Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(109,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 325.6 | ||
Character | \(\chi\) | \(=\) | 432.325 |
Dual form | 432.2.k.c.109.6 |
$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.680919 | − | 1.23950i | −0.481482 | − | 0.876456i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.07270 | + | 1.68799i | −0.536349 | + | 0.843996i | ||||
\(5\) | −2.24693 | − | 2.24693i | −1.00486 | − | 1.00486i | −0.999988 | − | 0.00487156i | \(-0.998449\pi\) |
−0.00487156 | − | 0.999988i | \(-0.501551\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.93534i | 1.48742i | 0.668502 | + | 0.743710i | \(0.266936\pi\) | ||||
−0.668502 | + | 0.743710i | \(0.733064\pi\) | |||||||
\(8\) | 2.82268 | + | 0.180219i | 0.997968 | + | 0.0637170i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.25508 | + | 4.31505i | −0.396893 | + | 1.36454i | ||||
\(11\) | 3.47488 | + | 3.47488i | 1.04771 | + | 1.04771i | 0.998803 | + | 0.0489112i | \(0.0155751\pi\) |
0.0489112 | + | 0.998803i | \(0.484425\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.14540 | − | 4.14540i | 1.14973 | − | 1.14973i | 0.163120 | − | 0.986606i | \(-0.447844\pi\) |
0.986606 | − | 0.163120i | \(-0.0521558\pi\) | |||||||
\(14\) | 4.87784 | − | 2.67965i | 1.30366 | − | 0.716167i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.69864 | − | 3.62141i | −0.424659 | − | 0.905353i | ||||
\(17\) | 0.326940 | 0.0792945 | 0.0396473 | − | 0.999214i | \(-0.487377\pi\) | ||||
0.0396473 | + | 0.999214i | \(0.487377\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.108711 | + | 0.108711i | −0.0249399 | + | 0.0249399i | −0.719467 | − | 0.694527i | \(-0.755614\pi\) |
0.694527 | + | 0.719467i | \(0.255614\pi\) | |||||||
\(20\) | 6.20309 | − | 1.38253i | 1.38705 | − | 0.309142i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.94098 | − | 6.67320i | 0.413819 | − | 1.42273i | ||||
\(23\) | − | 4.30494i | − | 0.897643i | −0.893622 | − | 0.448821i | \(-0.851844\pi\) | ||
0.893622 | − | 0.448821i | \(-0.148156\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.09743i | 1.01949i | ||||||||
\(26\) | −7.96088 | − | 2.31552i | −1.56126 | − | 0.454111i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −6.64283 | − | 4.22144i | −1.25538 | − | 0.797777i | ||||
\(29\) | 2.75677 | − | 2.75677i | 0.511919 | − | 0.511919i | −0.403195 | − | 0.915114i | \(-0.632100\pi\) |
0.915114 | + | 0.403195i | \(0.132100\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.45679 | 0.800464 | 0.400232 | − | 0.916414i | \(-0.368930\pi\) | ||||
0.400232 | + | 0.916414i | \(0.368930\pi\) | |||||||
\(32\) | −3.33209 | + | 4.57134i | −0.589036 | + | 0.808107i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.222619 | − | 0.405240i | −0.0381789 | − | 0.0694981i | ||||
\(35\) | 8.84246 | − | 8.84246i | 1.49465 | − | 1.49465i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.76428 | + | 4.76428i | 0.783242 | + | 0.783242i | 0.980377 | − | 0.197134i | \(-0.0631635\pi\) |
−0.197134 | + | 0.980377i | \(0.563163\pi\) | |||||||
\(38\) | 0.208769 | + | 0.0607231i | 0.0338668 | + | 0.00985059i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.93744 | − | 6.74732i | −0.938791 | − | 1.06684i | ||||
\(41\) | 9.19359i | 1.43580i | 0.696148 | + | 0.717898i | \(0.254896\pi\) | ||||
−0.696148 | + | 0.717898i | \(0.745104\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.45288 | + | 5.45288i | 0.831556 | + | 0.831556i | 0.987730 | − | 0.156173i | \(-0.0499158\pi\) |
−0.156173 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(44\) | −9.59306 | + | 2.13807i | −1.44621 | + | 0.322326i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.33596 | + | 2.93132i | −0.786744 | + | 0.432199i | ||||
\(47\) | 3.67052 | 0.535401 | 0.267700 | − | 0.963502i | \(-0.413736\pi\) | ||||
0.267700 | + | 0.963502i | \(0.413736\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8.48693 | −1.21242 | ||||||||
\(50\) | 6.31824 | − | 3.47094i | 0.893534 | − | 0.490865i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.55064 | + | 11.4442i | 0.353710 | + | 1.58702i | ||||
\(53\) | −2.59909 | − | 2.59909i | −0.357012 | − | 0.357012i | 0.505698 | − | 0.862710i | \(-0.331235\pi\) |
−0.862710 | + | 0.505698i | \(0.831235\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 15.6156i | − | 2.10561i | ||||||
\(56\) | −0.709223 | + | 11.1082i | −0.0947739 | + | 1.48440i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.29414 | − | 1.53987i | −0.695154 | − | 0.202194i | ||||
\(59\) | 0.326100 | + | 0.326100i | 0.0424546 | + | 0.0424546i | 0.728015 | − | 0.685561i | \(-0.240443\pi\) |
−0.685561 | + | 0.728015i | \(0.740443\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.26951 | − | 8.26951i | 1.05880 | − | 1.05880i | 0.0606422 | − | 0.998160i | \(-0.480685\pi\) |
0.998160 | − | 0.0606422i | \(-0.0193149\pi\) | |||||||
\(62\) | −3.03472 | − | 5.52418i | −0.385409 | − | 0.701571i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.93504 | + | 1.01740i | 0.991880 | + | 0.127175i | ||||
\(65\) | −18.6289 | −2.31063 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.31646 | − | 4.31646i | 0.527340 | − | 0.527340i | −0.392438 | − | 0.919778i | \(-0.628368\pi\) |
0.919778 | + | 0.392438i | \(0.128368\pi\) | |||||||
\(68\) | −0.350708 | + | 0.551872i | −0.0425296 | + | 0.0669243i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −16.9812 | − | 4.93919i | −2.02964 | − | 0.590346i | ||||
\(71\) | 6.88192i | 0.816733i | 0.912818 | + | 0.408367i | \(0.133901\pi\) | ||||
−0.912818 | + | 0.408367i | \(0.866099\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.15046i | 0.368734i | 0.982857 | + | 0.184367i | \(0.0590235\pi\) | ||||
−0.982857 | + | 0.184367i | \(0.940977\pi\) | |||||||
\(74\) | 2.66121 | − | 9.14939i | 0.309360 | − | 1.06359i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.0668889 | − | 0.300116i | −0.00767268 | − | 0.0344257i | ||||
\(77\) | −13.6748 | + | 13.6748i | −1.55839 | + | 1.55839i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.2305 | −1.15102 | −0.575512 | − | 0.817794i | \(-0.695197\pi\) | ||||
−0.575512 | + | 0.817794i | \(0.695197\pi\) | |||||||
\(80\) | −4.32036 | + | 11.9538i | −0.483030 | + | 1.33648i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 11.3954 | − | 6.26009i | 1.25841 | − | 0.691311i | ||||
\(83\) | −1.07814 | + | 1.07814i | −0.118341 | + | 0.118341i | −0.763797 | − | 0.645456i | \(-0.776667\pi\) |
0.645456 | + | 0.763797i | \(0.276667\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.734612 | − | 0.734612i | −0.0796799 | − | 0.0796799i | ||||
\(86\) | 3.04585 | − | 10.4718i | 0.328443 | − | 1.12920i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 9.18222 | + | 10.4347i | 0.978828 | + | 1.11234i | ||||
\(89\) | − | 5.77030i | − | 0.611650i | −0.952088 | − | 0.305825i | \(-0.901068\pi\) | ||
0.952088 | − | 0.305825i | \(-0.0989323\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.3136 | + | 16.3136i | 1.71013 | + | 1.71013i | ||||
\(92\) | 7.26671 | + | 4.61790i | 0.757607 | + | 0.481450i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.49933 | − | 4.54960i | −0.257786 | − | 0.469255i | ||||
\(95\) | 0.488531 | 0.0501222 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.82365 | 0.286698 | 0.143349 | − | 0.989672i | \(-0.454213\pi\) | ||||
0.143349 | + | 0.989672i | \(0.454213\pi\) | |||||||
\(98\) | 5.77891 | + | 10.5195i | 0.583758 | + | 1.06263i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.60442 | − | 5.46801i | −0.860442 | − | 0.546801i | ||||
\(101\) | 3.00490 | + | 3.00490i | 0.298998 | + | 0.298998i | 0.840621 | − | 0.541623i | \(-0.182190\pi\) |
−0.541623 | + | 0.840621i | \(0.682190\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 7.42721i | − | 0.731825i | −0.930649 | − | 0.365912i | \(-0.880757\pi\) | ||
0.930649 | − | 0.365912i | \(-0.119243\pi\) | |||||||
\(104\) | 12.4482 | − | 10.9540i | 1.22065 | − | 1.07413i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.45179 | + | 4.99133i | −0.141010 | + | 0.484801i | ||||
\(107\) | 3.48970 | + | 3.48970i | 0.337362 | + | 0.337362i | 0.855374 | − | 0.518011i | \(-0.173328\pi\) |
−0.518011 | + | 0.855374i | \(0.673328\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.9987 | + | 11.9987i | −1.14927 | + | 1.14927i | −0.162571 | + | 0.986697i | \(0.551979\pi\) |
−0.986697 | + | 0.162571i | \(0.948021\pi\) | |||||||
\(110\) | −19.3555 | + | 10.6330i | −1.84548 | + | 1.01382i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 14.2515 | − | 6.68472i | 1.34664 | − | 0.631646i | ||||
\(113\) | −2.81801 | −0.265096 | −0.132548 | − | 0.991177i | \(-0.542316\pi\) | ||||
