Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(499,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.499");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.o (of order \(6\), degree \(2\), not 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: | \(8.38429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 499.1 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.499 |
Dual form | 1050.2.o.c.949.1 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −1.73205 | + | 2.00000i | −0.654654 | + | 0.755929i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50000 | − | 2.59808i | −0.452267 | − | 0.783349i | 0.546259 | − | 0.837616i | \(-0.316051\pi\) |
−0.998526 | + | 0.0542666i | \(0.982718\pi\) | |||||||
\(12\) | 0.866025 | + | 0.500000i | 0.250000 | + | 0.144338i | ||||
\(13\) | 5.00000i | 1.38675i | 0.720577 | + | 0.693375i | \(0.243877\pi\) | ||||
−0.720577 | + | 0.693375i | \(0.756123\pi\) | |||||||
\(14\) | 2.50000 | − | 0.866025i | 0.668153 | − | 0.231455i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(18\) | −0.866025 | + | 0.500000i | −0.204124 | + | 0.117851i | ||||
\(19\) | 2.50000 | − | 4.33013i | 0.573539 | − | 0.993399i | −0.422659 | − | 0.906289i | \(-0.638903\pi\) |
0.996199 | − | 0.0871106i | \(-0.0277634\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.500000 | + | 2.59808i | −0.109109 | + | 0.566947i | ||||
\(22\) | 3.00000i | 0.639602i | ||||||||
\(23\) | 7.79423 | + | 4.50000i | 1.62521 | + | 0.938315i | 0.985496 | + | 0.169701i | \(0.0542803\pi\) |
0.639713 | + | 0.768613i | \(0.279053\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.50000 | − | 4.33013i | 0.490290 | − | 0.849208i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −2.59808 | − | 0.500000i | −0.490990 | − | 0.0944911i | ||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.00000 | + | 8.66025i | 0.898027 | + | 1.55543i | 0.830014 | + | 0.557743i | \(0.188333\pi\) |
0.0680129 | + | 0.997684i | \(0.478334\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | −2.59808 | − | 1.50000i | −0.452267 | − | 0.261116i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −0.866025 | − | 0.500000i | −0.142374 | − | 0.0821995i | 0.427121 | − | 0.904194i | \(-0.359528\pi\) |
−0.569495 | + | 0.821995i | \(0.692861\pi\) | |||||||
\(38\) | −4.33013 | + | 2.50000i | −0.702439 | + | 0.405554i | ||||
\(39\) | 2.50000 | + | 4.33013i | 0.400320 | + | 0.693375i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.00000 | 1.40556 | 0.702782 | − | 0.711405i | \(-0.251941\pi\) | ||||
0.702782 | + | 0.711405i | \(0.251941\pi\) | |||||||
\(42\) | 1.73205 | − | 2.00000i | 0.267261 | − | 0.308607i | ||||
\(43\) | 8.00000i | 1.21999i | 0.792406 | + | 0.609994i | \(0.208828\pi\) | ||||
−0.792406 | + | 0.609994i | \(0.791172\pi\) | |||||||
\(44\) | 1.50000 | − | 2.59808i | 0.226134 | − | 0.391675i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.50000 | − | 7.79423i | −0.663489 | − | 1.14920i | ||||
\(47\) | 2.59808 | + | 1.50000i | 0.378968 | + | 0.218797i | 0.677369 | − | 0.735643i | \(-0.263120\pi\) |
−0.298401 | + | 0.954441i | \(0.596453\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | −1.00000 | − | 6.92820i | −0.142857 | − | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.33013 | + | 2.50000i | −0.600481 | + | 0.346688i | ||||
\(53\) | −2.59808 | + | 1.50000i | −0.356873 | + | 0.206041i | −0.667708 | − | 0.744423i | \(-0.732725\pi\) |
0.310835 | + | 0.950464i | \(0.399391\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.00000 | + | 1.73205i | 0.267261 | + | 0.231455i | ||||
\(57\) | − | 5.00000i | − | 0.662266i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.00000 | + | 10.3923i | 0.781133 | + | 1.35296i | 0.931282 | + | 0.364299i | \(0.118692\pi\) |
−0.150148 | + | 0.988663i | \(0.547975\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.00000 | + | 6.92820i | −0.512148 | + | 0.887066i | 0.487753 | + | 0.872982i | \(0.337817\pi\) |
−0.999901 | + | 0.0140840i | \(0.995517\pi\) | |||||||
\(62\) | − | 10.0000i | − | 1.27000i | ||||||
\(63\) | 0.866025 | + | 2.50000i | 0.109109 | + | 0.314970i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.50000 | + | 2.59808i | 0.184637 | + | 0.319801i | ||||
\(67\) | −6.92820 | + | 4.00000i | −0.846415 | + | 0.488678i | −0.859440 | − | 0.511237i | \(-0.829187\pi\) |
0.0130248 | + | 0.999915i | \(0.495854\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.00000 | 1.08347 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | −0.866025 | − | 0.500000i | −0.102062 | − | 0.0589256i | ||||
\(73\) | 1.73205 | − | 1.00000i | 0.202721 | − | 0.117041i | −0.395203 | − | 0.918594i | \(-0.629326\pi\) |
0.597924 | + | 0.801553i | \(0.295992\pi\) | |||||||
\(74\) | 0.500000 | + | 0.866025i | 0.0581238 | + | 0.100673i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.00000 | 0.573539 | ||||||||
\(77\) | 7.79423 | + | 1.50000i | 0.888235 | + | 0.170941i | ||||
\(78\) | − | 5.00000i | − | 0.566139i | ||||||
\(79\) | 4.00000 | − | 6.92820i | 0.450035 | − | 0.779484i | −0.548352 | − | 0.836247i | \(-0.684745\pi\) |
0.998388 | + | 0.0567635i | \(0.0180781\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −7.79423 | − | 4.50000i | −0.860729 | − | 0.496942i | ||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | −2.50000 | + | 0.866025i | −0.272772 | + | 0.0944911i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.00000 | − | 6.92820i | 0.431331 | − | 0.747087i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.59808 | + | 1.50000i | −0.276956 | + | 0.159901i | ||||
\(89\) | 3.00000 | − | 5.19615i | 0.317999 | − | 0.550791i | −0.662071 | − | 0.749441i | \(-0.730322\pi\) |
0.980071 | + | 0.198650i | \(0.0636557\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.0000 | − | 8.66025i | −1.04828 | − | 0.907841i | ||||
\(92\) | 9.00000i | 0.938315i | ||||||||
\(93\) | 8.66025 | + | 5.00000i | 0.898027 | + | 0.518476i | ||||
\(94\) | −1.50000 | − | 2.59808i | −0.154713 | − | 0.267971i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.500000 | − | 0.866025i | 0.0510310 | − | 0.0883883i | ||||
\(97\) | − | 8.00000i | − | 0.812277i | −0.913812 | − | 0.406138i | \(-0.866875\pi\) | ||
0.913812 | − | 0.406138i | \(-0.133125\pi\) | |||||||
\(98\) | −2.59808 | + | 6.50000i | −0.262445 | + | 0.656599i | ||||
\(99\) | −3.00000 | −0.301511 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.92820 | − | 4.00000i | −0.682656 | − | 0.394132i | 0.118199 | − | 0.992990i | \(-0.462288\pi\) |
−0.800855 | + | 0.598858i | \(0.795621\pi\) | |||||||
\(104\) | 5.00000 | 0.490290 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.00000 | 0.291386 | ||||||||
\(107\) | 5.19615 | + | 3.00000i | 0.502331 | + | 0.290021i | 0.729676 | − | 0.683793i | \(-0.239671\pi\) |
−0.227345 | + | 0.973814i | \(0.573004\pi\) | |||||||
\(108\) | 0.866025 | − | 0.500000i | 0.0833333 | − | 0.0481125i | ||||
\(109\) | 7.00000 | + | 12.1244i | 0.670478 | + | 1.16130i | 0.977769 | + | 0.209687i | \(0.0672444\pi\) |
−0.307290 | + | 0.951616i | \(0.599422\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.00000 | −0.0949158 | ||||||||
\(112\) | −0.866025 | − | 2.50000i | −0.0818317 | − | 0.236228i | ||||
\(113\) | − | 18.0000i | − | 1.69330i | −0.532152 | − | 0.846649i | \(-0.678617\pi\) | ||
0.532152 | − | 0.846649i | \(-0.321383\pi\) | |||||||
\(114\) | −2.50000 | + | 4.33013i | −0.234146 | + | 0.405554i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.33013 | + | 2.50000i | 0.400320 | + | 0.231125i | ||||
\(118\) | − | 12.0000i | − | 1.10469i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | 6.92820 | − | 4.00000i | 0.627250 | − | 0.362143i | ||||
\(123\) | 7.79423 | − | 4.50000i | 0.702782 | − | 0.405751i | ||||
\(124\) | −5.00000 | + | 8.66025i | −0.449013 | + | 0.777714i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.500000 | − | 2.59808i | 0.0445435 | − | 0.231455i | ||||
\(127\) | 13.0000i | 1.15356i | 0.816898 | + | 0.576782i | \(0.195692\pi\) | ||||
−0.816898 | + | 0.576782i | \(0.804308\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 4.00000 | + | 6.92820i | 0.352180 | + | 0.609994i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.50000 | − | 7.79423i | 0.393167 | − | 0.680985i | −0.599699 | − | 0.800226i | \(-0.704713\pi\) |
0.992865 | + | 0.119241i | \(0.0380462\pi\) | |||||||
