Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,2,Mod(121,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.67685844245\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 121.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.121 |
Dual form | 210.2.i.c.151.1 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −2.00000 | − | 1.73205i | −0.755929 | − | 0.654654i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −0.500000 | − | 0.866025i | −0.158114 | − | 0.273861i | ||||
\(11\) | −1.50000 | − | 2.59808i | −0.452267 | − | 0.783349i | 0.546259 | − | 0.837616i | \(-0.316051\pi\) |
−0.998526 | + | 0.0542666i | \(0.982718\pi\) | |||||||
\(12\) | −0.500000 | + | 0.866025i | −0.144338 | + | 0.250000i | ||||
\(13\) | 5.00000 | 1.38675 | 0.693375 | − | 0.720577i | \(-0.256123\pi\) | ||||
0.693375 | + | 0.720577i | \(0.256123\pi\) | |||||||
\(14\) | −2.50000 | + | 0.866025i | −0.668153 | + | 0.231455i | ||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | 0.500000 | + | 0.866025i | 0.117851 | + | 0.204124i | ||||
\(19\) | −2.50000 | + | 4.33013i | −0.573539 | + | 0.993399i | 0.422659 | + | 0.906289i | \(0.361097\pi\) |
−0.996199 | + | 0.0871106i | \(0.972237\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −0.500000 | + | 2.59808i | −0.109109 | + | 0.566947i | ||||
\(22\) | −3.00000 | −0.639602 | ||||||||
\(23\) | 4.50000 | − | 7.79423i | 0.938315 | − | 1.62521i | 0.169701 | − | 0.985496i | \(-0.445720\pi\) |
0.768613 | − | 0.639713i | \(-0.220947\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 2.50000 | − | 4.33013i | 0.490290 | − | 0.849208i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.500000 | + | 2.59808i | −0.0944911 | + | 0.490990i | ||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | −0.500000 | + | 0.866025i | −0.0912871 | + | 0.158114i | ||||
\(31\) | 5.00000 | + | 8.66025i | 0.898027 | + | 1.55543i | 0.830014 | + | 0.557743i | \(0.188333\pi\) |
0.0680129 | + | 0.997684i | \(0.478334\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −1.50000 | + | 2.59808i | −0.261116 | + | 0.452267i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.50000 | + | 0.866025i | −0.422577 | + | 0.146385i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 0.500000 | − | 0.866025i | 0.0821995 | − | 0.142374i | −0.821995 | − | 0.569495i | \(-0.807139\pi\) |
0.904194 | + | 0.427121i | \(0.140472\pi\) | |||||||
\(38\) | 2.50000 | + | 4.33013i | 0.405554 | + | 0.702439i | ||||
\(39\) | −2.50000 | − | 4.33013i | −0.400320 | − | 0.693375i | ||||
\(40\) | −0.500000 | + | 0.866025i | −0.0790569 | + | 0.136931i | ||||
\(41\) | 9.00000 | 1.40556 | 0.702782 | − | 0.711405i | \(-0.251941\pi\) | ||||
0.702782 | + | 0.711405i | \(0.251941\pi\) | |||||||
\(42\) | 2.00000 | + | 1.73205i | 0.308607 | + | 0.267261i | ||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | −1.50000 | + | 2.59808i | −0.226134 | + | 0.391675i | ||||
\(45\) | 0.500000 | + | 0.866025i | 0.0745356 | + | 0.129099i | ||||
\(46\) | −4.50000 | − | 7.79423i | −0.663489 | − | 1.14920i | ||||
\(47\) | −1.50000 | + | 2.59808i | −0.218797 | + | 0.378968i | −0.954441 | − | 0.298401i | \(-0.903547\pi\) |
0.735643 | + | 0.677369i | \(0.236880\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 1.00000 | + | 6.92820i | 0.142857 | + | 0.989743i | ||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.50000 | − | 4.33013i | −0.346688 | − | 0.600481i | ||||
\(53\) | 1.50000 | + | 2.59808i | 0.206041 | + | 0.356873i | 0.950464 | − | 0.310835i | \(-0.100609\pi\) |
−0.744423 | + | 0.667708i | \(0.767275\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | −3.00000 | −0.404520 | ||||||||
\(56\) | 2.00000 | + | 1.73205i | 0.267261 | + | 0.231455i | ||||
\(57\) | 5.00000 | 0.662266 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.00000 | − | 10.3923i | −0.781133 | − | 1.35296i | −0.931282 | − | 0.364299i | \(-0.881308\pi\) |
0.150148 | − | 0.988663i | \(-0.452025\pi\) | |||||||
\(60\) | 0.500000 | + | 0.866025i | 0.0645497 | + | 0.111803i | ||||
\(61\) | −4.00000 | + | 6.92820i | −0.512148 | + | 0.887066i | 0.487753 | + | 0.872982i | \(0.337817\pi\) |
−0.999901 | + | 0.0140840i | \(0.995517\pi\) | |||||||
\(62\) | 10.0000 | 1.27000 | ||||||||
\(63\) | 2.50000 | − | 0.866025i | 0.314970 | − | 0.109109i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.50000 | − | 4.33013i | 0.310087 | − | 0.537086i | ||||
\(66\) | 1.50000 | + | 2.59808i | 0.184637 | + | 0.319801i | ||||
\(67\) | −4.00000 | − | 6.92820i | −0.488678 | − | 0.846415i | 0.511237 | − | 0.859440i | \(-0.329187\pi\) |
−0.999915 | + | 0.0130248i | \(0.995854\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.00000 | −1.08347 | ||||||||
\(70\) | −0.500000 | + | 2.59808i | −0.0597614 | + | 0.310530i | ||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | −1.00000 | − | 1.73205i | −0.117041 | − | 0.202721i | 0.801553 | − | 0.597924i | \(-0.204008\pi\) |
−0.918594 | + | 0.395203i | \(0.870674\pi\) | |||||||
\(74\) | −0.500000 | − | 0.866025i | −0.0581238 | − | 0.100673i | ||||
\(75\) | −0.500000 | + | 0.866025i | −0.0577350 | + | 0.100000i | ||||
\(76\) | 5.00000 | 0.573539 | ||||||||
\(77\) | −1.50000 | + | 7.79423i | −0.170941 | + | 0.888235i | ||||
\(78\) | −5.00000 | −0.566139 | ||||||||
\(79\) | −4.00000 | + | 6.92820i | −0.450035 | + | 0.779484i | −0.998388 | − | 0.0567635i | \(-0.981922\pi\) |
0.548352 | + | 0.836247i | \(0.315255\pi\) | |||||||
\(80\) | 0.500000 | + | 0.866025i | 0.0559017 | + | 0.0968246i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 4.50000 | − | 7.79423i | 0.496942 | − | 0.860729i | ||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 2.50000 | − | 0.866025i | 0.272772 | − | 0.0944911i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.00000 | − | 6.92820i | 0.431331 | − | 0.747087i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.50000 | + | 2.59808i | 0.159901 | + | 0.276956i | ||||
\(89\) | −3.00000 | + | 5.19615i | −0.317999 | + | 0.550791i | −0.980071 | − | 0.198650i | \(-0.936344\pi\) |
0.662071 | + | 0.749441i | \(0.269678\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | −10.0000 | − | 8.66025i | −1.04828 | − | 0.907841i | ||||
\(92\) | −9.00000 | −0.938315 | ||||||||
\(93\) | 5.00000 | − | 8.66025i | 0.518476 | − | 0.898027i | ||||
\(94\) | 1.50000 | + | 2.59808i | 0.154713 | + | 0.267971i | ||||
\(95\) | 2.50000 | + | 4.33013i | 0.256495 | + | 0.444262i | ||||
\(96\) | 0.500000 | − | 0.866025i | 0.0510310 | − | 0.0883883i | ||||
\(97\) | 8.00000 | 0.812277 | 0.406138 | − | 0.913812i | \(-0.366875\pi\) | ||||
0.406138 | + | 0.913812i | \(0.366875\pi\) | |||||||
\(98\) | 6.50000 | + | 2.59808i | 0.656599 | + | 0.262445i | ||||
\(99\) | 3.00000 | 0.301511 | ||||||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.00000 | + | 6.92820i | −0.394132 | + | 0.682656i | −0.992990 | − | 0.118199i | \(-0.962288\pi\) |
0.598858 | + | 0.800855i | \(0.295621\pi\) | |||||||
\(104\) | −5.00000 | −0.490290 | ||||||||
\(105\) | 2.00000 | + | 1.73205i | 0.195180 | + | 0.169031i | ||||
\(106\) | 3.00000 | 0.291386 | ||||||||
\(107\) | −3.00000 | + | 5.19615i | −0.290021 | + | 0.502331i | −0.973814 | − | 0.227345i | \(-0.926996\pi\) |
0.683793 | + | 0.729676i | \(0.260329\pi\) | |||||||
\(108\) | −0.500000 | − | 0.866025i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | −7.00000 | − | 12.1244i | −0.670478 | − | 1.16130i | −0.977769 | − | 0.209687i | \(-0.932756\pi\) |
0.307290 | − | 0.951616i | \(-0.400578\pi\) | |||||||
\(110\) | −1.50000 | + | 2.59808i | −0.143019 | + | 0.247717i | ||||
\(111\) | −1.00000 | −0.0949158 | ||||||||
\(112\) | 2.50000 | − | 0.866025i | 0.236228 | − | 0.0818317i | ||||
\(113\) | −18.0000 | −1.69330 | −0.846649 | − | 0.532152i | \(-0.821383\pi\) | ||||
−0.846649 | + | 0.532152i | \(0.821383\pi\) | |||||||
\(114\) | 2.50000 | − | 4.33013i | 0.234146 | − | 0.405554i | ||||
\(115\) | −4.50000 | − | 7.79423i | −0.419627 | − | 0.726816i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.50000 | + | 4.33013i | −0.231125 | + | 0.400320i | ||||
\(118\) | −12.0000 | −1.10469 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | 4.00000 | + | 6.92820i | 0.362143 | + | 0.627250i | ||||
\(123\) | −4.50000 | − | 7.79423i | −0.405751 | − | 0.702782i | ||||
\(124\) | 5.00000 | − | 8.66025i | 0.449013 | − | 0.777714i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0.500000 | − | 2.59808i | 0.0445435 | − | 0.231455i | ||||
\(127\) | −13.0000 | −1.15356 | −0.576782 | − | 0.816898i | \(-0.695692\pi\) | ||||
−0.576782 | + | 0.816898i | \(0.695692\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −4.00000 | − | 6.92820i | −0.352180 | − | 0.609994i | ||||
\(130\) | −2.50000 | − | 4.33013i | −0.219265 | − | 0.379777i | ||||
\(131\) | 4.50000 | − | 7.79423i | 0.393167 | − | 0.680985i | −0.599699 | − | 0.800226i | \(-0.704713\pi\) |
0.992865 | + | 0.119241i | \(0.0380462\pi\) | |||||||
\(132\) | 3.00000 | 0.261116 | ||||||||
\(133\) | 12.5000 | − | 4.33013i | 1.08389 | − | 0.375470i | ||||
