Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1078,2,Mod(67,1078)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1078, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1078.67");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1078 = 2 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1078.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.60787333789\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - x^{3} + 2x^{2} + x + 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 154) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.2 | ||
Root | \(-0.309017 + 0.535233i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1078.67 |
Dual form | 1078.2.e.n.177.2 |
$q$-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 \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(981\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0.618034 | − | 1.07047i | 0.356822 | − | 0.618034i | −0.630606 | − | 0.776103i | \(-0.717194\pi\) |
0.987428 | + | 0.158069i | \(0.0505269\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −0.618034 | − | 1.07047i | −0.276393 | − | 0.478727i | 0.694092 | − | 0.719886i | \(-0.255806\pi\) |
−0.970486 | + | 0.241159i | \(0.922473\pi\) | |||||||
\(6\) | −1.23607 | −0.504623 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.736068 | + | 1.27491i | 0.245356 | + | 0.424969i | ||||
\(10\) | −0.618034 | + | 1.07047i | −0.195440 | + | 0.338511i | ||||
\(11\) | −0.500000 | + | 0.866025i | −0.150756 | + | 0.261116i | ||||
\(12\) | 0.618034 | + | 1.07047i | 0.178411 | + | 0.309017i | ||||
\(13\) | 3.23607 | 0.897524 | 0.448762 | − | 0.893651i | \(-0.351865\pi\) | ||||
0.448762 | + | 0.893651i | \(0.351865\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.52786 | −0.394493 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.23607 | − | 2.14093i | 0.299791 | − | 0.519252i | −0.676297 | − | 0.736629i | \(-0.736417\pi\) |
0.976088 | + | 0.217376i | \(0.0697499\pi\) | |||||||
\(18\) | 0.736068 | − | 1.27491i | 0.173493 | − | 0.300498i | ||||
\(19\) | −3.61803 | − | 6.26662i | −0.830034 | − | 1.43766i | −0.898011 | − | 0.439974i | \(-0.854988\pi\) |
0.0679766 | − | 0.997687i | \(-0.478346\pi\) | |||||||
\(20\) | 1.23607 | 0.276393 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −2.00000 | − | 3.46410i | −0.417029 | − | 0.722315i | 0.578610 | − | 0.815604i | \(-0.303595\pi\) |
−0.995639 | + | 0.0932891i | \(0.970262\pi\) | |||||||
\(24\) | 0.618034 | − | 1.07047i | 0.126156 | − | 0.218508i | ||||
\(25\) | 1.73607 | − | 3.00696i | 0.347214 | − | 0.601392i | ||||
\(26\) | −1.61803 | − | 2.80252i | −0.317323 | − | 0.549619i | ||||
\(27\) | 5.52786 | 1.06384 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.47214 | 0.830455 | 0.415227 | − | 0.909718i | \(-0.363702\pi\) | ||||
0.415227 | + | 0.909718i | \(0.363702\pi\) | |||||||
\(30\) | 0.763932 | + | 1.32317i | 0.139474 | + | 0.241577i | ||||
\(31\) | 1.00000 | − | 1.73205i | 0.179605 | − | 0.311086i | −0.762140 | − | 0.647412i | \(-0.775851\pi\) |
0.941745 | + | 0.336327i | \(0.109185\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0.618034 | + | 1.07047i | 0.107586 | + | 0.186344i | ||||
\(34\) | −2.47214 | −0.423968 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.47214 | −0.245356 | ||||||||
\(37\) | −3.47214 | − | 6.01392i | −0.570816 | − | 0.988682i | −0.996482 | − | 0.0838017i | \(-0.973294\pi\) |
0.425667 | − | 0.904880i | \(-0.360040\pi\) | |||||||
\(38\) | −3.61803 | + | 6.26662i | −0.586923 | + | 1.01658i | ||||
\(39\) | 2.00000 | − | 3.46410i | 0.320256 | − | 0.554700i | ||||
\(40\) | −0.618034 | − | 1.07047i | −0.0977198 | − | 0.169256i | ||||
\(41\) | 2.47214 | 0.386083 | 0.193041 | − | 0.981191i | \(-0.438165\pi\) | ||||
0.193041 | + | 0.981191i | \(0.438165\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.4721 | −1.59699 | −0.798493 | − | 0.602004i | \(-0.794369\pi\) | ||||
−0.798493 | + | 0.602004i | \(0.794369\pi\) | |||||||
\(44\) | −0.500000 | − | 0.866025i | −0.0753778 | − | 0.130558i | ||||
\(45\) | 0.909830 | − | 1.57587i | 0.135629 | − | 0.234917i | ||||
\(46\) | −2.00000 | + | 3.46410i | −0.294884 | + | 0.510754i | ||||
\(47\) | −1.00000 | − | 1.73205i | −0.145865 | − | 0.252646i | 0.783830 | − | 0.620975i | \(-0.213263\pi\) |
−0.929695 | + | 0.368329i | \(0.879930\pi\) | |||||||
\(48\) | −1.23607 | −0.178411 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.47214 | −0.491034 | ||||||||
\(51\) | −1.52786 | − | 2.64634i | −0.213944 | − | 0.370561i | ||||
\(52\) | −1.61803 | + | 2.80252i | −0.224381 | + | 0.388639i | ||||
\(53\) | −4.23607 | + | 7.33708i | −0.581869 | + | 1.00783i | 0.413389 | + | 0.910554i | \(0.364345\pi\) |
−0.995258 | + | 0.0972717i | \(0.968988\pi\) | |||||||
\(54\) | −2.76393 | − | 4.78727i | −0.376124 | − | 0.651465i | ||||
\(55\) | 1.23607 | 0.166671 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.94427 | −1.18470 | ||||||||
\(58\) | −2.23607 | − | 3.87298i | −0.293610 | − | 0.508548i | ||||
\(59\) | 1.38197 | − | 2.39364i | 0.179917 | − | 0.311625i | −0.761935 | − | 0.647653i | \(-0.775751\pi\) |
0.941852 | + | 0.336029i | \(0.109084\pi\) | |||||||
\(60\) | 0.763932 | − | 1.32317i | 0.0986232 | − | 0.170820i | ||||
\(61\) | −0.381966 | − | 0.661585i | −0.0489057 | − | 0.0847072i | 0.840536 | − | 0.541755i | \(-0.182240\pi\) |
−0.889442 | + | 0.457048i | \(0.848907\pi\) | |||||||
\(62\) | −2.00000 | −0.254000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.00000 | − | 3.46410i | −0.248069 | − | 0.429669i | ||||
\(66\) | 0.618034 | − | 1.07047i | 0.0760747 | − | 0.131765i | ||||
\(67\) | −5.70820 | + | 9.88690i | −0.697368 | + | 1.20788i | 0.272008 | + | 0.962295i | \(0.412312\pi\) |
−0.969376 | + | 0.245582i | \(0.921021\pi\) | |||||||
\(68\) | 1.23607 | + | 2.14093i | 0.149895 | + | 0.259626i | ||||
\(69\) | −4.94427 | −0.595220 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.47214 | 0.768101 | 0.384051 | − | 0.923312i | \(-0.374529\pi\) | ||||
0.384051 | + | 0.923312i | \(0.374529\pi\) | |||||||
\(72\) | 0.736068 | + | 1.27491i | 0.0867464 | + | 0.150249i | ||||
\(73\) | 6.47214 | − | 11.2101i | 0.757506 | − | 1.31204i | −0.186612 | − | 0.982434i | \(-0.559751\pi\) |
0.944119 | − | 0.329606i | \(-0.106916\pi\) | |||||||
\(74\) | −3.47214 | + | 6.01392i | −0.403628 | + | 0.699104i | ||||
\(75\) | −2.14590 | − | 3.71680i | −0.247787 | − | 0.429180i | ||||
\(76\) | 7.23607 | 0.830034 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.00000 | −0.452911 | ||||||||
\(79\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(80\) | −0.618034 | + | 1.07047i | −0.0690983 | + | 0.119682i | ||||
\(81\) | 1.20820 | − | 2.09267i | 0.134245 | − | 0.232519i | ||||
\(82\) | −1.23607 | − | 2.14093i | −0.136501 | − | 0.236426i | ||||
\(83\) | 12.1803 | 1.33697 | 0.668483 | − | 0.743727i | \(-0.266944\pi\) | ||||
0.668483 | + | 0.743727i | \(0.266944\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.05573 | −0.331440 | ||||||||
\(86\) | 5.23607 | + | 9.06914i | 0.564620 | + | 0.977950i | ||||
\(87\) | 2.76393 | − | 4.78727i | 0.296325 | − | 0.513249i | ||||
\(88\) | −0.500000 | + | 0.866025i | −0.0533002 | + | 0.0923186i | ||||
\(89\) | 5.00000 | + | 8.66025i | 0.529999 | + | 0.917985i | 0.999388 | + | 0.0349934i | \(0.0111410\pi\) |
−0.469389 | + | 0.882992i | \(0.655526\pi\) | |||||||
\(90\) | −1.81966 | −0.191809 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.00000 | 0.417029 | ||||||||
\(93\) | −1.23607 | − | 2.14093i | −0.128174 | − | 0.222004i | ||||
\(94\) | −1.00000 | + | 1.73205i | −0.103142 | + | 0.178647i | ||||
\(95\) | −4.47214 | + | 7.74597i | −0.458831 | + | 0.794719i | ||||
\(96\) | 0.618034 | + | 1.07047i | 0.0630778 | + | 0.109254i | ||||
\(97\) | −12.4721 | −1.26635 | −0.633177 | − | 0.774007i | \(-0.718249\pi\) | ||||
−0.633177 | + | 0.774007i | \(0.718249\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.47214 | −0.147955 | ||||||||
\(100\) | 1.73607 | + | 3.00696i | 0.173607 | + | 0.300696i | ||||
\(101\) | 4.09017 | − | 7.08438i | 0.406987 | − | 0.704922i | −0.587563 | − | 0.809178i | \(-0.699913\pi\) |
0.994551 | + | 0.104256i | \(0.0332461\pi\) | |||||||
\(102\) | −1.52786 | + | 2.64634i | −0.151281 | + | 0.262027i | ||||
\(103\) | −7.47214 | − | 12.9421i | −0.736251 | − | 1.27522i | −0.954172 | − | 0.299258i | \(-0.903261\pi\) |
0.217921 | − | 0.975966i | \(-0.430073\pi\) | |||||||
\(104\) | 3.23607 | 0.317323 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.47214 | 0.822887 | ||||||||
\(107\) | −1.23607 | − | 2.14093i | −0.119495 | − | 0.206972i | 0.800073 | − | 0.599903i | \(-0.204794\pi\) |
−0.919568 | + | 0.392932i | \(0.871461\pi\) | |||||||
\(108\) | −2.76393 | + | 4.78727i | −0.265959 | + | 0.460655i | ||||
\(109\) | 5.00000 | − | 8.66025i | 0.478913 | − | 0.829502i | −0.520794 | − | 0.853682i | \(-0.674364\pi\) |
0.999708 | + | 0.0241802i | \(0.00769755\pi\) | |||||||
\(110\) | −0.618034 | − | 1.07047i | −0.0589272 | − | 0.102065i | ||||
