Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1170,2,Mod(451,1170)]
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, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1170.451");
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.i (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: | \(9.34249703649\) |
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: | no (minimal twist has level 390) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 991.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1170.991 |
Dual form | 1170.2.i.g.451.1 |
$q$-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 \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).
\(n\) | \(911\) | \(937\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.50000 | − | 4.33013i | 0.944911 | − | 1.63663i | 0.188982 | − | 0.981981i | \(-0.439481\pi\) |
0.755929 | − | 0.654654i | \(-0.227186\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.500000 | − | 0.866025i | −0.158114 | − | 0.273861i | ||||
\(11\) | −1.50000 | − | 2.59808i | −0.452267 | − | 0.783349i | 0.546259 | − | 0.837616i | \(-0.316051\pi\) |
−0.998526 | + | 0.0542666i | \(0.982718\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.50000 | − | 2.59808i | −0.693375 | − | 0.720577i | ||||
\(14\) | −5.00000 | −1.33631 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −4.00000 | + | 6.92820i | −0.970143 | + | 1.68034i | −0.275029 | + | 0.961436i | \(0.588688\pi\) |
−0.695113 | + | 0.718900i | \(0.744646\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.50000 | − | 4.33013i | 0.573539 | − | 0.993399i | −0.422659 | − | 0.906289i | \(-0.638903\pi\) |
0.996199 | − | 0.0871106i | \(-0.0277634\pi\) | |||||||
\(20\) | −0.500000 | + | 0.866025i | −0.111803 | + | 0.193649i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.50000 | + | 2.59808i | −0.319801 | + | 0.553912i | ||||
\(23\) | −2.00000 | − | 3.46410i | −0.417029 | − | 0.722315i | 0.578610 | − | 0.815604i | \(-0.303595\pi\) |
−0.995639 | + | 0.0932891i | \(0.970262\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.00000 | + | 3.46410i | −0.196116 | + | 0.679366i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.50000 | + | 4.33013i | 0.472456 | + | 0.818317i | ||||
\(29\) | −2.00000 | − | 3.46410i | −0.371391 | − | 0.643268i | 0.618389 | − | 0.785872i | \(-0.287786\pi\) |
−0.989780 | + | 0.142605i | \(0.954452\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | −0.359211 | −0.179605 | − | 0.983739i | \(-0.557482\pi\) | ||||
−0.179605 | + | 0.983739i | \(0.557482\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.00000 | 1.37199 | ||||||||
\(35\) | 2.50000 | − | 4.33013i | 0.422577 | − | 0.731925i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.50000 | + | 6.06218i | 0.575396 | + | 0.996616i | 0.995998 | + | 0.0893706i | \(0.0284856\pi\) |
−0.420602 | + | 0.907245i | \(0.638181\pi\) | |||||||
\(38\) | −5.00000 | −0.811107 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 3.00000 | + | 5.19615i | 0.468521 | + | 0.811503i | 0.999353 | − | 0.0359748i | \(-0.0114536\pi\) |
−0.530831 | + | 0.847477i | \(0.678120\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.00000 | + | 5.19615i | −0.457496 | + | 0.792406i | −0.998828 | − | 0.0484030i | \(-0.984587\pi\) |
0.541332 | + | 0.840809i | \(0.317920\pi\) | |||||||
\(44\) | 3.00000 | 0.452267 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.00000 | + | 3.46410i | −0.294884 | + | 0.510754i | ||||
\(47\) | 3.00000 | 0.437595 | 0.218797 | − | 0.975770i | \(-0.429787\pi\) | ||||
0.218797 | + | 0.975770i | \(0.429787\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9.00000 | − | 15.5885i | −1.28571 | − | 2.22692i | ||||
\(50\) | −0.500000 | − | 0.866025i | −0.0707107 | − | 0.122474i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.50000 | − | 0.866025i | 0.485363 | − | 0.120096i | ||||
\(53\) | −1.00000 | −0.137361 | −0.0686803 | − | 0.997639i | \(-0.521879\pi\) | ||||
−0.0686803 | + | 0.997639i | \(0.521879\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.50000 | − | 2.59808i | −0.202260 | − | 0.350325i | ||||
\(56\) | 2.50000 | − | 4.33013i | 0.334077 | − | 0.578638i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.00000 | + | 3.46410i | −0.262613 | + | 0.454859i | ||||
\(59\) | 6.00000 | − | 10.3923i | 0.781133 | − | 1.35296i | −0.150148 | − | 0.988663i | \(-0.547975\pi\) |
0.931282 | − | 0.364299i | \(-0.118692\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | + | 1.73205i | −0.128037 | + | 0.221766i | −0.922916 | − | 0.385002i | \(-0.874201\pi\) |
0.794879 | + | 0.606768i | \(0.207534\pi\) | |||||||
\(62\) | 1.00000 | + | 1.73205i | 0.127000 | + | 0.219971i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.50000 | − | 2.59808i | −0.310087 | − | 0.322252i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | − | 6.92820i | −0.488678 | − | 0.846415i | 0.511237 | − | 0.859440i | \(-0.329187\pi\) |
−0.999915 | + | 0.0130248i | \(0.995854\pi\) | |||||||
\(68\) | −4.00000 | − | 6.92820i | −0.485071 | − | 0.840168i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.00000 | −0.597614 | ||||||||
\(71\) | 1.00000 | − | 1.73205i | 0.118678 | − | 0.205557i | −0.800566 | − | 0.599245i | \(-0.795468\pi\) |
0.919244 | + | 0.393688i | \(0.128801\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(74\) | 3.50000 | − | 6.06218i | 0.406867 | − | 0.704714i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.50000 | + | 4.33013i | 0.286770 | + | 0.496700i | ||||
\(77\) | −15.0000 | −1.70941 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.00000 | −0.225018 | −0.112509 | − | 0.993651i | \(-0.535889\pi\) | ||||
−0.112509 | + | 0.993651i | \(0.535889\pi\) | |||||||
\(80\) | −0.500000 | − | 0.866025i | −0.0559017 | − | 0.0968246i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.00000 | − | 5.19615i | 0.331295 | − | 0.573819i | ||||
\(83\) | −8.00000 | −0.878114 | −0.439057 | − | 0.898459i | \(-0.644687\pi\) | ||||
−0.439057 | + | 0.898459i | \(0.644687\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.00000 | + | 6.92820i | −0.433861 | + | 0.751469i | ||||
\(86\) | 6.00000 | 0.646997 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.50000 | − | 2.59808i | −0.159901 | − | 0.276956i | ||||
\(89\) | −5.50000 | − | 9.52628i | −0.582999 | − | 1.00978i | −0.995122 | − | 0.0986553i | \(-0.968546\pi\) |
0.412123 | − | 0.911128i | \(-0.364787\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −17.5000 | + | 4.33013i | −1.83450 | + | 0.453921i | ||||
\(92\) | 4.00000 | 0.417029 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.50000 | − | 2.59808i | −0.154713 | − | 0.267971i | ||||
\(95\) | 2.50000 | − | 4.33013i | 0.256495 | − | 0.444262i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(98\) | −9.00000 | + | 15.5885i | −0.909137 | + | 1.57467i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | −4.00000 | − | 6.92820i | −0.398015 | − | 0.689382i | 0.595466 | − | 0.803380i | \(-0.296967\pi\) |
−0.993481 | + | 0.113998i | \(0.963634\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.00000 | −0.689730 | −0.344865 | − | 0.938652i | \(-0.612075\pi\) | ||||
−0.344865 | + | 0.938652i | \(0.612075\pi\) | |||||||
\(104\) | −2.50000 | − | 2.59808i | −0.245145 | − | 0.254762i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.500000 | + | 0.866025i | 0.0485643 | + | 0.0841158i | ||||
\(107\) | −3.00000 | − | 5.19615i | −0.290021 | − | 0.502331i | 0.683793 | − | 0.729676i | \(-0.260329\pi\) |
−0.973814 | + | 0.227345i | \(0.926996\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.0000 | 1.34096 | 0.670478 | − | 0.741929i | \(-0.266089\pi\) | ||||
0.670478 | + | 0.741929i | \(0.266089\pi\) | |||||||
\(110\) | −1.50000 | + | 2.59808i | −0.143019 | + | 0.247717i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −5.00000 | −0.472456 | ||||||||
\(113\) | 4.00000 | − | 6.92820i | 0.376288 | − | 0.651751i | −0.614231 | − | 0.789127i | \(-0.710534\pi\) |
0.990519 | + | 0.137376i | \(0.0438669\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.00000 | − | 3.46410i | −0.186501 | − | 0.323029i | ||||
\(116\) | 4.00000 | 0.371391 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.0000 | −1.10469 | ||||||||
