Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(491,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.491");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.q (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.08647060876\) |
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 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 589.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.589 |
Dual form | 637.2.q.b.491.1 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.50000 | + | 0.866025i | 1.06066 | + | 0.612372i | 0.925615 | − | 0.378467i | \(-0.123549\pi\) |
0.135045 | + | 0.990839i | \(0.456882\pi\) | |||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | −0.973494 | − | 0.228714i | \(-0.926548\pi\) |
0.684819 | + | 0.728714i | \(0.259881\pi\) | |||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | − | 1.73205i | − | 0.774597i | −0.921954 | − | 0.387298i | \(-0.873408\pi\) | ||
0.921954 | − | 0.387298i | \(-0.126592\pi\) | |||||||
\(6\) | −1.50000 | + | 0.866025i | −0.612372 | + | 0.353553i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.73205i | − | 0.612372i | ||||||
\(9\) | 1.00000 | + | 1.73205i | 0.333333 | + | 0.577350i | ||||
\(10\) | 1.50000 | − | 2.59808i | 0.474342 | − | 0.821584i | ||||
\(11\) | 4.50000 | + | 2.59808i | 1.35680 | + | 0.783349i | 0.989191 | − | 0.146631i | \(-0.0468429\pi\) |
0.367610 | + | 0.929980i | \(0.380176\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.00000 | − | 3.46410i | 0.277350 | − | 0.960769i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.50000 | + | 0.866025i | 0.387298 | + | 0.223607i | ||||
\(16\) | 2.50000 | − | 4.33013i | 0.625000 | − | 1.08253i | ||||
\(17\) | 3.00000 | + | 5.19615i | 0.727607 | + | 1.26025i | 0.957892 | + | 0.287129i | \(0.0927008\pi\) |
−0.230285 | + | 0.973123i | \(0.573966\pi\) | |||||||
\(18\) | 3.46410i | 0.816497i | ||||||||
\(19\) | −1.50000 | + | 0.866025i | −0.344124 | + | 0.198680i | −0.662094 | − | 0.749421i | \(-0.730332\pi\) |
0.317970 | + | 0.948101i | \(0.396999\pi\) | |||||||
\(20\) | 1.50000 | − | 0.866025i | 0.335410 | − | 0.193649i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.50000 | + | 7.79423i | 0.959403 | + | 1.66174i | ||||
\(23\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(24\) | 1.50000 | + | 0.866025i | 0.306186 | + | 0.176777i | ||||
\(25\) | 2.00000 | 0.400000 | ||||||||
\(26\) | 4.50000 | − | 4.33013i | 0.882523 | − | 0.849208i | ||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.50000 | + | 2.59808i | −0.278543 | + | 0.482451i | −0.971023 | − | 0.238987i | \(-0.923185\pi\) |
0.692480 | + | 0.721437i | \(0.256518\pi\) | |||||||
\(30\) | 1.50000 | + | 2.59808i | 0.273861 | + | 0.474342i | ||||
\(31\) | − | 1.73205i | − | 0.311086i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) | ||
0.987829 | − | 0.155543i | \(-0.0497126\pi\) | |||||||
\(32\) | 4.50000 | − | 2.59808i | 0.795495 | − | 0.459279i | ||||
\(33\) | −4.50000 | + | 2.59808i | −0.783349 | + | 0.452267i | ||||
\(34\) | 10.3923i | 1.78227i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | + | 1.73205i | −0.166667 | + | 0.288675i | ||||
\(37\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(38\) | −3.00000 | −0.486664 | ||||||||
\(39\) | 2.50000 | + | 2.59808i | 0.400320 | + | 0.416025i | ||||
\(40\) | −3.00000 | −0.474342 | ||||||||
\(41\) | 4.50000 | + | 2.59808i | 0.702782 | + | 0.405751i | 0.808383 | − | 0.588657i | \(-0.200343\pi\) |
−0.105601 | + | 0.994409i | \(0.533677\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.50000 | − | 9.52628i | −0.838742 | − | 1.45274i | −0.890947 | − | 0.454108i | \(-0.849958\pi\) |
0.0522047 | − | 0.998636i | \(-0.483375\pi\) | |||||||
\(44\) | 5.19615i | 0.783349i | ||||||||
\(45\) | 3.00000 | − | 1.73205i | 0.447214 | − | 0.258199i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 8.66025i | − | 1.26323i | −0.775283 | − | 0.631614i | \(-0.782393\pi\) | ||
0.775283 | − | 0.631614i | \(-0.217607\pi\) | |||||||
\(48\) | 2.50000 | + | 4.33013i | 0.360844 | + | 0.625000i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.00000 | + | 1.73205i | 0.424264 | + | 0.244949i | ||||
\(51\) | −6.00000 | −0.840168 | ||||||||
\(52\) | 3.50000 | − | 0.866025i | 0.485363 | − | 0.120096i | ||||
\(53\) | −9.00000 | −1.23625 | −0.618123 | − | 0.786082i | \(-0.712106\pi\) | ||||
−0.618123 | + | 0.786082i | \(0.712106\pi\) | |||||||
\(54\) | −7.50000 | − | 4.33013i | −1.02062 | − | 0.589256i | ||||
\(55\) | 4.50000 | − | 7.79423i | 0.606780 | − | 1.05097i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 1.73205i | − | 0.229416i | ||||||
\(58\) | −4.50000 | + | 2.59808i | −0.590879 | + | 0.341144i | ||||
\(59\) | −3.00000 | + | 1.73205i | −0.390567 | + | 0.225494i | −0.682406 | − | 0.730974i | \(-0.739066\pi\) |
0.291839 | + | 0.956467i | \(0.405733\pi\) | |||||||
\(60\) | 1.73205i | 0.223607i | ||||||||
\(61\) | 3.50000 | + | 6.06218i | 0.448129 | + | 0.776182i | 0.998264 | − | 0.0588933i | \(-0.0187572\pi\) |
−0.550135 | + | 0.835076i | \(0.685424\pi\) | |||||||
\(62\) | 1.50000 | − | 2.59808i | 0.190500 | − | 0.329956i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −6.00000 | − | 1.73205i | −0.744208 | − | 0.214834i | ||||
\(66\) | −9.00000 | −1.10782 | ||||||||
\(67\) | −7.50000 | − | 4.33013i | −0.916271 | − | 0.529009i | −0.0338274 | − | 0.999428i | \(-0.510770\pi\) |
−0.882443 | + | 0.470418i | \(0.844103\pi\) | |||||||
\(68\) | −3.00000 | + | 5.19615i | −0.363803 | + | 0.630126i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.50000 | − | 0.866025i | 0.178017 | − | 0.102778i | −0.408344 | − | 0.912828i | \(-0.633893\pi\) |
0.586361 | + | 0.810050i | \(0.300560\pi\) | |||||||
\(72\) | 3.00000 | − | 1.73205i | 0.353553 | − | 0.204124i | ||||
\(73\) | 8.66025i | 1.01361i | 0.862062 | + | 0.506803i | \(0.169173\pi\) | ||||
−0.862062 | + | 0.506803i | \(0.830827\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | + | 1.73205i | −0.115470 | + | 0.200000i | ||||
\(76\) | −1.50000 | − | 0.866025i | −0.172062 | − | 0.0993399i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.50000 | + | 6.06218i | 0.169842 | + | 0.686406i | ||||
\(79\) | −5.00000 | −0.562544 | −0.281272 | − | 0.959628i | \(-0.590756\pi\) | ||||
−0.281272 | + | 0.959628i | \(0.590756\pi\) | |||||||
\(80\) | −7.50000 | − | 4.33013i | −0.838525 | − | 0.484123i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 4.50000 | + | 7.79423i | 0.496942 | + | 0.860729i | ||||
\(83\) | 3.46410i | 0.380235i | 0.981761 | + | 0.190117i | \(0.0608868\pi\) | ||||
−0.981761 | + | 0.190117i | \(0.939113\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.00000 | − | 5.19615i | 0.976187 | − | 0.563602i | ||||
\(86\) | − | 19.0526i | − | 2.05449i | ||||||
\(87\) | −1.50000 | − | 2.59808i | −0.160817 | − | 0.278543i | ||||
\(88\) | 4.50000 | − | 7.79423i | 0.479702 | − | 0.830868i | ||||
\(89\) | −6.00000 | − | 3.46410i | −0.635999 | − | 0.367194i | 0.147073 | − | 0.989126i | \(-0.453015\pi\) |
−0.783072 | + | 0.621932i | \(0.786348\pi\) | |||||||
\(90\) | 6.00000 | 0.632456 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.50000 | + | 0.866025i | 0.155543 | + | 0.0898027i | ||||
\(94\) | 7.50000 | − | 12.9904i | 0.773566 | − | 1.33986i | ||||
\(95\) | 1.50000 | + | 2.59808i | 0.153897 | + | 0.266557i | ||||
\(96\) | 5.19615i | 0.530330i | ||||||||
\(97\) | 4.50000 | − | 2.59808i | 0.456906 | − | 0.263795i | −0.253837 | − | 0.967247i | \(-0.581693\pi\) |
0.710742 | + | 0.703452i | \(0.248359\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.3923i | 1.04447i | ||||||||
\(100\) | 1.00000 | + | 1.73205i | 0.100000 | + | 0.173205i | ||||
\(101\) | −4.50000 | + | 7.79423i | −0.447767 | + | 0.775555i | −0.998240 | − | 0.0592978i | \(-0.981114\pi\) |
0.550474 | + | 0.834853i | \(0.314447\pi\) | |||||||
\(102\) | −9.00000 | − | 5.19615i | −0.891133 | − | 0.514496i | ||||
\(103\) | 13.0000 | 1.28093 | 0.640464 | − | 0.767988i | \(-0.278742\pi\) | ||||
0.640464 | + | 0.767988i | \(0.278742\pi\) | |||||||
\(104\) | −6.00000 | − | 1.73205i | −0.588348 | − | 0.169842i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −13.5000 | − | 7.79423i | −1.31124 | − | 0.757042i | ||||
\(107\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(108\) | −2.50000 | − | 4.33013i | −0.240563 | − | 0.416667i | ||||
\(109\) | 5.19615i | 0.497701i | 0.968542 | + | 0.248851i | \(0.0800528\pi\) | ||||
−0.968542 | + | 0.248851i | \(0.919947\pi\) | |||||||
\(110\) | 13.5000 | − | 7.79423i | 1.28717 | − | 0.743151i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.50000 | − | 12.9904i | −0.705541 | − | 1.22203i | −0.966496 | − | 0.256681i | \(-0.917371\pi\) |
0.260955 | − | 0.965351i | \(-0.415962\pi\) | |||||||
\(114\) | 1.50000 | − | 2.59808i | 0.140488 | − | 0.243332i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.00000 | −0.278543 | ||||||||
