Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,6,Mod(67,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.67");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(23.5764215125\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{193})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 49x^{2} + 48x + 2304 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.2 | ||
Root | \(3.72311 + 6.44862i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.67 |
Dual form | 147.6.e.n.79.2 |
$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.22311 | + | 7.31464i | 0.746548 | + | 1.29306i | 0.949468 | + | 0.313863i | \(0.101623\pi\) |
−0.202921 | + | 0.979195i | \(0.565043\pi\) | |||||||
\(3\) | 4.50000 | − | 7.79423i | 0.288675 | − | 0.500000i | ||||
\(4\) | −19.6693 | + | 34.0683i | −0.614667 | + | 1.06463i | ||||
\(5\) | −18.0000 | − | 31.1769i | −0.321994 | − | 0.557710i | 0.658906 | − | 0.752226i | \(-0.271020\pi\) |
−0.980899 | + | 0.194516i | \(0.937686\pi\) | |||||||
\(6\) | 76.0160 | 0.862039 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −61.9840 | −0.342416 | ||||||||
\(9\) | −40.5000 | − | 70.1481i | −0.166667 | − | 0.288675i | ||||
\(10\) | 152.032 | − | 263.327i | 0.480767 | − | 0.832714i | ||||
\(11\) | −147.785 | + | 255.971i | −0.368255 | + | 0.637836i | −0.989293 | − | 0.145945i | \(-0.953378\pi\) |
0.621038 | + | 0.783780i | \(0.286711\pi\) | |||||||
\(12\) | 177.024 | + | 306.615i | 0.354878 | + | 0.614667i | ||||
\(13\) | 1148.13 | 1.88422 | 0.942111 | − | 0.335302i | \(-0.108838\pi\) | ||||
0.942111 | + | 0.335302i | \(0.108838\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −324.000 | −0.371806 | ||||||||
\(16\) | 367.653 | + | 636.794i | 0.359036 | + | 0.621869i | ||||
\(17\) | 516.192 | − | 894.071i | 0.433200 | − | 0.750325i | −0.563946 | − | 0.825811i | \(-0.690718\pi\) |
0.997147 | + | 0.0754862i | \(0.0240509\pi\) | |||||||
\(18\) | 342.072 | − | 592.486i | 0.248849 | − | 0.431019i | ||||
\(19\) | 1054.26 | + | 1826.02i | 0.669980 | + | 1.16044i | 0.977909 | + | 0.209031i | \(0.0670308\pi\) |
−0.307929 | + | 0.951409i | \(0.599636\pi\) | |||||||
\(20\) | 1416.19 | 0.791675 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2496.45 | −1.09968 | ||||||||
\(23\) | 320.494 | + | 555.112i | 0.126328 | + | 0.218807i | 0.922251 | − | 0.386591i | \(-0.126347\pi\) |
−0.795923 | + | 0.605398i | \(0.793014\pi\) | |||||||
\(24\) | −278.928 | + | 483.117i | −0.0988471 | + | 0.171208i | ||||
\(25\) | 914.500 | − | 1583.96i | 0.292640 | − | 0.506867i | ||||
\(26\) | 4848.67 | + | 8398.15i | 1.40666 | + | 2.43641i | ||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7631.58 | 1.68508 | 0.842538 | − | 0.538637i | \(-0.181060\pi\) | ||||
0.842538 | + | 0.538637i | \(0.181060\pi\) | |||||||
\(30\) | −1368.29 | − | 2369.94i | −0.277571 | − | 0.480767i | ||||
\(31\) | −483.488 | + | 837.426i | −0.0903611 | + | 0.156510i | −0.907663 | − | 0.419700i | \(-0.862135\pi\) |
0.817302 | + | 0.576210i | \(0.195469\pi\) | |||||||
\(32\) | −4097.03 | + | 7096.26i | −0.707284 | + | 1.22505i | ||||
\(33\) | 1330.06 | + | 2303.74i | 0.212612 | + | 0.368255i | ||||
\(34\) | 8719.74 | 1.29362 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3186.43 | 0.409778 | ||||||||
\(37\) | 886.605 | + | 1535.65i | 0.106470 | + | 0.184411i | 0.914338 | − | 0.404953i | \(-0.132712\pi\) |
−0.807868 | + | 0.589363i | \(0.799379\pi\) | |||||||
\(38\) | −8904.48 | + | 15423.0i | −1.00034 | + | 1.73265i | ||||
\(39\) | 5166.58 | − | 8948.77i | 0.543928 | − | 0.942111i | ||||
\(40\) | 1115.71 | + | 1932.47i | 0.110256 | + | 0.190969i | ||||
\(41\) | 11976.4 | 1.11267 | 0.556335 | − | 0.830958i | \(-0.312207\pi\) | ||||
0.556335 | + | 0.830958i | \(0.312207\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −19802.9 | −1.63327 | −0.816636 | − | 0.577153i | \(-0.804163\pi\) | ||||
−0.816636 | + | 0.577153i | \(0.804163\pi\) | |||||||
\(44\) | −5813.66 | − | 10069.6i | −0.452708 | − | 0.784113i | ||||
\(45\) | −1458.00 | + | 2525.33i | −0.107331 | + | 0.185903i | ||||
\(46\) | −2706.97 | + | 4688.60i | −0.188620 | + | 0.326700i | ||||
\(47\) | −13983.1 | − | 24219.4i | −0.923332 | − | 1.59926i | −0.794222 | − | 0.607628i | \(-0.792121\pi\) |
−0.129110 | − | 0.991630i | \(-0.541212\pi\) | |||||||
\(48\) | 6617.76 | 0.414580 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 15448.1 | 0.873879 | ||||||||
\(51\) | −4645.73 | − | 8046.64i | −0.250108 | − | 0.433200i | ||||
\(52\) | −22582.9 | + | 39114.8i | −1.15817 | + | 2.00601i | ||||
\(53\) | 3557.16 | − | 6161.19i | 0.173946 | − | 0.301283i | −0.765850 | − | 0.643019i | \(-0.777682\pi\) |
0.939796 | + | 0.341736i | \(0.111015\pi\) | |||||||
\(54\) | −3078.65 | − | 5332.37i | −0.143673 | − | 0.248849i | ||||
\(55\) | 10640.5 | 0.474303 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 18976.6 | 0.773627 | ||||||||
\(58\) | 32229.0 | + | 55822.3i | 1.25799 | + | 2.17890i | ||||
\(59\) | −10434.8 | + | 18073.5i | −0.390259 | + | 0.675948i | −0.992484 | − | 0.122379i | \(-0.960948\pi\) |
0.602225 | + | 0.798327i | \(0.294281\pi\) | |||||||
\(60\) | 6372.86 | − | 11038.1i | 0.228537 | − | 0.395838i | ||||
\(61\) | −11934.2 | − | 20670.6i | −0.410646 | − | 0.711259i | 0.584315 | − | 0.811527i | \(-0.301363\pi\) |
−0.994960 | + | 0.100268i | \(0.968030\pi\) | |||||||
\(62\) | −8167.30 | −0.269835 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −45679.0 | −1.39401 | ||||||||
\(65\) | −20666.3 | − | 35795.1i | −0.606708 | − | 1.05085i | ||||
\(66\) | −11234.0 | + | 19457.9i | −0.317450 | + | 0.549839i | ||||
\(67\) | −17335.8 | + | 30026.4i | −0.471798 | + | 0.817178i | −0.999479 | − | 0.0322646i | \(-0.989728\pi\) |
0.527682 | + | 0.849442i | \(0.323061\pi\) | |||||||
\(68\) | 20306.3 | + | 35171.5i | 0.532548 | + | 0.922400i | ||||
\(69\) | 5768.90 | 0.145871 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −28413.2 | −0.668921 | −0.334461 | − | 0.942410i | \(-0.608554\pi\) | ||||
−0.334461 | + | 0.942410i | \(0.608554\pi\) | |||||||
\(72\) | 2510.35 | + | 4348.06i | 0.0570694 | + | 0.0988471i | ||||
\(73\) | −7646.34 | + | 13243.8i | −0.167937 | + | 0.290875i | −0.937694 | − | 0.347461i | \(-0.887044\pi\) |
0.769757 | + | 0.638337i | \(0.220377\pi\) | |||||||
\(74\) | −7488.46 | + | 12970.4i | −0.158969 | + | 0.275343i | ||||
\(75\) | −8230.50 | − | 14255.6i | −0.168956 | − | 0.292640i | ||||
\(76\) | −82946.0 | −1.64726 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 87276.1 | 1.62427 | ||||||||
\(79\) | 36529.8 | + | 63271.4i | 0.658535 | + | 1.14062i | 0.980995 | + | 0.194033i | \(0.0621570\pi\) |
−0.322460 | + | 0.946583i | \(0.604510\pi\) | |||||||
\(80\) | 13235.5 | − | 22924.6i | 0.231215 | − | 0.400476i | ||||
\(81\) | −3280.50 | + | 5681.99i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 50577.6 | + | 87603.0i | 0.830661 | + | 1.43875i | ||||
\(83\) | 30340.9 | 0.483429 | 0.241715 | − | 0.970347i | \(-0.422290\pi\) | ||||
0.241715 | + | 0.970347i | \(0.422290\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −37165.8 | −0.557951 | ||||||||
\(86\) | −83630.0 | − | 144851.i | −1.21931 | − | 2.11192i | ||||
\(87\) | 34342.1 | − | 59482.3i | 0.486440 | − | 0.842538i | ||||
\(88\) | 9160.30 | − | 15866.1i | 0.126096 | − | 0.218406i | ||||
\(89\) | −18044.7 | − | 31254.4i | −0.241477 | − | 0.418250i | 0.719658 | − | 0.694328i | \(-0.244298\pi\) |
−0.961135 | + | 0.276078i | \(0.910965\pi\) | |||||||
\(90\) | −24629.2 | −0.320512 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −25215.6 | −0.310599 | ||||||||
\(93\) | 4351.39 | + | 7536.83i | 0.0521700 | + | 0.0903611i | ||||
\(94\) | 118104. | − | 204562.i | 1.37862 | − | 2.38784i | ||||
\(95\) | 37953.2 | − | 65736.9i | 0.431459 | − | 0.747309i | ||||
\(96\) | 36873.2 | + | 63866.3i | 0.408351 | + | 0.707284i | ||||
\(97\) | 153963. | 1.66145 | 0.830724 | − | 0.556685i | \(-0.187927\pi\) | ||||
0.830724 | + | 0.556685i | \(0.187927\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 23941.2 | 0.245503 | ||||||||
\(100\) | 35975.2 | + | 62310.9i | 0.359752 | + | 0.623109i | ||||
\(101\) | 69904.4 | − | 121078.i | 0.681869 | − | 1.18103i | −0.292541 | − | 0.956253i | \(-0.594501\pi\) |
0.974410 | − | 0.224779i | \(-0.0721659\pi\) | |||||||
\(102\) | 39238.8 | − | 67963.7i | 0.373436 | − | 0.646810i | ||||
\(103\) | −57962.7 | − | 100394.i | −0.538339 | − | 0.932430i | −0.998994 | − | 0.0448508i | \(-0.985719\pi\) |
0.460655 | − | 0.887579i | \(-0.347615\pi\) | |||||||
\(104\) | −71165.6 | −0.645188 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 60089.2 | 0.519436 | ||||||||
\(107\) | −41530.9 | − | 71933.6i | −0.350681 | − | 0.607397i | 0.635688 | − | 0.771946i | \(-0.280716\pi\) |
−0.986369 | + | 0.164549i | \(0.947383\pi\) | |||||||
\(108\) | 14338.9 | − | 24835.8i | 0.118293 | − | 0.204889i | ||||
\(109\) | −22678.1 | + | 39279.7i | −0.182827 | + | 0.316666i | −0.942842 | − | 0.333240i | \(-0.891858\pi\) |
0.760015 | + | 0.649906i | \(0.225192\pi\) | |||||||
\(110\) | 44936.1 | + | 77831.5i | 0.354090 | + | 0.613301i | ||||
\(111\) | 15958.9 | 0.122941 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −355.533 | −0.00261929 | −0.00130965 | − | 0.999999i | \(-0.500417\pi\) | ||||
