Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [810,3,Mod(269,810)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(810, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("810.269");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 810 = 2 \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 810.j (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(22.0709014132\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 270) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 539.2 | ||
Root | \(0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 810.539 |
Dual form | 810.3.j.b.269.2 |
$q$-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 \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).
\(n\) | \(487\) | \(731\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 1.22474i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | + | 1.73205i | −0.250000 | + | 0.433013i | ||||
\(5\) | 3.08725 | − | 3.93305i | 0.617449 | − | 0.786611i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 9.52628 | − | 5.50000i | 1.36090 | − | 0.785714i | 0.371154 | − | 0.928571i | \(-0.378962\pi\) |
0.989743 | + | 0.142857i | \(0.0456289\pi\) | |||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −7.00000 | − | 1.00000i | −0.700000 | − | 0.100000i | ||||
\(11\) | 6.12372 | − | 3.53553i | 0.556702 | − | 0.321412i | −0.195119 | − | 0.980780i | \(-0.562509\pi\) |
0.751821 | + | 0.659367i | \(0.229176\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −12.9904 | − | 7.50000i | −0.999260 | − | 0.576923i | −0.0912308 | − | 0.995830i | \(-0.529080\pi\) |
−0.908029 | + | 0.418907i | \(0.862413\pi\) | |||||||
\(14\) | −13.4722 | − | 7.77817i | −0.962300 | − | 0.555584i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.125000 | − | 0.216506i | ||||
\(17\) | 22.6274 | 1.33102 | 0.665512 | − | 0.746387i | \(-0.268213\pi\) | ||||
0.665512 | + | 0.746387i | \(0.268213\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.00000 | −0.157895 | −0.0789474 | − | 0.996879i | \(-0.525156\pi\) | ||||
−0.0789474 | + | 0.996879i | \(0.525156\pi\) | |||||||
\(20\) | 3.72500 | + | 9.28032i | 0.186250 | + | 0.464016i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.66025 | − | 5.00000i | −0.393648 | − | 0.227273i | ||||
\(23\) | 9.19239 | − | 15.9217i | 0.399669 | − | 0.692247i | −0.594016 | − | 0.804453i | \(-0.702458\pi\) |
0.993685 | + | 0.112206i | \(0.0357917\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.93782 | − | 24.2846i | −0.237513 | − | 0.971384i | ||||
\(26\) | 21.2132i | 0.815892i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 22.0000i | 0.785714i | ||||||||
\(29\) | −11.0227 | + | 6.36396i | −0.380093 | + | 0.219447i | −0.677859 | − | 0.735192i | \(-0.737092\pi\) |
0.297766 | + | 0.954639i | \(0.403759\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | − | 6.92820i | 0.129032 | − | 0.223490i | −0.794270 | − | 0.607565i | \(-0.792146\pi\) |
0.923302 | + | 0.384075i | \(0.125480\pi\) | |||||||
\(32\) | −2.82843 | + | 4.89898i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −16.0000 | − | 27.7128i | −0.470588 | − | 0.815083i | ||||
\(35\) | 7.77817 | − | 54.4472i | 0.222234 | − | 1.55563i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 65.0000i | 1.75676i | 0.477966 | + | 0.878378i | \(0.341374\pi\) | ||||
−0.477966 | + | 0.878378i | \(0.658626\pi\) | |||||||
\(38\) | 2.12132 | + | 3.67423i | 0.0558242 | + | 0.0966904i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 8.73205 | − | 11.1244i | 0.218301 | − | 0.278109i | ||||
\(41\) | 67.3610 | + | 38.8909i | 1.64295 | + | 0.948558i | 0.979777 | + | 0.200092i | \(0.0641241\pi\) |
0.663173 | + | 0.748466i | \(0.269209\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −27.7128 | + | 16.0000i | −0.644484 | + | 0.372093i | −0.786340 | − | 0.617794i | \(-0.788026\pi\) |
0.141856 | + | 0.989887i | \(0.454693\pi\) | |||||||
\(44\) | 14.1421i | 0.321412i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −26.0000 | −0.565217 | ||||||||
\(47\) | 28.2843 | + | 48.9898i | 0.601793 | + | 1.04234i | 0.992550 | + | 0.121842i | \(0.0388801\pi\) |
−0.390757 | + | 0.920494i | \(0.627787\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 36.0000 | − | 62.3538i | 0.734694 | − | 1.27253i | ||||
\(50\) | −25.5438 | + | 24.4441i | −0.510876 | + | 0.488883i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 25.9808 | − | 15.0000i | 0.499630 | − | 0.288462i | ||||
\(53\) | 12.7279 | 0.240149 | 0.120075 | − | 0.992765i | \(-0.461687\pi\) | ||||
0.120075 | + | 0.992765i | \(0.461687\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.00000 | − | 35.0000i | 0.0909091 | − | 0.636364i | ||||
\(56\) | 26.9444 | − | 15.5563i | 0.481150 | − | 0.277792i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 15.5885 | + | 9.00000i | 0.268767 | + | 0.155172i | ||||
\(59\) | −68.5857 | − | 39.5980i | −1.16247 | − | 0.671152i | −0.210575 | − | 0.977578i | \(-0.567534\pi\) |
−0.951895 | + | 0.306425i | \(0.900867\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −47.5000 | − | 82.2724i | −0.778689 | − | 1.34873i | −0.932698 | − | 0.360659i | \(-0.882552\pi\) |
0.154009 | − | 0.988069i | \(-0.450781\pi\) | |||||||
\(62\) | −11.3137 | −0.182479 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | −69.6024 | + | 27.9375i | −1.07081 | + | 0.429808i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −16.4545 | − | 9.50000i | −0.245589 | − | 0.141791i | 0.372154 | − | 0.928171i | \(-0.378619\pi\) |
−0.617743 | + | 0.786380i | \(0.711953\pi\) | |||||||
\(68\) | −22.6274 | + | 39.1918i | −0.332756 | + | 0.576351i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −72.1840 | + | 28.9737i | −1.03120 | + | 0.413910i | ||||
\(71\) | − | 4.24264i | − | 0.0597555i | −0.999554 | − | 0.0298778i | \(-0.990488\pi\) | ||
0.999554 | − | 0.0298778i | \(-0.00951180\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 119.000i | − | 1.63014i | −0.579365 | − | 0.815068i | \(-0.696699\pi\) | ||
0.579365 | − | 0.815068i | \(-0.303301\pi\) | |||||||
\(74\) | 79.6084 | − | 45.9619i | 1.07579 | − | 0.621107i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.00000 | − | 5.19615i | 0.0394737 | − | 0.0683704i | ||||
\(77\) | 38.8909 | − | 67.3610i | 0.505076 | − | 0.874818i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −49.5000 | − | 85.7365i | −0.626582 | − | 1.08527i | −0.988233 | − | 0.152959i | \(-0.951120\pi\) |
0.361650 | − | 0.932314i | \(-0.382213\pi\) | |||||||
\(80\) | −19.7990 | − | 2.82843i | −0.247487 | − | 0.0353553i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 110.000i | − | 1.34146i | ||||||
\(83\) | −54.4472 | − | 94.3054i | −0.655991 | − | 1.13621i | −0.981644 | − | 0.190720i | \(-0.938918\pi\) |
0.325654 | − | 0.945489i | \(-0.394416\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 69.8564 | − | 88.9948i | 0.821840 | − | 1.04700i | ||||
\(86\) | 39.1918 | + | 22.6274i | 0.455719 | + | 0.263109i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 17.3205 | − | 10.0000i | 0.196824 | − | 0.113636i | ||||
\(89\) | 90.5097i | 1.01696i | 0.861073 | + | 0.508481i | \(0.169793\pi\) | ||||
−0.861073 | + | 0.508481i | \(0.830207\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −165.000 | −1.81319 | ||||||||
\(92\) | 18.3848 | + | 31.8434i | 0.199835 | + | 0.346124i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 40.0000 | − | 69.2820i | 0.425532 | − | 0.737043i | ||||
\(95\) | −9.26174 | + | 11.7992i | −0.0974920 | + | 0.124202i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −82.2724 | + | 47.5000i | −0.848169 | + | 0.489691i | −0.860033 | − | 0.510239i | \(-0.829557\pi\) |
0.0118635 | + | 0.999930i | \(0.496224\pi\) | |||||||
\(98\) | −101.823 | −1.03901 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 48.0000 | + | 14.0000i | 0.480000 | + | 0.140000i | ||||
\(101\) | −97.9796 | + | 56.5685i | −0.970095 | + | 0.560085i | −0.899265 | − | 0.437404i | \(-0.855898\pi\) |
−0.0708298 | + | 0.997488i | \(0.522565\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 99.5929 | + | 57.5000i | 0.966922 | + | 0.558252i | 0.898296 | − | 0.439390i | \(-0.144805\pi\) |
0.0686252 | + | 0.997643i | \(0.478139\pi\) | |||||||
\(104\) | −36.7423 | − | 21.2132i | −0.353292 | − | 0.203973i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.00000 | − | 15.5885i | −0.0849057 | − | 0.147061i | ||||
\(107\) | 173.948 | 1.62568 | 0.812842 | − | 0.582484i | \(-0.197919\pi\) | ||||
0.812842 | + | 0.582484i | \(0.197919\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.00000 | 0.0733945 | 0.0366972 | − | 0.999326i | \(-0.488316\pi\) | ||||
0.0366972 | + | 0.999326i | \(0.488316\pi\) | |||||||
\(110\) | −46.4016 | + | 18.6250i | −0.421833 | + | 0.169318i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −38.1051 | − | 22.0000i | −0.340224 | − | 0.196429i | ||||