\(111\) | −8.58359 | −0.814719 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.472136 | −0.0444148 | −0.0222074 | − | 0.999753i | \(-0.507069\pi\) | ||||
−0.0222074 | + | 0.999753i | \(0.507069\pi\) | |||||||
\(114\) | 4.47214 | + | 7.74597i | 0.418854 | + | 0.725476i | ||||
\(115\) | −2.47214 | + | 4.28187i | −0.230528 | + | 0.399286i | ||||
\(116\) | −2.23607 | + | 3.87298i | −0.207614 | + | 0.359597i | ||||
\(117\) | 2.38197 | + | 4.12569i | 0.220213 | + | 0.381420i | ||||
\(118\) | −2.76393 | −0.254441 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.52786 | −0.139474 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | −0.381966 | + | 0.661585i | −0.0345816 | + | 0.0598970i | ||||
\(123\) | 1.52786 | − | 2.64634i | 0.137763 | − | 0.238612i | ||||
\(124\) | 1.00000 | + | 1.73205i | 0.0898027 | + | 0.155543i | ||||
\(125\) | −10.4721 | −0.936656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.0000 | −1.06483 | −0.532414 | − | 0.846484i | \(-0.678715\pi\) | ||||
−0.532414 | + | 0.846484i | \(0.678715\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | −6.47214 | + | 11.2101i | −0.569840 | + | 0.986991i | ||||
\(130\) | −2.00000 | + | 3.46410i | −0.175412 | + | 0.303822i | ||||
\(131\) | 2.38197 | + | 4.12569i | 0.208113 | + | 0.360463i | 0.951120 | − | 0.308821i | \(-0.0999344\pi\) |
−0.743007 | + | 0.669284i | \(0.766601\pi\) | |||||||
\(132\) | −1.23607 | −0.107586 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 11.4164 | 0.986227 | ||||||||
\(135\) | −3.41641 | − | 5.91739i | −0.294038 | − | 0.509288i | ||||
\(136\) | 1.23607 | − | 2.14093i | 0.105992 | − | 0.183583i | ||||
\(137\) | 9.94427 | − | 17.2240i | 0.849596 | − | 1.47154i | −0.0319723 | − | 0.999489i | \(-0.510179\pi\) |
0.881569 | − | 0.472056i | \(-0.156488\pi\) | |||||||
\(138\) | 2.47214 | + | 4.28187i | 0.210442 | + | 0.364497i | ||||
\(139\) | 21.7082 | 1.84127 | 0.920633 | − | 0.390429i | \(-0.127673\pi\) | ||||
0.920633 | + | 0.390429i | \(0.127673\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.47214 | −0.208191 | ||||||||
\(142\) | −3.23607 | − | 5.60503i | −0.271565 | − | 0.470364i | ||||
\(143\) | −1.61803 | + | 2.80252i | −0.135307 | + | 0.234358i | ||||
\(144\) | 0.736068 | − | 1.27491i | 0.0613390 | − | 0.106242i | ||||
\(145\) | −2.76393 | − | 4.78727i | −0.229532 | − | 0.397561i | ||||
\(146\) | −12.9443 | −1.07128 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.94427 | 0.570816 | ||||||||
\(149\) | 11.1803 | + | 19.3649i | 0.915929 | + | 1.58644i | 0.805535 | + | 0.592548i | \(0.201878\pi\) |
0.110394 | + | 0.993888i | \(0.464789\pi\) | |||||||
\(150\) | −2.14590 | + | 3.71680i | −0.175212 | + | 0.303476i | ||||
\(151\) | −6.00000 | + | 10.3923i | −0.488273 | + | 0.845714i | −0.999909 | − | 0.0134886i | \(-0.995706\pi\) |
0.511636 | + | 0.859202i | \(0.329040\pi\) | |||||||
\(152\) | −3.61803 | − | 6.26662i | −0.293461 | − | 0.508290i | ||||
\(153\) | 3.63932 | 0.294222 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.47214 | −0.198567 | ||||||||
\(156\) | 2.00000 | + | 3.46410i | 0.160128 | + | 0.277350i | ||||
\(157\) | −6.32624 | + | 10.9574i | −0.504889 | + | 0.874493i | 0.495095 | + | 0.868839i | \(0.335133\pi\) |
−0.999984 | + | 0.00565427i | \(0.998200\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.23607 | + | 9.06914i | 0.415247 | + | 0.719229i | ||||
\(160\) | 1.23607 | 0.0977198 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.41641 | −0.189851 | ||||||||
\(163\) | 9.70820 | + | 16.8151i | 0.760405 | + | 1.31706i | 0.942642 | + | 0.333806i | \(0.108333\pi\) |
−0.182237 | + | 0.983255i | \(0.558334\pi\) | |||||||
\(164\) | −1.23607 | + | 2.14093i | −0.0965207 | + | 0.167179i | ||||
\(165\) | 0.763932 | − | 1.32317i | 0.0594720 | − | 0.103009i | ||||
\(166\) | −6.09017 | − | 10.5485i | −0.472689 | − | 0.818721i | ||||
\(167\) | −11.4164 | −0.883428 | −0.441714 | − | 0.897156i | \(-0.645629\pi\) | ||||
−0.441714 | + | 0.897156i | \(0.645629\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.52786 | −0.194451 | ||||||||
\(170\) | 1.52786 | + | 2.64634i | 0.117182 | + | 0.202965i | ||||
\(171\) | 5.32624 | − | 9.22531i | 0.407308 | − | 0.705477i | ||||
\(172\) | 5.23607 | − | 9.06914i | 0.399246 | − | 0.691515i | ||||
\(173\) | −1.61803 | − | 2.80252i | −0.123017 | − | 0.213071i | 0.797939 | − | 0.602738i | \(-0.205924\pi\) |
−0.920956 | + | 0.389667i | \(0.872590\pi\) | |||||||
\(174\) | −5.52786 | −0.419066 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −1.70820 | − | 2.95870i | −0.128396 | − | 0.222389i | ||||
\(178\) | 5.00000 | − | 8.66025i | 0.374766 | − | 0.649113i | ||||
\(179\) | 4.47214 | − | 7.74597i | 0.334263 | − | 0.578961i | −0.649080 | − | 0.760720i | \(-0.724846\pi\) |
0.983343 | + | 0.181760i | \(0.0581792\pi\) | |||||||
\(180\) | 0.909830 | + | 1.57587i | 0.0678147 | + | 0.117459i | ||||
\(181\) | −9.23607 | −0.686512 | −0.343256 | − | 0.939242i | \(-0.611530\pi\) | ||||
−0.343256 | + | 0.939242i | \(0.611530\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.944272 | −0.0698026 | ||||||||
\(184\) | −2.00000 | − | 3.46410i | −0.147442 | − | 0.255377i | ||||
\(185\) | −4.29180 | + | 7.43361i | −0.315539 | + | 0.546530i | ||||
\(186\) | −1.23607 | + | 2.14093i | −0.0906329 | + | 0.156981i | ||||
\(187\) | 1.23607 | + | 2.14093i | 0.0903902 | + | 0.156560i | ||||
\(188\) | 2.00000 | 0.145865 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.94427 | 0.648886 | ||||||||
\(191\) | 1.23607 | + | 2.14093i | 0.0894387 | + | 0.154912i | 0.907274 | − | 0.420540i | \(-0.138159\pi\) |
−0.817835 | + | 0.575452i | \(0.804826\pi\) | |||||||
\(192\) | 0.618034 | − | 1.07047i | 0.0446028 | − | 0.0772542i | ||||
\(193\) | 7.47214 | − | 12.9421i | 0.537856 | − | 0.931594i | −0.461163 | − | 0.887315i | \(-0.652568\pi\) |
0.999019 | − | 0.0442787i | \(-0.0140990\pi\) | |||||||
\(194\) | 6.23607 | + | 10.8012i | 0.447724 | + | 0.775480i | ||||
\(195\) | −4.94427 | −0.354067 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | 0.736068 | + | 1.27491i | 0.0523101 | + | 0.0906037i | ||||
\(199\) | 9.47214 | − | 16.4062i | 0.671462 | − | 1.16301i | −0.306028 | − | 0.952023i | \(-0.599000\pi\) |
0.977490 | − | 0.210984i | \(-0.0676666\pi\) | |||||||
\(200\) | 1.73607 | − | 3.00696i | 0.122759 | − | 0.212624i | ||||
\(201\) | 7.05573 | + | 12.2209i | 0.497673 | + | 0.861994i | ||||
\(202\) | −8.18034 | −0.575567 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3.05573 | 0.213944 | ||||||||
\(205\) | −1.52786 | − | 2.64634i | −0.106711 | − | 0.184828i | ||||
\(206\) | −7.47214 | + | 12.9421i | −0.520608 | + | 0.901720i | ||||
\(207\) | 2.94427 | − | 5.09963i | 0.204641 | − | 0.354449i | ||||
\(208\) | −1.61803 | − | 2.80252i | −0.112190 | − | 0.194320i | ||||
\(209\) | 7.23607 | 0.500529 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.5279 | −0.931297 | −0.465648 | − | 0.884970i | \(-0.654179\pi\) | ||||
−0.465648 | + | 0.884970i | \(0.654179\pi\) | |||||||
\(212\) | −4.23607 | − | 7.33708i | −0.290934 | − | 0.503913i | ||||
\(213\) | 4.00000 | − | 6.92820i | 0.274075 | − | 0.474713i | ||||
\(214\) | −1.23607 | + | 2.14093i | −0.0844959 | + | 0.146351i | ||||
\(215\) | 6.47214 | + | 11.2101i | 0.441396 | + | 0.764520i | ||||
\(216\) | 5.52786 | 0.376124 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −10.0000 | −0.677285 | ||||||||
\(219\) | −8.00000 | − | 13.8564i | −0.540590 | − | 0.936329i | ||||
\(220\) | −0.618034 | + | 1.07047i | −0.0416678 | + | 0.0721708i | ||||
\(221\) | 4.00000 | − | 6.92820i | 0.269069 | − | 0.466041i | ||||
\(222\) | 4.29180 | + | 7.43361i | 0.288046 | + | 0.498911i | ||||
\(223\) | 0.472136 | 0.0316166 | 0.0158083 | − | 0.999875i | \(-0.494968\pi\) | ||||
0.0158083 | + | 0.999875i | \(0.494968\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.11146 | 0.340764 | ||||||||
\(226\) | 0.236068 | + | 0.408882i | 0.0157030 | + | 0.0271984i | ||||
\(227\) | −9.61803 | + | 16.6589i | −0.638371 | + | 1.10569i | 0.347419 | + | 0.937710i | \(0.387058\pi\) |
−0.985790 | + | 0.167982i | \(0.946275\pi\) | |||||||
\(228\) | 4.47214 | − | 7.74597i | 0.296174 | − | 0.512989i | ||||
\(229\) | 8.61803 | + | 14.9269i | 0.569496 | + | 0.986396i | 0.996616 | + | 0.0822006i | \(0.0261948\pi\) |
−0.427120 | + | 0.904195i | \(0.640472\pi\) | |||||||
\(230\) | 4.94427 | 0.326016 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.47214 | 0.293610 | ||||||||
\(233\) | 7.47214 | + | 12.9421i | 0.489516 | + | 0.847866i | 0.999927 | − | 0.0120640i | \(-0.00384018\pi\) |
−0.510411 | + | 0.859930i | \(0.670507\pi\) | |||||||
\(234\) | 2.38197 | − | 4.12569i | 0.155714 | − | 0.269705i | ||||
\(235\) | −1.23607 | + | 2.14093i | −0.0806322 | + | 0.139659i | ||||
\(236\) | 1.38197 | + | 2.39364i | 0.0899583 | + | 0.155812i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.0000 | 1.29369 | 0.646846 | − | 0.762620i | \(-0.276088\pi\) | ||||
0.646846 | + | 0.762620i | \(0.276088\pi\) | |||||||
\(240\) | 0.763932 | + | 1.32317i | 0.0493116 | + | 0.0854102i | ||||
\(241\) | 7.70820 | − | 13.3510i | 0.496529 | − | 0.860014i | −0.503463 | − | 0.864017i | \(-0.667941\pi\) |
