Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1890,2,Mod(541,1890)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1890, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1890.541");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1890.k (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: | \(15.0917259820\) |
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 | 541.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1890.541 |
Dual form | 1890.2.k.d.1621.1 |
$q$-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 \(\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(1081\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | + | 1.73205i | 0.755929 | + | 0.654654i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.500000 | − | 0.866025i | −0.158114 | − | 0.273861i | ||||
\(11\) | −1.00000 | − | 1.73205i | −0.301511 | − | 0.522233i | 0.674967 | − | 0.737848i | \(-0.264158\pi\) |
−0.976478 | + | 0.215615i | \(0.930824\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | 0.138675 | − | 0.990338i | \(-0.455716\pi\) | ||||
0.138675 | + | 0.990338i | \(0.455716\pi\) | |||||||
\(14\) | −2.50000 | + | 0.866025i | −0.668153 | + | 0.231455i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.50000 | − | 4.33013i | −0.606339 | − | 1.05021i | −0.991838 | − | 0.127502i | \(-0.959304\pi\) |
0.385499 | − | 0.922708i | \(-0.374029\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.50000 | + | 6.06218i | −0.802955 | + | 1.39076i | 0.114708 | + | 0.993399i | \(0.463407\pi\) |
−0.917663 | + | 0.397360i | \(0.869927\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.00000 | 0.426401 | ||||||||
\(23\) | −2.00000 | + | 3.46410i | −0.417029 | + | 0.722315i | −0.995639 | − | 0.0932891i | \(-0.970262\pi\) |
0.578610 | + | 0.815604i | \(0.303595\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | −0.500000 | + | 0.866025i | −0.0980581 | + | 0.169842i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.500000 | − | 2.59808i | 0.0944911 | − | 0.490990i | ||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.00000 | + | 5.19615i | 0.538816 | + | 0.933257i | 0.998968 | + | 0.0454165i | \(0.0144615\pi\) |
−0.460152 | + | 0.887840i | \(0.652205\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.00000 | 0.857493 | ||||||||
\(35\) | −2.50000 | + | 0.866025i | −0.422577 | + | 0.146385i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.00000 | + | 5.19615i | −0.493197 | + | 0.854242i | −0.999969 | − | 0.00783774i | \(-0.997505\pi\) |
0.506772 | + | 0.862080i | \(0.330838\pi\) | |||||||
\(38\) | −3.50000 | − | 6.06218i | −0.567775 | − | 0.983415i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.500000 | + | 0.866025i | −0.0790569 | + | 0.136931i | ||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000 | 0.304997 | 0.152499 | − | 0.988304i | \(-0.451268\pi\) | ||||
0.152499 | + | 0.988304i | \(0.451268\pi\) | |||||||
\(44\) | −1.00000 | + | 1.73205i | −0.150756 | + | 0.261116i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.00000 | − | 3.46410i | −0.294884 | − | 0.510754i | ||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | + | 6.92820i | 0.142857 | + | 0.989743i | ||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.500000 | − | 0.866025i | −0.0693375 | − | 0.120096i | ||||
\(53\) | 2.00000 | + | 3.46410i | 0.274721 | + | 0.475831i | 0.970065 | − | 0.242846i | \(-0.0780811\pi\) |
−0.695344 | + | 0.718677i | \(0.744748\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.00000 | 0.269680 | ||||||||
\(56\) | 2.00000 | + | 1.73205i | 0.267261 | + | 0.231455i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.00000 | − | 1.73205i | 0.131306 | − | 0.227429i | ||||
\(59\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | − | 3.46410i | 0.256074 | − | 0.443533i | −0.709113 | − | 0.705095i | \(-0.750904\pi\) |
0.965187 | + | 0.261562i | \(0.0842377\pi\) | |||||||
\(62\) | −6.00000 | −0.762001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.500000 | + | 0.866025i | −0.0620174 | + | 0.107417i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.00000 | + | 5.19615i | 0.366508 | + | 0.634811i | 0.989017 | − | 0.147802i | \(-0.0472198\pi\) |
−0.622509 | + | 0.782613i | \(0.713886\pi\) | |||||||
\(68\) | −2.50000 | + | 4.33013i | −0.303170 | + | 0.525105i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.500000 | − | 2.59808i | 0.0597614 | − | 0.310530i | ||||
\(71\) | 1.00000 | 0.118678 | 0.0593391 | − | 0.998238i | \(-0.481101\pi\) | ||||
0.0593391 | + | 0.998238i | \(0.481101\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.00000 | − | 13.8564i | −0.936329 | − | 1.62177i | −0.772246 | − | 0.635323i | \(-0.780867\pi\) |
−0.164083 | − | 0.986447i | \(-0.552466\pi\) | |||||||
\(74\) | −3.00000 | − | 5.19615i | −0.348743 | − | 0.604040i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.00000 | 0.802955 | ||||||||
\(77\) | 1.00000 | − | 5.19615i | 0.113961 | − | 0.592157i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.00000 | − | 1.73205i | 0.112509 | − | 0.194871i | −0.804272 | − | 0.594261i | \(-0.797445\pi\) |
0.916781 | + | 0.399390i | \(0.130778\pi\) | |||||||
\(80\) | −0.500000 | − | 0.866025i | −0.0559017 | − | 0.0968246i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.0000 | −1.64646 | −0.823232 | − | 0.567705i | \(-0.807831\pi\) | ||||
−0.823232 | + | 0.567705i | \(0.807831\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.00000 | 0.542326 | ||||||||
\(86\) | −1.00000 | + | 1.73205i | −0.107833 | + | 0.186772i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.00000 | − | 1.73205i | −0.106600 | − | 0.184637i | ||||
\(89\) | −8.00000 | + | 13.8564i | −0.847998 | + | 1.46878i | 0.0349934 | + | 0.999388i | \(0.488859\pi\) |
−0.882992 | + | 0.469389i | \(0.844474\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | + | 1.73205i | 0.209657 | + | 0.181568i | ||||
\(92\) | 4.00000 | 0.417029 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.50000 | − | 6.06218i | −0.359092 | − | 0.621966i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.0000 | −1.01535 | −0.507673 | − | 0.861550i | \(-0.669494\pi\) | ||||
−0.507673 | + | 0.861550i | \(0.669494\pi\) | |||||||
\(98\) | −6.50000 | − | 2.59808i | −0.656599 | − | 0.262445i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | −1.50000 | − | 2.59808i | −0.149256 | − | 0.258518i | 0.781697 | − | 0.623658i | \(-0.214354\pi\) |
−0.930953 | + | 0.365140i | \(0.881021\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.50000 | + | 11.2583i | −0.640464 | + | 1.10932i | 0.344865 | + | 0.938652i | \(0.387925\pi\) |
−0.985329 | + | 0.170664i | \(0.945409\pi\) | |||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.00000 | −0.388514 | ||||||||
\(107\) | −1.50000 | + | 2.59808i | −0.145010 | + | 0.251166i | −0.929377 | − | 0.369132i | \(-0.879655\pi\) |
0.784366 | + | 0.620298i | \(0.212988\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.00000 | + | 8.66025i | 0.478913 | + | 0.829502i | 0.999708 | − | 0.0241802i | \(-0.00769755\pi\) |
−0.520794 | + | 0.853682i | \(0.674364\pi\) | |||||||
\(110\) | −1.00000 | + | 1.73205i | −0.0953463 | + | 0.165145i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.50000 | + | 0.866025i | −0.236228 | + | 0.0818317i | ||||
\(113\) | −18.0000 | −1.69330 | −0.846649 | − | 0.532152i | \(-0.821383\pi\) | ||||
−0.846649 | + | 0.532152i | \(0.821383\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.00000 | − | 3.46410i | −0.186501 | − | 0.323029i | ||||
\(116\) | 1.00000 | + | 1.73205i | 0.0928477 | + | 0.160817i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.50000 | − | 12.9904i | 0.229175 | − | 1.19083i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | 2.00000 | + | 3.46410i | 0.181071 | + | 0.313625i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.00000 | − | 5.19615i | 0.269408 | − | 0.466628i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.00000 | −0.621150 | −0.310575 | − | 0.950549i | \(-0.600522\pi\) | ||||