−0.00130965 | + | 0.999999i | \(0.500417\pi\) | |||||||
\(114\) | 80140.3 | + | 138807.i | 0.577549 | + | 1.00034i | ||||
\(115\) | 11537.8 | − | 19984.0i | 0.0813538 | − | 0.140909i | ||||
\(116\) | −150108. | + | 259995.i | −1.03576 | + | 1.79399i | ||||
\(117\) | −46499.2 | − | 80538.9i | −0.314037 | − | 0.543928i | ||||
\(118\) | −176269. | −1.16539 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 20082.8 | 0.127313 | ||||||||
\(121\) | 36844.8 | + | 63817.0i | 0.228777 | + | 0.396253i | ||||
\(122\) | 100799. | − | 174588.i | 0.613133 | − | 1.06198i | ||||
\(123\) | 53893.7 | − | 93346.7i | 0.321200 | − | 0.556335i | ||||
\(124\) | −19019.8 | − | 32943.2i | −0.111084 | − | 0.192403i | ||||
\(125\) | −178344. | −1.02090 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 168967. | 0.929593 | 0.464797 | − | 0.885417i | \(-0.346127\pi\) | ||||
0.464797 | + | 0.885417i | \(0.346127\pi\) | |||||||
\(128\) | −61802.5 | − | 107045.i | −0.333412 | − | 0.577486i | ||||
\(129\) | −89113.2 | + | 154349.i | −0.471485 | + | 0.816636i | ||||
\(130\) | 174552. | − | 302333.i | 0.905872 | − | 1.56902i | ||||
\(131\) | −86984.6 | − | 150662.i | −0.442858 | − | 0.767052i | 0.555043 | − | 0.831822i | \(-0.312702\pi\) |
−0.997900 | + | 0.0647701i | \(0.979369\pi\) | |||||||
\(132\) | −104646. | −0.522742 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −292843. | −1.40888 | ||||||||
\(135\) | 13122.0 | + | 22728.0i | 0.0619677 | + | 0.107331i | ||||
\(136\) | −31995.6 | + | 55418.1i | −0.148335 | + | 0.256924i | ||||
\(137\) | −183862. | + | 318458.i | −0.836931 | + | 1.44961i | 0.0555168 | + | 0.998458i | \(0.482319\pi\) |
−0.892448 | + | 0.451150i | \(0.851014\pi\) | |||||||
\(138\) | 24362.7 | + | 42197.4i | 0.108900 | + | 0.188620i | ||||
\(139\) | −217967. | −0.956870 | −0.478435 | − | 0.878123i | \(-0.658796\pi\) | ||||
−0.478435 | + | 0.878123i | \(0.658796\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −251695. | −1.06617 | ||||||||
\(142\) | −119992. | − | 207833.i | −0.499381 | − | 0.864954i | ||||
\(143\) | −169676. | + | 293887.i | −0.693873 | + | 1.20182i | ||||
\(144\) | 29779.9 | − | 51580.3i | 0.119679 | − | 0.207290i | ||||
\(145\) | −137368. | − | 237929.i | −0.542584 | − | 0.939783i | ||||
\(146\) | −129165. | −0.501492 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −69755.7 | −0.261773 | ||||||||
\(149\) | 32453.0 | + | 56210.3i | 0.119754 | + | 0.207420i | 0.919670 | − | 0.392692i | \(-0.128456\pi\) |
−0.799916 | + | 0.600112i | \(0.795123\pi\) | |||||||
\(150\) | 69516.6 | − | 120406.i | 0.252267 | − | 0.436939i | ||||
\(151\) | 111889. | − | 193797.i | 0.399341 | − | 0.691678i | −0.594304 | − | 0.804240i | \(-0.702572\pi\) |
0.993645 | + | 0.112562i | \(0.0359057\pi\) | |||||||
\(152\) | −65347.0 | − | 113184.i | −0.229412 | − | 0.397354i | ||||
\(153\) | −83623.1 | −0.288800 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 34811.1 | 0.116383 | ||||||||
\(156\) | 203246. | + | 352033.i | 0.668669 | + | 1.15817i | ||||
\(157\) | −229986. | + | 398348.i | −0.744652 | + | 1.28977i | 0.205706 | + | 0.978614i | \(0.434051\pi\) |
−0.950357 | + | 0.311161i | \(0.899282\pi\) | |||||||
\(158\) | −308538. | + | 534404.i | −0.983256 | + | 1.70305i | ||||
\(159\) | −32014.5 | − | 55450.7i | −0.100428 | − | 0.173946i | ||||
\(160\) | 294986. | 0.910964 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −55415.7 | −0.165899 | ||||||||
\(163\) | −45534.3 | − | 78867.7i | −0.134236 | − | 0.232504i | 0.791069 | − | 0.611727i | \(-0.209525\pi\) |
−0.925305 | + | 0.379223i | \(0.876191\pi\) | |||||||
\(164\) | −235567. | + | 408015.i | −0.683921 | + | 1.18459i | ||||
\(165\) | 47882.3 | − | 82934.6i | 0.136919 | − | 0.237151i | ||||
\(166\) | 128133. | + | 221933.i | 0.360903 | + | 0.625103i | ||||
\(167\) | 314772. | 0.873384 | 0.436692 | − | 0.899611i | \(-0.356150\pi\) | ||||
0.436692 | + | 0.899611i | \(0.356150\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 946905. | 2.55029 | ||||||||
\(170\) | −156955. | − | 271855.i | −0.416537 | − | 0.721464i | ||||
\(171\) | 85394.7 | − | 147908.i | 0.223327 | − | 0.386813i | ||||
\(172\) | 389510. | − | 674652.i | 1.00392 | − | 1.73884i | ||||
\(173\) | −181071. | − | 313625.i | −0.459975 | − | 0.796701i | 0.538984 | − | 0.842316i | \(-0.318808\pi\) |
−0.998959 | + | 0.0456154i | \(0.985475\pi\) | |||||||
\(174\) | 580122. | 1.45260 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −217334. | −0.528867 | ||||||||
\(177\) | 93912.9 | + | 162662.i | 0.225316 | + | 0.390259i | ||||
\(178\) | 152410. | − | 263982.i | 0.360548 | − | 0.624487i | ||||
\(179\) | 86948.1 | − | 150599.i | 0.202828 | − | 0.351308i | −0.746611 | − | 0.665261i | \(-0.768320\pi\) |
0.949438 | + | 0.313953i | \(0.101653\pi\) | |||||||
\(180\) | −57355.8 | − | 99343.1i | −0.131946 | − | 0.228537i | ||||
\(181\) | −134973. | −0.306233 | −0.153116 | − | 0.988208i | \(-0.548931\pi\) | ||||
−0.153116 | + | 0.988208i | \(0.548931\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −214815. | −0.474173 | ||||||||
\(184\) | −19865.5 | − | 34408.1i | −0.0432569 | − | 0.0749231i | ||||
\(185\) | 31917.8 | − | 55283.2i | 0.0685652 | − | 0.118758i | ||||
\(186\) | −36752.8 | + | 63657.8i | −0.0778948 | + | 0.134918i | ||||
\(187\) | 152571. | + | 264260.i | 0.319056 | + | 0.552622i | ||||
\(188\) | 1.10015e6 | 2.27017 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 641123. | 1.28842 | ||||||||
\(191\) | −90706.7 | − | 157109.i | −0.179910 | − | 0.311614i | 0.761939 | − | 0.647648i | \(-0.224247\pi\) |
−0.941850 | + | 0.336035i | \(0.890914\pi\) | |||||||
\(192\) | −205555. | + | 356032.i | −0.402416 | + | 0.697006i | ||||
\(193\) | −482999. | + | 836579.i | −0.933369 | + | 1.61664i | −0.155851 | + | 0.987781i | \(0.549812\pi\) |
−0.777517 | + | 0.628861i | \(0.783521\pi\) | |||||||
\(194\) | 650202. | + | 1.12618e6i | 1.24035 | + | 2.14835i | ||||
\(195\) | −371993. | −0.700566 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −699058. | −1.28336 | −0.641679 | − | 0.766974i | \(-0.721762\pi\) | ||||
−0.641679 | + | 0.766974i | \(0.721762\pi\) | |||||||
\(198\) | 101106. | + | 175121.i | 0.183280 | + | 0.317450i | ||||
\(199\) | −208095. | + | 360432.i | −0.372503 | + | 0.645194i | −0.989950 | − | 0.141419i | \(-0.954834\pi\) |
0.617447 | + | 0.786612i | \(0.288167\pi\) | |||||||
\(200\) | −56684.4 | + | 98180.2i | −0.100205 | + | 0.173560i | ||||
\(201\) | 156022. | + | 270238.i | 0.272393 | + | 0.471798i | ||||
\(202\) | 1.18086e6 | 2.03619 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 365513. | 0.614933 | ||||||||
\(205\) | −215575. | − | 373387.i | −0.358273 | − | 0.620546i | ||||
\(206\) | 489566. | − | 847953.i | 0.803791 | − | 1.39221i | ||||
\(207\) | 25960.0 | − | 44964.1i | 0.0421094 | − | 0.0729357i | ||||
\(208\) | 422113. | + | 731121.i | 0.676504 | + | 1.17174i | ||||
\(209\) | −623212. | −0.986894 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −407152. | −0.629580 | −0.314790 | − | 0.949161i | \(-0.601934\pi\) | ||||
−0.314790 | + | 0.949161i | \(0.601934\pi\) | |||||||
\(212\) | 139934. | + | 242373.i | 0.213837 | + | 0.370377i | ||||
\(213\) | −127860. | + | 221459.i | −0.193101 | + | 0.334461i | ||||
\(214\) | 350779. | − | 607567.i | 0.523600 | − | 0.906901i | ||||
\(215\) | 356453. | + | 617394.i | 0.525903 | + | 0.910891i | ||||
\(216\) | 45186.3 | 0.0658981 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −383089. | −0.545957 | ||||||||
\(219\) | 68817.0 | + | 119195.i | 0.0969584 | + | 0.167937i | ||||
\(220\) | −209292. | + | 362504.i | −0.291538 | + | 0.504959i | ||||
\(221\) | 592654. | − | 1.02651e6i | 0.816246 | − | 1.41378i | ||||
\(222\) | 67396.2 | + | 116734.i | 0.0917810 | + | 0.158969i | ||||
\(223\) | −882022. | −1.18773 | −0.593865 | − | 0.804565i | \(-0.702398\pi\) | ||||
−0.593865 | + | 0.804565i | \(0.702398\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −148149. | −0.195093 | ||||||||
\(226\) | −1501.45 | − | 2600.60i | −0.00195542 | − | 0.00338690i | ||||
\(227\) | −563251. | + | 975579.i | −0.725499 | + | 1.25660i | 0.233269 | + | 0.972412i | \(0.425058\pi\) |
−0.958768 | + | 0.284189i | \(0.908276\pi\) | |||||||
\(228\) | −373257. | + | 646500.i | −0.475523 | + | 0.823629i | ||||
\(229\) | 155042. | + | 268541.i | 0.195371 | + | 0.338393i | 0.947022 | − | 0.321168i | \(-0.104075\pi\) |
−0.751651 | + | 0.659561i | \(0.770742\pi\) | |||||||
\(230\) | 194902. | 0.242938 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −473036. | −0.576998 | ||||||||
\(233\) | −568268. | − | 984268.i | −0.685746 | − | 1.18775i | −0.973202 | − | 0.229953i | \(-0.926143\pi\) |
0.287456 | − | 0.957794i | \(-0.407190\pi\) | |||||||
\(234\) | 392742. | − | 680250.i | 0.468887 | − | 0.812136i | ||||
\(235\) | −503391. | + | 871898.i | −0.594614 | + | 1.02990i | ||||
\(236\) | −410490. | − | 710989.i | −0.479758 | − | 0.830966i | ||||
\(237\) | 657536. | 0.760411 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 87506.8 | 0.0990940 | 0.0495470 | − | 0.998772i | \(-0.484222\pi\) | ||||
0.0495470 | + | 0.998772i | \(0.484222\pi\) | |||||||
\(240\) | −119120. | − | 206321.i | −0.133492 | − | 0.231215i | ||||
