Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2738,2,Mod(1,2738)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2738, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2738.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2738 = 2 \cdot 37^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2738.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: | \(21.8630400734\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{18})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 74) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.87939\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2738.1 |
$q$-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 | ||||||||
\(3\) | −1.87939 | −1.08506 | −0.542532 | − | 0.840035i | \(-0.682534\pi\) | ||||
−0.542532 | + | 0.840035i | \(0.682534\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.53209 | 1.57960 | 0.789799 | − | 0.613366i | \(-0.210185\pi\) | ||||
0.789799 | + | 0.613366i | \(0.210185\pi\) | |||||||
\(6\) | −1.87939 | −0.767256 | ||||||||
\(7\) | −0.879385 | −0.332376 | −0.166188 | − | 0.986094i | \(-0.553146\pi\) | ||||
−0.166188 | + | 0.986094i | \(0.553146\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.532089 | 0.177363 | ||||||||
\(10\) | 3.53209 | 1.11694 | ||||||||
\(11\) | 3.34730 | 1.00925 | 0.504624 | − | 0.863339i | \(-0.331631\pi\) | ||||
0.504624 | + | 0.863339i | \(0.331631\pi\) | |||||||
\(12\) | −1.87939 | −0.542532 | ||||||||
\(13\) | 6.41147 | 1.77822 | 0.889111 | − | 0.457691i | \(-0.151323\pi\) | ||||
0.889111 | + | 0.457691i | \(0.151323\pi\) | |||||||
\(14\) | −0.879385 | −0.235026 | ||||||||
\(15\) | −6.63816 | −1.71396 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.00000 | 0.727607 | 0.363803 | − | 0.931476i | \(-0.381478\pi\) | ||||
0.363803 | + | 0.931476i | \(0.381478\pi\) | |||||||
\(18\) | 0.532089 | 0.125415 | ||||||||
\(19\) | −4.63816 | −1.06407 | −0.532033 | − | 0.846724i | \(-0.678572\pi\) | ||||
−0.532033 | + | 0.846724i | \(0.678572\pi\) | |||||||
\(20\) | 3.53209 | 0.789799 | ||||||||
\(21\) | 1.65270 | 0.360650 | ||||||||
\(22\) | 3.34730 | 0.713646 | ||||||||
\(23\) | −5.83750 | −1.21720 | −0.608601 | − | 0.793476i | \(-0.708269\pi\) | ||||
−0.608601 | + | 0.793476i | \(0.708269\pi\) | |||||||
\(24\) | −1.87939 | −0.383628 | ||||||||
\(25\) | 7.47565 | 1.49513 | ||||||||
\(26\) | 6.41147 | 1.25739 | ||||||||
\(27\) | 4.63816 | 0.892613 | ||||||||
\(28\) | −0.879385 | −0.166188 | ||||||||
\(29\) | 3.26857 | 0.606958 | 0.303479 | − | 0.952838i | \(-0.401852\pi\) | ||||
0.303479 | + | 0.952838i | \(0.401852\pi\) | |||||||
\(30\) | −6.63816 | −1.21196 | ||||||||
\(31\) | 1.12061 | 0.201268 | 0.100634 | − | 0.994923i | \(-0.467913\pi\) | ||||
0.100634 | + | 0.994923i | \(0.467913\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −6.29086 | −1.09510 | ||||||||
\(34\) | 3.00000 | 0.514496 | ||||||||
\(35\) | −3.10607 | −0.525021 | ||||||||
\(36\) | 0.532089 | 0.0886815 | ||||||||
\(37\) | 0 | 0 | ||||||||
\(38\) | −4.63816 | −0.752408 | ||||||||
\(39\) | −12.0496 | −1.92948 | ||||||||
\(40\) | 3.53209 | 0.558472 | ||||||||
\(41\) | 8.58172 | 1.34024 | 0.670120 | − | 0.742253i | \(-0.266243\pi\) | ||||
0.670120 | + | 0.742253i | \(0.266243\pi\) | |||||||
\(42\) | 1.65270 | 0.255018 | ||||||||
\(43\) | −5.61587 | −0.856412 | −0.428206 | − | 0.903681i | \(-0.640854\pi\) | ||||
−0.428206 | + | 0.903681i | \(0.640854\pi\) | |||||||
\(44\) | 3.34730 | 0.504624 | ||||||||
\(45\) | 1.87939 | 0.280162 | ||||||||
\(46\) | −5.83750 | −0.860692 | ||||||||
\(47\) | −5.12836 | −0.748048 | −0.374024 | − | 0.927419i | \(-0.622022\pi\) | ||||
−0.374024 | + | 0.927419i | \(0.622022\pi\) | |||||||
\(48\) | −1.87939 | −0.271266 | ||||||||
\(49\) | −6.22668 | −0.889526 | ||||||||
\(50\) | 7.47565 | 1.05722 | ||||||||
\(51\) | −5.63816 | −0.789500 | ||||||||
\(52\) | 6.41147 | 0.889111 | ||||||||
\(53\) | 0.268571 | 0.0368910 | 0.0184455 | − | 0.999830i | \(-0.494128\pi\) | ||||
0.0184455 | + | 0.999830i | \(0.494128\pi\) | |||||||
\(54\) | 4.63816 | 0.631173 | ||||||||
\(55\) | 11.8229 | 1.59421 | ||||||||
\(56\) | −0.879385 | −0.117513 | ||||||||
\(57\) | 8.71688 | 1.15458 | ||||||||
\(58\) | 3.26857 | 0.429184 | ||||||||
\(59\) | −7.61856 | −0.991851 | −0.495926 | − | 0.868365i | \(-0.665171\pi\) | ||||
−0.495926 | + | 0.868365i | \(0.665171\pi\) | |||||||
\(60\) | −6.63816 | −0.856982 | ||||||||
\(61\) | −2.12836 | −0.272508 | −0.136254 | − | 0.990674i | \(-0.543506\pi\) | ||||
−0.136254 | + | 0.990674i | \(0.543506\pi\) | |||||||
\(62\) | 1.12061 | 0.142318 | ||||||||
\(63\) | −0.467911 | −0.0589513 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 22.6459 | 2.80888 | ||||||||
\(66\) | −6.29086 | −0.774351 | ||||||||
\(67\) | 8.53209 | 1.04236 | 0.521180 | − | 0.853447i | \(-0.325492\pi\) | ||||
0.521180 | + | 0.853447i | \(0.325492\pi\) | |||||||
\(68\) | 3.00000 | 0.363803 | ||||||||
\(69\) | 10.9709 | 1.32074 | ||||||||
\(70\) | −3.10607 | −0.371246 | ||||||||
\(71\) | 13.1480 | 1.56038 | 0.780188 | − | 0.625546i | \(-0.215124\pi\) | ||||
0.780188 | + | 0.625546i | \(0.215124\pi\) | |||||||
\(72\) | 0.532089 | 0.0627073 | ||||||||
\(73\) | −8.57398 | −1.00351 | −0.501754 | − | 0.865010i | \(-0.667312\pi\) | ||||
−0.501754 | + | 0.865010i | \(0.667312\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −14.0496 | −1.62231 | ||||||||
\(76\) | −4.63816 | −0.532033 | ||||||||
\(77\) | −2.94356 | −0.335450 | ||||||||
\(78\) | −12.0496 | −1.36435 | ||||||||
\(79\) | 11.5817 | 1.30305 | 0.651523 | − | 0.758629i | \(-0.274131\pi\) | ||||
0.651523 | + | 0.758629i | \(0.274131\pi\) | |||||||
\(80\) | 3.53209 | 0.394900 | ||||||||
\(81\) | −10.3131 | −1.14591 | ||||||||
\(82\) | 8.58172 | 0.947692 | ||||||||
\(83\) | 4.17024 | 0.457744 | 0.228872 | − | 0.973457i | \(-0.426496\pi\) | ||||
0.228872 | + | 0.973457i | \(0.426496\pi\) | |||||||
\(84\) | 1.65270 | 0.180325 | ||||||||
\(85\) | 10.5963 | 1.14933 | ||||||||
\(86\) | −5.61587 | −0.605575 | ||||||||
\(87\) | −6.14290 | −0.658588 | ||||||||
\(88\) | 3.34730 | 0.356823 | ||||||||
\(89\) | −8.37464 | −0.887710 | −0.443855 | − | 0.896099i | \(-0.646389\pi\) | ||||
−0.443855 | + | 0.896099i | \(0.646389\pi\) | |||||||
\(90\) | 1.87939 | 0.198105 | ||||||||
\(91\) | −5.63816 | −0.591039 | ||||||||
\(92\) | −5.83750 | −0.608601 | ||||||||
\(93\) | −2.10607 | −0.218389 | ||||||||
\(94\) | −5.12836 | −0.528949 | ||||||||
\(95\) | −16.3824 | −1.68080 | ||||||||
\(96\) | −1.87939 | −0.191814 | ||||||||
\(97\) | 17.0642 | 1.73260 | 0.866302 | − | 0.499520i | \(-0.166490\pi\) | ||||
0.866302 | + | 0.499520i | \(0.166490\pi\) | |||||||
\(98\) | −6.22668 | −0.628990 | ||||||||
\(99\) | 1.78106 | 0.179003 | ||||||||
\(100\) | 7.47565 | 0.747565 | ||||||||
\(101\) | 1.08647 | 0.108107 | 0.0540537 | − | 0.998538i | \(-0.482786\pi\) | ||||
0.0540537 | + | 0.998538i | \(0.482786\pi\) | |||||||
\(102\) | −5.63816 | −0.558261 | ||||||||
\(103\) | −11.2148 | −1.10503 | −0.552515 | − | 0.833503i | \(-0.686332\pi\) | ||||
−0.552515 | + | 0.833503i | \(0.686332\pi\) | |||||||
\(104\) | 6.41147 | 0.628697 | ||||||||
\(105\) | 5.83750 | 0.569681 | ||||||||
\(106\) | 0.268571 | 0.0260859 | ||||||||
\(107\) | 9.59627 | 0.927706 | 0.463853 | − | 0.885912i | \(-0.346467\pi\) | ||||
