Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [78,2,Mod(43,78)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(78, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("78.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 78 = 2 \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 78.i (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.622833135766\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 43.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 78.43 |
Dual form | 78.2.i.b.49.2 |
$q$-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 \(\left(\mathbb{Z}/78\mathbb{Z}\right)^\times\).
\(n\) | \(53\) | \(67\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | − | 1.73205i | − | 0.774597i | −0.921954 | − | 0.387298i | \(-0.873408\pi\) | ||
0.921954 | − | 0.387298i | \(-0.126592\pi\) | |||||||
\(6\) | 0.866025 | − | 0.500000i | 0.353553 | − | 0.204124i | ||||
\(7\) | −4.09808 | + | 2.36603i | −1.54893 | + | 0.894274i | −0.550703 | + | 0.834701i | \(0.685640\pi\) |
−0.998224 | + | 0.0595724i | \(0.981026\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0.866025 | − | 1.50000i | 0.273861 | − | 0.474342i | ||||
\(11\) | 4.09808 | + | 2.36603i | 1.23562 | + | 0.713384i | 0.968195 | − | 0.250196i | \(-0.0804951\pi\) |
0.267421 | + | 0.963580i | \(0.413828\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −3.59808 | + | 0.232051i | −0.997927 | + | 0.0643593i | ||||
\(14\) | −4.73205 | −1.26469 | ||||||||
\(15\) | −1.50000 | − | 0.866025i | −0.387298 | − | 0.223607i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.59808 | − | 4.50000i | −0.630126 | − | 1.09141i | −0.987526 | − | 0.157459i | \(-0.949670\pi\) |
0.357400 | − | 0.933952i | \(-0.383663\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | 1.09808 | − | 0.633975i | 0.251916 | − | 0.145444i | −0.368725 | − | 0.929538i | \(-0.620206\pi\) |
0.620641 | + | 0.784095i | \(0.286872\pi\) | |||||||
\(20\) | 1.50000 | − | 0.866025i | 0.335410 | − | 0.193649i | ||||
\(21\) | 4.73205i | 1.03262i | ||||||||
\(22\) | 2.36603 | + | 4.09808i | 0.504438 | + | 0.873713i | ||||
\(23\) | 1.09808 | − | 1.90192i | 0.228965 | − | 0.396579i | −0.728537 | − | 0.685007i | \(-0.759799\pi\) |
0.957502 | + | 0.288428i | \(0.0931326\pi\) | |||||||
\(24\) | 0.866025 | + | 0.500000i | 0.176777 | + | 0.102062i | ||||
\(25\) | 2.00000 | 0.400000 | ||||||||
\(26\) | −3.23205 | − | 1.59808i | −0.633857 | − | 0.313409i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −4.09808 | − | 2.36603i | −0.774464 | − | 0.447137i | ||||
\(29\) | 1.50000 | − | 2.59808i | 0.278543 | − | 0.482451i | −0.692480 | − | 0.721437i | \(-0.743482\pi\) |
0.971023 | + | 0.238987i | \(0.0768152\pi\) | |||||||
\(30\) | −0.866025 | − | 1.50000i | −0.158114 | − | 0.273861i | ||||
\(31\) | 2.53590i | 0.455461i | 0.973724 | + | 0.227730i | \(0.0731305\pi\) | ||||
−0.973724 | + | 0.227730i | \(0.926870\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 4.09808 | − | 2.36603i | 0.713384 | − | 0.411872i | ||||
\(34\) | − | 5.19615i | − | 0.891133i | ||||||
\(35\) | 4.09808 | + | 7.09808i | 0.692701 | + | 1.19979i | ||||
\(36\) | 0.500000 | − | 0.866025i | 0.0833333 | − | 0.144338i | ||||
\(37\) | 2.59808 | + | 1.50000i | 0.427121 | + | 0.246598i | 0.698119 | − | 0.715981i | \(-0.254020\pi\) |
−0.270998 | + | 0.962580i | \(0.587354\pi\) | |||||||
\(38\) | 1.26795 | 0.205689 | ||||||||
\(39\) | −1.59808 | + | 3.23205i | −0.255897 | + | 0.517542i | ||||
\(40\) | 1.73205 | 0.273861 | ||||||||
\(41\) | 0.401924 | + | 0.232051i | 0.0627700 | + | 0.0362402i | 0.531057 | − | 0.847336i | \(-0.321795\pi\) |
−0.468287 | + | 0.883577i | \(0.655129\pi\) | |||||||
\(42\) | −2.36603 | + | 4.09808i | −0.365086 | + | 0.632347i | ||||
\(43\) | 3.09808 | + | 5.36603i | 0.472452 | + | 0.818311i | 0.999503 | − | 0.0315225i | \(-0.0100356\pi\) |
−0.527051 | + | 0.849834i | \(0.676702\pi\) | |||||||
\(44\) | 4.73205i | 0.713384i | ||||||||
\(45\) | −1.50000 | + | 0.866025i | −0.223607 | + | 0.129099i | ||||
\(46\) | 1.90192 | − | 1.09808i | 0.280423 | − | 0.161903i | ||||
\(47\) | 1.26795i | 0.184949i | 0.995715 | + | 0.0924747i | \(0.0294777\pi\) | ||||
−0.995715 | + | 0.0924747i | \(0.970522\pi\) | |||||||
\(48\) | 0.500000 | + | 0.866025i | 0.0721688 | + | 0.125000i | ||||
\(49\) | 7.69615 | − | 13.3301i | 1.09945 | − | 1.90430i | ||||
\(50\) | 1.73205 | + | 1.00000i | 0.244949 | + | 0.141421i | ||||
\(51\) | −5.19615 | −0.727607 | ||||||||
\(52\) | −2.00000 | − | 3.00000i | −0.277350 | − | 0.416025i | ||||
\(53\) | 3.00000 | 0.412082 | 0.206041 | − | 0.978543i | \(-0.433942\pi\) | ||||
0.206041 | + | 0.978543i | \(0.433942\pi\) | |||||||
\(54\) | −0.866025 | − | 0.500000i | −0.117851 | − | 0.0680414i | ||||
\(55\) | 4.09808 | − | 7.09808i | 0.552584 | − | 0.957104i | ||||
\(56\) | −2.36603 | − | 4.09808i | −0.316173 | − | 0.547628i | ||||
\(57\) | − | 1.26795i | − | 0.167944i | ||||||
\(58\) | 2.59808 | − | 1.50000i | 0.341144 | − | 0.196960i | ||||
\(59\) | −12.0000 | + | 6.92820i | −1.56227 | + | 0.901975i | −0.565240 | + | 0.824927i | \(0.691216\pi\) |
−0.997027 | + | 0.0770484i | \(0.975450\pi\) | |||||||
\(60\) | − | 1.73205i | − | 0.223607i | ||||||
\(61\) | −2.40192 | − | 4.16025i | −0.307535 | − | 0.532666i | 0.670288 | − | 0.742101i | \(-0.266171\pi\) |
−0.977822 | + | 0.209435i | \(0.932837\pi\) | |||||||
\(62\) | −1.26795 | + | 2.19615i | −0.161030 | + | 0.278912i | ||||
\(63\) | 4.09808 | + | 2.36603i | 0.516309 | + | 0.298091i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0.401924 | + | 6.23205i | 0.0498525 | + | 0.772991i | ||||
\(66\) | 4.73205 | 0.582475 | ||||||||
\(67\) | −9.29423 | − | 5.36603i | −1.13547 | − | 0.655564i | −0.190166 | − | 0.981752i | \(-0.560903\pi\) |
−0.945305 | + | 0.326188i | \(0.894236\pi\) | |||||||
\(68\) | 2.59808 | − | 4.50000i | 0.315063 | − | 0.545705i | ||||
\(69\) | −1.09808 | − | 1.90192i | −0.132193 | − | 0.228965i | ||||
\(70\) | 8.19615i | 0.979628i | ||||||||
\(71\) | 7.09808 | − | 4.09808i | 0.842387 | − | 0.486352i | −0.0156881 | − | 0.999877i | \(-0.504994\pi\) |
0.858075 | + | 0.513525i | \(0.171661\pi\) | |||||||
\(72\) | 0.866025 | − | 0.500000i | 0.102062 | − | 0.0589256i | ||||
\(73\) | 12.1244i | 1.41905i | 0.704681 | + | 0.709524i | \(0.251090\pi\) | ||||
−0.704681 | + | 0.709524i | \(0.748910\pi\) | |||||||
\(74\) | 1.50000 | + | 2.59808i | 0.174371 | + | 0.302020i | ||||
\(75\) | 1.00000 | − | 1.73205i | 0.115470 | − | 0.200000i | ||||
\(76\) | 1.09808 | + | 0.633975i | 0.125958 | + | 0.0727219i | ||||
\(77\) | −22.3923 | −2.55184 | ||||||||
\(78\) | −3.00000 | + | 2.00000i | −0.339683 | + | 0.226455i | ||||
\(79\) | −12.3923 | −1.39424 | −0.697122 | − | 0.716953i | \(-0.745536\pi\) | ||||
−0.697122 | + | 0.716953i | \(0.745536\pi\) | |||||||
\(80\) | 1.50000 | + | 0.866025i | 0.167705 | + | 0.0968246i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0.232051 | + | 0.401924i | 0.0256257 | + | 0.0443851i | ||||
\(83\) | − | 11.6603i | − | 1.27988i | −0.768425 | − | 0.639940i | \(-0.778959\pi\) | ||
0.768425 | − | 0.639940i | \(-0.221041\pi\) | |||||||
\(84\) | −4.09808 | + | 2.36603i | −0.447137 | + | 0.258155i | ||||
\(85\) | −7.79423 | + | 4.50000i | −0.845403 | + | 0.488094i | ||||
\(86\) | 6.19615i | 0.668148i | ||||||||
\(87\) | −1.50000 | − | 2.59808i | −0.160817 | − | 0.278543i | ||||
\(88\) | −2.36603 | + | 4.09808i | −0.252219 | + | 0.436856i | ||||
\(89\) | 2.19615 | + | 1.26795i | 0.232792 | + | 0.134402i | 0.611859 | − | 0.790967i | \(-0.290422\pi\) |
−0.379068 | + | 0.925369i | \(0.623755\pi\) | |||||||
\(90\) | −1.73205 | −0.182574 | ||||||||
\(91\) | 14.1962 | − | 9.46410i | 1.48816 | − | 0.992107i | ||||
\(92\) | 2.19615 | 0.228965 | ||||||||
\(93\) | 2.19615 | + | 1.26795i | 0.227730 | + | 0.131480i | ||||
\(94\) | −0.633975 | + | 1.09808i | −0.0653895 | + | 0.113258i | ||||
\(95\) | −1.09808 | − | 1.90192i | −0.112660 | − | 0.195133i | ||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | 5.19615 | − | 3.00000i | 0.527589 | − | 0.304604i | −0.212445 | − | 0.977173i | \(-0.568143\pi\) |
0.740034 | + | 0.672569i | \(0.234809\pi\) | |||||||
\(98\) | 13.3301 | − | 7.69615i | 1.34655 | − | 0.777429i | ||||
\(99\) | − | 4.73205i | − | 0.475589i | ||||||
\(100\) | 1.00000 | + | 1.73205i | 0.100000 | + | 0.173205i | ||||
\(101\) | −0.696152 | + | 1.20577i | −0.0692698 | + | 0.119979i | −0.898580 | − | 0.438810i | \(-0.855400\pi\) |
0.829310 | + | 0.558788i | \(0.188734\pi\) | |||||||
\(102\) | −4.50000 | − | 2.59808i | −0.445566 | − | 0.257248i | ||||
\(103\) | 4.19615 | 0.413459 | 0.206730 | − | 0.978398i | \(-0.433718\pi\) | ||||
0.206730 | + | 0.978398i | \(0.433718\pi\) | |||||||
\(104\) | −0.232051 | − | 3.59808i | −0.0227545 | − | 0.352820i | ||||
\(105\) | 8.19615 | 0.799863 | ||||||||
\(106\) | 2.59808 | + | 1.50000i | 0.252347 | + | 0.145693i | ||||
\(107\) | −4.09808 | + | 7.09808i | −0.396176 | + | 0.686197i | −0.993251 | − | 0.115989i | \(-0.962996\pi\) |
0.597075 | + | 0.802186i | \(0.296330\pi\) | |||||||
\(108\) | −0.500000 | − | 0.866025i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | 16.3923i | 1.57010i | 0.619434 | + | 0.785049i | \(0.287362\pi\) | ||||
−0.619434 | + | 0.785049i | \(0.712638\pi\) | |||||||
\(110\) | 7.09808 | − | 4.09808i | 0.676775 | − | 0.390736i | ||||
\(111\) | 2.59808 | − | 1.50000i | 0.246598 | − | 0.142374i | ||||
\(112\) | − | 4.73205i | − | 0.447137i | ||||||
\(113\) | −5.59808 | − | 9.69615i | −0.526623 | − | 0.912137i | −0.999519 | − | 0.0310191i | \(-0.990125\pi\) |
0.472896 | − | 0.881118i | \(-0.343209\pi\) | |||||||
\(114\) | 0.633975 | − | 1.09808i | 0.0593772 | − | 0.102844i | ||||
\(115\) | −3.29423 | − | 1.90192i | −0.307188 | − | 0.177355i | ||||
