Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1170,2,Mod(361,1170)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1170, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1170.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1170.bs (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.34249703649\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 361.2 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1170.361 |
Dual form | 1170.2.bs.a.901.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).
\(n\) | \(911\) | \(937\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.50000 | − | 0.866025i | −0.566947 | − | 0.327327i | 0.188982 | − | 0.981981i | \(-0.439481\pi\) |
−0.755929 | + | 0.654654i | \(0.772814\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.500000 | + | 0.866025i | 0.158114 | + | 0.273861i | ||||
\(11\) | 2.59808 | − | 1.50000i | 0.783349 | − | 0.452267i | −0.0542666 | − | 0.998526i | \(-0.517282\pi\) |
0.837616 | + | 0.546259i | \(0.183949\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.50000 | + | 0.866025i | 0.970725 | + | 0.240192i | ||||
\(14\) | −1.73205 | −0.462910 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.50000 | + | 2.59808i | 1.03237 | + | 0.596040i | 0.917663 | − | 0.397360i | \(-0.130073\pi\) |
0.114708 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(20\) | 0.866025 | + | 0.500000i | 0.193649 | + | 0.111803i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.50000 | − | 2.59808i | 0.319801 | − | 0.553912i | ||||
\(23\) | 1.73205 | + | 3.00000i | 0.361158 | + | 0.625543i | 0.988152 | − | 0.153481i | \(-0.0490483\pi\) |
−0.626994 | + | 0.779024i | \(0.715715\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 3.46410 | − | 1.00000i | 0.679366 | − | 0.196116i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.50000 | + | 0.866025i | −0.283473 | + | 0.163663i | ||||
\(29\) | −3.46410 | − | 6.00000i | −0.643268 | − | 1.11417i | −0.984699 | − | 0.174265i | \(-0.944245\pi\) |
0.341431 | − | 0.939907i | \(-0.389088\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 10.3923i | − | 1.86651i | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||
0.359211 | − | 0.933257i | \(-0.383046\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.866025 | − | 1.50000i | 0.146385 | − | 0.253546i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.50000 | − | 4.33013i | 1.23299 | − | 0.711868i | 0.265340 | − | 0.964155i | \(-0.414516\pi\) |
0.967653 | + | 0.252286i | \(0.0811825\pi\) | |||||||
\(38\) | 5.19615 | 0.842927 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −5.19615 | + | 3.00000i | −0.811503 | + | 0.468521i | −0.847477 | − | 0.530831i | \(-0.821880\pi\) |
0.0359748 | + | 0.999353i | \(0.488546\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.00000 | − | 8.66025i | 0.762493 | − | 1.32068i | −0.179069 | − | 0.983836i | \(-0.557309\pi\) |
0.941562 | − | 0.336840i | \(-0.109358\pi\) | |||||||
\(44\) | − | 3.00000i | − | 0.452267i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.00000 | + | 1.73205i | 0.442326 | + | 0.255377i | ||||
\(47\) | 9.00000i | 1.31278i | 0.754420 | + | 0.656392i | \(0.227918\pi\) | ||||
−0.754420 | + | 0.656392i | \(0.772082\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.00000 | − | 3.46410i | −0.285714 | − | 0.494872i | ||||
\(50\) | −0.866025 | + | 0.500000i | −0.122474 | + | 0.0707107i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.50000 | − | 2.59808i | 0.346688 | − | 0.360288i | ||||
\(53\) | 12.1244 | 1.66541 | 0.832704 | − | 0.553718i | \(-0.186791\pi\) | ||||
0.832704 | + | 0.553718i | \(0.186791\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.50000 | + | 2.59808i | 0.202260 | + | 0.350325i | ||||
\(56\) | −0.866025 | + | 1.50000i | −0.115728 | + | 0.200446i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.00000 | − | 3.46410i | −0.787839 | − | 0.454859i | ||||
\(59\) | 10.3923 | + | 6.00000i | 1.35296 | + | 0.781133i | 0.988663 | − | 0.150148i | \(-0.0479752\pi\) |
0.364299 | + | 0.931282i | \(0.381308\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.00000 | + | 8.66025i | −0.640184 | + | 1.10883i | 0.345207 | + | 0.938527i | \(0.387809\pi\) |
−0.985391 | + | 0.170305i | \(0.945525\pi\) | |||||||
\(62\) | −5.19615 | − | 9.00000i | −0.659912 | − | 1.14300i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −0.866025 | + | 3.50000i | −0.107417 | + | 0.434122i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − | 1.73205i | − | 0.207020i | ||||||
\(71\) | −5.19615 | − | 3.00000i | −0.616670 | − | 0.356034i | 0.158901 | − | 0.987294i | \(-0.449205\pi\) |
−0.775571 | + | 0.631260i | \(0.782538\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.92820i | − | 0.810885i | −0.914121 | − | 0.405442i | \(-0.867117\pi\) | ||
0.914121 | − | 0.405442i | \(-0.132883\pi\) | |||||||
\(74\) | 4.33013 | − | 7.50000i | 0.503367 | − | 0.871857i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.50000 | − | 2.59808i | 0.516185 | − | 0.298020i | ||||
\(77\) | −5.19615 | −0.592157 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.0000 | 1.12509 | 0.562544 | − | 0.826767i | \(-0.309823\pi\) | ||||
0.562544 | + | 0.826767i | \(0.309823\pi\) | |||||||
\(80\) | 0.866025 | − | 0.500000i | 0.0968246 | − | 0.0559017i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.00000 | + | 5.19615i | −0.331295 | + | 0.573819i | ||||
\(83\) | 12.0000i | 1.31717i | 0.752506 | + | 0.658586i | \(0.228845\pi\) | ||||
−0.752506 | + | 0.658586i | \(0.771155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 10.0000i | − | 1.07833i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.50000 | − | 2.59808i | −0.159901 | − | 0.276956i | ||||
\(89\) | −12.9904 | + | 7.50000i | −1.37698 | + | 0.794998i | −0.991795 | − | 0.127842i | \(-0.959195\pi\) |
−0.385183 | + | 0.922840i | \(0.625862\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.50000 | − | 4.33013i | −0.471728 | − | 0.453921i | ||||
\(92\) | 3.46410 | 0.361158 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.50000 | + | 7.79423i | 0.464140 | + | 0.803913i | ||||
\(95\) | −2.59808 | + | 4.50000i | −0.266557 | + | 0.461690i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.00000 | − | 3.46410i | −0.609208 | − | 0.351726i | 0.163448 | − | 0.986552i | \(-0.447739\pi\) |
−0.772655 | + | 0.634826i | \(0.781072\pi\) | |||||||
\(98\) | −3.46410 | − | 2.00000i | −0.349927 | − | 0.202031i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | −6.92820 | − | 12.0000i | −0.689382 | − | 1.19404i | −0.972038 | − | 0.234823i | \(-0.924549\pi\) |
0.282656 | − | 0.959221i | \(-0.408784\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.00000 | −0.0985329 | −0.0492665 | − | 0.998786i | \(-0.515688\pi\) | ||||
−0.0492665 | + | 0.998786i | \(0.515688\pi\) | |||||||
\(104\) | 0.866025 | − | 3.50000i | 0.0849208 | − | 0.343203i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.5000 | − | 6.06218i | 1.01985 | − | 0.588811i | ||||
\(107\) | 1.73205 | + | 3.00000i | 0.167444 | + | 0.290021i | 0.937520 | − | 0.347930i | \(-0.113115\pi\) |
−0.770077 | + | 0.637951i | \(0.779782\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.3923i | 0.995402i | 0.867349 | + | 0.497701i | \(0.165822\pi\) | ||||
−0.867349 | + | 0.497701i | \(0.834178\pi\) | |||||||
\(110\) | 2.59808 | + | 1.50000i | 0.247717 | + | 0.143019i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.73205i | 0.163663i | ||||||||
\(113\) | −6.92820 | + | 12.0000i | −0.651751 | + | 1.12887i | 0.330947 | + | 0.943649i | \(0.392632\pi\) |
−0.982698 | + | 0.185216i | \(0.940702\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.00000 | + | 1.73205i | −0.279751 | + | 0.161515i | ||||
\(116\) | −6.92820 | −0.643268 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 12.0000 | 1.10469 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | + | 1.73205i | −0.0909091 | + | 0.157459i | ||||
