Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [27,6,Mod(10,27)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(27, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("27.10");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 27 = 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 27.c (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: | \(4.33036313495\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 40x^{6} + 568x^{4} + 3363x^{2} + 7056 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{8} \) |
Twist minimal: | no (minimal twist has level 9) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 10.2 | ||
Root | \(-3.84183i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 27.10 |
Dual form | 27.6.c.a.19.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/27\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.78978 | − | 3.09998i | −0.316391 | − | 0.548005i | 0.663341 | − | 0.748317i | \(-0.269138\pi\) |
−0.979732 | + | 0.200312i | \(0.935804\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 9.59340 | − | 16.6162i | 0.299794 | − | 0.519258i | ||||
\(5\) | −4.05388 | + | 7.02152i | −0.0725179 | + | 0.125605i | −0.900004 | − | 0.435881i | \(-0.856437\pi\) |
0.827486 | + | 0.561486i | \(0.189770\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −87.7139 | − | 151.925i | −0.676587 | − | 1.17188i | −0.976002 | − | 0.217760i | \(-0.930125\pi\) |
0.299416 | − | 0.954123i | \(-0.403208\pi\) | |||||||
\(8\) | −183.226 | −1.01219 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 29.0221 | 0.0917761 | ||||||||
\(11\) | −206.795 | − | 358.179i | −0.515298 | − | 0.892522i | −0.999842 | − | 0.0177554i | \(-0.994348\pi\) |
0.484545 | − | 0.874767i | \(-0.338985\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −61.8514 | + | 107.130i | −0.101506 | + | 0.175813i | −0.912305 | − | 0.409511i | \(-0.865699\pi\) |
0.810799 | + | 0.585324i | \(0.199033\pi\) | |||||||
\(14\) | −313.977 | + | 543.824i | −0.428132 | + | 0.741546i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 20.9448 | + | 36.2775i | 0.0204539 | + | 0.0354273i | ||||
\(17\) | 2223.70 | 1.86618 | 0.933092 | − | 0.359638i | \(-0.117100\pi\) | ||||
0.933092 | + | 0.359638i | \(0.117100\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 891.313 | 0.566430 | 0.283215 | − | 0.959056i | \(-0.408599\pi\) | ||||
0.283215 | + | 0.959056i | \(0.408599\pi\) | |||||||
\(20\) | 77.7809 | + | 134.720i | 0.0434808 | + | 0.0753110i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −740.234 | + | 1282.12i | −0.326071 | + | 0.564772i | ||||
\(23\) | −293.902 | + | 509.053i | −0.115846 | + | 0.200652i | −0.918118 | − | 0.396308i | \(-0.870291\pi\) |
0.802271 | + | 0.596960i | \(0.203625\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1529.63 | + | 2649.40i | 0.489482 | + | 0.847808i | ||||
\(26\) | 442.801 | 0.128462 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3365.90 | −0.811346 | ||||||||
\(29\) | −2467.97 | − | 4274.65i | −0.544936 | − | 0.943856i | −0.998611 | − | 0.0526894i | \(-0.983221\pi\) |
0.453675 | − | 0.891167i | \(-0.350113\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2832.69 | − | 4906.37i | 0.529414 | − | 0.916971i | −0.469998 | − | 0.882668i | \(-0.655745\pi\) |
0.999411 | − | 0.0343037i | \(-0.0109213\pi\) | |||||||
\(32\) | −2856.64 | + | 4947.85i | −0.493152 | + | 0.854164i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3979.93 | − | 6893.45i | −0.590444 | − | 1.02268i | ||||
\(35\) | 1422.33 | 0.196259 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1204.25 | 0.144614 | 0.0723071 | − | 0.997382i | \(-0.476964\pi\) | ||||
0.0723071 | + | 0.997382i | \(0.476964\pi\) | |||||||
\(38\) | −1595.25 | − | 2763.06i | −0.179213 | − | 0.310407i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 742.775 | − | 1286.52i | 0.0734019 | − | 0.127136i | ||||
\(41\) | 1194.48 | − | 2068.90i | 0.110973 | − | 0.192212i | −0.805190 | − | 0.593018i | \(-0.797936\pi\) |
0.916163 | + | 0.400806i | \(0.131270\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2885.71 | + | 4998.19i | 0.238002 | + | 0.412232i | 0.960141 | − | 0.279516i | \(-0.0901741\pi\) |
−0.722139 | + | 0.691748i | \(0.756841\pi\) | |||||||
\(44\) | −7935.46 | −0.617932 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2104.08 | 0.146611 | ||||||||
\(47\) | 3532.81 | + | 6119.00i | 0.233279 | + | 0.404051i | 0.958771 | − | 0.284180i | \(-0.0917212\pi\) |
−0.725492 | + | 0.688230i | \(0.758388\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6983.97 | + | 12096.6i | −0.415539 | + | 0.719735i | ||||
\(50\) | 5475.40 | − | 9483.67i | 0.309735 | − | 0.536478i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1186.73 | + | 2055.48i | 0.0608616 | + | 0.105415i | ||||
\(53\) | 11521.6 | 0.563406 | 0.281703 | − | 0.959502i | \(-0.409101\pi\) | ||||
0.281703 | + | 0.959502i | \(0.409101\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3353.28 | 0.149473 | ||||||||
\(56\) | 16071.5 | + | 27836.6i | 0.684834 | + | 1.18617i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8834.24 | + | 15301.4i | −0.344825 | + | 0.597255i | ||||
\(59\) | 4876.49 | − | 8446.33i | 0.182380 | − | 0.315892i | −0.760310 | − | 0.649560i | \(-0.774953\pi\) |
0.942691 | + | 0.333668i | \(0.108287\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 932.881 | + | 1615.80i | 0.0320997 | + | 0.0555984i | 0.881629 | − | 0.471943i | \(-0.156447\pi\) |
−0.849529 | + | 0.527542i | \(0.823114\pi\) | |||||||
\(62\) | −20279.5 | −0.670006 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 21791.5 | 0.665023 | ||||||||
\(65\) | −501.476 | − | 868.582i | −0.0147220 | − | 0.0254992i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 19671.5 | − | 34072.0i | 0.535366 | − | 0.927281i | −0.463780 | − | 0.885950i | \(-0.653507\pi\) |
0.999146 | − | 0.0413301i | \(-0.0131595\pi\) | |||||||
\(68\) | 21332.9 | − | 36949.6i | 0.559470 | − | 0.969031i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2545.65 | − | 4409.19i | −0.0620945 | − | 0.107551i | ||||
\(71\) | −43602.4 | −1.02651 | −0.513257 | − | 0.858235i | \(-0.671561\pi\) | ||||
−0.513257 | + | 0.858235i | \(0.671561\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −52142.6 | −1.14521 | −0.572605 | − | 0.819831i | \(-0.694067\pi\) | ||||
−0.572605 | + | 0.819831i | \(0.694067\pi\) | |||||||
\(74\) | −2155.33 | − | 3733.15i | −0.0457546 | − | 0.0792494i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8550.72 | − | 14810.3i | 0.169812 | − | 0.294123i | ||||
\(77\) | −36277.6 | + | 62834.6i | −0.697287 | + | 1.20774i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −25384.2 | − | 43966.8i | −0.457611 | − | 0.792605i | 0.541223 | − | 0.840879i | \(-0.317961\pi\) |
−0.998834 | + | 0.0482737i | \(0.984628\pi\) | |||||||
\(80\) | −339.631 | −0.00593311 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8551.41 | −0.140444 | ||||||||
\(83\) | −27810.6 | − | 48169.3i | −0.443113 | − | 0.767494i | 0.554806 | − | 0.831980i | \(-0.312793\pi\) |
−0.997919 | + | 0.0644858i | \(0.979459\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9014.62 | + | 15613.8i | −0.135332 | + | 0.234402i | ||||
\(86\) | 10329.5 | − | 17891.3i | 0.150604 | − | 0.260853i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 37890.2 | + | 65627.7i | 0.521579 | + | 0.903401i | ||||
\(89\) | 46554.3 | 0.622996 | 0.311498 | − | 0.950247i | \(-0.399169\pi\) | ||||
0.311498 | + | 0.950247i | \(0.399169\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 21700.9 | 0.274710 | ||||||||
\(92\) | 5639.04 | + | 9767.10i | 0.0694601 | + | 0.120308i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 12645.9 | − | 21903.3i | 0.147615 | − | 0.255676i | ||||
\(95\) | −3613.27 | + | 6258.38i | −0.0410764 | + | 0.0711463i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 21616.0 | + | 37440.1i | 0.233264 | + | 0.404024i | 0.958767 | − | 0.284195i | \(-0.0917262\pi\) |
−0.725503 | + | 0.688219i | \(0.758393\pi\) | |||||||
\(98\) | 49999.0 | 0.525891 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 58697.5 | 0.586975 | ||||||||
\(101\) | 37727.5 | + | 65345.9i | 0.368005 | + | 0.637404i | 0.989254 | − | 0.146210i | \(-0.0467075\pi\) |
−0.621248 | + | 0.783614i | \(0.713374\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −50758.5 | + | 87916.3i | −0.471428 | + | 0.816538i | −0.999466 | − | 0.0326834i | \(-0.989595\pi\) |
0.528038 | + | 0.849221i | \(0.322928\pi\) | |||||||
\(104\) | 11332.8 | − | 19629.0i | 0.102743 | − | 0.177956i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −20621.0 | − | 35716.7i | −0.178257 | − | 0.308750i | ||||