\(117\) | 7.00000 | − | 1.73205i | 0.647150 | − | 0.160128i | ||||
\(118\) | −6.00000 | −0.552345 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.50000 | − | 2.59808i | 0.136931 | − | 0.237171i | ||||
\(121\) | 8.00000 | + | 13.8564i | 0.727273 | + | 1.25967i | ||||
\(122\) | 12.1244i | 1.09769i | ||||||||
\(123\) | −4.50000 | + | 2.59808i | −0.405751 | + | 0.234261i | ||||
\(124\) | 1.50000 | − | 0.866025i | 0.134704 | − | 0.0777714i | ||||
\(125\) | − | 12.1244i | − | 1.08444i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.50000 | + | 11.2583i | −0.576782 | + | 0.999015i | 0.419064 | + | 0.907957i | \(0.362358\pi\) |
−0.995846 | + | 0.0910585i | \(0.970975\pi\) | |||||||
\(128\) | −10.5000 | − | 6.06218i | −0.928078 | − | 0.535826i | ||||
\(129\) | 11.0000 | 0.968496 | ||||||||
\(130\) | −7.50000 | − | 7.79423i | −0.657794 | − | 0.683599i | ||||
\(131\) | −15.0000 | −1.31056 | −0.655278 | − | 0.755388i | \(-0.727449\pi\) | ||||
−0.655278 | + | 0.755388i | \(0.727449\pi\) | |||||||
\(132\) | −4.50000 | − | 2.59808i | −0.391675 | − | 0.226134i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −7.50000 | − | 12.9904i | −0.647901 | − | 1.12220i | ||||
\(135\) | 8.66025i | 0.745356i | ||||||||
\(136\) | 9.00000 | − | 5.19615i | 0.771744 | − | 0.445566i | ||||
\(137\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.50000 | − | 11.2583i | −0.551323 | − | 0.954919i | −0.998179 | − | 0.0603135i | \(-0.980790\pi\) |
0.446857 | − | 0.894606i | \(-0.352543\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.50000 | + | 4.33013i | 0.631614 | + | 0.364662i | ||||
\(142\) | 3.00000 | 0.251754 | ||||||||
\(143\) | 13.5000 | − | 12.9904i | 1.12893 | − | 1.08631i | ||||
\(144\) | 10.0000 | 0.833333 | ||||||||
\(145\) | 4.50000 | + | 2.59808i | 0.373705 | + | 0.215758i | ||||
\(146\) | −7.50000 | + | 12.9904i | −0.620704 | + | 1.07509i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.5000 | − | 9.52628i | 1.35173 | − | 0.780423i | 0.363241 | − | 0.931695i | \(-0.381670\pi\) |
0.988492 | + | 0.151272i | \(0.0483370\pi\) | |||||||
\(150\) | −3.00000 | + | 1.73205i | −0.244949 | + | 0.141421i | ||||
\(151\) | − | 12.1244i | − | 0.986666i | −0.869841 | − | 0.493333i | \(-0.835778\pi\) | ||
0.869841 | − | 0.493333i | \(-0.164222\pi\) | |||||||
\(152\) | 1.50000 | + | 2.59808i | 0.121666 | + | 0.210732i | ||||
\(153\) | −6.00000 | + | 10.3923i | −0.485071 | + | 0.840168i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.00000 | −0.240966 | ||||||||
\(156\) | −1.00000 | + | 3.46410i | −0.0800641 | + | 0.277350i | ||||
\(157\) | −23.0000 | −1.83560 | −0.917800 | − | 0.397043i | \(-0.870036\pi\) | ||||
−0.917800 | + | 0.397043i | \(0.870036\pi\) | |||||||
\(158\) | −7.50000 | − | 4.33013i | −0.596668 | − | 0.344486i | ||||
\(159\) | 4.50000 | − | 7.79423i | 0.356873 | − | 0.618123i | ||||
\(160\) | −4.50000 | − | 7.79423i | −0.355756 | − | 0.616188i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.50000 | + | 0.866025i | −0.117851 | + | 0.0680414i | ||||
\(163\) | −10.5000 | + | 6.06218i | −0.822423 | + | 0.474826i | −0.851251 | − | 0.524758i | \(-0.824156\pi\) |
0.0288280 | + | 0.999584i | \(0.490822\pi\) | |||||||
\(164\) | 5.19615i | 0.405751i | ||||||||
\(165\) | 4.50000 | + | 7.79423i | 0.350325 | + | 0.606780i | ||||
\(166\) | −3.00000 | + | 5.19615i | −0.232845 | + | 0.403300i | ||||
\(167\) | 1.50000 | + | 0.866025i | 0.116073 | + | 0.0670151i | 0.556913 | − | 0.830571i | \(-0.311986\pi\) |
−0.440839 | + | 0.897586i | \(0.645319\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | − | 6.92820i | −0.846154 | − | 0.532939i | ||||
\(170\) | 18.0000 | 1.38054 | ||||||||
\(171\) | −3.00000 | − | 1.73205i | −0.229416 | − | 0.132453i | ||||
\(172\) | 5.50000 | − | 9.52628i | 0.419371 | − | 0.726372i | ||||
\(173\) | 7.50000 | + | 12.9904i | 0.570214 | + | 0.987640i | 0.996544 | + | 0.0830722i | \(0.0264732\pi\) |
−0.426329 | + | 0.904568i | \(0.640193\pi\) | |||||||
\(174\) | − | 5.19615i | − | 0.393919i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 22.5000 | − | 12.9904i | 1.69600 | − | 0.979187i | ||||
\(177\) | − | 3.46410i | − | 0.260378i | ||||||
\(178\) | −6.00000 | − | 10.3923i | −0.449719 | − | 0.778936i | ||||
\(179\) | −1.50000 | + | 2.59808i | −0.112115 | + | 0.194189i | −0.916623 | − | 0.399753i | \(-0.869096\pi\) |
0.804508 | + | 0.593942i | \(0.202429\pi\) | |||||||
\(180\) | 3.00000 | + | 1.73205i | 0.223607 | + | 0.129099i | ||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.00000 | −0.517455 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.50000 | + | 2.59808i | 0.109985 | + | 0.190500i | ||||
\(187\) | 31.1769i | 2.27988i | ||||||||
\(188\) | 7.50000 | − | 4.33013i | 0.546994 | − | 0.315807i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.19615i | 0.376969i | ||||||||
\(191\) | 7.50000 | + | 12.9904i | 0.542681 | + | 0.939951i | 0.998749 | + | 0.0500060i | \(0.0159241\pi\) |
−0.456068 | + | 0.889945i | \(0.650743\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | −1.50000 | − | 0.866025i | −0.107972 | − | 0.0623379i | 0.445041 | − | 0.895510i | \(-0.353189\pi\) |
−0.553014 | + | 0.833172i | \(0.686522\pi\) | |||||||
\(194\) | 9.00000 | 0.646162 | ||||||||
\(195\) | 4.50000 | − | 4.33013i | 0.322252 | − | 0.310087i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.5000 | + | 11.2583i | 1.38932 | + | 0.802123i | 0.993238 | − | 0.116094i | \(-0.0370372\pi\) |
0.396079 | + | 0.918216i | \(0.370371\pi\) | |||||||
\(198\) | −9.00000 | + | 15.5885i | −0.639602 | + | 1.10782i | ||||
\(199\) | 2.00000 | + | 3.46410i | 0.141776 | + | 0.245564i | 0.928166 | − | 0.372168i | \(-0.121385\pi\) |
−0.786389 | + | 0.617731i | \(0.788052\pi\) | |||||||
\(200\) | − | 3.46410i | − | 0.244949i | ||||||
\(201\) | 7.50000 | − | 4.33013i | 0.529009 | − | 0.305424i | ||||
\(202\) | −13.5000 | + | 7.79423i | −0.949857 | + | 0.548400i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3.00000 | − | 5.19615i | −0.210042 | − | 0.363803i | ||||
\(205\) | 4.50000 | − | 7.79423i | 0.314294 | − | 0.544373i | ||||
\(206\) | 19.5000 | + | 11.2583i | 1.35863 | + | 0.784405i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −12.5000 | − | 12.9904i | −0.866719 | − | 0.900721i | ||||
\(209\) | −9.00000 | −0.622543 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.50000 | + | 11.2583i | −0.447478 | + | 0.775055i | −0.998221 | − | 0.0596196i | \(-0.981011\pi\) |
0.550743 | + | 0.834675i | \(0.314345\pi\) | |||||||
\(212\) | −4.50000 | − | 7.79423i | −0.309061 | − | 0.535310i | ||||
\(213\) | 1.73205i | 0.118678i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −16.5000 | + | 9.52628i | −1.12529 | + | 0.649687i | ||||
\(216\) | 8.66025i | 0.589256i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −4.50000 | + | 7.79423i | −0.304778 | + | 0.527892i | ||||
\(219\) | −7.50000 | − | 4.33013i | −0.506803 | − | 0.292603i | ||||
\(220\) | 9.00000 | 0.606780 | ||||||||
\(221\) | 21.0000 | − | 5.19615i | 1.41261 | − | 0.349531i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.50000 | − | 2.59808i | −0.301342 | − | 0.173980i | 0.341703 | − | 0.939808i | \(-0.388996\pi\) |
−0.643046 | + | 0.765828i | \(0.722329\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.00000 | + | 3.46410i | 0.133333 | + | 0.230940i | ||||
\(226\) | − | 25.9808i | − | 1.72821i | ||||||
\(227\) | −15.0000 | + | 8.66025i | −0.995585 | + | 0.574801i | −0.906939 | − | 0.421262i | \(-0.861587\pi\) |
−0.0886460 | + | 0.996063i | \(0.528254\pi\) | |||||||
\(228\) | 1.50000 | − | 0.866025i | 0.0993399 | − | 0.0573539i | ||||
\(229\) | 12.1244i | 0.801200i | 0.916253 | + | 0.400600i | \(0.131198\pi\) | ||||
−0.916253 | + | 0.400600i | \(0.868802\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.50000 | + | 2.59808i | 0.295439 | + | 0.170572i | ||||
\(233\) | 3.00000 | 0.196537 | 0.0982683 | − | 0.995160i | \(-0.468670\pi\) | ||||
0.0982683 | + | 0.995160i | \(0.468670\pi\) | |||||||
\(234\) | 12.0000 | + | 3.46410i | 0.784465 | + | 0.226455i | ||||
\(235\) | −15.0000 | −0.978492 | ||||||||
\(236\) | −3.00000 | − | 1.73205i | −0.195283 | − | 0.112747i | ||||
\(237\) | 2.50000 | − | 4.33013i | 0.162392 | − | 0.281272i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 10.3923i | − | 0.672222i | −0.941822 | − | 0.336111i | \(-0.890888\pi\) | ||
0.941822 | − | 0.336111i | \(-0.109112\pi\) | |||||||
\(240\) | 7.50000 | − | 4.33013i | 0.484123 | − | 0.279508i | ||||
\(241\) | −6.00000 | + | 3.46410i | −0.386494 | + | 0.223142i | −0.680640 | − | 0.732618i | \(-0.738298\pi\) |
0.294146 | + | 0.955761i | \(0.404965\pi\) | |||||||
\(242\) | 27.7128i | 1.78145i | ||||||||
\(243\) | −8.00000 | − | 13.8564i | −0.513200 | − | 0.888889i | ||||
\(244\) | −3.50000 | + | 6.06218i | −0.224065 | + | 0.388091i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −9.00000 | −0.573819 | ||||||||