\(134\) | −8.00000 | −0.691095 | ||||||||
\(135\) | 0.500000 | − | 0.866025i | 0.0430331 | − | 0.0745356i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.00000 | + | 15.5885i | 0.768922 | + | 1.33181i | 0.938148 | + | 0.346235i | \(0.112540\pi\) |
−0.169226 | + | 0.985577i | \(0.554127\pi\) | |||||||
\(138\) | −4.50000 | + | 7.79423i | −0.383065 | + | 0.663489i | ||||
\(139\) | 20.0000 | 1.69638 | 0.848189 | − | 0.529694i | \(-0.177693\pi\) | ||||
0.848189 | + | 0.529694i | \(0.177693\pi\) | |||||||
\(140\) | 2.00000 | + | 1.73205i | 0.169031 | + | 0.146385i | ||||
\(141\) | 3.00000 | 0.252646 | ||||||||
\(142\) | −3.00000 | + | 5.19615i | −0.251754 | + | 0.436051i | ||||
\(143\) | −7.50000 | − | 12.9904i | −0.627182 | − | 1.08631i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.00000 | −0.165521 | ||||||||
\(147\) | 5.50000 | − | 4.33013i | 0.453632 | − | 0.357143i | ||||
\(148\) | −1.00000 | −0.0821995 | ||||||||
\(149\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(150\) | 0.500000 | + | 0.866025i | 0.0408248 | + | 0.0707107i | ||||
\(151\) | 5.00000 | + | 8.66025i | 0.406894 | + | 0.704761i | 0.994540 | − | 0.104357i | \(-0.0332784\pi\) |
−0.587646 | + | 0.809118i | \(0.699945\pi\) | |||||||
\(152\) | 2.50000 | − | 4.33013i | 0.202777 | − | 0.351220i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.00000 | + | 5.19615i | 0.483494 | + | 0.418718i | ||||
\(155\) | 10.0000 | 0.803219 | ||||||||
\(156\) | −2.50000 | + | 4.33013i | −0.200160 | + | 0.346688i | ||||
\(157\) | −2.50000 | − | 4.33013i | −0.199522 | − | 0.345582i | 0.748852 | − | 0.662738i | \(-0.230606\pi\) |
−0.948373 | + | 0.317156i | \(0.897272\pi\) | |||||||
\(158\) | 4.00000 | + | 6.92820i | 0.318223 | + | 0.551178i | ||||
\(159\) | 1.50000 | − | 2.59808i | 0.118958 | − | 0.206041i | ||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −22.5000 | + | 7.79423i | −1.77325 | + | 0.614271i | ||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 8.00000 | − | 13.8564i | 0.626608 | − | 1.08532i | −0.361619 | − | 0.932326i | \(-0.617776\pi\) |
0.988227 | − | 0.152992i | \(-0.0488907\pi\) | |||||||
\(164\) | −4.50000 | − | 7.79423i | −0.351391 | − | 0.608627i | ||||
\(165\) | 1.50000 | + | 2.59808i | 0.116775 | + | 0.202260i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.00000 | −0.232147 | −0.116073 | − | 0.993241i | \(-0.537031\pi\) | ||||
−0.116073 | + | 0.993241i | \(0.537031\pi\) | |||||||
\(168\) | 0.500000 | − | 2.59808i | 0.0385758 | − | 0.200446i | ||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.50000 | − | 4.33013i | −0.191180 | − | 0.331133i | ||||
\(172\) | −4.00000 | − | 6.92820i | −0.304997 | − | 0.528271i | ||||
\(173\) | −4.50000 | + | 7.79423i | −0.342129 | + | 0.592584i | −0.984828 | − | 0.173534i | \(-0.944481\pi\) |
0.642699 | + | 0.766119i | \(0.277815\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.500000 | + | 2.59808i | −0.0377964 | + | 0.196396i | ||||
\(176\) | 3.00000 | 0.226134 | ||||||||
\(177\) | −6.00000 | + | 10.3923i | −0.450988 | + | 0.781133i | ||||
\(178\) | 3.00000 | + | 5.19615i | 0.224860 | + | 0.389468i | ||||
\(179\) | 7.50000 | + | 12.9904i | 0.560576 | + | 0.970947i | 0.997446 | + | 0.0714220i | \(0.0227537\pi\) |
−0.436870 | + | 0.899525i | \(0.643913\pi\) | |||||||
\(180\) | 0.500000 | − | 0.866025i | 0.0372678 | − | 0.0645497i | ||||
\(181\) | 8.00000 | 0.594635 | 0.297318 | − | 0.954779i | \(-0.403908\pi\) | ||||
0.297318 | + | 0.954779i | \(0.403908\pi\) | |||||||
\(182\) | −12.5000 | + | 4.33013i | −0.926562 | + | 0.320970i | ||||
\(183\) | 8.00000 | 0.591377 | ||||||||
\(184\) | −4.50000 | + | 7.79423i | −0.331744 | + | 0.574598i | ||||
\(185\) | −0.500000 | − | 0.866025i | −0.0367607 | − | 0.0636715i | ||||
\(186\) | −5.00000 | − | 8.66025i | −0.366618 | − | 0.635001i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 3.00000 | 0.218797 | ||||||||
\(189\) | −2.00000 | − | 1.73205i | −0.145479 | − | 0.125988i | ||||
\(190\) | 5.00000 | 0.362738 | ||||||||
\(191\) | −9.00000 | + | 15.5885i | −0.651217 | + | 1.12794i | 0.331611 | + | 0.943416i | \(0.392408\pi\) |
−0.982828 | + | 0.184525i | \(0.940925\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | 5.00000 | + | 8.66025i | 0.359908 | + | 0.623379i | 0.987945 | − | 0.154805i | \(-0.0494748\pi\) |
−0.628037 | + | 0.778183i | \(0.716141\pi\) | |||||||
\(194\) | 4.00000 | − | 6.92820i | 0.287183 | − | 0.497416i | ||||
\(195\) | −5.00000 | −0.358057 | ||||||||
\(196\) | 5.50000 | − | 4.33013i | 0.392857 | − | 0.309295i | ||||
\(197\) | 15.0000 | 1.06871 | 0.534353 | − | 0.845262i | \(-0.320555\pi\) | ||||
0.534353 | + | 0.845262i | \(0.320555\pi\) | |||||||
\(198\) | 1.50000 | − | 2.59808i | 0.106600 | − | 0.184637i | ||||
\(199\) | 8.00000 | + | 13.8564i | 0.567105 | + | 0.982255i | 0.996850 | + | 0.0793045i | \(0.0252700\pi\) |
−0.429745 | + | 0.902950i | \(0.641397\pi\) | |||||||
\(200\) | 0.500000 | + | 0.866025i | 0.0353553 | + | 0.0612372i | ||||
\(201\) | −4.00000 | + | 6.92820i | −0.282138 | + | 0.488678i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.50000 | − | 7.79423i | 0.314294 | − | 0.544373i | ||||
\(206\) | 4.00000 | + | 6.92820i | 0.278693 | + | 0.482711i | ||||
\(207\) | 4.50000 | + | 7.79423i | 0.312772 | + | 0.541736i | ||||
\(208\) | −2.50000 | + | 4.33013i | −0.173344 | + | 0.300240i | ||||
\(209\) | 15.0000 | 1.03757 | ||||||||
\(210\) | 2.50000 | − | 0.866025i | 0.172516 | − | 0.0597614i | ||||
\(211\) | 5.00000 | 0.344214 | 0.172107 | − | 0.985078i | \(-0.444942\pi\) | ||||
0.172107 | + | 0.985078i | \(0.444942\pi\) | |||||||
\(212\) | 1.50000 | − | 2.59808i | 0.103020 | − | 0.178437i | ||||
\(213\) | 3.00000 | + | 5.19615i | 0.205557 | + | 0.356034i | ||||
\(214\) | 3.00000 | + | 5.19615i | 0.205076 | + | 0.355202i | ||||
\(215\) | 4.00000 | − | 6.92820i | 0.272798 | − | 0.472500i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 5.00000 | − | 25.9808i | 0.339422 | − | 1.76369i | ||||
\(218\) | −14.0000 | −0.948200 | ||||||||
\(219\) | −1.00000 | + | 1.73205i | −0.0675737 | + | 0.117041i | ||||
\(220\) | 1.50000 | + | 2.59808i | 0.101130 | + | 0.175162i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −0.500000 | + | 0.866025i | −0.0335578 | + | 0.0581238i | ||||
\(223\) | −28.0000 | −1.87502 | −0.937509 | − | 0.347960i | \(-0.886874\pi\) | ||||
−0.937509 | + | 0.347960i | \(0.886874\pi\) | |||||||
\(224\) | 0.500000 | − | 2.59808i | 0.0334077 | − | 0.173591i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −9.00000 | + | 15.5885i | −0.598671 | + | 1.03693i | ||||
\(227\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(228\) | −2.50000 | − | 4.33013i | −0.165567 | − | 0.286770i | ||||
\(229\) | −7.00000 | + | 12.1244i | −0.462573 | + | 0.801200i | −0.999088 | − | 0.0426906i | \(-0.986407\pi\) |
0.536515 | + | 0.843891i | \(0.319740\pi\) | |||||||
\(230\) | −9.00000 | −0.593442 | ||||||||
\(231\) | 7.50000 | − | 2.59808i | 0.493464 | − | 0.170941i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.00000 | − | 5.19615i | 0.196537 | − | 0.340411i | −0.750867 | − | 0.660454i | \(-0.770364\pi\) |
0.947403 | + | 0.320043i | \(0.103697\pi\) | |||||||
\(234\) | 2.50000 | + | 4.33013i | 0.163430 | + | 0.283069i | ||||
\(235\) | 1.50000 | + | 2.59808i | 0.0978492 | + | 0.169480i | ||||
\(236\) | −6.00000 | + | 10.3923i | −0.390567 | + | 0.676481i | ||||
\(237\) | 8.00000 | 0.519656 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 30.0000 | 1.94054 | 0.970269 | − | 0.242028i | \(-0.0778125\pi\) | ||||
0.970269 | + | 0.242028i | \(0.0778125\pi\) | |||||||
\(240\) | 0.500000 | − | 0.866025i | 0.0322749 | − | 0.0559017i | ||||
\(241\) | 0.500000 | + | 0.866025i | 0.0322078 | + | 0.0557856i | 0.881680 | − | 0.471848i | \(-0.156413\pi\) |
−0.849472 | + | 0.527633i | \(0.823079\pi\) | |||||||
\(242\) | −1.00000 | − | 1.73205i | −0.0642824 | − | 0.111340i | ||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 8.00000 | 0.512148 | ||||||||
\(245\) | 6.50000 | + | 2.59808i | 0.415270 | + | 0.165985i | ||||
\(246\) | −9.00000 | −0.573819 | ||||||||
\(247\) | −12.5000 | + | 21.6506i | −0.795356 | + | 1.37760i | ||||
\(248\) | −5.00000 | − | 8.66025i | −0.317500 | − | 0.549927i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.500000 | + | 0.866025i | −0.0316228 | + | 0.0547723i | ||||
\(251\) | 9.00000 | 0.568075 | 0.284037 | − | 0.958813i | \(-0.408326\pi\) | ||||
0.284037 | + | 0.958813i | \(0.408326\pi\) | |||||||
\(252\) | −2.00000 | − | 1.73205i | −0.125988 | − | 0.109109i | ||||
\(253\) | −27.0000 | −1.69748 | ||||||||
\(254\) | −6.50000 | + | 11.2583i | −0.407846 | + | 0.706410i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 6.00000 | − | 10.3923i | 0.374270 | − | 0.648254i | −0.615948 | − | 0.787787i | \(-0.711227\pi\) |
0.990217 | + | 0.139533i | \(0.0445601\pi\) | |||||||
\(258\) | −8.00000 | −0.498058 | ||||||||
\(259\) | −2.50000 | + | 0.866025i | −0.155342 | + | 0.0538122i | ||||
