Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1638,2,Mod(289,1638)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1638, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1638.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1638.m (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: | \(13.0794958511\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 289.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1638.289 |
Dual form | 1638.2.m.b.1621.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).
\(n\) | \(379\) | \(703\) | \(911\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | − | 1.73205i | 0.447214 | − | 0.774597i | −0.550990 | − | 0.834512i | \(-0.685750\pi\) |
0.998203 | + | 0.0599153i | \(0.0190830\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.50000 | + | 0.866025i | −0.944911 | + | 0.327327i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.00000 | + | 1.73205i | −0.316228 | + | 0.547723i | ||||
\(11\) | −1.00000 | + | 1.73205i | −0.301511 | + | 0.522233i | −0.976478 | − | 0.215615i | \(-0.930824\pi\) |
0.674967 | + | 0.737848i | \(0.264158\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.50000 | + | 0.866025i | −0.970725 | + | 0.240192i | ||||
\(14\) | 2.50000 | − | 0.866025i | 0.668153 | − | 0.231455i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.00000 | 0.970143 | 0.485071 | − | 0.874475i | \(-0.338794\pi\) | ||||
0.485071 | + | 0.874475i | \(0.338794\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.50000 | − | 4.33013i | −0.573539 | − | 0.993399i | −0.996199 | − | 0.0871106i | \(-0.972237\pi\) |
0.422659 | − | 0.906289i | \(-0.361097\pi\) | |||||||
\(20\) | 1.00000 | − | 1.73205i | 0.223607 | − | 0.387298i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | − | 1.73205i | 0.213201 | − | 0.369274i | ||||
\(23\) | 2.00000 | 0.417029 | 0.208514 | − | 0.978019i | \(-0.433137\pi\) | ||||
0.208514 | + | 0.978019i | \(0.433137\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | 3.50000 | − | 0.866025i | 0.686406 | − | 0.169842i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.50000 | + | 0.866025i | −0.472456 | + | 0.163663i | ||||
\(29\) | 4.00000 | + | 6.92820i | 0.742781 | + | 1.28654i | 0.951224 | + | 0.308500i | \(0.0998271\pi\) |
−0.208443 | + | 0.978035i | \(0.566840\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.00000 | −0.685994 | ||||||||
\(35\) | −1.00000 | + | 5.19615i | −0.169031 | + | 0.878310i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.00000 | 1.15079 | 0.575396 | − | 0.817875i | \(-0.304848\pi\) | ||||
0.575396 | + | 0.817875i | \(0.304848\pi\) | |||||||
\(38\) | 2.50000 | + | 4.33013i | 0.405554 | + | 0.702439i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | + | 1.73205i | −0.158114 | + | 0.273861i | ||||
\(41\) | 5.00000 | + | 8.66025i | 0.780869 | + | 1.35250i | 0.931436 | + | 0.363905i | \(0.118557\pi\) |
−0.150567 | + | 0.988600i | \(0.548110\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.50000 | + | 6.06218i | −0.533745 | + | 0.924473i | 0.465478 | + | 0.885059i | \(0.345882\pi\) |
−0.999223 | + | 0.0394140i | \(0.987451\pi\) | |||||||
\(44\) | −1.00000 | + | 1.73205i | −0.150756 | + | 0.261116i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.00000 | −0.294884 | ||||||||
\(47\) | 6.00000 | − | 10.3923i | 0.875190 | − | 1.51587i | 0.0186297 | − | 0.999826i | \(-0.494070\pi\) |
0.856560 | − | 0.516047i | \(-0.172597\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | −0.500000 | − | 0.866025i | −0.0707107 | − | 0.122474i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.50000 | + | 0.866025i | −0.485363 | + | 0.120096i | ||||
\(53\) | 3.00000 | + | 5.19615i | 0.412082 | + | 0.713746i | 0.995117 | − | 0.0987002i | \(-0.0314685\pi\) |
−0.583036 | + | 0.812447i | \(0.698135\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.00000 | + | 3.46410i | 0.269680 | + | 0.467099i | ||||
\(56\) | 2.50000 | − | 0.866025i | 0.334077 | − | 0.115728i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.00000 | − | 6.92820i | −0.525226 | − | 0.909718i | ||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.500000 | + | 0.866025i | 0.0640184 | + | 0.110883i | 0.896258 | − | 0.443533i | \(-0.146275\pi\) |
−0.832240 | + | 0.554416i | \(0.812942\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.00000 | + | 6.92820i | −0.248069 | + | 0.859338i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000 | − | 6.92820i | 0.488678 | − | 0.846415i | −0.511237 | − | 0.859440i | \(-0.670813\pi\) |
0.999915 | + | 0.0130248i | \(0.00414604\pi\) | |||||||
\(68\) | 4.00000 | 0.485071 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.00000 | − | 5.19615i | 0.119523 | − | 0.621059i | ||||
\(71\) | 4.00000 | − | 6.92820i | 0.474713 | − | 0.822226i | −0.524868 | − | 0.851184i | \(-0.675885\pi\) |
0.999581 | + | 0.0289572i | \(0.00921865\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.50000 | − | 7.79423i | −0.526685 | − | 0.912245i | −0.999517 | − | 0.0310925i | \(-0.990101\pi\) |
0.472831 | − | 0.881153i | \(-0.343232\pi\) | |||||||
\(74\) | −7.00000 | −0.813733 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.50000 | − | 4.33013i | −0.286770 | − | 0.496700i | ||||
\(77\) | 1.00000 | − | 5.19615i | 0.113961 | − | 0.592157i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | + | 6.92820i | −0.450035 | + | 0.779484i | −0.998388 | − | 0.0567635i | \(-0.981922\pi\) |
0.548352 | + | 0.836247i | \(0.315255\pi\) | |||||||
\(80\) | 1.00000 | − | 1.73205i | 0.111803 | − | 0.193649i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.00000 | − | 8.66025i | −0.552158 | − | 0.956365i | ||||
\(83\) | 14.0000 | 1.53670 | 0.768350 | − | 0.640030i | \(-0.221078\pi\) | ||||
0.768350 | + | 0.640030i | \(0.221078\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.00000 | − | 6.92820i | 0.433861 | − | 0.751469i | ||||
\(86\) | 3.50000 | − | 6.06218i | 0.377415 | − | 0.653701i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.00000 | − | 1.73205i | 0.106600 | − | 0.184637i | ||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.00000 | − | 5.19615i | 0.838628 | − | 0.544705i | ||||
\(92\) | 2.00000 | 0.208514 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.00000 | + | 10.3923i | −0.618853 | + | 1.07188i | ||||
\(95\) | −10.0000 | −1.02598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.50000 | + | 14.7224i | −0.863044 | + | 1.49484i | 0.00593185 | + | 0.999982i | \(0.498112\pi\) |
−0.868976 | + | 0.494854i | \(0.835222\pi\) | |||||||
\(98\) | −5.50000 | + | 4.33013i | −0.555584 | + | 0.437409i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.500000 | + | 0.866025i | 0.0500000 | + | 0.0866025i | ||||
\(101\) | −3.00000 | + | 5.19615i | −0.298511 | + | 0.517036i | −0.975796 | − | 0.218685i | \(-0.929823\pi\) |
0.677284 | + | 0.735721i | \(0.263157\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.50000 | − | 4.33013i | 0.246332 | − | 0.426660i | −0.716173 | − | 0.697923i | \(-0.754108\pi\) |
0.962505 | + | 0.271263i | \(0.0874412\pi\) | |||||||
\(104\) | 3.50000 | − | 0.866025i | 0.343203 | − | 0.0849208i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.00000 | − | 5.19615i | −0.291386 | − | 0.504695i | ||||
\(107\) | 12.0000 | 1.16008 | 0.580042 | − | 0.814587i | \(-0.303036\pi\) | ||||
0.580042 | + | 0.814587i | \(0.303036\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.50000 | + | 16.4545i | 0.909935 | + | 1.57605i | 0.814152 | + | 0.580651i | \(0.197202\pi\) |
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | −2.00000 | − | 3.46410i | −0.190693 | − | 0.330289i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.50000 | + | 0.866025i | −0.236228 | + | 0.0818317i | ||||
\(113\) | 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 | + | 6.92820i | 0.371391 | + | 0.643268i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.0000 | + | 3.46410i | −0.916698 | + | 0.317554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | + | 6.06218i | 0.318182 | + | 0.551107i | ||||