\(119\) | 20.0000 | + | 34.6410i | 1.83340 | + | 3.17554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | 2.00000 | 0.181071 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.00000 | − | 1.73205i | 0.0898027 | − | 0.155543i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.5000 | + | 18.1865i | 0.931724 | + | 1.61379i | 0.780373 | + | 0.625314i | \(0.215029\pi\) |
0.151351 | + | 0.988480i | \(0.451638\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.00000 | + | 3.46410i | −0.0877058 | + | 0.303822i | ||||
\(131\) | 19.0000 | 1.66004 | 0.830019 | − | 0.557735i | \(-0.188330\pi\) | ||||
0.830019 | + | 0.557735i | \(0.188330\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.5000 | − | 21.6506i | −1.08389 | − | 1.87735i | ||||
\(134\) | −4.00000 | + | 6.92820i | −0.345547 | + | 0.598506i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.00000 | + | 6.92820i | −0.342997 | + | 0.594089i | ||||
\(137\) | −6.00000 | + | 10.3923i | −0.512615 | + | 0.887875i | 0.487278 | + | 0.873247i | \(0.337990\pi\) |
−0.999893 | + | 0.0146279i | \(0.995344\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.50000 | + | 6.06218i | −0.296866 | + | 0.514187i | −0.975417 | − | 0.220366i | \(-0.929275\pi\) |
0.678551 | + | 0.734553i | \(0.262608\pi\) | |||||||
\(140\) | 2.50000 | + | 4.33013i | 0.211289 | + | 0.365963i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.00000 | −0.167836 | ||||||||
\(143\) | −3.00000 | + | 10.3923i | −0.250873 | + | 0.869048i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.00000 | − | 3.46410i | −0.166091 | − | 0.287678i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.00000 | −0.575396 | ||||||||
\(149\) | −1.00000 | + | 1.73205i | −0.0819232 | + | 0.141895i | −0.904076 | − | 0.427372i | \(-0.859440\pi\) |
0.822153 | + | 0.569267i | \(0.192773\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.0000 | 1.79033 | 0.895167 | − | 0.445730i | \(-0.147056\pi\) | ||||
0.895167 | + | 0.445730i | \(0.147056\pi\) | |||||||
\(152\) | 2.50000 | − | 4.33013i | 0.202777 | − | 0.351220i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.50000 | + | 12.9904i | 0.604367 | + | 1.04679i | ||||
\(155\) | −2.00000 | −0.160644 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.0000 | 1.19713 | 0.598565 | − | 0.801074i | \(-0.295738\pi\) | ||||
0.598565 | + | 0.801074i | \(0.295738\pi\) | |||||||
\(158\) | 1.00000 | + | 1.73205i | 0.0795557 | + | 0.137795i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.500000 | + | 0.866025i | −0.0395285 | + | 0.0684653i | ||||
\(161\) | −20.0000 | −1.57622 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.0000 | − | 17.3205i | 0.783260 | − | 1.35665i | −0.146772 | − | 0.989170i | \(-0.546888\pi\) |
0.930033 | − | 0.367477i | \(-0.119778\pi\) | |||||||
\(164\) | −6.00000 | −0.468521 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.00000 | + | 6.92820i | 0.310460 | + | 0.537733i | ||||
\(167\) | −11.5000 | − | 19.9186i | −0.889897 | − | 1.54135i | −0.839996 | − | 0.542592i | \(-0.817443\pi\) |
−0.0499004 | − | 0.998754i | \(-0.515890\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.500000 | + | 12.9904i | −0.0384615 | + | 0.999260i | ||||
\(170\) | 8.00000 | 0.613572 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.00000 | − | 5.19615i | −0.228748 | − | 0.396203i | ||||
\(173\) | 2.50000 | − | 4.33013i | 0.190071 | − | 0.329213i | −0.755202 | − | 0.655492i | \(-0.772461\pi\) |
0.945274 | + | 0.326278i | \(0.105795\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.50000 | − | 4.33013i | 0.188982 | − | 0.327327i | ||||
\(176\) | −1.50000 | + | 2.59808i | −0.113067 | + | 0.195837i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.50000 | + | 9.52628i | −0.412242 | + | 0.714025i | ||||
\(179\) | 2.00000 | + | 3.46410i | 0.149487 | + | 0.258919i | 0.931038 | − | 0.364922i | \(-0.118904\pi\) |
−0.781551 | + | 0.623841i | \(0.785571\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 12.5000 | + | 12.9904i | 0.926562 | + | 0.962911i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.00000 | − | 3.46410i | −0.147442 | − | 0.255377i | ||||
\(185\) | 3.50000 | + | 6.06218i | 0.257325 | + | 0.445700i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 24.0000 | 1.75505 | ||||||||
\(188\) | −1.50000 | + | 2.59808i | −0.109399 | + | 0.189484i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.00000 | −0.362738 | ||||||||
\(191\) | 1.00000 | − | 1.73205i | 0.0723575 | − | 0.125327i | −0.827577 | − | 0.561353i | \(-0.810281\pi\) |
0.899934 | + | 0.436026i | \(0.143614\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.0000 | − | 20.7846i | −0.863779 | − | 1.49611i | −0.868255 | − | 0.496119i | \(-0.834758\pi\) |
0.00447566 | − | 0.999990i | \(-0.498575\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 18.0000 | 1.28571 | ||||||||
\(197\) | 1.50000 | + | 2.59808i | 0.106871 | + | 0.185105i | 0.914501 | − | 0.404584i | \(-0.132584\pi\) |
−0.807630 | + | 0.589689i | \(0.799250\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.0000 | + | 19.0526i | −0.779769 | + | 1.35060i | 0.152305 | + | 0.988334i | \(0.451330\pi\) |
−0.932075 | + | 0.362267i | \(0.882003\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.00000 | + | 6.92820i | −0.281439 | + | 0.487467i | ||||
\(203\) | −20.0000 | −1.40372 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.00000 | + | 5.19615i | 0.209529 | + | 0.362915i | ||||
\(206\) | 3.50000 | + | 6.06218i | 0.243857 | + | 0.422372i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.00000 | + | 3.46410i | −0.0693375 | + | 0.240192i | ||||
\(209\) | −15.0000 | −1.03757 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.50000 | + | 12.9904i | 0.516321 | + | 0.894295i | 0.999820 | + | 0.0189499i | \(0.00603229\pi\) |
−0.483499 | + | 0.875345i | \(0.660634\pi\) | |||||||
\(212\) | 0.500000 | − | 0.866025i | 0.0343401 | − | 0.0594789i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.00000 | + | 5.19615i | −0.205076 | + | 0.355202i | ||||
\(215\) | −3.00000 | + | 5.19615i | −0.204598 | + | 0.354375i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.00000 | + | 8.66025i | −0.339422 | + | 0.587896i | ||||
\(218\) | −7.00000 | − | 12.1244i | −0.474100 | − | 0.821165i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.00000 | 0.202260 | ||||||||
\(221\) | 28.0000 | − | 6.92820i | 1.88348 | − | 0.466041i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.50000 | + | 2.59808i | 0.100447 | + | 0.173980i | 0.911869 | − | 0.410481i | \(-0.134639\pi\) |
−0.811422 | + | 0.584461i | \(0.801306\pi\) | |||||||
\(224\) | 2.50000 | + | 4.33013i | 0.167038 | + | 0.289319i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.00000 | −0.532152 | ||||||||
\(227\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.0000 | 0.925146 | 0.462573 | − | 0.886581i | \(-0.346926\pi\) | ||||
0.462573 | + | 0.886581i | \(0.346926\pi\) | |||||||
\(230\) | −2.00000 | + | 3.46410i | −0.131876 | + | 0.228416i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.00000 | − | 3.46410i | −0.131306 | − | 0.227429i | ||||
\(233\) | 14.0000 | 0.917170 | 0.458585 | − | 0.888650i | \(-0.348356\pi\) | ||||
0.458585 | + | 0.888650i | \(0.348356\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.00000 | 0.195698 | ||||||||
\(236\) | 6.00000 | + | 10.3923i | 0.390567 | + | 0.676481i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 20.0000 | − | 34.6410i | 1.29641 | − | 2.24544i | ||||
\(239\) | 18.0000 | 1.16432 | 0.582162 | − | 0.813073i | \(-0.302207\pi\) | ||||
0.582162 | + | 0.813073i | \(0.302207\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.5000 | − | 21.6506i | 0.805196 | − | 1.39464i | −0.110963 | − | 0.993825i | \(-0.535394\pi\) |
0.916159 | − | 0.400815i | \(-0.131273\pi\) | |||||||
\(242\) | −2.00000 | −0.128565 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.00000 | − | 1.73205i | −0.0640184 | − | 0.110883i | ||||
\(245\) | −9.00000 | − | 15.5885i | −0.574989 | − | 0.995910i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −17.5000 | + | 4.33013i | −1.11350 | + | 0.275519i | ||||