\(116\) | 3.00000 | 0.278543 | ||||||||
\(117\) | 2.00000 | + | 3.00000i | 0.184900 | + | 0.277350i | ||||
\(118\) | −13.8564 | −1.27559 | ||||||||
\(119\) | 21.2942 | + | 12.2942i | 1.95204 | + | 1.12701i | ||||
\(120\) | 0.866025 | − | 1.50000i | 0.0790569 | − | 0.136931i | ||||
\(121\) | 5.69615 | + | 9.86603i | 0.517832 | + | 0.896911i | ||||
\(122\) | − | 4.80385i | − | 0.434920i | ||||||
\(123\) | 0.401924 | − | 0.232051i | 0.0362402 | − | 0.0209233i | ||||
\(124\) | −2.19615 | + | 1.26795i | −0.197220 | + | 0.113865i | ||||
\(125\) | − | 12.1244i | − | 1.08444i | ||||||
\(126\) | 2.36603 | + | 4.09808i | 0.210782 | + | 0.365086i | ||||
\(127\) | −2.00000 | + | 3.46410i | −0.177471 | + | 0.307389i | −0.941014 | − | 0.338368i | \(-0.890125\pi\) |
0.763542 | + | 0.645758i | \(0.223458\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 6.19615 | 0.545541 | ||||||||
\(130\) | −2.76795 | + | 5.59808i | −0.242765 | + | 0.490984i | ||||
\(131\) | 16.3923 | 1.43220 | 0.716101 | − | 0.697997i | \(-0.245925\pi\) | ||||
0.716101 | + | 0.697997i | \(0.245925\pi\) | |||||||
\(132\) | 4.09808 | + | 2.36603i | 0.356692 | + | 0.205936i | ||||
\(133\) | −3.00000 | + | 5.19615i | −0.260133 | + | 0.450564i | ||||
\(134\) | −5.36603 | − | 9.29423i | −0.463554 | − | 0.802899i | ||||
\(135\) | 1.73205i | 0.149071i | ||||||||
\(136\) | 4.50000 | − | 2.59808i | 0.385872 | − | 0.222783i | ||||
\(137\) | 7.79423 | − | 4.50000i | 0.665906 | − | 0.384461i | −0.128618 | − | 0.991694i | \(-0.541054\pi\) |
0.794524 | + | 0.607233i | \(0.207721\pi\) | |||||||
\(138\) | − | 2.19615i | − | 0.186949i | ||||||
\(139\) | 2.00000 | + | 3.46410i | 0.169638 | + | 0.293821i | 0.938293 | − | 0.345843i | \(-0.112407\pi\) |
−0.768655 | + | 0.639664i | \(0.779074\pi\) | |||||||
\(140\) | −4.09808 | + | 7.09808i | −0.346351 | + | 0.599897i | ||||
\(141\) | 1.09808 | + | 0.633975i | 0.0924747 | + | 0.0533903i | ||||
\(142\) | 8.19615 | 0.687806 | ||||||||
\(143\) | −15.2942 | − | 7.56218i | −1.27897 | − | 0.632381i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −4.50000 | − | 2.59808i | −0.373705 | − | 0.215758i | ||||
\(146\) | −6.06218 | + | 10.5000i | −0.501709 | + | 0.868986i | ||||
\(147\) | −7.69615 | − | 13.3301i | −0.634768 | − | 1.09945i | ||||
\(148\) | 3.00000i | 0.246598i | ||||||||
\(149\) | −15.6962 | + | 9.06218i | −1.28588 | + | 0.742403i | −0.977916 | − | 0.208996i | \(-0.932980\pi\) |
−0.307962 | + | 0.951399i | \(0.599647\pi\) | |||||||
\(150\) | 1.73205 | − | 1.00000i | 0.141421 | − | 0.0816497i | ||||
\(151\) | − | 7.26795i | − | 0.591457i | −0.955272 | − | 0.295729i | \(-0.904438\pi\) | ||
0.955272 | − | 0.295729i | \(-0.0955624\pi\) | |||||||
\(152\) | 0.633975 | + | 1.09808i | 0.0514221 | + | 0.0890657i | ||||
\(153\) | −2.59808 | + | 4.50000i | −0.210042 | + | 0.363803i | ||||
\(154\) | −19.3923 | − | 11.1962i | −1.56268 | − | 0.902212i | ||||
\(155\) | 4.39230 | 0.352798 | ||||||||
\(156\) | −3.59808 | + | 0.232051i | −0.288077 | + | 0.0185789i | ||||
\(157\) | −3.19615 | −0.255081 | −0.127540 | − | 0.991833i | \(-0.540708\pi\) | ||||
−0.127540 | + | 0.991833i | \(0.540708\pi\) | |||||||
\(158\) | −10.7321 | − | 6.19615i | −0.853796 | − | 0.492939i | ||||
\(159\) | 1.50000 | − | 2.59808i | 0.118958 | − | 0.206041i | ||||
\(160\) | 0.866025 | + | 1.50000i | 0.0684653 | + | 0.118585i | ||||
\(161\) | 10.3923i | 0.819028i | ||||||||
\(162\) | −0.866025 | + | 0.500000i | −0.0680414 | + | 0.0392837i | ||||
\(163\) | −8.19615 | + | 4.73205i | −0.641972 | + | 0.370643i | −0.785374 | − | 0.619022i | \(-0.787529\pi\) |
0.143402 | + | 0.989665i | \(0.454196\pi\) | |||||||
\(164\) | 0.464102i | 0.0362402i | ||||||||
\(165\) | −4.09808 | − | 7.09808i | −0.319035 | − | 0.552584i | ||||
\(166\) | 5.83013 | − | 10.0981i | 0.452506 | − | 0.783763i | ||||
\(167\) | −2.19615 | − | 1.26795i | −0.169943 | − | 0.0981169i | 0.412616 | − | 0.910905i | \(-0.364615\pi\) |
−0.582559 | + | 0.812788i | \(0.697949\pi\) | |||||||
\(168\) | −4.73205 | −0.365086 | ||||||||
\(169\) | 12.8923 | − | 1.66987i | 0.991716 | − | 0.128452i | ||||
\(170\) | −9.00000 | −0.690268 | ||||||||
\(171\) | −1.09808 | − | 0.633975i | −0.0839720 | − | 0.0484812i | ||||
\(172\) | −3.09808 | + | 5.36603i | −0.236226 | + | 0.409156i | ||||
\(173\) | 8.19615 | + | 14.1962i | 0.623142 | + | 1.07931i | 0.988897 | + | 0.148602i | \(0.0474774\pi\) |
−0.365755 | + | 0.930711i | \(0.619189\pi\) | |||||||
\(174\) | − | 3.00000i | − | 0.227429i | ||||||
\(175\) | −8.19615 | + | 4.73205i | −0.619571 | + | 0.357709i | ||||
\(176\) | −4.09808 | + | 2.36603i | −0.308904 | + | 0.178346i | ||||
\(177\) | 13.8564i | 1.04151i | ||||||||
\(178\) | 1.26795 | + | 2.19615i | 0.0950368 | + | 0.164609i | ||||
\(179\) | −4.09808 | + | 7.09808i | −0.306305 | + | 0.530535i | −0.977551 | − | 0.210699i | \(-0.932426\pi\) |
0.671246 | + | 0.741234i | \(0.265759\pi\) | |||||||
\(180\) | −1.50000 | − | 0.866025i | −0.111803 | − | 0.0645497i | ||||
\(181\) | 11.5885 | 0.861363 | 0.430682 | − | 0.902504i | \(-0.358273\pi\) | ||||
0.430682 | + | 0.902504i | \(0.358273\pi\) | |||||||
\(182\) | 17.0263 | − | 1.09808i | 1.26207 | − | 0.0813948i | ||||
\(183\) | −4.80385 | −0.355111 | ||||||||
\(184\) | 1.90192 | + | 1.09808i | 0.140212 | + | 0.0809513i | ||||
\(185\) | 2.59808 | − | 4.50000i | 0.191014 | − | 0.330847i | ||||
\(186\) | 1.26795 | + | 2.19615i | 0.0929705 | + | 0.161030i | ||||
\(187\) | − | 24.5885i | − | 1.79809i | ||||||
\(188\) | −1.09808 | + | 0.633975i | −0.0800854 | + | 0.0462373i | ||||
\(189\) | 4.09808 | − | 2.36603i | 0.298091 | − | 0.172103i | ||||
\(190\) | − | 2.19615i | − | 0.159326i | ||||||
\(191\) | −10.3923 | − | 18.0000i | −0.751961 | − | 1.30243i | −0.946871 | − | 0.321613i | \(-0.895775\pi\) |
0.194910 | − | 0.980821i | \(-0.437558\pi\) | |||||||
\(192\) | −0.500000 | + | 0.866025i | −0.0360844 | + | 0.0625000i | ||||
\(193\) | −11.0885 | − | 6.40192i | −0.798165 | − | 0.460821i | 0.0446644 | − | 0.999002i | \(-0.485778\pi\) |
−0.842829 | + | 0.538181i | \(0.819111\pi\) | |||||||
\(194\) | 6.00000 | 0.430775 | ||||||||
\(195\) | 5.59808 | + | 2.76795i | 0.400887 | + | 0.198217i | ||||
\(196\) | 15.3923 | 1.09945 | ||||||||
\(197\) | −6.00000 | − | 3.46410i | −0.427482 | − | 0.246807i | 0.270791 | − | 0.962638i | \(-0.412715\pi\) |
−0.698273 | + | 0.715831i | \(0.746048\pi\) | |||||||
\(198\) | 2.36603 | − | 4.09808i | 0.168146 | − | 0.291238i | ||||
\(199\) | 4.29423 | + | 7.43782i | 0.304410 | + | 0.527253i | 0.977130 | − | 0.212644i | \(-0.0682074\pi\) |
−0.672720 | + | 0.739897i | \(0.734874\pi\) | |||||||
\(200\) | 2.00000i | 0.141421i | ||||||||
\(201\) | −9.29423 | + | 5.36603i | −0.655564 | + | 0.378490i | ||||
\(202\) | −1.20577 | + | 0.696152i | −0.0848378 | + | 0.0489811i | ||||
\(203\) | 14.1962i | 0.996375i | ||||||||
\(204\) | −2.59808 | − | 4.50000i | −0.181902 | − | 0.315063i | ||||
\(205\) | 0.401924 | − | 0.696152i | 0.0280716 | − | 0.0486214i | ||||
\(206\) | 3.63397 | + | 2.09808i | 0.253191 | + | 0.146180i | ||||
\(207\) | −2.19615 | −0.152643 | ||||||||
\(208\) | 1.59808 | − | 3.23205i | 0.110807 | − | 0.224102i | ||||
\(209\) | 6.00000 | 0.415029 | ||||||||
\(210\) | 7.09808 | + | 4.09808i | 0.489814 | + | 0.282794i | ||||
\(211\) | 1.80385 | − | 3.12436i | 0.124182 | − | 0.215090i | −0.797231 | − | 0.603674i | \(-0.793703\pi\) |
0.921413 | + | 0.388585i | \(0.127036\pi\) | |||||||
\(212\) | 1.50000 | + | 2.59808i | 0.103020 | + | 0.178437i | ||||
\(213\) | − | 8.19615i | − | 0.561591i | ||||||
\(214\) | −7.09808 | + | 4.09808i | −0.485215 | + | 0.280139i | ||||
\(215\) | 9.29423 | − | 5.36603i | 0.633861 | − | 0.365960i | ||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | −6.00000 | − | 10.3923i | −0.407307 | − | 0.705476i | ||||
\(218\) | −8.19615 | + | 14.1962i | −0.555113 | + | 0.961485i | ||||
\(219\) | 10.5000 | + | 6.06218i | 0.709524 | + | 0.409644i | ||||
\(220\) | 8.19615 | 0.552584 | ||||||||
\(221\) | 10.3923 | + | 15.5885i | 0.699062 | + | 1.04859i | ||||
\(222\) | 3.00000 | 0.201347 | ||||||||
\(223\) | 16.3923 | + | 9.46410i | 1.09771 | + | 0.633763i | 0.935619 | − | 0.353013i | \(-0.114843\pi\) |
0.162091 | + | 0.986776i | \(0.448176\pi\) | |||||||
\(224\) | 2.36603 | − | 4.09808i | 0.158087 | − | 0.273814i | ||||
\(225\) | −1.00000 | − | 1.73205i | −0.0666667 | − | 0.115470i | ||||
\(226\) | − | 11.1962i | − | 0.744757i | ||||||
\(227\) | −8.49038 | + | 4.90192i | −0.563526 | + | 0.325352i | −0.754560 | − | 0.656231i | \(-0.772149\pi\) |
0.191033 | + | 0.981584i | \(0.438816\pi\) | |||||||
\(228\) | 1.09808 | − | 0.633975i | 0.0727219 | − | 0.0419860i | ||||
\(229\) | − | 19.8564i | − | 1.31215i | −0.754696 | − | 0.656074i | \(-0.772216\pi\) | ||
0.754696 | − | 0.656074i | \(-0.227784\pi\) | |||||||
\(230\) | −1.90192 | − | 3.29423i | −0.125409 | − | 0.217215i | ||||
\(231\) | −11.1962 | + | 19.3923i | −0.736653 | + | 1.27592i | ||||
\(232\) | 2.59808 | + | 1.50000i | 0.170572 | + | 0.0984798i | ||||
\(233\) | 18.0000 | 1.17922 | 0.589610 | − | 0.807688i | \(-0.299282\pi\) | ||||
0.589610 | + | 0.807688i | \(0.299282\pi\) | |||||||
\(234\) | 0.232051 | + | 3.59808i | 0.0151696 | + | 0.235214i | ||||
\(235\) | 2.19615 | 0.143261 | ||||||||
\(236\) | −12.0000 | − | 6.92820i | −0.781133 | − | 0.450988i | ||||
\(237\) | −6.19615 | + | 10.7321i | −0.402483 | + | 0.697122i | ||||
\(238\) | 12.2942 | + | 21.2942i | 0.796916 | + | 1.38030i | ||||
\(239\) | − | 24.5885i | − | 1.59050i | −0.606285 | − | 0.795248i | \(-0.707341\pi\) | ||
0.606285 | − | 0.795248i | \(-0.292659\pi\) | |||||||
\(240\) | 1.50000 | − | 0.866025i | 0.0968246 | − | 0.0559017i | ||||
\(241\) | −0.696152 | + | 0.401924i | −0.0448431 | + | 0.0258902i | −0.522254 | − | 0.852790i | \(-0.674909\pi\) |