−0.132548 | + | 0.991177i | \(0.542316\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.67292 | + | 9.67292i | −0.902005 | + | 0.902005i | ||||
\(116\) | 1.69622 | + | 7.61058i | 0.157490 | + | 0.706625i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.182152 | − | 0.626248i | 0.0167684 | − | 0.0576508i | ||||
\(119\) | 1.28662i | 0.117944i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.1495i | 1.19541i | ||||||||
\(122\) | −15.8809 | − | 4.61915i | −1.43779 | − | 0.418198i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.78080 | + | 7.52303i | −0.429328 | + | 0.675588i | ||||
\(125\) | 0.218919 | − | 0.218919i | 0.0195807 | − | 0.0195807i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.8717 | −1.05344 | −0.526722 | − | 0.850038i | \(-0.676579\pi\) | ||||
−0.526722 | + | 0.850038i | \(0.676579\pi\) | |||||||
\(128\) | −4.14206 | − | 10.5282i | −0.366110 | − | 0.930572i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 12.6848 | + | 23.0904i | 1.11253 | + | 2.02516i | ||||
\(131\) | −8.54865 | + | 8.54865i | −0.746899 | + | 0.746899i | −0.973896 | − | 0.226996i | \(-0.927109\pi\) |
0.226996 | + | 0.973896i | \(0.427109\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.427813 | − | 0.427813i | −0.0370961 | − | 0.0370961i | ||||
\(134\) | −8.28940 | − | 2.41107i | −0.716095 | − | 0.208285i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.922846 | + | 0.0589207i | 0.0791334 | + | 0.00505241i | ||||
\(137\) | − | 4.96667i | − | 0.424332i | −0.977234 | − | 0.212166i | \(-0.931948\pi\) | ||
0.977234 | − | 0.212166i | \(-0.0680517\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.10134 | − | 2.10134i | −0.178234 | − | 0.178234i | 0.612352 | − | 0.790585i | \(-0.290224\pi\) |
−0.790585 | + | 0.612352i | \(0.790224\pi\) | |||||||
\(140\) | 5.44071 | + | 24.4113i | 0.459824 | + | 2.06313i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.53010 | − | 4.68603i | 0.715830 | − | 0.393243i | ||||
\(143\) | 28.8095 | 2.40917 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.3885 | −1.02881 | ||||||||
\(146\) | 3.90499 | − | 2.14521i | 0.323179 | − | 0.177539i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −13.1527 | + | 2.93143i | −1.08114 | + | 0.240962i | ||||
\(149\) | −7.78968 | − | 7.78968i | −0.638155 | − | 0.638155i | 0.311945 | − | 0.950100i | \(-0.399020\pi\) |
−0.950100 | + | 0.311945i | \(0.899020\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2.99839i | − | 0.244005i | −0.992530 | − | 0.122003i | \(-0.961068\pi\) | ||
0.992530 | − | 0.122003i | \(-0.0389316\pi\) | |||||||
\(152\) | −0.326447 | + | 0.287263i | −0.0264783 | + | 0.0233001i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 26.2613 | + | 7.63844i | 2.11620 | + | 0.615523i | ||||
\(155\) | −10.0141 | − | 10.0141i | −0.804354 | − | 0.804354i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.5844 | − | 13.5844i | 1.08415 | − | 1.08415i | 0.0880321 | − | 0.996118i | \(-0.471942\pi\) |
0.996118 | − | 0.0880321i | \(-0.0280578\pi\) | |||||||
\(158\) | 6.96616 | + | 12.6807i | 0.554198 | + | 1.00882i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 17.7585 | − | 2.78451i | 1.40393 | − | 0.220135i | ||||
\(161\) | 16.9414 | 1.33517 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.38524 | − | 7.38524i | 0.578457 | − | 0.578457i | −0.356021 | − | 0.934478i | \(-0.615867\pi\) |
0.934478 | + | 0.356021i | \(0.115867\pi\) | |||||||
\(164\) | −15.5187 | − | 9.86195i | −1.21181 | − | 0.770089i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.07047 | + | 0.602223i | 0.160700 | + | 0.0467416i | ||||
\(167\) | − | 4.04079i | − | 0.312686i | −0.987703 | − | 0.156343i | \(-0.950030\pi\) | ||
0.987703 | − | 0.156343i | \(-0.0499705\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 21.3686i | − | 1.64374i | ||||||
\(170\) | −0.410337 | + | 1.41076i | −0.0314714 | + | 0.108200i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −15.0537 | + | 3.35512i | −1.14784 | + | 0.255826i | ||||
\(173\) | −6.71115 | + | 6.71115i | −0.510239 | + | 0.510239i | −0.914600 | − | 0.404360i | \(-0.867494\pi\) |
0.404360 | + | 0.914600i | \(0.367494\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −20.0601 | −1.51640 | ||||||||
\(176\) | 6.68141 | − | 18.4865i | 0.503630 | − | 1.39347i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.15226 | + | 3.92910i | −0.536084 | + | 0.294499i | ||||
\(179\) | −3.48970 | + | 3.48970i | −0.260833 | + | 0.260833i | −0.825392 | − | 0.564560i | \(-0.809046\pi\) |
0.564560 | + | 0.825392i | \(0.309046\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.4293 | − | 17.4293i | −1.29551 | − | 1.29551i | −0.931328 | − | 0.364181i | \(-0.881349\pi\) |
−0.364181 | − | 0.931328i | \(-0.618651\pi\) | |||||||
\(182\) | 9.11237 | − | 31.3288i | 0.675454 | − | 2.32225i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.775832 | − | 12.1515i | 0.0571951 | − | 0.895819i | ||||
\(185\) | − | 21.4100i | − | 1.57410i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.13607 | + | 1.13607i | 0.0830780 | + | 0.0830780i | ||||
\(188\) | −3.93736 | + | 6.19581i | −0.287162 | + | 0.451876i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.332650 | − | 0.605532i | −0.0241330 | − | 0.0439299i | ||||
\(191\) | −3.50685 | −0.253747 | −0.126873 | − | 0.991919i | \(-0.540494\pi\) | ||||
−0.126873 | + | 0.991919i | \(0.540494\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.4842 | −0.754666 | −0.377333 | − | 0.926078i | \(-0.623159\pi\) | ||||
−0.377333 | + | 0.926078i | \(0.623159\pi\) | |||||||
\(194\) | −1.92268 | − | 3.49990i | −0.138040 | − | 0.251278i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.10391 | − | 14.3259i | 0.650280 | − | 1.02328i | ||||
\(197\) | 5.28098 | + | 5.28098i | 0.376255 | + | 0.376255i | 0.869749 | − | 0.493494i | \(-0.164281\pi\) |
−0.493494 | + | 0.869749i | \(0.664281\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 9.93981i | − | 0.704614i | −0.935884 | − | 0.352307i | \(-0.885397\pi\) | ||
0.935884 | − | 0.352307i | \(-0.114603\pi\) | |||||||
\(200\) | −0.918653 | + | 14.3884i | −0.0649586 | + | 1.01741i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.67846 | − | 5.77065i | 0.118096 | − | 0.406021i | ||||
\(203\) | 10.8488 | + | 10.8488i | 0.761438 | + | 0.761438i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20.6574 | − | 20.6574i | 1.44277 | − | 1.44277i | ||||
\(206\) | −9.20600 | + | 5.05733i | −0.641412 | + | 0.352361i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −22.0537 | − | 7.97068i | −1.52915 | − | 0.552667i | ||||
\(209\) | −0.755511 | −0.0522598 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.9210 | + | 10.9210i | −0.751830 | + | 0.751830i | −0.974821 | − | 0.222991i | \(-0.928418\pi\) |
0.222991 | + | 0.974821i | \(0.428418\pi\) | |||||||
\(212\) | 7.17528 | − | 1.59920i | 0.492800 | − | 0.109834i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.94927 | − | 6.70167i | 0.133249 | − | 0.458117i | ||||
\(215\) | − | 24.5045i | − | 1.67120i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.5390i | 1.19063i | ||||||||
\(218\) | 23.0425 | + | 6.70220i | 1.56063 | + | 0.453930i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 26.3591 | + | 16.7509i | 1.77713 | + | 1.12934i | ||||
\(221\) | 1.35529 | − | 1.35529i | 0.0911670 | − | 0.0911670i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.89438 | −0.595612 | −0.297806 | − | 0.954626i | \(-0.596255\pi\) | ||||
−0.297806 | + | 0.954626i | \(0.596255\pi\) | |||||||
\(224\) | −17.9898 | − | 13.1129i | −1.20199 | − | 0.876144i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.91884 | + | 3.49291i | 0.127639 | + | 0.232345i | ||||
\(227\) | 19.5902 | − | 19.5902i | 1.30025 | − | 1.30025i | 0.372028 | − | 0.928222i | \(-0.378663\pi\) |
0.928222 | − | 0.372028i | \(-0.121337\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.88839 | + | 8.88839i | 0.587361 | + | 0.587361i | 0.936916 | − | 0.349555i | \(-0.113667\pi\) |
−0.349555 | + | 0.936916i | \(0.613667\pi\) | |||||||
\(230\) | 18.5760 | + | 5.40307i | 1.22487 | + | 0.356268i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.27829 | − | 7.28465i | 0.543496 | − | 0.478261i | ||||
\(233\) | 13.5181i | 0.885602i | 0.896620 | + | 0.442801i | \(0.146015\pi\) | ||||
−0.896620 | + | 0.442801i | \(0.853985\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.24742 | − | 8.24742i | −0.538003 | − | 0.538003i | ||||
\(236\) | −0.900262 | + | 0.200647i | −0.0586021 | + | 0.0130610i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.59476 | − | 0.876084i | 0.103373 | − | 0.0567881i | ||||