\(248\) | −2.00000 | −0.127000 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.500000 | − | 0.866025i | −0.0316228 | − | 0.0547723i | ||||
\(251\) | 7.50000 | − | 12.9904i | 0.473396 | − | 0.819946i | −0.526140 | − | 0.850398i | \(-0.676361\pi\) |
0.999536 | + | 0.0304521i | \(0.00969471\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.00000 | + | 10.3923i | −0.377217 | + | 0.653359i | ||||
\(254\) | 10.5000 | − | 18.1865i | 0.658829 | − | 1.14112i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 14.0000 | + | 24.2487i | 0.873296 | + | 1.51259i | 0.858567 | + | 0.512702i | \(0.171355\pi\) |
0.0147291 | + | 0.999892i | \(0.495311\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 35.0000 | 2.17479 | ||||||||
\(260\) | 3.50000 | − | 0.866025i | 0.217061 | − | 0.0537086i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.50000 | − | 16.4545i | −0.586912 | − | 1.01656i | ||||
\(263\) | −7.50000 | − | 12.9904i | −0.462470 | − | 0.801021i | 0.536614 | − | 0.843828i | \(-0.319703\pi\) |
−0.999083 | + | 0.0428069i | \(0.986370\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.00000 | −0.0614295 | ||||||||
\(266\) | −12.5000 | + | 21.6506i | −0.766424 | + | 1.32749i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.00000 | 0.488678 | ||||||||
\(269\) | 2.00000 | − | 3.46410i | 0.121942 | − | 0.211210i | −0.798591 | − | 0.601874i | \(-0.794421\pi\) |
0.920534 | + | 0.390664i | \(0.127754\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.00000 | − | 3.46410i | −0.121491 | − | 0.210429i | 0.798865 | − | 0.601511i | \(-0.205434\pi\) |
−0.920356 | + | 0.391082i | \(0.872101\pi\) | |||||||
\(272\) | 8.00000 | 0.485071 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.0000 | 0.724947 | ||||||||
\(275\) | −1.50000 | − | 2.59808i | −0.0904534 | − | 0.156670i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.50000 | − | 12.9904i | 0.450631 | − | 0.780516i | −0.547794 | − | 0.836613i | \(-0.684532\pi\) |
0.998425 | + | 0.0560969i | \(0.0178656\pi\) | |||||||
\(278\) | 7.00000 | 0.419832 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.50000 | − | 4.33013i | 0.149404 | − | 0.258775i | ||||
\(281\) | −18.0000 | −1.07379 | −0.536895 | − | 0.843649i | \(-0.680403\pi\) | ||||
−0.536895 | + | 0.843649i | \(0.680403\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.00000 | + | 8.66025i | 0.297219 | + | 0.514799i | 0.975499 | − | 0.220005i | \(-0.0706075\pi\) |
−0.678280 | + | 0.734804i | \(0.737274\pi\) | |||||||
\(284\) | 1.00000 | + | 1.73205i | 0.0593391 | + | 0.102778i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.5000 | − | 2.59808i | 0.620878 | − | 0.153627i | ||||
\(287\) | 30.0000 | 1.77084 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −23.5000 | − | 40.7032i | −1.38235 | − | 2.39431i | ||||
\(290\) | −2.00000 | + | 3.46410i | −0.117444 | + | 0.203419i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.50000 | + | 7.79423i | −0.262893 | + | 0.455344i | −0.967009 | − | 0.254741i | \(-0.918010\pi\) |
0.704117 | + | 0.710084i | \(0.251343\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.00000 | − | 10.3923i | 0.349334 | − | 0.605063i | ||||
\(296\) | 3.50000 | + | 6.06218i | 0.203433 | + | 0.352357i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.00000 | 0.115857 | ||||||||
\(299\) | −4.00000 | + | 13.8564i | −0.231326 | + | 0.801337i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.0000 | + | 25.9808i | 0.864586 | + | 1.49751i | ||||
\(302\) | −11.0000 | − | 19.0526i | −0.632979 | − | 1.09635i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.00000 | −0.286770 | ||||||||
\(305\) | −1.00000 | + | 1.73205i | −0.0572598 | + | 0.0991769i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.00000 | −0.342438 | −0.171219 | − | 0.985233i | \(-0.554771\pi\) | ||||
−0.171219 | + | 0.985233i | \(0.554771\pi\) | |||||||
\(308\) | 7.50000 | − | 12.9904i | 0.427352 | − | 0.740196i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.00000 | + | 1.73205i | 0.0567962 | + | 0.0983739i | ||||
\(311\) | 12.0000 | 0.680458 | 0.340229 | − | 0.940343i | \(-0.389495\pi\) | ||||
0.340229 | + | 0.940343i | \(0.389495\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.00000 | −0.339140 | −0.169570 | − | 0.985518i | \(-0.554238\pi\) | ||||
−0.169570 | + | 0.985518i | \(0.554238\pi\) | |||||||
\(314\) | −7.50000 | − | 12.9904i | −0.423249 | − | 0.733090i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.00000 | − | 1.73205i | 0.0562544 | − | 0.0974355i | ||||
\(317\) | 23.0000 | 1.29181 | 0.645904 | − | 0.763418i | \(-0.276480\pi\) | ||||
0.645904 | + | 0.763418i | \(0.276480\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.00000 | + | 10.3923i | −0.335936 | + | 0.581857i | ||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 10.0000 | + | 17.3205i | 0.557278 | + | 0.965234i | ||||
\(323\) | 20.0000 | + | 34.6410i | 1.11283 | + | 1.92748i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.50000 | − | 2.59808i | −0.138675 | − | 0.144115i | ||||
\(326\) | −20.0000 | −1.10770 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.00000 | + | 5.19615i | 0.165647 | + | 0.286910i | ||||
\(329\) | 7.50000 | − | 12.9904i | 0.413488 | − | 0.716183i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.00000 | + | 3.46410i | −0.109930 | + | 0.190404i | −0.915742 | − | 0.401768i | \(-0.868396\pi\) |
0.805812 | + | 0.592172i | \(0.201729\pi\) | |||||||
\(332\) | 4.00000 | − | 6.92820i | 0.219529 | − | 0.380235i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −11.5000 | + | 19.9186i | −0.629252 | + | 1.08990i | ||||
\(335\) | −4.00000 | − | 6.92820i | −0.218543 | − | 0.378528i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.0000 | 0.762629 | 0.381314 | − | 0.924445i | \(-0.375472\pi\) | ||||
0.381314 | + | 0.924445i | \(0.375472\pi\) | |||||||
\(338\) | 11.5000 | − | 6.06218i | 0.625518 | − | 0.329739i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.00000 | − | 6.92820i | −0.216930 | − | 0.375735i | ||||
\(341\) | 3.00000 | + | 5.19615i | 0.162459 | + | 0.281387i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −55.0000 | −2.96972 | ||||||||
\(344\) | −3.00000 | + | 5.19615i | −0.161749 | + | 0.280158i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.00000 | −0.268802 | ||||||||
\(347\) | −8.00000 | + | 13.8564i | −0.429463 | + | 0.743851i | −0.996826 | − | 0.0796169i | \(-0.974630\pi\) |
0.567363 | + | 0.823468i | \(0.307964\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.00000 | − | 6.92820i | −0.214115 | − | 0.370858i | 0.738883 | − | 0.673833i | \(-0.235353\pi\) |
−0.952998 | + | 0.302975i | \(0.902020\pi\) | |||||||
\(350\) | −5.00000 | −0.267261 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.00000 | 0.159901 | ||||||||
\(353\) | 8.00000 | + | 13.8564i | 0.425797 | + | 0.737502i | 0.996495 | − | 0.0836583i | \(-0.0266604\pi\) |
−0.570697 | + | 0.821160i | \(0.693327\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.00000 | − | 1.73205i | 0.0530745 | − | 0.0919277i | ||||
\(356\) | 11.0000 | 0.582999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.00000 | − | 3.46410i | 0.105703 | − | 0.183083i | ||||
\(359\) | 18.0000 | 0.950004 | 0.475002 | − | 0.879985i | \(-0.342447\pi\) | ||||
0.475002 | + | 0.879985i | \(0.342447\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | − | 5.19615i | −0.157895 | − | 0.273482i | ||||
\(362\) | 1.00000 | + | 1.73205i | 0.0525588 | + | 0.0910346i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.00000 | − | 17.3205i | 0.262071 | − | 0.907841i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.00000 | + | 6.92820i | 0.208798 | + | 0.361649i | 0.951336 | − | 0.308155i | \(-0.0997115\pi\) |
−0.742538 | + | 0.669804i | \(0.766378\pi\) | |||||||
\(368\) | −2.00000 | + | 3.46410i | −0.104257 | + | 0.180579i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.50000 | − | 6.06218i | 0.181956 | − | 0.315158i | ||||
\(371\) | −2.50000 | + | 4.33013i | −0.129794 | + | 0.224809i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.0000 | + | 32.9090i | −0.983783 | + | 1.70396i | −0.336557 | + | 0.941663i | \(0.609263\pi\) |
−0.647225 | + | 0.762299i | \(0.724071\pi\) | |||||||
