Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [387,5,Mod(343,387)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(387, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("387.343");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 387 = 3^{2} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 387.b (of order \(2\), degree \(1\), 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: | \(40.0041757134\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 142x^{10} + 7173x^{8} + 157368x^{6} + 1510016x^{4} + 5098688x^{2} + 90352 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 43) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 343.2 | ||
Root | \(-6.72223i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 387.343 |
Dual form | 387.5.b.c.343.11 |
$q$-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 \(\left(\mathbb{Z}/387\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(173\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 6.72223i | − | 1.68056i | −0.542154 | − | 0.840279i | \(-0.682391\pi\) | ||
0.542154 | − | 0.840279i | \(-0.317609\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −29.1884 | −1.82427 | ||||||||
\(5\) | 1.48242i | 0.0592969i | 0.999560 | + | 0.0296484i | \(0.00943877\pi\) | ||||
−0.999560 | + | 0.0296484i | \(0.990561\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 13.7963i | 0.281556i | 0.990041 | + | 0.140778i | \(0.0449604\pi\) | ||||
−0.990041 | + | 0.140778i | \(0.955040\pi\) | |||||||
\(8\) | 88.6554i | 1.38524i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 9.96518 | 0.0996518 | ||||||||
\(11\) | 10.2025 | 0.0843185 | 0.0421592 | − | 0.999111i | \(-0.486576\pi\) | ||||
0.0421592 | + | 0.999111i | \(0.486576\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 98.4183 | 0.582357 | 0.291179 | − | 0.956669i | \(-0.405953\pi\) | ||||
0.291179 | + | 0.956669i | \(0.405953\pi\) | |||||||
\(14\) | 92.7416 | 0.473172 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 128.948 | 0.503703 | ||||||||
\(17\) | 286.515 | 0.991400 | 0.495700 | − | 0.868494i | \(-0.334911\pi\) | ||||
0.495700 | + | 0.868494i | \(0.334911\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 367.004i | 1.01663i | 0.861171 | + | 0.508316i | \(0.169732\pi\) | ||||
−0.861171 | + | 0.508316i | \(0.830268\pi\) | |||||||
\(20\) | − | 43.2695i | − | 0.108174i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 68.5838i | − | 0.141702i | ||||||
\(23\) | 242.039 | 0.457540 | 0.228770 | − | 0.973480i | \(-0.426530\pi\) | ||||
0.228770 | + | 0.973480i | \(0.426530\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 622.802 | 0.996484 | ||||||||
\(26\) | − | 661.591i | − | 0.978685i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 402.691i | − | 0.513636i | ||||||
\(29\) | − | 1147.40i | − | 1.36433i | −0.731199 | − | 0.682164i | \(-0.761039\pi\) | ||
0.731199 | − | 0.682164i | \(-0.238961\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 895.225 | 0.931556 | 0.465778 | − | 0.884902i | \(-0.345775\pi\) | ||||
0.465778 | + | 0.884902i | \(0.345775\pi\) | |||||||
\(32\) | 551.669i | 0.538739i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 1926.02i | − | 1.66611i | ||||||
\(35\) | −20.4519 | −0.0166954 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2295.69i | − | 1.67691i | −0.544969 | − | 0.838456i | \(-0.683459\pi\) | ||
0.544969 | − | 0.838456i | \(-0.316541\pi\) | |||||||
\(38\) | 2467.09 | 1.70851 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −131.425 | −0.0821405 | ||||||||
\(41\) | −1692.26 | −1.00670 | −0.503348 | − | 0.864084i | \(-0.667899\pi\) | ||||
−0.503348 | + | 0.864084i | \(0.667899\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1546.34 | + | 1013.73i | −0.836310 | + | 0.548257i | ||||
\(44\) | −297.796 | −0.153820 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 1627.04i | − | 0.768923i | ||||||
\(47\) | −743.419 | −0.336541 | −0.168271 | − | 0.985741i | \(-0.553818\pi\) | ||||
−0.168271 | + | 0.985741i | \(0.553818\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2210.66 | 0.920726 | ||||||||
\(50\) | − | 4186.62i | − | 1.67465i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2872.67 | −1.06238 | ||||||||
\(53\) | −99.3399 | −0.0353649 | −0.0176824 | − | 0.999844i | \(-0.505629\pi\) | ||||
−0.0176824 | + | 0.999844i | \(0.505629\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.1245i | 0.00499982i | ||||||||
\(56\) | −1223.11 | −0.390023 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7713.09 | −2.29283 | ||||||||
\(59\) | −3286.35 | −0.944082 | −0.472041 | − | 0.881577i | \(-0.656483\pi\) | ||||
−0.472041 | + | 0.881577i | \(0.656483\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 3223.22i | − | 0.866225i | −0.901340 | − | 0.433112i | \(-0.857415\pi\) | ||
0.901340 | − | 0.433112i | \(-0.142585\pi\) | |||||||
\(62\) | − | 6017.91i | − | 1.56553i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5771.61 | 1.40908 | ||||||||
\(65\) | 145.898i | 0.0345320i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5556.36 | 1.23777 | 0.618886 | − | 0.785481i | \(-0.287584\pi\) | ||||
0.618886 | + | 0.785481i | \(0.287584\pi\) | |||||||
\(68\) | −8362.90 | −1.80859 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 137.482i | 0.0280576i | ||||||||
\(71\) | − | 2953.33i | − | 0.585861i | −0.956134 | − | 0.292930i | \(-0.905370\pi\) | ||
0.956134 | − | 0.292930i | \(-0.0946305\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 3618.34i | − | 0.678991i | −0.940608 | − | 0.339496i | \(-0.889744\pi\) | ||
0.940608 | − | 0.339496i | \(-0.110256\pi\) | |||||||
\(74\) | −15432.2 | −2.81815 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 10712.3i | − | 1.85461i | ||||||
\(77\) | 140.757i | 0.0237404i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2380.74 | 0.381468 | 0.190734 | − | 0.981642i | \(-0.438913\pi\) | ||||
0.190734 | + | 0.981642i | \(0.438913\pi\) | |||||||
\(80\) | 191.155i | 0.0298680i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 11375.7i | 1.69181i | ||||||||
\(83\) | 6427.91 | 0.933069 | 0.466535 | − | 0.884503i | \(-0.345502\pi\) | ||||
0.466535 | + | 0.884503i | \(0.345502\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 424.736i | 0.0587869i | ||||||||
\(86\) | 6814.51 | + | 10394.8i | 0.921377 | + | 1.40547i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 904.510i | 0.116801i | ||||||||
\(89\) | − | 3293.36i | − | 0.415776i | −0.978153 | − | 0.207888i | \(-0.933341\pi\) | ||
0.978153 | − | 0.207888i | \(-0.0666590\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1357.80i | 0.163966i | ||||||||
\(92\) | −7064.72 | −0.834679 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4997.44i | 0.565577i | ||||||||
\(95\) | −544.055 | −0.0602831 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9329.95 | −0.991599 | −0.495799 | − | 0.868437i | \(-0.665125\pi\) | ||||
−0.495799 | + | 0.868437i | \(0.665125\pi\) | |||||||
\(98\) | − | 14860.6i | − | 1.54733i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −18178.6 | −1.81786 | ||||||||
\(101\) | 13572.8 | 1.33054 | 0.665270 | − | 0.746603i | \(-0.268317\pi\) | ||||