0.999992 | + | 0.00400327i | \(0.00127428\pi\) | |||||||
\(242\) | −0.500000 | + | 0.866025i | −0.0321412 | + | 0.0556702i | ||||
\(243\) | 6.79837 | + | 11.7751i | 0.436116 | + | 0.755375i | ||||
\(244\) | 0.763932 | 0.0489057 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.05573 | −0.194826 | ||||||||
\(247\) | −11.7082 | − | 20.2792i | −0.744975 | − | 1.29033i | ||||
\(248\) | 1.00000 | − | 1.73205i | 0.0635001 | − | 0.109985i | ||||
\(249\) | 7.52786 | − | 13.0386i | 0.477059 | − | 0.826290i | ||||
\(250\) | 5.23607 | + | 9.06914i | 0.331158 | + | 0.573583i | ||||
\(251\) | −29.2361 | −1.84536 | −0.922682 | − | 0.385562i | \(-0.874008\pi\) | ||||
−0.922682 | + | 0.385562i | \(0.874008\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.00000 | 0.251478 | ||||||||
\(254\) | 6.00000 | + | 10.3923i | 0.376473 | + | 0.652071i | ||||
\(255\) | −1.88854 | + | 3.27105i | −0.118265 | + | 0.204841i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 3.47214 | + | 6.01392i | 0.216586 | + | 0.375138i | 0.953762 | − | 0.300563i | \(-0.0971745\pi\) |
−0.737176 | + | 0.675701i | \(0.763841\pi\) | |||||||
\(258\) | 12.9443 | 0.805875 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.00000 | 0.248069 | ||||||||
\(261\) | 3.29180 | + | 5.70156i | 0.203757 | + | 0.352918i | ||||
\(262\) | 2.38197 | − | 4.12569i | 0.147158 | − | 0.254886i | ||||
\(263\) | 2.47214 | − | 4.28187i | 0.152438 | − | 0.264031i | −0.779685 | − | 0.626172i | \(-0.784621\pi\) |
0.932123 | + | 0.362141i | \(0.117954\pi\) | |||||||
\(264\) | 0.618034 | + | 1.07047i | 0.0380374 | + | 0.0658826i | ||||
\(265\) | 10.4721 | 0.643298 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.3607 | 0.756461 | ||||||||
\(268\) | −5.70820 | − | 9.88690i | −0.348684 | − | 0.603938i | ||||
\(269\) | −11.3820 | + | 19.7141i | −0.693971 | + | 1.20199i | 0.276556 | + | 0.960998i | \(0.410807\pi\) |
−0.970526 | + | 0.240995i | \(0.922526\pi\) | |||||||
\(270\) | −3.41641 | + | 5.91739i | −0.207916 | + | 0.360121i | ||||
\(271\) | 0.472136 | + | 0.817763i | 0.0286802 | + | 0.0496756i | 0.880009 | − | 0.474957i | \(-0.157536\pi\) |
−0.851329 | + | 0.524632i | \(0.824203\pi\) | |||||||
\(272\) | −2.47214 | −0.149895 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −19.8885 | −1.20151 | ||||||||
\(275\) | 1.73607 | + | 3.00696i | 0.104689 | + | 0.181326i | ||||
\(276\) | 2.47214 | − | 4.28187i | 0.148805 | − | 0.257738i | ||||
\(277\) | −1.76393 | + | 3.05522i | −0.105984 | + | 0.183570i | −0.914140 | − | 0.405399i | \(-0.867133\pi\) |
0.808156 | + | 0.588969i | \(0.200466\pi\) | |||||||
\(278\) | −10.8541 | − | 18.7999i | −0.650986 | − | 1.12754i | ||||
\(279\) | 2.94427 | 0.176269 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.8328 | 1.72002 | 0.860011 | − | 0.510276i | \(-0.170457\pi\) | ||||
0.860011 | + | 0.510276i | \(0.170457\pi\) | |||||||
\(282\) | 1.23607 | + | 2.14093i | 0.0736068 | + | 0.127491i | ||||
\(283\) | 7.32624 | − | 12.6894i | 0.435500 | − | 0.754308i | −0.561837 | − | 0.827248i | \(-0.689905\pi\) |
0.997336 | + | 0.0729407i | \(0.0232384\pi\) | |||||||
\(284\) | −3.23607 | + | 5.60503i | −0.192025 | + | 0.332598i | ||||
\(285\) | 5.52786 | + | 9.57454i | 0.327442 | + | 0.567147i | ||||
\(286\) | 3.23607 | 0.191353 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.47214 | −0.0867464 | ||||||||
\(289\) | 5.44427 | + | 9.42976i | 0.320251 | + | 0.554692i | ||||
\(290\) | −2.76393 | + | 4.78727i | −0.162304 | + | 0.281118i | ||||
\(291\) | −7.70820 | + | 13.3510i | −0.451863 | + | 0.782650i | ||||
\(292\) | 6.47214 | + | 11.2101i | 0.378753 | + | 0.656020i | ||||
\(293\) | 26.6525 | 1.55705 | 0.778527 | − | 0.627611i | \(-0.215967\pi\) | ||||
0.778527 | + | 0.627611i | \(0.215967\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.41641 | −0.198911 | ||||||||
\(296\) | −3.47214 | − | 6.01392i | −0.201814 | − | 0.349552i | ||||
\(297\) | −2.76393 | + | 4.78727i | −0.160380 | + | 0.277786i | ||||
\(298\) | 11.1803 | − | 19.3649i | 0.647660 | − | 1.12178i | ||||
\(299\) | −6.47214 | − | 11.2101i | −0.374293 | − | 0.648295i | ||||
\(300\) | 4.29180 | 0.247787 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 12.0000 | 0.690522 | ||||||||
\(303\) | −5.05573 | − | 8.75678i | −0.290444 | − | 0.503064i | ||||
\(304\) | −3.61803 | + | 6.26662i | −0.207508 | + | 0.359415i | ||||
\(305\) | −0.472136 | + | 0.817763i | −0.0270344 | + | 0.0468250i | ||||
\(306\) | −1.81966 | − | 3.15174i | −0.104023 | − | 0.180173i | ||||
\(307\) | 26.0689 | 1.48783 | 0.743915 | − | 0.668274i | \(-0.232967\pi\) | ||||
0.743915 | + | 0.668274i | \(0.232967\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.4721 | −1.05084 | ||||||||
\(310\) | 1.23607 | + | 2.14093i | 0.0702039 | + | 0.121597i | ||||
\(311\) | −10.7082 | + | 18.5472i | −0.607207 | + | 1.05171i | 0.384492 | + | 0.923128i | \(0.374377\pi\) |
−0.991699 | + | 0.128584i | \(0.958957\pi\) | |||||||
\(312\) | 2.00000 | − | 3.46410i | 0.113228 | − | 0.196116i | ||||
\(313\) | 9.76393 | + | 16.9116i | 0.551890 | + | 0.955902i | 0.998138 | + | 0.0609924i | \(0.0194265\pi\) |
−0.446248 | + | 0.894909i | \(0.647240\pi\) | |||||||
\(314\) | 12.6525 | 0.714021 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.4721 | + | 26.7985i | 0.869002 | + | 1.50516i | 0.863018 | + | 0.505173i | \(0.168571\pi\) |
0.00598366 | + | 0.999982i | \(0.498095\pi\) | |||||||
\(318\) | 5.23607 | − | 9.06914i | 0.293624 | − | 0.508572i | ||||
\(319\) | −2.23607 | + | 3.87298i | −0.125196 | + | 0.216845i | ||||
\(320\) | −0.618034 | − | 1.07047i | −0.0345492 | − | 0.0598409i | ||||
\(321\) | −3.05573 | −0.170554 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.8885 | −0.995345 | ||||||||
\(324\) | 1.20820 | + | 2.09267i | 0.0671224 | + | 0.116259i | ||||
\(325\) | 5.61803 | − | 9.73072i | 0.311632 | − | 0.539763i | ||||
\(326\) | 9.70820 | − | 16.8151i | 0.537688 | − | 0.931302i | ||||
\(327\) | −6.18034 | − | 10.7047i | −0.341774 | − | 0.591969i | ||||
\(328\) | 2.47214 | 0.136501 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.52786 | −0.0841061 | ||||||||
\(331\) | 8.47214 | + | 14.6742i | 0.465671 | + | 0.806565i | 0.999232 | − | 0.0391964i | \(-0.0124798\pi\) |
−0.533561 | + | 0.845762i | \(0.679146\pi\) | |||||||
\(332\) | −6.09017 | + | 10.5485i | −0.334241 | + | 0.578923i | ||||
\(333\) | 5.11146 | − | 8.85330i | 0.280106 | − | 0.485158i | ||||
\(334\) | 5.70820 | + | 9.88690i | 0.312339 | + | 0.540987i | ||||
\(335\) | 14.1115 | 0.770991 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.0000 | 0.980522 | 0.490261 | − | 0.871576i | \(-0.336901\pi\) | ||||
0.490261 | + | 0.871576i | \(0.336901\pi\) | |||||||
\(338\) | 1.26393 | + | 2.18919i | 0.0687488 | + | 0.119076i | ||||
\(339\) | −0.291796 | + | 0.505406i | −0.0158482 | + | 0.0274499i | ||||
\(340\) | 1.52786 | − | 2.64634i | 0.0828601 | − | 0.143518i | ||||
\(341\) | 1.00000 | + | 1.73205i | 0.0541530 | + | 0.0937958i | ||||
\(342\) | −10.6525 | −0.576020 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −10.4721 | −0.564620 | ||||||||
\(345\) | 3.05573 | + | 5.29268i | 0.164515 | + | 0.284948i | ||||
\(346\) | −1.61803 | + | 2.80252i | −0.0869860 | + | 0.150664i | ||||
\(347\) | −1.23607 | + | 2.14093i | −0.0663556 | + | 0.114931i | −0.897295 | − | 0.441432i | \(-0.854471\pi\) |
0.830939 | + | 0.556364i | \(0.187804\pi\) | |||||||
\(348\) | 2.76393 | + | 4.78727i | 0.148162 | + | 0.256625i | ||||
\(349\) | −21.7082 | −1.16201 | −0.581007 | − | 0.813899i | \(-0.697341\pi\) | ||||
−0.581007 | + | 0.813899i | \(0.697341\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 17.8885 | 0.954820 | ||||||||
\(352\) | −0.500000 | − | 0.866025i | −0.0266501 | − | 0.0461593i | ||||
\(353\) | −8.52786 | + | 14.7707i | −0.453892 | + | 0.786165i | −0.998624 | − | 0.0524459i | \(-0.983298\pi\) |
0.544731 | + | 0.838611i | \(0.316632\pi\) | |||||||
\(354\) | −1.70820 | + | 2.95870i | −0.0907900 | + | 0.157253i | ||||
\(355\) | −4.00000 | − | 6.92820i | −0.212298 | − | 0.367711i | ||||
\(356\) | −10.0000 | −0.529999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.94427 | −0.472719 | ||||||||
\(359\) | −13.4164 | − | 23.2379i | −0.708091 | − | 1.22645i | −0.965564 | − | 0.260164i | \(-0.916223\pi\) |
0.257473 | − | 0.966285i | \(-0.417110\pi\) | |||||||
\(360\) | 0.909830 | − | 1.57587i | 0.0479523 | − | 0.0830557i | ||||
\(361\) | −16.6803 | + | 28.8912i | −0.877913 | + | 1.52059i | ||||
\(362\) | 4.61803 | + | 7.99867i | 0.242718 | + | 0.420401i | ||||
\(363\) | −1.23607 | −0.0648767 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.0000 | −0.837478 | ||||||||
\(366\) | 0.472136 | + | 0.817763i | 0.0246789 | + | 0.0427452i | ||||
\(367\) | −2.70820 | + | 4.69075i | −0.141367 | + | 0.244855i | −0.928012 | − | 0.372551i | \(-0.878483\pi\) |
0.786645 | + | 0.617406i | \(0.211816\pi\) | |||||||
\(368\) | −2.00000 | + | 3.46410i | −0.104257 | + | 0.180579i | ||||
\(369\) | 1.81966 | + | 3.15174i | 0.0947277 | + | 0.164073i | ||||