\(247\) | 1.50000 | + | 6.06218i | 0.0954427 | + | 0.385727i | ||||
\(248\) | −3.00000 | −0.190500 | ||||||||
\(249\) | −3.00000 | − | 1.73205i | −0.190117 | − | 0.109764i | ||||
\(250\) | 10.5000 | − | 18.1865i | 0.664078 | − | 1.15022i | ||||
\(251\) | 1.50000 | + | 2.59808i | 0.0946792 | + | 0.163989i | 0.909475 | − | 0.415759i | \(-0.136484\pi\) |
−0.814795 | + | 0.579748i | \(0.803151\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −19.5000 | + | 11.2583i | −1.22354 | + | 0.706410i | ||||
\(255\) | 10.3923i | 0.650791i | ||||||||
\(256\) | −9.50000 | − | 16.4545i | −0.593750 | − | 1.02841i | ||||
\(257\) | 15.0000 | − | 25.9808i | 0.935674 | − | 1.62064i | 0.162247 | − | 0.986750i | \(-0.448126\pi\) |
0.773427 | − | 0.633885i | \(-0.218541\pi\) | |||||||
\(258\) | 16.5000 | + | 9.52628i | 1.02725 | + | 0.593080i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.50000 | − | 6.06218i | −0.0930261 | − | 0.375960i | ||||
\(261\) | −6.00000 | −0.371391 | ||||||||
\(262\) | −22.5000 | − | 12.9904i | −1.39005 | − | 0.802548i | ||||
\(263\) | −1.50000 | + | 2.59808i | −0.0924940 | + | 0.160204i | −0.908560 | − | 0.417755i | \(-0.862817\pi\) |
0.816066 | + | 0.577959i | \(0.196151\pi\) | |||||||
\(264\) | 4.50000 | + | 7.79423i | 0.276956 | + | 0.479702i | ||||
\(265\) | 15.5885i | 0.957591i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.00000 | − | 3.46410i | 0.367194 | − | 0.212000i | ||||
\(268\) | − | 8.66025i | − | 0.529009i | ||||||
\(269\) | −3.00000 | − | 5.19615i | −0.182913 | − | 0.316815i | 0.759958 | − | 0.649972i | \(-0.225219\pi\) |
−0.942871 | + | 0.333157i | \(0.891886\pi\) | |||||||
\(270\) | −7.50000 | + | 12.9904i | −0.456435 | + | 0.790569i | ||||
\(271\) | −15.0000 | − | 8.66025i | −0.911185 | − | 0.526073i | −0.0303728 | − | 0.999539i | \(-0.509669\pi\) |
−0.880812 | + | 0.473466i | \(0.843003\pi\) | |||||||
\(272\) | 30.0000 | 1.81902 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.00000 | + | 5.19615i | 0.542720 | + | 0.313340i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.00000 | + | 8.66025i | 0.300421 | + | 0.520344i | 0.976231 | − | 0.216731i | \(-0.0695395\pi\) |
−0.675810 | + | 0.737075i | \(0.736206\pi\) | |||||||
\(278\) | − | 22.5167i | − | 1.35046i | ||||||
\(279\) | 3.00000 | − | 1.73205i | 0.179605 | − | 0.103695i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.92820i | 0.413302i | 0.978415 | + | 0.206651i | \(0.0662565\pi\) | ||||
−0.978415 | + | 0.206651i | \(0.933744\pi\) | |||||||
\(282\) | 7.50000 | + | 12.9904i | 0.446619 | + | 0.773566i | ||||
\(283\) | 9.50000 | − | 16.4545i | 0.564716 | − | 0.978117i | −0.432360 | − | 0.901701i | \(-0.642319\pi\) |
0.997076 | − | 0.0764162i | \(-0.0243478\pi\) | |||||||
\(284\) | 1.50000 | + | 0.866025i | 0.0890086 | + | 0.0513892i | ||||
\(285\) | −3.00000 | −0.177705 | ||||||||
\(286\) | 31.5000 | − | 7.79423i | 1.86263 | − | 0.460882i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 9.00000 | + | 5.19615i | 0.530330 | + | 0.306186i | ||||
\(289\) | −9.50000 | + | 16.4545i | −0.558824 | + | 0.967911i | ||||
\(290\) | 4.50000 | + | 7.79423i | 0.264249 | + | 0.457693i | ||||
\(291\) | 5.19615i | 0.304604i | ||||||||
\(292\) | −7.50000 | + | 4.33013i | −0.438904 | + | 0.253402i | ||||
\(293\) | 22.5000 | − | 12.9904i | 1.31446 | − | 0.758906i | 0.331632 | − | 0.943409i | \(-0.392401\pi\) |
0.982832 | + | 0.184503i | \(0.0590674\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.00000 | + | 5.19615i | 0.174667 | + | 0.302532i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −22.5000 | − | 12.9904i | −1.30558 | − | 0.753778i | ||||
\(298\) | 33.0000 | 1.91164 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −2.00000 | −0.115470 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 10.5000 | − | 18.1865i | 0.604207 | − | 1.04652i | ||||
\(303\) | −4.50000 | − | 7.79423i | −0.258518 | − | 0.447767i | ||||
\(304\) | 8.66025i | 0.496700i | ||||||||
\(305\) | 10.5000 | − | 6.06218i | 0.601228 | − | 0.347119i | ||||
\(306\) | −18.0000 | + | 10.3923i | −1.02899 | + | 0.594089i | ||||
\(307\) | 24.2487i | 1.38395i | 0.721923 | + | 0.691974i | \(0.243259\pi\) | ||||
−0.721923 | + | 0.691974i | \(0.756741\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.50000 | + | 11.2583i | −0.369772 | + | 0.640464i | ||||
\(310\) | −4.50000 | − | 2.59808i | −0.255583 | − | 0.147561i | ||||
\(311\) | 15.0000 | 0.850572 | 0.425286 | − | 0.905059i | \(-0.360174\pi\) | ||||
0.425286 | + | 0.905059i | \(0.360174\pi\) | |||||||
\(312\) | 4.50000 | − | 4.33013i | 0.254762 | − | 0.245145i | ||||
\(313\) | −19.0000 | −1.07394 | −0.536972 | − | 0.843600i | \(-0.680432\pi\) | ||||
−0.536972 | + | 0.843600i | \(0.680432\pi\) | |||||||
\(314\) | −34.5000 | − | 19.9186i | −1.94695 | − | 1.12407i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.50000 | − | 4.33013i | −0.140636 | − | 0.243589i | ||||
\(317\) | − | 5.19615i | − | 0.291845i | −0.989296 | − | 0.145922i | \(-0.953385\pi\) | ||
0.989296 | − | 0.145922i | \(-0.0466150\pi\) | |||||||
\(318\) | 13.5000 | − | 7.79423i | 0.757042 | − | 0.437079i | ||||
\(319\) | −13.5000 | + | 7.79423i | −0.755855 | + | 0.436393i | ||||
\(320\) | 1.73205i | 0.0968246i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.00000 | − | 5.19615i | −0.500773 | − | 0.289122i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 2.00000 | − | 6.92820i | 0.110940 | − | 0.384308i | ||||
\(326\) | −21.0000 | −1.16308 | ||||||||
\(327\) | −4.50000 | − | 2.59808i | −0.248851 | − | 0.143674i | ||||
\(328\) | 4.50000 | − | 7.79423i | 0.248471 | − | 0.430364i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 15.5885i | 0.858116i | ||||||||
\(331\) | −28.5000 | + | 16.4545i | −1.56650 | + | 0.904420i | −0.569929 | + | 0.821694i | \(0.693029\pi\) |
−0.996572 | + | 0.0827265i | \(0.973637\pi\) | |||||||
\(332\) | −3.00000 | + | 1.73205i | −0.164646 | + | 0.0950586i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.50000 | + | 2.59808i | 0.0820763 | + | 0.142160i | ||||
\(335\) | −7.50000 | + | 12.9904i | −0.409769 | + | 0.709740i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.0000 | 1.19842 | 0.599208 | − | 0.800593i | \(-0.295482\pi\) | ||||
0.599208 | + | 0.800593i | \(0.295482\pi\) | |||||||
\(338\) | −10.5000 | − | 19.9186i | −0.571125 | − | 1.08343i | ||||
\(339\) | 15.0000 | 0.814688 | ||||||||
\(340\) | 9.00000 | + | 5.19615i | 0.488094 | + | 0.281801i | ||||
\(341\) | 4.50000 | − | 7.79423i | 0.243689 | − | 0.422081i | ||||
\(342\) | −3.00000 | − | 5.19615i | −0.162221 | − | 0.280976i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −16.5000 | + | 9.52628i | −0.889620 | + | 0.513623i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 25.9808i | 1.39673i | ||||||||
\(347\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(348\) | 1.50000 | − | 2.59808i | 0.0804084 | − | 0.139272i | ||||
\(349\) | 4.50000 | + | 2.59808i | 0.240879 | + | 0.139072i | 0.615581 | − | 0.788074i | \(-0.288921\pi\) |
−0.374701 | + | 0.927146i | \(0.622255\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.00000 | + | 17.3205i | −0.266880 | + | 0.924500i | ||||
\(352\) | 27.0000 | 1.43910 | ||||||||
\(353\) | 1.50000 | + | 0.866025i | 0.0798369 | + | 0.0460939i | 0.539387 | − | 0.842058i | \(-0.318656\pi\) |
−0.459550 | + | 0.888152i | \(0.651989\pi\) | |||||||
\(354\) | 3.00000 | − | 5.19615i | 0.159448 | − | 0.276172i | ||||
\(355\) | −1.50000 | − | 2.59808i | −0.0796117 | − | 0.137892i | ||||
\(356\) | − | 6.92820i | − | 0.367194i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.50000 | + | 2.59808i | −0.237832 | + | 0.137313i | ||||
\(359\) | − | 19.0526i | − | 1.00556i | −0.864416 | − | 0.502778i | \(-0.832311\pi\) | ||
0.864416 | − | 0.502778i | \(-0.167689\pi\) | |||||||
\(360\) | −3.00000 | − | 5.19615i | −0.158114 | − | 0.273861i | ||||
\(361\) | −8.00000 | + | 13.8564i | −0.421053 | + | 0.729285i | ||||
\(362\) | −3.00000 | − | 1.73205i | −0.157676 | − | 0.0910346i | ||||
\(363\) | −16.0000 | −0.839782 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.0000 | 0.785136 | ||||||||
\(366\) | −10.5000 | − | 6.06218i | −0.548844 | − | 0.316875i | ||||
\(367\) | 11.5000 | − | 19.9186i | 0.600295 | − | 1.03974i | −0.392481 | − | 0.919760i | \(-0.628383\pi\) |
0.992776 | − | 0.119982i | \(-0.0382835\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.3923i | 0.541002i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.73205i | 0.0898027i | ||||||||
\(373\) | −9.50000 | − | 16.4545i | −0.491891 | − | 0.851981i | 0.508065 | − | 0.861319i | \(-0.330361\pi\) |
−0.999956 | + | 0.00933789i | \(0.997028\pi\) | |||||||
\(374\) | −27.0000 | + | 46.7654i | −1.39614 | + | 2.41818i | ||||
\(375\) | 10.5000 | + | 6.06218i | 0.542218 | + | 0.313050i | ||||
\(376\) | −15.0000 | −0.773566 | ||||||||
