Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4030,2,Mod(1,4030)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4030, 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("4030.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4030.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: | \(32.1797120146\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 16x^{6} + 18x^{5} + 64x^{4} - 84x^{3} - 19x^{2} + 22x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-0.178838\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4030.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0.178838 | 0.103252 | 0.0516262 | − | 0.998666i | \(-0.483560\pi\) | ||||
0.0516262 | + | 0.998666i | \(0.483560\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0.178838 | 0.0730104 | ||||||||
\(7\) | −4.63233 | −1.75086 | −0.875428 | − | 0.483349i | \(-0.839420\pi\) | ||||
−0.875428 | + | 0.483349i | \(0.839420\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.96802 | −0.989339 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 5.33531 | 1.60866 | 0.804328 | − | 0.594185i | \(-0.202525\pi\) | ||||
0.804328 | + | 0.594185i | \(0.202525\pi\) | |||||||
\(12\) | 0.178838 | 0.0516262 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −4.63233 | −1.23804 | ||||||||
\(15\) | −0.178838 | −0.0461758 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.03643 | −1.46405 | −0.732025 | − | 0.681278i | \(-0.761425\pi\) | ||||
−0.732025 | + | 0.681278i | \(0.761425\pi\) | |||||||
\(18\) | −2.96802 | −0.699568 | ||||||||
\(19\) | −0.663724 | −0.152269 | −0.0761343 | − | 0.997098i | \(-0.524258\pi\) | ||||
−0.0761343 | + | 0.997098i | \(0.524258\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −0.828437 | −0.180780 | ||||||||
\(22\) | 5.33531 | 1.13749 | ||||||||
\(23\) | −1.20734 | −0.251748 | −0.125874 | − | 0.992046i | \(-0.540174\pi\) | ||||
−0.125874 | + | 0.992046i | \(0.540174\pi\) | |||||||
\(24\) | 0.178838 | 0.0365052 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −1.06731 | −0.205404 | ||||||||
\(28\) | −4.63233 | −0.875428 | ||||||||
\(29\) | 7.03585 | 1.30652 | 0.653262 | − | 0.757132i | \(-0.273400\pi\) | ||||
0.653262 | + | 0.757132i | \(0.273400\pi\) | |||||||
\(30\) | −0.178838 | −0.0326513 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.954158 | 0.166098 | ||||||||
\(34\) | −6.03643 | −1.03524 | ||||||||
\(35\) | 4.63233 | 0.783006 | ||||||||
\(36\) | −2.96802 | −0.494669 | ||||||||
\(37\) | 6.84984 | 1.12611 | 0.563053 | − | 0.826421i | \(-0.309627\pi\) | ||||
0.563053 | + | 0.826421i | \(0.309627\pi\) | |||||||
\(38\) | −0.663724 | −0.107670 | ||||||||
\(39\) | −0.178838 | −0.0286370 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 7.35666 | 1.14892 | 0.574459 | − | 0.818534i | \(-0.305213\pi\) | ||||
0.574459 | + | 0.818534i | \(0.305213\pi\) | |||||||
\(42\) | −0.828437 | −0.127831 | ||||||||
\(43\) | 12.4429 | 1.89753 | 0.948763 | − | 0.315989i | \(-0.102336\pi\) | ||||
0.948763 | + | 0.315989i | \(0.102336\pi\) | |||||||
\(44\) | 5.33531 | 0.804328 | ||||||||
\(45\) | 2.96802 | 0.442446 | ||||||||
\(46\) | −1.20734 | −0.178013 | ||||||||
\(47\) | 0.326660 | 0.0476482 | 0.0238241 | − | 0.999716i | \(-0.492416\pi\) | ||||
0.0238241 | + | 0.999716i | \(0.492416\pi\) | |||||||
\(48\) | 0.178838 | 0.0258131 | ||||||||
\(49\) | 14.4585 | 2.06549 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −1.07955 | −0.151167 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | 12.3242 | 1.69286 | 0.846430 | − | 0.532500i | \(-0.178747\pi\) | ||||
0.846430 | + | 0.532500i | \(0.178747\pi\) | |||||||
\(54\) | −1.06731 | −0.145242 | ||||||||
\(55\) | −5.33531 | −0.719413 | ||||||||
\(56\) | −4.63233 | −0.619021 | ||||||||
\(57\) | −0.118699 | −0.0157221 | ||||||||
\(58\) | 7.03585 | 0.923852 | ||||||||
\(59\) | 10.9205 | 1.42173 | 0.710865 | − | 0.703328i | \(-0.248304\pi\) | ||||
0.710865 | + | 0.703328i | \(0.248304\pi\) | |||||||
\(60\) | −0.178838 | −0.0230879 | ||||||||
\(61\) | −11.0097 | −1.40964 | −0.704822 | − | 0.709384i | \(-0.748973\pi\) | ||||
−0.704822 | + | 0.709384i | \(0.748973\pi\) | |||||||
\(62\) | −1.00000 | −0.127000 | ||||||||
\(63\) | 13.7488 | 1.73219 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | 0.954158 | 0.117449 | ||||||||
\(67\) | −3.23660 | −0.395414 | −0.197707 | − | 0.980261i | \(-0.563349\pi\) | ||||
−0.197707 | + | 0.980261i | \(0.563349\pi\) | |||||||
\(68\) | −6.03643 | −0.732025 | ||||||||
\(69\) | −0.215919 | −0.0259936 | ||||||||
\(70\) | 4.63233 | 0.553669 | ||||||||
\(71\) | −9.94396 | −1.18013 | −0.590066 | − | 0.807355i | \(-0.700898\pi\) | ||||
−0.590066 | + | 0.807355i | \(0.700898\pi\) | |||||||
\(72\) | −2.96802 | −0.349784 | ||||||||
\(73\) | 1.10218 | 0.129000 | 0.0645002 | − | 0.997918i | \(-0.479455\pi\) | ||||
0.0645002 | + | 0.997918i | \(0.479455\pi\) | |||||||
\(74\) | 6.84984 | 0.796277 | ||||||||
\(75\) | 0.178838 | 0.0206505 | ||||||||
\(76\) | −0.663724 | −0.0761343 | ||||||||
\(77\) | −24.7149 | −2.81652 | ||||||||
\(78\) | −0.178838 | −0.0202494 | ||||||||
\(79\) | 15.7918 | 1.77671 | 0.888356 | − | 0.459156i | \(-0.151848\pi\) | ||||
0.888356 | + | 0.459156i | \(0.151848\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 8.71317 | 0.968131 | ||||||||
\(82\) | 7.35666 | 0.812407 | ||||||||
\(83\) | −8.93682 | −0.980944 | −0.490472 | − | 0.871457i | \(-0.663176\pi\) | ||||
−0.490472 | + | 0.871457i | \(0.663176\pi\) | |||||||
\(84\) | −0.828437 | −0.0903899 | ||||||||
\(85\) | 6.03643 | 0.654743 | ||||||||
\(86\) | 12.4429 | 1.34175 | ||||||||
\(87\) | 1.25828 | 0.134902 | ||||||||
\(88\) | 5.33531 | 0.568746 | ||||||||
\(89\) | −0.384321 | −0.0407379 | −0.0203690 | − | 0.999793i | \(-0.506484\pi\) | ||||
−0.0203690 | + | 0.999793i | \(0.506484\pi\) | |||||||
\(90\) | 2.96802 | 0.312856 | ||||||||
\(91\) | 4.63233 | 0.485600 | ||||||||
\(92\) | −1.20734 | −0.125874 | ||||||||
\(93\) | −0.178838 | −0.0185447 | ||||||||
\(94\) | 0.326660 | 0.0336924 | ||||||||
\(95\) | 0.663724 | 0.0680966 | ||||||||
\(96\) | 0.178838 | 0.0182526 | ||||||||
\(97\) | −17.7548 | −1.80273 | −0.901365 | − | 0.433060i | \(-0.857434\pi\) | ||||
−0.901365 | + | 0.433060i | \(0.857434\pi\) | |||||||
\(98\) | 14.4585 | 1.46053 | ||||||||
\(99\) | −15.8353 | −1.59151 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 5.33151 | 0.530505 | 0.265252 | − | 0.964179i | \(-0.414545\pi\) | ||||
0.265252 | + | 0.964179i | \(0.414545\pi\) | |||||||
\(102\) | −1.07955 | −0.106891 | ||||||||
\(103\) | 0.761610 | 0.0750436 | 0.0375218 | − | 0.999296i | \(-0.488054\pi\) | ||||
0.0375218 | + | 0.999296i | \(0.488054\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0.828437 | 0.0808472 | ||||||||
\(106\) | 12.3242 | 1.19703 | ||||||||
\(107\) | −17.9697 | −1.73720 | −0.868598 | − | 0.495518i | \(-0.834978\pi\) | ||||
−0.868598 | + | 0.495518i | \(0.834978\pi\) | |||||||
\(108\) | −1.06731 | −0.102702 | ||||||||
\(109\) | 11.9278 | 1.14248 | 0.571238 | − | 0.820785i | \(-0.306463\pi\) | ||||
0.571238 | + | 0.820785i | \(0.306463\pi\) | |||||||
\(110\) | −5.33531 | −0.508702 | ||||||||
\(111\) | 1.22501 | 0.116273 | ||||||||
\(112\) | −4.63233 | −0.437714 | ||||||||