\(370\) | 8.58359 | 0.446240 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.47214 | 0.128174 | ||||||||
\(373\) | 3.00000 | + | 5.19615i | 0.155334 | + | 0.269047i | 0.933181 | − | 0.359408i | \(-0.117021\pi\) |
−0.777847 | + | 0.628454i | \(0.783688\pi\) | |||||||
\(374\) | 1.23607 | − | 2.14093i | 0.0639156 | − | 0.110705i | ||||
\(375\) | −6.47214 | + | 11.2101i | −0.334220 | + | 0.578885i | ||||
\(376\) | −1.00000 | − | 1.73205i | −0.0515711 | − | 0.0893237i | ||||
\(377\) | 14.4721 | 0.745353 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.4721 | 0.743384 | 0.371692 | − | 0.928356i | \(-0.378778\pi\) | ||||
0.371692 | + | 0.928356i | \(0.378778\pi\) | |||||||
\(380\) | −4.47214 | − | 7.74597i | −0.229416 | − | 0.397360i | ||||
\(381\) | −7.41641 | + | 12.8456i | −0.379954 | + | 0.658100i | ||||
\(382\) | 1.23607 | − | 2.14093i | 0.0632427 | − | 0.109540i | ||||
\(383\) | −11.9443 | − | 20.6881i | −0.610324 | − | 1.05711i | −0.991186 | − | 0.132480i | \(-0.957706\pi\) |
0.380862 | − | 0.924632i | \(-0.375627\pi\) | |||||||
\(384\) | −1.23607 | −0.0630778 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.9443 | −0.760643 | ||||||||
\(387\) | −7.70820 | − | 13.3510i | −0.391830 | − | 0.678670i | ||||
\(388\) | 6.23607 | − | 10.8012i | 0.316588 | − | 0.548347i | ||||
\(389\) | −16.7082 | + | 28.9395i | −0.847140 | + | 1.46729i | 0.0366105 | + | 0.999330i | \(0.488344\pi\) |
−0.883750 | + | 0.467959i | \(0.844989\pi\) | |||||||
\(390\) | 2.47214 | + | 4.28187i | 0.125181 | + | 0.216821i | ||||
\(391\) | −9.88854 | −0.500085 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.88854 | 0.297038 | ||||||||
\(394\) | −9.00000 | − | 15.5885i | −0.453413 | − | 0.785335i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.736068 | − | 1.27491i | 0.0369888 | − | 0.0640665i | ||||
\(397\) | −11.8541 | − | 20.5319i | −0.594940 | − | 1.03047i | −0.993555 | − | 0.113348i | \(-0.963842\pi\) |
0.398615 | − | 0.917118i | \(-0.369491\pi\) | |||||||
\(398\) | −18.9443 | −0.949591 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.47214 | −0.173607 | ||||||||
\(401\) | −7.18034 | − | 12.4367i | −0.358569 | − | 0.621060i | 0.629153 | − | 0.777282i | \(-0.283402\pi\) |
−0.987722 | + | 0.156222i | \(0.950069\pi\) | |||||||
\(402\) | 7.05573 | − | 12.2209i | 0.351908 | − | 0.609522i | ||||
\(403\) | 3.23607 | − | 5.60503i | 0.161200 | − | 0.279207i | ||||
\(404\) | 4.09017 | + | 7.08438i | 0.203494 | + | 0.352461i | ||||
\(405\) | −2.98684 | −0.148417 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.94427 | 0.344215 | ||||||||
\(408\) | −1.52786 | − | 2.64634i | −0.0756405 | − | 0.131013i | ||||
\(409\) | 1.70820 | − | 2.95870i | 0.0844652 | − | 0.146298i | −0.820698 | − | 0.571362i | \(-0.806415\pi\) |
0.905163 | + | 0.425064i | \(0.139748\pi\) | |||||||
\(410\) | −1.52786 | + | 2.64634i | −0.0754558 | + | 0.130693i | ||||
\(411\) | −12.2918 | − | 21.2900i | −0.606310 | − | 1.05016i | ||||
\(412\) | 14.9443 | 0.736251 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −5.88854 | −0.289406 | ||||||||
\(415\) | −7.52786 | − | 13.0386i | −0.369528 | − | 0.640042i | ||||
\(416\) | −1.61803 | + | 2.80252i | −0.0793306 | + | 0.137405i | ||||
\(417\) | 13.4164 | − | 23.2379i | 0.657004 | − | 1.13796i | ||||
\(418\) | −3.61803 | − | 6.26662i | −0.176964 | − | 0.306510i | ||||
\(419\) | −17.2361 | −0.842037 | −0.421019 | − | 0.907052i | \(-0.638327\pi\) | ||||
−0.421019 | + | 0.907052i | \(0.638327\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.4721 | 0.802803 | 0.401401 | − | 0.915902i | \(-0.368523\pi\) | ||||
0.401401 | + | 0.915902i | \(0.368523\pi\) | |||||||
\(422\) | 6.76393 | + | 11.7155i | 0.329263 | + | 0.570300i | ||||
\(423\) | 1.47214 | − | 2.54981i | 0.0715777 | − | 0.123976i | ||||
\(424\) | −4.23607 | + | 7.33708i | −0.205722 | + | 0.356320i | ||||
\(425\) | −4.29180 | − | 7.43361i | −0.208183 | − | 0.360583i | ||||
\(426\) | −8.00000 | −0.387601 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2.47214 | 0.119495 | ||||||||
\(429\) | 2.00000 | + | 3.46410i | 0.0965609 | + | 0.167248i | ||||
\(430\) | 6.47214 | − | 11.2101i | 0.312114 | − | 0.540597i | ||||
\(431\) | −11.5279 | + | 19.9668i | −0.555278 | + | 0.961769i | 0.442604 | + | 0.896717i | \(0.354055\pi\) |
−0.997882 | + | 0.0650521i | \(0.979279\pi\) | |||||||
\(432\) | −2.76393 | − | 4.78727i | −0.132980 | − | 0.230328i | ||||
\(433\) | −28.4721 | −1.36828 | −0.684142 | − | 0.729349i | \(-0.739823\pi\) | ||||
−0.684142 | + | 0.729349i | \(0.739823\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.83282 | −0.327608 | ||||||||
\(436\) | 5.00000 | + | 8.66025i | 0.239457 | + | 0.414751i | ||||
\(437\) | −14.4721 | + | 25.0665i | −0.692296 | + | 1.19909i | ||||
\(438\) | −8.00000 | + | 13.8564i | −0.382255 | + | 0.662085i | ||||
\(439\) | 4.47214 | + | 7.74597i | 0.213443 | + | 0.369695i | 0.952790 | − | 0.303630i | \(-0.0981988\pi\) |
−0.739347 | + | 0.673325i | \(0.764865\pi\) | |||||||
\(440\) | 1.23607 | 0.0589272 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8.00000 | −0.380521 | ||||||||
\(443\) | 12.4721 | + | 21.6024i | 0.592569 | + | 1.02636i | 0.993885 | + | 0.110420i | \(0.0352196\pi\) |
−0.401316 | + | 0.915940i | \(0.631447\pi\) | |||||||
\(444\) | 4.29180 | − | 7.43361i | 0.203680 | − | 0.352783i | ||||
\(445\) | 6.18034 | − | 10.7047i | 0.292976 | − | 0.507450i | ||||
\(446\) | −0.236068 | − | 0.408882i | −0.0111781 | − | 0.0193611i | ||||
\(447\) | 27.6393 | 1.30729 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.9443 | 0.894035 | 0.447018 | − | 0.894525i | \(-0.352486\pi\) | ||||
0.447018 | + | 0.894525i | \(0.352486\pi\) | |||||||
\(450\) | −2.55573 | − | 4.42665i | −0.120478 | − | 0.208674i | ||||
\(451\) | −1.23607 | + | 2.14093i | −0.0582042 | + | 0.100813i | ||||
\(452\) | 0.236068 | − | 0.408882i | 0.0111037 | − | 0.0192322i | ||||
\(453\) | 7.41641 | + | 12.8456i | 0.348453 | + | 0.603539i | ||||
\(454\) | 19.2361 | 0.902793 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8.94427 | −0.418854 | ||||||||
\(457\) | −13.4721 | − | 23.3344i | −0.630200 | − | 1.09154i | −0.987511 | − | 0.157553i | \(-0.949640\pi\) |
0.357311 | − | 0.933986i | \(-0.383694\pi\) | |||||||
\(458\) | 8.61803 | − | 14.9269i | 0.402694 | − | 0.697487i | ||||
\(459\) | 6.83282 | − | 11.8348i | 0.318929 | − | 0.552400i | ||||
\(460\) | −2.47214 | − | 4.28187i | −0.115264 | − | 0.199643i | ||||
\(461\) | −24.7639 | −1.15337 | −0.576686 | − | 0.816966i | \(-0.695654\pi\) | ||||
−0.576686 | + | 0.816966i | \(0.695654\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.4721 | −1.41616 | −0.708080 | − | 0.706132i | \(-0.750438\pi\) | ||||
−0.708080 | + | 0.706132i | \(0.750438\pi\) | |||||||
\(464\) | −2.23607 | − | 3.87298i | −0.103807 | − | 0.179799i | ||||
\(465\) | −1.52786 | + | 2.64634i | −0.0708530 | + | 0.122721i | ||||
\(466\) | 7.47214 | − | 12.9421i | 0.346140 | − | 0.599532i | ||||
\(467\) | −13.5623 | − | 23.4906i | −0.627589 | − | 1.08702i | −0.988034 | − | 0.154235i | \(-0.950709\pi\) |
0.360445 | − | 0.932780i | \(-0.382625\pi\) | |||||||
\(468\) | −4.76393 | −0.220213 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2.47214 | 0.114031 | ||||||||
\(471\) | 7.81966 | + | 13.5440i | 0.360311 | + | 0.624077i | ||||
\(472\) | 1.38197 | − | 2.39364i | 0.0636101 | − | 0.110176i | ||||
\(473\) | 5.23607 | − | 9.06914i | 0.240755 | − | 0.416999i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −25.1246 | −1.15280 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.4721 | −0.571060 | ||||||||
\(478\) | −10.0000 | − | 17.3205i | −0.457389 | − | 0.792222i | ||||
\(479\) | 6.18034 | − | 10.7047i | 0.282387 | − | 0.489109i | −0.689585 | − | 0.724205i | \(-0.742207\pi\) |
0.971972 | + | 0.235096i | \(0.0755405\pi\) | |||||||
\(480\) | 0.763932 | − | 1.32317i | 0.0348686 | − | 0.0603941i | ||||
\(481\) | −11.2361 | − | 19.4614i | −0.512321 | − | 0.887365i | ||||
\(482\) | −15.4164 | −0.702198 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 7.70820 | + | 13.3510i | 0.350012 | + | 0.606238i | ||||
\(486\) | 6.79837 | − | 11.7751i | 0.308381 | − | 0.534131i | ||||
\(487\) | −8.47214 | + | 14.6742i | −0.383909 | + | 0.664950i | −0.991617 | − | 0.129210i | \(-0.958756\pi\) |
0.607708 | + | 0.794160i | \(0.292089\pi\) | |||||||
\(488\) | −0.381966 | − | 0.661585i | −0.0172908 | − | 0.0299485i | ||||
\(489\) | 24.0000 | 1.08532 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.9443 | −0.764684 | −0.382342 | − | 0.924021i | \(-0.624882\pi\) | ||||
−0.382342 | + | 0.924021i | \(0.624882\pi\) | |||||||
\(492\) | 1.52786 | + | 2.64634i | 0.0688814 | + | 0.119306i | ||||
\(493\) | 5.52786 | − | 9.57454i | 0.248962 | − | 0.431216i | ||||
\(494\) | −11.7082 | + | 20.2792i | −0.526777 | + | 0.912405i | ||||
\(495\) | 0.909830 | + | 1.57587i | 0.0408938 | + | 0.0708302i | ||||
\(496\) | −2.00000 | −0.0898027 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −15.0557 | −0.674663 | ||||||||
