Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [189,2,Mod(109,189)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(189, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("189.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 189 = 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 189.e (of order \(3\), degree \(2\), 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: | \(1.50917259820\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 109.2 | ||
Root | \(-1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 189.109 |
Dual form | 189.2.e.d.163.2 |
$q$-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 \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(136\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.22474 | + | 2.12132i | 0.866025 | + | 1.50000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | + | 3.46410i | −1.00000 | + | 1.73205i | ||||
\(5\) | 1.22474 | + | 2.12132i | 0.547723 | + | 0.948683i | 0.998430 | + | 0.0560116i | \(0.0178384\pi\) |
−0.450708 | + | 0.892672i | \(0.648828\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | − | 2.59808i | −0.188982 | − | 0.981981i | ||||
\(8\) | −4.89898 | −1.73205 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.00000 | + | 5.19615i | −0.948683 | + | 1.64317i | ||||
\(11\) | 2.44949 | − | 4.24264i | 0.738549 | − | 1.27920i | −0.214600 | − | 0.976702i | \(-0.568845\pi\) |
0.953149 | − | 0.302502i | \(-0.0978220\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.00000 | −1.10940 | −0.554700 | − | 0.832050i | \(-0.687167\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | 4.89898 | − | 4.24264i | 1.30931 | − | 1.13389i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.500000 | − | 0.866025i | ||||
\(17\) | −1.22474 | + | 2.12132i | −0.297044 | + | 0.514496i | −0.975458 | − | 0.220184i | \(-0.929334\pi\) |
0.678414 | + | 0.734680i | \(0.262668\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.500000 | + | 0.866025i | 0.114708 | + | 0.198680i | 0.917663 | − | 0.397360i | \(-0.130073\pi\) |
−0.802955 | + | 0.596040i | \(0.796740\pi\) | |||||||
\(20\) | −9.79796 | −2.19089 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 12.0000 | 2.55841 | ||||||||
\(23\) | 1.22474 | + | 2.12132i | 0.255377 | + | 0.442326i | 0.964998 | − | 0.262258i | \(-0.0844671\pi\) |
−0.709621 | + | 0.704584i | \(0.751134\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | −4.89898 | − | 8.48528i | −0.960769 | − | 1.66410i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 10.0000 | + | 3.46410i | 1.88982 | + | 0.654654i | ||||
\(29\) | 7.34847 | 1.36458 | 0.682288 | − | 0.731083i | \(-0.260985\pi\) | ||||
0.682288 | + | 0.731083i | \(0.260985\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.50000 | − | 6.06218i | 0.628619 | − | 1.08880i | −0.359211 | − | 0.933257i | \(-0.616954\pi\) |
0.987829 | − | 0.155543i | \(-0.0497126\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.00000 | −1.02899 | ||||||||
\(35\) | 4.89898 | − | 4.24264i | 0.828079 | − | 0.717137i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | − | 6.92820i | −0.657596 | − | 1.13899i | −0.981236 | − | 0.192809i | \(-0.938240\pi\) |
0.323640 | − | 0.946180i | \(-0.395093\pi\) | |||||||
\(38\) | −1.22474 | + | 2.12132i | −0.198680 | + | 0.344124i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.00000 | − | 10.3923i | −0.948683 | − | 1.64317i | ||||
\(41\) | −7.34847 | −1.14764 | −0.573819 | − | 0.818982i | \(-0.694539\pi\) | ||||
−0.573819 | + | 0.818982i | \(0.694539\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.00000 | −0.152499 | −0.0762493 | − | 0.997089i | \(-0.524294\pi\) | ||||
−0.0762493 | + | 0.997089i | \(0.524294\pi\) | |||||||
\(44\) | 9.79796 | + | 16.9706i | 1.47710 | + | 2.55841i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.00000 | + | 5.19615i | −0.442326 | + | 0.766131i | ||||
\(47\) | 1.22474 | + | 2.12132i | 0.178647 | + | 0.309426i | 0.941417 | − | 0.337243i | \(-0.109495\pi\) |
−0.762770 | + | 0.646670i | \(0.776161\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.50000 | + | 2.59808i | −0.928571 | + | 0.371154i | ||||
\(50\) | −2.44949 | −0.346410 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 8.00000 | − | 13.8564i | 1.10940 | − | 1.92154i | ||||
\(53\) | −1.22474 | + | 2.12132i | −0.168232 | + | 0.291386i | −0.937798 | − | 0.347181i | \(-0.887139\pi\) |
0.769567 | + | 0.638567i | \(0.220472\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 12.0000 | 1.61808 | ||||||||
\(56\) | 2.44949 | + | 12.7279i | 0.327327 | + | 1.70084i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.00000 | + | 15.5885i | 1.18176 | + | 2.04686i | ||||
\(59\) | −4.89898 | + | 8.48528i | −0.637793 | + | 1.10469i | 0.348123 | + | 0.937449i | \(0.386819\pi\) |
−0.985916 | + | 0.167241i | \(0.946514\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.50000 | − | 4.33013i | −0.320092 | − | 0.554416i | 0.660415 | − | 0.750901i | \(-0.270381\pi\) |
−0.980507 | + | 0.196485i | \(0.937047\pi\) | |||||||
\(62\) | 17.1464 | 2.17760 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | −4.89898 | − | 8.48528i | −0.607644 | − | 1.05247i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00000 | + | 1.73205i | −0.122169 | + | 0.211604i | −0.920623 | − | 0.390453i | \(-0.872318\pi\) |
0.798454 | + | 0.602056i | \(0.205652\pi\) | |||||||
\(68\) | −4.89898 | − | 8.48528i | −0.594089 | − | 1.02899i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 15.0000 | + | 5.19615i | 1.79284 | + | 0.621059i | ||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.500000 | − | 0.866025i | 0.0585206 | − | 0.101361i | −0.835281 | − | 0.549823i | \(-0.814695\pi\) |
0.893801 | + | 0.448463i | \(0.148028\pi\) | |||||||
\(74\) | 9.79796 | − | 16.9706i | 1.13899 | − | 1.97279i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.00000 | −0.458831 | ||||||||
\(77\) | −12.2474 | − | 4.24264i | −1.39573 | − | 0.483494i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.00000 | + | 3.46410i | 0.225018 | + | 0.389742i | 0.956325 | − | 0.292306i | \(-0.0944227\pi\) |
−0.731307 | + | 0.682048i | \(0.761089\pi\) | |||||||
\(80\) | 4.89898 | − | 8.48528i | 0.547723 | − | 0.948683i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −9.00000 | − | 15.5885i | −0.993884 | − | 1.72146i | ||||
\(83\) | −14.6969 | −1.61320 | −0.806599 | − | 0.591099i | \(-0.798694\pi\) | ||||
−0.806599 | + | 0.591099i | \(0.798694\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.00000 | −0.650791 | ||||||||
\(86\) | −1.22474 | − | 2.12132i | −0.132068 | − | 0.228748i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −12.0000 | + | 20.7846i | −1.27920 | + | 2.21565i | ||||
\(89\) | 1.22474 | + | 2.12132i | 0.129823 | + | 0.224860i | 0.923608 | − | 0.383339i | \(-0.125226\pi\) |
−0.793785 | + | 0.608198i | \(0.791893\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | + | 10.3923i | 0.209657 | + | 1.08941i | ||||
\(92\) | −9.79796 | −1.02151 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.00000 | + | 5.19615i | −0.309426 | + | 0.535942i | ||||
\(95\) | −1.22474 | + | 2.12132i | −0.125656 | + | 0.217643i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.00000 | −0.101535 | −0.0507673 | − | 0.998711i | \(-0.516167\pi\) | ||||
−0.0507673 | + | 0.998711i | \(0.516167\pi\) | |||||||
\(98\) | −13.4722 | − | 10.6066i | −1.36090 | − | 1.07143i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.00000 | − | 3.46410i | −0.200000 | − | 0.346410i | ||||
\(101\) | 2.44949 | − | 4.24264i | 0.243733 | − | 0.422159i | −0.718041 | − | 0.696000i | \(-0.754961\pi\) |
0.961775 | + | 0.273842i | \(0.0882945\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.00000 | − | 1.73205i | −0.0985329 | − | 0.170664i | 0.812545 | − | 0.582899i | \(-0.198082\pi\) |
−0.911078 | + | 0.412235i | \(0.864748\pi\) | |||||||
\(104\) | 19.5959 | 1.92154 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | −9.79796 | − | 16.9706i | −0.947204 | − | 1.64061i | −0.751276 | − | 0.659988i | \(-0.770561\pi\) |
−0.195928 | − | 0.980618i | \(-0.562772\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.500000 | − | 0.866025i | 0.0478913 | − | 0.0829502i | −0.841086 | − | 0.540901i | \(-0.818083\pi\) |
0.888977 | + | 0.457951i | \(0.151417\pi\) | |||||||