0.477411 | + | 0.878680i | \(0.341575\pi\) | |||||||
\(242\) | 11.3923i | 0.732325i | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 2.40192 | − | 4.16025i | 0.153767 | − | 0.266333i | ||||
\(245\) | −23.0885 | − | 13.3301i | −1.47507 | − | 0.851631i | ||||
\(246\) | 0.464102 | 0.0295900 | ||||||||
\(247\) | −3.80385 | + | 2.53590i | −0.242033 | + | 0.161355i | ||||
\(248\) | −2.53590 | −0.161030 | ||||||||
\(249\) | −10.0981 | − | 5.83013i | −0.639940 | − | 0.369469i | ||||
\(250\) | 6.06218 | − | 10.5000i | 0.383406 | − | 0.664078i | ||||
\(251\) | −2.19615 | − | 3.80385i | −0.138620 | − | 0.240097i | 0.788355 | − | 0.615221i | \(-0.210933\pi\) |
−0.926974 | + | 0.375124i | \(0.877600\pi\) | |||||||
\(252\) | 4.73205i | 0.298091i | ||||||||
\(253\) | 9.00000 | − | 5.19615i | 0.565825 | − | 0.326679i | ||||
\(254\) | −3.46410 | + | 2.00000i | −0.217357 | + | 0.125491i | ||||
\(255\) | 9.00000i | 0.563602i | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 6.40192 | − | 11.0885i | 0.399341 | − | 0.691679i | −0.594304 | − | 0.804241i | \(-0.702572\pi\) |
0.993645 | + | 0.112562i | \(0.0359056\pi\) | |||||||
\(258\) | 5.36603 | + | 3.09808i | 0.334074 | + | 0.192878i | ||||
\(259\) | −14.1962 | −0.882106 | ||||||||
\(260\) | −5.19615 | + | 3.46410i | −0.322252 | + | 0.214834i | ||||
\(261\) | −3.00000 | −0.185695 | ||||||||
\(262\) | 14.1962 | + | 8.19615i | 0.877041 | + | 0.506360i | ||||
\(263\) | 1.09808 | − | 1.90192i | 0.0677103 | − | 0.117278i | −0.830183 | − | 0.557491i | \(-0.811764\pi\) |
0.897893 | + | 0.440214i | \(0.145097\pi\) | |||||||
\(264\) | 2.36603 | + | 4.09808i | 0.145619 | + | 0.252219i | ||||
\(265\) | − | 5.19615i | − | 0.319197i | ||||||
\(266\) | −5.19615 | + | 3.00000i | −0.318597 | + | 0.183942i | ||||
\(267\) | 2.19615 | − | 1.26795i | 0.134402 | − | 0.0775972i | ||||
\(268\) | − | 10.7321i | − | 0.655564i | ||||||
\(269\) | 14.1962 | + | 24.5885i | 0.865555 | + | 1.49918i | 0.866495 | + | 0.499185i | \(0.166367\pi\) |
−0.000940662 | 1.00000i | \(0.500299\pi\) | ||||||||
\(270\) | −0.866025 | + | 1.50000i | −0.0527046 | + | 0.0912871i | ||||
\(271\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(272\) | 5.19615 | 0.315063 | ||||||||
\(273\) | −1.09808 | − | 17.0263i | −0.0664586 | − | 1.03048i | ||||
\(274\) | 9.00000 | 0.543710 | ||||||||
\(275\) | 8.19615 | + | 4.73205i | 0.494247 | + | 0.285353i | ||||
\(276\) | 1.09808 | − | 1.90192i | 0.0660964 | − | 0.114482i | ||||
\(277\) | 7.59808 | + | 13.1603i | 0.456524 | + | 0.790723i | 0.998774 | − | 0.0494940i | \(-0.0157609\pi\) |
−0.542250 | + | 0.840217i | \(0.682428\pi\) | |||||||
\(278\) | 4.00000i | 0.239904i | ||||||||
\(279\) | 2.19615 | − | 1.26795i | 0.131480 | − | 0.0759101i | ||||
\(280\) | −7.09808 | + | 4.09808i | −0.424191 | + | 0.244907i | ||||
\(281\) | − | 24.4641i | − | 1.45941i | −0.683764 | − | 0.729703i | \(-0.739658\pi\) | ||
0.683764 | − | 0.729703i | \(-0.260342\pi\) | |||||||
\(282\) | 0.633975 | + | 1.09808i | 0.0377526 | + | 0.0653895i | ||||
\(283\) | −15.0981 | + | 26.1506i | −0.897487 | + | 1.55449i | −0.0667919 | + | 0.997767i | \(0.521276\pi\) |
−0.830696 | + | 0.556727i | \(0.812057\pi\) | |||||||
\(284\) | 7.09808 | + | 4.09808i | 0.421193 | + | 0.243176i | ||||
\(285\) | −2.19615 | −0.130089 | ||||||||
\(286\) | −9.46410 | − | 14.1962i | −0.559624 | − | 0.839436i | ||||
\(287\) | −2.19615 | −0.129635 | ||||||||
\(288\) | 0.866025 | + | 0.500000i | 0.0510310 | + | 0.0294628i | ||||
\(289\) | −5.00000 | + | 8.66025i | −0.294118 | + | 0.509427i | ||||
\(290\) | −2.59808 | − | 4.50000i | −0.152564 | − | 0.264249i | ||||
\(291\) | − | 6.00000i | − | 0.351726i | ||||||
\(292\) | −10.5000 | + | 6.06218i | −0.614466 | + | 0.354762i | ||||
\(293\) | 12.6962 | − | 7.33013i | 0.741717 | − | 0.428231i | −0.0809762 | − | 0.996716i | \(-0.525804\pi\) |
0.822693 | + | 0.568485i | \(0.192470\pi\) | |||||||
\(294\) | − | 15.3923i | − | 0.897697i | ||||||
\(295\) | 12.0000 | + | 20.7846i | 0.698667 | + | 1.21013i | ||||
\(296\) | −1.50000 | + | 2.59808i | −0.0871857 | + | 0.151010i | ||||
\(297\) | −4.09808 | − | 2.36603i | −0.237795 | − | 0.137291i | ||||
\(298\) | −18.1244 | −1.04992 | ||||||||
\(299\) | −3.50962 | + | 7.09808i | −0.202967 | + | 0.410492i | ||||
\(300\) | 2.00000 | 0.115470 | ||||||||
\(301\) | −25.3923 | − | 14.6603i | −1.46359 | − | 0.845003i | ||||
\(302\) | 3.63397 | − | 6.29423i | 0.209112 | − | 0.362192i | ||||
\(303\) | 0.696152 | + | 1.20577i | 0.0399929 | + | 0.0692698i | ||||
\(304\) | 1.26795i | 0.0727219i | ||||||||
\(305\) | −7.20577 | + | 4.16025i | −0.412601 | + | 0.238215i | ||||
\(306\) | −4.50000 | + | 2.59808i | −0.257248 | + | 0.148522i | ||||
\(307\) | − | 10.7321i | − | 0.612510i | −0.951949 | − | 0.306255i | \(-0.900924\pi\) | ||
0.951949 | − | 0.306255i | \(-0.0990761\pi\) | |||||||
\(308\) | −11.1962 | − | 19.3923i | −0.637960 | − | 1.10498i | ||||
\(309\) | 2.09808 | − | 3.63397i | 0.119355 | − | 0.206730i | ||||
\(310\) | 3.80385 | + | 2.19615i | 0.216044 | + | 0.124733i | ||||
\(311\) | −2.19615 | −0.124532 | −0.0622662 | − | 0.998060i | \(-0.519833\pi\) | ||||
−0.0622662 | + | 0.998060i | \(0.519833\pi\) | |||||||
\(312\) | −3.23205 | − | 1.59808i | −0.182979 | − | 0.0904732i | ||||
\(313\) | −24.3923 | −1.37873 | −0.689367 | − | 0.724412i | \(-0.742111\pi\) | ||||
−0.689367 | + | 0.724412i | \(0.742111\pi\) | |||||||
\(314\) | −2.76795 | − | 1.59808i | −0.156204 | − | 0.0901847i | ||||
\(315\) | 4.09808 | − | 7.09808i | 0.230900 | − | 0.399931i | ||||
\(316\) | −6.19615 | − | 10.7321i | −0.348561 | − | 0.603725i | ||||
\(317\) | 6.12436i | 0.343978i | 0.985099 | + | 0.171989i | \(0.0550194\pi\) | ||||
−0.985099 | + | 0.171989i | \(0.944981\pi\) | |||||||
\(318\) | 2.59808 | − | 1.50000i | 0.145693 | − | 0.0841158i | ||||
\(319\) | 12.2942 | − | 7.09808i | 0.688345 | − | 0.397416i | ||||
\(320\) | 1.73205i | 0.0968246i | ||||||||
\(321\) | 4.09808 | + | 7.09808i | 0.228732 | + | 0.396176i | ||||
\(322\) | −5.19615 | + | 9.00000i | −0.289570 | + | 0.501550i | ||||
\(323\) | −5.70577 | − | 3.29423i | −0.317478 | − | 0.183296i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | −7.19615 | + | 0.464102i | −0.399171 | + | 0.0257437i | ||||
\(326\) | −9.46410 | −0.524168 | ||||||||
\(327\) | 14.1962 | + | 8.19615i | 0.785049 | + | 0.453248i | ||||
\(328\) | −0.232051 | + | 0.401924i | −0.0128129 | + | 0.0221925i | ||||
\(329\) | −3.00000 | − | 5.19615i | −0.165395 | − | 0.286473i | ||||
\(330\) | − | 8.19615i | − | 0.451183i | ||||||
\(331\) | 10.3923 | − | 6.00000i | 0.571213 | − | 0.329790i | −0.186421 | − | 0.982470i | \(-0.559689\pi\) |
0.757634 | + | 0.652680i | \(0.226355\pi\) | |||||||
\(332\) | 10.0981 | − | 5.83013i | 0.554204 | − | 0.319970i | ||||
\(333\) | − | 3.00000i | − | 0.164399i | ||||||
\(334\) | −1.26795 | − | 2.19615i | −0.0693791 | − | 0.120168i | ||||
\(335\) | −9.29423 | + | 16.0981i | −0.507798 | + | 0.879532i | ||||
\(336\) | −4.09808 | − | 2.36603i | −0.223568 | − | 0.129077i | ||||
\(337\) | 31.0000 | 1.68868 | 0.844339 | − | 0.535810i | \(-0.179994\pi\) | ||||
0.844339 | + | 0.535810i | \(0.179994\pi\) | |||||||
\(338\) | 12.0000 | + | 5.00000i | 0.652714 | + | 0.271964i | ||||
\(339\) | −11.1962 | −0.608092 | ||||||||
\(340\) | −7.79423 | − | 4.50000i | −0.422701 | − | 0.244047i | ||||
\(341\) | −6.00000 | + | 10.3923i | −0.324918 | + | 0.562775i | ||||
\(342\) | −0.633975 | − | 1.09808i | −0.0342814 | − | 0.0593772i | ||||
\(343\) | 39.7128i | 2.14429i | ||||||||
\(344\) | −5.36603 | + | 3.09808i | −0.289317 | + | 0.167037i | ||||
\(345\) | −3.29423 | + | 1.90192i | −0.177355 | + | 0.102396i | ||||
\(346\) | 16.3923i | 0.881256i | ||||||||
\(347\) | 6.29423 | + | 10.9019i | 0.337892 | + | 0.585246i | 0.984036 | − | 0.177969i | \(-0.0569528\pi\) |
−0.646144 | + | 0.763215i | \(0.723620\pi\) | |||||||
\(348\) | 1.50000 | − | 2.59808i | 0.0804084 | − | 0.139272i | ||||
\(349\) | 2.19615 | + | 1.26795i | 0.117557 | + | 0.0678718i | 0.557626 | − | 0.830093i | \(-0.311712\pi\) |
−0.440068 | + | 0.897964i | \(0.645046\pi\) | |||||||
\(350\) | −9.46410 | −0.505878 | ||||||||
\(351\) | 3.59808 | − | 0.232051i | 0.192051 | − | 0.0123860i | ||||
\(352\) | −4.73205 | −0.252219 | ||||||||
\(353\) | −5.00962 | − | 2.89230i | −0.266635 | − | 0.153942i | 0.360722 | − | 0.932673i | \(-0.382530\pi\) |
−0.627358 | + | 0.778731i | \(0.715864\pi\) | |||||||
\(354\) | −6.92820 | + | 12.0000i | −0.368230 | + | 0.637793i | ||||
\(355\) | −7.09808 | − | 12.2942i | −0.376727 | − | 0.652510i | ||||
\(356\) | 2.53590i | 0.134402i | ||||||||
\(357\) | 21.2942 | − | 12.2942i | 1.12701 | − | 0.650680i | ||||
\(358\) | −7.09808 | + | 4.09808i | −0.375145 | + | 0.216590i | ||||
\(359\) | − | 22.0526i | − | 1.16389i | −0.813228 | − | 0.581945i | \(-0.802292\pi\) | ||
0.813228 | − | 0.581945i | \(-0.197708\pi\) | |||||||
\(360\) | −0.866025 | − | 1.50000i | −0.0456435 | − | 0.0790569i | ||||
\(361\) | −8.69615 | + | 15.0622i | −0.457692 | + | 0.792746i | ||||
\(362\) | 10.0359 | + | 5.79423i | 0.527475 | + | 0.304538i | ||||
\(363\) | 11.3923 | 0.597941 | ||||||||
\(364\) | 15.2942 | + | 7.56218i | 0.801635 | + | 0.396366i | ||||
\(365\) | 21.0000 | 1.09919 | ||||||||
\(366\) | −4.16025 | − | 2.40192i | −0.217460 | − | 0.125551i | ||||
\(367\) | 12.0981 | − | 20.9545i | 0.631514 | − | 1.09382i | −0.355728 | − | 0.934590i | \(-0.615767\pi\) |
0.987242 | − | 0.159225i | \(-0.0508997\pi\) | |||||||
\(368\) | 1.09808 | + | 1.90192i | 0.0572412 | + | 0.0991446i | ||||
\(369\) | − | 0.464102i | − | 0.0241602i | ||||||
\(370\) | 4.50000 | − | 2.59808i | 0.233944 | − | 0.135068i | ||||
