Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [41,6,Mod(9,41)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(41, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("41.9");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 41 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 41.c (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.57573661233\) |
Analytic rank: | \(0\) |
Dimension: | \(34\) |
Relative dimension: | \(17\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 9.5 | ||
Character | \(\chi\) | \(=\) | 41.9 |
Dual form | 41.6.c.a.32.13 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/41\mathbb{Z}\right)^\times\).
\(n\) | \(6\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 5.81352i | − | 1.02769i | −0.857882 | − | 0.513847i | \(-0.828220\pi\) | ||
0.857882 | − | 0.513847i | \(-0.171780\pi\) | |||||||
\(3\) | 3.20738 | + | 3.20738i | 0.205753 | + | 0.205753i | 0.802460 | − | 0.596706i | \(-0.203524\pi\) |
−0.596706 | + | 0.802460i | \(0.703524\pi\) | |||||||
\(4\) | −1.79697 | −0.0561553 | ||||||||
\(5\) | − | 42.7691i | − | 0.765076i | −0.923940 | − | 0.382538i | \(-0.875050\pi\) | ||
0.923940 | − | 0.382538i | \(-0.124950\pi\) | |||||||
\(6\) | 18.6461 | − | 18.6461i | 0.211452 | − | 0.211452i | ||||
\(7\) | 22.3392 | + | 22.3392i | 0.172315 | + | 0.172315i | 0.787996 | − | 0.615681i | \(-0.211119\pi\) |
−0.615681 | + | 0.787996i | \(0.711119\pi\) | |||||||
\(8\) | − | 175.586i | − | 0.969984i | ||||||
\(9\) | − | 222.425i | − | 0.915331i | ||||||
\(10\) | −248.639 | −0.786265 | ||||||||
\(11\) | 177.276 | + | 177.276i | 0.441742 | + | 0.441742i | 0.892597 | − | 0.450855i | \(-0.148881\pi\) |
−0.450855 | + | 0.892597i | \(0.648881\pi\) | |||||||
\(12\) | −5.76356 | − | 5.76356i | −0.0115541 | − | 0.0115541i | ||||
\(13\) | −580.171 | − | 580.171i | −0.952133 | − | 0.952133i | 0.0467729 | − | 0.998906i | \(-0.485106\pi\) |
−0.998906 | + | 0.0467729i | \(0.985106\pi\) | |||||||
\(14\) | 129.869 | − | 129.869i | 0.177087 | − | 0.177087i | ||||
\(15\) | 137.177 | − | 137.177i | 0.157417 | − | 0.157417i | ||||
\(16\) | −1078.27 | −1.05300 | ||||||||
\(17\) | −1112.05 | + | 1112.05i | −0.933258 | + | 0.933258i | −0.997908 | − | 0.0646503i | \(-0.979407\pi\) |
0.0646503 | + | 0.997908i | \(0.479407\pi\) | |||||||
\(18\) | −1293.07 | −0.940680 | ||||||||
\(19\) | 909.297 | − | 909.297i | 0.577859 | − | 0.577859i | −0.356454 | − | 0.934313i | \(-0.616014\pi\) |
0.934313 | + | 0.356454i | \(0.116014\pi\) | |||||||
\(20\) | 76.8547i | 0.0429631i | ||||||||
\(21\) | 143.300i | 0.0709086i | ||||||||
\(22\) | 1030.60 | − | 1030.60i | 0.453975 | − | 0.453975i | ||||
\(23\) | 4027.98 | 1.58770 | 0.793849 | − | 0.608115i | \(-0.208074\pi\) | ||||
0.793849 | + | 0.608115i | \(0.208074\pi\) | |||||||
\(24\) | 563.170 | − | 563.170i | 0.199577 | − | 0.199577i | ||||
\(25\) | 1295.81 | 0.414658 | ||||||||
\(26\) | −3372.83 | + | 3372.83i | −0.978501 | + | 0.978501i | ||||
\(27\) | 1492.80 | − | 1492.80i | 0.394086 | − | 0.394086i | ||||
\(28\) | −40.1428 | − | 40.1428i | −0.00967637 | − | 0.00967637i | ||||
\(29\) | 4259.20 | + | 4259.20i | 0.940444 | + | 0.940444i | 0.998324 | − | 0.0578799i | \(-0.0184341\pi\) |
−0.0578799 | + | 0.998324i | \(0.518434\pi\) | |||||||
\(30\) | −797.478 | − | 797.478i | −0.161777 | − | 0.161777i | ||||
\(31\) | 584.269 | 0.109197 | 0.0545983 | − | 0.998508i | \(-0.482612\pi\) | ||||
0.0545983 | + | 0.998508i | \(0.482612\pi\) | |||||||
\(32\) | 649.817i | 0.112180i | ||||||||
\(33\) | 1137.18i | 0.181780i | ||||||||
\(34\) | 6464.91 | + | 6464.91i | 0.959103 | + | 0.959103i | ||||
\(35\) | 955.426 | − | 955.426i | 0.131834 | − | 0.131834i | ||||
\(36\) | 399.692i | 0.0514007i | ||||||||
\(37\) | −6540.21 | −0.785393 | −0.392697 | − | 0.919668i | \(-0.628458\pi\) | ||||
−0.392697 | + | 0.919668i | \(0.628458\pi\) | |||||||
\(38\) | −5286.21 | − | 5286.21i | −0.593862 | − | 0.593862i | ||||
\(39\) | − | 3721.65i | − | 0.391809i | ||||||
\(40\) | −7509.64 | −0.742112 | ||||||||
\(41\) | 6314.48 | + | 8716.85i | 0.586648 | + | 0.809842i | ||||
\(42\) | 833.079 | 0.0728724 | ||||||||
\(43\) | 19713.1i | 1.62586i | 0.582358 | + | 0.812932i | \(0.302130\pi\) | ||||
−0.582358 | + | 0.812932i | \(0.697870\pi\) | |||||||
\(44\) | −318.559 | − | 318.559i | −0.0248061 | − | 0.0248061i | ||||
\(45\) | −9512.93 | −0.700298 | ||||||||
\(46\) | − | 23416.7i | − | 1.63167i | ||||||
\(47\) | −2649.01 | + | 2649.01i | −0.174920 | + | 0.174920i | −0.789137 | − | 0.614217i | \(-0.789472\pi\) |
0.614217 | + | 0.789137i | \(0.289472\pi\) | |||||||
\(48\) | −3458.43 | − | 3458.43i | −0.216659 | − | 0.216659i | ||||
\(49\) | − | 15808.9i | − | 0.940615i | ||||||
\(50\) | − | 7533.19i | − | 0.426142i | ||||||
\(51\) | −7133.52 | −0.384042 | ||||||||
\(52\) | 1042.55 | + | 1042.55i | 0.0534673 | + | 0.0534673i | ||||
\(53\) | 12245.4 | + | 12245.4i | 0.598801 | + | 0.598801i | 0.939994 | − | 0.341192i | \(-0.110831\pi\) |
−0.341192 | + | 0.939994i | \(0.610831\pi\) | |||||||
\(54\) | −8678.39 | − | 8678.39i | −0.405000 | − | 0.405000i | ||||
\(55\) | 7581.93 | − | 7581.93i | 0.337966 | − | 0.337966i | ||||
\(56\) | 3922.44 | − | 3922.44i | 0.167142 | − | 0.167142i | ||||
\(57\) | 5832.92 | 0.237793 | ||||||||
\(58\) | 24760.9 | − | 24760.9i | 0.966488 | − | 0.966488i | ||||
\(59\) | −18496.7 | −0.691775 | −0.345888 | − | 0.938276i | \(-0.612422\pi\) | ||||
−0.345888 | + | 0.938276i | \(0.612422\pi\) | |||||||
\(60\) | −246.502 | + | 246.502i | −0.00883980 | + | 0.00883980i | ||||
\(61\) | − | 15638.9i | − | 0.538124i | −0.963123 | − | 0.269062i | \(-0.913286\pi\) | ||
0.963123 | − | 0.269062i | \(-0.0867137\pi\) | |||||||
\(62\) | − | 3396.66i | − | 0.112221i | ||||||
\(63\) | 4968.80 | − | 4968.80i | 0.157725 | − | 0.157725i | ||||
\(64\) | −30727.0 | −0.937715 | ||||||||
\(65\) | −24813.4 | + | 24813.4i | −0.728454 | + | 0.728454i | ||||
\(66\) | 6611.03 | 0.186814 | ||||||||
\(67\) | 15672.6 | − | 15672.6i | 0.426536 | − | 0.426536i | −0.460911 | − | 0.887446i | \(-0.652477\pi\) |
0.887446 | + | 0.460911i | \(0.152477\pi\) | |||||||
\(68\) | 1998.32 | − | 1998.32i | 0.0524073 | − | 0.0524073i | ||||
\(69\) | 12919.3 | + | 12919.3i | 0.326674 | + | 0.326674i | ||||
\(70\) | −5554.38 | − | 5554.38i | −0.135485 | − | 0.135485i | ||||
\(71\) | 32943.1 | + | 32943.1i | 0.775566 | + | 0.775566i | 0.979073 | − | 0.203507i | \(-0.0652341\pi\) |
−0.203507 | + | 0.979073i | \(0.565234\pi\) | |||||||
\(72\) | −39054.8 | −0.887856 | ||||||||
\(73\) | 29040.6i | 0.637821i | 0.947785 | + | 0.318911i | \(0.103317\pi\) | ||||
−0.947785 | + | 0.318911i | \(0.896683\pi\) | |||||||
\(74\) | 38021.6i | 0.807144i | ||||||||
\(75\) | 4156.14 | + | 4156.14i | 0.0853173 | + | 0.0853173i | ||||
\(76\) | −1633.98 | + | 1633.98i | −0.0324498 | + | 0.0324498i | ||||
\(77\) | 7920.40i | 0.152237i | ||||||||
\(78\) | −21635.9 | −0.402660 | ||||||||
\(79\) | 12851.5 | + | 12851.5i | 0.231678 | + | 0.231678i | 0.813393 | − | 0.581715i | \(-0.197618\pi\) |
−0.581715 | + | 0.813393i | \(0.697618\pi\) | |||||||
\(80\) | 46116.8i | 0.805627i | ||||||||
\(81\) | −44473.5 | −0.753162 | ||||||||
\(82\) | 50675.6 | − | 36709.3i | 0.832270 | − | 0.602895i | ||||
\(83\) | −35969.0 | −0.573104 | −0.286552 | − | 0.958065i | \(-0.592509\pi\) | ||||
−0.286552 | + | 0.958065i | \(0.592509\pi\) | |||||||
\(84\) | − | 257.506i | − | 0.00398189i | ||||||
\(85\) | 47561.3 | + | 47561.3i | 0.714013 | + | 0.714013i | ||||
\(86\) | 114603. | 1.67089 | ||||||||
\(87\) | 27321.7i | 0.386999i | ||||||||
\(88\) | 31127.1 | − | 31127.1i | 0.428482 | − | 0.428482i | ||||
\(89\) | −25718.6 | − | 25718.6i | −0.344170 | − | 0.344170i | 0.513763 | − | 0.857932i | \(-0.328251\pi\) |
−0.857932 | + | 0.513763i | \(0.828251\pi\) | |||||||
\(90\) | 55303.6i | 0.719692i | ||||||||
\(91\) | − | 25921.1i | − | 0.328133i | ||||||
\(92\) | −7238.16 | −0.0891577 | ||||||||
\(93\) | 1873.97 | + | 1873.97i | 0.0224675 | + | 0.0224675i | ||||
\(94\) | 15400.1 | + | 15400.1i | 0.179764 | + | 0.179764i | ||||
\(95\) | −38889.8 | − | 38889.8i | −0.442106 | − | 0.442106i | ||||
\(96\) | −2084.21 | + | 2084.21i | −0.0230814 | + | 0.0230814i | ||||
\(97\) | 32563.1 | − | 32563.1i | 0.351395 | − | 0.351395i | −0.509233 | − | 0.860629i | \(-0.670071\pi\) |
0.860629 | + | 0.509233i | \(0.170071\pi\) | |||||||
\(98\) | −91905.4 | −0.966665 | ||||||||
\(99\) | 39430.7 | − | 39430.7i | 0.404340 | − | 0.404340i | ||||
\(100\) | −2328.52 | −0.0232852 | ||||||||
\(101\) | 91513.8 | − | 91513.8i | 0.892654 | − | 0.892654i | −0.102118 | − | 0.994772i | \(-0.532562\pi\) |
0.994772 | + | 0.102118i | \(0.0325619\pi\) | |||||||
\(102\) | 41470.8i | 0.394678i | ||||||||
\(103\) | − | 59937.7i | − | 0.556682i | −0.960482 | − | 0.278341i | \(-0.910215\pi\) | ||
0.960482 | − | 0.278341i | \(-0.0897846\pi\) | |||||||
\(104\) | −101870. | + | 101870.i | −0.923553 | + | 0.923553i | ||||
\(105\) | 6128.82 | 0.0542505 | ||||||||
\(106\) | 71188.7 | − | 71188.7i | 0.615385 | − | 0.615385i | ||||
\(107\) | −135996. | −1.14833 | −0.574164 | − | 0.818740i | \(-0.694673\pi\) | ||||
−0.574164 | + | 0.818740i | \(0.694673\pi\) | |||||||
\(108\) | −2682.51 | + | 2682.51i | −0.0221300 | + | 0.0221300i | ||||
\(109\) | −6503.28 | + | 6503.28i | −0.0524284 | + | 0.0524284i | −0.732835 | − | 0.680407i | \(-0.761803\pi\) |