\(110\) | 14.6969 | + | 25.4558i | 1.40130 | + | 2.42712i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −8.00000 | + | 6.92820i | −0.755929 | + | 0.654654i | ||||
\(113\) | 14.6969 | 1.38257 | 0.691286 | − | 0.722581i | \(-0.257045\pi\) | ||||
0.691286 | + | 0.722581i | \(0.257045\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.00000 | + | 5.19615i | −0.279751 | + | 0.484544i | ||||
\(116\) | −14.6969 | + | 25.4558i | −1.36458 | + | 2.36352i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −24.0000 | −2.20938 | ||||||||
\(119\) | 6.12372 | + | 2.12132i | 0.561361 | + | 0.194461i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.50000 | − | 11.2583i | −0.590909 | − | 1.02348i | ||||
\(122\) | 6.12372 | − | 10.6066i | 0.554416 | − | 0.960277i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 14.0000 | + | 24.2487i | 1.25724 | + | 2.17760i | ||||
\(125\) | 9.79796 | 0.876356 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.0000 | 0.976092 | 0.488046 | − | 0.872818i | \(-0.337710\pi\) | ||||
0.488046 | + | 0.872818i | \(0.337710\pi\) | |||||||
\(128\) | −9.79796 | − | 16.9706i | −0.866025 | − | 1.50000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 12.0000 | − | 20.7846i | 1.05247 | − | 1.82293i | ||||
\(131\) | 1.22474 | + | 2.12132i | 0.107006 | + | 0.185341i | 0.914556 | − | 0.404459i | \(-0.132540\pi\) |
−0.807550 | + | 0.589799i | \(0.799207\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.00000 | − | 1.73205i | 0.173422 | − | 0.150188i | ||||
\(134\) | −4.89898 | −0.423207 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.00000 | − | 10.3923i | 0.514496 | − | 0.891133i | ||||
\(137\) | −8.57321 | + | 14.8492i | −0.732459 | + | 1.26866i | 0.223370 | + | 0.974734i | \(0.428294\pi\) |
−0.955829 | + | 0.293923i | \(0.905039\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.0000 | 1.18746 | 0.593732 | − | 0.804663i | \(-0.297654\pi\) | ||||
0.593732 | + | 0.804663i | \(0.297654\pi\) | |||||||
\(140\) | 4.89898 | + | 25.4558i | 0.414039 | + | 2.15141i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.79796 | + | 16.9706i | −0.819346 | + | 1.41915i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.00000 | + | 15.5885i | 0.747409 | + | 1.29455i | ||||
\(146\) | 2.44949 | 0.202721 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 32.0000 | 2.63038 | ||||||||
\(149\) | 1.22474 | + | 2.12132i | 0.100335 | + | 0.173785i | 0.911823 | − | 0.410584i | \(-0.134675\pi\) |
−0.811488 | + | 0.584370i | \(0.801342\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.50000 | + | 4.33013i | −0.203447 | + | 0.352381i | −0.949637 | − | 0.313353i | \(-0.898548\pi\) |
0.746190 | + | 0.665733i | \(0.231881\pi\) | |||||||
\(152\) | −2.44949 | − | 4.24264i | −0.198680 | − | 0.344124i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.00000 | − | 31.1769i | −0.483494 | − | 2.51231i | ||||
\(155\) | 17.1464 | 1.37723 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.0000 | + | 17.3205i | −0.798087 | + | 1.38233i | 0.122774 | + | 0.992435i | \(0.460821\pi\) |
−0.920860 | + | 0.389892i | \(0.872512\pi\) | |||||||
\(158\) | −4.89898 | + | 8.48528i | −0.389742 | + | 0.675053i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.89898 | − | 4.24264i | 0.386094 | − | 0.334367i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.500000 | + | 0.866025i | 0.0391630 | + | 0.0678323i | 0.884943 | − | 0.465700i | \(-0.154198\pi\) |
−0.845780 | + | 0.533533i | \(0.820864\pi\) | |||||||
\(164\) | 14.6969 | − | 25.4558i | 1.14764 | − | 1.98777i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −18.0000 | − | 31.1769i | −1.39707 | − | 2.41980i | ||||
\(167\) | 14.6969 | 1.13728 | 0.568642 | − | 0.822585i | \(-0.307469\pi\) | ||||
0.568642 | + | 0.822585i | \(0.307469\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | −7.34847 | − | 12.7279i | −0.563602 | − | 0.976187i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.00000 | − | 3.46410i | 0.152499 | − | 0.264135i | ||||
\(173\) | 1.22474 | + | 2.12132i | 0.0931156 | + | 0.161281i | 0.908821 | − | 0.417187i | \(-0.136984\pi\) |
−0.815705 | + | 0.578468i | \(0.803651\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.50000 | + | 0.866025i | 0.188982 | + | 0.0654654i | ||||
\(176\) | −19.5959 | −1.47710 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.00000 | + | 5.19615i | −0.224860 | + | 0.389468i | ||||
\(179\) | −1.22474 | + | 2.12132i | −0.0915417 | + | 0.158555i | −0.908160 | − | 0.418623i | \(-0.862513\pi\) |
0.816618 | + | 0.577178i | \(0.195846\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.00000 | −0.520306 | −0.260153 | − | 0.965567i | \(-0.583773\pi\) | ||||
−0.260153 | + | 0.965567i | \(0.583773\pi\) | |||||||
\(182\) | −19.5959 | + | 16.9706i | −1.45255 | + | 1.25794i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.00000 | − | 10.3923i | −0.442326 | − | 0.766131i | ||||
\(185\) | 9.79796 | − | 16.9706i | 0.720360 | − | 1.24770i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.00000 | + | 10.3923i | 0.438763 | + | 0.759961i | ||||
\(188\) | −9.79796 | −0.714590 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.00000 | −0.435286 | ||||||||
\(191\) | 1.22474 | + | 2.12132i | 0.0886194 | + | 0.153493i | 0.906928 | − | 0.421286i | \(-0.138421\pi\) |
−0.818308 | + | 0.574779i | \(0.805088\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.0000 | + | 17.3205i | −0.719816 | + | 1.24676i | 0.241257 | + | 0.970461i | \(0.422440\pi\) |
−0.961073 | + | 0.276296i | \(0.910893\pi\) | |||||||
\(194\) | −1.22474 | − | 2.12132i | −0.0879316 | − | 0.152302i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.00000 | − | 27.7128i | 0.285714 | − | 1.97949i | ||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.50000 | − | 16.4545i | 0.673437 | − | 1.16643i | −0.303486 | − | 0.952836i | \(-0.598151\pi\) |
0.976923 | − | 0.213591i | \(-0.0685161\pi\) | |||||||
\(200\) | 2.44949 | − | 4.24264i | 0.173205 | − | 0.300000i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.0000 | 0.844317 | ||||||||
\(203\) | −3.67423 | − | 19.0919i | −0.257881 | − | 1.33999i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.00000 | − | 15.5885i | −0.628587 | − | 1.08875i | ||||
\(206\) | 2.44949 | − | 4.24264i | 0.170664 | − | 0.295599i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 8.00000 | + | 13.8564i | 0.554700 | + | 0.960769i | ||||
\(209\) | 4.89898 | 0.338869 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.00000 | 0.344214 | 0.172107 | − | 0.985078i | \(-0.444942\pi\) | ||||
0.172107 | + | 0.985078i | \(0.444942\pi\) | |||||||
\(212\) | −4.89898 | − | 8.48528i | −0.336463 | − | 0.582772i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 24.0000 | − | 41.5692i | 1.64061 | − | 2.84161i | ||||
\(215\) | −1.22474 | − | 2.12132i | −0.0835269 | − | 0.144673i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.5000 | − | 6.06218i | −1.18798 | − | 0.411527i | ||||
\(218\) | 2.44949 | 0.165900 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −24.0000 | + | 41.5692i | −1.61808 | + | 2.80260i | ||||
\(221\) | 4.89898 | − | 8.48528i | 0.329541 | − | 0.570782i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.0000 | 1.74109 | 0.870544 | − | 0.492090i | \(-0.163767\pi\) | ||||
0.870544 | + | 0.492090i | \(0.163767\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 18.0000 | + | 31.1769i | 1.19734 | + | 2.07386i | ||||
\(227\) | −8.57321 | + | 14.8492i | −0.569024 | + | 0.985579i | 0.427639 | + | 0.903950i | \(0.359346\pi\) |
−0.996663 | + | 0.0816290i | \(0.973988\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.50000 | + | 6.06218i | 0.231287 | + | 0.400600i | 0.958187 | − | 0.286143i | \(-0.0923732\pi\) |
−0.726900 | + | 0.686743i | \(0.759040\pi\) | |||||||
\(230\) | −14.6969 | −0.969087 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −36.0000 | −2.36352 | ||||||||
\(233\) | 1.22474 | + | 2.12132i | 0.0802357 | + | 0.138972i | 0.903351 | − | 0.428902i | \(-0.141099\pi\) |
−0.823115 | + | 0.567874i | \(0.807766\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.00000 | + | 5.19615i | −0.195698 | + | 0.338960i | ||||
\(236\) | −19.5959 | − | 33.9411i | −1.27559 | − | 2.20938i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.00000 | + | 15.5885i | 0.194461 | + | 1.01045i | ||||
\(239\) | −7.34847 | −0.475333 | −0.237666 | − | 0.971347i | \(-0.576383\pi\) | ||||
