Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [220,2,Mod(23,220)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(220, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("220.23");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 220 = 2^{2} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 220.l (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.75670884447\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} + 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 23.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 220.23 |
Dual form | 220.2.l.a.67.1 |
$q$-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 \(\left(\mathbb{Z}/220\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(111\) | \(177\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | − | 1.00000i | −0.707107 | − | 0.707107i | ||||
\(3\) | −2.00000 | + | 2.00000i | −1.15470 | + | 1.15470i | −0.169102 | + | 0.985599i | \(0.554087\pi\) |
−0.985599 | + | 0.169102i | \(0.945913\pi\) | |||||||
\(4\) | 2.00000i | 1.00000i | ||||||||
\(5\) | −1.00000 | + | 2.00000i | −0.447214 | + | 0.894427i | ||||
\(6\) | 4.00000 | 1.63299 | ||||||||
\(7\) | −1.00000 | − | 1.00000i | −0.377964 | − | 0.377964i | 0.492403 | − | 0.870367i | \(-0.336119\pi\) |
−0.870367 | + | 0.492403i | \(0.836119\pi\) | |||||||
\(8\) | 2.00000 | − | 2.00000i | 0.707107 | − | 0.707107i | ||||
\(9\) | − | 5.00000i | − | 1.66667i | ||||||
\(10\) | 3.00000 | − | 1.00000i | 0.948683 | − | 0.316228i | ||||
\(11\) | 1.00000i | 0.301511i | ||||||||
\(12\) | −4.00000 | − | 4.00000i | −1.15470 | − | 1.15470i | ||||
\(13\) | −4.00000 | − | 4.00000i | −1.10940 | − | 1.10940i | −0.993229 | − | 0.116171i | \(-0.962938\pi\) |
−0.116171 | − | 0.993229i | \(-0.537062\pi\) | |||||||
\(14\) | 2.00000i | 0.534522i | ||||||||
\(15\) | −2.00000 | − | 6.00000i | −0.516398 | − | 1.54919i | ||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 2.00000 | − | 2.00000i | 0.485071 | − | 0.485071i | −0.421676 | − | 0.906747i | \(-0.638558\pi\) |
0.906747 | + | 0.421676i | \(0.138558\pi\) | |||||||
\(18\) | −5.00000 | + | 5.00000i | −1.17851 | + | 1.17851i | ||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | −4.00000 | − | 2.00000i | −0.894427 | − | 0.447214i | ||||
\(21\) | 4.00000 | 0.872872 | ||||||||
\(22\) | 1.00000 | − | 1.00000i | 0.213201 | − | 0.213201i | ||||
\(23\) | −4.00000 | + | 4.00000i | −0.834058 | + | 0.834058i | −0.988069 | − | 0.154011i | \(-0.950781\pi\) |
0.154011 | + | 0.988069i | \(0.450781\pi\) | |||||||
\(24\) | 8.00000i | 1.63299i | ||||||||
\(25\) | −3.00000 | − | 4.00000i | −0.600000 | − | 0.800000i | ||||
\(26\) | 8.00000i | 1.56893i | ||||||||
\(27\) | 4.00000 | + | 4.00000i | 0.769800 | + | 0.769800i | ||||
\(28\) | 2.00000 | − | 2.00000i | 0.377964 | − | 0.377964i | ||||
\(29\) | 2.00000i | 0.371391i | 0.982607 | + | 0.185695i | \(0.0594537\pi\) | ||||
−0.982607 | + | 0.185695i | \(0.940546\pi\) | |||||||
\(30\) | −4.00000 | + | 8.00000i | −0.730297 | + | 1.46059i | ||||
\(31\) | − | 8.00000i | − | 1.43684i | −0.695608 | − | 0.718421i | \(-0.744865\pi\) | ||
0.695608 | − | 0.718421i | \(-0.255135\pi\) | |||||||
\(32\) | 4.00000 | + | 4.00000i | 0.707107 | + | 0.707107i | ||||
\(33\) | −2.00000 | − | 2.00000i | −0.348155 | − | 0.348155i | ||||
\(34\) | −4.00000 | −0.685994 | ||||||||
\(35\) | 3.00000 | − | 1.00000i | 0.507093 | − | 0.169031i | ||||
\(36\) | 10.0000 | 1.66667 | ||||||||
\(37\) | −5.00000 | + | 5.00000i | −0.821995 | + | 0.821995i | −0.986394 | − | 0.164399i | \(-0.947432\pi\) |
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | −2.00000 | − | 2.00000i | −0.324443 | − | 0.324443i | ||||
\(39\) | 16.0000 | 2.56205 | ||||||||
\(40\) | 2.00000 | + | 6.00000i | 0.316228 | + | 0.948683i | ||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | −4.00000 | − | 4.00000i | −0.617213 | − | 0.617213i | ||||
\(43\) | 1.00000 | − | 1.00000i | 0.152499 | − | 0.152499i | −0.626734 | − | 0.779233i | \(-0.715609\pi\) |
0.779233 | + | 0.626734i | \(0.215609\pi\) | |||||||
\(44\) | −2.00000 | −0.301511 | ||||||||
\(45\) | 10.0000 | + | 5.00000i | 1.49071 | + | 0.745356i | ||||
\(46\) | 8.00000 | 1.17954 | ||||||||
\(47\) | −4.00000 | − | 4.00000i | −0.583460 | − | 0.583460i | 0.352392 | − | 0.935852i | \(-0.385368\pi\) |
−0.935852 | + | 0.352392i | \(0.885368\pi\) | |||||||
\(48\) | 8.00000 | − | 8.00000i | 1.15470 | − | 1.15470i | ||||
\(49\) | − | 5.00000i | − | 0.714286i | ||||||
\(50\) | −1.00000 | + | 7.00000i | −0.141421 | + | 0.989949i | ||||
\(51\) | 8.00000i | 1.12022i | ||||||||
\(52\) | 8.00000 | − | 8.00000i | 1.10940 | − | 1.10940i | ||||
\(53\) | 9.00000 | + | 9.00000i | 1.23625 | + | 1.23625i | 0.961524 | + | 0.274721i | \(0.0885855\pi\) |
0.274721 | + | 0.961524i | \(0.411414\pi\) | |||||||
\(54\) | − | 8.00000i | − | 1.08866i | ||||||
\(55\) | −2.00000 | − | 1.00000i | −0.269680 | − | 0.134840i | ||||
\(56\) | −4.00000 | −0.534522 | ||||||||
\(57\) | −4.00000 | + | 4.00000i | −0.529813 | + | 0.529813i | ||||
\(58\) | 2.00000 | − | 2.00000i | 0.262613 | − | 0.262613i | ||||
\(59\) | −8.00000 | −1.04151 | −0.520756 | − | 0.853706i | \(-0.674350\pi\) | ||||
−0.520756 | + | 0.853706i | \(0.674350\pi\) | |||||||
\(60\) | 12.0000 | − | 4.00000i | 1.54919 | − | 0.516398i | ||||
\(61\) | −10.0000 | −1.28037 | −0.640184 | − | 0.768221i | \(-0.721142\pi\) | ||||
−0.640184 | + | 0.768221i | \(0.721142\pi\) | |||||||
\(62\) | −8.00000 | + | 8.00000i | −1.01600 | + | 1.01600i | ||||
\(63\) | −5.00000 | + | 5.00000i | −0.629941 | + | 0.629941i | ||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | 12.0000 | − | 4.00000i | 1.48842 | − | 0.496139i | ||||
\(66\) | 4.00000i | 0.492366i | ||||||||
\(67\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(68\) | 4.00000 | + | 4.00000i | 0.485071 | + | 0.485071i | ||||
\(69\) | − | 16.0000i | − | 1.92617i | ||||||
\(70\) | −4.00000 | − | 2.00000i | −0.478091 | − | 0.239046i | ||||
\(71\) | 12.0000i | 1.42414i | 0.702109 | + | 0.712069i | \(0.252242\pi\) | ||||
−0.702109 | + | 0.712069i | \(0.747758\pi\) | |||||||
\(72\) | −10.0000 | − | 10.0000i | −1.17851 | − | 1.17851i | ||||
\(73\) | 2.00000 | + | 2.00000i | 0.234082 | + | 0.234082i | 0.814394 | − | 0.580312i | \(-0.197069\pi\) |
−0.580312 | + | 0.814394i | \(0.697069\pi\) | |||||||
\(74\) | 10.0000 | 1.16248 | ||||||||
\(75\) | 14.0000 | + | 2.00000i | 1.61658 | + | 0.230940i | ||||
\(76\) | 4.00000i | 0.458831i | ||||||||
\(77\) | 1.00000 | − | 1.00000i | 0.113961 | − | 0.113961i | ||||
\(78\) | −16.0000 | − | 16.0000i | −1.81164 | − | 1.81164i | ||||
\(79\) | −10.0000 | −1.12509 | −0.562544 | − | 0.826767i | \(-0.690177\pi\) | ||||
−0.562544 | + | 0.826767i | \(0.690177\pi\) | |||||||
\(80\) | 4.00000 | − | 8.00000i | 0.447214 | − | 0.894427i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 6.00000 | + | 6.00000i | 0.662589 | + | 0.662589i | ||||
\(83\) | 1.00000 | − | 1.00000i | 0.109764 | − | 0.109764i | −0.650092 | − | 0.759856i | \(-0.725269\pi\) |
0.759856 | + | 0.650092i | \(0.225269\pi\) | |||||||
\(84\) | 8.00000i | 0.872872i | ||||||||