0.680407 | + | 0.732835i | \(0.261803\pi\) | |||||||
\(110\) | −44077.7 | − | 44077.7i | −0.347326 | − | 0.347326i | ||||
\(111\) | −20976.9 | − | 20976.9i | −0.161597 | − | 0.161597i | ||||
\(112\) | −24087.7 | − | 24087.7i | −0.181448 | − | 0.181448i | ||||
\(113\) | 191184. | 1.40850 | 0.704248 | − | 0.709954i | \(-0.251284\pi\) | ||||
0.704248 | + | 0.709954i | \(0.251284\pi\) | |||||||
\(114\) | − | 33909.8i | − | 0.244378i | ||||||
\(115\) | − | 172273.i | − | 1.21471i | ||||||
\(116\) | −7653.65 | − | 7653.65i | −0.0528109 | − | 0.0528109i | ||||
\(117\) | −129045. | + | 129045.i | −0.871517 | + | 0.871517i | ||||
\(118\) | 107531.i | 0.710933i | ||||||||
\(119\) | −49684.5 | −0.321628 | ||||||||
\(120\) | −24086.3 | − | 24086.3i | −0.152692 | − | 0.152692i | ||||
\(121\) | − | 98197.4i | − | 0.609729i | ||||||
\(122\) | −90917.2 | −0.553027 | ||||||||
\(123\) | −7705.33 | + | 48211.2i | −0.0459228 | + | 0.287333i | ||||
\(124\) | −1049.91 | −0.00613196 | ||||||||
\(125\) | − | 189074.i | − | 1.08232i | ||||||
\(126\) | −28886.2 | − | 28886.2i | −0.162093 | − | 0.162093i | ||||
\(127\) | −245230. | −1.34916 | −0.674581 | − | 0.738201i | \(-0.735676\pi\) | ||||
−0.674581 | + | 0.738201i | \(0.735676\pi\) | |||||||
\(128\) | 199426.i | 1.07586i | ||||||||
\(129\) | −63227.4 | + | 63227.4i | −0.334527 | + | 0.334527i | ||||
\(130\) | 144253. | + | 144253.i | 0.748628 | + | 0.748628i | ||||
\(131\) | − | 40003.9i | − | 0.203669i | −0.994801 | − | 0.101834i | \(-0.967529\pi\) | ||
0.994801 | − | 0.101834i | \(-0.0324711\pi\) | |||||||
\(132\) | − | 2043.48i | − | 0.0102079i | ||||||
\(133\) | 40625.9 | 0.199147 | ||||||||
\(134\) | −91113.2 | − | 91113.2i | −0.438348 | − | 0.438348i | ||||
\(135\) | −63845.5 | − | 63845.5i | −0.301506 | − | 0.301506i | ||||
\(136\) | 195260. | + | 195260.i | 0.905245 | + | 0.905245i | ||||
\(137\) | −204030. | + | 204030.i | −0.928738 | + | 0.928738i | −0.997624 | − | 0.0688870i | \(-0.978055\pi\) |
0.0688870 | + | 0.997624i | \(0.478055\pi\) | |||||||
\(138\) | 75106.3 | − | 75106.3i | 0.335721 | − | 0.335721i | ||||
\(139\) | 327570. | 1.43803 | 0.719014 | − | 0.694995i | \(-0.244594\pi\) | ||||
0.719014 | + | 0.694995i | \(0.244594\pi\) | |||||||
\(140\) | −1716.87 | + | 1716.87i | −0.00740316 | + | 0.00740316i | ||||
\(141\) | −16992.8 | −0.0719807 | ||||||||
\(142\) | 191515. | − | 191515.i | 0.797045 | − | 0.797045i | ||||
\(143\) | − | 205701.i | − | 0.841193i | ||||||
\(144\) | 239836.i | 0.963845i | ||||||||
\(145\) | 182162. | − | 182162.i | 0.719511 | − | 0.719511i | ||||
\(146\) | 168828. | 0.655485 | ||||||||
\(147\) | 50705.2 | − | 50705.2i | 0.193535 | − | 0.193535i | ||||
\(148\) | 11752.6 | 0.0441040 | ||||||||
\(149\) | −194580. | + | 194580.i | −0.718013 | + | 0.718013i | −0.968198 | − | 0.250185i | \(-0.919509\pi\) |
0.250185 | + | 0.968198i | \(0.419509\pi\) | |||||||
\(150\) | 24161.8 | − | 24161.8i | 0.0876801 | − | 0.0876801i | ||||
\(151\) | 112834. | + | 112834.i | 0.402716 | + | 0.402716i | 0.879189 | − | 0.476473i | \(-0.158085\pi\) |
−0.476473 | + | 0.879189i | \(0.658085\pi\) | |||||||
\(152\) | −159660. | − | 159660.i | −0.560514 | − | 0.560514i | ||||
\(153\) | 247348. | + | 247348.i | 0.854240 | + | 0.854240i | ||||
\(154\) | 46045.4 | 0.156453 | ||||||||
\(155\) | − | 24988.7i | − | 0.0835437i | ||||||
\(156\) | 6687.70i | 0.0220021i | ||||||||
\(157\) | 163272. | + | 163272.i | 0.528644 | + | 0.528644i | 0.920168 | − | 0.391524i | \(-0.128052\pi\) |
−0.391524 | + | 0.920168i | \(0.628052\pi\) | |||||||
\(158\) | 74712.3 | − | 74712.3i | 0.238094 | − | 0.238094i | ||||
\(159\) | 78551.1i | 0.246411i | ||||||||
\(160\) | 27792.1 | 0.0858264 | ||||||||
\(161\) | 89981.8 | + | 89981.8i | 0.273584 | + | 0.273584i | ||||
\(162\) | 258547.i | 0.774020i | ||||||||
\(163\) | −457039. | −1.34736 | −0.673680 | − | 0.739023i | \(-0.735288\pi\) | ||||
−0.673680 | + | 0.739023i | \(0.735288\pi\) | |||||||
\(164\) | −11346.9 | − | 15663.9i | −0.0329434 | − | 0.0454769i | ||||
\(165\) | 48636.2 | 0.139075 | ||||||||
\(166\) | 209107.i | 0.588976i | ||||||||
\(167\) | −160390. | − | 160390.i | −0.445028 | − | 0.445028i | 0.448670 | − | 0.893698i | \(-0.351898\pi\) |
−0.893698 | + | 0.448670i | \(0.851898\pi\) | |||||||
\(168\) | 25161.5 | 0.0687802 | ||||||||
\(169\) | 301903.i | 0.813113i | ||||||||
\(170\) | 276498. | − | 276498.i | 0.733787 | − | 0.733787i | ||||
\(171\) | −202251. | − | 202251.i | −0.528932 | − | 0.528932i | ||||
\(172\) | − | 35423.9i | − | 0.0913009i | ||||||
\(173\) | 30998.9i | 0.0787466i | 0.999225 | + | 0.0393733i | \(0.0125361\pi\) | ||||
−0.999225 | + | 0.0393733i | \(0.987464\pi\) | |||||||
\(174\) | 158835. | 0.397716 | ||||||||
\(175\) | 28947.3 | + | 28947.3i | 0.0714516 | + | 0.0714516i | ||||
\(176\) | −191152. | − | 191152.i | −0.465155 | − | 0.465155i | ||||
\(177\) | −59326.0 | − | 59326.0i | −0.142335 | − | 0.142335i | ||||
\(178\) | −149516. | + | 149516.i | −0.353701 | + | 0.353701i | ||||
\(179\) | −347619. | + | 347619.i | −0.810907 | + | 0.810907i | −0.984770 | − | 0.173863i | \(-0.944375\pi\) |
0.173863 | + | 0.984770i | \(0.444375\pi\) | |||||||
\(180\) | 17094.4 | 0.0393254 | ||||||||
\(181\) | 20242.8 | − | 20242.8i | 0.0459277 | − | 0.0459277i | −0.683770 | − | 0.729698i | \(-0.739661\pi\) |
0.729698 | + | 0.683770i | \(0.239661\pi\) | |||||||
\(182\) | −150693. | −0.337220 | ||||||||
\(183\) | 50160.0 | − | 50160.0i | 0.110721 | − | 0.110721i | ||||
\(184\) | − | 707257.i | − | 1.54004i | ||||||
\(185\) | 279719.i | 0.600886i | ||||||||
\(186\) | 10894.4 | − | 10894.4i | 0.0230898 | − | 0.0230898i | ||||
\(187\) | −394279. | −0.824517 | ||||||||
\(188\) | 4760.19 | − | 4760.19i | 0.00982267 | − | 0.00982267i | ||||
\(189\) | 66695.6 | 0.135813 | ||||||||
\(190\) | −226086. | + | 226086.i | −0.454350 | + | 0.454350i | ||||
\(191\) | 419728. | − | 419728.i | 0.832501 | − | 0.832501i | −0.155357 | − | 0.987858i | \(-0.549653\pi\) |
0.987858 | + | 0.155357i | \(0.0496529\pi\) | |||||||
\(192\) | −98553.2 | − | 98553.2i | −0.192938 | − | 0.192938i | ||||
\(193\) | −285876. | − | 285876.i | −0.552439 | − | 0.552439i | 0.374705 | − | 0.927144i | \(-0.377744\pi\) |
−0.927144 | + | 0.374705i | \(0.877744\pi\) | |||||||
\(194\) | −189306. | − | 189306.i | −0.361127 | − | 0.361127i | ||||
\(195\) | −159172. | −0.299764 | ||||||||
\(196\) | 28408.1i | 0.0528205i | ||||||||
\(197\) | 746196.i | 1.36990i | 0.728592 | + | 0.684948i | \(0.240175\pi\) | ||||
−0.728592 | + | 0.684948i | \(0.759825\pi\) | |||||||
\(198\) | −229231. | − | 229231.i | −0.415538 | − | 0.415538i | ||||
\(199\) | 505374. | − | 505374.i | 0.904650 | − | 0.904650i | −0.0911843 | − | 0.995834i | \(-0.529065\pi\) |
0.995834 | + | 0.0911843i | \(0.0290652\pi\) | |||||||
\(200\) | − | 227525.i | − | 0.402212i | ||||||
\(201\) | 100536. | 0.175522 | ||||||||
\(202\) | −532017. | − | 532017.i | −0.917376 | − | 0.917376i | ||||
\(203\) | 190294.i | 0.324104i | ||||||||
\(204\) | 12818.7 | 0.0215660 | ||||||||
\(205\) | 372812. | − | 270064.i | 0.619591 | − | 0.448831i | ||||
\(206\) | −348449. | −0.572099 | ||||||||
\(207\) | − | 895926.i | − | 1.45327i | ||||||
\(208\) | 625583. | + | 625583.i | 1.00260 | + | 1.00260i | ||||
\(209\) | 322393. | 0.510528 | ||||||||
\(210\) | − | 35630.0i | − | 0.0557529i | ||||||
\(211\) | 70844.0 | − | 70844.0i | 0.109546 | − | 0.109546i | −0.650209 | − | 0.759755i | \(-0.725319\pi\) |
0.759755 | + | 0.650209i | \(0.225319\pi\) | |||||||
\(212\) | −22004.6 | − | 22004.6i | −0.0336259 | − | 0.0336259i | ||||
\(213\) | 211322.i | 0.319151i | ||||||||
\(214\) | 790614.i | 1.18013i | ||||||||
\(215\) | 843112. | 1.24391 | ||||||||
\(216\) | −262114. | − | 262114.i | −0.382257 | − | 0.382257i | ||||
\(217\) | 13052.1 | + | 13052.1i | 0.0188162 | + | 0.0188162i | ||||
\(218\) | 37806.9 | + | 37806.9i | 0.0538803 | + | 0.0538803i | ||||
\(219\) | −93144.3 | + | 93144.3i | −0.131234 | + | 0.131234i | ||||
\(220\) | −13624.5 | + | 13624.5i | −0.0189786 | + | 0.0189786i | ||||
\(221\) | 1.29036e6 | 1.77717 | ||||||||
\(222\) | −121950. | + | 121950.i | −0.166073 | + | 0.166073i | ||||
\(223\) | −1.37201e6 | −1.84754 | −0.923772 | − | 0.382942i | \(-0.874911\pi\) | ||||
−0.923772 | + | 0.382942i | \(0.874911\pi\) | |||||||
\(224\) | −14516.4 | + | 14516.4i | −0.0193303 | + | 0.0193303i | ||||
\(225\) | − | 288220.i | − | 0.379550i | ||||||
\(226\) | − | 1.11145e6i | − | 1.44750i | ||||||
\(227\) | 184927. | − | 184927.i | 0.238196 | − | 0.238196i | −0.577907 | − | 0.816103i | \(-0.696130\pi\) |
0.816103 | + | 0.577907i | \(0.196130\pi\) | |||||||
\(228\) | −10481.6 | −0.0133533 | ||||||||
\(229\) | −797528. | + | 797528.i | −1.00498 | + | 1.00498i | −0.00499237 | + | 0.999988i | \(0.501589\pi\) |
−0.999988 | + | 0.00499237i | \(0.998411\pi\) | |||||||
\(230\) | −1.00151e6 | −1.24835 | ||||||||
\(231\) | −25403.7 | + | 25403.7i | −0.0313233 | + | 0.0313233i | ||||
\(232\) | 747855. | − | 747855.i | 0.912215 | − | 0.912215i | ||||
\(233\) | 904976. | + | 904976.i | 1.09206 | + | 1.09206i | 0.995308 | + | 0.0967540i | \(0.0308460\pi\) |
0.0967540 | + | 0.995308i | \(0.469154\pi\) | |||||||
\(234\) | 750204. | + | 750204.i | 0.895653 | + | 0.895653i | ||||
\(235\) | 113296. | + | 113296.i | 0.133827 | + | 0.133827i | ||||