−0.237666 | + | 0.971347i | \(0.576383\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.50000 | − | 11.2583i | 0.418702 | − | 0.725213i | −0.577107 | − | 0.816668i | \(-0.695819\pi\) |
0.995809 | + | 0.0914555i | \(0.0291519\pi\) | |||||||
\(242\) | 15.9217 | − | 27.5772i | 1.02348 | − | 1.77273i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 20.0000 | 1.28037 | ||||||||
\(245\) | −13.4722 | − | 10.6066i | −0.860707 | − | 0.677631i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.00000 | − | 3.46410i | −0.127257 | − | 0.220416i | ||||
\(248\) | −17.1464 | + | 29.6985i | −1.08880 | + | 1.88586i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 12.0000 | + | 20.7846i | 0.758947 | + | 1.31453i | ||||
\(251\) | 22.0454 | 1.39149 | 0.695747 | − | 0.718287i | \(-0.255074\pi\) | ||||
0.695747 | + | 0.718287i | \(0.255074\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.0000 | 0.754434 | ||||||||
\(254\) | 13.4722 | + | 23.3345i | 0.845321 | + | 1.46414i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | − | 27.7128i | 1.00000 | − | 1.73205i | ||||
\(257\) | 12.2474 | + | 21.2132i | 0.763975 | + | 1.32324i | 0.940787 | + | 0.338999i | \(0.110088\pi\) |
−0.176812 | + | 0.984245i | \(0.556578\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.0000 | + | 13.8564i | −0.994192 | + | 0.860995i | ||||
\(260\) | 39.1918 | 2.43057 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.00000 | + | 5.19615i | −0.185341 | + | 0.321019i | ||||
\(263\) | 2.44949 | − | 4.24264i | 0.151042 | − | 0.261612i | −0.780569 | − | 0.625070i | \(-0.785070\pi\) |
0.931611 | + | 0.363457i | \(0.118404\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.00000 | −0.368577 | ||||||||
\(266\) | 6.12372 | + | 2.12132i | 0.375470 | + | 0.130066i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.00000 | − | 6.92820i | −0.244339 | − | 0.423207i | ||||
\(269\) | −12.2474 | + | 21.2132i | −0.746740 | + | 1.29339i | 0.202637 | + | 0.979254i | \(0.435049\pi\) |
−0.949377 | + | 0.314138i | \(0.898285\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.500000 | + | 0.866025i | 0.0303728 | + | 0.0526073i | 0.880812 | − | 0.473466i | \(-0.156997\pi\) |
−0.850439 | + | 0.526073i | \(0.823664\pi\) | |||||||
\(272\) | 9.79796 | 0.594089 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −42.0000 | −2.53731 | ||||||||
\(275\) | 2.44949 | + | 4.24264i | 0.147710 | + | 0.255841i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.5000 | + | 19.9186i | −0.690968 | + | 1.19679i | 0.280553 | + | 0.959839i | \(0.409482\pi\) |
−0.971521 | + | 0.236953i | \(0.923851\pi\) | |||||||
\(278\) | 17.1464 | + | 29.6985i | 1.02837 | + | 1.78120i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −24.0000 | + | 20.7846i | −1.43427 | + | 1.24212i | ||||
\(281\) | −14.6969 | −0.876746 | −0.438373 | − | 0.898793i | \(-0.644445\pi\) | ||||
−0.438373 | + | 0.898793i | \(0.644445\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.5000 | − | 21.6506i | 0.743048 | − | 1.28700i | −0.208053 | − | 0.978117i | \(-0.566713\pi\) |
0.951101 | − | 0.308879i | \(-0.0999539\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −48.0000 | −2.83830 | ||||||||
\(287\) | 3.67423 | + | 19.0919i | 0.216883 | + | 1.12696i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.50000 | + | 9.52628i | 0.323529 | + | 0.560369i | ||||
\(290\) | −22.0454 | + | 38.1838i | −1.29455 | + | 2.24223i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.00000 | + | 3.46410i | 0.117041 | + | 0.202721i | ||||
\(293\) | −29.3939 | −1.71721 | −0.858604 | − | 0.512639i | \(-0.828668\pi\) | ||||
−0.858604 | + | 0.512639i | \(0.828668\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −24.0000 | −1.39733 | ||||||||
\(296\) | 19.5959 | + | 33.9411i | 1.13899 | + | 1.97279i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.00000 | + | 5.19615i | −0.173785 | + | 0.301005i | ||||
\(299\) | −4.89898 | − | 8.48528i | −0.283315 | − | 0.490716i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.500000 | + | 2.59808i | 0.0288195 | + | 0.149751i | ||||
\(302\) | −12.2474 | −0.704761 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.00000 | − | 3.46410i | 0.114708 | − | 0.198680i | ||||
\(305\) | 6.12372 | − | 10.6066i | 0.350643 | − | 0.607332i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.0000 | −1.42683 | −0.713413 | − | 0.700744i | \(-0.752851\pi\) | ||||
−0.713413 | + | 0.700744i | \(0.752851\pi\) | |||||||
\(308\) | 39.1918 | − | 33.9411i | 2.23316 | − | 1.93398i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 21.0000 | + | 36.3731i | 1.19272 | + | 2.06585i | ||||
\(311\) | 17.1464 | − | 29.6985i | 0.972285 | − | 1.68405i | 0.283666 | − | 0.958923i | \(-0.408449\pi\) |
0.688619 | − | 0.725123i | \(-0.258217\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.5000 | − | 19.9186i | −0.650018 | − | 1.12586i | −0.983118 | − | 0.182973i | \(-0.941428\pi\) |
0.333099 | − | 0.942892i | \(-0.391906\pi\) | |||||||
\(314\) | −48.9898 | −2.76465 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.0000 | −0.900070 | ||||||||
\(317\) | 12.2474 | + | 21.2132i | 0.687885 | + | 1.19145i | 0.972521 | + | 0.232816i | \(0.0747941\pi\) |
−0.284635 | + | 0.958636i | \(0.591873\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.0000 | − | 31.1769i | 1.00781 | − | 1.74557i | ||||
\(320\) | −9.79796 | − | 16.9706i | −0.547723 | − | 0.948683i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 15.0000 | + | 5.19615i | 0.835917 | + | 0.289570i | ||||
\(323\) | −2.44949 | −0.136293 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.00000 | − | 3.46410i | 0.110940 | − | 0.192154i | ||||
\(326\) | −1.22474 | + | 2.12132i | −0.0678323 | + | 0.117489i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 36.0000 | 1.98777 | ||||||||
\(329\) | 4.89898 | − | 4.24264i | 0.270089 | − | 0.233904i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.50000 | + | 11.2583i | 0.357272 | + | 0.618814i | 0.987504 | − | 0.157593i | \(-0.0503735\pi\) |
−0.630232 | + | 0.776407i | \(0.717040\pi\) | |||||||
\(332\) | 29.3939 | − | 50.9117i | 1.61320 | − | 2.79414i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 18.0000 | + | 31.1769i | 0.984916 | + | 1.70592i | ||||
\(335\) | −4.89898 | −0.267660 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.00000 | 0.272367 | 0.136184 | − | 0.990684i | \(-0.456516\pi\) | ||||
0.136184 | + | 0.990684i | \(0.456516\pi\) | |||||||
\(338\) | 3.67423 | + | 6.36396i | 0.199852 | + | 0.346154i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 12.0000 | − | 20.7846i | 0.650791 | − | 1.12720i | ||||
\(341\) | −17.1464 | − | 29.6985i | −0.928531 | − | 1.60826i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | + | 15.5885i | 0.539949 | + | 0.841698i | ||||
\(344\) | 4.89898 | 0.264135 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.00000 | + | 5.19615i | −0.161281 | + | 0.279347i | ||||
\(347\) | −4.89898 | + | 8.48528i | −0.262991 | + | 0.455514i | −0.967035 | − | 0.254642i | \(-0.918042\pi\) |
0.704044 | + | 0.710156i | \(0.251376\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 35.0000 | 1.87351 | 0.936754 | − | 0.349990i | \(-0.113815\pi\) | ||||
0.936754 | + | 0.349990i | \(0.113815\pi\) | |||||||
\(350\) | 1.22474 | + | 6.36396i | 0.0654654 | + | 0.340168i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.44949 | − | 4.24264i | 0.130373 | − | 0.225813i | −0.793447 | − | 0.608639i | \(-0.791716\pi\) |
0.923820 | + | 0.382826i | \(0.125049\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −9.79796 | −0.519291 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.00000 | −0.317110 | ||||||||
\(359\) | −9.79796 | − | 16.9706i | −0.517116 | − | 0.895672i | −0.999802 | − | 0.0198785i | \(-0.993672\pi\) |
0.482686 | − | 0.875794i | \(-0.339661\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | − | 15.5885i | 0.473684 | − | 0.820445i | ||||
\(362\) | −8.57321 | − | 14.8492i | −0.450598 | − | 0.780459i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −40.0000 | − | 13.8564i | −2.09657 | − | 0.726273i | ||||
\(365\) | 2.44949 | 0.128212 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.50000 | − | 11.2583i | 0.339297 | − | 0.587680i | −0.645003 | − | 0.764180i | \(-0.723144\pi\) |
0.984301 | + | 0.176500i | \(0.0564774\pi\) | |||||||