\(85\) | 2.00000 | + | 6.00000i | 0.216930 | + | 0.650791i | ||||
\(86\) | −2.00000 | −0.215666 | ||||||||
\(87\) | −4.00000 | − | 4.00000i | −0.428845 | − | 0.428845i | ||||
\(88\) | 2.00000 | + | 2.00000i | 0.213201 | + | 0.213201i | ||||
\(89\) | 6.00000i | 0.635999i | 0.948091 | + | 0.317999i | \(0.103011\pi\) | ||||
−0.948091 | + | 0.317999i | \(0.896989\pi\) | |||||||
\(90\) | −5.00000 | − | 15.0000i | −0.527046 | − | 1.58114i | ||||
\(91\) | 8.00000i | 0.838628i | ||||||||
\(92\) | −8.00000 | − | 8.00000i | −0.834058 | − | 0.834058i | ||||
\(93\) | 16.0000 | + | 16.0000i | 1.65912 | + | 1.65912i | ||||
\(94\) | 8.00000i | 0.825137i | ||||||||
\(95\) | −2.00000 | + | 4.00000i | −0.205196 | + | 0.410391i | ||||
\(96\) | −16.0000 | −1.63299 | ||||||||
\(97\) | −3.00000 | + | 3.00000i | −0.304604 | + | 0.304604i | −0.842812 | − | 0.538208i | \(-0.819101\pi\) |
0.538208 | + | 0.842812i | \(0.319101\pi\) | |||||||
\(98\) | −5.00000 | + | 5.00000i | −0.505076 | + | 0.505076i | ||||
\(99\) | 5.00000 | 0.502519 | ||||||||
\(100\) | 8.00000 | − | 6.00000i | 0.800000 | − | 0.600000i | ||||
\(101\) | −14.0000 | −1.39305 | −0.696526 | − | 0.717532i | \(-0.745272\pi\) | ||||
−0.696526 | + | 0.717532i | \(0.745272\pi\) | |||||||
\(102\) | 8.00000 | − | 8.00000i | 0.792118 | − | 0.792118i | ||||
\(103\) | −6.00000 | + | 6.00000i | −0.591198 | + | 0.591198i | −0.937955 | − | 0.346757i | \(-0.887283\pi\) |
0.346757 | + | 0.937955i | \(0.387283\pi\) | |||||||
\(104\) | −16.0000 | −1.56893 | ||||||||
\(105\) | −4.00000 | + | 8.00000i | −0.390360 | + | 0.780720i | ||||
\(106\) | − | 18.0000i | − | 1.74831i | ||||||
\(107\) | −13.0000 | − | 13.0000i | −1.25676 | − | 1.25676i | −0.952632 | − | 0.304125i | \(-0.901636\pi\) |
−0.304125 | − | 0.952632i | \(-0.598364\pi\) | |||||||
\(108\) | −8.00000 | + | 8.00000i | −0.769800 | + | 0.769800i | ||||
\(109\) | 2.00000i | 0.191565i | 0.995402 | + | 0.0957826i | \(0.0305354\pi\) | ||||
−0.995402 | + | 0.0957826i | \(0.969465\pi\) | |||||||
\(110\) | 1.00000 | + | 3.00000i | 0.0953463 | + | 0.286039i | ||||
\(111\) | − | 20.0000i | − | 1.89832i | ||||||
\(112\) | 4.00000 | + | 4.00000i | 0.377964 | + | 0.377964i | ||||
\(113\) | −1.00000 | − | 1.00000i | −0.0940721 | − | 0.0940721i | 0.658505 | − | 0.752577i | \(-0.271189\pi\) |
−0.752577 | + | 0.658505i | \(0.771189\pi\) | |||||||
\(114\) | 8.00000 | 0.749269 | ||||||||
\(115\) | −4.00000 | − | 12.0000i | −0.373002 | − | 1.11901i | ||||
\(116\) | −4.00000 | −0.371391 | ||||||||
\(117\) | −20.0000 | + | 20.0000i | −1.84900 | + | 1.84900i | ||||
\(118\) | 8.00000 | + | 8.00000i | 0.736460 | + | 0.736460i | ||||
\(119\) | −4.00000 | −0.366679 | ||||||||
\(120\) | −16.0000 | − | 8.00000i | −1.46059 | − | 0.730297i | ||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 10.0000 | + | 10.0000i | 0.905357 | + | 0.905357i | ||||
\(123\) | 12.0000 | − | 12.0000i | 1.08200 | − | 1.08200i | ||||
\(124\) | 16.0000 | 1.43684 | ||||||||
\(125\) | 11.0000 | − | 2.00000i | 0.983870 | − | 0.178885i | ||||
\(126\) | 10.0000 | 0.890871 | ||||||||
\(127\) | 1.00000 | + | 1.00000i | 0.0887357 | + | 0.0887357i | 0.750081 | − | 0.661346i | \(-0.230014\pi\) |
−0.661346 | + | 0.750081i | \(0.730014\pi\) | |||||||
\(128\) | −8.00000 | + | 8.00000i | −0.707107 | + | 0.707107i | ||||
\(129\) | 4.00000i | 0.352180i | ||||||||
\(130\) | −16.0000 | − | 8.00000i | −1.40329 | − | 0.701646i | ||||
\(131\) | 6.00000i | 0.524222i | 0.965038 | + | 0.262111i | \(0.0844187\pi\) | ||||
−0.965038 | + | 0.262111i | \(0.915581\pi\) | |||||||
\(132\) | 4.00000 | − | 4.00000i | 0.348155 | − | 0.348155i | ||||
\(133\) | −2.00000 | − | 2.00000i | −0.173422 | − | 0.173422i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −12.0000 | + | 4.00000i | −1.03280 | + | 0.344265i | ||||
\(136\) | − | 8.00000i | − | 0.685994i | ||||||
\(137\) | 7.00000 | − | 7.00000i | 0.598050 | − | 0.598050i | −0.341743 | − | 0.939793i | \(-0.611017\pi\) |
0.939793 | + | 0.341743i | \(0.111017\pi\) | |||||||
\(138\) | −16.0000 | + | 16.0000i | −1.36201 | + | 1.36201i | ||||
\(139\) | 20.0000 | 1.69638 | 0.848189 | − | 0.529694i | \(-0.177693\pi\) | ||||
0.848189 | + | 0.529694i | \(0.177693\pi\) | |||||||
\(140\) | 2.00000 | + | 6.00000i | 0.169031 | + | 0.507093i | ||||
\(141\) | 16.0000 | 1.34744 | ||||||||
\(142\) | 12.0000 | − | 12.0000i | 1.00702 | − | 1.00702i | ||||
\(143\) | 4.00000 | − | 4.00000i | 0.334497 | − | 0.334497i | ||||
\(144\) | 20.0000i | 1.66667i | ||||||||
\(145\) | −4.00000 | − | 2.00000i | −0.332182 | − | 0.166091i | ||||
\(146\) | − | 4.00000i | − | 0.331042i | ||||||
\(147\) | 10.0000 | + | 10.0000i | 0.824786 | + | 0.824786i | ||||
\(148\) | −10.0000 | − | 10.0000i | −0.821995 | − | 0.821995i | ||||
\(149\) | − | 18.0000i | − | 1.47462i | −0.675556 | − | 0.737309i | \(-0.736096\pi\) | ||
0.675556 | − | 0.737309i | \(-0.263904\pi\) | |||||||
\(150\) | −12.0000 | − | 16.0000i | −0.979796 | − | 1.30639i | ||||
\(151\) | − | 10.0000i | − | 0.813788i | −0.913475 | − | 0.406894i | \(-0.866612\pi\) | ||
0.913475 | − | 0.406894i | \(-0.133388\pi\) | |||||||
\(152\) | 4.00000 | − | 4.00000i | 0.324443 | − | 0.324443i | ||||
\(153\) | −10.0000 | − | 10.0000i | −0.808452 | − | 0.808452i | ||||
\(154\) | −2.00000 | −0.161165 | ||||||||
\(155\) | 16.0000 | + | 8.00000i | 1.28515 | + | 0.642575i | ||||
\(156\) | 32.0000i | 2.56205i | ||||||||
\(157\) | 3.00000 | − | 3.00000i | 0.239426 | − | 0.239426i | −0.577186 | − | 0.816612i | \(-0.695849\pi\) |
0.816612 | + | 0.577186i | \(0.195849\pi\) | |||||||
\(158\) | 10.0000 | + | 10.0000i | 0.795557 | + | 0.795557i | ||||
\(159\) | −36.0000 | −2.85499 | ||||||||
\(160\) | −12.0000 | + | 4.00000i | −0.948683 | + | 0.316228i | ||||
\(161\) | 8.00000 | 0.630488 | ||||||||
\(162\) | 1.00000 | + | 1.00000i | 0.0785674 | + | 0.0785674i | ||||
\(163\) | 6.00000 | − | 6.00000i | 0.469956 | − | 0.469956i | −0.431944 | − | 0.901900i | \(-0.642172\pi\) |
0.901900 | + | 0.431944i | \(0.142172\pi\) | |||||||
\(164\) | − | 12.0000i | − | 0.937043i | ||||||
\(165\) | 6.00000 | − | 2.00000i | 0.467099 | − | 0.155700i | ||||
\(166\) | −2.00000 | −0.155230 | ||||||||
\(167\) | 3.00000 | + | 3.00000i | 0.232147 | + | 0.232147i | 0.813588 | − | 0.581441i | \(-0.197511\pi\) |
−0.581441 | + | 0.813588i | \(0.697511\pi\) | |||||||
\(168\) | 8.00000 | − | 8.00000i | 0.617213 | − | 0.617213i | ||||
\(169\) | 19.0000i | 1.46154i | ||||||||
\(170\) | 4.00000 | − | 8.00000i | 0.306786 | − | 0.613572i | ||||
\(171\) | − | 10.0000i | − | 0.764719i | ||||||
\(172\) | 2.00000 | + | 2.00000i | 0.152499 | + | 0.152499i | ||||
\(173\) | −2.00000 | − | 2.00000i | −0.152057 | − | 0.152057i | 0.626979 | − | 0.779036i | \(-0.284291\pi\) |
−0.779036 | + | 0.626979i | \(0.784291\pi\) | |||||||
\(174\) | 8.00000i | 0.606478i | ||||||||
\(175\) | −1.00000 | + | 7.00000i | −0.0755929 | + | 0.529150i | ||||
\(176\) | − | 4.00000i | − | 0.301511i | ||||||
\(177\) | 16.0000 | − | 16.0000i | 1.20263 | − | 1.20263i | ||||
