Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [93,2,Mod(26,93)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(93, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("93.26");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 93 = 3 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 93.g (of order \(6\), 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: | \(0.742608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 68.2 | ||
Root | \(-1.18614 - 1.26217i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 93.68 |
Dual form | 93.2.g.e.26.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/93\mathbb{Z}\right)^\times\).
\(n\) | \(32\) | \(34\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.52434i | 1.78498i | 0.451071 | + | 0.892488i | \(0.351042\pi\) | ||||
−0.451071 | + | 0.892488i | \(0.648958\pi\) | |||||||
\(3\) | 1.68614 | + | 0.396143i | 0.973494 | + | 0.228714i | ||||
\(4\) | −4.37228 | −2.18614 | ||||||||
\(5\) | −2.18614 | − | 1.26217i | −0.977672 | − | 0.564459i | −0.0761054 | − | 0.997100i | \(-0.524249\pi\) |
−0.901566 | + | 0.432641i | \(0.857582\pi\) | |||||||
\(6\) | −1.00000 | + | 4.25639i | −0.408248 | + | 1.73766i | ||||
\(7\) | 1.18614 | + | 2.05446i | 0.448319 | + | 0.776511i | 0.998277 | − | 0.0586811i | \(-0.0186895\pi\) |
−0.549958 | + | 0.835192i | \(0.685356\pi\) | |||||||
\(8\) | − | 5.98844i | − | 2.11723i | ||||||
\(9\) | 2.68614 | + | 1.33591i | 0.895380 | + | 0.445302i | ||||
\(10\) | 3.18614 | − | 5.51856i | 1.00755 | − | 1.74512i | ||||
\(11\) | 2.18614 | − | 3.78651i | 0.659146 | − | 1.14167i | −0.321691 | − | 0.946845i | \(-0.604251\pi\) |
0.980837 | − | 0.194830i | \(-0.0624155\pi\) | |||||||
\(12\) | −7.37228 | − | 1.73205i | −2.12819 | − | 0.500000i | ||||
\(13\) | 1.50000 | + | 0.866025i | 0.416025 | + | 0.240192i | 0.693375 | − | 0.720577i | \(-0.256123\pi\) |
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | −5.18614 | + | 2.99422i | −1.38605 | + | 0.800239i | ||||
\(15\) | −3.18614 | − | 2.99422i | −0.822658 | − | 0.773104i | ||||
\(16\) | 6.37228 | 1.59307 | ||||||||
\(17\) | 0.813859 | + | 1.40965i | 0.197390 | + | 0.341889i | 0.947681 | − | 0.319218i | \(-0.103420\pi\) |
−0.750291 | + | 0.661107i | \(0.770087\pi\) | |||||||
\(18\) | −3.37228 | + | 6.78073i | −0.794854 | + | 1.59823i | ||||
\(19\) | −3.87228 | − | 6.70699i | −0.888362 | − | 1.53869i | −0.841811 | − | 0.539773i | \(-0.818510\pi\) |
−0.0465514 | − | 0.998916i | \(-0.514823\pi\) | |||||||
\(20\) | 9.55842 | + | 5.51856i | 2.13733 | + | 1.23399i | ||||
\(21\) | 1.18614 | + | 3.93398i | 0.258837 | + | 0.858466i | ||||
\(22\) | 9.55842 | + | 5.51856i | 2.03786 | + | 1.17656i | ||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 2.37228 | − | 10.0974i | 0.484240 | − | 2.06111i | ||||
\(25\) | 0.686141 | + | 1.18843i | 0.137228 | + | 0.237686i | ||||
\(26\) | −2.18614 | + | 3.78651i | −0.428737 | + | 0.742595i | ||||
\(27\) | 4.00000 | + | 3.31662i | 0.769800 | + | 0.638285i | ||||
\(28\) | −5.18614 | − | 8.98266i | −0.980088 | − | 1.69756i | ||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 7.55842 | − | 8.04290i | 1.37997 | − | 1.46843i | ||||
\(31\) | −2.00000 | + | 5.19615i | −0.359211 | + | 0.933257i | ||||
\(32\) | 4.10891i | 0.726360i | ||||||||
\(33\) | 5.18614 | − | 5.51856i | 0.902791 | − | 0.960658i | ||||
\(34\) | −3.55842 | + | 2.05446i | −0.610264 | + | 0.352336i | ||||
\(35\) | − | 5.98844i | − | 1.01223i | ||||||
\(36\) | −11.7446 | − | 5.84096i | −1.95743 | − | 0.973494i | ||||
\(37\) | 1.50000 | − | 0.866025i | 0.246598 | − | 0.142374i | −0.371607 | − | 0.928390i | \(-0.621193\pi\) |
0.618206 | + | 0.786016i | \(0.287860\pi\) | |||||||
\(38\) | 16.9307 | − | 9.77495i | 2.74652 | − | 1.58571i | ||||
\(39\) | 2.18614 | + | 2.05446i | 0.350063 | + | 0.328976i | ||||
\(40\) | −7.55842 | + | 13.0916i | −1.19509 | + | 2.06996i | ||||
\(41\) | −2.18614 | − | 1.26217i | −0.341418 | − | 0.197118i | 0.319481 | − | 0.947593i | \(-0.396491\pi\) |
−0.660899 | + | 0.750475i | \(0.729825\pi\) | |||||||
\(42\) | −9.93070 | + | 2.99422i | −1.53234 | + | 0.462018i | ||||
\(43\) | −7.50000 | + | 4.33013i | −1.14374 | + | 0.660338i | −0.947354 | − | 0.320189i | \(-0.896254\pi\) |
−0.196385 | + | 0.980527i | \(0.562920\pi\) | |||||||
\(44\) | −9.55842 | + | 16.5557i | −1.44099 | + | 2.49586i | ||||
\(45\) | −4.18614 | − | 6.31084i | −0.624033 | − | 0.940765i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.63325i | 0.967559i | 0.875190 | + | 0.483779i | \(0.160736\pi\) | ||||
−0.875190 | + | 0.483779i | \(0.839264\pi\) | |||||||
\(48\) | 10.7446 | + | 2.52434i | 1.55084 | + | 0.364357i | ||||
\(49\) | 0.686141 | − | 1.18843i | 0.0980201 | − | 0.169776i | ||||
\(50\) | −3.00000 | + | 1.73205i | −0.424264 | + | 0.244949i | ||||
\(51\) | 0.813859 | + | 2.69927i | 0.113963 | + | 0.377973i | ||||
\(52\) | −6.55842 | − | 3.78651i | −0.909489 | − | 0.525094i | ||||
\(53\) | 2.18614 | − | 3.78651i | 0.300290 | − | 0.520117i | −0.675912 | − | 0.736982i | \(-0.736250\pi\) |
0.976201 | + | 0.216866i | \(0.0695834\pi\) | |||||||
\(54\) | −8.37228 | + | 10.0974i | −1.13932 | + | 1.37408i | ||||
\(55\) | −9.55842 | + | 5.51856i | −1.28886 | + | 0.744122i | ||||
\(56\) | 12.3030 | − | 7.10313i | 1.64406 | − | 0.949196i | ||||
\(57\) | −3.87228 | − | 12.8429i | −0.512896 | − | 1.70108i | ||||
\(58\) | − | 15.1460i | − | 1.98877i | ||||||
\(59\) | −1.93070 | + | 1.11469i | −0.251356 | + | 0.145121i | −0.620385 | − | 0.784297i | \(-0.713024\pi\) |
0.369029 | + | 0.929418i | \(0.379690\pi\) | |||||||
\(60\) | 13.9307 | + | 13.0916i | 1.79845 | + | 1.69011i | ||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | −13.1168 | − | 5.04868i | −1.66584 | − | 0.641182i | ||||
\(63\) | 0.441578 | + | 7.10313i | 0.0556336 | + | 0.894910i | ||||
\(64\) | 2.37228 | 0.296535 | ||||||||
\(65\) | −2.18614 | − | 3.78651i | −0.271157 | − | 0.469658i | ||||
\(66\) | 13.9307 | + | 13.0916i | 1.71475 | + | 1.61146i | ||||
\(67\) | 5.55842 | − | 9.62747i | 0.679069 | − | 1.17618i | −0.296192 | − | 0.955128i | \(-0.595717\pi\) |
0.975262 | − | 0.221054i | \(-0.0709498\pi\) | |||||||
\(68\) | −3.55842 | − | 6.16337i | −0.431522 | − | 0.747418i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 15.1168 | 1.80681 | ||||||||
\(71\) | 1.93070 | + | 1.11469i | 0.229132 | + | 0.132290i | 0.610172 | − | 0.792269i | \(-0.291100\pi\) |
−0.381039 | + | 0.924559i | \(0.624434\pi\) | |||||||
\(72\) | 8.00000 | − | 16.0858i | 0.942809 | − | 1.89573i | ||||
\(73\) | 5.61684 | + | 3.24289i | 0.657402 | + | 0.379551i | 0.791286 | − | 0.611446i | \(-0.209412\pi\) |
−0.133884 | + | 0.990997i | \(0.542745\pi\) | |||||||
\(74\) | 2.18614 | + | 3.78651i | 0.254134 | + | 0.440172i | ||||
\(75\) | 0.686141 | + | 2.27567i | 0.0792287 | + | 0.262772i | ||||
\(76\) | 16.9307 | + | 29.3248i | 1.94208 | + | 3.36379i | ||||
\(77\) | 10.3723 | 1.18203 | ||||||||
\(78\) | −5.18614 | + | 5.51856i | −0.587215 | + | 0.624854i | ||||
\(79\) | −0.558422 | + | 0.322405i | −0.0628274 | + | 0.0362734i | −0.531085 | − | 0.847319i | \(-0.678215\pi\) |
0.468257 | + | 0.883592i | \(0.344882\pi\) | |||||||
\(80\) | −13.9307 | − | 8.04290i | −1.55750 | − | 0.899223i | ||||
\(81\) | 5.43070 | + | 7.17687i | 0.603411 | + | 0.797430i | ||||
\(82\) | 3.18614 | − | 5.51856i | 0.351850 | − | 0.609423i | ||||
\(83\) | −3.81386 | + | 6.60580i | −0.418625 | + | 0.725081i | −0.995801 | − | 0.0915392i | \(-0.970821\pi\) |
0.577176 | + | 0.816620i | \(0.304155\pi\) | |||||||
\(84\) | −5.18614 | − | 17.2005i | −0.565854 | − | 1.87673i | ||||
\(85\) | − | 4.10891i | − | 0.445674i | ||||||
\(86\) | −10.9307 | − | 18.9325i | −1.17869 | − | 2.04155i | ||||
\(87\) | −10.1168 | − | 2.37686i | −1.08464 | − | 0.254826i | ||||
\(88\) | −22.6753 | − | 13.0916i | −2.41719 | − | 1.39557i | ||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | 15.9307 | − | 10.5672i | 1.67924 | − | 1.11388i | ||||
\(91\) | 4.10891i | 0.430731i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.43070 | + | 7.96916i | −0.563138 | + | 0.826363i | ||||
\(94\) | −16.7446 | −1.72707 | ||||||||
\(95\) | 19.5499i | 2.00578i | ||||||||
\(96\) | −1.62772 | + | 6.92820i | −0.166128 | + | 0.707107i | ||||
\(97\) | −5.37228 | −0.545473 | −0.272736 | − | 0.962089i | \(-0.587929\pi\) | ||||
−0.272736 | + | 0.962089i | \(0.587929\pi\) | |||||||
\(98\) | 3.00000 | + | 1.73205i | 0.303046 | + | 0.174964i | ||||
\(99\) | 10.9307 | − | 7.25061i | 1.09858 | − | 0.728714i | ||||
\(100\) | −3.00000 | − | 5.19615i | −0.300000 | − | 0.519615i | ||||
\(101\) | 5.34363i | 0.531711i | 0.964013 | + | 0.265855i | \(0.0856544\pi\) | ||||
−0.964013 | + | 0.265855i | \(0.914346\pi\) | |||||||
\(102\) | −6.81386 | + | 2.05446i | −0.674673 | + | 0.203421i | ||||
\(103\) | −6.87228 | + | 11.9031i | −0.677146 | + | 1.17285i | 0.298691 | + | 0.954350i | \(0.403450\pi\) |
−0.975837 | + | 0.218501i | \(0.929883\pi\) | |||||||
\(104\) | 5.18614 | − | 8.98266i | 0.508543 | − | 0.880822i | ||||
\(105\) | 2.37228 | − | 10.0974i | 0.231511 | − | 0.985401i | ||||
\(106\) | 9.55842 | + | 5.51856i | 0.928396 | + | 0.536010i | ||||
\(107\) | 2.18614 | − | 1.26217i | 0.211342 | − | 0.122018i | −0.390593 | − | 0.920564i | \(-0.627730\pi\) |
0.601935 | + | 0.798545i | \(0.294397\pi\) | |||||||
\(108\) | −17.4891 | − | 14.5012i | −1.68289 | − | 1.39538i | ||||
\(109\) | 6.62772 | 0.634820 | 0.317410 | − | 0.948288i | \(-0.397187\pi\) | ||||
0.317410 | + | 0.948288i | \(0.397187\pi\) | |||||||
\(110\) | −13.9307 | − | 24.1287i | −1.32824 | − | 2.30058i | ||||
\(111\) | 2.87228 | − | 0.866025i | 0.272625 | − | 0.0821995i | ||||
\(112\) | 7.55842 | + | 13.0916i | 0.714204 | + | 1.23704i | ||||