0.463853 | + | 0.885912i | \(0.346467\pi\) | |||||||
\(108\) | 4.63816 | 0.446307 | ||||||||
\(109\) | 2.22163 | 0.212793 | 0.106397 | − | 0.994324i | \(-0.466069\pi\) | ||||
0.106397 | + | 0.994324i | \(0.466069\pi\) | |||||||
\(110\) | 11.8229 | 1.12727 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.879385 | −0.0830941 | ||||||||
\(113\) | 4.63041 | 0.435593 | 0.217796 | − | 0.975994i | \(-0.430113\pi\) | ||||
0.217796 | + | 0.975994i | \(0.430113\pi\) | |||||||
\(114\) | 8.71688 | 0.816411 | ||||||||
\(115\) | −20.6186 | −1.92269 | ||||||||
\(116\) | 3.26857 | 0.303479 | ||||||||
\(117\) | 3.41147 | 0.315391 | ||||||||
\(118\) | −7.61856 | −0.701345 | ||||||||
\(119\) | −2.63816 | −0.241839 | ||||||||
\(120\) | −6.63816 | −0.605978 | ||||||||
\(121\) | 0.204393 | 0.0185812 | ||||||||
\(122\) | −2.12836 | −0.192692 | ||||||||
\(123\) | −16.1284 | −1.45424 | ||||||||
\(124\) | 1.12061 | 0.100634 | ||||||||
\(125\) | 8.74422 | 0.782107 | ||||||||
\(126\) | −0.467911 | −0.0416848 | ||||||||
\(127\) | −5.08647 | −0.451351 | −0.225675 | − | 0.974203i | \(-0.572459\pi\) | ||||
−0.225675 | + | 0.974203i | \(0.572459\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 10.5544 | 0.929261 | ||||||||
\(130\) | 22.6459 | 1.98618 | ||||||||
\(131\) | −3.26083 | −0.284900 | −0.142450 | − | 0.989802i | \(-0.545498\pi\) | ||||
−0.142450 | + | 0.989802i | \(0.545498\pi\) | |||||||
\(132\) | −6.29086 | −0.547549 | ||||||||
\(133\) | 4.07873 | 0.353670 | ||||||||
\(134\) | 8.53209 | 0.737060 | ||||||||
\(135\) | 16.3824 | 1.40997 | ||||||||
\(136\) | 3.00000 | 0.257248 | ||||||||
\(137\) | −1.59627 | −0.136378 | −0.0681891 | − | 0.997672i | \(-0.521722\pi\) | ||||
−0.0681891 | + | 0.997672i | \(0.521722\pi\) | |||||||
\(138\) | 10.9709 | 0.933905 | ||||||||
\(139\) | 11.8033 | 1.00115 | 0.500573 | − | 0.865694i | \(-0.333123\pi\) | ||||
0.500573 | + | 0.865694i | \(0.333123\pi\) | |||||||
\(140\) | −3.10607 | −0.262511 | ||||||||
\(141\) | 9.63816 | 0.811679 | ||||||||
\(142\) | 13.1480 | 1.10335 | ||||||||
\(143\) | 21.4611 | 1.79467 | ||||||||
\(144\) | 0.532089 | 0.0443407 | ||||||||
\(145\) | 11.5449 | 0.958750 | ||||||||
\(146\) | −8.57398 | −0.709587 | ||||||||
\(147\) | 11.7023 | 0.965192 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.6604 | −1.03718 | −0.518592 | − | 0.855022i | \(-0.673544\pi\) | ||||
−0.518592 | + | 0.855022i | \(0.673544\pi\) | |||||||
\(150\) | −14.0496 | −1.14715 | ||||||||
\(151\) | −4.53983 | −0.369446 | −0.184723 | − | 0.982791i | \(-0.559139\pi\) | ||||
−0.184723 | + | 0.982791i | \(0.559139\pi\) | |||||||
\(152\) | −4.63816 | −0.376204 | ||||||||
\(153\) | 1.59627 | 0.129051 | ||||||||
\(154\) | −2.94356 | −0.237199 | ||||||||
\(155\) | 3.95811 | 0.317923 | ||||||||
\(156\) | −12.0496 | −0.964742 | ||||||||
\(157\) | −17.8794 | −1.42693 | −0.713465 | − | 0.700691i | \(-0.752875\pi\) | ||||
−0.713465 | + | 0.700691i | \(0.752875\pi\) | |||||||
\(158\) | 11.5817 | 0.921392 | ||||||||
\(159\) | −0.504748 | −0.0400291 | ||||||||
\(160\) | 3.53209 | 0.279236 | ||||||||
\(161\) | 5.13341 | 0.404569 | ||||||||
\(162\) | −10.3131 | −0.810277 | ||||||||
\(163\) | 2.26857 | 0.177688 | 0.0888441 | − | 0.996046i | \(-0.471683\pi\) | ||||
0.0888441 | + | 0.996046i | \(0.471683\pi\) | |||||||
\(164\) | 8.58172 | 0.670120 | ||||||||
\(165\) | −22.2199 | −1.72981 | ||||||||
\(166\) | 4.17024 | 0.323674 | ||||||||
\(167\) | 21.4466 | 1.65958 | 0.829792 | − | 0.558073i | \(-0.188459\pi\) | ||||
0.829792 | + | 0.558073i | \(0.188459\pi\) | |||||||
\(168\) | 1.65270 | 0.127509 | ||||||||
\(169\) | 28.1070 | 2.16208 | ||||||||
\(170\) | 10.5963 | 0.812697 | ||||||||
\(171\) | −2.46791 | −0.188726 | ||||||||
\(172\) | −5.61587 | −0.428206 | ||||||||
\(173\) | −11.2686 | −0.856734 | −0.428367 | − | 0.903605i | \(-0.640911\pi\) | ||||
−0.428367 | + | 0.903605i | \(0.640911\pi\) | |||||||
\(174\) | −6.14290 | −0.465692 | ||||||||
\(175\) | −6.57398 | −0.496946 | ||||||||
\(176\) | 3.34730 | 0.252312 | ||||||||
\(177\) | 14.3182 | 1.07622 | ||||||||
\(178\) | −8.37464 | −0.627706 | ||||||||
\(179\) | 6.43107 | 0.480681 | 0.240341 | − | 0.970689i | \(-0.422741\pi\) | ||||
0.240341 | + | 0.970689i | \(0.422741\pi\) | |||||||
\(180\) | 1.87939 | 0.140081 | ||||||||
\(181\) | 3.50299 | 0.260375 | 0.130188 | − | 0.991489i | \(-0.458442\pi\) | ||||
0.130188 | + | 0.991489i | \(0.458442\pi\) | |||||||
\(182\) | −5.63816 | −0.417928 | ||||||||
\(183\) | 4.00000 | 0.295689 | ||||||||
\(184\) | −5.83750 | −0.430346 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.10607 | −0.154424 | ||||||||
\(187\) | 10.0419 | 0.734336 | ||||||||
\(188\) | −5.12836 | −0.374024 | ||||||||
\(189\) | −4.07873 | −0.296684 | ||||||||
\(190\) | −16.3824 | −1.18850 | ||||||||
\(191\) | 13.9240 | 1.00750 | 0.503751 | − | 0.863849i | \(-0.331953\pi\) | ||||
0.503751 | + | 0.863849i | \(0.331953\pi\) | |||||||
\(192\) | −1.87939 | −0.135633 | ||||||||
\(193\) | 11.5767 | 0.833307 | 0.416653 | − | 0.909065i | \(-0.363203\pi\) | ||||
0.416653 | + | 0.909065i | \(0.363203\pi\) | |||||||
\(194\) | 17.0642 | 1.22514 | ||||||||
\(195\) | −42.5604 | −3.04781 | ||||||||
\(196\) | −6.22668 | −0.444763 | ||||||||
\(197\) | 14.4561 | 1.02995 | 0.514976 | − | 0.857205i | \(-0.327801\pi\) | ||||
0.514976 | + | 0.857205i | \(0.327801\pi\) | |||||||
\(198\) | 1.78106 | 0.126574 | ||||||||
\(199\) | 5.71688 | 0.405259 | 0.202629 | − | 0.979255i | \(-0.435051\pi\) | ||||
0.202629 | + | 0.979255i | \(0.435051\pi\) | |||||||
\(200\) | 7.47565 | 0.528608 | ||||||||
\(201\) | −16.0351 | −1.13103 | ||||||||
\(202\) | 1.08647 | 0.0764435 | ||||||||
\(203\) | −2.87433 | −0.201739 | ||||||||
\(204\) | −5.63816 | −0.394750 | ||||||||
\(205\) | 30.3114 | 2.11704 | ||||||||
\(206\) | −11.2148 | −0.781374 | ||||||||
\(207\) | −3.10607 | −0.215887 | ||||||||
\(208\) | 6.41147 | 0.444556 | ||||||||
\(209\) | −15.5253 | −1.07391 | ||||||||
\(210\) | 5.83750 | 0.402826 | ||||||||
\(211\) | −7.66550 | −0.527715 | −0.263857 | − | 0.964562i | \(-0.584995\pi\) | ||||
−0.263857 | + | 0.964562i | \(0.584995\pi\) | |||||||
\(212\) | 0.268571 | 0.0184455 | ||||||||
\(213\) | −24.7101 | −1.69311 | ||||||||
\(214\) | 9.59627 | 0.655987 | ||||||||
\(215\) | −19.8357 | −1.35279 | ||||||||
\(216\) | 4.63816 | 0.315587 | ||||||||
\(217\) | −0.985452 | −0.0668968 | ||||||||
\(218\) | 2.22163 | 0.150468 | ||||||||
\(219\) | 16.1138 | 1.08887 | ||||||||
\(220\) | 11.8229 | 0.797103 | ||||||||
\(221\) | 19.2344 | 1.29385 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.99226 | −0.133412 | −0.0667058 | − | 0.997773i | \(-0.521249\pi\) | ||||
−0.0667058 | + | 0.997773i | \(0.521249\pi\) | |||||||
\(224\) | −0.879385 | −0.0587564 | ||||||||
\(225\) | 3.97771 | 0.265181 | ||||||||
\(226\) | 4.63041 | 0.308011 | ||||||||
\(227\) | 19.4834 | 1.29316 | 0.646579 | − | 0.762847i | \(-0.276199\pi\) | ||||
0.646579 | + | 0.762847i | \(0.276199\pi\) | |||||||
\(228\) | 8.71688 | 0.577290 | ||||||||
\(229\) | −12.8152 | −0.846853 | −0.423426 | − | 0.905931i | \(-0.639173\pi\) | ||||
−0.423426 | + | 0.905931i | \(0.639173\pi\) | |||||||
\(230\) | −20.6186 | −1.35955 | ||||||||
\(231\) | 5.53209 | 0.363985 | ||||||||
\(232\) | 3.26857 | 0.214592 | ||||||||
