Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,5,Mod(42,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.42");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.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: | \(4.44490841261\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 42.2 | ||
Root | \(-6.72223i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 43.42 |
Dual form | 43.5.b.b.42.11 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 | \(-0.317609\pi\) | |||||||
\(3\) | − | 8.31879i | − | 0.924310i | −0.886799 | − | 0.462155i | \(-0.847076\pi\) | ||
0.886799 | − | 0.462155i | \(-0.152924\pi\) | |||||||
\(4\) | −29.1884 | −1.82427 | ||||||||
\(5\) | 1.48242i | 0.0592969i | 0.999560 | + | 0.0296484i | \(0.00943877\pi\) | ||||
−0.999560 | + | 0.0296484i | \(0.990561\pi\) | |||||||
\(6\) | −55.9208 | −1.55336 | ||||||||
\(7\) | − | 13.7963i | − | 0.281556i | −0.990041 | − | 0.140778i | \(-0.955040\pi\) | ||
0.990041 | − | 0.140778i | \(-0.0449604\pi\) | |||||||
\(8\) | 88.6554i | 1.38524i | ||||||||
\(9\) | 11.7977 | 0.145651 | ||||||||
\(10\) | 9.96518 | 0.0996518 | ||||||||
\(11\) | −10.2025 | −0.0843185 | −0.0421592 | − | 0.999111i | \(-0.513424\pi\) | ||||
−0.0421592 | + | 0.999111i | \(0.513424\pi\) | |||||||
\(12\) | 242.812i | 1.68620i | ||||||||
\(13\) | 98.4183 | 0.582357 | 0.291179 | − | 0.956669i | \(-0.405953\pi\) | ||||
0.291179 | + | 0.956669i | \(0.405953\pi\) | |||||||
\(14\) | −92.7416 | −0.473172 | ||||||||
\(15\) | 12.3320 | 0.0548087 | ||||||||
\(16\) | 128.948 | 0.503703 | ||||||||
\(17\) | −286.515 | −0.991400 | −0.495700 | − | 0.868494i | \(-0.665089\pi\) | ||||
−0.495700 | + | 0.868494i | \(0.665089\pi\) | |||||||
\(18\) | − | 79.3069i | − | 0.244775i | ||||||
\(19\) | − | 367.004i | − | 1.01663i | −0.861171 | − | 0.508316i | \(-0.830268\pi\) | ||
0.861171 | − | 0.508316i | \(-0.169732\pi\) | |||||||
\(20\) | − | 43.2695i | − | 0.108174i | ||||||
\(21\) | −114.768 | −0.260245 | ||||||||
\(22\) | 68.5838i | 0.141702i | ||||||||
\(23\) | −242.039 | −0.457540 | −0.228770 | − | 0.973480i | \(-0.573470\pi\) | ||||
−0.228770 | + | 0.973480i | \(0.573470\pi\) | |||||||
\(24\) | 737.506 | 1.28039 | ||||||||
\(25\) | 622.802 | 0.996484 | ||||||||
\(26\) | − | 661.591i | − | 0.978685i | ||||||
\(27\) | − | 771.965i | − | 1.05894i | ||||||
\(28\) | 402.691i | 0.513636i | ||||||||
\(29\) | − | 1147.40i | − | 1.36433i | −0.731199 | − | 0.682164i | \(-0.761039\pi\) | ||
0.731199 | − | 0.682164i | \(-0.238961\pi\) | |||||||
\(30\) | − | 82.8983i | − | 0.0921092i | ||||||
\(31\) | 895.225 | 0.931556 | 0.465778 | − | 0.884902i | \(-0.345775\pi\) | ||||
0.465778 | + | 0.884902i | \(0.345775\pi\) | |||||||
\(32\) | 551.669i | 0.538739i | ||||||||
\(33\) | 84.8728i | 0.0779364i | ||||||||
\(34\) | 1926.02i | 1.66611i | ||||||||
\(35\) | 20.4519 | 0.0166954 | ||||||||
\(36\) | −344.356 | −0.265707 | ||||||||
\(37\) | 2295.69i | 1.67691i | 0.544969 | + | 0.838456i | \(0.316541\pi\) | ||||
−0.544969 | + | 0.838456i | \(0.683459\pi\) | |||||||
\(38\) | −2467.09 | −1.70851 | ||||||||
\(39\) | − | 818.722i | − | 0.538279i | ||||||
\(40\) | −131.425 | −0.0821405 | ||||||||
\(41\) | 1692.26 | 1.00670 | 0.503348 | − | 0.864084i | \(-0.332101\pi\) | ||||
0.503348 | + | 0.864084i | \(0.332101\pi\) | |||||||
\(42\) | 771.498i | 0.437357i | ||||||||
\(43\) | −1546.34 | − | 1013.73i | −0.836310 | − | 0.548257i | ||||
\(44\) | 297.796 | 0.153820 | ||||||||
\(45\) | 17.4892i | 0.00863663i | ||||||||
\(46\) | 1627.04i | 0.768923i | ||||||||
\(47\) | 743.419 | 0.336541 | 0.168271 | − | 0.985741i | \(-0.446182\pi\) | ||||
0.168271 | + | 0.985741i | \(0.446182\pi\) | |||||||
\(48\) | − | 1072.69i | − | 0.465578i | ||||||
\(49\) | 2210.66 | 0.920726 | ||||||||
\(50\) | − | 4186.62i | − | 1.67465i | ||||||
\(51\) | 2383.46i | 0.916361i | ||||||||
\(52\) | −2872.67 | −1.06238 | ||||||||
\(53\) | 99.3399 | 0.0353649 | 0.0176824 | − | 0.999844i | \(-0.494371\pi\) | ||||
0.0176824 | + | 0.999844i | \(0.494371\pi\) | |||||||
\(54\) | −5189.33 | −1.77960 | ||||||||
\(55\) | − | 15.1245i | − | 0.00499982i | ||||||
\(56\) | 1223.11 | 0.390023 | ||||||||
\(57\) | −3053.03 | −0.939683 | ||||||||
\(58\) | −7713.09 | −2.29283 | ||||||||
\(59\) | 3286.35 | 0.944082 | 0.472041 | − | 0.881577i | \(-0.343517\pi\) | ||||
0.472041 | + | 0.881577i | \(0.343517\pi\) | |||||||
\(60\) | −359.950 | −0.0999861 | ||||||||
\(61\) | 3223.22i | 0.866225i | 0.901340 | + | 0.433112i | \(0.142585\pi\) | ||||
−0.901340 | + | 0.433112i | \(0.857415\pi\) | |||||||
\(62\) | − | 6017.91i | − | 1.56553i | ||||||
\(63\) | − | 162.764i | − | 0.0410089i | ||||||
\(64\) | 5771.61 | 1.40908 | ||||||||
\(65\) | 145.898i | 0.0345320i | ||||||||
\(66\) | 570.534 | 0.130977 | ||||||||
\(67\) | 5556.36 | 1.23777 | 0.618886 | − | 0.785481i | \(-0.287584\pi\) | ||||
0.618886 | + | 0.785481i | \(0.287584\pi\) | |||||||
\(68\) | 8362.90 | 1.80859 | ||||||||
\(69\) | 2013.47i | 0.422909i | ||||||||
\(70\) | − | 137.482i | − | 0.0280576i | ||||||
\(71\) | − | 2953.33i | − | 0.585861i | −0.956134 | − | 0.292930i | \(-0.905370\pi\) | ||
0.956134 | − | 0.292930i | \(-0.0946305\pi\) | |||||||
\(72\) | 1045.93i | 0.201761i | ||||||||
\(73\) | 3618.34i | 0.678991i | 0.940608 | + | 0.339496i | \(0.110256\pi\) | ||||
−0.940608 | + | 0.339496i | \(0.889744\pi\) | |||||||
\(74\) | 15432.2 | 2.81815 | ||||||||
\(75\) | − | 5180.96i | − | 0.921060i | ||||||
\(76\) | 10712.3i | 1.85461i | ||||||||
\(77\) | 140.757i | 0.0237404i | ||||||||
\(78\) | −5503.64 | −0.904608 | ||||||||
\(79\) | 2380.74 | 0.381468 | 0.190734 | − | 0.981642i | \(-0.438913\pi\) | ||||
0.190734 | + | 0.981642i | \(0.438913\pi\) | |||||||
\(80\) | 191.155i | 0.0298680i | ||||||||
\(81\) | −5466.20 | −0.833135 | ||||||||
\(82\) | − | 11375.7i | − | 1.69181i | ||||||
\(83\) | −6427.91 | −0.933069 | −0.466535 | − | 0.884503i | \(-0.654498\pi\) | ||||
−0.466535 | + | 0.884503i | \(0.654498\pi\) | |||||||
\(84\) | 3349.90 | 0.474759 | ||||||||
\(85\) | − | 424.736i | − | 0.0587869i | ||||||
\(86\) | −6814.51 | + | 10394.8i | −0.921377 | + | 1.40547i | ||||
\(87\) | −9544.98 | −1.26106 | ||||||||
\(88\) | − | 904.510i | − | 0.116801i | ||||||
\(89\) | − | 3293.36i | − | 0.415776i | −0.978153 | − | 0.207888i | \(-0.933341\pi\) | ||
0.978153 | − | 0.207888i | \(-0.0666590\pi\) | |||||||
\(90\) | 117.566 | 0.0145144 | ||||||||
\(91\) | − | 1357.80i | − | 0.163966i | ||||||
\(92\) | 7064.72 | 0.834679 | ||||||||
\(93\) | − | 7447.19i | − | 0.861046i | ||||||
\(94\) | − | 4997.44i | − | 0.565577i | ||||||
\(95\) | 544.055 | 0.0602831 | ||||||||
\(96\) | 4589.22 | 0.497962 | ||||||||
\(97\) | −9329.95 | −0.991599 | −0.495799 | − | 0.868437i | \(-0.665125\pi\) | ||||
−0.495799 | + | 0.868437i | \(0.665125\pi\) | |||||||
\(98\) | − | 14860.6i | − | 1.54733i | ||||||
\(99\) | −120.367 | −0.0122811 | ||||||||
\(100\) | −18178.6 | −1.81786 | ||||||||
\(101\) | −13572.8 | −1.33054 | −0.665270 | − | 0.746603i | \(-0.731683\pi\) | ||||
−0.665270 | + | 0.746603i | \(0.731683\pi\) | |||||||
\(102\) | 16022.1 | 1.54000 | ||||||||
\(103\) | −5527.90 | −0.521057 | −0.260529 | − | 0.965466i | \(-0.583897\pi\) | ||||
−0.260529 | + | 0.965466i | \(0.583897\pi\) | |||||||
\(104\) | 8725.32i | 0.806705i | ||||||||
\(105\) | − | 170.135i | − | 0.0154317i | ||||||
\(106\) | − | 667.786i | − | 0.0594327i | ||||||
\(107\) | −2435.69 | −0.212742 | −0.106371 | − | 0.994326i | \(-0.533923\pi\) | ||||
−0.106371 | + | 0.994326i | \(0.533923\pi\) | |||||||
\(108\) | 22532.4i | 1.93179i | ||||||||
\(109\) | 3235.93 | 0.272362 | 0.136181 | − | 0.990684i | \(-0.456517\pi\) | ||||