\(113\) | −13.8676 | −1.30455 | −0.652277 | − | 0.757981i | \(-0.726186\pi\) | ||||
−0.652277 | + | 0.757981i | \(0.726186\pi\) | |||||||
\(114\) | −0.118699 | −0.0111172 | ||||||||
\(115\) | 1.20734 | 0.112585 | ||||||||
\(116\) | 7.03585 | 0.653262 | ||||||||
\(117\) | 2.96802 | 0.274393 | ||||||||
\(118\) | 10.9205 | 1.00532 | ||||||||
\(119\) | 27.9627 | 2.56334 | ||||||||
\(120\) | −0.178838 | −0.0163256 | ||||||||
\(121\) | 17.4655 | 1.58778 | ||||||||
\(122\) | −11.0097 | −0.996769 | ||||||||
\(123\) | 1.31565 | 0.118628 | ||||||||
\(124\) | −1.00000 | −0.0898027 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 13.7488 | 1.22484 | ||||||||
\(127\) | 18.4024 | 1.63295 | 0.816473 | − | 0.577384i | \(-0.195926\pi\) | ||||
0.816473 | + | 0.577384i | \(0.195926\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 2.22527 | 0.195924 | ||||||||
\(130\) | 1.00000 | 0.0877058 | ||||||||
\(131\) | −7.02881 | −0.614110 | −0.307055 | − | 0.951692i | \(-0.599344\pi\) | ||||
−0.307055 | + | 0.951692i | \(0.599344\pi\) | |||||||
\(132\) | 0.954158 | 0.0830488 | ||||||||
\(133\) | 3.07459 | 0.266600 | ||||||||
\(134\) | −3.23660 | −0.279600 | ||||||||
\(135\) | 1.06731 | 0.0918594 | ||||||||
\(136\) | −6.03643 | −0.517620 | ||||||||
\(137\) | 15.3912 | 1.31496 | 0.657480 | − | 0.753472i | \(-0.271622\pi\) | ||||
0.657480 | + | 0.753472i | \(0.271622\pi\) | |||||||
\(138\) | −0.215919 | −0.0183802 | ||||||||
\(139\) | −5.33060 | −0.452136 | −0.226068 | − | 0.974112i | \(-0.572587\pi\) | ||||
−0.226068 | + | 0.974112i | \(0.572587\pi\) | |||||||
\(140\) | 4.63233 | 0.391503 | ||||||||
\(141\) | 0.0584192 | 0.00491979 | ||||||||
\(142\) | −9.94396 | −0.834479 | ||||||||
\(143\) | −5.33531 | −0.446161 | ||||||||
\(144\) | −2.96802 | −0.247335 | ||||||||
\(145\) | −7.03585 | −0.584295 | ||||||||
\(146\) | 1.10218 | 0.0912170 | ||||||||
\(147\) | 2.58573 | 0.213267 | ||||||||
\(148\) | 6.84984 | 0.563053 | ||||||||
\(149\) | 8.14501 | 0.667265 | 0.333633 | − | 0.942703i | \(-0.391726\pi\) | ||||
0.333633 | + | 0.942703i | \(0.391726\pi\) | |||||||
\(150\) | 0.178838 | 0.0146021 | ||||||||
\(151\) | −4.82349 | −0.392530 | −0.196265 | − | 0.980551i | \(-0.562881\pi\) | ||||
−0.196265 | + | 0.980551i | \(0.562881\pi\) | |||||||
\(152\) | −0.663724 | −0.0538351 | ||||||||
\(153\) | 17.9162 | 1.44844 | ||||||||
\(154\) | −24.7149 | −1.99158 | ||||||||
\(155\) | 1.00000 | 0.0803219 | ||||||||
\(156\) | −0.178838 | −0.0143185 | ||||||||
\(157\) | −9.18398 | −0.732961 | −0.366481 | − | 0.930426i | \(-0.619437\pi\) | ||||
−0.366481 | + | 0.930426i | \(0.619437\pi\) | |||||||
\(158\) | 15.7918 | 1.25632 | ||||||||
\(159\) | 2.20404 | 0.174792 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 5.59280 | 0.440774 | ||||||||
\(162\) | 8.71317 | 0.684572 | ||||||||
\(163\) | 4.50771 | 0.353071 | 0.176536 | − | 0.984294i | \(-0.443511\pi\) | ||||
0.176536 | + | 0.984294i | \(0.443511\pi\) | |||||||
\(164\) | 7.35666 | 0.574459 | ||||||||
\(165\) | −0.954158 | −0.0742811 | ||||||||
\(166\) | −8.93682 | −0.693632 | ||||||||
\(167\) | 4.88428 | 0.377957 | 0.188979 | − | 0.981981i | \(-0.439482\pi\) | ||||
0.188979 | + | 0.981981i | \(0.439482\pi\) | |||||||
\(168\) | −0.828437 | −0.0639153 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 6.03643 | 0.462973 | ||||||||
\(171\) | 1.96994 | 0.150645 | ||||||||
\(172\) | 12.4429 | 0.948763 | ||||||||
\(173\) | 3.37554 | 0.256637 | 0.128319 | − | 0.991733i | \(-0.459042\pi\) | ||||
0.128319 | + | 0.991733i | \(0.459042\pi\) | |||||||
\(174\) | 1.25828 | 0.0953899 | ||||||||
\(175\) | −4.63233 | −0.350171 | ||||||||
\(176\) | 5.33531 | 0.402164 | ||||||||
\(177\) | 1.95301 | 0.146797 | ||||||||
\(178\) | −0.384321 | −0.0288061 | ||||||||
\(179\) | −20.3213 | −1.51888 | −0.759441 | − | 0.650576i | \(-0.774527\pi\) | ||||
−0.759441 | + | 0.650576i | \(0.774527\pi\) | |||||||
\(180\) | 2.96802 | 0.221223 | ||||||||
\(181\) | 16.0859 | 1.19565 | 0.597827 | − | 0.801625i | \(-0.296031\pi\) | ||||
0.597827 | + | 0.801625i | \(0.296031\pi\) | |||||||
\(182\) | 4.63233 | 0.343371 | ||||||||
\(183\) | −1.96895 | −0.145549 | ||||||||
\(184\) | −1.20734 | −0.0890064 | ||||||||
\(185\) | −6.84984 | −0.503610 | ||||||||
\(186\) | −0.178838 | −0.0131131 | ||||||||
\(187\) | −32.2062 | −2.35515 | ||||||||
\(188\) | 0.326660 | 0.0238241 | ||||||||
\(189\) | 4.94413 | 0.359632 | ||||||||
\(190\) | 0.663724 | 0.0481516 | ||||||||
\(191\) | 3.94669 | 0.285572 | 0.142786 | − | 0.989754i | \(-0.454394\pi\) | ||||
0.142786 | + | 0.989754i | \(0.454394\pi\) | |||||||
\(192\) | 0.178838 | 0.0129065 | ||||||||
\(193\) | −1.51907 | −0.109345 | −0.0546725 | − | 0.998504i | \(-0.517411\pi\) | ||||
−0.0546725 | + | 0.998504i | \(0.517411\pi\) | |||||||
\(194\) | −17.7548 | −1.27472 | ||||||||
\(195\) | 0.178838 | 0.0128069 | ||||||||
\(196\) | 14.4585 | 1.03275 | ||||||||
\(197\) | 19.1945 | 1.36755 | 0.683776 | − | 0.729692i | \(-0.260336\pi\) | ||||
0.683776 | + | 0.729692i | \(0.260336\pi\) | |||||||
\(198\) | −15.8353 | −1.12537 | ||||||||
\(199\) | −3.45167 | −0.244682 | −0.122341 | − | 0.992488i | \(-0.539040\pi\) | ||||
−0.122341 | + | 0.992488i | \(0.539040\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −0.578829 | −0.0408274 | ||||||||
\(202\) | 5.33151 | 0.375124 | ||||||||
\(203\) | −32.5923 | −2.28753 | ||||||||
\(204\) | −1.07955 | −0.0755833 | ||||||||
\(205\) | −7.35666 | −0.513811 | ||||||||
\(206\) | 0.761610 | 0.0530639 | ||||||||
\(207\) | 3.58341 | 0.249064 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | −3.54117 | −0.244948 | ||||||||
\(210\) | 0.828437 | 0.0571676 | ||||||||
\(211\) | 19.5039 | 1.34271 | 0.671353 | − | 0.741138i | \(-0.265714\pi\) | ||||
0.671353 | + | 0.741138i | \(0.265714\pi\) | |||||||
\(212\) | 12.3242 | 0.846430 | ||||||||
\(213\) | −1.77836 | −0.121851 | ||||||||
\(214\) | −17.9697 | −1.22838 | ||||||||
\(215\) | −12.4429 | −0.848599 | ||||||||
\(216\) | −1.06731 | −0.0726212 | ||||||||
\(217\) | 4.63233 | 0.314463 | ||||||||
\(218\) | 11.9278 | 0.807852 | ||||||||
\(219\) | 0.197112 | 0.0133196 | ||||||||
\(220\) | −5.33531 | −0.359707 | ||||||||
\(221\) | 6.03643 | 0.406054 | ||||||||
\(222\) | 1.22501 | 0.0822175 | ||||||||
\(223\) | 21.7277 | 1.45500 | 0.727498 | − | 0.686110i | \(-0.240683\pi\) | ||||
0.727498 | + | 0.686110i | \(0.240683\pi\) | |||||||
\(224\) | −4.63233 | −0.309510 | ||||||||
\(225\) | −2.96802 | −0.197868 | ||||||||
\(226\) | −13.8676 | −0.922459 | ||||||||
\(227\) | 15.9688 | 1.05989 | 0.529943 | − | 0.848033i | \(-0.322213\pi\) | ||||
0.529943 | + | 0.848033i | \(0.322213\pi\) | |||||||
\(228\) | −0.118699 | −0.00786105 | ||||||||
\(229\) | 14.7883 | 0.977241 | 0.488620 | − | 0.872497i | \(-0.337500\pi\) | ||||
0.488620 | + | 0.872497i | \(0.337500\pi\) | |||||||
\(230\) | 1.20734 | 0.0796097 | ||||||||
\(231\) | −4.41997 | −0.290813 | ||||||||
\(232\) | 7.03585 | 0.461926 | ||||||||
\(233\) | 6.09633 | 0.399384 | 0.199692 | − | 0.979859i | \(-0.436006\pi\) | ||||
0.199692 | + | 0.979859i | \(0.436006\pi\) | |||||||
\(234\) | 2.96802 | 0.194025 | ||||||||
\(235\) | −0.326660 | −0.0213089 | ||||||||
