Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1003,2,Mod(1,1003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1003, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1003 = 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1003.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: | \(8.00899532273\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 3x^{9} - 10x^{8} + 34x^{7} + 28x^{6} - 129x^{5} - 3x^{4} + 178x^{3} - 56x^{2} - 56x + 15 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.08521\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.86330 | −1.31755 | −0.658777 | − | 0.752338i | \(-0.728926\pi\) | ||||
−0.658777 | + | 0.752338i | \(0.728926\pi\) | |||||||
\(3\) | 1.08521 | 0.626547 | 0.313273 | − | 0.949663i | \(-0.398574\pi\) | ||||
0.313273 | + | 0.949663i | \(0.398574\pi\) | |||||||
\(4\) | 1.47190 | 0.735950 | ||||||||
\(5\) | 0.335552 | 0.150064 | 0.0750318 | − | 0.997181i | \(-0.476094\pi\) | ||||
0.0750318 | + | 0.997181i | \(0.476094\pi\) | |||||||
\(6\) | −2.02208 | −0.825510 | ||||||||
\(7\) | −1.78229 | −0.673641 | −0.336821 | − | 0.941569i | \(-0.609352\pi\) | ||||
−0.336821 | + | 0.941569i | \(0.609352\pi\) | |||||||
\(8\) | 0.984011 | 0.347900 | ||||||||
\(9\) | −1.82232 | −0.607439 | ||||||||
\(10\) | −0.625236 | −0.197717 | ||||||||
\(11\) | −2.96686 | −0.894542 | −0.447271 | − | 0.894399i | \(-0.647604\pi\) | ||||
−0.447271 | + | 0.894399i | \(0.647604\pi\) | |||||||
\(12\) | 1.59732 | 0.461107 | ||||||||
\(13\) | 5.83034 | 1.61705 | 0.808523 | − | 0.588464i | \(-0.200267\pi\) | ||||
0.808523 | + | 0.588464i | \(0.200267\pi\) | |||||||
\(14\) | 3.32094 | 0.887559 | ||||||||
\(15\) | 0.364145 | 0.0940219 | ||||||||
\(16\) | −4.77731 | −1.19433 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 3.39553 | 0.800334 | ||||||||
\(19\) | 0.660752 | 0.151587 | 0.0757934 | − | 0.997124i | \(-0.475851\pi\) | ||||
0.0757934 | + | 0.997124i | \(0.475851\pi\) | |||||||
\(20\) | 0.493900 | 0.110439 | ||||||||
\(21\) | −1.93416 | −0.422068 | ||||||||
\(22\) | 5.52816 | 1.17861 | ||||||||
\(23\) | 2.34383 | 0.488722 | 0.244361 | − | 0.969684i | \(-0.421422\pi\) | ||||
0.244361 | + | 0.969684i | \(0.421422\pi\) | |||||||
\(24\) | 1.06786 | 0.217976 | ||||||||
\(25\) | −4.88740 | −0.977481 | ||||||||
\(26\) | −10.8637 | −2.13055 | ||||||||
\(27\) | −5.23323 | −1.00714 | ||||||||
\(28\) | −2.62335 | −0.495766 | ||||||||
\(29\) | −5.05539 | −0.938762 | −0.469381 | − | 0.882996i | \(-0.655523\pi\) | ||||
−0.469381 | + | 0.882996i | \(0.655523\pi\) | |||||||
\(30\) | −0.678513 | −0.123879 | ||||||||
\(31\) | −3.22725 | −0.579632 | −0.289816 | − | 0.957082i | \(-0.593594\pi\) | ||||
−0.289816 | + | 0.957082i | \(0.593594\pi\) | |||||||
\(32\) | 6.93356 | 1.22569 | ||||||||
\(33\) | −3.21967 | −0.560472 | ||||||||
\(34\) | 1.86330 | 0.319554 | ||||||||
\(35\) | −0.598051 | −0.101089 | ||||||||
\(36\) | −2.68227 | −0.447045 | ||||||||
\(37\) | 7.16306 | 1.17760 | 0.588800 | − | 0.808279i | \(-0.299600\pi\) | ||||
0.588800 | + | 0.808279i | \(0.299600\pi\) | |||||||
\(38\) | −1.23118 | −0.199724 | ||||||||
\(39\) | 6.32716 | 1.01316 | ||||||||
\(40\) | 0.330187 | 0.0522072 | ||||||||
\(41\) | −10.1061 | −1.57831 | −0.789157 | − | 0.614192i | \(-0.789482\pi\) | ||||
−0.789157 | + | 0.614192i | \(0.789482\pi\) | |||||||
\(42\) | 3.60392 | 0.556097 | ||||||||
\(43\) | −4.53751 | −0.691964 | −0.345982 | − | 0.938241i | \(-0.612454\pi\) | ||||
−0.345982 | + | 0.938241i | \(0.612454\pi\) | |||||||
\(44\) | −4.36692 | −0.658338 | ||||||||
\(45\) | −0.611483 | −0.0911545 | ||||||||
\(46\) | −4.36726 | −0.643918 | ||||||||
\(47\) | 3.42798 | 0.500022 | 0.250011 | − | 0.968243i | \(-0.419566\pi\) | ||||
0.250011 | + | 0.968243i | \(0.419566\pi\) | |||||||
\(48\) | −5.18439 | −0.748302 | ||||||||
\(49\) | −3.82345 | −0.546207 | ||||||||
\(50\) | 9.10672 | 1.28788 | ||||||||
\(51\) | −1.08521 | −0.151960 | ||||||||
\(52\) | 8.58168 | 1.19007 | ||||||||
\(53\) | −3.90662 | −0.536616 | −0.268308 | − | 0.963333i | \(-0.586464\pi\) | ||||
−0.268308 | + | 0.963333i | \(0.586464\pi\) | |||||||
\(54\) | 9.75110 | 1.32696 | ||||||||
\(55\) | −0.995537 | −0.134238 | ||||||||
\(56\) | −1.75379 | −0.234360 | ||||||||
\(57\) | 0.717055 | 0.0949763 | ||||||||
\(58\) | 9.41972 | 1.23687 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | 0.535985 | 0.0691954 | ||||||||
\(61\) | 1.20369 | 0.154116 | 0.0770580 | − | 0.997027i | \(-0.475447\pi\) | ||||
0.0770580 | + | 0.997027i | \(0.475447\pi\) | |||||||
\(62\) | 6.01335 | 0.763696 | ||||||||
\(63\) | 3.24789 | 0.409196 | ||||||||
\(64\) | −3.36470 | −0.420588 | ||||||||
\(65\) | 1.95639 | 0.242660 | ||||||||
\(66\) | 5.99922 | 0.738453 | ||||||||
\(67\) | 7.89572 | 0.964616 | 0.482308 | − | 0.876002i | \(-0.339799\pi\) | ||||
0.482308 | + | 0.876002i | \(0.339799\pi\) | |||||||
\(68\) | −1.47190 | −0.178494 | ||||||||
\(69\) | 2.54355 | 0.306207 | ||||||||
\(70\) | 1.11435 | 0.133190 | ||||||||
\(71\) | 4.37632 | 0.519374 | 0.259687 | − | 0.965693i | \(-0.416381\pi\) | ||||
0.259687 | + | 0.965693i | \(0.416381\pi\) | |||||||
\(72\) | −1.79318 | −0.211328 | ||||||||
\(73\) | −15.3323 | −1.79451 | −0.897254 | − | 0.441515i | \(-0.854441\pi\) | ||||
−0.897254 | + | 0.441515i | \(0.854441\pi\) | |||||||
\(74\) | −13.3470 | −1.55155 | ||||||||
\(75\) | −5.30387 | −0.612438 | ||||||||
\(76\) | 0.972560 | 0.111560 | ||||||||
\(77\) | 5.28780 | 0.602600 | ||||||||
\(78\) | −11.7894 | −1.33489 | ||||||||
\(79\) | 0.0651189 | 0.00732645 | 0.00366323 | − | 0.999993i | \(-0.498834\pi\) | ||||
0.00366323 | + | 0.999993i | \(0.498834\pi\) | |||||||
\(80\) | −1.60304 | −0.179225 | ||||||||
\(81\) | −0.212211 | −0.0235789 | ||||||||
\(82\) | 18.8308 | 2.07951 | ||||||||
\(83\) | −17.7551 | −1.94888 | −0.974439 | − | 0.224652i | \(-0.927875\pi\) | ||||
−0.974439 | + | 0.224652i | \(0.927875\pi\) | |||||||
\(84\) | −2.84689 | −0.310621 | ||||||||
\(85\) | −0.335552 | −0.0363958 | ||||||||
\(86\) | 8.45476 | 0.911700 | ||||||||
\(87\) | −5.48616 | −0.588179 | ||||||||
\(88\) | −2.91942 | −0.311211 | ||||||||
\(89\) | −10.4873 | −1.11166 | −0.555828 | − | 0.831297i | \(-0.687599\pi\) | ||||
−0.555828 | + | 0.831297i | \(0.687599\pi\) | |||||||
\(90\) | 1.13938 | 0.120101 | ||||||||
\(91\) | −10.3914 | −1.08931 | ||||||||
\(92\) | 3.44988 | 0.359675 | ||||||||
\(93\) | −3.50225 | −0.363166 | ||||||||
\(94\) | −6.38736 | −0.658806 | ||||||||
\(95\) | 0.221717 | 0.0227477 | ||||||||
\(96\) | 7.52437 | 0.767953 | ||||||||
\(97\) | 4.30637 | 0.437246 | 0.218623 | − | 0.975809i | \(-0.429844\pi\) | ||||
0.218623 | + | 0.975809i | \(0.429844\pi\) | |||||||
\(98\) | 7.12425 | 0.719658 | ||||||||
\(99\) | 5.40656 | 0.543380 | ||||||||
\(100\) | −7.19377 | −0.719377 | ||||||||
\(101\) | −16.9163 | −1.68324 | −0.841620 | − | 0.540071i | \(-0.818397\pi\) | ||||
−0.841620 | + | 0.540071i | \(0.818397\pi\) | |||||||
\(102\) | 2.02208 | 0.200216 | ||||||||
\(103\) | 1.32193 | 0.130254 | 0.0651268 | − | 0.997877i | \(-0.479255\pi\) | ||||
0.0651268 | + | 0.997877i | \(0.479255\pi\) | |||||||
\(104\) | 5.73712 | 0.562571 | ||||||||
\(105\) | −0.649011 | −0.0633370 | ||||||||
\(106\) | 7.27922 | 0.707020 | ||||||||