−0.310575 | + | 0.950549i | \(0.600522\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.500000 | − | 0.866025i | −0.0438529 | − | 0.0759555i | ||||
\(131\) | −7.00000 | + | 12.1244i | −0.611593 | + | 1.05931i | 0.379379 | + | 0.925241i | \(0.376138\pi\) |
−0.990972 | + | 0.134069i | \(0.957196\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −17.5000 | + | 6.06218i | −1.51744 | + | 0.525657i | ||||
\(134\) | −6.00000 | −0.518321 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.50000 | − | 4.33013i | −0.214373 | − | 0.371305i | ||||
\(137\) | 8.50000 | + | 14.7224i | 0.726204 | + | 1.25782i | 0.958477 | + | 0.285171i | \(0.0920506\pi\) |
−0.232273 | + | 0.972651i | \(0.574616\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.00000 | 0.424094 | 0.212047 | − | 0.977259i | \(-0.431987\pi\) | ||||
0.212047 | + | 0.977259i | \(0.431987\pi\) | |||||||
\(140\) | 2.00000 | + | 1.73205i | 0.169031 | + | 0.146385i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.500000 | + | 0.866025i | −0.0419591 | + | 0.0726752i | ||||
\(143\) | −1.00000 | − | 1.73205i | −0.0836242 | − | 0.144841i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.00000 | − | 1.73205i | 0.0830455 | − | 0.143839i | ||||
\(146\) | 16.0000 | 1.32417 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.00000 | 0.493197 | ||||||||
\(149\) | −2.50000 | + | 4.33013i | −0.204808 | + | 0.354738i | −0.950072 | − | 0.312032i | \(-0.898990\pi\) |
0.745264 | + | 0.666770i | \(0.232324\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.0000 | − | 19.0526i | −0.895167 | − | 1.55048i | −0.833597 | − | 0.552372i | \(-0.813723\pi\) |
−0.0615699 | − | 0.998103i | \(-0.519611\pi\) | |||||||
\(152\) | −3.50000 | + | 6.06218i | −0.283887 | + | 0.491708i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.00000 | + | 3.46410i | 0.322329 | + | 0.279145i | ||||
\(155\) | −6.00000 | −0.481932 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.5000 | + | 18.1865i | 0.837991 | + | 1.45144i | 0.891572 | + | 0.452880i | \(0.149603\pi\) |
−0.0535803 | + | 0.998564i | \(0.517063\pi\) | |||||||
\(158\) | 1.00000 | + | 1.73205i | 0.0795557 | + | 0.137795i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −10.0000 | + | 3.46410i | −0.788110 | + | 0.273009i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.00000 | − | 3.46410i | 0.156652 | − | 0.271329i | −0.777007 | − | 0.629492i | \(-0.783263\pi\) |
0.933659 | + | 0.358162i | \(0.116597\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.50000 | − | 12.9904i | 0.582113 | − | 1.00825i | ||||
\(167\) | −8.00000 | −0.619059 | −0.309529 | − | 0.950890i | \(-0.600171\pi\) | ||||
−0.309529 | + | 0.950890i | \(0.600171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | −2.50000 | + | 4.33013i | −0.191741 | + | 0.332106i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.00000 | − | 1.73205i | −0.0762493 | − | 0.132068i | ||||
\(173\) | −3.00000 | + | 5.19615i | −0.228086 | + | 0.395056i | −0.957241 | − | 0.289292i | \(-0.906580\pi\) |
0.729155 | + | 0.684349i | \(0.239913\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.500000 | − | 2.59808i | 0.0377964 | − | 0.196396i | ||||
\(176\) | 2.00000 | 0.150756 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.00000 | − | 13.8564i | −0.599625 | − | 1.03858i | ||||
\(179\) | 4.00000 | + | 6.92820i | 0.298974 | + | 0.517838i | 0.975901 | − | 0.218212i | \(-0.0700223\pi\) |
−0.676927 | + | 0.736050i | \(0.736689\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | −2.50000 | + | 0.866025i | −0.185312 | + | 0.0641941i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.00000 | + | 3.46410i | −0.147442 | + | 0.255377i | ||||
\(185\) | −3.00000 | − | 5.19615i | −0.220564 | − | 0.382029i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.00000 | + | 8.66025i | −0.365636 | + | 0.633300i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.00000 | 0.507833 | ||||||||
\(191\) | 8.00000 | − | 13.8564i | 0.578860 | − | 1.00261i | −0.416751 | − | 0.909021i | \(-0.636831\pi\) |
0.995610 | − | 0.0935936i | \(-0.0298354\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.00000 | + | 3.46410i | 0.143963 | + | 0.249351i | 0.928986 | − | 0.370116i | \(-0.120682\pi\) |
−0.785022 | + | 0.619467i | \(0.787349\pi\) | |||||||
\(194\) | 5.00000 | − | 8.66025i | 0.358979 | − | 0.621770i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.50000 | − | 4.33013i | 0.392857 | − | 0.309295i | ||||
\(197\) | 12.0000 | 0.854965 | 0.427482 | − | 0.904024i | \(-0.359401\pi\) | ||||
0.427482 | + | 0.904024i | \(0.359401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(200\) | −0.500000 | − | 0.866025i | −0.0353553 | − | 0.0612372i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.00000 | 0.211079 | ||||||||
\(203\) | −4.00000 | − | 3.46410i | −0.280745 | − | 0.243132i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6.50000 | − | 11.2583i | −0.452876 | − | 0.784405i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.500000 | + | 0.866025i | −0.0346688 | + | 0.0600481i | ||||
\(209\) | 14.0000 | 0.968400 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.00000 | −0.206529 | −0.103264 | − | 0.994654i | \(-0.532929\pi\) | ||||
−0.103264 | + | 0.994654i | \(0.532929\pi\) | |||||||
\(212\) | 2.00000 | − | 3.46410i | 0.137361 | − | 0.237915i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.50000 | − | 2.59808i | −0.102538 | − | 0.177601i | ||||
\(215\) | −1.00000 | + | 1.73205i | −0.0681994 | + | 0.118125i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.00000 | + | 15.5885i | −0.203653 | + | 1.05821i | ||||
\(218\) | −10.0000 | −0.677285 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.00000 | − | 1.73205i | −0.0674200 | − | 0.116775i | ||||
\(221\) | −2.50000 | − | 4.33013i | −0.168168 | − | 0.291276i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.0000 | 1.13840 | 0.569202 | − | 0.822198i | \(-0.307252\pi\) | ||||
0.569202 | + | 0.822198i | \(0.307252\pi\) | |||||||
\(224\) | 0.500000 | − | 2.59808i | 0.0334077 | − | 0.173591i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.00000 | − | 15.5885i | 0.598671 | − | 1.03693i | ||||
\(227\) | −14.0000 | − | 24.2487i | −0.929213 | − | 1.60944i | −0.784642 | − | 0.619949i | \(-0.787153\pi\) |
−0.144571 | − | 0.989494i | \(-0.546180\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.00000 | + | 6.92820i | −0.264327 | + | 0.457829i | −0.967387 | − | 0.253302i | \(-0.918483\pi\) |
0.703060 | + | 0.711131i | \(0.251817\pi\) | |||||||
\(230\) | 4.00000 | 0.263752 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.00000 | −0.131306 | ||||||||
\(233\) | 6.50000 | − | 11.2583i | 0.425829 | − | 0.737558i | −0.570668 | − | 0.821181i | \(-0.693316\pi\) |
0.996497 | + | 0.0836229i | \(0.0266491\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 10.0000 | + | 8.66025i | 0.648204 | + | 0.561361i | ||||
\(239\) | 21.0000 | 1.35838 | 0.679189 | − | 0.733964i | \(-0.262332\pi\) | ||||
0.679189 | + | 0.733964i | \(0.262332\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.00000 | − | 8.66025i | −0.322078 | − | 0.557856i | 0.658838 | − | 0.752285i | \(-0.271048\pi\) |
−0.980917 | + | 0.194429i | \(0.937715\pi\) | |||||||
\(242\) | 3.50000 | + | 6.06218i | 0.224989 | + | 0.389692i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.00000 | −0.256074 | ||||||||
\(245\) | −6.50000 | − | 2.59808i | −0.415270 | − | 0.165985i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.50000 | + | 6.06218i | −0.222700 | + | 0.385727i | ||||
\(248\) | 3.00000 | + | 5.19615i | 0.190500 | + | 0.329956i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.500000 | + | 0.866025i | −0.0316228 | + | 0.0547723i | ||||