\(241\) | 268884. | − | 465721.i | 0.298210 | − | 0.516515i | −0.677516 | − | 0.735508i | \(-0.736944\pi\) |
0.975727 | + | 0.218992i | \(0.0702770\pi\) | |||||||
\(242\) | −311199. | + | 539012.i | −0.341586 | + | 0.591644i | ||||
\(243\) | 29524.5 | + | 51137.9i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 938948. | 1.00964 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 910397. | 0.959164 | ||||||||
\(247\) | 1.21042e6 | + | 2.09651e6i | 1.26239 | + | 2.18653i | ||||
\(248\) | 29968.5 | − | 51907.0i | 0.0309411 | − | 0.0535916i | ||||
\(249\) | 136534. | − | 236484.i | 0.139554 | − | 0.241715i | ||||
\(250\) | −753167. | − | 1.30452e6i | −0.762151 | − | 1.32008i | ||||
\(251\) | −1.35353e6 | −1.35607 | −0.678036 | − | 0.735028i | \(-0.737169\pi\) | ||||
−0.678036 | + | 0.735028i | \(0.737169\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −189457. | −0.186084 | ||||||||
\(254\) | 713567. | + | 1.23593e6i | 0.693986 | + | 1.20202i | ||||
\(255\) | −167246. | + | 289679.i | −0.161067 | + | 0.278976i | ||||
\(256\) | −208866. | + | 361766.i | −0.199190 | + | 0.345007i | ||||
\(257\) | −488450. | − | 846020.i | −0.461304 | − | 0.799002i | 0.537722 | − | 0.843122i | \(-0.319285\pi\) |
−0.999026 | + | 0.0441199i | \(0.985952\pi\) | |||||||
\(258\) | −1.50534e6 | −1.40794 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.62597e6 | 1.49169 | ||||||||
\(261\) | −309079. | − | 535341.i | −0.280846 | − | 0.486440i | ||||
\(262\) | 734691. | − | 1.27252e6i | 0.661229 | − | 1.14528i | ||||
\(263\) | 621874. | − | 1.07712e6i | 0.554387 | − | 0.960227i | −0.443564 | − | 0.896243i | \(-0.646286\pi\) |
0.997951 | − | 0.0639842i | \(-0.0203807\pi\) | |||||||
\(264\) | −82442.7 | − | 142795.i | −0.0728018 | − | 0.126096i | ||||
\(265\) | −256116. | −0.224038 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −324805. | −0.278833 | ||||||||
\(268\) | −681966. | − | 1.18120e6i | −0.579997 | − | 1.00458i | ||||
\(269\) | −542042. | + | 938844.i | −0.456722 | + | 0.791066i | −0.998785 | − | 0.0492716i | \(-0.984310\pi\) |
0.542063 | + | 0.840338i | \(0.317643\pi\) | |||||||
\(270\) | −110831. | + | 191965.i | −0.0925237 | + | 0.160256i | ||||
\(271\) | −1.08314e6 | − | 1.87605e6i | −0.895900 | − | 1.55174i | −0.832687 | − | 0.553744i | \(-0.813199\pi\) |
−0.0632128 | − | 0.998000i | \(-0.520135\pi\) | |||||||
\(272\) | 759119. | 0.622139 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.10587e6 | −2.49924 | ||||||||
\(275\) | 270299. | + | 468171.i | 0.215532 | + | 0.373313i | ||||
\(276\) | −113470. | + | 196536.i | −0.0896622 | + | 0.155300i | ||||
\(277\) | −126929. | + | 219848.i | −0.0993946 | + | 0.172157i | −0.911434 | − | 0.411446i | \(-0.865024\pi\) |
0.812040 | + | 0.583602i | \(0.198357\pi\) | |||||||
\(278\) | −920497. | − | 1.59435e6i | −0.714349 | − | 1.23729i | ||||
\(279\) | 78325.1 | 0.0602407 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.14116e6 | 0.862143 | 0.431072 | − | 0.902318i | \(-0.358136\pi\) | ||||
0.431072 | + | 0.902318i | \(0.358136\pi\) | |||||||
\(282\) | −1.06294e6 | − | 1.84106e6i | −0.795948 | − | 1.37862i | ||||
\(283\) | −304959. | + | 528204.i | −0.226347 | + | 0.392045i | −0.956723 | − | 0.291001i | \(-0.906012\pi\) |
0.730376 | + | 0.683046i | \(0.239345\pi\) | |||||||
\(284\) | 558870. | − | 967990.i | 0.411164 | − | 0.712156i | ||||
\(285\) | −341579. | − | 591632.i | −0.249103 | − | 0.431459i | ||||
\(286\) | −2.86624e6 | −2.07204 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 663718. | 0.471523 | ||||||||
\(289\) | 177020. | + | 306608.i | 0.124675 | + | 0.215943i | ||||
\(290\) | 1.16024e6 | − | 2.00960e6i | 0.810130 | − | 1.40319i | ||||
\(291\) | 692833. | − | 1.20002e6i | 0.479618 | − | 0.830724i | ||||
\(292\) | −300797. | − | 520995.i | −0.206450 | − | 0.357583i | ||||
\(293\) | −156438. | −0.106457 | −0.0532283 | − | 0.998582i | \(-0.516951\pi\) | ||||
−0.0532283 | + | 0.998582i | \(0.516951\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 751303. | 0.502644 | ||||||||
\(296\) | −54955.3 | − | 95185.4i | −0.0364570 | − | 0.0631453i | ||||
\(297\) | 107735. | − | 186603.i | 0.0708707 | − | 0.122752i | ||||
\(298\) | −274106. | + | 474765.i | −0.178804 | + | 0.309698i | ||||
\(299\) | 367968. | + | 637340.i | 0.238030 | + | 0.412281i | ||||
\(300\) | 647554. | 0.415406 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.89007e6 | 1.19251 | ||||||||
\(303\) | −629139. | − | 1.08970e6i | −0.393677 | − | 0.681869i | ||||
\(304\) | −775201. | + | 1.34269e6i | −0.481095 | + | 0.833281i | ||||
\(305\) | −429630. | + | 744141.i | −0.264451 | + | 0.458042i | ||||
\(306\) | −353150. | − | 611673.i | −0.215603 | − | 0.373436i | ||||
\(307\) | −293229. | −0.177566 | −0.0887831 | − | 0.996051i | \(-0.528298\pi\) | ||||
−0.0887831 | + | 0.996051i | \(0.528298\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.04333e6 | −0.621620 | ||||||||
\(310\) | 147011. | + | 254631.i | 0.0868853 | + | 0.150490i | ||||
\(311\) | 1.22608e6 | − | 2.12363e6i | 0.718816 | − | 1.24503i | −0.242653 | − | 0.970113i | \(-0.578018\pi\) |
0.961469 | − | 0.274913i | \(-0.0886491\pi\) | |||||||
\(312\) | −320245. | + | 554681.i | −0.186250 | + | 0.322594i | ||||
\(313\) | 917705. | + | 1.58951e6i | 0.529471 | + | 0.917071i | 0.999409 | + | 0.0343716i | \(0.0109430\pi\) |
−0.469938 | + | 0.882700i | \(0.655724\pi\) | |||||||
\(314\) | −3.88503e6 | −2.22367 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.87406e6 | −1.61912 | ||||||||
\(317\) | −294980. | − | 510920.i | −0.164871 | − | 0.285565i | 0.771738 | − | 0.635940i | \(-0.219387\pi\) |
−0.936609 | + | 0.350375i | \(0.886054\pi\) | |||||||
\(318\) | 270401. | − | 468349.i | 0.149948 | − | 0.259718i | ||||
\(319\) | −1.12783e6 | + | 1.95346e6i | −0.620537 | + | 1.07480i | ||||
\(320\) | 822221. | + | 1.42413e6i | 0.448863 | + | 0.777454i | ||||
\(321\) | −747556. | −0.404931 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.17679e6 | 1.16094 | ||||||||
\(324\) | −129050. | − | 223522.i | −0.0682963 | − | 0.118293i | ||||
\(325\) | 1.04996e6 | − | 1.81859e6i | 0.551399 | − | 0.955050i | ||||
\(326\) | 384593. | − | 666134.i | 0.200427 | − | 0.347151i | ||||
\(327\) | 204103. | + | 353517.i | 0.105555 | + | 0.182827i | ||||
\(328\) | −742344. | −0.380996 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 808849. | 0.408868 | ||||||||
\(331\) | −88659.2 | − | 153562.i | −0.0444789 | − | 0.0770396i | 0.842929 | − | 0.538025i | \(-0.180829\pi\) |
−0.887408 | + | 0.460985i | \(0.847496\pi\) | |||||||
\(332\) | −596785. | + | 1.03366e6i | −0.297148 | + | 0.514675i | ||||
\(333\) | 71815.0 | − | 124387.i | 0.0354899 | − | 0.0614703i | ||||
\(334\) | 1.32932e6 | + | 2.30245e6i | 0.652023 | + | 1.12934i | ||||
\(335\) | 1.24817e6 | 0.607664 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.04781e6 | −1.46189 | −0.730943 | − | 0.682438i | \(-0.760920\pi\) | ||||
−0.730943 | + | 0.682438i | \(0.760920\pi\) | |||||||
\(338\) | 3.99888e6 | + | 6.92627e6i | 1.90391 | + | 3.29767i | ||||
\(339\) | −1599.90 | + | 2771.10i | −0.000756124 | + | 0.00130965i | ||||
\(340\) | 731027. | − | 1.26618e6i | 0.342954 | − | 0.594014i | ||||
\(341\) | −142904. | − | 247518.i | −0.0665518 | − | 0.115271i | ||||
\(342\) | 1.44253e6 | 0.666896 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.22747e6 | 0.559259 | ||||||||
\(345\) | −103840. | − | 179856.i | −0.0469697 | − | 0.0813538i | ||||
\(346\) | 1.52937e6 | − | 2.64895e6i | 0.686787 | − | 1.18955i | ||||
\(347\) | 1.21180e6 | − | 2.09891e6i | 0.540268 | − | 0.935771i | −0.458621 | − | 0.888632i | \(-0.651656\pi\) |
0.998888 | − | 0.0471388i | \(-0.0150103\pi\) | |||||||
\(348\) | 1.35097e6 | + | 2.33995e6i | 0.597996 | + | 1.03576i | ||||
\(349\) | 2.67690e6 | 1.17644 | 0.588218 | − | 0.808702i | \(-0.299830\pi\) | ||||
0.588218 | + | 0.808702i | \(0.299830\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −836985. | −0.362619 | ||||||||
\(352\) | −1.21096e6 | − | 2.09744e6i | −0.520921 | − | 0.902262i | ||||
\(353\) | 475206. | − | 823081.i | 0.202976 | − | 0.351565i | −0.746510 | − | 0.665374i | \(-0.768272\pi\) |
0.949486 | + | 0.313809i | \(0.101605\pi\) | |||||||
\(354\) | −793209. | + | 1.37388e6i | −0.336418 | + | 0.582694i | ||||
\(355\) | 511438. | + | 885837.i | 0.215388 | + | 0.373064i | ||||
\(356\) | 1.41971e6 | 0.593711 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.46877e6 | 0.605683 | ||||||||
\(359\) | −1.39441e6 | − | 2.41518e6i | −0.571022 | − | 0.989039i | −0.996461 | − | 0.0840524i | \(-0.973214\pi\) |
0.425439 | − | 0.904987i | \(-0.360120\pi\) | |||||||
\(360\) | 90372.7 | − | 156530.i | 0.0367520 | − | 0.0636563i | ||||
\(361\) | −984862. | + | 1.70583e6i | −0.397747 | + | 0.688919i | ||||
\(362\) | −570007. | − | 987282.i | −0.228617 | − | 0.395977i | ||||
\(363\) | 663206. | 0.264169 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 550536. | 0.216299 | ||||||||
\(366\) | −907187. | − | 1.57129e6i | −0.353993 | − | 0.613133i | ||||
\(367\) | 76940.7 | − | 133265.i | 0.0298189 | − | 0.0516478i | −0.850731 | − | 0.525602i | \(-0.823840\pi\) |
0.880550 | + | 0.473954i | \(0.157174\pi\) | |||||||
\(368\) | −235662. | + | 408178.i | −0.0907129 | + | 0.157119i | ||||