\(377\) | 7.50000 | + | 7.79423i | 0.386270 | + | 0.401423i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.50000 | − | 0.866025i | −0.0770498 | − | 0.0444847i | 0.460980 | − | 0.887410i | \(-0.347498\pi\) |
−0.538030 | + | 0.842926i | \(0.680831\pi\) | |||||||
\(380\) | −1.50000 | + | 2.59808i | −0.0769484 | + | 0.133278i | ||||
\(381\) | −6.50000 | − | 11.2583i | −0.333005 | − | 0.576782i | ||||
\(382\) | 25.9808i | 1.32929i | ||||||||
\(383\) | −13.5000 | + | 7.79423i | −0.689818 | + | 0.398266i | −0.803544 | − | 0.595246i | \(-0.797055\pi\) |
0.113726 | + | 0.993512i | \(0.463721\pi\) | |||||||
\(384\) | 10.5000 | − | 6.06218i | 0.535826 | − | 0.309359i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.50000 | − | 2.59808i | −0.0763480 | − | 0.132239i | ||||
\(387\) | 11.0000 | − | 19.0526i | 0.559161 | − | 0.968496i | ||||
\(388\) | 4.50000 | + | 2.59808i | 0.228453 | + | 0.131897i | ||||
\(389\) | 3.00000 | 0.152106 | 0.0760530 | − | 0.997104i | \(-0.475768\pi\) | ||||
0.0760530 | + | 0.997104i | \(0.475768\pi\) | |||||||
\(390\) | 10.5000 | − | 2.59808i | 0.531688 | − | 0.131559i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.50000 | − | 12.9904i | 0.378325 | − | 0.655278i | ||||
\(394\) | 19.5000 | + | 33.7750i | 0.982396 | + | 1.70156i | ||||
\(395\) | 8.66025i | 0.435745i | ||||||||
\(396\) | −9.00000 | + | 5.19615i | −0.452267 | + | 0.261116i | ||||
\(397\) | 31.5000 | − | 18.1865i | 1.58094 | − | 0.912756i | 0.586217 | − | 0.810154i | \(-0.300617\pi\) |
0.994722 | − | 0.102602i | \(-0.0327168\pi\) | |||||||
\(398\) | 6.92820i | 0.347279i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.00000 | − | 8.66025i | 0.250000 | − | 0.433013i | ||||
\(401\) | 6.00000 | + | 3.46410i | 0.299626 | + | 0.172989i | 0.642275 | − | 0.766475i | \(-0.277991\pi\) |
−0.342649 | + | 0.939463i | \(0.611324\pi\) | |||||||
\(402\) | 15.0000 | 0.748132 | ||||||||
\(403\) | −6.00000 | − | 1.73205i | −0.298881 | − | 0.0862796i | ||||
\(404\) | −9.00000 | −0.447767 | ||||||||
\(405\) | 1.50000 | + | 0.866025i | 0.0745356 | + | 0.0430331i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 10.3923i | 0.514496i | ||||||||
\(409\) | 6.00000 | − | 3.46410i | 0.296681 | − | 0.171289i | −0.344270 | − | 0.938871i | \(-0.611874\pi\) |
0.640951 | + | 0.767582i | \(0.278540\pi\) | |||||||
\(410\) | 13.5000 | − | 7.79423i | 0.666717 | − | 0.384930i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.50000 | + | 11.2583i | 0.320232 | + | 0.554658i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.00000 | 0.294528 | ||||||||
\(416\) | −4.50000 | − | 18.1865i | −0.220631 | − | 0.891668i | ||||
\(417\) | 13.0000 | 0.636613 | ||||||||
\(418\) | −13.5000 | − | 7.79423i | −0.660307 | − | 0.381228i | ||||
\(419\) | 10.5000 | − | 18.1865i | 0.512959 | − | 0.888470i | −0.486928 | − | 0.873442i | \(-0.661883\pi\) |
0.999887 | − | 0.0150285i | \(-0.00478389\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | −19.5000 | + | 11.2583i | −0.949245 | + | 0.548047i | ||||
\(423\) | 15.0000 | − | 8.66025i | 0.729325 | − | 0.421076i | ||||
\(424\) | 15.5885i | 0.757042i | ||||||||
\(425\) | 6.00000 | + | 10.3923i | 0.291043 | + | 0.504101i | ||||
\(426\) | −1.50000 | + | 2.59808i | −0.0726752 | + | 0.125877i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.50000 | + | 18.1865i | 0.217262 | + | 0.878054i | ||||
\(430\) | −33.0000 | −1.59140 | ||||||||
\(431\) | 28.5000 | + | 16.4545i | 1.37280 | + | 0.792585i | 0.991279 | − | 0.131777i | \(-0.0420683\pi\) |
0.381517 | + | 0.924362i | \(0.375402\pi\) | |||||||
\(432\) | −12.5000 | + | 21.6506i | −0.601407 | + | 1.04167i | ||||
\(433\) | 9.50000 | + | 16.4545i | 0.456541 | + | 0.790752i | 0.998775 | − | 0.0494752i | \(-0.0157549\pi\) |
−0.542234 | + | 0.840227i | \(0.682422\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.50000 | + | 2.59808i | −0.215758 | + | 0.124568i | ||||
\(436\) | −4.50000 | + | 2.59808i | −0.215511 | + | 0.124425i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −7.50000 | − | 12.9904i | −0.358364 | − | 0.620704i | ||||
\(439\) | 4.00000 | − | 6.92820i | 0.190910 | − | 0.330665i | −0.754642 | − | 0.656136i | \(-0.772190\pi\) |
0.945552 | + | 0.325471i | \(0.105523\pi\) | |||||||
\(440\) | −13.5000 | − | 7.79423i | −0.643587 | − | 0.371575i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 36.0000 | + | 10.3923i | 1.71235 | + | 0.494312i | ||||
\(443\) | 15.0000 | 0.712672 | 0.356336 | − | 0.934358i | \(-0.384026\pi\) | ||||
0.356336 | + | 0.934358i | \(0.384026\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.00000 | + | 10.3923i | −0.284427 | + | 0.492642i | ||||
\(446\) | −4.50000 | − | 7.79423i | −0.213081 | − | 0.369067i | ||||
\(447\) | 19.0526i | 0.901155i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.50000 | − | 0.866025i | 0.0707894 | − | 0.0408703i | −0.464188 | − | 0.885737i | \(-0.653654\pi\) |
0.534977 | + | 0.844867i | \(0.320320\pi\) | |||||||
\(450\) | 6.92820i | 0.326599i | ||||||||
\(451\) | 13.5000 | + | 23.3827i | 0.635690 | + | 1.10105i | ||||
\(452\) | 7.50000 | − | 12.9904i | 0.352770 | − | 0.611016i | ||||
\(453\) | 10.5000 | + | 6.06218i | 0.493333 | + | 0.284826i | ||||
\(454\) | −30.0000 | −1.40797 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.00000 | −0.140488 | ||||||||
\(457\) | 30.0000 | + | 17.3205i | 1.40334 | + | 0.810219i | 0.994734 | − | 0.102491i | \(-0.0326814\pi\) |
0.408607 | + | 0.912710i | \(0.366015\pi\) | |||||||
\(458\) | −10.5000 | + | 18.1865i | −0.490633 | + | 0.849801i | ||||
\(459\) | −15.0000 | − | 25.9808i | −0.700140 | − | 1.21268i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.5000 | + | 14.7224i | −1.18765 | + | 0.685692i | −0.957773 | − | 0.287527i | \(-0.907167\pi\) |
−0.229881 | + | 0.973219i | \(0.573834\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.2487i | 1.12693i | 0.826139 | + | 0.563467i | \(0.190533\pi\) | ||||
−0.826139 | + | 0.563467i | \(0.809467\pi\) | |||||||
\(464\) | 7.50000 | + | 12.9904i | 0.348179 | + | 0.603063i | ||||
\(465\) | 1.50000 | − | 2.59808i | 0.0695608 | − | 0.120483i | ||||
\(466\) | 4.50000 | + | 2.59808i | 0.208458 | + | 0.120354i | ||||
\(467\) | 21.0000 | 0.971764 | 0.485882 | − | 0.874024i | \(-0.338498\pi\) | ||||
0.485882 | + | 0.874024i | \(0.338498\pi\) | |||||||
\(468\) | 5.00000 | + | 5.19615i | 0.231125 | + | 0.240192i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −22.5000 | − | 12.9904i | −1.03785 | − | 0.599202i | ||||
\(471\) | 11.5000 | − | 19.9186i | 0.529892 | − | 0.917800i | ||||
\(472\) | 3.00000 | + | 5.19615i | 0.138086 | + | 0.239172i | ||||
\(473\) | − | 57.1577i | − | 2.62811i | ||||||
\(474\) | 7.50000 | − | 4.33013i | 0.344486 | − | 0.198889i | ||||
\(475\) | −3.00000 | + | 1.73205i | −0.137649 | + | 0.0794719i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.00000 | − | 15.5885i | −0.412082 | − | 0.713746i | ||||
\(478\) | 9.00000 | − | 15.5885i | 0.411650 | − | 0.712999i | ||||
\(479\) | 25.5000 | + | 14.7224i | 1.16512 | + | 0.672685i | 0.952527 | − | 0.304455i | \(-0.0984742\pi\) |
0.212598 | + | 0.977140i | \(0.431808\pi\) | |||||||
\(480\) | 9.00000 | 0.410792 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −12.0000 | −0.546585 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.00000 | + | 13.8564i | −0.363636 | + | 0.629837i | ||||
\(485\) | −4.50000 | − | 7.79423i | −0.204334 | − | 0.353918i | ||||
\(486\) | − | 27.7128i | − | 1.25708i | ||||||
\(487\) | 21.0000 | − | 12.1244i | 0.951601 | − | 0.549407i | 0.0580230 | − | 0.998315i | \(-0.481520\pi\) |
0.893578 | + | 0.448908i | \(0.148187\pi\) | |||||||
\(488\) | 10.5000 | − | 6.06218i | 0.475313 | − | 0.274422i | ||||
\(489\) | − | 12.1244i | − | 0.548282i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.5000 | − | 23.3827i | 0.609246 | − | 1.05525i | −0.382118 | − | 0.924113i | \(-0.624805\pi\) |
0.991365 | − | 0.131132i | \(-0.0418613\pi\) | |||||||
\(492\) | −4.50000 | − | 2.59808i | −0.202876 | − | 0.117130i | ||||
\(493\) | −18.0000 | −0.810679 | ||||||||
\(494\) | −3.00000 | + | 10.3923i | −0.134976 | + | 0.467572i | ||||
\(495\) | 18.0000 | 0.809040 | ||||||||
\(496\) | −7.50000 | − | 4.33013i | −0.336760 | − | 0.194428i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −3.00000 | − | 5.19615i | −0.134433 | − | 0.232845i | ||||
\(499\) | 1.73205i | 0.0775372i | 0.999248 | + | 0.0387686i | \(0.0123435\pi\) | ||||
−0.999248 | + | 0.0387686i | \(0.987656\pi\) | |||||||
\(500\) | 10.5000 | − | 6.06218i | 0.469574 | − | 0.271109i | ||||
\(501\) | −1.50000 | + | 0.866025i | −0.0670151 | + | 0.0386912i | ||||
\(502\) | 5.19615i | 0.231916i | ||||||||
\(503\) | −4.50000 | − | 7.79423i | −0.200645 | − | 0.347527i | 0.748091 | − | 0.663596i | \(-0.230970\pi\) |
