Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,5,Mod(31,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.31");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.f (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.2313552747\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 4 x^{13} + 15 x^{12} - 34 x^{11} + 62 x^{10} - 312 x^{9} + 1432 x^{8} - 4960 x^{7} + 11456 x^{6} - 19968 x^{5} + 31744 x^{4} - 139264 x^{3} + 491520 x^{2} + \cdots + 2097152 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{42} \) |
Twist minimal: | no (minimal twist has level 16) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 31.5 | ||
Root | \(2.79265 - 0.448449i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 128.31 |
Dual form | 128.5.f.b.95.5 |
$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 4.63552 | + | 4.63552i | 0.515058 | + | 0.515058i | 0.916072 | − | 0.401014i | \(-0.131342\pi\) |
−0.401014 | + | 0.916072i | \(0.631342\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 29.2002 | + | 29.2002i | 1.16801 | + | 1.16801i | 0.982676 | + | 0.185330i | \(0.0593353\pi\) |
0.185330 | + | 0.982676i | \(0.440665\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 59.6196 | 1.21673 | 0.608363 | − | 0.793659i | \(-0.291826\pi\) | ||||
0.608363 | + | 0.793659i | \(0.291826\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 38.0239i | − | 0.469431i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 18.0837 | − | 18.0837i | 0.149452 | − | 0.149452i | −0.628421 | − | 0.777873i | \(-0.716299\pi\) |
0.777873 | + | 0.628421i | \(0.216299\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −50.7721 | + | 50.7721i | −0.300427 | + | 0.300427i | −0.841181 | − | 0.540754i | \(-0.818139\pi\) |
0.540754 | + | 0.841181i | \(0.318139\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 270.716i | 1.20318i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −223.769 | −0.774289 | −0.387144 | − | 0.922019i | \(-0.626538\pi\) | ||||
−0.387144 | + | 0.922019i | \(0.626538\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −14.7360 | − | 14.7360i | −0.0408199 | − | 0.0408199i | 0.686402 | − | 0.727222i | \(-0.259189\pi\) |
−0.727222 | + | 0.686402i | \(0.759189\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 276.368 | + | 276.368i | 0.626684 | + | 0.626684i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 739.082 | 1.39713 | 0.698565 | − | 0.715547i | \(-0.253822\pi\) | ||||
0.698565 | + | 0.715547i | \(0.253822\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1080.30i | 1.72848i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 551.738 | − | 551.738i | 0.756842 | − | 0.756842i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −938.904 | + | 938.904i | −1.11641 | + | 1.11641i | −0.124150 | + | 0.992263i | \(0.539620\pi\) |
−0.992263 | + | 0.124150i | \(0.960380\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 938.741i | − | 0.976838i | −0.872609 | − | 0.488419i | \(-0.837574\pi\) | ||
0.872609 | − | 0.488419i | \(-0.162426\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 167.655 | 0.153953 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1740.90 | + | 1740.90i | 1.42114 | + | 1.42114i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −263.837 | − | 263.837i | −0.192722 | − | 0.192722i | 0.604149 | − | 0.796871i | \(-0.293513\pi\) |
−0.796871 | + | 0.604149i | \(0.793513\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −470.710 | −0.309474 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 248.841i | 0.148031i | 0.997257 | + | 0.0740157i | \(0.0235815\pi\) | ||||
−0.997257 | + | 0.0740157i | \(0.976418\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1035.00 | + | 1035.00i | −0.559765 | + | 0.559765i | −0.929240 | − | 0.369476i | \(-0.879537\pi\) |
0.369476 | + | 0.929240i | \(0.379537\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1110.31 | − | 1110.31i | 0.548299 | − | 0.548299i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2018.46i | 0.913746i | 0.889532 | + | 0.456873i | \(0.151031\pi\) | ||||
−0.889532 | + | 0.456873i | \(0.848969\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1153.50 | 0.480424 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1037.29 | − | 1037.29i | −0.398803 | − | 0.398803i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −833.240 | − | 833.240i | −0.296632 | − | 0.296632i | 0.543061 | − | 0.839693i | \(-0.317265\pi\) |
−0.839693 | + | 0.543061i | \(0.817265\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1056.09 | 0.349122 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 136.618i | − | 0.0420492i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2223.17 | − | 2223.17i | 0.638660 | − | 0.638660i | −0.311565 | − | 0.950225i | \(-0.600853\pi\) |
0.950225 | + | 0.311565i | \(0.100853\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 341.374 | − | 341.374i | 0.0917425 | − | 0.0917425i | −0.659746 | − | 0.751489i | \(-0.729336\pi\) |
0.751489 | + | 0.659746i | \(0.229336\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 2266.97i | − | 0.571170i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2965.11 | −0.701800 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4845.43 | − | 4845.43i | −1.07940 | − | 1.07940i | −0.996563 | − | 0.0828379i | \(-0.973602\pi\) |
−0.0828379 | − | 0.996563i | \(-0.526398\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3426.03 | + | 3426.03i | 0.719602 | + | 0.719602i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4180.93 | −0.829386 | −0.414693 | − | 0.909961i | \(-0.636111\pi\) | ||||
−0.414693 | + | 0.909961i | \(0.636111\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 9071.36i | − | 1.70226i | −0.524953 | − | 0.851131i | \(-0.675917\pi\) | ||
0.524953 | − | 0.851131i | \(-0.324083\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5007.74 | + | 5007.74i | −0.890265 | + | 0.890265i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1078.14 | − | 1078.14i | 0.181842 | − | 0.181842i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 735.536i | 0.117855i | 0.998262 | + | 0.0589277i | \(0.0187682\pi\) | ||||
−0.998262 | + | 0.0589277i | \(0.981232\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2035.24 | 0.310203 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1441.90 | − | 1441.90i | −0.209305 | − | 0.209305i | 0.594667 | − | 0.803972i | \(-0.297284\pi\) |
−0.803972 | + | 0.594667i | \(0.797284\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6534.10 | − | 6534.10i | −0.904374 | − | 0.904374i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8704.61 | −1.15003 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 5071.77i | − | 0.640294i | −0.947368 | − | 0.320147i | \(-0.896268\pi\) | ||
0.947368 | − | 0.320147i | \(-0.103732\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3027.01 | + | 3027.01i | −0.365537 | + | 0.365537i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4351.55 | − | 4351.55i | 0.503128 | − | 0.503128i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 860.586i | − | 0.0953558i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2523.85 | −0.268238 | −0.134119 | − | 0.990965i | \(-0.542820\pi\) | ||||
−0.134119 | + | 0.990965i | \(0.542820\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −687.613 | − | 687.613i | −0.0701575 | − | 0.0701575i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −425.990 | − | 425.990i | −0.0417596 | − | 0.0417596i | 0.685919 | − | 0.727678i | \(-0.259401\pi\) |
−0.727678 | + | 0.685919i | \(0.759401\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13178.6 | 1.24221 | 0.621103 | − | 0.783729i | \(-0.286685\pi\) | ||||