\(122\) | −0.500000 | − | 0.866025i | −0.0452679 | − | 0.0784063i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.50000 | − | 16.4545i | −0.842989 | − | 1.46010i | −0.887357 | − | 0.461084i | \(-0.847461\pi\) |
0.0443678 | − | 0.999015i | \(-0.485873\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.00000 | − | 6.92820i | 0.175412 | − | 0.607644i | ||||
\(131\) | −3.00000 | + | 5.19615i | −0.262111 | + | 0.453990i | −0.966803 | − | 0.255524i | \(-0.917752\pi\) |
0.704692 | + | 0.709514i | \(0.251085\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.0000 | + | 8.66025i | 0.867110 | + | 0.750939i | ||||
\(134\) | −4.00000 | + | 6.92820i | −0.345547 | + | 0.598506i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.00000 | −0.342997 | ||||||||
\(137\) | −2.00000 | −0.170872 | −0.0854358 | − | 0.996344i | \(-0.527228\pi\) | ||||
−0.0854358 | + | 0.996344i | \(0.527228\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.00000 | + | 3.46410i | −0.169638 | + | 0.293821i | −0.938293 | − | 0.345843i | \(-0.887593\pi\) |
0.768655 | + | 0.639664i | \(0.220926\pi\) | |||||||
\(140\) | −1.00000 | + | 5.19615i | −0.0845154 | + | 0.439155i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.00000 | + | 6.92820i | −0.335673 | + | 0.581402i | ||||
\(143\) | 2.00000 | − | 6.92820i | 0.167248 | − | 0.579365i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.0000 | 1.32873 | ||||||||
\(146\) | 4.50000 | + | 7.79423i | 0.372423 | + | 0.645055i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.00000 | 0.575396 | ||||||||
\(149\) | −3.00000 | − | 5.19615i | −0.245770 | − | 0.425685i | 0.716578 | − | 0.697507i | \(-0.245707\pi\) |
−0.962348 | + | 0.271821i | \(0.912374\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | + | 13.8564i | 0.651031 | + | 1.12762i | 0.982873 | + | 0.184284i | \(0.0589965\pi\) |
−0.331842 | + | 0.943335i | \(0.607670\pi\) | |||||||
\(152\) | 2.50000 | + | 4.33013i | 0.202777 | + | 0.351220i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.00000 | + | 5.19615i | −0.0805823 | + | 0.418718i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.50000 | + | 14.7224i | 0.678374 | + | 1.17498i | 0.975470 | + | 0.220131i | \(0.0706483\pi\) |
−0.297097 | + | 0.954847i | \(0.596018\pi\) | |||||||
\(158\) | 4.00000 | − | 6.92820i | 0.318223 | − | 0.551178i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.00000 | + | 1.73205i | −0.0790569 | + | 0.136931i | ||||
\(161\) | −5.00000 | + | 1.73205i | −0.394055 | + | 0.136505i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.50000 | + | 2.59808i | 0.117489 | + | 0.203497i | 0.918772 | − | 0.394789i | \(-0.129182\pi\) |
−0.801283 | + | 0.598286i | \(0.795849\pi\) | |||||||
\(164\) | 5.00000 | + | 8.66025i | 0.390434 | + | 0.676252i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.0000 | −1.08661 | ||||||||
\(167\) | −9.00000 | − | 15.5885i | −0.696441 | − | 1.20627i | −0.969693 | − | 0.244328i | \(-0.921432\pi\) |
0.273252 | − | 0.961943i | \(-0.411901\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.5000 | − | 6.06218i | 0.884615 | − | 0.466321i | ||||
\(170\) | −4.00000 | + | 6.92820i | −0.306786 | + | 0.531369i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.50000 | + | 6.06218i | −0.266872 | + | 0.462237i | ||||
\(173\) | −1.00000 | − | 1.73205i | −0.0760286 | − | 0.131685i | 0.825505 | − | 0.564396i | \(-0.190891\pi\) |
−0.901533 | + | 0.432710i | \(0.857557\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.00000 | − | 1.73205i | −0.151186 | − | 0.130931i | ||||
\(176\) | −1.00000 | + | 1.73205i | −0.0753778 | + | 0.130558i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.00000 | 0.449719 | ||||||||
\(179\) | 3.00000 | − | 5.19615i | 0.224231 | − | 0.388379i | −0.731858 | − | 0.681457i | \(-0.761346\pi\) |
0.956088 | + | 0.293079i | \(0.0946798\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.0000 | 0.966282 | 0.483141 | − | 0.875542i | \(-0.339496\pi\) | ||||
0.483141 | + | 0.875542i | \(0.339496\pi\) | |||||||
\(182\) | −8.00000 | + | 5.19615i | −0.592999 | + | 0.385164i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.00000 | −0.147442 | ||||||||
\(185\) | 7.00000 | − | 12.1244i | 0.514650 | − | 0.891400i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.00000 | + | 6.92820i | −0.292509 | + | 0.506640i | ||||
\(188\) | 6.00000 | − | 10.3923i | 0.437595 | − | 0.757937i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.0000 | 0.725476 | ||||||||
\(191\) | 12.0000 | + | 20.7846i | 0.868290 | + | 1.50392i | 0.863743 | + | 0.503932i | \(0.168114\pi\) |
0.00454614 | + | 0.999990i | \(0.498553\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.50000 | + | 9.52628i | −0.395899 | + | 0.685717i | −0.993215 | − | 0.116289i | \(-0.962900\pi\) |
0.597317 | + | 0.802005i | \(0.296234\pi\) | |||||||
\(194\) | 8.50000 | − | 14.7224i | 0.610264 | − | 1.05701i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.50000 | − | 4.33013i | 0.392857 | − | 0.309295i | ||||
\(197\) | 6.00000 | + | 10.3923i | 0.427482 | + | 0.740421i | 0.996649 | − | 0.0818013i | \(-0.0260673\pi\) |
−0.569166 | + | 0.822222i | \(0.692734\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.00000 | 0.496217 | 0.248108 | − | 0.968732i | \(-0.420191\pi\) | ||||
0.248108 | + | 0.968732i | \(0.420191\pi\) | |||||||
\(200\) | −0.500000 | − | 0.866025i | −0.0353553 | − | 0.0612372i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.00000 | − | 5.19615i | 0.211079 | − | 0.365600i | ||||
\(203\) | −16.0000 | − | 13.8564i | −1.12298 | − | 0.972529i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20.0000 | 1.39686 | ||||||||
\(206\) | −2.50000 | + | 4.33013i | −0.174183 | + | 0.301694i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.50000 | + | 0.866025i | −0.242681 | + | 0.0600481i | ||||
\(209\) | 10.0000 | 0.691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.50000 | − | 11.2583i | −0.447478 | − | 0.775055i | 0.550743 | − | 0.834675i | \(-0.314345\pi\) |
−0.998221 | + | 0.0596196i | \(0.981011\pi\) | |||||||
\(212\) | 3.00000 | + | 5.19615i | 0.206041 | + | 0.356873i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −12.0000 | −0.820303 | ||||||||
\(215\) | 7.00000 | + | 12.1244i | 0.477396 | + | 0.826874i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −9.50000 | − | 16.4545i | −0.643421 | − | 1.11444i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.00000 | + | 3.46410i | 0.134840 | + | 0.233550i | ||||
\(221\) | −14.0000 | + | 3.46410i | −0.941742 | + | 0.233021i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(224\) | 2.50000 | − | 0.866025i | 0.167038 | − | 0.0578638i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.00000 | + | 6.92820i | −0.266076 | + | 0.460857i | ||||
\(227\) | −2.00000 | −0.132745 | −0.0663723 | − | 0.997795i | \(-0.521143\pi\) | ||||
−0.0663723 | + | 0.997795i | \(0.521143\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.500000 | + | 0.866025i | −0.0330409 | + | 0.0572286i | −0.882073 | − | 0.471113i | \(-0.843853\pi\) |
0.849032 | + | 0.528341i | \(0.177186\pi\) | |||||||
\(230\) | −2.00000 | + | 3.46410i | −0.131876 | + | 0.228416i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.00000 | − | 6.92820i | −0.262613 | − | 0.454859i | ||||
\(233\) | −10.0000 | + | 17.3205i | −0.655122 | + | 1.13470i | 0.326741 | + | 0.945114i | \(0.394049\pi\) |
−0.981863 | + | 0.189590i | \(0.939284\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.0000 | − | 20.7846i | −0.782794 | − | 1.35584i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 10.0000 | − | 3.46410i | 0.648204 | − | 0.224544i | ||||
\(239\) | 18.0000 | 1.16432 | 0.582162 | − | 0.813073i | \(-0.302207\pi\) | ||||
0.582162 | + | 0.813073i | \(0.302207\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.0000 | −1.41714 | −0.708572 | − | 0.705638i | \(-0.750660\pi\) | ||||
−0.708572 | + | 0.705638i | \(0.750660\pi\) | |||||||
\(242\) | −3.50000 | − | 6.06218i | −0.224989 | − | 0.389692i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.500000 | + | 0.866025i | 0.0320092 | + | 0.0554416i | ||||
