Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.50751 | 1.06597 | 0.532984 | − | 0.846125i | \(-0.321071\pi\) | ||||
0.532984 | + | 0.846125i | \(0.321071\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.272577 | 0.136288 | ||||||||
\(5\) | −1.10903 | −0.495973 | −0.247987 | − | 0.968763i | \(-0.579769\pi\) | ||||
−0.247987 | + | 0.968763i | \(0.579769\pi\) | |||||||
\(6\) | −1.50751 | −0.615437 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.60410 | −0.920689 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.67187 | −0.528692 | ||||||||
\(11\) | 3.74096 | 1.12794 | 0.563971 | − | 0.825794i | \(-0.309273\pi\) | ||||
0.563971 | + | 0.825794i | \(0.309273\pi\) | |||||||
\(12\) | −0.272577 | −0.0786862 | ||||||||
\(13\) | −4.04957 | −1.12315 | −0.561575 | − | 0.827426i | \(-0.689804\pi\) | ||||
−0.561575 | + | 0.827426i | \(0.689804\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.10903 | 0.286350 | ||||||||
\(16\) | −4.47086 | −1.11771 | ||||||||
\(17\) | 1.28562 | 0.311808 | 0.155904 | − | 0.987772i | \(-0.450171\pi\) | ||||
0.155904 | + | 0.987772i | \(0.450171\pi\) | |||||||
\(18\) | 1.50751 | 0.355323 | ||||||||
\(19\) | −2.77400 | −0.636400 | −0.318200 | − | 0.948024i | \(-0.603078\pi\) | ||||
−0.318200 | + | 0.948024i | \(0.603078\pi\) | |||||||
\(20\) | −0.302296 | −0.0675955 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.63953 | 1.20235 | ||||||||
\(23\) | 8.14553 | 1.69846 | 0.849230 | − | 0.528023i | \(-0.177067\pi\) | ||||
0.849230 | + | 0.528023i | \(0.177067\pi\) | |||||||
\(24\) | 2.60410 | 0.531560 | ||||||||
\(25\) | −3.77005 | −0.754010 | ||||||||
\(26\) | −6.10476 | −1.19724 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.13225 | −0.210254 | −0.105127 | − | 0.994459i | \(-0.533525\pi\) | ||||
−0.105127 | + | 0.994459i | \(0.533525\pi\) | |||||||
\(30\) | 1.67187 | 0.305240 | ||||||||
\(31\) | −3.06661 | −0.550779 | −0.275390 | − | 0.961333i | \(-0.588807\pi\) | ||||
−0.275390 | + | 0.961333i | \(0.588807\pi\) | |||||||
\(32\) | −1.53164 | −0.270758 | ||||||||
\(33\) | −3.74096 | −0.651218 | ||||||||
\(34\) | 1.93807 | 0.332377 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.272577 | 0.0454295 | ||||||||
\(37\) | −8.99346 | −1.47852 | −0.739258 | − | 0.673423i | \(-0.764823\pi\) | ||||
−0.739258 | + | 0.673423i | \(0.764823\pi\) | |||||||
\(38\) | −4.18183 | −0.678382 | ||||||||
\(39\) | 4.04957 | 0.648450 | ||||||||
\(40\) | 2.88803 | 0.456637 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.07578 | 0.774050 | 0.387025 | − | 0.922069i | \(-0.373503\pi\) | ||||
0.387025 | + | 0.922069i | \(0.373503\pi\) | |||||||
\(44\) | 1.01970 | 0.153726 | ||||||||
\(45\) | −1.10903 | −0.165324 | ||||||||
\(46\) | 12.2794 | 1.81050 | ||||||||
\(47\) | 1.77524 | 0.258946 | 0.129473 | − | 0.991583i | \(-0.458671\pi\) | ||||
0.129473 | + | 0.991583i | \(0.458671\pi\) | |||||||
\(48\) | 4.47086 | 0.645312 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −5.68338 | −0.803751 | ||||||||
\(51\) | −1.28562 | −0.180022 | ||||||||
\(52\) | −1.10382 | −0.153072 | ||||||||
\(53\) | −1.43908 | −0.197673 | −0.0988365 | − | 0.995104i | \(-0.531512\pi\) | ||||
−0.0988365 | + | 0.995104i | \(0.531512\pi\) | |||||||
\(54\) | −1.50751 | −0.205146 | ||||||||
\(55\) | −4.14884 | −0.559430 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.77400 | 0.367425 | ||||||||
\(58\) | −1.70688 | −0.224124 | ||||||||
\(59\) | 11.8133 | 1.53796 | 0.768980 | − | 0.639273i | \(-0.220765\pi\) | ||||
0.768980 | + | 0.639273i | \(0.220765\pi\) | |||||||
\(60\) | 0.302296 | 0.0390263 | ||||||||
\(61\) | −6.29435 | −0.805908 | −0.402954 | − | 0.915220i | \(-0.632017\pi\) | ||||
−0.402954 | + | 0.915220i | \(0.632017\pi\) | |||||||
\(62\) | −4.62294 | −0.587113 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.63275 | 0.829094 | ||||||||
\(65\) | 4.49110 | 0.557052 | ||||||||
\(66\) | −5.63953 | −0.694178 | ||||||||
\(67\) | 1.53411 | 0.187421 | 0.0937107 | − | 0.995599i | \(-0.470127\pi\) | ||||
0.0937107 | + | 0.995599i | \(0.470127\pi\) | |||||||
\(68\) | 0.350429 | 0.0424958 | ||||||||
\(69\) | −8.14553 | −0.980606 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.4191 | 1.47388 | 0.736938 | − | 0.675960i | \(-0.236271\pi\) | ||||
0.736938 | + | 0.675960i | \(0.236271\pi\) | |||||||
\(72\) | −2.60410 | −0.306896 | ||||||||
\(73\) | −7.32700 | −0.857561 | −0.428780 | − | 0.903409i | \(-0.641057\pi\) | ||||
−0.428780 | + | 0.903409i | \(0.641057\pi\) | |||||||
\(74\) | −13.5577 | −1.57605 | ||||||||
\(75\) | 3.77005 | 0.435328 | ||||||||
\(76\) | −0.756129 | −0.0867339 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 6.10476 | 0.691228 | ||||||||
\(79\) | 3.06259 | 0.344568 | 0.172284 | − | 0.985047i | \(-0.444885\pi\) | ||||
0.172284 | + | 0.985047i | \(0.444885\pi\) | |||||||
\(80\) | 4.95832 | 0.554356 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.50751 | 0.166476 | ||||||||
\(83\) | 10.5895 | 1.16235 | 0.581175 | − | 0.813778i | \(-0.302593\pi\) | ||||
0.581175 | + | 0.813778i | \(0.302593\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.42579 | −0.154648 | ||||||||
\(86\) | 7.65178 | 0.825112 | ||||||||
\(87\) | 1.13225 | 0.121390 | ||||||||
\(88\) | −9.74185 | −1.03848 | ||||||||
\(89\) | 0.862204 | 0.0913935 | 0.0456967 | − | 0.998955i | \(-0.485449\pi\) | ||||
0.0456967 | + | 0.998955i | \(0.485449\pi\) | |||||||
\(90\) | −1.67187 | −0.176231 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.22028 | 0.231480 | ||||||||
\(93\) | 3.06661 | 0.317993 | ||||||||
\(94\) | 2.67619 | 0.276028 | ||||||||
\(95\) | 3.07645 | 0.315637 | ||||||||
\(96\) | 1.53164 | 0.156322 | ||||||||
\(97\) | 2.95888 | 0.300428 | 0.150214 | − | 0.988653i | \(-0.452004\pi\) | ||||
0.150214 | + | 0.988653i | \(0.452004\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.74096 | 0.375981 | ||||||||
\(100\) | −1.02763 | −0.102763 | ||||||||
\(101\) | −9.78581 | −0.973724 | −0.486862 | − | 0.873479i | \(-0.661859\pi\) | ||||
−0.486862 | + | 0.873479i | \(0.661859\pi\) | |||||||
\(102\) | −1.93807 | −0.191898 | ||||||||
\(103\) | −5.64685 | −0.556400 | −0.278200 | − | 0.960523i | \(-0.589738\pi\) | ||||
−0.278200 | + | 0.960523i | \(0.589738\pi\) | |||||||
\(104\) | 10.5455 | 1.03407 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.16942 | −0.210713 | ||||||||
\(107\) | 14.2514 | 1.37773 | 0.688866 | − | 0.724889i | \(-0.258109\pi\) | ||||
0.688866 | + | 0.724889i | \(0.258109\pi\) | |||||||
\(108\) | −0.272577 | −0.0262287 | ||||||||
\(109\) | −1.98301 | −0.189938 | −0.0949689 | − | 0.995480i | \(-0.530275\pi\) | ||||
−0.0949689 | + | 0.995480i | \(0.530275\pi\) | |||||||
\(110\) | −6.25441 | −0.596334 | ||||||||
\(111\) | 8.99346 | 0.853621 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.92257 | 0.180860 | 0.0904302 | − | 0.995903i | \(-0.471176\pi\) | ||||
0.0904302 | + | 0.995903i | \(0.471176\pi\) | |||||||
\(114\) | 4.18183 | 0.391664 | ||||||||