0.621103 | + | 0.783729i | \(0.286685\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 16140.0i | 1.46394i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10821.5 | − | 10821.5i | 0.945190 | − | 0.945190i | −0.0533845 | − | 0.998574i | \(-0.517001\pi\) |
0.998574 | + | 0.0533845i | \(0.0170009\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1428.57 | − | 1428.57i | 0.120240 | − | 0.120240i | −0.644426 | − | 0.764666i | \(-0.722904\pi\) |
0.764666 | + | 0.644426i | \(0.222904\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 2446.04i | − | 0.198526i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 20121.5 | 1.57581 | 0.787904 | − | 0.615798i | \(-0.211166\pi\) | ||||
0.787904 | + | 0.615798i | \(0.211166\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 21581.3 | + | 21581.3i | 1.63186 | + | 1.63186i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1930.56 | + | 1930.56i | 0.141030 | + | 0.141030i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −13341.0 | −0.942098 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13987.0i | 0.955328i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1153.51 | + | 1153.51i | −0.0762447 | + | 0.0762447i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −13294.8 | + | 13294.8i | −0.850865 | + | 0.850865i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2630.54i | 0.163094i | 0.996669 | + | 0.0815470i | \(0.0259861\pi\) | ||||
−0.996669 | + | 0.0815470i | \(0.974014\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9595.57 | −0.576622 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12437.0 | − | 12437.0i | −0.724722 | − | 0.724722i | 0.244841 | − | 0.969563i | \(-0.421264\pi\) |
−0.969563 | + | 0.244841i | \(0.921264\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −878.554 | − | 878.554i | −0.0496667 | − | 0.0496667i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 32221.6 | 1.76799 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 15392.0i | − | 0.820078i | −0.912068 | − | 0.410039i | \(-0.865515\pi\) | ||
0.912068 | − | 0.410039i | \(-0.134485\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12151.3 | + | 12151.3i | −0.628915 | + | 0.628915i | −0.947795 | − | 0.318880i | \(-0.896693\pi\) |
0.318880 | + | 0.947795i | \(0.396693\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9356.63 | + | 9356.63i | −0.470632 | + | 0.470632i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1836.29i | 0.0897987i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −54832.3 | −2.60796 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5347.06 | + | 5347.06i | 0.247446 | + | 0.247446i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20803.7 | + | 20803.7i | 0.937062 | + | 0.937062i | 0.998133 | − | 0.0610710i | \(-0.0194516\pi\) |
−0.0610710 | + | 0.998133i | \(0.519452\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7756.67 | −0.340190 | −0.170095 | − | 0.985428i | \(-0.554407\pi\) | ||||
−0.170095 | + | 0.985428i | \(0.554407\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8508.60i | 0.363475i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 27411.4 | − | 27411.4i | 1.14095 | − | 1.14095i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7040.20 | + | 7040.20i | −0.285618 | + | 0.285618i | −0.835345 | − | 0.549727i | \(-0.814732\pi\) |
0.549727 | + | 0.835345i | \(0.314732\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 7725.00i | − | 0.305565i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 44063.8 | 1.69993 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7273.43 | − | 7273.43i | −0.273756 | − | 0.273756i | 0.556854 | − | 0.830610i | \(-0.312008\pi\) |
−0.830610 | + | 0.556854i | \(0.812008\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4895.54 | + | 4895.54i | 0.179818 | + | 0.179818i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 30069.6 | 1.07819 | 0.539095 | − | 0.842245i | \(-0.318766\pi\) | ||||
0.539095 | + | 0.842245i | \(0.318766\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23405.4i | 0.819488i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −560.320 | + | 560.320i | −0.0191621 | + | 0.0191621i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8329.72 | − | 8329.72i | 0.278316 | − | 0.278316i | −0.554121 | − | 0.832436i | \(-0.686945\pi\) |
0.832436 | + | 0.554121i | \(0.186945\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 64406.9i | 2.10308i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 20611.1 | 0.657893 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7537.56 | + | 7537.56i | 0.235247 | + | 0.235247i | 0.814879 | − | 0.579632i | \(-0.196803\pi\) |
−0.579632 | + | 0.814879i | \(0.696803\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3802.64 | − | 3802.64i | −0.116072 | − | 0.116072i | 0.646685 | − | 0.762757i | \(-0.276155\pi\) |
−0.762757 | + | 0.646685i | \(0.776155\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3164.89 | 0.0945054 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 15408.2i | − | 0.450202i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4046.58 | + | 4046.58i | −0.115719 | + | 0.115719i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 32894.4 | − | 32894.4i | 0.920869 | − | 0.920869i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 52248.1i | − | 1.43220i | −0.697997 | − | 0.716100i | \(-0.745925\pi\) | ||
0.697997 | − | 0.716100i | \(-0.254075\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −24380.0 | −0.654514 | −0.327257 | − | 0.944935i | \(-0.606124\pi\) | ||||
−0.327257 | + | 0.944935i | \(0.606124\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −13744.8 | − | 13744.8i | −0.361468 | − | 0.361468i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −31537.9 | − | 31537.9i | −0.812644 | − | 0.812644i | 0.172386 | − | 0.985030i | \(-0.444852\pi\) |
−0.985030 | + | 0.172386i | \(0.944852\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −71129.4 | −1.79615 | −0.898076 | − | 0.439841i | \(-0.855035\pi\) | ||||
−0.898076 | + | 0.439841i | \(0.855035\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 44922.2i | − | 1.11191i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −55977.1 | + | 55977.1i | −1.35837 | + | 1.35837i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7266.19 | + | 7266.19i | −0.172902 | + | 0.172902i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 28102.8i | − | 0.655857i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −532.962 | −0.0122012 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13393.4 | + | 13393.4i | 0.300833 | + | 0.300833i | 0.841340 | − | 0.540507i | \(-0.181767\pi\) |
−0.540507 | + | 0.841340i | \(0.681767\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −19380.8 | − | 19380.8i | −0.427181 | − | 0.427181i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −60444.6 | −1.30762 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 55967.4i | − | 1.18854i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 42050.4 | − | 42050.4i | 0.876763 | − | 0.876763i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11361.2 | − | 11361.2i | 0.232617 | − | 0.232617i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 54266.9i | − | 1.09125i | −0.838029 | − | 0.545626i | \(-0.816292\pi\) | ||
0.838029 | − | 0.545626i | \(-0.183708\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 41077.2 | 0.811401 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14529.0 | − | 14529.0i | −0.281957 | − | 0.281957i | 0.551932 | − | 0.833889i | \(-0.313891\pi\) |
−0.833889 | + | 0.551932i | \(0.813891\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21618.1 | − | 21618.1i | −0.412237 | − | 0.412237i | 0.470280 | − | 0.882517i | \(-0.344153\pi\) |
