Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,3,Mod(145,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.145");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.be (of order \(6\), degree \(2\), not 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: | \(24.8502001097\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 6.0.6967728.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 8x^{4} + 5x^{3} + 50x^{2} - 7x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 57) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 145.2 | ||
Root | \(0.0702177 + 0.121621i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.145 |
Dual form | 912.3.be.d.673.2 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.50000 | + | 0.866025i | −0.500000 | + | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.140435 | − | 0.243241i | −0.0280871 | − | 0.0486482i | 0.851640 | − | 0.524127i | \(-0.175608\pi\) |
−0.879727 | + | 0.475479i | \(0.842275\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.24143 | 0.748775 | 0.374388 | − | 0.927272i | \(-0.377853\pi\) | ||||
0.374388 | + | 0.927272i | \(0.377853\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.15739 | 0.105217 | 0.0526085 | − | 0.998615i | \(-0.483246\pi\) | ||||
0.0526085 | + | 0.998615i | \(0.483246\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.32289 | − | 3.65052i | −0.486376 | − | 0.280809i | 0.236694 | − | 0.971584i | \(-0.423936\pi\) |
−0.723070 | + | 0.690775i | \(0.757270\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.421306 | + | 0.243241i | 0.0280871 | + | 0.0162161i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.52230 | + | 13.0290i | 0.442488 | + | 0.766412i | 0.997873 | − | 0.0651813i | \(-0.0207626\pi\) |
−0.555385 | + | 0.831593i | \(0.687429\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.52230 | + | 18.9389i | −0.0801209 | + | 0.996785i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.86214 | + | 4.53921i | −0.374388 | + | 0.216153i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 13.3819 | − | 23.1781i | 0.581820 | − | 1.00774i | −0.413444 | − | 0.910530i | \(-0.635674\pi\) |
0.995264 | − | 0.0972122i | \(-0.0309926\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.4606 | − | 21.5823i | 0.498422 | − | 0.863293i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.76372 | − | 4.48239i | −0.267715 | − | 0.154565i | 0.360134 | − | 0.932901i | \(-0.382731\pi\) |
−0.627849 | + | 0.778335i | \(0.716064\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 11.7968i | 0.380543i | 0.981732 | + | 0.190272i | \(0.0609368\pi\) | ||||
−0.981732 | + | 0.190272i | \(0.939063\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.73608 | + | 1.00233i | −0.0526085 | + | 0.0303736i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.736082 | − | 1.27493i | −0.0210309 | − | 0.0364266i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 36.1681i | − | 0.977516i | −0.872419 | − | 0.488758i | \(-0.837450\pi\) | ||
0.872419 | − | 0.488758i | \(-0.162550\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 12.6458 | 0.324251 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 40.3701 | − | 23.3077i | 0.984636 | − | 0.568480i | 0.0809691 | − | 0.996717i | \(-0.474198\pi\) |
0.903666 | + | 0.428237i | \(0.140865\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.64044 | − | 2.84132i | −0.0381497 | − | 0.0660771i | 0.846320 | − | 0.532675i | \(-0.178813\pi\) |
−0.884470 | + | 0.466597i | \(0.845480\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.842612 | −0.0187247 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −26.3199 | + | 45.5874i | −0.559998 | + | 0.969946i | 0.437497 | + | 0.899220i | \(0.355865\pi\) |
−0.997496 | + | 0.0707260i | \(0.977468\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −21.5274 | −0.439336 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −22.5669 | − | 13.0290i | −0.442488 | − | 0.255471i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 88.0273 | + | 50.8226i | 1.66089 | + | 0.958916i | 0.972291 | + | 0.233776i | \(0.0751082\pi\) |
0.688601 | + | 0.725140i | \(0.258225\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.162538 | − | 0.281524i | −0.00295524 | − | 0.00511863i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −14.1181 | − | 29.7267i | −0.247687 | − | 0.521521i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 39.8304 | − | 22.9961i | 0.675092 | − | 0.389764i | −0.122911 | − | 0.992418i | \(-0.539223\pi\) |
0.798003 | + | 0.602653i | \(0.205890\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −50.7162 | + | 87.8430i | −0.831413 | + | 1.44005i | 0.0655056 | + | 0.997852i | \(0.479134\pi\) |
−0.896918 | + | 0.442197i | \(0.854199\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.86214 | − | 13.6176i | 0.124796 | − | 0.216153i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.05065i | 0.0315485i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 50.9209 | + | 29.3992i | 0.760014 | + | 0.438794i | 0.829301 | − | 0.558803i | \(-0.188739\pi\) |
−0.0692870 | + | 0.997597i | \(0.522072\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 46.3561i | 0.671828i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 90.7243 | − | 52.3797i | 1.27781 | − | 0.737742i | 0.301362 | − | 0.953510i | \(-0.402559\pi\) |
0.976445 | + | 0.215768i | \(0.0692254\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 63.1115 | + | 109.312i | 0.864541 | + | 1.49743i | 0.867502 | + | 0.497433i | \(0.165724\pi\) |
−0.00296139 | + | 0.999996i | \(0.500943\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 43.1646i | 0.575528i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.06636 | 0.0787839 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 55.9406 | − | 32.2973i | 0.708109 | − | 0.408827i | −0.102251 | − | 0.994759i | \(-0.532605\pi\) |
0.810361 | + | 0.585931i | \(0.199271\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 22.0789 | 0.266011 | 0.133005 | − | 0.991115i | \(-0.457537\pi\) | ||||
0.133005 | + | 0.991115i | \(0.457537\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.11279 | − | 3.65947i | 0.0248564 | − | 0.0430525i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 15.5274 | 0.178476 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 107.579 | + | 62.1106i | 1.20875 | + | 0.697872i | 0.962486 | − | 0.271331i | \(-0.0874639\pi\) |
0.246263 | + | 0.969203i | \(0.420797\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −33.1410 | − | 19.1339i | −0.364186 | − | 0.210263i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.2164 | − | 17.6953i | −0.109853 | − | 0.190272i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.82051 | − | 2.28941i | 0.0507422 | − | 0.0240990i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 162.700 | − | 93.9348i | 1.67732 | − | 0.968400i | 0.713959 | − | 0.700188i | \(-0.246900\pi\) |
0.963360 | − | 0.268213i | \(-0.0864330\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.73608 | − | 3.00698i | 0.0175362 | − | 0.0303736i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 19.8478 | − | 34.3773i | 0.196513 | − | 0.340370i | −0.750883 | − | 0.660435i | \(-0.770372\pi\) |
0.947395 | + | 0.320066i | \(0.103705\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 26.7360i | 0.259573i | 0.991542 | + | 0.129787i | \(0.0414292\pi\) | ||||
−0.991542 | + | 0.129787i | \(0.958571\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.20825 | + | 1.27493i | 0.0210309 | + | 0.0121422i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 61.9439i | − | 0.578915i | −0.957191 | − | 0.289458i | \(-0.906525\pi\) | ||
0.957191 | − | 0.289458i | \(-0.0934749\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 30.9996 | − | 17.8976i | 0.284400 | − | 0.164198i | −0.351014 | − | 0.936370i | \(-0.614163\pi\) |