\(251\) | 18.0000 | 1.13615 | 0.568075 | − | 0.822977i | \(-0.307688\pi\) | ||||
0.568075 | + | 0.822977i | \(0.307688\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.00000 | 0.502956 | ||||||||
\(254\) | 3.50000 | − | 6.06218i | 0.219610 | − | 0.380375i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 1.00000 | − | 1.73205i | 0.0623783 | − | 0.108042i | −0.833150 | − | 0.553047i | \(-0.813465\pi\) |
0.895528 | + | 0.445005i | \(0.146798\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.0000 | + | 5.19615i | −0.932055 | + | 0.322873i | ||||
\(260\) | 1.00000 | 0.0620174 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.00000 | − | 12.1244i | −0.432461 | − | 0.749045i | ||||
\(263\) | 8.00000 | + | 13.8564i | 0.493301 | + | 0.854423i | 0.999970 | − | 0.00771799i | \(-0.00245674\pi\) |
−0.506669 | + | 0.862141i | \(0.669123\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.00000 | −0.245718 | ||||||||
\(266\) | 3.50000 | − | 18.1865i | 0.214599 | − | 1.11509i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.00000 | − | 5.19615i | 0.183254 | − | 0.317406i | ||||
\(269\) | −1.50000 | − | 2.59808i | −0.0914566 | − | 0.158408i | 0.816668 | − | 0.577108i | \(-0.195819\pi\) |
−0.908124 | + | 0.418701i | \(0.862486\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.0000 | − | 17.3205i | 0.607457 | − | 1.05215i | −0.384201 | − | 0.923249i | \(-0.625523\pi\) |
0.991658 | − | 0.128897i | \(-0.0411435\pi\) | |||||||
\(272\) | 5.00000 | 0.303170 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −17.0000 | −1.02701 | ||||||||
\(275\) | −1.00000 | + | 1.73205i | −0.0603023 | + | 0.104447i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.5000 | − | 26.8468i | −0.931305 | − | 1.61307i | −0.781094 | − | 0.624413i | \(-0.785338\pi\) |
−0.150210 | − | 0.988654i | \(-0.547995\pi\) | |||||||
\(278\) | −2.50000 | + | 4.33013i | −0.149940 | + | 0.259704i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.50000 | + | 0.866025i | −0.149404 | + | 0.0517549i | ||||
\(281\) | 18.0000 | 1.07379 | 0.536895 | − | 0.843649i | \(-0.319597\pi\) | ||||
0.536895 | + | 0.843649i | \(0.319597\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.0000 | + | 22.5167i | 0.772770 | + | 1.33848i | 0.936039 | + | 0.351895i | \(0.114463\pi\) |
−0.163270 | + | 0.986581i | \(0.552204\pi\) | |||||||
\(284\) | −0.500000 | − | 0.866025i | −0.0296695 | − | 0.0513892i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.00000 | 0.118262 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.00000 | + | 6.92820i | −0.235294 | + | 0.407541i | ||||
\(290\) | 1.00000 | + | 1.73205i | 0.0587220 | + | 0.101710i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.00000 | + | 13.8564i | −0.468165 | + | 0.810885i | ||||
\(293\) | 12.0000 | 0.701047 | 0.350524 | − | 0.936554i | \(-0.386004\pi\) | ||||
0.350524 | + | 0.936554i | \(0.386004\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.00000 | + | 5.19615i | −0.174371 | + | 0.302020i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.50000 | − | 4.33013i | −0.144821 | − | 0.250838i | ||||
\(299\) | −2.00000 | + | 3.46410i | −0.115663 | + | 0.200334i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.00000 | + | 3.46410i | 0.230556 | + | 0.199667i | ||||
\(302\) | 22.0000 | 1.26596 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.50000 | − | 6.06218i | −0.200739 | − | 0.347690i | ||||
\(305\) | 2.00000 | + | 3.46410i | 0.114520 | + | 0.198354i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.00000 | 0.456584 | 0.228292 | − | 0.973593i | \(-0.426686\pi\) | ||||
0.228292 | + | 0.973593i | \(0.426686\pi\) | |||||||
\(308\) | −5.00000 | + | 1.73205i | −0.284901 | + | 0.0986928i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.00000 | − | 5.19615i | 0.170389 | − | 0.295122i | ||||
\(311\) | 2.50000 | + | 4.33013i | 0.141762 | + | 0.245539i | 0.928160 | − | 0.372181i | \(-0.121390\pi\) |
−0.786398 | + | 0.617720i | \(0.788057\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(314\) | −21.0000 | −1.18510 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.00000 | −0.112509 | ||||||||
\(317\) | 4.00000 | − | 6.92820i | 0.224662 | − | 0.389127i | −0.731556 | − | 0.681782i | \(-0.761205\pi\) |
0.956218 | + | 0.292655i | \(0.0945387\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.00000 | + | 3.46410i | 0.111979 | + | 0.193952i | ||||
\(320\) | −0.500000 | + | 0.866025i | −0.0279508 | + | 0.0484123i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.00000 | − | 10.3923i | 0.111456 | − | 0.579141i | ||||
\(323\) | 35.0000 | 1.94745 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.500000 | − | 0.866025i | −0.0277350 | − | 0.0480384i | ||||
\(326\) | 2.00000 | + | 3.46410i | 0.110770 | + | 0.191859i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.5000 | − | 23.3827i | 0.742027 | − | 1.28523i | −0.209544 | − | 0.977799i | \(-0.567198\pi\) |
0.951571 | − | 0.307429i | \(-0.0994688\pi\) | |||||||
\(332\) | 7.50000 | + | 12.9904i | 0.411616 | + | 0.712940i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.00000 | − | 6.92820i | 0.218870 | − | 0.379094i | ||||
\(335\) | −6.00000 | −0.327815 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.0000 | −0.980522 | −0.490261 | − | 0.871576i | \(-0.663099\pi\) | ||||
−0.490261 | + | 0.871576i | \(0.663099\pi\) | |||||||
\(338\) | 6.00000 | − | 10.3923i | 0.326357 | − | 0.565267i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.50000 | − | 4.33013i | −0.135582 | − | 0.234834i | ||||
\(341\) | 6.00000 | − | 10.3923i | 0.324918 | − | 0.562775i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 2.00000 | 0.107833 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.00000 | − | 5.19615i | −0.161281 | − | 0.279347i | ||||
\(347\) | 2.00000 | + | 3.46410i | 0.107366 | + | 0.185963i | 0.914702 | − | 0.404128i | \(-0.132425\pi\) |
−0.807337 | + | 0.590091i | \(0.799092\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.00000 | −0.214115 | −0.107058 | − | 0.994253i | \(-0.534143\pi\) | ||||
−0.107058 | + | 0.994253i | \(0.534143\pi\) | |||||||
\(350\) | 2.00000 | + | 1.73205i | 0.106904 | + | 0.0925820i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.00000 | + | 1.73205i | −0.0533002 | + | 0.0923186i | ||||
\(353\) | −17.0000 | − | 29.4449i | −0.904819 | − | 1.56719i | −0.821160 | − | 0.570697i | \(-0.806673\pi\) |
−0.0836583 | − | 0.996495i | \(-0.526660\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.500000 | + | 0.866025i | −0.0265372 | + | 0.0459639i | ||||
\(356\) | 16.0000 | 0.847998 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.00000 | −0.422813 | ||||||||
\(359\) | 7.50000 | − | 12.9904i | 0.395835 | − | 0.685606i | −0.597372 | − | 0.801964i | \(-0.703789\pi\) |
0.993207 | + | 0.116358i | \(0.0371219\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | − | 25.9808i | −0.789474 | − | 1.36741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.500000 | − | 2.59808i | 0.0262071 | − | 0.136176i | ||||
\(365\) | 16.0000 | 0.837478 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.0000 | + | 27.7128i | 0.835193 | + | 1.44660i | 0.893873 | + | 0.448320i | \(0.147978\pi\) |
−0.0586798 | + | 0.998277i | \(0.518689\pi\) | |||||||
\(368\) | −2.00000 | − | 3.46410i | −0.104257 | − | 0.180579i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.00000 | 0.311925 | ||||||||
\(371\) | −2.00000 | + | 10.3923i | −0.103835 | + | 0.539542i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.50000 | + | 9.52628i | −0.284779 | + | 0.493252i | −0.972556 | − | 0.232671i | \(-0.925254\pi\) |
0.687776 | + | 0.725923i | \(0.258587\pi\) | |||||||
\(374\) | −5.00000 | − | 8.66025i | −0.258544 | − | 0.447811i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.00000 | −0.103005 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.0000 | 0.975964 | 0.487982 | − | 0.872854i | \(-0.337733\pi\) | ||||
