Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,4,Mod(383,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.383");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.f (of order \(2\), degree \(1\), 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: | \(45.3134668844\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 39x^{10} + 549x^{8} + 3500x^{6} + 10236x^{4} + 11952x^{2} + 4624 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{26}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 384) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 383.9 | ||
Root | \(3.14286i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.383 |
Dual form | 768.4.f.e.383.10 |
$q$-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 \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.16369 | − | 4.12202i | 0.608853 | − | 0.793283i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −21.4043 | −1.91446 | −0.957232 | − | 0.289323i | \(-0.906570\pi\) | ||||
−0.957232 | + | 0.289323i | \(0.906570\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 20.9034i | − | 1.12868i | −0.825543 | − | 0.564339i | \(-0.809131\pi\) | ||
0.825543 | − | 0.564339i | \(-0.190869\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6.98212 | − | 26.0816i | −0.258597 | − | 0.965985i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 9.94564i | 0.272611i | 0.990667 | + | 0.136306i | \(0.0435229\pi\) | ||||
−0.990667 | + | 0.136306i | \(0.956477\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 67.8290i | − | 1.44711i | −0.690268 | − | 0.723554i | \(-0.742507\pi\) | ||
0.690268 | − | 0.723554i | \(-0.257493\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −67.7167 | + | 88.2292i | −1.16563 | + | 1.51871i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 7.97348i | − | 0.113756i | −0.998381 | − | 0.0568780i | \(-0.981885\pi\) | ||
0.998381 | − | 0.0568780i | \(-0.0181146\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −62.4014 | −0.753466 | −0.376733 | − | 0.926322i | \(-0.622953\pi\) | ||||
−0.376733 | + | 0.926322i | \(0.622953\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −86.1644 | − | 66.1320i | −0.895362 | − | 0.687199i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −101.816 | −0.923049 | −0.461525 | − | 0.887127i | \(-0.652697\pi\) | ||||
−0.461525 | + | 0.887127i | \(0.652697\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 333.146 | 2.66517 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −129.598 | − | 53.7337i | −0.923748 | − | 0.383002i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −122.445 | −0.784051 | −0.392025 | − | 0.919954i | \(-0.628225\pi\) | ||||
−0.392025 | + | 0.919954i | \(0.628225\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 87.5072i | − | 0.506992i | −0.967336 | − | 0.253496i | \(-0.918419\pi\) | ||
0.967336 | − | 0.253496i | \(-0.0815805\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 40.9961 | + | 31.4649i | 0.216258 | + | 0.165980i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 447.424i | 2.16081i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 106.136i | − | 0.471587i | −0.971803 | − | 0.235794i | \(-0.924231\pi\) | ||
0.971803 | − | 0.235794i | \(-0.0757689\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −279.593 | − | 214.590i | −1.14797 | − | 0.881075i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 90.3818i | − | 0.344275i | −0.985073 | − | 0.172137i | \(-0.944933\pi\) | ||
0.985073 | − | 0.172137i | \(-0.0550673\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 451.366 | 1.60076 | 0.800380 | − | 0.599494i | \(-0.204631\pi\) | ||||
0.800380 | + | 0.599494i | \(0.204631\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 149.448 | + | 558.260i | 0.495075 | + | 1.84934i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 428.890 | 1.33106 | 0.665532 | − | 0.746369i | \(-0.268205\pi\) | ||||
0.665532 | + | 0.746369i | \(0.268205\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −93.9530 | −0.273916 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −32.8669 | − | 25.2256i | −0.0902408 | − | 0.0692607i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −362.452 | −0.939370 | −0.469685 | − | 0.882834i | \(-0.655633\pi\) | ||||
−0.469685 | + | 0.882834i | \(0.655633\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 212.880i | − | 0.521904i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −197.419 | + | 257.220i | −0.458750 | + | 0.597712i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 801.483i | 1.76855i | 0.466970 | + | 0.884273i | \(0.345346\pi\) | ||||
−0.466970 | + | 0.884273i | \(0.654654\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 647.903i | 1.35993i | 0.733247 | + | 0.679963i | \(0.238004\pi\) | ||||
−0.733247 | + | 0.679963i | \(0.761996\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −545.195 | + | 145.950i | −1.09029 | + | 0.291873i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1451.84i | 2.77043i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −957.240 | −1.74545 | −0.872727 | − | 0.488208i | \(-0.837651\pi\) | ||||
−0.872727 | + | 0.488208i | \(0.837651\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −322.115 | + | 419.688i | −0.562001 | + | 0.732240i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 224.090 | 0.374572 | 0.187286 | − | 0.982305i | \(-0.440031\pi\) | ||||
0.187286 | + | 0.982305i | \(0.440031\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 108.474 | 0.173916 | 0.0869582 | − | 0.996212i | \(-0.472285\pi\) | ||||
0.0869582 | + | 0.996212i | \(0.472285\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1053.97 | − | 1373.24i | 1.62269 | − | 2.11423i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 207.898 | 0.307690 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 615.569i | 0.876670i | 0.898812 | + | 0.438335i | \(0.144432\pi\) | ||||
−0.898812 | + | 0.438335i | \(0.855568\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −631.500 | + | 364.210i | −0.866255 | + | 0.499602i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 204.385i | − | 0.270291i | −0.990826 | − | 0.135145i | \(-0.956850\pi\) | ||
0.990826 | − | 0.135145i | \(-0.0431501\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 170.667i | 0.217782i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −387.378 | + | 504.721i | −0.477371 | + | 0.621974i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 454.067i | 0.540798i | 0.962748 | + | 0.270399i | \(0.0871556\pi\) | ||||
−0.962748 | + | 0.270399i | \(0.912844\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1417.86 | −1.63332 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −360.707 | − | 276.846i | −0.402189 | − | 0.308684i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1335.66 | 1.44248 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 740.490 | 0.775106 | 0.387553 | − | 0.921847i | \(-0.373320\pi\) | ||||
0.387553 | + | 0.921847i | \(0.373320\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 259.398 | − | 69.4417i | 0.263338 | − | 0.0704965i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −52.9454 | −0.0521610 | −0.0260805 | − | 0.999660i | \(-0.508303\pi\) | ||||
−0.0260805 | + | 0.999660i | \(0.508303\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 808.292i | − | 0.773236i | −0.922240 | − | 0.386618i | \(-0.873643\pi\) | ||