\(236\) | 33238.1 | 0.0388468 | ||||||||
\(237\) | 82439.1i | 0.0953372i | ||||||||
\(238\) | 288842.i | 0.330535i | ||||||||
\(239\) | 1.14442e6 | + | 1.14442e6i | 1.29596 | + | 1.29596i | 0.931041 | + | 0.364916i | \(0.118902\pi\) |
0.364916 | + | 0.931041i | \(0.381098\pi\) | |||||||
\(240\) | −147914. | + | 147914.i | −0.165760 | + | 0.165760i | ||||
\(241\) | 1.11242e6i | 1.23374i | 0.787063 | + | 0.616872i | \(0.211601\pi\) | ||||
−0.787063 | + | 0.616872i | \(0.788399\pi\) | |||||||
\(242\) | −570872. | −0.626615 | ||||||||
\(243\) | −505392. | − | 505392.i | −0.549051 | − | 0.549051i | ||||
\(244\) | 28102.7i | 0.0302185i | ||||||||
\(245\) | −676133. | −0.719643 | ||||||||
\(246\) | 280276. | + | 44795.0i | 0.295290 | + | 0.0471946i | ||||
\(247\) | −1.05510e6 | −1.10040 | ||||||||
\(248\) | − | 102589.i | − | 0.105919i | ||||||
\(249\) | −115366. | − | 115366.i | −0.117918 | − | 0.117918i | ||||
\(250\) | −1.09918e6 | −1.11230 | ||||||||
\(251\) | 680486.i | 0.681766i | 0.940106 | + | 0.340883i | \(0.110726\pi\) | ||||
−0.940106 | + | 0.340883i | \(0.889274\pi\) | |||||||
\(252\) | −8928.78 | + | 8928.78i | −0.00885709 | + | 0.00885709i | ||||
\(253\) | 714065. | + | 714065.i | 0.701352 | + | 0.701352i | ||||
\(254\) | 1.42565e6i | 1.38653i | ||||||||
\(255\) | 305094.i | 0.293821i | ||||||||
\(256\) | 176103. | 0.167945 | ||||||||
\(257\) | −1.12361e6 | − | 1.12361e6i | −1.06117 | − | 1.06117i | −0.998003 | − | 0.0631619i | \(-0.979882\pi\) |
−0.0631619 | − | 0.998003i | \(-0.520118\pi\) | |||||||
\(258\) | 367574. | + | 367574.i | 0.343792 | + | 0.343792i | ||||
\(259\) | −146103. | − | 146103.i | −0.135335 | − | 0.135335i | ||||
\(260\) | 44588.8 | − | 44588.8i | 0.0409066 | − | 0.0409066i | ||||
\(261\) | 947354. | − | 947354.i | 0.860817 | − | 0.860817i | ||||
\(262\) | −232563. | −0.209309 | ||||||||
\(263\) | 1.02660e6 | − | 1.02660e6i | 0.915191 | − | 0.915191i | −0.0814840 | − | 0.996675i | \(-0.525966\pi\) |
0.996675 | + | 0.0814840i | \(0.0259659\pi\) | |||||||
\(264\) | 199673. | 0.176323 | ||||||||
\(265\) | 523724. | − | 523724.i | 0.458129 | − | 0.458129i | ||||
\(266\) | − | 236179.i | − | 0.204662i | ||||||
\(267\) | − | 164979.i | − | 0.141628i | ||||||
\(268\) | −28163.3 | + | 28163.3i | −0.0239522 | + | 0.0239522i | ||||
\(269\) | 1.74306e6 | 1.46870 | 0.734349 | − | 0.678772i | \(-0.237487\pi\) | ||||
0.734349 | + | 0.678772i | \(0.237487\pi\) | |||||||
\(270\) | −371167. | + | 371167.i | −0.309856 | + | 0.309856i | ||||
\(271\) | −108772. | −0.0899694 | −0.0449847 | − | 0.998988i | \(-0.514324\pi\) | ||||
−0.0449847 | + | 0.998988i | \(0.514324\pi\) | |||||||
\(272\) | 1.19909e6 | − | 1.19909e6i | 0.982722 | − | 0.982722i | ||||
\(273\) | 83138.7 | − | 83138.7i | 0.0675144 | − | 0.0675144i | ||||
\(274\) | 1.18613e6 | + | 1.18613e6i | 0.954458 | + | 0.954458i | ||||
\(275\) | 229715. | + | 229715.i | 0.183172 | + | 0.183172i | ||||
\(276\) | −23215.5 | − | 23215.5i | −0.0183445 | − | 0.0183445i | ||||
\(277\) | −1.18958e6 | −0.931522 | −0.465761 | − | 0.884910i | \(-0.654219\pi\) | ||||
−0.465761 | + | 0.884910i | \(0.654219\pi\) | |||||||
\(278\) | − | 1.90433e6i | − | 1.47785i | ||||||
\(279\) | − | 129956.i | − | 0.0999510i | ||||||
\(280\) | −167759. | − | 167759.i | −0.127877 | − | 0.127877i | ||||
\(281\) | −871892. | + | 871892.i | −0.658714 | + | 0.658714i | −0.955076 | − | 0.296362i | \(-0.904227\pi\) |
0.296362 | + | 0.955076i | \(0.404227\pi\) | |||||||
\(282\) | 98787.6i | 0.0739741i | ||||||||
\(283\) | −1.28153e6 | −0.951178 | −0.475589 | − | 0.879668i | \(-0.657765\pi\) | ||||
−0.475589 | + | 0.879668i | \(0.657765\pi\) | |||||||
\(284\) | −59197.8 | − | 59197.8i | −0.0435521 | − | 0.0435521i | ||||
\(285\) | − | 249468.i | − | 0.181930i | ||||||
\(286\) | −1.19584e6 | −0.864489 | ||||||||
\(287\) | −53667.1 | + | 335788.i | −0.0384595 | + | 0.240636i | ||||
\(288\) | 144536. | 0.102682 | ||||||||
\(289\) | − | 1.05345e6i | − | 0.741940i | ||||||
\(290\) | −1.05900e6 | − | 1.05900e6i | −0.739437 | − | 0.739437i | ||||
\(291\) | 208884. | 0.144602 | ||||||||
\(292\) | − | 52185.1i | − | 0.0358170i | ||||||
\(293\) | 884746. | − | 884746.i | 0.602073 | − | 0.602073i | −0.338789 | − | 0.940862i | \(-0.610017\pi\) |
0.940862 | + | 0.338789i | \(0.110017\pi\) | |||||||
\(294\) | −294775. | − | 294775.i | −0.198895 | − | 0.198895i | ||||
\(295\) | 791088.i | 0.529261i | ||||||||
\(296\) | 1.14837e6i | 0.761819i | ||||||||
\(297\) | 529273. | 0.348168 | ||||||||
\(298\) | 1.13119e6 | + | 1.13119e6i | 0.737898 | + | 0.737898i | ||||
\(299\) | −2.33692e6 | − | 2.33692e6i | −1.51170 | − | 1.51170i | ||||
\(300\) | −7468.46 | − | 7468.46i | −0.00479102 | − | 0.00479102i | ||||
\(301\) | −440375. | + | 440375.i | −0.280160 | + | 0.280160i | ||||
\(302\) | 655965. | − | 655965.i | 0.413869 | − | 0.413869i | ||||
\(303\) | 587039. | 0.367333 | ||||||||
\(304\) | −980471. | + | 980471.i | −0.608486 | + | 0.608486i | ||||
\(305\) | −668863. | −0.411706 | ||||||||
\(306\) | 1.43796e6 | − | 1.43796e6i | 0.877897 | − | 0.877897i | ||||
\(307\) | − | 2.98062e6i | − | 1.80493i | −0.430759 | − | 0.902467i | \(-0.641754\pi\) | ||
0.430759 | − | 0.902467i | \(-0.358246\pi\) | |||||||
\(308\) | − | 14232.7i | − | 0.00854891i | ||||||
\(309\) | 192243. | − | 192243.i | 0.114539 | − | 0.114539i | ||||
\(310\) | −145272. | −0.0858573 | ||||||||
\(311\) | −1.23638e6 | + | 1.23638e6i | −0.724854 | + | 0.724854i | −0.969590 | − | 0.244736i | \(-0.921299\pi\) |
0.244736 | + | 0.969590i | \(0.421299\pi\) | |||||||
\(312\) | −653469. | −0.380048 | ||||||||
\(313\) | −1.62278e6 | + | 1.62278e6i | −0.936267 | + | 0.936267i | −0.998087 | − | 0.0618203i | \(-0.980309\pi\) |
0.0618203 | + | 0.998087i | \(0.480309\pi\) | |||||||
\(314\) | 949186. | − | 949186.i | 0.543284 | − | 0.543284i | ||||
\(315\) | −212511. | − | 212511.i | −0.120672 | − | 0.120672i | ||||
\(316\) | −23093.7 | − | 23093.7i | −0.0130100 | − | 0.0130100i | ||||
\(317\) | −991450. | − | 991450.i | −0.554144 | − | 0.554144i | 0.373490 | − | 0.927634i | \(-0.378161\pi\) |
−0.927634 | + | 0.373490i | \(0.878161\pi\) | |||||||
\(318\) | 456658. | 0.253235 | ||||||||
\(319\) | 1.51011e6i | 0.830866i | ||||||||
\(320\) | 1.31417e6i | 0.717424i | ||||||||
\(321\) | −436190. | − | 436190.i | −0.236272 | − | 0.236272i | ||||
\(322\) | 523111. | − | 523111.i | 0.281160 | − | 0.281160i | ||||
\(323\) | 2.02237e6i | 1.07858i | ||||||||
\(324\) | 79917.5 | 0.0422940 | ||||||||
\(325\) | −751789. | − | 751789.i | −0.394810 | − | 0.394810i | ||||
\(326\) | 2.65700e6i | 1.38467i | ||||||||
\(327\) | −41717.0 | −0.0215746 | ||||||||
\(328\) | 1.53056e6 | − | 1.10873e6i | 0.785533 | − | 0.569039i | ||||
\(329\) | −118353. | −0.0602825 | ||||||||
\(330\) | − | 282747.i | − | 0.142927i | ||||||
\(331\) | −1.03403e6 | − | 1.03403e6i | −0.518756 | − | 0.518756i | 0.398439 | − | 0.917195i | \(-0.369552\pi\) |
−0.917195 | + | 0.398439i | \(0.869552\pi\) | |||||||
\(332\) | 64635.2 | 0.0321828 | ||||||||
\(333\) | 1.45471e6i | 0.718895i | ||||||||
\(334\) | −932433. | + | 932433.i | −0.457353 | + | 0.457353i | ||||
\(335\) | −670305. | − | 670305.i | −0.326332 | − | 0.326332i | ||||
\(336\) | − | 154517.i | − | 0.0746669i | ||||||
\(337\) | 2.72705e6i | 1.30803i | 0.756480 | + | 0.654016i | \(0.226917\pi\) | ||||
−0.756480 | + | 0.654016i | \(0.773083\pi\) | |||||||
\(338\) | 1.75512e6 | 0.835632 | ||||||||
\(339\) | 613200. | + | 613200.i | 0.289803 | + | 0.289803i | ||||
\(340\) | −85466.2 | − | 85466.2i | −0.0400956 | − | 0.0400956i | ||||
\(341\) | 103577. | + | 103577.i | 0.0482366 | + | 0.0482366i | ||||
\(342\) | −1.17579e6 | + | 1.17579e6i | −0.543581 | + | 0.543581i | ||||
\(343\) | 728613. | − | 728613.i | 0.334396 | − | 0.334396i | ||||
\(344\) | 3.46135e6 | 1.57706 | ||||||||
\(345\) | 552545. | − | 552545.i | 0.249931 | − | 0.249931i | ||||
\(346\) | 180213. | 0.0809274 | ||||||||
\(347\) | 1.94035e6 | − | 1.94035e6i | 0.865078 | − | 0.865078i | −0.126844 | − | 0.991923i | \(-0.540485\pi\) |
0.991923 | + | 0.126844i | \(0.0404849\pi\) | |||||||
\(348\) | − | 49096.3i | − | 0.0217320i | ||||||
\(349\) | 711342.i | 0.312619i | 0.987708 | + | 0.156309i | \(0.0499597\pi\) | ||||
−0.987708 | + | 0.156309i | \(0.950040\pi\) | |||||||
\(350\) | 168285. | − | 168285.i | 0.0734304 | − | 0.0734304i | ||||
\(351\) | −1.73215e6 | −0.750444 | ||||||||
\(352\) | −115197. | + | 115197.i | −0.0495546 | + | 0.0495546i | ||||
\(353\) | −1.51777e6 | −0.648291 | −0.324146 | − | 0.946007i | \(-0.605077\pi\) | ||||
−0.324146 | + | 0.946007i | \(0.605077\pi\) | |||||||
\(354\) | −344893. | + | 344893.i | −0.146277 | + | 0.146277i | ||||
\(355\) | 1.40895e6 | − | 1.40895e6i | 0.593367 | − | 0.593367i | ||||
\(356\) | 46215.6 | + | 46215.6i | 0.0193269 | + | 0.0193269i | ||||
\(357\) | −159357. | − | 159357.i | −0.0661760 | − | 0.0661760i | ||||
\(358\) | 2.02089e6 | + | 2.02089e6i | 0.833364 | + | 0.833364i | ||||
\(359\) | 3.15206e6 | 1.29080 | 0.645400 | − | 0.763845i | \(-0.276691\pi\) | ||||
0.645400 | + | 0.763845i | \(0.276691\pi\) | |||||||
\(360\) | 1.67034e6i | 0.679278i | ||||||||
\(361\) | 822457.i | 0.332158i | ||||||||
\(362\) | −117682. | − | 117682.i | −0.0471996 | − | 0.0471996i | ||||
\(363\) | 314956. | − | 314956.i | 0.125454 | − | 0.125454i | ||||
