Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [490,2,Mod(361,490)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(490, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("490.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 490 = 2 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 490.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: | \(3.91266969904\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 471.1 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 490.471 |
Dual form | 490.2.e.i.361.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||
\(3\) | −1.70711 | − | 2.95680i | −0.985599 | − | 1.70711i | −0.639246 | − | 0.769002i | \(-0.720753\pi\) |
−0.346353 | − | 0.938104i | \(-0.612580\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | −3.41421 | −1.39385 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −4.32843 | + | 7.49706i | −1.44281 | + | 2.49902i | ||||
\(10\) | 0.500000 | + | 0.866025i | 0.158114 | + | 0.273861i | ||||
\(11\) | 0.414214 | + | 0.717439i | 0.124890 | + | 0.216316i | 0.921690 | − | 0.387927i | \(-0.126809\pi\) |
−0.796800 | + | 0.604243i | \(0.793476\pi\) | |||||||
\(12\) | −1.70711 | + | 2.95680i | −0.492799 | + | 0.853553i | ||||
\(13\) | −4.82843 | −1.33916 | −0.669582 | − | 0.742738i | \(-0.733527\pi\) | ||||
−0.669582 | + | 0.742738i | \(0.733527\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.41421 | 0.881546 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.29289 | − | 2.23936i | −0.313573 | − | 0.543124i | 0.665560 | − | 0.746344i | \(-0.268193\pi\) |
−0.979133 | + | 0.203220i | \(0.934859\pi\) | |||||||
\(18\) | 4.32843 | + | 7.49706i | 1.02022 | + | 1.76707i | ||||
\(19\) | −0.292893 | + | 0.507306i | −0.0671943 | + | 0.116384i | −0.897665 | − | 0.440678i | \(-0.854738\pi\) |
0.830471 | + | 0.557062i | \(0.188071\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.828427 | 0.176621 | ||||||||
\(23\) | 0.585786 | − | 1.01461i | 0.122145 | − | 0.211561i | −0.798468 | − | 0.602037i | \(-0.794356\pi\) |
0.920613 | + | 0.390476i | \(0.127689\pi\) | |||||||
\(24\) | 1.70711 | + | 2.95680i | 0.348462 | + | 0.603553i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | −2.41421 | + | 4.18154i | −0.473466 | + | 0.820068i | ||||
\(27\) | 19.3137 | 3.71692 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.82843 | −0.896616 | −0.448308 | − | 0.893879i | \(-0.647973\pi\) | ||||
−0.448308 | + | 0.893879i | \(0.647973\pi\) | |||||||
\(30\) | 1.70711 | − | 2.95680i | 0.311674 | − | 0.539835i | ||||
\(31\) | 1.41421 | + | 2.44949i | 0.254000 | + | 0.439941i | 0.964623 | − | 0.263631i | \(-0.0849203\pi\) |
−0.710623 | + | 0.703573i | \(0.751587\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 1.41421 | − | 2.44949i | 0.246183 | − | 0.426401i | ||||
\(34\) | −2.58579 | −0.443459 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 8.65685 | 1.44281 | ||||||||
\(37\) | 3.82843 | − | 6.63103i | 0.629390 | − | 1.09013i | −0.358285 | − | 0.933612i | \(-0.616638\pi\) |
0.987674 | − | 0.156522i | \(-0.0500283\pi\) | |||||||
\(38\) | 0.292893 | + | 0.507306i | 0.0475136 | + | 0.0822959i | ||||
\(39\) | 8.24264 | + | 14.2767i | 1.31988 | + | 2.28610i | ||||
\(40\) | 0.500000 | − | 0.866025i | 0.0790569 | − | 0.136931i | ||||
\(41\) | −3.07107 | −0.479620 | −0.239810 | − | 0.970820i | \(-0.577085\pi\) | ||||
−0.239810 | + | 0.970820i | \(0.577085\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.82843 | −1.34632 | −0.673161 | − | 0.739496i | \(-0.735064\pi\) | ||||
−0.673161 | + | 0.739496i | \(0.735064\pi\) | |||||||
\(44\) | 0.414214 | − | 0.717439i | 0.0624450 | − | 0.108158i | ||||
\(45\) | −4.32843 | − | 7.49706i | −0.645244 | − | 1.11760i | ||||
\(46\) | −0.585786 | − | 1.01461i | −0.0863695 | − | 0.149596i | ||||
\(47\) | −2.58579 | + | 4.47871i | −0.377176 | + | 0.653288i | −0.990650 | − | 0.136427i | \(-0.956438\pi\) |
0.613474 | + | 0.789715i | \(0.289771\pi\) | |||||||
\(48\) | 3.41421 | 0.492799 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −4.41421 | + | 7.64564i | −0.618114 | + | 1.07060i | ||||
\(52\) | 2.41421 | + | 4.18154i | 0.334791 | + | 0.579875i | ||||
\(53\) | −3.24264 | − | 5.61642i | −0.445411 | − | 0.771474i | 0.552670 | − | 0.833400i | \(-0.313609\pi\) |
−0.998081 | + | 0.0619259i | \(0.980276\pi\) | |||||||
\(54\) | 9.65685 | − | 16.7262i | 1.31413 | − | 2.27614i | ||||
\(55\) | −0.828427 | −0.111705 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.00000 | 0.264906 | ||||||||
\(58\) | −2.41421 | + | 4.18154i | −0.317002 | + | 0.549063i | ||||
\(59\) | −4.29289 | − | 7.43551i | −0.558887 | − | 0.968021i | −0.997590 | − | 0.0693885i | \(-0.977895\pi\) |
0.438703 | − | 0.898632i | \(-0.355438\pi\) | |||||||
\(60\) | −1.70711 | − | 2.95680i | −0.220387 | − | 0.381721i | ||||
\(61\) | −4.65685 | + | 8.06591i | −0.596249 | + | 1.03273i | 0.397120 | + | 0.917767i | \(0.370010\pi\) |
−0.993369 | + | 0.114967i | \(0.963324\pi\) | |||||||
\(62\) | 2.82843 | 0.359211 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.41421 | − | 4.18154i | 0.299446 | − | 0.518656i | ||||
\(66\) | −1.41421 | − | 2.44949i | −0.174078 | − | 0.301511i | ||||
\(67\) | −0.828427 | − | 1.43488i | −0.101208 | − | 0.175298i | 0.810974 | − | 0.585082i | \(-0.198938\pi\) |
−0.912183 | + | 0.409784i | \(0.865604\pi\) | |||||||
\(68\) | −1.29289 | + | 2.23936i | −0.156786 | + | 0.271562i | ||||
\(69\) | −4.00000 | −0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.48528 | −0.532305 | −0.266152 | − | 0.963931i | \(-0.585752\pi\) | ||||
−0.266152 | + | 0.963931i | \(0.585752\pi\) | |||||||
\(72\) | 4.32843 | − | 7.49706i | 0.510110 | − | 0.883536i | ||||
\(73\) | 4.70711 | + | 8.15295i | 0.550925 | + | 0.954230i | 0.998208 | + | 0.0598379i | \(0.0190584\pi\) |
−0.447283 | + | 0.894393i | \(0.647608\pi\) | |||||||
\(74\) | −3.82843 | − | 6.63103i | −0.445046 | − | 0.770842i | ||||
\(75\) | −1.70711 | + | 2.95680i | −0.197120 | + | 0.341421i | ||||
\(76\) | 0.585786 | 0.0671943 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 16.4853 | 1.86659 | ||||||||
\(79\) | 3.41421 | − | 5.91359i | 0.384129 | − | 0.665331i | −0.607519 | − | 0.794305i | \(-0.707835\pi\) |
0.991648 | + | 0.128974i | \(0.0411684\pi\) | |||||||
\(80\) | −0.500000 | − | 0.866025i | −0.0559017 | − | 0.0968246i | ||||
\(81\) | −19.9853 | − | 34.6155i | −2.22059 | − | 3.84617i | ||||
\(82\) | −1.53553 | + | 2.65962i | −0.169571 | + | 0.293706i | ||||
\(83\) | −2.24264 | −0.246162 | −0.123081 | − | 0.992397i | \(-0.539277\pi\) | ||||
−0.123081 | + | 0.992397i | \(0.539277\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.58579 | 0.280468 | ||||||||
\(86\) | −4.41421 | + | 7.64564i | −0.475997 | + | 0.824451i | ||||
\(87\) | 8.24264 | + | 14.2767i | 0.883704 | + | 1.53062i | ||||
\(88\) | −0.414214 | − | 0.717439i | −0.0441553 | − | 0.0764792i | ||||
\(89\) | −6.36396 | + | 11.0227i | −0.674579 | + | 1.16840i | 0.302013 | + | 0.953304i | \(0.402341\pi\) |
−0.976592 | + | 0.215101i | \(0.930992\pi\) | |||||||
\(90\) | −8.65685 | −0.912513 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.17157 | −0.122145 | ||||||||
\(93\) | 4.82843 | − | 8.36308i | 0.500685 | − | 0.867211i | ||||
\(94\) | 2.58579 | + | 4.47871i | 0.266704 | + | 0.461944i | ||||
\(95\) | −0.292893 | − | 0.507306i | −0.0300502 | − | 0.0520485i | ||||
\(96\) | 1.70711 | − | 2.95680i | 0.174231 | − | 0.301777i | ||||
\(97\) | −7.75736 | −0.787641 | −0.393820 | − | 0.919187i | \(-0.628847\pi\) | ||||
−0.393820 | + | 0.919187i | \(0.628847\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.17157 | −0.720770 | ||||||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | −6.65685 | − | 11.5300i | −0.662382 | − | 1.14728i | −0.979988 | − | 0.199056i | \(-0.936212\pi\) |
0.317606 | − | 0.948223i | \(-0.397121\pi\) | |||||||
\(102\) | 4.41421 | + | 7.64564i | 0.437072 | + | 0.757031i | ||||
\(103\) | 7.41421 | − | 12.8418i | 0.730544 | − | 1.26534i | −0.226107 | − | 0.974103i | \(-0.572600\pi\) |
0.956651 | − | 0.291237i | \(-0.0940669\pi\) | |||||||
\(104\) | 4.82843 | 0.473466 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.48528 | −0.629906 | ||||||||
\(107\) | −4.82843 | + | 8.36308i | −0.466782 | + | 0.808490i | −0.999280 | − | 0.0379415i | \(-0.987920\pi\) |
0.532498 | + | 0.846431i | \(0.321253\pi\) | |||||||
\(108\) | −9.65685 | − | 16.7262i | −0.929231 | − | 1.60948i | ||||
\(109\) | −1.24264 | − | 2.15232i | −0.119023 | − | 0.206155i | 0.800358 | − | 0.599523i | \(-0.204643\pi\) |
−0.919381 | + | 0.393368i | \(0.871310\pi\) | |||||||
\(110\) | −0.414214 | + | 0.717439i | −0.0394937 | + | 0.0684051i | ||||
\(111\) | −26.1421 | −2.48130 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.3137 | −1.44059 | −0.720296 | − | 0.693667i | \(-0.755994\pi\) | ||||
−0.720296 | + | 0.693667i | \(0.755994\pi\) | |||||||
\(114\) | 1.00000 | − | 1.73205i | 0.0936586 | − | 0.162221i | ||||
\(115\) | 0.585786 | + | 1.01461i | 0.0546249 | + | 0.0946130i | ||||
\(116\) | 2.41421 | + | 4.18154i | 0.224154 | + | 0.388246i | ||||