\(178\) | 6.00000 | − | 6.00000i | 0.449719 | − | 0.449719i | ||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | −10.0000 | + | 20.0000i | −0.745356 | + | 1.49071i | ||||
\(181\) | −16.0000 | −1.18927 | −0.594635 | − | 0.803996i | \(-0.702704\pi\) | ||||
−0.594635 | + | 0.803996i | \(0.702704\pi\) | |||||||
\(182\) | 8.00000 | − | 8.00000i | 0.592999 | − | 0.592999i | ||||
\(183\) | 20.0000 | − | 20.0000i | 1.47844 | − | 1.47844i | ||||
\(184\) | 16.0000i | 1.17954i | ||||||||
\(185\) | −5.00000 | − | 15.0000i | −0.367607 | − | 1.10282i | ||||
\(186\) | − | 32.0000i | − | 2.34635i | ||||||
\(187\) | 2.00000 | + | 2.00000i | 0.146254 | + | 0.146254i | ||||
\(188\) | 8.00000 | − | 8.00000i | 0.583460 | − | 0.583460i | ||||
\(189\) | − | 8.00000i | − | 0.581914i | ||||||
\(190\) | 6.00000 | − | 2.00000i | 0.435286 | − | 0.145095i | ||||
\(191\) | 4.00000i | 0.289430i | 0.989473 | + | 0.144715i | \(0.0462265\pi\) | ||||
−0.989473 | + | 0.144715i | \(0.953773\pi\) | |||||||
\(192\) | 16.0000 | + | 16.0000i | 1.15470 | + | 1.15470i | ||||
\(193\) | 10.0000 | + | 10.0000i | 0.719816 | + | 0.719816i | 0.968567 | − | 0.248752i | \(-0.0800203\pi\) |
−0.248752 | + | 0.968567i | \(0.580020\pi\) | |||||||
\(194\) | 6.00000 | 0.430775 | ||||||||
\(195\) | −16.0000 | + | 32.0000i | −1.14578 | + | 2.29157i | ||||
\(196\) | 10.0000 | 0.714286 | ||||||||
\(197\) | −2.00000 | + | 2.00000i | −0.142494 | + | 0.142494i | −0.774755 | − | 0.632261i | \(-0.782127\pi\) |
0.632261 | + | 0.774755i | \(0.282127\pi\) | |||||||
\(198\) | −5.00000 | − | 5.00000i | −0.355335 | − | 0.355335i | ||||
\(199\) | 4.00000 | 0.283552 | 0.141776 | − | 0.989899i | \(-0.454719\pi\) | ||||
0.141776 | + | 0.989899i | \(0.454719\pi\) | |||||||
\(200\) | −14.0000 | − | 2.00000i | −0.989949 | − | 0.141421i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 14.0000 | + | 14.0000i | 0.985037 | + | 0.985037i | ||||
\(203\) | 2.00000 | − | 2.00000i | 0.140372 | − | 0.140372i | ||||
\(204\) | −16.0000 | −1.12022 | ||||||||
\(205\) | 6.00000 | − | 12.0000i | 0.419058 | − | 0.838116i | ||||
\(206\) | 12.0000 | 0.836080 | ||||||||
\(207\) | 20.0000 | + | 20.0000i | 1.39010 | + | 1.39010i | ||||
\(208\) | 16.0000 | + | 16.0000i | 1.10940 | + | 1.10940i | ||||
\(209\) | 2.00000i | 0.138343i | ||||||||
\(210\) | 12.0000 | − | 4.00000i | 0.828079 | − | 0.276026i | ||||
\(211\) | 22.0000i | 1.51454i | 0.653101 | + | 0.757271i | \(0.273468\pi\) | ||||
−0.653101 | + | 0.757271i | \(0.726532\pi\) | |||||||
\(212\) | −18.0000 | + | 18.0000i | −1.23625 | + | 1.23625i | ||||
\(213\) | −24.0000 | − | 24.0000i | −1.64445 | − | 1.64445i | ||||
\(214\) | 26.0000i | 1.77732i | ||||||||
\(215\) | 1.00000 | + | 3.00000i | 0.0681994 | + | 0.204598i | ||||
\(216\) | 16.0000 | 1.08866 | ||||||||
\(217\) | −8.00000 | + | 8.00000i | −0.543075 | + | 0.543075i | ||||
\(218\) | 2.00000 | − | 2.00000i | 0.135457 | − | 0.135457i | ||||
\(219\) | −8.00000 | −0.540590 | ||||||||
\(220\) | 2.00000 | − | 4.00000i | 0.134840 | − | 0.269680i | ||||
\(221\) | −16.0000 | −1.07628 | ||||||||
\(222\) | −20.0000 | + | 20.0000i | −1.34231 | + | 1.34231i | ||||
\(223\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(224\) | − | 8.00000i | − | 0.534522i | ||||||
\(225\) | −20.0000 | + | 15.0000i | −1.33333 | + | 1.00000i | ||||
\(226\) | 2.00000i | 0.133038i | ||||||||
\(227\) | −5.00000 | − | 5.00000i | −0.331862 | − | 0.331862i | 0.521431 | − | 0.853293i | \(-0.325398\pi\) |
−0.853293 | + | 0.521431i | \(0.825398\pi\) | |||||||
\(228\) | −8.00000 | − | 8.00000i | −0.529813 | − | 0.529813i | ||||
\(229\) | − | 4.00000i | − | 0.264327i | −0.991228 | − | 0.132164i | \(-0.957808\pi\) | ||
0.991228 | − | 0.132164i | \(-0.0421925\pi\) | |||||||
\(230\) | −8.00000 | + | 16.0000i | −0.527504 | + | 1.05501i | ||||
\(231\) | 4.00000i | 0.263181i | ||||||||
\(232\) | 4.00000 | + | 4.00000i | 0.262613 | + | 0.262613i | ||||
\(233\) | 20.0000 | + | 20.0000i | 1.31024 | + | 1.31024i | 0.921234 | + | 0.389010i | \(0.127183\pi\) |
0.389010 | + | 0.921234i | \(0.372817\pi\) | |||||||
\(234\) | 40.0000 | 2.61488 | ||||||||
\(235\) | 12.0000 | − | 4.00000i | 0.782794 | − | 0.260931i | ||||
\(236\) | − | 16.0000i | − | 1.04151i | ||||||
\(237\) | 20.0000 | − | 20.0000i | 1.29914 | − | 1.29914i | ||||
\(238\) | 4.00000 | + | 4.00000i | 0.259281 | + | 0.259281i | ||||
\(239\) | 22.0000 | 1.42306 | 0.711531 | − | 0.702655i | \(-0.248002\pi\) | ||||
0.711531 | + | 0.702655i | \(0.248002\pi\) | |||||||
\(240\) | 8.00000 | + | 24.0000i | 0.516398 | + | 1.54919i | ||||
\(241\) | 10.0000 | 0.644157 | 0.322078 | − | 0.946713i | \(-0.395619\pi\) | ||||
0.322078 | + | 0.946713i | \(0.395619\pi\) | |||||||
\(242\) | 1.00000 | + | 1.00000i | 0.0642824 | + | 0.0642824i | ||||
\(243\) | −10.0000 | + | 10.0000i | −0.641500 | + | 0.641500i | ||||
\(244\) | − | 20.0000i | − | 1.28037i | ||||||
\(245\) | 10.0000 | + | 5.00000i | 0.638877 | + | 0.319438i | ||||
\(246\) | −24.0000 | −1.53018 | ||||||||
\(247\) | −8.00000 | − | 8.00000i | −0.509028 | − | 0.509028i | ||||
\(248\) | −16.0000 | − | 16.0000i | −1.01600 | − | 1.01600i | ||||
\(249\) | 4.00000i | 0.253490i | ||||||||
\(250\) | −13.0000 | − | 9.00000i | −0.822192 | − | 0.569210i | ||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | −10.0000 | − | 10.0000i | −0.629941 | − | 0.629941i | ||||
\(253\) | −4.00000 | − | 4.00000i | −0.251478 | − | 0.251478i | ||||
\(254\) | − | 2.00000i | − | 0.125491i | ||||||
\(255\) | −16.0000 | − | 8.00000i | −1.00196 | − | 0.500979i | ||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 1.00000 | − | 1.00000i | 0.0623783 | − | 0.0623783i | −0.675229 | − | 0.737608i | \(-0.735955\pi\) |
0.737608 | + | 0.675229i | \(0.235955\pi\) | |||||||
\(258\) | 4.00000 | − | 4.00000i | 0.249029 | − | 0.249029i | ||||
\(259\) | 10.0000 | 0.621370 | ||||||||
\(260\) | 8.00000 | + | 24.0000i | 0.496139 | + | 1.48842i | ||||
\(261\) | 10.0000 | 0.618984 | ||||||||
\(262\) | 6.00000 | − | 6.00000i | 0.370681 | − | 0.370681i | ||||
\(263\) | −5.00000 | + | 5.00000i | −0.308313 | + | 0.308313i | −0.844255 | − | 0.535942i | \(-0.819957\pi\) |
0.535942 | + | 0.844255i | \(0.319957\pi\) | |||||||
\(264\) | −8.00000 | −0.492366 | ||||||||
\(265\) | −27.0000 | + | 9.00000i | −1.65860 | + | 0.552866i | ||||
\(266\) | 4.00000i | 0.245256i | ||||||||
\(267\) | −12.0000 | − | 12.0000i | −0.734388 | − | 0.734388i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 26.0000i | − | 1.58525i | −0.609711 | − | 0.792624i | \(-0.708714\pi\) | ||
0.609711 | − | 0.792624i | \(-0.291286\pi\) | |||||||
\(270\) | 16.0000 | + | 8.00000i | 0.973729 | + | 0.486864i | ||||
\(271\) | − | 14.0000i | − | 0.850439i | −0.905090 | − | 0.425220i | \(-0.860197\pi\) | ||
0.905090 | − | 0.425220i | \(-0.139803\pi\) | |||||||
\(272\) | −8.00000 | + | 8.00000i | −0.485071 | + | 0.485071i | ||||
\(273\) | −16.0000 | − | 16.0000i | −0.968364 | − | 0.968364i | ||||
\(274\) | −14.0000 | −0.845771 | ||||||||
\(275\) | 4.00000 | − | 3.00000i | 0.241209 | − | 0.180907i | ||||
\(276\) | 32.0000 | 1.92617 | ||||||||
\(277\) | −8.00000 | + | 8.00000i | −0.480673 | + | 0.480673i | −0.905347 | − | 0.424673i | \(-0.860389\pi\) |