−0.882517 | + | 0.470280i | \(0.844153\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9995.50 | 0.187318 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 92103.6i | 1.69654i | 0.529562 | + | 0.848271i | \(0.322356\pi\) | ||||
−0.529562 | + | 0.848271i | \(0.677644\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −58939.5 | + | 58939.5i | −1.06726 | + | 1.06726i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3409.59 | + | 3409.59i | −0.0607024 | + | 0.0607024i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 70411.0i | 1.23266i | 0.787487 | + | 0.616332i | \(0.211382\pi\) | ||||
−0.787487 | + | 0.616332i | \(0.788618\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22402.6 | 0.385714 | 0.192857 | − | 0.981227i | \(-0.438225\pi\) | ||||
0.192857 | + | 0.981227i | \(0.438225\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −35256.4 | − | 35256.4i | −0.597070 | − | 0.597070i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 33682.3 | + | 33682.3i | 0.561138 | + | 0.561138i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1496.35 | 0.0245268 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 13367.9i | − | 0.215608i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 72407.6 | − | 72407.6i | 1.14931 | − | 1.14931i | 0.162621 | − | 0.986689i | \(-0.448005\pi\) |
0.986689 | − | 0.162621i | \(-0.0519947\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13365.3 | − | 13365.3i | 0.208804 | − | 0.208804i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 60577.9i | − | 0.931609i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −56466.3 | −0.854916 | −0.427458 | − | 0.904035i | \(-0.640591\pi\) | ||||
−0.427458 | + | 0.904035i | \(0.640591\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15729.9 | − | 15729.9i | −0.234490 | − | 0.234490i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 35700.8 | + | 35700.8i | 0.524080 | + | 0.524080i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 76515.5 | 1.10621 | 0.553105 | − | 0.833111i | \(-0.313443\pi\) | ||||
0.553105 | + | 0.833111i | \(0.313443\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 48661.5i | − | 0.692937i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 23510.3 | − | 23510.3i | 0.329788 | − | 0.329788i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1928.97 | + | 1928.97i | −0.0266576 | + | 0.0266576i | −0.720310 | − | 0.693652i | \(-0.756000\pi\) |
0.693652 | + | 0.720310i | \(0.256000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 128685.i | 1.75222i | 0.482109 | + | 0.876111i | \(0.339871\pi\) | ||||
−0.482109 | + | 0.876111i | \(0.660129\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −28063.5 | −0.376545 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 19535.8 | + | 19535.8i | 0.258324 | + | 0.258324i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −56674.5 | − | 56674.5i | −0.738632 | − | 0.738632i | 0.233681 | − | 0.972313i | \(-0.424923\pi\) |
−0.972313 | + | 0.233681i | \(0.924923\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −35694.6 | −0.458558 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 10599.7i | − | 0.134240i | −0.997745 | − | 0.0671200i | \(-0.978619\pi\) | ||
0.997745 | − | 0.0671200i | \(-0.0213810\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −63293.6 | + | 63293.6i | −0.790291 | + | 0.790291i | −0.981541 | − | 0.191251i | \(-0.938746\pi\) |
0.191251 | + | 0.981541i | \(0.438746\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3989.26 | − | 3989.26i | 0.0491137 | − | 0.0491137i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14835.8i | 0.180114i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −33448.2 | −0.400477 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11699.3 | − | 11699.3i | −0.138158 | − | 0.138158i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 89072.9 | + | 89072.9i | 1.03755 | + | 1.03755i | 0.999267 | + | 0.0382867i | \(0.0121900\pi\) |
0.0382867 | + | 0.999267i | \(0.487810\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 129834. | 1.49192 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 19954.9i | − | 0.226223i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −37524.7 | + | 37524.7i | −0.419735 | + | 0.419735i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −61706.6 | + | 61706.6i | −0.681080 | + | 0.681080i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 3949.36i | − | 0.0430172i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 19936.3 | 0.214312 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 124227. | + | 124227.i | 1.31807 | + | 1.31807i | 0.915302 | + | 0.402769i | \(0.131952\pi\) |
0.402769 | + | 0.915302i | \(0.368048\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 61089.5 | + | 61089.5i | 0.639808 | + | 0.639808i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15733.9 | 0.162673 | 0.0813364 | − | 0.996687i | \(-0.474081\pi\) | ||||
0.0813364 | + | 0.996687i | \(0.474081\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 104554.i | 1.06721i | 0.845733 | + | 0.533606i | \(0.179163\pi\) | ||||
−0.845733 | + | 0.533606i | \(0.820837\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 66196.0 | − | 66196.0i | 0.667130 | − | 0.667130i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −45847.9 | + | 45847.9i | −0.456248 | + | 0.456248i | −0.897422 | − | 0.441174i | \(-0.854562\pi\) |
0.441174 | + | 0.897422i | \(0.354562\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 33957.7i | 0.333700i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 100326. | 0.973654 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3297.46 | + | 3297.46i | 0.0316064 | + | 0.0316064i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −54849.0 | − | 54849.0i | −0.519281 | − | 0.519281i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13244.3 | 0.123861 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 120340.i | 1.11178i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 137545. | − | 137545.i | 1.25542 | − | 1.25542i | 0.302159 | − | 0.953258i | \(-0.402293\pi\) |
0.953258 | − | 0.302159i | \(-0.0977073\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10032.1 | + | 10032.1i | −0.0904700 | + | 0.0904700i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 282975.i | − | 2.52149i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −40849.6 | −0.359690 | −0.179845 | − | 0.983695i | \(-0.557560\pi\) | ||||
−0.179845 | + | 0.983695i | \(0.557560\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 93273.5 | + | 93273.5i | 0.811632 | + | 0.811632i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16975.9 | − | 16975.9i | −0.145990 | − | 0.145990i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −74375.6 | −0.632182 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 200081.i | 1.68100i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21361.1 | + | 21361.1i | −0.177404 | + | 0.177404i | −0.790223 | − | 0.612819i | \(-0.790035\pi\) |
0.612819 | + | 0.790223i | \(0.290035\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −139275. | + | 139275.i | −1.14347 | + | 1.14347i | −0.155654 | + | 0.987812i | \(0.549748\pi\) |
−0.987812 | + | 0.155654i | \(0.950252\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 56025.8i | 0.454751i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −100461. | −0.806209 | −0.403105 | − | 0.915154i | \(-0.632069\pi\) | ||||
−0.403105 | + | 0.915154i | \(0.632069\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −122084. | − | 122084.i | −0.968728 | − | 0.968728i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −61842.6 | − | 61842.6i | −0.485234 | − | 0.485234i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 96352.7 | 0.747609 | 0.373805 | − | 0.927507i | \(-0.378053\pi\) | ||||
