Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,5,Mod(7,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(4))
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("75.7");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.f (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.75274723129\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.1 | ||
Root | \(1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.43 |
Dual form | 75.5.f.d.7.1 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.550510 | − | 0.550510i | 0.137628 | − | 0.137628i | −0.634937 | − | 0.772564i | \(-0.718974\pi\) |
0.772564 | + | 0.634937i | \(0.218974\pi\) | |||||||
\(3\) | 3.67423 | + | 3.67423i | 0.408248 | + | 0.408248i | ||||
\(4\) | 15.3939i | 0.962117i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.04541 | 0.112372 | ||||||||
\(7\) | −16.7753 | + | 16.7753i | −0.342352 | + | 0.342352i | −0.857251 | − | 0.514899i | \(-0.827829\pi\) |
0.514899 | + | 0.857251i | \(0.327829\pi\) | |||||||
\(8\) | 17.2827 | + | 17.2827i | 0.270041 | + | 0.270041i | ||||
\(9\) | 27.0000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −197.060 | −1.62860 | −0.814298 | − | 0.580447i | \(-0.802878\pi\) | ||||
−0.814298 | + | 0.580447i | \(0.802878\pi\) | |||||||
\(12\) | −56.5607 | + | 56.5607i | −0.392783 | + | 0.392783i | ||||
\(13\) | 120.507 | + | 120.507i | 0.713062 | + | 0.713062i | 0.967175 | − | 0.254113i | \(-0.0817835\pi\) |
−0.254113 | + | 0.967175i | \(0.581784\pi\) | |||||||
\(14\) | 18.4699i | 0.0942342i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −227.273 | −0.887787 | ||||||||
\(17\) | 152.449 | − | 152.449i | 0.527507 | − | 0.527507i | −0.392321 | − | 0.919828i | \(-0.628328\pi\) |
0.919828 | + | 0.392321i | \(0.128328\pi\) | |||||||
\(18\) | 14.8638 | + | 14.8638i | 0.0458759 | + | 0.0458759i | ||||
\(19\) | 418.242i | 1.15856i | 0.815127 | + | 0.579282i | \(0.196667\pi\) | ||||
−0.815127 | + | 0.579282i | \(0.803333\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −123.272 | −0.279529 | ||||||||
\(22\) | −108.484 | + | 108.484i | −0.224140 | + | 0.224140i | ||||
\(23\) | 621.267 | + | 621.267i | 1.17442 | + | 1.17442i | 0.981145 | + | 0.193272i | \(0.0619101\pi\) |
0.193272 | + | 0.981145i | \(0.438090\pi\) | |||||||
\(24\) | 127.001i | 0.220488i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 132.681 | 0.196274 | ||||||||
\(27\) | −99.2043 | + | 99.2043i | −0.136083 | + | 0.136083i | ||||
\(28\) | −258.236 | − | 258.236i | −0.329383 | − | 0.329383i | ||||
\(29\) | − | 792.756i | − | 0.942635i | −0.881964 | − | 0.471318i | \(-0.843779\pi\) | ||
0.881964 | − | 0.471318i | \(-0.156221\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 208.426 | 0.216884 | 0.108442 | − | 0.994103i | \(-0.465414\pi\) | ||||
0.108442 | + | 0.994103i | \(0.465414\pi\) | |||||||
\(32\) | −401.639 | + | 401.639i | −0.392225 | + | 0.392225i | ||||
\(33\) | −724.045 | − | 724.045i | −0.664872 | − | 0.664872i | ||||
\(34\) | − | 167.850i | − | 0.145199i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −415.635 | −0.320706 | ||||||||
\(37\) | 460.132 | − | 460.132i | 0.336108 | − | 0.336108i | −0.518792 | − | 0.854900i | \(-0.673618\pi\) |
0.854900 | + | 0.518792i | \(0.173618\pi\) | |||||||
\(38\) | 230.246 | + | 230.246i | 0.159450 | + | 0.159450i | ||||
\(39\) | 885.545i | 0.582212i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2436.15 | 1.44923 | 0.724613 | − | 0.689156i | \(-0.242018\pi\) | ||||
0.724613 | + | 0.689156i | \(0.242018\pi\) | |||||||
\(42\) | −67.8627 | + | 67.8627i | −0.0384709 | + | 0.0384709i | ||||
\(43\) | −2114.72 | − | 2114.72i | −1.14371 | − | 1.14371i | −0.987766 | − | 0.155946i | \(-0.950157\pi\) |
−0.155946 | − | 0.987766i | \(-0.549843\pi\) | |||||||
\(44\) | − | 3033.52i | − | 1.56690i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 684.028 | 0.323264 | ||||||||
\(47\) | 2910.44 | − | 2910.44i | 1.31754 | − | 1.31754i | 0.401815 | − | 0.915721i | \(-0.368380\pi\) |
0.915721 | − | 0.401815i | \(-0.131620\pi\) | |||||||
\(48\) | −835.056 | − | 835.056i | −0.362438 | − | 0.362438i | ||||
\(49\) | 1838.18i | 0.765590i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1120.27 | 0.430708 | ||||||||
\(52\) | −1855.08 | + | 1855.08i | −0.686049 | + | 0.686049i | ||||
\(53\) | 1289.93 | + | 1289.93i | 0.459212 | + | 0.459212i | 0.898397 | − | 0.439185i | \(-0.144733\pi\) |
−0.439185 | + | 0.898397i | \(0.644733\pi\) | |||||||
\(54\) | 109.226i | 0.0374575i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −579.842 | −0.184899 | ||||||||
\(57\) | −1536.72 | + | 1536.72i | −0.472982 | + | 0.472982i | ||||
\(58\) | −436.420 | − | 436.420i | −0.129733 | − | 0.129733i | ||||
\(59\) | − | 1953.99i | − | 0.561331i | −0.959806 | − | 0.280665i | \(-0.909445\pi\) | ||
0.959806 | − | 0.280665i | \(-0.0905551\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1227.13 | 0.329784 | 0.164892 | − | 0.986312i | \(-0.447272\pi\) | ||||
0.164892 | + | 0.986312i | \(0.447272\pi\) | |||||||
\(62\) | 114.740 | − | 114.740i | 0.0298492 | − | 0.0298492i | ||||
\(63\) | −452.932 | − | 452.932i | −0.114117 | − | 0.114117i | ||||
\(64\) | − | 3194.16i | − | 0.779825i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −797.189 | −0.183009 | ||||||||
\(67\) | −1165.88 | + | 1165.88i | −0.259718 | + | 0.259718i | −0.824939 | − | 0.565221i | \(-0.808791\pi\) |
0.565221 | + | 0.824939i | \(0.308791\pi\) | |||||||
\(68\) | 2346.79 | + | 2346.79i | 0.507524 | + | 0.507524i | ||||
\(69\) | 4565.36i | 0.958908i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3109.97 | −0.616936 | −0.308468 | − | 0.951235i | \(-0.599816\pi\) | ||||
−0.308468 | + | 0.951235i | \(0.599816\pi\) | |||||||
\(72\) | −466.632 | + | 466.632i | −0.0900138 | + | 0.0900138i | ||||
\(73\) | 3457.41 | + | 3457.41i | 0.648791 | + | 0.648791i | 0.952701 | − | 0.303910i | \(-0.0982922\pi\) |
−0.303910 | + | 0.952701i | \(0.598292\pi\) | |||||||
\(74\) | − | 506.614i | − | 0.0925154i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6438.36 | −1.11468 | ||||||||
\(77\) | 3305.74 | − | 3305.74i | 0.557554 | − | 0.557554i | ||||
\(78\) | 487.502 | + | 487.502i | 0.0801285 | + | 0.0801285i | ||||
\(79\) | 9879.38i | 1.58298i | 0.611182 | + | 0.791490i | \(0.290694\pi\) | ||||
−0.611182 | + | 0.791490i | \(0.709306\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −729.000 | −0.111111 | ||||||||
\(82\) | 1341.13 | − | 1341.13i | 0.199454 | − | 0.199454i | ||||
\(83\) | 3296.81 | + | 3296.81i | 0.478562 | + | 0.478562i | 0.904671 | − | 0.426110i | \(-0.140116\pi\) |
−0.426110 | + | 0.904671i | \(0.640116\pi\) | |||||||
\(84\) | − | 1897.64i | − | 0.268940i | ||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2328.35 | −0.314813 | ||||||||
\(87\) | 2912.77 | − | 2912.77i | 0.384829 | − | 0.384829i | ||||
\(88\) | −3405.72 | − | 3405.72i | −0.439789 | − | 0.439789i | ||||
\(89\) | 6138.84i | 0.775008i | 0.921868 | + | 0.387504i | \(0.126663\pi\) | ||||
−0.921868 | + | 0.387504i | \(0.873337\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4043.08 | −0.488236 | ||||||||
\(92\) | −9563.71 | + | 9563.71i | −1.12993 | + | 1.12993i | ||||
\(93\) | 765.804 | + | 765.804i | 0.0885425 | + | 0.0885425i | ||||
\(94\) | − | 3204.45i | − | 0.362658i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2951.43 | −0.320251 | ||||||||
\(97\) | −728.123 | + | 728.123i | −0.0773858 | + | 0.0773858i | −0.744740 | − | 0.667354i | \(-0.767427\pi\) |
0.667354 | + | 0.744740i | \(0.267427\pi\) | |||||||
\(98\) | 1011.94 | + | 1011.94i | 0.105366 | + | 0.105366i | ||||
\(99\) | − | 5320.63i | − | 0.542866i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3284.75 | 0.322002 | 0.161001 | − | 0.986954i | \(-0.448528\pi\) | ||||
0.161001 | + | 0.986954i | \(0.448528\pi\) | |||||||
\(102\) | 616.720 | − | 616.720i | 0.0592772 | − | 0.0592772i | ||||
\(103\) | 6786.93 | + | 6786.93i | 0.639733 | + | 0.639733i | 0.950490 | − | 0.310756i | \(-0.100582\pi\) |
−0.310756 | + | 0.950490i | \(0.600582\pi\) | |||||||
\(104\) | 4165.37i | 0.385112i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1420.24 | 0.126401 | ||||||||
\(107\) | −1447.22 | + | 1447.22i | −0.126406 | + | 0.126406i | −0.767480 | − | 0.641073i | \(-0.778489\pi\) |
0.641073 | + | 0.767480i | \(0.278489\pi\) | |||||||
\(108\) | −1527.14 | − | 1527.14i | −0.130928 | − | 0.130928i | ||||
\(109\) | − | 13927.0i | − | 1.17221i | −0.810234 | − | 0.586106i | \(-0.800660\pi\) | ||