\(369\) | −485044. | − | 840120.i | −0.185445 | − | 0.321200i | ||||
\(370\) | 539169. | 0.204749 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −342356. | −0.128269 | ||||||||
\(373\) | 1.19191e6 | + | 2.06444e6i | 0.443578 | + | 0.768299i | 0.997952 | − | 0.0639683i | \(-0.0203757\pi\) |
−0.554374 | + | 0.832268i | \(0.687042\pi\) | |||||||
\(374\) | −1.28865e6 | + | 2.23200e6i | −0.476381 | + | 0.825117i | ||||
\(375\) | −802548. | + | 1.39005e6i | −0.294709 | + | 0.510450i | ||||
\(376\) | 866727. | + | 1.50121e6i | 0.316164 | + | 0.547612i | ||||
\(377\) | 8.76203e6 | 3.17506 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.65191e6 | 1.30594 | 0.652969 | − | 0.757385i | \(-0.273523\pi\) | ||||
0.652969 | + | 0.757385i | \(0.273523\pi\) | |||||||
\(380\) | 1.49303e6 | + | 2.58600e6i | 0.530407 | + | 0.918692i | ||||
\(381\) | 760352. | − | 1.31697e6i | 0.268350 | − | 0.464797i | ||||
\(382\) | 766129. | − | 1.32697e6i | 0.268623 | − | 0.465269i | ||||
\(383\) | 1.07865e6 | + | 1.86827e6i | 0.375736 | + | 0.650794i | 0.990437 | − | 0.137967i | \(-0.0440566\pi\) |
−0.614701 | + | 0.788760i | \(0.710723\pi\) | |||||||
\(384\) | −1.11245e6 | −0.384991 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.15904e6 | −2.78722 | ||||||||
\(387\) | 802019. | + | 1.38914e6i | 0.272212 | + | 0.471485i | ||||
\(388\) | −3.02835e6 | + | 5.24525e6i | −1.02124 | + | 1.76883i | ||||
\(389\) | 1.83236e6 | − | 3.17373e6i | 0.613954 | − | 1.06340i | −0.376613 | − | 0.926371i | \(-0.622911\pi\) |
0.990567 | − | 0.137029i | \(-0.0437553\pi\) | |||||||
\(390\) | −1.57097e6 | − | 2.72100e6i | −0.523006 | − | 0.905872i | ||||
\(391\) | 661746. | 0.218902 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.56572e6 | −0.511368 | ||||||||
\(394\) | −2.95220e6 | − | 5.11336e6i | −0.958087 | − | 1.65946i | ||||
\(395\) | 1.31507e6 | − | 2.27777e6i | 0.424089 | − | 0.734543i | ||||
\(396\) | −470906. | + | 815634.i | −0.150903 | + | 0.261371i | ||||
\(397\) | −1.97324e6 | − | 3.41775e6i | −0.628353 | − | 1.08834i | −0.987882 | − | 0.155205i | \(-0.950396\pi\) |
0.359529 | − | 0.933134i | \(-0.382937\pi\) | |||||||
\(398\) | −3.51524e6 | −1.11236 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.34488e6 | 0.420274 | ||||||||
\(401\) | −12508.0 | − | 21664.5i | −0.00388444 | − | 0.00672804i | 0.864077 | − | 0.503360i | \(-0.167903\pi\) |
−0.867961 | + | 0.496632i | \(0.834570\pi\) | |||||||
\(402\) | −1.31780e6 | + | 2.28249e6i | −0.406708 | + | 0.704439i | ||||
\(403\) | −555106. | + | 961472.i | −0.170260 | + | 0.294900i | ||||
\(404\) | 2.74994e6 | + | 4.76304e6i | 0.838244 | + | 1.45188i | ||||
\(405\) | 236196. | 0.0715542 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −524107. | −0.156832 | ||||||||
\(408\) | 287961. | + | 498763.i | 0.0856412 | + | 0.148335i | ||||
\(409\) | 416350. | − | 721139.i | 0.123069 | − | 0.213163i | −0.797907 | − | 0.602780i | \(-0.794060\pi\) |
0.920977 | + | 0.389618i | \(0.127393\pi\) | |||||||
\(410\) | 1.82079e6 | − | 3.15371e6i | 0.534935 | − | 0.926535i | ||||
\(411\) | 1.65476e6 | + | 2.86612e6i | 0.483203 | + | 0.836931i | ||||
\(412\) | 4.56035e6 | 1.32360 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 438528. | 0.125747 | ||||||||
\(415\) | −546136. | − | 945935.i | −0.155661 | − | 0.269613i | ||||
\(416\) | −4.70391e6 | + | 8.14741e6i | −1.33268 | + | 2.30827i | ||||
\(417\) | −980850. | + | 1.69888e6i | −0.276225 | + | 0.478435i | ||||
\(418\) | −2.63190e6 | − | 4.55858e6i | −0.736763 | − | 1.27611i | ||||
\(419\) | −3.95178e6 | −1.09966 | −0.549828 | − | 0.835278i | \(-0.685307\pi\) | ||||
−0.549828 | + | 0.835278i | \(0.685307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.72285e6 | 1.29867 | 0.649336 | − | 0.760502i | \(-0.275047\pi\) | ||||
0.649336 | + | 0.760502i | \(0.275047\pi\) | |||||||
\(422\) | −1.71945e6 | − | 2.97817e6i | −0.470011 | − | 0.814084i | ||||
\(423\) | −1.13263e6 | + | 1.96177e6i | −0.307777 | + | 0.533086i | ||||
\(424\) | −220487. | + | 381895.i | −0.0595619 | + | 0.103164i | ||||
\(425\) | −944115. | − | 1.63526e6i | −0.253544 | − | 0.439150i | ||||
\(426\) | −2.15986e6 | −0.576636 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3.26754e6 | 0.862207 | ||||||||
\(429\) | 1.52708e6 | + | 2.64499e6i | 0.400608 | + | 0.693873i | ||||
\(430\) | −3.01068e6 | + | 5.21465e6i | −0.785224 | + | 1.36005i | ||||
\(431\) | −2.03905e6 | + | 3.53174e6i | −0.528731 | + | 0.915789i | 0.470708 | + | 0.882289i | \(0.343999\pi\) |
−0.999439 | + | 0.0334995i | \(0.989335\pi\) | |||||||
\(432\) | −268019. | − | 464223.i | −0.0690966 | − | 0.119679i | ||||
\(433\) | 1.79927e6 | 0.461186 | 0.230593 | − | 0.973050i | \(-0.425933\pi\) | ||||
0.230593 | + | 0.973050i | \(0.425933\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.47263e6 | −0.626522 | ||||||||
\(436\) | −892127. | − | 1.54521e6i | −0.224756 | − | 0.389288i | ||||
\(437\) | −675766. | + | 1.17046e6i | −0.169275 | + | 0.293193i | ||||
\(438\) | −581244. | + | 1.00674e6i | −0.144768 | + | 0.250746i | ||||
\(439\) | 2.25913e6 | + | 3.91293e6i | 0.559475 | + | 0.969039i | 0.997540 | + | 0.0700959i | \(0.0223305\pi\) |
−0.438065 | + | 0.898943i | \(0.644336\pi\) | |||||||
\(440\) | −659542. | −0.162409 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.00114e7 | 2.43746 | ||||||||
\(443\) | 1.42628e6 | + | 2.47039e6i | 0.345299 | + | 0.598075i | 0.985408 | − | 0.170209i | \(-0.0544443\pi\) |
−0.640109 | + | 0.768284i | \(0.721111\pi\) | |||||||
\(444\) | −313901. | + | 543692.i | −0.0755675 | + | 0.130887i | ||||
\(445\) | −649611. | + | 1.12516e6i | −0.155508 | + | 0.269348i | ||||
\(446\) | −3.72488e6 | − | 6.45168e6i | −0.886696 | − | 1.53580i | ||||
\(447\) | 584155. | 0.138280 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.90246e6 | −0.445348 | −0.222674 | − | 0.974893i | \(-0.571478\pi\) | ||||
−0.222674 | + | 0.974893i | \(0.571478\pi\) | |||||||
\(450\) | −625650. | − | 1.08366e6i | −0.145646 | − | 0.252267i | ||||
\(451\) | −1.76993e6 | + | 3.06561e6i | −0.409746 | + | 0.709700i | ||||
\(452\) | 6993.09 | − | 12112.4i | 0.00160999 | − | 0.00278859i | ||||
\(453\) | −1.00700e6 | − | 1.74417e6i | −0.230559 | − | 0.399341i | ||||
\(454\) | −9.51468e6 | −2.16648 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.17625e6 | −0.264903 | ||||||||
\(457\) | −1.32417e6 | − | 2.29353e6i | −0.296588 | − | 0.513705i | 0.678765 | − | 0.734355i | \(-0.262515\pi\) |
−0.975353 | + | 0.220650i | \(0.929182\pi\) | |||||||
\(458\) | −1.30952e6 | + | 2.26815e6i | −0.291708 | + | 0.505253i | ||||
\(459\) | −376304. | + | 651778.i | −0.0833695 | + | 0.144400i | ||||
\(460\) | 453881. | + | 786146.i | 0.100011 | + | 0.173224i | ||||
\(461\) | −1.09031e6 | −0.238944 | −0.119472 | − | 0.992838i | \(-0.538120\pi\) | ||||
−0.119472 | + | 0.992838i | \(0.538120\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.50851e6 | −0.543831 | −0.271916 | − | 0.962321i | \(-0.587657\pi\) | ||||
−0.271916 | + | 0.962321i | \(0.587657\pi\) | |||||||
\(464\) | 2.80578e6 | + | 4.85975e6i | 0.605004 | + | 1.04790i | ||||
\(465\) | 156650. | − | 271326.i | 0.0335968 | − | 0.0581914i | ||||
\(466\) | 4.79971e6 | − | 8.31335e6i | 1.02388 | − | 1.77342i | ||||
\(467\) | −1.60468e6 | − | 2.77938e6i | −0.340483 | − | 0.589734i | 0.644040 | − | 0.764992i | \(-0.277257\pi\) |
−0.984522 | + | 0.175259i | \(0.943924\pi\) | |||||||
\(468\) | 3.65843e6 | 0.772112 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −8.50350e6 | −1.77563 | ||||||||
\(471\) | 2.06988e6 | + | 3.58513e6i | 0.429925 | + | 0.744652i | ||||
\(472\) | 646789. | − | 1.12027e6i | 0.133631 | − | 0.231456i | ||||
\(473\) | 2.92657e6 | − | 5.06898e6i | 0.601460 | − | 1.04176i | ||||
\(474\) | 2.77685e6 | + | 4.80964e6i | 0.567683 | + | 0.983256i | ||||
\(475\) | 3.85647e6 | 0.784252 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −576260. | −0.115964 | ||||||||
\(478\) | 369551. | + | 640081.i | 0.0739784 | + | 0.128134i | ||||
\(479\) | 1.15731e6 | − | 2.00452e6i | 0.230468 | − | 0.399182i | −0.727478 | − | 0.686131i | \(-0.759308\pi\) |
0.957946 | + | 0.286949i | \(0.0926410\pi\) | |||||||
\(480\) | 1.32744e6 | − | 2.29919e6i | 0.262973 | − | 0.455482i | ||||
\(481\) | 1.01794e6 | + | 1.76312e6i | 0.200612 | + | 0.347471i | ||||
\(482\) | 4.54211e6 | 0.890513 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.89885e6 | −0.562486 | ||||||||
\(485\) | −2.77133e6 | − | 4.80009e6i | −0.534976 | − | 0.926605i | ||||
\(486\) | −249370. | + | 431922.i | −0.0478911 | + | 0.0829497i | ||||
\(487\) | 2.31867e6 | − | 4.01606e6i | 0.443014 | − | 0.767322i | −0.554898 | − | 0.831919i | \(-0.687243\pi\) |
0.997911 | + | 0.0645962i | \(0.0205759\pi\) | |||||||
\(488\) | 739727. | + | 1.28124e6i | 0.140612 | + | 0.243547i | ||||
\(489\) | −819618. | −0.155003 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.02151e6 | 0.940007 | 0.470003 | − | 0.882665i | \(-0.344253\pi\) | ||||
0.470003 | + | 0.882665i | \(0.344253\pi\) | |||||||
\(492\) | 2.12011e6 | + | 3.67213e6i | 0.394862 | + | 0.683921i | ||||
\(493\) | 3.93936e6 | − | 6.82317e6i | 0.729976 | − | 1.26436i | ||||
\(494\) | −1.02235e7 | + | 1.77076e7i | −1.88487 | + | 3.26469i | ||||
\(495\) | −430941. | − | 746411.i | −0.0790505 | − | 0.136919i | ||||
