Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [45,2,Mod(16,45)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("45.16");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 45 = 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 45.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.359326809096\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 16.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 45.16 |
Dual form | 45.2.e.a.31.1 |
$q$-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 \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(37\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | −0.986869 | − | 0.161521i | \(-0.948360\pi\) |
0.633316 | + | 0.773893i | \(0.281693\pi\) | |||||||
\(3\) | −1.50000 | + | 0.866025i | −0.866025 | + | 0.500000i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | − | 1.73205i | − | 0.707107i | ||||||
\(7\) | 1.50000 | − | 2.59808i | 0.566947 | − | 0.981981i | −0.429919 | − | 0.902867i | \(-0.641458\pi\) |
0.996866 | − | 0.0791130i | \(-0.0252088\pi\) | |||||||
\(8\) | −3.00000 | −1.06066 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.500000 | − | 0.866025i | ||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 1.00000 | − | 1.73205i | 0.301511 | − | 0.522233i | −0.674967 | − | 0.737848i | \(-0.735842\pi\) |
0.976478 | + | 0.215615i | \(0.0691756\pi\) | |||||||
\(12\) | −1.50000 | − | 0.866025i | −0.433013 | − | 0.250000i | ||||
\(13\) | 1.00000 | + | 1.73205i | 0.277350 | + | 0.480384i | 0.970725 | − | 0.240192i | \(-0.0772105\pi\) |
−0.693375 | + | 0.720577i | \(0.743877\pi\) | |||||||
\(14\) | 1.50000 | + | 2.59808i | 0.400892 | + | 0.694365i | ||||
\(15\) | −1.50000 | − | 0.866025i | −0.387298 | − | 0.223607i | ||||
\(16\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(17\) | 4.00000 | 0.970143 | 0.485071 | − | 0.874475i | \(-0.338794\pi\) | ||||
0.485071 | + | 0.874475i | \(0.338794\pi\) | |||||||
\(18\) | 1.50000 | + | 2.59808i | 0.353553 | + | 0.612372i | ||||
\(19\) | −8.00000 | −1.83533 | −0.917663 | − | 0.397360i | \(-0.869927\pi\) | ||||
−0.917663 | + | 0.397360i | \(0.869927\pi\) | |||||||
\(20\) | −0.500000 | + | 0.866025i | −0.111803 | + | 0.193649i | ||||
\(21\) | 5.19615i | 1.13389i | ||||||||
\(22\) | 1.00000 | + | 1.73205i | 0.213201 | + | 0.369274i | ||||
\(23\) | −1.50000 | − | 2.59808i | −0.312772 | − | 0.541736i | 0.666190 | − | 0.745782i | \(-0.267924\pi\) |
−0.978961 | + | 0.204046i | \(0.934591\pi\) | |||||||
\(24\) | 4.50000 | − | 2.59808i | 0.918559 | − | 0.530330i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | −2.00000 | −0.392232 | ||||||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | 3.00000 | 0.566947 | ||||||||
\(29\) | 0.500000 | − | 0.866025i | 0.0928477 | − | 0.160817i | −0.815861 | − | 0.578249i | \(-0.803736\pi\) |
0.908708 | + | 0.417432i | \(0.137070\pi\) | |||||||
\(30\) | 1.50000 | − | 0.866025i | 0.273861 | − | 0.158114i | ||||
\(31\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(32\) | −2.50000 | − | 4.33013i | −0.441942 | − | 0.765466i | ||||
\(33\) | 3.46410i | 0.603023i | ||||||||
\(34\) | −2.00000 | + | 3.46410i | −0.342997 | + | 0.594089i | ||||
\(35\) | 3.00000 | 0.507093 | ||||||||
\(36\) | 3.00000 | 0.500000 | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | 4.00000 | − | 6.92820i | 0.648886 | − | 1.12390i | ||||
\(39\) | −3.00000 | − | 1.73205i | −0.480384 | − | 0.277350i | ||||
\(40\) | −1.50000 | − | 2.59808i | −0.237171 | − | 0.410792i | ||||
\(41\) | −2.50000 | − | 4.33013i | −0.390434 | − | 0.676252i | 0.602072 | − | 0.798441i | \(-0.294342\pi\) |
−0.992507 | + | 0.122189i | \(0.961009\pi\) | |||||||
\(42\) | −4.50000 | − | 2.59808i | −0.694365 | − | 0.400892i | ||||
\(43\) | 4.00000 | − | 6.92820i | 0.609994 | − | 1.05654i | −0.381246 | − | 0.924473i | \(-0.624505\pi\) |
0.991241 | − | 0.132068i | \(-0.0421616\pi\) | |||||||
\(44\) | 2.00000 | 0.301511 | ||||||||
\(45\) | 3.00000 | 0.447214 | ||||||||
\(46\) | 3.00000 | 0.442326 | ||||||||
\(47\) | −3.50000 | + | 6.06218i | −0.510527 | + | 0.884260i | 0.489398 | + | 0.872060i | \(0.337217\pi\) |
−0.999926 | + | 0.0121990i | \(0.996117\pi\) | |||||||
\(48\) | 1.73205i | 0.250000i | ||||||||
\(49\) | −1.00000 | − | 1.73205i | −0.142857 | − | 0.247436i | ||||
\(50\) | −0.500000 | − | 0.866025i | −0.0707107 | − | 0.122474i | ||||
\(51\) | −6.00000 | + | 3.46410i | −0.840168 | + | 0.485071i | ||||
\(52\) | −1.00000 | + | 1.73205i | −0.138675 | + | 0.240192i | ||||
\(53\) | −2.00000 | −0.274721 | −0.137361 | − | 0.990521i | \(-0.543862\pi\) | ||||
−0.137361 | + | 0.990521i | \(0.543862\pi\) | |||||||
\(54\) | −4.50000 | − | 2.59808i | −0.612372 | − | 0.353553i | ||||
\(55\) | 2.00000 | 0.269680 | ||||||||
\(56\) | −4.50000 | + | 7.79423i | −0.601338 | + | 1.04155i | ||||
\(57\) | 12.0000 | − | 6.92820i | 1.58944 | − | 0.917663i | ||||
\(58\) | 0.500000 | + | 0.866025i | 0.0656532 | + | 0.113715i | ||||
\(59\) | 7.00000 | + | 12.1244i | 0.911322 | + | 1.57846i | 0.812198 | + | 0.583382i | \(0.198271\pi\) |
0.0991242 | + | 0.995075i | \(0.468396\pi\) | |||||||
\(60\) | − | 1.73205i | − | 0.223607i | ||||||
\(61\) | −3.50000 | + | 6.06218i | −0.448129 | + | 0.776182i | −0.998264 | − | 0.0588933i | \(-0.981243\pi\) |
0.550135 | + | 0.835076i | \(0.314576\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.50000 | − | 7.79423i | −0.566947 | − | 0.981981i | ||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | −1.00000 | + | 1.73205i | −0.124035 | + | 0.214834i | ||||
\(66\) | −3.00000 | − | 1.73205i | −0.369274 | − | 0.213201i | ||||
\(67\) | 1.50000 | + | 2.59808i | 0.183254 | + | 0.317406i | 0.942987 | − | 0.332830i | \(-0.108004\pi\) |
−0.759733 | + | 0.650236i | \(0.774670\pi\) | |||||||
\(68\) | 2.00000 | + | 3.46410i | 0.242536 | + | 0.420084i | ||||
\(69\) | 4.50000 | + | 2.59808i | 0.541736 | + | 0.312772i | ||||
\(70\) | −1.50000 | + | 2.59808i | −0.179284 | + | 0.310530i | ||||
\(71\) | 2.00000 | 0.237356 | 0.118678 | − | 0.992933i | \(-0.462134\pi\) | ||||
0.118678 | + | 0.992933i | \(0.462134\pi\) | |||||||
\(72\) | −4.50000 | + | 7.79423i | −0.530330 | + | 0.918559i | ||||
\(73\) | 4.00000 | 0.468165 | 0.234082 | − | 0.972217i | \(-0.424791\pi\) | ||||
0.234082 | + | 0.972217i | \(0.424791\pi\) | |||||||
\(74\) | 2.00000 | − | 3.46410i | 0.232495 | − | 0.402694i | ||||
\(75\) | − | 1.73205i | − | 0.200000i | ||||||
\(76\) | −4.00000 | − | 6.92820i | −0.458831 | − | 0.794719i | ||||
\(77\) | −3.00000 | − | 5.19615i | −0.341882 | − | 0.592157i | ||||
\(78\) | 3.00000 | − | 1.73205i | 0.339683 | − | 0.196116i | ||||
\(79\) | 3.00000 | − | 5.19615i | 0.337526 | − | 0.584613i | −0.646440 | − | 0.762964i | \(-0.723743\pi\) |
0.983967 | + | 0.178352i | \(0.0570765\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 5.00000 | 0.552158 | ||||||||
\(83\) | −4.50000 | + | 7.79423i | −0.493939 | + | 0.855528i | −0.999976 | − | 0.00698436i | \(-0.997777\pi\) |
0.506036 | + | 0.862512i | \(0.331110\pi\) | |||||||
\(84\) | −4.50000 | + | 2.59808i | −0.490990 | + | 0.283473i | ||||
\(85\) | 2.00000 | + | 3.46410i | 0.216930 | + | 0.375735i | ||||
\(86\) | 4.00000 | + | 6.92820i | 0.431331 | + | 0.747087i | ||||
\(87\) | 1.73205i | 0.185695i | ||||||||
\(88\) | −3.00000 | + | 5.19615i | −0.319801 | + | 0.553912i | ||||
\(89\) | −15.0000 | −1.59000 | −0.794998 | − | 0.606612i | \(-0.792528\pi\) | ||||
−0.794998 | + | 0.606612i | \(0.792528\pi\) | |||||||
\(90\) | −1.50000 | + | 2.59808i | −0.158114 | + | 0.273861i | ||||
\(91\) | 6.00000 | 0.628971 | ||||||||
\(92\) | 1.50000 | − | 2.59808i | 0.156386 | − | 0.270868i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.50000 | − | 6.06218i | −0.360997 | − | 0.625266i | ||||
\(95\) | −4.00000 | − | 6.92820i | −0.410391 | − | 0.710819i | ||||
\(96\) | 7.50000 | + | 4.33013i | 0.765466 | + | 0.441942i | ||||
\(97\) | −1.00000 | + | 1.73205i | −0.101535 | + | 0.175863i | −0.912317 | − | 0.409484i | \(-0.865709\pi\) |
0.810782 | + | 0.585348i | \(0.199042\pi\) | |||||||
\(98\) | 2.00000 | 0.202031 | ||||||||
\(99\) | −3.00000 | − | 5.19615i | −0.301511 | − | 0.522233i | ||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | 9.00000 | − | 15.5885i | 0.895533 | − | 1.55111i | 0.0623905 | − | 0.998052i | \(-0.480128\pi\) |
0.833143 | − | 0.553058i | \(-0.186539\pi\) | |||||||
\(102\) | − | 6.92820i | − | 0.685994i | ||||||
\(103\) | −4.00000 | − | 6.92820i | −0.394132 | − | 0.682656i | 0.598858 | − | 0.800855i | \(-0.295621\pi\) |
−0.992990 | + | 0.118199i | \(0.962288\pi\) | |||||||
\(104\) | −3.00000 | − | 5.19615i | −0.294174 | − | 0.509525i | ||||
\(105\) | −4.50000 | + | 2.59808i | −0.439155 | + | 0.253546i | ||||
\(106\) | 1.00000 | − | 1.73205i | 0.0971286 | − | 0.168232i | ||||
\(107\) | 3.00000 | 0.290021 | 0.145010 | − | 0.989430i | \(-0.453678\pi\) | ||||
0.145010 | + | 0.989430i | \(0.453678\pi\) | |||||||
\(108\) | −4.50000 | + | 2.59808i | −0.433013 | + | 0.250000i | ||||
\(109\) | 5.00000 | 0.478913 | 0.239457 | − | 0.970907i | \(-0.423031\pi\) | ||||
0.239457 | + | 0.970907i | \(0.423031\pi\) | |||||||
\(110\) | −1.00000 | + | 1.73205i | −0.0953463 | + | 0.165145i | ||||
\(111\) | 6.00000 | − | 3.46410i | 0.569495 | − | 0.328798i | ||||
\(112\) | −1.50000 | − | 2.59808i | −0.141737 | − | 0.245495i | ||||
\(113\) | 4.00000 | + | 6.92820i | 0.376288 | + | 0.651751i | 0.990519 | − | 0.137376i | \(-0.0438669\pi\) |
−0.614231 | + | 0.789127i | \(0.710534\pi\) | |||||||
\(114\) | 13.8564i | 1.29777i | ||||||||
\(115\) | 1.50000 | − | 2.59808i | 0.139876 | − | 0.242272i | ||||
\(116\) | 1.00000 | 0.0928477 | ||||||||