\(371\) | −12.2942 | + | 7.09808i | −0.638285 | + | 0.368514i | ||||
\(372\) | 2.53590i | 0.131480i | ||||||||
\(373\) | −11.9904 | − | 20.7679i | −0.620838 | − | 1.07532i | −0.989330 | − | 0.145693i | \(-0.953459\pi\) |
0.368492 | − | 0.929631i | \(-0.379874\pi\) | |||||||
\(374\) | 12.2942 | − | 21.2942i | 0.635719 | − | 1.10110i | ||||
\(375\) | −10.5000 | − | 6.06218i | −0.542218 | − | 0.313050i | ||||
\(376\) | −1.26795 | −0.0653895 | ||||||||
\(377\) | −4.79423 | + | 9.69615i | −0.246915 | + | 0.499377i | ||||
\(378\) | 4.73205 | 0.243390 | ||||||||
\(379\) | 15.8038 | + | 9.12436i | 0.811789 | + | 0.468687i | 0.847577 | − | 0.530673i | \(-0.178061\pi\) |
−0.0357877 | + | 0.999359i | \(0.511394\pi\) | |||||||
\(380\) | 1.09808 | − | 1.90192i | 0.0563301 | − | 0.0975666i | ||||
\(381\) | 2.00000 | + | 3.46410i | 0.102463 | + | 0.177471i | ||||
\(382\) | − | 20.7846i | − | 1.06343i | ||||||
\(383\) | 9.80385 | − | 5.66025i | 0.500953 | − | 0.289225i | −0.228154 | − | 0.973625i | \(-0.573269\pi\) |
0.729107 | + | 0.684400i | \(0.239936\pi\) | |||||||
\(384\) | −0.866025 | + | 0.500000i | −0.0441942 | + | 0.0255155i | ||||
\(385\) | 38.7846i | 1.97665i | ||||||||
\(386\) | −6.40192 | − | 11.0885i | −0.325849 | − | 0.564388i | ||||
\(387\) | 3.09808 | − | 5.36603i | 0.157484 | − | 0.272770i | ||||
\(388\) | 5.19615 | + | 3.00000i | 0.263795 | + | 0.152302i | ||||
\(389\) | 13.3923 | 0.679017 | 0.339508 | − | 0.940603i | \(-0.389739\pi\) | ||||
0.339508 | + | 0.940603i | \(0.389739\pi\) | |||||||
\(390\) | 3.46410 | + | 5.19615i | 0.175412 | + | 0.263117i | ||||
\(391\) | −11.4115 | −0.577107 | ||||||||
\(392\) | 13.3301 | + | 7.69615i | 0.673273 | + | 0.388714i | ||||
\(393\) | 8.19615 | − | 14.1962i | 0.413441 | − | 0.716101i | ||||
\(394\) | −3.46410 | − | 6.00000i | −0.174519 | − | 0.302276i | ||||
\(395\) | 21.4641i | 1.07998i | ||||||||
\(396\) | 4.09808 | − | 2.36603i | 0.205936 | − | 0.118897i | ||||
\(397\) | 14.1962 | − | 8.19615i | 0.712484 | − | 0.411353i | −0.0994958 | − | 0.995038i | \(-0.531723\pi\) |
0.811980 | + | 0.583685i | \(0.198390\pi\) | |||||||
\(398\) | 8.58846i | 0.430500i | ||||||||
\(399\) | 3.00000 | + | 5.19615i | 0.150188 | + | 0.260133i | ||||
\(400\) | −1.00000 | + | 1.73205i | −0.0500000 | + | 0.0866025i | ||||
\(401\) | 18.1865 | + | 10.5000i | 0.908192 | + | 0.524345i | 0.879849 | − | 0.475253i | \(-0.157644\pi\) |
0.0283431 | + | 0.999598i | \(0.490977\pi\) | |||||||
\(402\) | −10.7321 | −0.535266 | ||||||||
\(403\) | −0.588457 | − | 9.12436i | −0.0293131 | − | 0.454517i | ||||
\(404\) | −1.39230 | −0.0692698 | ||||||||
\(405\) | 1.50000 | + | 0.866025i | 0.0745356 | + | 0.0430331i | ||||
\(406\) | −7.09808 | + | 12.2942i | −0.352272 | + | 0.610152i | ||||
\(407\) | 7.09808 | + | 12.2942i | 0.351839 | + | 0.609402i | ||||
\(408\) | − | 5.19615i | − | 0.257248i | ||||||
\(409\) | −2.89230 | + | 1.66987i | −0.143015 | + | 0.0825699i | −0.569800 | − | 0.821783i | \(-0.692979\pi\) |
0.426785 | + | 0.904353i | \(0.359646\pi\) | |||||||
\(410\) | 0.696152 | − | 0.401924i | 0.0343805 | − | 0.0198496i | ||||
\(411\) | − | 9.00000i | − | 0.443937i | ||||||
\(412\) | 2.09808 | + | 3.63397i | 0.103365 | + | 0.179033i | ||||
\(413\) | 32.7846 | − | 56.7846i | 1.61323 | − | 2.79419i | ||||
\(414\) | −1.90192 | − | 1.09808i | −0.0934745 | − | 0.0539675i | ||||
\(415\) | −20.1962 | −0.991390 | ||||||||
\(416\) | 3.00000 | − | 2.00000i | 0.147087 | − | 0.0980581i | ||||
\(417\) | 4.00000 | 0.195881 | ||||||||
\(418\) | 5.19615 | + | 3.00000i | 0.254152 | + | 0.146735i | ||||
\(419\) | −8.19615 | + | 14.1962i | −0.400408 | + | 0.693527i | −0.993775 | − | 0.111405i | \(-0.964465\pi\) |
0.593367 | + | 0.804932i | \(0.297798\pi\) | |||||||
\(420\) | 4.09808 | + | 7.09808i | 0.199966 | + | 0.346351i | ||||
\(421\) | 0.464102i | 0.0226189i | 0.999936 | + | 0.0113095i | \(0.00359999\pi\) | ||||
−0.999936 | + | 0.0113095i | \(0.996400\pi\) | |||||||
\(422\) | 3.12436 | − | 1.80385i | 0.152091 | − | 0.0878099i | ||||
\(423\) | 1.09808 | − | 0.633975i | 0.0533903 | − | 0.0308249i | ||||
\(424\) | 3.00000i | 0.145693i | ||||||||
\(425\) | −5.19615 | − | 9.00000i | −0.252050 | − | 0.436564i | ||||
\(426\) | 4.09808 | − | 7.09808i | 0.198552 | − | 0.343903i | ||||
\(427\) | 19.6865 | + | 11.3660i | 0.952698 | + | 0.550041i | ||||
\(428\) | −8.19615 | −0.396176 | ||||||||
\(429\) | −14.1962 | + | 9.46410i | −0.685397 | + | 0.456931i | ||||
\(430\) | 10.7321 | 0.517545 | ||||||||
\(431\) | −24.0788 | − | 13.9019i | −1.15984 | − | 0.669632i | −0.208572 | − | 0.978007i | \(-0.566882\pi\) |
−0.951265 | + | 0.308375i | \(0.900215\pi\) | |||||||
\(432\) | 0.500000 | − | 0.866025i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | −16.8923 | − | 29.2583i | −0.811792 | − | 1.40607i | −0.911608 | − | 0.411060i | \(-0.865159\pi\) |
0.0998161 | − | 0.995006i | \(-0.468175\pi\) | |||||||
\(434\) | − | 12.0000i | − | 0.576018i | ||||||
\(435\) | −4.50000 | + | 2.59808i | −0.215758 | + | 0.124568i | ||||
\(436\) | −14.1962 | + | 8.19615i | −0.679872 | + | 0.392525i | ||||
\(437\) | − | 2.78461i | − | 0.133206i | ||||||
\(438\) | 6.06218 | + | 10.5000i | 0.289662 | + | 0.501709i | ||||
\(439\) | 8.29423 | − | 14.3660i | 0.395862 | − | 0.685653i | −0.597349 | − | 0.801982i | \(-0.703779\pi\) |
0.993211 | + | 0.116329i | \(0.0371125\pi\) | |||||||
\(440\) | 7.09808 | + | 4.09808i | 0.338388 | + | 0.195368i | ||||
\(441\) | −15.3923 | −0.732967 | ||||||||
\(442\) | 1.20577 | + | 18.6962i | 0.0573527 | + | 0.889285i | ||||
\(443\) | −4.39230 | −0.208685 | −0.104342 | − | 0.994541i | \(-0.533274\pi\) | ||||
−0.104342 | + | 0.994541i | \(0.533274\pi\) | |||||||
\(444\) | 2.59808 | + | 1.50000i | 0.123299 | + | 0.0711868i | ||||
\(445\) | 2.19615 | − | 3.80385i | 0.104108 | − | 0.180320i | ||||
\(446\) | 9.46410 | + | 16.3923i | 0.448138 | + | 0.776198i | ||||
\(447\) | 18.1244i | 0.857253i | ||||||||
\(448\) | 4.09808 | − | 2.36603i | 0.193616 | − | 0.111784i | ||||
\(449\) | −28.9808 | + | 16.7321i | −1.36769 | + | 0.789634i | −0.990632 | − | 0.136557i | \(-0.956396\pi\) |
−0.377054 | + | 0.926191i | \(0.623063\pi\) | |||||||
\(450\) | − | 2.00000i | − | 0.0942809i | ||||||
\(451\) | 1.09808 | + | 1.90192i | 0.0517064 | + | 0.0895581i | ||||
\(452\) | 5.59808 | − | 9.69615i | 0.263311 | − | 0.456069i | ||||
\(453\) | −6.29423 | − | 3.63397i | −0.295729 | − | 0.170739i | ||||
\(454\) | −9.80385 | −0.460117 | ||||||||
\(455\) | −16.3923 | − | 24.5885i | −0.768483 | − | 1.15272i | ||||
\(456\) | 1.26795 | 0.0593772 | ||||||||
\(457\) | −17.3038 | − | 9.99038i | −0.809440 | − | 0.467330i | 0.0373215 | − | 0.999303i | \(-0.488117\pi\) |
−0.846761 | + | 0.531973i | \(0.821451\pi\) | |||||||
\(458\) | 9.92820 | − | 17.1962i | 0.463914 | − | 0.803523i | ||||
\(459\) | 2.59808 | + | 4.50000i | 0.121268 | + | 0.210042i | ||||
\(460\) | − | 3.80385i | − | 0.177355i | ||||||
\(461\) | −17.3038 | + | 9.99038i | −0.805921 | + | 0.465298i | −0.845537 | − | 0.533917i | \(-0.820720\pi\) |
0.0396167 | + | 0.999215i | \(0.487386\pi\) | |||||||
\(462\) | −19.3923 | + | 11.1962i | −0.902212 | + | 0.520892i | ||||
\(463\) | 26.1962i | 1.21744i | 0.793386 | + | 0.608719i | \(0.208316\pi\) | ||||
−0.793386 | + | 0.608719i | \(0.791684\pi\) | |||||||
\(464\) | 1.50000 | + | 2.59808i | 0.0696358 | + | 0.120613i | ||||
\(465\) | 2.19615 | − | 3.80385i | 0.101844 | − | 0.176399i | ||||
\(466\) | 15.5885 | + | 9.00000i | 0.722121 | + | 0.416917i | ||||
\(467\) | −36.5885 | −1.69311 | −0.846556 | − | 0.532300i | \(-0.821328\pi\) | ||||
−0.846556 | + | 0.532300i | \(0.821328\pi\) | |||||||
\(468\) | −1.59808 | + | 3.23205i | −0.0738711 | + | 0.149402i | ||||
\(469\) | 50.7846 | 2.34502 | ||||||||
\(470\) | 1.90192 | + | 1.09808i | 0.0877292 | + | 0.0506505i | ||||
\(471\) | −1.59808 | + | 2.76795i | −0.0736355 | + | 0.127540i | ||||
\(472\) | −6.92820 | − | 12.0000i | −0.318896 | − | 0.552345i | ||||
\(473\) | 29.3205i | 1.34816i | ||||||||
\(474\) | −10.7321 | + | 6.19615i | −0.492939 | + | 0.284599i | ||||
\(475\) | 2.19615 | − | 1.26795i | 0.100766 | − | 0.0581775i | ||||
\(476\) | 24.5885i | 1.12701i | ||||||||
\(477\) | −1.50000 | − | 2.59808i | −0.0686803 | − | 0.118958i | ||||
\(478\) | 12.2942 | − | 21.2942i | 0.562325 | − | 0.973975i | ||||
\(479\) | −30.5885 | − | 17.6603i | −1.39762 | − | 0.806918i | −0.403479 | − | 0.914989i | \(-0.632199\pi\) |
−0.994143 | + | 0.108071i | \(0.965533\pi\) | |||||||
\(480\) | 1.73205 | 0.0790569 | ||||||||
\(481\) | −9.69615 | − | 4.79423i | −0.442106 | − | 0.218598i | ||||
\(482\) | −0.803848 | −0.0366143 | ||||||||
\(483\) | 9.00000 | + | 5.19615i | 0.409514 | + | 0.236433i | ||||
\(484\) | −5.69615 | + | 9.86603i | −0.258916 | + | 0.448456i | ||||
\(485\) | −5.19615 | − | 9.00000i | −0.235945 | − | 0.408669i | ||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | 7.90192 | − | 4.56218i | 0.358070 | − | 0.206732i | −0.310164 | − | 0.950683i | \(-0.600384\pi\) |
0.668234 | + | 0.743951i | \(0.267051\pi\) | |||||||
\(488\) | 4.16025 | − | 2.40192i | 0.188326 | − | 0.108730i | ||||
\(489\) | 9.46410i | 0.427981i | ||||||||
\(490\) | −13.3301 | − | 23.0885i | −0.602194 | − | 1.04303i | ||||
\(491\) | 0.294229 | − | 0.509619i | 0.0132784 | − | 0.0229988i | −0.859310 | − | 0.511455i | \(-0.829107\pi\) |
0.872588 | + | 0.488457i | \(0.162440\pi\) | |||||||
\(492\) | 0.401924 | + | 0.232051i | 0.0181201 | + | 0.0104617i | ||||
\(493\) | −15.5885 | −0.702069 | ||||||||
\(494\) | −4.56218 | + | 0.294229i | −0.205262 | + | 0.0132380i | ||||
\(495\) | −8.19615 | −0.368390 | ||||||||
\(496\) | −2.19615 | − | 1.26795i | −0.0986102 | − | 0.0569326i | ||||
\(497\) | −19.3923 | + | 33.5885i | −0.869864 | + | 1.50665i | ||||