0.810234 | − | 0.586106i | \(-0.199340\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3381.26 | 0.274431 | ||||||||
\(112\) | 3812.57 | − | 3812.57i | 0.303936 | − | 0.303936i | ||||
\(113\) | −17279.9 | − | 17279.9i | −1.35327 | − | 1.35327i | −0.881980 | − | 0.471287i | \(-0.843790\pi\) |
−0.471287 | − | 0.881980i | \(-0.656210\pi\) | |||||||
\(114\) | 1691.96i | 0.130191i | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 12203.6 | 0.906926 | ||||||||
\(117\) | −3253.70 | + | 3253.70i | −0.237687 | + | 0.237687i | ||||
\(118\) | −1075.69 | − | 1075.69i | −0.0772546 | − | 0.0772546i | ||||
\(119\) | 5114.76i | 0.361186i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 24191.7 | 1.65233 | ||||||||
\(122\) | 675.546 | − | 675.546i | 0.0453874 | − | 0.0453874i | ||||
\(123\) | 8950.99 | + | 8950.99i | 0.591644 | + | 0.591644i | ||||
\(124\) | 3208.48i | 0.208668i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −498.687 | −0.0314114 | ||||||||
\(127\) | 9885.00 | − | 9885.00i | 0.612871 | − | 0.612871i | −0.330822 | − | 0.943693i | \(-0.607326\pi\) |
0.943693 | + | 0.330822i | \(0.107326\pi\) | |||||||
\(128\) | −8184.64 | − | 8184.64i | −0.499551 | − | 0.499551i | ||||
\(129\) | − | 15540.0i | − | 0.933837i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18900.4 | −1.10136 | −0.550680 | − | 0.834716i | \(-0.685632\pi\) | ||||
−0.550680 | + | 0.834716i | \(0.685632\pi\) | |||||||
\(132\) | 11145.9 | − | 11145.9i | 0.639685 | − | 0.639685i | ||||
\(133\) | −7016.11 | − | 7016.11i | −0.396637 | − | 0.396637i | ||||
\(134\) | 1283.65i | 0.0714888i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5269.46 | 0.284897 | ||||||||
\(137\) | 1922.12 | − | 1922.12i | 0.102409 | − | 0.102409i | −0.654046 | − | 0.756455i | \(-0.726930\pi\) |
0.756455 | + | 0.654046i | \(0.226930\pi\) | |||||||
\(138\) | 2513.28 | + | 2513.28i | 0.131972 | + | 0.131972i | ||||
\(139\) | − | 12035.8i | − | 0.622939i | −0.950256 | − | 0.311470i | \(-0.899179\pi\) | ||
0.950256 | − | 0.311470i | \(-0.100821\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 21387.3 | 1.07576 | ||||||||
\(142\) | −1712.07 | + | 1712.07i | −0.0849074 | + | 0.0849074i | ||||
\(143\) | −23747.2 | − | 23747.2i | −1.16129 | − | 1.16129i | ||||
\(144\) | − | 6136.38i | − | 0.295929i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3806.68 | 0.178583 | ||||||||
\(147\) | −6753.91 | + | 6753.91i | −0.312551 | + | 0.312551i | ||||
\(148\) | 7083.21 | + | 7083.21i | 0.323375 | + | 0.323375i | ||||
\(149\) | − | 2831.35i | − | 0.127533i | −0.997965 | − | 0.0637663i | \(-0.979689\pi\) | ||
0.997965 | − | 0.0637663i | \(-0.0203112\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11509.8 | −0.504794 | −0.252397 | − | 0.967624i | \(-0.581219\pi\) | ||||
−0.252397 | + | 0.967624i | \(0.581219\pi\) | |||||||
\(152\) | −7228.33 | + | 7228.33i | −0.312860 | + | 0.312860i | ||||
\(153\) | 4116.14 | + | 4116.14i | 0.175836 | + | 0.175836i | ||||
\(154\) | − | 3639.68i | − | 0.153469i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −13632.0 | −0.560157 | ||||||||
\(157\) | −16855.1 | + | 16855.1i | −0.683806 | + | 0.683806i | −0.960856 | − | 0.277050i | \(-0.910643\pi\) |
0.277050 | + | 0.960856i | \(0.410643\pi\) | |||||||
\(158\) | 5438.70 | + | 5438.70i | 0.217862 | + | 0.217862i | ||||
\(159\) | 9478.99i | 0.374945i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20843.8 | −0.804129 | ||||||||
\(162\) | −401.322 | + | 401.322i | −0.0152920 | + | 0.0152920i | ||||
\(163\) | 21091.4 | + | 21091.4i | 0.793836 | + | 0.793836i | 0.982116 | − | 0.188279i | \(-0.0602910\pi\) |
−0.188279 | + | 0.982116i | \(0.560291\pi\) | |||||||
\(164\) | 37501.8i | 1.39433i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3629.86 | 0.131727 | ||||||||
\(167\) | −14608.4 | + | 14608.4i | −0.523804 | + | 0.523804i | −0.918718 | − | 0.394914i | \(-0.870774\pi\) |
0.394914 | + | 0.918718i | \(0.370774\pi\) | |||||||
\(168\) | −2130.47 | − | 2130.47i | −0.0754845 | − | 0.0754845i | ||||
\(169\) | 483.065i | 0.0169134i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11292.5 | −0.386188 | ||||||||
\(172\) | 32553.8 | − | 32553.8i | 1.10038 | − | 1.10038i | ||||
\(173\) | 5686.94 | + | 5686.94i | 0.190014 | + | 0.190014i | 0.795702 | − | 0.605688i | \(-0.207102\pi\) |
−0.605688 | + | 0.795702i | \(0.707102\pi\) | |||||||
\(174\) | − | 3207.02i | − | 0.105926i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 44786.6 | 1.44585 | ||||||||
\(177\) | 7179.42 | − | 7179.42i | 0.229162 | − | 0.229162i | ||||
\(178\) | 3379.49 | + | 3379.49i | 0.106662 | + | 0.106662i | ||||
\(179\) | 18806.9i | 0.586965i | 0.955964 | + | 0.293482i | \(0.0948142\pi\) | ||||
−0.955964 | + | 0.293482i | \(0.905186\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −35653.8 | −1.08830 | −0.544150 | − | 0.838988i | \(-0.683148\pi\) | ||||
−0.544150 | + | 0.838988i | \(0.683148\pi\) | |||||||
\(182\) | −2225.76 | + | 2225.76i | −0.0671948 | + | 0.0671948i | ||||
\(183\) | 4508.75 | + | 4508.75i | 0.134634 | + | 0.134634i | ||||
\(184\) | 21474.3i | 0.634283i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 843.166 | 0.0243718 | ||||||||
\(187\) | −30041.7 | + | 30041.7i | −0.859096 | + | 0.859096i | ||||
\(188\) | 44802.9 | + | 44802.9i | 1.26762 | + | 1.26762i | ||||
\(189\) | − | 3328.36i | − | 0.0931765i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −58397.3 | −1.60076 | −0.800380 | − | 0.599493i | \(-0.795369\pi\) | ||||
−0.800380 | + | 0.599493i | \(0.795369\pi\) | |||||||
\(192\) | 11736.1 | − | 11736.1i | 0.318362 | − | 0.318362i | ||||
\(193\) | −12679.5 | − | 12679.5i | −0.340398 | − | 0.340398i | 0.516119 | − | 0.856517i | \(-0.327376\pi\) |
−0.856517 | + | 0.516119i | \(0.827376\pi\) | |||||||
\(194\) | 801.679i | 0.0213008i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −28296.7 | −0.736587 | ||||||||
\(197\) | 20420.8 | − | 20420.8i | 0.526187 | − | 0.526187i | −0.393246 | − | 0.919433i | \(-0.628648\pi\) |
0.919433 | + | 0.393246i | \(0.128648\pi\) | |||||||
\(198\) | −2929.06 | − | 2929.06i | −0.0747133 | − | 0.0747133i | ||||
\(199\) | − | 1036.13i | − | 0.0261643i | −0.999914 | − | 0.0130821i | \(-0.995836\pi\) | ||
0.999914 | − | 0.0130821i | \(-0.00416429\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8567.40 | −0.212059 | ||||||||
\(202\) | 1808.29 | − | 1808.29i | 0.0443164 | − | 0.0443164i | ||||
\(203\) | 13298.7 | + | 13298.7i | 0.322713 | + | 0.322713i | ||||
\(204\) | 17245.3i | 0.414391i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7472.55 | 0.176090 | ||||||||
\(207\) | −16774.2 | + | 16774.2i | −0.391472 | + | 0.391472i | ||||
\(208\) | −27388.1 | − | 27388.1i | −0.633047 | − | 0.633047i | ||||
\(209\) | − | 82418.8i | − | 1.88683i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22118.0 | 0.496800 | 0.248400 | − | 0.968658i | \(-0.420095\pi\) | ||||
0.248400 | + | 0.968658i | \(0.420095\pi\) | |||||||
\(212\) | −19857.0 | + | 19857.0i | −0.441816 | + | 0.441816i | ||||
\(213\) | −11426.8 | − | 11426.8i | −0.251863 | − | 0.251863i | ||||
\(214\) | 1593.42i | 0.0347940i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3429.03 | −0.0734960 | ||||||||
\(217\) | −3496.39 | + | 3496.39i | −0.0742507 | + | 0.0742507i | ||||
\(218\) | −7666.98 | − | 7666.98i | −0.161329 | − | 0.161329i | ||||
\(219\) | 25406.7i | 0.529736i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 36742.6 | 0.752290 | ||||||||
\(222\) | 1861.42 | − | 1861.42i | 0.0377693 | − | 0.0377693i | ||||
\(223\) | 30120.3 | + | 30120.3i | 0.605688 | + | 0.605688i | 0.941816 | − | 0.336128i | \(-0.109118\pi\) |
−0.336128 | + | 0.941816i | \(0.609118\pi\) | |||||||
\(224\) | − | 13475.2i | − | 0.268558i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −19025.5 | −0.372494 | ||||||||
\(227\) | 48275.2 | − | 48275.2i | 0.936855 | − | 0.936855i | −0.0612669 | − | 0.998121i | \(-0.519514\pi\) |
0.998121 | + | 0.0612669i | \(0.0195141\pi\) | |||||||
\(228\) | −23656.1 | − | 23656.1i | −0.455064 | − | 0.455064i | ||||
\(229\) | 3292.48i | 0.0627844i | 0.999507 | + | 0.0313922i | \(0.00999409\pi\) | ||||
−0.999507 | + | 0.0313922i | \(0.990006\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 24292.1 | 0.455241 | ||||||||
\(232\) | 13700.9 | − | 13700.9i | 0.254551 | − | 0.254551i | ||||
\(233\) | −14693.1 | − | 14693.1i | −0.270645 | − | 0.270645i | 0.558715 | − | 0.829360i | \(-0.311295\pi\) |
−0.829360 | + | 0.558715i | \(0.811295\pi\) | |||||||
\(234\) | 3582.39i | 0.0654246i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 30079.5 | 0.540066 | ||||||||