\(122\) | 10.0000i | 0.905357i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.00000 | − | 5.19615i | −0.808224 | − | 0.466628i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.50000 | + | 9.52628i | 0.488046 | + | 0.845321i | 0.999905 | − | 0.0137486i | \(-0.00437646\pi\) |
−0.511859 | + | 0.859069i | \(0.671043\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.00000 | + | 3.46410i | 0.0877058 | + | 0.303822i | ||||
\(131\) | −12.1244 | −1.05931 | −0.529655 | − | 0.848213i | \(-0.677679\pi\) | ||||
−0.529655 | + | 0.848213i | \(0.677679\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.50000 | − | 7.79423i | −0.390199 | − | 0.675845i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.3923 | − | 6.00000i | −0.887875 | − | 0.512615i | −0.0146279 | − | 0.999893i | \(-0.504656\pi\) |
−0.873247 | + | 0.487278i | \(0.837990\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.50000 | + | 4.33013i | −0.212047 | + | 0.367277i | −0.952355 | − | 0.304991i | \(-0.901346\pi\) |
0.740308 | + | 0.672268i | \(0.234680\pi\) | |||||||
\(140\) | −0.866025 | − | 1.50000i | −0.0731925 | − | 0.126773i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.00000 | −0.503509 | ||||||||
\(143\) | 10.3923 | − | 3.00000i | 0.869048 | − | 0.250873i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.00000 | − | 3.46410i | 0.498273 | − | 0.287678i | ||||
\(146\) | −3.46410 | − | 6.00000i | −0.286691 | − | 0.496564i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 8.66025i | − | 0.711868i | ||||||
\(149\) | −5.19615 | − | 3.00000i | −0.425685 | − | 0.245770i | 0.271821 | − | 0.962348i | \(-0.412374\pi\) |
−0.697507 | + | 0.716578i | \(0.745707\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 10.3923i | − | 0.845714i | −0.906196 | − | 0.422857i | \(-0.861027\pi\) | ||
0.906196 | − | 0.422857i | \(-0.138973\pi\) | |||||||
\(152\) | 2.59808 | − | 4.50000i | 0.210732 | − | 0.364998i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.50000 | + | 2.59808i | −0.362620 | + | 0.209359i | ||||
\(155\) | 10.3923 | 0.834730 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.0000 | 0.877896 | 0.438948 | − | 0.898513i | \(-0.355351\pi\) | ||||
0.438948 | + | 0.898513i | \(0.355351\pi\) | |||||||
\(158\) | 8.66025 | − | 5.00000i | 0.688973 | − | 0.397779i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.500000 | − | 0.866025i | 0.0395285 | − | 0.0684653i | ||||
\(161\) | − | 6.00000i | − | 0.472866i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.00000 | − | 3.46410i | −0.469956 | − | 0.271329i | 0.246265 | − | 0.969202i | \(-0.420797\pi\) |
−0.716221 | + | 0.697873i | \(0.754130\pi\) | |||||||
\(164\) | 6.00000i | 0.468521i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.00000 | + | 10.3923i | 0.465690 | + | 0.806599i | ||||
\(167\) | 2.59808 | − | 1.50000i | 0.201045 | − | 0.116073i | −0.396098 | − | 0.918208i | \(-0.629636\pi\) |
0.597143 | + | 0.802135i | \(0.296303\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.5000 | + | 6.06218i | 0.884615 | + | 0.466321i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.00000 | − | 8.66025i | −0.381246 | − | 0.660338i | ||||
\(173\) | −2.59808 | + | 4.50000i | −0.197528 | + | 0.342129i | −0.947726 | − | 0.319084i | \(-0.896625\pi\) |
0.750198 | + | 0.661213i | \(0.229958\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.50000 | + | 0.866025i | 0.113389 | + | 0.0654654i | ||||
\(176\) | −2.59808 | − | 1.50000i | −0.195837 | − | 0.113067i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.50000 | + | 12.9904i | −0.562149 | + | 0.973670i | ||||
\(179\) | −1.73205 | − | 3.00000i | −0.129460 | − | 0.224231i | 0.794008 | − | 0.607908i | \(-0.207991\pi\) |
−0.923467 | + | 0.383677i | \(0.874658\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | −6.06218 | − | 1.50000i | −0.449359 | − | 0.111187i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.00000 | − | 1.73205i | 0.221163 | − | 0.127688i | ||||
\(185\) | 4.33013 | + | 7.50000i | 0.318357 | + | 0.551411i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 7.79423 | + | 4.50000i | 0.568453 | + | 0.328196i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.19615i | 0.376969i | ||||||||
\(191\) | −8.66025 | + | 15.0000i | −0.626634 | + | 1.08536i | 0.361588 | + | 0.932338i | \(0.382235\pi\) |
−0.988222 | + | 0.153024i | \(0.951099\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.00000 | + | 3.46410i | −0.431889 | + | 0.249351i | −0.700151 | − | 0.713995i | \(-0.746884\pi\) |
0.268262 | + | 0.963346i | \(0.413551\pi\) | |||||||
\(194\) | −6.92820 | −0.497416 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.00000 | −0.285714 | ||||||||
\(197\) | 2.59808 | − | 1.50000i | 0.185105 | − | 0.106871i | −0.404584 | − | 0.914501i | \(-0.632584\pi\) |
0.589689 | + | 0.807630i | \(0.299250\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.0000 | + | 19.0526i | −0.779769 | + | 1.35060i | 0.152305 | + | 0.988334i | \(0.451330\pi\) |
−0.932075 | + | 0.362267i | \(0.882003\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −12.0000 | − | 6.92820i | −0.844317 | − | 0.487467i | ||||
\(203\) | 12.0000i | 0.842235i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.00000 | − | 5.19615i | −0.209529 | − | 0.362915i | ||||
\(206\) | −0.866025 | + | 0.500000i | −0.0603388 | + | 0.0348367i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.00000 | − | 3.46410i | −0.0693375 | − | 0.240192i | ||||
\(209\) | 15.5885 | 1.07828 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.50000 | + | 9.52628i | 0.378636 | + | 0.655816i | 0.990864 | − | 0.134865i | \(-0.0430600\pi\) |
−0.612228 | + | 0.790681i | \(0.709727\pi\) | |||||||
\(212\) | 6.06218 | − | 10.5000i | 0.416352 | − | 0.721143i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.00000 | + | 1.73205i | 0.205076 | + | 0.118401i | ||||
\(215\) | 8.66025 | + | 5.00000i | 0.590624 | + | 0.340997i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.00000 | + | 15.5885i | −0.610960 | + | 1.05821i | ||||
\(218\) | 5.19615 | + | 9.00000i | 0.351928 | + | 0.609557i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.00000 | 0.202260 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.5000 | + | 6.06218i | −0.703132 | + | 0.405953i | −0.808513 | − | 0.588478i | \(-0.799727\pi\) |
0.105381 | + | 0.994432i | \(0.466394\pi\) | |||||||
\(224\) | 0.866025 | + | 1.50000i | 0.0578638 | + | 0.100223i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.8564i | 0.921714i | ||||||||
\(227\) | −20.7846 | − | 12.0000i | −1.37952 | − | 0.796468i | −0.387421 | − | 0.921903i | \(-0.626634\pi\) |
−0.992102 | + | 0.125435i | \(0.959967\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 3.46410i | − | 0.228914i | −0.993428 | − | 0.114457i | \(-0.963487\pi\) | ||
0.993428 | − | 0.114457i | \(-0.0365129\pi\) | |||||||
\(230\) | −1.73205 | + | 3.00000i | −0.114208 | + | 0.197814i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.00000 | + | 3.46410i | −0.393919 | + | 0.227429i | ||||
\(233\) | 3.46410 | 0.226941 | 0.113470 | − | 0.993541i | \(-0.463803\pi\) | ||||
0.113470 | + | 0.993541i | \(0.463803\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.00000 | −0.587095 | ||||||||
\(236\) | 10.3923 | − | 6.00000i | 0.676481 | − | 0.390567i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 6.00000i | − | 0.388108i | −0.980991 | − | 0.194054i | \(-0.937836\pi\) | ||
0.980991 | − | 0.194054i | \(-0.0621637\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.5000 | − | 14.7224i | −1.64260 | − | 0.948355i | −0.979905 | − | 0.199465i | \(-0.936079\pi\) |
−0.662695 | − | 0.748890i | \(-0.730587\pi\) | |||||||
\(242\) | 2.00000i | 0.128565i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.00000 | + | 8.66025i | 0.320092 | + | 0.554416i | ||||
