i | \(0.825713\pi\) | |||||||
\(282\) | 528277. | 0.395584 | ||||||||
\(283\) | −1.81290e6 | −1.34558 | −0.672789 | − | 0.739835i | \(-0.734904\pi\) | ||||
−0.672789 | + | 0.739835i | \(0.734904\pi\) | |||||||
\(284\) | −265561. | −0.195375 | ||||||||
\(285\) | 324514. | 0.236658 | ||||||||
\(286\) | −312812. | −0.226136 | ||||||||
\(287\) | −11827.6 | −0.00847602 | ||||||||
\(288\) | −200526. | −0.142459 | ||||||||
\(289\) | −1.31161e6 | −0.923764 | ||||||||
\(290\) | 169112. | 0.118081 | ||||||||
\(291\) | 2610.55 | 0.00180717 | ||||||||
\(292\) | 44870.7 | 0.0307968 | ||||||||
\(293\) | −1.92999e6 | −1.31336 | −0.656682 | − | 0.754168i | \(-0.728041\pi\) | ||||
−0.656682 | + | 0.754168i | \(0.728041\pi\) | |||||||
\(294\) | 980167. | 0.661351 | ||||||||
\(295\) | 269130. | 0.180056 | ||||||||
\(296\) | −927563. | −0.615338 | ||||||||
\(297\) | −2.25451e6 | −1.48307 | ||||||||
\(298\) | 126067. | 0.0822356 | ||||||||
\(299\) | −41508.0 | −0.0268506 | ||||||||
\(300\) | −164407. | −0.105467 | ||||||||
\(301\) | 20531.5 | 0.0130618 | ||||||||
\(302\) | 1.45290e6 | 0.916680 | ||||||||
\(303\) | 736154. | 0.460640 | ||||||||
\(304\) | −2.48755e6 | −1.54379 | ||||||||
\(305\) | 359659. | 0.221381 | ||||||||
\(306\) | −199023. | −0.121507 | ||||||||
\(307\) | −2.35372e6 | −1.42531 | −0.712654 | − | 0.701515i | \(-0.752507\pi\) | ||||
−0.712654 | + | 0.701515i | \(0.752507\pi\) | |||||||
\(308\) | −29807.5 | −0.0179040 | ||||||||
\(309\) | −2.37600e6 | −1.41563 | ||||||||
\(310\) | 279628. | 0.165263 | ||||||||
\(311\) | 1.25933e6 | 0.738312 | 0.369156 | − | 0.929367i | \(-0.379647\pi\) | ||||
0.369156 | + | 0.929367i | \(0.379647\pi\) | |||||||
\(312\) | 232875. | 0.135436 | ||||||||
\(313\) | −1.21791e6 | −0.702676 | −0.351338 | − | 0.936249i | \(-0.614273\pi\) | ||||
−0.351338 | + | 0.936249i | \(0.614273\pi\) | |||||||
\(314\) | −532990. | −0.305067 | ||||||||
\(315\) | −12628.3 | −0.00717079 | ||||||||
\(316\) | −273732. | −0.154208 | ||||||||
\(317\) | 689890. | 0.385595 | 0.192798 | − | 0.981239i | \(-0.438244\pi\) | ||||
0.192798 | + | 0.981239i | \(0.438244\pi\) | |||||||
\(318\) | 600231. | 0.332852 | ||||||||
\(319\) | 1.84410e6 | 1.01463 | ||||||||
\(320\) | −353884. | −0.193191 | ||||||||
\(321\) | 1.78425e6 | 0.966480 | ||||||||
\(322\) | 22320.2 | 0.0119966 | ||||||||
\(323\) | 966649. | 0.515540 | ||||||||
\(324\) | 83782.0 | 0.0443392 | ||||||||
\(325\) | −326103. | −0.171256 | ||||||||
\(326\) | 2.31603e6 | 1.20698 | ||||||||
\(327\) | 967077. | 0.500140 | ||||||||
\(328\) | −204461. | −0.104936 | ||||||||
\(329\) | 99847.5 | 0.0508566 | ||||||||
\(330\) | −320911. | −0.162218 | ||||||||
\(331\) | 1.93331e6 | 0.969912 | 0.484956 | − | 0.874538i | \(-0.338836\pi\) | ||||
0.484956 | + | 0.874538i | \(0.338836\pi\) | |||||||
\(332\) | 28218.7 | 0.0140505 | ||||||||
\(333\) | −560658. | −0.277069 | ||||||||
\(334\) | −2.43602e6 | −1.19485 | ||||||||
\(335\) | 257516. | 0.125370 | ||||||||
\(336\) | −105937. | −0.0511917 | ||||||||
\(337\) | 347418. | 0.166639 | 0.0833196 | − | 0.996523i | \(-0.473448\pi\) | ||||
0.0833196 | + | 0.996523i | \(0.473448\pi\) | |||||||
\(338\) | −1.87539e6 | −0.892893 | ||||||||
\(339\) | −1.14828e6 | −0.542686 | ||||||||
\(340\) | 15534.1 | 0.00728765 | ||||||||
\(341\) | 3.04924e6 | 1.42006 | ||||||||
\(342\) | −1.77733e6 | −0.821678 | ||||||||
\(343\) | 371884. | 0.170676 | ||||||||
\(344\) | 354923. | 0.161710 | ||||||||
\(345\) | −42582.7 | −0.0192613 | ||||||||
\(346\) | 1.54553e6 | 0.694045 | ||||||||
\(347\) | −4.28700e6 | −1.91130 | −0.955652 | − | 0.294498i | \(-0.904847\pi\) | ||||
−0.955652 | + | 0.294498i | \(0.904847\pi\) | |||||||
\(348\) | −179618. | −0.0795062 | ||||||||
\(349\) | 2.58234e6 | 1.13488 | 0.567439 | − | 0.823415i | \(-0.307934\pi\) | ||||
0.567439 | + | 0.823415i | \(0.307934\pi\) | |||||||
\(350\) | 175356. | 0.0765156 | ||||||||
\(351\) | 435562. | 0.188704 | ||||||||
\(352\) | −963136. | −0.414315 | ||||||||
\(353\) | −2.31876e6 | −0.990419 | −0.495210 | − | 0.868774i | \(-0.664909\pi\) | ||||
−0.495210 | + | 0.868774i | \(0.664909\pi\) | |||||||
\(354\) | 1.61310e6 | 0.684152 | ||||||||
\(355\) | −540380. | −0.227577 | ||||||||
\(356\) | 206242. | 0.0862486 | ||||||||
\(357\) | 41166.5 | 0.0170952 | ||||||||
\(358\) | 1.10310e6 | 0.454892 | ||||||||
\(359\) | −1.41572e6 | −0.579752 | −0.289876 | − | 0.957064i | \(-0.593614\pi\) | ||||
−0.289876 | + | 0.957064i | \(0.593614\pi\) | |||||||
\(360\) | −218302. | −0.0887771 | ||||||||
\(361\) | 6.15632e6 | 2.48630 | ||||||||
\(362\) | −978979. | −0.392647 | ||||||||
\(363\) | −1.68465e6 | −0.671033 | ||||||||
\(364\) | 5758.68 | 0.00227808 | ||||||||
\(365\) | 91305.7 | 0.0358728 | ||||||||
\(366\) | 2.15571e6 | 0.841177 | ||||||||
\(367\) | 2.64620e6 | 1.02555 | 0.512776 | − | 0.858523i | \(-0.328617\pi\) | ||||
0.512776 | + | 0.858523i | \(0.328617\pi\) | |||||||
\(368\) | 326416. | 0.125647 | ||||||||
\(369\) | −123585. | −0.0472498 | ||||||||
\(370\) | −246947. | −0.0937777 | ||||||||
\(371\) | 113447. | 0.0427916 | ||||||||
\(372\) | −297000. | −0.111275 | ||||||||
\(373\) | 3.49265e6 | 1.29982 | 0.649910 | − | 0.760011i | \(-0.274806\pi\) | ||||