0.922240 | − | 0.386618i | \(-0.126357\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1844.29 | + | 1415.51i | 1.71414 | + | 1.31562i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 728.059i | − | 0.657796i | −0.944366 | − | 0.328898i | \(-0.893323\pi\) | ||
0.944366 | − | 0.328898i | \(-0.106677\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1488.85i | 1.30831i | 0.756358 | + | 0.654157i | \(0.226977\pi\) | ||||
−0.756358 | + | 0.654157i | \(0.773023\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −437.497 | − | 335.783i | −0.374102 | − | 0.287127i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 38.0071i | − | 0.0316408i | −0.999875 | − | 0.0158204i | \(-0.994964\pi\) | ||
0.999875 | − | 0.0158204i | \(-0.00503600\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2179.31 | 1.76714 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1769.09 | + | 473.591i | −1.39788 | + | 0.374218i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −166.673 | −0.128394 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1232.08 | 0.925683 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −372.556 | − | 285.940i | −0.273107 | − | 0.209613i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4455.23 | −3.18790 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 226.671i | 0.158376i | 0.996860 | + | 0.0791882i | \(0.0252328\pi\) | ||||
−0.996860 | + | 0.0791882i | \(0.974767\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1427.98 | − | 1860.54i | 0.974626 | − | 1.26986i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 1580.10i | − | 1.05385i | −0.849912 | − | 0.526925i | \(-0.823345\pi\) | ||
0.849912 | − | 0.526925i | \(-0.176655\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1304.40i | 0.850421i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2773.96 | + | 1150.13i | 1.76848 | + | 0.733243i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 543.435i | − | 0.338896i | −0.985539 | − | 0.169448i | \(-0.945801\pi\) | ||
0.985539 | − | 0.169448i | \(-0.0541985\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 29.7527 | 0.0181554 | 0.00907768 | − | 0.999959i | \(-0.497110\pi\) | ||||
0.00907768 | + | 0.999959i | \(0.497110\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1356.87 | − | 1767.89i | 0.810422 | − | 1.05591i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 674.603 | 0.394498 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2620.86 | 1.50104 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −297.238 | + | 387.276i | −0.166774 | + | 0.217293i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −489.426 | −0.269096 | −0.134548 | − | 0.990907i | \(-0.542958\pi\) | ||||
−0.134548 | + | 0.990907i | \(0.542958\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 396.852i | 0.213877i | 0.994266 | + | 0.106938i | \(0.0341047\pi\) | ||||
−0.994266 | + | 0.106938i | \(0.965895\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −207.961 | + | 55.6718i | −0.109887 | + | 0.0294170i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1873.04i | 0.970618i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 2542.51i | − | 1.29245i | −0.763148 | − | 0.646224i | \(-0.776347\pi\) | ||
0.763148 | − | 0.646224i | \(-0.223653\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1146.69 | + | 1494.03i | −0.571938 | + | 0.745187i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2128.31i | 1.04183i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1807.94 | −0.868765 | −0.434383 | − | 0.900728i | \(-0.643033\pi\) | ||||
−0.434383 | + | 0.900728i | \(0.643033\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −877.496 | − | 673.486i | −0.414018 | − | 0.317763i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −25.5944 | −0.0118596 | −0.00592980 | − | 0.999982i | \(-0.501888\pi\) | ||||
−0.00592980 | + | 0.999982i | \(0.501888\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2403.78 | −1.09412 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 435.694 | + | 1627.53i | 0.194844 | + | 0.727837i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −677.278 | −0.297644 | −0.148822 | − | 0.988864i | \(-0.547548\pi\) | ||||
−0.148822 | + | 0.988864i | \(0.547548\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 6963.89i | − | 3.00812i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3303.73 | + | 2535.64i | 1.40296 | + | 1.07678i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 3240.41i | − | 1.35307i | −0.736411 | − | 0.676535i | \(-0.763481\pi\) | ||
0.736411 | − | 0.676535i | \(-0.236519\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2123.69i | 0.872114i | 0.899919 | + | 0.436057i | \(0.143625\pi\) | ||||
−0.899919 | + | 0.436057i | \(0.856375\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2670.67 | + | 2049.76i | 1.07881 | + | 0.827994i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2271.78i | 0.902836i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 79.3014 | 0.0310112 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1123.22 | + | 2709.05i | −0.432286 | + | 1.04261i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3080.73 | −1.16709 | −0.583543 | − | 0.812082i | \(-0.698334\pi\) | ||||
−0.583543 | + | 0.812082i | \(0.698334\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2614.09 | −0.974955 | −0.487478 | − | 0.873135i | \(-0.662083\pi\) | ||||
−0.487478 | + | 0.873135i | \(0.662083\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5984.50 | + | 4593.16i | 2.19774 | + | 1.68679i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4223.51 | 1.52748 | 0.763738 | − | 0.645527i | \(-0.223362\pi\) | ||||
0.763738 | + | 0.645527i | \(0.223362\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 783.071i | − | 0.278947i | −0.990226 | − | 0.139474i | \(-0.955459\pi\) | ||
0.990226 | − | 0.139474i | \(-0.0445410\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3028.41 | + | 3945.76i | −1.06272 | + | 1.38464i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2559.52i | 0.884941i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1934.56i | 0.659101i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 710.893 | + | 2655.53i | 0.238698 | + | 0.891652i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 620.622i | − | 0.205403i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3515.60 | −1.14703 | −0.573516 | − | 0.819195i | \(-0.694421\pi\) | ||||
−0.573516 | + | 0.819195i | \(0.694421\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 708.952 | − | 923.705i | 0.228059 | − | 0.297142i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9661.19 | −3.06459 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1829.20 | −0.572232 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 343.177 | − | 447.131i | 0.105889 | − | 0.137965i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −540.834 | −0.164617 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1864.10i | − | 0.559772i | −0.960033 | − | 0.279886i | \(-0.909703\pi\) | ||
0.960033 | − | 0.279886i | \(-0.0902967\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2326.07 | − | 8688.98i | −0.689205 | − | 2.57451i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 2871.51i | − | 0.839600i | −0.907617 | − | 0.419800i | \(-0.862100\pi\) | ||
0.907617 | − | 0.419800i | \(-0.137900\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3048.58i | 0.879720i | 0.898066 | + | 0.439860i | \(0.144972\pi\) | ||||
−0.898066 | + | 0.439860i | \(0.855028\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 657.725 | − | 856.960i | 0.187338 | − | 0.244086i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 2078.46i | − | 0.584398i | −0.956358 | − | 0.292199i | \(-0.905613\pi\) | ||