\(364\) | 46579.4i | 0.0184264i | ||||||||
\(365\) | 1.24204e6 | 0.487982 | ||||||||
\(366\) | −291606. | − | 291606.i | −0.113787 | − | 0.113787i | ||||
\(367\) | 430477.i | 0.166834i | 0.996515 | + | 0.0834170i | \(0.0265833\pi\) | ||||
−0.996515 | + | 0.0834170i | \(0.973417\pi\) | |||||||
\(368\) | −4.34327e6 | −1.67185 | ||||||||
\(369\) | 1.93885e6 | − | 1.40450e6i | 0.741273 | − | 0.536978i | ||||
\(370\) | 1.62615e6 | 0.617527 | ||||||||
\(371\) | 547103.i | 0.206364i | ||||||||
\(372\) | −3367.47 | − | 3367.47i | −0.00126167 | − | 0.00126167i | ||||
\(373\) | −823447. | −0.306453 | −0.153226 | − | 0.988191i | \(-0.548966\pi\) | ||||
−0.153226 | + | 0.988191i | \(0.548966\pi\) | |||||||
\(374\) | 2.29215e6i | 0.847352i | ||||||||
\(375\) | 606431. | − | 606431.i | 0.222691 | − | 0.222691i | ||||
\(376\) | 465129. | + | 465129.i | 0.169669 | + | 0.169669i | ||||
\(377\) | − | 4.94212e6i | − | 1.79085i | ||||||
\(378\) | − | 387736.i | − | 0.139575i | ||||||
\(379\) | 4.01507e6 | 1.43580 | 0.717901 | − | 0.696145i | \(-0.245103\pi\) | ||||
0.717901 | + | 0.696145i | \(0.245103\pi\) | |||||||
\(380\) | 69883.7 | + | 69883.7i | 0.0248266 | + | 0.0248266i | ||||
\(381\) | −786544. | − | 786544.i | −0.277594 | − | 0.277594i | ||||
\(382\) | −2.44010e6 | − | 2.44010e6i | −0.855556 | − | 0.855556i | ||||
\(383\) | −1.49548e6 | + | 1.49548e6i | −0.520936 | + | 0.520936i | −0.917854 | − | 0.396918i | \(-0.870080\pi\) |
0.396918 | + | 0.917854i | \(0.370080\pi\) | |||||||
\(384\) | −639635. | + | 639635.i | −0.221363 | + | 0.221363i | ||||
\(385\) | 338748. | 0.116473 | ||||||||
\(386\) | −1.66195e6 | + | 1.66195e6i | −0.567739 | + | 0.567739i | ||||
\(387\) | 4.38470e6 | 1.48820 | ||||||||
\(388\) | −58514.8 | + | 58514.8i | −0.0197327 | + | 0.0197327i | ||||
\(389\) | 1.69724e6i | 0.568681i | 0.958723 | + | 0.284340i | \(0.0917746\pi\) | ||||
−0.958723 | + | 0.284340i | \(0.908225\pi\) | |||||||
\(390\) | 925347.i | 0.308065i | ||||||||
\(391\) | −4.47931e6 | + | 4.47931e6i | −1.48173 | + | 1.48173i | ||||
\(392\) | −2.77582e6 | −0.912382 | ||||||||
\(393\) | 128308. | − | 128308.i | 0.0419055 | − | 0.0419055i | ||||
\(394\) | 4.33802e6 | 1.40783 | ||||||||
\(395\) | 549646. | − | 549646.i | 0.177252 | − | 0.177252i | ||||
\(396\) | −70855.7 | + | 70855.7i | −0.0227058 | + | 0.0227058i | ||||
\(397\) | −731668. | − | 731668.i | −0.232990 | − | 0.232990i | 0.580949 | − | 0.813940i | \(-0.302681\pi\) |
−0.813940 | + | 0.580949i | \(0.802681\pi\) | |||||||
\(398\) | −2.93800e6 | − | 2.93800e6i | −0.929703 | − | 0.929703i | ||||
\(399\) | 130303. | + | 130303.i | 0.0409752 | + | 0.0409752i | ||||
\(400\) | −1.39723e6 | −0.436636 | ||||||||
\(401\) | − | 4.11597e6i | − | 1.27824i | −0.769108 | − | 0.639118i | \(-0.779299\pi\) | ||
0.769108 | − | 0.639118i | \(-0.220701\pi\) | |||||||
\(402\) | − | 584469.i | − | 0.180383i | ||||||
\(403\) | −338976. | − | 338976.i | −0.103970 | − | 0.103970i | ||||
\(404\) | −164448. | + | 164448.i | −0.0501273 | + | 0.0501273i | ||||
\(405\) | 1.90209e6i | 0.576227i | ||||||||
\(406\) | 1.10628e6 | 0.333080 | ||||||||
\(407\) | −1.15942e6 | − | 1.15942e6i | −0.346941 | − | 0.346941i | ||||
\(408\) | 1.25254e6i | 0.372514i | ||||||||
\(409\) | −3.79128e6 | −1.12067 | −0.560334 | − | 0.828266i | \(-0.689327\pi\) | ||||
−0.560334 | + | 0.828266i | \(0.689327\pi\) | |||||||
\(410\) | −1.57002e6 | − | 2.16735e6i | −0.461261 | − | 0.636750i | ||||
\(411\) | −1.30880e6 | −0.382182 | ||||||||
\(412\) | 107706.i | 0.0312606i | ||||||||
\(413\) | −413202. | − | 413202.i | −0.119203 | − | 0.119203i | ||||
\(414\) | −5.20848e6 | −1.49352 | ||||||||
\(415\) | 1.53836e6i | 0.438468i | ||||||||
\(416\) | 377005. | − | 377005.i | 0.106810 | − | 0.106810i | ||||
\(417\) | 1.05064e6 | + | 1.05064e6i | 0.295879 | + | 0.295879i | ||||
\(418\) | − | 1.87424e6i | − | 0.524667i | ||||||
\(419\) | 2.30732e6i | 0.642057i | 0.947070 | + | 0.321028i | \(0.104029\pi\) | ||||
−0.947070 | + | 0.321028i | \(0.895971\pi\) | |||||||
\(420\) | −11013.3 | −0.00304645 | ||||||||
\(421\) | 182088. | + | 182088.i | 0.0500698 | + | 0.0500698i | 0.731698 | − | 0.681629i | \(-0.238728\pi\) |
−0.681629 | + | 0.731698i | \(0.738728\pi\) | |||||||
\(422\) | −411853. | − | 411853.i | −0.112580 | − | 0.112580i | ||||
\(423\) | 589207. | + | 589207.i | 0.160110 | + | 0.160110i | ||||
\(424\) | 2.15012e6 | − | 2.15012e6i | 0.580827 | − | 0.580827i | ||||
\(425\) | −1.44100e6 | + | 1.44100e6i | −0.386983 | + | 0.386983i | ||||
\(426\) | 1.22852e6 | 0.327989 | ||||||||
\(427\) | 349361. | − | 349361.i | 0.0927266 | − | 0.0927266i | ||||
\(428\) | 244380. | 0.0644847 | ||||||||
\(429\) | 659760. | − | 659760.i | 0.173078 | − | 0.173078i | ||||
\(430\) | − | 4.90145e6i | − | 1.27836i | ||||||
\(431\) | − | 2.75129e6i | − | 0.713417i | −0.934216 | − | 0.356709i | \(-0.883899\pi\) | ||
0.934216 | − | 0.356709i | \(-0.116101\pi\) | |||||||
\(432\) | −1.60964e6 | + | 1.60964e6i | −0.414973 | + | 0.414973i | ||||
\(433\) | 6.26885e6 | 1.60682 | 0.803412 | − | 0.595423i | \(-0.203016\pi\) | ||||
0.803412 | + | 0.595423i | \(0.203016\pi\) | |||||||
\(434\) | 75878.5 | − | 75878.5i | 0.0193372 | − | 0.0193372i | ||||
\(435\) | 1.16852e6 | 0.296084 | ||||||||
\(436\) | 11686.2 | − | 11686.2i | 0.00294413 | − | 0.00294413i | ||||
\(437\) | 3.66263e6 | − | 3.66263e6i | 0.917466 | − | 0.917466i | ||||
\(438\) | 541496. | + | 541496.i | 0.134868 | + | 0.134868i | ||||
\(439\) | −1.04568e6 | − | 1.04568e6i | −0.258962 | − | 0.258962i | 0.565670 | − | 0.824632i | \(-0.308618\pi\) |
−0.824632 | + | 0.565670i | \(0.808618\pi\) | |||||||
\(440\) | −1.33128e6 | − | 1.33128e6i | −0.327822 | − | 0.327822i | ||||
\(441\) | −3.51631e6 | −0.860975 | ||||||||
\(442\) | − | 7.50151e6i | − | 1.82639i | ||||||
\(443\) | 500255.i | 0.121111i | 0.998165 | + | 0.0605553i | \(0.0192872\pi\) | ||||
−0.998165 | + | 0.0605553i | \(0.980713\pi\) | |||||||
\(444\) | 37694.9 | + | 37694.9i | 0.00907454 | + | 0.00907454i | ||||
\(445\) | −1.09996e6 | + | 1.09996e6i | −0.263316 | + | 0.263316i | ||||
\(446\) | 7.97620e6i | 1.89871i | ||||||||
\(447\) | −1.24818e6 | −0.295467 | ||||||||
\(448\) | −686417. | − | 686417.i | −0.161582 | − | 0.161582i | ||||
\(449\) | − | 271952.i | − | 0.0636615i | −0.999493 | − | 0.0318307i | \(-0.989866\pi\) | ||
0.999493 | − | 0.0318307i | \(-0.0101337\pi\) | |||||||
\(450\) | −1.67557e6 | −0.390061 | ||||||||
\(451\) | −425884. | + | 2.66469e6i | −0.0985938 | + | 0.616888i | ||||
\(452\) | −343552. | −0.0790945 | ||||||||
\(453\) | 723805.i | 0.165721i | ||||||||
\(454\) | −1.07507e6 | − | 1.07507e6i | −0.244793 | − | 0.244793i | ||||
\(455\) | −1.10862e6 | −0.251047 | ||||||||
\(456\) | − | 1.02418e6i | − | 0.230655i | ||||||
\(457\) | 1.97316e6 | − | 1.97316e6i | 0.441948 | − | 0.441948i | −0.450718 | − | 0.892666i | \(-0.648832\pi\) |
0.892666 | + | 0.450718i | \(0.148832\pi\) | |||||||
\(458\) | 4.63644e6 | + | 4.63644e6i | 1.03281 | + | 1.03281i | ||||
\(459\) | 3.32012e6i | 0.735567i | ||||||||
\(460\) | 309569.i | 0.0682124i | ||||||||
\(461\) | 752001. | 0.164803 | 0.0824017 | − | 0.996599i | \(-0.473741\pi\) | ||||
0.0824017 | + | 0.996599i | \(0.473741\pi\) | |||||||
\(462\) | 147685. | + | 147685.i | 0.0321907 | + | 0.0321907i | ||||
\(463\) | 4.54236e6 | + | 4.54236e6i | 0.984758 | + | 0.984758i | 0.999886 | − | 0.0151279i | \(-0.00481555\pi\) |
−0.0151279 | + | 0.999886i | \(0.504816\pi\) | |||||||
\(464\) | −4.59258e6 | − | 4.59258e6i | −0.990289 | − | 0.990289i | ||||
\(465\) | 80148.0 | − | 80148.0i | 0.0171894 | − | 0.0171894i | ||||
\(466\) | 5.26109e6 | − | 5.26109e6i | 1.12231 | − | 1.12231i | ||||
\(467\) | −4.40683e6 | −0.935049 | −0.467525 | − | 0.883980i | \(-0.654854\pi\) | ||||
−0.467525 | + | 0.883980i | \(0.654854\pi\) | |||||||
\(468\) | 231889. | − | 231889.i | 0.0489403 | − | 0.0489403i | ||||
\(469\) | 700228. | 0.146997 | ||||||||
\(470\) | 658646. | − | 658646.i | 0.137533 | − | 0.137533i | ||||
\(471\) | 1.04735e6i | 0.217541i | ||||||||
\(472\) | 3.24776e6i | 0.671011i | ||||||||
\(473\) | −3.49466e6 | + | 3.49466e6i | −0.718212 | + | 0.718212i | ||||
\(474\) | 479261. | 0.0979774 | ||||||||
\(475\) | 1.17827e6 | − | 1.17827e6i | 0.239614 | − | 0.239614i | ||||
\(476\) | 89281.5 | 0.0180611 | ||||||||
\(477\) | 2.72369e6 | − | 2.72369e6i | 0.548101 | − | 0.548101i | ||||
\(478\) | 6.65310e6 | − | 6.65310e6i | 1.33185 | − | 1.33185i | ||||
\(479\) | 6.01810e6 | + | 6.01810e6i | 1.19845 | + | 1.19845i | 0.974630 | + | 0.223823i | \(0.0718536\pi\) |
0.223823 | + | 0.974630i | \(0.428146\pi\) | |||||||
\(480\) | 89139.6 | + | 89139.6i | 0.0176591 | + | 0.0176591i | ||||
\(481\) | 3.79444e6 | + | 3.79444e6i | 0.747799 | + | 0.747799i | ||||
\(482\) | 6.46706e6 | 1.26791 | ||||||||
\(483\) | 577211.i | 0.112581i | ||||||||
\(484\) | 176458.i | 0.0342395i | ||||||||
\(485\) | −1.39269e6 | − | 1.39269e6i | −0.268844 | − | 0.268844i | ||||
\(486\) | −2.93811e6 | + | 2.93811e6i | −0.564257 | + | 0.564257i | ||||
\(487\) | 5.89407e6i | 1.12614i | 0.826409 | + | 0.563071i | \(0.190380\pi\) | ||||
−0.826409 | + | 0.563071i | \(0.809620\pi\) | |||||||
\(488\) | −2.74597e6 | −0.521972 | ||||||||
\(489\) | −1.46590e6 | − | 1.46590e6i | −0.277224 | − | 0.277224i | ||||
\(490\) | 3.93071e6i | 0.739572i | ||||||||