\(498\) | −5.83013 | − | 10.0981i | −0.261254 | − | 0.452506i | ||||
\(499\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(500\) | 10.5000 | − | 6.06218i | 0.469574 | − | 0.271109i | ||||
\(501\) | −2.19615 | + | 1.26795i | −0.0981169 | + | 0.0566478i | ||||
\(502\) | − | 4.39230i | − | 0.196038i | ||||||
\(503\) | 9.29423 | + | 16.0981i | 0.414409 | + | 0.717778i | 0.995366 | − | 0.0961565i | \(-0.0306549\pi\) |
−0.580957 | + | 0.813934i | \(0.697322\pi\) | |||||||
\(504\) | −2.36603 | + | 4.09808i | −0.105391 | + | 0.182543i | ||||
\(505\) | 2.08846 | + | 1.20577i | 0.0929351 | + | 0.0536561i | ||||
\(506\) | 10.3923 | 0.461994 | ||||||||
\(507\) | 5.00000 | − | 12.0000i | 0.222058 | − | 0.532939i | ||||
\(508\) | −4.00000 | −0.177471 | ||||||||
\(509\) | −8.08846 | − | 4.66987i | −0.358515 | − | 0.206988i | 0.309914 | − | 0.950764i | \(-0.399700\pi\) |
−0.668429 | + | 0.743776i | \(0.733033\pi\) | |||||||
\(510\) | −4.50000 | + | 7.79423i | −0.199263 | + | 0.345134i | ||||
\(511\) | −28.6865 | − | 49.6865i | −1.26902 | − | 2.19800i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −1.09808 | + | 0.633975i | −0.0484812 | + | 0.0279907i | ||||
\(514\) | 11.0885 | − | 6.40192i | 0.489091 | − | 0.282377i | ||||
\(515\) | − | 7.26795i | − | 0.320264i | ||||||
\(516\) | 3.09808 | + | 5.36603i | 0.136385 | + | 0.236226i | ||||
\(517\) | −3.00000 | + | 5.19615i | −0.131940 | + | 0.228527i | ||||
\(518\) | −12.2942 | − | 7.09808i | −0.540177 | − | 0.311872i | ||||
\(519\) | 16.3923 | 0.719542 | ||||||||
\(520\) | −6.23205 | + | 0.401924i | −0.273294 | + | 0.0176255i | ||||
\(521\) | −18.8038 | −0.823812 | −0.411906 | − | 0.911226i | \(-0.635137\pi\) | ||||
−0.411906 | + | 0.911226i | \(0.635137\pi\) | |||||||
\(522\) | −2.59808 | − | 1.50000i | −0.113715 | − | 0.0656532i | ||||
\(523\) | −0.705771 | + | 1.22243i | −0.0308612 | + | 0.0534532i | −0.881044 | − | 0.473035i | \(-0.843158\pi\) |
0.850182 | + | 0.526488i | \(0.176492\pi\) | |||||||
\(524\) | 8.19615 | + | 14.1962i | 0.358051 | + | 0.620162i | ||||
\(525\) | 9.46410i | 0.413047i | ||||||||
\(526\) | 1.90192 | − | 1.09808i | 0.0829278 | − | 0.0478784i | ||||
\(527\) | 11.4115 | − | 6.58846i | 0.497095 | − | 0.286998i | ||||
\(528\) | 4.73205i | 0.205936i | ||||||||
\(529\) | 9.08846 | + | 15.7417i | 0.395150 | + | 0.684420i | ||||
\(530\) | 2.59808 | − | 4.50000i | 0.112853 | − | 0.195468i | ||||
\(531\) | 12.0000 | + | 6.92820i | 0.520756 | + | 0.300658i | ||||
\(532\) | −6.00000 | −0.260133 | ||||||||
\(533\) | −1.50000 | − | 0.741670i | −0.0649722 | − | 0.0321253i | ||||
\(534\) | 2.53590 | 0.109739 | ||||||||
\(535\) | 12.2942 | + | 7.09808i | 0.531526 | + | 0.306877i | ||||
\(536\) | 5.36603 | − | 9.29423i | 0.231777 | − | 0.401450i | ||||
\(537\) | 4.09808 | + | 7.09808i | 0.176845 | + | 0.306305i | ||||
\(538\) | 28.3923i | 1.22408i | ||||||||
\(539\) | 63.0788 | − | 36.4186i | 2.71700 | − | 1.56866i | ||||
\(540\) | −1.50000 | + | 0.866025i | −0.0645497 | + | 0.0372678i | ||||
\(541\) | − | 16.8564i | − | 0.724714i | −0.932039 | − | 0.362357i | \(-0.881972\pi\) | ||
0.932039 | − | 0.362357i | \(-0.118028\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.79423 | − | 10.0359i | 0.248654 | − | 0.430682i | ||||
\(544\) | 4.50000 | + | 2.59808i | 0.192936 | + | 0.111392i | ||||
\(545\) | 28.3923 | 1.21619 | ||||||||
\(546\) | 7.56218 | − | 15.2942i | 0.323631 | − | 0.654533i | ||||
\(547\) | −6.19615 | −0.264928 | −0.132464 | − | 0.991188i | \(-0.542289\pi\) | ||||
−0.132464 | + | 0.991188i | \(0.542289\pi\) | |||||||
\(548\) | 7.79423 | + | 4.50000i | 0.332953 | + | 0.192230i | ||||
\(549\) | −2.40192 | + | 4.16025i | −0.102512 | + | 0.177555i | ||||
\(550\) | 4.73205 | + | 8.19615i | 0.201775 | + | 0.349485i | ||||
\(551\) | − | 3.80385i | − | 0.162049i | ||||||
\(552\) | 1.90192 | − | 1.09808i | 0.0809513 | − | 0.0467372i | ||||
\(553\) | 50.7846 | − | 29.3205i | 2.15958 | − | 1.24683i | ||||
\(554\) | 15.1962i | 0.645623i | ||||||||
\(555\) | −2.59808 | − | 4.50000i | −0.110282 | − | 0.191014i | ||||
\(556\) | −2.00000 | + | 3.46410i | −0.0848189 | + | 0.146911i | ||||
\(557\) | 19.2846 | + | 11.1340i | 0.817115 | + | 0.471762i | 0.849421 | − | 0.527716i | \(-0.176952\pi\) |
−0.0323055 | + | 0.999478i | \(0.510285\pi\) | |||||||
\(558\) | 2.53590 | 0.107353 | ||||||||
\(559\) | −12.3923 | − | 18.5885i | −0.524139 | − | 0.786208i | ||||
\(560\) | −8.19615 | −0.346351 | ||||||||
\(561\) | −21.2942 | − | 12.2942i | −0.899043 | − | 0.519063i | ||||
\(562\) | 12.2321 | − | 21.1865i | 0.515978 | − | 0.893700i | ||||
\(563\) | 4.39230 | + | 7.60770i | 0.185114 | + | 0.320626i | 0.943615 | − | 0.331046i | \(-0.107401\pi\) |
−0.758501 | + | 0.651672i | \(0.774068\pi\) | |||||||
\(564\) | 1.26795i | 0.0533903i | ||||||||
\(565\) | −16.7942 | + | 9.69615i | −0.706539 | + | 0.407920i | ||||
\(566\) | −26.1506 | + | 15.0981i | −1.09919 | + | 0.634619i | ||||
\(567\) | − | 4.73205i | − | 0.198727i | ||||||
\(568\) | 4.09808 | + | 7.09808i | 0.171951 | + | 0.297829i | ||||
\(569\) | −16.3923 | + | 28.3923i | −0.687201 | + | 1.19027i | 0.285538 | + | 0.958367i | \(0.407828\pi\) |
−0.972740 | + | 0.231900i | \(0.925506\pi\) | |||||||
\(570\) | −1.90192 | − | 1.09808i | −0.0796628 | − | 0.0459934i | ||||
\(571\) | 13.8038 | 0.577673 | 0.288837 | − | 0.957378i | \(-0.406732\pi\) | ||||
0.288837 | + | 0.957378i | \(0.406732\pi\) | |||||||
\(572\) | −1.09808 | − | 17.0263i | −0.0459129 | − | 0.711905i | ||||
\(573\) | −20.7846 | −0.868290 | ||||||||
\(574\) | −1.90192 | − | 1.09808i | −0.0793848 | − | 0.0458328i | ||||
\(575\) | 2.19615 | − | 3.80385i | 0.0915859 | − | 0.158631i | ||||
\(576\) | 0.500000 | + | 0.866025i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | − | 16.2679i | − | 0.677244i | −0.940923 | − | 0.338622i | \(-0.890039\pi\) | ||
0.940923 | − | 0.338622i | \(-0.109961\pi\) | |||||||
\(578\) | −8.66025 | + | 5.00000i | −0.360219 | + | 0.207973i | ||||
\(579\) | −11.0885 | + | 6.40192i | −0.460821 | + | 0.266055i | ||||
\(580\) | − | 5.19615i | − | 0.215758i | ||||||
\(581\) | 27.5885 | + | 47.7846i | 1.14456 | + | 1.98244i | ||||
\(582\) | 3.00000 | − | 5.19615i | 0.124354 | − | 0.215387i | ||||
\(583\) | 12.2942 | + | 7.09808i | 0.509175 | + | 0.293972i | ||||
\(584\) | −12.1244 | −0.501709 | ||||||||
\(585\) | 5.19615 | − | 3.46410i | 0.214834 | − | 0.143223i | ||||
\(586\) | 14.6603 | 0.605610 | ||||||||
\(587\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(588\) | 7.69615 | − | 13.3301i | 0.317384 | − | 0.549725i | ||||
\(589\) | 1.60770 | + | 2.78461i | 0.0662439 | + | 0.114738i | ||||
\(590\) | 24.0000i | 0.988064i | ||||||||
\(591\) | −6.00000 | + | 3.46410i | −0.246807 | + | 0.142494i | ||||
\(592\) | −2.59808 | + | 1.50000i | −0.106780 | + | 0.0616496i | ||||
\(593\) | 46.8564i | 1.92416i | 0.272764 | + | 0.962081i | \(0.412062\pi\) | ||||
−0.272764 | + | 0.962081i | \(0.587938\pi\) | |||||||
\(594\) | −2.36603 | − | 4.09808i | −0.0970792 | − | 0.168146i | ||||
\(595\) | 21.2942 | − | 36.8827i | 0.872978 | − | 1.51204i | ||||
\(596\) | −15.6962 | − | 9.06218i | −0.642939 | − | 0.371201i | ||||
\(597\) | 8.58846 | 0.351502 | ||||||||
\(598\) | −6.58846 | + | 4.39230i | −0.269422 | + | 0.179615i | ||||
\(599\) | −4.39230 | −0.179465 | −0.0897324 | − | 0.995966i | \(-0.528601\pi\) | ||||
−0.0897324 | + | 0.995966i | \(0.528601\pi\) | |||||||
\(600\) | 1.73205 | + | 1.00000i | 0.0707107 | + | 0.0408248i | ||||
\(601\) | −10.8923 | + | 18.8660i | −0.444306 | + | 0.769561i | −0.998004 | − | 0.0631568i | \(-0.979883\pi\) |
0.553697 | + | 0.832718i | \(0.313216\pi\) | |||||||
\(602\) | −14.6603 | − | 25.3923i | −0.597507 | − | 1.03491i | ||||
\(603\) | 10.7321i | 0.437043i | ||||||||
\(604\) | 6.29423 | − | 3.63397i | 0.256109 | − | 0.147864i | ||||
\(605\) | 17.0885 | − | 9.86603i | 0.694745 | − | 0.401111i | ||||
\(606\) | 1.39230i | 0.0565585i | ||||||||
\(607\) | 24.3923 | + | 42.2487i | 0.990053 | + | 1.71482i | 0.616871 | + | 0.787064i | \(0.288400\pi\) |
0.373182 | + | 0.927758i | \(0.378267\pi\) | |||||||
\(608\) | −0.633975 | + | 1.09808i | −0.0257111 | + | 0.0445329i | ||||
\(609\) | 12.2942 | + | 7.09808i | 0.498187 | + | 0.287629i | ||||
\(610\) | −8.32051 | −0.336888 | ||||||||
\(611\) | −0.294229 | − | 4.56218i | −0.0119032 | − | 0.184566i | ||||
\(612\) | −5.19615 | −0.210042 | ||||||||
\(613\) | 35.3827 | + | 20.4282i | 1.42909 | + | 0.825087i | 0.997049 | − | 0.0767652i | \(-0.0244592\pi\) |
0.432044 | + | 0.901853i | \(0.357793\pi\) | |||||||
\(614\) | 5.36603 | − | 9.29423i | 0.216555 | − | 0.375085i | ||||
\(615\) | −0.401924 | − | 0.696152i | −0.0162071 | − | 0.0280716i | ||||
\(616\) | − | 22.3923i | − | 0.902212i | ||||||
\(617\) | 9.18653 | − | 5.30385i | 0.369836 | − | 0.213525i | −0.303551 | − | 0.952815i | \(-0.598172\pi\) |
0.673387 | + | 0.739290i | \(0.264839\pi\) | |||||||
\(618\) | 3.63397 | − | 2.09808i | 0.146180 | − | 0.0843970i | ||||
\(619\) | 7.60770i | 0.305779i | 0.988243 | + | 0.152890i | \(0.0488579\pi\) | ||||
−0.988243 | + | 0.152890i | \(0.951142\pi\) | |||||||
\(620\) | 2.19615 | + | 3.80385i | 0.0881996 | + | 0.152766i | ||||
\(621\) | −1.09808 | + | 1.90192i | −0.0440643 | + | 0.0763216i | ||||
\(622\) | −1.90192 | − | 1.09808i | −0.0762602 | − | 0.0440288i | ||||
\(623\) | −12.0000 | −0.480770 | ||||||||
\(624\) | −2.00000 | − | 3.00000i | −0.0800641 | − | 0.120096i | ||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | −21.1244 | − | 12.1962i | −0.844299 | − | 0.487456i | ||||
\(627\) | 3.00000 | − | 5.19615i | 0.119808 | − | 0.207514i | ||||
\(628\) | −1.59808 | − | 2.76795i | −0.0637702 | − | 0.110453i | ||||
\(629\) | − | 15.5885i | − | 0.621552i | ||||||