\(260\) | −5.00000 | −0.310087 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.50000 | − | 7.79423i | −0.278011 | − | 0.481529i | ||||
\(263\) | 12.0000 | + | 20.7846i | 0.739952 | + | 1.28163i | 0.952517 | + | 0.304487i | \(0.0984850\pi\) |
−0.212565 | + | 0.977147i | \(0.568182\pi\) | |||||||
\(264\) | 1.50000 | − | 2.59808i | 0.0923186 | − | 0.159901i | ||||
\(265\) | 3.00000 | 0.184289 | ||||||||
\(266\) | 2.50000 | − | 12.9904i | 0.153285 | − | 0.796491i | ||||
\(267\) | 6.00000 | 0.367194 | ||||||||
\(268\) | −4.00000 | + | 6.92820i | −0.244339 | + | 0.423207i | ||||
\(269\) | −6.00000 | − | 10.3923i | −0.365826 | − | 0.633630i | 0.623082 | − | 0.782157i | \(-0.285880\pi\) |
−0.988908 | + | 0.148527i | \(0.952547\pi\) | |||||||
\(270\) | −0.500000 | − | 0.866025i | −0.0304290 | − | 0.0527046i | ||||
\(271\) | 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 | ||||||||
\(273\) | −2.50000 | + | 12.9904i | −0.151307 | + | 0.786214i | ||||
\(274\) | 18.0000 | 1.08742 | ||||||||
\(275\) | −1.50000 | + | 2.59808i | −0.0904534 | + | 0.156670i | ||||
\(276\) | 4.50000 | + | 7.79423i | 0.270868 | + | 0.469157i | ||||
\(277\) | −13.0000 | − | 22.5167i | −0.781094 | − | 1.35290i | −0.931305 | − | 0.364241i | \(-0.881328\pi\) |
0.150210 | − | 0.988654i | \(-0.452005\pi\) | |||||||
\(278\) | 10.0000 | − | 17.3205i | 0.599760 | − | 1.03882i | ||||
\(279\) | −10.0000 | −0.598684 | ||||||||
\(280\) | 2.50000 | − | 0.866025i | 0.149404 | − | 0.0517549i | ||||
\(281\) | −21.0000 | −1.25275 | −0.626377 | − | 0.779520i | \(-0.715463\pi\) | ||||
−0.626377 | + | 0.779520i | \(0.715463\pi\) | |||||||
\(282\) | 1.50000 | − | 2.59808i | 0.0893237 | − | 0.154713i | ||||
\(283\) | 11.0000 | + | 19.0526i | 0.653882 | + | 1.13256i | 0.982173 | + | 0.187980i | \(0.0601941\pi\) |
−0.328291 | + | 0.944577i | \(0.606473\pi\) | |||||||
\(284\) | 3.00000 | + | 5.19615i | 0.178017 | + | 0.308335i | ||||
\(285\) | 2.50000 | − | 4.33013i | 0.148087 | − | 0.256495i | ||||
\(286\) | −15.0000 | −0.886969 | ||||||||
\(287\) | −18.0000 | − | 15.5885i | −1.06251 | − | 0.920158i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 8.50000 | − | 14.7224i | 0.500000 | − | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.00000 | − | 6.92820i | −0.234484 | − | 0.406138i | ||||
\(292\) | −1.00000 | + | 1.73205i | −0.0585206 | + | 0.101361i | ||||
\(293\) | −21.0000 | −1.22683 | −0.613417 | − | 0.789760i | \(-0.710205\pi\) | ||||
−0.613417 | + | 0.789760i | \(0.710205\pi\) | |||||||
\(294\) | −1.00000 | − | 6.92820i | −0.0583212 | − | 0.404061i | ||||
\(295\) | −12.0000 | −0.698667 | ||||||||
\(296\) | −0.500000 | + | 0.866025i | −0.0290619 | + | 0.0503367i | ||||
\(297\) | −1.50000 | − | 2.59808i | −0.0870388 | − | 0.150756i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 22.5000 | − | 38.9711i | 1.30121 | − | 2.25376i | ||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | −16.0000 | − | 13.8564i | −0.922225 | − | 0.798670i | ||||
\(302\) | 10.0000 | 0.575435 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.50000 | − | 4.33013i | −0.143385 | − | 0.248350i | ||||
\(305\) | 4.00000 | + | 6.92820i | 0.229039 | + | 0.396708i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.0000 | −1.59804 | −0.799022 | − | 0.601302i | \(-0.794649\pi\) | ||||
−0.799022 | + | 0.601302i | \(0.794649\pi\) | |||||||
\(308\) | 7.50000 | − | 2.59808i | 0.427352 | − | 0.148039i | ||||
\(309\) | 8.00000 | 0.455104 | ||||||||
\(310\) | 5.00000 | − | 8.66025i | 0.283981 | − | 0.491869i | ||||
\(311\) | 6.00000 | + | 10.3923i | 0.340229 | + | 0.589294i | 0.984475 | − | 0.175525i | \(-0.0561621\pi\) |
−0.644246 | + | 0.764818i | \(0.722829\pi\) | |||||||
\(312\) | 2.50000 | + | 4.33013i | 0.141535 | + | 0.245145i | ||||
\(313\) | 2.00000 | − | 3.46410i | 0.113047 | − | 0.195803i | −0.803951 | − | 0.594696i | \(-0.797272\pi\) |
0.916997 | + | 0.398894i | \(0.130606\pi\) | |||||||
\(314\) | −5.00000 | −0.282166 | ||||||||
\(315\) | 0.500000 | − | 2.59808i | 0.0281718 | − | 0.146385i | ||||
\(316\) | 8.00000 | 0.450035 | ||||||||
\(317\) | 9.00000 | − | 15.5885i | 0.505490 | − | 0.875535i | −0.494489 | − | 0.869184i | \(-0.664645\pi\) |
0.999980 | − | 0.00635137i | \(-0.00202172\pi\) | |||||||
\(318\) | −1.50000 | − | 2.59808i | −0.0841158 | − | 0.145693i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.500000 | − | 0.866025i | 0.0279508 | − | 0.0484123i | ||||
\(321\) | 6.00000 | 0.334887 | ||||||||
\(322\) | −4.50000 | + | 23.3827i | −0.250775 | + | 1.30307i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | −2.50000 | − | 4.33013i | −0.138675 | − | 0.240192i | ||||
\(326\) | −8.00000 | − | 13.8564i | −0.443079 | − | 0.767435i | ||||
\(327\) | −7.00000 | + | 12.1244i | −0.387101 | + | 0.670478i | ||||
\(328\) | −9.00000 | −0.496942 | ||||||||
\(329\) | 7.50000 | − | 2.59808i | 0.413488 | − | 0.143237i | ||||
\(330\) | 3.00000 | 0.165145 | ||||||||
\(331\) | −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 | ||||||||
\(333\) | 0.500000 | + | 0.866025i | 0.0273998 | + | 0.0474579i | ||||
\(334\) | −1.50000 | + | 2.59808i | −0.0820763 | + | 0.142160i | ||||
\(335\) | −8.00000 | −0.437087 | ||||||||
\(336\) | −2.00000 | − | 1.73205i | −0.109109 | − | 0.0944911i | ||||
\(337\) | 20.0000 | 1.08947 | 0.544735 | − | 0.838608i | \(-0.316630\pi\) | ||||
0.544735 | + | 0.838608i | \(0.316630\pi\) | |||||||
\(338\) | 6.00000 | − | 10.3923i | 0.326357 | − | 0.565267i | ||||
\(339\) | 9.00000 | + | 15.5885i | 0.488813 | + | 0.846649i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.0000 | − | 25.9808i | 0.812296 | − | 1.40694i | ||||
\(342\) | −5.00000 | −0.270369 | ||||||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | −8.00000 | −0.431331 | ||||||||
\(345\) | −4.50000 | + | 7.79423i | −0.242272 | + | 0.419627i | ||||
\(346\) | 4.50000 | + | 7.79423i | 0.241921 | + | 0.419020i | ||||
\(347\) | −15.0000 | − | 25.9808i | −0.805242 | − | 1.39472i | −0.916127 | − | 0.400887i | \(-0.868702\pi\) |
0.110885 | − | 0.993833i | \(-0.464631\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.0000 | −1.49881 | −0.749403 | − | 0.662114i | \(-0.769659\pi\) | ||||
−0.749403 | + | 0.662114i | \(0.769659\pi\) | |||||||
\(350\) | 2.00000 | + | 1.73205i | 0.106904 | + | 0.0925820i | ||||
\(351\) | 5.00000 | 0.266880 | ||||||||
\(352\) | 1.50000 | − | 2.59808i | 0.0799503 | − | 0.138478i | ||||
\(353\) | −12.0000 | − | 20.7846i | −0.638696 | − | 1.10625i | −0.985719 | − | 0.168397i | \(-0.946141\pi\) |
0.347024 | − | 0.937856i | \(-0.387192\pi\) | |||||||
\(354\) | 6.00000 | + | 10.3923i | 0.318896 | + | 0.552345i | ||||
\(355\) | −3.00000 | + | 5.19615i | −0.159223 | + | 0.275783i | ||||
\(356\) | 6.00000 | 0.317999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 15.0000 | 0.792775 | ||||||||
\(359\) | −6.00000 | + | 10.3923i | −0.316668 | + | 0.548485i | −0.979791 | − | 0.200026i | \(-0.935897\pi\) |
0.663123 | + | 0.748511i | \(0.269231\pi\) | |||||||
\(360\) | −0.500000 | − | 0.866025i | −0.0263523 | − | 0.0456435i | ||||
\(361\) | −3.00000 | − | 5.19615i | −0.157895 | − | 0.273482i | ||||
\(362\) | 4.00000 | − | 6.92820i | 0.210235 | − | 0.364138i | ||||
\(363\) | −2.00000 | −0.104973 | ||||||||
\(364\) | −2.50000 | + | 12.9904i | −0.131036 | + | 0.680881i | ||||
\(365\) | −2.00000 | −0.104685 | ||||||||
\(366\) | 4.00000 | − | 6.92820i | 0.209083 | − | 0.362143i | ||||
\(367\) | 9.50000 | + | 16.4545i | 0.495896 | + | 0.858917i | 0.999989 | − | 0.00473247i | \(-0.00150640\pi\) |
−0.504093 | + | 0.863649i | \(0.668173\pi\) | |||||||
\(368\) | 4.50000 | + | 7.79423i | 0.234579 | + | 0.406302i | ||||
\(369\) | −4.50000 | + | 7.79423i | −0.234261 | + | 0.405751i | ||||
\(370\) | −1.00000 | −0.0519875 | ||||||||
\(371\) | 1.50000 | − | 7.79423i | 0.0778761 | − | 0.404656i | ||||
\(372\) | −10.0000 | −0.518476 | ||||||||
\(373\) | 5.00000 | − | 8.66025i | 0.258890 | − | 0.448411i | −0.707055 | − | 0.707159i | \(-0.749977\pi\) |
0.965945 | + | 0.258748i | \(0.0833099\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.500000 | + | 0.866025i | 0.0258199 | + | 0.0447214i | ||||
\(376\) | 1.50000 | − | 2.59808i | 0.0773566 | − | 0.133986i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2.50000 | + | 0.866025i | −0.128586 | + | 0.0445435i | ||||
\(379\) | −19.0000 | −0.975964 | −0.487982 | − | 0.872854i | \(-0.662267\pi\) | ||||
−0.487982 | + | 0.872854i | \(0.662267\pi\) | |||||||
\(380\) | 2.50000 | − | 4.33013i | 0.128247 | − | 0.222131i | ||||
\(381\) | 6.50000 | + | 11.2583i | 0.333005 | + | 0.576782i | ||||
\(382\) | 9.00000 | + | 15.5885i | 0.460480 | + | 0.797575i | ||||
\(383\) | −13.5000 | + | 23.3827i | −0.689818 | + | 1.19480i | 0.282079 | + | 0.959391i | \(0.408976\pi\) |
−0.971897 | + | 0.235408i | \(0.924357\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 6.00000 | + | 5.19615i | 0.305788 | + | 0.264820i | ||||
\(386\) | 10.0000 | 0.508987 | ||||||||
\(387\) | −4.00000 | + | 6.92820i | −0.203331 | + | 0.352180i | ||||