\(239\) | −5.79042 | −0.374551 | −0.187276 | − | 0.982307i | \(-0.559966\pi\) | ||||
−0.187276 | + | 0.982307i | \(0.559966\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.3050 | −1.82329 | −0.911643 | − | 0.410984i | \(-0.865185\pi\) | ||||
−0.911643 | + | 0.410984i | \(0.865185\pi\) | |||||||
\(242\) | 16.2988 | − | 8.95376i | 1.04772 | − | 0.575569i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.08818 | + | 22.8295i | 0.325737 | + | 1.46151i | ||||
\(245\) | 19.0696 | + | 19.0696i | 1.21831 | + | 1.21831i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.901296i | 0.0573481i | ||||||||
\(248\) | 12.5801 | + | 0.803198i | 0.798837 | + | 0.0510031i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.420415 | − | 0.122283i | −0.0265894 | − | 0.00773385i | ||||
\(251\) | −12.6583 | − | 12.6583i | −0.798982 | − | 0.798982i | 0.183953 | − | 0.982935i | \(-0.441111\pi\) |
−0.982935 | + | 0.183953i | \(0.941111\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.9591 | − | 14.9591i | 0.940473 | − | 0.940473i | ||||
\(254\) | 8.08368 | + | 14.7149i | 0.507215 | + | 0.923297i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.2293 | + | 12.3029i | −0.639329 | + | 0.768933i | ||||
\(257\) | 24.8277 | 1.54871 | 0.774356 | − | 0.632750i | \(-0.218074\pi\) | ||||
0.774356 | + | 0.632750i | \(0.218074\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −18.7491 | + | 18.7491i | −1.16501 | + | 1.16501i | ||||
\(260\) | 19.9832 | − | 31.4454i | 1.23930 | − | 1.95016i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 16.4170 | + | 4.77508i | 1.01424 | + | 0.295005i | ||||
\(263\) | 28.3171i | 1.74610i | 0.487626 | + | 0.873052i | \(0.337863\pi\) | ||||
−0.487626 | + | 0.873052i | \(0.662137\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.6800i | 0.717495i | ||||||||
\(266\) | −0.238966 | + | 0.821579i | −0.0146520 | + | 0.0503742i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.65589 | + | 11.9164i | 0.162235 | + | 0.727911i | ||||
\(269\) | 16.4900 | − | 16.4900i | 1.00541 | − | 1.00541i | 0.00542517 | − | 0.999985i | \(-0.498273\pi\) |
0.999985 | − | 0.00542517i | \(-0.00172689\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.2088 | 0.923867 | 0.461933 | − | 0.886915i | \(-0.347156\pi\) | ||||
0.461933 | + | 0.886915i | \(0.347156\pi\) | |||||||
\(272\) | −0.555352 | − | 1.18398i | −0.0336731 | − | 0.0717896i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.15617 | + | 3.38190i | −0.371908 | + | 0.204308i | ||||
\(275\) | −17.7129 | + | 17.7129i | −1.06813 | + | 1.06813i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.25572 | + | 3.25572i | 0.195617 | + | 0.195617i | 0.798118 | − | 0.602501i | \(-0.205829\pi\) |
−0.602501 | + | 0.798118i | \(0.705829\pi\) | |||||||
\(278\) | −1.17376 | + | 4.03545i | −0.0703975 | + | 0.242030i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 26.5530 | − | 23.3659i | 1.58685 | − | 1.39638i | ||||
\(281\) | 13.1484i | 0.784367i | 0.919887 | + | 0.392183i | \(0.128280\pi\) | ||||
−0.919887 | + | 0.392183i | \(0.871720\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.18485 | + | 9.18485i | 0.545983 | + | 0.545983i | 0.925276 | − | 0.379294i | \(-0.123833\pi\) |
−0.379294 | + | 0.925276i | \(0.623833\pi\) | |||||||
\(284\) | −11.6166 | − | 7.38222i | −0.689320 | − | 0.438054i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −19.6169 | − | 35.7092i | −1.15997 | − | 2.11153i | ||||
\(287\) | −36.1799 | −2.13563 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8931 | −0.993712 | ||||||||
\(290\) | 8.43560 | + | 15.3556i | 0.495355 | + | 0.901709i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.31796 | − | 3.37950i | −0.311210 | − | 0.197770i | ||||
\(293\) | −14.6906 | − | 14.6906i | −0.858234 | − | 0.858234i | 0.132896 | − | 0.991130i | \(-0.457572\pi\) |
−0.991130 | + | 0.132896i | \(0.957572\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 1.46545i | − | 0.0853219i | ||||||
\(296\) | 12.5894 | + | 14.3066i | 0.731745 | + | 0.831557i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.35113 | + | 14.9594i | −0.252054 | + | 0.866576i | ||||
\(299\) | −17.8457 | − | 17.8457i | −1.03204 | − | 1.03204i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.4590 | + | 21.4590i | −1.23687 | + | 1.23687i | ||||
\(302\) | −3.71649 | + | 2.04166i | −0.213860 | + | 0.117484i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.578345 | + | 0.209026i | 0.0331704 | + | 0.0119885i | ||||
\(305\) | −37.1621 | −2.12789 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.7587 | − | 23.7587i | 1.35598 | − | 1.35598i | 0.477173 | − | 0.878809i | \(-0.341662\pi\) |
0.878809 | − | 0.477173i | \(-0.158338\pi\) | |||||||
\(308\) | −8.41404 | − | 37.7520i | −0.479434 | − | 2.15112i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.59365 | + | 19.2313i | −0.317698 | + | 1.09226i | ||||
\(311\) | − | 8.59248i | − | 0.487235i | −0.969871 | − | 0.243617i | \(-0.921666\pi\) | ||
0.969871 | − | 0.243617i | \(-0.0783341\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.35592i | 0.472304i | 0.971716 | + | 0.236152i | \(0.0758864\pi\) | ||||
−0.971716 | + | 0.236152i | \(0.924114\pi\) | |||||||
\(314\) | −26.0876 | − | 7.58790i | −1.47221 | − | 0.428210i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.9743 | − | 17.2690i | 0.617350 | − | 0.971459i | ||||
\(317\) | 23.6909 | − | 23.6909i | 1.33061 | − | 1.33061i | 0.425790 | − | 0.904822i | \(-0.359996\pi\) |
0.904822 | − | 0.425790i | \(-0.140004\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.1588 | 1.07269 | ||||||||
\(320\) | −15.5435 | − | 20.1156i | −0.868907 | − | 1.12449i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −11.5357 | − | 20.9988i | −0.642862 | − | 1.17022i | ||||
\(323\) | −0.0355418 | + | 0.0355418i | −0.00197760 | + | 0.00197760i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.1309 | + | 21.1309i | 1.17213 | + | 1.17213i | ||||
\(326\) | −14.1827 | − | 4.12522i | −0.785508 | − | 0.228475i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.65686 | + | 25.9506i | −0.0914846 | + | 1.43288i | ||||
\(329\) | 14.4448i | 0.796366i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.37674 | + | 4.37674i | 0.240567 | + | 0.240567i | 0.817085 | − | 0.576518i | \(-0.195589\pi\) |
−0.576518 | + | 0.817085i | \(0.695589\pi\) | |||||||
\(332\) | −0.663372 | − | 2.97641i | −0.0364073 | − | 0.163352i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.00854 | + | 2.75145i | −0.274055 | + | 0.150553i | ||||
\(335\) | −19.3976 | −1.05981 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.946967 | −0.0515846 | −0.0257923 | − | 0.999667i | \(-0.508211\pi\) | ||||
−0.0257923 | + | 0.999667i | \(0.508211\pi\) | |||||||
\(338\) | −26.4863 | + | 14.5503i | −1.44067 | + | 0.791432i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.02804 | − | 0.452002i | 0.109986 | − | 0.0245133i | ||||
\(341\) | 15.4868 | + | 15.4868i | 0.838657 | + | 0.838657i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 5.85157i | − | 0.315955i | ||||||
\(344\) | 14.4090 | + | 16.3744i | 0.776883 | + | 0.882851i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.8882 | + | 3.74869i | 0.692873 | + | 0.201531i | ||||
\(347\) | 17.3176 | + | 17.3176i | 0.929656 | + | 0.929656i | 0.997683 | − | 0.0680274i | \(-0.0216705\pi\) |
−0.0680274 | + | 0.997683i | \(0.521671\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.862655 | + | 0.862655i | −0.0461769 | + | 0.0461769i | −0.729818 | − | 0.683641i | \(-0.760395\pi\) |
0.683641 | + | 0.729818i | \(0.260395\pi\) | |||||||
\(350\) | 13.6593 | + | 24.8645i | 0.730122 | + | 1.32906i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −27.4634 | + | 4.30624i | −1.46381 | + | 0.229523i | ||||
\(353\) | 19.2982 | 1.02714 | 0.513570 | − | 0.858048i | \(-0.328323\pi\) | ||||
0.513570 | + | 0.858048i | \(0.328323\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.4632 | − | 15.4632i | 0.820702 | − | 0.820702i | ||||
\(356\) | 9.74021 | + | 6.18979i | 0.516230 | + | 0.328058i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.70167 | + | 1.94927i | 0.354194 | + | 0.103022i | ||||
\(359\) | 23.4266i | 1.23641i | 0.786018 | + | 0.618203i | \(0.212139\pi\) | ||||
−0.786018 | + | 0.618203i | \(0.787861\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.9764i | 0.998756i | ||||||||
\(362\) | −9.73559 | + | 33.4715i | −0.511691 | + | 1.75922i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −45.0367 | + | 10.0376i | −2.36056 | + | 0.526115i | ||||
\(365\) | 7.07889 | − | 7.07889i | 0.370526 | − | 0.370526i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.53294 | −0.0800186 | −0.0400093 | − | 0.999199i | \(-0.512739\pi\) | ||||