\(107\) | 5.87500 | 0.567957 | 0.283979 | − | 0.958831i | \(-0.408346\pi\) | ||||
0.283979 | + | 0.958831i | \(0.408346\pi\) | |||||||
\(108\) | −7.70279 | −0.741202 | ||||||||
\(109\) | 9.54324 | 0.914076 | 0.457038 | − | 0.889447i | \(-0.348910\pi\) | ||||
0.457038 | + | 0.889447i | \(0.348910\pi\) | |||||||
\(110\) | 1.85499 | 0.176866 | ||||||||
\(111\) | 7.77344 | 0.737822 | ||||||||
\(112\) | 8.51454 | 0.804548 | ||||||||
\(113\) | −15.5885 | −1.46644 | −0.733222 | − | 0.679989i | \(-0.761984\pi\) | ||||
−0.733222 | + | 0.679989i | \(0.761984\pi\) | |||||||
\(114\) | −1.33609 | −0.125136 | ||||||||
\(115\) | 0.786477 | 0.0733394 | ||||||||
\(116\) | −7.44103 | −0.690882 | ||||||||
\(117\) | −10.6247 | −0.982257 | ||||||||
\(118\) | 1.86330 | 0.171531 | ||||||||
\(119\) | 1.78229 | 0.163382 | ||||||||
\(120\) | 0.358323 | 0.0327102 | ||||||||
\(121\) | −2.19774 | −0.199795 | ||||||||
\(122\) | −2.24283 | −0.203056 | ||||||||
\(123\) | −10.9673 | −0.988888 | ||||||||
\(124\) | −4.75019 | −0.426580 | ||||||||
\(125\) | −3.31774 | −0.296748 | ||||||||
\(126\) | −6.05181 | −0.539138 | ||||||||
\(127\) | 5.88880 | 0.522547 | 0.261273 | − | 0.965265i | \(-0.415858\pi\) | ||||
0.261273 | + | 0.965265i | \(0.415858\pi\) | |||||||
\(128\) | −7.59766 | −0.671544 | ||||||||
\(129\) | −4.92416 | −0.433548 | ||||||||
\(130\) | −3.64534 | −0.319718 | ||||||||
\(131\) | 9.61177 | 0.839785 | 0.419892 | − | 0.907574i | \(-0.362068\pi\) | ||||
0.419892 | + | 0.907574i | \(0.362068\pi\) | |||||||
\(132\) | −4.73903 | −0.412480 | ||||||||
\(133\) | −1.17765 | −0.102115 | ||||||||
\(134\) | −14.7121 | −1.27093 | ||||||||
\(135\) | −1.75602 | −0.151134 | ||||||||
\(136\) | −0.984011 | −0.0843782 | ||||||||
\(137\) | −20.5821 | −1.75845 | −0.879223 | − | 0.476410i | \(-0.841938\pi\) | ||||
−0.879223 | + | 0.476410i | \(0.841938\pi\) | |||||||
\(138\) | −4.73940 | −0.403445 | ||||||||
\(139\) | 1.51139 | 0.128194 | 0.0640971 | − | 0.997944i | \(-0.479583\pi\) | ||||
0.0640971 | + | 0.997944i | \(0.479583\pi\) | |||||||
\(140\) | −0.880271 | −0.0743965 | ||||||||
\(141\) | 3.72008 | 0.313287 | ||||||||
\(142\) | −8.15442 | −0.684303 | ||||||||
\(143\) | −17.2978 | −1.44652 | ||||||||
\(144\) | 8.70577 | 0.725481 | ||||||||
\(145\) | −1.69635 | −0.140874 | ||||||||
\(146\) | 28.5687 | 2.36436 | ||||||||
\(147\) | −4.14925 | −0.342225 | ||||||||
\(148\) | 10.5433 | 0.866655 | ||||||||
\(149\) | −9.99932 | −0.819177 | −0.409588 | − | 0.912270i | \(-0.634328\pi\) | ||||
−0.409588 | + | 0.912270i | \(0.634328\pi\) | |||||||
\(150\) | 9.88271 | 0.806920 | ||||||||
\(151\) | −11.6818 | −0.950648 | −0.475324 | − | 0.879811i | \(-0.657669\pi\) | ||||
−0.475324 | + | 0.879811i | \(0.657669\pi\) | |||||||
\(152\) | 0.650187 | 0.0527371 | ||||||||
\(153\) | 1.82232 | 0.147326 | ||||||||
\(154\) | −9.85277 | −0.793959 | ||||||||
\(155\) | −1.08291 | −0.0869816 | ||||||||
\(156\) | 9.31294 | 0.745632 | ||||||||
\(157\) | −1.38132 | −0.110241 | −0.0551206 | − | 0.998480i | \(-0.517554\pi\) | ||||
−0.0551206 | + | 0.998480i | \(0.517554\pi\) | |||||||
\(158\) | −0.121336 | −0.00965300 | ||||||||
\(159\) | −4.23951 | −0.336215 | ||||||||
\(160\) | 2.32657 | 0.183932 | ||||||||
\(161\) | −4.17738 | −0.329223 | ||||||||
\(162\) | 0.395413 | 0.0310665 | ||||||||
\(163\) | 6.47260 | 0.506973 | 0.253487 | − | 0.967339i | \(-0.418423\pi\) | ||||
0.253487 | + | 0.967339i | \(0.418423\pi\) | |||||||
\(164\) | −14.8752 | −1.16156 | ||||||||
\(165\) | −1.08037 | −0.0841065 | ||||||||
\(166\) | 33.0832 | 2.56775 | ||||||||
\(167\) | −4.61493 | −0.357114 | −0.178557 | − | 0.983930i | \(-0.557143\pi\) | ||||
−0.178557 | + | 0.983930i | \(0.557143\pi\) | |||||||
\(168\) | −1.90323 | −0.146838 | ||||||||
\(169\) | 20.9929 | 1.61484 | ||||||||
\(170\) | 0.625236 | 0.0479534 | ||||||||
\(171\) | −1.20410 | −0.0920798 | ||||||||
\(172\) | −6.67876 | −0.509251 | ||||||||
\(173\) | 16.8344 | 1.27990 | 0.639948 | − | 0.768418i | \(-0.278956\pi\) | ||||
0.639948 | + | 0.768418i | \(0.278956\pi\) | |||||||
\(174\) | 10.2224 | 0.774957 | ||||||||
\(175\) | 8.71076 | 0.658472 | ||||||||
\(176\) | 14.1736 | 1.06838 | ||||||||
\(177\) | −1.08521 | −0.0815695 | ||||||||
\(178\) | 19.5411 | 1.46467 | ||||||||
\(179\) | 5.62749 | 0.420618 | 0.210309 | − | 0.977635i | \(-0.432553\pi\) | ||||
0.210309 | + | 0.977635i | \(0.432553\pi\) | |||||||
\(180\) | −0.900041 | −0.0670851 | ||||||||
\(181\) | −11.9052 | −0.884904 | −0.442452 | − | 0.896792i | \(-0.645891\pi\) | ||||
−0.442452 | + | 0.896792i | \(0.645891\pi\) | |||||||
\(182\) | 19.3622 | 1.43522 | ||||||||
\(183\) | 1.30625 | 0.0965610 | ||||||||
\(184\) | 2.30635 | 0.170027 | ||||||||
\(185\) | 2.40358 | 0.176715 | ||||||||
\(186\) | 6.52576 | 0.478492 | ||||||||
\(187\) | 2.96686 | 0.216958 | ||||||||
\(188\) | 5.04564 | 0.367991 | ||||||||
\(189\) | 9.32712 | 0.678448 | ||||||||
\(190\) | −0.413126 | −0.0299713 | ||||||||
\(191\) | −25.4738 | −1.84322 | −0.921611 | − | 0.388115i | \(-0.873126\pi\) | ||||
−0.921611 | + | 0.388115i | \(0.873126\pi\) | |||||||
\(192\) | −3.65141 | −0.263518 | ||||||||
\(193\) | 10.9178 | 0.785881 | 0.392940 | − | 0.919564i | \(-0.371458\pi\) | ||||
0.392940 | + | 0.919564i | \(0.371458\pi\) | |||||||
\(194\) | −8.02408 | −0.576095 | ||||||||
\(195\) | 2.12309 | 0.152038 | ||||||||
\(196\) | −5.62774 | −0.401981 | ||||||||
\(197\) | 12.7677 | 0.909662 | 0.454831 | − | 0.890578i | \(-0.349700\pi\) | ||||
0.454831 | + | 0.890578i | \(0.349700\pi\) | |||||||
\(198\) | −10.0741 | −0.715932 | ||||||||
\(199\) | 8.19687 | 0.581061 | 0.290530 | − | 0.956866i | \(-0.406168\pi\) | ||||
0.290530 | + | 0.956866i | \(0.406168\pi\) | |||||||
\(200\) | −4.80926 | −0.340066 | ||||||||
\(201\) | 8.56853 | 0.604377 | ||||||||
\(202\) | 31.5203 | 2.21776 | ||||||||
\(203\) | 9.01016 | 0.632389 | ||||||||
\(204\) | −1.59732 | −0.111835 | ||||||||
\(205\) | −3.39114 | −0.236847 | ||||||||
\(206\) | −2.46316 | −0.171616 | ||||||||
\(207\) | −4.27120 | −0.296869 | ||||||||
\(208\) | −27.8534 | −1.93128 | ||||||||
\(209\) | −1.96036 | −0.135601 | ||||||||
\(210\) | 1.20931 | 0.0834500 | ||||||||
\(211\) | 21.1312 | 1.45473 | 0.727367 | − | 0.686249i | \(-0.240744\pi\) | ||||
0.727367 | + | 0.686249i | \(0.240744\pi\) | |||||||
\(212\) | −5.75015 | −0.394922 | ||||||||
\(213\) | 4.74923 | 0.325412 | ||||||||
\(214\) | −10.9469 | −0.748315 | ||||||||
\(215\) | −1.52257 | −0.103839 | ||||||||
\(216\) | −5.14956 | −0.350383 | ||||||||
\(217\) | 5.75189 | 0.390464 | ||||||||
\(218\) | −17.7819 | −1.20435 | ||||||||
\(219\) | −16.6388 | −1.12434 | ||||||||
\(220\) | −1.46533 | −0.0987926 | ||||||||
\(221\) | −5.83034 | −0.392191 | ||||||||
\(222\) | −14.4843 | −0.972121 | ||||||||
\(223\) | −20.0111 | −1.34004 | −0.670020 | − | 0.742343i | \(-0.733714\pi\) | ||||
−0.670020 | + | 0.742343i | \(0.733714\pi\) | |||||||
\(224\) | −12.3576 | −0.825676 | ||||||||
\(225\) | 8.90640 | 0.593760 | ||||||||
\(226\) | 29.0461 | 1.93212 | ||||||||
\(227\) | 11.1459 | 0.739778 | 0.369889 | − | 0.929076i | \(-0.379396\pi\) | ||||
0.369889 | + | 0.929076i | \(0.379396\pi\) | |||||||
\(228\) | 1.05543 | 0.0698978 | ||||||||
\(229\) | 20.2955 | 1.34116 | 0.670581 | − | 0.741836i | \(-0.266045\pi\) | ||||