\(368\) | 4.89898 | − | 8.48528i | 0.255377 | − | 0.442326i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 48.0000 | 2.49540 | ||||||||
\(371\) | 6.12372 | + | 2.12132i | 0.317928 | + | 0.110133i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.50000 | − | 9.52628i | −0.284779 | − | 0.493252i | 0.687776 | − | 0.725923i | \(-0.258587\pi\) |
−0.972556 | + | 0.232671i | \(0.925254\pi\) | |||||||
\(374\) | −14.6969 | + | 25.4558i | −0.759961 | + | 1.31629i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.00000 | − | 10.3923i | −0.309426 | − | 0.535942i | ||||
\(377\) | −29.3939 | −1.51386 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −34.0000 | −1.74646 | −0.873231 | − | 0.487306i | \(-0.837980\pi\) | ||||
−0.873231 | + | 0.487306i | \(0.837980\pi\) | |||||||
\(380\) | −4.89898 | − | 8.48528i | −0.251312 | − | 0.435286i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.00000 | + | 5.19615i | −0.153493 | + | 0.265858i | ||||
\(383\) | −9.79796 | − | 16.9706i | −0.500652 | − | 0.867155i | −1.00000 | 0.000753393i | \(-0.999760\pi\) | |
0.499347 | − | 0.866402i | \(-0.333573\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.00000 | − | 31.1769i | −0.305788 | − | 1.58892i | ||||
\(386\) | −48.9898 | −2.49351 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.00000 | − | 3.46410i | 0.101535 | − | 0.175863i | ||||
\(389\) | −8.57321 | + | 14.8492i | −0.434679 | + | 0.752886i | −0.997269 | − | 0.0738494i | \(-0.976472\pi\) |
0.562590 | + | 0.826736i | \(0.309805\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.00000 | −0.303433 | ||||||||
\(392\) | 31.8434 | − | 12.7279i | 1.60833 | − | 0.642857i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.89898 | + | 8.48528i | −0.246494 | + | 0.426941i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.50000 | − | 14.7224i | −0.426603 | − | 0.738898i | 0.569966 | − | 0.821668i | \(-0.306956\pi\) |
−0.996569 | + | 0.0827707i | \(0.973623\pi\) | |||||||
\(398\) | 46.5403 | 2.33285 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.00000 | 0.200000 | ||||||||
\(401\) | 12.2474 | + | 21.2132i | 0.611608 | + | 1.05934i | 0.990969 | + | 0.134088i | \(0.0428105\pi\) |
−0.379361 | + | 0.925249i | \(0.623856\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.0000 | + | 24.2487i | −0.697390 | + | 1.20791i | ||||
\(404\) | 9.79796 | + | 16.9706i | 0.487467 | + | 0.844317i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 36.0000 | − | 31.1769i | 1.78665 | − | 1.54728i | ||||
\(407\) | −39.1918 | −1.94267 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.0000 | + | 17.3205i | −0.494468 | + | 0.856444i | −0.999980 | − | 0.00637586i | \(-0.997970\pi\) |
0.505511 | + | 0.862820i | \(0.331304\pi\) | |||||||
\(410\) | 22.0454 | − | 38.1838i | 1.08875 | − | 1.88576i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.00000 | 0.394132 | ||||||||
\(413\) | 24.4949 | + | 8.48528i | 1.20532 | + | 0.417533i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.0000 | − | 31.1769i | −0.883585 | − | 1.53041i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.00000 | + | 10.3923i | 0.293470 | + | 0.508304i | ||||
\(419\) | −7.34847 | −0.358996 | −0.179498 | − | 0.983758i | \(-0.557447\pi\) | ||||
−0.179498 | + | 0.983758i | \(0.557447\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.0000 | 1.70580 | 0.852898 | − | 0.522078i | \(-0.174843\pi\) | ||||
0.852898 | + | 0.522078i | \(0.174843\pi\) | |||||||
\(422\) | 6.12372 | + | 10.6066i | 0.298098 | + | 0.516321i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.00000 | − | 10.3923i | 0.291386 | − | 0.504695i | ||||
\(425\) | −1.22474 | − | 2.12132i | −0.0594089 | − | 0.102899i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.0000 | + | 8.66025i | −0.483934 | + | 0.419099i | ||||
\(428\) | 78.3837 | 3.78882 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.00000 | − | 5.19615i | 0.144673 | − | 0.250581i | ||||
\(431\) | 9.79796 | − | 16.9706i | 0.471951 | − | 0.817443i | −0.527534 | − | 0.849534i | \(-0.676883\pi\) |
0.999485 | + | 0.0320907i | \(0.0102166\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.00000 | −0.336399 | −0.168199 | − | 0.985753i | \(-0.553795\pi\) | ||||
−0.168199 | + | 0.985753i | \(0.553795\pi\) | |||||||
\(434\) | −8.57321 | − | 44.5477i | −0.411527 | − | 2.13836i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.00000 | + | 3.46410i | 0.0957826 | + | 0.165900i | ||||
\(437\) | −1.22474 | + | 2.12132i | −0.0585875 | + | 0.101477i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.00000 | − | 12.1244i | −0.334092 | − | 0.578664i | 0.649218 | − | 0.760602i | \(-0.275096\pi\) |
−0.983310 | + | 0.181938i | \(0.941763\pi\) | |||||||
\(440\) | −58.7878 | −2.80260 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 24.0000 | 1.14156 | ||||||||
\(443\) | 1.22474 | + | 2.12132i | 0.0581894 | + | 0.100787i | 0.893653 | − | 0.448759i | \(-0.148134\pi\) |
−0.835463 | + | 0.549546i | \(0.814801\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.00000 | + | 5.19615i | −0.142214 | + | 0.246321i | ||||
\(446\) | 31.8434 | + | 55.1543i | 1.50783 | + | 2.61163i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.00000 | + | 20.7846i | 0.188982 | + | 0.981981i | ||||
\(449\) | −22.0454 | −1.04039 | −0.520194 | − | 0.854048i | \(-0.674140\pi\) | ||||
−0.520194 | + | 0.854048i | \(0.674140\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.0000 | + | 31.1769i | −0.847587 | + | 1.46806i | ||||
\(452\) | −29.3939 | + | 50.9117i | −1.38257 | + | 2.39468i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −42.0000 | −1.97116 | ||||||||
\(455\) | −19.5959 | + | 16.9706i | −0.918671 | + | 0.795592i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.5000 | − | 19.9186i | −0.537947 | − | 0.931752i | −0.999014 | − | 0.0443868i | \(-0.985867\pi\) |
0.461067 | − | 0.887365i | \(-0.347467\pi\) | |||||||
\(458\) | −8.57321 | + | 14.8492i | −0.400600 | + | 0.693860i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −12.0000 | − | 20.7846i | −0.559503 | − | 0.969087i | ||||
\(461\) | 29.3939 | 1.36901 | 0.684505 | − | 0.729008i | \(-0.260019\pi\) | ||||
0.684505 | + | 0.729008i | \(0.260019\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.0000 | 1.06890 | 0.534450 | − | 0.845200i | \(-0.320519\pi\) | ||||
0.534450 | + | 0.845200i | \(0.320519\pi\) | |||||||
\(464\) | −14.6969 | − | 25.4558i | −0.682288 | − | 1.18176i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.00000 | + | 5.19615i | −0.138972 | + | 0.240707i | ||||
\(467\) | 12.2474 | + | 21.2132i | 0.566744 | + | 0.981630i | 0.996885 | + | 0.0788681i | \(0.0251306\pi\) |
−0.430141 | + | 0.902762i | \(0.641536\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.00000 | + | 1.73205i | 0.230879 | + | 0.0799787i | ||||
\(470\) | −14.6969 | −0.677919 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 24.0000 | − | 41.5692i | 1.10469 | − | 1.91338i | ||||
\(473\) | −2.44949 | + | 4.24264i | −0.112628 | + | 0.195077i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.00000 | −0.0458831 | ||||||||
\(476\) | −19.5959 | + | 16.9706i | −0.898177 | + | 0.777844i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −9.00000 | − | 15.5885i | −0.411650 | − | 0.712999i | ||||
\(479\) | 13.4722 | − | 23.3345i | 0.615560 | − | 1.06618i | −0.374726 | − | 0.927136i | \(-0.622263\pi\) |
0.990286 | − | 0.139046i | \(-0.0444036\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.0000 | + | 27.7128i | 0.729537 | + | 1.26360i | ||||
\(482\) | 31.8434 | 1.45043 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 52.0000 | 2.36364 | ||||||||
\(485\) | −1.22474 | − | 2.12132i | −0.0556128 | − | 0.0963242i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.50000 | − | 16.4545i | 0.430486 | − | 0.745624i | −0.566429 | − | 0.824110i | \(-0.691675\pi\) |
0.996915 | + | 0.0784867i | \(0.0250088\pi\) | |||||||
\(488\) | 12.2474 | + | 21.2132i | 0.554416 | + | 0.960277i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6.00000 | − | 41.5692i | 0.271052 | − | 1.87791i | ||||
\(491\) | 14.6969 | 0.663264 | 0.331632 | − | 0.943409i | \(-0.392401\pi\) | ||||
0.331632 | + | 0.943409i | \(0.392401\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.00000 | + | 15.5885i | −0.405340 | + | 0.702069i | ||||