\(107\) | 178800. | 1.50976 | 0.754882 | − | 0.655860i | \(-0.227694\pi\) | ||||
0.754882 | + | 0.655860i | \(0.227694\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −37985.3 | −0.306231 | −0.153116 | − | 0.988208i | \(-0.548931\pi\) | ||||
−0.153116 | + | 0.988208i | \(0.548931\pi\) | |||||||
\(110\) | −6001.63 | − | 10395.1i | −0.0472920 | − | 0.0819121i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3674.31 | − | 6364.09i | 0.0276777 | − | 0.0479392i | ||||
\(113\) | −100834. | + | 174650.i | −0.742867 | + | 1.28668i | 0.208318 | + | 0.978061i | \(0.433201\pi\) |
−0.951185 | + | 0.308622i | \(0.900132\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2382.88 | − | 4127.28i | −0.0168019 | − | 0.0291017i | ||||
\(116\) | −94705.0 | −0.653473 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −34911.3 | −0.230814 | ||||||||
\(119\) | −195050. | − | 337836.i | −1.26264 | − | 2.18695i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5002.82 | + | 8665.14i | −0.0310636 | + | 0.0538037i | ||||
\(122\) | 3339.30 | − | 5783.83i | 0.0203121 | − | 0.0351816i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −54350.3 | − | 94137.4i | −0.317430 | − | 0.549804i | ||||
\(125\) | −50140.5 | −0.287021 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 255248. | 1.40428 | 0.702138 | − | 0.712041i | \(-0.252229\pi\) | ||||
0.702138 | + | 0.712041i | \(0.252229\pi\) | |||||||
\(128\) | 52410.6 | + | 90777.9i | 0.282745 | + | 0.489728i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1795.06 | + | 3109.14i | −0.00931581 | + | 0.0161355i | ||||
\(131\) | 16914.0 | − | 29295.9i | 0.0861129 | − | 0.149152i | −0.819752 | − | 0.572719i | \(-0.805889\pi\) |
0.905865 | + | 0.423567i | \(0.139222\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −78180.6 | − | 135413.i | −0.383239 | − | 0.663790i | ||||
\(134\) | −140830. | −0.677539 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −407440. | −1.88893 | ||||||||
\(137\) | 93918.5 | + | 162672.i | 0.427514 | + | 0.740475i | 0.996651 | − | 0.0817669i | \(-0.0260563\pi\) |
−0.569138 | + | 0.822242i | \(0.692723\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 169712. | − | 293951.i | 0.745035 | − | 1.29044i | −0.205144 | − | 0.978732i | \(-0.565766\pi\) |
0.950178 | − | 0.311706i | \(-0.100901\pi\) | |||||||
\(140\) | 13644.9 | − | 23633.7i | 0.0588371 | − | 0.101909i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 78038.6 | + | 135167.i | 0.324780 | + | 0.562535i | ||||
\(143\) | 51162.2 | 0.209223 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 40019.4 | 0.158070 | ||||||||
\(146\) | 93323.6 | + | 161641.i | 0.362334 | + | 0.627581i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 11552.8 | − | 20010.1i | 0.0433544 | − | 0.0750921i | ||||
\(149\) | 193953. | − | 335937.i | 0.715700 | − | 1.23963i | −0.246988 | − | 0.969018i | \(-0.579441\pi\) |
0.962689 | − | 0.270611i | \(-0.0872257\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 138084. | + | 239168.i | 0.492833 | + | 0.853611i | 0.999966 | − | 0.00825649i | \(-0.00262815\pi\) |
−0.507133 | + | 0.861868i | \(0.669295\pi\) | |||||||
\(152\) | −163312. | −0.573335 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 259715. | 0.882461 | ||||||||
\(155\) | 22966.8 | + | 39779.6i | 0.0767840 | + | 0.132994i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −256623. | + | 444485.i | −0.830897 | + | 1.43916i | 0.0664312 | + | 0.997791i | \(0.478839\pi\) |
−0.897328 | + | 0.441364i | \(0.854495\pi\) | |||||||
\(158\) | −90864.2 | + | 157381.i | −0.289568 | + | 0.501546i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −23160.9 | − | 40115.9i | −0.0715247 | − | 0.123884i | ||||
\(161\) | 103117. | 0.313521 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −236294. | −0.696601 | −0.348300 | − | 0.937383i | \(-0.613241\pi\) | ||||
−0.348300 | + | 0.937383i | \(0.613241\pi\) | |||||||
\(164\) | −22918.2 | − | 39695.5i | −0.0665383 | − | 0.115248i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −99549.4 | + | 172425.i | −0.280394 | + | 0.485656i | ||||
\(167\) | 125015. | − | 216533.i | 0.346875 | − | 0.600805i | −0.638818 | − | 0.769358i | \(-0.720576\pi\) |
0.985693 | + | 0.168553i | \(0.0539096\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 177995. | + | 308297.i | 0.479393 | + | 0.830333i | ||||
\(170\) | 64536.6 | 0.171271 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 110735. | 0.285406 | ||||||||
\(173\) | 255819. | + | 443091.i | 0.649856 | + | 1.12558i | 0.983157 | + | 0.182763i | \(0.0585041\pi\) |
−0.333301 | + | 0.942820i | \(0.608163\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 268340. | − | 464779.i | 0.662354 | − | 1.14723i | ||||
\(176\) | 8662.58 | − | 15004.0i | 0.0210797 | − | 0.0365112i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −83321.9 | − | 144318.i | −0.197110 | − | 0.341405i | ||||
\(179\) | −254552. | −0.593806 | −0.296903 | − | 0.954908i | \(-0.595954\pi\) | ||||
−0.296903 | + | 0.954908i | \(0.595954\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −42413.6 | −0.0962296 | −0.0481148 | − | 0.998842i | \(-0.515321\pi\) | ||||
−0.0481148 | + | 0.998842i | \(0.515321\pi\) | |||||||
\(182\) | −38839.8 | − | 67272.5i | −0.0869158 | − | 0.150543i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 53850.4 | − | 93271.7i | 0.117259 | − | 0.203098i | ||||
\(185\) | −4881.87 | + | 8455.64i | −0.0104871 | + | 0.0181642i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −459851. | − | 796485.i | −0.961640 | − | 1.66561i | ||||
\(188\) | 135566. | 0.279742 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 25867.8 | 0.0519847 | ||||||||
\(191\) | −133628. | − | 231451.i | −0.265042 | − | 0.459067i | 0.702532 | − | 0.711652i | \(-0.252053\pi\) |
−0.967575 | + | 0.252585i | \(0.918719\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −127808. | + | 221370.i | −0.246982 | + | 0.427786i | −0.962687 | − | 0.270617i | \(-0.912772\pi\) |
0.715705 | + | 0.698403i | \(0.246106\pi\) | |||||||
\(194\) | 77375.8 | − | 134019.i | 0.147605 | − | 0.255659i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 134000. | + | 232095.i | 0.249152 | + | 0.431544i | ||||
\(197\) | −650944. | −1.19503 | −0.597514 | − | 0.801859i | \(-0.703845\pi\) | ||||
−0.597514 | + | 0.801859i | \(0.703845\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 395656. | 0.708248 | 0.354124 | − | 0.935199i | \(-0.384779\pi\) | ||||
0.354124 | + | 0.935199i | \(0.384779\pi\) | |||||||
\(200\) | −280268. | − | 485439.i | −0.495449 | − | 0.858143i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 135047. | − | 233909.i | 0.232867 | − | 0.403338i | ||||
\(203\) | −432951. | + | 749893.i | −0.737393 | + | 1.27720i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9684.54 | + | 16774.1i | 0.0160951 | + | 0.0278776i | ||||
\(206\) | 363386. | 0.596622 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5181.87 | −0.00830478 | ||||||||
\(209\) | −184319. | − | 319250.i | −0.291880 | − | 0.505551i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −309289. | + | 535705.i | −0.478254 | + | 0.828361i | −0.999689 | − | 0.0249304i | \(-0.992064\pi\) |
0.521435 | + | 0.853291i | \(0.325397\pi\) | |||||||
\(212\) | 110531. | − | 191445.i | 0.168906 | − | 0.292553i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −320013. | − | 554279.i | −0.477676 | − | 0.827359i | ||||
\(215\) | −46793.2 | −0.0690378 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −993866. | −1.43278 | ||||||||
\(218\) | 67985.2 | + | 117754.i | 0.0968888 | + | 0.167816i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 32169.4 | − | 55719.0i | 0.0448112 | − | 0.0776152i | ||||
\(221\) | −137539. | + | 238225.i | −0.189429 | + | 0.328100i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 438618. | + | 759708.i | 0.590642 | + | 1.02302i | 0.994146 | + | 0.108044i | \(0.0344586\pi\) |
−0.403504 | + | 0.914978i | \(0.632208\pi\) | |||||||
\(224\) | 1.00227e6 | 1.33464 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 721881. | 0.940145 | ||||||||
\(227\) | 265882. | + | 460521.i | 0.342471 | + | 0.593177i | 0.984891 | − | 0.173176i | \(-0.0554028\pi\) |
−0.642420 | + | 0.766353i | \(0.722069\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 571507. | − | 989880.i | 0.720167 | − | 1.24737i | −0.240766 | − | 0.970583i | \(-0.577399\pi\) |
0.960933 | − | 0.276782i | \(-0.0892681\pi\) | |||||||
\(230\) | −8529.66 | + | 14773.8i | −0.0106319 | + | 0.0184151i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 452196. | + | 783227.i | 0.551578 | + | 0.955362i | ||||
\(233\) | 818670. | 0.987913 | 0.493957 | − | 0.869487i | \(-0.335550\pi\) | ||||