\(491\) | 1.65538e6 | 0.309881 | 0.154940 | − | 0.987924i | \(-0.450481\pi\) | ||||
0.154940 | + | 0.987924i | \(0.450481\pi\) | |||||||
\(492\) | 13846.2 | − | 86634.0i | 0.00257881 | − | 0.0161352i | ||||
\(493\) | −9.47287e6 | −1.75535 | ||||||||
\(494\) | 6.13381e6i | 1.13087i | ||||||||
\(495\) | −1.68641e6 | − | 1.68641e6i | −0.309351 | − | 0.309351i | ||||
\(496\) | −630002. | −0.114984 | ||||||||
\(497\) | 1.47184e6i | 0.267283i | ||||||||
\(498\) | −670683. | + | 670683.i | −0.121184 | + | 0.121184i | ||||
\(499\) | −6.47246e6 | − | 6.47246e6i | −1.16364 | − | 1.16364i | −0.983673 | − | 0.179966i | \(-0.942401\pi\) |
−0.179966 | − | 0.983673i | \(-0.557599\pi\) | |||||||
\(500\) | 339760.i | 0.0607781i | ||||||||
\(501\) | − | 1.02887e6i | − | 0.183132i | ||||||
\(502\) | 3.95602e6 | 0.700647 | ||||||||
\(503\) | 7.76956e6 | + | 7.76956e6i | 1.36923 | + | 1.36923i | 0.861540 | + | 0.507689i | \(0.169500\pi\) |
0.507689 | + | 0.861540i | \(0.330500\pi\) | |||||||
\(504\) | −872451. | − | 872451.i | −0.152991 | − | 0.152991i | ||||
\(505\) | −3.91396e6 | − | 3.91396e6i | −0.682949 | − | 0.682949i | ||||
\(506\) | 4.15123e6 | − | 4.15123e6i | 0.720776 | − | 0.720776i | ||||
\(507\) | −968317. | + | 968317.i | −0.167301 | + | 0.167301i | ||||
\(508\) | 440670. | 0.0757625 | ||||||||
\(509\) | −4.48141e6 | + | 4.48141e6i | −0.766691 | + | 0.766691i | −0.977522 | − | 0.210831i | \(-0.932383\pi\) |
0.210831 | + | 0.977522i | \(0.432383\pi\) | |||||||
\(510\) | 1.77367e6 | 0.301958 | ||||||||
\(511\) | −648744. | + | 648744.i | −0.109906 | + | 0.109906i | ||||
\(512\) | 5.35787e6i | 0.903269i | ||||||||
\(513\) | − | 2.71479e6i | − | 0.455452i | ||||||
\(514\) | −6.53213e6 | + | 6.53213e6i | −1.09055 | + | 1.09055i | ||||
\(515\) | −2.56348e6 | −0.425904 | ||||||||
\(516\) | 113618. | − | 113618.i | 0.0187855 | − | 0.0187855i | ||||
\(517\) | −939212. | −0.154539 | ||||||||
\(518\) | −849371. | + | 849371.i | −0.139083 | + | 0.139083i | ||||
\(519\) | −99425.3 | + | 99425.3i | −0.0162024 | + | 0.0162024i | ||||
\(520\) | 4.35687e6 | + | 4.35687e6i | 0.706589 | + | 0.706589i | ||||
\(521\) | 3.25748e6 | + | 3.25748e6i | 0.525759 | + | 0.525759i | 0.919305 | − | 0.393546i | \(-0.128752\pi\) |
−0.393546 | + | 0.919305i | \(0.628752\pi\) | |||||||
\(522\) | −5.50746e6 | − | 5.50746e6i | −0.884657 | − | 0.884657i | ||||
\(523\) | 3.98076e6 | 0.636374 | 0.318187 | − | 0.948028i | \(-0.396926\pi\) | ||||
0.318187 | + | 0.948028i | \(0.396926\pi\) | |||||||
\(524\) | 71885.7i | 0.0114371i | ||||||||
\(525\) | 185690.i | 0.0294028i | ||||||||
\(526\) | −5.96815e6 | − | 5.96815e6i | −0.940536 | − | 0.940536i | ||||
\(527\) | −649736. | + | 649736.i | −0.101908 | + | 0.101908i | ||||
\(528\) | − | 1.22619e6i | − | 0.191414i | ||||||
\(529\) | 9.78830e6 | 1.52079 | ||||||||
\(530\) | −3.04468e6 | − | 3.04468e6i | −0.470816 | − | 0.470816i | ||||
\(531\) | 4.11414e6i | 0.633203i | ||||||||
\(532\) | −73003.5 | −0.0111832 | ||||||||
\(533\) | 1.39379e6 | − | 8.72074e6i | 0.212510 | − | 1.32964i | ||||
\(534\) | −959106. | −0.145550 | ||||||||
\(535\) | 5.81642e6i | 0.878559i | ||||||||
\(536\) | −2.75189e6 | − | 2.75189e6i | −0.413733 | − | 0.413733i | ||||
\(537\) | −2.22989e6 | −0.333694 | ||||||||
\(538\) | − | 1.01333e7i | − | 1.50937i | ||||||
\(539\) | 2.80254e6 | − | 2.80254e6i | 0.415509 | − | 0.415509i | ||||
\(540\) | 114728. | + | 114728.i | 0.0169311 | + | 0.0169311i | ||||
\(541\) | − | 9.44255e6i | − | 1.38706i | −0.720427 | − | 0.693531i | \(-0.756054\pi\) | ||
0.720427 | − | 0.693531i | \(-0.243946\pi\) | |||||||
\(542\) | 632349.i | 0.0924610i | ||||||||
\(543\) | 129853. | 0.0188996 | ||||||||
\(544\) | −722628. | − | 722628.i | −0.104693 | − | 0.104693i | ||||
\(545\) | 278139. | + | 278139.i | 0.0401117 | + | 0.0401117i | ||||
\(546\) | −483328. | − | 483328.i | −0.0693841 | − | 0.0693841i | ||||
\(547\) | −1.11156e6 | + | 1.11156e6i | −0.158842 | + | 0.158842i | −0.782053 | − | 0.623212i | \(-0.785828\pi\) |
0.623212 | + | 0.782053i | \(0.285828\pi\) | |||||||
\(548\) | 366636. | − | 366636.i | 0.0521535 | − | 0.0521535i | ||||
\(549\) | −3.47850e6 | −0.492562 | ||||||||
\(550\) | 1.33545e6 | − | 1.33545e6i | 0.188245 | − | 0.188245i | ||||
\(551\) | 7.74575e6 | 1.08689 | ||||||||
\(552\) | 2.26844e6 | − | 2.26844e6i | 0.316869 | − | 0.316869i | ||||
\(553\) | 574183.i | 0.0798431i | ||||||||
\(554\) | 6.91563e6i | 0.957320i | ||||||||
\(555\) | −897163. | + | 897163.i | −0.123634 | + | 0.123634i | ||||
\(556\) | −588634. | −0.0807529 | ||||||||
\(557\) | −7.66574e6 | + | 7.66574e6i | −1.04693 | + | 1.04693i | −0.0480829 | + | 0.998843i | \(0.515311\pi\) |
−0.998843 | + | 0.0480829i | \(0.984689\pi\) | |||||||
\(558\) | −755503. | −0.102719 | ||||||||
\(559\) | 1.14370e7 | − | 1.14370e7i | 1.54804 | − | 1.54804i | ||||
\(560\) | −1.03021e6 | + | 1.03021e6i | −0.138821 | + | 0.138821i | ||||
\(561\) | −1.26460e6 | − | 1.26460e6i | −0.169647 | − | 0.169647i | ||||
\(562\) | 5.06876e6 | + | 5.06876e6i | 0.676956 | + | 0.676956i | ||||
\(563\) | −9.00928e6 | − | 9.00928e6i | −1.19790 | − | 1.19790i | −0.974795 | − | 0.223101i | \(-0.928382\pi\) |
−0.223101 | − | 0.974795i | \(-0.571618\pi\) | |||||||
\(564\) | 30535.4 | 0.00404210 | ||||||||
\(565\) | − | 8.17677e6i | − | 1.07761i | ||||||
\(566\) | 7.45018e6i | 0.977520i | ||||||||
\(567\) | −993501. | − | 993501.i | −0.129781 | − | 0.129781i | ||||
\(568\) | 5.78434e6 | − | 5.78434e6i | 0.752286 | − | 0.752286i | ||||
\(569\) | − | 4.87526e6i | − | 0.631273i | −0.948880 | − | 0.315636i | \(-0.897782\pi\) | ||
0.948880 | − | 0.315636i | \(-0.102218\pi\) | |||||||
\(570\) | −1.45029e6 | −0.186968 | ||||||||
\(571\) | −4.46036e6 | − | 4.46036e6i | −0.572505 | − | 0.572505i | 0.360322 | − | 0.932828i | \(-0.382667\pi\) |
−0.932828 | + | 0.360322i | \(0.882667\pi\) | |||||||
\(572\) | 369638.i | 0.0472374i | ||||||||
\(573\) | 2.69245e6 | 0.342580 | ||||||||
\(574\) | 1.95211e6 | + | 311994.i | 0.247300 | + | 0.0395246i | ||||
\(575\) | 5.21949e6 | 0.658352 | ||||||||
\(576\) | 6.83448e6i | 0.858320i | ||||||||
\(577\) | −6.40864e6 | − | 6.40864e6i | −0.801357 | − | 0.801357i | 0.181951 | − | 0.983308i | \(-0.441759\pi\) |
−0.983308 | + | 0.181951i | \(0.941759\pi\) | |||||||
\(578\) | −6.12424e6 | −0.762487 | ||||||||
\(579\) | − | 1.83383e6i | − | 0.227333i | ||||||
\(580\) | −327339. | + | 327339.i | −0.0404044 | + | 0.0404044i | ||||
\(581\) | −803518. | − | 803518.i | −0.0987542 | − | 0.0987542i | ||||
\(582\) | − | 1.21435e6i | − | 0.148606i | ||||||
\(583\) | 4.34163e6i | 0.529031i | ||||||||
\(584\) | 5.09912e6 | 0.618676 | ||||||||
\(585\) | 5.51912e6 | + | 5.51912e6i | 0.666777 | + | 0.666777i | ||||
\(586\) | −5.14348e6 | − | 5.14348e6i | −0.618747 | − | 0.618747i | ||||
\(587\) | −7.08270e6 | − | 7.08270e6i | −0.848406 | − | 0.848406i | 0.141528 | − | 0.989934i | \(-0.454798\pi\) |
−0.989934 | + | 0.141528i | \(0.954798\pi\) | |||||||
\(588\) | −91115.6 | + | 91115.6i | −0.0108680 | + | 0.0108680i | ||||
\(589\) | 531274. | − | 531274.i | 0.0631002 | − | 0.0631002i | ||||
\(590\) | 4.59900e6 | 0.543918 | ||||||||
\(591\) | −2.39333e6 | + | 2.39333e6i | −0.281861 | + | 0.281861i | ||||
\(592\) | 7.05214e6 | 0.827021 | ||||||||
\(593\) | −2.14214e6 | + | 2.14214e6i | −0.250156 | + | 0.250156i | −0.821034 | − | 0.570879i | \(-0.806603\pi\) |
0.570879 | + | 0.821034i | \(0.306603\pi\) | |||||||
\(594\) | − | 3.07694e6i | − | 0.357810i | ||||||
\(595\) | 2.12496e6i | 0.246070i | ||||||||
\(596\) | 349654. | − | 349654.i | 0.0403202 | − | 0.0403202i | ||||
\(597\) | 3.24185e6 | 0.372269 | ||||||||
\(598\) | −1.35857e7 | + | 1.35857e7i | −1.55356 | + | 1.55356i | ||||
\(599\) | 3.12893e6 | 0.356311 | 0.178156 | − | 0.984002i | \(-0.442987\pi\) | ||||
0.178156 | + | 0.984002i | \(0.442987\pi\) | |||||||
\(600\) | 729759. | − | 729759.i | 0.0827564 | − | 0.0827564i | ||||
\(601\) | −8.31693e6 | + | 8.31693e6i | −0.939240 | + | 0.939240i | −0.998257 | − | 0.0590168i | \(-0.981203\pi\) |
0.0590168 | + | 0.998257i | \(0.481203\pi\) | |||||||
\(602\) | 2.56013e6 | + | 2.56013e6i | 0.287919 | + | 0.287919i | ||||
\(603\) | −3.48600e6 | − | 3.48600e6i | −0.390421 | − | 0.390421i | ||||
\(604\) | −202760. | − | 202760.i | −0.0226147 | − | 0.0226147i | ||||
\(605\) | −4.19981e6 | −0.466489 | ||||||||
\(606\) | − | 3.41276e6i | − | 0.377506i | ||||||
\(607\) | 1.08265e7i | 1.19266i | 0.802741 | + | 0.596328i | \(0.203374\pi\) | ||||
−0.802741 | + | 0.596328i | \(0.796626\pi\) | |||||||
\(608\) | 590877. | + | 590877.i | 0.0648243 | + | 0.0648243i | ||||
\(609\) | −610344. | + | 610344.i | −0.0666855 | + | 0.0666855i | ||||
\(610\) | 3.88844e6i | 0.423108i | ||||||||
\(611\) | 3.07376e6 | 0.333094 | ||||||||
\(612\) | −444477. | − | 444477.i | −0.0479701 | − | 0.0479701i | ||||
\(613\) | 9.17949e6i | 0.986659i | 0.869842 | + | 0.493330i | \(0.164220\pi\) | ||||
−0.869842 | + | 0.493330i | \(0.835780\pi\) | |||||||
\(614\) | −1.73279e7 | −1.85492 | ||||||||
\(615\) | 2.06195e6 | + | 329550.i | 0.219831 | + | 0.0351344i | ||||
\(616\) | 1.39071e6 | 0.147667 | ||||||||
\(617\) | − | 1.17721e7i | − | 1.24492i | −0.782652 | − | 0.622460i | \(-0.786133\pi\) | ||
0.782652 | − | 0.622460i | \(-0.213867\pi\) | |||||||
\(618\) | −1.11761e6 | − | 1.11761e6i | −0.117711 | − | 0.117711i | ||||