\(233\) | 2.91622 | 0.191048 | 0.0955240 | − | 0.995427i | \(-0.469547\pi\) | ||||
0.0955240 | + | 0.995427i | \(0.469547\pi\) | |||||||
\(234\) | 3.41147 | 0.223015 | ||||||||
\(235\) | −18.1138 | −1.18161 | ||||||||
\(236\) | −7.61856 | −0.495926 | ||||||||
\(237\) | −21.7665 | −1.41389 | ||||||||
\(238\) | −2.63816 | −0.171006 | ||||||||
\(239\) | −16.0128 | −1.03578 | −0.517891 | − | 0.855447i | \(-0.673283\pi\) | ||||
−0.517891 | + | 0.855447i | \(0.673283\pi\) | |||||||
\(240\) | −6.63816 | −0.428491 | ||||||||
\(241\) | −9.78880 | −0.630552 | −0.315276 | − | 0.949000i | \(-0.602097\pi\) | ||||
−0.315276 | + | 0.949000i | \(0.602097\pi\) | |||||||
\(242\) | 0.204393 | 0.0131389 | ||||||||
\(243\) | 5.46791 | 0.350767 | ||||||||
\(244\) | −2.12836 | −0.136254 | ||||||||
\(245\) | −21.9932 | −1.40509 | ||||||||
\(246\) | −16.1284 | −1.02831 | ||||||||
\(247\) | −29.7374 | −1.89215 | ||||||||
\(248\) | 1.12061 | 0.0711591 | ||||||||
\(249\) | −7.83750 | −0.496681 | ||||||||
\(250\) | 8.74422 | 0.553033 | ||||||||
\(251\) | −16.7442 | −1.05689 | −0.528443 | − | 0.848969i | \(-0.677224\pi\) | ||||
−0.528443 | + | 0.848969i | \(0.677224\pi\) | |||||||
\(252\) | −0.467911 | −0.0294756 | ||||||||
\(253\) | −19.5398 | −1.22846 | ||||||||
\(254\) | −5.08647 | −0.319153 | ||||||||
\(255\) | −19.9145 | −1.24709 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 21.7716 | 1.35807 | 0.679036 | − | 0.734105i | \(-0.262398\pi\) | ||||
0.679036 | + | 0.734105i | \(0.262398\pi\) | |||||||
\(258\) | 10.5544 | 0.657087 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 22.6459 | 1.40444 | ||||||||
\(261\) | 1.73917 | 0.107652 | ||||||||
\(262\) | −3.26083 | −0.201455 | ||||||||
\(263\) | 21.1857 | 1.30637 | 0.653184 | − | 0.757199i | \(-0.273433\pi\) | ||||
0.653184 | + | 0.757199i | \(0.273433\pi\) | |||||||
\(264\) | −6.29086 | −0.387176 | ||||||||
\(265\) | 0.948615 | 0.0582730 | ||||||||
\(266\) | 4.07873 | 0.250083 | ||||||||
\(267\) | 15.7392 | 0.963222 | ||||||||
\(268\) | 8.53209 | 0.521180 | ||||||||
\(269\) | 20.2317 | 1.23355 | 0.616775 | − | 0.787139i | \(-0.288439\pi\) | ||||
0.616775 | + | 0.787139i | \(0.288439\pi\) | |||||||
\(270\) | 16.3824 | 0.997000 | ||||||||
\(271\) | −13.3405 | −0.810377 | −0.405189 | − | 0.914233i | \(-0.632794\pi\) | ||||
−0.405189 | + | 0.914233i | \(0.632794\pi\) | |||||||
\(272\) | 3.00000 | 0.181902 | ||||||||
\(273\) | 10.5963 | 0.641315 | ||||||||
\(274\) | −1.59627 | −0.0964340 | ||||||||
\(275\) | 25.0232 | 1.50896 | ||||||||
\(276\) | 10.9709 | 0.660371 | ||||||||
\(277\) | −32.2627 | −1.93848 | −0.969239 | − | 0.246122i | \(-0.920844\pi\) | ||||
−0.969239 | + | 0.246122i | \(0.920844\pi\) | |||||||
\(278\) | 11.8033 | 0.707918 | ||||||||
\(279\) | 0.596267 | 0.0356976 | ||||||||
\(280\) | −3.10607 | −0.185623 | ||||||||
\(281\) | −4.31727 | −0.257547 | −0.128773 | − | 0.991674i | \(-0.541104\pi\) | ||||
−0.128773 | + | 0.991674i | \(0.541104\pi\) | |||||||
\(282\) | 9.63816 | 0.573944 | ||||||||
\(283\) | −1.34224 | −0.0797881 | −0.0398941 | − | 0.999204i | \(-0.512702\pi\) | ||||
−0.0398941 | + | 0.999204i | \(0.512702\pi\) | |||||||
\(284\) | 13.1480 | 0.780188 | ||||||||
\(285\) | 30.7888 | 1.82377 | ||||||||
\(286\) | 21.4611 | 1.26902 | ||||||||
\(287\) | −7.54664 | −0.445464 | ||||||||
\(288\) | 0.532089 | 0.0313536 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 11.5449 | 0.677939 | ||||||||
\(291\) | −32.0702 | −1.87999 | ||||||||
\(292\) | −8.57398 | −0.501754 | ||||||||
\(293\) | 2.75877 | 0.161169 | 0.0805845 | − | 0.996748i | \(-0.474321\pi\) | ||||
0.0805845 | + | 0.996748i | \(0.474321\pi\) | |||||||
\(294\) | 11.7023 | 0.682494 | ||||||||
\(295\) | −26.9094 | −1.56673 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 15.5253 | 0.900868 | ||||||||
\(298\) | −12.6604 | −0.733400 | ||||||||
\(299\) | −37.4270 | −2.16446 | ||||||||
\(300\) | −14.0496 | −0.811156 | ||||||||
\(301\) | 4.93851 | 0.284651 | ||||||||
\(302\) | −4.53983 | −0.261238 | ||||||||
\(303\) | −2.04189 | −0.117303 | ||||||||
\(304\) | −4.63816 | −0.266016 | ||||||||
\(305\) | −7.51754 | −0.430453 | ||||||||
\(306\) | 1.59627 | 0.0912525 | ||||||||
\(307\) | −6.58853 | −0.376027 | −0.188014 | − | 0.982166i | \(-0.560205\pi\) | ||||
−0.188014 | + | 0.982166i | \(0.560205\pi\) | |||||||
\(308\) | −2.94356 | −0.167725 | ||||||||
\(309\) | 21.0770 | 1.19903 | ||||||||
\(310\) | 3.95811 | 0.224806 | ||||||||
\(311\) | 19.0351 | 1.07938 | 0.539690 | − | 0.841864i | \(-0.318541\pi\) | ||||
0.539690 | + | 0.841864i | \(0.318541\pi\) | |||||||
\(312\) | −12.0496 | −0.682176 | ||||||||
\(313\) | 12.8152 | 0.724358 | 0.362179 | − | 0.932108i | \(-0.382033\pi\) | ||||
0.362179 | + | 0.932108i | \(0.382033\pi\) | |||||||
\(314\) | −17.8794 | −1.00899 | ||||||||
\(315\) | −1.65270 | −0.0931193 | ||||||||
\(316\) | 11.5817 | 0.651523 | ||||||||
\(317\) | −19.5449 | −1.09775 | −0.548875 | − | 0.835904i | \(-0.684944\pi\) | ||||
−0.548875 | + | 0.835904i | \(0.684944\pi\) | |||||||
\(318\) | −0.504748 | −0.0283048 | ||||||||
\(319\) | 10.9409 | 0.612571 | ||||||||
\(320\) | 3.53209 | 0.197450 | ||||||||
\(321\) | −18.0351 | −1.00662 | ||||||||
\(322\) | 5.13341 | 0.286074 | ||||||||
\(323\) | −13.9145 | −0.774222 | ||||||||
\(324\) | −10.3131 | −0.572953 | ||||||||
\(325\) | 47.9299 | 2.65868 | ||||||||
\(326\) | 2.26857 | 0.125645 | ||||||||
\(327\) | −4.17530 | −0.230894 | ||||||||
\(328\) | 8.58172 | 0.473846 | ||||||||
\(329\) | 4.50980 | 0.248633 | ||||||||
\(330\) | −22.2199 | −1.22316 | ||||||||
\(331\) | −13.6973 | −0.752871 | −0.376435 | − | 0.926443i | \(-0.622850\pi\) | ||||
−0.376435 | + | 0.926443i | \(0.622850\pi\) | |||||||
\(332\) | 4.17024 | 0.228872 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 21.4466 | 1.17350 | ||||||||
\(335\) | 30.1361 | 1.64651 | ||||||||
\(336\) | 1.65270 | 0.0901624 | ||||||||
\(337\) | −5.11381 | −0.278567 | −0.139283 | − | 0.990253i | \(-0.544480\pi\) | ||||
−0.139283 | + | 0.990253i | \(0.544480\pi\) | |||||||
\(338\) | 28.1070 | 1.52882 | ||||||||
\(339\) | −8.70233 | −0.472646 | ||||||||
\(340\) | 10.5963 | 0.574663 | ||||||||
\(341\) | 3.75103 | 0.203130 | ||||||||
\(342\) | −2.46791 | −0.133449 | ||||||||
\(343\) | 11.6313 | 0.628034 | ||||||||
\(344\) | −5.61587 | −0.302787 | ||||||||
\(345\) | 38.7502 | 2.08624 | ||||||||
\(346\) | −11.2686 | −0.605802 | ||||||||
\(347\) | −14.9632 | −0.803265 | −0.401632 | − | 0.915801i | \(-0.631557\pi\) | ||||
−0.401632 | + | 0.915801i | \(0.631557\pi\) | |||||||
\(348\) | −6.14290 | −0.329294 | ||||||||
\(349\) | −13.3628 | −0.715293 | −0.357647 | − | 0.933857i | \(-0.616421\pi\) | ||||
−0.357647 | + | 0.933857i | \(0.616421\pi\) | |||||||
\(350\) | −6.57398 | −0.351394 | ||||||||
\(351\) | 29.7374 | 1.58727 | ||||||||
\(352\) | 3.34730 | 0.178411 | ||||||||
\(353\) | −8.15301 | −0.433941 | −0.216970 | − | 0.976178i | \(-0.569618\pi\) | ||||
−0.216970 | + | 0.976178i | \(0.569618\pi\) | |||||||
\(354\) | 14.3182 | 0.761004 | ||||||||
\(355\) | 46.4397 | 2.46477 | ||||||||
\(356\) | −8.37464 | −0.443855 | ||||||||
\(357\) | 4.95811 | 0.262411 | ||||||||
\(358\) | 6.43107 | 0.339893 | ||||||||
\(359\) | 1.08647 | 0.0573415 | 0.0286708 | − | 0.999589i | \(-0.490873\pi\) | ||||
