Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4029,2,Mod(1,4029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4029, 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("4029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4029 = 3 \cdot 17 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4029.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1717269744\) |
Analytic rank: | \(0\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 4029.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.22001 | −1.56978 | −0.784890 | − | 0.619635i | \(-0.787281\pi\) | ||||
−0.784890 | + | 0.619635i | \(0.787281\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 2.92842 | 1.46421 | ||||||||
\(5\) | −1.63428 | −0.730873 | −0.365437 | − | 0.930836i | \(-0.619080\pi\) | ||||
−0.365437 | + | 0.930836i | \(0.619080\pi\) | |||||||
\(6\) | −2.22001 | −0.906313 | ||||||||
\(7\) | −1.90265 | −0.719134 | −0.359567 | − | 0.933119i | \(-0.617076\pi\) | ||||
−0.359567 | + | 0.933119i | \(0.617076\pi\) | |||||||
\(8\) | −2.06110 | −0.728710 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.62811 | 1.14731 | ||||||||
\(11\) | −4.46342 | −1.34577 | −0.672886 | − | 0.739746i | \(-0.734946\pi\) | ||||
−0.672886 | + | 0.739746i | \(0.734946\pi\) | |||||||
\(12\) | 2.92842 | 0.845363 | ||||||||
\(13\) | −1.29449 | −0.359028 | −0.179514 | − | 0.983755i | \(-0.557453\pi\) | ||||
−0.179514 | + | 0.983755i | \(0.557453\pi\) | |||||||
\(14\) | 4.22389 | 1.12888 | ||||||||
\(15\) | −1.63428 | −0.421970 | ||||||||
\(16\) | −1.28119 | −0.320296 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −2.22001 | −0.523260 | ||||||||
\(19\) | −6.67824 | −1.53209 | −0.766047 | − | 0.642785i | \(-0.777779\pi\) | ||||
−0.766047 | + | 0.642785i | \(0.777779\pi\) | |||||||
\(20\) | −4.78587 | −1.07015 | ||||||||
\(21\) | −1.90265 | −0.415192 | ||||||||
\(22\) | 9.90882 | 2.11257 | ||||||||
\(23\) | 5.41253 | 1.12859 | 0.564295 | − | 0.825573i | \(-0.309148\pi\) | ||||
0.564295 | + | 0.825573i | \(0.309148\pi\) | |||||||
\(24\) | −2.06110 | −0.420721 | ||||||||
\(25\) | −2.32912 | −0.465824 | ||||||||
\(26\) | 2.87378 | 0.563596 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −5.57176 | −1.05296 | ||||||||
\(29\) | −0.385878 | −0.0716557 | −0.0358278 | − | 0.999358i | \(-0.511407\pi\) | ||||
−0.0358278 | + | 0.999358i | \(0.511407\pi\) | |||||||
\(30\) | 3.62811 | 0.662400 | ||||||||
\(31\) | −4.16741 | −0.748490 | −0.374245 | − | 0.927330i | \(-0.622098\pi\) | ||||
−0.374245 | + | 0.927330i | \(0.622098\pi\) | |||||||
\(32\) | 6.96645 | 1.23151 | ||||||||
\(33\) | −4.46342 | −0.776982 | ||||||||
\(34\) | −2.22001 | −0.380728 | ||||||||
\(35\) | 3.10947 | 0.525596 | ||||||||
\(36\) | 2.92842 | 0.488070 | ||||||||
\(37\) | −6.13298 | −1.00826 | −0.504128 | − | 0.863629i | \(-0.668186\pi\) | ||||
−0.504128 | + | 0.863629i | \(0.668186\pi\) | |||||||
\(38\) | 14.8257 | 2.40505 | ||||||||
\(39\) | −1.29449 | −0.207285 | ||||||||
\(40\) | 3.36842 | 0.532595 | ||||||||
\(41\) | −9.88644 | −1.54400 | −0.772002 | − | 0.635621i | \(-0.780744\pi\) | ||||
−0.772002 | + | 0.635621i | \(0.780744\pi\) | |||||||
\(42\) | 4.22389 | 0.651761 | ||||||||
\(43\) | 2.00780 | 0.306187 | 0.153093 | − | 0.988212i | \(-0.451077\pi\) | ||||
0.153093 | + | 0.988212i | \(0.451077\pi\) | |||||||
\(44\) | −13.0708 | −1.97050 | ||||||||
\(45\) | −1.63428 | −0.243624 | ||||||||
\(46\) | −12.0158 | −1.77164 | ||||||||
\(47\) | 3.04402 | 0.444017 | 0.222008 | − | 0.975045i | \(-0.428739\pi\) | ||||
0.222008 | + | 0.975045i | \(0.428739\pi\) | |||||||
\(48\) | −1.28119 | −0.184923 | ||||||||
\(49\) | −3.37992 | −0.482846 | ||||||||
\(50\) | 5.17066 | 0.731242 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −3.79083 | −0.525693 | ||||||||
\(53\) | 11.1495 | 1.53151 | 0.765754 | − | 0.643133i | \(-0.222366\pi\) | ||||
0.765754 | + | 0.643133i | \(0.222366\pi\) | |||||||
\(54\) | −2.22001 | −0.302104 | ||||||||
\(55\) | 7.29449 | 0.983589 | ||||||||
\(56\) | 3.92156 | 0.524040 | ||||||||
\(57\) | −6.67824 | −0.884555 | ||||||||
\(58\) | 0.856651 | 0.112484 | ||||||||
\(59\) | 3.07457 | 0.400275 | 0.200137 | − | 0.979768i | \(-0.435861\pi\) | ||||
0.200137 | + | 0.979768i | \(0.435861\pi\) | |||||||
\(60\) | −4.78587 | −0.617853 | ||||||||
\(61\) | 11.5138 | 1.47420 | 0.737099 | − | 0.675785i | \(-0.236195\pi\) | ||||
0.737099 | + | 0.675785i | \(0.236195\pi\) | |||||||
\(62\) | 9.25168 | 1.17496 | ||||||||
\(63\) | −1.90265 | −0.239711 | ||||||||
\(64\) | −12.9032 | −1.61290 | ||||||||
\(65\) | 2.11557 | 0.262404 | ||||||||
\(66\) | 9.90882 | 1.21969 | ||||||||
\(67\) | −10.5512 | −1.28904 | −0.644519 | − | 0.764588i | \(-0.722942\pi\) | ||||
−0.644519 | + | 0.764588i | \(0.722942\pi\) | |||||||
\(68\) | 2.92842 | 0.355123 | ||||||||
\(69\) | 5.41253 | 0.651592 | ||||||||
\(70\) | −6.90303 | −0.825070 | ||||||||
\(71\) | −9.15147 | −1.08608 | −0.543040 | − | 0.839707i | \(-0.682727\pi\) | ||||
−0.543040 | + | 0.839707i | \(0.682727\pi\) | |||||||
\(72\) | −2.06110 | −0.242903 | ||||||||
\(73\) | −3.90855 | −0.457461 | −0.228730 | − | 0.973490i | \(-0.573457\pi\) | ||||
−0.228730 | + | 0.973490i | \(0.573457\pi\) | |||||||
\(74\) | 13.6152 | 1.58274 | ||||||||
\(75\) | −2.32912 | −0.268944 | ||||||||
\(76\) | −19.5567 | −2.24331 | ||||||||
\(77\) | 8.49233 | 0.967791 | ||||||||
\(78\) | 2.87378 | 0.325392 | ||||||||
\(79\) | 1.00000 | 0.112509 | ||||||||
\(80\) | 2.09382 | 0.234096 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 21.9480 | 2.42375 | ||||||||
\(83\) | 9.32483 | 1.02353 | 0.511766 | − | 0.859125i | \(-0.328991\pi\) | ||||
0.511766 | + | 0.859125i | \(0.328991\pi\) | |||||||
\(84\) | −5.57176 | −0.607929 | ||||||||
\(85\) | −1.63428 | −0.177263 | ||||||||
\(86\) | −4.45732 | −0.480646 | ||||||||
\(87\) | −0.385878 | −0.0413704 | ||||||||
\(88\) | 9.19958 | 0.980678 | ||||||||
\(89\) | −2.90621 | −0.308058 | −0.154029 | − | 0.988066i | \(-0.549225\pi\) | ||||
−0.154029 | + | 0.988066i | \(0.549225\pi\) | |||||||
\(90\) | 3.62811 | 0.382437 | ||||||||
\(91\) | 2.46297 | 0.258189 | ||||||||
\(92\) | 15.8502 | 1.65249 | ||||||||
\(93\) | −4.16741 | −0.432141 | ||||||||
\(94\) | −6.75775 | −0.697009 | ||||||||
\(95\) | 10.9141 | 1.11977 | ||||||||
\(96\) | 6.96645 | 0.711010 | ||||||||
\(97\) | −0.111051 | −0.0112755 | −0.00563777 | − | 0.999984i | \(-0.501795\pi\) | ||||
−0.00563777 | + | 0.999984i | \(0.501795\pi\) | |||||||
\(98\) | 7.50345 | 0.757963 | ||||||||
\(99\) | −4.46342 | −0.448591 | ||||||||
\(100\) | −6.82066 | −0.682066 | ||||||||
\(101\) | −4.06378 | −0.404361 | −0.202181 | − | 0.979348i | \(-0.564803\pi\) | ||||
−0.202181 | + | 0.979348i | \(0.564803\pi\) | |||||||
\(102\) | −2.22001 | −0.219813 | ||||||||
\(103\) | 2.71058 | 0.267082 | 0.133541 | − | 0.991043i | \(-0.457365\pi\) | ||||
0.133541 | + | 0.991043i | \(0.457365\pi\) | |||||||
\(104\) | 2.66809 | 0.261628 | ||||||||
\(105\) | 3.10947 | 0.303453 | ||||||||
\(106\) | −24.7521 | −2.40413 | ||||||||
\(107\) | −14.6277 | −1.41411 | −0.707056 | − | 0.707157i | \(-0.749977\pi\) | ||||
−0.707056 | + | 0.707157i | \(0.749977\pi\) | |||||||
\(108\) | 2.92842 | 0.281788 | ||||||||