\(113\) | 74.2462 | − | 128.598i | 0.657046 | − | 1.13804i | −0.324331 | − | 0.945944i | \(-0.605139\pi\) |
0.981377 | − | 0.192093i | \(-0.0615277\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −34.2417 | − | 85.3083i | −0.297754 | − | 0.741811i | ||||
\(116\) | − | 25.4558i | − | 0.219447i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 112.000i | 0.949153i | ||||||||
\(119\) | 215.555 | − | 124.451i | 1.81139 | − | 1.04580i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −35.5000 | + | 61.4878i | −0.293388 | + | 0.508164i | ||||
\(122\) | −67.1751 | + | 116.351i | −0.550616 | + | 0.953695i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.00000 | + | 13.8564i | 0.0645161 | + | 0.111745i | ||||
\(125\) | −113.844 | − | 51.6188i | −0.910754 | − | 0.412950i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 104.000i | 0.818898i | 0.912333 | + | 0.409449i | \(0.134279\pi\) | ||||
−0.912333 | + | 0.409449i | \(0.865721\pi\) | |||||||
\(128\) | −5.65685 | − | 9.79796i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 83.4327 | + | 65.4904i | 0.641790 | + | 0.503772i | ||||
\(131\) | −58.7878 | − | 33.9411i | −0.448761 | − | 0.259093i | 0.258546 | − | 0.965999i | \(-0.416757\pi\) |
−0.707307 | + | 0.706907i | \(0.750090\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −28.5788 | + | 16.5000i | −0.214878 | + | 0.124060i | ||||
\(134\) | 26.8701i | 0.200523i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 64.0000 | 0.470588 | ||||||||
\(137\) | −44.5477 | − | 77.1589i | −0.325166 | − | 0.563204i | 0.656380 | − | 0.754430i | \(-0.272087\pi\) |
−0.981546 | + | 0.191227i | \(0.938753\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −41.5000 | + | 71.8801i | −0.298561 | + | 0.517123i | −0.975807 | − | 0.218634i | \(-0.929840\pi\) |
0.677246 | + | 0.735757i | \(0.263173\pi\) | |||||||
\(140\) | 86.5272 | + | 67.9194i | 0.618051 | + | 0.485139i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.19615 | + | 3.00000i | −0.0365926 | + | 0.0211268i | ||||
\(143\) | −106.066 | −0.741720 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.00000 | + | 63.0000i | −0.0620690 | + | 0.434483i | ||||
\(146\) | −145.745 | + | 84.1457i | −0.998251 | + | 0.576340i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −112.583 | − | 65.0000i | −0.760698 | − | 0.439189i | ||||
\(149\) | −68.5857 | − | 39.5980i | −0.460307 | − | 0.265758i | 0.251866 | − | 0.967762i | \(-0.418956\pi\) |
−0.712173 | + | 0.702004i | \(0.752289\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 77.5000 | + | 134.234i | 0.513245 | + | 0.888966i | 0.999882 | + | 0.0153622i | \(0.00489013\pi\) |
−0.486637 | + | 0.873604i | \(0.661777\pi\) | |||||||
\(152\) | −8.48528 | −0.0558242 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −110.000 | −0.714286 | ||||||||
\(155\) | −14.9000 | − | 37.1213i | −0.0961291 | − | 0.239492i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.66025 | − | 5.00000i | −0.0551609 | − | 0.0318471i | 0.472166 | − | 0.881510i | \(-0.343472\pi\) |
−0.527327 | + | 0.849663i | \(0.676806\pi\) | |||||||
\(158\) | −70.0036 | + | 121.250i | −0.443061 | + | 0.767403i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 10.5359 | + | 26.2487i | 0.0658494 | + | 0.164054i | ||||
\(161\) | − | 202.233i | − | 1.25610i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 53.0000i | 0.325153i | 0.986696 | + | 0.162577i | \(0.0519805\pi\) | ||||
−0.986696 | + | 0.162577i | \(0.948020\pi\) | |||||||
\(164\) | −134.722 | + | 77.7817i | −0.821475 | + | 0.474279i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −77.0000 | + | 133.368i | −0.463855 | + | 0.803421i | ||||
\(167\) | 67.8823 | − | 117.576i | 0.406481 | − | 0.704045i | −0.588012 | − | 0.808852i | \(-0.700089\pi\) |
0.994493 | + | 0.104807i | \(0.0334226\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 28.0000 | + | 48.4974i | 0.165680 | + | 0.286967i | ||||
\(170\) | −158.392 | − | 22.6274i | −0.931717 | − | 0.133102i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 64.0000i | − | 0.372093i | ||||||
\(173\) | −62.2254 | − | 107.778i | −0.359684 | − | 0.622992i | 0.628224 | − | 0.778033i | \(-0.283782\pi\) |
−0.987908 | + | 0.155041i | \(0.950449\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −190.131 | − | 198.684i | −1.08646 | − | 1.13534i | ||||
\(176\) | −24.4949 | − | 14.1421i | −0.139176 | − | 0.0803530i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 110.851 | − | 64.0000i | 0.622760 | − | 0.359551i | ||||
\(179\) | 287.085i | 1.60383i | 0.597439 | + | 0.801914i | \(0.296185\pi\) | ||||
−0.597439 | + | 0.801914i | \(0.703815\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 113.000 | 0.624309 | 0.312155 | − | 0.950031i | \(-0.398949\pi\) | ||||
0.312155 | + | 0.950031i | \(0.398949\pi\) | |||||||
\(182\) | 116.673 | + | 202.083i | 0.641058 | + | 1.11035i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 26.0000 | − | 45.0333i | 0.141304 | − | 0.244746i | ||||
\(185\) | 255.648 | + | 200.671i | 1.38188 | + | 1.08471i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 138.564 | − | 80.0000i | 0.740984 | − | 0.427807i | ||||
\(188\) | −113.137 | −0.601793 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 21.0000 | + | 3.00000i | 0.110526 | + | 0.0157895i | ||||
\(191\) | 117.576 | − | 67.8823i | 0.615579 | − | 0.355404i | −0.159567 | − | 0.987187i | \(-0.551010\pi\) |
0.775146 | + | 0.631783i | \(0.217676\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −63.2199 | − | 36.5000i | −0.327564 | − | 0.189119i | 0.327195 | − | 0.944957i | \(-0.393897\pi\) |
−0.654759 | + | 0.755838i | \(0.727230\pi\) | |||||||
\(194\) | 116.351 | + | 67.1751i | 0.599746 | + | 0.346264i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 72.0000 | + | 124.708i | 0.367347 | + | 0.636264i | ||||
\(197\) | 214.960 | 1.09117 | 0.545585 | − | 0.838056i | \(-0.316308\pi\) | ||||
0.545585 | + | 0.838056i | \(0.316308\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 123.000 | 0.618090 | 0.309045 | − | 0.951047i | \(-0.399991\pi\) | ||||
0.309045 | + | 0.951047i | \(0.399991\pi\) | |||||||
\(200\) | −16.7947 | − | 68.6872i | −0.0839735 | − | 0.343436i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 138.564 | + | 80.0000i | 0.685961 | + | 0.396040i | ||||
\(203\) | −70.0036 | + | 121.250i | −0.344845 | + | 0.597289i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 360.920 | − | 144.869i | 1.76058 | − | 0.706676i | ||||
\(206\) | − | 162.635i | − | 0.789488i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 60.0000i | 0.288462i | ||||||||
\(209\) | −18.3712 | + | 10.6066i | −0.0879003 | + | 0.0507493i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −130.500 | + | 226.033i | −0.618483 | + | 1.07124i | 0.371279 | + | 0.928521i | \(0.378919\pi\) |
−0.989763 | + | 0.142723i | \(0.954414\pi\) | |||||||
\(212\) | −12.7279 | + | 22.0454i | −0.0600374 | + | 0.103988i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −123.000 | − | 213.042i | −0.574766 | − | 0.995525i | ||||
\(215\) | −22.6274 | + | 158.392i | −0.105244 | + | 0.736707i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 88.0000i | − | 0.405530i | ||||||
\(218\) | −5.65685 | − | 9.79796i | −0.0259489 | − | 0.0449448i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 55.6218 | + | 43.6603i | 0.252826 | + | 0.198456i | ||||
\(221\) | −293.939 | − | 169.706i | −1.33004 | − | 0.767899i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −48.4974 | + | 28.0000i | −0.217477 | + | 0.125561i | −0.604782 | − | 0.796391i | \(-0.706740\pi\) |
0.387304 | + | 0.921952i | \(0.373406\pi\) | |||||||
\(224\) | 62.2254i | 0.277792i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −210.000 | −0.929204 | ||||||||
\(227\) | 211.425 | + | 366.199i | 0.931387 | + | 1.61321i | 0.780953 | + | 0.624590i | \(0.214734\pi\) |
0.150435 | + | 0.988620i | \(0.451933\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.0000 | + | 34.6410i | −0.0873362 | + | 0.151271i | −0.906384 | − | 0.422454i | \(-0.861169\pi\) |
0.819048 | + | 0.573725i | \(0.194502\pi\) | |||||||
\(230\) | −80.2684 | + | 102.259i | −0.348993 | + | 0.444606i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −31.1769 | + | 18.0000i | −0.134383 | + | 0.0775862i | ||||
\(233\) | 90.5097 | 0.388454 | 0.194227 | − | 0.980957i | \(-0.437780\pi\) | ||||
0.194227 | + | 0.980957i | \(0.437780\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 280.000 | + | 40.0000i | 1.19149 | + | 0.170213i | ||||
\(236\) | 137.171 | − | 79.1960i | 0.581235 | − | 0.335576i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −304.841 | − | 176.000i | −1.28084 | − | 0.739496i | ||||