\(113\) | 1.93070 | + | 1.11469i | 0.181625 | + | 0.104861i | 0.588056 | − | 0.808820i | \(-0.299893\pi\) |
−0.406431 | + | 0.913682i | \(0.633227\pi\) | |||||||
\(114\) | 32.4198 | − | 9.77495i | 3.03640 | − | 0.915508i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 26.2337 | 2.43574 | ||||||||
\(117\) | 2.87228 | + | 4.33013i | 0.265543 | + | 0.400320i | ||||
\(118\) | −2.81386 | − | 4.87375i | −0.259037 | − | 0.448665i | ||||
\(119\) | −1.93070 | + | 3.34408i | −0.176987 | + | 0.306551i | ||||
\(120\) | −17.9307 | + | 19.0800i | −1.63684 | + | 1.74176i | ||||
\(121\) | −4.05842 | − | 7.02939i | −0.368947 | − | 0.639036i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.18614 | − | 2.99422i | −0.287285 | − | 0.269980i | ||||
\(124\) | 8.74456 | − | 22.7190i | 0.785285 | − | 2.04023i | ||||
\(125\) | 9.15759i | 0.819080i | ||||||||
\(126\) | −17.9307 | + | 1.11469i | −1.59739 | + | 0.0993047i | ||||
\(127\) | −11.6168 | + | 6.70699i | −1.03083 | + | 0.595149i | −0.917222 | − | 0.398377i | \(-0.869574\pi\) |
−0.113606 | + | 0.993526i | \(0.536240\pi\) | |||||||
\(128\) | 14.2063i | 1.25567i | ||||||||
\(129\) | −14.3614 | + | 4.33013i | −1.26445 | + | 0.381246i | ||||
\(130\) | 9.55842 | − | 5.51856i | 0.838329 | − | 0.484010i | ||||
\(131\) | −9.81386 | + | 5.66603i | −0.857441 | + | 0.495044i | −0.863154 | − | 0.504940i | \(-0.831515\pi\) |
0.00571360 | + | 0.999984i | \(0.498181\pi\) | |||||||
\(132\) | −22.6753 | + | 24.1287i | −1.97363 | + | 2.10013i | ||||
\(133\) | 9.18614 | − | 15.9109i | 0.796539 | − | 1.37965i | ||||
\(134\) | 24.3030 | + | 14.0313i | 2.09946 | + | 1.21212i | ||||
\(135\) | −4.55842 | − | 12.2993i | −0.392326 | − | 1.05855i | ||||
\(136\) | 8.44158 | − | 4.87375i | 0.723859 | − | 0.417920i | ||||
\(137\) | 8.18614 | − | 14.1788i | 0.699389 | − | 1.21138i | −0.269289 | − | 0.963059i | \(-0.586789\pi\) |
0.968678 | − | 0.248318i | \(-0.0798779\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.3923i | 0.881464i | 0.897639 | + | 0.440732i | \(0.145281\pi\) | ||||
−0.897639 | + | 0.440732i | \(0.854719\pi\) | |||||||
\(140\) | 26.1831i | 2.21288i | ||||||||
\(141\) | −2.62772 | + | 11.1846i | −0.221294 | + | 0.941913i | ||||
\(142\) | −2.81386 | + | 4.87375i | −0.236134 | + | 0.408996i | ||||
\(143\) | 6.55842 | − | 3.78651i | 0.548443 | − | 0.316644i | ||||
\(144\) | 17.1168 | + | 8.51278i | 1.42640 | + | 0.709398i | ||||
\(145\) | 13.1168 | + | 7.57301i | 1.08929 | + | 0.628905i | ||||
\(146\) | −8.18614 | + | 14.1788i | −0.677490 | + | 1.17345i | ||||
\(147\) | 1.62772 | − | 1.73205i | 0.134252 | − | 0.142857i | ||||
\(148\) | −6.55842 | + | 3.78651i | −0.539099 | + | 0.311249i | ||||
\(149\) | −0.813859 | + | 0.469882i | −0.0666740 | + | 0.0384942i | −0.532966 | − | 0.846136i | \(-0.678923\pi\) |
0.466292 | + | 0.884631i | \(0.345589\pi\) | |||||||
\(150\) | −5.74456 | + | 1.73205i | −0.469042 | + | 0.141421i | ||||
\(151\) | − | 23.1615i | − | 1.88485i | −0.334412 | − | 0.942427i | \(-0.608538\pi\) | ||
0.334412 | − | 0.942427i | \(-0.391462\pi\) | |||||||
\(152\) | −40.1644 | + | 23.1889i | −3.25776 | + | 1.88087i | ||||
\(153\) | 0.302985 | + | 4.87375i | 0.0244949 | + | 0.394019i | ||||
\(154\) | 26.1831i | 2.10990i | ||||||||
\(155\) | 10.9307 | − | 8.83518i | 0.877975 | − | 0.709659i | ||||
\(156\) | −9.55842 | − | 8.98266i | −0.765286 | − | 0.719188i | ||||
\(157\) | 6.62772 | 0.528950 | 0.264475 | − | 0.964393i | \(-0.414801\pi\) | ||||
0.264475 | + | 0.964393i | \(0.414801\pi\) | |||||||
\(158\) | −0.813859 | − | 1.40965i | −0.0647472 | − | 0.112145i | ||||
\(159\) | 5.18614 | − | 5.51856i | 0.411288 | − | 0.437650i | ||||
\(160\) | 5.18614 | − | 8.98266i | 0.410000 | − | 0.710142i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −18.1168 | + | 13.7089i | −1.42339 | + | 1.07708i | ||||
\(163\) | 0.627719 | 0.0491667 | 0.0245834 | − | 0.999698i | \(-0.492174\pi\) | ||||
0.0245834 | + | 0.999698i | \(0.492174\pi\) | |||||||
\(164\) | 9.55842 | + | 5.51856i | 0.746387 | + | 0.430927i | ||||
\(165\) | −18.3030 | + | 5.51856i | −1.42489 | + | 0.429619i | ||||
\(166\) | −16.6753 | − | 9.62747i | −1.29425 | − | 0.747237i | ||||
\(167\) | −8.18614 | − | 14.1788i | −0.633463 | − | 1.09719i | −0.986839 | − | 0.161708i | \(-0.948300\pi\) |
0.353376 | − | 0.935481i | \(-0.385034\pi\) | |||||||
\(168\) | 23.5584 | − | 7.10313i | 1.81757 | − | 0.548018i | ||||
\(169\) | −5.00000 | − | 8.66025i | −0.384615 | − | 0.666173i | ||||
\(170\) | 10.3723 | 0.795518 | ||||||||
\(171\) | −1.44158 | − | 23.1889i | −0.110240 | − | 1.77330i | ||||
\(172\) | 32.7921 | − | 18.9325i | 2.50037 | − | 1.44359i | ||||
\(173\) | −12.3030 | − | 7.10313i | −0.935379 | − | 0.540041i | −0.0468700 | − | 0.998901i | \(-0.514925\pi\) |
−0.888509 | + | 0.458860i | \(0.848258\pi\) | |||||||
\(174\) | 6.00000 | − | 25.5383i | 0.454859 | − | 1.93606i | ||||
\(175\) | −1.62772 | + | 2.81929i | −0.123044 | + | 0.213118i | ||||
\(176\) | 13.9307 | − | 24.1287i | 1.05007 | − | 1.81877i | ||||
\(177\) | −3.69702 | + | 1.11469i | −0.277885 | + | 0.0837854i | ||||
\(178\) | 15.1460i | 1.13524i | ||||||||
\(179\) | 3.81386 | + | 6.60580i | 0.285061 | + | 0.493741i | 0.972624 | − | 0.232384i | \(-0.0746527\pi\) |
−0.687563 | + | 0.726125i | \(0.741319\pi\) | |||||||
\(180\) | 18.3030 | + | 27.5928i | 1.36422 | + | 2.05664i | ||||
\(181\) | 5.61684 | + | 3.24289i | 0.417497 | + | 0.241042i | 0.694006 | − | 0.719969i | \(-0.255844\pi\) |
−0.276509 | + | 0.961011i | \(0.589178\pi\) | |||||||
\(182\) | −10.3723 | −0.768845 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.37228 | −0.321457 | ||||||||
\(186\) | −20.1168 | − | 13.7089i | −1.47504 | − | 1.00519i | ||||
\(187\) | 7.11684 | 0.520435 | ||||||||
\(188\) | − | 29.0024i | − | 2.11522i | ||||||
\(189\) | −2.06930 | + | 12.1518i | −0.150519 | + | 0.883914i | ||||
\(190\) | −49.3505 | −3.58026 | ||||||||
\(191\) | 15.8139 | + | 9.13014i | 1.14425 | + | 0.660633i | 0.947480 | − | 0.319816i | \(-0.103621\pi\) |
0.196771 | + | 0.980449i | \(0.436954\pi\) | |||||||
\(192\) | 4.00000 | + | 0.939764i | 0.288675 | + | 0.0678216i | ||||
\(193\) | −0.872281 | − | 1.51084i | −0.0627882 | − | 0.108752i | 0.832923 | − | 0.553390i | \(-0.186666\pi\) |
−0.895711 | + | 0.444637i | \(0.853333\pi\) | |||||||
\(194\) | − | 13.5615i | − | 0.973656i | ||||||
\(195\) | −2.18614 | − | 7.25061i | −0.156553 | − | 0.519227i | ||||
\(196\) | −3.00000 | + | 5.19615i | −0.214286 | + | 0.371154i | ||||
\(197\) | 12.3030 | − | 21.3094i | 0.876551 | − | 1.51823i | 0.0214504 | − | 0.999770i | \(-0.493172\pi\) |
0.855101 | − | 0.518462i | \(-0.173495\pi\) | |||||||
\(198\) | 18.3030 | + | 27.5928i | 1.30074 | + | 1.96093i | ||||
\(199\) | −5.44158 | − | 3.14170i | −0.385743 | − | 0.222709i | 0.294571 | − | 0.955630i | \(-0.404823\pi\) |
−0.680314 | + | 0.732921i | \(0.738157\pi\) | |||||||
\(200\) | 7.11684 | − | 4.10891i | 0.503237 | − | 0.290544i | ||||
\(201\) | 13.1861 | − | 14.0313i | 0.930079 | − | 0.989694i | ||||
\(202\) | −13.4891 | −0.949092 | ||||||||
\(203\) | −7.11684 | − | 12.3267i | −0.499505 | − | 0.865167i | ||||
\(204\) | −3.55842 | − | 11.8020i | −0.249139 | − | 0.826302i | ||||
\(205\) | 3.18614 | + | 5.51856i | 0.222530 | + | 0.385433i | ||||
\(206\) | −30.0475 | − | 17.3480i | −2.09351 | − | 1.20869i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 9.55842 | + | 5.51856i | 0.662757 | + | 0.382643i | ||||
\(209\) | −33.8614 | −2.34224 | ||||||||
\(210\) | 25.4891 | + | 5.98844i | 1.75892 | + | 0.413242i | ||||
\(211\) | 12.2446 | + | 21.2082i | 0.842950 | + | 1.46003i | 0.887389 | + | 0.461021i | \(0.152517\pi\) |
−0.0444388 | + | 0.999012i | \(0.514150\pi\) | |||||||
\(212\) | −9.55842 | + | 16.5557i | −0.656475 | + | 1.13705i | ||||
\(213\) | 2.81386 | + | 2.64436i | 0.192802 | + | 0.181189i | ||||
\(214\) | 3.18614 | + | 5.51856i | 0.217800 | + | 0.377241i | ||||
\(215\) | 21.8614 | 1.49094 | ||||||||
\(216\) | 19.8614 | − | 23.9538i | 1.35140 | − | 1.62985i | ||||
\(217\) | −13.0475 | + | 2.05446i | −0.885725 | + | 0.139466i | ||||
\(218\) | 16.7306i | 1.13314i | ||||||||
\(219\) | 8.18614 | + | 7.69304i | 0.553168 | + | 0.519847i | ||||
\(220\) | 41.7921 | − | 24.1287i | 2.81762 | − | 1.62676i | ||||
\(221\) | 2.81929i | 0.189646i | ||||||||
\(222\) | 2.18614 | + | 7.25061i | 0.146724 | + | 0.486629i | ||||
\(223\) | −7.50000 | + | 4.33013i | −0.502237 | + | 0.289967i | −0.729637 | − | 0.683835i | \(-0.760311\pi\) |
0.227400 | + | 0.973801i | \(0.426978\pi\) | |||||||
\(224\) | −8.44158 | + | 4.87375i | −0.564027 | + | 0.325641i | ||||
\(225\) | 0.255437 | + | 4.10891i | 0.0170292 | + | 0.273927i | ||||
\(226\) | −2.81386 | + | 4.87375i | −0.187175 | + | 0.324197i | ||||
\(227\) | −12.3030 | − | 7.10313i | −0.816578 | − | 0.471451i | 0.0326571 | − | 0.999467i | \(-0.489603\pi\) |
−0.849235 | + | 0.528015i | \(0.822936\pi\) | |||||||
\(228\) | 16.9307 | + | 56.1528i | 1.12126 | + | 3.71881i | ||||
\(229\) | −2.61684 | + | 1.51084i | −0.172926 | + | 0.0998388i | −0.583965 | − | 0.811779i | \(-0.698499\pi\) |
0.411039 | + | 0.911618i | \(0.365166\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 17.4891 | + | 4.10891i | 1.15070 | + | 0.270347i | ||||
\(232\) | 35.9306i | 2.35896i | ||||||||
\(233\) | 10.0974i | 0.661499i | 0.943719 | + | 0.330750i | \(0.107302\pi\) | ||||
−0.943719 | + | 0.330750i | \(0.892698\pi\) | |||||||
\(234\) | −10.9307 | + | 7.25061i | −0.714562 | + | 0.473987i | ||||
\(235\) | 8.37228 | − | 14.5012i | 0.546147 | − | 0.945955i | ||||
\(236\) | 8.44158 | − | 4.87375i | 0.549500 | − | 0.317254i | ||||
\(237\) | −1.06930 | + | 0.322405i | −0.0694583 | + | 0.0209425i | ||||