\(117\) | 6.00000 | 0.554700 | ||||||||
\(118\) | −14.0000 | −1.28880 | ||||||||
\(119\) | 6.00000 | − | 10.3923i | 0.550019 | − | 0.952661i | ||||
\(120\) | 4.50000 | + | 2.59808i | 0.410792 | + | 0.237171i | ||||
\(121\) | 3.50000 | + | 6.06218i | 0.318182 | + | 0.551107i | ||||
\(122\) | −3.50000 | − | 6.06218i | −0.316875 | − | 0.548844i | ||||
\(123\) | 7.50000 | + | 4.33013i | 0.676252 | + | 0.390434i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 9.00000 | 0.801784 | ||||||||
\(127\) | −5.00000 | −0.443678 | −0.221839 | − | 0.975083i | \(-0.571206\pi\) | ||||
−0.221839 | + | 0.975083i | \(0.571206\pi\) | |||||||
\(128\) | 1.50000 | − | 2.59808i | 0.132583 | − | 0.229640i | ||||
\(129\) | 13.8564i | 1.21999i | ||||||||
\(130\) | −1.00000 | − | 1.73205i | −0.0877058 | − | 0.151911i | ||||
\(131\) | 3.00000 | + | 5.19615i | 0.262111 | + | 0.453990i | 0.966803 | − | 0.255524i | \(-0.0822479\pi\) |
−0.704692 | + | 0.709514i | \(0.748915\pi\) | |||||||
\(132\) | −3.00000 | + | 1.73205i | −0.261116 | + | 0.150756i | ||||
\(133\) | −12.0000 | + | 20.7846i | −1.04053 | + | 1.80225i | ||||
\(134\) | −3.00000 | −0.259161 | ||||||||
\(135\) | −4.50000 | + | 2.59808i | −0.387298 | + | 0.223607i | ||||
\(136\) | −12.0000 | −1.02899 | ||||||||
\(137\) | −6.00000 | + | 10.3923i | −0.512615 | + | 0.887875i | 0.487278 | + | 0.873247i | \(0.337990\pi\) |
−0.999893 | + | 0.0146279i | \(0.995344\pi\) | |||||||
\(138\) | −4.50000 | + | 2.59808i | −0.383065 | + | 0.221163i | ||||
\(139\) | 8.00000 | + | 13.8564i | 0.678551 | + | 1.17529i | 0.975417 | + | 0.220366i | \(0.0707252\pi\) |
−0.296866 | + | 0.954919i | \(0.595942\pi\) | |||||||
\(140\) | 1.50000 | + | 2.59808i | 0.126773 | + | 0.219578i | ||||
\(141\) | − | 12.1244i | − | 1.02105i | ||||||
\(142\) | −1.00000 | + | 1.73205i | −0.0839181 | + | 0.145350i | ||||
\(143\) | 4.00000 | 0.334497 | ||||||||
\(144\) | −1.50000 | − | 2.59808i | −0.125000 | − | 0.216506i | ||||
\(145\) | 1.00000 | 0.0830455 | ||||||||
\(146\) | −2.00000 | + | 3.46410i | −0.165521 | + | 0.286691i | ||||
\(147\) | 3.00000 | + | 1.73205i | 0.247436 | + | 0.142857i | ||||
\(148\) | −2.00000 | − | 3.46410i | −0.164399 | − | 0.284747i | ||||
\(149\) | −8.50000 | − | 14.7224i | −0.696347 | − | 1.20611i | −0.969724 | − | 0.244202i | \(-0.921474\pi\) |
0.273377 | − | 0.961907i | \(-0.411859\pi\) | |||||||
\(150\) | 1.50000 | + | 0.866025i | 0.122474 | + | 0.0707107i | ||||
\(151\) | 1.00000 | − | 1.73205i | 0.0813788 | − | 0.140952i | −0.822464 | − | 0.568818i | \(-0.807401\pi\) |
0.903842 | + | 0.427865i | \(0.140734\pi\) | |||||||
\(152\) | 24.0000 | 1.94666 | ||||||||
\(153\) | 6.00000 | − | 10.3923i | 0.485071 | − | 0.840168i | ||||
\(154\) | 6.00000 | 0.483494 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | − | 3.46410i | − | 0.277350i | ||||||
\(157\) | −7.00000 | − | 12.1244i | −0.558661 | − | 0.967629i | −0.997609 | − | 0.0691164i | \(-0.977982\pi\) |
0.438948 | − | 0.898513i | \(-0.355351\pi\) | |||||||
\(158\) | 3.00000 | + | 5.19615i | 0.238667 | + | 0.413384i | ||||
\(159\) | 3.00000 | − | 1.73205i | 0.237915 | − | 0.137361i | ||||
\(160\) | 2.50000 | − | 4.33013i | 0.197642 | − | 0.342327i | ||||
\(161\) | −9.00000 | −0.709299 | ||||||||
\(162\) | 9.00000 | 0.707107 | ||||||||
\(163\) | −4.00000 | −0.313304 | −0.156652 | − | 0.987654i | \(-0.550070\pi\) | ||||
−0.156652 | + | 0.987654i | \(0.550070\pi\) | |||||||
\(164\) | 2.50000 | − | 4.33013i | 0.195217 | − | 0.338126i | ||||
\(165\) | −3.00000 | + | 1.73205i | −0.233550 | + | 0.134840i | ||||
\(166\) | −4.50000 | − | 7.79423i | −0.349268 | − | 0.604949i | ||||
\(167\) | 4.50000 | + | 7.79423i | 0.348220 | + | 0.603136i | 0.985933 | − | 0.167139i | \(-0.0534527\pi\) |
−0.637713 | + | 0.770274i | \(0.720119\pi\) | |||||||
\(168\) | − | 15.5885i | − | 1.20268i | ||||||
\(169\) | 4.50000 | − | 7.79423i | 0.346154 | − | 0.599556i | ||||
\(170\) | −4.00000 | −0.306786 | ||||||||
\(171\) | −12.0000 | + | 20.7846i | −0.917663 | + | 1.58944i | ||||
\(172\) | 8.00000 | 0.609994 | ||||||||
\(173\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(174\) | −1.50000 | − | 0.866025i | −0.113715 | − | 0.0656532i | ||||
\(175\) | 1.50000 | + | 2.59808i | 0.113389 | + | 0.196396i | ||||
\(176\) | −1.00000 | − | 1.73205i | −0.0753778 | − | 0.130558i | ||||
\(177\) | −21.0000 | − | 12.1244i | −1.57846 | − | 0.911322i | ||||
\(178\) | 7.50000 | − | 12.9904i | 0.562149 | − | 0.973670i | ||||
\(179\) | −2.00000 | −0.149487 | −0.0747435 | − | 0.997203i | \(-0.523814\pi\) | ||||
−0.0747435 | + | 0.997203i | \(0.523814\pi\) | |||||||
\(180\) | 1.50000 | + | 2.59808i | 0.111803 | + | 0.193649i | ||||
\(181\) | −7.00000 | −0.520306 | −0.260153 | − | 0.965567i | \(-0.583773\pi\) | ||||
−0.260153 | + | 0.965567i | \(0.583773\pi\) | |||||||
\(182\) | −3.00000 | + | 5.19615i | −0.222375 | + | 0.385164i | ||||
\(183\) | − | 12.1244i | − | 0.896258i | ||||||
\(184\) | 4.50000 | + | 7.79423i | 0.331744 | + | 0.574598i | ||||
\(185\) | −2.00000 | − | 3.46410i | −0.147043 | − | 0.254686i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.00000 | − | 6.92820i | 0.292509 | − | 0.506640i | ||||
\(188\) | −7.00000 | −0.510527 | ||||||||
\(189\) | 13.5000 | + | 7.79423i | 0.981981 | + | 0.566947i | ||||
\(190\) | 8.00000 | 0.580381 | ||||||||
\(191\) | −4.00000 | + | 6.92820i | −0.289430 | + | 0.501307i | −0.973674 | − | 0.227946i | \(-0.926799\pi\) |
0.684244 | + | 0.729253i | \(0.260132\pi\) | |||||||
\(192\) | −10.5000 | + | 6.06218i | −0.757772 | + | 0.437500i | ||||
\(193\) | 5.00000 | + | 8.66025i | 0.359908 | + | 0.623379i | 0.987945 | − | 0.154805i | \(-0.0494748\pi\) |
−0.628037 | + | 0.778183i | \(0.716141\pi\) | |||||||
\(194\) | −1.00000 | − | 1.73205i | −0.0717958 | − | 0.124354i | ||||
\(195\) | − | 3.46410i | − | 0.248069i | ||||||
\(196\) | 1.00000 | − | 1.73205i | 0.0714286 | − | 0.123718i | ||||
\(197\) | −12.0000 | −0.854965 | −0.427482 | − | 0.904024i | \(-0.640599\pi\) | ||||
−0.427482 | + | 0.904024i | \(0.640599\pi\) | |||||||
\(198\) | 6.00000 | 0.426401 | ||||||||
\(199\) | 4.00000 | 0.283552 | 0.141776 | − | 0.989899i | \(-0.454719\pi\) | ||||
0.141776 | + | 0.989899i | \(0.454719\pi\) | |||||||
\(200\) | 1.50000 | − | 2.59808i | 0.106066 | − | 0.183712i | ||||
\(201\) | −4.50000 | − | 2.59808i | −0.317406 | − | 0.183254i | ||||
\(202\) | 9.00000 | + | 15.5885i | 0.633238 | + | 1.09680i | ||||
\(203\) | −1.50000 | − | 2.59808i | −0.105279 | − | 0.182349i | ||||
\(204\) | −6.00000 | − | 3.46410i | −0.420084 | − | 0.242536i | ||||
\(205\) | 2.50000 | − | 4.33013i | 0.174608 | − | 0.302429i | ||||
\(206\) | 8.00000 | 0.557386 | ||||||||
\(207\) | −9.00000 | −0.625543 | ||||||||
\(208\) | 2.00000 | 0.138675 | ||||||||
\(209\) | −8.00000 | + | 13.8564i | −0.553372 | + | 0.958468i | ||||
\(210\) | − | 5.19615i | − | 0.358569i | ||||||
\(211\) | 11.0000 | + | 19.0526i | 0.757271 | + | 1.31163i | 0.944237 | + | 0.329266i | \(0.106801\pi\) |
−0.186966 | + | 0.982366i | \(0.559865\pi\) | |||||||
\(212\) | −1.00000 | − | 1.73205i | −0.0686803 | − | 0.118958i | ||||
\(213\) | −3.00000 | + | 1.73205i | −0.205557 | + | 0.118678i | ||||
\(214\) | −1.50000 | + | 2.59808i | −0.102538 | + | 0.177601i | ||||
\(215\) | 8.00000 | 0.545595 | ||||||||
\(216\) | − | 15.5885i | − | 1.06066i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.50000 | + | 4.33013i | −0.169321 | + | 0.293273i | ||||
\(219\) | −6.00000 | + | 3.46410i | −0.405442 | + | 0.234082i | ||||
\(220\) | 1.00000 | + | 1.73205i | 0.0674200 | + | 0.116775i | ||||
\(221\) | 4.00000 | + | 6.92820i | 0.269069 | + | 0.466041i | ||||
\(222\) | 6.92820i | 0.464991i | ||||||||
\(223\) | 9.50000 | − | 16.4545i | 0.636167 | − | 1.10187i | −0.350100 | − | 0.936713i | \(-0.613852\pi\) |
0.986267 | − | 0.165161i | \(-0.0528144\pi\) | |||||||
\(224\) | −15.0000 | −1.00223 | ||||||||
\(225\) | 1.50000 | + | 2.59808i | 0.100000 | + | 0.173205i | ||||
\(226\) | −8.00000 | −0.532152 | ||||||||
\(227\) | 2.00000 | − | 3.46410i | 0.132745 | − | 0.229920i | −0.791989 | − | 0.610535i | \(-0.790954\pi\) |
0.924734 | + | 0.380615i | \(0.124288\pi\) | |||||||
\(228\) | 12.0000 | + | 6.92820i | 0.794719 | + | 0.458831i | ||||
\(229\) | −7.50000 | − | 12.9904i | −0.495614 | − | 0.858429i | 0.504373 | − | 0.863486i | \(-0.331724\pi\) |
−0.999987 | + | 0.00505719i | \(0.998390\pi\) | |||||||
\(230\) | 1.50000 | + | 2.59808i | 0.0989071 | + | 0.171312i | ||||
\(231\) | 9.00000 | + | 5.19615i | 0.592157 | + | 0.341882i | ||||
\(232\) | −1.50000 | + | 2.59808i | −0.0984798 | + | 0.170572i | ||||
\(233\) | 24.0000 | 1.57229 | 0.786146 | − | 0.618041i | \(-0.212073\pi\) | ||||
0.786146 | + | 0.618041i | \(0.212073\pi\) | |||||||
\(234\) | −3.00000 | + | 5.19615i | −0.196116 | + | 0.339683i | ||||
\(235\) | −7.00000 | −0.456630 | ||||||||
\(236\) | −7.00000 | + | 12.1244i | −0.455661 | + | 0.789228i | ||||
\(237\) | 10.3923i | 0.675053i | ||||||||
\(238\) | 6.00000 | + | 10.3923i | 0.388922 | + | 0.673633i | ||||
\(239\) | 4.00000 | + | 6.92820i | 0.258738 | + | 0.448148i | 0.965904 | − | 0.258900i | \(-0.0833599\pi\) |
−0.707166 | + | 0.707048i | \(0.750027\pi\) | |||||||
\(240\) | −1.50000 | + | 0.866025i | −0.0968246 | + | 0.0559017i | ||||
\(241\) | 5.50000 | − | 9.52628i | 0.354286 | − | 0.613642i | −0.632709 | − | 0.774389i | \(-0.718057\pi\) |
0.986996 | + | 0.160748i | \(0.0513906\pi\) | |||||||
\(242\) | −7.00000 | −0.449977 | ||||||||
\(243\) | 13.5000 | + | 7.79423i | 0.866025 | + | 0.500000i | ||||
\(244\) | −7.00000 | −0.448129 | ||||||||