0.493957 | + | 0.869487i | \(0.335550\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −57286.2 | −0.0676676 | ||||||||
\(236\) | −93564.2 | − | 162058.i | −0.109353 | − | 0.189405i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −698191. | + | 1.20930e6i | −0.798973 | + | 1.38386i | ||||
\(239\) | 94237.4 | − | 163224.i | 0.106716 | − | 0.184837i | −0.807722 | − | 0.589563i | \(-0.799300\pi\) |
0.914438 | + | 0.404726i | \(0.132633\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22511.4 | − | 38990.8i | −0.0249666 | − | 0.0432434i | 0.853272 | − | 0.521466i | \(-0.174615\pi\) |
−0.878239 | + | 0.478222i | \(0.841281\pi\) | |||||||
\(242\) | 35815.7 | 0.0393129 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 35798.0 | 0.0384932 | ||||||||
\(245\) | −56624.3 | − | 98076.1i | −0.0602681 | − | 0.104387i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −55129.0 | + | 95486.2i | −0.0574960 | + | 0.0995860i | ||||
\(248\) | −519022. | + | 898973.i | −0.535867 | + | 0.928149i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 89740.3 | + | 155435.i | 0.0908108 | + | 0.157289i | ||||
\(251\) | 556667. | 0.557713 | 0.278857 | − | 0.960333i | \(-0.410045\pi\) | ||||
0.278857 | + | 0.960333i | \(0.410045\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 243110. | 0.238782 | ||||||||
\(254\) | −456837. | − | 791264.i | −0.444300 | − | 0.769551i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 536270. | − | 928847.i | 0.511427 | − | 0.885818i | ||||
\(257\) | 290077. | − | 502428.i | 0.273956 | − | 0.474505i | −0.695915 | − | 0.718124i | \(-0.745001\pi\) |
0.969871 | + | 0.243618i | \(0.0783345\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −105629. | − | 182955.i | −0.0978441 | − | 0.169471i | ||||
\(260\) | −19243.4 | −0.0176542 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −121089. | −0.108981 | ||||||||
\(263\) | 30271.7 | + | 52432.1i | 0.0269865 | + | 0.0467420i | 0.879203 | − | 0.476447i | \(-0.158076\pi\) |
−0.852217 | + | 0.523189i | \(0.824742\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −46707.0 | + | 80898.9i | −0.0408571 | + | 0.0707665i | ||||
\(266\) | −279852. | + | 484717.i | −0.242507 | + | 0.420034i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −377433. | − | 653733.i | −0.320998 | − | 0.555986i | ||||
\(269\) | −2.17306e6 | −1.83101 | −0.915507 | − | 0.402301i | \(-0.868211\pi\) | ||||
−0.915507 | + | 0.402301i | \(0.868211\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.72652e6 | −1.42806 | −0.714032 | − | 0.700113i | \(-0.753133\pi\) | ||||
−0.714032 | + | 0.700113i | \(0.753133\pi\) | |||||||
\(272\) | 46575.1 | + | 80670.4i | 0.0381708 | + | 0.0661138i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 336186. | − | 582292.i | 0.270523 | − | 0.468559i | ||||
\(275\) | 632640. | − | 1.09577e6i | 0.504458 | − | 0.873747i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −523243. | − | 906283.i | −0.409736 | − | 0.709683i | 0.585124 | − | 0.810944i | \(-0.301046\pi\) |
−0.994860 | + | 0.101260i | \(0.967712\pi\) | |||||||
\(278\) | −1.21499e6 | −0.942889 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −260607. | −0.198651 | ||||||||
\(281\) | 673149. | + | 1.16593e6i | 0.508564 | + | 0.880858i | 0.999951 | + | 0.00991669i | \(0.00315663\pi\) |
−0.491387 | + | 0.870941i | \(0.663510\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −284960. | + | 493565.i | −0.211503 | + | 0.366335i | −0.952185 | − | 0.305521i | \(-0.901169\pi\) |
0.740682 | + | 0.671856i | \(0.234503\pi\) | |||||||
\(284\) | −418295. | + | 724509.i | −0.307742 | + | 0.533025i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −91569.0 | − | 158602.i | −0.0661963 | − | 0.114655i | ||||
\(287\) | −419090. | −0.300333 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.52500e6 | 2.48264 | ||||||||
\(290\) | −71625.8 | − | 124060.i | −0.0500121 | − | 0.0866234i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −500225. | + | 866414.i | −0.343327 | + | 0.594660i | ||||
\(293\) | 1.22915e6 | − | 2.12896e6i | 0.836444 | − | 1.44876i | −0.0564045 | − | 0.998408i | \(-0.517964\pi\) |
0.892849 | − | 0.450356i | \(-0.148703\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 39537.4 | + | 68480.8i | 0.0264517 | + | 0.0458156i | ||||
\(296\) | −220649. | −0.146377 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.38853e6 | −0.905764 | ||||||||
\(299\) | −36356.5 | − | 62971.3i | −0.0235182 | − | 0.0407347i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 506234. | − | 876822.i | 0.322058 | − | 0.557822i | ||||
\(302\) | 494277. | − | 856114.i | 0.311855 | − | 0.540150i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 18668.4 | + | 32334.6i | 0.0115857 | + | 0.0200671i | ||||
\(305\) | −15127.1 | −0.00931123 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.25805e6 | 0.761819 | 0.380910 | − | 0.924612i | \(-0.375611\pi\) | ||||
0.380910 | + | 0.924612i | \(0.375611\pi\) | |||||||
\(308\) | 696051. | + | 1.20560e6i | 0.418085 | + | 0.724144i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 82210.8 | − | 142393.i | 0.0485875 | − | 0.0841560i | ||||
\(311\) | −1.02249e6 | + | 1.77101e6i | −0.599457 | + | 1.03829i | 0.393444 | + | 0.919349i | \(0.371284\pi\) |
−0.992901 | + | 0.118942i | \(0.962050\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 473219. | + | 819640.i | 0.273025 | + | 0.472892i | 0.969635 | − | 0.244557i | \(-0.0786426\pi\) |
−0.696610 | + | 0.717450i | \(0.745309\pi\) | |||||||
\(314\) | 1.83719e6 | 1.05155 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −974084. | −0.548755 | ||||||||
\(317\) | 197117. | + | 341417.i | 0.110173 | + | 0.190826i | 0.915840 | − | 0.401543i | \(-0.131526\pi\) |
−0.805667 | + | 0.592369i | \(0.798193\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.02073e6 | + | 1.76795e6i | −0.561608 | + | 0.972734i | ||||
\(320\) | −88339.9 | + | 153009.i | −0.0482261 | + | 0.0835301i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −184557. | − | 319662.i | −0.0991951 | − | 0.171811i | ||||
\(323\) | 1.98202e6 | 1.05706 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −378440. | −0.198741 | ||||||||
\(326\) | 422914. | + | 732508.i | 0.220398 | + | 0.381741i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −218860. | + | 379076.i | −0.112326 | + | 0.194555i | ||||
\(329\) | 619752. | − | 1.07344e6i | 0.315667 | − | 0.546750i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.36828e6 | + | 2.36992e6i | 0.686442 | + | 1.18895i | 0.972981 | + | 0.230884i | \(0.0741617\pi\) |
−0.286539 | + | 0.958068i | \(0.592505\pi\) | |||||||
\(332\) | −1.06719e6 | −0.531370 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −894999. | −0.438992 | ||||||||
\(335\) | 159492. | + | 276248.i | 0.0776472 | + | 0.134489i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13015.1 | − | 22542.8i | 0.00624269 | − | 0.0108127i | −0.862887 | − | 0.505397i | \(-0.831346\pi\) |
0.869130 | + | 0.494584i | \(0.164680\pi\) | |||||||
\(338\) | 637144. | − | 1.10357e6i | 0.303351 | − | 0.525420i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 172962. | + | 299578.i | 0.0811432 | + | 0.140544i | ||||
\(341\) | −2.34315e6 | −1.09122 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −498052. | −0.228580 | ||||||||
\(344\) | −528736. | − | 915798.i | −0.240904 | − | 0.417257i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 915717. | − | 1.58607e6i | 0.411217 | − | 0.712249i | ||||
\(347\) | −935583. | + | 1.62048e6i | −0.417118 | + | 0.722469i | −0.995648 | − | 0.0931918i | \(-0.970293\pi\) |
0.578531 | + | 0.815661i | \(0.303626\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −644297. | − | 1.11595e6i | −0.283154 | − | 0.490437i | 0.689006 | − | 0.724756i | \(-0.258047\pi\) |
−0.972160 | + | 0.234319i | \(0.924714\pi\) | |||||||
\(350\) | −1.92108e6 | −0.838252 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.36296e6 | 1.01648 | ||||||||
\(353\) | −697250. | − | 1.20767e6i | −0.297818 | − | 0.515837i | 0.677818 | − | 0.735230i | \(-0.262926\pi\) |
−0.975637 | + | 0.219393i | \(0.929592\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 176759. | − | 306155.i | 0.0744407 | − | 0.128935i | ||||
\(356\) | 446614. | − | 773559.i | 0.186770 | − | 0.323495i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 455592. | + | 789108.i | 0.187875 | + | 0.325408i | ||||
\(359\) | 3.14929e6 | 1.28967 | 0.644833 | − | 0.764324i | \(-0.276927\pi\) | ||||
0.644833 | + | 0.764324i | \(0.276927\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.68166e6 | −0.679157 | ||||||||