0.635414 | + | 0.772172i | \(0.280830\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 31.3225 | + | 54.2522i | 0.282185 | + | 0.488758i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 106.018i | 0.938215i | 0.883141 | + | 0.469108i | \(0.155424\pi\) | ||||
−0.883141 | + | 0.469108i | \(0.844576\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.51715 | −0.0653665 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −18.9687 | + | 10.9516i | −0.162125 | + | 0.0936031i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 39.4276 | + | 68.2906i | 0.331324 | + | 0.573870i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −119.660 | −0.988929 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −40.3701 | + | 69.9230i | −0.328212 | + | 0.568480i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −14.0214 | −0.112171 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 97.9362 | + | 56.5435i | 0.771151 | + | 0.445224i | 0.833285 | − | 0.552844i | \(-0.186457\pi\) |
−0.0621341 | + | 0.998068i | \(0.519791\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.92131 | + | 2.84132i | 0.0381497 | + | 0.0220257i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 64.7582 | + | 112.164i | 0.494337 | + | 0.856217i | 0.999979 | − | 0.00652644i | \(-0.00207745\pi\) |
−0.505641 | + | 0.862744i | \(0.668744\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.97901 | + | 99.2669i | −0.0599926 | + | 0.746368i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.26392 | − | 0.729724i | 0.00936236 | − | 0.00540536i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 21.4880 | − | 37.2183i | 0.156847 | − | 0.271667i | −0.776883 | − | 0.629645i | \(-0.783200\pi\) |
0.933730 | + | 0.357978i | \(0.116534\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −104.196 | + | 180.473i | −0.749613 | + | 1.29837i | 0.198395 | + | 0.980122i | \(0.436427\pi\) |
−0.948008 | + | 0.318246i | \(0.896906\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 91.1749i | − | 0.646630i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.31804 | − | 4.22507i | −0.0511751 | − | 0.0295459i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.51794i | 0.0173651i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 32.2912 | − | 18.6433i | 0.219668 | − | 0.126825i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −69.2344 | − | 119.917i | −0.464660 | − | 0.804815i | 0.534526 | − | 0.845152i | \(-0.320490\pi\) |
−0.999186 | + | 0.0403369i | \(0.987157\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 265.635i | − | 1.75917i | −0.475739 | − | 0.879586i | \(-0.657819\pi\) | ||
0.475739 | − | 0.879586i | \(-0.342181\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 45.1338 | 0.294992 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.86948 | − | 1.65669i | 0.0185128 | − | 0.0106883i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −52.4464 | − | 90.8398i | −0.334053 | − | 0.578597i | 0.649249 | − | 0.760576i | \(-0.275083\pi\) |
−0.983303 | + | 0.181978i | \(0.941750\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −176.055 | −1.10726 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 70.1400 | − | 121.486i | 0.435652 | − | 0.754572i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −89.1556 | −0.546967 | −0.273483 | − | 0.961877i | \(-0.588176\pi\) | ||||
−0.273483 | + | 0.961877i | \(0.588176\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.487615 | + | 0.281524i | 0.00295524 | + | 0.00170621i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.7589 | − | 11.9852i | −0.124305 | − | 0.0717674i | 0.436558 | − | 0.899676i | \(-0.356197\pi\) |
−0.560863 | + | 0.827909i | \(0.689531\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −57.8474 | − | 100.195i | −0.342292 | − | 0.592867i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 46.9213 | + | 32.3634i | 0.274394 | + | 0.189260i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 48.4169 | − | 27.9535i | 0.279866 | − | 0.161581i | −0.353497 | − | 0.935436i | \(-0.615007\pi\) |
0.633363 | + | 0.773855i | \(0.281674\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 65.3111 | − | 113.122i | 0.373206 | − | 0.646412i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −39.8304 | + | 68.9883i | −0.225031 | + | 0.389764i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 191.121i | 1.06771i | 0.845575 | + | 0.533856i | \(0.179258\pi\) | ||||
−0.845575 | + | 0.533856i | \(0.820742\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 74.2912 | + | 42.8920i | 0.410448 | + | 0.236973i | 0.690982 | − | 0.722872i | \(-0.257178\pi\) |
−0.280534 | + | 0.959844i | \(0.590512\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 175.686i | − | 0.960033i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.79757 | + | 5.07928i | −0.0475545 | + | 0.0274556i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.70621 | + | 15.0796i | 0.0465573 | + | 0.0806396i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 27.2353i | 0.144102i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 328.175 | 1.71820 | 0.859098 | − | 0.511811i | \(-0.171025\pi\) | ||||
0.859098 | + | 0.511811i | \(0.171025\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −187.491 | + | 108.248i | −0.971456 | + | 0.560871i | −0.899680 | − | 0.436550i | \(-0.856200\pi\) |
−0.0717764 | + | 0.997421i | \(0.522867\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.77591 | − | 3.07597i | −0.00910726 | − | 0.0157742i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 86.2234 | 0.437682 | 0.218841 | − | 0.975761i | \(-0.429772\pi\) | ||||
0.218841 | + | 0.975761i | \(0.429772\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.2768 | + | 36.8525i | −0.106919 | + | 0.185188i | −0.914520 | − | 0.404540i | \(-0.867432\pi\) |
0.807602 | + | 0.589728i | \(0.200765\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −101.842 | −0.506676 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −40.6930 | − | 23.4941i | −0.200458 | − | 0.115735i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.3388 | − | 6.54644i | −0.0553111 | − | 0.0319339i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −40.1456 | − | 69.5342i | −0.193940 | − | 0.335914i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.76189 | + | 21.9197i | −0.00843009 | + | 0.104879i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −278.518 | + | 160.803i | −1.31999 | + | 0.762098i | −0.983727 | − | 0.179670i | \(-0.942497\pi\) |
−0.336265 | + | 0.941767i | \(0.609164\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −90.7243 | + | 157.139i | −0.425936 | + | 0.737742i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.460750 | + | 0.798043i | −0.00214302 | + | 0.00371183i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 61.8322i | 0.284941i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −189.334 | − | 109.312i | −0.864541 | − | 0.499143i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 109.841i | − | 0.497019i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −227.577 | + | 131.392i | −1.02053 | + | 0.589201i | −0.914257 | − | 0.405136i | \(-0.867224\pi\) |
−0.106270 | + | 0.994337i | \(0.533891\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −37.3817 | − | 64.7469i | −0.166141 | − | 0.287764i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 424.986i | − | 1.87219i | −0.351752 | − | 0.936093i | \(-0.614414\pi\) | ||
0.351752 | − | 0.936093i | \(-0.385586\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 65.9830 | 0.288135 | 0.144068 | − | 0.989568i | \(-0.453982\pi\) | ||||
0.144068 | + | 0.989568i | \(0.453982\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.09954 | + | 5.25362i | −0.0393920 | + | 0.0227430i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −25.7144 | − | 44.5386i | −0.110362 | − | 0.191153i | 0.805554 | − | 0.592522i | \(-0.201868\pi\) |