\(245\) | 3.46410 | − | 2.00000i | 0.221313 | − | 0.127775i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.5000 | + | 12.9904i | 0.858984 | + | 0.826558i | ||||
\(248\) | −10.3923 | −0.659912 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.500000 | − | 0.866025i | −0.0316228 | − | 0.0547723i | ||||
\(251\) | 2.59808 | − | 4.50000i | 0.163989 | − | 0.284037i | −0.772307 | − | 0.635250i | \(-0.780897\pi\) |
0.936296 | + | 0.351212i | \(0.114230\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.00000 | + | 5.19615i | 0.565825 | + | 0.326679i | ||||
\(254\) | 9.52628 | + | 5.50000i | 0.597732 | + | 0.345101i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −6.92820 | − | 12.0000i | −0.432169 | − | 0.748539i | 0.564890 | − | 0.825166i | \(-0.308918\pi\) |
−0.997060 | + | 0.0766265i | \(0.975585\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.0000 | −0.932055 | ||||||||
\(260\) | 2.59808 | + | 2.50000i | 0.161126 | + | 0.155043i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.5000 | + | 6.06218i | −0.648692 | + | 0.374523i | ||||
\(263\) | 7.79423 | + | 13.5000i | 0.480613 | + | 0.832446i | 0.999753 | − | 0.0222436i | \(-0.00708096\pi\) |
−0.519140 | + | 0.854689i | \(0.673748\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.1244i | 0.744793i | ||||||||
\(266\) | −7.79423 | − | 4.50000i | −0.477895 | − | 0.275913i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.46410 | + | 6.00000i | −0.211210 | + | 0.365826i | −0.952093 | − | 0.305807i | \(-0.901074\pi\) |
0.740883 | + | 0.671634i | \(0.234407\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.0000 | −0.724947 | ||||||||
\(275\) | −2.59808 | + | 1.50000i | −0.156670 | + | 0.0904534i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.50000 | − | 16.4545i | 0.570800 | − | 0.988654i | −0.425684 | − | 0.904872i | \(-0.639967\pi\) |
0.996484 | − | 0.0837823i | \(-0.0267000\pi\) | |||||||
\(278\) | 5.00000i | 0.299880i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.50000 | − | 0.866025i | −0.0896421 | − | 0.0517549i | ||||
\(281\) | − | 18.0000i | − | 1.07379i | −0.843649 | − | 0.536895i | \(-0.819597\pi\) | ||
0.843649 | − | 0.536895i | \(-0.180403\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.00000 | + | 12.1244i | 0.416107 | + | 0.720718i | 0.995544 | − | 0.0942988i | \(-0.0300609\pi\) |
−0.579437 | + | 0.815017i | \(0.696728\pi\) | |||||||
\(284\) | −5.19615 | + | 3.00000i | −0.308335 | + | 0.178017i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.50000 | − | 7.79423i | 0.443484 | − | 0.460882i | ||||
\(287\) | 10.3923 | 0.613438 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.50000 | + | 14.7224i | 0.500000 | + | 0.866025i | ||||
\(290\) | 3.46410 | − | 6.00000i | 0.203419 | − | 0.352332i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.00000 | − | 3.46410i | −0.351123 | − | 0.202721i | ||||
\(293\) | 28.5788 | + | 16.5000i | 1.66959 | + | 0.963940i | 0.967856 | + | 0.251505i | \(0.0809254\pi\) |
0.701737 | + | 0.712436i | \(0.252408\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.00000 | + | 10.3923i | −0.349334 | + | 0.605063i | ||||
\(296\) | −4.33013 | − | 7.50000i | −0.251684 | − | 0.435929i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.00000 | −0.347571 | ||||||||
\(299\) | 3.46410 | + | 12.0000i | 0.200334 | + | 0.693978i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.0000 | + | 8.66025i | −0.864586 | + | 0.499169i | ||||
\(302\) | −5.19615 | − | 9.00000i | −0.299005 | − | 0.517892i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 5.19615i | − | 0.298020i | ||||||
\(305\) | −8.66025 | − | 5.00000i | −0.495885 | − | 0.286299i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 10.3923i | − | 0.593120i | −0.955014 | − | 0.296560i | \(-0.904160\pi\) | ||
0.955014 | − | 0.296560i | \(-0.0958395\pi\) | |||||||
\(308\) | −2.59808 | + | 4.50000i | −0.148039 | + | 0.256411i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 9.00000 | − | 5.19615i | 0.511166 | − | 0.295122i | ||||
\(311\) | 27.7128 | 1.57145 | 0.785725 | − | 0.618576i | \(-0.212290\pi\) | ||||
0.785725 | + | 0.618576i | \(0.212290\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.00000 | −0.113047 | −0.0565233 | − | 0.998401i | \(-0.518002\pi\) | ||||
−0.0565233 | + | 0.998401i | \(0.518002\pi\) | |||||||
\(314\) | 9.52628 | − | 5.50000i | 0.537599 | − | 0.310383i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.00000 | − | 8.66025i | 0.281272 | − | 0.487177i | ||||
\(317\) | − | 9.00000i | − | 0.505490i | −0.967533 | − | 0.252745i | \(-0.918667\pi\) | ||
0.967533 | − | 0.252745i | \(-0.0813334\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.0000 | − | 10.3923i | −1.00781 | − | 0.581857i | ||||
\(320\) | − | 1.00000i | − | 0.0559017i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.00000 | − | 5.19615i | −0.167183 | − | 0.289570i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.50000 | − | 0.866025i | −0.194145 | − | 0.0480384i | ||||
\(326\) | −6.92820 | −0.383718 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.00000 | + | 5.19615i | 0.165647 | + | 0.286910i | ||||
\(329\) | 7.79423 | − | 13.5000i | 0.429710 | − | 0.744279i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.0000 | − | 8.66025i | −0.824475 | − | 0.476011i | 0.0274825 | − | 0.999622i | \(-0.491251\pi\) |
−0.851957 | + | 0.523612i | \(0.824584\pi\) | |||||||
\(332\) | 10.3923 | + | 6.00000i | 0.570352 | + | 0.329293i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.50000 | − | 2.59808i | 0.0820763 | − | 0.142160i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.0000 | −1.41631 | −0.708155 | − | 0.706057i | \(-0.750472\pi\) | ||||
−0.708155 | + | 0.706057i | \(0.750472\pi\) | |||||||
\(338\) | 12.9904 | − | 0.500000i | 0.706584 | − | 0.0271964i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.5885 | − | 27.0000i | −0.844162 | − | 1.46213i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.0526i | 1.02874i | ||||||||
\(344\) | −8.66025 | − | 5.00000i | −0.466930 | − | 0.269582i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.19615i | 0.279347i | ||||||||
\(347\) | −3.46410 | + | 6.00000i | −0.185963 | + | 0.322097i | −0.943901 | − | 0.330230i | \(-0.892874\pi\) |
0.757938 | + | 0.652327i | \(0.226207\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.0000 | − | 6.92820i | 0.642345 | − | 0.370858i | −0.143172 | − | 0.989698i | \(-0.545730\pi\) |
0.785517 | + | 0.618840i | \(0.212397\pi\) | |||||||
\(350\) | 1.73205 | 0.0925820 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.00000 | −0.159901 | ||||||||
\(353\) | 10.3923 | − | 6.00000i | 0.553127 | − | 0.319348i | −0.197256 | − | 0.980352i | \(-0.563203\pi\) |
0.750382 | + | 0.661004i | \(0.229870\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.00000 | − | 5.19615i | 0.159223 | − | 0.275783i | ||||
\(356\) | 15.0000i | 0.794998i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.00000 | − | 1.73205i | −0.158555 | − | 0.0915417i | ||||
\(359\) | − | 6.00000i | − | 0.316668i | −0.987386 | − | 0.158334i | \(-0.949388\pi\) | ||
0.987386 | − | 0.158334i | \(-0.0506123\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.00000 | + | 6.92820i | 0.210526 | + | 0.364642i | ||||
\(362\) | −8.66025 | + | 5.00000i | −0.455173 | + | 0.262794i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.00000 | + | 1.73205i | −0.314485 | + | 0.0907841i | ||||
\(365\) | 6.92820 | 0.362639 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.00000 | + | 13.8564i | 0.417597 | + | 0.723299i | 0.995697 | − | 0.0926670i | \(-0.0295392\pi\) |
−0.578101 | + | 0.815966i | \(0.696206\pi\) | |||||||
\(368\) | 1.73205 | − | 3.00000i | 0.0902894 | − | 0.156386i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7.50000 | + | 4.33013i | 0.389906 | + | 0.225113i | ||||