\(494\) | 4.89898 | − | 8.48528i | 0.220416 | − | 0.381771i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −28.0000 | −1.25724 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.50000 | + | 6.06218i | 0.156682 | + | 0.271380i | 0.933670 | − | 0.358134i | \(-0.116587\pi\) |
−0.776989 | + | 0.629515i | \(0.783254\pi\) | |||||||
\(500\) | −19.5959 | + | 33.9411i | −0.876356 | + | 1.51789i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 27.0000 | + | 46.7654i | 1.20507 | + | 2.08724i | ||||
\(503\) | 22.0454 | 0.982956 | 0.491478 | − | 0.870890i | \(-0.336457\pi\) | ||||
0.491478 | + | 0.870890i | \(0.336457\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.0000 | 0.533993 | ||||||||
\(506\) | 14.6969 | + | 25.4558i | 0.653359 | + | 1.13165i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −22.0000 | + | 38.1051i | −0.976092 | + | 1.69064i | ||||
\(509\) | −9.79796 | − | 16.9706i | −0.434287 | − | 0.752207i | 0.562950 | − | 0.826491i | \(-0.309666\pi\) |
−0.997237 | + | 0.0742838i | \(0.976333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.50000 | − | 0.866025i | −0.110593 | − | 0.0383107i | ||||
\(512\) | 39.1918 | 1.73205 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −30.0000 | + | 51.9615i | −1.32324 | + | 2.29192i | ||||
\(515\) | 2.44949 | − | 4.24264i | 0.107937 | − | 0.186953i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.0000 | 0.527759 | ||||||||
\(518\) | −48.9898 | − | 16.9706i | −2.15249 | − | 0.745644i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 24.0000 | + | 41.5692i | 1.05247 | + | 1.82293i | ||||
\(521\) | 9.79796 | − | 16.9706i | 0.429256 | − | 0.743494i | −0.567551 | − | 0.823338i | \(-0.692109\pi\) |
0.996807 | + | 0.0798444i | \(0.0254423\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.00000 | − | 6.92820i | −0.174908 | − | 0.302949i | 0.765222 | − | 0.643767i | \(-0.222629\pi\) |
−0.940129 | + | 0.340818i | \(0.889296\pi\) | |||||||
\(524\) | −9.79796 | −0.428026 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.0000 | 0.523225 | ||||||||
\(527\) | 8.57321 | + | 14.8492i | 0.373455 | + | 0.646843i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.50000 | − | 14.7224i | 0.369565 | − | 0.640106i | ||||
\(530\) | −7.34847 | − | 12.7279i | −0.319197 | − | 0.552866i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.00000 | + | 10.3923i | 0.0867110 | + | 0.450564i | ||||
\(533\) | 29.3939 | 1.27319 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 24.0000 | − | 41.5692i | 1.03761 | − | 1.79719i | ||||
\(536\) | 4.89898 | − | 8.48528i | 0.211604 | − | 0.366508i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −60.0000 | −2.58678 | ||||||||
\(539\) | −4.89898 | + | 33.9411i | −0.211014 | + | 1.46195i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.5000 | − | 30.3109i | −0.752384 | − | 1.30317i | −0.946664 | − | 0.322221i | \(-0.895571\pi\) |
0.194281 | − | 0.980946i | \(-0.437763\pi\) | |||||||
\(542\) | −1.22474 | + | 2.12132i | −0.0526073 | + | 0.0911185i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.44949 | 0.104925 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −37.0000 | −1.58201 | −0.791003 | − | 0.611812i | \(-0.790441\pi\) | ||||
−0.791003 | + | 0.611812i | \(0.790441\pi\) | |||||||
\(548\) | −34.2929 | − | 59.3970i | −1.46492 | − | 2.53731i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.00000 | + | 10.3923i | −0.255841 | + | 0.443129i | ||||
\(551\) | 3.67423 | + | 6.36396i | 0.156528 | + | 0.271114i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.00000 | − | 6.92820i | 0.340195 | − | 0.294617i | ||||
\(554\) | −56.3383 | −2.39358 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −28.0000 | + | 48.4974i | −1.18746 | + | 2.05675i | ||||
\(557\) | 20.8207 | − | 36.0624i | 0.882200 | − | 1.52801i | 0.0333100 | − | 0.999445i | \(-0.489395\pi\) |
0.848890 | − | 0.528570i | \(-0.177272\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.00000 | 0.169182 | ||||||||
\(560\) | −24.4949 | − | 8.48528i | −1.03510 | − | 0.358569i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −18.0000 | − | 31.1769i | −0.759284 | − | 1.31512i | ||||
\(563\) | 6.12372 | − | 10.6066i | 0.258084 | − | 0.447015i | −0.707644 | − | 0.706569i | \(-0.750242\pi\) |
0.965729 | + | 0.259554i | \(0.0835755\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.0000 | + | 31.1769i | 0.757266 | + | 1.31162i | ||||
\(566\) | 61.2372 | 2.57399 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.79796 | − | 16.9706i | −0.410752 | − | 0.711443i | 0.584220 | − | 0.811595i | \(-0.301400\pi\) |
−0.994972 | + | 0.100152i | \(0.968067\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.5000 | + | 25.1147i | −0.606806 | + | 1.05102i | 0.384957 | + | 0.922934i | \(0.374216\pi\) |
−0.991763 | + | 0.128085i | \(0.959117\pi\) | |||||||
\(572\) | −39.1918 | − | 67.8823i | −1.63869 | − | 2.83830i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −36.0000 | + | 31.1769i | −1.50261 | + | 1.30130i | ||||
\(575\) | −2.44949 | −0.102151 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.00000 | + | 6.92820i | −0.166522 | + | 0.288425i | −0.937195 | − | 0.348806i | \(-0.886587\pi\) |
0.770673 | + | 0.637231i | \(0.219920\pi\) | |||||||
\(578\) | −13.4722 | + | 23.3345i | −0.560369 | + | 0.970588i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −72.0000 | −2.98964 | ||||||||
\(581\) | 7.34847 | + | 38.1838i | 0.304866 | + | 1.58413i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.00000 | + | 10.3923i | 0.248495 | + | 0.430405i | ||||
\(584\) | −2.44949 | + | 4.24264i | −0.101361 | + | 0.175562i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −36.0000 | − | 62.3538i | −1.48715 | − | 2.57581i | ||||
\(587\) | 7.34847 | 0.303304 | 0.151652 | − | 0.988434i | \(-0.451541\pi\) | ||||
0.151652 | + | 0.988434i | \(0.451541\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.00000 | 0.288430 | ||||||||
\(590\) | −29.3939 | − | 50.9117i | −1.21013 | − | 2.09600i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −16.0000 | + | 27.7128i | −0.657596 | + | 1.13899i | ||||
\(593\) | 12.2474 | + | 21.2132i | 0.502942 | + | 0.871122i | 0.999994 | + | 0.00340097i | \(0.00108257\pi\) |
−0.497052 | + | 0.867721i | \(0.665584\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.00000 | + | 15.5885i | 0.122988 | + | 0.639064i | ||||
\(596\) | −9.79796 | −0.401340 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 12.0000 | − | 20.7846i | 0.490716 | − | 0.849946i | ||||
\(599\) | −15.9217 | + | 27.5772i | −0.650542 | + | 1.12677i | 0.332449 | + | 0.943121i | \(0.392125\pi\) |
−0.982991 | + | 0.183651i | \(0.941208\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.0000 | 0.693444 | 0.346722 | − | 0.937968i | \(-0.387295\pi\) | ||||
0.346722 | + | 0.937968i | \(0.387295\pi\) | |||||||
\(602\) | −4.89898 | + | 4.24264i | −0.199667 | + | 0.172917i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −10.0000 | − | 17.3205i | −0.406894 | − | 0.704761i | ||||
\(605\) | 15.9217 | − | 27.5772i | 0.647308 | − | 1.12117i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.5000 | − | 25.1147i | −0.588537 | − | 1.01938i | −0.994424 | − | 0.105453i | \(-0.966371\pi\) |
0.405887 | − | 0.913923i | \(-0.366962\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 30.0000 | 1.21466 | ||||||||
\(611\) | −4.89898 | − | 8.48528i | −0.198191 | − | 0.343278i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.50000 | + | 14.7224i | −0.343312 | + | 0.594633i | −0.985046 | − | 0.172294i | \(-0.944882\pi\) |
0.641734 | + | 0.766927i | \(0.278215\pi\) | |||||||
\(614\) | −30.6186 | − | 53.0330i | −1.23567 | − | 2.14024i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 60.0000 | + | 20.7846i | 2.41747 | + | 0.837436i | ||||
\(617\) | −29.3939 | −1.18335 | −0.591676 | − | 0.806176i | \(-0.701534\pi\) | ||||
−0.591676 | + | 0.806176i | \(0.701534\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.00000 | + | 12.1244i | −0.281354 | + | 0.487319i | −0.971718 | − | 0.236143i | \(-0.924117\pi\) |
0.690365 | + | 0.723462i | \(0.257450\pi\) | |||||||
\(620\) | −34.2929 | + | 59.3970i | −1.37723 | + | 2.38544i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 84.0000 | 3.36809 | ||||||||
\(623\) | 4.89898 | − | 4.24264i | 0.196273 | − | 0.169978i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | + | 25.1147i | 0.580000 | + | 1.00459i | ||||