\(245\) | −2.00000 | − | 13.8564i | −0.127775 | − | 0.885253i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.5000 | + | 12.9904i | 0.795356 | + | 0.826558i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −12.0000 | −0.758947 | ||||||||
\(251\) | −4.00000 | + | 6.92820i | −0.252478 | + | 0.437304i | −0.964207 | − | 0.265149i | \(-0.914579\pi\) |
0.711730 | + | 0.702454i | \(0.247912\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.00000 | + | 3.46410i | −0.125739 | + | 0.217786i | ||||
\(254\) | 9.50000 | + | 16.4545i | 0.596083 | + | 1.03245i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −6.00000 | −0.374270 | −0.187135 | − | 0.982334i | \(-0.559920\pi\) | ||||
−0.187135 | + | 0.982334i | \(0.559920\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.5000 | + | 6.06218i | −1.08740 | + | 0.376685i | ||||
\(260\) | −2.00000 | + | 6.92820i | −0.124035 | + | 0.429669i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.00000 | − | 5.19615i | 0.185341 | − | 0.321019i | ||||
\(263\) | −2.00000 | + | 3.46410i | −0.123325 | + | 0.213606i | −0.921077 | − | 0.389380i | \(-0.872689\pi\) |
0.797752 | + | 0.602986i | \(0.206023\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.0000 | 0.737154 | ||||||||
\(266\) | −10.0000 | − | 8.66025i | −0.613139 | − | 0.530994i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.00000 | − | 6.92820i | 0.244339 | − | 0.423207i | ||||
\(269\) | −12.0000 | −0.731653 | −0.365826 | − | 0.930683i | \(-0.619214\pi\) | ||||
−0.365826 | + | 0.930683i | \(0.619214\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.00000 | 0.182237 | 0.0911185 | − | 0.995840i | \(-0.470956\pi\) | ||||
0.0911185 | + | 0.995840i | \(0.470956\pi\) | |||||||
\(272\) | 4.00000 | 0.242536 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.00000 | 0.120824 | ||||||||
\(275\) | −2.00000 | −0.120605 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.0000 | 0.781094 | 0.390547 | − | 0.920583i | \(-0.372286\pi\) | ||||
0.390547 | + | 0.920583i | \(0.372286\pi\) | |||||||
\(278\) | 2.00000 | − | 3.46410i | 0.119952 | − | 0.207763i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.00000 | − | 5.19615i | 0.0597614 | − | 0.310530i | ||||
\(281\) | −8.00000 | −0.477240 | −0.238620 | − | 0.971113i | \(-0.576695\pi\) | ||||
−0.238620 | + | 0.971113i | \(0.576695\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.50000 | − | 11.2583i | 0.386385 | − | 0.669238i | −0.605575 | − | 0.795788i | \(-0.707057\pi\) |
0.991960 | + | 0.126550i | \(0.0403903\pi\) | |||||||
\(284\) | 4.00000 | − | 6.92820i | 0.237356 | − | 0.411113i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.00000 | + | 6.92820i | −0.118262 | + | 0.409673i | ||||
\(287\) | −20.0000 | − | 17.3205i | −1.18056 | − | 1.02240i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | −16.0000 | −0.939552 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.50000 | − | 7.79423i | −0.263343 | − | 0.456123i | ||||
\(293\) | 14.0000 | − | 24.2487i | 0.817889 | − | 1.41662i | −0.0893462 | − | 0.996001i | \(-0.528478\pi\) |
0.907235 | − | 0.420624i | \(-0.138189\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7.00000 | −0.406867 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.00000 | + | 5.19615i | 0.173785 | + | 0.301005i | ||||
\(299\) | −7.00000 | + | 1.73205i | −0.404820 | + | 0.100167i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.50000 | − | 18.1865i | 0.201737 | − | 1.04825i | ||||
\(302\) | −8.00000 | − | 13.8564i | −0.460348 | − | 0.797347i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.50000 | − | 4.33013i | −0.143385 | − | 0.248350i | ||||
\(305\) | 2.00000 | 0.114520 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.0000 | −0.684876 | −0.342438 | − | 0.939540i | \(-0.611253\pi\) | ||||
−0.342438 | + | 0.939540i | \(0.611253\pi\) | |||||||
\(308\) | 1.00000 | − | 5.19615i | 0.0569803 | − | 0.296078i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.0000 | + | 25.9808i | 0.850572 | + | 1.47323i | 0.880693 | + | 0.473688i | \(0.157077\pi\) |
−0.0301210 | + | 0.999546i | \(0.509589\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.5000 | − | 18.1865i | 0.593495 | − | 1.02796i | −0.400262 | − | 0.916401i | \(-0.631081\pi\) |
0.993757 | − | 0.111563i | \(-0.0355857\pi\) | |||||||
\(314\) | −8.50000 | − | 14.7224i | −0.479683 | − | 0.830835i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.00000 | + | 6.92820i | −0.225018 | + | 0.389742i | ||||
\(317\) | −1.00000 | + | 1.73205i | −0.0561656 | + | 0.0972817i | −0.892741 | − | 0.450570i | \(-0.851221\pi\) |
0.836576 | + | 0.547852i | \(0.184554\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.0000 | −0.895828 | ||||||||
\(320\) | 1.00000 | − | 1.73205i | 0.0559017 | − | 0.0968246i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.00000 | − | 1.73205i | 0.278639 | − | 0.0965234i | ||||
\(323\) | −10.0000 | − | 17.3205i | −0.556415 | − | 0.963739i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.50000 | − | 2.59808i | −0.138675 | − | 0.144115i | ||||
\(326\) | −1.50000 | − | 2.59808i | −0.0830773 | − | 0.143894i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.00000 | − | 8.66025i | −0.276079 | − | 0.478183i | ||||
\(329\) | −6.00000 | + | 31.1769i | −0.330791 | + | 1.71884i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.50000 | + | 12.9904i | 0.412237 | + | 0.714016i | 0.995134 | − | 0.0985303i | \(-0.0314141\pi\) |
−0.582897 | + | 0.812546i | \(0.698081\pi\) | |||||||
\(332\) | 14.0000 | 0.768350 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9.00000 | + | 15.5885i | 0.492458 | + | 0.852962i | ||||
\(335\) | −8.00000 | − | 13.8564i | −0.437087 | − | 0.757056i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.00000 | −0.163420 | −0.0817102 | − | 0.996656i | \(-0.526038\pi\) | ||||
−0.0817102 | + | 0.996656i | \(0.526038\pi\) | |||||||
\(338\) | −11.5000 | + | 6.06218i | −0.625518 | + | 0.329739i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.00000 | − | 6.92820i | 0.216930 | − | 0.375735i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 3.50000 | − | 6.06218i | 0.188707 | − | 0.326851i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.00000 | + | 1.73205i | 0.0537603 | + | 0.0931156i | ||||
\(347\) | −8.00000 | −0.429463 | −0.214731 | − | 0.976673i | \(-0.568888\pi\) | ||||
−0.214731 | + | 0.976673i | \(0.568888\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.500000 | + | 0.866025i | 0.0267644 | + | 0.0463573i | 0.879097 | − | 0.476642i | \(-0.158146\pi\) |
−0.852333 | + | 0.523000i | \(0.824813\pi\) | |||||||
\(350\) | 2.00000 | + | 1.73205i | 0.106904 | + | 0.0925820i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.00000 | − | 1.73205i | 0.0533002 | − | 0.0923186i | ||||
\(353\) | 7.00000 | − | 12.1244i | 0.372572 | − | 0.645314i | −0.617388 | − | 0.786659i | \(-0.711809\pi\) |
0.989960 | + | 0.141344i | \(0.0451425\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.00000 | − | 13.8564i | −0.424596 | − | 0.735422i | ||||
\(356\) | −6.00000 | −0.317999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.00000 | + | 5.19615i | −0.158555 | + | 0.274625i | ||||
\(359\) | −18.0000 | + | 31.1769i | −0.950004 | + | 1.64545i | −0.204595 | + | 0.978847i | \(0.565588\pi\) |
−0.745409 | + | 0.666608i | \(0.767746\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | + | 5.19615i | −0.157895 | + | 0.273482i | ||||
\(362\) | −13.0000 | −0.683265 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.00000 | − | 5.19615i | 0.419314 | − | 0.272352i | ||||
\(365\) | −18.0000 | −0.942163 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.5000 | + | 28.5788i | −0.861293 | + | 1.49180i | 0.00938849 | + | 0.999956i | \(0.497012\pi\) |
−0.870681 | + | 0.491847i | \(0.836322\pi\) | |||||||
\(368\) | 2.00000 | 0.104257 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −7.00000 | + | 12.1244i | −0.363913 | + | 0.630315i | ||||
\(371\) | −12.0000 | − | 10.3923i | −0.623009 | − | 0.539542i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.0000 | − | 29.4449i | −0.880227 | − | 1.52460i | −0.851089 | − | 0.525022i | \(-0.824057\pi\) |
