Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(49,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.y (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.5708283941\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 390) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.49 |
Dual form | 1950.2.y.f.199.2 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) |
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 | ||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.866025 | + | 0.500000i | 0.353553 | + | 0.204124i | ||||
\(7\) | −1.00000 | + | 1.73205i | −0.377964 | + | 0.654654i | −0.990766 | − | 0.135583i | \(-0.956709\pi\) |
0.612801 | + | 0.790237i | \(0.290043\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.401924 | − | 0.232051i | 0.121185 | − | 0.0699660i | −0.438182 | − | 0.898886i | \(-0.644378\pi\) |
0.559367 | + | 0.828920i | \(0.311044\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | 3.46410 | − | 1.00000i | 0.960769 | − | 0.277350i | ||||
\(14\) | −2.00000 | −0.534522 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 3.46410 | + | 2.00000i | 0.840168 | + | 0.485071i | 0.857321 | − | 0.514782i | \(-0.172127\pi\) |
−0.0171533 | + | 0.999853i | \(0.505460\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 0.464102 | + | 0.267949i | 0.106472 | + | 0.0614718i | 0.552291 | − | 0.833652i | \(-0.313754\pi\) |
−0.445818 | + | 0.895123i | \(0.647087\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000i | 0.436436i | ||||||||
\(22\) | 0.401924 | + | 0.232051i | 0.0856904 | + | 0.0494734i | ||||
\(23\) | −0.232051 | + | 0.133975i | −0.0483859 | + | 0.0279356i | −0.523998 | − | 0.851720i | \(-0.675560\pi\) |
0.475612 | + | 0.879655i | \(0.342227\pi\) | |||||||
\(24\) | −0.866025 | + | 0.500000i | −0.176777 | + | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.59808 | + | 2.50000i | 0.509525 | + | 0.490290i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −1.00000 | − | 1.73205i | −0.188982 | − | 0.327327i | ||||
\(29\) | 1.86603 | + | 3.23205i | 0.346512 | + | 0.600177i | 0.985627 | − | 0.168934i | \(-0.0540326\pi\) |
−0.639115 | + | 0.769111i | \(0.720699\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.73205i | 0.311086i | 0.987829 | + | 0.155543i | \(0.0497126\pi\) | ||||
−0.987829 | + | 0.155543i | \(0.950287\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 0.232051 | − | 0.401924i | 0.0403949 | − | 0.0699660i | ||||
\(34\) | 4.00000i | 0.685994i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.500000 | + | 0.866025i | 0.0833333 | + | 0.144338i | ||||
\(37\) | 0.598076 | + | 1.03590i | 0.0983231 | + | 0.170301i | 0.910991 | − | 0.412427i | \(-0.135319\pi\) |
−0.812668 | + | 0.582728i | \(0.801985\pi\) | |||||||
\(38\) | 0.535898i | 0.0869342i | ||||||||
\(39\) | 2.50000 | − | 2.59808i | 0.400320 | − | 0.416025i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.73205 | + | 1.00000i | −0.270501 | + | 0.156174i | −0.629115 | − | 0.777312i | \(-0.716583\pi\) |
0.358614 | + | 0.933486i | \(0.383249\pi\) | |||||||
\(42\) | −1.73205 | + | 1.00000i | −0.267261 | + | 0.154303i | ||||
\(43\) | −1.66987 | − | 0.964102i | −0.254653 | − | 0.147024i | 0.367240 | − | 0.930126i | \(-0.380303\pi\) |
−0.621893 | + | 0.783102i | \(0.713636\pi\) | |||||||
\(44\) | 0.464102i | 0.0699660i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.232051 | − | 0.133975i | −0.0342140 | − | 0.0197535i | ||||
\(47\) | 10.4641 | 1.52635 | 0.763173 | − | 0.646194i | \(-0.223640\pi\) | ||||
0.763173 | + | 0.646194i | \(0.223640\pi\) | |||||||
\(48\) | −0.866025 | − | 0.500000i | −0.125000 | − | 0.0721688i | ||||
\(49\) | 1.50000 | + | 2.59808i | 0.214286 | + | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.00000 | 0.560112 | ||||||||
\(52\) | −0.866025 | + | 3.50000i | −0.120096 | + | 0.485363i | ||||
\(53\) | 12.9282i | 1.77583i | 0.460012 | + | 0.887913i | \(0.347845\pi\) | ||||
−0.460012 | + | 0.887913i | \(0.652155\pi\) | |||||||
\(54\) | 0.866025 | − | 0.500000i | 0.117851 | − | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | − | 1.73205i | 0.133631 | − | 0.231455i | ||||
\(57\) | 0.535898 | 0.0709815 | ||||||||
\(58\) | −1.86603 | + | 3.23205i | −0.245021 | + | 0.424389i | ||||
\(59\) | 1.33013 | + | 0.767949i | 0.173168 | + | 0.0999785i | 0.584079 | − | 0.811697i | \(-0.301456\pi\) |
−0.410911 | + | 0.911676i | \(0.634789\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.19615 | + | 9.00000i | −0.665299 | + | 1.15233i | 0.313905 | + | 0.949454i | \(0.398363\pi\) |
−0.979204 | + | 0.202878i | \(0.934971\pi\) | |||||||
\(62\) | −1.50000 | + | 0.866025i | −0.190500 | + | 0.109985i | ||||
\(63\) | 1.00000 | + | 1.73205i | 0.125988 | + | 0.218218i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.464102 | 0.0571270 | ||||||||
\(67\) | 2.26795 | + | 3.92820i | 0.277074 | + | 0.479906i | 0.970656 | − | 0.240471i | \(-0.0773019\pi\) |
−0.693582 | + | 0.720377i | \(0.743969\pi\) | |||||||
\(68\) | −3.46410 | + | 2.00000i | −0.420084 | + | 0.242536i | ||||
\(69\) | −0.133975 | + | 0.232051i | −0.0161286 | + | 0.0279356i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.26795 | − | 4.19615i | −0.862547 | − | 0.497992i | 0.00231747 | − | 0.999997i | \(-0.499262\pi\) |
−0.864864 | + | 0.502006i | \(0.832596\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | 2.00000 | 0.234082 | 0.117041 | − | 0.993127i | \(-0.462659\pi\) | ||||
0.117041 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(74\) | −0.598076 | + | 1.03590i | −0.0695249 | + | 0.120421i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.464102 | + | 0.267949i | −0.0532361 | + | 0.0307359i | ||||
\(77\) | 0.928203i | 0.105779i | ||||||||
\(78\) | 3.50000 | + | 0.866025i | 0.396297 | + | 0.0980581i | ||||
\(79\) | 0.0717968 | 0.00807777 | 0.00403888 | − | 0.999992i | \(-0.498714\pi\) | ||||
0.00403888 | + | 0.999992i | \(0.498714\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −1.73205 | − | 1.00000i | −0.191273 | − | 0.110432i | ||||
\(83\) | −4.92820 | −0.540941 | −0.270470 | − | 0.962728i | \(-0.587179\pi\) | ||||
−0.270470 | + | 0.962728i | \(0.587179\pi\) | |||||||
\(84\) | −1.73205 | − | 1.00000i | −0.188982 | − | 0.109109i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 1.92820i | − | 0.207924i | ||||||
\(87\) | 3.23205 | + | 1.86603i | 0.346512 | + | 0.200059i | ||||
\(88\) | −0.401924 | + | 0.232051i | −0.0428452 | + | 0.0247367i | ||||
\(89\) | −6.46410 | + | 3.73205i | −0.685193 | + | 0.395597i | −0.801809 | − | 0.597581i | \(-0.796129\pi\) |
0.116615 | + | 0.993177i | \(0.462795\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.73205 | + | 7.00000i | −0.181568 | + | 0.733799i | ||||
\(92\) | − | 0.267949i | − | 0.0279356i | ||||||
\(93\) | 0.866025 | + | 1.50000i | 0.0898027 | + | 0.155543i | ||||
\(94\) | 5.23205 | + | 9.06218i | 0.539645 | + | 0.934692i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | 3.73205 | − | 6.46410i | 0.378932 | − | 0.656330i | −0.611975 | − | 0.790877i | \(-0.709625\pi\) |
0.990907 | + | 0.134547i | \(0.0429580\pi\) | |||||||
\(98\) | −1.50000 | + | 2.59808i | −0.151523 | + | 0.262445i | ||||
\(99\) | − | 0.464102i | − | 0.0466440i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.46410 | + | 9.46410i | 0.543698 | + | 0.941713i | 0.998688 | + | 0.0512163i | \(0.0163098\pi\) |
−0.454989 | + | 0.890497i | \(0.650357\pi\) | |||||||
\(102\) | 2.00000 | + | 3.46410i | 0.198030 | + | 0.342997i | ||||
\(103\) | − | 15.8564i | − | 1.56238i | −0.624295 | − | 0.781189i | \(-0.714613\pi\) | ||
0.624295 | − | 0.781189i | \(-0.285387\pi\) | |||||||
\(104\) | −3.46410 | + | 1.00000i | −0.339683 | + | 0.0980581i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.1962 | + | 6.46410i | −1.08747 | + | 0.627849i | ||||
\(107\) | 17.1962 | − | 9.92820i | 1.66241 | − | 0.959796i | 0.690858 | − | 0.722991i | \(-0.257233\pi\) |
0.971557 | − | 0.236805i | \(-0.0761002\pi\) | |||||||
\(108\) | 0.866025 | + | 0.500000i | 0.0833333 | + | 0.0481125i | ||||
\(109\) | − | 11.8564i | − | 1.13564i | −0.823154 | − | 0.567819i | \(-0.807787\pi\) | ||
0.823154 | − | 0.567819i | \(-0.192213\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.03590 | + | 0.598076i | 0.0983231 | + | 0.0567669i | ||||
\(112\) | 2.00000 | 0.188982 | ||||||||
\(113\) | 9.69615 | + | 5.59808i | 0.912137 | + | 0.526623i | 0.881118 | − | 0.472896i | \(-0.156791\pi\) |
0.0310191 | + | 0.999519i | \(0.490125\pi\) | |||||||
\(114\) | 0.267949 | + | 0.464102i | 0.0250957 | + | 0.0434671i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.73205 | −0.346512 | ||||||||
\(117\) | 0.866025 | − | 3.50000i | 0.0800641 | − | 0.323575i | ||||
\(118\) | 1.53590i | 0.141391i | ||||||||
\(119\) | −6.92820 | + | 4.00000i | −0.635107 | + | 0.366679i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.39230 | + | 9.33975i | −0.490210 | + | 0.849068i | ||||
\(122\) | −10.3923 | −0.940875 | ||||||||
\(123\) | −1.00000 | + | 1.73205i | −0.0901670 | + | 0.156174i | ||||