\(109\) | −1.86669 | −0.178797 | −0.0893983 | − | 0.995996i | \(-0.528494\pi\) | ||||
−0.0893983 | + | 0.995996i | \(0.528494\pi\) | |||||||
\(110\) | −16.1938 | −1.54402 | ||||||||
\(111\) | −6.13298 | −0.582117 | ||||||||
\(112\) | 2.43765 | 0.230336 | ||||||||
\(113\) | 14.1312 | 1.32935 | 0.664674 | − | 0.747133i | \(-0.268570\pi\) | ||||
0.664674 | + | 0.747133i | \(0.268570\pi\) | |||||||
\(114\) | 14.8257 | 1.38856 | ||||||||
\(115\) | −8.84560 | −0.824856 | ||||||||
\(116\) | −1.13001 | −0.104919 | ||||||||
\(117\) | −1.29449 | −0.119676 | ||||||||
\(118\) | −6.82556 | −0.628343 | ||||||||
\(119\) | −1.90265 | −0.174416 | ||||||||
\(120\) | 3.36842 | 0.307494 | ||||||||
\(121\) | 8.92215 | 0.811104 | ||||||||
\(122\) | −25.5608 | −2.31417 | ||||||||
\(123\) | −9.88644 | −0.891431 | ||||||||
\(124\) | −12.2039 | −1.09595 | ||||||||
\(125\) | 11.9779 | 1.07133 | ||||||||
\(126\) | 4.22389 | 0.376294 | ||||||||
\(127\) | −4.97589 | −0.441539 | −0.220769 | − | 0.975326i | \(-0.570857\pi\) | ||||
−0.220769 | + | 0.975326i | \(0.570857\pi\) | |||||||
\(128\) | 14.7122 | 1.30039 | ||||||||
\(129\) | 2.00780 | 0.176777 | ||||||||
\(130\) | −4.69657 | −0.411917 | ||||||||
\(131\) | 17.1743 | 1.50052 | 0.750261 | − | 0.661142i | \(-0.229928\pi\) | ||||
0.750261 | + | 0.661142i | \(0.229928\pi\) | |||||||
\(132\) | −13.0708 | −1.13767 | ||||||||
\(133\) | 12.7064 | 1.10178 | ||||||||
\(134\) | 23.4238 | 2.02351 | ||||||||
\(135\) | −1.63428 | −0.140657 | ||||||||
\(136\) | −2.06110 | −0.176738 | ||||||||
\(137\) | 6.69309 | 0.571829 | 0.285915 | − | 0.958255i | \(-0.407703\pi\) | ||||
0.285915 | + | 0.958255i | \(0.407703\pi\) | |||||||
\(138\) | −12.0158 | −1.02286 | ||||||||
\(139\) | 14.9696 | 1.26970 | 0.634852 | − | 0.772634i | \(-0.281061\pi\) | ||||
0.634852 | + | 0.772634i | \(0.281061\pi\) | |||||||
\(140\) | 9.10583 | 0.769583 | ||||||||
\(141\) | 3.04402 | 0.256353 | ||||||||
\(142\) | 20.3163 | 1.70491 | ||||||||
\(143\) | 5.77788 | 0.483170 | ||||||||
\(144\) | −1.28119 | −0.106765 | ||||||||
\(145\) | 0.630633 | 0.0523712 | ||||||||
\(146\) | 8.67700 | 0.718113 | ||||||||
\(147\) | −3.37992 | −0.278771 | ||||||||
\(148\) | −17.9600 | −1.47630 | ||||||||
\(149\) | −7.16380 | −0.586882 | −0.293441 | − | 0.955977i | \(-0.594800\pi\) | ||||
−0.293441 | + | 0.955977i | \(0.594800\pi\) | |||||||
\(150\) | 5.17066 | 0.422183 | ||||||||
\(151\) | 21.9170 | 1.78358 | 0.891790 | − | 0.452450i | \(-0.149450\pi\) | ||||
0.891790 | + | 0.452450i | \(0.149450\pi\) | |||||||
\(152\) | 13.7645 | 1.11645 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −18.8530 | −1.51922 | ||||||||
\(155\) | 6.81073 | 0.547051 | ||||||||
\(156\) | −3.79083 | −0.303509 | ||||||||
\(157\) | −17.8477 | −1.42440 | −0.712200 | − | 0.701977i | \(-0.752301\pi\) | ||||
−0.712200 | + | 0.701977i | \(0.752301\pi\) | |||||||
\(158\) | −2.22001 | −0.176614 | ||||||||
\(159\) | 11.1495 | 0.884217 | ||||||||
\(160\) | −11.3851 | −0.900074 | ||||||||
\(161\) | −10.2981 | −0.811607 | ||||||||
\(162\) | −2.22001 | −0.174420 | ||||||||
\(163\) | 9.39482 | 0.735859 | 0.367930 | − | 0.929854i | \(-0.380067\pi\) | ||||
0.367930 | + | 0.929854i | \(0.380067\pi\) | |||||||
\(164\) | −28.9517 | −2.26075 | ||||||||
\(165\) | 7.29449 | 0.567875 | ||||||||
\(166\) | −20.7012 | −1.60672 | ||||||||
\(167\) | −4.89296 | −0.378628 | −0.189314 | − | 0.981917i | \(-0.560626\pi\) | ||||
−0.189314 | + | 0.981917i | \(0.560626\pi\) | |||||||
\(168\) | 3.92156 | 0.302555 | ||||||||
\(169\) | −11.3243 | −0.871099 | ||||||||
\(170\) | 3.62811 | 0.278264 | ||||||||
\(171\) | −6.67824 | −0.510698 | ||||||||
\(172\) | 5.87968 | 0.448322 | ||||||||
\(173\) | 22.1087 | 1.68090 | 0.840448 | − | 0.541891i | \(-0.182292\pi\) | ||||
0.840448 | + | 0.541891i | \(0.182292\pi\) | |||||||
\(174\) | 0.856651 | 0.0649425 | ||||||||
\(175\) | 4.43150 | 0.334990 | ||||||||
\(176\) | 5.71847 | 0.431046 | ||||||||
\(177\) | 3.07457 | 0.231099 | ||||||||
\(178\) | 6.45180 | 0.483583 | ||||||||
\(179\) | −15.7268 | −1.17547 | −0.587737 | − | 0.809052i | \(-0.699981\pi\) | ||||
−0.587737 | + | 0.809052i | \(0.699981\pi\) | |||||||
\(180\) | −4.78587 | −0.356718 | ||||||||
\(181\) | 15.6878 | 1.16606 | 0.583031 | − | 0.812450i | \(-0.301867\pi\) | ||||
0.583031 | + | 0.812450i | \(0.301867\pi\) | |||||||
\(182\) | −5.46781 | −0.405301 | ||||||||
\(183\) | 11.5138 | 0.851128 | ||||||||
\(184\) | −11.1558 | −0.822415 | ||||||||
\(185\) | 10.0230 | 0.736907 | ||||||||
\(186\) | 9.25168 | 0.678366 | ||||||||
\(187\) | −4.46342 | −0.326398 | ||||||||
\(188\) | 8.91419 | 0.650134 | ||||||||
\(189\) | −1.90265 | −0.138397 | ||||||||
\(190\) | −24.2294 | −1.75779 | ||||||||
\(191\) | 19.6849 | 1.42435 | 0.712176 | − | 0.702001i | \(-0.247710\pi\) | ||||
0.712176 | + | 0.702001i | \(0.247710\pi\) | |||||||
\(192\) | −12.9032 | −0.931206 | ||||||||
\(193\) | 4.07050 | 0.293001 | 0.146500 | − | 0.989211i | \(-0.453199\pi\) | ||||
0.146500 | + | 0.989211i | \(0.453199\pi\) | |||||||
\(194\) | 0.246534 | 0.0177001 | ||||||||
\(195\) | 2.11557 | 0.151499 | ||||||||
\(196\) | −9.89785 | −0.706989 | ||||||||
\(197\) | −20.3233 | −1.44797 | −0.723987 | − | 0.689814i | \(-0.757692\pi\) | ||||
−0.723987 | + | 0.689814i | \(0.757692\pi\) | |||||||
\(198\) | 9.90882 | 0.704189 | ||||||||
\(199\) | −10.5630 | −0.748789 | −0.374395 | − | 0.927269i | \(-0.622149\pi\) | ||||
−0.374395 | + | 0.927269i | \(0.622149\pi\) | |||||||
\(200\) | 4.80056 | 0.339451 | ||||||||
\(201\) | −10.5512 | −0.744227 | ||||||||
\(202\) | 9.02162 | 0.634759 | ||||||||
\(203\) | 0.734190 | 0.0515300 | ||||||||
\(204\) | 2.92842 | 0.205031 | ||||||||
\(205\) | 16.1572 | 1.12847 | ||||||||
\(206\) | −6.01751 | −0.419260 | ||||||||
\(207\) | 5.41253 | 0.376197 | ||||||||
\(208\) | 1.65849 | 0.114995 | ||||||||
\(209\) | 29.8078 | 2.06185 | ||||||||
\(210\) | −6.90303 | −0.476354 | ||||||||
\(211\) | 19.0212 | 1.30947 | 0.654735 | − | 0.755858i | \(-0.272780\pi\) | ||||
0.654735 | + | 0.755858i | \(0.272780\pi\) | |||||||
\(212\) | 32.6506 | 2.24245 | ||||||||
\(213\) | −9.15147 | −0.627048 | ||||||||
\(214\) | 32.4736 | 2.21985 | ||||||||
\(215\) | −3.28131 | −0.223783 | ||||||||
\(216\) | −2.06110 | −0.140240 | ||||||||
\(217\) | 7.92913 | 0.538264 | ||||||||
\(218\) | 4.14406 | 0.280671 | ||||||||
\(219\) | −3.90855 | −0.264115 | ||||||||
\(220\) | 21.3614 | 1.44018 | ||||||||
\(221\) | −1.29449 | −0.0870771 | ||||||||
\(222\) | 13.6152 | 0.913795 | ||||||||
\(223\) | 8.55625 | 0.572969 | 0.286485 | − | 0.958085i | \(-0.407513\pi\) | ||||
0.286485 | + | 0.958085i | \(0.407513\pi\) | |||||||
\(224\) | −13.2547 | −0.885617 | ||||||||
\(225\) | −2.32912 | −0.155275 | ||||||||
\(226\) | −31.3713 | −2.08679 | ||||||||
\(227\) | 8.88220 | 0.589532 | 0.294766 | − | 0.955569i | \(-0.404758\pi\) | ||||
0.294766 | + | 0.955569i | \(0.404758\pi\) | |||||||
\(228\) | −19.5567 | −1.29518 | ||||||||
\(229\) | −29.3221 | −1.93766 | −0.968830 | − | 0.247725i | \(-0.920317\pi\) | ||||
−0.968830 | + | 0.247725i | \(0.920317\pi\) | |||||||
\(230\) | 19.6373 | 1.29484 | ||||||||
\(231\) | 8.49233 | 0.558754 | ||||||||
\(232\) | 0.795334 | 0.0522162 | ||||||||