0.424673 | + | 0.905347i | \(0.360389\pi\) | |||||||
\(278\) | −20.0000 | − | 20.0000i | −1.19952 | − | 1.19952i | ||||
\(279\) | −40.0000 | −2.39474 | ||||||||
\(280\) | 4.00000 | − | 8.00000i | 0.239046 | − | 0.478091i | ||||
\(281\) | −10.0000 | −0.596550 | −0.298275 | − | 0.954480i | \(-0.596411\pi\) | ||||
−0.298275 | + | 0.954480i | \(0.596411\pi\) | |||||||
\(282\) | −16.0000 | − | 16.0000i | −0.952786 | − | 0.952786i | ||||
\(283\) | −21.0000 | + | 21.0000i | −1.24832 | + | 1.24832i | −0.291859 | + | 0.956461i | \(0.594274\pi\) |
−0.956461 | + | 0.291859i | \(0.905726\pi\) | |||||||
\(284\) | −24.0000 | −1.42414 | ||||||||
\(285\) | −4.00000 | − | 12.0000i | −0.236940 | − | 0.710819i | ||||
\(286\) | −8.00000 | −0.473050 | ||||||||
\(287\) | 6.00000 | + | 6.00000i | 0.354169 | + | 0.354169i | ||||
\(288\) | 20.0000 | − | 20.0000i | 1.17851 | − | 1.17851i | ||||
\(289\) | 9.00000i | 0.529412i | ||||||||
\(290\) | 2.00000 | + | 6.00000i | 0.117444 | + | 0.352332i | ||||
\(291\) | − | 12.0000i | − | 0.703452i | ||||||
\(292\) | −4.00000 | + | 4.00000i | −0.234082 | + | 0.234082i | ||||
\(293\) | −8.00000 | − | 8.00000i | −0.467365 | − | 0.467365i | 0.433695 | − | 0.901060i | \(-0.357210\pi\) |
−0.901060 | + | 0.433695i | \(0.857210\pi\) | |||||||
\(294\) | − | 20.0000i | − | 1.16642i | ||||||
\(295\) | 8.00000 | − | 16.0000i | 0.465778 | − | 0.931556i | ||||
\(296\) | 20.0000i | 1.16248i | ||||||||
\(297\) | −4.00000 | + | 4.00000i | −0.232104 | + | 0.232104i | ||||
\(298\) | −18.0000 | + | 18.0000i | −1.04271 | + | 1.04271i | ||||
\(299\) | 32.0000 | 1.85061 | ||||||||
\(300\) | −4.00000 | + | 28.0000i | −0.230940 | + | 1.61658i | ||||
\(301\) | −2.00000 | −0.115278 | ||||||||
\(302\) | −10.0000 | + | 10.0000i | −0.575435 | + | 0.575435i | ||||
\(303\) | 28.0000 | − | 28.0000i | 1.60856 | − | 1.60856i | ||||
\(304\) | −8.00000 | −0.458831 | ||||||||
\(305\) | 10.0000 | − | 20.0000i | 0.572598 | − | 1.14520i | ||||
\(306\) | 20.0000i | 1.14332i | ||||||||
\(307\) | 15.0000 | + | 15.0000i | 0.856095 | + | 0.856095i | 0.990876 | − | 0.134780i | \(-0.0430329\pi\) |
−0.134780 | + | 0.990876i | \(0.543033\pi\) | |||||||
\(308\) | 2.00000 | + | 2.00000i | 0.113961 | + | 0.113961i | ||||
\(309\) | − | 24.0000i | − | 1.36531i | ||||||
\(310\) | −8.00000 | − | 24.0000i | −0.454369 | − | 1.36311i | ||||
\(311\) | 4.00000i | 0.226819i | 0.993548 | + | 0.113410i | \(0.0361772\pi\) | ||||
−0.993548 | + | 0.113410i | \(0.963823\pi\) | |||||||
\(312\) | 32.0000 | − | 32.0000i | 1.81164 | − | 1.81164i | ||||
\(313\) | −9.00000 | − | 9.00000i | −0.508710 | − | 0.508710i | 0.405420 | − | 0.914130i | \(-0.367125\pi\) |
−0.914130 | + | 0.405420i | \(0.867125\pi\) | |||||||
\(314\) | −6.00000 | −0.338600 | ||||||||
\(315\) | −5.00000 | − | 15.0000i | −0.281718 | − | 0.845154i | ||||
\(316\) | − | 20.0000i | − | 1.12509i | ||||||
\(317\) | −21.0000 | + | 21.0000i | −1.17948 | + | 1.17948i | −0.199600 | + | 0.979877i | \(0.563964\pi\) |
−0.979877 | + | 0.199600i | \(0.936036\pi\) | |||||||
\(318\) | 36.0000 | + | 36.0000i | 2.01878 | + | 2.01878i | ||||
\(319\) | −2.00000 | −0.111979 | ||||||||
\(320\) | 16.0000 | + | 8.00000i | 0.894427 | + | 0.447214i | ||||
\(321\) | 52.0000 | 2.90236 | ||||||||
\(322\) | −8.00000 | − | 8.00000i | −0.445823 | − | 0.445823i | ||||
\(323\) | 4.00000 | − | 4.00000i | 0.222566 | − | 0.222566i | ||||
\(324\) | − | 2.00000i | − | 0.111111i | ||||||
\(325\) | −4.00000 | + | 28.0000i | −0.221880 | + | 1.55316i | ||||
\(326\) | −12.0000 | −0.664619 | ||||||||
\(327\) | −4.00000 | − | 4.00000i | −0.221201 | − | 0.221201i | ||||
\(328\) | −12.0000 | + | 12.0000i | −0.662589 | + | 0.662589i | ||||
\(329\) | 8.00000i | 0.441054i | ||||||||
\(330\) | −8.00000 | − | 4.00000i | −0.440386 | − | 0.220193i | ||||
\(331\) | − | 8.00000i | − | 0.439720i | −0.975531 | − | 0.219860i | \(-0.929440\pi\) | ||
0.975531 | − | 0.219860i | \(-0.0705600\pi\) | |||||||
\(332\) | 2.00000 | + | 2.00000i | 0.109764 | + | 0.109764i | ||||
\(333\) | 25.0000 | + | 25.0000i | 1.36999 | + | 1.36999i | ||||
\(334\) | − | 6.00000i | − | 0.328305i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −16.0000 | −0.872872 | ||||||||
\(337\) | 18.0000 | − | 18.0000i | 0.980522 | − | 0.980522i | −0.0192914 | − | 0.999814i | \(-0.506141\pi\) |
0.999814 | + | 0.0192914i | \(0.00614103\pi\) | |||||||
\(338\) | 19.0000 | − | 19.0000i | 1.03346 | − | 1.03346i | ||||
\(339\) | 4.00000 | 0.217250 | ||||||||
\(340\) | −12.0000 | + | 4.00000i | −0.650791 | + | 0.216930i | ||||
\(341\) | 8.00000 | 0.433224 | ||||||||
\(342\) | −10.0000 | + | 10.0000i | −0.540738 | + | 0.540738i | ||||
\(343\) | −12.0000 | + | 12.0000i | −0.647939 | + | 0.647939i | ||||
\(344\) | − | 4.00000i | − | 0.215666i | ||||||
\(345\) | 32.0000 | + | 16.0000i | 1.72282 | + | 0.861411i | ||||
\(346\) | 4.00000i | 0.215041i | ||||||||
\(347\) | 5.00000 | + | 5.00000i | 0.268414 | + | 0.268414i | 0.828461 | − | 0.560047i | \(-0.189217\pi\) |
−0.560047 | + | 0.828461i | \(0.689217\pi\) | |||||||
\(348\) | 8.00000 | − | 8.00000i | 0.428845 | − | 0.428845i | ||||
\(349\) | 6.00000i | 0.321173i | 0.987022 | + | 0.160586i | \(0.0513385\pi\) | ||||
−0.987022 | + | 0.160586i | \(0.948662\pi\) | |||||||
\(350\) | 8.00000 | − | 6.00000i | 0.427618 | − | 0.320713i | ||||
\(351\) | − | 32.0000i | − | 1.70803i | ||||||
\(352\) | −4.00000 | + | 4.00000i | −0.213201 | + | 0.213201i | ||||
\(353\) | 13.0000 | + | 13.0000i | 0.691920 | + | 0.691920i | 0.962654 | − | 0.270734i | \(-0.0872664\pi\) |
−0.270734 | + | 0.962654i | \(0.587266\pi\) | |||||||
\(354\) | −32.0000 | −1.70078 | ||||||||
\(355\) | −24.0000 | − | 12.0000i | −1.27379 | − | 0.636894i | ||||
\(356\) | −12.0000 | −0.635999 | ||||||||
\(357\) | 8.00000 | − | 8.00000i | 0.423405 | − | 0.423405i | ||||
\(358\) | 12.0000 | + | 12.0000i | 0.634220 | + | 0.634220i | ||||
\(359\) | −22.0000 | −1.16112 | −0.580558 | − | 0.814219i | \(-0.697165\pi\) | ||||
−0.580558 | + | 0.814219i | \(0.697165\pi\) | |||||||
\(360\) | 30.0000 | − | 10.0000i | 1.58114 | − | 0.527046i | ||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 16.0000 | + | 16.0000i | 0.840941 | + | 0.840941i | ||||
\(363\) | 2.00000 | − | 2.00000i | 0.104973 | − | 0.104973i | ||||
\(364\) | −16.0000 | −0.838628 | ||||||||
\(365\) | −6.00000 | + | 2.00000i | −0.314054 | + | 0.104685i | ||||
\(366\) | −40.0000 | −2.09083 | ||||||||
\(367\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(368\) | 16.0000 | − | 16.0000i | 0.834058 | − | 0.834058i | ||||
\(369\) | 30.0000i | 1.56174i | ||||||||
\(370\) | −10.0000 | + | 20.0000i | −0.519875 | + | 1.03975i | ||||
\(371\) | − | 18.0000i | − | 0.934513i | ||||||
\(372\) | −32.0000 | + | 32.0000i | −1.65912 | + | 1.65912i | ||||
\(373\) | −14.0000 | − | 14.0000i | −0.724893 | − | 0.724893i | 0.244705 | − | 0.969598i | \(-0.421309\pi\) |
−0.969598 | + | 0.244705i | \(0.921309\pi\) | |||||||
\(374\) | − | 4.00000i | − | 0.206835i | ||||||
\(375\) | −18.0000 | + | 26.0000i | −0.929516 | + | 1.34263i | ||||