0.136181 | + | 0.990684i | \(0.456517\pi\) | |||||||
\(110\) | −101.670 | −0.00840249 | ||||||||
\(111\) | 19097.4 | 1.54999 | ||||||||
\(112\) | − | 1779.00i | − | 0.141821i | ||||||
\(113\) | 14680.9i | 1.14973i | 0.818247 | + | 0.574867i | \(0.194946\pi\) | ||||
−0.818247 | + | 0.574867i | \(0.805054\pi\) | |||||||
\(114\) | 20523.2i | 1.57919i | ||||||||
\(115\) | − | 358.803i | − | 0.0271307i | ||||||
\(116\) | 33490.7i | 2.48891i | ||||||||
\(117\) | 1161.11 | 0.0848207 | ||||||||
\(118\) | − | 22091.6i | − | 1.58658i | ||||||
\(119\) | 3952.83i | 0.279135i | ||||||||
\(120\) | 1093.29i | 0.0759233i | ||||||||
\(121\) | −14536.9 | −0.992890 | ||||||||
\(122\) | 21667.2 | 1.45574 | ||||||||
\(123\) | − | 14077.5i | − | 0.930499i | ||||||
\(124\) | −26130.2 | −1.69941 | ||||||||
\(125\) | 1849.77i | 0.118385i | ||||||||
\(126\) | −1094.14 | −0.0689178 | ||||||||
\(127\) | 27000.0 | 1.67400 | 0.837001 | − | 0.547201i | \(-0.184307\pi\) | ||||
0.837001 | + | 0.547201i | \(0.184307\pi\) | |||||||
\(128\) | − | 29971.4i | − | 1.82931i | ||||||
\(129\) | −8432.98 | + | 12863.7i | −0.506759 | + | 0.773010i | ||||
\(130\) | 980.757 | 0.0580329 | ||||||||
\(131\) | 17222.3i | 1.00357i | 0.864991 | + | 0.501787i | \(0.167324\pi\) | ||||
−0.864991 | + | 0.501787i | \(0.832676\pi\) | |||||||
\(132\) | − | 2477.30i | − | 0.142177i | ||||||
\(133\) | −5063.28 | −0.286239 | ||||||||
\(134\) | − | 37351.1i | − | 2.08015i | ||||||
\(135\) | 1144.38 | 0.0627916 | ||||||||
\(136\) | − | 25401.1i | − | 1.37333i | ||||||
\(137\) | − | 1880.48i | − | 0.100191i | −0.998744 | − | 0.0500955i | \(-0.984047\pi\) | ||
0.998744 | − | 0.0500955i | \(-0.0159526\pi\) | |||||||
\(138\) | 13535.0 | 0.710723 | ||||||||
\(139\) | 20668.9 | 1.06977 | 0.534883 | − | 0.844926i | \(-0.320356\pi\) | ||||
0.534883 | + | 0.844926i | \(0.320356\pi\) | |||||||
\(140\) | −596.957 | −0.0304570 | ||||||||
\(141\) | − | 6184.35i | − | 0.311068i | ||||||
\(142\) | −19852.9 | −0.984573 | ||||||||
\(143\) | −1004.12 | −0.0491035 | ||||||||
\(144\) | 1521.29 | 0.0733647 | ||||||||
\(145\) | 1700.93 | 0.0809004 | ||||||||
\(146\) | 24323.3 | 1.14108 | ||||||||
\(147\) | − | 18390.0i | − | 0.851036i | ||||||
\(148\) | − | 67007.6i | − | 3.05915i | ||||||
\(149\) | − | 13651.5i | − | 0.614904i | −0.951564 | − | 0.307452i | \(-0.900524\pi\) | ||
0.951564 | − | 0.307452i | \(-0.0994763\pi\) | |||||||
\(150\) | −34827.6 | −1.54789 | ||||||||
\(151\) | 41870.6i | 1.83635i | 0.396175 | + | 0.918175i | \(0.370338\pi\) | ||||
−0.396175 | + | 0.918175i | \(0.629662\pi\) | |||||||
\(152\) | 32536.9 | 1.40828 | ||||||||
\(153\) | −3380.22 | −0.144398 | ||||||||
\(154\) | 946.200 | 0.0398971 | ||||||||
\(155\) | 1327.10i | 0.0552383i | ||||||||
\(156\) | 23897.2i | 0.981968i | ||||||||
\(157\) | 41348.7i | 1.67750i | 0.544517 | + | 0.838750i | \(0.316713\pi\) | ||||
−0.544517 | + | 0.838750i | \(0.683287\pi\) | |||||||
\(158\) | − | 16003.9i | − | 0.641079i | ||||||
\(159\) | − | 826.388i | − | 0.0326881i | ||||||
\(160\) | −817.806 | −0.0319455 | ||||||||
\(161\) | 3339.23i | 0.128823i | ||||||||
\(162\) | 36745.1i | 1.40013i | ||||||||
\(163\) | − | 6111.31i | − | 0.230017i | −0.993365 | − | 0.115008i | \(-0.963311\pi\) | ||
0.993365 | − | 0.115008i | \(-0.0366895\pi\) | |||||||
\(164\) | −49394.2 | −1.83649 | ||||||||
\(165\) | −125.817 | −0.00462139 | ||||||||
\(166\) | 43209.9i | 1.56808i | ||||||||
\(167\) | 34991.0 | 1.25465 | 0.627326 | − | 0.778757i | \(-0.284149\pi\) | ||||
0.627326 | + | 0.778757i | \(0.284149\pi\) | |||||||
\(168\) | − | 10174.8i | − | 0.360503i | ||||||
\(169\) | −18874.8 | −0.660860 | ||||||||
\(170\) | −2855.17 | −0.0987949 | ||||||||
\(171\) | − | 4329.81i | − | 0.148073i | ||||||
\(172\) | 45135.1 | + | 29589.1i | 1.52566 | + | 1.00017i | ||||
\(173\) | −4597.15 | −0.153602 | −0.0768009 | − | 0.997046i | \(-0.524471\pi\) | ||||
−0.0768009 | + | 0.997046i | \(0.524471\pi\) | |||||||
\(174\) | 64163.5i | 2.11929i | ||||||||
\(175\) | − | 8592.34i | − | 0.280566i | ||||||
\(176\) | −1315.60 | −0.0424715 | ||||||||
\(177\) | − | 27338.5i | − | 0.872624i | ||||||
\(178\) | −22138.7 | −0.698736 | ||||||||
\(179\) | − | 26315.3i | − | 0.821301i | −0.911793 | − | 0.410650i | \(-0.865302\pi\) | ||
0.911793 | − | 0.410650i | \(-0.134698\pi\) | |||||||
\(180\) | − | 510.481i | − | 0.0157556i | ||||||
\(181\) | 48133.4 | 1.46923 | 0.734614 | − | 0.678485i | \(-0.237363\pi\) | ||||
0.734614 | + | 0.678485i | \(0.237363\pi\) | |||||||
\(182\) | −9127.48 | −0.275555 | ||||||||
\(183\) | 26813.3 | 0.800660 | ||||||||
\(184\) | − | 21458.0i | − | 0.633803i | ||||||
\(185\) | −3403.19 | −0.0994357 | ||||||||
\(186\) | −50061.7 | −1.44704 | ||||||||
\(187\) | 2923.18 | 0.0835934 | ||||||||
\(188\) | −21699.2 | −0.613943 | ||||||||
\(189\) | −10650.2 | −0.298150 | ||||||||
\(190\) | − | 3657.26i | − | 0.101309i | ||||||
\(191\) | − | 46954.1i | − | 1.28708i | −0.765411 | − | 0.643542i | \(-0.777464\pi\) | ||
0.765411 | − | 0.643542i | \(-0.222536\pi\) | |||||||
\(192\) | − | 48012.8i | − | 1.30243i | ||||||
\(193\) | 18967.8 | 0.509215 | 0.254608 | − | 0.967044i | \(-0.418054\pi\) | ||||
0.254608 | + | 0.967044i | \(0.418054\pi\) | |||||||
\(194\) | 62718.1i | 1.66644i | ||||||||
\(195\) | 1213.69 | 0.0319182 | ||||||||
\(196\) | −64525.7 | −1.67966 | ||||||||
\(197\) | −77177.1 | −1.98864 | −0.994320 | − | 0.106435i | \(-0.966056\pi\) | ||||
−0.994320 | + | 0.106435i | \(0.966056\pi\) | |||||||
\(198\) | 809.132i | 0.0206390i | ||||||||
\(199\) | 2250.86i | 0.0568385i | 0.999596 | + | 0.0284192i | \(0.00904734\pi\) | ||||
−0.999596 | + | 0.0284192i | \(0.990953\pi\) | |||||||
\(200\) | 55214.8i | 1.38037i | ||||||||
\(201\) | − | 46222.2i | − | 1.14409i | ||||||
\(202\) | 91239.7i | 2.23605i | ||||||||
\(203\) | −15829.8 | −0.384135 | ||||||||
\(204\) | − | 69569.3i | − | 1.67169i | ||||||
\(205\) | 2508.64i | 0.0596939i | ||||||||
\(206\) | 37159.8i | 0.875667i | ||||||||
\(207\) | −2855.50 | −0.0666411 | ||||||||
\(208\) | 12690.8 | 0.293335 | ||||||||
\(209\) | 3744.37i | 0.0857208i | ||||||||
\(210\) | −1143.69 | −0.0259339 | ||||||||
\(211\) | − | 64198.9i | − | 1.44199i | −0.692939 | − | 0.720996i | \(-0.743685\pi\) | ||
0.692939 | − | 0.720996i | \(-0.256315\pi\) | |||||||
\(212\) | −2899.57 | −0.0645152 | ||||||||
\(213\) | −24568.1 | −0.541517 | ||||||||
\(214\) | 16373.2i | 0.357526i | ||||||||
\(215\) | 1502.77 | − | 2292.32i | 0.0325099 | − | 0.0495906i | ||||
\(216\) | 68438.9 | 1.46688 | ||||||||
\(217\) | − | 12350.8i | − | 0.262285i | ||||||
\(218\) | − | 21752.7i | − | 0.457720i | ||||||
\(219\) | 30100.2 | 0.627598 | ||||||||
\(220\) | 441.459i | 0.00912105i | ||||||||
\(221\) | −28198.3 | −0.577349 | ||||||||
\(222\) | − | 128377.i | − | 2.60484i | ||||||
\(223\) | 53407.6i | 1.07397i | 0.843591 | + | 0.536987i | \(0.180437\pi\) | ||||
−0.843591 | + | 0.536987i | \(0.819563\pi\) | |||||||
\(224\) | 7610.96 | 0.151685 | ||||||||
\(225\) | 7347.64 | 0.145139 | ||||||||
\(226\) | 98688.7 | 1.93219 | ||||||||
\(227\) | − | 43494.8i | − | 0.844084i | −0.906576 | − | 0.422042i | \(-0.861313\pi\) | ||
0.906576 | − | 0.422042i | \(-0.138687\pi\) | |||||||
\(228\) | 89113.0 | 1.71424 | ||||||||
\(229\) | 67145.4 | 1.28040 | 0.640199 | − | 0.768209i | \(-0.278852\pi\) | ||||
0.640199 | + | 0.768209i | \(0.278852\pi\) | |||||||
\(230\) | −2411.96 | −0.0455947 | ||||||||
\(231\) | 1170.93 | 0.0219435 | ||||||||
\(232\) | 101723. | 1.88992 | ||||||||
\(233\) | 76734.0i | 1.41344i | 0.707496 | + | 0.706718i | \(0.249825\pi\) | ||||