\(630\) | 7.09808 | − | 4.09808i | 0.282794 | − | 0.163271i | ||||
\(631\) | −22.3923 | + | 12.9282i | −0.891424 | + | 0.514664i | −0.874408 | − | 0.485192i | \(-0.838750\pi\) |
−0.0170157 | + | 0.999855i | \(0.505417\pi\) | |||||||
\(632\) | − | 12.3923i | − | 0.492939i | ||||||
\(633\) | −1.80385 | − | 3.12436i | −0.0716965 | − | 0.124182i | ||||
\(634\) | −3.06218 | + | 5.30385i | −0.121615 | + | 0.210643i | ||||
\(635\) | 6.00000 | + | 3.46410i | 0.238103 | + | 0.137469i | ||||
\(636\) | 3.00000 | 0.118958 | ||||||||
\(637\) | −24.5981 | + | 49.7487i | −0.974611 | + | 1.97112i | ||||
\(638\) | 14.1962 | 0.562031 | ||||||||
\(639\) | −7.09808 | − | 4.09808i | −0.280796 | − | 0.162117i | ||||
\(640\) | −0.866025 | + | 1.50000i | −0.0342327 | + | 0.0592927i | ||||
\(641\) | −15.4019 | − | 26.6769i | −0.608339 | − | 1.05367i | −0.991514 | − | 0.129999i | \(-0.958503\pi\) |
0.383175 | − | 0.923676i | \(-0.374831\pi\) | |||||||
\(642\) | 8.19615i | 0.323476i | ||||||||
\(643\) | −24.0000 | + | 13.8564i | −0.946468 | + | 0.546443i | −0.891982 | − | 0.452071i | \(-0.850685\pi\) |
−0.0544858 | + | 0.998515i | \(0.517352\pi\) | |||||||
\(644\) | −9.00000 | + | 5.19615i | −0.354650 | + | 0.204757i | ||||
\(645\) | − | 10.7321i | − | 0.422574i | ||||||
\(646\) | −3.29423 | − | 5.70577i | −0.129610 | − | 0.224491i | ||||
\(647\) | 6.58846 | − | 11.4115i | 0.259019 | − | 0.448634i | −0.706960 | − | 0.707253i | \(-0.749934\pi\) |
0.965979 | + | 0.258619i | \(0.0832674\pi\) | |||||||
\(648\) | −0.866025 | − | 0.500000i | −0.0340207 | − | 0.0196419i | ||||
\(649\) | −65.5692 | −2.57382 | ||||||||
\(650\) | −6.46410 | − | 3.19615i | −0.253543 | − | 0.125363i | ||||
\(651\) | −12.0000 | −0.470317 | ||||||||
\(652\) | −8.19615 | − | 4.73205i | −0.320986 | − | 0.185321i | ||||
\(653\) | 24.5885 | − | 42.5885i | 0.962221 | − | 1.66662i | 0.245317 | − | 0.969443i | \(-0.421108\pi\) |
0.716904 | − | 0.697172i | \(-0.245559\pi\) | |||||||
\(654\) | 8.19615 | + | 14.1962i | 0.320495 | + | 0.555113i | ||||
\(655\) | − | 28.3923i | − | 1.10938i | ||||||
\(656\) | −0.401924 | + | 0.232051i | −0.0156925 | + | 0.00906006i | ||||
\(657\) | 10.5000 | − | 6.06218i | 0.409644 | − | 0.236508i | ||||
\(658\) | − | 6.00000i | − | 0.233904i | ||||||
\(659\) | −12.5885 | − | 21.8038i | −0.490377 | − | 0.849357i | 0.509562 | − | 0.860434i | \(-0.329807\pi\) |
−0.999939 | + | 0.0110766i | \(0.996474\pi\) | |||||||
\(660\) | 4.09808 | − | 7.09808i | 0.159517 | − | 0.276292i | ||||
\(661\) | 7.79423 | + | 4.50000i | 0.303160 | + | 0.175030i | 0.643862 | − | 0.765142i | \(-0.277331\pi\) |
−0.340701 | + | 0.940172i | \(0.610665\pi\) | |||||||
\(662\) | 12.0000 | 0.466393 | ||||||||
\(663\) | 18.6962 | − | 1.20577i | 0.726098 | − | 0.0468283i | ||||
\(664\) | 11.6603 | 0.452506 | ||||||||
\(665\) | 9.00000 | + | 5.19615i | 0.349005 | + | 0.201498i | ||||
\(666\) | 1.50000 | − | 2.59808i | 0.0581238 | − | 0.100673i | ||||
\(667\) | −3.29423 | − | 5.70577i | −0.127553 | − | 0.220928i | ||||
\(668\) | − | 2.53590i | − | 0.0981169i | ||||||
\(669\) | 16.3923 | − | 9.46410i | 0.633763 | − | 0.365903i | ||||
\(670\) | −16.0981 | + | 9.29423i | −0.621923 | + | 0.359067i | ||||
\(671\) | − | 22.7321i | − | 0.877561i | ||||||
\(672\) | −2.36603 | − | 4.09808i | −0.0912714 | − | 0.158087i | ||||
\(673\) | 0.500000 | − | 0.866025i | 0.0192736 | − | 0.0333828i | −0.856228 | − | 0.516599i | \(-0.827198\pi\) |
0.875501 | + | 0.483216i | \(0.160531\pi\) | |||||||
\(674\) | 26.8468 | + | 15.5000i | 1.03410 | + | 0.597038i | ||||
\(675\) | −2.00000 | −0.0769800 | ||||||||
\(676\) | 7.89230 | + | 10.3301i | 0.303550 | + | 0.397313i | ||||
\(677\) | 4.39230 | 0.168810 | 0.0844050 | − | 0.996432i | \(-0.473101\pi\) | ||||
0.0844050 | + | 0.996432i | \(0.473101\pi\) | |||||||
\(678\) | −9.69615 | − | 5.59808i | −0.372378 | − | 0.214993i | ||||
\(679\) | −14.1962 | + | 24.5885i | −0.544798 | + | 0.943618i | ||||
\(680\) | −4.50000 | − | 7.79423i | −0.172567 | − | 0.298895i | ||||
\(681\) | 9.80385i | 0.375684i | ||||||||
\(682\) | −10.3923 | + | 6.00000i | −0.397942 | + | 0.229752i | ||||
\(683\) | −24.0000 | + | 13.8564i | −0.918334 | + | 0.530201i | −0.883103 | − | 0.469179i | \(-0.844550\pi\) |
−0.0352311 | + | 0.999379i | \(0.511217\pi\) | |||||||
\(684\) | − | 1.26795i | − | 0.0484812i | ||||||
\(685\) | −7.79423 | − | 13.5000i | −0.297802 | − | 0.515808i | ||||
\(686\) | −19.8564 | + | 34.3923i | −0.758121 | + | 1.31310i | ||||
\(687\) | −17.1962 | − | 9.92820i | −0.656074 | − | 0.378785i | ||||
\(688\) | −6.19615 | −0.236226 | ||||||||
\(689\) | −10.7942 | + | 0.696152i | −0.411227 | + | 0.0265213i | ||||
\(690\) | −3.80385 | −0.144810 | ||||||||
\(691\) | 16.9019 | + | 9.75833i | 0.642979 | + | 0.371224i | 0.785761 | − | 0.618530i | \(-0.212271\pi\) |
−0.142782 | + | 0.989754i | \(0.545605\pi\) | |||||||
\(692\) | −8.19615 | + | 14.1962i | −0.311571 | + | 0.539657i | ||||
\(693\) | 11.1962 | + | 19.3923i | 0.425307 | + | 0.736653i | ||||
\(694\) | 12.5885i | 0.477851i | ||||||||
\(695\) | 6.00000 | − | 3.46410i | 0.227593 | − | 0.131401i | ||||
\(696\) | 2.59808 | − | 1.50000i | 0.0984798 | − | 0.0568574i | ||||
\(697\) | − | 2.41154i | − | 0.0913437i | ||||||
\(698\) | 1.26795 | + | 2.19615i | 0.0479926 | + | 0.0831256i | ||||
\(699\) | 9.00000 | − | 15.5885i | 0.340411 | − | 0.589610i | ||||
\(700\) | −8.19615 | − | 4.73205i | −0.309785 | − | 0.178855i | ||||
\(701\) | −4.39230 | −0.165895 | −0.0829475 | − | 0.996554i | \(-0.526433\pi\) | ||||
−0.0829475 | + | 0.996554i | \(0.526433\pi\) | |||||||
\(702\) | 3.23205 | + | 1.59808i | 0.121986 | + | 0.0603155i | ||||
\(703\) | 3.80385 | 0.143465 | ||||||||
\(704\) | −4.09808 | − | 2.36603i | −0.154452 | − | 0.0891729i | ||||
\(705\) | 1.09808 | − | 1.90192i | 0.0413559 | − | 0.0716306i | ||||
\(706\) | −2.89230 | − | 5.00962i | −0.108853 | − | 0.188539i | ||||
\(707\) | − | 6.58846i | − | 0.247784i | ||||||
\(708\) | −12.0000 | + | 6.92820i | −0.450988 | + | 0.260378i | ||||
\(709\) | −2.81347 | + | 1.62436i | −0.105662 | + | 0.0610040i | −0.551900 | − | 0.833910i | \(-0.686097\pi\) |
0.446238 | + | 0.894914i | \(0.352764\pi\) | |||||||
\(710\) | − | 14.1962i | − | 0.532772i | ||||||
\(711\) | 6.19615 | + | 10.7321i | 0.232374 | + | 0.402483i | ||||
\(712\) | −1.26795 | + | 2.19615i | −0.0475184 | + | 0.0823043i | ||||
\(713\) | 4.82309 | + | 2.78461i | 0.180626 | + | 0.104284i | ||||
\(714\) | 24.5885 | 0.920200 | ||||||||
\(715\) | −13.0981 | + | 26.4904i | −0.489840 | + | 0.990684i | ||||
\(716\) | −8.19615 | −0.306305 | ||||||||
\(717\) | −21.2942 | − | 12.2942i | −0.795248 | − | 0.459136i | ||||
\(718\) | 11.0263 | − | 19.0981i | 0.411497 | − | 0.712734i | ||||
\(719\) | 26.1962 | + | 45.3731i | 0.976952 | + | 1.69213i | 0.673338 | + | 0.739335i | \(0.264860\pi\) |
0.303613 | + | 0.952795i | \(0.401807\pi\) | |||||||
\(720\) | − | 1.73205i | − | 0.0645497i | ||||||
\(721\) | −17.1962 | + | 9.92820i | −0.640418 | + | 0.369746i | ||||
\(722\) | −15.0622 | + | 8.69615i | −0.560556 | + | 0.323637i | ||||
\(723\) | 0.803848i | 0.0298954i | ||||||||
\(724\) | 5.79423 | + | 10.0359i | 0.215341 | + | 0.372981i | ||||
\(725\) | 3.00000 | − | 5.19615i | 0.111417 | − | 0.192980i | ||||
\(726\) | 9.86603 | + | 5.69615i | 0.366163 | + | 0.211404i | ||||
\(727\) | 24.1962 | 0.897386 | 0.448693 | − | 0.893686i | \(-0.351890\pi\) | ||||
0.448693 | + | 0.893686i | \(0.351890\pi\) | |||||||
\(728\) | 9.46410 | + | 14.1962i | 0.350763 | + | 0.526144i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 18.1865 | + | 10.5000i | 0.673114 | + | 0.388622i | ||||
\(731\) | 16.0981 | − | 27.8827i | 0.595409 | − | 1.03128i | ||||
\(732\) | −2.40192 | − | 4.16025i | −0.0887777 | − | 0.153767i | ||||
\(733\) | − | 14.3205i | − | 0.528940i | −0.964394 | − | 0.264470i | \(-0.914803\pi\) | ||
0.964394 | − | 0.264470i | \(-0.0851970\pi\) | |||||||
\(734\) | 20.9545 | − | 12.0981i | 0.773444 | − | 0.446548i | ||||
\(735\) | −23.0885 | + | 13.3301i | −0.851631 | + | 0.491689i | ||||
\(736\) | 2.19615i | 0.0809513i | ||||||||
\(737\) | −25.3923 | − | 43.9808i | −0.935338 | − | 1.62005i | ||||
\(738\) | 0.232051 | − | 0.401924i | 0.00854191 | − | 0.0147950i | ||||
\(739\) | −16.3923 | − | 9.46410i | −0.603001 | − | 0.348143i | 0.167220 | − | 0.985920i | \(-0.446521\pi\) |
−0.770221 | + | 0.637777i | \(0.779854\pi\) | |||||||
\(740\) | 5.19615 | 0.191014 | ||||||||
\(741\) | 0.294229 | + | 4.56218i | 0.0108088 | + | 0.167596i | ||||
\(742\) | −14.1962 | −0.521157 | ||||||||
\(743\) | −3.80385 | − | 2.19615i | −0.139550 | − | 0.0805690i | 0.428600 | − | 0.903494i | \(-0.359007\pi\) |
−0.568149 | + | 0.822925i | \(0.692340\pi\) | |||||||
\(744\) | −1.26795 | + | 2.19615i | −0.0464853 | + | 0.0805149i | ||||
\(745\) | 15.6962 | + | 27.1865i | 0.575063 | + | 0.996038i | ||||
\(746\) | − | 23.9808i | − | 0.877998i | ||||||
\(747\) | −10.0981 | + | 5.83013i | −0.369469 | + | 0.213313i | ||||
\(748\) | 21.2942 | − | 12.2942i | 0.778594 | − | 0.449522i | ||||
\(749\) | − | 38.7846i | − | 1.41716i | ||||||
\(750\) | −6.06218 | − | 10.5000i | −0.221359 | − | 0.383406i | ||||
\(751\) | −12.4904 | + | 21.6340i | −0.455780 | + | 0.789435i | −0.998733 | − | 0.0503286i | \(-0.983973\pi\) |
0.542952 | + | 0.839764i | \(0.317306\pi\) | |||||||
\(752\) | −1.09808 | − | 0.633975i | −0.0400427 | − | 0.0231187i | ||||
\(753\) | −4.39230 | −0.160064 | ||||||||
\(754\) | −9.00000 | + | 6.00000i | −0.327761 | + | 0.218507i | ||||
\(755\) | −12.5885 | −0.458141 | ||||||||
\(756\) | 4.09808 | + | 2.36603i | 0.149046 | + | 0.0860515i | ||||
\(757\) | −9.39230 | + | 16.2679i | −0.341369 | + | 0.591269i | −0.984687 | − | 0.174330i | \(-0.944224\pi\) |
0.643318 | + | 0.765599i | \(0.277557\pi\) | |||||||