\(239\) | −199.633 | − | 115.258i | −0.835286 | − | 0.482253i | 0.0203729 | − | 0.999792i | \(-0.493515\pi\) |
−0.855659 | + | 0.517540i | \(0.826848\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 104.500 | + | 180.999i | 0.433610 | + | 0.751034i | 0.997181 | − | 0.0750331i | \(-0.0239062\pi\) |
−0.563571 | + | 0.826068i | \(0.690573\pi\) | |||||||
\(242\) | 100.409 | 0.414914 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 190.000 | 0.778689 | ||||||||
\(245\) | −134.100 | − | 334.092i | −0.547347 | − | 1.36364i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 38.9711 | + | 22.5000i | 0.157778 | + | 0.0910931i | ||||
\(248\) | 11.3137 | − | 19.5959i | 0.0456198 | − | 0.0790158i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 17.2801 | + | 175.930i | 0.0691206 | + | 0.703720i | ||||
\(251\) | 207.889i | 0.828245i | 0.910221 | + | 0.414122i | \(0.135911\pi\) | ||||
−0.910221 | + | 0.414122i | \(0.864089\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 130.000i | − | 0.513834i | ||||||
\(254\) | 127.373 | − | 73.5391i | 0.501470 | − | 0.289524i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 220.617 | − | 382.120i | 0.858433 | − | 1.48685i | −0.0149899 | − | 0.999888i | \(-0.504772\pi\) |
0.873423 | − | 0.486962i | \(-0.161895\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 357.500 | + | 619.208i | 1.38031 | + | 2.39077i | ||||
\(260\) | 21.2132 | − | 148.492i | 0.0815892 | − | 0.571125i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 96.0000i | 0.366412i | ||||||||
\(263\) | 96.1665 | + | 166.565i | 0.365652 | + | 0.633328i | 0.988881 | − | 0.148712i | \(-0.0475126\pi\) |
−0.623228 | + | 0.782040i | \(0.714179\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 39.2942 | − | 50.0596i | 0.148280 | − | 0.188904i | ||||
\(266\) | 40.4166 | + | 23.3345i | 0.151942 | + | 0.0877238i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 32.9090 | − | 19.0000i | 0.122795 | − | 0.0708955i | ||||
\(269\) | − | 407.294i | − | 1.51410i | −0.653356 | − | 0.757051i | \(-0.726639\pi\) | ||
0.653356 | − | 0.757051i | \(-0.273361\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −101.000 | −0.372694 | −0.186347 | − | 0.982484i | \(-0.559665\pi\) | ||||
−0.186347 | + | 0.982484i | \(0.559665\pi\) | |||||||
\(272\) | −45.2548 | − | 78.3837i | −0.166378 | − | 0.288175i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −63.0000 | + | 109.119i | −0.229927 | + | 0.398245i | ||||
\(275\) | −122.221 | − | 127.719i | −0.444439 | − | 0.464432i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −159.349 | + | 92.0000i | −0.575266 | + | 0.332130i | −0.759250 | − | 0.650799i | \(-0.774434\pi\) |
0.183984 | + | 0.982929i | \(0.441101\pi\) | |||||||
\(278\) | 117.380 | 0.422229 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 22.0000 | − | 154.000i | 0.0785714 | − | 0.550000i | ||||
\(281\) | −176.363 | + | 101.823i | −0.627627 | + | 0.362361i | −0.779833 | − | 0.625988i | \(-0.784696\pi\) |
0.152205 | + | 0.988349i | \(0.451362\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 471.118 | + | 272.000i | 1.66473 | + | 0.961131i | 0.970410 | + | 0.241461i | \(0.0776267\pi\) |
0.694317 | + | 0.719669i | \(0.255707\pi\) | |||||||
\(284\) | 7.34847 | + | 4.24264i | 0.0258749 | + | 0.0149389i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 75.0000 | + | 129.904i | 0.262238 | + | 0.454209i | ||||
\(287\) | 855.599 | 2.98118 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 223.000 | 0.771626 | ||||||||
\(290\) | 83.5229 | − | 33.5250i | 0.288010 | − | 0.115604i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 206.114 | + | 119.000i | 0.705870 | + | 0.407534i | ||||
\(293\) | 40.3051 | − | 69.8105i | 0.137560 | − | 0.238261i | −0.789012 | − | 0.614377i | \(-0.789407\pi\) |
0.926572 | + | 0.376116i | \(0.122741\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −367.482 | + | 147.503i | −1.24570 | + | 0.500009i | ||||
\(296\) | 183.848i | 0.621107i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 112.000i | 0.375839i | ||||||||
\(299\) | −238.825 | + | 137.886i | −0.798747 | + | 0.461157i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −176.000 | + | 304.841i | −0.584718 | + | 1.01276i | ||||
\(302\) | 109.602 | − | 189.835i | 0.362919 | − | 0.628594i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.00000 | + | 10.3923i | 0.0197368 | + | 0.0341852i | ||||
\(305\) | −470.226 | − | 67.1751i | −1.54172 | − | 0.220246i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 282.000i | − | 0.918567i | −0.888290 | − | 0.459283i | \(-0.848106\pi\) | ||
0.888290 | − | 0.459283i | \(-0.151894\pi\) | |||||||
\(308\) | 77.7817 | + | 134.722i | 0.252538 | + | 0.437409i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −34.9282 | + | 44.4974i | −0.112672 | + | 0.143540i | ||||
\(311\) | 264.545 | + | 152.735i | 0.850627 | + | 0.491110i | 0.860862 | − | 0.508838i | \(-0.169925\pi\) |
−0.0102356 | + | 0.999948i | \(0.503258\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −165.411 | + | 95.5000i | −0.528469 | + | 0.305112i | −0.740393 | − | 0.672174i | \(-0.765361\pi\) |
0.211924 | + | 0.977286i | \(0.432027\pi\) | |||||||
\(314\) | 14.1421i | 0.0450386i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 198.000 | 0.626582 | ||||||||
\(317\) | 124.451 | + | 215.555i | 0.392589 | + | 0.679985i | 0.992790 | − | 0.119865i | \(-0.0382461\pi\) |
−0.600201 | + | 0.799849i | \(0.704913\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −45.0000 | + | 77.9423i | −0.141066 | + | 0.244333i | ||||
\(320\) | 24.6980 | − | 31.4644i | 0.0771812 | − | 0.0983263i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −247.683 | + | 143.000i | −0.769203 | + | 0.444099i | ||||
\(323\) | −67.8823 | −0.210162 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −105.000 | + | 360.000i | −0.323077 | + | 1.10769i | ||||
\(326\) | 64.9115 | − | 37.4767i | 0.199115 | − | 0.114959i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 190.526 | + | 110.000i | 0.580871 | + | 0.335366i | ||||
\(329\) | 538.888 | + | 311.127i | 1.63796 | + | 0.945675i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −78.5000 | − | 135.966i | −0.237160 | − | 0.410773i | 0.722738 | − | 0.691122i | \(-0.242883\pi\) |
−0.959898 | + | 0.280349i | \(0.909550\pi\) | |||||||
\(332\) | 217.789 | 0.655991 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −192.000 | −0.574850 | ||||||||
\(335\) | −88.1630 | + | 35.3875i | −0.263173 | + | 0.105634i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 167.143 | + | 96.5000i | 0.495973 | + | 0.286350i | 0.727049 | − | 0.686586i | \(-0.240891\pi\) |
−0.231076 | + | 0.972936i | \(0.574225\pi\) | |||||||
\(338\) | 39.5980 | − | 68.5857i | 0.117154 | − | 0.202916i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 84.2872 | + | 209.990i | 0.247903 | + | 0.617617i | ||||
\(341\) | − | 56.5685i | − | 0.165890i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 253.000i | − | 0.737609i | ||||||
\(344\) | −78.3837 | + | 45.2548i | −0.227860 | + | 0.131555i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −88.0000 | + | 152.420i | −0.254335 | + | 0.440522i | ||||
\(347\) | −167.584 | + | 290.265i | −0.482952 | + | 0.836497i | −0.999808 | − | 0.0195748i | \(-0.993769\pi\) |
0.516857 | + | 0.856072i | \(0.327102\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 171.500 | + | 297.047i | 0.491404 | + | 0.851137i | 0.999951 | − | 0.00989751i | \(-0.00315053\pi\) |
−0.508547 | + | 0.861034i | \(0.669817\pi\) | |||||||
\(350\) | −108.894 | + | 373.352i | −0.311127 | + | 1.06672i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 40.0000i | 0.113636i | ||||||||
\(353\) | −113.137 | − | 195.959i | −0.320502 | − | 0.555125i | 0.660090 | − | 0.751187i | \(-0.270518\pi\) |
−0.980592 | + | 0.196061i | \(0.937185\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.6865 | − | 13.0981i | −0.0470043 | − | 0.0368960i | ||||
\(356\) | −156.767 | − | 90.5097i | −0.440358 | − | 0.254241i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 351.606 | − | 203.000i | 0.982141 | − | 0.567039i | ||||
\(359\) | − | 411.536i | − | 1.14634i | −0.819436 | − | 0.573170i | \(-0.805713\pi\) | ||
0.819436 | − | 0.573170i | \(-0.194287\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −352.000 | −0.975069 | ||||||||
\(362\) | −79.9031 | − | 138.396i | −0.220727 | − | 0.382310i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 165.000 | − | 285.788i | 0.453297 | − | 0.785133i | ||||
\(365\) | −468.033 | − | 367.382i | −1.28228 | − | 1.00653i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 399.238 | − | 230.500i | 1.08784 | − | 0.628065i | 0.154840 | − | 0.987940i | \(-0.450514\pi\) |
0.933001 | + | 0.359874i | \(0.117180\pi\) | |||||||