\(124\) | −1.50000 | − | 0.866025i | −0.134704 | − | 0.0777714i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.00000 | + | 1.73205i | −0.0890871 | + | 0.154303i | ||||
\(127\) | 7.73205 | − | 4.46410i | 0.686109 | − | 0.396125i | −0.116044 | − | 0.993244i | \(-0.537021\pi\) |
0.802153 | + | 0.597119i | \(0.203688\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −1.92820 | −0.169769 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.33975 | −0.117054 | −0.0585271 | − | 0.998286i | \(-0.518640\pi\) | ||||
−0.0585271 | + | 0.998286i | \(0.518640\pi\) | |||||||
\(132\) | 0.232051 | + | 0.401924i | 0.0201974 | + | 0.0349830i | ||||
\(133\) | −0.928203 | + | 0.535898i | −0.0804854 | + | 0.0464683i | ||||
\(134\) | −2.26795 | + | 3.92820i | −0.195921 | + | 0.339345i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.46410 | − | 2.00000i | −0.297044 | − | 0.171499i | ||||
\(137\) | 2.23205 | − | 3.86603i | 0.190697 | − | 0.330297i | −0.754784 | − | 0.655973i | \(-0.772259\pi\) |
0.945481 | + | 0.325676i | \(0.105592\pi\) | |||||||
\(138\) | −0.267949 | −0.0228093 | ||||||||
\(139\) | 0.464102 | − | 0.803848i | 0.0393646 | − | 0.0681815i | −0.845672 | − | 0.533703i | \(-0.820800\pi\) |
0.885036 | + | 0.465522i | \(0.154133\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.06218 | − | 5.23205i | 0.763173 | − | 0.440618i | ||||
\(142\) | − | 8.39230i | − | 0.704267i | ||||||
\(143\) | 1.16025 | − | 1.20577i | 0.0970253 | − | 0.100832i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.00000 | + | 1.73205i | 0.0827606 | + | 0.143346i | ||||
\(147\) | 2.59808 | + | 1.50000i | 0.214286 | + | 0.123718i | ||||
\(148\) | −1.19615 | −0.0983231 | ||||||||
\(149\) | −17.7224 | − | 10.2321i | −1.45188 | − | 0.838242i | −0.453290 | − | 0.891363i | \(-0.649750\pi\) |
−0.998588 | + | 0.0531208i | \(0.983083\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.3923i | 0.845714i | 0.906196 | + | 0.422857i | \(0.138973\pi\) | ||||
−0.906196 | + | 0.422857i | \(0.861027\pi\) | |||||||
\(152\) | −0.464102 | − | 0.267949i | −0.0376436 | − | 0.0217335i | ||||
\(153\) | 3.46410 | − | 2.00000i | 0.280056 | − | 0.161690i | ||||
\(154\) | −0.803848 | + | 0.464102i | −0.0647759 | + | 0.0373984i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.00000 | + | 3.46410i | 0.0800641 | + | 0.277350i | ||||
\(157\) | − | 5.00000i | − | 0.399043i | −0.979893 | − | 0.199522i | \(-0.936061\pi\) | ||
0.979893 | − | 0.199522i | \(-0.0639388\pi\) | |||||||
\(158\) | 0.0358984 | + | 0.0621778i | 0.00285592 | + | 0.00494660i | ||||
\(159\) | 6.46410 | + | 11.1962i | 0.512637 | + | 0.887913i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 0.535898i | − | 0.0422347i | ||||||
\(162\) | 0.500000 | − | 0.866025i | 0.0392837 | − | 0.0680414i | ||||
\(163\) | 11.5263 | − | 19.9641i | 0.902808 | − | 1.56371i | 0.0789748 | − | 0.996877i | \(-0.474835\pi\) |
0.823833 | − | 0.566833i | \(-0.191831\pi\) | |||||||
\(164\) | − | 2.00000i | − | 0.156174i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.46410 | − | 4.26795i | −0.191251 | − | 0.331257i | ||||
\(167\) | 9.16025 | + | 15.8660i | 0.708842 | + | 1.22775i | 0.965287 | + | 0.261191i | \(0.0841153\pi\) |
−0.256445 | + | 0.966559i | \(0.582551\pi\) | |||||||
\(168\) | − | 2.00000i | − | 0.154303i | ||||||
\(169\) | 11.0000 | − | 6.92820i | 0.846154 | − | 0.532939i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.464102 | − | 0.267949i | 0.0354907 | − | 0.0204906i | ||||
\(172\) | 1.66987 | − | 0.964102i | 0.127327 | − | 0.0735121i | ||||
\(173\) | −2.53590 | − | 1.46410i | −0.192801 | − | 0.111314i | 0.400492 | − | 0.916300i | \(-0.368839\pi\) |
−0.593293 | + | 0.804987i | \(0.702172\pi\) | |||||||
\(174\) | 3.73205i | 0.282926i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.401924 | − | 0.232051i | −0.0302961 | − | 0.0174915i | ||||
\(177\) | 1.53590 | 0.115445 | ||||||||
\(178\) | −6.46410 | − | 3.73205i | −0.484505 | − | 0.279729i | ||||
\(179\) | −8.13397 | − | 14.0885i | −0.607962 | − | 1.05302i | −0.991576 | − | 0.129527i | \(-0.958654\pi\) |
0.383614 | − | 0.923494i | \(-0.374679\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.9282 | 0.812287 | 0.406143 | − | 0.913809i | \(-0.366873\pi\) | ||||
0.406143 | + | 0.913809i | \(0.366873\pi\) | |||||||
\(182\) | −6.92820 | + | 2.00000i | −0.513553 | + | 0.148250i | ||||
\(183\) | 10.3923i | 0.768221i | ||||||||
\(184\) | 0.232051 | − | 0.133975i | 0.0171070 | − | 0.00987674i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.866025 | + | 1.50000i | −0.0635001 | + | 0.109985i | ||||
\(187\) | 1.85641 | 0.135754 | ||||||||
\(188\) | −5.23205 | + | 9.06218i | −0.381587 | + | 0.660927i | ||||
\(189\) | 1.73205 | + | 1.00000i | 0.125988 | + | 0.0727393i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.26795 | + | 12.5885i | −0.525890 | + | 0.910869i | 0.473655 | + | 0.880711i | \(0.342934\pi\) |
−0.999545 | + | 0.0301582i | \(0.990399\pi\) | |||||||
\(192\) | 0.866025 | − | 0.500000i | 0.0625000 | − | 0.0360844i | ||||
\(193\) | −11.6603 | − | 20.1962i | −0.839323 | − | 1.45375i | −0.890461 | − | 0.455059i | \(-0.849618\pi\) |
0.0511377 | − | 0.998692i | \(-0.483715\pi\) | |||||||
\(194\) | 7.46410 | 0.535891 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | 8.19615 | + | 14.1962i | 0.583952 | + | 1.01143i | 0.995005 | + | 0.0998228i | \(0.0318276\pi\) |
−0.411054 | + | 0.911611i | \(0.634839\pi\) | |||||||
\(198\) | 0.401924 | − | 0.232051i | 0.0285635 | − | 0.0164911i | ||||
\(199\) | −9.46410 | + | 16.3923i | −0.670892 | + | 1.16202i | 0.306759 | + | 0.951787i | \(0.400755\pi\) |
−0.977651 | + | 0.210232i | \(0.932578\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.92820 | + | 2.26795i | 0.277074 | + | 0.159969i | ||||
\(202\) | −5.46410 | + | 9.46410i | −0.384453 | + | 0.665892i | ||||
\(203\) | −7.46410 | −0.523877 | ||||||||
\(204\) | −2.00000 | + | 3.46410i | −0.140028 | + | 0.242536i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 13.7321 | − | 7.92820i | 0.956757 | − | 0.552384i | ||||
\(207\) | 0.267949i | 0.0186238i | ||||||||
\(208\) | −2.59808 | − | 2.50000i | −0.180144 | − | 0.173344i | ||||
\(209\) | 0.248711 | 0.0172037 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.6603 | − | 20.1962i | −0.802725 | − | 1.39036i | −0.917816 | − | 0.397006i | \(-0.870049\pi\) |
0.115091 | − | 0.993355i | \(-0.463284\pi\) | |||||||
\(212\) | −11.1962 | − | 6.46410i | −0.768955 | − | 0.443956i | ||||
\(213\) | −8.39230 | −0.575031 | ||||||||
\(214\) | 17.1962 | + | 9.92820i | 1.17550 | + | 0.678678i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | −3.00000 | − | 1.73205i | −0.203653 | − | 0.117579i | ||||
\(218\) | 10.2679 | − | 5.92820i | 0.695433 | − | 0.401509i | ||||
\(219\) | 1.73205 | − | 1.00000i | 0.117041 | − | 0.0675737i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.0000 | + | 3.46410i | 0.941742 | + | 0.233021i | ||||
\(222\) | 1.19615i | 0.0802805i | ||||||||
\(223\) | −13.7321 | − | 23.7846i | −0.919566 | − | 1.59274i | −0.800075 | − | 0.599900i | \(-0.795207\pi\) |
−0.119491 | − | 0.992835i | \(-0.538126\pi\) | |||||||
\(224\) | 1.00000 | + | 1.73205i | 0.0668153 | + | 0.115728i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.1962i | 0.744757i | ||||||||
\(227\) | 2.19615 | − | 3.80385i | 0.145764 | − | 0.252470i | −0.783894 | − | 0.620895i | \(-0.786769\pi\) |
0.929658 | + | 0.368425i | \(0.120103\pi\) | |||||||
\(228\) | −0.267949 | + | 0.464102i | −0.0177454 | + | 0.0307359i | ||||
\(229\) | − | 19.8564i | − | 1.31215i | −0.754696 | − | 0.656074i | \(-0.772216\pi\) | ||
0.754696 | − | 0.656074i | \(-0.227784\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.464102 | + | 0.803848i | 0.0305356 | + | 0.0528893i | ||||
\(232\) | −1.86603 | − | 3.23205i | −0.122511 | − | 0.212195i | ||||
\(233\) | 18.1244i | 1.18737i | 0.804699 | + | 0.593683i | \(0.202327\pi\) | ||||
−0.804699 | + | 0.593683i | \(0.797673\pi\) | |||||||
\(234\) | 3.46410 | − | 1.00000i | 0.226455 | − | 0.0653720i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.33013 | + | 0.767949i | −0.0865839 | + | 0.0499892i | ||||
\(237\) | 0.0621778 | − | 0.0358984i | 0.00403888 | − | 0.00233185i | ||||
\(238\) | −6.92820 | − | 4.00000i | −0.449089 | − | 0.259281i | ||||
\(239\) | − | 4.39230i | − | 0.284115i | −0.989858 | − | 0.142057i | \(-0.954628\pi\) | ||
0.989858 | − | 0.142057i | \(-0.0453717\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.3564 | − | 7.13397i | −0.795946 | − | 0.459540i | 0.0461056 | − | 0.998937i | \(-0.485319\pi\) |
−0.842052 | + | 0.539397i | \(0.818652\pi\) | |||||||
\(242\) | −10.7846 | −0.693261 | ||||||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | −5.19615 | − | 9.00000i | −0.332650 | − | 0.576166i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.00000 | −0.127515 | ||||||||
\(247\) | 1.87564 | + | 0.464102i | 0.119344 | + | 0.0295301i | ||||
\(248\) | − | 1.73205i | − | 0.109985i | ||||||