−0.0291379 | − | 0.999575i | \(-0.509276\pi\) | |||||||
\(374\) | 4.00000 | − | 6.92820i | 0.206835 | − | 0.358249i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.00000 | + | 10.3923i | −0.309426 | + | 0.535942i | ||||
\(377\) | −20.0000 | − | 20.7846i | −1.03005 | − | 1.07046i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.0000 | − | 24.2487i | −0.719132 | − | 1.24557i | −0.961344 | − | 0.275349i | \(-0.911206\pi\) |
0.242213 | − | 0.970223i | \(-0.422127\pi\) | |||||||
\(380\) | −10.0000 | −0.512989 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −12.0000 | − | 20.7846i | −0.613973 | − | 1.06343i | ||||
\(383\) | −18.0000 | − | 31.1769i | −0.919757 | − | 1.59307i | −0.799783 | − | 0.600289i | \(-0.795052\pi\) |
−0.119974 | − | 0.992777i | \(-0.538281\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.00000 | − | 6.92820i | −0.407718 | − | 0.353094i | ||||
\(386\) | 5.50000 | − | 9.52628i | 0.279943 | − | 0.484875i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.50000 | + | 14.7224i | −0.431522 | + | 0.747418i | ||||
\(389\) | −19.0000 | − | 32.9090i | −0.963338 | − | 1.66855i | −0.714015 | − | 0.700130i | \(-0.753125\pi\) |
−0.249323 | − | 0.968420i | \(-0.580208\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.00000 | 0.404577 | ||||||||
\(392\) | −5.50000 | + | 4.33013i | −0.277792 | + | 0.218704i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.00000 | − | 10.3923i | −0.302276 | − | 0.523557i | ||||
\(395\) | 8.00000 | + | 13.8564i | 0.402524 | + | 0.697191i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.5000 | + | 21.6506i | 0.627357 | + | 1.08661i | 0.988080 | + | 0.153941i | \(0.0491966\pi\) |
−0.360723 | + | 0.932673i | \(0.617470\pi\) | |||||||
\(398\) | −7.00000 | −0.350878 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.500000 | + | 0.866025i | 0.0250000 | + | 0.0433013i | ||||
\(401\) | −10.0000 | −0.499376 | −0.249688 | − | 0.968326i | \(-0.580328\pi\) | ||||
−0.249688 | + | 0.968326i | \(0.580328\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −3.00000 | + | 5.19615i | −0.149256 | + | 0.258518i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 16.0000 | + | 13.8564i | 0.794067 | + | 0.687682i | ||||
\(407\) | −7.00000 | + | 12.1244i | −0.346977 | + | 0.600982i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.0000 | −0.939490 | −0.469745 | − | 0.882802i | \(-0.655654\pi\) | ||||
−0.469745 | + | 0.882802i | \(0.655654\pi\) | |||||||
\(410\) | −20.0000 | −0.987730 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.50000 | − | 4.33013i | 0.123166 | − | 0.213330i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.0000 | − | 24.2487i | 0.687233 | − | 1.19032i | ||||
\(416\) | 3.50000 | − | 0.866025i | 0.171602 | − | 0.0424604i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −10.0000 | −0.489116 | ||||||||
\(419\) | 5.00000 | + | 8.66025i | 0.244266 | + | 0.423081i | 0.961925 | − | 0.273314i | \(-0.0881197\pi\) |
−0.717659 | + | 0.696395i | \(0.754786\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.0000 | 1.07221 | 0.536107 | − | 0.844150i | \(-0.319894\pi\) | ||||
0.536107 | + | 0.844150i | \(0.319894\pi\) | |||||||
\(422\) | 6.50000 | + | 11.2583i | 0.316415 | + | 0.548047i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.00000 | − | 5.19615i | −0.145693 | − | 0.252347i | ||||
\(425\) | 2.00000 | + | 3.46410i | 0.0970143 | + | 0.168034i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.00000 | − | 1.73205i | −0.0967868 | − | 0.0838198i | ||||
\(428\) | 12.0000 | 0.580042 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7.00000 | − | 12.1244i | −0.337570 | − | 0.584688i | ||||
\(431\) | −7.00000 | + | 12.1244i | −0.337178 | + | 0.584010i | −0.983901 | − | 0.178716i | \(-0.942806\pi\) |
0.646723 | + | 0.762725i | \(0.276139\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.00000 | − | 15.5885i | 0.432512 | − | 0.749133i | −0.564577 | − | 0.825381i | \(-0.690961\pi\) |
0.997089 | + | 0.0762473i | \(0.0242938\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.50000 | + | 16.4545i | 0.454967 | + | 0.788027i | ||||
\(437\) | −5.00000 | − | 8.66025i | −0.239182 | − | 0.414276i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.0000 | 1.19318 | 0.596592 | − | 0.802544i | \(-0.296521\pi\) | ||||
0.596592 | + | 0.802544i | \(0.296521\pi\) | |||||||
\(440\) | −2.00000 | − | 3.46410i | −0.0953463 | − | 0.165145i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 14.0000 | − | 3.46410i | 0.665912 | − | 0.164771i | ||||
\(443\) | −3.00000 | + | 5.19615i | −0.142534 | + | 0.246877i | −0.928450 | − | 0.371457i | \(-0.878858\pi\) |
0.785916 | + | 0.618333i | \(0.212192\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.00000 | + | 10.3923i | −0.284427 | + | 0.492642i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.50000 | + | 0.866025i | −0.118114 | + | 0.0409159i | ||||
\(449\) | −9.00000 | + | 15.5885i | −0.424736 | + | 0.735665i | −0.996396 | − | 0.0848262i | \(-0.972967\pi\) |
0.571660 | + | 0.820491i | \(0.306300\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −20.0000 | −0.941763 | ||||||||
\(452\) | 4.00000 | − | 6.92820i | 0.188144 | − | 0.325875i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.00000 | 0.0938647 | ||||||||
\(455\) | −1.00000 | − | 19.0526i | −0.0468807 | − | 0.893198i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.00000 | 0.280668 | 0.140334 | − | 0.990104i | \(-0.455182\pi\) | ||||
0.140334 | + | 0.990104i | \(0.455182\pi\) | |||||||
\(458\) | 0.500000 | − | 0.866025i | 0.0233635 | − | 0.0404667i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.00000 | − | 3.46410i | 0.0932505 | − | 0.161515i | ||||
\(461\) | 16.0000 | − | 27.7128i | 0.745194 | − | 1.29071i | −0.204910 | − | 0.978781i | \(-0.565690\pi\) |
0.950104 | − | 0.311933i | \(-0.100977\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.0000 | −1.25480 | −0.627398 | − | 0.778699i | \(-0.715880\pi\) | ||||
−0.627398 | + | 0.778699i | \(0.715880\pi\) | |||||||
\(464\) | 4.00000 | + | 6.92820i | 0.185695 | + | 0.321634i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.0000 | − | 17.3205i | 0.463241 | − | 0.802357i | ||||
\(467\) | 1.00000 | − | 1.73205i | 0.0462745 | − | 0.0801498i | −0.841960 | − | 0.539539i | \(-0.818598\pi\) |
0.888235 | + | 0.459390i | \(0.151932\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.00000 | + | 20.7846i | −0.184703 | + | 0.959744i | ||||
\(470\) | 12.0000 | + | 20.7846i | 0.553519 | + | 0.958723i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.00000 | − | 12.1244i | −0.321860 | − | 0.557478i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.50000 | − | 4.33013i | 0.114708 | − | 0.198680i | ||||
\(476\) | −10.0000 | + | 3.46410i | −0.458349 | + | 0.158777i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −18.0000 | −0.823301 | ||||||||
\(479\) | 12.0000 | − | 20.7846i | 0.548294 | − | 0.949673i | −0.450098 | − | 0.892979i | \(-0.648611\pi\) |
0.998392 | − | 0.0566937i | \(-0.0180558\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.5000 | + | 6.06218i | −1.11710 | + | 0.276412i | ||||
\(482\) | 22.0000 | 1.00207 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.50000 | + | 6.06218i | 0.159091 | + | 0.275554i | ||||
\(485\) | 17.0000 | + | 29.4449i | 0.771930 | + | 1.33702i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.0000 | −1.13286 | −0.566429 | − | 0.824110i | \(-0.691675\pi\) | ||||
−0.566429 | + | 0.824110i | \(0.691675\pi\) | |||||||
\(488\) | −0.500000 | − | 0.866025i | −0.0226339 | − | 0.0392031i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.00000 | + | 13.8564i | 0.0903508 | + | 0.625969i | ||||
\(491\) | 4.00000 | + | 6.92820i | 0.180517 | + | 0.312665i | 0.942057 | − | 0.335453i | \(-0.108889\pi\) |
−0.761539 | + | 0.648119i | \(0.775556\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.0000 | + | 27.7128i | 0.720604 | + | 1.24812i | ||||