\(236\) | 10.9205 | 0.710865 | ||||||||
\(237\) | 2.82417 | 0.183450 | ||||||||
\(238\) | 27.9627 | 1.81256 | ||||||||
\(239\) | 27.2233 | 1.76093 | 0.880464 | − | 0.474113i | \(-0.157231\pi\) | ||||
0.880464 | + | 0.474113i | \(0.157231\pi\) | |||||||
\(240\) | −0.178838 | −0.0115440 | ||||||||
\(241\) | −8.85643 | −0.570493 | −0.285246 | − | 0.958454i | \(-0.592075\pi\) | ||||
−0.285246 | + | 0.958454i | \(0.592075\pi\) | |||||||
\(242\) | 17.4655 | 1.12273 | ||||||||
\(243\) | 4.76018 | 0.305366 | ||||||||
\(244\) | −11.0097 | −0.704822 | ||||||||
\(245\) | −14.4585 | −0.923717 | ||||||||
\(246\) | 1.31565 | 0.0838829 | ||||||||
\(247\) | 0.663724 | 0.0422317 | ||||||||
\(248\) | −1.00000 | −0.0635001 | ||||||||
\(249\) | −1.59825 | −0.101285 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −6.59287 | −0.416139 | −0.208069 | − | 0.978114i | \(-0.566718\pi\) | ||||
−0.208069 | + | 0.978114i | \(0.566718\pi\) | |||||||
\(252\) | 13.7488 | 0.866095 | ||||||||
\(253\) | −6.44154 | −0.404976 | ||||||||
\(254\) | 18.4024 | 1.15467 | ||||||||
\(255\) | 1.07955 | 0.0676038 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.16043 | 0.197142 | 0.0985710 | − | 0.995130i | \(-0.468573\pi\) | ||||
0.0985710 | + | 0.995130i | \(0.468573\pi\) | |||||||
\(258\) | 2.22527 | 0.138539 | ||||||||
\(259\) | −31.7307 | −1.97165 | ||||||||
\(260\) | 1.00000 | 0.0620174 | ||||||||
\(261\) | −20.8825 | −1.29260 | ||||||||
\(262\) | −7.02881 | −0.434241 | ||||||||
\(263\) | 2.92844 | 0.180575 | 0.0902876 | − | 0.995916i | \(-0.471221\pi\) | ||||
0.0902876 | + | 0.995916i | \(0.471221\pi\) | |||||||
\(264\) | 0.954158 | 0.0587243 | ||||||||
\(265\) | −12.3242 | −0.757070 | ||||||||
\(266\) | 3.07459 | 0.188515 | ||||||||
\(267\) | −0.0687313 | −0.00420628 | ||||||||
\(268\) | −3.23660 | −0.197707 | ||||||||
\(269\) | 16.7347 | 1.02033 | 0.510167 | − | 0.860075i | \(-0.329584\pi\) | ||||
0.510167 | + | 0.860075i | \(0.329584\pi\) | |||||||
\(270\) | 1.06731 | 0.0649544 | ||||||||
\(271\) | 28.1642 | 1.71085 | 0.855425 | − | 0.517926i | \(-0.173296\pi\) | ||||
0.855425 | + | 0.517926i | \(0.173296\pi\) | |||||||
\(272\) | −6.03643 | −0.366013 | ||||||||
\(273\) | 0.828437 | 0.0501393 | ||||||||
\(274\) | 15.3912 | 0.929817 | ||||||||
\(275\) | 5.33531 | 0.321731 | ||||||||
\(276\) | −0.215919 | −0.0129968 | ||||||||
\(277\) | −4.18271 | −0.251315 | −0.125657 | − | 0.992074i | \(-0.540104\pi\) | ||||
−0.125657 | + | 0.992074i | \(0.540104\pi\) | |||||||
\(278\) | −5.33060 | −0.319708 | ||||||||
\(279\) | 2.96802 | 0.177691 | ||||||||
\(280\) | 4.63233 | 0.276835 | ||||||||
\(281\) | −29.5778 | −1.76446 | −0.882231 | − | 0.470816i | \(-0.843959\pi\) | ||||
−0.882231 | + | 0.470816i | \(0.843959\pi\) | |||||||
\(282\) | 0.0584192 | 0.00347881 | ||||||||
\(283\) | −21.8936 | −1.30144 | −0.650721 | − | 0.759317i | \(-0.725533\pi\) | ||||
−0.650721 | + | 0.759317i | \(0.725533\pi\) | |||||||
\(284\) | −9.94396 | −0.590066 | ||||||||
\(285\) | 0.118699 | 0.00703113 | ||||||||
\(286\) | −5.33531 | −0.315484 | ||||||||
\(287\) | −34.0785 | −2.01159 | ||||||||
\(288\) | −2.96802 | −0.174892 | ||||||||
\(289\) | 19.4385 | 1.14344 | ||||||||
\(290\) | −7.03585 | −0.413159 | ||||||||
\(291\) | −3.17524 | −0.186136 | ||||||||
\(292\) | 1.10218 | 0.0645002 | ||||||||
\(293\) | −31.6771 | −1.85059 | −0.925297 | − | 0.379242i | \(-0.876185\pi\) | ||||
−0.925297 | + | 0.379242i | \(0.876185\pi\) | |||||||
\(294\) | 2.58573 | 0.150803 | ||||||||
\(295\) | −10.9205 | −0.635817 | ||||||||
\(296\) | 6.84984 | 0.398139 | ||||||||
\(297\) | −5.69443 | −0.330424 | ||||||||
\(298\) | 8.14501 | 0.471828 | ||||||||
\(299\) | 1.20734 | 0.0698224 | ||||||||
\(300\) | 0.178838 | 0.0103252 | ||||||||
\(301\) | −57.6396 | −3.32229 | ||||||||
\(302\) | −4.82349 | −0.277560 | ||||||||
\(303\) | 0.953478 | 0.0547759 | ||||||||
\(304\) | −0.663724 | −0.0380672 | ||||||||
\(305\) | 11.0097 | 0.630412 | ||||||||
\(306\) | 17.9162 | 1.02420 | ||||||||
\(307\) | −15.6792 | −0.894860 | −0.447430 | − | 0.894319i | \(-0.647661\pi\) | ||||
−0.447430 | + | 0.894319i | \(0.647661\pi\) | |||||||
\(308\) | −24.7149 | −1.40826 | ||||||||
\(309\) | 0.136205 | 0.00774843 | ||||||||
\(310\) | 1.00000 | 0.0567962 | ||||||||
\(311\) | 1.60738 | 0.0911462 | 0.0455731 | − | 0.998961i | \(-0.485489\pi\) | ||||
0.0455731 | + | 0.998961i | \(0.485489\pi\) | |||||||
\(312\) | −0.178838 | −0.0101247 | ||||||||
\(313\) | 33.2099 | 1.87714 | 0.938568 | − | 0.345096i | \(-0.112154\pi\) | ||||
0.938568 | + | 0.345096i | \(0.112154\pi\) | |||||||
\(314\) | −9.18398 | −0.518282 | ||||||||
\(315\) | −13.7488 | −0.774659 | ||||||||
\(316\) | 15.7918 | 0.888356 | ||||||||
\(317\) | −28.2205 | −1.58502 | −0.792511 | − | 0.609858i | \(-0.791226\pi\) | ||||
−0.792511 | + | 0.609858i | \(0.791226\pi\) | |||||||
\(318\) | 2.20404 | 0.123596 | ||||||||
\(319\) | 37.5384 | 2.10175 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −3.21367 | −0.179370 | ||||||||
\(322\) | 5.59280 | 0.311675 | ||||||||
\(323\) | 4.00652 | 0.222929 | ||||||||
\(324\) | 8.71317 | 0.484065 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | 4.50771 | 0.249659 | ||||||||
\(327\) | 2.13315 | 0.117963 | ||||||||
\(328\) | 7.35666 | 0.406204 | ||||||||
\(329\) | −1.51319 | −0.0834251 | ||||||||
\(330\) | −0.954158 | −0.0525246 | ||||||||
\(331\) | 15.1107 | 0.830558 | 0.415279 | − | 0.909694i | \(-0.363684\pi\) | ||||
0.415279 | + | 0.909694i | \(0.363684\pi\) | |||||||
\(332\) | −8.93682 | −0.490472 | ||||||||
\(333\) | −20.3304 | −1.11410 | ||||||||
\(334\) | 4.88428 | 0.267256 | ||||||||
\(335\) | 3.23660 | 0.176835 | ||||||||
\(336\) | −0.828437 | −0.0451950 | ||||||||
\(337\) | −17.3733 | −0.946385 | −0.473193 | − | 0.880959i | \(-0.656899\pi\) | ||||
−0.473193 | + | 0.880959i | \(0.656899\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | −2.48006 | −0.134698 | ||||||||
\(340\) | 6.03643 | 0.327372 | ||||||||
\(341\) | −5.33531 | −0.288923 | ||||||||
\(342\) | 1.96994 | 0.106522 | ||||||||
\(343\) | −34.5500 | −1.86553 | ||||||||
\(344\) | 12.4429 | 0.670877 | ||||||||
\(345\) | 0.215919 | 0.0116247 | ||||||||
\(346\) | 3.37554 | 0.181470 | ||||||||
\(347\) | 5.03025 | 0.270038 | 0.135019 | − | 0.990843i | \(-0.456890\pi\) | ||||
0.135019 | + | 0.990843i | \(0.456890\pi\) | |||||||
\(348\) | 1.25828 | 0.0674508 | ||||||||
\(349\) | 3.33672 | 0.178611 | 0.0893053 | − | 0.996004i | \(-0.471535\pi\) | ||||
0.0893053 | + | 0.996004i | \(0.471535\pi\) | |||||||
\(350\) | −4.63233 | −0.247608 | ||||||||
\(351\) | 1.06731 | 0.0569688 | ||||||||
\(352\) | 5.33531 | 0.284373 | ||||||||
\(353\) | 10.8928 | 0.579768 | 0.289884 | − | 0.957062i | \(-0.406383\pi\) | ||||
0.289884 | + | 0.957062i | \(0.406383\pi\) | |||||||
\(354\) | 1.95301 | 0.103801 | ||||||||
\(355\) | 9.94396 | 0.527771 | ||||||||
\(356\) | −0.384321 | −0.0203690 | ||||||||
\(357\) | 5.00081 | 0.264671 | ||||||||
\(358\) | −20.3213 | −1.07401 | ||||||||
\(359\) | −14.7587 | −0.778937 | −0.389468 | − | 0.921040i | \(-0.627341\pi\) | ||||
−0.389468 | + | 0.921040i | \(0.627341\pi\) | |||||||
\(360\) | 2.96802 | 0.156428 | ||||||||
\(361\) | −18.5595 | −0.976814 | ||||||||