\(626\) | 28.1691 | − | 48.7904i | 1.12586 | − | 1.95006i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −40.0000 | − | 69.2820i | −1.59617 | − | 2.76465i | ||||
\(629\) | 19.5959 | 0.781340 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.0000 | −0.995234 | −0.497617 | − | 0.867397i | \(-0.665792\pi\) | ||||
−0.497617 | + | 0.867397i | \(0.665792\pi\) | |||||||
\(632\) | −9.79796 | − | 16.9706i | −0.389742 | − | 0.675053i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −30.0000 | + | 51.9615i | −1.19145 | + | 2.06366i | ||||
\(635\) | 13.4722 | + | 23.3345i | 0.534628 | + | 0.926002i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.0000 | − | 10.3923i | 1.03016 | − | 0.411758i | ||||
\(638\) | 88.1816 | 3.49114 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 24.0000 | − | 41.5692i | 0.948683 | − | 1.64317i | ||||
\(641\) | 13.4722 | − | 23.3345i | 0.532120 | − | 0.921658i | −0.467177 | − | 0.884164i | \(-0.654729\pi\) |
0.999297 | − | 0.0374946i | \(-0.0119377\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.00000 | 0.197181 | 0.0985904 | − | 0.995128i | \(-0.468567\pi\) | ||||
0.0985904 | + | 0.995128i | \(0.468567\pi\) | |||||||
\(644\) | 4.89898 | + | 25.4558i | 0.193047 | + | 1.00310i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.00000 | − | 5.19615i | −0.118033 | − | 0.204440i | ||||
\(647\) | 9.79796 | − | 16.9706i | 0.385198 | − | 0.667182i | −0.606599 | − | 0.795008i | \(-0.707467\pi\) |
0.991797 | + | 0.127826i | \(0.0408000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.0000 | + | 41.5692i | 0.942082 | + | 1.63173i | ||||
\(650\) | 9.79796 | 0.384308 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.00000 | −0.156652 | ||||||||
\(653\) | 1.22474 | + | 2.12132i | 0.0479280 | + | 0.0830137i | 0.888994 | − | 0.457919i | \(-0.151405\pi\) |
−0.841066 | + | 0.540932i | \(0.818072\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.00000 | + | 5.19615i | −0.117220 | + | 0.203030i | ||||
\(656\) | 14.6969 | + | 25.4558i | 0.573819 | + | 0.993884i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 15.0000 | + | 5.19615i | 0.584761 | + | 0.202567i | ||||
\(659\) | 7.34847 | 0.286256 | 0.143128 | − | 0.989704i | \(-0.454284\pi\) | ||||
0.143128 | + | 0.989704i | \(0.454284\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.50000 | + | 9.52628i | −0.213925 | + | 0.370529i | −0.952940 | − | 0.303160i | \(-0.901958\pi\) |
0.739014 | + | 0.673690i | \(0.235292\pi\) | |||||||
\(662\) | −15.9217 | + | 27.5772i | −0.618814 | + | 1.07182i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 72.0000 | 2.79414 | ||||||||
\(665\) | 6.12372 | + | 2.12132i | 0.237468 | + | 0.0822613i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.00000 | + | 15.5885i | 0.348481 | + | 0.603587i | ||||
\(668\) | −29.3939 | + | 50.9117i | −1.13728 | + | 1.96983i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.00000 | − | 10.3923i | −0.231800 | − | 0.401490i | ||||
\(671\) | −24.4949 | −0.945615 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.0000 | 0.655302 | 0.327651 | − | 0.944799i | \(-0.393743\pi\) | ||||
0.327651 | + | 0.944799i | \(0.393743\pi\) | |||||||
\(674\) | 6.12372 | + | 10.6066i | 0.235877 | + | 0.408551i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.00000 | + | 10.3923i | −0.230769 | + | 0.399704i | ||||
\(677\) | −9.79796 | − | 16.9706i | −0.376566 | − | 0.652232i | 0.613994 | − | 0.789311i | \(-0.289562\pi\) |
−0.990560 | + | 0.137079i | \(0.956229\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.500000 | + | 2.59808i | 0.0191882 | + | 0.0997050i | ||||
\(680\) | 29.3939 | 1.12720 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 42.0000 | − | 72.7461i | 1.60826 | − | 2.78559i | ||||
\(683\) | −12.2474 | + | 21.2132i | −0.468636 | + | 0.811701i | −0.999357 | − | 0.0358455i | \(-0.988588\pi\) |
0.530722 | + | 0.847546i | \(0.321921\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −42.0000 | −1.60474 | ||||||||
\(686\) | −20.8207 | + | 40.3051i | −0.794937 | + | 1.53886i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.00000 | + | 3.46410i | 0.0762493 | + | 0.132068i | ||||
\(689\) | 4.89898 | − | 8.48528i | 0.186636 | − | 0.323263i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.5000 | − | 35.5070i | −0.779857 | − | 1.35075i | −0.932024 | − | 0.362397i | \(-0.881959\pi\) |
0.152167 | − | 0.988355i | \(-0.451375\pi\) | |||||||
\(692\) | −9.79796 | −0.372463 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −24.0000 | −0.911028 | ||||||||
\(695\) | 17.1464 | + | 29.6985i | 0.650401 | + | 1.12653i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.00000 | − | 15.5885i | 0.340899 | − | 0.590455i | ||||
\(698\) | 42.8661 | + | 74.2462i | 1.62250 | + | 2.81026i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8.00000 | + | 6.92820i | −0.302372 | + | 0.261861i | ||||
\(701\) | −22.0454 | −0.832644 | −0.416322 | − | 0.909217i | \(-0.636681\pi\) | ||||
−0.416322 | + | 0.909217i | \(0.636681\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.00000 | − | 6.92820i | 0.150863 | − | 0.261302i | ||||
\(704\) | −19.5959 | + | 33.9411i | −0.738549 | + | 1.27920i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.0000 | 0.451626 | ||||||||
\(707\) | −12.2474 | − | 4.24264i | −0.460613 | − | 0.159561i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.5000 | + | 42.4352i | 0.920117 | + | 1.59369i | 0.799232 | + | 0.601023i | \(0.205240\pi\) |
0.120885 | + | 0.992667i | \(0.461427\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.00000 | − | 10.3923i | −0.224860 | − | 0.389468i | ||||
\(713\) | 17.1464 | 0.642139 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −48.0000 | −1.79510 | ||||||||
\(716\) | −4.89898 | − | 8.48528i | −0.183083 | − | 0.317110i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 24.0000 | − | 41.5692i | 0.895672 | − | 1.55135i | ||||
\(719\) | −9.79796 | − | 16.9706i | −0.365402 | − | 0.632895i | 0.623438 | − | 0.781872i | \(-0.285735\pi\) |
−0.988841 | + | 0.148977i | \(0.952402\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.00000 | + | 3.46410i | −0.148968 | + | 0.129010i | ||||
\(722\) | 44.0908 | 1.64089 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14.0000 | − | 24.2487i | 0.520306 | − | 0.901196i | ||||
\(725\) | −3.67423 | + | 6.36396i | −0.136458 | + | 0.236352i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.0000 | −0.704671 | −0.352335 | − | 0.935874i | \(-0.614612\pi\) | ||||
−0.352335 | + | 0.935874i | \(0.614612\pi\) | |||||||
\(728\) | −9.79796 | − | 50.9117i | −0.363137 | − | 1.88691i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.00000 | + | 5.19615i | 0.111035 | + | 0.192318i | ||||
\(731\) | 1.22474 | − | 2.12132i | 0.0452988 | − | 0.0784599i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.50000 | − | 9.52628i | −0.203147 | − | 0.351861i | 0.746394 | − | 0.665505i | \(-0.231784\pi\) |
−0.949541 | + | 0.313644i | \(0.898450\pi\) | |||||||
\(734\) | 31.8434 | 1.17536 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.89898 | + | 8.48528i | 0.180456 | + | 0.312559i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.50000 | − | 16.4545i | 0.349463 | − | 0.605288i | −0.636691 | − | 0.771119i | \(-0.719697\pi\) |
0.986154 | + | 0.165831i | \(0.0530307\pi\) | |||||||
\(740\) | 39.1918 | + | 67.8823i | 1.44072 | + | 2.49540i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.00000 | + | 15.5885i | 0.110133 | + | 0.572270i | ||||
\(743\) | −7.34847 | −0.269589 | −0.134795 | − | 0.990874i | \(-0.543037\pi\) | ||||
−0.134795 | + | 0.990874i | \(0.543037\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.00000 | + | 5.19615i | −0.109911 | + | 0.190372i | ||||
\(746\) | 13.4722 | − | 23.3345i | 0.493252 | − | 0.854338i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −48.0000 | −1.75505 | ||||||||
\(749\) | −39.1918 | + | 33.9411i | −1.43204 | + | 1.24018i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.5000 | + | 37.2391i | 0.784546 | + | 1.35887i | 0.929270 | + | 0.369402i | \(0.120437\pi\) |
−0.144724 | + | 0.989472i | \(0.546229\pi\) | |||||||
\(752\) | 4.89898 | − | 8.48528i | 0.178647 | − | 0.309426i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −36.0000 | − | 62.3538i | −1.31104 | − | 2.27079i | ||||
\(755\) | −12.2474 | −0.445730 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 47.0000 | 1.70824 | 0.854122 | − | 0.520073i | \(-0.174095\pi\) | ||||
