Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7605,2,Mod(1,7605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7605, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7605.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7605 = 3^{2} \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7605.a (trivial) |
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: | yes |
Analytic conductor: | \(60.7262307372\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.756.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - 6x - 2 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 195) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.339877\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7605.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.339877 | −0.240329 | −0.120165 | − | 0.992754i | \(-0.538342\pi\) | ||||
−0.120165 | + | 0.992754i | \(0.538342\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.88448 | −0.942242 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.660123 | −0.249503 | −0.124752 | − | 0.992188i | \(-0.539813\pi\) | ||||
−0.124752 | + | 0.992188i | \(0.539813\pi\) | |||||||
\(8\) | 1.32025 | 0.466778 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.339877 | −0.107479 | ||||||||
\(11\) | 0.679754 | 0.204953 | 0.102477 | − | 0.994735i | \(-0.467323\pi\) | ||||
0.102477 | + | 0.994735i | \(0.467323\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.224361 | 0.0599629 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.32025 | 0.830062 | ||||||||
\(17\) | −7.42909 | −1.80182 | −0.900910 | − | 0.434007i | \(-0.857099\pi\) | ||||
−0.900910 | + | 0.434007i | \(0.857099\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.115516 | −0.0265013 | −0.0132506 | − | 0.999912i | \(-0.504218\pi\) | ||||
−0.0132506 | + | 0.999912i | \(0.504218\pi\) | |||||||
\(20\) | −1.88448 | −0.421383 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.231033 | −0.0492563 | ||||||||
\(23\) | 7.76897 | 1.61994 | 0.809971 | − | 0.586470i | \(-0.199483\pi\) | ||||
0.809971 | + | 0.586470i | \(0.199483\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.24399 | 0.235092 | ||||||||
\(29\) | −5.54461 | −1.02961 | −0.514804 | − | 0.857308i | \(-0.672135\pi\) | ||||
−0.514804 | + | 0.857308i | \(0.672135\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.97370 | 1.79133 | 0.895664 | − | 0.444730i | \(-0.146701\pi\) | ||||
0.895664 | + | 0.444730i | \(0.146701\pi\) | |||||||
\(32\) | −3.76897 | −0.666266 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.52498 | 0.433030 | ||||||||
\(35\) | −0.660123 | −0.111581 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.76897 | −1.60601 | −0.803004 | − | 0.595973i | \(-0.796766\pi\) | ||||
−0.803004 | + | 0.595973i | \(0.796766\pi\) | |||||||
\(38\) | 0.0392613 | 0.00636903 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.32025 | 0.208749 | ||||||||
\(41\) | 4.22436 | 0.659734 | 0.329867 | − | 0.944027i | \(-0.392996\pi\) | ||||
0.329867 | + | 0.944027i | \(0.392996\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.544607 | −0.0830518 | −0.0415259 | − | 0.999137i | \(-0.513222\pi\) | ||||
−0.0415259 | + | 0.999137i | \(0.513222\pi\) | |||||||
\(44\) | −1.28098 | −0.193116 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.64049 | −0.389319 | ||||||||
\(47\) | −5.01963 | −0.732188 | −0.366094 | − | 0.930578i | \(-0.619305\pi\) | ||||
−0.366094 | + | 0.930578i | \(0.619305\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.56424 | −0.937748 | ||||||||
\(50\) | −0.339877 | −0.0480659 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.679754 | −0.0933714 | −0.0466857 | − | 0.998910i | \(-0.514866\pi\) | ||||
−0.0466857 | + | 0.998910i | \(0.514866\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.679754 | 0.0916580 | ||||||||
\(56\) | −0.871525 | −0.116462 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.88448 | 0.247445 | ||||||||
\(59\) | 2.22436 | 0.289587 | 0.144794 | − | 0.989462i | \(-0.453748\pi\) | ||||
0.144794 | + | 0.989462i | \(0.453748\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.20473 | −0.538361 | −0.269180 | − | 0.963090i | \(-0.586753\pi\) | ||||
−0.269180 | + | 0.963090i | \(0.586753\pi\) | |||||||
\(62\) | −3.38983 | −0.430509 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.35951 | −0.669938 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.63382 | 0.932620 | 0.466310 | − | 0.884621i | \(-0.345583\pi\) | ||||
0.466310 | + | 0.884621i | \(0.345583\pi\) | |||||||
\(68\) | 14.0000 | 1.69775 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.224361 | 0.0268162 | ||||||||
\(71\) | 7.31357 | 0.867962 | 0.433981 | − | 0.900922i | \(-0.357109\pi\) | ||||
0.433981 | + | 0.900922i | \(0.357109\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.01963 | −0.938627 | −0.469313 | − | 0.883032i | \(-0.655499\pi\) | ||||
−0.469313 | + | 0.883032i | \(0.655499\pi\) | |||||||
\(74\) | 3.32025 | 0.385971 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.217689 | 0.0249706 | ||||||||
\(77\) | −0.448721 | −0.0511365 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.97370 | 1.12213 | 0.561064 | − | 0.827772i | \(-0.310392\pi\) | ||||
0.561064 | + | 0.827772i | \(0.310392\pi\) | |||||||
\(80\) | 3.32025 | 0.371215 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.43576 | −0.158553 | ||||||||
\(83\) | 1.76897 | 0.194169 | 0.0970847 | − | 0.995276i | \(-0.469048\pi\) | ||||
0.0970847 | + | 0.995276i | \(0.469048\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.42909 | −0.805798 | ||||||||
\(86\) | 0.185099 | 0.0199598 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.897442 | 0.0956677 | ||||||||
\(89\) | 13.5446 | 1.43573 | 0.717863 | − | 0.696185i | \(-0.245121\pi\) | ||||
0.717863 | + | 0.696185i | \(0.245121\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −14.6405 | −1.52638 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.70606 | 0.175966 | ||||||||
\(95\) | −0.115516 | −0.0118517 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.90411 | −1.00561 | −0.502805 | − | 0.864400i | \(-0.667699\pi\) | ||||
−0.502805 | + | 0.864400i | \(0.667699\pi\) | |||||||
\(98\) | 2.23103 | 0.225368 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.88448 | −0.188448 | ||||||||
\(101\) | 9.35951 | 0.931306 | 0.465653 | − | 0.884967i | \(-0.345820\pi\) | ||||
0.465653 | + | 0.884967i | \(0.345820\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.50535 | 0.443925 | 0.221962 | − | 0.975055i | \(-0.428754\pi\) | ||||
0.221962 | + | 0.975055i | \(0.428754\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.231033 | 0.0224399 | ||||||||