\(499\) | 16.1803 | + | 28.0252i | 0.724331 | + | 1.25458i | 0.959249 | + | 0.282564i | \(0.0911848\pi\) |
−0.234917 | + | 0.972015i | \(0.575482\pi\) | |||||||
\(500\) | 5.23607 | − | 9.06914i | 0.234164 | − | 0.405584i | ||||
\(501\) | −7.05573 | + | 12.2209i | −0.315227 | + | 0.545989i | ||||
\(502\) | 14.6180 | + | 25.3192i | 0.652435 | + | 1.13005i | ||||
\(503\) | −4.00000 | −0.178351 | −0.0891756 | − | 0.996016i | \(-0.528423\pi\) | ||||
−0.0891756 | + | 0.996016i | \(0.528423\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.1115 | −0.449954 | ||||||||
\(506\) | −2.00000 | − | 3.46410i | −0.0889108 | − | 0.153998i | ||||
\(507\) | −1.56231 | + | 2.70599i | −0.0693844 | + | 0.120177i | ||||
\(508\) | 6.00000 | − | 10.3923i | 0.266207 | − | 0.461084i | ||||
\(509\) | 12.0344 | + | 20.8443i | 0.533417 | + | 0.923906i | 0.999238 | + | 0.0390268i | \(0.0124258\pi\) |
−0.465821 | + | 0.884879i | \(0.654241\pi\) | |||||||
\(510\) | 3.77709 | 0.167252 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −20.0000 | − | 34.6410i | −0.883022 | − | 1.52944i | ||||
\(514\) | 3.47214 | − | 6.01392i | 0.153149 | − | 0.265262i | ||||
\(515\) | −9.23607 | + | 15.9973i | −0.406990 | + | 0.704927i | ||||
\(516\) | −6.47214 | − | 11.2101i | −0.284920 | − | 0.493496i | ||||
\(517\) | 2.00000 | 0.0879599 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.00000 | −0.175581 | ||||||||
\(520\) | −2.00000 | − | 3.46410i | −0.0877058 | − | 0.151911i | ||||
\(521\) | −5.18034 | + | 8.97261i | −0.226955 | + | 0.393097i | −0.956904 | − | 0.290404i | \(-0.906210\pi\) |
0.729949 | + | 0.683501i | \(0.239544\pi\) | |||||||
\(522\) | 3.29180 | − | 5.70156i | 0.144078 | − | 0.249550i | ||||
\(523\) | −7.14590 | − | 12.3771i | −0.312468 | − | 0.541211i | 0.666428 | − | 0.745570i | \(-0.267822\pi\) |
−0.978896 | + | 0.204359i | \(0.934489\pi\) | |||||||
\(524\) | −4.76393 | −0.208113 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.94427 | −0.215580 | ||||||||
\(527\) | −2.47214 | − | 4.28187i | −0.107688 | − | 0.186521i | ||||
\(528\) | 0.618034 | − | 1.07047i | 0.0268965 | − | 0.0465861i | ||||
\(529\) | 3.50000 | − | 6.06218i | 0.152174 | − | 0.263573i | ||||
\(530\) | −5.23607 | − | 9.06914i | −0.227440 | − | 0.393938i | ||||
\(531\) | 4.06888 | 0.176575 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.00000 | 0.346518 | ||||||||
\(534\) | −6.18034 | − | 10.7047i | −0.267449 | − | 0.463236i | ||||
\(535\) | −1.52786 | + | 2.64634i | −0.0660553 | + | 0.114411i | ||||
\(536\) | −5.70820 | + | 9.88690i | −0.246557 | + | 0.427049i | ||||
\(537\) | −5.52786 | − | 9.57454i | −0.238545 | − | 0.413172i | ||||
\(538\) | 22.7639 | 0.981423 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 6.83282 | 0.294038 | ||||||||
\(541\) | 13.4721 | + | 23.3344i | 0.579212 | + | 1.00323i | 0.995570 | + | 0.0940243i | \(0.0299731\pi\) |
−0.416358 | + | 0.909201i | \(0.636694\pi\) | |||||||
\(542\) | 0.472136 | − | 0.817763i | 0.0202800 | − | 0.0351259i | ||||
\(543\) | −5.70820 | + | 9.88690i | −0.244962 | + | 0.424287i | ||||
\(544\) | 1.23607 | + | 2.14093i | 0.0529960 | + | 0.0917917i | ||||
\(545\) | −12.3607 | −0.529473 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.944272 | −0.0403742 | −0.0201871 | − | 0.999796i | \(-0.506426\pi\) | ||||
−0.0201871 | + | 0.999796i | \(0.506426\pi\) | |||||||
\(548\) | 9.94427 | + | 17.2240i | 0.424798 | + | 0.735772i | ||||
\(549\) | 0.562306 | − | 0.973942i | 0.0239986 | − | 0.0415668i | ||||
\(550\) | 1.73607 | − | 3.00696i | 0.0740262 | − | 0.128217i | ||||
\(551\) | −16.1803 | − | 28.0252i | −0.689306 | − | 1.19391i | ||||
\(552\) | −4.94427 | −0.210442 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3.52786 | 0.149885 | ||||||||
\(555\) | 5.30495 | + | 9.18845i | 0.225183 | + | 0.390028i | ||||
\(556\) | −10.8541 | + | 18.7999i | −0.460316 | + | 0.797291i | ||||
\(557\) | −12.4164 | + | 21.5058i | −0.526100 | + | 0.911232i | 0.473438 | + | 0.880827i | \(0.343013\pi\) |
−0.999538 | + | 0.0304047i | \(0.990320\pi\) | |||||||
\(558\) | −1.47214 | − | 2.54981i | −0.0623205 | − | 0.107942i | ||||
\(559\) | −33.8885 | −1.43333 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.05573 | 0.129013 | ||||||||
\(562\) | −14.4164 | − | 24.9700i | −0.608119 | − | 1.05329i | ||||
\(563\) | 15.6180 | − | 27.0512i | 0.658222 | − | 1.14007i | −0.322854 | − | 0.946449i | \(-0.604642\pi\) |
0.981076 | − | 0.193625i | \(-0.0620244\pi\) | |||||||
\(564\) | 1.23607 | − | 2.14093i | 0.0520479 | − | 0.0901495i | ||||
\(565\) | 0.291796 | + | 0.505406i | 0.0122760 | + | 0.0212626i | ||||
\(566\) | −14.6525 | −0.615889 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.47214 | 0.271565 | ||||||||
\(569\) | 18.4164 | + | 31.8982i | 0.772056 | + | 1.33724i | 0.936434 | + | 0.350843i | \(0.114105\pi\) |
−0.164378 | + | 0.986397i | \(0.552562\pi\) | |||||||
\(570\) | 5.52786 | − | 9.57454i | 0.231537 | − | 0.401033i | ||||
\(571\) | 5.05573 | − | 8.75678i | 0.211576 | − | 0.366460i | −0.740632 | − | 0.671911i | \(-0.765474\pi\) |
0.952208 | + | 0.305451i | \(0.0988072\pi\) | |||||||
\(572\) | −1.61803 | − | 2.80252i | −0.0676534 | − | 0.117179i | ||||
\(573\) | 3.05573 | 0.127655 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.8885 | −0.579192 | ||||||||
\(576\) | 0.736068 | + | 1.27491i | 0.0306695 | + | 0.0531211i | ||||
\(577\) | 13.4721 | − | 23.3344i | 0.560852 | − | 0.971425i | −0.436570 | − | 0.899670i | \(-0.643807\pi\) |
0.997422 | − | 0.0717545i | \(-0.0228598\pi\) | |||||||
\(578\) | 5.44427 | − | 9.42976i | 0.226452 | − | 0.392226i | ||||
\(579\) | −9.23607 | − | 15.9973i | −0.383838 | − | 0.664827i | ||||
\(580\) | 5.52786 | 0.229532 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 15.4164 | 0.639031 | ||||||||
\(583\) | −4.23607 | − | 7.33708i | −0.175440 | − | 0.303871i | ||||
\(584\) | 6.47214 | − | 11.2101i | 0.267819 | − | 0.463876i | ||||
\(585\) | 2.94427 | − | 5.09963i | 0.121731 | − | 0.210844i | ||||
\(586\) | −13.3262 | − | 23.0817i | −0.550502 | − | 0.953497i | ||||
\(587\) | 5.81966 | 0.240203 | 0.120102 | − | 0.992762i | \(-0.461678\pi\) | ||||
0.120102 | + | 0.992762i | \(0.461678\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.4721 | −0.596314 | ||||||||
\(590\) | 1.70820 | + | 2.95870i | 0.0703256 | + | 0.121808i | ||||
\(591\) | 11.1246 | − | 19.2684i | 0.457605 | − | 0.792596i | ||||
\(592\) | −3.47214 | + | 6.01392i | −0.142704 | + | 0.247170i | ||||
\(593\) | 12.0000 | + | 20.7846i | 0.492781 | + | 0.853522i | 0.999965 | − | 0.00831589i | \(-0.00264706\pi\) |
−0.507184 | + | 0.861838i | \(0.669314\pi\) | |||||||
\(594\) | 5.52786 | 0.226811 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −22.3607 | −0.915929 | ||||||||
\(597\) | −11.7082 | − | 20.2792i | −0.479185 | − | 0.829973i | ||||
\(598\) | −6.47214 | + | 11.2101i | −0.264665 | + | 0.458414i | ||||
\(599\) | 16.1803 | − | 28.0252i | 0.661111 | − | 1.14508i | −0.319213 | − | 0.947683i | \(-0.603419\pi\) |
0.980324 | − | 0.197395i | \(-0.0632480\pi\) | |||||||
\(600\) | −2.14590 | − | 3.71680i | −0.0876059 | − | 0.151738i | ||||
\(601\) | 34.8328 | 1.42086 | 0.710430 | − | 0.703768i | \(-0.248500\pi\) | ||||
0.710430 | + | 0.703768i | \(0.248500\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16.8065 | −0.684414 | ||||||||
\(604\) | −6.00000 | − | 10.3923i | −0.244137 | − | 0.422857i | ||||
\(605\) | −0.618034 | + | 1.07047i | −0.0251267 | + | 0.0435206i | ||||
\(606\) | −5.05573 | + | 8.75678i | −0.205375 | + | 0.355720i | ||||
\(607\) | −16.0000 | − | 27.7128i | −0.649420 | − | 1.12483i | −0.983262 | − | 0.182199i | \(-0.941678\pi\) |
0.333842 | − | 0.942629i | \(-0.391655\pi\) | |||||||
\(608\) | 7.23607 | 0.293461 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.944272 | 0.0382325 | ||||||||
\(611\) | −3.23607 | − | 5.60503i | −0.130917 | − | 0.226755i | ||||
\(612\) | −1.81966 | + | 3.15174i | −0.0735554 | + | 0.127402i | ||||
\(613\) | −14.2361 | + | 24.6576i | −0.574989 | + | 0.995911i | 0.421053 | + | 0.907036i | \(0.361660\pi\) |
−0.996043 | + | 0.0888750i | \(0.971673\pi\) | |||||||
\(614\) | −13.0344 | − | 22.5763i | −0.526027 | − | 0.911106i | ||||
\(615\) | −3.77709 | −0.152307 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.4164 | 0.862192 | 0.431096 | − | 0.902306i | \(-0.358127\pi\) | ||||
0.431096 | + | 0.902306i | \(0.358127\pi\) | |||||||
\(618\) | 9.23607 | + | 15.9973i | 0.371529 | + | 0.643507i | ||||
\(619\) | 9.27051 | − | 16.0570i | 0.372613 | − | 0.645385i | −0.617353 | − | 0.786686i | \(-0.711795\pi\) |
0.989967 | + | 0.141301i | \(0.0451285\pi\) | |||||||
\(620\) | 1.23607 | − | 2.14093i | 0.0496417 | − | 0.0859819i | ||||
\(621\) | −11.0557 | − | 19.1491i | −0.443651 | − | 0.768426i | ||||
\(622\) | 21.4164 | 0.858720 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −4.00000 | −0.160128 | ||||||||
\(625\) | −2.20820 | − | 3.82472i | −0.0883282 | − | 0.152989i | ||||
\(626\) | 9.76393 | − | 16.9116i | 0.390245 | − | 0.675925i | ||||
\(627\) | 4.47214 | − | 7.74597i | 0.178600 | − | 0.309344i | ||||