\(362\) | 75910.9 | + | 131482.i | 0.0304462 | + | 0.0527343i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 208186. | − | 360588.i | 0.0823563 | − | 0.142645i | ||||
\(365\) | 211380. | − | 366120.i | 0.0830483 | − | 0.143844i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.79452e6 | − | 3.10820e6i | −0.695478 | − | 1.20460i | −0.970019 | − | 0.243028i | \(-0.921859\pi\) |
0.274541 | − | 0.961575i | \(-0.411474\pi\) | |||||||
\(368\) | −24622.9 | −0.00947807 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 34949.8 | 0.0132721 | ||||||||
\(371\) | −1.01060e6 | − | 1.75041e6i | −0.381193 | − | 0.660246i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.68552e6 | − | 2.91941e6i | 0.627280 | − | 1.08648i | −0.360815 | − | 0.932638i | \(-0.617501\pi\) |
0.988095 | − | 0.153844i | \(-0.0491654\pi\) | |||||||
\(374\) | −1.64606e6 | + | 2.85106e6i | −0.608509 | + | 1.05397i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −647301. | − | 1.12116e6i | −0.236122 | − | 0.408976i | ||||
\(377\) | 610590. | 0.221257 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.82703e6 | −0.653352 | −0.326676 | − | 0.945136i | \(-0.605929\pi\) | ||||
−0.326676 | + | 0.945136i | \(0.605929\pi\) | |||||||
\(380\) | 69327.1 | + | 120078.i | 0.0246289 | + | 0.0426584i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −478330. | + | 828492.i | −0.167714 | + | 0.290489i | ||||
\(383\) | −2.84772e6 | + | 4.93239e6i | −0.991973 | + | 1.71815i | −0.386480 | + | 0.922298i | \(0.626309\pi\) |
−0.605494 | + | 0.795850i | \(0.707024\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −294130. | − | 509448.i | −0.101132 | − | 0.175165i | ||||
\(386\) | 914993. | 0.312572 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 829485. | 0.279724 | ||||||||
\(389\) | −1.43125e6 | − | 2.47899e6i | −0.479557 | − | 0.830617i | 0.520168 | − | 0.854064i | \(-0.325869\pi\) |
−0.999725 | + | 0.0234470i | \(0.992536\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −653551. | + | 1.13198e6i | −0.216191 | + | 0.374454i | ||||
\(392\) | 1.27964e6 | − | 2.21641e6i | 0.420604 | − | 0.728508i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.16504e6 | + | 2.01792e6i | 0.378096 | + | 0.654881i | ||||
\(395\) | 411618. | 0.132740 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −373432. | −0.118915 | −0.0594574 | − | 0.998231i | \(-0.518937\pi\) | ||||
−0.0594574 | + | 0.998231i | \(0.518937\pi\) | |||||||
\(398\) | −708136. | − | 1.22653e6i | −0.224083 | − | 0.388123i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −64075.8 | + | 110983.i | −0.0200237 | + | 0.0346820i | ||||
\(401\) | 1.18967e6 | − | 2.06056e6i | 0.369457 | − | 0.639918i | −0.620024 | − | 0.784583i | \(-0.712877\pi\) |
0.989481 | + | 0.144665i | \(0.0462104\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 350412. | + | 606931.i | 0.107477 | + | 0.186156i | ||||
\(404\) | 1.44774e6 | 0.441303 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.09954e6 | 0.933217 | ||||||||
\(407\) | −249032. | − | 431336.i | −0.0745194 | − | 0.129071i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.02677e6 | + | 3.51046e6i | −0.599094 | + | 1.03766i | 0.393861 | + | 0.919170i | \(0.371139\pi\) |
−0.992955 | + | 0.118492i | \(0.962194\pi\) | |||||||
\(410\) | 34666.3 | − | 60043.9i | 0.0101847 | − | 0.0176404i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 973893. | + | 1.68683e6i | 0.282662 | + | 0.489586i | ||||
\(413\) | −1.71094e6 | −0.493584 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 450962. | 0.128535 | ||||||||
\(416\) | −353375. | − | 612063.i | −0.100116 | − | 0.173405i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −659780. | + | 1.14277e6i | −0.184697 | + | 0.319904i | ||||
\(419\) | −2.01845e6 | + | 3.49605e6i | −0.561671 | + | 0.972843i | 0.435680 | + | 0.900102i | \(0.356508\pi\) |
−0.997351 | + | 0.0727412i | \(0.976825\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 295419. | + | 511680.i | 0.0812330 | + | 0.140700i | 0.903780 | − | 0.427998i | \(-0.140781\pi\) |
−0.822547 | + | 0.568697i | \(0.807448\pi\) | |||||||
\(422\) | 2.21424e6 | 0.605261 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.11105e6 | −0.570274 | ||||||||
\(425\) | 3.40145e6 | + | 5.89148e6i | 0.913464 | + | 1.58217i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 163653. | − | 283456.i | 0.0434365 | − | 0.0752343i | ||||
\(428\) | 1.71530e6 | − | 2.97099e6i | 0.452618 | − | 0.783957i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 83749.4 | + | 145058.i | 0.0218429 | + | 0.0378330i | ||||
\(431\) | 5.06059e6 | 1.31222 | 0.656112 | − | 0.754663i | \(-0.272200\pi\) | ||||
0.656112 | + | 0.754663i | \(0.272200\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.37592e6 | 0.865312 | 0.432656 | − | 0.901559i | \(-0.357576\pi\) | ||||
0.432656 | + | 0.901559i | \(0.357576\pi\) | |||||||
\(434\) | 1.77880e6 | + | 3.08097e6i | 0.453317 | + | 0.785169i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −364408. | + | 631173.i | −0.0918062 | + | 0.159013i | ||||
\(437\) | −261959. | + | 453726.i | −0.0656190 | + | 0.113655i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.69856e6 | − | 2.94199e6i | −0.420648 | − | 0.728584i | 0.575355 | − | 0.817904i | \(-0.304864\pi\) |
−0.996003 | + | 0.0893200i | \(0.971531\pi\) | |||||||
\(440\) | −614409. | −0.151295 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 984658. | 0.239734 | ||||||||
\(443\) | −2.12190e6 | − | 3.67523e6i | −0.513706 | − | 0.889765i | −0.999874 | − | 0.0158995i | \(-0.994939\pi\) |
0.486167 | − | 0.873866i | \(-0.338395\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −188726. | + | 326882.i | −0.0451784 | + | 0.0782512i | ||||
\(446\) | 1.57006e6 | − | 2.71942e6i | 0.373747 | − | 0.647349i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.91142e6 | − | 3.31067e6i | −0.449946 | − | 0.779329i | ||||
\(449\) | −519362. | −0.121578 | −0.0607889 | − | 0.998151i | \(-0.519362\pi\) | ||||
−0.0607889 | + | 0.998151i | \(0.519362\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −988049. | −0.228737 | ||||||||
\(452\) | 1.93468e6 | + | 3.35097e6i | 0.445413 | + | 0.771479i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 951738. | − | 1.64846e6i | 0.216709 | − | 0.375352i | ||||
\(455\) | −87972.8 | + | 152373.i | −0.0199214 | + | 0.0345049i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.02545e6 | + | 6.97228e6i | 0.901621 | + | 1.56165i | 0.825390 | + | 0.564563i | \(0.190955\pi\) |
0.0762309 | + | 0.997090i | \(0.475711\pi\) | |||||||
\(458\) | −4.09148e6 | −0.911417 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −91439.8 | −0.0201484 | ||||||||
\(461\) | −1.76486e6 | − | 3.05683e6i | −0.386775 | − | 0.669914i | 0.605239 | − | 0.796044i | \(-0.293078\pi\) |
−0.992014 | + | 0.126130i | \(0.959744\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.80617e6 | − | 6.59248e6i | 0.825156 | − | 1.42921i | −0.0766442 | − | 0.997059i | \(-0.524421\pi\) |
0.901800 | − | 0.432153i | \(-0.142246\pi\) | |||||||
\(464\) | 103383. | − | 179064.i | 0.0222922 | − | 0.0386112i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.46524e6 | − | 2.53786e6i | −0.312567 | − | 0.541382i | ||||
\(467\) | −7.10090e6 | −1.50668 | −0.753340 | − | 0.657631i | \(-0.771559\pi\) | ||||
−0.753340 | + | 0.657631i | \(0.771559\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.90186e6 | −1.44889 | ||||||||
\(470\) | 102530. | + | 177586.i | 0.0214094 | + | 0.0370822i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −893499. | + | 1.54759e6i | −0.184603 | + | 0.319742i | ||||
\(473\) | 1.19350e6 | − | 2.06720e6i | 0.245284 | − | 0.424845i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.36338e6 | + | 2.36145e6i | 0.277258 | + | 0.480224i | ||||
\(476\) | −7.48476e6 | −1.51412 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −674656. | −0.135056 | ||||||||
\(479\) | −564151. | − | 977138.i | −0.112346 | − | 0.194589i | 0.804370 | − | 0.594129i | \(-0.202503\pi\) |
−0.916716 | + | 0.399540i | \(0.869170\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −74484.4 | + | 129011.i | −0.0146792 | + | 0.0254251i | ||||
\(482\) | −80580.6 | + | 139570.i | −0.0157984 | + | 0.0273636i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 95988.1 | + | 166256.i | 0.0186253 | + | 0.0322600i | ||||
\(485\) | −350515. | −0.0676632 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.19304e6 | 0.419009 | 0.209505 | − | 0.977808i | \(-0.432815\pi\) | ||||
0.209505 | + | 0.977808i | \(0.432815\pi\) | |||||||
\(488\) | −170928. | − | 296056.i | −0.0324910 | − | 0.0562761i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −202690. | + | 351069.i | −0.0381365 | + | 0.0660544i | ||||