0.670581 | + | 0.741836i | \(0.266045\pi\) | |||||||
\(230\) | −1.46545 | −0.0966286 | ||||||||
\(231\) | 5.73838 | 0.377557 | ||||||||
\(232\) | −4.97456 | −0.326596 | ||||||||
\(233\) | −5.04130 | −0.330267 | −0.165133 | − | 0.986271i | \(-0.552805\pi\) | ||||
−0.165133 | + | 0.986271i | \(0.552805\pi\) | |||||||
\(234\) | 19.7971 | 1.29418 | ||||||||
\(235\) | 1.15027 | 0.0750351 | ||||||||
\(236\) | −1.47190 | −0.0958125 | ||||||||
\(237\) | 0.0706678 | 0.00459037 | ||||||||
\(238\) | −3.32094 | −0.215265 | ||||||||
\(239\) | 24.7860 | 1.60327 | 0.801637 | − | 0.597812i | \(-0.203963\pi\) | ||||
0.801637 | + | 0.597812i | \(0.203963\pi\) | |||||||
\(240\) | −1.73963 | −0.112293 | ||||||||
\(241\) | 11.3279 | 0.729697 | 0.364848 | − | 0.931067i | \(-0.381121\pi\) | ||||
0.364848 | + | 0.931067i | \(0.381121\pi\) | |||||||
\(242\) | 4.09506 | 0.263241 | ||||||||
\(243\) | 15.4694 | 0.992363 | ||||||||
\(244\) | 1.77170 | 0.113422 | ||||||||
\(245\) | −1.28297 | −0.0819658 | ||||||||
\(246\) | 20.4354 | 1.30291 | ||||||||
\(247\) | 3.85241 | 0.245123 | ||||||||
\(248\) | −3.17565 | −0.201654 | ||||||||
\(249\) | −19.2681 | −1.22106 | ||||||||
\(250\) | 6.18196 | 0.390982 | ||||||||
\(251\) | 9.31329 | 0.587850 | 0.293925 | − | 0.955829i | \(-0.405038\pi\) | ||||
0.293925 | + | 0.955829i | \(0.405038\pi\) | |||||||
\(252\) | 4.78057 | 0.301148 | ||||||||
\(253\) | −6.95381 | −0.437182 | ||||||||
\(254\) | −10.9726 | −0.688484 | ||||||||
\(255\) | −0.364145 | −0.0228037 | ||||||||
\(256\) | 20.8861 | 1.30538 | ||||||||
\(257\) | 17.0007 | 1.06048 | 0.530238 | − | 0.847849i | \(-0.322103\pi\) | ||||
0.530238 | + | 0.847849i | \(0.322103\pi\) | |||||||
\(258\) | 9.17520 | 0.571223 | ||||||||
\(259\) | −12.7666 | −0.793280 | ||||||||
\(260\) | 2.87960 | 0.178585 | ||||||||
\(261\) | 9.21252 | 0.570241 | ||||||||
\(262\) | −17.9097 | −1.10646 | ||||||||
\(263\) | −9.94021 | −0.612940 | −0.306470 | − | 0.951880i | \(-0.599148\pi\) | ||||
−0.306470 | + | 0.951880i | \(0.599148\pi\) | |||||||
\(264\) | −3.16819 | −0.194989 | ||||||||
\(265\) | −1.31088 | −0.0805265 | ||||||||
\(266\) | 2.19432 | 0.134542 | ||||||||
\(267\) | −11.3810 | −0.696504 | ||||||||
\(268\) | 11.6217 | 0.709909 | ||||||||
\(269\) | 4.02855 | 0.245625 | 0.122813 | − | 0.992430i | \(-0.460809\pi\) | ||||
0.122813 | + | 0.992430i | \(0.460809\pi\) | |||||||
\(270\) | 3.27200 | 0.199128 | ||||||||
\(271\) | 15.7817 | 0.958670 | 0.479335 | − | 0.877632i | \(-0.340878\pi\) | ||||
0.479335 | + | 0.877632i | \(0.340878\pi\) | |||||||
\(272\) | 4.77731 | 0.289667 | ||||||||
\(273\) | −11.2768 | −0.682504 | ||||||||
\(274\) | 38.3507 | 2.31685 | ||||||||
\(275\) | 14.5002 | 0.874398 | ||||||||
\(276\) | 3.74385 | 0.225353 | ||||||||
\(277\) | 15.7930 | 0.948909 | 0.474454 | − | 0.880280i | \(-0.342645\pi\) | ||||
0.474454 | + | 0.880280i | \(0.342645\pi\) | |||||||
\(278\) | −2.81617 | −0.168903 | ||||||||
\(279\) | 5.88108 | 0.352091 | ||||||||
\(280\) | −0.588488 | −0.0351689 | ||||||||
\(281\) | −7.57142 | −0.451673 | −0.225837 | − | 0.974165i | \(-0.572512\pi\) | ||||
−0.225837 | + | 0.974165i | \(0.572512\pi\) | |||||||
\(282\) | −6.93163 | −0.412773 | ||||||||
\(283\) | 15.7493 | 0.936200 | 0.468100 | − | 0.883675i | \(-0.344939\pi\) | ||||
0.468100 | + | 0.883675i | \(0.344939\pi\) | |||||||
\(284\) | 6.44151 | 0.382233 | ||||||||
\(285\) | 0.240610 | 0.0142525 | ||||||||
\(286\) | 32.2311 | 1.90586 | ||||||||
\(287\) | 18.0120 | 1.06322 | ||||||||
\(288\) | −12.6351 | −0.744533 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 3.16081 | 0.185609 | ||||||||
\(291\) | 4.67332 | 0.273955 | ||||||||
\(292\) | −22.5676 | −1.32067 | ||||||||
\(293\) | 2.58099 | 0.150783 | 0.0753916 | − | 0.997154i | \(-0.475979\pi\) | ||||
0.0753916 | + | 0.997154i | \(0.475979\pi\) | |||||||
\(294\) | 7.73132 | 0.450899 | ||||||||
\(295\) | −0.335552 | −0.0195366 | ||||||||
\(296\) | 7.04853 | 0.409688 | ||||||||
\(297\) | 15.5263 | 0.900925 | ||||||||
\(298\) | 18.6318 | 1.07931 | ||||||||
\(299\) | 13.6653 | 0.790286 | ||||||||
\(300\) | −7.80676 | −0.450723 | ||||||||
\(301\) | 8.08715 | 0.466135 | ||||||||
\(302\) | 21.7667 | 1.25253 | ||||||||
\(303\) | −18.3578 | −1.05463 | ||||||||
\(304\) | −3.15662 | −0.181044 | ||||||||
\(305\) | 0.403899 | 0.0231272 | ||||||||
\(306\) | −3.39553 | −0.194109 | ||||||||
\(307\) | −15.8745 | −0.906005 | −0.453002 | − | 0.891509i | \(-0.649647\pi\) | ||||
−0.453002 | + | 0.891509i | \(0.649647\pi\) | |||||||
\(308\) | 7.78311 | 0.443484 | ||||||||
\(309\) | 1.43457 | 0.0816100 | ||||||||
\(310\) | 2.01779 | 0.114603 | ||||||||
\(311\) | −6.04920 | −0.343018 | −0.171509 | − | 0.985183i | \(-0.554864\pi\) | ||||
−0.171509 | + | 0.985183i | \(0.554864\pi\) | |||||||
\(312\) | 6.22599 | 0.352477 | ||||||||
\(313\) | 28.0638 | 1.58626 | 0.793130 | − | 0.609053i | \(-0.208450\pi\) | ||||
0.793130 | + | 0.609053i | \(0.208450\pi\) | |||||||
\(314\) | 2.57381 | 0.145249 | ||||||||
\(315\) | 1.08984 | 0.0614054 | ||||||||
\(316\) | 0.0958485 | 0.00539190 | ||||||||
\(317\) | −24.9206 | −1.39968 | −0.699840 | − | 0.714300i | \(-0.746745\pi\) | ||||
−0.699840 | + | 0.714300i | \(0.746745\pi\) | |||||||
\(318\) | 7.89949 | 0.442981 | ||||||||
\(319\) | 14.9986 | 0.839762 | ||||||||
\(320\) | −1.12903 | −0.0631149 | ||||||||
\(321\) | 6.37561 | 0.355852 | ||||||||
\(322\) | 7.78372 | 0.433770 | ||||||||
\(323\) | −0.660752 | −0.0367652 | ||||||||
\(324\) | −0.312353 | −0.0173529 | ||||||||
\(325\) | −28.4953 | −1.58063 | ||||||||
\(326\) | −12.0604 | −0.667965 | ||||||||
\(327\) | 10.3564 | 0.572712 | ||||||||
\(328\) | −9.94455 | −0.549096 | ||||||||
\(329\) | −6.10964 | −0.336835 | ||||||||
\(330\) | 2.01305 | 0.110815 | ||||||||
\(331\) | −6.25862 | −0.344005 | −0.172003 | − | 0.985097i | \(-0.555024\pi\) | ||||
−0.172003 | + | 0.985097i | \(0.555024\pi\) | |||||||
\(332\) | −26.1338 | −1.43428 | ||||||||
\(333\) | −13.0534 | −0.715320 | ||||||||
\(334\) | 8.59901 | 0.470517 | ||||||||
\(335\) | 2.64943 | 0.144754 | ||||||||
\(336\) | 9.24007 | 0.504087 | ||||||||
\(337\) | −14.5926 | −0.794910 | −0.397455 | − | 0.917622i | \(-0.630107\pi\) | ||||
−0.397455 | + | 0.917622i | \(0.630107\pi\) | |||||||
\(338\) | −39.1162 | −2.12764 | ||||||||
\(339\) | −16.9168 | −0.918796 | ||||||||
\(340\) | −0.493900 | −0.0267855 | ||||||||
\(341\) | 9.57481 | 0.518505 | ||||||||
\(342\) | 2.24360 | 0.121320 | ||||||||
\(343\) | 19.2905 | 1.04159 | ||||||||
\(344\) | −4.46496 | −0.240734 | ||||||||
\(345\) | 0.853494 | 0.0459506 | ||||||||
\(346\) | −31.3676 | −1.68633 | ||||||||
\(347\) | −29.6944 | −1.59408 | −0.797038 | − | 0.603929i | \(-0.793601\pi\) | ||||
−0.797038 | + | 0.603929i | \(0.793601\pi\) | |||||||
\(348\) | −8.07509 | −0.432870 | ||||||||
\(349\) | 28.5347 | 1.52743 | 0.763714 | − | 0.645555i | \(-0.223374\pi\) | ||||
0.763714 | + | 0.645555i | \(0.223374\pi\) | |||||||
\(350\) | −16.2308 | −0.867572 | ||||||||
\(351\) | −30.5115 | −1.62859 | ||||||||
\(352\) | −20.5709 | −1.09643 | ||||||||
\(353\) | 9.76145 | 0.519549 | 0.259775 | − | 0.965669i | \(-0.416352\pi\) | ||||
0.259775 | + | 0.965669i | \(0.416352\pi\) | |||||||
\(354\) | 2.02208 | 0.107472 | ||||||||
\(355\) | 1.46849 | 0.0779391 | ||||||||