\(628\) | −6.32624 | − | 10.9574i | −0.252444 | − | 0.437246i | ||||
\(629\) | −17.1672 | −0.684500 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.4164 | −1.25067 | −0.625334 | − | 0.780357i | \(-0.715037\pi\) | ||||
−0.625334 | + | 0.780357i | \(0.715037\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.36068 | + | 14.4811i | −0.332307 | + | 0.575573i | ||||
\(634\) | 15.4721 | − | 26.7985i | 0.614477 | − | 1.06431i | ||||
\(635\) | 7.41641 | + | 12.8456i | 0.294311 | + | 0.509762i | ||||
\(636\) | −10.4721 | −0.415247 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.47214 | 0.177054 | ||||||||
\(639\) | 4.76393 | + | 8.25137i | 0.188458 | + | 0.326419i | ||||
\(640\) | −0.618034 | + | 1.07047i | −0.0244299 | + | 0.0423139i | ||||
\(641\) | −13.7639 | + | 23.8398i | −0.543643 | + | 0.941617i | 0.455048 | + | 0.890467i | \(0.349622\pi\) |
−0.998691 | + | 0.0511499i | \(0.983711\pi\) | |||||||
\(642\) | 1.52786 | + | 2.64634i | 0.0603000 | + | 0.104443i | ||||
\(643\) | 18.7639 | 0.739977 | 0.369989 | − | 0.929036i | \(-0.379362\pi\) | ||||
0.369989 | + | 0.929036i | \(0.379362\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 16.0000 | 0.629999 | ||||||||
\(646\) | 8.94427 | + | 15.4919i | 0.351908 | + | 0.609522i | ||||
\(647\) | −14.4164 | + | 24.9700i | −0.566767 | + | 0.981670i | 0.430115 | + | 0.902774i | \(0.358473\pi\) |
−0.996883 | + | 0.0788961i | \(0.974860\pi\) | |||||||
\(648\) | 1.20820 | − | 2.09267i | 0.0474627 | − | 0.0822079i | ||||
\(649\) | 1.38197 | + | 2.39364i | 0.0542469 | + | 0.0939584i | ||||
\(650\) | −11.2361 | −0.440715 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −19.4164 | −0.760405 | ||||||||
\(653\) | −23.1803 | − | 40.1495i | −0.907117 | − | 1.57117i | −0.818050 | − | 0.575147i | \(-0.804945\pi\) |
−0.0890665 | − | 0.996026i | \(-0.528388\pi\) | |||||||
\(654\) | −6.18034 | + | 10.7047i | −0.241670 | + | 0.418585i | ||||
\(655\) | 2.94427 | − | 5.09963i | 0.115042 | − | 0.199259i | ||||
\(656\) | −1.23607 | − | 2.14093i | −0.0482603 | − | 0.0835894i | ||||
\(657\) | 19.0557 | 0.743435 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.5836 | 0.646005 | 0.323003 | − | 0.946398i | \(-0.395308\pi\) | ||||
0.323003 | + | 0.946398i | \(0.395308\pi\) | |||||||
\(660\) | 0.763932 | + | 1.32317i | 0.0297360 | + | 0.0515043i | ||||
\(661\) | −1.56231 | + | 2.70599i | −0.0607667 | + | 0.105251i | −0.894808 | − | 0.446451i | \(-0.852688\pi\) |
0.834042 | + | 0.551701i | \(0.186021\pi\) | |||||||
\(662\) | 8.47214 | − | 14.6742i | 0.329279 | − | 0.570328i | ||||
\(663\) | −4.94427 | − | 8.56373i | −0.192020 | − | 0.332588i | ||||
\(664\) | 12.1803 | 0.472689 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −10.2229 | −0.396130 | ||||||||
\(667\) | −8.94427 | − | 15.4919i | −0.346324 | − | 0.599850i | ||||
\(668\) | 5.70820 | − | 9.88690i | 0.220857 | − | 0.382536i | ||||
\(669\) | 0.291796 | − | 0.505406i | 0.0112815 | − | 0.0195401i | ||||
\(670\) | −7.05573 | − | 12.2209i | −0.272587 | − | 0.472134i | ||||
\(671\) | 0.763932 | 0.0294913 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.88854 | −0.149892 | −0.0749462 | − | 0.997188i | \(-0.523878\pi\) | ||||
−0.0749462 | + | 0.997188i | \(0.523878\pi\) | |||||||
\(674\) | −9.00000 | − | 15.5885i | −0.346667 | − | 0.600445i | ||||
\(675\) | 9.59675 | − | 16.6221i | 0.369379 | − | 0.639783i | ||||
\(676\) | 1.26393 | − | 2.18919i | 0.0486128 | − | 0.0841998i | ||||
\(677\) | −13.0344 | − | 22.5763i | −0.500954 | − | 0.867678i | −0.999999 | − | 0.00110228i | \(-0.999649\pi\) |
0.499045 | − | 0.866576i | \(-0.333684\pi\) | |||||||
\(678\) | 0.583592 | 0.0224127 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.05573 | −0.117182 | ||||||||
\(681\) | 11.8885 | + | 20.5916i | 0.455570 | + | 0.789070i | ||||
\(682\) | 1.00000 | − | 1.73205i | 0.0382920 | − | 0.0663237i | ||||
\(683\) | −16.4721 | + | 28.5306i | −0.630289 | + | 1.09169i | 0.357204 | + | 0.934026i | \(0.383730\pi\) |
−0.987493 | + | 0.157666i | \(0.949603\pi\) | |||||||
\(684\) | 5.32624 | + | 9.22531i | 0.203654 | + | 0.352739i | ||||
\(685\) | −24.5836 | −0.939291 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.3050 | 0.812835 | ||||||||
\(688\) | 5.23607 | + | 9.06914i | 0.199623 | + | 0.345758i | ||||
\(689\) | −13.7082 | + | 23.7433i | −0.522241 | + | 0.904548i | ||||
\(690\) | 3.05573 | − | 5.29268i | 0.116330 | − | 0.201489i | ||||
\(691\) | 6.32624 | + | 10.9574i | 0.240661 | + | 0.416838i | 0.960903 | − | 0.276886i | \(-0.0893023\pi\) |
−0.720241 | + | 0.693723i | \(0.755969\pi\) | |||||||
\(692\) | 3.23607 | 0.123017 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.47214 | 0.0938410 | ||||||||
\(695\) | −13.4164 | − | 23.2379i | −0.508913 | − | 0.881464i | ||||
\(696\) | 2.76393 | − | 4.78727i | 0.104767 | − | 0.181461i | ||||
\(697\) | 3.05573 | − | 5.29268i | 0.115744 | − | 0.200474i | ||||
\(698\) | 10.8541 | + | 18.7999i | 0.410834 | + | 0.711585i | ||||
\(699\) | 18.4721 | 0.698680 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −42.7214 | −1.61356 | −0.806782 | − | 0.590850i | \(-0.798793\pi\) | ||||
−0.806782 | + | 0.590850i | \(0.798793\pi\) | |||||||
\(702\) | −8.94427 | − | 15.4919i | −0.337580 | − | 0.584705i | ||||
\(703\) | −25.1246 | + | 43.5171i | −0.947593 | + | 1.64128i | ||||
\(704\) | −0.500000 | + | 0.866025i | −0.0188445 | + | 0.0326396i | ||||
\(705\) | 1.52786 | + | 2.64634i | 0.0575427 | + | 0.0996669i | ||||
\(706\) | 17.0557 | 0.641901 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 3.41641 | 0.128396 | ||||||||
\(709\) | −2.23607 | − | 3.87298i | −0.0839773 | − | 0.145453i | 0.820978 | − | 0.570960i | \(-0.193429\pi\) |
−0.904955 | + | 0.425507i | \(0.860096\pi\) | |||||||
\(710\) | −4.00000 | + | 6.92820i | −0.150117 | + | 0.260011i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.00000 | + | 8.66025i | 0.187383 | + | 0.324557i | ||||
\(713\) | −8.00000 | −0.299602 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.00000 | 0.149592 | ||||||||
\(716\) | 4.47214 | + | 7.74597i | 0.167132 | + | 0.289480i | ||||
\(717\) | 12.3607 | − | 21.4093i | 0.461618 | − | 0.799546i | ||||
\(718\) | −13.4164 | + | 23.2379i | −0.500696 | + | 0.867231i | ||||
\(719\) | 8.41641 | + | 14.5776i | 0.313879 | + | 0.543654i | 0.979199 | − | 0.202904i | \(-0.0650380\pi\) |
−0.665320 | + | 0.746559i | \(0.731705\pi\) | |||||||
\(720\) | −1.81966 | −0.0678147 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 33.3607 | 1.24156 | ||||||||
\(723\) | −9.52786 | − | 16.5027i | −0.354345 | − | 0.613744i | ||||
\(724\) | 4.61803 | − | 7.99867i | 0.171628 | − | 0.297268i | ||||
\(725\) | 7.76393 | − | 13.4475i | 0.288345 | − | 0.499429i | ||||
\(726\) | 0.618034 | + | 1.07047i | 0.0229374 | + | 0.0397287i | ||||
\(727\) | −18.0000 | −0.667583 | −0.333792 | − | 0.942647i | \(-0.608328\pi\) | ||||
−0.333792 | + | 0.942647i | \(0.608328\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.0557 | 0.890953 | ||||||||
\(730\) | 8.00000 | + | 13.8564i | 0.296093 | + | 0.512849i | ||||
\(731\) | −12.9443 | + | 22.4201i | −0.478761 | + | 0.829239i | ||||
\(732\) | 0.472136 | − | 0.817763i | 0.0174506 | − | 0.0302254i | ||||
\(733\) | 24.5623 | + | 42.5432i | 0.907229 | + | 1.57137i | 0.817896 | + | 0.575366i | \(0.195140\pi\) |
0.0893332 | + | 0.996002i | \(0.471526\pi\) | |||||||
\(734\) | 5.41641 | 0.199923 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.00000 | 0.147442 | ||||||||
\(737\) | −5.70820 | − | 9.88690i | −0.210264 | − | 0.364189i | ||||
\(738\) | 1.81966 | − | 3.15174i | 0.0669826 | − | 0.116017i | ||||
\(739\) | −10.0000 | + | 17.3205i | −0.367856 | + | 0.637145i | −0.989230 | − | 0.146369i | \(-0.953241\pi\) |
0.621374 | + | 0.783514i | \(0.286575\pi\) | |||||||
\(740\) | −4.29180 | − | 7.43361i | −0.157770 | − | 0.273265i | ||||
\(741\) | −28.9443 | −1.06329 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.8885 | 0.803013 | 0.401506 | − | 0.915856i | \(-0.368487\pi\) | ||||
0.401506 | + | 0.915856i | \(0.368487\pi\) | |||||||
\(744\) | −1.23607 | − | 2.14093i | −0.0453165 | − | 0.0784904i | ||||
\(745\) | 13.8197 | − | 23.9364i | 0.506313 | − | 0.876960i | ||||
\(746\) | 3.00000 | − | 5.19615i | 0.109838 | − | 0.190245i | ||||
\(747\) | 8.96556 | + | 15.5288i | 0.328033 | + | 0.568169i | ||||
\(748\) | −2.47214 | −0.0903902 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 12.9443 | 0.472658 | ||||||||
\(751\) | 8.47214 | + | 14.6742i | 0.309153 | + | 0.535468i | 0.978177 | − | 0.207772i | \(-0.0666213\pi\) |
−0.669025 | + | 0.743240i | \(0.733288\pi\) | |||||||
\(752\) | −1.00000 | + | 1.73205i | −0.0364662 | + | 0.0631614i | ||||
\(753\) | −18.0689 | + | 31.2962i | −0.658467 | + | 1.14050i | ||||
\(754\) | −7.23607 | − | 12.5332i | −0.263522 | − | 0.456434i | ||||
\(755\) | 14.8328 | 0.539821 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.3050 | −0.847033 | −0.423516 | − | 0.905888i | \(-0.639204\pi\) | ||||
−0.423516 | + | 0.905888i | \(0.639204\pi\) | |||||||