−0.915916 | + | 0.401369i | \(0.868534\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.7850 | 0.0629149 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −55.9406 | + | 96.8920i | −0.236036 | + | 0.408827i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 239.866 | 1.00362 | 0.501811 | − | 0.864977i | \(-0.332667\pi\) | ||||
0.501811 | + | 0.864977i | \(0.332667\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −165.208 | − | 95.3831i | −0.685512 | − | 0.395781i | 0.116416 | − | 0.993200i | \(-0.462859\pi\) |
−0.801929 | + | 0.597420i | \(0.796193\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.5000 | + | 7.79423i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.02322 | + | 5.23636i | 0.0123397 | + | 0.0213729i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 78.7623 | − | 114.192i | 0.318876 | − | 0.462314i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −33.1183 | + | 19.1209i | −0.133005 | + | 0.0767907i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −103.899 | + | 179.959i | −0.413942 | + | 0.716968i | −0.995317 | − | 0.0966678i | \(-0.969182\pi\) |
0.581375 | + | 0.813636i | \(0.302515\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.4880 | − | 26.8260i | 0.0612174 | − | 0.106032i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.31893i | 0.0287017i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −58.1843 | − | 33.5927i | −0.226398 | − | 0.130711i | 0.382511 | − | 0.923951i | \(-0.375059\pi\) |
−0.608909 | + | 0.793240i | \(0.708393\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 189.572i | − | 0.731940i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −23.2912 | + | 13.4472i | −0.0892382 | + | 0.0515217i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −142.093 | − | 246.111i | −0.540276 | − | 0.935785i | −0.998888 | − | 0.0471484i | \(-0.984987\pi\) |
0.458612 | − | 0.888637i | \(-0.348347\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 28.5491i | − | 0.107733i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −215.157 | −0.805833 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 61.8223 | − | 35.6931i | 0.229823 | − | 0.132688i | −0.380667 | − | 0.924712i | \(-0.624306\pi\) |
0.610490 | + | 0.792024i | \(0.290972\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −35.5404 | − | 61.5577i | −0.131145 | − | 0.227150i | 0.792973 | − | 0.609257i | \(-0.208532\pi\) |
−0.924118 | + | 0.382106i | \(0.875199\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 66.2819 | 0.242791 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 14.4217 | − | 24.9791i | 0.0524425 | − | 0.0908331i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −476.997 | −1.72201 | −0.861005 | − | 0.508597i | \(-0.830164\pi\) | ||||
−0.861005 | + | 0.508597i | \(0.830164\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 30.6491 | + | 17.6953i | 0.109853 | + | 0.0634238i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 126.681 | + | 73.1394i | 0.450822 | + | 0.260282i | 0.708177 | − | 0.706034i | \(-0.249518\pi\) |
−0.257355 | + | 0.966317i | \(0.582851\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −76.0571 | − | 131.735i | −0.268753 | − | 0.465494i | 0.699787 | − | 0.714352i | \(-0.253278\pi\) |
−0.968540 | + | 0.248858i | \(0.919945\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.24808 | + | 7.60880i | −0.0184143 | + | 0.0266975i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 211.597 | − | 122.165i | 0.737271 | − | 0.425663i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 31.3301 | − | 54.2653i | 0.108409 | − | 0.187769i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −162.700 | + | 281.804i | −0.559106 | + | 0.968400i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 350.693i | − | 1.19690i | −0.801159 | − | 0.598452i | \(-0.795783\pi\) | ||
0.801159 | − | 0.598452i | \(-0.204217\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.1872 | − | 6.45893i | −0.0379227 | − | 0.0218947i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.01396i | 0.0202490i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −169.224 | + | 97.7016i | −0.565967 | + | 0.326761i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.59822 | − | 14.8926i | −0.0285655 | − | 0.0494769i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 68.7547i | 0.226913i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 28.4894 | 0.0934078 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −412.362 | + | 238.077i | −1.34320 | + | 0.775497i | −0.987276 | − | 0.159018i | \(-0.949167\pi\) |
−0.355924 | + | 0.934515i | \(0.615834\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −23.1541 | − | 40.1041i | −0.0749323 | − | 0.129787i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 468.952 | 1.50788 | 0.753942 | − | 0.656942i | \(-0.228150\pi\) | ||||
0.753942 | + | 0.656942i | \(0.228150\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.6786 | + | 30.6203i | −0.0564812 | + | 0.0978284i | −0.892884 | − | 0.450288i | \(-0.851321\pi\) |
0.836402 | + | 0.548116i | \(0.184655\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.41649 | −0.0140206 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 377.554 | + | 217.981i | 1.19102 | + | 0.687637i | 0.958539 | − | 0.284963i | \(-0.0919812\pi\) |
0.232484 | + | 0.972600i | \(0.425315\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.98564 | − | 5.18786i | −0.0281681 | − | 0.0162629i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 53.6450 | + | 92.9159i | 0.167118 | + | 0.289458i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −258.206 | + | 122.630i | −0.799400 | + | 0.379660i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −157.573 | + | 90.9751i | −0.484841 | + | 0.279923i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −30.9996 | + | 53.6929i | −0.0948000 | + | 0.164198i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −137.954 | + | 238.943i | −0.419313 | + | 0.726271i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.06641i | 0.0273910i | 0.999906 | + | 0.0136955i | \(0.00435954\pi\) | ||||
−0.999906 | + | 0.0136955i | \(0.995640\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −93.9675 | − | 54.2522i | −0.282185 | − | 0.162919i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 16.5148i | − | 0.0492978i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 364.175 | − | 210.256i | 1.08064 | − | 0.623906i | 0.149569 | − | 0.988751i | \(-0.452211\pi\) |
0.931068 | + | 0.364845i | \(0.118878\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −91.8146 | − | 159.028i | −0.270839 | − | 0.469108i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.6535i | 0.0400396i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −369.664 | −1.07774 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11.2757 | − | 6.51004i | 0.0326832 | − | 0.0188697i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 32.2864 | + | 55.9216i | 0.0930443 | + | 0.161157i | 0.908791 | − | 0.417252i | \(-0.137007\pi\) |
−0.815746 | + | 0.578410i | \(0.803674\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −242.722 | −0.695477 | −0.347739 | − | 0.937592i | \(-0.613050\pi\) | ||||
−0.347739 | + | 0.937592i | \(0.613050\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.9687 | − | 32.8547i | 0.0540418 | − | 0.0936031i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −560.267 | −1.58716 | −0.793579 | − | 0.608467i | \(-0.791785\pi\) | ||||
−0.793579 | + | 0.608467i | \(0.791785\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −25.4818 | − | 14.7119i | −0.0717797 | − | 0.0414420i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −118.283 | − | 68.2906i | −0.331324 | − | 0.191290i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −219.906 | − | 380.889i | −0.612552 | − | 1.06097i | −0.990809 | − | 0.135271i | \(-0.956810\pi\) |