\(356\) | −15.4363 | −0.818123 | ||||||||
\(357\) | 1.93416 | 0.102367 | ||||||||
\(358\) | −10.4857 | −0.554188 | ||||||||
\(359\) | 22.9107 | 1.20918 | 0.604590 | − | 0.796537i | \(-0.293337\pi\) | ||||
0.604590 | + | 0.796537i | \(0.293337\pi\) | |||||||
\(360\) | −0.601706 | −0.0317127 | ||||||||
\(361\) | −18.5634 | −0.977021 | ||||||||
\(362\) | 22.1829 | 1.16591 | ||||||||
\(363\) | −2.38501 | −0.125181 | ||||||||
\(364\) | −15.2950 | −0.801677 | ||||||||
\(365\) | −5.14478 | −0.269290 | ||||||||
\(366\) | −2.43394 | −0.127224 | ||||||||
\(367\) | −7.95154 | −0.415067 | −0.207533 | − | 0.978228i | \(-0.566544\pi\) | ||||
−0.207533 | + | 0.978228i | \(0.566544\pi\) | |||||||
\(368\) | −11.1972 | −0.583694 | ||||||||
\(369\) | 18.4166 | 0.958729 | ||||||||
\(370\) | −4.47861 | −0.232832 | ||||||||
\(371\) | 6.96272 | 0.361486 | ||||||||
\(372\) | −5.15496 | −0.267272 | ||||||||
\(373\) | 9.27783 | 0.480388 | 0.240194 | − | 0.970725i | \(-0.422789\pi\) | ||||
0.240194 | + | 0.970725i | \(0.422789\pi\) | |||||||
\(374\) | −5.52816 | −0.285854 | ||||||||
\(375\) | −3.60045 | −0.185926 | ||||||||
\(376\) | 3.37317 | 0.173958 | ||||||||
\(377\) | −29.4747 | −1.51802 | ||||||||
\(378\) | −17.3793 | −0.893893 | ||||||||
\(379\) | 7.95324 | 0.408531 | 0.204265 | − | 0.978916i | \(-0.434519\pi\) | ||||
0.204265 | + | 0.978916i | \(0.434519\pi\) | |||||||
\(380\) | 0.326345 | 0.0167411 | ||||||||
\(381\) | 6.39059 | 0.327400 | ||||||||
\(382\) | 47.4655 | 2.42855 | ||||||||
\(383\) | −20.2576 | −1.03511 | −0.517557 | − | 0.855648i | \(-0.673159\pi\) | ||||
−0.517557 | + | 0.855648i | \(0.673159\pi\) | |||||||
\(384\) | −8.24506 | −0.420754 | ||||||||
\(385\) | 1.77433 | 0.0904284 | ||||||||
\(386\) | −20.3432 | −1.03544 | ||||||||
\(387\) | 8.26878 | 0.420326 | ||||||||
\(388\) | 6.33855 | 0.321791 | ||||||||
\(389\) | 5.39968 | 0.273775 | 0.136887 | − | 0.990587i | \(-0.456290\pi\) | ||||
0.136887 | + | 0.990587i | \(0.456290\pi\) | |||||||
\(390\) | −3.95596 | −0.200318 | ||||||||
\(391\) | −2.34383 | −0.118532 | ||||||||
\(392\) | −3.76232 | −0.190026 | ||||||||
\(393\) | 10.4308 | 0.526164 | ||||||||
\(394\) | −23.7901 | −1.19853 | ||||||||
\(395\) | 0.0218508 | 0.00109943 | ||||||||
\(396\) | 7.95791 | 0.399900 | ||||||||
\(397\) | 6.75805 | 0.339177 | 0.169588 | − | 0.985515i | \(-0.445756\pi\) | ||||
0.169588 | + | 0.985515i | \(0.445756\pi\) | |||||||
\(398\) | −15.2733 | −0.765579 | ||||||||
\(399\) | −1.27800 | −0.0639799 | ||||||||
\(400\) | 23.3486 | 1.16743 | ||||||||
\(401\) | 7.86655 | 0.392837 | 0.196418 | − | 0.980520i | \(-0.437069\pi\) | ||||
0.196418 | + | 0.980520i | \(0.437069\pi\) | |||||||
\(402\) | −15.9658 | −0.796300 | ||||||||
\(403\) | −18.8160 | −0.937292 | ||||||||
\(404\) | −24.8992 | −1.23878 | ||||||||
\(405\) | −0.0712078 | −0.00353834 | ||||||||
\(406\) | −16.7887 | −0.833207 | ||||||||
\(407\) | −21.2518 | −1.05341 | ||||||||
\(408\) | −1.06786 | −0.0528669 | ||||||||
\(409\) | −29.2041 | −1.44405 | −0.722024 | − | 0.691868i | \(-0.756788\pi\) | ||||
−0.722024 | + | 0.691868i | \(0.756788\pi\) | |||||||
\(410\) | 6.31872 | 0.312059 | ||||||||
\(411\) | −22.3359 | −1.10175 | ||||||||
\(412\) | 1.94575 | 0.0958601 | ||||||||
\(413\) | 1.78229 | 0.0877006 | ||||||||
\(414\) | 7.95854 | 0.391141 | ||||||||
\(415\) | −5.95777 | −0.292456 | ||||||||
\(416\) | 40.4250 | 1.98200 | ||||||||
\(417\) | 1.64017 | 0.0803197 | ||||||||
\(418\) | 3.65274 | 0.178661 | ||||||||
\(419\) | 25.2775 | 1.23488 | 0.617442 | − | 0.786616i | \(-0.288169\pi\) | ||||
0.617442 | + | 0.786616i | \(0.288169\pi\) | |||||||
\(420\) | −0.955280 | −0.0466129 | ||||||||
\(421\) | −26.9567 | −1.31379 | −0.656894 | − | 0.753983i | \(-0.728130\pi\) | ||||
−0.656894 | + | 0.753983i | \(0.728130\pi\) | |||||||
\(422\) | −39.3739 | −1.91669 | ||||||||
\(423\) | −6.24686 | −0.303733 | ||||||||
\(424\) | −3.84416 | −0.186689 | ||||||||
\(425\) | 4.88740 | 0.237074 | ||||||||
\(426\) | −8.84926 | −0.428748 | ||||||||
\(427\) | −2.14531 | −0.103819 | ||||||||
\(428\) | 8.64741 | 0.417988 | ||||||||
\(429\) | −18.7718 | −0.906310 | ||||||||
\(430\) | 2.83701 | 0.136813 | ||||||||
\(431\) | −22.9758 | −1.10671 | −0.553353 | − | 0.832947i | \(-0.686652\pi\) | ||||
−0.553353 | + | 0.832947i | \(0.686652\pi\) | |||||||
\(432\) | 25.0008 | 1.20285 | ||||||||
\(433\) | 15.9134 | 0.764751 | 0.382376 | − | 0.924007i | \(-0.375106\pi\) | ||||
0.382376 | + | 0.924007i | \(0.375106\pi\) | |||||||
\(434\) | −10.7175 | −0.514457 | ||||||||
\(435\) | −1.84090 | −0.0882642 | ||||||||
\(436\) | 14.0467 | 0.672714 | ||||||||
\(437\) | 1.54869 | 0.0740838 | ||||||||
\(438\) | 31.0031 | 1.48138 | ||||||||
\(439\) | 6.10811 | 0.291524 | 0.145762 | − | 0.989320i | \(-0.453437\pi\) | ||||
0.145762 | + | 0.989320i | \(0.453437\pi\) | |||||||
\(440\) | −0.979619 | −0.0467015 | ||||||||
\(441\) | 6.96754 | 0.331788 | ||||||||
\(442\) | 10.8637 | 0.516734 | ||||||||
\(443\) | 3.55001 | 0.168666 | 0.0843330 | − | 0.996438i | \(-0.473124\pi\) | ||||
0.0843330 | + | 0.996438i | \(0.473124\pi\) | |||||||
\(444\) | 11.4417 | 0.543000 | ||||||||
\(445\) | −3.51905 | −0.166819 | ||||||||
\(446\) | 37.2867 | 1.76558 | ||||||||
\(447\) | −10.8514 | −0.513253 | ||||||||
\(448\) | 5.99686 | 0.283325 | ||||||||
\(449\) | −32.8083 | −1.54832 | −0.774161 | − | 0.632989i | \(-0.781828\pi\) | ||||
−0.774161 | + | 0.632989i | \(0.781828\pi\) | |||||||
\(450\) | −16.5953 | −0.782311 | ||||||||
\(451\) | 29.9835 | 1.41187 | ||||||||
\(452\) | −22.9447 | −1.07923 | ||||||||
\(453\) | −12.6772 | −0.595626 | ||||||||
\(454\) | −20.7682 | −0.974698 | ||||||||
\(455\) | −3.48684 | −0.163466 | ||||||||
\(456\) | 0.705590 | 0.0330423 | ||||||||
\(457\) | −7.85695 | −0.367533 | −0.183766 | − | 0.982970i | \(-0.558829\pi\) | ||||
−0.183766 | + | 0.982970i | \(0.558829\pi\) | |||||||
\(458\) | −37.8166 | −1.76705 | ||||||||
\(459\) | 5.23323 | 0.244266 | ||||||||
\(460\) | 1.15762 | 0.0539741 | ||||||||
\(461\) | 10.5628 | 0.491957 | 0.245978 | − | 0.969275i | \(-0.420891\pi\) | ||||
0.245978 | + | 0.969275i | \(0.420891\pi\) | |||||||
\(462\) | −10.6923 | −0.497452 | ||||||||
\(463\) | −32.3816 | −1.50490 | −0.752450 | − | 0.658649i | \(-0.771128\pi\) | ||||
−0.752450 | + | 0.658649i | \(0.771128\pi\) | |||||||
\(464\) | 24.1512 | 1.12119 | ||||||||
\(465\) | −1.17519 | −0.0544981 | ||||||||
\(466\) | 9.39348 | 0.435144 | ||||||||
\(467\) | 4.58631 | 0.212229 | 0.106115 | − | 0.994354i | \(-0.466159\pi\) | ||||
0.106115 | + | 0.994354i | \(0.466159\pi\) | |||||||
\(468\) | −15.6385 | −0.722892 | ||||||||
\(469\) | −14.0724 | −0.649805 | ||||||||
\(470\) | −2.14329 | −0.0988628 | ||||||||
\(471\) | −1.49902 | −0.0690712 | ||||||||
\(472\) | −0.984011 | −0.0452928 | ||||||||
\(473\) | 13.4622 | 0.618991 | ||||||||
\(474\) | −0.131676 | −0.00604806 | ||||||||
\(475\) | −3.22936 | −0.148173 | ||||||||
\(476\) | 2.62335 | 0.120241 | ||||||||
\(477\) | 7.11910 | 0.325961 | ||||||||
\(478\) | −46.1838 | −2.11240 | ||||||||
\(479\) | −0.613626 | −0.0280373 | −0.0140186 | − | 0.999902i | \(-0.504462\pi\) | ||||
−0.0140186 | + | 0.999902i | \(0.504462\pi\) | |||||||
\(480\) | 2.52482 | 0.115242 | ||||||||
\(481\) | 41.7631 | 1.90423 | ||||||||