\(362\) | 16.0859 | 0.845456 | ||||||||
\(363\) | 3.12351 | 0.163942 | ||||||||
\(364\) | 4.63233 | 0.242800 | ||||||||
\(365\) | −1.10218 | −0.0576907 | ||||||||
\(366\) | −1.96895 | −0.102919 | ||||||||
\(367\) | 19.5687 | 1.02148 | 0.510739 | − | 0.859736i | \(-0.329372\pi\) | ||||
0.510739 | + | 0.859736i | \(0.329372\pi\) | |||||||
\(368\) | −1.20734 | −0.0629370 | ||||||||
\(369\) | −21.8347 | −1.13667 | ||||||||
\(370\) | −6.84984 | −0.356106 | ||||||||
\(371\) | −57.0898 | −2.96395 | ||||||||
\(372\) | −0.178838 | −0.00927233 | ||||||||
\(373\) | −23.4343 | −1.21338 | −0.606690 | − | 0.794938i | \(-0.707503\pi\) | ||||
−0.606690 | + | 0.794938i | \(0.707503\pi\) | |||||||
\(374\) | −32.2062 | −1.66535 | ||||||||
\(375\) | −0.178838 | −0.00923517 | ||||||||
\(376\) | 0.326660 | 0.0168462 | ||||||||
\(377\) | −7.03585 | −0.362365 | ||||||||
\(378\) | 4.94413 | 0.254299 | ||||||||
\(379\) | −9.95784 | −0.511500 | −0.255750 | − | 0.966743i | \(-0.582322\pi\) | ||||
−0.255750 | + | 0.966743i | \(0.582322\pi\) | |||||||
\(380\) | 0.663724 | 0.0340483 | ||||||||
\(381\) | 3.29105 | 0.168605 | ||||||||
\(382\) | 3.94669 | 0.201930 | ||||||||
\(383\) | 15.5114 | 0.792598 | 0.396299 | − | 0.918122i | \(-0.370294\pi\) | ||||
0.396299 | + | 0.918122i | \(0.370294\pi\) | |||||||
\(384\) | 0.178838 | 0.00912630 | ||||||||
\(385\) | 24.7149 | 1.25959 | ||||||||
\(386\) | −1.51907 | −0.0773187 | ||||||||
\(387\) | −36.9308 | −1.87730 | ||||||||
\(388\) | −17.7548 | −0.901365 | ||||||||
\(389\) | 5.09129 | 0.258139 | 0.129069 | − | 0.991636i | \(-0.458801\pi\) | ||||
0.129069 | + | 0.991636i | \(0.458801\pi\) | |||||||
\(390\) | 0.178838 | 0.00905583 | ||||||||
\(391\) | 7.28804 | 0.368572 | ||||||||
\(392\) | 14.4585 | 0.730263 | ||||||||
\(393\) | −1.25702 | −0.0634083 | ||||||||
\(394\) | 19.1945 | 0.967006 | ||||||||
\(395\) | −15.7918 | −0.794569 | ||||||||
\(396\) | −15.8353 | −0.795753 | ||||||||
\(397\) | 23.7475 | 1.19185 | 0.595926 | − | 0.803039i | \(-0.296785\pi\) | ||||
0.595926 | + | 0.803039i | \(0.296785\pi\) | |||||||
\(398\) | −3.45167 | −0.173016 | ||||||||
\(399\) | 0.549854 | 0.0275271 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −7.89202 | −0.394109 | −0.197054 | − | 0.980393i | \(-0.563138\pi\) | ||||
−0.197054 | + | 0.980393i | \(0.563138\pi\) | |||||||
\(402\) | −0.578829 | −0.0288694 | ||||||||
\(403\) | 1.00000 | 0.0498135 | ||||||||
\(404\) | 5.33151 | 0.265252 | ||||||||
\(405\) | −8.71317 | −0.432961 | ||||||||
\(406\) | −32.5923 | −1.61753 | ||||||||
\(407\) | 36.5460 | 1.81152 | ||||||||
\(408\) | −1.07955 | −0.0534455 | ||||||||
\(409\) | −37.3652 | −1.84759 | −0.923796 | − | 0.382886i | \(-0.874930\pi\) | ||||
−0.923796 | + | 0.382886i | \(0.874930\pi\) | |||||||
\(410\) | −7.35666 | −0.363320 | ||||||||
\(411\) | 2.75254 | 0.135773 | ||||||||
\(412\) | 0.761610 | 0.0375218 | ||||||||
\(413\) | −50.5874 | −2.48924 | ||||||||
\(414\) | 3.58341 | 0.176115 | ||||||||
\(415\) | 8.93682 | 0.438691 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −0.953316 | −0.0466841 | ||||||||
\(418\) | −3.54117 | −0.173204 | ||||||||
\(419\) | −16.2972 | −0.796168 | −0.398084 | − | 0.917349i | \(-0.630325\pi\) | ||||
−0.398084 | + | 0.917349i | \(0.630325\pi\) | |||||||
\(420\) | 0.828437 | 0.0404236 | ||||||||
\(421\) | −11.5930 | −0.565008 | −0.282504 | − | 0.959266i | \(-0.591165\pi\) | ||||
−0.282504 | + | 0.959266i | \(0.591165\pi\) | |||||||
\(422\) | 19.5039 | 0.949436 | ||||||||
\(423\) | −0.969531 | −0.0471402 | ||||||||
\(424\) | 12.3242 | 0.598516 | ||||||||
\(425\) | −6.03643 | −0.292810 | ||||||||
\(426\) | −1.77836 | −0.0861619 | ||||||||
\(427\) | 51.0004 | 2.46808 | ||||||||
\(428\) | −17.9697 | −0.868598 | ||||||||
\(429\) | −0.954158 | −0.0460672 | ||||||||
\(430\) | −12.4429 | −0.600050 | ||||||||
\(431\) | 16.9740 | 0.817610 | 0.408805 | − | 0.912622i | \(-0.365946\pi\) | ||||
0.408805 | + | 0.912622i | \(0.365946\pi\) | |||||||
\(432\) | −1.06731 | −0.0513510 | ||||||||
\(433\) | 26.3107 | 1.26441 | 0.632205 | − | 0.774801i | \(-0.282150\pi\) | ||||
0.632205 | + | 0.774801i | \(0.282150\pi\) | |||||||
\(434\) | 4.63233 | 0.222359 | ||||||||
\(435\) | −1.25828 | −0.0603298 | ||||||||
\(436\) | 11.9278 | 0.571238 | ||||||||
\(437\) | 0.801341 | 0.0383333 | ||||||||
\(438\) | 0.197112 | 0.00941837 | ||||||||
\(439\) | 26.8813 | 1.28298 | 0.641488 | − | 0.767133i | \(-0.278318\pi\) | ||||
0.641488 | + | 0.767133i | \(0.278318\pi\) | |||||||
\(440\) | −5.33531 | −0.254351 | ||||||||
\(441\) | −42.9130 | −2.04347 | ||||||||
\(442\) | 6.03643 | 0.287124 | ||||||||
\(443\) | −4.26704 | −0.202733 | −0.101366 | − | 0.994849i | \(-0.532321\pi\) | ||||
−0.101366 | + | 0.994849i | \(0.532321\pi\) | |||||||
\(444\) | 1.22501 | 0.0581365 | ||||||||
\(445\) | 0.384321 | 0.0182186 | ||||||||
\(446\) | 21.7277 | 1.02884 | ||||||||
\(447\) | 1.45664 | 0.0688967 | ||||||||
\(448\) | −4.63233 | −0.218857 | ||||||||
\(449\) | 0.342985 | 0.0161865 | 0.00809323 | − | 0.999967i | \(-0.497424\pi\) | ||||
0.00809323 | + | 0.999967i | \(0.497424\pi\) | |||||||
\(450\) | −2.96802 | −0.139914 | ||||||||
\(451\) | 39.2501 | 1.84821 | ||||||||
\(452\) | −13.8676 | −0.652277 | ||||||||
\(453\) | −0.862624 | −0.0405296 | ||||||||
\(454\) | 15.9688 | 0.749453 | ||||||||
\(455\) | −4.63233 | −0.217167 | ||||||||
\(456\) | −0.118699 | −0.00555860 | ||||||||
\(457\) | −12.6480 | −0.591649 | −0.295824 | − | 0.955242i | \(-0.595594\pi\) | ||||
−0.295824 | + | 0.955242i | \(0.595594\pi\) | |||||||
\(458\) | 14.7883 | 0.691013 | ||||||||
\(459\) | 6.44274 | 0.300722 | ||||||||
\(460\) | 1.20734 | 0.0562926 | ||||||||
\(461\) | −11.1326 | −0.518497 | −0.259249 | − | 0.965811i | \(-0.583475\pi\) | ||||
−0.259249 | + | 0.965811i | \(0.583475\pi\) | |||||||
\(462\) | −4.41997 | −0.205636 | ||||||||
\(463\) | −36.7366 | −1.70730 | −0.853648 | − | 0.520850i | \(-0.825615\pi\) | ||||
−0.853648 | + | 0.520850i | \(0.825615\pi\) | |||||||
\(464\) | 7.03585 | 0.326631 | ||||||||
\(465\) | 0.178838 | 0.00829343 | ||||||||
\(466\) | 6.09633 | 0.282407 | ||||||||
\(467\) | 15.6133 | 0.722497 | 0.361249 | − | 0.932470i | \(-0.382351\pi\) | ||||
0.361249 | + | 0.932470i | \(0.382351\pi\) | |||||||
\(468\) | 2.96802 | 0.137197 | ||||||||
\(469\) | 14.9930 | 0.692313 | ||||||||
\(470\) | −0.326660 | −0.0150677 | ||||||||
\(471\) | −1.64245 | −0.0756800 | ||||||||
\(472\) | 10.9205 | 0.502658 | ||||||||
\(473\) | 66.3868 | 3.05247 | ||||||||
\(474\) | 2.82417 | 0.129718 | ||||||||
\(475\) | −0.663724 | −0.0304537 | ||||||||
\(476\) | 27.9627 | 1.28167 | ||||||||
\(477\) | −36.5785 | −1.67481 | ||||||||
\(478\) | 27.2233 | 1.24516 | ||||||||
\(479\) | −4.03715 | −0.184462 | −0.0922310 | − | 0.995738i | \(-0.529400\pi\) | ||||
−0.0922310 | + | 0.995738i | \(0.529400\pi\) | |||||||
\(480\) | −0.178838 | −0.00816281 | ||||||||
\(481\) | −6.84984 | −0.312326 | ||||||||
\(482\) | −8.85643 | −0.403399 | ||||||||
\(483\) | 1.00021 | 0.0455110 | ||||||||
\(484\) | 17.4655 | 0.793888 | ||||||||
\(485\) | 17.7548 | 0.806205 | ||||||||
\(486\) | 4.76018 | 0.215926 | ||||||||
\(487\) | 40.9020 | 1.85344 | 0.926722 | − | 0.375747i | \(-0.122614\pi\) | ||||