\(368\) | −73.5391 | −0.199835 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 65.0000 | − | 455.000i | 0.175676 | − | 1.22973i | ||||
\(371\) | 121.250 | − | 70.0036i | 0.326819 | − | 0.188689i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −137.698 | − | 79.5000i | −0.369164 | − | 0.213137i | 0.303929 | − | 0.952695i | \(-0.401701\pi\) |
−0.673093 | + | 0.739558i | \(0.735035\pi\) | |||||||
\(374\) | −195.959 | − | 113.137i | −0.523955 | − | 0.302506i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 80.0000 | + | 138.564i | 0.212766 | + | 0.368521i | ||||
\(377\) | 190.919 | 0.506416 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 37.0000 | 0.0976253 | 0.0488127 | − | 0.998808i | \(-0.484456\pi\) | ||||
0.0488127 | + | 0.998808i | \(0.484456\pi\) | |||||||
\(380\) | −11.1750 | − | 27.8410i | −0.0294079 | − | 0.0732657i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −166.277 | − | 96.0000i | −0.435280 | − | 0.251309i | ||||
\(383\) | −231.931 | + | 401.716i | −0.605564 | + | 1.04887i | 0.386398 | + | 0.922332i | \(0.373719\pi\) |
−0.991962 | + | 0.126536i | \(0.959614\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −144.869 | − | 360.920i | −0.376282 | − | 0.937454i | ||||
\(386\) | 103.238i | 0.267455i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 190.000i | − | 0.489691i | ||||||
\(389\) | −39.1918 | + | 22.6274i | −0.100750 | + | 0.0581682i | −0.549529 | − | 0.835475i | \(-0.685193\pi\) |
0.448778 | + | 0.893643i | \(0.351859\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 208.000 | − | 360.267i | 0.531969 | − | 0.921398i | ||||
\(392\) | 101.823 | − | 176.363i | 0.259754 | − | 0.449906i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −152.000 | − | 263.272i | −0.385787 | − | 0.668202i | ||||
\(395\) | −490.025 | − | 70.0036i | −1.24057 | − | 0.177224i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 40.0000i | − | 0.100756i | −0.998730 | − | 0.0503778i | \(-0.983957\pi\) | ||
0.998730 | − | 0.0503778i | \(-0.0160426\pi\) | |||||||
\(398\) | −86.9741 | − | 150.644i | −0.218528 | − | 0.378502i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −72.2487 | + | 69.1384i | −0.180622 | + | 0.172846i | ||||
\(401\) | 549.910 | + | 317.491i | 1.37135 | + | 0.791748i | 0.991098 | − | 0.133136i | \(-0.0425046\pi\) |
0.380250 | + | 0.924884i | \(0.375838\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −103.923 | + | 60.0000i | −0.257874 | + | 0.148883i | ||||
\(404\) | − | 226.274i | − | 0.560085i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 198.000 | 0.487685 | ||||||||
\(407\) | 229.810 | + | 398.042i | 0.564643 | + | 0.977990i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −384.500 | + | 665.974i | −0.940098 | + | 1.62830i | −0.174817 | + | 0.984601i | \(0.555933\pi\) |
−0.765281 | + | 0.643696i | \(0.777400\pi\) | |||||||
\(410\) | −432.636 | − | 339.597i | −1.05521 | − | 0.828286i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −199.186 | + | 115.000i | −0.483461 | + | 0.279126i | ||||
\(413\) | −871.156 | −2.10934 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −539.000 | − | 77.0000i | −1.29880 | − | 0.185542i | ||||
\(416\) | 73.4847 | − | 42.4264i | 0.176646 | − | 0.101987i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 25.9808 | + | 15.0000i | 0.0621549 | + | 0.0358852i | ||||
\(419\) | 421.312 | + | 243.245i | 1.00552 | + | 0.580536i | 0.909876 | − | 0.414879i | \(-0.136176\pi\) |
0.0956421 | + | 0.995416i | \(0.469510\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 83.5000 | + | 144.626i | 0.198337 | + | 0.343530i | 0.947989 | − | 0.318302i | \(-0.103113\pi\) |
−0.749652 | + | 0.661832i | \(0.769779\pi\) | |||||||
\(422\) | 369.110 | 0.874668 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 36.0000 | 0.0849057 | ||||||||
\(425\) | −134.358 | − | 549.498i | −0.316135 | − | 1.29294i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −904.997 | − | 522.500i | −2.11943 | − | 1.22365i | ||||
\(428\) | −173.948 | + | 301.287i | −0.406421 | + | 0.703942i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 209.990 | − | 84.2872i | 0.488348 | − | 0.196017i | ||||
\(431\) | 422.850i | 0.981090i | 0.871416 | + | 0.490545i | \(0.163202\pi\) | ||||
−0.871416 | + | 0.490545i | \(0.836798\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 32.0000i | − | 0.0739030i | −0.999317 | − | 0.0369515i | \(-0.988235\pi\) | ||
0.999317 | − | 0.0369515i | \(-0.0117647\pi\) | |||||||
\(434\) | −107.778 | + | 62.2254i | −0.248335 | + | 0.143376i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.00000 | + | 13.8564i | −0.0183486 | + | 0.0317807i | ||||
\(437\) | −27.5772 | + | 47.7650i | −0.0631056 | + | 0.109302i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −324.000 | − | 561.184i | −0.738041 | − | 1.27832i | −0.953376 | − | 0.301784i | \(-0.902418\pi\) |
0.215335 | − | 0.976540i | \(-0.430916\pi\) | |||||||
\(440\) | 14.1421 | − | 98.9949i | 0.0321412 | − | 0.224989i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 480.000i | 1.08597i | ||||||||
\(443\) | 220.617 | + | 382.120i | 0.498007 | + | 0.862574i | 0.999997 | − | 0.00229923i | \(-0.000731869\pi\) |
−0.501990 | + | 0.864873i | \(0.667399\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 355.979 | + | 279.426i | 0.799954 | + | 0.627923i | ||||
\(446\) | 68.5857 | + | 39.5980i | 0.153780 | + | 0.0887847i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 76.2102 | − | 44.0000i | 0.170112 | − | 0.0982143i | ||||
\(449\) | − | 101.823i | − | 0.226778i | −0.993551 | − | 0.113389i | \(-0.963829\pi\) | ||
0.993551 | − | 0.113389i | \(-0.0361707\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 550.000 | 1.21951 | ||||||||
\(452\) | 148.492 | + | 257.196i | 0.328523 | + | 0.569019i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 299.000 | − | 517.883i | 0.658590 | − | 1.14071i | ||||
\(455\) | −509.396 | + | 648.954i | −1.11955 | + | 1.42627i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 318.697 | − | 184.000i | 0.697368 | − | 0.402626i | −0.108998 | − | 0.994042i | \(-0.534764\pi\) |
0.806367 | + | 0.591416i | \(0.201431\pi\) | |||||||
\(458\) | 56.5685 | 0.123512 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 182.000 | + | 26.0000i | 0.395652 | + | 0.0565217i | ||||
\(461\) | 382.120 | − | 220.617i | 0.828895 | − | 0.478563i | −0.0245795 | − | 0.999698i | \(-0.507825\pi\) |
0.853474 | + | 0.521135i | \(0.174491\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 59.7558 | + | 34.5000i | 0.129062 | + | 0.0745140i | 0.563141 | − | 0.826361i | \(-0.309593\pi\) |
−0.434079 | + | 0.900875i | \(0.642926\pi\) | |||||||
\(464\) | 44.0908 | + | 25.4558i | 0.0950233 | + | 0.0548617i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −64.0000 | − | 110.851i | −0.137339 | − | 0.237878i | ||||
\(467\) | −475.176 | −1.01751 | −0.508753 | − | 0.860912i | \(-0.669894\pi\) | ||||
−0.508753 | + | 0.860912i | \(0.669894\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −209.000 | −0.445629 | ||||||||
\(470\) | −149.000 | − | 371.213i | −0.317021 | − | 0.789815i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −193.990 | − | 112.000i | −0.410995 | − | 0.237288i | ||||
\(473\) | −113.137 | + | 195.959i | −0.239190 | + | 0.414290i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 17.8135 | + | 72.8538i | 0.0375020 | + | 0.153376i | ||||
\(476\) | 497.803i | 1.04580i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 326.000i | 0.682008i | ||||||||
\(479\) | −476.426 | + | 275.065i | −0.994626 | + | 0.574247i | −0.906654 | − | 0.421875i | \(-0.861372\pi\) |
−0.0879720 | + | 0.996123i | \(0.528039\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 487.500 | − | 844.375i | 1.01351 | − | 1.75546i | ||||
\(482\) | 147.785 | − | 255.972i | 0.306609 | − | 0.531062i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −71.0000 | − | 122.976i | −0.146694 | − | 0.254082i | ||||
\(485\) | −67.1751 | + | 470.226i | −0.138505 | + | 0.969538i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 507.000i | 1.04107i | 0.853841 | + | 0.520534i | \(0.174267\pi\) | ||||
−0.853841 | + | 0.520534i | \(0.825733\pi\) | |||||||
\(488\) | −134.350 | − | 232.702i | −0.275308 | − | 0.476847i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −314.354 | + | 400.477i | −0.641538 | + | 0.817300i | ||||
\(491\) | −25.7196 | − | 14.8492i | −0.0523822 | − | 0.0302429i | 0.473580 | − | 0.880751i | \(-0.342961\pi\) |
−0.525962 | + | 0.850508i | \(0.676295\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −249.415 | + | 144.000i | −0.505913 | + | 0.292089i | ||||
\(494\) | − | 63.6396i | − | 0.128825i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −32.0000 | −0.0645161 | ||||||||