\(491\) | 2.08709e6 | − | 3.61494e6i | 0.390694 | − | 0.676701i | −0.601847 | − | 0.798611i | \(-0.705568\pi\) |
0.992541 | + | 0.121910i | \(0.0389018\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.48804e6 | − | 9.50556e6i | −1.01695 | − | 1.76141i | ||||
\(494\) | 394674. | 0.0727649 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 237321. | 0.0433144 | ||||||||
\(497\) | 3.82454e6 | + | 6.62430e6i | 0.694526 | + | 1.20295i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.01487e6 | + | 3.48985e6i | −0.362239 | + | 0.627416i | −0.988329 | − | 0.152335i | \(-0.951321\pi\) |
0.626090 | + | 0.779751i | \(0.284654\pi\) | |||||||
\(500\) | −481018. | + | 833147.i | −0.0860470 | + | 0.149038i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −996309. | − | 1.72566e6i | −0.176455 | − | 0.305630i | ||||
\(503\) | 3.13647e6 | 0.552740 | 0.276370 | − | 0.961051i | \(-0.410868\pi\) | ||||
0.276370 | + | 0.961051i | \(0.410868\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −611770. | −0.106748 | ||||||||
\(506\) | −435112. | − | 753637.i | −0.0755484 | − | 0.130854i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.44869e6 | − | 4.24126e6i | 0.420993 | − | 0.729181i | ||||
\(509\) | −2.68135e6 | + | 4.64424e6i | −0.458733 | + | 0.794548i | −0.998894 | − | 0.0470129i | \(-0.985030\pi\) |
0.540161 | + | 0.841561i | \(0.318363\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.57363e6 | + | 7.92176e6i | 0.774834 | + | 1.34205i | ||||
\(512\) | −484936. | −0.0817542 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.07669e6 | −0.346708 | ||||||||
\(515\) | −411537. | − | 712803.i | −0.0683740 | − | 0.118427i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.46113e6 | − | 2.53076e6i | 0.240416 | − | 0.416413i | ||||
\(518\) | −378106. | + | 654898.i | −0.0619140 | + | 0.107238i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 91883.4 | + | 159147.i | 0.0149015 | + | 0.0258101i | ||||
\(521\) | 7.05392e6 | 1.13851 | 0.569254 | − | 0.822162i | \(-0.307232\pi\) | ||||
0.569254 | + | 0.822162i | \(0.307232\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.48751e6 | 0.877246 | 0.438623 | − | 0.898671i | \(-0.355466\pi\) | ||||
0.438623 | + | 0.898671i | \(0.355466\pi\) | |||||||
\(524\) | −324526. | − | 562095.i | −0.0516322 | − | 0.0894296i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 108359. | − | 187683.i | 0.0170766 | − | 0.0295775i | ||||
\(527\) | 6.29906e6 | − | 1.09103e7i | 0.987983 | − | 1.71124i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.04541e6 | + | 5.27481e6i | 0.473159 | + | 0.819536i | ||||
\(530\) | 334380. | 0.0517072 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.00007e6 | −0.459571 | ||||||||
\(533\) | 147760. | + | 255929.i | 0.0225289 | + | 0.0390212i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −724835. | + | 1.25545e6i | −0.109485 | + | 0.189634i | ||||
\(536\) | −3.60433e6 | + | 6.24288e6i | −0.541892 | + | 0.938584i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.88930e6 | + | 6.73647e6i | 0.579316 | + | 1.00341i | ||||
\(539\) | 5.77700e6 | 0.856506 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.61784e6 | 1.41281 | 0.706406 | − | 0.707807i | \(-0.250315\pi\) | ||||
0.706406 | + | 0.707807i | \(0.250315\pi\) | |||||||
\(542\) | 3.09008e6 | + | 5.35218e6i | 0.451827 | + | 0.782587i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.35232e6 | + | 1.10025e7i | −0.920312 | + | 1.59403i | ||||
\(545\) | 153988. | − | 266715.i | 0.0222073 | − | 0.0384641i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.52168e6 | − | 6.09973e6i | −0.503247 | − | 0.871650i | −0.999993 | − | 0.00375395i | \(-0.998805\pi\) |
0.496745 | − | 0.867896i | \(-0.334528\pi\) | |||||||
\(548\) | 3.60399e6 | 0.512663 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.52914e6 | −0.638424 | ||||||||
\(551\) | −2.19974e6 | − | 3.81006e6i | −0.308668 | − | 0.534629i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.45310e6 | + | 7.71300e6i | −0.619227 | + | 1.07253i | ||||
\(554\) | −1.87298e6 | + | 3.24409e6i | −0.259273 | + | 0.449075i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.25624e6 | − | 5.63997e6i | −0.446713 | − | 0.773730i | ||||
\(557\) | −1.13517e7 | −1.55032 | −0.775162 | − | 0.631762i | \(-0.782332\pi\) | ||||
−0.775162 | + | 0.631762i | \(0.782332\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −713941. | −0.0966346 | ||||||||
\(560\) | 29790.4 | + | 51598.5i | 0.00401426 | + | 0.00695291i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.40957e6 | − | 4.17350e6i | 0.321810 | − | 0.557391i | ||||
\(563\) | 1.47052e6 | − | 2.54702e6i | 0.195524 | − | 0.338658i | −0.751548 | − | 0.659678i | \(-0.770692\pi\) |
0.947072 | + | 0.321020i | \(0.104026\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −817537. | − | 1.41602e6i | −0.107742 | − | 0.186615i | ||||
\(566\) | 2.04006e6 | 0.267671 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.98909e6 | 1.03903 | ||||||||
\(569\) | 2.60302e6 | + | 4.50857e6i | 0.337052 | + | 0.583792i | 0.983877 | − | 0.178847i | \(-0.0572368\pi\) |
−0.646825 | + | 0.762639i | \(0.723903\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.43649e6 | − | 5.95217e6i | 0.441087 | − | 0.763986i | −0.556683 | − | 0.830725i | \(-0.687926\pi\) |
0.997770 | + | 0.0667391i | \(0.0212595\pi\) | |||||||
\(572\) | 490820. | − | 850125.i | 0.0627237 | − | 0.108641i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 750078. | + | 1.29917e6i | 0.0950225 | + | 0.164584i | ||||
\(575\) | −1.79825e6 | −0.226819 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.61342e6 | −0.826964 | −0.413482 | − | 0.910512i | \(-0.635688\pi\) | ||||
−0.413482 | + | 0.910512i | \(0.635688\pi\) | |||||||
\(578\) | −6.30896e6 | − | 1.09274e7i | −0.785485 | − | 1.36050i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 383922. | − | 664973.i | 0.0473885 | − | 0.0820793i | ||||
\(581\) | −4.87875e6 | + | 8.45024e6i | −0.599609 | + | 1.03855i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.38260e6 | − | 4.12679e6i | −0.290322 | − | 0.502853i | ||||
\(584\) | 9.55387e6 | 1.15917 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.79964e6 | −1.05857 | ||||||||
\(587\) | −3.31969e6 | − | 5.74987e6i | −0.397651 | − | 0.688751i | 0.595785 | − | 0.803144i | \(-0.296841\pi\) |
−0.993436 | + | 0.114393i | \(0.963508\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.52482e6 | − | 4.37311e6i | 0.299876 | − | 0.519400i | ||||
\(590\) | 141526. | − | 245131.i | 0.0167381 | − | 0.0289913i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 25222.8 | + | 43687.1i | 0.00295793 | + | 0.00512329i | ||||
\(593\) | 2.49082e6 | 0.290875 | 0.145437 | − | 0.989367i | \(-0.453541\pi\) | ||||
0.145437 | + | 0.989367i | \(0.453541\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.16283e6 | 0.366255 | ||||||||
\(596\) | −3.72134e6 | − | 6.44555e6i | −0.429125 | − | 0.743266i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −130140. | + | 225409.i | −0.0148819 | + | 0.0257762i | ||||
\(599\) | −6.54109e6 | + | 1.13295e7i | −0.744875 | + | 1.29016i | 0.205378 | + | 0.978683i | \(0.434158\pi\) |
−0.950253 | + | 0.311478i | \(0.899176\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.50119e6 | − | 2.60013e6i | −0.169531 | − | 0.293636i | 0.768724 | − | 0.639580i | \(-0.220892\pi\) |
−0.938255 | + | 0.345944i | \(0.887559\pi\) | |||||||
\(602\) | −3.62418e6 | −0.407585 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.29876e6 | 0.590992 | ||||||||
\(605\) | −40561.6 | − | 70254.8i | −0.00450533 | − | 0.00780347i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 757606. | − | 1.31221e6i | 0.0834587 | − | 0.144555i | −0.821275 | − | 0.570533i | \(-0.806737\pi\) |
0.904733 | + | 0.425978i | \(0.140070\pi\) | |||||||
\(608\) | −2.54616e6 | + | 4.41008e6i | −0.279336 | + | 0.483824i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 27074.2 | + | 46893.9i | 0.00294599 | + | 0.00510260i | ||||
\(611\) | −874036. | −0.0947166 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.71159e6 | −0.721397 | −0.360698 | − | 0.932683i | \(-0.617462\pi\) | ||||
−0.360698 | + | 0.932683i | \(0.617462\pi\) | |||||||
\(614\) | −2.25163e6 | − | 3.89994e6i | −0.241033 | − | 0.417481i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.64700e6 | − | 1.15129e7i | 0.705787 | − | 1.22246i | ||||
\(617\) | 3.98994e6 | − | 6.91077e6i | 0.421942 | − | 0.730826i | −0.574187 | − | 0.818724i | \(-0.694682\pi\) |
0.996129 | + | 0.0878986i | \(0.0280151\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 335377. | + | 580890.i | 0.0351809 | + | 0.0609351i | 0.883080 | − | 0.469223i | \(-0.155466\pi\) |
