Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [231,2,Mod(76,231)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(231, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("231.76");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 231 = 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 231.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(1.84454428669\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + x^{14} - 4x^{12} - 49x^{10} + 11x^{8} + 395x^{6} + 900x^{4} + 1125x^{2} + 625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{13} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 76.16 | ||
Root | \(-0.917186 + 1.66637i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 231.76 |
Dual form | 231.2.c.a.76.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/231\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.30927i | 1.63290i | 0.577414 | + | 0.816452i | \(0.304062\pi\) | ||||
−0.577414 | + | 0.816452i | \(0.695938\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −3.33275 | −1.66637 | ||||||||
\(5\) | 3.77447i | 1.68799i | 0.536349 | + | 0.843997i | \(0.319803\pi\) | ||||
−0.536349 | + | 0.843997i | \(0.680197\pi\) | |||||||
\(6\) | −2.30927 | −0.942757 | ||||||||
\(7\) | −0.474903 | − | 2.60278i | −0.179496 | − | 0.983759i | ||||
\(8\) | − | 3.07768i | − | 1.08813i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −8.71628 | −2.75633 | ||||||||
\(11\) | 3.23607 | − | 0.726543i | 0.975711 | − | 0.219061i | ||||
\(12\) | − | 3.33275i | − | 0.962082i | ||||||
\(13\) | 3.32932 | 0.923388 | 0.461694 | − | 0.887039i | \(-0.347242\pi\) | ||||
0.461694 | + | 0.887039i | \(0.347242\pi\) | |||||||
\(14\) | 6.01054 | − | 1.09668i | 1.60638 | − | 0.293100i | ||||
\(15\) | −3.77447 | −0.974563 | ||||||||
\(16\) | 0.441718 | 0.110430 | ||||||||
\(17\) | −5.12183 | −1.24223 | −0.621113 | − | 0.783721i | \(-0.713319\pi\) | ||||
−0.621113 | + | 0.783721i | \(0.713319\pi\) | |||||||
\(18\) | − | 2.30927i | − | 0.544301i | ||||||
\(19\) | 2.74231 | 0.629129 | 0.314565 | − | 0.949236i | \(-0.398141\pi\) | ||||
0.314565 | + | 0.949236i | \(0.398141\pi\) | |||||||
\(20\) | − | 12.5794i | − | 2.81283i | ||||||
\(21\) | 2.60278 | − | 0.474903i | 0.567973 | − | 0.103632i | ||||
\(22\) | 1.67779 | + | 7.47297i | 0.357705 | + | 1.59324i | ||||
\(23\) | 2.19336 | 0.457348 | 0.228674 | − | 0.973503i | \(-0.426561\pi\) | ||||
0.228674 | + | 0.973503i | \(0.426561\pi\) | |||||||
\(24\) | 3.07768 | 0.628230 | ||||||||
\(25\) | −9.24660 | −1.84932 | ||||||||
\(26\) | 7.68832i | 1.50780i | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 1.58273 | + | 8.67441i | 0.299108 | + | 1.63931i | ||||
\(29\) | 4.27913i | 0.794614i | 0.917686 | + | 0.397307i | \(0.130055\pi\) | ||||
−0.917686 | + | 0.397307i | \(0.869945\pi\) | |||||||
\(30\) | − | 8.71628i | − | 1.59137i | ||||||
\(31\) | 1.11656i | 0.200541i | 0.994960 | + | 0.100270i | \(0.0319708\pi\) | ||||
−0.994960 | + | 0.100270i | \(0.968029\pi\) | |||||||
\(32\) | − | 5.13532i | − | 0.907805i | ||||||
\(33\) | 0.726543 | + | 3.23607i | 0.126475 | + | 0.563327i | ||||
\(34\) | − | 11.8277i | − | 2.02844i | ||||||
\(35\) | 9.82411 | − | 1.79251i | 1.66058 | − | 0.302989i | ||||
\(36\) | 3.33275 | 0.555458 | ||||||||
\(37\) | 8.24660 | 1.35573 | 0.677867 | − | 0.735185i | \(-0.262905\pi\) | ||||
0.677867 | + | 0.735185i | \(0.262905\pi\) | |||||||
\(38\) | 6.33275i | 1.02731i | ||||||||
\(39\) | 3.32932i | 0.533118i | ||||||||
\(40\) | 11.6166 | 1.83675 | ||||||||
\(41\) | −3.75248 | −0.586038 | −0.293019 | − | 0.956107i | \(-0.594660\pi\) | ||||
−0.293019 | + | 0.956107i | \(0.594660\pi\) | |||||||
\(42\) | 1.09668 | + | 6.01054i | 0.169222 | + | 0.927446i | ||||
\(43\) | 6.74238i | 1.02820i | 0.857729 | + | 0.514102i | \(0.171875\pi\) | ||||
−0.857729 | + | 0.514102i | \(0.828125\pi\) | |||||||
\(44\) | −10.7850 | + | 2.42138i | −1.62590 | + | 0.365037i | ||||
\(45\) | − | 3.77447i | − | 0.562664i | ||||||
\(46\) | 5.06508i | 0.746805i | ||||||||
\(47\) | − | 5.58111i | − | 0.814088i | −0.913409 | − | 0.407044i | \(-0.866560\pi\) | ||
0.913409 | − | 0.407044i | \(-0.133440\pi\) | |||||||
\(48\) | 0.441718i | 0.0637565i | ||||||||
\(49\) | −6.54893 | + | 2.47214i | −0.935562 | + | 0.353162i | ||||
\(50\) | − | 21.3529i | − | 3.01976i | ||||||
\(51\) | − | 5.12183i | − | 0.717199i | ||||||
\(52\) | −11.0958 | −1.53871 | ||||||||
\(53\) | 6.66550 | 0.915577 | 0.457788 | − | 0.889061i | \(-0.348642\pi\) | ||||
0.457788 | + | 0.889061i | \(0.348642\pi\) | |||||||
\(54\) | 2.30927 | 0.314252 | ||||||||
\(55\) | 2.74231 | + | 12.2144i | 0.369773 | + | 1.64699i | ||||
\(56\) | −8.01054 | + | 1.46160i | −1.07045 | + | 0.195315i | ||||
\(57\) | 2.74231i | 0.363228i | ||||||||
\(58\) | −9.88168 | −1.29753 | ||||||||
\(59\) | 7.36317i | 0.958603i | 0.877650 | + | 0.479301i | \(0.159110\pi\) | ||||
−0.877650 | + | 0.479301i | \(0.840890\pi\) | |||||||
\(60\) | 12.5794 | 1.62399 | ||||||||
\(61\) | −9.23710 | −1.18269 | −0.591345 | − | 0.806419i | \(-0.701403\pi\) | ||||
−0.591345 | + | 0.806419i | \(0.701403\pi\) | |||||||
\(62\) | −2.57845 | −0.327464 | ||||||||
\(63\) | 0.474903 | + | 2.60278i | 0.0598321 | + | 0.327920i | ||||
\(64\) | 12.7423 | 1.59279 | ||||||||
\(65\) | 12.5664i | 1.55867i | ||||||||
\(66\) | −7.47297 | + | 1.67779i | −0.919859 | + | 0.206521i | ||||
\(67\) | 1.96783 | 0.240409 | 0.120204 | − | 0.992749i | \(-0.461645\pi\) | ||||
0.120204 | + | 0.992749i | \(0.461645\pi\) | |||||||
\(68\) | 17.0698 | 2.07001 | ||||||||
\(69\) | 2.19336i | 0.264050i | ||||||||
\(70\) | 4.13939 | + | 22.6866i | 0.494751 | + | 2.71156i | ||||
\(71\) | −5.07680 | −0.602505 | −0.301253 | − | 0.953544i | \(-0.597405\pi\) | ||||
−0.301253 | + | 0.953544i | \(0.597405\pi\) | |||||||
\(72\) | 3.07768i | 0.362708i | ||||||||
\(73\) | 12.7339 | 1.49039 | 0.745194 | − | 0.666847i | \(-0.232357\pi\) | ||||
0.745194 | + | 0.666847i | \(0.232357\pi\) | |||||||
\(74\) | 19.0437i | 2.21378i | ||||||||
\(75\) | − | 9.24660i | − | 1.06771i | ||||||
\(76\) | −9.13943 | −1.04837 | ||||||||
\(77\) | −3.42785 | − | 8.07774i | −0.390640 | − | 0.920544i | ||||
\(78\) | −7.68832 | −0.870531 | ||||||||
\(79\) | − | 5.88440i | − | 0.662047i | −0.943623 | − | 0.331023i | \(-0.892606\pi\) | ||
0.943623 | − | 0.331023i | \(-0.107394\pi\) | |||||||
\(80\) | 1.66725i | 0.186404i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 8.66550i | − | 0.956944i | ||||||
\(83\) | 16.2585 | 1.78461 | 0.892303 | − | 0.451437i | \(-0.149088\pi\) | ||||
0.892303 | + | 0.451437i | \(0.149088\pi\) | |||||||
\(84\) | −8.67441 | + | 1.58273i | −0.946456 | + | 0.172690i | ||||
\(85\) | − | 19.3322i | − | 2.09687i | ||||||
\(86\) | −15.5700 | −1.67896 | ||||||||
\(87\) | −4.27913 | −0.458771 | ||||||||
\(88\) | −2.23607 | − | 9.95959i | −0.238366 | − | 1.06170i | ||||
\(89\) | − | 10.0211i | − | 1.06223i | −0.847299 | − | 0.531116i | \(-0.821773\pi\) | ||
0.847299 | − | 0.531116i | \(-0.178227\pi\) | |||||||
\(90\) | 8.71628 | 0.918777 | ||||||||
\(91\) | −1.58111 | − | 8.66550i | −0.165745 | − | 0.908391i | ||||
\(92\) | −7.30993 | −0.762112 | ||||||||
\(93\) | −1.11656 | −0.115782 | ||||||||
\(94\) | 12.8883 | 1.32933 | ||||||||
\(95\) | 10.3508i | 1.06197i | ||||||||
\(96\) | 5.13532 | 0.524121 | ||||||||
\(97\) | − | 14.4476i | − | 1.46693i | −0.679729 | − | 0.733464i | \(-0.737902\pi\) | ||
0.679729 | − | 0.733464i | \(-0.262098\pi\) | |||||||
\(98\) | −5.70884 | − | 15.1233i | −0.576680 | − | 1.52768i | ||||
\(99\) | −3.23607 | + | 0.726543i | −0.325237 | + | 0.0730203i | ||||
\(100\) | 30.8166 | 3.08166 | ||||||||
\(101\) | −15.5797 | −1.55024 | −0.775119 | − | 0.631815i | \(-0.782310\pi\) | ||||
−0.775119 | + | 0.631815i | \(0.782310\pi\) | |||||||
\(102\) | 11.8277 | 1.17112 | ||||||||
\(103\) | − | 16.4932i | − | 1.62512i | −0.582875 | − | 0.812562i | \(-0.698072\pi\) | ||
0.582875 | − | 0.812562i | \(-0.301928\pi\) | |||||||
\(104\) | − | 10.2466i | − | 1.00476i | ||||||
\(105\) | 1.79251 | + | 9.82411i | 0.174931 | + | 0.958735i | ||||
\(106\) | 15.3925i | 1.49505i | ||||||||
\(107\) | 5.09846i | 0.492886i | 0.969157 | + | 0.246443i | \(0.0792619\pi\) | ||||
−0.969157 | + | 0.246443i | \(0.920738\pi\) | |||||||
\(108\) | 3.33275i | 0.320694i | ||||||||