\(497\) | −23.3345 | − | 40.4166i | −0.0469508 | − | 0.0813211i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 237.000 | − | 410.496i | 0.474950 | − | 0.822637i | −0.524639 | − | 0.851325i | \(-0.675800\pi\) |
0.999588 | + | 0.0286877i | \(0.00913284\pi\) | |||||||
\(500\) | 203.251 | − | 145.565i | 0.406501 | − | 0.291130i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 254.611 | − | 147.000i | 0.507194 | − | 0.292829i | ||||
\(503\) | 165.463 | 0.328952 | 0.164476 | − | 0.986381i | \(-0.447407\pi\) | ||||
0.164476 | + | 0.986381i | \(0.447407\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −80.0000 | + | 560.000i | −0.158416 | + | 1.10891i | ||||
\(506\) | −159.217 | + | 91.9239i | −0.314658 | + | 0.181668i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −180.133 | − | 104.000i | −0.354593 | − | 0.204724i | ||||
\(509\) | −481.325 | − | 277.893i | −0.945628 | − | 0.545959i | −0.0539080 | − | 0.998546i | \(-0.517168\pi\) |
−0.891720 | + | 0.452587i | \(0.850501\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −654.500 | − | 1133.63i | −1.28082 | − | 2.21845i | ||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −624.000 | −1.21401 | ||||||||
\(515\) | 533.618 | − | 214.188i | 1.03615 | − | 0.415898i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 346.410 | + | 200.000i | 0.670039 | + | 0.386847i | ||||
\(518\) | 505.581 | − | 875.693i | 0.976026 | − | 1.69053i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −196.865 | + | 79.0192i | −0.378587 | + | 0.151960i | ||||
\(521\) | 281.428i | 0.540170i | 0.962837 | + | 0.270085i | \(0.0870518\pi\) | ||||
−0.962837 | + | 0.270085i | \(0.912948\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 851.000i | 1.62715i | 0.581459 | + | 0.813576i | \(0.302482\pi\) | ||||
−0.581459 | + | 0.813576i | \(0.697518\pi\) | |||||||
\(524\) | 117.576 | − | 67.8823i | 0.224381 | − | 0.129546i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 136.000 | − | 235.559i | 0.258555 | − | 0.447831i | ||||
\(527\) | 90.5097 | − | 156.767i | 0.171745 | − | 0.297471i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 95.5000 | + | 165.411i | 0.180529 | + | 0.312686i | ||||
\(530\) | −89.0955 | − | 12.7279i | −0.168105 | − | 0.0240149i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 66.0000i | − | 0.124060i | ||||||
\(533\) | −583.363 | − | 1010.41i | −1.09449 | − | 1.89571i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 537.021 | − | 684.148i | 1.00378 | − | 1.27878i | ||||
\(536\) | −46.5403 | − | 26.8701i | −0.0868289 | − | 0.0501307i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −498.831 | + | 288.000i | −0.927194 | + | 0.535316i | ||||
\(539\) | − | 509.117i | − | 0.944558i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 73.0000 | 0.134935 | 0.0674677 | − | 0.997721i | \(-0.478508\pi\) | ||||
0.0674677 | + | 0.997721i | \(0.478508\pi\) | |||||||
\(542\) | 71.4178 | + | 123.699i | 0.131767 | + | 0.228227i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −64.0000 | + | 110.851i | −0.117647 | + | 0.203771i | ||||
\(545\) | 24.6980 | − | 31.4644i | 0.0453174 | − | 0.0577329i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 217.372 | − | 125.500i | 0.397390 | − | 0.229433i | −0.287967 | − | 0.957640i | \(-0.592979\pi\) |
0.685357 | + | 0.728207i | \(0.259646\pi\) | |||||||
\(548\) | 178.191 | 0.325166 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −70.0000 | + | 240.000i | −0.127273 | + | 0.436364i | ||||
\(551\) | 33.0681 | − | 19.0919i | 0.0600147 | − | 0.0346495i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −943.102 | − | 544.500i | −1.70543 | − | 0.984629i | ||||
\(554\) | 225.353 | + | 130.108i | 0.406774 | + | 0.234851i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −83.0000 | − | 143.760i | −0.149281 | − | 0.258562i | ||||
\(557\) | 441.235 | 0.792163 | 0.396081 | − | 0.918215i | \(-0.370370\pi\) | ||||
0.396081 | + | 0.918215i | \(0.370370\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 480.000 | 0.858676 | ||||||||
\(560\) | −204.167 | + | 81.9501i | −0.364584 | + | 0.146339i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 249.415 | + | 144.000i | 0.443799 | + | 0.256228i | ||||
\(563\) | −164.049 | + | 284.141i | −0.291383 | + | 0.504691i | −0.974137 | − | 0.225958i | \(-0.927449\pi\) |
0.682754 | + | 0.730649i | \(0.260782\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −276.567 | − | 689.029i | −0.489500 | − | 1.21952i | ||||
\(566\) | − | 769.332i | − | 1.35924i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 12.0000i | − | 0.0211268i | ||||||
\(569\) | −862.220 | + | 497.803i | −1.51533 | + | 0.874874i | −0.515487 | + | 0.856897i | \(0.672389\pi\) |
−0.999838 | + | 0.0179766i | \(0.994278\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.5000 | − | 30.3109i | 0.0306480 | − | 0.0530839i | −0.850295 | − | 0.526307i | \(-0.823576\pi\) |
0.880943 | + | 0.473223i | \(0.156910\pi\) | |||||||
\(572\) | 106.066 | − | 183.712i | 0.185430 | − | 0.321174i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −605.000 | − | 1047.89i | −1.05401 | − | 1.82559i | ||||
\(575\) | −441.235 | − | 128.693i | −0.767365 | − | 0.223815i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 337.000i | − | 0.584055i | −0.956410 | − | 0.292028i | \(-0.905670\pi\) | ||
0.956410 | − | 0.292028i | \(-0.0943300\pi\) | |||||||
\(578\) | −157.685 | − | 273.118i | −0.272811 | − | 0.472523i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −100.119 | − | 78.5885i | −0.172619 | − | 0.135497i | ||||
\(581\) | −1037.36 | − | 598.919i | −1.78547 | − | 1.03084i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 77.9423 | − | 45.0000i | 0.133692 | − | 0.0771870i | ||||
\(584\) | − | 336.583i | − | 0.576340i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −114.000 | −0.194539 | ||||||||
\(587\) | 235.467 | + | 407.840i | 0.401136 | + | 0.694787i | 0.993863 | − | 0.110616i | \(-0.0352823\pi\) |
−0.592728 | + | 0.805403i | \(0.701949\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.0000 | + | 20.7846i | −0.0203735 | + | 0.0352880i | ||||
\(590\) | 440.502 | + | 345.772i | 0.746614 | + | 0.586054i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 225.167 | − | 130.000i | 0.380349 | − | 0.219595i | ||||
\(593\) | −666.095 | −1.12326 | −0.561631 | − | 0.827388i | \(-0.689826\pi\) | ||||
−0.561631 | + | 0.827388i | \(0.689826\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 176.000 | − | 1232.00i | 0.295798 | − | 2.07059i | ||||
\(596\) | 137.171 | − | 79.1960i | 0.230153 | − | 0.132879i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 337.750 | + | 195.000i | 0.564799 | + | 0.326087i | ||||
\(599\) | 591.552 | + | 341.533i | 0.987566 | + | 0.570171i | 0.904546 | − | 0.426377i | \(-0.140210\pi\) |
0.0830198 | + | 0.996548i | \(0.473544\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −304.000 | − | 526.543i | −0.505824 | − | 0.876112i | −0.999977 | − | 0.00673765i | \(-0.997855\pi\) |
0.494154 | − | 0.869375i | \(-0.335478\pi\) | |||||||
\(602\) | 497.803 | 0.826916 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −310.000 | −0.513245 | ||||||||
\(605\) | 132.238 | + | 329.451i | 0.218575 | + | 0.544548i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −364.597 | − | 210.500i | −0.600654 | − | 0.346787i | 0.168645 | − | 0.985677i | \(-0.446061\pi\) |
−0.769299 | + | 0.638889i | \(0.779394\pi\) | |||||||
\(608\) | 8.48528 | − | 14.6969i | 0.0139561 | − | 0.0241726i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 250.228 | + | 623.407i | 0.410209 | + | 1.02198i | ||||
\(611\) | − | 848.528i | − | 1.38875i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 761.000i | − | 1.24144i | −0.784034 | − | 0.620718i | \(-0.786841\pi\) | ||
0.784034 | − | 0.620718i | \(-0.213159\pi\) | |||||||
\(614\) | −345.378 | + | 199.404i | −0.562505 | + | 0.324762i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 110.000 | − | 190.526i | 0.178571 | − | 0.309295i | ||||
\(617\) | 50.2046 | − | 86.9569i | 0.0813689 | − | 0.140935i | −0.822469 | − | 0.568810i | \(-0.807404\pi\) |
0.903838 | + | 0.427875i | \(0.140737\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 470.500 | + | 814.930i | 0.760097 | + | 1.31653i | 0.942800 | + | 0.333358i | \(0.108182\pi\) |
−0.182703 | + | 0.983168i | \(0.558485\pi\) | |||||||
\(620\) | 79.1960 | + | 11.3137i | 0.127735 | + | 0.0182479i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 432.000i | − | 0.694534i | ||||||
\(623\) | 497.803 | + | 862.220i | 0.799042 | + | 1.38398i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −554.485 | + | 288.395i | −0.887175 | + | 0.461433i | ||||
\(626\) | 233.926 | + | 135.057i | 0.373684 | + | 0.215747i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 17.3205 | − | 10.0000i | 0.0275804 | − | 0.0159236i | ||||