\(249\) | −4.26795 | + | 2.46410i | −0.270470 | + | 0.156156i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.13397 | + | 10.6244i | −0.387173 | + | 0.670603i | −0.992068 | − | 0.125702i | \(-0.959882\pi\) |
0.604895 | + | 0.796305i | \(0.293215\pi\) | |||||||
\(252\) | −2.00000 | −0.125988 | ||||||||
\(253\) | −0.0621778 | + | 0.107695i | −0.00390909 | + | 0.00677074i | ||||
\(254\) | 7.73205 | + | 4.46410i | 0.485152 | + | 0.280103i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −19.6244 | + | 11.3301i | −1.22413 | + | 0.706754i | −0.965797 | − | 0.259301i | \(-0.916508\pi\) |
−0.258337 | + | 0.966055i | \(0.583175\pi\) | |||||||
\(258\) | −0.964102 | − | 1.66987i | −0.0600223 | − | 0.103962i | ||||
\(259\) | −2.39230 | −0.148651 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.73205 | 0.231008 | ||||||||
\(262\) | −0.669873 | − | 1.16025i | −0.0413849 | − | 0.0716807i | ||||
\(263\) | 15.6962 | − | 9.06218i | 0.967866 | − | 0.558798i | 0.0692812 | − | 0.997597i | \(-0.477929\pi\) |
0.898585 | + | 0.438799i | \(0.144596\pi\) | |||||||
\(264\) | −0.232051 | + | 0.401924i | −0.0142817 | + | 0.0247367i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.928203 | − | 0.535898i | −0.0569118 | − | 0.0328580i | ||||
\(267\) | −3.73205 | + | 6.46410i | −0.228398 | + | 0.395597i | ||||
\(268\) | −4.53590 | −0.277074 | ||||||||
\(269\) | 6.00000 | − | 10.3923i | 0.365826 | − | 0.633630i | −0.623082 | − | 0.782157i | \(-0.714120\pi\) |
0.988908 | + | 0.148527i | \(0.0474530\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.96410 | − | 4.59808i | 0.483785 | − | 0.279313i | −0.238208 | − | 0.971214i | \(-0.576560\pi\) |
0.721992 | + | 0.691901i | \(0.243227\pi\) | |||||||
\(272\) | − | 4.00000i | − | 0.242536i | ||||||
\(273\) | 2.00000 | + | 6.92820i | 0.121046 | + | 0.419314i | ||||
\(274\) | 4.46410 | 0.269686 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.133975 | − | 0.232051i | −0.00806432 | − | 0.0139678i | ||||
\(277\) | −8.59808 | − | 4.96410i | −0.516608 | − | 0.298264i | 0.218938 | − | 0.975739i | \(-0.429741\pi\) |
−0.735546 | + | 0.677475i | \(0.763074\pi\) | |||||||
\(278\) | 0.928203 | 0.0556699 | ||||||||
\(279\) | 1.50000 | + | 0.866025i | 0.0898027 | + | 0.0518476i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.92820i | 0.293992i | 0.989137 | + | 0.146996i | \(0.0469604\pi\) | ||||
−0.989137 | + | 0.146996i | \(0.953040\pi\) | |||||||
\(282\) | 9.06218 | + | 5.23205i | 0.539645 | + | 0.311564i | ||||
\(283\) | −3.40192 | + | 1.96410i | −0.202223 | + | 0.116754i | −0.597692 | − | 0.801726i | \(-0.703915\pi\) |
0.395469 | + | 0.918479i | \(0.370582\pi\) | |||||||
\(284\) | 7.26795 | − | 4.19615i | 0.431273 | − | 0.248996i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.62436 | + | 0.401924i | 0.0960502 | + | 0.0237663i | ||||
\(287\) | − | 4.00000i | − | 0.236113i | ||||||
\(288\) | −0.500000 | − | 0.866025i | −0.0294628 | − | 0.0510310i | ||||
\(289\) | −0.500000 | − | 0.866025i | −0.0294118 | − | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 7.46410i | − | 0.437553i | ||||||
\(292\) | −1.00000 | + | 1.73205i | −0.0585206 | + | 0.101361i | ||||
\(293\) | 2.07180 | − | 3.58846i | 0.121036 | − | 0.209640i | −0.799141 | − | 0.601144i | \(-0.794712\pi\) |
0.920176 | + | 0.391504i | \(0.128045\pi\) | |||||||
\(294\) | 3.00000i | 0.174964i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.598076 | − | 1.03590i | −0.0347625 | − | 0.0602104i | ||||
\(297\) | −0.232051 | − | 0.401924i | −0.0134650 | − | 0.0233220i | ||||
\(298\) | − | 20.4641i | − | 1.18545i | ||||||
\(299\) | −0.669873 | + | 0.696152i | −0.0387398 | + | 0.0402595i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.33975 | − | 1.92820i | 0.192500 | − | 0.111140i | ||||
\(302\) | −9.00000 | + | 5.19615i | −0.517892 | + | 0.299005i | ||||
\(303\) | 9.46410 | + | 5.46410i | 0.543698 | + | 0.313904i | ||||
\(304\) | − | 0.535898i | − | 0.0307359i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.46410 | + | 2.00000i | 0.198030 | + | 0.114332i | ||||
\(307\) | −12.5359 | −0.715462 | −0.357731 | − | 0.933825i | \(-0.616449\pi\) | ||||
−0.357731 | + | 0.933825i | \(0.616449\pi\) | |||||||
\(308\) | −0.803848 | − | 0.464102i | −0.0458035 | − | 0.0264446i | ||||
\(309\) | −7.92820 | − | 13.7321i | −0.451020 | − | 0.781189i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.60770 | −0.431393 | −0.215696 | − | 0.976460i | \(-0.569202\pi\) | ||||
−0.215696 | + | 0.976460i | \(0.569202\pi\) | |||||||
\(312\) | −2.50000 | + | 2.59808i | −0.141535 | + | 0.147087i | ||||
\(313\) | 28.0000i | 1.58265i | 0.611393 | + | 0.791327i | \(0.290609\pi\) | ||||
−0.611393 | + | 0.791327i | \(0.709391\pi\) | |||||||
\(314\) | 4.33013 | − | 2.50000i | 0.244363 | − | 0.141083i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.0358984 | + | 0.0621778i | −0.00201944 | + | 0.00349778i | ||||
\(317\) | −21.4641 | −1.20554 | −0.602772 | − | 0.797913i | \(-0.705937\pi\) | ||||
−0.602772 | + | 0.797913i | \(0.705937\pi\) | |||||||
\(318\) | −6.46410 | + | 11.1962i | −0.362489 | + | 0.627849i | ||||
\(319\) | 1.50000 | + | 0.866025i | 0.0839839 | + | 0.0484881i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.92820 | − | 17.1962i | 0.554138 | − | 0.959796i | ||||
\(322\) | 0.464102 | − | 0.267949i | 0.0258634 | − | 0.0149322i | ||||
\(323\) | 1.07180 | + | 1.85641i | 0.0596364 | + | 0.103293i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 23.0526 | 1.27676 | ||||||||
\(327\) | −5.92820 | − | 10.2679i | −0.327830 | − | 0.567819i | ||||
\(328\) | 1.73205 | − | 1.00000i | 0.0956365 | − | 0.0552158i | ||||
\(329\) | −10.4641 | + | 18.1244i | −0.576905 | + | 0.999228i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.4641 | − | 12.3923i | −1.17977 | − | 0.681143i | −0.223812 | − | 0.974632i | \(-0.571850\pi\) |
−0.955962 | + | 0.293490i | \(0.905183\pi\) | |||||||
\(332\) | 2.46410 | − | 4.26795i | 0.135235 | − | 0.234234i | ||||
\(333\) | 1.19615 | 0.0655487 | ||||||||
\(334\) | −9.16025 | + | 15.8660i | −0.501227 | + | 0.868150i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.73205 | − | 1.00000i | 0.0944911 | − | 0.0545545i | ||||
\(337\) | − | 25.3205i | − | 1.37930i | −0.724145 | − | 0.689648i | \(-0.757765\pi\) | ||
0.724145 | − | 0.689648i | \(-0.242235\pi\) | |||||||
\(338\) | 11.5000 | + | 6.06218i | 0.625518 | + | 0.329739i | ||||
\(339\) | 11.1962 | 0.608092 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.401924 | + | 0.696152i | 0.0217654 | + | 0.0376988i | ||||
\(342\) | 0.464102 | + | 0.267949i | 0.0250957 | + | 0.0144890i | ||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | 1.66987 | + | 0.964102i | 0.0900335 | + | 0.0519809i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 2.92820i | − | 0.157421i | ||||||
\(347\) | −19.3923 | − | 11.1962i | −1.04103 | − | 0.601041i | −0.120908 | − | 0.992664i | \(-0.538580\pi\) |
−0.920126 | + | 0.391623i | \(0.871914\pi\) | |||||||
\(348\) | −3.23205 | + | 1.86603i | −0.173256 | + | 0.100029i | ||||
\(349\) | 12.5885 | − | 7.26795i | 0.673845 | − | 0.389044i | −0.123687 | − | 0.992321i | \(-0.539472\pi\) |
0.797532 | + | 0.603277i | \(0.206139\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | − | 3.46410i | −0.0533761 | − | 0.184900i | ||||
\(352\) | − | 0.464102i | − | 0.0247367i | ||||||
\(353\) | 1.00000 | + | 1.73205i | 0.0532246 | + | 0.0921878i | 0.891410 | − | 0.453197i | \(-0.149717\pi\) |
−0.838186 | + | 0.545385i | \(0.816383\pi\) | |||||||
\(354\) | 0.767949 | + | 1.33013i | 0.0408160 | + | 0.0706955i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 7.46410i | − | 0.395597i | ||||||
\(357\) | −4.00000 | + | 6.92820i | −0.211702 | + | 0.366679i | ||||
\(358\) | 8.13397 | − | 14.0885i | 0.429894 | − | 0.744598i | ||||
\(359\) | − | 18.9282i | − | 0.998992i | −0.866316 | − | 0.499496i | \(-0.833518\pi\) | ||
0.866316 | − | 0.499496i | \(-0.166482\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.35641 | − | 16.2058i | −0.492442 | − | 0.852935i | ||||
\(362\) | 5.46410 | + | 9.46410i | 0.287187 | + | 0.497422i | ||||
\(363\) | 10.7846i | 0.566045i | ||||||||
\(364\) | −5.19615 | − | 5.00000i | −0.272352 | − | 0.262071i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −9.00000 | + | 5.19615i | −0.470438 | + | 0.271607i | ||||
\(367\) | 31.5167 | − | 18.1962i | 1.64516 | − | 0.949831i | 0.666197 | − | 0.745776i | \(-0.267921\pi\) |
0.978959 | − | 0.204056i | \(-0.0654123\pi\) | |||||||
\(368\) | 0.232051 | + | 0.133975i | 0.0120965 | + | 0.00698391i | ||||
\(369\) | 2.00000i | 0.104116i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −22.3923 | − | 12.9282i | −1.16255 | − | 0.671199i | ||||
\(372\) | −1.73205 | −0.0898027 | ||||||||
\(373\) | 22.3301 | + | 12.8923i | 1.15621 | + | 0.667538i | 0.950393 | − | 0.311052i | \(-0.100681\pi\) |
0.205817 | + | 0.978590i | \(0.434015\pi\) | |||||||
\(374\) | 0.928203 | + | 1.60770i | 0.0479962 | + | 0.0831319i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.4641 | −0.539645 | ||||||||