0.0286708 | + | 0.999589i | \(0.490873\pi\) | |||||||
\(360\) | 1.87939 | 0.0990523 | ||||||||
\(361\) | 2.51249 | 0.132236 | ||||||||
\(362\) | 3.50299 | 0.184113 | ||||||||
\(363\) | −0.384133 | −0.0201618 | ||||||||
\(364\) | −5.63816 | −0.295520 | ||||||||
\(365\) | −30.2841 | −1.58514 | ||||||||
\(366\) | 4.00000 | 0.209083 | ||||||||
\(367\) | −31.7124 | −1.65538 | −0.827688 | − | 0.561189i | \(-0.810344\pi\) | ||||
−0.827688 | + | 0.561189i | \(0.810344\pi\) | |||||||
\(368\) | −5.83750 | −0.304301 | ||||||||
\(369\) | 4.56624 | 0.237709 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.236177 | −0.0122617 | ||||||||
\(372\) | −2.10607 | −0.109194 | ||||||||
\(373\) | 3.52023 | 0.182271 | 0.0911353 | − | 0.995839i | \(-0.470950\pi\) | ||||
0.0911353 | + | 0.995839i | \(0.470950\pi\) | |||||||
\(374\) | 10.0419 | 0.519254 | ||||||||
\(375\) | −16.4338 | −0.848636 | ||||||||
\(376\) | −5.12836 | −0.264475 | ||||||||
\(377\) | 20.9564 | 1.07931 | ||||||||
\(378\) | −4.07873 | −0.209787 | ||||||||
\(379\) | −12.3277 | −0.633231 | −0.316616 | − | 0.948554i | \(-0.602547\pi\) | ||||
−0.316616 | + | 0.948554i | \(0.602547\pi\) | |||||||
\(380\) | −16.3824 | −0.840398 | ||||||||
\(381\) | 9.55943 | 0.489744 | ||||||||
\(382\) | 13.9240 | 0.712412 | ||||||||
\(383\) | −24.4593 | −1.24981 | −0.624907 | − | 0.780699i | \(-0.714863\pi\) | ||||
−0.624907 | + | 0.780699i | \(0.714863\pi\) | |||||||
\(384\) | −1.87939 | −0.0959070 | ||||||||
\(385\) | −10.3969 | −0.529876 | ||||||||
\(386\) | 11.5767 | 0.589237 | ||||||||
\(387\) | −2.98814 | −0.151896 | ||||||||
\(388\) | 17.0642 | 0.866302 | ||||||||
\(389\) | −14.0865 | −0.714212 | −0.357106 | − | 0.934064i | \(-0.616237\pi\) | ||||
−0.357106 | + | 0.934064i | \(0.616237\pi\) | |||||||
\(390\) | −42.5604 | −2.15513 | ||||||||
\(391\) | −17.5125 | −0.885645 | ||||||||
\(392\) | −6.22668 | −0.314495 | ||||||||
\(393\) | 6.12836 | 0.309135 | ||||||||
\(394\) | 14.4561 | 0.728285 | ||||||||
\(395\) | 40.9077 | 2.05829 | ||||||||
\(396\) | 1.78106 | 0.0895016 | ||||||||
\(397\) | −16.3482 | −0.820494 | −0.410247 | − | 0.911974i | \(-0.634558\pi\) | ||||
−0.410247 | + | 0.911974i | \(0.634558\pi\) | |||||||
\(398\) | 5.71688 | 0.286561 | ||||||||
\(399\) | −7.66550 | −0.383755 | ||||||||
\(400\) | 7.47565 | 0.373783 | ||||||||
\(401\) | −32.2763 | −1.61180 | −0.805901 | − | 0.592050i | \(-0.798319\pi\) | ||||
−0.805901 | + | 0.592050i | \(0.798319\pi\) | |||||||
\(402\) | −16.0351 | −0.799757 | ||||||||
\(403\) | 7.18479 | 0.357900 | ||||||||
\(404\) | 1.08647 | 0.0540537 | ||||||||
\(405\) | −36.4270 | −1.81007 | ||||||||
\(406\) | −2.87433 | −0.142651 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −5.63816 | −0.279130 | ||||||||
\(409\) | 14.9932 | 0.741366 | 0.370683 | − | 0.928760i | \(-0.379124\pi\) | ||||
0.370683 | + | 0.928760i | \(0.379124\pi\) | |||||||
\(410\) | 30.3114 | 1.49697 | ||||||||
\(411\) | 3.00000 | 0.147979 | ||||||||
\(412\) | −11.2148 | −0.552515 | ||||||||
\(413\) | 6.69965 | 0.329668 | ||||||||
\(414\) | −3.10607 | −0.152655 | ||||||||
\(415\) | 14.7297 | 0.723051 | ||||||||
\(416\) | 6.41147 | 0.314348 | ||||||||
\(417\) | −22.1830 | −1.08631 | ||||||||
\(418\) | −15.5253 | −0.759366 | ||||||||
\(419\) | −34.7401 | −1.69717 | −0.848583 | − | 0.529063i | \(-0.822544\pi\) | ||||
−0.848583 | + | 0.529063i | \(0.822544\pi\) | |||||||
\(420\) | 5.83750 | 0.284841 | ||||||||
\(421\) | −15.8452 | −0.772250 | −0.386125 | − | 0.922447i | \(-0.626187\pi\) | ||||
−0.386125 | + | 0.922447i | \(0.626187\pi\) | |||||||
\(422\) | −7.66550 | −0.373151 | ||||||||
\(423\) | −2.72874 | −0.132676 | ||||||||
\(424\) | 0.268571 | 0.0130429 | ||||||||
\(425\) | 22.4270 | 1.08787 | ||||||||
\(426\) | −24.7101 | −1.19721 | ||||||||
\(427\) | 1.87164 | 0.0905752 | ||||||||
\(428\) | 9.59627 | 0.463853 | ||||||||
\(429\) | −40.3337 | −1.94733 | ||||||||
\(430\) | −19.8357 | −0.956564 | ||||||||
\(431\) | 22.4688 | 1.08229 | 0.541143 | − | 0.840931i | \(-0.317992\pi\) | ||||
0.541143 | + | 0.840931i | \(0.317992\pi\) | |||||||
\(432\) | 4.63816 | 0.223153 | ||||||||
\(433\) | −4.86247 | −0.233676 | −0.116838 | − | 0.993151i | \(-0.537276\pi\) | ||||
−0.116838 | + | 0.993151i | \(0.537276\pi\) | |||||||
\(434\) | −0.985452 | −0.0473032 | ||||||||
\(435\) | −21.6973 | −1.04031 | ||||||||
\(436\) | 2.22163 | 0.106397 | ||||||||
\(437\) | 27.0752 | 1.29518 | ||||||||
\(438\) | 16.1138 | 0.769948 | ||||||||
\(439\) | 32.3655 | 1.54472 | 0.772360 | − | 0.635185i | \(-0.219076\pi\) | ||||
0.772360 | + | 0.635185i | \(0.219076\pi\) | |||||||
\(440\) | 11.8229 | 0.563637 | ||||||||
\(441\) | −3.31315 | −0.157769 | ||||||||
\(442\) | 19.2344 | 0.914888 | ||||||||
\(443\) | −19.8844 | −0.944738 | −0.472369 | − | 0.881401i | \(-0.656601\pi\) | ||||
−0.472369 | + | 0.881401i | \(0.656601\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −29.5800 | −1.40222 | ||||||||
\(446\) | −1.99226 | −0.0943362 | ||||||||
\(447\) | 23.7939 | 1.12541 | ||||||||
\(448\) | −0.879385 | −0.0415470 | ||||||||
\(449\) | −15.2713 | −0.720695 | −0.360348 | − | 0.932818i | \(-0.617342\pi\) | ||||
−0.360348 | + | 0.932818i | \(0.617342\pi\) | |||||||
\(450\) | 3.97771 | 0.187511 | ||||||||
\(451\) | 28.7256 | 1.35263 | ||||||||
\(452\) | 4.63041 | 0.217796 | ||||||||
\(453\) | 8.53209 | 0.400873 | ||||||||
\(454\) | 19.4834 | 0.914401 | ||||||||
\(455\) | −19.9145 | −0.933605 | ||||||||
\(456\) | 8.71688 | 0.408205 | ||||||||
\(457\) | 13.4602 | 0.629640 | 0.314820 | − | 0.949151i | \(-0.398056\pi\) | ||||
0.314820 | + | 0.949151i | \(0.398056\pi\) | |||||||
\(458\) | −12.8152 | −0.598815 | ||||||||
\(459\) | 13.9145 | 0.649472 | ||||||||
\(460\) | −20.6186 | −0.961345 | ||||||||
\(461\) | 13.2422 | 0.616749 | 0.308375 | − | 0.951265i | \(-0.400215\pi\) | ||||
0.308375 | + | 0.951265i | \(0.400215\pi\) | |||||||
\(462\) | 5.53209 | 0.257376 | ||||||||
\(463\) | −10.7065 | −0.497571 | −0.248786 | − | 0.968559i | \(-0.580031\pi\) | ||||
−0.248786 | + | 0.968559i | \(0.580031\pi\) | |||||||
\(464\) | 3.26857 | 0.151740 | ||||||||
\(465\) | −7.43882 | −0.344967 | ||||||||
\(466\) | 2.91622 | 0.135091 | ||||||||
\(467\) | 15.7229 | 0.727568 | 0.363784 | − | 0.931483i | \(-0.381485\pi\) | ||||
0.363784 | + | 0.931483i | \(0.381485\pi\) | |||||||
\(468\) | 3.41147 | 0.157695 | ||||||||
\(469\) | −7.50299 | −0.346456 | ||||||||
\(470\) | −18.1138 | −0.835528 | ||||||||
\(471\) | 33.6023 | 1.54831 | ||||||||
\(472\) | −7.61856 | −0.350672 | ||||||||
\(473\) | −18.7980 | −0.864332 | ||||||||
\(474\) | −21.7665 | −0.999769 | ||||||||
\(475\) | −34.6732 | −1.59092 | ||||||||
\(476\) | −2.63816 | −0.120920 | ||||||||
\(477\) | 0.142903 | 0.00654310 | ||||||||
\(478\) | −16.0128 | −0.732408 | ||||||||
\(479\) | −29.8093 | −1.36202 | −0.681012 | − | 0.732273i | \(-0.738460\pi\) | ||||
−0.681012 | + | 0.732273i | \(0.738460\pi\) | |||||||
\(480\) | −6.63816 | −0.302989 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −9.78880 | −0.445868 | ||||||||
\(483\) | −9.64765 | −0.438983 | ||||||||
\(484\) | 0.204393 | 0.00929059 | ||||||||
\(485\) | 60.2722 | 2.73682 | ||||||||
\(486\) | 5.46791 | 0.248029 | ||||||||
\(487\) | 11.2550 | 0.510011 | 0.255005 | − | 0.966940i | \(-0.417923\pi\) | ||||