\(629\) | 1470.78i | 2.33829i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −805.000 | −1.27575 | −0.637876 | − | 0.770139i | \(-0.720187\pi\) | ||||
−0.637876 | + | 0.770139i | \(0.720187\pi\) | |||||||
\(632\) | −140.007 | − | 242.499i | −0.221530 | − | 0.383702i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 176.000 | − | 304.841i | 0.277603 | − | 0.480822i | ||||
\(635\) | 409.038 | + | 321.074i | 0.644154 | + | 0.505628i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −935.307 | + | 540.000i | −1.46830 | + | 0.847724i | ||||
\(638\) | 127.279 | 0.199497 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −56.0000 | − | 8.00000i | −0.0875000 | − | 0.0125000i | ||||
\(641\) | 68.5857 | − | 39.5980i | 0.106998 | − | 0.0617753i | −0.445546 | − | 0.895259i | \(-0.646990\pi\) |
0.552544 | + | 0.833484i | \(0.313657\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 956.092 | + | 552.000i | 1.48692 | + | 0.858476i | 0.999889 | − | 0.0149066i | \(-0.00474509\pi\) |
0.487035 | + | 0.873382i | \(0.338078\pi\) | |||||||
\(644\) | 350.277 | + | 202.233i | 0.543908 | + | 0.314026i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 48.0000 | + | 83.1384i | 0.0743034 | + | 0.128697i | ||||
\(647\) | 750.947 | 1.16066 | 0.580330 | − | 0.814381i | \(-0.302923\pi\) | ||||
0.580330 | + | 0.814381i | \(0.302923\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −560.000 | −0.862866 | ||||||||
\(650\) | 515.154 | − | 125.960i | 0.792545 | − | 0.193785i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −91.7987 | − | 53.0000i | −0.140796 | − | 0.0812883i | ||||
\(653\) | −73.5391 | + | 127.373i | −0.112617 | + | 0.195059i | −0.916825 | − | 0.399290i | \(-0.869257\pi\) |
0.804207 | + | 0.594349i | \(0.202590\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −314.985 | + | 126.431i | −0.480892 | + | 0.193024i | ||||
\(656\) | − | 311.127i | − | 0.474279i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 880.000i | − | 1.33739i | ||||||
\(659\) | 862.220 | − | 497.803i | 1.30838 | − | 0.755392i | 0.326552 | − | 0.945179i | \(-0.394113\pi\) |
0.981825 | + | 0.189788i | \(0.0607799\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 624.500 | − | 1081.67i | 0.944781 | − | 1.63641i | 0.188591 | − | 0.982056i | \(-0.439608\pi\) |
0.756190 | − | 0.654352i | \(-0.227059\pi\) | |||||||
\(662\) | −111.016 | + | 192.285i | −0.167698 | + | 0.290461i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −154.000 | − | 266.736i | −0.231928 | − | 0.401711i | ||||
\(665\) | −23.3345 | + | 163.342i | −0.0350895 | + | 0.245627i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 234.000i | 0.350825i | ||||||||
\(668\) | 135.765 | + | 235.151i | 0.203240 | + | 0.352022i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 105.681 | + | 82.9545i | 0.157733 | + | 0.123813i | ||||
\(671\) | −581.754 | − | 335.876i | −0.866995 | − | 0.500560i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 735.256 | − | 424.500i | 1.09250 | − | 0.630758i | 0.158262 | − | 0.987397i | \(-0.449411\pi\) |
0.934242 | + | 0.356639i | \(0.116077\pi\) | |||||||
\(674\) | − | 272.943i | − | 0.404960i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −112.000 | −0.165680 | ||||||||
\(677\) | −282.843 | − | 489.898i | −0.417788 | − | 0.723631i | 0.577928 | − | 0.816088i | \(-0.303861\pi\) |
−0.995717 | + | 0.0924569i | \(0.970528\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −522.500 | + | 904.997i | −0.769514 | + | 1.33284i | ||||
\(680\) | 197.584 | − | 251.715i | 0.290564 | − | 0.370170i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −69.2820 | + | 40.0000i | −0.101587 | + | 0.0586510i | ||||
\(683\) | 117.380 | 0.171859 | 0.0859295 | − | 0.996301i | \(-0.472614\pi\) | ||||
0.0859295 | + | 0.996301i | \(0.472614\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −441.000 | − | 63.0000i | −0.643796 | − | 0.0919708i | ||||
\(686\) | −309.860 | + | 178.898i | −0.451692 | + | 0.260784i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 110.851 | + | 64.0000i | 0.161121 | + | 0.0930233i | ||||
\(689\) | −165.341 | − | 95.4594i | −0.239972 | − | 0.138548i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.00000 | − | 13.8564i | −0.0115774 | − | 0.0200527i | 0.860179 | − | 0.509993i | \(-0.170352\pi\) |
−0.871756 | + | 0.489940i | \(0.837019\pi\) | |||||||
\(692\) | 248.902 | 0.359684 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 474.000 | 0.682997 | ||||||||
\(695\) | 154.588 | + | 385.133i | 0.222428 | + | 0.554149i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1524.20 | + | 880.000i | 2.18681 | + | 1.26255i | ||||
\(698\) | 242.538 | − | 420.087i | 0.347475 | − | 0.601845i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 534.261 | − | 130.632i | 0.763231 | − | 0.186617i | ||||
\(701\) | 1016.82i | 1.45053i | 0.688471 | + | 0.725264i | \(0.258282\pi\) | ||||
−0.688471 | + | 0.725264i | \(0.741718\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 195.000i | − | 0.277383i | ||||||
\(704\) | 48.9898 | − | 28.2843i | 0.0695878 | − | 0.0401765i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −160.000 | + | 277.128i | −0.226629 | + | 0.392533i | ||||
\(707\) | −622.254 | + | 1077.78i | −0.880133 | + | 1.52443i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −115.500 | − | 200.052i | −0.162906 | − | 0.282161i | 0.773004 | − | 0.634401i | \(-0.218753\pi\) |
−0.935910 | + | 0.352241i | \(0.885420\pi\) | |||||||
\(710\) | −4.24264 | + | 29.6985i | −0.00597555 | + | 0.0418289i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 256.000i | 0.359551i | ||||||||
\(713\) | −73.5391 | − | 127.373i | −0.103140 | − | 0.178644i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −327.452 | + | 417.163i | −0.457975 | + | 0.583445i | ||||
\(716\) | −497.246 | − | 287.085i | −0.694478 | − | 0.400957i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −504.027 | + | 291.000i | −0.701987 | + | 0.405292i | ||||
\(719\) | 120.208i | 0.167188i | 0.996500 | + | 0.0835940i | \(0.0266399\pi\) | ||||
−0.996500 | + | 0.0835940i | \(0.973360\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1265.00 | 1.75451 | ||||||||
\(722\) | 248.902 | + | 431.110i | 0.344739 | + | 0.597106i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −113.000 | + | 195.722i | −0.156077 | + | 0.270334i | ||||
\(725\) | 219.997 | + | 229.894i | 0.303444 | + | 0.317095i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −935.307 | + | 540.000i | −1.28653 | + | 0.742779i | −0.978034 | − | 0.208447i | \(-0.933159\pi\) |
−0.308496 | + | 0.951225i | \(0.599826\pi\) | |||||||
\(728\) | −466.690 | −0.641058 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −119.000 | + | 833.000i | −0.163014 | + | 1.14110i | ||||
\(731\) | −627.069 | + | 362.039i | −0.857824 | + | 0.495265i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −297.913 | − | 172.000i | −0.406429 | − | 0.234652i | 0.282825 | − | 0.959172i | \(-0.408728\pi\) |
−0.689254 | + | 0.724519i | \(0.742062\pi\) | |||||||
\(734\) | −564.607 | − | 325.976i | −0.769220 | − | 0.444109i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 52.0000 | + | 90.0666i | 0.0706522 | + | 0.122373i | ||||
\(737\) | −134.350 | −0.182293 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −640.000 | −0.866035 | −0.433018 | − | 0.901385i | \(-0.642551\pi\) | ||||
−0.433018 | + | 0.901385i | \(0.642551\pi\) | |||||||
\(740\) | −603.221 | + | 242.125i | −0.815163 | + | 0.327196i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −171.473 | − | 99.0000i | −0.231096 | − | 0.133423i | ||||
\(743\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −367.482 | + | 147.503i | −0.493264 | + | 0.197990i | ||||
\(746\) | 224.860i | 0.301421i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 320.000i | 0.427807i | ||||||||
\(749\) | 1657.08 | − | 956.715i | 2.21239 | − | 1.27732i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 150.500 | − | 260.674i | 0.200399 | − | 0.347102i | −0.748258 | − | 0.663408i | \(-0.769109\pi\) |
0.948657 | + | 0.316306i | \(0.102443\pi\) | |||||||
\(752\) | 113.137 | − | 195.959i | 0.150448 | − | 0.260584i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −135.000 | − | 233.827i | −0.179045 | − | 0.310115i | ||||
\(755\) | 767.211 | + | 109.602i | 1.01617 | + | 0.145168i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 367.000i | − | 0.484808i | −0.970175 | − | 0.242404i | \(-0.922064\pi\) | ||
0.970175 | − | 0.242404i | \(-0.0779360\pi\) | |||||||
\(758\) | −26.1630 | − | 45.3156i | −0.0345158 | − | 0.0597831i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −26.1962 | + | 33.3731i | −0.0344686 | + | 0.0439119i | ||||
\(761\) | 69.8105 | + | 40.3051i | 0.0917352 | + | 0.0529633i | 0.545166 | − | 0.838328i | \(-0.316467\pi\) |