\(109\) | − | 13.6801i | − | 1.31031i | −0.755492 | − | 0.655157i | \(-0.772602\pi\) | ||
0.755492 | − | 0.655157i | \(-0.227398\pi\) | |||||||
\(110\) | −28.2065 | + | 6.33275i | −2.68938 | + | 0.603804i | ||||
\(111\) | 8.24660i | 0.782733i | ||||||||
\(112\) | −0.209773 | − | 1.14970i | −0.0198217 | − | 0.108636i | ||||
\(113\) | 17.0979 | 1.60843 | 0.804216 | − | 0.594337i | \(-0.202585\pi\) | ||||
0.804216 | + | 0.594337i | \(0.202585\pi\) | |||||||
\(114\) | −6.33275 | −0.593116 | ||||||||
\(115\) | 8.27877i | 0.772000i | ||||||||
\(116\) | − | 14.2613i | − | 1.32413i | ||||||
\(117\) | −3.32932 | −0.307796 | ||||||||
\(118\) | −17.0036 | −1.56531 | ||||||||
\(119\) | 2.43237 | + | 13.3310i | 0.222975 | + | 1.22205i | ||||
\(120\) | 11.6166i | 1.06045i | ||||||||
\(121\) | 9.94427 | − | 4.70228i | 0.904025 | − | 0.427480i | ||||
\(122\) | − | 21.3310i | − | 1.93122i | ||||||
\(123\) | − | 3.75248i | − | 0.338349i | ||||||
\(124\) | − | 3.72123i | − | 0.334176i | ||||||
\(125\) | − | 16.0287i | − | 1.43365i | ||||||
\(126\) | −6.01054 | + | 1.09668i | −0.535461 | + | 0.0977001i | ||||
\(127\) | 3.66874i | 0.325548i | 0.986663 | + | 0.162774i | \(0.0520442\pi\) | ||||
−0.986663 | + | 0.162774i | \(0.947956\pi\) | |||||||
\(128\) | 19.1548i | 1.69306i | ||||||||
\(129\) | −6.74238 | −0.593633 | ||||||||
\(130\) | −29.0193 | −2.54516 | ||||||||
\(131\) | 8.55826 | 0.747738 | 0.373869 | − | 0.927481i | \(-0.378031\pi\) | ||||
0.373869 | + | 0.927481i | \(0.378031\pi\) | |||||||
\(132\) | −2.42138 | − | 10.7850i | −0.210754 | − | 0.938714i | ||||
\(133\) | −1.30233 | − | 7.13763i | −0.112926 | − | 0.618911i | ||||
\(134\) | 4.54426i | 0.392564i | ||||||||
\(135\) | 3.77447 | 0.324854 | ||||||||
\(136\) | 15.7634i | 1.35170i | ||||||||
\(137\) | −8.44756 | −0.721724 | −0.360862 | − | 0.932619i | \(-0.617517\pi\) | ||||
−0.360862 | + | 0.932619i | \(0.617517\pi\) | |||||||
\(138\) | −5.06508 | −0.431168 | ||||||||
\(139\) | 2.12383 | 0.180141 | 0.0900705 | − | 0.995935i | \(-0.471291\pi\) | ||||
0.0900705 | + | 0.995935i | \(0.471291\pi\) | |||||||
\(140\) | −32.7413 | + | 5.97397i | −2.76714 | + | 0.504893i | ||||
\(141\) | 5.58111 | 0.470014 | ||||||||
\(142\) | − | 11.7237i | − | 0.983833i | ||||||
\(143\) | 10.7739 | − | 2.41889i | 0.900960 | − | 0.202278i | ||||
\(144\) | −0.441718 | −0.0368099 | ||||||||
\(145\) | −16.1514 | −1.34130 | ||||||||
\(146\) | 29.4060i | 2.43366i | ||||||||
\(147\) | −2.47214 | − | 6.54893i | −0.203898 | − | 0.540147i | ||||
\(148\) | −27.4839 | −2.25916 | ||||||||
\(149\) | − | 5.45315i | − | 0.446740i | −0.974734 | − | 0.223370i | \(-0.928294\pi\) | ||
0.974734 | − | 0.223370i | \(-0.0717058\pi\) | |||||||
\(150\) | 21.3529 | 1.74346 | ||||||||
\(151\) | 7.42122i | 0.603930i | 0.953319 | + | 0.301965i | \(0.0976426\pi\) | ||||
−0.953319 | + | 0.301965i | \(0.902357\pi\) | |||||||
\(152\) | − | 8.43997i | − | 0.684572i | ||||||
\(153\) | 5.12183 | 0.414075 | ||||||||
\(154\) | 18.6537 | − | 7.91584i | 1.50316 | − | 0.637877i | ||||
\(155\) | −4.21443 | −0.338511 | ||||||||
\(156\) | − | 11.0958i | − | 0.888375i | ||||||
\(157\) | 1.83121i | 0.146147i | 0.997327 | + | 0.0730734i | \(0.0232807\pi\) | ||||
−0.997327 | + | 0.0730734i | \(0.976719\pi\) | |||||||
\(158\) | 13.5887 | 1.08106 | ||||||||
\(159\) | 6.66550i | 0.528608i | ||||||||
\(160\) | 19.3831 | 1.53237 | ||||||||
\(161\) | −1.04163 | − | 5.70884i | −0.0820923 | − | 0.449920i | ||||
\(162\) | 2.30927i | 0.181434i | ||||||||
\(163\) | −7.73470 | −0.605829 | −0.302914 | − | 0.953018i | \(-0.597960\pi\) | ||||
−0.302914 | + | 0.953018i | \(0.597960\pi\) | |||||||
\(164\) | 12.5061 | 0.976559 | ||||||||
\(165\) | −12.2144 | + | 2.74231i | −0.950892 | + | 0.213489i | ||||
\(166\) | 37.5454i | 2.91409i | ||||||||
\(167\) | 0.316047 | 0.0244564 | 0.0122282 | − | 0.999925i | \(-0.496108\pi\) | ||||
0.0122282 | + | 0.999925i | \(0.496108\pi\) | |||||||
\(168\) | −1.46160 | − | 8.01054i | −0.112765 | − | 0.618026i | ||||
\(169\) | −1.91561 | −0.147354 | ||||||||
\(170\) | 44.6433 | 3.42398 | ||||||||
\(171\) | −2.74231 | −0.209710 | ||||||||
\(172\) | − | 22.4707i | − | 1.71337i | ||||||
\(173\) | −20.1434 | −1.53147 | −0.765737 | − | 0.643153i | \(-0.777626\pi\) | ||||
−0.765737 | + | 0.643153i | \(0.777626\pi\) | |||||||
\(174\) | − | 9.88168i | − | 0.749129i | ||||||
\(175\) | 4.39124 | + | 24.0669i | 0.331946 | + | 1.81929i | ||||
\(176\) | 1.42943 | − | 0.320927i | 0.107747 | − | 0.0241908i | ||||
\(177\) | −7.36317 | −0.553450 | ||||||||
\(178\) | 23.1414 | 1.73452 | ||||||||
\(179\) | 8.25420 | 0.616948 | 0.308474 | − | 0.951233i | \(-0.400182\pi\) | ||||
0.308474 | + | 0.951233i | \(0.400182\pi\) | |||||||
\(180\) | 12.5794i | 0.937610i | ||||||||
\(181\) | 10.4324i | 0.775432i | 0.921779 | + | 0.387716i | \(0.126736\pi\) | ||||
−0.921779 | + | 0.387716i | \(0.873264\pi\) | |||||||
\(182\) | 20.0110 | − | 3.65121i | 1.48332 | − | 0.270645i | ||||
\(183\) | − | 9.23710i | − | 0.682826i | ||||||
\(184\) | − | 6.75047i | − | 0.497652i | ||||||
\(185\) | 31.1265i | 2.28847i | ||||||||
\(186\) | − | 2.57845i | − | 0.189061i | ||||||
\(187\) | −16.5746 | + | 3.72123i | −1.21205 | + | 0.272123i | ||||
\(188\) | 18.6004i | 1.35658i | ||||||||
\(189\) | −2.60278 | + | 0.474903i | −0.189324 | + | 0.0345441i | ||||
\(190\) | −23.9028 | −1.73409 | ||||||||
\(191\) | −10.2998 | −0.745271 | −0.372635 | − | 0.927978i | \(-0.621546\pi\) | ||||
−0.372635 | + | 0.927978i | \(0.621546\pi\) | |||||||
\(192\) | 12.7423i | 0.919596i | ||||||||
\(193\) | − | 0.195328i | − | 0.0140600i | −0.999975 | − | 0.00703000i | \(-0.997762\pi\) | ||
0.999975 | − | 0.00703000i | \(-0.00223774\pi\) | |||||||
\(194\) | 33.3634 | 2.39535 | ||||||||
\(195\) | −12.5664 | −0.899900 | ||||||||
\(196\) | 21.8260 | − | 8.23901i | 1.55900 | − | 0.588501i | ||||
\(197\) | − | 5.87631i | − | 0.418669i | −0.977844 | − | 0.209335i | \(-0.932870\pi\) | ||
0.977844 | − | 0.209335i | \(-0.0671298\pi\) | |||||||
\(198\) | −1.67779 | − | 7.47297i | −0.119235 | − | 0.531081i | ||||
\(199\) | 0.214433i | 0.0152007i | 0.999971 | + | 0.00760037i | \(0.00241929\pi\) | ||||
−0.999971 | + | 0.00760037i | \(0.997581\pi\) | |||||||
\(200\) | 28.4581i | 2.01229i | ||||||||
\(201\) | 1.96783i | 0.138800i | ||||||||
\(202\) | − | 35.9778i | − | 2.53139i | ||||||
\(203\) | 11.1376 | − | 2.03217i | 0.781709 | − | 0.142630i | ||||
\(204\) | 17.0698i | 1.19512i | ||||||||
\(205\) | − | 14.1636i | − | 0.989229i | ||||||
\(206\) | 38.0873 | 2.65367 | ||||||||
\(207\) | −2.19336 | −0.152449 | ||||||||
\(208\) | 1.47062 | 0.101969 | ||||||||
\(209\) | 8.87430 | − | 1.99241i | 0.613848 | − | 0.137818i | ||||
\(210\) | −22.6866 | + | 4.13939i | −1.56552 | + | 0.285645i | ||||
\(211\) | − | 19.2017i | − | 1.32190i | −0.750430 | − | 0.660950i | \(-0.770154\pi\) | ||
0.750430 | − | 0.660950i | \(-0.229846\pi\) | |||||||
\(212\) | −22.2144 | −1.52569 | ||||||||
\(213\) | − | 5.07680i | − | 0.347857i | ||||||
\(214\) | −11.7737 | −0.804836 | ||||||||
\(215\) | −25.4489 | −1.73560 | ||||||||
\(216\) | −3.07768 | −0.209410 | ||||||||
\(217\) | 2.90617 | − | 0.530259i | 0.197284 | − | 0.0359963i | ||||
\(218\) | 31.5911 | 2.13962 | ||||||||
\(219\) | 12.7339i | 0.860476i | ||||||||
\(220\) | −9.13943 | − | 40.7076i | −0.616181 | − | 2.74451i | ||||
\(221\) | −17.0522 | −1.14706 | ||||||||
\(222\) | −19.0437 | −1.27813 | ||||||||
\(223\) | 3.62846i | 0.242980i | 0.992593 | + | 0.121490i | \(0.0387672\pi\) | ||||
−0.992593 | + | 0.121490i | \(0.961233\pi\) | |||||||
\(224\) | −13.3661 | + | 2.43878i | −0.893061 | + | 0.162948i | ||||
\(225\) | 9.24660 | 0.616440 | ||||||||
\(226\) | 39.4837i | 2.62641i | ||||||||
\(227\) | −3.07364 | −0.204004 | −0.102002 | − | 0.994784i | \(-0.532525\pi\) | ||||
−0.102002 | + | 0.994784i | \(0.532525\pi\) | |||||||
\(228\) | − | 9.13943i | − | 0.605274i | ||||||
\(229\) | 15.3766i | 1.01612i | 0.861323 | + | 0.508059i | \(0.169637\pi\) | ||||
−0.861323 | + | 0.508059i | \(0.830363\pi\) | |||||||
\(230\) | −19.1180 | −1.26060 | ||||||||
\(231\) | 8.07774 | − | 3.42785i | 0.531476 | − | 0.225536i | ||||
\(232\) | 13.1698 | 0.864640 | ||||||||
\(233\) | 16.2874i | 1.06702i | 0.845792 | + | 0.533512i | \(0.179128\pi\) | ||||
−0.845792 | + | 0.533512i | \(0.820872\pi\) | |||||||
