Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, 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("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 5 x^{15} - 36 x^{14} + 196 x^{13} + 498 x^{12} - 3101 x^{11} - 3150 x^{10} + 25368 x^{9} + \cdots - 66432 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(0.808021\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.808021 | 0.361358 | 0.180679 | − | 0.983542i | \(-0.442170\pi\) | ||||
0.180679 | + | 0.983542i | \(0.442170\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 3.24300 | 1.22574 | 0.612869 | − | 0.790184i | \(-0.290015\pi\) | ||||
0.612869 | + | 0.790184i | \(0.290015\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.808021 | 0.255519 | ||||||||
\(11\) | 4.15216 | 1.25192 | 0.625962 | − | 0.779853i | \(-0.284706\pi\) | ||||
0.625962 | + | 0.779853i | \(0.284706\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 3.24300 | 0.866728 | ||||||||
\(15\) | 0.808021 | 0.208630 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.76632 | 1.88361 | 0.941805 | − | 0.336159i | \(-0.109128\pi\) | ||||
0.941805 | + | 0.336159i | \(0.109128\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 8.59590 | 1.97204 | 0.986018 | − | 0.166641i | \(-0.0532922\pi\) | ||||
0.986018 | + | 0.166641i | \(0.0532922\pi\) | |||||||
\(20\) | 0.808021 | 0.180679 | ||||||||
\(21\) | 3.24300 | 0.707680 | ||||||||
\(22\) | 4.15216 | 0.885244 | ||||||||
\(23\) | −8.64744 | −1.80312 | −0.901558 | − | 0.432657i | \(-0.857576\pi\) | ||||
−0.901558 | + | 0.432657i | \(0.857576\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.34710 | −0.869420 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 3.24300 | 0.612869 | ||||||||
\(29\) | 4.23930 | 0.787219 | 0.393610 | − | 0.919278i | \(-0.371226\pi\) | ||||
0.393610 | + | 0.919278i | \(0.371226\pi\) | |||||||
\(30\) | 0.808021 | 0.147524 | ||||||||
\(31\) | −6.26307 | −1.12488 | −0.562440 | − | 0.826838i | \(-0.690137\pi\) | ||||
−0.562440 | + | 0.826838i | \(0.690137\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 4.15216 | 0.722799 | ||||||||
\(34\) | 7.76632 | 1.33191 | ||||||||
\(35\) | 2.62041 | 0.442930 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 5.67059 | 0.932239 | 0.466120 | − | 0.884722i | \(-0.345652\pi\) | ||||
0.466120 | + | 0.884722i | \(0.345652\pi\) | |||||||
\(38\) | 8.59590 | 1.39444 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0.808021 | 0.127759 | ||||||||
\(41\) | 1.67856 | 0.262146 | 0.131073 | − | 0.991373i | \(-0.458158\pi\) | ||||
0.131073 | + | 0.991373i | \(0.458158\pi\) | |||||||
\(42\) | 3.24300 | 0.500406 | ||||||||
\(43\) | 0.621687 | 0.0948064 | 0.0474032 | − | 0.998876i | \(-0.484905\pi\) | ||||
0.0474032 | + | 0.998876i | \(0.484905\pi\) | |||||||
\(44\) | 4.15216 | 0.625962 | ||||||||
\(45\) | 0.808021 | 0.120453 | ||||||||
\(46\) | −8.64744 | −1.27500 | ||||||||
\(47\) | −10.5592 | −1.54022 | −0.770108 | − | 0.637914i | \(-0.779798\pi\) | ||||
−0.770108 | + | 0.637914i | \(0.779798\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 3.51704 | 0.502434 | ||||||||
\(50\) | −4.34710 | −0.614773 | ||||||||
\(51\) | 7.76632 | 1.08750 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | 6.13590 | 0.842831 | 0.421415 | − | 0.906868i | \(-0.361533\pi\) | ||||
0.421415 | + | 0.906868i | \(0.361533\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 3.35504 | 0.452393 | ||||||||
\(56\) | 3.24300 | 0.433364 | ||||||||
\(57\) | 8.59590 | 1.13856 | ||||||||
\(58\) | 4.23930 | 0.556648 | ||||||||
\(59\) | −12.2258 | −1.59167 | −0.795835 | − | 0.605514i | \(-0.792968\pi\) | ||||
−0.795835 | + | 0.605514i | \(0.792968\pi\) | |||||||
\(60\) | 0.808021 | 0.104315 | ||||||||
\(61\) | −10.0049 | −1.28100 | −0.640498 | − | 0.767960i | \(-0.721272\pi\) | ||||
−0.640498 | + | 0.767960i | \(0.721272\pi\) | |||||||
\(62\) | −6.26307 | −0.795411 | ||||||||
\(63\) | 3.24300 | 0.408579 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.808021 | −0.100223 | ||||||||
\(66\) | 4.15216 | 0.511096 | ||||||||
\(67\) | −11.2176 | −1.37045 | −0.685227 | − | 0.728330i | \(-0.740297\pi\) | ||||
−0.685227 | + | 0.728330i | \(0.740297\pi\) | |||||||
\(68\) | 7.76632 | 0.941805 | ||||||||
\(69\) | −8.64744 | −1.04103 | ||||||||
\(70\) | 2.62041 | 0.313199 | ||||||||
\(71\) | 4.12480 | 0.489524 | 0.244762 | − | 0.969583i | \(-0.421290\pi\) | ||||
0.244762 | + | 0.969583i | \(0.421290\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 13.8673 | 1.62305 | 0.811525 | − | 0.584318i | \(-0.198638\pi\) | ||||
0.811525 | + | 0.584318i | \(0.198638\pi\) | |||||||
\(74\) | 5.67059 | 0.659193 | ||||||||
\(75\) | −4.34710 | −0.501960 | ||||||||
\(76\) | 8.59590 | 0.986018 | ||||||||
\(77\) | 13.4655 | 1.53453 | ||||||||
\(78\) | −1.00000 | −0.113228 | ||||||||
\(79\) | −14.1068 | −1.58714 | −0.793568 | − | 0.608482i | \(-0.791779\pi\) | ||||
−0.793568 | + | 0.608482i | \(0.791779\pi\) | |||||||
\(80\) | 0.808021 | 0.0903395 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.67856 | 0.185366 | ||||||||
\(83\) | −14.9176 | −1.63742 | −0.818709 | − | 0.574208i | \(-0.805310\pi\) | ||||
−0.818709 | + | 0.574208i | \(0.805310\pi\) | |||||||
\(84\) | 3.24300 | 0.353840 | ||||||||
\(85\) | 6.27535 | 0.680658 | ||||||||
\(86\) | 0.621687 | 0.0670383 | ||||||||
\(87\) | 4.23930 | 0.454501 | ||||||||
\(88\) | 4.15216 | 0.442622 | ||||||||
\(89\) | −8.36437 | −0.886622 | −0.443311 | − | 0.896368i | \(-0.646196\pi\) | ||||
−0.443311 | + | 0.896368i | \(0.646196\pi\) | |||||||
\(90\) | 0.808021 | 0.0851729 | ||||||||
\(91\) | −3.24300 | −0.339959 | ||||||||
\(92\) | −8.64744 | −0.901558 | ||||||||
\(93\) | −6.26307 | −0.649450 | ||||||||
\(94\) | −10.5592 | −1.08910 | ||||||||
\(95\) | 6.94567 | 0.712611 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 3.02487 | 0.307129 | 0.153564 | − | 0.988139i | \(-0.450925\pi\) | ||||
0.153564 | + | 0.988139i | \(0.450925\pi\) | |||||||
\(98\) | 3.51704 | 0.355275 | ||||||||
\(99\) | 4.15216 | 0.417308 | ||||||||
\(100\) | −4.34710 | −0.434710 | ||||||||
\(101\) | 12.2137 | 1.21531 | 0.607653 | − | 0.794202i | \(-0.292111\pi\) | ||||
0.607653 | + | 0.794202i | \(0.292111\pi\) | |||||||
\(102\) | 7.76632 | 0.768981 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 2.62041 | 0.255726 | ||||||||
\(106\) | 6.13590 | 0.595971 | ||||||||
\(107\) | 0.530297 | 0.0512657 | 0.0256328 | − | 0.999671i | \(-0.491840\pi\) | ||||
0.0256328 | + | 0.999671i | \(0.491840\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −1.40297 | −0.134380 | −0.0671902 | − | 0.997740i | \(-0.521403\pi\) | ||||
−0.0671902 | + | 0.997740i | \(0.521403\pi\) | |||||||
\(110\) | 3.35504 | 0.319890 | ||||||||
\(111\) | 5.67059 | 0.538228 | ||||||||
\(112\) | 3.24300 | 0.306435 | ||||||||
\(113\) | −15.9476 | −1.50022 | −0.750111 | − | 0.661312i | \(-0.770000\pi\) | ||||
−0.750111 | + | 0.661312i | \(0.770000\pi\) | |||||||
\(114\) | 8.59590 | 0.805080 | ||||||||
\(115\) | −6.98732 | −0.651571 | ||||||||
\(116\) | 4.23930 | 0.393610 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | −12.2258 | −1.12548 | ||||||||