−0.453431 | + | 0.891292i | \(0.649800\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 76.2102 | − | 44.0000i | 0.0998824 | − | 0.0576671i | ||||
\(764\) | 271.529i | 0.355404i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 656.000 | 0.856397 | ||||||||
\(767\) | 593.970 | + | 1028.79i | 0.774406 | + | 1.34131i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 208.500 | − | 361.133i | 0.271131 | − | 0.469613i | −0.698020 | − | 0.716078i | \(-0.745936\pi\) |
0.969152 | + | 0.246465i | \(0.0792689\pi\) | |||||||
\(770\) | −339.597 | + | 432.636i | −0.441035 | + | 0.561865i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 126.440 | − | 73.0000i | 0.163782 | − | 0.0945596i | ||||
\(773\) | 292.742 | 0.378709 | 0.189355 | − | 0.981909i | \(-0.439360\pi\) | ||||
0.189355 | + | 0.981909i | \(0.439360\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −192.000 | − | 56.0000i | −0.247742 | − | 0.0722581i | ||||
\(776\) | −232.702 | + | 134.350i | −0.299873 | + | 0.173132i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 55.4256 | + | 32.0000i | 0.0712412 | + | 0.0411311i | ||||
\(779\) | −202.083 | − | 116.673i | −0.259413 | − | 0.149772i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.0000 | − | 25.9808i | −0.0192061 | − | 0.0332660i | ||||
\(782\) | −588.313 | −0.752318 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −288.000 | −0.367347 | ||||||||
\(785\) | −46.4016 | + | 18.6250i | −0.0591103 | + | 0.0237261i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 328.224 | + | 189.500i | 0.417057 | + | 0.240788i | 0.693817 | − | 0.720151i | \(-0.255928\pi\) |
−0.276761 | + | 0.960939i | \(0.589261\pi\) | |||||||
\(788\) | −214.960 | + | 372.322i | −0.272792 | + | 0.472490i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 260.763 | + | 649.656i | 0.330080 | + | 0.822349i | ||||
\(791\) | − | 1633.42i | − | 2.06500i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1425.00i | 1.79697i | ||||||||
\(794\) | −48.9898 | + | 28.2843i | −0.0617000 | + | 0.0356225i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −123.000 | + | 213.042i | −0.154523 | + | 0.267641i | ||||
\(797\) | 345.068 | − | 597.675i | 0.432959 | − | 0.749907i | −0.564168 | − | 0.825660i | \(-0.690803\pi\) |
0.997127 | + | 0.0757536i | \(0.0241362\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 640.000 | + | 1108.51i | 0.801001 | + | 1.38737i | ||||
\(800\) | 135.765 | + | 39.5980i | 0.169706 | + | 0.0494975i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 898.000i | − | 1.11970i | ||||||
\(803\) | −420.729 | − | 728.723i | −0.523946 | − | 0.907501i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −795.391 | − | 624.342i | −0.988064 | − | 0.775580i | ||||
\(806\) | 146.969 | + | 84.8528i | 0.182344 | + | 0.105276i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −277.128 | + | 160.000i | −0.342980 | + | 0.198020i | ||||
\(809\) | − | 644.881i | − | 0.797134i | −0.917139 | − | 0.398567i | \(-0.869508\pi\) | ||
0.917139 | − | 0.398567i | \(-0.130492\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 64.0000 | 0.0789149 | 0.0394575 | − | 0.999221i | \(-0.487437\pi\) | ||||
0.0394575 | + | 0.999221i | \(0.487437\pi\) | |||||||
\(812\) | −140.007 | − | 242.499i | −0.172423 | − | 0.298645i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 325.000 | − | 562.917i | 0.399263 | − | 0.691544i | ||||
\(815\) | 208.452 | + | 163.624i | 0.255769 | + | 0.200766i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 83.1384 | − | 48.0000i | 0.101761 | − | 0.0587515i | ||||
\(818\) | 1087.53 | 1.32950 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −110.000 | + | 770.000i | −0.134146 | + | 0.939024i | ||||
\(821\) | 166.565 | − | 96.1665i | 0.202881 | − | 0.117133i | −0.395118 | − | 0.918631i | \(-0.629296\pi\) |
0.597999 | + | 0.801497i | \(0.295963\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −293.583 | − | 169.500i | −0.356722 | − | 0.205954i | 0.310920 | − | 0.950436i | \(-0.399363\pi\) |
−0.667642 | + | 0.744482i | \(0.732696\pi\) | |||||||
\(824\) | 281.691 | + | 162.635i | 0.341858 | + | 0.197372i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 616.000 | + | 1066.94i | 0.745763 | + | 1.29170i | ||||
\(827\) | −724.077 | −0.875547 | −0.437773 | − | 0.899085i | \(-0.644233\pi\) | ||||
−0.437773 | + | 0.899085i | \(0.644233\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 639.000 | 0.770808 | 0.385404 | − | 0.922748i | \(-0.374062\pi\) | ||||
0.385404 | + | 0.922748i | \(0.374062\pi\) | |||||||
\(830\) | 286.825 | + | 714.585i | 0.345573 | + | 0.860945i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −103.923 | − | 60.0000i | −0.124908 | − | 0.0721154i | ||||
\(833\) | 814.587 | − | 1410.91i | 0.977896 | − | 1.69376i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −252.862 | − | 629.969i | −0.302828 | − | 0.754454i | ||||
\(836\) | − | 42.4264i | − | 0.0507493i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 688.000i | − | 0.821002i | ||||||
\(839\) | 244.949 | − | 141.421i | 0.291953 | − | 0.168559i | −0.346869 | − | 0.937914i | \(-0.612755\pi\) |
0.638822 | + | 0.769354i | \(0.279422\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −339.500 | + | 588.031i | −0.403686 | + | 0.699205i | ||||
\(842\) | 118.087 | − | 204.532i | 0.140246 | − | 0.242913i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −261.000 | − | 452.065i | −0.309242 | − | 0.535622i | ||||
\(845\) | 277.186 | + | 39.5980i | 0.328031 | + | 0.0468615i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 781.000i | 0.922078i | ||||||||
\(848\) | −25.4558 | − | 44.0908i | −0.0300187 | − | 0.0519939i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −577.990 | + | 553.108i | −0.679988 | + | 0.650715i | ||||
\(851\) | 1034.91 | + | 597.505i | 1.21611 | + | 0.702121i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 830.518 | − | 479.500i | 0.973644 | − | 0.562134i | 0.0732988 | − | 0.997310i | \(-0.476647\pi\) |
0.900345 | + | 0.435176i | \(0.143314\pi\) | |||||||
\(854\) | 1477.85i | 1.73051i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 492.000 | 0.574766 | ||||||||
\(857\) | −91.2168 | − | 157.992i | −0.106437 | − | 0.184355i | 0.807887 | − | 0.589337i | \(-0.200611\pi\) |
−0.914325 | + | 0.404982i | \(0.867278\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −573.500 | + | 993.331i | −0.667637 | + | 1.15638i | 0.310926 | + | 0.950434i | \(0.399361\pi\) |
−0.978563 | + | 0.205947i | \(0.933973\pi\) | |||||||
\(860\) | −251.715 | − | 197.584i | −0.292692 | − | 0.229749i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 517.883 | − | 299.000i | 0.600793 | − | 0.346868i | ||||
\(863\) | 746.705 | 0.865243 | 0.432622 | − | 0.901576i | \(-0.357589\pi\) | ||||
0.432622 | + | 0.901576i | \(0.357589\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −616.000 | − | 88.0000i | −0.712139 | − | 0.101734i | ||||
\(866\) | −39.1918 | + | 22.6274i | −0.0452562 | + | 0.0261287i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 152.420 | + | 88.0000i | 0.175600 | + | 0.101382i | ||||
\(869\) | −606.249 | − | 350.018i | −0.697639 | − | 0.402782i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 142.500 | + | 246.817i | 0.163605 | + | 0.283372i | ||||
\(872\) | 22.6274 | 0.0259489 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 78.0000 | 0.0892449 | ||||||||
\(875\) | −1368.41 | + | 134.408i | −1.56390 | + | 0.153609i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −567.247 | − | 327.500i | −0.646803 | − | 0.373432i | 0.140427 | − | 0.990091i | \(-0.455152\pi\) |
−0.787230 | + | 0.616659i | \(0.788486\pi\) | |||||||
\(878\) | −458.205 | + | 793.635i | −0.521874 | + | 0.903912i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −131.244 | + | 52.6795i | −0.149140 | + | 0.0598631i | ||||
\(881\) | − | 318.198i | − | 0.361178i | −0.983559 | − | 0.180589i | \(-0.942200\pi\) | ||
0.983559 | − | 0.180589i | \(-0.0578004\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 261.000i | 0.295583i | 0.989019 | + | 0.147792i | \(0.0472165\pi\) | ||||
−0.989019 | + | 0.147792i | \(0.952784\pi\) | |||||||
\(884\) | 587.878 | − | 339.411i | 0.665020 | − | 0.383949i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 312.000 | − | 540.400i | 0.352144 | − | 0.609932i | ||||
\(887\) | 390.323 | − | 676.059i | 0.440048 | − | 0.762186i | −0.557644 | − | 0.830080i | \(-0.688295\pi\) |
0.997693 | + | 0.0678939i | \(0.0216279\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 572.000 | + | 990.733i | 0.643420 | + | 1.11444i | ||||
\(890\) | 90.5097 | − | 633.568i | 0.101696 | − | 0.711874i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 112.000i | − | 0.125561i | ||||||
\(893\) | −84.8528 | − | 146.969i | −0.0950199 | − | 0.164579i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1129.12 | + | 886.303i | 1.26159 | + | 0.990283i | ||||