\(245\) | 1.00000 | − | 1.73205i | 0.0638877 | − | 0.110657i | ||||
\(246\) | −7.50000 | + | 4.33013i | −0.478183 | + | 0.276079i | ||||
\(247\) | −8.00000 | − | 13.8564i | −0.509028 | − | 0.881662i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 15.5885i | − | 0.987878i | ||||||
\(250\) | 0.500000 | − | 0.866025i | 0.0316228 | − | 0.0547723i | ||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 4.50000 | − | 7.79423i | 0.283473 | − | 0.490990i | ||||
\(253\) | −6.00000 | −0.377217 | ||||||||
\(254\) | 2.50000 | − | 4.33013i | 0.156864 | − | 0.271696i | ||||
\(255\) | −6.00000 | − | 3.46410i | −0.375735 | − | 0.216930i | ||||
\(256\) | 8.50000 | + | 14.7224i | 0.531250 | + | 0.920152i | ||||
\(257\) | 3.00000 | + | 5.19615i | 0.187135 | + | 0.324127i | 0.944294 | − | 0.329104i | \(-0.106747\pi\) |
−0.757159 | + | 0.653231i | \(0.773413\pi\) | |||||||
\(258\) | −12.0000 | − | 6.92820i | −0.747087 | − | 0.431331i | ||||
\(259\) | −6.00000 | + | 10.3923i | −0.372822 | + | 0.645746i | ||||
\(260\) | −2.00000 | −0.124035 | ||||||||
\(261\) | −1.50000 | − | 2.59808i | −0.0928477 | − | 0.160817i | ||||
\(262\) | −6.00000 | −0.370681 | ||||||||
\(263\) | 8.00000 | − | 13.8564i | 0.493301 | − | 0.854423i | −0.506669 | − | 0.862141i | \(-0.669123\pi\) |
0.999970 | + | 0.00771799i | \(0.00245674\pi\) | |||||||
\(264\) | − | 10.3923i | − | 0.639602i | ||||||
\(265\) | −1.00000 | − | 1.73205i | −0.0614295 | − | 0.106399i | ||||
\(266\) | −12.0000 | − | 20.7846i | −0.735767 | − | 1.27439i | ||||
\(267\) | 22.5000 | − | 12.9904i | 1.37698 | − | 0.794998i | ||||
\(268\) | −1.50000 | + | 2.59808i | −0.0916271 | + | 0.158703i | ||||
\(269\) | 25.0000 | 1.52428 | 0.762138 | − | 0.647414i | \(-0.224150\pi\) | ||||
0.762138 | + | 0.647414i | \(0.224150\pi\) | |||||||
\(270\) | − | 5.19615i | − | 0.316228i | ||||||
\(271\) | −8.00000 | −0.485965 | −0.242983 | − | 0.970031i | \(-0.578126\pi\) | ||||
−0.242983 | + | 0.970031i | \(0.578126\pi\) | |||||||
\(272\) | 2.00000 | − | 3.46410i | 0.121268 | − | 0.210042i | ||||
\(273\) | −9.00000 | + | 5.19615i | −0.544705 | + | 0.314485i | ||||
\(274\) | −6.00000 | − | 10.3923i | −0.362473 | − | 0.627822i | ||||
\(275\) | 1.00000 | + | 1.73205i | 0.0603023 | + | 0.104447i | ||||
\(276\) | 5.19615i | 0.312772i | ||||||||
\(277\) | −6.00000 | + | 10.3923i | −0.360505 | + | 0.624413i | −0.988044 | − | 0.154172i | \(-0.950729\pi\) |
0.627539 | + | 0.778585i | \(0.284062\pi\) | |||||||
\(278\) | −16.0000 | −0.959616 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −9.00000 | −0.537853 | ||||||||
\(281\) | 7.50000 | − | 12.9904i | 0.447412 | − | 0.774941i | −0.550804 | − | 0.834634i | \(-0.685679\pi\) |
0.998217 | + | 0.0596933i | \(0.0190123\pi\) | |||||||
\(282\) | 10.5000 | + | 6.06218i | 0.625266 | + | 0.360997i | ||||
\(283\) | −10.5000 | − | 18.1865i | −0.624160 | − | 1.08108i | −0.988703 | − | 0.149890i | \(-0.952108\pi\) |
0.364542 | − | 0.931187i | \(-0.381225\pi\) | |||||||
\(284\) | 1.00000 | + | 1.73205i | 0.0593391 | + | 0.102778i | ||||
\(285\) | 12.0000 | + | 6.92820i | 0.710819 | + | 0.410391i | ||||
\(286\) | −2.00000 | + | 3.46410i | −0.118262 | + | 0.204837i | ||||
\(287\) | −15.0000 | −0.885422 | ||||||||
\(288\) | −15.0000 | −0.883883 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | −0.500000 | + | 0.866025i | −0.0293610 | + | 0.0508548i | ||||
\(291\) | − | 3.46410i | − | 0.203069i | ||||||
\(292\) | 2.00000 | + | 3.46410i | 0.117041 | + | 0.202721i | ||||
\(293\) | −6.00000 | − | 10.3923i | −0.350524 | − | 0.607125i | 0.635818 | − | 0.771839i | \(-0.280663\pi\) |
−0.986341 | + | 0.164714i | \(0.947330\pi\) | |||||||
\(294\) | −3.00000 | + | 1.73205i | −0.174964 | + | 0.101015i | ||||
\(295\) | −7.00000 | + | 12.1244i | −0.407556 | + | 0.705907i | ||||
\(296\) | 12.0000 | 0.697486 | ||||||||
\(297\) | 9.00000 | + | 5.19615i | 0.522233 | + | 0.301511i | ||||
\(298\) | 17.0000 | 0.984784 | ||||||||
\(299\) | 3.00000 | − | 5.19615i | 0.173494 | − | 0.300501i | ||||
\(300\) | 1.50000 | − | 0.866025i | 0.0866025 | − | 0.0500000i | ||||
\(301\) | −12.0000 | − | 20.7846i | −0.691669 | − | 1.19800i | ||||
\(302\) | 1.00000 | + | 1.73205i | 0.0575435 | + | 0.0996683i | ||||
\(303\) | 31.1769i | 1.79107i | ||||||||
\(304\) | −4.00000 | + | 6.92820i | −0.229416 | + | 0.397360i | ||||
\(305\) | −7.00000 | −0.400819 | ||||||||
\(306\) | 6.00000 | + | 10.3923i | 0.342997 | + | 0.594089i | ||||
\(307\) | 7.00000 | 0.399511 | 0.199756 | − | 0.979846i | \(-0.435985\pi\) | ||||
0.199756 | + | 0.979846i | \(0.435985\pi\) | |||||||
\(308\) | 3.00000 | − | 5.19615i | 0.170941 | − | 0.296078i | ||||
\(309\) | 12.0000 | + | 6.92820i | 0.682656 | + | 0.394132i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(312\) | 9.00000 | + | 5.19615i | 0.509525 | + | 0.294174i | ||||
\(313\) | −7.00000 | + | 12.1244i | −0.395663 | + | 0.685309i | −0.993186 | − | 0.116543i | \(-0.962819\pi\) |
0.597522 | + | 0.801852i | \(0.296152\pi\) | |||||||
\(314\) | 14.0000 | 0.790066 | ||||||||
\(315\) | 4.50000 | − | 7.79423i | 0.253546 | − | 0.439155i | ||||
\(316\) | 6.00000 | 0.337526 | ||||||||
\(317\) | 17.0000 | − | 29.4449i | 0.954815 | − | 1.65379i | 0.220024 | − | 0.975494i | \(-0.429386\pi\) |
0.734791 | − | 0.678294i | \(-0.237280\pi\) | |||||||
\(318\) | 3.46410i | 0.194257i | ||||||||
\(319\) | −1.00000 | − | 1.73205i | −0.0559893 | − | 0.0969762i | ||||
\(320\) | 3.50000 | + | 6.06218i | 0.195656 | + | 0.338886i | ||||
\(321\) | −4.50000 | + | 2.59808i | −0.251166 | + | 0.145010i | ||||
\(322\) | 4.50000 | − | 7.79423i | 0.250775 | − | 0.434355i | ||||
\(323\) | −32.0000 | −1.78053 | ||||||||
\(324\) | 4.50000 | − | 7.79423i | 0.250000 | − | 0.433013i | ||||
\(325\) | −2.00000 | −0.110940 | ||||||||
\(326\) | 2.00000 | − | 3.46410i | 0.110770 | − | 0.191859i | ||||
\(327\) | −7.50000 | + | 4.33013i | −0.414751 | + | 0.239457i | ||||
\(328\) | 7.50000 | + | 12.9904i | 0.414118 | + | 0.717274i | ||||
\(329\) | 10.5000 | + | 18.1865i | 0.578884 | + | 1.00266i | ||||
\(330\) | − | 3.46410i | − | 0.190693i | ||||||
\(331\) | 3.00000 | − | 5.19615i | 0.164895 | − | 0.285606i | −0.771723 | − | 0.635959i | \(-0.780605\pi\) |
0.936618 | + | 0.350352i | \(0.113938\pi\) | |||||||
\(332\) | −9.00000 | −0.493939 | ||||||||
\(333\) | −6.00000 | + | 10.3923i | −0.328798 | + | 0.569495i | ||||
\(334\) | −9.00000 | −0.492458 | ||||||||
\(335\) | −1.50000 | + | 2.59808i | −0.0819538 | + | 0.141948i | ||||
\(336\) | 4.50000 | + | 2.59808i | 0.245495 | + | 0.141737i | ||||
\(337\) | 4.00000 | + | 6.92820i | 0.217894 | + | 0.377403i | 0.954164 | − | 0.299285i | \(-0.0967480\pi\) |
−0.736270 | + | 0.676688i | \(0.763415\pi\) | |||||||
\(338\) | 4.50000 | + | 7.79423i | 0.244768 | + | 0.423950i | ||||
\(339\) | −12.0000 | − | 6.92820i | −0.651751 | − | 0.376288i | ||||
\(340\) | −2.00000 | + | 3.46410i | −0.108465 | + | 0.187867i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −12.0000 | − | 20.7846i | −0.648886 | − | 1.12390i | ||||
\(343\) | 15.0000 | 0.809924 | ||||||||
\(344\) | −12.0000 | + | 20.7846i | −0.646997 | + | 1.12063i | ||||
\(345\) | 5.19615i | 0.279751i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.00000 | − | 3.46410i | −0.107366 | − | 0.185963i | 0.807337 | − | 0.590091i | \(-0.200908\pi\) |
−0.914702 | + | 0.404128i | \(0.867575\pi\) | |||||||
\(348\) | −1.50000 | + | 0.866025i | −0.0804084 | + | 0.0464238i | ||||
\(349\) | 2.50000 | − | 4.33013i | 0.133822 | − | 0.231786i | −0.791325 | − | 0.611396i | \(-0.790608\pi\) |
0.925147 | + | 0.379610i | \(0.123942\pi\) | |||||||
\(350\) | −3.00000 | −0.160357 | ||||||||
\(351\) | −9.00000 | + | 5.19615i | −0.480384 | + | 0.277350i | ||||
\(352\) | −10.0000 | −0.533002 | ||||||||
\(353\) | −12.0000 | + | 20.7846i | −0.638696 | + | 1.10625i | 0.347024 | + | 0.937856i | \(0.387192\pi\) |
−0.985719 | + | 0.168397i | \(0.946141\pi\) | |||||||
\(354\) | 21.0000 | − | 12.1244i | 1.11614 | − | 0.644402i | ||||
\(355\) | 1.00000 | + | 1.73205i | 0.0530745 | + | 0.0919277i | ||||
\(356\) | −7.50000 | − | 12.9904i | −0.397499 | − | 0.688489i | ||||
\(357\) | 20.7846i | 1.10004i | ||||||||
\(358\) | 1.00000 | − | 1.73205i | 0.0528516 | − | 0.0915417i | ||||
\(359\) | 24.0000 | 1.26667 | 0.633336 | − | 0.773877i | \(-0.281685\pi\) | ||||
0.633336 | + | 0.773877i | \(0.281685\pi\) | |||||||
\(360\) | −9.00000 | −0.474342 | ||||||||
\(361\) | 45.0000 | 2.36842 | ||||||||
\(362\) | 3.50000 | − | 6.06218i | 0.183956 | − | 0.318621i | ||||
\(363\) | −10.5000 | − | 6.06218i | −0.551107 | − | 0.318182i | ||||
\(364\) | 3.00000 | + | 5.19615i | 0.157243 | + | 0.272352i | ||||
\(365\) | 2.00000 | + | 3.46410i | 0.104685 | + | 0.181319i | ||||
\(366\) | 10.5000 | + | 6.06218i | 0.548844 | + | 0.316875i | ||||
\(367\) | −12.0000 | + | 20.7846i | −0.626395 | + | 1.08495i | 0.361874 | + | 0.932227i | \(0.382137\pi\) |
−0.988269 | + | 0.152721i | \(0.951196\pi\) | |||||||
\(368\) | −3.00000 | −0.156386 | ||||||||
\(369\) | −15.0000 | −0.780869 | ||||||||
\(370\) | 4.00000 | 0.207950 | ||||||||
\(371\) | −3.00000 | + | 5.19615i | −0.155752 | + | 0.269771i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.00000 | − | 8.66025i | −0.258890 | − | 0.448411i | 0.707055 | − | 0.707159i | \(-0.250023\pi\) |
−0.965945 | + | 0.258748i | \(0.916690\pi\) | |||||||
\(374\) | 4.00000 | + | 6.92820i | 0.206835 | + | 0.358249i | ||||
\(375\) | 1.50000 | − | 0.866025i | 0.0774597 | − | 0.0447214i | ||||
\(376\) | 10.5000 | − | 18.1865i | 0.541496 | − | 0.937899i | ||||
\(377\) | 2.00000 | 0.103005 | ||||||||
\(378\) | −13.5000 | + | 7.79423i | −0.694365 | + | 0.400892i | ||||