\(376\) | −16.0000 | −0.825137 | ||||||||
\(377\) | 8.00000 | − | 8.00000i | 0.412021 | − | 0.412021i | ||||
\(378\) | −8.00000 | + | 8.00000i | −0.411476 | + | 0.411476i | ||||
\(379\) | 24.0000 | 1.23280 | 0.616399 | − | 0.787434i | \(-0.288591\pi\) | ||||
0.616399 | + | 0.787434i | \(0.288591\pi\) | |||||||
\(380\) | −8.00000 | − | 4.00000i | −0.410391 | − | 0.205196i | ||||
\(381\) | −4.00000 | −0.204926 | ||||||||
\(382\) | 4.00000 | − | 4.00000i | 0.204658 | − | 0.204658i | ||||
\(383\) | 2.00000 | − | 2.00000i | 0.102195 | − | 0.102195i | −0.654161 | − | 0.756356i | \(-0.726978\pi\) |
0.756356 | + | 0.654161i | \(0.226978\pi\) | |||||||
\(384\) | − | 32.0000i | − | 1.63299i | ||||||
\(385\) | 1.00000 | + | 3.00000i | 0.0509647 | + | 0.152894i | ||||
\(386\) | − | 20.0000i | − | 1.01797i | ||||||
\(387\) | −5.00000 | − | 5.00000i | −0.254164 | − | 0.254164i | ||||
\(388\) | −6.00000 | − | 6.00000i | −0.304604 | − | 0.304604i | ||||
\(389\) | 26.0000i | 1.31825i | 0.752032 | + | 0.659126i | \(0.229074\pi\) | ||||
−0.752032 | + | 0.659126i | \(0.770926\pi\) | |||||||
\(390\) | 48.0000 | − | 16.0000i | 2.43057 | − | 0.810191i | ||||
\(391\) | 16.0000i | 0.809155i | ||||||||
\(392\) | −10.0000 | − | 10.0000i | −0.505076 | − | 0.505076i | ||||
\(393\) | −12.0000 | − | 12.0000i | −0.605320 | − | 0.605320i | ||||
\(394\) | 4.00000 | 0.201517 | ||||||||
\(395\) | 10.0000 | − | 20.0000i | 0.503155 | − | 1.00631i | ||||
\(396\) | 10.0000i | 0.502519i | ||||||||
\(397\) | −9.00000 | + | 9.00000i | −0.451697 | + | 0.451697i | −0.895918 | − | 0.444220i | \(-0.853481\pi\) |
0.444220 | + | 0.895918i | \(0.353481\pi\) | |||||||
\(398\) | −4.00000 | − | 4.00000i | −0.200502 | − | 0.200502i | ||||
\(399\) | 8.00000 | 0.400501 | ||||||||
\(400\) | 12.0000 | + | 16.0000i | 0.600000 | + | 0.800000i | ||||
\(401\) | 8.00000 | 0.399501 | 0.199750 | − | 0.979847i | \(-0.435987\pi\) | ||||
0.199750 | + | 0.979847i | \(0.435987\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −32.0000 | + | 32.0000i | −1.59403 | + | 1.59403i | ||||
\(404\) | − | 28.0000i | − | 1.39305i | ||||||
\(405\) | 1.00000 | − | 2.00000i | 0.0496904 | − | 0.0993808i | ||||
\(406\) | −4.00000 | −0.198517 | ||||||||
\(407\) | −5.00000 | − | 5.00000i | −0.247841 | − | 0.247841i | ||||
\(408\) | 16.0000 | + | 16.0000i | 0.792118 | + | 0.792118i | ||||
\(409\) | − | 6.00000i | − | 0.296681i | −0.988936 | − | 0.148340i | \(-0.952607\pi\) | ||
0.988936 | − | 0.148340i | \(-0.0473931\pi\) | |||||||
\(410\) | −18.0000 | + | 6.00000i | −0.888957 | + | 0.296319i | ||||
\(411\) | 28.0000i | 1.38114i | ||||||||
\(412\) | −12.0000 | − | 12.0000i | −0.591198 | − | 0.591198i | ||||
\(413\) | 8.00000 | + | 8.00000i | 0.393654 | + | 0.393654i | ||||
\(414\) | − | 40.0000i | − | 1.96589i | ||||||
\(415\) | 1.00000 | + | 3.00000i | 0.0490881 | + | 0.147264i | ||||
\(416\) | − | 32.0000i | − | 1.56893i | ||||||
\(417\) | −40.0000 | + | 40.0000i | −1.95881 | + | 1.95881i | ||||
\(418\) | 2.00000 | − | 2.00000i | 0.0978232 | − | 0.0978232i | ||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | −16.0000 | − | 8.00000i | −0.780720 | − | 0.390360i | ||||
\(421\) | 6.00000 | 0.292422 | 0.146211 | − | 0.989253i | \(-0.453292\pi\) | ||||
0.146211 | + | 0.989253i | \(0.453292\pi\) | |||||||
\(422\) | 22.0000 | − | 22.0000i | 1.07094 | − | 1.07094i | ||||
\(423\) | −20.0000 | + | 20.0000i | −0.972433 | + | 0.972433i | ||||
\(424\) | 36.0000 | 1.74831 | ||||||||
\(425\) | −14.0000 | − | 2.00000i | −0.679100 | − | 0.0970143i | ||||
\(426\) | 48.0000i | 2.32561i | ||||||||
\(427\) | 10.0000 | + | 10.0000i | 0.483934 | + | 0.483934i | ||||
\(428\) | 26.0000 | − | 26.0000i | 1.25676 | − | 1.25676i | ||||
\(429\) | 16.0000i | 0.772487i | ||||||||
\(430\) | 2.00000 | − | 4.00000i | 0.0964486 | − | 0.192897i | ||||
\(431\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(432\) | −16.0000 | − | 16.0000i | −0.769800 | − | 0.769800i | ||||
\(433\) | −21.0000 | − | 21.0000i | −1.00920 | − | 1.00920i | −0.999957 | − | 0.00923827i | \(-0.997059\pi\) |
−0.00923827 | − | 0.999957i | \(-0.502941\pi\) | |||||||
\(434\) | 16.0000 | 0.768025 | ||||||||
\(435\) | 12.0000 | − | 4.00000i | 0.575356 | − | 0.191785i | ||||
\(436\) | −4.00000 | −0.191565 | ||||||||
\(437\) | −8.00000 | + | 8.00000i | −0.382692 | + | 0.382692i | ||||
\(438\) | 8.00000 | + | 8.00000i | 0.382255 | + | 0.382255i | ||||
\(439\) | 8.00000 | 0.381819 | 0.190910 | − | 0.981608i | \(-0.438856\pi\) | ||||
0.190910 | + | 0.981608i | \(0.438856\pi\) | |||||||
\(440\) | −6.00000 | + | 2.00000i | −0.286039 | + | 0.0953463i | ||||
\(441\) | −25.0000 | −1.19048 | ||||||||
\(442\) | 16.0000 | + | 16.0000i | 0.761042 | + | 0.761042i | ||||
\(443\) | −10.0000 | + | 10.0000i | −0.475114 | + | 0.475114i | −0.903565 | − | 0.428451i | \(-0.859060\pi\) |
0.428451 | + | 0.903565i | \(0.359060\pi\) | |||||||
\(444\) | 40.0000 | 1.89832 | ||||||||
\(445\) | −12.0000 | − | 6.00000i | −0.568855 | − | 0.284427i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 36.0000 | + | 36.0000i | 1.70274 | + | 1.70274i | ||||
\(448\) | −8.00000 | + | 8.00000i | −0.377964 | + | 0.377964i | ||||
\(449\) | 12.0000i | 0.566315i | 0.959073 | + | 0.283158i | \(0.0913819\pi\) | ||||
−0.959073 | + | 0.283158i | \(0.908618\pi\) | |||||||
\(450\) | 35.0000 | + | 5.00000i | 1.64992 | + | 0.235702i | ||||
\(451\) | − | 6.00000i | − | 0.282529i | ||||||
\(452\) | 2.00000 | − | 2.00000i | 0.0940721 | − | 0.0940721i | ||||
\(453\) | 20.0000 | + | 20.0000i | 0.939682 | + | 0.939682i | ||||
\(454\) | 10.0000i | 0.469323i | ||||||||
\(455\) | −16.0000 | − | 8.00000i | −0.750092 | − | 0.375046i | ||||
\(456\) | 16.0000i | 0.749269i | ||||||||
\(457\) | 16.0000 | − | 16.0000i | 0.748448 | − | 0.748448i | −0.225739 | − | 0.974188i | \(-0.572480\pi\) |
0.974188 | + | 0.225739i | \(0.0724798\pi\) | |||||||
\(458\) | −4.00000 | + | 4.00000i | −0.186908 | + | 0.186908i | ||||
\(459\) | 16.0000 | 0.746816 | ||||||||
\(460\) | 24.0000 | − | 8.00000i | 1.11901 | − | 0.373002i | ||||
\(461\) | 10.0000 | 0.465746 | 0.232873 | − | 0.972507i | \(-0.425187\pi\) | ||||
0.232873 | + | 0.972507i | \(0.425187\pi\) | |||||||
\(462\) | 4.00000 | − | 4.00000i | 0.186097 | − | 0.186097i | ||||
\(463\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(464\) | − | 8.00000i | − | 0.371391i | ||||||
\(465\) | −48.0000 | + | 16.0000i | −2.22595 | + | 0.741982i | ||||
\(466\) | − | 40.0000i | − | 1.85296i | ||||||
\(467\) | 12.0000 | + | 12.0000i | 0.555294 | + | 0.555294i | 0.927964 | − | 0.372670i | \(-0.121558\pi\) |
−0.372670 | + | 0.927964i | \(0.621558\pi\) | |||||||
\(468\) | −40.0000 | − | 40.0000i | −1.84900 | − | 1.84900i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −16.0000 | − | 8.00000i | −0.738025 | − | 0.369012i | ||||
\(471\) | 12.0000i | 0.552931i | ||||||||
\(472\) | −16.0000 | + | 16.0000i | −0.736460 | + | 0.736460i | ||||
\(473\) | 1.00000 | + | 1.00000i | 0.0459800 | + | 0.0459800i | ||||
\(474\) | −40.0000 | −1.83726 | ||||||||
\(475\) | −6.00000 | − | 8.00000i | −0.275299 | − | 0.367065i | ||||