\(482\) | −21.1074 | −0.961416 | ||||||||
\(483\) | −4.53333 | −0.206274 | ||||||||
\(484\) | −3.23486 | −0.147039 | ||||||||
\(485\) | 1.44501 | 0.0656147 | ||||||||
\(486\) | −28.8242 | −1.30749 | ||||||||
\(487\) | 10.6801 | 0.483962 | 0.241981 | − | 0.970281i | \(-0.422203\pi\) | ||||
0.241981 | + | 0.970281i | \(0.422203\pi\) | |||||||
\(488\) | 1.18444 | 0.0536170 | ||||||||
\(489\) | 7.02414 | 0.317642 | ||||||||
\(490\) | 2.39056 | 0.107994 | ||||||||
\(491\) | 38.8940 | 1.75526 | 0.877630 | − | 0.479338i | \(-0.159123\pi\) | ||||
0.877630 | + | 0.479338i | \(0.159123\pi\) | |||||||
\(492\) | −16.1428 | −0.727772 | ||||||||
\(493\) | 5.05539 | 0.227683 | ||||||||
\(494\) | −7.17821 | −0.322963 | ||||||||
\(495\) | 1.81418 | 0.0815415 | ||||||||
\(496\) | 15.4176 | 0.692270 | ||||||||
\(497\) | −7.79986 | −0.349872 | ||||||||
\(498\) | 35.9022 | 1.60882 | ||||||||
\(499\) | −35.7847 | −1.60194 | −0.800970 | − | 0.598704i | \(-0.795683\pi\) | ||||
−0.800970 | + | 0.598704i | \(0.795683\pi\) | |||||||
\(500\) | −4.88338 | −0.218392 | ||||||||
\(501\) | −5.00817 | −0.223749 | ||||||||
\(502\) | −17.3535 | −0.774524 | ||||||||
\(503\) | 17.2649 | 0.769802 | 0.384901 | − | 0.922958i | \(-0.374236\pi\) | ||||
0.384901 | + | 0.922958i | \(0.374236\pi\) | |||||||
\(504\) | 3.19596 | 0.142359 | ||||||||
\(505\) | −5.67632 | −0.252593 | ||||||||
\(506\) | 12.9571 | 0.576011 | ||||||||
\(507\) | 22.7818 | 1.01177 | ||||||||
\(508\) | 8.66773 | 0.384568 | ||||||||
\(509\) | 16.2983 | 0.722411 | 0.361206 | − | 0.932486i | \(-0.382365\pi\) | ||||
0.361206 | + | 0.932486i | \(0.382365\pi\) | |||||||
\(510\) | 0.678513 | 0.0300451 | ||||||||
\(511\) | 27.3265 | 1.20885 | ||||||||
\(512\) | −23.7219 | −1.04837 | ||||||||
\(513\) | −3.45787 | −0.152669 | ||||||||
\(514\) | −31.6775 | −1.39723 | ||||||||
\(515\) | 0.443577 | 0.0195463 | ||||||||
\(516\) | −7.24786 | −0.319069 | ||||||||
\(517\) | −10.1703 | −0.447290 | ||||||||
\(518\) | 23.7881 | 1.04519 | ||||||||
\(519\) | 18.2689 | 0.801915 | ||||||||
\(520\) | 1.92511 | 0.0844214 | ||||||||
\(521\) | −33.4699 | −1.46634 | −0.733172 | − | 0.680044i | \(-0.761961\pi\) | ||||
−0.733172 | + | 0.680044i | \(0.761961\pi\) | |||||||
\(522\) | −17.1657 | −0.751323 | ||||||||
\(523\) | 1.80809 | 0.0790621 | 0.0395311 | − | 0.999218i | \(-0.487414\pi\) | ||||
0.0395311 | + | 0.999218i | \(0.487414\pi\) | |||||||
\(524\) | 14.1476 | 0.618039 | ||||||||
\(525\) | 9.45301 | 0.412563 | ||||||||
\(526\) | 18.5216 | 0.807581 | ||||||||
\(527\) | 3.22725 | 0.140581 | ||||||||
\(528\) | 15.3814 | 0.669388 | ||||||||
\(529\) | −17.5065 | −0.761151 | ||||||||
\(530\) | 2.44256 | 0.106098 | ||||||||
\(531\) | 1.82232 | 0.0790818 | ||||||||
\(532\) | −1.73338 | −0.0751516 | ||||||||
\(533\) | −58.9223 | −2.55221 | ||||||||
\(534\) | 21.2062 | 0.917682 | ||||||||
\(535\) | 1.97137 | 0.0852297 | ||||||||
\(536\) | 7.76948 | 0.335590 | ||||||||
\(537\) | 6.10701 | 0.263537 | ||||||||
\(538\) | −7.50642 | −0.323625 | ||||||||
\(539\) | 11.3436 | 0.488605 | ||||||||
\(540\) | −2.58469 | −0.111227 | ||||||||
\(541\) | 6.67089 | 0.286804 | 0.143402 | − | 0.989665i | \(-0.454196\pi\) | ||||
0.143402 | + | 0.989665i | \(0.454196\pi\) | |||||||
\(542\) | −29.4061 | −1.26310 | ||||||||
\(543\) | −12.9196 | −0.554434 | ||||||||
\(544\) | −6.93356 | −0.297274 | ||||||||
\(545\) | 3.20226 | 0.137170 | ||||||||
\(546\) | 21.0121 | 0.899236 | ||||||||
\(547\) | −2.92387 | −0.125016 | −0.0625078 | − | 0.998044i | \(-0.519910\pi\) | ||||
−0.0625078 | + | 0.998044i | \(0.519910\pi\) | |||||||
\(548\) | −30.2948 | −1.29413 | ||||||||
\(549\) | −2.19350 | −0.0936161 | ||||||||
\(550\) | −27.0184 | −1.15207 | ||||||||
\(551\) | −3.34036 | −0.142304 | ||||||||
\(552\) | 2.50288 | 0.106530 | ||||||||
\(553\) | −0.116061 | −0.00493540 | ||||||||
\(554\) | −29.4271 | −1.25024 | ||||||||
\(555\) | 2.60840 | 0.110720 | ||||||||
\(556\) | 2.22461 | 0.0943445 | ||||||||
\(557\) | −15.5279 | −0.657940 | −0.328970 | − | 0.944340i | \(-0.606702\pi\) | ||||
−0.328970 | + | 0.944340i | \(0.606702\pi\) | |||||||
\(558\) | −10.9582 | −0.463899 | ||||||||
\(559\) | −26.4552 | −1.11894 | ||||||||
\(560\) | 2.85707 | 0.120733 | ||||||||
\(561\) | 3.21967 | 0.135935 | ||||||||
\(562\) | 14.1079 | 0.595104 | ||||||||
\(563\) | −26.3223 | −1.10935 | −0.554677 | − | 0.832066i | \(-0.687158\pi\) | ||||
−0.554677 | + | 0.832066i | \(0.687158\pi\) | |||||||
\(564\) | 5.47558 | 0.230564 | ||||||||
\(565\) | −5.23076 | −0.220060 | ||||||||
\(566\) | −29.3458 | −1.23349 | ||||||||
\(567\) | 0.378220 | 0.0158838 | ||||||||
\(568\) | 4.30635 | 0.180690 | ||||||||
\(569\) | 21.2835 | 0.892251 | 0.446125 | − | 0.894970i | \(-0.352804\pi\) | ||||
0.446125 | + | 0.894970i | \(0.352804\pi\) | |||||||
\(570\) | −0.448329 | −0.0187784 | ||||||||
\(571\) | 14.0880 | 0.589563 | 0.294782 | − | 0.955565i | \(-0.404753\pi\) | ||||
0.294782 | + | 0.955565i | \(0.404753\pi\) | |||||||
\(572\) | −25.4607 | −1.06456 | ||||||||
\(573\) | −27.6445 | −1.15486 | ||||||||
\(574\) | −33.5619 | −1.40085 | ||||||||
\(575\) | −11.4552 | −0.477716 | ||||||||
\(576\) | 6.13155 | 0.255481 | ||||||||
\(577\) | −22.5707 | −0.939630 | −0.469815 | − | 0.882765i | \(-0.655679\pi\) | ||||
−0.469815 | + | 0.882765i | \(0.655679\pi\) | |||||||
\(578\) | −1.86330 | −0.0775032 | ||||||||
\(579\) | 11.8481 | 0.492391 | ||||||||
\(580\) | −2.49685 | −0.103676 | ||||||||
\(581\) | 31.6447 | 1.31284 | ||||||||
\(582\) | −8.70782 | −0.360951 | ||||||||
\(583\) | 11.5904 | 0.480025 | ||||||||
\(584\) | −15.0871 | −0.624310 | ||||||||
\(585\) | −3.56516 | −0.147401 | ||||||||
\(586\) | −4.80917 | −0.198665 | ||||||||
\(587\) | 41.4964 | 1.71274 | 0.856371 | − | 0.516361i | \(-0.172714\pi\) | ||||
0.856371 | + | 0.516361i | \(0.172714\pi\) | |||||||
\(588\) | −6.10728 | −0.251860 | ||||||||
\(589\) | −2.13241 | −0.0878645 | ||||||||
\(590\) | 0.625236 | 0.0257406 | ||||||||
\(591\) | 13.8557 | 0.569946 | ||||||||
\(592\) | −34.2202 | −1.40644 | ||||||||
\(593\) | −12.0523 | −0.494928 | −0.247464 | − | 0.968897i | \(-0.579597\pi\) | ||||
−0.247464 | + | 0.968897i | \(0.579597\pi\) | |||||||
\(594\) | −28.9301 | −1.18702 | ||||||||
\(595\) | 0.598051 | 0.0245177 | ||||||||
\(596\) | −14.7180 | −0.602873 | ||||||||
\(597\) | 8.89533 | 0.364062 | ||||||||
\(598\) | −25.4627 | −1.04125 | ||||||||
\(599\) | −7.94051 | −0.324441 | −0.162220 | − | 0.986755i | \(-0.551866\pi\) | ||||
−0.162220 | + | 0.986755i | \(0.551866\pi\) | |||||||
\(600\) | −5.21906 | −0.213067 | ||||||||
\(601\) | −34.8574 | −1.42186 | −0.710932 | − | 0.703261i | \(-0.751727\pi\) | ||||
−0.710932 | + | 0.703261i | \(0.751727\pi\) | |||||||
\(602\) | −15.0688 | −0.614159 | ||||||||
\(603\) | −14.3885 | −0.585945 | ||||||||
\(604\) | −17.1944 | −0.699629 | ||||||||
\(605\) | −0.737458 | −0.0299819 | ||||||||
\(606\) | 34.2062 | 1.38953 | ||||||||
\(607\) | 40.2138 | 1.63223 | 0.816115 | − | 0.577890i | \(-0.196124\pi\) | ||||
0.816115 | + | 0.577890i | \(0.196124\pi\) | |||||||
\(608\) | 4.58136 | 0.185799 | ||||||||
\(609\) | 9.77792 | 0.396221 | ||||||||
\(610\) | −0.752587 | −0.0304714 | ||||||||
\(611\) | 19.9863 | 0.808559 | ||||||||
\(612\) | 2.68227 | 0.108424 | ||||||||