0.487982 | + | 0.872854i | \(0.337733\pi\) | |||||||
\(380\) | −3.50000 | + | 6.06218i | −0.179546 | + | 0.310983i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8.00000 | + | 13.8564i | 0.409316 | + | 0.708955i | ||||
\(383\) | −17.0000 | + | 29.4449i | −0.868659 | + | 1.50456i | −0.00529229 | + | 0.999986i | \(0.501685\pi\) |
−0.863367 | + | 0.504576i | \(0.831649\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.00000 | + | 3.46410i | 0.203859 | + | 0.176547i | ||||
\(386\) | −4.00000 | −0.203595 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.00000 | + | 8.66025i | 0.253837 | + | 0.439658i | ||||
\(389\) | 17.5000 | + | 30.3109i | 0.887285 | + | 1.53682i | 0.843072 | + | 0.537801i | \(0.180745\pi\) |
0.0442134 | + | 0.999022i | \(0.485922\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.0000 | 1.01144 | ||||||||
\(392\) | 1.00000 | + | 6.92820i | 0.0505076 | + | 0.349927i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.00000 | + | 10.3923i | −0.302276 | + | 0.523557i | ||||
\(395\) | 1.00000 | + | 1.73205i | 0.0503155 | + | 0.0871489i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.5000 | + | 28.5788i | −0.828111 | + | 1.43433i | 0.0714068 | + | 0.997447i | \(0.477251\pi\) |
−0.899518 | + | 0.436884i | \(0.856082\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −2.00000 | + | 3.46410i | −0.0998752 | + | 0.172989i | −0.911633 | − | 0.411005i | \(-0.865178\pi\) |
0.811758 | + | 0.583994i | \(0.198511\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.00000 | + | 5.19615i | 0.149441 | + | 0.258839i | ||||
\(404\) | −1.50000 | + | 2.59808i | −0.0746278 | + | 0.129259i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.00000 | − | 1.73205i | 0.248146 | − | 0.0859602i | ||||
\(407\) | 12.0000 | 0.594818 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.00000 | + | 1.73205i | 0.0494468 | + | 0.0856444i | 0.889689 | − | 0.456566i | \(-0.150921\pi\) |
−0.840243 | + | 0.542211i | \(0.817588\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 13.0000 | 0.640464 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.50000 | − | 12.9904i | 0.368161 | − | 0.637673i | ||||
\(416\) | −0.500000 | − | 0.866025i | −0.0245145 | − | 0.0424604i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7.00000 | + | 12.1244i | −0.342381 | + | 0.593022i | ||||
\(419\) | −16.0000 | −0.781651 | −0.390826 | − | 0.920465i | \(-0.627810\pi\) | ||||
−0.390826 | + | 0.920465i | \(0.627810\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.00000 | −0.0974740 | −0.0487370 | − | 0.998812i | \(-0.515520\pi\) | ||||
−0.0487370 | + | 0.998812i | \(0.515520\pi\) | |||||||
\(422\) | 1.50000 | − | 2.59808i | 0.0730189 | − | 0.126472i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.00000 | + | 3.46410i | 0.0971286 | + | 0.168232i | ||||
\(425\) | −2.50000 | + | 4.33013i | −0.121268 | + | 0.210042i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.0000 | − | 3.46410i | 0.483934 | − | 0.167640i | ||||
\(428\) | 3.00000 | 0.145010 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.00000 | − | 1.73205i | −0.0482243 | − | 0.0835269i | ||||
\(431\) | −1.50000 | − | 2.59808i | −0.0722525 | − | 0.125145i | 0.827636 | − | 0.561266i | \(-0.189685\pi\) |
−0.899888 | + | 0.436121i | \(0.856352\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −38.0000 | −1.82616 | −0.913082 | − | 0.407777i | \(-0.866304\pi\) | ||||
−0.913082 | + | 0.407777i | \(0.866304\pi\) | |||||||
\(434\) | −12.0000 | − | 10.3923i | −0.576018 | − | 0.498847i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.00000 | − | 8.66025i | 0.239457 | − | 0.414751i | ||||
\(437\) | −14.0000 | − | 24.2487i | −0.669711 | − | 1.15997i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.00000 | + | 3.46410i | −0.0954548 | + | 0.165333i | −0.909798 | − | 0.415051i | \(-0.863764\pi\) |
0.814344 | + | 0.580383i | \(0.197097\pi\) | |||||||
\(440\) | 2.00000 | 0.0953463 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.00000 | 0.237826 | ||||||||
\(443\) | −10.5000 | + | 18.1865i | −0.498870 | + | 0.864068i | −0.999999 | − | 0.00130426i | \(-0.999585\pi\) |
0.501129 | + | 0.865373i | \(0.332918\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.00000 | − | 13.8564i | −0.379236 | − | 0.656857i | ||||
\(446\) | −8.50000 | + | 14.7224i | −0.402487 | + | 0.697127i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.00000 | + | 1.73205i | 0.0944911 | + | 0.0818317i | ||||
\(449\) | 20.0000 | 0.943858 | 0.471929 | − | 0.881636i | \(-0.343558\pi\) | ||||
0.471929 | + | 0.881636i | \(0.343558\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 9.00000 | + | 15.5885i | 0.423324 | + | 0.733219i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 28.0000 | 1.31411 | ||||||||
\(455\) | −2.50000 | + | 0.866025i | −0.117202 | + | 0.0405999i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.0000 | + | 24.2487i | −0.654892 | + | 1.13431i | 0.327028 | + | 0.945015i | \(0.393953\pi\) |
−0.981921 | + | 0.189292i | \(0.939381\pi\) | |||||||
\(458\) | −4.00000 | − | 6.92820i | −0.186908 | − | 0.323734i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.00000 | + | 3.46410i | −0.0932505 | + | 0.161515i | ||||
\(461\) | 38.0000 | 1.76984 | 0.884918 | − | 0.465746i | \(-0.154214\pi\) | ||||
0.884918 | + | 0.465746i | \(0.154214\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.0000 | 1.11537 | 0.557687 | − | 0.830051i | \(-0.311689\pi\) | ||||
0.557687 | + | 0.830051i | \(0.311689\pi\) | |||||||
\(464\) | 1.00000 | − | 1.73205i | 0.0464238 | − | 0.0804084i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.50000 | + | 11.2583i | 0.301107 | + | 0.521532i | ||||
\(467\) | −1.50000 | + | 2.59808i | −0.0694117 | + | 0.120225i | −0.898642 | − | 0.438682i | \(-0.855446\pi\) |
0.829231 | + | 0.558906i | \(0.188779\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.00000 | + | 15.5885i | −0.138527 | + | 0.719808i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.00000 | − | 3.46410i | −0.0919601 | − | 0.159280i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.00000 | 0.321182 | ||||||||
\(476\) | −12.5000 | + | 4.33013i | −0.572937 | + | 0.198471i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −10.5000 | + | 18.1865i | −0.480259 | + | 0.831833i | ||||
\(479\) | 8.00000 | + | 13.8564i | 0.365529 | + | 0.633115i | 0.988861 | − | 0.148842i | \(-0.0475547\pi\) |
−0.623332 | + | 0.781958i | \(0.714221\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.00000 | + | 5.19615i | −0.136788 | + | 0.236924i | ||||
\(482\) | 10.0000 | 0.455488 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.00000 | −0.318182 | ||||||||
\(485\) | 5.00000 | − | 8.66025i | 0.227038 | − | 0.393242i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.50000 | − | 16.4545i | −0.430486 | − | 0.745624i | 0.566429 | − | 0.824110i | \(-0.308325\pi\) |
−0.996915 | + | 0.0784867i | \(0.974991\pi\) | |||||||
\(488\) | 2.00000 | − | 3.46410i | 0.0905357 | − | 0.156813i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 5.50000 | − | 4.33013i | 0.248465 | − | 0.195615i | ||||
\(491\) | 36.0000 | 1.62466 | 0.812329 | − | 0.583200i | \(-0.198200\pi\) | ||||
0.812329 | + | 0.583200i | \(0.198200\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.00000 | + | 8.66025i | 0.225189 | + | 0.390038i | ||||
\(494\) | −3.50000 | − | 6.06218i | −0.157472 | − | 0.272750i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.00000 | −0.269408 | ||||||||
\(497\) | 2.00000 | + | 1.73205i | 0.0897123 | + | 0.0776931i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.5000 | − | 23.3827i | 0.604343 | − | 1.04675i | −0.387812 | − | 0.921739i | \(-0.626769\pi\) |
0.992155 | − | 0.125014i | \(-0.0398977\pi\) | |||||||