0.665270 | + | 0.746603i | \(0.268317\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5527.90 | −0.521057 | −0.260529 | − | 0.965466i | \(-0.583897\pi\) | ||||
−0.260529 | + | 0.965466i | \(0.583897\pi\) | |||||||
\(104\) | 8725.32i | 0.806705i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 667.786i | 0.0594327i | ||||||||
\(107\) | 2435.69 | 0.212742 | 0.106371 | − | 0.994326i | \(-0.466077\pi\) | ||||
0.106371 | + | 0.994326i | \(0.466077\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3235.93 | 0.272362 | 0.136181 | − | 0.990684i | \(-0.456517\pi\) | ||||
0.136181 | + | 0.990684i | \(0.456517\pi\) | |||||||
\(110\) | 101.670 | 0.00840249 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1779.00i | 0.141821i | ||||||||
\(113\) | 14680.9i | 1.14973i | 0.818247 | + | 0.574867i | \(0.194946\pi\) | ||||
−0.818247 | + | 0.574867i | \(0.805054\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 358.803i | 0.0271307i | ||||||||
\(116\) | 33490.7i | 2.48891i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 22091.6i | 1.58658i | ||||||||
\(119\) | 3952.83i | 0.279135i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14536.9 | −0.992890 | ||||||||
\(122\) | −21667.2 | −1.45574 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −26130.2 | −1.69941 | ||||||||
\(125\) | 1849.77i | 0.118385i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 27000.0 | 1.67400 | 0.837001 | − | 0.547201i | \(-0.184307\pi\) | ||||
0.837001 | + | 0.547201i | \(0.184307\pi\) | |||||||
\(128\) | − | 29971.4i | − | 1.82931i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 980.757 | 0.0580329 | ||||||||
\(131\) | 17222.3i | 1.00357i | 0.864991 | + | 0.501787i | \(0.167324\pi\) | ||||
−0.864991 | + | 0.501787i | \(0.832676\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5063.28 | −0.286239 | ||||||||
\(134\) | − | 37351.1i | − | 2.08015i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 25401.1i | 1.37333i | ||||||||
\(137\) | − | 1880.48i | − | 0.100191i | −0.998744 | − | 0.0500955i | \(-0.984047\pi\) | ||
0.998744 | − | 0.0500955i | \(-0.0159526\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20668.9 | 1.06977 | 0.534883 | − | 0.844926i | \(-0.320356\pi\) | ||||
0.534883 | + | 0.844926i | \(0.320356\pi\) | |||||||
\(140\) | 596.957 | 0.0304570 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −19852.9 | −0.984573 | ||||||||
\(143\) | 1004.12 | 0.0491035 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1700.93 | 0.0809004 | ||||||||
\(146\) | −24323.3 | −1.14108 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 67007.6i | 3.05915i | ||||||||
\(149\) | − | 13651.5i | − | 0.614904i | −0.951564 | − | 0.307452i | \(-0.900524\pi\) | ||
0.951564 | − | 0.307452i | \(-0.0994763\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 41870.6i | − | 1.83635i | −0.396175 | − | 0.918175i | \(-0.629662\pi\) | ||
0.396175 | − | 0.918175i | \(-0.370338\pi\) | |||||||
\(152\) | −32536.9 | −1.40828 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 946.200 | 0.0398971 | ||||||||
\(155\) | 1327.10i | 0.0552383i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 41348.7i | − | 1.67750i | −0.544517 | − | 0.838750i | \(-0.683287\pi\) | ||
0.544517 | − | 0.838750i | \(-0.316713\pi\) | |||||||
\(158\) | − | 16003.9i | − | 0.641079i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −817.806 | −0.0319455 | ||||||||
\(161\) | 3339.23i | 0.128823i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6111.31i | 0.230017i | 0.993365 | + | 0.115008i | \(0.0366895\pi\) | ||||
−0.993365 | + | 0.115008i | \(0.963311\pi\) | |||||||
\(164\) | 49394.2 | 1.83649 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 43209.9i | − | 1.56808i | ||||||
\(167\) | −34991.0 | −1.25465 | −0.627326 | − | 0.778757i | \(-0.715851\pi\) | ||||
−0.627326 | + | 0.778757i | \(0.715851\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −18874.8 | −0.660860 | ||||||||
\(170\) | 2855.17 | 0.0987949 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 45135.1 | − | 29589.1i | 1.52566 | − | 1.00017i | ||||
\(173\) | 4597.15 | 0.153602 | 0.0768009 | − | 0.997046i | \(-0.475529\pi\) | ||||
0.0768009 | + | 0.997046i | \(0.475529\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8592.34i | 0.280566i | ||||||||
\(176\) | 1315.60 | 0.0424715 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −22138.7 | −0.698736 | ||||||||
\(179\) | − | 26315.3i | − | 0.821301i | −0.911793 | − | 0.410650i | \(-0.865302\pi\) | ||
0.911793 | − | 0.410650i | \(-0.134698\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 48133.4 | 1.46923 | 0.734614 | − | 0.678485i | \(-0.237363\pi\) | ||||
0.734614 | + | 0.678485i | \(0.237363\pi\) | |||||||
\(182\) | 9127.48 | 0.275555 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 21458.0i | 0.633803i | ||||||||
\(185\) | 3403.19 | 0.0994357 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2923.18 | 0.0835934 | ||||||||
\(188\) | 21699.2 | 0.613943 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3657.26i | 0.101309i | ||||||||
\(191\) | − | 46954.1i | − | 1.28708i | −0.765411 | − | 0.643542i | \(-0.777464\pi\) | ||
0.765411 | − | 0.643542i | \(-0.222536\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18967.8 | 0.509215 | 0.254608 | − | 0.967044i | \(-0.418054\pi\) | ||||
0.254608 | + | 0.967044i | \(0.418054\pi\) | |||||||
\(194\) | 62718.1i | 1.66644i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −64525.7 | −1.67966 | ||||||||
\(197\) | 77177.1 | 1.98864 | 0.994320 | − | 0.106435i | \(-0.0339435\pi\) | ||||
0.994320 | + | 0.106435i | \(0.0339435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 2250.86i | − | 0.0568385i | −0.999596 | − | 0.0284192i | \(-0.990953\pi\) | ||
0.999596 | − | 0.0284192i | \(-0.00904734\pi\) | |||||||
\(200\) | 55214.8i | 1.38037i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 91239.7i | − | 2.23605i | ||||||
\(203\) | 15829.8 | 0.384135 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 2508.64i | − | 0.0596939i | ||||||
\(206\) | 37159.8i | 0.875667i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 12690.8 | 0.293335 | ||||||||
\(209\) | 3744.37i | 0.0857208i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 64198.9i | 1.44199i | 0.692939 | + | 0.720996i | \(0.256315\pi\) | ||||
−0.692939 | + | 0.720996i | \(0.743685\pi\) | |||||||
\(212\) | 2899.57 | 0.0645152 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 16373.2i | − | 0.357526i | ||||||
\(215\) | −1502.77 | − | 2292.32i | −0.0325099 | − | 0.0495906i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12350.8i | 0.262285i | ||||||||
\(218\) | − | 21752.7i | − | 0.457720i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 441.459i | − | 0.00912105i | ||||||
\(221\) | 28198.3 | 0.577349 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 53407.6i | − | 1.07397i | −0.843591 | − | 0.536987i | \(-0.819563\pi\) | ||
0.843591 | − | 0.536987i | \(-0.180437\pi\) | |||||||
\(224\) | −7610.96 | −0.151685 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 98688.7 | 1.93219 | ||||||||
\(227\) | − | 43494.8i | − | 0.844084i | −0.906576 | − | 0.422042i | \(-0.861313\pi\) | ||