\(494\) | −12.5000 | − | 12.9904i | −0.562402 | − | 0.584465i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.00000 | + | 20.7846i | −0.179425 | + | 0.932317i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.5000 | + | 21.6506i | −0.559577 | + | 0.969216i | 0.437955 | + | 0.898997i | \(0.355703\pi\) |
−0.997532 | + | 0.0702185i | \(0.977630\pi\) | |||||||
\(500\) | 12.0000 | 0.536656 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.00000 | − | 6.92820i | 0.178529 | − | 0.309221i | ||||
\(503\) | −7.00000 | + | 12.1244i | −0.312115 | + | 0.540598i | −0.978820 | − | 0.204723i | \(-0.934371\pi\) |
0.666705 | + | 0.745321i | \(0.267704\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000 | + | 10.3923i | 0.266996 | + | 0.462451i | ||||
\(506\) | 2.00000 | − | 3.46410i | 0.0889108 | − | 0.153998i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −9.50000 | − | 16.4545i | −0.421494 | − | 0.730050i | ||||
\(509\) | 6.00000 | 0.265945 | 0.132973 | − | 0.991120i | \(-0.457548\pi\) | ||||
0.132973 | + | 0.991120i | \(0.457548\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.0000 | + | 15.5885i | 0.796273 | + | 0.689593i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.00000 | 0.264649 | ||||||||
\(515\) | −5.00000 | − | 8.66025i | −0.220326 | − | 0.381616i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.0000 | + | 20.7846i | 0.527759 | + | 0.914106i | ||||
\(518\) | 17.5000 | − | 6.06218i | 0.768906 | − | 0.266357i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.00000 | − | 6.92820i | 0.0877058 | − | 0.303822i | ||||
\(521\) | 18.0000 | + | 31.1769i | 0.788594 | + | 1.36589i | 0.926828 | + | 0.375486i | \(0.122524\pi\) |
−0.138234 | + | 0.990400i | \(0.544143\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.00000 | −0.393543 | −0.196771 | − | 0.980449i | \(-0.563046\pi\) | ||||
−0.196771 | + | 0.980449i | \(0.563046\pi\) | |||||||
\(524\) | −3.00000 | + | 5.19615i | −0.131056 | + | 0.226995i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.00000 | − | 3.46410i | 0.0872041 | − | 0.151042i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.0000 | −0.826087 | ||||||||
\(530\) | −12.0000 | −0.521247 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 10.0000 | + | 8.66025i | 0.433555 | + | 0.375470i | ||||
\(533\) | −25.0000 | − | 25.9808i | −1.08287 | − | 1.12535i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.0000 | − | 20.7846i | 0.518805 | − | 0.898597i | ||||
\(536\) | −4.00000 | + | 6.92820i | −0.172774 | + | 0.299253i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 12.0000 | 0.517357 | ||||||||
\(539\) | 2.00000 | + | 13.8564i | 0.0861461 | + | 0.596838i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.50000 | − | 9.52628i | 0.236463 | − | 0.409567i | −0.723234 | − | 0.690604i | \(-0.757345\pi\) |
0.959697 | + | 0.281037i | \(0.0906783\pi\) | |||||||
\(542\) | −3.00000 | −0.128861 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.00000 | −0.171499 | ||||||||
\(545\) | 38.0000 | 1.62774 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.0000 | −1.06892 | −0.534461 | − | 0.845193i | \(-0.679486\pi\) | ||||
−0.534461 | + | 0.845193i | \(0.679486\pi\) | |||||||
\(548\) | −2.00000 | −0.0854358 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.00000 | 0.0852803 | ||||||||
\(551\) | 20.0000 | − | 34.6410i | 0.852029 | − | 1.47576i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.00000 | − | 20.7846i | 0.170097 | − | 0.883852i | ||||
\(554\) | −13.0000 | −0.552317 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.00000 | + | 3.46410i | −0.0848189 | + | 0.146911i | ||||
\(557\) | 19.0000 | − | 32.9090i | 0.805056 | − | 1.39440i | −0.111198 | − | 0.993798i | \(-0.535469\pi\) |
0.916253 | − | 0.400599i | \(-0.131198\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.00000 | − | 24.2487i | 0.296068 | − | 1.02561i | ||||
\(560\) | −1.00000 | + | 5.19615i | −0.0422577 | + | 0.219578i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.00000 | 0.337460 | ||||||||
\(563\) | 26.0000 | 1.09577 | 0.547885 | − | 0.836554i | \(-0.315433\pi\) | ||||
0.547885 | + | 0.836554i | \(0.315433\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.00000 | − | 13.8564i | −0.336563 | − | 0.582943i | ||||
\(566\) | −6.50000 | + | 11.2583i | −0.273215 | + | 0.473223i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.00000 | + | 6.92820i | −0.167836 | + | 0.290701i | ||||
\(569\) | 20.0000 | 0.838444 | 0.419222 | − | 0.907884i | \(-0.362303\pi\) | ||||
0.419222 | + | 0.907884i | \(0.362303\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.50000 | + | 16.4545i | 0.397563 | + | 0.688599i | 0.993425 | − | 0.114488i | \(-0.0365228\pi\) |
−0.595862 | + | 0.803087i | \(0.703189\pi\) | |||||||
\(572\) | 2.00000 | − | 6.92820i | 0.0836242 | − | 0.289683i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 20.0000 | + | 17.3205i | 0.834784 | + | 0.722944i | ||||
\(575\) | 1.00000 | + | 1.73205i | 0.0417029 | + | 0.0722315i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.5000 | − | 23.3827i | −0.562012 | − | 0.973434i | −0.997321 | − | 0.0731526i | \(-0.976694\pi\) |
0.435308 | − | 0.900281i | \(-0.356639\pi\) | |||||||
\(578\) | 1.00000 | 0.0415945 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 16.0000 | 0.664364 | ||||||||
\(581\) | −35.0000 | + | 12.1244i | −1.45204 | + | 0.503003i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.0000 | −0.496989 | ||||||||
\(584\) | 4.50000 | + | 7.79423i | 0.186211 | + | 0.322527i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.0000 | + | 24.2487i | −0.578335 | + | 1.00171i | ||||
\(587\) | 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 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7.00000 | 0.287698 | ||||||||
\(593\) | −16.0000 | + | 27.7128i | −0.657041 | + | 1.13803i | 0.324337 | + | 0.945942i | \(0.394859\pi\) |
−0.981378 | + | 0.192087i | \(0.938474\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.00000 | + | 20.7846i | −0.163984 | + | 0.852086i | ||||
\(596\) | −3.00000 | − | 5.19615i | −0.122885 | − | 0.212843i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.00000 | − | 1.73205i | 0.286251 | − | 0.0708288i | ||||
\(599\) | −6.00000 | − | 10.3923i | −0.245153 | − | 0.424618i | 0.717021 | − | 0.697051i | \(-0.245505\pi\) |
−0.962175 | + | 0.272433i | \(0.912172\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.500000 | + | 0.866025i | 0.0203954 | + | 0.0353259i | 0.876043 | − | 0.482233i | \(-0.160174\pi\) |
−0.855648 | + | 0.517559i | \(0.826841\pi\) | |||||||
\(602\) | −3.50000 | + | 18.1865i | −0.142649 | + | 0.741228i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.00000 | + | 13.8564i | 0.325515 | + | 0.563809i | ||||
\(605\) | 14.0000 | 0.569181 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.5000 | − | 19.9186i | −0.466771 | − | 0.808470i | 0.532509 | − | 0.846424i | \(-0.321249\pi\) |
−0.999279 | + | 0.0379540i | \(0.987916\pi\) | |||||||
\(608\) | 2.50000 | + | 4.33013i | 0.101388 | + | 0.175610i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.00000 | −0.0809776 | ||||||||
\(611\) | −12.0000 | + | 41.5692i | −0.485468 | + | 1.68171i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.50000 | + | 9.52628i | −0.222143 | + | 0.384763i | −0.955458 | − | 0.295126i | \(-0.904638\pi\) |
0.733316 | + | 0.679888i | \(0.237972\pi\) | |||||||
\(614\) | 12.0000 | 0.484281 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.00000 | + | 5.19615i | −0.0402911 | + | 0.209359i | ||||
\(617\) | 10.0000 | − | 17.3205i | 0.402585 | − | 0.697297i | −0.591452 | − | 0.806340i | \(-0.701445\pi\) |
0.994037 | + | 0.109043i | \(0.0347785\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.50000 | + | 6.06218i | 0.140677 | + | 0.243659i | 0.927752 | − | 0.373198i | \(-0.121739\pi\) |
−0.787075 | + | 0.616858i | \(0.788405\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −15.0000 | − | 25.9808i | −0.601445 | − | 1.04173i | ||||
\(623\) | 15.0000 | − | 5.19615i | 0.600962 | − | 0.208179i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.50000 | − | 16.4545i | 0.380000 | − | 0.658179i | ||||