\(107\) | −0.570909 | −0.0551919 | −0.0275960 | − | 0.999619i | \(-0.508785\pi\) | ||||
−0.0275960 | + | 0.999619i | \(0.508785\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.4095 | −1.47596 | −0.737979 | − | 0.674823i | \(-0.764220\pi\) | ||||
−0.737979 | + | 0.674823i | \(0.764220\pi\) | |||||||
\(110\) | −0.231033 | −0.0220281 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.19177 | −0.207103 | ||||||||
\(113\) | 5.32025 | 0.500487 | 0.250243 | − | 0.968183i | \(-0.419489\pi\) | ||||
0.250243 | + | 0.968183i | \(0.419489\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.76897 | 0.724460 | ||||||||
\(116\) | 10.4487 | 0.970139 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.756009 | −0.0695962 | ||||||||
\(119\) | 4.90411 | 0.449559 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.5379 | −0.957994 | ||||||||
\(122\) | 1.42909 | 0.129384 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −18.7953 | −1.68787 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.0196 | −1.06657 | −0.533285 | − | 0.845936i | \(-0.679043\pi\) | ||||
−0.533285 | + | 0.845936i | \(0.679043\pi\) | |||||||
\(128\) | 9.35951 | 0.827271 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.9041 | −0.952697 | −0.476348 | − | 0.879257i | \(-0.658040\pi\) | ||||
−0.476348 | + | 0.879257i | \(0.658040\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.0762550 | 0.00661215 | ||||||||
\(134\) | −2.59456 | −0.224136 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.80823 | −0.841049 | ||||||||
\(137\) | 3.38983 | 0.289613 | 0.144806 | − | 0.989460i | \(-0.453744\pi\) | ||||
0.144806 | + | 0.989460i | \(0.453744\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.8082 | 1.25602 | 0.628009 | − | 0.778206i | \(-0.283870\pi\) | ||||
0.628009 | + | 0.778206i | \(0.283870\pi\) | |||||||
\(140\) | 1.24399 | 0.105136 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.48571 | −0.208597 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.54461 | −0.460455 | ||||||||
\(146\) | 2.72569 | 0.225579 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 18.4095 | 1.51325 | ||||||||
\(149\) | −17.0892 | −1.40000 | −0.700001 | − | 0.714141i | \(-0.746817\pi\) | ||||
−0.700001 | + | 0.714141i | \(0.746817\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.0130 | −1.05898 | −0.529490 | − | 0.848316i | \(-0.677617\pi\) | ||||
−0.529490 | + | 0.848316i | \(0.677617\pi\) | |||||||
\(152\) | −0.152510 | −0.0123702 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.152510 | 0.0122896 | ||||||||
\(155\) | 9.97370 | 0.801107 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.775639 | −0.0619028 | −0.0309514 | − | 0.999521i | \(-0.509854\pi\) | ||||
−0.0309514 | + | 0.999521i | \(0.509854\pi\) | |||||||
\(158\) | −3.38983 | −0.269680 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.76897 | −0.297963 | ||||||||
\(161\) | −5.12847 | −0.404180 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.1981 | −0.955426 | −0.477713 | − | 0.878516i | \(-0.658534\pi\) | ||||
−0.477713 | + | 0.878516i | \(0.658534\pi\) | |||||||
\(164\) | −7.96074 | −0.621629 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.601231 | −0.0466646 | ||||||||
\(167\) | −1.59054 | −0.123080 | −0.0615398 | − | 0.998105i | \(-0.519601\pi\) | ||||
−0.0615398 | + | 0.998105i | \(0.519601\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 2.52498 | 0.193657 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.02630 | 0.0782548 | ||||||||
\(173\) | −12.7493 | −0.969314 | −0.484657 | − | 0.874704i | \(-0.661056\pi\) | ||||
−0.484657 | + | 0.874704i | \(0.661056\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.660123 | −0.0499006 | ||||||||
\(176\) | 2.25695 | 0.170124 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.60350 | −0.345047 | ||||||||
\(179\) | −17.7623 | −1.32762 | −0.663808 | − | 0.747903i | \(-0.731061\pi\) | ||||
−0.663808 | + | 0.747903i | \(0.731061\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.02630 | 0.522261 | 0.261130 | − | 0.965304i | \(-0.415905\pi\) | ||||
0.261130 | + | 0.965304i | \(0.415905\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 10.2569 | 0.756152 | ||||||||
\(185\) | −9.76897 | −0.718229 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.04995 | −0.369289 | ||||||||
\(188\) | 9.45941 | 0.689899 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.0392613 | 0.00284832 | ||||||||
\(191\) | 13.9541 | 1.00968 | 0.504840 | − | 0.863213i | \(-0.331551\pi\) | ||||
0.504840 | + | 0.863213i | \(0.331551\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23.7493 | −1.70951 | −0.854757 | − | 0.519028i | \(-0.826294\pi\) | ||||
−0.854757 | + | 0.519028i | \(0.826294\pi\) | |||||||
\(194\) | 3.36618 | 0.241678 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.3702 | 0.883586 | ||||||||
\(197\) | 15.8082 | 1.12629 | 0.563145 | − | 0.826358i | \(-0.309591\pi\) | ||||
0.563145 | + | 0.826358i | \(0.309591\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.76897 | 0.621616 | 0.310808 | − | 0.950473i | \(-0.399400\pi\) | ||||
0.310808 | + | 0.950473i | \(0.399400\pi\) | |||||||
\(200\) | 1.32025 | 0.0933555 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.18108 | −0.223820 | ||||||||
\(203\) | 3.66012 | 0.256890 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.22436 | 0.295042 | ||||||||
\(206\) | −1.53126 | −0.106688 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.0785226 | −0.00543152 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.80823 | 0.606383 | 0.303192 | − | 0.952930i | \(-0.401948\pi\) | ||||
0.303192 | + | 0.952930i | \(0.401948\pi\) | |||||||
\(212\) | 1.28098 | 0.0879784 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.194039 | 0.0132642 | ||||||||
\(215\) | −0.544607 | −0.0371419 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.58387 | −0.446942 | ||||||||
\(218\) | 5.23732 | 0.354716 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.28098 | −0.0863640 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.0393 | −0.672279 | −0.336139 | − | 0.941812i | \(-0.609121\pi\) | ||||
−0.336139 | + | 0.941812i | \(0.609121\pi\) | |||||||
\(224\) | 2.48798 | 0.166235 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.80823 | −0.120282 | ||||||||
\(227\) | 1.21140 | 0.0804036 | 0.0402018 | − | 0.999192i | \(-0.487200\pi\) | ||||
0.0402018 | + | 0.999192i | \(0.487200\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.2440 | −1.27168 | −0.635839 | − | 0.771821i | \(-0.719346\pi\) | ||||
−0.635839 | + | 0.771821i | \(0.719346\pi\) | |||||||
\(230\) | −2.64049 | −0.174109 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.32025 | −0.480598 | ||||||||