0.906576 | − | 0.422042i | \(-0.138687\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 67145.4 | 1.28040 | 0.640199 | − | 0.768209i | \(-0.278852\pi\) | ||||
0.640199 | + | 0.768209i | \(0.278852\pi\) | |||||||
\(230\) | 2411.96 | 0.0455947 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 101723. | 1.88992 | ||||||||
\(233\) | 76734.0i | 1.41344i | 0.707496 | + | 0.706718i | \(0.249825\pi\) | ||||
−0.707496 | + | 0.706718i | \(0.750175\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 1102.06i | − | 0.0199558i | ||||||
\(236\) | 95923.2 | 1.72226 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 26571.8 | 0.469103 | ||||||||
\(239\) | 26767.6 | 0.468613 | 0.234307 | − | 0.972163i | \(-0.424718\pi\) | ||||
0.234307 | + | 0.972163i | \(0.424718\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 100445.i | − | 1.72939i | −0.502297 | − | 0.864695i | \(-0.667512\pi\) | ||
0.502297 | − | 0.864695i | \(-0.332488\pi\) | |||||||
\(242\) | 97720.5i | 1.66861i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 94080.7i | 1.58023i | ||||||||
\(245\) | 3277.14i | 0.0545962i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 36119.9i | 0.592043i | ||||||||
\(248\) | 79366.5i | 1.29043i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 12434.6 | 0.198953 | ||||||||
\(251\) | 71737.6 | 1.13867 | 0.569337 | − | 0.822104i | \(-0.307200\pi\) | ||||
0.569337 | + | 0.822104i | \(0.307200\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2469.41 | 0.0385791 | ||||||||
\(254\) | − | 181500.i | − | 2.81326i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −109129. | −1.66518 | ||||||||
\(257\) | − | 7267.88i | − | 0.110038i | −0.998485 | − | 0.0550189i | \(-0.982478\pi\) | ||
0.998485 | − | 0.0550189i | \(-0.0175219\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 31672.0 | 0.472145 | ||||||||
\(260\) | − | 4258.51i | − | 0.0629958i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 115773. | 1.68656 | ||||||||
\(263\) | 73838.4i | 1.06751i | 0.845640 | + | 0.533754i | \(0.179219\pi\) | ||||
−0.845640 | + | 0.533754i | \(0.820781\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 147.264i | − | 0.00209703i | ||||||
\(266\) | 34036.6i | 0.481041i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −162181. | −2.25804 | ||||||||
\(269\) | −127266. | −1.75877 | −0.879384 | − | 0.476113i | \(-0.842045\pi\) | ||||
−0.879384 | + | 0.476113i | \(0.842045\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 44182.9 | 0.601610 | 0.300805 | − | 0.953686i | \(-0.402745\pi\) | ||||
0.300805 | + | 0.953686i | \(0.402745\pi\) | |||||||
\(272\) | 36945.5 | 0.499371 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12641.0 | −0.168377 | ||||||||
\(275\) | 6354.17 | 0.0840220 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 31197.7i | 0.406596i | 0.979117 | + | 0.203298i | \(0.0651660\pi\) | ||||
−0.979117 | + | 0.203298i | \(0.934834\pi\) | |||||||
\(278\) | − | 138941.i | − | 1.79780i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | − | 1813.17i | − | 0.0231272i | ||||||
\(281\) | 140212. | 1.77572 | 0.887859 | − | 0.460116i | \(-0.152192\pi\) | ||||
0.887859 | + | 0.460116i | \(0.152192\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2024.17 | 0.0252740 | 0.0126370 | − | 0.999920i | \(-0.495977\pi\) | ||||
0.0126370 | + | 0.999920i | \(0.495977\pi\) | |||||||
\(284\) | 86202.8i | 1.06877i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 6749.91i | − | 0.0825212i | ||||||
\(287\) | − | 23346.8i | − | 0.283442i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1430.31 | −0.0171252 | ||||||||
\(290\) | − | 11434.0i | − | 0.135958i | ||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 105614.i | 1.23867i | ||||||||
\(293\) | −75732.9 | −0.882164 | −0.441082 | − | 0.897467i | \(-0.645405\pi\) | ||||
−0.441082 | + | 0.897467i | \(0.645405\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 4871.76i | − | 0.0559811i | ||||||
\(296\) | 203526. | 2.32293 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −91768.4 | −1.03338 | ||||||||
\(299\) | 23821.0 | 0.266452 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13985.6 | − | 21333.7i | −0.154365 | − | 0.235468i | ||||
\(302\) | −281464. | −3.08609 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 47324.4i | 0.512080i | ||||||||
\(305\) | 4778.18 | 0.0513644 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −158838. | −1.68530 | −0.842652 | − | 0.538458i | \(-0.819007\pi\) | ||||
−0.842652 | + | 0.538458i | \(0.819007\pi\) | |||||||
\(308\) | − | 4108.47i | − | 0.0433090i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 8921.08 | 0.0928312 | ||||||||
\(311\) | 49344.1 | 0.510169 | 0.255085 | − | 0.966919i | \(-0.417897\pi\) | ||||
0.255085 | + | 0.966919i | \(0.417897\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 66350.6i | 0.677261i | 0.940919 | + | 0.338631i | \(0.109964\pi\) | ||||
−0.940919 | + | 0.338631i | \(0.890036\pi\) | |||||||
\(314\) | −277955. | −2.81914 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −69490.0 | −0.695903 | ||||||||
\(317\) | −15717.4 | −0.156409 | −0.0782046 | − | 0.996937i | \(-0.524919\pi\) | ||||
−0.0782046 | + | 0.996937i | \(0.524919\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 11706.4i | − | 0.115038i | ||||||
\(320\) | 8555.96i | 0.0835543i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 22447.1 | 0.216495 | ||||||||
\(323\) | 105152.i | 1.00789i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 61295.2 | 0.580309 | ||||||||
\(326\) | 41081.6 | 0.386556 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 150028.i | − | 1.39452i | ||||||
\(329\) | − | 10256.4i | − | 0.0947553i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 85452.6i | 0.779954i | 0.920825 | + | 0.389977i | \(0.127517\pi\) | ||||
−0.920825 | + | 0.389977i | \(0.872483\pi\) | |||||||
\(332\) | −187620. | −1.70217 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 235218.i | 2.10852i | ||||||||
\(335\) | 8236.87i | 0.0733960i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −146925. | −1.29371 | −0.646855 | − | 0.762613i | \(-0.723916\pi\) | ||||
−0.646855 | + | 0.762613i | \(0.723916\pi\) | |||||||
\(338\) | 126881.i | 1.11061i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − | 12397.4i | − | 0.107244i | ||||||
\(341\) | 9133.57 | 0.0785474 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 63623.7i | 0.540793i | ||||||||
\(344\) | −89872.4 | − | 137091.i | −0.759468 | − | 1.15849i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 30903.1i | − | 0.258137i | ||||||
\(347\) | − | 78623.4i | − | 0.652969i | −0.945203 | − | 0.326485i | \(-0.894136\pi\) | ||
0.945203 | − | 0.326485i | \(-0.105864\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 165981.i | 1.36273i | 0.731945 | + | 0.681363i | \(0.238613\pi\) | ||||
−0.731945 | + | 0.681363i | \(0.761387\pi\) | |||||||
\(350\) | 57759.7 | 0.471508 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5628.42i | 0.0454257i | ||||||||
\(353\) | −53106.9 | −0.426188 | −0.213094 | − | 0.977032i | \(-0.568354\pi\) | ||||