0.956358 | − | 0.292199i | \(-0.0943870\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9180.11 | −2.54827 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2537.39 | + | 1947.47i | 0.695448 | + | 0.533763i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2778.79 | −0.752072 | −0.376036 | − | 0.926605i | \(-0.622713\pi\) | ||||
−0.376036 | + | 0.926605i | \(0.622713\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2838.97 | −0.758815 | −0.379408 | − | 0.925230i | \(-0.623872\pi\) | ||||
−0.379408 | + | 0.925230i | \(0.623872\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −496.589 | + | 3755.30i | −0.131095 | + | 0.991370i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2011.00 | 0.524401 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4232.63i | 1.09035i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −842.478 | − | 646.610i | −0.214417 | − | 0.164567i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 5339.24i | − | 1.34267i | −0.741155 | − | 0.671334i | \(-0.765722\pi\) | ||
0.741155 | − | 0.671334i | \(-0.234278\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 1012.63i | − | 0.251634i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 703.494 | + | 539.938i | 0.172763 | + | 0.132597i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6223.99i | 1.51067i | 0.655339 | + | 0.755335i | \(0.272526\pi\) | ||||
−0.655339 | + | 0.755335i | \(0.727474\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2218.61 | −0.532270 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 854.926 | + | 3193.56i | 0.202753 | + | 0.757381i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4779.81 | 1.12067 | 0.560334 | − | 0.828267i | \(-0.310673\pi\) | ||||
0.560334 | + | 0.828267i | \(0.310673\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7758.05 | 1.79839 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1871.67 | + | 1436.53i | 0.429006 | + | 0.329266i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3916.03 | 0.887601 | 0.443800 | − | 0.896126i | \(-0.353630\pi\) | ||||
0.443800 | + | 0.896126i | \(0.353630\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6412.78i | 1.43745i | 0.695295 | + | 0.718725i | \(0.255274\pi\) | ||||
−0.695295 | + | 0.718725i | \(0.744726\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4485.67 | + | 5844.45i | −0.994450 | + | 1.29568i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3313.35i | 0.726555i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 3745.22i | − | 0.812376i | −0.913789 | − | 0.406188i | \(-0.866858\pi\) | ||
0.913789 | − | 0.406188i | \(-0.133142\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2282.33 | + | 610.986i | −0.489747 | + | 0.131107i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 6656.43i | − | 1.41313i | −0.707648 | − | 0.706565i | \(-0.750244\pi\) | ||
0.707648 | − | 0.706565i | \(-0.249756\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6460.77 | 1.35708 | 0.678539 | − | 0.734564i | \(-0.262613\pi\) | ||||
0.678539 | + | 0.734564i | \(0.262613\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4225.62 | − | 5505.62i | 0.878260 | − | 1.14430i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1889.29 | −0.388576 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4849.42 | 0.987060 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2342.68 | − | 3052.31i | 0.471925 | − | 0.614879i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2620.84 | −0.522564 | −0.261282 | − | 0.965263i | \(-0.584145\pi\) | ||||
−0.261282 | + | 0.965263i | \(0.584145\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 17155.2i | − | 3.38582i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 534.416 | − | 1288.94i | 0.104411 | − | 0.251824i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6906.09i | 1.33575i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 9435.09i | − | 1.80674i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −167.503 | + | 218.242i | −0.0317584 | + | 0.0413785i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 13867.9i | − | 2.60353i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −952.063 | −0.176994 | −0.0884969 | − | 0.996076i | \(-0.528206\pi\) | ||||
−0.0884969 | + | 0.996076i | \(0.528206\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3331.80 | − | 2557.18i | −0.613395 | − | 0.470787i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −464.965 | −0.0847773 | −0.0423887 | − | 0.999101i | \(-0.513497\pi\) | ||||
−0.0423887 | + | 0.999101i | \(0.513497\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5656.16 | −1.02142 | −0.510711 | − | 0.859752i | \(-0.670618\pi\) | ||||
−0.510711 | + | 0.859752i | \(0.670618\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 11669.5 | − | 3123.97i | 2.08731 | − | 0.558780i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4593.57 | 0.813883 | 0.406941 | − | 0.913454i | \(-0.366595\pi\) | ||||
0.406941 | + | 0.913454i | \(0.366595\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1217.79i | − | 0.213741i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3001.08 | − | 2303.35i | −0.521818 | − | 0.400501i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 497.556i | 0.0857113i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 22597.0i | − | 3.85678i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6137.09 | + | 4710.27i | 1.03786 | + | 0.796571i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 8965.26i | − | 1.50234i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6709.02 | −1.11408 | −0.557041 | − | 0.830485i | \(-0.688063\pi\) | ||||
−0.557041 | + | 0.830485i | \(0.688063\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2768.21 | + | 741.058i | −0.455546 | + | 0.121951i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 20489.1 | 3.34161 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3712.30 | −0.600064 | −0.300032 | − | 0.953929i | \(-0.596997\pi\) | ||||
−0.300032 | + | 0.953929i | \(0.596997\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −156.666 | − | 120.243i | −0.0251001 | − | 0.0192646i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 870.316 | 0.138212 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 5205.93i | − | 0.819516i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6894.66 | − | 8983.16i | 1.07593 | − | 1.40185i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 6331.12i | − | 0.979459i | −0.871874 | − | 0.489729i | \(-0.837096\pi\) | ||
0.871874 | − | 0.489729i | \(-0.162904\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8328.66i | 1.27743i | 0.769444 | + | 0.638714i | \(0.220533\pi\) | ||||
−0.769444 | + | 0.638714i | \(0.779467\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3644.70 | + | 8790.52i | −0.554245 | + | 1.33676i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1494.95i | 0.225406i | 0.993629 | + | 0.112703i | \(0.0359508\pi\) | ||||
−0.993629 | + | 0.112703i | \(0.964049\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4796.51 | −0.717104 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −527.302 | + | 687.030i | −0.0781730 | + | 0.101853i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2701.95 | 0.397223 | 0.198612 | − | 0.980078i | \(-0.436357\pi\) | ||||