\(619\) | −5.19479e6 | −0.544931 | −0.272466 | − | 0.962166i | \(-0.587839\pi\) | ||||
−0.272466 | + | 0.962166i | \(0.587839\pi\) | |||||||
\(620\) | 44903.8i | 0.00469142i | ||||||||
\(621\) | 6.01295e6 | − | 6.01295e6i | 0.625689 | − | 0.625689i | ||||
\(622\) | 7.18771e6 | + | 7.18771e6i | 0.744928 | + | 0.744928i | ||||
\(623\) | − | 1.14907e6i | − | 0.118611i | ||||||
\(624\) | 4.01296e6i | 0.412576i | ||||||||
\(625\) | −4.03711e6 | −0.413400 | ||||||||
\(626\) | 9.43408e6 | + | 9.43408e6i | 0.962196 | + | 0.962196i | ||||
\(627\) | 1.03404e6 | + | 1.03404e6i | 0.105043 | + | 0.105043i | ||||
\(628\) | −293395. | − | 293395.i | −0.0296862 | − | 0.0296862i | ||||
\(629\) | 7.27303e6 | − | 7.27303e6i | 0.732974 | − | 0.732974i | ||||
\(630\) | −1.23544e6 | + | 1.23544e6i | −0.124013 | + | 0.124013i | ||||
\(631\) | 9.81154e6 | 0.980988 | 0.490494 | − | 0.871444i | \(-0.336816\pi\) | ||||
0.490494 | + | 0.871444i | \(0.336816\pi\) | |||||||
\(632\) | 2.25654e6 | − | 2.25654e6i | 0.224724 | − | 0.224724i | ||||
\(633\) | 454447. | 0.0450790 | ||||||||
\(634\) | −5.76381e6 | + | 5.76381e6i | −0.569491 | + | 0.569491i | ||||
\(635\) | 1.04882e7i | 1.03221i | ||||||||
\(636\) | − | 141154.i | − | 0.0138373i | ||||||
\(637\) | −9.17187e6 | + | 9.17187e6i | −0.895591 | + | 0.895591i | ||||
\(638\) | 8.77903e6 | 0.853876 | ||||||||
\(639\) | 7.32739e6 | − | 7.32739e6i | 0.709900 | − | 0.709900i | ||||
\(640\) | 8.52928e6 | 0.823118 | ||||||||
\(641\) | 8.18261e6 | − | 8.18261e6i | 0.786587 | − | 0.786587i | −0.194346 | − | 0.980933i | \(-0.562258\pi\) |
0.980933 | + | 0.194346i | \(0.0622585\pi\) | |||||||
\(642\) | −2.53580e6 | + | 2.53580e6i | −0.242816 | + | 0.242816i | ||||
\(643\) | −7.16404e6 | − | 7.16404e6i | −0.683330 | − | 0.683330i | 0.277419 | − | 0.960749i | \(-0.410521\pi\) |
−0.960749 | + | 0.277419i | \(0.910521\pi\) | |||||||
\(644\) | −161695. | − | 161695.i | −0.0153632 | − | 0.0153632i | ||||
\(645\) | 2.70418e6 | + | 2.70418e6i | 0.255939 | + | 0.255939i | ||||
\(646\) | 1.17571e7 | 1.10845 | ||||||||
\(647\) | 7.19483e6i | 0.675709i | 0.941198 | + | 0.337855i | \(0.109701\pi\) | ||||
−0.941198 | + | 0.337855i | \(0.890299\pi\) | |||||||
\(648\) | 7.80891e6i | 0.730555i | ||||||||
\(649\) | −3.27903e6 | − | 3.27903e6i | −0.305586 | − | 0.305586i | ||||
\(650\) | −4.37054e6 | + | 4.37054e6i | −0.405743 | + | 0.405743i | ||||
\(651\) | 83726.0i | 0.00774297i | ||||||||
\(652\) | 821284. | 0.0756614 | ||||||||
\(653\) | 11077.2 | + | 11077.2i | 0.00101660 | + | 0.00101660i | 0.707615 | − | 0.706598i | \(-0.249771\pi\) |
−0.706598 | + | 0.707615i | \(0.749771\pi\) | |||||||
\(654\) | 242522.i | 0.0221721i | ||||||||
\(655\) | −1.71093e6 | −0.155822 | ||||||||
\(656\) | −6.80874e6 | − | 9.39916e6i | −0.617742 | − | 0.852765i | ||||
\(657\) | 6.45938e6 | 0.583818 | ||||||||
\(658\) | 688049.i | 0.0619519i | ||||||||
\(659\) | −1.19515e7 | − | 1.19515e7i | −1.07203 | − | 1.07203i | −0.997196 | − | 0.0748369i | \(-0.976156\pi\) |
−0.0748369 | − | 0.997196i | \(-0.523844\pi\) | |||||||
\(660\) | −87397.8 | −0.00780981 | ||||||||
\(661\) | − | 1.39032e7i | − | 1.23769i | −0.785513 | − | 0.618845i | \(-0.787601\pi\) | ||
0.785513 | − | 0.618845i | \(-0.212399\pi\) | |||||||
\(662\) | −6.01135e6 | + | 6.01135e6i | −0.533122 | + | 0.533122i | ||||
\(663\) | 4.13866e6 | + | 4.13866e6i | 0.365659 | + | 0.365659i | ||||
\(664\) | 6.31565e6i | 0.555902i | ||||||||
\(665\) | − | 1.73753e6i | − | 0.152363i | ||||||
\(666\) | 8.45697e6 | 0.738804 | ||||||||
\(667\) | 1.71560e7 | + | 1.71560e7i | 1.49314 | + | 1.49314i | ||||
\(668\) | 288217. | + | 288217.i | 0.0249907 | + | 0.0249907i | ||||
\(669\) | −4.40055e6 | − | 4.40055e6i | −0.380139 | − | 0.380139i | ||||
\(670\) | −3.89683e6 | + | 3.89683e6i | −0.335370 | + | 0.335370i | ||||
\(671\) | 2.77241e6 | − | 2.77241e6i | 0.237712 | − | 0.237712i | ||||
\(672\) | −93119.0 | −0.00795454 | ||||||||
\(673\) | −1.27602e7 | + | 1.27602e7i | −1.08598 | + | 1.08598i | −0.0900380 | + | 0.995938i | \(0.528699\pi\) |
−0.995938 | + | 0.0900380i | \(0.971301\pi\) | |||||||
\(674\) | 1.58538e7 | 1.34426 | ||||||||
\(675\) | 1.93437e6 | − | 1.93437e6i | 0.163411 | − | 0.163411i | ||||
\(676\) | − | 542511.i | − | 0.0456606i | ||||||
\(677\) | 1.69659e7i | 1.42267i | 0.702853 | + | 0.711335i | \(0.251909\pi\) | ||||
−0.702853 | + | 0.711335i | \(0.748091\pi\) | |||||||
\(678\) | 3.56485e6 | − | 3.56485e6i | 0.297829 | − | 0.297829i | ||||
\(679\) | 1.45486e6 | 0.121101 | ||||||||
\(680\) | 8.35109e6 | − | 8.35109e6i | 0.692581 | − | 0.692581i | ||||
\(681\) | 1.18626e6 | 0.0980194 | ||||||||
\(682\) | 602146. | − | 602146.i | 0.0495725 | − | 0.0495725i | ||||
\(683\) | 2.53820e6 | − | 2.53820e6i | 0.208197 | − | 0.208197i | −0.595304 | − | 0.803501i | \(-0.702968\pi\) |
0.803501 | + | 0.595304i | \(0.202968\pi\) | |||||||
\(684\) | 363438. | + | 363438.i | 0.0297023 | + | 0.0297023i | ||||
\(685\) | 8.72618e6 | + | 8.72618e6i | 0.710555 | + | 0.710555i | ||||
\(686\) | −4.23580e6 | − | 4.23580e6i | −0.343657 | − | 0.343657i | ||||
\(687\) | −5.11595e6 | −0.413556 | ||||||||
\(688\) | − | 2.12562e7i | − | 1.71204i | ||||||
\(689\) | − | 1.42088e7i | − | 1.14028i | ||||||
\(690\) | −3.21223e6 | − | 3.21223e6i | −0.256852 | − | 0.256852i | ||||
\(691\) | 7.74824e6 | − | 7.74824e6i | 0.617317 | − | 0.617317i | −0.327526 | − | 0.944842i | \(-0.606215\pi\) |
0.944842 | + | 0.327526i | \(0.106215\pi\) | |||||||
\(692\) | − | 55704.1i | − | 0.00442204i | ||||||
\(693\) | 1.76170e6 | 0.139347 | ||||||||
\(694\) | −1.12802e7 | − | 1.12802e7i | −0.889036 | − | 0.889036i | ||||
\(695\) | − | 1.40099e7i | − | 1.10020i | ||||||
\(696\) | 4.79730e6 | 0.375383 | ||||||||
\(697\) | −1.67156e7 | − | 2.67156e6i | −1.30329 | − | 0.208297i | ||||
\(698\) | 4.13540e6 | 0.321276 | ||||||||
\(699\) | 5.80520e6i | 0.449391i | ||||||||
\(700\) | −52017.3 | − | 52017.3i | −0.00401239 | − | 0.00401239i | ||||
\(701\) | −1.99725e7 | −1.53510 | −0.767552 | − | 0.640987i | \(-0.778525\pi\) | ||||
−0.767552 | + | 0.640987i | \(0.778525\pi\) | |||||||
\(702\) | 1.00699e7i | 0.771227i | ||||||||
\(703\) | −5.94699e6 | + | 5.94699e6i | −0.453846 | + | 0.453846i | ||||
\(704\) | −5.44717e6 | − | 5.44717e6i | −0.414228 | − | 0.414228i | ||||
\(705\) | 726764.i | 0.0550707i | ||||||||
\(706\) | 8.82360e6i | 0.666245i | ||||||||
\(707\) | 4.08869e6 | 0.307635 | ||||||||
\(708\) | 106607. | + | 106607.i | 0.00799287 | + | 0.00799287i | ||||
\(709\) | 8.66267e6 | + | 8.66267e6i | 0.647196 | + | 0.647196i | 0.952315 | − | 0.305118i | \(-0.0986959\pi\) |
−0.305118 | + | 0.952315i | \(0.598696\pi\) | |||||||
\(710\) | −8.19093e6 | − | 8.19093e6i | −0.609800 | − | 0.609800i | ||||
\(711\) | 2.85850e6 | − | 2.85850e6i | 0.212062 | − | 0.212062i | ||||
\(712\) | −4.51582e6 | + | 4.51582e6i | −0.333839 | + | 0.333839i | ||||
\(713\) | 2.35343e6 | 0.173371 | ||||||||
\(714\) | −926424. | + | 926424.i | −0.0680087 | + | 0.0680087i | ||||
\(715\) | −8.79763e6 | −0.643577 | ||||||||
\(716\) | 624661. | − | 624661.i | 0.0455367 | − | 0.0455367i | ||||
\(717\) | 7.34117e6i | 0.533295i | ||||||||
\(718\) | − | 1.83246e7i | − | 1.32655i | ||||||
\(719\) | −1.30749e7 | + | 1.30749e7i | −0.943230 | + | 0.943230i | −0.998473 | − | 0.0552429i | \(-0.982407\pi\) |
0.0552429 | + | 0.998473i | \(0.482407\pi\) | |||||||
\(720\) | 1.02575e7 | 0.737415 | ||||||||
\(721\) | 1.33896e6 | − | 1.33896e6i | 0.0959245 | − | 0.0959245i | ||||
\(722\) | 4.78137e6 | 0.341357 | ||||||||
\(723\) | −3.56794e6 | + | 3.56794e6i | −0.253847 | + | 0.253847i | ||||
\(724\) | −36375.7 | + | 36375.7i | −0.00257908 | + | 0.00257908i | ||||
\(725\) | 5.51910e6 | + | 5.51910e6i | 0.389963 | + | 0.389963i | ||||
\(726\) | −1.83100e6 | − | 1.83100e6i | −0.128928 | − | 0.128928i | ||||
\(727\) | −1.60959e7 | − | 1.60959e7i | −1.12948 | − | 1.12948i | −0.990262 | − | 0.139219i | \(-0.955541\pi\) |
−0.139219 | − | 0.990262i | \(-0.544459\pi\) | |||||||
\(728\) | −4.55137e6 | −0.318283 | ||||||||
\(729\) | 7.56509e6i | 0.527224i | ||||||||
\(730\) | − | 7.22063e6i | − | 0.501496i | ||||||
\(731\) | −2.19220e7 | − | 2.19220e7i | −1.51735 | − | 1.51735i | ||||
\(732\) | −90135.9 | + | 90135.9i | −0.00621756 | + | 0.00621756i | ||||
\(733\) | 1.60770e7i | 1.10521i | 0.833443 | + | 0.552605i | \(0.186366\pi\) | ||||
−0.833443 | + | 0.552605i | \(0.813634\pi\) | |||||||
\(734\) | 2.50258e6 | 0.171454 | ||||||||
\(735\) | −2.16861e6 | − | 2.16861e6i | −0.148069 | − | 0.148069i | ||||
\(736\) | 2.61745e6i | 0.178108i | ||||||||
\(737\) | 5.55677e6 | 0.376837 | ||||||||
\(738\) | −8.16509e6 | − | 1.12715e7i | −0.551849 | − | 0.761802i | ||||
\(739\) | −2.14388e7 | −1.44407 | −0.722037 | − | 0.691855i | \(-0.756794\pi\) | ||||
−0.722037 | + | 0.691855i | \(0.756794\pi\) | |||||||
\(740\) | − | 502646.i | − | 0.0337429i | ||||||
\(741\) | −3.38409e6 | − | 3.38409e6i | −0.226410 | − | 0.226410i | ||||
\(742\) | 3.18059e6 | 0.212079 | ||||||||
\(743\) | − | 104279.i | − | 0.00692989i | −0.999994 | − | 0.00346495i | \(-0.998897\pi\) | ||
0.999994 | − | 0.00346495i | \(-0.00110293\pi\) | |||||||
\(744\) | 329043. | − | 329043.i | 0.0217932 | − | 0.0217932i | ||||
\(745\) | 8.32200e6 | + | 8.32200e6i | 0.549335 | + | 0.549335i | ||||
\(746\) | 4.78712e6i | 0.314940i | ||||||||
\(747\) | 8.00043e6i | 0.524580i | ||||||||