\(496\) | −711024. | −0.129772 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2.30639e6 | 0.416735 | ||||||||
\(499\) | −1.68911e6 | − | 2.92562e6i | −0.303673 | − | 0.525978i | 0.673292 | − | 0.739377i | \(-0.264880\pi\) |
−0.976965 | + | 0.213399i | \(0.931546\pi\) | |||||||
\(500\) | 3.50791e6 | − | 6.07587e6i | 0.627514 | − | 1.08689i | ||||
\(501\) | 1.41648e6 | − | 2.45341e6i | 0.252124 | − | 0.436692i | ||||
\(502\) | −5.71610e6 | − | 9.90057e6i | −1.01237 | − | 1.75348i | ||||
\(503\) | −5.03743e6 | −0.887747 | −0.443873 | − | 0.896090i | \(-0.646396\pi\) | ||||
−0.443873 | + | 0.896090i | \(0.646396\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.03311e6 | −0.878230 | ||||||||
\(506\) | −800097. | − | 1.38581e6i | −0.138921 | − | 0.240617i | ||||
\(507\) | 4.26107e6 | − | 7.38039e6i | 0.736205 | − | 1.27515i | ||||
\(508\) | −3.32347e6 | + | 5.75642e6i | −0.571390 | + | 0.989677i | ||||
\(509\) | 3.36233e6 | + | 5.82373e6i | 0.575236 | + | 0.996338i | 0.996016 | + | 0.0891752i | \(0.0284231\pi\) |
−0.420780 | + | 0.907163i | \(0.638244\pi\) | |||||||
\(510\) | −2.82520e6 | −0.480976 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −7.48361e6 | −1.26164 | ||||||||
\(513\) | −768553. | − | 1.33117e6i | −0.128938 | − | 0.223327i | ||||
\(514\) | 4.12556e6 | − | 7.14568e6i | 0.688771 | − | 1.19299i | ||||
\(515\) | −2.08666e6 | + | 3.61420e6i | −0.346684 | + | 0.600473i | ||||
\(516\) | −3.50559e6 | − | 6.07187e6i | −0.579612 | − | 1.00392i | ||||
\(517\) | 8.26595e6 | 1.36009 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.25929e6 | −0.531134 | ||||||||
\(520\) | 1.28098e6 | + | 2.21872e6i | 0.207747 | + | 0.359828i | ||||
\(521\) | 2.21385e6 | − | 3.83450e6i | 0.357317 | − | 0.618892i | −0.630194 | − | 0.776437i | \(-0.717025\pi\) |
0.987512 | + | 0.157546i | \(0.0503582\pi\) | |||||||
\(522\) | 2.61055e6 | − | 4.52161e6i | 0.419330 | − | 0.726301i | ||||
\(523\) | 4.47955e6 | + | 7.75882e6i | 0.716111 | + | 1.24034i | 0.962529 | + | 0.271178i | \(0.0874131\pi\) |
−0.246418 | + | 0.969164i | \(0.579254\pi\) | |||||||
\(524\) | 6.84372e6 | 1.08884 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.05050e7 | 1.65551 | ||||||||
\(527\) | 499145. | + | 864545.i | 0.0782889 | + | 0.135600i | ||||
\(528\) | −978005. | + | 1.69395e6i | −0.152671 | + | 0.264434i | ||||
\(529\) | 3.01274e6 | − | 5.21822e6i | 0.468082 | − | 0.810742i | ||||
\(530\) | −1.08161e6 | − | 1.87340e6i | −0.167255 | − | 0.289694i | ||||
\(531\) | 1.69043e6 | 0.260173 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.37504e7 | 2.09652 | ||||||||
\(534\) | −1.37169e6 | − | 2.37583e6i | −0.208162 | − | 0.360548i | ||||
\(535\) | −1.49511e6 | + | 2.58961e6i | −0.225834 | + | 0.391156i | ||||
\(536\) | 1.07454e6 | − | 1.86116e6i | 0.161551 | − | 0.279815i | ||||
\(537\) | −782533. | − | 1.35539e6i | −0.117103 | − | 0.202828i | ||||
\(538\) | −9.15641e6 | −1.36386 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.03240e6 | −0.152358 | ||||||||
\(541\) | 5.02337e6 | + | 8.70073e6i | 0.737907 | + | 1.27809i | 0.953436 | + | 0.301595i | \(0.0975192\pi\) |
−0.215529 | + | 0.976498i | \(0.569147\pi\) | |||||||
\(542\) | 9.14840e6 | − | 1.58455e7i | 1.33766 | − | 2.31690i | ||||
\(543\) | −607380. | + | 1.05201e6i | −0.0884018 | + | 0.153116i | ||||
\(544\) | 4.22970e6 | + | 7.32606e6i | 0.612791 | + | 1.06139i | ||||
\(545\) | 1.63282e6 | 0.235477 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.31426e7 | −1.87808 | −0.939039 | − | 0.343811i | \(-0.888282\pi\) | ||||
−0.939039 | + | 0.343811i | \(0.888282\pi\) | |||||||
\(548\) | −7.23287e6 | − | 1.25277e7i | −1.02887 | − | 1.78205i | ||||
\(549\) | −966667. | + | 1.67432e6i | −0.136882 | + | 0.237086i | ||||
\(550\) | −2.28300e6 | + | 3.95427e6i | −0.321810 | + | 0.557391i | ||||
\(551\) | 8.04564e6 | + | 1.39355e7i | 1.12897 | + | 1.95543i | ||||
\(552\) | −357579. | −0.0499487 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2.14415e6 | −0.296811 | ||||||||
\(555\) | −287260. | − | 497549.i | −0.0395861 | − | 0.0685652i | ||||
\(556\) | 4.28726e6 | − | 7.42575e6i | 0.588156 | − | 1.01872i | ||||
\(557\) | −4.53376e6 | + | 7.85270e6i | −0.619185 | + | 1.07246i | 0.370450 | + | 0.928853i | \(0.379204\pi\) |
−0.989635 | + | 0.143607i | \(0.954130\pi\) | |||||||
\(558\) | 330775. | + | 572920.i | 0.0449726 | + | 0.0778948i | ||||
\(559\) | −2.27363e7 | −3.07744 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.74627e6 | 0.368414 | ||||||||
\(562\) | 4.81923e6 | + | 8.34715e6i | 0.643631 | + | 1.11480i | ||||
\(563\) | −5.25898e6 | + | 9.10882e6i | −0.699247 | + | 1.21113i | 0.269481 | + | 0.963006i | \(0.413148\pi\) |
−0.968728 | + | 0.248126i | \(0.920185\pi\) | |||||||
\(564\) | 4.95068e6 | − | 8.57483e6i | 0.655340 | − | 1.13508i | ||||
\(565\) | 6399.59 | + | 11084.4i | 0.000843395 | + | 0.00146080i | ||||
\(566\) | −5.15150e6 | −0.675916 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.76117e6 | 0.229050 | ||||||||
\(569\) | −3.66153e6 | − | 6.34196e6i | −0.474114 | − | 0.821189i | 0.525447 | − | 0.850826i | \(-0.323898\pi\) |
−0.999561 | + | 0.0296373i | \(0.990565\pi\) | |||||||
\(570\) | 2.88505e6 | − | 4.99706e6i | 0.371934 | − | 0.644209i | ||||
\(571\) | 3.48990e6 | − | 6.04469e6i | 0.447943 | − | 0.775861i | −0.550309 | − | 0.834961i | \(-0.685490\pi\) |
0.998252 | + | 0.0591007i | \(0.0188233\pi\) | |||||||
\(572\) | −6.67483e6 | − | 1.15611e7i | −0.853002 | − | 1.47744i | ||||
\(573\) | −1.63272e6 | −0.207743 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.17237e6 | 0.147875 | ||||||||
\(576\) | 1.85000e6 | + | 3.20429e6i | 0.232335 | + | 0.402416i | ||||
\(577\) | 2.90605e6 | − | 5.03343e6i | 0.363382 | − | 0.629397i | −0.625133 | − | 0.780518i | \(-0.714955\pi\) |
0.988515 | + | 0.151122i | \(0.0482886\pi\) | |||||||
\(578\) | −1.49515e6 | + | 2.58968e6i | −0.186151 | + | 0.322423i | ||||
\(579\) | 4.34699e6 | + | 7.52921e6i | 0.538881 | + | 0.933369i | ||||
\(580\) | 1.08078e7 | 1.33403 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.17036e7 | 1.43223 | ||||||||
\(583\) | 1.05139e6 | + | 1.82106e6i | 0.128113 | + | 0.221898i | ||||
\(584\) | 473951. | − | 820906.i | 0.0575044 | − | 0.0996005i | ||||
\(585\) | −1.67397e6 | + | 2.89940e6i | −0.202236 | + | 0.350283i | ||||
\(586\) | −660654. | − | 1.14429e6i | −0.0794750 | − | 0.137655i | ||||
\(587\) | −7.37446e6 | −0.883355 | −0.441677 | − | 0.897174i | \(-0.645616\pi\) | ||||
−0.441677 | + | 0.897174i | \(0.645616\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.03888e6 | −0.242161 | ||||||||
\(590\) | 3.17284e6 | + | 5.49552e6i | 0.375247 | + | 0.649948i | ||||
\(591\) | −3.14576e6 | + | 5.44862e6i | −0.370473 | + | 0.641679i | ||||
\(592\) | −651927. | + | 1.12917e6i | −0.0764530 | + | 0.132420i | ||||
\(593\) | −4.73264e6 | − | 8.19717e6i | −0.552671 | − | 0.957254i | −0.998081 | − | 0.0619274i | \(-0.980275\pi\) |
0.445410 | − | 0.895327i | \(-0.353058\pi\) | |||||||
\(594\) | 1.81991e6 | 0.211633 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.55332e6 | −0.294435 | ||||||||
\(597\) | 1.87286e6 | + | 3.24388e6i | 0.215065 | + | 0.372503i | ||||
\(598\) | −3.10794e6 | + | 5.38311e6i | −0.355402 | + | 0.615575i | ||||
\(599\) | 4.26098e6 | − | 7.38023e6i | 0.485224 | − | 0.840432i | −0.514632 | − | 0.857411i | \(-0.672071\pi\) |
0.999856 | + | 0.0169788i | \(0.00540478\pi\) | |||||||
\(600\) | 510159. | + | 883622.i | 0.0578532 | + | 0.100205i | ||||
\(601\) | −657065. | −0.0742031 | −0.0371016 | − | 0.999311i | \(-0.511813\pi\) | ||||
−0.0371016 | + | 0.999311i | \(0.511813\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.80839e6 | 0.314532 | ||||||||
\(604\) | 4.40155e6 | + | 7.62371e6i | 0.490923 | + | 0.850303i | ||||
\(605\) | 1.32641e6 | − | 2.29741e6i | 0.147330 | − | 0.255182i | ||||
\(606\) | 5.31385e6 | − | 9.20386e6i | 0.587798 | − | 1.01810i | ||||
\(607\) | −2.93443e6 | − | 5.08257e6i | −0.323260 | − | 0.559902i | 0.657899 | − | 0.753106i | \(-0.271445\pi\) |
−0.981159 | + | 0.193204i | \(0.938112\pi\) | |||||||
\(608\) | −1.72773e7 | −1.89547 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.25750e6 | −0.789700 | ||||||||
\(611\) | −1.60544e7 | − | 2.78070e7i | −1.73976 | − | 3.01336i | ||||
\(612\) | 1.64481e6 | − | 2.84890e6i | 0.177516 | − | 0.307467i | ||||
\(613\) | −1.92201e6 | + | 3.32902e6i | −0.206588 | + | 0.357820i | −0.950637 | − | 0.310304i | \(-0.899569\pi\) |
0.744050 | + | 0.668124i | \(0.232902\pi\) | |||||||
\(614\) | −1.23834e6 | − | 2.14486e6i | −0.132562 | − | 0.229603i | ||||
\(615\) | −3.88035e6 | −0.413698 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.44660e6 | 0.681739 | 0.340869 | − | 0.940111i | \(-0.389279\pi\) | ||||
0.340869 | + | 0.940111i | \(0.389279\pi\) | |||||||
\(618\) | −4.40609e6 | − | 7.63158e6i | −0.464069 | − | 0.803791i | ||||
\(619\) | −3.36870e6 | + | 5.83476e6i | −0.353375 | + | 0.612063i | −0.986838 | − | 0.161709i | \(-0.948299\pi\) |
0.633464 | + | 0.773772i | \(0.281633\pi\) | |||||||
\(620\) | −684712. | + | 1.18596e6i | −0.0715367 | + | 0.123905i | ||||
\(621\) | −233640. | − | 404677.i | −0.0243119 | − | 0.0421094i | ||||