0.926722 | + | 0.375747i | \(0.122614\pi\) | |||||||
\(488\) | −11.0097 | −0.498385 | ||||||||
\(489\) | 0.806152 | 0.0364554 | ||||||||
\(490\) | −14.4585 | −0.653167 | ||||||||
\(491\) | 30.5529 | 1.37883 | 0.689417 | − | 0.724365i | \(-0.257867\pi\) | ||||
0.689417 | + | 0.724365i | \(0.257867\pi\) | |||||||
\(492\) | 1.31565 | 0.0593142 | ||||||||
\(493\) | −42.4714 | −1.91282 | ||||||||
\(494\) | 0.663724 | 0.0298623 | ||||||||
\(495\) | 15.8353 | 0.711743 | ||||||||
\(496\) | −1.00000 | −0.0449013 | ||||||||
\(497\) | 46.0637 | 2.06624 | ||||||||
\(498\) | −1.59825 | −0.0716191 | ||||||||
\(499\) | 26.9218 | 1.20519 | 0.602593 | − | 0.798048i | \(-0.294134\pi\) | ||||
0.602593 | + | 0.798048i | \(0.294134\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 0.873497 | 0.0390250 | ||||||||
\(502\) | −6.59287 | −0.294254 | ||||||||
\(503\) | −36.0604 | −1.60785 | −0.803926 | − | 0.594730i | \(-0.797259\pi\) | ||||
−0.803926 | + | 0.594730i | \(0.797259\pi\) | |||||||
\(504\) | 13.7488 | 0.612421 | ||||||||
\(505\) | −5.33151 | −0.237249 | ||||||||
\(506\) | −6.44154 | −0.286361 | ||||||||
\(507\) | 0.178838 | 0.00794249 | ||||||||
\(508\) | 18.4024 | 0.816473 | ||||||||
\(509\) | −30.9960 | −1.37387 | −0.686936 | − | 0.726718i | \(-0.741045\pi\) | ||||
−0.686936 | + | 0.726718i | \(0.741045\pi\) | |||||||
\(510\) | 1.07955 | 0.0478031 | ||||||||
\(511\) | −5.10566 | −0.225861 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0.708399 | 0.0312766 | ||||||||
\(514\) | 3.16043 | 0.139400 | ||||||||
\(515\) | −0.761610 | −0.0335605 | ||||||||
\(516\) | 2.22527 | 0.0979620 | ||||||||
\(517\) | 1.74283 | 0.0766496 | ||||||||
\(518\) | −31.7307 | −1.39417 | ||||||||
\(519\) | 0.603675 | 0.0264984 | ||||||||
\(520\) | 1.00000 | 0.0438529 | ||||||||
\(521\) | −8.33312 | −0.365081 | −0.182540 | − | 0.983198i | \(-0.558432\pi\) | ||||
−0.182540 | + | 0.983198i | \(0.558432\pi\) | |||||||
\(522\) | −20.8825 | −0.914003 | ||||||||
\(523\) | −4.55325 | −0.199100 | −0.0995498 | − | 0.995033i | \(-0.531740\pi\) | ||||
−0.0995498 | + | 0.995033i | \(0.531740\pi\) | |||||||
\(524\) | −7.02881 | −0.307055 | ||||||||
\(525\) | −0.828437 | −0.0361560 | ||||||||
\(526\) | 2.92844 | 0.127686 | ||||||||
\(527\) | 6.03643 | 0.262951 | ||||||||
\(528\) | 0.954158 | 0.0415244 | ||||||||
\(529\) | −21.5423 | −0.936623 | ||||||||
\(530\) | −12.3242 | −0.535329 | ||||||||
\(531\) | −32.4123 | −1.40657 | ||||||||
\(532\) | 3.07459 | 0.133300 | ||||||||
\(533\) | −7.35666 | −0.318652 | ||||||||
\(534\) | −0.0687313 | −0.00297429 | ||||||||
\(535\) | 17.9697 | 0.776898 | ||||||||
\(536\) | −3.23660 | −0.139800 | ||||||||
\(537\) | −3.63422 | −0.156828 | ||||||||
\(538\) | 16.7347 | 0.721485 | ||||||||
\(539\) | 77.1404 | 3.32267 | ||||||||
\(540\) | 1.06731 | 0.0459297 | ||||||||
\(541\) | 20.1042 | 0.864347 | 0.432173 | − | 0.901791i | \(-0.357747\pi\) | ||||
0.432173 | + | 0.901791i | \(0.357747\pi\) | |||||||
\(542\) | 28.1642 | 1.20975 | ||||||||
\(543\) | 2.87677 | 0.123454 | ||||||||
\(544\) | −6.03643 | −0.258810 | ||||||||
\(545\) | −11.9278 | −0.510930 | ||||||||
\(546\) | 0.828437 | 0.0354539 | ||||||||
\(547\) | −12.6527 | −0.540992 | −0.270496 | − | 0.962721i | \(-0.587188\pi\) | ||||
−0.270496 | + | 0.962721i | \(0.587188\pi\) | |||||||
\(548\) | 15.3912 | 0.657480 | ||||||||
\(549\) | 32.6769 | 1.39462 | ||||||||
\(550\) | 5.33531 | 0.227498 | ||||||||
\(551\) | −4.66986 | −0.198943 | ||||||||
\(552\) | −0.215919 | −0.00919012 | ||||||||
\(553\) | −73.1526 | −3.11076 | ||||||||
\(554\) | −4.18271 | −0.177706 | ||||||||
\(555\) | −1.22501 | −0.0519989 | ||||||||
\(556\) | −5.33060 | −0.226068 | ||||||||
\(557\) | 9.98212 | 0.422956 | 0.211478 | − | 0.977383i | \(-0.432172\pi\) | ||||
0.211478 | + | 0.977383i | \(0.432172\pi\) | |||||||
\(558\) | 2.96802 | 0.125646 | ||||||||
\(559\) | −12.4429 | −0.526279 | ||||||||
\(560\) | 4.63233 | 0.195752 | ||||||||
\(561\) | −5.75971 | −0.243175 | ||||||||
\(562\) | −29.5778 | −1.24766 | ||||||||
\(563\) | 42.7653 | 1.80234 | 0.901171 | − | 0.433464i | \(-0.142709\pi\) | ||||
0.901171 | + | 0.433464i | \(0.142709\pi\) | |||||||
\(564\) | 0.0584192 | 0.00245989 | ||||||||
\(565\) | 13.8676 | 0.583414 | ||||||||
\(566\) | −21.8936 | −0.920258 | ||||||||
\(567\) | −40.3623 | −1.69506 | ||||||||
\(568\) | −9.94396 | −0.417239 | ||||||||
\(569\) | 17.3053 | 0.725476 | 0.362738 | − | 0.931891i | \(-0.381842\pi\) | ||||
0.362738 | + | 0.931891i | \(0.381842\pi\) | |||||||
\(570\) | 0.118699 | 0.00497176 | ||||||||
\(571\) | 35.4528 | 1.48365 | 0.741827 | − | 0.670592i | \(-0.233960\pi\) | ||||
0.741827 | + | 0.670592i | \(0.233960\pi\) | |||||||
\(572\) | −5.33531 | −0.223081 | ||||||||
\(573\) | 0.705819 | 0.0294860 | ||||||||
\(574\) | −34.0785 | −1.42241 | ||||||||
\(575\) | −1.20734 | −0.0503496 | ||||||||
\(576\) | −2.96802 | −0.123667 | ||||||||
\(577\) | 13.3304 | 0.554953 | 0.277477 | − | 0.960732i | \(-0.410502\pi\) | ||||
0.277477 | + | 0.960732i | \(0.410502\pi\) | |||||||
\(578\) | 19.4385 | 0.808536 | ||||||||
\(579\) | −0.271668 | −0.0112901 | ||||||||
\(580\) | −7.03585 | −0.292148 | ||||||||
\(581\) | 41.3983 | 1.71749 | ||||||||
\(582\) | −3.17524 | −0.131618 | ||||||||
\(583\) | 65.7535 | 2.72323 | ||||||||
\(584\) | 1.10218 | 0.0456085 | ||||||||
\(585\) | −2.96802 | −0.122712 | ||||||||
\(586\) | −31.6771 | −1.30857 | ||||||||
\(587\) | 19.6700 | 0.811868 | 0.405934 | − | 0.913902i | \(-0.366946\pi\) | ||||
0.405934 | + | 0.913902i | \(0.366946\pi\) | |||||||
\(588\) | 2.58573 | 0.106634 | ||||||||
\(589\) | 0.663724 | 0.0273483 | ||||||||
\(590\) | −10.9205 | −0.449591 | ||||||||
\(591\) | 3.43271 | 0.141203 | ||||||||
\(592\) | 6.84984 | 0.281527 | ||||||||
\(593\) | 24.8311 | 1.01969 | 0.509845 | − | 0.860266i | \(-0.329703\pi\) | ||||
0.509845 | + | 0.860266i | \(0.329703\pi\) | |||||||
\(594\) | −5.69443 | −0.233645 | ||||||||
\(595\) | −27.9627 | −1.14636 | ||||||||
\(596\) | 8.14501 | 0.333633 | ||||||||
\(597\) | −0.617290 | −0.0252640 | ||||||||
\(598\) | 1.20734 | 0.0493719 | ||||||||
\(599\) | −18.9916 | −0.775977 | −0.387989 | − | 0.921664i | \(-0.626830\pi\) | ||||
−0.387989 | + | 0.921664i | \(0.626830\pi\) | |||||||
\(600\) | 0.178838 | 0.00730104 | ||||||||
\(601\) | −32.2369 | −1.31497 | −0.657486 | − | 0.753467i | \(-0.728380\pi\) | ||||
−0.657486 | + | 0.753467i | \(0.728380\pi\) | |||||||
\(602\) | −57.6396 | −2.34922 | ||||||||
\(603\) | 9.60630 | 0.391199 | ||||||||
\(604\) | −4.82349 | −0.196265 | ||||||||
\(605\) | −17.4655 | −0.710075 | ||||||||
\(606\) | 0.953478 | 0.0387324 | ||||||||
\(607\) | −22.8430 | −0.927169 | −0.463585 | − | 0.886053i | \(-0.653437\pi\) | ||||
−0.463585 | + | 0.886053i | \(0.653437\pi\) | |||||||
\(608\) | −0.663724 | −0.0269175 | ||||||||
\(609\) | −5.82876 | −0.236193 | ||||||||
\(610\) | 11.0097 | 0.445769 | ||||||||
\(611\) | −0.326660 | −0.0132152 | ||||||||
\(612\) | 17.9162 | 0.724221 | ||||||||
\(613\) | 48.2963 | 1.95067 | 0.975335 | − | 0.220728i | \(-0.0708432\pi\) | ||||
0.975335 | + | 0.220728i | \(0.0708432\pi\) | |||||||
\(614\) | −15.6792 | −0.632761 | ||||||||