\(374\) | −12.0000 | − | 20.7846i | −0.620505 | − | 1.07475i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.00000 | 0.154713 | ||||||||
\(377\) | −4.00000 | + | 13.8564i | −0.206010 | + | 0.713641i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.5000 | + | 21.6506i | 0.642082 | + | 1.11212i | 0.984967 | + | 0.172741i | \(0.0552624\pi\) |
−0.342885 | + | 0.939377i | \(0.611404\pi\) | |||||||
\(380\) | 2.50000 | + | 4.33013i | 0.128247 | + | 0.222131i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.00000 | −0.102329 | ||||||||
\(383\) | −14.0000 | + | 24.2487i | −0.715367 | + | 1.23905i | 0.247451 | + | 0.968900i | \(0.420407\pi\) |
−0.962818 | + | 0.270151i | \(0.912926\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −15.0000 | −0.764471 | ||||||||
\(386\) | −12.0000 | + | 20.7846i | −0.610784 | + | 1.05791i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 32.0000 | 1.62246 | 0.811232 | − | 0.584724i | \(-0.198797\pi\) | ||||
0.811232 | + | 0.584724i | \(0.198797\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 32.0000 | 1.61831 | ||||||||
\(392\) | −9.00000 | − | 15.5885i | −0.454569 | − | 0.787336i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.50000 | − | 2.59808i | 0.0755689 | − | 0.130889i | ||||
\(395\) | −2.00000 | −0.100631 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.5000 | + | 21.6506i | −0.627357 | + | 1.08661i | 0.360723 | + | 0.932673i | \(0.382530\pi\) |
−0.988080 | + | 0.153941i | \(0.950803\pi\) | |||||||
\(398\) | 22.0000 | 1.10276 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.500000 | − | 0.866025i | −0.0250000 | − | 0.0433013i | ||||
\(401\) | −9.50000 | − | 16.4545i | −0.474407 | − | 0.821698i | 0.525163 | − | 0.851002i | \(-0.324004\pi\) |
−0.999571 | + | 0.0293039i | \(0.990671\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.00000 | + | 5.19615i | 0.249068 | + | 0.258839i | ||||
\(404\) | 8.00000 | 0.398015 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10.0000 | + | 17.3205i | 0.496292 | + | 0.859602i | ||||
\(407\) | 10.5000 | − | 18.1865i | 0.520466 | − | 0.901473i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.5000 | + | 21.6506i | −0.618085 | + | 1.07056i | 0.371750 | + | 0.928333i | \(0.378758\pi\) |
−0.989835 | + | 0.142222i | \(0.954575\pi\) | |||||||
\(410\) | 3.00000 | − | 5.19615i | 0.148159 | − | 0.256620i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.50000 | − | 6.06218i | 0.172433 | − | 0.298662i | ||||
\(413\) | −30.0000 | − | 51.9615i | −1.47620 | − | 2.55686i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.00000 | −0.392705 | ||||||||
\(416\) | 3.50000 | − | 0.866025i | 0.171602 | − | 0.0424604i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.50000 | + | 12.9904i | 0.366837 | + | 0.635380i | ||||
\(419\) | −6.00000 | − | 10.3923i | −0.293119 | − | 0.507697i | 0.681426 | − | 0.731887i | \(-0.261360\pi\) |
−0.974546 | + | 0.224189i | \(0.928027\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.0000 | 0.584844 | 0.292422 | − | 0.956289i | \(-0.405539\pi\) | ||||
0.292422 | + | 0.956289i | \(0.405539\pi\) | |||||||
\(422\) | 7.50000 | − | 12.9904i | 0.365094 | − | 0.632362i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.00000 | −0.0485643 | ||||||||
\(425\) | −4.00000 | + | 6.92820i | −0.194029 | + | 0.336067i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.00000 | + | 8.66025i | 0.241967 | + | 0.419099i | ||||
\(428\) | 6.00000 | 0.290021 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.00000 | 0.289346 | ||||||||
\(431\) | 6.00000 | + | 10.3923i | 0.289010 | + | 0.500580i | 0.973574 | − | 0.228373i | \(-0.0733406\pi\) |
−0.684564 | + | 0.728953i | \(0.740007\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.00000 | + | 13.8564i | −0.384455 | + | 0.665896i | −0.991693 | − | 0.128624i | \(-0.958944\pi\) |
0.607238 | + | 0.794520i | \(0.292277\pi\) | |||||||
\(434\) | 10.0000 | 0.480015 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.00000 | + | 12.1244i | −0.335239 | + | 0.580651i | ||||
\(437\) | −20.0000 | −0.956730 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.00000 | − | 8.66025i | −0.238637 | − | 0.413331i | 0.721686 | − | 0.692220i | \(-0.243367\pi\) |
−0.960323 | + | 0.278889i | \(0.910034\pi\) | |||||||
\(440\) | −1.50000 | − | 2.59808i | −0.0715097 | − | 0.123858i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −20.0000 | − | 20.7846i | −0.951303 | − | 0.988623i | ||||
\(443\) | −6.00000 | −0.285069 | −0.142534 | − | 0.989790i | \(-0.545525\pi\) | ||||
−0.142534 | + | 0.989790i | \(0.545525\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.50000 | − | 9.52628i | −0.260725 | − | 0.451589i | ||||
\(446\) | 1.50000 | − | 2.59808i | 0.0710271 | − | 0.123022i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.50000 | − | 4.33013i | 0.118114 | − | 0.204579i | ||||
\(449\) | −13.5000 | + | 23.3827i | −0.637104 | + | 1.10350i | 0.348961 | + | 0.937137i | \(0.386535\pi\) |
−0.986065 | + | 0.166360i | \(0.946799\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.00000 | − | 15.5885i | 0.423793 | − | 0.734032i | ||||
\(452\) | 4.00000 | + | 6.92820i | 0.188144 | + | 0.325875i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −17.5000 | + | 4.33013i | −0.820413 | + | 0.202999i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.0000 | − | 25.9808i | −0.701670 | − | 1.21533i | −0.967880 | − | 0.251414i | \(-0.919105\pi\) |
0.266209 | − | 0.963915i | \(-0.414229\pi\) | |||||||
\(458\) | −7.00000 | − | 12.1244i | −0.327089 | − | 0.566534i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.00000 | 0.186501 | ||||||||
\(461\) | 4.00000 | − | 6.92820i | 0.186299 | − | 0.322679i | −0.757715 | − | 0.652586i | \(-0.773684\pi\) |
0.944013 | + | 0.329907i | \(0.107017\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.00000 | 0.371792 | 0.185896 | − | 0.982569i | \(-0.440481\pi\) | ||||
0.185896 | + | 0.982569i | \(0.440481\pi\) | |||||||
\(464\) | −2.00000 | + | 3.46410i | −0.0928477 | + | 0.160817i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.00000 | − | 12.1244i | −0.324269 | − | 0.561650i | ||||
\(467\) | 24.0000 | 1.11059 | 0.555294 | − | 0.831654i | \(-0.312606\pi\) | ||||
0.555294 | + | 0.831654i | \(0.312606\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −40.0000 | −1.84703 | ||||||||
\(470\) | −1.50000 | − | 2.59808i | −0.0691898 | − | 0.119840i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.00000 | − | 10.3923i | 0.276172 | − | 0.478345i | ||||
\(473\) | 18.0000 | 0.827641 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.50000 | − | 4.33013i | 0.114708 | − | 0.198680i | ||||
\(476\) | −40.0000 | −1.83340 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −9.00000 | − | 15.5885i | −0.411650 | − | 0.712999i | ||||
\(479\) | −14.0000 | − | 24.2487i | −0.639676 | − | 1.10795i | −0.985504 | − | 0.169654i | \(-0.945735\pi\) |
0.345827 | − | 0.938298i | \(-0.387598\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.00000 | − | 24.2487i | 0.319173 | − | 1.10565i | ||||
\(482\) | −25.0000 | −1.13872 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | + | 1.73205i | 0.0454545 | + | 0.0787296i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.5000 | + | 32.0429i | −0.838315 | + | 1.45200i | 0.0529875 | + | 0.998595i | \(0.483126\pi\) |
−0.891303 | + | 0.453409i | \(0.850208\pi\) | |||||||
\(488\) | −1.00000 | + | 1.73205i | −0.0452679 | + | 0.0784063i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −9.00000 | + | 15.5885i | −0.406579 | + | 0.704215i | ||||
\(491\) | 10.5000 | + | 18.1865i | 0.473858 | + | 0.820747i | 0.999552 | − | 0.0299272i | \(-0.00952753\pi\) |
−0.525694 | + | 0.850674i | \(0.676194\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 32.0000 | 1.44121 | ||||||||
\(494\) | 12.5000 | + | 12.9904i | 0.562402 | + | 0.584465i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.00000 | + | 1.73205i | 0.0449013 | + | 0.0777714i | ||||
\(497\) | −5.00000 | − | 8.66025i | −0.224281 | − | 0.388465i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.00000 | 0.179065 | 0.0895323 | − | 0.995984i | \(-0.471463\pi\) | ||||
0.0895323 | + | 0.995984i | \(0.471463\pi\) | |||||||