0.198612 | + | 0.980078i | \(0.436357\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2965.07 | −0.432289 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3897.93 | − | 5078.68i | 0.563605 | − | 0.734329i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2321.81 | −0.332956 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 11089.3i | − | 1.57727i | −0.614861 | − | 0.788636i | \(-0.710788\pi\) | ||
0.614861 | − | 0.788636i | \(-0.289212\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2357.30 | + | 631.057i | −0.332564 | + | 0.0890285i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7576.49i | 1.06025i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 1299.98i | − | 0.180456i | −0.995921 | − | 0.0902282i | \(-0.971240\pi\) | ||
0.995921 | − | 0.0902282i | \(-0.0287597\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −14095.0 | + | 18364.6i | −1.94096 | + | 2.52891i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8305.33i | 1.13461i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2953.18 | −0.400250 | −0.200125 | − | 0.979770i | \(-0.564135\pi\) | ||||
−0.200125 | + | 0.979770i | \(0.564135\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 934.343 | + | 717.117i | 0.125637 | + | 0.0964279i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2647.22 | 0.353176 | 0.176588 | − | 0.984285i | \(-0.443494\pi\) | ||||
0.176588 | + | 0.984285i | \(0.443494\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4449.92 | −0.589062 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3151.49 | − | 11772.3i | −0.413952 | − | 1.54631i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3585.34 | 0.467310 | 0.233655 | − | 0.972320i | \(-0.424931\pi\) | ||||
0.233655 | + | 0.972320i | \(0.424931\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 811.829i | 0.105002i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6513.22 | − | 4998.96i | −0.836001 | − | 0.641639i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 13175.9i | − | 1.67835i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6502.91i | 0.822094i | 0.911614 | + | 0.411047i | \(0.134837\pi\) | ||||
−0.911614 | + | 0.411047i | \(0.865163\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5376.77 | + | 4126.73i | 0.674625 | + | 0.517781i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 6673.49i | − | 0.831068i | −0.909578 | − | 0.415534i | \(-0.863595\pi\) | ||
0.909578 | − | 0.415534i | \(-0.136405\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5935.53 | −0.733672 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13516.8 | − | 7795.68i | 1.65841 | − | 0.956470i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1055.59 | 0.128560 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2660.34 | 0.321627 | 0.160814 | − | 0.986985i | \(-0.448588\pi\) | ||||
0.160814 | + | 0.986985i | \(0.448588\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2240.05 | − | 1719.26i | −0.268841 | − | 0.206338i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 16753.7 | 1.99612 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4374.72i | 0.517461i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 94.1285 | − | 122.641i | 0.0110539 | − | 0.0144023i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8957.94i | 1.04445i | 0.852808 | + | 0.522224i | \(0.174898\pi\) | ||||
−0.852808 | + | 0.522224i | \(0.825102\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12070.2i | 1.39730i | 0.715461 | + | 0.698652i | \(0.246217\pi\) | ||||
−0.715461 | + | 0.698652i | \(0.753783\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2994.56 | − | 11186.1i | −0.344209 | − | 1.28579i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 2656.33i | − | 0.303179i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13543.4 | 1.53492 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2134.24 | − | 2780.73i | 0.240191 | − | 0.312948i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14197.2 | −1.58667 | −0.793334 | − | 0.608787i | \(-0.791656\pi\) | ||||
−0.793334 | + | 0.608787i | \(0.791656\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7129.67 | −0.791294 | −0.395647 | − | 0.918403i | \(-0.629480\pi\) | ||||
−0.395647 | + | 0.918403i | \(0.629480\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8291.58 | − | 10803.2i | 0.913909 | − | 1.19075i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6353.47 | 0.695487 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5206.56i | 0.566049i | 0.959113 | + | 0.283025i | \(0.0913378\pi\) | ||||
−0.959113 | + | 0.283025i | \(0.908662\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 655.992 | + | 2450.45i | 0.0708338 | + | 0.264598i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17034.3i | 1.82692i | 0.406930 | + | 0.913459i | \(0.366599\pi\) | ||||
−0.406930 | + | 0.913459i | \(0.633401\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 9719.01i | − | 1.03534i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1548.39 | + | 2017.42i | −0.163840 | + | 0.213470i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9312.78i | 0.978836i | 0.872049 | + | 0.489418i | \(0.162791\pi\) | ||||
−0.872049 | + | 0.489418i | \(0.837209\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 898.905 | 0.0938532 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1635.83 | + | 1255.52i | 0.169665 | + | 0.130219i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 30348.4 | 3.12693 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13276.6 | −1.35898 | −0.679488 | − | 0.733687i | \(-0.737798\pi\) | ||||
−0.679488 | + | 0.733687i | \(0.737798\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −428.444 | + | 1033.35i | −0.0435688 | + | 0.105082i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 507.329 | 0.0512552 | 0.0256276 | − | 0.999672i | \(-0.491842\pi\) | ||||
0.0256276 | + | 0.999672i | \(0.491842\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 4468.90i | − | 0.448569i | −0.974524 | − | 0.224284i | \(-0.927996\pi\) | ||
0.974524 | − | 0.224284i | \(-0.0720044\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7720.69 | + | 5925.70i | 0.769975 | + | 0.590963i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 12258.9i | − | 1.21472i | −0.794428 | − | 0.607358i | \(-0.792229\pi\) | ||
0.794428 | − | 0.607358i | \(-0.207771\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20009.6i | 1.97006i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10480.3 | − | 8043.71i | −1.02528 | − | 0.786910i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4489.12i | 0.436385i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20788.8 | −2.00811 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2530.68 | + | 9453.33i | 0.242918 | + | 0.907418i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5781.56 | −0.551495 | −0.275747 | − | 0.961230i | \(-0.588925\pi\) | ||||
−0.275747 | + | 0.961230i | \(0.588925\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7199.13 | −0.682437 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8772.92 | + | 6733.30i | 0.826463 | + | 0.634318i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15849.7 | −1.48391 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 8699.77i | − | 0.809495i | −0.914429 | − | 0.404747i | \(-0.867359\pi\) | ||
0.914429 | − | 0.404747i | \(-0.132641\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5719.76 | + | 7452.36i | −0.528950 | + | 0.689177i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6084.95i | 0.559287i | 0.960104 | + | 0.279643i | \(0.0902163\pi\) | ||||