0.255005 | + | 0.966940i | \(0.417923\pi\) | |||||||
\(488\) | −2.12836 | −0.0963461 | ||||||||
\(489\) | −4.26352 | −0.192803 | ||||||||
\(490\) | −21.9932 | −0.993551 | ||||||||
\(491\) | 1.03952 | 0.0469131 | 0.0234566 | − | 0.999725i | \(-0.492533\pi\) | ||||
0.0234566 | + | 0.999725i | \(0.492533\pi\) | |||||||
\(492\) | −16.1284 | −0.727122 | ||||||||
\(493\) | 9.80571 | 0.441627 | ||||||||
\(494\) | −29.7374 | −1.33795 | ||||||||
\(495\) | 6.29086 | 0.282753 | ||||||||
\(496\) | 1.12061 | 0.0503171 | ||||||||
\(497\) | −11.5621 | −0.518632 | ||||||||
\(498\) | −7.83750 | −0.351207 | ||||||||
\(499\) | −35.6810 | −1.59730 | −0.798650 | − | 0.601796i | \(-0.794452\pi\) | ||||
−0.798650 | + | 0.601796i | \(0.794452\pi\) | |||||||
\(500\) | 8.74422 | 0.391054 | ||||||||
\(501\) | −40.3063 | −1.80075 | ||||||||
\(502\) | −16.7442 | −0.747331 | ||||||||
\(503\) | −25.4260 | −1.13369 | −0.566845 | − | 0.823824i | \(-0.691836\pi\) | ||||
−0.566845 | + | 0.823824i | \(0.691836\pi\) | |||||||
\(504\) | −0.467911 | −0.0208424 | ||||||||
\(505\) | 3.83750 | 0.170766 | ||||||||
\(506\) | −19.5398 | −0.868651 | ||||||||
\(507\) | −52.8239 | −2.34599 | ||||||||
\(508\) | −5.08647 | −0.225675 | ||||||||
\(509\) | 0.00680713 | 0.000301721 0 | 0.000150860 | − | 1.00000i | \(-0.499952\pi\) | ||||
0.000150860 | 1.00000i | \(0.499952\pi\) | ||||||||
\(510\) | −19.9145 | −0.881827 | ||||||||
\(511\) | 7.53983 | 0.333542 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −21.5125 | −0.949800 | ||||||||
\(514\) | 21.7716 | 0.960303 | ||||||||
\(515\) | −39.6117 | −1.74550 | ||||||||
\(516\) | 10.5544 | 0.464631 | ||||||||
\(517\) | −17.1661 | −0.754965 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.1780 | 0.929610 | ||||||||
\(520\) | 22.6459 | 0.993088 | ||||||||
\(521\) | 6.97864 | 0.305740 | 0.152870 | − | 0.988246i | \(-0.451148\pi\) | ||||
0.152870 | + | 0.988246i | \(0.451148\pi\) | |||||||
\(522\) | 1.73917 | 0.0761214 | ||||||||
\(523\) | −39.5408 | −1.72900 | −0.864498 | − | 0.502636i | \(-0.832364\pi\) | ||||
−0.864498 | + | 0.502636i | \(0.832364\pi\) | |||||||
\(524\) | −3.26083 | −0.142450 | ||||||||
\(525\) | 12.3550 | 0.539218 | ||||||||
\(526\) | 21.1857 | 0.923742 | ||||||||
\(527\) | 3.36184 | 0.146444 | ||||||||
\(528\) | −6.29086 | −0.273775 | ||||||||
\(529\) | 11.0764 | 0.481581 | ||||||||
\(530\) | 0.948615 | 0.0412052 | ||||||||
\(531\) | −4.05375 | −0.175918 | ||||||||
\(532\) | 4.07873 | 0.176835 | ||||||||
\(533\) | 55.0215 | 2.38324 | ||||||||
\(534\) | 15.7392 | 0.681101 | ||||||||
\(535\) | 33.8949 | 1.46540 | ||||||||
\(536\) | 8.53209 | 0.368530 | ||||||||
\(537\) | −12.0865 | −0.521570 | ||||||||
\(538\) | 20.2317 | 0.872252 | ||||||||
\(539\) | −20.8425 | −0.897752 | ||||||||
\(540\) | 16.3824 | 0.704985 | ||||||||
\(541\) | 11.8111 | 0.507798 | 0.253899 | − | 0.967231i | \(-0.418287\pi\) | ||||
0.253899 | + | 0.967231i | \(0.418287\pi\) | |||||||
\(542\) | −13.3405 | −0.573023 | ||||||||
\(543\) | −6.58347 | −0.282524 | ||||||||
\(544\) | 3.00000 | 0.128624 | ||||||||
\(545\) | 7.84699 | 0.336128 | ||||||||
\(546\) | 10.5963 | 0.453478 | ||||||||
\(547\) | −42.1165 | −1.80077 | −0.900386 | − | 0.435093i | \(-0.856716\pi\) | ||||
−0.900386 | + | 0.435093i | \(0.856716\pi\) | |||||||
\(548\) | −1.59627 | −0.0681891 | ||||||||
\(549\) | −1.13247 | −0.0483328 | ||||||||
\(550\) | 25.0232 | 1.06699 | ||||||||
\(551\) | −15.1601 | −0.645844 | ||||||||
\(552\) | 10.9709 | 0.466953 | ||||||||
\(553\) | −10.1848 | −0.433101 | ||||||||
\(554\) | −32.2627 | −1.37071 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11.8033 | 0.500573 | ||||||||
\(557\) | −12.3301 | −0.522441 | −0.261221 | − | 0.965279i | \(-0.584125\pi\) | ||||
−0.261221 | + | 0.965279i | \(0.584125\pi\) | |||||||
\(558\) | 0.596267 | 0.0252420 | ||||||||
\(559\) | −36.0060 | −1.52289 | ||||||||
\(560\) | −3.10607 | −0.131255 | ||||||||
\(561\) | −18.8726 | −0.796801 | ||||||||
\(562\) | −4.31727 | −0.182113 | ||||||||
\(563\) | −8.37733 | −0.353062 | −0.176531 | − | 0.984295i | \(-0.556488\pi\) | ||||
−0.176531 | + | 0.984295i | \(0.556488\pi\) | |||||||
\(564\) | 9.63816 | 0.405840 | ||||||||
\(565\) | 16.3550 | 0.688062 | ||||||||
\(566\) | −1.34224 | −0.0564187 | ||||||||
\(567\) | 9.06923 | 0.380872 | ||||||||
\(568\) | 13.1480 | 0.551676 | ||||||||
\(569\) | 8.29086 | 0.347571 | 0.173785 | − | 0.984784i | \(-0.444400\pi\) | ||||
0.173785 | + | 0.984784i | \(0.444400\pi\) | |||||||
\(570\) | 30.7888 | 1.28960 | ||||||||
\(571\) | 0.0196004 | 0.000820250 0 | 0.000410125 | − | 1.00000i | \(-0.499869\pi\) | ||||
0.000410125 | 1.00000i | \(0.499869\pi\) | ||||||||
\(572\) | 21.4611 | 0.897334 | ||||||||
\(573\) | −26.1685 | −1.09320 | ||||||||
\(574\) | −7.54664 | −0.314991 | ||||||||
\(575\) | −43.6391 | −1.81988 | ||||||||
\(576\) | 0.532089 | 0.0221704 | ||||||||
\(577\) | −5.80840 | −0.241807 | −0.120903 | − | 0.992664i | \(-0.538579\pi\) | ||||
−0.120903 | + | 0.992664i | \(0.538579\pi\) | |||||||
\(578\) | −8.00000 | −0.332756 | ||||||||
\(579\) | −21.7570 | −0.904191 | ||||||||
\(580\) | 11.5449 | 0.479375 | ||||||||
\(581\) | −3.66725 | −0.152143 | ||||||||
\(582\) | −32.0702 | −1.32935 | ||||||||
\(583\) | 0.898986 | 0.0372322 | ||||||||
\(584\) | −8.57398 | −0.354794 | ||||||||
\(585\) | 12.0496 | 0.498191 | ||||||||
\(586\) | 2.75877 | 0.113964 | ||||||||
\(587\) | 1.60307 | 0.0661659 | 0.0330830 | − | 0.999453i | \(-0.489467\pi\) | ||||
0.0330830 | + | 0.999453i | \(0.489467\pi\) | |||||||
\(588\) | 11.7023 | 0.482596 | ||||||||
\(589\) | −5.19759 | −0.214163 | ||||||||
\(590\) | −26.9094 | −1.10784 | ||||||||
\(591\) | −27.1685 | −1.11756 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26.7543 | 1.09867 | 0.549334 | − | 0.835603i | \(-0.314881\pi\) | ||||
0.549334 | + | 0.835603i | \(0.314881\pi\) | |||||||
\(594\) | 15.5253 | 0.637010 | ||||||||
\(595\) | −9.31820 | −0.382009 | ||||||||
\(596\) | −12.6604 | −0.518592 | ||||||||
\(597\) | −10.7442 | −0.439732 | ||||||||
\(598\) | −37.4270 | −1.53050 | ||||||||
\(599\) | −14.3746 | −0.587332 | −0.293666 | − | 0.955908i | \(-0.594875\pi\) | ||||
−0.293666 | + | 0.955908i | \(0.594875\pi\) | |||||||
\(600\) | −14.0496 | −0.573574 | ||||||||
\(601\) | 1.92303 | 0.0784420 | 0.0392210 | − | 0.999231i | \(-0.487512\pi\) | ||||
0.0392210 | + | 0.999231i | \(0.487512\pi\) | |||||||
\(602\) | 4.93851 | 0.201279 | ||||||||
\(603\) | 4.53983 | 0.184876 | ||||||||
\(604\) | −4.53983 | −0.184723 | ||||||||
\(605\) | 0.721934 | 0.0293508 | ||||||||
\(606\) | −2.04189 | −0.0829461 | ||||||||
\(607\) | −27.0678 | −1.09865 | −0.549324 | − | 0.835609i | \(-0.685115\pi\) | ||||
−0.549324 | + | 0.835609i | \(0.685115\pi\) | |||||||
\(608\) | −4.63816 | −0.188102 | ||||||||
\(609\) | 5.40198 | 0.218899 | ||||||||
\(610\) | −7.51754 | −0.304376 | ||||||||
\(611\) | −32.8803 | −1.33020 | ||||||||
\(612\) | 1.59627 | 0.0645253 | ||||||||
\(613\) | 30.1516 | 1.21781 | 0.608905 | − | 0.793243i | \(-0.291609\pi\) | ||||
0.608905 | + | 0.793243i | \(0.291609\pi\) | |||||||
\(614\) | −6.58853 | −0.265891 | ||||||||
\(615\) | −56.9668 | −2.29712 | ||||||||
\(616\) | −2.94356 | −0.118600 | ||||||||
\(617\) | −18.7050 | −0.753036 | −0.376518 | − | 0.926409i | \(-0.622879\pi\) | ||||