\(115\) | −9.03364 | −0.842391 | ||||||||
\(116\) | −0.308626 | −0.0286552 | ||||||||
\(117\) | −4.04957 | −0.374383 | ||||||||
\(118\) | 17.8086 | 1.63942 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.88803 | −0.263640 | ||||||||
\(121\) | 2.99480 | 0.272255 | ||||||||
\(122\) | −9.48877 | −0.859073 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | −0.835887 | −0.0750649 | ||||||||
\(125\) | 9.72625 | 0.869943 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.05248 | 0.537071 | 0.268536 | − | 0.963270i | \(-0.413460\pi\) | ||||
0.268536 | + | 0.963270i | \(0.413460\pi\) | |||||||
\(128\) | 13.0622 | 1.15455 | ||||||||
\(129\) | −5.07578 | −0.446898 | ||||||||
\(130\) | 6.77036 | 0.593800 | ||||||||
\(131\) | −10.1642 | −0.888055 | −0.444027 | − | 0.896013i | \(-0.646451\pi\) | ||||
−0.444027 | + | 0.896013i | \(0.646451\pi\) | |||||||
\(132\) | −1.01970 | −0.0887535 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.31268 | 0.199785 | ||||||||
\(135\) | 1.10903 | 0.0954501 | ||||||||
\(136\) | −3.34788 | −0.287078 | ||||||||
\(137\) | 10.4749 | 0.894928 | 0.447464 | − | 0.894302i | \(-0.352327\pi\) | ||||
0.447464 | + | 0.894302i | \(0.352327\pi\) | |||||||
\(138\) | −12.2794 | −1.04530 | ||||||||
\(139\) | 5.03683 | 0.427219 | 0.213609 | − | 0.976919i | \(-0.431478\pi\) | ||||
0.213609 | + | 0.976919i | \(0.431478\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.77524 | −0.149503 | ||||||||
\(142\) | 18.7219 | 1.57110 | ||||||||
\(143\) | −15.1493 | −1.26685 | ||||||||
\(144\) | −4.47086 | −0.372571 | ||||||||
\(145\) | 1.25570 | 0.104280 | ||||||||
\(146\) | −11.0455 | −0.914132 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.45141 | −0.201505 | ||||||||
\(149\) | 12.4511 | 1.02003 | 0.510016 | − | 0.860165i | \(-0.329640\pi\) | ||||
0.510016 | + | 0.860165i | \(0.329640\pi\) | |||||||
\(150\) | 5.68338 | 0.464046 | ||||||||
\(151\) | 1.01228 | 0.0823779 | 0.0411889 | − | 0.999151i | \(-0.486885\pi\) | ||||
0.0411889 | + | 0.999151i | \(0.486885\pi\) | |||||||
\(152\) | 7.22378 | 0.585926 | ||||||||
\(153\) | 1.28562 | 0.103936 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.40096 | 0.273172 | ||||||||
\(156\) | 1.10382 | 0.0883763 | ||||||||
\(157\) | 3.97214 | 0.317011 | 0.158506 | − | 0.987358i | \(-0.449332\pi\) | ||||
0.158506 | + | 0.987358i | \(0.449332\pi\) | |||||||
\(158\) | 4.61688 | 0.367299 | ||||||||
\(159\) | 1.43908 | 0.114127 | ||||||||
\(160\) | 1.69864 | 0.134289 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.50751 | 0.118441 | ||||||||
\(163\) | 22.6056 | 1.77061 | 0.885304 | − | 0.465013i | \(-0.153950\pi\) | ||||
0.885304 | + | 0.465013i | \(0.153950\pi\) | |||||||
\(164\) | 0.272577 | 0.0212847 | ||||||||
\(165\) | 4.14884 | 0.322987 | ||||||||
\(166\) | 15.9638 | 1.23903 | ||||||||
\(167\) | 10.2870 | 0.796035 | 0.398017 | − | 0.917378i | \(-0.369698\pi\) | ||||
0.398017 | + | 0.917378i | \(0.369698\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.39903 | 0.261464 | ||||||||
\(170\) | −2.14938 | −0.164850 | ||||||||
\(171\) | −2.77400 | −0.212133 | ||||||||
\(172\) | 1.38354 | 0.105494 | ||||||||
\(173\) | 8.31332 | 0.632050 | 0.316025 | − | 0.948751i | \(-0.397652\pi\) | ||||
0.316025 | + | 0.948751i | \(0.397652\pi\) | |||||||
\(174\) | 1.70688 | 0.129398 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −16.7253 | −1.26072 | ||||||||
\(177\) | −11.8133 | −0.887942 | ||||||||
\(178\) | 1.29978 | 0.0974225 | ||||||||
\(179\) | 5.82288 | 0.435222 | 0.217611 | − | 0.976036i | \(-0.430174\pi\) | ||||
0.217611 | + | 0.976036i | \(0.430174\pi\) | |||||||
\(180\) | −0.302296 | −0.0225318 | ||||||||
\(181\) | 16.9447 | 1.25949 | 0.629746 | − | 0.776801i | \(-0.283159\pi\) | ||||
0.629746 | + | 0.776801i | \(0.283159\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.29435 | 0.465291 | ||||||||
\(184\) | −21.2118 | −1.56375 | ||||||||
\(185\) | 9.97402 | 0.733304 | ||||||||
\(186\) | 4.62294 | 0.338970 | ||||||||
\(187\) | 4.80944 | 0.351701 | ||||||||
\(188\) | 0.483891 | 0.0352913 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.63777 | 0.336459 | ||||||||
\(191\) | 12.9496 | 0.937001 | 0.468501 | − | 0.883463i | \(-0.344794\pi\) | ||||
0.468501 | + | 0.883463i | \(0.344794\pi\) | |||||||
\(192\) | −6.63275 | −0.478678 | ||||||||
\(193\) | −1.53674 | −0.110617 | −0.0553084 | − | 0.998469i | \(-0.517614\pi\) | ||||
−0.0553084 | + | 0.998469i | \(0.517614\pi\) | |||||||
\(194\) | 4.46053 | 0.320247 | ||||||||
\(195\) | −4.49110 | −0.321614 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.6537 | 1.04403 | 0.522017 | − | 0.852935i | \(-0.325180\pi\) | ||||
0.522017 | + | 0.852935i | \(0.325180\pi\) | |||||||
\(198\) | 5.63953 | 0.400784 | ||||||||
\(199\) | 15.9626 | 1.13156 | 0.565780 | − | 0.824556i | \(-0.308575\pi\) | ||||
0.565780 | + | 0.824556i | \(0.308575\pi\) | |||||||
\(200\) | 9.81760 | 0.694209 | ||||||||
\(201\) | −1.53411 | −0.108208 | ||||||||
\(202\) | −14.7522 | −1.03796 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.350429 | −0.0245350 | ||||||||
\(205\) | −1.10903 | −0.0774580 | ||||||||
\(206\) | −8.51266 | −0.593105 | ||||||||
\(207\) | 8.14553 | 0.566153 | ||||||||
\(208\) | 18.1050 | 1.25536 | ||||||||
\(209\) | −10.3774 | −0.717822 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.5174 | 1.61901 | 0.809503 | − | 0.587116i | \(-0.199737\pi\) | ||||
0.809503 | + | 0.587116i | \(0.199737\pi\) | |||||||
\(212\) | −0.392260 | −0.0269405 | ||||||||
\(213\) | −12.4191 | −0.850943 | ||||||||
\(214\) | 21.4840 | 1.46862 | ||||||||
\(215\) | −5.62920 | −0.383908 | ||||||||
\(216\) | 2.60410 | 0.177187 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.98940 | −0.202468 | ||||||||
\(219\) | 7.32700 | 0.495113 | ||||||||
\(220\) | −1.13088 | −0.0762438 | ||||||||
\(221\) | −5.20619 | −0.350206 | ||||||||
\(222\) | 13.5577 | 0.909933 | ||||||||
\(223\) | 22.1230 | 1.48146 | 0.740732 | − | 0.671801i | \(-0.234479\pi\) | ||||
0.740732 | + | 0.671801i | \(0.234479\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.77005 | −0.251337 | ||||||||
\(226\) | 2.89829 | 0.192791 | ||||||||
\(227\) | −21.8654 | −1.45126 | −0.725630 | − | 0.688085i | \(-0.758451\pi\) | ||||
−0.725630 | + | 0.688085i | \(0.758451\pi\) | |||||||
\(228\) | 0.756129 | 0.0500758 | ||||||||
\(229\) | 14.7855 | 0.977054 | 0.488527 | − | 0.872549i | \(-0.337534\pi\) | ||||
0.488527 | + | 0.872549i | \(0.337534\pi\) | |||||||
\(230\) | −13.6183 | −0.897962 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.94850 | 0.193578 | ||||||||
\(233\) | −27.2105 | −1.78262 | −0.891310 | − | 0.453394i | \(-0.850213\pi\) | ||||
−0.891310 | + | 0.453394i | \(0.850213\pi\) | |||||||
\(234\) | −6.10476 | −0.399080 | ||||||||
\(235\) | −1.96880 | −0.128430 | ||||||||
\(236\) | 3.22003 | 0.209606 | ||||||||
\(237\) | −3.06259 | −0.198937 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.9634 | −1.55006 | −0.775031 | − | 0.631924i | \(-0.782266\pi\) | ||||