\(615\) | −1.31565 | −0.0530522 | ||||||||
\(616\) | −24.7149 | −0.995792 | ||||||||
\(617\) | 14.6017 | 0.587844 | 0.293922 | − | 0.955829i | \(-0.405039\pi\) | ||||
0.293922 | + | 0.955829i | \(0.405039\pi\) | |||||||
\(618\) | 0.136205 | 0.00547897 | ||||||||
\(619\) | −14.6378 | −0.588342 | −0.294171 | − | 0.955753i | \(-0.595043\pi\) | ||||
−0.294171 | + | 0.955753i | \(0.595043\pi\) | |||||||
\(620\) | 1.00000 | 0.0401610 | ||||||||
\(621\) | 1.28861 | 0.0517100 | ||||||||
\(622\) | 1.60738 | 0.0644501 | ||||||||
\(623\) | 1.78030 | 0.0713262 | ||||||||
\(624\) | −0.178838 | −0.00715926 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 33.2099 | 1.32733 | ||||||||
\(627\) | −0.633297 | −0.0252914 | ||||||||
\(628\) | −9.18398 | −0.366481 | ||||||||
\(629\) | −41.3486 | −1.64868 | ||||||||
\(630\) | −13.7488 | −0.547766 | ||||||||
\(631\) | 6.72848 | 0.267857 | 0.133928 | − | 0.990991i | \(-0.457241\pi\) | ||||
0.133928 | + | 0.990991i | \(0.457241\pi\) | |||||||
\(632\) | 15.7918 | 0.628162 | ||||||||
\(633\) | 3.48805 | 0.138637 | ||||||||
\(634\) | −28.2205 | −1.12078 | ||||||||
\(635\) | −18.4024 | −0.730275 | ||||||||
\(636\) | 2.20404 | 0.0873959 | ||||||||
\(637\) | −14.4585 | −0.572865 | ||||||||
\(638\) | 37.5384 | 1.48616 | ||||||||
\(639\) | 29.5139 | 1.16755 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 21.2546 | 0.839508 | 0.419754 | − | 0.907638i | \(-0.362116\pi\) | ||||
0.419754 | + | 0.907638i | \(0.362116\pi\) | |||||||
\(642\) | −3.21367 | −0.126833 | ||||||||
\(643\) | −15.5072 | −0.611543 | −0.305772 | − | 0.952105i | \(-0.598914\pi\) | ||||
−0.305772 | + | 0.952105i | \(0.598914\pi\) | |||||||
\(644\) | 5.59280 | 0.220387 | ||||||||
\(645\) | −2.22527 | −0.0876198 | ||||||||
\(646\) | 4.00652 | 0.157635 | ||||||||
\(647\) | −7.68131 | −0.301983 | −0.150992 | − | 0.988535i | \(-0.548247\pi\) | ||||
−0.150992 | + | 0.988535i | \(0.548247\pi\) | |||||||
\(648\) | 8.71317 | 0.342286 | ||||||||
\(649\) | 58.2643 | 2.28708 | ||||||||
\(650\) | −1.00000 | −0.0392232 | ||||||||
\(651\) | 0.828437 | 0.0324690 | ||||||||
\(652\) | 4.50771 | 0.176536 | ||||||||
\(653\) | −34.2319 | −1.33960 | −0.669799 | − | 0.742543i | \(-0.733620\pi\) | ||||
−0.669799 | + | 0.742543i | \(0.733620\pi\) | |||||||
\(654\) | 2.13315 | 0.0834126 | ||||||||
\(655\) | 7.02881 | 0.274638 | ||||||||
\(656\) | 7.35666 | 0.287229 | ||||||||
\(657\) | −3.27129 | −0.127625 | ||||||||
\(658\) | −1.51319 | −0.0589904 | ||||||||
\(659\) | −1.15499 | −0.0449919 | −0.0224960 | − | 0.999747i | \(-0.507161\pi\) | ||||
−0.0224960 | + | 0.999747i | \(0.507161\pi\) | |||||||
\(660\) | −0.954158 | −0.0371405 | ||||||||
\(661\) | 1.95963 | 0.0762207 | 0.0381103 | − | 0.999274i | \(-0.487866\pi\) | ||||
0.0381103 | + | 0.999274i | \(0.487866\pi\) | |||||||
\(662\) | 15.1107 | 0.587293 | ||||||||
\(663\) | 1.07955 | 0.0419261 | ||||||||
\(664\) | −8.93682 | −0.346816 | ||||||||
\(665\) | −3.07459 | −0.119227 | ||||||||
\(666\) | −20.3304 | −0.787788 | ||||||||
\(667\) | −8.49467 | −0.328915 | ||||||||
\(668\) | 4.88428 | 0.188979 | ||||||||
\(669\) | 3.88575 | 0.150232 | ||||||||
\(670\) | 3.23660 | 0.125041 | ||||||||
\(671\) | −58.7400 | −2.26763 | ||||||||
\(672\) | −0.828437 | −0.0319577 | ||||||||
\(673\) | −33.5909 | −1.29483 | −0.647417 | − | 0.762136i | \(-0.724151\pi\) | ||||
−0.647417 | + | 0.762136i | \(0.724151\pi\) | |||||||
\(674\) | −17.3733 | −0.669195 | ||||||||
\(675\) | −1.06731 | −0.0410808 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 8.34855 | 0.320861 | 0.160430 | − | 0.987047i | \(-0.448712\pi\) | ||||
0.160430 | + | 0.987047i | \(0.448712\pi\) | |||||||
\(678\) | −2.48006 | −0.0952460 | ||||||||
\(679\) | 82.2462 | 3.15632 | ||||||||
\(680\) | 6.03643 | 0.231487 | ||||||||
\(681\) | 2.85583 | 0.109436 | ||||||||
\(682\) | −5.33531 | −0.204300 | ||||||||
\(683\) | 0.0400037 | 0.00153070 | 0.000765350 | − | 1.00000i | \(-0.499756\pi\) | ||||
0.000765350 | 1.00000i | \(0.499756\pi\) | ||||||||
\(684\) | 1.96994 | 0.0753227 | ||||||||
\(685\) | −15.3912 | −0.588068 | ||||||||
\(686\) | −34.5500 | −1.31913 | ||||||||
\(687\) | 2.64472 | 0.100902 | ||||||||
\(688\) | 12.4429 | 0.474381 | ||||||||
\(689\) | −12.3242 | −0.469515 | ||||||||
\(690\) | 0.215919 | 0.00821989 | ||||||||
\(691\) | 16.2070 | 0.616542 | 0.308271 | − | 0.951299i | \(-0.400250\pi\) | ||||
0.308271 | + | 0.951299i | \(0.400250\pi\) | |||||||
\(692\) | 3.37554 | 0.128319 | ||||||||
\(693\) | 73.3543 | 2.78650 | ||||||||
\(694\) | 5.03025 | 0.190946 | ||||||||
\(695\) | 5.33060 | 0.202201 | ||||||||
\(696\) | 1.25828 | 0.0476949 | ||||||||
\(697\) | −44.4080 | −1.68207 | ||||||||
\(698\) | 3.33672 | 0.126297 | ||||||||
\(699\) | 1.09026 | 0.0412373 | ||||||||
\(700\) | −4.63233 | −0.175086 | ||||||||
\(701\) | −21.9164 | −0.827772 | −0.413886 | − | 0.910329i | \(-0.635829\pi\) | ||||
−0.413886 | + | 0.910329i | \(0.635829\pi\) | |||||||
\(702\) | 1.06731 | 0.0402830 | ||||||||
\(703\) | −4.54640 | −0.171471 | ||||||||
\(704\) | 5.33531 | 0.201082 | ||||||||
\(705\) | −0.0584192 | −0.00220020 | ||||||||
\(706\) | 10.8928 | 0.409958 | ||||||||
\(707\) | −24.6973 | −0.928837 | ||||||||
\(708\) | 1.95301 | 0.0733985 | ||||||||
\(709\) | −36.5413 | −1.37234 | −0.686169 | − | 0.727442i | \(-0.740709\pi\) | ||||
−0.686169 | + | 0.727442i | \(0.740709\pi\) | |||||||
\(710\) | 9.94396 | 0.373190 | ||||||||
\(711\) | −46.8702 | −1.75777 | ||||||||
\(712\) | −0.384321 | −0.0144030 | ||||||||
\(713\) | 1.20734 | 0.0452153 | ||||||||
\(714\) | 5.00081 | 0.187151 | ||||||||
\(715\) | 5.33531 | 0.199529 | ||||||||
\(716\) | −20.3213 | −0.759441 | ||||||||
\(717\) | 4.86857 | 0.181820 | ||||||||
\(718\) | −14.7587 | −0.550791 | ||||||||
\(719\) | −0.635175 | −0.0236880 | −0.0118440 | − | 0.999930i | \(-0.503770\pi\) | ||||
−0.0118440 | + | 0.999930i | \(0.503770\pi\) | |||||||
\(720\) | 2.96802 | 0.110611 | ||||||||
\(721\) | −3.52803 | −0.131391 | ||||||||
\(722\) | −18.5595 | −0.690712 | ||||||||
\(723\) | −1.58387 | −0.0589047 | ||||||||
\(724\) | 16.0859 | 0.597827 | ||||||||
\(725\) | 7.03585 | 0.261305 | ||||||||
\(726\) | 3.12351 | 0.115924 | ||||||||
\(727\) | −23.1672 | −0.859223 | −0.429611 | − | 0.903014i | \(-0.641349\pi\) | ||||
−0.429611 | + | 0.903014i | \(0.641349\pi\) | |||||||
\(728\) | 4.63233 | 0.171685 | ||||||||
\(729\) | −25.2882 | −0.936601 | ||||||||
\(730\) | −1.10218 | −0.0407935 | ||||||||
\(731\) | −75.1108 | −2.77807 | ||||||||
\(732\) | −1.96895 | −0.0727746 | ||||||||
\(733\) | 28.9507 | 1.06932 | 0.534659 | − | 0.845068i | \(-0.320440\pi\) | ||||
0.534659 | + | 0.845068i | \(0.320440\pi\) | |||||||
\(734\) | 19.5687 | 0.722294 | ||||||||
\(735\) | −2.58573 | −0.0953759 | ||||||||
\(736\) | −1.20734 | −0.0445032 | ||||||||
\(737\) | −17.2683 | −0.636086 | ||||||||
\(738\) | −21.8347 | −0.803746 | ||||||||
\(739\) | 4.15374 | 0.152798 | 0.0763989 | − | 0.997077i | \(-0.475658\pi\) | ||||
0.0763989 | + | 0.997077i | \(0.475658\pi\) | |||||||
\(740\) | −6.84984 | −0.251805 | ||||||||
\(741\) | 0.118699 | 0.00436052 | ||||||||
\(742\) | −57.0898 | −2.09583 | ||||||||
\(743\) | 2.66887 | 0.0979114 | 0.0489557 | − | 0.998801i | \(-0.484411\pi\) | ||||