−0.960104 | + | 0.279643i | \(0.909784\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 976.313i | 0.0891905i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5552.25 | + | 1486.35i | −0.504152 | + | 0.134963i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 4684.25i | − | 0.422772i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6970.12 | −0.625301 | −0.312651 | − | 0.949868i | \(-0.601217\pi\) | ||||
−0.312651 | + | 0.949868i | \(0.601217\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −80.9728 | + | 105.501i | −0.00722075 | + | 0.00940803i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15721.2 | −1.39359 | −0.696795 | − | 0.717271i | \(-0.745391\pi\) | ||||
−0.696795 | + | 0.717271i | \(0.745391\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1133.26 | 0.0998604 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7604.82 | + | 9908.43i | −0.666157 | + | 0.867947i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11249.3 | 0.979602 | 0.489801 | − | 0.871834i | \(-0.337069\pi\) | ||||
0.489801 | + | 0.871834i | \(0.337069\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 2267.47i | − | 0.196296i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8087.11 | + | 3353.05i | 0.696013 | + | 0.288579i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17301.0i | 1.48033i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4265.58i | 0.362863i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2142.70 | + | 2791.75i | −0.181222 | + | 0.236116i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12276.2i | 1.03231i | 0.856496 | + | 0.516153i | \(0.172636\pi\) | ||||
−0.856496 | + | 0.516153i | \(0.827364\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −770.278 | −0.0644013 | −0.0322007 | − | 0.999481i | \(-0.510252\pi\) | ||||
−0.0322007 | + | 0.999481i | \(0.510252\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −28705.3 | − | 22031.6i | −2.38629 | − | 1.83150i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −697.737 | −0.0576735 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1800.47 | −0.147980 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 20904.0 | − | 5596.05i | 1.70839 | − | 0.457341i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6130.51 | −0.498202 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15583.6i | 1.25933i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13357.0 | − | 10251.6i | −1.07337 | − | 0.823820i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 934.423i | − | 0.0746725i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 14469.7i | − | 1.14991i | −0.818184 | − | 0.574956i | \(-0.805019\pi\) | ||
0.818184 | − | 0.574956i | \(-0.194981\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8753.90 | + | 6718.70i | 0.691834 | + | 0.530989i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 31867.9i | − | 2.50472i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1150.14 | −0.0899021 | −0.0449511 | − | 0.998989i | \(-0.514313\pi\) | ||||
−0.0449511 | + | 0.998989i | \(0.514313\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 16898.3 | − | 4523.74i | 1.31367 | − | 0.351673i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7640.74 | 0.590756 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12867.5 | 0.989479 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9364.33 | + | 7187.21i | 0.716205 | + | 0.549694i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −24347.5 | −1.85213 | −0.926066 | − | 0.377361i | \(-0.876832\pi\) | ||||
−0.926066 | + | 0.377361i | \(0.876832\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 30615.7i | − | 2.31647i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 250.885 | − | 326.882i | 0.0188812 | − | 0.0246007i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15515.2i | 1.16144i | 0.814105 | + | 0.580718i | \(0.197228\pi\) | ||||
−0.814105 | + | 0.580718i | \(0.802772\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 813.518i | 0.0605752i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7613.23 | + | 13200.5i | 0.563890 | + | 0.977724i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10960.4i | 0.807531i | 0.914863 | + | 0.403765i | \(0.132299\pi\) | ||||
−0.914863 | + | 0.403765i | \(0.867701\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24367.3 | −1.78588 | −0.892941 | − | 0.450174i | \(-0.851362\pi\) | ||||
−0.892941 | + | 0.450174i | \(0.851362\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9746.46 | + | 12698.8i | −0.710583 | + | 0.925830i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −33919.7 | −2.46008 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17109.4 | 1.23445 | 0.617223 | − | 0.786788i | \(-0.288258\pi\) | ||||
0.617223 | + | 0.786788i | \(0.288258\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8270.17 | + | 10775.3i | −0.593604 | + | 0.773416i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4272.34 | −0.305071 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 3604.82i | − | 0.256083i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 37866.2 | − | 10136.9i | 2.67620 | − | 0.716426i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 13267.9i | − | 0.932921i | −0.884542 | − | 0.466460i | \(-0.845529\pi\) | ||
0.884542 | − | 0.466460i | \(-0.154471\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5460.57i | 0.382002i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13361.9 | − | 17409.4i | 0.930007 | − | 1.21172i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16312.5i | 1.12963i | 0.825216 | + | 0.564817i | \(0.191053\pi\) | ||||
−0.825216 | + | 0.564817i | \(0.808947\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3567.53 | 0.245806 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3227.84 | − | 2477.40i | −0.221284 | − | 0.169838i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15038.9 | −1.02583 | −0.512915 | − | 0.858440i | \(-0.671434\pi\) | ||||
−0.512915 | + | 0.858440i | \(0.671434\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4408.70 | 0.299226 | 0.149613 | − | 0.988745i | \(-0.452197\pi\) | ||||
0.149613 | + | 0.988745i | \(0.452197\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6683.57 | + | 24966.3i | 0.451370 | + | 1.68608i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −26372.0 | −1.77219 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1271.09i | − | 0.0849950i | −0.999097 | − | 0.0424975i | \(-0.986469\pi\) | ||
0.999097 | − | 0.0424975i | \(-0.0135315\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10550.4 | + | 8097.53i | 0.702009 | + | 0.538799i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 29091.2i | − | 1.92619i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 21306.8i | − | 1.40387i | −0.712239 | − | 0.701937i | \(-0.752319\pi\) | ||
0.712239 | − | 0.701937i | \(-0.247681\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7974.31 | + | 6120.36i | 0.522854 | + | 0.401295i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26964.4i | 1.75940i | 0.475533 | + | 0.879698i | \(0.342255\pi\) | ||||
−0.475533 | + | 0.879698i | \(0.657745\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17633.6 | 1.14500 | 0.572500 | − | 0.819905i | \(-0.305974\pi\) | ||||