\(748\) | 708507. | 0.0463010 | ||||||||
\(749\) | −3.03803e6 | − | 3.03803e6i | −0.197874 | − | 0.197874i | ||||
\(750\) | −3.52550e6 | − | 3.52550e6i | −0.228859 | − | 0.228859i | ||||
\(751\) | 1.90142e7 | + | 1.90142e7i | 1.23021 | + | 1.23021i | 0.963884 | + | 0.266323i | \(0.0858087\pi\) |
0.266323 | + | 0.963884i | \(0.414191\pi\) | |||||||
\(752\) | 2.85636e6 | − | 2.85636e6i | 0.184191 | − | 0.184191i | ||||
\(753\) | −2.18258e6 | + | 2.18258e6i | −0.140276 | + | 0.140276i | ||||
\(754\) | −2.87311e7 | −1.84045 | ||||||||
\(755\) | 4.82582e6 | − | 4.82582e6i | 0.308109 | − | 0.308109i | ||||
\(756\) | −119850. | −0.00762664 | ||||||||
\(757\) | 4.23966e6 | − | 4.23966e6i | 0.268900 | − | 0.268900i | −0.559757 | − | 0.828657i | \(-0.689105\pi\) |
0.828657 | + | 0.559757i | \(0.189105\pi\) | |||||||
\(758\) | − | 2.33416e7i | − | 1.47557i | ||||||
\(759\) | 4.58055e6i | 0.288611i | ||||||||
\(760\) | −6.82849e6 | + | 6.82849e6i | −0.428836 | + | 0.428836i | ||||
\(761\) | 1.28108e7 | 0.801889 | 0.400944 | − | 0.916102i | \(-0.368682\pi\) | ||||
0.400944 | + | 0.916102i | \(0.368682\pi\) | |||||||
\(762\) | −4.57259e6 | + | 4.57259e6i | −0.285282 | + | 0.285282i | ||||
\(763\) | −290556. | −0.0180683 | ||||||||
\(764\) | −754239. | + | 754239.i | −0.0467493 | + | 0.0467493i | ||||
\(765\) | 1.05788e7 | − | 1.05788e7i | 0.653559 | − | 0.653559i | ||||
\(766\) | 8.69402e6 | + | 8.69402e6i | 0.535363 | + | 0.535363i | ||||
\(767\) | 1.07313e7 | + | 1.07313e7i | 0.658662 | + | 0.658662i | ||||
\(768\) | 564828. | + | 564828.i | 0.0345552 | + | 0.0345552i | ||||
\(769\) | 1.04373e7 | 0.636460 | 0.318230 | − | 0.948014i | \(-0.396912\pi\) | ||||
0.318230 | + | 0.948014i | \(0.396912\pi\) | |||||||
\(770\) | − | 1.96932e6i | − | 0.119699i | ||||||
\(771\) | − | 7.20769e6i | − | 0.436677i | ||||||
\(772\) | 513711. | + | 513711.i | 0.0310224 | + | 0.0310224i | ||||
\(773\) | 4.38411e6 | − | 4.38411e6i | 0.263896 | − | 0.263896i | −0.562739 | − | 0.826635i | \(-0.690252\pi\) |
0.826635 | + | 0.562739i | \(0.190252\pi\) | |||||||
\(774\) | − | 2.54905e7i | − | 1.52942i | ||||||
\(775\) | 757100. | 0.0452792 | ||||||||
\(776\) | −5.71761e6 | − | 5.71761e6i | −0.340848 | − | 0.340848i | ||||
\(777\) | − | 937214.i | − | 0.0556911i | ||||||
\(778\) | 9.86691e6 | 0.584430 | ||||||||
\(779\) | 1.36679e7 | + | 2.18447e6i | 0.806974 | + | 0.128974i | ||||
\(780\) | 286027. | 0.0168333 | ||||||||
\(781\) | 1.16800e7i | 0.685199i | ||||||||
\(782\) | 2.60406e7 | + | 2.60406e7i | 1.52277 | + | 1.52277i | ||||
\(783\) | 1.27162e7 | 0.741231 | ||||||||
\(784\) | 1.70463e7i | 0.990470i | ||||||||
\(785\) | 6.98300e6 | − | 6.98300e6i | 0.404453 | − | 0.404453i | ||||
\(786\) | −745918. | − | 745918.i | −0.0430660 | − | 0.0430660i | ||||
\(787\) | − | 2.13605e7i | − | 1.22935i | −0.788781 | − | 0.614675i | \(-0.789287\pi\) | ||
0.788781 | − | 0.614675i | \(-0.210713\pi\) | |||||||
\(788\) | − | 1.34089e6i | − | 0.0769269i | ||||||
\(789\) | 6.58538e6 | 0.376607 | ||||||||
\(790\) | −3.19537e6 | − | 3.19537e6i | −0.182160 | − | 0.182160i | ||||
\(791\) | 4.27089e6 | + | 4.27089e6i | 0.242704 | + | 0.242704i | ||||
\(792\) | −6.92347e6 | − | 6.92347e6i | −0.392203 | − | 0.392203i | ||||
\(793\) | −9.07325e6 | + | 9.07325e6i | −0.512366 | + | 0.512366i | ||||
\(794\) | −4.25356e6 | + | 4.25356e6i | −0.239443 | + | 0.239443i | ||||
\(795\) | 3.35956e6 | 0.188523 | ||||||||
\(796\) | −908142. | + | 908142.i | −0.0508009 | + | 0.0508009i | ||||
\(797\) | 2.36313e6 | 0.131778 | 0.0658888 | − | 0.997827i | \(-0.479012\pi\) | ||||
0.0658888 | + | 0.997827i | \(0.479012\pi\) | |||||||
\(798\) | 757516. | − | 757516.i | 0.0421099 | − | 0.0421099i | ||||
\(799\) | − | 5.89166e6i | − | 0.326490i | ||||||
\(800\) | 842037.i | 0.0465164i | ||||||||
\(801\) | −5.72047e6 | + | 5.72047e6i | −0.315029 | + | 0.315029i | ||||
\(802\) | −2.39283e7 | −1.31364 | ||||||||
\(803\) | −5.14821e6 | + | 5.14821e6i | −0.281752 | + | 0.281752i | ||||
\(804\) | −180660. | −0.00985651 | ||||||||
\(805\) | 3.84844e6 | − | 3.84844e6i | 0.209312 | − | 0.209312i | ||||
\(806\) | −1.97064e6 | + | 1.97064e6i | −0.106849 | + | 0.106849i | ||||
\(807\) | 5.59066e6 | + | 5.59066e6i | 0.302190 | + | 0.302190i | ||||
\(808\) | −1.60685e7 | − | 1.60685e7i | −0.865860 | − | 0.865860i | ||||
\(809\) | 1.84991e7 | + | 1.84991e7i | 0.993757 | + | 0.993757i | 0.999981 | − | 0.00622355i | \(-0.00198103\pi\) |
−0.00622355 | + | 0.999981i | \(0.501981\pi\) | |||||||
\(810\) | 1.10578e7 | 0.592185 | ||||||||
\(811\) | − | 1.39863e7i | − | 0.746708i | −0.927689 | − | 0.373354i | \(-0.878208\pi\) | ||
0.927689 | − | 0.373354i | \(-0.121792\pi\) | |||||||
\(812\) | − | 341952.i | − | 0.0182002i | ||||||
\(813\) | −348873. | − | 348873.i | −0.0185115 | − | 0.0185115i | ||||
\(814\) | −6.74032e6 | + | 6.74032e6i | −0.356549 | + | 0.356549i | ||||
\(815\) | 1.95471e7i | 1.03083i | ||||||||
\(816\) | 7.69189e6 | 0.404397 | ||||||||
\(817\) | 1.79251e7 | + | 1.79251e7i | 0.939520 | + | 0.939520i | ||||
\(818\) | 2.20407e7i | 1.15170i | ||||||||
\(819\) | −5.76551e6 | −0.300350 | ||||||||
\(820\) | −669931. | + | 485297.i | −0.0347933 | + | 0.0252042i | ||||
\(821\) | −616890. | −0.0319411 | −0.0159705 | − | 0.999872i | \(-0.505084\pi\) | ||||
−0.0159705 | + | 0.999872i | \(0.505084\pi\) | |||||||
\(822\) | 7.60875e6i | 0.392766i | ||||||||
\(823\) | −1.30109e7 | − | 1.30109e7i | −0.669589 | − | 0.669589i | 0.288032 | − | 0.957621i | \(-0.406999\pi\) |
−0.957621 | + | 0.288032i | \(0.906999\pi\) | |||||||
\(824\) | −1.05242e7 | −0.539973 | ||||||||
\(825\) | 1.47357e6i | 0.0753764i | ||||||||
\(826\) | −2.40215e6 | + | 2.40215e6i | −0.122504 | + | 0.122504i | ||||
\(827\) | −2.66329e6 | − | 2.66329e6i | −0.135411 | − | 0.135411i | 0.636152 | − | 0.771563i | \(-0.280525\pi\) |
−0.771563 | + | 0.636152i | \(0.780525\pi\) | |||||||
\(828\) | 1.60995e6i | 0.0816088i | ||||||||
\(829\) | − | 3.17236e7i | − | 1.60323i | −0.597839 | − | 0.801616i | \(-0.703974\pi\) | ||
0.597839 | − | 0.801616i | \(-0.296026\pi\) | |||||||
\(830\) | 8.94329e6 | 0.450611 | ||||||||
\(831\) | −3.81542e6 | − | 3.81542e6i | −0.191664 | − | 0.191664i | ||||
\(832\) | 1.78269e7 | + | 1.78269e7i | 0.892829 | + | 0.892829i | ||||
\(833\) | 1.75803e7 | + | 1.75803e7i | 0.877837 | + | 0.877837i | ||||
\(834\) | 6.10792e6 | − | 6.10792e6i | 0.304073 | − | 0.304073i | ||||
\(835\) | −6.85975e6 | + | 6.85975e6i | −0.340480 | + | 0.340480i | ||||
\(836\) | −579330. | −0.0286689 | ||||||||
\(837\) | 872194. | − | 872194.i | 0.0430328 | − | 0.0430328i | ||||
\(838\) | 1.34137e7 | 0.659838 | ||||||||
\(839\) | −8.94703e6 | + | 8.94703e6i | −0.438807 | + | 0.438807i | −0.891610 | − | 0.452803i | \(-0.850424\pi\) |
0.452803 | + | 0.891610i | \(0.350424\pi\) | |||||||
\(840\) | − | 1.07613e6i | − | 0.0526221i | ||||||
\(841\) | 1.57704e7i | 0.768868i | ||||||||
\(842\) | 1.05857e6 | − | 1.05857e6i | 0.0514564 | − | 0.0514564i | ||||
\(843\) | −5.59297e6 | −0.271065 | ||||||||
\(844\) | −127305. | + | 127305.i | −0.00615160 | + | 0.00615160i | ||||
\(845\) | 1.29121e7 | 0.622094 | ||||||||
\(846\) | 3.42537e6 | − | 3.42537e6i | 0.164544 | − | 0.164544i | ||||
\(847\) | 2.19365e6 | − | 2.19365e6i | 0.105065 | − | 0.105065i | ||||
\(848\) | −1.32039e7 | − | 1.32039e7i | −0.630539 | − | 0.630539i | ||||
\(849\) | −4.11034e6 | − | 4.11034e6i | −0.195708 | − | 0.195708i | ||||
\(850\) | 8.37728e6 | + | 8.37728e6i | 0.397700 | + | 0.397700i | ||||
\(851\) | −2.63438e7 | −1.24697 | ||||||||
\(852\) | − | 379739.i | − | 0.0179220i | ||||||
\(853\) | 1.50424e7i | 0.707855i | 0.935273 | + | 0.353927i | \(0.115154\pi\) | ||||
−0.935273 | + | 0.353927i | \(0.884846\pi\) | |||||||
\(854\) | −2.03101e6 | − | 2.03101e6i | −0.0952946 | − | 0.0952946i | ||||
\(855\) | −8.65008e6 | + | 8.65008e6i | −0.404674 | + | 0.404674i | ||||
\(856\) | 2.38789e7i | 1.11386i | ||||||||
\(857\) | 944309. | 0.0439200 | 0.0219600 | − | 0.999759i | \(-0.493009\pi\) | ||||
0.0219600 | + | 0.999759i | \(0.493009\pi\) | |||||||
\(858\) | −3.83552e6 | − | 3.83552e6i | −0.177872 | − | 0.177872i | ||||
\(859\) | − | 1.65499e7i | − | 0.765265i | −0.923901 | − | 0.382633i | \(-0.875017\pi\) | ||
0.923901 | − | 0.382633i | \(-0.124983\pi\) | |||||||
\(860\) | −1.51505e6 | −0.0698522 | ||||||||
\(861\) | −1.24913e6 | + | 904867.i | −0.0574247 | + | 0.0415984i | ||||
\(862\) | −1.59947e7 | −0.733175 | ||||||||
\(863\) | − | 9.59137e6i | − | 0.438383i | −0.975682 | − | 0.219191i | \(-0.929658\pi\) | ||
0.975682 | − | 0.219191i | \(-0.0703419\pi\) | |||||||
\(864\) | 970044. | + | 970044.i | 0.0442086 | + | 0.0442086i | ||||
\(865\) | 1.32580e6 | 0.0602471 | ||||||||
\(866\) | − | 3.64441e7i | − | 1.65132i | ||||||
\(867\) | 3.37881e6 | − | 3.37881e6i | 0.152657 | − | 0.152657i | ||||
\(868\) | −23454.2 | − | 23454.2i | −0.00105663 | − | 0.00105663i | ||||
\(869\) | 4.55652e6i | 0.204684i | ||||||||
\(870\) | − | 6.79323e6i | − | 0.304283i | ||||||
\(871\) | −1.81856e7 | −0.812237 | ||||||||
\(872\) | 1.14188e6 | + | 1.14188e6i | 0.0508547 | + | 0.0508547i | ||||
\(873\) | −7.24286e6 | − | 7.24286e6i | −0.321643 | − | 0.321643i | ||||
\(874\) | −2.12928e7 | − | 2.12928e7i | −0.942874 | − | 0.942874i | ||||
\(875\) | 4.22375e6 | − | 4.22375e6i | 0.186500 | − | 0.186500i | ||||