0.0489557 | + | 0.998801i | \(0.484411\pi\) | |||||||
\(744\) | −0.178838 | −0.00655653 | ||||||||
\(745\) | −8.14501 | −0.298410 | ||||||||
\(746\) | −23.4343 | −0.857990 | ||||||||
\(747\) | 26.5246 | 0.970486 | ||||||||
\(748\) | −32.2062 | −1.17758 | ||||||||
\(749\) | 83.2415 | 3.04158 | ||||||||
\(750\) | −0.178838 | −0.00653025 | ||||||||
\(751\) | 2.49405 | 0.0910090 | 0.0455045 | − | 0.998964i | \(-0.485510\pi\) | ||||
0.0455045 | + | 0.998964i | \(0.485510\pi\) | |||||||
\(752\) | 0.326660 | 0.0119120 | ||||||||
\(753\) | −1.17906 | −0.0429673 | ||||||||
\(754\) | −7.03585 | −0.256230 | ||||||||
\(755\) | 4.82349 | 0.175545 | ||||||||
\(756\) | 4.94413 | 0.179816 | ||||||||
\(757\) | −43.2745 | −1.57284 | −0.786419 | − | 0.617693i | \(-0.788068\pi\) | ||||
−0.786419 | + | 0.617693i | \(0.788068\pi\) | |||||||
\(758\) | −9.95784 | −0.361685 | ||||||||
\(759\) | −1.15199 | −0.0418147 | ||||||||
\(760\) | 0.663724 | 0.0240758 | ||||||||
\(761\) | 11.3170 | 0.410242 | 0.205121 | − | 0.978737i | \(-0.434241\pi\) | ||||
0.205121 | + | 0.978737i | \(0.434241\pi\) | |||||||
\(762\) | 3.29105 | 0.119222 | ||||||||
\(763\) | −55.2534 | −2.00031 | ||||||||
\(764\) | 3.94669 | 0.142786 | ||||||||
\(765\) | −17.9162 | −0.647763 | ||||||||
\(766\) | 15.5114 | 0.560451 | ||||||||
\(767\) | −10.9205 | −0.394317 | ||||||||
\(768\) | 0.178838 | 0.00645327 | ||||||||
\(769\) | 42.9251 | 1.54792 | 0.773959 | − | 0.633236i | \(-0.218274\pi\) | ||||
0.773959 | + | 0.633236i | \(0.218274\pi\) | |||||||
\(770\) | 24.7149 | 0.890663 | ||||||||
\(771\) | 0.565205 | 0.0203554 | ||||||||
\(772\) | −1.51907 | −0.0546725 | ||||||||
\(773\) | 29.2341 | 1.05148 | 0.525739 | − | 0.850646i | \(-0.323789\pi\) | ||||
0.525739 | + | 0.850646i | \(0.323789\pi\) | |||||||
\(774\) | −36.9308 | −1.32745 | ||||||||
\(775\) | −1.00000 | −0.0359211 | ||||||||
\(776\) | −17.7548 | −0.637361 | ||||||||
\(777\) | −5.67466 | −0.203577 | ||||||||
\(778\) | 5.09129 | 0.182532 | ||||||||
\(779\) | −4.88279 | −0.174944 | ||||||||
\(780\) | 0.178838 | 0.00640344 | ||||||||
\(781\) | −53.0541 | −1.89843 | ||||||||
\(782\) | 7.28804 | 0.260620 | ||||||||
\(783\) | −7.50943 | −0.268365 | ||||||||
\(784\) | 14.4585 | 0.516374 | ||||||||
\(785\) | 9.18398 | 0.327790 | ||||||||
\(786\) | −1.25702 | −0.0448364 | ||||||||
\(787\) | 5.72717 | 0.204151 | 0.102076 | − | 0.994777i | \(-0.467452\pi\) | ||||
0.102076 | + | 0.994777i | \(0.467452\pi\) | |||||||
\(788\) | 19.1945 | 0.683776 | ||||||||
\(789\) | 0.523716 | 0.0186448 | ||||||||
\(790\) | −15.7918 | −0.561845 | ||||||||
\(791\) | 64.2392 | 2.28408 | ||||||||
\(792\) | −15.8353 | −0.562683 | ||||||||
\(793\) | 11.0097 | 0.390965 | ||||||||
\(794\) | 23.7475 | 0.842767 | ||||||||
\(795\) | −2.20404 | −0.0781692 | ||||||||
\(796\) | −3.45167 | −0.122341 | ||||||||
\(797\) | −51.1198 | −1.81075 | −0.905377 | − | 0.424608i | \(-0.860412\pi\) | ||||
−0.905377 | + | 0.424608i | \(0.860412\pi\) | |||||||
\(798\) | 0.549854 | 0.0194646 | ||||||||
\(799\) | −1.97186 | −0.0697593 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 1.14067 | 0.0403036 | ||||||||
\(802\) | −7.89202 | −0.278677 | ||||||||
\(803\) | 5.88047 | 0.207517 | ||||||||
\(804\) | −0.578829 | −0.0204137 | ||||||||
\(805\) | −5.59280 | −0.197120 | ||||||||
\(806\) | 1.00000 | 0.0352235 | ||||||||
\(807\) | 2.99281 | 0.105352 | ||||||||
\(808\) | 5.33151 | 0.187562 | ||||||||
\(809\) | −39.5674 | −1.39112 | −0.695558 | − | 0.718470i | \(-0.744843\pi\) | ||||
−0.695558 | + | 0.718470i | \(0.744843\pi\) | |||||||
\(810\) | −8.71317 | −0.306150 | ||||||||
\(811\) | −11.7083 | −0.411136 | −0.205568 | − | 0.978643i | \(-0.565904\pi\) | ||||
−0.205568 | + | 0.978643i | \(0.565904\pi\) | |||||||
\(812\) | −32.5923 | −1.14377 | ||||||||
\(813\) | 5.03683 | 0.176649 | ||||||||
\(814\) | 36.5460 | 1.28094 | ||||||||
\(815\) | −4.50771 | −0.157898 | ||||||||
\(816\) | −1.07955 | −0.0377916 | ||||||||
\(817\) | −8.25865 | −0.288934 | ||||||||
\(818\) | −37.3652 | −1.30644 | ||||||||
\(819\) | −13.7488 | −0.480423 | ||||||||
\(820\) | −7.35666 | −0.256906 | ||||||||
\(821\) | −21.6045 | −0.754001 | −0.377000 | − | 0.926213i | \(-0.623044\pi\) | ||||
−0.377000 | + | 0.926213i | \(0.623044\pi\) | |||||||
\(822\) | 2.75254 | 0.0960058 | ||||||||
\(823\) | −15.1764 | −0.529015 | −0.264507 | − | 0.964384i | \(-0.585209\pi\) | ||||
−0.264507 | + | 0.964384i | \(0.585209\pi\) | |||||||
\(824\) | 0.761610 | 0.0265319 | ||||||||
\(825\) | 0.954158 | 0.0332195 | ||||||||
\(826\) | −50.5874 | −1.76016 | ||||||||
\(827\) | 18.6439 | 0.648311 | 0.324155 | − | 0.946004i | \(-0.394920\pi\) | ||||
0.324155 | + | 0.946004i | \(0.394920\pi\) | |||||||
\(828\) | 3.58341 | 0.124532 | ||||||||
\(829\) | −29.6882 | −1.03111 | −0.515557 | − | 0.856855i | \(-0.672415\pi\) | ||||
−0.515557 | + | 0.856855i | \(0.672415\pi\) | |||||||
\(830\) | 8.93682 | 0.310202 | ||||||||
\(831\) | −0.748028 | −0.0259488 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | −87.2775 | −3.02399 | ||||||||
\(834\) | −0.953316 | −0.0330106 | ||||||||
\(835\) | −4.88428 | −0.169028 | ||||||||
\(836\) | −3.54117 | −0.122474 | ||||||||
\(837\) | 1.06731 | 0.0368916 | ||||||||
\(838\) | −16.2972 | −0.562976 | ||||||||
\(839\) | 20.8238 | 0.718919 | 0.359459 | − | 0.933161i | \(-0.382961\pi\) | ||||
0.359459 | + | 0.933161i | \(0.382961\pi\) | |||||||
\(840\) | 0.828437 | 0.0285838 | ||||||||
\(841\) | 20.5031 | 0.707005 | ||||||||
\(842\) | −11.5930 | −0.399521 | ||||||||
\(843\) | −5.28964 | −0.182185 | ||||||||
\(844\) | 19.5039 | 0.671353 | ||||||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | −0.969531 | −0.0333332 | ||||||||
\(847\) | −80.9061 | −2.77997 | ||||||||
\(848\) | 12.3242 | 0.423215 | ||||||||
\(849\) | −3.91542 | −0.134377 | ||||||||
\(850\) | −6.03643 | −0.207048 | ||||||||
\(851\) | −8.27009 | −0.283495 | ||||||||
\(852\) | −1.77836 | −0.0609257 | ||||||||
\(853\) | 45.2753 | 1.55020 | 0.775098 | − | 0.631841i | \(-0.217700\pi\) | ||||
0.775098 | + | 0.631841i | \(0.217700\pi\) | |||||||
\(854\) | 51.0004 | 1.74520 | ||||||||
\(855\) | −1.96994 | −0.0673706 | ||||||||
\(856\) | −17.9697 | −0.614191 | ||||||||
\(857\) | 52.3546 | 1.78840 | 0.894200 | − | 0.447668i | \(-0.147745\pi\) | ||||
0.894200 | + | 0.447668i | \(0.147745\pi\) | |||||||
\(858\) | −0.954158 | −0.0325744 | ||||||||
\(859\) | 29.1940 | 0.996087 | 0.498043 | − | 0.867152i | \(-0.334052\pi\) | ||||
0.498043 | + | 0.867152i | \(0.334052\pi\) | |||||||
\(860\) | −12.4429 | −0.424300 | ||||||||
\(861\) | −6.09453 | −0.207701 | ||||||||
\(862\) | 16.9740 | 0.578137 | ||||||||
\(863\) | 17.6919 | 0.602239 | 0.301120 | − | 0.953586i | \(-0.402640\pi\) | ||||
0.301120 | + | 0.953586i | \(0.402640\pi\) | |||||||
\(864\) | −1.06731 | −0.0363106 | ||||||||
\(865\) | −3.37554 | −0.114772 | ||||||||
\(866\) | 26.3107 | 0.894073 | ||||||||
\(867\) | 3.47635 | 0.118063 | ||||||||
\(868\) | 4.63233 | 0.157231 | ||||||||
\(869\) | 84.2539 | 2.85812 | ||||||||
\(870\) | −1.25828 | −0.0426596 | ||||||||
\(871\) | 3.23660 | 0.109668 | ||||||||
\(872\) | 11.9278 | 0.403926 | ||||||||