\(500\) | −0.500000 | − | 0.866025i | −0.0223607 | − | 0.0387298i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9.00000 | + | 15.5885i | −0.401690 | + | 0.695747i | ||||
\(503\) | 28.0000 | 1.24846 | 0.624229 | − | 0.781241i | \(-0.285413\pi\) | ||||
0.624229 | + | 0.781241i | \(0.285413\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.00000 | 0.133498 | ||||||||
\(506\) | −4.00000 | + | 6.92820i | −0.177822 | + | 0.307996i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.50000 | + | 6.06218i | 0.155287 | + | 0.268966i | ||||
\(509\) | −22.5000 | + | 38.9711i | −0.997295 | + | 1.72737i | −0.434992 | + | 0.900434i | \(0.643249\pi\) |
−0.562303 | + | 0.826931i | \(0.690085\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.00000 | − | 41.5692i | 0.353899 | − | 1.83891i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.00000 | + | 1.73205i | 0.0441081 | + | 0.0763975i | ||||
\(515\) | −6.50000 | − | 11.2583i | −0.286424 | − | 0.496101i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 3.00000 | − | 15.5885i | 0.131812 | − | 0.684917i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.500000 | + | 0.866025i | −0.0219265 | + | 0.0379777i | ||||
\(521\) | 15.0000 | + | 25.9808i | 0.657162 | + | 1.13824i | 0.981347 | + | 0.192244i | \(0.0615766\pi\) |
−0.324185 | + | 0.945994i | \(0.605090\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.0000 | − | 27.7128i | 0.699631 | − | 1.21180i | −0.268963 | − | 0.963150i | \(-0.586681\pi\) |
0.968594 | − | 0.248646i | \(-0.0799857\pi\) | |||||||
\(524\) | 14.0000 | 0.611593 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.0000 | −0.697633 | ||||||||
\(527\) | 15.0000 | − | 25.9808i | 0.653410 | − | 1.13174i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | + | 6.06218i | 0.152174 | + | 0.263573i | ||||
\(530\) | 2.00000 | − | 3.46410i | 0.0868744 | − | 0.150471i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 14.0000 | + | 12.1244i | 0.606977 | + | 0.525657i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.50000 | − | 2.59808i | −0.0648507 | − | 0.112325i | ||||
\(536\) | 3.00000 | + | 5.19615i | 0.129580 | + | 0.224440i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.00000 | 0.129339 | ||||||||
\(539\) | 11.0000 | − | 8.66025i | 0.473804 | − | 0.373024i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.0000 | − | 24.2487i | 0.601907 | − | 1.04253i | −0.390625 | − | 0.920550i | \(-0.627741\pi\) |
0.992532 | − | 0.121984i | \(-0.0389256\pi\) | |||||||
\(542\) | 10.0000 | + | 17.3205i | 0.429537 | + | 0.743980i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.50000 | + | 4.33013i | −0.107187 | + | 0.185653i | ||||
\(545\) | −10.0000 | −0.428353 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.0000 | 0.513083 | 0.256541 | − | 0.966533i | \(-0.417417\pi\) | ||||
0.256541 | + | 0.966533i | \(0.417417\pi\) | |||||||
\(548\) | 8.50000 | − | 14.7224i | 0.363102 | − | 0.628911i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.00000 | − | 1.73205i | −0.0426401 | − | 0.0738549i | ||||
\(551\) | 7.00000 | − | 12.1244i | 0.298210 | − | 0.516515i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.00000 | − | 1.73205i | 0.212622 | − | 0.0736543i | ||||
\(554\) | 31.0000 | 1.31706 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.50000 | − | 4.33013i | −0.106024 | − | 0.183638i | ||||
\(557\) | −15.0000 | − | 25.9808i | −0.635570 | − | 1.10084i | −0.986394 | − | 0.164399i | \(-0.947432\pi\) |
0.350824 | − | 0.936442i | \(-0.385902\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.00000 | 0.0845910 | ||||||||
\(560\) | 0.500000 | − | 2.59808i | 0.0211289 | − | 0.109789i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.00000 | + | 15.5885i | −0.379642 | + | 0.657559i | ||||
\(563\) | 9.50000 | + | 16.4545i | 0.400377 | + | 0.693474i | 0.993771 | − | 0.111438i | \(-0.0355457\pi\) |
−0.593394 | + | 0.804912i | \(0.702212\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.00000 | − | 15.5885i | 0.378633 | − | 0.655811i | ||||
\(566\) | −26.0000 | −1.09286 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.00000 | 0.0419591 | ||||||||
\(569\) | 17.0000 | − | 29.4449i | 0.712677 | − | 1.23439i | −0.251172 | − | 0.967943i | \(-0.580816\pi\) |
0.963849 | − | 0.266450i | \(-0.0858508\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.5000 | + | 40.7032i | 0.983444 | + | 1.70338i | 0.648655 | + | 0.761083i | \(0.275332\pi\) |
0.334790 | + | 0.942293i | \(0.391335\pi\) | |||||||
\(572\) | −1.00000 | + | 1.73205i | −0.0418121 | + | 0.0724207i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.00000 | 0.166812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.00000 | + | 12.1244i | 0.291414 | + | 0.504744i | 0.974144 | − | 0.225927i | \(-0.0725410\pi\) |
−0.682730 | + | 0.730670i | \(0.739208\pi\) | |||||||
\(578\) | −4.00000 | − | 6.92820i | −0.166378 | − | 0.288175i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.00000 | −0.0830455 | ||||||||
\(581\) | −30.0000 | − | 25.9808i | −1.24461 | − | 1.07786i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.00000 | − | 6.92820i | 0.165663 | − | 0.286937i | ||||
\(584\) | −8.00000 | − | 13.8564i | −0.331042 | − | 0.573382i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.00000 | + | 10.3923i | −0.247858 | + | 0.429302i | ||||
\(587\) | 3.00000 | 0.123823 | 0.0619116 | − | 0.998082i | \(-0.480280\pi\) | ||||
0.0619116 | + | 0.998082i | \(0.480280\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −42.0000 | −1.73058 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.00000 | − | 5.19615i | −0.123299 | − | 0.213561i | ||||
\(593\) | 13.5000 | − | 23.3827i | 0.554379 | − | 0.960212i | −0.443573 | − | 0.896238i | \(-0.646289\pi\) |
0.997952 | − | 0.0639736i | \(-0.0203773\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.0000 | + | 8.66025i | 0.409960 | + | 0.355036i | ||||
\(596\) | 5.00000 | 0.204808 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.00000 | − | 3.46410i | −0.0817861 | − | 0.141658i | ||||
\(599\) | −4.50000 | − | 7.79423i | −0.183865 | − | 0.318464i | 0.759328 | − | 0.650708i | \(-0.225528\pi\) |
−0.943193 | + | 0.332244i | \(0.892194\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.0000 | 1.01977 | 0.509886 | − | 0.860242i | \(-0.329688\pi\) | ||||
0.509886 | + | 0.860242i | \(0.329688\pi\) | |||||||
\(602\) | −5.00000 | + | 1.73205i | −0.203785 | + | 0.0705931i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −11.0000 | + | 19.0526i | −0.447584 | + | 0.775238i | ||||
\(605\) | 3.50000 | + | 6.06218i | 0.142295 | + | 0.246463i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.5000 | + | 26.8468i | −0.629126 | + | 1.08968i | 0.358602 | + | 0.933491i | \(0.383254\pi\) |
−0.987728 | + | 0.156187i | \(0.950080\pi\) | |||||||
\(608\) | 7.00000 | 0.283887 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.00000 | −0.161955 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.50000 | + | 2.59808i | 0.0605844 | + | 0.104935i | 0.894727 | − | 0.446614i | \(-0.147370\pi\) |
−0.834142 | + | 0.551549i | \(0.814037\pi\) | |||||||
\(614\) | −4.00000 | + | 6.92820i | −0.161427 | + | 0.279600i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.00000 | − | 5.19615i | 0.0402911 | − | 0.209359i | ||||
\(617\) | −25.0000 | −1.00646 | −0.503231 | − | 0.864152i | \(-0.667856\pi\) | ||||
−0.503231 | + | 0.864152i | \(0.667856\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.00000 | + | 3.46410i | 0.0803868 | + | 0.139234i | 0.903416 | − | 0.428765i | \(-0.141051\pi\) |
−0.823029 | + | 0.567999i | \(0.807718\pi\) | |||||||
\(620\) | 3.00000 | + | 5.19615i | 0.120483 | + | 0.208683i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.00000 | −0.200482 | ||||||||