\(238\) | −8.44158 | − | 4.87375i | −0.547186 | − | 0.315918i | ||||
\(239\) | −7.93070 | + | 13.7364i | −0.512995 | + | 0.888533i | 0.486892 | + | 0.873462i | \(0.338131\pi\) |
−0.999886 | + | 0.0150704i | \(0.995203\pi\) | |||||||
\(240\) | −20.3030 | − | 19.0800i | −1.31055 | − | 1.23161i | ||||
\(241\) | 23.6168 | − | 13.6352i | 1.52129 | − | 0.878320i | 0.521611 | − | 0.853184i | \(-0.325331\pi\) |
0.999684 | − | 0.0251362i | \(-0.00800195\pi\) | |||||||
\(242\) | 17.7446 | − | 10.2448i | 1.14066 | − | 0.658562i | ||||
\(243\) | 6.31386 | + | 14.2525i | 0.405034 | + | 0.914302i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.00000 | + | 1.73205i | −0.191663 | + | 0.110657i | ||||
\(246\) | 7.55842 | − | 8.04290i | 0.481907 | − | 0.512796i | ||||
\(247\) | − | 13.4140i | − | 0.853511i | ||||||
\(248\) | 31.1168 | + | 11.9769i | 1.97592 | + | 0.760533i | ||||
\(249\) | −9.04755 | + | 9.62747i | −0.573365 | + | 0.610116i | ||||
\(250\) | −23.1168 | −1.46204 | ||||||||
\(251\) | −8.18614 | − | 14.1788i | −0.516705 | − | 0.894959i | −0.999812 | − | 0.0193975i | \(-0.993825\pi\) |
0.483107 | − | 0.875561i | \(-0.339508\pi\) | |||||||
\(252\) | −1.93070 | − | 31.0569i | −0.121623 | − | 1.95640i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −16.9307 | − | 29.3248i | −1.06233 | − | 1.84000i | ||||
\(255\) | 1.62772 | − | 6.92820i | 0.101932 | − | 0.433861i | ||||
\(256\) | −31.1168 | −1.94480 | ||||||||
\(257\) | 24.0475 | + | 13.8839i | 1.50004 | + | 0.866051i | 1.00000 | 5.17161e-5i | \(1.64617e-5\pi\) | |
0.500045 | + | 0.866000i | \(0.333317\pi\) | |||||||
\(258\) | −10.9307 | − | 36.2530i | −0.680516 | − | 2.25702i | ||||
\(259\) | 3.55842 | + | 2.05446i | 0.221110 | + | 0.127658i | ||||
\(260\) | 9.55842 | + | 16.5557i | 0.592788 | + | 1.02674i | ||||
\(261\) | −16.1168 | − | 8.01544i | −0.997608 | − | 0.496144i | ||||
\(262\) | −14.3030 | − | 24.7735i | −0.883641 | − | 1.53051i | ||||
\(263\) | −24.0000 | −1.47990 | −0.739952 | − | 0.672660i | \(-0.765152\pi\) | ||||
−0.739952 | + | 0.672660i | \(0.765152\pi\) | |||||||
\(264\) | −33.0475 | − | 31.0569i | −2.03394 | − | 1.91142i | ||||
\(265\) | −9.55842 | + | 5.51856i | −0.587169 | + | 0.339002i | ||||
\(266\) | 40.1644 | + | 23.1889i | 2.46264 | + | 1.42180i | ||||
\(267\) | 10.1168 | + | 2.37686i | 0.619141 | + | 0.145462i | ||||
\(268\) | −24.3030 | + | 42.0940i | −1.48454 | + | 2.57130i | ||||
\(269\) | −7.93070 | + | 13.7364i | −0.483544 | + | 0.837522i | −0.999821 | − | 0.0188992i | \(-0.993984\pi\) |
0.516278 | + | 0.856421i | \(0.327317\pi\) | |||||||
\(270\) | 31.0475 | − | 11.5070i | 1.88949 | − | 0.700294i | ||||
\(271\) | − | 2.37686i | − | 0.144384i | −0.997391 | − | 0.0721920i | \(-0.977001\pi\) | ||
0.997391 | − | 0.0721920i | \(-0.0229994\pi\) | |||||||
\(272\) | 5.18614 | + | 8.98266i | 0.314456 | + | 0.544654i | ||||
\(273\) | −1.62772 | + | 6.92820i | −0.0985140 | + | 0.419314i | ||||
\(274\) | 35.7921 | + | 20.6646i | 2.16228 | + | 1.24839i | ||||
\(275\) | 6.00000 | 0.361814 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 8.01544i | − | 0.481601i | −0.970575 | − | 0.240801i | \(-0.922590\pi\) | ||
0.970575 | − | 0.240801i | \(-0.0774100\pi\) | |||||||
\(278\) | −26.2337 | −1.57339 | ||||||||
\(279\) | −12.3139 | + | 11.2858i | −0.737211 | + | 0.675662i | ||||
\(280\) | −35.8614 | −2.14313 | ||||||||
\(281\) | 14.8511i | 0.885941i | 0.896536 | + | 0.442970i | \(0.146075\pi\) | ||||
−0.896536 | + | 0.442970i | \(0.853925\pi\) | |||||||
\(282\) | −28.2337 | − | 6.63325i | −1.68129 | − | 0.395004i | ||||
\(283\) | 26.3505 | 1.56638 | 0.783188 | − | 0.621785i | \(-0.213592\pi\) | ||||
0.783188 | + | 0.621785i | \(0.213592\pi\) | |||||||
\(284\) | −8.44158 | − | 4.87375i | −0.500915 | − | 0.289204i | ||||
\(285\) | −7.74456 | + | 32.9639i | −0.458748 | + | 1.95261i | ||||
\(286\) | 9.55842 | + | 16.5557i | 0.565201 | + | 0.978957i | ||||
\(287\) | − | 5.98844i | − | 0.353486i | ||||||
\(288\) | −5.48913 | + | 11.0371i | −0.323450 | + | 0.650368i | ||||
\(289\) | 7.17527 | − | 12.4279i | 0.422074 | − | 0.731054i | ||||
\(290\) | −19.1168 | + | 33.1113i | −1.12258 | + | 1.94437i | ||||
\(291\) | −9.05842 | − | 2.12819i | −0.531014 | − | 0.124757i | ||||
\(292\) | −24.5584 | − | 14.1788i | −1.43717 | − | 0.829752i | ||||
\(293\) | 17.1861 | − | 9.92242i | 1.00403 | − | 0.579674i | 0.0945883 | − | 0.995516i | \(-0.469847\pi\) |
0.909437 | + | 0.415842i | \(0.136513\pi\) | |||||||
\(294\) | 4.37228 | + | 4.10891i | 0.254997 | + | 0.239637i | ||||
\(295\) | 5.62772 | 0.327658 | ||||||||
\(296\) | −5.18614 | − | 8.98266i | −0.301438 | − | 0.522106i | ||||
\(297\) | 21.3030 | − | 7.89542i | 1.23612 | − | 0.458139i | ||||
\(298\) | −1.18614 | − | 2.05446i | −0.0687113 | − | 0.119011i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −3.00000 | − | 9.94987i | −0.173205 | − | 0.574456i | ||||
\(301\) | −17.7921 | − | 10.2723i | −1.02552 | − | 0.592084i | ||||
\(302\) | 58.4674 | 3.36442 | ||||||||
\(303\) | −2.11684 | + | 9.01011i | −0.121610 | + | 0.517617i | ||||
\(304\) | −24.6753 | − | 42.7388i | −1.41522 | − | 2.45124i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −12.3030 | + | 0.764836i | −0.703315 | + | 0.0437227i | ||||
\(307\) | 2.12772 | + | 3.68532i | 0.121435 | + | 0.210332i | 0.920334 | − | 0.391134i | \(-0.127917\pi\) |
−0.798899 | + | 0.601466i | \(0.794584\pi\) | |||||||
\(308\) | −45.3505 | −2.58409 | ||||||||
\(309\) | −16.3030 | + | 17.3480i | −0.927444 | + | 0.986891i | ||||
\(310\) | 22.3030 | + | 27.5928i | 1.26672 | + | 1.56717i | ||||
\(311\) | − | 30.5870i | − | 1.73443i | −0.497934 | − | 0.867215i | \(-0.665908\pi\) | ||
0.497934 | − | 0.867215i | \(-0.334092\pi\) | |||||||
\(312\) | 12.3030 | − | 13.0916i | 0.696519 | − | 0.741164i | ||||
\(313\) | −2.61684 | + | 1.51084i | −0.147913 | + | 0.0853975i | −0.572130 | − | 0.820163i | \(-0.693883\pi\) |
0.424217 | + | 0.905561i | \(0.360549\pi\) | |||||||
\(314\) | 16.7306i | 0.944162i | ||||||||
\(315\) | 8.00000 | − | 16.0858i | 0.450749 | − | 0.906332i | ||||
\(316\) | 2.44158 | − | 1.40965i | 0.137349 | − | 0.0792988i | ||||
\(317\) | 7.06930 | − | 4.08146i | 0.397051 | − | 0.229238i | −0.288160 | − | 0.957582i | \(-0.593043\pi\) |
0.685211 | + | 0.728345i | \(0.259710\pi\) | |||||||
\(318\) | 13.9307 | + | 13.0916i | 0.781195 | + | 0.734139i | ||||
\(319\) | −13.1168 | + | 22.7190i | −0.734402 | + | 1.27202i | ||||
\(320\) | −5.18614 | − | 2.99422i | −0.289914 | − | 0.167382i | ||||
\(321\) | 4.18614 | − | 1.26217i | 0.233648 | − | 0.0704474i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.30298 | − | 10.9171i | 0.350707 | − | 0.607443i | ||||
\(324\) | −23.7446 | − | 31.3793i | −1.31914 | − | 1.74329i | ||||
\(325\) | 2.37686i | 0.131845i | ||||||||
\(326\) | 1.58457i | 0.0877614i | ||||||||
\(327\) | 11.1753 | + | 2.62553i | 0.617994 | + | 0.145192i | ||||
\(328\) | −7.55842 | + | 13.0916i | −0.417344 | + | 0.722861i | ||||
\(329\) | −13.6277 | + | 7.86797i | −0.751320 | + | 0.433775i | ||||
\(330\) | −13.9307 | − | 46.2029i | −0.766860 | − | 2.54339i | ||||
\(331\) | 1.50000 | + | 0.866025i | 0.0824475 | + | 0.0476011i | 0.540657 | − | 0.841243i | \(-0.318176\pi\) |
−0.458209 | + | 0.888844i | \(0.651509\pi\) | |||||||
\(332\) | 16.6753 | − | 28.8824i | 0.915174 | − | 1.58513i | ||||
\(333\) | 5.18614 | − | 0.322405i | 0.284199 | − | 0.0176677i | ||||
\(334\) | 35.7921 | − | 20.6646i | 1.95846 | − | 1.13072i | ||||
\(335\) | −24.3030 | + | 14.0313i | −1.32781 | + | 0.766614i | ||||
\(336\) | 7.55842 | + | 25.0684i | 0.412346 | + | 1.36760i | ||||
\(337\) | 9.50744i | 0.517903i | 0.965890 | + | 0.258952i | \(0.0833771\pi\) | ||||
−0.965890 | + | 0.258952i | \(0.916623\pi\) | |||||||
\(338\) | 21.8614 | − | 12.6217i | 1.18910 | − | 0.686529i | ||||
\(339\) | 2.81386 | + | 2.64436i | 0.152828 | + | 0.143622i | ||||
\(340\) | 17.9653i | 0.974306i | ||||||||
\(341\) | 15.3030 | + | 18.9325i | 0.828703 | + | 1.02525i | ||||
\(342\) | 58.5367 | − | 3.63903i | 3.16530 | − | 0.196776i | ||||
\(343\) | 19.8614 | 1.07242 | ||||||||
\(344\) | 25.9307 | + | 44.9133i | 1.39809 | + | 2.42156i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 17.9307 | − | 31.0569i | 0.963961 | − | 1.66963i | ||||
\(347\) | −2.18614 | − | 3.78651i | −0.117358 | − | 0.203270i | 0.801362 | − | 0.598180i | \(-0.204109\pi\) |
−0.918720 | + | 0.394910i | \(0.870776\pi\) | |||||||
\(348\) | 44.2337 | + | 10.3923i | 2.37117 | + | 0.557086i | ||||
\(349\) | 12.1168 | 0.648600 | 0.324300 | − | 0.945954i | \(-0.394871\pi\) | ||||
0.324300 | + | 0.945954i | \(0.394871\pi\) | |||||||
\(350\) | −7.11684 | − | 4.10891i | −0.380411 | − | 0.219631i | ||||
\(351\) | 3.12772 | + | 8.43904i | 0.166945 | + | 0.450443i | ||||
\(352\) | 15.5584 | + | 8.98266i | 0.829267 | + | 0.478777i | ||||
\(353\) | 6.81386 | + | 11.8020i | 0.362665 | + | 0.628154i | 0.988399 | − | 0.151883i | \(-0.0485335\pi\) |
−0.625733 | + | 0.780037i | \(0.715200\pi\) | |||||||
\(354\) | −2.81386 | − | 9.33252i | −0.149555 | − | 0.496018i | ||||
\(355\) | −2.81386 | − | 4.87375i | −0.149344 | − | 0.258672i | ||||
\(356\) | −26.2337 | −1.39038 | ||||||||
\(357\) | −4.58017 | + | 4.87375i | −0.242408 | + | 0.257946i | ||||
\(358\) | −16.6753 | + | 9.62747i | −0.881315 | + | 0.508828i | ||||
\(359\) | 15.8139 | + | 9.13014i | 0.834624 | + | 0.481870i | 0.855433 | − | 0.517913i | \(-0.173291\pi\) |
−0.0208095 | + | 0.999783i | \(0.506624\pi\) | |||||||
\(360\) | −37.7921 | + | 25.0684i | −1.99182 | + | 1.32122i | ||||
\(361\) | −20.4891 | + | 35.4882i | −1.07838 | + | 1.86780i | ||||
\(362\) | −8.18614 | + | 14.1788i | −0.430254 | + | 0.745222i | ||||