\(233\) | 23.9081 | 1.56627 | 0.783137 | − | 0.621849i | \(-0.213618\pi\) | ||||
0.783137 | + | 0.621849i | \(0.213618\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.01963 | −0.327445 | ||||||||
\(236\) | −4.19177 | −0.272861 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.66680 | −0.108042 | ||||||||
\(239\) | 18.6798 | 1.20829 | 0.604146 | − | 0.796873i | \(-0.293514\pi\) | ||||
0.604146 | + | 0.796873i | \(0.293514\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.11552 | −0.393935 | −0.196968 | − | 0.980410i | \(-0.563109\pi\) | ||||
−0.196968 | + | 0.980410i | \(0.563109\pi\) | |||||||
\(242\) | 3.58160 | 0.230234 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.92375 | 0.507266 | ||||||||
\(245\) | −6.56424 | −0.419374 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 13.1677 | 0.836152 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.339877 | −0.0214957 | ||||||||
\(251\) | −3.35951 | −0.212050 | −0.106025 | − | 0.994363i | \(-0.533812\pi\) | ||||
−0.106025 | + | 0.994363i | \(0.533812\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.28098 | 0.332013 | ||||||||
\(254\) | 4.08519 | 0.256328 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.53793 | 0.471121 | ||||||||
\(257\) | 10.1088 | 0.630572 | 0.315286 | − | 0.948997i | \(-0.397899\pi\) | ||||
0.315286 | + | 0.948997i | \(0.397899\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.44872 | 0.400704 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.70606 | 0.228961 | ||||||||
\(263\) | 22.5183 | 1.38854 | 0.694269 | − | 0.719716i | \(-0.255728\pi\) | ||||
0.694269 | + | 0.719716i | \(0.255728\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.679754 | −0.0417569 | ||||||||
\(266\) | −0.0259173 | −0.00158909 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −14.3858 | −0.878753 | ||||||||
\(269\) | −8.49465 | −0.517928 | −0.258964 | − | 0.965887i | \(-0.583381\pi\) | ||||
−0.258964 | + | 0.965887i | \(0.583381\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.37020 | −0.569199 | −0.284600 | − | 0.958647i | \(-0.591861\pi\) | ||||
−0.284600 | + | 0.958647i | \(0.591861\pi\) | |||||||
\(272\) | −24.6664 | −1.49562 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.15212 | −0.0696024 | ||||||||
\(275\) | 0.679754 | 0.0409907 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.719015 | 0.0432014 | 0.0216007 | − | 0.999767i | \(-0.493124\pi\) | ||||
0.0216007 | + | 0.999767i | \(0.493124\pi\) | |||||||
\(278\) | −5.03297 | −0.301858 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.871525 | −0.0520836 | ||||||||
\(281\) | 1.54461 | 0.0921435 | 0.0460718 | − | 0.998938i | \(-0.485330\pi\) | ||||
0.0460718 | + | 0.998938i | \(0.485330\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.1195 | −1.07709 | −0.538547 | − | 0.842595i | \(-0.681027\pi\) | ||||
−0.538547 | + | 0.842595i | \(0.681027\pi\) | |||||||
\(284\) | −13.7823 | −0.817830 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.78860 | −0.164606 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 38.1914 | 2.24655 | ||||||||
\(290\) | 1.88448 | 0.110661 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 15.1129 | 0.884413 | ||||||||
\(293\) | −30.5050 | −1.78212 | −0.891059 | − | 0.453887i | \(-0.850037\pi\) | ||||
−0.891059 | + | 0.453887i | \(0.850037\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.22436 | 0.129507 | ||||||||
\(296\) | −12.8974 | −0.749649 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.80823 | 0.336462 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.359508 | 0.0207217 | ||||||||
\(302\) | 4.42280 | 0.254504 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.383543 | −0.0219977 | ||||||||
\(305\) | −4.20473 | −0.240762 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.77564 | 0.272560 | 0.136280 | − | 0.990670i | \(-0.456485\pi\) | ||||
0.136280 | + | 0.990670i | \(0.456485\pi\) | |||||||
\(308\) | 0.845608 | 0.0481830 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.38983 | −0.192529 | ||||||||
\(311\) | −30.5812 | −1.73410 | −0.867051 | − | 0.498220i | \(-0.833987\pi\) | ||||
−0.867051 | + | 0.498220i | \(0.833987\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.7230 | −1.51048 | −0.755238 | − | 0.655451i | \(-0.772479\pi\) | ||||
−0.755238 | + | 0.655451i | \(0.772479\pi\) | |||||||
\(314\) | 0.263622 | 0.0148770 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −18.7953 | −1.05732 | ||||||||
\(317\) | −20.6271 | −1.15854 | −0.579268 | − | 0.815137i | \(-0.696662\pi\) | ||||
−0.579268 | + | 0.815137i | \(0.696662\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.76897 | −0.211022 | ||||||||
\(320\) | −5.35951 | −0.299606 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.74305 | 0.0971364 | ||||||||
\(323\) | 0.858181 | 0.0477505 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.14584 | 0.229617 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.57720 | 0.307949 | ||||||||
\(329\) | 3.31357 | 0.182683 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.37020 | −0.295173 | −0.147586 | − | 0.989049i | \(-0.547150\pi\) | ||||
−0.147586 | + | 0.989049i | \(0.547150\pi\) | |||||||
\(332\) | −3.33359 | −0.182955 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.540588 | 0.0295797 | ||||||||
\(335\) | 7.63382 | 0.417080 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.7623 | 1.56678 | 0.783391 | − | 0.621529i | \(-0.213488\pi\) | ||||
0.783391 | + | 0.621529i | \(0.213488\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 14.0000 | 0.759257 | ||||||||
\(341\) | 6.77966 | 0.367139 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.95407 | 0.483474 | ||||||||
\(344\) | −0.719015 | −0.0387667 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.33320 | 0.232955 | ||||||||
\(347\) | −22.3961 | −1.20229 | −0.601143 | − | 0.799141i | \(-0.705288\pi\) | ||||
−0.601143 | + | 0.799141i | \(0.705288\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.9737 | 0.640937 | 0.320469 | − | 0.947259i | \(-0.396160\pi\) | ||||
0.320469 | + | 0.947259i | \(0.396160\pi\) | |||||||
\(350\) | 0.224361 | 0.0119926 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.56197 | −0.136553 | ||||||||
\(353\) | −17.0366 | −0.906767 | −0.453384 | − | 0.891316i | \(-0.649783\pi\) | ||||
−0.453384 | + | 0.891316i | \(0.649783\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.31357 | 0.388164 | ||||||||
\(356\) | −25.5246 | −1.35280 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.03699 | 0.319065 | ||||||||
\(359\) | −35.0825 | −1.85159 | −0.925793 | − | 0.378031i | \(-0.876601\pi\) | ||||
−0.925793 | + | 0.378031i | \(0.876601\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9867 | −0.999298 | ||||||||
