Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,7,Mod(65,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.65");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.h (of order \(2\), degree \(1\), 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: | \(88.3407681100\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 172x^{6} + 13179x^{4} - 522628x^{2} + 8755681 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{26}\cdot 3^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 65.5 | ||
Root | \(7.10120 + 0.847848i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.65 |
Dual form | 384.7.h.e.65.7 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 4.41641 | − | 26.6364i | 0.163571 | − | 0.986532i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −127.030 | −1.01624 | −0.508121 | − | 0.861286i | \(-0.669660\pi\) | ||||
−0.508121 | + | 0.861286i | \(0.669660\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 467.888 | 1.36410 | 0.682052 | − | 0.731304i | \(-0.261088\pi\) | ||||
0.682052 | + | 0.731304i | \(0.261088\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −689.991 | − | 235.274i | −0.946489 | − | 0.322735i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −554.827 | −0.416849 | −0.208425 | − | 0.978038i | \(-0.566834\pi\) | ||||
−0.208425 | + | 0.978038i | \(0.566834\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 357.218i | − | 0.162594i | −0.996690 | − | 0.0812968i | \(-0.974094\pi\) | ||
0.996690 | − | 0.0812968i | \(-0.0259062\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −561.017 | + | 3383.62i | −0.166227 | + | 1.00255i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4495.52i | − | 0.915026i | −0.889203 | − | 0.457513i | \(-0.848740\pi\) | ||
0.889203 | − | 0.457513i | \(-0.151260\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 3243.70i | − | 0.472911i | −0.971642 | − | 0.236456i | \(-0.924014\pi\) | ||
0.971642 | − | 0.236456i | \(-0.0759858\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2066.38 | − | 12462.8i | 0.223127 | − | 1.34573i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 17444.0i | 1.43371i | 0.697221 | + | 0.716856i | \(0.254419\pi\) | ||||
−0.697221 | + | 0.716856i | \(0.745581\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 511.656 | 0.0327460 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −9314.12 | + | 17339.8i | −0.473206 | + | 0.880952i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −17419.5 | −0.714235 | −0.357118 | − | 0.934059i | \(-0.616241\pi\) | ||||
−0.357118 | + | 0.934059i | \(0.616241\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8039.04 | 0.269848 | 0.134924 | − | 0.990856i | \(-0.456921\pi\) | ||||
0.134924 | + | 0.990856i | \(0.456921\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2450.34 | + | 14778.6i | −0.0681843 | + | 0.411235i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −59435.8 | −1.38626 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 79420.8i | − | 1.56794i | −0.620800 | − | 0.783969i | \(-0.713192\pi\) | ||
0.620800 | − | 0.783969i | \(-0.286808\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9514.99 | − | 1577.62i | −0.160404 | − | 0.0265956i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 61806.9i | 0.896779i | 0.893838 | + | 0.448389i | \(0.148002\pi\) | ||||
−0.893838 | + | 0.448389i | \(0.851998\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 45444.9i | 0.571584i | 0.958292 | + | 0.285792i | \(0.0922566\pi\) | ||||
−0.958292 | + | 0.285792i | \(0.907743\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 87649.6 | + | 29886.9i | 0.961861 | + | 0.327977i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 159556.i | − | 1.53681i | −0.639965 | − | 0.768404i | \(-0.721051\pi\) | ||
0.639965 | − | 0.768404i | \(-0.278949\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 101270. | 0.860781 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −119744. | − | 19854.1i | −0.902702 | − | 0.149671i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −190908. | −1.28232 | −0.641159 | − | 0.767408i | \(-0.721546\pi\) | ||||
−0.641159 | + | 0.767408i | \(0.721546\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 70479.7 | 0.423620 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −86400.3 | − | 14325.5i | −0.466542 | − | 0.0773544i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −306549. | −1.49260 | −0.746300 | − | 0.665610i | \(-0.768171\pi\) | ||||
−0.746300 | + | 0.665610i | \(0.768171\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 251837.i | 1.10951i | 0.832015 | + | 0.554753i | \(0.187187\pi\) | ||||
−0.832015 | + | 0.554753i | \(0.812813\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −322838. | − | 110082.i | −1.29111 | − | 0.440245i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 45377.5i | 0.165234i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 202398.i | 0.672949i | 0.941693 | + | 0.336475i | \(0.109235\pi\) | ||||