−0.847899 | + | 0.530158i | \(0.822133\pi\) | |||||||
\(620\) | 881317. | 0.0920774 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7.32012e6 | 0.758652 | ||||||||
\(623\) | −4.08346e6 | − | 7.07277e6i | −0.421511 | − | 0.730078i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.57684e6 | + | 7.92731e6i | −0.468668 | + | 0.811757i | ||||
\(626\) | 1.69391e6 | − | 2.93395e6i | 0.172765 | − | 0.299238i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.92378e6 | + | 8.52824e6i | 0.498195 | + | 0.862899i | ||||
\(629\) | 2.67789e6 | 0.269877 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.37169e6 | −0.437095 | −0.218548 | − | 0.975826i | \(-0.570132\pi\) | ||||
−0.218548 | + | 0.975826i | \(0.570132\pi\) | |||||||
\(632\) | 4.65105e6 | + | 8.05585e6i | 0.463189 | + | 0.802267i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 705591. | − | 1.22212e6i | 0.0697156 | − | 0.120751i | ||||
\(635\) | −1.03474e6 | + | 1.79223e6i | −0.101835 | + | 0.176384i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −863936. | − | 1.49638e6i | −0.0843593 | − | 0.146115i | ||||
\(638\) | 7.30751e6 | 0.710751 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −849865. | −0.0820163 | ||||||||
\(641\) | 6.89117e6 | + | 1.19359e7i | 0.662442 | + | 1.14738i | 0.979972 | + | 0.199135i | \(0.0638133\pi\) |
−0.317530 | + | 0.948248i | \(0.602853\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 746906. | − | 1.29368e6i | 0.0712424 | − | 0.123395i | −0.828204 | − | 0.560427i | \(-0.810637\pi\) |
0.899446 | + | 0.437032i | \(0.143970\pi\) | |||||||
\(644\) | 989244. | − | 1.71342e6i | 0.0939915 | − | 0.162798i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.54737e6 | − | 6.14422e6i | −0.334445 | − | 0.579276i | ||||
\(647\) | −1.27773e7 | −1.19999 | −0.599997 | − | 0.800002i | \(-0.704832\pi\) | ||||
−0.599997 | + | 0.800002i | \(0.704832\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.03374e6 | −0.375920 | ||||||||
\(650\) | 677323. | + | 1.17316e6i | 0.0628799 | + | 0.108911i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.26686e6 | + | 3.92632e6i | −0.208836 | + | 0.361715i | ||||
\(653\) | 2.42085e6 | − | 4.19304e6i | 0.222170 | − | 0.384810i | −0.733297 | − | 0.679909i | \(-0.762019\pi\) |
0.955467 | + | 0.295099i | \(0.0953526\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 137135. | + | 237524.i | 0.0124895 | + | 0.0216324i | ||||
\(656\) | 100073. | 0.00907938 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.43688e6 | −0.399496 | ||||||||
\(659\) | 6.63829e6 | + | 1.14979e7i | 0.595447 | + | 1.03134i | 0.993484 | + | 0.113975i | \(0.0363582\pi\) |
−0.398037 | + | 0.917369i | \(0.630308\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.76351e6 | + | 1.51788e7i | −0.780143 | + | 1.35125i | 0.151715 | + | 0.988424i | \(0.451520\pi\) |
−0.931858 | + | 0.362823i | \(0.881813\pi\) | |||||||
\(662\) | 4.89782e6 | − | 8.48327e6i | 0.434368 | − | 0.752347i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.09561e6 | + | 8.82586e6i | 0.448514 | + | 0.776850i | ||||
\(665\) | 1.26774e6 | 0.111167 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.90137e6 | 0.252516 | ||||||||
\(668\) | −2.39865e6 | − | 4.15458e6i | −0.207982 | − | 0.360235i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 570909. | − | 988843.i | 0.0491338 | − | 0.0851022i | ||||
\(671\) | 385830. | − | 668277.i | 0.0330819 | − | 0.0572995i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.25108e6 | + | 1.60233e7i | 0.787326 | + | 1.36369i | 0.927599 | + | 0.373576i | \(0.121869\pi\) |
−0.140273 | + | 0.990113i | \(0.544798\pi\) | |||||||
\(674\) | −93176.3 | −0.00790052 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.83032e6 | 0.574876 | ||||||||
\(677\) | 1.97541e6 | + | 3.42152e6i | 0.165648 | + | 0.286911i | 0.936885 | − | 0.349637i | \(-0.113695\pi\) |
−0.771237 | + | 0.636548i | \(0.780362\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.79206e6 | − | 6.56803e6i | 0.315646 | − | 0.546715i | ||||
\(680\) | 1.65171e6 | − | 2.86085e6i | 0.136981 | − | 0.237259i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.19371e6 | + | 7.26372e6i | 0.345253 | + | 0.597995i | ||||
\(683\) | −746853. | −0.0612609 | −0.0306304 | − | 0.999531i | \(-0.509751\pi\) | ||||
−0.0306304 | + | 0.999531i | \(0.509751\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.52294e6 | −0.124010 | ||||||||
\(686\) | 891401. | + | 1.54395e6i | 0.0723208 | + | 0.125263i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −120881. | + | 209373.i | −0.00973618 | + | 0.0168636i | ||||
\(689\) | −712625. | + | 1.23430e6i | −0.0571891 | + | 0.0990544i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.00126e6 | − | 6.93039e6i | −0.318788 | − | 0.552157i | 0.661448 | − | 0.749991i | \(-0.269942\pi\) |
−0.980235 | + | 0.197835i | \(0.936609\pi\) | |||||||
\(692\) | 9.81668e6 | 0.779291 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.69794e6 | 0.527889 | ||||||||
\(695\) | 1.37599e6 | + | 2.38328e6i | 0.108057 | + | 0.187160i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.65617e6 | − | 4.60062e6i | 0.207097 | − | 0.358702i | ||||
\(698\) | −2.30629e6 | + | 3.99462e6i | −0.179175 | + | 0.310339i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5.14859e6 | − | 8.91761e6i | −0.397139 | − | 0.687865i | ||||
\(701\) | −1.57926e7 | −1.21383 | −0.606914 | − | 0.794767i | \(-0.707593\pi\) | ||||
−0.606914 | + | 0.794767i | \(0.707593\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.07336e6 | 0.0819139 | ||||||||
\(704\) | −4.50637e6 | − | 7.80526e6i | −0.342685 | − | 0.593548i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.49584e6 | + | 4.32293e6i | −0.188454 | + | 0.326412i | ||||
\(707\) | 6.61845e6 | − | 1.14635e7i | 0.497975 | − | 0.862518i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.54046e6 | − | 1.65246e7i | −0.712777 | − | 1.23457i | −0.963811 | − | 0.266588i | \(-0.914104\pi\) |
0.251033 | − | 0.967978i | \(-0.419230\pi\) | |||||||
\(710\) | −1.26544e6 | −0.0942094 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8.52996e6 | −0.630590 | ||||||||
\(713\) | 1.66507e6 | + | 2.88398e6i | 0.122661 | + | 0.212456i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −207405. | + | 359237.i | −0.0151724 | + | 0.0262794i | ||||
\(716\) | −2.44202e6 | + | 4.22970e6i | −0.178019 | + | 0.308338i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.63653e6 | − | 9.76276e6i | −0.408038 | − | 0.706743i | ||||
\(719\) | −1.74493e6 | −0.125880 | −0.0629399 | − | 0.998017i | \(-0.520048\pi\) | ||||
−0.0629399 | + | 0.998017i | \(0.520048\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.78089e7 | 1.27585 | ||||||||
\(722\) | 3.00980e6 | + | 5.21312e6i | 0.214879 | + | 0.372181i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −406890. | + | 704755.i | −0.0288490 | + | 0.0499680i | ||||
\(725\) | 7.55018e6 | − | 1.30773e7i | 0.533473 | − | 0.924002i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.04470e6 | − | 1.80947e6i | −0.0733087 | − | 0.126974i | 0.827041 | − | 0.562142i | \(-0.190022\pi\) |
−0.900350 | + | 0.435167i | \(0.856689\pi\) | |||||||
\(728\) | −3.97617e6 | −0.278059 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.51329e6 | −0.105103 | ||||||||
\(731\) | 6.41696e6 | + | 1.11145e7i | 0.444156 | + | 0.769301i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.00097e7 | − | 1.73373e7i | 0.688114 | − | 1.19185i | −0.284333 | − | 0.958726i | \(-0.591772\pi\) |
0.972447 | − | 0.233123i | \(-0.0748946\pi\) | |||||||
\(734\) | −6.42359e6 | + | 1.11260e7i | −0.440086 | + | 0.762251i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.67914e6 | − | 2.90836e6i | −0.114260 | − | 0.197904i | ||||
\(737\) | −1.62719e7 | −1.10349 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.93522e6 | −0.130353 | −0.0651763 | − | 0.997874i | \(-0.520761\pi\) | ||||
−0.0651763 | + | 0.997874i | \(0.520761\pi\) | |||||||
\(740\) | 93667.4 | + | 162237.i | 0.00628795 | + | 0.0108910i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.61750e6 | + | 6.26570e6i | −0.241212 | + | 0.417792i | ||||
\(743\) | −4.52092e6 | + | 7.83046e6i | −0.300438 | + | 0.520373i | −0.976235 | − | 0.216714i | \(-0.930466\pi\) |
0.675797 | + | 0.737087i | \(0.263799\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.57252e6 | + | 2.72369e6i | 0.103802 | + | 0.179791i | ||||
\(746\) | −1.20668e7 | −0.793863 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.76461e7 | −1.15317 | ||||||||
\(749\) | −1.56833e7 | − | 2.71643e7i | −1.02149 | − | 1.76927i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.16416e6 | + | 1.58728e7i | −0.592915 | + | 1.02696i | 0.400922 | + | 0.916112i | \(0.368690\pi\) |