\(476\) | − | 8.00000i | − | 0.366679i | ||||||
\(477\) | 45.0000 | − | 45.0000i | 2.06041 | − | 2.06041i | ||||
\(478\) | −22.0000 | − | 22.0000i | −1.00626 | − | 1.00626i | ||||
\(479\) | 18.0000 | 0.822441 | 0.411220 | − | 0.911536i | \(-0.365103\pi\) | ||||
0.411220 | + | 0.911536i | \(0.365103\pi\) | |||||||
\(480\) | 16.0000 | − | 32.0000i | 0.730297 | − | 1.46059i | ||||
\(481\) | 40.0000 | 1.82384 | ||||||||
\(482\) | −10.0000 | − | 10.0000i | −0.455488 | − | 0.455488i | ||||
\(483\) | −16.0000 | + | 16.0000i | −0.728025 | + | 0.728025i | ||||
\(484\) | − | 2.00000i | − | 0.0909091i | ||||||
\(485\) | −3.00000 | − | 9.00000i | −0.136223 | − | 0.408669i | ||||
\(486\) | 20.0000 | 0.907218 | ||||||||
\(487\) | 16.0000 | + | 16.0000i | 0.725029 | + | 0.725029i | 0.969625 | − | 0.244596i | \(-0.0786553\pi\) |
−0.244596 | + | 0.969625i | \(0.578655\pi\) | |||||||
\(488\) | −20.0000 | + | 20.0000i | −0.905357 | + | 0.905357i | ||||
\(489\) | 24.0000i | 1.08532i | ||||||||
\(490\) | −5.00000 | − | 15.0000i | −0.225877 | − | 0.677631i | ||||
\(491\) | − | 12.0000i | − | 0.541552i | −0.962642 | − | 0.270776i | \(-0.912720\pi\) | ||
0.962642 | − | 0.270776i | \(-0.0872803\pi\) | |||||||
\(492\) | 24.0000 | + | 24.0000i | 1.08200 | + | 1.08200i | ||||
\(493\) | 4.00000 | + | 4.00000i | 0.180151 | + | 0.180151i | ||||
\(494\) | 16.0000i | 0.719874i | ||||||||
\(495\) | −5.00000 | + | 10.0000i | −0.224733 | + | 0.449467i | ||||
\(496\) | 32.0000i | 1.43684i | ||||||||
\(497\) | 12.0000 | − | 12.0000i | 0.538274 | − | 0.538274i | ||||
\(498\) | 4.00000 | − | 4.00000i | 0.179244 | − | 0.179244i | ||||
\(499\) | 8.00000 | 0.358129 | 0.179065 | − | 0.983837i | \(-0.442693\pi\) | ||||
0.179065 | + | 0.983837i | \(0.442693\pi\) | |||||||
\(500\) | 4.00000 | + | 22.0000i | 0.178885 | + | 0.983870i | ||||
\(501\) | −12.0000 | −0.536120 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.0000 | − | 19.0000i | 0.847168 | − | 0.847168i | −0.142611 | − | 0.989779i | \(-0.545550\pi\) |
0.989779 | + | 0.142611i | \(0.0455497\pi\) | |||||||
\(504\) | 20.0000i | 0.890871i | ||||||||
\(505\) | 14.0000 | − | 28.0000i | 0.622992 | − | 1.24598i | ||||
\(506\) | 8.00000i | 0.355643i | ||||||||
\(507\) | −38.0000 | − | 38.0000i | −1.68764 | − | 1.68764i | ||||
\(508\) | −2.00000 | + | 2.00000i | −0.0887357 | + | 0.0887357i | ||||
\(509\) | 28.0000i | 1.24108i | 0.784176 | + | 0.620539i | \(0.213086\pi\) | ||||
−0.784176 | + | 0.620539i | \(0.786914\pi\) | |||||||
\(510\) | 8.00000 | + | 24.0000i | 0.354246 | + | 1.06274i | ||||
\(511\) | − | 4.00000i | − | 0.176950i | ||||||
\(512\) | −16.0000 | − | 16.0000i | −0.707107 | − | 0.707107i | ||||
\(513\) | 8.00000 | + | 8.00000i | 0.353209 | + | 0.353209i | ||||
\(514\) | −2.00000 | −0.0882162 | ||||||||
\(515\) | −6.00000 | − | 18.0000i | −0.264392 | − | 0.793175i | ||||
\(516\) | −8.00000 | −0.352180 | ||||||||
\(517\) | 4.00000 | − | 4.00000i | 0.175920 | − | 0.175920i | ||||
\(518\) | −10.0000 | − | 10.0000i | −0.439375 | − | 0.439375i | ||||
\(519\) | 8.00000 | 0.351161 | ||||||||
\(520\) | 16.0000 | − | 32.0000i | 0.701646 | − | 1.40329i | ||||
\(521\) | −24.0000 | −1.05146 | −0.525730 | − | 0.850652i | \(-0.676208\pi\) | ||||
−0.525730 | + | 0.850652i | \(0.676208\pi\) | |||||||
\(522\) | −10.0000 | − | 10.0000i | −0.437688 | − | 0.437688i | ||||
\(523\) | −3.00000 | + | 3.00000i | −0.131181 | + | 0.131181i | −0.769649 | − | 0.638468i | \(-0.779569\pi\) |
0.638468 | + | 0.769649i | \(0.279569\pi\) | |||||||
\(524\) | −12.0000 | −0.524222 | ||||||||
\(525\) | −12.0000 | − | 16.0000i | −0.523723 | − | 0.698297i | ||||
\(526\) | 10.0000 | 0.436021 | ||||||||
\(527\) | −16.0000 | − | 16.0000i | −0.696971 | − | 0.696971i | ||||
\(528\) | 8.00000 | + | 8.00000i | 0.348155 | + | 0.348155i | ||||
\(529\) | − | 9.00000i | − | 0.391304i | ||||||
\(530\) | 36.0000 | + | 18.0000i | 1.56374 | + | 0.781870i | ||||
\(531\) | 40.0000i | 1.73585i | ||||||||
\(532\) | 4.00000 | − | 4.00000i | 0.173422 | − | 0.173422i | ||||
\(533\) | 24.0000 | + | 24.0000i | 1.03956 | + | 1.03956i | ||||
\(534\) | 24.0000i | 1.03858i | ||||||||
\(535\) | 39.0000 | − | 13.0000i | 1.68612 | − | 0.562039i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 24.0000 | − | 24.0000i | 1.03568 | − | 1.03568i | ||||
\(538\) | −26.0000 | + | 26.0000i | −1.12094 | + | 1.12094i | ||||
\(539\) | 5.00000 | 0.215365 | ||||||||
\(540\) | −8.00000 | − | 24.0000i | −0.344265 | − | 1.03280i | ||||
\(541\) | 6.00000 | 0.257960 | 0.128980 | − | 0.991647i | \(-0.458830\pi\) | ||||
0.128980 | + | 0.991647i | \(0.458830\pi\) | |||||||
\(542\) | −14.0000 | + | 14.0000i | −0.601351 | + | 0.601351i | ||||
\(543\) | 32.0000 | − | 32.0000i | 1.37325 | − | 1.37325i | ||||
\(544\) | 16.0000 | 0.685994 | ||||||||
\(545\) | −4.00000 | − | 2.00000i | −0.171341 | − | 0.0856706i | ||||
\(546\) | 32.0000i | 1.36947i | ||||||||
\(547\) | −31.0000 | − | 31.0000i | −1.32546 | − | 1.32546i | −0.909281 | − | 0.416184i | \(-0.863367\pi\) |
−0.416184 | − | 0.909281i | \(-0.636633\pi\) | |||||||
\(548\) | 14.0000 | + | 14.0000i | 0.598050 | + | 0.598050i | ||||
\(549\) | 50.0000i | 2.13395i | ||||||||
\(550\) | −7.00000 | − | 1.00000i | −0.298481 | − | 0.0426401i | ||||
\(551\) | 4.00000i | 0.170406i | ||||||||
\(552\) | −32.0000 | − | 32.0000i | −1.36201 | − | 1.36201i | ||||
\(553\) | 10.0000 | + | 10.0000i | 0.425243 | + | 0.425243i | ||||
\(554\) | 16.0000 | 0.679775 | ||||||||
\(555\) | 40.0000 | + | 20.0000i | 1.69791 | + | 0.848953i | ||||
\(556\) | 40.0000i | 1.69638i | ||||||||
\(557\) | 10.0000 | − | 10.0000i | 0.423714 | − | 0.423714i | −0.462767 | − | 0.886480i | \(-0.653143\pi\) |
0.886480 | + | 0.462767i | \(0.153143\pi\) | |||||||
\(558\) | 40.0000 | + | 40.0000i | 1.69334 | + | 1.69334i | ||||
\(559\) | −8.00000 | −0.338364 | ||||||||
\(560\) | −12.0000 | + | 4.00000i | −0.507093 | + | 0.169031i | ||||
\(561\) | −8.00000 | −0.337760 | ||||||||
\(562\) | 10.0000 | + | 10.0000i | 0.421825 | + | 0.421825i | ||||
\(563\) | 9.00000 | − | 9.00000i | 0.379305 | − | 0.379305i | −0.491547 | − | 0.870851i | \(-0.663568\pi\) |
0.870851 | + | 0.491547i | \(0.163568\pi\) | |||||||
\(564\) | 32.0000i | 1.34744i | ||||||||
\(565\) | 3.00000 | − | 1.00000i | 0.126211 | − | 0.0420703i | ||||
\(566\) | 42.0000 | 1.76539 | ||||||||
\(567\) | 1.00000 | + | 1.00000i | 0.0419961 | + | 0.0419961i | ||||
\(568\) | 24.0000 | + | 24.0000i | 1.00702 | + | 1.00702i | ||||
\(569\) | 10.0000i | 0.419222i | 0.977785 | + | 0.209611i | \(0.0672197\pi\) | ||||
−0.977785 | + | 0.209611i | \(0.932780\pi\) | |||||||
\(570\) | −8.00000 | + | 16.0000i | −0.335083 | + | 0.670166i | ||||
\(571\) | − | 4.00000i | − | 0.167395i | −0.996491 | − | 0.0836974i | \(-0.973327\pi\) | ||
0.996491 | − | 0.0836974i | \(-0.0266729\pi\) | |||||||
\(572\) | 8.00000 | + | 8.00000i | 0.334497 | + | 0.334497i | ||||
\(573\) | −8.00000 | − | 8.00000i | −0.334205 | − | 0.334205i | ||||
\(574\) | − | 12.0000i | − | 0.500870i | ||||||
\(575\) | 28.0000 | + | 4.00000i | 1.16768 | + | 0.166812i | ||||