0.649910 | + | 0.760011i | \(0.274806\pi\) | |||||||
\(374\) | −955917. | −0.353379 | ||||||||
\(375\) | −679703. | −0.249598 | ||||||||
\(376\) | 1.72604e6 | 0.629624 | ||||||||
\(377\) | −356273. | −0.129101 | ||||||||
\(378\) | −234216. | −0.0843114 | ||||||||
\(379\) | 1.42204e6 | 0.508526 | 0.254263 | − | 0.967135i | \(-0.418167\pi\) | ||||
0.254263 | + | 0.967135i | \(0.418167\pi\) | |||||||
\(380\) | 138723. | 0.0492822 | ||||||||
\(381\) | −1.23840e6 | −0.437068 | ||||||||
\(382\) | −3.41999e6 | −1.19913 | ||||||||
\(383\) | −2.81442e6 | −0.980373 | −0.490187 | − | 0.871618i | \(-0.663071\pi\) | ||||
−0.490187 | + | 0.871618i | \(0.663071\pi\) | |||||||
\(384\) | −1.49790e6 | −0.518387 | ||||||||
\(385\) | −60654.1 | −0.0208549 | ||||||||
\(386\) | 2.34823e6 | 0.802182 | ||||||||
\(387\) | 214530. | 0.0728134 | ||||||||
\(388\) | 1115.95 | 0.000376329 0 | ||||||||
\(389\) | −165325. | −0.0553943 | −0.0276971 | − | 0.999616i | \(-0.508817\pi\) | ||||
−0.0276971 | + | 0.999616i | \(0.508817\pi\) | |||||||
\(390\) | 61998.7 | 0.0206405 | ||||||||
\(391\) | −126844. | −0.0419591 | ||||||||
\(392\) | 3.20250e6 | 1.05263 | ||||||||
\(393\) | 893695. | 0.291882 | ||||||||
\(394\) | −5.07366e6 | −1.64657 | ||||||||
\(395\) | −557006. | −0.179625 | ||||||||
\(396\) | −311455. | −0.0998061 | ||||||||
\(397\) | −3.79445e6 | −1.20830 | −0.604148 | − | 0.796872i | \(-0.706486\pi\) | ||||
−0.604148 | + | 0.796872i | \(0.706486\pi\) | |||||||
\(398\) | 1.35474e6 | 0.428694 | ||||||||
\(399\) | 367628. | 0.115605 | ||||||||
\(400\) | 2.56445e6 | 0.801390 | ||||||||
\(401\) | 4.59396e6 | 1.42668 | 0.713339 | − | 0.700819i | \(-0.247182\pi\) | ||||
0.713339 | + | 0.700819i | \(0.247182\pi\) | |||||||
\(402\) | 1.54349e6 | 0.476363 | ||||||||
\(403\) | −589100. | −0.180687 | ||||||||
\(404\) | 314690. | 0.0959246 | ||||||||
\(405\) | 170485. | 0.0516473 | ||||||||
\(406\) | 191579. | 0.0576811 | ||||||||
\(407\) | −2.69287e6 | −0.805804 | ||||||||
\(408\) | 711637. | 0.211645 | ||||||||
\(409\) | 3.83956e6 | 1.13494 | 0.567471 | − | 0.823393i | \(-0.307922\pi\) | ||||
0.567471 | + | 0.823393i | \(0.307922\pi\) | |||||||
\(410\) | −54434.1 | −0.0159923 | ||||||||
\(411\) | 4.05850e6 | 1.18512 | ||||||||
\(412\) | −1.01569e6 | −0.294793 | ||||||||
\(413\) | 304885. | 0.0879551 | ||||||||
\(414\) | 233221. | 0.0668753 | ||||||||
\(415\) | 57421.2 | 0.0163663 | ||||||||
\(416\) | 186074. | 0.0527171 | ||||||||
\(417\) | −3.72785e6 | −1.04983 | ||||||||
\(418\) | −8.53658e6 | −2.38970 | ||||||||
\(419\) | 2.87922e6 | 0.801199 | 0.400600 | − | 0.916253i | \(-0.368802\pi\) | ||||
0.400600 | + | 0.916253i | \(0.368802\pi\) | |||||||
\(420\) | 5907.78 | 0.00163419 | ||||||||
\(421\) | 1.41982e6 | 0.390417 | 0.195208 | − | 0.980762i | \(-0.437462\pi\) | ||||
0.195208 | + | 0.980762i | \(0.437462\pi\) | |||||||
\(422\) | −3.23857e6 | −0.885262 | ||||||||
\(423\) | 1.04329e6 | 0.283501 | ||||||||
\(424\) | 1.96114e6 | 0.529777 | ||||||||
\(425\) | −996531. | −0.267620 | ||||||||
\(426\) | −3.23891e6 | −0.864718 | ||||||||
\(427\) | 407441. | 0.108142 | ||||||||
\(428\) | 762729. | 0.201262 | ||||||||
\(429\) | 676074. | 0.177358 | ||||||||
\(430\) | 94491.8 | 0.0246447 | ||||||||
\(431\) | −4.77968e6 | −1.23938 | −0.619691 | − | 0.784846i | \(-0.712742\pi\) | ||||
−0.619691 | + | 0.784846i | \(0.712742\pi\) | |||||||
\(432\) | −3.42523e6 | −0.883040 | ||||||||
\(433\) | 213516. | 0.0547282 | 0.0273641 | − | 0.999626i | \(-0.491289\pi\) | ||||
0.0273641 | + | 0.999626i | \(0.491289\pi\) | |||||||
\(434\) | 316778. | 0.0807293 | ||||||||
\(435\) | −365497. | −0.0926106 | ||||||||
\(436\) | 413405. | 0.104150 | ||||||||
\(437\) | −1.13275e6 | −0.283745 | ||||||||
\(438\) | 547264. | 0.136305 | ||||||||
\(439\) | 555761. | 0.137634 | 0.0688172 | − | 0.997629i | \(-0.478077\pi\) | ||||
0.0688172 | + | 0.997629i | \(0.478077\pi\) | |||||||
\(440\) | −1.04851e6 | −0.258192 | ||||||||
\(441\) | 1.93573e6 | 0.473967 | ||||||||
\(442\) | 184679. | 0.0449637 | ||||||||
\(443\) | −1.23542e6 | −0.299092 | −0.149546 | − | 0.988755i | \(-0.547781\pi\) | ||||
−0.149546 | + | 0.988755i | \(0.547781\pi\) | |||||||
\(444\) | 262289. | 0.0631425 | ||||||||
\(445\) | 419674. | 0.100464 | ||||||||
\(446\) | −4.06470e6 | −0.967591 | ||||||||
\(447\) | −272465. | −0.0644974 | ||||||||
\(448\) | −400900. | −0.0943715 | ||||||||
\(449\) | 1.61043e6 | 0.376986 | 0.188493 | − | 0.982074i | \(-0.439640\pi\) | ||||
0.188493 | + | 0.982074i | \(0.439640\pi\) | |||||||
\(450\) | 1.83227e6 | 0.426538 | ||||||||
\(451\) | −593584. | −0.137417 | ||||||||
\(452\) | −490866. | −0.113010 | ||||||||
\(453\) | −3.14011e6 | −0.718951 | ||||||||
\(454\) | 4.14713e6 | 0.944295 | ||||||||
\(455\) | 11718.1 | 0.00265356 | ||||||||
\(456\) | 6.35510e6 | 1.43123 | ||||||||
\(457\) | 4.44189e6 | 0.994894 | 0.497447 | − | 0.867494i | \(-0.334271\pi\) | ||||
0.497447 | + | 0.867494i | \(0.334271\pi\) | |||||||
\(458\) | −3.66515e6 | −0.816447 | ||||||||
\(459\) | 1.33102e6 | 0.294886 | ||||||||
\(460\) | −18203.2 | −0.00401101 | ||||||||
\(461\) | −8.65627e6 | −1.89705 | −0.948524 | − | 0.316705i | \(-0.897423\pi\) | ||||