−0.948736 | + | 0.316068i | \(0.897637\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.5000 | + | 7.79423i | 0.600742 | + | 0.346839i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.5000 | − | 6.06218i | 0.510733 | − | 0.269231i | ||||
\(508\) | −13.0000 | −0.576782 | ||||||||
\(509\) | −6.00000 | − | 3.46410i | −0.265945 | − | 0.153544i | 0.361098 | − | 0.932528i | \(-0.382402\pi\) |
−0.627044 | + | 0.778984i | \(0.715735\pi\) | |||||||
\(510\) | −9.00000 | + | 15.5885i | −0.398527 | + | 0.690268i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 8.66025i | − | 0.382733i | ||||||
\(513\) | 7.50000 | − | 4.33013i | 0.331133 | − | 0.191180i | ||||
\(514\) | 45.0000 | − | 25.9808i | 1.98486 | − | 1.14596i | ||||
\(515\) | − | 22.5167i | − | 0.992203i | ||||||
\(516\) | 5.50000 | + | 9.52628i | 0.242124 | + | 0.419371i | ||||
\(517\) | 22.5000 | − | 38.9711i | 0.989549 | − | 1.71395i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.0000 | −0.658427 | ||||||||
\(520\) | −3.00000 | + | 10.3923i | −0.131559 | + | 0.455733i | ||||
\(521\) | −39.0000 | −1.70862 | −0.854311 | − | 0.519763i | \(-0.826020\pi\) | ||||
−0.854311 | + | 0.519763i | \(0.826020\pi\) | |||||||
\(522\) | −9.00000 | − | 5.19615i | −0.393919 | − | 0.227429i | ||||
\(523\) | −2.00000 | + | 3.46410i | −0.0874539 | + | 0.151475i | −0.906434 | − | 0.422347i | \(-0.861206\pi\) |
0.818980 | + | 0.573822i | \(0.194540\pi\) | |||||||
\(524\) | −7.50000 | − | 12.9904i | −0.327639 | − | 0.567487i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.50000 | + | 2.59808i | −0.196209 | + | 0.113282i | ||||
\(527\) | 9.00000 | − | 5.19615i | 0.392046 | − | 0.226348i | ||||
\(528\) | 25.9808i | 1.13067i | ||||||||
\(529\) | 11.5000 | + | 19.9186i | 0.500000 | + | 0.866025i | ||||
\(530\) | −13.5000 | + | 23.3827i | −0.586403 | + | 1.01568i | ||||
\(531\) | −6.00000 | − | 3.46410i | −0.260378 | − | 0.150329i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.5000 | − | 12.9904i | 0.584750 | − | 0.562676i | ||||
\(534\) | 12.0000 | 0.519291 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.50000 | + | 12.9904i | −0.323951 | + | 0.561099i | ||||
\(537\) | −1.50000 | − | 2.59808i | −0.0647298 | − | 0.112115i | ||||
\(538\) | − | 10.3923i | − | 0.448044i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −7.50000 | + | 4.33013i | −0.322749 | + | 0.186339i | ||||
\(541\) | − | 12.1244i | − | 0.521267i | −0.965438 | − | 0.260633i | \(-0.916069\pi\) | ||
0.965438 | − | 0.260633i | \(-0.0839314\pi\) | |||||||
\(542\) | −15.0000 | − | 25.9808i | −0.644305 | − | 1.11597i | ||||
\(543\) | 1.00000 | − | 1.73205i | 0.0429141 | − | 0.0743294i | ||||
\(544\) | 27.0000 | + | 15.5885i | 1.15762 | + | 0.668350i | ||||
\(545\) | 9.00000 | 0.385518 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.0000 | −1.19719 | −0.598597 | − | 0.801050i | \(-0.704275\pi\) | ||||
−0.598597 | + | 0.801050i | \(0.704275\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.00000 | + | 12.1244i | −0.298753 | + | 0.517455i | ||||
\(550\) | 9.00000 | + | 15.5885i | 0.383761 | + | 0.664694i | ||||
\(551\) | − | 5.19615i | − | 0.221364i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 17.3205i | 0.735878i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.50000 | − | 11.2583i | 0.275661 | − | 0.477460i | ||||
\(557\) | −13.5000 | − | 7.79423i | −0.572013 | − | 0.330252i | 0.185940 | − | 0.982561i | \(-0.440467\pi\) |
−0.757953 | + | 0.652309i | \(0.773800\pi\) | |||||||
\(558\) | 6.00000 | 0.254000 | ||||||||
\(559\) | −38.5000 | + | 9.52628i | −1.62838 | + | 0.402919i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −27.0000 | − | 15.5885i | −1.13994 | − | 0.658145i | ||||
\(562\) | −6.00000 | + | 10.3923i | −0.253095 | + | 0.438373i | ||||
\(563\) | −18.0000 | − | 31.1769i | −0.758610 | − | 1.31395i | −0.943560 | − | 0.331202i | \(-0.892546\pi\) |
0.184950 | − | 0.982748i | \(-0.440788\pi\) | |||||||
\(564\) | 8.66025i | 0.364662i | ||||||||
\(565\) | −22.5000 | + | 12.9904i | −0.946582 | + | 0.546509i | ||||
\(566\) | 28.5000 | − | 16.4545i | 1.19794 | − | 0.691633i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.50000 | − | 2.59808i | −0.0629386 | − | 0.109013i | ||||
\(569\) | 3.00000 | − | 5.19615i | 0.125767 | − | 0.217834i | −0.796266 | − | 0.604947i | \(-0.793194\pi\) |
0.922032 | + | 0.387113i | \(0.126528\pi\) | |||||||
\(570\) | −4.50000 | − | 2.59808i | −0.188484 | − | 0.108821i | ||||
\(571\) | −23.0000 | −0.962520 | −0.481260 | − | 0.876578i | \(-0.659821\pi\) | ||||
−0.481260 | + | 0.876578i | \(0.659821\pi\) | |||||||
\(572\) | 18.0000 | + | 5.19615i | 0.752618 | + | 0.217262i | ||||
\(573\) | −15.0000 | −0.626634 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.00000 | − | 1.73205i | −0.0416667 | − | 0.0721688i | ||||
\(577\) | 15.5885i | 0.648956i | 0.945893 | + | 0.324478i | \(0.105189\pi\) | ||||
−0.945893 | + | 0.324478i | \(0.894811\pi\) | |||||||
\(578\) | −28.5000 | + | 16.4545i | −1.18544 | + | 0.684416i | ||||
\(579\) | 1.50000 | − | 0.866025i | 0.0623379 | − | 0.0359908i | ||||
\(580\) | 5.19615i | 0.215758i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −4.50000 | + | 7.79423i | −0.186531 | + | 0.323081i | ||||
\(583\) | −40.5000 | − | 23.3827i | −1.67734 | − | 0.968412i | ||||
\(584\) | 15.0000 | 0.620704 | ||||||||
\(585\) | −3.00000 | − | 12.1244i | −0.124035 | − | 0.501280i | ||||
\(586\) | 45.0000 | 1.85893 | ||||||||
\(587\) | 13.5000 | + | 7.79423i | 0.557205 | + | 0.321702i | 0.752023 | − | 0.659137i | \(-0.229078\pi\) |
−0.194818 | + | 0.980839i | \(0.562412\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.50000 | + | 2.59808i | 0.0618064 | + | 0.107052i | ||||
\(590\) | 10.3923i | 0.427844i | ||||||||
\(591\) | −19.5000 | + | 11.2583i | −0.802123 | + | 0.463106i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.19615i | 0.213380i | 0.994292 | + | 0.106690i | \(0.0340253\pi\) | ||||
−0.994292 | + | 0.106690i | \(0.965975\pi\) | |||||||
\(594\) | −22.5000 | − | 38.9711i | −0.923186 | − | 1.59901i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.5000 | + | 9.52628i | 0.675866 | + | 0.390212i | ||||
\(597\) | −4.00000 | −0.163709 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.00000 | 0.367730 | 0.183865 | − | 0.982952i | \(-0.441139\pi\) | ||||
0.183865 | + | 0.982952i | \(0.441139\pi\) | |||||||
\(600\) | 3.00000 | + | 1.73205i | 0.122474 | + | 0.0707107i | ||||
\(601\) | 9.50000 | − | 16.4545i | 0.387513 | − | 0.671192i | −0.604601 | − | 0.796528i | \(-0.706668\pi\) |
0.992114 | + | 0.125336i | \(0.0400009\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 17.3205i | − | 0.705346i | ||||||
\(604\) | 10.5000 | − | 6.06218i | 0.427239 | − | 0.246667i | ||||
\(605\) | 24.0000 | − | 13.8564i | 0.975739 | − | 0.563343i | ||||
\(606\) | − | 15.5885i | − | 0.633238i | ||||||
\(607\) | −21.5000 | − | 37.2391i | −0.872658 | − | 1.51149i | −0.859237 | − | 0.511578i | \(-0.829061\pi\) |
−0.0134214 | − | 0.999910i | \(-0.504272\pi\) | |||||||
\(608\) | −4.50000 | + | 7.79423i | −0.182499 | + | 0.316098i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 21.0000 | 0.850265 | ||||||||
\(611\) | −30.0000 | − | 8.66025i | −1.21367 | − | 0.350356i | ||||
\(612\) | −12.0000 | −0.485071 | ||||||||
\(613\) | −31.5000 | − | 18.1865i | −1.27227 | − | 0.734547i | −0.296858 | − | 0.954922i | \(-0.595939\pi\) |
−0.975415 | + | 0.220375i | \(0.929272\pi\) | |||||||
\(614\) | −21.0000 | + | 36.3731i | −0.847491 | + | 1.46790i | ||||
\(615\) | 4.50000 | + | 7.79423i | 0.181458 | + | 0.314294i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 37.5000 | − | 21.6506i | 1.50969 | − | 0.871622i | 0.509757 | − | 0.860318i | \(-0.329735\pi\) |
0.999936 | − | 0.0113033i | \(-0.00359804\pi\) | |||||||
\(618\) | −19.5000 | + | 11.2583i | −0.784405 | + | 0.452876i | ||||
\(619\) | 19.0526i | 0.765787i | 0.923792 | + | 0.382893i | \(0.125072\pi\) | ||||
−0.923792 | + | 0.382893i | \(0.874928\pi\) | |||||||
\(620\) | −1.50000 | − | 2.59808i | −0.0602414 | − | 0.104341i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 22.5000 | + | 12.9904i | 0.902168 | + | 0.520867i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 17.5000 | − | 4.33013i | 0.700561 | − | 0.173344i | ||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | −28.5000 | − | 16.4545i | −1.13909 | − | 0.657653i | ||||
\(627\) | 4.50000 | − | 7.79423i | 0.179713 | − | 0.311272i | ||||
\(628\) | −11.5000 | − | 19.9186i | −0.458900 | − | 0.794838i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.5000 | + | 23.3827i | −1.61228 | + | 0.930850i | −0.623439 | + | 0.781872i | \(0.714265\pi\) |
−0.988841 | + | 0.148978i | \(0.952402\pi\) | |||||||
\(632\) | 8.66025i | 0.344486i | ||||||||
\(633\) | −6.50000 | − | 11.2583i | −0.258352 | − | 0.447478i | ||||
\(634\) | 4.50000 | − | 7.79423i | 0.178718 | − | 0.309548i | ||||
\(635\) | 19.5000 | + | 11.2583i | 0.773834 | + | 0.446773i | ||||