\(119\) | 25.1862 | 2.30881 | ||||||||
\(120\) | 0.808021 | 0.0737619 | ||||||||
\(121\) | 6.24047 | 0.567316 | ||||||||
\(122\) | −10.0049 | −0.905801 | ||||||||
\(123\) | 1.67856 | 0.151350 | ||||||||
\(124\) | −6.26307 | −0.562440 | ||||||||
\(125\) | −7.55266 | −0.675530 | ||||||||
\(126\) | 3.24300 | 0.288909 | ||||||||
\(127\) | −5.15738 | −0.457644 | −0.228822 | − | 0.973468i | \(-0.573487\pi\) | ||||
−0.228822 | + | 0.973468i | \(0.573487\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0.621687 | 0.0547365 | ||||||||
\(130\) | −0.808021 | −0.0708681 | ||||||||
\(131\) | 0.509744 | 0.0445366 | 0.0222683 | − | 0.999752i | \(-0.492911\pi\) | ||||
0.0222683 | + | 0.999752i | \(0.492911\pi\) | |||||||
\(132\) | 4.15216 | 0.361400 | ||||||||
\(133\) | 27.8765 | 2.41720 | ||||||||
\(134\) | −11.2176 | −0.969057 | ||||||||
\(135\) | 0.808021 | 0.0695434 | ||||||||
\(136\) | 7.76632 | 0.665957 | ||||||||
\(137\) | −8.22378 | −0.702605 | −0.351302 | − | 0.936262i | \(-0.614261\pi\) | ||||
−0.351302 | + | 0.936262i | \(0.614261\pi\) | |||||||
\(138\) | −8.64744 | −0.736119 | ||||||||
\(139\) | −14.5980 | −1.23819 | −0.619094 | − | 0.785317i | \(-0.712500\pi\) | ||||
−0.619094 | + | 0.785317i | \(0.712500\pi\) | |||||||
\(140\) | 2.62041 | 0.221465 | ||||||||
\(141\) | −10.5592 | −0.889244 | ||||||||
\(142\) | 4.12480 | 0.346146 | ||||||||
\(143\) | −4.15216 | −0.347221 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 3.42545 | 0.284468 | ||||||||
\(146\) | 13.8673 | 1.14767 | ||||||||
\(147\) | 3.51704 | 0.290081 | ||||||||
\(148\) | 5.67059 | 0.466120 | ||||||||
\(149\) | −3.96159 | −0.324546 | −0.162273 | − | 0.986746i | \(-0.551883\pi\) | ||||
−0.162273 | + | 0.986746i | \(0.551883\pi\) | |||||||
\(150\) | −4.34710 | −0.354939 | ||||||||
\(151\) | −2.69321 | −0.219171 | −0.109585 | − | 0.993977i | \(-0.534952\pi\) | ||||
−0.109585 | + | 0.993977i | \(0.534952\pi\) | |||||||
\(152\) | 8.59590 | 0.697220 | ||||||||
\(153\) | 7.76632 | 0.627870 | ||||||||
\(154\) | 13.4655 | 1.08508 | ||||||||
\(155\) | −5.06069 | −0.406485 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | −18.1386 | −1.44762 | −0.723809 | − | 0.690000i | \(-0.757610\pi\) | ||||
−0.723809 | + | 0.690000i | \(0.757610\pi\) | |||||||
\(158\) | −14.1068 | −1.12227 | ||||||||
\(159\) | 6.13590 | 0.486609 | ||||||||
\(160\) | 0.808021 | 0.0638797 | ||||||||
\(161\) | −28.0436 | −2.21015 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 15.9190 | 1.24687 | 0.623436 | − | 0.781874i | \(-0.285736\pi\) | ||||
0.623436 | + | 0.781874i | \(0.285736\pi\) | |||||||
\(164\) | 1.67856 | 0.131073 | ||||||||
\(165\) | 3.35504 | 0.261189 | ||||||||
\(166\) | −14.9176 | −1.15783 | ||||||||
\(167\) | 21.7955 | 1.68658 | 0.843292 | − | 0.537456i | \(-0.180614\pi\) | ||||
0.843292 | + | 0.537456i | \(0.180614\pi\) | |||||||
\(168\) | 3.24300 | 0.250203 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 6.27535 | 0.481298 | ||||||||
\(171\) | 8.59590 | 0.657345 | ||||||||
\(172\) | 0.621687 | 0.0474032 | ||||||||
\(173\) | −7.22504 | −0.549310 | −0.274655 | − | 0.961543i | \(-0.588564\pi\) | ||||
−0.274655 | + | 0.961543i | \(0.588564\pi\) | |||||||
\(174\) | 4.23930 | 0.321381 | ||||||||
\(175\) | −14.0976 | −1.06568 | ||||||||
\(176\) | 4.15216 | 0.312981 | ||||||||
\(177\) | −12.2258 | −0.918951 | ||||||||
\(178\) | −8.36437 | −0.626936 | ||||||||
\(179\) | 1.51059 | 0.112907 | 0.0564534 | − | 0.998405i | \(-0.482021\pi\) | ||||
0.0564534 | + | 0.998405i | \(0.482021\pi\) | |||||||
\(180\) | 0.808021 | 0.0602263 | ||||||||
\(181\) | 4.03456 | 0.299886 | 0.149943 | − | 0.988695i | \(-0.452091\pi\) | ||||
0.149943 | + | 0.988695i | \(0.452091\pi\) | |||||||
\(182\) | −3.24300 | −0.240387 | ||||||||
\(183\) | −10.0049 | −0.739583 | ||||||||
\(184\) | −8.64744 | −0.637498 | ||||||||
\(185\) | 4.58196 | 0.336872 | ||||||||
\(186\) | −6.26307 | −0.459230 | ||||||||
\(187\) | 32.2471 | 2.35814 | ||||||||
\(188\) | −10.5592 | −0.770108 | ||||||||
\(189\) | 3.24300 | 0.235893 | ||||||||
\(190\) | 6.94567 | 0.503892 | ||||||||
\(191\) | 11.5886 | 0.838518 | 0.419259 | − | 0.907867i | \(-0.362290\pi\) | ||||
0.419259 | + | 0.907867i | \(0.362290\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −1.16862 | −0.0841194 | −0.0420597 | − | 0.999115i | \(-0.513392\pi\) | ||||
−0.0420597 | + | 0.999115i | \(0.513392\pi\) | |||||||
\(194\) | 3.02487 | 0.217173 | ||||||||
\(195\) | −0.808021 | −0.0578636 | ||||||||
\(196\) | 3.51704 | 0.251217 | ||||||||
\(197\) | −22.7068 | −1.61780 | −0.808898 | − | 0.587950i | \(-0.799935\pi\) | ||||
−0.808898 | + | 0.587950i | \(0.799935\pi\) | |||||||
\(198\) | 4.15216 | 0.295081 | ||||||||
\(199\) | −21.8807 | −1.55108 | −0.775541 | − | 0.631297i | \(-0.782523\pi\) | ||||
−0.775541 | + | 0.631297i | \(0.782523\pi\) | |||||||
\(200\) | −4.34710 | −0.307387 | ||||||||
\(201\) | −11.2176 | −0.791232 | ||||||||
\(202\) | 12.2137 | 0.859352 | ||||||||
\(203\) | 13.7481 | 0.964924 | ||||||||
\(204\) | 7.76632 | 0.543751 | ||||||||
\(205\) | 1.35631 | 0.0947287 | ||||||||
\(206\) | 1.00000 | 0.0696733 | ||||||||
\(207\) | −8.64744 | −0.601039 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | 35.6916 | 2.46884 | ||||||||
\(210\) | 2.62041 | 0.180826 | ||||||||
\(211\) | 0.590099 | 0.0406241 | 0.0203120 | − | 0.999794i | \(-0.493534\pi\) | ||||
0.0203120 | + | 0.999794i | \(0.493534\pi\) | |||||||
\(212\) | 6.13590 | 0.421415 | ||||||||
\(213\) | 4.12480 | 0.282627 | ||||||||
\(214\) | 0.530297 | 0.0362503 | ||||||||
\(215\) | 0.502336 | 0.0342591 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −20.3111 | −1.37881 | ||||||||
\(218\) | −1.40297 | −0.0950213 | ||||||||
\(219\) | 13.8673 | 0.937068 | ||||||||
\(220\) | 3.35504 | 0.226197 | ||||||||
\(221\) | −7.76632 | −0.522419 | ||||||||
\(222\) | 5.67059 | 0.380585 | ||||||||
\(223\) | 23.7424 | 1.58991 | 0.794954 | − | 0.606670i | \(-0.207495\pi\) | ||||
0.794954 | + | 0.606670i | \(0.207495\pi\) | |||||||
\(224\) | 3.24300 | 0.216682 | ||||||||
\(225\) | −4.34710 | −0.289807 | ||||||||
\(226\) | −15.9476 | −1.06082 | ||||||||
\(227\) | −2.77610 | −0.184256 | −0.0921280 | − | 0.995747i | \(-0.529367\pi\) | ||||
−0.0921280 | + | 0.995747i | \(0.529367\pi\) | |||||||
\(228\) | 8.59590 | 0.569278 | ||||||||
\(229\) | −26.2266 | −1.73310 | −0.866551 | − | 0.499089i | \(-0.833668\pi\) | ||||
−0.866551 | + | 0.499089i | \(0.833668\pi\) | |||||||
\(230\) | −6.98732 | −0.460730 | ||||||||
\(231\) | 13.4655 | 0.885962 | ||||||||
\(232\) | 4.23930 | 0.278324 | ||||||||
\(233\) | 2.40864 | 0.157795 | 0.0788975 | − | 0.996883i | \(-0.474860\pi\) | ||||
0.0788975 | + | 0.996883i | \(0.474860\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | −8.53204 | −0.556569 | ||||||||
\(236\) | −12.2258 | −0.795835 | ||||||||
\(237\) | −14.1068 | −0.916333 | ||||||||
\(238\) | 25.1862 | 1.63258 | ||||||||
\(239\) | 6.82164 | 0.441255 | 0.220628 | − | 0.975358i | \(-0.429189\pi\) | ||||
0.220628 | + | 0.975358i | \(0.429189\pi\) | |||||||