\(132\) | − | 3.00000i | − | 0.261116i | ||||||
\(133\) | 4.33013 | + | 12.5000i | 0.375470 | + | 1.08389i | ||||
\(134\) | 8.00000 | 0.691095 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.5885 | − | 9.00000i | 1.33181 | − | 0.768922i | 0.346235 | − | 0.938148i | \(-0.387460\pi\) |
0.985577 | + | 0.169226i | \(0.0541268\pi\) | |||||||
\(138\) | −7.79423 | − | 4.50000i | −0.663489 | − | 0.383065i | ||||
\(139\) | −20.0000 | −1.69638 | −0.848189 | − | 0.529694i | \(-0.822307\pi\) | ||||
−0.848189 | + | 0.529694i | \(0.822307\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.00000 | 0.252646 | ||||||||
\(142\) | 5.19615 | + | 3.00000i | 0.436051 | + | 0.251754i | ||||
\(143\) | 12.9904 | − | 7.50000i | 1.08631 | − | 0.627182i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.00000 | −0.165521 | ||||||||
\(147\) | −4.33013 | − | 5.50000i | −0.357143 | − | 0.453632i | ||||
\(148\) | − | 1.00000i | − | 0.0821995i | ||||||
\(149\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.00000 | + | 8.66025i | 0.406894 | + | 0.704761i | 0.994540 | − | 0.104357i | \(-0.0332784\pi\) |
−0.587646 | + | 0.809118i | \(0.699945\pi\) | |||||||
\(152\) | −4.33013 | − | 2.50000i | −0.351220 | − | 0.202777i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.00000 | − | 5.19615i | −0.483494 | − | 0.418718i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.50000 | + | 4.33013i | −0.200160 | + | 0.346688i | ||||
\(157\) | −4.33013 | + | 2.50000i | −0.345582 | + | 0.199522i | −0.662738 | − | 0.748852i | \(-0.730606\pi\) |
0.317156 | + | 0.948373i | \(0.397272\pi\) | |||||||
\(158\) | −6.92820 | + | 4.00000i | −0.551178 | + | 0.318223i | ||||
\(159\) | −1.50000 | + | 2.59808i | −0.118958 | + | 0.206041i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −22.5000 | + | 7.79423i | −1.77325 | + | 0.614271i | ||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 13.8564 | + | 8.00000i | 1.08532 | + | 0.626608i | 0.932326 | − | 0.361619i | \(-0.117776\pi\) |
0.152992 | + | 0.988227i | \(0.451109\pi\) | |||||||
\(164\) | 4.50000 | + | 7.79423i | 0.351391 | + | 0.608627i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.00000i | 0.232147i | 0.993241 | + | 0.116073i | \(0.0370308\pi\) | ||||
−0.993241 | + | 0.116073i | \(0.962969\pi\) | |||||||
\(168\) | 2.59808 | + | 0.500000i | 0.200446 | + | 0.0385758i | ||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.50000 | − | 4.33013i | −0.191180 | − | 0.331133i | ||||
\(172\) | −6.92820 | + | 4.00000i | −0.528271 | + | 0.304997i | ||||
\(173\) | −7.79423 | − | 4.50000i | −0.592584 | − | 0.342129i | 0.173534 | − | 0.984828i | \(-0.444481\pi\) |
−0.766119 | + | 0.642699i | \(0.777815\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.00000 | 0.226134 | ||||||||
\(177\) | 10.3923 | + | 6.00000i | 0.781133 | + | 0.450988i | ||||
\(178\) | −5.19615 | + | 3.00000i | −0.389468 | + | 0.224860i | ||||
\(179\) | −7.50000 | − | 12.9904i | −0.560576 | − | 0.970947i | −0.997446 | − | 0.0714220i | \(-0.977246\pi\) |
0.436870 | − | 0.899525i | \(-0.356087\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.00000 | 0.594635 | 0.297318 | − | 0.954779i | \(-0.403908\pi\) | ||||
0.297318 | + | 0.954779i | \(0.403908\pi\) | |||||||
\(182\) | 4.33013 | + | 12.5000i | 0.320970 | + | 0.926562i | ||||
\(183\) | 8.00000i | 0.591377i | ||||||||
\(184\) | 4.50000 | − | 7.79423i | 0.331744 | − | 0.574598i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −5.00000 | − | 8.66025i | −0.366618 | − | 0.635001i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 3.00000i | 0.218797i | ||||||||
\(189\) | 2.00000 | + | 1.73205i | 0.145479 | + | 0.125988i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.00000 | + | 15.5885i | −0.651217 | + | 1.12794i | 0.331611 | + | 0.943416i | \(0.392408\pi\) |
−0.982828 | + | 0.184525i | \(0.940925\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | −8.66025 | + | 5.00000i | −0.623379 | + | 0.359908i | −0.778183 | − | 0.628037i | \(-0.783859\pi\) |
0.154805 | + | 0.987945i | \(0.450525\pi\) | |||||||
\(194\) | −4.00000 | + | 6.92820i | −0.287183 | + | 0.497416i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.50000 | − | 4.33013i | 0.392857 | − | 0.309295i | ||||
\(197\) | − | 15.0000i | − | 1.06871i | −0.845262 | − | 0.534353i | \(-0.820555\pi\) | ||
0.845262 | − | 0.534353i | \(-0.179445\pi\) | |||||||
\(198\) | 2.59808 | + | 1.50000i | 0.184637 | + | 0.106600i | ||||
\(199\) | −8.00000 | − | 13.8564i | −0.567105 | − | 0.982255i | −0.996850 | − | 0.0793045i | \(-0.974730\pi\) |
0.429745 | − | 0.902950i | \(-0.358603\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.00000 | + | 6.92820i | −0.282138 | + | 0.488678i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.00000 | + | 6.92820i | 0.278693 | + | 0.482711i | ||||
\(207\) | 7.79423 | − | 4.50000i | 0.541736 | − | 0.312772i | ||||
\(208\) | −4.33013 | − | 2.50000i | −0.300240 | − | 0.173344i | ||||
\(209\) | −15.0000 | −1.03757 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.00000 | 0.344214 | 0.172107 | − | 0.985078i | \(-0.444942\pi\) | ||||
0.172107 | + | 0.985078i | \(0.444942\pi\) | |||||||
\(212\) | −2.59808 | − | 1.50000i | −0.178437 | − | 0.103020i | ||||
\(213\) | −5.19615 | + | 3.00000i | −0.356034 | + | 0.205557i | ||||
\(214\) | −3.00000 | − | 5.19615i | −0.205076 | − | 0.355202i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −25.9808 | − | 5.00000i | −1.76369 | − | 0.339422i | ||||
\(218\) | − | 14.0000i | − | 0.948200i | ||||||
\(219\) | 1.00000 | − | 1.73205i | 0.0675737 | − | 0.117041i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0.866025 | + | 0.500000i | 0.0581238 | + | 0.0335578i | ||||
\(223\) | − | 28.0000i | − | 1.87502i | −0.347960 | − | 0.937509i | \(-0.613126\pi\) | ||
0.347960 | − | 0.937509i | \(-0.386874\pi\) | |||||||
\(224\) | −0.500000 | + | 2.59808i | −0.0334077 | + | 0.173591i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.00000 | + | 15.5885i | −0.598671 | + | 1.03693i | ||||
\(227\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(228\) | 4.33013 | − | 2.50000i | 0.286770 | − | 0.165567i | ||||
\(229\) | 7.00000 | − | 12.1244i | 0.462573 | − | 0.801200i | −0.536515 | − | 0.843891i | \(-0.680260\pi\) |
0.999088 | + | 0.0426906i | \(0.0135930\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.50000 | − | 2.59808i | 0.493464 | − | 0.170941i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.19615 | + | 3.00000i | 0.340411 | + | 0.196537i | 0.660454 | − | 0.750867i | \(-0.270364\pi\) |
−0.320043 | + | 0.947403i | \(0.603697\pi\) | |||||||
\(234\) | −2.50000 | − | 4.33013i | −0.163430 | − | 0.283069i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.00000 | + | 10.3923i | −0.390567 | + | 0.676481i | ||||
\(237\) | − | 8.00000i | − | 0.519656i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −30.0000 | −1.94054 | −0.970269 | − | 0.242028i | \(-0.922188\pi\) | ||||
−0.970269 | + | 0.242028i | \(0.922188\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.500000 | + | 0.866025i | 0.0322078 | + | 0.0557856i | 0.881680 | − | 0.471848i | \(-0.156413\pi\) |
−0.849472 | + | 0.527633i | \(0.823079\pi\) | |||||||
\(242\) | −1.73205 | + | 1.00000i | −0.111340 | + | 0.0642824i | ||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | −8.00000 | −0.512148 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −9.00000 | −0.573819 | ||||||||
\(247\) | 21.6506 | + | 12.5000i | 1.37760 | + | 0.795356i | ||||
\(248\) | 8.66025 | − | 5.00000i | 0.549927 | − | 0.317500i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.00000 | 0.568075 | 0.284037 | − | 0.958813i | \(-0.408326\pi\) | ||||
0.284037 | + | 0.958813i | \(0.408326\pi\) | |||||||
\(252\) | −1.73205 | + | 2.00000i | −0.109109 | + | 0.125988i | ||||
\(253\) | − | 27.0000i | − | 1.69748i | ||||||
\(254\) | 6.50000 | − | 11.2583i | 0.407846 | − | 0.706410i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −10.3923 | − | 6.00000i | −0.648254 | − | 0.374270i | 0.139533 | − | 0.990217i | \(-0.455440\pi\) |
−0.787787 | + | 0.615948i | \(0.788773\pi\) | |||||||
\(258\) | − | 8.00000i | − | 0.498058i | ||||||
\(259\) | 2.50000 | − | 0.866025i | 0.155342 | − | 0.0538122i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.79423 | + | 4.50000i | −0.481529 | + | 0.278011i | ||||