\(636\) | 9.00000 | 0.356873 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −27.0000 | −1.06894 | ||||||||
\(639\) | 3.00000 | + | 1.73205i | 0.118678 | + | 0.0685189i | ||||
\(640\) | −10.5000 | + | 18.1865i | −0.415049 | + | 0.718886i | ||||
\(641\) | −15.0000 | − | 25.9808i | −0.592464 | − | 1.02618i | −0.993899 | − | 0.110291i | \(-0.964822\pi\) |
0.401435 | − | 0.915888i | \(-0.368512\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.50000 | − | 2.59808i | 0.177463 | − | 0.102458i | −0.408637 | − | 0.912697i | \(-0.633996\pi\) |
0.586100 | + | 0.810239i | \(0.300663\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 19.0526i | − | 0.750194i | ||||||
\(646\) | −9.00000 | − | 15.5885i | −0.354100 | − | 0.613320i | ||||
\(647\) | −4.50000 | + | 7.79423i | −0.176913 | + | 0.306423i | −0.940822 | − | 0.338902i | \(-0.889945\pi\) |
0.763908 | + | 0.645325i | \(0.223278\pi\) | |||||||
\(648\) | 1.50000 | + | 0.866025i | 0.0589256 | + | 0.0340207i | ||||
\(649\) | −18.0000 | −0.706562 | ||||||||
\(650\) | 9.00000 | − | 8.66025i | 0.353009 | − | 0.339683i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.5000 | − | 6.06218i | −0.411212 | − | 0.237413i | ||||
\(653\) | 15.0000 | − | 25.9808i | 0.586995 | − | 1.01671i | −0.407628 | − | 0.913148i | \(-0.633644\pi\) |
0.994623 | − | 0.103558i | \(-0.0330227\pi\) | |||||||
\(654\) | −4.50000 | − | 7.79423i | −0.175964 | − | 0.304778i | ||||
\(655\) | 25.9808i | 1.01515i | ||||||||
\(656\) | 22.5000 | − | 12.9904i | 0.878477 | − | 0.507189i | ||||
\(657\) | −15.0000 | + | 8.66025i | −0.585206 | + | 0.337869i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.50000 | − | 12.9904i | −0.292159 | − | 0.506033i | 0.682161 | − | 0.731202i | \(-0.261040\pi\) |
−0.974320 | + | 0.225168i | \(0.927707\pi\) | |||||||
\(660\) | −4.50000 | + | 7.79423i | −0.175162 | + | 0.303390i | ||||
\(661\) | 31.5000 | + | 18.1865i | 1.22521 | + | 0.707374i | 0.966024 | − | 0.258454i | \(-0.0832129\pi\) |
0.259184 | + | 0.965828i | \(0.416546\pi\) | |||||||
\(662\) | −57.0000 | −2.21537 | ||||||||
\(663\) | −6.00000 | + | 20.7846i | −0.233021 | + | 0.807207i | ||||
\(664\) | 6.00000 | 0.232845 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 1.73205i | 0.0670151i | ||||||||
\(669\) | 4.50000 | − | 2.59808i | 0.173980 | − | 0.100447i | ||||
\(670\) | −22.5000 | + | 12.9904i | −0.869251 | + | 0.501862i | ||||
\(671\) | 36.3731i | 1.40417i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.500000 | − | 0.866025i | 0.0192736 | − | 0.0333828i | −0.856228 | − | 0.516599i | \(-0.827198\pi\) |
0.875501 | + | 0.483216i | \(0.160531\pi\) | |||||||
\(674\) | 33.0000 | + | 19.0526i | 1.27111 | + | 0.733877i | ||||
\(675\) | −10.0000 | −0.384900 | ||||||||
\(676\) | 0.500000 | − | 12.9904i | 0.0192308 | − | 0.499630i | ||||
\(677\) | −27.0000 | −1.03769 | −0.518847 | − | 0.854867i | \(-0.673639\pi\) | ||||
−0.518847 | + | 0.854867i | \(0.673639\pi\) | |||||||
\(678\) | 22.5000 | + | 12.9904i | 0.864107 | + | 0.498893i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −9.00000 | − | 15.5885i | −0.345134 | − | 0.597790i | ||||
\(681\) | − | 17.3205i | − | 0.663723i | ||||||
\(682\) | 13.5000 | − | 7.79423i | 0.516942 | − | 0.298456i | ||||
\(683\) | −21.0000 | + | 12.1244i | −0.803543 | + | 0.463926i | −0.844708 | − | 0.535227i | \(-0.820226\pi\) |
0.0411658 | + | 0.999152i | \(0.486893\pi\) | |||||||
\(684\) | − | 3.46410i | − | 0.132453i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.5000 | − | 6.06218i | −0.400600 | − | 0.231287i | ||||
\(688\) | −55.0000 | −2.09686 | ||||||||
\(689\) | −9.00000 | + | 31.1769i | −0.342873 | + | 1.18775i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.0000 | + | 15.5885i | 1.02713 | + | 0.593013i | 0.916161 | − | 0.400811i | \(-0.131272\pi\) |
0.110968 | + | 0.993824i | \(0.464605\pi\) | |||||||
\(692\) | −7.50000 | + | 12.9904i | −0.285107 | + | 0.493820i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −19.5000 | + | 11.2583i | −0.739677 | + | 0.427053i | ||||
\(696\) | −4.50000 | + | 2.59808i | −0.170572 | + | 0.0984798i | ||||
\(697\) | 31.1769i | 1.18091i | ||||||||
\(698\) | 4.50000 | + | 7.79423i | 0.170328 | + | 0.295016i | ||||
\(699\) | −1.50000 | + | 2.59808i | −0.0567352 | + | 0.0982683i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.00000 | −0.226617 | −0.113308 | − | 0.993560i | \(-0.536145\pi\) | ||||
−0.113308 | + | 0.993560i | \(0.536145\pi\) | |||||||
\(702\) | −22.5000 | + | 21.6506i | −0.849208 | + | 0.817151i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −4.50000 | − | 2.59808i | −0.169600 | − | 0.0979187i | ||||
\(705\) | 7.50000 | − | 12.9904i | 0.282466 | − | 0.489246i | ||||
\(706\) | 1.50000 | + | 2.59808i | 0.0564532 | + | 0.0977799i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 3.00000 | − | 1.73205i | 0.112747 | − | 0.0650945i | ||||
\(709\) | 10.5000 | − | 6.06218i | 0.394336 | − | 0.227670i | −0.289701 | − | 0.957117i | \(-0.593556\pi\) |
0.684037 | + | 0.729447i | \(0.260223\pi\) | |||||||
\(710\) | − | 5.19615i | − | 0.195008i | ||||||
\(711\) | −5.00000 | − | 8.66025i | −0.187515 | − | 0.324785i | ||||
\(712\) | −6.00000 | + | 10.3923i | −0.224860 | + | 0.389468i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −22.5000 | − | 23.3827i | −0.841452 | − | 0.874463i | ||||
\(716\) | −3.00000 | −0.112115 | ||||||||
\(717\) | 9.00000 | + | 5.19615i | 0.336111 | + | 0.194054i | ||||
\(718\) | 16.5000 | − | 28.5788i | 0.615775 | − | 1.06655i | ||||
\(719\) | −7.50000 | − | 12.9904i | −0.279703 | − | 0.484459i | 0.691608 | − | 0.722273i | \(-0.256903\pi\) |
−0.971311 | + | 0.237814i | \(0.923569\pi\) | |||||||
\(720\) | − | 17.3205i | − | 0.645497i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −24.0000 | + | 13.8564i | −0.893188 | + | 0.515682i | ||||
\(723\) | − | 6.92820i | − | 0.257663i | ||||||
\(724\) | −1.00000 | − | 1.73205i | −0.0371647 | − | 0.0643712i | ||||
\(725\) | −3.00000 | + | 5.19615i | −0.111417 | + | 0.192980i | ||||
\(726\) | −24.0000 | − | 13.8564i | −0.890724 | − | 0.514259i | ||||
\(727\) | 32.0000 | 1.18681 | 0.593407 | − | 0.804902i | \(-0.297782\pi\) | ||||
0.593407 | + | 0.804902i | \(0.297782\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 22.5000 | + | 12.9904i | 0.832762 | + | 0.480796i | ||||
\(731\) | 33.0000 | − | 57.1577i | 1.22055 | − | 2.11405i | ||||
\(732\) | −3.50000 | − | 6.06218i | −0.129364 | − | 0.224065i | ||||
\(733\) | − | 50.2295i | − | 1.85527i | −0.373491 | − | 0.927634i | \(-0.621839\pi\) | ||
0.373491 | − | 0.927634i | \(-0.378161\pi\) | |||||||
\(734\) | 34.5000 | − | 19.9186i | 1.27342 | − | 0.735208i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22.5000 | − | 38.9711i | −0.828798 | − | 1.43552i | ||||
\(738\) | −9.00000 | + | 15.5885i | −0.331295 | + | 0.573819i | ||||
\(739\) | 34.5000 | + | 19.9186i | 1.26910 | + | 0.732717i | 0.974818 | − | 0.223001i | \(-0.0715853\pi\) |
0.294285 | + | 0.955718i | \(0.404919\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.00000 | − | 1.73205i | −0.220416 | − | 0.0636285i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.50000 | − | 0.866025i | −0.0550297 | − | 0.0317714i | 0.472233 | − | 0.881474i | \(-0.343448\pi\) |
−0.527262 | + | 0.849703i | \(0.676782\pi\) | |||||||
\(744\) | 1.50000 | − | 2.59808i | 0.0549927 | − | 0.0952501i | ||||
\(745\) | −16.5000 | − | 28.5788i | −0.604513 | − | 1.04705i | ||||
\(746\) | − | 32.9090i | − | 1.20488i | ||||||
\(747\) | −6.00000 | + | 3.46410i | −0.219529 | + | 0.126745i | ||||
\(748\) | −27.0000 | + | 15.5885i | −0.987218 | + | 0.569970i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 10.5000 | + | 18.1865i | 0.383406 | + | 0.664078i | ||||
\(751\) | −10.0000 | + | 17.3205i | −0.364905 | + | 0.632034i | −0.988761 | − | 0.149505i | \(-0.952232\pi\) |
0.623856 | + | 0.781540i | \(0.285565\pi\) | |||||||
\(752\) | −37.5000 | − | 21.6506i | −1.36748 | − | 0.789517i | ||||
\(753\) | −3.00000 | −0.109326 | ||||||||
\(754\) | 4.50000 | + | 18.1865i | 0.163880 | + | 0.662314i | ||||
\(755\) | −21.0000 | −0.764268 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.50000 | − | 14.7224i | 0.308938 | − | 0.535096i | −0.669193 | − | 0.743089i | \(-0.733360\pi\) |
0.978130 | + | 0.207993i | \(0.0666932\pi\) | |||||||
\(758\) | −1.50000 | − | 2.59808i | −0.0544825 | − | 0.0943664i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.50000 | − | 2.59808i | 0.163232 | − | 0.0942421i | ||||
\(761\) | 25.5000 | − | 14.7224i | 0.924374 | − | 0.533688i | 0.0393463 | − | 0.999226i | \(-0.487472\pi\) |
0.885028 | + | 0.465538i | \(0.154139\pi\) | |||||||
\(762\) | − | 22.5167i | − | 0.815693i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −7.50000 | + | 12.9904i | −0.271340 | + | 0.469975i | ||||
\(765\) | 18.0000 | + | 10.3923i | 0.650791 | + | 0.375735i | ||||