\(500\) | −0.500000 | + | 0.866025i | −0.0223607 | + | 0.0387298i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −15.0000 | −0.669483 | ||||||||
\(503\) | −5.50000 | + | 9.52628i | −0.245233 | + | 0.424756i | −0.962197 | − | 0.272354i | \(-0.912198\pi\) |
0.716964 | + | 0.697110i | \(0.245531\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.00000 | − | 6.92820i | −0.177998 | − | 0.308301i | ||||
\(506\) | 12.0000 | 0.533465 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −21.0000 | −0.931724 | ||||||||
\(509\) | 5.00000 | + | 8.66025i | 0.221621 | + | 0.383859i | 0.955300 | − | 0.295637i | \(-0.0955319\pi\) |
−0.733679 | + | 0.679496i | \(0.762199\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 14.0000 | − | 24.2487i | 0.617514 | − | 1.06956i | ||||
\(515\) | −7.00000 | −0.308457 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.50000 | − | 7.79423i | −0.197910 | − | 0.342790i | ||||
\(518\) | −17.5000 | − | 30.3109i | −0.768906 | − | 1.33178i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.50000 | − | 2.59808i | −0.109632 | − | 0.113933i | ||||
\(521\) | −5.00000 | −0.219054 | −0.109527 | − | 0.993984i | \(-0.534934\pi\) | ||||
−0.109527 | + | 0.993984i | \(0.534934\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.00000 | + | 8.66025i | 0.218635 | + | 0.378686i | 0.954391 | − | 0.298560i | \(-0.0965063\pi\) |
−0.735756 | + | 0.677247i | \(0.763173\pi\) | |||||||
\(524\) | −9.50000 | + | 16.4545i | −0.415009 | + | 0.718817i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.50000 | + | 12.9904i | −0.327016 | + | 0.566408i | ||||
\(527\) | 8.00000 | − | 13.8564i | 0.348485 | − | 0.603595i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | − | 6.06218i | 0.152174 | − | 0.263573i | ||||
\(530\) | 0.500000 | + | 0.866025i | 0.0217186 | + | 0.0376177i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 25.0000 | 1.08389 | ||||||||
\(533\) | 6.00000 | − | 20.7846i | 0.259889 | − | 0.900281i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.00000 | − | 5.19615i | −0.129701 | − | 0.224649i | ||||
\(536\) | −4.00000 | − | 6.92820i | −0.172774 | − | 0.299253i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.00000 | −0.172452 | ||||||||
\(539\) | −27.0000 | + | 46.7654i | −1.16297 | + | 2.01433i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.0000 | 1.46177 | 0.730887 | − | 0.682498i | \(-0.239107\pi\) | ||||
0.730887 | + | 0.682498i | \(0.239107\pi\) | |||||||
\(542\) | −2.00000 | + | 3.46410i | −0.0859074 | + | 0.148796i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.00000 | − | 6.92820i | −0.171499 | − | 0.297044i | ||||
\(545\) | 14.0000 | 0.599694 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.00000 | 0.256541 | 0.128271 | − | 0.991739i | \(-0.459057\pi\) | ||||
0.128271 | + | 0.991739i | \(0.459057\pi\) | |||||||
\(548\) | −6.00000 | − | 10.3923i | −0.256307 | − | 0.443937i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.50000 | + | 2.59808i | −0.0639602 | + | 0.110782i | ||||
\(551\) | −20.0000 | −0.852029 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.00000 | + | 8.66025i | −0.212622 | + | 0.368271i | ||||
\(554\) | −15.0000 | −0.637289 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.50000 | − | 6.06218i | −0.148433 | − | 0.257094i | ||||
\(557\) | 7.50000 | + | 12.9904i | 0.317785 | + | 0.550420i | 0.980026 | − | 0.198871i | \(-0.0637276\pi\) |
−0.662240 | + | 0.749291i | \(0.730394\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.0000 | − | 5.19615i | 0.888205 | − | 0.219774i | ||||
\(560\) | −5.00000 | −0.211289 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.00000 | + | 15.5885i | 0.379642 | + | 0.657559i | ||||
\(563\) | 18.0000 | − | 31.1769i | 0.758610 | − | 1.31395i | −0.184950 | − | 0.982748i | \(-0.559212\pi\) |
0.943560 | − | 0.331202i | \(-0.107454\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.00000 | − | 6.92820i | 0.168281 | − | 0.291472i | ||||
\(566\) | 5.00000 | − | 8.66025i | 0.210166 | − | 0.364018i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.00000 | − | 1.73205i | 0.0419591 | − | 0.0726752i | ||||
\(569\) | −7.50000 | − | 12.9904i | −0.314416 | − | 0.544585i | 0.664897 | − | 0.746935i | \(-0.268475\pi\) |
−0.979313 | + | 0.202350i | \(0.935142\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.0000 | −1.38101 | −0.690504 | − | 0.723329i | \(-0.742611\pi\) | ||||
−0.690504 | + | 0.723329i | \(0.742611\pi\) | |||||||
\(572\) | −7.50000 | − | 7.79423i | −0.313591 | − | 0.325893i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −15.0000 | − | 25.9808i | −0.626088 | − | 1.08442i | ||||
\(575\) | −2.00000 | − | 3.46410i | −0.0834058 | − | 0.144463i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.00000 | 0.0832611 | 0.0416305 | − | 0.999133i | \(-0.486745\pi\) | ||||
0.0416305 | + | 0.999133i | \(0.486745\pi\) | |||||||
\(578\) | −23.5000 | + | 40.7032i | −0.977471 | + | 1.69303i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.00000 | 0.166091 | ||||||||
\(581\) | −20.0000 | + | 34.6410i | −0.829740 | + | 1.43715i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.50000 | + | 2.59808i | 0.0621237 | + | 0.107601i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.00000 | 0.371787 | ||||||||
\(587\) | 9.00000 | + | 15.5885i | 0.371470 | + | 0.643404i | 0.989792 | − | 0.142520i | \(-0.0455206\pi\) |
−0.618322 | + | 0.785925i | \(0.712187\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.00000 | + | 8.66025i | −0.206021 | + | 0.356840i | ||||
\(590\) | −12.0000 | −0.494032 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.50000 | − | 6.06218i | 0.143849 | − | 0.249154i | ||||
\(593\) | −20.0000 | −0.821302 | −0.410651 | − | 0.911793i | \(-0.634698\pi\) | ||||
−0.410651 | + | 0.911793i | \(0.634698\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20.0000 | + | 34.6410i | 0.819920 | + | 1.42014i | ||||
\(596\) | −1.00000 | − | 1.73205i | −0.0409616 | − | 0.0709476i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 14.0000 | − | 3.46410i | 0.572503 | − | 0.141658i | ||||
\(599\) | −34.0000 | −1.38920 | −0.694601 | − | 0.719395i | \(-0.744419\pi\) | ||||
−0.694601 | + | 0.719395i | \(0.744419\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.5000 | − | 32.0429i | −0.754631 | − | 1.30706i | −0.945558 | − | 0.325455i | \(-0.894483\pi\) |
0.190927 | − | 0.981604i | \(-0.438851\pi\) | |||||||
\(602\) | 15.0000 | − | 25.9808i | 0.611354 | − | 1.05890i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −11.0000 | + | 19.0526i | −0.447584 | + | 0.775238i | ||||
\(605\) | 1.00000 | − | 1.73205i | 0.0406558 | − | 0.0704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.5000 | − | 25.1147i | 0.588537 | − | 1.01938i | −0.405887 | − | 0.913923i | \(-0.633038\pi\) |
0.994424 | − | 0.105453i | \(-0.0336291\pi\) | |||||||
\(608\) | 2.50000 | + | 4.33013i | 0.101388 | + | 0.175610i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.00000 | 0.0809776 | ||||||||
\(611\) | −7.50000 | − | 7.79423i | −0.303418 | − | 0.315321i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.5000 | − | 21.6506i | −0.504870 | − | 0.874461i | −0.999984 | − | 0.00563283i | \(-0.998207\pi\) |
0.495114 | − | 0.868828i | \(-0.335126\pi\) | |||||||
\(614\) | 3.00000 | + | 5.19615i | 0.121070 | + | 0.209700i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −15.0000 | −0.604367 | ||||||||
\(617\) | −7.00000 | + | 12.1244i | −0.281809 | + | 0.488108i | −0.971830 | − | 0.235681i | \(-0.924268\pi\) |
0.690021 | + | 0.723789i | \(0.257601\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.0000 | 0.683288 | 0.341644 | − | 0.939829i | \(-0.389016\pi\) | ||||
0.341644 | + | 0.939829i | \(0.389016\pi\) | |||||||
\(620\) | 1.00000 | − | 1.73205i | 0.0401610 | − | 0.0695608i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6.00000 | − | 10.3923i | −0.240578 | − | 0.416693i | ||||
\(623\) | −55.0000 | −2.20353 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 3.00000 | + | 5.19615i | 0.119904 | + | 0.207680i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.50000 | + | 12.9904i | −0.299283 | + | 0.518373i | ||||