\(371\) | −18.1865 | − | 10.5000i | −0.944198 | − | 0.545133i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.0000 | + | 19.0526i | −0.569558 | + | 0.986504i | 0.427051 | + | 0.904227i | \(0.359552\pi\) |
−0.996610 | + | 0.0822766i | \(0.973781\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.00000 | 0.464140 | ||||||||
\(377\) | −6.92820 | − | 24.0000i | −0.356821 | − | 1.23606i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.5000 | − | 12.9904i | 1.15575 | − | 0.667271i | 0.205466 | − | 0.978664i | \(-0.434129\pi\) |
0.950281 | + | 0.311393i | \(0.100796\pi\) | |||||||
\(380\) | 2.59808 | + | 4.50000i | 0.133278 | + | 0.230845i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 17.3205i | 0.886194i | ||||||||
\(383\) | 31.1769 | + | 18.0000i | 1.59307 | + | 0.919757i | 0.992777 | + | 0.119974i | \(0.0382810\pi\) |
0.600289 | + | 0.799783i | \(0.295052\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 5.19615i | − | 0.264820i | ||||||
\(386\) | −3.46410 | + | 6.00000i | −0.176318 | + | 0.305392i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6.00000 | + | 3.46410i | −0.304604 | + | 0.175863i | ||||
\(389\) | −27.7128 | −1.40510 | −0.702548 | − | 0.711637i | \(-0.747954\pi\) | ||||
−0.702548 | + | 0.711637i | \(0.747954\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −3.46410 | + | 2.00000i | −0.174964 | + | 0.101015i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.50000 | − | 2.59808i | 0.0755689 | − | 0.130889i | ||||
\(395\) | 10.0000i | 0.503155i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.5000 | + | 9.52628i | 0.828111 | + | 0.478110i | 0.853206 | − | 0.521575i | \(-0.174655\pi\) |
−0.0250943 | + | 0.999685i | \(0.507989\pi\) | |||||||
\(398\) | 22.0000i | 1.10276i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.500000 | + | 0.866025i | 0.0250000 | + | 0.0433013i | ||||
\(401\) | −28.5788 | + | 16.5000i | −1.42716 | + | 0.823971i | −0.996896 | − | 0.0787327i | \(-0.974913\pi\) |
−0.430263 | + | 0.902703i | \(0.641579\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.00000 | − | 36.3731i | 0.448322 | − | 1.81187i | ||||
\(404\) | −13.8564 | −0.689382 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.00000 | + | 10.3923i | 0.297775 | + | 0.515761i | ||||
\(407\) | 12.9904 | − | 22.5000i | 0.643909 | − | 1.11528i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.50000 | + | 0.866025i | 0.0741702 | + | 0.0428222i | 0.536626 | − | 0.843820i | \(-0.319698\pi\) |
−0.462456 | + | 0.886642i | \(0.653032\pi\) | |||||||
\(410\) | −5.19615 | − | 3.00000i | −0.256620 | − | 0.148159i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.500000 | + | 0.866025i | −0.0246332 | + | 0.0426660i | ||||
\(413\) | −10.3923 | − | 18.0000i | −0.511372 | − | 0.885722i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.0000 | −0.589057 | ||||||||
\(416\) | −2.59808 | − | 2.50000i | −0.127381 | − | 0.122573i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 13.5000 | − | 7.79423i | 0.660307 | − | 0.381228i | ||||
\(419\) | 12.1244 | + | 21.0000i | 0.592314 | + | 1.02592i | 0.993920 | + | 0.110105i | \(0.0351186\pi\) |
−0.401606 | + | 0.915812i | \(0.631548\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | 9.52628 | + | 5.50000i | 0.463732 | + | 0.267736i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 12.1244i | − | 0.588811i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.0000 | − | 8.66025i | 0.725901 | − | 0.419099i | ||||
\(428\) | 3.46410 | 0.167444 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10.0000 | 0.482243 | ||||||||
\(431\) | 10.3923 | − | 6.00000i | 0.500580 | − | 0.289010i | −0.228373 | − | 0.973574i | \(-0.573341\pi\) |
0.728953 | + | 0.684564i | \(0.240007\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.00000 | + | 3.46410i | −0.0961139 | + | 0.166474i | −0.910073 | − | 0.414448i | \(-0.863975\pi\) |
0.813959 | + | 0.580922i | \(0.197308\pi\) | |||||||
\(434\) | 18.0000i | 0.864028i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.00000 | + | 5.19615i | 0.431022 | + | 0.248851i | ||||
\(437\) | 18.0000i | 0.861057i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.00000 | − | 12.1244i | −0.334092 | − | 0.578664i | 0.649218 | − | 0.760602i | \(-0.275096\pi\) |
−0.983310 | + | 0.181938i | \(0.941763\pi\) | |||||||
\(440\) | 2.59808 | − | 1.50000i | 0.123858 | − | 0.0715097i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.3923 | 0.493753 | 0.246877 | − | 0.969047i | \(-0.420596\pi\) | ||||
0.246877 | + | 0.969047i | \(0.420596\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.50000 | − | 12.9904i | −0.355534 | − | 0.615803i | ||||
\(446\) | −6.06218 | + | 10.5000i | −0.287052 | + | 0.497189i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.50000 | + | 0.866025i | 0.0708683 | + | 0.0409159i | ||||
\(449\) | −28.5788 | − | 16.5000i | −1.34872 | − | 0.778683i | −0.360651 | − | 0.932701i | \(-0.617445\pi\) |
−0.988068 | + | 0.154018i | \(0.950779\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.00000 | + | 15.5885i | −0.423793 | + | 0.734032i | ||||
\(452\) | 6.92820 | + | 12.0000i | 0.325875 | + | 0.564433i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −24.0000 | −1.12638 | ||||||||
\(455\) | 4.33013 | − | 4.50000i | 0.202999 | − | 0.210963i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 33.0000 | − | 19.0526i | 1.54367 | − | 0.891241i | 0.545073 | − | 0.838389i | \(-0.316502\pi\) |
0.998602 | − | 0.0528522i | \(-0.0168312\pi\) | |||||||
\(458\) | −1.73205 | − | 3.00000i | −0.0809334 | − | 0.140181i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.46410i | 0.161515i | ||||||||
\(461\) | −10.3923 | − | 6.00000i | −0.484018 | − | 0.279448i | 0.238071 | − | 0.971248i | \(-0.423485\pi\) |
−0.722089 | + | 0.691800i | \(0.756818\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 24.2487i | − | 1.12693i | −0.826139 | − | 0.563467i | \(-0.809467\pi\) | ||
0.826139 | − | 0.563467i | \(-0.190533\pi\) | |||||||
\(464\) | −3.46410 | + | 6.00000i | −0.160817 | + | 0.278543i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.00000 | − | 1.73205i | 0.138972 | − | 0.0802357i | ||||
\(467\) | 34.6410 | 1.60300 | 0.801498 | − | 0.597998i | \(-0.204037\pi\) | ||||
0.801498 | + | 0.597998i | \(0.204037\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −7.79423 | + | 4.50000i | −0.359521 | + | 0.207570i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.00000 | − | 10.3923i | 0.276172 | − | 0.478345i | ||||
\(473\) | − | 30.0000i | − | 1.37940i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.50000 | − | 2.59808i | −0.206474 | − | 0.119208i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.00000 | − | 5.19615i | −0.137217 | − | 0.237666i | ||||
\(479\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 30.0000 | − | 8.66025i | 1.36788 | − | 0.394874i | ||||
\(482\) | −29.4449 | −1.34118 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | + | 1.73205i | 0.0454545 | + | 0.0787296i | ||||
\(485\) | 3.46410 | − | 6.00000i | 0.157297 | − | 0.272446i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.50000 | + | 0.866025i | 0.0679715 | + | 0.0392434i | 0.533601 | − | 0.845737i | \(-0.320839\pi\) |
−0.465629 | + | 0.884980i | \(0.654172\pi\) | |||||||
\(488\) | 8.66025 | + | 5.00000i | 0.392031 | + | 0.226339i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.00000 | − | 3.46410i | 0.0903508 | − | 0.156492i | ||||
\(491\) | −6.06218 | − | 10.5000i | −0.273582 | − | 0.473858i | 0.696194 | − | 0.717853i | \(-0.254875\pi\) |
−0.969776 | + | 0.243995i | \(0.921542\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 18.1865 | + | 4.50000i | 0.818251 | + | 0.202465i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9.00000 | + | 5.19615i | −0.404112 | + | 0.233314i | ||||