\(613\) | 13.0768 | 0.528166 | 0.264083 | − | 0.964500i | \(-0.414931\pi\) | ||||
0.264083 | + | 0.964500i | \(0.414931\pi\) | |||||||
\(614\) | 29.5790 | 1.19371 | ||||||||
\(615\) | −3.68010 | −0.148396 | ||||||||
\(616\) | 5.20325 | 0.209645 | ||||||||
\(617\) | −13.5140 | −0.544055 | −0.272027 | − | 0.962289i | \(-0.587694\pi\) | ||||
−0.272027 | + | 0.962289i | \(0.587694\pi\) | |||||||
\(618\) | −2.67304 | −0.107526 | ||||||||
\(619\) | 42.1820 | 1.69544 | 0.847718 | − | 0.530447i | \(-0.177976\pi\) | ||||
0.847718 | + | 0.530447i | \(0.177976\pi\) | |||||||
\(620\) | −1.59394 | −0.0640141 | ||||||||
\(621\) | −12.2658 | −0.492209 | ||||||||
\(622\) | 11.2715 | 0.451945 | ||||||||
\(623\) | 18.6914 | 0.748857 | ||||||||
\(624\) | −30.2268 | −1.21004 | ||||||||
\(625\) | 23.3237 | 0.932950 | ||||||||
\(626\) | −52.2914 | −2.08998 | ||||||||
\(627\) | −2.12740 | −0.0849603 | ||||||||
\(628\) | −2.03316 | −0.0811319 | ||||||||
\(629\) | −7.16306 | −0.285610 | ||||||||
\(630\) | −2.03070 | −0.0809050 | ||||||||
\(631\) | −24.2876 | −0.966876 | −0.483438 | − | 0.875379i | \(-0.660612\pi\) | ||||
−0.483438 | + | 0.875379i | \(0.660612\pi\) | |||||||
\(632\) | 0.0640777 | 0.00254887 | ||||||||
\(633\) | 22.9318 | 0.911459 | ||||||||
\(634\) | 46.4346 | 1.84415 | ||||||||
\(635\) | 1.97600 | 0.0784152 | ||||||||
\(636\) | −6.24013 | −0.247437 | ||||||||
\(637\) | −22.2920 | −0.883243 | ||||||||
\(638\) | −27.9470 | −1.10643 | ||||||||
\(639\) | −7.97504 | −0.315488 | ||||||||
\(640\) | −2.54941 | −0.100774 | ||||||||
\(641\) | 0.958607 | 0.0378627 | 0.0189313 | − | 0.999821i | \(-0.493974\pi\) | ||||
0.0189313 | + | 0.999821i | \(0.493974\pi\) | |||||||
\(642\) | −11.8797 | −0.468854 | ||||||||
\(643\) | −35.7827 | −1.41113 | −0.705566 | − | 0.708644i | \(-0.749307\pi\) | ||||
−0.705566 | + | 0.708644i | \(0.749307\pi\) | |||||||
\(644\) | −6.14868 | −0.242292 | ||||||||
\(645\) | −1.65231 | −0.0650597 | ||||||||
\(646\) | 1.23118 | 0.0484402 | ||||||||
\(647\) | 49.7798 | 1.95705 | 0.978524 | − | 0.206135i | \(-0.0660885\pi\) | ||||
0.978524 | + | 0.206135i | \(0.0660885\pi\) | |||||||
\(648\) | −0.208817 | −0.00820312 | ||||||||
\(649\) | 2.96686 | 0.116459 | ||||||||
\(650\) | 53.0953 | 2.08257 | ||||||||
\(651\) | 6.24202 | 0.244644 | ||||||||
\(652\) | 9.52702 | 0.373107 | ||||||||
\(653\) | 34.6089 | 1.35435 | 0.677176 | − | 0.735821i | \(-0.263204\pi\) | ||||
0.677176 | + | 0.735821i | \(0.263204\pi\) | |||||||
\(654\) | −19.2972 | −0.754579 | ||||||||
\(655\) | 3.22525 | 0.126021 | ||||||||
\(656\) | 48.2802 | 1.88502 | ||||||||
\(657\) | 27.9403 | 1.09005 | ||||||||
\(658\) | 11.3841 | 0.443799 | ||||||||
\(659\) | 38.8265 | 1.51247 | 0.756233 | − | 0.654302i | \(-0.227038\pi\) | ||||
0.756233 | + | 0.654302i | \(0.227038\pi\) | |||||||
\(660\) | −1.59019 | −0.0618982 | ||||||||
\(661\) | −40.7428 | −1.58471 | −0.792356 | − | 0.610058i | \(-0.791146\pi\) | ||||
−0.792356 | + | 0.610058i | \(0.791146\pi\) | |||||||
\(662\) | 11.6617 | 0.453245 | ||||||||
\(663\) | −6.32716 | −0.245726 | ||||||||
\(664\) | −17.4712 | −0.678015 | ||||||||
\(665\) | −0.395163 | −0.0153238 | ||||||||
\(666\) | 24.3224 | 0.942474 | ||||||||
\(667\) | −11.8490 | −0.458794 | ||||||||
\(668\) | −6.79271 | −0.262818 | ||||||||
\(669\) | −21.7162 | −0.839598 | ||||||||
\(670\) | −4.93669 | −0.190721 | ||||||||
\(671\) | −3.57117 | −0.137863 | ||||||||
\(672\) | −13.4106 | −0.517325 | ||||||||
\(673\) | 27.1195 | 1.04538 | 0.522690 | − | 0.852523i | \(-0.324928\pi\) | ||||
0.522690 | + | 0.852523i | \(0.324928\pi\) | |||||||
\(674\) | 27.1905 | 1.04734 | ||||||||
\(675\) | 25.5769 | 0.984456 | ||||||||
\(676\) | 30.8995 | 1.18844 | ||||||||
\(677\) | 50.8005 | 1.95242 | 0.976210 | − | 0.216827i | \(-0.0695707\pi\) | ||||
0.976210 | + | 0.216827i | \(0.0695707\pi\) | |||||||
\(678\) | 31.5212 | 1.21056 | ||||||||
\(679\) | −7.67520 | −0.294547 | ||||||||
\(680\) | −0.330187 | −0.0126621 | ||||||||
\(681\) | 12.0956 | 0.463506 | ||||||||
\(682\) | −17.8408 | −0.683158 | ||||||||
\(683\) | −11.4679 | −0.438807 | −0.219404 | − | 0.975634i | \(-0.570411\pi\) | ||||
−0.219404 | + | 0.975634i | \(0.570411\pi\) | |||||||
\(684\) | −1.77231 | −0.0677661 | ||||||||
\(685\) | −6.90637 | −0.263879 | ||||||||
\(686\) | −35.9441 | −1.37235 | ||||||||
\(687\) | 22.0249 | 0.840301 | ||||||||
\(688\) | 21.6771 | 0.826431 | ||||||||
\(689\) | −22.7769 | −0.867732 | ||||||||
\(690\) | −1.59032 | −0.0605424 | ||||||||
\(691\) | 3.16212 | 0.120293 | 0.0601464 | − | 0.998190i | \(-0.480843\pi\) | ||||
0.0601464 | + | 0.998190i | \(0.480843\pi\) | |||||||
\(692\) | 24.7786 | 0.941939 | ||||||||
\(693\) | −9.63604 | −0.366043 | ||||||||
\(694\) | 55.3296 | 2.10028 | ||||||||
\(695\) | 0.507150 | 0.0192373 | ||||||||
\(696\) | −5.39845 | −0.204628 | ||||||||
\(697\) | 10.1061 | 0.382797 | ||||||||
\(698\) | −53.1688 | −2.01247 | ||||||||
\(699\) | −5.47088 | −0.206928 | ||||||||
\(700\) | 12.8214 | 0.484602 | ||||||||
\(701\) | 30.4979 | 1.15189 | 0.575945 | − | 0.817488i | \(-0.304634\pi\) | ||||
0.575945 | + | 0.817488i | \(0.304634\pi\) | |||||||
\(702\) | 56.8523 | 2.14575 | ||||||||
\(703\) | 4.73301 | 0.178509 | ||||||||
\(704\) | 9.98260 | 0.376233 | ||||||||
\(705\) | 1.24828 | 0.0470130 | ||||||||
\(706\) | −18.1885 | −0.684535 | ||||||||
\(707\) | 30.1498 | 1.13390 | ||||||||
\(708\) | −1.59732 | −0.0600310 | ||||||||
\(709\) | −44.4812 | −1.67052 | −0.835262 | − | 0.549852i | \(-0.814684\pi\) | ||||
−0.835262 | + | 0.549852i | \(0.814684\pi\) | |||||||
\(710\) | −2.73623 | −0.102689 | ||||||||
\(711\) | −0.118667 | −0.00445037 | ||||||||
\(712\) | −10.3197 | −0.386745 | ||||||||
\(713\) | −7.56413 | −0.283279 | ||||||||
\(714\) | −3.60392 | −0.134873 | ||||||||
\(715\) | −5.80432 | −0.217069 | ||||||||
\(716\) | 8.28310 | 0.309554 | ||||||||
\(717\) | 26.8980 | 1.00453 | ||||||||
\(718\) | −42.6896 | −1.59316 | ||||||||
\(719\) | 7.93928 | 0.296085 | 0.148043 | − | 0.988981i | \(-0.452703\pi\) | ||||
0.148043 | + | 0.988981i | \(0.452703\pi\) | |||||||
\(720\) | 2.92124 | 0.108868 | ||||||||
\(721\) | −2.35606 | −0.0877442 | ||||||||
\(722\) | 34.5893 | 1.28728 | ||||||||
\(723\) | 12.2932 | 0.457189 | ||||||||
\(724\) | −17.5232 | −0.651245 | ||||||||
\(725\) | 24.7077 | 0.917622 | ||||||||
\(726\) | 4.44401 | 0.164933 | ||||||||
\(727\) | −46.0250 | −1.70697 | −0.853487 | − | 0.521114i | \(-0.825516\pi\) | ||||
−0.853487 | + | 0.521114i | \(0.825516\pi\) | |||||||
\(728\) | −10.2252 | −0.378971 | ||||||||
\(729\) | 17.4242 | 0.645341 | ||||||||
\(730\) | 9.58629 | 0.354805 | ||||||||
\(731\) | 4.53751 | 0.167826 | ||||||||
\(732\) | 1.92267 | 0.0710640 | ||||||||
\(733\) | −19.9668 | −0.737491 | −0.368745 | − | 0.929530i | \(-0.620213\pi\) | ||||
−0.368745 | + | 0.929530i | \(0.620213\pi\) | |||||||
\(734\) | 14.8161 | 0.546873 | ||||||||
\(735\) | −1.39229 | −0.0513554 | ||||||||
\(736\) | 16.2511 | 0.599022 | ||||||||
\(737\) | −23.4255 | −0.862889 | ||||||||
\(738\) | −34.3157 | −1.26318 | ||||||||
\(739\) | 47.7707 | 1.75727 | 0.878636 | − | 0.477492i | \(-0.158454\pi\) | ||||
0.878636 | + | 0.477492i | \(0.158454\pi\) | |||||||
\(740\) | 3.53783 | 0.130053 | ||||||||
\(741\) | 4.18068 | 0.153581 | ||||||||