\(233\) | 2.85833 | 0.187256 | 0.0936278 | − | 0.995607i | \(-0.470154\pi\) | ||||
0.0936278 | + | 0.995607i | \(0.470154\pi\) | |||||||
\(234\) | 2.87378 | 0.187865 | ||||||||
\(235\) | −4.97479 | −0.324520 | ||||||||
\(236\) | 9.00363 | 0.586087 | ||||||||
\(237\) | 1.00000 | 0.0649570 | ||||||||
\(238\) | 4.22389 | 0.273794 | ||||||||
\(239\) | −24.0944 | −1.55854 | −0.779270 | − | 0.626689i | \(-0.784410\pi\) | ||||
−0.779270 | + | 0.626689i | \(0.784410\pi\) | |||||||
\(240\) | 2.09382 | 0.135155 | ||||||||
\(241\) | 0.357116 | 0.0230039 | 0.0115019 | − | 0.999934i | \(-0.496339\pi\) | ||||
0.0115019 | + | 0.999934i | \(0.496339\pi\) | |||||||
\(242\) | −19.8072 | −1.27326 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 33.7174 | 2.15854 | ||||||||
\(245\) | 5.52375 | 0.352899 | ||||||||
\(246\) | 21.9480 | 1.39935 | ||||||||
\(247\) | 8.64495 | 0.550065 | ||||||||
\(248\) | 8.58947 | 0.545432 | ||||||||
\(249\) | 9.32483 | 0.590937 | ||||||||
\(250\) | −26.5909 | −1.68176 | ||||||||
\(251\) | −9.94112 | −0.627478 | −0.313739 | − | 0.949509i | \(-0.601582\pi\) | ||||
−0.313739 | + | 0.949509i | \(0.601582\pi\) | |||||||
\(252\) | −5.57176 | −0.350988 | ||||||||
\(253\) | −24.1584 | −1.51883 | ||||||||
\(254\) | 11.0465 | 0.693119 | ||||||||
\(255\) | −1.63428 | −0.102343 | ||||||||
\(256\) | −6.85486 | −0.428429 | ||||||||
\(257\) | −30.7848 | −1.92030 | −0.960150 | − | 0.279485i | \(-0.909836\pi\) | ||||
−0.960150 | + | 0.279485i | \(0.909836\pi\) | |||||||
\(258\) | −4.45732 | −0.277501 | ||||||||
\(259\) | 11.6689 | 0.725071 | ||||||||
\(260\) | 6.19528 | 0.384215 | ||||||||
\(261\) | −0.385878 | −0.0238852 | ||||||||
\(262\) | −38.1269 | −2.35549 | ||||||||
\(263\) | −14.0747 | −0.867885 | −0.433943 | − | 0.900941i | \(-0.642878\pi\) | ||||
−0.433943 | + | 0.900941i | \(0.642878\pi\) | |||||||
\(264\) | 9.19958 | 0.566195 | ||||||||
\(265\) | −18.2215 | −1.11934 | ||||||||
\(266\) | −28.2082 | −1.72955 | ||||||||
\(267\) | −2.90621 | −0.177857 | ||||||||
\(268\) | −30.8985 | −1.88743 | ||||||||
\(269\) | −29.9446 | −1.82575 | −0.912877 | − | 0.408235i | \(-0.866144\pi\) | ||||
−0.912877 | + | 0.408235i | \(0.866144\pi\) | |||||||
\(270\) | 3.62811 | 0.220800 | ||||||||
\(271\) | 22.7835 | 1.38400 | 0.692000 | − | 0.721898i | \(-0.256730\pi\) | ||||
0.692000 | + | 0.721898i | \(0.256730\pi\) | |||||||
\(272\) | −1.28119 | −0.0776833 | ||||||||
\(273\) | 2.46297 | 0.149066 | ||||||||
\(274\) | −14.8587 | −0.897646 | ||||||||
\(275\) | 10.3959 | 0.626894 | ||||||||
\(276\) | 15.8502 | 0.954068 | ||||||||
\(277\) | 26.0724 | 1.56654 | 0.783269 | − | 0.621682i | \(-0.213551\pi\) | ||||
0.783269 | + | 0.621682i | \(0.213551\pi\) | |||||||
\(278\) | −33.2326 | −1.99316 | ||||||||
\(279\) | −4.16741 | −0.249497 | ||||||||
\(280\) | −6.40893 | −0.383007 | ||||||||
\(281\) | 31.1424 | 1.85780 | 0.928898 | − | 0.370335i | \(-0.120757\pi\) | ||||
0.928898 | + | 0.370335i | \(0.120757\pi\) | |||||||
\(282\) | −6.75775 | −0.402418 | ||||||||
\(283\) | −4.82456 | −0.286791 | −0.143395 | − | 0.989665i | \(-0.545802\pi\) | ||||
−0.143395 | + | 0.989665i | \(0.545802\pi\) | |||||||
\(284\) | −26.7994 | −1.59025 | ||||||||
\(285\) | 10.9141 | 0.646497 | ||||||||
\(286\) | −12.8269 | −0.758472 | ||||||||
\(287\) | 18.8104 | 1.11035 | ||||||||
\(288\) | 6.96645 | 0.410502 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −1.40001 | −0.0822113 | ||||||||
\(291\) | −0.111051 | −0.00650993 | ||||||||
\(292\) | −11.4459 | −0.669820 | ||||||||
\(293\) | 14.7399 | 0.861115 | 0.430557 | − | 0.902563i | \(-0.358317\pi\) | ||||
0.430557 | + | 0.902563i | \(0.358317\pi\) | |||||||
\(294\) | 7.50345 | 0.437610 | ||||||||
\(295\) | −5.02471 | −0.292550 | ||||||||
\(296\) | 12.6407 | 0.734726 | ||||||||
\(297\) | −4.46342 | −0.258994 | ||||||||
\(298\) | 15.9037 | 0.921275 | ||||||||
\(299\) | −7.00649 | −0.405196 | ||||||||
\(300\) | −6.82066 | −0.393791 | ||||||||
\(301\) | −3.82014 | −0.220189 | ||||||||
\(302\) | −48.6558 | −2.79983 | ||||||||
\(303\) | −4.06378 | −0.233458 | ||||||||
\(304\) | 8.55607 | 0.490724 | ||||||||
\(305\) | −18.8169 | −1.07745 | ||||||||
\(306\) | −2.22001 | −0.126909 | ||||||||
\(307\) | −9.51663 | −0.543143 | −0.271571 | − | 0.962418i | \(-0.587543\pi\) | ||||
−0.271571 | + | 0.962418i | \(0.587543\pi\) | |||||||
\(308\) | 24.8691 | 1.41705 | ||||||||
\(309\) | 2.71058 | 0.154200 | ||||||||
\(310\) | −15.1199 | −0.858750 | ||||||||
\(311\) | 10.6710 | 0.605098 | 0.302549 | − | 0.953134i | \(-0.402162\pi\) | ||||
0.302549 | + | 0.953134i | \(0.402162\pi\) | |||||||
\(312\) | 2.66809 | 0.151051 | ||||||||
\(313\) | −20.8019 | −1.17579 | −0.587897 | − | 0.808936i | \(-0.700044\pi\) | ||||
−0.587897 | + | 0.808936i | \(0.700044\pi\) | |||||||
\(314\) | 39.6219 | 2.23600 | ||||||||
\(315\) | 3.10947 | 0.175199 | ||||||||
\(316\) | 2.92842 | 0.164737 | ||||||||
\(317\) | 17.2323 | 0.967861 | 0.483930 | − | 0.875106i | \(-0.339209\pi\) | ||||
0.483930 | + | 0.875106i | \(0.339209\pi\) | |||||||
\(318\) | −24.7521 | −1.38803 | ||||||||
\(319\) | 1.72234 | 0.0964323 | ||||||||
\(320\) | 21.0874 | 1.17882 | ||||||||
\(321\) | −14.6277 | −0.816438 | ||||||||
\(322\) | 22.8619 | 1.27405 | ||||||||
\(323\) | −6.67824 | −0.371587 | ||||||||
\(324\) | 2.92842 | 0.162690 | ||||||||
\(325\) | 3.01504 | 0.167244 | ||||||||
\(326\) | −20.8566 | −1.15514 | ||||||||
\(327\) | −1.86669 | −0.103228 | ||||||||
\(328\) | 20.3770 | 1.12513 | ||||||||
\(329\) | −5.79171 | −0.319307 | ||||||||
\(330\) | −16.1938 | −0.891440 | ||||||||
\(331\) | 26.6575 | 1.46523 | 0.732614 | − | 0.680645i | \(-0.238300\pi\) | ||||
0.732614 | + | 0.680645i | \(0.238300\pi\) | |||||||
\(332\) | 27.3070 | 1.49867 | ||||||||
\(333\) | −6.13298 | −0.336085 | ||||||||
\(334\) | 10.8624 | 0.594363 | ||||||||
\(335\) | 17.2437 | 0.942124 | ||||||||
\(336\) | 2.43765 | 0.132985 | ||||||||
\(337\) | −12.8716 | −0.701163 | −0.350582 | − | 0.936532i | \(-0.614016\pi\) | ||||
−0.350582 | + | 0.936532i | \(0.614016\pi\) | |||||||
\(338\) | 25.1400 | 1.36743 | ||||||||
\(339\) | 14.1312 | 0.767500 | ||||||||
\(340\) | −4.78587 | −0.259550 | ||||||||
\(341\) | 18.6009 | 1.00730 | ||||||||
\(342\) | 14.8257 | 0.801684 | ||||||||
\(343\) | 19.7494 | 1.06637 | ||||||||
\(344\) | −4.13828 | −0.223121 | ||||||||
\(345\) | −8.84560 | −0.476231 | ||||||||
\(346\) | −49.0815 | −2.63864 | ||||||||
\(347\) | 19.9735 | 1.07223 | 0.536117 | − | 0.844144i | \(-0.319891\pi\) | ||||
0.536117 | + | 0.844144i | \(0.319891\pi\) | |||||||
\(348\) | −1.13001 | −0.0605751 | ||||||||
\(349\) | −16.2872 | −0.871833 | −0.435916 | − | 0.899987i | \(-0.643576\pi\) | ||||
−0.435916 | + | 0.899987i | \(0.643576\pi\) | |||||||
\(350\) | −9.83796 | −0.525861 | ||||||||
\(351\) | −1.29449 | −0.0690950 | ||||||||
\(352\) | −31.0942 | −1.65733 | ||||||||
\(353\) | −14.3591 | −0.764258 | −0.382129 | − | 0.924109i | \(-0.624809\pi\) | ||||
−0.382129 | + | 0.924109i | \(0.624809\pi\) | |||||||
\(354\) | −6.82556 | −0.362774 | ||||||||
\(355\) | 14.9561 | 0.793786 | ||||||||
\(356\) | −8.51062 | −0.451062 | ||||||||
\(357\) | −1.90265 | −0.100699 | ||||||||