\(758\) | 9.12436 | + | 15.8038i | 0.331412 | + | 0.574022i | ||||
\(759\) | − | 10.3923i | − | 0.377217i | ||||||
\(760\) | 1.90192 | − | 1.09808i | 0.0689900 | − | 0.0398314i | ||||
\(761\) | 3.80385 | − | 2.19615i | 0.137889 | − | 0.0796105i | −0.429468 | − | 0.903082i | \(-0.641299\pi\) |
0.567358 | + | 0.823471i | \(0.307966\pi\) | |||||||
\(762\) | 4.00000i | 0.144905i | ||||||||
\(763\) | −38.7846 | − | 67.1769i | −1.40410 | − | 2.43197i | ||||
\(764\) | 10.3923 | − | 18.0000i | 0.375980 | − | 0.651217i | ||||
\(765\) | 7.79423 | + | 4.50000i | 0.281801 | + | 0.162698i | ||||
\(766\) | 11.3205 | 0.409027 | ||||||||
\(767\) | 41.5692 | − | 27.7128i | 1.50098 | − | 1.00065i | ||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −29.1962 | − | 16.8564i | −1.05284 | − | 0.607858i | −0.129397 | − | 0.991593i | \(-0.541304\pi\) |
−0.923443 | + | 0.383735i | \(0.874638\pi\) | |||||||
\(770\) | −19.3923 | + | 33.5885i | −0.698850 | + | 1.21044i | ||||
\(771\) | −6.40192 | − | 11.0885i | −0.230560 | − | 0.399341i | ||||
\(772\) | − | 12.8038i | − | 0.460821i | ||||||
\(773\) | −43.9808 | + | 25.3923i | −1.58188 | + | 0.913298i | −0.587293 | + | 0.809375i | \(0.699806\pi\) |
−0.994585 | + | 0.103923i | \(0.966860\pi\) | |||||||
\(774\) | 5.36603 | − | 3.09808i | 0.192878 | − | 0.111358i | ||||
\(775\) | 5.07180i | 0.182184i | ||||||||
\(776\) | 3.00000 | + | 5.19615i | 0.107694 | + | 0.186531i | ||||
\(777\) | −7.09808 | + | 12.2942i | −0.254642 | + | 0.441053i | ||||
\(778\) | 11.5981 | + | 6.69615i | 0.415811 | + | 0.240069i | ||||
\(779\) | 0.588457 | 0.0210837 | ||||||||
\(780\) | 0.401924 | + | 6.23205i | 0.0143912 | + | 0.223143i | ||||
\(781\) | 38.7846 | 1.38782 | ||||||||
\(782\) | −9.88269 | − | 5.70577i | −0.353404 | − | 0.204038i | ||||
\(783\) | −1.50000 | + | 2.59808i | −0.0536056 | + | 0.0928477i | ||||
\(784\) | 7.69615 | + | 13.3301i | 0.274863 | + | 0.476076i | ||||
\(785\) | 5.53590i | 0.197585i | ||||||||
\(786\) | 14.1962 | − | 8.19615i | 0.506360 | − | 0.292347i | ||||
\(787\) | 12.5885 | − | 7.26795i | 0.448730 | − | 0.259074i | −0.258564 | − | 0.965994i | \(-0.583249\pi\) |
0.707294 | + | 0.706920i | \(0.249916\pi\) | |||||||
\(788\) | − | 6.92820i | − | 0.246807i | ||||||
\(789\) | −1.09808 | − | 1.90192i | −0.0390925 | − | 0.0677103i | ||||
\(790\) | −10.7321 | + | 18.5885i | −0.381829 | + | 0.661348i | ||||
\(791\) | 45.8827 | + | 26.4904i | 1.63140 | + | 0.941890i | ||||
\(792\) | 4.73205 | 0.168146 | ||||||||
\(793\) | 9.60770 | + | 14.4115i | 0.341179 | + | 0.511769i | ||||
\(794\) | 16.3923 | 0.581741 | ||||||||
\(795\) | −4.50000 | − | 2.59808i | −0.159599 | − | 0.0921443i | ||||
\(796\) | −4.29423 | + | 7.43782i | −0.152205 | + | 0.263627i | ||||
\(797\) | 3.00000 | + | 5.19615i | 0.106265 | + | 0.184057i | 0.914255 | − | 0.405140i | \(-0.132777\pi\) |
−0.807989 | + | 0.589197i | \(0.799444\pi\) | |||||||
\(798\) | 6.00000i | 0.212398i | ||||||||
\(799\) | 5.70577 | − | 3.29423i | 0.201856 | − | 0.116541i | ||||
\(800\) | −1.73205 | + | 1.00000i | −0.0612372 | + | 0.0353553i | ||||
\(801\) | − | 2.53590i | − | 0.0896016i | ||||||
\(802\) | 10.5000 | + | 18.1865i | 0.370768 | + | 0.642189i | ||||
\(803\) | −28.6865 | + | 49.6865i | −1.01233 | + | 1.75340i | ||||
\(804\) | −9.29423 | − | 5.36603i | −0.327782 | − | 0.189245i | ||||
\(805\) | 18.0000 | 0.634417 | ||||||||
\(806\) | 4.05256 | − | 8.19615i | 0.142745 | − | 0.288697i | ||||
\(807\) | 28.3923 | 0.999456 | ||||||||
\(808\) | −1.20577 | − | 0.696152i | −0.0424189 | − | 0.0244906i | ||||
\(809\) | 23.5981 | − | 40.8731i | 0.829664 | − | 1.43702i | −0.0686377 | − | 0.997642i | \(-0.521865\pi\) |
0.898302 | − | 0.439379i | \(-0.144801\pi\) | |||||||
\(810\) | 0.866025 | + | 1.50000i | 0.0304290 | + | 0.0527046i | ||||
\(811\) | 4.39230i | 0.154235i | 0.997022 | + | 0.0771173i | \(0.0245716\pi\) | ||||
−0.997022 | + | 0.0771173i | \(0.975428\pi\) | |||||||
\(812\) | −12.2942 | + | 7.09808i | −0.431443 | + | 0.249094i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 14.1962i | 0.497575i | ||||||||
\(815\) | 8.19615 | + | 14.1962i | 0.287099 | + | 0.497270i | ||||
\(816\) | 2.59808 | − | 4.50000i | 0.0909509 | − | 0.157532i | ||||
\(817\) | 6.80385 | + | 3.92820i | 0.238036 | + | 0.137430i | ||||
\(818\) | −3.33975 | −0.116771 | ||||||||
\(819\) | −15.2942 | − | 7.56218i | −0.534424 | − | 0.264244i | ||||
\(820\) | 0.803848 | 0.0280716 | ||||||||
\(821\) | 35.1962 | + | 20.3205i | 1.22835 | + | 0.709191i | 0.966685 | − | 0.255967i | \(-0.0823939\pi\) |
0.261669 | + | 0.965158i | \(0.415727\pi\) | |||||||
\(822\) | 4.50000 | − | 7.79423i | 0.156956 | − | 0.271855i | ||||
\(823\) | −16.0000 | − | 27.7128i | −0.557725 | − | 0.966008i | −0.997686 | − | 0.0679910i | \(-0.978341\pi\) |
0.439961 | − | 0.898017i | \(-0.354992\pi\) | |||||||
\(824\) | 4.19615i | 0.146180i | ||||||||
\(825\) | 8.19615 | − | 4.73205i | 0.285353 | − | 0.164749i | ||||
\(826\) | 56.7846 | − | 32.7846i | 1.97579 | − | 1.14072i | ||||
\(827\) | 32.1051i | 1.11640i | 0.829705 | + | 0.558202i | \(0.188509\pi\) | ||||
−0.829705 | + | 0.558202i | \(0.811491\pi\) | |||||||
\(828\) | −1.09808 | − | 1.90192i | −0.0381608 | − | 0.0660964i | ||||
\(829\) | −5.99038 | + | 10.3756i | −0.208055 | + | 0.360361i | −0.951102 | − | 0.308878i | \(-0.900046\pi\) |
0.743047 | + | 0.669239i | \(0.233380\pi\) | |||||||
\(830\) | −17.4904 | − | 10.0981i | −0.607100 | − | 0.350509i | ||||
\(831\) | 15.1962 | 0.527149 | ||||||||
\(832\) | 3.59808 | − | 0.232051i | 0.124741 | − | 0.00804491i | ||||
\(833\) | −79.9808 | −2.77117 | ||||||||
\(834\) | 3.46410 | + | 2.00000i | 0.119952 | + | 0.0692543i | ||||
\(835\) | −2.19615 | + | 3.80385i | −0.0760010 | + | 0.131638i | ||||
\(836\) | 3.00000 | + | 5.19615i | 0.103757 | + | 0.179713i | ||||
\(837\) | − | 2.53590i | − | 0.0876535i | ||||||
\(838\) | −14.1962 | + | 8.19615i | −0.490398 | + | 0.283131i | ||||
\(839\) | 10.3923 | − | 6.00000i | 0.358782 | − | 0.207143i | −0.309764 | − | 0.950813i | \(-0.600250\pi\) |
0.668546 | + | 0.743670i | \(0.266917\pi\) | |||||||
\(840\) | 8.19615i | 0.282794i | ||||||||
\(841\) | 10.0000 | + | 17.3205i | 0.344828 | + | 0.597259i | ||||
\(842\) | −0.232051 | + | 0.401924i | −0.00799700 | + | 0.0138512i | ||||
\(843\) | −21.1865 | − | 12.2321i | −0.729703 | − | 0.421294i | ||||
\(844\) | 3.60770 | 0.124182 | ||||||||
\(845\) | −2.89230 | − | 22.3301i | −0.0994983 | − | 0.768180i | ||||
\(846\) | 1.26795 | 0.0435930 | ||||||||
\(847\) | −46.6865 | − | 26.9545i | −1.60417 | − | 0.926167i | ||||
\(848\) | −1.50000 | + | 2.59808i | −0.0515102 | + | 0.0892183i | ||||
\(849\) | 15.0981 | + | 26.1506i | 0.518165 | + | 0.897487i | ||||
\(850\) | − | 10.3923i | − | 0.356453i | ||||||
\(851\) | 5.70577 | − | 3.29423i | 0.195591 | − | 0.112925i | ||||
\(852\) | 7.09808 | − | 4.09808i | 0.243176 | − | 0.140398i | ||||
\(853\) | − | 9.00000i | − | 0.308154i | −0.988059 | − | 0.154077i | \(-0.950760\pi\) | ||
0.988059 | − | 0.154077i | \(-0.0492404\pi\) | |||||||
\(854\) | 11.3660 | + | 19.6865i | 0.388937 | + | 0.673659i | ||||
\(855\) | −1.09808 | + | 1.90192i | −0.0375534 | + | 0.0650444i | ||||
\(856\) | −7.09808 | − | 4.09808i | −0.242607 | − | 0.140069i | ||||
\(857\) | 54.3731 | 1.85735 | 0.928674 | − | 0.370896i | \(-0.120949\pi\) | ||||
0.928674 | + | 0.370896i | \(0.120949\pi\) | |||||||
\(858\) | −17.0263 | + | 1.09808i | −0.581268 | + | 0.0374877i | ||||
\(859\) | 10.5885 | 0.361273 | 0.180637 | − | 0.983550i | \(-0.442184\pi\) | ||||
0.180637 | + | 0.983550i | \(0.442184\pi\) | |||||||
\(860\) | 9.29423 | + | 5.36603i | 0.316931 | + | 0.182980i | ||||
\(861\) | −1.09808 | + | 1.90192i | −0.0374223 | + | 0.0648174i | ||||
\(862\) | −13.9019 | − | 24.0788i | −0.473501 | − | 0.820128i | ||||
\(863\) | 4.48334i | 0.152615i | 0.997084 | + | 0.0763073i | \(0.0243130\pi\) | ||||
−0.997084 | + | 0.0763073i | \(0.975687\pi\) | |||||||
\(864\) | 0.866025 | − | 0.500000i | 0.0294628 | − | 0.0170103i | ||||
\(865\) | 24.5885 | − | 14.1962i | 0.836033 | − | 0.482684i | ||||
\(866\) | − | 33.7846i | − | 1.14805i | ||||||
\(867\) | 5.00000 | + | 8.66025i | 0.169809 | + | 0.294118i | ||||
\(868\) | 6.00000 | − | 10.3923i | 0.203653 | − | 0.352738i | ||||
\(869\) | −50.7846 | − | 29.3205i | −1.72275 | − | 0.994630i | ||||
\(870\) | −5.19615 | −0.176166 | ||||||||
\(871\) | 34.6865 | + | 17.1506i | 1.17531 | + | 0.581127i | ||||
\(872\) | −16.3923 | −0.555113 | ||||||||
\(873\) | −5.19615 | − | 3.00000i | −0.175863 | − | 0.101535i | ||||
\(874\) | 1.39230 | − | 2.41154i | 0.0470954 | − | 0.0815716i | ||||
\(875\) | 28.6865 | + | 49.6865i | 0.969782 | + | 1.67971i | ||||
\(876\) | 12.1244i | 0.409644i | ||||||||
\(877\) | 37.5788 | − | 21.6962i | 1.26895 | − | 0.732627i | 0.294158 | − | 0.955757i | \(-0.404961\pi\) |
0.974789 | + | 0.223130i | \(0.0716273\pi\) | |||||||
\(878\) | 14.3660 | − | 8.29423i | 0.484830 | − | 0.279917i | ||||
\(879\) | − | 14.6603i | − | 0.494478i | ||||||
\(880\) | 4.09808 | + | 7.09808i | 0.138146 | + | 0.239276i | ||||
\(881\) | 18.9904 | − | 32.8923i | 0.639802 | − | 1.10817i | −0.345674 | − | 0.938355i | \(-0.612350\pi\) |
0.985476 | − | 0.169815i | \(-0.0543171\pi\) | |||||||
\(882\) | −13.3301 | − | 7.69615i | −0.448849 | − | 0.259143i | ||||
\(883\) | 24.7846 | 0.834069 | 0.417034 | − | 0.908891i | \(-0.363070\pi\) | ||||
0.417034 | + | 0.908891i | \(0.363070\pi\) | |||||||
\(884\) | −8.30385 | + | 16.7942i | −0.279289 | + | 0.564851i | ||||
\(885\) | 24.0000 | 0.806751 | ||||||||
\(886\) | −3.80385 | − | 2.19615i | −0.127793 | − | 0.0737812i | ||||
\(887\) | −24.0000 | + | 41.5692i | −0.805841 | + | 1.39576i | 0.109881 | + | 0.993945i | \(0.464953\pi\) |