\(377\) | 9.69615 | + | 9.33013i | 0.499377 | + | 0.480526i | ||||
\(378\) | 2.00000i | 0.102869i | ||||||||
\(379\) | 0.124356 | − | 0.0717968i | 0.00638772 | − | 0.00368795i | −0.496803 | − | 0.867863i | \(-0.665493\pi\) |
0.503190 | + | 0.864176i | \(0.332159\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.46410 | − | 7.73205i | 0.228703 | − | 0.396125i | ||||
\(382\) | −14.5359 | −0.743721 | ||||||||
\(383\) | −2.30385 | + | 3.99038i | −0.117721 | + | 0.203899i | −0.918864 | − | 0.394574i | \(-0.870892\pi\) |
0.801143 | + | 0.598473i | \(0.204226\pi\) | |||||||
\(384\) | 0.866025 | + | 0.500000i | 0.0441942 | + | 0.0255155i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11.6603 | − | 20.1962i | 0.593491 | − | 1.02796i | ||||
\(387\) | −1.66987 | + | 0.964102i | −0.0848844 | + | 0.0490080i | ||||
\(388\) | 3.73205 | + | 6.46410i | 0.189466 | + | 0.328165i | ||||
\(389\) | 20.2679 | 1.02763 | 0.513813 | − | 0.857902i | \(-0.328233\pi\) | ||||
0.513813 | + | 0.857902i | \(0.328233\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.07180 | −0.0542031 | ||||||||
\(392\) | −1.50000 | − | 2.59808i | −0.0757614 | − | 0.131223i | ||||
\(393\) | −1.16025 | + | 0.669873i | −0.0585271 | + | 0.0337906i | ||||
\(394\) | −8.19615 | + | 14.1962i | −0.412916 | + | 0.715192i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.401924 | + | 0.232051i | 0.0201974 | + | 0.0116610i | ||||
\(397\) | −6.06218 | + | 10.5000i | −0.304252 | + | 0.526980i | −0.977095 | − | 0.212806i | \(-0.931740\pi\) |
0.672843 | + | 0.739786i | \(0.265073\pi\) | |||||||
\(398\) | −18.9282 | −0.948785 | ||||||||
\(399\) | −0.535898 | + | 0.928203i | −0.0268285 | + | 0.0464683i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.7128 | − | 16.0000i | 1.38391 | − | 0.799002i | 0.391292 | − | 0.920267i | \(-0.372028\pi\) |
0.992620 | + | 0.121265i | \(0.0386950\pi\) | |||||||
\(402\) | 4.53590i | 0.226230i | ||||||||
\(403\) | 1.73205 | + | 6.00000i | 0.0862796 | + | 0.298881i | ||||
\(404\) | −10.9282 | −0.543698 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.73205 | − | 6.46410i | −0.185219 | − | 0.320808i | ||||
\(407\) | 0.480762 | + | 0.277568i | 0.0238305 | + | 0.0137585i | ||||
\(408\) | −4.00000 | −0.198030 | ||||||||
\(409\) | 3.46410 | + | 2.00000i | 0.171289 | + | 0.0988936i | 0.583193 | − | 0.812333i | \(-0.301803\pi\) |
−0.411905 | + | 0.911227i | \(0.635136\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 4.46410i | − | 0.220198i | ||||||
\(412\) | 13.7321 | + | 7.92820i | 0.676530 | + | 0.390595i | ||||
\(413\) | −2.66025 | + | 1.53590i | −0.130903 | + | 0.0755766i | ||||
\(414\) | −0.232051 | + | 0.133975i | −0.0114047 | + | 0.00658449i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.866025 | − | 3.50000i | 0.0424604 | − | 0.171602i | ||||
\(417\) | − | 0.928203i | − | 0.0454543i | ||||||
\(418\) | 0.124356 | + | 0.215390i | 0.00608243 | + | 0.0105351i | ||||
\(419\) | 0.803848 | + | 1.39230i | 0.0392705 | + | 0.0680185i | 0.884993 | − | 0.465605i | \(-0.154163\pi\) |
−0.845722 | + | 0.533624i | \(0.820830\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 16.3923i | − | 0.798912i | −0.916752 | − | 0.399456i | \(-0.869199\pi\) | ||
0.916752 | − | 0.399456i | \(-0.130801\pi\) | |||||||
\(422\) | 11.6603 | − | 20.1962i | 0.567612 | − | 0.983133i | ||||
\(423\) | 5.23205 | − | 9.06218i | 0.254391 | − | 0.440618i | ||||
\(424\) | − | 12.9282i | − | 0.627849i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.19615 | − | 7.26795i | −0.203304 | − | 0.352133i | ||||
\(427\) | −10.3923 | − | 18.0000i | −0.502919 | − | 0.871081i | ||||
\(428\) | 19.8564i | 0.959796i | ||||||||
\(429\) | 0.401924 | − | 1.62436i | 0.0194051 | − | 0.0784246i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.58846 | + | 3.80385i | −0.317355 | + | 0.183225i | −0.650213 | − | 0.759752i | \(-0.725320\pi\) |
0.332858 | + | 0.942977i | \(0.391987\pi\) | |||||||
\(432\) | −0.866025 | + | 0.500000i | −0.0416667 | + | 0.0240563i | ||||
\(433\) | −13.2679 | − | 7.66025i | −0.637617 | − | 0.368128i | 0.146079 | − | 0.989273i | \(-0.453335\pi\) |
−0.783696 | + | 0.621145i | \(0.786668\pi\) | |||||||
\(434\) | − | 3.46410i | − | 0.166282i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.2679 | + | 5.92820i | 0.491746 | + | 0.283909i | ||||
\(437\) | −0.143594 | −0.00686901 | ||||||||
\(438\) | 1.73205 | + | 1.00000i | 0.0827606 | + | 0.0477818i | ||||
\(439\) | 4.92820 | + | 8.53590i | 0.235210 | + | 0.407396i | 0.959334 | − | 0.282274i | \(-0.0910888\pi\) |
−0.724123 | + | 0.689670i | \(0.757755\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.00000 | 0.142857 | ||||||||
\(442\) | 4.00000 | + | 13.8564i | 0.190261 | + | 0.659082i | ||||
\(443\) | 4.39230i | 0.208685i | 0.994541 | + | 0.104342i | \(0.0332738\pi\) | ||||
−0.994541 | + | 0.104342i | \(0.966726\pi\) | |||||||
\(444\) | −1.03590 | + | 0.598076i | −0.0491616 | + | 0.0283834i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 13.7321 | − | 23.7846i | 0.650231 | − | 1.12623i | ||||
\(447\) | −20.4641 | −0.967919 | ||||||||
\(448\) | −1.00000 | + | 1.73205i | −0.0472456 | + | 0.0818317i | ||||
\(449\) | 34.3923 | + | 19.8564i | 1.62307 | + | 0.937082i | 0.986092 | + | 0.166203i | \(0.0531506\pi\) |
0.636982 | + | 0.770879i | \(0.280183\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.464102 | + | 0.803848i | −0.0218537 | + | 0.0378517i | ||||
\(452\) | −9.69615 | + | 5.59808i | −0.456069 | + | 0.263311i | ||||
\(453\) | 5.19615 | + | 9.00000i | 0.244137 | + | 0.422857i | ||||
\(454\) | 4.39230 | 0.206141 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.535898 | −0.0250957 | ||||||||
\(457\) | −15.7321 | − | 27.2487i | −0.735914 | − | 1.27464i | −0.954321 | − | 0.298783i | \(-0.903419\pi\) |
0.218407 | − | 0.975858i | \(-0.429914\pi\) | |||||||
\(458\) | 17.1962 | − | 9.92820i | 0.803523 | − | 0.463914i | ||||
\(459\) | 2.00000 | − | 3.46410i | 0.0933520 | − | 0.161690i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.59808 | + | 3.23205i | 0.260728 | + | 0.150532i | 0.624667 | − | 0.780891i | \(-0.285235\pi\) |
−0.363938 | + | 0.931423i | \(0.618568\pi\) | |||||||
\(462\) | −0.464102 | + | 0.803848i | −0.0215920 | + | 0.0373984i | ||||
\(463\) | 20.9282 | 0.972616 | 0.486308 | − | 0.873787i | \(-0.338343\pi\) | ||||
0.486308 | + | 0.873787i | \(0.338343\pi\) | |||||||
\(464\) | 1.86603 | − | 3.23205i | 0.0866281 | − | 0.150044i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −15.6962 | + | 9.06218i | −0.727110 | + | 0.419797i | ||||
\(467\) | 11.8564i | 0.548649i | 0.961637 | + | 0.274325i | \(0.0884542\pi\) | ||||
−0.961637 | + | 0.274325i | \(0.911546\pi\) | |||||||
\(468\) | 2.59808 | + | 2.50000i | 0.120096 | + | 0.115563i | ||||
\(469\) | −9.07180 | −0.418897 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.50000 | − | 4.33013i | −0.115194 | − | 0.199522i | ||||
\(472\) | −1.33013 | − | 0.767949i | −0.0612241 | − | 0.0353477i | ||||
\(473\) | −0.894882 | −0.0411467 | ||||||||
\(474\) | 0.0621778 | + | 0.0358984i | 0.00285592 | + | 0.00164887i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 8.00000i | − | 0.366679i | ||||||
\(477\) | 11.1962 | + | 6.46410i | 0.512637 | + | 0.295971i | ||||
\(478\) | 3.80385 | − | 2.19615i | 0.173984 | − | 0.100450i | ||||
\(479\) | −1.26795 | + | 0.732051i | −0.0579341 | + | 0.0334483i | −0.528687 | − | 0.848817i | \(-0.677316\pi\) |
0.470753 | + | 0.882265i | \(0.343982\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.10770 | + | 2.99038i | 0.141699 | + | 0.136350i | ||||
\(482\) | − | 14.2679i | − | 0.649887i | ||||||
\(483\) | −0.267949 | − | 0.464102i | −0.0121921 | − | 0.0211174i | ||||
\(484\) | −5.39230 | − | 9.33975i | −0.245105 | − | 0.424534i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | −19.5885 | + | 33.9282i | −0.887638 | + | 1.53743i | −0.0449775 | + | 0.998988i | \(0.514322\pi\) |
−0.842660 | + | 0.538446i | \(0.819012\pi\) | |||||||
\(488\) | 5.19615 | − | 9.00000i | 0.235219 | − | 0.407411i | ||||
\(489\) | − | 23.0526i | − | 1.04247i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.66025 | − | 15.0000i | −0.390832 | − | 0.676941i | 0.601728 | − | 0.798701i | \(-0.294479\pi\) |
−0.992559 | + | 0.121761i | \(0.961146\pi\) | |||||||
\(492\) | −1.00000 | − | 1.73205i | −0.0450835 | − | 0.0780869i | ||||
\(493\) | 14.9282i | 0.672332i | ||||||||
\(494\) | 0.535898 | + | 1.85641i | 0.0241112 | + | 0.0835237i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.50000 | − | 0.866025i | 0.0673520 | − | 0.0388857i | ||||
\(497\) | 14.5359 | − | 8.39230i | 0.652024 | − | 0.376446i | ||||
\(498\) | −4.26795 | − | 2.46410i | −0.191251 | − | 0.110419i | ||||
\(499\) | − | 13.4641i | − | 0.602736i | −0.953508 | − | 0.301368i | \(-0.902557\pi\) | ||
0.953508 | − | 0.301368i | \(-0.0974433\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 15.8660 | + | 9.16025i | 0.708842 | + | 0.409250i | ||||