−0.948524 | + | 0.316705i | \(0.897423\pi\) | |||||||
\(462\) | −363546. | −0.0792419 | ||||||||
\(463\) | −8.50880e6 | −1.84466 | −0.922329 | − | 0.386404i | \(-0.873717\pi\) | ||||
−0.922329 | + | 0.386404i | \(0.873717\pi\) | |||||||
\(464\) | 2.80170e6 | 0.604126 | ||||||||
\(465\) | −604353. | −0.129616 | ||||||||
\(466\) | −1.14351e6 | −0.243936 | ||||||||
\(467\) | −692449. | −0.146925 | −0.0734625 | − | 0.997298i | \(-0.523405\pi\) | ||||
−0.0734625 | + | 0.997298i | \(0.523405\pi\) | |||||||
\(468\) | 60171.7 | 0.0126992 | ||||||||
\(469\) | 291728. | 0.0612416 | ||||||||
\(470\) | 459527. | 0.0959548 | ||||||||
\(471\) | 1.15194e6 | 0.239264 | ||||||||
\(472\) | 5.27048e6 | 1.08892 | ||||||||
\(473\) | 1.03040e6 | 0.211764 | ||||||||
\(474\) | −3.33856e6 | −0.682517 | ||||||||
\(475\) | −8.89927e6 | −1.80976 | ||||||||
\(476\) | 17597.8 | 0.00355993 | ||||||||
\(477\) | 1.18539e6 | 0.238543 | ||||||||
\(478\) | 9.13176e6 | 1.82804 | ||||||||
\(479\) | −7.63881e6 | −1.52120 | −0.760601 | − | 0.649220i | \(-0.775095\pi\) | ||||
−0.760601 | + | 0.649220i | \(0.775095\pi\) | |||||||
\(480\) | 190891. | 0.0378166 | ||||||||
\(481\) | 520250. | 0.102530 | ||||||||
\(482\) | 5.13865e6 | 1.00747 | ||||||||
\(483\) | −48240.1 | −0.00940893 | ||||||||
\(484\) | −720154. | −0.139737 | ||||||||
\(485\) | 2270.81 | 0.000438356 0 | ||||||||
\(486\) | −4.10369e6 | −0.788104 | ||||||||
\(487\) | 4.82019e6 | 0.920962 | 0.460481 | − | 0.887670i | \(-0.347677\pi\) | ||||
0.460481 | + | 0.887670i | \(0.347677\pi\) | |||||||
\(488\) | 7.04335e6 | 1.33884 | ||||||||
\(489\) | −5.00557e6 | −0.946633 | ||||||||
\(490\) | 852609. | 0.160420 | ||||||||
\(491\) | 66664.0 | 0.0124792 | 0.00623961 | − | 0.999981i | \(-0.498014\pi\) | ||||
0.00623961 | + | 0.999981i | \(0.498014\pi\) | |||||||
\(492\) | 57815.8 | 0.0107680 | ||||||||
\(493\) | −1.08873e6 | −0.201744 | ||||||||
\(494\) | 1.64923e6 | 0.304063 | ||||||||
\(495\) | −633767. | −0.116256 | ||||||||
\(496\) | 4.63265e6 | 0.845522 | ||||||||
\(497\) | −612172. | −0.111169 | ||||||||
\(498\) | 344169. | 0.0621868 | ||||||||
\(499\) | −2.93211e6 | −0.527144 | −0.263572 | − | 0.964640i | \(-0.584901\pi\) | ||||
−0.263572 | + | 0.964640i | \(0.584901\pi\) | |||||||
\(500\) | −290559. | −0.0519768 | ||||||||
\(501\) | 5.26490e6 | 0.937122 | ||||||||
\(502\) | 657669. | 0.116479 | ||||||||
\(503\) | −3.90093e6 | −0.687462 | −0.343731 | − | 0.939068i | \(-0.611691\pi\) | ||||
−0.343731 | + | 0.939068i | \(0.611691\pi\) | |||||||
\(504\) | −247305. | −0.0433666 | ||||||||
\(505\) | 640351. | 0.111735 | ||||||||
\(506\) | 1.12017e6 | 0.194495 | ||||||||
\(507\) | 4.05323e6 | 0.700296 | ||||||||
\(508\) | −529391. | −0.0910159 | ||||||||
\(509\) | 2.09591e6 | 0.358573 | 0.179287 | − | 0.983797i | \(-0.442621\pi\) | ||||
0.179287 | + | 0.983797i | \(0.442621\pi\) | |||||||
\(510\) | 189460. | 0.0322547 | ||||||||
\(511\) | 103436. | 0.0175235 | ||||||||
\(512\) | −6.66386e6 | −1.12344 | ||||||||
\(513\) | 1.18864e7 | 1.99414 | ||||||||
\(514\) | 8.12994e6 | 1.35731 | ||||||||
\(515\) | −2.06678e6 | −0.343382 | ||||||||
\(516\) | −100362. | −0.0165938 | ||||||||
\(517\) | 5.01098e6 | 0.824511 | ||||||||
\(518\) | −279755. | −0.0458093 | ||||||||
\(519\) | −3.34032e6 | −0.544339 | ||||||||
\(520\) | 202568. | 0.0328521 | ||||||||
\(521\) | 3.34502e6 | 0.539889 | 0.269944 | − | 0.962876i | \(-0.412995\pi\) | ||||
0.269944 | + | 0.962876i | \(0.412995\pi\) | |||||||
\(522\) | 2.00178e6 | 0.321544 | ||||||||
\(523\) | −1.04450e7 | −1.66976 | −0.834878 | − | 0.550434i | \(-0.814462\pi\) | ||||
−0.834878 | + | 0.550434i | \(0.814462\pi\) | |||||||
\(524\) | 382036. | 0.0607821 | ||||||||
\(525\) | −378992. | −0.0600112 | ||||||||
\(526\) | −559378. | −0.0881538 | ||||||||
\(527\) | −1.80022e6 | −0.282357 | ||||||||
\(528\) | −5.31660e6 | −0.829944 | ||||||||
\(529\) | −6.28770e6 | −0.976906 | ||||||||
\(530\) | 522117. | 0.0807381 | ||||||||
\(531\) | 3.18570e6 | 0.490308 | ||||||||
\(532\) | 157153. | 0.0240738 | ||||||||
\(533\) | 114678. | 0.0174848 | ||||||||
\(534\) | 2.51542e6 | 0.381731 | ||||||||
\(535\) | 1.55205e6 | 0.234434 | ||||||||
\(536\) | 5.04304e6 | 0.758195 | ||||||||
\(537\) | −2.38411e6 | −0.356771 | ||||||||
\(538\) | 4.32463e6 | 0.644159 | ||||||||
\(539\) | 9.29739e6 | 1.37844 | ||||||||
\(540\) | 191014. | 0.0281891 | ||||||||
\(541\) | 5.88573e6 | 0.864584 | 0.432292 | − | 0.901734i | \(-0.357705\pi\) | ||||
0.432292 | + | 0.901734i | \(0.357705\pi\) | |||||||
\(542\) | 1.16180e7 | 1.69877 | ||||||||
\(543\) | 2.11584e6 | 0.307952 | ||||||||
\(544\) | 568618. | 0.0823803 | ||||||||
\(545\) | 841222. | 0.121316 | ||||||||
\(546\) | 70235.6 | 0.0100827 | ||||||||
\(547\) | −2.94922e6 | −0.421444 | −0.210722 | − | 0.977546i | \(-0.567581\pi\) | ||||
−0.210722 | + | 0.977546i | \(0.567581\pi\) | |||||||
\(548\) | 1.73492e6 | 0.246791 | ||||||||
\(549\) | 4.25730e6 | 0.602842 | ||||||||
\(550\) | 8.80048e6 | 1.24051 | ||||||||
\(551\) | −9.72260e6 | −1.36428 | ||||||||
\(552\) | −833915. | −0.116486 | ||||||||
\(553\) | −631007. | −0.0877448 | ||||||||
\(554\) | −8.20990e6 | −1.13648 | ||||||||
\(555\) | 533720. | 0.0735498 | ||||||||