\(234\) | − | 7.68832i | − | 0.502601i | ||||||
\(235\) | 21.0657 | 1.37417 | ||||||||
\(236\) | − | 24.5396i | − | 1.59739i | ||||||
\(237\) | 5.88440 | 0.382233 | ||||||||
\(238\) | −30.7849 | + | 5.61701i | −1.99549 | + | 0.364097i | ||||
\(239\) | 13.8242i | 0.894212i | 0.894481 | + | 0.447106i | \(0.147545\pi\) | ||||
−0.894481 | + | 0.447106i | \(0.852455\pi\) | |||||||
\(240\) | −1.66725 | −0.107621 | ||||||||
\(241\) | −5.22893 | −0.336825 | −0.168413 | − | 0.985717i | \(-0.553864\pi\) | ||||
−0.168413 | + | 0.985717i | \(0.553864\pi\) | |||||||
\(242\) | 10.8589 | + | 22.9641i | 0.698034 | + | 1.47619i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 30.7849 | 1.97080 | ||||||||
\(245\) | −9.33100 | − | 24.7187i | −0.596135 | − | 1.57922i | ||||
\(246\) | 8.66550 | 0.552492 | ||||||||
\(247\) | 9.13004 | 0.580931 | ||||||||
\(248\) | 3.43643 | 0.218213 | ||||||||
\(249\) | 16.2585i | 1.03034i | ||||||||
\(250\) | 37.0146 | 2.34101 | ||||||||
\(251\) | 1.19438i | 0.0753886i | 0.999289 | + | 0.0376943i | \(0.0120013\pi\) | ||||
−0.999289 | + | 0.0376943i | \(0.987999\pi\) | |||||||
\(252\) | −1.58273 | − | 8.67441i | −0.0997027 | − | 0.546437i | ||||
\(253\) | 7.09787 | − | 1.59357i | 0.446239 | − | 0.100187i | ||||
\(254\) | −8.47214 | −0.531589 | ||||||||
\(255\) | 19.3322 | 1.21063 | ||||||||
\(256\) | −18.7492 | −1.17182 | ||||||||
\(257\) | − | 15.8166i | − | 0.986613i | −0.869856 | − | 0.493306i | \(-0.835788\pi\) | ||
0.869856 | − | 0.493306i | \(-0.164212\pi\) | |||||||
\(258\) | − | 15.5700i | − | 0.969346i | ||||||
\(259\) | −3.91634 | − | 21.4641i | −0.243349 | − | 1.33371i | ||||
\(260\) | − | 41.8807i | − | 2.59733i | ||||||
\(261\) | − | 4.27913i | − | 0.264871i | ||||||
\(262\) | 19.7634i | 1.22098i | ||||||||
\(263\) | − | 24.7467i | − | 1.52595i | −0.646431 | − | 0.762973i | \(-0.723739\pi\) | ||
0.646431 | − | 0.762973i | \(-0.276261\pi\) | |||||||
\(264\) | 9.95959 | − | 2.23607i | 0.612971 | − | 0.137620i | ||||
\(265\) | 25.1587i | 1.54549i | ||||||||
\(266\) | 16.4828 | − | 3.00744i | 1.01062 | − | 0.184398i | ||||
\(267\) | 10.0211 | 0.613280 | ||||||||
\(268\) | −6.55828 | −0.400611 | ||||||||
\(269\) | 13.0768i | 0.797306i | 0.917102 | + | 0.398653i | \(0.130522\pi\) | ||||
−0.917102 | + | 0.398653i | \(0.869478\pi\) | |||||||
\(270\) | 8.71628i | 0.530456i | ||||||||
\(271\) | 24.8015 | 1.50658 | 0.753292 | − | 0.657686i | \(-0.228464\pi\) | ||||
0.753292 | + | 0.657686i | \(0.228464\pi\) | |||||||
\(272\) | −2.26240 | −0.137178 | ||||||||
\(273\) | 8.66550 | − | 1.58111i | 0.524460 | − | 0.0956928i | ||||
\(274\) | − | 19.5077i | − | 1.17851i | ||||||
\(275\) | −29.9226 | + | 6.71805i | −1.80440 | + | 0.405114i | ||||
\(276\) | − | 7.30993i | − | 0.440006i | ||||||
\(277\) | 4.26385i | 0.256190i | 0.991762 | + | 0.128095i | \(0.0408862\pi\) | ||||
−0.991762 | + | 0.128095i | \(0.959114\pi\) | |||||||
\(278\) | 4.90451i | 0.294153i | ||||||||
\(279\) | − | 1.11656i | − | 0.0668469i | ||||||
\(280\) | −5.51676 | − | 30.2355i | −0.329690 | − | 1.80692i | ||||
\(281\) | 17.4290i | 1.03972i | 0.854250 | + | 0.519862i | \(0.174017\pi\) | ||||
−0.854250 | + | 0.519862i | \(0.825983\pi\) | |||||||
\(282\) | 12.8883i | 0.767487i | ||||||||
\(283\) | −10.5750 | −0.628617 | −0.314309 | − | 0.949321i | \(-0.601773\pi\) | ||||
−0.314309 | + | 0.949321i | \(0.601773\pi\) | |||||||
\(284\) | 16.9197 | 1.00400 | ||||||||
\(285\) | −10.3508 | −0.613126 | ||||||||
\(286\) | 5.58589 | + | 24.8799i | 0.330301 | + | 1.47118i | ||||
\(287\) | 1.78206 | + | 9.76687i | 0.105192 | + | 0.576520i | ||||
\(288\) | 5.13532i | 0.302602i | ||||||||
\(289\) | 9.23313 | 0.543125 | ||||||||
\(290\) | − | 37.2981i | − | 2.19022i | ||||||
\(291\) | 14.4476 | 0.846931 | ||||||||
\(292\) | −42.4389 | −2.48355 | ||||||||
\(293\) | −21.3804 | −1.24905 | −0.624527 | − | 0.781003i | \(-0.714708\pi\) | ||||
−0.624527 | + | 0.781003i | \(0.714708\pi\) | |||||||
\(294\) | 15.1233 | − | 5.70884i | 0.882008 | − | 0.332946i | ||||
\(295\) | −27.7920 | −1.61811 | ||||||||
\(296\) | − | 25.3804i | − | 1.47521i | ||||||
\(297\) | −0.726543 | − | 3.23607i | −0.0421583 | − | 0.187776i | ||||
\(298\) | 12.5928 | 0.729483 | ||||||||
\(299\) | 7.30241 | 0.422309 | ||||||||
\(300\) | 30.8166i | 1.77920i | ||||||||
\(301\) | 17.5489 | − | 3.20198i | 1.01150 | − | 0.184559i | ||||
\(302\) | −17.1376 | −0.986160 | ||||||||
\(303\) | − | 15.5797i | − | 0.895030i | ||||||
\(304\) | 1.21133 | 0.0694745 | ||||||||
\(305\) | − | 34.8651i | − | 1.99637i | ||||||
\(306\) | 11.8277i | 0.676145i | ||||||||
\(307\) | 26.2034 | 1.49551 | 0.747753 | − | 0.663977i | \(-0.231133\pi\) | ||||
0.747753 | + | 0.663977i | \(0.231133\pi\) | |||||||
\(308\) | 11.4242 | + | 26.9211i | 0.650952 | + | 1.53397i | ||||
\(309\) | 16.4932 | 0.938266 | ||||||||
\(310\) | − | 9.73228i | − | 0.552756i | ||||||
\(311\) | − | 17.3731i | − | 0.985140i | −0.870273 | − | 0.492570i | \(-0.836058\pi\) | ||
0.870273 | − | 0.492570i | \(-0.163942\pi\) | |||||||
\(312\) | 10.2466 | 0.580100 | ||||||||
\(313\) | − | 3.33450i | − | 0.188477i | −0.995550 | − | 0.0942386i | \(-0.969958\pi\) | ||
0.995550 | − | 0.0942386i | \(-0.0300417\pi\) | |||||||
\(314\) | −4.22878 | −0.238644 | ||||||||
\(315\) | −9.82411 | + | 1.79251i | −0.553526 | + | 0.100996i | ||||
\(316\) | 19.6112i | 1.10322i | ||||||||
\(317\) | −4.83428 | −0.271520 | −0.135760 | − | 0.990742i | \(-0.543348\pi\) | ||||
−0.135760 | + | 0.990742i | \(0.543348\pi\) | |||||||
\(318\) | −15.3925 | −0.863167 | ||||||||
\(319\) | 3.10897 | + | 13.8476i | 0.174069 | + | 0.775314i | ||||
\(320\) | 48.0954i | 2.68861i | ||||||||
\(321\) | −5.09846 | −0.284568 | ||||||||
\(322\) | 13.1833 | − | 2.40542i | 0.734676 | − | 0.134049i | ||||
\(323\) | −14.0456 | −0.781521 | ||||||||
\(324\) | −3.33275 | −0.185153 | ||||||||
\(325\) | −30.7849 | −1.70764 | ||||||||
\(326\) | − | 17.8616i | − | 0.989260i | ||||||
\(327\) | 13.6801 | 0.756511 | ||||||||
\(328\) | 11.5489i | 0.637683i | ||||||||
\(329\) | −14.5264 | + | 2.65048i | −0.800866 | + | 0.146126i | ||||
\(330\) | −6.33275 | − | 28.2065i | −0.348606 | − | 1.55272i | ||||
\(331\) | −9.71772 | −0.534134 | −0.267067 | − | 0.963678i | \(-0.586055\pi\) | ||||
−0.267067 | + | 0.963678i | \(0.586055\pi\) | |||||||
\(332\) | −54.1856 | −2.97382 | ||||||||
\(333\) | −8.24660 | −0.451911 | ||||||||
\(334\) | 0.729839i | 0.0399350i | ||||||||
\(335\) | 7.42751i | 0.405808i | ||||||||
\(336\) | 1.14970 | − | 0.209773i | 0.0627210 | − | 0.0114441i | ||||
\(337\) | 22.5895i | 1.23053i | 0.788322 | + | 0.615263i | \(0.210950\pi\) | ||||
−0.788322 | + | 0.615263i | \(0.789050\pi\) | |||||||
\(338\) | − | 4.42366i | − | 0.240616i | ||||||
\(339\) | 17.0979i | 0.928629i | ||||||||
\(340\) | 64.4293i | 3.49417i | ||||||||
\(341\) | 0.811231 | + | 3.61328i | 0.0439306 | + | 0.195670i | ||||
\(342\) | − | 6.33275i | − | 0.342436i | ||||||
\(343\) | 9.54454 | + | 15.8714i | 0.515356 | + | 0.856976i | ||||
\(344\) | 20.7509 | 1.11881 | ||||||||
\(345\) | −8.27877 | −0.445714 | ||||||||
\(346\) | − | 46.5167i | − | 2.50075i | ||||||
\(347\) | − | 9.12550i | − | 0.489883i | −0.969538 | − | 0.244941i | \(-0.921231\pi\) | ||
0.969538 | − | 0.244941i | \(-0.0787687\pi\) | |||||||
\(348\) | 14.2613 | 0.764484 | ||||||||
\(349\) | −21.8035 | −1.16712 | −0.583558 | − | 0.812072i | \(-0.698340\pi\) | ||||
−0.583558 | + | 0.812072i | \(0.698340\pi\) | |||||||
\(350\) | −55.5770 | + | 10.1406i | −2.97072 | + | 0.542037i | ||||
\(351\) | − | 3.32932i | − | 0.177706i | ||||||
\(352\) | −3.73103 | − | 16.6182i | −0.198864 | − | 0.885755i | ||||
\(353\) | 2.50080i | 0.133104i | 0.997783 | + | 0.0665521i | \(0.0211999\pi\) | ||||
−0.997783 | + | 0.0665521i | \(0.978800\pi\) | |||||||
\(354\) | − | 17.0036i | − | 0.903730i | ||||||
\(355\) | − | 19.1622i | − | 1.01702i | ||||||
\(356\) | 33.3977i | 1.77008i | ||||||||
\(357\) | −13.3310 | + | 2.43237i | −0.705551 | + | 0.128735i | ||||
\(358\) | 19.0612i | 1.00742i | ||||||||
\(359\) | − | 32.0706i | − | 1.69262i | −0.532692 | − | 0.846309i | \(-0.678819\pi\) | ||
0.532692 | − | 0.846309i | \(-0.321181\pi\) | |||||||
\(360\) | −11.6166 | −0.612249 | ||||||||
\(361\) | −11.4797 | −0.604196 | ||||||||
\(362\) | −24.0912 | −1.26621 | ||||||||