\(379\) | −26.0000 | −1.33553 | −0.667765 | − | 0.744372i | \(-0.732749\pi\) | ||||
−0.667765 | + | 0.744372i | \(0.732749\pi\) | |||||||
\(380\) | 4.00000 | − | 6.92820i | 0.205196 | − | 0.355409i | ||||
\(381\) | 7.50000 | − | 4.33013i | 0.384237 | − | 0.221839i | ||||
\(382\) | −4.00000 | − | 6.92820i | −0.204658 | − | 0.354478i | ||||
\(383\) | −18.0000 | − | 31.1769i | −0.919757 | − | 1.59307i | −0.799783 | − | 0.600289i | \(-0.795052\pi\) |
−0.119974 | − | 0.992777i | \(-0.538281\pi\) | |||||||
\(384\) | 5.19615i | 0.265165i | ||||||||
\(385\) | 3.00000 | − | 5.19615i | 0.152894 | − | 0.264820i | ||||
\(386\) | −10.0000 | −0.508987 | ||||||||
\(387\) | −12.0000 | − | 20.7846i | −0.609994 | − | 1.05654i | ||||
\(388\) | −2.00000 | −0.101535 | ||||||||
\(389\) | −16.5000 | + | 28.5788i | −0.836583 | + | 1.44900i | 0.0561516 | + | 0.998422i | \(0.482117\pi\) |
−0.892735 | + | 0.450582i | \(0.851216\pi\) | |||||||
\(390\) | 3.00000 | + | 1.73205i | 0.151911 | + | 0.0877058i | ||||
\(391\) | −6.00000 | − | 10.3923i | −0.303433 | − | 0.525561i | ||||
\(392\) | 3.00000 | + | 5.19615i | 0.151523 | + | 0.262445i | ||||
\(393\) | −9.00000 | − | 5.19615i | −0.453990 | − | 0.262111i | ||||
\(394\) | 6.00000 | − | 10.3923i | 0.302276 | − | 0.523557i | ||||
\(395\) | 6.00000 | 0.301893 | ||||||||
\(396\) | 3.00000 | − | 5.19615i | 0.150756 | − | 0.261116i | ||||
\(397\) | 34.0000 | 1.70641 | 0.853206 | − | 0.521575i | \(-0.174655\pi\) | ||||
0.853206 | + | 0.521575i | \(0.174655\pi\) | |||||||
\(398\) | −2.00000 | + | 3.46410i | −0.100251 | + | 0.173640i | ||||
\(399\) | − | 41.5692i | − | 2.08106i | ||||||
\(400\) | 0.500000 | + | 0.866025i | 0.0250000 | + | 0.0433013i | ||||
\(401\) | 9.00000 | + | 15.5885i | 0.449439 | + | 0.778450i | 0.998350 | − | 0.0574304i | \(-0.0182907\pi\) |
−0.548911 | + | 0.835881i | \(0.684957\pi\) | |||||||
\(402\) | 4.50000 | − | 2.59808i | 0.224440 | − | 0.129580i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 18.0000 | 0.895533 | ||||||||
\(405\) | 4.50000 | − | 7.79423i | 0.223607 | − | 0.387298i | ||||
\(406\) | 3.00000 | 0.148888 | ||||||||
\(407\) | −4.00000 | + | 6.92820i | −0.198273 | + | 0.343418i | ||||
\(408\) | 18.0000 | − | 10.3923i | 0.891133 | − | 0.514496i | ||||
\(409\) | −7.00000 | − | 12.1244i | −0.346128 | − | 0.599511i | 0.639430 | − | 0.768849i | \(-0.279170\pi\) |
−0.985558 | + | 0.169338i | \(0.945837\pi\) | |||||||
\(410\) | 2.50000 | + | 4.33013i | 0.123466 | + | 0.213850i | ||||
\(411\) | − | 20.7846i | − | 1.02523i | ||||||
\(412\) | 4.00000 | − | 6.92820i | 0.197066 | − | 0.341328i | ||||
\(413\) | 42.0000 | 2.06668 | ||||||||
\(414\) | 4.50000 | − | 7.79423i | 0.221163 | − | 0.383065i | ||||
\(415\) | −9.00000 | −0.441793 | ||||||||
\(416\) | 5.00000 | − | 8.66025i | 0.245145 | − | 0.424604i | ||||
\(417\) | −24.0000 | − | 13.8564i | −1.17529 | − | 0.678551i | ||||
\(418\) | −8.00000 | − | 13.8564i | −0.391293 | − | 0.677739i | ||||
\(419\) | −13.0000 | − | 22.5167i | −0.635092 | − | 1.10001i | −0.986496 | − | 0.163787i | \(-0.947629\pi\) |
0.351404 | − | 0.936224i | \(-0.385704\pi\) | |||||||
\(420\) | −4.50000 | − | 2.59808i | −0.219578 | − | 0.126773i | ||||
\(421\) | −17.0000 | + | 29.4449i | −0.828529 | + | 1.43505i | 0.0706626 | + | 0.997500i | \(0.477489\pi\) |
−0.899192 | + | 0.437555i | \(0.855845\pi\) | |||||||
\(422\) | −22.0000 | −1.07094 | ||||||||
\(423\) | 10.5000 | + | 18.1865i | 0.510527 | + | 0.884260i | ||||
\(424\) | 6.00000 | 0.291386 | ||||||||
\(425\) | −2.00000 | + | 3.46410i | −0.0970143 | + | 0.168034i | ||||
\(426\) | − | 3.46410i | − | 0.167836i | ||||||
\(427\) | 10.5000 | + | 18.1865i | 0.508131 | + | 0.880108i | ||||
\(428\) | 1.50000 | + | 2.59808i | 0.0725052 | + | 0.125583i | ||||
\(429\) | −6.00000 | + | 3.46410i | −0.289683 | + | 0.167248i | ||||
\(430\) | −4.00000 | + | 6.92820i | −0.192897 | + | 0.334108i | ||||
\(431\) | −30.0000 | −1.44505 | −0.722525 | − | 0.691345i | \(-0.757018\pi\) | ||||
−0.722525 | + | 0.691345i | \(0.757018\pi\) | |||||||
\(432\) | 4.50000 | + | 2.59808i | 0.216506 | + | 0.125000i | ||||
\(433\) | 28.0000 | 1.34559 | 0.672797 | − | 0.739827i | \(-0.265093\pi\) | ||||
0.672797 | + | 0.739827i | \(0.265093\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.50000 | + | 0.866025i | −0.0719195 | + | 0.0415227i | ||||
\(436\) | 2.50000 | + | 4.33013i | 0.119728 | + | 0.207375i | ||||
\(437\) | 12.0000 | + | 20.7846i | 0.574038 | + | 0.994263i | ||||
\(438\) | − | 6.92820i | − | 0.331042i | ||||||
\(439\) | −14.0000 | + | 24.2487i | −0.668184 | + | 1.15733i | 0.310228 | + | 0.950662i | \(0.399595\pi\) |
−0.978412 | + | 0.206666i | \(0.933739\pi\) | |||||||
\(440\) | −6.00000 | −0.286039 | ||||||||
\(441\) | −6.00000 | −0.285714 | ||||||||
\(442\) | −8.00000 | −0.380521 | ||||||||
\(443\) | −7.50000 | + | 12.9904i | −0.356336 | + | 0.617192i | −0.987346 | − | 0.158583i | \(-0.949307\pi\) |
0.631010 | + | 0.775775i | \(0.282641\pi\) | |||||||
\(444\) | 6.00000 | + | 3.46410i | 0.284747 | + | 0.164399i | ||||
\(445\) | −7.50000 | − | 12.9904i | −0.355534 | − | 0.615803i | ||||
\(446\) | 9.50000 | + | 16.4545i | 0.449838 | + | 0.779142i | ||||
\(447\) | 25.5000 | + | 14.7224i | 1.20611 | + | 0.696347i | ||||
\(448\) | 10.5000 | − | 18.1865i | 0.496078 | − | 0.859233i | ||||
\(449\) | −26.0000 | −1.22702 | −0.613508 | − | 0.789689i | \(-0.710242\pi\) | ||||
−0.613508 | + | 0.789689i | \(0.710242\pi\) | |||||||
\(450\) | −3.00000 | −0.141421 | ||||||||
\(451\) | −10.0000 | −0.470882 | ||||||||
\(452\) | −4.00000 | + | 6.92820i | −0.188144 | + | 0.325875i | ||||
\(453\) | 3.46410i | 0.162758i | ||||||||
\(454\) | 2.00000 | + | 3.46410i | 0.0938647 | + | 0.162578i | ||||
\(455\) | 3.00000 | + | 5.19615i | 0.140642 | + | 0.243599i | ||||
\(456\) | −36.0000 | + | 20.7846i | −1.68585 | + | 0.973329i | ||||
\(457\) | 10.0000 | − | 17.3205i | 0.467780 | − | 0.810219i | −0.531542 | − | 0.847032i | \(-0.678387\pi\) |
0.999322 | + | 0.0368128i | \(0.0117205\pi\) | |||||||
\(458\) | 15.0000 | 0.700904 | ||||||||
\(459\) | 20.7846i | 0.970143i | ||||||||
\(460\) | 3.00000 | 0.139876 | ||||||||
\(461\) | −4.50000 | + | 7.79423i | −0.209586 | + | 0.363013i | −0.951584 | − | 0.307388i | \(-0.900545\pi\) |
0.741998 | + | 0.670402i | \(0.233878\pi\) | |||||||
\(462\) | −9.00000 | + | 5.19615i | −0.418718 | + | 0.241747i | ||||
\(463\) | 18.0000 | + | 31.1769i | 0.836531 | + | 1.44891i | 0.892778 | + | 0.450497i | \(0.148753\pi\) |
−0.0562469 | + | 0.998417i | \(0.517913\pi\) | |||||||
\(464\) | −0.500000 | − | 0.866025i | −0.0232119 | − | 0.0402042i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.0000 | + | 20.7846i | −0.555889 | + | 0.962828i | ||||
\(467\) | 20.0000 | 0.925490 | 0.462745 | − | 0.886492i | \(-0.346865\pi\) | ||||
0.462745 | + | 0.886492i | \(0.346865\pi\) | |||||||
\(468\) | 3.00000 | + | 5.19615i | 0.138675 | + | 0.240192i | ||||
\(469\) | 9.00000 | 0.415581 | ||||||||
\(470\) | 3.50000 | − | 6.06218i | 0.161443 | − | 0.279627i | ||||
\(471\) | 21.0000 | + | 12.1244i | 0.967629 | + | 0.558661i | ||||
\(472\) | −21.0000 | − | 36.3731i | −0.966603 | − | 1.67421i | ||||
\(473\) | −8.00000 | − | 13.8564i | −0.367840 | − | 0.637118i | ||||
\(474\) | −9.00000 | − | 5.19615i | −0.413384 | − | 0.238667i | ||||
\(475\) | 4.00000 | − | 6.92820i | 0.183533 | − | 0.317888i | ||||
\(476\) | 12.0000 | 0.550019 | ||||||||
\(477\) | −3.00000 | + | 5.19615i | −0.137361 | + | 0.237915i | ||||
\(478\) | −8.00000 | −0.365911 | ||||||||
\(479\) | 9.00000 | − | 15.5885i | 0.411220 | − | 0.712255i | −0.583803 | − | 0.811895i | \(-0.698436\pi\) |
0.995023 | + | 0.0996406i | \(0.0317693\pi\) | |||||||
\(480\) | 8.66025i | 0.395285i | ||||||||
\(481\) | −4.00000 | − | 6.92820i | −0.182384 | − | 0.315899i | ||||
\(482\) | 5.50000 | + | 9.52628i | 0.250518 | + | 0.433910i | ||||
\(483\) | 13.5000 | − | 7.79423i | 0.614271 | − | 0.354650i | ||||
\(484\) | −3.50000 | + | 6.06218i | −0.159091 | + | 0.275554i | ||||
\(485\) | −2.00000 | −0.0908153 | ||||||||
\(486\) | −13.5000 | + | 7.79423i | −0.612372 | + | 0.353553i | ||||
\(487\) | −16.0000 | −0.725029 | −0.362515 | − | 0.931978i | \(-0.618082\pi\) | ||||
−0.362515 | + | 0.931978i | \(0.618082\pi\) | |||||||
\(488\) | 10.5000 | − | 18.1865i | 0.475313 | − | 0.823266i | ||||
\(489\) | 6.00000 | − | 3.46410i | 0.271329 | − | 0.156652i | ||||
\(490\) | 1.00000 | + | 1.73205i | 0.0451754 | + | 0.0782461i | ||||
\(491\) | −10.0000 | − | 17.3205i | −0.451294 | − | 0.781664i | 0.547173 | − | 0.837020i | \(-0.315704\pi\) |
−0.998467 | + | 0.0553560i | \(0.982371\pi\) | |||||||
\(492\) | 8.66025i | 0.390434i | ||||||||
\(493\) | 2.00000 | − | 3.46410i | 0.0900755 | − | 0.156015i | ||||
\(494\) | 16.0000 | 0.719874 | ||||||||
\(495\) | 3.00000 | − | 5.19615i | 0.134840 | − | 0.233550i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.00000 | − | 5.19615i | 0.134568 | − | 0.233079i | ||||
\(498\) | 13.5000 | + | 7.79423i | 0.604949 | + | 0.349268i | ||||
\(499\) | 16.0000 | + | 27.7128i | 0.716258 | + | 1.24060i | 0.962472 | + | 0.271380i | \(0.0874801\pi\) |
−0.246214 | + | 0.969216i | \(0.579187\pi\) | |||||||
\(500\) | −0.500000 | − | 0.866025i | −0.0223607 | − | 0.0387298i | ||||
\(501\) | −13.5000 | − | 7.79423i | −0.603136 | − | 0.348220i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.00000 | −0.312115 | −0.156057 | − | 0.987748i | \(-0.549878\pi\) | ||||
−0.156057 | + | 0.987748i | \(0.549878\pi\) | |||||||
\(504\) | 13.5000 | + | 23.3827i | 0.601338 | + | 1.04155i | ||||
\(505\) | 18.0000 | 0.800989 | ||||||||