\(629\) | −56.0000 | −2.23287 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.00000 | + | 10.3923i | −0.238856 | + | 0.413711i | −0.960386 | − | 0.278672i | \(-0.910106\pi\) |
0.721530 | + | 0.692383i | \(0.243439\pi\) | |||||||
\(632\) | −2.00000 | −0.0795557 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −11.5000 | − | 19.9186i | −0.456723 | − | 0.791068i | ||||
\(635\) | 10.5000 | + | 18.1865i | 0.416680 | + | 0.721711i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.0000 | + | 62.3538i | −0.713186 | + | 2.47055i | ||||
\(638\) | 12.0000 | 0.475085 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.500000 | − | 0.866025i | −0.0197642 | − | 0.0342327i | ||||
\(641\) | 13.5000 | − | 23.3827i | 0.533218 | − | 0.923561i | −0.466029 | − | 0.884769i | \(-0.654316\pi\) |
0.999247 | − | 0.0387913i | \(-0.0123508\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.0000 | − | 38.1051i | 0.867595 | − | 1.50272i | 0.00314839 | − | 0.999995i | \(-0.498998\pi\) |
0.864447 | − | 0.502724i | \(-0.167669\pi\) | |||||||
\(644\) | 10.0000 | − | 17.3205i | 0.394055 | − | 0.682524i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 20.0000 | − | 34.6410i | 0.786889 | − | 1.36293i | ||||
\(647\) | 1.50000 | + | 2.59808i | 0.0589711 | + | 0.102141i | 0.894004 | − | 0.448059i | \(-0.147885\pi\) |
−0.835033 | + | 0.550200i | \(0.814551\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −36.0000 | −1.41312 | ||||||||
\(650\) | −1.00000 | + | 3.46410i | −0.0392232 | + | 0.135873i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.0000 | + | 17.3205i | 0.391630 | + | 0.678323i | ||||
\(653\) | 13.5000 | + | 23.3827i | 0.528296 | + | 0.915035i | 0.999456 | + | 0.0329874i | \(0.0105021\pi\) |
−0.471160 | + | 0.882048i | \(0.656165\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19.0000 | 0.742391 | ||||||||
\(656\) | 3.00000 | − | 5.19615i | 0.117130 | − | 0.202876i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −15.0000 | −0.584761 | ||||||||
\(659\) | 18.0000 | − | 31.1769i | 0.701180 | − | 1.21448i | −0.266872 | − | 0.963732i | \(-0.585990\pi\) |
0.968052 | − | 0.250748i | \(-0.0806766\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.00000 | + | 8.66025i | 0.194477 | + | 0.336845i | 0.946729 | − | 0.322031i | \(-0.104366\pi\) |
−0.752252 | + | 0.658876i | \(0.771032\pi\) | |||||||
\(662\) | 4.00000 | 0.155464 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.00000 | −0.310460 | ||||||||
\(665\) | −12.5000 | − | 21.6506i | −0.484729 | − | 0.839576i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.00000 | + | 13.8564i | −0.309761 | + | 0.536522i | ||||
\(668\) | 23.0000 | 0.889897 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.00000 | + | 6.92820i | −0.154533 | + | 0.267660i | ||||
\(671\) | 6.00000 | 0.231627 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.0000 | + | 27.7128i | 0.616755 | + | 1.06825i | 0.990074 | + | 0.140548i | \(0.0448863\pi\) |
−0.373319 | + | 0.927703i | \(0.621780\pi\) | |||||||
\(674\) | −7.00000 | − | 12.1244i | −0.269630 | − | 0.467013i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.0000 | − | 6.92820i | −0.423077 | − | 0.266469i | ||||
\(677\) | 22.0000 | 0.845529 | 0.422764 | − | 0.906240i | \(-0.361060\pi\) | ||||
0.422764 | + | 0.906240i | \(0.361060\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −4.00000 | + | 6.92820i | −0.153393 | + | 0.265684i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.00000 | − | 5.19615i | 0.114876 | − | 0.198971i | ||||
\(683\) | 15.0000 | − | 25.9808i | 0.573959 | − | 0.994126i | −0.422195 | − | 0.906505i | \(-0.638740\pi\) |
0.996154 | − | 0.0876211i | \(-0.0279265\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.00000 | + | 10.3923i | −0.229248 | + | 0.397070i | ||||
\(686\) | 27.5000 | + | 47.6314i | 1.04995 | + | 1.81858i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.00000 | 0.228748 | ||||||||
\(689\) | 2.50000 | + | 2.59808i | 0.0952424 | + | 0.0989788i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.50000 | − | 14.7224i | −0.323355 | − | 0.560068i | 0.657823 | − | 0.753173i | \(-0.271478\pi\) |
−0.981178 | + | 0.193105i | \(0.938144\pi\) | |||||||
\(692\) | 2.50000 | + | 4.33013i | 0.0950357 | + | 0.164607i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16.0000 | 0.607352 | ||||||||
\(695\) | −3.50000 | + | 6.06218i | −0.132763 | + | 0.229952i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −48.0000 | −1.81813 | ||||||||
\(698\) | −4.00000 | + | 6.92820i | −0.151402 | + | 0.262236i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.50000 | + | 4.33013i | 0.0944911 | + | 0.163663i | ||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 35.0000 | 1.32005 | ||||||||
\(704\) | −1.50000 | − | 2.59808i | −0.0565334 | − | 0.0979187i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.00000 | − | 13.8564i | 0.301084 | − | 0.521493i | ||||
\(707\) | −40.0000 | −1.50435 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.0000 | + | 27.7128i | −0.600893 | + | 1.04078i | 0.391794 | + | 0.920053i | \(0.371855\pi\) |
−0.992686 | + | 0.120723i | \(0.961479\pi\) | |||||||
\(710\) | −2.00000 | −0.0750587 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.50000 | − | 9.52628i | −0.206121 | − | 0.357012i | ||||
\(713\) | 4.00000 | + | 6.92820i | 0.149801 | + | 0.259463i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.00000 | + | 10.3923i | −0.112194 | + | 0.388650i | ||||
\(716\) | −4.00000 | −0.149487 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.00000 | − | 15.5885i | −0.335877 | − | 0.581756i | ||||
\(719\) | −10.0000 | + | 17.3205i | −0.372937 | + | 0.645946i | −0.990016 | − | 0.140955i | \(-0.954983\pi\) |
0.617079 | + | 0.786901i | \(0.288316\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.5000 | + | 30.3109i | −0.651734 | + | 1.12884i | ||||
\(722\) | −3.00000 | + | 5.19615i | −0.111648 | + | 0.193381i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.00000 | − | 1.73205i | 0.0371647 | − | 0.0643712i | ||||
\(725\) | −2.00000 | − | 3.46410i | −0.0742781 | − | 0.128654i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.0000 | −0.407967 | −0.203984 | − | 0.978974i | \(-0.565389\pi\) | ||||
−0.203984 | + | 0.978974i | \(0.565389\pi\) | |||||||
\(728\) | −17.5000 | + | 4.33013i | −0.648593 | + | 0.160485i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24.0000 | − | 41.5692i | −0.887672 | − | 1.53749i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −43.0000 | −1.58824 | −0.794121 | − | 0.607760i | \(-0.792068\pi\) | ||||
−0.794121 | + | 0.607760i | \(0.792068\pi\) | |||||||
\(734\) | 4.00000 | − | 6.92820i | 0.147643 | − | 0.255725i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.00000 | 0.147442 | ||||||||
\(737\) | −12.0000 | + | 20.7846i | −0.442026 | + | 0.765611i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.50000 | − | 16.4545i | −0.349463 | − | 0.605288i | 0.636691 | − | 0.771119i | \(-0.280303\pi\) |
−0.986154 | + | 0.165831i | \(0.946969\pi\) | |||||||
\(740\) | −7.00000 | −0.257325 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.00000 | 0.183556 | ||||||||
\(743\) | −8.00000 | − | 13.8564i | −0.293492 | − | 0.508342i | 0.681141 | − | 0.732152i | \(-0.261484\pi\) |
−0.974633 | + | 0.223810i | \(0.928151\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.00000 | + | 1.73205i | −0.0366372 | + | 0.0634574i | ||||
\(746\) | 38.0000 | 1.39128 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −12.0000 | + | 20.7846i | −0.438763 | + | 0.759961i | ||||
\(749\) | −30.0000 | −1.09618 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.00000 | + | 6.92820i | 0.145962 | + | 0.252814i | 0.929731 | − | 0.368238i | \(-0.120039\pi\) |
−0.783769 | + | 0.621052i | \(0.786706\pi\) | |||||||
\(752\) | −1.50000 | − | 2.59808i | −0.0546994 | − | 0.0947421i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 14.0000 | − | 3.46410i | 0.509850 | − | 0.126155i | ||||
\(755\) | 22.0000 | 0.800662 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.50000 | − | 14.7224i | −0.308938 | − | 0.535096i | 0.669193 | − | 0.743089i | \(-0.266640\pi\) |
−0.978130 | + | 0.207993i | \(0.933307\pi\) | |||||||
\(758\) | 12.5000 | − | 21.6506i | 0.454020 | − | 0.786386i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.50000 | − | 4.33013i | 0.0906845 | − | 0.157070i | ||||