\(117\) | 20.8995 | − | 36.1990i | 1.93216 | − | 3.34660i | ||||
\(118\) | −8.58579 | −0.790386 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.41421 | −0.311674 | ||||||||
\(121\) | 5.15685 | − | 8.93193i | 0.468805 | − | 0.811994i | ||||
\(122\) | 4.65685 | + | 8.06591i | 0.421612 | + | 0.730253i | ||||
\(123\) | 5.24264 | + | 9.08052i | 0.472713 | + | 0.818763i | ||||
\(124\) | 1.41421 | − | 2.44949i | 0.127000 | − | 0.219971i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.82843 | 0.250982 | 0.125491 | − | 0.992095i | \(-0.459949\pi\) | ||||
0.125491 | + | 0.992095i | \(0.459949\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 15.0711 | + | 26.1039i | 1.32693 | + | 2.29832i | ||||
\(130\) | −2.41421 | − | 4.18154i | −0.211741 | − | 0.366745i | ||||
\(131\) | 3.12132 | − | 5.40629i | 0.272711 | − | 0.472349i | −0.696844 | − | 0.717223i | \(-0.745413\pi\) |
0.969555 | + | 0.244873i | \(0.0787464\pi\) | |||||||
\(132\) | −2.82843 | −0.246183 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.65685 | −0.143130 | ||||||||
\(135\) | −9.65685 | + | 16.7262i | −0.831130 | + | 1.43956i | ||||
\(136\) | 1.29289 | + | 2.23936i | 0.110865 | + | 0.192023i | ||||
\(137\) | 8.00000 | + | 13.8564i | 0.683486 | + | 1.18383i | 0.973910 | + | 0.226935i | \(0.0728704\pi\) |
−0.290424 | + | 0.956898i | \(0.593796\pi\) | |||||||
\(138\) | −2.00000 | + | 3.46410i | −0.170251 | + | 0.294884i | ||||
\(139\) | 19.8995 | 1.68785 | 0.843927 | − | 0.536459i | \(-0.180238\pi\) | ||||
0.843927 | + | 0.536459i | \(0.180238\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.6569 | 1.48698 | ||||||||
\(142\) | −2.24264 | + | 3.88437i | −0.188198 | + | 0.325969i | ||||
\(143\) | −2.00000 | − | 3.46410i | −0.167248 | − | 0.289683i | ||||
\(144\) | −4.32843 | − | 7.49706i | −0.360702 | − | 0.624755i | ||||
\(145\) | 2.41421 | − | 4.18154i | 0.200490 | − | 0.347258i | ||||
\(146\) | 9.41421 | 0.779126 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.65685 | −0.629390 | ||||||||
\(149\) | 3.00000 | − | 5.19615i | 0.245770 | − | 0.425685i | −0.716578 | − | 0.697507i | \(-0.754293\pi\) |
0.962348 | + | 0.271821i | \(0.0876260\pi\) | |||||||
\(150\) | 1.70711 | + | 2.95680i | 0.139385 | + | 0.241421i | ||||
\(151\) | 5.65685 | + | 9.79796i | 0.460348 | + | 0.797347i | 0.998978 | − | 0.0451959i | \(-0.0143912\pi\) |
−0.538630 | + | 0.842542i | \(0.681058\pi\) | |||||||
\(152\) | 0.292893 | − | 0.507306i | 0.0237568 | − | 0.0411479i | ||||
\(153\) | 22.3848 | 1.80970 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.82843 | −0.227185 | ||||||||
\(156\) | 8.24264 | − | 14.2767i | 0.659939 | − | 1.14305i | ||||
\(157\) | −3.24264 | − | 5.61642i | −0.258791 | − | 0.448239i | 0.707127 | − | 0.707086i | \(-0.249991\pi\) |
−0.965918 | + | 0.258847i | \(0.916657\pi\) | |||||||
\(158\) | −3.41421 | − | 5.91359i | −0.271620 | − | 0.470460i | ||||
\(159\) | −11.0711 | + | 19.1757i | −0.877993 | + | 1.52073i | ||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −39.9706 | −3.14038 | ||||||||
\(163\) | 10.0711 | − | 17.4436i | 0.788827 | − | 1.36629i | −0.137859 | − | 0.990452i | \(-0.544022\pi\) |
0.926686 | − | 0.375836i | \(-0.122645\pi\) | |||||||
\(164\) | 1.53553 | + | 2.65962i | 0.119905 | + | 0.207682i | ||||
\(165\) | 1.41421 | + | 2.44949i | 0.110096 | + | 0.190693i | ||||
\(166\) | −1.12132 | + | 1.94218i | −0.0870313 | + | 0.150743i | ||||
\(167\) | 15.7990 | 1.22256 | 0.611281 | − | 0.791413i | \(-0.290654\pi\) | ||||
0.611281 | + | 0.791413i | \(0.290654\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.3137 | 0.793362 | ||||||||
\(170\) | 1.29289 | − | 2.23936i | 0.0991604 | − | 0.171751i | ||||
\(171\) | −2.53553 | − | 4.39167i | −0.193897 | − | 0.335840i | ||||
\(172\) | 4.41421 | + | 7.64564i | 0.336581 | + | 0.582975i | ||||
\(173\) | 4.41421 | − | 7.64564i | 0.335606 | − | 0.581287i | −0.647995 | − | 0.761645i | \(-0.724392\pi\) |
0.983601 | + | 0.180357i | \(0.0577254\pi\) | |||||||
\(174\) | 16.4853 | 1.24975 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.828427 | −0.0624450 | ||||||||
\(177\) | −14.6569 | + | 25.3864i | −1.10168 | + | 1.90816i | ||||
\(178\) | 6.36396 | + | 11.0227i | 0.476999 | + | 0.826187i | ||||
\(179\) | −2.00000 | − | 3.46410i | −0.149487 | − | 0.258919i | 0.781551 | − | 0.623841i | \(-0.214429\pi\) |
−0.931038 | + | 0.364922i | \(0.881096\pi\) | |||||||
\(180\) | −4.32843 | + | 7.49706i | −0.322622 | + | 0.558798i | ||||
\(181\) | −2.48528 | −0.184730 | −0.0923648 | − | 0.995725i | \(-0.529443\pi\) | ||||
−0.0923648 | + | 0.995725i | \(0.529443\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 31.7990 | 2.35065 | ||||||||
\(184\) | −0.585786 | + | 1.01461i | −0.0431847 | + | 0.0747982i | ||||
\(185\) | 3.82843 | + | 6.63103i | 0.281472 | + | 0.487523i | ||||
\(186\) | −4.82843 | − | 8.36308i | −0.354037 | − | 0.613211i | ||||
\(187\) | 1.07107 | − | 1.85514i | 0.0783242 | − | 0.135662i | ||||
\(188\) | 5.17157 | 0.377176 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.585786 | −0.0424974 | ||||||||
\(191\) | −5.07107 | + | 8.78335i | −0.366930 | + | 0.635541i | −0.989084 | − | 0.147354i | \(-0.952924\pi\) |
0.622154 | + | 0.782895i | \(0.286258\pi\) | |||||||
\(192\) | −1.70711 | − | 2.95680i | −0.123200 | − | 0.213388i | ||||
\(193\) | −2.82843 | − | 4.89898i | −0.203595 | − | 0.352636i | 0.746089 | − | 0.665846i | \(-0.231929\pi\) |
−0.949684 | + | 0.313210i | \(0.898596\pi\) | |||||||
\(194\) | −3.87868 | + | 6.71807i | −0.278473 | + | 0.482329i | ||||
\(195\) | −16.4853 | −1.18054 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −25.7990 | −1.83810 | −0.919051 | − | 0.394139i | \(-0.871043\pi\) | ||||
−0.919051 | + | 0.394139i | \(0.871043\pi\) | |||||||
\(198\) | −3.58579 | + | 6.21076i | −0.254831 | + | 0.441380i | ||||
\(199\) | −8.24264 | − | 14.2767i | −0.584305 | − | 1.01205i | −0.994962 | − | 0.100256i | \(-0.968034\pi\) |
0.410656 | − | 0.911790i | \(-0.365300\pi\) | |||||||
\(200\) | 0.500000 | + | 0.866025i | 0.0353553 | + | 0.0612372i | ||||
\(201\) | −2.82843 | + | 4.89898i | −0.199502 | + | 0.345547i | ||||
\(202\) | −13.3137 | −0.936749 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 8.82843 | 0.618114 | ||||||||
\(205\) | 1.53553 | − | 2.65962i | 0.107246 | − | 0.185756i | ||||
\(206\) | −7.41421 | − | 12.8418i | −0.516573 | − | 0.894730i | ||||
\(207\) | 5.07107 | + | 8.78335i | 0.352464 | + | 0.610485i | ||||
\(208\) | 2.41421 | − | 4.18154i | 0.167396 | − | 0.289938i | ||||
\(209\) | −0.485281 | −0.0335676 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.6274 | 1.28236 | 0.641182 | − | 0.767389i | \(-0.278444\pi\) | ||||
0.641182 | + | 0.767389i | \(0.278444\pi\) | |||||||
\(212\) | −3.24264 | + | 5.61642i | −0.222705 | + | 0.385737i | ||||
\(213\) | 7.65685 | + | 13.2621i | 0.524639 | + | 0.908701i | ||||
\(214\) | 4.82843 | + | 8.36308i | 0.330064 | + | 0.571688i | ||||
\(215\) | 4.41421 | − | 7.64564i | 0.301047 | − | 0.521428i | ||||
\(216\) | −19.3137 | −1.31413 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.48528 | −0.168324 | ||||||||
\(219\) | 16.0711 | − | 27.8359i | 1.08598 | − | 1.88098i | ||||
\(220\) | 0.414214 | + | 0.717439i | 0.0279263 | + | 0.0483697i | ||||
\(221\) | 6.24264 | + | 10.8126i | 0.419925 | + | 0.727332i | ||||
\(222\) | −13.0711 | + | 22.6398i | −0.877273 | + | 1.51948i | ||||
\(223\) | −7.31371 | −0.489762 | −0.244881 | − | 0.969553i | \(-0.578749\pi\) | ||||
−0.244881 | + | 0.969553i | \(0.578749\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.65685 | 0.577124 | ||||||||
\(226\) | −7.65685 | + | 13.2621i | −0.509326 | + | 0.882179i | ||||
\(227\) | −9.12132 | − | 15.7986i | −0.605403 | − | 1.04859i | −0.991988 | − | 0.126335i | \(-0.959679\pi\) |
0.386584 | − | 0.922254i | \(-0.373655\pi\) | |||||||
\(228\) | −1.00000 | − | 1.73205i | −0.0662266 | − | 0.114708i | ||||
\(229\) | 8.07107 | − | 13.9795i | 0.533351 | − | 0.923791i | −0.465890 | − | 0.884843i | \(-0.654266\pi\) |
0.999241 | − | 0.0389487i | \(-0.0124009\pi\) | |||||||
\(230\) | 1.17157 | 0.0772512 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.82843 | 0.317002 | ||||||||
\(233\) | −11.6569 | + | 20.1903i | −0.763666 | + | 1.32271i | 0.177283 | + | 0.984160i | \(0.443269\pi\) |
−0.940949 | + | 0.338548i | \(0.890064\pi\) | |||||||
\(234\) | −20.8995 | − | 36.1990i | −1.36624 | − | 2.36640i | ||||
\(235\) | −2.58579 | − | 4.47871i | −0.168678 | − | 0.292159i | ||||
\(236\) | −4.29289 | + | 7.43551i | −0.279444 | + | 0.484010i | ||||
\(237\) | −23.3137 | −1.51439 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.65685 | 0.107173 | 0.0535865 | − | 0.998563i | \(-0.482935\pi\) | ||||
0.0535865 | + | 0.998563i | \(0.482935\pi\) | |||||||
\(240\) | −1.70711 | + | 2.95680i | −0.110193 | + | 0.190860i | ||||
\(241\) | 6.70711 | + | 11.6170i | 0.432043 | + | 0.748320i | 0.997049 | − | 0.0767666i | \(-0.0244596\pi\) |
−0.565006 | + | 0.825087i | \(0.691126\pi\) | |||||||
\(242\) | −5.15685 | − | 8.93193i | −0.331495 | − | 0.574166i | ||||