\(766\) | −27.0000 | −0.975550 | ||||||||
\(767\) | 3.00000 | + | 12.1244i | 0.108324 | + | 0.437785i | ||||
\(768\) | 19.0000 | 0.685603 | ||||||||
\(769\) | 16.5000 | + | 9.52628i | 0.595005 | + | 0.343526i | 0.767074 | − | 0.641558i | \(-0.221712\pi\) |
−0.172069 | + | 0.985085i | \(0.555045\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.0000 | + | 25.9808i | 0.540212 | + | 0.935674i | ||||
\(772\) | − | 1.73205i | − | 0.0623379i | ||||||
\(773\) | −12.0000 | + | 6.92820i | −0.431610 | + | 0.249190i | −0.700032 | − | 0.714111i | \(-0.746831\pi\) |
0.268422 | + | 0.963301i | \(0.413498\pi\) | |||||||
\(774\) | 33.0000 | − | 19.0526i | 1.18616 | − | 0.684830i | ||||
\(775\) | − | 3.46410i | − | 0.124434i | ||||||
\(776\) | −4.50000 | − | 7.79423i | −0.161541 | − | 0.279797i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.50000 | + | 2.59808i | 0.161333 | + | 0.0931455i | ||||
\(779\) | −9.00000 | −0.322458 | ||||||||
\(780\) | 6.00000 | + | 1.73205i | 0.214834 | + | 0.0620174i | ||||
\(781\) | 9.00000 | 0.322045 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.50000 | − | 12.9904i | 0.268028 | − | 0.464238i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 39.8372i | 1.42185i | ||||||||
\(786\) | 22.5000 | − | 12.9904i | 0.802548 | − | 0.463352i | ||||
\(787\) | −27.0000 | + | 15.5885i | −0.962446 | + | 0.555668i | −0.896925 | − | 0.442183i | \(-0.854204\pi\) |
−0.0655211 | + | 0.997851i | \(0.520871\pi\) | |||||||
\(788\) | 22.5167i | 0.802123i | ||||||||
\(789\) | −1.50000 | − | 2.59808i | −0.0534014 | − | 0.0924940i | ||||
\(790\) | −7.50000 | + | 12.9904i | −0.266838 | + | 0.462177i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 18.0000 | 0.639602 | ||||||||
\(793\) | 24.5000 | − | 6.06218i | 0.870021 | − | 0.215274i | ||||
\(794\) | 63.0000 | 2.23579 | ||||||||
\(795\) | −13.5000 | − | 7.79423i | −0.478796 | − | 0.276433i | ||||
\(796\) | −2.00000 | + | 3.46410i | −0.0708881 | + | 0.122782i | ||||
\(797\) | −16.5000 | − | 28.5788i | −0.584460 | − | 1.01231i | −0.994943 | − | 0.100446i | \(-0.967973\pi\) |
0.410483 | − | 0.911868i | \(-0.365360\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 45.0000 | − | 25.9808i | 1.59199 | − | 0.919133i | ||||
\(800\) | 9.00000 | − | 5.19615i | 0.318198 | − | 0.183712i | ||||
\(801\) | − | 13.8564i | − | 0.489592i | ||||||
\(802\) | 6.00000 | + | 10.3923i | 0.211867 | + | 0.366965i | ||||
\(803\) | −22.5000 | + | 38.9711i | −0.794008 | + | 1.37526i | ||||
\(804\) | 7.50000 | + | 4.33013i | 0.264505 | + | 0.152712i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.50000 | − | 7.79423i | −0.264176 | − | 0.274540i | ||||
\(807\) | 6.00000 | 0.211210 | ||||||||
\(808\) | 13.5000 | + | 7.79423i | 0.474928 | + | 0.274200i | ||||
\(809\) | 10.5000 | − | 18.1865i | 0.369160 | − | 0.639404i | −0.620274 | − | 0.784385i | \(-0.712979\pi\) |
0.989434 | + | 0.144981i | \(0.0463120\pi\) | |||||||
\(810\) | 1.50000 | + | 2.59808i | 0.0527046 | + | 0.0912871i | ||||
\(811\) | − | 3.46410i | − | 0.121641i | −0.998149 | − | 0.0608205i | \(-0.980628\pi\) | ||
0.998149 | − | 0.0608205i | \(-0.0193717\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15.0000 | − | 8.66025i | 0.526073 | − | 0.303728i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.5000 | + | 18.1865i | 0.367799 | + | 0.637046i | ||||
\(816\) | −15.0000 | + | 25.9808i | −0.525105 | + | 0.909509i | ||||
\(817\) | 16.5000 | + | 9.52628i | 0.577262 | + | 0.333282i | ||||
\(818\) | 12.0000 | 0.419570 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.00000 | 0.314294 | ||||||||
\(821\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.0000 | − | 27.7128i | −0.557725 | − | 0.966008i | −0.997686 | − | 0.0679910i | \(-0.978341\pi\) |
0.439961 | − | 0.898017i | \(-0.354992\pi\) | |||||||
\(824\) | − | 22.5167i | − | 0.784405i | ||||||
\(825\) | −9.00000 | + | 5.19615i | −0.313340 | + | 0.180907i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 10.3923i | − | 0.361376i | −0.983540 | − | 0.180688i | \(-0.942168\pi\) | ||
0.983540 | − | 0.180688i | \(-0.0578324\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.50000 | − | 6.06218i | 0.121560 | − | 0.210548i | −0.798823 | − | 0.601566i | \(-0.794544\pi\) |
0.920383 | + | 0.391018i | \(0.127877\pi\) | |||||||
\(830\) | 9.00000 | + | 5.19615i | 0.312395 | + | 0.180361i | ||||
\(831\) | −10.0000 | −0.346896 | ||||||||
\(832\) | −1.00000 | + | 3.46410i | −0.0346688 | + | 0.120096i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 19.5000 | + | 11.2583i | 0.675230 | + | 0.389844i | ||||
\(835\) | 1.50000 | − | 2.59808i | 0.0519096 | − | 0.0899101i | ||||
\(836\) | −4.50000 | − | 7.79423i | −0.155636 | − | 0.269569i | ||||
\(837\) | 8.66025i | 0.299342i | ||||||||
\(838\) | 31.5000 | − | 18.1865i | 1.08815 | − | 0.628243i | ||||
\(839\) | −1.50000 | + | 0.866025i | −0.0517858 | + | 0.0298985i | −0.525669 | − | 0.850689i | \(-0.676185\pi\) |
0.473884 | + | 0.880587i | \(0.342852\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0000 | + | 17.3205i | 0.344828 | + | 0.597259i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.00000 | − | 3.46410i | −0.206651 | − | 0.119310i | ||||
\(844\) | −13.0000 | −0.447478 | ||||||||
\(845\) | −12.0000 | + | 19.0526i | −0.412813 | + | 0.655428i | ||||
\(846\) | 30.0000 | 1.03142 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −22.5000 | + | 38.9711i | −0.772653 | + | 1.33827i | ||||
\(849\) | 9.50000 | + | 16.4545i | 0.326039 | + | 0.564716i | ||||
\(850\) | 20.7846i | 0.712906i | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −1.50000 | + | 0.866025i | −0.0513892 | + | 0.0296695i | ||||
\(853\) | 41.5692i | 1.42330i | 0.702533 | + | 0.711651i | \(0.252052\pi\) | ||||
−0.702533 | + | 0.711651i | \(0.747948\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.00000 | + | 5.19615i | −0.102598 | + | 0.177705i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 33.0000 | 1.12726 | 0.563629 | − | 0.826028i | \(-0.309405\pi\) | ||||
0.563629 | + | 0.826028i | \(0.309405\pi\) | |||||||
\(858\) | −9.00000 | + | 31.1769i | −0.307255 | + | 1.06436i | ||||
\(859\) | 29.0000 | 0.989467 | 0.494734 | − | 0.869045i | \(-0.335266\pi\) | ||||
0.494734 | + | 0.869045i | \(0.335266\pi\) | |||||||
\(860\) | −16.5000 | − | 9.52628i | −0.562645 | − | 0.324843i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 28.5000 | + | 49.3634i | 0.970714 | + | 1.68133i | ||||
\(863\) | 1.73205i | 0.0589597i | 0.999565 | + | 0.0294798i | \(0.00938509\pi\) | ||||
−0.999565 | + | 0.0294798i | \(0.990615\pi\) | |||||||
\(864\) | −22.5000 | + | 12.9904i | −0.765466 | + | 0.441942i | ||||
\(865\) | 22.5000 | − | 12.9904i | 0.765023 | − | 0.441686i | ||||
\(866\) | 32.9090i | 1.11829i | ||||||||
\(867\) | −9.50000 | − | 16.4545i | −0.322637 | − | 0.558824i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22.5000 | − | 12.9904i | −0.763260 | − | 0.440668i | ||||
\(870\) | −9.00000 | −0.305129 | ||||||||
\(871\) | −22.5000 | + | 21.6506i | −0.762383 | + | 0.733604i | ||||
\(872\) | 9.00000 | 0.304778 | ||||||||
\(873\) | 9.00000 | + | 5.19615i | 0.304604 | + | 0.175863i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 8.66025i | − | 0.292603i | ||||||
\(877\) | −1.50000 | + | 0.866025i | −0.0506514 | + | 0.0292436i | −0.525112 | − | 0.851033i | \(-0.675977\pi\) |
0.474460 | + | 0.880277i | \(0.342643\pi\) | |||||||
\(878\) | 12.0000 | − | 6.92820i | 0.404980 | − | 0.233816i | ||||
\(879\) | 25.9808i | 0.876309i | ||||||||
\(880\) | −22.5000 | − | 38.9711i | −0.758475 | − | 1.31372i | ||||
\(881\) | −16.5000 | + | 28.5788i | −0.555899 | + | 0.962846i | 0.441934 | + | 0.897048i | \(0.354293\pi\) |
−0.997833 | + | 0.0657979i | \(0.979041\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.0000 | −1.48072 | −0.740359 | − | 0.672212i | \(-0.765344\pi\) | ||||
−0.740359 | + | 0.672212i | \(0.765344\pi\) | |||||||
\(884\) | 15.0000 | + | 15.5885i | 0.504505 | + | 0.524297i | ||||
\(885\) | −6.00000 | −0.201688 | ||||||||
\(886\) | 22.5000 | + | 12.9904i | 0.755902 | + | 0.436420i | ||||
\(887\) | 12.0000 | − | 20.7846i | 0.402921 | − | 0.697879i | −0.591156 | − | 0.806557i | \(-0.701328\pi\) |
0.994077 | + | 0.108678i | \(0.0346618\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −18.0000 | + | 10.3923i | −0.603361 | + | 0.348351i | ||||
\(891\) | −4.50000 | + | 2.59808i | −0.150756 | + | 0.0870388i | ||||
\(892\) | − | 5.19615i | − | 0.173980i | ||||||
\(893\) | 7.50000 | + | 12.9904i | 0.250978 | + | 0.434707i | ||||
\(894\) | −16.5000 | + | 28.5788i | −0.551843 | + | 0.955819i | ||||
\(895\) | 4.50000 | + | 2.59808i | 0.150418 | + | 0.0868441i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.00000 | 0.100111 | ||||||||
\(899\) | 4.50000 | + | 2.59808i | 0.150083 | + | 0.0866507i | ||||