\(237\) | −36299.2 | + | 36299.2i | −0.646249 | + | 0.646249i | ||||
\(238\) | 2815.73 | + | 2815.73i | 0.0497092 | + | 0.0497092i | ||||
\(239\) | − | 33152.5i | − | 0.580390i | −0.956968 | − | 0.290195i | \(-0.906280\pi\) | ||
0.956968 | − | 0.290195i | \(-0.0937202\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 110527. | 1.90299 | 0.951493 | − | 0.307671i | \(-0.0995497\pi\) | ||||
0.951493 | + | 0.307671i | \(0.0995497\pi\) | |||||||
\(242\) | 13317.8 | − | 13317.8i | 0.227406 | − | 0.227406i | ||||
\(243\) | −2678.52 | − | 2678.52i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 18890.2i | 0.317291i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9855.22 | 0.162853 | ||||||||
\(247\) | −50401.2 | + | 50401.2i | −0.826128 | + | 0.826128i | ||||
\(248\) | 3602.15 | + | 3602.15i | 0.0585677 | + | 0.0585677i | ||||
\(249\) | 24226.5i | 0.390744i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2118.00 | 0.0336185 | 0.0168093 | − | 0.999859i | \(-0.494649\pi\) | ||||
0.0168093 | + | 0.999859i | \(0.494649\pi\) | |||||||
\(252\) | 6972.38 | − | 6972.38i | 0.109794 | − | 0.109794i | ||||
\(253\) | −122427. | − | 122427.i | −1.91265 | − | 1.91265i | ||||
\(254\) | − | 10883.6i | − | 0.168696i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 42095.2 | 0.642321 | ||||||||
\(257\) | 77692.9 | − | 77692.9i | 1.17629 | − | 1.17629i | 0.195610 | − | 0.980682i | \(-0.437331\pi\) |
0.980682 | − | 0.195610i | \(-0.0626685\pi\) | |||||||
\(258\) | −8554.92 | − | 8554.92i | −0.128522 | − | 0.128522i | ||||
\(259\) | 15437.7i | 0.230134i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 21404.4 | 0.314212 | ||||||||
\(262\) | −10404.9 | + | 10404.9i | −0.151578 | + | 0.151578i | ||||
\(263\) | 55670.1 | + | 55670.1i | 0.804842 | + | 0.804842i | 0.983848 | − | 0.179006i | \(-0.0572880\pi\) |
−0.179006 | + | 0.983848i | \(0.557288\pi\) | |||||||
\(264\) | − | 25026.8i | − | 0.359086i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −7724.88 | −0.109176 | ||||||||
\(267\) | −22555.5 | + | 22555.5i | −0.316396 | + | 0.316396i | ||||
\(268\) | −17947.3 | − | 17947.3i | −0.249880 | − | 0.249880i | ||||
\(269\) | − | 105854.i | − | 1.46286i | −0.681917 | − | 0.731430i | \(-0.738853\pi\) | ||
0.681917 | − | 0.731430i | \(-0.261147\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −98922.9 | −1.34697 | −0.673486 | − | 0.739200i | \(-0.735204\pi\) | ||||
−0.673486 | + | 0.739200i | \(0.735204\pi\) | |||||||
\(272\) | −34647.7 | + | 34647.7i | −0.468314 | + | 0.468314i | ||||
\(273\) | −14855.2 | − | 14855.2i | −0.199322 | − | 0.199322i | ||||
\(274\) | − | 2116.30i | − | 0.0281887i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −70278.6 | −0.922582 | ||||||||
\(277\) | 63861.7 | − | 63861.7i | 0.832302 | − | 0.832302i | −0.155529 | − | 0.987831i | \(-0.549708\pi\) |
0.987831 | + | 0.155529i | \(0.0497083\pi\) | |||||||
\(278\) | −6625.84 | − | 6625.84i | −0.0857336 | − | 0.0857336i | ||||
\(279\) | 5627.49i | 0.0722947i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 32035.4 | 0.405712 | 0.202856 | − | 0.979209i | \(-0.434978\pi\) | ||||
0.202856 | + | 0.979209i | \(0.434978\pi\) | |||||||
\(282\) | 11773.9 | − | 11773.9i | 0.148055 | − | 0.148055i | ||||
\(283\) | 63944.4 | + | 63944.4i | 0.798417 | + | 0.798417i | 0.982846 | − | 0.184429i | \(-0.0590436\pi\) |
−0.184429 | + | 0.982846i | \(0.559044\pi\) | |||||||
\(284\) | − | 47874.6i | − | 0.593565i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −26146.2 | −0.319651 | ||||||||
\(287\) | −40867.0 | + | 40867.0i | −0.496146 | + | 0.496146i | ||||
\(288\) | −10844.2 | − | 10844.2i | −0.130742 | − | 0.130742i | ||||
\(289\) | 37039.3i | 0.443473i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5350.59 | −0.0631853 | ||||||||
\(292\) | −53222.9 | + | 53222.9i | −0.624213 | + | 0.624213i | ||||
\(293\) | −13864.2 | − | 13864.2i | −0.161495 | − | 0.161495i | 0.621734 | − | 0.783229i | \(-0.286429\pi\) |
−0.783229 | + | 0.621734i | \(0.786429\pi\) | |||||||
\(294\) | 7436.19i | 0.0860312i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 15904.6 | 0.181526 | ||||||||
\(297\) | 19549.2 | − | 19549.2i | 0.221624 | − | 0.221624i | ||||
\(298\) | −1558.69 | − | 1558.69i | −0.0175520 | − | 0.0175520i | ||||
\(299\) | 149734.i | 1.67486i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 70950.0 | 0.783104 | ||||||||
\(302\) | −6336.26 | + | 6336.26i | −0.0694735 | + | 0.0694735i | ||||
\(303\) | 12068.9 | + | 12068.9i | 0.131457 | + | 0.131457i | ||||
\(304\) | − | 95055.3i | − | 1.02856i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4531.95 | 0.0483997 | ||||||||
\(307\) | 94399.9 | − | 94399.9i | 1.00160 | − | 1.00160i | 0.00160232 | − | 0.999999i | \(-0.499490\pi\) |
0.999999 | − | 0.00160232i | \(-0.000510033\pi\) | |||||||
\(308\) | 50888.1 | + | 50888.1i | 0.536432 | + | 0.536432i | ||||
\(309\) | 49873.5i | 0.522340i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −88072.6 | −0.910584 | −0.455292 | − | 0.890342i | \(-0.650465\pi\) | ||||
−0.455292 | + | 0.890342i | \(0.650465\pi\) | |||||||
\(312\) | −15304.6 | + | 15304.6i | −0.157221 | + | 0.157221i | ||||
\(313\) | 88635.0 | + | 88635.0i | 0.904725 | + | 0.904725i | 0.995840 | − | 0.0911152i | \(-0.0290431\pi\) |
−0.0911152 | + | 0.995840i | \(0.529043\pi\) | |||||||
\(314\) | 18557.8i | 0.188221i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −152082. | −1.52301 | ||||||||
\(317\) | −40191.1 | + | 40191.1i | −0.399955 | + | 0.399955i | −0.878217 | − | 0.478262i | \(-0.841267\pi\) |
0.478262 | + | 0.878217i | \(0.341267\pi\) | |||||||
\(318\) | 5218.28 | + | 5218.28i | 0.0516028 | + | 0.0516028i | ||||
\(319\) | 156221.i | 1.53517i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10634.9 | −0.103210 | ||||||||
\(322\) | −11474.7 | + | 11474.7i | −0.110670 | + | 0.110670i | ||||
\(323\) | 63760.8 | + | 63760.8i | 0.611151 | + | 0.611151i | ||||
\(324\) | − | 11222.1i | − | 0.106902i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 23222.1 | 0.218508 | ||||||||
\(327\) | 51171.2 | − | 51171.2i | 0.478553 | − | 0.478553i | ||||
\(328\) | 42103.1 | + | 42103.1i | 0.391351 | + | 0.391351i | ||||
\(329\) | 97646.6i | 0.902122i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3414.71 | 0.0311672 | 0.0155836 | − | 0.999879i | \(-0.495039\pi\) | ||||
0.0155836 | + | 0.999879i | \(0.495039\pi\) | |||||||
\(332\) | −50750.7 | + | 50750.7i | −0.460432 | + | 0.460432i | ||||
\(333\) | 12423.6 | + | 12423.6i | 0.112036 | + | 0.112036i | ||||
\(334\) | 16084.1i | 0.144180i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 28016.6 | 0.248163 | ||||||||
\(337\) | −123560. | + | 123560.i | −1.08797 | + | 1.08797i | −0.0922321 | + | 0.995738i | \(0.529400\pi\) |
−0.995738 | + | 0.0922321i | \(0.970600\pi\) | |||||||
\(338\) | 265.932 | + | 265.932i | 0.00232776 | + | 0.00232776i | ||||
\(339\) | − | 126981.i | − | 1.10494i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −41072.4 | −0.353217 | ||||||||
\(342\) | −6216.65 | + | 6216.65i | −0.0531501 | + | 0.0531501i | ||||
\(343\) | −71113.4 | − | 71113.4i | −0.604454 | − | 0.604454i | ||||
\(344\) | − | 73096.0i | − | 0.617699i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6261.44 | 0.0523025 | ||||||||
\(347\) | 28249.8 | − | 28249.8i | 0.234615 | − | 0.234615i | −0.580001 | − | 0.814616i | \(-0.696948\pi\) |
0.814616 | + | 0.580001i | \(0.196948\pi\) | |||||||
\(348\) | 44838.9 | + | 44838.9i | 0.370251 | + | 0.370251i | ||||
\(349\) | − | 105370.i | − | 0.865102i | −0.901610 | − | 0.432551i | \(-0.857614\pi\) | ||
0.901610 | − | 0.432551i | \(-0.142386\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −23909.7 | −0.194071 | ||||||||
\(352\) | 79147.0 | − | 79147.0i | 0.638777 | − | 0.638777i | ||||
\(353\) | −121429. | − | 121429.i | −0.974482 | − | 0.974482i | 0.0252004 | − | 0.999682i | \(-0.491978\pi\) |
−0.999682 | + | 0.0252004i | \(0.991978\pi\) | |||||||
\(354\) | − | 7904.69i | − | 0.0630781i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −94500.5 | −0.745649 | ||||||||
\(357\) | −18792.8 | + | 18792.8i | −0.147454 | + | 0.147454i | ||||
\(358\) | 10353.4 | + | 10353.4i | 0.0807825 | + | 0.0807825i | ||||
\(359\) | 200543.i | 1.55603i | 0.628245 | + | 0.778016i | \(0.283774\pi\) | ||||
−0.628245 | + | 0.778016i | \(0.716226\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −44605.2 | −0.342272 | ||||||||
\(362\) | −19627.8 | + | 19627.8i | −0.149780 | + | 0.149780i | ||||