\(363\) | −4.05842 | − | 13.4603i | −0.213012 | − | 0.706481i | ||||
\(364\) | − | 17.9653i | − | 0.941639i | ||||||
\(365\) | −8.18614 | − | 14.1788i | −0.428482 | − | 0.742153i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.8505 | − | 16.6569i | −1.50599 | − | 0.869481i | −0.999976 | − | 0.00695334i | \(-0.997787\pi\) |
−0.506010 | − | 0.862528i | \(-0.668880\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.18614 | − | 6.31084i | −0.217922 | − | 0.328529i | ||||
\(370\) | − | 11.0371i | − | 0.573792i | ||||||
\(371\) | 10.3723 | 0.538502 | ||||||||
\(372\) | 23.7446 | − | 34.8434i | 1.23110 | − | 1.80655i | ||||
\(373\) | 14.8614 | 0.769494 | 0.384747 | − | 0.923022i | \(-0.374289\pi\) | ||||
0.384747 | + | 0.923022i | \(0.374289\pi\) | |||||||
\(374\) | 17.9653i | 0.928964i | ||||||||
\(375\) | −3.62772 | + | 15.4410i | −0.187335 | + | 0.797369i | ||||
\(376\) | 39.7228 | 2.04855 | ||||||||
\(377\) | −9.00000 | − | 5.19615i | −0.463524 | − | 0.267615i | ||||
\(378\) | −30.6753 | − | 5.22360i | −1.57777 | − | 0.268673i | ||||
\(379\) | −12.6168 | − | 21.8530i | −0.648084 | − | 1.12251i | −0.983580 | − | 0.180472i | \(-0.942237\pi\) |
0.335496 | − | 0.942042i | \(-0.391096\pi\) | |||||||
\(380\) | − | 85.4776i | − | 4.38491i | ||||||
\(381\) | −22.2446 | + | 6.70699i | −1.13962 | + | 0.343609i | ||||
\(382\) | −23.0475 | + | 39.9195i | −1.17922 | + | 2.04246i | ||||
\(383\) | 2.18614 | − | 3.78651i | 0.111707 | − | 0.193481i | −0.804752 | − | 0.593611i | \(-0.797702\pi\) |
0.916458 | + | 0.400130i | \(0.131035\pi\) | |||||||
\(384\) | −5.62772 | + | 23.9538i | −0.287188 | + | 1.22239i | ||||
\(385\) | −22.6753 | − | 13.0916i | −1.15564 | − | 0.667208i | ||||
\(386\) | 3.81386 | − | 2.20193i | 0.194120 | − | 0.112075i | ||||
\(387\) | −25.9307 | + | 1.61203i | −1.31813 | + | 0.0819439i | ||||
\(388\) | 23.4891 | 1.19248 | ||||||||
\(389\) | −11.1861 | − | 19.3750i | −0.567160 | − | 0.982350i | −0.996845 | − | 0.0793710i | \(-0.974709\pi\) |
0.429685 | − | 0.902979i | \(-0.358624\pi\) | |||||||
\(390\) | 18.3030 | − | 5.51856i | 0.926808 | − | 0.279443i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −7.11684 | − | 4.10891i | −0.359455 | − | 0.207531i | ||||
\(393\) | −18.7921 | + | 5.66603i | −0.947937 | + | 0.285814i | ||||
\(394\) | 53.7921 | + | 31.0569i | 2.71001 | + | 1.56462i | ||||
\(395\) | 1.62772 | 0.0818994 | ||||||||
\(396\) | −47.7921 | + | 31.7017i | −2.40164 | + | 1.59307i | ||||
\(397\) | −7.81386 | − | 13.5340i | −0.392166 | − | 0.679252i | 0.600569 | − | 0.799573i | \(-0.294941\pi\) |
−0.992735 | + | 0.120321i | \(0.961608\pi\) | |||||||
\(398\) | 7.93070 | − | 13.7364i | 0.397530 | − | 0.688543i | ||||
\(399\) | 21.7921 | − | 23.1889i | 1.09097 | − | 1.16090i | ||||
\(400\) | 4.37228 | + | 7.57301i | 0.218614 | + | 0.378651i | ||||
\(401\) | −14.2337 | −0.710796 | −0.355398 | − | 0.934715i | \(-0.615655\pi\) | ||||
−0.355398 | + | 0.934715i | \(0.615655\pi\) | |||||||
\(402\) | 35.4198 | + | 33.2863i | 1.76658 | + | 1.66017i | ||||
\(403\) | −7.50000 | + | 6.06218i | −0.373602 | + | 0.301979i | ||||
\(404\) | − | 23.3639i | − | 1.16240i | ||||||
\(405\) | −2.81386 | − | 22.5441i | −0.139822 | − | 1.12023i | ||||
\(406\) | 31.1168 | − | 17.9653i | 1.54430 | − | 0.891604i | ||||
\(407\) | − | 7.57301i | − | 0.375380i | ||||||
\(408\) | 16.1644 | − | 4.87375i | 0.800257 | − | 0.241286i | ||||
\(409\) | −20.6168 | + | 11.9031i | −1.01944 | + | 0.588572i | −0.913941 | − | 0.405847i | \(-0.866976\pi\) |
−0.105496 | + | 0.994420i | \(0.533643\pi\) | |||||||
\(410\) | −13.9307 | + | 8.04290i | −0.687988 | + | 0.397210i | ||||
\(411\) | 19.4198 | − | 20.6646i | 0.957910 | − | 1.01931i | ||||
\(412\) | 30.0475 | − | 52.0439i | 1.48034 | − | 2.56402i | ||||
\(413\) | −4.58017 | − | 2.64436i | −0.225376 | − | 0.130121i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.6753 | − | 9.62747i | 0.818557 | − | 0.472594i | ||||
\(416\) | −3.55842 | + | 6.16337i | −0.174466 | + | 0.302184i | ||||
\(417\) | −4.11684 | + | 17.5229i | −0.201603 | + | 0.858100i | ||||
\(418\) | − | 85.4776i | − | 4.18085i | ||||||
\(419\) | − | 35.3407i | − | 1.72651i | −0.504770 | − | 0.863254i | \(-0.668423\pi\) | ||
0.504770 | − | 0.863254i | \(-0.331577\pi\) | |||||||
\(420\) | −10.3723 | + | 44.1485i | −0.506116 | + | 2.15422i | ||||
\(421\) | 10.1861 | − | 17.6429i | 0.496442 | − | 0.859863i | −0.503549 | − | 0.863966i | \(-0.667973\pi\) |
0.999992 | + | 0.00410343i | \(0.00130616\pi\) | |||||||
\(422\) | −53.5367 | + | 30.9094i | −2.60612 | + | 1.50465i | ||||
\(423\) | −8.86141 | + | 17.8178i | −0.430856 | + | 0.866333i | ||||
\(424\) | −22.6753 | − | 13.0916i | −1.10121 | − | 0.635783i | ||||
\(425\) | −1.11684 | + | 1.93443i | −0.0541749 | + | 0.0938337i | ||||
\(426\) | −6.67527 | + | 7.10313i | −0.323418 | + | 0.344148i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −9.55842 | + | 5.51856i | −0.462024 | + | 0.266750i | ||||
\(429\) | 12.5584 | − | 3.78651i | 0.606326 | − | 0.182814i | ||||
\(430\) | 55.1856i | 2.66128i | ||||||||
\(431\) | −13.9307 | + | 8.04290i | −0.671018 | + | 0.387413i | −0.796462 | − | 0.604688i | \(-0.793298\pi\) |
0.125444 | + | 0.992101i | \(0.459964\pi\) | |||||||
\(432\) | 25.4891 | + | 21.1345i | 1.22635 | + | 1.01683i | ||||
\(433\) | 28.8001i | 1.38404i | 0.721877 | + | 0.692021i | \(0.243280\pi\) | ||||
−0.721877 | + | 0.692021i | \(0.756720\pi\) | |||||||
\(434\) | −5.18614 | − | 32.9364i | −0.248943 | − | 1.58100i | ||||
\(435\) | 19.1168 | + | 17.9653i | 0.916583 | + | 0.861371i | ||||
\(436\) | −28.9783 | −1.38781 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −19.4198 | + | 20.6646i | −0.927915 | + | 0.987392i | ||||
\(439\) | −16.9891 | + | 29.4260i | −0.810847 | + | 1.40443i | 0.101425 | + | 0.994843i | \(0.467660\pi\) |
−0.912272 | + | 0.409585i | \(0.865674\pi\) | |||||||
\(440\) | 33.0475 | + | 57.2400i | 1.57548 | + | 2.72881i | ||||
\(441\) | 3.43070 | − | 2.27567i | 0.163367 | − | 0.108365i | ||||
\(442\) | −7.11684 | −0.338514 | ||||||||
\(443\) | 19.9307 | + | 11.5070i | 0.946936 | + | 0.546714i | 0.892128 | − | 0.451783i | \(-0.149212\pi\) |
0.0548084 | + | 0.998497i | \(0.482545\pi\) | |||||||
\(444\) | −12.5584 | + | 3.78651i | −0.595996 | + | 0.179700i | ||||
\(445\) | −13.1168 | − | 7.57301i | −0.621798 | − | 0.358995i | ||||
\(446\) | −10.9307 | − | 18.9325i | −0.517584 | − | 0.896481i | ||||
\(447\) | −1.55842 | + | 0.469882i | −0.0737108 | + | 0.0222247i | ||||
\(448\) | 2.81386 | + | 4.87375i | 0.132942 | + | 0.230263i | ||||
\(449\) | 38.2337 | 1.80436 | 0.902180 | − | 0.431361i | \(-0.141966\pi\) | ||||
0.902180 | + | 0.431361i | \(0.141966\pi\) | |||||||
\(450\) | −10.3723 | + | 0.644810i | −0.488954 | + | 0.0303966i | ||||
\(451\) | −9.55842 | + | 5.51856i | −0.450089 | + | 0.259859i | ||||
\(452\) | −8.44158 | − | 4.87375i | −0.397058 | − | 0.229242i | ||||
\(453\) | 9.17527 | − | 39.0535i | 0.431092 | − | 1.83489i | ||||
\(454\) | 17.9307 | − | 31.0569i | 0.841530 | − | 1.45757i | ||||
\(455\) | 5.18614 | − | 8.98266i | 0.243130 | − | 0.421114i | ||||
\(456\) | −76.9090 | + | 23.1889i | −3.60159 | + | 1.08592i | ||||
\(457\) | 12.7692i | 0.597316i | 0.954360 | + | 0.298658i | \(0.0965390\pi\) | ||||
−0.954360 | + | 0.298658i | \(0.903461\pi\) | |||||||
\(458\) | −3.81386 | − | 6.60580i | −0.178210 | − | 0.308669i | ||||
\(459\) | −1.41983 | + | 8.33785i | −0.0662719 | + | 0.389177i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.00000 | −0.279448 | −0.139724 | − | 0.990190i | \(-0.544622\pi\) | ||||
−0.139724 | + | 0.990190i | \(0.544622\pi\) | |||||||
\(462\) | −10.3723 | + | 44.1485i | −0.482562 | + | 2.05397i | ||||
\(463\) | − | 18.4077i | − | 0.855481i | −0.903902 | − | 0.427740i | \(-0.859310\pi\) | ||
0.903902 | − | 0.427740i | \(-0.140690\pi\) | |||||||
\(464\) | −38.2337 | −1.77495 | ||||||||
\(465\) | 21.9307 | − | 10.5672i | 1.01701 | − | 0.490044i | ||||
\(466\) | −25.4891 | −1.18076 | ||||||||
\(467\) | 15.7359i | 0.728172i | 0.931365 | + | 0.364086i | \(0.118619\pi\) | ||||
−0.931365 | + | 0.364086i | \(0.881381\pi\) | |||||||
\(468\) | −12.5584 | − | 18.9325i | −0.580513 | − | 0.875157i | ||||
\(469\) | 26.3723 | 1.21776 | ||||||||
\(470\) | 36.6060 | + | 21.1345i | 1.68851 | + | 0.974860i | ||||
\(471\) | 11.1753 | + | 2.62553i | 0.514929 | + | 0.120978i | ||||
\(472\) | 6.67527 | + | 11.5619i | 0.307254 | + | 0.532180i | ||||
\(473\) | 37.8651i | 1.74104i | ||||||||
\(474\) | −0.813859 | − | 2.69927i | −0.0373818 | − | 0.123981i | ||||
\(475\) | 5.31386 | − | 9.20387i | 0.243817 | − | 0.422303i | ||||
\(476\) | 8.44158 | − | 14.6212i | 0.386919 | − | 0.670164i | ||||
\(477\) | 10.9307 | − | 7.25061i | 0.500483 | − | 0.331983i | ||||
\(478\) | −34.6753 | − | 20.0198i | −1.58601 | − | 0.915683i | ||||
\(479\) | −19.9307 | + | 11.5070i | −0.910657 | + | 0.525768i | −0.880643 | − | 0.473781i | \(-0.842889\pi\) |
−0.0300146 | + | 0.999549i | \(0.509555\pi\) | |||||||
\(480\) | 12.3030 | − | 13.0916i | 0.561552 | − | 0.597546i | ||||
\(481\) | 3.00000 | 0.136788 | ||||||||
\(482\) | 34.4198 | + | 59.6169i | 1.56778 | + | 2.71548i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 17.7446 | + | 30.7345i | 0.806571 | + | 1.39702i | ||||
\(485\) | 11.7446 | + | 6.78073i | 0.533293 | + | 0.307897i | ||||
\(486\) | −35.9783 | + | 15.9383i | −1.63201 | + | 0.722977i | ||||
\(487\) | 23.6168 | + | 13.6352i | 1.07018 | + | 0.617869i | 0.928231 | − | 0.372004i | \(-0.121329\pi\) |
0.141950 | + | 0.989874i | \(0.454663\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.05842 | + | 0.248667i | 0.0478635 | + | 0.0112451i | ||||