\(263\) | −20.7846 | + | 12.0000i | −1.28163 | + | 0.739952i | −0.977147 | − | 0.212565i | \(-0.931818\pi\) |
−0.304487 | + | 0.952517i | \(0.598485\pi\) | |||||||
\(264\) | −1.50000 | + | 2.59808i | −0.0923186 | + | 0.159901i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.50000 | − | 12.9904i | 0.153285 | − | 0.796491i | ||||
\(267\) | − | 6.00000i | − | 0.367194i | ||||||
\(268\) | −6.92820 | − | 4.00000i | −0.423207 | − | 0.244339i | ||||
\(269\) | 6.00000 | + | 10.3923i | 0.365826 | + | 0.633630i | 0.988908 | − | 0.148527i | \(-0.0474530\pi\) |
−0.623082 | + | 0.782157i | \(0.714120\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | − | 13.8564i | 0.485965 | − | 0.841717i | −0.513905 | − | 0.857847i | \(-0.671801\pi\) |
0.999870 | + | 0.0161307i | \(0.00513477\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −12.9904 | − | 2.50000i | −0.786214 | − | 0.151307i | ||||
\(274\) | −18.0000 | −1.08742 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.50000 | + | 7.79423i | 0.270868 | + | 0.469157i | ||||
\(277\) | −22.5167 | + | 13.0000i | −1.35290 | + | 0.781094i | −0.988654 | − | 0.150210i | \(-0.952005\pi\) |
−0.364241 | + | 0.931305i | \(0.618672\pi\) | |||||||
\(278\) | 17.3205 | + | 10.0000i | 1.03882 | + | 0.599760i | ||||
\(279\) | 10.0000 | 0.598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.0000 | −1.25275 | −0.626377 | − | 0.779520i | \(-0.715463\pi\) | ||||
−0.626377 | + | 0.779520i | \(0.715463\pi\) | |||||||
\(282\) | −2.59808 | − | 1.50000i | −0.154713 | − | 0.0893237i | ||||
\(283\) | −19.0526 | + | 11.0000i | −1.13256 | + | 0.653882i | −0.944577 | − | 0.328291i | \(-0.893527\pi\) |
−0.187980 | + | 0.982173i | \(0.560194\pi\) | |||||||
\(284\) | −3.00000 | − | 5.19615i | −0.178017 | − | 0.308335i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −15.0000 | −0.886969 | ||||||||
\(287\) | −15.5885 | + | 18.0000i | −0.920158 | + | 1.06251i | ||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | −8.50000 | + | 14.7224i | −0.500000 | + | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.00000 | − | 6.92820i | −0.234484 | − | 0.406138i | ||||
\(292\) | 1.73205 | + | 1.00000i | 0.101361 | + | 0.0585206i | ||||
\(293\) | − | 21.0000i | − | 1.22683i | −0.789760 | − | 0.613417i | \(-0.789795\pi\) | ||
0.789760 | − | 0.613417i | \(-0.210205\pi\) | |||||||
\(294\) | 1.00000 | + | 6.92820i | 0.0583212 | + | 0.404061i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.500000 | + | 0.866025i | −0.0290619 | + | 0.0503367i | ||||
\(297\) | −2.59808 | + | 1.50000i | −0.150756 | + | 0.0870388i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −22.5000 | + | 38.9711i | −1.30121 | + | 2.25376i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.0000 | − | 13.8564i | −0.922225 | − | 0.798670i | ||||
\(302\) | − | 10.0000i | − | 0.575435i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.50000 | + | 4.33013i | 0.143385 | + | 0.248350i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.0000i | 1.59804i | 0.601302 | + | 0.799022i | \(0.294649\pi\) | ||||
−0.601302 | + | 0.799022i | \(0.705351\pi\) | |||||||
\(308\) | 2.59808 | + | 7.50000i | 0.148039 | + | 0.427352i | ||||
\(309\) | −8.00000 | −0.455104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.00000 | + | 10.3923i | 0.340229 | + | 0.589294i | 0.984475 | − | 0.175525i | \(-0.0561621\pi\) |
−0.644246 | + | 0.764818i | \(0.722829\pi\) | |||||||
\(312\) | 4.33013 | − | 2.50000i | 0.245145 | − | 0.141535i | ||||
\(313\) | 3.46410 | + | 2.00000i | 0.195803 | + | 0.113047i | 0.594696 | − | 0.803951i | \(-0.297272\pi\) |
−0.398894 | + | 0.916997i | \(0.630606\pi\) | |||||||
\(314\) | 5.00000 | 0.282166 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.00000 | 0.450035 | ||||||||
\(317\) | −15.5885 | − | 9.00000i | −0.875535 | − | 0.505490i | −0.00635137 | − | 0.999980i | \(-0.502022\pi\) |
−0.869184 | + | 0.494489i | \(0.835355\pi\) | |||||||
\(318\) | 2.59808 | − | 1.50000i | 0.145693 | − | 0.0841158i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.00000 | 0.334887 | ||||||||
\(322\) | 23.3827 | + | 4.50000i | 1.30307 | + | 0.250775i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.00000 | − | 13.8564i | −0.443079 | − | 0.767435i | ||||
\(327\) | 12.1244 | + | 7.00000i | 0.670478 | + | 0.387101i | ||||
\(328\) | − | 9.00000i | − | 0.496942i | ||||||
\(329\) | −7.50000 | + | 2.59808i | −0.413488 | + | 0.143237i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.50000 | + | 9.52628i | −0.302307 | + | 0.523612i | −0.976658 | − | 0.214799i | \(-0.931090\pi\) |
0.674351 | + | 0.738411i | \(0.264424\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.866025 | + | 0.500000i | −0.0474579 | + | 0.0273998i | ||||
\(334\) | 1.50000 | − | 2.59808i | 0.0820763 | − | 0.142160i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.00000 | − | 1.73205i | −0.109109 | − | 0.0944911i | ||||
\(337\) | − | 20.0000i | − | 1.08947i | −0.838608 | − | 0.544735i | \(-0.816630\pi\) | ||
0.838608 | − | 0.544735i | \(-0.183370\pi\) | |||||||
\(338\) | 10.3923 | + | 6.00000i | 0.565267 | + | 0.326357i | ||||
\(339\) | −9.00000 | − | 15.5885i | −0.488813 | − | 0.846649i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.0000 | − | 25.9808i | 0.812296 | − | 1.40694i | ||||
\(342\) | 5.00000i | 0.270369i | ||||||||
\(343\) | 15.5885 | + | 10.0000i | 0.841698 | + | 0.539949i | ||||
\(344\) | 8.00000 | 0.431331 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.50000 | + | 7.79423i | 0.241921 | + | 0.419020i | ||||
\(347\) | −25.9808 | + | 15.0000i | −1.39472 | + | 0.805242i | −0.993833 | − | 0.110885i | \(-0.964631\pi\) |
−0.400887 | + | 0.916127i | \(0.631298\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.0000 | 1.49881 | 0.749403 | − | 0.662114i | \(-0.230341\pi\) | ||||
0.749403 | + | 0.662114i | \(0.230341\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.00000 | 0.266880 | ||||||||
\(352\) | −2.59808 | − | 1.50000i | −0.138478 | − | 0.0799503i | ||||
\(353\) | 20.7846 | − | 12.0000i | 1.10625 | − | 0.638696i | 0.168397 | − | 0.985719i | \(-0.446141\pi\) |
0.937856 | + | 0.347024i | \(0.112808\pi\) | |||||||
\(354\) | −6.00000 | − | 10.3923i | −0.318896 | − | 0.552345i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.00000 | 0.317999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 15.0000i | 0.792775i | ||||||||
\(359\) | 6.00000 | − | 10.3923i | 0.316668 | − | 0.548485i | −0.663123 | − | 0.748511i | \(-0.730769\pi\) |
0.979791 | + | 0.200026i | \(0.0641026\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | − | 5.19615i | −0.157895 | − | 0.273482i | ||||
\(362\) | −6.92820 | − | 4.00000i | −0.364138 | − | 0.210235i | ||||
\(363\) | − | 2.00000i | − | 0.104973i | ||||||
\(364\) | 2.50000 | − | 12.9904i | 0.131036 | − | 0.680881i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.00000 | − | 6.92820i | 0.209083 | − | 0.362143i | ||||
\(367\) | 16.4545 | − | 9.50000i | 0.858917 | − | 0.495896i | −0.00473247 | − | 0.999989i | \(-0.501506\pi\) |
0.863649 | + | 0.504093i | \(0.168173\pi\) | |||||||
\(368\) | −7.79423 | + | 4.50000i | −0.406302 | + | 0.234579i | ||||
\(369\) | 4.50000 | − | 7.79423i | 0.234261 | − | 0.405751i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.50000 | − | 7.79423i | 0.0778761 | − | 0.404656i | ||||
\(372\) | 10.0000i | 0.518476i | ||||||||
\(373\) | 8.66025 | + | 5.00000i | 0.448411 | + | 0.258890i | 0.707159 | − | 0.707055i | \(-0.249977\pi\) |
−0.258748 | + | 0.965945i | \(0.583310\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.50000 | − | 2.59808i | 0.0773566 | − | 0.133986i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.866025 | − | 2.50000i | −0.0445435 | − | 0.128586i | ||||
\(379\) | 19.0000 | 0.975964 | 0.487982 | − | 0.872854i | \(-0.337733\pi\) | ||||
0.487982 | + | 0.872854i | \(0.337733\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.50000 | + | 11.2583i | 0.333005 | + | 0.576782i | ||||
\(382\) | 15.5885 | − | 9.00000i | 0.797575 | − | 0.460480i | ||||
\(383\) | −23.3827 | − | 13.5000i | −1.19480 | − | 0.689818i | −0.235408 | − | 0.971897i | \(-0.575643\pi\) |
−0.959391 | + | 0.282079i | \(0.908976\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10.0000 | 0.508987 | ||||||||
\(387\) | 6.92820 | + | 4.00000i | 0.352180 | + | 0.203331i | ||||