\(362\) | −2.38808 | −0.125515 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.01963 | −0.419767 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.0825 | 1.04830 | 0.524150 | − | 0.851626i | \(-0.324383\pi\) | ||||
0.524150 | + | 0.851626i | \(0.324383\pi\) | |||||||
\(368\) | 25.7949 | 1.34465 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.32025 | 0.172611 | ||||||||
\(371\) | 0.448721 | 0.0232964 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.4790 | −1.21570 | −0.607849 | − | 0.794052i | \(-0.707968\pi\) | ||||
−0.607849 | + | 0.794052i | \(0.707968\pi\) | |||||||
\(374\) | 1.71636 | 0.0887510 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.62715 | −0.341769 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.1414 | −1.08596 | −0.542981 | − | 0.839745i | \(-0.682705\pi\) | ||||
−0.542981 | + | 0.839745i | \(0.682705\pi\) | |||||||
\(380\) | 0.217689 | 0.0111672 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.74266 | −0.242656 | ||||||||
\(383\) | 1.73865 | 0.0888406 | 0.0444203 | − | 0.999013i | \(-0.485856\pi\) | ||||
0.0444203 | + | 0.999013i | \(0.485856\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.448721 | −0.0228689 | ||||||||
\(386\) | 8.07185 | 0.410846 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 18.6641 | 0.947528 | ||||||||
\(389\) | 26.6664 | 1.35204 | 0.676020 | − | 0.736883i | \(-0.263703\pi\) | ||||
0.676020 | + | 0.736883i | \(0.263703\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −57.7164 | −2.91884 | ||||||||
\(392\) | −8.66641 | −0.437720 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.37285 | −0.270680 | ||||||||
\(395\) | 9.97370 | 0.501831 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.5446 | −0.729973 | −0.364986 | − | 0.931013i | \(-0.618926\pi\) | ||||
−0.364986 | + | 0.931013i | \(0.618926\pi\) | |||||||
\(398\) | −2.98037 | −0.149392 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.32025 | 0.166012 | ||||||||
\(401\) | −8.37020 | −0.417988 | −0.208994 | − | 0.977917i | \(-0.567019\pi\) | ||||
−0.208994 | + | 0.977917i | \(0.567019\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −17.6378 | −0.877515 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.24399 | −0.0617382 | ||||||||
\(407\) | −6.64049 | −0.329157 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.2547 | −0.853189 | −0.426595 | − | 0.904443i | \(-0.640287\pi\) | ||||
−0.426595 | + | 0.904443i | \(0.640287\pi\) | |||||||
\(410\) | −1.43576 | −0.0709073 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8.49025 | −0.418285 | ||||||||
\(413\) | −1.46835 | −0.0722529 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.76897 | 0.0868352 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.0266880 | 0.00130535 | ||||||||
\(419\) | −12.8649 | −0.628489 | −0.314245 | − | 0.949342i | \(-0.601751\pi\) | ||||
−0.314245 | + | 0.949342i | \(0.601751\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.5616 | −1.19706 | −0.598529 | − | 0.801101i | \(-0.704248\pi\) | ||||
−0.598529 | + | 0.801101i | \(0.704248\pi\) | |||||||
\(422\) | −2.99371 | −0.145732 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.897442 | −0.0435837 | ||||||||
\(425\) | −7.42909 | −0.360364 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.77564 | 0.134323 | ||||||||
\(428\) | 1.07587 | 0.0520041 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.185099 | 0.00892628 | ||||||||
\(431\) | 24.7797 | 1.19359 | 0.596797 | − | 0.802392i | \(-0.296440\pi\) | ||||
0.596797 | + | 0.802392i | \(0.296440\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.0589 | −0.675627 | −0.337814 | − | 0.941213i | \(-0.609687\pi\) | ||||
−0.337814 | + | 0.941213i | \(0.609687\pi\) | |||||||
\(434\) | 2.23770 | 0.107413 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 29.0389 | 1.39071 | ||||||||
\(437\) | −0.897442 | −0.0429305 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.8452 | 0.994888 | 0.497444 | − | 0.867496i | \(-0.334272\pi\) | ||||
0.497444 | + | 0.867496i | \(0.334272\pi\) | |||||||
\(440\) | 0.897442 | 0.0427839 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.4291 | 0.543012 | 0.271506 | − | 0.962437i | \(-0.412478\pi\) | ||||
0.271506 | + | 0.962437i | \(0.412478\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.5446 | 0.642076 | ||||||||
\(446\) | 3.41211 | 0.161568 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.53793 | 0.167152 | ||||||||
\(449\) | 25.9081 | 1.22268 | 0.611340 | − | 0.791368i | \(-0.290631\pi\) | ||||
0.611340 | + | 0.791368i | \(0.290631\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.87153 | 0.135215 | ||||||||
\(452\) | −10.0259 | −0.471579 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −0.411728 | −0.0193233 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.90411 | −0.276183 | −0.138091 | − | 0.990419i | \(-0.544097\pi\) | ||||
−0.138091 | + | 0.990419i | \(0.544097\pi\) | |||||||
\(458\) | 6.54059 | 0.305622 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −14.6405 | −0.682616 | ||||||||
\(461\) | −15.4920 | −0.721534 | −0.360767 | − | 0.932656i | \(-0.617485\pi\) | ||||
−0.360767 | + | 0.932656i | \(0.617485\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.4420 | −0.810601 | −0.405300 | − | 0.914184i | \(-0.632833\pi\) | ||||
−0.405300 | + | 0.914184i | \(0.632833\pi\) | |||||||
\(464\) | −18.4095 | −0.854638 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.12582 | −0.376421 | ||||||||
\(467\) | 20.4790 | 0.947657 | 0.473829 | − | 0.880617i | \(-0.342872\pi\) | ||||
0.473829 | + | 0.880617i | \(0.342872\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.03926 | −0.232691 | ||||||||
\(470\) | 1.70606 | 0.0786945 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.93670 | 0.135173 | ||||||||
\(473\) | −0.370199 | −0.0170217 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.115516 | −0.00530025 | ||||||||
\(476\) | −9.24172 | −0.423594 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.34882 | −0.290388 | ||||||||
\(479\) | −40.9907 | −1.87291 | −0.936456 | − | 0.350785i | \(-0.885915\pi\) | ||||
−0.936456 | + | 0.350785i | \(0.885915\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 2.07852 | 0.0946741 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 19.8586 | 0.902662 | ||||||||
\(485\) | −9.90411 | −0.449723 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.0629 | −1.09039 | −0.545197 | − | 0.838308i | \(-0.683545\pi\) | ||||
−0.545197 | + | 0.838308i | \(0.683545\pi\) | |||||||
\(488\) | −5.55128 | −0.251295 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.23103 | 0.100788 | ||||||||