\(358\) | 34.9135 | 1.84524 | ||||||||
\(359\) | 9.07260 | 0.478834 | 0.239417 | − | 0.970917i | \(-0.423044\pi\) | ||||
0.239417 | + | 0.970917i | \(0.423044\pi\) | |||||||
\(360\) | 3.36842 | 0.177532 | ||||||||
\(361\) | 25.5989 | 1.34731 | ||||||||
\(362\) | −34.8269 | −1.83046 | ||||||||
\(363\) | 8.92215 | 0.468291 | ||||||||
\(364\) | 7.21262 | 0.378044 | ||||||||
\(365\) | 6.38767 | 0.334346 | ||||||||
\(366\) | −25.5608 | −1.33608 | ||||||||
\(367\) | −22.8469 | −1.19260 | −0.596299 | − | 0.802762i | \(-0.703363\pi\) | ||||
−0.596299 | + | 0.802762i | \(0.703363\pi\) | |||||||
\(368\) | −6.93445 | −0.361483 | ||||||||
\(369\) | −9.88644 | −0.514668 | ||||||||
\(370\) | −22.2511 | −1.15678 | ||||||||
\(371\) | −21.2137 | −1.10136 | ||||||||
\(372\) | −12.2039 | −0.632745 | ||||||||
\(373\) | −17.2152 | −0.891369 | −0.445684 | − | 0.895190i | \(-0.647040\pi\) | ||||
−0.445684 | + | 0.895190i | \(0.647040\pi\) | |||||||
\(374\) | 9.90882 | 0.512373 | ||||||||
\(375\) | 11.9779 | 0.618534 | ||||||||
\(376\) | −6.27405 | −0.323559 | ||||||||
\(377\) | 0.499517 | 0.0257264 | ||||||||
\(378\) | 4.22389 | 0.217254 | ||||||||
\(379\) | −2.54211 | −0.130580 | −0.0652898 | − | 0.997866i | \(-0.520797\pi\) | ||||
−0.0652898 | + | 0.997866i | \(0.520797\pi\) | |||||||
\(380\) | 31.9612 | 1.63957 | ||||||||
\(381\) | −4.97589 | −0.254923 | ||||||||
\(382\) | −43.7007 | −2.23592 | ||||||||
\(383\) | 30.8515 | 1.57644 | 0.788220 | − | 0.615394i | \(-0.211003\pi\) | ||||
0.788220 | + | 0.615394i | \(0.211003\pi\) | |||||||
\(384\) | 14.7122 | 0.750780 | ||||||||
\(385\) | −13.8789 | −0.707332 | ||||||||
\(386\) | −9.03653 | −0.459947 | ||||||||
\(387\) | 2.00780 | 0.102062 | ||||||||
\(388\) | −0.325205 | −0.0165098 | ||||||||
\(389\) | 9.85490 | 0.499663 | 0.249832 | − | 0.968289i | \(-0.419625\pi\) | ||||
0.249832 | + | 0.968289i | \(0.419625\pi\) | |||||||
\(390\) | −4.69657 | −0.237820 | ||||||||
\(391\) | 5.41253 | 0.273723 | ||||||||
\(392\) | 6.96637 | 0.351855 | ||||||||
\(393\) | 17.1743 | 0.866326 | ||||||||
\(394\) | 45.1178 | 2.27300 | ||||||||
\(395\) | −1.63428 | −0.0822297 | ||||||||
\(396\) | −13.0708 | −0.656832 | ||||||||
\(397\) | 18.2723 | 0.917061 | 0.458531 | − | 0.888679i | \(-0.348376\pi\) | ||||
0.458531 | + | 0.888679i | \(0.348376\pi\) | |||||||
\(398\) | 23.4499 | 1.17544 | ||||||||
\(399\) | 12.7064 | 0.636113 | ||||||||
\(400\) | 2.98404 | 0.149202 | ||||||||
\(401\) | 10.6339 | 0.531030 | 0.265515 | − | 0.964107i | \(-0.414458\pi\) | ||||
0.265515 | + | 0.964107i | \(0.414458\pi\) | |||||||
\(402\) | 23.4238 | 1.16827 | ||||||||
\(403\) | 5.39469 | 0.268729 | ||||||||
\(404\) | −11.9005 | −0.592071 | ||||||||
\(405\) | −1.63428 | −0.0812081 | ||||||||
\(406\) | −1.62991 | −0.0808909 | ||||||||
\(407\) | 27.3741 | 1.35688 | ||||||||
\(408\) | −2.06110 | −0.102040 | ||||||||
\(409\) | 20.1190 | 0.994822 | 0.497411 | − | 0.867515i | \(-0.334284\pi\) | ||||
0.497411 | + | 0.867515i | \(0.334284\pi\) | |||||||
\(410\) | −35.8691 | −1.77145 | ||||||||
\(411\) | 6.69309 | 0.330146 | ||||||||
\(412\) | 7.93774 | 0.391064 | ||||||||
\(413\) | −5.84982 | −0.287851 | ||||||||
\(414\) | −12.0158 | −0.590546 | ||||||||
\(415\) | −15.2394 | −0.748072 | ||||||||
\(416\) | −9.01803 | −0.442145 | ||||||||
\(417\) | 14.9696 | 0.733064 | ||||||||
\(418\) | −66.1735 | −3.23665 | ||||||||
\(419\) | 18.7028 | 0.913690 | 0.456845 | − | 0.889546i | \(-0.348979\pi\) | ||||
0.456845 | + | 0.889546i | \(0.348979\pi\) | |||||||
\(420\) | 9.10583 | 0.444319 | ||||||||
\(421\) | 12.0322 | 0.586415 | 0.293208 | − | 0.956049i | \(-0.405277\pi\) | ||||
0.293208 | + | 0.956049i | \(0.405277\pi\) | |||||||
\(422\) | −42.2271 | −2.05558 | ||||||||
\(423\) | 3.04402 | 0.148006 | ||||||||
\(424\) | −22.9804 | −1.11603 | ||||||||
\(425\) | −2.32912 | −0.112979 | ||||||||
\(426\) | 20.3163 | 0.984328 | ||||||||
\(427\) | −21.9068 | −1.06015 | ||||||||
\(428\) | −42.8361 | −2.07056 | ||||||||
\(429\) | 5.77788 | 0.278959 | ||||||||
\(430\) | 7.28453 | 0.351291 | ||||||||
\(431\) | 32.4481 | 1.56297 | 0.781484 | − | 0.623925i | \(-0.214463\pi\) | ||||
0.781484 | + | 0.623925i | \(0.214463\pi\) | |||||||
\(432\) | −1.28119 | −0.0616411 | ||||||||
\(433\) | −33.4347 | −1.60677 | −0.803384 | − | 0.595461i | \(-0.796969\pi\) | ||||
−0.803384 | + | 0.595461i | \(0.796969\pi\) | |||||||
\(434\) | −17.6027 | −0.844957 | ||||||||
\(435\) | 0.630633 | 0.0302365 | ||||||||
\(436\) | −5.46646 | −0.261796 | ||||||||
\(437\) | −36.1462 | −1.72911 | ||||||||
\(438\) | 8.67700 | 0.414603 | ||||||||
\(439\) | 13.4602 | 0.642421 | 0.321210 | − | 0.947008i | \(-0.395910\pi\) | ||||
0.321210 | + | 0.947008i | \(0.395910\pi\) | |||||||
\(440\) | −15.0347 | −0.716751 | ||||||||
\(441\) | −3.37992 | −0.160949 | ||||||||
\(442\) | 2.87378 | 0.136692 | ||||||||
\(443\) | 24.6866 | 1.17289 | 0.586447 | − | 0.809988i | \(-0.300526\pi\) | ||||
0.586447 | + | 0.809988i | \(0.300526\pi\) | |||||||
\(444\) | −17.9600 | −0.852342 | ||||||||
\(445\) | 4.74957 | 0.225151 | ||||||||
\(446\) | −18.9949 | −0.899436 | ||||||||
\(447\) | −7.16380 | −0.338836 | ||||||||
\(448\) | 24.5502 | 1.15989 | ||||||||
\(449\) | 33.3851 | 1.57554 | 0.787769 | − | 0.615971i | \(-0.211236\pi\) | ||||
0.787769 | + | 0.615971i | \(0.211236\pi\) | |||||||
\(450\) | 5.17066 | 0.243747 | ||||||||
\(451\) | 44.1274 | 2.07788 | ||||||||
\(452\) | 41.3821 | 1.94645 | ||||||||
\(453\) | 21.9170 | 1.02975 | ||||||||
\(454\) | −19.7185 | −0.925437 | ||||||||
\(455\) | −4.02519 | −0.188704 | ||||||||
\(456\) | 13.7645 | 0.644584 | ||||||||
\(457\) | 14.2678 | 0.667418 | 0.333709 | − | 0.942676i | \(-0.391700\pi\) | ||||
0.333709 | + | 0.942676i | \(0.391700\pi\) | |||||||
\(458\) | 65.0953 | 3.04170 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −25.9036 | −1.20776 | ||||||||
\(461\) | −8.54505 | −0.397983 | −0.198991 | − | 0.980001i | \(-0.563767\pi\) | ||||
−0.198991 | + | 0.980001i | \(0.563767\pi\) | |||||||
\(462\) | −18.8530 | −0.877122 | ||||||||
\(463\) | 6.34967 | 0.295094 | 0.147547 | − | 0.989055i | \(-0.452862\pi\) | ||||
0.147547 | + | 0.989055i | \(0.452862\pi\) | |||||||
\(464\) | 0.494381 | 0.0229511 | ||||||||
\(465\) | 6.81073 | 0.315840 | ||||||||
\(466\) | −6.34551 | −0.293950 | ||||||||
\(467\) | 5.83527 | 0.270024 | 0.135012 | − | 0.990844i | \(-0.456893\pi\) | ||||
0.135012 | + | 0.990844i | \(0.456893\pi\) | |||||||
\(468\) | −3.79083 | −0.175231 | ||||||||
\(469\) | 20.0753 | 0.926991 | ||||||||
\(470\) | 11.0441 | 0.509425 | ||||||||
\(471\) | −17.8477 | −0.822378 | ||||||||
\(472\) | −6.33700 | −0.291684 | ||||||||
\(473\) | −8.96166 | −0.412057 | ||||||||
\(474\) | −2.22001 | −0.101968 | ||||||||
\(475\) | 15.5544 | 0.713687 | ||||||||
\(476\) | −5.57176 | −0.255381 | ||||||||
\(477\) | 11.1495 | 0.510503 | ||||||||
\(478\) | 53.4898 | 2.44657 | ||||||||
\(479\) | 10.9464 | 0.500155 | 0.250077 | − | 0.968226i | \(-0.419544\pi\) | ||||
0.250077 | + | 0.968226i | \(0.419544\pi\) | |||||||
\(480\) | −11.3851 | −0.519658 | ||||||||
\(481\) | 7.93911 | 0.361992 | ||||||||
\(482\) | −0.792799 | −0.0361110 | ||||||||
\(483\) | −10.2981 | −0.468582 | ||||||||