\(576\) | −40.0000 | −1.66667 | ||||||||
\(577\) | 13.0000 | − | 13.0000i | 0.541197 | − | 0.541197i | −0.382683 | − | 0.923880i | \(-0.625000\pi\) |
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(578\) | 9.00000 | − | 9.00000i | 0.374351 | − | 0.374351i | ||||
\(579\) | −40.0000 | −1.66234 | ||||||||
\(580\) | 4.00000 | − | 8.00000i | 0.166091 | − | 0.332182i | ||||
\(581\) | −2.00000 | −0.0829740 | ||||||||
\(582\) | −12.0000 | + | 12.0000i | −0.497416 | + | 0.497416i | ||||
\(583\) | −9.00000 | + | 9.00000i | −0.372742 | + | 0.372742i | ||||
\(584\) | 8.00000 | 0.331042 | ||||||||
\(585\) | −20.0000 | − | 60.0000i | −0.826898 | − | 2.48069i | ||||
\(586\) | 16.0000i | 0.660954i | ||||||||
\(587\) | −24.0000 | − | 24.0000i | −0.990586 | − | 0.990586i | 0.00937009 | − | 0.999956i | \(-0.497017\pi\) |
−0.999956 | + | 0.00937009i | \(0.997017\pi\) | |||||||
\(588\) | −20.0000 | + | 20.0000i | −0.824786 | + | 0.824786i | ||||
\(589\) | − | 16.0000i | − | 0.659269i | ||||||
\(590\) | −24.0000 | + | 8.00000i | −0.988064 | + | 0.329355i | ||||
\(591\) | − | 8.00000i | − | 0.329076i | ||||||
\(592\) | 20.0000 | − | 20.0000i | 0.821995 | − | 0.821995i | ||||
\(593\) | −22.0000 | − | 22.0000i | −0.903432 | − | 0.903432i | 0.0922996 | − | 0.995731i | \(-0.470578\pi\) |
−0.995731 | + | 0.0922996i | \(0.970578\pi\) | |||||||
\(594\) | 8.00000 | 0.328244 | ||||||||
\(595\) | 4.00000 | − | 8.00000i | 0.163984 | − | 0.327968i | ||||
\(596\) | 36.0000 | 1.47462 | ||||||||
\(597\) | −8.00000 | + | 8.00000i | −0.327418 | + | 0.327418i | ||||
\(598\) | −32.0000 | − | 32.0000i | −1.30858 | − | 1.30858i | ||||
\(599\) | −20.0000 | −0.817178 | −0.408589 | − | 0.912719i | \(-0.633979\pi\) | ||||
−0.408589 | + | 0.912719i | \(0.633979\pi\) | |||||||
\(600\) | 32.0000 | − | 24.0000i | 1.30639 | − | 0.979796i | ||||
\(601\) | 34.0000 | 1.38689 | 0.693444 | − | 0.720510i | \(-0.256092\pi\) | ||||
0.693444 | + | 0.720510i | \(0.256092\pi\) | |||||||
\(602\) | 2.00000 | + | 2.00000i | 0.0815139 | + | 0.0815139i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 20.0000 | 0.813788 | ||||||||
\(605\) | 1.00000 | − | 2.00000i | 0.0406558 | − | 0.0813116i | ||||
\(606\) | −56.0000 | −2.27484 | ||||||||
\(607\) | −15.0000 | − | 15.0000i | −0.608831 | − | 0.608831i | 0.333809 | − | 0.942641i | \(-0.391666\pi\) |
−0.942641 | + | 0.333809i | \(0.891666\pi\) | |||||||
\(608\) | 8.00000 | + | 8.00000i | 0.324443 | + | 0.324443i | ||||
\(609\) | 8.00000i | 0.324176i | ||||||||
\(610\) | −30.0000 | + | 10.0000i | −1.21466 | + | 0.404888i | ||||
\(611\) | 32.0000i | 1.29458i | ||||||||
\(612\) | 20.0000 | − | 20.0000i | 0.808452 | − | 0.808452i | ||||
\(613\) | −2.00000 | − | 2.00000i | −0.0807792 | − | 0.0807792i | 0.665563 | − | 0.746342i | \(-0.268192\pi\) |
−0.746342 | + | 0.665563i | \(0.768192\pi\) | |||||||
\(614\) | − | 30.0000i | − | 1.21070i | ||||||
\(615\) | 12.0000 | + | 36.0000i | 0.483887 | + | 1.45166i | ||||
\(616\) | − | 4.00000i | − | 0.161165i | ||||||
\(617\) | 11.0000 | − | 11.0000i | 0.442843 | − | 0.442843i | −0.450123 | − | 0.892966i | \(-0.648620\pi\) |
0.892966 | + | 0.450123i | \(0.148620\pi\) | |||||||
\(618\) | −24.0000 | + | 24.0000i | −0.965422 | + | 0.965422i | ||||
\(619\) | −36.0000 | −1.44696 | −0.723481 | − | 0.690344i | \(-0.757459\pi\) | ||||
−0.723481 | + | 0.690344i | \(0.757459\pi\) | |||||||
\(620\) | −16.0000 | + | 32.0000i | −0.642575 | + | 1.28515i | ||||
\(621\) | −32.0000 | −1.28412 | ||||||||
\(622\) | 4.00000 | − | 4.00000i | 0.160385 | − | 0.160385i | ||||
\(623\) | 6.00000 | − | 6.00000i | 0.240385 | − | 0.240385i | ||||
\(624\) | −64.0000 | −2.56205 | ||||||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | 18.0000i | 0.719425i | ||||||||
\(627\) | −4.00000 | − | 4.00000i | −0.159745 | − | 0.159745i | ||||
\(628\) | 6.00000 | + | 6.00000i | 0.239426 | + | 0.239426i | ||||
\(629\) | 20.0000i | 0.797452i | ||||||||
\(630\) | −10.0000 | + | 20.0000i | −0.398410 | + | 0.796819i | ||||
\(631\) | 28.0000i | 1.11466i | 0.830290 | + | 0.557331i | \(0.188175\pi\) | ||||
−0.830290 | + | 0.557331i | \(0.811825\pi\) | |||||||
\(632\) | −20.0000 | + | 20.0000i | −0.795557 | + | 0.795557i | ||||
\(633\) | −44.0000 | − | 44.0000i | −1.74884 | − | 1.74884i | ||||
\(634\) | 42.0000 | 1.66803 | ||||||||
\(635\) | −3.00000 | + | 1.00000i | −0.119051 | + | 0.0396838i | ||||
\(636\) | − | 72.0000i | − | 2.85499i | ||||||
\(637\) | −20.0000 | + | 20.0000i | −0.792429 | + | 0.792429i | ||||
\(638\) | 2.00000 | + | 2.00000i | 0.0791808 | + | 0.0791808i | ||||
\(639\) | 60.0000 | 2.37356 | ||||||||
\(640\) | −8.00000 | − | 24.0000i | −0.316228 | − | 0.948683i | ||||
\(641\) | −30.0000 | −1.18493 | −0.592464 | − | 0.805597i | \(-0.701845\pi\) | ||||
−0.592464 | + | 0.805597i | \(0.701845\pi\) | |||||||
\(642\) | −52.0000 | − | 52.0000i | −2.05228 | − | 2.05228i | ||||
\(643\) | 10.0000 | − | 10.0000i | 0.394362 | − | 0.394362i | −0.481877 | − | 0.876239i | \(-0.660045\pi\) |
0.876239 | + | 0.481877i | \(0.160045\pi\) | |||||||
\(644\) | 16.0000i | 0.630488i | ||||||||
\(645\) | −8.00000 | − | 4.00000i | −0.315000 | − | 0.157500i | ||||
\(646\) | −8.00000 | −0.314756 | ||||||||
\(647\) | −30.0000 | − | 30.0000i | −1.17942 | − | 1.17942i | −0.979892 | − | 0.199530i | \(-0.936058\pi\) |
−0.199530 | − | 0.979892i | \(-0.563942\pi\) | |||||||
\(648\) | −2.00000 | + | 2.00000i | −0.0785674 | + | 0.0785674i | ||||
\(649\) | − | 8.00000i | − | 0.314027i | ||||||
\(650\) | 32.0000 | − | 24.0000i | 1.25514 | − | 0.941357i | ||||
\(651\) | − | 32.0000i | − | 1.25418i | ||||||
\(652\) | 12.0000 | + | 12.0000i | 0.469956 | + | 0.469956i | ||||
\(653\) | −19.0000 | − | 19.0000i | −0.743527 | − | 0.743527i | 0.229728 | − | 0.973255i | \(-0.426216\pi\) |
−0.973255 | + | 0.229728i | \(0.926216\pi\) | |||||||
\(654\) | 8.00000i | 0.312825i | ||||||||
\(655\) | −12.0000 | − | 6.00000i | −0.468879 | − | 0.234439i | ||||
\(656\) | 24.0000 | 0.937043 | ||||||||
\(657\) | 10.0000 | − | 10.0000i | 0.390137 | − | 0.390137i | ||||
\(658\) | 8.00000 | − | 8.00000i | 0.311872 | − | 0.311872i | ||||
\(659\) | −12.0000 | −0.467454 | −0.233727 | − | 0.972302i | \(-0.575092\pi\) | ||||
−0.233727 | + | 0.972302i | \(0.575092\pi\) | |||||||
\(660\) | 4.00000 | + | 12.0000i | 0.155700 | + | 0.467099i | ||||
\(661\) | 40.0000 | 1.55582 | 0.777910 | − | 0.628376i | \(-0.216280\pi\) | ||||
0.777910 | + | 0.628376i | \(0.216280\pi\) | |||||||
\(662\) | −8.00000 | + | 8.00000i | −0.310929 | + | 0.310929i | ||||
\(663\) | 32.0000 | − | 32.0000i | 1.24278 | − | 1.24278i | ||||
\(664\) | − | 4.00000i | − | 0.155230i | ||||||
\(665\) | 6.00000 | − | 2.00000i | 0.232670 | − | 0.0775567i | ||||
\(666\) | − | 50.0000i | − | 1.93746i | ||||||
\(667\) | −8.00000 | − | 8.00000i | −0.309761 | − | 0.309761i | ||||
\(668\) | −6.00000 | + | 6.00000i | −0.232147 | + | 0.232147i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 10.0000i | − | 0.386046i | ||||||
\(672\) | 16.0000 | + | 16.0000i | 0.617213 | + | 0.617213i | ||||