\(243\) | −39.2635 | + | 68.0063i | −2.51875 | + | 4.36261i | ||||
\(244\) | 9.31371 | 0.596249 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 10.4853 | 0.668517 | ||||||||
\(247\) | 1.41421 | − | 2.44949i | 0.0899843 | − | 0.155857i | ||||
\(248\) | −1.41421 | − | 2.44949i | −0.0898027 | − | 0.155543i | ||||
\(249\) | 3.82843 | + | 6.63103i | 0.242617 | + | 0.420224i | ||||
\(250\) | 0.500000 | − | 0.866025i | 0.0316228 | − | 0.0547723i | ||||
\(251\) | 0.585786 | 0.0369745 | 0.0184873 | − | 0.999829i | \(-0.494115\pi\) | ||||
0.0184873 | + | 0.999829i | \(0.494115\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.970563 | 0.0610188 | ||||||||
\(254\) | 1.41421 | − | 2.44949i | 0.0887357 | − | 0.153695i | ||||
\(255\) | −4.41421 | − | 7.64564i | −0.276429 | − | 0.478789i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 4.94975 | − | 8.57321i | 0.308757 | − | 0.534782i | −0.669334 | − | 0.742962i | \(-0.733420\pi\) |
0.978091 | + | 0.208179i | \(0.0667538\pi\) | |||||||
\(258\) | 30.1421 | 1.87657 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −4.82843 | −0.299446 | ||||||||
\(261\) | 20.8995 | − | 36.1990i | 1.29365 | − | 2.24066i | ||||
\(262\) | −3.12132 | − | 5.40629i | −0.192836 | − | 0.334001i | ||||
\(263\) | −14.0000 | − | 24.2487i | −0.863277 | − | 1.49524i | −0.868748 | − | 0.495255i | \(-0.835075\pi\) |
0.00547092 | − | 0.999985i | \(-0.498259\pi\) | |||||||
\(264\) | −1.41421 | + | 2.44949i | −0.0870388 | + | 0.150756i | ||||
\(265\) | 6.48528 | 0.398388 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 43.4558 | 2.65945 | ||||||||
\(268\) | −0.828427 | + | 1.43488i | −0.0506042 | + | 0.0876491i | ||||
\(269\) | −9.24264 | − | 16.0087i | −0.563534 | − | 0.976069i | −0.997184 | − | 0.0749880i | \(-0.976108\pi\) |
0.433651 | − | 0.901081i | \(-0.357225\pi\) | |||||||
\(270\) | 9.65685 | + | 16.7262i | 0.587697 | + | 1.01792i | ||||
\(271\) | −6.00000 | + | 10.3923i | −0.364474 | + | 0.631288i | −0.988692 | − | 0.149963i | \(-0.952085\pi\) |
0.624218 | + | 0.781251i | \(0.285418\pi\) | |||||||
\(272\) | 2.58579 | 0.156786 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.0000 | 0.966595 | ||||||||
\(275\) | 0.414214 | − | 0.717439i | 0.0249780 | − | 0.0432632i | ||||
\(276\) | 2.00000 | + | 3.46410i | 0.120386 | + | 0.208514i | ||||
\(277\) | 4.07107 | + | 7.05130i | 0.244607 | + | 0.423671i | 0.962021 | − | 0.272976i | \(-0.0880078\pi\) |
−0.717414 | + | 0.696647i | \(0.754674\pi\) | |||||||
\(278\) | 9.94975 | − | 17.2335i | 0.596746 | − | 1.03359i | ||||
\(279\) | −24.4853 | −1.46590 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.00000 | 0.477240 | 0.238620 | − | 0.971113i | \(-0.423305\pi\) | ||||
0.238620 | + | 0.971113i | \(0.423305\pi\) | |||||||
\(282\) | 8.82843 | − | 15.2913i | 0.525725 | − | 0.910583i | ||||
\(283\) | 1.12132 | + | 1.94218i | 0.0666556 | + | 0.115451i | 0.897427 | − | 0.441163i | \(-0.145434\pi\) |
−0.830772 | + | 0.556613i | \(0.812100\pi\) | |||||||
\(284\) | 2.24264 | + | 3.88437i | 0.133076 | + | 0.230495i | ||||
\(285\) | −1.00000 | + | 1.73205i | −0.0592349 | + | 0.102598i | ||||
\(286\) | −4.00000 | −0.236525 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −8.65685 | −0.510110 | ||||||||
\(289\) | 5.15685 | − | 8.93193i | 0.303344 | − | 0.525408i | ||||
\(290\) | −2.41421 | − | 4.18154i | −0.141768 | − | 0.245549i | ||||
\(291\) | 13.2426 | + | 22.9369i | 0.776297 | + | 1.34459i | ||||
\(292\) | 4.70711 | − | 8.15295i | 0.275463 | − | 0.477115i | ||||
\(293\) | −8.34315 | −0.487412 | −0.243706 | − | 0.969849i | \(-0.578363\pi\) | ||||
−0.243706 | + | 0.969849i | \(0.578363\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.58579 | 0.499884 | ||||||||
\(296\) | −3.82843 | + | 6.63103i | −0.222523 | + | 0.385421i | ||||
\(297\) | 8.00000 | + | 13.8564i | 0.464207 | + | 0.804030i | ||||
\(298\) | −3.00000 | − | 5.19615i | −0.173785 | − | 0.301005i | ||||
\(299\) | −2.82843 | + | 4.89898i | −0.163572 | + | 0.283315i | ||||
\(300\) | 3.41421 | 0.197120 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 11.3137 | 0.651031 | ||||||||
\(303\) | −22.7279 | + | 39.3659i | −1.30569 | + | 2.26151i | ||||
\(304\) | −0.292893 | − | 0.507306i | −0.0167986 | − | 0.0290960i | ||||
\(305\) | −4.65685 | − | 8.06591i | −0.266651 | − | 0.461853i | ||||
\(306\) | 11.1924 | − | 19.3858i | 0.639826 | − | 1.10821i | ||||
\(307\) | 14.9289 | 0.852039 | 0.426020 | − | 0.904714i | \(-0.359915\pi\) | ||||
0.426020 | + | 0.904714i | \(0.359915\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −50.6274 | −2.88009 | ||||||||
\(310\) | −1.41421 | + | 2.44949i | −0.0803219 | + | 0.139122i | ||||
\(311\) | −2.00000 | − | 3.46410i | −0.113410 | − | 0.196431i | 0.803733 | − | 0.594990i | \(-0.202844\pi\) |
−0.917143 | + | 0.398559i | \(0.869511\pi\) | |||||||
\(312\) | −8.24264 | − | 14.2767i | −0.466648 | − | 0.808257i | ||||
\(313\) | −7.19239 | + | 12.4576i | −0.406538 | + | 0.704144i | −0.994499 | − | 0.104745i | \(-0.966597\pi\) |
0.587961 | + | 0.808889i | \(0.299931\pi\) | |||||||
\(314\) | −6.48528 | −0.365986 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.82843 | −0.384129 | ||||||||
\(317\) | −5.24264 | + | 9.08052i | −0.294456 | + | 0.510013i | −0.974858 | − | 0.222826i | \(-0.928472\pi\) |
0.680402 | + | 0.732839i | \(0.261805\pi\) | |||||||
\(318\) | 11.0711 | + | 19.1757i | 0.620835 | + | 1.07532i | ||||
\(319\) | −2.00000 | − | 3.46410i | −0.111979 | − | 0.193952i | ||||
\(320\) | −0.500000 | + | 0.866025i | −0.0279508 | + | 0.0484123i | ||||
\(321\) | 32.9706 | 1.84024 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.51472 | 0.0842812 | ||||||||
\(324\) | −19.9853 | + | 34.6155i | −1.11029 | + | 1.92308i | ||||
\(325\) | 2.41421 | + | 4.18154i | 0.133916 | + | 0.231950i | ||||
\(326\) | −10.0711 | − | 17.4436i | −0.557785 | − | 0.966112i | ||||
\(327\) | −4.24264 | + | 7.34847i | −0.234619 | + | 0.406371i | ||||
\(328\) | 3.07107 | 0.169571 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.82843 | 0.155700 | ||||||||
\(331\) | −16.8995 | + | 29.2708i | −0.928880 | + | 1.60887i | −0.143681 | + | 0.989624i | \(0.545894\pi\) |
−0.785199 | + | 0.619244i | \(0.787439\pi\) | |||||||
\(332\) | 1.12132 | + | 1.94218i | 0.0615404 | + | 0.106591i | ||||
\(333\) | 33.1421 | + | 57.4039i | 1.81618 | + | 3.14571i | ||||
\(334\) | 7.89949 | − | 13.6823i | 0.432241 | − | 0.748664i | ||||
\(335\) | 1.65685 | 0.0905236 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.00000 | 0.326841 | 0.163420 | − | 0.986557i | \(-0.447747\pi\) | ||||
0.163420 | + | 0.986557i | \(0.447747\pi\) | |||||||
\(338\) | 5.15685 | − | 8.93193i | 0.280496 | − | 0.485833i | ||||
\(339\) | 26.1421 | + | 45.2795i | 1.41985 | + | 2.45925i | ||||
\(340\) | −1.29289 | − | 2.23936i | −0.0701170 | − | 0.121446i | ||||
\(341\) | −1.17157 | + | 2.02922i | −0.0634442 | + | 0.109889i | ||||
\(342\) | −5.07107 | −0.274212 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 8.82843 | 0.475997 | ||||||||
\(345\) | 2.00000 | − | 3.46410i | 0.107676 | − | 0.186501i | ||||
\(346\) | −4.41421 | − | 7.64564i | −0.237310 | − | 0.411032i | ||||
\(347\) | 1.58579 | + | 2.74666i | 0.0851295 | + | 0.147449i | 0.905446 | − | 0.424461i | \(-0.139536\pi\) |
−0.820317 | + | 0.571909i | \(0.806203\pi\) | |||||||
\(348\) | 8.24264 | − | 14.2767i | 0.441852 | − | 0.765310i | ||||
\(349\) | 2.48528 | 0.133034 | 0.0665170 | − | 0.997785i | \(-0.478811\pi\) | ||||
0.0665170 | + | 0.997785i | \(0.478811\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −93.2548 | −4.97757 | ||||||||
\(352\) | −0.414214 | + | 0.717439i | −0.0220777 | + | 0.0382396i | ||||
\(353\) | 1.19239 | + | 2.06528i | 0.0634644 | + | 0.109924i | 0.896012 | − | 0.444030i | \(-0.146452\pi\) |
−0.832547 | + | 0.553954i | \(0.813118\pi\) | |||||||
\(354\) | 14.6569 | + | 25.3864i | 0.779003 | + | 1.34927i | ||||
\(355\) | 2.24264 | − | 3.88437i | 0.119027 | − | 0.206161i | ||||
\(356\) | 12.7279 | 0.674579 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.00000 | −0.211407 | ||||||||
\(359\) | −14.1421 | + | 24.4949i | −0.746393 | + | 1.29279i | 0.203148 | + | 0.979148i | \(0.434883\pi\) |
−0.949541 | + | 0.313643i | \(0.898450\pi\) | |||||||
\(360\) | 4.32843 | + | 7.49706i | 0.228128 | + | 0.395130i | ||||
\(361\) | 9.32843 | + | 16.1573i | 0.490970 | + | 0.850385i | ||||
\(362\) | −1.24264 | + | 2.15232i | −0.0653117 | + | 0.113123i | ||||
\(363\) | −35.2132 | −1.84821 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.41421 | −0.492762 | ||||||||
\(366\) | 15.8995 | − | 27.5387i | 0.831080 | − | 1.43947i | ||||
\(367\) | −12.4853 | − | 21.6251i | −0.651726 | − | 1.12882i | −0.982704 | − | 0.185185i | \(-0.940712\pi\) |
0.330977 | − | 0.943639i | \(-0.392622\pi\) | |||||||
\(368\) | 0.585786 | + | 1.01461i | 0.0305362 | + | 0.0528903i | ||||
\(369\) | 13.2929 | − | 23.0240i | 0.692000 | − | 1.19858i | ||||
\(370\) | 7.65685 | 0.398061 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −9.65685 | −0.500685 | ||||||||