\(623\) | −40.0000 | + | 13.8564i | −1.60257 | + | 0.555145i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.5000 | − | 18.1865i | 0.418996 | − | 0.725722i | ||||
\(629\) | 30.0000 | 1.19618 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.0000 | 1.03504 | 0.517522 | − | 0.855670i | \(-0.326855\pi\) | ||||
0.517522 | + | 0.855670i | \(0.326855\pi\) | |||||||
\(632\) | 1.00000 | − | 1.73205i | 0.0397779 | − | 0.0688973i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.00000 | + | 6.92820i | 0.158860 | + | 0.275154i | ||||
\(635\) | 3.50000 | − | 6.06218i | 0.138893 | − | 0.240570i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | + | 6.92820i | 0.0396214 | + | 0.274505i | ||||
\(638\) | −4.00000 | −0.158362 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.500000 | − | 0.866025i | −0.0197642 | − | 0.0342327i | ||||
\(641\) | 13.0000 | + | 22.5167i | 0.513469 | + | 0.889355i | 0.999878 | + | 0.0156233i | \(0.00497325\pi\) |
−0.486409 | + | 0.873731i | \(0.661693\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.0000 | 1.02534 | 0.512670 | − | 0.858586i | \(-0.328656\pi\) | ||||
0.512670 | + | 0.858586i | \(0.328656\pi\) | |||||||
\(644\) | 8.00000 | + | 6.92820i | 0.315244 | + | 0.273009i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −17.5000 | + | 30.3109i | −0.688528 | + | 1.19257i | ||||
\(647\) | −18.0000 | − | 31.1769i | −0.707653 | − | 1.22569i | −0.965726 | − | 0.259565i | \(-0.916421\pi\) |
0.258073 | − | 0.966126i | \(-0.416913\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 1.00000 | 0.0392232 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.00000 | −0.156652 | ||||||||
\(653\) | 8.00000 | − | 13.8564i | 0.313064 | − | 0.542243i | −0.665960 | − | 0.745988i | \(-0.731978\pi\) |
0.979024 | + | 0.203744i | \(0.0653112\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.00000 | − | 12.1244i | −0.273513 | − | 0.473738i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −30.0000 | −1.16863 | −0.584317 | − | 0.811525i | \(-0.698638\pi\) | ||||
−0.584317 | + | 0.811525i | \(0.698638\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.00000 | + | 8.66025i | 0.194477 | + | 0.336845i | 0.946729 | − | 0.322031i | \(-0.104366\pi\) |
−0.752252 | + | 0.658876i | \(0.771032\pi\) | |||||||
\(662\) | 13.5000 | + | 23.3827i | 0.524692 | + | 0.908794i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15.0000 | −0.582113 | ||||||||
\(665\) | 3.50000 | − | 18.1865i | 0.135724 | − | 0.705244i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.00000 | − | 6.92820i | 0.154881 | − | 0.268261i | ||||
\(668\) | 4.00000 | + | 6.92820i | 0.154765 | + | 0.268060i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.00000 | − | 5.19615i | 0.115900 | − | 0.200745i | ||||
\(671\) | −8.00000 | −0.308837 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.0000 | −1.15642 | −0.578208 | − | 0.815890i | \(-0.696248\pi\) | ||||
−0.578208 | + | 0.815890i | \(0.696248\pi\) | |||||||
\(674\) | 9.00000 | − | 15.5885i | 0.346667 | − | 0.600445i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.00000 | + | 10.3923i | 0.230769 | + | 0.399704i | ||||
\(677\) | −20.0000 | + | 34.6410i | −0.768662 | + | 1.33136i | 0.169626 | + | 0.985509i | \(0.445744\pi\) |
−0.938288 | + | 0.345854i | \(0.887589\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20.0000 | − | 17.3205i | −0.767530 | − | 0.664700i | ||||
\(680\) | 5.00000 | 0.191741 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.00000 | + | 10.3923i | 0.229752 | + | 0.397942i | ||||
\(683\) | 12.0000 | + | 20.7846i | 0.459167 | + | 0.795301i | 0.998917 | − | 0.0465244i | \(-0.0148145\pi\) |
−0.539750 | + | 0.841825i | \(0.681481\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.0000 | −0.649537 | ||||||||
\(686\) | −8.50000 | − | 16.4545i | −0.324532 | − | 0.628235i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.00000 | + | 1.73205i | −0.0381246 | + | 0.0660338i | ||||
\(689\) | 2.00000 | + | 3.46410i | 0.0761939 | + | 0.131972i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.50000 | − | 2.59808i | 0.0570627 | − | 0.0988355i | −0.836083 | − | 0.548603i | \(-0.815160\pi\) |
0.893146 | + | 0.449768i | \(0.148493\pi\) | |||||||
\(692\) | 6.00000 | 0.228086 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.00000 | −0.151838 | ||||||||
\(695\) | −2.50000 | + | 4.33013i | −0.0948304 | + | 0.164251i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 2.00000 | − | 3.46410i | 0.0757011 | − | 0.131118i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.50000 | + | 0.866025i | −0.0944911 | + | 0.0327327i | ||||
\(701\) | −15.0000 | −0.566542 | −0.283271 | − | 0.959040i | \(-0.591420\pi\) | ||||
−0.283271 | + | 0.959040i | \(0.591420\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21.0000 | − | 36.3731i | −0.792030 | − | 1.37184i | ||||
\(704\) | −1.00000 | − | 1.73205i | −0.0376889 | − | 0.0652791i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 34.0000 | 1.27961 | ||||||||
\(707\) | 1.50000 | − | 7.79423i | 0.0564133 | − | 0.293132i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.0000 | − | 22.5167i | 0.488225 | − | 0.845631i | −0.511683 | − | 0.859174i | \(-0.670978\pi\) |
0.999908 | + | 0.0135434i | \(0.00431112\pi\) | |||||||
\(710\) | −0.500000 | − | 0.866025i | −0.0187647 | − | 0.0325014i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8.00000 | + | 13.8564i | −0.299813 | + | 0.519291i | ||||
\(713\) | −24.0000 | −0.898807 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.00000 | 0.0747958 | ||||||||
\(716\) | 4.00000 | − | 6.92820i | 0.149487 | − | 0.258919i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 7.50000 | + | 12.9904i | 0.279898 | + | 0.484797i | ||||
\(719\) | −2.50000 | + | 4.33013i | −0.0932343 | + | 0.161486i | −0.908870 | − | 0.417079i | \(-0.863054\pi\) |
0.815636 | + | 0.578565i | \(0.196387\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32.5000 | + | 11.2583i | −1.21036 | + | 0.419282i | ||||
\(722\) | 30.0000 | 1.11648 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.00000 | + | 1.73205i | 0.0371391 | + | 0.0643268i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −37.0000 | −1.37225 | −0.686127 | − | 0.727482i | \(-0.740691\pi\) | ||||
−0.686127 | + | 0.727482i | \(0.740691\pi\) | |||||||
\(728\) | 2.00000 | + | 1.73205i | 0.0741249 | + | 0.0641941i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8.00000 | + | 13.8564i | −0.296093 | + | 0.512849i | ||||
\(731\) | −5.00000 | − | 8.66025i | −0.184932 | − | 0.320311i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.5000 | − | 25.1147i | 0.535570 | − | 0.927634i | −0.463566 | − | 0.886062i | \(-0.653430\pi\) |
0.999136 | − | 0.0415715i | \(-0.0132364\pi\) | |||||||
\(734\) | −32.0000 | −1.18114 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.00000 | 0.147442 | ||||||||
\(737\) | 6.00000 | − | 10.3923i | 0.221013 | − | 0.382805i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.5000 | + | 37.2391i | 0.790890 | + | 1.36986i | 0.925416 | + | 0.378952i | \(0.123715\pi\) |
−0.134526 | + | 0.990910i | \(0.542951\pi\) | |||||||
\(740\) | −3.00000 | + | 5.19615i | −0.110282 | + | 0.191014i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.00000 | − | 6.92820i | −0.293689 | − | 0.254342i | ||||
\(743\) | 36.0000 | 1.32071 | 0.660356 | − | 0.750953i | \(-0.270405\pi\) | ||||
0.660356 | + | 0.750953i | \(0.270405\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.50000 | − | 4.33013i | −0.0915929 | − | 0.158644i | ||||
\(746\) | −5.50000 | − | 9.52628i | −0.201369 | − | 0.348782i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 10.0000 | 0.365636 | ||||||||
\(749\) | −7.50000 | + | 2.59808i | −0.274044 | + | 0.0949316i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.0000 | − | 43.3013i | 0.912263 | − | 1.58009i | 0.101403 | − | 0.994845i | \(-0.467667\pi\) |