\(240\) | 0.808021 | 0.0521575 | ||||||||
\(241\) | 26.0809 | 1.68002 | 0.840011 | − | 0.542570i | \(-0.182549\pi\) | ||||
0.840011 | + | 0.542570i | \(0.182549\pi\) | |||||||
\(242\) | 6.24047 | 0.401153 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −10.0049 | −0.640498 | ||||||||
\(245\) | 2.84184 | 0.181559 | ||||||||
\(246\) | 1.67856 | 0.107021 | ||||||||
\(247\) | −8.59590 | −0.546944 | ||||||||
\(248\) | −6.26307 | −0.397705 | ||||||||
\(249\) | −14.9176 | −0.945364 | ||||||||
\(250\) | −7.55266 | −0.477672 | ||||||||
\(251\) | −1.74155 | −0.109925 | −0.0549627 | − | 0.998488i | \(-0.517504\pi\) | ||||
−0.0549627 | + | 0.998488i | \(0.517504\pi\) | |||||||
\(252\) | 3.24300 | 0.204290 | ||||||||
\(253\) | −35.9056 | −2.25737 | ||||||||
\(254\) | −5.15738 | −0.323603 | ||||||||
\(255\) | 6.27535 | 0.392978 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.3840 | 0.772495 | 0.386247 | − | 0.922395i | \(-0.373771\pi\) | ||||
0.386247 | + | 0.922395i | \(0.373771\pi\) | |||||||
\(258\) | 0.621687 | 0.0387046 | ||||||||
\(259\) | 18.3897 | 1.14268 | ||||||||
\(260\) | −0.808021 | −0.0501113 | ||||||||
\(261\) | 4.23930 | 0.262406 | ||||||||
\(262\) | 0.509744 | 0.0314921 | ||||||||
\(263\) | 14.1956 | 0.875339 | 0.437670 | − | 0.899136i | \(-0.355804\pi\) | ||||
0.437670 | + | 0.899136i | \(0.355804\pi\) | |||||||
\(264\) | 4.15216 | 0.255548 | ||||||||
\(265\) | 4.95794 | 0.304564 | ||||||||
\(266\) | 27.8765 | 1.70922 | ||||||||
\(267\) | −8.36437 | −0.511891 | ||||||||
\(268\) | −11.2176 | −0.685227 | ||||||||
\(269\) | 2.89416 | 0.176460 | 0.0882300 | − | 0.996100i | \(-0.471879\pi\) | ||||
0.0882300 | + | 0.996100i | \(0.471879\pi\) | |||||||
\(270\) | 0.808021 | 0.0491746 | ||||||||
\(271\) | −3.63848 | −0.221022 | −0.110511 | − | 0.993875i | \(-0.535249\pi\) | ||||
−0.110511 | + | 0.993875i | \(0.535249\pi\) | |||||||
\(272\) | 7.76632 | 0.470903 | ||||||||
\(273\) | −3.24300 | −0.196275 | ||||||||
\(274\) | −8.22378 | −0.496816 | ||||||||
\(275\) | −18.0499 | −1.08845 | ||||||||
\(276\) | −8.64744 | −0.520515 | ||||||||
\(277\) | 24.7013 | 1.48416 | 0.742080 | − | 0.670312i | \(-0.233840\pi\) | ||||
0.742080 | + | 0.670312i | \(0.233840\pi\) | |||||||
\(278\) | −14.5980 | −0.875531 | ||||||||
\(279\) | −6.26307 | −0.374960 | ||||||||
\(280\) | 2.62041 | 0.156600 | ||||||||
\(281\) | 7.92008 | 0.472473 | 0.236236 | − | 0.971696i | \(-0.424086\pi\) | ||||
0.236236 | + | 0.971696i | \(0.424086\pi\) | |||||||
\(282\) | −10.5592 | −0.628790 | ||||||||
\(283\) | 21.6308 | 1.28582 | 0.642910 | − | 0.765942i | \(-0.277727\pi\) | ||||
0.642910 | + | 0.765942i | \(0.277727\pi\) | |||||||
\(284\) | 4.12480 | 0.244762 | ||||||||
\(285\) | 6.94567 | 0.411426 | ||||||||
\(286\) | −4.15216 | −0.245523 | ||||||||
\(287\) | 5.44355 | 0.321323 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 43.3158 | 2.54799 | ||||||||
\(290\) | 3.42545 | 0.201149 | ||||||||
\(291\) | 3.02487 | 0.177321 | ||||||||
\(292\) | 13.8673 | 0.811525 | ||||||||
\(293\) | 10.9756 | 0.641203 | 0.320601 | − | 0.947214i | \(-0.396115\pi\) | ||||
0.320601 | + | 0.947214i | \(0.396115\pi\) | |||||||
\(294\) | 3.51704 | 0.205118 | ||||||||
\(295\) | −9.87874 | −0.575163 | ||||||||
\(296\) | 5.67059 | 0.329596 | ||||||||
\(297\) | 4.15216 | 0.240933 | ||||||||
\(298\) | −3.96159 | −0.229489 | ||||||||
\(299\) | 8.64744 | 0.500095 | ||||||||
\(300\) | −4.34710 | −0.250980 | ||||||||
\(301\) | 2.01613 | 0.116208 | ||||||||
\(302\) | −2.69321 | −0.154977 | ||||||||
\(303\) | 12.2137 | 0.701658 | ||||||||
\(304\) | 8.59590 | 0.493009 | ||||||||
\(305\) | −8.08417 | −0.462898 | ||||||||
\(306\) | 7.76632 | 0.443971 | ||||||||
\(307\) | −14.0960 | −0.804504 | −0.402252 | − | 0.915529i | \(-0.631772\pi\) | ||||
−0.402252 | + | 0.915529i | \(0.631772\pi\) | |||||||
\(308\) | 13.4655 | 0.767266 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | −5.06069 | −0.287428 | ||||||||
\(311\) | −5.20425 | −0.295106 | −0.147553 | − | 0.989054i | \(-0.547140\pi\) | ||||
−0.147553 | + | 0.989054i | \(0.547140\pi\) | |||||||
\(312\) | −1.00000 | −0.0566139 | ||||||||
\(313\) | 4.00558 | 0.226409 | 0.113204 | − | 0.993572i | \(-0.463889\pi\) | ||||
0.113204 | + | 0.993572i | \(0.463889\pi\) | |||||||
\(314\) | −18.1386 | −1.02362 | ||||||||
\(315\) | 2.62041 | 0.147643 | ||||||||
\(316\) | −14.1068 | −0.793568 | ||||||||
\(317\) | −3.26012 | −0.183106 | −0.0915532 | − | 0.995800i | \(-0.529183\pi\) | ||||
−0.0915532 | + | 0.995800i | \(0.529183\pi\) | |||||||
\(318\) | 6.13590 | 0.344084 | ||||||||
\(319\) | 17.6023 | 0.985539 | ||||||||
\(320\) | 0.808021 | 0.0451698 | ||||||||
\(321\) | 0.530297 | 0.0295983 | ||||||||
\(322\) | −28.0436 | −1.56281 | ||||||||
\(323\) | 66.7586 | 3.71455 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 4.34710 | 0.241134 | ||||||||
\(326\) | 15.9190 | 0.881672 | ||||||||
\(327\) | −1.40297 | −0.0775846 | ||||||||
\(328\) | 1.67856 | 0.0926828 | ||||||||
\(329\) | −34.2434 | −1.88790 | ||||||||
\(330\) | 3.35504 | 0.184689 | ||||||||
\(331\) | −2.80347 | −0.154092 | −0.0770462 | − | 0.997028i | \(-0.524549\pi\) | ||||
−0.0770462 | + | 0.997028i | \(0.524549\pi\) | |||||||
\(332\) | −14.9176 | −0.818709 | ||||||||
\(333\) | 5.67059 | 0.310746 | ||||||||
\(334\) | 21.7955 | 1.19259 | ||||||||
\(335\) | −9.06409 | −0.495224 | ||||||||
\(336\) | 3.24300 | 0.176920 | ||||||||
\(337\) | −9.53649 | −0.519486 | −0.259743 | − | 0.965678i | \(-0.583638\pi\) | ||||
−0.259743 | + | 0.965678i | \(0.583638\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | −15.9476 | −0.866154 | ||||||||
\(340\) | 6.27535 | 0.340329 | ||||||||
\(341\) | −26.0053 | −1.40827 | ||||||||
\(342\) | 8.59590 | 0.464813 | ||||||||
\(343\) | −11.2952 | −0.609885 | ||||||||
\(344\) | 0.621687 | 0.0335191 | ||||||||
\(345\) | −6.98732 | −0.376185 | ||||||||
\(346\) | −7.22504 | −0.388421 | ||||||||
\(347\) | 8.47381 | 0.454898 | 0.227449 | − | 0.973790i | \(-0.426962\pi\) | ||||
0.227449 | + | 0.973790i | \(0.426962\pi\) | |||||||
\(348\) | 4.23930 | 0.227251 | ||||||||
\(349\) | −12.1276 | −0.649173 | −0.324586 | − | 0.945856i | \(-0.605225\pi\) | ||||
−0.324586 | + | 0.945856i | \(0.605225\pi\) | |||||||
\(350\) | −14.0976 | −0.753551 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 4.15216 | 0.221311 | ||||||||
\(353\) | 2.41300 | 0.128431 | 0.0642156 | − | 0.997936i | \(-0.479545\pi\) | ||||
0.0642156 | + | 0.997936i | \(0.479545\pi\) | |||||||
\(354\) | −12.2258 | −0.649796 | ||||||||
\(355\) | 3.33293 | 0.176893 | ||||||||
\(356\) | −8.36437 | −0.443311 | ||||||||
\(357\) | 25.1862 | 1.33299 | ||||||||
\(358\) | 1.51059 | 0.0798372 | ||||||||
\(359\) | −4.29733 | −0.226804 | −0.113402 | − | 0.993549i | \(-0.536175\pi\) | ||||
−0.113402 | + | 0.993549i | \(0.536175\pi\) | |||||||
\(360\) | 0.808021 | 0.0425864 | ||||||||
\(361\) | 54.8895 | 2.88892 | ||||||||
\(362\) | 4.03456 | 0.212052 | ||||||||
\(363\) | 6.24047 | 0.327540 | ||||||||
\(364\) | −3.24300 | −0.169979 | ||||||||
\(365\) | 11.2051 | 0.586502 | ||||||||
\(366\) | −10.0049 | −0.522964 | ||||||||