\(373\) | 15.2426 | − | 26.4010i | 0.789234 | − | 1.36699i | −0.137203 | − | 0.990543i | \(-0.543811\pi\) |
0.926437 | − | 0.376450i | \(-0.122855\pi\) | |||||||
\(374\) | −1.07107 | − | 1.85514i | −0.0553836 | − | 0.0959272i | ||||
\(375\) | −1.70711 | − | 2.95680i | −0.0881546 | − | 0.152688i | ||||
\(376\) | 2.58579 | − | 4.47871i | 0.133352 | − | 0.230972i | ||||
\(377\) | 23.3137 | 1.20072 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.4853 | 1.77139 | 0.885695 | − | 0.464268i | \(-0.153682\pi\) | ||||
0.885695 | + | 0.464268i | \(0.153682\pi\) | |||||||
\(380\) | −0.292893 | + | 0.507306i | −0.0150251 | + | 0.0260242i | ||||
\(381\) | −4.82843 | − | 8.36308i | −0.247368 | − | 0.428454i | ||||
\(382\) | 5.07107 | + | 8.78335i | 0.259458 | + | 0.449395i | ||||
\(383\) | 16.2426 | − | 28.1331i | 0.829960 | − | 1.43753i | −0.0681085 | − | 0.997678i | \(-0.521696\pi\) |
0.898069 | − | 0.439855i | \(-0.144970\pi\) | |||||||
\(384\) | −3.41421 | −0.174231 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.65685 | −0.287926 | ||||||||
\(387\) | 38.2132 | − | 66.1872i | 1.94249 | − | 3.36448i | ||||
\(388\) | 3.87868 | + | 6.71807i | 0.196910 | + | 0.341058i | ||||
\(389\) | −14.0711 | − | 24.3718i | −0.713431 | − | 1.23570i | −0.963561 | − | 0.267487i | \(-0.913807\pi\) |
0.250130 | − | 0.968212i | \(-0.419527\pi\) | |||||||
\(390\) | −8.24264 | + | 14.2767i | −0.417382 | + | 0.722927i | ||||
\(391\) | −3.02944 | −0.153205 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −21.3137 | −1.07513 | ||||||||
\(394\) | −12.8995 | + | 22.3426i | −0.649867 | + | 1.12560i | ||||
\(395\) | 3.41421 | + | 5.91359i | 0.171788 | + | 0.297545i | ||||
\(396\) | 3.58579 | + | 6.21076i | 0.180193 | + | 0.312103i | ||||
\(397\) | −16.8995 | + | 29.2708i | −0.848161 | + | 1.46906i | 0.0346859 | + | 0.999398i | \(0.488957\pi\) |
−0.882847 | + | 0.469660i | \(0.844376\pi\) | |||||||
\(398\) | −16.4853 | −0.826332 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 3.00000 | − | 5.19615i | 0.149813 | − | 0.259483i | −0.781345 | − | 0.624099i | \(-0.785466\pi\) |
0.931158 | + | 0.364615i | \(0.118800\pi\) | |||||||
\(402\) | 2.82843 | + | 4.89898i | 0.141069 | + | 0.244339i | ||||
\(403\) | −6.82843 | − | 11.8272i | −0.340148 | − | 0.589154i | ||||
\(404\) | −6.65685 | + | 11.5300i | −0.331191 | + | 0.573639i | ||||
\(405\) | 39.9706 | 1.98615 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.34315 | 0.314418 | ||||||||
\(408\) | 4.41421 | − | 7.64564i | 0.218536 | − | 0.378516i | ||||
\(409\) | 5.29289 | + | 9.16756i | 0.261717 | + | 0.453307i | 0.966698 | − | 0.255919i | \(-0.0823781\pi\) |
−0.704981 | + | 0.709226i | \(0.749045\pi\) | |||||||
\(410\) | −1.53553 | − | 2.65962i | −0.0758346 | − | 0.131349i | ||||
\(411\) | 27.3137 | − | 47.3087i | 1.34729 | − | 2.33357i | ||||
\(412\) | −14.8284 | −0.730544 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 10.1421 | 0.498459 | ||||||||
\(415\) | 1.12132 | − | 1.94218i | 0.0550435 | − | 0.0953381i | ||||
\(416\) | −2.41421 | − | 4.18154i | −0.118367 | − | 0.205017i | ||||
\(417\) | −33.9706 | − | 58.8387i | −1.66355 | − | 2.88135i | ||||
\(418\) | −0.242641 | + | 0.420266i | −0.0118679 | + | 0.0205559i | ||||
\(419\) | −20.8701 | −1.01957 | −0.509785 | − | 0.860302i | \(-0.670275\pi\) | ||||
−0.509785 | + | 0.860302i | \(0.670275\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.3137 | 0.843819 | 0.421909 | − | 0.906638i | \(-0.361360\pi\) | ||||
0.421909 | + | 0.906638i | \(0.361360\pi\) | |||||||
\(422\) | 9.31371 | − | 16.1318i | 0.453384 | − | 0.785285i | ||||
\(423\) | −22.3848 | − | 38.7716i | −1.08839 | − | 1.88514i | ||||
\(424\) | 3.24264 | + | 5.61642i | 0.157477 | + | 0.272757i | ||||
\(425\) | −1.29289 | + | 2.23936i | −0.0627145 | + | 0.108625i | ||||
\(426\) | 15.3137 | 0.741952 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 9.65685 | 0.466782 | ||||||||
\(429\) | −6.82843 | + | 11.8272i | −0.329680 | + | 0.571022i | ||||
\(430\) | −4.41421 | − | 7.64564i | −0.212872 | − | 0.368706i | ||||
\(431\) | 11.1716 | + | 19.3497i | 0.538116 | + | 0.932044i | 0.999006 | + | 0.0445864i | \(0.0141970\pi\) |
−0.460890 | + | 0.887457i | \(0.652470\pi\) | |||||||
\(432\) | −9.65685 | + | 16.7262i | −0.464616 | + | 0.804738i | ||||
\(433\) | 10.5858 | 0.508720 | 0.254360 | − | 0.967110i | \(-0.418135\pi\) | ||||
0.254360 | + | 0.967110i | \(0.418135\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −16.4853 | −0.790409 | ||||||||
\(436\) | −1.24264 | + | 2.15232i | −0.0595117 | + | 0.103077i | ||||
\(437\) | 0.343146 | + | 0.594346i | 0.0164149 | + | 0.0284314i | ||||
\(438\) | −16.0711 | − | 27.8359i | −0.767905 | − | 1.33005i | ||||
\(439\) | 12.4853 | − | 21.6251i | 0.595890 | − | 1.03211i | −0.397531 | − | 0.917589i | \(-0.630133\pi\) |
0.993421 | − | 0.114523i | \(-0.0365339\pi\) | |||||||
\(440\) | 0.828427 | 0.0394937 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12.4853 | 0.593864 | ||||||||
\(443\) | −1.51472 | + | 2.62357i | −0.0719665 | + | 0.124650i | −0.899763 | − | 0.436379i | \(-0.856261\pi\) |
0.827797 | + | 0.561028i | \(0.189594\pi\) | |||||||
\(444\) | 13.0711 | + | 22.6398i | 0.620325 | + | 1.07444i | ||||
\(445\) | −6.36396 | − | 11.0227i | −0.301681 | − | 0.522526i | ||||
\(446\) | −3.65685 | + | 6.33386i | −0.173157 | + | 0.299917i | ||||
\(447\) | −20.4853 | −0.968921 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.6274 | −0.784696 | −0.392348 | − | 0.919817i | \(-0.628337\pi\) | ||||
−0.392348 | + | 0.919817i | \(0.628337\pi\) | |||||||
\(450\) | 4.32843 | − | 7.49706i | 0.204044 | − | 0.353415i | ||||
\(451\) | −1.27208 | − | 2.20330i | −0.0598998 | − | 0.103750i | ||||
\(452\) | 7.65685 | + | 13.2621i | 0.360148 | + | 0.623795i | ||||
\(453\) | 19.3137 | − | 33.4523i | 0.907437 | − | 1.57173i | ||||
\(454\) | −18.2426 | −0.856170 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.00000 | −0.0936586 | ||||||||
\(457\) | −10.8284 | + | 18.7554i | −0.506532 | + | 0.877340i | 0.493439 | + | 0.869780i | \(0.335740\pi\) |
−0.999971 | + | 0.00755953i | \(0.997594\pi\) | |||||||
\(458\) | −8.07107 | − | 13.9795i | −0.377136 | − | 0.653219i | ||||
\(459\) | −24.9706 | − | 43.2503i | −1.16553 | − | 2.01875i | ||||
\(460\) | 0.585786 | − | 1.01461i | 0.0273124 | − | 0.0473065i | ||||
\(461\) | −12.8284 | −0.597479 | −0.298740 | − | 0.954335i | \(-0.596566\pi\) | ||||
−0.298740 | + | 0.954335i | \(0.596566\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.9706 | −0.788689 | −0.394344 | − | 0.918963i | \(-0.629028\pi\) | ||||
−0.394344 | + | 0.918963i | \(0.629028\pi\) | |||||||
\(464\) | 2.41421 | − | 4.18154i | 0.112077 | − | 0.194123i | ||||
\(465\) | 4.82843 | + | 8.36308i | 0.223913 | + | 0.387829i | ||||
\(466\) | 11.6569 | + | 20.1903i | 0.539993 | + | 0.935296i | ||||
\(467\) | 7.94975 | − | 13.7694i | 0.367870 | − | 0.637170i | −0.621362 | − | 0.783524i | \(-0.713420\pi\) |
0.989232 | + | 0.146353i | \(0.0467537\pi\) | |||||||
\(468\) | −41.7990 | −1.93216 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −5.17157 | −0.238547 | ||||||||
\(471\) | −11.0711 | + | 19.1757i | −0.510128 | + | 0.883567i | ||||
\(472\) | 4.29289 | + | 7.43551i | 0.197596 | + | 0.342247i | ||||
\(473\) | −3.65685 | − | 6.33386i | −0.168142 | − | 0.291231i | ||||
\(474\) | −11.6569 | + | 20.1903i | −0.535417 | + | 0.927370i | ||||
\(475\) | 0.585786 | 0.0268777 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 56.1421 | 2.57057 | ||||||||
\(478\) | 0.828427 | − | 1.43488i | 0.0378914 | − | 0.0656298i | ||||
\(479\) | 8.58579 | + | 14.8710i | 0.392295 | + | 0.679474i | 0.992752 | − | 0.120183i | \(-0.0383480\pi\) |
−0.600457 | + | 0.799657i | \(0.705015\pi\) | |||||||
\(480\) | 1.70711 | + | 2.95680i | 0.0779184 | + | 0.134959i | ||||
\(481\) | −18.4853 | + | 32.0174i | −0.842856 | + | 1.45987i | ||||
\(482\) | 13.4142 | 0.611001 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.3137 | −0.468805 | ||||||||
\(485\) | 3.87868 | − | 6.71807i | 0.176122 | − | 0.305052i | ||||
\(486\) | 39.2635 | + | 68.0063i | 1.78103 | + | 3.08483i | ||||
\(487\) | −15.8995 | − | 27.5387i | −0.720475 | − | 1.24790i | −0.960810 | − | 0.277209i | \(-0.910591\pi\) |
0.240335 | − | 0.970690i | \(-0.422743\pi\) | |||||||
\(488\) | 4.65685 | − | 8.06591i | 0.210806 | − | 0.365127i | ||||
\(489\) | −68.7696 | −3.10987 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.2843 | 1.45697 | 0.728484 | − | 0.685062i | \(-0.240225\pi\) | ||||
0.728484 | + | 0.685062i | \(0.240225\pi\) | |||||||
\(492\) | 5.24264 | − | 9.08052i | 0.236356 | − | 0.409381i | ||||
\(493\) | 6.24264 | + | 10.8126i | 0.281154 | + | 0.486974i | ||||
\(494\) | −1.41421 | − | 2.44949i | −0.0636285 | − | 0.110208i | ||||
\(495\) | 3.58579 | − | 6.21076i | 0.161169 | − | 0.279153i | ||||
\(496\) | −2.82843 | −0.127000 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 7.65685 | 0.343112 | ||||||||
\(499\) | −15.1716 | + | 26.2779i | −0.679173 | + | 1.17636i | 0.296057 | + | 0.955170i | \(0.404328\pi\) |