\(502\) | −12.2679 | −0.547545 | ||||||||
\(503\) | 27.0000 | + | 15.5885i | 1.20387 | + | 0.695055i | 0.961414 | − | 0.275107i | \(-0.0887134\pi\) |
0.242457 | + | 0.970162i | \(0.422047\pi\) | |||||||
\(504\) | −1.00000 | − | 1.73205i | −0.0445435 | − | 0.0771517i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.124356 | −0.00552828 | ||||||||
\(507\) | 6.06218 | − | 11.5000i | 0.269231 | − | 0.510733i | ||||
\(508\) | 8.92820i | 0.396125i | ||||||||
\(509\) | −16.7942 | + | 9.69615i | −0.744391 | + | 0.429774i | −0.823664 | − | 0.567079i | \(-0.808074\pi\) |
0.0792726 | + | 0.996853i | \(0.474740\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.00000 | + | 3.46410i | −0.0884748 | + | 0.153243i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0.267949 | − | 0.464102i | 0.0118302 | − | 0.0204906i | ||||
\(514\) | −19.6244 | − | 11.3301i | −0.865593 | − | 0.499750i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.964102 | − | 1.66987i | 0.0424422 | − | 0.0735121i | ||||
\(517\) | 4.20577 | − | 2.42820i | 0.184970 | − | 0.106792i | ||||
\(518\) | −1.19615 | − | 2.07180i | −0.0525559 | − | 0.0910295i | ||||
\(519\) | −2.92820 | −0.128534 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.3205 | 0.758825 | 0.379413 | − | 0.925228i | \(-0.376126\pi\) | ||||
0.379413 | + | 0.925228i | \(0.376126\pi\) | |||||||
\(522\) | 1.86603 | + | 3.23205i | 0.0816737 | + | 0.141463i | ||||
\(523\) | 25.7942 | − | 14.8923i | 1.12790 | − | 0.651195i | 0.184496 | − | 0.982833i | \(-0.440935\pi\) |
0.943407 | + | 0.331638i | \(0.107601\pi\) | |||||||
\(524\) | 0.669873 | − | 1.16025i | 0.0292635 | − | 0.0506859i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.6962 | + | 9.06218i | 0.684385 | + | 0.395130i | ||||
\(527\) | −3.46410 | + | 6.00000i | −0.150899 | + | 0.261364i | ||||
\(528\) | −0.464102 | −0.0201974 | ||||||||
\(529\) | −11.4641 | + | 19.8564i | −0.498439 | + | 0.863322i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.33013 | − | 0.767949i | 0.0577226 | − | 0.0333262i | ||||
\(532\) | − | 1.07180i | − | 0.0464683i | ||||||
\(533\) | −5.00000 | + | 5.19615i | −0.216574 | + | 0.225070i | ||||
\(534\) | −7.46410 | −0.323003 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.26795 | − | 3.92820i | −0.0979605 | − | 0.169673i | ||||
\(537\) | −14.0885 | − | 8.13397i | −0.607962 | − | 0.351007i | ||||
\(538\) | 12.0000 | 0.517357 | ||||||||
\(539\) | 1.20577 | + | 0.696152i | 0.0519362 | + | 0.0299854i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.0718i | 0.562000i | 0.959708 | + | 0.281000i | \(0.0906662\pi\) | ||||
−0.959708 | + | 0.281000i | \(0.909334\pi\) | |||||||
\(542\) | 7.96410 | + | 4.59808i | 0.342087 | + | 0.197504i | ||||
\(543\) | 9.46410 | − | 5.46410i | 0.406143 | − | 0.234487i | ||||
\(544\) | 3.46410 | − | 2.00000i | 0.148522 | − | 0.0857493i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −5.00000 | + | 5.19615i | −0.213980 | + | 0.222375i | ||||
\(547\) | 9.07180i | 0.387882i | 0.981013 | + | 0.193941i | \(0.0621270\pi\) | ||||
−0.981013 | + | 0.193941i | \(0.937873\pi\) | |||||||
\(548\) | 2.23205 | + | 3.86603i | 0.0953485 | + | 0.165148i | ||||
\(549\) | 5.19615 | + | 9.00000i | 0.221766 | + | 0.384111i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.00000i | 0.0852029i | ||||||||
\(552\) | 0.133975 | − | 0.232051i | 0.00570234 | − | 0.00987674i | ||||
\(553\) | −0.0717968 | + | 0.124356i | −0.00305311 | + | 0.00528814i | ||||
\(554\) | − | 9.92820i | − | 0.421809i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.464102 | + | 0.803848i | 0.0196823 | + | 0.0340907i | ||||
\(557\) | 18.8564 | + | 32.6603i | 0.798972 | + | 1.38386i | 0.920286 | + | 0.391245i | \(0.127956\pi\) |
−0.121315 | + | 0.992614i | \(0.538711\pi\) | |||||||
\(558\) | 1.73205i | 0.0733236i | ||||||||
\(559\) | −6.74871 | − | 1.66987i | −0.285440 | − | 0.0706281i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.60770 | − | 0.928203i | 0.0678769 | − | 0.0391888i | ||||
\(562\) | −4.26795 | + | 2.46410i | −0.180033 | + | 0.103942i | ||||
\(563\) | −34.0526 | − | 19.6603i | −1.43514 | − | 0.828581i | −0.437637 | − | 0.899152i | \(-0.644185\pi\) |
−0.997507 | + | 0.0705706i | \(0.977518\pi\) | |||||||
\(564\) | 10.4641i | 0.440618i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3.40192 | − | 1.96410i | −0.142994 | − | 0.0825573i | ||||
\(567\) | 2.00000 | 0.0839921 | ||||||||
\(568\) | 7.26795 | + | 4.19615i | 0.304956 | + | 0.176067i | ||||
\(569\) | −2.66025 | − | 4.60770i | −0.111524 | − | 0.193165i | 0.804861 | − | 0.593463i | \(-0.202240\pi\) |
−0.916385 | + | 0.400299i | \(0.868906\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 45.1769 | 1.89060 | 0.945298 | − | 0.326209i | \(-0.105771\pi\) | ||||
0.945298 | + | 0.326209i | \(0.105771\pi\) | |||||||
\(572\) | 0.464102 | + | 1.60770i | 0.0194051 | + | 0.0672211i | ||||
\(573\) | 14.5359i | 0.607246i | ||||||||
\(574\) | 3.46410 | − | 2.00000i | 0.144589 | − | 0.0834784i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | 10.0000 | 0.416305 | 0.208153 | − | 0.978096i | \(-0.433255\pi\) | ||||
0.208153 | + | 0.978096i | \(0.433255\pi\) | |||||||
\(578\) | 0.500000 | − | 0.866025i | 0.0207973 | − | 0.0360219i | ||||
\(579\) | −20.1962 | − | 11.6603i | −0.839323 | − | 0.484584i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.92820 | − | 8.53590i | 0.204456 | − | 0.354129i | ||||
\(582\) | 6.46410 | − | 3.73205i | 0.267946 | − | 0.154698i | ||||
\(583\) | 3.00000 | + | 5.19615i | 0.124247 | + | 0.215203i | ||||
\(584\) | −2.00000 | −0.0827606 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.14359 | 0.171170 | ||||||||
\(587\) | −9.19615 | − | 15.9282i | −0.379566 | − | 0.657427i | 0.611433 | − | 0.791296i | \(-0.290593\pi\) |
−0.990999 | + | 0.133869i | \(0.957260\pi\) | |||||||
\(588\) | −2.59808 | + | 1.50000i | −0.107143 | + | 0.0618590i | ||||
\(589\) | −0.464102 | + | 0.803848i | −0.0191230 | + | 0.0331220i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.1962 | + | 8.19615i | 0.583952 | + | 0.337145i | ||||
\(592\) | 0.598076 | − | 1.03590i | 0.0245808 | − | 0.0425752i | ||||
\(593\) | −31.1051 | −1.27733 | −0.638667 | − | 0.769483i | \(-0.720514\pi\) | ||||
−0.638667 | + | 0.769483i | \(0.720514\pi\) | |||||||
\(594\) | 0.232051 | − | 0.401924i | 0.00952116 | − | 0.0164911i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 17.7224 | − | 10.2321i | 0.725939 | − | 0.419121i | ||||
\(597\) | 18.9282i | 0.774680i | ||||||||
\(598\) | −0.937822 | − | 0.232051i | −0.0383504 | − | 0.00948926i | ||||
\(599\) | −10.3923 | −0.424618 | −0.212309 | − | 0.977203i | \(-0.568098\pi\) | ||||
−0.212309 | + | 0.977203i | \(0.568098\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.8923 | − | 18.8660i | −0.444306 | − | 0.769561i | 0.553697 | − | 0.832718i | \(-0.313216\pi\) |
−0.998004 | + | 0.0631568i | \(0.979883\pi\) | |||||||
\(602\) | 3.33975 | + | 1.92820i | 0.136118 | + | 0.0785877i | ||||
\(603\) | 4.53590 | 0.184716 | ||||||||
\(604\) | −9.00000 | − | 5.19615i | −0.366205 | − | 0.211428i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 10.9282i | 0.443928i | ||||||||
\(607\) | −37.3923 | − | 21.5885i | −1.51771 | − | 0.876248i | −0.999783 | − | 0.0208216i | \(-0.993372\pi\) |
−0.517924 | − | 0.855427i | \(-0.673295\pi\) | |||||||
\(608\) | 0.464102 | − | 0.267949i | 0.0188218 | − | 0.0108668i | ||||
\(609\) | −6.46410 | + | 3.73205i | −0.261939 | + | 0.151230i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 36.2487 | − | 10.4641i | 1.46647 | − | 0.423332i | ||||
\(612\) | 4.00000i | 0.161690i | ||||||||
\(613\) | −0.473721 | − | 0.820508i | −0.0191334 | − | 0.0331400i | 0.856300 | − | 0.516478i | \(-0.172757\pi\) |
−0.875434 | + | 0.483338i | \(0.839424\pi\) | |||||||
\(614\) | −6.26795 | − | 10.8564i | −0.252954 | − | 0.438129i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 0.928203i | − | 0.0373984i | ||||||
\(617\) | −7.76795 | + | 13.4545i | −0.312726 | + | 0.541657i | −0.978951 | − | 0.204093i | \(-0.934575\pi\) |
0.666226 | + | 0.745750i | \(0.267909\pi\) | |||||||
\(618\) | 7.92820 | − | 13.7321i | 0.318919 | − | 0.552384i | ||||
\(619\) | − | 24.2487i | − | 0.974638i | −0.873224 | − | 0.487319i | \(-0.837975\pi\) | ||
0.873224 | − | 0.487319i | \(-0.162025\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.133975 | + | 0.232051i | 0.00537622 | + | 0.00931188i | ||||
\(622\) | −3.80385 | − | 6.58846i | −0.152520 | − | 0.264173i | ||||
\(623\) | − | 14.9282i | − | 0.598086i | ||||||
\(624\) | −3.50000 | − | 0.866025i | −0.140112 | − | 0.0346688i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −24.2487 | + | 14.0000i | −0.969173 | + | 0.559553i | ||||
\(627\) | 0.215390 | − | 0.124356i | 0.00860186 | − | 0.00496629i | ||||
\(628\) | 4.33013 | + | 2.50000i | 0.172791 | + | 0.0997609i | ||||
\(629\) | 4.78461i | 0.190775i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.2487 | − | 12.2679i | −0.845898 | − | 0.488379i | 0.0133668 | − | 0.999911i | \(-0.495745\pi\) |