\(490\) | −4.37228 | − | 7.57301i | −0.197520 | − | 0.342114i | ||||
\(491\) | −19.9307 | + | 34.5210i | −0.899460 | + | 1.55791i | −0.0712743 | + | 0.997457i | \(0.522707\pi\) |
−0.828186 | + | 0.560454i | \(0.810627\pi\) | |||||||
\(492\) | 13.9307 | + | 13.0916i | 0.628045 | + | 0.590214i | ||||
\(493\) | −4.88316 | − | 8.45787i | −0.219926 | − | 0.380924i | ||||
\(494\) | 33.8614 | 1.52350 | ||||||||
\(495\) | −33.0475 | + | 2.05446i | −1.48538 | + | 0.0923409i | ||||
\(496\) | −12.7446 | + | 33.1113i | −0.572248 | + | 1.48674i | ||||
\(497\) | 5.28873i | 0.237232i | ||||||||
\(498\) | −24.3030 | − | 22.8391i | −1.08904 | − | 1.02344i | ||||
\(499\) | −0.558422 | + | 0.322405i | −0.0249984 | + | 0.0144328i | −0.512447 | − | 0.858719i | \(-0.671261\pi\) |
0.487449 | + | 0.873152i | \(0.337928\pi\) | |||||||
\(500\) | − | 40.0395i | − | 1.79062i | ||||||
\(501\) | −8.18614 | − | 27.1504i | −0.365730 | − | 1.21299i | ||||
\(502\) | 35.7921 | − | 20.6646i | 1.59748 | − | 0.922306i | ||||
\(503\) | 16.0693 | − | 9.27761i | 0.716495 | − | 0.413668i | −0.0969666 | − | 0.995288i | \(-0.530914\pi\) |
0.813461 | + | 0.581619i | \(0.197581\pi\) | |||||||
\(504\) | 42.5367 | − | 2.64436i | 1.89473 | − | 0.117789i | ||||
\(505\) | 6.74456 | − | 11.6819i | 0.300129 | − | 0.519839i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.00000 | − | 16.5831i | −0.222058 | − | 0.736482i | ||||
\(508\) | 50.7921 | − | 29.3248i | 2.25354 | − | 1.30108i | ||||
\(509\) | −7.93070 | + | 13.7364i | −0.351522 | + | 0.608854i | −0.986516 | − | 0.163663i | \(-0.947669\pi\) |
0.634994 | + | 0.772517i | \(0.281003\pi\) | |||||||
\(510\) | 17.4891 | + | 4.10891i | 0.774431 | + | 0.181946i | ||||
\(511\) | 15.3861i | 0.680640i | ||||||||
\(512\) | − | 50.1369i | − | 2.21576i | ||||||
\(513\) | 6.75544 | − | 39.6709i | 0.298260 | − | 1.75151i | ||||
\(514\) | −35.0475 | + | 60.7041i | −1.54588 | + | 2.67754i | ||||
\(515\) | 30.0475 | − | 17.3480i | 1.32405 | − | 0.764442i | ||||
\(516\) | 62.7921 | − | 18.9325i | 2.76427 | − | 0.833458i | ||||
\(517\) | 25.1168 | + | 14.5012i | 1.10464 | + | 0.637763i | ||||
\(518\) | −5.18614 | + | 8.98266i | −0.227866 | + | 0.394675i | ||||
\(519\) | −17.9307 | − | 16.8506i | −0.787071 | − | 0.739660i | ||||
\(520\) | −22.6753 | + | 13.0916i | −0.994376 | + | 0.574103i | ||||
\(521\) | −4.93070 | + | 2.84674i | −0.216018 | + | 0.124718i | −0.604105 | − | 0.796905i | \(-0.706469\pi\) |
0.388087 | + | 0.921623i | \(0.373136\pi\) | |||||||
\(522\) | 20.2337 | − | 40.6844i | 0.885604 | − | 1.78071i | ||||
\(523\) | 19.8997i | 0.870155i | 0.900393 | + | 0.435078i | \(0.143279\pi\) | ||||
−0.900393 | + | 0.435078i | \(0.856721\pi\) | |||||||
\(524\) | 42.9090 | − | 24.7735i | 1.87449 | − | 1.08224i | ||||
\(525\) | −3.86141 | + | 4.10891i | −0.168526 | + | 0.179328i | ||||
\(526\) | − | 60.5841i | − | 2.64159i | ||||||
\(527\) | −8.95245 | + | 1.40965i | −0.389975 | + | 0.0614051i | ||||
\(528\) | 33.0475 | − | 35.1658i | 1.43821 | − | 1.53040i | ||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | −13.9307 | − | 24.1287i | −0.605111 | − | 1.04808i | ||||
\(531\) | −6.67527 | + | 0.414979i | −0.289682 | + | 0.0180086i | ||||
\(532\) | −40.1644 | + | 69.5668i | −1.74135 | + | 3.01610i | ||||
\(533\) | −2.18614 | − | 3.78651i | −0.0946923 | − | 0.164012i | ||||
\(534\) | −6.00000 | + | 25.5383i | −0.259645 | + | 1.10515i | ||||
\(535\) | −6.37228 | −0.275498 | ||||||||
\(536\) | −57.6535 | − | 33.2863i | −2.49025 | − | 1.43775i | ||||
\(537\) | 3.81386 | + | 12.6491i | 0.164580 | + | 0.545851i | ||||
\(538\) | −34.6753 | − | 20.0198i | −1.49496 | − | 0.863114i | ||||
\(539\) | −3.00000 | − | 5.19615i | −0.129219 | − | 0.223814i | ||||
\(540\) | 19.9307 | + | 53.7759i | 0.857681 | + | 2.31415i | ||||
\(541\) | −4.98913 | − | 8.64142i | −0.214499 | − | 0.371524i | 0.738618 | − | 0.674124i | \(-0.235479\pi\) |
−0.953118 | + | 0.302600i | \(0.902145\pi\) | |||||||
\(542\) | 6.00000 | 0.257722 | ||||||||
\(543\) | 8.18614 | + | 7.69304i | 0.351301 | + | 0.330140i | ||||
\(544\) | −5.79211 | + | 3.34408i | −0.248335 | + | 0.143376i | ||||
\(545\) | −14.4891 | − | 8.36530i | −0.620646 | − | 0.358330i | ||||
\(546\) | −17.4891 | − | 4.10891i | −0.748465 | − | 0.175845i | ||||
\(547\) | 7.36141 | − | 12.7503i | 0.314751 | − | 0.545165i | −0.664634 | − | 0.747170i | \(-0.731412\pi\) |
0.979385 | + | 0.202005i | \(0.0647456\pi\) | |||||||
\(548\) | −35.7921 | + | 61.9938i | −1.52896 | + | 2.64824i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 15.1460i | 0.645829i | ||||||||
\(551\) | 23.2337 | + | 40.2419i | 0.989788 | + | 1.71436i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.32473 | − | 0.764836i | −0.0563334 | − | 0.0325241i | ||||
\(554\) | 20.2337 | 0.859647 | ||||||||
\(555\) | −7.37228 | − | 1.73205i | −0.312936 | − | 0.0735215i | ||||
\(556\) | − | 45.4381i | − | 1.92700i | ||||||
\(557\) | 14.2337 | 0.603101 | 0.301550 | − | 0.953450i | \(-0.402496\pi\) | ||||
0.301550 | + | 0.953450i | \(0.402496\pi\) | |||||||
\(558\) | −28.4891 | − | 31.0843i | −1.20604 | − | 1.31591i | ||||
\(559\) | −15.0000 | −0.634432 | ||||||||
\(560\) | − | 38.1600i | − | 1.61256i | ||||||
\(561\) | 12.0000 | + | 2.81929i | 0.506640 | + | 0.119031i | ||||
\(562\) | −37.4891 | −1.58138 | ||||||||
\(563\) | −20.1861 | − | 11.6545i | −0.850744 | − | 0.491178i | 0.0101576 | − | 0.999948i | \(-0.496767\pi\) |
−0.860902 | + | 0.508771i | \(0.830100\pi\) | |||||||
\(564\) | 11.4891 | − | 48.9022i | 0.483779 | − | 2.05915i | ||||
\(565\) | −2.81386 | − | 4.87375i | −0.118380 | − | 0.205040i | ||||
\(566\) | 66.5176i | 2.79595i | ||||||||
\(567\) | −8.30298 | + | 19.6699i | −0.348693 | + | 0.826059i | ||||
\(568\) | 6.67527 | − | 11.5619i | 0.280088 | − | 0.485127i | ||||
\(569\) | 6.30298 | − | 10.9171i | 0.264235 | − | 0.457668i | −0.703128 | − | 0.711063i | \(-0.748214\pi\) |
0.967363 | + | 0.253395i | \(0.0815473\pi\) | |||||||
\(570\) | −83.2119 | − | 19.5499i | −3.48536 | − | 0.818855i | ||||
\(571\) | 23.6168 | + | 13.6352i | 0.988334 | + | 0.570615i | 0.904776 | − | 0.425888i | \(-0.140038\pi\) |
0.0835582 | + | 0.996503i | \(0.473372\pi\) | |||||||
\(572\) | −28.6753 | + | 16.5557i | −1.19897 | + | 0.692227i | ||||
\(573\) | 23.0475 | + | 21.6593i | 0.962825 | + | 0.904828i | ||||
\(574\) | 15.1168 | 0.630965 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6.37228 | + | 3.16915i | 0.265512 | + | 0.132048i | ||||
\(577\) | 7.44158 | + | 12.8892i | 0.309797 | + | 0.536584i | 0.978318 | − | 0.207109i | \(-0.0664056\pi\) |
−0.668521 | + | 0.743693i | \(0.733072\pi\) | |||||||
\(578\) | 31.3723 | + | 18.1128i | 1.30491 | + | 0.753393i | ||||
\(579\) | −0.872281 | − | 2.89303i | −0.0362508 | − | 0.120230i | ||||
\(580\) | −57.3505 | − | 33.1113i | −2.38135 | − | 1.37487i | ||||
\(581\) | −18.0951 | −0.750711 | ||||||||
\(582\) | 5.37228 | − | 22.8665i | 0.222688 | − | 0.947848i | ||||
\(583\) | −9.55842 | − | 16.5557i | −0.395869 | − | 0.685666i | ||||
\(584\) | 19.4198 | − | 33.6361i | 0.803598 | − | 1.39187i | ||||
\(585\) | −0.813859 | − | 13.0916i | −0.0336489 | − | 0.541270i | ||||
\(586\) | 25.0475 | + | 43.3836i | 1.03470 | + | 1.79216i | ||||
\(587\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(588\) | −7.11684 | + | 7.57301i | −0.293494 | + | 0.312306i | ||||
\(589\) | 42.5951 | − | 6.70699i | 1.75510 | − | 0.276357i | ||||
\(590\) | 14.2063i | 0.584863i | ||||||||
\(591\) | 29.1861 | − | 31.0569i | 1.20056 | − | 1.27751i | ||||
\(592\) | 9.55842 | − | 5.51856i | 0.392849 | − | 0.226811i | ||||
\(593\) | − | 29.7021i | − | 1.21972i | −0.792509 | − | 0.609860i | \(-0.791225\pi\) | ||
0.792509 | − | 0.609860i | \(-0.208775\pi\) | |||||||
\(594\) | 19.9307 | + | 53.7759i | 0.817767 | + | 2.20645i | ||||
\(595\) | 8.44158 | − | 4.87375i | 0.346071 | − | 0.199804i | ||||
\(596\) | 3.55842 | − | 2.05446i | 0.145759 | − | 0.0841538i | ||||
\(597\) | −7.93070 | − | 7.45299i | −0.324582 | − | 0.305030i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.8139 | + | 9.13014i | 0.646137 | + | 0.373047i | 0.786975 | − | 0.616985i | \(-0.211646\pi\) |
−0.140838 | + | 0.990033i | \(0.544980\pi\) | |||||||
\(600\) | 13.6277 | − | 4.10891i | 0.556349 | − | 0.167746i | ||||
\(601\) | −1.32473 | + | 0.764836i | −0.0540370 | + | 0.0311983i | −0.526775 | − | 0.850005i | \(-0.676599\pi\) |
0.472738 | + | 0.881203i | \(0.343266\pi\) | |||||||
\(602\) | 25.9307 | − | 44.9133i | 1.05686 | − | 1.83053i | ||||
\(603\) | 27.7921 | − | 18.4352i | 1.13178 | − | 0.750739i | ||||
\(604\) | 101.268i | 4.12056i | ||||||||
\(605\) | 20.4897i | 0.833023i | ||||||||
\(606\) | −22.7446 | − | 5.34363i | −0.923935 | − | 0.217070i | ||||
\(607\) | −5.50000 | + | 9.52628i | −0.223238 | + | 0.386660i | −0.955789 | − | 0.294052i | \(-0.904996\pi\) |
0.732551 | + | 0.680712i | \(0.238329\pi\) | |||||||
\(608\) | 27.5584 | − | 15.9109i | 1.11764 | − | 0.645271i | ||||
\(609\) | −7.11684 | − | 23.6039i | −0.288389 | − | 0.956478i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.74456 | + | 9.94987i | −0.232400 | + | 0.402529i | ||||
\(612\) | −1.32473 | − | 21.3094i | −0.0535492 | − | 0.861381i | ||||
\(613\) | −12.3832 | + | 7.14942i | −0.500151 | + | 0.288762i | −0.728776 | − | 0.684752i | \(-0.759910\pi\) |
0.228625 | + | 0.973515i | \(0.426577\pi\) | |||||||
\(614\) | −9.30298 | + | 5.37108i | −0.375438 | + | 0.216759i | ||||
\(615\) | 3.18614 | + | 10.5672i | 0.128478 | + | 0.426112i | ||||
\(616\) | − | 62.1138i | − | 2.50264i | ||||||
\(617\) | 29.5367 | − | 17.0530i | 1.18910 | − | 0.686528i | 0.230999 | − | 0.972954i | \(-0.425801\pi\) |
0.958102 | + | 0.286426i | \(0.0924672\pi\) | |||||||