\(761\) | 4.50000 | − | 7.79423i | 0.163125 | − | 0.282541i | −0.772863 | − | 0.634573i | \(-0.781176\pi\) |
0.935988 | + | 0.352032i | \(0.114509\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 35.0000 | − | 60.6218i | 1.26709 | − | 2.19466i | ||||
\(764\) | 1.00000 | + | 1.73205i | 0.0361787 | + | 0.0626634i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 28.0000 | 1.01168 | ||||||||
\(767\) | −42.0000 | + | 10.3923i | −1.51653 | + | 0.375244i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.0000 | + | 29.4449i | 0.613036 | + | 1.06181i | 0.990726 | + | 0.135877i | \(0.0433852\pi\) |
−0.377690 | + | 0.925932i | \(0.623282\pi\) | |||||||
\(770\) | 7.50000 | + | 12.9904i | 0.270281 | + | 0.468141i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 24.0000 | 0.863779 | ||||||||
\(773\) | 0.500000 | − | 0.866025i | 0.0179838 | − | 0.0311488i | −0.856893 | − | 0.515494i | \(-0.827609\pi\) |
0.874877 | + | 0.484345i | \(0.160942\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.00000 | −0.0718421 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −16.0000 | − | 27.7128i | −0.573628 | − | 0.993552i | ||||
\(779\) | 30.0000 | 1.07486 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.00000 | −0.214697 | ||||||||
\(782\) | −16.0000 | − | 27.7128i | −0.572159 | − | 0.991008i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −9.00000 | + | 15.5885i | −0.321429 | + | 0.556731i | ||||
\(785\) | 15.0000 | 0.535373 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.0000 | − | 24.2487i | 0.499046 | − | 0.864373i | −0.500953 | − | 0.865474i | \(-0.667017\pi\) |
0.999999 | + | 0.00110111i | \(0.000350496\pi\) | |||||||
\(788\) | −3.00000 | −0.106871 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.00000 | + | 1.73205i | 0.0355784 | + | 0.0616236i | ||||
\(791\) | −20.0000 | − | 34.6410i | −0.711118 | − | 1.23169i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.00000 | − | 1.73205i | 0.248577 | − | 0.0615069i | ||||
\(794\) | 25.0000 | 0.887217 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.0000 | − | 19.0526i | −0.389885 | − | 0.675300i | ||||
\(797\) | −5.00000 | + | 8.66025i | −0.177109 | + | 0.306762i | −0.940889 | − | 0.338715i | \(-0.890008\pi\) |
0.763780 | + | 0.645477i | \(0.223341\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.0000 | + | 20.7846i | −0.424529 | + | 0.735307i | ||||
\(800\) | −0.500000 | + | 0.866025i | −0.0176777 | + | 0.0306186i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9.50000 | + | 16.4545i | −0.335457 | + | 0.581028i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −20.0000 | −0.704907 | ||||||||
\(806\) | 2.00000 | − | 6.92820i | 0.0704470 | − | 0.244036i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.00000 | − | 6.92820i | −0.140720 | − | 0.243733i | ||||
\(809\) | −13.0000 | − | 22.5167i | −0.457056 | − | 0.791644i | 0.541748 | − | 0.840541i | \(-0.317763\pi\) |
−0.998804 | + | 0.0488972i | \(0.984429\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.0000 | 0.877869 | 0.438934 | − | 0.898519i | \(-0.355356\pi\) | ||||
0.438934 | + | 0.898519i | \(0.355356\pi\) | |||||||
\(812\) | 10.0000 | − | 17.3205i | 0.350931 | − | 0.607831i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −21.0000 | −0.736050 | ||||||||
\(815\) | 10.0000 | − | 17.3205i | 0.350285 | − | 0.606711i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.0000 | + | 25.9808i | 0.524784 | + | 0.908952i | ||||
\(818\) | 25.0000 | 0.874105 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.00000 | −0.209529 | ||||||||
\(821\) | −11.0000 | − | 19.0526i | −0.383903 | − | 0.664939i | 0.607714 | − | 0.794156i | \(-0.292087\pi\) |
−0.991616 | + | 0.129217i | \(0.958754\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.5000 | − | 30.3109i | 0.610012 | − | 1.05657i | −0.381226 | − | 0.924482i | \(-0.624498\pi\) |
0.991238 | − | 0.132089i | \(-0.0421686\pi\) | |||||||
\(824\) | −7.00000 | −0.243857 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −30.0000 | + | 51.9615i | −1.04383 | + | 1.80797i | ||||
\(827\) | −6.00000 | −0.208640 | −0.104320 | − | 0.994544i | \(-0.533267\pi\) | ||||
−0.104320 | + | 0.994544i | \(0.533267\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.00000 | + | 13.8564i | 0.277851 | + | 0.481253i | 0.970851 | − | 0.239686i | \(-0.0770444\pi\) |
−0.692999 | + | 0.720938i | \(0.743711\pi\) | |||||||
\(830\) | 4.00000 | + | 6.92820i | 0.138842 | + | 0.240481i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.50000 | − | 2.59808i | −0.0866719 | − | 0.0900721i | ||||
\(833\) | 144.000 | 4.98930 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.5000 | − | 19.9186i | −0.397974 | − | 0.689311i | ||||
\(836\) | 7.50000 | − | 12.9904i | 0.259393 | − | 0.449282i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.00000 | + | 10.3923i | −0.207267 | + | 0.358996i | ||||
\(839\) | −7.00000 | + | 12.1244i | −0.241667 | + | 0.418579i | −0.961189 | − | 0.275890i | \(-0.911027\pi\) |
0.719522 | + | 0.694469i | \(0.244361\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.50000 | − | 11.2583i | 0.224138 | − | 0.388218i | ||||
\(842\) | −6.00000 | − | 10.3923i | −0.206774 | − | 0.358142i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −15.0000 | −0.516321 | ||||||||
\(845\) | −0.500000 | + | 12.9904i | −0.0172005 | + | 0.446883i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.00000 | − | 8.66025i | −0.171802 | − | 0.297570i | ||||
\(848\) | 0.500000 | + | 0.866025i | 0.0171701 | + | 0.0297394i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 8.00000 | 0.274398 | ||||||||
\(851\) | 14.0000 | − | 24.2487i | 0.479914 | − | 0.831235i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.0000 | −0.890223 | −0.445112 | − | 0.895475i | \(-0.646836\pi\) | ||||
−0.445112 | + | 0.895475i | \(0.646836\pi\) | |||||||
\(854\) | 5.00000 | − | 8.66025i | 0.171096 | − | 0.296348i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.00000 | − | 5.19615i | −0.102538 | − | 0.177601i | ||||
\(857\) | −38.0000 | −1.29806 | −0.649028 | − | 0.760765i | \(-0.724824\pi\) | ||||
−0.649028 | + | 0.760765i | \(0.724824\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.00000 | 0.102359 | 0.0511793 | − | 0.998689i | \(-0.483702\pi\) | ||||
0.0511793 | + | 0.998689i | \(0.483702\pi\) | |||||||
\(860\) | −3.00000 | − | 5.19615i | −0.102299 | − | 0.177187i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.00000 | − | 10.3923i | 0.204361 | − | 0.353963i | ||||
\(863\) | 24.0000 | 0.816970 | 0.408485 | − | 0.912765i | \(-0.366057\pi\) | ||||
0.408485 | + | 0.912765i | \(0.366057\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.50000 | − | 4.33013i | 0.0850026 | − | 0.147229i | ||||
\(866\) | 16.0000 | 0.543702 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.00000 | − | 8.66025i | −0.169711 | − | 0.293948i | ||||
\(869\) | 3.00000 | + | 5.19615i | 0.101768 | + | 0.176267i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.00000 | + | 27.7128i | −0.271070 | + | 0.939013i | ||||
\(872\) | 14.0000 | 0.474100 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 10.0000 | + | 17.3205i | 0.338255 | + | 0.585875i | ||||
\(875\) | 2.50000 | − | 4.33013i | 0.0845154 | − | 0.146385i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.0000 | − | 46.7654i | 0.911725 | − | 1.57915i | 0.100099 | − | 0.994977i | \(-0.468084\pi\) |
0.811626 | − | 0.584177i | \(-0.198583\pi\) | |||||||
\(878\) | −5.00000 | + | 8.66025i | −0.168742 | + | 0.292269i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.50000 | + | 2.59808i | −0.0505650 | + | 0.0875811i | ||||
\(881\) | −7.50000 | − | 12.9904i | −0.252681 | − | 0.437657i | 0.711582 | − | 0.702603i | \(-0.247979\pi\) |
−0.964263 | + | 0.264946i | \(0.914646\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.0000 | 1.00958 | 0.504790 | − | 0.863242i | \(-0.331570\pi\) | ||||
0.504790 | + | 0.863242i | \(0.331570\pi\) | |||||||
\(884\) | −8.00000 | + | 27.7128i | −0.269069 | + | 0.932083i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.00000 | + | 5.19615i | 0.100787 | + | 0.174568i | ||||