\(484\) | 26.1278 | 1.18763 | ||||||||
\(485\) | 0.181489 | 0.00824099 | ||||||||
\(486\) | −2.22001 | −0.100701 | ||||||||
\(487\) | −7.31707 | −0.331568 | −0.165784 | − | 0.986162i | \(-0.553015\pi\) | ||||
−0.165784 | + | 0.986162i | \(0.553015\pi\) | |||||||
\(488\) | −23.7312 | −1.07426 | ||||||||
\(489\) | 9.39482 | 0.424849 | ||||||||
\(490\) | −12.2628 | −0.553975 | ||||||||
\(491\) | −11.9953 | −0.541339 | −0.270670 | − | 0.962672i | \(-0.587245\pi\) | ||||
−0.270670 | + | 0.962672i | \(0.587245\pi\) | |||||||
\(492\) | −28.9517 | −1.30524 | ||||||||
\(493\) | −0.385878 | −0.0173791 | ||||||||
\(494\) | −19.1918 | −0.863481 | ||||||||
\(495\) | 7.29449 | 0.327863 | ||||||||
\(496\) | 5.33923 | 0.239738 | ||||||||
\(497\) | 17.4120 | 0.781036 | ||||||||
\(498\) | −20.7012 | −0.927641 | ||||||||
\(499\) | 14.1153 | 0.631889 | 0.315945 | − | 0.948778i | \(-0.397679\pi\) | ||||
0.315945 | + | 0.948778i | \(0.397679\pi\) | |||||||
\(500\) | 35.0762 | 1.56866 | ||||||||
\(501\) | −4.89296 | −0.218601 | ||||||||
\(502\) | 22.0693 | 0.985002 | ||||||||
\(503\) | 23.3365 | 1.04052 | 0.520261 | − | 0.854007i | \(-0.325835\pi\) | ||||
0.520261 | + | 0.854007i | \(0.325835\pi\) | |||||||
\(504\) | 3.92156 | 0.174680 | ||||||||
\(505\) | 6.64137 | 0.295537 | ||||||||
\(506\) | 53.6318 | 2.38422 | ||||||||
\(507\) | −11.3243 | −0.502929 | ||||||||
\(508\) | −14.5715 | −0.646506 | ||||||||
\(509\) | 32.1813 | 1.42641 | 0.713206 | − | 0.700954i | \(-0.247242\pi\) | ||||
0.713206 | + | 0.700954i | \(0.247242\pi\) | |||||||
\(510\) | 3.62811 | 0.160656 | ||||||||
\(511\) | 7.43660 | 0.328976 | ||||||||
\(512\) | −14.2066 | −0.627850 | ||||||||
\(513\) | −6.67824 | −0.294852 | ||||||||
\(514\) | 68.3423 | 3.01445 | ||||||||
\(515\) | −4.42986 | −0.195203 | ||||||||
\(516\) | 5.87968 | 0.258839 | ||||||||
\(517\) | −13.5868 | −0.597545 | ||||||||
\(518\) | −25.9050 | −1.13820 | ||||||||
\(519\) | 22.1087 | 0.970466 | ||||||||
\(520\) | −4.36041 | −0.191217 | ||||||||
\(521\) | 11.4869 | 0.503251 | 0.251625 | − | 0.967825i | \(-0.419035\pi\) | ||||
0.251625 | + | 0.967825i | \(0.419035\pi\) | |||||||
\(522\) | 0.856651 | 0.0374946 | ||||||||
\(523\) | 3.23156 | 0.141306 | 0.0706531 | − | 0.997501i | \(-0.477492\pi\) | ||||
0.0706531 | + | 0.997501i | \(0.477492\pi\) | |||||||
\(524\) | 50.2935 | 2.19708 | ||||||||
\(525\) | 4.43150 | 0.193407 | ||||||||
\(526\) | 31.2460 | 1.36239 | ||||||||
\(527\) | −4.16741 | −0.181535 | ||||||||
\(528\) | 5.71847 | 0.248865 | ||||||||
\(529\) | 6.29545 | 0.273715 | ||||||||
\(530\) | 40.4518 | 1.75712 | ||||||||
\(531\) | 3.07457 | 0.133425 | ||||||||
\(532\) | 37.2096 | 1.61324 | ||||||||
\(533\) | 12.7979 | 0.554341 | ||||||||
\(534\) | 6.45180 | 0.279197 | ||||||||
\(535\) | 23.9058 | 1.03354 | ||||||||
\(536\) | 21.7472 | 0.939336 | ||||||||
\(537\) | −15.7268 | −0.678660 | ||||||||
\(538\) | 66.4771 | 2.86603 | ||||||||
\(539\) | 15.0860 | 0.649802 | ||||||||
\(540\) | −4.78587 | −0.205951 | ||||||||
\(541\) | −5.01331 | −0.215539 | −0.107770 | − | 0.994176i | \(-0.534371\pi\) | ||||
−0.107770 | + | 0.994176i | \(0.534371\pi\) | |||||||
\(542\) | −50.5795 | −2.17258 | ||||||||
\(543\) | 15.6878 | 0.673226 | ||||||||
\(544\) | 6.96645 | 0.298684 | ||||||||
\(545\) | 3.05070 | 0.130678 | ||||||||
\(546\) | −5.46781 | −0.234000 | ||||||||
\(547\) | −22.2531 | −0.951472 | −0.475736 | − | 0.879588i | \(-0.657818\pi\) | ||||
−0.475736 | + | 0.879588i | \(0.657818\pi\) | |||||||
\(548\) | 19.6002 | 0.837279 | ||||||||
\(549\) | 11.5138 | 0.491399 | ||||||||
\(550\) | −23.0789 | −0.984086 | ||||||||
\(551\) | 2.57698 | 0.109783 | ||||||||
\(552\) | −11.1558 | −0.474821 | ||||||||
\(553\) | −1.90265 | −0.0809089 | ||||||||
\(554\) | −57.8809 | −2.45912 | ||||||||
\(555\) | 10.0230 | 0.425453 | ||||||||
\(556\) | 43.8373 | 1.85912 | ||||||||
\(557\) | −0.355109 | −0.0150464 | −0.00752322 | − | 0.999972i | \(-0.502395\pi\) | ||||
−0.00752322 | + | 0.999972i | \(0.502395\pi\) | |||||||
\(558\) | 9.25168 | 0.391655 | ||||||||
\(559\) | −2.59909 | −0.109930 | ||||||||
\(560\) | −3.98380 | −0.168346 | ||||||||
\(561\) | −4.46342 | −0.188446 | ||||||||
\(562\) | −69.1362 | −2.91633 | ||||||||
\(563\) | −38.8358 | −1.63673 | −0.818367 | − | 0.574697i | \(-0.805120\pi\) | ||||
−0.818367 | + | 0.574697i | \(0.805120\pi\) | |||||||
\(564\) | 8.91419 | 0.375355 | ||||||||
\(565\) | −23.0943 | −0.971585 | ||||||||
\(566\) | 10.7106 | 0.450198 | ||||||||
\(567\) | −1.90265 | −0.0799038 | ||||||||
\(568\) | 18.8621 | 0.791437 | ||||||||
\(569\) | 8.40024 | 0.352156 | 0.176078 | − | 0.984376i | \(-0.443659\pi\) | ||||
0.176078 | + | 0.984376i | \(0.443659\pi\) | |||||||
\(570\) | −24.2294 | −1.01486 | ||||||||
\(571\) | 15.9096 | 0.665797 | 0.332899 | − | 0.942963i | \(-0.391973\pi\) | ||||
0.332899 | + | 0.942963i | \(0.391973\pi\) | |||||||
\(572\) | 16.9201 | 0.707464 | ||||||||
\(573\) | 19.6849 | 0.822350 | ||||||||
\(574\) | −41.7593 | −1.74300 | ||||||||
\(575\) | −12.6064 | −0.525725 | ||||||||
\(576\) | −12.9032 | −0.537632 | ||||||||
\(577\) | 10.4062 | 0.433216 | 0.216608 | − | 0.976259i | \(-0.430501\pi\) | ||||
0.216608 | + | 0.976259i | \(0.430501\pi\) | |||||||
\(578\) | −2.22001 | −0.0923400 | ||||||||
\(579\) | 4.07050 | 0.169164 | ||||||||
\(580\) | 1.84676 | 0.0766825 | ||||||||
\(581\) | −17.7419 | −0.736057 | ||||||||
\(582\) | 0.246534 | 0.0102192 | ||||||||
\(583\) | −49.7652 | −2.06106 | ||||||||
\(584\) | 8.05592 | 0.333356 | ||||||||
\(585\) | 2.11557 | 0.0874680 | ||||||||
\(586\) | −32.7227 | −1.35176 | ||||||||
\(587\) | 29.6498 | 1.22378 | 0.611888 | − | 0.790944i | \(-0.290410\pi\) | ||||
0.611888 | + | 0.790944i | \(0.290410\pi\) | |||||||
\(588\) | −9.89785 | −0.408180 | ||||||||
\(589\) | 27.8310 | 1.14676 | ||||||||
\(590\) | 11.1549 | 0.459239 | ||||||||
\(591\) | −20.3233 | −0.835988 | ||||||||
\(592\) | 7.85748 | 0.322941 | ||||||||
\(593\) | 44.7799 | 1.83889 | 0.919445 | − | 0.393219i | \(-0.128639\pi\) | ||||
0.919445 | + | 0.393219i | \(0.128639\pi\) | |||||||
\(594\) | 9.90882 | 0.406564 | ||||||||
\(595\) | 3.10947 | 0.127476 | ||||||||
\(596\) | −20.9786 | −0.859319 | ||||||||
\(597\) | −10.5630 | −0.432314 | ||||||||
\(598\) | 15.5544 | 0.636068 | ||||||||
\(599\) | −24.6038 | −1.00529 | −0.502643 | − | 0.864494i | \(-0.667639\pi\) | ||||
−0.502643 | + | 0.864494i | \(0.667639\pi\) | |||||||
\(600\) | 4.80056 | 0.195982 | ||||||||
\(601\) | 20.3776 | 0.831219 | 0.415609 | − | 0.909543i | \(-0.363568\pi\) | ||||
0.415609 | + | 0.909543i | \(0.363568\pi\) | |||||||
\(602\) | 8.48073 | 0.345649 | ||||||||
\(603\) | −10.5512 | −0.429680 | ||||||||
\(604\) | 64.1822 | 2.61154 | ||||||||
\(605\) | −14.5813 | −0.592814 | ||||||||
\(606\) | 9.02162 | 0.366478 | ||||||||
\(607\) | 4.01090 | 0.162797 | 0.0813987 | − | 0.996682i | \(-0.474061\pi\) | ||||
0.0813987 | + | 0.996682i | \(0.474061\pi\) | |||||||
\(608\) | −46.5236 | −1.88678 | ||||||||
\(609\) | 0.734190 | 0.0297509 | ||||||||
\(610\) | 41.7736 | 1.69136 | ||||||||
\(611\) | −3.94047 | −0.159414 | ||||||||
\(612\) | 2.92842 | 0.118374 | ||||||||
\(613\) | −19.0827 | −0.770743 | −0.385372 | − | 0.922761i | \(-0.625927\pi\) | ||||