\(388\) | 6.92820 | − | 4.00000i | 0.351726 | − | 0.203069i | ||||
\(389\) | −3.00000 | − | 5.19615i | −0.152106 | − | 0.263455i | 0.779895 | − | 0.625910i | \(-0.215272\pi\) |
−0.932002 | + | 0.362454i | \(0.881939\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −6.92820 | + | 1.00000i | −0.349927 | + | 0.0505076i | ||||
\(393\) | − | 9.00000i | − | 0.453990i | ||||||
\(394\) | −7.50000 | + | 12.9904i | −0.377845 | + | 0.654446i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.50000 | − | 2.59808i | −0.0753778 | − | 0.130558i | ||||
\(397\) | 12.1244 | + | 7.00000i | 0.608504 | + | 0.351320i | 0.772380 | − | 0.635161i | \(-0.219066\pi\) |
−0.163876 | + | 0.986481i | \(0.552400\pi\) | |||||||
\(398\) | 16.0000i | 0.802008i | ||||||||
\(399\) | 10.0000 | + | 8.66025i | 0.500626 | + | 0.433555i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.50000 | + | 12.9904i | −0.374532 | + | 0.648709i | −0.990257 | − | 0.139253i | \(-0.955530\pi\) |
0.615725 | + | 0.787961i | \(0.288863\pi\) | |||||||
\(402\) | 6.92820 | − | 4.00000i | 0.345547 | − | 0.199502i | ||||
\(403\) | −43.3013 | + | 25.0000i | −2.15699 | + | 1.24534i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.00000i | 0.148704i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.00000 | + | 1.73205i | 0.0494468 | + | 0.0856444i | 0.889689 | − | 0.456566i | \(-0.150921\pi\) |
−0.840243 | + | 0.542211i | \(0.817588\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.00000 | − | 15.5885i | 0.443937 | − | 0.768922i | ||||
\(412\) | − | 8.00000i | − | 0.394132i | ||||||
\(413\) | −31.1769 | − | 6.00000i | −1.53412 | − | 0.295241i | ||||
\(414\) | −9.00000 | −0.442326 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.50000 | + | 4.33013i | 0.122573 | + | 0.212302i | ||||
\(417\) | −17.3205 | + | 10.0000i | −0.848189 | + | 0.489702i | ||||
\(418\) | 12.9904 | + | 7.50000i | 0.635380 | + | 0.366837i | ||||
\(419\) | 9.00000 | 0.439679 | 0.219839 | − | 0.975536i | \(-0.429447\pi\) | ||||
0.219839 | + | 0.975536i | \(0.429447\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.0000 | 0.682318 | 0.341159 | − | 0.940006i | \(-0.389181\pi\) | ||||
0.341159 | + | 0.940006i | \(0.389181\pi\) | |||||||
\(422\) | −4.33013 | − | 2.50000i | −0.210787 | − | 0.121698i | ||||
\(423\) | 2.59808 | − | 1.50000i | 0.126323 | − | 0.0729325i | ||||
\(424\) | 1.50000 | + | 2.59808i | 0.0728464 | + | 0.126174i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.00000 | 0.290701 | ||||||||
\(427\) | −6.92820 | − | 20.0000i | −0.335279 | − | 0.967868i | ||||
\(428\) | 6.00000i | 0.290021i | ||||||||
\(429\) | 7.50000 | − | 12.9904i | 0.362103 | − | 0.627182i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.0000 | + | 20.7846i | 0.578020 | + | 1.00116i | 0.995706 | + | 0.0925683i | \(0.0295076\pi\) |
−0.417687 | + | 0.908591i | \(0.637159\pi\) | |||||||
\(432\) | 0.866025 | + | 0.500000i | 0.0416667 | + | 0.0240563i | ||||
\(433\) | − | 16.0000i | − | 0.768911i | −0.923144 | − | 0.384455i | \(-0.874389\pi\) | ||
0.923144 | − | 0.384455i | \(-0.125611\pi\) | |||||||
\(434\) | 20.0000 | + | 17.3205i | 0.960031 | + | 0.831411i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.00000 | + | 12.1244i | −0.335239 | + | 0.580651i | ||||
\(437\) | 38.9711 | − | 22.5000i | 1.86424 | − | 1.07632i | ||||
\(438\) | −1.73205 | + | 1.00000i | −0.0827606 | + | 0.0477818i | ||||
\(439\) | 4.00000 | − | 6.92820i | 0.190910 | − | 0.330665i | −0.754642 | − | 0.656136i | \(-0.772190\pi\) |
0.945552 | + | 0.325471i | \(0.105523\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.50000 | − | 2.59808i | −0.309524 | − | 0.123718i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.7846 | + | 12.0000i | 0.987507 | + | 0.570137i | 0.904528 | − | 0.426414i | \(-0.140223\pi\) |
0.0829786 | + | 0.996551i | \(0.473557\pi\) | |||||||
\(444\) | −0.500000 | − | 0.866025i | −0.0237289 | − | 0.0410997i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −14.0000 | + | 24.2487i | −0.662919 | + | 1.14821i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.73205 | − | 2.00000i | 0.0818317 | − | 0.0944911i | ||||
\(449\) | 33.0000 | 1.55737 | 0.778683 | − | 0.627417i | \(-0.215888\pi\) | ||||
0.778683 | + | 0.627417i | \(0.215888\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.5000 | − | 23.3827i | −0.635690 | − | 1.10105i | ||||
\(452\) | 15.5885 | − | 9.00000i | 0.733219 | − | 0.423324i | ||||
\(453\) | 8.66025 | + | 5.00000i | 0.406894 | + | 0.234920i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.00000 | −0.234146 | ||||||||
\(457\) | −8.66025 | − | 5.00000i | −0.405110 | − | 0.233890i | 0.283577 | − | 0.958950i | \(-0.408479\pi\) |
−0.688686 | + | 0.725059i | \(0.741812\pi\) | |||||||
\(458\) | −12.1244 | + | 7.00000i | −0.566534 | + | 0.327089i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.0000 | 0.558896 | 0.279448 | − | 0.960161i | \(-0.409849\pi\) | ||||
0.279448 | + | 0.960161i | \(0.409849\pi\) | |||||||
\(462\) | −7.79423 | − | 1.50000i | −0.362620 | − | 0.0697863i | ||||
\(463\) | − | 1.00000i | − | 0.0464739i | −0.999730 | − | 0.0232370i | \(-0.992603\pi\) | ||
0.999730 | − | 0.0232370i | \(-0.00739722\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.00000 | − | 5.19615i | −0.138972 | − | 0.240707i | ||||
\(467\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(468\) | 5.00000i | 0.231125i | ||||||||
\(469\) | 4.00000 | − | 20.7846i | 0.184703 | − | 0.959744i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.50000 | + | 4.33013i | −0.115194 | + | 0.199522i | ||||
\(472\) | 10.3923 | − | 6.00000i | 0.478345 | − | 0.276172i | ||||
\(473\) | 20.7846 | − | 12.0000i | 0.955677 | − | 0.551761i | ||||
\(474\) | −4.00000 | + | 6.92820i | −0.183726 | + | 0.318223i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.00000i | 0.137361i | ||||||||
\(478\) | 25.9808 | + | 15.0000i | 1.18833 | + | 0.686084i | ||||
\(479\) | −9.00000 | − | 15.5885i | −0.411220 | − | 0.712255i | 0.583803 | − | 0.811895i | \(-0.301564\pi\) |
−0.995023 | + | 0.0996406i | \(0.968231\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.50000 | − | 4.33013i | 0.113990 | − | 0.197437i | ||||
\(482\) | − | 1.00000i | − | 0.0455488i | ||||||
\(483\) | −15.5885 | + | 18.0000i | −0.709299 | + | 0.819028i | ||||
\(484\) | 2.00000 | 0.0909091 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.500000 | + | 0.866025i | 0.0226805 | + | 0.0392837i | ||||
\(487\) | 34.6410 | − | 20.0000i | 1.56973 | − | 0.906287i | 0.573535 | − | 0.819181i | \(-0.305572\pi\) |
0.996199 | − | 0.0871056i | \(-0.0277618\pi\) | |||||||
\(488\) | 6.92820 | + | 4.00000i | 0.313625 | + | 0.181071i | ||||
\(489\) | 16.0000 | 0.723545 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.0000 | 0.541552 | 0.270776 | − | 0.962642i | \(-0.412720\pi\) | ||||
0.270776 | + | 0.962642i | \(0.412720\pi\) | |||||||
\(492\) | 7.79423 | + | 4.50000i | 0.351391 | + | 0.202876i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −12.5000 | − | 21.6506i | −0.562402 | − | 0.974108i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.0000 | −0.449013 | ||||||||
\(497\) | 10.3923 | − | 12.0000i | 0.466159 | − | 0.538274i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.00000 | + | 13.8564i | −0.358129 | + | 0.620298i | −0.987648 | − | 0.156687i | \(-0.949919\pi\) |
0.629519 | + | 0.776985i | \(0.283252\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.50000 | + | 2.59808i | 0.0670151 | + | 0.116073i | ||||
\(502\) | −7.79423 | − | 4.50000i | −0.347873 | − | 0.200845i | ||||
\(503\) | − | 12.0000i | − | 0.535054i | −0.963550 | − | 0.267527i | \(-0.913794\pi\) | ||
0.963550 | − | 0.267527i | \(-0.0862064\pi\) | |||||||
\(504\) | 2.50000 | − | 0.866025i | 0.111359 | − | 0.0385758i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −13.5000 | + | 23.3827i | −0.600148 | + | 1.03949i | ||||
\(507\) | −10.3923 | + | 6.00000i | −0.461538 | + | 0.266469i | ||||
\(508\) | −11.2583 | + | 6.50000i | −0.499508 | + | 0.288391i | ||||
\(509\) | 3.00000 | − | 5.19615i | 0.132973 | − | 0.230315i | −0.791849 | − | 0.610718i | \(-0.790881\pi\) |
0.924821 | + | 0.380402i | \(0.124214\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.00000 | + | 5.19615i | −0.0442374 | + | 0.229864i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −4.33013 | − | 2.50000i | −0.191180 | − | 0.110378i | ||||