\(758\) | −7.23607 | − | 12.5332i | −0.262826 | − | 0.455228i | ||||
\(759\) | 2.47214 | − | 4.28187i | 0.0897329 | − | 0.155422i | ||||
\(760\) | −4.47214 | + | 7.74597i | −0.162221 | + | 0.280976i | ||||
\(761\) | −5.70820 | − | 9.88690i | −0.206922 | − | 0.358400i | 0.743821 | − | 0.668379i | \(-0.233011\pi\) |
−0.950743 | + | 0.309979i | \(0.899678\pi\) | |||||||
\(762\) | 14.8328 | 0.537336 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.47214 | −0.0894387 | ||||||||
\(765\) | −2.24922 | − | 3.89577i | −0.0813209 | − | 0.140852i | ||||
\(766\) | −11.9443 | + | 20.6881i | −0.431564 | + | 0.747491i | ||||
\(767\) | 4.47214 | − | 7.74597i | 0.161479 | − | 0.279691i | ||||
\(768\) | 0.618034 | + | 1.07047i | 0.0223014 | + | 0.0386271i | ||||
\(769\) | 43.4164 | 1.56564 | 0.782818 | − | 0.622251i | \(-0.213782\pi\) | ||||
0.782818 | + | 0.622251i | \(0.213782\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.58359 | 0.309131 | ||||||||
\(772\) | 7.47214 | + | 12.9421i | 0.268928 | + | 0.465797i | ||||
\(773\) | 7.85410 | − | 13.6037i | 0.282492 | − | 0.489291i | −0.689506 | − | 0.724280i | \(-0.742172\pi\) |
0.971998 | + | 0.234989i | \(0.0755055\pi\) | |||||||
\(774\) | −7.70820 | + | 13.3510i | −0.277066 | + | 0.479892i | ||||
\(775\) | −3.47214 | − | 6.01392i | −0.124723 | − | 0.216026i | ||||
\(776\) | −12.4721 | −0.447724 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 33.4164 | 1.19804 | ||||||||
\(779\) | −8.94427 | − | 15.4919i | −0.320462 | − | 0.555056i | ||||
\(780\) | 2.47214 | − | 4.28187i | 0.0885167 | − | 0.153315i | ||||
\(781\) | −3.23607 | + | 5.60503i | −0.115796 | + | 0.200564i | ||||
\(782\) | 4.94427 | + | 8.56373i | 0.176807 | + | 0.306238i | ||||
\(783\) | 24.7214 | 0.883469 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.6393 | 0.558191 | ||||||||
\(786\) | −2.94427 | − | 5.09963i | −0.105019 | − | 0.181898i | ||||
\(787\) | −14.0902 | + | 24.4049i | −0.502260 | + | 0.869940i | 0.497736 | + | 0.867328i | \(0.334165\pi\) |
−0.999997 | + | 0.00261196i | \(0.999169\pi\) | |||||||
\(788\) | −9.00000 | + | 15.5885i | −0.320612 | + | 0.555316i | ||||
\(789\) | −3.05573 | − | 5.29268i | −0.108787 | − | 0.188424i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.47214 | −0.0523101 | ||||||||
\(793\) | −1.23607 | − | 2.14093i | −0.0438941 | − | 0.0760267i | ||||
\(794\) | −11.8541 | + | 20.5319i | −0.420686 | + | 0.728650i | ||||
\(795\) | 6.47214 | − | 11.2101i | 0.229543 | − | 0.397580i | ||||
\(796\) | 9.47214 | + | 16.4062i | 0.335731 | + | 0.581503i | ||||
\(797\) | 41.5967 | 1.47343 | 0.736716 | − | 0.676202i | \(-0.236375\pi\) | ||||
0.736716 | + | 0.676202i | \(0.236375\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.94427 | −0.174916 | ||||||||
\(800\) | 1.73607 | + | 3.00696i | 0.0613793 | + | 0.106312i | ||||
\(801\) | −7.36068 | + | 12.7491i | −0.260077 | + | 0.450466i | ||||
\(802\) | −7.18034 | + | 12.4367i | −0.253547 | + | 0.439156i | ||||
\(803\) | 6.47214 | + | 11.2101i | 0.228397 | + | 0.395595i | ||||
\(804\) | −14.1115 | −0.497673 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.47214 | −0.227971 | ||||||||
\(807\) | 14.0689 | + | 24.3680i | 0.495248 | + | 0.857795i | ||||
\(808\) | 4.09017 | − | 7.08438i | 0.143892 | − | 0.249228i | ||||
\(809\) | 10.5279 | − | 18.2348i | 0.370140 | − | 0.641101i | −0.619447 | − | 0.785039i | \(-0.712643\pi\) |
0.989587 | + | 0.143937i | \(0.0459764\pi\) | |||||||
\(810\) | 1.49342 | + | 2.58668i | 0.0524735 | + | 0.0908868i | ||||
\(811\) | −4.76393 | −0.167284 | −0.0836421 | − | 0.996496i | \(-0.526655\pi\) | ||||
−0.0836421 | + | 0.996496i | \(0.526655\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.16718 | 0.0409349 | ||||||||
\(814\) | −3.47214 | − | 6.01392i | −0.121698 | − | 0.210788i | ||||
\(815\) | 12.0000 | − | 20.7846i | 0.420342 | − | 0.728053i | ||||
\(816\) | −1.52786 | + | 2.64634i | −0.0534859 | + | 0.0926404i | ||||
\(817\) | 37.8885 | + | 65.6249i | 1.32555 | + | 2.29592i | ||||
\(818\) | −3.41641 | −0.119452 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.05573 | 0.106711 | ||||||||
\(821\) | 0.708204 | + | 1.22665i | 0.0247165 | + | 0.0428102i | 0.878119 | − | 0.478442i | \(-0.158798\pi\) |
−0.853403 | + | 0.521252i | \(0.825465\pi\) | |||||||
\(822\) | −12.2918 | + | 21.2900i | −0.428726 | + | 0.742575i | ||||
\(823\) | 23.1246 | − | 40.0530i | 0.806073 | − | 1.39616i | −0.109491 | − | 0.993988i | \(-0.534922\pi\) |
0.915564 | − | 0.402172i | \(-0.131745\pi\) | |||||||
\(824\) | −7.47214 | − | 12.9421i | −0.260304 | − | 0.450860i | ||||
\(825\) | 4.29180 | 0.149421 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.9443 | 0.589210 | 0.294605 | − | 0.955619i | \(-0.404812\pi\) | ||||
0.294605 | + | 0.955619i | \(0.404812\pi\) | |||||||
\(828\) | 2.94427 | + | 5.09963i | 0.102321 | + | 0.177224i | ||||
\(829\) | 5.85410 | − | 10.1396i | 0.203321 | − | 0.352163i | −0.746275 | − | 0.665637i | \(-0.768160\pi\) |
0.949597 | + | 0.313475i | \(0.101493\pi\) | |||||||
\(830\) | −7.52786 | + | 13.0386i | −0.261296 | + | 0.452578i | ||||
\(831\) | 2.18034 | + | 3.77646i | 0.0756352 | + | 0.131004i | ||||
\(832\) | 3.23607 | 0.112190 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −26.8328 | −0.929144 | ||||||||
\(835\) | 7.05573 | + | 12.2209i | 0.244174 | + | 0.422921i | ||||
\(836\) | −3.61803 | + | 6.26662i | −0.125132 | + | 0.216736i | ||||
\(837\) | 5.52786 | − | 9.57454i | 0.191071 | − | 0.330945i | ||||
\(838\) | 8.61803 | + | 14.9269i | 0.297705 | + | 0.515640i | ||||
\(839\) | −16.8328 | −0.581133 | −0.290567 | − | 0.956855i | \(-0.593844\pi\) | ||||
−0.290567 | + | 0.956855i | \(0.593844\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | −8.23607 | − | 14.2653i | −0.283834 | − | 0.491614i | ||||
\(843\) | 17.8197 | − | 30.8646i | 0.613742 | − | 1.06303i | ||||
\(844\) | 6.76393 | − | 11.7155i | 0.232824 | − | 0.403263i | ||||
\(845\) | 1.56231 | + | 2.70599i | 0.0537450 | + | 0.0930890i | ||||
\(846\) | −2.94427 | −0.101226 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.47214 | 0.290934 | ||||||||
\(849\) | −9.05573 | − | 15.6850i | −0.310792 | − | 0.538307i | ||||
\(850\) | −4.29180 | + | 7.43361i | −0.147207 | + | 0.254971i | ||||
\(851\) | −13.8885 | + | 24.0557i | −0.476093 | + | 0.824618i | ||||
\(852\) | 4.00000 | + | 6.92820i | 0.137038 | + | 0.237356i | ||||
\(853\) | −32.5410 | −1.11418 | −0.557092 | − | 0.830451i | \(-0.688083\pi\) | ||||
−0.557092 | + | 0.830451i | \(0.688083\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −13.1672 | −0.450308 | ||||||||
\(856\) | −1.23607 | − | 2.14093i | −0.0422479 | − | 0.0731756i | ||||
\(857\) | −23.2361 | + | 40.2461i | −0.793729 | + | 1.37478i | 0.129914 | + | 0.991525i | \(0.458530\pi\) |
−0.923643 | + | 0.383254i | \(0.874804\pi\) | |||||||
\(858\) | 2.00000 | − | 3.46410i | 0.0682789 | − | 0.118262i | ||||
\(859\) | 7.56231 | + | 13.0983i | 0.258023 | + | 0.446908i | 0.965712 | − | 0.259615i | \(-0.0835958\pi\) |
−0.707690 | + | 0.706524i | \(0.750262\pi\) | |||||||
\(860\) | −12.9443 | −0.441396 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 23.0557 | 0.785281 | ||||||||
\(863\) | −0.291796 | − | 0.505406i | −0.00993285 | − | 0.0172042i | 0.861016 | − | 0.508577i | \(-0.169828\pi\) |
−0.870949 | + | 0.491373i | \(0.836495\pi\) | |||||||
\(864\) | −2.76393 | + | 4.78727i | −0.0940309 | + | 0.162866i | ||||
\(865\) | −2.00000 | + | 3.46410i | −0.0680020 | + | 0.117783i | ||||
\(866\) | 14.2361 | + | 24.6576i | 0.483761 | + | 0.837899i | ||||
\(867\) | 13.4590 | 0.457091 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 3.41641 | + | 5.91739i | 0.115827 | + | 0.200618i | ||||
\(871\) | −18.4721 | + | 31.9947i | −0.625904 | + | 1.08410i | ||||
\(872\) | 5.00000 | − | 8.66025i | 0.169321 | − | 0.293273i | ||||
\(873\) | −9.18034 | − | 15.9008i | −0.310707 | − | 0.538161i | ||||
\(874\) | 28.9443 | 0.979055 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 16.0000 | 0.540590 | ||||||||
\(877\) | −4.52786 | − | 7.84249i | −0.152895 | − | 0.264822i | 0.779395 | − | 0.626532i | \(-0.215526\pi\) |
−0.932291 | + | 0.361710i | \(0.882193\pi\) | |||||||
\(878\) | 4.47214 | − | 7.74597i | 0.150927 | − | 0.261414i | ||||
\(879\) | 16.4721 | − | 28.5306i | 0.555591 | − | 0.962312i | ||||
\(880\) | −0.618034 | − | 1.07047i | −0.0208339 | − | 0.0360854i | ||||
\(881\) | −28.8328 | −0.971402 | −0.485701 | − | 0.874125i | \(-0.661436\pi\) | ||||
−0.485701 | + | 0.874125i | \(0.661436\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.83282 | −0.0953318 | −0.0476659 | − | 0.998863i | \(-0.515178\pi\) | ||||
−0.0476659 | + | 0.998863i | \(0.515178\pi\) | |||||||
\(884\) | 4.00000 | + | 6.92820i | 0.134535 | + | 0.233021i | ||||
\(885\) | −2.11146 | + | 3.65715i | −0.0709758 | + | 0.122934i | ||||
\(886\) | 12.4721 | − | 21.6024i | 0.419010 | − | 0.725746i | ||||
\(887\) | −22.1803 | − | 38.4175i | −0.744743 | − | 1.28993i | −0.950315 | − | 0.311291i | \(-0.899239\pi\) |
0.205572 | − | 0.978642i | \(-0.434095\pi\) | |||||||