−0.993837 | + | 0.110847i | \(0.964644\pi\) | |||||||
\(752\) | −147988. | + | 256323.i | −0.00954294 | + | 0.0165289i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.09282e6 | − | 1.89282e6i | −0.0700036 | − | 0.121250i | ||||
\(755\) | −2.23909e6 | −0.142957 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.00372e7 | −1.27086 | −0.635429 | − | 0.772159i | \(-0.719177\pi\) | ||||
−0.635429 | + | 0.772159i | \(0.719177\pi\) | |||||||
\(758\) | 3.26997e6 | + | 5.66376e6i | 0.206715 | + | 0.358040i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 662045. | − | 1.14670e6i | 0.0415771 | − | 0.0720136i | ||||
\(761\) | 7.82878e6 | − | 1.35598e7i | 0.490041 | − | 0.848776i | −0.509893 | − | 0.860238i | \(-0.670315\pi\) |
0.999934 | + | 0.0114616i | \(0.00364841\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.33184e6 | + | 5.77092e6i | 0.207192 | + | 0.358867i | ||||
\(764\) | −5.12780e6 | −0.317832 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.03871e7 | 1.25541 | ||||||||
\(767\) | 603236. | + | 1.04483e6i | 0.0370253 | + | 0.0641297i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.33840e6 | − | 1.44425e7i | 0.508472 | − | 0.880699i | −0.491480 | − | 0.870889i | \(-0.663544\pi\) |
0.999952 | − | 0.00981049i | \(-0.00312282\pi\) | |||||||
\(770\) | −1.05285e6 | + | 1.82360e6i | −0.0639943 | + | 0.110841i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.45223e6 | + | 4.24739e6i | 0.148087 | + | 0.256495i | ||||
\(773\) | 1.89296e7 | 1.13944 | 0.569721 | − | 0.821838i | \(-0.307051\pi\) | ||||
0.569721 | + | 0.821838i | \(0.307051\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.73319e7 | 1.03655 | ||||||||
\(776\) | −3.96062e6 | − | 6.85999e6i | −0.236107 | − | 0.408949i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.12322e6 | + | 8.87368e6i | −0.303455 | + | 0.525599i | ||||
\(779\) | 1.06466e6 | − | 1.84404e6i | 0.0628587 | − | 0.108874i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.01676e6 | + | 1.56175e7i | 0.528960 | + | 0.916186i | ||||
\(782\) | 4.67884e6 | 0.273603 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −585112. | −0.0339977 | ||||||||
\(785\) | −2.08064e6 | − | 3.60377e6i | −0.120510 | − | 0.208729i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.87371e6 | − | 3.24536e6i | 0.107837 | − | 0.186778i | −0.807057 | − | 0.590473i | \(-0.798941\pi\) |
0.914894 | + | 0.403695i | \(0.132274\pi\) | |||||||
\(788\) | −6.24476e6 | + | 1.08162e7i | −0.358262 | + | 0.620527i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −736705. | − | 1.27601e6i | −0.0419977 | − | 0.0727422i | ||||
\(791\) | 3.53782e7 | 2.01045 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −230800. | −0.0130333 | ||||||||
\(794\) | 668361. | + | 1.15763e6i | 0.0376235 | + | 0.0651659i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.79568e6 | − | 6.57432e6i | 0.212328 | − | 0.367763i | ||||
\(797\) | −7.58701e6 | + | 1.31411e7i | −0.423082 | + | 0.732800i | −0.996239 | − | 0.0866454i | \(-0.972385\pi\) |
0.573157 | + | 0.819446i | \(0.305719\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.85591e6 | + | 1.36068e7i | 0.435341 | + | 0.754033i | ||||
\(800\) | −1.74784e7 | −0.965557 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8.51694e6 | −0.467571 | ||||||||
\(803\) | 1.07828e7 | + | 1.86764e7i | 0.590125 | + | 1.02213i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −418024. | + | 724039.i | −0.0227359 | + | 0.0393797i | ||||
\(806\) | 1.25432e6 | − | 2.17254e6i | 0.0680096 | − | 0.117796i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.91265e6 | − | 1.19731e7i | −0.372491 | − | 0.645174i | ||||
\(809\) | 3.67446e7 | 1.97389 | 0.986943 | − | 0.161067i | \(-0.0514936\pi\) | ||||
0.986943 | + | 0.161067i | \(0.0514936\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.10069e7 | −1.65541 | −0.827706 | − | 0.561162i | \(-0.810355\pi\) | ||||
−0.827706 | + | 0.561162i | \(0.810355\pi\) | |||||||
\(812\) | 8.30694e6 | + | 1.43880e7i | 0.442131 | + | 0.765794i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −891424. | + | 1.54399e6i | −0.0471545 | + | 0.0816740i | ||||
\(815\) | 957907. | − | 1.65914e6i | 0.0505160 | − | 0.0874963i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.57207e6 | + | 4.45496e6i | 0.134812 | + | 0.233501i | ||||
\(818\) | 1.45098e7 | 0.758192 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 371631. | 0.0193009 | ||||||||
\(821\) | −2.14433e6 | − | 3.71409e6i | −0.111028 | − | 0.192307i | 0.805157 | − | 0.593062i | \(-0.202081\pi\) |
−0.916185 | + | 0.400755i | \(0.868748\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.66686e6 | + | 1.15473e7i | −0.343101 | + | 0.594268i | −0.985007 | − | 0.172515i | \(-0.944811\pi\) |
0.641906 | + | 0.766783i | \(0.278144\pi\) | |||||||
\(824\) | 9.30027e6 | − | 1.61085e7i | 0.477175 | − | 0.826491i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.06221e6 | + | 5.30390e6i | 0.156165 | + | 0.270486i | ||||
\(827\) | −6.58421e6 | −0.334765 | −0.167382 | − | 0.985892i | \(-0.553531\pi\) | ||||
−0.167382 | + | 0.985892i | \(0.553531\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.49408e7 | 1.76582 | 0.882909 | − | 0.469544i | \(-0.155582\pi\) | ||||
0.882909 | + | 0.469544i | \(0.155582\pi\) | |||||||
\(830\) | −807122. | − | 1.39798e6i | −0.0406672 | − | 0.0704376i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.34783e6 | + | 2.33452e6i | −0.0675038 | + | 0.116920i | ||||
\(833\) | −1.55303e7 | + | 2.68992e7i | −0.775472 | + | 1.34316i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.01359e6 | + | 1.75560e6i | 0.0503093 | + | 0.0871382i | ||||
\(836\) | −7.07299e6 | −0.350015 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.44503e7 | 0.710831 | ||||||||
\(839\) | −1.85769e7 | − | 3.21761e7i | −0.911105 | − | 1.57808i | −0.812507 | − | 0.582952i | \(-0.801898\pi\) |
−0.0985980 | − | 0.995127i | \(-0.531436\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.92620e6 | + | 3.33628e6i | −0.0939100 | + | 0.162657i | ||||
\(842\) | 1.05747e6 | − | 1.83159e6i | 0.0514028 | − | 0.0890322i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.93427e6 | + | 1.02785e7i | 0.286755 | + | 0.496674i | ||||
\(845\) | −2.88628e6 | −0.139058 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.75527e6 | 0.0840688 | ||||||||
\(848\) | 241317. | + | 417974.i | 0.0115239 | + | 0.0199600i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.21757e7 | − | 2.10889e7i | 0.578023 | − | 1.00117i | ||||
\(851\) | −353931. | + | 613026.i | −0.0167531 | + | 0.0290171i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.28069e6 | − | 1.08785e7i | −0.295552 | − | 0.511912i | 0.679561 | − | 0.733619i | \(-0.262170\pi\) |
−0.975113 | + | 0.221707i | \(0.928837\pi\) | |||||||
\(854\) | −1.17161e6 | −0.0549717 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.27609e7 | −1.52817 | ||||||||
\(857\) | −1.88788e7 | − | 3.26990e7i | −0.878055 | − | 1.52084i | −0.853472 | − | 0.521138i | \(-0.825508\pi\) |
−0.0245827 | − | 0.999698i | \(-0.507826\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.11422e6 | + | 7.12604e6i | −0.190241 | + | 0.329507i | −0.945330 | − | 0.326115i | \(-0.894260\pi\) |
0.755089 | + | 0.655622i | \(0.227594\pi\) | |||||||
\(860\) | −448906. | + | 777528.i | −0.0206971 | + | 0.0358484i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9.05733e6 | − | 1.56878e7i | −0.415176 | − | 0.719105i | ||||
\(863\) | −2.85773e7 | −1.30615 | −0.653077 | − | 0.757291i | \(-0.726522\pi\) | ||||
−0.653077 | + | 0.757291i | \(0.726522\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.14823e6 | −0.188505 | ||||||||
\(866\) | −6.04215e6 | − | 1.04653e7i | −0.273777 | − | 0.474195i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −9.53455e6 | + | 1.65143e7i | −0.429537 | + | 0.743980i | ||||
\(869\) | −1.04987e7 | + | 1.81842e7i | −0.471612 | + | 0.816855i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.43342e6 | + | 4.21481e6i | 0.108686 | + | 0.188249i | ||||
\(872\) | 6.95989e6 | 0.309964 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.87539e6 | 0.0830450 | ||||||||
\(875\) | 4.39802e6 | + | 7.61759e6i | 0.194195 | + | 0.336355i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.58797e7 | − | 2.75045e7i | 0.697180 | − | 1.20755i | −0.272261 | − | 0.962223i | \(-0.587771\pi\) |
0.969440 | − | 0.245327i | \(-0.0788953\pi\) | |||||||
\(878\) | −6.08008e6 | + | 1.05310e7i | −0.266178 | + | 0.461035i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 70234.0 | + | 121649.i | 0.00305732 | + | 0.00529543i | ||||
\(881\) | 1.74609e7 | 0.757924 | 0.378962 | − | 0.925412i | \(-0.376281\pi\) | ||||