−0.385372 | + | 0.922761i | \(0.625927\pi\) | |||||||
\(614\) | 21.1270 | 0.852615 | ||||||||
\(615\) | 16.1572 | 0.651523 | ||||||||
\(616\) | −17.5036 | −0.705239 | ||||||||
\(617\) | −43.6562 | −1.75753 | −0.878767 | − | 0.477251i | \(-0.841633\pi\) | ||||
−0.878767 | + | 0.477251i | \(0.841633\pi\) | |||||||
\(618\) | −6.01751 | −0.242060 | ||||||||
\(619\) | 21.0467 | 0.845937 | 0.422969 | − | 0.906144i | \(-0.360988\pi\) | ||||
0.422969 | + | 0.906144i | \(0.360988\pi\) | |||||||
\(620\) | 19.9447 | 0.800998 | ||||||||
\(621\) | 5.41253 | 0.217197 | ||||||||
\(622\) | −23.6897 | −0.949870 | ||||||||
\(623\) | 5.52950 | 0.221535 | ||||||||
\(624\) | 1.65849 | 0.0663926 | ||||||||
\(625\) | −7.92958 | −0.317183 | ||||||||
\(626\) | 46.1803 | 1.84574 | ||||||||
\(627\) | 29.8078 | 1.19041 | ||||||||
\(628\) | −52.2655 | −2.08562 | ||||||||
\(629\) | −6.13298 | −0.244538 | ||||||||
\(630\) | −6.90303 | −0.275023 | ||||||||
\(631\) | −23.1984 | −0.923513 | −0.461757 | − | 0.887007i | \(-0.652781\pi\) | ||||
−0.461757 | + | 0.887007i | \(0.652781\pi\) | |||||||
\(632\) | −2.06110 | −0.0819863 | ||||||||
\(633\) | 19.0212 | 0.756023 | ||||||||
\(634\) | −38.2557 | −1.51933 | ||||||||
\(635\) | 8.13201 | 0.322709 | ||||||||
\(636\) | 32.6506 | 1.29468 | ||||||||
\(637\) | 4.37529 | 0.173355 | ||||||||
\(638\) | −3.82359 | −0.151378 | ||||||||
\(639\) | −9.15147 | −0.362026 | ||||||||
\(640\) | −24.0439 | −0.950419 | ||||||||
\(641\) | 4.56317 | 0.180234 | 0.0901172 | − | 0.995931i | \(-0.471276\pi\) | ||||
0.0901172 | + | 0.995931i | \(0.471276\pi\) | |||||||
\(642\) | 32.4736 | 1.28163 | ||||||||
\(643\) | 38.5256 | 1.51930 | 0.759651 | − | 0.650331i | \(-0.225370\pi\) | ||||
0.759651 | + | 0.650331i | \(0.225370\pi\) | |||||||
\(644\) | −30.1573 | −1.18836 | ||||||||
\(645\) | −3.28131 | −0.129201 | ||||||||
\(646\) | 14.8257 | 0.583311 | ||||||||
\(647\) | −40.2058 | −1.58065 | −0.790326 | − | 0.612687i | \(-0.790089\pi\) | ||||
−0.790326 | + | 0.612687i | \(0.790089\pi\) | |||||||
\(648\) | −2.06110 | −0.0809678 | ||||||||
\(649\) | −13.7231 | −0.538679 | ||||||||
\(650\) | −6.69340 | −0.262537 | ||||||||
\(651\) | 7.92913 | 0.310767 | ||||||||
\(652\) | 27.5120 | 1.07745 | ||||||||
\(653\) | 46.1148 | 1.80461 | 0.902305 | − | 0.431098i | \(-0.141874\pi\) | ||||
0.902305 | + | 0.431098i | \(0.141874\pi\) | |||||||
\(654\) | 4.14406 | 0.162046 | ||||||||
\(655\) | −28.0676 | −1.09669 | ||||||||
\(656\) | 12.6664 | 0.494539 | ||||||||
\(657\) | −3.90855 | −0.152487 | ||||||||
\(658\) | 12.8576 | 0.501243 | ||||||||
\(659\) | 8.17654 | 0.318513 | 0.159256 | − | 0.987237i | \(-0.449090\pi\) | ||||
0.159256 | + | 0.987237i | \(0.449090\pi\) | |||||||
\(660\) | 21.3614 | 0.831490 | ||||||||
\(661\) | −1.66625 | −0.0648096 | −0.0324048 | − | 0.999475i | \(-0.510317\pi\) | ||||
−0.0324048 | + | 0.999475i | \(0.510317\pi\) | |||||||
\(662\) | −59.1797 | −2.30009 | ||||||||
\(663\) | −1.29449 | −0.0502740 | ||||||||
\(664\) | −19.2194 | −0.745859 | ||||||||
\(665\) | −20.7658 | −0.805262 | ||||||||
\(666\) | 13.6152 | 0.527580 | ||||||||
\(667\) | −2.08857 | −0.0808699 | ||||||||
\(668\) | −14.3286 | −0.554392 | ||||||||
\(669\) | 8.55625 | 0.330804 | ||||||||
\(670\) | −38.2811 | −1.47893 | ||||||||
\(671\) | −51.3912 | −1.98393 | ||||||||
\(672\) | −13.2547 | −0.511311 | ||||||||
\(673\) | −28.9598 | −1.11632 | −0.558159 | − | 0.829734i | \(-0.688492\pi\) | ||||
−0.558159 | + | 0.829734i | \(0.688492\pi\) | |||||||
\(674\) | 28.5751 | 1.10067 | ||||||||
\(675\) | −2.32912 | −0.0896480 | ||||||||
\(676\) | −33.1623 | −1.27547 | ||||||||
\(677\) | −27.2001 | −1.04539 | −0.522693 | − | 0.852521i | \(-0.675073\pi\) | ||||
−0.522693 | + | 0.852521i | \(0.675073\pi\) | |||||||
\(678\) | −31.3713 | −1.20481 | ||||||||
\(679\) | 0.211291 | 0.00810862 | ||||||||
\(680\) | 3.36842 | 0.129173 | ||||||||
\(681\) | 8.88220 | 0.340367 | ||||||||
\(682\) | −41.2942 | −1.58124 | ||||||||
\(683\) | −2.31369 | −0.0885307 | −0.0442654 | − | 0.999020i | \(-0.514095\pi\) | ||||
−0.0442654 | + | 0.999020i | \(0.514095\pi\) | |||||||
\(684\) | −19.5567 | −0.747770 | ||||||||
\(685\) | −10.9384 | −0.417935 | ||||||||
\(686\) | −43.8437 | −1.67396 | ||||||||
\(687\) | −29.3221 | −1.11871 | ||||||||
\(688\) | −2.57236 | −0.0980704 | ||||||||
\(689\) | −14.4330 | −0.549855 | ||||||||
\(690\) | 19.6373 | 0.747578 | ||||||||
\(691\) | −12.9395 | −0.492243 | −0.246122 | − | 0.969239i | \(-0.579156\pi\) | ||||
−0.246122 | + | 0.969239i | \(0.579156\pi\) | |||||||
\(692\) | 64.7438 | 2.46119 | ||||||||
\(693\) | 8.49233 | 0.322597 | ||||||||
\(694\) | −44.3413 | −1.68317 | ||||||||
\(695\) | −24.4645 | −0.927993 | ||||||||
\(696\) | 0.795334 | 0.0301471 | ||||||||
\(697\) | −9.88644 | −0.374476 | ||||||||
\(698\) | 36.1576 | 1.36859 | ||||||||
\(699\) | 2.85833 | 0.108112 | ||||||||
\(700\) | 12.9773 | 0.490496 | ||||||||
\(701\) | −17.5815 | −0.664043 | −0.332021 | − | 0.943272i | \(-0.607731\pi\) | ||||
−0.332021 | + | 0.943272i | \(0.607731\pi\) | |||||||
\(702\) | 2.87378 | 0.108464 | ||||||||
\(703\) | 40.9575 | 1.54474 | ||||||||
\(704\) | 57.5923 | 2.17059 | ||||||||
\(705\) | −4.97479 | −0.187362 | ||||||||
\(706\) | 31.8773 | 1.19972 | ||||||||
\(707\) | 7.73195 | 0.290790 | ||||||||
\(708\) | 9.00363 | 0.338377 | ||||||||
\(709\) | −24.5669 | −0.922628 | −0.461314 | − | 0.887237i | \(-0.652622\pi\) | ||||
−0.461314 | + | 0.887237i | \(0.652622\pi\) | |||||||
\(710\) | −33.2026 | −1.24607 | ||||||||
\(711\) | 1.00000 | 0.0375029 | ||||||||
\(712\) | 5.99000 | 0.224485 | ||||||||
\(713\) | −22.5562 | −0.844738 | ||||||||
\(714\) | 4.22389 | 0.158075 | ||||||||
\(715\) | −9.44268 | −0.353136 | ||||||||
\(716\) | −46.0546 | −1.72114 | ||||||||
\(717\) | −24.0944 | −0.899823 | ||||||||
\(718\) | −20.1412 | −0.751664 | ||||||||
\(719\) | −37.4207 | −1.39556 | −0.697778 | − | 0.716314i | \(-0.745828\pi\) | ||||
−0.697778 | + | 0.716314i | \(0.745828\pi\) | |||||||
\(720\) | 2.09382 | 0.0780320 | ||||||||
\(721\) | −5.15729 | −0.192068 | ||||||||
\(722\) | −56.8297 | −2.11498 | ||||||||
\(723\) | 0.357116 | 0.0132813 | ||||||||
\(724\) | 45.9404 | 1.70736 | ||||||||
\(725\) | 0.898756 | 0.0333790 | ||||||||
\(726\) | −19.8072 | −0.735115 | ||||||||
\(727\) | −13.6349 | −0.505692 | −0.252846 | − | 0.967507i | \(-0.581367\pi\) | ||||
−0.252846 | + | 0.967507i | \(0.581367\pi\) | |||||||
\(728\) | −5.07644 | −0.188145 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −14.1807 | −0.524850 | ||||||||
\(731\) | 2.00780 | 0.0742611 | ||||||||
\(732\) | 33.7174 | 1.24623 | ||||||||
\(733\) | 14.8079 | 0.546944 | 0.273472 | − | 0.961880i | \(-0.411828\pi\) | ||||
0.273472 | + | 0.961880i | \(0.411828\pi\) | |||||||
\(734\) | 50.7203 | 1.87212 | ||||||||
\(735\) | 5.52375 | 0.203747 | ||||||||
\(736\) | 37.7061 | 1.38986 | ||||||||
\(737\) | 47.0946 | 1.73475 | ||||||||
\(738\) | 21.9480 | 0.807915 | ||||||||
\(739\) | −9.86864 | −0.363024 | −0.181512 | − | 0.983389i | \(-0.558099\pi\) | ||||
−0.181512 | + | 0.983389i | \(0.558099\pi\) | |||||||
\(740\) | 29.3516 | 1.07899 | ||||||||
\(741\) | 8.64495 | 0.317580 | ||||||||