−0.213094 | + | 0.977032i | \(0.568354\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4378.07 | 0.0347397 | ||||||||
\(356\) | 96127.9i | 0.758490i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −176897. | −1.38024 | ||||||||
\(359\) | 120101. | 0.931879 | 0.465939 | − | 0.884817i | \(-0.345716\pi\) | ||||
0.465939 | + | 0.884817i | \(0.345716\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4370.92 | −0.0335396 | ||||||||
\(362\) | − | 323564.i | − | 2.46912i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 39632.1i | − | 0.299120i | ||||||
\(365\) | 5363.91 | 0.0402620 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −37702.0 | −0.279919 | −0.139959 | − | 0.990157i | \(-0.544697\pi\) | ||||
−0.139959 | + | 0.990157i | \(0.544697\pi\) | |||||||
\(368\) | 31210.4 | 0.230464 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 22877.0i | − | 0.167107i | ||||||
\(371\) | − | 1370.52i | − | 0.00995720i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 139388.i | 1.00186i | 0.865488 | + | 0.500930i | \(0.167009\pi\) | ||||
−0.865488 | + | 0.500930i | \(0.832991\pi\) | |||||||
\(374\) | − | 19650.3i | − | 0.140484i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 65908.1i | − | 0.466190i | ||||||
\(377\) | − | 112925.i | − | 0.794526i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −88126.5 | −0.613519 | −0.306759 | − | 0.951787i | \(-0.599245\pi\) | ||||
−0.306759 | + | 0.951787i | \(0.599245\pi\) | |||||||
\(380\) | 15880.1 | 0.109973 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −315636. | −2.16302 | ||||||||
\(383\) | 250818.i | 1.70986i | 0.518743 | + | 0.854930i | \(0.326400\pi\) | ||||
−0.518743 | + | 0.854930i | \(0.673600\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −208.661 | −0.00140773 | ||||||||
\(386\) | − | 127506.i | − | 0.855766i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 272326. | 1.80895 | ||||||||
\(389\) | 34015.7i | 0.224792i | 0.993664 | + | 0.112396i | \(0.0358524\pi\) | ||||
−0.993664 | + | 0.112396i | \(0.964148\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 69347.7 | 0.453605 | ||||||||
\(392\) | 195987.i | 1.27543i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 518802.i | − | 3.34202i | ||||||
\(395\) | 3529.26i | 0.0226199i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 206559. | 1.31058 | 0.655291 | − | 0.755377i | \(-0.272546\pi\) | ||||
0.655291 | + | 0.755377i | \(0.272546\pi\) | |||||||
\(398\) | −15130.8 | −0.0955203 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 80309.1 | 0.501932 | ||||||||
\(401\) | −85162.0 | −0.529611 | −0.264806 | − | 0.964302i | \(-0.585308\pi\) | ||||
−0.264806 | + | 0.964302i | \(0.585308\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 88106.5 | 0.542498 | ||||||||
\(404\) | −396169. | −2.42727 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 106412.i | − | 0.645561i | ||||||
\(407\) | − | 23421.9i | − | 0.141395i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 216421.i | − | 1.29375i | −0.762594 | − | 0.646877i | \(-0.776075\pi\) | ||
0.762594 | − | 0.646877i | \(-0.223925\pi\) | |||||||
\(410\) | −16863.6 | −0.100319 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 161350. | 0.950552 | ||||||||
\(413\) | − | 45339.3i | − | 0.265812i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9528.88i | 0.0553281i | ||||||||
\(416\) | 54294.3i | 0.313738i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 25170.5 | 0.144059 | ||||||||
\(419\) | 195727.i | 1.11487i | 0.830222 | + | 0.557433i | \(0.188214\pi\) | ||||
−0.830222 | + | 0.557433i | \(0.811786\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 216454.i | 1.22124i | 0.791924 | + | 0.610620i | \(0.209080\pi\) | ||||
−0.791924 | + | 0.610620i | \(0.790920\pi\) | |||||||
\(422\) | 431560. | 2.42335 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 8807.02i | − | 0.0489889i | ||||||
\(425\) | 178442. | 0.987915 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 44468.4 | 0.243891 | ||||||||
\(428\) | −71093.8 | −0.388100 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −15409.5 | + | 10102.0i | −0.0833398 | + | 0.0546348i | ||||
\(431\) | 219971. | 1.18416 | 0.592082 | − | 0.805878i | \(-0.298306\pi\) | ||||
0.592082 | + | 0.805878i | \(0.298306\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 141123.i | − | 0.752699i | −0.926478 | − | 0.376349i | \(-0.877179\pi\) | ||
0.926478 | − | 0.376349i | \(-0.122821\pi\) | |||||||
\(434\) | 83024.6 | 0.440786 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −94451.7 | −0.496863 | ||||||||
\(437\) | 88829.2i | 0.465150i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18660.8 | −0.0968279 | −0.0484139 | − | 0.998827i | \(-0.515417\pi\) | ||||
−0.0484139 | + | 0.998827i | \(0.515417\pi\) | |||||||
\(440\) | −1340.87 | −0.00692596 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 189556.i | − | 0.970268i | ||||||
\(443\) | −21366.2 | −0.108873 | −0.0544366 | − | 0.998517i | \(-0.517336\pi\) | ||||
−0.0544366 | + | 0.998517i | \(0.517336\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4882.15 | 0.0246542 | ||||||||
\(446\) | −359018. | −1.80487 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 79626.7i | 0.396737i | ||||||||
\(449\) | 101517.i | 0.503553i | 0.967785 | + | 0.251777i | \(0.0810148\pi\) | ||||
−0.967785 | + | 0.251777i | \(0.918985\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17265.3 | −0.0848831 | ||||||||
\(452\) | − | 428513.i | − | 2.09743i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −292382. | −1.41853 | ||||||||
\(455\) | −2012.84 | −0.00972269 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 308003.i | 1.47477i | 0.675475 | + | 0.737383i | \(0.263939\pi\) | ||||
−0.675475 | + | 0.737383i | \(0.736061\pi\) | |||||||
\(458\) | − | 451367.i | − | 2.15178i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 10472.9i | − | 0.0494938i | ||||||
\(461\) | −156343. | −0.735660 | −0.367830 | − | 0.929893i | \(-0.619899\pi\) | ||||
−0.367830 | + | 0.929893i | \(0.619899\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 203393.i | 0.948800i | 0.880309 | + | 0.474400i | \(0.157335\pi\) | ||||
−0.880309 | + | 0.474400i | \(0.842665\pi\) | |||||||
\(464\) | − | 147955.i | − | 0.687216i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 515824. | 2.37536 | ||||||||
\(467\) | − | 208975.i | − | 0.958209i | −0.877758 | − | 0.479104i | \(-0.840962\pi\) | ||
0.877758 | − | 0.479104i | \(-0.159038\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 76657.0i | 0.348503i | ||||||||
\(470\) | −7408.31 | −0.0335369 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 291353.i | − | 1.30778i | ||||||
\(473\) | −15776.6 | + | 10342.6i | −0.0705164 | + | 0.0462282i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 228571.i | 1.01306i | ||||||||
\(476\) | − | 115377.i | − | 0.509219i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 179938.i | − | 0.787531i | ||||||
\(479\) | −98547.6 | −0.429512 | −0.214756 | − | 0.976668i | \(-0.568896\pi\) | ||||
−0.214756 | + | 0.976668i | \(0.568896\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 225938.i | − | 0.976562i | ||||||