−0.0400093 | + | 0.999199i | \(0.512739\pi\) | |||||||
\(368\) | −15.5900 | + | 7.31253i | −0.812684 | + | 0.381192i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −26.5376 | + | 14.5785i | −1.37963 | + | 0.757900i | ||||
\(371\) | 10.2283 | − | 10.2283i | 0.531027 | − | 0.531027i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.7693 | − | 14.7693i | −0.764727 | − | 0.764727i | 0.212446 | − | 0.977173i | \(-0.431857\pi\) |
−0.977173 | + | 0.212446i | \(0.931857\pi\) | |||||||
\(374\) | 0.634585 | − | 2.18173i | 0.0328136 | − | 0.112815i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.3607 | + | 0.661497i | 0.534313 | + | 0.0341141i | ||||
\(377\) | − | 22.8558i | − | 1.17713i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.8578 | − | 18.8578i | −0.968659 | − | 0.968659i | 0.0308646 | − | 0.999524i | \(-0.490174\pi\) |
−0.999524 | + | 0.0308646i | \(0.990174\pi\) | |||||||
\(380\) | −0.524046 | + | 0.824636i | −0.0268830 | + | 0.0423029i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.38788 | + | 4.34673i | 0.122175 | + | 0.222398i | ||||
\(383\) | 0.241783 | 0.0123546 | 0.00617728 | − | 0.999981i | \(-0.498034\pi\) | ||||
0.00617728 | + | 0.999981i | \(0.498034\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 61.4529 | 3.13193 | ||||||||
\(386\) | 7.13886 | + | 12.9951i | 0.363359 | + | 0.661431i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.02892 | + | 4.76629i | −0.153770 | + | 0.241972i | ||||
\(389\) | −22.1081 | − | 22.1081i | −1.12093 | − | 1.12093i | −0.991602 | − | 0.129325i | \(-0.958719\pi\) |
−0.129325 | − | 0.991602i | \(-0.541281\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1.40746i | − | 0.0711781i | ||||||
\(392\) | −23.9559 | − | 1.52950i | −1.20995 | − | 0.0772516i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.94983 | − | 10.1417i | 0.148610 | − | 0.510930i | ||||
\(395\) | 22.9873 | + | 22.9873i | 1.15662 | + | 1.15662i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.22027 | + | 7.22027i | −0.362375 | + | 0.362375i | −0.864687 | − | 0.502312i | \(-0.832483\pi\) |
0.502312 | + | 0.864687i | \(0.332483\pi\) | |||||||
\(398\) | −12.3203 | + | 6.76820i | −0.617563 | + | 0.339259i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 18.4599 | − | 8.65868i | 0.922995 | − | 0.432934i | ||||
\(401\) | 35.9448 | 1.79500 | 0.897499 | − | 0.441017i | \(-0.145382\pi\) | ||||
0.897499 | + | 0.441017i | \(0.145382\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.4752 | − | 18.4752i | 0.920314 | − | 0.920314i | ||||
\(404\) | −8.29559 | + | 1.84889i | −0.412721 | + | 0.0919859i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.05990 | − | 20.8342i | 0.300748 | − | 1.03399i | ||||
\(407\) | 33.1105i | 1.64123i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 15.5816i | − | 0.770460i | −0.922821 | − | 0.385230i | \(-0.874122\pi\) | ||
0.922821 | − | 0.385230i | \(-0.125878\pi\) | |||||||
\(410\) | −39.6707 | − | 11.5387i | −1.95920 | − | 0.569857i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 12.5371 | + | 7.96716i | 0.617657 | + | 0.392514i | ||||
\(413\) | −1.28332 | + | 1.28332i | −0.0631479 | + | 0.0631479i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.84501 | 0.237832 | ||||||||
\(416\) | 5.13718 | + | 32.7629i | 0.251871 | + | 1.60633i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.514442 | + | 0.936452i | 0.0251622 | + | 0.0458034i | ||||
\(419\) | −17.7897 | + | 17.7897i | −0.869084 | + | 0.869084i | −0.992371 | − | 0.123287i | \(-0.960656\pi\) |
0.123287 | + | 0.992371i | \(0.460656\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.1522 | − | 17.1522i | −0.835945 | − | 0.835945i | 0.152377 | − | 0.988322i | \(-0.451307\pi\) |
−0.988322 | + | 0.152377i | \(0.951307\pi\) | |||||||
\(422\) | 20.9728 | + | 6.10019i | 1.02094 | + | 0.296953i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.86799 | − | 7.80480i | −0.333539 | − | 0.379035i | ||||
\(425\) | 1.66655i | 0.0808397i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 32.5433 | + | 32.5433i | 1.57488 | + | 1.57488i | ||||
\(428\) | −9.63399 | + | 2.14719i | −0.465676 | + | 0.103788i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −30.3733 | + | 16.6856i | −1.46473 | + | 0.804651i | ||||
\(431\) | −36.1086 | −1.73929 | −0.869645 | − | 0.493677i | \(-0.835653\pi\) | ||||
−0.869645 | + | 0.493677i | \(0.835653\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.7206 | 0.659372 | 0.329686 | − | 0.944091i | \(-0.393057\pi\) | ||||
0.329686 | + | 0.944091i | \(0.393057\pi\) | |||||||
\(434\) | 21.7395 | − | 11.9426i | 1.04353 | − | 0.573265i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.38273 | − | 33.1247i | −0.353569 | − | 1.58639i | ||||
\(437\) | 0.467993 | + | 0.467993i | 0.0223871 | + | 0.0223871i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.1895i | 1.34541i | 0.739909 | + | 0.672707i | \(0.234868\pi\) | ||||
−0.739909 | + | 0.672707i | \(0.765132\pi\) | |||||||
\(440\) | 2.81423 | − | 44.0779i | 0.134163 | − | 2.10133i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.60273 | − | 0.757036i | −0.123799 | − | 0.0360085i | ||||
\(443\) | 1.74454 | + | 1.74454i | 0.0828854 | + | 0.0828854i | 0.747334 | − | 0.664449i | \(-0.231334\pi\) |
−0.664449 | + | 0.747334i | \(0.731334\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.9655 | + | 12.9655i | −0.614623 | + | 0.614623i | ||||
\(446\) | 6.05635 | + | 11.0245i | 0.286777 | + | 0.522027i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.00382 | + | 31.2271i | −0.189163 | + | 1.47534i | ||||
\(449\) | 1.12449 | 0.0530679 | 0.0265339 | − | 0.999648i | \(-0.491553\pi\) | ||||
0.0265339 | + | 0.999648i | \(0.491553\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −31.9466 | + | 31.9466i | −1.50431 | + | 1.50431i | ||||
\(452\) | 3.02287 | − | 4.75678i | 0.142184 | − | 0.223740i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −37.6214 | − | 10.9426i | −1.76566 | − | 0.513564i | ||||
\(455\) | − | 73.3110i | − | 3.43687i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 37.2983i | − | 1.74474i | −0.488843 | − | 0.872372i | \(-0.662581\pi\) | ||
0.488843 | − | 0.872372i | \(-0.337419\pi\) | |||||||
\(458\) | 4.96484 | − | 17.0694i | 0.231992 | − | 0.797600i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5.95169 | − | 26.7040i | −0.277499 | − | 1.24508i | ||||
\(461\) | −3.09234 | + | 3.09234i | −0.144025 | + | 0.144025i | −0.775443 | − | 0.631418i | \(-0.782473\pi\) |
0.631418 | + | 0.775443i | \(0.282473\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.58611 | −0.213134 | −0.106567 | − | 0.994305i | \(-0.533986\pi\) | ||||
−0.106567 | + | 0.994305i | \(0.533986\pi\) | |||||||
\(464\) | −14.6661 | − | 5.30065i | −0.680858 | − | 0.246076i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 16.7557 | − | 9.20476i | 0.776191 | − | 0.426402i | ||||
\(467\) | −24.4064 | + | 24.4064i | −1.12939 | + | 1.12939i | −0.139116 | + | 0.990276i | \(0.544426\pi\) |
−0.990276 | + | 0.139116i | \(0.955574\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.9868 | + | 16.9868i | 0.784376 | + | 0.784376i | ||||
\(470\) | −4.60682 | + | 15.8385i | −0.212497 | + | 0.730574i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.861707 | + | 0.979246i | 0.0396633 | + | 0.0450734i | ||||
\(473\) | 37.8962i | 1.74247i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.554144 | − | 0.554144i | −0.0254259 | − | 0.0254259i | ||||
\(476\) | −2.17180 | − | 1.38016i | −0.0995445 | − | 0.0632593i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.94281 | + | 7.17720i | 0.180340 | + | 0.328277i | ||||
\(479\) | −1.12295 | −0.0513089 | −0.0256545 | − | 0.999671i | \(-0.508167\pi\) | ||||
−0.0256545 | + | 0.999671i | \(0.508167\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 39.4996 | 1.80103 | ||||||||
\(482\) | 19.2734 | + | 35.0839i | 0.877880 | + | 1.59803i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −22.1963 | − | 14.1055i | −1.00892 | − | 0.641157i | ||||
\(485\) | −6.34455 | − | 6.34455i | −0.288091 | − | 0.288091i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.5301i | 0.884991i | 0.896771 | + | 0.442496i | \(0.145907\pi\) | ||||
−0.896771 | + | 0.442496i | \(0.854093\pi\) | |||||||
\(488\) | 24.8325 | − | 21.8518i | 1.12411 | − | 0.989187i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 10.6518 | − | 36.6215i | 0.481200 | − | 1.65439i | ||||
\(491\) | −22.6135 | − | 22.6135i | −1.02053 | − | 1.02053i | −0.999785 | − | 0.0207472i | \(-0.993395\pi\) |