0.378256 | − | 0.925701i | \(-0.376524\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −356.365 | − | 57.6613i | −0.987161 | − | 0.159727i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 179.491 | − | 103.629i | 0.494465 | − | 0.285479i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 17.7262 | − | 30.7026i | 0.0485648 | − | 0.0841168i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 66.5853 | − | 115.329i | 0.181431 | − | 0.314248i | −0.760937 | − | 0.648826i | \(-0.775260\pi\) |
0.942368 | + | 0.334578i | \(0.108594\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 139.846i | − | 0.378986i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 461.388 | + | 266.383i | 1.24363 | + | 0.718013i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 340.051i | 0.911666i | 0.890065 | + | 0.455833i | \(0.150659\pi\) | ||||
−0.890065 | + | 0.455833i | \(0.849341\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 21.0321 | − | 12.1429i | 0.0560855 | − | 0.0323810i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 32.7261 | + | 56.6833i | 0.0868067 | + | 0.150354i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 71.0281i | 0.187409i | 0.995600 | + | 0.0937046i | \(0.0298709\pi\) | ||||
−0.995600 | + | 0.0937046i | \(0.970129\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −195.872 | −0.514101 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −296.523 | + | 171.198i | −0.774213 | + | 0.446992i | −0.834375 | − | 0.551197i | \(-0.814171\pi\) |
0.0601627 | + | 0.998189i | \(0.480838\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.851932 | − | 1.47559i | −0.00221281 | − | 0.00383270i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.84261 | −0.0254331 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 38.8478 | − | 67.2864i | 0.0998659 | − | 0.172973i | −0.811763 | − | 0.583987i | \(-0.801492\pi\) |
0.911629 | + | 0.411014i | \(0.134825\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 402.649 | 1.02979 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −194.275 | − | 112.164i | −0.494337 | − | 0.285406i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.7121 | − | 9.07138i | −0.0397774 | − | 0.0229655i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 47.6985 | + | 82.6162i | 0.120147 | + | 0.208101i | 0.919826 | − | 0.392327i | \(-0.128330\pi\) |
−0.799678 | + | 0.600429i | \(0.794997\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −73.9992 | − | 155.810i | −0.185462 | − | 0.390502i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −93.1614 | + | 53.7868i | −0.232323 | + | 0.134132i | −0.611643 | − | 0.791134i | \(-0.709491\pi\) |
0.379320 | + | 0.925265i | \(0.376158\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 43.0646 | − | 74.5901i | 0.106860 | − | 0.185087i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.26392 | + | 2.18917i | −0.00312079 | + | 0.00540536i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 41.8605i | − | 0.102851i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 423.796 | + | 244.679i | 1.03618 | + | 0.598237i | 0.918748 | − | 0.394845i | \(-0.129202\pi\) |
0.117428 | + | 0.993081i | \(0.462535\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 74.4366i | 0.181111i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 208.768 | − | 120.532i | 0.505492 | − | 0.291846i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.10066 | − | 5.37050i | −0.00747146 | − | 0.0129410i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 360.946i | − | 0.865579i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 160.772 | 0.383705 | 0.191853 | − | 0.981424i | \(-0.438550\pi\) | ||||
0.191853 | + | 0.981424i | \(0.438550\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 304.122 | − | 175.585i | 0.722381 | − | 0.417067i | −0.0932477 | − | 0.995643i | \(-0.529725\pi\) |
0.815628 | + | 0.578576i | \(0.196392\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 78.9598 | + | 136.762i | 0.186666 | + | 0.323315i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 374.928 | 0.882184 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −265.825 | + | 460.423i | −0.622541 | + | 1.07827i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 14.6361 | 0.0341167 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.5476 | − | 8.39908i | −0.0337532 | − | 0.0194874i | 0.483028 | − | 0.875605i | \(-0.339537\pi\) |
−0.516782 | + | 0.856117i | \(0.672870\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −360.314 | − | 208.027i | −0.832133 | − | 0.480432i | 0.0224496 | − | 0.999748i | \(-0.492853\pi\) |
−0.854582 | + | 0.519316i | \(0.826187\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.18060 | − | 3.77691i | −0.00501288 | − | 0.00868256i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 418.596 | + | 288.722i | 0.957886 | + | 0.660691i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 561.428 | − | 324.140i | 1.27888 | − | 0.738361i | 0.302237 | − | 0.953233i | \(-0.402267\pi\) |
0.976642 | + | 0.214872i | \(0.0689334\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −32.2912 | + | 55.9299i | −0.0732226 | + | 0.126825i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −341.171 | + | 590.925i | −0.770137 | + | 1.33392i | 0.167351 | + | 0.985897i | \(0.446479\pi\) |
−0.937488 | + | 0.348019i | \(0.886855\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 34.8901i | − | 0.0784047i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 207.703 | + | 119.917i | 0.464660 | + | 0.268272i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 185.741i | − | 0.413677i | −0.978375 | − | 0.206839i | \(-0.933682\pi\) | ||
0.978375 | − | 0.206839i | \(-0.0663175\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 46.7238 | − | 26.9760i | 0.103600 | − | 0.0598138i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 230.047 | + | 398.453i | 0.507829 | + | 0.879586i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.7483i | 0.0236227i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −311.871 | −0.682430 | −0.341215 | − | 0.939985i | \(-0.610838\pi\) | ||||
−0.341215 | + | 0.939985i | \(0.610838\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −67.7007 | + | 39.0870i | −0.147496 | + | 0.0851569i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −428.769 | − | 742.649i | −0.930084 | − | 1.61095i | −0.783174 | − | 0.621803i | \(-0.786400\pi\) |
−0.146910 | − | 0.989150i | \(-0.546933\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −140.408 | −0.303258 | −0.151629 | − | 0.988438i | \(-0.548452\pi\) | ||||
−0.151629 | + | 0.988438i | \(0.548452\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.86948 | + | 4.97008i | −0.00617092 | + | 0.0106883i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −416.647 | −0.892178 | −0.446089 | − | 0.894989i | \(-0.647183\pi\) | ||||
−0.446089 | + | 0.894989i | \(0.647183\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 266.898 | + | 154.094i | 0.569079 | + | 0.328558i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 157.339 | + | 90.8398i | 0.334053 | + | 0.192866i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.89862 | − | 3.28851i | −0.00401400 | − | 0.00695244i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 389.777 | + | 268.844i | 0.820583 | + | 0.565988i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 264.082 | − | 152.468i | 0.553631 | − | 0.319639i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 78.9373 | − | 136.723i | 0.164796 | − | 0.285435i | −0.771787 | − | 0.635881i | \(-0.780637\pi\) |
0.936583 | + | 0.350446i | \(0.113970\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −132.032 | + | 228.687i | −0.274496 | + | 0.475441i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 242.972i | 0.503048i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −45.6976 | − | 26.3835i | −0.0942219 | − | 0.0543991i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 69.9652i | − | 0.143666i | −0.997417 | − | 0.0718329i | \(-0.977115\pi\) | ||