\(367\) | 9.13736 | 0.476966 | 0.238483 | − | 0.971147i | \(-0.423350\pi\) | ||||
0.238483 | + | 0.971147i | \(0.423350\pi\) | |||||||
\(368\) | −8.64744 | −0.450779 | ||||||||
\(369\) | 1.67856 | 0.0873821 | ||||||||
\(370\) | 4.58196 | 0.238205 | ||||||||
\(371\) | 19.8987 | 1.03309 | ||||||||
\(372\) | −6.26307 | −0.324725 | ||||||||
\(373\) | 16.1454 | 0.835979 | 0.417990 | − | 0.908452i | \(-0.362735\pi\) | ||||
0.417990 | + | 0.908452i | \(0.362735\pi\) | |||||||
\(374\) | 32.2471 | 1.66746 | ||||||||
\(375\) | −7.55266 | −0.390017 | ||||||||
\(376\) | −10.5592 | −0.544548 | ||||||||
\(377\) | −4.23930 | −0.218335 | ||||||||
\(378\) | 3.24300 | 0.166802 | ||||||||
\(379\) | −25.5292 | −1.31135 | −0.655673 | − | 0.755045i | \(-0.727615\pi\) | ||||
−0.655673 | + | 0.755045i | \(0.727615\pi\) | |||||||
\(380\) | 6.94567 | 0.356305 | ||||||||
\(381\) | −5.15738 | −0.264221 | ||||||||
\(382\) | 11.5886 | 0.592922 | ||||||||
\(383\) | 27.4748 | 1.40390 | 0.701948 | − | 0.712229i | \(-0.252314\pi\) | ||||
0.701948 | + | 0.712229i | \(0.252314\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 10.8804 | 0.554515 | ||||||||
\(386\) | −1.16862 | −0.0594814 | ||||||||
\(387\) | 0.621687 | 0.0316021 | ||||||||
\(388\) | 3.02487 | 0.153564 | ||||||||
\(389\) | 9.21329 | 0.467132 | 0.233566 | − | 0.972341i | \(-0.424960\pi\) | ||||
0.233566 | + | 0.972341i | \(0.424960\pi\) | |||||||
\(390\) | −0.808021 | −0.0409157 | ||||||||
\(391\) | −67.1589 | −3.39637 | ||||||||
\(392\) | 3.51704 | 0.177637 | ||||||||
\(393\) | 0.509744 | 0.0257132 | ||||||||
\(394\) | −22.7068 | −1.14395 | ||||||||
\(395\) | −11.3986 | −0.573524 | ||||||||
\(396\) | 4.15216 | 0.208654 | ||||||||
\(397\) | −1.52055 | −0.0763142 | −0.0381571 | − | 0.999272i | \(-0.512149\pi\) | ||||
−0.0381571 | + | 0.999272i | \(0.512149\pi\) | |||||||
\(398\) | −21.8807 | −1.09678 | ||||||||
\(399\) | 27.8765 | 1.39557 | ||||||||
\(400\) | −4.34710 | −0.217355 | ||||||||
\(401\) | 5.91594 | 0.295428 | 0.147714 | − | 0.989030i | \(-0.452809\pi\) | ||||
0.147714 | + | 0.989030i | \(0.452809\pi\) | |||||||
\(402\) | −11.2176 | −0.559485 | ||||||||
\(403\) | 6.26307 | 0.311986 | ||||||||
\(404\) | 12.2137 | 0.607653 | ||||||||
\(405\) | 0.808021 | 0.0401509 | ||||||||
\(406\) | 13.7481 | 0.682305 | ||||||||
\(407\) | 23.5452 | 1.16709 | ||||||||
\(408\) | 7.76632 | 0.384490 | ||||||||
\(409\) | −16.6091 | −0.821268 | −0.410634 | − | 0.911800i | \(-0.634693\pi\) | ||||
−0.410634 | + | 0.911800i | \(0.634693\pi\) | |||||||
\(410\) | 1.35631 | 0.0669833 | ||||||||
\(411\) | −8.22378 | −0.405649 | ||||||||
\(412\) | 1.00000 | 0.0492665 | ||||||||
\(413\) | −39.6484 | −1.95097 | ||||||||
\(414\) | −8.64744 | −0.424999 | ||||||||
\(415\) | −12.0537 | −0.591694 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −14.5980 | −0.714868 | ||||||||
\(418\) | 35.6916 | 1.74573 | ||||||||
\(419\) | 1.71675 | 0.0838686 | 0.0419343 | − | 0.999120i | \(-0.486648\pi\) | ||||
0.0419343 | + | 0.999120i | \(0.486648\pi\) | |||||||
\(420\) | 2.62041 | 0.127863 | ||||||||
\(421\) | −32.9663 | −1.60668 | −0.803340 | − | 0.595520i | \(-0.796946\pi\) | ||||
−0.803340 | + | 0.595520i | \(0.796946\pi\) | |||||||
\(422\) | 0.590099 | 0.0287256 | ||||||||
\(423\) | −10.5592 | −0.513405 | ||||||||
\(424\) | 6.13590 | 0.297986 | ||||||||
\(425\) | −33.7610 | −1.63765 | ||||||||
\(426\) | 4.12480 | 0.199847 | ||||||||
\(427\) | −32.4459 | −1.57017 | ||||||||
\(428\) | 0.530297 | 0.0256328 | ||||||||
\(429\) | −4.15216 | −0.200468 | ||||||||
\(430\) | 0.502336 | 0.0242248 | ||||||||
\(431\) | 23.5251 | 1.13317 | 0.566583 | − | 0.824005i | \(-0.308265\pi\) | ||||
0.566583 | + | 0.824005i | \(0.308265\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 26.4575 | 1.27146 | 0.635732 | − | 0.771910i | \(-0.280698\pi\) | ||||
0.635732 | + | 0.771910i | \(0.280698\pi\) | |||||||
\(434\) | −20.3111 | −0.974965 | ||||||||
\(435\) | 3.42545 | 0.164238 | ||||||||
\(436\) | −1.40297 | −0.0671902 | ||||||||
\(437\) | −74.3326 | −3.55581 | ||||||||
\(438\) | 13.8673 | 0.662607 | ||||||||
\(439\) | −1.55491 | −0.0742118 | −0.0371059 | − | 0.999311i | \(-0.511814\pi\) | ||||
−0.0371059 | + | 0.999311i | \(0.511814\pi\) | |||||||
\(440\) | 3.35504 | 0.159945 | ||||||||
\(441\) | 3.51704 | 0.167478 | ||||||||
\(442\) | −7.76632 | −0.369406 | ||||||||
\(443\) | 3.72538 | 0.176998 | 0.0884990 | − | 0.996076i | \(-0.471793\pi\) | ||||
0.0884990 | + | 0.996076i | \(0.471793\pi\) | |||||||
\(444\) | 5.67059 | 0.269114 | ||||||||
\(445\) | −6.75859 | −0.320388 | ||||||||
\(446\) | 23.7424 | 1.12423 | ||||||||
\(447\) | −3.96159 | −0.187377 | ||||||||
\(448\) | 3.24300 | 0.153217 | ||||||||
\(449\) | 26.2702 | 1.23977 | 0.619884 | − | 0.784694i | \(-0.287180\pi\) | ||||
0.619884 | + | 0.784694i | \(0.287180\pi\) | |||||||
\(450\) | −4.34710 | −0.204924 | ||||||||
\(451\) | 6.96964 | 0.328188 | ||||||||
\(452\) | −15.9476 | −0.750111 | ||||||||
\(453\) | −2.69321 | −0.126538 | ||||||||
\(454\) | −2.77610 | −0.130289 | ||||||||
\(455\) | −2.62041 | −0.122847 | ||||||||
\(456\) | 8.59590 | 0.402540 | ||||||||
\(457\) | −17.1670 | −0.803037 | −0.401518 | − | 0.915851i | \(-0.631517\pi\) | ||||
−0.401518 | + | 0.915851i | \(0.631517\pi\) | |||||||
\(458\) | −26.2266 | −1.22549 | ||||||||
\(459\) | 7.76632 | 0.362501 | ||||||||
\(460\) | −6.98732 | −0.325785 | ||||||||
\(461\) | −2.59128 | −0.120688 | −0.0603439 | − | 0.998178i | \(-0.519220\pi\) | ||||
−0.0603439 | + | 0.998178i | \(0.519220\pi\) | |||||||
\(462\) | 13.4655 | 0.626470 | ||||||||
\(463\) | −30.8714 | −1.43472 | −0.717358 | − | 0.696705i | \(-0.754649\pi\) | ||||
−0.717358 | + | 0.696705i | \(0.754649\pi\) | |||||||
\(464\) | 4.23930 | 0.196805 | ||||||||
\(465\) | −5.06069 | −0.234684 | ||||||||
\(466\) | 2.40864 | 0.111578 | ||||||||
\(467\) | 19.7850 | 0.915541 | 0.457771 | − | 0.889070i | \(-0.348648\pi\) | ||||
0.457771 | + | 0.889070i | \(0.348648\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | −36.3788 | −1.67982 | ||||||||
\(470\) | −8.53204 | −0.393554 | ||||||||
\(471\) | −18.1386 | −0.835783 | ||||||||
\(472\) | −12.2258 | −0.562740 | ||||||||
\(473\) | 2.58135 | 0.118691 | ||||||||
\(474\) | −14.1068 | −0.647945 | ||||||||
\(475\) | −37.3673 | −1.71453 | ||||||||
\(476\) | 25.1862 | 1.15441 | ||||||||
\(477\) | 6.13590 | 0.280944 | ||||||||
\(478\) | 6.82164 | 0.312015 | ||||||||
\(479\) | −10.1618 | −0.464306 | −0.232153 | − | 0.972679i | \(-0.574577\pi\) | ||||
−0.232153 | + | 0.972679i | \(0.574577\pi\) | |||||||
\(480\) | 0.808021 | 0.0368809 | ||||||||
\(481\) | −5.67059 | −0.258557 | ||||||||
\(482\) | 26.0809 | 1.18795 | ||||||||
\(483\) | −28.0436 | −1.27603 | ||||||||
\(484\) | 6.24047 | 0.283658 | ||||||||
\(485\) | 2.44416 | 0.110983 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −39.4004 | −1.78540 | −0.892702 | − | 0.450647i | \(-0.851193\pi\) | ||||
−0.892702 | + | 0.450647i | \(0.851193\pi\) | |||||||
\(488\) | −10.0049 | −0.452900 | ||||||||
\(489\) | 15.9190 | 0.719882 | ||||||||