−0.0207472 | − | 0.999785i | \(-0.506605\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.901296 | − | 0.901296i | 0.0405924 | − | 0.0405924i | ||||
\(494\) | 1.11715 | − | 0.613710i | 0.0502631 | − | 0.0276121i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.57047 | − | 16.1399i | −0.339924 | − | 0.724703i | ||||
\(497\) | −27.0827 | −1.21483 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.4100 | + | 12.4100i | −0.555547 | + | 0.555547i | −0.928036 | − | 0.372489i | \(-0.878504\pi\) |
0.372489 | + | 0.928036i | \(0.378504\pi\) | |||||||
\(500\) | 0.134699 | + | 0.604368i | 0.00602394 | + | 0.0270281i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −7.07061 | + | 24.3091i | −0.315577 | + | 1.08497i | ||||
\(503\) | 11.7678i | 0.524698i | 0.964973 | + | 0.262349i | \(0.0844972\pi\) | ||||
−0.964973 | + | 0.262349i | \(0.915503\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 13.5036i | − | 0.600903i | ||||||
\(506\) | −28.7277 | − | 8.35582i | −1.27710 | − | 0.371462i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 12.7348 | − | 20.0394i | 0.565014 | − | 0.889103i | ||||
\(509\) | −15.3964 | + | 15.3964i | −0.682434 | + | 0.682434i | −0.960548 | − | 0.278114i | \(-0.910291\pi\) |
0.278114 | + | 0.960548i | \(0.410291\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.3982 | −0.548462 | ||||||||
\(512\) | 22.2147 | + | 4.30184i | 0.981762 | + | 0.190116i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −16.9057 | − | 30.7739i | −0.745678 | − | 1.35738i | ||||
\(515\) | −16.6885 | + | 16.6885i | −0.735381 | + | 0.735381i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.7546 | + | 12.7546i | 0.560947 | + | 0.560947i | ||||
\(518\) | 36.0060 | + | 10.4728i | 1.58201 | + | 0.460148i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −52.5833 | − | 3.35727i | −2.30593 | − | 0.147226i | ||||
\(521\) | 11.8344i | 0.518474i | 0.965814 | + | 0.259237i | \(0.0834711\pi\) | ||||
−0.965814 | + | 0.259237i | \(0.916529\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.49118 | − | 1.49118i | −0.0652049 | − | 0.0652049i | 0.673752 | − | 0.738957i | \(-0.264681\pi\) |
−0.738957 | + | 0.673752i | \(0.764681\pi\) | |||||||
\(524\) | −5.25993 | − | 23.6002i | −0.229781 | − | 1.03098i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 35.0989 | − | 19.2816i | 1.53038 | − | 0.840719i | ||||
\(527\) | 1.45710 | 0.0634724 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.46747 | 0.194238 | ||||||||
\(530\) | 14.4773 | − | 7.95311i | 0.628852 | − | 0.345461i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.18106 | − | 0.263231i | 0.0512054 | − | 0.0114125i | ||||
\(533\) | 38.1111 | + | 38.1111i | 1.65077 | + | 1.65077i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 15.6823i | − | 0.678003i | ||||||
\(536\) | 12.9619 | − | 11.4061i | 0.559869 | − | 0.492668i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −31.6676 | − | 9.21090i | −1.36529 | − | 0.397110i | ||||
\(539\) | −29.4910 | − | 29.4910i | −1.27027 | − | 1.27027i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.54651 | − | 7.54651i | 0.324450 | − | 0.324450i | −0.526021 | − | 0.850471i | \(-0.676317\pi\) |
0.850471 | + | 0.526021i | \(0.176317\pi\) | |||||||
\(542\) | −10.3559 | − | 18.8512i | −0.444826 | − | 0.809728i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.08939 | + | 1.49455i | −0.0467073 | + | 0.0640784i | ||||
\(545\) | 53.9206 | 2.30971 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.75678 | − | 8.75678i | 0.374413 | − | 0.374413i | −0.494669 | − | 0.869082i | \(-0.664711\pi\) |
0.869082 | + | 0.494669i | \(0.164711\pi\) | |||||||
\(548\) | 8.38371 | + | 5.32774i | 0.358134 | + | 0.227590i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 34.0162 | + | 9.89403i | 1.45045 | + | 0.421883i | ||||
\(551\) | 0.599379i | 0.0255344i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 40.2606i | − | 1.71206i | ||||||
\(554\) | 1.81857 | − | 6.25233i | 0.0772636 | − | 0.265636i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.80116 | − | 1.29294i | 0.246024 | − | 0.0548330i | ||||
\(557\) | −19.9006 | + | 19.9006i | −0.843215 | + | 0.843215i | −0.989276 | − | 0.146061i | \(-0.953341\pi\) |
0.146061 | + | 0.989276i | \(0.453341\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 45.2087 | 1.91212 | ||||||||
\(560\) | −47.0423 | − | 17.0021i | −1.98790 | − | 0.718469i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 16.2974 | − | 8.95299i | 0.687463 | − | 0.377659i | ||||
\(563\) | 24.1922 | − | 24.1922i | 1.01958 | − | 1.01958i | 0.0197747 | − | 0.999804i | \(-0.493705\pi\) |
0.999804 | − | 0.0197747i | \(-0.00629490\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.33188 | + | 6.33188i | 0.266384 | + | 0.266384i | ||||
\(566\) | 5.13044 | − | 17.6387i | 0.215649 | − | 0.741411i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.24025 | + | 19.4254i | −0.0520398 | + | 0.815073i | ||||
\(569\) | − | 38.1466i | − | 1.59919i | −0.600540 | − | 0.799594i | \(-0.705048\pi\) | ||
0.600540 | − | 0.799594i | \(-0.294952\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.3968 | − | 22.3968i | −0.937277 | − | 0.937277i | 0.0608686 | − | 0.998146i | \(-0.480613\pi\) |
−0.998146 | + | 0.0608686i | \(0.980613\pi\) | |||||||
\(572\) | −30.9039 | + | 48.6302i | −1.29216 | + | 2.03333i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 24.6356 | + | 44.8448i | 1.02827 | + | 1.87179i | ||||
\(575\) | 21.9441 | 0.915134 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.2349 | −1.09217 | −0.546086 | − | 0.837729i | \(-0.683883\pi\) | ||||
−0.546086 | + | 0.837729i | \(0.683883\pi\) | |||||||
\(578\) | 11.5028 | + | 20.9389i | 0.478455 | + | 0.870945i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 13.2892 | − | 20.9118i | 0.551803 | − | 0.868314i | ||||
\(581\) | −4.24285 | − | 4.24285i | −0.176023 | − | 0.176023i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 18.0630i | − | 0.748094i | ||||||
\(584\) | −0.567773 | + | 8.89275i | −0.0234946 | + | 0.367985i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.20582 | + | 28.2120i | −0.338979 | + | 1.16543i | ||||
\(587\) | −3.63391 | − | 3.63391i | −0.149988 | − | 0.149988i | 0.628125 | − | 0.778113i | \(-0.283823\pi\) |
−0.778113 | + | 0.628125i | \(0.783823\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.484500 | + | 0.484500i | −0.0199635 | + | 0.0199635i | ||||
\(590\) | −1.81642 | + | 0.997854i | −0.0747809 | + | 0.0410810i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9.16064 | − | 25.3462i | 0.376500 | − | 1.04172i | ||||
\(593\) | −13.6076 | −0.558796 | −0.279398 | − | 0.960175i | \(-0.590135\pi\) | ||||
−0.279398 | + | 0.960175i | \(0.590135\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.89095 | − | 2.89095i | 0.118517 | − | 0.118517i | ||||
\(596\) | 21.5049 | − | 4.79294i | 0.880875 | − | 0.196327i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.96819 | + | 34.2711i | −0.407629 | + | 1.40145i | ||||
\(599\) | − | 5.25611i | − | 0.214759i | −0.994218 | − | 0.107379i | \(-0.965754\pi\) | ||
0.994218 | − | 0.107379i | \(-0.0342459\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.7190i | 1.41622i | 0.706103 | + | 0.708109i | \(0.250451\pi\) | ||||
−0.706103 | + | 0.708109i | \(0.749549\pi\) | |||||||
\(602\) | 41.2101 | + | 11.9865i | 1.67960 | + | 0.488532i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.06126 | + | 3.21637i | 0.205940 | + | 0.130872i | ||||
\(605\) | 29.5461 | − | 29.5461i | 1.20122 | − | 1.20122i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.2796 | −0.579590 | −0.289795 | − | 0.957089i | \(-0.593587\pi\) | ||||
−0.289795 | + | 0.957089i | \(0.593587\pi\) | |||||||
\(608\) | −0.134719 | − | 0.859186i | −0.00546359 | − | 0.0348446i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 25.3044 | + | 46.0622i | 1.02454 | + | 1.86501i | ||||
\(611\) | 15.2158 | − | 15.2158i | 0.615564 | − | 0.615564i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.3421 | − | 15.3421i | −0.619660 | − | 0.619660i | 0.325784 | − | 0.945444i | \(-0.394372\pi\) |
−0.945444 | + | 0.325784i | \(0.894372\pi\) | |||||||
\(614\) | −45.6266 | − | 13.2711i | −1.84134 | − | 0.535577i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −41.0641 | + | 36.1352i | −1.65452 | + | 1.45593i | ||||
\(617\) | − | 43.4143i | − | 1.74779i | −0.486112 | − | 0.873897i | \(-0.661585\pi\) | ||
0.486112 | − | 0.873897i | \(-0.338415\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.34752 | + | 9.34752i | 0.375709 | + | 0.375709i | 0.869551 | − | 0.493843i | \(-0.164408\pi\) |
−0.493843 | + | 0.869551i | \(0.664408\pi\) | |||||||