−0.775031 | + | 0.631924i | \(0.782266\pi\) | |||||||
\(240\) | −4.95832 | −0.320058 | ||||||||
\(241\) | −12.9104 | −0.831632 | −0.415816 | − | 0.909449i | \(-0.636504\pi\) | ||||
−0.415816 | + | 0.909449i | \(0.636504\pi\) | |||||||
\(242\) | 4.51468 | 0.290215 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −1.71569 | −0.109836 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.50751 | −0.0961151 | ||||||||
\(247\) | 11.2335 | 0.714772 | ||||||||
\(248\) | 7.98577 | 0.507097 | ||||||||
\(249\) | −10.5895 | −0.671083 | ||||||||
\(250\) | 14.6624 | 0.927331 | ||||||||
\(251\) | 13.4903 | 0.851497 | 0.425749 | − | 0.904841i | \(-0.360011\pi\) | ||||
0.425749 | + | 0.904841i | \(0.360011\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 30.4721 | 1.91577 | ||||||||
\(254\) | 9.12416 | 0.572501 | ||||||||
\(255\) | 1.42579 | 0.0892863 | ||||||||
\(256\) | 6.42585 | 0.401616 | ||||||||
\(257\) | 4.35831 | 0.271864 | 0.135932 | − | 0.990718i | \(-0.456597\pi\) | ||||
0.135932 | + | 0.990718i | \(0.456597\pi\) | |||||||
\(258\) | −7.65178 | −0.476379 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.22417 | 0.0759198 | ||||||||
\(261\) | −1.13225 | −0.0700846 | ||||||||
\(262\) | −15.3227 | −0.946638 | ||||||||
\(263\) | −14.2904 | −0.881182 | −0.440591 | − | 0.897708i | \(-0.645231\pi\) | ||||
−0.440591 | + | 0.897708i | \(0.645231\pi\) | |||||||
\(264\) | 9.74185 | 0.599569 | ||||||||
\(265\) | 1.59598 | 0.0980405 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.862204 | −0.0527660 | ||||||||
\(268\) | 0.418163 | 0.0255434 | ||||||||
\(269\) | 20.3295 | 1.23951 | 0.619755 | − | 0.784795i | \(-0.287232\pi\) | ||||
0.619755 | + | 0.784795i | \(0.287232\pi\) | |||||||
\(270\) | 1.67187 | 0.101747 | ||||||||
\(271\) | −21.1831 | −1.28678 | −0.643392 | − | 0.765537i | \(-0.722473\pi\) | ||||
−0.643392 | + | 0.765537i | \(0.722473\pi\) | |||||||
\(272\) | −5.74780 | −0.348512 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.7909 | 0.953965 | ||||||||
\(275\) | −14.1036 | −0.850480 | ||||||||
\(276\) | −2.22028 | −0.133645 | ||||||||
\(277\) | 3.20291 | 0.192444 | 0.0962221 | − | 0.995360i | \(-0.469324\pi\) | ||||
0.0962221 | + | 0.995360i | \(0.469324\pi\) | |||||||
\(278\) | 7.59306 | 0.455401 | ||||||||
\(279\) | −3.06661 | −0.183593 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.8668 | −1.00619 | −0.503094 | − | 0.864231i | \(-0.667805\pi\) | ||||
−0.503094 | + | 0.864231i | \(0.667805\pi\) | |||||||
\(282\) | −2.67619 | −0.159365 | ||||||||
\(283\) | −29.0207 | −1.72510 | −0.862551 | − | 0.505971i | \(-0.831134\pi\) | ||||
−0.862551 | + | 0.505971i | \(0.831134\pi\) | |||||||
\(284\) | 3.38516 | 0.200872 | ||||||||
\(285\) | −3.07645 | −0.182233 | ||||||||
\(286\) | −22.8377 | −1.35042 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.53164 | −0.0902528 | ||||||||
\(289\) | −15.3472 | −0.902776 | ||||||||
\(290\) | 1.89298 | 0.111160 | ||||||||
\(291\) | −2.95888 | −0.173452 | ||||||||
\(292\) | −1.99717 | −0.116876 | ||||||||
\(293\) | 33.4645 | 1.95502 | 0.977509 | − | 0.210896i | \(-0.0676380\pi\) | ||||
0.977509 | + | 0.210896i | \(0.0676380\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.1013 | −0.762787 | ||||||||
\(296\) | 23.4199 | 1.36125 | ||||||||
\(297\) | −3.74096 | −0.217073 | ||||||||
\(298\) | 18.7701 | 1.08732 | ||||||||
\(299\) | −32.9859 | −1.90762 | ||||||||
\(300\) | 1.02763 | 0.0593302 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.52601 | 0.0878122 | ||||||||
\(303\) | 9.78581 | 0.562180 | ||||||||
\(304\) | 12.4022 | 0.711313 | ||||||||
\(305\) | 6.98062 | 0.399709 | ||||||||
\(306\) | 1.93807 | 0.110792 | ||||||||
\(307\) | 12.0971 | 0.690419 | 0.345209 | − | 0.938526i | \(-0.387808\pi\) | ||||
0.345209 | + | 0.938526i | \(0.387808\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.64685 | 0.321238 | ||||||||
\(310\) | 5.12698 | 0.291193 | ||||||||
\(311\) | 4.23825 | 0.240329 | 0.120165 | − | 0.992754i | \(-0.461658\pi\) | ||||
0.120165 | + | 0.992754i | \(0.461658\pi\) | |||||||
\(312\) | −10.5455 | −0.597021 | ||||||||
\(313\) | −23.4002 | −1.32266 | −0.661329 | − | 0.750096i | \(-0.730007\pi\) | ||||
−0.661329 | + | 0.750096i | \(0.730007\pi\) | |||||||
\(314\) | 5.98802 | 0.337924 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.834792 | 0.0469607 | ||||||||
\(317\) | 7.71467 | 0.433299 | 0.216650 | − | 0.976249i | \(-0.430487\pi\) | ||||
0.216650 | + | 0.976249i | \(0.430487\pi\) | |||||||
\(318\) | 2.16942 | 0.121655 | ||||||||
\(319\) | −4.23571 | −0.237154 | ||||||||
\(320\) | −7.35592 | −0.411209 | ||||||||
\(321\) | −14.2514 | −0.795434 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.56630 | −0.198434 | ||||||||
\(324\) | 0.272577 | 0.0151432 | ||||||||
\(325\) | 15.2671 | 0.846866 | ||||||||
\(326\) | 34.0781 | 1.88741 | ||||||||
\(327\) | 1.98301 | 0.109661 | ||||||||
\(328\) | −2.60410 | −0.143787 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 6.25441 | 0.344294 | ||||||||
\(331\) | 0.784765 | 0.0431346 | 0.0215673 | − | 0.999767i | \(-0.493134\pi\) | ||||
0.0215673 | + | 0.999767i | \(0.493134\pi\) | |||||||
\(332\) | 2.88646 | 0.158415 | ||||||||
\(333\) | −8.99346 | −0.492838 | ||||||||
\(334\) | 15.5078 | 0.848548 | ||||||||
\(335\) | −1.70138 | −0.0929561 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.6836 | −0.636447 | −0.318224 | − | 0.948016i | \(-0.603086\pi\) | ||||
−0.318224 | + | 0.948016i | \(0.603086\pi\) | |||||||
\(338\) | 5.12406 | 0.278712 | ||||||||
\(339\) | −1.92257 | −0.104420 | ||||||||
\(340\) | −0.388637 | −0.0210768 | ||||||||
\(341\) | −11.4721 | −0.621248 | ||||||||
\(342\) | −4.18183 | −0.226127 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −13.2179 | −0.712659 | ||||||||
\(345\) | 9.03364 | 0.486355 | ||||||||
\(346\) | 12.5324 | 0.673745 | ||||||||
\(347\) | 1.28541 | 0.0690042 | 0.0345021 | − | 0.999405i | \(-0.489015\pi\) | ||||
0.0345021 | + | 0.999405i | \(0.489015\pi\) | |||||||
\(348\) | 0.308626 | 0.0165441 | ||||||||
\(349\) | 30.6569 | 1.64103 | 0.820513 | − | 0.571628i | \(-0.193688\pi\) | ||||
0.820513 | + | 0.571628i | \(0.193688\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.04957 | 0.216150 | ||||||||
\(352\) | −5.72981 | −0.305400 | ||||||||
\(353\) | 0.656222 | 0.0349271 | 0.0174636 | − | 0.999848i | \(-0.494441\pi\) | ||||
0.0174636 | + | 0.999848i | \(0.494441\pi\) | |||||||
\(354\) | −17.8086 | −0.946518 | ||||||||
\(355\) | −13.7732 | −0.731003 | ||||||||
\(356\) | 0.235017 | 0.0124559 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.77803 | 0.463933 | ||||||||
\(359\) | −0.670115 | −0.0353673 | −0.0176837 | − | 0.999844i | \(-0.505629\pi\) | ||||
−0.0176837 | + | 0.999844i | \(0.505629\pi\) | |||||||
\(360\) | 2.88803 | 0.152212 | ||||||||
\(361\) | −11.3049 | −0.594996 | ||||||||
\(362\) | 25.5443 | 1.34258 | ||||||||
\(363\) | −2.99480 | −0.157186 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.12587 | 0.425327 | ||||||||