\(363\) | 88886.1 | + | 88886.1i | 0.674560 | + | 0.674560i | ||||
\(364\) | − | 62238.7i | − | 0.469741i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4964.23 | 0.0370586 | ||||||||
\(367\) | −23362.1 | + | 23362.1i | −0.173452 | + | 0.173452i | −0.788494 | − | 0.615042i | \(-0.789139\pi\) |
0.615042 | + | 0.788494i | \(0.289139\pi\) | |||||||
\(368\) | −141197. | − | 141197.i | −1.04263 | − | 1.04263i | ||||
\(369\) | 65776.0i | 0.483076i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −43277.7 | −0.314425 | ||||||||
\(372\) | −11788.7 | + | 11788.7i | −0.0851883 | + | 0.0851883i | ||||
\(373\) | 83015.4 | + | 83015.4i | 0.596680 | + | 0.596680i | 0.939427 | − | 0.342748i | \(-0.111358\pi\) |
−0.342748 | + | 0.939427i | \(0.611358\pi\) | |||||||
\(374\) | 33076.6i | 0.236471i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 100600. | 0.711578 | ||||||||
\(377\) | 95533.0 | − | 95533.0i | 0.672157 | − | 0.672157i | ||||
\(378\) | −1832.29 | − | 1832.29i | −0.0128236 | − | 0.0128236i | ||||
\(379\) | − | 158522.i | − | 1.10360i | −0.833977 | − | 0.551800i | \(-0.813941\pi\) | ||
0.833977 | − | 0.551800i | \(-0.186059\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 72639.6 | 0.500407 | ||||||||
\(382\) | −32148.3 | + | 32148.3i | −0.220309 | + | 0.220309i | ||||
\(383\) | −166677. | − | 166677.i | −1.13626 | − | 1.13626i | −0.989114 | − | 0.147148i | \(-0.952991\pi\) |
−0.147148 | − | 0.989114i | \(-0.547009\pi\) | |||||||
\(384\) | − | 60144.6i | − | 0.407882i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13960.4 | −0.0936963 | ||||||||
\(387\) | 57097.5 | − | 57097.5i | 0.381237 | − | 0.381237i | ||||
\(388\) | −11208.6 | − | 11208.6i | −0.0744542 | − | 0.0744542i | ||||
\(389\) | 8918.27i | 0.0589361i | 0.999566 | + | 0.0294680i | \(0.00938133\pi\) | ||||
−0.999566 | + | 0.0294680i | \(0.990619\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 189424. | 1.23903 | ||||||||
\(392\) | −31768.7 | + | 31768.7i | −0.206741 | + | 0.206741i | ||||
\(393\) | −69444.7 | − | 69444.7i | −0.449629 | − | 0.449629i | ||||
\(394\) | − | 22483.7i | − | 0.144836i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 81905.1 | 0.522300 | ||||||||
\(397\) | 219532. | − | 219532.i | 1.39289 | − | 1.39289i | 0.574115 | − | 0.818775i | \(-0.305346\pi\) |
0.818775 | − | 0.574115i | \(-0.194654\pi\) | |||||||
\(398\) | −570.401 | − | 570.401i | −0.00360092 | − | 0.00360092i | ||||
\(399\) | − | 51557.7i | − | 0.323853i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 278202. | 1.73010 | 0.865050 | − | 0.501686i | \(-0.167287\pi\) | ||||
0.865050 | + | 0.501686i | \(0.167287\pi\) | |||||||
\(402\) | −4716.44 | + | 4716.44i | −0.0291852 | + | 0.0291852i | ||||
\(403\) | 25116.8 | + | 25116.8i | 0.154652 | + | 0.154652i | ||||
\(404\) | 50565.0i | 0.309804i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 14642.1 | 0.0888284 | ||||||||
\(407\) | −90673.6 | + | 90673.6i | −0.547384 | + | 0.547384i | ||||
\(408\) | 19361.2 | + | 19361.2i | 0.116309 | + | 0.116309i | ||||
\(409\) | − | 31311.9i | − | 0.187182i | −0.995611 | − | 0.0935908i | \(-0.970165\pi\) | ||
0.995611 | − | 0.0935908i | \(-0.0298346\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14124.7 | 0.0836169 | ||||||||
\(412\) | −104477. | + | 104477.i | −0.615498 | + | 0.615498i | ||||
\(413\) | 32778.7 | + | 32778.7i | 0.192173 | + | 0.192173i | ||||
\(414\) | 18468.7i | 0.107755i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −96800.9 | −0.559362 | ||||||||
\(417\) | 44222.4 | − | 44222.4i | 0.254314 | − | 0.254314i | ||||
\(418\) | −45372.4 | − | 45372.4i | −0.259680 | − | 0.259680i | ||||
\(419\) | − | 83155.1i | − | 0.473653i | −0.971552 | − | 0.236827i | \(-0.923893\pi\) | ||
0.971552 | − | 0.236827i | \(-0.0761074\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4396.02 | 0.0248025 | 0.0124012 | − | 0.999923i | \(-0.496052\pi\) | ||||
0.0124012 | + | 0.999923i | \(0.496052\pi\) | |||||||
\(422\) | 12176.2 | − | 12176.2i | 0.0683734 | − | 0.0683734i | ||||
\(423\) | 78581.8 | + | 78581.8i | 0.439179 | + | 0.439179i | ||||
\(424\) | 44586.7i | 0.248013i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −12581.1 | −0.0693266 | ||||||||
\(427\) | −20585.4 | + | 20585.4i | −0.112902 | + | 0.112902i | ||||
\(428\) | −22278.4 | − | 22278.4i | −0.121618 | − | 0.121618i | ||||
\(429\) | − | 174506.i | − | 0.948189i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 97154.1 | 0.523006 | 0.261503 | − | 0.965203i | \(-0.415782\pi\) | ||||
0.261503 | + | 0.965203i | \(0.415782\pi\) | |||||||
\(432\) | 22546.5 | − | 22546.5i | 0.120813 | − | 0.120813i | ||||
\(433\) | −152799. | − | 152799.i | −0.814978 | − | 0.814978i | 0.170397 | − | 0.985375i | \(-0.445495\pi\) |
−0.985375 | + | 0.170397i | \(0.945495\pi\) | |||||||
\(434\) | 3849.60i | 0.0204379i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 214391. | 1.12781 | ||||||||
\(437\) | −259840. | + | 259840.i | −1.36064 | + | 1.36064i | ||||
\(438\) | 13986.6 | + | 13986.6i | 0.0729062 | + | 0.0729062i | ||||
\(439\) | − | 30829.0i | − | 0.159967i | −0.996796 | − | 0.0799836i | \(-0.974513\pi\) | ||
0.996796 | − | 0.0799836i | \(-0.0254868\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −49630.9 | −0.255197 | ||||||||
\(442\) | 20227.2 | − | 20227.2i | 0.103536 | − | 0.103536i | ||||
\(443\) | −126571. | − | 126571.i | −0.644952 | − | 0.644952i | 0.306817 | − | 0.951769i | \(-0.400736\pi\) |
−0.951769 | + | 0.306817i | \(0.900736\pi\) | |||||||
\(444\) | 52050.7i | 0.264035i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 33163.0 | 0.166719 | ||||||||
\(447\) | 10403.0 | − | 10403.0i | 0.0520650 | − | 0.0520650i | ||||
\(448\) | 53582.9 | + | 53582.9i | 0.266975 | + | 0.266975i | ||||
\(449\) | − | 135018.i | − | 0.669728i | −0.942266 | − | 0.334864i | \(-0.891310\pi\) | ||
0.942266 | − | 0.334864i | \(-0.108690\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −480068. | −2.36021 | ||||||||
\(452\) | 266004. | − | 266004.i | 1.30200 | − | 1.30200i | ||||
\(453\) | −42289.7 | − | 42289.7i | −0.206081 | − | 0.206081i | ||||
\(454\) | − | 53152.0i | − | 0.257874i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −53117.1 | −0.255449 | ||||||||
\(457\) | −6037.20 | + | 6037.20i | −0.0289070 | + | 0.0289070i | −0.721413 | − | 0.692506i | \(-0.756507\pi\) |
0.692506 | + | 0.721413i | \(0.256507\pi\) | |||||||
\(458\) | 1812.54 | + | 1812.54i | 0.00864087 | + | 0.00864087i | ||||
\(459\) | 30247.3i | 0.143569i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 35960.5 | 0.169209 | 0.0846046 | − | 0.996415i | \(-0.473037\pi\) | ||||
0.0846046 | + | 0.996415i | \(0.473037\pi\) | |||||||
\(462\) | 13373.0 | − | 13373.0i | 0.0626537 | − | 0.0626537i | ||||
\(463\) | 155969. | + | 155969.i | 0.727571 | + | 0.727571i | 0.970135 | − | 0.242565i | \(-0.0779886\pi\) |
−0.242565 | + | 0.970135i | \(0.577989\pi\) | |||||||
\(464\) | 180172.i | 0.836859i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16177.4 | −0.0744965 | ||||||||
\(467\) | −162294. | + | 162294.i | −0.744164 | + | 0.744164i | −0.973376 | − | 0.229212i | \(-0.926385\pi\) |
0.229212 | + | 0.973376i | \(0.426385\pi\) | |||||||
\(468\) | −50087.1 | − | 50087.1i | −0.228683 | − | 0.228683i | ||||
\(469\) | − | 39115.7i | − | 0.177830i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −123859. | −0.558325 | ||||||||
\(472\) | 33770.2 | − | 33770.2i | 0.151583 | − | 0.151583i | ||||
\(473\) | 416728. | + | 416728.i | 1.86265 | + | 1.86265i | ||||
\(474\) | 39966.1i | 0.177883i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −78736.0 | −0.347504 | ||||||||
\(477\) | −34828.0 | + | 34828.0i | −0.153071 | + | 0.153071i | ||||
\(478\) | −18250.8 | − | 18250.8i | −0.0798776 | − | 0.0798776i | ||||
\(479\) | 148721.i | 0.648190i | 0.946025 | + | 0.324095i | \(0.105060\pi\) | ||||
−0.946025 | + | 0.324095i | \(0.894940\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 110899. | 0.479331 | ||||||||
\(482\) | 60846.4 | − | 60846.4i | 0.261903 | − | 0.261903i | ||||
\(483\) | −76585.1 | − | 76585.1i | −0.328284 | − | 0.328284i | ||||
\(484\) | 372404.i | 1.58973i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2949.10 | −0.0124858 | ||||||||
\(487\) | 194156. | − | 194156.i | 0.818639 | − | 0.818639i | −0.167272 | − | 0.985911i | \(-0.553496\pi\) |
0.985911 | + | 0.167272i | \(0.0534957\pi\) | |||||||
\(488\) | 21208.0 | + | 21208.0i | 0.0890554 | + | 0.0890554i | ||||