\(490\) | 2.84184 | 0.128381 | ||||||||
\(491\) | 26.2570 | 1.18496 | 0.592480 | − | 0.805585i | \(-0.298149\pi\) | ||||
0.592480 | + | 0.805585i | \(0.298149\pi\) | |||||||
\(492\) | 1.67856 | 0.0756752 | ||||||||
\(493\) | 32.9238 | 1.48281 | ||||||||
\(494\) | −8.59590 | −0.386748 | ||||||||
\(495\) | 3.35504 | 0.150798 | ||||||||
\(496\) | −6.26307 | −0.281220 | ||||||||
\(497\) | 13.3767 | 0.600028 | ||||||||
\(498\) | −14.9176 | −0.668473 | ||||||||
\(499\) | −6.57128 | −0.294171 | −0.147086 | − | 0.989124i | \(-0.546989\pi\) | ||||
−0.147086 | + | 0.989124i | \(0.546989\pi\) | |||||||
\(500\) | −7.55266 | −0.337765 | ||||||||
\(501\) | 21.7955 | 0.973750 | ||||||||
\(502\) | −1.74155 | −0.0777290 | ||||||||
\(503\) | 40.4174 | 1.80212 | 0.901062 | − | 0.433690i | \(-0.142789\pi\) | ||||
0.901062 | + | 0.433690i | \(0.142789\pi\) | |||||||
\(504\) | 3.24300 | 0.144455 | ||||||||
\(505\) | 9.86891 | 0.439161 | ||||||||
\(506\) | −35.9056 | −1.59620 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | −5.15738 | −0.228822 | ||||||||
\(509\) | −9.13173 | −0.404757 | −0.202378 | − | 0.979307i | \(-0.564867\pi\) | ||||
−0.202378 | + | 0.979307i | \(0.564867\pi\) | |||||||
\(510\) | 6.27535 | 0.277877 | ||||||||
\(511\) | 44.9718 | 1.98943 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 8.59590 | 0.379518 | ||||||||
\(514\) | 12.3840 | 0.546236 | ||||||||
\(515\) | 0.808021 | 0.0356057 | ||||||||
\(516\) | 0.621687 | 0.0273683 | ||||||||
\(517\) | −43.8435 | −1.92823 | ||||||||
\(518\) | 18.3897 | 0.807997 | ||||||||
\(519\) | −7.22504 | −0.317144 | ||||||||
\(520\) | −0.808021 | −0.0354341 | ||||||||
\(521\) | 13.9197 | 0.609832 | 0.304916 | − | 0.952379i | \(-0.401372\pi\) | ||||
0.304916 | + | 0.952379i | \(0.401372\pi\) | |||||||
\(522\) | 4.23930 | 0.185549 | ||||||||
\(523\) | 6.81800 | 0.298131 | 0.149065 | − | 0.988827i | \(-0.452374\pi\) | ||||
0.149065 | + | 0.988827i | \(0.452374\pi\) | |||||||
\(524\) | 0.509744 | 0.0222683 | ||||||||
\(525\) | −14.0976 | −0.615272 | ||||||||
\(526\) | 14.1956 | 0.618958 | ||||||||
\(527\) | −48.6410 | −2.11884 | ||||||||
\(528\) | 4.15216 | 0.180700 | ||||||||
\(529\) | 51.7783 | 2.25123 | ||||||||
\(530\) | 4.95794 | 0.215359 | ||||||||
\(531\) | −12.2258 | −0.530557 | ||||||||
\(532\) | 27.8765 | 1.20860 | ||||||||
\(533\) | −1.67856 | −0.0727063 | ||||||||
\(534\) | −8.36437 | −0.361962 | ||||||||
\(535\) | 0.428491 | 0.0185253 | ||||||||
\(536\) | −11.2176 | −0.484529 | ||||||||
\(537\) | 1.51059 | 0.0651868 | ||||||||
\(538\) | 2.89416 | 0.124776 | ||||||||
\(539\) | 14.6033 | 0.629010 | ||||||||
\(540\) | 0.808021 | 0.0347717 | ||||||||
\(541\) | −36.1087 | −1.55243 | −0.776216 | − | 0.630467i | \(-0.782863\pi\) | ||||
−0.776216 | + | 0.630467i | \(0.782863\pi\) | |||||||
\(542\) | −3.63848 | −0.156286 | ||||||||
\(543\) | 4.03456 | 0.173139 | ||||||||
\(544\) | 7.76632 | 0.332978 | ||||||||
\(545\) | −1.13363 | −0.0485595 | ||||||||
\(546\) | −3.24300 | −0.138788 | ||||||||
\(547\) | −21.2363 | −0.907997 | −0.453999 | − | 0.891002i | \(-0.650003\pi\) | ||||
−0.453999 | + | 0.891002i | \(0.650003\pi\) | |||||||
\(548\) | −8.22378 | −0.351302 | ||||||||
\(549\) | −10.0049 | −0.426999 | ||||||||
\(550\) | −18.0499 | −0.769650 | ||||||||
\(551\) | 36.4406 | 1.55242 | ||||||||
\(552\) | −8.64744 | −0.368060 | ||||||||
\(553\) | −45.7482 | −1.94541 | ||||||||
\(554\) | 24.7013 | 1.04946 | ||||||||
\(555\) | 4.58196 | 0.194493 | ||||||||
\(556\) | −14.5980 | −0.619094 | ||||||||
\(557\) | −34.7050 | −1.47050 | −0.735250 | − | 0.677796i | \(-0.762935\pi\) | ||||
−0.735250 | + | 0.677796i | \(0.762935\pi\) | |||||||
\(558\) | −6.26307 | −0.265137 | ||||||||
\(559\) | −0.621687 | −0.0262946 | ||||||||
\(560\) | 2.62041 | 0.110733 | ||||||||
\(561\) | 32.2471 | 1.36147 | ||||||||
\(562\) | 7.92008 | 0.334089 | ||||||||
\(563\) | −23.1255 | −0.974622 | −0.487311 | − | 0.873228i | \(-0.662022\pi\) | ||||
−0.487311 | + | 0.873228i | \(0.662022\pi\) | |||||||
\(564\) | −10.5592 | −0.444622 | ||||||||
\(565\) | −12.8860 | −0.542117 | ||||||||
\(566\) | 21.6308 | 0.909212 | ||||||||
\(567\) | 3.24300 | 0.136193 | ||||||||
\(568\) | 4.12480 | 0.173073 | ||||||||
\(569\) | 31.6380 | 1.32634 | 0.663168 | − | 0.748471i | \(-0.269212\pi\) | ||||
0.663168 | + | 0.748471i | \(0.269212\pi\) | |||||||
\(570\) | 6.94567 | 0.290922 | ||||||||
\(571\) | 14.9369 | 0.625089 | 0.312544 | − | 0.949903i | \(-0.398819\pi\) | ||||
0.312544 | + | 0.949903i | \(0.398819\pi\) | |||||||
\(572\) | −4.15216 | −0.173611 | ||||||||
\(573\) | 11.5886 | 0.484119 | ||||||||
\(574\) | 5.44355 | 0.227210 | ||||||||
\(575\) | 37.5913 | 1.56767 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 25.2735 | 1.05215 | 0.526074 | − | 0.850439i | \(-0.323663\pi\) | ||||
0.526074 | + | 0.850439i | \(0.323663\pi\) | |||||||
\(578\) | 43.3158 | 1.80170 | ||||||||
\(579\) | −1.16862 | −0.0485663 | ||||||||
\(580\) | 3.42545 | 0.142234 | ||||||||
\(581\) | −48.3777 | −2.00705 | ||||||||
\(582\) | 3.02487 | 0.125385 | ||||||||
\(583\) | 25.4773 | 1.05516 | ||||||||
\(584\) | 13.8673 | 0.573835 | ||||||||
\(585\) | −0.808021 | −0.0334076 | ||||||||
\(586\) | 10.9756 | 0.453399 | ||||||||
\(587\) | 17.8524 | 0.736846 | 0.368423 | − | 0.929658i | \(-0.379898\pi\) | ||||
0.368423 | + | 0.929658i | \(0.379898\pi\) | |||||||
\(588\) | 3.51704 | 0.145040 | ||||||||
\(589\) | −53.8367 | −2.21830 | ||||||||
\(590\) | −9.87874 | −0.406701 | ||||||||
\(591\) | −22.7068 | −0.934035 | ||||||||
\(592\) | 5.67059 | 0.233060 | ||||||||
\(593\) | 44.5806 | 1.83071 | 0.915353 | − | 0.402653i | \(-0.131912\pi\) | ||||
0.915353 | + | 0.402653i | \(0.131912\pi\) | |||||||
\(594\) | 4.15216 | 0.170365 | ||||||||
\(595\) | 20.3510 | 0.834308 | ||||||||
\(596\) | −3.96159 | −0.162273 | ||||||||
\(597\) | −21.8807 | −0.895517 | ||||||||
\(598\) | 8.64744 | 0.353620 | ||||||||
\(599\) | −5.96523 | −0.243733 | −0.121866 | − | 0.992547i | \(-0.538888\pi\) | ||||
−0.121866 | + | 0.992547i | \(0.538888\pi\) | |||||||
\(600\) | −4.34710 | −0.177470 | ||||||||
\(601\) | 26.5651 | 1.08361 | 0.541806 | − | 0.840504i | \(-0.317741\pi\) | ||||
0.541806 | + | 0.840504i | \(0.317741\pi\) | |||||||
\(602\) | 2.01613 | 0.0821714 | ||||||||
\(603\) | −11.2176 | −0.456818 | ||||||||
\(604\) | −2.69321 | −0.109585 | ||||||||
\(605\) | 5.04243 | 0.205004 | ||||||||
\(606\) | 12.2137 | 0.496147 | ||||||||
\(607\) | −24.3019 | −0.986383 | −0.493192 | − | 0.869921i | \(-0.664170\pi\) | ||||
−0.493192 | + | 0.869921i | \(0.664170\pi\) | |||||||
\(608\) | 8.59590 | 0.348610 | ||||||||
\(609\) | 13.7481 | 0.557099 | ||||||||
\(610\) | −8.08417 | −0.327318 | ||||||||
\(611\) | 10.5592 | 0.427179 | ||||||||
\(612\) | 7.76632 | 0.313935 | ||||||||
\(613\) | −0.617576 | −0.0249437 | −0.0124718 | − | 0.999922i | \(-0.503970\pi\) | ||||
−0.0124718 | + | 0.999922i | \(0.503970\pi\) | |||||||
\(614\) | −14.0960 | −0.568870 | ||||||||
\(615\) | 1.35631 | 0.0546916 | ||||||||
\(616\) | 13.4655 | 0.542539 | ||||||||
\(617\) | −22.5973 | −0.909732 | −0.454866 | − | 0.890560i | \(-0.650313\pi\) | ||||