0.997417 | − | 0.0718329i | \(-0.0228848\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 133.733 | − | 77.2110i | 0.273483 | − | 0.157896i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −187.193 | − | 324.228i | −0.381249 | − | 0.660342i | 0.609992 | − | 0.792407i | \(-0.291172\pi\) |
−0.991241 | + | 0.132065i | \(0.957839\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 134.871i | − | 0.273573i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.975229 | −0.00197016 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 475.525 | − | 274.544i | 0.956790 | − | 0.552403i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −269.212 | − | 466.288i | −0.539502 | − | 0.934446i | −0.998931 | − | 0.0462308i | \(-0.985279\pi\) |
0.459428 | − | 0.888215i | \(-0.348054\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 41.5178 | 0.0828699 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 370.028 | − | 640.906i | 0.735641 | − | 1.27417i | −0.218800 | − | 0.975770i | \(-0.570214\pi\) |
0.954441 | − | 0.298398i | \(-0.0964523\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.1493 | −0.0220778 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 173.542 | + | 100.195i | 0.342292 | + | 0.197622i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 36.2456 | + | 20.9264i | 0.0712094 | + | 0.0411128i | 0.535182 | − | 0.844737i | \(-0.320243\pi\) |
−0.463973 | + | 0.885850i | \(0.653576\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 330.794 | + | 572.952i | 0.647347 | + | 1.12124i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −98.4095 | − | 7.91009i | −0.191831 | − | 0.0154193i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.50331 | − | 3.75469i | 0.0126278 | − | 0.00729065i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −30.4624 | + | 52.7624i | −0.0589214 | + | 0.102055i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −48.4169 | + | 83.8605i | −0.0932888 | + | 0.161581i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 881.594i | 1.69212i | 0.533089 | + | 0.846059i | \(0.321031\pi\) | ||||
−0.533089 | + | 0.846059i | \(0.678969\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −447.114 | − | 258.142i | −0.854903 | − | 0.493578i | 0.00739916 | − | 0.999973i | \(-0.497645\pi\) |
−0.862302 | + | 0.506394i | \(0.830978\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 226.244i | 0.430941i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −153.701 | + | 88.7393i | −0.291653 | + | 0.168386i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −93.6485 | − | 162.204i | −0.177029 | − | 0.306624i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 137.977i | − | 0.259843i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −340.341 | −0.638538 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.0673 | + | 8.69912i | −0.0281632 | + | 0.0162600i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −165.515 | − | 286.681i | −0.308222 | − | 0.533856i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −24.9156 | −0.0462256 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 163.097 | − | 282.493i | 0.301474 | − | 0.522168i | −0.674996 | − | 0.737821i | \(-0.735855\pi\) |
0.976470 | + | 0.215654i | \(0.0691882\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −148.582 | −0.273632 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.70688 | − | 5.02692i | −0.0159759 | − | 0.00922371i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 420.124 | + | 242.559i | 0.768052 | + | 0.443435i | 0.832179 | − | 0.554507i | \(-0.187093\pi\) |
−0.0641274 | + | 0.997942i | \(0.520426\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 152.148 | + | 263.529i | 0.277138 | + | 0.480016i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 96.7103 | − | 140.213i | 0.175518 | − | 0.254470i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 293.209 | − | 169.284i | 0.530215 | − | 0.306120i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.79757 | − | 15.2378i | 0.0158515 | − | 0.0274556i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 45.2381 | − | 78.3548i | 0.0812175 | − | 0.140673i | −0.822556 | − | 0.568685i | \(-0.807452\pi\) |
0.903773 | + | 0.428012i | \(0.140786\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23.9538i | 0.0428511i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −26.1186 | − | 15.0796i | −0.0465573 | − | 0.0268799i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 126.463i | − | 0.224624i | −0.993673 | − | 0.112312i | \(-0.964174\pi\) | ||
0.993673 | − | 0.112312i | \(-0.0358256\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 25.7880 | − | 14.8887i | 0.0456425 | − | 0.0263517i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −23.5864 | − | 40.8529i | −0.0415986 | − | 0.0720509i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 857.322i | 1.50672i | 0.657610 | + | 0.753359i | \(0.271568\pi\) | ||||
−0.657610 | + | 0.753359i | \(0.728432\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 99.1009 | 0.173557 | 0.0867784 | − | 0.996228i | \(-0.472343\pi\) | ||||
0.0867784 | + | 0.996228i | \(0.472343\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −492.263 | + | 284.208i | −0.859098 | + | 0.496000i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −333.491 | − | 577.623i | −0.579984 | − | 1.00456i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 777.423 | 1.34735 | 0.673677 | − | 0.739026i | \(-0.264714\pi\) | ||||
0.673677 | + | 0.739026i | \(0.264714\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 187.491 | − | 324.744i | 0.323819 | − | 0.560871i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 115.725 | 0.199182 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 101.882 | + | 58.8214i | 0.174754 | + | 0.100894i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.32774 | + | 3.07597i | 0.00910726 | + | 0.00525808i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 265.805 | + | 460.388i | 0.452820 | + | 0.784307i | 0.998560 | − | 0.0536475i | \(-0.0170847\pi\) |
−0.545740 | + | 0.837955i | \(0.683751\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −223.419 | − | 17.9583i | −0.379320 | − | 0.0304895i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −129.335 | + | 74.6716i | −0.218841 | + | 0.126348i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −340.521 | + | 589.799i | −0.574234 | + | 0.994603i | 0.421890 | + | 0.906647i | \(0.361367\pi\) |
−0.996124 | + | 0.0879557i | \(0.971967\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.0741 | − | 19.1808i | 0.0186118 | − | 0.0322367i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 73.7050i | − | 0.123459i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 281.589 | + | 162.575i | 0.470098 | + | 0.271411i | 0.716281 | − | 0.697812i | \(-0.245843\pi\) |
−0.246183 | + | 0.969223i | \(0.579176\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 331.221i | − | 0.551117i | −0.961284 | − | 0.275558i | \(-0.911137\pi\) | ||
0.961284 | − | 0.275558i | \(-0.0888628\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 152.763 | − | 88.1976i | 0.253338 | − | 0.146265i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 16.8046 | + | 29.1064i | 0.0277761 | + | 0.0481097i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 819.129i | − | 1.34947i | −0.738060 | − | 0.674735i | \(-0.764258\pi\) | ||
0.738060 | − | 0.674735i | \(-0.235742\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 81.3860 | 0.133639 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 332.836 | − | 192.163i | 0.544740 | − | 0.314506i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 161.068 | + | 278.978i | 0.262754 | + | 0.455103i | 0.966973 | − | 0.254880i | \(-0.0820359\pi\) |
−0.704219 | + | 0.709983i | \(0.748703\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 22.6775 | 0.0368740 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −570.525 | + | 988.179i | −0.924676 | + | 1.60159i | −0.132595 | + | 0.991170i | \(0.542331\pi\) |