−0.707496 | + | 0.706718i | \(0.750175\pi\) | |||||||
\(234\) | − | 7805.26i | − | 0.142546i | ||||||
\(235\) | 1102.06i | 0.0199558i | ||||||||
\(236\) | −95923.2 | −1.72226 | ||||||||
\(237\) | − | 19804.9i | − | 0.352595i | ||||||
\(238\) | 26571.8 | 0.469103 | ||||||||
\(239\) | −26767.6 | −0.468613 | −0.234307 | − | 0.972163i | \(-0.575282\pi\) | ||||
−0.234307 | + | 0.972163i | \(0.575282\pi\) | |||||||
\(240\) | 1590.18 | 0.0276073 | ||||||||
\(241\) | 100445.i | 1.72939i | 0.502297 | + | 0.864695i | \(0.332488\pi\) | ||||
−0.502297 | + | 0.864695i | \(0.667512\pi\) | |||||||
\(242\) | 97720.5i | 1.66861i | ||||||||
\(243\) | − | 17057.0i | − | 0.288861i | ||||||
\(244\) | − | 94080.7i | − | 1.58023i | ||||||
\(245\) | 3277.14i | 0.0545962i | ||||||||
\(246\) | −94632.4 | −1.56376 | ||||||||
\(247\) | − | 36119.9i | − | 0.592043i | ||||||
\(248\) | 79366.5i | 1.29043i | ||||||||
\(249\) | 53472.5i | 0.862445i | ||||||||
\(250\) | 12434.6 | 0.198953 | ||||||||
\(251\) | −71737.6 | −1.13867 | −0.569337 | − | 0.822104i | \(-0.692800\pi\) | ||||
−0.569337 | + | 0.822104i | \(0.692800\pi\) | |||||||
\(252\) | 4750.83i | 0.0748115i | ||||||||
\(253\) | 2469.41 | 0.0385791 | ||||||||
\(254\) | − | 181500.i | − | 2.81326i | ||||||
\(255\) | −3533.29 | −0.0543374 | ||||||||
\(256\) | −109129. | −1.66518 | ||||||||
\(257\) | − | 7267.88i | − | 0.110038i | −0.998485 | − | 0.0550189i | \(-0.982478\pi\) | ||
0.998485 | − | 0.0550189i | \(-0.0175219\pi\) | |||||||
\(258\) | 86472.5 | + | 56688.5i | 1.29909 | + | 0.851638i | ||||
\(259\) | 31672.0 | 0.472145 | ||||||||
\(260\) | − | 4258.51i | − | 0.0629958i | ||||||
\(261\) | − | 13536.7i | − | 0.198715i | ||||||
\(262\) | 115773. | 1.68656 | ||||||||
\(263\) | 73838.4i | 1.06751i | 0.845640 | + | 0.533754i | \(0.179219\pi\) | ||||
−0.845640 | + | 0.533754i | \(0.820781\pi\) | |||||||
\(264\) | −7524.43 | −0.107961 | ||||||||
\(265\) | 147.264i | 0.00209703i | ||||||||
\(266\) | 34036.6i | 0.481041i | ||||||||
\(267\) | −27396.8 | −0.384306 | ||||||||
\(268\) | −162181. | −2.25804 | ||||||||
\(269\) | 127266. | 1.75877 | 0.879384 | − | 0.476113i | \(-0.157955\pi\) | ||||
0.879384 | + | 0.476113i | \(0.157955\pi\) | |||||||
\(270\) | − | 7692.77i | − | 0.105525i | ||||||
\(271\) | 44182.9 | 0.601610 | 0.300805 | − | 0.953686i | \(-0.402745\pi\) | ||||
0.300805 | + | 0.953686i | \(0.402745\pi\) | |||||||
\(272\) | −36945.5 | −0.499371 | ||||||||
\(273\) | −11295.3 | −0.151556 | ||||||||
\(274\) | −12641.0 | −0.168377 | ||||||||
\(275\) | −6354.17 | −0.0840220 | ||||||||
\(276\) | − | 58769.9i | − | 0.771502i | ||||||
\(277\) | − | 31197.7i | − | 0.406596i | −0.979117 | − | 0.203298i | \(-0.934834\pi\) | ||
0.979117 | − | 0.203298i | \(-0.0651660\pi\) | |||||||
\(278\) | − | 138941.i | − | 1.79780i | ||||||
\(279\) | 10561.6 | 0.135682 | ||||||||
\(280\) | 1813.17i | 0.0231272i | ||||||||
\(281\) | −140212. | −1.77572 | −0.887859 | − | 0.460116i | \(-0.847808\pi\) | ||||
−0.887859 | + | 0.460116i | \(0.847808\pi\) | |||||||
\(282\) | −41572.6 | −0.522768 | ||||||||
\(283\) | 2024.17 | 0.0252740 | 0.0126370 | − | 0.999920i | \(-0.495977\pi\) | ||||
0.0126370 | + | 0.999920i | \(0.495977\pi\) | |||||||
\(284\) | 86202.8i | 1.06877i | ||||||||
\(285\) | − | 4525.88i | − | 0.0557203i | ||||||
\(286\) | 6749.91i | 0.0825212i | ||||||||
\(287\) | − | 23346.8i | − | 0.283442i | ||||||
\(288\) | 6508.43i | 0.0784677i | ||||||||
\(289\) | −1430.31 | −0.0171252 | ||||||||
\(290\) | − | 11434.0i | − | 0.135958i | ||||||
\(291\) | 77613.9i | 0.916545i | ||||||||
\(292\) | − | 105614.i | − | 1.23867i | ||||||
\(293\) | 75732.9 | 0.882164 | 0.441082 | − | 0.897467i | \(-0.354595\pi\) | ||||
0.441082 | + | 0.897467i | \(0.354595\pi\) | |||||||
\(294\) | −123622. | −1.43022 | ||||||||
\(295\) | 4871.76i | 0.0559811i | ||||||||
\(296\) | −203526. | −2.32293 | ||||||||
\(297\) | 7876.00i | 0.0892879i | ||||||||
\(298\) | −91768.4 | −1.03338 | ||||||||
\(299\) | −23821.0 | −0.266452 | ||||||||
\(300\) | 151224.i | 1.68027i | ||||||||
\(301\) | −13985.6 | + | 21333.7i | −0.154365 | + | 0.235468i | ||||
\(302\) | 281464. | 3.08609 | ||||||||
\(303\) | 112910.i | 1.22983i | ||||||||
\(304\) | − | 47324.4i | − | 0.512080i | ||||||
\(305\) | −4778.18 | −0.0513644 | ||||||||
\(306\) | 22722.6i | 0.242670i | ||||||||
\(307\) | −158838. | −1.68530 | −0.842652 | − | 0.538458i | \(-0.819007\pi\) | ||||
−0.842652 | + | 0.538458i | \(0.819007\pi\) | |||||||
\(308\) | − | 4108.47i | − | 0.0433090i | ||||||
\(309\) | 45985.4i | 0.481619i | ||||||||
\(310\) | 8921.08 | 0.0928312 | ||||||||
\(311\) | −49344.1 | −0.510169 | −0.255085 | − | 0.966919i | \(-0.582103\pi\) | ||||
−0.255085 | + | 0.966919i | \(0.582103\pi\) | |||||||
\(312\) | 72584.1 | 0.745645 | ||||||||
\(313\) | − | 66350.6i | − | 0.677261i | −0.940919 | − | 0.338631i | \(-0.890036\pi\) | ||
0.940919 | − | 0.338631i | \(-0.109964\pi\) | |||||||
\(314\) | 277955. | 2.81914 | ||||||||
\(315\) | 241.285 | 0.00243170 | ||||||||
\(316\) | −69490.0 | −0.695903 | ||||||||
\(317\) | 15717.4 | 0.156409 | 0.0782046 | − | 0.996937i | \(-0.475081\pi\) | ||||
0.0782046 | + | 0.996937i | \(0.475081\pi\) | |||||||
\(318\) | −5555.17 | −0.0549342 | ||||||||
\(319\) | 11706.4i | 0.115038i | ||||||||
\(320\) | 8555.96i | 0.0835543i | ||||||||
\(321\) | 20262.0i | 0.196640i | ||||||||
\(322\) | 22447.1 | 0.216495 | ||||||||
\(323\) | 105152.i | 1.00789i | ||||||||
\(324\) | 159550. | 1.51987 | ||||||||
\(325\) | 61295.2 | 0.580309 | ||||||||
\(326\) | −41081.6 | −0.386556 | ||||||||
\(327\) | − | 26919.1i | − | 0.251747i | ||||||
\(328\) | 150028.i | 1.39452i | ||||||||
\(329\) | − | 10256.4i | − | 0.0947553i | ||||||
\(330\) | 845.773i | 0.00776651i | ||||||||
\(331\) | − | 85452.6i | − | 0.779954i | −0.920825 | − | 0.389977i | \(-0.872483\pi\) | ||
0.920825 | − | 0.389977i | \(-0.127517\pi\) | |||||||
\(332\) | 187620. | 1.70217 | ||||||||
\(333\) | 27083.9i | 0.244244i | ||||||||
\(334\) | − | 235218.i | − | 2.10852i | ||||||
\(335\) | 8236.87i | 0.0733960i | ||||||||
\(336\) | −14799.1 | −0.131086 | ||||||||
\(337\) | −146925. | −1.29371 | −0.646855 | − | 0.762613i | \(-0.723916\pi\) | ||||
−0.646855 | + | 0.762613i | \(0.723916\pi\) | |||||||
\(338\) | 126881.i | 1.11061i | ||||||||
\(339\) | 122128. | 1.06271 | ||||||||
\(340\) | 12397.4i | 0.107244i | ||||||||
\(341\) | −9133.57 | −0.0785474 | ||||||||
\(342\) | −29106.0 | −0.248845 | ||||||||
\(343\) | − | 63623.7i | − | 0.540793i | ||||||
\(344\) | 89872.4 | − | 137091.i | 0.759468 | − | 1.15849i | ||||
\(345\) | −2984.81 | −0.0250772 | ||||||||
\(346\) | 30903.1i | 0.258137i | ||||||||
\(347\) | − | 78623.4i | − | 0.652969i | −0.945203 | − | 0.326485i | \(-0.894136\pi\) | ||
0.945203 | − | 0.326485i | \(-0.105864\pi\) | |||||||
\(348\) | 278603. | 2.30052 | ||||||||
\(349\) | − | 165981.i | − | 1.36273i | −0.731945 | − | 0.681363i | \(-0.761387\pi\) | ||
0.731945 | − | 0.681363i | \(-0.238613\pi\) | |||||||
\(350\) | −57759.7 | −0.471508 | ||||||||
\(351\) | − | 75975.5i | − | 0.616679i | ||||||
\(352\) | − | 5628.42i | − | 0.0454257i | ||||||
\(353\) | 53106.9 | 0.426188 | 0.213094 | − | 0.977032i | \(-0.431646\pi\) | ||||
0.213094 | + | 0.977032i | \(0.431646\pi\) | |||||||
\(354\) | −183775. | −1.46650 | ||||||||
\(355\) | 4378.07 | 0.0347397 | ||||||||
\(356\) | 96127.9i | 0.758490i | ||||||||
\(357\) | 32882.8 | 0.258007 | ||||||||
\(358\) | −176897. | −1.38024 | ||||||||
\(359\) | −120101. | −0.931879 | −0.465939 | − | 0.884817i | \(-0.654284\pi\) | ||||
−0.465939 | + | 0.884817i | \(0.654284\pi\) | |||||||