0.373805 | + | 0.927507i | \(0.378053\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 129887.i | − | 0.996667i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −64836.8 | + | 64836.8i | −0.492049 | + | 0.492049i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 264885. | − | 264885.i | 1.98825 | − | 1.98825i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 190661.i | 1.41557i | 0.706429 | + | 0.707784i | \(0.250305\pi\) | ||||
−0.706429 | + | 0.707784i | \(0.749695\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9461.91 | 0.0694906 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −49677.5 | − | 49677.5i | −0.360920 | − | 0.360920i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −51771.9 | − | 51771.9i | −0.372114 | − | 0.372114i | 0.496133 | − | 0.868247i | \(-0.334753\pi\) |
−0.868247 | + | 0.496133i | \(0.834753\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −123256. | −0.876489 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 95340.2i | − | 0.670801i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −121232. | + | 121232.i | −0.843990 | + | 0.843990i | −0.989375 | − | 0.145385i | \(-0.953558\pi\) |
0.145385 | + | 0.989375i | \(0.453558\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12193.9 | + | 12193.9i | −0.0840028 | + | 0.0840028i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 8262.20i | − | 0.0563246i | −0.999603 | − | 0.0281623i | \(-0.991034\pi\) | ||
0.999603 | − | 0.0281623i | \(-0.00896552\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 62963.9 | 0.424786 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 39355.0 | + | 39355.0i | 0.262771 | + | 0.262771i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −43964.9 | − | 43964.9i | −0.290541 | − | 0.290541i | 0.546753 | − | 0.837294i | \(-0.315864\pi\) |
−0.837294 | + | 0.546753i | \(0.815864\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −165384. | −1.08178 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 115303.i | − | 0.746547i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −21477.8 | + | 21477.8i | −0.137656 | + | 0.137656i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −72864.3 | + | 72864.3i | −0.462311 | + | 0.462311i | −0.899412 | − | 0.437101i | \(-0.856005\pi\) |
0.437101 | + | 0.899412i | \(0.356005\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 8145.10i | − | 0.0511624i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 237249. | 1.47542 | 0.737711 | − | 0.675116i | \(-0.235907\pi\) | ||||
0.737711 | + | 0.675116i | \(0.235907\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 47661.9 | + | 47661.9i | 0.293468 | + | 0.293468i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 59429.3 | + | 59429.3i | 0.362319 | + | 0.362319i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9542.29 | −0.0576055 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 150042.i | − | 0.896945i | −0.893797 | − | 0.448473i | \(-0.851968\pi\) | ||
0.893797 | − | 0.448473i | \(-0.148032\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 71350.1 | − | 71350.1i | 0.422387 | − | 0.422387i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 132545. | − | 132545.i | 0.777074 | − | 0.777074i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 84207.5i | − | 0.488939i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −112655. | −0.647855 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −71760.1 | − | 71760.1i | −0.408747 | − | 0.408747i | 0.472554 | − | 0.881302i | \(-0.343332\pi\) |
−0.881302 | + | 0.472554i | \(0.843332\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 209821. | + | 209821.i | 1.18382 | + | 1.18382i | 0.978747 | + | 0.205070i | \(0.0657424\pi\) |
0.205070 | + | 0.978747i | \(0.434258\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 76750.0 | 0.428941 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 241738.i | − | 1.33834i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20352.6 | − | 20352.6i | 0.111626 | − | 0.111626i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8512.18 | + | 8512.18i | −0.0462515 | + | 0.0462515i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 123853.i | − | 0.666731i | −0.942798 | − | 0.333366i | \(-0.891816\pi\) | ||
0.942798 | − | 0.333366i | \(-0.108184\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −265114. | −1.41402 | −0.707012 | − | 0.707202i | \(-0.749957\pi\) | ||||
−0.707012 | + | 0.707202i | \(0.749957\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −254176. | − | 254176.i | −1.34325 | − | 1.34325i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10891.1 | − | 10891.1i | −0.0570307 | − | 0.0570307i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 186089. | 0.965590 | 0.482795 | − | 0.875734i | \(-0.339622\pi\) | ||||
0.482795 | + | 0.875734i | \(0.339622\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 43860.5i | − | 0.225526i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25618.8 | + | 25618.8i | −0.130542 | + | 0.130542i | −0.769359 | − | 0.638817i | \(-0.779424\pi\) |
0.638817 | + | 0.769359i | \(0.279424\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 148096. | − | 148096.i | 0.747867 | − | 0.747867i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 192872.i | 0.965282i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2307.59 | −0.0114463 | −0.00572316 | − | 0.999984i | \(-0.501822\pi\) | ||||
−0.00572316 | + | 0.999984i | \(0.501822\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4499.96 | + | 4499.96i | 0.0221236 | + | 0.0221236i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −35956.2 | − | 35956.2i | −0.175217 | − | 0.175217i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −176778. | −0.853899 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 262378.i | 1.25631i | 0.778090 | + | 0.628153i | \(0.216189\pi\) | ||||
−0.778090 | + | 0.628153i | \(0.783811\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −123462. | + | 123462.i | −0.586014 | + | 0.586014i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −136771. | + | 136771.i | −0.643564 | + | 0.643564i | −0.951430 | − | 0.307866i | \(-0.900385\pi\) |
0.307866 | + | 0.951430i | \(0.400385\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22250.8i | 0.103797i | 0.998652 | + | 0.0518983i | \(0.0165272\pi\) | ||||
−0.998652 | + | 0.0518983i | \(0.983473\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 254132. | 1.17531 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −175541. | − | 175541.i | −0.804906 | − | 0.804906i | 0.178952 | − | 0.983858i | \(-0.442729\pi\) |
−0.983858 | + | 0.178952i | \(0.942729\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −288883. | − | 288883.i | −1.31334 | − | 1.31334i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −65269.9 | −0.294219 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 37433.4i | 0.167316i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15919.3 | − | 15919.3i | 0.0705563 | − | 0.0705563i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −31683.1 | + | 31683.1i | −0.139249 | + | 0.139249i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 117920.i | 0.513945i | 0.966419 | + | 0.256973i | \(0.0827250\pi\) | ||||
−0.966419 | + | 0.256973i | \(0.917275\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 26791.1 | 0.115798 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 204258. | + | 204258.i | 0.875559 | + | 0.875559i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −73696.7 | − | 73696.7i | −0.313303 | − | 0.313303i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −449942. | −1.89714 | −0.948568 | − | 0.316574i | \(-0.897467\pi\) | ||||