−0.792081 | + | 0.610416i | \(0.791002\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 56.7606 | 0.0916972 | 0.0458486 | − | 0.998948i | \(-0.485401\pi\) | ||||
0.0458486 | + | 0.998948i | \(0.485401\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 120.437 | + | 69.5342i | 0.193940 | + | 0.111971i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 563.866 | + | 325.548i | 0.905082 | + | 0.522549i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −309.545 | − | 536.147i | −0.495272 | − | 0.857836i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.3402 | − | 34.4053i | −0.0260609 | − | 0.0548730i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 471.234 | − | 272.067i | 0.749180 | − | 0.432539i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −568.803 | + | 985.195i | −0.901430 | + | 1.56132i | −0.0757921 | + | 0.997124i | \(0.524149\pi\) |
−0.825638 | + | 0.564200i | \(0.809185\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 278.518 | − | 482.408i | 0.439997 | − | 0.762098i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 31.7628i | − | 0.0500202i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 136.116 | + | 78.5864i | 0.213682 | + | 0.123370i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 314.278i | − | 0.491828i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 65.0480 | − | 37.5555i | 0.101479 | − | 0.0585889i | −0.448402 | − | 0.893832i | \(-0.648007\pi\) |
0.549881 | + | 0.835243i | \(0.314673\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 154.393 | + | 267.417i | 0.240114 | + | 0.415889i | 0.960746 | − | 0.277428i | \(-0.0894820\pi\) |
−0.720633 | + | 0.693317i | \(0.756149\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 1.59609i | − | 0.00247455i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −121.571 | −0.187900 | −0.0939498 | − | 0.995577i | \(-0.529949\pi\) | ||||
−0.0939498 | + | 0.995577i | \(0.529949\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 46.0992 | − | 26.6154i | 0.0710312 | − | 0.0410099i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −53.5483 | − | 92.7484i | −0.0822555 | − | 0.142471i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1258.75 | 1.92764 | 0.963819 | − | 0.266559i | \(-0.0858867\pi\) | ||||
0.963819 | + | 0.266559i | \(0.0858867\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.1887 | − | 31.5037i | 0.0277690 | − | 0.0480973i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 378.669 | 0.576361 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −851.135 | − | 491.403i | −1.29156 | − | 0.745680i | −0.312625 | − | 0.949876i | \(-0.601208\pi\) |
−0.978930 | + | 0.204197i | \(0.934542\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 249.208 | + | 143.880i | 0.377017 | + | 0.217671i | 0.676519 | − | 0.736425i | \(-0.263487\pi\) |
−0.299503 | + | 0.954095i | \(0.596821\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 95.1253 | + | 164.762i | 0.143477 | + | 0.248510i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 25.2663 | − | 11.9998i | 0.0379945 | − | 0.0180448i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −207.786 | + | 119.965i | −0.311523 | + | 0.179858i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 227.577 | − | 394.176i | 0.340176 | − | 0.589201i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −58.6983 | + | 101.668i | −0.0874788 | + | 0.151518i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 252.012i | 0.374460i | 0.982316 | + | 0.187230i | \(0.0599510\pi\) | ||||
−0.982316 | + | 0.187230i | \(0.940049\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 112.145 | + | 64.7469i | 0.166141 | + | 0.0959214i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 293.002i | − | 0.432795i | −0.976305 | − | 0.216397i | \(-0.930569\pi\) | ||
0.976305 | − | 0.216397i | \(-0.0694306\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 852.780 | − | 492.353i | 1.25593 | − | 0.725114i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 368.049 | + | 637.479i | 0.540454 | + | 0.936093i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 532.042i | 0.778979i | 0.921031 | + | 0.389489i | \(0.127349\pi\) | ||||
−0.921031 | + | 0.389489i | \(0.872651\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.0707 | −0.0176215 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −98.9745 | + | 57.1429i | −0.144068 | + | 0.0831775i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −371.058 | − | 642.691i | −0.538545 | − | 0.932788i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 806.065 | 1.16652 | 0.583260 | − | 0.812286i | \(-0.301777\pi\) | ||||
0.583260 | + | 0.812286i | \(0.301777\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.09954 | − | 15.7609i | 0.0131307 | − | 0.0227430i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 58.5314 | 0.0842178 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 607.351 | + | 350.654i | 0.871379 | + | 0.503091i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 77.1431 | + | 44.5386i | 0.110362 | + | 0.0637176i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −395.041 | − | 684.230i | −0.563539 | − | 0.976077i | −0.997184 | − | 0.0749939i | \(-0.976106\pi\) |
0.433645 | − | 0.901084i | \(-0.357227\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 684.985 | + | 55.0586i | 0.974374 | + | 0.0783195i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −22.1775 | + | 12.8042i | −0.0314574 | + | 0.0181620i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 104.031 | − | 180.186i | 0.147144 | − | 0.254860i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −497.856 | + | 862.312i | −0.702195 | + | 1.21624i | 0.265499 | + | 0.964111i | \(0.414463\pi\) |
−0.967694 | + | 0.252126i | \(0.918870\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 193.784i | − | 0.272551i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 273.428 | + | 157.864i | 0.383489 | + | 0.221408i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.37340i | 0.00331944i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −359.799 | + | 207.730i | −0.501811 | + | 0.289721i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 600.858 | + | 1040.72i | 0.835686 | + | 1.44745i | 0.893471 | + | 0.449122i | \(0.148263\pi\) |
−0.0577845 | + | 0.998329i | \(0.518404\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 140.135i | 0.194362i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 330.417 | 0.457008 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −193.481 | + | 111.706i | −0.266870 | + | 0.154077i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.3246 | − | 21.3468i | −0.0169527 | − | 0.0293629i | 0.857425 | − | 0.514610i | \(-0.172063\pi\) |
−0.874377 | + | 0.485247i | \(0.838730\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.6797 | − | 42.7465i | 0.0337615 | − | 0.0584767i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 68.8594 | 0.0939419 | 0.0469710 | − | 0.998896i | \(-0.485043\pi\) | ||||
0.0469710 | + | 0.998896i | \(0.485043\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9.06965 | − | 5.23636i | −0.0123397 | − | 0.00712430i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 58.9352 | + | 34.0263i | 0.0799664 | + | 0.0461686i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 497.408 | + | 861.536i | 0.673083 | + | 1.16581i | 0.977025 | + | 0.213123i | \(0.0683635\pi\) |
−0.303943 | + | 0.952690i | \(0.598303\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −19.2506 | + | 239.497i | −0.0259793 | + | 0.323208i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −341.188 | + | 196.985i | −0.459204 | + | 0.265121i | −0.711709 | − | 0.702474i | \(-0.752079\pi\) |
0.252506 | + | 0.967595i | \(0.418745\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.4459 | + | 33.6813i | −0.0261019 | + | 0.0452098i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 33.1183 | − | 57.3626i | 0.0443351 | − | 0.0767907i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 324.674i | − | 0.433477i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −153.043 | − | 88.3594i | −0.203786 | − | 0.117656i | 0.394634 | − | 0.918838i | \(-0.370871\pi\) |