\(360\) | −1550.51 | −0.0119638 | ||||||||
\(361\) | −4370.92 | −0.0335396 | ||||||||
\(362\) | − | 323564.i | − | 2.46912i | ||||||
\(363\) | 120930.i | 0.917739i | ||||||||
\(364\) | 39632.1i | 0.299120i | ||||||||
\(365\) | −5363.91 | −0.0402620 | ||||||||
\(366\) | − | 180245.i | − | 1.34556i | ||||||
\(367\) | −37702.0 | −0.279919 | −0.139959 | − | 0.990157i | \(-0.544697\pi\) | ||||
−0.139959 | + | 0.990157i | \(0.544697\pi\) | |||||||
\(368\) | −31210.4 | −0.230464 | ||||||||
\(369\) | 19964.7 | 0.146626 | ||||||||
\(370\) | 22877.0i | 0.167107i | ||||||||
\(371\) | − | 1370.52i | − | 0.00995720i | ||||||
\(372\) | 217371.i | 1.57078i | ||||||||
\(373\) | − | 139388.i | − | 1.00186i | −0.865488 | − | 0.500930i | \(-0.832991\pi\) | ||
0.865488 | − | 0.500930i | \(-0.167009\pi\) | |||||||
\(374\) | − | 19650.3i | − | 0.140484i | ||||||
\(375\) | 15387.8 | 0.109425 | ||||||||
\(376\) | 65908.1i | 0.466190i | ||||||||
\(377\) | − | 112925.i | − | 0.794526i | ||||||
\(378\) | 71593.3i | 0.501059i | ||||||||
\(379\) | −88126.5 | −0.613519 | −0.306759 | − | 0.951787i | \(-0.599245\pi\) | ||||
−0.306759 | + | 0.951787i | \(0.599245\pi\) | |||||||
\(380\) | −15880.1 | −0.109973 | ||||||||
\(381\) | − | 224607.i | − | 1.54730i | ||||||
\(382\) | −315636. | −2.16302 | ||||||||
\(383\) | 250818.i | 1.70986i | 0.518743 | + | 0.854930i | \(0.326400\pi\) | ||||
−0.518743 | + | 0.854930i | \(0.673600\pi\) | |||||||
\(384\) | −249326. | −1.69085 | ||||||||
\(385\) | −208.661 | −0.00140773 | ||||||||
\(386\) | − | 127506.i | − | 0.855766i | ||||||
\(387\) | −18243.2 | − | 11959.7i | −0.121809 | − | 0.0798540i | ||||
\(388\) | 272326. | 1.80895 | ||||||||
\(389\) | 34015.7i | 0.224792i | 0.993664 | + | 0.112396i | \(0.0358524\pi\) | ||||
−0.993664 | + | 0.112396i | \(0.964148\pi\) | |||||||
\(390\) | − | 8158.71i | − | 0.0536404i | ||||||
\(391\) | 69347.7 | 0.453605 | ||||||||
\(392\) | 195987.i | 1.27543i | ||||||||
\(393\) | 143269. | 0.927614 | ||||||||
\(394\) | 518802.i | 3.34202i | ||||||||
\(395\) | 3529.26i | 0.0226199i | ||||||||
\(396\) | 3513.31 | 0.0224040 | ||||||||
\(397\) | 206559. | 1.31058 | 0.655291 | − | 0.755377i | \(-0.272546\pi\) | ||||
0.655291 | + | 0.755377i | \(0.272546\pi\) | |||||||
\(398\) | 15130.8 | 0.0955203 | ||||||||
\(399\) | 42120.4i | 0.264574i | ||||||||
\(400\) | 80309.1 | 0.501932 | ||||||||
\(401\) | 85162.0 | 0.529611 | 0.264806 | − | 0.964302i | \(-0.414692\pi\) | ||||
0.264806 | + | 0.964302i | \(0.414692\pi\) | |||||||
\(402\) | −310716. | −1.92270 | ||||||||
\(403\) | 88106.5 | 0.542498 | ||||||||
\(404\) | 396169. | 2.42727 | ||||||||
\(405\) | − | 8103.21i | − | 0.0494023i | ||||||
\(406\) | 106412.i | 0.645561i | ||||||||
\(407\) | − | 23421.9i | − | 0.141395i | ||||||
\(408\) | −211306. | −1.26938 | ||||||||
\(409\) | 216421.i | 1.29375i | 0.762594 | + | 0.646877i | \(0.223925\pi\) | ||||
−0.762594 | + | 0.646877i | \(0.776075\pi\) | |||||||
\(410\) | 16863.6 | 0.100319 | ||||||||
\(411\) | −15643.3 | −0.0926075 | ||||||||
\(412\) | 161350. | 0.950552 | ||||||||
\(413\) | − | 45339.3i | − | 0.265812i | ||||||
\(414\) | 19195.3i | 0.111994i | ||||||||
\(415\) | − | 9528.88i | − | 0.0553281i | ||||||
\(416\) | 54294.3i | 0.313738i | ||||||||
\(417\) | − | 171941.i | − | 0.988795i | ||||||
\(418\) | 25170.5 | 0.144059 | ||||||||
\(419\) | 195727.i | 1.11487i | 0.830222 | + | 0.557433i | \(0.188214\pi\) | ||||
−0.830222 | + | 0.557433i | \(0.811786\pi\) | |||||||
\(420\) | 4965.96i | 0.0281517i | ||||||||
\(421\) | − | 216454.i | − | 1.22124i | −0.791924 | − | 0.610620i | \(-0.790920\pi\) | ||
0.791924 | − | 0.610620i | \(-0.209080\pi\) | |||||||
\(422\) | −431560. | −2.42335 | ||||||||
\(423\) | 8770.65 | 0.0490175 | ||||||||
\(424\) | 8807.02i | 0.0489889i | ||||||||
\(425\) | −178442. | −0.987915 | ||||||||
\(426\) | 165152.i | 0.910051i | ||||||||
\(427\) | 44468.4 | 0.243891 | ||||||||
\(428\) | 71093.8 | 0.388100 | ||||||||
\(429\) | 8353.04i | 0.0453868i | ||||||||
\(430\) | −15409.5 | − | 10102.0i | −0.0833398 | − | 0.0546348i | ||||
\(431\) | −219971. | −1.18416 | −0.592082 | − | 0.805878i | \(-0.701694\pi\) | ||||
−0.592082 | + | 0.805878i | \(0.701694\pi\) | |||||||
\(432\) | − | 99543.3i | − | 0.533390i | ||||||
\(433\) | 141123.i | 0.752699i | 0.926478 | + | 0.376349i | \(0.122821\pi\) | ||||
−0.926478 | + | 0.376349i | \(0.877179\pi\) | |||||||
\(434\) | −83024.6 | −0.440786 | ||||||||
\(435\) | − | 14149.7i | − | 0.0747770i | ||||||
\(436\) | −94451.7 | −0.496863 | ||||||||
\(437\) | 88829.2i | 0.465150i | ||||||||
\(438\) | − | 202341.i | − | 1.05472i | ||||||
\(439\) | −18660.8 | −0.0968279 | −0.0484139 | − | 0.998827i | \(-0.515417\pi\) | ||||
−0.0484139 | + | 0.998827i | \(0.515417\pi\) | |||||||
\(440\) | 1340.87 | 0.00692596 | ||||||||
\(441\) | 26080.8 | 0.134104 | ||||||||
\(442\) | 189556.i | 0.970268i | ||||||||
\(443\) | 21366.2 | 0.108873 | 0.0544366 | − | 0.998517i | \(-0.482664\pi\) | ||||
0.0544366 | + | 0.998517i | \(0.482664\pi\) | |||||||
\(444\) | −557422. | −2.82760 | ||||||||
\(445\) | 4882.15 | 0.0246542 | ||||||||
\(446\) | 359018. | 1.80487 | ||||||||
\(447\) | −113564. | −0.568362 | ||||||||
\(448\) | − | 79626.7i | − | 0.396737i | ||||||
\(449\) | 101517.i | 0.503553i | 0.967785 | + | 0.251777i | \(0.0810148\pi\) | ||||
−0.967785 | + | 0.251777i | \(0.918985\pi\) | |||||||
\(450\) | − | 49392.6i | − | 0.243914i | ||||||
\(451\) | −17265.3 | −0.0848831 | ||||||||
\(452\) | − | 428513.i | − | 2.09743i | ||||||
\(453\) | 348313. | 1.69736 | ||||||||
\(454\) | −292382. | −1.41853 | ||||||||
\(455\) | 2012.84 | 0.00972269 | ||||||||
\(456\) | − | 270668.i | − | 1.30169i | ||||||
\(457\) | − | 308003.i | − | 1.47477i | −0.675475 | − | 0.737383i | \(-0.736061\pi\) | ||
0.675475 | − | 0.737383i | \(-0.263939\pi\) | |||||||
\(458\) | − | 451367.i | − | 2.15178i | ||||||
\(459\) | 221179.i | 1.04983i | ||||||||
\(460\) | 10472.9i | 0.0494938i | ||||||||
\(461\) | 156343. | 0.735660 | 0.367830 | − | 0.929893i | \(-0.380101\pi\) | ||||
0.367830 | + | 0.929893i | \(0.380101\pi\) | |||||||
\(462\) | − | 7871.24i | − | 0.0368773i | ||||||
\(463\) | − | 203393.i | − | 0.948800i | −0.880309 | − | 0.474400i | \(-0.842665\pi\) | ||
0.880309 | − | 0.474400i | \(-0.157335\pi\) | |||||||
\(464\) | − | 147955.i | − | 0.687216i | ||||||
\(465\) | 11039.9 | 0.0510573 | ||||||||
\(466\) | 515824. | 2.37536 | ||||||||
\(467\) | − | 208975.i | − | 0.958209i | −0.877758 | − | 0.479104i | \(-0.840962\pi\) | ||
0.877758 | − | 0.479104i | \(-0.159038\pi\) | |||||||
\(468\) | −33891.0 | −0.154736 | ||||||||
\(469\) | − | 76657.0i | − | 0.348503i | ||||||
\(470\) | 7408.31 | 0.0335369 | ||||||||
\(471\) | 343971. | 1.55053 | ||||||||
\(472\) | 291353.i | 1.30778i | ||||||||
\(473\) | 15776.6 | + | 10342.6i | 0.0705164 | + | 0.0462282i | ||||
\(474\) | −133133. | −0.592556 | ||||||||
\(475\) | − | 228571.i | − | 1.01306i | ||||||
\(476\) | − | 115377.i | − | 0.509219i | ||||||
\(477\) | 1171.98 | 0.00515092 | ||||||||
\(478\) | 179938.i | 0.787531i | ||||||||
\(479\) | 98547.6 | 0.429512 | 0.214756 | − | 0.976668i | \(-0.431104\pi\) | ||||
0.214756 | + | 0.976668i | \(0.431104\pi\) | |||||||
\(480\) | 6803.16i | 0.0295276i | ||||||||
\(481\) | 225938.i | 0.976562i | ||||||||
\(482\) | 675212. | 2.90634 | ||||||||
\(483\) | 27778.3 | 0.119073 | ||||||||
\(484\) | 424309. | 1.81130 | ||||||||
\(485\) | − | 13830.9i | − | 0.0587987i | ||||||
\(486\) | −114661. | −0.485448 | ||||||||
\(487\) | −319902. | −1.34884 | −0.674418 | − | 0.738350i | \(-0.735605\pi\) | ||||
−0.674418 | + | 0.738350i | \(0.735605\pi\) | |||||||