\(497\) | 5.19615 | + | 9.00000i | 0.233079 | + | 0.403705i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.2487i | 1.08552i | 0.839887 | + | 0.542761i | \(0.182621\pi\) | ||||
−0.839887 | + | 0.542761i | \(0.817379\pi\) | |||||||
\(500\) | −0.866025 | − | 0.500000i | −0.0387298 | − | 0.0223607i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 5.19615i | − | 0.231916i | ||||||
\(503\) | −9.52628 | + | 16.5000i | −0.424756 | + | 0.735699i | −0.996398 | − | 0.0848047i | \(-0.972973\pi\) |
0.571642 | + | 0.820503i | \(0.306307\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.0000 | − | 6.92820i | 0.533993 | − | 0.308301i | ||||
\(506\) | 10.3923 | 0.461994 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 11.0000 | 0.488046 | ||||||||
\(509\) | 5.19615 | − | 3.00000i | 0.230315 | − | 0.132973i | −0.380402 | − | 0.924821i | \(-0.624214\pi\) |
0.610718 | + | 0.791849i | \(0.290881\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.00000 | + | 10.3923i | −0.265424 | + | 0.459728i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −12.0000 | − | 6.92820i | −0.529297 | − | 0.305590i | ||||
\(515\) | − | 1.00000i | − | 0.0440653i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.5000 | + | 23.3827i | 0.593729 | + | 1.02837i | ||||
\(518\) | −12.9904 | + | 7.50000i | −0.570765 | + | 0.329531i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.50000 | + | 0.866025i | 0.153485 | + | 0.0379777i | ||||
\(521\) | 12.1244 | 0.531178 | 0.265589 | − | 0.964086i | \(-0.414434\pi\) | ||||
0.265589 | + | 0.964086i | \(0.414434\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.0000 | + | 29.4449i | 0.743358 | + | 1.28753i | 0.950958 | + | 0.309320i | \(0.100101\pi\) |
−0.207600 | + | 0.978214i | \(0.566565\pi\) | |||||||
\(524\) | −6.06218 | + | 10.5000i | −0.264827 | + | 0.458695i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13.5000 | + | 7.79423i | 0.588628 | + | 0.339845i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.50000 | − | 9.52628i | 0.239130 | − | 0.414186i | ||||
\(530\) | 6.06218 | + | 10.5000i | 0.263324 | + | 0.456091i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −9.00000 | −0.390199 | ||||||||
\(533\) | −20.7846 | + | 6.00000i | −0.900281 | + | 0.259889i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.00000 | + | 1.73205i | −0.129701 | + | 0.0748831i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.92820i | 0.298696i | ||||||||
\(539\) | −10.3923 | − | 6.00000i | −0.447628 | − | 0.258438i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.46410i | 0.148933i | 0.997224 | + | 0.0744667i | \(0.0237254\pi\) | ||||
−0.997224 | + | 0.0744667i | \(0.976275\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.3923 | −0.445157 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.0000 | −0.940652 | −0.470326 | − | 0.882493i | \(-0.655864\pi\) | ||||
−0.470326 | + | 0.882493i | \(0.655864\pi\) | |||||||
\(548\) | −10.3923 | + | 6.00000i | −0.443937 | + | 0.256307i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.50000 | + | 2.59808i | −0.0639602 | + | 0.110782i | ||||
\(551\) | − | 36.0000i | − | 1.53365i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.0000 | − | 8.66025i | −0.637865 | − | 0.368271i | ||||
\(554\) | − | 19.0000i | − | 0.807233i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.50000 | + | 4.33013i | 0.106024 | + | 0.183638i | ||||
\(557\) | 7.79423 | − | 4.50000i | 0.330252 | − | 0.190671i | −0.325701 | − | 0.945473i | \(-0.605600\pi\) |
0.655953 | + | 0.754802i | \(0.272267\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 25.0000 | − | 25.9808i | 1.05739 | − | 1.09887i | ||||
\(560\) | −1.73205 | −0.0731925 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.00000 | − | 15.5885i | −0.379642 | − | 0.657559i | ||||
\(563\) | −6.92820 | + | 12.0000i | −0.291989 | + | 0.505740i | −0.974280 | − | 0.225341i | \(-0.927650\pi\) |
0.682291 | + | 0.731081i | \(0.260984\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.0000 | − | 6.92820i | −0.504844 | − | 0.291472i | ||||
\(566\) | 12.1244 | + | 7.00000i | 0.509625 | + | 0.294232i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.00000 | + | 5.19615i | −0.125877 | + | 0.218026i | ||||
\(569\) | −9.52628 | − | 16.5000i | −0.399362 | − | 0.691716i | 0.594285 | − | 0.804255i | \(-0.297435\pi\) |
−0.993647 | + | 0.112539i | \(0.964102\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.00000 | −0.209243 | −0.104622 | − | 0.994512i | \(-0.533363\pi\) | ||||
−0.104622 | + | 0.994512i | \(0.533363\pi\) | |||||||
\(572\) | 2.59808 | − | 10.5000i | 0.108631 | − | 0.439027i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 9.00000 | − | 5.19615i | 0.375653 | − | 0.216883i | ||||
\(575\) | −1.73205 | − | 3.00000i | −0.0722315 | − | 0.125109i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.3923i | 0.432637i | 0.976323 | + | 0.216319i | \(0.0694050\pi\) | ||||
−0.976323 | + | 0.216319i | \(0.930595\pi\) | |||||||
\(578\) | 14.7224 | + | 8.50000i | 0.612372 | + | 0.353553i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 6.92820i | − | 0.287678i | ||||||
\(581\) | 10.3923 | − | 18.0000i | 0.431145 | − | 0.746766i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 31.5000 | − | 18.1865i | 1.30460 | − | 0.753209i | ||||
\(584\) | −6.92820 | −0.286691 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 33.0000 | 1.36322 | ||||||||
\(587\) | −36.3731 | + | 21.0000i | −1.50128 | + | 0.866763i | −0.501278 | + | 0.865286i | \(0.667137\pi\) |
−0.999999 | + | 0.00147660i | \(0.999530\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.0000 | − | 46.7654i | 1.11252 | − | 1.92693i | ||||
\(590\) | 12.0000i | 0.494032i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.50000 | − | 4.33013i | −0.308248 | − | 0.177967i | ||||
\(593\) | 36.0000i | 1.47834i | 0.673517 | + | 0.739171i | \(0.264783\pi\) | ||||
−0.673517 | + | 0.739171i | \(0.735217\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.19615 | + | 3.00000i | −0.212843 | + | 0.122885i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9.00000 | + | 8.66025i | 0.368037 | + | 0.354144i | ||||
\(599\) | 24.2487 | 0.990775 | 0.495388 | − | 0.868672i | \(-0.335026\pi\) | ||||
0.495388 | + | 0.868672i | \(0.335026\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.5000 | − | 32.0429i | −0.754631 | − | 1.30706i | −0.945558 | − | 0.325455i | \(-0.894483\pi\) |
0.190927 | − | 0.981604i | \(-0.438851\pi\) | |||||||
\(602\) | −8.66025 | + | 15.0000i | −0.352966 | + | 0.611354i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −9.00000 | − | 5.19615i | −0.366205 | − | 0.211428i | ||||
\(605\) | −1.73205 | − | 1.00000i | −0.0704179 | − | 0.0406558i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.50000 | + | 9.52628i | −0.223238 | + | 0.386660i | −0.955789 | − | 0.294052i | \(-0.904996\pi\) |
0.732551 | + | 0.680712i | \(0.238329\pi\) | |||||||
\(608\) | −2.59808 | − | 4.50000i | −0.105366 | − | 0.182499i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −10.0000 | −0.404888 | ||||||||
\(611\) | −7.79423 | + | 31.5000i | −0.315321 | + | 1.27435i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.5000 | + | 11.2583i | −0.787598 | + | 0.454720i | −0.839116 | − | 0.543952i | \(-0.816927\pi\) |
0.0515185 | + | 0.998672i | \(0.483594\pi\) | |||||||
\(614\) | −5.19615 | − | 9.00000i | −0.209700 | − | 0.363210i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.19615i | 0.209359i | ||||||||
\(617\) | −5.19615 | − | 3.00000i | −0.209189 | − | 0.120775i | 0.391745 | − | 0.920074i | \(-0.371871\pi\) |
−0.600935 | + | 0.799298i | \(0.705205\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 12.1244i | − | 0.487319i | −0.969861 | − | 0.243659i | \(-0.921652\pi\) | ||
0.969861 | − | 0.243659i | \(-0.0783479\pi\) | |||||||
\(620\) | 5.19615 | − | 9.00000i | 0.208683 | − | 0.361449i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 24.0000 | − | 13.8564i | 0.962312 | − | 0.555591i | ||||