\(626\) | −10.5000 | + | 18.1865i | −0.419664 | + | 0.726880i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.50000 | + | 14.7224i | 0.339187 | + | 0.587489i | ||||
\(629\) | 28.0000 | 1.11643 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.5000 | + | 21.6506i | −0.497617 | + | 0.861898i | −0.999996 | − | 0.00274930i | \(-0.999125\pi\) |
0.502379 | + | 0.864647i | \(0.332458\pi\) | |||||||
\(632\) | 4.00000 | − | 6.92820i | 0.159111 | − | 0.275589i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.00000 | − | 1.73205i | 0.0397151 | − | 0.0687885i | ||||
\(635\) | −38.0000 | −1.50798 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.5000 | + | 19.9186i | −0.614132 | + | 0.789203i | ||||
\(638\) | 16.0000 | 0.633446 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.00000 | + | 1.73205i | −0.0395285 | + | 0.0684653i | ||||
\(641\) | −34.0000 | −1.34292 | −0.671460 | − | 0.741041i | \(-0.734332\pi\) | ||||
−0.671460 | + | 0.741041i | \(0.734332\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.50000 | − | 11.2583i | 0.256335 | − | 0.443985i | −0.708922 | − | 0.705287i | \(-0.750818\pi\) |
0.965257 | + | 0.261301i | \(0.0841516\pi\) | |||||||
\(644\) | −5.00000 | + | 1.73205i | −0.197028 | + | 0.0682524i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10.0000 | + | 17.3205i | 0.393445 | + | 0.681466i | ||||
\(647\) | −6.00000 | + | 10.3923i | −0.235884 | + | 0.408564i | −0.959529 | − | 0.281609i | \(-0.909132\pi\) |
0.723645 | + | 0.690172i | \(0.242465\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.50000 | + | 2.59808i | 0.0980581 | + | 0.101905i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.50000 | + | 2.59808i | 0.0587445 | + | 0.101749i | ||||
\(653\) | −36.0000 | −1.40879 | −0.704394 | − | 0.709809i | \(-0.748781\pi\) | ||||
−0.704394 | + | 0.709809i | \(0.748781\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.00000 | + | 10.3923i | 0.234439 | + | 0.406061i | ||||
\(656\) | 5.00000 | + | 8.66025i | 0.195217 | + | 0.338126i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.00000 | − | 31.1769i | 0.233904 | − | 1.21540i | ||||
\(659\) | 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 | ||||||||
\(661\) | 19.0000 | − | 32.9090i | 0.739014 | − | 1.28001i | −0.213925 | − | 0.976850i | \(-0.568625\pi\) |
0.952940 | − | 0.303160i | \(-0.0980418\pi\) | |||||||
\(662\) | −7.50000 | − | 12.9904i | −0.291496 | − | 0.504885i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −14.0000 | −0.543305 | ||||||||
\(665\) | 25.0000 | − | 8.66025i | 0.969458 | − | 0.335830i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.00000 | + | 13.8564i | 0.309761 | + | 0.536522i | ||||
\(668\) | −9.00000 | − | 15.5885i | −0.348220 | − | 0.603136i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8.00000 | + | 13.8564i | 0.309067 | + | 0.535320i | ||||
\(671\) | −2.00000 | −0.0772091 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.50000 | − | 12.9904i | −0.289104 | − | 0.500742i | 0.684492 | − | 0.729020i | \(-0.260024\pi\) |
−0.973596 | + | 0.228278i | \(0.926691\pi\) | |||||||
\(674\) | 3.00000 | 0.115556 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.5000 | − | 6.06218i | 0.442308 | − | 0.233161i | ||||
\(677\) | 1.00000 | − | 1.73205i | 0.0384331 | − | 0.0665681i | −0.846169 | − | 0.532915i | \(-0.821097\pi\) |
0.884602 | + | 0.466347i | \(0.154430\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.50000 | − | 44.1673i | 0.326200 | − | 1.69499i | ||||
\(680\) | −4.00000 | + | 6.92820i | −0.153393 | + | 0.265684i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.0000 | 0.382639 | 0.191320 | − | 0.981528i | \(-0.438723\pi\) | ||||
0.191320 | + | 0.981528i | \(0.438723\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.00000 | + | 3.46410i | −0.0764161 | + | 0.132357i | ||||
\(686\) | 10.0000 | − | 15.5885i | 0.381802 | − | 0.595170i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.50000 | + | 6.06218i | −0.133436 | + | 0.231118i | ||||
\(689\) | −15.0000 | − | 15.5885i | −0.571454 | − | 0.593873i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.0000 | −0.874961 | −0.437481 | − | 0.899228i | \(-0.644129\pi\) | ||||
−0.437481 | + | 0.899228i | \(0.644129\pi\) | |||||||
\(692\) | −1.00000 | − | 1.73205i | −0.0380143 | − | 0.0658427i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.00000 | 0.303676 | ||||||||
\(695\) | 4.00000 | + | 6.92820i | 0.151729 | + | 0.262802i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.0000 | + | 34.6410i | 0.757554 | + | 1.31212i | ||||
\(698\) | −0.500000 | − | 0.866025i | −0.0189253 | − | 0.0327795i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.00000 | − | 1.73205i | −0.0755929 | − | 0.0654654i | ||||
\(701\) | 48.0000 | 1.81293 | 0.906467 | − | 0.422276i | \(-0.138769\pi\) | ||||
0.906467 | + | 0.422276i | \(0.138769\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.5000 | − | 30.3109i | −0.660025 | − | 1.14320i | ||||
\(704\) | −1.00000 | + | 1.73205i | −0.0376889 | + | 0.0652791i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.00000 | + | 12.1244i | −0.263448 | + | 0.456306i | ||||
\(707\) | 3.00000 | − | 15.5885i | 0.112827 | − | 0.586264i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.5000 | − | 38.9711i | −0.845005 | − | 1.46359i | −0.885617 | − | 0.464417i | \(-0.846264\pi\) |
0.0406114 | − | 0.999175i | \(-0.487069\pi\) | |||||||
\(710\) | 8.00000 | + | 13.8564i | 0.300235 | + | 0.520022i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.00000 | 0.224860 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.0000 | − | 10.3923i | −0.373979 | − | 0.388650i | ||||
\(716\) | 3.00000 | − | 5.19615i | 0.112115 | − | 0.194189i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 18.0000 | − | 31.1769i | 0.671754 | − | 1.16351i | ||||
\(719\) | 5.00000 | + | 8.66025i | 0.186469 | + | 0.322973i | 0.944070 | − | 0.329744i | \(-0.106962\pi\) |
−0.757602 | + | 0.652717i | \(0.773629\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.50000 | + | 12.9904i | −0.0931049 | + | 0.483787i | ||||
\(722\) | 3.00000 | − | 5.19615i | 0.111648 | − | 0.193381i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 13.0000 | 0.483141 | ||||||||
\(725\) | −4.00000 | + | 6.92820i | −0.148556 | + | 0.257307i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.0000 | 0.890111 | 0.445055 | − | 0.895503i | \(-0.353184\pi\) | ||||
0.445055 | + | 0.895503i | \(0.353184\pi\) | |||||||
\(728\) | −8.00000 | + | 5.19615i | −0.296500 | + | 0.192582i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 18.0000 | 0.666210 | ||||||||
\(731\) | −14.0000 | + | 24.2487i | −0.517809 | + | 0.896871i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.0000 | − | 25.9808i | 0.554038 | − | 0.959621i | −0.443940 | − | 0.896056i | \(-0.646420\pi\) |
0.997978 | − | 0.0635649i | \(-0.0202470\pi\) | |||||||
\(734\) | 16.5000 | − | 28.5788i | 0.609026 | − | 1.05486i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.00000 | −0.0737210 | ||||||||
\(737\) | 8.00000 | + | 13.8564i | 0.294684 | + | 0.510407i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.5000 | − | 19.9186i | 0.423034 | − | 0.732717i | −0.573200 | − | 0.819415i | \(-0.694298\pi\) |
0.996235 | + | 0.0866983i | \(0.0276316\pi\) | |||||||
\(740\) | 7.00000 | − | 12.1244i | 0.257325 | − | 0.445700i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12.0000 | + | 10.3923i | 0.440534 | + | 0.381514i | ||||
\(743\) | 25.0000 | + | 43.3013i | 0.917161 | + | 1.58857i | 0.803706 | + | 0.595026i | \(0.202858\pi\) |
0.113455 | + | 0.993543i | \(0.463808\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.0000 | −0.439646 | ||||||||
\(746\) | 17.0000 | + | 29.4449i | 0.622414 | + | 1.07805i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.00000 | + | 6.92820i | −0.146254 | + | 0.253320i | ||||
\(749\) | −30.0000 | + | 10.3923i | −1.09618 | + | 0.379727i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.0000 | −1.27717 | −0.638584 | − | 0.769552i | \(-0.720480\pi\) | ||||
−0.638584 | + | 0.769552i | \(0.720480\pi\) | |||||||