0.378962 | + | 0.925412i | \(0.376281\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.63763e7 | −0.706829 | −0.353415 | − | 0.935467i | \(-0.614979\pi\) | ||||
−0.353415 | + | 0.935467i | \(0.614979\pi\) | |||||||
\(884\) | 2.63894e6 | + | 4.57077e6i | 0.113579 | + | 0.196725i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.59544e6 | + | 1.31557e7i | −0.325064 | + | 0.563027i | ||||
\(887\) | −2.53921e6 | + | 4.39804e6i | −0.108365 | + | 0.187694i | −0.915108 | − | 0.403209i | \(-0.867895\pi\) |
0.806743 | + | 0.590903i | \(0.201228\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.23888e7 | − | 3.87785e7i | −0.950115 | − | 1.64565i | ||||
\(890\) | 1.35111e6 | 0.0571761 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.68313e7 | 0.708282 | ||||||||
\(893\) | 3.14884e6 | + | 5.45395e6i | 0.132136 | + | 0.228866i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.03192e6 | − | 1.78734e6i | 0.0430616 | − | 0.0745848i | ||||
\(896\) | 9.19429e6 | − | 1.59250e7i | 0.382603 | − | 0.662687i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 929542. | + | 1.61001e6i | 0.0384661 | + | 0.0666252i | ||||
\(899\) | −2.79640e7 | −1.15399 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.56205e7 | 1.05142 | ||||||||
\(902\) | 1.76839e6 | + | 3.06294e6i | 0.0723704 | + | 0.125349i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.84754e7 | − | 3.20003e7i | 0.751922 | − | 1.30237i | ||||
\(905\) | 171939. | − | 297808.i | 0.00697837 | − | 0.0120869i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 923315. | + | 1.59923e6i | 0.0372676 | + | 0.0645494i | 0.884058 | − | 0.467378i | \(-0.154801\pi\) |
−0.846790 | + | 0.531927i | \(0.821468\pi\) | |||||||
\(908\) | 1.02028e7 | 0.410682 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 629807. | 0.0252118 | ||||||||
\(911\) | 2.19578e7 | + | 3.80320e7i | 0.876582 | + | 1.51829i | 0.855067 | + | 0.518517i | \(0.173516\pi\) |
0.0215150 | + | 0.999769i | \(0.493151\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.15022e7 | + | 1.99223e7i | −0.456670 | + | 0.790976i | ||||
\(914\) | 1.44093e7 | − | 2.49577e7i | 0.570529 | − | 0.988186i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.09654e7 | − | 1.89926e7i | −0.431803 | − | 0.747904i | ||||
\(917\) | −5.93438e6 | −0.233051 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.53760e7 | −0.991140 | −0.495570 | − | 0.868568i | \(-0.665041\pi\) | ||||
−0.495570 | + | 0.868568i | \(0.665041\pi\) | |||||||
\(920\) | 436606. | + | 756224.i | 0.0170067 | + | 0.0294565i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −6.31742e6 | + | 1.09421e7i | −0.244744 | + | 0.423909i | ||||
\(923\) | 2.69687e6 | − | 4.67112e6i | 0.104197 | − | 0.180475i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.84205e6 | + | 3.19053e6i | 0.0707861 | + | 0.122605i | ||||
\(926\) | −2.72488e7 | −1.04429 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.82004e7 | 1.07494 | ||||||||
\(929\) | −2.02111e7 | − | 3.50067e7i | −0.768336 | − | 1.33080i | −0.938465 | − | 0.345375i | \(-0.887752\pi\) |
0.170129 | − | 0.985422i | \(-0.445582\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.22490e6 | + | 1.07818e7i | −0.235374 | + | 0.407680i | ||||
\(932\) | 7.85382e6 | − | 1.36032e7i | 0.296170 | − | 0.512982i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.27090e7 | + | 2.20127e7i | 0.476700 | + | 0.825668i | ||||
\(935\) | 7.45671e6 | 0.278945 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.79012e7 | 0.666089 | 0.333044 | − | 0.942911i | \(-0.391924\pi\) | ||||
0.333044 | + | 0.942911i | \(0.391924\pi\) | |||||||
\(938\) | 1.23528e7 | + | 2.13957e7i | 0.458414 | + | 0.793996i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −549569. | + | 951882.i | −0.0202863 | + | 0.0351369i | ||||
\(941\) | −412928. | + | 715212.i | −0.0152020 | + | 0.0263306i | −0.873526 | − | 0.486777i | \(-0.838172\pi\) |
0.858324 | + | 0.513108i | \(0.171506\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 702120. | + | 1.21611e6i | 0.0257118 | + | 0.0445341i | ||||
\(944\) | 408549. | 0.0149216 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.54440e6 | −0.310423 | ||||||||
\(947\) | 2.71734e7 | + | 4.70657e7i | 0.984620 | + | 1.70541i | 0.643614 | + | 0.765351i | \(0.277434\pi\) |
0.341006 | + | 0.940061i | \(0.389232\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.22509e6 | − | 5.58602e6i | 0.116246 | − | 0.201343i | ||||
\(950\) | 4.88030e6 | − | 8.45293e6i | 0.175444 | − | 0.303877i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.57382e7 | + | 6.19003e7i | 1.27803 | + | 2.21361i | ||||
\(953\) | −4.00436e6 | −0.142824 | −0.0714119 | − | 0.997447i | \(-0.522750\pi\) | ||||
−0.0714119 | + | 0.997447i | \(0.522750\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.16685e6 | 0.0768813 | ||||||||
\(956\) | −1.80811e6 | − | 3.13174e6i | −0.0639854 | − | 0.110826i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.01941e6 | + | 3.49772e6i | −0.0710903 | + | 0.123132i | ||||
\(959\) | 1.64759e7 | − | 2.85371e7i | 0.578500 | − | 1.00199i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.73371e6 | − | 3.00287e6i | −0.0605574 | − | 0.104889i | ||||
\(962\) | 533242. | 0.0185775 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −863842. | −0.0299393 | ||||||||
\(965\) | −1.03624e6 | − | 1.79482e6i | −0.0358213 | − | 0.0620443i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.61712e7 | + | 2.80093e7i | −0.556130 | + | 0.963245i | 0.441685 | + | 0.897170i | \(0.354381\pi\) |
−0.997815 | + | 0.0660745i | \(0.978952\pi\) | |||||||
\(968\) | 916646. | − | 1.58768e6i | 0.0314422 | − | 0.0544595i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 627344. | + | 1.08659e6i | 0.0214080 | + | 0.0370798i | ||||
\(971\) | 2.08060e7 | 0.708176 | 0.354088 | − | 0.935212i | \(-0.384791\pi\) | ||||
0.354088 | + | 0.935212i | \(0.384791\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.95446e7 | −2.01632 | ||||||||
\(974\) | −3.92505e6 | − | 6.79838e6i | −0.132571 | − | 0.229619i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −39078.1 | + | 67685.2i | −0.00131313 | + | 0.00227441i | ||||
\(977\) | −1.24444e7 | + | 2.15543e7i | −0.417097 | + | 0.722433i | −0.995646 | − | 0.0932148i | \(-0.970286\pi\) |
0.578549 | + | 0.815647i | \(0.303619\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.62720e6 | − | 1.66748e7i | −0.321028 | − | 0.556037i | ||||
\(980\) | −2.17288e6 | −0.0722719 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.49417e7 | −0.494448 | ||||||||
\(983\) | −2.11280e6 | − | 3.65948e6i | −0.0697388 | − | 0.120791i | 0.829047 | − | 0.559178i | \(-0.188883\pi\) |
−0.898786 | + | 0.438387i | \(0.855550\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.63885e6 | − | 4.57062e6i | 0.0866610 | − | 0.150101i | ||||
\(986\) | −1.96447e7 | + | 3.40257e7i | −0.643508 | + | 1.11459i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.05775e6 | + | 1.83207e6i | 0.0344739 | + | 0.0597105i | ||||
\(989\) | −3.39246e6 | −0.110287 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.01661e7 | 0.975741 | 0.487871 | − | 0.872916i | \(-0.337774\pi\) | ||||
0.487871 | + | 0.872916i | \(0.337774\pi\) | |||||||
\(992\) | 1.61840e7 | + | 2.80315e7i | 0.522163 | + | 0.904412i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.36901e7 | − | 2.37120e7i | 0.439483 | − | 0.761207i | ||||
\(995\) | −1.60394e6 | + | 2.77811e6i | −0.0513607 | + | 0.0889593i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.97488e6 | + | 6.88470e6i | 0.126645 | + | 0.219355i | 0.922375 | − | 0.386297i | \(-0.126246\pi\) |
−0.795730 | + | 0.605652i | \(0.792913\pi\) | |||||||
\(998\) | 1.44246e7 | 0.458436 | ||||||||
\(999\) | 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 | 27.6.c.a.10.2 | 8 | ||
3.2 | odd | 2 | 9.6.c.a.4.3 | ✓ | 8 | ||
4.3 | odd | 2 | 432.6.i.c.145.3 | 8 | |||
9.2 | odd | 6 | 9.6.c.a.7.3 | yes | 8 | ||
9.4 | even | 3 | 81.6.a.d.1.3 | 4 | |||
9.5 | odd | 6 | 81.6.a.c.1.2 | 4 | |||
9.7 | even | 3 | inner | 27.6.c.a.19.2 | 8 | ||
12.11 | even | 2 | 144.6.i.c.49.2 | 8 | |||
36.7 | odd | 6 | 432.6.i.c.289.3 | 8 | |||
36.11 | even | 6 | 144.6.i.c.97.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9.6.c.a.4.3 | ✓ | 8 | 3.2 | odd | 2 | ||
9.6.c.a.7.3 | yes | 8 | 9.2 | odd | 6 | ||
27.6.c.a.10.2 | 8 | 1.1 | even | 1 | trivial | ||
27.6.c.a.19.2 | 8 | 9.7 | even | 3 | inner | ||
81.6.a.c.1.2 | 4 | 9.5 | odd | 6 | |||
81.6.a.d.1.3 | 4 | 9.4 | even | 3 | |||
144.6.i.c.49.2 | 8 | 12.11 | even | 2 | |||
144.6.i.c.97.2 | 8 | 36.11 | even | 6 | |||
432.6.i.c.145.3 | 8 | 4.3 | odd | 2 | |||
432.6.i.c.289.3 | 8 | 36.7 | odd | 6 |