\(388\) | −4.00000 | − | 6.92820i | −0.203069 | − | 0.351726i | ||||
\(389\) | 3.00000 | + | 5.19615i | 0.152106 | + | 0.263455i | 0.932002 | − | 0.362454i | \(-0.118061\pi\) |
−0.779895 | + | 0.625910i | \(0.784728\pi\) | |||||||
\(390\) | −2.50000 | + | 4.33013i | −0.126592 | + | 0.219265i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −1.00000 | − | 6.92820i | −0.0505076 | − | 0.349927i | ||||
\(393\) | −9.00000 | −0.453990 | ||||||||
\(394\) | 7.50000 | − | 12.9904i | 0.377845 | − | 0.654446i | ||||
\(395\) | 4.00000 | + | 6.92820i | 0.201262 | + | 0.348596i | ||||
\(396\) | −1.50000 | − | 2.59808i | −0.0753778 | − | 0.130558i | ||||
\(397\) | −7.00000 | + | 12.1244i | −0.351320 | + | 0.608504i | −0.986481 | − | 0.163876i | \(-0.947600\pi\) |
0.635161 | + | 0.772380i | \(0.280934\pi\) | |||||||
\(398\) | 16.0000 | 0.802008 | ||||||||
\(399\) | −10.0000 | − | 8.66025i | −0.500626 | − | 0.433555i | ||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −7.50000 | + | 12.9904i | −0.374532 | + | 0.648709i | −0.990257 | − | 0.139253i | \(-0.955530\pi\) |
0.615725 | + | 0.787961i | \(0.288863\pi\) | |||||||
\(402\) | 4.00000 | + | 6.92820i | 0.199502 | + | 0.345547i | ||||
\(403\) | 25.0000 | + | 43.3013i | 1.24534 | + | 2.15699i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.00000 | −0.148704 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.00000 | − | 1.73205i | −0.0494468 | − | 0.0856444i | 0.840243 | − | 0.542211i | \(-0.182412\pi\) |
−0.889689 | + | 0.456566i | \(0.849079\pi\) | |||||||
\(410\) | −4.50000 | − | 7.79423i | −0.222239 | − | 0.384930i | ||||
\(411\) | 9.00000 | − | 15.5885i | 0.443937 | − | 0.768922i | ||||
\(412\) | 8.00000 | 0.394132 | ||||||||
\(413\) | −6.00000 | + | 31.1769i | −0.295241 | + | 1.53412i | ||||
\(414\) | 9.00000 | 0.442326 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.50000 | + | 4.33013i | 0.122573 | + | 0.212302i | ||||
\(417\) | −10.0000 | − | 17.3205i | −0.489702 | − | 0.848189i | ||||
\(418\) | 7.50000 | − | 12.9904i | 0.366837 | − | 0.635380i | ||||
\(419\) | −9.00000 | −0.439679 | −0.219839 | − | 0.975536i | \(-0.570553\pi\) | ||||
−0.219839 | + | 0.975536i | \(0.570553\pi\) | |||||||
\(420\) | 0.500000 | − | 2.59808i | 0.0243975 | − | 0.126773i | ||||
\(421\) | 14.0000 | 0.682318 | 0.341159 | − | 0.940006i | \(-0.389181\pi\) | ||||
0.341159 | + | 0.940006i | \(0.389181\pi\) | |||||||
\(422\) | 2.50000 | − | 4.33013i | 0.121698 | − | 0.210787i | ||||
\(423\) | −1.50000 | − | 2.59808i | −0.0729325 | − | 0.126323i | ||||
\(424\) | −1.50000 | − | 2.59808i | −0.0728464 | − | 0.126174i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.00000 | 0.290701 | ||||||||
\(427\) | 20.0000 | − | 6.92820i | 0.967868 | − | 0.335279i | ||||
\(428\) | 6.00000 | 0.290021 | ||||||||
\(429\) | −7.50000 | + | 12.9904i | −0.362103 | + | 0.627182i | ||||
\(430\) | −4.00000 | − | 6.92820i | −0.192897 | − | 0.334108i | ||||
\(431\) | 12.0000 | + | 20.7846i | 0.578020 | + | 1.00116i | 0.995706 | + | 0.0925683i | \(0.0295076\pi\) |
−0.417687 | + | 0.908591i | \(0.637159\pi\) | |||||||
\(432\) | −0.500000 | + | 0.866025i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | −16.0000 | −0.768911 | −0.384455 | − | 0.923144i | \(-0.625611\pi\) | ||||
−0.384455 | + | 0.923144i | \(0.625611\pi\) | |||||||
\(434\) | −20.0000 | − | 17.3205i | −0.960031 | − | 0.831411i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.00000 | + | 12.1244i | −0.335239 | + | 0.580651i | ||||
\(437\) | 22.5000 | + | 38.9711i | 1.07632 | + | 1.86424i | ||||
\(438\) | 1.00000 | + | 1.73205i | 0.0477818 | + | 0.0827606i | ||||
\(439\) | −4.00000 | + | 6.92820i | −0.190910 | + | 0.330665i | −0.945552 | − | 0.325471i | \(-0.894477\pi\) |
0.754642 | + | 0.656136i | \(0.227810\pi\) | |||||||
\(440\) | 3.00000 | 0.143019 | ||||||||
\(441\) | −6.50000 | − | 2.59808i | −0.309524 | − | 0.123718i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.0000 | − | 20.7846i | 0.570137 | − | 0.987507i | −0.426414 | − | 0.904528i | \(-0.640223\pi\) |
0.996551 | − | 0.0829786i | \(-0.0264433\pi\) | |||||||
\(444\) | 0.500000 | + | 0.866025i | 0.0237289 | + | 0.0410997i | ||||
\(445\) | 3.00000 | + | 5.19615i | 0.142214 | + | 0.246321i | ||||
\(446\) | −14.0000 | + | 24.2487i | −0.662919 | + | 1.14821i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.00000 | − | 1.73205i | −0.0944911 | − | 0.0818317i | ||||
\(449\) | −33.0000 | −1.55737 | −0.778683 | − | 0.627417i | \(-0.784112\pi\) | ||||
−0.778683 | + | 0.627417i | \(0.784112\pi\) | |||||||
\(450\) | 0.500000 | − | 0.866025i | 0.0235702 | − | 0.0408248i | ||||
\(451\) | −13.5000 | − | 23.3827i | −0.635690 | − | 1.10105i | ||||
\(452\) | 9.00000 | + | 15.5885i | 0.423324 | + | 0.733219i | ||||
\(453\) | 5.00000 | − | 8.66025i | 0.234920 | − | 0.406894i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.5000 | + | 4.33013i | −0.586009 | + | 0.202999i | ||||
\(456\) | −5.00000 | −0.234146 | ||||||||
\(457\) | 5.00000 | − | 8.66025i | 0.233890 | − | 0.405110i | −0.725059 | − | 0.688686i | \(-0.758188\pi\) |
0.958950 | + | 0.283577i | \(0.0915211\pi\) | |||||||
\(458\) | 7.00000 | + | 12.1244i | 0.327089 | + | 0.566534i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.50000 | + | 7.79423i | −0.209814 | + | 0.363408i | ||||
\(461\) | 12.0000 | 0.558896 | 0.279448 | − | 0.960161i | \(-0.409849\pi\) | ||||
0.279448 | + | 0.960161i | \(0.409849\pi\) | |||||||
\(462\) | 1.50000 | − | 7.79423i | 0.0697863 | − | 0.362620i | ||||
\(463\) | −1.00000 | −0.0464739 | −0.0232370 | − | 0.999730i | \(-0.507397\pi\) | ||||
−0.0232370 | + | 0.999730i | \(0.507397\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.00000 | − | 8.66025i | −0.231869 | − | 0.401610i | ||||
\(466\) | −3.00000 | − | 5.19615i | −0.138972 | − | 0.240707i | ||||
\(467\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(468\) | 5.00000 | 0.231125 | ||||||||
\(469\) | −4.00000 | + | 20.7846i | −0.184703 | + | 0.959744i | ||||
\(470\) | 3.00000 | 0.138380 | ||||||||
\(471\) | −2.50000 | + | 4.33013i | −0.115194 | + | 0.199522i | ||||
\(472\) | 6.00000 | + | 10.3923i | 0.276172 | + | 0.478345i | ||||
\(473\) | −12.0000 | − | 20.7846i | −0.551761 | − | 0.955677i | ||||
\(474\) | 4.00000 | − | 6.92820i | 0.183726 | − | 0.318223i | ||||
\(475\) | 5.00000 | 0.229416 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.00000 | −0.137361 | ||||||||
\(478\) | 15.0000 | − | 25.9808i | 0.686084 | − | 1.18833i | ||||
\(479\) | 9.00000 | + | 15.5885i | 0.411220 | + | 0.712255i | 0.995023 | − | 0.0996406i | \(-0.0317693\pi\) |
−0.583803 | + | 0.811895i | \(0.698436\pi\) | |||||||
\(480\) | −0.500000 | − | 0.866025i | −0.0228218 | − | 0.0395285i | ||||
\(481\) | 2.50000 | − | 4.33013i | 0.113990 | − | 0.197437i | ||||
\(482\) | 1.00000 | 0.0455488 | ||||||||
\(483\) | 18.0000 | + | 15.5885i | 0.819028 | + | 0.709299i | ||||
\(484\) | −2.00000 | −0.0909091 | ||||||||
\(485\) | 4.00000 | − | 6.92820i | 0.181631 | − | 0.314594i | ||||
\(486\) | 0.500000 | + | 0.866025i | 0.0226805 | + | 0.0392837i | ||||
\(487\) | 20.0000 | + | 34.6410i | 0.906287 | + | 1.56973i | 0.819181 | + | 0.573535i | \(0.194428\pi\) |
0.0871056 | + | 0.996199i | \(0.472238\pi\) | |||||||
\(488\) | 4.00000 | − | 6.92820i | 0.181071 | − | 0.313625i | ||||
\(489\) | −16.0000 | −0.723545 | ||||||||
\(490\) | 5.50000 | − | 4.33013i | 0.248465 | − | 0.195615i | ||||
\(491\) | 12.0000 | 0.541552 | 0.270776 | − | 0.962642i | \(-0.412720\pi\) | ||||
0.270776 | + | 0.962642i | \(0.412720\pi\) | |||||||
\(492\) | −4.50000 | + | 7.79423i | −0.202876 | + | 0.351391i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 12.5000 | + | 21.6506i | 0.562402 | + | 0.974108i | ||||
\(495\) | 1.50000 | − | 2.59808i | 0.0674200 | − | 0.116775i | ||||
\(496\) | −10.0000 | −0.449013 | ||||||||
\(497\) | 12.0000 | + | 10.3923i | 0.538274 | + | 0.466159i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.00000 | − | 13.8564i | 0.358129 | − | 0.620298i | −0.629519 | − | 0.776985i | \(-0.716748\pi\) |
0.987648 | + | 0.156687i | \(0.0500814\pi\) | |||||||
\(500\) | 0.500000 | + | 0.866025i | 0.0223607 | + | 0.0387298i | ||||
\(501\) | 1.50000 | + | 2.59808i | 0.0670151 | + | 0.116073i | ||||
\(502\) | 4.50000 | − | 7.79423i | 0.200845 | − | 0.347873i | ||||
\(503\) | −12.0000 | −0.535054 | −0.267527 | − | 0.963550i | \(-0.586206\pi\) | ||||
−0.267527 | + | 0.963550i | \(0.586206\pi\) | |||||||
\(504\) | −2.50000 | + | 0.866025i | −0.111359 | + | 0.0385758i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −13.5000 | + | 23.3827i | −0.600148 | + | 1.03949i | ||||
\(507\) | −6.00000 | − | 10.3923i | −0.266469 | − | 0.461538i | ||||
\(508\) | 6.50000 | + | 11.2583i | 0.288391 | + | 0.499508i | ||||
\(509\) | −3.00000 | + | 5.19615i | −0.132973 | + | 0.230315i | −0.924821 | − | 0.380402i | \(-0.875786\pi\) |