−0.975230 | + | 0.221192i | \(0.929005\pi\) | |||||||
\(500\) | −0.500000 | − | 0.866025i | −0.0223607 | − | 0.0387298i | ||||
\(501\) | −26.9706 | − | 46.7144i | −1.20496 | − | 2.08704i | ||||
\(502\) | 0.292893 | − | 0.507306i | 0.0130725 | − | 0.0226422i | ||||
\(503\) | 17.6569 | 0.787280 | 0.393640 | − | 0.919265i | \(-0.371216\pi\) | ||||
0.393640 | + | 0.919265i | \(0.371216\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.3137 | 0.592452 | ||||||||
\(506\) | 0.485281 | − | 0.840532i | 0.0215734 | − | 0.0373662i | ||||
\(507\) | −17.6066 | − | 30.4955i | −0.781937 | − | 1.35435i | ||||
\(508\) | −1.41421 | − | 2.44949i | −0.0627456 | − | 0.108679i | ||||
\(509\) | −2.89949 | + | 5.02207i | −0.128518 | + | 0.222599i | −0.923103 | − | 0.384554i | \(-0.874355\pi\) |
0.794585 | + | 0.607153i | \(0.207689\pi\) | |||||||
\(510\) | −8.82843 | −0.390929 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −5.65685 | + | 9.79796i | −0.249756 | + | 0.432590i | ||||
\(514\) | −4.94975 | − | 8.57321i | −0.218324 | − | 0.378148i | ||||
\(515\) | 7.41421 | + | 12.8418i | 0.326709 | + | 0.565877i | ||||
\(516\) | 15.0711 | − | 26.1039i | 0.663467 | − | 1.14916i | ||||
\(517\) | −4.28427 | −0.188422 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −30.1421 | −1.32309 | ||||||||
\(520\) | −2.41421 | + | 4.18154i | −0.105870 | + | 0.183373i | ||||
\(521\) | −9.53553 | − | 16.5160i | −0.417759 | − | 0.723580i | 0.577954 | − | 0.816069i | \(-0.303851\pi\) |
−0.995714 | + | 0.0924887i | \(0.970518\pi\) | |||||||
\(522\) | −20.8995 | − | 36.1990i | −0.914746 | − | 1.58439i | ||||
\(523\) | −11.9497 | + | 20.6976i | −0.522526 | + | 0.905042i | 0.477131 | + | 0.878832i | \(0.341677\pi\) |
−0.999656 | + | 0.0262091i | \(0.991656\pi\) | |||||||
\(524\) | −6.24264 | −0.272711 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −28.0000 | −1.22086 | ||||||||
\(527\) | 3.65685 | − | 6.33386i | 0.159295 | − | 0.275907i | ||||
\(528\) | 1.41421 | + | 2.44949i | 0.0615457 | + | 0.106600i | ||||
\(529\) | 10.8137 | + | 18.7299i | 0.470161 | + | 0.814343i | ||||
\(530\) | 3.24264 | − | 5.61642i | 0.140851 | − | 0.243962i | ||||
\(531\) | 74.3259 | 3.22547 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.8284 | 0.642290 | ||||||||
\(534\) | 21.7279 | − | 37.6339i | 0.940259 | − | 1.62858i | ||||
\(535\) | −4.82843 | − | 8.36308i | −0.208751 | − | 0.361568i | ||||
\(536\) | 0.828427 | + | 1.43488i | 0.0357826 | + | 0.0619773i | ||||
\(537\) | −6.82843 | + | 11.8272i | −0.294668 | + | 0.510381i | ||||
\(538\) | −18.4853 | −0.796957 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 19.3137 | 0.831130 | ||||||||
\(541\) | 7.48528 | − | 12.9649i | 0.321817 | − | 0.557404i | −0.659046 | − | 0.752103i | \(-0.729040\pi\) |
0.980863 | + | 0.194699i | \(0.0623730\pi\) | |||||||
\(542\) | 6.00000 | + | 10.3923i | 0.257722 | + | 0.446388i | ||||
\(543\) | 4.24264 | + | 7.34847i | 0.182069 | + | 0.315353i | ||||
\(544\) | 1.29289 | − | 2.23936i | 0.0554323 | − | 0.0960116i | ||||
\(545\) | 2.48528 | 0.106458 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.4853 | −0.448318 | −0.224159 | − | 0.974553i | \(-0.571964\pi\) | ||||
−0.224159 | + | 0.974553i | \(0.571964\pi\) | |||||||
\(548\) | 8.00000 | − | 13.8564i | 0.341743 | − | 0.591916i | ||||
\(549\) | −40.3137 | − | 69.8254i | −1.72055 | − | 2.98008i | ||||
\(550\) | −0.414214 | − | 0.717439i | −0.0176621 | − | 0.0305917i | ||||
\(551\) | 1.41421 | − | 2.44949i | 0.0602475 | − | 0.104352i | ||||
\(552\) | 4.00000 | 0.170251 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 8.14214 | 0.345926 | ||||||||
\(555\) | 13.0711 | − | 22.6398i | 0.554836 | − | 0.961004i | ||||
\(556\) | −9.94975 | − | 17.2335i | −0.421963 | − | 0.730862i | ||||
\(557\) | −7.58579 | − | 13.1390i | −0.321420 | − | 0.556716i | 0.659361 | − | 0.751826i | \(-0.270827\pi\) |
−0.980781 | + | 0.195110i | \(0.937493\pi\) | |||||||
\(558\) | −12.2426 | + | 21.2049i | −0.518272 | + | 0.897674i | ||||
\(559\) | 42.6274 | 1.80295 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.31371 | −0.308785 | ||||||||
\(562\) | 4.00000 | − | 6.92820i | 0.168730 | − | 0.292249i | ||||
\(563\) | 18.2929 | + | 31.6842i | 0.770954 | + | 1.33533i | 0.937041 | + | 0.349220i | \(0.113553\pi\) |
−0.166087 | + | 0.986111i | \(0.553113\pi\) | |||||||
\(564\) | −8.82843 | − | 15.2913i | −0.371744 | − | 0.643879i | ||||
\(565\) | 7.65685 | − | 13.2621i | 0.322126 | − | 0.557939i | ||||
\(566\) | 2.24264 | 0.0942652 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.48528 | 0.188198 | ||||||||
\(569\) | 14.6569 | − | 25.3864i | 0.614447 | − | 1.06425i | −0.376034 | − | 0.926606i | \(-0.622712\pi\) |
0.990481 | − | 0.137648i | \(-0.0439543\pi\) | |||||||
\(570\) | 1.00000 | + | 1.73205i | 0.0418854 | + | 0.0725476i | ||||
\(571\) | 1.10051 | + | 1.90613i | 0.0460547 | + | 0.0797691i | 0.888134 | − | 0.459585i | \(-0.152002\pi\) |
−0.842079 | + | 0.539354i | \(0.818668\pi\) | |||||||
\(572\) | −2.00000 | + | 3.46410i | −0.0836242 | + | 0.144841i | ||||
\(573\) | 34.6274 | 1.44658 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.17157 | −0.0488580 | ||||||||
\(576\) | −4.32843 | + | 7.49706i | −0.180351 | + | 0.312377i | ||||
\(577\) | −3.05025 | − | 5.28319i | −0.126984 | − | 0.219942i | 0.795523 | − | 0.605923i | \(-0.207196\pi\) |
−0.922507 | + | 0.385981i | \(0.873863\pi\) | |||||||
\(578\) | −5.15685 | − | 8.93193i | −0.214497 | − | 0.371519i | ||||
\(579\) | −9.65685 | + | 16.7262i | −0.401325 | + | 0.695116i | ||||
\(580\) | −4.82843 | −0.200490 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 26.4853 | 1.09785 | ||||||||
\(583\) | 2.68629 | − | 4.65279i | 0.111255 | − | 0.192699i | ||||
\(584\) | −4.70711 | − | 8.15295i | −0.194781 | − | 0.337371i | ||||
\(585\) | 20.8995 | + | 36.1990i | 0.864088 | + | 1.49664i | ||||
\(586\) | −4.17157 | + | 7.22538i | −0.172326 | + | 0.298478i | ||||
\(587\) | 17.0711 | 0.704598 | 0.352299 | − | 0.935887i | \(-0.385400\pi\) | ||||
0.352299 | + | 0.935887i | \(0.385400\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.65685 | −0.0682695 | ||||||||
\(590\) | 4.29289 | − | 7.43551i | 0.176736 | − | 0.306115i | ||||
\(591\) | 44.0416 | + | 76.2823i | 1.81163 | + | 3.13784i | ||||
\(592\) | 3.82843 | + | 6.63103i | 0.157347 | + | 0.272534i | ||||
\(593\) | −1.63604 | + | 2.83370i | −0.0671841 | + | 0.116366i | −0.897661 | − | 0.440687i | \(-0.854735\pi\) |
0.830477 | + | 0.557053i | \(0.188068\pi\) | |||||||
\(594\) | 16.0000 | 0.656488 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.00000 | −0.245770 | ||||||||
\(597\) | −28.1421 | + | 48.7436i | −1.15178 | + | 1.99494i | ||||
\(598\) | 2.82843 | + | 4.89898i | 0.115663 | + | 0.200334i | ||||
\(599\) | 5.41421 | + | 9.37769i | 0.221219 | + | 0.383162i | 0.955178 | − | 0.296031i | \(-0.0956632\pi\) |
−0.733960 | + | 0.679193i | \(0.762330\pi\) | |||||||
\(600\) | 1.70711 | − | 2.95680i | 0.0696923 | − | 0.120711i | ||||
\(601\) | 6.58579 | 0.268640 | 0.134320 | − | 0.990938i | \(-0.457115\pi\) | ||||
0.134320 | + | 0.990938i | \(0.457115\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.3431 | 0.584098 | ||||||||
\(604\) | 5.65685 | − | 9.79796i | 0.230174 | − | 0.398673i | ||||
\(605\) | 5.15685 | + | 8.93193i | 0.209656 | + | 0.363135i | ||||
\(606\) | 22.7279 | + | 39.3659i | 0.923259 | + | 1.59913i | ||||
\(607\) | −8.14214 | + | 14.1026i | −0.330479 | + | 0.572407i | −0.982606 | − | 0.185703i | \(-0.940544\pi\) |
0.652127 | + | 0.758110i | \(0.273877\pi\) | |||||||
\(608\) | −0.585786 | −0.0237568 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.31371 | −0.377101 | ||||||||
\(611\) | 12.4853 | − | 21.6251i | 0.505100 | − | 0.874860i | ||||
\(612\) | −11.1924 | − | 19.3858i | −0.452425 | − | 0.783624i | ||||
\(613\) | 6.17157 | + | 10.6895i | 0.249267 | + | 0.431744i | 0.963323 | − | 0.268345i | \(-0.0864768\pi\) |
−0.714055 | + | 0.700089i | \(0.753144\pi\) | |||||||
\(614\) | 7.46447 | − | 12.9288i | 0.301241 | − | 0.521765i | ||||
\(615\) | −10.4853 | −0.422807 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −33.3137 | −1.34116 | −0.670580 | − | 0.741837i | \(-0.733955\pi\) | ||||
−0.670580 | + | 0.741837i | \(0.733955\pi\) | |||||||
\(618\) | −25.3137 | + | 43.8446i | −1.01827 | + | 1.76369i | ||||
\(619\) | −14.5355 | − | 25.1763i | −0.584232 | − | 1.01192i | −0.994971 | − | 0.100167i | \(-0.968062\pi\) |
0.410738 | − | 0.911753i | \(-0.365271\pi\) | |||||||
\(620\) | 1.41421 | + | 2.44949i | 0.0567962 | + | 0.0983739i | ||||
\(621\) | 11.3137 | − | 19.5959i | 0.454003 | − | 0.786357i | ||||
\(622\) | −4.00000 | −0.160385 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −16.4853 | −0.659939 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 7.19239 | + | 12.4576i | 0.287466 | + | 0.497905i | ||||
\(627\) | 0.828427 | + | 1.43488i | 0.0330842 | + | 0.0573035i | ||||
\(628\) | −3.24264 | + | 5.61642i | −0.129395 | + | 0.224119i | ||||
\(629\) | −19.7990 | −0.789437 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.4853 | −0.497031 | −0.248516 | − | 0.968628i | \(-0.579943\pi\) | ||||