−0.598420 | + | 0.801183i | \(0.704205\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 359.918i | − | 0.477979i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −64.6134 | + | 37.3046i | −0.0855807 | + | 0.0494100i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 591.818 | + | 1025.06i | 0.781793 | + | 1.35411i | 0.930896 | + | 0.365284i | \(0.119028\pi\) |
−0.149103 | + | 0.988822i | \(0.547639\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 53.6520i | 0.0706878i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −517.695 | −0.680282 | −0.340141 | − | 0.940374i | \(-0.610475\pi\) | ||||
−0.340141 | + | 0.940374i | \(0.610475\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 162.482 | − | 93.8091i | 0.212952 | − | 0.122948i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.33838 | − | 10.9784i | −0.00828546 | − | 0.0143508i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −335.791 | −0.437798 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 476.376 | − | 825.107i | 0.619474 | − | 1.07296i | −0.370107 | − | 0.928989i | \(-0.620679\pi\) |
0.989582 | − | 0.143972i | \(-0.0459875\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 116.369 | 0.150932 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1088.18 | − | 628.259i | −1.40773 | − | 0.812754i | −0.412561 | − | 0.910930i | \(-0.635366\pi\) |
−0.995169 | + | 0.0981762i | \(0.968699\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 254.603 | + | 146.995i | 0.328520 | + | 0.189671i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 164.175 | + | 284.359i | 0.211293 | + | 0.365970i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 379.967 | + | 800.046i | 0.487762 | + | 1.02702i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 105.003 | − | 60.6236i | 0.134447 | − | 0.0776231i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 23.2912 | − | 40.3415i | 0.0297461 | − | 0.0515217i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.7307 | + | 25.5142i | −0.0187652 | + | 0.0325022i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 981.332i | − | 1.24693i | −0.781852 | − | 0.623464i | \(-0.785725\pi\) | ||
0.781852 | − | 0.623464i | \(-0.214275\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 426.278 | + | 246.111i | 0.540276 | + | 0.311928i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 555.687i | 0.702512i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 641.345 | − | 370.281i | 0.808758 | − | 0.466937i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 24.7243 | + | 42.8237i | 0.0310997 | + | 0.0538663i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 943.008i | − | 1.18320i | −0.806233 | − | 0.591599i | \(-0.798497\pi\) | ||
0.806233 | − | 0.591599i | \(-0.201503\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −791.945 | −0.991171 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 322.736 | − | 186.332i | 0.402916 | − | 0.232624i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 73.0445 | + | 126.517i | 0.0909645 | + | 0.157555i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −39.4006 | −0.0489448 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −61.8223 | + | 107.079i | −0.0766076 | + | 0.132688i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 942.078 | 1.16450 | 0.582249 | − | 0.813011i | \(-0.302173\pi\) | ||||
0.582249 | + | 0.813011i | \(0.302173\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −556.679 | − | 321.399i | −0.686411 | − | 0.396300i | 0.115855 | − | 0.993266i | \(-0.463039\pi\) |
−0.802266 | + | 0.596967i | \(0.796373\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 106.621 | + | 61.5577i | 0.131145 | + | 0.0757167i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.5206 | + | 21.6863i | 0.0153627 | + | 0.0266090i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 56.3087 | − | 26.7427i | 0.0689213 | − | 0.0327329i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −99.4229 | + | 57.4018i | −0.121395 | + | 0.0700877i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −428.109 | + | 741.507i | −0.521449 | + | 0.903176i | 0.478240 | + | 0.878229i | \(0.341275\pi\) |
−0.999689 | + | 0.0249465i | \(0.992058\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −705.555 | + | 1222.06i | −0.857297 | + | 1.48488i | 0.0172014 | + | 0.999852i | \(0.494524\pi\) |
−0.874498 | + | 0.485029i | \(0.838809\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 49.9582i | 0.0605554i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 790.058 | + | 456.140i | 0.955330 | + | 0.551560i | 0.894733 | − | 0.446602i | \(-0.147366\pi\) |
0.0605975 | + | 0.998162i | \(0.480699\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1182.75i | − | 1.42672i | −0.700799 | − | 0.713359i | \(-0.747173\pi\) | ||
0.700799 | − | 0.713359i | \(-0.252827\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 715.495 | − | 413.091i | 0.861005 | − | 0.497101i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −161.936 | − | 280.481i | −0.194401 | − | 0.336712i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.73256i | 0.00806295i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −61.2982 | −0.0732356 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −791.646 | + | 457.057i | −0.943559 | + | 0.544764i | −0.891074 | − | 0.453858i | \(-0.850047\pi\) |
−0.0524848 | + | 0.998622i | \(0.516714\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −380.316 | − | 658.727i | −0.452219 | − | 0.783267i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −253.362 | −0.300548 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −16.2476 | + | 28.1417i | −0.0192280 | + | 0.0333038i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −627.191 | −0.740486 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 228.171 | + | 131.735i | 0.268753 | + | 0.155165i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −838.307 | − | 483.997i | −0.985084 | − | 0.568739i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 241.160 | + | 417.701i | 0.282720 | + | 0.489685i | 0.972054 | − | 0.234759i | \(-0.0754301\pi\) |
−0.689334 | + | 0.724444i | \(0.742097\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.28271 | − | 15.9582i | 0.00150024 | − | 0.0186645i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −965.678 | + | 557.534i | −1.12681 | + | 0.650565i | −0.943131 | − | 0.332421i | \(-0.892135\pi\) |
−0.183681 | + | 0.982986i | \(0.558801\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 103.471 | − | 179.217i | 0.120455 | − | 0.208635i | −0.799492 | − | 0.600677i | \(-0.794898\pi\) |
0.919947 | + | 0.392042i | \(0.128231\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −211.597 | + | 366.496i | −0.245757 | + | 0.425663i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 562.589i | 0.651899i | 0.945387 | + | 0.325949i | \(0.105684\pi\) | ||||
−0.945387 | + | 0.325949i | \(0.894316\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.5989 | − | 7.85132i | −0.0157213 | − | 0.00907667i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 108.531i | 0.125179i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 64.7450 | − | 37.3806i | 0.0745052 | − | 0.0430156i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −214.645 | − | 371.776i | −0.246435 | − | 0.426838i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 563.609i | − | 0.645600i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −73.4920 | −0.0839909 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −446.560 | + | 257.821i | −0.509190 | + | 0.293981i | −0.732501 | − | 0.680766i | \(-0.761647\pi\) |