−0.454866 | + | 0.890560i | \(0.650313\pi\) | |||||||
\(618\) | 1.00000 | 0.0402259 | ||||||||
\(619\) | −32.9642 | −1.32494 | −0.662472 | − | 0.749086i | \(-0.730493\pi\) | ||||
−0.662472 | + | 0.749086i | \(0.730493\pi\) | |||||||
\(620\) | −5.06069 | −0.203242 | ||||||||
\(621\) | −8.64744 | −0.347010 | ||||||||
\(622\) | −5.20425 | −0.208672 | ||||||||
\(623\) | −27.1256 | −1.08677 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | 15.6328 | 0.625312 | ||||||||
\(626\) | 4.00558 | 0.160095 | ||||||||
\(627\) | 35.6916 | 1.42539 | ||||||||
\(628\) | −18.1386 | −0.723809 | ||||||||
\(629\) | 44.0396 | 1.75598 | ||||||||
\(630\) | 2.62041 | 0.104400 | ||||||||
\(631\) | 35.3071 | 1.40555 | 0.702777 | − | 0.711410i | \(-0.251943\pi\) | ||||
0.702777 | + | 0.711410i | \(0.251943\pi\) | |||||||
\(632\) | −14.1068 | −0.561137 | ||||||||
\(633\) | 0.590099 | 0.0234543 | ||||||||
\(634\) | −3.26012 | −0.129476 | ||||||||
\(635\) | −4.16728 | −0.165373 | ||||||||
\(636\) | 6.13590 | 0.243304 | ||||||||
\(637\) | −3.51704 | −0.139350 | ||||||||
\(638\) | 17.6023 | 0.696881 | ||||||||
\(639\) | 4.12480 | 0.163175 | ||||||||
\(640\) | 0.808021 | 0.0319398 | ||||||||
\(641\) | −6.18105 | −0.244137 | −0.122068 | − | 0.992522i | \(-0.538953\pi\) | ||||
−0.122068 | + | 0.992522i | \(0.538953\pi\) | |||||||
\(642\) | 0.530297 | 0.0209291 | ||||||||
\(643\) | 35.9717 | 1.41859 | 0.709293 | − | 0.704914i | \(-0.249014\pi\) | ||||
0.709293 | + | 0.704914i | \(0.249014\pi\) | |||||||
\(644\) | −28.0436 | −1.10507 | ||||||||
\(645\) | 0.502336 | 0.0197795 | ||||||||
\(646\) | 66.7586 | 2.62658 | ||||||||
\(647\) | −25.7896 | −1.01389 | −0.506946 | − | 0.861978i | \(-0.669226\pi\) | ||||
−0.506946 | + | 0.861978i | \(0.669226\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −50.7637 | −1.99265 | ||||||||
\(650\) | 4.34710 | 0.170507 | ||||||||
\(651\) | −20.3111 | −0.796056 | ||||||||
\(652\) | 15.9190 | 0.623436 | ||||||||
\(653\) | −6.09455 | −0.238498 | −0.119249 | − | 0.992864i | \(-0.538049\pi\) | ||||
−0.119249 | + | 0.992864i | \(0.538049\pi\) | |||||||
\(654\) | −1.40297 | −0.0548606 | ||||||||
\(655\) | 0.411884 | 0.0160936 | ||||||||
\(656\) | 1.67856 | 0.0655366 | ||||||||
\(657\) | 13.8673 | 0.541017 | ||||||||
\(658\) | −34.2434 | −1.33495 | ||||||||
\(659\) | 8.89271 | 0.346411 | 0.173205 | − | 0.984886i | \(-0.444588\pi\) | ||||
0.173205 | + | 0.984886i | \(0.444588\pi\) | |||||||
\(660\) | 3.35504 | 0.130595 | ||||||||
\(661\) | 41.6401 | 1.61961 | 0.809806 | − | 0.586698i | \(-0.199573\pi\) | ||||
0.809806 | + | 0.586698i | \(0.199573\pi\) | |||||||
\(662\) | −2.80347 | −0.108960 | ||||||||
\(663\) | −7.76632 | −0.301619 | ||||||||
\(664\) | −14.9176 | −0.578915 | ||||||||
\(665\) | 22.5248 | 0.873474 | ||||||||
\(666\) | 5.67059 | 0.219731 | ||||||||
\(667\) | −36.6591 | −1.41945 | ||||||||
\(668\) | 21.7955 | 0.843292 | ||||||||
\(669\) | 23.7424 | 0.917934 | ||||||||
\(670\) | −9.06409 | −0.350177 | ||||||||
\(671\) | −41.5420 | −1.60371 | ||||||||
\(672\) | 3.24300 | 0.125101 | ||||||||
\(673\) | −5.75620 | −0.221885 | −0.110943 | − | 0.993827i | \(-0.535387\pi\) | ||||
−0.110943 | + | 0.993827i | \(0.535387\pi\) | |||||||
\(674\) | −9.53649 | −0.367332 | ||||||||
\(675\) | −4.34710 | −0.167320 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 49.1410 | 1.88864 | 0.944321 | − | 0.329027i | \(-0.106721\pi\) | ||||
0.944321 | + | 0.329027i | \(0.106721\pi\) | |||||||
\(678\) | −15.9476 | −0.612463 | ||||||||
\(679\) | 9.80964 | 0.376459 | ||||||||
\(680\) | 6.27535 | 0.240649 | ||||||||
\(681\) | −2.77610 | −0.106380 | ||||||||
\(682\) | −26.0053 | −0.995794 | ||||||||
\(683\) | −22.0907 | −0.845278 | −0.422639 | − | 0.906298i | \(-0.638896\pi\) | ||||
−0.422639 | + | 0.906298i | \(0.638896\pi\) | |||||||
\(684\) | 8.59590 | 0.328673 | ||||||||
\(685\) | −6.64498 | −0.253892 | ||||||||
\(686\) | −11.2952 | −0.431254 | ||||||||
\(687\) | −26.2266 | −1.00061 | ||||||||
\(688\) | 0.621687 | 0.0237016 | ||||||||
\(689\) | −6.13590 | −0.233759 | ||||||||
\(690\) | −6.98732 | −0.266003 | ||||||||
\(691\) | 50.7375 | 1.93015 | 0.965073 | − | 0.261980i | \(-0.0843756\pi\) | ||||
0.965073 | + | 0.261980i | \(0.0843756\pi\) | |||||||
\(692\) | −7.22504 | −0.274655 | ||||||||
\(693\) | 13.4655 | 0.511511 | ||||||||
\(694\) | 8.47381 | 0.321661 | ||||||||
\(695\) | −11.7955 | −0.447429 | ||||||||
\(696\) | 4.23930 | 0.160690 | ||||||||
\(697\) | 13.0362 | 0.493782 | ||||||||
\(698\) | −12.1276 | −0.459035 | ||||||||
\(699\) | 2.40864 | 0.0911030 | ||||||||
\(700\) | −14.0976 | −0.532841 | ||||||||
\(701\) | 29.9644 | 1.13174 | 0.565871 | − | 0.824494i | \(-0.308540\pi\) | ||||
0.565871 | + | 0.824494i | \(0.308540\pi\) | |||||||
\(702\) | −1.00000 | −0.0377426 | ||||||||
\(703\) | 48.7438 | 1.83841 | ||||||||
\(704\) | 4.15216 | 0.156491 | ||||||||
\(705\) | −8.53204 | −0.321335 | ||||||||
\(706\) | 2.41300 | 0.0908146 | ||||||||
\(707\) | 39.6090 | 1.48965 | ||||||||
\(708\) | −12.2258 | −0.459475 | ||||||||
\(709\) | −17.5704 | −0.659870 | −0.329935 | − | 0.944004i | \(-0.607027\pi\) | ||||
−0.329935 | + | 0.944004i | \(0.607027\pi\) | |||||||
\(710\) | 3.33293 | 0.125083 | ||||||||
\(711\) | −14.1068 | −0.529045 | ||||||||
\(712\) | −8.36437 | −0.313468 | ||||||||
\(713\) | 54.1595 | 2.02829 | ||||||||
\(714\) | 25.1862 | 0.942569 | ||||||||
\(715\) | −3.35504 | −0.125471 | ||||||||
\(716\) | 1.51059 | 0.0564534 | ||||||||
\(717\) | 6.82164 | 0.254759 | ||||||||
\(718\) | −4.29733 | −0.160375 | ||||||||
\(719\) | 15.9090 | 0.593304 | 0.296652 | − | 0.954986i | \(-0.404130\pi\) | ||||
0.296652 | + | 0.954986i | \(0.404130\pi\) | |||||||
\(720\) | 0.808021 | 0.0301132 | ||||||||
\(721\) | 3.24300 | 0.120776 | ||||||||
\(722\) | 54.8895 | 2.04278 | ||||||||
\(723\) | 26.0809 | 0.969961 | ||||||||
\(724\) | 4.03456 | 0.149943 | ||||||||
\(725\) | −18.4287 | −0.684424 | ||||||||
\(726\) | 6.24047 | 0.231606 | ||||||||
\(727\) | −22.5620 | −0.836778 | −0.418389 | − | 0.908268i | \(-0.637405\pi\) | ||||
−0.418389 | + | 0.908268i | \(0.637405\pi\) | |||||||
\(728\) | −3.24300 | −0.120194 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 11.2051 | 0.414720 | ||||||||
\(731\) | 4.82822 | 0.178578 | ||||||||
\(732\) | −10.0049 | −0.369792 | ||||||||
\(733\) | −5.95341 | −0.219894 | −0.109947 | − | 0.993937i | \(-0.535068\pi\) | ||||
−0.109947 | + | 0.993937i | \(0.535068\pi\) | |||||||
\(734\) | 9.13736 | 0.337266 | ||||||||
\(735\) | 2.84184 | 0.104823 | ||||||||
\(736\) | −8.64744 | −0.318749 | ||||||||
\(737\) | −46.5775 | −1.71570 | ||||||||
\(738\) | 1.67856 | 0.0617885 | ||||||||
\(739\) | 32.8439 | 1.20818 | 0.604090 | − | 0.796916i | \(-0.293537\pi\) | ||||
0.604090 | + | 0.796916i | \(0.293537\pi\) | |||||||
\(740\) | 4.58196 | 0.168436 | ||||||||
\(741\) | −8.59590 | −0.315778 | ||||||||
\(742\) | 19.8987 | 0.730505 | ||||||||
\(743\) | −24.8183 | −0.910493 | −0.455247 | − | 0.890365i | \(-0.650449\pi\) | ||||
−0.455247 | + | 0.890365i | \(0.650449\pi\) | |||||||