−0.948568 | + | 0.316574i | \(0.897467\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 67432.3i | − | 0.282001i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 122509. | − | 122509.i | 0.508166 | − | 0.508166i | −0.405797 | − | 0.913963i | \(-0.633006\pi\) |
0.913963 | + | 0.405797i | \(0.133006\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 210098. | − | 210098.i | 0.864426 | − | 0.864426i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 40156.8i | − | 0.163889i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −249266. | −1.00914 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 44886.9 | + | 44886.9i | 0.180268 | + | 0.180268i | 0.791473 | − | 0.611205i | \(-0.209315\pi\) |
−0.611205 | + | 0.791473i | \(0.709315\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 139388. | + | 139388.i | 0.555330 | + | 0.555330i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 235778. | 0.931896 | 0.465948 | − | 0.884812i | \(-0.345713\pi\) | ||||
0.465948 | + | 0.884812i | \(0.345713\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 24877.9i | − | 0.0975509i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −108496. | + | 108496.i | −0.422083 | + | 0.422083i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −227812. | + | 227812.i | −0.879308 | + | 0.879308i | −0.993463 | − | 0.114155i | \(-0.963584\pi\) |
0.114155 | + | 0.993463i | \(0.463584\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 540831.i | − | 2.07119i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −16260.8 | −0.0617884 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 384816. | + | 384816.i | 1.45090 | + | 1.45090i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 36501.3 | + | 36501.3i | 0.136561 | + | 0.136561i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 77225.1 | 0.286697 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 539683.i | 1.98822i | 0.108395 | + | 0.994108i | \(0.465429\pi\) | ||||
−0.108395 | + | 0.994108i | \(0.534571\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 175071. | − | 175071.i | 0.640044 | − | 0.640044i | −0.310522 | − | 0.950566i | \(-0.600504\pi\) |
0.950566 | + | 0.310522i | \(0.100504\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −298560. | + | 298560.i | −1.08321 | + | 1.08321i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 210062.i | 0.756354i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 266401. | 0.951972 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −84533.9 | − | 84533.9i | −0.299807 | − | 0.299807i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12634.2 | − | 12634.2i | −0.0444726 | − | 0.0444726i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 631977. | 2.20797 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 69880.9i | 0.242332i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 20859.5 | − | 20859.5i | 0.0718003 | − | 0.0718003i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 142203. | − | 142203.i | 0.485863 | − | 0.485863i | −0.421135 | − | 0.906998i | \(-0.638368\pi\) |
0.906998 | + | 0.421135i | \(0.138368\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 35254.4i | − | 0.119568i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 83428.9 | 0.280882 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 265412. | + | 265412.i | 0.887045 | + | 0.887045i | 0.994238 | − | 0.107193i | \(-0.0341862\pi\) |
−0.107193 | + | 0.994238i | \(0.534186\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12980.4 | − | 12980.4i | −0.0430668 | − | 0.0430668i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 27671.3 | 0.0911438 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 43852.4i | 0.143398i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 71424.8 | − | 71424.8i | 0.231880 | − | 0.231880i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −168105. | + | 168105.i | −0.541837 | + | 0.541837i | −0.924067 | − | 0.382230i | \(-0.875156\pi\) |
0.382230 | + | 0.924067i | \(0.375156\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 105099.i | − | 0.336336i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −37516.0 | −0.119204 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 181113. | + | 181113.i | 0.571389 | + | 0.571389i | 0.932517 | − | 0.361127i | \(-0.117608\pi\) |
−0.361127 | + | 0.932517i | \(0.617608\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 587551. | + | 587551.i | 1.84055 | + | 1.84055i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 121340. | 0.377432 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 124083.i | − | 0.383254i | −0.981468 | − | 0.191627i | \(-0.938624\pi\) | ||
0.981468 | − | 0.191627i | \(-0.0613765\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 92801.0 | − | 92801.0i | 0.284630 | − | 0.284630i | −0.550322 | − | 0.834952i | \(-0.685495\pi\) |
0.834952 | + | 0.550322i | \(0.185495\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 242197. | − | 242197.i | 0.737666 | − | 0.737666i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 798429.i | 2.41491i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 182478. | 0.548098 | 0.274049 | − | 0.961716i | \(-0.411637\pi\) | ||||
0.274049 | + | 0.961716i | \(0.411637\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −113014. | − | 113014.i | −0.337112 | − | 0.337112i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −85965.6 | − | 85965.6i | −0.254667 | − | 0.254667i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −30136.1 | −0.0886646 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 112745.i | 0.329447i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −197015. | + | 197015.i | −0.571772 | + | 0.571772i | −0.932623 | − | 0.360851i | \(-0.882486\pi\) |
0.360851 | + | 0.932623i | \(0.382486\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13833.3 | + | 13833.3i | −0.0398744 | + | 0.0398744i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 292389.i | − | 0.837116i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −478257. | −1.36004 | −0.680020 | − | 0.733194i | \(-0.738029\pi\) | ||||
−0.680020 | + | 0.733194i | \(0.738029\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −389561. | − | 389561.i | −1.10038 | − | 1.10038i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −329722. | − | 329722.i | −0.925121 | − | 0.925121i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −141800. | −0.395206 | −0.197603 | − | 0.980282i | \(-0.563316\pi\) | ||||
−0.197603 | + | 0.980282i | \(0.563316\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 50813.1i | 0.140678i | 0.997523 | + | 0.0703391i | \(0.0224081\pi\) | ||||
−0.997523 | + | 0.0703391i | \(0.977592\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −184242. | + | 184242.i | −0.506705 | + | 0.506705i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −408421. | + | 408421.i | −1.11583 | + | 1.11583i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 448023.i | 1.21597i | 0.793948 | + | 0.607985i | \(0.208022\pi\) | ||||
−0.793948 | + | 0.607985i | \(0.791978\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −518965. | −1.39928 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −102482. | − | 102482.i | −0.274514 | − | 0.274514i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8742.04 | − | 8742.04i | −0.0232644 | − | 0.0232644i | 0.695379 | − | 0.718643i | \(-0.255237\pi\) |
−0.718643 | + | 0.695379i | \(0.755237\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −67365.1 | −0.178109 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 488336.i | − | 1.28277i | −0.767220 | − | 0.641384i | \(-0.778361\pi\) | ||
0.767220 | − | 0.641384i | \(-0.221639\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 416206. | − | 416206.i | 1.08624 | − | 1.08624i | 0.0903309 | − | 0.995912i | \(-0.471208\pi\) |