0.791849 | + | 0.610718i | \(0.209119\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.00000 | + | 5.19615i | −0.0442374 | + | 0.229864i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −2.50000 | + | 4.33013i | −0.110378 | + | 0.191180i | ||||
\(514\) | −6.00000 | − | 10.3923i | −0.264649 | − | 0.458385i | ||||
\(515\) | 4.00000 | + | 6.92820i | 0.176261 | + | 0.305293i | ||||
\(516\) | −4.00000 | + | 6.92820i | −0.176090 | + | 0.304997i | ||||
\(517\) | 9.00000 | 0.395820 | ||||||||
\(518\) | −0.500000 | + | 2.59808i | −0.0219687 | + | 0.114153i | ||||
\(519\) | 9.00000 | 0.395056 | ||||||||
\(520\) | −2.50000 | + | 4.33013i | −0.109632 | + | 0.189889i | ||||
\(521\) | −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 | ||||||||
\(523\) | 11.0000 | − | 19.0526i | 0.480996 | − | 0.833110i | −0.518766 | − | 0.854916i | \(-0.673608\pi\) |
0.999762 | + | 0.0218062i | \(0.00694167\pi\) | |||||||
\(524\) | −9.00000 | −0.393167 | ||||||||
\(525\) | 2.50000 | − | 0.866025i | 0.109109 | − | 0.0377964i | ||||
\(526\) | 24.0000 | 1.04645 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −1.50000 | − | 2.59808i | −0.0652791 | − | 0.113067i | ||||
\(529\) | −29.0000 | − | 50.2295i | −1.26087 | − | 2.18389i | ||||
\(530\) | 1.50000 | − | 2.59808i | 0.0651558 | − | 0.112853i | ||||
\(531\) | 12.0000 | 0.520756 | ||||||||
\(532\) | −10.0000 | − | 8.66025i | −0.433555 | − | 0.375470i | ||||
\(533\) | 45.0000 | 1.94917 | ||||||||
\(534\) | 3.00000 | − | 5.19615i | 0.129823 | − | 0.224860i | ||||
\(535\) | 3.00000 | + | 5.19615i | 0.129701 | + | 0.224649i | ||||
\(536\) | 4.00000 | + | 6.92820i | 0.172774 | + | 0.299253i | ||||
\(537\) | 7.50000 | − | 12.9904i | 0.323649 | − | 0.560576i | ||||
\(538\) | −12.0000 | −0.517357 | ||||||||
\(539\) | 16.5000 | − | 12.9904i | 0.710705 | − | 0.559535i | ||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | 5.00000 | − | 8.66025i | 0.214967 | − | 0.372333i | −0.738296 | − | 0.674477i | \(-0.764369\pi\) |
0.953262 | + | 0.302144i | \(0.0977023\pi\) | |||||||
\(542\) | −8.00000 | − | 13.8564i | −0.343629 | − | 0.595184i | ||||
\(543\) | −4.00000 | − | 6.92820i | −0.171656 | − | 0.297318i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.0000 | −0.599694 | ||||||||
\(546\) | 10.0000 | + | 8.66025i | 0.427960 | + | 0.370625i | ||||
\(547\) | 8.00000 | 0.342055 | 0.171028 | − | 0.985266i | \(-0.445291\pi\) | ||||
0.171028 | + | 0.985266i | \(0.445291\pi\) | |||||||
\(548\) | 9.00000 | − | 15.5885i | 0.384461 | − | 0.665906i | ||||
\(549\) | −4.00000 | − | 6.92820i | −0.170716 | − | 0.295689i | ||||
\(550\) | 1.50000 | + | 2.59808i | 0.0639602 | + | 0.110782i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 9.00000 | 0.383065 | ||||||||
\(553\) | 20.0000 | − | 6.92820i | 0.850487 | − | 0.294617i | ||||
\(554\) | −26.0000 | −1.10463 | ||||||||
\(555\) | −0.500000 | + | 0.866025i | −0.0212238 | + | 0.0367607i | ||||
\(556\) | −10.0000 | − | 17.3205i | −0.424094 | − | 0.734553i | ||||
\(557\) | −19.5000 | − | 33.7750i | −0.826242 | − | 1.43109i | −0.900967 | − | 0.433888i | \(-0.857141\pi\) |
0.0747252 | − | 0.997204i | \(-0.476192\pi\) | |||||||
\(558\) | −5.00000 | + | 8.66025i | −0.211667 | + | 0.366618i | ||||
\(559\) | 40.0000 | 1.69182 | ||||||||
\(560\) | 0.500000 | − | 2.59808i | 0.0211289 | − | 0.109789i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10.5000 | + | 18.1865i | −0.442916 | + | 0.767153i | ||||
\(563\) | 3.00000 | + | 5.19615i | 0.126435 | + | 0.218992i | 0.922293 | − | 0.386492i | \(-0.126313\pi\) |
−0.795858 | + | 0.605483i | \(0.792980\pi\) | |||||||
\(564\) | −1.50000 | − | 2.59808i | −0.0631614 | − | 0.109399i | ||||
\(565\) | −9.00000 | + | 15.5885i | −0.378633 | + | 0.655811i | ||||
\(566\) | 22.0000 | 0.924729 | ||||||||
\(567\) | −0.500000 | + | 2.59808i | −0.0209980 | + | 0.109109i | ||||
\(568\) | 6.00000 | 0.251754 | ||||||||
\(569\) | −13.5000 | + | 23.3827i | −0.565949 | + | 0.980253i | 0.431011 | + | 0.902347i | \(0.358157\pi\) |
−0.996961 | + | 0.0779066i | \(0.975176\pi\) | |||||||
\(570\) | −2.50000 | − | 4.33013i | −0.104713 | − | 0.181369i | ||||
\(571\) | 8.00000 | + | 13.8564i | 0.334790 | + | 0.579873i | 0.983444 | − | 0.181210i | \(-0.0580014\pi\) |
−0.648655 | + | 0.761083i | \(0.724668\pi\) | |||||||
\(572\) | −7.50000 | + | 12.9904i | −0.313591 | + | 0.543155i | ||||
\(573\) | 18.0000 | 0.751961 | ||||||||
\(574\) | −22.5000 | + | 7.79423i | −0.939132 | + | 0.325325i | ||||
\(575\) | −9.00000 | −0.375326 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 11.0000 | + | 19.0526i | 0.457936 | + | 0.793168i | 0.998852 | − | 0.0479084i | \(-0.0152556\pi\) |
−0.540916 | + | 0.841077i | \(0.681922\pi\) | |||||||
\(578\) | −8.50000 | − | 14.7224i | −0.353553 | − | 0.612372i | ||||
\(579\) | 5.00000 | − | 8.66025i | 0.207793 | − | 0.359908i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −8.00000 | −0.331611 | ||||||||
\(583\) | 4.50000 | − | 7.79423i | 0.186371 | − | 0.322804i | ||||
\(584\) | 1.00000 | + | 1.73205i | 0.0413803 | + | 0.0716728i | ||||
\(585\) | 2.50000 | + | 4.33013i | 0.103362 | + | 0.179029i | ||||
\(586\) | −10.5000 | + | 18.1865i | −0.433751 | + | 0.751279i | ||||
\(587\) | −42.0000 | −1.73353 | −0.866763 | − | 0.498721i | \(-0.833803\pi\) | ||||
−0.866763 | + | 0.498721i | \(0.833803\pi\) | |||||||
\(588\) | −6.50000 | − | 2.59808i | −0.268055 | − | 0.107143i | ||||
\(589\) | −50.0000 | −2.06021 | ||||||||
\(590\) | −6.00000 | + | 10.3923i | −0.247016 | + | 0.427844i | ||||
\(591\) | −7.50000 | − | 12.9904i | −0.308509 | − | 0.534353i | ||||
\(592\) | 0.500000 | + | 0.866025i | 0.0205499 | + | 0.0355934i | ||||
\(593\) | −12.0000 | + | 20.7846i | −0.492781 | + | 0.853522i | −0.999965 | − | 0.00831589i | \(-0.997353\pi\) |
0.507184 | + | 0.861838i | \(0.330686\pi\) | |||||||
\(594\) | −3.00000 | −0.123091 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.00000 | − | 13.8564i | 0.327418 | − | 0.567105i | ||||
\(598\) | −22.5000 | − | 38.9711i | −0.920093 | − | 1.59365i | ||||
\(599\) | −9.00000 | − | 15.5885i | −0.367730 | − | 0.636927i | 0.621480 | − | 0.783430i | \(-0.286532\pi\) |
−0.989210 | + | 0.146503i | \(0.953198\pi\) | |||||||
\(600\) | 0.500000 | − | 0.866025i | 0.0204124 | − | 0.0353553i | ||||
\(601\) | 38.0000 | 1.55005 | 0.775026 | − | 0.631929i | \(-0.217737\pi\) | ||||
0.775026 | + | 0.631929i | \(0.217737\pi\) | |||||||
\(602\) | −20.0000 | + | 6.92820i | −0.815139 | + | 0.282372i | ||||
\(603\) | 8.00000 | 0.325785 | ||||||||
\(604\) | 5.00000 | − | 8.66025i | 0.203447 | − | 0.352381i | ||||
\(605\) | −1.00000 | − | 1.73205i | −0.0406558 | − | 0.0704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.5000 | − | 21.6506i | 0.507359 | − | 0.878772i | −0.492604 | − | 0.870253i | \(-0.663955\pi\) |
0.999964 | − | 0.00851879i | \(-0.00271165\pi\) | |||||||
\(608\) | −5.00000 | −0.202777 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.00000 | 0.323911 | ||||||||
\(611\) | −7.50000 | + | 12.9904i | −0.303418 | + | 0.525535i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.50000 | − | 9.52628i | −0.222143 | − | 0.384763i | 0.733316 | − | 0.679888i | \(-0.237972\pi\) |
−0.955458 | + | 0.295126i | \(0.904638\pi\) | |||||||
\(614\) | −14.0000 | + | 24.2487i | −0.564994 | + | 0.978598i | ||||
\(615\) | −9.00000 | −0.362915 | ||||||||
\(616\) | 1.50000 | − | 7.79423i | 0.0604367 | − | 0.314038i | ||||
\(617\) | 12.0000 | 0.483102 | 0.241551 | − | 0.970388i | \(-0.422344\pi\) | ||||
0.241551 | + | 0.970388i | \(0.422344\pi\) | |||||||
\(618\) | 4.00000 | − | 6.92820i | 0.160904 | − | 0.278693i | ||||
\(619\) | −14.5000 | − | 25.1147i | −0.582804 | − | 1.00945i | −0.995145 | − | 0.0984169i | \(-0.968622\pi\) |
0.412341 | − | 0.911030i | \(-0.364711\pi\) | |||||||
\(620\) | −5.00000 | − | 8.66025i | −0.200805 | − | 0.347804i | ||||
\(621\) | 4.50000 | − | 7.79423i | 0.180579 | − | 0.312772i | ||||
\(622\) | 12.0000 | 0.481156 | ||||||||
\(623\) | 15.0000 | − | 5.19615i | 0.600962 | − | 0.208179i | ||||
\(624\) | 5.00000 | 0.200160 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −2.00000 | − | 3.46410i | −0.0799361 | − | 0.138453i | ||||
\(627\) | −7.50000 | − | 12.9904i | −0.299521 | − | 0.518786i | ||||
\(628\) | −2.50000 | + | 4.33013i | −0.0997609 | + | 0.172791i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −2.00000 | − | 1.73205i | −0.0796819 | − | 0.0690066i | ||||
\(631\) | −34.0000 | −1.35352 | −0.676759 | − | 0.736204i | \(-0.736616\pi\) | ||||
−0.676759 | + | 0.736204i | \(0.736616\pi\) | |||||||
\(632\) | 4.00000 | − | 6.92820i | 0.159111 | − | 0.275589i | ||||
\(633\) | −2.50000 | − | 4.33013i | −0.0993661 | − | 0.172107i | ||||
\(634\) | −9.00000 | − | 15.5885i | −0.357436 | − | 0.619097i | ||||
\(635\) | −6.50000 | + | 11.2583i | −0.257945 | + | 0.446773i | ||||
\(636\) | −3.00000 | −0.118958 | ||||||||
\(637\) | 5.00000 | + | 34.6410i | 0.198107 | + | 1.37253i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.00000 | − | 5.19615i | 0.118678 | − | 0.205557i | ||||
\(640\) | −0.500000 | − | 0.866025i | −0.0197642 | − | 0.0342327i | ||||