\(673\) | −30.0000 | − | 30.0000i | −1.15642 | − | 1.15642i | −0.985241 | − | 0.171174i | \(-0.945244\pi\) |
−0.171174 | − | 0.985241i | \(-0.554756\pi\) | |||||||
\(674\) | −36.0000 | −1.38667 | ||||||||
\(675\) | 4.00000 | − | 28.0000i | 0.153960 | − | 1.07772i | ||||
\(676\) | −38.0000 | −1.46154 | ||||||||
\(677\) | 16.0000 | − | 16.0000i | 0.614930 | − | 0.614930i | −0.329297 | − | 0.944227i | \(-0.606812\pi\) |
0.944227 | + | 0.329297i | \(0.106812\pi\) | |||||||
\(678\) | −4.00000 | − | 4.00000i | −0.153619 | − | 0.153619i | ||||
\(679\) | 6.00000 | 0.230259 | ||||||||
\(680\) | 16.0000 | + | 8.00000i | 0.613572 | + | 0.306786i | ||||
\(681\) | 20.0000 | 0.766402 | ||||||||
\(682\) | −8.00000 | − | 8.00000i | −0.306336 | − | 0.306336i | ||||
\(683\) | 4.00000 | − | 4.00000i | 0.153056 | − | 0.153056i | −0.626426 | − | 0.779481i | \(-0.715483\pi\) |
0.779481 | + | 0.626426i | \(0.215483\pi\) | |||||||
\(684\) | 20.0000 | 0.764719 | ||||||||
\(685\) | 7.00000 | + | 21.0000i | 0.267456 | + | 0.802369i | ||||
\(686\) | 24.0000 | 0.916324 | ||||||||
\(687\) | 8.00000 | + | 8.00000i | 0.305219 | + | 0.305219i | ||||
\(688\) | −4.00000 | + | 4.00000i | −0.152499 | + | 0.152499i | ||||
\(689\) | − | 72.0000i | − | 2.74298i | ||||||
\(690\) | −16.0000 | − | 48.0000i | −0.609110 | − | 1.82733i | ||||
\(691\) | 8.00000i | 0.304334i | 0.988355 | + | 0.152167i | \(0.0486252\pi\) | ||||
−0.988355 | + | 0.152167i | \(0.951375\pi\) | |||||||
\(692\) | 4.00000 | − | 4.00000i | 0.152057 | − | 0.152057i | ||||
\(693\) | −5.00000 | − | 5.00000i | −0.189934 | − | 0.189934i | ||||
\(694\) | − | 10.0000i | − | 0.379595i | ||||||
\(695\) | −20.0000 | + | 40.0000i | −0.758643 | + | 1.51729i | ||||
\(696\) | −16.0000 | −0.606478 | ||||||||
\(697\) | −12.0000 | + | 12.0000i | −0.454532 | + | 0.454532i | ||||
\(698\) | 6.00000 | − | 6.00000i | 0.227103 | − | 0.227103i | ||||
\(699\) | −80.0000 | −3.02588 | ||||||||
\(700\) | −14.0000 | − | 2.00000i | −0.529150 | − | 0.0755929i | ||||
\(701\) | −18.0000 | −0.679851 | −0.339925 | − | 0.940452i | \(-0.610402\pi\) | ||||
−0.339925 | + | 0.940452i | \(0.610402\pi\) | |||||||
\(702\) | −32.0000 | + | 32.0000i | −1.20776 | + | 1.20776i | ||||
\(703\) | −10.0000 | + | 10.0000i | −0.377157 | + | 0.377157i | ||||
\(704\) | 8.00000 | 0.301511 | ||||||||
\(705\) | −16.0000 | + | 32.0000i | −0.602595 | + | 1.20519i | ||||
\(706\) | − | 26.0000i | − | 0.978523i | ||||||
\(707\) | 14.0000 | + | 14.0000i | 0.526524 | + | 0.526524i | ||||
\(708\) | 32.0000 | + | 32.0000i | 1.20263 | + | 1.20263i | ||||
\(709\) | − | 38.0000i | − | 1.42712i | −0.700594 | − | 0.713560i | \(-0.747082\pi\) | ||
0.700594 | − | 0.713560i | \(-0.252918\pi\) | |||||||
\(710\) | 12.0000 | + | 36.0000i | 0.450352 | + | 1.35106i | ||||
\(711\) | 50.0000i | 1.87515i | ||||||||
\(712\) | 12.0000 | + | 12.0000i | 0.449719 | + | 0.449719i | ||||
\(713\) | 32.0000 | + | 32.0000i | 1.19841 | + | 1.19841i | ||||
\(714\) | −16.0000 | −0.598785 | ||||||||
\(715\) | 4.00000 | + | 12.0000i | 0.149592 | + | 0.448775i | ||||
\(716\) | − | 24.0000i | − | 0.896922i | ||||||
\(717\) | −44.0000 | + | 44.0000i | −1.64321 | + | 1.64321i | ||||
\(718\) | 22.0000 | + | 22.0000i | 0.821033 | + | 0.821033i | ||||
\(719\) | −20.0000 | −0.745874 | −0.372937 | − | 0.927857i | \(-0.621649\pi\) | ||||
−0.372937 | + | 0.927857i | \(0.621649\pi\) | |||||||
\(720\) | −40.0000 | − | 20.0000i | −1.49071 | − | 0.745356i | ||||
\(721\) | 12.0000 | 0.446903 | ||||||||
\(722\) | 15.0000 | + | 15.0000i | 0.558242 | + | 0.558242i | ||||
\(723\) | −20.0000 | + | 20.0000i | −0.743808 | + | 0.743808i | ||||
\(724\) | − | 32.0000i | − | 1.18927i | ||||||
\(725\) | 8.00000 | − | 6.00000i | 0.297113 | − | 0.222834i | ||||
\(726\) | −4.00000 | −0.148454 | ||||||||
\(727\) | 2.00000 | + | 2.00000i | 0.0741759 | + | 0.0741759i | 0.743221 | − | 0.669046i | \(-0.233297\pi\) |
−0.669046 | + | 0.743221i | \(0.733297\pi\) | |||||||
\(728\) | 16.0000 | + | 16.0000i | 0.592999 | + | 0.592999i | ||||
\(729\) | − | 43.0000i | − | 1.59259i | ||||||
\(730\) | 8.00000 | + | 4.00000i | 0.296093 | + | 0.148047i | ||||
\(731\) | − | 4.00000i | − | 0.147945i | ||||||
\(732\) | 40.0000 | + | 40.0000i | 1.47844 | + | 1.47844i | ||||
\(733\) | 6.00000 | + | 6.00000i | 0.221615 | + | 0.221615i | 0.809178 | − | 0.587563i | \(-0.199913\pi\) |
−0.587563 | + | 0.809178i | \(0.699913\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −30.0000 | + | 10.0000i | −1.10657 | + | 0.368856i | ||||
\(736\) | −32.0000 | −1.17954 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 30.0000 | − | 30.0000i | 1.10432 | − | 1.10432i | ||||
\(739\) | 36.0000 | 1.32428 | 0.662141 | − | 0.749380i | \(-0.269648\pi\) | ||||
0.662141 | + | 0.749380i | \(0.269648\pi\) | |||||||
\(740\) | 30.0000 | − | 10.0000i | 1.10282 | − | 0.367607i | ||||
\(741\) | 32.0000 | 1.17555 | ||||||||
\(742\) | −18.0000 | + | 18.0000i | −0.660801 | + | 0.660801i | ||||
\(743\) | −19.0000 | + | 19.0000i | −0.697042 | + | 0.697042i | −0.963772 | − | 0.266729i | \(-0.914057\pi\) |
0.266729 | + | 0.963772i | \(0.414057\pi\) | |||||||
\(744\) | 64.0000 | 2.34635 | ||||||||
\(745\) | 36.0000 | + | 18.0000i | 1.31894 | + | 0.659469i | ||||
\(746\) | 28.0000i | 1.02515i | ||||||||
\(747\) | −5.00000 | − | 5.00000i | −0.182940 | − | 0.182940i | ||||
\(748\) | −4.00000 | + | 4.00000i | −0.146254 | + | 0.146254i | ||||
\(749\) | 26.0000i | 0.950019i | ||||||||
\(750\) | 44.0000 | − | 8.00000i | 1.60665 | − | 0.292119i | ||||
\(751\) | − | 32.0000i | − | 1.16770i | −0.811863 | − | 0.583848i | \(-0.801546\pi\) | ||
0.811863 | − | 0.583848i | \(-0.198454\pi\) | |||||||
\(752\) | 16.0000 | + | 16.0000i | 0.583460 | + | 0.583460i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −16.0000 | −0.582686 | ||||||||
\(755\) | 20.0000 | + | 10.0000i | 0.727875 | + | 0.363937i | ||||
\(756\) | 16.0000 | 0.581914 | ||||||||
\(757\) | −15.0000 | + | 15.0000i | −0.545184 | + | 0.545184i | −0.925044 | − | 0.379860i | \(-0.875972\pi\) |
0.379860 | + | 0.925044i | \(0.375972\pi\) | |||||||
\(758\) | −24.0000 | − | 24.0000i | −0.871719 | − | 0.871719i | ||||
\(759\) | 16.0000 | 0.580763 | ||||||||
\(760\) | 4.00000 | + | 12.0000i | 0.145095 | + | 0.435286i | ||||
\(761\) | −22.0000 | −0.797499 | −0.398750 | − | 0.917060i | \(-0.630556\pi\) | ||||
−0.398750 | + | 0.917060i | \(0.630556\pi\) | |||||||
\(762\) | 4.00000 | + | 4.00000i | 0.144905 | + | 0.144905i | ||||
\(763\) | 2.00000 | − | 2.00000i | 0.0724049 | − | 0.0724049i | ||||
\(764\) | −8.00000 | −0.289430 | ||||||||
\(765\) | 30.0000 | − | 10.0000i | 1.08465 | − | 0.361551i | ||||
\(766\) | −4.00000 | −0.144526 | ||||||||
\(767\) | 32.0000 | + | 32.0000i | 1.15545 | + | 1.15545i | ||||
\(768\) | −32.0000 | + | 32.0000i | −1.15470 | + | 1.15470i | ||||
\(769\) | − | 10.0000i | − | 0.360609i | −0.983611 | − | 0.180305i | \(-0.942292\pi\) | ||
0.983611 | − | 0.180305i | \(-0.0577084\pi\) | |||||||
\(770\) | 2.00000 | − | 4.00000i | 0.0720750 | − | 0.144150i | ||||
\(771\) | 4.00000i | 0.144056i | ||||||||
\(772\) | −20.0000 | + | 20.0000i | −0.719816 | + | 0.719816i |