0.995912 | − | 0.0903309i | \(-0.0287925\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 407779. | − | 407779.i | 1.05741 | − | 1.05741i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 302377.i | − | 0.779062i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −101233. | −0.259155 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2470.56 | − | 2470.56i | −0.00628434 | − | 0.00628434i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 59038.6 | + | 59038.6i | 0.149223 | + | 0.149223i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 77166.0 | 0.193806 | 0.0969030 | − | 0.995294i | \(-0.469106\pi\) | ||||
0.0969030 | + | 0.995294i | \(0.469106\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 124171.i | 0.309893i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −76812.3 | + | 76812.3i | −0.190495 | + | 0.190495i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −58565.5 | + | 58565.5i | −0.144332 | + | 0.144332i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 158976.i | 0.389340i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 692532. | 1.68548 | 0.842740 | − | 0.538321i | \(-0.180941\pi\) | ||||
0.842740 | + | 0.538321i | \(0.180941\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −515879. | − | 515879.i | −1.24774 | − | 1.24774i | −0.956714 | − | 0.291031i | \(-0.906002\pi\) |
−0.291031 | − | 0.956714i | \(-0.593998\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −280192. | − | 280192.i | −0.673498 | − | 0.673498i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −187947. | −0.448980 | −0.224490 | − | 0.974476i | \(-0.572072\pi\) | ||||
−0.224490 | + | 0.974476i | \(0.572072\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 80406.4i | − | 0.190898i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 259438. | − | 259438.i | 0.612169 | − | 0.612169i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −363478. | + | 363478.i | −0.852415 | + | 0.852415i | −0.990430 | − | 0.138015i | \(-0.955928\pi\) |
0.138015 | + | 0.990430i | \(0.455928\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 726322.i | − | 1.69296i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −344929. | −0.799096 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 59401.3 | + | 59401.3i | 0.136781 | + | 0.136781i | 0.772182 | − | 0.635401i | \(-0.219165\pi\) |
−0.635401 | + | 0.772182i | \(0.719165\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 352242. | + | 352242.i | 0.806191 | + | 0.806191i | 0.984055 | − | 0.177864i | \(-0.0569187\pi\) |
−0.177864 | + | 0.984055i | \(0.556919\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 105331. | 0.239622 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 51307.8i | − | 0.116022i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −693927. | + | 693927.i | −1.55977 | + | 1.55977i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 251555. | − | 251555.i | 0.562058 | − | 0.562058i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 12346.6i | − | 0.0274222i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 678354. | 1.49771 | 0.748853 | − | 0.662736i | \(-0.230605\pi\) | ||||
0.748853 | + | 0.662736i | \(0.230605\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 596041. | + | 596041.i | 1.30818 | + | 1.30818i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 348304. | + | 348304.i | 0.759943 | + | 0.759943i | 0.976312 | − | 0.216369i | \(-0.0694214\pi\) |
−0.216369 | + | 0.976312i | \(0.569421\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −150471. | −0.326372 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 134699.i | − | 0.290448i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 218970. | − | 218970.i | 0.469401 | − | 0.469401i | −0.432319 | − | 0.901721i | \(-0.642305\pi\) |
0.901721 | + | 0.432319i | \(0.142305\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 449450. | − | 449450.i | 0.957856 | − | 0.957856i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 200422.i | − | 0.424652i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 84610.7 | 0.178233 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −166441. | − | 166441.i | −0.348581 | − | 0.348581i | 0.511000 | − | 0.859581i | \(-0.329275\pi\) |
−0.859581 | + | 0.511000i | \(0.829275\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −40995.2 | − | 40995.2i | −0.0853625 | − | 0.0853625i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −709638. | −1.46915 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 55683.0i | − | 0.114619i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −426948. | + | 426948.i | −0.873817 | + | 0.873817i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 606601. | − | 606601.i | 1.23443 | − | 1.23443i | 0.272188 | − | 0.962244i | \(-0.412253\pi\) |
0.962244 | − | 0.272188i | \(-0.0877473\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7775.80i | 0.0157338i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −546430. | −1.09940 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −25397.3 | − | 25397.3i | −0.0508100 | − | 0.0508100i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −590171. | − | 590171.i | −1.17405 | − | 1.17405i | −0.981236 | − | 0.192811i | \(-0.938240\pi\) |
−0.192811 | − | 0.981236i | \(-0.561760\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 27968.0 | 0.0553251 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 693806.i | − | 1.36477i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −53620.1 | + | 53620.1i | −0.104885 | + | 0.104885i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −326391. | + | 326391.i | −0.634893 | + | 0.634893i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 319294.i | 0.617637i | 0.951121 | + | 0.308819i | \(0.0999336\pi\) | ||||
−0.951121 | + | 0.308819i | \(0.900066\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 785701. | 1.51143 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 103848. | + | 103848.i | 0.198665 | + | 0.198665i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.01430e6 | − | 1.01430e6i | −1.92969 | − | 1.92969i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −295780. | −0.559628 | −0.279814 | − | 0.960054i | \(-0.590273\pi\) | ||||
−0.279814 | + | 0.960054i | \(0.590273\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 491717.i | − | 0.925253i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 231602. | − | 231602.i | 0.433419 | − | 0.433419i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −353645. | + | 353645.i | −0.658203 | + | 0.658203i | −0.954955 | − | 0.296752i | \(-0.904097\pi\) |
0.296752 | + | 0.954955i | \(0.404097\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 312270.i | 0.578036i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −175247. | −0.322637 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23782.9 | + | 23782.9i | 0.0435488 | + | 0.0435488i | 0.728546 | − | 0.684997i | \(-0.240197\pi\) |
−0.684997 | + | 0.728546i | \(0.740197\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6936.38 | + | 6936.38i | 0.0126327 | + | 0.0126327i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −912931. | −1.65371 | −0.826857 | − | 0.562412i | \(-0.809873\pi\) | ||||
−0.826857 | + | 0.562412i | \(0.809873\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.21494e6i | 2.18899i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −54826.8 | + | 54826.8i | −0.0982543 | + | 0.0982543i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 645172. | − | 645172.i | 1.15004 | − | 1.15004i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 799005.i | − | 1.41667i | −0.705875 | − | 0.708336i | \(-0.749446\pi\) | ||