\(744\) | −6.26307 | −0.229615 | ||||||||
\(745\) | −3.20105 | −0.117277 | ||||||||
\(746\) | 16.1454 | 0.591127 | ||||||||
\(747\) | −14.9176 | −0.545806 | ||||||||
\(748\) | 32.2471 | 1.17907 | ||||||||
\(749\) | 1.71975 | 0.0628383 | ||||||||
\(750\) | −7.55266 | −0.275784 | ||||||||
\(751\) | 35.1991 | 1.28443 | 0.642217 | − | 0.766523i | \(-0.278015\pi\) | ||||
0.642217 | + | 0.766523i | \(0.278015\pi\) | |||||||
\(752\) | −10.5592 | −0.385054 | ||||||||
\(753\) | −1.74155 | −0.0634655 | ||||||||
\(754\) | −4.23930 | −0.154386 | ||||||||
\(755\) | −2.17617 | −0.0791991 | ||||||||
\(756\) | 3.24300 | 0.117947 | ||||||||
\(757\) | −32.5090 | −1.18156 | −0.590781 | − | 0.806832i | \(-0.701180\pi\) | ||||
−0.590781 | + | 0.806832i | \(0.701180\pi\) | |||||||
\(758\) | −25.5292 | −0.927261 | ||||||||
\(759\) | −35.9056 | −1.30329 | ||||||||
\(760\) | 6.94567 | 0.251946 | ||||||||
\(761\) | 9.02410 | 0.327123 | 0.163562 | − | 0.986533i | \(-0.447702\pi\) | ||||
0.163562 | + | 0.986533i | \(0.447702\pi\) | |||||||
\(762\) | −5.15738 | −0.186832 | ||||||||
\(763\) | −4.54984 | −0.164715 | ||||||||
\(764\) | 11.5886 | 0.419259 | ||||||||
\(765\) | 6.27535 | 0.226886 | ||||||||
\(766\) | 27.4748 | 0.992704 | ||||||||
\(767\) | 12.2258 | 0.441450 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −22.2013 | −0.800598 | −0.400299 | − | 0.916385i | \(-0.631094\pi\) | ||||
−0.400299 | + | 0.916385i | \(0.631094\pi\) | |||||||
\(770\) | 10.8804 | 0.392102 | ||||||||
\(771\) | 12.3840 | 0.446000 | ||||||||
\(772\) | −1.16862 | −0.0420597 | ||||||||
\(773\) | −7.83404 | −0.281771 | −0.140885 | − | 0.990026i | \(-0.544995\pi\) | ||||
−0.140885 | + | 0.990026i | \(0.544995\pi\) | |||||||
\(774\) | 0.621687 | 0.0223461 | ||||||||
\(775\) | 27.2262 | 0.977994 | ||||||||
\(776\) | 3.02487 | 0.108586 | ||||||||
\(777\) | 18.3897 | 0.659727 | ||||||||
\(778\) | 9.21329 | 0.330312 | ||||||||
\(779\) | 14.4287 | 0.516962 | ||||||||
\(780\) | −0.808021 | −0.0289318 | ||||||||
\(781\) | 17.1269 | 0.612847 | ||||||||
\(782\) | −67.1589 | −2.40160 | ||||||||
\(783\) | 4.23930 | 0.151500 | ||||||||
\(784\) | 3.51704 | 0.125609 | ||||||||
\(785\) | −14.6564 | −0.523108 | ||||||||
\(786\) | 0.509744 | 0.0181820 | ||||||||
\(787\) | −27.5116 | −0.980681 | −0.490341 | − | 0.871531i | \(-0.663128\pi\) | ||||
−0.490341 | + | 0.871531i | \(0.663128\pi\) | |||||||
\(788\) | −22.7068 | −0.808898 | ||||||||
\(789\) | 14.1956 | 0.505377 | ||||||||
\(790\) | −11.3986 | −0.405543 | ||||||||
\(791\) | −51.7180 | −1.83888 | ||||||||
\(792\) | 4.15216 | 0.147541 | ||||||||
\(793\) | 10.0049 | 0.355284 | ||||||||
\(794\) | −1.52055 | −0.0539623 | ||||||||
\(795\) | 4.95794 | 0.175840 | ||||||||
\(796\) | −21.8807 | −0.775541 | ||||||||
\(797\) | 32.3472 | 1.14580 | 0.572898 | − | 0.819626i | \(-0.305819\pi\) | ||||
0.572898 | + | 0.819626i | \(0.305819\pi\) | |||||||
\(798\) | 27.8765 | 0.986817 | ||||||||
\(799\) | −82.0060 | −2.90117 | ||||||||
\(800\) | −4.34710 | −0.153693 | ||||||||
\(801\) | −8.36437 | −0.295541 | ||||||||
\(802\) | 5.91594 | 0.208899 | ||||||||
\(803\) | 57.5795 | 2.03194 | ||||||||
\(804\) | −11.2176 | −0.395616 | ||||||||
\(805\) | −22.6599 | −0.798655 | ||||||||
\(806\) | 6.26307 | 0.220607 | ||||||||
\(807\) | 2.89416 | 0.101879 | ||||||||
\(808\) | 12.2137 | 0.429676 | ||||||||
\(809\) | 17.7588 | 0.624366 | 0.312183 | − | 0.950022i | \(-0.398940\pi\) | ||||
0.312183 | + | 0.950022i | \(0.398940\pi\) | |||||||
\(810\) | 0.808021 | 0.0283910 | ||||||||
\(811\) | 4.09101 | 0.143655 | 0.0718273 | − | 0.997417i | \(-0.477117\pi\) | ||||
0.0718273 | + | 0.997417i | \(0.477117\pi\) | |||||||
\(812\) | 13.7481 | 0.482462 | ||||||||
\(813\) | −3.63848 | −0.127607 | ||||||||
\(814\) | 23.5452 | 0.825259 | ||||||||
\(815\) | 12.8629 | 0.450567 | ||||||||
\(816\) | 7.76632 | 0.271876 | ||||||||
\(817\) | 5.34396 | 0.186962 | ||||||||
\(818\) | −16.6091 | −0.580724 | ||||||||
\(819\) | −3.24300 | −0.113320 | ||||||||
\(820\) | 1.35631 | 0.0473644 | ||||||||
\(821\) | 21.4712 | 0.749349 | 0.374674 | − | 0.927156i | \(-0.377755\pi\) | ||||
0.374674 | + | 0.927156i | \(0.377755\pi\) | |||||||
\(822\) | −8.22378 | −0.286837 | ||||||||
\(823\) | 24.8955 | 0.867802 | 0.433901 | − | 0.900961i | \(-0.357137\pi\) | ||||
0.433901 | + | 0.900961i | \(0.357137\pi\) | |||||||
\(824\) | 1.00000 | 0.0348367 | ||||||||
\(825\) | −18.0499 | −0.628416 | ||||||||
\(826\) | −39.6484 | −1.37954 | ||||||||
\(827\) | −6.08948 | −0.211752 | −0.105876 | − | 0.994379i | \(-0.533765\pi\) | ||||
−0.105876 | + | 0.994379i | \(0.533765\pi\) | |||||||
\(828\) | −8.64744 | −0.300519 | ||||||||
\(829\) | 4.42657 | 0.153741 | 0.0768705 | − | 0.997041i | \(-0.475507\pi\) | ||||
0.0768705 | + | 0.997041i | \(0.475507\pi\) | |||||||
\(830\) | −12.0537 | −0.418391 | ||||||||
\(831\) | 24.7013 | 0.856880 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 27.3145 | 0.946390 | ||||||||
\(834\) | −14.5980 | −0.505488 | ||||||||
\(835\) | 17.6112 | 0.609461 | ||||||||
\(836\) | 35.6916 | 1.23442 | ||||||||
\(837\) | −6.26307 | −0.216483 | ||||||||
\(838\) | 1.71675 | 0.0593040 | ||||||||
\(839\) | 21.4548 | 0.740701 | 0.370350 | − | 0.928892i | \(-0.379238\pi\) | ||||
0.370350 | + | 0.928892i | \(0.379238\pi\) | |||||||
\(840\) | 2.62041 | 0.0904128 | ||||||||
\(841\) | −11.0283 | −0.380286 | ||||||||
\(842\) | −32.9663 | −1.13609 | ||||||||
\(843\) | 7.92008 | 0.272782 | ||||||||
\(844\) | 0.590099 | 0.0203120 | ||||||||
\(845\) | 0.808021 | 0.0277968 | ||||||||
\(846\) | −10.5592 | −0.363032 | ||||||||
\(847\) | 20.2378 | 0.695380 | ||||||||
\(848\) | 6.13590 | 0.210708 | ||||||||
\(849\) | 21.6308 | 0.742368 | ||||||||
\(850\) | −33.7610 | −1.15799 | ||||||||
\(851\) | −49.0361 | −1.68094 | ||||||||
\(852\) | 4.12480 | 0.141313 | ||||||||
\(853\) | −9.35371 | −0.320265 | −0.160132 | − | 0.987096i | \(-0.551192\pi\) | ||||
−0.160132 | + | 0.987096i | \(0.551192\pi\) | |||||||
\(854\) | −32.4459 | −1.11027 | ||||||||
\(855\) | 6.94567 | 0.237537 | ||||||||
\(856\) | 0.530297 | 0.0181252 | ||||||||
\(857\) | 16.8397 | 0.575232 | 0.287616 | − | 0.957746i | \(-0.407137\pi\) | ||||
0.287616 | + | 0.957746i | \(0.407137\pi\) | |||||||
\(858\) | −4.15216 | −0.141753 | ||||||||
\(859\) | −10.2004 | −0.348035 | −0.174017 | − | 0.984743i | \(-0.555675\pi\) | ||||
−0.174017 | + | 0.984743i | \(0.555675\pi\) | |||||||
\(860\) | 0.502336 | 0.0171295 | ||||||||
\(861\) | 5.44355 | 0.185516 | ||||||||
\(862\) | 23.5251 | 0.801270 | ||||||||
\(863\) | −40.2954 | −1.37167 | −0.685836 | − | 0.727756i | \(-0.740563\pi\) | ||||
−0.685836 | + | 0.727756i | \(0.740563\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −5.83798 | −0.198497 | ||||||||
\(866\) | 26.4575 | 0.899061 | ||||||||
\(867\) | 43.3158 | 1.47108 | ||||||||
\(868\) | −20.3111 | −0.689404 | ||||||||
\(869\) | −58.5736 | −1.98697 | ||||||||
\(870\) | 3.42545 | 0.116134 | ||||||||
\(871\) | 11.2176 | 0.380095 | ||||||||
\(872\) | −1.40297 | −0.0475107 | ||||||||
\(873\) | 3.02487 | 0.102376 | ||||||||