\(514\) | 6.00000 | + | 10.3923i | 0.264649 | + | 0.458385i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.00000 | + | 6.92820i | −0.176090 | + | 0.304997i | ||||
\(517\) | − | 9.00000i | − | 0.395820i | ||||||
\(518\) | −2.59808 | − | 0.500000i | −0.114153 | − | 0.0219687i | ||||
\(519\) | −9.00000 | −0.395056 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.5000 | − | 23.3827i | −0.591446 | − | 1.02441i | −0.994038 | − | 0.109035i | \(-0.965224\pi\) |
0.402592 | − | 0.915379i | \(-0.368109\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.0526 | + | 11.0000i | 0.833110 | + | 0.480996i | 0.854916 | − | 0.518766i | \(-0.173608\pi\) |
−0.0218062 | + | 0.999762i | \(0.506942\pi\) | |||||||
\(524\) | 9.00000 | 0.393167 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.0000 | 1.04645 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 2.59808 | − | 1.50000i | 0.113067 | − | 0.0652791i | ||||
\(529\) | 29.0000 | + | 50.2295i | 1.26087 | + | 2.18389i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.0000 | 0.520756 | ||||||||
\(532\) | −8.66025 | + | 10.0000i | −0.375470 | + | 0.433555i | ||||
\(533\) | 45.0000i | 1.94917i | ||||||||
\(534\) | −3.00000 | + | 5.19615i | −0.129823 | + | 0.224860i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.00000 | + | 6.92820i | 0.172774 | + | 0.299253i | ||||
\(537\) | −12.9904 | − | 7.50000i | −0.560576 | − | 0.323649i | ||||
\(538\) | − | 12.0000i | − | 0.517357i | ||||||
\(539\) | −16.5000 | + | 12.9904i | −0.710705 | + | 0.559535i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.00000 | − | 8.66025i | 0.214967 | − | 0.372333i | −0.738296 | − | 0.674477i | \(-0.764369\pi\) |
0.953262 | + | 0.302144i | \(0.0977023\pi\) | |||||||
\(542\) | −13.8564 | + | 8.00000i | −0.595184 | + | 0.343629i | ||||
\(543\) | 6.92820 | − | 4.00000i | 0.297318 | − | 0.171656i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 10.0000 | + | 8.66025i | 0.427960 | + | 0.370625i | ||||
\(547\) | − | 8.00000i | − | 0.342055i | −0.985266 | − | 0.171028i | \(-0.945291\pi\) | ||
0.985266 | − | 0.171028i | \(-0.0547087\pi\) | |||||||
\(548\) | 15.5885 | + | 9.00000i | 0.665906 | + | 0.384461i | ||||
\(549\) | 4.00000 | + | 6.92820i | 0.170716 | + | 0.295689i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | − | 9.00000i | − | 0.383065i | ||||||
\(553\) | 6.92820 | + | 20.0000i | 0.294617 | + | 0.850487i | ||||
\(554\) | 26.0000 | 1.10463 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.0000 | − | 17.3205i | −0.424094 | − | 0.734553i | ||||
\(557\) | −33.7750 | + | 19.5000i | −1.43109 | + | 0.826242i | −0.997204 | − | 0.0747252i | \(-0.976192\pi\) |
−0.433888 | + | 0.900967i | \(0.642859\pi\) | |||||||
\(558\) | −8.66025 | − | 5.00000i | −0.366618 | − | 0.211667i | ||||
\(559\) | −40.0000 | −1.69182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 18.1865 | + | 10.5000i | 0.767153 | + | 0.442916i | ||||
\(563\) | −5.19615 | + | 3.00000i | −0.218992 | + | 0.126435i | −0.605483 | − | 0.795858i | \(-0.707020\pi\) |
0.386492 | + | 0.922293i | \(0.373687\pi\) | |||||||
\(564\) | 1.50000 | + | 2.59808i | 0.0631614 | + | 0.109399i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 22.0000 | 0.924729 | ||||||||
\(567\) | 2.59808 | + | 0.500000i | 0.109109 | + | 0.0209980i | ||||
\(568\) | 6.00000i | 0.251754i | ||||||||
\(569\) | 13.5000 | − | 23.3827i | 0.565949 | − | 0.980253i | −0.431011 | − | 0.902347i | \(-0.641843\pi\) |
0.996961 | − | 0.0779066i | \(-0.0248236\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.00000 | + | 13.8564i | 0.334790 | + | 0.579873i | 0.983444 | − | 0.181210i | \(-0.0580014\pi\) |
−0.648655 | + | 0.761083i | \(0.724668\pi\) | |||||||
\(572\) | 12.9904 | + | 7.50000i | 0.543155 | + | 0.313591i | ||||
\(573\) | 18.0000i | 0.751961i | ||||||||
\(574\) | 22.5000 | − | 7.79423i | 0.939132 | − | 0.325325i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 19.0526 | − | 11.0000i | 0.793168 | − | 0.457936i | −0.0479084 | − | 0.998852i | \(-0.515256\pi\) |
0.841077 | + | 0.540916i | \(0.181922\pi\) | |||||||
\(578\) | 14.7224 | − | 8.50000i | 0.612372 | − | 0.353553i | ||||
\(579\) | −5.00000 | + | 8.66025i | −0.207793 | + | 0.359908i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 8.00000i | 0.331611i | ||||||||
\(583\) | 7.79423 | + | 4.50000i | 0.322804 | + | 0.186371i | ||||
\(584\) | −1.00000 | − | 1.73205i | −0.0413803 | − | 0.0716728i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.5000 | + | 18.1865i | −0.433751 | + | 0.751279i | ||||
\(587\) | 42.0000i | 1.73353i | 0.498721 | + | 0.866763i | \(0.333803\pi\) | ||||
−0.498721 | + | 0.866763i | \(0.666197\pi\) | |||||||
\(588\) | 2.59808 | − | 6.50000i | 0.107143 | − | 0.268055i | ||||
\(589\) | 50.0000 | 2.06021 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.50000 | − | 12.9904i | −0.308509 | − | 0.534353i | ||||
\(592\) | 0.866025 | − | 0.500000i | 0.0355934 | − | 0.0205499i | ||||
\(593\) | −20.7846 | − | 12.0000i | −0.853522 | − | 0.492781i | 0.00831589 | − | 0.999965i | \(-0.497353\pi\) |
−0.861838 | + | 0.507184i | \(0.830686\pi\) | |||||||
\(594\) | 3.00000 | 0.123091 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13.8564 | − | 8.00000i | −0.567105 | − | 0.327418i | ||||
\(598\) | 38.9711 | − | 22.5000i | 1.59365 | − | 0.920093i | ||||
\(599\) | 9.00000 | + | 15.5885i | 0.367730 | + | 0.636927i | 0.989210 | − | 0.146503i | \(-0.0468017\pi\) |
−0.621480 | + | 0.783430i | \(0.713468\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.0000 | 1.55005 | 0.775026 | − | 0.631929i | \(-0.217737\pi\) | ||||
0.775026 | + | 0.631929i | \(0.217737\pi\) | |||||||
\(602\) | 6.92820 | + | 20.0000i | 0.282372 | + | 0.815139i | ||||
\(603\) | 8.00000i | 0.325785i | ||||||||
\(604\) | −5.00000 | + | 8.66025i | −0.203447 | + | 0.352381i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.6506 | − | 12.5000i | −0.878772 | − | 0.507359i | −0.00851879 | − | 0.999964i | \(-0.502712\pi\) |
−0.870253 | + | 0.492604i | \(0.836045\pi\) | |||||||
\(608\) | − | 5.00000i | − | 0.202777i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.50000 | + | 12.9904i | −0.303418 | + | 0.525535i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.52628 | − | 5.50000i | 0.384763 | − | 0.222143i | −0.295126 | − | 0.955458i | \(-0.595362\pi\) |
0.679888 | + | 0.733316i | \(0.262028\pi\) | |||||||
\(614\) | 14.0000 | − | 24.2487i | 0.564994 | − | 0.978598i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.50000 | − | 7.79423i | 0.0604367 | − | 0.314038i | ||||
\(617\) | − | 12.0000i | − | 0.483102i | −0.970388 | − | 0.241551i | \(-0.922344\pi\) | ||
0.970388 | − | 0.241551i | \(-0.0776561\pi\) | |||||||
\(618\) | 6.92820 | + | 4.00000i | 0.278693 | + | 0.160904i | ||||
\(619\) | 14.5000 | + | 25.1147i | 0.582804 | + | 1.00945i | 0.995145 | + | 0.0984169i | \(0.0313779\pi\) |
−0.412341 | + | 0.911030i | \(0.635289\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.50000 | − | 7.79423i | 0.180579 | − | 0.312772i | ||||
\(622\) | − | 12.0000i | − | 0.481156i | ||||||
\(623\) | 5.19615 | + | 15.0000i | 0.208179 | + | 0.600962i | ||||
\(624\) | −5.00000 | −0.200160 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.00000 | − | 3.46410i | −0.0799361 | − | 0.138453i | ||||
\(627\) | −12.9904 | + | 7.50000i | −0.518786 | + | 0.299521i | ||||
\(628\) | −4.33013 | − | 2.50000i | −0.172791 | − | 0.0997609i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.0000 | −1.35352 | −0.676759 | − | 0.736204i | \(-0.736616\pi\) | ||||
−0.676759 | + | 0.736204i | \(0.736616\pi\) | |||||||
\(632\) | −6.92820 | − | 4.00000i | −0.275589 | − | 0.159111i | ||||
\(633\) | 4.33013 | − | 2.50000i | 0.172107 | − | 0.0993661i | ||||
\(634\) | 9.00000 | + | 15.5885i | 0.357436 | + | 0.619097i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.00000 | −0.118958 | ||||||||
\(637\) | 34.6410 | − | 5.00000i | 1.37253 | − | 0.198107i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.00000 | + | 5.19615i | −0.118678 | + | 0.205557i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.5000 | − | 28.5788i | −0.651711 | − | 1.12880i | −0.982708 | − | 0.185164i | \(-0.940718\pi\) |
0.330997 | − | 0.943632i | \(-0.392615\pi\) | |||||||