\(556\) | −1.59358e6 | −0.218618 | ||||||||
\(557\) | −1.44836e7 | −1.97806 | −0.989029 | − | 0.147723i | \(-0.952805\pi\) | ||||
−0.989029 | + | 0.147723i | \(0.952805\pi\) | |||||||
\(558\) | 3.30997e6 | 0.450027 | ||||||||
\(559\) | −199069. | −0.0269447 | ||||||||
\(560\) | −92150.4 | −0.0124173 | ||||||||
\(561\) | 2.06600e6 | 0.277155 | ||||||||
\(562\) | −1.17843e7 | −1.57385 | ||||||||
\(563\) | 6.77740e6 | 0.901139 | 0.450570 | − | 0.892741i | \(-0.351221\pi\) | ||||
0.450570 | + | 0.892741i | \(0.351221\pi\) | |||||||
\(564\) | −488076. | −0.0646084 | ||||||||
\(565\) | −998842. | −0.131636 | ||||||||
\(566\) | −9.45200e6 | −1.24017 | ||||||||
\(567\) | 193134. | 0.0252291 | ||||||||
\(568\) | −1.05825e7 | −1.37631 | ||||||||
\(569\) | 1.03288e7 | 1.33742 | 0.668710 | − | 0.743523i | \(-0.266847\pi\) | ||||
0.668710 | + | 0.743523i | \(0.266847\pi\) | |||||||
\(570\) | 1.69193e6 | 0.218120 | ||||||||
\(571\) | −9.52868e6 | −1.22304 | −0.611522 | − | 0.791227i | \(-0.709443\pi\) | ||||
−0.611522 | + | 0.791227i | \(0.709443\pi\) | |||||||
\(572\) | 289007. | 0.0369334 | ||||||||
\(573\) | 7.39155e6 | 0.940478 | ||||||||
\(574\) | −61666.0 | −0.00781206 | ||||||||
\(575\) | 1.16776e6 | 0.147294 | ||||||||
\(576\) | −4.18895e6 | −0.526076 | ||||||||
\(577\) | 5.58573e6 | 0.698458 | 0.349229 | − | 0.937037i | \(-0.386444\pi\) | ||||
0.349229 | + | 0.937037i | \(0.386444\pi\) | |||||||
\(578\) | −6.83840e6 | −0.851403 | ||||||||
\(579\) | −5.07518e6 | −0.629151 | ||||||||
\(580\) | −156242. | −0.0192854 | ||||||||
\(581\) | 65049.9 | 0.00799478 | ||||||||
\(582\) | 13610.7 | 0.00166561 | ||||||||
\(583\) | 5.69350e6 | 0.693758 | ||||||||
\(584\) | 1.78808e6 | 0.216947 | ||||||||
\(585\) | 122441. | 0.0147923 | ||||||||
\(586\) | −1.00624e7 | −1.21048 | ||||||||
\(587\) | −1.34089e7 | −1.60619 | −0.803096 | − | 0.595849i | \(-0.796816\pi\) | ||||
−0.803096 | + | 0.595849i | \(0.796816\pi\) | |||||||
\(588\) | −905577. | −0.108014 | ||||||||
\(589\) | −1.60764e7 | −1.90942 | ||||||||
\(590\) | 1.40317e6 | 0.165951 | ||||||||
\(591\) | 1.09656e7 | 1.29141 | ||||||||
\(592\) | −4.09121e6 | −0.479786 | ||||||||
\(593\) | −1.46278e7 | −1.70821 | −0.854106 | − | 0.520099i | \(-0.825895\pi\) | ||||
−0.854106 | + | 0.520099i | \(0.825895\pi\) | |||||||
\(594\) | −1.17544e7 | −1.36690 | ||||||||
\(595\) | 35809.1 | 0.00414669 | ||||||||
\(596\) | −116473. | −0.0134311 | ||||||||
\(597\) | −2.92796e6 | −0.336224 | ||||||||
\(598\) | −216412. | −0.0247473 | ||||||||
\(599\) | 1.02632e7 | 1.16873 | 0.584367 | − | 0.811489i | \(-0.301343\pi\) | ||||
0.584367 | + | 0.811489i | \(0.301343\pi\) | |||||||
\(600\) | −6.55155e6 | −0.742961 | ||||||||
\(601\) | 9.07707e6 | 1.02508 | 0.512542 | − | 0.858662i | \(-0.328704\pi\) | ||||
0.512542 | + | 0.858662i | \(0.328704\pi\) | |||||||
\(602\) | 107046. | 0.0120386 | ||||||||
\(603\) | 3.04823e6 | 0.341393 | ||||||||
\(604\) | −1.34233e6 | −0.149716 | ||||||||
\(605\) | −1.46541e6 | −0.162769 | ||||||||
\(606\) | 3.83811e6 | 0.424557 | ||||||||
\(607\) | −1.20707e7 | −1.32972 | −0.664862 | − | 0.746966i | \(-0.731510\pi\) | ||||
−0.664862 | + | 0.746966i | \(0.731510\pi\) | |||||||
\(608\) | 5.07791e6 | 0.557091 | ||||||||
\(609\) | −414055. | −0.0452392 | ||||||||
\(610\) | 1.87517e6 | 0.204040 | ||||||||
\(611\) | −968100. | −0.104910 | ||||||||
\(612\) | 183877. | 0.0198449 | ||||||||
\(613\) | 1.40958e6 | 0.151509 | 0.0757544 | − | 0.997127i | \(-0.475864\pi\) | ||||
0.0757544 | + | 0.997127i | \(0.475864\pi\) | |||||||
\(614\) | −1.22717e7 | −1.31366 | ||||||||
\(615\) | 117647. | 0.0125428 | ||||||||
\(616\) | −1.18782e6 | −0.126124 | ||||||||
\(617\) | 1.51488e7 | 1.60201 | 0.801005 | − | 0.598658i | \(-0.204299\pi\) | ||||
0.801005 | + | 0.598658i | \(0.204299\pi\) | |||||||
\(618\) | −1.23878e7 | −1.30474 | ||||||||
\(619\) | 1.58021e7 | 1.65763 | 0.828816 | − | 0.559521i | \(-0.189015\pi\) | ||||
0.828816 | + | 0.559521i | \(0.189015\pi\) | |||||||
\(620\) | −258348. | −0.0269915 | ||||||||
\(621\) | −1.55973e6 | −0.162301 | ||||||||
\(622\) | 6.56584e6 | 0.680478 | ||||||||
\(623\) | 475430. | 0.0490757 | ||||||||
\(624\) | 1.02714e6 | 0.105601 | ||||||||
\(625\) | 8.87414e6 | 0.908712 | ||||||||
\(626\) | −6.34988e6 | −0.647634 | ||||||||
\(627\) | 1.84499e7 | 1.87424 | ||||||||
\(628\) | 492430. | 0.0498247 | ||||||||
\(629\) | 1.58982e6 | 0.160222 | ||||||||
\(630\) | −65840.4 | −0.00660908 | ||||||||
\(631\) | −1.08922e7 | −1.08904 | −0.544519 | − | 0.838749i | \(-0.683288\pi\) | ||||
−0.544519 | + | 0.838749i | \(0.683288\pi\) | |||||||
\(632\) | −1.09081e7 | −1.08631 | ||||||||
\(633\) | 6.99944e6 | 0.694311 | ||||||||
\(634\) | 3.59690e6 | 0.355390 | ||||||||
\(635\) | −1.07724e6 | −0.106017 | ||||||||
\(636\) | −554554. | −0.0543627 | ||||||||
\(637\) | −1.79622e6 | −0.175392 | ||||||||
\(638\) | 9.61466e6 | 0.935152 | ||||||||
\(639\) | −6.39650e6 | −0.619712 | ||||||||
\(640\) | −1.30296e6 | −0.125742 | ||||||||
\(641\) | 2.41942e6 | 0.232577 | 0.116289 | − | 0.993215i | \(-0.462900\pi\) | ||||
0.116289 | + | 0.993215i | \(0.462900\pi\) | |||||||
\(642\) | 9.30260e6 | 0.890772 | ||||||||