\(363\) | 4.70228 | + | 9.94427i | 0.246806 | + | 0.521939i | ||||
\(364\) | 5.26943 | + | 28.8799i | 0.276193 | + | 1.51372i | ||||
\(365\) | 48.0636i | 2.51577i | ||||||||
\(366\) | 21.3310 | 1.11499 | ||||||||
\(367\) | 4.77345i | 0.249172i | 0.992209 | + | 0.124586i | \(0.0397603\pi\) | ||||
−0.992209 | + | 0.124586i | \(0.960240\pi\) | |||||||
\(368\) | 0.968848 | 0.0505047 | ||||||||
\(369\) | 3.75248 | 0.195346 | ||||||||
\(370\) | −71.8797 | −3.73685 | ||||||||
\(371\) | −3.16546 | − | 17.3488i | −0.164343 | − | 0.900706i | ||||
\(372\) | 3.72123 | 0.192937 | ||||||||
\(373\) | 4.27552i | 0.221378i | 0.993855 | + | 0.110689i | \(0.0353058\pi\) | ||||
−0.993855 | + | 0.110689i | \(0.964694\pi\) | |||||||
\(374\) | −8.59333 | − | 38.2753i | −0.444351 | − | 1.97917i | ||||
\(375\) | 16.0287 | 0.827717 | ||||||||
\(376\) | −17.1769 | −0.885830 | ||||||||
\(377\) | 14.2466i | 0.733737i | ||||||||
\(378\) | −1.09668 | − | 6.01054i | −0.0564072 | − | 0.309149i | ||||
\(379\) | −2.41889 | −0.124250 | −0.0621251 | − | 0.998068i | \(-0.519788\pi\) | ||||
−0.0621251 | + | 0.998068i | \(0.519788\pi\) | |||||||
\(380\) | − | 34.4965i | − | 1.76963i | ||||||
\(381\) | −3.66874 | −0.187955 | ||||||||
\(382\) | − | 23.7852i | − | 1.21696i | ||||||
\(383\) | − | 24.9443i | − | 1.27459i | −0.770619 | − | 0.637296i | \(-0.780053\pi\) | ||
0.770619 | − | 0.637296i | \(-0.219947\pi\) | |||||||
\(384\) | −19.1548 | −0.977491 | ||||||||
\(385\) | 30.4892 | − | 12.9383i | 1.55387 | − | 0.659397i | ||||
\(386\) | 0.451065 | 0.0229586 | ||||||||
\(387\) | − | 6.74238i | − | 0.342734i | ||||||
\(388\) | 48.1501i | 2.44445i | ||||||||
\(389\) | −24.2753 | −1.23080 | −0.615402 | − | 0.788213i | \(-0.711007\pi\) | ||||
−0.615402 | + | 0.788213i | \(0.711007\pi\) | |||||||
\(390\) | − | 29.0193i | − | 1.46945i | ||||||
\(391\) | −11.2340 | −0.568129 | ||||||||
\(392\) | 7.60845 | + | 20.1555i | 0.384285 | + | 1.01801i | ||||
\(393\) | 8.55826i | 0.431707i | ||||||||
\(394\) | 13.5700 | 0.683647 | ||||||||
\(395\) | 22.2105 | 1.11753 | ||||||||
\(396\) | 10.7850 | − | 2.42138i | 0.541967 | − | 0.121679i | ||||
\(397\) | − | 29.0944i | − | 1.46020i | −0.683338 | − | 0.730102i | \(-0.739472\pi\) | ||
0.683338 | − | 0.730102i | \(-0.260528\pi\) | |||||||
\(398\) | −0.495184 | −0.0248213 | ||||||||
\(399\) | 7.13763 | − | 1.30233i | 0.357329 | − | 0.0651981i | ||||
\(400\) | −4.08439 | −0.204220 | ||||||||
\(401\) | −12.0456 | −0.601531 | −0.300765 | − | 0.953698i | \(-0.597242\pi\) | ||||
−0.300765 | + | 0.953698i | \(0.597242\pi\) | |||||||
\(402\) | −4.54426 | −0.226647 | ||||||||
\(403\) | 3.71740i | 0.185177i | ||||||||
\(404\) | 51.9232 | 2.58328 | ||||||||
\(405\) | 3.77447i | 0.187555i | ||||||||
\(406\) | 4.69284 | + | 25.7199i | 0.232902 | + | 1.27645i | ||||
\(407\) | 26.6866 | − | 5.99151i | 1.32280 | − | 0.296988i | ||||
\(408\) | −15.7634 | −0.780403 | ||||||||
\(409\) | 14.9359 | 0.738534 | 0.369267 | − | 0.929323i | \(-0.379609\pi\) | ||||
0.369267 | + | 0.929323i | \(0.379609\pi\) | |||||||
\(410\) | 32.7076 | 1.61532 | ||||||||
\(411\) | − | 8.44756i | − | 0.416687i | ||||||
\(412\) | 54.9677i | 2.70807i | ||||||||
\(413\) | 19.1647 | − | 3.49679i | 0.943034 | − | 0.172066i | ||||
\(414\) | − | 5.06508i | − | 0.248935i | ||||||
\(415\) | 61.3673i | 3.01240i | ||||||||
\(416\) | − | 17.0971i | − | 0.838256i | ||||||
\(417\) | 2.12383i | 0.104004i | ||||||||
\(418\) | 4.60101 | + | 20.4932i | 0.225043 | + | 1.00236i | ||||
\(419\) | − | 8.29225i | − | 0.405103i | −0.979272 | − | 0.202551i | \(-0.935077\pi\) | ||
0.979272 | − | 0.202551i | \(-0.0649233\pi\) | |||||||
\(420\) | −5.97397 | − | 32.7413i | −0.291500 | − | 1.59761i | ||||
\(421\) | −2.54407 | −0.123990 | −0.0619952 | − | 0.998076i | \(-0.519746\pi\) | ||||
−0.0619952 | + | 0.998076i | \(0.519746\pi\) | |||||||
\(422\) | 44.3420 | 2.15853 | ||||||||
\(423\) | 5.58111i | 0.271363i | ||||||||
\(424\) | − | 20.5143i | − | 0.996262i | ||||||
\(425\) | 47.3595 | 2.29727 | ||||||||
\(426\) | 11.7237 | 0.568016 | ||||||||
\(427\) | 4.38672 | + | 24.0421i | 0.212288 | + | 1.16348i | ||||
\(428\) | − | 16.9919i | − | 0.821333i | ||||||
\(429\) | 2.41889 | + | 10.7739i | 0.116785 | + | 0.520170i | ||||
\(430\) | − | 58.7685i | − | 2.83407i | ||||||
\(431\) | − | 22.4454i | − | 1.08116i | −0.841294 | − | 0.540578i | \(-0.818206\pi\) | ||
0.841294 | − | 0.540578i | \(-0.181794\pi\) | |||||||
\(432\) | − | 0.441718i | − | 0.0212522i | ||||||
\(433\) | − | 28.4137i | − | 1.36547i | −0.730664 | − | 0.682737i | \(-0.760789\pi\) | ||
0.730664 | − | 0.682737i | \(-0.239211\pi\) | |||||||
\(434\) | 1.22451 | + | 6.71114i | 0.0587786 | + | 0.322145i | ||||
\(435\) | − | 16.1514i | − | 0.774402i | ||||||
\(436\) | 45.5923i | 2.18347i | ||||||||
\(437\) | 6.01488 | 0.287731 | ||||||||
\(438\) | −29.4060 | −1.40508 | ||||||||
\(439\) | 23.3503 | 1.11445 | 0.557226 | − | 0.830361i | \(-0.311866\pi\) | ||||
0.557226 | + | 0.830361i | \(0.311866\pi\) | |||||||
\(440\) | 37.5922 | − | 8.43997i | 1.79214 | − | 0.402360i | ||||
\(441\) | 6.54893 | − | 2.47214i | 0.311854 | − | 0.117721i | ||||
\(442\) | − | 39.3783i | − | 1.87303i | ||||||
\(443\) | −7.37427 | −0.350362 | −0.175181 | − | 0.984536i | \(-0.556051\pi\) | ||||
−0.175181 | + | 0.984536i | \(0.556051\pi\) | |||||||
\(444\) | − | 27.4839i | − | 1.30433i | ||||||
\(445\) | 37.8242 | 1.79304 | ||||||||
\(446\) | −8.37912 | −0.396763 | ||||||||
\(447\) | 5.45315 | 0.257925 | ||||||||
\(448\) | −6.05135 | − | 33.1654i | −0.285900 | − | 1.56692i | ||||
\(449\) | −26.0270 | −1.22829 | −0.614144 | − | 0.789194i | \(-0.710499\pi\) | ||||
−0.614144 | + | 0.789194i | \(0.710499\pi\) | |||||||
\(450\) | 21.3529i | 1.00659i | ||||||||
\(451\) | −12.1433 | + | 2.72633i | −0.571804 | + | 0.128378i | ||||
\(452\) | −56.9829 | −2.68025 | ||||||||
\(453\) | −7.42122 | −0.348679 | ||||||||
\(454\) | − | 7.09787i | − | 0.333120i | ||||||
\(455\) | 32.7076 | − | 5.96783i | 1.53336 | − | 0.279776i | ||||
\(456\) | 8.43997 | 0.395238 | ||||||||
\(457\) | − | 11.2853i | − | 0.527904i | −0.964536 | − | 0.263952i | \(-0.914974\pi\) | ||
0.964536 | − | 0.263952i | \(-0.0850260\pi\) | |||||||
\(458\) | −35.5089 | −1.65922 | ||||||||
\(459\) | 5.12183i | 0.239066i | ||||||||
\(460\) | − | 27.5911i | − | 1.28644i | ||||||
\(461\) | 11.1367 | 0.518688 | 0.259344 | − | 0.965785i | \(-0.416494\pi\) | ||||
0.259344 | + | 0.965785i | \(0.416494\pi\) | |||||||
\(462\) | 7.91584 | + | 18.6537i | 0.368278 | + | 0.867849i | ||||
\(463\) | 0.572492 | 0.0266060 | 0.0133030 | − | 0.999912i | \(-0.495765\pi\) | ||||
0.0133030 | + | 0.999912i | \(0.495765\pi\) | |||||||
\(464\) | 1.89017i | 0.0877489i | ||||||||
\(465\) | − | 4.21443i | − | 0.195440i | ||||||
\(466\) | −37.6121 | −1.74235 | ||||||||
\(467\) | 9.06570i | 0.419510i | 0.977754 | + | 0.209755i | \(0.0672667\pi\) | ||||
−0.977754 | + | 0.209755i | \(0.932733\pi\) | |||||||
\(468\) | 11.0958 | 0.512903 | ||||||||
\(469\) | −0.934528 | − | 5.12183i | −0.0431525 | − | 0.236504i | ||||
\(470\) | 48.6465i | 2.24389i | ||||||||
\(471\) | −1.83121 | −0.0843779 | ||||||||
\(472\) | 22.6615 | 1.04308 | ||||||||
\(473\) | 4.89863 | + | 21.8188i | 0.225239 | + | 1.00323i | ||||
\(474\) | 13.5887i | 0.624150i | ||||||||
\(475\) | −25.3571 | −1.16346 | ||||||||
\(476\) | −8.10648 | − | 44.4289i | −0.371560 | − | 2.03639i | ||||
\(477\) | −6.66550 | −0.305192 | ||||||||
\(478\) | −31.9238 | −1.46016 | ||||||||
\(479\) | −36.0275 | −1.64614 | −0.823069 | − | 0.567942i | \(-0.807740\pi\) | ||||
−0.823069 | + | 0.567942i | \(0.807740\pi\) | |||||||
\(480\) | 19.3831i | 0.884713i | ||||||||
\(481\) | 27.4556 | 1.25187 | ||||||||
\(482\) | − | 12.0750i | − | 0.550003i | ||||||
\(483\) | 5.70884 | − | 1.04163i | 0.259761 | − | 0.0473960i | ||||
\(484\) | −33.1418 | + | 15.6715i | −1.50644 | + | 0.712342i | ||||
\(485\) | 54.5318 | 2.47616 | ||||||||
\(486\) | −2.30927 | −0.104751 | ||||||||
\(487\) | −36.8156 | −1.66827 | −0.834137 | − | 0.551558i | \(-0.814034\pi\) | ||||
−0.834137 | + | 0.551558i | \(0.814034\pi\) | |||||||
\(488\) | 28.4289i | 1.28691i | ||||||||
\(489\) | − | 7.73470i | − | 0.349775i | ||||||
\(490\) | 57.0824 | − | 21.5478i | 2.57872 | − | 0.973432i | ||||
\(491\) | 8.85093i | 0.399437i | 0.979853 | + | 0.199718i | \(0.0640028\pi\) | ||||