\(642\) | −5.19615 | − | 3.00000i | −0.205076 | − | 0.118401i | ||||
\(643\) | − | 34.0000i | − | 1.34083i | −0.741987 | − | 0.670415i | \(-0.766116\pi\) | ||
0.741987 | − | 0.670415i | \(-0.233884\pi\) | |||||||
\(644\) | −18.0000 | − | 15.5885i | −0.709299 | − | 0.614271i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.79423 | − | 4.50000i | 0.306423 | − | 0.176913i | −0.338902 | − | 0.940822i | \(-0.610055\pi\) |
0.645325 | + | 0.763908i | \(0.276722\pi\) | |||||||
\(648\) | −0.866025 | + | 0.500000i | −0.0340207 | + | 0.0196419i | ||||
\(649\) | 18.0000 | − | 31.1769i | 0.706562 | − | 1.22380i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −25.0000 | + | 8.66025i | −0.979827 | + | 0.339422i | ||||
\(652\) | 16.0000i | 0.626608i | ||||||||
\(653\) | −33.7750 | − | 19.5000i | −1.32172 | − | 0.763094i | −0.337715 | − | 0.941248i | \(-0.609654\pi\) |
−0.984003 | + | 0.178154i | \(0.942987\pi\) | |||||||
\(654\) | −7.00000 | − | 12.1244i | −0.273722 | − | 0.474100i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.50000 | + | 7.79423i | −0.175695 | + | 0.304314i | ||||
\(657\) | − | 2.00000i | − | 0.0780274i | ||||||
\(658\) | 7.79423 | + | 1.50000i | 0.303851 | + | 0.0584761i | ||||
\(659\) | −12.0000 | −0.467454 | −0.233727 | − | 0.972302i | \(-0.575092\pi\) | ||||
−0.233727 | + | 0.972302i | \(0.575092\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.0000 | + | 34.6410i | 0.777910 | + | 1.34738i | 0.933144 | + | 0.359502i | \(0.117053\pi\) |
−0.155235 | + | 0.987878i | \(0.549613\pi\) | |||||||
\(662\) | 9.52628 | − | 5.50000i | 0.370249 | − | 0.213764i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.00000 | 0.0387492 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −2.59808 | + | 1.50000i | −0.100523 | + | 0.0580367i | ||||
\(669\) | −14.0000 | − | 24.2487i | −0.541271 | − | 0.937509i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.0000 | 0.926510 | ||||||||
\(672\) | 0.866025 | + | 2.50000i | 0.0334077 | + | 0.0964396i | ||||
\(673\) | 20.0000i | 0.770943i | 0.922720 | + | 0.385472i | \(0.125961\pi\) | ||||
−0.922720 | + | 0.385472i | \(0.874039\pi\) | |||||||
\(674\) | −10.0000 | + | 17.3205i | −0.385186 | + | 0.667161i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.00000 | − | 10.3923i | −0.230769 | − | 0.399704i | ||||
\(677\) | 2.59808 | + | 1.50000i | 0.0998522 | + | 0.0576497i | 0.549095 | − | 0.835760i | \(-0.314973\pi\) |
−0.449242 | + | 0.893410i | \(0.648306\pi\) | |||||||
\(678\) | 18.0000i | 0.691286i | ||||||||
\(679\) | 16.0000 | + | 13.8564i | 0.614024 | + | 0.531760i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −25.9808 | + | 15.0000i | −0.994855 | + | 0.574380i | ||||
\(683\) | −10.3923 | + | 6.00000i | −0.397650 | + | 0.229584i | −0.685470 | − | 0.728101i | \(-0.740403\pi\) |
0.287819 | + | 0.957685i | \(0.407070\pi\) | |||||||
\(684\) | 2.50000 | − | 4.33013i | 0.0955899 | − | 0.165567i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.50000 | − | 16.4545i | −0.324532 | − | 0.628235i | ||||
\(687\) | − | 14.0000i | − | 0.534133i | ||||||
\(688\) | −6.92820 | − | 4.00000i | −0.264135 | − | 0.152499i | ||||
\(689\) | −7.50000 | − | 12.9904i | −0.285727 | − | 0.494894i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.0000 | − | 24.2487i | 0.532585 | − | 0.922464i | −0.466691 | − | 0.884420i | \(-0.654554\pi\) |
0.999276 | − | 0.0380440i | \(-0.0121127\pi\) | |||||||
\(692\) | − | 9.00000i | − | 0.342129i | ||||||
\(693\) | 5.19615 | − | 6.00000i | 0.197386 | − | 0.227921i | ||||
\(694\) | 30.0000 | 1.13878 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −24.2487 | − | 14.0000i | −0.917827 | − | 0.529908i | ||||
\(699\) | 6.00000 | 0.226941 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −42.0000 | −1.58632 | −0.793159 | − | 0.609015i | \(-0.791565\pi\) | ||||
−0.793159 | + | 0.609015i | \(0.791565\pi\) | |||||||
\(702\) | −4.33013 | − | 2.50000i | −0.163430 | − | 0.0943564i | ||||
\(703\) | −4.33013 | + | 2.50000i | −0.163314 | + | 0.0942893i | ||||
\(704\) | 1.50000 | + | 2.59808i | 0.0565334 | + | 0.0979187i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −24.0000 | −0.903252 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 12.0000i | 0.450988i | ||||||||
\(709\) | −14.0000 | + | 24.2487i | −0.525781 | + | 0.910679i | 0.473768 | + | 0.880650i | \(0.342894\pi\) |
−0.999549 | + | 0.0300298i | \(0.990440\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.00000 | − | 6.92820i | −0.150012 | − | 0.259828i | ||||
\(712\) | −5.19615 | − | 3.00000i | −0.194734 | − | 0.112430i | ||||
\(713\) | 90.0000i | 3.37053i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.50000 | − | 12.9904i | 0.280288 | − | 0.485473i | ||||
\(717\) | −25.9808 | + | 15.0000i | −0.970269 | + | 0.560185i | ||||
\(718\) | −10.3923 | + | 6.00000i | −0.387837 | + | 0.223918i | ||||
\(719\) | 9.00000 | − | 15.5885i | 0.335643 | − | 0.581351i | −0.647965 | − | 0.761670i | \(-0.724380\pi\) |
0.983608 | + | 0.180319i | \(0.0577130\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.0000 | − | 6.92820i | 0.744839 | − | 0.258020i | ||||
\(722\) | 6.00000i | 0.223297i | ||||||||
\(723\) | 0.866025 | + | 0.500000i | 0.0322078 | + | 0.0185952i | ||||
\(724\) | 4.00000 | + | 6.92820i | 0.148659 | + | 0.257485i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.00000 | + | 1.73205i | −0.0371135 | + | 0.0642824i | ||||
\(727\) | − | 23.0000i | − | 0.853023i | −0.904482 | − | 0.426511i | \(-0.859742\pi\) | ||
0.904482 | − | 0.426511i | \(-0.140258\pi\) | |||||||
\(728\) | −8.66025 | + | 10.0000i | −0.320970 | + | 0.370625i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −6.92820 | + | 4.00000i | −0.256074 | + | 0.147844i | ||||
\(733\) | 0.866025 | + | 0.500000i | 0.0319874 | + | 0.0184679i | 0.515908 | − | 0.856644i | \(-0.327454\pi\) |
−0.483921 | + | 0.875112i | \(0.660788\pi\) | |||||||
\(734\) | −19.0000 | −0.701303 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.00000 | 0.331744 | ||||||||
\(737\) | 20.7846 | + | 12.0000i | 0.765611 | + | 0.442026i | ||||
\(738\) | −7.79423 | + | 4.50000i | −0.286910 | + | 0.165647i | ||||
\(739\) | 2.50000 | + | 4.33013i | 0.0919640 | + | 0.159286i | 0.908337 | − | 0.418238i | \(-0.137352\pi\) |
−0.816373 | + | 0.577524i | \(0.804019\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 25.0000 | 0.918398 | ||||||||
\(742\) | −5.19615 | + | 6.00000i | −0.190757 | + | 0.220267i | ||||
\(743\) | − | 39.0000i | − | 1.43077i | −0.698730 | − | 0.715386i | \(-0.746251\pi\) | ||
0.698730 | − | 0.715386i | \(-0.253749\pi\) | |||||||
\(744\) | 5.00000 | − | 8.66025i | 0.183309 | − | 0.317500i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −5.00000 | − | 8.66025i | −0.183063 | − | 0.317074i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.0000 | + | 5.19615i | −0.548088 | + | 0.189863i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | + | 1.73205i | −0.0364905 | + | 0.0632034i | −0.883694 | − | 0.468065i | \(-0.844951\pi\) |
0.847203 | + | 0.531269i | \(0.178285\pi\) | |||||||
\(752\) | −2.59808 | + | 1.50000i | −0.0947421 | + | 0.0546994i | ||||
\(753\) | 7.79423 | − | 4.50000i | 0.284037 | − | 0.163989i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.500000 | + | 2.59808i | −0.0181848 | + | 0.0944911i | ||||
\(757\) | − | 2.00000i | − | 0.0726912i | −0.999339 | − | 0.0363456i | \(-0.988428\pi\) | ||
0.999339 | − | 0.0363456i | \(-0.0115717\pi\) | |||||||
\(758\) | −16.4545 | − | 9.50000i | −0.597654 | − | 0.345056i | ||||
\(759\) | −13.5000 | − | 23.3827i | −0.490019 | − | 0.848738i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.5000 | − | 28.5788i | 0.598125 | − | 1.03598i | −0.394973 | − | 0.918693i | \(-0.629246\pi\) |
0.993098 | − | 0.117289i | \(-0.0374205\pi\) | |||||||
\(762\) | − | 13.0000i | − | 0.470940i | ||||||
\(763\) | −36.3731 | − | 7.00000i | −1.31679 | − | 0.253417i | ||||
\(764\) | −18.0000 | −0.651217 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13.5000 | + | 23.3827i | 0.487775 | + | 0.844851i | ||||
\(767\) | −51.9615 | + | 30.0000i | −1.87622 | + | 1.08324i | ||||
\(768\) | −0.866025 | − | 0.500000i | −0.0312500 | − | 0.0180422i | ||||
\(769\) | −35.0000 | −1.26213 | −0.631066 | − | 0.775729i | \(-0.717382\pi\) | ||||