\(643\) | 1.38769e7 | 1.32363 | 0.661814 | − | 0.749668i | \(-0.269787\pi\) | ||||
0.661814 | + | 0.749668i | \(0.269787\pi\) | |||||||
\(644\) | −20621.6 | −0.00195933 | ||||||||
\(645\) | −204223. | −0.0193288 | ||||||||
\(646\) | 5.03985e6 | 0.475156 | ||||||||
\(647\) | −7.58249e6 | −0.712116 | −0.356058 | − | 0.934464i | \(-0.615880\pi\) | ||||
−0.356058 | + | 0.934464i | \(0.615880\pi\) | |||||||
\(648\) | 3.33867e6 | 0.312346 | ||||||||
\(649\) | 1.53011e7 | 1.42597 | ||||||||
\(650\) | −1.70021e6 | −0.157841 | ||||||||
\(651\) | −684645. | −0.0633159 | ||||||||
\(652\) | −2.13978e6 | −0.197129 | ||||||||
\(653\) | 3.26919e6 | 0.300025 | 0.150012 | − | 0.988684i | \(-0.452069\pi\) | ||||
0.150012 | + | 0.988684i | \(0.452069\pi\) | |||||||
\(654\) | 5.04208e6 | 0.460962 | ||||||||
\(655\) | 777389. | 0.0708003 | ||||||||
\(656\) | −901819. | −0.0818201 | ||||||||
\(657\) | 1.08079e6 | 0.0976850 | ||||||||
\(658\) | 520578. | 0.0468728 | ||||||||
\(659\) | 1.94787e6 | 0.174721 | 0.0873606 | − | 0.996177i | \(-0.472157\pi\) | ||||
0.0873606 | + | 0.996177i | \(0.472157\pi\) | |||||||
\(660\) | 296490. | 0.0264942 | ||||||||
\(661\) | −1.04897e7 | −0.933810 | −0.466905 | − | 0.884307i | \(-0.654631\pi\) | ||||
−0.466905 | + | 0.884307i | \(0.654631\pi\) | |||||||
\(662\) | 1.00798e7 | 0.893936 | ||||||||
\(663\) | −399142. | −0.0352650 | ||||||||
\(664\) | 1.12450e6 | 0.0989784 | ||||||||
\(665\) | 319785. | 0.0280417 | ||||||||
\(666\) | −2.92312e6 | −0.255365 | ||||||||
\(667\) | 1.27580e6 | 0.111037 | ||||||||
\(668\) | 2.25064e6 | 0.195148 | ||||||||
\(669\) | 8.78494e6 | 0.758881 | ||||||||
\(670\) | 1.34262e6 | 0.115549 | ||||||||
\(671\) | 2.04480e7 | 1.75325 | ||||||||
\(672\) | 216252. | 0.0184730 | ||||||||
\(673\) | −1.81198e6 | −0.154211 | −0.0771054 | − | 0.997023i | \(-0.524568\pi\) | ||||
−0.0771054 | + | 0.997023i | \(0.524568\pi\) | |||||||
\(674\) | 1.81134e6 | 0.153586 | ||||||||
\(675\) | −1.22538e7 | −1.03517 | ||||||||
\(676\) | 1.73267e6 | 0.145831 | ||||||||
\(677\) | −1.71538e7 | −1.43843 | −0.719216 | − | 0.694786i | \(-0.755499\pi\) | ||||
−0.719216 | + | 0.694786i | \(0.755499\pi\) | |||||||
\(678\) | −5.98682e6 | −0.500175 | ||||||||
\(679\) | 2572.50 | 0.000214132 0 | ||||||||
\(680\) | 619024. | 0.0513376 | ||||||||
\(681\) | −8.96308e6 | −0.740610 | ||||||||
\(682\) | 1.58979e7 | 1.30882 | ||||||||
\(683\) | 1.80610e7 | 1.48146 | 0.740732 | − | 0.671801i | \(-0.234479\pi\) | ||||
0.740732 | + | 0.671801i | \(0.234479\pi\) | |||||||
\(684\) | 1.64207e6 | 0.134200 | ||||||||
\(685\) | 3.53033e6 | 0.287467 | ||||||||
\(686\) | 1.93890e6 | 0.157306 | ||||||||
\(687\) | 7.92140e6 | 0.640339 | ||||||||
\(688\) | 1.56546e6 | 0.126087 | ||||||||
\(689\) | −1.09996e6 | −0.0882732 | ||||||||
\(690\) | −222015. | −0.0177525 | ||||||||
\(691\) | −1.44368e7 | −1.15021 | −0.575105 | − | 0.818080i | \(-0.695039\pi\) | ||||
−0.575105 | + | 0.818080i | \(0.695039\pi\) | |||||||
\(692\) | −1.42792e6 | −0.113354 | ||||||||
\(693\) | −717966. | −0.0567899 | ||||||||
\(694\) | −2.23513e7 | −1.76159 | ||||||||
\(695\) | −3.24271e6 | −0.254651 | ||||||||
\(696\) | −7.15768e6 | −0.560079 | ||||||||
\(697\) | 350442. | 0.0273233 | ||||||||
\(698\) | 1.34636e7 | 1.04598 | ||||||||
\(699\) | 2.47145e6 | 0.191319 | ||||||||
\(700\) | −162011. | −0.0124968 | ||||||||
\(701\) | −1.39926e7 | −1.07549 | −0.537743 | − | 0.843109i | \(-0.680723\pi\) | ||||
−0.537743 | + | 0.843109i | \(0.680723\pi\) | |||||||
\(702\) | 2.27090e6 | 0.173923 | ||||||||
\(703\) | 1.41975e7 | 1.08349 | ||||||||
\(704\) | −2.01197e7 | −1.53000 | ||||||||
\(705\) | −993165. | −0.0752573 | ||||||||
\(706\) | −1.20894e7 | −0.912836 | ||||||||
\(707\) | 725425. | 0.0545813 | ||||||||
\(708\) | −1.49034e6 | −0.111738 | ||||||||
\(709\) | −1.37678e7 | −1.02860 | −0.514302 | − | 0.857609i | \(-0.671949\pi\) | ||||
−0.514302 | + | 0.857609i | \(0.671949\pi\) | |||||||
\(710\) | −2.81740e6 | −0.209750 | ||||||||
\(711\) | −6.59331e6 | −0.489136 | ||||||||
\(712\) | 8.21864e6 | 0.607575 | ||||||||
\(713\) | 2.10955e6 | 0.155405 | ||||||||
\(714\) | 214631. | 0.0157561 | ||||||||
\(715\) | 588090. | 0.0430208 | ||||||||
\(716\) | −1.01916e6 | −0.0742947 | ||||||||
\(717\) | −1.97362e7 | −1.43373 | ||||||||
\(718\) | −7.38120e6 | −0.534338 | ||||||||
\(719\) | −8.26505e6 | −0.596243 | −0.298121 | − | 0.954528i | \(-0.596360\pi\) | ||||
−0.298121 | + | 0.954528i | \(0.596360\pi\) | |||||||
\(720\) | −962867. | −0.0692205 | ||||||||
\(721\) | −2.34137e6 | −0.167738 | ||||||||
\(722\) | 3.20974e7 | 2.29154 | ||||||||
\(723\) | −1.11060e7 | −0.790158 | ||||||||
\(724\) | 904479. | 0.0641286 | ||||||||
\(725\) | 1.00232e7 | 0.708206 | ||||||||
\(726\) | −8.78333e6 | −0.618469 | ||||||||
\(727\) | 7.18688e6 | 0.504318 | 0.252159 | − | 0.967686i | \(-0.418859\pi\) | ||||
0.252159 | + | 0.967686i | \(0.418859\pi\) | |||||||
\(728\) | 229481. | 0.0160479 | ||||||||
\(729\) | 1.30957e7 | 0.912663 | ||||||||
\(730\) | 476043. | 0.0330628 | ||||||||
\(731\) | −608330. | −0.0421062 | ||||||||
\(732\) | −1.99166e6 | −0.137384 | ||||||||
\(733\) | −1.10728e6 | −0.0761196 | −0.0380598 | − | 0.999275i | \(-0.512118\pi\) | ||||