\(366\) | 9.48877 | 0.495986 | ||||||||
\(367\) | 24.0081 | 1.25321 | 0.626607 | − | 0.779335i | \(-0.284443\pi\) | ||||
0.626607 | + | 0.779335i | \(0.284443\pi\) | |||||||
\(368\) | −36.4175 | −1.89839 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | 15.0359 | 0.781679 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.835887 | 0.0433387 | ||||||||
\(373\) | −3.48977 | −0.180694 | −0.0903468 | − | 0.995910i | \(-0.528798\pi\) | ||||
−0.0903468 | + | 0.995910i | \(0.528798\pi\) | |||||||
\(374\) | 7.25027 | 0.374902 | ||||||||
\(375\) | −9.72625 | −0.502262 | ||||||||
\(376\) | −4.62292 | −0.238409 | ||||||||
\(377\) | 4.58513 | 0.236146 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.7705 | 1.52921 | 0.764603 | − | 0.644501i | \(-0.222935\pi\) | ||||
0.764603 | + | 0.644501i | \(0.222935\pi\) | |||||||
\(380\) | 0.838570 | 0.0430177 | ||||||||
\(381\) | −6.05248 | −0.310078 | ||||||||
\(382\) | 19.5216 | 0.998814 | ||||||||
\(383\) | 9.44326 | 0.482528 | 0.241264 | − | 0.970460i | \(-0.422438\pi\) | ||||
0.241264 | + | 0.970460i | \(0.422438\pi\) | |||||||
\(384\) | −13.0622 | −0.666578 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.31664 | −0.117914 | ||||||||
\(387\) | 5.07578 | 0.258017 | ||||||||
\(388\) | 0.806521 | 0.0409449 | ||||||||
\(389\) | 31.9855 | 1.62173 | 0.810864 | − | 0.585235i | \(-0.198998\pi\) | ||||
0.810864 | + | 0.585235i | \(0.198998\pi\) | |||||||
\(390\) | −6.77036 | −0.342831 | ||||||||
\(391\) | 10.4720 | 0.529593 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.1642 | 0.512719 | ||||||||
\(394\) | 22.0906 | 1.11291 | ||||||||
\(395\) | −3.39651 | −0.170897 | ||||||||
\(396\) | 1.01970 | 0.0512419 | ||||||||
\(397\) | 21.0779 | 1.05787 | 0.528934 | − | 0.848663i | \(-0.322592\pi\) | ||||
0.528934 | + | 0.848663i | \(0.322592\pi\) | |||||||
\(398\) | 24.0638 | 1.20621 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 16.8554 | 0.842768 | ||||||||
\(401\) | −21.5312 | −1.07522 | −0.537609 | − | 0.843194i | \(-0.680672\pi\) | ||||
−0.537609 | + | 0.843194i | \(0.680672\pi\) | |||||||
\(402\) | −2.31268 | −0.115346 | ||||||||
\(403\) | 12.4185 | 0.618607 | ||||||||
\(404\) | −2.66739 | −0.132707 | ||||||||
\(405\) | −1.10903 | −0.0551082 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −33.6442 | −1.66768 | ||||||||
\(408\) | 3.34788 | 0.165745 | ||||||||
\(409\) | −35.8518 | −1.77276 | −0.886379 | − | 0.462961i | \(-0.846787\pi\) | ||||
−0.886379 | + | 0.462961i | \(0.846787\pi\) | |||||||
\(410\) | −1.67187 | −0.0825678 | ||||||||
\(411\) | −10.4749 | −0.516687 | ||||||||
\(412\) | −1.53920 | −0.0758310 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 12.2794 | 0.603501 | ||||||||
\(415\) | −11.7441 | −0.576495 | ||||||||
\(416\) | 6.20249 | 0.304102 | ||||||||
\(417\) | −5.03683 | −0.246655 | ||||||||
\(418\) | −15.6441 | −0.765176 | ||||||||
\(419\) | 9.75270 | 0.476451 | 0.238225 | − | 0.971210i | \(-0.423434\pi\) | ||||
0.238225 | + | 0.971210i | \(0.423434\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.117163 | 0.00571015 | 0.00285508 | − | 0.999996i | \(-0.499091\pi\) | ||||
0.00285508 | + | 0.999996i | \(0.499091\pi\) | |||||||
\(422\) | 35.4527 | 1.72581 | ||||||||
\(423\) | 1.77524 | 0.0863153 | ||||||||
\(424\) | 3.74751 | 0.181995 | ||||||||
\(425\) | −4.84684 | −0.235106 | ||||||||
\(426\) | −18.7219 | −0.907078 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3.88459 | 0.187769 | ||||||||
\(429\) | 15.1493 | 0.731415 | ||||||||
\(430\) | −8.48605 | −0.409234 | ||||||||
\(431\) | 21.1818 | 1.02029 | 0.510146 | − | 0.860088i | \(-0.329591\pi\) | ||||
0.510146 | + | 0.860088i | \(0.329591\pi\) | |||||||
\(432\) | 4.47086 | 0.215104 | ||||||||
\(433\) | 23.6911 | 1.13852 | 0.569260 | − | 0.822157i | \(-0.307230\pi\) | ||||
0.569260 | + | 0.822157i | \(0.307230\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.25570 | −0.0602063 | ||||||||
\(436\) | −0.540523 | −0.0258863 | ||||||||
\(437\) | −22.5957 | −1.08090 | ||||||||
\(438\) | 11.0455 | 0.527775 | ||||||||
\(439\) | 17.5444 | 0.837349 | 0.418675 | − | 0.908136i | \(-0.362495\pi\) | ||||
0.418675 | + | 0.908136i | \(0.362495\pi\) | |||||||
\(440\) | 10.8040 | 0.515061 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7.84837 | −0.373309 | ||||||||
\(443\) | 4.89678 | 0.232653 | 0.116327 | − | 0.993211i | \(-0.462888\pi\) | ||||
0.116327 | + | 0.993211i | \(0.462888\pi\) | |||||||
\(444\) | 2.45141 | 0.116339 | ||||||||
\(445\) | −0.956211 | −0.0453287 | ||||||||
\(446\) | 33.3505 | 1.57919 | ||||||||
\(447\) | −12.4511 | −0.588915 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.8031 | −1.21772 | −0.608862 | − | 0.793276i | \(-0.708374\pi\) | ||||
−0.608862 | + | 0.793276i | \(0.708374\pi\) | |||||||
\(450\) | −5.68338 | −0.267917 | ||||||||
\(451\) | 3.74096 | 0.176155 | ||||||||
\(452\) | 0.524049 | 0.0246492 | ||||||||
\(453\) | −1.01228 | −0.0475609 | ||||||||
\(454\) | −32.9623 | −1.54700 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.22378 | −0.338285 | ||||||||
\(457\) | −10.7604 | −0.503349 | −0.251675 | − | 0.967812i | \(-0.580981\pi\) | ||||
−0.251675 | + | 0.967812i | \(0.580981\pi\) | |||||||
\(458\) | 22.2893 | 1.04151 | ||||||||
\(459\) | −1.28562 | −0.0600074 | ||||||||
\(460\) | −2.46236 | −0.114808 | ||||||||
\(461\) | −4.73851 | −0.220694 | −0.110347 | − | 0.993893i | \(-0.535196\pi\) | ||||
−0.110347 | + | 0.993893i | \(0.535196\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.8446 | −0.643413 | −0.321707 | − | 0.946839i | \(-0.604256\pi\) | ||||
−0.321707 | + | 0.946839i | \(0.604256\pi\) | |||||||
\(464\) | 5.06213 | 0.235004 | ||||||||
\(465\) | −3.40096 | −0.157716 | ||||||||
\(466\) | −41.0200 | −1.90022 | ||||||||
\(467\) | −11.5666 | −0.535238 | −0.267619 | − | 0.963525i | \(-0.586237\pi\) | ||||
−0.267619 | + | 0.963525i | \(0.586237\pi\) | |||||||
\(468\) | −1.10382 | −0.0510241 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2.96798 | −0.136903 | ||||||||
\(471\) | −3.97214 | −0.183026 | ||||||||
\(472\) | −30.7630 | −1.41598 | ||||||||
\(473\) | 18.9883 | 0.873084 | ||||||||
\(474\) | −4.61688 | −0.212060 | ||||||||
\(475\) | 10.4581 | 0.479852 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.43908 | −0.0658910 | ||||||||
\(478\) | −36.1249 | −1.65232 | ||||||||
\(479\) | −11.9744 | −0.547123 | −0.273562 | − | 0.961854i | \(-0.588202\pi\) | ||||
−0.273562 | + | 0.961854i | \(0.588202\pi\) | |||||||
\(480\) | −1.69864 | −0.0775318 | ||||||||
\(481\) | 36.4196 | 1.66059 | ||||||||
\(482\) | −19.4625 | −0.886494 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.816313 | 0.0371052 | ||||||||
\(485\) | −3.28148 | −0.149004 | ||||||||
\(486\) | −1.50751 | −0.0683819 | ||||||||
\(487\) | −11.7895 | −0.534235 | −0.267118 | − | 0.963664i | \(-0.586071\pi\) | ||||
−0.267118 | + | 0.963664i | \(0.586071\pi\) | |||||||
\(488\) | 16.3911 | 0.741991 | ||||||||