\(622\) | 2.07115e7 | 2.14652 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 7.59804e6 | 0.781160 | ||||||||
\(625\) | 352380. | + | 610339.i | 0.0360837 | + | 0.0624987i | ||||
\(626\) | −7.75114e6 | + | 1.34254e7i | −0.790551 | + | 1.36927i | ||||
\(627\) | −2.80446e6 | + | 4.85746e6i | −0.284892 | + | 0.493447i | ||||
\(628\) | −9.04736e6 | − | 1.56705e7i | −0.915425 | − | 1.58556i | ||||
\(629\) | 1.83063e6 | 0.184491 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.14514e6 | −0.914360 | −0.457180 | − | 0.889374i | \(-0.651140\pi\) | ||||
−0.457180 | + | 0.889374i | \(0.651140\pi\) | |||||||
\(632\) | −2.26426e6 | − | 3.92181e6i | −0.225493 | − | 0.390566i | ||||
\(633\) | −1.83219e6 | + | 3.17344e6i | −0.181744 | + | 0.314790i | ||||
\(634\) | 2.49147e6 | − | 4.31534e6i | 0.246168 | − | 0.426376i | ||||
\(635\) | −3.04141e6 | − | 5.26787e6i | −0.299323 | − | 0.518443i | ||||
\(636\) | 2.51881e6 | 0.246918 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.90518e7 | −1.85304 | ||||||||
\(639\) | 1.15074e6 | + | 1.99313e6i | 0.111487 | + | 0.193101i | ||||
\(640\) | −2.22489e6 | + | 3.85362e6i | −0.214713 | + | 0.371894i | ||||
\(641\) | 520442. | − | 901432.i | 0.0500296 | − | 0.0866538i | −0.839926 | − | 0.542701i | \(-0.817402\pi\) |
0.889956 | + | 0.456047i | \(0.150735\pi\) | |||||||
\(642\) | −3.15701e6 | − | 5.46811e6i | −0.302300 | − | 0.523600i | ||||
\(643\) | −9.08713e6 | −0.866761 | −0.433381 | − | 0.901211i | \(-0.642679\pi\) | ||||
−0.433381 | + | 0.901211i | \(0.642679\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.41615e6 | 0.607261 | ||||||||
\(646\) | 9.19284e6 | + | 1.59225e7i | 0.866699 | + | 1.50117i | ||||
\(647\) | −1.10356e6 | + | 1.91141e6i | −0.103641 | + | 0.179512i | −0.913182 | − | 0.407551i | \(-0.866383\pi\) |
0.809541 | + | 0.587064i | \(0.199716\pi\) | |||||||
\(648\) | 203339. | − | 352193.i | 0.0190231 | − | 0.0329490i | ||||
\(649\) | −3.08420e6 | − | 5.34199e6i | −0.287429 | − | 0.497842i | ||||
\(650\) | 1.77364e7 | 1.64658 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.58252e6 | 0.330042 | ||||||||
\(653\) | 9.18048e6 | + | 1.59011e7i | 0.842524 | + | 1.45929i | 0.887754 | + | 0.460318i | \(0.152265\pi\) |
−0.0452296 | + | 0.998977i | \(0.514402\pi\) | |||||||
\(654\) | −1.72390e6 | + | 2.98588e6i | −0.157604 | + | 0.272978i | ||||
\(655\) | −3.13145e6 | + | 5.42382e6i | −0.285195 | + | 0.493972i | ||||
\(656\) | 4.40316e6 | + | 7.62649e6i | 0.399489 | + | 0.691935i | ||||
\(657\) | 1.23871e6 | 0.111958 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.21208e6 | 0.557216 | 0.278608 | − | 0.960405i | \(-0.410127\pi\) | ||||
0.278608 | + | 0.960405i | \(0.410127\pi\) | |||||||
\(660\) | 1.88363e6 | + | 3.26254e6i | 0.168320 | + | 0.291538i | ||||
\(661\) | −7.71149e6 | + | 1.33567e7i | −0.686491 | + | 1.18904i | 0.286475 | + | 0.958088i | \(0.407517\pi\) |
−0.972966 | + | 0.230950i | \(0.925817\pi\) | |||||||
\(662\) | 748835. | − | 1.29702e6i | 0.0664112 | − | 0.115028i | ||||
\(663\) | −5.33389e6 | − | 9.23857e6i | −0.471260 | − | 0.816246i | ||||
\(664\) | −1.88065e6 | −0.165534 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.21313e6 | 0.105980 | ||||||||
\(667\) | 2.44588e6 | + | 4.23638e6i | 0.212873 | + | 0.368707i | ||||
\(668\) | −6.19136e6 | + | 1.07238e7i | −0.536840 | + | 0.929834i | ||||
\(669\) | −3.96910e6 | + | 6.87468e6i | −0.342868 | + | 0.593865i | ||||
\(670\) | 5.27118e6 | + | 9.12995e6i | 0.453650 | + | 0.785745i | ||||
\(671\) | 7.05475e6 | 0.604889 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.27201e7 | −1.93362 | −0.966811 | − | 0.255491i | \(-0.917763\pi\) | ||||
−0.966811 | + | 0.255491i | \(0.917763\pi\) | |||||||
\(674\) | −1.28713e7 | − | 2.22937e7i | −1.09137 | − | 1.89030i | ||||
\(675\) | −666670. | + | 1.15471e6i | −0.0563186 | + | 0.0975467i | ||||
\(676\) | −1.86250e7 | + | 3.22594e7i | −1.56758 | + | 2.71513i | ||||
\(677\) | −6.80867e6 | − | 1.17930e7i | −0.570940 | − | 0.988897i | −0.996470 | − | 0.0839525i | \(-0.973246\pi\) |
0.425530 | − | 0.904944i | \(-0.360088\pi\) | |||||||
\(678\) | −27026.2 | −0.00225793 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2.30369e6 | 0.191052 | ||||||||
\(681\) | 5.06926e6 | + | 8.78021e6i | 0.418867 | + | 0.725499i | ||||
\(682\) | 1.20700e6 | − | 2.09059e6i | 0.0993682 | − | 0.172111i | ||||
\(683\) | −1.19993e6 | + | 2.07833e6i | −0.0984245 | + | 0.170476i | −0.911033 | − | 0.412334i | \(-0.864714\pi\) |
0.812608 | + | 0.582810i | \(0.198047\pi\) | |||||||
\(684\) | 3.35931e6 | + | 5.81850e6i | 0.274543 | + | 0.475523i | ||||
\(685\) | 1.32380e7 | 1.07795 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.79076e6 | 0.225595 | ||||||||
\(688\) | −7.28061e6 | − | 1.26104e7i | −0.586404 | − | 1.01568i | ||||
\(689\) | 4.08408e6 | − | 7.07383e6i | 0.327753 | − | 0.567684i | ||||
\(690\) | 877057. | − | 1.51911e6i | 0.0701302 | − | 0.121469i | ||||
\(691\) | 701824. | + | 1.21560e6i | 0.0559156 | + | 0.0968487i | 0.892628 | − | 0.450793i | \(-0.148859\pi\) |
−0.836713 | + | 0.547642i | \(0.815526\pi\) | |||||||
\(692\) | 1.42462e7 | 1.13093 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.04703e7 | 1.61334 | ||||||||
\(695\) | 3.92340e6 | + | 6.79553e6i | 0.308106 | + | 0.533656i | ||||
\(696\) | −2.12866e6 | + | 3.68695e6i | −0.166565 | + | 0.288499i | ||||
\(697\) | 6.18211e6 | − | 1.07077e7i | 0.482009 | − | 0.834864i | ||||
\(698\) | 1.13048e7 | + | 1.95806e7i | 0.878266 | + | 1.52120i | ||||
\(699\) | −1.02288e7 | −0.791831 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.78991e6 | −0.445017 | −0.222509 | − | 0.974931i | \(-0.571425\pi\) | ||||
−0.222509 | + | 0.974931i | \(0.571425\pi\) | |||||||
\(702\) | −3.53468e6 | − | 6.12225e6i | −0.270712 | − | 0.468887i | ||||
\(703\) | −1.86942e6 | + | 3.23793e6i | −0.142665 | + | 0.247103i | ||||
\(704\) | 6.75066e6 | − | 1.16925e7i | 0.513351 | − | 0.889150i | ||||
\(705\) | 4.53052e6 | + | 7.84708e6i | 0.343301 | + | 0.594614i | ||||
\(706\) | 8.02739e6 | 0.606126 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −7.38882e6 | −0.553977 | ||||||||
\(709\) | 5.65716e6 | + | 9.79849e6i | 0.422652 | + | 0.732055i | 0.996198 | − | 0.0871187i | \(-0.0277659\pi\) |
−0.573546 | + | 0.819173i | \(0.694433\pi\) | |||||||
\(710\) | −4.31972e6 | + | 7.48198e6i | −0.321595 | + | 0.557020i | ||||
\(711\) | 2.95891e6 | − | 5.12498e6i | 0.219512 | − | 0.380206i | ||||
\(712\) | 1.11848e6 | + | 1.93727e6i | 0.0826857 | + | 0.143216i | ||||
\(713\) | −619821. | −0.0456607 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.22167e7 | 0.893692 | ||||||||
\(716\) | 3.42042e6 | + | 5.92435e6i | 0.249343 | + | 0.431875i | ||||
\(717\) | 393781. | − | 682048.i | 0.0286060 | − | 0.0495470i | ||||
\(718\) | 1.17775e7 | − | 2.03992e7i | 0.852591 | − | 1.47673i | ||||
\(719\) | 1.36890e7 | + | 2.37101e7i | 0.987529 | + | 1.71045i | 0.630109 | + | 0.776507i | \(0.283010\pi\) |
0.357420 | + | 0.933944i | \(0.383656\pi\) | |||||||
\(720\) | −2.14415e6 | −0.154143 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.66367e7 | −1.18775 | ||||||||
\(723\) | −2.41996e6 | − | 4.19149e6i | −0.172172 | − | 0.298210i | ||||
\(724\) | 2.65484e6 | − | 4.59831e6i | 0.188231 | − | 0.326026i | ||||
\(725\) | 6.97908e6 | − | 1.20881e7i | 0.493121 | − | 0.854110i | ||||
\(726\) | 2.80079e6 | + | 4.85111e6i | 0.197215 | + | 0.341586i | ||||
\(727\) | −9.86471e6 | −0.692226 | −0.346113 | − | 0.938193i | \(-0.612499\pi\) | ||||
−0.346113 | + | 0.938193i | \(0.612499\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 2.32498e6 | + | 4.02698e6i | 0.161477 | + | 0.279687i | ||||
\(731\) | −1.02221e7 | + | 1.77052e7i | −0.707534 | + | 1.22548i | ||||
\(732\) | 4.22527e6 | − | 7.31837e6i | 0.291458 | − | 0.504820i | ||||
\(733\) | −1.93938e6 | − | 3.35911e6i | −0.133322 | − | 0.230921i | 0.791633 | − | 0.610997i | \(-0.209231\pi\) |
−0.924955 | + | 0.380076i | \(0.875898\pi\) | |||||||
\(734\) | 1.29972e6 | 0.0890448 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.25229e6 | −0.357400 | ||||||||
\(737\) | −5.12393e6 | − | 8.87490e6i | −0.347483 | − | 0.601859i | ||||
\(738\) | 4.09679e6 | − | 7.09584e6i | 0.276887 | − | 0.479582i | ||||
\(739\) | 3.97749e6 | − | 6.88922e6i | 0.267916 | − | 0.464044i | −0.700408 | − | 0.713743i | \(-0.746998\pi\) |
0.968323 | + | 0.249699i | \(0.0803318\pi\) | |||||||
\(740\) | 1.25560e6 | + | 2.17477e6i | 0.0842894 | + | 0.145994i | ||||
\(741\) | 2.17876e7 | 1.45768 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.65977e7 | 1.10300 | 0.551500 | − | 0.834175i | \(-0.314056\pi\) | ||||
0.551500 | + | 0.834175i | \(0.314056\pi\) | |||||||
\(744\) | −269717. | − | 467163.i | −0.0178639 | − | 0.0309411i | ||||
\(745\) | 1.16831e6 | − | 2.02357e6i | 0.0771200 | − | 0.133576i | ||||
\(746\) | −1.00671e7 | + | 1.74367e7i | −0.662304 | + | 1.14714i | ||||
\(747\) | −1.22881e6 | − | 2.12835e6i | −0.0805716 | − | 0.139554i | ||||
\(748\) | −1.20039e7 | −0.784453 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.35570e7 | −0.880056 | ||||||||
\(751\) | −7.55359e6 | − | 1.30832e7i | −0.488713 | − | 0.846475i | 0.511203 | − | 0.859460i | \(-0.329200\pi\) |
−0.999916 | + | 0.0129846i | \(0.995867\pi\) | |||||||
\(752\) | 1.02818e7 | − | 1.78087e7i | 0.663020 | − | 1.14838i | ||||