−0.0380598 | + | 0.999275i | \(0.512118\pi\) | |||||||
\(734\) | 1.37966e7 | 0.945217 | ||||||||
\(735\) | −1.84272e6 | −0.125818 | ||||||||
\(736\) | −666322. | −0.0453409 | ||||||||
\(737\) | 1.46408e7 | 0.992878 | ||||||||
\(738\) | −644339. | −0.0435485 | ||||||||
\(739\) | 1.98449e7 | 1.33671 | 0.668356 | − | 0.743841i | \(-0.266998\pi\) | ||||
0.668356 | + | 0.743841i | \(0.266998\pi\) | |||||||
\(740\) | 228154. | 0.0153161 | ||||||||
\(741\) | −3.56444e6 | −0.238477 | ||||||||
\(742\) | 591484. | 0.0394396 | ||||||||
\(743\) | −2.19204e7 | −1.45672 | −0.728360 | − | 0.685194i | \(-0.759717\pi\) | ||||
−0.728360 | + | 0.685194i | \(0.759717\pi\) | |||||||
\(744\) | −1.18353e7 | −0.783875 | ||||||||
\(745\) | −237006. | −0.0156448 | ||||||||
\(746\) | 1.82098e7 | 1.19800 | ||||||||
\(747\) | 679697. | 0.0445671 | ||||||||
\(748\) | 883172. | 0.0577153 | ||||||||
\(749\) | 1.75825e6 | 0.114518 | ||||||||
\(750\) | −3.54379e6 | −0.230046 | ||||||||
\(751\) | −1.62135e7 | −1.04900 | −0.524502 | − | 0.851409i | \(-0.675748\pi\) | ||||
−0.524502 | + | 0.851409i | \(0.675748\pi\) | |||||||
\(752\) | 7.61307e6 | 0.490925 | ||||||||
\(753\) | −1.42140e6 | −0.0913545 | ||||||||
\(754\) | −1.85751e6 | −0.118988 | ||||||||
\(755\) | −2.73146e6 | −0.174392 | ||||||||
\(756\) | 216392. | 0.0137701 | ||||||||
\(757\) | 1.31863e7 | 0.836342 | 0.418171 | − | 0.908368i | \(-0.362671\pi\) | ||||
0.418171 | + | 0.908368i | \(0.362671\pi\) | |||||||
\(758\) | 7.41412e6 | 0.468691 | ||||||||
\(759\) | −2.42099e6 | −0.152542 | ||||||||
\(760\) | 5.52805e6 | 0.347166 | ||||||||
\(761\) | −1.92620e7 | −1.20570 | −0.602851 | − | 0.797854i | \(-0.705969\pi\) | ||||
−0.602851 | + | 0.797854i | \(0.705969\pi\) | |||||||
\(762\) | −6.45670e6 | −0.402831 | ||||||||
\(763\) | 952983. | 0.0592617 | ||||||||
\(764\) | 3.15973e6 | 0.195847 | ||||||||
\(765\) | 374165. | 0.0231158 | ||||||||
\(766\) | −1.46736e7 | −0.903577 | ||||||||
\(767\) | −2.95610e6 | −0.181439 | ||||||||
\(768\) | 5.20888e6 | 0.318670 | ||||||||
\(769\) | −456438. | −0.0278334 | −0.0139167 | − | 0.999903i | \(-0.504430\pi\) | ||||
−0.0139167 | + | 0.999903i | \(0.504430\pi\) | |||||||
\(770\) | −316235. | −0.0192213 | ||||||||
\(771\) | −1.75710e7 | −1.06454 | ||||||||
\(772\) | −2.16953e6 | −0.131016 | ||||||||
\(773\) | −6.14461e6 | −0.369867 | −0.184933 | − | 0.982751i | \(-0.559207\pi\) | ||||
−0.184933 | + | 0.982751i | \(0.559207\pi\) | |||||||
\(774\) | 1.11850e6 | 0.0671097 | ||||||||
\(775\) | 1.65734e7 | 0.991191 | ||||||||
\(776\) | 44470.2 | 0.00265103 | ||||||||
\(777\) | 604628. | 0.0359282 | ||||||||
\(778\) | −861961. | −0.0510551 | ||||||||
\(779\) | 3.12953e6 | 0.184772 | ||||||||
\(780\) | −57280.6 | −0.00337110 | ||||||||
\(781\) | −3.07227e7 | −1.80232 | ||||||||
\(782\) | −661328. | −0.0386723 | ||||||||
\(783\) | −1.33875e7 | −0.780361 | ||||||||
\(784\) | 1.41253e7 | 0.820745 | ||||||||
\(785\) | 1.00203e6 | 0.0580369 | ||||||||
\(786\) | 4.65949e6 | 0.269018 | ||||||||
\(787\) | 8.50558e6 | 0.489516 | 0.244758 | − | 0.969584i | \(-0.421291\pi\) | ||||
0.244758 | + | 0.969584i | \(0.421291\pi\) | |||||||
\(788\) | 4.68755e6 | 0.268925 | ||||||||
\(789\) | 1.20897e6 | 0.0691389 | ||||||||
\(790\) | −2.90408e6 | −0.165554 | ||||||||
\(791\) | −1.13154e6 | −0.0643029 | ||||||||
\(792\) | −1.24113e7 | −0.703080 | ||||||||
\(793\) | −3.95047e6 | −0.223082 | ||||||||
\(794\) | −1.97833e7 | −1.11365 | ||||||||
\(795\) | −1.12844e6 | −0.0633228 | ||||||||
\(796\) | −1.25164e6 | −0.0700160 | ||||||||
\(797\) | 1.28439e7 | 0.716227 | 0.358113 | − | 0.933678i | \(-0.383420\pi\) | ||||
0.358113 | + | 0.933678i | \(0.383420\pi\) | |||||||
\(798\) | 1.91671e6 | 0.106549 | ||||||||
\(799\) | −2.95840e6 | −0.163942 | ||||||||
\(800\) | −5.23488e6 | −0.289189 | ||||||||
\(801\) | 4.96770e6 | 0.273573 | ||||||||
\(802\) | 2.39517e7 | 1.31492 | ||||||||
\(803\) | 5.19108e6 | 0.284099 | ||||||||
\(804\) | −1.42603e6 | −0.0778016 | ||||||||
\(805\) | −41962.1 | −0.00228227 | ||||||||
\(806\) | −3.07141e6 | −0.166533 | ||||||||
\(807\) | −9.34670e6 | −0.505213 | ||||||||
\(808\) | 1.25403e7 | 0.675738 | ||||||||
\(809\) | 2.98801e7 | 1.60513 | 0.802567 | − | 0.596562i | \(-0.203467\pi\) | ||||
0.802567 | + | 0.596562i | \(0.203467\pi\) | |||||||
\(810\) | 888861. | 0.0476016 | ||||||||
\(811\) | −2.05001e7 | −1.09447 | −0.547234 | − | 0.836980i | \(-0.684319\pi\) | ||||
−0.547234 | + | 0.836980i | \(0.684319\pi\) | |||||||
\(812\) | −177000. | −0.00942070 | ||||||||
\(813\) | −2.51098e7 | −1.33234 | ||||||||
\(814\) | −1.40399e7 | −0.742682 | ||||||||
\(815\) | −4.35415e6 | −0.229620 | ||||||||
\(816\) | 3.13882e6 | 0.165022 | ||||||||
\(817\) | −5.43254e6 | −0.284740 | ||||||||
\(818\) | 2.00185e7 | 1.04604 | ||||||||
\(819\) | 138708. | 0.00722589 | ||||||||
\(820\) | 50291.7 | 0.00261193 | ||||||||
\(821\) | 2.20698e7 | 1.14272 | 0.571360 | − | 0.820699i | \(-0.306416\pi\) | ||||
0.571360 | + | 0.820699i | \(0.306416\pi\) | |||||||
\(822\) | 2.11599e7 | 1.09228 | ||||||||
\(823\) | 1.59817e6 | 0.0822476 | 0.0411238 | − | 0.999154i | \(-0.486906\pi\) | ||||
0.0411238 | + | 0.999154i | \(0.486906\pi\) | |||||||
\(824\) | −4.04747e7 | −2.07666 | ||||||||