\(489\) | −22.6056 | −1.02226 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −41.8155 | −1.88711 | −0.943553 | − | 0.331222i | \(-0.892539\pi\) | ||||
−0.943553 | + | 0.331222i | \(0.892539\pi\) | |||||||
\(492\) | −0.272577 | −0.0122887 | ||||||||
\(493\) | −1.45564 | −0.0655588 | ||||||||
\(494\) | 16.9346 | 0.761924 | ||||||||
\(495\) | −4.14884 | −0.186477 | ||||||||
\(496\) | 13.7104 | 0.615614 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −15.9638 | −0.715354 | ||||||||
\(499\) | −18.7923 | −0.841260 | −0.420630 | − | 0.907232i | \(-0.638191\pi\) | ||||
−0.420630 | + | 0.907232i | \(0.638191\pi\) | |||||||
\(500\) | 2.65115 | 0.118563 | ||||||||
\(501\) | −10.2870 | −0.459591 | ||||||||
\(502\) | 20.3367 | 0.907669 | ||||||||
\(503\) | −5.66329 | −0.252514 | −0.126257 | − | 0.991998i | \(-0.540296\pi\) | ||||
−0.126257 | + | 0.991998i | \(0.540296\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.8528 | 0.482941 | ||||||||
\(506\) | 45.9369 | 2.04215 | ||||||||
\(507\) | −3.39903 | −0.150956 | ||||||||
\(508\) | 1.64977 | 0.0731966 | ||||||||
\(509\) | 16.0628 | 0.711970 | 0.355985 | − | 0.934492i | \(-0.384145\pi\) | ||||
0.355985 | + | 0.934492i | \(0.384145\pi\) | |||||||
\(510\) | 2.14938 | 0.0951763 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −16.4374 | −0.726437 | ||||||||
\(513\) | 2.77400 | 0.122475 | ||||||||
\(514\) | 6.57018 | 0.289798 | ||||||||
\(515\) | 6.26253 | 0.275960 | ||||||||
\(516\) | −1.38354 | −0.0609070 | ||||||||
\(517\) | 6.64112 | 0.292076 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.31332 | −0.364914 | ||||||||
\(520\) | −11.6953 | −0.512872 | ||||||||
\(521\) | 29.4204 | 1.28893 | 0.644465 | − | 0.764634i | \(-0.277080\pi\) | ||||
0.644465 | + | 0.764634i | \(0.277080\pi\) | |||||||
\(522\) | −1.70688 | −0.0747080 | ||||||||
\(523\) | −1.46912 | −0.0642401 | −0.0321201 | − | 0.999484i | \(-0.510226\pi\) | ||||
−0.0321201 | + | 0.999484i | \(0.510226\pi\) | |||||||
\(524\) | −2.77054 | −0.121032 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −21.5428 | −0.939312 | ||||||||
\(527\) | −3.94248 | −0.171737 | ||||||||
\(528\) | 16.7253 | 0.727875 | ||||||||
\(529\) | 43.3496 | 1.88477 | ||||||||
\(530\) | 2.40596 | 0.104508 | ||||||||
\(531\) | 11.8133 | 0.512653 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.04957 | −0.175406 | ||||||||
\(534\) | −1.29978 | −0.0562469 | ||||||||
\(535\) | −15.8052 | −0.683318 | ||||||||
\(536\) | −3.99498 | −0.172557 | ||||||||
\(537\) | −5.82288 | −0.251276 | ||||||||
\(538\) | 30.6468 | 1.32128 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.302296 | 0.0130088 | ||||||||
\(541\) | 14.1541 | 0.608534 | 0.304267 | − | 0.952587i | \(-0.401588\pi\) | ||||
0.304267 | + | 0.952587i | \(0.401588\pi\) | |||||||
\(542\) | −31.9337 | −1.37167 | ||||||||
\(543\) | −16.9447 | −0.727168 | ||||||||
\(544\) | −1.96910 | −0.0844246 | ||||||||
\(545\) | 2.19922 | 0.0942042 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.1112 | −1.54401 | −0.772003 | − | 0.635619i | \(-0.780745\pi\) | ||||
−0.772003 | + | 0.635619i | \(0.780745\pi\) | |||||||
\(548\) | 2.85521 | 0.121968 | ||||||||
\(549\) | −6.29435 | −0.268636 | ||||||||
\(550\) | −21.2613 | −0.906585 | ||||||||
\(551\) | 3.14087 | 0.133805 | ||||||||
\(552\) | 21.2118 | 0.902834 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 4.82841 | 0.205139 | ||||||||
\(555\) | −9.97402 | −0.423373 | ||||||||
\(556\) | 1.37292 | 0.0582250 | ||||||||
\(557\) | −28.3038 | −1.19927 | −0.599635 | − | 0.800274i | \(-0.704687\pi\) | ||||
−0.599635 | + | 0.800274i | \(0.704687\pi\) | |||||||
\(558\) | −4.62294 | −0.195704 | ||||||||
\(559\) | −20.5547 | −0.869373 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.80944 | −0.203055 | ||||||||
\(562\) | −25.4268 | −1.07257 | ||||||||
\(563\) | 28.6819 | 1.20880 | 0.604399 | − | 0.796682i | \(-0.293413\pi\) | ||||
0.604399 | + | 0.796682i | \(0.293413\pi\) | |||||||
\(564\) | −0.483891 | −0.0203755 | ||||||||
\(565\) | −2.13219 | −0.0897019 | ||||||||
\(566\) | −43.7489 | −1.83890 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −32.3406 | −1.35698 | ||||||||
\(569\) | −25.3316 | −1.06195 | −0.530977 | − | 0.847386i | \(-0.678175\pi\) | ||||
−0.530977 | + | 0.847386i | \(0.678175\pi\) | |||||||
\(570\) | −4.63777 | −0.194255 | ||||||||
\(571\) | −44.5188 | −1.86305 | −0.931526 | − | 0.363674i | \(-0.881522\pi\) | ||||
−0.931526 | + | 0.363674i | \(0.881522\pi\) | |||||||
\(572\) | −4.12935 | −0.172657 | ||||||||
\(573\) | −12.9496 | −0.540978 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −30.7091 | −1.28066 | ||||||||
\(576\) | 6.63275 | 0.276365 | ||||||||
\(577\) | −8.77810 | −0.365437 | −0.182718 | − | 0.983165i | \(-0.558490\pi\) | ||||
−0.182718 | + | 0.983165i | \(0.558490\pi\) | |||||||
\(578\) | −23.1360 | −0.962331 | ||||||||
\(579\) | 1.53674 | 0.0638646 | ||||||||
\(580\) | 0.342275 | 0.0142122 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −4.46053 | −0.184895 | ||||||||
\(583\) | −5.38355 | −0.222964 | ||||||||
\(584\) | 19.0803 | 0.789547 | ||||||||
\(585\) | 4.49110 | 0.185684 | ||||||||
\(586\) | 50.4480 | 2.08399 | ||||||||
\(587\) | −8.35115 | −0.344689 | −0.172344 | − | 0.985037i | \(-0.555134\pi\) | ||||
−0.172344 | + | 0.985037i | \(0.555134\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.50678 | 0.350516 | ||||||||
\(590\) | −19.7503 | −0.813107 | ||||||||
\(591\) | −14.6537 | −0.602773 | ||||||||
\(592\) | 40.2084 | 1.65256 | ||||||||
\(593\) | −6.68553 | −0.274542 | −0.137271 | − | 0.990534i | \(-0.543833\pi\) | ||||
−0.137271 | + | 0.990534i | \(0.543833\pi\) | |||||||
\(594\) | −5.63953 | −0.231393 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.39387 | 0.139018 | ||||||||
\(597\) | −15.9626 | −0.653306 | ||||||||
\(598\) | −49.7265 | −2.03347 | ||||||||
\(599\) | 6.46648 | 0.264213 | 0.132107 | − | 0.991236i | \(-0.457826\pi\) | ||||
0.132107 | + | 0.991236i | \(0.457826\pi\) | |||||||
\(600\) | −9.81760 | −0.400802 | ||||||||
\(601\) | −40.0959 | −1.63554 | −0.817772 | − | 0.575542i | \(-0.804791\pi\) | ||||
−0.817772 | + | 0.575542i | \(0.804791\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.53411 | 0.0624738 | ||||||||
\(604\) | 0.275923 | 0.0112272 | ||||||||
\(605\) | −3.32132 | −0.135031 | ||||||||
\(606\) | 14.7522 | 0.599266 | ||||||||
\(607\) | −2.40461 | −0.0976000 | −0.0488000 | − | 0.998809i | \(-0.515540\pi\) | ||||
−0.0488000 | + | 0.998809i | \(0.515540\pi\) | |||||||
\(608\) | 4.24877 | 0.172311 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10.5233 | 0.426077 | ||||||||
\(611\) | −7.18898 | −0.290835 | ||||||||
\(612\) | 0.350429 | 0.0141653 | ||||||||
\(613\) | −21.6500 | −0.874435 | −0.437218 | − | 0.899356i | \(-0.644036\pi\) | ||||
−0.437218 | + | 0.899356i | \(0.644036\pi\) | |||||||
\(614\) | 18.2365 | 0.735964 | ||||||||
\(615\) | 1.10903 | 0.0447204 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.55725 | −0.223726 | −0.111863 | − | 0.993724i | \(-0.535682\pi\) | ||||