\(641\) | −16.5000 | − | 28.5788i | −0.651711 | − | 1.12880i | −0.982708 | − | 0.185164i | \(-0.940718\pi\) |
0.330997 | − | 0.943632i | \(-0.392615\pi\) | |||||||
\(642\) | 3.00000 | − | 5.19615i | 0.118401 | − | 0.205076i | ||||
\(643\) | −34.0000 | −1.34083 | −0.670415 | − | 0.741987i | \(-0.733884\pi\) | ||||
−0.670415 | + | 0.741987i | \(0.733884\pi\) | |||||||
\(644\) | 18.0000 | + | 15.5885i | 0.709299 | + | 0.614271i | ||||
\(645\) | −8.00000 | −0.315000 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.50000 | + | 7.79423i | 0.176913 | + | 0.306423i | 0.940822 | − | 0.338902i | \(-0.110055\pi\) |
−0.763908 | + | 0.645325i | \(0.776722\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | −18.0000 | + | 31.1769i | −0.706562 | + | 1.22380i | ||||
\(650\) | −5.00000 | −0.196116 | ||||||||
\(651\) | −25.0000 | + | 8.66025i | −0.979827 | + | 0.339422i | ||||
\(652\) | −16.0000 | −0.626608 | ||||||||
\(653\) | −19.5000 | + | 33.7750i | −0.763094 | + | 1.32172i | 0.178154 | + | 0.984003i | \(0.442987\pi\) |
−0.941248 | + | 0.337715i | \(0.890346\pi\) | |||||||
\(654\) | 7.00000 | + | 12.1244i | 0.273722 | + | 0.474100i | ||||
\(655\) | −4.50000 | − | 7.79423i | −0.175830 | − | 0.304546i | ||||
\(656\) | −4.50000 | + | 7.79423i | −0.175695 | + | 0.304314i | ||||
\(657\) | 2.00000 | 0.0780274 | ||||||||
\(658\) | 1.50000 | − | 7.79423i | 0.0584761 | − | 0.303851i | ||||
\(659\) | 12.0000 | 0.467454 | 0.233727 | − | 0.972302i | \(-0.424908\pi\) | ||||
0.233727 | + | 0.972302i | \(0.424908\pi\) | |||||||
\(660\) | 1.50000 | − | 2.59808i | 0.0583874 | − | 0.101130i | ||||
\(661\) | 20.0000 | + | 34.6410i | 0.777910 | + | 1.34738i | 0.933144 | + | 0.359502i | \(0.117053\pi\) |
−0.155235 | + | 0.987878i | \(0.549613\pi\) | |||||||
\(662\) | 5.50000 | + | 9.52628i | 0.213764 | + | 0.370249i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.50000 | − | 12.9904i | 0.0969458 | − | 0.503745i | ||||
\(666\) | 1.00000 | 0.0387492 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 1.50000 | + | 2.59808i | 0.0580367 | + | 0.100523i | ||||
\(669\) | 14.0000 | + | 24.2487i | 0.541271 | + | 0.937509i | ||||
\(670\) | −4.00000 | + | 6.92820i | −0.154533 | + | 0.267660i | ||||
\(671\) | 24.0000 | 0.926510 | ||||||||
\(672\) | −2.50000 | + | 0.866025i | −0.0964396 | + | 0.0334077i | ||||
\(673\) | 20.0000 | 0.770943 | 0.385472 | − | 0.922720i | \(-0.374039\pi\) | ||||
0.385472 | + | 0.922720i | \(0.374039\pi\) | |||||||
\(674\) | 10.0000 | − | 17.3205i | 0.385186 | − | 0.667161i | ||||
\(675\) | −0.500000 | − | 0.866025i | −0.0192450 | − | 0.0333333i | ||||
\(676\) | −6.00000 | − | 10.3923i | −0.230769 | − | 0.399704i | ||||
\(677\) | −1.50000 | + | 2.59808i | −0.0576497 | + | 0.0998522i | −0.893410 | − | 0.449242i | \(-0.851694\pi\) |
0.835760 | + | 0.549095i | \(0.185027\pi\) | |||||||
\(678\) | 18.0000 | 0.691286 | ||||||||
\(679\) | −16.0000 | − | 13.8564i | −0.614024 | − | 0.531760i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −15.0000 | − | 25.9808i | −0.574380 | − | 0.994855i | ||||
\(683\) | 6.00000 | + | 10.3923i | 0.229584 | + | 0.397650i | 0.957685 | − | 0.287819i | \(-0.0929302\pi\) |
−0.728101 | + | 0.685470i | \(0.759597\pi\) | |||||||
\(684\) | −2.50000 | + | 4.33013i | −0.0955899 | + | 0.165567i | ||||
\(685\) | 18.0000 | 0.687745 | ||||||||
\(686\) | −8.50000 | − | 16.4545i | −0.324532 | − | 0.628235i | ||||
\(687\) | 14.0000 | 0.534133 | ||||||||
\(688\) | −4.00000 | + | 6.92820i | −0.152499 | + | 0.264135i | ||||
\(689\) | 7.50000 | + | 12.9904i | 0.285727 | + | 0.494894i | ||||
\(690\) | 4.50000 | + | 7.79423i | 0.171312 | + | 0.296721i | ||||
\(691\) | 14.0000 | − | 24.2487i | 0.532585 | − | 0.922464i | −0.466691 | − | 0.884420i | \(-0.654554\pi\) |
0.999276 | − | 0.0380440i | \(-0.0121127\pi\) | |||||||
\(692\) | 9.00000 | 0.342129 | ||||||||
\(693\) | −6.00000 | − | 5.19615i | −0.227921 | − | 0.197386i | ||||
\(694\) | −30.0000 | −1.13878 | ||||||||
\(695\) | 10.0000 | − | 17.3205i | 0.379322 | − | 0.657004i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −14.0000 | + | 24.2487i | −0.529908 | + | 0.917827i | ||||
\(699\) | −6.00000 | −0.226941 | ||||||||
\(700\) | 2.50000 | − | 0.866025i | 0.0944911 | − | 0.0327327i | ||||
\(701\) | −42.0000 | −1.58632 | −0.793159 | − | 0.609015i | \(-0.791565\pi\) | ||||
−0.793159 | + | 0.609015i | \(0.791565\pi\) | |||||||
\(702\) | 2.50000 | − | 4.33013i | 0.0943564 | − | 0.163430i | ||||
\(703\) | 2.50000 | + | 4.33013i | 0.0942893 | + | 0.163314i | ||||
\(704\) | −1.50000 | − | 2.59808i | −0.0565334 | − | 0.0979187i | ||||
\(705\) | 1.50000 | − | 2.59808i | 0.0564933 | − | 0.0978492i | ||||
\(706\) | −24.0000 | −0.903252 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 12.0000 | 0.450988 | ||||||||
\(709\) | 14.0000 | − | 24.2487i | 0.525781 | − | 0.910679i | −0.473768 | − | 0.880650i | \(-0.657106\pi\) |
0.999549 | − | 0.0300298i | \(-0.00956021\pi\) | |||||||
\(710\) | 3.00000 | + | 5.19615i | 0.112588 | + | 0.195008i | ||||
\(711\) | −4.00000 | − | 6.92820i | −0.150012 | − | 0.259828i | ||||
\(712\) | 3.00000 | − | 5.19615i | 0.112430 | − | 0.194734i | ||||
\(713\) | 90.0000 | 3.37053 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.0000 | −0.560968 | ||||||||
\(716\) | 7.50000 | − | 12.9904i | 0.280288 | − | 0.485473i | ||||
\(717\) | −15.0000 | − | 25.9808i | −0.560185 | − | 0.970269i | ||||
\(718\) | 6.00000 | + | 10.3923i | 0.223918 | + | 0.387837i | ||||
\(719\) | −9.00000 | + | 15.5885i | −0.335643 | + | 0.581351i | −0.983608 | − | 0.180319i | \(-0.942287\pi\) |
0.647965 | + | 0.761670i | \(0.275620\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | 20.0000 | − | 6.92820i | 0.744839 | − | 0.258020i | ||||
\(722\) | −6.00000 | −0.223297 | ||||||||
\(723\) | 0.500000 | − | 0.866025i | 0.0185952 | − | 0.0322078i | ||||
\(724\) | −4.00000 | − | 6.92820i | −0.148659 | − | 0.257485i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.00000 | + | 1.73205i | −0.0371135 | + | 0.0642824i | ||||
\(727\) | 23.0000 | 0.853023 | 0.426511 | − | 0.904482i | \(-0.359742\pi\) | ||||
0.426511 | + | 0.904482i | \(0.359742\pi\) | |||||||
\(728\) | 10.0000 | + | 8.66025i | 0.370625 | + | 0.320970i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.00000 | + | 1.73205i | −0.0370117 | + | 0.0641061i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −4.00000 | − | 6.92820i | −0.147844 | − | 0.256074i | ||||
\(733\) | 0.500000 | − | 0.866025i | 0.0184679 | − | 0.0319874i | −0.856644 | − | 0.515908i | \(-0.827454\pi\) |
0.875112 | + | 0.483921i | \(0.160788\pi\) | |||||||
\(734\) | 19.0000 | 0.701303 | ||||||||
\(735\) | −1.00000 | − | 6.92820i | −0.0368856 | − | 0.255551i | ||||
\(736\) | 9.00000 | 0.331744 | ||||||||
\(737\) | −12.0000 | + | 20.7846i | −0.442026 | + | 0.765611i | ||||
\(738\) | 4.50000 | + | 7.79423i | 0.165647 | + | 0.286910i | ||||
\(739\) | −2.50000 | − | 4.33013i | −0.0919640 | − | 0.159286i | 0.816373 | − | 0.577524i | \(-0.195981\pi\) |
−0.908337 | + | 0.418238i | \(0.862648\pi\) | |||||||
\(740\) | −0.500000 | + | 0.866025i | −0.0183804 | + | 0.0318357i | ||||
\(741\) | 25.0000 | 0.918398 | ||||||||
\(742\) | −6.00000 | − | 5.19615i | −0.220267 | − | 0.190757i | ||||
\(743\) | −39.0000 | −1.43077 | −0.715386 | − | 0.698730i | \(-0.753749\pi\) | ||||
−0.715386 | + | 0.698730i | \(0.753749\pi\) | |||||||
\(744\) | −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 | ||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | −1.00000 | + | 1.73205i | −0.0364905 | + | 0.0632034i | −0.883694 | − | 0.468065i | \(-0.844951\pi\) |
0.847203 | + | 0.531269i | \(0.178285\pi\) | |||||||
\(752\) | −1.50000 | − | 2.59808i | −0.0546994 | − | 0.0947421i | ||||
\(753\) | −4.50000 | − | 7.79423i | −0.163989 | − | 0.284037i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.0000 | 0.363937 | ||||||||
\(756\) | −0.500000 | + | 2.59808i | −0.0181848 | + | 0.0944911i | ||||
\(757\) | 2.00000 | 0.0726912 | 0.0363456 | − | 0.999339i | \(-0.488428\pi\) | ||||
0.0363456 | + | 0.999339i | \(0.488428\pi\) | |||||||
\(758\) | −9.50000 | + | 16.4545i | −0.345056 | + | 0.597654i | ||||
\(759\) | 13.5000 | + | 23.3827i | 0.490019 | + | 0.848738i | ||||
\(760\) | −2.50000 | − | 4.33013i | −0.0906845 | − | 0.157070i | ||||
\(761\) | 16.5000 | − | 28.5788i | 0.598125 | − | 1.03598i | −0.394973 | − | 0.918693i | \(-0.629246\pi\) |
0.993098 | − | 0.117289i | \(-0.0374205\pi\) | |||||||
\(762\) | 13.0000 | 0.470940 | ||||||||
\(763\) | −7.00000 | + | 36.3731i | −0.253417 | + | 1.31679i | ||||
\(764\) | 18.0000 | 0.651217 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13.5000 | + | 23.3827i | 0.487775 | + | 0.844851i | ||||
\(767\) | −30.0000 | − | 51.9615i | −1.08324 | − | 1.87622i | ||||
\(768\) | −0.500000 | + | 0.866025i | −0.0180422 | + | 0.0312500i | ||||
\(769\) | 35.0000 | 1.26213 | 0.631066 | − | 0.775729i | \(-0.282618\pi\) | ||||
0.631066 | + | 0.775729i | \(0.282618\pi\) | |||||||