\(506\) | 3.00000 | − | 5.19615i | 0.133366 | − | 0.230997i | ||||
\(507\) | 15.5885i | 0.692308i | ||||||||
\(508\) | −2.50000 | − | 4.33013i | −0.110920 | − | 0.192118i | ||||
\(509\) | −21.5000 | − | 37.2391i | −0.952971 | − | 1.65059i | −0.738945 | − | 0.673766i | \(-0.764676\pi\) |
−0.214026 | − | 0.976828i | \(-0.568658\pi\) | |||||||
\(510\) | 6.00000 | − | 3.46410i | 0.265684 | − | 0.153393i | ||||
\(511\) | 6.00000 | − | 10.3923i | 0.265424 | − | 0.459728i | ||||
\(512\) | −11.0000 | −0.486136 | ||||||||
\(513\) | − | 41.5692i | − | 1.83533i | ||||||
\(514\) | −6.00000 | −0.264649 | ||||||||
\(515\) | 4.00000 | − | 6.92820i | 0.176261 | − | 0.305293i | ||||
\(516\) | −12.0000 | + | 6.92820i | −0.528271 | + | 0.304997i | ||||
\(517\) | 7.00000 | + | 12.1244i | 0.307860 | + | 0.533229i | ||||
\(518\) | −6.00000 | − | 10.3923i | −0.263625 | − | 0.456612i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.00000 | − | 5.19615i | 0.131559 | − | 0.227866i | ||||
\(521\) | 11.0000 | 0.481919 | 0.240959 | − | 0.970535i | \(-0.422538\pi\) | ||||
0.240959 | + | 0.970535i | \(0.422538\pi\) | |||||||
\(522\) | 3.00000 | 0.131306 | ||||||||
\(523\) | −29.0000 | −1.26808 | −0.634041 | − | 0.773300i | \(-0.718605\pi\) | ||||
−0.634041 | + | 0.773300i | \(0.718605\pi\) | |||||||
\(524\) | −3.00000 | + | 5.19615i | −0.131056 | + | 0.226995i | ||||
\(525\) | −4.50000 | − | 2.59808i | −0.196396 | − | 0.113389i | ||||
\(526\) | 8.00000 | + | 13.8564i | 0.348817 | + | 0.604168i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 3.00000 | + | 1.73205i | 0.130558 | + | 0.0753778i | ||||
\(529\) | 7.00000 | − | 12.1244i | 0.304348 | − | 0.527146i | ||||
\(530\) | 2.00000 | 0.0868744 | ||||||||
\(531\) | 42.0000 | 1.82264 | ||||||||
\(532\) | −24.0000 | −1.04053 | ||||||||
\(533\) | 5.00000 | − | 8.66025i | 0.216574 | − | 0.375117i | ||||
\(534\) | 25.9808i | 1.12430i | ||||||||
\(535\) | 1.50000 | + | 2.59808i | 0.0648507 | + | 0.112325i | ||||
\(536\) | −4.50000 | − | 7.79423i | −0.194370 | − | 0.336659i | ||||
\(537\) | 3.00000 | − | 1.73205i | 0.129460 | − | 0.0747435i | ||||
\(538\) | −12.5000 | + | 21.6506i | −0.538913 | + | 0.933425i | ||||
\(539\) | −4.00000 | −0.172292 | ||||||||
\(540\) | −4.50000 | − | 2.59808i | −0.193649 | − | 0.111803i | ||||
\(541\) | −39.0000 | −1.67674 | −0.838370 | − | 0.545101i | \(-0.816491\pi\) | ||||
−0.838370 | + | 0.545101i | \(0.816491\pi\) | |||||||
\(542\) | 4.00000 | − | 6.92820i | 0.171815 | − | 0.297592i | ||||
\(543\) | 10.5000 | − | 6.06218i | 0.450598 | − | 0.260153i | ||||
\(544\) | −10.0000 | − | 17.3205i | −0.428746 | − | 0.742611i | ||||
\(545\) | 2.50000 | + | 4.33013i | 0.107088 | + | 0.185482i | ||||
\(546\) | − | 10.3923i | − | 0.444750i | ||||||
\(547\) | 14.5000 | − | 25.1147i | 0.619975 | − | 1.07383i | −0.369514 | − | 0.929225i | \(-0.620476\pi\) |
0.989490 | − | 0.144604i | \(-0.0461907\pi\) | |||||||
\(548\) | −12.0000 | −0.512615 | ||||||||
\(549\) | 10.5000 | + | 18.1865i | 0.448129 | + | 0.776182i | ||||
\(550\) | −2.00000 | −0.0852803 | ||||||||
\(551\) | −4.00000 | + | 6.92820i | −0.170406 | + | 0.295151i | ||||
\(552\) | −13.5000 | − | 7.79423i | −0.574598 | − | 0.331744i | ||||
\(553\) | −9.00000 | − | 15.5885i | −0.382719 | − | 0.662889i | ||||
\(554\) | −6.00000 | − | 10.3923i | −0.254916 | − | 0.441527i | ||||
\(555\) | 6.00000 | + | 3.46410i | 0.254686 | + | 0.147043i | ||||
\(556\) | −8.00000 | + | 13.8564i | −0.339276 | + | 0.587643i | ||||
\(557\) | −30.0000 | −1.27114 | −0.635570 | − | 0.772043i | \(-0.719235\pi\) | ||||
−0.635570 | + | 0.772043i | \(0.719235\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.0000 | 0.676728 | ||||||||
\(560\) | 1.50000 | − | 2.59808i | 0.0633866 | − | 0.109789i | ||||
\(561\) | 13.8564i | 0.585018i | ||||||||
\(562\) | 7.50000 | + | 12.9904i | 0.316368 | + | 0.547966i | ||||
\(563\) | 10.5000 | + | 18.1865i | 0.442522 | + | 0.766471i | 0.997876 | − | 0.0651433i | \(-0.0207504\pi\) |
−0.555354 | + | 0.831614i | \(0.687417\pi\) | |||||||
\(564\) | 10.5000 | − | 6.06218i | 0.442130 | − | 0.255264i | ||||
\(565\) | −4.00000 | + | 6.92820i | −0.168281 | + | 0.291472i | ||||
\(566\) | 21.0000 | 0.882696 | ||||||||
\(567\) | −27.0000 | −1.13389 | ||||||||
\(568\) | −6.00000 | −0.251754 | ||||||||
\(569\) | 3.00000 | − | 5.19615i | 0.125767 | − | 0.217834i | −0.796266 | − | 0.604947i | \(-0.793194\pi\) |
0.922032 | + | 0.387113i | \(0.126528\pi\) | |||||||
\(570\) | −12.0000 | + | 6.92820i | −0.502625 | + | 0.290191i | ||||
\(571\) | −16.0000 | − | 27.7128i | −0.669579 | − | 1.15975i | −0.978022 | − | 0.208502i | \(-0.933141\pi\) |
0.308443 | − | 0.951243i | \(-0.400192\pi\) | |||||||
\(572\) | 2.00000 | + | 3.46410i | 0.0836242 | + | 0.144841i | ||||
\(573\) | − | 13.8564i | − | 0.578860i | ||||||
\(574\) | 7.50000 | − | 12.9904i | 0.313044 | − | 0.542208i | ||||
\(575\) | 3.00000 | 0.125109 | ||||||||
\(576\) | 10.5000 | − | 18.1865i | 0.437500 | − | 0.757772i | ||||
\(577\) | −10.0000 | −0.416305 | −0.208153 | − | 0.978096i | \(-0.566745\pi\) | ||||
−0.208153 | + | 0.978096i | \(0.566745\pi\) | |||||||
\(578\) | 0.500000 | − | 0.866025i | 0.0207973 | − | 0.0360219i | ||||
\(579\) | −15.0000 | − | 8.66025i | −0.623379 | − | 0.359908i | ||||
\(580\) | 0.500000 | + | 0.866025i | 0.0207614 | + | 0.0359597i | ||||
\(581\) | 13.5000 | + | 23.3827i | 0.560074 | + | 0.970077i | ||||
\(582\) | 3.00000 | + | 1.73205i | 0.124354 | + | 0.0717958i | ||||
\(583\) | −2.00000 | + | 3.46410i | −0.0828315 | + | 0.143468i | ||||
\(584\) | −12.0000 | −0.496564 | ||||||||
\(585\) | 3.00000 | + | 5.19615i | 0.124035 | + | 0.214834i | ||||
\(586\) | 12.0000 | 0.495715 | ||||||||
\(587\) | 16.5000 | − | 28.5788i | 0.681028 | − | 1.17957i | −0.293640 | − | 0.955916i | \(-0.594867\pi\) |
0.974668 | − | 0.223659i | \(-0.0718001\pi\) | |||||||
\(588\) | 3.46410i | 0.142857i | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −7.00000 | − | 12.1244i | −0.288185 | − | 0.499152i | ||||
\(591\) | 18.0000 | − | 10.3923i | 0.740421 | − | 0.427482i | ||||
\(592\) | −2.00000 | + | 3.46410i | −0.0821995 | + | 0.142374i | ||||
\(593\) | 20.0000 | 0.821302 | 0.410651 | − | 0.911793i | \(-0.365302\pi\) | ||||
0.410651 | + | 0.911793i | \(0.365302\pi\) | |||||||
\(594\) | −9.00000 | + | 5.19615i | −0.369274 | + | 0.213201i | ||||
\(595\) | 12.0000 | 0.491952 | ||||||||
\(596\) | 8.50000 | − | 14.7224i | 0.348174 | − | 0.603054i | ||||
\(597\) | −6.00000 | + | 3.46410i | −0.245564 | + | 0.141776i | ||||
\(598\) | 3.00000 | + | 5.19615i | 0.122679 | + | 0.212486i | ||||
\(599\) | 5.00000 | + | 8.66025i | 0.204294 | + | 0.353848i | 0.949908 | − | 0.312531i | \(-0.101177\pi\) |
−0.745613 | + | 0.666379i | \(0.767843\pi\) | |||||||
\(600\) | 5.19615i | 0.212132i | ||||||||
\(601\) | −1.00000 | + | 1.73205i | −0.0407909 | + | 0.0706518i | −0.885700 | − | 0.464258i | \(-0.846321\pi\) |
0.844909 | + | 0.534910i | \(0.179654\pi\) | |||||||
\(602\) | 24.0000 | 0.978167 | ||||||||
\(603\) | 9.00000 | 0.366508 | ||||||||
\(604\) | 2.00000 | 0.0813788 | ||||||||
\(605\) | −3.50000 | + | 6.06218i | −0.142295 | + | 0.246463i | ||||
\(606\) | −27.0000 | − | 15.5885i | −1.09680 | − | 0.633238i | ||||
\(607\) | 20.5000 | + | 35.5070i | 0.832069 | + | 1.44119i | 0.896394 | + | 0.443257i | \(0.146177\pi\) |
−0.0643251 | + | 0.997929i | \(0.520489\pi\) | |||||||
\(608\) | 20.0000 | + | 34.6410i | 0.811107 | + | 1.40488i | ||||
\(609\) | 4.50000 | + | 2.59808i | 0.182349 | + | 0.105279i | ||||
\(610\) | 3.50000 | − | 6.06218i | 0.141711 | − | 0.245450i | ||||
\(611\) | −14.0000 | −0.566379 | ||||||||
\(612\) | 12.0000 | 0.485071 | ||||||||
\(613\) | −44.0000 | −1.77714 | −0.888572 | − | 0.458738i | \(-0.848302\pi\) | ||||
−0.888572 | + | 0.458738i | \(0.848302\pi\) | |||||||
\(614\) | −3.50000 | + | 6.06218i | −0.141249 | + | 0.244650i | ||||
\(615\) | 8.66025i | 0.349215i | ||||||||
\(616\) | 9.00000 | + | 15.5885i | 0.362620 | + | 0.628077i | ||||
\(617\) | 18.0000 | + | 31.1769i | 0.724653 | + | 1.25514i | 0.959117 | + | 0.283011i | \(0.0913331\pi\) |
−0.234464 | + | 0.972125i | \(0.575334\pi\) | |||||||
\(618\) | −12.0000 | + | 6.92820i | −0.482711 | + | 0.278693i | ||||
\(619\) | 2.00000 | − | 3.46410i | 0.0803868 | − | 0.139234i | −0.823029 | − | 0.567999i | \(-0.807718\pi\) |
0.903416 | + | 0.428765i | \(0.141051\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13.5000 | − | 7.79423i | 0.541736 | − | 0.312772i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −22.5000 | + | 38.9711i | −0.901443 | + | 1.56135i | ||||
\(624\) | −3.00000 | + | 1.73205i | −0.120096 | + | 0.0693375i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −7.00000 | − | 12.1244i | −0.279776 | − | 0.484587i | ||||
\(627\) | − | 27.7128i | − | 1.10674i | ||||||
\(628\) | 7.00000 | − | 12.1244i | 0.279330 | − | 0.483814i | ||||
\(629\) | −16.0000 | −0.637962 | ||||||||
\(630\) | 4.50000 | + | 7.79423i | 0.179284 | + | 0.310530i | ||||
\(631\) | 16.0000 | 0.636950 | 0.318475 | − | 0.947931i | \(-0.396829\pi\) | ||||
0.318475 | + | 0.947931i | \(0.396829\pi\) | |||||||
\(632\) | −9.00000 | + | 15.5885i | −0.358001 | + | 0.620076i | ||||
\(633\) | −33.0000 | − | 19.0526i | −1.31163 | − | 0.757271i | ||||
\(634\) | 17.0000 | + | 29.4449i | 0.675156 | + | 1.16940i | ||||
\(635\) | −2.50000 | − | 4.33013i | −0.0992095 | − | 0.171836i | ||||
\(636\) | 3.00000 | + | 1.73205i | 0.118958 | + | 0.0686803i | ||||
\(637\) | 2.00000 | − | 3.46410i | 0.0792429 | − | 0.137253i | ||||
\(638\) | 2.00000 | 0.0791808 | ||||||||