−0.248516 | + | 0.968628i | \(0.579943\pi\) | |||||||
\(632\) | −3.41421 | + | 5.91359i | −0.135810 | + | 0.235230i | ||||
\(633\) | −31.7990 | − | 55.0775i | −1.26390 | − | 2.18913i | ||||
\(634\) | 5.24264 | + | 9.08052i | 0.208212 | + | 0.360634i | ||||
\(635\) | −1.41421 | + | 2.44949i | −0.0561214 | + | 0.0972050i | ||||
\(636\) | 22.1421 | 0.877993 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4.00000 | −0.158362 | ||||||||
\(639\) | 19.4142 | − | 33.6264i | 0.768014 | − | 1.33024i | ||||
\(640\) | 0.500000 | + | 0.866025i | 0.0197642 | + | 0.0342327i | ||||
\(641\) | 12.3137 | + | 21.3280i | 0.486362 | + | 0.842404i | 0.999877 | − | 0.0156766i | \(-0.00499021\pi\) |
−0.513515 | + | 0.858081i | \(0.671657\pi\) | |||||||
\(642\) | 16.4853 | − | 28.5533i | 0.650622 | − | 1.12691i | ||||
\(643\) | 4.78680 | 0.188773 | 0.0943864 | − | 0.995536i | \(-0.469911\pi\) | ||||
0.0943864 | + | 0.995536i | \(0.469911\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −30.1421 | −1.18685 | ||||||||
\(646\) | 0.757359 | − | 1.31178i | 0.0297979 | − | 0.0516115i | ||||
\(647\) | 11.5563 | + | 20.0162i | 0.454327 | + | 0.786917i | 0.998649 | − | 0.0519588i | \(-0.0165465\pi\) |
−0.544322 | + | 0.838876i | \(0.683213\pi\) | |||||||
\(648\) | 19.9853 | + | 34.6155i | 0.785096 | + | 1.35983i | ||||
\(649\) | 3.55635 | − | 6.15978i | 0.139599 | − | 0.241792i | ||||
\(650\) | 4.82843 | 0.189386 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −20.1421 | −0.788827 | ||||||||
\(653\) | −2.17157 | + | 3.76127i | −0.0849802 | + | 0.147190i | −0.905383 | − | 0.424596i | \(-0.860416\pi\) |
0.820403 | + | 0.571786i | \(0.193749\pi\) | |||||||
\(654\) | 4.24264 | + | 7.34847i | 0.165900 | + | 0.287348i | ||||
\(655\) | 3.12132 | + | 5.40629i | 0.121960 | + | 0.211241i | ||||
\(656\) | 1.53553 | − | 2.65962i | 0.0599525 | − | 0.103841i | ||||
\(657\) | −81.4975 | −3.17952 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27.1716 | −1.05845 | −0.529227 | − | 0.848480i | \(-0.677518\pi\) | ||||
−0.529227 | + | 0.848480i | \(0.677518\pi\) | |||||||
\(660\) | 1.41421 | − | 2.44949i | 0.0550482 | − | 0.0953463i | ||||
\(661\) | 19.1421 | + | 33.1552i | 0.744543 | + | 1.28959i | 0.950408 | + | 0.311006i | \(0.100666\pi\) |
−0.205865 | + | 0.978580i | \(0.566001\pi\) | |||||||
\(662\) | 16.8995 | + | 29.2708i | 0.656818 | + | 1.13764i | ||||
\(663\) | 21.3137 | − | 36.9164i | 0.827756 | − | 1.43372i | ||||
\(664\) | 2.24264 | 0.0870313 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 66.2843 | 2.56846 | ||||||||
\(667\) | −2.82843 | + | 4.89898i | −0.109517 | + | 0.189689i | ||||
\(668\) | −7.89949 | − | 13.6823i | −0.305641 | − | 0.529385i | ||||
\(669\) | 12.4853 | + | 21.6251i | 0.482709 | + | 0.836076i | ||||
\(670\) | 0.828427 | − | 1.43488i | 0.0320049 | − | 0.0554342i | ||||
\(671\) | −7.71573 | −0.297862 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −48.0000 | −1.85026 | −0.925132 | − | 0.379646i | \(-0.876046\pi\) | ||||
−0.925132 | + | 0.379646i | \(0.876046\pi\) | |||||||
\(674\) | 3.00000 | − | 5.19615i | 0.115556 | − | 0.200148i | ||||
\(675\) | −9.65685 | − | 16.7262i | −0.371692 | − | 0.643790i | ||||
\(676\) | −5.15685 | − | 8.93193i | −0.198341 | − | 0.343536i | ||||
\(677\) | −19.7279 | + | 34.1698i | −0.758206 | + | 1.31325i | 0.185559 | + | 0.982633i | \(0.440590\pi\) |
−0.943765 | + | 0.330618i | \(0.892743\pi\) | |||||||
\(678\) | 52.2843 | 2.00797 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.58579 | −0.0991604 | ||||||||
\(681\) | −31.1421 | + | 53.9398i | −1.19337 | + | 2.06698i | ||||
\(682\) | 1.17157 | + | 2.02922i | 0.0448618 | + | 0.0777030i | ||||
\(683\) | −16.8284 | − | 29.1477i | −0.643922 | − | 1.11531i | −0.984549 | − | 0.175107i | \(-0.943973\pi\) |
0.340628 | − | 0.940198i | \(-0.389360\pi\) | |||||||
\(684\) | −2.53553 | + | 4.39167i | −0.0969486 | + | 0.167920i | ||||
\(685\) | −16.0000 | −0.611329 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −55.1127 | −2.10268 | ||||||||
\(688\) | 4.41421 | − | 7.64564i | 0.168290 | − | 0.291487i | ||||
\(689\) | 15.6569 | + | 27.1185i | 0.596479 | + | 1.03313i | ||||
\(690\) | −2.00000 | − | 3.46410i | −0.0761387 | − | 0.131876i | ||||
\(691\) | −0.878680 | + | 1.52192i | −0.0334265 | + | 0.0578965i | −0.882255 | − | 0.470772i | \(-0.843975\pi\) |
0.848828 | + | 0.528669i | \(0.177309\pi\) | |||||||
\(692\) | −8.82843 | −0.335606 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.17157 | 0.120391 | ||||||||
\(695\) | −9.94975 | + | 17.2335i | −0.377415 | + | 0.653703i | ||||
\(696\) | −8.24264 | − | 14.2767i | −0.312436 | − | 0.541156i | ||||
\(697\) | 3.97056 | + | 6.87722i | 0.150396 | + | 0.260493i | ||||
\(698\) | 1.24264 | − | 2.15232i | 0.0470346 | − | 0.0814664i | ||||
\(699\) | 79.5980 | 3.01067 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.48528 | 0.0938678 | 0.0469339 | − | 0.998898i | \(-0.485055\pi\) | ||||
0.0469339 | + | 0.998898i | \(0.485055\pi\) | |||||||
\(702\) | −46.6274 | + | 80.7611i | −1.75984 | + | 3.04813i | ||||
\(703\) | 2.24264 | + | 3.88437i | 0.0845828 | + | 0.146502i | ||||
\(704\) | 0.414214 | + | 0.717439i | 0.0156113 | + | 0.0270395i | ||||
\(705\) | −8.82843 | + | 15.2913i | −0.332498 | + | 0.575903i | ||||
\(706\) | 2.38478 | 0.0897522 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 29.3137 | 1.10168 | ||||||||
\(709\) | −22.5563 | + | 39.0687i | −0.847121 | + | 1.46726i | 0.0366445 | + | 0.999328i | \(0.488333\pi\) |
−0.883766 | + | 0.467929i | \(0.845000\pi\) | |||||||
\(710\) | −2.24264 | − | 3.88437i | −0.0841648 | − | 0.145778i | ||||
\(711\) | 29.5563 | + | 51.1931i | 1.10845 | + | 1.91989i | ||||
\(712\) | 6.36396 | − | 11.0227i | 0.238500 | − | 0.413093i | ||||
\(713\) | 3.31371 | 0.124099 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.00000 | 0.149592 | ||||||||
\(716\) | −2.00000 | + | 3.46410i | −0.0747435 | + | 0.129460i | ||||
\(717\) | −2.82843 | − | 4.89898i | −0.105630 | − | 0.182956i | ||||
\(718\) | 14.1421 | + | 24.4949i | 0.527780 | + | 0.914141i | ||||
\(719\) | −20.7279 | + | 35.9018i | −0.773021 | + | 1.33891i | 0.162879 | + | 0.986646i | \(0.447922\pi\) |
−0.935900 | + | 0.352266i | \(0.885411\pi\) | |||||||
\(720\) | 8.65685 | 0.322622 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 18.6569 | 0.694336 | ||||||||
\(723\) | 22.8995 | − | 39.6631i | 0.851641 | − | 1.47509i | ||||
\(724\) | 1.24264 | + | 2.15232i | 0.0461824 | + | 0.0799902i | ||||
\(725\) | 2.41421 | + | 4.18154i | 0.0896616 | + | 0.155299i | ||||
\(726\) | −17.6066 | + | 30.4955i | −0.653442 | + | 1.13180i | ||||
\(727\) | −3.51472 | −0.130354 | −0.0651768 | − | 0.997874i | \(-0.520761\pi\) | ||||
−0.0651768 | + | 0.997874i | \(0.520761\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 148.196 | 5.48874 | ||||||||
\(730\) | −4.70711 | + | 8.15295i | −0.174218 | + | 0.301754i | ||||
\(731\) | 11.4142 | + | 19.7700i | 0.422170 | + | 0.731220i | ||||
\(732\) | −15.8995 | − | 27.5387i | −0.587662 | − | 1.01786i | ||||
\(733\) | −17.0000 | + | 29.4449i | −0.627909 | + | 1.08757i | 0.360061 | + | 0.932929i | \(0.382756\pi\) |
−0.987971 | + | 0.154642i | \(0.950578\pi\) | |||||||
\(734\) | −24.9706 | −0.921680 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.17157 | 0.0431847 | ||||||||
\(737\) | 0.686292 | − | 1.18869i | 0.0252799 | − | 0.0437860i | ||||
\(738\) | −13.2929 | − | 23.0240i | −0.489318 | − | 0.847524i | ||||
\(739\) | −1.58579 | − | 2.74666i | −0.0583341 | − | 0.101038i | 0.835384 | − | 0.549667i | \(-0.185246\pi\) |
−0.893718 | + | 0.448630i | \(0.851912\pi\) | |||||||
\(740\) | 3.82843 | − | 6.63103i | 0.140736 | − | 0.243762i | ||||
\(741\) | −9.65685 | −0.354753 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 51.7990 | 1.90032 | 0.950160 | − | 0.311762i | \(-0.100919\pi\) | ||||
0.950160 | + | 0.311762i | \(0.100919\pi\) | |||||||
\(744\) | −4.82843 | + | 8.36308i | −0.177019 | + | 0.306605i | ||||
\(745\) | 3.00000 | + | 5.19615i | 0.109911 | + | 0.190372i | ||||
\(746\) | −15.2426 | − | 26.4010i | −0.558073 | − | 0.966610i | ||||
\(747\) | 9.70711 | − | 16.8132i | 0.355164 | − | 0.615163i | ||||
\(748\) | −2.14214 | −0.0783242 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −3.41421 | −0.124669 | ||||||||
\(751\) | 19.6569 | − | 34.0467i | 0.717289 | − | 1.24238i | −0.244781 | − | 0.969578i | \(-0.578716\pi\) |
0.962070 | − | 0.272802i | \(-0.0879505\pi\) | |||||||
\(752\) | −2.58579 | − | 4.47871i | −0.0942939 | − | 0.163322i | ||||
\(753\) | −1.00000 | − | 1.73205i | −0.0364420 | − | 0.0631194i | ||||
\(754\) | 11.6569 | − | 20.1903i | 0.424518 | − | 0.735286i | ||||
\(755\) | −11.3137 | −0.411748 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.65685 | 0.132911 | 0.0664553 | − | 0.997789i | \(-0.478831\pi\) | ||||
0.0664553 | + | 0.997789i | \(0.478831\pi\) | |||||||
\(758\) | 17.2426 | − | 29.8651i | 0.626281 | − | 1.08475i | ||||
\(759\) | −1.65685 | − | 2.86976i | −0.0601400 | − | 0.104166i | ||||