−0.941693 | + | 0.336475i | \(0.890765\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 464644. | + | 77039.7i | 1.41440 | + | 0.234513i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 362276.i | 1.01219i | 0.862476 | + | 0.506097i | \(0.168912\pi\) | ||||
−0.862476 | + | 0.506097i | \(0.831088\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −349729. | −0.899008 | −0.449504 | − | 0.893278i | \(-0.648399\pi\) | ||||
−0.449504 | + | 0.893278i | \(0.648399\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2259.68 | − | 13628.7i | 0.00535629 | − | 0.0323050i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −259597. | −0.568626 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 718180. | 1.45664 | 0.728320 | − | 0.685238i | \(-0.240302\pi\) | ||||
0.728320 | + | 0.685238i | \(0.240302\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 420733. | + | 324674.i | 0.791684 | + | 0.610931i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 138716. | 0.242601 | 0.121300 | − | 0.992616i | \(-0.461294\pi\) | ||||
0.121300 | + | 0.992616i | \(0.461294\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 571067.i | 0.929887i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −76931.6 | + | 463992.i | −0.116828 | + | 0.704616i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.22054e6i | 1.73134i | 0.500618 | + | 0.865668i | \(0.333106\pi\) | ||||
−0.500618 | + | 0.865668i | \(0.666894\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 167138.i | − | 0.221795i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 35503.7 | − | 214131.i | 0.0441392 | − | 0.266214i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 412047.i | 0.480592i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.15946e6 | 1.27040 | 0.635198 | − | 0.772350i | \(-0.280919\pi\) | ||||
0.635198 | + | 0.772350i | \(0.280919\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 382825. | + | 130536.i | 0.394544 | + | 0.134532i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −533156. | −0.517476 | −0.258738 | − | 0.965948i | \(-0.583307\pi\) | ||||
−0.258738 | + | 0.965948i | \(0.583307\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1966.17 | −0.00179933 | −0.000899663 | − | 1.00000i | \(-0.500286\pi\) | ||||
−0.000899663 | 1.00000i | \(0.500286\pi\) | ||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −262493. | + | 1.58315e6i | −0.226751 | + | 1.36759i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.25359e6 | 1.02331 | 0.511653 | − | 0.859192i | \(-0.329033\pi\) | ||||
0.511653 | + | 0.859192i | \(0.329033\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 2.18389e6i | − | 1.68637i | −0.537627 | − | 0.843183i | \(-0.680679\pi\) | ||
0.537627 | − | 0.843183i | \(-0.319321\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.11548e6 | − | 350755.i | −1.54682 | − | 0.256469i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.18039e6i | 1.51112i | 0.655082 | + | 0.755558i | \(0.272634\pi\) | ||||
−0.655082 | + | 0.755558i | \(0.727366\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 2.21591e6i | − | 1.45700i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −84044.2 | + | 246477.i | −0.0524747 | + | 0.153893i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 2.10340e6i | − | 1.24819i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.46373e6 | −0.826237 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.64631e6 | + | 272964.i | 0.884701 | + | 0.146687i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.91985e6 | 0.982963 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.67367e6 | 1.30526 | 0.652630 | − | 0.757677i | \(-0.273666\pi\) | ||||
0.652630 | + | 0.757677i | \(0.273666\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.21049e6 | + | 200703.i | 0.563885 | + | 0.0934943i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.37296e6 | 0.610722 | 0.305361 | − | 0.952237i | \(-0.401223\pi\) | ||||
0.305361 | + | 0.952237i | \(0.401223\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 1.51769e6i | − | 0.645100i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.18317e6 | − | 2.20267e6i | 0.480892 | − | 0.895259i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.93934e6i | 1.53201i | 0.642835 | + | 0.766005i | \(0.277758\pi\) | ||||
−0.642835 | + | 0.766005i | \(0.722242\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.06914e6i | 1.14281i | 0.820670 | + | 0.571403i | \(0.193601\pi\) | ||||
−0.820670 | + | 0.571403i | \(0.806399\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.24999e6 | − | 704664.i | −1.51611 | − | 0.251377i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 198194.i | 0.0677771i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.21280e6 | 0.725835 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 447249. | − | 2.69746e6i | 0.140798 | − | 0.849187i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.04539e6 | 0.316024 | 0.158012 | − | 0.987437i | \(-0.449492\pi\) | ||||