\(491\) | −36.7730 | −1.65954 | −0.829771 | − | 0.558104i | \(-0.811529\pi\) | ||||
−0.829771 | + | 0.558104i | \(0.811529\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 41.1914 | 1.85517 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 33.1151 | 1.48691 | ||||||||
\(497\) | −4.82786 | −0.216559 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −34.8212 | −1.55881 | −0.779405 | − | 0.626520i | \(-0.784479\pi\) | ||||
−0.779405 | + | 0.626520i | \(0.784479\pi\) | |||||||
\(500\) | −1.88448 | −0.0842767 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.14182 | 0.0509619 | ||||||||
\(503\) | 32.0259 | 1.42797 | 0.713983 | − | 0.700164i | \(-0.246890\pi\) | ||||
0.713983 | + | 0.700164i | \(0.246890\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.35951 | 0.416493 | ||||||||
\(506\) | −1.79488 | −0.0797924 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 22.6508 | 1.00497 | ||||||||
\(509\) | −41.3462 | −1.83264 | −0.916318 | − | 0.400451i | \(-0.868854\pi\) | ||||
−0.916318 | + | 0.400451i | \(0.868854\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.29394 | 0.234190 | ||||||||
\(512\) | −21.2810 | −0.940496 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.43576 | −0.151545 | ||||||||
\(515\) | 4.50535 | 0.198529 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.41211 | −0.150065 | ||||||||
\(518\) | −2.19177 | −0.0963009 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.40279 | −0.192890 | −0.0964448 | − | 0.995338i | \(-0.530747\pi\) | ||||
−0.0964448 | + | 0.995338i | \(0.530747\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −32.4487 | −1.41888 | −0.709442 | − | 0.704764i | \(-0.751053\pi\) | ||||
−0.709442 | + | 0.704764i | \(0.751053\pi\) | |||||||
\(524\) | 20.5486 | 0.897671 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.65345 | −0.333706 | ||||||||
\(527\) | −74.0955 | −3.22765 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 37.3569 | 1.62421 | ||||||||
\(530\) | 0.231033 | 0.0100354 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.143701 | −0.00623024 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.570909 | −0.0246826 | ||||||||
\(536\) | 10.0785 | 0.435326 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.88714 | 0.124473 | ||||||||
\(539\) | −4.46207 | −0.192195 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.57720 | 0.368762 | 0.184381 | − | 0.982855i | \(-0.440972\pi\) | ||||
0.184381 | + | 0.982855i | \(0.440972\pi\) | |||||||
\(542\) | 3.18471 | 0.136795 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 28.0000 | 1.20049 | ||||||||
\(545\) | −15.4095 | −0.660069 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.4920 | −1.38926 | −0.694629 | − | 0.719368i | \(-0.744431\pi\) | ||||
−0.694629 | + | 0.719368i | \(0.744431\pi\) | |||||||
\(548\) | −6.38808 | −0.272885 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.231033 | −0.00985126 | ||||||||
\(551\) | 0.640492 | 0.0272859 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.58387 | −0.279975 | ||||||||
\(554\) | −0.244377 | −0.0103826 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −27.9059 | −1.18347 | ||||||||
\(557\) | −41.2150 | −1.74634 | −0.873169 | − | 0.487418i | \(-0.837939\pi\) | ||||
−0.873169 | + | 0.487418i | \(0.837939\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2.19177 | −0.0926192 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.524976 | −0.0221448 | ||||||||
\(563\) | 12.1784 | 0.513260 | 0.256630 | − | 0.966510i | \(-0.417388\pi\) | ||||
0.256630 | + | 0.966510i | \(0.417388\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.32025 | 0.223824 | ||||||||
\(566\) | 6.15841 | 0.258857 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.65572 | 0.405145 | ||||||||
\(569\) | −6.94338 | −0.291081 | −0.145541 | − | 0.989352i | \(-0.546492\pi\) | ||||
−0.145541 | + | 0.989352i | \(0.546492\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.51429 | 0.147068 | 0.0735341 | − | 0.997293i | \(-0.476572\pi\) | ||||
0.0735341 | + | 0.997293i | \(0.476572\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.947780 | 0.0395596 | ||||||||
\(575\) | 7.76897 | 0.323988 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.14182 | −0.130796 | −0.0653978 | − | 0.997859i | \(-0.520832\pi\) | ||||
−0.0653978 | + | 0.997859i | \(0.520832\pi\) | |||||||
\(578\) | −12.9804 | −0.539912 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 10.4487 | 0.433860 | ||||||||
\(581\) | −1.16774 | −0.0484459 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.462065 | −0.0191368 | ||||||||
\(584\) | −10.5879 | −0.438130 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.3679 | 0.428295 | ||||||||
\(587\) | 37.9777 | 1.56751 | 0.783754 | − | 0.621071i | \(-0.213302\pi\) | ||||
0.783754 | + | 0.621071i | \(0.213302\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.15212 | −0.0474725 | ||||||||
\(590\) | −0.756009 | −0.0311244 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −32.4354 | −1.33309 | ||||||||
\(593\) | 10.4487 | 0.429078 | 0.214539 | − | 0.976715i | \(-0.431175\pi\) | ||||
0.214539 | + | 0.976715i | \(0.431175\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.90411 | 0.201049 | ||||||||
\(596\) | 32.2043 | 1.31914 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 45.5705 | 1.86196 | 0.930981 | − | 0.365069i | \(-0.118955\pi\) | ||||
0.930981 | + | 0.365069i | \(0.118955\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.7819 | −0.602967 | −0.301484 | − | 0.953471i | \(-0.597482\pi\) | ||||
−0.301484 | + | 0.953471i | \(0.597482\pi\) | |||||||
\(602\) | −0.122188 | −0.00498002 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 24.5227 | 0.997815 | ||||||||
\(605\) | −10.5379 | −0.428428 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.9344 | −0.768525 | −0.384263 | − | 0.923224i | \(-0.625544\pi\) | ||||
−0.384263 | + | 0.923224i | \(0.625544\pi\) | |||||||
\(608\) | 0.435377 | 0.0176569 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.42909 | 0.0578622 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.58387 | 0.104361 | 0.0521807 | − | 0.998638i | \(-0.483383\pi\) | ||||
0.0521807 | + | 0.998638i | \(0.483383\pi\) | |||||||
\(614\) | −1.62313 | −0.0655042 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.592422 | −0.0238694 | ||||||||
\(617\) | 14.0393 | 0.565199 | 0.282600 | − | 0.959238i | \(-0.408803\pi\) | ||||
0.282600 | + | 0.959238i | \(0.408803\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.8582 | 0.717781 | 0.358890 | − | 0.933380i | \(-0.383155\pi\) | ||||
0.358890 | + | 0.933380i | \(0.383155\pi\) | |||||||
\(620\) | −18.7953 | −0.754836 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10.3938 | 0.416755 | ||||||||