\(760\) | 0.292893 | + | 0.507306i | 0.0106244 | + | 0.0184019i | ||||
\(761\) | −11.1924 | + | 19.3858i | −0.405724 | + | 0.702734i | −0.994405 | − | 0.105631i | \(-0.966314\pi\) |
0.588682 | + | 0.808365i | \(0.299647\pi\) | |||||||
\(762\) | −9.65685 | −0.349831 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 10.1421 | 0.366930 | ||||||||
\(765\) | −11.1924 | + | 19.3858i | −0.404662 | + | 0.700895i | ||||
\(766\) | −16.2426 | − | 28.1331i | −0.586870 | − | 1.01649i | ||||
\(767\) | 20.7279 | + | 35.9018i | 0.748442 | + | 1.29634i | ||||
\(768\) | −1.70711 | + | 2.95680i | −0.0615999 | + | 0.106694i | ||||
\(769\) | 19.5563 | 0.705220 | 0.352610 | − | 0.935770i | \(-0.385294\pi\) | ||||
0.352610 | + | 0.935770i | \(0.385294\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −33.7990 | −1.21724 | ||||||||
\(772\) | −2.82843 | + | 4.89898i | −0.101797 | + | 0.176318i | ||||
\(773\) | 1.00000 | + | 1.73205i | 0.0359675 | + | 0.0622975i | 0.883449 | − | 0.468528i | \(-0.155215\pi\) |
−0.847481 | + | 0.530825i | \(0.821882\pi\) | |||||||
\(774\) | −38.2132 | − | 66.1872i | −1.37355 | − | 2.37905i | ||||
\(775\) | 1.41421 | − | 2.44949i | 0.0508001 | − | 0.0879883i | ||||
\(776\) | 7.75736 | 0.278473 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −28.1421 | −1.00894 | ||||||||
\(779\) | 0.899495 | − | 1.55797i | 0.0322278 | − | 0.0558201i | ||||
\(780\) | 8.24264 | + | 14.2767i | 0.295134 | + | 0.511187i | ||||
\(781\) | −1.85786 | − | 3.21792i | −0.0664796 | − | 0.115146i | ||||
\(782\) | −1.51472 | + | 2.62357i | −0.0541662 | + | 0.0938187i | ||||
\(783\) | −93.2548 | −3.33266 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.48528 | 0.231470 | ||||||||
\(786\) | −10.6569 | + | 18.4582i | −0.380117 | + | 0.658383i | ||||
\(787\) | 0.636039 | + | 1.10165i | 0.0226723 | + | 0.0392696i | 0.877139 | − | 0.480237i | \(-0.159449\pi\) |
−0.854467 | + | 0.519506i | \(0.826116\pi\) | |||||||
\(788\) | 12.8995 | + | 22.3426i | 0.459525 | + | 0.795921i | ||||
\(789\) | −47.7990 | + | 82.7903i | −1.70169 | + | 2.94741i | ||||
\(790\) | 6.82843 | 0.242945 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 7.17157 | 0.254831 | ||||||||
\(793\) | 22.4853 | − | 38.9456i | 0.798476 | − | 1.38300i | ||||
\(794\) | 16.8995 | + | 29.2708i | 0.599741 | + | 1.03878i | ||||
\(795\) | −11.0711 | − | 19.1757i | −0.392650 | − | 0.680090i | ||||
\(796\) | −8.24264 | + | 14.2767i | −0.292153 | + | 0.506023i | ||||
\(797\) | −41.7990 | −1.48060 | −0.740298 | − | 0.672279i | \(-0.765316\pi\) | ||||
−0.740298 | + | 0.672279i | \(0.765316\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.3726 | 0.473088 | ||||||||
\(800\) | 0.500000 | − | 0.866025i | 0.0176777 | − | 0.0306186i | ||||
\(801\) | −55.0919 | − | 95.4219i | −1.94658 | − | 3.37157i | ||||
\(802\) | −3.00000 | − | 5.19615i | −0.105934 | − | 0.183483i | ||||
\(803\) | −3.89949 | + | 6.75412i | −0.137610 | + | 0.238348i | ||||
\(804\) | 5.65685 | 0.199502 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −13.6569 | −0.481042 | ||||||||
\(807\) | −31.5563 | + | 54.6572i | −1.11084 | + | 1.92402i | ||||
\(808\) | 6.65685 | + | 11.5300i | 0.234187 | + | 0.405624i | ||||
\(809\) | −1.51472 | − | 2.62357i | −0.0532547 | − | 0.0922398i | 0.838169 | − | 0.545410i | \(-0.183626\pi\) |
−0.891424 | + | 0.453171i | \(0.850293\pi\) | |||||||
\(810\) | 19.9853 | − | 34.6155i | 0.702211 | − | 1.21627i | ||||
\(811\) | 32.5858 | 1.14424 | 0.572121 | − | 0.820169i | \(-0.306121\pi\) | ||||
0.572121 | + | 0.820169i | \(0.306121\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 40.9706 | 1.43690 | ||||||||
\(814\) | 3.17157 | − | 5.49333i | 0.111164 | − | 0.192541i | ||||
\(815\) | 10.0711 | + | 17.4436i | 0.352774 | + | 0.611023i | ||||
\(816\) | −4.41421 | − | 7.64564i | −0.154528 | − | 0.267651i | ||||
\(817\) | 2.58579 | − | 4.47871i | 0.0904652 | − | 0.156690i | ||||
\(818\) | 10.5858 | 0.370123 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.07107 | −0.107246 | ||||||||
\(821\) | −8.65685 | + | 14.9941i | −0.302126 | + | 0.523298i | −0.976617 | − | 0.214985i | \(-0.931030\pi\) |
0.674491 | + | 0.738283i | \(0.264363\pi\) | |||||||
\(822\) | −27.3137 | − | 47.3087i | −0.952675 | − | 1.65008i | ||||
\(823\) | −10.1421 | − | 17.5667i | −0.353533 | − | 0.612336i | 0.633333 | − | 0.773879i | \(-0.281686\pi\) |
−0.986866 | + | 0.161543i | \(0.948353\pi\) | |||||||
\(824\) | −7.41421 | + | 12.8418i | −0.258286 | + | 0.447365i | ||||
\(825\) | −2.82843 | −0.0984732 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.37258 | −0.186823 | −0.0934115 | − | 0.995628i | \(-0.529777\pi\) | ||||
−0.0934115 | + | 0.995628i | \(0.529777\pi\) | |||||||
\(828\) | 5.07107 | − | 8.78335i | 0.176232 | − | 0.305242i | ||||
\(829\) | 2.51472 | + | 4.35562i | 0.0873398 | + | 0.151277i | 0.906386 | − | 0.422451i | \(-0.138830\pi\) |
−0.819046 | + | 0.573728i | \(0.805497\pi\) | |||||||
\(830\) | −1.12132 | − | 1.94218i | −0.0389216 | − | 0.0674142i | ||||
\(831\) | 13.8995 | − | 24.0746i | 0.482168 | − | 0.835140i | ||||
\(832\) | −4.82843 | −0.167396 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −67.9411 | −2.35261 | ||||||||
\(835\) | −7.89949 | + | 13.6823i | −0.273373 | + | 0.473496i | ||||
\(836\) | 0.242641 | + | 0.420266i | 0.00839190 | + | 0.0145352i | ||||
\(837\) | 27.3137 | + | 47.3087i | 0.944100 | + | 1.63523i | ||||
\(838\) | −10.4350 | + | 18.0740i | −0.360472 | + | 0.624356i | ||||
\(839\) | −42.1421 | −1.45491 | −0.727454 | − | 0.686156i | \(-0.759297\pi\) | ||||
−0.727454 | + | 0.686156i | \(0.759297\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.68629 | −0.196079 | ||||||||
\(842\) | 8.65685 | − | 14.9941i | 0.298335 | − | 0.516731i | ||||
\(843\) | −13.6569 | − | 23.6544i | −0.470367 | − | 0.814700i | ||||
\(844\) | −9.31371 | − | 16.1318i | −0.320591 | − | 0.555280i | ||||
\(845\) | −5.15685 | + | 8.93193i | −0.177401 | + | 0.307268i | ||||
\(846\) | −44.7696 | −1.53921 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.48528 | 0.222705 | ||||||||
\(849\) | 3.82843 | − | 6.63103i | 0.131391 | − | 0.227576i | ||||
\(850\) | 1.29289 | + | 2.23936i | 0.0443459 | + | 0.0768093i | ||||
\(851\) | −4.48528 | − | 7.76874i | −0.153753 | − | 0.266309i | ||||
\(852\) | 7.65685 | − | 13.2621i | 0.262320 | − | 0.454351i | ||||
\(853\) | −43.1716 | −1.47817 | −0.739083 | − | 0.673614i | \(-0.764741\pi\) | ||||
−0.739083 | + | 0.673614i | \(0.764741\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.07107 | 0.173427 | ||||||||
\(856\) | 4.82843 | − | 8.36308i | 0.165032 | − | 0.285844i | ||||
\(857\) | 2.46447 | + | 4.26858i | 0.0841846 | + | 0.145812i | 0.905043 | − | 0.425319i | \(-0.139838\pi\) |
−0.820859 | + | 0.571131i | \(0.806505\pi\) | |||||||
\(858\) | 6.82843 | + | 11.8272i | 0.233119 | + | 0.403773i | ||||
\(859\) | 3.60660 | − | 6.24682i | 0.123056 | − | 0.213139i | −0.797916 | − | 0.602769i | \(-0.794064\pi\) |
0.920971 | + | 0.389631i | \(0.127397\pi\) | |||||||
\(860\) | −8.82843 | −0.301047 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 22.3431 | 0.761011 | ||||||||
\(863\) | 2.48528 | − | 4.30463i | 0.0846000 | − | 0.146531i | −0.820621 | − | 0.571473i | \(-0.806372\pi\) |
0.905221 | + | 0.424942i | \(0.139705\pi\) | |||||||
\(864\) | 9.65685 | + | 16.7262i | 0.328533 | + | 0.569036i | ||||
\(865\) | 4.41421 | + | 7.64564i | 0.150088 | + | 0.259960i | ||||
\(866\) | 5.29289 | − | 9.16756i | 0.179860 | − | 0.311526i | ||||
\(867\) | −35.2132 | −1.19590 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.65685 | 0.191896 | ||||||||
\(870\) | −8.24264 | + | 14.2767i | −0.279452 | + | 0.484025i | ||||
\(871\) | 4.00000 | + | 6.92820i | 0.135535 | + | 0.234753i | ||||
\(872\) | 1.24264 | + | 2.15232i | 0.0420811 | + | 0.0728866i | ||||
\(873\) | 33.5772 | − | 58.1574i | 1.13641 | − | 1.96833i | ||||
\(874\) | 0.686292 | 0.0232142 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −32.1421 | −1.08598 | ||||||||
\(877\) | 15.1421 | − | 26.2269i | 0.511314 | − | 0.885621i | −0.488600 | − | 0.872508i | \(-0.662492\pi\) |
0.999914 | − | 0.0131135i | \(-0.00417426\pi\) | |||||||
\(878\) | −12.4853 | − | 21.6251i | −0.421358 | − | 0.729813i | ||||
\(879\) | 14.2426 | + | 24.6690i | 0.480392 | + | 0.832064i | ||||
\(880\) | 0.414214 | − | 0.717439i | 0.0139631 | − | 0.0241849i | ||||
\(881\) | −2.38478 | −0.0803452 | −0.0401726 | − | 0.999193i | \(-0.512791\pi\) | ||||
−0.0401726 | + | 0.999193i | \(0.512791\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −41.6569 | −1.40186 | −0.700932 | − | 0.713228i | \(-0.747233\pi\) | ||||
−0.700932 | + | 0.713228i | \(0.747233\pi\) | |||||||
\(884\) | 6.24264 | − | 10.8126i | 0.209963 | − | 0.363666i | ||||
\(885\) | −14.6569 | − | 25.3864i | −0.492685 | − | 0.853355i | ||||
\(886\) | 1.51472 | + | 2.62357i | 0.0508880 | + | 0.0881405i | ||||
\(887\) | 27.5563 | − | 47.7290i | 0.925252 | − | 1.60258i | 0.134096 | − | 0.990968i | \(-0.457187\pi\) |
0.791156 | − | 0.611614i | \(-0.209480\pi\) | |||||||