\(623\) | 25.9808 | 1.04090 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −1.73205 | + | 1.00000i | −0.0692267 | + | 0.0399680i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.50000 | − | 9.52628i | 0.219474 | − | 0.380140i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.0000 | − | 20.7846i | −1.43314 | − | 0.827422i | −0.435779 | − | 0.900054i | \(-0.643527\pi\) |
−0.997359 | + | 0.0726317i | \(0.976860\pi\) | |||||||
\(632\) | − | 10.0000i | − | 0.397779i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.50000 | − | 7.79423i | −0.178718 | − | 0.309548i | ||||
\(635\) | −9.52628 | + | 5.50000i | −0.378039 | + | 0.218261i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.00000 | − | 13.8564i | −0.158486 | − | 0.549011i | ||||
\(638\) | −20.7846 | −0.822871 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.500000 | − | 0.866025i | −0.0197642 | − | 0.0342327i | ||||
\(641\) | −6.06218 | + | 10.5000i | −0.239442 | + | 0.414725i | −0.960554 | − | 0.278093i | \(-0.910298\pi\) |
0.721113 | + | 0.692818i | \(0.243631\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.00000 | − | 3.46410i | −0.236617 | − | 0.136611i | 0.377004 | − | 0.926212i | \(-0.376954\pi\) |
−0.613621 | + | 0.789601i | \(0.710288\pi\) | |||||||
\(644\) | −5.19615 | − | 3.00000i | −0.204757 | − | 0.118217i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.1865 | − | 31.5000i | −0.714986 | − | 1.23839i | −0.962965 | − | 0.269627i | \(-0.913100\pi\) |
0.247978 | − | 0.968766i | \(-0.420234\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 36.0000 | 1.41312 | ||||||||
\(650\) | −3.46410 | + | 1.00000i | −0.135873 | + | 0.0392232i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.00000 | + | 3.46410i | −0.234978 | + | 0.135665i | ||||
\(653\) | −23.3827 | − | 40.5000i | −0.915035 | − | 1.58489i | −0.806850 | − | 0.590757i | \(-0.798829\pi\) |
−0.108185 | − | 0.994131i | \(-0.534504\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 12.1244i | − | 0.473738i | ||||||
\(656\) | 5.19615 | + | 3.00000i | 0.202876 | + | 0.117130i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 15.5885i | − | 0.607701i | ||||||
\(659\) | 12.1244 | − | 21.0000i | 0.472298 | − | 0.818044i | −0.527200 | − | 0.849741i | \(-0.676758\pi\) |
0.999498 | + | 0.0316976i | \(0.0100913\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.00000 | − | 5.19615i | 0.350059 | − | 0.202107i | −0.314652 | − | 0.949207i | \(-0.601888\pi\) |
0.664711 | + | 0.747100i | \(0.268554\pi\) | |||||||
\(662\) | −17.3205 | −0.673181 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.0000 | 0.465690 | ||||||||
\(665\) | 7.79423 | − | 4.50000i | 0.302247 | − | 0.174503i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.0000 | − | 20.7846i | 0.464642 | − | 0.804783i | ||||
\(668\) | − | 3.00000i | − | 0.116073i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 30.0000i | 1.15814i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.0000 | + | 34.6410i | 0.770943 | + | 1.33531i | 0.937046 | + | 0.349205i | \(0.113548\pi\) |
−0.166103 | + | 0.986108i | \(0.553118\pi\) | |||||||
\(674\) | −22.5167 | + | 13.0000i | −0.867309 | + | 0.500741i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.0000 | − | 6.92820i | 0.423077 | − | 0.266469i | ||||
\(677\) | −27.7128 | −1.06509 | −0.532545 | − | 0.846402i | \(-0.678764\pi\) | ||||
−0.532545 | + | 0.846402i | \(0.678764\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.00000 | + | 10.3923i | 0.230259 | + | 0.398820i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −27.0000 | − | 15.5885i | −1.03388 | − | 0.596913i | ||||
\(683\) | −25.9808 | − | 15.0000i | −0.994126 | − | 0.573959i | −0.0876211 | − | 0.996154i | \(-0.527926\pi\) |
−0.906505 | + | 0.422195i | \(0.861260\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.00000 | − | 10.3923i | 0.229248 | − | 0.397070i | ||||
\(686\) | 9.52628 | + | 16.5000i | 0.363715 | + | 0.629973i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −10.0000 | −0.381246 | ||||||||
\(689\) | 42.4352 | + | 10.5000i | 1.61665 | + | 0.400018i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.5000 | − | 14.7224i | 0.970066 | − | 0.560068i | 0.0708094 | − | 0.997490i | \(-0.477442\pi\) |
0.899256 | + | 0.437422i | \(0.144108\pi\) | |||||||
\(692\) | 2.59808 | + | 4.50000i | 0.0987640 | + | 0.171064i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.92820i | 0.262991i | ||||||||
\(695\) | −4.33013 | − | 2.50000i | −0.164251 | − | 0.0948304i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 6.92820 | − | 12.0000i | 0.262236 | − | 0.454207i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.50000 | − | 0.866025i | 0.0566947 | − | 0.0327327i | ||||
\(701\) | 13.8564 | 0.523349 | 0.261675 | − | 0.965156i | \(-0.415725\pi\) | ||||
0.261675 | + | 0.965156i | \(0.415725\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 45.0000 | 1.69721 | ||||||||
\(704\) | −2.59808 | + | 1.50000i | −0.0979187 | + | 0.0565334i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.00000 | − | 10.3923i | 0.225813 | − | 0.391120i | ||||
\(707\) | 24.0000i | 0.902613i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −42.0000 | − | 24.2487i | −1.57734 | − | 0.910679i | −0.995228 | − | 0.0975728i | \(-0.968892\pi\) |
−0.582115 | − | 0.813107i | \(-0.697775\pi\) | |||||||
\(710\) | − | 6.00000i | − | 0.225176i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.50000 | + | 12.9904i | 0.281074 | + | 0.486835i | ||||
\(713\) | 31.1769 | − | 18.0000i | 1.16758 | − | 0.674105i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.00000 | + | 10.3923i | 0.112194 | + | 0.388650i | ||||
\(716\) | −3.46410 | −0.129460 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.00000 | − | 5.19615i | −0.111959 | − | 0.193919i | ||||
\(719\) | 6.92820 | − | 12.0000i | 0.258378 | − | 0.447524i | −0.707429 | − | 0.706784i | \(-0.750145\pi\) |
0.965808 | + | 0.259260i | \(0.0834785\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.50000 | + | 0.866025i | 0.0558629 | + | 0.0322525i | ||||
\(722\) | 6.92820 | + | 4.00000i | 0.257841 | + | 0.148865i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.00000 | + | 8.66025i | −0.185824 | + | 0.321856i | ||||
\(725\) | 3.46410 | + | 6.00000i | 0.128654 | + | 0.222834i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.0000 | 1.37225 | 0.686127 | − | 0.727482i | \(-0.259309\pi\) | ||||
0.686127 | + | 0.727482i | \(0.259309\pi\) | |||||||
\(728\) | −4.33013 | + | 4.50000i | −0.160485 | + | 0.166781i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.00000 | − | 3.46410i | 0.222070 | − | 0.128212i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.4449i | 1.08757i | 0.839224 | + | 0.543785i | \(0.183009\pi\) | ||||
−0.839224 | + | 0.543785i | \(0.816991\pi\) | |||||||
\(734\) | 13.8564 | + | 8.00000i | 0.511449 | + | 0.295285i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 3.46410i | − | 0.127688i | ||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −40.5000 | + | 23.3827i | −1.48982 | + | 0.860146i | −0.999932 | − | 0.0116414i | \(-0.996294\pi\) |
−0.489884 | + | 0.871787i | \(0.662961\pi\) | |||||||
\(740\) | 8.66025 | 0.318357 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −21.0000 | −0.770934 | ||||||||
\(743\) | 20.7846 | − | 12.0000i | 0.762513 | − | 0.440237i | −0.0676840 | − | 0.997707i | \(-0.521561\pi\) |
0.830197 | + | 0.557470i | \(0.188228\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.00000 | − | 5.19615i | 0.109911 | − | 0.190372i | ||||
\(746\) | 22.0000i | 0.805477i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 6.00000i | − | 0.219235i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.00000 | + | 3.46410i | 0.0729810 | + | 0.126407i | 0.900207 | − | 0.435463i | \(-0.143415\pi\) |