\(482\) | −675212. | −2.90634 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 424309. | 1.81130 | ||||||||
\(485\) | − | 13830.9i | − | 0.0587987i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −319902. | −1.34884 | −0.674418 | − | 0.738350i | \(-0.735605\pi\) | ||||
−0.674418 | + | 0.738350i | \(0.735605\pi\) | |||||||
\(488\) | 285756. | 1.19993 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 22029.7 | 0.0917520 | ||||||||
\(491\) | 454263.i | 1.88428i | 0.335226 | + | 0.942138i | \(0.391187\pi\) | ||||
−0.335226 | + | 0.942138i | \(0.608813\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 328747.i | − | 1.35260i | ||||||
\(494\) | 242806. | 0.994962 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 115437. | 0.469227 | ||||||||
\(497\) | 40744.8 | 0.164953 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 336510.i | − | 1.35144i | −0.737158 | − | 0.675720i | \(-0.763833\pi\) | ||
0.737158 | − | 0.675720i | \(-0.236167\pi\) | |||||||
\(500\) | − | 53991.8i | − | 0.215967i | ||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 482237.i | − | 1.91361i | ||||||
\(503\) | − | 313054.i | − | 1.23732i | −0.785658 | − | 0.618661i | \(-0.787675\pi\) | ||
0.785658 | − | 0.618661i | \(-0.212325\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20120.7i | 0.0788968i | ||||||||
\(506\) | − | 16599.9i | − | 0.0648344i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −788086. | −3.05384 | ||||||||
\(509\) | −406043. | −1.56724 | −0.783621 | − | 0.621239i | \(-0.786630\pi\) | ||||
−0.783621 | + | 0.621239i | \(0.786630\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 49919.6 | 0.191174 | ||||||||
\(512\) | 254048.i | 0.969114i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −48856.4 | −0.184925 | ||||||||
\(515\) | − | 8194.68i | − | 0.0308971i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7584.76 | −0.0283766 | ||||||||
\(518\) | − | 212906.i | − | 0.793467i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −12934.6 | −0.0478351 | ||||||||
\(521\) | 221529.i | 0.816122i | 0.912955 | + | 0.408061i | \(0.133795\pi\) | ||||
−0.912955 | + | 0.408061i | \(0.866205\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 146666.i | − | 0.536199i | −0.963391 | − | 0.268099i | \(-0.913604\pi\) | ||
0.963391 | − | 0.268099i | \(-0.0863955\pi\) | |||||||
\(524\) | − | 502692.i | − | 1.83080i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 496359. | 1.79401 | ||||||||
\(527\) | 256495. | 0.923545 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −221258. | −0.790657 | ||||||||
\(530\) | −989.940 | −0.00352417 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 147789. | 0.522179 | ||||||||
\(533\) | −166549. | −0.586257 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3610.71i | 0.0126150i | ||||||||
\(536\) | 492601.i | 1.71461i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 855513.i | 2.95571i | ||||||||
\(539\) | 22554.4 | 0.0776342 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 38164.1 | 0.130395 | 0.0651974 | − | 0.997872i | \(-0.479232\pi\) | ||||
0.0651974 | + | 0.997872i | \(0.479232\pi\) | |||||||
\(542\) | − | 297007.i | − | 1.01104i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 158061.i | 0.534106i | ||||||||
\(545\) | 4797.02i | 0.0161502i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 105758. | 0.353459 | 0.176730 | − | 0.984259i | \(-0.443448\pi\) | ||||
0.176730 | + | 0.984259i | \(0.443448\pi\) | |||||||
\(548\) | 54888.3i | 0.182776i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | − | 42714.2i | − | 0.141204i | ||||||
\(551\) | 421100. | 1.38702 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 32845.3i | 0.107405i | ||||||||
\(554\) | 209718. | 0.683308 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −603293. | −1.95155 | ||||||||
\(557\) | −280135. | −0.902936 | −0.451468 | − | 0.892287i | \(-0.649100\pi\) | ||||
−0.451468 | + | 0.892287i | \(0.649100\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −152188. | + | 99769.3i | −0.487031 | + | 0.319281i | ||||
\(560\) | −2637.23 | −0.00840953 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 942541.i | − | 2.98420i | ||||||
\(563\) | 403332. | 1.27247 | 0.636233 | − | 0.771497i | \(-0.280492\pi\) | ||||
0.636233 | + | 0.771497i | \(0.280492\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21763.3 | −0.0681756 | ||||||||
\(566\) | − | 13606.9i | − | 0.0424744i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 261828. | 0.811559 | ||||||||
\(569\) | 72865.2 | 0.225059 | 0.112529 | − | 0.993648i | \(-0.464105\pi\) | ||||
0.112529 | + | 0.993648i | \(0.464105\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 280074.i | 0.859015i | 0.903063 | + | 0.429507i | \(0.141313\pi\) | ||||
−0.903063 | + | 0.429507i | \(0.858687\pi\) | |||||||
\(572\) | −29308.6 | −0.0895782 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −156943. | −0.476340 | ||||||||
\(575\) | 150742. | 0.455931 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 205999.i | − | 0.618748i | −0.950940 | − | 0.309374i | \(-0.899881\pi\) | ||
0.950940 | − | 0.309374i | \(-0.100119\pi\) | |||||||
\(578\) | 9614.89i | 0.0287799i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −49647.4 | −0.147584 | ||||||||
\(581\) | 88681.2i | 0.262712i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1013.52 | −0.00298191 | ||||||||
\(584\) | 320786. | 0.940566 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 509094.i | 1.48253i | ||||||||
\(587\) | − | 466185.i | − | 1.35295i | −0.736464 | − | 0.676476i | \(-0.763506\pi\) | ||
0.736464 | − | 0.676476i | \(-0.236494\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 328551.i | 0.947049i | ||||||||
\(590\) | −32749.1 | −0.0940795 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 296025.i | − | 0.844666i | ||||||
\(593\) | 284311.i | 0.808507i | 0.914647 | + | 0.404253i | \(0.132469\pi\) | ||||
−0.914647 | + | 0.404253i | \(0.867531\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5859.76 | −0.0165518 | ||||||||
\(596\) | 398465.i | 1.12175i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 160131.i | − | 0.447787i | ||||||
\(599\) | −438880. | −1.22318 | −0.611592 | − | 0.791173i | \(-0.709471\pi\) | ||||
−0.611592 | + | 0.791173i | \(0.709471\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 52157.2i | − | 0.144399i | −0.997390 | − | 0.0721997i | \(-0.976998\pi\) | ||
0.997390 | − | 0.0721997i | \(-0.0230019\pi\) | |||||||
\(602\) | −143410. | + | 94014.7i | −0.395718 | + | 0.259420i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.22214e6i | 3.35001i | ||||||||
\(605\) | − | 21549.8i | − | 0.0588753i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 328500.i | 0.891575i | 0.895139 | + | 0.445788i | \(0.147076\pi\) | ||||
−0.895139 | + | 0.445788i | \(0.852924\pi\) | |||||||
\(608\) | −202465. | −0.547699 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 32120.0i | − | 0.0863209i | ||||||
\(611\) | −73166.1 | −0.195987 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −194249. | −0.516937 | −0.258468 | − | 0.966020i | \(-0.583218\pi\) | ||||
−0.258468 | + | 0.966020i | \(0.583218\pi\) | |||||||