\(623\) | −8.94111 | −0.358218 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 9.08254 | 0.363011 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.46168 | 0.0583274 | ||||||||
\(629\) | 72.5745 | 2.89374 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.9630 | 0.993762 | 0.496881 | − | 0.867819i | \(-0.334479\pi\) | ||||
0.496881 | + | 0.867819i | \(0.334479\pi\) | |||||||
\(632\) | 13.1677 | 0.523784 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.01069 | 0.278430 | ||||||||
\(635\) | −12.0196 | −0.476984 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.28098 | 0.0507147 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 9.35951 | 0.369967 | ||||||||
\(641\) | −23.3069 | −0.920567 | −0.460284 | − | 0.887772i | \(-0.652252\pi\) | ||||
−0.460284 | + | 0.887772i | \(0.652252\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −45.4790 | −1.79352 | −0.896759 | − | 0.442519i | \(-0.854085\pi\) | ||||
−0.896759 | + | 0.442519i | \(0.854085\pi\) | |||||||
\(644\) | 9.66453 | 0.380836 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.291676 | −0.0114758 | ||||||||
\(647\) | −6.40946 | −0.251982 | −0.125991 | − | 0.992031i | \(-0.540211\pi\) | ||||
−0.125991 | + | 0.992031i | \(0.540211\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.51202 | 0.0593519 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 22.9870 | 0.900242 | ||||||||
\(653\) | −1.48170 | −0.0579832 | −0.0289916 | − | 0.999580i | \(-0.509230\pi\) | ||||
−0.0289916 | + | 0.999580i | \(0.509230\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.9041 | −0.426059 | ||||||||
\(656\) | 14.0259 | 0.547620 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.12621 | −0.0439041 | ||||||||
\(659\) | 7.08921 | 0.276157 | 0.138078 | − | 0.990421i | \(-0.455907\pi\) | ||||
0.138078 | + | 0.990421i | \(0.455907\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.17843 | −0.0458355 | −0.0229178 | − | 0.999737i | \(-0.507296\pi\) | ||||
−0.0229178 | + | 0.999737i | \(0.507296\pi\) | |||||||
\(662\) | 1.82521 | 0.0709387 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.33547 | 0.0906339 | ||||||||
\(665\) | 0.0762550 | 0.00295704 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −43.0759 | −1.66790 | ||||||||
\(668\) | 2.99735 | 0.115971 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.59456 | −0.100237 | ||||||||
\(671\) | −2.85818 | −0.110339 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.5576 | 0.522606 | 0.261303 | − | 0.965257i | \(-0.415848\pi\) | ||||
0.261303 | + | 0.965257i | \(0.415848\pi\) | |||||||
\(674\) | −9.77564 | −0.376544 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.53793 | −0.366573 | −0.183286 | − | 0.983060i | \(-0.558674\pi\) | ||||
−0.183286 | + | 0.983060i | \(0.558674\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.53793 | 0.250903 | ||||||||
\(680\) | −9.80823 | −0.376128 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.30425 | −0.0882343 | ||||||||
\(683\) | −44.5183 | −1.70345 | −0.851723 | − | 0.523993i | \(-0.824442\pi\) | ||||
−0.851723 | + | 0.523993i | \(0.824442\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.38983 | 0.129519 | ||||||||
\(686\) | −3.04328 | −0.116193 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.80823 | −0.0689381 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.28060 | 0.200883 | 0.100442 | − | 0.994943i | \(-0.467974\pi\) | ||||
0.100442 | + | 0.994943i | \(0.467974\pi\) | |||||||
\(692\) | 24.0259 | 0.913328 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.61192 | 0.288945 | ||||||||
\(695\) | 14.8082 | 0.561708 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −31.3832 | −1.18872 | ||||||||
\(698\) | −4.06958 | −0.154036 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.24399 | 0.0470184 | ||||||||
\(701\) | −20.1392 | −0.760646 | −0.380323 | − | 0.924854i | \(-0.624187\pi\) | ||||
−0.380323 | + | 0.924854i | \(0.624187\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.12847 | 0.0425612 | ||||||||
\(704\) | −3.64315 | −0.137306 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.79035 | 0.217923 | ||||||||
\(707\) | −6.17843 | −0.232364 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.54059 | −0.0578580 | −0.0289290 | − | 0.999581i | \(-0.509210\pi\) | ||||
−0.0289290 | + | 0.999581i | \(0.509210\pi\) | |||||||
\(710\) | −2.48571 | −0.0932872 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 17.8822 | 0.670164 | ||||||||
\(713\) | 77.4853 | 2.90185 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 33.4728 | 1.25094 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 11.9237 | 0.444990 | ||||||||
\(719\) | −37.0040 | −1.38002 | −0.690009 | − | 0.723801i | \(-0.742393\pi\) | ||||
−0.690009 | + | 0.723801i | \(0.742393\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.97408 | −0.110761 | ||||||||
\(722\) | 6.45313 | 0.240160 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −13.2410 | −0.492096 | ||||||||
\(725\) | −5.54461 | −0.205922 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −44.9015 | −1.66530 | −0.832652 | − | 0.553797i | \(-0.813178\pi\) | ||||
−0.832652 | + | 0.553797i | \(0.813178\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.72569 | 0.100882 | ||||||||
\(731\) | 4.04593 | 0.149644 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.94072 | 0.182490 | 0.0912449 | − | 0.995828i | \(-0.470915\pi\) | ||||
0.0912449 | + | 0.995828i | \(0.470915\pi\) | |||||||
\(734\) | −6.82559 | −0.251937 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −29.2810 | −1.07931 | ||||||||
\(737\) | 5.18912 | 0.191144 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.03926 | −0.222158 | −0.111079 | − | 0.993812i | \(-0.535431\pi\) | ||||
−0.111079 | + | 0.993812i | \(0.535431\pi\) | |||||||
\(740\) | 18.4095 | 0.676745 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.152510 | −0.00559882 | ||||||||
\(743\) | −13.0589 | −0.479084 | −0.239542 | − | 0.970886i | \(-0.576997\pi\) | ||||
−0.239542 | + | 0.970886i | \(0.576997\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17.0892 | −0.626100 | ||||||||
\(746\) | 7.97998 | 0.292168 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9.51655 | 0.347960 | ||||||||
\(749\) | 0.376871 | 0.0137706 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 48.0236 | 1.75241 | 0.876204 | − | 0.481941i | \(-0.160068\pi\) | ||||
0.876204 | + | 0.481941i | \(0.160068\pi\) | |||||||
\(752\) | −16.6664 | −0.607761 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13.0130 | −0.473590 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.56424 | −0.165890 | −0.0829450 | − | 0.996554i | \(-0.526433\pi\) | ||||