\(887\) | 20.5000 | + | 35.5070i | 0.688323 | + | 1.19221i | 0.972380 | + | 0.233403i | \(0.0749860\pi\) |
−0.284058 | + | 0.958807i | \(0.591681\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 105.000 | 3.52159 | ||||||||
\(890\) | −5.50000 | + | 9.52628i | −0.184360 | + | 0.319322i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.00000 | −0.100447 | ||||||||
\(893\) | 7.50000 | − | 12.9904i | 0.250978 | − | 0.434707i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.00000 | + | 3.46410i | 0.0668526 | + | 0.115792i | ||||
\(896\) | −5.00000 | −0.167038 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 27.0000 | 0.901002 | ||||||||
\(899\) | 4.00000 | + | 6.92820i | 0.133407 | + | 0.231069i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.00000 | − | 6.92820i | 0.133259 | − | 0.230812i | ||||
\(902\) | −18.0000 | −0.599334 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.00000 | − | 6.92820i | 0.133038 | − | 0.230429i | ||||
\(905\) | −2.00000 | −0.0664822 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.00000 | − | 8.66025i | −0.166022 | − | 0.287559i | 0.770996 | − | 0.636841i | \(-0.219759\pi\) |
−0.937018 | + | 0.349281i | \(0.886426\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 12.5000 | + | 12.9904i | 0.414371 | + | 0.430627i | ||||
\(911\) | 20.0000 | 0.662630 | 0.331315 | − | 0.943520i | \(-0.392508\pi\) | ||||
0.331315 | + | 0.943520i | \(0.392508\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.0000 | + | 20.7846i | 0.397142 | + | 0.687870i | ||||
\(914\) | −15.0000 | + | 25.9808i | −0.496156 | + | 0.859367i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.00000 | + | 12.1244i | −0.231287 | + | 0.400600i | ||||
\(917\) | 47.5000 | − | 82.2724i | 1.56859 | − | 2.71687i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.00000 | − | 1.73205i | 0.0329870 | − | 0.0571351i | −0.849061 | − | 0.528295i | \(-0.822831\pi\) |
0.882048 | + | 0.471160i | \(0.156165\pi\) | |||||||
\(920\) | −2.00000 | − | 3.46410i | −0.0659380 | − | 0.114208i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −8.00000 | −0.263466 | ||||||||
\(923\) | −7.00000 | + | 1.73205i | −0.230408 | + | 0.0570111i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.50000 | + | 6.06218i | 0.115079 | + | 0.199323i | ||||
\(926\) | −4.00000 | − | 6.92820i | −0.131448 | − | 0.227675i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.00000 | 0.131306 | ||||||||
\(929\) | 1.00000 | − | 1.73205i | 0.0328089 | − | 0.0568267i | −0.849155 | − | 0.528144i | \(-0.822888\pi\) |
0.881964 | + | 0.471317i | \(0.156221\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −90.0000 | −2.94963 | ||||||||
\(932\) | −7.00000 | + | 12.1244i | −0.229293 | + | 0.397146i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −12.0000 | − | 20.7846i | −0.392652 | − | 0.680093i | ||||
\(935\) | 24.0000 | 0.784884 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.0000 | 0.980057 | 0.490029 | − | 0.871706i | \(-0.336986\pi\) | ||||
0.490029 | + | 0.871706i | \(0.336986\pi\) | |||||||
\(938\) | 20.0000 | + | 34.6410i | 0.653023 | + | 1.13107i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.50000 | + | 2.59808i | −0.0489246 | + | 0.0847399i | ||||
\(941\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.0000 | − | 20.7846i | 0.390774 | − | 0.676840i | ||||
\(944\) | −12.0000 | −0.390567 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.00000 | − | 15.5885i | −0.292615 | − | 0.506824i | ||||
\(947\) | 29.0000 | + | 50.2295i | 0.942373 | + | 1.63224i | 0.760927 | + | 0.648838i | \(0.224745\pi\) |
0.181447 | + | 0.983401i | \(0.441922\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −5.00000 | −0.162221 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 20.0000 | + | 34.6410i | 0.648204 | + | 1.12272i | ||||
\(953\) | −27.0000 | + | 46.7654i | −0.874616 | + | 1.51488i | −0.0174443 | + | 0.999848i | \(0.505553\pi\) |
−0.857171 | + | 0.515031i | \(0.827780\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.00000 | − | 1.73205i | 0.0323592 | − | 0.0560478i | ||||
\(956\) | −9.00000 | + | 15.5885i | −0.291081 | + | 0.504167i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −14.0000 | + | 24.2487i | −0.452319 | + | 0.783440i | ||||
\(959\) | 30.0000 | + | 51.9615i | 0.968751 | + | 1.67793i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | −24.5000 | + | 6.06218i | −0.789912 | + | 0.195452i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 12.5000 | + | 21.6506i | 0.402598 | + | 0.697320i | ||||
\(965\) | −12.0000 | − | 20.7846i | −0.386294 | − | 0.669080i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.0000 | −0.996893 | −0.498446 | − | 0.866921i | \(-0.666096\pi\) | ||||
−0.498446 | + | 0.866921i | \(0.666096\pi\) | |||||||
\(968\) | 1.00000 | − | 1.73205i | 0.0321412 | − | 0.0556702i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.50000 | − | 12.9904i | 0.240686 | − | 0.416881i | −0.720224 | − | 0.693742i | \(-0.755961\pi\) |
0.960910 | + | 0.276861i | \(0.0892941\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.5000 | + | 30.3109i | 0.561024 | + | 0.971722i | ||||
\(974\) | 37.0000 | 1.18556 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.00000 | 0.0640184 | ||||||||
\(977\) | 10.0000 | + | 17.3205i | 0.319928 | + | 0.554132i | 0.980473 | − | 0.196655i | \(-0.0630078\pi\) |
−0.660544 | + | 0.750787i | \(0.729674\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.5000 | + | 28.5788i | −0.527342 | + | 0.913384i | ||||
\(980\) | 18.0000 | 0.574989 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 10.5000 | − | 18.1865i | 0.335068 | − | 0.580356i | ||||
\(983\) | −23.0000 | −0.733586 | −0.366793 | − | 0.930303i | \(-0.619544\pi\) | ||||
−0.366793 | + | 0.930303i | \(0.619544\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.50000 | + | 2.59808i | 0.0477940 | + | 0.0827816i | ||||
\(986\) | −16.0000 | − | 27.7128i | −0.509544 | − | 0.882556i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.00000 | − | 17.3205i | 0.159071 | − | 0.551039i | ||||
\(989\) | 24.0000 | 0.763156 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.00000 | − | 8.66025i | −0.158830 | − | 0.275102i | 0.775617 | − | 0.631204i | \(-0.217439\pi\) |
−0.934447 | + | 0.356102i | \(0.884106\pi\) | |||||||
\(992\) | 1.00000 | − | 1.73205i | 0.0317500 | − | 0.0549927i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5.00000 | + | 8.66025i | −0.158590 | + | 0.274687i | ||||
\(995\) | −11.0000 | + | 19.0526i | −0.348723 | + | 0.604007i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.500000 | − | 0.866025i | 0.0158352 | − | 0.0274273i | −0.857999 | − | 0.513651i | \(-0.828293\pi\) |
0.873834 | + | 0.486224i | \(0.161626\pi\) | |||||||
\(998\) | −2.00000 | − | 3.46410i | −0.0633089 | − | 0.109654i | ||||
\(999\) | 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.i.g.991.1 | 2 | ||
3.2 | odd | 2 | 390.2.i.d.211.1 | yes | 2 | ||
13.9 | even | 3 | inner | 1170.2.i.g.451.1 | 2 | ||
15.2 | even | 4 | 1950.2.z.j.1849.1 | 4 | |||
15.8 | even | 4 | 1950.2.z.j.1849.2 | 4 | |||
15.14 | odd | 2 | 1950.2.i.i.601.1 | 2 | |||
39.2 | even | 12 | 5070.2.b.l.1351.2 | 2 | |||
39.11 | even | 12 | 5070.2.b.l.1351.1 | 2 | |||
39.23 | odd | 6 | 5070.2.a.x.1.1 | 1 | |||
39.29 | odd | 6 | 5070.2.a.i.1.1 | 1 | |||
39.35 | odd | 6 | 390.2.i.d.61.1 | ✓ | 2 | ||
195.74 | odd | 6 | 1950.2.i.i.451.1 | 2 | |||
195.113 | even | 12 | 1950.2.z.j.1699.1 | 4 | |||
195.152 | even | 12 | 1950.2.z.j.1699.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.i.d.61.1 | ✓ | 2 | 39.35 | odd | 6 | ||
390.2.i.d.211.1 | yes | 2 | 3.2 | odd | 2 | ||
1170.2.i.g.451.1 | 2 | 13.9 | even | 3 | inner | ||
1170.2.i.g.991.1 | 2 | 1.1 | even | 1 | trivial | ||
1950.2.i.i.451.1 | 2 | 195.74 | odd | 6 | |||
1950.2.i.i.601.1 | 2 | 15.14 | odd | 2 | |||
1950.2.z.j.1699.1 | 4 | 195.113 | even | 12 | |||
1950.2.z.j.1699.2 | 4 | 195.152 | even | 12 | |||
1950.2.z.j.1849.1 | 4 | 15.2 | even | 4 | |||
1950.2.z.j.1849.2 | 4 | 15.8 | even | 4 | |||
5070.2.a.i.1.1 | 1 | 39.29 | odd | 6 | |||
5070.2.a.x.1.1 | 1 | 39.23 | odd | 6 | |||
5070.2.b.l.1351.1 | 2 | 39.11 | even | 12 | |||
5070.2.b.l.1351.2 | 2 | 39.2 | even | 12 |