\(742\) | 47.0945 | 1.72889 | ||||||||
\(743\) | 26.6119 | 0.976295 | 0.488148 | − | 0.872761i | \(-0.337673\pi\) | ||||
0.488148 | + | 0.872761i | \(0.337673\pi\) | |||||||
\(744\) | 8.58947 | 0.314905 | ||||||||
\(745\) | 11.7077 | 0.428936 | ||||||||
\(746\) | 38.2178 | 1.39925 | ||||||||
\(747\) | 9.32483 | 0.341178 | ||||||||
\(748\) | −13.0708 | −0.477915 | ||||||||
\(749\) | 27.8314 | 1.01694 | ||||||||
\(750\) | −26.5909 | −0.970962 | ||||||||
\(751\) | −32.8146 | −1.19742 | −0.598712 | − | 0.800965i | \(-0.704320\pi\) | ||||
−0.598712 | + | 0.800965i | \(0.704320\pi\) | |||||||
\(752\) | −3.89996 | −0.142217 | ||||||||
\(753\) | −9.94112 | −0.362274 | ||||||||
\(754\) | −1.10893 | −0.0403848 | ||||||||
\(755\) | −35.8185 | −1.30357 | ||||||||
\(756\) | −5.57176 | −0.202643 | ||||||||
\(757\) | −42.5526 | −1.54660 | −0.773300 | − | 0.634040i | \(-0.781395\pi\) | ||||
−0.773300 | + | 0.634040i | \(0.781395\pi\) | |||||||
\(758\) | 5.64351 | 0.204981 | ||||||||
\(759\) | −24.1584 | −0.876894 | ||||||||
\(760\) | −22.4952 | −0.815985 | ||||||||
\(761\) | 20.5221 | 0.743924 | 0.371962 | − | 0.928248i | \(-0.378685\pi\) | ||||
0.371962 | + | 0.928248i | \(0.378685\pi\) | |||||||
\(762\) | 11.0465 | 0.400172 | ||||||||
\(763\) | 3.55166 | 0.128579 | ||||||||
\(764\) | 57.6458 | 2.08555 | ||||||||
\(765\) | −1.63428 | −0.0590876 | ||||||||
\(766\) | −68.4906 | −2.47466 | ||||||||
\(767\) | −3.98001 | −0.143710 | ||||||||
\(768\) | −6.85486 | −0.247353 | ||||||||
\(769\) | 13.8634 | 0.499928 | 0.249964 | − | 0.968255i | \(-0.419581\pi\) | ||||
0.249964 | + | 0.968255i | \(0.419581\pi\) | |||||||
\(770\) | 30.8111 | 1.11036 | ||||||||
\(771\) | −30.7848 | −1.10869 | ||||||||
\(772\) | 11.9201 | 0.429015 | ||||||||
\(773\) | 16.6664 | 0.599447 | 0.299724 | − | 0.954026i | \(-0.403106\pi\) | ||||
0.299724 | + | 0.954026i | \(0.403106\pi\) | |||||||
\(774\) | −4.45732 | −0.160215 | ||||||||
\(775\) | 9.70642 | 0.348665 | ||||||||
\(776\) | 0.228888 | 0.00821660 | ||||||||
\(777\) | 11.6689 | 0.418620 | ||||||||
\(778\) | −21.8779 | −0.784361 | ||||||||
\(779\) | 66.0241 | 2.36556 | ||||||||
\(780\) | 6.19528 | 0.221827 | ||||||||
\(781\) | 40.8469 | 1.46162 | ||||||||
\(782\) | −12.0158 | −0.429685 | ||||||||
\(783\) | −0.385878 | −0.0137901 | ||||||||
\(784\) | 4.33031 | 0.154654 | ||||||||
\(785\) | 29.1681 | 1.04106 | ||||||||
\(786\) | −38.1269 | −1.35994 | ||||||||
\(787\) | 38.5395 | 1.37379 | 0.686893 | − | 0.726759i | \(-0.258974\pi\) | ||||
0.686893 | + | 0.726759i | \(0.258974\pi\) | |||||||
\(788\) | −59.5152 | −2.12014 | ||||||||
\(789\) | −14.0747 | −0.501074 | ||||||||
\(790\) | 3.62811 | 0.129083 | ||||||||
\(791\) | −26.8867 | −0.955980 | ||||||||
\(792\) | 9.19958 | 0.326893 | ||||||||
\(793\) | −14.9046 | −0.529278 | ||||||||
\(794\) | −40.5646 | −1.43958 | ||||||||
\(795\) | −18.2215 | −0.646250 | ||||||||
\(796\) | −30.9329 | −1.09639 | ||||||||
\(797\) | 49.0978 | 1.73913 | 0.869566 | − | 0.493817i | \(-0.164399\pi\) | ||||
0.869566 | + | 0.493817i | \(0.164399\pi\) | |||||||
\(798\) | −28.2082 | −0.998558 | ||||||||
\(799\) | 3.04402 | 0.107690 | ||||||||
\(800\) | −16.2257 | −0.573665 | ||||||||
\(801\) | −2.90621 | −0.102686 | ||||||||
\(802\) | −23.6072 | −0.833600 | ||||||||
\(803\) | 17.4455 | 0.615639 | ||||||||
\(804\) | −30.8985 | −1.08971 | ||||||||
\(805\) | 16.8301 | 0.593182 | ||||||||
\(806\) | −11.9762 | −0.421845 | ||||||||
\(807\) | −29.9446 | −1.05410 | ||||||||
\(808\) | 8.37588 | 0.294662 | ||||||||
\(809\) | −27.4817 | −0.966204 | −0.483102 | − | 0.875564i | \(-0.660490\pi\) | ||||
−0.483102 | + | 0.875564i | \(0.660490\pi\) | |||||||
\(810\) | 3.62811 | 0.127479 | ||||||||
\(811\) | −20.6161 | −0.723930 | −0.361965 | − | 0.932192i | \(-0.617894\pi\) | ||||
−0.361965 | + | 0.932192i | \(0.617894\pi\) | |||||||
\(812\) | 2.15002 | 0.0754509 | ||||||||
\(813\) | 22.7835 | 0.799052 | ||||||||
\(814\) | −60.7706 | −2.13001 | ||||||||
\(815\) | −15.3538 | −0.537820 | ||||||||
\(816\) | −1.28119 | −0.0448505 | ||||||||
\(817\) | −13.4086 | −0.469106 | ||||||||
\(818\) | −44.6643 | −1.56165 | ||||||||
\(819\) | 2.46297 | 0.0860631 | ||||||||
\(820\) | 47.3152 | 1.65232 | ||||||||
\(821\) | −52.2856 | −1.82478 | −0.912391 | − | 0.409321i | \(-0.865766\pi\) | ||||
−0.912391 | + | 0.409321i | \(0.865766\pi\) | |||||||
\(822\) | −14.8587 | −0.518256 | ||||||||
\(823\) | −2.33779 | −0.0814903 | −0.0407451 | − | 0.999170i | \(-0.512973\pi\) | ||||
−0.0407451 | + | 0.999170i | \(0.512973\pi\) | |||||||
\(824\) | −5.58679 | −0.194625 | ||||||||
\(825\) | 10.3959 | 0.361937 | ||||||||
\(826\) | 12.9866 | 0.451863 | ||||||||
\(827\) | 26.2013 | 0.911107 | 0.455553 | − | 0.890208i | \(-0.349441\pi\) | ||||
0.455553 | + | 0.890208i | \(0.349441\pi\) | |||||||
\(828\) | 15.8502 | 0.550831 | ||||||||
\(829\) | 22.0549 | 0.766000 | 0.383000 | − | 0.923748i | \(-0.374891\pi\) | ||||
0.383000 | + | 0.923748i | \(0.374891\pi\) | |||||||
\(830\) | 33.8315 | 1.17431 | ||||||||
\(831\) | 26.0724 | 0.904442 | ||||||||
\(832\) | 16.7031 | 0.579075 | ||||||||
\(833\) | −3.37992 | −0.117107 | ||||||||
\(834\) | −33.2326 | −1.15075 | ||||||||
\(835\) | 7.99647 | 0.276729 | ||||||||
\(836\) | 87.2899 | 3.01898 | ||||||||
\(837\) | −4.16741 | −0.144047 | ||||||||
\(838\) | −41.5203 | −1.43429 | ||||||||
\(839\) | −16.5348 | −0.570843 | −0.285422 | − | 0.958402i | \(-0.592134\pi\) | ||||
−0.285422 | + | 0.958402i | \(0.592134\pi\) | |||||||
\(840\) | −6.40893 | −0.221129 | ||||||||
\(841\) | −28.8511 | −0.994865 | ||||||||
\(842\) | −26.7116 | −0.920543 | ||||||||
\(843\) | 31.1424 | 1.07260 | ||||||||
\(844\) | 55.7020 | 1.91734 | ||||||||
\(845\) | 18.5071 | 0.636663 | ||||||||
\(846\) | −6.75775 | −0.232336 | ||||||||
\(847\) | −16.9757 | −0.583293 | ||||||||
\(848\) | −14.2846 | −0.490537 | ||||||||
\(849\) | −4.82456 | −0.165579 | ||||||||
\(850\) | 5.17066 | 0.177352 | ||||||||
\(851\) | −33.1949 | −1.13791 | ||||||||
\(852\) | −26.7994 | −0.918131 | ||||||||
\(853\) | 43.3295 | 1.48357 | 0.741787 | − | 0.670636i | \(-0.233979\pi\) | ||||
0.741787 | + | 0.670636i | \(0.233979\pi\) | |||||||
\(854\) | 48.6332 | 1.66420 | ||||||||
\(855\) | 10.9141 | 0.373255 | ||||||||
\(856\) | 30.1492 | 1.03048 | ||||||||
\(857\) | 1.52979 | 0.0522565 | 0.0261283 | − | 0.999659i | \(-0.491682\pi\) | ||||
0.0261283 | + | 0.999659i | \(0.491682\pi\) | |||||||
\(858\) | −12.8269 | −0.437904 | ||||||||
\(859\) | 5.96544 | 0.203538 | 0.101769 | − | 0.994808i | \(-0.467550\pi\) | ||||
0.101769 | + | 0.994808i | \(0.467550\pi\) | |||||||
\(860\) | −9.60906 | −0.327666 | ||||||||
\(861\) | 18.8104 | 0.641058 | ||||||||
\(862\) | −72.0349 | −2.45352 | ||||||||
\(863\) | −4.67341 | −0.159085 | −0.0795423 | − | 0.996831i | \(-0.525346\pi\) | ||||
−0.0795423 | + | 0.996831i | \(0.525346\pi\) | |||||||
\(864\) | 6.96645 | 0.237003 | ||||||||
\(865\) | −36.1319 | −1.22852 | ||||||||
\(866\) | 74.2251 | 2.52227 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 23.2198 | 0.788133 | ||||||||
\(869\) | −4.46342 | −0.151411 | ||||||||
\(870\) | −1.40001 | −0.0474647 | ||||||||
\(871\) | 13.6585 | 0.462801 | ||||||||