0.705875 | − | 0.708336i | \(-0.250554\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 671294. | 1.18392 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −226496. | − | 226496.i | −0.397344 | − | 0.397344i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24122.0 | + | 24122.0i | 0.0420940 | + | 0.0420940i | 0.727841 | − | 0.685746i | \(-0.240524\pi\) |
−0.685746 | + | 0.727841i | \(0.740524\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 123910. | 0.215092 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 97444.6i | 0.168263i | 0.996455 | + | 0.0841315i | \(0.0268116\pi\) | ||||
−0.996455 | + | 0.0841315i | \(0.973188\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 85170.8 | − | 85170.8i | 0.146299 | − | 0.146299i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −248452. | + | 248452.i | −0.424542 | + | 0.424542i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 225750.i | 0.383741i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −747937. | −1.26477 | −0.632386 | − | 0.774653i | \(-0.717924\pi\) | ||||
−0.632386 | + | 0.774653i | \(0.717924\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −261751. | − | 261751.i | −0.440331 | − | 0.440331i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 328529. | + | 328529.i | 0.549813 | + | 0.549813i | 0.926387 | − | 0.376574i | \(-0.122898\pi\) |
−0.376574 | + | 0.926387i | \(0.622898\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.01412e6 | 1.68844 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 145832.i | − | 0.241552i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3666.92 | − | 3666.92i | 0.00604263 | − | 0.00604263i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −75606.7 | + | 75606.7i | −0.123953 | + | 0.123953i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.03606e6i | 1.68990i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −411150. | −0.667207 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 76254.3 | + | 76254.3i | 0.123116 | + | 0.123116i | 0.765980 | − | 0.642864i | \(-0.222254\pi\) |
−0.642864 | + | 0.765980i | \(0.722254\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 354689. | + | 354689.i | 0.569762 | + | 0.569762i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.19964e6 | 1.91733 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 34664.5i | 0.0551238i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 225571. | − | 225571.i | 0.356902 | − | 0.356902i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10472.2 | + | 10472.2i | −0.0164862 | + | 0.0164862i | −0.715302 | − | 0.698816i | \(-0.753711\pi\) |
0.698816 | + | 0.715302i | \(0.253711\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 451671.i | − | 0.707503i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −192849. | −0.300574 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −164044. | − | 164044.i | −0.254407 | − | 0.254407i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.28667e6 | + | 1.28667e6i | 1.98552 | + | 1.98552i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −17883.5 | −0.0274604 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 569939.i | 0.870826i | 0.900231 | + | 0.435413i | \(0.143398\pi\) | ||||
−0.900231 | + | 0.435413i | \(0.856602\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 207525. | − | 207525.i | 0.315521 | − | 0.315521i | −0.531523 | − | 0.847044i | \(-0.678380\pi\) |
0.847044 | + | 0.531523i | \(0.178380\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −596522. | + | 596522.i | −0.902496 | + | 0.902496i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 424771.i | − | 0.639498i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 30503.6 | 0.0456991 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 115099. | + | 115099.i | 0.171595 | + | 0.171595i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 597985. | + | 597985.i | 0.887163 | + | 0.887163i | 0.994250 | − | 0.107086i | \(-0.0341521\pi\) |
−0.107086 | + | 0.994250i | \(0.534152\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17487.0 | −0.0258176 | −0.0129088 | − | 0.999917i | \(-0.504109\pi\) | ||||
−0.0129088 | + | 0.999917i | \(0.504109\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 181117.i | 0.266104i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −108277. | + | 108277.i | −0.158316 | + | 0.158316i | −0.781820 | − | 0.623504i | \(-0.785709\pi\) |
0.623504 | + | 0.781820i | \(0.285709\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −368289. | + | 368289.i | −0.535895 | + | 0.535895i | −0.922321 | − | 0.386426i | \(-0.873710\pi\) |
0.386426 | + | 0.922321i | \(0.373710\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 525431.i | − | 0.760876i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −258117. | −0.371987 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 878038. | + | 878038.i | 1.25933 | + | 1.25933i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −517939. | − | 517939.i | −0.739311 | − | 0.739311i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −105615. | −0.150038 | −0.0750188 | − | 0.997182i | \(-0.523902\pi\) | ||||
−0.0750188 | + | 0.997182i | \(0.523902\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 1.05580e6i | − | 1.49276i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 49135.2 | − | 49135.2i | 0.0691414 | − | 0.0691414i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −683441. | + | 683441.i | −0.957167 | + | 0.957167i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 833897.i | 1.16237i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −586797. | −0.814090 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −194997. | − | 194997.i | −0.269258 | − | 0.269258i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.00366e6 | − | 1.00366e6i | −1.37939 | − | 1.37939i | −0.845647 | − | 0.533742i | \(-0.820785\pi\) |
−0.533742 | − | 0.845647i | \(-0.679215\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −32722.9 | −0.0447630 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 677179.i | 0.922024i | 0.887394 | + | 0.461012i | \(0.152513\pi\) | ||||
−0.887394 | + | 0.461012i | \(0.847487\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 750520. | − | 750520.i | 1.01713 | − | 1.01713i | 0.0172783 | − | 0.999851i | \(-0.494500\pi\) |
0.999851 | − | 0.0172783i | \(-0.00550014\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −68771.6 | + | 68771.6i | −0.0927690 | + | 0.0927690i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 61525.8i | − | 0.0826106i | −0.999147 | − | 0.0413053i | \(-0.986848\pi\) | ||
0.999147 | − | 0.0413053i | \(-0.0131516\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 486458. | 0.650149 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −155050. | − | 155050.i | −0.206269 | − | 0.206269i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13301.2 | + | 13301.2i | 0.0176137 | + | 0.0176137i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 492025. | 0.648562 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 95966.7i | 0.125919i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −792629. | + | 792629.i | −1.03527 | + | 1.03527i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 818941. | − | 818941.i | 1.06476 | − | 1.06476i | 0.0670114 | − | 0.997752i | \(-0.478654\pi\) |
0.997752 | − | 0.0670114i | \(-0.0213464\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 825798.i | 1.06880i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 349159. | 0.449853 | 0.224927 | − | 0.974376i | \(-0.427786\pi\) | ||||
0.224927 | + | 0.974376i | \(0.427786\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −353886. | − | 353886.i | −0.453881 | − | 0.453881i | 0.442760 | − | 0.896640i | \(-0.353999\pi\) |