\(753\) | −6.09088e6 | + | 1.05497e7i | −0.391464 | + | 0.678036i | ||||
\(754\) | 3.70030e7 | + | 6.40911e7i | 2.37033 | + | 4.10553i | ||||
\(755\) | −8.05598e6 | −0.514341 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.80923e6 | 0.368450 | 0.184225 | − | 0.982884i | \(-0.441022\pi\) | ||||
0.184225 | + | 0.982884i | \(0.441022\pi\) | |||||||
\(758\) | 1.54224e7 | + | 2.67124e7i | 0.974944 | + | 1.68865i | ||||
\(759\) | −852556. | + | 1.47667e6i | −0.0537178 | + | 0.0930420i | ||||
\(760\) | −2.35249e6 | + | 4.07464e6i | −0.147739 | + | 0.255891i | ||||
\(761\) | −1.27135e7 | − | 2.20204e7i | −0.795799 | − | 1.37836i | −0.922331 | − | 0.386402i | \(-0.873718\pi\) |
0.126531 | − | 0.991963i | \(-0.459616\pi\) | |||||||
\(762\) | 1.28442e7 | 0.801346 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 7.13656e6 | 0.442340 | ||||||||
\(765\) | 1.50522e6 | + | 2.60711e6i | 0.0929919 | + | 0.161067i | ||||
\(766\) | −9.11050e6 | + | 1.57798e7i | −0.561010 | + | 0.971697i | ||||
\(767\) | −1.19804e7 | + | 2.07507e7i | −0.735334 | + | 1.27364i | ||||
\(768\) | 1.87979e6 | + | 3.25589e6i | 0.115002 | + | 0.199190i | ||||
\(769\) | 1.53909e7 | 0.938532 | 0.469266 | − | 0.883057i | \(-0.344519\pi\) | ||||
0.469266 | + | 0.883057i | \(0.344519\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.79210e6 | −0.532668 | ||||||||
\(772\) | −1.90005e7 | − | 3.29099e7i | −1.14742 | − | 1.98739i | ||||
\(773\) | −452696. | + | 784093.i | −0.0272495 | + | 0.0471975i | −0.879329 | − | 0.476216i | \(-0.842008\pi\) |
0.852079 | + | 0.523413i | \(0.175342\pi\) | |||||||
\(774\) | −6.77403e6 | + | 1.17330e7i | −0.406438 | + | 0.703972i | ||||
\(775\) | 884300. | + | 1.53165e6i | 0.0528865 | + | 0.0916022i | ||||
\(776\) | −9.54323e6 | −0.568907 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.09530e7 | 1.83338 | ||||||||
\(779\) | 1.26262e7 | + | 2.18692e7i | 0.745467 | + | 1.29119i | ||||
\(780\) | 7.31686e6 | − | 1.26732e7i | 0.430614 | − | 0.745846i | ||||
\(781\) | 4.19905e6 | − | 7.27296e6i | 0.246333 | − | 0.426662i | ||||
\(782\) | 2.79463e6 | + | 4.84044e6i | 0.163421 | + | 0.283053i | ||||
\(783\) | −5.56342e6 | −0.324293 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.65590e7 | 0.959093 | ||||||||
\(786\) | −6.61222e6 | − | 1.14527e7i | −0.381760 | − | 0.661229i | ||||
\(787\) | 1.39667e7 | − | 2.41910e7i | 0.803817 | − | 1.39225i | −0.113271 | − | 0.993564i | \(-0.536133\pi\) |
0.917087 | − | 0.398687i | \(-0.130534\pi\) | |||||||
\(788\) | 1.37500e7 | − | 2.38157e7i | 0.788837 | − | 1.36631i | ||||
\(789\) | −5.59687e6 | − | 9.69406e6i | −0.320076 | − | 0.554387i | ||||
\(790\) | 2.22148e7 | 1.26641 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.48397e6 | −0.0840643 | ||||||||
\(793\) | −1.37019e7 | − | 2.37325e7i | −0.773747 | − | 1.34017i | ||||
\(794\) | 1.66664e7 | − | 2.88671e7i | 0.938191 | − | 1.62499i | ||||
\(795\) | −1.15252e6 | + | 1.99622e6i | −0.0646742 | + | 0.112019i | ||||
\(796\) | −8.18619e6 | − | 1.41789e7i | −0.457930 | − | 0.793158i | ||||
\(797\) | 2.18824e7 | 1.22025 | 0.610126 | − | 0.792304i | \(-0.291119\pi\) | ||||
0.610126 | + | 0.792304i | \(0.291119\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.88718e7 | −1.59995 | ||||||||
\(800\) | 7.49346e6 | + | 1.29791e7i | 0.413959 | + | 0.716998i | ||||
\(801\) | −1.46162e6 | + | 2.53161e6i | −0.0804923 | + | 0.139417i | ||||
\(802\) | 105646. | − | 182983.i | 0.00579983 | − | 0.0100456i | ||||
\(803\) | −2.26003e6 | − | 3.91448e6i | −0.123687 | − | 0.214232i | ||||
\(804\) | −1.22754e7 | −0.669722 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9.37710e6 | −0.508430 | ||||||||
\(807\) | 4.87838e6 | + | 8.44960e6i | 0.263689 | + | 0.456722i | ||||
\(808\) | −4.33295e6 | + | 7.50489e6i | −0.233483 | + | 0.404405i | ||||
\(809\) | −1.22097e7 | + | 2.11478e7i | −0.655893 | + | 1.13604i | 0.325776 | + | 0.945447i | \(0.394375\pi\) |
−0.981669 | + | 0.190594i | \(0.938959\pi\) | |||||||
\(810\) | 997482. | + | 1.72769e6i | 0.0534186 | + | 0.0925237i | ||||
\(811\) | 4.46711e6 | 0.238492 | 0.119246 | − | 0.992865i | \(-0.461952\pi\) | ||||
0.119246 | + | 0.992865i | \(0.461952\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.94964e7 | −1.03450 | ||||||||
\(814\) | −2.21336e6 | − | 3.83366e6i | −0.117082 | − | 0.202793i | ||||
\(815\) | −1.63924e6 | + | 2.83924e6i | −0.0864465 | + | 0.149730i | ||||
\(816\) | 3.41603e6 | − | 5.91675e6i | 0.179596 | − | 0.311070i | ||||
\(817\) | −2.08774e7 | − | 3.61606e7i | −1.09426 | − | 1.89531i | ||||
\(818\) | 7.03317e6 | 0.367509 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.69609e7 | 0.880873 | ||||||||
\(821\) | −6.73539e6 | − | 1.16660e7i | −0.348743 | − | 0.604040i | 0.637284 | − | 0.770629i | \(-0.280058\pi\) |
−0.986026 | + | 0.166589i | \(0.946725\pi\) | |||||||
\(822\) | −1.39764e7 | + | 2.42079e7i | −0.721467 | + | 1.24962i | ||||
\(823\) | 2.01979e6 | − | 3.49838e6i | 0.103946 | − | 0.180039i | −0.809361 | − | 0.587311i | \(-0.800187\pi\) |
0.913307 | + | 0.407272i | \(0.133520\pi\) | |||||||
\(824\) | 3.59276e6 | + | 6.22285e6i | 0.184336 | + | 0.319279i | ||||
\(825\) | 4.86537e6 | 0.248875 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.24927e7 | 0.635175 | 0.317588 | − | 0.948229i | \(-0.397127\pi\) | ||||
0.317588 | + | 0.948229i | \(0.397127\pi\) | |||||||
\(828\) | 1.02123e6 | + | 1.76883e6i | 0.0517665 | + | 0.0896622i | ||||
\(829\) | 7.29902e6 | − | 1.26423e7i | 0.368874 | − | 0.638909i | −0.620515 | − | 0.784194i | \(-0.713077\pi\) |
0.989390 | + | 0.145285i | \(0.0464099\pi\) | |||||||
\(830\) | 4.61279e6 | − | 7.98958e6i | 0.232417 | − | 0.402558i | ||||
\(831\) | 1.14237e6 | + | 1.97863e6i | 0.0573855 | + | 0.0993946i | ||||
\(832\) | −5.24453e7 | −2.62663 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1.65690e7 | −0.824859 | ||||||||
\(835\) | −5.66590e6 | − | 9.81363e6i | −0.281224 | − | 0.487095i | ||||
\(836\) | 1.22582e7 | − | 2.12318e7i | 0.606611 | − | 1.05068i | ||||
\(837\) | 352463. | − | 610483.i | 0.0173900 | − | 0.0301204i | ||||
\(838\) | −1.66888e7 | − | 2.89058e7i | −0.820946 | − | 1.42192i | ||||
\(839\) | −9.15983e6 | −0.449244 | −0.224622 | − | 0.974446i | \(-0.572115\pi\) | ||||
−0.224622 | + | 0.974446i | \(0.572115\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.77299e7 | 1.83948 | ||||||||
\(842\) | 1.99451e7 | + | 3.45460e7i | 0.969520 | + | 1.67926i | ||||
\(843\) | 5.13521e6 | − | 8.89444e6i | 0.248879 | − | 0.431072i | ||||
\(844\) | 8.00842e6 | − | 1.38710e7i | 0.386982 | − | 0.670272i | ||||
\(845\) | −1.70443e7 | − | 2.95216e7i | −0.821178 | − | 1.42232i | ||||
\(846\) | −1.91329e7 | −0.919082 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5.23121e6 | 0.249812 | ||||||||
\(849\) | 2.74463e6 | + | 4.75384e6i | 0.130682 | + | 0.226347i | ||||
\(850\) | 7.97421e6 | − | 1.38117e7i | 0.378565 | − | 0.655693i | ||||
\(851\) | −568304. | + | 984331.i | −0.0269003 | + | 0.0465926i | ||||
\(852\) | −5.02983e6 | − | 8.71191e6i | −0.237385 | − | 0.411164i | ||||
\(853\) | −8.68253e6 | −0.408577 | −0.204289 | − | 0.978911i | \(-0.565488\pi\) | ||||
−0.204289 | + | 0.978911i | \(0.565488\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.14842e6 | −0.287639 | ||||||||
\(856\) | 2.57425e6 | + | 4.45873e6i | 0.120079 | + | 0.207983i | ||||
\(857\) | −5.24941e6 | + | 9.09225e6i | −0.244151 | + | 0.422882i | −0.961893 | − | 0.273428i | \(-0.911843\pi\) |
0.717742 | + | 0.696310i | \(0.245176\pi\) | |||||||
\(858\) | −1.28981e7 | + | 2.23401e7i | −0.598146 | + | 1.03602i | ||||
\(859\) | −4.51890e6 | − | 7.82697e6i | −0.208954 | − | 0.361918i | 0.742432 | − | 0.669922i | \(-0.233672\pi\) |
−0.951385 | + | 0.308004i | \(0.900339\pi\) | |||||||
\(860\) | −2.80448e7 | −1.29302 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.44445e7 | −1.57889 | ||||||||
\(863\) | 7.99288e6 | + | 1.38441e7i | 0.365322 | + | 0.632757i | 0.988828 | − | 0.149062i | \(-0.0476255\pi\) |
−0.623506 | + | 0.781819i | \(0.714292\pi\) | |||||||
\(864\) | 2.98673e6 | − | 5.17317e6i | 0.136117 | − | 0.235761i | ||||
\(865\) | −6.51857e6 | + | 1.12905e7i | −0.296218 | + | 0.513065i | ||||
\(866\) | 7.59850e6 | + | 1.31610e7i | 0.344297 | + | 0.596340i | ||||
\(867\) | 3.18636e6 | 0.143962 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.15942e7 | −0.970035 | ||||||||
\(870\) | −1.04422e7 | − | 1.80864e7i | −0.467729 | − | 0.810130i | ||||
\(871\) | −1.99037e7 | + | 3.44742e7i | −0.888971 | + | 1.53974i | ||||
\(872\) | 1.40568e6 | − | 2.43471e6i | 0.0626030 | − | 0.108432i | ||||
\(873\) | −6.23549e6 | − | 1.08002e7i | −0.276908 | − | 0.479618i | ||||
\(874\) | −1.14153e7 | −0.505487 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.41434e6 | −0.238388 | ||||||||
\(877\) | −1.33727e7 | − | 2.31621e7i | −0.587109 | − | 1.01690i | −0.994609 | − | 0.103697i | \(-0.966933\pi\) |
0.407500 | − | 0.913205i | \(-0.366401\pi\) | |||||||
\(878\) | −1.90811e7 | + | 3.30495e7i | −0.835349 | + | 1.44687i | ||||
\(879\) | −703970. | + | 1.21931e6i | −0.0307314 | + | 0.0532283i | ||||
\(880\) | 3.91202e6 | + | 6.77582e6i | 0.170292 | + | 0.294954i | ||||
\(881\) | −6.40715e6 | −0.278115 | −0.139058 | − | 0.990284i | \(-0.544407\pi\) | ||||