\(825\) | −1.90202e7 | −0.972929 | ||||||||
\(826\) | 1.58959e6 | 0.0810653 | ||||||||
\(827\) | −1.49218e7 | −0.758680 | −0.379340 | − | 0.925257i | \(-0.623849\pi\) | ||||
−0.379340 | + | 0.925257i | \(0.623849\pi\) | |||||||
\(828\) | −215473. | −0.0109223 | ||||||||
\(829\) | 7.71986e6 | 0.390142 | 0.195071 | − | 0.980789i | \(-0.437506\pi\) | ||||
0.195071 | + | 0.980789i | \(0.437506\pi\) | |||||||
\(830\) | 299379. | 0.0150843 | ||||||||
\(831\) | 1.77439e7 | 0.891344 | ||||||||
\(832\) | 3.88704e6 | 0.194675 | ||||||||
\(833\) | −5.48902e6 | −0.274083 | ||||||||
\(834\) | −1.94360e7 | −0.967592 | ||||||||
\(835\) | 4.57973e6 | 0.227313 | ||||||||
\(836\) | 7.88695e6 | 0.390295 | ||||||||
\(837\) | −2.21364e7 | −1.09218 | ||||||||
\(838\) | 1.50115e7 | 0.738439 | ||||||||
\(839\) | 3.50556e7 | 1.71930 | 0.859652 | − | 0.510880i | \(-0.170680\pi\) | ||||
0.859652 | + | 0.510880i | \(0.170680\pi\) | |||||||
\(840\) | 235422. | 0.0115120 | ||||||||
\(841\) | −9.56068e6 | −0.466121 | ||||||||
\(842\) | 7.40258e6 | 0.359834 | ||||||||
\(843\) | 2.54692e7 | 1.23437 | ||||||||
\(844\) | 2.99211e6 | 0.144585 | ||||||||
\(845\) | 3.52575e6 | 0.169867 | ||||||||
\(846\) | 5.43945e6 | 0.261294 | ||||||||
\(847\) | −1.66010e6 | −0.0795108 | ||||||||
\(848\) | 8.65001e6 | 0.413073 | ||||||||
\(849\) | 2.04284e7 | 0.972668 | ||||||||
\(850\) | −5.19565e6 | −0.246656 | ||||||||
\(851\) | −1.86300e6 | −0.0881837 | ||||||||
\(852\) | 2.99243e6 | 0.141229 | ||||||||
\(853\) | −2.21072e7 | −1.04031 | −0.520153 | − | 0.854073i | \(-0.674125\pi\) | ||||
−0.520153 | + | 0.854073i | \(0.674125\pi\) | |||||||
\(854\) | 2.12429e6 | 0.0996712 | ||||||||
\(855\) | 3.34139e6 | 0.156319 | ||||||||
\(856\) | 3.03944e7 | 1.41778 | ||||||||
\(857\) | 1.60053e7 | 0.744410 | 0.372205 | − | 0.928151i | \(-0.378602\pi\) | ||||
0.372205 | + | 0.928151i | \(0.378602\pi\) | |||||||
\(858\) | 3.52487e6 | 0.163465 | ||||||||
\(859\) | −2.09057e7 | −0.966677 | −0.483338 | − | 0.875434i | \(-0.660576\pi\) | ||||
−0.483338 | + | 0.875434i | \(0.660576\pi\) | |||||||
\(860\) | −87301.0 | −0.00402507 | ||||||||
\(861\) | 133277. | 0.00612700 | ||||||||
\(862\) | −2.49200e7 | −1.14230 | ||||||||
\(863\) | 1.41874e7 | 0.648449 | 0.324224 | − | 0.945980i | \(-0.394897\pi\) | ||||
0.324224 | + | 0.945980i | \(0.394897\pi\) | |||||||
\(864\) | 6.99201e6 | 0.318653 | ||||||||
\(865\) | −2.90561e6 | −0.132037 | ||||||||
\(866\) | 1.11322e6 | 0.0504412 | ||||||||
\(867\) | 1.47797e7 | 0.667755 | ||||||||
\(868\) | −292671. | −0.0131850 | ||||||||
\(869\) | −3.16680e7 | −1.42256 | ||||||||
\(870\) | −1.90560e6 | −0.0853561 | ||||||||
\(871\) | −2.82854e6 | −0.126333 | ||||||||
\(872\) | 1.64740e7 | 0.733682 | ||||||||
\(873\) | 26879.7 | 0.00119368 | ||||||||
\(874\) | −5.90583e6 | −0.261519 | ||||||||
\(875\) | −669798. | −0.0295749 | ||||||||
\(876\) | −505618. | −0.0222619 | ||||||||
\(877\) | 2.06566e7 | 0.906901 | 0.453450 | − | 0.891282i | \(-0.350193\pi\) | ||||
0.453450 | + | 0.891282i | \(0.350193\pi\) | |||||||
\(878\) | 2.89759e6 | 0.126853 | ||||||||
\(879\) | 2.17477e7 | 0.949382 | ||||||||
\(880\) | −4.62470e6 | −0.201315 | ||||||||
\(881\) | −1.35902e7 | −0.589909 | −0.294955 | − | 0.955511i | \(-0.595305\pi\) | ||||
−0.294955 | + | 0.955511i | \(0.595305\pi\) | |||||||
\(882\) | 1.00924e7 | 0.436839 | ||||||||
\(883\) | 1.20900e7 | 0.521824 | 0.260912 | − | 0.965363i | \(-0.415977\pi\) | ||||
0.260912 | + | 0.965363i | \(0.415977\pi\) | |||||||
\(884\) | −170625. | −0.00734365 | ||||||||
\(885\) | −3.03264e6 | −0.130155 | ||||||||
\(886\) | −6.44115e6 | −0.275663 | ||||||||
\(887\) | 1.83559e7 | 0.783371 | 0.391685 | − | 0.920099i | \(-0.371892\pi\) | ||||
0.391685 | + | 0.920099i | \(0.371892\pi\) | |||||||
\(888\) | 1.04521e7 | 0.444805 | ||||||||
\(889\) | −1.22035e6 | −0.0517883 | ||||||||
\(890\) | 2.18807e6 | 0.0925946 | ||||||||
\(891\) | 9.69271e6 | 0.409026 | ||||||||
\(892\) | 3.75538e6 | 0.158031 | ||||||||
\(893\) | −2.64192e7 | −1.10864 | ||||||||
\(894\) | −1.42056e6 | −0.0594451 | ||||||||
\(895\) | −2.07384e6 | −0.0865401 | ||||||||
\(896\) | −1.47607e6 | −0.0614238 | ||||||||
\(897\) | 467725. | 0.0194093 | ||||||||
\(898\) | 8.39635e6 | 0.347456 | ||||||||
\(899\) | 1.81067e7 | 0.747206 | ||||||||
\(900\) | −1.69283e6 | −0.0696639 | ||||||||
\(901\) | −3.36134e6 | −0.137943 | ||||||||
\(902\) | −3.09479e6 | −0.126653 | ||||||||
\(903\) | −231355. | −0.00944190 | ||||||||
\(904\) | −1.95608e7 | −0.796094 | ||||||||
\(905\) | 1.84049e6 | 0.0746984 | ||||||||
\(906\) | −1.63717e7 | −0.662634 | ||||||||
\(907\) | 1.78761e7 | 0.721531 | 0.360765 | − | 0.932657i | \(-0.382515\pi\) | ||||
0.360765 | + | 0.932657i | \(0.382515\pi\) | |||||||
\(908\) | −3.83153e6 | −0.154226 | ||||||||
\(909\) | 7.57987e6 | 0.304265 | ||||||||
\(910\) | 61095.1 | 0.00244570 | ||||||||
\(911\) | −1.47994e7 | −0.590809 | −0.295405 | − | 0.955372i | \(-0.595454\pi\) | ||||
−0.295405 | + | 0.955372i | \(0.595454\pi\) | |||||||
\(912\) | 2.80305e7 | 1.11595 | ||||||||
\(913\) | 3.26462e6 | 0.129615 | ||||||||
\(914\) | 2.31588e7 | 0.916961 | ||||||||
\(915\) | −4.05275e6 | −0.160028 | ||||||||