\(874\) | −74.3326 | −2.51434 | ||||||||
\(875\) | −24.4932 | −0.828023 | ||||||||
\(876\) | 13.8673 | 0.468534 | ||||||||
\(877\) | −43.1234 | −1.45617 | −0.728087 | − | 0.685485i | \(-0.759590\pi\) | ||||
−0.728087 | + | 0.685485i | \(0.759590\pi\) | |||||||
\(878\) | −1.55491 | −0.0524757 | ||||||||
\(879\) | 10.9756 | 0.370199 | ||||||||
\(880\) | 3.35504 | 0.113098 | ||||||||
\(881\) | −36.4338 | −1.22749 | −0.613743 | − | 0.789506i | \(-0.710337\pi\) | ||||
−0.613743 | + | 0.789506i | \(0.710337\pi\) | |||||||
\(882\) | 3.51704 | 0.118425 | ||||||||
\(883\) | −42.8201 | −1.44101 | −0.720506 | − | 0.693449i | \(-0.756090\pi\) | ||||
−0.720506 | + | 0.693449i | \(0.756090\pi\) | |||||||
\(884\) | −7.76632 | −0.261210 | ||||||||
\(885\) | −9.87874 | −0.332070 | ||||||||
\(886\) | 3.72538 | 0.125156 | ||||||||
\(887\) | −37.5568 | −1.26104 | −0.630518 | − | 0.776175i | \(-0.717157\pi\) | ||||
−0.630518 | + | 0.776175i | \(0.717157\pi\) | |||||||
\(888\) | 5.67059 | 0.190292 | ||||||||
\(889\) | −16.7254 | −0.560952 | ||||||||
\(890\) | −6.75859 | −0.226548 | ||||||||
\(891\) | 4.15216 | 0.139103 | ||||||||
\(892\) | 23.7424 | 0.794954 | ||||||||
\(893\) | −90.7657 | −3.03736 | ||||||||
\(894\) | −3.96159 | −0.132495 | ||||||||
\(895\) | 1.22059 | 0.0407998 | ||||||||
\(896\) | 3.24300 | 0.108341 | ||||||||
\(897\) | 8.64744 | 0.288730 | ||||||||
\(898\) | 26.2702 | 0.876648 | ||||||||
\(899\) | −26.5511 | −0.885527 | ||||||||
\(900\) | −4.34710 | −0.144903 | ||||||||
\(901\) | 47.6534 | 1.58756 | ||||||||
\(902\) | 6.96964 | 0.232064 | ||||||||
\(903\) | 2.01613 | 0.0670926 | ||||||||
\(904\) | −15.9476 | −0.530409 | ||||||||
\(905\) | 3.26001 | 0.108366 | ||||||||
\(906\) | −2.69321 | −0.0894761 | ||||||||
\(907\) | −50.1342 | −1.66468 | −0.832339 | − | 0.554267i | \(-0.812999\pi\) | ||||
−0.832339 | + | 0.554267i | \(0.812999\pi\) | |||||||
\(908\) | −2.77610 | −0.0921280 | ||||||||
\(909\) | 12.2137 | 0.405102 | ||||||||
\(910\) | −2.62041 | −0.0868658 | ||||||||
\(911\) | −46.5932 | −1.54370 | −0.771851 | − | 0.635803i | \(-0.780669\pi\) | ||||
−0.771851 | + | 0.635803i | \(0.780669\pi\) | |||||||
\(912\) | 8.59590 | 0.284639 | ||||||||
\(913\) | −61.9403 | −2.04993 | ||||||||
\(914\) | −17.1670 | −0.567833 | ||||||||
\(915\) | −8.08417 | −0.267254 | ||||||||
\(916\) | −26.2266 | −0.866551 | ||||||||
\(917\) | 1.65310 | 0.0545902 | ||||||||
\(918\) | 7.76632 | 0.256327 | ||||||||
\(919\) | −14.2416 | −0.469786 | −0.234893 | − | 0.972021i | \(-0.575474\pi\) | ||||
−0.234893 | + | 0.972021i | \(0.575474\pi\) | |||||||
\(920\) | −6.98732 | −0.230365 | ||||||||
\(921\) | −14.0960 | −0.464480 | ||||||||
\(922\) | −2.59128 | −0.0853391 | ||||||||
\(923\) | −4.12480 | −0.135770 | ||||||||
\(924\) | 13.4655 | 0.442981 | ||||||||
\(925\) | −24.6506 | −0.810508 | ||||||||
\(926\) | −30.8714 | −1.01450 | ||||||||
\(927\) | 1.00000 | 0.0328443 | ||||||||
\(928\) | 4.23930 | 0.139162 | ||||||||
\(929\) | 3.79770 | 0.124599 | 0.0622993 | − | 0.998058i | \(-0.480157\pi\) | ||||
0.0622993 | + | 0.998058i | \(0.480157\pi\) | |||||||
\(930\) | −5.06069 | −0.165947 | ||||||||
\(931\) | 30.2321 | 0.990818 | ||||||||
\(932\) | 2.40864 | 0.0788975 | ||||||||
\(933\) | −5.20425 | −0.170380 | ||||||||
\(934\) | 19.7850 | 0.647386 | ||||||||
\(935\) | 26.0563 | 0.852132 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | 27.3691 | 0.894111 | 0.447055 | − | 0.894506i | \(-0.352473\pi\) | ||||
0.447055 | + | 0.894506i | \(0.352473\pi\) | |||||||
\(938\) | −36.3788 | −1.18781 | ||||||||
\(939\) | 4.00558 | 0.130717 | ||||||||
\(940\) | −8.53204 | −0.278285 | ||||||||
\(941\) | 30.6755 | 0.999994 | 0.499997 | − | 0.866027i | \(-0.333334\pi\) | ||||
0.499997 | + | 0.866027i | \(0.333334\pi\) | |||||||
\(942\) | −18.1386 | −0.590988 | ||||||||
\(943\) | −14.5152 | −0.472681 | ||||||||
\(944\) | −12.2258 | −0.397917 | ||||||||
\(945\) | 2.62041 | 0.0852420 | ||||||||
\(946\) | 2.58135 | 0.0839269 | ||||||||
\(947\) | −10.6801 | −0.347056 | −0.173528 | − | 0.984829i | \(-0.555517\pi\) | ||||
−0.173528 | + | 0.984829i | \(0.555517\pi\) | |||||||
\(948\) | −14.1068 | −0.458166 | ||||||||
\(949\) | −13.8673 | −0.450153 | ||||||||
\(950\) | −37.3673 | −1.21235 | ||||||||
\(951\) | −3.26012 | −0.105716 | ||||||||
\(952\) | 25.1862 | 0.816289 | ||||||||
\(953\) | −35.7031 | −1.15654 | −0.578268 | − | 0.815847i | \(-0.696271\pi\) | ||||
−0.578268 | + | 0.815847i | \(0.696271\pi\) | |||||||
\(954\) | 6.13590 | 0.198657 | ||||||||
\(955\) | 9.36380 | 0.303005 | ||||||||
\(956\) | 6.82164 | 0.220628 | ||||||||
\(957\) | 17.6023 | 0.569001 | ||||||||
\(958\) | −10.1618 | −0.328314 | ||||||||
\(959\) | −26.6697 | −0.861209 | ||||||||
\(960\) | 0.808021 | 0.0260788 | ||||||||
\(961\) | 8.22603 | 0.265356 | ||||||||
\(962\) | −5.67059 | −0.182827 | ||||||||
\(963\) | 0.530297 | 0.0170886 | ||||||||
\(964\) | 26.0809 | 0.840011 | ||||||||
\(965\) | −0.944272 | −0.0303972 | ||||||||
\(966\) | −28.0436 | −0.902290 | ||||||||
\(967\) | 8.09442 | 0.260299 | 0.130149 | − | 0.991494i | \(-0.458454\pi\) | ||||
0.130149 | + | 0.991494i | \(0.458454\pi\) | |||||||
\(968\) | 6.24047 | 0.200576 | ||||||||
\(969\) | 66.7586 | 2.14459 | ||||||||
\(970\) | 2.44416 | 0.0784771 | ||||||||
\(971\) | −48.2088 | −1.54709 | −0.773547 | − | 0.633739i | \(-0.781519\pi\) | ||||
−0.773547 | + | 0.633739i | \(0.781519\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −47.3414 | −1.51769 | ||||||||
\(974\) | −39.4004 | −1.26247 | ||||||||
\(975\) | 4.34710 | 0.139219 | ||||||||
\(976\) | −10.0049 | −0.320249 | ||||||||
\(977\) | 42.5120 | 1.36008 | 0.680040 | − | 0.733175i | \(-0.261963\pi\) | ||||
0.680040 | + | 0.733175i | \(0.261963\pi\) | |||||||
\(978\) | 15.9190 | 0.509034 | ||||||||
\(979\) | −34.7302 | −1.10998 | ||||||||
\(980\) | 2.84184 | 0.0907793 | ||||||||
\(981\) | −1.40297 | −0.0447935 | ||||||||
\(982\) | 26.2570 | 0.837894 | ||||||||
\(983\) | −47.8717 | −1.52687 | −0.763435 | − | 0.645884i | \(-0.776489\pi\) | ||||
−0.763435 | + | 0.645884i | \(0.776489\pi\) | |||||||
\(984\) | 1.67856 | 0.0535104 | ||||||||
\(985\) | −18.3476 | −0.584603 | ||||||||
\(986\) | 32.9238 | 1.04851 | ||||||||
\(987\) | −34.2434 | −1.08998 | ||||||||
\(988\) | −8.59590 | −0.273472 | ||||||||
\(989\) | −5.37601 | −0.170947 | ||||||||
\(990\) | 3.35504 | 0.106630 | ||||||||
\(991\) | 19.7180 | 0.626362 | 0.313181 | − | 0.949693i | \(-0.398605\pi\) | ||||
0.313181 | + | 0.949693i | \(0.398605\pi\) | |||||||
\(992\) | −6.26307 | −0.198853 | ||||||||
\(993\) | −2.80347 | −0.0889653 | ||||||||
\(994\) | 13.3767 | 0.424284 | ||||||||
\(995\) | −17.6801 | −0.560496 | ||||||||
\(996\) | −14.9176 | −0.472682 | ||||||||
\(997\) | −37.0099 | −1.17212 | −0.586058 | − | 0.810269i | \(-0.699321\pi\) | ||||
−0.586058 | + | 0.810269i | \(0.699321\pi\) | |||||||
\(998\) | −6.57128 | −0.208010 | ||||||||
\(999\) | 5.67059 | 0.179409 |
(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 | 8034.2.a.bd.1.9 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.bd.1.9 | ✓ | 16 | 1.1 | even | 1 | trivial |