−0.896640 | + | 0.442760i | \(0.853999\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 601848. | + | 601848.i | 0.768423 | + | 0.768423i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.16958e6 | 1.48656 | 0.743282 | − | 0.668978i | \(-0.233268\pi\) | ||||
0.743282 | + | 0.668978i | \(0.233268\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 156832.i | 0.198441i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 36804.6 | − | 36804.6i | 0.0463604 | − | 0.0463604i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 29744.1 | − | 29744.1i | 0.0372990 | − | 0.0372990i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 440196.i | 0.549540i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −347893. | −0.432375 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 881387. | + | 881387.i | 1.09055 | + | 1.09055i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 186454. | + | 186454.i | 0.229679 | + | 0.229679i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −572084. | −0.701591 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 222075.i | − | 0.271146i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −110870. | + | 110870.i | −0.134772 | + | 0.134772i | −0.771274 | − | 0.636503i | \(-0.780380\pi\) |
0.636503 | + | 0.771274i | \(0.280380\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −16197.8 | + | 16197.8i | −0.0196033 | + | 0.0196033i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 162563.i | − | 0.195877i | −0.995192 | − | 0.0979387i | \(-0.968775\pi\) | ||
0.995192 | − | 0.0979387i | \(-0.0312249\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −52149.8 | −0.0625621 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 92415.3 | + | 92415.3i | 0.110383 | + | 0.110383i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −741487. | − | 741487.i | −0.881789 | − | 0.881789i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −615695. | −0.729012 | −0.364506 | − | 0.931201i | \(-0.618762\pi\) | ||||
−0.364506 | + | 0.931201i | \(0.618762\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.15171e6i | 1.35776i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 212275. | − | 212275.i | 0.249170 | − | 0.249170i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 285023. | − | 285023.i | 0.333116 | − | 0.333116i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 501101.i | − | 0.583131i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 228015. | 0.264199 | 0.132099 | − | 0.991236i | \(-0.457828\pi\) | ||||
0.132099 | + | 0.991236i | \(0.457828\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16997.9 | − | 16997.9i | −0.0196108 | − | 0.0196108i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 72934.7 | + | 72934.7i | 0.0837859 | + | 0.0837859i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −236321. | −0.270321 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 431768.i | 0.491781i | 0.969298 | + | 0.245890i | \(0.0790803\pi\) | ||||
−0.969298 | + | 0.245890i | \(0.920920\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −484660. | + | 484660.i | −0.549675 | + | 0.549675i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 532946. | − | 532946.i | 0.601871 | − | 0.601871i | −0.338938 | − | 0.940809i | \(-0.610068\pi\) |
0.940809 | + | 0.338938i | \(0.110068\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 183914.i | 0.206819i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.92104e6 | 2.15116 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.02432e6 | + | 1.02432e6i | 1.14218 | + | 1.14218i | 0.988051 | + | 0.154128i | \(0.0492569\pi\) |
0.154128 | + | 0.988051i | \(0.450743\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 460572. | + | 460572.i | 0.511405 | + | 0.511405i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −425057. | −0.469988 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 264733.i | 0.291490i | 0.989322 | + | 0.145745i | \(0.0465578\pi\) | ||||
−0.989322 | + | 0.145745i | \(0.953442\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.52565e6 | − | 1.52565e6i | 1.67282 | − | 1.67282i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −157411. | + | 157411.i | −0.171875 | + | 0.171875i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 917667.i | − | 0.997810i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 42286.5 | 0.0457883 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −411475. | − | 411475.i | −0.443702 | − | 0.443702i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −711899. | − | 711899.i | −0.764476 | − | 0.764476i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 61058.3 | 0.0652967 | 0.0326484 | − | 0.999467i | \(-0.489606\pi\) | ||||
0.0326484 | + | 0.999467i | \(0.489606\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 30570.9i | 0.0325582i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −404297. | + | 404297.i | −0.428807 | + | 0.428807i | −0.888222 | − | 0.459415i | \(-0.848059\pi\) |
0.459415 | + | 0.888222i | \(0.348059\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −724454. | + | 724454.i | −0.765218 | + | 0.765218i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 508507.i | − | 0.534919i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.83431e6 | −1.92169 | −0.960845 | − | 0.277086i | \(-0.910631\pi\) | ||||
−0.960845 | + | 0.277086i | \(0.910631\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −91716.3 | − | 91716.3i | −0.0956932 | − | 0.0956932i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −54319.9 | − | 54319.9i | −0.0564444 | − | 0.0564444i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 586823. | 0.607296 | 0.303648 | − | 0.952784i | \(-0.401795\pi\) | ||||
0.303648 | + | 0.952784i | \(0.401795\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 1.84182e6i | − | 1.89835i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −557839. | + | 557839.i | −0.572630 | + | 0.572630i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −764953. | + | 764953.i | −0.782064 | + | 0.782064i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.20757e6i | − | 1.22961i | −0.788680 | − | 0.614804i | \(-0.789235\pi\) | ||
0.788680 | − | 0.614804i | \(-0.210765\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.27518e6 | 1.29322 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.07699e6 | − | 2.07699e6i | −2.09792 | − | 2.09792i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −833662. | − | 833662.i | −0.838686 | − | 0.838686i | 0.150000 | − | 0.988686i | \(-0.452073\pi\) |
−0.988686 | + | 0.150000i | \(0.952073\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −291138. | −0.291721 |
(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 | 128.5.f.b.31.5 | 14 | ||
4.3 | odd | 2 | 128.5.f.a.31.3 | 14 | |||
8.3 | odd | 2 | 64.5.f.a.15.5 | 14 | |||
8.5 | even | 2 | 16.5.f.a.11.3 | yes | 14 | ||
16.3 | odd | 4 | inner | 128.5.f.b.95.5 | 14 | ||
16.5 | even | 4 | 64.5.f.a.47.5 | 14 | |||
16.11 | odd | 4 | 16.5.f.a.3.3 | ✓ | 14 | ||
16.13 | even | 4 | 128.5.f.a.95.3 | 14 | |||
24.5 | odd | 2 | 144.5.m.a.91.5 | 14 | |||
24.11 | even | 2 | 576.5.m.a.271.7 | 14 | |||
48.5 | odd | 4 | 576.5.m.a.559.7 | 14 | |||
48.11 | even | 4 | 144.5.m.a.19.5 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.5.f.a.3.3 | ✓ | 14 | 16.11 | odd | 4 | ||
16.5.f.a.11.3 | yes | 14 | 8.5 | even | 2 | ||
64.5.f.a.15.5 | 14 | 8.3 | odd | 2 | |||
64.5.f.a.47.5 | 14 | 16.5 | even | 4 | |||
128.5.f.a.31.3 | 14 | 4.3 | odd | 2 | |||
128.5.f.a.95.3 | 14 | 16.13 | even | 4 | |||
128.5.f.b.31.5 | 14 | 1.1 | even | 1 | trivial | ||
128.5.f.b.95.5 | 14 | 16.3 | odd | 4 | inner | ||
144.5.m.a.19.5 | 14 | 48.11 | even | 4 | |||
144.5.m.a.91.5 | 14 | 24.5 | odd | 2 | |||
576.5.m.a.271.7 | 14 | 24.11 | even | 2 | |||
576.5.m.a.559.7 | 14 | 48.5 | odd | 4 |