−0.979853 | + | 0.199718i | \(0.935997\pi\) | |||||||
\(492\) | 12.5061i | 0.563817i | ||||||||
\(493\) | − | 21.9170i | − | 0.987090i | ||||||
\(494\) | 21.0838i | 0.948604i | ||||||||
\(495\) | −2.74231 | − | 12.2144i | −0.123258 | − | 0.548998i | ||||
\(496\) | 0.493206i | 0.0221456i | ||||||||
\(497\) | 2.41099 | + | 13.2138i | 0.108148 | + | 0.592720i | ||||
\(498\) | −37.5454 | −1.68245 | ||||||||
\(499\) | 20.3074 | 0.909086 | 0.454543 | − | 0.890725i | \(-0.349803\pi\) | ||||
0.454543 | + | 0.890725i | \(0.349803\pi\) | |||||||
\(500\) | 53.4195i | 2.38899i | ||||||||
\(501\) | 0.316047i | 0.0141199i | ||||||||
\(502\) | −2.75815 | −0.123102 | ||||||||
\(503\) | −14.0240 | −0.625299 | −0.312650 | − | 0.949869i | \(-0.601217\pi\) | ||||
−0.312650 | + | 0.949869i | \(0.601217\pi\) | |||||||
\(504\) | 8.01054 | − | 1.46160i | 0.356818 | − | 0.0651049i | ||||
\(505\) | − | 58.8051i | − | 2.61679i | ||||||
\(506\) | 3.67999 | + | 16.3909i | 0.163596 | + | 0.728666i | ||||
\(507\) | − | 1.91561i | − | 0.0850751i | ||||||
\(508\) | − | 12.2270i | − | 0.542485i | ||||||
\(509\) | 16.2963i | 0.722323i | 0.932503 | + | 0.361161i | \(0.117620\pi\) | ||||
−0.932503 | + | 0.361161i | \(0.882380\pi\) | |||||||
\(510\) | 44.6433i | 1.97684i | ||||||||
\(511\) | −6.04736 | − | 33.1435i | −0.267519 | − | 1.46618i | ||||
\(512\) | − | 4.98730i | − | 0.220410i | ||||||
\(513\) | − | 2.74231i | − | 0.121076i | ||||||
\(514\) | 36.5249 | 1.61104 | ||||||||
\(515\) | 62.2531 | 2.74320 | ||||||||
\(516\) | 22.4707 | 0.989216 | ||||||||
\(517\) | −4.05491 | − | 18.0608i | −0.178335 | − | 0.794315i | ||||
\(518\) | 49.5665 | − | 9.04389i | 2.17783 | − | 0.397366i | ||||
\(519\) | − | 20.1434i | − | 0.884197i | ||||||
\(520\) | 38.6755 | 1.69603 | ||||||||
\(521\) | − | 6.83020i | − | 0.299236i | −0.988744 | − | 0.149618i | \(-0.952196\pi\) | ||
0.988744 | − | 0.149618i | \(-0.0478044\pi\) | |||||||
\(522\) | 9.88168 | 0.432510 | ||||||||
\(523\) | 18.7983 | 0.821993 | 0.410996 | − | 0.911637i | \(-0.365181\pi\) | ||||
0.410996 | + | 0.911637i | \(0.365181\pi\) | |||||||
\(524\) | −28.5225 | −1.24601 | ||||||||
\(525\) | −24.0669 | + | 4.39124i | −1.05036 | + | 0.191649i | ||||
\(526\) | 57.1469 | 2.49172 | ||||||||
\(527\) | − | 5.71885i | − | 0.249117i | ||||||
\(528\) | 0.320927 | + | 1.42943i | 0.0139666 | + | 0.0622080i | ||||
\(529\) | −18.1892 | −0.790833 | ||||||||
\(530\) | −58.0984 | −2.52363 | ||||||||
\(531\) | − | 7.36317i | − | 0.319534i | ||||||
\(532\) | 4.34034 | + | 23.7879i | 0.188178 | + | 1.03134i | ||||
\(533\) | −12.4932 | −0.541141 | ||||||||
\(534\) | 23.1414i | 1.00143i | ||||||||
\(535\) | −19.2440 | −0.831989 | ||||||||
\(536\) | − | 6.05636i | − | 0.261595i | ||||||
\(537\) | 8.25420i | 0.356195i | ||||||||
\(538\) | −30.1979 | −1.30192 | ||||||||
\(539\) | −19.3967 | + | 12.7581i | −0.835474 | + | 0.549529i | ||||
\(540\) | −12.5794 | −0.541329 | ||||||||
\(541\) | 5.76559i | 0.247882i | 0.992290 | + | 0.123941i | \(0.0395534\pi\) | ||||
−0.992290 | + | 0.123941i | \(0.960447\pi\) | |||||||
\(542\) | 57.2735i | 2.46011i | ||||||||
\(543\) | −10.4324 | −0.447696 | ||||||||
\(544\) | 26.3022i | 1.12770i | ||||||||
\(545\) | 51.6350 | 2.21180 | ||||||||
\(546\) | 3.65121 | + | 20.0110i | 0.156257 | + | 0.856392i | ||||
\(547\) | − | 13.2686i | − | 0.567326i | −0.958924 | − | 0.283663i | \(-0.908450\pi\) | ||
0.958924 | − | 0.283663i | \(-0.0915497\pi\) | |||||||
\(548\) | 28.1536 | 1.20266 | ||||||||
\(549\) | 9.23710 | 0.394230 | ||||||||
\(550\) | −15.5138 | − | 69.0996i | −0.661512 | − | 2.94642i | ||||
\(551\) | 11.7347i | 0.499915i | ||||||||
\(552\) | 6.75047 | 0.287319 | ||||||||
\(553\) | −15.3158 | + | 2.79452i | −0.651294 | + | 0.118835i | ||||
\(554\) | −9.84640 | −0.418334 | ||||||||
\(555\) | −31.1265 | −1.32125 | ||||||||
\(556\) | −7.07819 | −0.300182 | ||||||||
\(557\) | 26.6733i | 1.13018i | 0.825028 | + | 0.565091i | \(0.191159\pi\) | ||||
−0.825028 | + | 0.565091i | \(0.808841\pi\) | |||||||
\(558\) | 2.57845 | 0.109155 | ||||||||
\(559\) | 22.4476i | 0.949431i | ||||||||
\(560\) | 4.33949 | − | 0.791782i | 0.183377 | − | 0.0334589i | ||||
\(561\) | −3.72123 | − | 16.5746i | −0.157110 | − | 0.699780i | ||||
\(562\) | −40.2482 | −1.69777 | ||||||||
\(563\) | 18.7902 | 0.791914 | 0.395957 | − | 0.918269i | \(-0.370413\pi\) | ||||
0.395957 | + | 0.918269i | \(0.370413\pi\) | |||||||
\(564\) | −18.6004 | −0.783219 | ||||||||
\(565\) | 64.5353i | 2.71502i | ||||||||
\(566\) | − | 24.4205i | − | 1.02647i | ||||||
\(567\) | −0.474903 | − | 2.60278i | −0.0199440 | − | 0.109307i | ||||
\(568\) | 15.6248i | 0.655601i | ||||||||
\(569\) | − | 35.6007i | − | 1.49246i | −0.665688 | − | 0.746230i | \(-0.731862\pi\) | ||
0.665688 | − | 0.746230i | \(-0.268138\pi\) | |||||||
\(570\) | − | 23.9028i | − | 1.00118i | ||||||
\(571\) | 35.3746i | 1.48038i | 0.672398 | + | 0.740190i | \(0.265265\pi\) | ||||
−0.672398 | + | 0.740190i | \(0.734735\pi\) | |||||||
\(572\) | −35.9068 | + | 8.06157i | −1.50134 | + | 0.337071i | ||||
\(573\) | − | 10.2998i | − | 0.430282i | ||||||
\(574\) | −22.5544 | + | 4.11527i | −0.941402 | + | 0.171768i | ||||
\(575\) | −20.2811 | −0.845782 | ||||||||
\(576\) | −12.7423 | −0.530929 | ||||||||
\(577\) | 36.2144i | 1.50763i | 0.657089 | + | 0.753813i | \(0.271788\pi\) | ||||
−0.657089 | + | 0.753813i | \(0.728212\pi\) | |||||||
\(578\) | 21.3218i | 0.886871i | ||||||||
\(579\) | 0.195328 | 0.00811754 | ||||||||
\(580\) | 53.8287 | 2.23511 | ||||||||
\(581\) | −7.72123 | − | 42.3174i | −0.320330 | − | 1.75562i | ||||
\(582\) | 33.3634i | 1.38296i | ||||||||
\(583\) | 21.5700 | − | 4.84277i | 0.893338 | − | 0.200567i | ||||
\(584\) | − | 39.1909i | − | 1.62173i | ||||||
\(585\) | − | 12.5664i | − | 0.519558i | ||||||
\(586\) | − | 49.3731i | − | 2.03959i | ||||||
\(587\) | 6.46104i | 0.266675i | 0.991071 | + | 0.133338i | \(0.0425695\pi\) | ||||
−0.991071 | + | 0.133338i | \(0.957430\pi\) | |||||||
\(588\) | 8.23901 | + | 21.8260i | 0.339771 | + | 0.900087i | ||||
\(589\) | 3.06196i | 0.126166i | ||||||||
\(590\) | − | 64.1794i | − | 2.64223i | ||||||
\(591\) | 5.87631 | 0.241719 | ||||||||
\(592\) | 3.64267 | 0.149713 | ||||||||
\(593\) | 42.9282 | 1.76285 | 0.881425 | − | 0.472324i | \(-0.156585\pi\) | ||||
0.881425 | + | 0.472324i | \(0.156585\pi\) | |||||||
\(594\) | 7.47297 | − | 1.67779i | 0.306620 | − | 0.0688404i | ||||
\(595\) | −50.3174 | + | 9.18090i | −2.06281 | + | 0.376380i | ||||
\(596\) | 18.1740i | 0.744436i | ||||||||
\(597\) | −0.214433 | −0.00877615 | ||||||||
\(598\) | 16.8633i | 0.689591i | ||||||||
\(599\) | −33.0698 | −1.35119 | −0.675597 | − | 0.737271i | \(-0.736114\pi\) | ||||
−0.675597 | + | 0.737271i | \(0.736114\pi\) | |||||||
\(600\) | −28.4581 | −1.16180 | ||||||||
\(601\) | 25.2049 | 1.02813 | 0.514064 | − | 0.857752i | \(-0.328139\pi\) | ||||
0.514064 | + | 0.857752i | \(0.328139\pi\) | |||||||
\(602\) | 7.39424 | + | 40.5253i | 0.301367 | + | 1.65169i | ||||
\(603\) | −1.96783 | −0.0801362 | ||||||||
\(604\) | − | 24.7331i | − | 1.00637i | ||||||
\(605\) | 17.7486 | + | 37.5343i | 0.721584 | + | 1.52599i | ||||
\(606\) | 35.9778 | 1.46150 | ||||||||
\(607\) | −26.0963 | −1.05921 | −0.529607 | − | 0.848243i | \(-0.677661\pi\) | ||||
−0.529607 | + | 0.848243i | \(0.677661\pi\) | |||||||
\(608\) | − | 14.0826i | − | 0.571126i | ||||||
\(609\) | 2.03217 | + | 11.1376i | 0.0823477 | + | 0.451320i | ||||
\(610\) | 80.5131 | 3.25988 | ||||||||
\(611\) | − | 18.5813i | − | 0.751719i | ||||||
\(612\) | −17.0698 | −0.690005 | ||||||||
\(613\) | 14.0078i | 0.565770i | 0.959154 | + | 0.282885i | \(0.0912915\pi\) | ||||
−0.959154 | + | 0.282885i | \(0.908709\pi\) | |||||||
\(614\) | 60.5108i | 2.44202i | ||||||||
\(615\) | 14.1636 | 0.571131 | ||||||||
\(616\) | −24.8607 | + | 10.5498i | −1.00167 | + | 0.425065i | ||||
\(617\) | 23.7025 | 0.954228 | 0.477114 | − | 0.878841i | \(-0.341683\pi\) | ||||
0.477114 | + | 0.878841i | \(0.341683\pi\) | |||||||
\(618\) | 38.0873i | 1.53210i | ||||||||
\(619\) | 17.4881i | 0.702906i | 0.936206 | + | 0.351453i | \(0.114312\pi\) | ||||
−0.936206 | + | 0.351453i | \(0.885688\pi\) | |||||||
\(620\) | 14.0456 | 0.564087 | ||||||||
\(621\) | − | 2.19336i | − | 0.0880166i | ||||||