\(620\) | 27.6459 | − | 6.16163i | 1.11029 | − | 0.247457i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −10.6503 | + | 5.85078i | −0.427040 | + | 0.234595i | ||||
\(623\) | 22.7081 | 0.909781 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.5034 | 0.980134 | ||||||||
\(626\) | 10.3571 | − | 5.68970i | 0.413954 | − | 0.227406i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.35837 | + | 37.5022i | 0.333535 | + | 1.49650i | ||||
\(629\) | 1.55763 | + | 1.55763i | 0.0621068 | + | 0.0621068i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.7747i | 1.42417i | 0.702095 | + | 0.712084i | \(0.252248\pi\) | ||||
−0.702095 | + | 0.712084i | \(0.747752\pi\) | |||||||
\(632\) | −28.8775 | − | 1.84373i | −1.14868 | − | 0.0733397i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −45.4963 | − | 13.2332i | −1.80689 | − | 0.525556i | ||||
\(635\) | 26.6750 | + | 26.6750i | 1.05856 | + | 1.05856i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −35.1817 | + | 35.1817i | −1.39395 | + | 1.39395i | ||||
\(638\) | −13.0456 | − | 23.7473i | −0.516481 | − | 0.940165i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −14.3493 | + | 32.9631i | −0.567205 | + | 1.30298i | ||||
\(641\) | −27.8292 | −1.09919 | −0.549593 | − | 0.835432i | \(-0.685217\pi\) | ||||
−0.549593 | + | 0.835432i | \(0.685217\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.87219 | − | 1.87219i | 0.0738321 | − | 0.0738321i | −0.669226 | − | 0.743059i | \(-0.733374\pi\) |
0.743059 | + | 0.669226i | \(0.233374\pi\) | |||||||
\(644\) | −18.1730 | + | 28.5970i | −0.716118 | + | 1.12688i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.0682550 | + | 0.0198528i | 0.00268546 | + | 0.000781098i | ||||
\(647\) | 22.2507i | 0.874767i | 0.899275 | + | 0.437383i | \(0.144095\pi\) | ||||
−0.899275 | + | 0.437383i | \(0.855905\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.26632i | 0.0889607i | ||||||||
\(650\) | 11.8032 | − | 40.5800i | 0.462960 | − | 1.59168i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.54409 | + | 20.3884i | 0.177960 | + | 0.798470i | ||||
\(653\) | −4.80129 | + | 4.80129i | −0.187889 | + | 0.187889i | −0.794783 | − | 0.606894i | \(-0.792415\pi\) |
0.606894 | + | 0.794783i | \(0.292415\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 38.4165 | 1.50106 | ||||||||
\(656\) | 33.2938 | − | 15.6166i | 1.29990 | − | 0.609724i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 17.9042 | − | 9.83572i | 0.697979 | − | 0.383436i | ||||
\(659\) | 24.9687 | − | 24.9687i | 0.972642 | − | 0.972642i | −0.0269940 | − | 0.999636i | \(-0.508593\pi\) |
0.999636 | + | 0.0269940i | \(0.00859350\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.42481 | + | 5.42481i | 0.211001 | + | 0.211001i | 0.804692 | − | 0.593692i | \(-0.202330\pi\) |
−0.593692 | + | 0.804692i | \(0.702330\pi\) | |||||||
\(662\) | 2.44474 | − | 8.40515i | 0.0950176 | − | 0.326675i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.23754 | + | 2.84894i | −0.125641 | + | 0.110560i | ||||
\(665\) | 1.92254i | 0.0745528i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.8677 | − | 11.8677i | −0.459520 | − | 0.459520i | ||||
\(668\) | 6.82082 | + | 4.33455i | 0.263905 | + | 0.167709i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 13.2082 | + | 24.0433i | 0.510278 | + | 0.928872i | ||||
\(671\) | 57.4710 | 2.21864 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.3041 | −1.09104 | −0.545521 | − | 0.838097i | \(-0.683668\pi\) | ||||
−0.545521 | + | 0.838097i | \(0.683668\pi\) | |||||||
\(674\) | 0.644808 | + | 1.17376i | 0.0248371 | + | 0.0452116i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 36.0701 | + | 22.9221i | 1.38731 | + | 0.881619i | ||||
\(677\) | −4.48694 | − | 4.48694i | −0.172447 | − | 0.172447i | 0.615607 | − | 0.788054i | \(-0.288911\pi\) |
−0.788054 | + | 0.615607i | \(0.788911\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.1120i | 0.426440i | ||||||||
\(680\) | −1.94118 | − | 2.20597i | −0.0744410 | − | 0.0845949i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.65056 | − | 29.7411i | 0.331247 | − | 1.13884i | ||||
\(683\) | −11.5502 | − | 11.5502i | −0.441955 | − | 0.441955i | 0.450713 | − | 0.892669i | \(-0.351170\pi\) |
−0.892669 | + | 0.450713i | \(0.851170\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.1598 | + | 11.1598i | −0.426394 | + | 0.426394i | ||||
\(686\) | −7.25299 | + | 3.98445i | −0.276921 | + | 0.152127i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 10.4847 | − | 29.0096i | 0.399725 | − | 1.10598i | ||||
\(689\) | −21.5485 | −0.820933 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.0962 | + | 11.0962i | −0.422118 | + | 0.422118i | −0.885932 | − | 0.463815i | \(-0.846480\pi\) |
0.463815 | + | 0.885932i | \(0.346480\pi\) | |||||||
\(692\) | −4.12933 | − | 18.5274i | −0.156974 | − | 0.704306i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.67319 | − | 33.2569i | 0.367189 | − | 1.26242i | ||||
\(695\) | 9.44316i | 0.358200i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.00575i | 0.113851i | ||||||||
\(698\) | 1.65666 | + | 0.481859i | 0.0627053 | + | 0.0182386i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 21.5185 | − | 33.8614i | 0.813322 | − | 1.27984i | ||||
\(701\) | 3.52654 | − | 3.52654i | 0.133196 | − | 0.133196i | −0.637366 | − | 0.770561i | \(-0.719976\pi\) |
0.770561 | + | 0.637366i | \(0.219976\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.03585 | −0.0390680 | ||||||||
\(704\) | 24.0379 | + | 31.1086i | 0.905964 | + | 1.17245i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13.1405 | − | 23.9201i | −0.494550 | − | 0.900243i | ||||
\(707\) | −11.8253 | + | 11.8253i | −0.444736 | + | 0.444736i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.22384 | + | 8.22384i | 0.308853 | + | 0.308853i | 0.844464 | − | 0.535612i | \(-0.179919\pi\) |
−0.535612 | + | 0.844464i | \(0.679919\pi\) | |||||||
\(710\) | −29.6958 | − | 8.63739i | −1.11446 | − | 0.324155i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.03992 | − | 16.2877i | 0.0389725 | − | 0.610407i | ||||
\(713\) | − | 19.1862i | − | 0.718530i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −64.7330 | − | 64.7330i | −2.42088 | − | 2.42088i | ||||
\(716\) | −2.14719 | − | 9.63399i | −0.0802443 | − | 0.360039i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 29.0371 | − | 15.9516i | 1.08366 | − | 0.595308i | ||||
\(719\) | 37.5128 | 1.39899 | 0.699496 | − | 0.714637i | \(-0.253408\pi\) | ||||
0.699496 | + | 0.714637i | \(0.253408\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 29.2286 | 1.08853 | ||||||||
\(722\) | 23.5211 | − | 12.9214i | 0.875365 | − | 0.480884i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 48.1169 | − | 10.7241i | 1.78825 | − | 0.398559i | ||||
\(725\) | 14.0524 | + | 14.0524i | 0.521894 | + | 0.521894i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 52.5708i | 1.94974i | 0.222765 | + | 0.974872i | \(0.428492\pi\) | ||||
−0.222765 | + | 0.974872i | \(0.571508\pi\) | |||||||
\(728\) | 43.1079 | + | 48.9880i | 1.59769 | + | 1.81561i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −13.5944 | − | 3.95410i | −0.503151 | − | 0.146348i | ||||
\(731\) | 1.78276 | + | 1.78276i | 0.0659379 | + | 0.0659379i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.339705 | − | 0.339705i | 0.0125473 | − | 0.0125473i | −0.700805 | − | 0.713353i | \(-0.747176\pi\) |
0.713353 | + | 0.700805i | \(0.247176\pi\) | |||||||
\(734\) | 1.04381 | + | 1.90007i | 0.0385276 | + | 0.0701328i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 19.6794 | + | 14.3445i | 0.725391 | + | 0.528744i | ||||
\(737\) | 29.9983 | 1.10500 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.8772 | − | 26.8772i | 0.988693 | − | 0.988693i | −0.0112434 | − | 0.999937i | \(-0.503579\pi\) |
0.999937 | + | 0.0112434i | \(0.00357897\pi\) | |||||||
\(740\) | 36.1400 | + | 22.9665i | 1.32853 | + | 0.844266i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −19.6426 | − | 5.71329i | −0.721102 | − | 0.209742i | ||||
\(743\) | 14.2143i | 0.521474i | 0.965410 | + | 0.260737i | \(0.0839655\pi\) | ||||
−0.965410 | + | 0.260737i | \(0.916035\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 35.0058i | 1.28251i | ||||||||
\(746\) | −8.24980 | + | 28.3632i | −0.302047 | + | 1.03845i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.13635 | + | 0.699020i | −0.114676 | + | 0.0255587i | ||||
\(749\) | −13.7332 | + | 13.7332i | −0.501799 | + | 0.501799i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.3087 | 0.887037 | 0.443519 | − | 0.896265i | \(-0.353730\pi\) | ||||
0.443519 | + | 0.896265i | \(0.353730\pi\) | |||||||