−0.111863 | + | 0.993724i | \(0.535682\pi\) | |||||||
\(618\) | 8.51266 | 0.342429 | ||||||||
\(619\) | 39.3059 | 1.57984 | 0.789918 | − | 0.613212i | \(-0.210123\pi\) | ||||
0.789918 | + | 0.613212i | \(0.210123\pi\) | |||||||
\(620\) | 0.927024 | 0.0372302 | ||||||||
\(621\) | −8.14553 | −0.326869 | ||||||||
\(622\) | 6.38920 | 0.256183 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −18.1050 | −0.724782 | ||||||||
\(625\) | 8.06355 | 0.322542 | ||||||||
\(626\) | −35.2760 | −1.40991 | ||||||||
\(627\) | 10.3774 | 0.414435 | ||||||||
\(628\) | 1.08271 | 0.0432049 | ||||||||
\(629\) | −11.5621 | −0.461012 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.34175 | −0.0534142 | −0.0267071 | − | 0.999643i | \(-0.508502\pi\) | ||||
−0.0267071 | + | 0.999643i | \(0.508502\pi\) | |||||||
\(632\) | −7.97530 | −0.317240 | ||||||||
\(633\) | −23.5174 | −0.934733 | ||||||||
\(634\) | 11.6299 | 0.461883 | ||||||||
\(635\) | −6.71239 | −0.266373 | ||||||||
\(636\) | 0.392260 | 0.0155541 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −6.38536 | −0.252799 | ||||||||
\(639\) | 12.4191 | 0.491292 | ||||||||
\(640\) | −14.4864 | −0.572624 | ||||||||
\(641\) | 21.6189 | 0.853894 | 0.426947 | − | 0.904277i | \(-0.359589\pi\) | ||||
0.426947 | + | 0.904277i | \(0.359589\pi\) | |||||||
\(642\) | −21.4840 | −0.847907 | ||||||||
\(643\) | 24.8621 | 0.980465 | 0.490233 | − | 0.871592i | \(-0.336912\pi\) | ||||
0.490233 | + | 0.871592i | \(0.336912\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.62920 | 0.221649 | ||||||||
\(646\) | −5.37622 | −0.211525 | ||||||||
\(647\) | 29.3258 | 1.15292 | 0.576459 | − | 0.817126i | \(-0.304434\pi\) | ||||
0.576459 | + | 0.817126i | \(0.304434\pi\) | |||||||
\(648\) | −2.60410 | −0.102299 | ||||||||
\(649\) | 44.1931 | 1.73473 | ||||||||
\(650\) | 23.0152 | 0.902732 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.16177 | 0.241313 | ||||||||
\(653\) | 40.3928 | 1.58069 | 0.790346 | − | 0.612661i | \(-0.209901\pi\) | ||||
0.790346 | + | 0.612661i | \(0.209901\pi\) | |||||||
\(654\) | 2.98940 | 0.116895 | ||||||||
\(655\) | 11.2725 | 0.440452 | ||||||||
\(656\) | −4.47086 | −0.174558 | ||||||||
\(657\) | −7.32700 | −0.285854 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.6015 | 1.42579 | 0.712895 | − | 0.701271i | \(-0.247384\pi\) | ||||
0.712895 | + | 0.701271i | \(0.247384\pi\) | |||||||
\(660\) | 1.13088 | 0.0440194 | ||||||||
\(661\) | −35.4309 | −1.37810 | −0.689050 | − | 0.724714i | \(-0.741972\pi\) | ||||
−0.689050 | + | 0.724714i | \(0.741972\pi\) | |||||||
\(662\) | 1.18304 | 0.0459801 | ||||||||
\(663\) | 5.20619 | 0.202192 | ||||||||
\(664\) | −27.5762 | −1.07016 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −13.5577 | −0.525350 | ||||||||
\(667\) | −9.22279 | −0.357108 | ||||||||
\(668\) | 2.80401 | 0.108490 | ||||||||
\(669\) | −22.1230 | −0.855323 | ||||||||
\(670\) | −2.56484 | −0.0990882 | ||||||||
\(671\) | −23.5469 | −0.909018 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.09653 | 0.157910 | 0.0789549 | − | 0.996878i | \(-0.474842\pi\) | ||||
0.0789549 | + | 0.996878i | \(0.474842\pi\) | |||||||
\(674\) | −17.6131 | −0.678432 | ||||||||
\(675\) | 3.77005 | 0.145109 | ||||||||
\(676\) | 0.926497 | 0.0356345 | ||||||||
\(677\) | −46.9399 | −1.80405 | −0.902023 | − | 0.431687i | \(-0.857919\pi\) | ||||
−0.902023 | + | 0.431687i | \(0.857919\pi\) | |||||||
\(678\) | −2.89829 | −0.111308 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3.71290 | 0.142383 | ||||||||
\(681\) | 21.8654 | 0.837885 | ||||||||
\(682\) | −17.2942 | −0.662230 | ||||||||
\(683\) | 43.8835 | 1.67916 | 0.839578 | − | 0.543239i | \(-0.182802\pi\) | ||||
0.839578 | + | 0.543239i | \(0.182802\pi\) | |||||||
\(684\) | −0.756129 | −0.0289113 | ||||||||
\(685\) | −11.6169 | −0.443861 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.7855 | −0.564103 | ||||||||
\(688\) | −22.6931 | −0.865166 | ||||||||
\(689\) | 5.82766 | 0.222016 | ||||||||
\(690\) | 13.6183 | 0.518439 | ||||||||
\(691\) | −13.1815 | −0.501446 | −0.250723 | − | 0.968059i | \(-0.580668\pi\) | ||||
−0.250723 | + | 0.968059i | \(0.580668\pi\) | |||||||
\(692\) | 2.26602 | 0.0861411 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.93776 | 0.0735563 | ||||||||
\(695\) | −5.58600 | −0.211889 | ||||||||
\(696\) | −2.94850 | −0.111763 | ||||||||
\(697\) | 1.28562 | 0.0486962 | ||||||||
\(698\) | 46.2155 | 1.74928 | ||||||||
\(699\) | 27.2105 | 1.02920 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21.8416 | −0.824945 | −0.412472 | − | 0.910970i | \(-0.635335\pi\) | ||||
−0.412472 | + | 0.910970i | \(0.635335\pi\) | |||||||
\(702\) | 6.10476 | 0.230409 | ||||||||
\(703\) | 24.9479 | 0.940926 | ||||||||
\(704\) | 24.8129 | 0.935170 | ||||||||
\(705\) | 1.96880 | 0.0741493 | ||||||||
\(706\) | 0.989258 | 0.0372312 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −3.22003 | −0.121016 | ||||||||
\(709\) | −23.7312 | −0.891243 | −0.445622 | − | 0.895221i | \(-0.647017\pi\) | ||||
−0.445622 | + | 0.895221i | \(0.647017\pi\) | |||||||
\(710\) | −20.7631 | −0.779226 | ||||||||
\(711\) | 3.06259 | 0.114856 | ||||||||
\(712\) | −2.24527 | −0.0841450 | ||||||||
\(713\) | −24.9792 | −0.935477 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.8010 | 0.628323 | ||||||||
\(716\) | 1.58718 | 0.0593158 | ||||||||
\(717\) | 23.9634 | 0.894928 | ||||||||
\(718\) | −1.01020 | −0.0377005 | ||||||||
\(719\) | 14.4356 | 0.538358 | 0.269179 | − | 0.963090i | \(-0.413248\pi\) | ||||
0.269179 | + | 0.963090i | \(0.413248\pi\) | |||||||
\(720\) | 4.95832 | 0.184785 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −17.0422 | −0.634246 | ||||||||
\(723\) | 12.9104 | 0.480143 | ||||||||
\(724\) | 4.61874 | 0.171654 | ||||||||
\(725\) | 4.26865 | 0.158534 | ||||||||
\(726\) | −4.51468 | −0.167556 | ||||||||
\(727\) | 7.96786 | 0.295512 | 0.147756 | − | 0.989024i | \(-0.452795\pi\) | ||||
0.147756 | + | 0.989024i | \(0.452795\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 12.2498 | 0.453385 | ||||||||
\(731\) | 6.52551 | 0.241355 | ||||||||
\(732\) | 1.71569 | 0.0634138 | ||||||||
\(733\) | −33.3492 | −1.23178 | −0.615890 | − | 0.787832i | \(-0.711204\pi\) | ||||
−0.615890 | + | 0.787832i | \(0.711204\pi\) | |||||||
\(734\) | 36.1924 | 1.33589 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −12.4760 | −0.459872 | ||||||||
\(737\) | 5.73905 | 0.211401 | ||||||||
\(738\) | 1.50751 | 0.0554921 | ||||||||
\(739\) | −14.8315 | −0.545584 | −0.272792 | − | 0.962073i | \(-0.587947\pi\) | ||||
−0.272792 | + | 0.962073i | \(0.587947\pi\) | |||||||
\(740\) | 2.71869 | 0.0999409 | ||||||||
\(741\) | −11.2335 | −0.412674 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.1321 | 1.14213 | 0.571063 | − | 0.820906i | \(-0.306531\pi\) | ||||
0.571063 | + | 0.820906i | \(0.306531\pi\) | |||||||
\(744\) | −7.98577 | −0.292772 | ||||||||