\(900\) | −2.00000 | + | 3.46410i | −0.0666667 | + | 0.115470i | ||||
\(901\) | −27.0000 | − | 46.7654i | −0.899500 | − | 1.55798i | ||||
\(902\) | 46.7654i | 1.55712i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −22.5000 | + | 12.9904i | −0.748339 | + | 0.432054i | ||||
\(905\) | 3.46410i | 0.115151i | ||||||||
\(906\) | 10.5000 | + | 18.1865i | 0.348839 | + | 0.604207i | ||||
\(907\) | 14.5000 | − | 25.1147i | 0.481465 | − | 0.833921i | −0.518309 | − | 0.855193i | \(-0.673438\pi\) |
0.999774 | + | 0.0212722i | \(0.00677166\pi\) | |||||||
\(908\) | −15.0000 | − | 8.66025i | −0.497792 | − | 0.287401i | ||||
\(909\) | −18.0000 | −0.597022 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | −7.50000 | − | 4.33013i | −0.248350 | − | 0.143385i | ||||
\(913\) | −9.00000 | + | 15.5885i | −0.297857 | + | 0.515903i | ||||
\(914\) | 30.0000 | + | 51.9615i | 0.992312 | + | 1.71873i | ||||
\(915\) | 12.1244i | 0.400819i | ||||||||
\(916\) | −10.5000 | + | 6.06218i | −0.346930 | + | 0.200300i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 51.9615i | − | 1.71499i | ||||||
\(919\) | 23.5000 | + | 40.7032i | 0.775193 | + | 1.34267i | 0.934686 | + | 0.355475i | \(0.115681\pi\) |
−0.159492 | + | 0.987199i | \(0.550986\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.0000 | − | 12.1244i | −0.691974 | − | 0.399511i | ||||
\(922\) | −51.0000 | −1.67960 | ||||||||
\(923\) | −1.50000 | − | 6.06218i | −0.0493731 | − | 0.199539i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −21.0000 | + | 36.3731i | −0.690103 | + | 1.19529i | ||||
\(927\) | 13.0000 | + | 22.5167i | 0.426976 | + | 0.739544i | ||||
\(928\) | 15.5885i | 0.511716i | ||||||||
\(929\) | −40.5000 | + | 23.3827i | −1.32876 | + | 0.767161i | −0.985108 | − | 0.171935i | \(-0.944998\pi\) |
−0.343654 | + | 0.939096i | \(0.611665\pi\) | |||||||
\(930\) | 4.50000 | − | 2.59808i | 0.147561 | − | 0.0851943i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.50000 | + | 2.59808i | 0.0491341 | + | 0.0851028i | ||||
\(933\) | −7.50000 | + | 12.9904i | −0.245539 | + | 0.425286i | ||||
\(934\) | 31.5000 | + | 18.1865i | 1.03071 | + | 0.595082i | ||||
\(935\) | 54.0000 | 1.76599 | ||||||||
\(936\) | −3.00000 | − | 12.1244i | −0.0980581 | − | 0.396297i | ||||
\(937\) | −22.0000 | −0.718709 | −0.359354 | − | 0.933201i | \(-0.617003\pi\) | ||||
−0.359354 | + | 0.933201i | \(0.617003\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.50000 | − | 16.4545i | 0.310021 | − | 0.536972i | ||||
\(940\) | −7.50000 | − | 12.9904i | −0.244623 | − | 0.423700i | ||||
\(941\) | − | 5.19615i | − | 0.169390i | −0.996407 | − | 0.0846949i | \(-0.973008\pi\) | ||
0.996407 | − | 0.0846949i | \(-0.0269915\pi\) | |||||||
\(942\) | 34.5000 | − | 19.9186i | 1.12407 | − | 0.648983i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 17.3205i | 0.563735i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 49.5000 | − | 85.7365i | 1.60938 | − | 2.78753i | ||||
\(947\) | 33.0000 | + | 19.0526i | 1.07236 | + | 0.619125i | 0.928824 | − | 0.370521i | \(-0.120821\pi\) |
0.143532 | + | 0.989646i | \(0.454154\pi\) | |||||||
\(948\) | 5.00000 | 0.162392 | ||||||||
\(949\) | 30.0000 | + | 8.66025i | 0.973841 | + | 0.281124i | ||||
\(950\) | −6.00000 | −0.194666 | ||||||||
\(951\) | 4.50000 | + | 2.59808i | 0.145922 | + | 0.0842484i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28.5000 | + | 49.3634i | 0.923206 | + | 1.59904i | 0.794422 | + | 0.607366i | \(0.207774\pi\) |
0.128784 | + | 0.991673i | \(0.458893\pi\) | |||||||
\(954\) | − | 31.1769i | − | 1.00939i | ||||||
\(955\) | 22.5000 | − | 12.9904i | 0.728083 | − | 0.420359i | ||||
\(956\) | 9.00000 | − | 5.19615i | 0.291081 | − | 0.168056i | ||||
\(957\) | − | 15.5885i | − | 0.503903i | ||||||
\(958\) | 25.5000 | + | 44.1673i | 0.823868 | + | 1.42698i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.50000 | − | 0.866025i | −0.0484123 | − | 0.0279508i | ||||
\(961\) | 28.0000 | 0.903226 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6.00000 | − | 3.46410i | −0.193247 | − | 0.111571i | ||||
\(965\) | −1.50000 | + | 2.59808i | −0.0482867 | + | 0.0836350i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.3923i | 0.334194i | 0.985940 | + | 0.167097i | \(0.0534393\pi\) | ||||
−0.985940 | + | 0.167097i | \(0.946561\pi\) | |||||||
\(968\) | 24.0000 | − | 13.8564i | 0.771389 | − | 0.445362i | ||||
\(969\) | 9.00000 | − | 5.19615i | 0.289122 | − | 0.166924i | ||||
\(970\) | − | 15.5885i | − | 0.500515i | ||||||
\(971\) | 10.5000 | + | 18.1865i | 0.336961 | + | 0.583634i | 0.983860 | − | 0.178942i | \(-0.0572676\pi\) |
−0.646899 | + | 0.762576i | \(0.723934\pi\) | |||||||
\(972\) | 8.00000 | − | 13.8564i | 0.256600 | − | 0.444444i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 42.0000 | 1.34577 | ||||||||
\(975\) | 5.00000 | + | 5.19615i | 0.160128 | + | 0.166410i | ||||
\(976\) | 35.0000 | 1.12032 | ||||||||
\(977\) | 16.5000 | + | 9.52628i | 0.527882 | + | 0.304773i | 0.740153 | − | 0.672438i | \(-0.234753\pi\) |
−0.212272 | + | 0.977211i | \(0.568086\pi\) | |||||||
\(978\) | 10.5000 | − | 18.1865i | 0.335753 | − | 0.581541i | ||||
\(979\) | −18.0000 | − | 31.1769i | −0.575282 | − | 0.996419i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.00000 | + | 5.19615i | −0.287348 | + | 0.165900i | ||||
\(982\) | 40.5000 | − | 23.3827i | 1.29241 | − | 0.746171i | ||||
\(983\) | − | 36.3731i | − | 1.16012i | −0.814574 | − | 0.580060i | \(-0.803029\pi\) | ||
0.814574 | − | 0.580060i | \(-0.196971\pi\) | |||||||
\(984\) | 4.50000 | + | 7.79423i | 0.143455 | + | 0.248471i | ||||
\(985\) | 19.5000 | − | 33.7750i | 0.621322 | − | 1.07616i | ||||
\(986\) | −27.0000 | − | 15.5885i | −0.859855 | − | 0.496438i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.50000 | + | 4.33013i | −0.143164 | + | 0.137760i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 27.0000 | + | 15.5885i | 0.858116 | + | 0.495434i | ||||
\(991\) | −29.5000 | + | 51.0955i | −0.937098 | + | 1.62310i | −0.166250 | + | 0.986084i | \(0.553166\pi\) |
−0.770849 | + | 0.637018i | \(0.780168\pi\) | |||||||
\(992\) | −4.50000 | − | 7.79423i | −0.142875 | − | 0.247467i | ||||
\(993\) | − | 32.9090i | − | 1.04433i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.00000 | − | 3.46410i | 0.190213 | − | 0.109819i | ||||
\(996\) | − | 3.46410i | − | 0.109764i | ||||||
\(997\) | 1.00000 | + | 1.73205i | 0.0316703 | + | 0.0548546i | 0.881426 | − | 0.472322i | \(-0.156584\pi\) |
−0.849756 | + | 0.527176i | \(0.823251\pi\) | |||||||
\(998\) | −1.50000 | + | 2.59808i | −0.0474817 | + | 0.0822407i | ||||
\(999\) | 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 | 637.2.q.b.589.1 | 2 | ||
7.2 | even | 3 | 637.2.k.b.459.1 | 2 | |||
7.3 | odd | 6 | 91.2.u.a.30.1 | yes | 2 | ||
7.4 | even | 3 | 637.2.u.a.30.1 | 2 | |||
7.5 | odd | 6 | 91.2.k.a.4.1 | ✓ | 2 | ||
7.6 | odd | 2 | 637.2.q.c.589.1 | 2 | |||
13.6 | odd | 12 | 8281.2.a.w.1.1 | 2 | |||
13.7 | odd | 12 | 8281.2.a.w.1.2 | 2 | |||
13.10 | even | 6 | inner | 637.2.q.b.491.1 | 2 | ||
21.5 | even | 6 | 819.2.bm.a.550.1 | 2 | |||
21.17 | even | 6 | 819.2.do.c.667.1 | 2 | |||
91.6 | even | 12 | 8281.2.a.s.1.1 | 2 | |||
91.10 | odd | 6 | 91.2.k.a.23.1 | yes | 2 | ||
91.19 | even | 12 | 1183.2.e.e.508.2 | 4 | |||
91.20 | even | 12 | 8281.2.a.s.1.2 | 2 | |||
91.23 | even | 6 | 637.2.u.a.361.1 | 2 | |||
91.33 | even | 12 | 1183.2.e.e.508.1 | 4 | |||
91.45 | even | 12 | 1183.2.e.e.170.2 | 4 | |||
91.59 | even | 12 | 1183.2.e.e.170.1 | 4 | |||
91.62 | odd | 6 | 637.2.q.c.491.1 | 2 | |||
91.75 | odd | 6 | 91.2.u.a.88.1 | yes | 2 | ||
91.88 | even | 6 | 637.2.k.b.569.1 | 2 | |||
273.101 | even | 6 | 819.2.bm.a.478.1 | 2 | |||
273.257 | even | 6 | 819.2.do.c.361.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.k.a.4.1 | ✓ | 2 | 7.5 | odd | 6 | ||
91.2.k.a.23.1 | yes | 2 | 91.10 | odd | 6 | ||
91.2.u.a.30.1 | yes | 2 | 7.3 | odd | 6 | ||
91.2.u.a.88.1 | yes | 2 | 91.75 | odd | 6 | ||
637.2.k.b.459.1 | 2 | 7.2 | even | 3 | |||
637.2.k.b.569.1 | 2 | 91.88 | even | 6 | |||
637.2.q.b.491.1 | 2 | 13.10 | even | 6 | inner | ||
637.2.q.b.589.1 | 2 | 1.1 | even | 1 | trivial | ||
637.2.q.c.491.1 | 2 | 91.62 | odd | 6 | |||
637.2.q.c.589.1 | 2 | 7.6 | odd | 2 | |||
637.2.u.a.30.1 | 2 | 7.4 | even | 3 | |||
637.2.u.a.361.1 | 2 | 91.23 | even | 6 | |||
819.2.bm.a.478.1 | 2 | 273.101 | even | 6 | |||
819.2.bm.a.550.1 | 2 | 21.5 | even | 6 | |||
819.2.do.c.361.1 | 2 | 273.257 | even | 6 | |||
819.2.do.c.667.1 | 2 | 21.17 | even | 6 | |||
1183.2.e.e.170.1 | 4 | 91.59 | even | 12 | |||
1183.2.e.e.170.2 | 4 | 91.45 | even | 12 | |||
1183.2.e.e.508.1 | 4 | 91.33 | even | 12 | |||
1183.2.e.e.508.2 | 4 | 91.19 | even | 12 | |||
8281.2.a.s.1.1 | 2 | 91.6 | even | 12 | |||
8281.2.a.s.1.2 | 2 | 91.20 | even | 12 | |||
8281.2.a.w.1.1 | 2 | 13.6 | odd | 12 | |||
8281.2.a.w.1.2 | 2 | 13.7 | odd | 12 |