0.854122 | + | 0.520073i | \(0.174095\pi\) | |||||||
\(758\) | −41.6413 | − | 72.1249i | −1.51248 | − | 2.61969i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.00000 | − | 10.3923i | 0.217643 | − | 0.376969i | ||||
\(761\) | −9.79796 | − | 16.9706i | −0.355176 | − | 0.615182i | 0.631972 | − | 0.774991i | \(-0.282246\pi\) |
−0.987148 | + | 0.159809i | \(0.948912\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.50000 | − | 0.866025i | −0.0905061 | − | 0.0313522i | ||||
\(764\) | −9.79796 | −0.354478 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.0000 | − | 41.5692i | 0.867155 | − | 1.50196i | ||||
\(767\) | 19.5959 | − | 33.9411i | 0.707568 | − | 1.22554i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.00000 | 0.180305 | 0.0901523 | − | 0.995928i | \(-0.471265\pi\) | ||||
0.0901523 | + | 0.995928i | \(0.471265\pi\) | |||||||
\(770\) | 58.7878 | − | 50.9117i | 2.11856 | − | 1.83473i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −40.0000 | − | 69.2820i | −1.43963 | − | 2.49351i | ||||
\(773\) | −23.2702 | + | 40.3051i | −0.836969 | + | 1.44967i | 0.0554478 | + | 0.998462i | \(0.482341\pi\) |
−0.892417 | + | 0.451212i | \(0.850992\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.50000 | + | 6.06218i | 0.125724 | + | 0.217760i | ||||
\(776\) | 4.89898 | 0.175863 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −42.0000 | −1.50577 | ||||||||
\(779\) | −3.67423 | − | 6.36396i | −0.131643 | − | 0.228013i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −7.34847 | − | 12.7279i | −0.262781 | − | 0.455150i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 22.0000 | + | 17.3205i | 0.785714 | + | 0.618590i | ||||
\(785\) | −48.9898 | −1.74852 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.50000 | − | 6.06218i | 0.124762 | − | 0.216093i | −0.796878 | − | 0.604140i | \(-0.793517\pi\) |
0.921640 | + | 0.388047i | \(0.126850\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −24.0000 | −0.853882 | ||||||||
\(791\) | −7.34847 | − | 38.1838i | −0.261281 | − | 1.35766i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.0000 | + | 17.3205i | 0.355110 | + | 0.615069i | ||||
\(794\) | 20.8207 | − | 36.0624i | 0.738898 | − | 1.27981i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 38.0000 | + | 65.8179i | 1.34687 | + | 2.33285i | ||||
\(797\) | 14.6969 | 0.520592 | 0.260296 | − | 0.965529i | \(-0.416180\pi\) | ||||
0.260296 | + | 0.965529i | \(0.416180\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.00000 | −0.212265 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −30.0000 | + | 51.9615i | −1.05934 | + | 1.83483i | ||||
\(803\) | −2.44949 | − | 4.24264i | −0.0864406 | − | 0.149720i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.0000 | + | 5.19615i | 0.528681 | + | 0.183140i | ||||
\(806\) | −68.5857 | −2.41583 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −12.0000 | + | 20.7846i | −0.422159 | + | 0.731200i | ||||
\(809\) | −12.2474 | + | 21.2132i | −0.430597 | + | 0.745817i | −0.996925 | − | 0.0783638i | \(-0.975030\pi\) |
0.566327 | + | 0.824180i | \(0.308364\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.00000 | 0.0702295 | 0.0351147 | − | 0.999383i | \(-0.488820\pi\) | ||||
0.0351147 | + | 0.999383i | \(0.488820\pi\) | |||||||
\(812\) | 73.4847 | + | 25.4558i | 2.57881 | + | 0.893325i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −48.0000 | − | 83.1384i | −1.68240 | − | 2.91400i | ||||
\(815\) | −1.22474 | + | 2.12132i | −0.0429009 | + | 0.0743066i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.500000 | − | 0.866025i | −0.0174928 | − | 0.0302984i | ||||
\(818\) | −48.9898 | −1.71289 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 72.0000 | 2.51435 | ||||||||
\(821\) | −9.79796 | − | 16.9706i | −0.341951 | − | 0.592277i | 0.642844 | − | 0.765997i | \(-0.277754\pi\) |
−0.984795 | + | 0.173721i | \(0.944421\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.5000 | − | 21.6506i | 0.435723 | − | 0.754694i | −0.561632 | − | 0.827387i | \(-0.689826\pi\) |
0.997354 | + | 0.0726937i | \(0.0231595\pi\) | |||||||
\(824\) | 4.89898 | + | 8.48528i | 0.170664 | + | 0.295599i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.0000 | + | 62.3538i | 0.417533 | + | 2.16957i | ||||
\(827\) | −44.0908 | −1.53319 | −0.766594 | − | 0.642132i | \(-0.778050\pi\) | ||||
−0.766594 | + | 0.642132i | \(0.778050\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.5000 | − | 47.6314i | 0.955114 | − | 1.65431i | 0.221009 | − | 0.975272i | \(-0.429065\pi\) |
0.734106 | − | 0.679035i | \(-0.237602\pi\) | |||||||
\(830\) | 44.0908 | − | 76.3675i | 1.53041 | − | 2.65076i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 32.0000 | 1.10940 | ||||||||
\(833\) | 2.44949 | − | 16.9706i | 0.0848698 | − | 0.587995i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.0000 | + | 31.1769i | 0.622916 | + | 1.07892i | ||||
\(836\) | −9.79796 | + | 16.9706i | −0.338869 | + | 0.586939i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −9.00000 | − | 15.5885i | −0.310900 | − | 0.538494i | ||||
\(839\) | −14.6969 | −0.507395 | −0.253697 | − | 0.967284i | \(-0.581647\pi\) | ||||
−0.253697 | + | 0.967284i | \(0.581647\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.0000 | 0.862069 | ||||||||
\(842\) | 42.8661 | + | 74.2462i | 1.47726 | + | 2.55869i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.0000 | + | 17.3205i | −0.344214 | + | 0.596196i | ||||
\(845\) | 3.67423 | + | 6.36396i | 0.126398 | + | 0.218927i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −26.0000 | + | 22.5167i | −0.893371 | + | 0.773682i | ||||
\(848\) | 9.79796 | 0.336463 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.00000 | − | 5.19615i | 0.102899 | − | 0.178227i | ||||
\(851\) | 9.79796 | − | 16.9706i | 0.335870 | − | 0.581743i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.0000 | −0.650548 | −0.325274 | − | 0.945620i | \(-0.605456\pi\) | ||||
−0.325274 | + | 0.945620i | \(0.605456\pi\) | |||||||
\(854\) | −30.6186 | − | 10.6066i | −1.04775 | − | 0.362950i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 48.0000 | + | 83.1384i | 1.64061 | + | 2.84161i | ||||
\(857\) | −19.5959 | + | 33.9411i | −0.669384 | + | 1.15941i | 0.308693 | + | 0.951162i | \(0.400108\pi\) |
−0.978077 | + | 0.208245i | \(0.933225\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.5000 | + | 21.6506i | 0.426494 | + | 0.738710i | 0.996559 | − | 0.0828900i | \(-0.0264150\pi\) |
−0.570064 | + | 0.821600i | \(0.693082\pi\) | |||||||
\(860\) | 9.79796 | 0.334108 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 48.0000 | 1.63489 | ||||||||
\(863\) | 1.22474 | + | 2.12132i | 0.0416908 | + | 0.0722106i | 0.886118 | − | 0.463460i | \(-0.153392\pi\) |
−0.844427 | + | 0.535671i | \(0.820059\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.00000 | + | 5.19615i | −0.102003 | + | 0.176674i | ||||
\(866\) | −8.57321 | − | 14.8492i | −0.291330 | − | 0.504598i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 56.0000 | − | 48.4974i | 1.90076 | − | 1.64611i | ||||
\(869\) | 19.5959 | 0.664746 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.00000 | − | 6.92820i | 0.135535 | − | 0.234753i | ||||
\(872\) | −2.44949 | + | 4.24264i | −0.0829502 | + | 0.143674i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.00000 | −0.202953 | ||||||||
\(875\) | −4.89898 | − | 25.4558i | −0.165616 | − | 0.860565i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.5000 | − | 40.7032i | −0.793539 | − | 1.37445i | −0.923763 | − | 0.382965i | \(-0.874903\pi\) |
0.130224 | − | 0.991485i | \(-0.458430\pi\) | |||||||
\(878\) | 17.1464 | − | 29.6985i | 0.578664 | − | 1.00228i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −24.0000 | − | 41.5692i | −0.809040 | − | 1.40130i | ||||
\(881\) | 22.0454 | 0.742729 | 0.371364 | − | 0.928487i | \(-0.378890\pi\) | ||||
0.371364 | + | 0.928487i | \(0.378890\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.00000 | −0.235569 | −0.117784 | − | 0.993039i | \(-0.537579\pi\) | ||||
−0.117784 | + | 0.993039i | \(0.537579\pi\) | |||||||
\(884\) | 19.5959 | + | 33.9411i | 0.659082 | + | 1.14156i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.00000 | + | 5.19615i | −0.100787 | + | 0.174568i | ||||