\(489\) | 154990.i | 0.648165i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −209053. | −0.867148 | −0.433574 | − | 0.901118i | \(-0.642748\pi\) | ||||
−0.433574 | + | 0.901118i | \(0.642748\pi\) | |||||||
\(492\) | −137790. | + | 137790.i | −0.569231 | + | 0.569231i | ||||
\(493\) | −120855. | − | 120855.i | −0.497246 | − | 0.497246i | ||||
\(494\) | 55492.8i | 0.227396i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −47369.6 | −0.192547 | ||||||||
\(497\) | 52170.6 | − | 52170.6i | 0.211209 | − | 0.211209i | ||||
\(498\) | 13336.9 | + | 13336.9i | 0.0537771 | + | 0.0537771i | ||||
\(499\) | 71012.3i | 0.285189i | 0.989781 | + | 0.142594i | \(0.0455445\pi\) | ||||
−0.989781 | + | 0.142594i | \(0.954456\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −107349. | −0.427684 | ||||||||
\(502\) | 1165.98 | − | 1165.98i | 0.00462683 | − | 0.00462683i | ||||
\(503\) | 31136.6 | + | 31136.6i | 0.123065 | + | 0.123065i | 0.765957 | − | 0.642892i | \(-0.222266\pi\) |
−0.642892 | + | 0.765957i | \(0.722266\pi\) | |||||||
\(504\) | − | 15655.7i | − | 0.0616328i | ||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −134795. | −0.526467 | ||||||||
\(507\) | −1774.89 | + | 1774.89i | −0.00690489 | + | 0.00690489i | ||||
\(508\) | 152169. | + | 152169.i | 0.589654 | + | 0.589654i | ||||
\(509\) | − | 223266.i | − | 0.861763i | −0.902409 | − | 0.430881i | \(-0.858203\pi\) | ||
0.902409 | − | 0.430881i | \(-0.141797\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −115998. | −0.444230 | ||||||||
\(512\) | 154128. | − | 154128.i | 0.587952 | − | 0.587952i | ||||
\(513\) | −41491.4 | − | 41491.4i | −0.157661 | − | 0.157661i | ||||
\(514\) | − | 85541.4i | − | 0.323780i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 239221. | 0.898461 | ||||||||
\(517\) | −573531. | + | 573531.i | −2.14573 | + | 2.14573i | ||||
\(518\) | 8498.59 | + | 8498.59i | 0.0316728 | + | 0.0316728i | ||||
\(519\) | 41790.3i | 0.155146i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −88774.7 | −0.327050 | −0.163525 | − | 0.986539i | \(-0.552286\pi\) | ||||
−0.163525 | + | 0.986539i | \(0.552286\pi\) | |||||||
\(522\) | 11783.3 | − | 11783.3i | 0.0432442 | − | 0.0432442i | ||||
\(523\) | 64718.9 | + | 64718.9i | 0.236607 | + | 0.236607i | 0.815444 | − | 0.578837i | \(-0.196493\pi\) |
−0.578837 | + | 0.815444i | \(0.696493\pi\) | |||||||
\(524\) | − | 290951.i | − | 1.05964i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 61294.0 | 0.221537 | ||||||||
\(527\) | 31774.4 | − | 31774.4i | 0.114408 | − | 0.114408i | ||||
\(528\) | 164556. | + | 164556.i | 0.590265 | + | 0.590265i | ||||
\(529\) | 492104.i | 1.75851i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 52757.8 | 0.187110 | ||||||||
\(532\) | 108005. | − | 108005.i | 0.381611 | − | 0.381611i | ||||
\(533\) | 293574. | + | 293574.i | 1.03339 | + | 1.03339i | ||||
\(534\) | 24834.1i | 0.0870895i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −40298.9 | −0.140269 | ||||||||
\(537\) | −69101.1 | + | 69101.1i | −0.239627 | + | 0.239627i | ||||
\(538\) | −58273.7 | − | 58273.7i | −0.201330 | − | 0.201330i | ||||
\(539\) | − | 362232.i | − | 1.24684i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −376988. | −1.28805 | −0.644026 | − | 0.765004i | \(-0.722737\pi\) | ||||
−0.644026 | + | 0.765004i | \(0.722737\pi\) | |||||||
\(542\) | −54458.1 | + | 54458.1i | −0.185380 | + | 0.185380i | ||||
\(543\) | −131000. | − | 131000.i | −0.444296 | − | 0.444296i | ||||
\(544\) | 122459.i | 0.413803i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −16355.9 | −0.0548643 | ||||||||
\(547\) | −103549. | + | 103549.i | −0.346075 | + | 0.346075i | −0.858645 | − | 0.512570i | \(-0.828693\pi\) |
0.512570 | + | 0.858645i | \(0.328693\pi\) | |||||||
\(548\) | 29588.9 | + | 29588.9i | 0.0985299 | + | 0.0985299i | ||||
\(549\) | 33132.4i | 0.109928i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 331564. | 1.09210 | ||||||||
\(552\) | −78901.5 | + | 78901.5i | −0.258945 | + | 0.258945i | ||||
\(553\) | −165729. | − | 165729.i | −0.541937 | − | 0.541937i | ||||
\(554\) | − | 70313.0i | − | 0.229095i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 185278. | 0.599341 | ||||||||
\(557\) | 171898. | − | 171898.i | 0.554065 | − | 0.554065i | −0.373547 | − | 0.927611i | \(-0.621858\pi\) |
0.927611 | + | 0.373547i | \(0.121858\pi\) | |||||||
\(558\) | 3097.99 | + | 3097.99i | 0.00994974 | + | 0.00994974i | ||||
\(559\) | − | 509680.i | − | 1.63107i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −220761. | −0.701449 | ||||||||
\(562\) | 17635.8 | − | 17635.8i | 0.0558372 | − | 0.0558372i | ||||
\(563\) | −129088. | − | 129088.i | −0.407258 | − | 0.407258i | 0.473523 | − | 0.880781i | \(-0.342982\pi\) |
−0.880781 | + | 0.473523i | \(0.842982\pi\) | |||||||
\(564\) | 329233.i | 1.03501i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 70404.1 | 0.219768 | ||||||||
\(567\) | 12229.2 | − | 12229.2i | 0.0380391 | − | 0.0380391i | ||||
\(568\) | −53748.6 | − | 53748.6i | −0.166598 | − | 0.166598i | ||||
\(569\) | − | 259535.i | − | 0.801624i | −0.916160 | − | 0.400812i | \(-0.868728\pi\) | ||
0.916160 | − | 0.400812i | \(-0.131272\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 597642. | 1.83303 | 0.916514 | − | 0.400004i | \(-0.130991\pi\) | ||||
0.916514 | + | 0.400004i | \(0.130991\pi\) | |||||||
\(572\) | 365562. | − | 365562.i | 1.11730 | − | 1.11730i | ||||
\(573\) | −214566. | − | 214566.i | −0.653508 | − | 0.653508i | ||||
\(574\) | 44995.4i | 0.136567i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 86242.4 | 0.259942 | ||||||||
\(577\) | 335792. | − | 335792.i | 1.00860 | − | 1.00860i | 0.00863725 | − | 0.999963i | \(-0.497251\pi\) |
0.999963 | − | 0.00863725i | \(-0.00274936\pi\) | |||||||
\(578\) | 20390.5 | + | 20390.5i | 0.0610341 | + | 0.0610341i | ||||
\(579\) | − | 93174.8i | − | 0.277934i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −110610. | −0.327673 | ||||||||
\(582\) | −2945.56 | + | 2945.56i | −0.00869603 | + | 0.00869603i | ||||
\(583\) | −254193. | − | 254193.i | −0.747872 | − | 0.747872i | ||||
\(584\) | 119506.i | 0.350401i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15264.8 | −0.0444523 | ||||||||
\(587\) | −189572. | + | 189572.i | −0.550171 | + | 0.550171i | −0.926490 | − | 0.376319i | \(-0.877190\pi\) |
0.376319 | + | 0.926490i | \(0.377190\pi\) | |||||||
\(588\) | −103969. | − | 103969.i | −0.300711 | − | 0.300711i | ||||
\(589\) | 87172.3i | 0.251274i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 150061. | 0.429630 | ||||||||
\(592\) | −104576. | + | 104576.i | −0.298392 | + | 0.298392i | ||||
\(593\) | 152696. | + | 152696.i | 0.434228 | + | 0.434228i | 0.890064 | − | 0.455836i | \(-0.150660\pi\) |
−0.455836 | + | 0.890064i | \(0.650660\pi\) | |||||||
\(594\) | − | 21524.1i | − | 0.0610031i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 43585.5 | 0.122701 | ||||||||
\(597\) | 3806.99 | − | 3806.99i | 0.0106815 | − | 0.0106815i | ||||
\(598\) | 82430.4 | + | 82430.4i | 0.230507 | + | 0.230507i | ||||
\(599\) | 232126.i | 0.646949i | 0.946237 | + | 0.323474i | \(0.104851\pi\) | ||||
−0.946237 | + | 0.323474i | \(0.895149\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −277987. | −0.769618 | −0.384809 | − | 0.922996i | \(-0.625733\pi\) | ||||
−0.384809 | + | 0.922996i | \(0.625733\pi\) | |||||||
\(602\) | 39058.7 | − | 39058.7i | 0.107777 | − | 0.107777i | ||||
\(603\) | −31478.6 | − | 31478.6i | −0.0865728 | − | 0.0865728i | ||||
\(604\) | − | 177180.i | − | 0.485671i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 13288.1 | 0.0361842 | ||||||||
\(607\) | 83749.1 | − | 83749.1i | 0.227302 | − | 0.227302i | −0.584263 | − | 0.811565i | \(-0.698616\pi\) |
0.811565 | + | 0.584263i | \(0.198616\pi\) | |||||||
\(608\) | −167982. | − | 167982.i | −0.454418 | − | 0.454418i | ||||
\(609\) | 97725.0i | 0.263494i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 701458. | 1.87897 | ||||||||
\(612\) | −63363.3 | + | 63363.3i | −0.169175 | + | 0.169175i | ||||
\(613\) | −167541. | − | 167541.i | −0.445861 | − | 0.445861i | 0.448115 | − | 0.893976i | \(-0.352096\pi\) |
−0.893976 | + | 0.448115i | \(0.852096\pi\) | |||||||
\(614\) | − | 103936.i | − | 0.275696i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 114264. | 0.301125 | ||||||||
\(617\) | 98951.6 | − | 98951.6i | 0.259928 | − | 0.259928i | −0.565097 | − | 0.825025i | \(-0.691161\pi\) |
0.825025 | + | 0.565097i | \(0.191161\pi\) | |||||||
\(618\) | 27455.9 | + | 27455.9i | 0.0718884 | + | 0.0718884i | ||||