−0.376518 | + | 0.926409i | \(0.622879\pi\) | |||||||
\(618\) | 21.0770 | 0.847840 | ||||||||
\(619\) | −23.3783 | −0.939652 | −0.469826 | − | 0.882759i | \(-0.655683\pi\) | ||||
−0.469826 | + | 0.882759i | \(0.655683\pi\) | |||||||
\(620\) | 3.95811 | 0.158962 | ||||||||
\(621\) | −27.0752 | −1.08649 | ||||||||
\(622\) | 19.0351 | 0.763237 | ||||||||
\(623\) | 7.36453 | 0.295054 | ||||||||
\(624\) | −12.0496 | −0.482371 | ||||||||
\(625\) | −6.49289 | −0.259716 | ||||||||
\(626\) | 12.8152 | 0.512199 | ||||||||
\(627\) | 29.1780 | 1.16526 | ||||||||
\(628\) | −17.8794 | −0.713465 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −1.65270 | −0.0658453 | ||||||||
\(631\) | −21.5493 | −0.857865 | −0.428933 | − | 0.903337i | \(-0.641110\pi\) | ||||
−0.428933 | + | 0.903337i | \(0.641110\pi\) | |||||||
\(632\) | 11.5817 | 0.460696 | ||||||||
\(633\) | 14.4064 | 0.572604 | ||||||||
\(634\) | −19.5449 | −0.776226 | ||||||||
\(635\) | −17.9659 | −0.712953 | ||||||||
\(636\) | −0.504748 | −0.0200145 | ||||||||
\(637\) | −39.9222 | −1.58178 | ||||||||
\(638\) | 10.9409 | 0.433153 | ||||||||
\(639\) | 6.99588 | 0.276753 | ||||||||
\(640\) | 3.53209 | 0.139618 | ||||||||
\(641\) | −5.67324 | −0.224079 | −0.112040 | − | 0.993704i | \(-0.535738\pi\) | ||||
−0.112040 | + | 0.993704i | \(0.535738\pi\) | |||||||
\(642\) | −18.0351 | −0.711788 | ||||||||
\(643\) | 25.8958 | 1.02123 | 0.510615 | − | 0.859809i | \(-0.329418\pi\) | ||||
0.510615 | + | 0.859809i | \(0.329418\pi\) | |||||||
\(644\) | 5.13341 | 0.202285 | ||||||||
\(645\) | 37.2790 | 1.46786 | ||||||||
\(646\) | −13.9145 | −0.547457 | ||||||||
\(647\) | −10.2558 | −0.403196 | −0.201598 | − | 0.979468i | \(-0.564613\pi\) | ||||
−0.201598 | + | 0.979468i | \(0.564613\pi\) | |||||||
\(648\) | −10.3131 | −0.405139 | ||||||||
\(649\) | −25.5016 | −1.00102 | ||||||||
\(650\) | 47.9299 | 1.87997 | ||||||||
\(651\) | 1.85204 | 0.0725873 | ||||||||
\(652\) | 2.26857 | 0.0888441 | ||||||||
\(653\) | 33.1557 | 1.29748 | 0.648741 | − | 0.761009i | \(-0.275296\pi\) | ||||
0.648741 | + | 0.761009i | \(0.275296\pi\) | |||||||
\(654\) | −4.17530 | −0.163267 | ||||||||
\(655\) | −11.5175 | −0.450028 | ||||||||
\(656\) | 8.58172 | 0.335060 | ||||||||
\(657\) | −4.56212 | −0.177985 | ||||||||
\(658\) | 4.50980 | 0.175810 | ||||||||
\(659\) | 12.2335 | 0.476549 | 0.238275 | − | 0.971198i | \(-0.423418\pi\) | ||||
0.238275 | + | 0.971198i | \(0.423418\pi\) | |||||||
\(660\) | −22.2199 | −0.864907 | ||||||||
\(661\) | −16.5098 | −0.642157 | −0.321078 | − | 0.947053i | \(-0.604045\pi\) | ||||
−0.321078 | + | 0.947053i | \(0.604045\pi\) | |||||||
\(662\) | −13.6973 | −0.532360 | ||||||||
\(663\) | −36.1489 | −1.40391 | ||||||||
\(664\) | 4.17024 | 0.161837 | ||||||||
\(665\) | 14.4064 | 0.558657 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.0803 | −0.738791 | ||||||||
\(668\) | 21.4466 | 0.829792 | ||||||||
\(669\) | 3.74422 | 0.144760 | ||||||||
\(670\) | 30.1361 | 1.16426 | ||||||||
\(671\) | −7.12424 | −0.275028 | ||||||||
\(672\) | 1.65270 | 0.0637544 | ||||||||
\(673\) | −47.4475 | −1.82897 | −0.914483 | − | 0.404624i | \(-0.867402\pi\) | ||||
−0.914483 | + | 0.404624i | \(0.867402\pi\) | |||||||
\(674\) | −5.11381 | −0.196977 | ||||||||
\(675\) | 34.6732 | 1.33457 | ||||||||
\(676\) | 28.1070 | 1.08104 | ||||||||
\(677\) | −8.83244 | −0.339458 | −0.169729 | − | 0.985491i | \(-0.554289\pi\) | ||||
−0.169729 | + | 0.985491i | \(0.554289\pi\) | |||||||
\(678\) | −8.70233 | −0.334211 | ||||||||
\(679\) | −15.0060 | −0.575877 | ||||||||
\(680\) | 10.5963 | 0.406348 | ||||||||
\(681\) | −36.6168 | −1.40316 | ||||||||
\(682\) | 3.75103 | 0.143634 | ||||||||
\(683\) | −41.0077 | −1.56912 | −0.784559 | − | 0.620054i | \(-0.787111\pi\) | ||||
−0.784559 | + | 0.620054i | \(0.787111\pi\) | |||||||
\(684\) | −2.46791 | −0.0943629 | ||||||||
\(685\) | −5.63816 | −0.215423 | ||||||||
\(686\) | 11.6313 | 0.444087 | ||||||||
\(687\) | 24.0847 | 0.918889 | ||||||||
\(688\) | −5.61587 | −0.214103 | ||||||||
\(689\) | 1.72193 | 0.0656005 | ||||||||
\(690\) | 38.7502 | 1.47520 | ||||||||
\(691\) | 46.3779 | 1.76430 | 0.882150 | − | 0.470969i | \(-0.156096\pi\) | ||||
0.882150 | + | 0.470969i | \(0.156096\pi\) | |||||||
\(692\) | −11.2686 | −0.428367 | ||||||||
\(693\) | −1.56624 | −0.0594964 | ||||||||
\(694\) | −14.9632 | −0.567994 | ||||||||
\(695\) | 41.6905 | 1.58141 | ||||||||
\(696\) | −6.14290 | −0.232846 | ||||||||
\(697\) | 25.7452 | 0.975167 | ||||||||
\(698\) | −13.3628 | −0.505789 | ||||||||
\(699\) | −5.48070 | −0.207299 | ||||||||
\(700\) | −6.57398 | −0.248473 | ||||||||
\(701\) | −6.57129 | −0.248194 | −0.124097 | − | 0.992270i | \(-0.539603\pi\) | ||||
−0.124097 | + | 0.992270i | \(0.539603\pi\) | |||||||
\(702\) | 29.7374 | 1.12237 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 3.34730 | 0.126156 | ||||||||
\(705\) | 34.0428 | 1.28213 | ||||||||
\(706\) | −8.15301 | −0.306843 | ||||||||
\(707\) | −0.955423 | −0.0359324 | ||||||||
\(708\) | 14.3182 | 0.538111 | ||||||||
\(709\) | 13.3105 | 0.499885 | 0.249942 | − | 0.968261i | \(-0.419588\pi\) | ||||
0.249942 | + | 0.968261i | \(0.419588\pi\) | |||||||
\(710\) | 46.4397 | 1.74285 | ||||||||
\(711\) | 6.16250 | 0.231112 | ||||||||
\(712\) | −8.37464 | −0.313853 | ||||||||
\(713\) | −6.54158 | −0.244984 | ||||||||
\(714\) | 4.95811 | 0.185553 | ||||||||
\(715\) | 75.8025 | 2.83485 | ||||||||
\(716\) | 6.43107 | 0.240341 | ||||||||
\(717\) | 30.0942 | 1.12389 | ||||||||
\(718\) | 1.08647 | 0.0405466 | ||||||||
\(719\) | 18.5280 | 0.690977 | 0.345488 | − | 0.938423i | \(-0.387713\pi\) | ||||
0.345488 | + | 0.938423i | \(0.387713\pi\) | |||||||
\(720\) | 1.87939 | 0.0700406 | ||||||||
\(721\) | 9.86215 | 0.367286 | ||||||||
\(722\) | 2.51249 | 0.0935051 | ||||||||
\(723\) | 18.3969 | 0.684189 | ||||||||
\(724\) | 3.50299 | 0.130188 | ||||||||
\(725\) | 24.4347 | 0.907482 | ||||||||
\(726\) | −0.384133 | −0.0142565 | ||||||||
\(727\) | 22.4279 | 0.831804 | 0.415902 | − | 0.909409i | \(-0.363466\pi\) | ||||
0.415902 | + | 0.909409i | \(0.363466\pi\) | |||||||
\(728\) | −5.63816 | −0.208964 | ||||||||
\(729\) | 20.6631 | 0.765301 | ||||||||
\(730\) | −30.2841 | −1.12086 | ||||||||
\(731\) | −16.8476 | −0.623131 | ||||||||
\(732\) | 4.00000 | 0.147844 | ||||||||
\(733\) | −25.0300 | −0.924505 | −0.462253 | − | 0.886748i | \(-0.652959\pi\) | ||||
−0.462253 | + | 0.886748i | \(0.652959\pi\) | |||||||
\(734\) | −31.7124 | −1.17053 | ||||||||
\(735\) | 41.3337 | 1.52462 | ||||||||
\(736\) | −5.83750 | −0.215173 | ||||||||
\(737\) | 28.5594 | 1.05200 | ||||||||
\(738\) | 4.56624 | 0.168086 | ||||||||
\(739\) | 27.2327 | 1.00177 | 0.500885 | − | 0.865514i | \(-0.333008\pi\) | ||||
0.500885 | + | 0.865514i | \(0.333008\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 55.8881 | 2.05310 | ||||||||
\(742\) | −0.236177 | −0.00867033 | ||||||||
\(743\) | −2.23349 | −0.0819388 | −0.0409694 | − | 0.999160i | \(-0.513045\pi\) | ||||
−0.0409694 | + | 0.999160i | \(0.513045\pi\) | |||||||
\(744\) | −2.10607 | −0.0772122 | ||||||||
\(745\) | −44.7178 | −1.63833 | ||||||||
\(746\) | 3.52023 | 0.128885 | ||||||||
\(747\) | 2.21894 | 0.0811868 | ||||||||
\(748\) | 10.0419 | 0.367168 | ||||||||