\(622\) | 40.1193 | 1.60864 | ||||||||
\(623\) | −26.0826 | + | 4.75903i | −1.04498 | + | 0.190667i | ||||
\(624\) | 1.47062i | 0.0588720i | ||||||||
\(625\) | 14.2667 | 0.570666 | ||||||||
\(626\) | 7.70028 | 0.307765 | ||||||||
\(627\) | 1.99241 | + | 8.87430i | 0.0795690 | + | 0.354406i | ||||
\(628\) | − | 6.10298i | − | 0.243535i | ||||||
\(629\) | −42.2377 | −1.68413 | ||||||||
\(630\) | −4.13939 | − | 22.6866i | −0.164917 | − | 0.903855i | ||||
\(631\) | −3.00658 | −0.119690 | −0.0598449 | − | 0.998208i | \(-0.519061\pi\) | ||||
−0.0598449 | + | 0.998208i | \(0.519061\pi\) | |||||||
\(632\) | −18.1103 | −0.720390 | ||||||||
\(633\) | 19.2017 | 0.763199 | ||||||||
\(634\) | − | 11.1637i | − | 0.443367i | ||||||
\(635\) | −13.8476 | −0.549523 | ||||||||
\(636\) | − | 22.2144i | − | 0.880860i | ||||||
\(637\) | −21.8035 | + | 8.23054i | −0.863887 | + | 0.326106i | ||||
\(638\) | −31.9778 | + | 7.17946i | −1.26601 | + | 0.284238i | ||||
\(639\) | 5.07680 | 0.200835 | ||||||||
\(640\) | −72.2993 | −2.85788 | ||||||||
\(641\) | 14.1501 | 0.558895 | 0.279448 | − | 0.960161i | \(-0.409849\pi\) | ||||
0.279448 | + | 0.960161i | \(0.409849\pi\) | |||||||
\(642\) | − | 11.7737i | − | 0.464672i | ||||||
\(643\) | 13.4238i | 0.529381i | 0.964333 | + | 0.264691i | \(0.0852699\pi\) | ||||
−0.964333 | + | 0.264691i | \(0.914730\pi\) | |||||||
\(644\) | 3.47150 | + | 19.0261i | 0.136796 | + | 0.749735i | ||||
\(645\) | − | 25.4489i | − | 1.00205i | ||||||
\(646\) | − | 32.4353i | − | 1.27615i | ||||||
\(647\) | − | 21.0809i | − | 0.828775i | −0.910100 | − | 0.414388i | \(-0.863996\pi\) | ||
0.910100 | − | 0.414388i | \(-0.136004\pi\) | |||||||
\(648\) | − | 3.07768i | − | 0.120903i | ||||||
\(649\) | 5.34965 | + | 23.8277i | 0.209992 | + | 0.935319i | ||||
\(650\) | − | 71.0909i | − | 2.78841i | ||||||
\(651\) | 0.530259 | + | 2.90617i | 0.0207825 | + | 0.113902i | ||||
\(652\) | 25.7778 | 1.00954 | ||||||||
\(653\) | −2.87993 | −0.112700 | −0.0563502 | − | 0.998411i | \(-0.517946\pi\) | ||||
−0.0563502 | + | 0.998411i | \(0.517946\pi\) | |||||||
\(654\) | 31.5911i | 1.23531i | ||||||||
\(655\) | 32.3029i | 1.26218i | ||||||||
\(656\) | −1.65754 | −0.0647160 | ||||||||
\(657\) | −12.7339 | −0.496796 | ||||||||
\(658\) | −6.12069 | − | 33.5454i | −0.238609 | − | 1.30774i | ||||
\(659\) | 41.2473i | 1.60677i | 0.595462 | + | 0.803383i | \(0.296969\pi\) | ||||
−0.595462 | + | 0.803383i | \(0.703031\pi\) | |||||||
\(660\) | 40.7076 | − | 9.13943i | 1.58454 | − | 0.355752i | ||||
\(661\) | − | 3.22802i | − | 0.125555i | −0.998028 | − | 0.0627777i | \(-0.980004\pi\) | ||
0.998028 | − | 0.0627777i | \(-0.0199959\pi\) | |||||||
\(662\) | − | 22.4409i | − | 0.872190i | ||||||
\(663\) | − | 17.0522i | − | 0.662253i | ||||||
\(664\) | − | 50.0386i | − | 1.94188i | ||||||
\(665\) | 26.9408 | − | 4.91561i | 1.04472 | − | 0.190619i | ||||
\(666\) | − | 19.0437i | − | 0.737927i | ||||||
\(667\) | 9.38568i | 0.363415i | ||||||||
\(668\) | −1.05331 | −0.0407536 | ||||||||
\(669\) | −3.62846 | −0.140285 | ||||||||
\(670\) | −17.1522 | −0.662646 | ||||||||
\(671\) | −29.8919 | + | 6.71114i | −1.15396 | + | 0.259081i | ||||
\(672\) | −2.43878 | − | 13.3661i | −0.0940779 | − | 0.515609i | ||||
\(673\) | − | 15.0845i | − | 0.581465i | −0.956804 | − | 0.290733i | \(-0.906101\pi\) | ||
0.956804 | − | 0.290733i | \(-0.0938990\pi\) | |||||||
\(674\) | −52.1653 | −2.00933 | ||||||||
\(675\) | 9.24660i | 0.355902i | ||||||||
\(676\) | 6.38424 | 0.245548 | ||||||||
\(677\) | −24.9654 | −0.959497 | −0.479749 | − | 0.877406i | \(-0.659272\pi\) | ||||
−0.479749 | + | 0.877406i | \(0.659272\pi\) | |||||||
\(678\) | −39.4837 | −1.51636 | ||||||||
\(679\) | −37.6038 | + | 6.86119i | −1.44310 | + | 0.263308i | ||||
\(680\) | −59.4983 | −2.28166 | ||||||||
\(681\) | − | 3.07364i | − | 0.117782i | ||||||
\(682\) | −8.34405 | + | 1.87335i | −0.319510 | + | 0.0717345i | ||||
\(683\) | 6.67138 | 0.255273 | 0.127637 | − | 0.991821i | \(-0.459261\pi\) | ||||
0.127637 | + | 0.991821i | \(0.459261\pi\) | |||||||
\(684\) | 9.13943 | 0.349455 | ||||||||
\(685\) | − | 31.8850i | − | 1.21826i | ||||||
\(686\) | −36.6515 | + | 22.0410i | −1.39936 | + | 0.841527i | ||||
\(687\) | −15.3766 | −0.586656 | ||||||||
\(688\) | 2.97823i | 0.113544i | ||||||||
\(689\) | 22.1916 | 0.845433 | ||||||||
\(690\) | − | 19.1180i | − | 0.727808i | ||||||
\(691\) | − | 37.8885i | − | 1.44135i | −0.693274 | − | 0.720674i | \(-0.743832\pi\) | ||
0.693274 | − | 0.720674i | \(-0.256168\pi\) | |||||||
\(692\) | 67.1329 | 2.55201 | ||||||||
\(693\) | 3.42785 | + | 8.07774i | 0.130213 | + | 0.306848i | ||||
\(694\) | 21.0733 | 0.799931 | ||||||||
\(695\) | 8.01633i | 0.304077i | ||||||||
\(696\) | 13.1698i | 0.499200i | ||||||||
\(697\) | 19.2195 | 0.727992 | ||||||||
\(698\) | − | 50.3503i | − | 1.90579i | ||||||
\(699\) | −16.2874 | −0.616047 | ||||||||
\(700\) | −14.6349 | − | 80.2089i | −0.553147 | − | 3.03161i | ||||
\(701\) | − | 18.3545i | − | 0.693240i | −0.938006 | − | 0.346620i | \(-0.887329\pi\) | ||
0.938006 | − | 0.346620i | \(-0.112671\pi\) | |||||||
\(702\) | 7.68832 | 0.290177 | ||||||||
\(703\) | 22.6148 | 0.852931 | ||||||||
\(704\) | 41.2349 | − | 9.25782i | 1.55410 | − | 0.348917i | ||||
\(705\) | 21.0657i | 0.793380i | ||||||||
\(706\) | −5.77504 | −0.217346 | ||||||||
\(707\) | 7.39884 | + | 40.5505i | 0.278262 | + | 1.52506i | ||||
\(708\) | 24.5396 | 0.922254 | ||||||||
\(709\) | −10.2937 | −0.386589 | −0.193294 | − | 0.981141i | \(-0.561917\pi\) | ||||
−0.193294 | + | 0.981141i | \(0.561917\pi\) | |||||||
\(710\) | 44.2508 | 1.66070 | ||||||||
\(711\) | 5.88440i | 0.220682i | ||||||||
\(712\) | −30.8417 | −1.15584 | ||||||||
\(713\) | 2.44903i | 0.0917168i | ||||||||
\(714\) | −5.61701 | − | 30.7849i | −0.210211 | − | 1.15210i | ||||
\(715\) | 9.13004 | + | 40.6658i | 0.341444 | + | 1.52081i | ||||
\(716\) | −27.5092 | −1.02807 | ||||||||
\(717\) | −13.8242 | −0.516273 | ||||||||
\(718\) | 74.0597 | 2.76388 | ||||||||
\(719\) | 31.8412i | 1.18748i | 0.804659 | + | 0.593738i | \(0.202348\pi\) | ||||
−0.804659 | + | 0.593738i | \(0.797652\pi\) | |||||||
\(720\) | − | 1.66725i | − | 0.0621348i | ||||||
\(721\) | −42.9282 | + | 7.83267i | −1.59873 | + | 0.291704i | ||||
\(722\) | − | 26.5098i | − | 0.986594i | ||||||
\(723\) | − | 5.22893i | − | 0.194466i | ||||||
\(724\) | − | 34.7685i | − | 1.29216i | ||||||
\(725\) | − | 39.5674i | − | 1.46950i | ||||||
\(726\) | −22.9641 | + | 10.8589i | −0.852276 | + | 0.403010i | ||||
\(727\) | − | 20.1501i | − | 0.747326i | −0.927565 | − | 0.373663i | \(-0.878102\pi\) | ||
0.927565 | − | 0.373663i | \(-0.121898\pi\) | |||||||
\(728\) | −26.6697 | + | 4.86614i | −0.988443 | + | 0.180351i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −110.992 | −4.10800 | ||||||||
\(731\) | − | 34.5333i | − | 1.27726i | ||||||
\(732\) | 30.7849i | 1.13784i | ||||||||
\(733\) | 16.7421 | 0.618382 | 0.309191 | − | 0.951000i | \(-0.399942\pi\) | ||||
0.309191 | + | 0.951000i | \(0.399942\pi\) | |||||||
\(734\) | −11.0232 | −0.406874 | ||||||||
\(735\) | 24.7187 | − | 9.33100i | 0.911764 | − | 0.344179i | ||||
\(736\) | − | 11.2636i | − | 0.415182i | ||||||
\(737\) | 6.36803 | − | 1.42971i | 0.234569 | − | 0.0526641i | ||||
\(738\) | 8.66550i | 0.318981i | ||||||||
\(739\) | − | 9.60180i | − | 0.353208i | −0.984282 | − | 0.176604i | \(-0.943489\pi\) | ||
0.984282 | − | 0.176604i | \(-0.0565112\pi\) | |||||||
\(740\) | − | 103.737i | − | 3.81345i | ||||||
\(741\) | 9.13004i | 0.335400i | ||||||||
\(742\) | 40.0632 | − | 7.30993i | 1.47077 | − | 0.268356i | ||||
\(743\) | − | 9.95098i | − | 0.365066i | −0.983200 | − | 0.182533i | \(-0.941570\pi\) | ||
0.983200 | − | 0.182533i | \(-0.0584297\pi\) | |||||||
\(744\) | 3.43643i | 0.125986i | ||||||||
\(745\) | 20.5827 | 0.754094 | ||||||||
\(746\) | −9.87335 | −0.361489 | ||||||||
\(747\) | −16.2585 | −0.594869 | ||||||||
\(748\) | 55.2389 | − | 12.4019i | 2.01974 | − | 0.453459i | ||||
\(749\) | 13.2702 | − | 2.42127i | 0.484881 | − | 0.0884713i | ||||
\(750\) | 37.0146i | 1.35158i | ||||||||
\(751\) | 53.5437 | 1.95384 | 0.976919 | − | 0.213610i | \(-0.0685222\pi\) | ||||
0.976919 | + | 0.213610i | \(0.0685222\pi\) | |||||||
\(752\) | − | 2.46528i | − | 0.0898994i | ||||||
\(753\) | −1.19438 | −0.0435257 | ||||||||