−0.827225 | + | 0.561870i | \(0.810082\pi\) | |||||||
\(752\) | 7.79423 | − | 4.50000i | 0.284226 | − | 0.164098i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −18.0000 | − | 17.3205i | −0.655521 | − | 0.630776i | ||||
\(755\) | 10.3923 | 0.378215 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.5000 | + | 25.1147i | 0.527011 | + | 0.912811i | 0.999505 | + | 0.0314762i | \(0.0100208\pi\) |
−0.472493 | + | 0.881334i | \(0.656646\pi\) | |||||||
\(758\) | 12.9904 | − | 22.5000i | 0.471832 | − | 0.817237i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.50000 | + | 2.59808i | 0.163232 | + | 0.0942421i | ||||
\(761\) | −18.1865 | − | 10.5000i | −0.659261 | − | 0.380625i | 0.132734 | − | 0.991152i | \(-0.457624\pi\) |
−0.791995 | + | 0.610527i | \(0.790958\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.00000 | − | 15.5885i | 0.325822 | − | 0.564340i | ||||
\(764\) | 8.66025 | + | 15.0000i | 0.313317 | + | 0.542681i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 36.0000 | 1.30073 | ||||||||
\(767\) | 31.1769 | + | 30.0000i | 1.12573 | + | 1.08324i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.00000 | + | 3.46410i | −0.216366 | + | 0.124919i | −0.604266 | − | 0.796782i | \(-0.706534\pi\) |
0.387901 | + | 0.921701i | \(0.373200\pi\) | |||||||
\(770\) | −2.59808 | − | 4.50000i | −0.0936282 | − | 0.162169i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.92820i | 0.249351i | ||||||||
\(773\) | −33.7750 | − | 19.5000i | −1.21480 | − | 0.701366i | −0.251000 | − | 0.967987i | \(-0.580760\pi\) |
−0.963802 | + | 0.266621i | \(0.914093\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.3923i | 0.373303i | ||||||||
\(776\) | −3.46410 | + | 6.00000i | −0.124354 | + | 0.215387i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24.0000 | + | 13.8564i | −0.860442 | + | 0.496776i | ||||
\(779\) | −31.1769 | −1.11703 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.0000 | −0.644091 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.00000 | + | 3.46410i | −0.0714286 | + | 0.123718i | ||||
\(785\) | 11.0000i | 0.392607i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.0000 | − | 13.8564i | −0.855508 | − | 0.493928i | 0.00699773 | − | 0.999976i | \(-0.497773\pi\) |
−0.862505 | + | 0.506048i | \(0.831106\pi\) | |||||||
\(788\) | − | 3.00000i | − | 0.106871i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.00000 | + | 8.66025i | 0.177892 | + | 0.308118i | ||||
\(791\) | 20.7846 | − | 12.0000i | 0.739016 | − | 0.426671i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −25.0000 | + | 25.9808i | −0.887776 | + | 0.922604i | ||||
\(794\) | 19.0526 | 0.676150 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.0000 | + | 19.0526i | 0.389885 | + | 0.675300i | ||||
\(797\) | 6.92820 | − | 12.0000i | 0.245410 | − | 0.425062i | −0.716837 | − | 0.697241i | \(-0.754411\pi\) |
0.962247 | + | 0.272179i | \(0.0877442\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.866025 | + | 0.500000i | 0.0306186 | + | 0.0176777i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −16.5000 | + | 28.5788i | −0.582635 | + | 1.00915i | ||||
\(803\) | −10.3923 | − | 18.0000i | −0.366736 | − | 0.635206i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.00000 | 0.211472 | ||||||||
\(806\) | −10.3923 | − | 36.0000i | −0.366053 | − | 1.26805i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −12.0000 | + | 6.92820i | −0.422159 | + | 0.243733i | ||||
\(809\) | 10.3923 | + | 18.0000i | 0.365374 | + | 0.632846i | 0.988836 | − | 0.149007i | \(-0.0476078\pi\) |
−0.623462 | + | 0.781854i | \(0.714274\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.4449i | 1.03395i | 0.856001 | + | 0.516975i | \(0.172942\pi\) | ||||
−0.856001 | + | 0.516975i | \(0.827058\pi\) | |||||||
\(812\) | 10.3923 | + | 6.00000i | 0.364698 | + | 0.210559i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 25.9808i | − | 0.910625i | ||||||
\(815\) | 3.46410 | − | 6.00000i | 0.121342 | − | 0.210171i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 45.0000 | − | 25.9808i | 1.57435 | − | 0.908952i | ||||
\(818\) | 1.73205 | 0.0605597 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.00000 | −0.209529 | ||||||||
\(821\) | 15.5885 | − | 9.00000i | 0.544041 | − | 0.314102i | −0.202674 | − | 0.979246i | \(-0.564963\pi\) |
0.746715 | + | 0.665144i | \(0.231630\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.50000 | − | 11.2583i | 0.226576 | − | 0.392441i | −0.730215 | − | 0.683217i | \(-0.760580\pi\) |
0.956791 | + | 0.290776i | \(0.0939136\pi\) | |||||||
\(824\) | 1.00000i | 0.0348367i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −18.0000 | − | 10.3923i | −0.626300 | − | 0.361595i | ||||
\(827\) | 6.00000i | 0.208640i | 0.994544 | + | 0.104320i | \(0.0332667\pi\) | ||||
−0.994544 | + | 0.104320i | \(0.966733\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.00000 | − | 13.8564i | −0.277851 | − | 0.481253i | 0.692999 | − | 0.720938i | \(-0.256289\pi\) |
−0.970851 | + | 0.239686i | \(0.922956\pi\) | |||||||
\(830\) | −10.3923 | + | 6.00000i | −0.360722 | + | 0.208263i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.50000 | − | 0.866025i | −0.121341 | − | 0.0300240i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.50000 | + | 2.59808i | 0.0519096 | + | 0.0899101i | ||||
\(836\) | 7.79423 | − | 13.5000i | 0.269569 | − | 0.466907i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 21.0000 | + | 12.1244i | 0.725433 | + | 0.418829i | ||||
\(839\) | 36.3731 | + | 21.0000i | 1.25574 | + | 0.725001i | 0.972243 | − | 0.233973i | \(-0.0751728\pi\) |
0.283495 | + | 0.958974i | \(0.408506\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.50000 | + | 16.4545i | −0.327586 | + | 0.567396i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 11.0000 | 0.378636 | ||||||||
\(845\) | −6.06218 | + | 11.5000i | −0.208545 | + | 0.395612i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.00000 | − | 1.73205i | 0.103081 | − | 0.0595140i | ||||
\(848\) | −6.06218 | − | 10.5000i | −0.208176 | − | 0.360571i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 25.9808 | + | 15.0000i | 0.890609 | + | 0.514193i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 13.8564i | − | 0.474434i | −0.971457 | − | 0.237217i | \(-0.923765\pi\) | ||
0.971457 | − | 0.237217i | \(-0.0762353\pi\) | |||||||
\(854\) | 8.66025 | − | 15.0000i | 0.296348 | − | 0.513289i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.00000 | − | 1.73205i | 0.102538 | − | 0.0592003i | ||||
\(857\) | −3.46410 | −0.118331 | −0.0591657 | − | 0.998248i | \(-0.518844\pi\) | ||||
−0.0591657 | + | 0.998248i | \(0.518844\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.0000 | 1.05771 | 0.528853 | − | 0.848713i | \(-0.322622\pi\) | ||||
0.528853 | + | 0.848713i | \(0.322622\pi\) | |||||||
\(860\) | 8.66025 | − | 5.00000i | 0.295312 | − | 0.170499i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.00000 | − | 10.3923i | 0.204361 | − | 0.353963i | ||||
\(863\) | − | 24.0000i | − | 0.816970i | −0.912765 | − | 0.408485i | \(-0.866057\pi\) | ||
0.912765 | − | 0.408485i | \(-0.133943\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.50000 | − | 2.59808i | −0.153005 | − | 0.0883372i | ||||
\(866\) | 4.00000i | 0.135926i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 9.00000 | + | 15.5885i | 0.305480 | + | 0.529107i | ||||
\(869\) | 25.9808 | − | 15.0000i | 0.881337 | − | 0.508840i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 10.3923 | 0.351928 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9.00000 | + | 15.5885i | 0.304430 | + | 0.527287i | ||||
\(875\) | −0.866025 | + | 1.50000i | −0.0292770 | + | 0.0507093i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36.0000 | − | 20.7846i | −1.21563 | − | 0.701846i | −0.251653 | − | 0.967818i | \(-0.580974\pi\) |