\(745\) | −13.8086 | −0.505908 | ||||||||
\(746\) | −5.26086 | −0.192614 | ||||||||
\(747\) | 10.5895 | 0.387450 | ||||||||
\(748\) | 1.31094 | 0.0479328 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −14.6624 | −0.535395 | ||||||||
\(751\) | 3.96823 | 0.144803 | 0.0724014 | − | 0.997376i | \(-0.476934\pi\) | ||||
0.0724014 | + | 0.997376i | \(0.476934\pi\) | |||||||
\(752\) | −7.93686 | −0.289427 | ||||||||
\(753\) | −13.4903 | −0.491612 | ||||||||
\(754\) | 6.91212 | 0.251725 | ||||||||
\(755\) | −1.12265 | −0.0408572 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28.9528 | −1.05231 | −0.526153 | − | 0.850390i | \(-0.676366\pi\) | ||||
−0.526153 | + | 0.850390i | \(0.676366\pi\) | |||||||
\(758\) | 44.8792 | 1.63009 | ||||||||
\(759\) | −30.4721 | −1.10607 | ||||||||
\(760\) | −8.01139 | −0.290604 | ||||||||
\(761\) | −12.6480 | −0.458490 | −0.229245 | − | 0.973369i | \(-0.573626\pi\) | ||||
−0.229245 | + | 0.973369i | \(0.573626\pi\) | |||||||
\(762\) | −9.12416 | −0.330533 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 3.52977 | 0.127702 | ||||||||
\(765\) | −1.42579 | −0.0515494 | ||||||||
\(766\) | 14.2358 | 0.514359 | ||||||||
\(767\) | −47.8388 | −1.72736 | ||||||||
\(768\) | −6.42585 | −0.231873 | ||||||||
\(769\) | −22.8838 | −0.825210 | −0.412605 | − | 0.910910i | \(-0.635381\pi\) | ||||
−0.412605 | + | 0.910910i | \(0.635381\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.35831 | −0.156961 | ||||||||
\(772\) | −0.418879 | −0.0150758 | ||||||||
\(773\) | 0.777954 | 0.0279811 | 0.0139905 | − | 0.999902i | \(-0.495547\pi\) | ||||
0.0139905 | + | 0.999902i | \(0.495547\pi\) | |||||||
\(774\) | 7.65178 | 0.275037 | ||||||||
\(775\) | 11.5613 | 0.415293 | ||||||||
\(776\) | −7.70521 | −0.276601 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 48.2183 | 1.72871 | ||||||||
\(779\) | −2.77400 | −0.0993889 | ||||||||
\(780\) | −1.22417 | −0.0438323 | ||||||||
\(781\) | 46.4594 | 1.66245 | ||||||||
\(782\) | 15.7866 | 0.564529 | ||||||||
\(783\) | 1.13225 | 0.0404634 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.40522 | −0.157229 | ||||||||
\(786\) | 15.3227 | 0.546542 | ||||||||
\(787\) | 29.3699 | 1.04692 | 0.523462 | − | 0.852049i | \(-0.324640\pi\) | ||||
0.523462 | + | 0.852049i | \(0.324640\pi\) | |||||||
\(788\) | 3.99426 | 0.142290 | ||||||||
\(789\) | 14.2904 | 0.508751 | ||||||||
\(790\) | −5.12026 | −0.182171 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −9.74185 | −0.346162 | ||||||||
\(793\) | 25.4894 | 0.905155 | ||||||||
\(794\) | 31.7750 | 1.12765 | ||||||||
\(795\) | −1.59598 | −0.0566037 | ||||||||
\(796\) | 4.35104 | 0.154219 | ||||||||
\(797\) | 22.5919 | 0.800247 | 0.400124 | − | 0.916461i | \(-0.368967\pi\) | ||||
0.400124 | + | 0.916461i | \(0.368967\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.28228 | 0.0807413 | ||||||||
\(800\) | 5.77437 | 0.204155 | ||||||||
\(801\) | 0.862204 | 0.0304645 | ||||||||
\(802\) | −32.4585 | −1.14615 | ||||||||
\(803\) | −27.4100 | −0.967279 | ||||||||
\(804\) | −0.418163 | −0.0147475 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 18.7209 | 0.659416 | ||||||||
\(807\) | −20.3295 | −0.715632 | ||||||||
\(808\) | 25.4832 | 0.896497 | ||||||||
\(809\) | 31.0716 | 1.09242 | 0.546209 | − | 0.837649i | \(-0.316070\pi\) | ||||
0.546209 | + | 0.837649i | \(0.316070\pi\) | |||||||
\(810\) | −1.67187 | −0.0587436 | ||||||||
\(811\) | 32.1947 | 1.13051 | 0.565254 | − | 0.824917i | \(-0.308778\pi\) | ||||
0.565254 | + | 0.824917i | \(0.308778\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.1831 | 0.742925 | ||||||||
\(814\) | −50.7188 | −1.77769 | ||||||||
\(815\) | −25.0703 | −0.878175 | ||||||||
\(816\) | 5.74780 | 0.201213 | ||||||||
\(817\) | −14.0802 | −0.492605 | ||||||||
\(818\) | −54.0468 | −1.88970 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.302296 | −0.0105566 | ||||||||
\(821\) | −21.4757 | −0.749509 | −0.374754 | − | 0.927124i | \(-0.622273\pi\) | ||||
−0.374754 | + | 0.927124i | \(0.622273\pi\) | |||||||
\(822\) | −15.7909 | −0.550772 | ||||||||
\(823\) | 27.4356 | 0.956345 | 0.478172 | − | 0.878266i | \(-0.341299\pi\) | ||||
0.478172 | + | 0.878266i | \(0.341299\pi\) | |||||||
\(824\) | 14.7050 | 0.512272 | ||||||||
\(825\) | 14.1036 | 0.491025 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.26418 | 0.183053 | 0.0915267 | − | 0.995803i | \(-0.470825\pi\) | ||||
0.0915267 | + | 0.995803i | \(0.470825\pi\) | |||||||
\(828\) | 2.22028 | 0.0771602 | ||||||||
\(829\) | −36.4033 | −1.26434 | −0.632169 | − | 0.774831i | \(-0.717835\pi\) | ||||
−0.632169 | + | 0.774831i | \(0.717835\pi\) | |||||||
\(830\) | −17.7043 | −0.614525 | ||||||||
\(831\) | −3.20291 | −0.111108 | ||||||||
\(832\) | −26.8598 | −0.931196 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −7.59306 | −0.262926 | ||||||||
\(835\) | −11.4086 | −0.394812 | ||||||||
\(836\) | −2.82865 | −0.0978309 | ||||||||
\(837\) | 3.06661 | 0.105998 | ||||||||
\(838\) | 14.7023 | 0.507881 | ||||||||
\(839\) | −35.5047 | −1.22576 | −0.612880 | − | 0.790176i | \(-0.709989\pi\) | ||||
−0.612880 | + | 0.790176i | \(0.709989\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.7180 | −0.955793 | ||||||||
\(842\) | 0.176623 | 0.00608684 | ||||||||
\(843\) | 16.8668 | 0.580923 | ||||||||
\(844\) | 6.41030 | 0.220652 | ||||||||
\(845\) | −3.76963 | −0.129679 | ||||||||
\(846\) | 2.67619 | 0.0920094 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.43392 | 0.220942 | ||||||||
\(849\) | 29.0207 | 0.995988 | ||||||||
\(850\) | −7.30664 | −0.250616 | ||||||||
\(851\) | −73.2564 | −2.51120 | ||||||||
\(852\) | −3.38516 | −0.115974 | ||||||||
\(853\) | 28.0973 | 0.962035 | 0.481017 | − | 0.876711i | \(-0.340267\pi\) | ||||
0.481017 | + | 0.876711i | \(0.340267\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.07645 | 0.105212 | ||||||||
\(856\) | −37.1120 | −1.26846 | ||||||||
\(857\) | −45.0276 | −1.53811 | −0.769056 | − | 0.639181i | \(-0.779273\pi\) | ||||
−0.769056 | + | 0.639181i | \(0.779273\pi\) | |||||||
\(858\) | 22.8377 | 0.779665 | ||||||||
\(859\) | −19.7121 | −0.672568 | −0.336284 | − | 0.941761i | \(-0.609170\pi\) | ||||
−0.336284 | + | 0.941761i | \(0.609170\pi\) | |||||||
\(860\) | −1.53439 | −0.0523222 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 31.9317 | 1.08760 | ||||||||
\(863\) | −8.30927 | −0.282851 | −0.141425 | − | 0.989949i | \(-0.545169\pi\) | ||||
−0.141425 | + | 0.989949i | \(0.545169\pi\) | |||||||
\(864\) | 1.53164 | 0.0521075 | ||||||||
\(865\) | −9.21972 | −0.313480 | ||||||||
\(866\) | 35.7145 | 1.21363 | ||||||||
\(867\) | 15.3472 | 0.521218 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.4570 | 0.388653 | ||||||||
\(870\) | −1.89298 | −0.0641780 | ||||||||
\(871\) | −6.21249 | −0.210502 | ||||||||
\(872\) | 5.16396 | 0.174874 | ||||||||
\(873\) | 2.95888 | 0.100143 | ||||||||
\(874\) | −34.0632 | −1.15220 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.99717 | 0.0674782 | ||||||||