−0.859265 | + | 0.511531i | \(0.829078\pi\) | |||||||
\(632\) | −0.0717968 | −0.00285592 | ||||||||
\(633\) | −20.1962 | − | 11.6603i | −0.802725 | − | 0.463453i | ||||
\(634\) | −10.7321 | − | 18.5885i | −0.426224 | − | 0.738242i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −12.9282 | −0.512637 | ||||||||
\(637\) | 7.79423 | + | 7.50000i | 0.308819 | + | 0.297161i | ||||
\(638\) | 1.73205i | 0.0685725i | ||||||||
\(639\) | −7.26795 | + | 4.19615i | −0.287516 | + | 0.165997i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.9282 | + | 24.1244i | −0.550131 | + | 0.952855i | 0.448134 | + | 0.893967i | \(0.352089\pi\) |
−0.998265 | + | 0.0588882i | \(0.981244\pi\) | |||||||
\(642\) | 19.8564 | 0.783670 | ||||||||
\(643\) | 13.7321 | − | 23.7846i | 0.541539 | − | 0.937973i | −0.457277 | − | 0.889324i | \(-0.651175\pi\) |
0.998816 | − | 0.0486490i | \(-0.0154916\pi\) | |||||||
\(644\) | 0.464102 | + | 0.267949i | 0.0182882 | + | 0.0105587i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.07180 | + | 1.85641i | −0.0421693 | + | 0.0730393i | ||||
\(647\) | 18.4641 | − | 10.6603i | 0.725899 | − | 0.419098i | −0.0910212 | − | 0.995849i | \(-0.529013\pi\) |
0.816920 | + | 0.576751i | \(0.195680\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | 0.712813 | 0.0279804 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.46410 | −0.135769 | ||||||||
\(652\) | 11.5263 | + | 19.9641i | 0.451404 | + | 0.781855i | ||||
\(653\) | 38.3205 | − | 22.1244i | 1.49960 | − | 0.865793i | 0.499597 | − | 0.866258i | \(-0.333481\pi\) |
1.00000 | 0.000464739i | \(0.000147931\pi\) | ||||||||
\(654\) | 5.92820 | − | 10.2679i | 0.231811 | − | 0.401509i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.73205 | + | 1.00000i | 0.0676252 | + | 0.0390434i | ||||
\(657\) | 1.00000 | − | 1.73205i | 0.0390137 | − | 0.0675737i | ||||
\(658\) | −20.9282 | −0.815866 | ||||||||
\(659\) | −1.86603 | + | 3.23205i | −0.0726900 | + | 0.125903i | −0.900079 | − | 0.435726i | \(-0.856492\pi\) |
0.827389 | + | 0.561629i | \(0.189825\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.5167 | − | 21.6603i | 1.45923 | − | 0.842486i | 0.460256 | − | 0.887786i | \(-0.347758\pi\) |
0.998973 | + | 0.0453002i | \(0.0144244\pi\) | |||||||
\(662\) | − | 24.7846i | − | 0.963281i | ||||||
\(663\) | 13.8564 | − | 4.00000i | 0.538138 | − | 0.155347i | ||||
\(664\) | 4.92820 | 0.191251 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.598076 | + | 1.03590i | 0.0231750 | + | 0.0401402i | ||||
\(667\) | −0.866025 | − | 0.500000i | −0.0335326 | − | 0.0193601i | ||||
\(668\) | −18.3205 | −0.708842 | ||||||||
\(669\) | −23.7846 | − | 13.7321i | −0.919566 | − | 0.530912i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.82309i | 0.186193i | ||||||||
\(672\) | 1.73205 | + | 1.00000i | 0.0668153 | + | 0.0385758i | ||||
\(673\) | −27.7128 | + | 16.0000i | −1.06825 | + | 0.616755i | −0.927703 | − | 0.373319i | \(-0.878220\pi\) |
−0.140548 | + | 0.990074i | \(0.544886\pi\) | |||||||
\(674\) | 21.9282 | − | 12.6603i | 0.844643 | − | 0.487655i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.500000 | + | 12.9904i | 0.0192308 | + | 0.499630i | ||||
\(677\) | 11.6077i | 0.446120i | 0.974805 | + | 0.223060i | \(0.0716046\pi\) | ||||
−0.974805 | + | 0.223060i | \(0.928395\pi\) | |||||||
\(678\) | 5.59808 | + | 9.69615i | 0.214993 | + | 0.372378i | ||||
\(679\) | 7.46410 | + | 12.9282i | 0.286446 | + | 0.496139i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 4.39230i | − | 0.168313i | ||||||
\(682\) | −0.401924 | + | 0.696152i | −0.0153905 | + | 0.0266571i | ||||
\(683\) | −0.392305 | + | 0.679492i | −0.0150111 | + | 0.0260000i | −0.873433 | − | 0.486944i | \(-0.838112\pi\) |
0.858422 | + | 0.512944i | \(0.171445\pi\) | |||||||
\(684\) | 0.535898i | 0.0204906i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −10.0000 | − | 17.3205i | −0.381802 | − | 0.661300i | ||||
\(687\) | −9.92820 | − | 17.1962i | −0.378785 | − | 0.656074i | ||||
\(688\) | 1.92820i | 0.0735121i | ||||||||
\(689\) | 12.9282 | + | 44.7846i | 0.492525 | + | 1.70616i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.4641 | + | 17.5885i | −1.15891 | + | 0.669096i | −0.951042 | − | 0.309061i | \(-0.899985\pi\) |
−0.207867 | + | 0.978157i | \(0.566652\pi\) | |||||||
\(692\) | 2.53590 | − | 1.46410i | 0.0964004 | − | 0.0556568i | ||||
\(693\) | 0.803848 | + | 0.464102i | 0.0305356 | + | 0.0176298i | ||||
\(694\) | − | 22.3923i | − | 0.850000i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.23205 | − | 1.86603i | −0.122511 | − | 0.0707315i | ||||
\(697\) | −8.00000 | −0.303022 | ||||||||
\(698\) | 12.5885 | + | 7.26795i | 0.476480 | + | 0.275096i | ||||
\(699\) | 9.06218 | + | 15.6962i | 0.342763 | + | 0.593683i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.73205 | −0.140958 | −0.0704788 | − | 0.997513i | \(-0.522453\pi\) | ||||
−0.0704788 | + | 0.997513i | \(0.522453\pi\) | |||||||
\(702\) | 2.50000 | − | 2.59808i | 0.0943564 | − | 0.0980581i | ||||
\(703\) | 0.641016i | 0.0241764i | ||||||||
\(704\) | 0.401924 | − | 0.232051i | 0.0151481 | − | 0.00874574i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.00000 | + | 1.73205i | −0.0376355 | + | 0.0651866i | ||||
\(707\) | −21.8564 | −0.821995 | ||||||||
\(708\) | −0.767949 | + | 1.33013i | −0.0288613 | + | 0.0499892i | ||||
\(709\) | −7.85641 | − | 4.53590i | −0.295054 | − | 0.170349i | 0.345165 | − | 0.938542i | \(-0.387823\pi\) |
−0.640219 | + | 0.768193i | \(0.721156\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.0358984 | − | 0.0621778i | 0.00134629 | − | 0.00233185i | ||||
\(712\) | 6.46410 | − | 3.73205i | 0.242252 | − | 0.139865i | ||||
\(713\) | −0.232051 | − | 0.401924i | −0.00869037 | − | 0.0150522i | ||||
\(714\) | −8.00000 | −0.299392 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.2679 | 0.607962 | ||||||||
\(717\) | −2.19615 | − | 3.80385i | −0.0820168 | − | 0.142057i | ||||
\(718\) | 16.3923 | − | 9.46410i | 0.611755 | − | 0.353197i | ||||
\(719\) | 17.3205 | − | 30.0000i | 0.645946 | − | 1.11881i | −0.338136 | − | 0.941097i | \(-0.609796\pi\) |
0.984082 | − | 0.177714i | \(-0.0568702\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.4641 | + | 15.8564i | 1.02282 | + | 0.590523i | ||||
\(722\) | 9.35641 | − | 16.2058i | 0.348209 | − | 0.603116i | ||||
\(723\) | −14.2679 | −0.530631 | ||||||||
\(724\) | −5.46410 | + | 9.46410i | −0.203072 | + | 0.351731i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −9.33975 | + | 5.39230i | −0.346630 | + | 0.200127i | ||||
\(727\) | 23.7128i | 0.879460i | 0.898130 | + | 0.439730i | \(0.144926\pi\) | ||||
−0.898130 | + | 0.439730i | \(0.855074\pi\) | |||||||
\(728\) | 1.73205 | − | 7.00000i | 0.0641941 | − | 0.259437i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.85641 | − | 6.67949i | −0.142634 | − | 0.247050i | ||||
\(732\) | −9.00000 | − | 5.19615i | −0.332650 | − | 0.192055i | ||||
\(733\) | −37.0718 | −1.36928 | −0.684639 | − | 0.728882i | \(-0.740040\pi\) | ||||
−0.684639 | + | 0.728882i | \(0.740040\pi\) | |||||||
\(734\) | 31.5167 | + | 18.1962i | 1.16330 | + | 0.671632i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.267949i | 0.00987674i | ||||||||
\(737\) | 1.82309 | + | 1.05256i | 0.0671542 | + | 0.0387715i | ||||
\(738\) | −1.73205 | + | 1.00000i | −0.0637577 | + | 0.0368105i | ||||
\(739\) | 13.2679 | − | 7.66025i | 0.488069 | − | 0.281787i | −0.235704 | − | 0.971825i | \(-0.575740\pi\) |
0.723773 | + | 0.690038i | \(0.242406\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.85641 | − | 0.535898i | 0.0681968 | − | 0.0196867i | ||||
\(742\) | − | 25.8564i | − | 0.949219i | ||||||
\(743\) | −16.7679 | − | 29.0429i | −0.615156 | − | 1.06548i | −0.990357 | − | 0.138539i | \(-0.955760\pi\) |
0.375201 | − | 0.926944i | \(-0.377574\pi\) | |||||||
\(744\) | −0.866025 | − | 1.50000i | −0.0317500 | − | 0.0549927i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 25.7846i | 0.944042i | ||||||||
\(747\) | −2.46410 | + | 4.26795i | −0.0901568 | + | 0.156156i | ||||
\(748\) | −0.928203 | + | 1.60770i | −0.0339385 | + | 0.0587832i | ||||
\(749\) | 39.7128i | 1.45107i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.9641 | − | 24.1865i | −0.509557 | − | 0.882579i | −0.999939 | − | 0.0110712i | \(-0.996476\pi\) |
0.490381 | − | 0.871508i | \(-0.336857\pi\) | |||||||
\(752\) | −5.23205 | − | 9.06218i | −0.190793 | − | 0.330464i | ||||
\(753\) | 12.2679i | 0.447069i | ||||||||
\(754\) | −3.23205 | + | 13.0622i | −0.117704 | + | 0.475696i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.73205 | + | 1.00000i | −0.0629941 | + | 0.0363696i | ||||
\(757\) | −15.5885 | + | 9.00000i | −0.566572 | + | 0.327111i | −0.755779 | − | 0.654827i | \(-0.772742\pi\) |
0.189207 | + | 0.981937i | \(0.439408\pi\) | |||||||
\(758\) | 0.124356 | + | 0.0717968i | 0.00451680 | + | 0.00260778i | ||||