0.572500 | + | 0.819905i | \(0.305974\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13195.2 | + | 5470.95i | 0.852665 | + | 0.353529i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9491.56 | 0.610387 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 53718.1 | 3.43796 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2558.22 | − | 1963.46i | −0.162943 | − | 0.125060i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −846.277 | −0.0536459 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 168.115i | 0.0106062i | 0.999986 | + | 0.00530312i | \(0.00168804\pi\) | ||||
−0.999986 | + | 0.00530312i | \(0.998312\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11122.3 | + | 14491.4i | −0.698373 | + | 0.909921i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 4851.75i | − | 0.303206i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6372.74i | 0.396385i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1564.63 | − | 5844.63i | −0.0968633 | − | 0.361831i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 823.334i | − | 0.0507328i | −0.999678 | − | 0.0253664i | \(-0.991925\pi\) | ||
0.999678 | − | 0.0253664i | \(-0.00807525\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17860.7 | 1.09543 | 0.547713 | − | 0.836666i | \(-0.315499\pi\) | ||||
0.547713 | + | 0.836666i | \(0.315499\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −30565.0 | + | 39823.6i | −1.86589 | + | 2.43109i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2518.14 | −0.153011 | −0.0765057 | − | 0.997069i | \(-0.524376\pi\) | ||||
−0.0765057 | + | 0.997069i | \(0.524376\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7971.26 | −0.482126 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5787.03 | + | 7540.01i | −0.348405 | + | 0.453942i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18937.3 | 1.13488 | 0.567439 | − | 0.823416i | \(-0.307934\pi\) | ||||
0.567439 | + | 0.823416i | \(0.307934\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 33821.1i | 2.01756i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −757.377 | − | 2829.17i | −0.0449743 | − | 0.168001i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 10400.8i | − | 0.614807i | −0.951579 | − | 0.307404i | \(-0.900540\pi\) | ||
0.951579 | − | 0.307404i | \(-0.0994602\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3225.88i | 0.189822i | 0.995486 | + | 0.0949108i | \(0.0302566\pi\) | ||||
−0.995486 | + | 0.0949108i | \(0.969743\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1711.03 | + | 2229.33i | −0.100228 | + | 0.130588i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 27919.9i | − | 1.62810i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12466.9 | 0.723717 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7683.85 | − | 5897.43i | −0.444058 | − | 0.340819i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6443.81 | −0.370731 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1215.38 | 0.0696128 | 0.0348064 | − | 0.999394i | \(-0.488919\pi\) | ||||
0.0348064 | + | 0.999394i | \(0.488919\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −43175.1 | − | 17901.2i | −2.46194 | − | 1.02076i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3901.92 | 0.221511 | 0.110755 | − | 0.993848i | \(-0.464673\pi\) | ||||
0.110755 | + | 0.993848i | \(0.464673\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 15478.8i | − | 0.874846i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11836.4 | − | 9084.58i | −0.666040 | − | 0.511192i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 31547.8i | − | 1.76742i | −0.468039 | − | 0.883708i | \(-0.655040\pi\) | ||
0.468039 | − | 0.883708i | \(-0.344960\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11631.9i | 0.648805i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12566.3 | + | 9644.76i | 0.697867 | + | 0.535620i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 24584.8i | 1.35937i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2791.51 | 0.153682 | 0.0768408 | − | 0.997043i | \(-0.475517\pi\) | ||||
0.0768408 | + | 0.997043i | \(0.475517\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1451.57 | − | 5422.31i | −0.0795679 | − | 0.297224i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −636.838 | −0.0347578 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −720.657 | −0.0391633 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8567.48 | − | 6575.62i | −0.463593 | − | 0.355812i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9830.35 | 0.529653 | 0.264827 | − | 0.964296i | \(-0.414685\pi\) | ||||
0.264827 | + | 0.964296i | \(0.414685\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6623.06i | 0.355325i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −29043.0 | + | 37840.6i | −1.55152 | + | 2.02150i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1106.74i | 0.0588730i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3029.84i | 0.160491i | 0.996775 | + | 0.0802455i | \(0.0255704\pi\) | ||||
−0.996775 | + | 0.0802455i | \(0.974430\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 16055.0 | − | 4297.98i | 0.846850 | − | 0.226704i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8909.65i | 0.467979i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14439.4 | −0.755251 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8791.24 | + | 11454.2i | −0.457901 | + | 0.596606i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −28359.2 | −1.47096 | −0.735479 | − | 0.677548i | \(-0.763043\pi\) | ||||
−0.735479 | + | 0.677548i | \(0.763043\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16896.1 | −0.872735 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8981.64 | + | 11702.3i | −0.462006 | + | 0.601955i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −40792.1 | −2.08963 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24702.5i | 1.26020i | 0.776514 | + | 0.630100i | \(0.216986\pi\) | ||||
−0.776514 | + | 0.630100i | \(0.783014\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13908.4 | + | 13927.6i | 0.706619 | + | 0.707594i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 3598.96i | − | 0.182096i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30507.1i | 1.53725i | 0.639698 | + | 0.768627i | \(0.279060\pi\) | ||||
−0.639698 | + | 0.768627i | \(0.720940\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6362.19 | − | 8289.40i | 0.319283 | − | 0.415999i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 9520.36i | − | 0.475831i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4105.52 | 0.204363 | 0.102181 | − | 0.994766i | \(-0.467418\pi\) | ||||
0.102181 | + | 0.994766i | \(0.467418\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17447.0 | + | 13390.7i | 0.864954 | + | 0.663860i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4140.87 | 0.204460 | 0.102230 | − | 0.994761i | \(-0.467402\pi\) | ||||
0.102230 | + | 0.994761i | \(0.467402\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10475.8 | 0.515175 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5330.68 | + | 1427.04i | −0.261097 | + | 0.0698964i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15218.9 | −0.742440 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22033.0i | 1.07057i | 0.844672 | + | 0.535284i | \(0.179796\pi\) | ||||
−0.844672 | + | 0.535284i | \(0.820204\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −22008.5 | − | 16891.7i | −1.06512 | − | 0.817487i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 8494.36i | − | 0.409459i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37525.3i | 1.80169i | 0.434137 | + | 0.900847i | \(0.357053\pi\) | ||||