\(618\) | −43.7921 | − | 41.1542i | −1.76158 | − | 1.65547i | ||||
\(619\) | − | 18.4077i | − | 0.739870i | −0.929058 | − | 0.369935i | \(-0.879380\pi\) | ||
0.929058 | − | 0.369935i | \(-0.120620\pi\) | |||||||
\(620\) | −47.7921 | + | 38.6299i | −1.91938 | + | 1.55141i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 77.2119 | 3.09592 | ||||||||
\(623\) | 7.11684 | + | 12.3267i | 0.285130 | + | 0.493860i | ||||
\(624\) | 13.9307 | + | 13.0916i | 0.557674 | + | 0.524082i | ||||
\(625\) | 14.9891 | − | 25.9619i | 0.599565 | − | 1.03848i | ||||
\(626\) | −3.81386 | − | 6.60580i | −0.152432 | − | 0.264021i | ||||
\(627\) | −57.0951 | − | 13.4140i | −2.28016 | − | 0.535703i | ||||
\(628\) | −28.9783 | −1.15636 | ||||||||
\(629\) | 2.44158 | + | 1.40965i | 0.0973521 | + | 0.0562063i | ||||
\(630\) | 40.6060 | + | 20.1947i | 1.61778 | + | 0.804576i | ||||
\(631\) | −5.44158 | − | 3.14170i | −0.216626 | − | 0.125069i | 0.387761 | − | 0.921760i | \(-0.373249\pi\) |
−0.604387 | + | 0.796691i | \(0.706582\pi\) | |||||||
\(632\) | 1.93070 | + | 3.34408i | 0.0767993 | + | 0.133020i | ||||
\(633\) | 12.2446 | + | 40.6106i | 0.486678 | + | 1.61413i | ||||
\(634\) | 10.3030 | + | 17.8453i | 0.409184 | + | 0.708727i | ||||
\(635\) | 33.8614 | 1.34375 | ||||||||
\(636\) | −22.6753 | + | 24.1287i | −0.899133 | + | 0.956765i | ||||
\(637\) | 2.05842 | − | 1.18843i | 0.0815576 | − | 0.0470873i | ||||
\(638\) | −57.3505 | − | 33.1113i | −2.27053 | − | 1.31089i | ||||
\(639\) | 3.69702 | + | 5.57346i | 0.146252 | + | 0.220483i | ||||
\(640\) | 17.9307 | − | 31.0569i | 0.708773 | − | 1.22763i | ||||
\(641\) | 14.1861 | − | 24.5711i | 0.560319 | − | 0.970501i | −0.437149 | − | 0.899389i | \(-0.644012\pi\) |
0.997468 | − | 0.0711119i | \(-0.0226547\pi\) | |||||||
\(642\) | 3.18614 | + | 10.5672i | 0.125747 | + | 0.417055i | ||||
\(643\) | 27.9152i | 1.10087i | 0.834879 | + | 0.550434i | \(0.185538\pi\) | ||||
−0.834879 | + | 0.550434i | \(0.814462\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 36.8614 | + | 8.66025i | 1.45142 | + | 0.340997i | ||||
\(646\) | 27.5584 | + | 15.9109i | 1.08427 | + | 0.626005i | ||||
\(647\) | −32.2337 | −1.26724 | −0.633619 | − | 0.773646i | \(-0.718431\pi\) | ||||
−0.633619 | + | 0.773646i | \(0.718431\pi\) | |||||||
\(648\) | 42.9783 | − | 32.5214i | 1.68835 | − | 1.27756i | ||||
\(649\) | 9.74749i | 0.382623i | ||||||||
\(650\) | −6.00000 | −0.235339 | ||||||||
\(651\) | −22.8139 | − | 1.70460i | −0.894146 | − | 0.0668085i | ||||
\(652\) | −2.74456 | −0.107485 | ||||||||
\(653\) | − | 8.51278i | − | 0.333131i | −0.986030 | − | 0.166565i | \(-0.946732\pi\) | ||
0.986030 | − | 0.166565i | \(-0.0532677\pi\) | |||||||
\(654\) | −6.62772 | + | 28.2101i | −0.259164 | + | 1.10310i | ||||
\(655\) | 28.6060 | 1.11773 | ||||||||
\(656\) | −13.9307 | − | 8.04290i | −0.543903 | − | 0.314022i | ||||
\(657\) | 10.7554 | + | 16.2144i | 0.419610 | + | 0.632585i | ||||
\(658\) | −19.8614 | − | 34.4010i | −0.774278 | − | 1.34109i | ||||
\(659\) | − | 0.294954i | − | 0.0114898i | −0.999983 | − | 0.00574488i | \(-0.998171\pi\) | ||
0.999983 | − | 0.00574488i | \(-0.00182866\pi\) | |||||||
\(660\) | 80.0258 | − | 24.1287i | 3.11500 | − | 0.939208i | ||||
\(661\) | −16.9891 | + | 29.4260i | −0.660800 | + | 1.14454i | 0.319605 | + | 0.947551i | \(0.396450\pi\) |
−0.980406 | + | 0.196989i | \(0.936884\pi\) | |||||||
\(662\) | −2.18614 | + | 3.78651i | −0.0849668 | + | 0.147167i | ||||
\(663\) | −1.11684 | + | 4.75372i | −0.0433746 | + | 0.184619i | ||||
\(664\) | 39.5584 | + | 22.8391i | 1.53516 | + | 0.886328i | ||||
\(665\) | −40.1644 | + | 23.1889i | −1.55751 | + | 0.899228i | ||||
\(666\) | 0.813859 | + | 13.0916i | 0.0315364 | + | 0.507288i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 35.7921 | + | 61.9938i | 1.38484 | + | 2.39861i | ||||
\(669\) | −14.3614 | + | 4.33013i | −0.555244 | + | 0.167412i | ||||
\(670\) | −35.4198 | − | 61.3489i | −1.36839 | − | 2.37012i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −16.1644 | + | 4.87375i | −0.623555 | + | 0.188009i | ||||
\(673\) | −35.7921 | − | 20.6646i | −1.37968 | − | 0.796561i | −0.387563 | − | 0.921843i | \(-0.626683\pi\) |
−0.992121 | + | 0.125282i | \(0.960016\pi\) | |||||||
\(674\) | −24.0000 | −0.924445 | ||||||||
\(675\) | −1.19702 | + | 7.02939i | −0.0460731 | + | 0.270561i | ||||
\(676\) | 21.8614 | + | 37.8651i | 0.840823 | + | 1.45635i | ||||
\(677\) | 16.4198 | − | 28.4400i | 0.631065 | − | 1.09304i | −0.356269 | − | 0.934383i | \(-0.615951\pi\) |
0.987334 | − | 0.158654i | \(-0.0507153\pi\) | |||||||
\(678\) | −6.67527 | + | 7.10313i | −0.256362 | + | 0.272794i | ||||
\(679\) | −6.37228 | − | 11.0371i | −0.244546 | − | 0.423566i | ||||
\(680\) | −24.6060 | −0.943596 | ||||||||
\(681\) | −17.9307 | − | 16.8506i | −0.687106 | − | 0.645717i | ||||
\(682\) | −47.7921 | + | 38.6299i | −1.83005 | + | 1.47922i | ||||
\(683\) | − | 35.3407i | − | 1.35228i | −0.736775 | − | 0.676138i | \(-0.763652\pi\) | ||
0.736775 | − | 0.676138i | \(-0.236348\pi\) | |||||||
\(684\) | 6.30298 | + | 101.388i | 0.241001 | + | 3.87669i | ||||
\(685\) | −35.7921 | + | 20.6646i | −1.36755 | + | 0.789553i | ||||
\(686\) | 50.1369i | 1.91424i | ||||||||
\(687\) | −5.01087 | + | 1.51084i | −0.191177 | + | 0.0576420i | ||||
\(688\) | −47.7921 | + | 27.5928i | −1.82206 | + | 1.05197i | ||||
\(689\) | 6.55842 | − | 3.78651i | 0.249856 | − | 0.144254i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.0692967 | − | 0.120025i | 0.00263617 | − | 0.00456598i | −0.864704 | − | 0.502281i | \(-0.832494\pi\) |
0.867340 | + | 0.497715i | \(0.165828\pi\) | |||||||
\(692\) | 53.7921 | + | 31.0569i | 2.04487 | + | 1.18061i | ||||
\(693\) | 27.8614 | + | 13.8564i | 1.05837 | + | 0.526361i | ||||
\(694\) | 9.55842 | − | 5.51856i | 0.362833 | − | 0.209482i | ||||
\(695\) | 13.1168 | − | 22.7190i | 0.497550 | − | 0.861782i | ||||
\(696\) | −14.2337 | + | 60.5841i | −0.539527 | + | 2.29643i | ||||
\(697\) | − | 4.10891i | − | 0.155636i | ||||||
\(698\) | 30.5870i | 1.15774i | ||||||||
\(699\) | −4.00000 | + | 17.0256i | −0.151294 | + | 0.643966i | ||||
\(700\) | 7.11684 | − | 12.3267i | 0.268991 | − | 0.465907i | ||||
\(701\) | −15.0475 | + | 8.68771i | −0.568338 | + | 0.328130i | −0.756485 | − | 0.654011i | \(-0.773085\pi\) |
0.188147 | + | 0.982141i | \(0.439752\pi\) | |||||||
\(702\) | −21.3030 | + | 7.89542i | −0.804029 | + | 0.297993i | ||||
\(703\) | −11.6168 | − | 6.70699i | −0.438138 | − | 0.252959i | ||||
\(704\) | 5.18614 | − | 8.98266i | 0.195460 | − | 0.338547i | ||||
\(705\) | 19.8614 | − | 21.1345i | 0.748024 | − | 0.795970i | ||||
\(706\) | −29.7921 | + | 17.2005i | −1.12124 | + | 0.647349i | ||||
\(707\) | −10.9783 | + | 6.33830i | −0.412880 | + | 0.238376i | ||||
\(708\) | 16.1644 | − | 4.87375i | 0.607495 | − | 0.183167i | ||||
\(709\) | − | 22.2766i | − | 0.836616i | −0.908305 | − | 0.418308i | \(-0.862623\pi\) | ||
0.908305 | − | 0.418308i | \(-0.137377\pi\) | |||||||
\(710\) | 12.3030 | − | 7.10313i | 0.461723 | − | 0.266576i | ||||
\(711\) | −1.93070 | + | 0.120025i | −0.0724070 | + | 0.00450130i | ||||
\(712\) | − | 35.9306i | − | 1.34656i | ||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −12.3030 | − | 11.5619i | −0.460428 | − | 0.432693i | ||||
\(715\) | −19.1168 | −0.714929 | ||||||||
\(716\) | −16.6753 | − | 28.8824i | −0.623184 | − | 1.07939i | ||||
\(717\) | −18.8139 | + | 20.0198i | −0.702616 | + | 0.747652i | ||||
\(718\) | −23.0475 | + | 39.9195i | −0.860127 | + | 1.48978i | ||||
\(719\) | −10.0693 | − | 17.4405i | −0.375521 | − | 0.650422i | 0.614884 | − | 0.788618i | \(-0.289203\pi\) |
−0.990405 | + | 0.138196i | \(0.955870\pi\) | |||||||
\(720\) | −26.6753 | − | 40.2145i | −0.994128 | − | 1.49871i | ||||
\(721\) | −32.6060 | −1.21431 | ||||||||
\(722\) | −89.5842 | − | 51.7215i | −3.33398 | − | 1.92487i | ||||
\(723\) | 45.2228 | − | 13.6352i | 1.68185 | − | 0.507098i | ||||
\(724\) | −24.5584 | − | 14.1788i | −0.912707 | − | 0.526951i | ||||
\(725\) | −4.11684 | − | 7.13058i | −0.152896 | − | 0.264823i | ||||
\(726\) | 33.9783 | − | 10.2448i | 1.26105 | − | 0.380221i | ||||
\(727\) | −1.98913 | − | 3.44527i | −0.0737726 | − | 0.127778i | 0.826779 | − | 0.562526i | \(-0.190171\pi\) |
−0.900552 | + | 0.434749i | \(0.856837\pi\) | |||||||
\(728\) | 24.6060 | 0.911958 | ||||||||
\(729\) | 5.00000 | + | 26.5330i | 0.185185 | + | 0.982704i | ||||
\(730\) | 35.7921 | − | 20.6646i | 1.32473 | − | 0.764831i | ||||
\(731\) | −12.2079 | − | 7.04823i | −0.451525 | − | 0.260688i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.9891 | + | 19.0337i | −0.405893 | + | 0.703027i | −0.994425 | − | 0.105447i | \(-0.966373\pi\) |
0.588532 | + | 0.808474i | \(0.299706\pi\) | |||||||
\(734\) | 42.0475 | − | 72.8285i | 1.55200 | − | 2.68815i | ||||
\(735\) | −5.74456 | + | 1.73205i | −0.211891 | + | 0.0638877i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −24.3030 | − | 42.0940i | −0.895212 | − | 1.55055i | ||||
\(738\) | 15.9307 | − | 10.5672i | 0.586417 | − | 0.388985i | ||||
\(739\) | −38.6168 | − | 22.2954i | −1.42054 | − | 0.820151i | −0.424198 | − | 0.905569i | \(-0.639444\pi\) |
−0.996345 | + | 0.0854181i | \(0.972777\pi\) | |||||||
\(740\) | 19.1168 | 0.702749 | ||||||||
\(741\) | 5.31386 | − | 22.6179i | 0.195210 | − | 0.830887i | ||||
\(742\) | 26.1831i | 0.961213i | ||||||||
\(743\) | 24.0000 | 0.880475 | 0.440237 | − | 0.897881i | \(-0.354894\pi\) | ||||
0.440237 | + | 0.897881i | \(0.354894\pi\) | |||||||
\(744\) | 47.7228 | + | 32.5214i | 1.74960 | + | 1.19229i | ||||
\(745\) | 2.37228 | 0.0869137 | ||||||||
\(746\) | 37.5152i | 1.37353i | ||||||||