\(752\) | −6.23488 | − | 13.2925i | −0.227363 | − | 0.484727i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −28.3296 | + | 15.5629i | −1.03170 | + | 0.566769i | ||||
\(755\) | −6.73718 | + | 6.73718i | −0.245191 | + | 0.245191i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.1423 | − | 32.1423i | −1.16823 | − | 1.16823i | −0.982624 | − | 0.185606i | \(-0.940575\pi\) |
−0.185606 | − | 0.982624i | \(-0.559425\pi\) | |||||||
\(758\) | −10.5335 | + | 36.2148i | −0.382594 | + | 1.31538i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.37897 | + | 0.0880425i | 0.0500204 | + | 0.00319364i | ||||
\(761\) | − | 44.1704i | − | 1.60117i | −0.599216 | − | 0.800587i | \(-0.704521\pi\) | ||
0.599216 | − | 0.800587i | \(-0.295479\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −47.2190 | − | 47.2190i | −1.70944 | − | 1.70944i | ||||
\(764\) | 3.76180 | − | 5.91954i | 0.136097 | − | 0.214161i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.164635 | − | 0.299689i | −0.00594850 | − | 0.0108282i | ||||
\(767\) | 2.70363 | 0.0976224 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.4844 | −1.13536 | −0.567678 | − | 0.823251i | \(-0.692158\pi\) | ||||
−0.567678 | + | 0.823251i | \(0.692158\pi\) | |||||||
\(770\) | −41.8444 | − | 76.1706i | −1.50797 | − | 2.74500i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 11.2463 | − | 17.6972i | 0.404765 | − | 0.636935i | ||||
\(773\) | −20.6072 | − | 20.6072i | −0.741188 | − | 0.741188i | 0.231619 | − | 0.972807i | \(-0.425598\pi\) |
−0.972807 | + | 0.231619i | \(0.925598\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 22.7182i | 0.816062i | ||||||||
\(776\) | 7.97025 | + | 0.508874i | 0.286115 | + | 0.0182675i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −12.3491 | + | 42.4568i | −0.442736 | + | 1.52215i | ||||
\(779\) | −0.999440 | − | 0.999440i | −0.0358086 | − | 0.0358086i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23.9138 | + | 23.9138i | −0.855703 | + | 0.855703i | ||||
\(782\) | −1.74454 | + | 0.958364i | −0.0623845 | + | 0.0342710i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 14.4162 | + | 30.7347i | 0.514864 | + | 1.09767i | ||||
\(785\) | −61.0463 | −2.17884 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.9633 | − | 17.9633i | 0.640321 | − | 0.640321i | −0.310313 | − | 0.950634i | \(-0.600434\pi\) |
0.950634 | + | 0.310313i | \(0.100434\pi\) | |||||||
\(788\) | −14.5792 | + | 3.24936i | −0.519361 | + | 0.115754i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 12.8402 | − | 44.1452i | 0.456833 | − | 1.57061i | ||||
\(791\) | − | 11.0898i | − | 0.394309i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 68.5608i | − | 2.43466i | ||||||
\(794\) | 13.8659 | + | 4.03307i | 0.492083 | + | 0.143128i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.7783 | + | 10.6624i | 0.594692 | + | 0.377919i | ||||
\(797\) | 3.15069 | − | 3.15069i | 0.111603 | − | 0.111603i | −0.649100 | − | 0.760703i | \(-0.724854\pi\) |
0.760703 | + | 0.649100i | \(0.224854\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.20004 | 0.0424543 | ||||||||
\(800\) | −23.3021 | − | 16.9851i | −0.823853 | − | 0.600514i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −24.4755 | − | 44.5534i | −0.864260 | − | 1.57324i | ||||
\(803\) | −10.9475 | + | 10.9475i | −0.386328 | + | 0.386328i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −38.0663 | − | 38.0663i | −1.34166 | − | 1.34166i | ||||
\(806\) | −35.4800 | − | 10.3198i | −1.24973 | − | 0.363499i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.94032 | + | 9.02340i | 0.279340 | + | 0.317442i | ||||
\(809\) | 49.4194i | 1.73749i | 0.495257 | + | 0.868746i | \(0.335074\pi\) | ||||
−0.495257 | + | 0.868746i | \(0.664926\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.3643 | − | 11.3643i | −0.399054 | − | 0.399054i | 0.478845 | − | 0.877899i | \(-0.341056\pi\) |
−0.877899 | + | 0.478845i | \(0.841056\pi\) | |||||||
\(812\) | −29.9502 | + | 6.67521i | −1.05105 | + | 0.234254i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 41.0404 | − | 22.5456i | 1.43846 | − | 0.790223i | ||||
\(815\) | −33.1883 | −1.16254 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.18557 | −0.0414779 | ||||||||
\(818\) | −19.3133 | + | 10.6098i | −0.675274 | + | 0.370963i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12.7104 | + | 57.0287i | 0.443865 | + | 1.99153i | ||||
\(821\) | 10.7322 | + | 10.7322i | 0.374557 | + | 0.374557i | 0.869134 | − | 0.494577i | \(-0.164677\pi\) |
−0.494577 | + | 0.869134i | \(0.664677\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1.72914i | − | 0.0602739i | −0.999546 | − | 0.0301370i | \(-0.990406\pi\) | ||
0.999546 | − | 0.0301370i | \(-0.00959435\pi\) | |||||||
\(824\) | 1.33852 | − | 20.9646i | 0.0466297 | − | 0.730338i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.46450 | + | 0.716830i | 0.0857509 | + | 0.0249417i | ||||
\(827\) | 14.7644 | + | 14.7644i | 0.513410 | + | 0.513410i | 0.915570 | − | 0.402160i | \(-0.131740\pi\) |
−0.402160 | + | 0.915570i | \(0.631740\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.9876 | + | 12.9876i | −0.451080 | + | 0.451080i | −0.895713 | − | 0.444633i | \(-0.853334\pi\) |
0.444633 | + | 0.895713i | \(0.353334\pi\) | |||||||
\(830\) | −3.29906 | − | 6.00537i | −0.114512 | − | 0.208450i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 37.1114 | − | 28.6764i | 1.28661 | − | 0.994174i | ||||
\(833\) | −2.77471 | −0.0961381 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.07939 | + | 9.07939i | −0.314205 | + | 0.314205i | ||||
\(836\) | 0.810435 | − | 1.27530i | 0.0280295 | − | 0.0441071i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 34.1636 | + | 9.93691i | 1.18016 | + | 0.343265i | ||||
\(839\) | − | 43.9697i | − | 1.51800i | −0.651089 | − | 0.759001i | \(-0.725688\pi\) | ||
0.651089 | − | 0.759001i | \(-0.274312\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.8005i | 0.475878i | ||||||||
\(842\) | −9.58079 | + | 32.9393i | −0.330176 | + | 1.13516i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.71960 | − | 30.1494i | −0.231298 | − | 1.03778i | ||||
\(845\) | −48.0139 | + | 48.0139i | −1.65173 | + | 1.65173i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −51.7479 | −1.77808 | ||||||||
\(848\) | −4.99747 | + | 13.8273i | −0.171614 | + | 0.474831i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.06568 | − | 1.13479i | 0.0708524 | − | 0.0389229i | ||||
\(851\) | 20.5099 | − | 20.5099i | 0.703072 | − | 0.703072i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.7069 | + | 14.7069i | 0.503553 | + | 0.503553i | 0.912540 | − | 0.408987i | \(-0.134118\pi\) |
−0.408987 | + | 0.912540i | \(0.634118\pi\) | |||||||
\(854\) | 18.1779 | − | 62.4967i | 0.622037 | − | 2.13859i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.22140 | + | 10.4792i | 0.315181 | + | 0.358172i | ||||
\(857\) | 12.0017i | 0.409971i | 0.978765 | + | 0.204985i | \(0.0657147\pi\) | ||||
−0.978765 | + | 0.204985i | \(0.934285\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.8440 | + | 12.8440i | 0.438231 | + | 0.438231i | 0.891416 | − | 0.453185i | \(-0.149712\pi\) |
−0.453185 | + | 0.891416i | \(0.649712\pi\) | |||||||
\(860\) | 41.3635 | + | 26.2860i | 1.41048 | + | 0.896344i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 24.5870 | + | 44.7565i | 0.837438 | + | 1.52441i | ||||
\(863\) | −26.2593 | −0.893877 | −0.446938 | − | 0.894565i | \(-0.647486\pi\) | ||||
−0.446938 | + | 0.894565i | \(0.647486\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 30.1590 | 1.02544 | ||||||||
\(866\) | −9.34265 | − | 17.0067i | −0.317476 | − | 0.577910i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −29.6057 | − | 18.8141i | −1.00488 | − | 0.638591i | ||||
\(869\) | −35.5498 | − | 35.5498i | −1.20594 | − | 1.20594i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 35.7869i | − | 1.21259i | ||||||
\(872\) | −36.0309 | + | 31.7061i | −1.22016 | + | 1.07370i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.261410 | − | 0.898740i | 0.00884231 | − | 0.0304003i | ||||
\(875\) | 0.861521 | + | 0.861521i | 0.0291247 | + | 0.0291247i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.26743 | − | 5.26743i | 0.177868 | − | 0.177868i | −0.612558 | − | 0.790426i | \(-0.709859\pi\) |
0.790426 | + | 0.612558i | \(0.209859\pi\) | |||||||
\(878\) | 34.9408 | − | 19.1948i | 1.17919 | − | 0.647793i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −56.5507 | + | 26.5253i | −1.90632 | + | 0.894167i | ||||
\(881\) | −5.66368 | −0.190814 | −0.0954071 | − | 0.995438i | \(-0.530415\pi\) | ||||