\(888\) | 26.1421 | 0.877273 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −12.7279 | −0.426641 | ||||||||
\(891\) | 16.5563 | − | 28.6764i | 0.554659 | − | 0.960697i | ||||
\(892\) | 3.65685 | + | 6.33386i | 0.122441 | + | 0.212073i | ||||
\(893\) | −1.51472 | − | 2.62357i | −0.0506881 | − | 0.0877944i | ||||
\(894\) | −10.2426 | + | 17.7408i | −0.342565 | + | 0.593340i | ||||
\(895\) | 4.00000 | 0.133705 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 19.3137 | 0.644866 | ||||||||
\(898\) | −8.31371 | + | 14.3998i | −0.277432 | + | 0.480526i | ||||
\(899\) | −6.82843 | − | 11.8272i | −0.227741 | − | 0.394459i | ||||
\(900\) | −4.32843 | − | 7.49706i | −0.144281 | − | 0.249902i | ||||
\(901\) | −8.38478 | + | 14.5229i | −0.279337 | + | 0.483827i | ||||
\(902\) | −2.54416 | −0.0847111 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 15.3137 | 0.509326 | ||||||||
\(905\) | 1.24264 | − | 2.15232i | 0.0413068 | − | 0.0715454i | ||||
\(906\) | −19.3137 | − | 33.4523i | −0.641655 | − | 1.11138i | ||||
\(907\) | −0.142136 | − | 0.246186i | −0.00471954 | − | 0.00817448i | 0.863656 | − | 0.504082i | \(-0.168169\pi\) |
−0.868376 | + | 0.495907i | \(0.834836\pi\) | |||||||
\(908\) | −9.12132 | + | 15.7986i | −0.302702 | + | 0.524295i | ||||
\(909\) | 115.255 | 3.82276 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36.2843 | 1.20215 | 0.601076 | − | 0.799192i | \(-0.294739\pi\) | ||||
0.601076 | + | 0.799192i | \(0.294739\pi\) | |||||||
\(912\) | −1.00000 | + | 1.73205i | −0.0331133 | + | 0.0573539i | ||||
\(913\) | −0.928932 | − | 1.60896i | −0.0307432 | − | 0.0532487i | ||||
\(914\) | 10.8284 | + | 18.7554i | 0.358173 | + | 0.620373i | ||||
\(915\) | −15.8995 | + | 27.5387i | −0.525621 | + | 0.910402i | ||||
\(916\) | −16.1421 | −0.533351 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −49.9411 | −1.64830 | ||||||||
\(919\) | −7.75736 | + | 13.4361i | −0.255892 | + | 0.443217i | −0.965137 | − | 0.261744i | \(-0.915702\pi\) |
0.709246 | + | 0.704961i | \(0.249036\pi\) | |||||||
\(920\) | −0.585786 | − | 1.01461i | −0.0193128 | − | 0.0334508i | ||||
\(921\) | −25.4853 | − | 44.1418i | −0.839769 | − | 1.45452i | ||||
\(922\) | −6.41421 | + | 11.1097i | −0.211241 | + | 0.365880i | ||||
\(923\) | 21.6569 | 0.712844 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.65685 | −0.251756 | ||||||||
\(926\) | −8.48528 | + | 14.6969i | −0.278844 | + | 0.482971i | ||||
\(927\) | 64.1838 | + | 111.170i | 2.10807 | + | 3.65129i | ||||
\(928\) | −2.41421 | − | 4.18154i | −0.0792504 | − | 0.137266i | ||||
\(929\) | 8.60660 | − | 14.9071i | 0.282373 | − | 0.489085i | −0.689595 | − | 0.724195i | \(-0.742212\pi\) |
0.971969 | + | 0.235110i | \(0.0755449\pi\) | |||||||
\(930\) | 9.65685 | 0.316661 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 23.3137 | 0.763666 | ||||||||
\(933\) | −6.82843 | + | 11.8272i | −0.223553 | + | 0.387205i | ||||
\(934\) | −7.94975 | − | 13.7694i | −0.260124 | − | 0.450547i | ||||
\(935\) | 1.07107 | + | 1.85514i | 0.0350277 | + | 0.0606697i | ||||
\(936\) | −20.8995 | + | 36.1990i | −0.683121 | + | 1.18320i | ||||
\(937\) | 20.2426 | 0.661298 | 0.330649 | − | 0.943754i | \(-0.392732\pi\) | ||||
0.330649 | + | 0.943754i | \(0.392732\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 49.1127 | 1.60273 | ||||||||
\(940\) | −2.58579 | + | 4.47871i | −0.0843391 | + | 0.146080i | ||||
\(941\) | 25.0000 | + | 43.3013i | 0.814977 | + | 1.41158i | 0.909345 | + | 0.416044i | \(0.136584\pi\) |
−0.0943679 | + | 0.995537i | \(0.530083\pi\) | |||||||
\(942\) | 11.0711 | + | 19.1757i | 0.360715 | + | 0.624777i | ||||
\(943\) | −1.79899 | + | 3.11594i | −0.0585832 | + | 0.101469i | ||||
\(944\) | 8.58579 | 0.279444 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.31371 | −0.237789 | ||||||||
\(947\) | 2.41421 | − | 4.18154i | 0.0784514 | − | 0.135882i | −0.824131 | − | 0.566400i | \(-0.808336\pi\) |
0.902582 | + | 0.430518i | \(0.141669\pi\) | |||||||
\(948\) | 11.6569 | + | 20.1903i | 0.378597 | + | 0.655749i | ||||
\(949\) | −22.7279 | − | 39.3659i | −0.737780 | − | 1.27787i | ||||
\(950\) | 0.292893 | − | 0.507306i | 0.00950271 | − | 0.0164592i | ||||
\(951\) | 35.7990 | 1.16086 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.343146 | 0.0111156 | 0.00555779 | − | 0.999985i | \(-0.498231\pi\) | ||||
0.00555779 | + | 0.999985i | \(0.498231\pi\) | |||||||
\(954\) | 28.0711 | − | 48.6205i | 0.908834 | − | 1.57415i | ||||
\(955\) | −5.07107 | − | 8.78335i | −0.164096 | − | 0.284222i | ||||
\(956\) | −0.828427 | − | 1.43488i | −0.0267932 | − | 0.0464073i | ||||
\(957\) | −6.82843 | + | 11.8272i | −0.220732 | + | 0.382319i | ||||
\(958\) | 17.1716 | 0.554788 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 3.41421 | 0.110193 | ||||||||
\(961\) | 11.5000 | − | 19.9186i | 0.370968 | − | 0.642535i | ||||
\(962\) | 18.4853 | + | 32.0174i | 0.595989 | + | 1.03228i | ||||
\(963\) | −41.7990 | − | 72.3980i | −1.34695 | − | 2.33299i | ||||
\(964\) | 6.70711 | − | 11.6170i | 0.216021 | − | 0.374160i | ||||
\(965\) | 5.65685 | 0.182101 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.4558 | −1.20450 | −0.602249 | − | 0.798308i | \(-0.705729\pi\) | ||||
−0.602249 | + | 0.798308i | \(0.705729\pi\) | |||||||
\(968\) | −5.15685 | + | 8.93193i | −0.165748 | + | 0.287083i | ||||
\(969\) | −2.58579 | − | 4.47871i | −0.0830674 | − | 0.143877i | ||||
\(970\) | −3.87868 | − | 6.71807i | −0.124537 | − | 0.215704i | ||||
\(971\) | 16.6777 | − | 28.8866i | 0.535212 | − | 0.927014i | −0.463941 | − | 0.885866i | \(-0.653565\pi\) |
0.999153 | − | 0.0411482i | \(-0.0131016\pi\) | |||||||
\(972\) | 78.5269 | 2.51875 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −31.7990 | −1.01891 | ||||||||
\(975\) | 8.24264 | − | 14.2767i | 0.263976 | − | 0.457219i | ||||
\(976\) | −4.65685 | − | 8.06591i | −0.149062 | − | 0.258183i | ||||
\(977\) | 6.34315 | + | 10.9867i | 0.202935 | + | 0.351494i | 0.949473 | − | 0.313849i | \(-0.101619\pi\) |
−0.746538 | + | 0.665343i | \(0.768285\pi\) | |||||||
\(978\) | −34.3848 | + | 59.5562i | −1.09950 | + | 1.90440i | ||||
\(979\) | −10.5442 | −0.336993 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 21.5147 | 0.686912 | ||||||||
\(982\) | 16.1421 | − | 27.9590i | 0.515116 | − | 0.892208i | ||||
\(983\) | 6.10051 | + | 10.5664i | 0.194576 | + | 0.337015i | 0.946761 | − | 0.321936i | \(-0.104334\pi\) |
−0.752186 | + | 0.658951i | \(0.771000\pi\) | |||||||
\(984\) | −5.24264 | − | 9.08052i | −0.167129 | − | 0.289476i | ||||
\(985\) | 12.8995 | − | 22.3426i | 0.411012 | − | 0.711894i | ||||
\(986\) | 12.4853 | 0.397612 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.82843 | −0.0899843 | ||||||||
\(989\) | −5.17157 | + | 8.95743i | −0.164446 | + | 0.284830i | ||||
\(990\) | −3.58579 | − | 6.21076i | −0.113964 | − | 0.197391i | ||||
\(991\) | −22.3848 | − | 38.7716i | −0.711076 | − | 1.23162i | −0.964454 | − | 0.264252i | \(-0.914875\pi\) |
0.253378 | − | 0.967367i | \(-0.418458\pi\) | |||||||
\(992\) | −1.41421 | + | 2.44949i | −0.0449013 | + | 0.0777714i | ||||
\(993\) | 115.397 | 3.66201 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.4853 | 0.522619 | ||||||||
\(996\) | 3.82843 | − | 6.63103i | 0.121308 | − | 0.210112i | ||||
\(997\) | 9.14214 | + | 15.8346i | 0.289534 | + | 0.501488i | 0.973699 | − | 0.227840i | \(-0.0731662\pi\) |
−0.684164 | + | 0.729328i | \(0.739833\pi\) | |||||||
\(998\) | 15.1716 | + | 26.2779i | 0.480248 | + | 0.831813i | ||||
\(999\) | 73.9411 | − | 128.070i | 2.33939 | − | 4.05195i |
(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 | 490.2.e.i.471.1 | 4 | ||
7.2 | even | 3 | 490.2.a.m.1.2 | yes | 2 | ||
7.3 | odd | 6 | 490.2.e.j.361.2 | 4 | |||
7.4 | even | 3 | inner | 490.2.e.i.361.1 | 4 | ||
7.5 | odd | 6 | 490.2.a.l.1.1 | ✓ | 2 | ||
7.6 | odd | 2 | 490.2.e.j.471.2 | 4 | |||
21.2 | odd | 6 | 4410.2.a.bt.1.2 | 2 | |||
21.5 | even | 6 | 4410.2.a.by.1.2 | 2 | |||
28.19 | even | 6 | 3920.2.a.ca.1.2 | 2 | |||
28.23 | odd | 6 | 3920.2.a.bm.1.1 | 2 | |||
35.2 | odd | 12 | 2450.2.c.t.99.1 | 4 | |||
35.9 | even | 6 | 2450.2.a.bn.1.1 | 2 | |||
35.12 | even | 12 | 2450.2.c.w.99.2 | 4 | |||
35.19 | odd | 6 | 2450.2.a.bs.1.2 | 2 | |||
35.23 | odd | 12 | 2450.2.c.t.99.4 | 4 | |||
35.33 | even | 12 | 2450.2.c.w.99.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
490.2.a.l.1.1 | ✓ | 2 | 7.5 | odd | 6 | ||
490.2.a.m.1.2 | yes | 2 | 7.2 | even | 3 | ||
490.2.e.i.361.1 | 4 | 7.4 | even | 3 | inner | ||
490.2.e.i.471.1 | 4 | 1.1 | even | 1 | trivial | ||
490.2.e.j.361.2 | 4 | 7.3 | odd | 6 | |||
490.2.e.j.471.2 | 4 | 7.6 | odd | 2 | |||
2450.2.a.bn.1.1 | 2 | 35.9 | even | 6 | |||
2450.2.a.bs.1.2 | 2 | 35.19 | odd | 6 | |||
2450.2.c.t.99.1 | 4 | 35.2 | odd | 12 | |||
2450.2.c.t.99.4 | 4 | 35.23 | odd | 12 | |||
2450.2.c.w.99.2 | 4 | 35.12 | even | 12 | |||
2450.2.c.w.99.3 | 4 | 35.33 | even | 12 | |||
3920.2.a.bm.1.1 | 2 | 28.23 | odd | 6 | |||
3920.2.a.ca.1.2 | 2 | 28.19 | even | 6 | |||
4410.2.a.bt.1.2 | 2 | 21.2 | odd | 6 | |||
4410.2.a.by.1.2 | 2 | 21.5 | even | 6 |