\(619\) | − | 390730.i | − | 1.01975i | −0.860247 | − | 0.509877i | \(-0.829691\pi\) | ||
0.860247 | − | 0.509877i | \(-0.170309\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −123265. | −0.319636 | ||||||||
\(622\) | −48484.9 | + | 48484.9i | −0.125321 | + | 0.125321i | ||||
\(623\) | −102981. | − | 102981.i | −0.265326 | − | 0.265326i | ||||
\(624\) | − | 201261.i | − | 0.516881i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 97589.0 | 0.249030 | ||||||||
\(627\) | 302826. | − | 302826.i | 0.770297 | − | 0.770297i | ||||
\(628\) | −259466. | − | 259466.i | −0.657901 | − | 0.657901i | ||||
\(629\) | − | 140294.i | − | 0.354598i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 47450.1 | 0.119173 | 0.0595865 | − | 0.998223i | \(-0.481022\pi\) | ||||
0.0595865 | + | 0.998223i | \(0.481022\pi\) | |||||||
\(632\) | −170742. | + | 170742.i | −0.427470 | + | 0.427470i | ||||
\(633\) | 81266.8 | + | 81266.8i | 0.202818 | + | 0.202818i | ||||
\(634\) | 44251.2i | 0.110090i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −145918. | −0.360741 | ||||||||
\(637\) | −221514. | + | 221514.i | −0.545913 | + | 0.545913i | ||||
\(638\) | 86001.1 | + | 86001.1i | 0.211282 | + | 0.211282i | ||||
\(639\) | − | 83969.3i | − | 0.205645i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 461671. | 1.12361 | 0.561807 | − | 0.827269i | \(-0.310106\pi\) | ||||
0.561807 | + | 0.827269i | \(0.310106\pi\) | |||||||
\(642\) | −5854.61 | + | 5854.61i | −0.0142046 | + | 0.0142046i | ||||
\(643\) | −47437.8 | − | 47437.8i | −0.114737 | − | 0.114737i | 0.647407 | − | 0.762144i | \(-0.275853\pi\) |
−0.762144 | + | 0.647407i | \(0.775853\pi\) | |||||||
\(644\) | − | 320867.i | − | 0.773666i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 70201.9 | 0.168222 | ||||||||
\(647\) | −480099. | + | 480099.i | −1.14689 | + | 1.14689i | −0.159731 | + | 0.987161i | \(0.551063\pi\) |
−0.987161 | + | 0.159731i | \(0.948937\pi\) | |||||||
\(648\) | −12599.1 | − | 12599.1i | −0.0300046 | − | 0.0300046i | ||||
\(649\) | 385054.i | 0.914181i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −25693.1 | −0.0606254 | ||||||||
\(652\) | −324679. | + | 324679.i | −0.763764 | + | 0.763764i | ||||
\(653\) | 259012. | + | 259012.i | 0.607426 | + | 0.607426i | 0.942273 | − | 0.334847i | \(-0.108685\pi\) |
−0.334847 | + | 0.942273i | \(0.608685\pi\) | |||||||
\(654\) | − | 56340.6i | − | 0.131724i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −553672. | −1.28660 | ||||||||
\(657\) | −93350.0 | + | 93350.0i | −0.216264 | + | 0.216264i | ||||
\(658\) | 53755.5 | + | 53755.5i | 0.124157 | + | 0.124157i | ||||
\(659\) | 347700.i | 0.800633i | 0.916377 | + | 0.400316i | \(0.131100\pi\) | ||||
−0.916377 | + | 0.400316i | \(0.868900\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −573427. | −1.31243 | −0.656214 | − | 0.754575i | \(-0.727843\pi\) | ||||
−0.656214 | + | 0.754575i | \(0.727843\pi\) | |||||||
\(662\) | 1879.84 | − | 1879.84i | 0.00428947 | − | 0.00428947i | ||||
\(663\) | 135001. | + | 135001.i | 0.307121 | + | 0.307121i | ||||
\(664\) | 113955.i | 0.258463i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 13678.6 | 0.0308385 | ||||||||
\(667\) | 492513. | − | 492513.i | 1.10705 | − | 1.10705i | ||||
\(668\) | −224879. | − | 224879.i | −0.503961 | − | 0.503961i | ||||
\(669\) | 221338.i | 0.494542i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −241818. | −0.537085 | ||||||||
\(672\) | 49511.0 | − | 49511.0i | 0.109639 | − | 0.109639i | ||||
\(673\) | 430119. | + | 430119.i | 0.949639 | + | 0.949639i | 0.998791 | − | 0.0491520i | \(-0.0156519\pi\) |
−0.0491520 | + | 0.998791i | \(0.515652\pi\) | |||||||
\(674\) | 136042.i | 0.299469i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7436.24 | −0.0162727 | ||||||||
\(677\) | 232285. | − | 232285.i | 0.506809 | − | 0.506809i | −0.406737 | − | 0.913545i | \(-0.633333\pi\) |
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(678\) | −69904.1 | − | 69904.1i | −0.152070 | − | 0.152070i | ||||
\(679\) | − | 24428.9i | − | 0.0529864i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 354749. | 0.764939 | ||||||||
\(682\) | −22610.8 | + | 22610.8i | −0.0486123 | + | 0.0486123i | ||||
\(683\) | −306372. | − | 306372.i | −0.656761 | − | 0.656761i | 0.297851 | − | 0.954612i | \(-0.403730\pi\) |
−0.954612 | + | 0.297851i | \(0.903730\pi\) | |||||||
\(684\) | − | 173836.i | − | 0.371558i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −78297.3 | −0.166379 | ||||||||
\(687\) | −12097.3 | + | 12097.3i | −0.0256316 | + | 0.0256316i | ||||
\(688\) | 480620. | + | 480620.i | 1.01537 | + | 1.01537i | ||||
\(689\) | 310892.i | 0.654893i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 568078. | 1.18974 | 0.594870 | − | 0.803822i | \(-0.297204\pi\) | ||||
0.594870 | + | 0.803822i | \(0.297204\pi\) | |||||||
\(692\) | −87544.1 | + | 87544.1i | −0.182816 | + | 0.182816i | ||||
\(693\) | 89254.8 | + | 89254.8i | 0.185851 | + | 0.185851i | ||||
\(694\) | − | 31103.6i | − | 0.0645791i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 100681. | 0.207840 | ||||||||
\(697\) | 371390. | − | 371390.i | 0.764477 | − | 0.764477i | ||||
\(698\) | −58007.4 | − | 58007.4i | −0.119062 | − | 0.119062i | ||||
\(699\) | − | 107972.i | − | 0.220981i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −773879. | −1.57484 | −0.787421 | − | 0.616416i | \(-0.788584\pi\) | ||||
−0.787421 | + | 0.616416i | \(0.788584\pi\) | |||||||
\(702\) | −13162.5 | + | 13162.5i | −0.0267095 | + | 0.0267095i | ||||
\(703\) | 192446. | + | 192446.i | 0.389403 | + | 0.389403i | ||||
\(704\) | 629442.i | 1.27002i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −133696. | −0.268231 | ||||||||
\(707\) | −55102.4 | + | 55102.4i | −0.110238 | + | 0.110238i | ||||
\(708\) | 110519. | + | 110519.i | 0.220481 | + | 0.220481i | ||||
\(709\) | − | 296312.i | − | 0.589463i | −0.955580 | − | 0.294732i | \(-0.904770\pi\) | ||
0.955580 | − | 0.294732i | \(-0.0952302\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −266743. | −0.527660 | ||||||||
\(712\) | −106095. | + | 106095.i | −0.209284 | + | 0.209284i | ||||
\(713\) | 129488. | + | 129488.i | 0.254712 | + | 0.254712i | ||||
\(714\) | 20691.3i | 0.0405874i | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −289512. | −0.564729 | ||||||||
\(717\) | 121810. | − | 121810.i | 0.236943 | − | 0.236943i | ||||
\(718\) | 110401. | + | 110401.i | 0.214153 | + | 0.214153i | ||||
\(719\) | 620357.i | 1.20001i | 0.799997 | + | 0.600004i | \(0.204834\pi\) | ||||
−0.799997 | + | 0.600004i | \(0.795166\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −227705. | −0.438028 | ||||||||
\(722\) | −24555.6 | + | 24555.6i | −0.0471061 | + | 0.0471061i | ||||
\(723\) | 406103. | + | 406103.i | 0.776891 | + | 0.776891i | ||||
\(724\) | − | 548850.i | − | 1.04707i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 97865.4 | 0.185676 | ||||||||
\(727\) | 27652.4 | − | 27652.4i | 0.0523195 | − | 0.0523195i | −0.680463 | − | 0.732782i | \(-0.738221\pi\) |
0.732782 | + | 0.680463i | \(0.238221\pi\) | |||||||
\(728\) | −69875.2 | − | 69875.2i | −0.131844 | − | 0.131844i | ||||
\(729\) | − | 19683.0i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −644777. | −1.20663 | ||||||||
\(732\) | −69407.2 | + | 69407.2i | −0.129533 | + | 0.129533i | ||||
\(733\) | 269452. | + | 269452.i | 0.501503 | + | 0.501503i | 0.911905 | − | 0.410402i | \(-0.134612\pi\) |
−0.410402 | + | 0.911905i | \(0.634612\pi\) | |||||||
\(734\) | 25722.1i | 0.0477435i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −499050. | −0.921273 | ||||||||
\(737\) | 229748. | − | 229748.i | 0.422976 | − | 0.422976i | ||||
\(738\) | 36210.4 | + | 36210.4i | 0.0664845 | + | 0.0664845i | ||||
\(739\) | 672746.i | 1.23186i | 0.787800 | + | 0.615931i | \(0.211220\pi\) | ||||
−0.787800 | + | 0.615931i | \(0.788780\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −370372. | −0.674531 | ||||||||
\(742\) | −23824.8 | + | 23824.8i | −0.0432735 | + | 0.0432735i | ||||
\(743\) | −413904. | − | 413904.i | −0.749759 | − | 0.749759i | 0.224675 | − | 0.974434i | \(-0.427868\pi\) |
−0.974434 | + | 0.224675i | \(0.927868\pi\) | |||||||
\(744\) | 26470.3i | 0.0478203i | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 91401.7 | 0.164239 | ||||||||
\(747\) | −89013.9 | + | 89013.9i | −0.159521 | + | 0.159521i | ||||
\(748\) | −462459. | − | 462459.i | −0.826551 | − | 0.826551i | ||||