\(872\) | 3.84744 | 0.130291 | ||||||||
\(873\) | −0.111051 | −0.00375851 | ||||||||
\(874\) | 80.2447 | 2.71432 | ||||||||
\(875\) | −22.7897 | −0.770431 | ||||||||
\(876\) | −11.4459 | −0.386721 | ||||||||
\(877\) | 26.2398 | 0.886055 | 0.443027 | − | 0.896508i | \(-0.353904\pi\) | ||||
0.443027 | + | 0.896508i | \(0.353904\pi\) | |||||||
\(878\) | −29.8817 | −1.00846 | ||||||||
\(879\) | 14.7399 | 0.497165 | ||||||||
\(880\) | −9.34560 | −0.315040 | ||||||||
\(881\) | −39.1655 | −1.31952 | −0.659760 | − | 0.751477i | \(-0.729342\pi\) | ||||
−0.659760 | + | 0.751477i | \(0.729342\pi\) | |||||||
\(882\) | 7.50345 | 0.252654 | ||||||||
\(883\) | −48.0021 | −1.61540 | −0.807700 | − | 0.589594i | \(-0.799288\pi\) | ||||
−0.807700 | + | 0.589594i | \(0.799288\pi\) | |||||||
\(884\) | −3.79083 | −0.127499 | ||||||||
\(885\) | −5.02471 | −0.168904 | ||||||||
\(886\) | −54.8043 | −1.84119 | ||||||||
\(887\) | 15.5810 | 0.523158 | 0.261579 | − | 0.965182i | \(-0.415757\pi\) | ||||
0.261579 | + | 0.965182i | \(0.415757\pi\) | |||||||
\(888\) | 12.6407 | 0.424194 | ||||||||
\(889\) | 9.46737 | 0.317526 | ||||||||
\(890\) | −10.5441 | −0.353438 | ||||||||
\(891\) | −4.46342 | −0.149530 | ||||||||
\(892\) | 25.0563 | 0.838948 | ||||||||
\(893\) | −20.3287 | −0.680275 | ||||||||
\(894\) | 15.9037 | 0.531899 | ||||||||
\(895\) | 25.7020 | 0.859122 | ||||||||
\(896\) | −27.9922 | −0.935154 | ||||||||
\(897\) | −7.00649 | −0.233940 | ||||||||
\(898\) | −74.1150 | −2.47325 | ||||||||
\(899\) | 1.60811 | 0.0536335 | ||||||||
\(900\) | −6.82066 | −0.227355 | ||||||||
\(901\) | 11.1495 | 0.371445 | ||||||||
\(902\) | −97.9630 | −3.26181 | ||||||||
\(903\) | −3.82014 | −0.127126 | ||||||||
\(904\) | −29.1258 | −0.968710 | ||||||||
\(905\) | −25.6382 | −0.852243 | ||||||||
\(906\) | −48.6558 | −1.61648 | ||||||||
\(907\) | 6.98488 | 0.231929 | 0.115965 | − | 0.993253i | \(-0.463004\pi\) | ||||
0.115965 | + | 0.993253i | \(0.463004\pi\) | |||||||
\(908\) | 26.0108 | 0.863200 | ||||||||
\(909\) | −4.06378 | −0.134787 | ||||||||
\(910\) | 8.93594 | 0.296223 | ||||||||
\(911\) | −45.3891 | −1.50381 | −0.751905 | − | 0.659272i | \(-0.770865\pi\) | ||||
−0.751905 | + | 0.659272i | \(0.770865\pi\) | |||||||
\(912\) | 8.55607 | 0.283320 | ||||||||
\(913\) | −41.6206 | −1.37744 | ||||||||
\(914\) | −31.6745 | −1.04770 | ||||||||
\(915\) | −18.8169 | −0.622067 | ||||||||
\(916\) | −85.8676 | −2.83715 | ||||||||
\(917\) | −32.6766 | −1.07908 | ||||||||
\(918\) | −2.22001 | −0.0732711 | ||||||||
\(919\) | 0.150106 | 0.00495153 | 0.00247577 | − | 0.999997i | \(-0.499212\pi\) | ||||
0.00247577 | + | 0.999997i | \(0.499212\pi\) | |||||||
\(920\) | 18.2317 | 0.601081 | ||||||||
\(921\) | −9.51663 | −0.313584 | ||||||||
\(922\) | 18.9701 | 0.624746 | ||||||||
\(923\) | 11.8465 | 0.389933 | ||||||||
\(924\) | 24.8691 | 0.818134 | ||||||||
\(925\) | 14.2845 | 0.469670 | ||||||||
\(926\) | −14.0963 | −0.463233 | ||||||||
\(927\) | 2.71058 | 0.0890273 | ||||||||
\(928\) | −2.68820 | −0.0882444 | ||||||||
\(929\) | 34.2867 | 1.12491 | 0.562455 | − | 0.826828i | \(-0.309857\pi\) | ||||
0.562455 | + | 0.826828i | \(0.309857\pi\) | |||||||
\(930\) | −15.1199 | −0.495799 | ||||||||
\(931\) | 22.5720 | 0.739766 | ||||||||
\(932\) | 8.37040 | 0.274182 | ||||||||
\(933\) | 10.6710 | 0.349353 | ||||||||
\(934\) | −12.9543 | −0.423879 | ||||||||
\(935\) | 7.29449 | 0.238555 | ||||||||
\(936\) | 2.66809 | 0.0872092 | ||||||||
\(937\) | 58.5314 | 1.91214 | 0.956069 | − | 0.293143i | \(-0.0947011\pi\) | ||||
0.956069 | + | 0.293143i | \(0.0947011\pi\) | |||||||
\(938\) | −44.5673 | −1.45517 | ||||||||
\(939\) | −20.8019 | −0.678844 | ||||||||
\(940\) | −14.5683 | −0.475166 | ||||||||
\(941\) | −7.10197 | −0.231518 | −0.115759 | − | 0.993277i | \(-0.536930\pi\) | ||||
−0.115759 | + | 0.993277i | \(0.536930\pi\) | |||||||
\(942\) | 39.6219 | 1.29095 | ||||||||
\(943\) | −53.5106 | −1.74255 | ||||||||
\(944\) | −3.93909 | −0.128206 | ||||||||
\(945\) | 3.10947 | 0.101151 | ||||||||
\(946\) | 19.8949 | 0.646840 | ||||||||
\(947\) | 20.7604 | 0.674623 | 0.337312 | − | 0.941393i | \(-0.390482\pi\) | ||||
0.337312 | + | 0.941393i | \(0.390482\pi\) | |||||||
\(948\) | 2.92842 | 0.0951108 | ||||||||
\(949\) | 5.05960 | 0.164241 | ||||||||
\(950\) | −34.5309 | −1.12033 | ||||||||
\(951\) | 17.2323 | 0.558795 | ||||||||
\(952\) | 3.92156 | 0.127098 | ||||||||
\(953\) | 2.03780 | 0.0660108 | 0.0330054 | − | 0.999455i | \(-0.489492\pi\) | ||||
0.0330054 | + | 0.999455i | \(0.489492\pi\) | |||||||
\(954\) | −24.7521 | −0.801377 | ||||||||
\(955\) | −32.1708 | −1.04102 | ||||||||
\(956\) | −70.5587 | −2.28203 | ||||||||
\(957\) | 1.72234 | 0.0556752 | ||||||||
\(958\) | −24.3011 | −0.785134 | ||||||||
\(959\) | −12.7346 | −0.411222 | ||||||||
\(960\) | 21.0874 | 0.680594 | ||||||||
\(961\) | −13.6327 | −0.439763 | ||||||||
\(962\) | −17.6249 | −0.568248 | ||||||||
\(963\) | −14.6277 | −0.471371 | ||||||||
\(964\) | 1.04579 | 0.0336825 | ||||||||
\(965\) | −6.65234 | −0.214146 | ||||||||
\(966\) | 22.8619 | 0.735570 | ||||||||
\(967\) | −45.6011 | −1.46643 | −0.733216 | − | 0.679996i | \(-0.761982\pi\) | ||||
−0.733216 | + | 0.679996i | \(0.761982\pi\) | |||||||
\(968\) | −18.3895 | −0.591060 | ||||||||
\(969\) | −6.67824 | −0.214536 | ||||||||
\(970\) | −0.402906 | −0.0129365 | ||||||||
\(971\) | 16.9241 | 0.543121 | 0.271561 | − | 0.962421i | \(-0.412460\pi\) | ||||
0.271561 | + | 0.962421i | \(0.412460\pi\) | |||||||
\(972\) | 2.92842 | 0.0939292 | ||||||||
\(973\) | −28.4819 | −0.913087 | ||||||||
\(974\) | 16.2439 | 0.520489 | ||||||||
\(975\) | 3.01504 | 0.0965584 | ||||||||
\(976\) | −14.7514 | −0.472180 | ||||||||
\(977\) | 8.46580 | 0.270845 | 0.135422 | − | 0.990788i | \(-0.456761\pi\) | ||||
0.135422 | + | 0.990788i | \(0.456761\pi\) | |||||||
\(978\) | −20.8566 | −0.666919 | ||||||||
\(979\) | 12.9717 | 0.414576 | ||||||||
\(980\) | 16.1759 | 0.516719 | ||||||||
\(981\) | −1.86669 | −0.0595988 | ||||||||
\(982\) | 26.6296 | 0.849784 | ||||||||
\(983\) | −51.5719 | −1.64489 | −0.822444 | − | 0.568846i | \(-0.807390\pi\) | ||||
−0.822444 | + | 0.568846i | \(0.807390\pi\) | |||||||
\(984\) | 20.3770 | 0.649594 | ||||||||
\(985\) | 33.2140 | 1.05829 | ||||||||
\(986\) | 0.856651 | 0.0272813 | ||||||||
\(987\) | −5.79171 | −0.184352 | ||||||||
\(988\) | 25.3161 | 0.805411 | ||||||||
\(989\) | 10.8673 | 0.345559 | ||||||||
\(990\) | −16.1938 | −0.514673 | ||||||||
\(991\) | 15.8735 | 0.504237 | 0.252118 | − | 0.967696i | \(-0.418873\pi\) | ||||
0.252118 | + | 0.967696i | \(0.418873\pi\) | |||||||
\(992\) | −29.0321 | −0.921769 | ||||||||
\(993\) | 26.6575 | 0.845949 | ||||||||
\(994\) | −38.6548 | −1.22606 | ||||||||
\(995\) | 17.2629 | 0.547270 | ||||||||
\(996\) | 27.3070 | 0.865256 | ||||||||
\(997\) | 11.4346 | 0.362139 | 0.181069 | − | 0.983470i | \(-0.442044\pi\) | ||||
0.181069 | + | 0.983470i | \(0.442044\pi\) | |||||||
\(998\) | −31.3361 | −0.991927 | ||||||||
\(999\) | −6.13298 | −0.194039 |
(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 | 4029.2.a.k.1.5 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4029.2.a.k.1.5 | ✓ | 31 | 1.1 | even | 1 | trivial |