\(876\) | 167377. | − | 167377.i | 0.00736948 | − | 0.00736948i | ||||
\(877\) | 2.51563e7 | 1.10446 | 0.552228 | − | 0.833693i | \(-0.313778\pi\) | ||||
0.552228 | + | 0.833693i | \(0.313778\pi\) | |||||||
\(878\) | −6.07906e6 | + | 6.07906e6i | −0.266134 | + | 0.266134i | ||||
\(879\) | 5.67543e6 | 0.247757 | ||||||||
\(880\) | −8.17540e6 | + | 8.17540e6i | −0.355879 | + | 0.355879i | ||||
\(881\) | 1.55724e7i | 0.675950i | 0.941155 | + | 0.337975i | \(0.109742\pi\) | ||||
−0.941155 | + | 0.337975i | \(0.890258\pi\) | |||||||
\(882\) | 2.04421e7i | 0.884818i | ||||||||
\(883\) | 2.38010e7 | − | 2.38010e7i | 1.02729 | − | 1.02729i | 0.0276745 | − | 0.999617i | \(-0.491190\pi\) |
0.999617 | − | 0.0276745i | \(-0.00881018\pi\) | |||||||
\(884\) | −2.31873e6 | −0.0997975 | ||||||||
\(885\) | −2.53732e6 | + | 2.53732e6i | −0.108897 | + | 0.108897i | ||||
\(886\) | 2.90824e6 | 0.124465 | ||||||||
\(887\) | −1.02362e7 | + | 1.02362e7i | −0.436849 | + | 0.436849i | −0.890950 | − | 0.454101i | \(-0.849960\pi\) |
0.454101 | + | 0.890950i | \(0.349960\pi\) | |||||||
\(888\) | −3.68325e6 | + | 3.68325e6i | −0.156747 | + | 0.156747i | ||||
\(889\) | −5.47823e6 | − | 5.47823e6i | −0.232480 | − | 0.232480i | ||||
\(890\) | 6.39464e6 | + | 6.39464e6i | 0.270608 | + | 0.270608i | ||||
\(891\) | −7.88408e6 | − | 7.88408e6i | −0.332703 | − | 0.332703i | ||||
\(892\) | 2.46546e6 | 0.103749 | ||||||||
\(893\) | 4.81747e6i | 0.202158i | ||||||||
\(894\) | 7.25633e6i | 0.303650i | ||||||||
\(895\) | 1.48673e7 | + | 1.48673e7i | 0.620406 | + | 0.620406i | ||||
\(896\) | −4.45502e6 | + | 4.45502e6i | −0.185387 | + | 0.185387i | ||||
\(897\) | − | 1.49908e7i | − | 0.622074i | ||||||
\(898\) | −1.58100e6 | −0.0654245 | ||||||||
\(899\) | 2.48852e6 | + | 2.48852e6i | 0.102693 | + | 0.102693i | ||||
\(900\) | 517923.i | 0.0213137i | ||||||||
\(901\) | −2.72349e7 | −1.11767 | ||||||||
\(902\) | 1.54912e7 | + | 2.47588e6i | 0.633972 | + | 0.101324i | ||||
\(903\) | −2.82490e6 | −0.115288 | ||||||||
\(904\) | − | 3.35692e7i | − | 1.36622i | ||||||
\(905\) | −865767. | − | 865767.i | −0.0351382 | − | 0.0351382i | ||||
\(906\) | 4.20785e6 | 0.170310 | ||||||||
\(907\) | − | 1.90099e7i | − | 0.767295i | −0.923480 | − | 0.383647i | \(-0.874668\pi\) | ||
0.923480 | − | 0.383647i | \(-0.125332\pi\) | |||||||
\(908\) | −332308. | + | 332308.i | −0.0133760 | + | 0.0133760i | ||||
\(909\) | −2.03550e7 | − | 2.03550e7i | −0.817074 | − | 0.817074i | ||||
\(910\) | 6.44498e6i | 0.257999i | ||||||||
\(911\) | − | 4.45025e6i | − | 0.177660i | −0.996047 | − | 0.0888298i | \(-0.971687\pi\) | ||
0.996047 | − | 0.0888298i | \(-0.0283127\pi\) | |||||||
\(912\) | −6.28948e6 | −0.250396 | ||||||||
\(913\) | −6.37644e6 | − | 6.37644e6i | −0.253164 | − | 0.253164i | ||||
\(914\) | −1.14710e7 | − | 1.14710e7i | −0.454188 | − | 0.454188i | ||||
\(915\) | −2.14529e6 | − | 2.14529e6i | −0.0847099 | − | 0.0847099i | ||||
\(916\) | 1.43313e6 | − | 1.43313e6i | 0.0564349 | − | 0.0564349i | ||||
\(917\) | 893654. | − | 893654.i | 0.0350951 | − | 0.0350951i | ||||
\(918\) | 1.93016e7 | 0.755938 | ||||||||
\(919\) | 2.62852e7 | − | 2.62852e7i | 1.02665 | − | 1.02665i | 0.0270166 | − | 0.999635i | \(-0.491399\pi\) |
0.999635 | − | 0.0270166i | \(-0.00860068\pi\) | |||||||
\(920\) | −3.02487e7 | −1.17825 | ||||||||
\(921\) | 9.55999e6 | − | 9.55999e6i | 0.371371 | − | 0.371371i | ||||
\(922\) | − | 4.37177e6i | − | 0.169368i | ||||||
\(923\) | − | 3.82253e7i | − | 1.47688i | ||||||
\(924\) | 45649.7 | − | 45649.7i | 0.00175897 | − | 0.00175897i | ||||
\(925\) | −8.47484e6 | −0.325670 | ||||||||
\(926\) | 2.64071e7 | − | 2.64071e7i | 1.01203 | − | 1.01203i | ||||
\(927\) | −1.33317e7 | −0.509549 | ||||||||
\(928\) | −2.76770e6 | + | 2.76770e6i | −0.105499 | + | 0.105499i | ||||
\(929\) | 398304. | − | 398304.i | 0.0151417 | − | 0.0151417i | −0.699495 | − | 0.714637i | \(-0.746592\pi\) |
0.714637 | + | 0.699495i | \(0.246592\pi\) | |||||||
\(930\) | −465942. | − | 465942.i | −0.0176654 | − | 0.0176654i | ||||
\(931\) | −1.43750e7 | − | 1.43750e7i | −0.543543 | − | 0.543543i | ||||
\(932\) | −1.62621e6 | − | 1.62621e6i | −0.0613251 | − | 0.0613251i | ||||
\(933\) | −7.93107e6 | −0.298282 | ||||||||
\(934\) | 2.56192e7i | 0.960944i | ||||||||
\(935\) | 1.68630e7i | 0.630819i | ||||||||
\(936\) | 2.26584e7 | + | 2.26584e7i | 0.845357 | + | 0.845357i | ||||
\(937\) | 6.17562e6 | − | 6.17562e6i | 0.229790 | − | 0.229790i | −0.582815 | − | 0.812605i | \(-0.698049\pi\) |
0.812605 | + | 0.582815i | \(0.198049\pi\) | |||||||
\(938\) | − | 4.07079e6i | − | 0.151068i | ||||||
\(939\) | −1.04098e7 | −0.385280 | ||||||||
\(940\) | −203589. | − | 203589.i | −0.00751509 | − | 0.00751509i | ||||
\(941\) | 2.16511e7i | 0.797087i | 0.917149 | + | 0.398544i | \(0.130484\pi\) | ||||
−0.917149 | + | 0.398544i | \(0.869516\pi\) | |||||||
\(942\) | 6.08880e6 | 0.223565 | ||||||||
\(943\) | 2.54346e7 | + | 3.51113e7i | 0.931421 | + | 1.28578i | ||||
\(944\) | 1.99445e7 | 0.728441 | ||||||||
\(945\) | − | 2.85251e6i | − | 0.103908i | ||||||
\(946\) | 2.03163e7 | + | 2.03163e7i | 0.738102 | + | 0.738102i | ||||
\(947\) | 1.13945e7 | 0.412877 | 0.206439 | − | 0.978460i | \(-0.433813\pi\) | ||||
0.206439 | + | 0.978460i | \(0.433813\pi\) | |||||||
\(948\) | − | 148140.i | − | 0.00535369i | ||||||
\(949\) | 1.68485e7 | − | 1.68485e7i | 0.607291 | − | 0.607291i | ||||
\(950\) | −6.84991e6 | − | 6.84991e6i | −0.246250 | − | 0.246250i | ||||
\(951\) | − | 6.35991e6i | − | 0.228034i | ||||||
\(952\) | 8.72389e6i | 0.311974i | ||||||||
\(953\) | −2.22603e7 | −0.793962 | −0.396981 | − | 0.917827i | \(-0.629942\pi\) | ||||
−0.396981 | + | 0.917827i | \(0.629942\pi\) | |||||||
\(954\) | −1.58342e7 | − | 1.58342e7i | −0.563281 | − | 0.563281i | ||||
\(955\) | −1.79514e7 | − | 1.79514e7i | −0.636927 | − | 0.636927i | ||||
\(956\) | −2.05649e6 | − | 2.05649e6i | −0.0727748 | − | 0.0727748i | ||||
\(957\) | −4.84348e6 | + | 4.84348e6i | −0.170953 | + | 0.170953i | ||||
\(958\) | 3.49863e7 | − | 3.49863e7i | 1.23164 | − | 1.23164i | ||||
\(959\) | −9.11573e6 | −0.320070 | ||||||||
\(960\) | −4.21503e6 | + | 4.21503e6i | −0.147612 | + | 0.147612i | ||||
\(961\) | −2.82878e7 | −0.988076 | ||||||||
\(962\) | 2.20590e7 | − | 2.20590e7i | 0.768508 | − | 0.768508i | ||||
\(963\) | 3.02489e7i | 1.05110i | ||||||||
\(964\) | − | 1.99898e6i | − | 0.0692813i | ||||||
\(965\) | −1.22267e7 | + | 1.22267e7i | −0.422658 | + | 0.422658i | ||||
\(966\) | 3.35563e6 | 0.115699 | ||||||||
\(967\) | −7.61422e6 | + | 7.61422e6i | −0.261854 | + | 0.261854i | −0.825807 | − | 0.563953i | \(-0.809280\pi\) |
0.563953 | + | 0.825807i | \(0.309280\pi\) | |||||||
\(968\) | −1.72421e7 | −0.591427 | ||||||||
\(969\) | −6.48649e6 | + | 6.48649e6i | −0.221922 | + | 0.221922i | ||||
\(970\) | −8.09644e6 | + | 8.09644e6i | −0.276290 | + | 0.276290i | ||||
\(971\) | −1.61275e7 | − | 1.61275e7i | −0.548933 | − | 0.548933i | 0.377199 | − | 0.926132i | \(-0.376887\pi\) |
−0.926132 | + | 0.377199i | \(0.876887\pi\) | |||||||
\(972\) | 908175. | + | 908175.i | 0.0308321 | + | 0.0308321i | ||||
\(973\) | 7.31765e6 | + | 7.31765e6i | 0.247793 | + | 0.247793i | ||||
\(974\) | 3.42653e7 | 1.15733 | ||||||||
\(975\) | − | 4.82254e6i | − | 0.162467i | ||||||
\(976\) | 1.68631e7i | 0.566646i | ||||||||
\(977\) | 1.59230e7 | + | 1.59230e7i | 0.533691 | + | 0.533691i | 0.921669 | − | 0.387978i | \(-0.126826\pi\) |
−0.387978 | + | 0.921669i | \(0.626826\pi\) | |||||||
\(978\) | −8.52201e6 | + | 8.52201e6i | −0.284901 | + | 0.284901i | ||||
\(979\) | − | 9.11859e6i | − | 0.304068i | ||||||
\(980\) | 1.21499e6 | 0.0404117 | ||||||||
\(981\) | 1.44650e6 | + | 1.44650e6i | 0.0479893 | + | 0.0479893i | ||||
\(982\) | − | 9.62359e6i | − | 0.318463i | ||||||
\(983\) | −1.62120e7 | −0.535121 | −0.267560 | − | 0.963541i | \(-0.586218\pi\) | ||||
−0.267560 | + | 0.963541i | \(0.586218\pi\) | |||||||
\(984\) | 8.46520e6 | + | 1.35295e6i | 0.278708 | + | 0.0445444i | ||||
\(985\) | 3.19141e7 | 1.04807 | ||||||||
\(986\) | 5.50707e7i | 1.80397i | ||||||||
\(987\) | −379604. | − | 379604.i | −0.0124033 | − | 0.0124033i | ||||
\(988\) | 1.89597e6 | 0.0617931 | ||||||||
\(989\) | 7.94041e7i | 2.58138i | ||||||||
\(990\) | −9.80400e6 | + | 9.80400e6i | −0.317918 | + | 0.317918i | ||||
\(991\) | 1.29471e7 | + | 1.29471e7i | 0.418781 | + | 0.418781i | 0.884783 | − | 0.466002i | \(-0.154306\pi\) |
−0.466002 | + | 0.884783i | \(0.654306\pi\) | |||||||
\(992\) | 379668.i | 0.0122497i | ||||||||
\(993\) | − | 6.63305e6i | − | 0.213471i | ||||||
\(994\) | 8.55659e6 | 0.274685 | ||||||||
\(995\) | −2.16144e7 | − | 2.16144e7i | −0.692126 | − | 0.692126i | ||||
\(996\) | 207310. | + | 207310.i | 0.00662172 | + | 0.00662172i | ||||
\(997\) | 1.26639e7 | + | 1.26639e7i | 0.403486 | + | 0.403486i | 0.879460 | − | 0.475973i | \(-0.157904\pi\) |
−0.475973 | + | 0.879460i | \(0.657904\pi\) | |||||||
\(998\) | −3.76278e7 | + | 3.76278e7i | −1.19586 | + | 1.19586i | ||||
\(999\) | −9.76319e6 | + | 9.76319e6i | −0.309512 | + | 0.309512i |
(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 | 41.6.c.a.9.5 | ✓ | 34 | |
41.32 | even | 4 | inner | 41.6.c.a.32.13 | yes | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
41.6.c.a.9.5 | ✓ | 34 | 1.1 | even | 1 | trivial | |
41.6.c.a.32.13 | yes | 34 | 41.32 | even | 4 | inner |