\(488\) | −285756. | −1.19993 | ||||||||
\(489\) | −50838.7 | −0.212607 | ||||||||
\(490\) | 22029.7 | 0.0917520 | ||||||||
\(491\) | 454263.i | 1.88428i | 0.335226 | + | 0.942138i | \(0.391187\pi\) | ||||
−0.335226 | + | 0.942138i | \(0.608813\pi\) | |||||||
\(492\) | 410900.i | 1.69749i | ||||||||
\(493\) | 328747.i | 1.35260i | ||||||||
\(494\) | −242806. | −0.994962 | ||||||||
\(495\) | − | 178.434i | − | 0.000728228i | ||||||
\(496\) | 115437. | 0.469227 | ||||||||
\(497\) | −40744.8 | −0.164953 | ||||||||
\(498\) | 359454. | 1.44939 | ||||||||
\(499\) | 336510.i | 1.35144i | 0.737158 | + | 0.675720i | \(0.236167\pi\) | ||||
−0.737158 | + | 0.675720i | \(0.763833\pi\) | |||||||
\(500\) | − | 53991.8i | − | 0.215967i | ||||||
\(501\) | − | 291083.i | − | 1.15969i | ||||||
\(502\) | 482237.i | 1.91361i | ||||||||
\(503\) | − | 313054.i | − | 1.23732i | −0.785658 | − | 0.618661i | \(-0.787675\pi\) | ||
0.785658 | − | 0.618661i | \(-0.212325\pi\) | |||||||
\(504\) | 14429.9 | 0.0568072 | ||||||||
\(505\) | − | 20120.7i | − | 0.0788968i | ||||||
\(506\) | − | 16599.9i | − | 0.0648344i | ||||||
\(507\) | 157016.i | 0.610840i | ||||||||
\(508\) | −788086. | −3.05384 | ||||||||
\(509\) | 406043. | 1.56724 | 0.783621 | − | 0.621239i | \(-0.213370\pi\) | ||||
0.783621 | + | 0.621239i | \(0.213370\pi\) | |||||||
\(510\) | 23751.6i | 0.0913171i | ||||||||
\(511\) | 49919.6 | 0.191174 | ||||||||
\(512\) | 254048.i | 0.969114i | ||||||||
\(513\) | −283314. | −1.07655 | ||||||||
\(514\) | −48856.4 | −0.184925 | ||||||||
\(515\) | − | 8194.68i | − | 0.0308971i | ||||||
\(516\) | 246145. | − | 375469.i | 0.924468 | − | 1.41018i | ||||
\(517\) | −7584.76 | −0.0283766 | ||||||||
\(518\) | − | 212906.i | − | 0.793467i | ||||||
\(519\) | 38242.7i | 0.141976i | ||||||||
\(520\) | −12934.6 | −0.0478351 | ||||||||
\(521\) | 221529.i | 0.816122i | 0.912955 | + | 0.408061i | \(0.133795\pi\) | ||||
−0.912955 | + | 0.408061i | \(0.866205\pi\) | |||||||
\(522\) | −90996.8 | −0.333953 | ||||||||
\(523\) | 146666.i | 0.536199i | 0.963391 | + | 0.268099i | \(0.0863955\pi\) | ||||
−0.963391 | + | 0.268099i | \(0.913604\pi\) | |||||||
\(524\) | − | 502692.i | − | 1.83080i | ||||||
\(525\) | −71477.9 | −0.259330 | ||||||||
\(526\) | 496359. | 1.79401 | ||||||||
\(527\) | −256495. | −0.923545 | ||||||||
\(528\) | 10944.2i | 0.0392568i | ||||||||
\(529\) | −221258. | −0.790657 | ||||||||
\(530\) | 989.940 | 0.00352417 | ||||||||
\(531\) | 38771.4 | 0.137506 | ||||||||
\(532\) | 147789. | 0.522179 | ||||||||
\(533\) | 166549. | 0.586257 | ||||||||
\(534\) | 184168.i | 0.645848i | ||||||||
\(535\) | − | 3610.71i | − | 0.0126150i | ||||||
\(536\) | 492601.i | 1.71461i | ||||||||
\(537\) | −218911. | −0.759137 | ||||||||
\(538\) | − | 855513.i | − | 2.95571i | ||||||
\(539\) | −22554.4 | −0.0776342 | ||||||||
\(540\) | −33402.5 | −0.114549 | ||||||||
\(541\) | 38164.1 | 0.130395 | 0.0651974 | − | 0.997872i | \(-0.479232\pi\) | ||||
0.0651974 | + | 0.997872i | \(0.479232\pi\) | |||||||
\(542\) | − | 297007.i | − | 1.01104i | ||||||
\(543\) | − | 400411.i | − | 1.35802i | ||||||
\(544\) | − | 158061.i | − | 0.534106i | ||||||
\(545\) | 4797.02i | 0.0161502i | ||||||||
\(546\) | 75929.6i | 0.254698i | ||||||||
\(547\) | 105758. | 0.353459 | 0.176730 | − | 0.984259i | \(-0.443448\pi\) | ||||
0.176730 | + | 0.984259i | \(0.443448\pi\) | |||||||
\(548\) | 54888.3i | 0.182776i | ||||||||
\(549\) | 38026.6i | 0.126166i | ||||||||
\(550\) | 42714.2i | 0.141204i | ||||||||
\(551\) | −421100. | −1.38702 | ||||||||
\(552\) | −178505. | −0.585831 | ||||||||
\(553\) | − | 32845.3i | − | 0.107405i | ||||||
\(554\) | −209718. | −0.683308 | ||||||||
\(555\) | 28310.4i | 0.0919094i | ||||||||
\(556\) | −603293. | −1.95155 | ||||||||
\(557\) | 280135. | 0.902936 | 0.451468 | − | 0.892287i | \(-0.350900\pi\) | ||||
0.451468 | + | 0.892287i | \(0.350900\pi\) | |||||||
\(558\) | − | 70997.5i | − | 0.228021i | ||||||
\(559\) | −152188. | − | 99769.3i | −0.487031 | − | 0.319281i | ||||
\(560\) | 2637.23 | 0.00840953 | ||||||||
\(561\) | − | 24317.3i | − | 0.0772662i | ||||||
\(562\) | 942541.i | 2.98420i | ||||||||
\(563\) | −403332. | −1.27247 | −0.636233 | − | 0.771497i | \(-0.719508\pi\) | ||||
−0.636233 | + | 0.771497i | \(0.719508\pi\) | |||||||
\(564\) | 180511.i | 0.567474i | ||||||||
\(565\) | −21763.3 | −0.0681756 | ||||||||
\(566\) | − | 13606.9i | − | 0.0424744i | ||||||
\(567\) | 75413.1i | 0.234574i | ||||||||
\(568\) | 261828. | 0.811559 | ||||||||
\(569\) | −72865.2 | −0.225059 | −0.112529 | − | 0.993648i | \(-0.535895\pi\) | ||||
−0.112529 | + | 0.993648i | \(0.535895\pi\) | |||||||
\(570\) | −30424.0 | −0.0936411 | ||||||||
\(571\) | − | 280074.i | − | 0.859015i | −0.903063 | − | 0.429507i | \(-0.858687\pi\) | ||
0.903063 | − | 0.429507i | \(-0.141313\pi\) | |||||||
\(572\) | 29308.6 | 0.0895782 | ||||||||
\(573\) | −390601. | −1.18966 | ||||||||
\(574\) | −156943. | −0.476340 | ||||||||
\(575\) | −150742. | −0.455931 | ||||||||
\(576\) | 68091.8 | 0.205234 | ||||||||
\(577\) | 205999.i | 0.618748i | 0.950940 | + | 0.309374i | \(0.100119\pi\) | ||||
−0.950940 | + | 0.309374i | \(0.899881\pi\) | |||||||
\(578\) | 9614.89i | 0.0287799i | ||||||||
\(579\) | − | 157789.i | − | 0.470673i | ||||||
\(580\) | −49647.4 | −0.147584 | ||||||||
\(581\) | 88681.2i | 0.262712i | ||||||||
\(582\) | 521739. | 1.54031 | ||||||||
\(583\) | −1013.52 | −0.00298191 | ||||||||
\(584\) | −320786. | −0.940566 | ||||||||
\(585\) | 1721.26i | 0.00502960i | ||||||||
\(586\) | − | 509094.i | − | 1.48253i | ||||||
\(587\) | − | 466185.i | − | 1.35295i | −0.736464 | − | 0.676476i | \(-0.763506\pi\) | ||
0.736464 | − | 0.676476i | \(-0.236494\pi\) | |||||||
\(588\) | 536776.i | 1.55252i | ||||||||
\(589\) | − | 328551.i | − | 0.947049i | ||||||
\(590\) | 32749.1 | 0.0940795 | ||||||||
\(591\) | 642020.i | 1.83812i | ||||||||
\(592\) | 296025.i | 0.844666i | ||||||||
\(593\) | 284311.i | 0.808507i | 0.914647 | + | 0.404253i | \(0.132469\pi\) | ||||
−0.914647 | + | 0.404253i | \(0.867531\pi\) | |||||||
\(594\) | 52944.3 | 0.150054 | ||||||||
\(595\) | −5859.76 | −0.0165518 | ||||||||
\(596\) | 398465.i | 1.12175i | ||||||||
\(597\) | 18724.4 | 0.0525364 | ||||||||
\(598\) | 160131.i | 0.447787i | ||||||||
\(599\) | 438880. | 1.22318 | 0.611592 | − | 0.791173i | \(-0.290529\pi\) | ||||
0.611592 | + | 0.791173i | \(0.290529\pi\) | |||||||
\(600\) | 459320. | 1.27589 | ||||||||
\(601\) | 52157.2i | 0.144399i | 0.997390 | + | 0.0721997i | \(0.0230019\pi\) | ||||
−0.997390 | + | 0.0721997i | \(0.976998\pi\) | |||||||
\(602\) | 143410. | + | 94014.7i | 0.395718 | + | 0.259420i | ||||
\(603\) | 65552.3 | 0.180282 | ||||||||
\(604\) | − | 1.22214e6i | − | 3.35001i | ||||||
\(605\) | − | 21549.8i | − | 0.0588753i | ||||||
\(606\) | 759004. | 2.06680 | ||||||||
\(607\) | − | 328500.i | − | 0.891575i | −0.895139 | − | 0.445788i | \(-0.852924\pi\) | ||
0.895139 | − | 0.445788i | \(-0.147076\pi\) | |||||||
\(608\) | 202465. | 0.547699 | ||||||||
\(609\) | 131685.i | 0.355060i | ||||||||
\(610\) | 32120.0i | 0.0863209i | ||||||||
\(611\) | 73166.1 | 0.195987 | ||||||||
\(612\) | 98663.1 | 0.263422 | ||||||||
\(613\) | −194249. | −0.516937 | −0.258468 | − | 0.966020i | \(-0.583218\pi\) | ||||
−0.258468 | + | 0.966020i | \(0.583218\pi\) | |||||||
\(614\) | 1.06775e6i | 2.83225i | ||||||||
\(615\) | 20868.8 | 0.0551757 | ||||||||
\(616\) | −12478.9 | −0.0328862 | ||||||||
\(617\) | −203384. | −0.534253 | −0.267126 | − | 0.963662i | \(-0.586074\pi\) | ||||
−0.267126 | + | 0.963662i | \(0.586074\pi\) | |||||||