\(742\) | −12.9737 | −0.476278 | ||||||||
\(743\) | −12.5372 | −0.459945 | −0.229972 | − | 0.973197i | \(-0.573864\pi\) | ||||
−0.229972 | + | 0.973197i | \(0.573864\pi\) | |||||||
\(744\) | −3.44625 | −0.126346 | ||||||||
\(745\) | −3.35530 | −0.122929 | ||||||||
\(746\) | −17.2874 | −0.632937 | ||||||||
\(747\) | 32.3555 | 1.18382 | ||||||||
\(748\) | 4.36692 | 0.159670 | ||||||||
\(749\) | −10.4709 | −0.382600 | ||||||||
\(750\) | 6.70873 | 0.244968 | ||||||||
\(751\) | 14.9786 | 0.546576 | 0.273288 | − | 0.961932i | \(-0.411889\pi\) | ||||
0.273288 | + | 0.961932i | \(0.411889\pi\) | |||||||
\(752\) | −16.3765 | −0.597190 | ||||||||
\(753\) | 10.1069 | 0.368315 | ||||||||
\(754\) | 54.9202 | 2.00008 | ||||||||
\(755\) | −3.91984 | −0.142658 | ||||||||
\(756\) | 13.7286 | 0.499304 | ||||||||
\(757\) | −17.1376 | −0.622878 | −0.311439 | − | 0.950266i | \(-0.600811\pi\) | ||||
−0.311439 | + | 0.950266i | \(0.600811\pi\) | |||||||
\(758\) | −14.8193 | −0.538261 | ||||||||
\(759\) | −7.54635 | −0.273915 | ||||||||
\(760\) | 0.218172 | 0.00791392 | ||||||||
\(761\) | −9.58584 | −0.347486 | −0.173743 | − | 0.984791i | \(-0.555586\pi\) | ||||
−0.173743 | + | 0.984791i | \(0.555586\pi\) | |||||||
\(762\) | −11.9076 | −0.431367 | ||||||||
\(763\) | −17.0088 | −0.615759 | ||||||||
\(764\) | −37.4949 | −1.35652 | ||||||||
\(765\) | 0.611483 | 0.0221082 | ||||||||
\(766\) | 37.7461 | 1.36382 | ||||||||
\(767\) | −5.83034 | −0.210522 | ||||||||
\(768\) | 22.6659 | 0.817884 | ||||||||
\(769\) | −28.3985 | −1.02408 | −0.512038 | − | 0.858963i | \(-0.671109\pi\) | ||||
−0.512038 | + | 0.858963i | \(0.671109\pi\) | |||||||
\(770\) | −3.30612 | −0.119144 | ||||||||
\(771\) | 18.4494 | 0.664438 | ||||||||
\(772\) | 16.0699 | 0.578369 | ||||||||
\(773\) | −17.5482 | −0.631165 | −0.315582 | − | 0.948898i | \(-0.602200\pi\) | ||||
−0.315582 | + | 0.948898i | \(0.602200\pi\) | |||||||
\(774\) | −15.4072 | −0.553802 | ||||||||
\(775\) | 15.7729 | 0.566579 | ||||||||
\(776\) | 4.23752 | 0.152118 | ||||||||
\(777\) | −13.8545 | −0.497027 | ||||||||
\(778\) | −10.0612 | −0.360713 | ||||||||
\(779\) | −6.67765 | −0.239252 | ||||||||
\(780\) | 3.12498 | 0.111892 | ||||||||
\(781\) | −12.9839 | −0.464602 | ||||||||
\(782\) | 4.36726 | 0.156173 | ||||||||
\(783\) | 26.4560 | 0.945461 | ||||||||
\(784\) | 18.2658 | 0.652351 | ||||||||
\(785\) | −0.463504 | −0.0165432 | ||||||||
\(786\) | −19.4358 | −0.693250 | ||||||||
\(787\) | −37.2633 | −1.32829 | −0.664146 | − | 0.747603i | \(-0.731205\pi\) | ||||
−0.664146 | + | 0.747603i | \(0.731205\pi\) | |||||||
\(788\) | 18.7928 | 0.669466 | ||||||||
\(789\) | −10.7872 | −0.384035 | ||||||||
\(790\) | −0.0407147 | −0.00144856 | ||||||||
\(791\) | 27.7832 | 0.987857 | ||||||||
\(792\) | 5.32011 | 0.189042 | ||||||||
\(793\) | 7.01790 | 0.249213 | ||||||||
\(794\) | −12.5923 | −0.446884 | ||||||||
\(795\) | −1.42258 | −0.0504536 | ||||||||
\(796\) | 12.0650 | 0.427632 | ||||||||
\(797\) | −40.9410 | −1.45020 | −0.725102 | − | 0.688642i | \(-0.758207\pi\) | ||||
−0.725102 | + | 0.688642i | \(0.758207\pi\) | |||||||
\(798\) | 2.38130 | 0.0842971 | ||||||||
\(799\) | −3.42798 | −0.121273 | ||||||||
\(800\) | −33.8871 | −1.19809 | ||||||||
\(801\) | 19.1113 | 0.675263 | ||||||||
\(802\) | −14.6578 | −0.517584 | ||||||||
\(803\) | 45.4887 | 1.60526 | ||||||||
\(804\) | 12.6120 | 0.444791 | ||||||||
\(805\) | −1.40173 | −0.0494044 | ||||||||
\(806\) | 35.0599 | 1.23493 | ||||||||
\(807\) | 4.37183 | 0.153896 | ||||||||
\(808\) | −16.6459 | −0.585600 | ||||||||
\(809\) | −38.5922 | −1.35683 | −0.678414 | − | 0.734680i | \(-0.737332\pi\) | ||||
−0.678414 | + | 0.734680i | \(0.737332\pi\) | |||||||
\(810\) | 0.132682 | 0.00466196 | ||||||||
\(811\) | −52.3127 | −1.83695 | −0.918474 | − | 0.395481i | \(-0.870578\pi\) | ||||
−0.918474 | + | 0.395481i | \(0.870578\pi\) | |||||||
\(812\) | 13.2620 | 0.465407 | ||||||||
\(813\) | 17.1265 | 0.600652 | ||||||||
\(814\) | 39.5986 | 1.38793 | ||||||||
\(815\) | 2.17190 | 0.0760782 | ||||||||
\(816\) | 5.18439 | 0.181490 | ||||||||
\(817\) | −2.99817 | −0.104893 | ||||||||
\(818\) | 54.4161 | 1.90261 | ||||||||
\(819\) | 18.9363 | 0.661689 | ||||||||
\(820\) | −4.99142 | −0.174308 | ||||||||
\(821\) | 46.8691 | 1.63574 | 0.817871 | − | 0.575402i | \(-0.195154\pi\) | ||||
0.817871 | + | 0.575402i | \(0.195154\pi\) | |||||||
\(822\) | 41.6186 | 1.45161 | ||||||||
\(823\) | −30.8025 | −1.07371 | −0.536854 | − | 0.843675i | \(-0.680387\pi\) | ||||
−0.536854 | + | 0.843675i | \(0.680387\pi\) | |||||||
\(824\) | 1.30079 | 0.0453153 | ||||||||
\(825\) | 15.7358 | 0.547851 | ||||||||
\(826\) | −3.32094 | −0.115550 | ||||||||
\(827\) | 31.4859 | 1.09487 | 0.547435 | − | 0.836848i | \(-0.315604\pi\) | ||||
0.547435 | + | 0.836848i | \(0.315604\pi\) | |||||||
\(828\) | −6.28678 | −0.218481 | ||||||||
\(829\) | −3.11446 | −0.108170 | −0.0540849 | − | 0.998536i | \(-0.517224\pi\) | ||||
−0.0540849 | + | 0.998536i | \(0.517224\pi\) | |||||||
\(830\) | 11.1011 | 0.385326 | ||||||||
\(831\) | 17.1387 | 0.594536 | ||||||||
\(832\) | −19.6174 | −0.680110 | ||||||||
\(833\) | 3.82345 | 0.132475 | ||||||||
\(834\) | −3.05614 | −0.105826 | ||||||||
\(835\) | −1.54855 | −0.0535898 | ||||||||
\(836\) | −2.88545 | −0.0997954 | ||||||||
\(837\) | 16.8890 | 0.583768 | ||||||||
\(838\) | −47.0996 | −1.62703 | ||||||||
\(839\) | −31.2075 | −1.07740 | −0.538701 | − | 0.842497i | \(-0.681085\pi\) | ||||
−0.538701 | + | 0.842497i | \(0.681085\pi\) | |||||||
\(840\) | −0.638634 | −0.0220350 | ||||||||
\(841\) | −3.44304 | −0.118725 | ||||||||
\(842\) | 50.2285 | 1.73099 | ||||||||
\(843\) | −8.21659 | −0.282995 | ||||||||
\(844\) | 31.1031 | 1.07061 | ||||||||
\(845\) | 7.04423 | 0.242329 | ||||||||
\(846\) | 11.6398 | 0.400184 | ||||||||
\(847\) | 3.91701 | 0.134590 | ||||||||
\(848\) | 18.6631 | 0.640895 | ||||||||
\(849\) | 17.0913 | 0.586573 | ||||||||
\(850\) | −9.10672 | −0.312358 | ||||||||
\(851\) | 16.7890 | 0.575519 | ||||||||
\(852\) | 6.99039 | 0.239487 | ||||||||
\(853\) | −16.3030 | −0.558206 | −0.279103 | − | 0.960261i | \(-0.590037\pi\) | ||||
−0.279103 | + | 0.960261i | \(0.590037\pi\) | |||||||
\(854\) | 3.99737 | 0.136787 | ||||||||
\(855\) | −0.404038 | −0.0138178 | ||||||||
\(856\) | 5.78106 | 0.197593 | ||||||||
\(857\) | −40.9532 | −1.39894 | −0.699468 | − | 0.714664i | \(-0.746580\pi\) | ||||
−0.699468 | + | 0.714664i | \(0.746580\pi\) | |||||||
\(858\) | 34.9775 | 1.19411 | ||||||||
\(859\) | −9.97437 | −0.340321 | −0.170161 | − | 0.985416i | \(-0.554429\pi\) | ||||
−0.170161 | + | 0.985416i | \(0.554429\pi\) | |||||||
\(860\) | −2.24107 | −0.0764200 | ||||||||
\(861\) | 19.5469 | 0.666156 | ||||||||
\(862\) | 42.8109 | 1.45815 | ||||||||
\(863\) | 28.9286 | 0.984742 | 0.492371 | − | 0.870385i | \(-0.336130\pi\) | ||||
0.492371 | + | 0.870385i | \(0.336130\pi\) | |||||||
\(864\) | −36.2849 | −1.23444 | ||||||||
\(865\) | 5.64883 | 0.192066 | ||||||||
\(866\) | −29.6516 | −1.00760 | ||||||||
\(867\) | 1.08521 | 0.0368557 | ||||||||
\(868\) | 8.46621 | 0.287362 | ||||||||
\(869\) | −0.193199 | −0.00655382 | ||||||||
\(870\) | 3.43015 | 0.116293 | ||||||||
\(871\) | 46.0348 | 1.55983 | ||||||||
\(872\) | 9.39065 | 0.318007 | ||||||||