\(877\) | 36.4096 | 1.22947 | 0.614733 | − | 0.788735i | \(-0.289264\pi\) | ||||
0.614733 | + | 0.788735i | \(0.289264\pi\) | |||||||
\(878\) | 26.4483 | 0.892588 | ||||||||
\(879\) | −33.4645 | −1.12873 | ||||||||
\(880\) | 18.5489 | 0.625282 | ||||||||
\(881\) | 41.2925 | 1.39118 | 0.695590 | − | 0.718439i | \(-0.255143\pi\) | ||||
0.695590 | + | 0.718439i | \(0.255143\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27.7916 | −0.935261 | −0.467631 | − | 0.883924i | \(-0.654892\pi\) | ||||
−0.467631 | + | 0.883924i | \(0.654892\pi\) | |||||||
\(884\) | −1.41909 | −0.0477291 | ||||||||
\(885\) | 13.1013 | 0.440395 | ||||||||
\(886\) | 7.38193 | 0.248001 | ||||||||
\(887\) | 22.4719 | 0.754534 | 0.377267 | − | 0.926105i | \(-0.376864\pi\) | ||||
0.377267 | + | 0.926105i | \(0.376864\pi\) | |||||||
\(888\) | −23.4199 | −0.785920 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1.44149 | −0.0483190 | ||||||||
\(891\) | 3.74096 | 0.125327 | ||||||||
\(892\) | 6.03021 | 0.201906 | ||||||||
\(893\) | −4.92453 | −0.164793 | ||||||||
\(894\) | −18.7701 | −0.627765 | ||||||||
\(895\) | −6.45775 | −0.215859 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 32.9859 | 1.10137 | ||||||||
\(898\) | −38.8984 | −1.29806 | ||||||||
\(899\) | 3.47217 | 0.115803 | ||||||||
\(900\) | −1.02763 | −0.0342543 | ||||||||
\(901\) | −1.85010 | −0.0616359 | ||||||||
\(902\) | 5.63953 | 0.187776 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.00657 | −0.166516 | ||||||||
\(905\) | −18.7922 | −0.624675 | ||||||||
\(906\) | −1.52601 | −0.0506984 | ||||||||
\(907\) | −48.2992 | −1.60375 | −0.801875 | − | 0.597492i | \(-0.796164\pi\) | ||||
−0.801875 | + | 0.597492i | \(0.796164\pi\) | |||||||
\(908\) | −5.96001 | −0.197790 | ||||||||
\(909\) | −9.78581 | −0.324575 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.4429 | 1.24054 | 0.620269 | − | 0.784389i | \(-0.287023\pi\) | ||||
0.620269 | + | 0.784389i | \(0.287023\pi\) | |||||||
\(912\) | −12.4022 | −0.410677 | ||||||||
\(913\) | 39.6150 | 1.31106 | ||||||||
\(914\) | −16.2213 | −0.536554 | ||||||||
\(915\) | −6.98062 | −0.230772 | ||||||||
\(916\) | 4.03019 | 0.133161 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −1.93807 | −0.0639660 | ||||||||
\(919\) | −11.5498 | −0.380992 | −0.190496 | − | 0.981688i | \(-0.561010\pi\) | ||||
−0.190496 | + | 0.981688i | \(0.561010\pi\) | |||||||
\(920\) | 23.5245 | 0.775580 | ||||||||
\(921\) | −12.0971 | −0.398613 | ||||||||
\(922\) | −7.14334 | −0.235253 | ||||||||
\(923\) | −50.2920 | −1.65538 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 33.9058 | 1.11482 | ||||||||
\(926\) | −20.8708 | −0.685858 | ||||||||
\(927\) | −5.64685 | −0.185467 | ||||||||
\(928\) | 1.73420 | 0.0569280 | ||||||||
\(929\) | −2.48031 | −0.0813764 | −0.0406882 | − | 0.999172i | \(-0.512955\pi\) | ||||
−0.0406882 | + | 0.999172i | \(0.512955\pi\) | |||||||
\(930\) | −5.12698 | −0.168120 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −7.41696 | −0.242951 | ||||||||
\(933\) | −4.23825 | −0.138754 | ||||||||
\(934\) | −17.4367 | −0.570547 | ||||||||
\(935\) | −5.33382 | −0.174434 | ||||||||
\(936\) | 10.5455 | 0.344690 | ||||||||
\(937\) | 20.6957 | 0.676098 | 0.338049 | − | 0.941128i | \(-0.390233\pi\) | ||||
0.338049 | + | 0.941128i | \(0.390233\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 23.4002 | 0.763637 | ||||||||
\(940\) | −0.536649 | −0.0175036 | ||||||||
\(941\) | 19.6088 | 0.639230 | 0.319615 | − | 0.947547i | \(-0.396446\pi\) | ||||
0.319615 | + | 0.947547i | \(0.396446\pi\) | |||||||
\(942\) | −5.98802 | −0.195100 | ||||||||
\(943\) | 8.14553 | 0.265255 | ||||||||
\(944\) | −52.8155 | −1.71900 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 28.6250 | 0.930679 | ||||||||
\(947\) | 51.2866 | 1.66659 | 0.833296 | − | 0.552828i | \(-0.186451\pi\) | ||||
0.833296 | + | 0.552828i | \(0.186451\pi\) | |||||||
\(948\) | −0.834792 | −0.0271128 | ||||||||
\(949\) | 29.6712 | 0.963168 | ||||||||
\(950\) | 15.7657 | 0.511507 | ||||||||
\(951\) | −7.71467 | −0.250165 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 49.5293 | 1.60441 | 0.802205 | − | 0.597048i | \(-0.203660\pi\) | ||||
0.802205 | + | 0.597048i | \(0.203660\pi\) | |||||||
\(954\) | −2.16942 | −0.0702377 | ||||||||
\(955\) | −14.3615 | −0.464728 | ||||||||
\(956\) | −6.53186 | −0.211255 | ||||||||
\(957\) | 4.23571 | 0.136921 | ||||||||
\(958\) | −18.0515 | −0.583216 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 7.35592 | 0.237411 | ||||||||
\(961\) | −21.5959 | −0.696642 | ||||||||
\(962\) | 54.9029 | 1.77014 | ||||||||
\(963\) | 14.2514 | 0.459244 | ||||||||
\(964\) | −3.51908 | −0.113342 | ||||||||
\(965\) | 1.70429 | 0.0548630 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.8164 | −0.733727 | −0.366863 | − | 0.930275i | \(-0.619568\pi\) | ||||
−0.366863 | + | 0.930275i | \(0.619568\pi\) | |||||||
\(968\) | −7.79877 | −0.250662 | ||||||||
\(969\) | 3.56630 | 0.114566 | ||||||||
\(970\) | −4.94686 | −0.158834 | ||||||||
\(971\) | −24.2347 | −0.777729 | −0.388864 | − | 0.921295i | \(-0.627133\pi\) | ||||
−0.388864 | + | 0.921295i | \(0.627133\pi\) | |||||||
\(972\) | −0.272577 | −0.00874291 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −17.7728 | −0.569478 | ||||||||
\(975\) | −15.2671 | −0.488938 | ||||||||
\(976\) | 28.1411 | 0.900775 | ||||||||
\(977\) | −33.0385 | −1.05700 | −0.528498 | − | 0.848934i | \(-0.677245\pi\) | ||||
−0.528498 | + | 0.848934i | \(0.677245\pi\) | |||||||
\(978\) | −34.0781 | −1.08970 | ||||||||
\(979\) | 3.22547 | 0.103087 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.98301 | −0.0633126 | ||||||||
\(982\) | −63.0371 | −2.01159 | ||||||||
\(983\) | −21.3362 | −0.680518 | −0.340259 | − | 0.940332i | \(-0.610515\pi\) | ||||
−0.340259 | + | 0.940332i | \(0.610515\pi\) | |||||||
\(984\) | 2.60410 | 0.0830157 | ||||||||
\(985\) | −16.2514 | −0.517813 | ||||||||
\(986\) | −2.19439 | −0.0698836 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.06200 | 0.0974151 | ||||||||
\(989\) | 41.3449 | 1.31469 | ||||||||
\(990\) | −6.25441 | −0.198778 | ||||||||
\(991\) | 6.34983 | 0.201709 | 0.100854 | − | 0.994901i | \(-0.467842\pi\) | ||||
0.100854 | + | 0.994901i | \(0.467842\pi\) | |||||||
\(992\) | 4.69695 | 0.149128 | ||||||||
\(993\) | −0.784765 | −0.0249038 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −17.7030 | −0.561224 | ||||||||
\(996\) | −2.88646 | −0.0914609 | ||||||||
\(997\) | 39.8519 | 1.26212 | 0.631061 | − | 0.775733i | \(-0.282620\pi\) | ||||
0.631061 | + | 0.775733i | \(0.282620\pi\) | |||||||
\(998\) | −28.3296 | −0.896757 | ||||||||
\(999\) | 8.99346 | 0.284540 |
(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 | 6027.2.a.bn.1.16 | ✓ | 24 | |
7.6 | odd | 2 | 6027.2.a.bo.1.16 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6027.2.a.bn.1.16 | ✓ | 24 | 1.1 | even | 1 | trivial | |
6027.2.a.bo.1.16 | yes | 24 | 7.6 | odd | 2 |