\(747\) | −19.0693 | + | 12.6491i | −0.697709 | + | 0.462808i | ||||
\(748\) | −31.1168 | −1.13774 | ||||||||
\(749\) | 5.18614 | + | 2.99422i | 0.189497 | + | 0.109406i | ||||
\(750\) | −38.9783 | − | 9.15759i | −1.42328 | − | 0.334388i | ||||
\(751\) | 12.2446 | + | 21.2082i | 0.446810 | + | 0.773898i | 0.998176 | − | 0.0603651i | \(-0.0192265\pi\) |
−0.551366 | + | 0.834264i | \(0.685893\pi\) | |||||||
\(752\) | 42.2689i | 1.54139i | ||||||||
\(753\) | −8.18614 | − | 27.1504i | −0.298320 | − | 0.989414i | ||||
\(754\) | 13.1168 | − | 22.7190i | 0.477687 | − | 0.827379i | ||||
\(755\) | −29.2337 | + | 50.6342i | −1.06392 | + | 1.84277i | ||||
\(756\) | 9.04755 | − | 53.1311i | 0.329056 | − | 1.93236i | ||||
\(757\) | 34.6753 | + | 20.0198i | 1.26029 | + | 0.727631i | 0.973131 | − | 0.230251i | \(-0.0739546\pi\) |
0.287163 | + | 0.957882i | \(0.407288\pi\) | |||||||
\(758\) | 55.1644 | − | 31.8492i | 2.00366 | − | 1.15681i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 117.073 | 4.24670 | ||||||||
\(761\) | −1.06930 | − | 1.85208i | −0.0387620 | − | 0.0671377i | 0.845994 | − | 0.533193i | \(-0.179008\pi\) |
−0.884756 | + | 0.466055i | \(0.845675\pi\) | |||||||
\(762\) | −16.9307 | − | 56.1528i | −0.613335 | − | 2.03420i | ||||
\(763\) | 7.86141 | + | 13.6164i | 0.284602 | + | 0.492945i | ||||
\(764\) | −69.1426 | − | 39.9195i | −2.50149 | − | 1.44424i | ||||
\(765\) | 5.48913 | − | 11.0371i | 0.198460 | − | 0.399048i | ||||
\(766\) | 9.55842 | + | 5.51856i | 0.345360 | + | 0.199394i | ||||
\(767\) | −3.86141 | −0.139427 | ||||||||
\(768\) | −52.4674 | − | 12.3267i | −1.89325 | − | 0.444803i | ||||
\(769\) | −7.81386 | − | 13.5340i | −0.281775 | − | 0.488049i | 0.690047 | − | 0.723765i | \(-0.257590\pi\) |
−0.971822 | + | 0.235716i | \(0.924256\pi\) | |||||||
\(770\) | 33.0475 | − | 57.2400i | 1.19095 | − | 2.06279i | ||||
\(771\) | 35.0475 | + | 32.9364i | 1.26221 | + | 1.18618i | ||||
\(772\) | 3.81386 | + | 6.60580i | 0.137264 | + | 0.237748i | ||||
\(773\) | 26.2337 | 0.943560 | 0.471780 | − | 0.881716i | \(-0.343612\pi\) | ||||
0.471780 | + | 0.881716i | \(0.343612\pi\) | |||||||
\(774\) | −4.06930 | − | 65.4579i | −0.146268 | − | 2.35283i | ||||
\(775\) | −7.54755 | + | 1.18843i | −0.271116 | + | 0.0426897i | ||||
\(776\) | 32.1716i | 1.15489i | ||||||||
\(777\) | 5.18614 | + | 4.87375i | 0.186052 | + | 0.174845i | ||||
\(778\) | 48.9090 | − | 28.2376i | 1.75347 | − | 1.01237i | ||||
\(779\) | 19.5499i | 0.700448i | ||||||||
\(780\) | 9.55842 | + | 31.7017i | 0.342246 | + | 1.13510i | ||||
\(781\) | 8.44158 | − | 4.87375i | 0.302063 | − | 0.174396i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −24.0000 | − | 19.8997i | −0.857690 | − | 0.711159i | ||||
\(784\) | 4.37228 | − | 7.57301i | 0.156153 | − | 0.270465i | ||||
\(785\) | −14.4891 | − | 8.36530i | −0.517139 | − | 0.298570i | ||||
\(786\) | −14.3030 | − | 47.4376i | −0.510171 | − | 1.69204i | ||||
\(787\) | −33.7337 | + | 19.4762i | −1.20248 | + | 0.694250i | −0.961105 | − | 0.276183i | \(-0.910930\pi\) |
−0.241371 | + | 0.970433i | \(0.577597\pi\) | |||||||
\(788\) | −53.7921 | + | 93.1707i | −1.91626 | + | 3.31907i | ||||
\(789\) | −40.4674 | − | 9.50744i | −1.44068 | − | 0.338474i | ||||
\(790\) | 4.10891i | 0.146189i | ||||||||
\(791\) | 5.28873i | 0.188045i | ||||||||
\(792\) | −43.4198 | − | 65.4579i | −1.54286 | − | 2.32594i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 34.1644 | − | 19.7248i | 1.21245 | − | 0.700008i | ||||
\(795\) | −18.3030 | + | 5.51856i | −0.649140 | + | 0.195723i | ||||
\(796\) | 23.7921 | + | 13.7364i | 0.843289 | + | 0.486873i | ||||
\(797\) | −19.9307 | + | 34.5210i | −0.705982 | + | 1.22280i | 0.260354 | + | 0.965513i | \(0.416161\pi\) |
−0.966336 | + | 0.257283i | \(0.917173\pi\) | |||||||
\(798\) | 58.5367 | + | 55.0106i | 2.07218 | + | 1.94736i | ||||
\(799\) | −9.35053 | + | 5.39853i | −0.330798 | + | 0.190986i | ||||
\(800\) | −4.88316 | + | 2.81929i | −0.172646 | + | 0.0996770i | ||||
\(801\) | 16.1168 | + | 8.01544i | 0.569461 | + | 0.283212i | ||||
\(802\) | − | 35.9306i | − | 1.26875i | ||||||
\(803\) | 24.5584 | − | 14.1788i | 0.866648 | − | 0.500359i | ||||
\(804\) | −57.6535 | + | 61.3489i | −2.03328 | + | 2.16361i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −15.3030 | − | 18.9325i | −0.539025 | − | 0.666870i | ||||
\(807\) | −18.8139 | + | 20.0198i | −0.662279 | + | 0.704729i | ||||
\(808\) | 32.0000 | 1.12576 | ||||||||
\(809\) | −3.30298 | − | 5.72094i | −0.116127 | − | 0.201137i | 0.802103 | − | 0.597186i | \(-0.203715\pi\) |
−0.918230 | + | 0.396048i | \(0.870381\pi\) | |||||||
\(810\) | 56.9090 | − | 7.10313i | 1.99958 | − | 0.249579i | ||||
\(811\) | 0.500000 | − | 0.866025i | 0.0175574 | − | 0.0304103i | −0.857113 | − | 0.515128i | \(-0.827744\pi\) |
0.874671 | + | 0.484718i | \(0.161078\pi\) | |||||||
\(812\) | 31.1168 | + | 53.8960i | 1.09199 | + | 1.89138i | ||||
\(813\) | 0.941578 | − | 4.00772i | 0.0330226 | − | 0.140557i | ||||
\(814\) | 19.1168 | 0.670045 | ||||||||
\(815\) | −1.37228 | − | 0.792287i | −0.0480689 | − | 0.0277526i | ||||
\(816\) | 5.18614 | + | 17.2005i | 0.181551 | + | 0.602137i | ||||
\(817\) | 58.0842 | + | 33.5349i | 2.03211 | + | 1.17324i | ||||
\(818\) | −30.0475 | − | 52.0439i | −1.05059 | − | 1.81967i | ||||
\(819\) | −5.48913 | + | 11.0371i | −0.191806 | + | 0.385668i | ||||
\(820\) | −13.9307 | − | 24.1287i | −0.486481 | − | 0.842610i | ||||
\(821\) | −50.2337 | −1.75317 | −0.876584 | − | 0.481249i | \(-0.840183\pi\) | ||||
−0.876584 | + | 0.481249i | \(0.840183\pi\) | |||||||
\(822\) | 52.1644 | + | 49.0222i | 1.81944 | + | 1.70985i | ||||
\(823\) | 25.6753 | − | 14.8236i | 0.894984 | − | 0.516719i | 0.0194142 | − | 0.999812i | \(-0.493820\pi\) |
0.875569 | + | 0.483093i | \(0.160487\pi\) | |||||||
\(824\) | 71.2812 | + | 41.1542i | 2.48320 | + | 1.43368i | ||||
\(825\) | 10.1168 | + | 2.37686i | 0.352223 | + | 0.0827517i | ||||
\(826\) | 6.67527 | − | 11.5619i | 0.232262 | − | 0.402290i | ||||
\(827\) | −18.0475 | + | 31.2593i | −0.627575 | + | 1.08699i | 0.360462 | + | 0.932774i | \(0.382619\pi\) |
−0.988037 | + | 0.154217i | \(0.950714\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 52.5687i | − | 1.82579i | −0.408200 | − | 0.912893i | \(-0.633843\pi\) | ||
0.408200 | − | 0.912893i | \(-0.366157\pi\) | |||||||
\(830\) | 24.3030 | + | 42.0940i | 0.843569 | + | 1.46110i | ||||
\(831\) | 3.17527 | − | 13.5152i | 0.110149 | − | 0.468836i | ||||
\(832\) | 3.55842 | + | 2.05446i | 0.123366 | + | 0.0712254i | ||||
\(833\) | 2.23369 | 0.0773927 | ||||||||
\(834\) | −44.2337 | − | 10.3923i | −1.53169 | − | 0.359856i | ||||
\(835\) | 41.3292i | 1.43025i | ||||||||
\(836\) | 148.052 | 5.12047 | ||||||||
\(837\) | −25.2337 | + | 14.1514i | −0.872204 | + | 0.489143i | ||||
\(838\) | 89.2119 | 3.08178 | ||||||||
\(839\) | − | 28.4125i | − | 0.980909i | −0.871467 | − | 0.490455i | \(-0.836831\pi\) | ||
0.871467 | − | 0.490455i | \(-0.163169\pi\) | |||||||
\(840\) | −60.4674 | − | 14.2063i | −2.08632 | − | 0.490163i | ||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 44.5367 | + | 25.7133i | 1.53484 | + | 0.886137i | ||||
\(843\) | −5.88316 | + | 25.0410i | −0.202627 | + | 0.862458i | ||||
\(844\) | −53.5367 | − | 92.7282i | −1.84281 | − | 3.19184i | ||||
\(845\) | 25.2434i | 0.868399i | ||||||||
\(846\) | −44.9783 | − | 22.3692i | −1.54638 | − | 0.769068i | ||||
\(847\) | 9.62772 | − | 16.6757i | 0.330812 | − | 0.572984i | ||||
\(848\) | 13.9307 | − | 24.1287i | 0.478382 | − | 0.828582i | ||||
\(849\) | 44.4307 | + | 10.4386i | 1.52486 | + | 0.358252i | ||||
\(850\) | −4.88316 | − | 2.81929i | −0.167491 | − | 0.0967009i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −12.3030 | − | 11.5619i | −0.421493 | − | 0.396104i | ||||
\(853\) | −4.35053 | −0.148959 | −0.0744797 | − | 0.997223i | \(-0.523730\pi\) | ||||
−0.0744797 | + | 0.997223i | \(0.523730\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −26.1168 | + | 52.5138i | −0.893177 | + | 1.79593i | ||||
\(856\) | −7.55842 | − | 13.0916i | −0.258342 | − | 0.447461i | ||||
\(857\) | 48.3981 | + | 27.9426i | 1.65325 | + | 0.954503i | 0.975725 | + | 0.219000i | \(0.0702795\pi\) |
0.677522 | + | 0.735502i | \(0.263054\pi\) | |||||||
\(858\) | 9.55842 | + | 31.7017i | 0.326319 | + | 1.08228i | ||||
\(859\) | −28.8505 | − | 16.6569i | −0.984367 | − | 0.568325i | −0.0807816 | − | 0.996732i | \(-0.525742\pi\) |
−0.903586 | + | 0.428407i | \(0.859075\pi\) | |||||||
\(860\) | −95.5842 | −3.25939 | ||||||||
\(861\) | 2.37228 | − | 10.0974i | 0.0808471 | − | 0.344117i | ||||
\(862\) | −20.3030 | − | 35.1658i | −0.691522 | − | 1.19775i | ||||
\(863\) | −18.0475 | + | 31.2593i | −0.614346 | + | 1.06408i | 0.376153 | + | 0.926557i | \(0.377247\pi\) |
−0.990499 | + | 0.137520i | \(0.956087\pi\) | |||||||
\(864\) | −13.6277 | + | 16.4356i | −0.463624 | + | 0.559152i | ||||
\(865\) | 17.9307 | + | 31.0569i | 0.609662 | + | 1.05597i | ||||
\(866\) | −72.7011 | −2.47048 | ||||||||
\(867\) | 17.0217 | − | 18.1128i | 0.578089 | − | 0.615143i | ||||
\(868\) | 57.0475 | − | 8.98266i | 1.93632 | − | 0.304891i | ||||
\(869\) | 2.81929i | 0.0956379i | ||||||||
\(870\) | −45.3505 | + | 48.2574i | −1.53753 | + | 1.63608i | ||||
\(871\) | 16.6753 | − | 9.62747i | 0.565020 | − | 0.326214i | ||||
\(872\) | − | 39.6897i | − | 1.34406i | ||||||
\(873\) | −14.4307 | − | 7.17687i | −0.488405 | − | 0.242900i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −18.8139 | + | 10.8622i | −0.636025 | + | 0.367209i | ||||
\(876\) | −35.7921 | − | 33.6361i | −1.20930 | − | 1.13646i | ||||
\(877\) | −6.87228 | + | 11.9031i | −0.232060 | + | 0.401940i | −0.958414 | − | 0.285380i | \(-0.907880\pi\) |