\(749\) | −8.43882 | −0.308348 | ||||||||
\(750\) | −16.4338 | −0.600076 | ||||||||
\(751\) | −0.167881 | −0.00612605 | −0.00306302 | − | 0.999995i | \(-0.500975\pi\) | ||||
−0.00306302 | + | 0.999995i | \(0.500975\pi\) | |||||||
\(752\) | −5.12836 | −0.187012 | ||||||||
\(753\) | 31.4688 | 1.14679 | ||||||||
\(754\) | 20.9564 | 0.763185 | ||||||||
\(755\) | −16.0351 | −0.583576 | ||||||||
\(756\) | −4.07873 | −0.148342 | ||||||||
\(757\) | 34.9195 | 1.26917 | 0.634586 | − | 0.772852i | \(-0.281171\pi\) | ||||
0.634586 | + | 0.772852i | \(0.281171\pi\) | |||||||
\(758\) | −12.3277 | −0.447762 | ||||||||
\(759\) | 36.7229 | 1.33296 | ||||||||
\(760\) | −16.3824 | −0.594251 | ||||||||
\(761\) | −2.21719 | −0.0803729 | −0.0401865 | − | 0.999192i | \(-0.512795\pi\) | ||||
−0.0401865 | + | 0.999192i | \(0.512795\pi\) | |||||||
\(762\) | 9.55943 | 0.346302 | ||||||||
\(763\) | −1.95367 | −0.0707275 | ||||||||
\(764\) | 13.9240 | 0.503751 | ||||||||
\(765\) | 5.63816 | 0.203848 | ||||||||
\(766\) | −24.4593 | −0.883752 | ||||||||
\(767\) | −48.8462 | −1.76373 | ||||||||
\(768\) | −1.87939 | −0.0678165 | ||||||||
\(769\) | 52.1421 | 1.88029 | 0.940146 | − | 0.340772i | \(-0.110689\pi\) | ||||
0.940146 | + | 0.340772i | \(0.110689\pi\) | |||||||
\(770\) | −10.3969 | −0.374679 | ||||||||
\(771\) | −40.9172 | −1.47360 | ||||||||
\(772\) | 11.5767 | 0.416653 | ||||||||
\(773\) | 44.9786 | 1.61777 | 0.808885 | − | 0.587967i | \(-0.200072\pi\) | ||||
0.808885 | + | 0.587967i | \(0.200072\pi\) | |||||||
\(774\) | −2.98814 | −0.107406 | ||||||||
\(775\) | 8.37733 | 0.300922 | ||||||||
\(776\) | 17.0642 | 0.612568 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −14.0865 | −0.505024 | ||||||||
\(779\) | −39.8033 | −1.42610 | ||||||||
\(780\) | −42.5604 | −1.52391 | ||||||||
\(781\) | 44.0101 | 1.57481 | ||||||||
\(782\) | −17.5125 | −0.626245 | ||||||||
\(783\) | 15.1601 | 0.541779 | ||||||||
\(784\) | −6.22668 | −0.222381 | ||||||||
\(785\) | −63.1516 | −2.25398 | ||||||||
\(786\) | 6.12836 | 0.218591 | ||||||||
\(787\) | 54.9968 | 1.96042 | 0.980212 | − | 0.197949i | \(-0.0634280\pi\) | ||||
0.980212 | + | 0.197949i | \(0.0634280\pi\) | |||||||
\(788\) | 14.4561 | 0.514976 | ||||||||
\(789\) | −39.8161 | −1.41749 | ||||||||
\(790\) | 40.9077 | 1.45543 | ||||||||
\(791\) | −4.07192 | −0.144781 | ||||||||
\(792\) | 1.78106 | 0.0632872 | ||||||||
\(793\) | −13.6459 | −0.484580 | ||||||||
\(794\) | −16.3482 | −0.580177 | ||||||||
\(795\) | −1.78281 | −0.0632299 | ||||||||
\(796\) | 5.71688 | 0.202629 | ||||||||
\(797\) | 21.1138 | 0.747889 | 0.373945 | − | 0.927451i | \(-0.378005\pi\) | ||||
0.373945 | + | 0.927451i | \(0.378005\pi\) | |||||||
\(798\) | −7.66550 | −0.271356 | ||||||||
\(799\) | −15.3851 | −0.544285 | ||||||||
\(800\) | 7.47565 | 0.264304 | ||||||||
\(801\) | −4.45605 | −0.157447 | ||||||||
\(802\) | −32.2763 | −1.13972 | ||||||||
\(803\) | −28.6996 | −1.01279 | ||||||||
\(804\) | −16.0351 | −0.565514 | ||||||||
\(805\) | 18.1317 | 0.639057 | ||||||||
\(806\) | 7.18479 | 0.253074 | ||||||||
\(807\) | −38.0232 | −1.33848 | ||||||||
\(808\) | 1.08647 | 0.0382218 | ||||||||
\(809\) | −47.1634 | −1.65818 | −0.829089 | − | 0.559117i | \(-0.811140\pi\) | ||||
−0.829089 | + | 0.559117i | \(0.811140\pi\) | |||||||
\(810\) | −36.4270 | −1.27991 | ||||||||
\(811\) | −17.7466 | −0.623167 | −0.311583 | − | 0.950219i | \(-0.600859\pi\) | ||||
−0.311583 | + | 0.950219i | \(0.600859\pi\) | |||||||
\(812\) | −2.87433 | −0.100869 | ||||||||
\(813\) | 25.0719 | 0.879311 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.01279 | 0.280676 | ||||||||
\(816\) | −5.63816 | −0.197375 | ||||||||
\(817\) | 26.0473 | 0.911278 | ||||||||
\(818\) | 14.9932 | 0.524225 | ||||||||
\(819\) | −3.00000 | −0.104828 | ||||||||
\(820\) | 30.3114 | 1.05852 | ||||||||
\(821\) | −0.352349 | −0.0122971 | −0.00614853 | − | 0.999981i | \(-0.501957\pi\) | ||||
−0.00614853 | + | 0.999981i | \(0.501957\pi\) | |||||||
\(822\) | 3.00000 | 0.104637 | ||||||||
\(823\) | 45.1661 | 1.57439 | 0.787196 | − | 0.616703i | \(-0.211532\pi\) | ||||
0.787196 | + | 0.616703i | \(0.211532\pi\) | |||||||
\(824\) | −11.2148 | −0.390687 | ||||||||
\(825\) | −47.0283 | −1.63731 | ||||||||
\(826\) | 6.69965 | 0.233110 | ||||||||
\(827\) | 1.03003 | 0.0358176 | 0.0179088 | − | 0.999840i | \(-0.494299\pi\) | ||||
0.0179088 | + | 0.999840i | \(0.494299\pi\) | |||||||
\(828\) | −3.10607 | −0.107943 | ||||||||
\(829\) | 45.5553 | 1.58220 | 0.791101 | − | 0.611686i | \(-0.209508\pi\) | ||||
0.791101 | + | 0.611686i | \(0.209508\pi\) | |||||||
\(830\) | 14.7297 | 0.511274 | ||||||||
\(831\) | 60.6340 | 2.10337 | ||||||||
\(832\) | 6.41147 | 0.222278 | ||||||||
\(833\) | −18.6800 | −0.647225 | ||||||||
\(834\) | −22.1830 | −0.768136 | ||||||||
\(835\) | 75.7511 | 2.62148 | ||||||||
\(836\) | −15.5253 | −0.536953 | ||||||||
\(837\) | 5.19759 | 0.179655 | ||||||||
\(838\) | −34.7401 | −1.20008 | ||||||||
\(839\) | −38.8786 | −1.34224 | −0.671119 | − | 0.741350i | \(-0.734186\pi\) | ||||
−0.671119 | + | 0.741350i | \(0.734186\pi\) | |||||||
\(840\) | 5.83750 | 0.201413 | ||||||||
\(841\) | −18.3164 | −0.631602 | ||||||||
\(842\) | −15.8452 | −0.546063 | ||||||||
\(843\) | 8.11381 | 0.279454 | ||||||||
\(844\) | −7.66550 | −0.263857 | ||||||||
\(845\) | 99.2764 | 3.41521 | ||||||||
\(846\) | −2.72874 | −0.0938160 | ||||||||
\(847\) | −0.179740 | −0.00617594 | ||||||||
\(848\) | 0.268571 | 0.00922275 | ||||||||
\(849\) | 2.52259 | 0.0865752 | ||||||||
\(850\) | 22.4270 | 0.769238 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −24.7101 | −0.846553 | ||||||||
\(853\) | 38.6783 | 1.32432 | 0.662160 | − | 0.749363i | \(-0.269640\pi\) | ||||
0.662160 | + | 0.749363i | \(0.269640\pi\) | |||||||
\(854\) | 1.87164 | 0.0640464 | ||||||||
\(855\) | −8.71688 | −0.298111 | ||||||||
\(856\) | 9.59627 | 0.327994 | ||||||||
\(857\) | −43.6965 | −1.49264 | −0.746321 | − | 0.665586i | \(-0.768182\pi\) | ||||
−0.746321 | + | 0.665586i | \(0.768182\pi\) | |||||||
\(858\) | −40.3337 | −1.37697 | ||||||||
\(859\) | 43.3364 | 1.47862 | 0.739309 | − | 0.673366i | \(-0.235152\pi\) | ||||
0.739309 | + | 0.673366i | \(0.235152\pi\) | |||||||
\(860\) | −19.8357 | −0.676393 | ||||||||
\(861\) | 14.1830 | 0.483357 | ||||||||
\(862\) | 22.4688 | 0.765292 | ||||||||
\(863\) | −40.0847 | −1.36450 | −0.682250 | − | 0.731119i | \(-0.738998\pi\) | ||||
−0.682250 | + | 0.731119i | \(0.738998\pi\) | |||||||
\(864\) | 4.63816 | 0.157793 | ||||||||
\(865\) | −39.8016 | −1.35329 | ||||||||
\(866\) | −4.86247 | −0.165234 | ||||||||
\(867\) | 15.0351 | 0.510618 | ||||||||
\(868\) | −0.985452 | −0.0334484 | ||||||||
\(869\) | 38.7674 | 1.31510 | ||||||||
\(870\) | −21.6973 | −0.735607 | ||||||||
\(871\) | 54.7033 | 1.85355 | ||||||||
\(872\) | 2.22163 | 0.0752339 | ||||||||
\(873\) | 9.07966 | 0.307300 | ||||||||
\(874\) | 27.0752 | 0.915833 | ||||||||
\(875\) | −7.68954 | −0.259954 | ||||||||
\(876\) | 16.1138 | 0.544435 | ||||||||
\(877\) | −52.2731 | −1.76514 | −0.882569 | − | 0.470183i | \(-0.844188\pi\) | ||||
−0.882569 | + | 0.470183i | \(0.844188\pi\) | |||||||
\(878\) | 32.3655 | 1.09228 | ||||||||
\(879\) | −5.18479 | −0.174879 | ||||||||
\(880\) | 11.8229 | 0.398552 | ||||||||