\(749\) | − | 48555.1i | − | 0.0865509i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 320818. | 0.568825 | 0.284413 | − | 0.958702i | \(-0.408201\pi\) | ||||
0.284413 | + | 0.958702i | \(0.408201\pi\) | |||||||
\(752\) | −661465. | + | 661465.i | −1.16969 | + | 1.16969i | ||||
\(753\) | 7782.03 | + | 7782.03i | 0.0137247 | + | 0.0137247i | ||||
\(754\) | − | 105184.i | − | 0.185015i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 51236.3 | 0.0896467 | ||||||||
\(757\) | −435523. | + | 435523.i | −0.760011 | + | 0.760011i | −0.976324 | − | 0.216313i | \(-0.930597\pi\) |
0.216313 | + | 0.976324i | \(0.430597\pi\) | |||||||
\(758\) | −87268.0 | − | 87268.0i | −0.151886 | − | 0.151886i | ||||
\(759\) | − | 899651.i | − | 1.56167i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 479713. | 0.828347 | 0.414174 | − | 0.910198i | \(-0.364071\pi\) | ||||
0.414174 | + | 0.910198i | \(0.364071\pi\) | |||||||
\(762\) | 39988.9 | − | 39988.9i | 0.0688699 | − | 0.0688699i | ||||
\(763\) | 233630. | + | 233630.i | 0.401309 | + | 0.401309i | ||||
\(764\) | − | 898961.i | − | 1.54012i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −183515. | −0.312762 | ||||||||
\(767\) | 235470. | − | 235470.i | 0.400263 | − | 0.400263i | ||||
\(768\) | 154667. | + | 154667.i | 0.262226 | + | 0.262226i | ||||
\(769\) | 682193.i | 1.15360i | 0.816886 | + | 0.576799i | \(0.195699\pi\) | ||||
−0.816886 | + | 0.576799i | \(0.804301\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 570924. | 0.960438 | ||||||||
\(772\) | 195186. | − | 195186.i | 0.327503 | − | 0.327503i | ||||
\(773\) | −264976. | − | 264976.i | −0.443452 | − | 0.443452i | 0.449718 | − | 0.893171i | \(-0.351524\pi\) |
−0.893171 | + | 0.449718i | \(0.851524\pi\) | |||||||
\(774\) | − | 62865.5i | − | 0.104938i | ||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −25167.8 | −0.0417948 | ||||||||
\(777\) | −56721.6 | + | 56721.6i | −0.0939520 | + | 0.0939520i | ||||
\(778\) | 4909.60 | + | 4909.60i | 0.00811123 | + | 0.00811123i | ||||
\(779\) | 1.01890e6i | 1.67902i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 612852. | 1.00474 | ||||||||
\(782\) | 104280. | − | 104280.i | 0.170524 | − | 0.170524i | ||||
\(783\) | 78644.8 | + | 78644.8i | 0.128276 | + | 0.128276i | ||||
\(784\) | − | 417770.i | − | 0.679681i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −76460.0 | −0.123763 | ||||||||
\(787\) | −163669. | + | 163669.i | −0.264252 | + | 0.264252i | −0.826779 | − | 0.562527i | \(-0.809829\pi\) |
0.562527 | + | 0.826779i | \(0.309829\pi\) | |||||||
\(788\) | 314355. | + | 314355.i | 0.506253 | + | 0.506253i | ||||
\(789\) | 409090.i | 0.657151i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 579748. | 0.926588 | ||||||||
\(792\) | 91954.5 | − | 91954.5i | 0.146596 | − | 0.146596i | ||||
\(793\) | 147878. | + | 147878.i | 0.235156 | + | 0.235156i | ||||
\(794\) | − | 241709.i | − | 0.383400i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 15950.1 | 0.0251731 | ||||||||
\(797\) | −511390. | + | 511390.i | −0.805074 | + | 0.805074i | −0.983884 | − | 0.178809i | \(-0.942775\pi\) |
0.178809 | + | 0.983884i | \(0.442775\pi\) | |||||||
\(798\) | −28383.0 | − | 28383.0i | −0.0445711 | − | 0.0445711i | ||||
\(799\) | − | 887389.i | − | 1.39002i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −165749. | −0.258336 | ||||||||
\(802\) | 153153. | − | 153153.i | 0.238109 | − | 0.238109i | ||||
\(803\) | −681317. | − | 681317.i | −1.05662 | − | 1.05662i | ||||
\(804\) | − | 131886.i | − | 0.204026i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 27654.1 | 0.0425687 | ||||||||
\(807\) | 388932. | − | 388932.i | 0.597210 | − | 0.597210i | ||||
\(808\) | 56769.1 | + | 56769.1i | 0.0869540 | + | 0.0869540i | ||||
\(809\) | 973697.i | 1.48774i | 0.668324 | + | 0.743870i | \(0.267012\pi\) | ||||
−0.668324 | + | 0.743870i | \(0.732988\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 426534. | 0.648504 | 0.324252 | − | 0.945971i | \(-0.394887\pi\) | ||||
0.324252 | + | 0.945971i | \(0.394887\pi\) | |||||||
\(812\) | −204718. | + | 204718.i | −0.310488 | + | 0.310488i | ||||
\(813\) | −363466. | − | 363466.i | −0.549899 | − | 0.549899i | ||||
\(814\) | 99833.5i | 0.150670i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −254608. | −0.382377 | ||||||||
\(817\) | 884466. | − | 884466.i | 1.32506 | − | 1.32506i | ||||
\(818\) | −17237.5 | − | 17237.5i | −0.0257614 | − | 0.0257614i | ||||
\(819\) | − | 109163.i | − | 0.162745i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −263379. | −0.390747 | −0.195373 | − | 0.980729i | \(-0.562592\pi\) | ||||
−0.195373 | + | 0.980729i | \(0.562592\pi\) | |||||||
\(822\) | 7775.77 | − | 7775.77i | 0.0115080 | − | 0.0115080i | ||||
\(823\) | −704572. | − | 704572.i | −1.04022 | − | 1.04022i | −0.999156 | − | 0.0410646i | \(-0.986925\pi\) |
−0.0410646 | − | 0.999156i | \(-0.513075\pi\) | |||||||
\(824\) | 234592.i | 0.345509i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 36090.0 | 0.0528965 | ||||||||
\(827\) | −103507. | + | 103507.i | −0.151342 | + | 0.151342i | −0.778717 | − | 0.627375i | \(-0.784129\pi\) |
0.627375 | + | 0.778717i | \(0.284129\pi\) | |||||||
\(828\) | −258220. | − | 258220.i | −0.376642 | − | 0.376642i | ||||
\(829\) | − | 575466.i | − | 0.837357i | −0.908134 | − | 0.418679i | \(-0.862493\pi\) | ||
0.908134 | − | 0.418679i | \(-0.137507\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 469286. | 0.679572 | ||||||||
\(832\) | 384920. | − | 384920.i | 0.556063 | − | 0.556063i | ||||
\(833\) | 280230. | + | 280230.i | 0.403854 | + | 0.403854i | ||||
\(834\) | − | 48689.8i | − | 0.0700012i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.26875e6 | 1.81536 | ||||||||
\(837\) | −20676.7 | + | 20676.7i | −0.0295142 | + | 0.0295142i | ||||
\(838\) | −45777.7 | − | 45777.7i | −0.0651878 | − | 0.0651878i | ||||
\(839\) | − | 1.07622e6i | − | 1.52889i | −0.644688 | − | 0.764446i | \(-0.723013\pi\) | ||
0.644688 | − | 0.764446i | \(-0.276987\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 78818.8 | 0.111439 | ||||||||
\(842\) | 2420.05 | − | 2420.05i | 0.00341351 | − | 0.00341351i | ||||
\(843\) | 117706. | + | 117706.i | 0.165631 | + | 0.165631i | ||||
\(844\) | 340482.i | 0.477980i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 86520.1 | 0.120886 | ||||||||
\(847\) | −405822. | + | 405822.i | −0.565678 | + | 0.565678i | ||||
\(848\) | −293166. | − | 293166.i | −0.407683 | − | 0.407683i | ||||
\(849\) | 469894.i | 0.651905i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 571729. | 0.789462 | ||||||||
\(852\) | 175902. | − | 175902.i | 0.242322 | − | 0.242322i | ||||
\(853\) | −21249.1 | − | 21249.1i | −0.0292040 | − | 0.0292040i | 0.692354 | − | 0.721558i | \(-0.256574\pi\) |
−0.721558 | + | 0.692354i | \(0.756574\pi\) | |||||||
\(854\) | 22664.9i | 0.0310769i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −50023.8 | −0.0682698 | ||||||||
\(857\) | 165230. | − | 165230.i | 0.224971 | − | 0.224971i | −0.585617 | − | 0.810588i | \(-0.699148\pi\) |
0.810588 | + | 0.585617i | \(0.199148\pi\) | |||||||
\(858\) | −96067.2 | − | 96067.2i | −0.130497 | − | 0.130497i | ||||
\(859\) | − | 249324.i | − | 0.337891i | −0.985625 | − | 0.168946i | \(-0.945964\pi\) | ||
0.985625 | − | 0.168946i | \(-0.0540363\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −300310. | −0.405101 | ||||||||
\(862\) | 53484.3 | − | 53484.3i | 0.0719800 | − | 0.0719800i | ||||
\(863\) | −325199. | − | 325199.i | −0.436644 | − | 0.436644i | 0.454237 | − | 0.890881i | \(-0.349912\pi\) |
−0.890881 | + | 0.454237i | \(0.849912\pi\) | |||||||
\(864\) | − | 79688.6i | − | 0.106750i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −168235. | −0.224327 | ||||||||
\(867\) | −136091. | + | 136091.i | −0.181047 | + | 0.181047i | ||||
\(868\) | −53823.0 | − | 53823.0i | −0.0714379 | − | 0.0714379i | ||||
\(869\) | − | 1.94683e6i | − | 2.57804i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −280993. | −0.370390 | ||||||||
\(872\) | 240696. | − | 240696.i | 0.316546 | − | 0.316546i | ||||
\(873\) | −19659.3 | − | 19659.3i | −0.0257953 | − | 0.0257953i | ||||
\(874\) | 286089.i | 0.374523i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −391107. | −0.509668 | ||||||||
\(877\) | −578651. | + | 578651.i | −0.752346 | + | 0.752346i | −0.974917 | − | 0.222571i | \(-0.928555\pi\) |
0.222571 | + | 0.974917i | \(0.428555\pi\) | |||||||
\(878\) | −16971.7 | − | 16971.7i | −0.0220159 | − | 0.0220159i | ||||
\(879\) | − | 101881.i | − | 0.131860i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.10283e6 | −1.42087 | −0.710436 | − | 0.703762i | \(-0.751502\pi\) | ||||