−0.631066 | + | 0.775729i | \(0.717382\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.0000 | −0.432169 | ||||||||
\(772\) | −8.66025 | − | 5.00000i | −0.311689 | − | 0.179954i | ||||
\(773\) | 28.5788 | − | 16.5000i | 1.02791 | − | 0.593464i | 0.111524 | − | 0.993762i | \(-0.464427\pi\) |
0.916385 | + | 0.400298i | \(0.131093\pi\) | |||||||
\(774\) | −4.00000 | − | 6.92820i | −0.143777 | − | 0.249029i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.00000 | −0.287183 | ||||||||
\(777\) | 1.73205 | − | 2.00000i | 0.0621370 | − | 0.0717496i | ||||
\(778\) | 6.00000i | 0.215110i | ||||||||
\(779\) | 22.5000 | − | 38.9711i | 0.806146 | − | 1.39629i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.00000 | + | 15.5885i | 0.322045 | + | 0.557799i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.50000 | + | 2.59808i | 0.232143 | + | 0.0927884i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.50000 | + | 7.79423i | −0.160510 | + | 0.278011i | ||||
\(787\) | −12.1244 | + | 7.00000i | −0.432187 | + | 0.249523i | −0.700278 | − | 0.713871i | \(-0.746941\pi\) |
0.268091 | + | 0.963394i | \(0.413607\pi\) | |||||||
\(788\) | 12.9904 | − | 7.50000i | 0.462763 | − | 0.267176i | ||||
\(789\) | −12.0000 | + | 20.7846i | −0.427211 | + | 0.739952i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 36.0000 | + | 31.1769i | 1.28001 | + | 1.10852i | ||||
\(792\) | 3.00000i | 0.106600i | ||||||||
\(793\) | −34.6410 | − | 20.0000i | −1.23014 | − | 0.710221i | ||||
\(794\) | −7.00000 | − | 12.1244i | −0.248421 | − | 0.430277i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.00000 | − | 13.8564i | 0.283552 | − | 0.491127i | ||||
\(797\) | − | 30.0000i | − | 1.06265i | −0.847167 | − | 0.531327i | \(-0.821693\pi\) | ||
0.847167 | − | 0.531327i | \(-0.178307\pi\) | |||||||
\(798\) | −4.33013 | − | 12.5000i | −0.153285 | − | 0.442495i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.00000 | − | 5.19615i | −0.106000 | − | 0.183597i | ||||
\(802\) | 12.9904 | − | 7.50000i | 0.458706 | − | 0.264834i | ||||
\(803\) | −5.19615 | − | 3.00000i | −0.183368 | − | 0.105868i | ||||
\(804\) | −8.00000 | −0.282138 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 50.0000 | 1.76117 | ||||||||
\(807\) | 10.3923 | + | 6.00000i | 0.365826 | + | 0.211210i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13.5000 | − | 23.3827i | −0.474635 | − | 0.822091i | 0.524943 | − | 0.851137i | \(-0.324086\pi\) |
−0.999578 | + | 0.0290457i | \(0.990753\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.00000 | −0.245803 | −0.122902 | − | 0.992419i | \(-0.539220\pi\) | ||||
−0.122902 | + | 0.992419i | \(0.539220\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 16.0000i | − | 0.561144i | ||||||
\(814\) | 1.50000 | − | 2.59808i | 0.0525750 | − | 0.0910625i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34.6410 | + | 20.0000i | 1.21194 | + | 0.699711i | ||||
\(818\) | − | 2.00000i | − | 0.0699284i | ||||||
\(819\) | −12.5000 | + | 4.33013i | −0.436785 | + | 0.151307i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.0000 | − | 25.9808i | 0.523504 | − | 0.906735i | −0.476122 | − | 0.879379i | \(-0.657958\pi\) |
0.999626 | − | 0.0273557i | \(-0.00870868\pi\) | |||||||
\(822\) | −15.5885 | + | 9.00000i | −0.543710 | + | 0.313911i | ||||
\(823\) | 27.7128 | − | 16.0000i | 0.966008 | − | 0.557725i | 0.0679910 | − | 0.997686i | \(-0.478341\pi\) |
0.898017 | + | 0.439961i | \(0.145008\pi\) | |||||||
\(824\) | −4.00000 | + | 6.92820i | −0.139347 | + | 0.241355i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 24.0000 | + | 20.7846i | 0.835067 | + | 0.723189i | ||||
\(827\) | − | 6.00000i | − | 0.208640i | −0.994544 | − | 0.104320i | \(-0.966733\pi\) | ||
0.994544 | − | 0.104320i | \(-0.0332667\pi\) | |||||||
\(828\) | 7.79423 | + | 4.50000i | 0.270868 | + | 0.156386i | ||||
\(829\) | −20.0000 | − | 34.6410i | −0.694629 | − | 1.20313i | −0.970306 | − | 0.241882i | \(-0.922235\pi\) |
0.275677 | − | 0.961250i | \(-0.411098\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.0000 | + | 22.5167i | −0.450965 | + | 0.781094i | ||||
\(832\) | − | 5.00000i | − | 0.173344i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 20.0000 | 0.692543 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −7.50000 | − | 12.9904i | −0.259393 | − | 0.449282i | ||||
\(837\) | 8.66025 | − | 5.00000i | 0.299342 | − | 0.172825i | ||||
\(838\) | −7.79423 | − | 4.50000i | −0.269247 | − | 0.155450i | ||||
\(839\) | 24.0000 | 0.828572 | 0.414286 | − | 0.910147i | \(-0.364031\pi\) | ||||
0.414286 | + | 0.910147i | \(0.364031\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | −12.1244 | − | 7.00000i | −0.417833 | − | 0.241236i | ||||
\(843\) | −18.1865 | + | 10.5000i | −0.626377 | + | 0.361639i | ||||
\(844\) | 2.50000 | + | 4.33013i | 0.0860535 | + | 0.149049i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.00000 | −0.103142 | ||||||||
\(847\) | 1.73205 | + | 5.00000i | 0.0595140 | + | 0.171802i | ||||
\(848\) | − | 3.00000i | − | 0.103020i | ||||||
\(849\) | −11.0000 | + | 19.0526i | −0.377519 | + | 0.653882i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.50000 | − | 7.79423i | −0.154258 | − | 0.267183i | ||||
\(852\) | −5.19615 | − | 3.00000i | −0.178017 | − | 0.102778i | ||||
\(853\) | − | 37.0000i | − | 1.26686i | −0.773802 | − | 0.633428i | \(-0.781647\pi\) | ||
0.773802 | − | 0.633428i | \(-0.218353\pi\) | |||||||
\(854\) | −4.00000 | + | 20.7846i | −0.136877 | + | 0.711235i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.00000 | − | 5.19615i | 0.102538 | − | 0.177601i | ||||
\(857\) | 5.19615 | − | 3.00000i | 0.177497 | − | 0.102478i | −0.408619 | − | 0.912705i | \(-0.633990\pi\) |
0.586116 | + | 0.810227i | \(0.300656\pi\) | |||||||
\(858\) | −12.9904 | + | 7.50000i | −0.443484 | + | 0.256046i | ||||
\(859\) | −2.00000 | + | 3.46410i | −0.0682391 | + | 0.118194i | −0.898126 | − | 0.439738i | \(-0.855071\pi\) |
0.829887 | + | 0.557931i | \(0.188405\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.50000 | + | 23.3827i | −0.153360 | + | 0.796880i | ||||
\(862\) | − | 24.0000i | − | 0.817443i | ||||||
\(863\) | 18.1865 | + | 10.5000i | 0.619077 | + | 0.357424i | 0.776509 | − | 0.630106i | \(-0.216988\pi\) |
−0.157433 | + | 0.987530i | \(0.550322\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −8.00000 | + | 13.8564i | −0.271851 | + | 0.470860i | ||||
\(867\) | 17.0000i | 0.577350i | ||||||||
\(868\) | −8.66025 | − | 25.0000i | −0.293948 | − | 0.848555i | ||||
\(869\) | −24.0000 | −0.814144 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.0000 | − | 34.6410i | −0.677674 | − | 1.17377i | ||||
\(872\) | 12.1244 | − | 7.00000i | 0.410582 | − | 0.237050i | ||||
\(873\) | −6.92820 | − | 4.00000i | −0.234484 | − | 0.135379i | ||||
\(874\) | −45.0000 | −1.52215 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.00000 | 0.0675737 | ||||||||
\(877\) | 4.33013 | + | 2.50000i | 0.146218 | + | 0.0844190i | 0.571324 | − | 0.820724i | \(-0.306430\pi\) |
−0.425106 | + | 0.905143i | \(0.639763\pi\) | |||||||
\(878\) | −6.92820 | + | 4.00000i | −0.233816 | + | 0.134993i | ||||
\(879\) | −10.5000 | − | 18.1865i | −0.354156 | − | 0.613417i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33.0000 | −1.11180 | −0.555899 | − | 0.831250i | \(-0.687626\pi\) | ||||
−0.555899 | + | 0.831250i | \(0.687626\pi\) | |||||||
\(882\) | 4.33013 | + | 5.50000i | 0.145803 | + | 0.185195i | ||||
\(883\) | 14.0000i | 0.471138i | 0.971858 | + | 0.235569i | \(0.0756953\pi\) | ||||
−0.971858 | + | 0.235569i | \(0.924305\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.0000 | − | 20.7846i | −0.403148 | − | 0.698273i | ||||
\(887\) | 10.3923 | + | 6.00000i | 0.348939 | + | 0.201460i | 0.664218 | − | 0.747539i | \(-0.268765\pi\) |
−0.315279 | + | 0.948999i | \(0.602098\pi\) | |||||||
\(888\) | 1.00000i | 0.0335578i | ||||||||
\(889\) | −26.0000 | − | 22.5167i | −0.872012 | − | 0.755185i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.50000 | + | 2.59808i | −0.0502519 | + | 0.0870388i | ||||
\(892\) | 24.2487 | − | 14.0000i | 0.811907 | − | 0.468755i | ||||
\(893\) | 12.9904 | − | 7.50000i | 0.434707 | − | 0.250978i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.50000 | + | 0.866025i | −0.0835191 | + | 0.0289319i | ||||
\(897\) | 45.0000i | 1.50251i | ||||||||