−0.915722 | + | 0.401813i | \(0.868380\pi\) | |||||||
\(888\) | 1.50000 | + | 2.59808i | 0.0503367 | + | 0.0871857i | ||||
\(889\) | − | 18.9282i | − | 0.634832i | ||||||
\(890\) | 3.80385 | − | 2.19615i | 0.127505 | − | 0.0736152i | ||||
\(891\) | −4.09808 | + | 2.36603i | −0.137291 | + | 0.0792648i | ||||
\(892\) | 18.9282i | 0.633763i | ||||||||
\(893\) | 0.803848 | + | 1.39230i | 0.0268997 | + | 0.0465917i | ||||
\(894\) | −9.06218 | + | 15.6962i | −0.303085 | + | 0.524958i | ||||
\(895\) | 12.2942 | + | 7.09808i | 0.410951 | + | 0.237263i | ||||
\(896\) | 4.73205 | 0.158087 | ||||||||
\(897\) | 4.39230 | + | 6.58846i | 0.146655 | + | 0.219982i | ||||
\(898\) | −33.4641 | −1.11671 | ||||||||
\(899\) | 6.58846 | + | 3.80385i | 0.219737 | + | 0.126865i | ||||
\(900\) | 1.00000 | − | 1.73205i | 0.0333333 | − | 0.0577350i | ||||
\(901\) | −7.79423 | − | 13.5000i | −0.259663 | − | 0.449750i | ||||
\(902\) | 2.19615i | 0.0731239i | ||||||||
\(903\) | −25.3923 | + | 14.6603i | −0.845003 | + | 0.487863i | ||||
\(904\) | 9.69615 | − | 5.59808i | 0.322489 | − | 0.186189i | ||||
\(905\) | − | 20.0718i | − | 0.667209i | ||||||
\(906\) | −3.63397 | − | 6.29423i | −0.120731 | − | 0.209112i | ||||
\(907\) | −20.5885 | + | 35.6603i | −0.683629 | + | 1.18408i | 0.290237 | + | 0.956955i | \(0.406266\pi\) |
−0.973866 | + | 0.227125i | \(0.927068\pi\) | |||||||
\(908\) | −8.49038 | − | 4.90192i | −0.281763 | − | 0.162676i | ||||
\(909\) | 1.39230 | 0.0461798 | ||||||||
\(910\) | −1.90192 | − | 29.4904i | −0.0630482 | − | 0.977597i | ||||
\(911\) | 37.1769 | 1.23173 | 0.615863 | − | 0.787853i | \(-0.288807\pi\) | ||||
0.615863 | + | 0.787853i | \(0.288807\pi\) | |||||||
\(912\) | 1.09808 | + | 0.633975i | 0.0363609 | + | 0.0209930i | ||||
\(913\) | 27.5885 | − | 47.7846i | 0.913045 | − | 1.58144i | ||||
\(914\) | −9.99038 | − | 17.3038i | −0.330452 | − | 0.572360i | ||||
\(915\) | 8.32051i | 0.275068i | ||||||||
\(916\) | 17.1962 | − | 9.92820i | 0.568177 | − | 0.328037i | ||||
\(917\) | −67.1769 | + | 38.7846i | −2.21838 | + | 1.28078i | ||||
\(918\) | 5.19615i | 0.171499i | ||||||||
\(919\) | −16.1962 | − | 28.0526i | −0.534262 | − | 0.925369i | −0.999199 | − | 0.0400247i | \(-0.987256\pi\) |
0.464937 | − | 0.885344i | \(-0.346077\pi\) | |||||||
\(920\) | 1.90192 | − | 3.29423i | 0.0627046 | − | 0.108608i | ||||
\(921\) | −9.29423 | − | 5.36603i | −0.306255 | − | 0.176817i | ||||
\(922\) | −19.9808 | −0.658031 | ||||||||
\(923\) | −24.5885 | + | 16.3923i | −0.809339 | + | 0.539559i | ||||
\(924\) | −22.3923 | −0.736653 | ||||||||
\(925\) | 5.19615 | + | 3.00000i | 0.170848 | + | 0.0986394i | ||||
\(926\) | −13.0981 | + | 22.6865i | −0.430429 | + | 0.745526i | ||||
\(927\) | −2.09808 | − | 3.63397i | −0.0689099 | − | 0.119355i | ||||
\(928\) | 3.00000i | 0.0984798i | ||||||||
\(929\) | −29.9711 | + | 17.3038i | −0.983321 | + | 0.567721i | −0.903271 | − | 0.429070i | \(-0.858841\pi\) |
−0.0800501 | + | 0.996791i | \(0.525508\pi\) | |||||||
\(930\) | 3.80385 | − | 2.19615i | 0.124733 | − | 0.0720147i | ||||
\(931\) | − | 19.5167i | − | 0.639633i | ||||||
\(932\) | 9.00000 | + | 15.5885i | 0.294805 | + | 0.510617i | ||||
\(933\) | −1.09808 | + | 1.90192i | −0.0359494 | + | 0.0622662i | ||||
\(934\) | −31.6865 | − | 18.2942i | −1.03682 | − | 0.598605i | ||||
\(935\) | −42.5885 | −1.39279 | ||||||||
\(936\) | −3.00000 | + | 2.00000i | −0.0980581 | + | 0.0653720i | ||||
\(937\) | 5.39230 | 0.176159 | 0.0880795 | − | 0.996113i | \(-0.471927\pi\) | ||||
0.0880795 | + | 0.996113i | \(0.471927\pi\) | |||||||
\(938\) | 43.9808 | + | 25.3923i | 1.43602 | + | 0.829088i | ||||
\(939\) | −12.1962 | + | 21.1244i | −0.398006 | + | 0.689367i | ||||
\(940\) | 1.09808 | + | 1.90192i | 0.0358153 | + | 0.0620339i | ||||
\(941\) | 2.78461i | 0.0907757i | 0.998969 | + | 0.0453878i | \(0.0144524\pi\) | ||||
−0.998969 | + | 0.0453878i | \(0.985548\pi\) | |||||||
\(942\) | −2.76795 | + | 1.59808i | −0.0901847 | + | 0.0520681i | ||||
\(943\) | 0.882686 | − | 0.509619i | 0.0287442 | − | 0.0165955i | ||||
\(944\) | − | 13.8564i | − | 0.450988i | ||||||
\(945\) | −4.09808 | − | 7.09808i | −0.133310 | − | 0.230900i | ||||
\(946\) | −14.6603 | + | 25.3923i | −0.476646 | + | 0.825575i | ||||
\(947\) | −37.1769 | − | 21.4641i | −1.20809 | − | 0.697490i | −0.245746 | − | 0.969334i | \(-0.579033\pi\) |
−0.962341 | + | 0.271845i | \(0.912366\pi\) | |||||||
\(948\) | −12.3923 | −0.402483 | ||||||||
\(949\) | −2.81347 | − | 43.6244i | −0.0913290 | − | 1.41611i | ||||
\(950\) | 2.53590 | 0.0822754 | ||||||||
\(951\) | 5.30385 | + | 3.06218i | 0.171989 | + | 0.0992979i | ||||
\(952\) | −12.2942 | + | 21.2942i | −0.398458 | + | 0.690150i | ||||
\(953\) | −12.0000 | − | 20.7846i | −0.388718 | − | 0.673280i | 0.603559 | − | 0.797318i | \(-0.293749\pi\) |
−0.992277 | + | 0.124039i | \(0.960415\pi\) | |||||||
\(954\) | − | 3.00000i | − | 0.0971286i | ||||||
\(955\) | −31.1769 | + | 18.0000i | −1.00886 | + | 0.582466i | ||||
\(956\) | 21.2942 | − | 12.2942i | 0.688705 | − | 0.397624i | ||||
\(957\) | − | 14.1962i | − | 0.458896i | ||||||
\(958\) | −17.6603 | − | 30.5885i | −0.570577 | − | 0.988268i | ||||
\(959\) | −21.2942 | + | 36.8827i | −0.687627 | + | 1.19100i | ||||
\(960\) | 1.50000 | + | 0.866025i | 0.0484123 | + | 0.0279508i | ||||
\(961\) | 24.5692 | 0.792555 | ||||||||
\(962\) | −6.00000 | − | 9.00000i | −0.193448 | − | 0.290172i | ||||
\(963\) | 8.19615 | 0.264117 | ||||||||
\(964\) | −0.696152 | − | 0.401924i | −0.0224216 | − | 0.0129451i | ||||
\(965\) | −11.0885 | + | 19.2058i | −0.356950 | + | 0.618256i | ||||
\(966\) | 5.19615 | + | 9.00000i | 0.167183 | + | 0.289570i | ||||
\(967\) | − | 14.8756i | − | 0.478368i | −0.970974 | − | 0.239184i | \(-0.923120\pi\) | ||
0.970974 | − | 0.239184i | \(-0.0768800\pi\) | |||||||
\(968\) | −9.86603 | + | 5.69615i | −0.317106 | + | 0.183081i | ||||
\(969\) | −5.70577 | + | 3.29423i | −0.183296 | + | 0.105826i | ||||
\(970\) | − | 10.3923i | − | 0.333677i | ||||||
\(971\) | 6.58846 | + | 11.4115i | 0.211434 | + | 0.366214i | 0.952163 | − | 0.305589i | \(-0.0988534\pi\) |
−0.740730 | + | 0.671803i | \(0.765520\pi\) | |||||||
\(972\) | −0.500000 | + | 0.866025i | −0.0160375 | + | 0.0277778i | ||||
\(973\) | −16.3923 | − | 9.46410i | −0.525513 | − | 0.303405i | ||||
\(974\) | 9.12436 | 0.292363 | ||||||||
\(975\) | −3.19615 | + | 6.46410i | −0.102359 | + | 0.207017i | ||||
\(976\) | 4.80385 | 0.153767 | ||||||||
\(977\) | 14.5981 | + | 8.42820i | 0.467034 | + | 0.269642i | 0.714997 | − | 0.699127i | \(-0.246428\pi\) |
−0.247963 | + | 0.968769i | \(0.579761\pi\) | |||||||
\(978\) | −4.73205 | + | 8.19615i | −0.151314 | + | 0.262084i | ||||
\(979\) | 6.00000 | + | 10.3923i | 0.191761 | + | 0.332140i | ||||
\(980\) | − | 26.6603i | − | 0.851631i | ||||||
\(981\) | 14.1962 | − | 8.19615i | 0.453248 | − | 0.261683i | ||||
\(982\) | 0.509619 | − | 0.294229i | 0.0162626 | − | 0.00938921i | ||||
\(983\) | 20.7846i | 0.662926i | 0.943468 | + | 0.331463i | \(0.107542\pi\) | ||||
−0.943468 | + | 0.331463i | \(0.892458\pi\) | |||||||
\(984\) | 0.232051 | + | 0.401924i | 0.00739751 | + | 0.0128129i | ||||
\(985\) | −6.00000 | + | 10.3923i | −0.191176 | + | 0.331126i | ||||
\(986\) | −13.5000 | − | 7.79423i | −0.429928 | − | 0.248219i | ||||
\(987\) | −6.00000 | −0.190982 | ||||||||
\(988\) | −4.09808 | − | 2.02628i | −0.130377 | − | 0.0644645i | ||||
\(989\) | 13.6077 | 0.432700 | ||||||||
\(990\) | −7.09808 | − | 4.09808i | −0.225592 | − | 0.130245i | ||||
\(991\) | −14.6865 | + | 25.4378i | −0.466533 | + | 0.808059i | −0.999269 | − | 0.0382223i | \(-0.987830\pi\) |
0.532736 | + | 0.846281i | \(0.321164\pi\) | |||||||
\(992\) | −1.26795 | − | 2.19615i | −0.0402574 | − | 0.0697279i | ||||
\(993\) | − | 12.0000i | − | 0.380808i | ||||||
\(994\) | −33.5885 | + | 19.3923i | −1.06536 | + | 0.615087i | ||||
\(995\) | 12.8827 | − | 7.43782i | 0.408409 | − | 0.235795i | ||||
\(996\) | − | 11.6603i | − | 0.369469i | ||||||
\(997\) | −6.59808 | − | 11.4282i | −0.208963 | − | 0.361935i | 0.742425 | − | 0.669929i | \(-0.233676\pi\) |
−0.951388 | + | 0.307994i | \(0.900342\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.59808 | − | 1.50000i | −0.0821995 | − | 0.0474579i |
(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 twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
78.2.i.b.43.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
78.2.i.b.49.2 | yes | 4 | 13.10 | even | 6 | inner | |
234.2.l.a.127.1 | 4 | 39.23 | odd | 6 | |||
234.2.l.a.199.1 | 4 | 3.2 | odd | 2 | |||
624.2.bv.d.49.2 | 4 | 52.23 | odd | 6 | |||
624.2.bv.d.433.2 | 4 | 4.3 | odd | 2 | |||
1014.2.a.h.1.1 | 2 | 13.6 | odd | 12 | |||
1014.2.a.j.1.2 | 2 | 13.7 | odd | 12 | |||
1014.2.b.d.337.1 | 4 | 13.9 | even | 3 | |||
1014.2.b.d.337.4 | 4 | 13.4 | even | 6 | |||
1014.2.e.h.529.2 | 4 | 13.8 | odd | 4 | |||
1014.2.e.h.991.2 | 4 | 13.11 | odd | 12 | |||
1014.2.e.j.529.1 | 4 | 13.5 | odd | 4 | |||
1014.2.e.j.991.1 | 4 | 13.2 | odd | 12 | |||
1014.2.i.f.361.1 | 4 | 13.3 | even | 3 | |||
1014.2.i.f.823.1 | 4 | 13.12 | even | 2 | |||
1872.2.by.k.433.2 | 4 | 12.11 | even | 2 | |||
1872.2.by.k.1297.2 | 4 | 156.23 | even | 6 | |||
1950.2.y.a.49.1 | 4 | 65.23 | odd | 12 | |||
1950.2.y.a.199.1 | 4 | 5.2 | odd | 4 | |||
1950.2.y.h.49.2 | 4 | 65.62 | odd | 12 | |||
1950.2.y.h.199.2 | 4 | 5.3 | odd | 4 | |||
1950.2.bc.c.751.1 | 4 | 65.49 | even | 6 | |||
1950.2.bc.c.901.1 | 4 | 5.4 | even | 2 | |||
3042.2.a.s.1.1 | 2 | 39.20 | even | 12 | |||
3042.2.a.v.1.2 | 2 | 39.32 | even | 12 | |||
3042.2.b.l.1351.1 | 4 | 39.17 | odd | 6 | |||
3042.2.b.l.1351.4 | 4 | 39.35 | odd | 6 | |||
8112.2.a.bq.1.1 | 2 | 52.19 | even | 12 | |||
8112.2.a.bx.1.2 | 2 | 52.7 | even | 12 |