\(639\) | 3.00000 | − | 5.19615i | 0.118678 | − | 0.205557i | ||||
\(640\) | 3.00000 | 0.118585 | ||||||||
\(641\) | −16.5000 | + | 28.5788i | −0.651711 | + | 1.12880i | 0.330997 | + | 0.943632i | \(0.392615\pi\) |
−0.982708 | + | 0.185164i | \(0.940718\pi\) | |||||||
\(642\) | − | 5.19615i | − | 0.205076i | ||||||
\(643\) | 4.50000 | + | 7.79423i | 0.177463 | + | 0.307374i | 0.941011 | − | 0.338377i | \(-0.109878\pi\) |
−0.763548 | + | 0.645751i | \(0.776544\pi\) | |||||||
\(644\) | −4.50000 | − | 7.79423i | −0.177325 | − | 0.307136i | ||||
\(645\) | −12.0000 | + | 6.92820i | −0.472500 | + | 0.272798i | ||||
\(646\) | 16.0000 | − | 27.7128i | 0.629512 | − | 1.09035i | ||||
\(647\) | −17.0000 | −0.668339 | −0.334169 | − | 0.942513i | \(-0.608456\pi\) | ||||
−0.334169 | + | 0.942513i | \(0.608456\pi\) | |||||||
\(648\) | 13.5000 | + | 23.3827i | 0.530330 | + | 0.918559i | ||||
\(649\) | 28.0000 | 1.09910 | ||||||||
\(650\) | 1.00000 | − | 1.73205i | 0.0392232 | − | 0.0679366i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.00000 | − | 3.46410i | −0.0783260 | − | 0.135665i | ||||
\(653\) | 2.00000 | + | 3.46410i | 0.0782660 | + | 0.135561i | 0.902502 | − | 0.430686i | \(-0.141728\pi\) |
−0.824236 | + | 0.566247i | \(0.808395\pi\) | |||||||
\(654\) | − | 8.66025i | − | 0.338643i | ||||||
\(655\) | −3.00000 | + | 5.19615i | −0.117220 | + | 0.203030i | ||||
\(656\) | −5.00000 | −0.195217 | ||||||||
\(657\) | 6.00000 | − | 10.3923i | 0.234082 | − | 0.405442i | ||||
\(658\) | −21.0000 | −0.818665 | ||||||||
\(659\) | 4.00000 | − | 6.92820i | 0.155818 | − | 0.269884i | −0.777539 | − | 0.628835i | \(-0.783532\pi\) |
0.933357 | + | 0.358951i | \(0.116865\pi\) | |||||||
\(660\) | −3.00000 | − | 1.73205i | −0.116775 | − | 0.0674200i | ||||
\(661\) | 7.00000 | + | 12.1244i | 0.272268 | + | 0.471583i | 0.969442 | − | 0.245319i | \(-0.0788928\pi\) |
−0.697174 | + | 0.716902i | \(0.745559\pi\) | |||||||
\(662\) | 3.00000 | + | 5.19615i | 0.116598 | + | 0.201954i | ||||
\(663\) | −12.0000 | − | 6.92820i | −0.466041 | − | 0.269069i | ||||
\(664\) | 13.5000 | − | 23.3827i | 0.523902 | − | 0.907424i | ||||
\(665\) | −24.0000 | −0.930680 | ||||||||
\(666\) | −6.00000 | − | 10.3923i | −0.232495 | − | 0.402694i | ||||
\(667\) | −3.00000 | −0.116160 | ||||||||
\(668\) | −4.50000 | + | 7.79423i | −0.174110 | + | 0.301568i | ||||
\(669\) | 32.9090i | 1.27233i | ||||||||
\(670\) | −1.50000 | − | 2.59808i | −0.0579501 | − | 0.100372i | ||||
\(671\) | 7.00000 | + | 12.1244i | 0.270232 | + | 0.468056i | ||||
\(672\) | 22.5000 | − | 12.9904i | 0.867956 | − | 0.501115i | ||||
\(673\) | −3.00000 | + | 5.19615i | −0.115642 | + | 0.200297i | −0.918036 | − | 0.396497i | \(-0.870226\pi\) |
0.802395 | + | 0.596794i | \(0.203559\pi\) | |||||||
\(674\) | −8.00000 | −0.308148 | ||||||||
\(675\) | −4.50000 | − | 2.59808i | −0.173205 | − | 0.100000i | ||||
\(676\) | 9.00000 | 0.346154 | ||||||||
\(677\) | 21.0000 | − | 36.3731i | 0.807096 | − | 1.39793i | −0.107772 | − | 0.994176i | \(-0.534372\pi\) |
0.914867 | − | 0.403755i | \(-0.132295\pi\) | |||||||
\(678\) | 12.0000 | − | 6.92820i | 0.460857 | − | 0.266076i | ||||
\(679\) | 3.00000 | + | 5.19615i | 0.115129 | + | 0.199410i | ||||
\(680\) | −6.00000 | − | 10.3923i | −0.230089 | − | 0.398527i | ||||
\(681\) | 6.92820i | 0.265489i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.0000 | 0.459167 | 0.229584 | − | 0.973289i | \(-0.426264\pi\) | ||||
0.229584 | + | 0.973289i | \(0.426264\pi\) | |||||||
\(684\) | −24.0000 | −0.917663 | ||||||||
\(685\) | −12.0000 | −0.458496 | ||||||||
\(686\) | −7.50000 | + | 12.9904i | −0.286351 | + | 0.495975i | ||||
\(687\) | 22.5000 | + | 12.9904i | 0.858429 | + | 0.495614i | ||||
\(688\) | −4.00000 | − | 6.92820i | −0.152499 | − | 0.264135i | ||||
\(689\) | −2.00000 | − | 3.46410i | −0.0761939 | − | 0.131972i | ||||
\(690\) | −4.50000 | − | 2.59808i | −0.171312 | − | 0.0989071i | ||||
\(691\) | 7.00000 | − | 12.1244i | 0.266293 | − | 0.461232i | −0.701609 | − | 0.712562i | \(-0.747535\pi\) |
0.967901 | + | 0.251330i | \(0.0808679\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −18.0000 | −0.683763 | ||||||||
\(694\) | 4.00000 | 0.151838 | ||||||||
\(695\) | −8.00000 | + | 13.8564i | −0.303457 | + | 0.525603i | ||||
\(696\) | − | 5.19615i | − | 0.196960i | ||||||
\(697\) | −10.0000 | − | 17.3205i | −0.378777 | − | 0.656061i | ||||
\(698\) | 2.50000 | + | 4.33013i | 0.0946264 | + | 0.163898i | ||||
\(699\) | −36.0000 | + | 20.7846i | −1.36165 | + | 0.786146i | ||||
\(700\) | −1.50000 | + | 2.59808i | −0.0566947 | + | 0.0981981i | ||||
\(701\) | 23.0000 | 0.868698 | 0.434349 | − | 0.900745i | \(-0.356978\pi\) | ||||
0.434349 | + | 0.900745i | \(0.356978\pi\) | |||||||
\(702\) | − | 10.3923i | − | 0.392232i | ||||||
\(703\) | 32.0000 | 1.20690 | ||||||||
\(704\) | 7.00000 | − | 12.1244i | 0.263822 | − | 0.456954i | ||||
\(705\) | 10.5000 | − | 6.06218i | 0.395453 | − | 0.228315i | ||||
\(706\) | −12.0000 | − | 20.7846i | −0.451626 | − | 0.782239i | ||||
\(707\) | −27.0000 | − | 46.7654i | −1.01544 | − | 1.75879i | ||||
\(708\) | − | 24.2487i | − | 0.911322i | ||||||
\(709\) | 20.5000 | − | 35.5070i | 0.769894 | − | 1.33349i | −0.167727 | − | 0.985834i | \(-0.553643\pi\) |
0.937620 | − | 0.347661i | \(-0.113024\pi\) | |||||||
\(710\) | −2.00000 | −0.0750587 | ||||||||
\(711\) | −9.00000 | − | 15.5885i | −0.337526 | − | 0.584613i | ||||
\(712\) | 45.0000 | 1.68645 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −18.0000 | − | 10.3923i | −0.673633 | − | 0.388922i | ||||
\(715\) | 2.00000 | + | 3.46410i | 0.0747958 | + | 0.129550i | ||||
\(716\) | −1.00000 | − | 1.73205i | −0.0373718 | − | 0.0647298i | ||||
\(717\) | −12.0000 | − | 6.92820i | −0.448148 | − | 0.258738i | ||||
\(718\) | −12.0000 | + | 20.7846i | −0.447836 | + | 0.775675i | ||||
\(719\) | 6.00000 | 0.223762 | 0.111881 | − | 0.993722i | \(-0.464312\pi\) | ||||
0.111881 | + | 0.993722i | \(0.464312\pi\) | |||||||
\(720\) | 1.50000 | − | 2.59808i | 0.0559017 | − | 0.0968246i | ||||
\(721\) | −24.0000 | −0.893807 | ||||||||
\(722\) | −22.5000 | + | 38.9711i | −0.837363 | + | 1.45036i | ||||
\(723\) | 19.0526i | 0.708572i | ||||||||
\(724\) | −3.50000 | − | 6.06218i | −0.130076 | − | 0.225299i | ||||
\(725\) | 0.500000 | + | 0.866025i | 0.0185695 | + | 0.0321634i | ||||
\(726\) | 10.5000 | − | 6.06218i | 0.389692 | − | 0.224989i | ||||
\(727\) | −11.5000 | + | 19.9186i | −0.426511 | + | 0.738739i | −0.996560 | − | 0.0828714i | \(-0.973591\pi\) |
0.570049 | + | 0.821611i | \(0.306924\pi\) | |||||||
\(728\) | −18.0000 | −0.667124 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | −4.00000 | −0.148047 | ||||||||
\(731\) | 16.0000 | − | 27.7128i | 0.591781 | − | 1.02500i | ||||
\(732\) | 10.5000 | − | 6.06218i | 0.388091 | − | 0.224065i | ||||
\(733\) | 17.0000 | + | 29.4449i | 0.627909 | + | 1.08757i | 0.987971 | + | 0.154642i | \(0.0494225\pi\) |
−0.360061 | + | 0.932929i | \(0.617244\pi\) | |||||||
\(734\) | −12.0000 | − | 20.7846i | −0.442928 | − | 0.767174i | ||||
\(735\) | 3.46410i | 0.127775i | ||||||||
\(736\) | −7.50000 | + | 12.9904i | −0.276454 | + | 0.478832i | ||||
\(737\) | 6.00000 | 0.221013 | ||||||||
\(738\) | 7.50000 | − | 12.9904i | 0.276079 | − | 0.478183i | ||||
\(739\) | −2.00000 | −0.0735712 | −0.0367856 | − | 0.999323i | \(-0.511712\pi\) | ||||
−0.0367856 | + | 0.999323i | \(0.511712\pi\) | |||||||
\(740\) | 2.00000 | − | 3.46410i | 0.0735215 | − | 0.127343i | ||||
\(741\) | 24.0000 | + | 13.8564i | 0.881662 | + | 0.509028i | ||||
\(742\) | −3.00000 | − | 5.19615i | −0.110133 | − | 0.190757i | ||||
\(743\) | 14.5000 | + | 25.1147i | 0.531953 | + | 0.921370i | 0.999304 | + | 0.0372984i | \(0.0118752\pi\) |
−0.467351 | + | 0.884072i | \(0.654791\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.50000 | − | 14.7224i | 0.311416 | − | 0.539388i | ||||
\(746\) | 10.0000 | 0.366126 | ||||||||
\(747\) | 13.5000 | + | 23.3827i | 0.493939 | + | 0.855528i | ||||
\(748\) | 8.00000 | 0.292509 | ||||||||
\(749\) | 4.50000 | − | 7.79423i | 0.164426 | − | 0.284795i | ||||
\(750\) | 1.73205i | 0.0632456i | ||||||||
\(751\) | −5.00000 | − | 8.66025i | −0.182453 | − | 0.316017i | 0.760263 | − | 0.649616i | \(-0.225070\pi\) |
−0.942715 | + | 0.333599i | \(0.891737\pi\) | |||||||
\(752\) | 3.50000 | + | 6.06218i | 0.127632 | + | 0.221065i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.00000 | + | 1.73205i | −0.0364179 | + | 0.0630776i | ||||
\(755\) | 2.00000 | 0.0727875 | ||||||||
\(756\) | 15.5885i | 0.566947i | ||||||||
\(757\) | −26.0000 | −0.944986 | −0.472493 | − | 0.881334i | \(-0.656646\pi\) | ||||
−0.472493 | + | 0.881334i | \(0.656646\pi\) | |||||||
\(758\) | 13.0000 | − | 22.5167i | 0.472181 | − | 0.817842i | ||||
\(759\) | 9.00000 | − | 5.19615i | 0.326679 | − | 0.188608i | ||||
\(760\) | 12.0000 | + | 20.7846i | 0.435286 | + | 0.753937i | ||||
\(761\) | −7.50000 | − | 12.9904i | −0.271875 | − | 0.470901i | 0.697467 | − | 0.716617i | \(-0.254310\pi\) |
−0.969342 | + | 0.245716i | \(0.920977\pi\) | |||||||
\(762\) | 8.66025i | 0.313728i | ||||||||
\(763\) | 7.50000 | − | 12.9904i | 0.271518 | − | 0.470283i | ||||
\(764\) | −8.00000 | −0.289430 | ||||||||
\(765\) | 12.0000 | 0.433861 | ||||||||
\(766\) | 36.0000 | 1.30073 | ||||||||
\(767\) | −14.0000 | + | 24.2487i | −0.505511 | + | 0.875570i | ||||
\(768\) | −25.5000 | − | 14.7224i | −0.920152 | − | 0.531250i | ||||
\(769\) | −2.50000 | − | 4.33013i | −0.0901523 | − | 0.156148i | 0.817423 | − | 0.576038i | \(-0.195402\pi\) |
−0.907575 | + | 0.419890i | \(0.862069\pi\) | |||||||