0.810860 | − | 0.585240i | \(-0.199000\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.00000 | − | 1.73205i | 0.0364179 | − | 0.0630776i | ||||
\(755\) | 22.0000 | 0.800662 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.0000 | 0.690567 | 0.345283 | − | 0.938498i | \(-0.387783\pi\) | ||||
0.345283 | + | 0.938498i | \(0.387783\pi\) | |||||||
\(758\) | −9.50000 | + | 16.4545i | −0.345056 | + | 0.597654i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.50000 | − | 6.06218i | −0.126958 | − | 0.219898i | ||||
\(761\) | −17.0000 | + | 29.4449i | −0.616250 | + | 1.06738i | 0.373914 | + | 0.927463i | \(0.378015\pi\) |
−0.990164 | + | 0.139912i | \(0.955318\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.00000 | + | 25.9808i | −0.181012 | + | 0.940567i | ||||
\(764\) | −16.0000 | −0.578860 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −17.0000 | − | 29.4449i | −0.614235 | − | 1.06389i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29.0000 | −1.04577 | −0.522883 | − | 0.852404i | \(-0.675144\pi\) | ||||
−0.522883 | + | 0.852404i | \(0.675144\pi\) | |||||||
\(770\) | −5.00000 | + | 1.73205i | −0.180187 | + | 0.0624188i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.00000 | − | 3.46410i | 0.0719816 | − | 0.124676i | ||||
\(773\) | 16.0000 | + | 27.7128i | 0.575480 | + | 0.996761i | 0.995989 | + | 0.0894724i | \(0.0285181\pi\) |
−0.420509 | + | 0.907288i | \(0.638149\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.00000 | − | 5.19615i | 0.107763 | − | 0.186651i | ||||
\(776\) | −10.0000 | −0.358979 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −35.0000 | −1.25481 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.00000 | − | 1.73205i | −0.0357828 | − | 0.0619777i | ||||
\(782\) | −10.0000 | + | 17.3205i | −0.357599 | + | 0.619380i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.50000 | − | 2.59808i | −0.232143 | − | 0.0927884i | ||||
\(785\) | −21.0000 | −0.749522 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.00000 | − | 6.92820i | −0.142585 | − | 0.246964i | 0.785885 | − | 0.618373i | \(-0.212208\pi\) |
−0.928469 | + | 0.371409i | \(0.878875\pi\) | |||||||
\(788\) | −6.00000 | − | 10.3923i | −0.213741 | − | 0.370211i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.00000 | −0.0711568 | ||||||||
\(791\) | −36.0000 | − | 31.1769i | −1.28001 | − | 1.10852i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.00000 | − | 3.46410i | 0.0710221 | − | 0.123014i | ||||
\(794\) | −16.5000 | − | 28.5788i | −0.585563 | − | 1.01423i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −36.0000 | −1.27519 | −0.637593 | − | 0.770374i | \(-0.720070\pi\) | ||||
−0.637593 | + | 0.770374i | \(0.720070\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.500000 | + | 0.866025i | −0.0176777 | + | 0.0306186i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.00000 | − | 3.46410i | −0.0706225 | − | 0.122322i | ||||
\(803\) | −16.0000 | + | 27.7128i | −0.564628 | + | 0.977964i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.00000 | − | 10.3923i | 0.0704907 | − | 0.366281i | ||||
\(806\) | −6.00000 | −0.211341 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.50000 | − | 2.59808i | −0.0527698 | − | 0.0914000i | ||||
\(809\) | 14.0000 | + | 24.2487i | 0.492214 | + | 0.852539i | 0.999960 | − | 0.00896753i | \(-0.00285449\pi\) |
−0.507746 | + | 0.861507i | \(0.669521\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.00000 | 0.245803 | 0.122902 | − | 0.992419i | \(-0.460780\pi\) | ||||
0.122902 | + | 0.992419i | \(0.460780\pi\) | |||||||
\(812\) | −1.00000 | + | 5.19615i | −0.0350931 | + | 0.182349i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.00000 | + | 10.3923i | −0.210300 | + | 0.364250i | ||||
\(815\) | 2.00000 | + | 3.46410i | 0.0700569 | + | 0.121342i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.00000 | + | 12.1244i | −0.244899 | + | 0.424178i | ||||
\(818\) | −2.00000 | −0.0699284 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.0000 | + | 39.8372i | −0.802706 | + | 1.39033i | 0.115124 | + | 0.993351i | \(0.463274\pi\) |
−0.917829 | + | 0.396976i | \(0.870060\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.0000 | − | 41.5692i | −0.836587 | − | 1.44901i | −0.892731 | − | 0.450589i | \(-0.851214\pi\) |
0.0561440 | − | 0.998423i | \(-0.482119\pi\) | |||||||
\(824\) | −6.50000 | + | 11.2583i | −0.226438 | + | 0.392203i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.00000 | −0.278187 | −0.139094 | − | 0.990279i | \(-0.544419\pi\) | ||||
−0.139094 | + | 0.990279i | \(0.544419\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.00000 | − | 15.5885i | −0.312583 | − | 0.541409i | 0.666338 | − | 0.745650i | \(-0.267861\pi\) |
−0.978921 | + | 0.204240i | \(0.934528\pi\) | |||||||
\(830\) | 7.50000 | + | 12.9904i | 0.260329 | + | 0.450903i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 27.5000 | − | 21.6506i | 0.952819 | − | 0.750150i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.00000 | − | 6.92820i | 0.138426 | − | 0.239760i | ||||
\(836\) | −7.00000 | − | 12.1244i | −0.242100 | − | 0.419330i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.00000 | − | 13.8564i | 0.276355 | − | 0.478662i | ||||
\(839\) | −13.0000 | −0.448810 | −0.224405 | − | 0.974496i | \(-0.572044\pi\) | ||||
−0.224405 | + | 0.974496i | \(0.572044\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 1.00000 | − | 1.73205i | 0.0344623 | − | 0.0596904i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.50000 | + | 2.59808i | 0.0516321 | + | 0.0894295i | ||||
\(845\) | 6.00000 | − | 10.3923i | 0.206406 | − | 0.357506i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.5000 | − | 6.06218i | 0.601307 | − | 0.208299i | ||||
\(848\) | −4.00000 | −0.137361 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.50000 | − | 4.33013i | −0.0857493 | − | 0.148522i | ||||
\(851\) | −12.0000 | − | 20.7846i | −0.411355 | − | 0.712487i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.0000 | 0.445112 | 0.222556 | − | 0.974920i | \(-0.428560\pi\) | ||||
0.222556 | + | 0.974920i | \(0.428560\pi\) | |||||||
\(854\) | −2.00000 | + | 10.3923i | −0.0684386 | + | 0.355617i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.50000 | + | 2.59808i | −0.0512689 | + | 0.0888004i | ||||
\(857\) | −2.50000 | − | 4.33013i | −0.0853984 | − | 0.147914i | 0.820163 | − | 0.572131i | \(-0.193883\pi\) |
−0.905561 | + | 0.424216i | \(0.860550\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.5000 | − | 35.5070i | 0.699451 | − | 1.21148i | −0.269206 | − | 0.963083i | \(-0.586761\pi\) |
0.968657 | − | 0.248402i | \(-0.0799054\pi\) | |||||||
\(860\) | 2.00000 | 0.0681994 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.00000 | 0.102180 | ||||||||
\(863\) | 2.00000 | − | 3.46410i | 0.0680808 | − | 0.117919i | −0.829976 | − | 0.557800i | \(-0.811646\pi\) |
0.898056 | + | 0.439880i | \(0.144979\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.00000 | − | 5.19615i | −0.102003 | − | 0.176674i | ||||
\(866\) | 19.0000 | − | 32.9090i | 0.645646 | − | 1.11829i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 15.0000 | − | 5.19615i | 0.509133 | − | 0.176369i | ||||
\(869\) | −4.00000 | −0.135691 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.00000 | + | 5.19615i | 0.101651 | + | 0.176065i | ||||
\(872\) | 5.00000 | + | 8.66025i | 0.169321 | + | 0.293273i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 28.0000 | 0.947114 | ||||||||
\(875\) | 2.00000 | + | 1.73205i | 0.0676123 | + | 0.0585540i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.5000 | − | 42.4352i | 0.827306 | − | 1.43294i | −0.0728377 | − | 0.997344i | \(-0.523206\pi\) |
0.900144 | − | 0.435593i | \(-0.143461\pi\) | |||||||
\(878\) | −2.00000 | − | 3.46410i | −0.0674967 | − | 0.116908i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.00000 | + | 1.73205i | −0.0337100 | + | 0.0583874i | ||||