−0.139058 | + | 0.990284i | \(0.544407\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.96462e6 | 0.214281 | 0.107141 | − | 0.994244i | \(-0.465831\pi\) | ||||
0.107141 | + | 0.994244i | \(0.465831\pi\) | |||||||
\(884\) | 2.33142e7 | + | 4.03814e7i | 1.00344 | + | 1.73801i | ||||
\(885\) | 3.38086e6 | − | 5.85583e6i | 0.145101 | − | 0.251322i | ||||
\(886\) | −1.20467e7 | + | 2.08654e7i | −0.515564 | + | 0.892983i | ||||
\(887\) | −4.35813e6 | − | 7.54849e6i | −0.185990 | − | 0.322145i | 0.757919 | − | 0.652348i | \(-0.226216\pi\) |
−0.943910 | + | 0.330203i | \(0.892883\pi\) | |||||||
\(888\) | −989196. | −0.0420969 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1.09735e7 | −0.464377 | ||||||||
\(891\) | −969617. | − | 1.67943e6i | −0.0409172 | − | 0.0708707i | ||||
\(892\) | 1.73488e7 | − | 3.00490e7i | 0.730057 | − | 1.26450i | ||||
\(893\) | 2.94835e7 | − | 5.10669e7i | 1.23723 | − | 2.14294i | ||||
\(894\) | 2.46695e6 | + | 4.27288e6i | 0.103233 | + | 0.178804i | ||||
\(895\) | −6.26026e6 | −0.261237 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.62343e6 | 0.274854 | ||||||||
\(898\) | −8.03429e6 | − | 1.39158e7i | −0.332473 | − | 0.575861i | ||||
\(899\) | −3.68978e6 | + | 6.39088e6i | −0.152265 | + | 0.263731i | ||||
\(900\) | 2.91399e6 | − | 5.04718e6i | 0.119917 | − | 0.207703i | ||||
\(901\) | −3.67236e6 | − | 6.36071e6i | −0.150707 | − | 0.261032i | ||||
\(902\) | −2.98984e7 | −1.22358 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 22037.4 | 0.000896888 | ||||||||
\(905\) | 2.42952e6 | + | 4.20805e6i | 0.0986050 | + | 0.170789i | ||||
\(906\) | 8.50533e6 | − | 1.47317e7i | 0.344247 | − | 0.596254i | ||||
\(907\) | 1.18128e7 | − | 2.04603e7i | 0.476797 | − | 0.825836i | −0.522850 | − | 0.852425i | \(-0.675131\pi\) |
0.999646 | + | 0.0265886i | \(0.00846441\pi\) | |||||||
\(908\) | −2.21575e7 | − | 3.83780e7i | −0.891880 | − | 1.54478i | ||||
\(909\) | −1.13245e7 | −0.454579 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.69360e7 | −0.676105 | −0.338053 | − | 0.941127i | \(-0.609768\pi\) | ||||
−0.338053 | + | 0.941127i | \(0.609768\pi\) | |||||||
\(912\) | 6.97681e6 | + | 1.20842e7i | 0.277760 | + | 0.481095i | ||||
\(913\) | −4.48393e6 | + | 7.76639e6i | −0.178025 | + | 0.308349i | ||||
\(914\) | 1.11842e7 | − | 1.93717e7i | 0.442834 | − | 0.767011i | ||||
\(915\) | 3.86667e6 | + | 6.69726e6i | 0.152681 | + | 0.264451i | ||||
\(916\) | −1.21983e7 | −0.480353 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −6.35669e6 | −0.248957 | ||||||||
\(919\) | 1.56902e7 | + | 2.71762e7i | 0.612829 | + | 1.06145i | 0.990761 | + | 0.135617i | \(0.0433018\pi\) |
−0.377933 | + | 0.925833i | \(0.623365\pi\) | |||||||
\(920\) | −715159. | + | 1.23869e6i | −0.0278569 | + | 0.0482496i | ||||
\(921\) | −1.31953e6 | + | 2.28549e6i | −0.0512590 | + | 0.0887831i | ||||
\(922\) | −4.60448e6 | − | 7.97519e6i | −0.178383 | − | 0.308968i | ||||
\(923\) | −3.26220e7 | −1.26040 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.24320e6 | 0.124629 | ||||||||
\(926\) | −1.05937e7 | − | 1.83489e7i | −0.405996 | − | 0.703206i | ||||
\(927\) | −4.69498e6 | + | 8.13194e6i | −0.179446 | + | 0.310810i | ||||
\(928\) | −3.12668e7 | + | 5.41557e7i | −1.19183 | + | 2.06431i | ||||
\(929\) | 7.15444e6 | + | 1.23919e7i | 0.271980 | + | 0.471082i | 0.969369 | − | 0.245610i | \(-0.0789884\pi\) |
−0.697389 | + | 0.716693i | \(0.745655\pi\) | |||||||
\(930\) | 2.64620e6 | 0.100327 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 4.47098e7 | 1.68602 | ||||||||
\(933\) | −1.10347e7 | − | 1.91127e7i | −0.415009 | − | 0.718816i | ||||
\(934\) | 1.35535e7 | − | 2.34753e7i | 0.508373 | − | 0.880528i | ||||
\(935\) | 5.49255e6 | − | 9.51337e6i | 0.205468 | − | 0.355881i | ||||
\(936\) | 2.88221e6 | + | 4.99213e6i | 0.107531 | + | 0.186250i | ||||
\(937\) | 2.81206e7 | 1.04635 | 0.523173 | − | 0.852227i | \(-0.324748\pi\) | ||||
0.523173 | + | 0.852227i | \(0.324748\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.65187e7 | 0.611381 | ||||||||
\(940\) | −1.98027e7 | − | 3.42993e7i | −0.730979 | − | 1.26609i | ||||
\(941\) | 1.64785e7 | − | 2.85415e7i | 0.606656 | − | 1.05076i | −0.385131 | − | 0.922862i | \(-0.625844\pi\) |
0.991787 | − | 0.127898i | \(-0.0408229\pi\) | |||||||
\(942\) | −1.74827e7 | + | 3.02808e7i | −0.641919 | + | 1.11184i | ||||
\(943\) | 3.83836e6 | + | 6.64824e6i | 0.140562 | + | 0.243460i | ||||
\(944\) | −1.53455e7 | −0.560469 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.94370e7 | 1.79607 | ||||||||
\(947\) | −8.14874e6 | − | 1.41140e7i | −0.295268 | − | 0.511418i | 0.679780 | − | 0.733417i | \(-0.262075\pi\) |
−0.975047 | + | 0.221998i | \(0.928742\pi\) | |||||||
\(948\) | −1.29333e7 | + | 2.24011e7i | −0.467399 | + | 0.809559i | ||||
\(949\) | −8.77897e6 | + | 1.52056e7i | −0.316430 | + | 0.548073i | ||||
\(950\) | 1.62863e7 | + | 2.82087e7i | 0.585482 | + | 1.01408i | ||||
\(951\) | −5.30964e6 | −0.190377 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.03230e7 | −1.08153 | −0.540767 | − | 0.841172i | \(-0.681866\pi\) | ||||
−0.540767 | + | 0.841172i | \(0.681866\pi\) | |||||||
\(954\) | −2.43361e6 | − | 4.21514e6i | −0.0865726 | − | 0.149948i | ||||
\(955\) | −3.26544e6 | + | 5.65591e6i | −0.115860 | + | 0.200675i | ||||
\(956\) | −1.72120e6 | + | 2.98121e6i | −0.0609098 | + | 0.105499i | ||||
\(957\) | 1.01505e7 | + | 1.75812e7i | 0.358267 | + | 0.620537i | ||||
\(958\) | 1.95498e7 | 0.688221 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.48000e7 | 0.518302 | ||||||||
\(961\) | 1.38471e7 | + | 2.39838e7i | 0.483670 | + | 0.837741i | ||||
\(962\) | −8.59772e6 | + | 1.48917e7i | −0.299533 | + | 0.518807i | ||||
\(963\) | −3.36400e6 | + | 5.82662e6i | −0.116894 | + | 0.202466i | ||||
\(964\) | 1.05775e7 | + | 1.83208e7i | 0.366600 | + | 0.634970i | ||||
\(965\) | 3.47759e7 | 1.20216 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.49059e7 | −0.512616 | −0.256308 | − | 0.966595i | \(-0.582506\pi\) | ||||
−0.256308 | + | 0.966595i | \(0.582506\pi\) | |||||||
\(968\) | −2.28379e6 | − | 3.95563e6i | −0.0783370 | − | 0.135684i | ||||
\(969\) | 9.79557e6 | − | 1.69664e7i | 0.335135 | − | 0.580472i | ||||
\(970\) | 2.34073e7 | − | 4.05426e7i | 0.798770 | − | 1.38351i | ||||
\(971\) | −8.28038e6 | − | 1.43420e7i | −0.281840 | − | 0.488161i | 0.689998 | − | 0.723811i | \(-0.257611\pi\) |
−0.971838 | + | 0.235650i | \(0.924278\pi\) | |||||||
\(972\) | −2.32291e6 | −0.0788618 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 3.91681e7 | 1.32292 | ||||||||
\(975\) | −9.44967e6 | − | 1.63673e7i | −0.318350 | − | 0.551399i | ||||
\(976\) | 8.77527e6 | − | 1.51992e7i | 0.294874 | − | 0.510736i | ||||
\(977\) | −3.78431e6 | + | 6.55462e6i | −0.126838 | + | 0.219690i | −0.922450 | − | 0.386117i | \(-0.873816\pi\) |
0.795612 | + | 0.605807i | \(0.207150\pi\) | |||||||
\(978\) | −3.46134e6 | − | 5.99521e6i | −0.115717 | − | 0.200427i | ||||
\(979\) | 1.06670e7 | 0.355700 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.67386e6 | 0.121885 | ||||||||
\(982\) | 2.12064e7 | + | 3.67306e7i | 0.701760 | + | 1.21548i | ||||
\(983\) | 1.66021e7 | − | 2.87556e7i | 0.547998 | − | 0.949160i | −0.450414 | − | 0.892820i | \(-0.648724\pi\) |
0.998412 | − | 0.0563398i | \(-0.0179430\pi\) | |||||||
\(984\) | −3.34055e6 | + | 5.78600e6i | −0.109984 | + | 0.190498i | ||||
\(985\) | 1.25830e7 | + | 2.17945e7i | 0.413233 | + | 0.715741i | ||||
\(986\) | 6.65454e7 | 2.17985 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9.52327e7 | −3.10380 | ||||||||
\(989\) | −6.34673e6 | − | 1.09929e7i | −0.206328 | − | 0.357371i | ||||
\(990\) | 3.63982e6 | − | 6.30436e6i | 0.118030 | − | 0.204434i | ||||
\(991\) | −1.74001e7 | + | 3.01379e7i | −0.562819 | + | 0.974831i | 0.434430 | + | 0.900706i | \(0.356950\pi\) |
−0.997249 | + | 0.0741255i | \(0.976383\pi\) | |||||||
\(992\) | −3.96173e6 | − | 6.86191e6i | −0.127822 | − | 0.221394i | ||||
\(993\) | −1.59586e6 | −0.0513598 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.49829e7 | 0.479774 | ||||||||
\(996\) | 5.37107e6 | + | 9.30296e6i | 0.171558 | + | 0.297148i | ||||
\(997\) | −4.70426e6 | + | 8.14802e6i | −0.149883 | + | 0.259606i | −0.931184 | − | 0.364549i | \(-0.881223\pi\) |
0.781301 | + | 0.624155i | \(0.214557\pi\) | |||||||
\(998\) | 1.42666e7 | − | 2.47105e7i | 0.453413 | − | 0.785335i | ||||
\(999\) | −646335. | − | 1.11949e6i | −0.0204901 | − | 0.0354899i |
(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 | 147.6.e.n.67.2 | 4 | ||
7.2 | even | 3 | inner | 147.6.e.n.79.2 | 4 | ||
7.3 | odd | 6 | 147.6.a.j.1.1 | yes | 2 | ||
7.4 | even | 3 | 147.6.a.h.1.1 | ✓ | 2 | ||
7.5 | odd | 6 | 147.6.e.m.79.2 | 4 | |||
7.6 | odd | 2 | 147.6.e.m.67.2 | 4 | |||
21.11 | odd | 6 | 441.6.a.q.1.2 | 2 | |||
21.17 | even | 6 | 441.6.a.r.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
147.6.a.h.1.1 | ✓ | 2 | 7.4 | even | 3 | ||
147.6.a.j.1.1 | yes | 2 | 7.3 | odd | 6 | ||
147.6.e.m.67.2 | 4 | 7.6 | odd | 2 | |||
147.6.e.m.79.2 | 4 | 7.5 | odd | 6 | |||
147.6.e.n.67.2 | 4 | 1.1 | even | 1 | trivial | ||
147.6.e.n.79.2 | 4 | 7.2 | even | 3 | inner | ||
441.6.a.q.1.2 | 2 | 21.11 | odd | 6 | |||
441.6.a.r.1.2 | 2 | 21.17 | even | 6 |