−0.963981 | + | 0.265971i | \(0.914307\pi\) | |||||||
\(878\) | −12.1244 | − | 7.00000i | −0.409177 | − | 0.236239i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.50000 | − | 2.59808i | 0.0505650 | − | 0.0875811i | ||||
\(881\) | 16.4545 | + | 28.5000i | 0.554366 | + | 0.960189i | 0.997953 | + | 0.0639581i | \(0.0203724\pi\) |
−0.443587 | + | 0.896231i | \(0.646294\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.00000 | −0.0673054 | −0.0336527 | − | 0.999434i | \(-0.510714\pi\) | ||||
−0.0336527 | + | 0.999434i | \(0.510714\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.00000 | − | 5.19615i | 0.302361 | − | 0.174568i | ||||
\(887\) | 12.9904 | + | 22.5000i | 0.436174 | + | 0.755476i | 0.997391 | − | 0.0721931i | \(-0.0229998\pi\) |
−0.561216 | + | 0.827669i | \(0.689666\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 19.0526i | − | 0.639002i | ||||||
\(890\) | −12.9904 | − | 7.50000i | −0.435439 | − | 0.251401i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 12.1244i | 0.405953i | ||||||||
\(893\) | −23.3827 | + | 40.5000i | −0.782472 | + | 1.35528i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.00000 | − | 1.73205i | 0.100279 | − | 0.0578961i | ||||
\(896\) | 1.73205 | 0.0578638 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −33.0000 | −1.10122 | ||||||||
\(899\) | −62.3538 | + | 36.0000i | −2.07962 | + | 1.20067i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 18.0000i | 0.599334i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12.0000 | + | 6.92820i | 0.399114 | + | 0.230429i | ||||
\(905\) | − | 10.0000i | − | 0.332411i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.0000 | + | 22.5167i | 0.431658 | + | 0.747653i | 0.997016 | − | 0.0771920i | \(-0.0245954\pi\) |
−0.565358 | + | 0.824845i | \(0.691262\pi\) | |||||||
\(908\) | −20.7846 | + | 12.0000i | −0.689761 | + | 0.398234i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.50000 | − | 6.06218i | 0.0497245 | − | 0.200959i | ||||
\(911\) | 34.6410 | 1.14771 | 0.573854 | − | 0.818958i | \(-0.305448\pi\) | ||||
0.573854 | + | 0.818958i | \(0.305448\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.0000 | + | 31.1769i | 0.595713 | + | 1.03181i | ||||
\(914\) | 19.0526 | − | 33.0000i | 0.630203 | − | 1.09154i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.00000 | − | 1.73205i | −0.0991228 | − | 0.0572286i | ||||
\(917\) | 18.1865 | + | 10.5000i | 0.600572 | + | 0.346741i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.0000 | + | 39.8372i | −0.758700 | + | 1.31411i | 0.184814 | + | 0.982774i | \(0.440832\pi\) |
−0.943514 | + | 0.331333i | \(0.892502\pi\) | |||||||
\(920\) | 1.73205 | + | 3.00000i | 0.0571040 | + | 0.0989071i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12.0000 | −0.395199 | ||||||||
\(923\) | −15.5885 | − | 15.0000i | −0.513100 | − | 0.493731i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.50000 | + | 4.33013i | −0.246598 | + | 0.142374i | ||||
\(926\) | −12.1244 | − | 21.0000i | −0.398431 | − | 0.690103i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.92820i | 0.227429i | ||||||||
\(929\) | −36.3731 | − | 21.0000i | −1.19336 | − | 0.688988i | −0.234294 | − | 0.972166i | \(-0.575278\pi\) |
−0.959067 | + | 0.283178i | \(0.908611\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 20.7846i | − | 0.681188i | ||||||
\(932\) | 1.73205 | − | 3.00000i | 0.0567352 | − | 0.0982683i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 30.0000 | − | 17.3205i | 0.981630 | − | 0.566744i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.0000 | 0.718709 | 0.359354 | − | 0.933201i | \(-0.382997\pi\) | ||||
0.359354 | + | 0.933201i | \(0.382997\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.50000 | + | 7.79423i | −0.146774 | + | 0.254220i | ||||
\(941\) | 12.0000i | 0.391189i | 0.980685 | + | 0.195594i | \(0.0626636\pi\) | ||||
−0.980685 | + | 0.195594i | \(0.937336\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.0000 | − | 10.3923i | −0.586161 | − | 0.338420i | ||||
\(944\) | − | 12.0000i | − | 0.390567i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −15.0000 | − | 25.9808i | −0.487692 | − | 0.844707i | ||||
\(947\) | 15.5885 | − | 9.00000i | 0.506557 | − | 0.292461i | −0.224860 | − | 0.974391i | \(-0.572193\pi\) |
0.731417 | + | 0.681930i | \(0.238859\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.00000 | − | 24.2487i | 0.194768 | − | 0.787146i | ||||
\(950\) | −5.19615 | −0.168585 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15.5885 | + | 27.0000i | −0.504960 | + | 0.874616i | 0.495024 | + | 0.868879i | \(0.335159\pi\) |
−0.999984 | + | 0.00573642i | \(0.998174\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.0000 | − | 8.66025i | −0.485389 | − | 0.280239i | ||||
\(956\) | −5.19615 | − | 3.00000i | −0.168056 | − | 0.0970269i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.3923 | + | 18.0000i | 0.335585 | + | 0.581250i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −77.0000 | −2.48387 | ||||||||
\(962\) | 21.6506 | − | 22.5000i | 0.698044 | − | 0.725429i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −25.5000 | + | 14.7224i | −0.821300 | + | 0.474178i | ||||
\(965\) | −3.46410 | − | 6.00000i | −0.111513 | − | 0.193147i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.0526i | 0.612689i | 0.951921 | + | 0.306344i | \(0.0991059\pi\) | ||||
−0.951921 | + | 0.306344i | \(0.900894\pi\) | |||||||
\(968\) | 1.73205 | + | 1.00000i | 0.0556702 | + | 0.0321412i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | − | 6.92820i | − | 0.222451i | ||||||
\(971\) | −23.3827 | + | 40.5000i | −0.750386 | + | 1.29971i | 0.197250 | + | 0.980353i | \(0.436799\pi\) |
−0.947636 | + | 0.319354i | \(0.896534\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.50000 | − | 4.33013i | 0.240439 | − | 0.138817i | ||||
\(974\) | 1.73205 | 0.0554985 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.0000 | 0.320092 | ||||||||
\(977\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −22.5000 | + | 38.9711i | −0.719103 | + | 1.24552i | ||||
\(980\) | − | 4.00000i | − | 0.127775i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −10.5000 | − | 6.06218i | −0.335068 | − | 0.193452i | ||||
\(983\) | − | 51.0000i | − | 1.62665i | −0.581811 | − | 0.813324i | \(-0.697656\pi\) | ||
0.581811 | − | 0.813324i | \(-0.302344\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.50000 | + | 2.59808i | 0.0477940 | + | 0.0827816i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 18.0000 | − | 5.19615i | 0.572656 | − | 0.165312i | ||||
\(989\) | 34.6410 | 1.10152 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.0000 | + | 19.0526i | 0.349427 | + | 0.605224i | 0.986148 | − | 0.165870i | \(-0.0530431\pi\) |
−0.636721 | + | 0.771094i | \(0.719710\pi\) | |||||||
\(992\) | −5.19615 | + | 9.00000i | −0.164978 | + | 0.285750i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 9.00000 | + | 5.19615i | 0.285463 | + | 0.164812i | ||||
\(995\) | −19.0526 | − | 11.0000i | −0.604007 | − | 0.348723i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.5000 | + | 45.8993i | −0.839263 | + | 1.45365i | 0.0512480 | + | 0.998686i | \(0.483680\pi\) |
−0.890511 | + | 0.454961i | \(0.849653\pi\) | |||||||
\(998\) | 12.1244 | + | 21.0000i | 0.383790 | + | 0.664743i | ||||
\(999\) | 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 | 1170.2.bs.a.361.2 | yes | 4 | |
3.2 | odd | 2 | inner | 1170.2.bs.a.361.1 | ✓ | 4 | |
13.4 | even | 6 | inner | 1170.2.bs.a.901.2 | yes | 4 | |
39.17 | odd | 6 | inner | 1170.2.bs.a.901.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1170.2.bs.a.361.1 | ✓ | 4 | 3.2 | odd | 2 | inner | |
1170.2.bs.a.361.2 | yes | 4 | 1.1 | even | 1 | trivial | |
1170.2.bs.a.901.1 | yes | 4 | 39.17 | odd | 6 | inner | |
1170.2.bs.a.901.2 | yes | 4 | 13.4 | even | 6 | inner |