\(881\) | −58.0000 | −1.95407 | −0.977035 | − | 0.213080i | \(-0.931651\pi\) | ||||
−0.977035 | + | 0.213080i | \(0.931651\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.00000 | −0.134611 | −0.0673054 | − | 0.997732i | \(-0.521440\pi\) | ||||
−0.0673054 | + | 0.997732i | \(0.521440\pi\) | |||||||
\(884\) | −2.50000 | + | 4.33013i | −0.0840841 | + | 0.145638i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.5000 | − | 18.1865i | −0.352754 | − | 0.610989i | ||||
\(887\) | −19.0000 | + | 32.9090i | −0.637958 | + | 1.10497i | 0.347923 | + | 0.937523i | \(0.386887\pi\) |
−0.985880 | + | 0.167452i | \(0.946446\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.0000 | − | 12.1244i | −0.469545 | − | 0.406638i | ||||
\(890\) | 16.0000 | 0.536321 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.50000 | − | 14.7224i | −0.284601 | − | 0.492943i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.00000 | −0.267411 | ||||||||
\(896\) | −2.50000 | + | 0.866025i | −0.0835191 | + | 0.0289319i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −10.0000 | + | 17.3205i | −0.333704 | + | 0.577993i | ||||
\(899\) | −6.00000 | − | 10.3923i | −0.200111 | − | 0.346603i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.0000 | − | 17.3205i | 0.333148 | − | 0.577030i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −18.0000 | −0.598671 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.0000 | + | 17.3205i | 0.332045 | + | 0.575118i | 0.982913 | − | 0.184073i | \(-0.0589282\pi\) |
−0.650868 | + | 0.759191i | \(0.725595\pi\) | |||||||
\(908\) | −14.0000 | + | 24.2487i | −0.464606 | + | 0.804722i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.500000 | − | 2.59808i | 0.0165748 | − | 0.0861254i | ||||
\(911\) | 35.0000 | 1.15960 | 0.579801 | − | 0.814758i | \(-0.303130\pi\) | ||||
0.579801 | + | 0.814758i | \(0.303130\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.0000 | + | 25.9808i | 0.496428 | + | 0.859838i | ||||
\(914\) | −14.0000 | − | 24.2487i | −0.463079 | − | 0.802076i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.00000 | 0.264327 | ||||||||
\(917\) | −35.0000 | + | 12.1244i | −1.15580 | + | 0.400381i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.00000 | + | 13.8564i | −0.263896 | + | 0.457081i | −0.967274 | − | 0.253735i | \(-0.918341\pi\) |
0.703378 | + | 0.710816i | \(0.251674\pi\) | |||||||
\(920\) | −2.00000 | − | 3.46410i | −0.0659380 | − | 0.114208i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −19.0000 | + | 32.9090i | −0.625732 | + | 1.08380i | ||||
\(923\) | 1.00000 | 0.0329154 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000 | 0.197279 | ||||||||
\(926\) | −12.0000 | + | 20.7846i | −0.394344 | + | 0.683025i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.00000 | + | 1.73205i | 0.0328266 | + | 0.0568574i | ||||
\(929\) | −20.0000 | + | 34.6410i | −0.656179 | + | 1.13653i | 0.325418 | + | 0.945570i | \(0.394495\pi\) |
−0.981597 | + | 0.190965i | \(0.938838\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −45.5000 | − | 18.1865i | −1.49120 | − | 0.596040i | ||||
\(932\) | −13.0000 | −0.425829 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.50000 | − | 2.59808i | −0.0490815 | − | 0.0850117i | ||||
\(935\) | −5.00000 | − | 8.66025i | −0.163517 | − | 0.283221i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.0000 | −0.849383 | −0.424691 | − | 0.905338i | \(-0.639617\pi\) | ||||
−0.424691 | + | 0.905338i | \(0.639617\pi\) | |||||||
\(938\) | −12.0000 | − | 10.3923i | −0.391814 | − | 0.339321i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.5000 | − | 28.5788i | −0.537885 | − | 0.931644i | −0.999018 | − | 0.0443125i | \(-0.985890\pi\) |
0.461133 | − | 0.887331i | \(-0.347443\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.00000 | 0.130051 | ||||||||
\(947\) | 26.5000 | − | 45.8993i | 0.861134 | − | 1.49153i | −0.00970072 | − | 0.999953i | \(-0.503088\pi\) |
0.870835 | − | 0.491575i | \(-0.163579\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.00000 | − | 13.8564i | −0.259691 | − | 0.449798i | ||||
\(950\) | −3.50000 | + | 6.06218i | −0.113555 | + | 0.196683i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.50000 | − | 12.9904i | 0.0810255 | − | 0.421021i | ||||
\(953\) | 59.0000 | 1.91120 | 0.955599 | − | 0.294671i | \(-0.0952101\pi\) | ||||
0.955599 | + | 0.294671i | \(0.0952101\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.00000 | + | 13.8564i | 0.258874 | + | 0.448383i | ||||
\(956\) | −10.5000 | − | 18.1865i | −0.339594 | − | 0.588195i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −16.0000 | −0.516937 | ||||||||
\(959\) | −8.50000 | + | 44.1673i | −0.274479 | + | 1.42624i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.50000 | + | 4.33013i | −0.0806452 | + | 0.139682i | ||||
\(962\) | −3.00000 | − | 5.19615i | −0.0967239 | − | 0.167531i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.00000 | + | 8.66025i | −0.161039 | + | 0.278928i | ||||
\(965\) | −4.00000 | −0.128765 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 49.0000 | 1.57573 | 0.787867 | − | 0.615846i | \(-0.211185\pi\) | ||||
0.787867 | + | 0.615846i | \(0.211185\pi\) | |||||||
\(968\) | 3.50000 | − | 6.06218i | 0.112494 | − | 0.194846i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.00000 | + | 8.66025i | 0.160540 | + | 0.278064i | ||||
\(971\) | −17.0000 | + | 29.4449i | −0.545556 | + | 0.944931i | 0.453016 | + | 0.891503i | \(0.350348\pi\) |
−0.998572 | + | 0.0534281i | \(0.982985\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.0000 | + | 8.66025i | 0.320585 | + | 0.277635i | ||||
\(974\) | 19.0000 | 0.608799 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.00000 | + | 3.46410i | 0.0640184 | + | 0.110883i | ||||
\(977\) | −22.5000 | − | 38.9711i | −0.719839 | − | 1.24680i | −0.961063 | − | 0.276328i | \(-0.910882\pi\) |
0.241225 | − | 0.970469i | \(-0.422451\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 32.0000 | 1.02272 | ||||||||
\(980\) | 1.00000 | + | 6.92820i | 0.0319438 | + | 0.221313i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −18.0000 | + | 31.1769i | −0.574403 | + | 0.994895i | ||||
\(983\) | −21.0000 | − | 36.3731i | −0.669796 | − | 1.16012i | −0.977961 | − | 0.208788i | \(-0.933048\pi\) |
0.308165 | − | 0.951333i | \(-0.400285\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.00000 | + | 10.3923i | −0.191176 | + | 0.331126i | ||||
\(986\) | −10.0000 | −0.318465 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.00000 | 0.222700 | ||||||||
\(989\) | −4.00000 | + | 6.92820i | −0.127193 | + | 0.220304i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.0000 | − | 24.2487i | −0.444725 | − | 0.770286i | 0.553308 | − | 0.832977i | \(-0.313365\pi\) |
−0.998033 | + | 0.0626908i | \(0.980032\pi\) | |||||||
\(992\) | 3.00000 | − | 5.19615i | 0.0952501 | − | 0.164978i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.50000 | + | 0.866025i | −0.0792952 | + | 0.0274687i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.0000 | + | 22.5167i | 0.411714 | + | 0.713110i | 0.995077 | − | 0.0991016i | \(-0.0315969\pi\) |
−0.583363 | + | 0.812211i | \(0.698264\pi\) | |||||||
\(998\) | 13.5000 | + | 23.3827i | 0.427335 | + | 0.740166i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1890.2.k.d.541.1 | ✓ | 2 | |
3.2 | odd | 2 | 1890.2.k.bf.541.1 | yes | 2 | ||
7.4 | even | 3 | inner | 1890.2.k.d.1621.1 | yes | 2 | |
21.11 | odd | 6 | 1890.2.k.bf.1621.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1890.2.k.d.541.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1890.2.k.d.1621.1 | yes | 2 | 7.4 | even | 3 | inner | |
1890.2.k.bf.541.1 | yes | 2 | 3.2 | odd | 2 | ||
1890.2.k.bf.1621.1 | yes | 2 | 21.11 | odd | 6 |