\(881\) | −23.9195 | −0.805869 | −0.402935 | − | 0.915229i | \(-0.632010\pi\) | ||||
−0.402935 | + | 0.915229i | \(0.632010\pi\) | |||||||
\(882\) | −3.31315 | −0.111559 | ||||||||
\(883\) | −13.4311 | −0.451992 | −0.225996 | − | 0.974128i | \(-0.572564\pi\) | ||||
−0.225996 | + | 0.974128i | \(0.572564\pi\) | |||||||
\(884\) | 19.2344 | 0.646924 | ||||||||
\(885\) | 50.5732 | 1.70000 | ||||||||
\(886\) | −19.8844 | −0.668031 | ||||||||
\(887\) | 49.3242 | 1.65614 | 0.828072 | − | 0.560622i | \(-0.189438\pi\) | ||||
0.828072 | + | 0.560622i | \(0.189438\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.47296 | 0.150018 | ||||||||
\(890\) | −29.5800 | −0.991523 | ||||||||
\(891\) | −34.5212 | −1.15650 | ||||||||
\(892\) | −1.99226 | −0.0667058 | ||||||||
\(893\) | 23.7861 | 0.795972 | ||||||||
\(894\) | 23.7939 | 0.795785 | ||||||||
\(895\) | 22.7151 | 0.759283 | ||||||||
\(896\) | −0.879385 | −0.0293782 | ||||||||
\(897\) | 70.3397 | 2.34857 | ||||||||
\(898\) | −15.2713 | −0.509609 | ||||||||
\(899\) | 3.66281 | 0.122162 | ||||||||
\(900\) | 3.97771 | 0.132590 | ||||||||
\(901\) | 0.805712 | 0.0268422 | ||||||||
\(902\) | 28.7256 | 0.956456 | ||||||||
\(903\) | −9.28136 | −0.308864 | ||||||||
\(904\) | 4.63041 | 0.154005 | ||||||||
\(905\) | 12.3729 | 0.411289 | ||||||||
\(906\) | 8.53209 | 0.283460 | ||||||||
\(907\) | 43.9522 | 1.45941 | 0.729705 | − | 0.683762i | \(-0.239657\pi\) | ||||
0.729705 | + | 0.683762i | \(0.239657\pi\) | |||||||
\(908\) | 19.4834 | 0.646579 | ||||||||
\(909\) | 0.578097 | 0.0191743 | ||||||||
\(910\) | −19.9145 | −0.660158 | ||||||||
\(911\) | −16.0597 | −0.532083 | −0.266041 | − | 0.963962i | \(-0.585716\pi\) | ||||
−0.266041 | + | 0.963962i | \(0.585716\pi\) | |||||||
\(912\) | 8.71688 | 0.288645 | ||||||||
\(913\) | 13.9590 | 0.461977 | ||||||||
\(914\) | 13.4602 | 0.445223 | ||||||||
\(915\) | 14.1284 | 0.467069 | ||||||||
\(916\) | −12.8152 | −0.423426 | ||||||||
\(917\) | 2.86753 | 0.0946940 | ||||||||
\(918\) | 13.9145 | 0.459246 | ||||||||
\(919\) | −34.6468 | −1.14289 | −0.571447 | − | 0.820639i | \(-0.693618\pi\) | ||||
−0.571447 | + | 0.820639i | \(0.693618\pi\) | |||||||
\(920\) | −20.6186 | −0.679774 | ||||||||
\(921\) | 12.3824 | 0.408013 | ||||||||
\(922\) | 13.2422 | 0.436107 | ||||||||
\(923\) | 84.2978 | 2.77470 | ||||||||
\(924\) | 5.53209 | 0.181992 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −10.7065 | −0.351836 | ||||||||
\(927\) | −5.96728 | −0.195991 | ||||||||
\(928\) | 3.26857 | 0.107296 | ||||||||
\(929\) | −48.5577 | −1.59313 | −0.796563 | − | 0.604556i | \(-0.793351\pi\) | ||||
−0.796563 | + | 0.604556i | \(0.793351\pi\) | |||||||
\(930\) | −7.43882 | −0.243928 | ||||||||
\(931\) | 28.8803 | 0.946514 | ||||||||
\(932\) | 2.91622 | 0.0955240 | ||||||||
\(933\) | −35.7743 | −1.17120 | ||||||||
\(934\) | 15.7229 | 0.514468 | ||||||||
\(935\) | 35.4688 | 1.15996 | ||||||||
\(936\) | 3.41147 | 0.111508 | ||||||||
\(937\) | 48.9617 | 1.59951 | 0.799755 | − | 0.600326i | \(-0.204963\pi\) | ||||
0.799755 | + | 0.600326i | \(0.204963\pi\) | |||||||
\(938\) | −7.50299 | −0.244981 | ||||||||
\(939\) | −24.0847 | −0.785975 | ||||||||
\(940\) | −18.1138 | −0.590807 | ||||||||
\(941\) | −17.5012 | −0.570524 | −0.285262 | − | 0.958450i | \(-0.592081\pi\) | ||||
−0.285262 | + | 0.958450i | \(0.592081\pi\) | |||||||
\(942\) | 33.6023 | 1.09482 | ||||||||
\(943\) | −50.0958 | −1.63134 | ||||||||
\(944\) | −7.61856 | −0.247963 | ||||||||
\(945\) | −14.4064 | −0.468641 | ||||||||
\(946\) | −18.7980 | −0.611175 | ||||||||
\(947\) | 17.3223 | 0.562900 | 0.281450 | − | 0.959576i | \(-0.409185\pi\) | ||||
0.281450 | + | 0.959576i | \(0.409185\pi\) | |||||||
\(948\) | −21.7665 | −0.706943 | ||||||||
\(949\) | −54.9718 | −1.78446 | ||||||||
\(950\) | −34.6732 | −1.12495 | ||||||||
\(951\) | 36.7324 | 1.19113 | ||||||||
\(952\) | −2.63816 | −0.0855031 | ||||||||
\(953\) | −38.8522 | −1.25854 | −0.629272 | − | 0.777185i | \(-0.716647\pi\) | ||||
−0.629272 | + | 0.777185i | \(0.716647\pi\) | |||||||
\(954\) | 0.142903 | 0.00462667 | ||||||||
\(955\) | 49.1807 | 1.59145 | ||||||||
\(956\) | −16.0128 | −0.517891 | ||||||||
\(957\) | −20.5621 | −0.664679 | ||||||||
\(958\) | −29.8093 | −0.963096 | ||||||||
\(959\) | 1.40373 | 0.0453289 | ||||||||
\(960\) | −6.63816 | −0.214246 | ||||||||
\(961\) | −29.7442 | −0.959491 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.10607 | 0.164541 | ||||||||
\(964\) | −9.78880 | −0.315276 | ||||||||
\(965\) | 40.8898 | 1.31629 | ||||||||
\(966\) | −9.64765 | −0.310408 | ||||||||
\(967\) | 44.5827 | 1.43368 | 0.716841 | − | 0.697237i | \(-0.245587\pi\) | ||||
0.716841 | + | 0.697237i | \(0.245587\pi\) | |||||||
\(968\) | 0.204393 | 0.00656944 | ||||||||
\(969\) | 26.1506 | 0.840080 | ||||||||
\(970\) | 60.2722 | 1.93522 | ||||||||
\(971\) | −57.1525 | −1.83411 | −0.917056 | − | 0.398759i | \(-0.869441\pi\) | ||||
−0.917056 | + | 0.398759i | \(0.869441\pi\) | |||||||
\(972\) | 5.46791 | 0.175383 | ||||||||
\(973\) | −10.3797 | −0.332758 | ||||||||
\(974\) | 11.2550 | 0.360632 | ||||||||
\(975\) | −90.0788 | −2.88483 | ||||||||
\(976\) | −2.12836 | −0.0681270 | ||||||||
\(977\) | 34.8489 | 1.11491 | 0.557457 | − | 0.830206i | \(-0.311777\pi\) | ||||
0.557457 | + | 0.830206i | \(0.311777\pi\) | |||||||
\(978\) | −4.26352 | −0.136332 | ||||||||
\(979\) | −28.0324 | −0.895919 | ||||||||
\(980\) | −21.9932 | −0.702547 | ||||||||
\(981\) | 1.18210 | 0.0377417 | ||||||||
\(982\) | 1.03952 | 0.0331726 | ||||||||
\(983\) | −1.06955 | −0.0341135 | −0.0170567 | − | 0.999855i | \(-0.505430\pi\) | ||||
−0.0170567 | + | 0.999855i | \(0.505430\pi\) | |||||||
\(984\) | −16.1284 | −0.514153 | ||||||||
\(985\) | 51.0601 | 1.62691 | ||||||||
\(986\) | 9.80571 | 0.312277 | ||||||||
\(987\) | −8.47565 | −0.269783 | ||||||||
\(988\) | −29.7374 | −0.946073 | ||||||||
\(989\) | 32.7826 | 1.04243 | ||||||||
\(990\) | 6.29086 | 0.199937 | ||||||||
\(991\) | 20.3250 | 0.645645 | 0.322823 | − | 0.946460i | \(-0.395368\pi\) | ||||
0.322823 | + | 0.946460i | \(0.395368\pi\) | |||||||
\(992\) | 1.12061 | 0.0355796 | ||||||||
\(993\) | 25.7425 | 0.816913 | ||||||||
\(994\) | −11.5621 | −0.366728 | ||||||||
\(995\) | 20.1925 | 0.640146 | ||||||||
\(996\) | −7.83750 | −0.248341 | ||||||||
\(997\) | 46.2404 | 1.46445 | 0.732224 | − | 0.681064i | \(-0.238482\pi\) | ||||
0.732224 | + | 0.681064i | \(0.238482\pi\) | |||||||
\(998\) | −35.6810 | −1.12946 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2738.2.a.p.1.1 | 3 | ||
37.21 | even | 18 | 74.2.f.a.71.1 | yes | 6 | ||
37.30 | even | 18 | 74.2.f.a.49.1 | ✓ | 6 | ||
37.36 | even | 2 | 2738.2.a.m.1.1 | 3 | |||
111.95 | odd | 18 | 666.2.x.c.145.1 | 6 | |||
111.104 | odd | 18 | 666.2.x.c.271.1 | 6 | |||
148.67 | odd | 18 | 592.2.bc.b.49.1 | 6 | |||
148.95 | odd | 18 | 592.2.bc.b.145.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.2.f.a.49.1 | ✓ | 6 | 37.30 | even | 18 | ||
74.2.f.a.71.1 | yes | 6 | 37.21 | even | 18 | ||
592.2.bc.b.49.1 | 6 | 148.67 | odd | 18 | |||
592.2.bc.b.145.1 | 6 | 148.95 | odd | 18 | |||
666.2.x.c.145.1 | 6 | 111.95 | odd | 18 | |||
666.2.x.c.271.1 | 6 | 111.104 | odd | 18 | |||
2738.2.a.m.1.1 | 3 | 37.36 | even | 2 | |||
2738.2.a.p.1.1 | 3 | 1.1 | even | 1 | trivial |