\(873\) | 52.6966 | 1.78351 | ||||||||
\(874\) | 0.801341 | 0.0271058 | ||||||||
\(875\) | 4.63233 | 0.156601 | ||||||||
\(876\) | 0.197112 | 0.00665979 | ||||||||
\(877\) | −25.9751 | −0.877117 | −0.438559 | − | 0.898703i | \(-0.644511\pi\) | ||||
−0.438559 | + | 0.898703i | \(0.644511\pi\) | |||||||
\(878\) | 26.8813 | 0.907200 | ||||||||
\(879\) | −5.66507 | −0.191078 | ||||||||
\(880\) | −5.33531 | −0.179853 | ||||||||
\(881\) | 9.35799 | 0.315279 | 0.157639 | − | 0.987497i | \(-0.449612\pi\) | ||||
0.157639 | + | 0.987497i | \(0.449612\pi\) | |||||||
\(882\) | −42.9130 | −1.44495 | ||||||||
\(883\) | 21.1305 | 0.711098 | 0.355549 | − | 0.934658i | \(-0.384294\pi\) | ||||
0.355549 | + | 0.934658i | \(0.384294\pi\) | |||||||
\(884\) | 6.03643 | 0.203027 | ||||||||
\(885\) | −1.95301 | −0.0656496 | ||||||||
\(886\) | −4.26704 | −0.143354 | ||||||||
\(887\) | 30.8744 | 1.03666 | 0.518331 | − | 0.855180i | \(-0.326554\pi\) | ||||
0.518331 | + | 0.855180i | \(0.326554\pi\) | |||||||
\(888\) | 1.22501 | 0.0411087 | ||||||||
\(889\) | −85.2458 | −2.85905 | ||||||||
\(890\) | 0.384321 | 0.0128825 | ||||||||
\(891\) | 46.4875 | 1.55739 | ||||||||
\(892\) | 21.7277 | 0.727498 | ||||||||
\(893\) | −0.216812 | −0.00725533 | ||||||||
\(894\) | 1.45664 | 0.0487173 | ||||||||
\(895\) | 20.3213 | 0.679265 | ||||||||
\(896\) | −4.63233 | −0.154755 | ||||||||
\(897\) | 0.215919 | 0.00720932 | ||||||||
\(898\) | 0.342985 | 0.0114456 | ||||||||
\(899\) | −7.03585 | −0.234659 | ||||||||
\(900\) | −2.96802 | −0.0989339 | ||||||||
\(901\) | −74.3943 | −2.47843 | ||||||||
\(902\) | 39.2501 | 1.30688 | ||||||||
\(903\) | −10.3082 | −0.343034 | ||||||||
\(904\) | −13.8676 | −0.461229 | ||||||||
\(905\) | −16.0859 | −0.534713 | ||||||||
\(906\) | −0.862624 | −0.0286588 | ||||||||
\(907\) | −25.3403 | −0.841410 | −0.420705 | − | 0.907197i | \(-0.638217\pi\) | ||||
−0.420705 | + | 0.907197i | \(0.638217\pi\) | |||||||
\(908\) | 15.9688 | 0.529943 | ||||||||
\(909\) | −15.8240 | −0.524849 | ||||||||
\(910\) | −4.63233 | −0.153560 | ||||||||
\(911\) | 47.5468 | 1.57530 | 0.787648 | − | 0.616125i | \(-0.211298\pi\) | ||||
0.787648 | + | 0.616125i | \(0.211298\pi\) | |||||||
\(912\) | −0.118699 | −0.00393052 | ||||||||
\(913\) | −47.6807 | −1.57800 | ||||||||
\(914\) | −12.6480 | −0.418359 | ||||||||
\(915\) | 1.96895 | 0.0650915 | ||||||||
\(916\) | 14.7883 | 0.488620 | ||||||||
\(917\) | 32.5598 | 1.07522 | ||||||||
\(918\) | 6.44274 | 0.212642 | ||||||||
\(919\) | −47.8058 | −1.57697 | −0.788485 | − | 0.615055i | \(-0.789134\pi\) | ||||
−0.788485 | + | 0.615055i | \(0.789134\pi\) | |||||||
\(920\) | 1.20734 | 0.0398049 | ||||||||
\(921\) | −2.80404 | −0.0923964 | ||||||||
\(922\) | −11.1326 | −0.366633 | ||||||||
\(923\) | 9.94396 | 0.327310 | ||||||||
\(924\) | −4.41997 | −0.145406 | ||||||||
\(925\) | 6.84984 | 0.225221 | ||||||||
\(926\) | −36.7366 | −1.20724 | ||||||||
\(927\) | −2.26047 | −0.0742436 | ||||||||
\(928\) | 7.03585 | 0.230963 | ||||||||
\(929\) | −42.0246 | −1.37878 | −0.689391 | − | 0.724390i | \(-0.742122\pi\) | ||||
−0.689391 | + | 0.724390i | \(0.742122\pi\) | |||||||
\(930\) | 0.178838 | 0.00586434 | ||||||||
\(931\) | −9.59642 | −0.314510 | ||||||||
\(932\) | 6.09633 | 0.199692 | ||||||||
\(933\) | 0.287461 | 0.00941106 | ||||||||
\(934\) | 15.6133 | 0.510883 | ||||||||
\(935\) | 32.2062 | 1.05326 | ||||||||
\(936\) | 2.96802 | 0.0970127 | ||||||||
\(937\) | −30.8158 | −1.00671 | −0.503354 | − | 0.864080i | \(-0.667901\pi\) | ||||
−0.503354 | + | 0.864080i | \(0.667901\pi\) | |||||||
\(938\) | 14.9930 | 0.489539 | ||||||||
\(939\) | 5.93920 | 0.193819 | ||||||||
\(940\) | −0.326660 | −0.0106545 | ||||||||
\(941\) | 14.0282 | 0.457306 | 0.228653 | − | 0.973508i | \(-0.426568\pi\) | ||||
0.228653 | + | 0.973508i | \(0.426568\pi\) | |||||||
\(942\) | −1.64245 | −0.0535138 | ||||||||
\(943\) | −8.88200 | −0.289238 | ||||||||
\(944\) | 10.9205 | 0.355433 | ||||||||
\(945\) | −4.94413 | −0.160833 | ||||||||
\(946\) | 66.3868 | 2.15842 | ||||||||
\(947\) | −44.8909 | −1.45876 | −0.729379 | − | 0.684110i | \(-0.760191\pi\) | ||||
−0.729379 | + | 0.684110i | \(0.760191\pi\) | |||||||
\(948\) | 2.82417 | 0.0917248 | ||||||||
\(949\) | −1.10218 | −0.0357783 | ||||||||
\(950\) | −0.663724 | −0.0215340 | ||||||||
\(951\) | −5.04691 | −0.163657 | ||||||||
\(952\) | 27.9627 | 0.906278 | ||||||||
\(953\) | 44.7485 | 1.44955 | 0.724773 | − | 0.688988i | \(-0.241945\pi\) | ||||
0.724773 | + | 0.688988i | \(0.241945\pi\) | |||||||
\(954\) | −36.5785 | −1.18427 | ||||||||
\(955\) | −3.94669 | −0.127712 | ||||||||
\(956\) | 27.2233 | 0.880464 | ||||||||
\(957\) | 6.71331 | 0.217010 | ||||||||
\(958\) | −4.03715 | −0.130434 | ||||||||
\(959\) | −71.2972 | −2.30231 | ||||||||
\(960\) | −0.178838 | −0.00577198 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | −6.84984 | −0.220848 | ||||||||
\(963\) | 53.3344 | 1.71868 | ||||||||
\(964\) | −8.85643 | −0.285246 | ||||||||
\(965\) | 1.51907 | 0.0489006 | ||||||||
\(966\) | 1.00021 | 0.0321811 | ||||||||
\(967\) | −2.51505 | −0.0808786 | −0.0404393 | − | 0.999182i | \(-0.512876\pi\) | ||||
−0.0404393 | + | 0.999182i | \(0.512876\pi\) | |||||||
\(968\) | 17.4655 | 0.561364 | ||||||||
\(969\) | 0.716520 | 0.0230179 | ||||||||
\(970\) | 17.7548 | 0.570073 | ||||||||
\(971\) | −25.2644 | −0.810773 | −0.405386 | − | 0.914145i | \(-0.632863\pi\) | ||||
−0.405386 | + | 0.914145i | \(0.632863\pi\) | |||||||
\(972\) | 4.76018 | 0.152683 | ||||||||
\(973\) | 24.6931 | 0.791624 | ||||||||
\(974\) | 40.9020 | 1.31058 | ||||||||
\(975\) | −0.178838 | −0.00572741 | ||||||||
\(976\) | −11.0097 | −0.352411 | ||||||||
\(977\) | −41.9063 | −1.34070 | −0.670350 | − | 0.742045i | \(-0.733856\pi\) | ||||
−0.670350 | + | 0.742045i | \(0.733856\pi\) | |||||||
\(978\) | 0.806152 | 0.0257779 | ||||||||
\(979\) | −2.05047 | −0.0655333 | ||||||||
\(980\) | −14.4585 | −0.461859 | ||||||||
\(981\) | −35.4019 | −1.13030 | ||||||||
\(982\) | 30.5529 | 0.974982 | ||||||||
\(983\) | 47.9142 | 1.52823 | 0.764113 | − | 0.645082i | \(-0.223177\pi\) | ||||
0.764113 | + | 0.645082i | \(0.223177\pi\) | |||||||
\(984\) | 1.31565 | 0.0419415 | ||||||||
\(985\) | −19.1945 | −0.611588 | ||||||||
\(986\) | −42.4714 | −1.35257 | ||||||||
\(987\) | −0.270617 | −0.00861383 | ||||||||
\(988\) | 0.663724 | 0.0211159 | ||||||||
\(989\) | −15.0228 | −0.477698 | ||||||||
\(990\) | 15.8353 | 0.503279 | ||||||||
\(991\) | −27.8008 | −0.883120 | −0.441560 | − | 0.897232i | \(-0.645575\pi\) | ||||
−0.441560 | + | 0.897232i | \(0.645575\pi\) | |||||||
\(992\) | −1.00000 | −0.0317500 | ||||||||
\(993\) | 2.70237 | 0.0857571 | ||||||||
\(994\) | 46.0637 | 1.46105 | ||||||||
\(995\) | 3.45167 | 0.109425 | ||||||||
\(996\) | −1.59825 | −0.0506424 | ||||||||
\(997\) | −59.8817 | −1.89647 | −0.948236 | − | 0.317567i | \(-0.897134\pi\) | ||||
−0.948236 | + | 0.317567i | \(0.897134\pi\) | |||||||
\(998\) | 26.9218 | 0.852196 | ||||||||
\(999\) | −7.31090 | −0.231307 |
(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 | 4030.2.a.n.1.5 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4030.2.a.n.1.5 | ✓ | 8 | 1.1 | even | 1 | trivial |