−0.0954071 | + | 0.995438i | \(0.530415\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.9671 | + | 17.9671i | −0.604640 | + | 0.604640i | −0.941540 | − | 0.336900i | \(-0.890621\pi\) |
0.336900 | + | 0.941540i | \(0.390621\pi\) | |||||||
\(884\) | 0.833905 | + | 3.74155i | 0.0280472 | + | 0.125842i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.974457 | − | 3.35023i | 0.0327375 | − | 0.112553i | ||||
\(887\) | 38.0932i | 1.27905i | 0.768772 | + | 0.639523i | \(0.220868\pi\) | ||||
−0.768772 | + | 0.639523i | \(0.779132\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 46.7193i | − | 1.56691i | ||||||
\(890\) | 24.8991 | + | 7.24221i | 0.834619 | + | 0.242759i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 9.54099 | − | 15.0136i | 0.319456 | − | 0.502694i | ||||
\(893\) | −0.399024 | + | 0.399024i | −0.0133528 | + | 0.0133528i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.6823 | 0.524200 | ||||||||
\(896\) | 41.4321 | − | 16.3004i | 1.38415 | − | 0.544559i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.765685 | − | 1.39380i | −0.0255512 | − | 0.0465116i | ||||
\(899\) | 12.2863 | − | 12.2863i | 0.409772 | − | 0.409772i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.849745 | − | 0.849745i | −0.0283091 | − | 0.0283091i | ||||
\(902\) | 61.3507 | + | 17.8446i | 2.04275 | + | 0.594160i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.95433 | − | 0.507858i | −0.264557 | − | 0.0168911i | ||||
\(905\) | 78.3250i | 2.60361i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.7306 | − | 25.7306i | −0.854372 | − | 0.854372i | 0.136296 | − | 0.990668i | \(-0.456480\pi\) |
−0.990668 | + | 0.136296i | \(0.956480\pi\) | |||||||
\(908\) | 12.0537 | + | 54.0826i | 0.400018 | + | 1.79479i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −90.8687 | + | 49.9189i | −3.01227 | + | 1.65479i | ||||
\(911\) | −2.17398 | −0.0720271 | −0.0360136 | − | 0.999351i | \(-0.511466\pi\) | ||||
−0.0360136 | + | 0.999351i | \(0.511466\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.49279 | −0.247975 | ||||||||
\(914\) | −46.2311 | + | 25.3972i | −1.52919 | + | 0.840063i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −24.5381 | + | 5.46897i | −0.810761 | + | 0.180700i | ||||
\(917\) | −33.6419 | − | 33.6419i | −1.11095 | − | 1.11095i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 8.61338i | − | 0.284129i | −0.989857 | − | 0.142065i | \(-0.954626\pi\) | ||
0.989857 | − | 0.142065i | \(-0.0453741\pi\) | |||||||
\(920\) | −29.0468 | + | 25.5603i | −0.957645 | + | 0.842699i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5.93857 | + | 1.72731i | 0.195576 | + | 0.0568858i | ||||
\(923\) | 28.5283 | + | 28.5283i | 0.939019 | + | 0.939019i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.2856 | + | 24.2856i | −0.798505 | + | 0.798505i | ||||
\(926\) | 3.12277 | + | 5.68446i | 0.102621 | + | 0.186803i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.41632 | + | 21.7879i | 0.112146 | + | 0.715224i | ||||
\(929\) | 5.86822 | 0.192530 | 0.0962650 | − | 0.995356i | \(-0.469310\pi\) | ||||
0.0962650 | + | 0.995356i | \(0.469310\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.922618 | − | 0.922618i | 0.0302376 | − | 0.0302376i | ||||
\(932\) | −22.8185 | − | 14.5009i | −0.747445 | − | 0.474992i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 46.8704 | + | 13.6328i | 1.53364 | + | 0.446080i | ||||
\(935\) | − | 5.10537i | − | 0.166963i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.7635i | 0.384296i | 0.981366 | + | 0.192148i | \(0.0615454\pi\) | ||||
−0.981366 | + | 0.192148i | \(0.938455\pi\) | |||||||
\(938\) | 9.48841 | − | 32.6216i | 0.309807 | − | 1.06513i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 22.7686 | − | 5.07459i | 0.742629 | − | 0.165515i | ||||
\(941\) | −40.7052 | + | 40.7052i | −1.32695 | + | 1.32695i | −0.418934 | + | 0.908017i | \(0.637596\pi\) |
−0.908017 | + | 0.418934i | \(0.862404\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 39.5779 | 1.28883 | ||||||||
\(944\) | 0.627018 | − | 1.73487i | 0.0204077 | − | 0.0564652i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 46.9721 | − | 25.8042i | 1.52720 | − | 0.838967i | ||||
\(947\) | 6.21975 | − | 6.21975i | 0.202115 | − | 0.202115i | −0.598791 | − | 0.800906i | \(-0.704352\pi\) |
0.800906 | + | 0.598791i | \(0.204352\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.0599 | + | 13.0599i | 0.423943 | + | 0.423943i | ||||
\(950\) | −0.309532 | + | 1.06419i | −0.0100425 | + | 0.0345268i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.231873 | + | 3.63172i | −0.00751505 | + | 0.117705i | ||||
\(953\) | − | 39.5189i | − | 1.28014i | −0.768316 | − | 0.640071i | \(-0.778905\pi\) | ||
0.768316 | − | 0.640071i | \(-0.221095\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.87967 | + | 7.87967i | 0.254980 | + | 0.254980i | ||||
\(956\) | 6.21137 | − | 9.77418i | 0.200890 | − | 0.316120i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.764638 | + | 1.39189i | 0.0247043 | + | 0.0449700i | ||||
\(959\) | 19.5456 | 0.631159 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.1370 | −0.359258 | ||||||||
\(962\) | −26.8961 | − | 48.9596i | −0.867164 | − | 1.57852i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 30.3627 | − | 47.7786i | 0.977918 | − | 1.53885i | ||||
\(965\) | 23.5572 | + | 23.5572i | 0.758334 | + | 0.758334i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 57.8455i | 1.86018i | 0.367326 | + | 0.930092i | \(0.380273\pi\) | ||||
−0.367326 | + | 0.930092i | \(0.619727\pi\) | |||||||
\(968\) | −2.36979 | + | 37.1169i | −0.0761679 | + | 1.19298i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.54392 | + | 12.1842i | −0.113788 | + | 0.391210i | ||||
\(971\) | −7.90060 | − | 7.90060i | −0.253542 | − | 0.253542i | 0.568879 | − | 0.822421i | \(-0.307377\pi\) |
−0.822421 | + | 0.568879i | \(0.807377\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.26951 | − | 8.26951i | 0.265108 | − | 0.265108i | ||||
\(974\) | 24.2074 | − | 13.2984i | 0.775656 | − | 0.426108i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −43.9942 | − | 15.9004i | −1.40822 | − | 0.508960i | ||||
\(977\) | −17.1759 | −0.549507 | −0.274753 | − | 0.961515i | \(-0.588596\pi\) | ||||
−0.274753 | + | 0.961515i | \(0.588596\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.0511 | − | 20.0511i | 0.640835 | − | 0.640835i | ||||
\(980\) | −52.6452 | + | 11.7334i | −1.68169 | + | 0.374809i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −12.6314 | + | 43.4273i | −0.403083 | + | 1.38582i | ||||
\(983\) | − | 22.1702i | − | 0.707120i | −0.935412 | − | 0.353560i | \(-0.884971\pi\) | ||
0.935412 | − | 0.353560i | \(-0.115029\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 23.7321i | − | 0.756166i | ||||||
\(986\) | −1.73086 | − | 0.503443i | −0.0551219 | − | 0.0160329i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.52138 | − | 0.966819i | −0.0484016 | − | 0.0307586i | ||||
\(989\) | 23.4743 | − | 23.4743i | 0.746440 | − | 0.746440i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.23742 | −0.229904 | −0.114952 | − | 0.993371i | \(-0.536671\pi\) | ||||
−0.114952 | + | 0.993371i | \(0.536671\pi\) | |||||||
\(992\) | −14.8504 | + | 20.3735i | −0.471502 | + | 0.646860i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 18.4411 | + | 33.5689i | 0.584917 | + | 1.06474i | ||||
\(995\) | −22.3341 | + | 22.3341i | −0.708039 | + | 0.708039i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.5321 | − | 13.5321i | −0.428566 | − | 0.428566i | 0.459573 | − | 0.888140i | \(-0.348002\pi\) |
−0.888140 | + | 0.459573i | \(0.848002\pi\) | |||||||
\(998\) | 23.8323 | + | 6.93192i | 0.754399 | + | 0.219426i | ||||
\(999\) | 0 | 0 |
(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 | 432.2.k.c.325.6 | yes | 24 | |
3.2 | odd | 2 | inner | 432.2.k.c.325.7 | yes | 24 | |
4.3 | odd | 2 | 1728.2.k.c.433.3 | 24 | |||
12.11 | even | 2 | 1728.2.k.c.433.10 | 24 | |||
16.3 | odd | 4 | 1728.2.k.c.1297.3 | 24 | |||
16.13 | even | 4 | inner | 432.2.k.c.109.6 | ✓ | 24 | |
48.29 | odd | 4 | inner | 432.2.k.c.109.7 | yes | 24 | |
48.35 | even | 4 | 1728.2.k.c.1297.10 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
432.2.k.c.109.6 | ✓ | 24 | 16.13 | even | 4 | inner | |
432.2.k.c.109.7 | yes | 24 | 48.29 | odd | 4 | inner | |
432.2.k.c.325.6 | yes | 24 | 1.1 | even | 1 | trivial | |
432.2.k.c.325.7 | yes | 24 | 3.2 | odd | 2 | inner | |
1728.2.k.c.433.3 | 24 | 4.3 | odd | 2 | |||
1728.2.k.c.433.10 | 24 | 12.11 | even | 2 | |||
1728.2.k.c.1297.3 | 24 | 16.3 | odd | 4 | |||
1728.2.k.c.1297.10 | 24 | 48.35 | even | 4 |