−0.434137 | + | 0.900847i | \(0.642947\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4174.07 | − | 3203.64i | −0.199617 | − | 0.153208i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32680.8i | 1.55674i | 0.627806 | + | 0.778369i | \(0.283953\pi\) | ||||
−0.627806 | + | 0.778369i | \(0.716047\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 31122.1 | 1.47667 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4451.27 | − | 1191.62i | 0.210374 | − | 0.0563177i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 54363.8 | 2.55928 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27457.2 | −1.28756 | −0.643779 | − | 0.765212i | \(-0.722634\pi\) | ||||
−0.643779 | + | 0.765212i | \(0.722634\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 25655.4 | + | 19690.8i | 1.19839 | + | 0.919775i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8851.25 | −0.411847 | −0.205923 | − | 0.978568i | \(-0.566020\pi\) | ||||
−0.205923 | + | 0.978568i | \(0.566020\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 29152.7i | − | 1.35122i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7019.01 | + | 9145.18i | −0.324074 | + | 0.422241i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5639.95i | 0.259399i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2228.72i | 0.102113i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 15868.7 | + | 6579.42i | 0.724265 | + | 0.300293i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 54420.8i | 2.47434i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3892.16 | 0.176290 | 0.0881452 | − | 0.996108i | \(-0.471906\pi\) | ||||
0.0881452 | + | 0.996108i | \(0.471906\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15121.8 | − | 19702.5i | 0.682321 | − | 0.889007i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −794.479 | −0.0357123 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 43946.6 | 1.96796 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 24544.1 | − | 31978.8i | 1.09495 | − | 1.42663i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −16462.8 | −0.731672 | −0.365836 | − | 0.930679i | \(-0.619217\pi\) | ||||
−0.365836 | + | 0.930679i | \(0.619217\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 3419.74i | − | 0.151417i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11842.8 | − | 3170.35i | 0.522403 | − | 0.139849i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1078.84i | 0.0474116i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 45555.0i | − | 1.99454i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12389.1 | − | 16142.0i | 0.540418 | − | 0.704119i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2287.89i | 0.0994287i | 0.998763 | + | 0.0497144i | \(0.0158311\pi\) | ||||
−0.998763 | + | 0.0497144i | \(0.984169\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2892.28 | 0.125230 | 0.0626150 | − | 0.998038i | \(-0.480056\pi\) | ||||
0.0626150 | + | 0.998038i | \(0.480056\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 26433.6 | + | 20288.1i | 1.14031 | + | 0.875195i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 38697.8 | 1.66322 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −28165.8 | −1.20612 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9899.67 | + | 36980.0i | 0.422372 | + | 1.57776i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 37351.7 | 1.58780 | 0.793899 | − | 0.608049i | \(-0.208048\pi\) | ||||
0.793899 | + | 0.608049i | \(0.208048\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 25859.6i | − | 1.09527i | −0.836717 | − | 0.547636i | \(-0.815528\pi\) | ||
0.836717 | − | 0.547636i | \(-0.184472\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 13657.7 | + | 10482.4i | 0.576364 | + | 0.442365i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 32182.0i | − | 1.35318i | −0.736361 | − | 0.676589i | \(-0.763457\pi\) | ||
0.736361 | − | 0.676589i | \(-0.236543\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 16710.7i | − | 0.700105i | −0.936730 | − | 0.350053i | \(-0.886164\pi\) | ||
0.936730 | − | 0.350053i | \(-0.113836\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15437.9 | − | 11848.7i | −0.644445 | − | 0.494617i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 749.133i | 0.0311595i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 547.831 | 0.0227048 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4702.08 | + | 11340.8i | −0.194179 | + | 0.468333i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19182.4 | −0.789334 | −0.394667 | − | 0.918824i | \(-0.629140\pi\) | ||||
−0.394667 | + | 0.918824i | \(0.629140\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9396.22 | −0.385265 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −27438.0 | − | 21058.9i | −1.12101 | − | 0.860388i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 51451.3 | 2.09465 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 25754.8i | − | 1.04480i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 20439.9 | − | 26631.4i | 0.826260 | − | 1.07655i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10806.4i | 0.435298i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16306.8i | 0.654552i | 0.944929 | + | 0.327276i | \(0.106131\pi\) | ||||
−0.944929 | + | 0.327276i | \(0.893869\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9325.75 | − | 34836.2i | −0.373022 | − | 1.39342i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 42374.8i | − | 1.68903i | −0.535534 | − | 0.844514i | \(-0.679890\pi\) | ||
0.535534 | − | 0.844514i | \(-0.320110\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21561.9 | 0.856442 | 0.428221 | − | 0.903674i | \(-0.359140\pi\) | ||||
0.428221 | + | 0.903674i | \(0.359140\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5977.12 | + | 7787.69i | −0.236585 | + | 0.308251i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16679.1 | −0.657894 | −0.328947 | − | 0.944348i | \(-0.606694\pi\) | ||||
−0.328947 | + | 0.944348i | \(0.606694\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14496.7 | 0.569829 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15342.1 | − | 19989.4i | 0.600974 | − | 0.783018i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6122.23 | −0.238990 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 64928.7i | 2.52586i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5170.19 | − | 19313.2i | −0.200440 | − | 0.748741i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 93129.6i | 3.59812i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14094.6i | 0.542690i | 0.962482 | + | 0.271345i | \(0.0874685\pi\) | ||||
−0.962482 | + | 0.271345i | \(0.912532\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8291.53 | + | 10803.2i | −0.318164 | + | 0.414541i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 12553.3i | − | 0.480057i | −0.970766 | − | 0.240028i | \(-0.922843\pi\) | ||
0.970766 | − | 0.240028i | \(-0.0771568\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −43192.3 | −1.64613 | −0.823067 | − | 0.567944i | \(-0.807739\pi\) | ||||
−0.823067 | + | 0.567944i | \(0.807739\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −70714.2 | − | 54273.8i | −2.68591 | − | 2.06146i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17930.0 | 0.678725 | 0.339362 | − | 0.940656i | \(-0.389789\pi\) | ||||