\(873\) | −7.84758 | −0.265600 | ||||||||
\(874\) | −2.88568 | −0.0976095 | ||||||||
\(875\) | 5.91317 | 0.199902 | ||||||||
\(876\) | −24.4906 | −0.827460 | ||||||||
\(877\) | −41.3086 | −1.39489 | −0.697447 | − | 0.716637i | \(-0.745681\pi\) | ||||
−0.697447 | + | 0.716637i | \(0.745681\pi\) | |||||||
\(878\) | −11.3813 | −0.384099 | ||||||||
\(879\) | 2.80092 | 0.0944728 | ||||||||
\(880\) | 4.75599 | 0.160324 | ||||||||
\(881\) | −25.6855 | −0.865365 | −0.432683 | − | 0.901546i | \(-0.642433\pi\) | ||||
−0.432683 | + | 0.901546i | \(0.642433\pi\) | |||||||
\(882\) | −12.9826 | −0.437148 | ||||||||
\(883\) | −24.4200 | −0.821799 | −0.410900 | − | 0.911681i | \(-0.634785\pi\) | ||||
−0.410900 | + | 0.911681i | \(0.634785\pi\) | |||||||
\(884\) | −8.58168 | −0.288633 | ||||||||
\(885\) | −0.364145 | −0.0122406 | ||||||||
\(886\) | −6.61474 | −0.222227 | ||||||||
\(887\) | −11.7041 | −0.392984 | −0.196492 | − | 0.980505i | \(-0.562955\pi\) | ||||
−0.196492 | + | 0.980505i | \(0.562955\pi\) | |||||||
\(888\) | 7.64915 | 0.256689 | ||||||||
\(889\) | −10.4955 | −0.352009 | ||||||||
\(890\) | 6.55706 | 0.219793 | ||||||||
\(891\) | 0.629599 | 0.0210924 | ||||||||
\(892\) | −29.4543 | −0.986202 | ||||||||
\(893\) | 2.26504 | 0.0757967 | ||||||||
\(894\) | 20.2194 | 0.676238 | ||||||||
\(895\) | 1.88832 | 0.0631195 | ||||||||
\(896\) | 13.5412 | 0.452380 | ||||||||
\(897\) | 14.8298 | 0.495151 | ||||||||
\(898\) | 61.1319 | 2.04000 | ||||||||
\(899\) | 16.3150 | 0.544136 | ||||||||
\(900\) | 13.1093 | 0.436978 | ||||||||
\(901\) | 3.90662 | 0.130148 | ||||||||
\(902\) | −55.8684 | −1.86021 | ||||||||
\(903\) | 8.77626 | 0.292056 | ||||||||
\(904\) | −15.3393 | −0.510176 | ||||||||
\(905\) | −3.99481 | −0.132792 | ||||||||
\(906\) | 23.6214 | 0.784769 | ||||||||
\(907\) | 24.1452 | 0.801728 | 0.400864 | − | 0.916138i | \(-0.368710\pi\) | ||||
0.400864 | + | 0.916138i | \(0.368710\pi\) | |||||||
\(908\) | 16.4056 | 0.544440 | ||||||||
\(909\) | 30.8269 | 1.02247 | ||||||||
\(910\) | 6.49705 | 0.215375 | ||||||||
\(911\) | 25.2852 | 0.837737 | 0.418868 | − | 0.908047i | \(-0.362427\pi\) | ||||
0.418868 | + | 0.908047i | \(0.362427\pi\) | |||||||
\(912\) | −3.42559 | −0.113433 | ||||||||
\(913\) | 52.6770 | 1.74335 | ||||||||
\(914\) | 14.6399 | 0.484244 | ||||||||
\(915\) | 0.438316 | 0.0144903 | ||||||||
\(916\) | 29.8729 | 0.987028 | ||||||||
\(917\) | −17.1309 | −0.565714 | ||||||||
\(918\) | −9.75110 | −0.321834 | ||||||||
\(919\) | 18.3380 | 0.604914 | 0.302457 | − | 0.953163i | \(-0.402193\pi\) | ||||
0.302457 | + | 0.953163i | \(0.402193\pi\) | |||||||
\(920\) | 0.773902 | 0.0255148 | ||||||||
\(921\) | −17.2272 | −0.567655 | ||||||||
\(922\) | −19.6816 | −0.648180 | ||||||||
\(923\) | 25.5155 | 0.839852 | ||||||||
\(924\) | 8.44631 | 0.277863 | ||||||||
\(925\) | −35.0088 | −1.15108 | ||||||||
\(926\) | 60.3367 | 1.98279 | ||||||||
\(927\) | −2.40898 | −0.0791211 | ||||||||
\(928\) | −35.0518 | −1.15063 | ||||||||
\(929\) | 35.7491 | 1.17289 | 0.586445 | − | 0.809989i | \(-0.300527\pi\) | ||||
0.586445 | + | 0.809989i | \(0.300527\pi\) | |||||||
\(930\) | 2.18973 | 0.0718042 | ||||||||
\(931\) | −2.52635 | −0.0827978 | ||||||||
\(932\) | −7.42029 | −0.243060 | ||||||||
\(933\) | −6.56465 | −0.214917 | ||||||||
\(934\) | −8.54569 | −0.279623 | ||||||||
\(935\) | 0.995537 | 0.0325575 | ||||||||
\(936\) | −10.4549 | −0.341728 | ||||||||
\(937\) | 20.7094 | 0.676548 | 0.338274 | − | 0.941048i | \(-0.390157\pi\) | ||||
0.338274 | + | 0.941048i | \(0.390157\pi\) | |||||||
\(938\) | 26.2212 | 0.856154 | ||||||||
\(939\) | 30.4551 | 0.993866 | ||||||||
\(940\) | 1.69308 | 0.0552220 | ||||||||
\(941\) | −17.2905 | −0.563655 | −0.281828 | − | 0.959465i | \(-0.590941\pi\) | ||||
−0.281828 | + | 0.959465i | \(0.590941\pi\) | |||||||
\(942\) | 2.79313 | 0.0910051 | ||||||||
\(943\) | −23.6871 | −0.771357 | ||||||||
\(944\) | 4.77731 | 0.155488 | ||||||||
\(945\) | 3.12974 | 0.101810 | ||||||||
\(946\) | −25.0841 | −0.815554 | ||||||||
\(947\) | −12.8393 | −0.417221 | −0.208610 | − | 0.977999i | \(-0.566894\pi\) | ||||
−0.208610 | + | 0.977999i | \(0.566894\pi\) | |||||||
\(948\) | 0.104016 | 0.00337828 | ||||||||
\(949\) | −89.3925 | −2.90180 | ||||||||
\(950\) | 6.01728 | 0.195226 | ||||||||
\(951\) | −27.0441 | −0.876965 | ||||||||
\(952\) | 1.75379 | 0.0568407 | ||||||||
\(953\) | 31.1210 | 1.00811 | 0.504054 | − | 0.863672i | \(-0.331841\pi\) | ||||
0.504054 | + | 0.863672i | \(0.331841\pi\) | |||||||
\(954\) | −13.2650 | −0.429472 | ||||||||
\(955\) | −8.54781 | −0.276600 | ||||||||
\(956\) | 36.4825 | 1.17993 | ||||||||
\(957\) | 16.2767 | 0.526150 | ||||||||
\(958\) | 1.14337 | 0.0369406 | ||||||||
\(959\) | 36.6832 | 1.18456 | ||||||||
\(960\) | −1.22524 | −0.0395444 | ||||||||
\(961\) | −20.5848 | −0.664027 | ||||||||
\(962\) | −77.8174 | −2.50893 | ||||||||
\(963\) | −10.7061 | −0.344999 | ||||||||
\(964\) | 16.6736 | 0.537020 | ||||||||
\(965\) | 3.66349 | 0.117932 | ||||||||
\(966\) | 8.44698 | 0.271777 | ||||||||
\(967\) | −11.3986 | −0.366554 | −0.183277 | − | 0.983061i | \(-0.558671\pi\) | ||||
−0.183277 | + | 0.983061i | \(0.558671\pi\) | |||||||
\(968\) | −2.16260 | −0.0695087 | ||||||||
\(969\) | −0.717055 | −0.0230351 | ||||||||
\(970\) | −2.69250 | −0.0864509 | ||||||||
\(971\) | −58.6062 | −1.88076 | −0.940381 | − | 0.340122i | \(-0.889532\pi\) | ||||
−0.940381 | + | 0.340122i | \(0.889532\pi\) | |||||||
\(972\) | 22.7694 | 0.730329 | ||||||||
\(973\) | −2.69373 | −0.0863569 | ||||||||
\(974\) | −19.9003 | −0.637646 | ||||||||
\(975\) | −30.9234 | −0.990340 | ||||||||
\(976\) | −5.75038 | −0.184065 | ||||||||
\(977\) | 13.0114 | 0.416272 | 0.208136 | − | 0.978100i | \(-0.433260\pi\) | ||||
0.208136 | + | 0.978100i | \(0.433260\pi\) | |||||||
\(978\) | −13.0881 | −0.418511 | ||||||||
\(979\) | 31.1145 | 0.994422 | ||||||||
\(980\) | −1.88840 | −0.0603228 | ||||||||
\(981\) | −17.3908 | −0.555245 | ||||||||
\(982\) | −72.4713 | −2.31265 | ||||||||
\(983\) | −7.81190 | −0.249161 | −0.124580 | − | 0.992210i | \(-0.539758\pi\) | ||||
−0.124580 | + | 0.992210i | \(0.539758\pi\) | |||||||
\(984\) | −10.7919 | −0.344034 | ||||||||
\(985\) | 4.28424 | 0.136507 | ||||||||
\(986\) | −9.41972 | −0.299985 | ||||||||
\(987\) | −6.63025 | −0.211043 | ||||||||
\(988\) | 5.67036 | 0.180398 | ||||||||
\(989\) | −10.6351 | −0.338178 | ||||||||
\(990\) | −3.38037 | −0.107435 | ||||||||
\(991\) | 56.6951 | 1.80098 | 0.900489 | − | 0.434879i | \(-0.143209\pi\) | ||||
0.900489 | + | 0.434879i | \(0.143209\pi\) | |||||||
\(992\) | −22.3763 | −0.710450 | ||||||||
\(993\) | −6.79193 | −0.215535 | ||||||||
\(994\) | 14.5335 | 0.460975 | ||||||||
\(995\) | 2.75048 | 0.0871960 | ||||||||
\(996\) | −28.3607 | −0.898642 | ||||||||
\(997\) | −13.1729 | −0.417189 | −0.208594 | − | 0.978002i | \(-0.566889\pi\) | ||||
−0.208594 | + | 0.978002i | \(0.566889\pi\) | |||||||
\(998\) | 66.6777 | 2.11064 | ||||||||
\(999\) | −37.4860 | −1.18600 |
(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 | 1003.2.a.g.1.3 | ✓ | 10 | |
3.2 | odd | 2 | 9027.2.a.j.1.8 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1003.2.a.g.1.3 | ✓ | 10 | 1.1 | even | 1 | trivial | |
9027.2.a.j.1.8 | 10 | 3.2 | odd | 2 |