\(759\) | 0.124356i | 0.00451382i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.3923 | − | 9.46410i | −0.594221 | − | 0.343073i | 0.172544 | − | 0.985002i | \(-0.444801\pi\) |
−0.766765 | + | 0.641928i | \(0.778135\pi\) | |||||||
\(762\) | 8.92820 | 0.323435 | ||||||||
\(763\) | 20.5359 | + | 11.8564i | 0.743449 | + | 0.429231i | ||||
\(764\) | −7.26795 | − | 12.5885i | −0.262945 | − | 0.455434i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.60770 | −0.166483 | ||||||||
\(767\) | 5.37564 | + | 1.33013i | 0.194103 | + | 0.0480281i | ||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | 16.9641 | − | 9.79423i | 0.611741 | − | 0.353189i | −0.161905 | − | 0.986806i | \(-0.551764\pi\) |
0.773647 | + | 0.633617i | \(0.218431\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.3301 | + | 19.6244i | −0.408045 | + | 0.706754i | ||||
\(772\) | 23.3205 | 0.839323 | ||||||||
\(773\) | 13.8564 | − | 24.0000i | 0.498380 | − | 0.863220i | −0.501618 | − | 0.865089i | \(-0.667262\pi\) |
0.999998 | + | 0.00186926i | \(0.000595004\pi\) | |||||||
\(774\) | −1.66987 | − | 0.964102i | −0.0600223 | − | 0.0346539i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3.73205 | + | 6.46410i | −0.133973 | + | 0.232048i | ||||
\(777\) | −2.07180 | + | 1.19615i | −0.0743253 | + | 0.0429117i | ||||
\(778\) | 10.1340 | + | 17.5526i | 0.363321 | + | 0.629290i | ||||
\(779\) | −1.07180 | −0.0384011 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.89488 | −0.139370 | ||||||||
\(782\) | −0.535898 | − | 0.928203i | −0.0191637 | − | 0.0331925i | ||||
\(783\) | 3.23205 | − | 1.86603i | 0.115504 | − | 0.0666863i | ||||
\(784\) | 1.50000 | − | 2.59808i | 0.0535714 | − | 0.0927884i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.16025 | − | 0.669873i | −0.0413849 | − | 0.0238936i | ||||
\(787\) | −0.866025 | + | 1.50000i | −0.0308705 | + | 0.0534692i | −0.881048 | − | 0.473027i | \(-0.843161\pi\) |
0.850177 | + | 0.526496i | \(0.176495\pi\) | |||||||
\(788\) | −16.3923 | −0.583952 | ||||||||
\(789\) | 9.06218 | − | 15.6962i | 0.322622 | − | 0.558798i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19.3923 | + | 11.1962i | −0.689511 | + | 0.398089i | ||||
\(792\) | 0.464102i | 0.0164911i | ||||||||
\(793\) | −9.00000 | + | 36.3731i | −0.319599 | + | 1.29165i | ||||
\(794\) | −12.1244 | −0.430277 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.46410 | − | 16.3923i | −0.335446 | − | 0.581010i | ||||
\(797\) | 32.7846 | + | 18.9282i | 1.16129 | + | 0.670471i | 0.951613 | − | 0.307299i | \(-0.0994253\pi\) |
0.209678 | + | 0.977771i | \(0.432759\pi\) | |||||||
\(798\) | −1.07180 | −0.0379412 | ||||||||
\(799\) | 36.2487 | + | 20.9282i | 1.28239 | + | 0.740387i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.46410i | 0.263731i | ||||||||
\(802\) | 27.7128 | + | 16.0000i | 0.978573 | + | 0.564980i | ||||
\(803\) | 0.803848 | − | 0.464102i | 0.0283672 | − | 0.0163778i | ||||
\(804\) | −3.92820 | + | 2.26795i | −0.138537 | + | 0.0799844i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.33013 | + | 4.50000i | −0.152522 | + | 0.158506i | ||||
\(807\) | − | 12.0000i | − | 0.422420i | ||||||
\(808\) | −5.46410 | − | 9.46410i | −0.192226 | − | 0.332946i | ||||
\(809\) | −0.607695 | − | 1.05256i | −0.0213654 | − | 0.0370060i | 0.855145 | − | 0.518389i | \(-0.173468\pi\) |
−0.876510 | + | 0.481383i | \(0.840135\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 0.784610i | − | 0.0275514i | −0.999905 | − | 0.0137757i | \(-0.995615\pi\) | ||
0.999905 | − | 0.0137757i | \(-0.00438508\pi\) | |||||||
\(812\) | 3.73205 | − | 6.46410i | 0.130969 | − | 0.226845i | ||||
\(813\) | 4.59808 | − | 7.96410i | 0.161262 | − | 0.279313i | ||||
\(814\) | 0.555136i | 0.0194575i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.00000 | − | 3.46410i | −0.0700140 | − | 0.121268i | ||||
\(817\) | −0.516660 | − | 0.894882i | −0.0180757 | − | 0.0313080i | ||||
\(818\) | 4.00000i | 0.139857i | ||||||||
\(819\) | 5.19615 | + | 5.00000i | 0.181568 | + | 0.174714i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.6506 | + | 17.6962i | −1.06971 | + | 0.617600i | −0.928103 | − | 0.372322i | \(-0.878562\pi\) |
−0.141611 | + | 0.989922i | \(0.545228\pi\) | |||||||
\(822\) | 3.86603 | − | 2.23205i | 0.134843 | − | 0.0778517i | ||||
\(823\) | −20.0718 | − | 11.5885i | −0.699659 | − | 0.403948i | 0.107561 | − | 0.994198i | \(-0.465696\pi\) |
−0.807220 | + | 0.590250i | \(0.799029\pi\) | |||||||
\(824\) | 15.8564i | 0.552384i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.66025 | − | 1.53590i | −0.0925621 | − | 0.0534407i | ||||
\(827\) | 17.3205 | 0.602293 | 0.301147 | − | 0.953578i | \(-0.402631\pi\) | ||||
0.301147 | + | 0.953578i | \(0.402631\pi\) | |||||||
\(828\) | −0.232051 | − | 0.133975i | −0.00806432 | − | 0.00465594i | ||||
\(829\) | 11.7321 | + | 20.3205i | 0.407471 | + | 0.705760i | 0.994606 | − | 0.103729i | \(-0.0330774\pi\) |
−0.587135 | + | 0.809489i | \(0.699744\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.92820 | −0.344406 | ||||||||
\(832\) | 3.46410 | − | 1.00000i | 0.120096 | − | 0.0346688i | ||||
\(833\) | 12.0000i | 0.415775i | ||||||||
\(834\) | 0.803848 | − | 0.464102i | 0.0278350 | − | 0.0160705i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.124356 | + | 0.215390i | −0.00430093 | + | 0.00744943i | ||||
\(837\) | 1.73205 | 0.0598684 | ||||||||
\(838\) | −0.803848 | + | 1.39230i | −0.0277685 | + | 0.0480964i | ||||
\(839\) | 34.2679 | + | 19.7846i | 1.18306 | + | 0.683041i | 0.956721 | − | 0.291008i | \(-0.0939905\pi\) |
0.226340 | + | 0.974048i | \(0.427324\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.53590 | − | 13.0526i | 0.259859 | − | 0.450088i | ||||
\(842\) | 14.1962 | − | 8.19615i | 0.489232 | − | 0.282458i | ||||
\(843\) | 2.46410 | + | 4.26795i | 0.0848682 | + | 0.146996i | ||||
\(844\) | 23.3205 | 0.802725 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 10.4641 | 0.359763 | ||||||||
\(847\) | −10.7846 | − | 18.6795i | −0.370564 | − | 0.641835i | ||||
\(848\) | 11.1962 | − | 6.46410i | 0.384477 | − | 0.221978i | ||||
\(849\) | −1.96410 | + | 3.40192i | −0.0674078 | + | 0.116754i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.277568 | − | 0.160254i | −0.00951491 | − | 0.00549344i | ||||
\(852\) | 4.19615 | − | 7.26795i | 0.143758 | − | 0.248996i | ||||
\(853\) | −35.8372 | −1.22704 | −0.613521 | − | 0.789679i | \(-0.710247\pi\) | ||||
−0.613521 | + | 0.789679i | \(0.710247\pi\) | |||||||
\(854\) | 10.3923 | − | 18.0000i | 0.355617 | − | 0.615947i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −17.1962 | + | 9.92820i | −0.587752 | + | 0.339339i | ||||
\(857\) | − | 20.5167i | − | 0.700836i | −0.936593 | − | 0.350418i | \(-0.886040\pi\) | ||
0.936593 | − | 0.350418i | \(-0.113960\pi\) | |||||||
\(858\) | 1.60770 | − | 0.464102i | 0.0548858 | − | 0.0158442i | ||||
\(859\) | −27.1769 | −0.927264 | −0.463632 | − | 0.886028i | \(-0.653454\pi\) | ||||
−0.463632 | + | 0.886028i | \(0.653454\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.00000 | − | 3.46410i | −0.0681598 | − | 0.118056i | ||||
\(862\) | −6.58846 | − | 3.80385i | −0.224404 | − | 0.129560i | ||||
\(863\) | 42.4641 | 1.44549 | 0.722747 | − | 0.691112i | \(-0.242879\pi\) | ||||
0.722747 | + | 0.691112i | \(0.242879\pi\) | |||||||
\(864\) | −0.866025 | − | 0.500000i | −0.0294628 | − | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 15.3205i | − | 0.520612i | ||||||
\(867\) | −0.866025 | − | 0.500000i | −0.0294118 | − | 0.0169809i | ||||
\(868\) | 3.00000 | − | 1.73205i | 0.101827 | − | 0.0587896i | ||||
\(869\) | 0.0288568 | − | 0.0166605i | 0.000978901 | − | 0.000565169i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.7846 | + | 11.3397i | 0.399306 | + | 0.384233i | ||||
\(872\) | 11.8564i | 0.401509i | ||||||||
\(873\) | −3.73205 | − | 6.46410i | −0.126311 | − | 0.218777i | ||||
\(874\) | −0.0717968 | − | 0.124356i | −0.00242856 | − | 0.00420639i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.00000i | 0.0675737i | ||||||||
\(877\) | −14.0622 | + | 24.3564i | −0.474846 | + | 0.822457i | −0.999585 | − | 0.0288057i | \(-0.990830\pi\) |
0.524739 | + | 0.851263i | \(0.324163\pi\) | |||||||
\(878\) | −4.92820 | + | 8.53590i | −0.166319 | + | 0.288073i | ||||
\(879\) | − | 4.14359i | − | 0.139760i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.00000 | + | 12.1244i | 0.235836 | + | 0.408480i | 0.959515 | − | 0.281656i | \(-0.0908839\pi\) |
−0.723679 | + | 0.690136i | \(0.757551\pi\) | |||||||
\(882\) | 1.50000 | + | 2.59808i | 0.0505076 | + | 0.0874818i | ||||
\(883\) | − | 16.0718i | − | 0.540859i | −0.962740 | − | 0.270430i | \(-0.912834\pi\) | ||
0.962740 | − | 0.270430i | \(-0.0871657\pi\) | |||||||
\(884\) | −10.0000 | + | 10.3923i | −0.336336 | + | 0.349531i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.80385 | + | 2.19615i | −0.127793 | + | 0.0737812i | ||||
\(887\) | −8.76795 | + | 5.06218i | −0.294399 | + | 0.169971i | −0.639924 | − | 0.768438i | \(-0.721034\pi\) |