−0.0829450 | + | 0.996554i | \(0.526433\pi\) | |||||||
\(758\) | 7.18548 | 0.260989 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.152510 | −0.00553212 | ||||||||
\(761\) | 21.0892 | 0.764483 | 0.382242 | − | 0.924062i | \(-0.375152\pi\) | ||||
0.382242 | + | 0.924062i | \(0.375152\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.1721 | 0.368256 | ||||||||
\(764\) | −26.2962 | −0.951364 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.590926 | −0.0213510 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −42.3332 | −1.52657 | −0.763287 | − | 0.646059i | \(-0.776416\pi\) | ||||
−0.763287 | + | 0.646059i | \(0.776416\pi\) | |||||||
\(770\) | 0.152510 | 0.00549608 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 44.7552 | 1.61078 | ||||||||
\(773\) | 50.2436 | 1.80714 | 0.903568 | − | 0.428444i | \(-0.140938\pi\) | ||||
0.903568 | + | 0.428444i | \(0.140938\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.97370 | 0.358266 | ||||||||
\(776\) | −13.0759 | −0.469396 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.06330 | −0.324935 | ||||||||
\(779\) | −0.487982 | −0.0174838 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.97143 | 0.177892 | ||||||||
\(782\) | 19.6165 | 0.701483 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −21.7949 | −0.778389 | ||||||||
\(785\) | −0.775639 | −0.0276838 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.5816 | 0.377193 | 0.188597 | − | 0.982055i | \(-0.439606\pi\) | ||||
0.188597 | + | 0.982055i | \(0.439606\pi\) | |||||||
\(788\) | −29.7903 | −1.06124 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3.38983 | −0.120605 | ||||||||
\(791\) | −3.51202 | −0.124873 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 4.94338 | 0.175434 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −16.5250 | −0.585712 | ||||||||
\(797\) | 20.1481 | 0.713683 | 0.356841 | − | 0.934165i | \(-0.383854\pi\) | ||||
0.356841 | + | 0.934165i | \(0.383854\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 37.2913 | 1.31927 | ||||||||
\(800\) | −3.76897 | −0.133253 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.84484 | 0.100455 | ||||||||
\(803\) | −5.45137 | −0.192375 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.12847 | −0.180755 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 12.3569 | 0.434713 | ||||||||
\(809\) | −12.9108 | −0.453919 | −0.226960 | − | 0.973904i | \(-0.572879\pi\) | ||||
−0.226960 | + | 0.973904i | \(0.572879\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.8974 | 0.558235 | 0.279117 | − | 0.960257i | \(-0.409958\pi\) | ||||
0.279117 | + | 0.960257i | \(0.409958\pi\) | |||||||
\(812\) | −6.89744 | −0.242053 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.25695 | 0.0791061 | ||||||||
\(815\) | −12.1981 | −0.427279 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.0629110 | 0.00220098 | ||||||||
\(818\) | 5.86447 | 0.205046 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.96074 | −0.278001 | ||||||||
\(821\) | −37.2284 | −1.29928 | −0.649640 | − | 0.760242i | \(-0.725080\pi\) | ||||
−0.649640 | + | 0.760242i | \(0.725080\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.89744 | −0.170714 | −0.0853571 | − | 0.996350i | \(-0.527203\pi\) | ||||
−0.0853571 | + | 0.996350i | \(0.527203\pi\) | |||||||
\(824\) | 5.94817 | 0.207214 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.499059 | 0.0173645 | ||||||||
\(827\) | 37.6334 | 1.30864 | 0.654321 | − | 0.756217i | \(-0.272954\pi\) | ||||
0.654321 | + | 0.756217i | \(0.272954\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −48.9104 | −1.69873 | −0.849364 | − | 0.527807i | \(-0.823014\pi\) | ||||
−0.849364 | + | 0.527807i | \(0.823014\pi\) | |||||||
\(830\) | −0.601231 | −0.0208690 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 48.7663 | 1.68965 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.59054 | −0.0550429 | ||||||||
\(836\) | 0.147975 | 0.00511781 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.37247 | 0.151044 | ||||||||
\(839\) | 48.2783 | 1.66675 | 0.833377 | − | 0.552706i | \(-0.186405\pi\) | ||||
0.833377 | + | 0.552706i | \(0.186405\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.74266 | 0.0600919 | ||||||||
\(842\) | 8.34791 | 0.287688 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −16.5990 | −0.571360 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.95633 | 0.239022 | ||||||||
\(848\) | −2.25695 | −0.0775040 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.52498 | 0.0866060 | ||||||||
\(851\) | −75.8948 | −2.60164 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.4291 | 0.494043 | 0.247021 | − | 0.969010i | \(-0.420548\pi\) | ||||
0.247021 | + | 0.969010i | \(0.420548\pi\) | |||||||
\(854\) | −0.943376 | −0.0322817 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.753741 | −0.0257623 | ||||||||
\(857\) | −3.64678 | −0.124572 | −0.0622858 | − | 0.998058i | \(-0.519839\pi\) | ||||
−0.0622858 | + | 0.998058i | \(0.519839\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.7427 | 0.741850 | 0.370925 | − | 0.928663i | \(-0.379041\pi\) | ||||
0.370925 | + | 0.928663i | \(0.379041\pi\) | |||||||
\(860\) | 1.02630 | 0.0349966 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.42203 | −0.286856 | ||||||||
\(863\) | −17.0892 | −0.581724 | −0.290862 | − | 0.956765i | \(-0.593942\pi\) | ||||
−0.290862 | + | 0.956765i | \(0.593942\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.7493 | −0.433490 | ||||||||
\(866\) | 4.77829 | 0.162373 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 12.4072 | 0.421128 | ||||||||
\(869\) | 6.77966 | 0.229984 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −20.3443 | −0.688944 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.305020 | 0.0103175 | ||||||||
\(875\) | −0.660123 | −0.0223162 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.85818 | 0.164049 | 0.0820246 | − | 0.996630i | \(-0.473861\pi\) | ||||
0.0820246 | + | 0.996630i | \(0.473861\pi\) | |||||||
\(878\) | −7.08481 | −0.239101 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.25695 | 0.0760818 | ||||||||
\(881\) | 23.3202 | 0.785679 | 0.392840 | − | 0.919607i | \(-0.371493\pi\) | ||||
0.392840 | + | 0.919607i | \(0.371493\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.8934 | −0.433898 | −0.216949 | − | 0.976183i | \(-0.569611\pi\) | ||||
−0.216949 | + | 0.976183i | \(0.569611\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.88448 | −0.130502 | ||||||||
\(887\) | −30.9278 | −1.03845 | −0.519226 | − | 0.854637i | \(-0.673780\pi\) | ||||
−0.519226 | + | 0.854637i | \(0.673780\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.93444 | 0.266112 | ||||||||