0.726354 | + | 0.687321i | \(0.241213\pi\) | |||||||
\(878\) | −74.2812 | − | 42.8863i | −2.50687 | − | 1.44734i | ||||
\(879\) | 32.9090 | − | 9.92242i | 1.10999 | − | 0.334675i | ||||
\(880\) | −60.9090 | + | 35.1658i | −2.05324 | + | 1.18544i | ||||
\(881\) | 12.3030 | − | 21.3094i | 0.414498 | − | 0.717932i | −0.580878 | − | 0.813991i | \(-0.697290\pi\) |
0.995376 | + | 0.0960592i | \(0.0306238\pi\) | |||||||
\(882\) | 5.74456 | + | 8.66025i | 0.193429 | + | 0.291606i | ||||
\(883\) | − | 27.9152i | − | 0.939421i | −0.882820 | − | 0.469711i | \(-0.844358\pi\) | ||
0.882820 | − | 0.469711i | \(-0.155642\pi\) | |||||||
\(884\) | − | 12.3267i | − | 0.414593i | ||||||
\(885\) | 9.48913 | + | 2.22938i | 0.318973 | + | 0.0749399i | ||||
\(886\) | −29.0475 | + | 50.3118i | −0.975871 | + | 1.69026i | ||||
\(887\) | 2.18614 | − | 1.26217i | 0.0734034 | − | 0.0423795i | −0.462849 | − | 0.886437i | \(-0.653173\pi\) |
0.536253 | + | 0.844058i | \(0.319839\pi\) | |||||||
\(888\) | −5.18614 | − | 17.2005i | −0.174035 | − | 0.577210i | ||||
\(889\) | −27.5584 | − | 15.9109i | −0.924280 | − | 0.533633i | ||||
\(890\) | 19.1168 | − | 33.1113i | 0.640798 | − | 1.10989i | ||||
\(891\) | 39.0475 | − | 4.87375i | 1.30814 | − | 0.163277i | ||||
\(892\) | 32.7921 | − | 18.9325i | 1.09796 | − | 0.633908i | ||||
\(893\) | 44.4891 | − | 25.6858i | 1.48877 | − | 0.859543i | ||||
\(894\) | −1.18614 | − | 3.93398i | −0.0396705 | − | 0.131572i | ||||
\(895\) | − | 19.2549i | − | 0.643622i | ||||||
\(896\) | −29.1861 | + | 16.8506i | −0.975041 | + | 0.562940i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 96.5147i | 3.22074i | ||||||||
\(899\) | 12.0000 | − | 31.1769i | 0.400222 | − | 1.03981i | ||||
\(900\) | −1.11684 | − | 17.9653i | −0.0372281 | − | 0.598844i | ||||
\(901\) | 7.11684 | 0.237096 | ||||||||
\(902\) | −13.9307 | − | 24.1287i | −0.463842 | − | 0.803397i | ||||
\(903\) | −25.9307 | − | 24.3687i | −0.862920 | − | 0.810941i | ||||
\(904\) | 6.67527 | − | 11.5619i | 0.222016 | − | 0.384543i | ||||
\(905\) | −8.18614 | − | 14.1788i | −0.272117 | − | 0.471320i | ||||
\(906\) | 98.5842 | + | 23.1615i | 3.27524 | + | 0.769488i | ||||
\(907\) | 54.9783 | 1.82552 | 0.912761 | − | 0.408493i | \(-0.133946\pi\) | ||||
0.912761 | + | 0.408493i | \(0.133946\pi\) | |||||||
\(908\) | 53.7921 | + | 31.0569i | 1.78515 | + | 1.03066i | ||||
\(909\) | −7.13859 | + | 14.3537i | −0.236772 | + | 0.476083i | ||||
\(910\) | 22.6753 | + | 13.0916i | 0.751678 | + | 0.433981i | ||||
\(911\) | 19.9307 | + | 34.5210i | 0.660334 | + | 1.14373i | 0.980528 | + | 0.196380i | \(0.0629185\pi\) |
−0.320194 | + | 0.947352i | \(0.603748\pi\) | |||||||
\(912\) | −24.6753 | − | 81.8386i | −0.817080 | − | 2.70995i | ||||
\(913\) | 16.6753 | + | 28.8824i | 0.551871 | + | 0.955868i | ||||
\(914\) | −32.2337 | −1.06620 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 11.4416 | − | 6.60580i | 0.378040 | − | 0.218262i | ||||
\(917\) | −23.2812 | − | 13.4414i | −0.768814 | − | 0.443875i | ||||
\(918\) | −21.0475 | − | 3.58413i | −0.694673 | − | 0.118294i | ||||
\(919\) | 22.6168 | − | 39.1735i | 0.746061 | − | 1.29222i | −0.203637 | − | 0.979047i | \(-0.565276\pi\) |
0.949697 | − | 0.313169i | \(-0.101391\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.12772 | + | 7.05684i | 0.0701107 | + | 0.232531i | ||||
\(922\) | − | 15.1460i | − | 0.498808i | ||||||
\(923\) | 1.93070 | + | 3.34408i | 0.0635499 | + | 0.110072i | ||||
\(924\) | −76.4674 | − | 17.9653i | −2.51559 | − | 0.591016i | ||||
\(925\) | 2.05842 | + | 1.18843i | 0.0676805 | + | 0.0390754i | ||||
\(926\) | 46.4674 | 1.52701 | ||||||||
\(927\) | −34.3614 | + | 22.7928i | −1.12858 | + | 0.748613i | ||||
\(928\) | − | 24.6535i | − | 0.809290i | ||||||
\(929\) | 26.2337 | 0.860699 | 0.430350 | − | 0.902662i | \(-0.358390\pi\) | ||||
0.430350 | + | 0.902662i | \(0.358390\pi\) | |||||||
\(930\) | 26.6753 | + | 55.3605i | 0.874716 | + | 1.81534i | ||||
\(931\) | −10.6277 | −0.348309 | ||||||||
\(932\) | − | 44.1485i | − | 1.44613i | ||||||
\(933\) | 12.1168 | − | 51.5740i | 0.396688 | − | 1.68846i | ||||
\(934\) | −39.7228 | −1.29977 | ||||||||
\(935\) | −15.5584 | − | 8.98266i | −0.508815 | − | 0.293764i | ||||
\(936\) | 25.9307 | − | 17.2005i | 0.847572 | − | 0.562215i | ||||
\(937\) | 22.6168 | + | 39.1735i | 0.738860 | + | 1.27974i | 0.953009 | + | 0.302942i | \(0.0979689\pi\) |
−0.214149 | + | 0.976801i | \(0.568698\pi\) | |||||||
\(938\) | 66.5725i | 2.17367i | ||||||||
\(939\) | −5.01087 | + | 1.51084i | −0.163524 | + | 0.0493043i | ||||
\(940\) | −36.6060 | + | 63.4034i | −1.19396 | + | 2.06799i | ||||
\(941\) | −1.93070 | + | 3.34408i | −0.0629391 | + | 0.109014i | −0.895778 | − | 0.444502i | \(-0.853381\pi\) |
0.832839 | + | 0.553516i | \(0.186714\pi\) | |||||||
\(942\) | −6.62772 | + | 28.2101i | −0.215943 | + | 0.919136i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −12.3030 | + | 7.10313i | −0.400428 | + | 0.231187i | ||||
\(945\) | 19.8614 | − | 23.9538i | 0.646092 | − | 0.779216i | ||||
\(946\) | −95.5842 | −3.10771 | ||||||||
\(947\) | 1.93070 | + | 3.34408i | 0.0627394 | + | 0.108668i | 0.895689 | − | 0.444681i | \(-0.146683\pi\) |
−0.832950 | + | 0.553349i | \(0.813350\pi\) | |||||||
\(948\) | 4.67527 | − | 1.40965i | 0.151846 | − | 0.0457832i | ||||
\(949\) | 5.61684 | + | 9.72866i | 0.182330 | + | 0.315806i | ||||
\(950\) | 23.2337 | + | 13.4140i | 0.753800 | + | 0.435207i | ||||
\(951\) | 13.5367 | − | 4.08146i | 0.438957 | − | 0.132350i | ||||
\(952\) | 20.0258 | + | 11.5619i | 0.649040 | + | 0.374723i | ||||
\(953\) | −34.4674 | −1.11651 | −0.558254 | − | 0.829670i | \(-0.688528\pi\) | ||||
−0.558254 | + | 0.829670i | \(0.688528\pi\) | |||||||
\(954\) | 18.3030 | + | 27.5928i | 0.592581 | + | 0.893349i | ||||
\(955\) | −23.0475 | − | 39.9195i | −0.745801 | − | 1.29177i | ||||
\(956\) | 34.6753 | − | 60.0593i | 1.12148 | − | 1.94246i | ||||
\(957\) | −31.1168 | + | 33.1113i | −1.00586 | + | 1.07034i | ||||
\(958\) | −29.0475 | − | 50.3118i | −0.938484 | − | 1.62550i | ||||
\(959\) | 38.8397 | 1.25420 | ||||||||
\(960\) | −7.55842 | − | 7.10313i | −0.243947 | − | 0.229253i | ||||
\(961\) | −23.0000 | − | 20.7846i | −0.741935 | − | 0.670471i | ||||
\(962\) | 7.57301i | 0.244164i | ||||||||
\(963\) | 7.55842 | − | 0.469882i | 0.243567 | − | 0.0151417i | ||||
\(964\) | −103.259 | + | 59.6169i | −3.32576 | + | 1.92013i | ||||
\(965\) | 4.40387i | 0.141765i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.558422 | + | 0.322405i | −0.0179576 | + | 0.0103678i | −0.508952 | − | 0.860795i | \(-0.669967\pi\) |
0.490994 | + | 0.871163i | \(0.336634\pi\) | |||||||
\(968\) | −42.0951 | + | 24.3036i | −1.35299 | + | 0.781148i | ||||
\(969\) | 14.9525 | − | 15.9109i | 0.480342 | − | 0.511131i | ||||
\(970\) | −17.1168 | + | 29.6472i | −0.549589 | + | 0.951916i | ||||
\(971\) | 13.9307 | + | 8.04290i | 0.447058 | + | 0.258109i | 0.706587 | − | 0.707626i | \(-0.250234\pi\) |
−0.259529 | + | 0.965735i | \(0.583567\pi\) | |||||||
\(972\) | −27.6060 | − | 62.3162i | −0.885462 | − | 1.99879i | ||||
\(973\) | −21.3505 | + | 12.3267i | −0.684467 | + | 0.395177i | ||||
\(974\) | −34.4198 | + | 59.6169i | −1.10288 | + | 1.91025i | ||||
\(975\) | −0.941578 | + | 4.00772i | −0.0301546 | + | 0.128350i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 40.9793i | − | 1.31104i | −0.755176 | − | 0.655522i | \(-0.772449\pi\) | ||
0.755176 | − | 0.655522i | \(-0.227551\pi\) | |||||||
\(978\) | −0.627719 | + | 2.67181i | −0.0200722 | + | 0.0854352i | ||||
\(979\) | 13.1168 | − | 22.7190i | 0.419216 | − | 0.726104i | ||||
\(980\) | 13.1168 | − | 7.57301i | 0.419002 | − | 0.241911i | ||||
\(981\) | 17.8030 | + | 8.85402i | 0.568406 | + | 0.282687i | ||||
\(982\) | −87.1426 | − | 50.3118i | −2.78083 | − | 1.60551i | ||||
\(983\) | −13.9307 | + | 24.1287i | −0.444320 | + | 0.769586i | −0.998005 | − | 0.0631412i | \(-0.979888\pi\) |
0.553684 | + | 0.832727i | \(0.313221\pi\) | |||||||
\(984\) | −17.9307 | + | 19.0800i | −0.571610 | + | 0.608249i | ||||
\(985\) | −53.7921 | + | 31.0569i | −1.71396 | + | 0.989555i | ||||
\(986\) | 21.3505 | − | 12.3267i | 0.679939 | − | 0.392563i | ||||
\(987\) | −26.0951 | + | 7.86797i | −0.830616 | + | 0.250440i | ||||
\(988\) | 58.6497i | 1.86589i | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −5.18614 | − | 83.4232i | −0.164826 | − | 2.65136i | ||||
\(991\) | − | 13.6540i | − | 0.433734i | −0.976201 | − | 0.216867i | \(-0.930416\pi\) | ||
0.976201 | − | 0.216867i | \(-0.0695839\pi\) | |||||||
\(992\) | −21.3505 | − | 8.21782i | −0.677880 | − | 0.260916i | ||||
\(993\) | 2.18614 | + | 2.05446i | 0.0693751 | + | 0.0651962i | ||||
\(994\) | −13.3505 | −0.423453 | ||||||||
\(995\) | 7.93070 | + | 13.7364i | 0.251420 | + | 0.435473i | ||||
\(996\) | 39.5584 | − | 42.0940i | 1.25346 | − | 1.33380i | ||||
\(997\) | 16.1861 | − | 28.0352i | 0.512620 | − | 0.887884i | −0.487273 | − | 0.873250i | \(-0.662008\pi\) |
0.999893 | − | 0.0146344i | \(-0.00465844\pi\) | |||||||
\(998\) | −0.813859 | − | 1.40965i | −0.0257623 | − | 0.0446216i | ||||
\(999\) | 8.87228 | + | 1.51084i | 0.280707 | + | 0.0478007i |
(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 | 93.2.g.e.68.2 | yes | 4 | |
3.2 | odd | 2 | 93.2.g.f.68.1 | yes | 4 | ||
31.26 | odd | 6 | 93.2.g.f.26.2 | yes | 4 | ||
93.26 | even | 6 | inner | 93.2.g.e.26.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
93.2.g.e.26.1 | ✓ | 4 | 93.26 | even | 6 | inner | |
93.2.g.e.68.2 | yes | 4 | 1.1 | even | 1 | trivial | |
93.2.g.f.26.2 | yes | 4 | 31.26 | odd | 6 | ||
93.2.g.f.68.1 | yes | 4 | 3.2 | odd | 2 |