\(614\) | 1.06775e6i | 2.83225i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12478.9 | −0.0328862 | ||||||||
\(617\) | 203384. | 0.534253 | 0.267126 | − | 0.963662i | \(-0.413926\pi\) | ||||
0.267126 | + | 0.963662i | \(0.413926\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 504248. | 1.31602 | 0.658011 | − | 0.753008i | \(-0.271398\pi\) | ||||
0.658011 | + | 0.753008i | \(0.271398\pi\) | |||||||
\(620\) | − | 38735.9i | − | 0.100770i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 331702.i | − | 0.857369i | ||||||
\(623\) | 45436.1 | 0.117064 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 386509. | 0.989464 | ||||||||
\(626\) | 446024. | 1.13818 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.20690e6i | 3.06022i | ||||||||
\(629\) | − | 657750.i | − | 1.66249i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 612948.i | 1.53945i | 0.638376 | + | 0.769724i | \(0.279606\pi\) | ||||
−0.638376 | + | 0.769724i | \(0.720394\pi\) | |||||||
\(632\) | 211066.i | 0.528425i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 105656.i | 0.262855i | ||||||||
\(635\) | 40025.4i | 0.0992631i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 217570. | 0.536191 | ||||||||
\(638\) | −78693.0 | −0.193328 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 44430.3 | 0.108472 | ||||||||
\(641\) | 571747.i | 1.39151i | 0.718277 | + | 0.695757i | \(0.244931\pi\) | ||||
−0.718277 | + | 0.695757i | \(0.755069\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −530650. | −1.28347 | −0.641736 | − | 0.766926i | \(-0.721785\pi\) | ||||
−0.641736 | + | 0.766926i | \(0.721785\pi\) | |||||||
\(644\) | − | 97466.7i | − | 0.235009i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 706856. | 1.69382 | ||||||||
\(647\) | 481379.i | 1.14995i | 0.818171 | + | 0.574975i | \(0.194988\pi\) | ||||
−0.818171 | + | 0.574975i | \(0.805012\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −33529.1 | −0.0796036 | ||||||||
\(650\) | − | 412040.i | − | 0.975244i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 178379.i | − | 0.419613i | ||||||
\(653\) | 293363.i | 0.687984i | 0.938973 | + | 0.343992i | \(0.111779\pi\) | ||||
−0.938973 | + | 0.343992i | \(0.888221\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −25530.8 | −0.0595088 | ||||||||
\(656\) | −218213. | −0.507076 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −68945.9 | −0.159242 | ||||||||
\(659\) | −657906. | −1.51493 | −0.757466 | − | 0.652875i | \(-0.773563\pi\) | ||||
−0.757466 | + | 0.652875i | \(0.773563\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −267844. | −0.613026 | −0.306513 | − | 0.951866i | \(-0.599162\pi\) | ||||
−0.306513 | + | 0.951866i | \(0.599162\pi\) | |||||||
\(662\) | 574432. | 1.31076 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 569869.i | 1.29253i | ||||||||
\(665\) | − | 7505.92i | − | 0.0169731i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 277715.i | − | 0.624235i | ||||||
\(668\) | 1.02133e6 | 2.28883 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 55370.1 | 0.123346 | ||||||||
\(671\) | − | 32885.0i | − | 0.0730388i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 48089.2i | 0.106174i | 0.998590 | + | 0.0530869i | \(0.0169060\pi\) | ||||
−0.998590 | + | 0.0530869i | \(0.983094\pi\) | |||||||
\(674\) | 987667.i | 2.17416i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 550926. | 1.20559 | ||||||||
\(677\) | 84879.3i | 0.185193i | 0.995704 | + | 0.0925964i | \(0.0295166\pi\) | ||||
−0.995704 | + | 0.0925964i | \(0.970483\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 128718.i | − | 0.279191i | ||||||
\(680\) | −37655.1 | −0.0814341 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 61397.9i | − | 0.132003i | ||||||
\(683\) | 707010. | 1.51560 | 0.757799 | − | 0.652488i | \(-0.226275\pi\) | ||||
0.757799 | + | 0.652488i | \(0.226275\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2787.67 | 0.00594101 | ||||||||
\(686\) | 427693. | 0.908833 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −199397. | + | 130718.i | −0.421252 | + | 0.276159i | ||||
\(689\) | −9776.87 | −0.0205950 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 316021.i | − | 0.661851i | −0.943657 | − | 0.330925i | \(-0.892639\pi\) | ||
0.943657 | − | 0.330925i | \(-0.107361\pi\) | |||||||
\(692\) | −134183. | −0.280212 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −528525. | −1.09735 | ||||||||
\(695\) | 30640.1i | 0.0634338i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −484856. | −0.998039 | ||||||||
\(698\) | 1.11577e6 | 2.29014 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | − | 250797.i | − | 0.511830i | ||||||
\(701\) | −790342. | −1.60835 | −0.804173 | − | 0.594396i | \(-0.797391\pi\) | ||||
−0.804173 | + | 0.594396i | \(0.797391\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 842529. | 1.70480 | ||||||||
\(704\) | 58885.1 | 0.118812 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 356997.i | 0.716234i | ||||||||
\(707\) | 187254.i | 0.374622i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 218246. | 0.434165 | 0.217082 | − | 0.976153i | \(-0.430346\pi\) | ||||
0.217082 | + | 0.976153i | \(0.430346\pi\) | |||||||
\(710\) | − | 29430.4i | − | 0.0583821i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 291974. | 0.575950 | ||||||||
\(713\) | 216679. | 0.426224 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1488.52i | 0.00291168i | ||||||||
\(716\) | 768101.i | 1.49828i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 807350.i | − | 1.56608i | ||||||
\(719\) | −733807. | −1.41946 | −0.709732 | − | 0.704472i | \(-0.751184\pi\) | ||||
−0.709732 | + | 0.704472i | \(0.751184\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 76264.3i | − | 0.146707i | ||||||
\(722\) | 29382.3i | 0.0563653i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.40494e6 | −2.68027 | ||||||||
\(725\) | − | 714603.i | − | 1.35953i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 250259.i | − | 0.473501i | −0.971570 | − | 0.236750i | \(-0.923918\pi\) | ||
0.971570 | − | 0.236750i | \(-0.0760824\pi\) | |||||||
\(728\) | −120377. | −0.227133 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | − | 36057.5i | − | 0.0676627i | ||||||
\(731\) | −443048. | + | 290448.i | −0.829118 | + | 0.543542i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 610120.i | − | 1.13555i | −0.823183 | − | 0.567776i | \(-0.807804\pi\) | ||
0.823183 | − | 0.567776i | \(-0.192196\pi\) | |||||||
\(734\) | 253441.i | 0.470419i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 133525.i | 0.246495i | ||||||||
\(737\) | 56689.0 | 0.104367 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 67964.4i | − | 0.124449i | −0.998062 | − | 0.0622246i | \(-0.980180\pi\) | ||
0.998062 | − | 0.0622246i | \(-0.0198195\pi\) | |||||||
\(740\) | −99333.5 | −0.181398 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9212.95 | −0.0167337 | ||||||||
\(743\) | − | 707585.i | − | 1.28174i | −0.767648 | − | 0.640871i | \(-0.778573\pi\) | ||
0.767648 | − | 0.640871i | \(-0.221427\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20237.3 | 0.0364619 | ||||||||