\(752\) | 6.00000 | − | 10.3923i | 0.218797 | − | 0.378968i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 20.0000 | + | 20.7846i | 0.728357 | + | 0.756931i | ||||
\(755\) | 32.0000 | 1.16460 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.00000 | + | 1.73205i | 0.0363456 | + | 0.0629525i | 0.883626 | − | 0.468193i | \(-0.155095\pi\) |
−0.847280 | + | 0.531146i | \(0.821762\pi\) | |||||||
\(758\) | 14.0000 | + | 24.2487i | 0.508503 | + | 0.880753i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 10.0000 | 0.362738 | ||||||||
\(761\) | −11.0000 | − | 19.0526i | −0.398750 | − | 0.690655i | 0.594822 | − | 0.803857i | \(-0.297222\pi\) |
−0.993572 | + | 0.113203i | \(0.963889\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −38.0000 | − | 32.9090i | −1.37569 | − | 1.19138i | ||||
\(764\) | 12.0000 | + | 20.7846i | 0.434145 | + | 0.751961i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18.0000 | + | 31.1769i | 0.650366 | + | 1.12647i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.5000 | + | 35.5070i | 0.739249 | + | 1.28042i | 0.952834 | + | 0.303492i | \(0.0981526\pi\) |
−0.213585 | + | 0.976924i | \(0.568514\pi\) | |||||||
\(770\) | 8.00000 | + | 6.92820i | 0.288300 | + | 0.249675i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.50000 | + | 9.52628i | −0.197949 | + | 0.342858i | ||||
\(773\) | −4.00000 | −0.143870 | −0.0719350 | − | 0.997409i | \(-0.522917\pi\) | ||||
−0.0719350 | + | 0.997409i | \(0.522917\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 8.50000 | − | 14.7224i | 0.305132 | − | 0.528505i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 19.0000 | + | 32.9090i | 0.681183 | + | 1.17984i | ||||
\(779\) | 25.0000 | − | 43.3013i | 0.895718 | − | 1.55143i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.00000 | + | 13.8564i | 0.286263 | + | 0.495821i | ||||
\(782\) | −8.00000 | −0.286079 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.50000 | − | 4.33013i | 0.196429 | − | 0.154647i | ||||
\(785\) | 34.0000 | 1.21351 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.0000 | 1.03374 | 0.516869 | − | 0.856064i | \(-0.327097\pi\) | ||||
0.516869 | + | 0.856064i | \(0.327097\pi\) | |||||||
\(788\) | 6.00000 | + | 10.3923i | 0.213741 | + | 0.370211i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.00000 | − | 13.8564i | −0.284627 | − | 0.492989i | ||||
\(791\) | −4.00000 | + | 20.7846i | −0.142224 | + | 0.739016i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.50000 | − | 2.59808i | −0.0887776 | − | 0.0922604i | ||||
\(794\) | −12.5000 | − | 21.6506i | −0.443608 | − | 0.768352i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.00000 | 0.248108 | ||||||||
\(797\) | −9.00000 | + | 15.5885i | −0.318796 | + | 0.552171i | −0.980237 | − | 0.197826i | \(-0.936612\pi\) |
0.661441 | + | 0.749997i | \(0.269945\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.0000 | − | 41.5692i | 0.849059 | − | 1.47061i | ||||
\(800\) | −0.500000 | − | 0.866025i | −0.0176777 | − | 0.0306186i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 10.0000 | 0.353112 | ||||||||
\(803\) | 18.0000 | 0.635206 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.00000 | + | 10.3923i | −0.0704907 | + | 0.366281i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.00000 | − | 5.19615i | 0.105540 | − | 0.182800i | ||||
\(809\) | 6.00000 | − | 10.3923i | 0.210949 | − | 0.365374i | −0.741063 | − | 0.671436i | \(-0.765678\pi\) |
0.952012 | + | 0.306062i | \(0.0990113\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −49.0000 | −1.72062 | −0.860311 | − | 0.509769i | \(-0.829731\pi\) | ||||
−0.860311 | + | 0.509769i | \(0.829731\pi\) | |||||||
\(812\) | −16.0000 | − | 13.8564i | −0.561490 | − | 0.486265i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.00000 | − | 12.1244i | 0.245350 | − | 0.424958i | ||||
\(815\) | 6.00000 | 0.210171 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 35.0000 | 1.22449 | ||||||||
\(818\) | 19.0000 | 0.664319 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 20.0000 | 0.698430 | ||||||||
\(821\) | 34.0000 | 1.18661 | 0.593304 | − | 0.804978i | \(-0.297823\pi\) | ||||
0.593304 | + | 0.804978i | \(0.297823\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.00000 | −0.278862 | −0.139431 | − | 0.990232i | \(-0.544527\pi\) | ||||
−0.139431 | + | 0.990232i | \(0.544527\pi\) | |||||||
\(824\) | −2.50000 | + | 4.33013i | −0.0870916 | + | 0.150847i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.00000 | −0.278187 | −0.139094 | − | 0.990279i | \(-0.544419\pi\) | ||||
−0.139094 | + | 0.990279i | \(0.544419\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.50000 | − | 2.59808i | 0.0520972 | − | 0.0902349i | −0.838801 | − | 0.544438i | \(-0.816743\pi\) |
0.890898 | + | 0.454204i | \(0.150076\pi\) | |||||||
\(830\) | −14.0000 | + | 24.2487i | −0.485947 | + | 0.841685i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.50000 | + | 0.866025i | −0.121341 | + | 0.0300240i | ||||
\(833\) | 22.0000 | − | 17.3205i | 0.762255 | − | 0.600120i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −36.0000 | −1.24583 | ||||||||
\(836\) | 10.0000 | 0.345857 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5.00000 | − | 8.66025i | −0.172722 | − | 0.299164i | ||||
\(839\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.5000 | + | 30.3109i | −0.603448 | + | 1.04520i | ||||
\(842\) | −22.0000 | −0.758170 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.50000 | − | 11.2583i | −0.223739 | − | 0.387528i | ||||
\(845\) | 1.00000 | − | 25.9808i | 0.0344010 | − | 0.893765i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.0000 | − | 12.1244i | −0.481046 | − | 0.416598i | ||||
\(848\) | 3.00000 | + | 5.19615i | 0.103020 | + | 0.178437i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.00000 | − | 3.46410i | −0.0685994 | − | 0.118818i | ||||
\(851\) | 14.0000 | 0.479914 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.0000 | 0.753266 | 0.376633 | − | 0.926363i | \(-0.377082\pi\) | ||||
0.376633 | + | 0.926363i | \(0.377082\pi\) | |||||||
\(854\) | 2.00000 | + | 1.73205i | 0.0684386 | + | 0.0592696i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.0000 | −0.410152 | ||||||||
\(857\) | 12.0000 | + | 20.7846i | 0.409912 | + | 0.709989i | 0.994880 | − | 0.101068i | \(-0.0322260\pi\) |
−0.584967 | + | 0.811057i | \(0.698893\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.50000 | + | 11.2583i | −0.221777 | + | 0.384129i | −0.955348 | − | 0.295484i | \(-0.904519\pi\) |
0.733571 | + | 0.679613i | \(0.237852\pi\) | |||||||
\(860\) | 7.00000 | + | 12.1244i | 0.238698 | + | 0.413437i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.00000 | − | 12.1244i | 0.238421 | − | 0.412957i | ||||
\(863\) | −15.0000 | + | 25.9808i | −0.510606 | + | 0.884395i | 0.489319 | + | 0.872105i | \(0.337246\pi\) |
−0.999924 | + | 0.0122903i | \(0.996088\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.00000 | −0.136004 | ||||||||
\(866\) | −9.00000 | + | 15.5885i | −0.305832 | + | 0.529717i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.00000 | − | 13.8564i | −0.271381 | − | 0.470046i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.00000 | + | 27.7128i | −0.271070 | + | 0.939013i | ||||
\(872\) | −9.50000 | − | 16.4545i | −0.321711 | − | 0.557219i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5.00000 | + | 8.66025i | 0.169128 | + | 0.292937i | ||||
\(875\) | −30.0000 | + | 10.3923i | −1.01419 | + | 0.351324i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.0000 | + | 19.0526i | 0.371444 | + | 0.643359i | 0.989788 | − | 0.142548i | \(-0.0455296\pi\) |
−0.618344 | + | 0.785907i | \(0.712196\pi\) | |||||||
\(878\) | −25.0000 | −0.843709 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.00000 | + | 3.46410i | 0.0674200 | + | 0.116775i | ||||
\(881\) | −14.0000 | − | 24.2487i | −0.471672 | − | 0.816960i | 0.527803 | − | 0.849367i | \(-0.323016\pi\) |
−0.999475 | + | 0.0324071i | \(0.989683\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.0000 | 0.975928 | 0.487964 | − | 0.872864i | \(-0.337740\pi\) | ||||