−0.710436 | + | 0.703762i | \(0.751502\pi\) | |||||||
\(882\) | −27322.3 | + | 27322.3i | −0.0351221 | + | 0.0351221i | ||||
\(883\) | −402039. | − | 402039.i | −0.515640 | − | 0.515640i | 0.400609 | − | 0.916249i | \(-0.368799\pi\) |
−0.916249 | + | 0.400609i | \(0.868799\pi\) | |||||||
\(884\) | 565611.i | 0.723791i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −139357. | −0.177526 | ||||||||
\(887\) | 725066. | − | 725066.i | 0.921575 | − | 0.921575i | −0.0755662 | − | 0.997141i | \(-0.524076\pi\) |
0.997141 | + | 0.0755662i | \(0.0240764\pi\) | |||||||
\(888\) | 58437.2 | + | 58437.2i | 0.0741077 | + | 0.0741077i | ||||
\(889\) | 331647.i | 0.419636i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 143657. | 0.180955 | ||||||||
\(892\) | −463668. | + | 463668.i | −0.582743 | + | 0.582743i | ||||
\(893\) | 1.21727e6 | + | 1.21727e6i | 1.52645 | + | 1.52645i | ||||
\(894\) | − | 11454.0i | − | 0.0143311i | ||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 274599. | 0.342045 | ||||||||
\(897\) | −550160. | + | 550160.i | −0.683760 | + | 0.683760i | ||||
\(898\) | −74328.7 | − | 74328.7i | −0.0921731 | − | 0.0921731i | ||||
\(899\) | − | 165231.i | − | 0.204442i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 393298. | 0.484475 | ||||||||
\(902\) | −264282. | + | 264282.i | −0.324829 | + | 0.324829i | ||||
\(903\) | 260687. | + | 260687.i | 0.319701 | + | 0.319701i | ||||
\(904\) | − | 597284.i | − | 0.730876i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −46561.8 | −0.0567249 | ||||||||
\(907\) | 118169. | − | 118169.i | 0.143644 | − | 0.143644i | −0.631628 | − | 0.775272i | \(-0.717613\pi\) |
0.775272 | + | 0.631628i | \(0.217613\pi\) | |||||||
\(908\) | 743142. | + | 743142.i | 0.901364 | + | 0.901364i | ||||
\(909\) | 88688.1i | 0.107334i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 291846. | 0.351655 | 0.175827 | − | 0.984421i | \(-0.443740\pi\) | ||||
0.175827 | + | 0.984421i | \(0.443740\pi\) | |||||||
\(912\) | 349255. | − | 349255.i | 0.419907 | − | 0.419907i | ||||
\(913\) | −649670. | − | 649670.i | −0.779384 | − | 0.779384i | ||||
\(914\) | 6647.08i | 0.00795680i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −50684.0 | −0.0604060 | ||||||||
\(917\) | 317060. | − | 317060.i | 0.377053 | − | 0.377053i | ||||
\(918\) | 16651.4 | + | 16651.4i | 0.0197591 | + | 0.0197591i | ||||
\(919\) | 487999.i | 0.577814i | 0.957357 | + | 0.288907i | \(0.0932918\pi\) | ||||
−0.957357 | + | 0.288907i | \(0.906708\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 693695. | 0.817804 | ||||||||
\(922\) | 19796.6 | − | 19796.6i | 0.0232878 | − | 0.0232878i | ||||
\(923\) | −374775. | − | 374775.i | −0.439913 | − | 0.439913i | ||||
\(924\) | 373949.i | 0.437995i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 171725. | 0.200268 | ||||||||
\(927\) | −183247. | + | 183247.i | −0.213244 | + | 0.213244i | ||||
\(928\) | 318402. | + | 318402.i | 0.369725 | + | 0.369725i | ||||
\(929\) | 480347.i | 0.556575i | 0.960498 | + | 0.278288i | \(0.0897669\pi\) | ||||
−0.960498 | + | 0.278288i | \(0.910233\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −768804. | −0.886986 | ||||||||
\(932\) | 226183. | − | 226183.i | 0.260393 | − | 0.260393i | ||||
\(933\) | −323599. | − | 323599.i | −0.371744 | − | 0.371744i | ||||
\(934\) | 178689.i | 0.204835i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −112465. | −0.128371 | ||||||||
\(937\) | −684823. | + | 684823.i | −0.780008 | + | 0.780008i | −0.979832 | − | 0.199824i | \(-0.935963\pi\) |
0.199824 | + | 0.979832i | \(0.435963\pi\) | |||||||
\(938\) | −21533.6 | − | 21533.6i | −0.0244743 | − | 0.0244743i | ||||
\(939\) | 651332.i | 0.738705i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.18932e6 | −1.34313 | −0.671565 | − | 0.740946i | \(-0.734377\pi\) | ||||
−0.671565 | + | 0.740946i | \(0.734377\pi\) | |||||||
\(942\) | −68185.9 | + | 68185.9i | −0.0768409 | + | 0.0768409i | ||||
\(943\) | 1.51350e6 | + | 1.51350e6i | 1.70200 | + | 1.70200i | ||||
\(944\) | 444090.i | 0.498342i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 458826. | 0.512703 | ||||||||
\(947\) | 242748. | − | 242748.i | 0.270679 | − | 0.270679i | −0.558694 | − | 0.829374i | \(-0.688698\pi\) |
0.829374 | + | 0.558694i | \(0.188698\pi\) | |||||||
\(948\) | −558785. | − | 558785.i | −0.621767 | − | 0.621767i | ||||
\(949\) | 833286.i | 0.925256i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −295343. | −0.326562 | ||||||||
\(952\) | −88396.6 | + | 88396.6i | −0.0975352 | + | 0.0975352i | ||||
\(953\) | 851307. | + | 851307.i | 0.937347 | + | 0.937347i | 0.998150 | − | 0.0608027i | \(-0.0193660\pi\) |
−0.0608027 | + | 0.998150i | \(0.519366\pi\) | |||||||
\(954\) | 38346.4i | 0.0421335i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 510345. | 0.558403 | ||||||||
\(957\) | −573991. | + | 573991.i | −0.626732 | + | 0.626732i | ||||
\(958\) | 81872.7 | + | 81872.7i | 0.0892088 | + | 0.0892088i | ||||
\(959\) | 64488.2i | 0.0701202i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −880080. | −0.952961 | ||||||||
\(962\) | 61050.8 | − | 61050.8i | 0.0659692 | − | 0.0659692i | ||||
\(963\) | −39075.1 | − | 39075.1i | −0.0421354 | − | 0.0421354i | ||||
\(964\) | 1.70144e6i | 1.83090i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −84321.7 | −0.0903619 | ||||||||
\(967\) | 444643. | − | 444643.i | 0.475509 | − | 0.475509i | −0.428183 | − | 0.903692i | \(-0.640846\pi\) |
0.903692 | + | 0.428183i | \(0.140846\pi\) | |||||||
\(968\) | 418097. | + | 418097.i | 0.446197 | + | 0.446197i | ||||
\(969\) | 468544.i | 0.499003i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.65301e6 | −1.75322 | −0.876609 | − | 0.481204i | \(-0.840200\pi\) | ||||
−0.876609 | + | 0.481204i | \(0.840200\pi\) | |||||||
\(972\) | 41232.8 | − | 41232.8i | 0.0436425 | − | 0.0436425i | ||||
\(973\) | 201904. | + | 201904.i | 0.213265 | + | 0.213265i | ||||
\(974\) | − | 213770.i | − | 0.225335i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −278893. | −0.292778 | ||||||||
\(977\) | 738999. | − | 738999.i | 0.774202 | − | 0.774202i | −0.204636 | − | 0.978838i | \(-0.565601\pi\) |
0.978838 | + | 0.204636i | \(0.0656010\pi\) | |||||||
\(978\) | 85323.5 | + | 85323.5i | 0.0892053 | + | 0.0892053i | ||||
\(979\) | − | 1.20972e6i | − | 1.26218i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 376030. | 0.390737 | ||||||||
\(982\) | −115086. | + | 115086.i | −0.119344 | + | 0.119344i | ||||
\(983\) | 246723. | + | 246723.i | 0.255330 | + | 0.255330i | 0.823152 | − | 0.567821i | \(-0.192214\pi\) |
−0.567821 | + | 0.823152i | \(0.692214\pi\) | |||||||
\(984\) | 309394.i | 0.319537i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −133064. | −0.136870 | ||||||||
\(987\) | −358777. | + | 358777.i | −0.368290 | + | 0.368290i | ||||
\(988\) | −775870. | − | 775870.i | −0.794832 | − | 0.794832i | ||||
\(989\) | − | 2.62761e6i | − | 2.68639i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 136401. | 0.138890 | 0.0694449 | − | 0.997586i | \(-0.477877\pi\) | ||||
0.0694449 | + | 0.997586i | \(0.477877\pi\) | |||||||
\(992\) | −83711.8 | + | 83711.8i | −0.0850674 | + | 0.0850674i | ||||
\(993\) | 12546.5 | + | 12546.5i | 0.0127240 | + | 0.0127240i | ||||
\(994\) | − | 57440.9i | − | 0.0581365i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −372940. | −0.375941 | ||||||||
\(997\) | −1.13742e6 | + | 1.13742e6i | −1.14427 | + | 1.14427i | −0.156613 | + | 0.987660i | \(0.550057\pi\) |
−0.987660 | + | 0.156613i | \(0.949943\pi\) | |||||||
\(998\) | 39093.0 | + | 39093.0i | 0.0392498 | + | 0.0392498i | ||||
\(999\) | 91294.1i | 0.0914770i |
(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 | 75.5.f.d.43.1 | yes | 4 | |
3.2 | odd | 2 | 225.5.g.d.118.2 | 4 | |||
5.2 | odd | 4 | inner | 75.5.f.d.7.1 | yes | 4 | |
5.3 | odd | 4 | 75.5.f.a.7.2 | ✓ | 4 | ||
5.4 | even | 2 | 75.5.f.a.43.2 | yes | 4 | ||
15.2 | even | 4 | 225.5.g.d.82.2 | 4 | |||
15.8 | even | 4 | 225.5.g.l.82.1 | 4 | |||
15.14 | odd | 2 | 225.5.g.l.118.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.5.f.a.7.2 | ✓ | 4 | 5.3 | odd | 4 | ||
75.5.f.a.43.2 | yes | 4 | 5.4 | even | 2 | ||
75.5.f.d.7.1 | yes | 4 | 5.2 | odd | 4 | inner | |
75.5.f.d.43.1 | yes | 4 | 1.1 | even | 1 | trivial | |
225.5.g.d.82.2 | 4 | 15.2 | even | 4 | |||
225.5.g.d.118.2 | 4 | 3.2 | odd | 2 | |||
225.5.g.l.82.1 | 4 | 15.8 | even | 4 | |||
225.5.g.l.118.1 | 4 | 15.14 | odd | 2 |