0.345525 | + | 0.938410i | \(0.387701\pi\) | |||||||
\(888\) | −1.03590 | − | 0.598076i | −0.0347625 | − | 0.0200701i | ||||
\(889\) | 17.8564i | 0.598885i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.401924 | − | 0.232051i | −0.0134650 | − | 0.00777399i | ||||
\(892\) | 27.4641 | 0.919566 | ||||||||
\(893\) | 4.85641 | + | 2.80385i | 0.162513 | + | 0.0938272i | ||||
\(894\) | −10.2321 | − | 17.7224i | −0.342211 | − | 0.592727i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.00000 | −0.0668153 | ||||||||
\(897\) | −0.232051 | + | 0.937822i | −0.00774795 | + | 0.0313130i | ||||
\(898\) | 39.7128i | 1.32523i | ||||||||
\(899\) | −5.59808 | + | 3.23205i | −0.186706 | + | 0.107795i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −25.8564 | + | 44.7846i | −0.861402 | + | 1.49199i | ||||
\(902\) | −0.928203 | −0.0309058 | ||||||||
\(903\) | 1.92820 | − | 3.33975i | 0.0641666 | − | 0.111140i | ||||
\(904\) | −9.69615 | − | 5.59808i | −0.322489 | − | 0.186189i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −5.19615 | + | 9.00000i | −0.172631 | + | 0.299005i | ||||
\(907\) | 5.93782 | − | 3.42820i | 0.197162 | − | 0.113832i | −0.398169 | − | 0.917312i | \(-0.630354\pi\) |
0.595331 | + | 0.803480i | \(0.297021\pi\) | |||||||
\(908\) | 2.19615 | + | 3.80385i | 0.0728819 | + | 0.126235i | ||||
\(909\) | 10.9282 | 0.362466 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.2487 | −0.803396 | −0.401698 | − | 0.915772i | \(-0.631580\pi\) | ||||
−0.401698 | + | 0.915772i | \(0.631580\pi\) | |||||||
\(912\) | −0.267949 | − | 0.464102i | −0.00887268 | − | 0.0153679i | ||||
\(913\) | −1.98076 | + | 1.14359i | −0.0655537 | + | 0.0378474i | ||||
\(914\) | 15.7321 | − | 27.2487i | 0.520370 | − | 0.901307i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17.1962 | + | 9.92820i | 0.568177 | + | 0.328037i | ||||
\(917\) | 1.33975 | − | 2.32051i | 0.0442423 | − | 0.0766299i | ||||
\(918\) | 4.00000 | 0.132020 | ||||||||
\(919\) | −27.3205 | + | 47.3205i | −0.901220 | + | 1.56096i | −0.0753085 | + | 0.997160i | \(0.523994\pi\) |
−0.825912 | + | 0.563799i | \(0.809339\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.8564 | + | 6.26795i | −0.357731 | + | 0.206536i | ||||
\(922\) | 6.46410i | 0.212884i | ||||||||
\(923\) | −29.3731 | − | 7.26795i | −0.966826 | − | 0.239227i | ||||
\(924\) | −0.928203 | −0.0305356 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 10.4641 | + | 18.1244i | 0.343872 | + | 0.595603i | ||||
\(927\) | −13.7321 | − | 7.92820i | −0.451020 | − | 0.260396i | ||||
\(928\) | 3.73205 | 0.122511 | ||||||||
\(929\) | −29.3205 | − | 16.9282i | −0.961975 | − | 0.555396i | −0.0651944 | − | 0.997873i | \(-0.520767\pi\) |
−0.896780 | + | 0.442476i | \(0.854100\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.60770i | 0.0526901i | ||||||||
\(932\) | −15.6962 | − | 9.06218i | −0.514145 | − | 0.296842i | ||||
\(933\) | −6.58846 | + | 3.80385i | −0.215696 | + | 0.124532i | ||||
\(934\) | −10.2679 | + | 5.92820i | −0.335978 | + | 0.193977i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.866025 | + | 3.50000i | −0.0283069 | + | 0.114401i | ||||
\(937\) | 44.6410i | 1.45836i | 0.684323 | + | 0.729179i | \(0.260098\pi\) | ||||
−0.684323 | + | 0.729179i | \(0.739902\pi\) | |||||||
\(938\) | −4.53590 | − | 7.85641i | −0.148102 | − | 0.256521i | ||||
\(939\) | 14.0000 | + | 24.2487i | 0.456873 | + | 0.791327i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.7846i | 0.873153i | 0.899667 | + | 0.436577i | \(0.143809\pi\) | ||||
−0.899667 | + | 0.436577i | \(0.856191\pi\) | |||||||
\(942\) | 2.50000 | − | 4.33013i | 0.0814544 | − | 0.141083i | ||||
\(943\) | 0.267949 | − | 0.464102i | 0.00872563 | − | 0.0151132i | ||||
\(944\) | − | 1.53590i | − | 0.0499892i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.447441 | − | 0.774991i | −0.0145476 | − | 0.0251971i | ||||
\(947\) | −1.26795 | − | 2.19615i | −0.0412028 | − | 0.0713654i | 0.844689 | − | 0.535258i | \(-0.179786\pi\) |
−0.885891 | + | 0.463893i | \(0.846452\pi\) | |||||||
\(948\) | 0.0717968i | 0.00233185i | ||||||||
\(949\) | 6.92820 | − | 2.00000i | 0.224899 | − | 0.0649227i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.5885 | + | 10.7321i | −0.602772 | + | 0.348011i | ||||
\(952\) | 6.92820 | − | 4.00000i | 0.224544 | − | 0.129641i | ||||
\(953\) | −13.6244 | − | 7.86603i | −0.441336 | − | 0.254806i | 0.262828 | − | 0.964843i | \(-0.415345\pi\) |
−0.704164 | + | 0.710037i | \(0.748678\pi\) | |||||||
\(954\) | 12.9282i | 0.418566i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.80385 | + | 2.19615i | 0.123025 | + | 0.0710286i | ||||
\(957\) | 1.73205 | 0.0559893 | ||||||||
\(958\) | −1.26795 | − | 0.732051i | −0.0409656 | − | 0.0236515i | ||||
\(959\) | 4.46410 | + | 7.73205i | 0.144153 | + | 0.249681i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.0000 | 0.903226 | ||||||||
\(962\) | −1.03590 | + | 4.18653i | −0.0333987 | + | 0.134979i | ||||
\(963\) | − | 19.8564i | − | 0.639864i | ||||||
\(964\) | 12.3564 | − | 7.13397i | 0.397973 | − | 0.229770i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.267949 | − | 0.464102i | 0.00862112 | − | 0.0149322i | ||||
\(967\) | 34.5359 | 1.11060 | 0.555300 | − | 0.831650i | \(-0.312604\pi\) | ||||
0.555300 | + | 0.831650i | \(0.312604\pi\) | |||||||
\(968\) | 5.39230 | − | 9.33975i | 0.173315 | − | 0.300191i | ||||
\(969\) | 1.85641 | + | 1.07180i | 0.0596364 | + | 0.0344311i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.73205 | + | 9.92820i | −0.183950 | + | 0.318611i | −0.943222 | − | 0.332162i | \(-0.892222\pi\) |
0.759272 | + | 0.650773i | \(0.225555\pi\) | |||||||
\(972\) | 0.866025 | − | 0.500000i | 0.0277778 | − | 0.0160375i | ||||
\(973\) | 0.928203 | + | 1.60770i | 0.0297568 | + | 0.0515403i | ||||
\(974\) | −39.1769 | −1.25531 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.3923 | 0.332650 | ||||||||
\(977\) | −16.6962 | − | 28.9186i | −0.534157 | − | 0.925187i | −0.999204 | − | 0.0399012i | \(-0.987296\pi\) |
0.465046 | − | 0.885286i | \(-0.346038\pi\) | |||||||
\(978\) | 19.9641 | − | 11.5263i | 0.638382 | − | 0.368570i | ||||
\(979\) | −1.73205 | + | 3.00000i | −0.0553566 | + | 0.0958804i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.2679 | − | 5.92820i | −0.327830 | − | 0.189273i | ||||
\(982\) | 8.66025 | − | 15.0000i | 0.276360 | − | 0.478669i | ||||
\(983\) | −57.3923 | −1.83053 | −0.915265 | − | 0.402852i | \(-0.868019\pi\) | ||||
−0.915265 | + | 0.402852i | \(0.868019\pi\) | |||||||
\(984\) | 1.00000 | − | 1.73205i | 0.0318788 | − | 0.0552158i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −12.9282 | + | 7.46410i | −0.411718 | + | 0.237705i | ||||
\(987\) | 20.9282i | 0.666152i | ||||||||
\(988\) | −1.33975 | + | 1.39230i | −0.0426230 | + | 0.0442951i | ||||
\(989\) | 0.516660 | 0.0164288 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.5718 | + | 21.7750i | 0.399356 | + | 0.691705i | 0.993647 | − | 0.112545i | \(-0.0359003\pi\) |
−0.594290 | + | 0.804251i | \(0.702567\pi\) | |||||||
\(992\) | 1.50000 | + | 0.866025i | 0.0476250 | + | 0.0274963i | ||||
\(993\) | −24.7846 | −0.786516 | ||||||||
\(994\) | 14.5359 | + | 8.39230i | 0.461051 | + | 0.266188i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 4.92820i | − | 0.156156i | ||||||
\(997\) | 41.1962 | + | 23.7846i | 1.30470 | + | 0.753266i | 0.981206 | − | 0.192966i | \(-0.0618106\pi\) |
0.323490 | + | 0.946232i | \(0.395144\pi\) | |||||||
\(998\) | 11.6603 | − | 6.73205i | 0.369099 | − | 0.213099i | ||||
\(999\) | 1.03590 | − | 0.598076i | 0.0327744 | − | 0.0189223i |
(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 | 1950.2.y.f.49.2 | 4 | ||
5.2 | odd | 4 | 1950.2.bc.b.751.1 | 4 | |||
5.3 | odd | 4 | 390.2.bb.b.361.2 | yes | 4 | ||
5.4 | even | 2 | 1950.2.y.c.49.1 | 4 | |||
13.4 | even | 6 | 1950.2.y.c.199.1 | 4 | |||
15.8 | even | 4 | 1170.2.bs.e.361.1 | 4 | |||
65.3 | odd | 12 | 5070.2.b.o.1351.4 | 4 | |||
65.4 | even | 6 | inner | 1950.2.y.f.199.2 | 4 | ||
65.17 | odd | 12 | 1950.2.bc.b.901.1 | 4 | |||
65.23 | odd | 12 | 5070.2.b.o.1351.1 | 4 | |||
65.28 | even | 12 | 5070.2.a.bg.1.1 | 2 | |||
65.43 | odd | 12 | 390.2.bb.b.121.2 | ✓ | 4 | ||
65.63 | even | 12 | 5070.2.a.y.1.2 | 2 | |||
195.173 | even | 12 | 1170.2.bs.e.901.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.bb.b.121.2 | ✓ | 4 | 65.43 | odd | 12 | ||
390.2.bb.b.361.2 | yes | 4 | 5.3 | odd | 4 | ||
1170.2.bs.e.361.1 | 4 | 15.8 | even | 4 | |||
1170.2.bs.e.901.1 | 4 | 195.173 | even | 12 | |||
1950.2.y.c.49.1 | 4 | 5.4 | even | 2 | |||
1950.2.y.c.199.1 | 4 | 13.4 | even | 6 | |||
1950.2.y.f.49.2 | 4 | 1.1 | even | 1 | trivial | ||
1950.2.y.f.199.2 | 4 | 65.4 | even | 6 | inner | ||
1950.2.bc.b.751.1 | 4 | 5.2 | odd | 4 | |||
1950.2.bc.b.901.1 | 4 | 65.17 | odd | 12 | |||
5070.2.a.y.1.2 | 2 | 65.63 | even | 12 | |||
5070.2.a.bg.1.1 | 2 | 65.28 | even | 12 | |||
5070.2.b.o.1351.1 | 4 | 65.23 | odd | 12 | |||
5070.2.b.o.1351.4 | 4 | 65.3 | odd | 12 |