\(754\) | −32.8993 | −1.19812 | ||||||||
\(755\) | −28.0112 | −1.01943 | ||||||||
\(756\) | 8.67441 | − | 1.58273i | 0.315485 | − | 0.0575634i | ||||
\(757\) | −38.4423 | −1.39721 | −0.698605 | − | 0.715507i | \(-0.746196\pi\) | ||||
−0.698605 | + | 0.715507i | \(0.746196\pi\) | |||||||
\(758\) | − | 5.58589i | − | 0.202889i | ||||||
\(759\) | 1.59357 | + | 7.09787i | 0.0578430 | + | 0.257636i | ||||
\(760\) | 31.8564 | 1.15555 | ||||||||
\(761\) | −34.1863 | −1.23925 | −0.619626 | − | 0.784897i | \(-0.712716\pi\) | ||||
−0.619626 | + | 0.784897i | \(0.712716\pi\) | |||||||
\(762\) | − | 8.47214i | − | 0.306913i | ||||||
\(763\) | −35.6063 | + | 6.49671i | −1.28903 | + | 0.235197i | ||||
\(764\) | 34.3268 | 1.24190 | ||||||||
\(765\) | 19.3322i | 0.698956i | ||||||||
\(766\) | 57.6032 | 2.08129 | ||||||||
\(767\) | 24.5144i | 0.885162i | ||||||||
\(768\) | − | 18.7492i | − | 0.676552i | ||||||
\(769\) | 1.52320 | 0.0549282 | 0.0274641 | − | 0.999623i | \(-0.491257\pi\) | ||||
0.0274641 | + | 0.999623i | \(0.491257\pi\) | |||||||
\(770\) | 29.8781 | + | 70.4078i | 1.07673 | + | 2.53732i | ||||
\(771\) | 15.8166 | 0.569621 | ||||||||
\(772\) | 0.650978i | 0.0234292i | ||||||||
\(773\) | 43.8809i | 1.57829i | 0.614208 | + | 0.789144i | \(0.289476\pi\) | ||||
−0.614208 | + | 0.789144i | \(0.710524\pi\) | |||||||
\(774\) | 15.5700 | 0.559652 | ||||||||
\(775\) | − | 10.3244i | − | 0.370864i | ||||||
\(776\) | −44.4650 | −1.59620 | ||||||||
\(777\) | 21.4641 | − | 3.91634i | 0.770020 | − | 0.140498i | ||||
\(778\) | − | 56.0583i | − | 2.00979i | ||||||
\(779\) | −10.2905 | −0.368694 | ||||||||
\(780\) | 41.8807 | 1.49957 | ||||||||
\(781\) | −16.4289 | + | 3.68851i | −0.587871 | + | 0.131985i | ||||
\(782\) | − | 25.9424i | − | 0.927700i | ||||||
\(783\) | 4.27913 | 0.152924 | ||||||||
\(784\) | −2.89278 | + | 1.09199i | −0.103314 | + | 0.0389996i | ||||
\(785\) | −6.91186 | −0.246695 | ||||||||
\(786\) | −19.7634 | −0.704936 | ||||||||
\(787\) | 7.83628 | 0.279333 | 0.139667 | − | 0.990199i | \(-0.455397\pi\) | ||||
0.139667 | + | 0.990199i | \(0.455397\pi\) | |||||||
\(788\) | 19.5843i | 0.697660i | ||||||||
\(789\) | 24.7467 | 0.881005 | ||||||||
\(790\) | 51.2901i | 1.82482i | ||||||||
\(791\) | −8.11983 | − | 44.5020i | −0.288708 | − | 1.58231i | ||||
\(792\) | 2.23607 | + | 9.95959i | 0.0794552 | + | 0.353899i | ||||
\(793\) | −30.7533 | −1.09208 | ||||||||
\(794\) | 67.1869 | 2.38437 | ||||||||
\(795\) | −25.1587 | −0.892287 | ||||||||
\(796\) | − | 0.714650i | − | 0.0253301i | ||||||
\(797\) | − | 12.2255i | − | 0.433051i | −0.976277 | − | 0.216525i | \(-0.930528\pi\) | ||
0.976277 | − | 0.216525i | \(-0.0694724\pi\) | |||||||
\(798\) | 3.00744 | + | 16.4828i | 0.106462 | + | 0.583483i | ||||
\(799\) | 28.5855i | 1.01128i | ||||||||
\(800\) | 47.4843i | 1.67882i | ||||||||
\(801\) | 10.0211i | 0.354077i | ||||||||
\(802\) | − | 27.8167i | − | 0.982242i | ||||||
\(803\) | 41.2077 | − | 9.25171i | 1.45419 | − | 0.326486i | ||||
\(804\) | − | 6.55828i | − | 0.231293i | ||||||
\(805\) | 21.5478 | − | 3.93161i | 0.759461 | − | 0.138571i | ||||
\(806\) | −8.58450 | −0.302376 | ||||||||
\(807\) | −13.0768 | −0.460325 | ||||||||
\(808\) | 47.9494i | 1.68685i | ||||||||
\(809\) | 5.29290i | 0.186088i | 0.995662 | + | 0.0930442i | \(0.0296598\pi\) | ||||
−0.995662 | + | 0.0930442i | \(0.970340\pi\) | |||||||
\(810\) | −8.71628 | −0.306259 | ||||||||
\(811\) | −43.0993 | −1.51342 | −0.756710 | − | 0.653751i | \(-0.773195\pi\) | ||||
−0.756710 | + | 0.653751i | \(0.773195\pi\) | |||||||
\(812\) | −37.1189 | + | 6.77271i | −1.30262 | + | 0.237676i | ||||
\(813\) | 24.8015i | 0.869827i | ||||||||
\(814\) | 13.8360 | + | 61.6266i | 0.484953 | + | 2.16001i | ||||
\(815\) | − | 29.1944i | − | 1.02263i | ||||||
\(816\) | − | 2.26240i | − | 0.0792000i | ||||||
\(817\) | 18.4897i | 0.646873i | ||||||||
\(818\) | 34.4912i | 1.20596i | ||||||||
\(819\) | 1.58111 | + | 8.66550i | 0.0552483 | + | 0.302797i | ||||
\(820\) | 47.2037i | 1.64843i | ||||||||
\(821\) | 44.6289i | 1.55756i | 0.627298 | + | 0.778779i | \(0.284161\pi\) | ||||
−0.627298 | + | 0.778779i | \(0.715839\pi\) | |||||||
\(822\) | 19.5077 | 0.680410 | ||||||||
\(823\) | −12.6942 | −0.442491 | −0.221245 | − | 0.975218i | \(-0.571012\pi\) | ||||
−0.221245 | + | 0.975218i | \(0.571012\pi\) | |||||||
\(824\) | −50.7609 | −1.76834 | ||||||||
\(825\) | −6.71805 | − | 29.9226i | −0.233892 | − | 1.04177i | ||||
\(826\) | 8.07505 | + | 44.2566i | 0.280967 | + | 1.53988i | ||||
\(827\) | − | 0.667138i | − | 0.0231987i | −0.999933 | − | 0.0115993i | \(-0.996308\pi\) | ||
0.999933 | − | 0.0115993i | \(-0.00369227\pi\) | |||||||
\(828\) | 7.30993 | 0.254037 | ||||||||
\(829\) | − | 3.13526i | − | 0.108892i | −0.998517 | − | 0.0544460i | \(-0.982661\pi\) | ||
0.998517 | − | 0.0544460i | \(-0.0173393\pi\) | |||||||
\(830\) | −141.714 | −4.91896 | ||||||||
\(831\) | −4.26385 | −0.147911 | ||||||||
\(832\) | 42.4232 | 1.47076 | ||||||||
\(833\) | 33.5425 | − | 12.6619i | 1.16218 | − | 0.438707i | ||||
\(834\) | −4.90451 | −0.169829 | ||||||||
\(835\) | 1.19291i | 0.0412823i | ||||||||
\(836\) | −29.5758 | + | 6.64019i | −1.02290 | + | 0.229656i | ||||
\(837\) | 1.11656 | 0.0385941 | ||||||||
\(838\) | 19.1491 | 0.661494 | ||||||||
\(839\) | 11.7195i | 0.404603i | 0.979323 | + | 0.202301i | \(0.0648420\pi\) | ||||
−0.979323 | + | 0.202301i | \(0.935158\pi\) | |||||||
\(840\) | 30.2355 | − | 5.51676i | 1.04322 | − | 0.190346i | ||||
\(841\) | 10.6891 | 0.368588 | ||||||||
\(842\) | − | 5.87496i | − | 0.202464i | ||||||
\(843\) | −17.4290 | −0.600285 | ||||||||
\(844\) | 63.9944i | 2.20278i | ||||||||
\(845\) | − | 7.23040i | − | 0.248733i | ||||||
\(846\) | −12.8883 | −0.443109 | ||||||||
\(847\) | −16.9616 | − | 23.6496i | −0.582807 | − | 0.812611i | ||||
\(848\) | 2.94427 | 0.101107 | ||||||||
\(849\) | − | 10.5750i | − | 0.362932i | ||||||
\(850\) | 109.366i | 3.75123i | ||||||||
\(851\) | 18.0878 | 0.620041 | ||||||||
\(852\) | 16.9197i | 0.579659i | ||||||||
\(853\) | 9.96269 | 0.341116 | 0.170558 | − | 0.985348i | \(-0.445443\pi\) | ||||
0.170558 | + | 0.985348i | \(0.445443\pi\) | |||||||
\(854\) | −55.5199 | + | 10.1302i | −1.89985 | + | 0.346647i | ||||
\(855\) | − | 10.3508i | − | 0.353989i | ||||||
\(856\) | 15.6914 | 0.536322 | ||||||||
\(857\) | −49.5868 | −1.69385 | −0.846927 | − | 0.531709i | \(-0.821550\pi\) | ||||
−0.846927 | + | 0.531709i | \(0.821550\pi\) | |||||||
\(858\) | −24.8799 | + | 5.58589i | −0.849387 | + | 0.190699i | ||||
\(859\) | − | 42.5977i | − | 1.45341i | −0.686948 | − | 0.726707i | \(-0.741050\pi\) | ||
0.686948 | − | 0.726707i | \(-0.258950\pi\) | |||||||
\(860\) | 84.8148 | 2.89216 | ||||||||
\(861\) | −9.76687 | + | 1.78206i | −0.332854 | + | 0.0607325i | ||||
\(862\) | 51.8325 | 1.76542 | ||||||||
\(863\) | 41.7996 | 1.42288 | 0.711438 | − | 0.702749i | \(-0.248044\pi\) | ||||
0.711438 | + | 0.702749i | \(0.248044\pi\) | |||||||
\(864\) | −5.13532 | −0.174707 | ||||||||
\(865\) | − | 76.0306i | − | 2.58512i | ||||||
\(866\) | 65.6150 | 2.22969 | ||||||||
\(867\) | 9.23313i | 0.313573i | ||||||||
\(868\) | −9.68554 | + | 1.76722i | −0.328749 | + | 0.0599834i | ||||
\(869\) | −4.27527 | − | 19.0423i | −0.145029 | − | 0.645967i | ||||
\(870\) | 37.2981 | 1.26452 | ||||||||
\(871\) | 6.55154 | 0.221990 | ||||||||
\(872\) | −42.1030 | −1.42579 | ||||||||
\(873\) | 14.4476i | 0.488976i | ||||||||
\(874\) | 13.8900i | 0.469837i | ||||||||
\(875\) | −41.7191 | + | 7.61206i | −1.41036 | + | 0.257335i | ||||
\(876\) | − | 42.4389i | − | 1.43388i | ||||||
\(877\) | − | 30.2663i | − | 1.02202i | −0.859574 | − | 0.511011i | \(-0.829271\pi\) | ||
0.859574 | − | 0.511011i | \(-0.170729\pi\) | |||||||
\(878\) | 53.9224i | 1.81979i | ||||||||
\(879\) | − | 21.3804i | − | 0.721142i | ||||||
\(880\) | 1.21133 | + | 5.39534i | 0.0408339 | + | 0.181877i | ||||
\(881\) | 36.1238i | 1.21704i | 0.793538 | + | 0.608521i | \(0.208237\pi\) | ||||
−0.793538 | + | 0.608521i | \(0.791763\pi\) | |||||||
\(882\) | 5.70884 | + | 15.1233i | 0.192227 | + | 0.509228i | ||||
\(883\) | 45.6654 | 1.53676 | 0.768381 | − | 0.639992i | \(-0.221062\pi\) | ||||
0.768381 | + | 0.639992i | \(0.221062\pi\) | |||||||
\(884\) | 56.8308 | 1.91143 | ||||||||