\(618\) | 309125. | 0.809388 | ||||||||
\(619\) | 504248. | 1.31602 | 0.658011 | − | 0.753008i | \(-0.271398\pi\) | ||||
0.658011 | + | 0.753008i | \(0.271398\pi\) | |||||||
\(620\) | − | 38735.9i | − | 0.100770i | ||||||
\(621\) | 186845.i | 0.484506i | ||||||||
\(622\) | 331702.i | 0.857369i | ||||||||
\(623\) | −45436.1 | −0.117064 | ||||||||
\(624\) | − | 105572.i | − | 0.271133i | ||||||
\(625\) | 386509. | 0.989464 | ||||||||
\(626\) | −446024. | −1.13818 | ||||||||
\(627\) | 31148.6 | 0.0792326 | ||||||||
\(628\) | − | 1.20690e6i | − | 3.06022i | ||||||
\(629\) | − | 657750.i | − | 1.66249i | ||||||
\(630\) | − | 1621.98i | − | 0.00408661i | ||||||
\(631\) | − | 612948.i | − | 1.53945i | −0.638376 | − | 0.769724i | \(-0.720394\pi\) | ||
0.638376 | − | 0.769724i | \(-0.279606\pi\) | |||||||
\(632\) | 211066.i | 0.528425i | ||||||||
\(633\) | −534057. | −1.33285 | ||||||||
\(634\) | − | 105656.i | − | 0.262855i | ||||||
\(635\) | 40025.4i | 0.0992631i | ||||||||
\(636\) | 24120.9i | 0.0596321i | ||||||||
\(637\) | 217570. | 0.536191 | ||||||||
\(638\) | 78693.0 | 0.193328 | ||||||||
\(639\) | − | 34842.5i | − | 0.0853311i | ||||||
\(640\) | 44430.3 | 0.108472 | ||||||||
\(641\) | 571747.i | 1.39151i | 0.718277 | + | 0.695757i | \(0.244931\pi\) | ||||
−0.718277 | + | 0.695757i | \(0.755069\pi\) | |||||||
\(642\) | 136206. | 0.330465 | ||||||||
\(643\) | −530650. | −1.28347 | −0.641736 | − | 0.766926i | \(-0.721785\pi\) | ||||
−0.641736 | + | 0.766926i | \(0.721785\pi\) | |||||||
\(644\) | − | 97466.7i | − | 0.235009i | ||||||
\(645\) | −19069.4 | − | 12501.2i | −0.0458371 | − | 0.0300492i | ||||
\(646\) | 706856. | 1.69382 | ||||||||
\(647\) | 481379.i | 1.14995i | 0.818171 | + | 0.574975i | \(0.194988\pi\) | ||||
−0.818171 | + | 0.574975i | \(0.805012\pi\) | |||||||
\(648\) | − | 484608.i | − | 1.15409i | ||||||
\(649\) | −33529.1 | −0.0796036 | ||||||||
\(650\) | − | 412040.i | − | 0.975244i | ||||||
\(651\) | −102743. | −0.242433 | ||||||||
\(652\) | 178379.i | 0.419613i | ||||||||
\(653\) | 293363.i | 0.687984i | 0.938973 | + | 0.343992i | \(0.111779\pi\) | ||||
−0.938973 | + | 0.343992i | \(0.888221\pi\) | |||||||
\(654\) | −180956. | −0.423076 | ||||||||
\(655\) | −25530.8 | −0.0595088 | ||||||||
\(656\) | 218213. | 0.507076 | ||||||||
\(657\) | 42688.2i | 0.0988956i | ||||||||
\(658\) | −68945.9 | −0.159242 | ||||||||
\(659\) | 657906. | 1.51493 | 0.757466 | − | 0.652875i | \(-0.226437\pi\) | ||||
0.757466 | + | 0.652875i | \(0.226437\pi\) | |||||||
\(660\) | 3672.40 | 0.00843068 | ||||||||
\(661\) | −267844. | −0.613026 | −0.306513 | − | 0.951866i | \(-0.599162\pi\) | ||||
−0.306513 | + | 0.951866i | \(0.599162\pi\) | |||||||
\(662\) | −574432. | −1.31076 | ||||||||
\(663\) | 234576.i | 0.533650i | ||||||||
\(664\) | − | 569869.i | − | 1.29253i | ||||||
\(665\) | − | 7505.92i | − | 0.0169731i | ||||||
\(666\) | 182064. | 0.410465 | ||||||||
\(667\) | 277715.i | 0.624235i | ||||||||
\(668\) | −1.02133e6 | −2.28883 | ||||||||
\(669\) | 444287. | 0.992685 | ||||||||
\(670\) | 55370.1 | 0.123346 | ||||||||
\(671\) | − | 32885.0i | − | 0.0730388i | ||||||
\(672\) | − | 63314.0i | − | 0.140204i | ||||||
\(673\) | − | 48089.2i | − | 0.106174i | −0.998590 | − | 0.0530869i | \(-0.983094\pi\) | ||
0.998590 | − | 0.0530869i | \(-0.0169060\pi\) | |||||||
\(674\) | 987667.i | 2.17416i | ||||||||
\(675\) | − | 480782.i | − | 1.05521i | ||||||
\(676\) | 550926. | 1.20559 | ||||||||
\(677\) | 84879.3i | 0.185193i | 0.995704 | + | 0.0925964i | \(0.0295166\pi\) | ||||
−0.995704 | + | 0.0925964i | \(0.970483\pi\) | |||||||
\(678\) | − | 820971.i | − | 1.78595i | ||||||
\(679\) | 128718.i | 0.279191i | ||||||||
\(680\) | 37655.1 | 0.0814341 | ||||||||
\(681\) | −361824. | −0.780195 | ||||||||
\(682\) | 61397.9i | 0.132003i | ||||||||
\(683\) | −707010. | −1.51560 | −0.757799 | − | 0.652488i | \(-0.773725\pi\) | ||||
−0.757799 | + | 0.652488i | \(0.773725\pi\) | |||||||
\(684\) | 126380.i | 0.270126i | ||||||||
\(685\) | 2787.67 | 0.00594101 | ||||||||
\(686\) | −427693. | −0.908833 | ||||||||
\(687\) | − | 558568.i | − | 1.18348i | ||||||
\(688\) | −199397. | − | 130718.i | −0.421252 | − | 0.276159i | ||||
\(689\) | 9776.87 | 0.0205950 | ||||||||
\(690\) | 20064.6i | 0.0421436i | ||||||||
\(691\) | 316021.i | 0.661851i | 0.943657 | + | 0.330925i | \(0.107361\pi\) | ||||
−0.943657 | + | 0.330925i | \(0.892639\pi\) | |||||||
\(692\) | 134183. | 0.280212 | ||||||||
\(693\) | 1660.61i | 0.00345781i | ||||||||
\(694\) | −528525. | −1.09735 | ||||||||
\(695\) | 30640.1i | 0.0634338i | ||||||||
\(696\) | − | 846214.i | − | 1.74687i | ||||||
\(697\) | −484856. | −0.998039 | ||||||||
\(698\) | −1.11577e6 | −2.29014 | ||||||||
\(699\) | 638334. | 1.30645 | ||||||||
\(700\) | 250797.i | 0.511830i | ||||||||
\(701\) | 790342. | 1.60835 | 0.804173 | − | 0.594396i | \(-0.202609\pi\) | ||||
0.804173 | + | 0.594396i | \(0.202609\pi\) | |||||||
\(702\) | −510725. | −1.03637 | ||||||||
\(703\) | 842529. | 1.70480 | ||||||||
\(704\) | −58885.1 | −0.118812 | ||||||||
\(705\) | 9167.81 | 0.0184454 | ||||||||
\(706\) | − | 356997.i | − | 0.716234i | ||||||
\(707\) | 187254.i | 0.374622i | ||||||||
\(708\) | 797965.i | 1.59191i | ||||||||
\(709\) | 218246. | 0.434165 | 0.217082 | − | 0.976153i | \(-0.430346\pi\) | ||||
0.217082 | + | 0.976153i | \(0.430346\pi\) | |||||||
\(710\) | − | 29430.4i | − | 0.0583821i | ||||||
\(711\) | 28087.3 | 0.0555611 | ||||||||
\(712\) | 291974. | 0.575950 | ||||||||
\(713\) | −216679. | −0.426224 | ||||||||
\(714\) | − | 221046.i | − | 0.433596i | ||||||
\(715\) | − | 1488.52i | − | 0.00291168i | ||||||
\(716\) | 768101.i | 1.49828i | ||||||||
\(717\) | 222674.i | 0.433144i | ||||||||
\(718\) | 807350.i | 1.56608i | ||||||||
\(719\) | 733807. | 1.41946 | 0.709732 | − | 0.704472i | \(-0.248816\pi\) | ||||
0.709732 | + | 0.704472i | \(0.248816\pi\) | |||||||
\(720\) | 2255.19i | 0.00435030i | ||||||||
\(721\) | 76264.3i | 0.146707i | ||||||||
\(722\) | 29382.3i | 0.0563653i | ||||||||
\(723\) | 835578. | 1.59849 | ||||||||
\(724\) | −1.40494e6 | −2.68027 | ||||||||
\(725\) | − | 714603.i | − | 1.35953i | ||||||
\(726\) | 812916. | 1.54231 | ||||||||
\(727\) | 250259.i | 0.473501i | 0.971570 | + | 0.236750i | \(0.0760824\pi\) | ||||
−0.971570 | + | 0.236750i | \(0.923918\pi\) | |||||||
\(728\) | 120377. | 0.227133 | ||||||||
\(729\) | −584656. | −1.10013 | ||||||||
\(730\) | 36057.5i | 0.0676627i | ||||||||
\(731\) | 443048. | + | 290448.i | 0.829118 | + | 0.543542i | ||||
\(732\) | −782638. | −1.46062 | ||||||||
\(733\) | 610120.i | 1.13555i | 0.823183 | + | 0.567776i | \(0.192196\pi\) | ||||
−0.823183 | + | 0.567776i | \(0.807804\pi\) | |||||||
\(734\) | 253441.i | 0.470419i | ||||||||
\(735\) | 27261.8 | 0.0504638 | ||||||||
\(736\) | − | 133525.i | − | 0.246495i | ||||||
\(737\) | −56689.0 | −0.104367 | ||||||||
\(738\) | − | 134208.i | − | 0.246414i | ||||||
\(739\) | 67964.4i | 0.124449i | 0.998062 | + | 0.0622246i | \(0.0198195\pi\) | ||||
−0.998062 | + | 0.0622246i | \(0.980180\pi\) | |||||||
\(740\) | 99333.5 | 0.181398 | ||||||||
\(741\) | −300474. | −0.547231 | ||||||||
\(742\) | −9212.95 | −0.0167337 | ||||||||
\(743\) | − | 707585.i | − | 1.28174i | −0.767648 | − | 0.640871i | \(-0.778573\pi\) | ||
0.767648 | − | 0.640871i | \(-0.221427\pi\) | |||||||
\(744\) | 660234. | 1.19276 | ||||||||
\(745\) | 20237.3 | 0.0364619 | ||||||||
\(746\) | −936998. | −1.68368 | ||||||||
\(747\) | −75834.7 | −0.135902 | ||||||||
\(748\) | −85322.8 | −0.152497 | ||||||||
\(749\) | 33603.4i | 0.0598989i | ||||||||