\(770\) | 7.50000 | − | 2.59808i | 0.270281 | − | 0.0936282i | ||||
\(771\) | −12.0000 | −0.432169 | ||||||||
\(772\) | 5.00000 | − | 8.66025i | 0.179954 | − | 0.311689i | ||||
\(773\) | −16.5000 | − | 28.5788i | −0.593464 | − | 1.02791i | −0.993762 | − | 0.111524i | \(-0.964427\pi\) |
0.400298 | − | 0.916385i | \(-0.368907\pi\) | |||||||
\(774\) | 4.00000 | + | 6.92820i | 0.143777 | + | 0.249029i | ||||
\(775\) | 5.00000 | − | 8.66025i | 0.179605 | − | 0.311086i | ||||
\(776\) | −8.00000 | −0.287183 | ||||||||
\(777\) | 2.00000 | + | 1.73205i | 0.0717496 | + | 0.0621370i | ||||
\(778\) | 6.00000 | 0.215110 | ||||||||
\(779\) | −22.5000 | + | 38.9711i | −0.806146 | + | 1.39629i | ||||
\(780\) | 2.50000 | + | 4.33013i | 0.0895144 | + | 0.155043i | ||||
\(781\) | 9.00000 | + | 15.5885i | 0.322045 | + | 0.557799i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.50000 | − | 2.59808i | −0.232143 | − | 0.0927884i | ||||
\(785\) | −5.00000 | −0.178458 | ||||||||
\(786\) | −4.50000 | + | 7.79423i | −0.160510 | + | 0.278011i | ||||
\(787\) | −7.00000 | − | 12.1244i | −0.249523 | − | 0.432187i | 0.713871 | − | 0.700278i | \(-0.246941\pi\) |
−0.963394 | + | 0.268091i | \(0.913607\pi\) | |||||||
\(788\) | −7.50000 | − | 12.9904i | −0.267176 | − | 0.462763i | ||||
\(789\) | 12.0000 | − | 20.7846i | 0.427211 | − | 0.739952i | ||||
\(790\) | 8.00000 | 0.284627 | ||||||||
\(791\) | 36.0000 | + | 31.1769i | 1.28001 | + | 1.10852i | ||||
\(792\) | −3.00000 | −0.106600 | ||||||||
\(793\) | −20.0000 | + | 34.6410i | −0.710221 | + | 1.23014i | ||||
\(794\) | 7.00000 | + | 12.1244i | 0.248421 | + | 0.430277i | ||||
\(795\) | −1.50000 | − | 2.59808i | −0.0531995 | − | 0.0921443i | ||||
\(796\) | 8.00000 | − | 13.8564i | 0.283552 | − | 0.491127i | ||||
\(797\) | 30.0000 | 1.06265 | 0.531327 | − | 0.847167i | \(-0.321693\pi\) | ||||
0.531327 | + | 0.847167i | \(0.321693\pi\) | |||||||
\(798\) | −12.5000 | + | 4.33013i | −0.442495 | + | 0.153285i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.500000 | − | 0.866025i | 0.0176777 | − | 0.0306186i | ||||
\(801\) | −3.00000 | − | 5.19615i | −0.106000 | − | 0.183597i | ||||
\(802\) | 7.50000 | + | 12.9904i | 0.264834 | + | 0.458706i | ||||
\(803\) | −3.00000 | + | 5.19615i | −0.105868 | + | 0.183368i | ||||
\(804\) | 8.00000 | 0.282138 | ||||||||
\(805\) | −4.50000 | + | 23.3827i | −0.158604 | + | 0.824131i | ||||
\(806\) | 50.0000 | 1.76117 | ||||||||
\(807\) | −6.00000 | + | 10.3923i | −0.211210 | + | 0.365826i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.5000 | + | 23.3827i | 0.474635 | + | 0.822091i | 0.999578 | − | 0.0290457i | \(-0.00924684\pi\) |
−0.524943 | + | 0.851137i | \(0.675914\pi\) | |||||||
\(810\) | −0.500000 | + | 0.866025i | −0.0175682 | + | 0.0304290i | ||||
\(811\) | −7.00000 | −0.245803 | −0.122902 | − | 0.992419i | \(-0.539220\pi\) | ||||
−0.122902 | + | 0.992419i | \(0.539220\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.0000 | −0.561144 | ||||||||
\(814\) | −1.50000 | + | 2.59808i | −0.0525750 | + | 0.0910625i | ||||
\(815\) | −8.00000 | − | 13.8564i | −0.280228 | − | 0.485369i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.0000 | + | 34.6410i | −0.699711 | + | 1.21194i | ||||
\(818\) | −2.00000 | −0.0699284 | ||||||||
\(819\) | 12.5000 | − | 4.33013i | 0.436785 | − | 0.151307i | ||||
\(820\) | −9.00000 | −0.314294 | ||||||||
\(821\) | 15.0000 | − | 25.9808i | 0.523504 | − | 0.906735i | −0.476122 | − | 0.879379i | \(-0.657958\pi\) |
0.999626 | − | 0.0273557i | \(-0.00870868\pi\) | |||||||
\(822\) | −9.00000 | − | 15.5885i | −0.313911 | − | 0.543710i | ||||
\(823\) | −16.0000 | − | 27.7128i | −0.557725 | − | 0.966008i | −0.997686 | − | 0.0679910i | \(-0.978341\pi\) |
0.439961 | − | 0.898017i | \(-0.354992\pi\) | |||||||
\(824\) | 4.00000 | − | 6.92820i | 0.139347 | − | 0.241355i | ||||
\(825\) | 3.00000 | 0.104447 | ||||||||
\(826\) | 24.0000 | + | 20.7846i | 0.835067 | + | 0.723189i | ||||
\(827\) | 6.00000 | 0.208640 | 0.104320 | − | 0.994544i | \(-0.466733\pi\) | ||||
0.104320 | + | 0.994544i | \(0.466733\pi\) | |||||||
\(828\) | 4.50000 | − | 7.79423i | 0.156386 | − | 0.270868i | ||||
\(829\) | 20.0000 | + | 34.6410i | 0.694629 | + | 1.20313i | 0.970306 | + | 0.241882i | \(0.0777647\pi\) |
−0.275677 | + | 0.961250i | \(0.588902\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.0000 | + | 22.5167i | −0.450965 | + | 0.781094i | ||||
\(832\) | 5.00000 | 0.173344 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −20.0000 | −0.692543 | ||||||||
\(835\) | −1.50000 | + | 2.59808i | −0.0519096 | + | 0.0899101i | ||||
\(836\) | −7.50000 | − | 12.9904i | −0.259393 | − | 0.449282i | ||||
\(837\) | 5.00000 | + | 8.66025i | 0.172825 | + | 0.299342i | ||||
\(838\) | −4.50000 | + | 7.79423i | −0.155450 | + | 0.269247i | ||||
\(839\) | −24.0000 | −0.828572 | −0.414286 | − | 0.910147i | \(-0.635969\pi\) | ||||
−0.414286 | + | 0.910147i | \(0.635969\pi\) | |||||||
\(840\) | −2.00000 | − | 1.73205i | −0.0690066 | − | 0.0597614i | ||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 7.00000 | − | 12.1244i | 0.241236 | − | 0.417833i | ||||
\(843\) | 10.5000 | + | 18.1865i | 0.361639 | + | 0.626377i | ||||
\(844\) | −2.50000 | − | 4.33013i | −0.0860535 | − | 0.149049i | ||||
\(845\) | 6.00000 | − | 10.3923i | 0.206406 | − | 0.357506i | ||||
\(846\) | −3.00000 | −0.103142 | ||||||||
\(847\) | −5.00000 | + | 1.73205i | −0.171802 | + | 0.0595140i | ||||
\(848\) | −3.00000 | −0.103020 | ||||||||
\(849\) | 11.0000 | − | 19.0526i | 0.377519 | − | 0.653882i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.50000 | − | 7.79423i | −0.154258 | − | 0.267183i | ||||
\(852\) | 3.00000 | − | 5.19615i | 0.102778 | − | 0.178017i | ||||
\(853\) | −37.0000 | −1.26686 | −0.633428 | − | 0.773802i | \(-0.718353\pi\) | ||||
−0.633428 | + | 0.773802i | \(0.718353\pi\) | |||||||
\(854\) | 4.00000 | − | 20.7846i | 0.136877 | − | 0.711235i | ||||
\(855\) | −5.00000 | −0.170996 | ||||||||
\(856\) | 3.00000 | − | 5.19615i | 0.102538 | − | 0.177601i | ||||
\(857\) | 3.00000 | + | 5.19615i | 0.102478 | + | 0.177497i | 0.912705 | − | 0.408619i | \(-0.133990\pi\) |
−0.810227 | + | 0.586116i | \(0.800656\pi\) | |||||||
\(858\) | 7.50000 | + | 12.9904i | 0.256046 | + | 0.443484i | ||||
\(859\) | 2.00000 | − | 3.46410i | 0.0682391 | − | 0.118194i | −0.829887 | − | 0.557931i | \(-0.811595\pi\) |
0.898126 | + | 0.439738i | \(0.144929\pi\) | |||||||
\(860\) | −8.00000 | −0.272798 | ||||||||
\(861\) | −4.50000 | + | 23.3827i | −0.153360 | + | 0.796880i | ||||
\(862\) | 24.0000 | 0.817443 | ||||||||
\(863\) | 10.5000 | − | 18.1865i | 0.357424 | − | 0.619077i | −0.630106 | − | 0.776509i | \(-0.716988\pi\) |
0.987530 | + | 0.157433i | \(0.0503217\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | 4.50000 | + | 7.79423i | 0.153005 | + | 0.265012i | ||||
\(866\) | −8.00000 | + | 13.8564i | −0.271851 | + | 0.470860i | ||||
\(867\) | −17.0000 | −0.577350 | ||||||||
\(868\) | −25.0000 | + | 8.66025i | −0.848555 | + | 0.293948i | ||||
\(869\) | 24.0000 | 0.814144 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.0000 | − | 34.6410i | −0.677674 | − | 1.17377i | ||||
\(872\) | 7.00000 | + | 12.1244i | 0.237050 | + | 0.410582i | ||||
\(873\) | −4.00000 | + | 6.92820i | −0.135379 | + | 0.234484i | ||||
\(874\) | 45.0000 | 1.52215 | ||||||||
\(875\) | 2.00000 | + | 1.73205i | 0.0676123 | + | 0.0585540i | ||||
\(876\) | 2.00000 | 0.0675737 | ||||||||
\(877\) | −2.50000 | + | 4.33013i | −0.0844190 | + | 0.146218i | −0.905143 | − | 0.425106i | \(-0.860237\pi\) |
0.820724 | + | 0.571324i | \(0.193570\pi\) | |||||||
\(878\) | 4.00000 | + | 6.92820i | 0.134993 | + | 0.233816i | ||||
\(879\) | 10.5000 | + | 18.1865i | 0.354156 | + | 0.613417i | ||||
\(880\) | 1.50000 | − | 2.59808i | 0.0505650 | − | 0.0875811i | ||||
\(881\) | −33.0000 | −1.11180 | −0.555899 | − | 0.831250i | \(-0.687626\pi\) | ||||
−0.555899 | + | 0.831250i | \(0.687626\pi\) | |||||||
\(882\) | −5.50000 | + | 4.33013i | −0.185195 | + | 0.145803i | ||||
\(883\) | 14.0000 | 0.471138 | 0.235569 | − | 0.971858i | \(-0.424305\pi\) | ||||
0.235569 | + | 0.971858i | \(0.424305\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.00000 | + | 10.3923i | 0.201688 | + | 0.349334i | ||||
\(886\) | −12.0000 | − | 20.7846i | −0.403148 | − | 0.698273i | ||||
\(887\) | −6.00000 | + | 10.3923i | −0.201460 | + | 0.348939i | −0.948999 | − | 0.315279i | \(-0.897902\pi\) |
0.747539 | + | 0.664218i | \(0.231235\pi\) | |||||||
\(888\) | 1.00000 | 0.0335578 | ||||||||
\(889\) | 26.0000 | + | 22.5167i | 0.872012 | + | 0.755185i | ||||
\(890\) | 6.00000 | 0.201120 | ||||||||
\(891\) | −1.50000 | + | 2.59808i | −0.0502519 | + | 0.0870388i | ||||
\(892\) | 14.0000 | + | 24.2487i | 0.468755 | + | 0.811907i | ||||
\(893\) | −7.50000 | − | 12.9904i | −0.250978 | − | 0.434707i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.0000 | 0.501395 | ||||||||