\(916\) | 3.38623e6 | 0.133345 | ||||||||
\(917\) | 880670. | 0.0345852 | ||||||||
\(918\) | 6.93961e6 | 0.271787 | ||||||||
\(919\) | −2.50852e6 | −0.0979780 | −0.0489890 | − | 0.998799i | \(-0.515600\pi\) | ||||
−0.0489890 | + | 0.998799i | \(0.515600\pi\) | |||||||
\(920\) | −725390. | −0.0282554 | ||||||||
\(921\) | 2.65225e7 | 1.03030 | ||||||||
\(922\) | −4.51315e7 | −1.74845 | ||||||||
\(923\) | 5.93549e6 | 0.229325 | ||||||||
\(924\) | 335881. | 0.0129421 | ||||||||
\(925\) | −1.46364e7 | −0.562445 | ||||||||
\(926\) | −4.43626e7 | −1.70016 | ||||||||
\(927\) | −2.44646e7 | −0.935060 | ||||||||
\(928\) | −5.71919e6 | −0.218004 | ||||||||
\(929\) | −9.51733e6 | −0.361806 | −0.180903 | − | 0.983501i | \(-0.557902\pi\) | ||||
−0.180903 | + | 0.983501i | \(0.557902\pi\) | |||||||
\(930\) | −3.15094e6 | −0.119463 | ||||||||
\(931\) | −4.90183e7 | −1.85347 | ||||||||
\(932\) | 1.05649e6 | 0.0398407 | ||||||||
\(933\) | −1.41906e7 | −0.533698 | ||||||||
\(934\) | −3.61025e6 | −0.135416 | ||||||||
\(935\) | 1.79713e6 | 0.0672281 | ||||||||
\(936\) | 2.39781e6 | 0.0894593 | ||||||||
\(937\) | 4.27838e6 | 0.159195 | 0.0795977 | − | 0.996827i | \(-0.474636\pi\) | ||||
0.0795977 | + | 0.996827i | \(0.474636\pi\) | |||||||
\(938\) | 1.52099e6 | 0.0564444 | ||||||||
\(939\) | 1.37238e7 | 0.507939 | ||||||||
\(940\) | −424557. | −0.0156717 | ||||||||
\(941\) | −3.20489e7 | −1.17988 | −0.589941 | − | 0.807446i | \(-0.700849\pi\) | ||||
−0.589941 | + | 0.807446i | \(0.700849\pi\) | |||||||
\(942\) | 6.00590e6 | 0.220521 | ||||||||
\(943\) | −410657. | −0.0150384 | ||||||||
\(944\) | 2.32466e7 | 0.849041 | ||||||||
\(945\) | 440327. | 0.0160397 | ||||||||
\(946\) | 5.37223e6 | 0.195176 | ||||||||
\(947\) | 1.34081e7 | 0.485841 | 0.242920 | − | 0.970046i | \(-0.421895\pi\) | ||||
0.242920 | + | 0.970046i | \(0.421895\pi\) | |||||||
\(948\) | 3.08450e6 | 0.111471 | ||||||||
\(949\) | −1.00289e6 | −0.0361485 | ||||||||
\(950\) | −4.63985e7 | −1.66799 | ||||||||
\(951\) | −7.77389e6 | −0.278732 | ||||||||
\(952\) | 701265. | 0.0250778 | ||||||||
\(953\) | 4.23589e7 | 1.51082 | 0.755409 | − | 0.655254i | \(-0.227438\pi\) | ||||
0.755409 | + | 0.655254i | \(0.227438\pi\) | |||||||
\(954\) | 6.18033e6 | 0.219857 | ||||||||
\(955\) | 6.42961e6 | 0.228127 | ||||||||
\(956\) | −8.43683e6 | −0.298562 | ||||||||
\(957\) | −2.07799e7 | −0.733440 | ||||||||
\(958\) | −3.98267e7 | −1.40204 | ||||||||
\(959\) | 3.99935e6 | 0.140425 | ||||||||
\(960\) | 3.98768e6 | 0.139650 | ||||||||
\(961\) | 1.31048e6 | 0.0457745 | ||||||||
\(962\) | 2.71245e6 | 0.0944982 | ||||||||
\(963\) | 1.83717e7 | 0.638385 | ||||||||
\(964\) | −4.74760e6 | −0.164544 | ||||||||
\(965\) | −4.41470e6 | −0.152610 | ||||||||
\(966\) | −251511. | −0.00867190 | ||||||||
\(967\) | −4.12202e7 | −1.41757 | −0.708785 | − | 0.705425i | \(-0.750756\pi\) | ||||
−0.708785 | + | 0.705425i | \(0.750756\pi\) | |||||||
\(968\) | −2.86978e7 | −0.984373 | ||||||||
\(969\) | −1.08925e7 | −0.372665 | ||||||||
\(970\) | 11839.4 | 0.000404018 0 | ||||||||
\(971\) | −1.13026e7 | −0.384708 | −0.192354 | − | 0.981326i | \(-0.561612\pi\) | ||||
−0.192354 | + | 0.981326i | \(0.561612\pi\) | |||||||
\(972\) | 3.79140e6 | 0.128716 | ||||||||
\(973\) | −3.67352e6 | −0.124394 | ||||||||
\(974\) | 2.51312e7 | 0.848820 | ||||||||
\(975\) | 3.67463e6 | 0.123795 | ||||||||
\(976\) | 3.10662e7 | 1.04391 | ||||||||
\(977\) | −2.79073e7 | −0.935367 | −0.467684 | − | 0.883896i | \(-0.654911\pi\) | ||||
−0.467684 | + | 0.883896i | \(0.654911\pi\) | |||||||
\(978\) | −2.60977e7 | −0.872480 | ||||||||
\(979\) | 2.38601e7 | 0.795638 | ||||||||
\(980\) | −787725. | −0.0262005 | ||||||||
\(981\) | 9.95758e6 | 0.330355 | ||||||||
\(982\) | 347568. | 0.0115017 | ||||||||
\(983\) | −1.22161e7 | −0.403226 | −0.201613 | − | 0.979465i | \(-0.564618\pi\) | ||||
−0.201613 | + | 0.979465i | \(0.564618\pi\) | |||||||
\(984\) | 2.30393e6 | 0.0758546 | ||||||||
\(985\) | 9.53852e6 | 0.313249 | ||||||||
\(986\) | −5.67633e6 | −0.185941 | ||||||||
\(987\) | −1.12511e6 | −0.0367623 | ||||||||
\(988\) | −1.52372e6 | −0.0496608 | ||||||||
\(989\) | 712858. | 0.0231746 | ||||||||
\(990\) | −3.30429e6 | −0.107150 | ||||||||
\(991\) | 2.47723e7 | 0.801277 | 0.400638 | − | 0.916236i | \(-0.368788\pi\) | ||||
0.400638 | + | 0.916236i | \(0.368788\pi\) | |||||||
\(992\) | −9.45675e6 | −0.305114 | ||||||||
\(993\) | −2.17852e7 | −0.701113 | ||||||||
\(994\) | −3.19170e6 | −0.102461 | ||||||||
\(995\) | −2.54691e6 | −0.0815561 | ||||||||
\(996\) | −317978. | −0.0101566 | ||||||||
\(997\) | 2.12381e7 | 0.676670 | 0.338335 | − | 0.941026i | \(-0.390136\pi\) | ||||
0.338335 | + | 0.941026i | \(0.390136\pi\) | |||||||
\(998\) | −1.52873e7 | −0.485851 | ||||||||
\(999\) | 1.95493e7 | 0.619750 |
(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 | 43.6.a.a.1.7 | ✓ | 8 | |
3.2 | odd | 2 | 387.6.a.c.1.2 | 8 | |||
4.3 | odd | 2 | 688.6.a.e.1.6 | 8 | |||
5.4 | even | 2 | 1075.6.a.a.1.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.6.a.a.1.7 | ✓ | 8 | 1.1 | even | 1 | trivial | |
387.6.a.c.1.2 | 8 | 3.2 | odd | 2 | |||
688.6.a.e.1.6 | 8 | 4.3 | odd | 2 | |||
1075.6.a.a.1.2 | 8 | 5.4 | even | 2 |