\(898\) | −28.5788 | − | 16.5000i | −0.953688 | − | 0.550612i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 27.0000i | 0.899002i | ||||||||
\(903\) | −20.7846 | − | 4.00000i | −0.691669 | − | 0.133112i | ||||
\(904\) | −18.0000 | −0.598671 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −5.00000 | − | 8.66025i | −0.166114 | − | 0.287718i | ||||
\(907\) | 8.66025 | − | 5.00000i | 0.287559 | − | 0.166022i | −0.349281 | − | 0.937018i | \(-0.613574\pi\) |
0.636841 | + | 0.770996i | \(0.280241\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.00000 | 0.198789 | 0.0993944 | − | 0.995048i | \(-0.468309\pi\) | ||||
0.0993944 | + | 0.995048i | \(0.468309\pi\) | |||||||
\(912\) | 4.33013 | + | 2.50000i | 0.143385 | + | 0.0827833i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 5.00000 | + | 8.66025i | 0.165385 | + | 0.286456i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.0000 | 0.462573 | ||||||||
\(917\) | 7.79423 | + | 22.5000i | 0.257388 | + | 0.743015i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.0000 | + | 24.2487i | −0.461817 | + | 0.799891i | −0.999052 | − | 0.0435419i | \(-0.986136\pi\) |
0.537234 | + | 0.843433i | \(0.319469\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.0000 | + | 24.2487i | 0.461316 | + | 0.799022i | ||||
\(922\) | −10.3923 | − | 6.00000i | −0.342252 | − | 0.197599i | ||||
\(923\) | − | 30.0000i | − | 0.987462i | ||||||
\(924\) | 6.00000 | + | 5.19615i | 0.197386 | + | 0.170941i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −0.500000 | + | 0.866025i | −0.0164310 | + | 0.0284594i | ||||
\(927\) | −6.92820 | + | 4.00000i | −0.227552 | + | 0.131377i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.5000 | − | 33.7750i | 0.639774 | − | 1.10812i | −0.345708 | − | 0.938342i | \(-0.612361\pi\) |
0.985482 | − | 0.169779i | \(-0.0543055\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32.5000 | − | 12.9904i | −1.06514 | − | 0.425743i | ||||
\(932\) | 6.00000i | 0.196537i | ||||||||
\(933\) | 10.3923 | + | 6.00000i | 0.340229 | + | 0.196431i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.50000 | − | 4.33013i | 0.0817151 | − | 0.141535i | ||||
\(937\) | − | 44.0000i | − | 1.43742i | −0.695311 | − | 0.718709i | \(-0.744734\pi\) | ||
0.695311 | − | 0.718709i | \(-0.255266\pi\) | |||||||
\(938\) | −13.8564 | + | 16.0000i | −0.452428 | + | 0.522419i | ||||
\(939\) | 4.00000 | 0.130535 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.00000 | + | 15.5885i | 0.293392 | + | 0.508169i | 0.974609 | − | 0.223912i | \(-0.0718827\pi\) |
−0.681218 | + | 0.732081i | \(0.738549\pi\) | |||||||
\(942\) | 4.33013 | − | 2.50000i | 0.141083 | − | 0.0814544i | ||||
\(943\) | 70.1481 | + | 40.5000i | 2.28434 | + | 1.31886i | ||||
\(944\) | −12.0000 | −0.390567 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −24.0000 | −0.780307 | ||||||||
\(947\) | −15.5885 | − | 9.00000i | −0.506557 | − | 0.292461i | 0.224860 | − | 0.974391i | \(-0.427807\pi\) |
−0.731417 | + | 0.681930i | \(0.761141\pi\) | |||||||
\(948\) | 6.92820 | − | 4.00000i | 0.225018 | − | 0.129914i | ||||
\(949\) | 5.00000 | + | 8.66025i | 0.162307 | + | 0.281124i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.0000 | −0.583690 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.0000i | 0.388718i | 0.980930 | + | 0.194359i | \(0.0622627\pi\) | ||||
−0.980930 | + | 0.194359i | \(0.937737\pi\) | |||||||
\(954\) | 1.50000 | − | 2.59808i | 0.0485643 | − | 0.0841158i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −15.0000 | − | 25.9808i | −0.485135 | − | 0.840278i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 18.0000i | 0.581554i | ||||||||
\(959\) | −9.00000 | + | 46.7654i | −0.290625 | + | 1.51013i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −34.5000 | + | 59.7558i | −1.11290 | + | 1.92760i | ||||
\(962\) | −4.33013 | + | 2.50000i | −0.139609 | + | 0.0806032i | ||||
\(963\) | 5.19615 | − | 3.00000i | 0.167444 | − | 0.0966736i | ||||
\(964\) | −0.500000 | + | 0.866025i | −0.0161039 | + | 0.0278928i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 22.5000 | − | 7.79423i | 0.723926 | − | 0.250775i | ||||
\(967\) | 28.0000i | 0.900419i | 0.892923 | + | 0.450210i | \(0.148651\pi\) | ||||
−0.892923 | + | 0.450210i | \(0.851349\pi\) | |||||||
\(968\) | −1.73205 | − | 1.00000i | −0.0556702 | − | 0.0321412i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.50000 | + | 12.9904i | −0.240686 | + | 0.416881i | −0.960910 | − | 0.276861i | \(-0.910706\pi\) |
0.720224 | + | 0.693742i | \(0.244039\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | 34.6410 | − | 40.0000i | 1.11054 | − | 1.28234i | ||||
\(974\) | −40.0000 | −1.28168 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.00000 | − | 6.92820i | −0.128037 | − | 0.221766i | ||||
\(977\) | −5.19615 | + | 3.00000i | −0.166240 | + | 0.0959785i | −0.580812 | − | 0.814038i | \(-0.697265\pi\) |
0.414572 | + | 0.910017i | \(0.363931\pi\) | |||||||
\(978\) | −13.8564 | − | 8.00000i | −0.443079 | − | 0.255812i | ||||
\(979\) | −18.0000 | −0.575282 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.0000 | 0.446986 | ||||||||
\(982\) | −10.3923 | − | 6.00000i | −0.331632 | − | 0.191468i | ||||
\(983\) | 7.79423 | − | 4.50000i | 0.248597 | − | 0.143528i | −0.370525 | − | 0.928823i | \(-0.620822\pi\) |
0.619122 | + | 0.785295i | \(0.287489\pi\) | |||||||
\(984\) | −4.50000 | − | 7.79423i | −0.143455 | − | 0.248471i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.19615 | + | 6.00000i | −0.165395 | + | 0.190982i | ||||
\(988\) | 25.0000i | 0.795356i | ||||||||
\(989\) | −36.0000 | + | 62.3538i | −1.14473 | + | 1.98274i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.0000 | + | 50.2295i | 0.921215 | + | 1.59559i | 0.797537 | + | 0.603269i | \(0.206136\pi\) |
0.123678 | + | 0.992322i | \(0.460531\pi\) | |||||||
\(992\) | 8.66025 | + | 5.00000i | 0.274963 | + | 0.158750i | ||||
\(993\) | 11.0000i | 0.349074i | ||||||||
\(994\) | −15.0000 | + | 5.19615i | −0.475771 | + | 0.164812i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.1244 | + | 7.00000i | −0.383982 | + | 0.221692i | −0.679549 | − | 0.733630i | \(-0.737825\pi\) |
0.295567 | + | 0.955322i | \(0.404491\pi\) | |||||||
\(998\) | 13.8564 | − | 8.00000i | 0.438617 | − | 0.253236i | ||||
\(999\) | −0.500000 | + | 0.866025i | −0.0158193 | + | 0.0273998i |
(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 | 1050.2.o.c.499.1 | 4 | ||
5.2 | odd | 4 | 210.2.i.c.121.1 | ✓ | 2 | ||
5.3 | odd | 4 | 1050.2.i.i.751.1 | 2 | |||
5.4 | even | 2 | inner | 1050.2.o.c.499.2 | 4 | ||
7.4 | even | 3 | inner | 1050.2.o.c.949.2 | 4 | ||
15.2 | even | 4 | 630.2.k.a.541.1 | 2 | |||
20.7 | even | 4 | 1680.2.bg.n.961.1 | 2 | |||
35.2 | odd | 12 | 1470.2.a.f.1.1 | 1 | |||
35.4 | even | 6 | inner | 1050.2.o.c.949.1 | 4 | ||
35.12 | even | 12 | 1470.2.a.e.1.1 | 1 | |||
35.17 | even | 12 | 1470.2.i.p.361.1 | 2 | |||
35.18 | odd | 12 | 1050.2.i.i.151.1 | 2 | |||
35.23 | odd | 12 | 7350.2.a.cd.1.1 | 1 | |||
35.27 | even | 4 | 1470.2.i.p.961.1 | 2 | |||
35.32 | odd | 12 | 210.2.i.c.151.1 | yes | 2 | ||
35.33 | even | 12 | 7350.2.a.cx.1.1 | 1 | |||
105.2 | even | 12 | 4410.2.a.bh.1.1 | 1 | |||
105.32 | even | 12 | 630.2.k.a.361.1 | 2 | |||
105.47 | odd | 12 | 4410.2.a.w.1.1 | 1 | |||
140.67 | even | 12 | 1680.2.bg.n.1201.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.i.c.121.1 | ✓ | 2 | 5.2 | odd | 4 | ||
210.2.i.c.151.1 | yes | 2 | 35.32 | odd | 12 | ||
630.2.k.a.361.1 | 2 | 105.32 | even | 12 | |||
630.2.k.a.541.1 | 2 | 15.2 | even | 4 | |||
1050.2.i.i.151.1 | 2 | 35.18 | odd | 12 | |||
1050.2.i.i.751.1 | 2 | 5.3 | odd | 4 | |||
1050.2.o.c.499.1 | 4 | 1.1 | even | 1 | trivial | ||
1050.2.o.c.499.2 | 4 | 5.4 | even | 2 | inner | ||
1050.2.o.c.949.1 | 4 | 35.4 | even | 6 | inner | ||
1050.2.o.c.949.2 | 4 | 7.4 | even | 3 | inner | ||
1470.2.a.e.1.1 | 1 | 35.12 | even | 12 | |||
1470.2.a.f.1.1 | 1 | 35.2 | odd | 12 | |||
1470.2.i.p.361.1 | 2 | 35.17 | even | 12 | |||
1470.2.i.p.961.1 | 2 | 35.27 | even | 4 | |||
1680.2.bg.n.961.1 | 2 | 20.7 | even | 4 | |||
1680.2.bg.n.1201.1 | 2 | 140.67 | even | 12 | |||
4410.2.a.w.1.1 | 1 | 105.47 | odd | 12 | |||
4410.2.a.bh.1.1 | 1 | 105.2 | even | 12 | |||
7350.2.a.cd.1.1 | 1 | 35.23 | odd | 12 | |||
7350.2.a.cx.1.1 | 1 | 35.33 | even | 12 |