\(770\) | 3.00000 | + | 5.19615i | 0.108112 | + | 0.187256i | ||||
\(771\) | −9.00000 | − | 5.19615i | −0.324127 | − | 0.187135i | ||||
\(772\) | −5.00000 | + | 8.66025i | −0.179954 | + | 0.311689i | ||||
\(773\) | −24.0000 | −0.863220 | −0.431610 | − | 0.902060i | \(-0.642054\pi\) | ||||
−0.431610 | + | 0.902060i | \(0.642054\pi\) | |||||||
\(774\) | 24.0000 | 0.862662 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.00000 | − | 5.19615i | 0.107694 | − | 0.186531i | ||||
\(777\) | − | 20.7846i | − | 0.745644i | ||||||
\(778\) | −16.5000 | − | 28.5788i | −0.591554 | − | 1.02460i | ||||
\(779\) | 20.0000 | + | 34.6410i | 0.716574 | + | 1.24114i | ||||
\(780\) | 3.00000 | − | 1.73205i | 0.107417 | − | 0.0620174i | ||||
\(781\) | 2.00000 | − | 3.46410i | 0.0715656 | − | 0.123955i | ||||
\(782\) | 12.0000 | 0.429119 | ||||||||
\(783\) | 4.50000 | + | 2.59808i | 0.160817 | + | 0.0928477i | ||||
\(784\) | −2.00000 | −0.0714286 | ||||||||
\(785\) | 7.00000 | − | 12.1244i | 0.249841 | − | 0.432737i | ||||
\(786\) | 9.00000 | − | 5.19615i | 0.321019 | − | 0.185341i | ||||
\(787\) | −14.0000 | − | 24.2487i | −0.499046 | − | 0.864373i | 0.500953 | − | 0.865474i | \(-0.332983\pi\) |
−0.999999 | + | 0.00110111i | \(0.999650\pi\) | |||||||
\(788\) | −6.00000 | − | 10.3923i | −0.213741 | − | 0.370211i | ||||
\(789\) | 27.7128i | 0.986602i | ||||||||
\(790\) | −3.00000 | + | 5.19615i | −0.106735 | + | 0.184871i | ||||
\(791\) | 24.0000 | 0.853342 | ||||||||
\(792\) | 9.00000 | + | 15.5885i | 0.319801 | + | 0.553912i | ||||
\(793\) | −14.0000 | −0.497155 | ||||||||
\(794\) | −17.0000 | + | 29.4449i | −0.603307 | + | 1.04496i | ||||
\(795\) | 3.00000 | + | 1.73205i | 0.106399 | + | 0.0614295i | ||||
\(796\) | 2.00000 | + | 3.46410i | 0.0708881 | + | 0.122782i | ||||
\(797\) | −13.0000 | − | 22.5167i | −0.460484 | − | 0.797581i | 0.538501 | − | 0.842625i | \(-0.318991\pi\) |
−0.998985 | + | 0.0450436i | \(0.985657\pi\) | |||||||
\(798\) | 36.0000 | + | 20.7846i | 1.27439 | + | 0.735767i | ||||
\(799\) | −14.0000 | + | 24.2487i | −0.495284 | + | 0.857858i | ||||
\(800\) | 5.00000 | 0.176777 | ||||||||
\(801\) | −22.5000 | + | 38.9711i | −0.794998 | + | 1.37698i | ||||
\(802\) | −18.0000 | −0.635602 | ||||||||
\(803\) | 4.00000 | − | 6.92820i | 0.141157 | − | 0.244491i | ||||
\(804\) | − | 5.19615i | − | 0.183254i | ||||||
\(805\) | −4.50000 | − | 7.79423i | −0.158604 | − | 0.274710i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −37.5000 | + | 21.6506i | −1.32006 | + | 0.762138i | ||||
\(808\) | −27.0000 | + | 46.7654i | −0.949857 | + | 1.64520i | ||||
\(809\) | 26.0000 | 0.914111 | 0.457056 | − | 0.889438i | \(-0.348904\pi\) | ||||
0.457056 | + | 0.889438i | \(0.348904\pi\) | |||||||
\(810\) | 4.50000 | + | 7.79423i | 0.158114 | + | 0.273861i | ||||
\(811\) | −42.0000 | −1.47482 | −0.737410 | − | 0.675446i | \(-0.763951\pi\) | ||||
−0.737410 | + | 0.675446i | \(0.763951\pi\) | |||||||
\(812\) | 1.50000 | − | 2.59808i | 0.0526397 | − | 0.0911746i | ||||
\(813\) | 12.0000 | − | 6.92820i | 0.420858 | − | 0.242983i | ||||
\(814\) | −4.00000 | − | 6.92820i | −0.140200 | − | 0.242833i | ||||
\(815\) | −2.00000 | − | 3.46410i | −0.0700569 | − | 0.121342i | ||||
\(816\) | 6.92820i | 0.242536i | ||||||||
\(817\) | −32.0000 | + | 55.4256i | −1.11954 | + | 1.93910i | ||||
\(818\) | 14.0000 | 0.489499 | ||||||||
\(819\) | 9.00000 | − | 15.5885i | 0.314485 | − | 0.544705i | ||||
\(820\) | 5.00000 | 0.174608 | ||||||||
\(821\) | −7.50000 | + | 12.9904i | −0.261752 | + | 0.453367i | −0.966708 | − | 0.255884i | \(-0.917634\pi\) |
0.704956 | + | 0.709251i | \(0.250967\pi\) | |||||||
\(822\) | 18.0000 | + | 10.3923i | 0.627822 | + | 0.362473i | ||||
\(823\) | −26.5000 | − | 45.8993i | −0.923732 | − | 1.59995i | −0.793588 | − | 0.608456i | \(-0.791789\pi\) |
−0.130144 | − | 0.991495i | \(-0.541544\pi\) | |||||||
\(824\) | 12.0000 | + | 20.7846i | 0.418040 | + | 0.724066i | ||||
\(825\) | −3.00000 | − | 1.73205i | −0.104447 | − | 0.0603023i | ||||
\(826\) | −21.0000 | + | 36.3731i | −0.730683 | + | 1.26558i | ||||
\(827\) | 37.0000 | 1.28662 | 0.643308 | − | 0.765607i | \(-0.277561\pi\) | ||||
0.643308 | + | 0.765607i | \(0.277561\pi\) | |||||||
\(828\) | −4.50000 | − | 7.79423i | −0.156386 | − | 0.270868i | ||||
\(829\) | −3.00000 | −0.104194 | −0.0520972 | − | 0.998642i | \(-0.516591\pi\) | ||||
−0.0520972 | + | 0.998642i | \(0.516591\pi\) | |||||||
\(830\) | 4.50000 | − | 7.79423i | 0.156197 | − | 0.270542i | ||||
\(831\) | − | 20.7846i | − | 0.721010i | ||||||
\(832\) | 7.00000 | + | 12.1244i | 0.242681 | + | 0.420336i | ||||
\(833\) | −4.00000 | − | 6.92820i | −0.138592 | − | 0.240048i | ||||
\(834\) | 24.0000 | − | 13.8564i | 0.831052 | − | 0.479808i | ||||
\(835\) | −4.50000 | + | 7.79423i | −0.155729 | + | 0.269730i | ||||
\(836\) | −16.0000 | −0.553372 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 26.0000 | 0.898155 | ||||||||
\(839\) | 20.0000 | − | 34.6410i | 0.690477 | − | 1.19594i | −0.281205 | − | 0.959648i | \(-0.590734\pi\) |
0.971682 | − | 0.236293i | \(-0.0759325\pi\) | |||||||
\(840\) | 13.5000 | − | 7.79423i | 0.465794 | − | 0.268926i | ||||
\(841\) | 14.0000 | + | 24.2487i | 0.482759 | + | 0.836162i | ||||
\(842\) | −17.0000 | − | 29.4449i | −0.585859 | − | 1.01474i | ||||
\(843\) | 25.9808i | 0.894825i | ||||||||
\(844\) | −11.0000 | + | 19.0526i | −0.378636 | + | 0.655816i | ||||
\(845\) | 9.00000 | 0.309609 | ||||||||
\(846\) | −21.0000 | −0.721995 | ||||||||
\(847\) | 21.0000 | 0.721569 | ||||||||
\(848\) | −1.00000 | + | 1.73205i | −0.0343401 | + | 0.0594789i | ||||
\(849\) | 31.5000 | + | 18.1865i | 1.08108 | + | 0.624160i | ||||
\(850\) | −2.00000 | − | 3.46410i | −0.0685994 | − | 0.118818i | ||||
\(851\) | 6.00000 | + | 10.3923i | 0.205677 | + | 0.356244i | ||||
\(852\) | −3.00000 | − | 1.73205i | −0.102778 | − | 0.0593391i | ||||
\(853\) | 27.0000 | − | 46.7654i | 0.924462 | − | 1.60122i | 0.132039 | − | 0.991245i | \(-0.457848\pi\) |
0.792424 | − | 0.609971i | \(-0.208819\pi\) | |||||||
\(854\) | −21.0000 | −0.718605 | ||||||||
\(855\) | −24.0000 | −0.820783 | ||||||||
\(856\) | −9.00000 | −0.307614 | ||||||||
\(857\) | −5.00000 | + | 8.66025i | −0.170797 | + | 0.295829i | −0.938699 | − | 0.344739i | \(-0.887967\pi\) |
0.767902 | + | 0.640567i | \(0.221301\pi\) | |||||||
\(858\) | − | 6.92820i | − | 0.236525i | ||||||
\(859\) | −11.0000 | − | 19.0526i | −0.375315 | − | 0.650065i | 0.615059 | − | 0.788481i | \(-0.289132\pi\) |
−0.990374 | + | 0.138416i | \(0.955799\pi\) | |||||||
\(860\) | 4.00000 | + | 6.92820i | 0.136399 | + | 0.236250i | ||||
\(861\) | 22.5000 | − | 12.9904i | 0.766798 | − | 0.442711i | ||||
\(862\) | 15.0000 | − | 25.9808i | 0.510902 | − | 0.884908i | ||||
\(863\) | 17.0000 | 0.578687 | 0.289343 | − | 0.957225i | \(-0.406563\pi\) | ||||
0.289343 | + | 0.957225i | \(0.406563\pi\) | |||||||
\(864\) | 22.5000 | − | 12.9904i | 0.765466 | − | 0.441942i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −14.0000 | + | 24.2487i | −0.475739 | + | 0.824005i | ||||
\(867\) | 1.50000 | − | 0.866025i | 0.0509427 | − | 0.0294118i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.00000 | − | 10.3923i | −0.203536 | − | 0.352535i | ||||
\(870\) | − | 1.73205i | − | 0.0587220i | ||||||
\(871\) | −3.00000 | + | 5.19615i | −0.101651 | + | 0.176065i | ||||
\(872\) | −15.0000 | −0.507964 | ||||||||
\(873\) | 3.00000 | + | 5.19615i | 0.101535 | + | 0.175863i | ||||
\(874\) | −24.0000 | −0.811812 | ||||||||
\(875\) | −1.50000 | + | 2.59808i | −0.0507093 | + | 0.0878310i | ||||
\(876\) | −6.00000 | − | 3.46410i | −0.202721 | − | 0.117041i | ||||
\(877\) | 9.00000 | + | 15.5885i | 0.303908 | + | 0.526385i | 0.977018 | − | 0.213158i | \(-0.0683750\pi\) |
−0.673109 | + | 0.739543i | \(0.735042\pi\) | |||||||
\(878\) | −14.0000 | − | 24.2487i | −0.472477 | − | 0.818354i | ||||
\(879\) | 18.0000 | + | 10.3923i | 0.607125 | + | 0.350524i | ||||
\(880\) | 1.00000 | − | 1.73205i | 0.0337100 | − | 0.0583874i | ||||
\(881\) | −35.0000 | −1.17918 | −0.589590 | − | 0.807703i | \(-0.700711\pi\) | ||||
−0.589590 | + | 0.807703i | \(0.700711\pi\) | |||||||
\(882\) | 3.00000 | − | 5.19615i | 0.101015 | − | 0.174964i | ||||
\(883\) | 23.0000 | 0.774012 | 0.387006 | − | 0.922077i | \(-0.373509\pi\) | ||||
0.387006 | + | 0.922077i | \(0.373509\pi\) | |||||||
\(884\) | −4.00000 | + | 6.92820i | −0.134535 | + | 0.233021i | ||||
\(885\) | − | 24.2487i | − | 0.815112i | ||||||
\(886\) | −7.50000 | − | 12.9904i | −0.251967 | − | 0.436420i | ||||
\(887\) | −18.0000 | − | 31.1769i | −0.604381 | − | 1.04682i | −0.992149 | − | 0.125061i | \(-0.960087\pi\) |
0.387768 | − | 0.921757i | \(-0.373246\pi\) | |||||||
\(888\) | −18.0000 | + | 10.3923i | −0.604040 | + | 0.348743i | ||||
\(889\) | −7.50000 | + | 12.9904i | −0.251542 | + | 0.435683i | ||||
\(890\) | 15.0000 | 0.502801 | ||||||||
\(891\) | −18.0000 | −0.603023 | ||||||||
\(892\) | 19.0000 | 0.636167 | ||||||||
\(893\) | 28.0000 | − | 48.4974i | 0.936984 | − | 1.62290i | ||||
\(894\) | −25.5000 | + | 14.7224i | −0.852848 | + | 0.492392i | ||||
\(895\) | −1.00000 | − | 1.73205i | −0.0334263 | − | 0.0578961i | ||||
\(896\) | −4.50000 | − | 7.79423i | −0.150334 | − | 0.260387i | ||||
\(897\) | 10.3923i | 0.346989i | ||||||||
\(898\) | 13.0000 | − | 22.5167i | 0.433816 | − | 0.751391i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −1.50000 | + | 2.59808i | −0.0500000 | + | 0.0866025i | ||||
\(901\) | −8.00000 | −0.266519 | ||||||||
\(902\) | 5.00000 | − | 8.66025i | 0.166482 | − | 0.288355i | ||||
\(903\) | 36.0000 | + | 20.7846i | 1.19800 | + | 0.691669i | ||||