\(888\) | −8.58359 | −0.288046 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −12.3607 | −0.414331 | ||||||||
\(891\) | 1.20820 | + | 2.09267i | 0.0404764 | + | 0.0701071i | ||||
\(892\) | −0.236068 | + | 0.408882i | −0.00790414 | + | 0.0136904i | ||||
\(893\) | −7.23607 | + | 12.5332i | −0.242146 | + | 0.419409i | ||||
\(894\) | −13.8197 | − | 23.9364i | −0.462199 | − | 0.800551i | ||||
\(895\) | −11.0557 | −0.369552 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16.0000 | −0.534224 | ||||||||
\(898\) | −9.47214 | − | 16.4062i | −0.316089 | − | 0.547483i | ||||
\(899\) | 4.47214 | − | 7.74597i | 0.149154 | − | 0.258342i | ||||
\(900\) | −2.55573 | + | 4.42665i | −0.0851909 | + | 0.147555i | ||||
\(901\) | 10.4721 | + | 18.1383i | 0.348877 | + | 0.604273i | ||||
\(902\) | 2.47214 | 0.0823131 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.472136 | −0.0157030 | ||||||||
\(905\) | 5.70820 | + | 9.88690i | 0.189747 | + | 0.328652i | ||||
\(906\) | 7.41641 | − | 12.8456i | 0.246394 | − | 0.426766i | ||||
\(907\) | 12.1803 | − | 21.0970i | 0.404442 | − | 0.700513i | −0.589815 | − | 0.807539i | \(-0.700799\pi\) |
0.994256 | + | 0.107025i | \(0.0341326\pi\) | |||||||
\(908\) | −9.61803 | − | 16.6589i | −0.319186 | − | 0.552846i | ||||
\(909\) | 12.0426 | 0.399427 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.0000 | −0.927681 | −0.463841 | − | 0.885919i | \(-0.653529\pi\) | ||||
−0.463841 | + | 0.885919i | \(0.653529\pi\) | |||||||
\(912\) | 4.47214 | + | 7.74597i | 0.148087 | + | 0.256495i | ||||
\(913\) | −6.09017 | + | 10.5485i | −0.201555 | + | 0.349104i | ||||
\(914\) | −13.4721 | + | 23.3344i | −0.445619 | + | 0.771834i | ||||
\(915\) | 0.583592 | + | 1.01081i | 0.0192930 | + | 0.0334164i | ||||
\(916\) | −17.2361 | −0.569496 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −13.6656 | −0.451033 | ||||||||
\(919\) | 11.0557 | + | 19.1491i | 0.364695 | + | 0.631670i | 0.988727 | − | 0.149729i | \(-0.0478400\pi\) |
−0.624032 | + | 0.781399i | \(0.714507\pi\) | |||||||
\(920\) | −2.47214 | + | 4.28187i | −0.0815039 | + | 0.141169i | ||||
\(921\) | 16.1115 | − | 27.9059i | 0.530891 | − | 0.919529i | ||||
\(922\) | 12.3820 | + | 21.4462i | 0.407778 | + | 0.706293i | ||||
\(923\) | 20.9443 | 0.689389 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.1115 | −0.792780 | ||||||||
\(926\) | 15.2361 | + | 26.3896i | 0.500688 | + | 0.867218i | ||||
\(927\) | 11.0000 | − | 19.0526i | 0.361287 | − | 0.625768i | ||||
\(928\) | −2.23607 | + | 3.87298i | −0.0734025 | + | 0.127137i | ||||
\(929\) | 20.1246 | + | 34.8569i | 0.660267 | + | 1.14362i | 0.980545 | + | 0.196293i | \(0.0628903\pi\) |
−0.320278 | + | 0.947324i | \(0.603776\pi\) | |||||||
\(930\) | 3.05573 | 0.100201 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −14.9443 | −0.489516 | ||||||||
\(933\) | 13.2361 | + | 22.9255i | 0.433329 | + | 0.750549i | ||||
\(934\) | −13.5623 | + | 23.4906i | −0.443772 | + | 0.768636i | ||||
\(935\) | 1.52786 | − | 2.64634i | 0.0499665 | − | 0.0865445i | ||||
\(936\) | 2.38197 | + | 4.12569i | 0.0778570 | + | 0.134852i | ||||
\(937\) | 3.05573 | 0.0998263 | 0.0499131 | − | 0.998754i | \(-0.484106\pi\) | ||||
0.0499131 | + | 0.998754i | \(0.484106\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24.1378 | 0.787706 | ||||||||
\(940\) | −1.23607 | − | 2.14093i | −0.0403161 | − | 0.0698295i | ||||
\(941\) | −5.90983 | + | 10.2361i | −0.192655 | + | 0.333688i | −0.946129 | − | 0.323789i | \(-0.895043\pi\) |
0.753474 | + | 0.657477i | \(0.228376\pi\) | |||||||
\(942\) | 7.81966 | − | 13.5440i | 0.254778 | − | 0.441289i | ||||
\(943\) | −4.94427 | − | 8.56373i | −0.161008 | − | 0.278873i | ||||
\(944\) | −2.76393 | −0.0899583 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.4721 | −0.340479 | ||||||||
\(947\) | −8.47214 | − | 14.6742i | −0.275307 | − | 0.476846i | 0.694905 | − | 0.719101i | \(-0.255446\pi\) |
−0.970213 | + | 0.242255i | \(0.922113\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.9443 | − | 36.2765i | 0.679880 | − | 1.17759i | ||||
\(950\) | 12.5623 | + | 21.7586i | 0.407575 | + | 0.705941i | ||||
\(951\) | 38.2492 | 1.24032 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.9443 | 0.743238 | 0.371619 | − | 0.928385i | \(-0.378803\pi\) | ||||
0.371619 | + | 0.928385i | \(0.378803\pi\) | |||||||
\(954\) | 6.23607 | + | 10.8012i | 0.201900 | + | 0.349701i | ||||
\(955\) | 1.52786 | − | 2.64634i | 0.0494405 | − | 0.0856335i | ||||
\(956\) | −10.0000 | + | 17.3205i | −0.323423 | + | 0.560185i | ||||
\(957\) | 2.76393 | + | 4.78727i | 0.0893452 | + | 0.154750i | ||||
\(958\) | −12.3607 | −0.399355 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.52786 | −0.0493116 | ||||||||
\(961\) | 13.5000 | + | 23.3827i | 0.435484 | + | 0.754280i | ||||
\(962\) | −11.2361 | + | 19.4614i | −0.362265 | + | 0.627462i | ||||
\(963\) | 1.81966 | − | 3.15174i | 0.0586377 | − | 0.101564i | ||||
\(964\) | 7.70820 | + | 13.3510i | 0.248265 | + | 0.430007i | ||||
\(965\) | −18.4721 | −0.594639 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45.8885 | 1.47568 | 0.737838 | − | 0.674978i | \(-0.235847\pi\) | ||||
0.737838 | + | 0.674978i | \(0.235847\pi\) | |||||||
\(968\) | −0.500000 | − | 0.866025i | −0.0160706 | − | 0.0278351i | ||||
\(969\) | −11.0557 | + | 19.1491i | −0.355161 | + | 0.615157i | ||||
\(970\) | 7.70820 | − | 13.3510i | 0.247496 | − | 0.428675i | ||||
\(971\) | 25.2705 | + | 43.7698i | 0.810969 | + | 1.40464i | 0.912186 | + | 0.409776i | \(0.134393\pi\) |
−0.101217 | + | 0.994864i | \(0.532274\pi\) | |||||||
\(972\) | −13.5967 | −0.436116 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 16.9443 | 0.542929 | ||||||||
\(975\) | −6.94427 | − | 12.0278i | −0.222395 | − | 0.385199i | ||||
\(976\) | −0.381966 | + | 0.661585i | −0.0122264 | + | 0.0211768i | ||||
\(977\) | 14.4164 | − | 24.9700i | 0.461222 | − | 0.798860i | −0.537800 | − | 0.843072i | \(-0.680745\pi\) |
0.999022 | + | 0.0442127i | \(0.0140779\pi\) | |||||||
\(978\) | −12.0000 | − | 20.7846i | −0.383718 | − | 0.664619i | ||||
\(979\) | −10.0000 | −0.319601 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.7214 | 0.470017 | ||||||||
\(982\) | 8.47214 | + | 14.6742i | 0.270357 | + | 0.468272i | ||||
\(983\) | 7.00000 | − | 12.1244i | 0.223265 | − | 0.386707i | −0.732532 | − | 0.680732i | \(-0.761662\pi\) |
0.955798 | + | 0.294025i | \(0.0949950\pi\) | |||||||
\(984\) | 1.52786 | − | 2.64634i | 0.0487065 | − | 0.0843622i | ||||
\(985\) | −11.1246 | − | 19.2684i | −0.354460 | − | 0.613942i | ||||
\(986\) | −11.0557 | −0.352086 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 23.4164 | 0.744975 | ||||||||
\(989\) | 20.9443 | + | 36.2765i | 0.665989 | + | 1.15353i | ||||
\(990\) | 0.909830 | − | 1.57587i | 0.0289163 | − | 0.0500845i | ||||
\(991\) | 0.180340 | − | 0.312358i | 0.00572869 | − | 0.00992237i | −0.863147 | − | 0.504953i | \(-0.831510\pi\) |
0.868876 | + | 0.495031i | \(0.164843\pi\) | |||||||
\(992\) | 1.00000 | + | 1.73205i | 0.0317500 | + | 0.0549927i | ||||
\(993\) | 20.9443 | 0.664646 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23.4164 | −0.742350 | ||||||||
\(996\) | 7.52786 | + | 13.0386i | 0.238529 | + | 0.413145i | ||||
\(997\) | 12.0902 | − | 20.9408i | 0.382900 | − | 0.663201i | −0.608576 | − | 0.793496i | \(-0.708259\pi\) |
0.991475 | + | 0.130294i | \(0.0415922\pi\) | |||||||
\(998\) | 16.1803 | − | 28.0252i | 0.512180 | − | 0.887121i | ||||
\(999\) | −19.1935 | − | 33.2441i | −0.607255 | − | 1.05180i |
(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 | 1078.2.e.n.67.2 | 4 | ||
7.2 | even | 3 | inner | 1078.2.e.n.177.2 | 4 | ||
7.3 | odd | 6 | 154.2.a.d.1.2 | ✓ | 2 | ||
7.4 | even | 3 | 1078.2.a.w.1.1 | 2 | |||
7.5 | odd | 6 | 1078.2.e.q.177.1 | 4 | |||
7.6 | odd | 2 | 1078.2.e.q.67.1 | 4 | |||
21.11 | odd | 6 | 9702.2.a.cu.1.1 | 2 | |||
21.17 | even | 6 | 1386.2.a.m.1.2 | 2 | |||
28.3 | even | 6 | 1232.2.a.p.1.1 | 2 | |||
28.11 | odd | 6 | 8624.2.a.bf.1.2 | 2 | |||
35.3 | even | 12 | 3850.2.c.q.1849.2 | 4 | |||
35.17 | even | 12 | 3850.2.c.q.1849.3 | 4 | |||
35.24 | odd | 6 | 3850.2.a.bj.1.1 | 2 | |||
56.3 | even | 6 | 4928.2.a.bk.1.2 | 2 | |||
56.45 | odd | 6 | 4928.2.a.bt.1.1 | 2 | |||
77.10 | even | 6 | 1694.2.a.l.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.a.d.1.2 | ✓ | 2 | 7.3 | odd | 6 | ||
1078.2.a.w.1.1 | 2 | 7.4 | even | 3 | |||
1078.2.e.n.67.2 | 4 | 1.1 | even | 1 | trivial | ||
1078.2.e.n.177.2 | 4 | 7.2 | even | 3 | inner | ||
1078.2.e.q.67.1 | 4 | 7.6 | odd | 2 | |||
1078.2.e.q.177.1 | 4 | 7.5 | odd | 6 | |||
1232.2.a.p.1.1 | 2 | 28.3 | even | 6 | |||
1386.2.a.m.1.2 | 2 | 21.17 | even | 6 | |||
1694.2.a.l.1.2 | 2 | 77.10 | even | 6 | |||
3850.2.a.bj.1.1 | 2 | 35.24 | odd | 6 | |||
3850.2.c.q.1849.2 | 4 | 35.3 | even | 12 | |||
3850.2.c.q.1849.3 | 4 | 35.17 | even | 12 | |||
4928.2.a.bk.1.2 | 2 | 56.3 | even | 6 | |||
4928.2.a.bt.1.1 | 2 | 56.45 | odd | 6 | |||
8624.2.a.bf.1.2 | 2 | 28.11 | odd | 6 | |||
9702.2.a.cu.1.1 | 2 | 21.11 | odd | 6 |