0.158012 | + | 0.987437i | \(0.449492\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.78383e6 | −1.09901 | −0.549504 | − | 0.835491i | \(-0.685183\pi\) | ||||
−0.549504 | + | 0.835491i | \(0.685183\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.05768e6 | + | 3.10187e6i | −0.295311 | + | 0.866062i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.02120e6 | −0.274231 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.20728e6i | 1.86240i | 0.364511 | + | 0.931199i | \(0.381236\pi\) | ||||
−0.364511 | + | 0.931199i | \(0.618764\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −843126. | + | 5.08508e6i | −0.209750 | + | 1.26505i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.16182e6i | 1.95573i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 650337.i | − | 0.150167i | −0.997177 | − | 0.0750837i | \(-0.976078\pi\) | ||
0.997177 | − | 0.0750837i | \(-0.0239224\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 311267. | − | 1.87732e6i | 0.0692917 | − | 0.417914i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.36276e6i | 0.722015i | 0.932563 | + | 0.361007i | \(0.117567\pi\) | ||||
−0.932563 | + | 0.361007i | \(0.882433\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.69920e6 | 0.973563 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −763158. | + | 2.23812e6i | −0.152625 | + | 0.447605i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.62335e6 | 1.47234 | 0.736169 | − | 0.676797i | \(-0.236633\pi\) | ||||
0.736169 | + | 0.676797i | \(0.236633\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 239398. | 0.0446690 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.35384e6 | + | 8.16534e6i | −0.244145 | + | 1.47250i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.30814e6 | −1.62295 | −0.811473 | − | 0.584390i | \(-0.801334\pi\) | ||||
−0.811473 | + | 0.584390i | \(0.801334\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.67832e6i | 0.283035i | 0.989936 | + | 0.141517i | \(0.0451981\pi\) | ||||
−0.989936 | + | 0.141517i | \(0.954802\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.70801e6 | + | 1.11221e6i | 1.09456 | + | 0.181483i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.00888e7i | 1.59340i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.49424e6i | 0.381428i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.35796e6 | + | 8.11307e6i | −0.645503 | + | 1.20171i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.83352e6i | 0.550171i | 0.961420 | + | 0.275085i | \(0.0887061\pi\) | ||||
−0.961420 | + | 0.275085i | \(0.911294\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.24738e6 | −0.312612 | −0.156306 | − | 0.987709i | \(-0.549959\pi\) | ||||
−0.156306 | + | 0.987709i | \(0.549959\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.20869e6 | + | 200405.i | 0.163009 | + | 0.0270275i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.35513e6 | −0.962036 | −0.481018 | − | 0.876711i | \(-0.659733\pi\) | ||||
−0.481018 | + | 0.876711i | \(0.659733\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.71907e6 | −0.471927 | −0.235964 | − | 0.971762i | \(-0.575825\pi\) | ||||
−0.235964 | + | 0.971762i | \(0.575825\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.39115e6 | + | 893873.i | 0.663885 | + | 0.110075i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.15037e6 | −0.974292 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 7.85134e6i | − | 0.911343i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.10411e6 | − | 1.20362e7i | 0.462709 | − | 1.35699i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.79969e6i | 0.197133i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 6.61991e6i | − | 0.704701i | −0.935868 | − | 0.352350i | \(-0.885383\pi\) | ||
0.935868 | − | 0.352350i | \(-0.114617\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.64970e6 | + | 1.59996e6i | 0.998562 | + | 0.165565i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 5.77287e6i | − | 0.580867i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.76137e6 | 0.368101 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.54455e6 | + | 9.31551e6i | −0.147051 | + | 0.886900i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.60588e6 | −0.148777 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.10450e7 | −0.995982 | −0.497991 | − | 0.867182i | \(-0.665929\pi\) | ||||
−0.497991 | + | 0.867182i | \(0.665929\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −353038. | − | 120379.i | −0.0309937 | − | 0.0105683i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.13090e7 | −0.966821 | −0.483411 | − | 0.875394i | \(-0.660602\pi\) | ||||
−0.483411 | + | 0.875394i | \(0.660602\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 2.64496e6i | − | 0.220248i | −0.993918 | − | 0.110124i | \(-0.964875\pi\) | ||
0.993918 | − | 0.110124i | \(-0.0351248\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.14648e6 | + | 6.91471e6i | −0.0930105 | + | 0.560968i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 2.97617e6i | − | 0.235283i | −0.993056 | − | 0.117641i | \(-0.962467\pi\) | ||