\(750\) | − | 103441.i | − | 0.183895i | ||||||
\(751\) | 613506.i | 1.08778i | 0.839158 | + | 0.543888i | \(0.183048\pi\) | ||||
−0.839158 | + | 0.543888i | \(0.816952\pi\) | |||||||
\(752\) | 95862.4 | 0.169517 | ||||||||
\(753\) | 596770.i | 1.05249i | ||||||||
\(754\) | −759109. | −1.33525 | ||||||||
\(755\) | −62069.9 | −0.108890 | ||||||||
\(756\) | 310863. | 0.543908 | ||||||||
\(757\) | 132879.i | 0.231880i | 0.993256 | + | 0.115940i | \(0.0369881\pi\) | ||||
−0.993256 | + | 0.115940i | \(0.963012\pi\) | |||||||
\(758\) | 592406.i | 1.03105i | ||||||||
\(759\) | − | 20542.5i | − | 0.0356590i | ||||||
\(760\) | 48233.4i | 0.0835066i | ||||||||
\(761\) | − | 790123.i | − | 1.36435i | −0.731190 | − | 0.682174i | \(-0.761035\pi\) | ||
0.731190 | − | 0.682174i | \(-0.238965\pi\) | |||||||
\(762\) | −1.50986e6 | −2.60032 | ||||||||
\(763\) | − | 44643.8i | − | 0.0766853i | ||||||
\(764\) | 1.37051e6i | 2.34799i | ||||||||
\(765\) | − | 5010.91i | − | 0.00856236i | ||||||
\(766\) | 1.68605e6 | 2.87352 | ||||||||
\(767\) | 323437. | 0.549793 | ||||||||
\(768\) | 907821.i | 1.53914i | ||||||||
\(769\) | −204245. | −0.345382 | −0.172691 | − | 0.984976i | \(-0.555246\pi\) | ||||
−0.172691 | + | 0.984976i | \(0.555246\pi\) | |||||||
\(770\) | 1402.67i | 0.00236577i | ||||||||
\(771\) | −60460.0 | −0.101709 | ||||||||
\(772\) | −553638. | −0.928948 | ||||||||
\(773\) | − | 824077.i | − | 1.37914i | −0.724218 | − | 0.689571i | \(-0.757799\pi\) | ||
0.724218 | − | 0.689571i | \(-0.242201\pi\) | |||||||
\(774\) | −80395.6 | + | 122635.i | −0.134199 | + | 0.204707i | ||||
\(775\) | 557548. | 0.928280 | ||||||||
\(776\) | − | 827151.i | − | 1.37360i | ||||||
\(777\) | − | 263473.i | − | 0.436409i | ||||||
\(778\) | 228661. | 0.377775 | ||||||||
\(779\) | − | 621065.i | − | 1.02344i | ||||||
\(780\) | −35425.7 | −0.0582276 | ||||||||
\(781\) | 30131.4i | 0.0493989i | ||||||||
\(782\) | − | 466171.i | − | 0.762310i | ||||||
\(783\) | −885752. | −1.44474 | ||||||||
\(784\) | 285061. | 0.463772 | ||||||||
\(785\) | −61296.2 | −0.0994705 | ||||||||
\(786\) | − | 963088.i | − | 1.55891i | ||||||
\(787\) | 347326. | 0.560774 | 0.280387 | − | 0.959887i | \(-0.409537\pi\) | ||||
0.280387 | + | 0.959887i | \(0.409537\pi\) | |||||||
\(788\) | 2.25268e6 | 3.62782 | ||||||||
\(789\) | 614246. | 0.986708 | ||||||||
\(790\) | 23724.5 | 0.0380140 | ||||||||
\(791\) | 202542. | 0.323715 | ||||||||
\(792\) | − | 10671.2i | − | 0.0170122i | ||||||
\(793\) | 317224.i | 0.504452i | ||||||||
\(794\) | − | 1.38854e6i | − | 2.20251i | ||||||
\(795\) | 1225.06 | 0.00193830 | ||||||||
\(796\) | − | 65699.0i | − | 0.103689i | ||||||
\(797\) | −550267. | −0.866278 | −0.433139 | − | 0.901327i | \(-0.642594\pi\) | ||||
−0.433139 | + | 0.901327i | \(0.642594\pi\) | |||||||
\(798\) | 283143. | 0.444631 | ||||||||
\(799\) | −213001. | −0.333647 | ||||||||
\(800\) | 343581.i | 0.536845i | ||||||||
\(801\) | − | 38854.1i | − | 0.0605581i | ||||||
\(802\) | − | 572479.i | − | 0.890042i | ||||||
\(803\) | − | 36916.3i | − | 0.0572515i | ||||||
\(804\) | 1.34915e6i | 2.08713i | ||||||||
\(805\) | −4950.15 | −0.00763882 | ||||||||
\(806\) | − | 592273.i | − | 0.911699i | ||||||
\(807\) | − | 1.05870e6i | − | 1.62565i | ||||||
\(808\) | − | 1.20331e6i | − | 1.84312i | ||||||
\(809\) | −237489. | −0.362866 | −0.181433 | − | 0.983403i | \(-0.558074\pi\) | ||||
−0.181433 | + | 0.983403i | \(0.558074\pi\) | |||||||
\(810\) | −54471.7 | −0.0830234 | ||||||||
\(811\) | − | 1.00555e6i | − | 1.52884i | −0.644717 | − | 0.764422i | \(-0.723025\pi\) | ||
0.644717 | − | 0.764422i | \(-0.276975\pi\) | |||||||
\(812\) | 462047. | 0.700768 | ||||||||
\(813\) | − | 367548.i | − | 0.556074i | ||||||
\(814\) | −157447. | −0.237622 | ||||||||
\(815\) | 9059.54 | 0.0136393 | ||||||||
\(816\) | 307342.i | 0.461574i | ||||||||
\(817\) | −372042. | + | 567512.i | −0.557375 | + | 0.850219i | ||||
\(818\) | 1.45483e6 | 2.17423 | ||||||||
\(819\) | − | 16019.0i | − | 0.0238818i | ||||||
\(820\) | − | 73223.1i | − | 0.108898i | ||||||
\(821\) | −259037. | −0.384305 | −0.192152 | − | 0.981365i | \(-0.561547\pi\) | ||||
−0.192152 | + | 0.981365i | \(0.561547\pi\) | |||||||
\(822\) | 105158.i | 0.155632i | ||||||||
\(823\) | −70048.9 | −0.103419 | −0.0517097 | − | 0.998662i | \(-0.516467\pi\) | ||||
−0.0517097 | + | 0.998662i | \(0.516467\pi\) | |||||||
\(824\) | − | 490078.i | − | 0.721790i | ||||||
\(825\) | 52859.0i | 0.0776624i | ||||||||
\(826\) | −304781. | −0.446713 | ||||||||
\(827\) | −771588. | −1.12817 | −0.564085 | − | 0.825717i | \(-0.690771\pi\) | ||||
−0.564085 | + | 0.825717i | \(0.690771\pi\) | |||||||
\(828\) | 83347.5 | 0.121572 | ||||||||
\(829\) | − | 131193.i | − | 0.190898i | −0.995434 | − | 0.0954489i | \(-0.969571\pi\) | ||
0.995434 | − | 0.0954489i | \(-0.0304286\pi\) | |||||||
\(830\) | −64055.3 | −0.0929821 | ||||||||
\(831\) | −259527. | −0.375821 | ||||||||
\(832\) | 568033. | 0.820591 | ||||||||
\(833\) | −633388. | −0.912808 | ||||||||
\(834\) | −1.15582e6 | −1.66173 | ||||||||
\(835\) | 51871.4i | 0.0743970i | ||||||||
\(836\) | − | 109292.i | − | 0.156378i | ||||||
\(837\) | − | 691082.i | − | 0.986458i | ||||||
\(838\) | 1.31572e6 | 1.87360 | ||||||||
\(839\) | 473423.i | 0.672552i | 0.941764 | + | 0.336276i | \(0.109167\pi\) | ||||
−0.941764 | + | 0.336276i | \(0.890833\pi\) | |||||||
\(840\) | 15083.4 | 0.0213767 | ||||||||
\(841\) | −609245. | −0.861390 | ||||||||
\(842\) | −1.45505e6 | −2.05236 | ||||||||
\(843\) | 1.16640e6i | 1.64131i | ||||||||
\(844\) | 1.87386e6i | 2.63059i | ||||||||
\(845\) | − | 27980.5i | − | 0.0391869i | ||||||
\(846\) | − | 58958.3i | − | 0.0823767i | ||||||
\(847\) | 200555.i | 0.279555i | ||||||||
\(848\) | 12809.7 | 0.0178134 | ||||||||
\(849\) | − | 16838.6i | − | 0.0233610i | ||||||
\(850\) | 1.19953e6i | 1.66025i | ||||||||
\(851\) | − | 555647.i | − | 0.767255i | ||||||
\(852\) | 717103. | 0.987876 | ||||||||
\(853\) | −535509. | −0.735985 | −0.367992 | − | 0.929829i | \(-0.619955\pi\) | ||||
−0.367992 | + | 0.929829i | \(0.619955\pi\) | |||||||
\(854\) | − | 298927.i | − | 0.409873i | ||||||
\(855\) | 6418.60 | 0.00878027 | ||||||||
\(856\) | − | 215937.i | − | 0.294699i | ||||||
\(857\) | 1.28191e6 | 1.74540 | 0.872699 | − | 0.488258i | \(-0.162368\pi\) | ||||
0.872699 | + | 0.488258i | \(0.162368\pi\) | |||||||
\(858\) | 56151.1 | 0.0762752 | ||||||||
\(859\) | 683886.i | 0.926825i | 0.886143 | + | 0.463412i | \(0.153375\pi\) | ||||
−0.886143 | + | 0.463412i | \(0.846625\pi\) | |||||||
\(860\) | −43863.5 | + | 66909.3i | −0.0593070 | + | 0.0904668i | ||||
\(861\) | −194217. | −0.261988 | ||||||||
\(862\) | 1.47870e6i | 1.99005i | ||||||||
\(863\) | 423128.i | 0.568134i | 0.958804 | + | 0.284067i | \(0.0916838\pi\) | ||||
−0.958804 | + | 0.284067i | \(0.908316\pi\) | |||||||
\(864\) | 425869. | 0.570490 | ||||||||
\(865\) | − | 6814.91i | − | 0.00910810i | ||||||
\(866\) | 948660. | 1.26495 | ||||||||
\(867\) | 11898.5i | 0.0158290i | ||||||||
\(868\) | 360499.i | 0.478480i | ||||||||
\(869\) | −24289.6 | −0.0321648 | ||||||||
\(870\) | −95117.4 | −0.125667 | ||||||||
\(871\) | 546848. | 0.720825 | ||||||||
\(872\) | 286883.i | 0.377287i | ||||||||
\(873\) | −110072. | −0.144427 | ||||||||
\(874\) | 597130. | 0.781711 | ||||||||
\(875\) | 25519.9 | 0.0333321 | ||||||||
\(876\) | −878578. | −1.14491 | ||||||||
\(877\) | 543060. | 0.706071 | 0.353036 | − | 0.935610i | \(-0.385149\pi\) | ||||
0.353036 | + | 0.935610i | \(0.385149\pi\) | |||||||
\(878\) | 125442.i | 0.162725i | ||||||||
\(879\) | − | 630006.i | − | 0.815393i | ||||||