\(887\) | −9.79796 | − | 16.9706i | −0.328983 | − | 0.569816i | 0.653327 | − | 0.757076i | \(-0.273373\pi\) |
−0.982310 | + | 0.187260i | \(0.940039\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.50000 | − | 28.5788i | −0.184464 | − | 0.958503i | ||||
\(890\) | −14.6969 | −0.492642 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −52.0000 | + | 90.0666i | −1.74109 | + | 3.01565i | ||||
\(893\) | −1.22474 | + | 2.12132i | −0.0409845 | + | 0.0709873i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.00000 | −0.200558 | ||||||||
\(896\) | −39.1918 | + | 33.9411i | −1.30931 | + | 1.13389i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −27.0000 | − | 46.7654i | −0.901002 | − | 1.56058i | ||||
\(899\) | 25.7196 | − | 44.5477i | 0.857798 | − | 1.48575i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.00000 | − | 5.19615i | −0.0999445 | − | 0.173109i | ||||
\(902\) | −88.1816 | −2.93613 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −72.0000 | −2.39468 | ||||||||
\(905\) | −8.57321 | − | 14.8492i | −0.284983 | − | 0.493606i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.0000 | + | 27.7128i | −0.531271 | + | 0.920189i | 0.468063 | + | 0.883695i | \(0.344952\pi\) |
−0.999334 | + | 0.0364935i | \(0.988381\pi\) | |||||||
\(908\) | −34.2929 | − | 59.3970i | −1.13805 | − | 1.97116i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −60.0000 | − | 20.7846i | −1.98898 | − | 0.689003i | ||||
\(911\) | 7.34847 | 0.243466 | 0.121733 | − | 0.992563i | \(-0.461155\pi\) | ||||
0.121733 | + | 0.992563i | \(0.461155\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −36.0000 | + | 62.3538i | −1.19143 | + | 2.06361i | ||||
\(914\) | 28.1691 | − | 48.7904i | 0.931752 | − | 1.61384i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −28.0000 | −0.925146 | ||||||||
\(917\) | 4.89898 | − | 4.24264i | 0.161779 | − | 0.140104i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.500000 | + | 0.866025i | 0.0164935 | + | 0.0285675i | 0.874154 | − | 0.485648i | \(-0.161416\pi\) |
−0.857661 | + | 0.514216i | \(0.828083\pi\) | |||||||
\(920\) | 14.6969 | − | 25.4558i | 0.484544 | − | 0.839254i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 36.0000 | + | 62.3538i | 1.18560 | + | 2.05351i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.00000 | 0.263038 | ||||||||
\(926\) | 28.1691 | + | 48.7904i | 0.925695 | + | 1.60335i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.2702 | + | 40.3051i | 0.763469 | + | 1.32237i | 0.941052 | + | 0.338261i | \(0.109839\pi\) |
−0.177583 | + | 0.984106i | \(0.556828\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.50000 | − | 4.33013i | −0.180255 | − | 0.141914i | ||||
\(932\) | −9.79796 | −0.320943 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −30.0000 | + | 51.9615i | −0.981630 | + | 1.70023i | ||||
\(935\) | −14.6969 | + | 25.4558i | −0.480641 | + | 0.832495i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.0000 | −0.522697 | −0.261349 | − | 0.965244i | \(-0.584167\pi\) | ||||
−0.261349 | + | 0.965244i | \(0.584167\pi\) | |||||||
\(938\) | 2.44949 | + | 12.7279i | 0.0799787 | + | 0.415581i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −12.0000 | − | 20.7846i | −0.391397 | − | 0.677919i | ||||
\(941\) | −4.89898 | + | 8.48528i | −0.159702 | + | 0.276612i | −0.934761 | − | 0.355276i | \(-0.884387\pi\) |
0.775059 | + | 0.631889i | \(0.217720\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.00000 | − | 15.5885i | −0.293080 | − | 0.507630i | ||||
\(944\) | 39.1918 | 1.27559 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.0000 | −0.390154 | ||||||||
\(947\) | 23.2702 | + | 40.3051i | 0.756178 | + | 1.30974i | 0.944786 | + | 0.327687i | \(0.106269\pi\) |
−0.188608 | + | 0.982052i | \(0.560398\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.00000 | + | 3.46410i | −0.0649227 | + | 0.112449i | ||||
\(950\) | −1.22474 | − | 2.12132i | −0.0397360 | − | 0.0688247i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −30.0000 | − | 10.3923i | −0.972306 | − | 0.336817i | ||||
\(953\) | 22.0454 | 0.714121 | 0.357060 | − | 0.934081i | \(-0.383779\pi\) | ||||
0.357060 | + | 0.934081i | \(0.383779\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.00000 | + | 5.19615i | −0.0970777 | + | 0.168144i | ||||
\(956\) | 14.6969 | − | 25.4558i | 0.475333 | − | 0.823301i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 66.0000 | 2.13236 | ||||||||
\(959\) | 42.8661 | + | 14.8492i | 1.38422 | + | 0.479507i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.00000 | − | 15.5885i | −0.290323 | − | 0.502853i | ||||
\(962\) | −39.1918 | + | 67.8823i | −1.26360 | + | 2.18861i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 26.0000 | + | 45.0333i | 0.837404 | + | 1.45043i | ||||
\(965\) | −48.9898 | −1.57704 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.0000 | −0.707472 | −0.353736 | − | 0.935345i | \(-0.615089\pi\) | ||||
−0.353736 | + | 0.935345i | \(0.615089\pi\) | |||||||
\(968\) | 31.8434 | + | 55.1543i | 1.02348 | + | 1.77273i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.00000 | − | 5.19615i | 0.0963242 | − | 0.166838i | ||||
\(971\) | −20.8207 | − | 36.0624i | −0.668167 | − | 1.15730i | −0.978416 | − | 0.206644i | \(-0.933746\pi\) |
0.310249 | − | 0.950655i | \(-0.399587\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.00000 | − | 36.3731i | −0.224410 | − | 1.16607i | ||||
\(974\) | 46.5403 | 1.49125 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.0000 | + | 17.3205i | −0.320092 | + | 0.554416i | ||||
\(977\) | −4.89898 | + | 8.48528i | −0.156732 | + | 0.271468i | −0.933688 | − | 0.358086i | \(-0.883429\pi\) |
0.776956 | + | 0.629555i | \(0.216763\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.0000 | 0.383522 | ||||||||
\(980\) | 63.6867 | − | 25.4558i | 2.03440 | − | 0.813157i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 18.0000 | + | 31.1769i | 0.574403 | + | 0.994895i | ||||
\(983\) | −19.5959 | + | 33.9411i | −0.625013 | + | 1.08255i | 0.363526 | + | 0.931584i | \(0.381573\pi\) |
−0.988538 | + | 0.150970i | \(0.951760\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −44.0908 | −1.40414 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 16.0000 | 0.509028 | ||||||||
\(989\) | −1.22474 | − | 2.12132i | −0.0389446 | − | 0.0674541i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.00000 | − | 8.66025i | 0.158830 | − | 0.275102i | −0.775617 | − | 0.631204i | \(-0.782561\pi\) |
0.934447 | + | 0.356102i | \(0.115894\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 46.5403 | 1.47543 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.5000 | + | 35.5070i | −0.649242 | + | 1.12452i | 0.334063 | + | 0.942551i | \(0.391580\pi\) |
−0.983304 | + | 0.181968i | \(0.941753\pi\) | |||||||
\(998\) | −8.57321 | + | 14.8492i | −0.271380 | + | 0.470045i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 189.2.e.d.109.2 | yes | 4 | |
3.2 | odd | 2 | inner | 189.2.e.d.109.1 | ✓ | 4 | |
7.2 | even | 3 | inner | 189.2.e.d.163.2 | yes | 4 | |
7.3 | odd | 6 | 1323.2.a.u.1.1 | 2 | |||
7.4 | even | 3 | 1323.2.a.v.1.1 | 2 | |||
9.2 | odd | 6 | 567.2.g.g.109.1 | 4 | |||
9.4 | even | 3 | 567.2.h.g.298.1 | 4 | |||
9.5 | odd | 6 | 567.2.h.g.298.2 | 4 | |||
9.7 | even | 3 | 567.2.g.g.109.2 | 4 | |||
21.2 | odd | 6 | inner | 189.2.e.d.163.1 | yes | 4 | |
21.11 | odd | 6 | 1323.2.a.v.1.2 | 2 | |||
21.17 | even | 6 | 1323.2.a.u.1.2 | 2 | |||
63.2 | odd | 6 | 567.2.h.g.352.2 | 4 | |||
63.16 | even | 3 | 567.2.h.g.352.1 | 4 | |||
63.23 | odd | 6 | 567.2.g.g.541.1 | 4 | |||
63.58 | even | 3 | 567.2.g.g.541.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
189.2.e.d.109.1 | ✓ | 4 | 3.2 | odd | 2 | inner | |
189.2.e.d.109.2 | yes | 4 | 1.1 | even | 1 | trivial | |
189.2.e.d.163.1 | yes | 4 | 21.2 | odd | 6 | inner | |
189.2.e.d.163.2 | yes | 4 | 7.2 | even | 3 | inner | |
567.2.g.g.109.1 | 4 | 9.2 | odd | 6 | |||
567.2.g.g.109.2 | 4 | 9.7 | even | 3 | |||
567.2.g.g.541.1 | 4 | 63.23 | odd | 6 | |||
567.2.g.g.541.2 | 4 | 63.58 | even | 3 | |||
567.2.h.g.298.1 | 4 | 9.4 | even | 3 | |||
567.2.h.g.298.2 | 4 | 9.5 | odd | 6 | |||
567.2.h.g.352.1 | 4 | 63.16 | even | 3 | |||
567.2.h.g.352.2 | 4 | 63.2 | odd | 6 | |||
1323.2.a.u.1.1 | 2 | 7.3 | odd | 6 | |||
1323.2.a.u.1.2 | 2 | 21.17 | even | 6 | |||
1323.2.a.v.1.1 | 2 | 7.4 | even | 3 | |||
1323.2.a.v.1.2 | 2 | 21.11 | odd | 6 |