\(746\) | 936998. | 1.68368 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −85322.8 | −0.152497 | ||||||||
\(749\) | 33603.4i | 0.0598989i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 613506.i | − | 1.08778i | −0.839158 | − | 0.543888i | \(-0.816952\pi\) | ||
0.839158 | − | 0.543888i | \(-0.183048\pi\) | |||||||
\(752\) | −95862.4 | −0.169517 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −759109. | −1.33525 | ||||||||
\(755\) | 62069.9 | 0.108890 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 132879.i | − | 0.231880i | −0.993256 | − | 0.115940i | \(-0.963012\pi\) | ||
0.993256 | − | 0.115940i | \(-0.0369881\pi\) | |||||||
\(758\) | 592406.i | 1.03105i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | − | 48233.4i | − | 0.0835066i | ||||||
\(761\) | − | 790123.i | − | 1.36435i | −0.731190 | − | 0.682174i | \(-0.761035\pi\) | ||
0.731190 | − | 0.682174i | \(-0.238965\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 44643.8i | 0.0766853i | ||||||||
\(764\) | 1.37051e6i | 2.34799i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.68605e6 | 2.87352 | ||||||||
\(767\) | −323437. | −0.549793 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −204245. | −0.345382 | −0.172691 | − | 0.984976i | \(-0.555246\pi\) | ||||
−0.172691 | + | 0.984976i | \(0.555246\pi\) | |||||||
\(770\) | 1402.67i | 0.00236577i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −553638. | −0.928948 | ||||||||
\(773\) | − | 824077.i | − | 1.37914i | −0.724218 | − | 0.689571i | \(-0.757799\pi\) | ||
0.724218 | − | 0.689571i | \(-0.242201\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 557548. | 0.928280 | ||||||||
\(776\) | − | 827151.i | − | 1.37360i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 228661. | 0.377775 | ||||||||
\(779\) | − | 621065.i | − | 1.02344i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 30131.4i | − | 0.0493989i | ||||||
\(782\) | − | 466171.i | − | 0.762310i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 285061. | 0.463772 | ||||||||
\(785\) | 61296.2 | 0.0994705 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 347326. | 0.560774 | 0.280387 | − | 0.959887i | \(-0.409537\pi\) | ||||
0.280387 | + | 0.959887i | \(0.409537\pi\) | |||||||
\(788\) | −2.25268e6 | −3.62782 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 23724.5 | 0.0380140 | ||||||||
\(791\) | −202542. | −0.323715 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 317224.i | − | 0.504452i | ||||||
\(794\) | − | 1.38854e6i | − | 2.20251i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 65699.0i | 0.103689i | ||||||||
\(797\) | 550267. | 0.866278 | 0.433139 | − | 0.901327i | \(-0.357406\pi\) | ||||
0.433139 | + | 0.901327i | \(0.357406\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −213001. | −0.333647 | ||||||||
\(800\) | 343581.i | 0.536845i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 572479.i | 0.890042i | ||||||||
\(803\) | − | 36916.3i | − | 0.0572515i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4950.15 | −0.00763882 | ||||||||
\(806\) | − | 592273.i | − | 0.911699i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.20331e6i | 1.84312i | ||||||||
\(809\) | 237489. | 0.362866 | 0.181433 | − | 0.983403i | \(-0.441926\pi\) | ||||
0.181433 | + | 0.983403i | \(0.441926\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.00555e6i | 1.52884i | 0.644717 | + | 0.764422i | \(0.276975\pi\) | ||||
−0.644717 | + | 0.764422i | \(0.723025\pi\) | |||||||
\(812\) | −462047. | −0.700768 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −157447. | −0.237622 | ||||||||
\(815\) | −9059.54 | −0.0136393 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −372042. | − | 567512.i | −0.557375 | − | 0.850219i | ||||
\(818\) | −1.45483e6 | −2.17423 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 73223.1i | 0.108898i | ||||||||
\(821\) | 259037. | 0.384305 | 0.192152 | − | 0.981365i | \(-0.438453\pi\) | ||||
0.192152 | + | 0.981365i | \(0.438453\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −70048.9 | −0.103419 | −0.0517097 | − | 0.998662i | \(-0.516467\pi\) | ||||
−0.0517097 | + | 0.998662i | \(0.516467\pi\) | |||||||
\(824\) | − | 490078.i | − | 0.721790i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −304781. | −0.446713 | ||||||||
\(827\) | 771588. | 1.12817 | 0.564085 | − | 0.825717i | \(-0.309229\pi\) | ||||
0.564085 | + | 0.825717i | \(0.309229\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 131193.i | 0.190898i | 0.995434 | + | 0.0954489i | \(0.0304286\pi\) | ||||
−0.995434 | + | 0.0954489i | \(0.969571\pi\) | |||||||
\(830\) | 64055.3 | 0.0929821 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 568033. | 0.820591 | ||||||||
\(833\) | 633388. | 0.912808 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 51871.4i | − | 0.0743970i | ||||||
\(836\) | − | 109292.i | − | 0.156378i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.31572e6 | 1.87360 | ||||||||
\(839\) | 473423.i | 0.672552i | 0.941764 | + | 0.336276i | \(0.109167\pi\) | ||||
−0.941764 | + | 0.336276i | \(0.890833\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −609245. | −0.861390 | ||||||||
\(842\) | 1.45505e6 | 2.05236 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 1.87386e6i | − | 2.63059i | ||||||
\(845\) | − | 27980.5i | − | 0.0391869i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 200555.i | − | 0.279555i | ||||||
\(848\) | −12809.7 | −0.0178134 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 1.19953e6i | − | 1.66025i | ||||||
\(851\) | − | 555647.i | − | 0.767255i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −535509. | −0.735985 | −0.367992 | − | 0.929829i | \(-0.619955\pi\) | ||||
−0.367992 | + | 0.929829i | \(0.619955\pi\) | |||||||
\(854\) | − | 298927.i | − | 0.409873i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 215937.i | 0.294699i | ||||||||
\(857\) | −1.28191e6 | −1.74540 | −0.872699 | − | 0.488258i | \(-0.837632\pi\) | ||||
−0.872699 | + | 0.488258i | \(0.837632\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 683886.i | − | 0.926825i | −0.886143 | − | 0.463412i | \(-0.846625\pi\) | ||
0.886143 | − | 0.463412i | \(-0.153375\pi\) | |||||||
\(860\) | 43863.5 | + | 66909.3i | 0.0593070 | + | 0.0904668i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 1.47870e6i | − | 1.99005i | ||||||
\(863\) | 423128.i | 0.568134i | 0.958804 | + | 0.284067i | \(0.0916838\pi\) | ||||
−0.958804 | + | 0.284067i | \(0.908316\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6814.91i | 0.00910810i | ||||||||
\(866\) | −948660. | −1.26495 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 360499.i | − | 0.478480i | ||||||
\(869\) | 24289.6 | 0.0321648 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 546848. | 0.720825 | ||||||||
\(872\) | 286883.i | 0.377287i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 597130. | 0.781711 | ||||||||
\(875\) | −25519.9 | −0.0333321 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 543060. | 0.706071 | 0.353036 | − | 0.935610i | \(-0.385149\pi\) | ||||
0.353036 | + | 0.935610i | \(0.385149\pi\) | |||||||