0.339362 | + | 0.940656i | \(0.389789\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4738.20 | 0.178756 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3622.30 | − | 6280.67i | −0.136197 | − | 0.236151i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −26763.3 | −1.00291 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 69358.8i | 2.59040i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 28467.1 | + | 21848.7i | 1.05963 | + | 0.813276i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10714.8i | 0.397508i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2890.00i | 0.106859i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −38891.6 | − | 29849.7i | −1.43326 | − | 1.10004i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 45456.2i | − | 1.66963i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5289.85 | −0.193657 | −0.0968283 | − | 0.995301i | \(-0.530870\pi\) | ||||
−0.0968283 | + | 0.995301i | \(0.530870\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 369.671 | + | 1380.90i | 0.0134887 | + | 0.0503868i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4585.72 | 0.166774 | 0.0833872 | − | 0.996517i | \(-0.473426\pi\) | ||||
0.0833872 | + | 0.996517i | \(0.473426\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2032.74 | 0.0736843 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −57163.9 | − | 43873.9i | −2.06533 | − | 1.58516i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −33029.6 | −1.18946 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43234.5i | 1.55188i | 0.630809 | + | 0.775939i | \(0.282723\pi\) | ||||
−0.630809 | + | 0.775939i | \(0.717277\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3012.03 | + | 3924.42i | −0.107763 | + | 0.140406i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 15199.8i | − | 0.542046i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 35358.9i | − | 1.25686i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −21081.5 | + | 5643.59i | −0.746935 | + | 0.199957i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 695.704i | 0.0245697i | 0.999925 | + | 0.0122849i | \(0.00391050\pi\) | ||||
−0.999925 | + | 0.0122849i | \(0.996090\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5862.80 | 0.206386 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1471.01 | + | 1916.60i | −0.0516169 | + | 0.0672525i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1697.39 | −0.0593698 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21092.2 | 0.735381 | 0.367691 | − | 0.929948i | \(-0.380149\pi\) | ||||
0.367691 | + | 0.929948i | \(0.380149\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17894.3 | + | 23314.8i | −0.621896 | + | 0.810277i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11392.6 | −0.394676 | −0.197338 | − | 0.980336i | \(-0.563230\pi\) | ||||
−0.197338 | + | 0.980336i | \(0.563230\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9202.33i | 0.317783i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 24041.7 | − | 57985.4i | 0.827595 | − | 1.99605i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3540.41i | 0.121487i | 0.998153 | + | 0.0607433i | \(0.0193471\pi\) | ||||
−0.998153 | + | 0.0607433i | \(0.980653\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 7357.67i | − | 0.251676i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14532.6 | − | 18934.8i | 0.495535 | − | 0.645640i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 29360.7i | − | 0.997992i | −0.866604 | − | 0.498996i | \(-0.833702\pi\) | ||
0.866604 | − | 0.498996i | \(-0.166298\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 65940.9 | 2.23434 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5019.77 | − | 3852.72i | −0.169557 | − | 0.130137i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11359.7 | −0.382505 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22133.5 | 0.742959 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −18989.0 | + | 5083.40i | −0.635421 | + | 0.170104i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 55952.9 | 1.86652 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27094.7i | 0.901043i | 0.892766 | + | 0.450521i | \(0.148762\pi\) | ||||
−0.892766 | + | 0.450521i | \(0.851238\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2050.94 | + | 1574.11i | 0.0679934 | + | 0.0521856i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10806.5i | 0.357154i | 0.983926 | + | 0.178577i | \(0.0571494\pi\) | ||||
−0.983926 | + | 0.178577i | \(0.942851\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 621.934i | − | 0.0204916i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −93145.2 | − | 71489.9i | −3.05952 | − | 2.34821i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 14327.6i | − | 0.469172i | −0.972095 | − | 0.234586i | \(-0.924627\pi\) | ||
0.972095 | − | 0.234586i | \(-0.0753734\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4515.99 | −0.147428 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 38831.7 | − | 10395.4i | 1.26381 | − | 0.338327i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25691.9 | −0.833617 | −0.416808 | − | 0.908994i | \(-0.636851\pi\) | ||||
−0.416808 | + | 0.908994i | \(0.636851\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −90401.5 | −2.92430 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −36955.0 | − | 28363.3i | −1.19178 | − | 0.914706i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −45956.3 | −1.47758 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 49378.3i | − | 1.58280i | −0.611300 | − | 0.791399i | \(-0.709353\pi\) | ||
0.611300 | − | 0.791399i | \(-0.290647\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −21225.3 | + | 27654.7i | −0.678311 | + | 0.883782i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16761.1i | 0.534034i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 22705.1i | − | 0.721241i | −0.932713 | − | 0.360621i | \(-0.882565\pi\) | ||
0.932713 | − | 0.360621i | \(-0.117435\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5703.10 | + | 13755.1i | −0.180619 | + | 0.435627i |
(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 | 768.4.f.e.383.9 | 12 | ||
3.2 | odd | 2 | 768.4.f.f.383.10 | 12 | |||
4.3 | odd | 2 | 768.4.f.g.383.4 | 12 | |||
8.3 | odd | 2 | 768.4.f.f.383.9 | 12 | |||
8.5 | even | 2 | 768.4.f.h.383.4 | 12 | |||
12.11 | even | 2 | 768.4.f.h.383.3 | 12 | |||
16.3 | odd | 4 | 384.4.c.b.383.3 | yes | 12 | ||
16.5 | even | 4 | 384.4.c.a.383.3 | ✓ | 12 | ||
16.11 | odd | 4 | 384.4.c.d.383.10 | yes | 12 | ||
16.13 | even | 4 | 384.4.c.c.383.10 | yes | 12 | ||
24.5 | odd | 2 | 768.4.f.g.383.3 | 12 | |||
24.11 | even | 2 | inner | 768.4.f.e.383.10 | 12 | ||
48.5 | odd | 4 | 384.4.c.d.383.9 | yes | 12 | ||
48.11 | even | 4 | 384.4.c.a.383.4 | yes | 12 | ||
48.29 | odd | 4 | 384.4.c.b.383.4 | yes | 12 | ||
48.35 | even | 4 | 384.4.c.c.383.9 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.4.c.a.383.3 | ✓ | 12 | 16.5 | even | 4 | ||
384.4.c.a.383.4 | yes | 12 | 48.11 | even | 4 | ||
384.4.c.b.383.3 | yes | 12 | 16.3 | odd | 4 | ||
384.4.c.b.383.4 | yes | 12 | 48.29 | odd | 4 | ||
384.4.c.c.383.9 | yes | 12 | 48.35 | even | 4 | ||
384.4.c.c.383.10 | yes | 12 | 16.13 | even | 4 | ||
384.4.c.d.383.9 | yes | 12 | 48.5 | odd | 4 | ||
384.4.c.d.383.10 | yes | 12 | 16.11 | odd | 4 | ||
768.4.f.e.383.9 | 12 | 1.1 | even | 1 | trivial | ||
768.4.f.e.383.10 | 12 | 24.11 | even | 2 | inner | ||
768.4.f.f.383.9 | 12 | 8.3 | odd | 2 | |||
768.4.f.f.383.10 | 12 | 3.2 | odd | 2 | |||
768.4.f.g.383.3 | 12 | 24.5 | odd | 2 | |||
768.4.f.g.383.4 | 12 | 4.3 | odd | 2 | |||
768.4.f.h.383.3 | 12 | 12.11 | even | 2 | |||
768.4.f.h.383.4 | 12 | 8.5 | even | 2 |