\(880\) | − | 1950.27i | − | 0.00251843i | ||||||
\(881\) | −747183. | −0.962665 | −0.481333 | − | 0.876538i | \(-0.659847\pi\) | ||||
−0.481333 | + | 0.876538i | \(0.659847\pi\) | |||||||
\(882\) | − | 175321.i | − | 0.225370i | ||||||
\(883\) | 908500. | 1.16521 | 0.582604 | − | 0.812756i | \(-0.302034\pi\) | ||||
0.582604 | + | 0.812756i | \(0.302034\pi\) | |||||||
\(884\) | 823063. | 1.05324 | ||||||||
\(885\) | 40527.1 | 0.0517439 | ||||||||
\(886\) | − | 143629.i | − | 0.182968i | ||||||
\(887\) | − | 283934.i | − | 0.360886i | −0.983585 | − | 0.180443i | \(-0.942247\pi\) | ||
0.983585 | − | 0.180443i | \(-0.0577531\pi\) | |||||||
\(888\) | 1.69309e6i | 2.14711i | ||||||||
\(889\) | − | 372499.i | − | 0.471326i | ||||||
\(890\) | − | 32819.0i | − | 0.0414328i | ||||||
\(891\) | 55769.1 | 0.0702487 | ||||||||
\(892\) | − | 1.55888e6i | − | 1.95922i | ||||||
\(893\) | − | 272838.i | − | 0.342138i | ||||||
\(894\) | 763402.i | 0.955165i | ||||||||
\(895\) | 39010.4 | 0.0487006 | ||||||||
\(896\) | −413493. | −0.515054 | ||||||||
\(897\) | 198162.i | 0.246284i | ||||||||
\(898\) | 682420. | 0.846250 | ||||||||
\(899\) | − | 1.02718e6i | − | 1.27095i | ||||||
\(900\) | −214466. | −0.264773 | ||||||||
\(901\) | −28462.3 | −0.0350607 | ||||||||
\(902\) | 116061.i | 0.142651i | ||||||||
\(903\) | 177470. | + | 116344.i | 0.217646 | + | 0.142681i | ||||
\(904\) | −1.30155e6 | −1.59266 | ||||||||
\(905\) | 71354.0i | 0.0871206i | ||||||||
\(906\) | − | 2.34144e6i | − | 2.85251i | ||||||
\(907\) | −329783. | −0.400880 | −0.200440 | − | 0.979706i | \(-0.564237\pi\) | ||||
−0.200440 | + | 0.979706i | \(0.564237\pi\) | |||||||
\(908\) | 1.26954e6i | 1.53984i | ||||||||
\(909\) | −160128. | −0.193794 | ||||||||
\(910\) | − | 13530.8i | − | 0.0163395i | ||||||
\(911\) | 1.20039e6i | 1.44639i | 0.690642 | + | 0.723197i | \(0.257328\pi\) | ||||
−0.690642 | + | 0.723197i | \(0.742672\pi\) | |||||||
\(912\) | −393682. | −0.473321 | ||||||||
\(913\) | 65581.0 | 0.0786750 | ||||||||
\(914\) | −2.07047e6 | −2.47843 | ||||||||
\(915\) | 39748.6i | 0.0474767i | ||||||||
\(916\) | −1.95986e6 | −2.33580 | ||||||||
\(917\) | 237604. | 0.282563 | ||||||||
\(918\) | 1.48682e6 | 1.76430 | ||||||||
\(919\) | −775338. | −0.918037 | −0.459018 | − | 0.888427i | \(-0.651799\pi\) | ||||
−0.459018 | + | 0.888427i | \(0.651799\pi\) | |||||||
\(920\) | 31809.9 | 0.0375826 | ||||||||
\(921\) | 1.32134e6i | 1.55774i | ||||||||
\(922\) | − | 1.05098e6i | − | 1.23632i | ||||||
\(923\) | − | 290661.i | − | 0.341180i | ||||||
\(924\) | −34177.5 | −0.0400310 | ||||||||
\(925\) | 1.42976e6i | 1.67102i | ||||||||
\(926\) | −1.36726e6 | −1.59451 | ||||||||
\(927\) | −65216.5 | −0.0758924 | ||||||||
\(928\) | 632985. | 0.735017 | ||||||||
\(929\) | 763445.i | 0.884599i | 0.896867 | + | 0.442300i | \(0.145837\pi\) | ||||
−0.896867 | + | 0.442300i | \(0.854163\pi\) | |||||||
\(930\) | − | 74212.6i | − | 0.0858048i | ||||||
\(931\) | − | 811322.i | − | 0.936039i | ||||||
\(932\) | − | 2.23974e6i | − | 2.57849i | ||||||
\(933\) | 410483.i | 0.471555i | ||||||||
\(934\) | −1.40478e6 | −1.61033 | ||||||||
\(935\) | 4333.38i | 0.00495683i | ||||||||
\(936\) | 102939.i | 0.117497i | ||||||||
\(937\) | 1.72023e6i | 1.95932i | 0.200654 | + | 0.979662i | \(0.435693\pi\) | ||||
−0.200654 | + | 0.979662i | \(0.564307\pi\) | |||||||
\(938\) | −515306. | −0.585679 | ||||||||
\(939\) | −551957. | −0.625999 | ||||||||
\(940\) | − | 32167.4i | − | 0.0364049i | ||||||
\(941\) | 657189. | 0.742183 | 0.371092 | − | 0.928596i | \(-0.378984\pi\) | ||||
0.371092 | + | 0.928596i | \(0.378984\pi\) | |||||||
\(942\) | − | 2.31225e6i | − | 2.60576i | ||||||
\(943\) | −409591. | −0.460604 | ||||||||
\(944\) | 423768. | 0.475537 | ||||||||
\(945\) | − | 15788.1i | − | 0.0176794i | ||||||
\(946\) | 69525.3 | − | 106054.i | 0.0776891 | − | 0.118507i | ||||
\(947\) | −829200. | −0.924612 | −0.462306 | − | 0.886721i | \(-0.652978\pi\) | ||||
−0.462306 | + | 0.886721i | \(0.652978\pi\) | |||||||
\(948\) | 578073.i | 0.643230i | ||||||||
\(949\) | 356111.i | 0.395415i | ||||||||
\(950\) | −1.53651e6 | −1.70250 | ||||||||
\(951\) | − | 130750.i | − | 0.144571i | ||||||
\(952\) | −350440. | −0.386669 | ||||||||
\(953\) | − | 1.33377e6i | − | 1.46858i | −0.678838 | − | 0.734288i | \(-0.737516\pi\) | ||
0.678838 | − | 0.734288i | \(-0.262484\pi\) | |||||||
\(954\) | − | 7878.34i | − | 0.00865642i | ||||||
\(955\) | 69605.8 | 0.0763200 | ||||||||
\(956\) | 781305. | 0.854879 | ||||||||
\(957\) | 97383.0 | 0.106331 | ||||||||
\(958\) | − | 662460.i | − | 0.721819i | ||||||
\(959\) | −25943.6 | −0.0282094 | ||||||||
\(960\) | 71175.3 | 0.0772301 | ||||||||
\(961\) | −122093. | −0.132204 | ||||||||
\(962\) | 1.51881e6 | 1.64117 | ||||||||
\(963\) | −28735.5 | −0.0309861 | ||||||||
\(964\) | − | 2.93182e6i | − | 3.15488i | ||||||
\(965\) | 28118.2i | 0.0301949i | ||||||||
\(966\) | − | 186732.i | − | 0.200109i | ||||||
\(967\) | 788889. | 0.843652 | 0.421826 | − | 0.906677i | \(-0.361389\pi\) | ||||
0.421826 | + | 0.906677i | \(0.361389\pi\) | |||||||
\(968\) | − | 1.28878e6i | − | 1.37539i | ||||||
\(969\) | 874738. | 0.931602 | ||||||||
\(970\) | −92974.7 | −0.0988146 | ||||||||
\(971\) | −1.20251e6 | −1.27541 | −0.637704 | − | 0.770282i | \(-0.720115\pi\) | ||||
−0.637704 | + | 0.770282i | \(0.720115\pi\) | |||||||
\(972\) | 497866.i | 0.526962i | ||||||||
\(973\) | − | 285154.i | − | 0.301199i | ||||||
\(974\) | 2.15046e6i | 2.26680i | ||||||||
\(975\) | − | 509902.i | − | 0.536386i | ||||||
\(976\) | 415628.i | 0.436320i | ||||||||
\(977\) | 634645. | 0.664878 | 0.332439 | − | 0.943125i | \(-0.392128\pi\) | ||||
0.332439 | + | 0.943125i | \(0.392128\pi\) | |||||||
\(978\) | 341750.i | 0.357298i | ||||||||
\(979\) | 33600.7i | 0.0350576i | ||||||||
\(980\) | − | 95654.3i | − | 0.0995984i | ||||||
\(981\) | 38176.6 | 0.0396698 | ||||||||
\(982\) | 3.05366e6 | 3.16663 | ||||||||
\(983\) | 1.63591e6i | 1.69298i | 0.532403 | + | 0.846491i | \(0.321289\pi\) | ||||
−0.532403 | + | 0.846491i | \(0.678711\pi\) | |||||||
\(984\) | 1.24805e6 | 1.28897 | ||||||||
\(985\) | − | 114409.i | − | 0.117920i | ||||||
\(986\) | 2.20991e6 | 2.27311 | ||||||||
\(987\) | −85320.9 | −0.0875832 | ||||||||
\(988\) | 1.05428e6i | 1.08005i | ||||||||
\(989\) | 374273. | + | 245361.i | 0.382645 | + | 0.250849i | ||||
\(990\) | −1199.48 | −0.00122383 | ||||||||
\(991\) | 1.20041e6i | 1.22231i | 0.791510 | + | 0.611156i | \(0.209295\pi\) | ||||
−0.791510 | + | 0.611156i | \(0.790705\pi\) | |||||||
\(992\) | 493868.i | 0.501865i | ||||||||
\(993\) | −710862. | −0.720920 | ||||||||
\(994\) | 273896.i | 0.277213i | ||||||||
\(995\) | −3336.72 | −0.00337034 | ||||||||
\(996\) | − | 1.56078e6i | − | 1.57334i | ||||||
\(997\) | 1.25293e6i | 1.26048i | 0.776401 | + | 0.630239i | \(0.217043\pi\) | ||||
−0.776401 | + | 0.630239i | \(0.782957\pi\) | |||||||
\(998\) | 2.26210e6 | 2.27117 | ||||||||
\(999\) | 1.77219e6 | 1.77574 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 43.5.b.b.42.2 | ✓ | 12 | |
3.2 | odd | 2 | 387.5.b.c.343.11 | 12 | |||
4.3 | odd | 2 | 688.5.b.d.257.9 | 12 | |||
43.42 | odd | 2 | inner | 43.5.b.b.42.11 | yes | 12 | |
129.128 | even | 2 | 387.5.b.c.343.2 | 12 | |||
172.171 | even | 2 | 688.5.b.d.257.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.5.b.b.42.2 | ✓ | 12 | 1.1 | even | 1 | trivial | |
43.5.b.b.42.11 | yes | 12 | 43.42 | odd | 2 | inner | |
387.5.b.c.343.2 | 12 | 129.128 | even | 2 | |||
387.5.b.c.343.11 | 12 | 3.2 | odd | 2 | |||
688.5.b.d.257.4 | 12 | 172.171 | even | 2 | |||
688.5.b.d.257.9 | 12 | 4.3 | odd | 2 |