\(890\) | −4.60350 | −0.154310 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 18.9188 | 0.633449 | ||||||||
\(893\) | 0.579849 | 0.0194039 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −17.7623 | −0.593728 | ||||||||
\(896\) | −6.17843 | −0.206407 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −8.80558 | −0.293846 | ||||||||
\(899\) | −55.3002 | −1.84437 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.04995 | 0.168238 | ||||||||
\(902\) | −0.975965 | −0.0324961 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.02404 | 0.233616 | ||||||||
\(905\) | 7.02630 | 0.233562 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.9604 | −0.563159 | −0.281580 | − | 0.959538i | \(-0.590858\pi\) | ||||
−0.281580 | + | 0.959538i | \(0.590858\pi\) | |||||||
\(908\) | −2.28287 | −0.0757596 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.7297 | −1.25004 | −0.625020 | − | 0.780608i | \(-0.714909\pi\) | ||||
−0.625020 | + | 0.780608i | \(0.714909\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.20246 | 0.0397957 | ||||||||
\(914\) | 2.00667 | 0.0663748 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 36.2650 | 1.19823 | ||||||||
\(917\) | 7.19806 | 0.237701 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.1628 | 1.32485 | 0.662425 | − | 0.749129i | \(-0.269528\pi\) | ||||
0.662425 | + | 0.749129i | \(0.269528\pi\) | |||||||
\(920\) | 10.2569 | 0.338162 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5.26537 | 0.173406 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.76897 | −0.321202 | ||||||||
\(926\) | 5.92815 | 0.194811 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 20.8974 | 0.685992 | ||||||||
\(929\) | 23.7690 | 0.779835 | 0.389917 | − | 0.920850i | \(-0.372504\pi\) | ||||
0.389917 | + | 0.920850i | \(0.372504\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.758276 | 0.0248515 | ||||||||
\(932\) | −45.0545 | −1.47581 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6.96035 | −0.227750 | ||||||||
\(935\) | −5.04995 | −0.165151 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.43803 | −0.242990 | −0.121495 | − | 0.992592i | \(-0.538769\pi\) | ||||
−0.121495 | + | 0.992592i | \(0.538769\pi\) | |||||||
\(938\) | 1.71273 | 0.0559226 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9.45941 | 0.308532 | ||||||||
\(941\) | −19.3528 | −0.630884 | −0.315442 | − | 0.948945i | \(-0.602153\pi\) | ||||
−0.315442 | + | 0.948945i | \(0.602153\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32.8189 | 1.06873 | ||||||||
\(944\) | 7.38542 | 0.240375 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.125822 | 0.00409082 | ||||||||
\(947\) | 13.9171 | 0.452244 | 0.226122 | − | 0.974099i | \(-0.427395\pi\) | ||||
0.226122 | + | 0.974099i | \(0.427395\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0.0392613 | 0.00127381 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.47464 | 0.209844 | ||||||||
\(953\) | 10.6271 | 0.344247 | 0.172124 | − | 0.985075i | \(-0.444937\pi\) | ||||
0.172124 | + | 0.985075i | \(0.444937\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.9541 | 0.451543 | ||||||||
\(956\) | −35.2017 | −1.13850 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 13.9318 | 0.450115 | ||||||||
\(959\) | −2.23770 | −0.0722593 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 68.4746 | 2.20886 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11.5246 | 0.371182 | ||||||||
\(965\) | −23.7493 | −0.764518 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −51.6771 | −1.66182 | −0.830912 | − | 0.556404i | \(-0.812181\pi\) | ||||
−0.830912 | + | 0.556404i | \(0.812181\pi\) | |||||||
\(968\) | −13.9127 | −0.447170 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.36618 | 0.108082 | ||||||||
\(971\) | 42.8974 | 1.37664 | 0.688322 | − | 0.725405i | \(-0.258348\pi\) | ||||
0.688322 | + | 0.725405i | \(0.258348\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.77525 | −0.313380 | ||||||||
\(974\) | 8.17843 | 0.262054 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −13.9607 | −0.446872 | ||||||||
\(977\) | 18.1651 | 0.581153 | 0.290576 | − | 0.956852i | \(-0.406153\pi\) | ||||
0.290576 | + | 0.956852i | \(0.406153\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.20700 | 0.294257 | ||||||||
\(980\) | 12.3702 | 0.395151 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12.4983 | 0.398836 | ||||||||
\(983\) | −10.8582 | −0.346322 | −0.173161 | − | 0.984894i | \(-0.555398\pi\) | ||||
−0.173161 | + | 0.984894i | \(0.555398\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.8082 | 0.503692 | ||||||||
\(986\) | −14.0000 | −0.445851 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.23103 | −0.134539 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.3725 | −0.710685 | −0.355342 | − | 0.934736i | \(-0.615636\pi\) | ||||
−0.355342 | + | 0.934736i | \(0.615636\pi\) | |||||||
\(992\) | −37.5905 | −1.19350 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.64088 | 0.0520455 | ||||||||
\(995\) | 8.76897 | 0.277995 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.2373 | −0.767604 | −0.383802 | − | 0.923415i | \(-0.625385\pi\) | ||||
−0.383802 | + | 0.923415i | \(0.625385\pi\) | |||||||
\(998\) | 11.8349 | 0.374628 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 7605.2.a.bw.1.2 | 3 | ||
3.2 | odd | 2 | 2535.2.a.ba.1.2 | 3 | |||
13.4 | even | 6 | 585.2.j.f.406.2 | 6 | |||
13.10 | even | 6 | 585.2.j.f.451.2 | 6 | |||
13.12 | even | 2 | 7605.2.a.bv.1.2 | 3 | |||
39.17 | odd | 6 | 195.2.i.d.16.2 | ✓ | 6 | ||
39.23 | odd | 6 | 195.2.i.d.61.2 | yes | 6 | ||
39.38 | odd | 2 | 2535.2.a.bb.1.2 | 3 | |||
195.17 | even | 12 | 975.2.bb.k.874.3 | 12 | |||
195.23 | even | 12 | 975.2.bb.k.724.3 | 12 | |||
195.62 | even | 12 | 975.2.bb.k.724.4 | 12 | |||
195.134 | odd | 6 | 975.2.i.l.601.2 | 6 | |||
195.173 | even | 12 | 975.2.bb.k.874.4 | 12 | |||
195.179 | odd | 6 | 975.2.i.l.451.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
195.2.i.d.16.2 | ✓ | 6 | 39.17 | odd | 6 | ||
195.2.i.d.61.2 | yes | 6 | 39.23 | odd | 6 | ||
585.2.j.f.406.2 | 6 | 13.4 | even | 6 | |||
585.2.j.f.451.2 | 6 | 13.10 | even | 6 | |||
975.2.i.l.451.2 | 6 | 195.179 | odd | 6 | |||
975.2.i.l.601.2 | 6 | 195.134 | odd | 6 | |||
975.2.bb.k.724.3 | 12 | 195.23 | even | 12 | |||
975.2.bb.k.724.4 | 12 | 195.62 | even | 12 | |||
975.2.bb.k.874.3 | 12 | 195.17 | even | 12 | |||
975.2.bb.k.874.4 | 12 | 195.173 | even | 12 | |||
2535.2.a.ba.1.2 | 3 | 3.2 | odd | 2 | |||
2535.2.a.bb.1.2 | 3 | 39.38 | odd | 2 | |||
7605.2.a.bv.1.2 | 3 | 13.12 | even | 2 | |||
7605.2.a.bw.1.2 | 3 | 1.1 | even | 1 | trivial |