\(885\) | − | 27.7920i | − | 0.934219i | ||||||
\(886\) | − | 17.0292i | − | 0.572107i | ||||||
\(887\) | −14.2454 | −0.478314 | −0.239157 | − | 0.970981i | \(-0.576871\pi\) | ||||
−0.239157 | + | 0.970981i | \(0.576871\pi\) | |||||||
\(888\) | 25.3804 | 0.851712 | ||||||||
\(889\) | 9.54893 | − | 1.74230i | 0.320261 | − | 0.0584348i | ||||
\(890\) | 87.3465i | 2.92786i | ||||||||
\(891\) | 3.23607 | − | 0.726543i | 0.108412 | − | 0.0243401i | ||||
\(892\) | − | 12.0928i | − | 0.404896i | ||||||
\(893\) | − | 15.3051i | − | 0.512167i | ||||||
\(894\) | 12.5928i | 0.421167i | ||||||||
\(895\) | 31.1552i | 1.04140i | ||||||||
\(896\) | 49.8558 | − | 9.09668i | 1.66557 | − | 0.303899i | ||||
\(897\) | 7.30241i | 0.243820i | ||||||||
\(898\) | − | 60.1034i | − | 2.00568i | ||||||
\(899\) | −4.77792 | −0.159353 | ||||||||
\(900\) | −30.8166 | −1.02722 | ||||||||
\(901\) | −34.1395 | −1.13735 | ||||||||
\(902\) | −6.29585 | − | 28.0421i | −0.209629 | − | 0.933701i | ||||
\(903\) | 3.20198 | + | 17.5489i | 0.106555 | + | 0.583992i | ||||
\(904\) | − | 52.6218i | − | 1.75018i | ||||||
\(905\) | −39.3766 | −1.30892 | ||||||||
\(906\) | − | 17.1376i | − | 0.569360i | ||||||
\(907\) | 19.1774 | 0.636775 | 0.318388 | − | 0.947961i | \(-0.396859\pi\) | ||||
0.318388 | + | 0.947961i | \(0.396859\pi\) | |||||||
\(908\) | 10.2437 | 0.339948 | ||||||||
\(909\) | 15.5797 | 0.516746 | ||||||||
\(910\) | 13.7814 | + | 75.5309i | 0.456848 | + | 2.50383i | ||||
\(911\) | 23.4737 | 0.777720 | 0.388860 | − | 0.921297i | \(-0.372869\pi\) | ||||
0.388860 | + | 0.921297i | \(0.372869\pi\) | |||||||
\(912\) | 1.21133i | 0.0401111i | ||||||||
\(913\) | 52.6137 | − | 11.8125i | 1.74126 | − | 0.390937i | ||||
\(914\) | 26.0608 | 0.862016 | ||||||||
\(915\) | 34.8651 | 1.15261 | ||||||||
\(916\) | − | 51.2465i | − | 1.69323i | ||||||
\(917\) | −4.06434 | − | 22.2753i | −0.134216 | − | 0.735594i | ||||
\(918\) | −11.8277 | −0.390373 | ||||||||
\(919\) | 12.8519i | 0.423944i | 0.977276 | + | 0.211972i | \(0.0679886\pi\) | ||||
−0.977276 | + | 0.211972i | \(0.932011\pi\) | |||||||
\(920\) | 25.4794 | 0.840032 | ||||||||
\(921\) | 26.2034i | 0.863430i | ||||||||
\(922\) | 25.7177i | 0.846968i | ||||||||
\(923\) | −16.9023 | −0.556346 | ||||||||
\(924\) | −26.9211 | + | 11.4242i | −0.885638 | + | 0.375827i | ||||
\(925\) | −76.2531 | −2.50719 | ||||||||
\(926\) | 1.32204i | 0.0434450i | ||||||||
\(927\) | 16.4932i | 0.541708i | ||||||||
\(928\) | 21.9747 | 0.721355 | ||||||||
\(929\) | − | 12.9195i | − | 0.423873i | −0.977283 | − | 0.211937i | \(-0.932023\pi\) | ||
0.977283 | − | 0.211937i | \(-0.0679771\pi\) | |||||||
\(930\) | 9.73228 | 0.319134 | ||||||||
\(931\) | −17.9592 | + | 6.77937i | −0.588590 | + | 0.222185i | ||||
\(932\) | − | 54.2819i | − | 1.77806i | ||||||
\(933\) | 17.3731 | 0.568771 | ||||||||
\(934\) | −20.9352 | −0.685020 | ||||||||
\(935\) | −14.0456 | − | 62.5602i | −0.459342 | − | 2.04594i | ||||
\(936\) | 10.2466i | 0.334921i | ||||||||
\(937\) | 5.64487 | 0.184410 | 0.0922050 | − | 0.995740i | \(-0.470608\pi\) | ||||
0.0922050 | + | 0.995740i | \(0.470608\pi\) | |||||||
\(938\) | 11.8277 | − | 2.15808i | 0.386188 | − | 0.0704639i | ||||
\(939\) | 3.33450 | 0.108817 | ||||||||
\(940\) | −70.2067 | −2.28989 | ||||||||
\(941\) | −20.5341 | −0.669391 | −0.334696 | − | 0.942326i | \(-0.608633\pi\) | ||||
−0.334696 | + | 0.942326i | \(0.608633\pi\) | |||||||
\(942\) | − | 4.22878i | − | 0.137781i | ||||||
\(943\) | −8.23054 | −0.268023 | ||||||||
\(944\) | 3.25244i | 0.105858i | ||||||||
\(945\) | −1.79251 | − | 9.82411i | −0.0583102 | − | 0.319578i | ||||
\(946\) | −50.3856 | + | 11.3123i | −1.63818 | + | 0.367794i | ||||
\(947\) | −28.7170 | −0.933178 | −0.466589 | − | 0.884474i | \(-0.654517\pi\) | ||||
−0.466589 | + | 0.884474i | \(0.654517\pi\) | |||||||
\(948\) | −19.6112 | −0.636943 | ||||||||
\(949\) | 42.3952 | 1.37621 | ||||||||
\(950\) | − | 58.5564i | − | 1.89982i | ||||||
\(951\) | − | 4.83428i | − | 0.156762i | ||||||
\(952\) | 41.0286 | − | 7.48607i | 1.32974 | − | 0.242625i | ||||
\(953\) | 33.3085i | 1.07897i | 0.841996 | + | 0.539484i | \(0.181381\pi\) | ||||
−0.841996 | + | 0.539484i | \(0.818619\pi\) | |||||||
\(954\) | − | 15.3925i | − | 0.498349i | ||||||
\(955\) | − | 38.8764i | − | 1.25801i | ||||||
\(956\) | − | 46.0725i | − | 1.49009i | ||||||
\(957\) | −13.8476 | + | 3.10897i | −0.447628 | + | 0.100499i | ||||
\(958\) | − | 83.1973i | − | 2.68798i | ||||||
\(959\) | 4.01177 | + | 21.9871i | 0.129547 | + | 0.710002i | ||||
\(960\) | −48.0954 | −1.55227 | ||||||||
\(961\) | 29.7533 | 0.959783 | ||||||||
\(962\) | 63.4025i | 2.04418i | ||||||||
\(963\) | − | 5.09846i | − | 0.164295i | ||||||
\(964\) | 17.4267 | 0.561277 | ||||||||
\(965\) | 0.737258 | 0.0237332 | ||||||||
\(966\) | 2.40542 | + | 13.1833i | 0.0773931 | + | 0.424165i | ||||
\(967\) | − | 4.50338i | − | 0.144819i | −0.997375 | − | 0.0724094i | \(-0.976931\pi\) | ||
0.997375 | − | 0.0724094i | \(-0.0230688\pi\) | |||||||
\(968\) | −14.4721 | − | 30.6053i | −0.465152 | − | 0.983692i | ||||
\(969\) | − | 14.0456i | − | 0.451211i | ||||||
\(970\) | 125.929i | 4.04334i | ||||||||
\(971\) | − | 28.7585i | − | 0.922904i | −0.887165 | − | 0.461452i | \(-0.847329\pi\) | ||
0.887165 | − | 0.461452i | \(-0.152671\pi\) | |||||||
\(972\) | − | 3.33275i | − | 0.106898i | ||||||
\(973\) | −1.00861 | − | 5.52786i | −0.0323346 | − | 0.177215i | ||||
\(974\) | − | 85.0173i | − | 2.72413i | ||||||
\(975\) | − | 30.7849i | − | 0.985907i | ||||||
\(976\) | −4.08019 | −0.130604 | ||||||||
\(977\) | 47.5454 | 1.52111 | 0.760557 | − | 0.649272i | \(-0.224926\pi\) | ||||
0.760557 | + | 0.649272i | \(0.224926\pi\) | |||||||
\(978\) | 17.8616 | 0.571149 | ||||||||
\(979\) | −7.28073 | − | 32.4289i | −0.232693 | − | 1.03643i | ||||
\(980\) | 31.0979 | + | 82.3814i | 0.993385 | + | 2.63158i | ||||
\(981\) | 13.6801i | 0.436772i | ||||||||
\(982\) | −20.4392 | −0.652242 | ||||||||
\(983\) | − | 33.3731i | − | 1.06444i | −0.846607 | − | 0.532219i | \(-0.821358\pi\) | ||
0.846607 | − | 0.532219i | \(-0.178642\pi\) | |||||||
\(984\) | −11.5489 | −0.368167 | ||||||||
\(985\) | 22.1799 | 0.706711 | ||||||||
\(986\) | 50.6123 | 1.61182 | ||||||||
\(987\) | −2.65048 | − | 14.5264i | −0.0843658 | − | 0.462380i | ||||
\(988\) | −30.4281 | −0.968048 | ||||||||
\(989\) | 14.7885i | 0.470246i | ||||||||
\(990\) | 28.2065 | − | 6.33275i | 0.896461 | − | 0.201268i | ||||
\(991\) | −24.1788 | −0.768064 | −0.384032 | − | 0.923320i | \(-0.625465\pi\) | ||||
−0.384032 | + | 0.923320i | \(0.625465\pi\) | |||||||
\(992\) | 5.73391 | 0.182052 | ||||||||
\(993\) | − | 9.71772i | − | 0.308383i | ||||||
\(994\) | −30.5143 | + | 5.56763i | −0.967854 | + | 0.176594i | ||||
\(995\) | −0.809369 | −0.0256587 | ||||||||
\(996\) | − | 54.1856i | − | 1.71694i | ||||||
\(997\) | 5.14071 | 0.162808 | 0.0814040 | − | 0.996681i | \(-0.474060\pi\) | ||||
0.0814040 | + | 0.996681i | \(0.474060\pi\) | |||||||
\(998\) | 46.8955i | 1.48445i | ||||||||
\(999\) | − | 8.24660i | − | 0.260911i |
(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 | 231.2.c.a.76.16 | yes | 16 | |
3.2 | odd | 2 | 693.2.c.e.307.1 | 16 | |||
4.3 | odd | 2 | 3696.2.q.e.769.8 | 16 | |||
7.6 | odd | 2 | inner | 231.2.c.a.76.15 | yes | 16 | |
11.10 | odd | 2 | inner | 231.2.c.a.76.2 | yes | 16 | |
21.20 | even | 2 | 693.2.c.e.307.2 | 16 | |||
28.27 | even | 2 | 3696.2.q.e.769.9 | 16 | |||
33.32 | even | 2 | 693.2.c.e.307.15 | 16 | |||
44.43 | even | 2 | 3696.2.q.e.769.7 | 16 | |||
77.76 | even | 2 | inner | 231.2.c.a.76.1 | ✓ | 16 | |
231.230 | odd | 2 | 693.2.c.e.307.16 | 16 | |||
308.307 | odd | 2 | 3696.2.q.e.769.10 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.c.a.76.1 | ✓ | 16 | 77.76 | even | 2 | inner | |
231.2.c.a.76.2 | yes | 16 | 11.10 | odd | 2 | inner | |
231.2.c.a.76.15 | yes | 16 | 7.6 | odd | 2 | inner | |
231.2.c.a.76.16 | yes | 16 | 1.1 | even | 1 | trivial | |
693.2.c.e.307.1 | 16 | 3.2 | odd | 2 | |||
693.2.c.e.307.2 | 16 | 21.20 | even | 2 | |||
693.2.c.e.307.15 | 16 | 33.32 | even | 2 | |||
693.2.c.e.307.16 | 16 | 231.230 | odd | 2 | |||
3696.2.q.e.769.7 | 16 | 44.43 | even | 2 | |||
3696.2.q.e.769.8 | 16 | 4.3 | odd | 2 | |||
3696.2.q.e.769.9 | 16 | 28.27 | even | 2 | |||
3696.2.q.e.769.10 | 16 | 308.307 | odd | 2 |