\(896\) | −2.50000 | + | 0.866025i | −0.0835191 | + | 0.0289319i | ||||
\(897\) | −45.0000 | −1.50251 | ||||||||
\(898\) | −16.5000 | + | 28.5788i | −0.550612 | + | 0.953688i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.500000 | − | 0.866025i | −0.0166667 | − | 0.0288675i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −27.0000 | −0.899002 | ||||||||
\(903\) | −4.00000 | + | 20.7846i | −0.133112 | + | 0.691669i | ||||
\(904\) | 18.0000 | 0.598671 | ||||||||
\(905\) | 4.00000 | − | 6.92820i | 0.132964 | − | 0.230301i | ||||
\(906\) | −5.00000 | − | 8.66025i | −0.166114 | − | 0.287718i | ||||
\(907\) | 5.00000 | + | 8.66025i | 0.166022 | + | 0.287559i | 0.937018 | − | 0.349281i | \(-0.113574\pi\) |
−0.770996 | + | 0.636841i | \(0.780241\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.50000 | + | 12.9904i | −0.0828742 | + | 0.430627i | ||||
\(911\) | 6.00000 | 0.198789 | 0.0993944 | − | 0.995048i | \(-0.468309\pi\) | ||||
0.0993944 | + | 0.995048i | \(0.468309\pi\) | |||||||
\(912\) | −2.50000 | + | 4.33013i | −0.0827833 | + | 0.143385i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −5.00000 | − | 8.66025i | −0.165385 | − | 0.286456i | ||||
\(915\) | 4.00000 | − | 6.92820i | 0.132236 | − | 0.229039i | ||||
\(916\) | 14.0000 | 0.462573 | ||||||||
\(917\) | −22.5000 | + | 7.79423i | −0.743015 | + | 0.257388i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.0000 | − | 24.2487i | 0.461817 | − | 0.799891i | −0.537234 | − | 0.843433i | \(-0.680531\pi\) |
0.999052 | + | 0.0435419i | \(0.0138642\pi\) | |||||||
\(920\) | 4.50000 | + | 7.79423i | 0.148361 | + | 0.256968i | ||||
\(921\) | 14.0000 | + | 24.2487i | 0.461316 | + | 0.799022i | ||||
\(922\) | 6.00000 | − | 10.3923i | 0.197599 | − | 0.342252i | ||||
\(923\) | −30.0000 | −0.987462 | ||||||||
\(924\) | −6.00000 | − | 5.19615i | −0.197386 | − | 0.170941i | ||||
\(925\) | −1.00000 | −0.0328798 | ||||||||
\(926\) | −0.500000 | + | 0.866025i | −0.0164310 | + | 0.0284594i | ||||
\(927\) | −4.00000 | − | 6.92820i | −0.131377 | − | 0.227552i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.5000 | + | 33.7750i | −0.639774 | + | 1.10812i | 0.345708 | + | 0.938342i | \(0.387639\pi\) |
−0.985482 | + | 0.169779i | \(0.945695\pi\) | |||||||
\(930\) | −10.0000 | −0.327913 | ||||||||
\(931\) | −32.5000 | − | 12.9904i | −1.06514 | − | 0.425743i | ||||
\(932\) | −6.00000 | −0.196537 | ||||||||
\(933\) | 6.00000 | − | 10.3923i | 0.196431 | − | 0.340229i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.50000 | − | 4.33013i | 0.0817151 | − | 0.141535i | ||||
\(937\) | 44.0000 | 1.43742 | 0.718709 | − | 0.695311i | \(-0.244734\pi\) | ||||
0.718709 | + | 0.695311i | \(0.244734\pi\) | |||||||
\(938\) | 16.0000 | + | 13.8564i | 0.522419 | + | 0.452428i | ||||
\(939\) | −4.00000 | −0.130535 | ||||||||
\(940\) | 1.50000 | − | 2.59808i | 0.0489246 | − | 0.0847399i | ||||
\(941\) | 9.00000 | + | 15.5885i | 0.293392 | + | 0.508169i | 0.974609 | − | 0.223912i | \(-0.0718827\pi\) |
−0.681218 | + | 0.732081i | \(0.738549\pi\) | |||||||
\(942\) | 2.50000 | + | 4.33013i | 0.0814544 | + | 0.141083i | ||||
\(943\) | 40.5000 | − | 70.1481i | 1.31886 | − | 2.28434i | ||||
\(944\) | 12.0000 | 0.390567 | ||||||||
\(945\) | −2.50000 | + | 0.866025i | −0.0813250 | + | 0.0281718i | ||||
\(946\) | −24.0000 | −0.780307 | ||||||||
\(947\) | 9.00000 | − | 15.5885i | 0.292461 | − | 0.506557i | −0.681930 | − | 0.731417i | \(-0.738859\pi\) |
0.974391 | + | 0.224860i | \(0.0721926\pi\) | |||||||
\(948\) | −4.00000 | − | 6.92820i | −0.129914 | − | 0.225018i | ||||
\(949\) | −5.00000 | − | 8.66025i | −0.162307 | − | 0.281124i | ||||
\(950\) | 2.50000 | − | 4.33013i | 0.0811107 | − | 0.140488i | ||||
\(951\) | −18.0000 | −0.583690 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.0000 | 0.388718 | 0.194359 | − | 0.980930i | \(-0.437737\pi\) | ||||
0.194359 | + | 0.980930i | \(0.437737\pi\) | |||||||
\(954\) | −1.50000 | + | 2.59808i | −0.0485643 | + | 0.0841158i | ||||
\(955\) | 9.00000 | + | 15.5885i | 0.291233 | + | 0.504431i | ||||
\(956\) | −15.0000 | − | 25.9808i | −0.485135 | − | 0.840278i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 18.0000 | 0.581554 | ||||||||
\(959\) | 9.00000 | − | 46.7654i | 0.290625 | − | 1.51013i | ||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | −34.5000 | + | 59.7558i | −1.11290 | + | 1.92760i | ||||
\(962\) | −2.50000 | − | 4.33013i | −0.0806032 | − | 0.139609i | ||||
\(963\) | −3.00000 | − | 5.19615i | −0.0966736 | − | 0.167444i | ||||
\(964\) | 0.500000 | − | 0.866025i | 0.0161039 | − | 0.0278928i | ||||
\(965\) | 10.0000 | 0.321911 | ||||||||
\(966\) | 22.5000 | − | 7.79423i | 0.723926 | − | 0.250775i | ||||
\(967\) | −28.0000 | −0.900419 | −0.450210 | − | 0.892923i | \(-0.648651\pi\) | ||||
−0.450210 | + | 0.892923i | \(0.648651\pi\) | |||||||
\(968\) | −1.00000 | + | 1.73205i | −0.0321412 | + | 0.0556702i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.00000 | − | 6.92820i | −0.128432 | − | 0.222451i | ||||
\(971\) | −7.50000 | + | 12.9904i | −0.240686 | + | 0.416881i | −0.960910 | − | 0.276861i | \(-0.910706\pi\) |
0.720224 | + | 0.693742i | \(0.244039\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −40.0000 | − | 34.6410i | −1.28234 | − | 1.11054i | ||||
\(974\) | 40.0000 | 1.28168 | ||||||||
\(975\) | −2.50000 | + | 4.33013i | −0.0800641 | + | 0.138675i | ||||
\(976\) | −4.00000 | − | 6.92820i | −0.128037 | − | 0.221766i | ||||
\(977\) | −3.00000 | − | 5.19615i | −0.0959785 | − | 0.166240i | 0.814038 | − | 0.580812i | \(-0.197265\pi\) |
−0.910017 | + | 0.414572i | \(0.863931\pi\) | |||||||
\(978\) | −8.00000 | + | 13.8564i | −0.255812 | + | 0.443079i | ||||
\(979\) | 18.0000 | 0.575282 | ||||||||
\(980\) | −1.00000 | − | 6.92820i | −0.0319438 | − | 0.221313i | ||||
\(981\) | 14.0000 | 0.446986 | ||||||||
\(982\) | 6.00000 | − | 10.3923i | 0.191468 | − | 0.331632i | ||||
\(983\) | −4.50000 | − | 7.79423i | −0.143528 | − | 0.248597i | 0.785295 | − | 0.619122i | \(-0.212511\pi\) |
−0.928823 | + | 0.370525i | \(0.879178\pi\) | |||||||
\(984\) | 4.50000 | + | 7.79423i | 0.143455 | + | 0.248471i | ||||
\(985\) | 7.50000 | − | 12.9904i | 0.238970 | − | 0.413908i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.00000 | − | 5.19615i | −0.190982 | − | 0.165395i | ||||
\(988\) | 25.0000 | 0.795356 | ||||||||
\(989\) | 36.0000 | − | 62.3538i | 1.14473 | − | 1.98274i | ||||
\(990\) | −1.50000 | − | 2.59808i | −0.0476731 | − | 0.0825723i | ||||
\(991\) | 29.0000 | + | 50.2295i | 0.921215 | + | 1.59559i | 0.797537 | + | 0.603269i | \(0.206136\pi\) |
0.123678 | + | 0.992322i | \(0.460531\pi\) | |||||||
\(992\) | −5.00000 | + | 8.66025i | −0.158750 | + | 0.274963i | ||||
\(993\) | 11.0000 | 0.349074 | ||||||||
\(994\) | 15.0000 | − | 5.19615i | 0.475771 | − | 0.164812i | ||||
\(995\) | 16.0000 | 0.507234 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.00000 | − | 12.1244i | −0.221692 | − | 0.383982i | 0.733630 | − | 0.679549i | \(-0.237825\pi\) |
−0.955322 | + | 0.295567i | \(0.904491\pi\) | |||||||
\(998\) | −8.00000 | − | 13.8564i | −0.253236 | − | 0.438617i | ||||
\(999\) | 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 | 210.2.i.c.121.1 | ✓ | 2 | |
3.2 | odd | 2 | 630.2.k.a.541.1 | 2 | |||
4.3 | odd | 2 | 1680.2.bg.n.961.1 | 2 | |||
5.2 | odd | 4 | 1050.2.o.c.499.2 | 4 | |||
5.3 | odd | 4 | 1050.2.o.c.499.1 | 4 | |||
5.4 | even | 2 | 1050.2.i.i.751.1 | 2 | |||
7.2 | even | 3 | 1470.2.a.f.1.1 | 1 | |||
7.3 | odd | 6 | 1470.2.i.p.361.1 | 2 | |||
7.4 | even | 3 | inner | 210.2.i.c.151.1 | yes | 2 | |
7.5 | odd | 6 | 1470.2.a.e.1.1 | 1 | |||
7.6 | odd | 2 | 1470.2.i.p.961.1 | 2 | |||
21.2 | odd | 6 | 4410.2.a.bh.1.1 | 1 | |||
21.5 | even | 6 | 4410.2.a.w.1.1 | 1 | |||
21.11 | odd | 6 | 630.2.k.a.361.1 | 2 | |||
28.11 | odd | 6 | 1680.2.bg.n.1201.1 | 2 | |||
35.4 | even | 6 | 1050.2.i.i.151.1 | 2 | |||
35.9 | even | 6 | 7350.2.a.cd.1.1 | 1 | |||
35.18 | odd | 12 | 1050.2.o.c.949.2 | 4 | |||
35.19 | odd | 6 | 7350.2.a.cx.1.1 | 1 | |||
35.32 | odd | 12 | 1050.2.o.c.949.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.i.c.121.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
210.2.i.c.151.1 | yes | 2 | 7.4 | even | 3 | inner | |
630.2.k.a.361.1 | 2 | 21.11 | odd | 6 | |||
630.2.k.a.541.1 | 2 | 3.2 | odd | 2 | |||
1050.2.i.i.151.1 | 2 | 35.4 | even | 6 | |||
1050.2.i.i.751.1 | 2 | 5.4 | even | 2 | |||
1050.2.o.c.499.1 | 4 | 5.3 | odd | 4 | |||
1050.2.o.c.499.2 | 4 | 5.2 | odd | 4 | |||
1050.2.o.c.949.1 | 4 | 35.32 | odd | 12 | |||
1050.2.o.c.949.2 | 4 | 35.18 | odd | 12 | |||
1470.2.a.e.1.1 | 1 | 7.5 | odd | 6 | |||
1470.2.a.f.1.1 | 1 | 7.2 | even | 3 | |||
1470.2.i.p.361.1 | 2 | 7.3 | odd | 6 | |||
1470.2.i.p.961.1 | 2 | 7.6 | odd | 2 | |||
1680.2.bg.n.961.1 | 2 | 4.3 | odd | 2 | |||
1680.2.bg.n.1201.1 | 2 | 28.11 | odd | 6 | |||
4410.2.a.w.1.1 | 1 | 21.5 | even | 6 | |||
4410.2.a.bh.1.1 | 1 | 21.2 | odd | 6 | |||
7350.2.a.cd.1.1 | 1 | 35.9 | even | 6 | |||
7350.2.a.cx.1.1 | 1 | 35.19 | odd | 6 |