\(904\) | −12.0000 | − | 20.7846i | −0.399114 | − | 0.691286i | ||||
\(905\) | −3.50000 | − | 6.06218i | −0.116344 | − | 0.201514i | ||||
\(906\) | −3.00000 | − | 1.73205i | −0.0996683 | − | 0.0575435i | ||||
\(907\) | 25.5000 | − | 44.1673i | 0.846714 | − | 1.46655i | −0.0374111 | − | 0.999300i | \(-0.511911\pi\) |
0.884125 | − | 0.467251i | \(-0.154756\pi\) | |||||||
\(908\) | 4.00000 | 0.132745 | ||||||||
\(909\) | −27.0000 | − | 46.7654i | −0.895533 | − | 1.55111i | ||||
\(910\) | −6.00000 | −0.198898 | ||||||||
\(911\) | 25.0000 | − | 43.3013i | 0.828287 | − | 1.43464i | −0.0710941 | − | 0.997470i | \(-0.522649\pi\) |
0.899381 | − | 0.437165i | \(-0.144018\pi\) | |||||||
\(912\) | − | 13.8564i | − | 0.458831i | ||||||
\(913\) | 9.00000 | + | 15.5885i | 0.297857 | + | 0.515903i | ||||
\(914\) | 10.0000 | + | 17.3205i | 0.330771 | + | 0.572911i | ||||
\(915\) | 10.5000 | − | 6.06218i | 0.347119 | − | 0.200409i | ||||
\(916\) | 7.50000 | − | 12.9904i | 0.247807 | − | 0.429214i | ||||
\(917\) | 18.0000 | 0.594412 | ||||||||
\(918\) | −18.0000 | − | 10.3923i | −0.594089 | − | 0.342997i | ||||
\(919\) | 10.0000 | 0.329870 | 0.164935 | − | 0.986304i | \(-0.447259\pi\) | ||||
0.164935 | + | 0.986304i | \(0.447259\pi\) | |||||||
\(920\) | −4.50000 | + | 7.79423i | −0.148361 | + | 0.256968i | ||||
\(921\) | −10.5000 | + | 6.06218i | −0.345987 | + | 0.199756i | ||||
\(922\) | −4.50000 | − | 7.79423i | −0.148200 | − | 0.256689i | ||||
\(923\) | 2.00000 | + | 3.46410i | 0.0658308 | + | 0.114022i | ||||
\(924\) | 10.3923i | 0.341882i | ||||||||
\(925\) | 2.00000 | − | 3.46410i | 0.0657596 | − | 0.113899i | ||||
\(926\) | −36.0000 | −1.18303 | ||||||||
\(927\) | −24.0000 | −0.788263 | ||||||||
\(928\) | −5.00000 | −0.164133 | ||||||||
\(929\) | −7.00000 | + | 12.1244i | −0.229663 | + | 0.397787i | −0.957708 | − | 0.287742i | \(-0.907096\pi\) |
0.728046 | + | 0.685529i | \(0.240429\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.00000 | + | 13.8564i | 0.262189 | + | 0.454125i | ||||
\(932\) | 12.0000 | + | 20.7846i | 0.393073 | + | 0.680823i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −10.0000 | + | 17.3205i | −0.327210 | + | 0.566744i | ||||
\(935\) | 8.00000 | 0.261628 | ||||||||
\(936\) | −18.0000 | −0.588348 | ||||||||
\(937\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(938\) | −4.50000 | + | 7.79423i | −0.146930 | + | 0.254491i | ||||
\(939\) | − | 24.2487i | − | 0.791327i | ||||||
\(940\) | −3.50000 | − | 6.06218i | −0.114157 | − | 0.197726i | ||||
\(941\) | 3.50000 | + | 6.06218i | 0.114097 | + | 0.197621i | 0.917418 | − | 0.397924i | \(-0.130269\pi\) |
−0.803322 | + | 0.595545i | \(0.796936\pi\) | |||||||
\(942\) | −21.0000 | + | 12.1244i | −0.684217 | + | 0.395033i | ||||
\(943\) | −7.50000 | + | 12.9904i | −0.244234 | + | 0.423025i | ||||
\(944\) | 14.0000 | 0.455661 | ||||||||
\(945\) | 15.5885i | 0.507093i | ||||||||
\(946\) | 16.0000 | 0.520205 | ||||||||
\(947\) | −28.5000 | + | 49.3634i | −0.926126 | + | 1.60410i | −0.136385 | + | 0.990656i | \(0.543548\pi\) |
−0.789741 | + | 0.613441i | \(0.789785\pi\) | |||||||
\(948\) | −9.00000 | + | 5.19615i | −0.292306 | + | 0.168763i | ||||
\(949\) | 4.00000 | + | 6.92820i | 0.129845 | + | 0.224899i | ||||
\(950\) | 4.00000 | + | 6.92820i | 0.129777 | + | 0.224781i | ||||
\(951\) | 58.8897i | 1.90963i | ||||||||
\(952\) | −18.0000 | + | 31.1769i | −0.583383 | + | 1.01045i | ||||
\(953\) | −26.0000 | −0.842223 | −0.421111 | − | 0.907009i | \(-0.638360\pi\) | ||||
−0.421111 | + | 0.907009i | \(0.638360\pi\) | |||||||
\(954\) | −3.00000 | − | 5.19615i | −0.0971286 | − | 0.168232i | ||||
\(955\) | −8.00000 | −0.258874 | ||||||||
\(956\) | −4.00000 | + | 6.92820i | −0.129369 | + | 0.224074i | ||||
\(957\) | 3.00000 | + | 1.73205i | 0.0969762 | + | 0.0559893i | ||||
\(958\) | 9.00000 | + | 15.5885i | 0.290777 | + | 0.503640i | ||||
\(959\) | 18.0000 | + | 31.1769i | 0.581250 | + | 1.00676i | ||||
\(960\) | −10.5000 | − | 6.06218i | −0.338886 | − | 0.195656i | ||||
\(961\) | 15.5000 | − | 26.8468i | 0.500000 | − | 0.866025i | ||||
\(962\) | 8.00000 | 0.257930 | ||||||||
\(963\) | 4.50000 | − | 7.79423i | 0.145010 | − | 0.251166i | ||||
\(964\) | 11.0000 | 0.354286 | ||||||||
\(965\) | −5.00000 | + | 8.66025i | −0.160956 | + | 0.278783i | ||||
\(966\) | 15.5885i | 0.501550i | ||||||||
\(967\) | −20.5000 | − | 35.5070i | −0.659236 | − | 1.14183i | −0.980814 | − | 0.194946i | \(-0.937547\pi\) |
0.321578 | − | 0.946883i | \(-0.395787\pi\) | |||||||
\(968\) | −10.5000 | − | 18.1865i | −0.337483 | − | 0.584537i | ||||
\(969\) | 48.0000 | − | 27.7128i | 1.54198 | − | 0.890264i | ||||
\(970\) | 1.00000 | − | 1.73205i | 0.0321081 | − | 0.0556128i | ||||
\(971\) | −36.0000 | −1.15529 | −0.577647 | − | 0.816286i | \(-0.696029\pi\) | ||||
−0.577647 | + | 0.816286i | \(0.696029\pi\) | |||||||
\(972\) | 15.5885i | 0.500000i | ||||||||
\(973\) | 48.0000 | 1.53881 | ||||||||
\(974\) | 8.00000 | − | 13.8564i | 0.256337 | − | 0.443988i | ||||
\(975\) | 3.00000 | − | 1.73205i | 0.0960769 | − | 0.0554700i | ||||
\(976\) | 3.50000 | + | 6.06218i | 0.112032 | + | 0.194046i | ||||
\(977\) | 19.0000 | + | 32.9090i | 0.607864 | + | 1.05285i | 0.991592 | + | 0.129405i | \(0.0413067\pi\) |
−0.383728 | + | 0.923446i | \(0.625360\pi\) | |||||||
\(978\) | 6.92820i | 0.221540i | ||||||||
\(979\) | −15.0000 | + | 25.9808i | −0.479402 | + | 0.830349i | ||||
\(980\) | 2.00000 | 0.0638877 | ||||||||
\(981\) | 7.50000 | − | 12.9904i | 0.239457 | − | 0.414751i | ||||
\(982\) | 20.0000 | 0.638226 | ||||||||
\(983\) | −1.50000 | + | 2.59808i | −0.0478426 | + | 0.0828658i | −0.888955 | − | 0.457995i | \(-0.848568\pi\) |
0.841112 | + | 0.540860i | \(0.181901\pi\) | |||||||
\(984\) | −22.5000 | − | 12.9904i | −0.717274 | − | 0.414118i | ||||
\(985\) | −6.00000 | − | 10.3923i | −0.191176 | − | 0.331126i | ||||
\(986\) | 2.00000 | + | 3.46410i | 0.0636930 | + | 0.110319i | ||||
\(987\) | −31.5000 | − | 18.1865i | −1.00266 | − | 0.578884i | ||||
\(988\) | 8.00000 | − | 13.8564i | 0.254514 | − | 0.440831i | ||||
\(989\) | −24.0000 | −0.763156 | ||||||||
\(990\) | 3.00000 | + | 5.19615i | 0.0953463 | + | 0.165145i | ||||
\(991\) | 26.0000 | 0.825917 | 0.412959 | − | 0.910750i | \(-0.364495\pi\) | ||||
0.412959 | + | 0.910750i | \(0.364495\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 10.3923i | 0.329790i | ||||||||
\(994\) | 3.00000 | + | 5.19615i | 0.0951542 | + | 0.164812i | ||||
\(995\) | 2.00000 | + | 3.46410i | 0.0634043 | + | 0.109819i | ||||
\(996\) | 13.5000 | − | 7.79423i | 0.427764 | − | 0.246970i | ||||
\(997\) | 9.00000 | − | 15.5885i | 0.285033 | − | 0.493691i | −0.687584 | − | 0.726105i | \(-0.741329\pi\) |
0.972617 | + | 0.232413i | \(0.0746622\pi\) | |||||||
\(998\) | −32.0000 | −1.01294 | ||||||||
\(999\) | − | 20.7846i | − | 0.657596i |
(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 | 45.2.e.a.16.1 | ✓ | 2 | |
3.2 | odd | 2 | 135.2.e.a.46.1 | 2 | |||
4.3 | odd | 2 | 720.2.q.d.241.1 | 2 | |||
5.2 | odd | 4 | 225.2.k.a.124.1 | 4 | |||
5.3 | odd | 4 | 225.2.k.a.124.2 | 4 | |||
5.4 | even | 2 | 225.2.e.a.151.1 | 2 | |||
9.2 | odd | 6 | 405.2.a.b.1.1 | 1 | |||
9.4 | even | 3 | inner | 45.2.e.a.31.1 | yes | 2 | |
9.5 | odd | 6 | 135.2.e.a.91.1 | 2 | |||
9.7 | even | 3 | 405.2.a.e.1.1 | 1 | |||
12.11 | even | 2 | 2160.2.q.a.721.1 | 2 | |||
15.2 | even | 4 | 675.2.k.a.424.2 | 4 | |||
15.8 | even | 4 | 675.2.k.a.424.1 | 4 | |||
15.14 | odd | 2 | 675.2.e.a.451.1 | 2 | |||
36.7 | odd | 6 | 6480.2.a.k.1.1 | 1 | |||
36.11 | even | 6 | 6480.2.a.x.1.1 | 1 | |||
36.23 | even | 6 | 2160.2.q.a.1441.1 | 2 | |||
36.31 | odd | 6 | 720.2.q.d.481.1 | 2 | |||
45.2 | even | 12 | 2025.2.b.d.649.1 | 2 | |||
45.4 | even | 6 | 225.2.e.a.76.1 | 2 | |||
45.7 | odd | 12 | 2025.2.b.c.649.2 | 2 | |||
45.13 | odd | 12 | 225.2.k.a.49.1 | 4 | |||
45.14 | odd | 6 | 675.2.e.a.226.1 | 2 | |||
45.22 | odd | 12 | 225.2.k.a.49.2 | 4 | |||
45.23 | even | 12 | 675.2.k.a.199.2 | 4 | |||
45.29 | odd | 6 | 2025.2.a.e.1.1 | 1 | |||
45.32 | even | 12 | 675.2.k.a.199.1 | 4 | |||
45.34 | even | 6 | 2025.2.a.b.1.1 | 1 | |||
45.38 | even | 12 | 2025.2.b.d.649.2 | 2 | |||
45.43 | odd | 12 | 2025.2.b.c.649.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.2.e.a.16.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
45.2.e.a.31.1 | yes | 2 | 9.4 | even | 3 | inner | |
135.2.e.a.46.1 | 2 | 3.2 | odd | 2 | |||
135.2.e.a.91.1 | 2 | 9.5 | odd | 6 | |||
225.2.e.a.76.1 | 2 | 45.4 | even | 6 | |||
225.2.e.a.151.1 | 2 | 5.4 | even | 2 | |||
225.2.k.a.49.1 | 4 | 45.13 | odd | 12 | |||
225.2.k.a.49.2 | 4 | 45.22 | odd | 12 | |||
225.2.k.a.124.1 | 4 | 5.2 | odd | 4 | |||
225.2.k.a.124.2 | 4 | 5.3 | odd | 4 | |||
405.2.a.b.1.1 | 1 | 9.2 | odd | 6 | |||
405.2.a.e.1.1 | 1 | 9.7 | even | 3 | |||
675.2.e.a.226.1 | 2 | 45.14 | odd | 6 | |||
675.2.e.a.451.1 | 2 | 15.14 | odd | 2 | |||
675.2.k.a.199.1 | 4 | 45.32 | even | 12 | |||
675.2.k.a.199.2 | 4 | 45.23 | even | 12 | |||
675.2.k.a.424.1 | 4 | 15.8 | even | 4 | |||
675.2.k.a.424.2 | 4 | 15.2 | even | 4 | |||
720.2.q.d.241.1 | 2 | 4.3 | odd | 2 | |||
720.2.q.d.481.1 | 2 | 36.31 | odd | 6 | |||
2025.2.a.b.1.1 | 1 | 45.34 | even | 6 | |||
2025.2.a.e.1.1 | 1 | 45.29 | odd | 6 | |||
2025.2.b.c.649.1 | 2 | 45.43 | odd | 12 | |||
2025.2.b.c.649.2 | 2 | 45.7 | odd | 12 | |||
2025.2.b.d.649.1 | 2 | 45.2 | even | 12 | |||
2025.2.b.d.649.2 | 2 | 45.38 | even | 12 | |||
2160.2.q.a.721.1 | 2 | 12.11 | even | 2 | |||
2160.2.q.a.1441.1 | 2 | 36.23 | even | 6 | |||
6480.2.a.k.1.1 | 1 | 36.7 | odd | 6 | |||
6480.2.a.x.1.1 | 1 | 36.11 | even | 6 |