\(896\) | −107.778 | − | 62.2254i | −0.120287 | − | 0.0694480i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −124.708 | + | 72.0000i | −0.138873 | + | 0.0801782i | ||||
\(899\) | 101.823i | 0.113263i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 288.000 | 0.319645 | ||||||||
\(902\) | −388.909 | − | 673.610i | −0.431163 | − | 0.746796i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 210.000 | − | 363.731i | 0.232301 | − | 0.402357i | ||||
\(905\) | 348.859 | − | 444.435i | 0.385479 | − | 0.491088i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 454.663 | − | 262.500i | 0.501283 | − | 0.289416i | −0.227960 | − | 0.973670i | \(-0.573206\pi\) |
0.729243 | + | 0.684255i | \(0.239872\pi\) | |||||||
\(908\) | −845.700 | −0.931387 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1155.00 | + | 165.000i | 1.26923 | + | 0.181319i | ||||
\(911\) | −440.908 | + | 254.558i | −0.483983 | + | 0.279427i | −0.722075 | − | 0.691815i | \(-0.756811\pi\) |
0.238092 | + | 0.971243i | \(0.423478\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −666.840 | − | 385.000i | −0.730383 | − | 0.421687i | ||||
\(914\) | −450.706 | − | 260.215i | −0.493114 | − | 0.284699i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −40.0000 | − | 69.2820i | −0.0436681 | − | 0.0756354i | ||||
\(917\) | −746.705 | −0.814291 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1272.00 | 1.38411 | 0.692057 | − | 0.721843i | \(-0.256705\pi\) | ||||
0.692057 | + | 0.721843i | \(0.256705\pi\) | |||||||
\(920\) | −96.8501 | − | 241.288i | −0.105272 | − | 0.262270i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −540.400 | − | 312.000i | −0.586117 | − | 0.338395i | ||||
\(923\) | −31.8198 | + | 55.1135i | −0.0344743 | + | 0.0597113i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1578.50 | − | 385.958i | 1.70649 | − | 0.417252i | ||||
\(926\) | − | 97.5807i | − | 0.105379i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 72.0000i | − | 0.0775862i | ||||||
\(929\) | −481.325 | + | 277.893i | −0.518111 | + | 0.299131i | −0.736161 | − | 0.676806i | \(-0.763364\pi\) |
0.218051 | + | 0.975937i | \(0.430030\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −108.000 | + | 187.061i | −0.116004 | + | 0.200925i | ||||
\(932\) | −90.5097 | + | 156.767i | −0.0971134 | + | 0.168205i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 336.000 | + | 581.969i | 0.359743 | + | 0.623093i | ||||
\(935\) | 113.137 | − | 791.960i | 0.121002 | − | 0.847016i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1265.00i | − | 1.35005i | −0.737793 | − | 0.675027i | \(-0.764132\pi\) | ||
0.737793 | − | 0.675027i | \(-0.235868\pi\) | |||||||
\(938\) | 147.785 | + | 255.972i | 0.157554 | + | 0.272891i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −349.282 | + | 444.974i | −0.371577 | + | 0.473377i | ||||
\(941\) | 978.571 | + | 564.978i | 1.03993 | + | 0.600402i | 0.919813 | − | 0.392358i | \(-0.128341\pi\) |
0.120114 | + | 0.992760i | \(0.461674\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1238.42 | − | 715.000i | 1.31327 | − | 0.758218i | ||||
\(944\) | 316.784i | 0.335576i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 320.000 | 0.338266 | ||||||||
\(947\) | −390.323 | − | 676.059i | −0.412168 | − | 0.713896i | 0.582959 | − | 0.812502i | \(-0.301895\pi\) |
−0.995127 | + | 0.0986061i | \(0.968562\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −892.500 | + | 1545.86i | −0.940464 | + | 1.62893i | ||||
\(950\) | 76.6313 | − | 73.3324i | 0.0806646 | − | 0.0771920i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 609.682 | − | 352.000i | 0.640422 | − | 0.369748i | ||||
\(953\) | 463.862 | 0.486739 | 0.243369 | − | 0.969934i | \(-0.421747\pi\) | ||||
0.243369 | + | 0.969934i | \(0.421747\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 96.0000 | − | 672.000i | 0.100524 | − | 0.703665i | ||||
\(956\) | 399.267 | − | 230.517i | 0.417643 | − | 0.241126i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 673.768 | + | 389.000i | 0.703307 | + | 0.406054i | ||||
\(959\) | −848.748 | − | 490.025i | −0.885035 | − | 0.510975i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 448.500 | + | 776.825i | 0.466701 | + | 0.808350i | ||||
\(962\) | −1378.86 | −1.43332 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −418.000 | −0.433610 | ||||||||
\(965\) | −338.732 | + | 135.963i | −0.351017 | + | 0.140894i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −993.331 | − | 573.500i | −1.02723 | − | 0.593071i | −0.111040 | − | 0.993816i | \(-0.535418\pi\) |
−0.916190 | + | 0.400745i | \(0.868751\pi\) | |||||||
\(968\) | −100.409 | + | 173.914i | −0.103728 | + | 0.179663i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 623.407 | − | 250.228i | 0.642688 | − | 0.257967i | ||||
\(971\) | 814.587i | 0.838916i | 0.907775 | + | 0.419458i | \(0.137780\pi\) | ||||
−0.907775 | + | 0.419458i | \(0.862220\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 913.000i | 0.938335i | ||||||||
\(974\) | 620.946 | − | 358.503i | 0.637521 | − | 0.368073i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −190.000 | + | 329.090i | −0.194672 | + | 0.337182i | ||||
\(977\) | −468.812 | + | 812.006i | −0.479848 | + | 0.831122i | −0.999733 | − | 0.0231149i | \(-0.992642\pi\) |
0.519885 | + | 0.854237i | \(0.325975\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 320.000 | + | 554.256i | 0.326864 | + | 0.566145i | ||||
\(980\) | 712.764 | + | 101.823i | 0.727310 | + | 0.103901i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 42.0000i | 0.0427699i | ||||||||
\(983\) | 682.358 | + | 1181.88i | 0.694159 | + | 1.20232i | 0.970463 | + | 0.241248i | \(0.0775568\pi\) |
−0.276305 | + | 0.961070i | \(0.589110\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 663.636 | − | 845.451i | 0.673742 | − | 0.858326i | ||||
\(986\) | 352.727 | + | 203.647i | 0.357735 | + | 0.206538i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −77.9423 | + | 45.0000i | −0.0788890 | + | 0.0455466i | ||||
\(989\) | 588.313i | 0.594856i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1115.00 | −1.12513 | −0.562563 | − | 0.826754i | \(-0.690185\pi\) | ||||
−0.562563 | + | 0.826754i | \(0.690185\pi\) | |||||||
\(992\) | 22.6274 | + | 39.1918i | 0.0228099 | + | 0.0395079i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −33.0000 | + | 57.1577i | −0.0331992 | + | 0.0575027i | ||||
\(995\) | 379.731 | − | 483.766i | 0.381639 | − | 0.486197i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1143.15 | + | 660.000i | −1.14659 | + | 0.661986i | −0.948055 | − | 0.318107i | \(-0.896953\pi\) |
−0.198539 | + | 0.980093i | \(0.563619\pi\) | |||||||
\(998\) | −670.337 | −0.671681 | ||||||||
\(999\) | 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 | 810.3.j.b.539.2 | 8 | ||
3.2 | odd | 2 | inner | 810.3.j.b.539.3 | 8 | ||
5.4 | even | 2 | inner | 810.3.j.b.539.4 | 8 | ||
9.2 | odd | 6 | inner | 810.3.j.b.269.4 | 8 | ||
9.4 | even | 3 | 270.3.b.b.269.3 | yes | 4 | ||
9.5 | odd | 6 | 270.3.b.b.269.2 | yes | 4 | ||
9.7 | even | 3 | inner | 810.3.j.b.269.1 | 8 | ||
15.14 | odd | 2 | inner | 810.3.j.b.539.1 | 8 | ||
36.23 | even | 6 | 2160.3.c.j.1889.4 | 4 | |||
36.31 | odd | 6 | 2160.3.c.j.1889.1 | 4 | |||
45.4 | even | 6 | 270.3.b.b.269.1 | ✓ | 4 | ||
45.13 | odd | 12 | 1350.3.d.j.701.1 | 2 | |||
45.14 | odd | 6 | 270.3.b.b.269.4 | yes | 4 | ||
45.22 | odd | 12 | 1350.3.d.b.701.2 | 2 | |||
45.23 | even | 12 | 1350.3.d.j.701.2 | 2 | |||
45.29 | odd | 6 | inner | 810.3.j.b.269.2 | 8 | ||
45.32 | even | 12 | 1350.3.d.b.701.1 | 2 | |||
45.34 | even | 6 | inner | 810.3.j.b.269.3 | 8 | ||
180.59 | even | 6 | 2160.3.c.j.1889.2 | 4 | |||
180.139 | odd | 6 | 2160.3.c.j.1889.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
270.3.b.b.269.1 | ✓ | 4 | 45.4 | even | 6 | ||
270.3.b.b.269.2 | yes | 4 | 9.5 | odd | 6 | ||
270.3.b.b.269.3 | yes | 4 | 9.4 | even | 3 | ||
270.3.b.b.269.4 | yes | 4 | 45.14 | odd | 6 | ||
810.3.j.b.269.1 | 8 | 9.7 | even | 3 | inner | ||
810.3.j.b.269.2 | 8 | 45.29 | odd | 6 | inner | ||
810.3.j.b.269.3 | 8 | 45.34 | even | 6 | inner | ||
810.3.j.b.269.4 | 8 | 9.2 | odd | 6 | inner | ||
810.3.j.b.539.1 | 8 | 15.14 | odd | 2 | inner | ||
810.3.j.b.539.2 | 8 | 1.1 | even | 1 | trivial | ||
810.3.j.b.539.3 | 8 | 3.2 | odd | 2 | inner | ||
810.3.j.b.539.4 | 8 | 5.4 | even | 2 | inner | ||
1350.3.d.b.701.1 | 2 | 45.32 | even | 12 | |||
1350.3.d.b.701.2 | 2 | 45.22 | odd | 12 | |||
1350.3.d.j.701.1 | 2 | 45.13 | odd | 12 | |||
1350.3.d.j.701.2 | 2 | 45.23 | even | 12 | |||
2160.3.c.j.1889.1 | 4 | 36.31 | odd | 6 | |||
2160.3.c.j.1889.2 | 4 | 180.59 | even | 6 | |||
2160.3.c.j.1889.3 | 4 | 180.139 | odd | 6 | |||
2160.3.c.j.1889.4 | 4 | 36.23 | even | 6 |