\(878\) | 125442.i | 0.162725i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1950.27i | 0.00251843i | ||||||||
\(881\) | 747183. | 0.962665 | 0.481333 | − | 0.876538i | \(-0.340153\pi\) | ||||
0.481333 | + | 0.876538i | \(0.340153\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 908500. | 1.16521 | 0.582604 | − | 0.812756i | \(-0.302034\pi\) | ||||
0.582604 | + | 0.812756i | \(0.302034\pi\) | |||||||
\(884\) | −823063. | −1.05324 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 143629.i | 0.182968i | ||||||||
\(887\) | − | 283934.i | − | 0.360886i | −0.983585 | − | 0.180443i | \(-0.942247\pi\) | ||
0.983585 | − | 0.180443i | \(-0.0577531\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 372499.i | 0.471326i | ||||||||
\(890\) | − | 32819.0i | − | 0.0414328i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.55888e6i | 1.95922i | ||||||||
\(893\) | − | 272838.i | − | 0.342138i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 39010.4 | 0.0487006 | ||||||||
\(896\) | 413493. | 0.515054 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 682420. | 0.846250 | ||||||||
\(899\) | − | 1.02718e6i | − | 1.27095i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28462.3 | −0.0350607 | ||||||||
\(902\) | 116061.i | 0.142651i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.30155e6 | −1.59266 | ||||||||
\(905\) | 71354.0i | 0.0871206i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −329783. | −0.400880 | −0.200440 | − | 0.979706i | \(-0.564237\pi\) | ||||
−0.200440 | + | 0.979706i | \(0.564237\pi\) | |||||||
\(908\) | 1.26954e6i | 1.53984i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 13530.8i | 0.0163395i | ||||||||
\(911\) | 1.20039e6i | 1.44639i | 0.690642 | + | 0.723197i | \(0.257328\pi\) | ||||
−0.690642 | + | 0.723197i | \(0.742672\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 65581.0 | 0.0786750 | ||||||||
\(914\) | 2.07047e6 | 2.47843 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.95986e6 | −2.33580 | ||||||||
\(917\) | −237604. | −0.282563 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −775338. | −0.918037 | −0.459018 | − | 0.888427i | \(-0.651799\pi\) | ||||
−0.459018 | + | 0.888427i | \(0.651799\pi\) | |||||||
\(920\) | −31809.9 | −0.0375826 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.05098e6i | 1.23632i | ||||||||
\(923\) | − | 290661.i | − | 0.341180i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 1.42976e6i | − | 1.67102i | ||||||
\(926\) | 1.36726e6 | 1.59451 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 632985. | 0.735017 | ||||||||
\(929\) | 763445.i | 0.884599i | 0.896867 | + | 0.442300i | \(0.145837\pi\) | ||||
−0.896867 | + | 0.442300i | \(0.854163\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 811322.i | 0.936039i | ||||||||
\(932\) | − | 2.23974e6i | − | 2.57849i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.40478e6 | −1.61033 | ||||||||
\(935\) | 4333.38i | 0.00495683i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1.72023e6i | − | 1.95932i | −0.200654 | − | 0.979662i | \(-0.564307\pi\) | ||
0.200654 | − | 0.979662i | \(-0.435693\pi\) | |||||||
\(938\) | 515306. | 0.585679 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 32167.4i | 0.0364049i | ||||||||
\(941\) | −657189. | −0.742183 | −0.371092 | − | 0.928596i | \(-0.621016\pi\) | ||||
−0.371092 | + | 0.928596i | \(0.621016\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −409591. | −0.460604 | ||||||||
\(944\) | −423768. | −0.475537 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 69525.3 | + | 106054.i | 0.0776891 | + | 0.118507i | ||||
\(947\) | 829200. | 0.924612 | 0.462306 | − | 0.886721i | \(-0.347022\pi\) | ||||
0.462306 | + | 0.886721i | \(0.347022\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 356111.i | − | 0.395415i | ||||||
\(950\) | 1.53651e6 | 1.70250 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −350440. | −0.386669 | ||||||||
\(953\) | − | 1.33377e6i | − | 1.46858i | −0.678838 | − | 0.734288i | \(-0.737516\pi\) | ||
0.678838 | − | 0.734288i | \(-0.262484\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 69605.8 | 0.0763200 | ||||||||
\(956\) | −781305. | −0.854879 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 662460.i | 0.721819i | ||||||||
\(959\) | 25943.6 | 0.0282094 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −122093. | −0.132204 | ||||||||
\(962\) | −1.51881e6 | −1.64117 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.93182e6i | 3.15488i | ||||||||
\(965\) | 28118.2i | 0.0301949i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 788889. | 0.843652 | 0.421826 | − | 0.906677i | \(-0.361389\pi\) | ||||
0.421826 | + | 0.906677i | \(0.361389\pi\) | |||||||
\(968\) | − | 1.28878e6i | − | 1.37539i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −92974.7 | −0.0988146 | ||||||||
\(971\) | 1.20251e6 | 1.27541 | 0.637704 | − | 0.770282i | \(-0.279885\pi\) | ||||
0.637704 | + | 0.770282i | \(0.279885\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 285154.i | 0.301199i | ||||||||
\(974\) | 2.15046e6i | 2.26680i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 415628.i | − | 0.436320i | ||||||
\(977\) | −634645. | −0.664878 | −0.332439 | − | 0.943125i | \(-0.607872\pi\) | ||||
−0.332439 | + | 0.943125i | \(0.607872\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 33600.7i | − | 0.0350576i | ||||||
\(980\) | − | 95654.3i | − | 0.0995984i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.05366e6 | 3.16663 | ||||||||
\(983\) | 1.63591e6i | 1.69298i | 0.532403 | + | 0.846491i | \(0.321289\pi\) | ||||
−0.532403 | + | 0.846491i | \(0.678711\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 114409.i | 0.117920i | ||||||||
\(986\) | −2.20991e6 | −2.27311 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 1.05428e6i | − | 1.08005i | ||||||
\(989\) | −374273. | + | 245361.i | −0.382645 | + | 0.250849i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.20041e6i | − | 1.22231i | −0.791510 | − | 0.611156i | \(-0.790705\pi\) | ||
0.791510 | − | 0.611156i | \(-0.209295\pi\) | |||||||
\(992\) | 493868.i | 0.501865i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 273896.i | − | 0.277213i | ||||||
\(995\) | 3336.72 | 0.00337034 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1.25293e6i | − | 1.26048i | −0.776401 | − | 0.630239i | \(-0.782957\pi\) | ||
0.776401 | − | 0.630239i | \(-0.217043\pi\) | |||||||
\(998\) | −2.26210e6 | −2.27117 | ||||||||
\(999\) | 0 | 0 |
(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 | 387.5.b.c.343.2 | 12 | ||
3.2 | odd | 2 | 43.5.b.b.42.11 | yes | 12 | ||
12.11 | even | 2 | 688.5.b.d.257.4 | 12 | |||
43.42 | odd | 2 | inner | 387.5.b.c.343.11 | 12 | ||
129.128 | even | 2 | 43.5.b.b.42.2 | ✓ | 12 | ||
516.515 | odd | 2 | 688.5.b.d.257.9 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.5.b.b.42.2 | ✓ | 12 | 129.128 | even | 2 | ||
43.5.b.b.42.11 | yes | 12 | 3.2 | odd | 2 | ||
387.5.b.c.343.2 | 12 | 1.1 | even | 1 | trivial | ||
387.5.b.c.343.11 | 12 | 43.42 | odd | 2 | inner | ||
688.5.b.d.257.4 | 12 | 12.11 | even | 2 | |||
688.5.b.d.257.9 | 12 | 516.515 | odd | 2 |