0.487964 | + | 0.872864i | \(0.337740\pi\) | |||||||
\(884\) | −14.0000 | + | 3.46410i | −0.470871 | + | 0.116510i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.00000 | − | 5.19615i | 0.100787 | − | 0.174568i | ||||
\(887\) | 50.0000 | 1.67884 | 0.839418 | − | 0.543487i | \(-0.182896\pi\) | ||||
0.839418 | + | 0.543487i | \(0.182896\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 38.0000 | + | 32.9090i | 1.27448 | + | 1.10373i | ||||
\(890\) | 6.00000 | − | 10.3923i | 0.201120 | − | 0.348351i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −60.0000 | −2.00782 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.00000 | − | 10.3923i | −0.200558 | − | 0.347376i | ||||
\(896\) | 2.50000 | − | 0.866025i | 0.0835191 | − | 0.0289319i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.00000 | − | 15.5885i | 0.300334 | − | 0.520194i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.0000 | + | 20.7846i | 0.399778 | + | 0.692436i | ||||
\(902\) | 20.0000 | 0.665927 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.00000 | + | 6.92820i | −0.133038 | + | 0.230429i | ||||
\(905\) | 13.0000 | − | 22.5167i | 0.432135 | − | 0.748479i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.5000 | + | 33.7750i | −0.647487 | + | 1.12148i | 0.336234 | + | 0.941778i | \(0.390847\pi\) |
−0.983721 | + | 0.179702i | \(0.942487\pi\) | |||||||
\(908\) | −2.00000 | −0.0663723 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.00000 | + | 19.0526i | 0.0331497 | + | 0.631586i | ||||
\(911\) | 36.0000 | 1.19273 | 0.596367 | − | 0.802712i | \(-0.296610\pi\) | ||||
0.596367 | + | 0.802712i | \(0.296610\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.0000 | + | 24.2487i | −0.463332 | + | 0.802515i | ||||
\(914\) | −6.00000 | −0.198462 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.500000 | + | 0.866025i | −0.0165205 | + | 0.0286143i | ||||
\(917\) | 3.00000 | − | 15.5885i | 0.0990687 | − | 0.514776i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.500000 | + | 0.866025i | 0.0164935 | + | 0.0285675i | 0.874154 | − | 0.485648i | \(-0.161416\pi\) |
−0.857661 | + | 0.514216i | \(0.828083\pi\) | |||||||
\(920\) | −2.00000 | + | 3.46410i | −0.0659380 | + | 0.114208i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −16.0000 | + | 27.7128i | −0.526932 | + | 0.912673i | ||||
\(923\) | −8.00000 | + | 27.7128i | −0.263323 | + | 0.912178i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.50000 | + | 6.06218i | 0.115079 | + | 0.199323i | ||||
\(926\) | 27.0000 | 0.887275 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.00000 | − | 6.92820i | −0.131306 | − | 0.227429i | ||||
\(929\) | 24.0000 | + | 41.5692i | 0.787414 | + | 1.36384i | 0.927546 | + | 0.373709i | \(0.121914\pi\) |
−0.140132 | + | 0.990133i | \(0.544753\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32.5000 | − | 12.9904i | −1.06514 | − | 0.425743i | ||||
\(932\) | −10.0000 | + | 17.3205i | −0.327561 | + | 0.567352i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.00000 | + | 1.73205i | −0.0327210 | + | 0.0566744i | ||||
\(935\) | 8.00000 | + | 13.8564i | 0.261628 | + | 0.453153i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.00000 | 0.0980057 | 0.0490029 | − | 0.998799i | \(-0.484396\pi\) | ||||
0.0490029 | + | 0.998799i | \(0.484396\pi\) | |||||||
\(938\) | 4.00000 | − | 20.7846i | 0.130605 | − | 0.678642i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −12.0000 | − | 20.7846i | −0.391397 | − | 0.677919i | ||||
\(941\) | 26.0000 | + | 45.0333i | 0.847576 | + | 1.46804i | 0.883365 | + | 0.468685i | \(0.155272\pi\) |
−0.0357896 | + | 0.999359i | \(0.511395\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.0000 | + | 17.3205i | 0.325645 | + | 0.564033i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.00000 | + | 12.1244i | 0.227590 | + | 0.394197i | ||||
\(947\) | −32.0000 | −1.03986 | −0.519930 | − | 0.854209i | \(-0.674042\pi\) | ||||
−0.519930 | + | 0.854209i | \(0.674042\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22.5000 | + | 23.3827i | 0.730381 | + | 0.759034i | ||||
\(950\) | −2.50000 | + | 4.33013i | −0.0811107 | + | 0.140488i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 10.0000 | − | 3.46410i | 0.324102 | − | 0.112272i | ||||
\(953\) | −25.0000 | + | 43.3013i | −0.809829 | + | 1.40267i | 0.103152 | + | 0.994666i | \(0.467107\pi\) |
−0.912982 | + | 0.408000i | \(0.866226\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 48.0000 | 1.55324 | ||||||||
\(956\) | 18.0000 | 0.582162 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12.0000 | + | 20.7846i | −0.387702 | + | 0.671520i | ||||
\(959\) | 5.00000 | − | 1.73205i | 0.161458 | − | 0.0559308i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.5000 | − | 26.8468i | 0.500000 | − | 0.866025i | ||||
\(962\) | 24.5000 | − | 6.06218i | 0.789912 | − | 0.195452i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −22.0000 | −0.708572 | ||||||||
\(965\) | 11.0000 | + | 19.0526i | 0.354103 | + | 0.613324i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.0000 | −0.675314 | −0.337657 | − | 0.941269i | \(-0.609634\pi\) | ||||
−0.337657 | + | 0.941269i | \(0.609634\pi\) | |||||||
\(968\) | −3.50000 | − | 6.06218i | −0.112494 | − | 0.194846i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −17.0000 | − | 29.4449i | −0.545837 | − | 0.945418i | ||||
\(971\) | 9.00000 | + | 15.5885i | 0.288824 | + | 0.500257i | 0.973529 | − | 0.228562i | \(-0.0734025\pi\) |
−0.684706 | + | 0.728820i | \(0.740069\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.00000 | − | 10.3923i | 0.0641171 | − | 0.333162i | ||||
\(974\) | 25.0000 | 0.801052 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.500000 | + | 0.866025i | 0.0160046 | + | 0.0277208i | ||||
\(977\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.00000 | − | 10.3923i | 0.191761 | − | 0.332140i | ||||
\(980\) | −2.00000 | − | 13.8564i | −0.0638877 | − | 0.442627i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.00000 | − | 6.92820i | −0.127645 | − | 0.221088i | ||||
\(983\) | 2.00000 | + | 3.46410i | 0.0637901 | + | 0.110488i | 0.896157 | − | 0.443738i | \(-0.146348\pi\) |
−0.832367 | + | 0.554226i | \(0.813015\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 24.0000 | 0.764704 | ||||||||
\(986\) | −16.0000 | − | 27.7128i | −0.509544 | − | 0.882556i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 12.5000 | + | 12.9904i | 0.397678 | + | 0.413279i | ||||
\(989\) | −7.00000 | + | 12.1244i | −0.222587 | + | 0.385532i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.5000 | + | 38.9711i | −0.714736 | + | 1.23796i | 0.248325 | + | 0.968677i | \(0.420120\pi\) |
−0.963061 | + | 0.269282i | \(0.913213\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4.00000 | − | 20.7846i | 0.126872 | − | 0.659248i | ||||
\(995\) | 7.00000 | − | 12.1244i | 0.221915 | − | 0.384368i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.0000 | 0.601736 | 0.300868 | − | 0.953666i | \(-0.402724\pi\) | ||||
0.300868 | + | 0.953666i | \(0.402724\pi\) | |||||||
\(998\) | 12.5000 | − | 21.6506i | 0.395681 | − | 0.685339i | ||||
\(999\) | 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 | 1638.2.m.b.289.1 | ✓ | 2 | |
3.2 | odd | 2 | 1638.2.m.d.289.1 | yes | 2 | ||
7.4 | even | 3 | 1638.2.p.e.991.1 | yes | 2 | ||
13.9 | even | 3 | 1638.2.p.e.919.1 | yes | 2 | ||
21.11 | odd | 6 | 1638.2.p.b.991.1 | yes | 2 | ||
39.35 | odd | 6 | 1638.2.p.b.919.1 | yes | 2 | ||
91.74 | even | 3 | inner | 1638.2.m.b.1621.1 | yes | 2 | |
273.74 | odd | 6 | 1638.2.m.d.1621.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1638.2.m.b.289.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1638.2.m.b.1621.1 | yes | 2 | 91.74 | even | 3 | inner | |
1638.2.m.d.289.1 | yes | 2 | 3.2 | odd | 2 | ||
1638.2.m.d.1621.1 | yes | 2 | 273.74 | odd | 6 | ||
1638.2.p.b.919.1 | yes | 2 | 39.35 | odd | 6 | ||
1638.2.p.b.991.1 | yes | 2 | 21.11 | odd | 6 | ||
1638.2.p.e.919.1 | yes | 2 | 13.9 | even | 3 | ||
1638.2.p.e.991.1 | yes | 2 | 7.4 | even | 3 |