0.223311 | + | 0.974747i | \(0.428314\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 303.709 | + | 526.039i | 0.345516 | + | 0.598452i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −830.527 | −0.942709 | −0.471355 | − | 0.881944i | \(-0.656235\pi\) | ||||
−0.471355 | + | 0.881944i | \(0.656235\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 387.441 | − | 671.068i | 0.438778 | − | 0.759986i | −0.558817 | − | 0.829291i | \(-0.688745\pi\) |
0.997596 | + | 0.0693046i | \(0.0220780\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 22.3744 | 0.0252818 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −419.897 | − | 242.428i | −0.473390 | − | 0.273312i | 0.244268 | − | 0.969708i | \(-0.421452\pi\) |
−0.717658 | + | 0.696396i | \(0.754786\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 513.325 | + | 296.368i | 0.577419 | + | 0.333373i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.20825 | − | 9.02094i | −0.00584539 | − | 0.0101245i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −823.310 | − | 567.869i | −0.921960 | − | 0.635911i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 46.4884 | − | 26.8401i | 0.0519423 | − | 0.0299889i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 169.224 | − | 293.105i | 0.188656 | − | 0.326761i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 52.8780 | − | 91.5874i | 0.0588187 | − | 0.101877i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1529.21i | 1.69724i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 25.7947 | + | 14.8926i | 0.0285655 | + | 0.0164923i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 24.0942i | − | 0.0266235i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 606.666 | − | 350.259i | 0.668871 | − | 0.386173i | −0.126778 | − | 0.991931i | \(-0.540464\pi\) |
0.795649 | + | 0.605759i | \(0.207130\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −59.5433 | − | 103.132i | −0.0655042 | − | 0.113457i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1216.56i | − | 1.33541i | −0.744426 | − | 0.667706i | \(-0.767277\pi\) | ||
0.744426 | − | 0.667706i | \(-0.232723\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.5538 | 0.0279889 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −42.7341 | + | 24.6725i | −0.0467039 | + | 0.0269645i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 339.425 | + | 587.902i | 0.370148 | + | 0.641114i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1332.61 | 1.45006 | 0.725030 | − | 0.688717i | \(-0.241826\pi\) | ||||
0.725030 | + | 0.688717i | \(0.241826\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 412.362 | − | 714.232i | 0.447733 | − | 0.775497i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −764.853 | −0.828660 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −780.592 | − | 450.675i | −0.843883 | − | 0.487216i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 69.4623 | + | 40.1041i | 0.0749323 | + | 0.0432622i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 297.945 | + | 516.056i | 0.320716 | + | 0.555497i | 0.980636 | − | 0.195839i | \(-0.0627431\pi\) |
−0.659920 | + | 0.751336i | \(0.729410\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 32.7712 | − | 407.707i | 0.0352000 | − | 0.437923i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −703.427 | + | 406.124i | −0.753942 | + | 0.435288i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.44532 | − | 4.23542i | 0.00261532 | − | 0.00452986i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −330.843 | + | 573.037i | −0.353087 | + | 0.611565i | −0.986789 | − | 0.162013i | \(-0.948201\pi\) |
0.633701 | + | 0.773578i | \(0.281535\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 61.2406i | − | 0.0652189i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −289.896 | − | 167.371i | −0.308072 | − | 0.177865i | 0.337992 | − | 0.941149i | \(-0.390252\pi\) |
−0.646063 | + | 0.763284i | \(0.723586\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1247.60i | − | 1.32301i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.62474 | − | 3.82479i | 0.00701030 | − | 0.00404740i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −523.600 | − | 906.901i | −0.552904 | − | 0.957657i | −0.998063 | − | 0.0622060i | \(-0.980186\pi\) |
0.445160 | − | 0.895451i | \(-0.353147\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 921.560i | − | 0.971085i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −755.109 | −0.794015 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1349.22 | + | 778.975i | −1.41577 | + | 0.817393i | −0.995923 | − | 0.0902041i | \(-0.971248\pi\) |
−0.419843 | + | 0.907597i | \(0.637915\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −46.0874 | − | 79.8258i | −0.0482591 | − | 0.0835872i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 17.9713 | 0.0187788 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 112.628 | − | 195.077i | 0.117443 | − | 0.203417i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 821.835 | 0.855187 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −160.935 | − | 92.9159i | −0.167118 | − | 0.0964858i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 52.6608 | + | 30.4037i | 0.0545707 | + | 0.0315064i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −575.086 | − | 996.077i | −0.594711 | − | 1.03007i | −0.993588 | − | 0.113065i | \(-0.963933\pi\) |
0.398877 | − | 0.917005i | \(-0.369400\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 281.109 | − | 407.558i | 0.290102 | − | 0.420597i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 970.030 | − | 560.047i | 0.999001 | − | 0.576774i | 0.0910487 | − | 0.995846i | \(-0.470978\pi\) |
0.907953 | + | 0.419073i | \(0.137645\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −546.137 | + | 945.937i | −0.561292 | + | 0.972186i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 157.573 | − | 272.925i | 0.161614 | − | 0.279923i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 106.000i | 0.108496i | 0.998528 | + | 0.0542478i | \(0.0172761\pi\) | ||||
−0.998528 | + | 0.0542478i | \(0.982724\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 124.510 | + | 71.8860i | 0.127181 | + | 0.0734280i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 107.386i | − | 0.109466i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1529.14 | + | 882.852i | −1.55559 | + | 0.898120i | −0.557919 | + | 0.829896i | \(0.688400\pi\) |
−0.997670 | + | 0.0682241i | \(0.978267\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.1088 | − | 20.9731i | −0.0122932 | − | 0.0212925i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 477.887i | − | 0.484181i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −87.8083 | −0.0887850 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1144.85 | + | 660.979i | −1.15525 | + | 0.666982i | −0.950160 | − | 0.311762i | \(-0.899081\pi\) |
−0.205087 | + | 0.978744i | \(0.565748\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.85174 | − | 13.5996i | −0.00790709 | − | 0.0136955i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.9521 | 0.0120121 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.4622 | − | 73.5468i | 0.0425900 | − | 0.0737681i | −0.843945 | − | 0.536430i | \(-0.819772\pi\) |
0.886535 | + | 0.462662i | \(0.153106\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 187.935 | 0.188123 |
(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 | 912.3.be.d.145.2 | 6 | ||
4.3 | odd | 2 | 57.3.g.a.31.3 | ✓ | 6 | ||
12.11 | even | 2 | 171.3.p.e.145.1 | 6 | |||
19.8 | odd | 6 | inner | 912.3.be.d.673.2 | 6 | ||
76.27 | even | 6 | 57.3.g.a.46.3 | yes | 6 | ||
228.179 | odd | 6 | 171.3.p.e.46.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
57.3.g.a.31.3 | ✓ | 6 | 4.3 | odd | 2 | ||
57.3.g.a.46.3 | yes | 6 | 76.27 | even | 6 | ||
171.3.p.e.46.1 | 6 | 228.179 | odd | 6 | |||
171.3.p.e.145.1 | 6 | 12.11 | even | 2 | |||
912.3.be.d.145.2 | 6 | 1.1 | even | 1 | trivial | ||
912.3.be.d.673.2 | 6 | 19.8 | odd | 6 | inner |