0.993056 | − | 0.117641i | \(-0.0375333\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.02684e7i | 1.56177i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.17178e6 | − | 1.91297e7i | 0.238263 | − | 1.43702i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 2.10038e7i | − | 1.53852i | −0.638935 | − | 0.769261i | \(-0.720625\pi\) | ||
0.638935 | − | 0.769261i | \(-0.279375\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.05051e7 | −1.46491 | −0.732455 | − | 0.680816i | \(-0.761625\pi\) | ||||
−0.732455 | + | 0.680816i | \(0.761625\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.05063e7 | − | 9.77291e6i | 0.732199 | − | 0.681091i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.28643e7 | −0.874761 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.15871e6 | −0.0768923 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 612626. | − | 3.69489e6i | 0.0396824 | − | 0.239333i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.33028e6 | 0.0841246 | 0.0420623 | − | 0.999115i | \(-0.486607\pi\) | ||||
0.0420623 | + | 0.999115i | \(0.486607\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 9.67838e6i | − | 0.597642i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.52111e7 | + | 2.52206e6i | 0.917363 | + | 0.152102i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.94766e6i | 0.468209i | 0.972211 | + | 0.234104i | \(0.0752158\pi\) | ||||
−0.972211 | + | 0.234104i | \(0.924784\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 3.71600e7i | − | 2.13883i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.20193e7 | + | 4.09835e6i | 0.676016 | + | 0.230509i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.89010e7i | 1.03901i | 0.854469 | + | 0.519503i | \(0.173883\pi\) | ||||
−0.854469 | + | 0.519503i | \(0.826117\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.42510e7 | 1.30314 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.25107e7 | + | 5.39040e6i | 1.70802 | + | 0.283196i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.87304e7 | −0.962255 | −0.481127 | − | 0.876651i | \(-0.659773\pi\) | ||||
−0.481127 | + | 0.876651i | \(0.659773\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.32087e7 | −0.663668 | −0.331834 | − | 0.943338i | \(-0.607667\pi\) | ||||
−0.331834 | + | 0.943338i | \(0.607667\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.45195e6 | − | 738150.i | −0.218807 | − | 0.0362791i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −283881. | −0.0136502 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.70493e6i | 0.456618i | 0.973589 | + | 0.228309i | \(0.0733197\pi\) | ||||
−0.973589 | + | 0.228309i | \(0.926680\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.54686e6 | − | 1.89138e6i | −0.255408 | − | 0.0870895i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.56440e7i | − | 0.705065i | −0.935800 | − | 0.352533i | \(-0.885321\pi\) | ||
0.935800 | − | 0.352533i | \(-0.114679\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.52214e7i | 1.55399i | 0.629510 | + | 0.776993i | \(0.283256\pi\) | ||||
−0.629510 | + | 0.776993i | \(0.716744\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.09754e7 | + | 1.81977e6i | 0.474119 | + | 0.0786107i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.89187e7i | 1.22330i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.92784e6 | 0.162727 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.12063e6 | − | 3.08837e7i | 0.207799 | − | 1.25329i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.23222e6 | 0.287520 | 0.143760 | − | 0.989613i | \(-0.454081\pi\) | ||||
0.143760 | + | 0.989613i | \(0.454081\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.89409e7 | 1.51684 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.16772e6 | − | 9.62057e6i | 0.197256 | − | 0.367224i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.23131e6 | 0.233112 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.12631e7i | 0.779700i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.35463e6 | + | 1.42013e7i | −0.0846438 | + | 0.510506i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 3.19908e7i | − | 1.12752i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2.78268e7i | − | 0.961719i | −0.876798 | − | 0.480859i | \(-0.840325\pi\) | ||
0.876798 | − | 0.480859i | \(-0.159675\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8683.42 | + | 52371.7i | −0.000294317 | + | 0.00177509i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 4.86634e6i | − | 0.161779i | −0.996723 | − | 0.0808893i | \(-0.974224\pi\) | ||
0.996723 | − | 0.0808893i | \(-0.0257760\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.79223e7 | −1.23669 | −0.618346 | − | 0.785906i | \(-0.712197\pi\) | ||||
−0.618346 | + | 0.785906i | \(0.712197\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.10102e7 | + | 1.39837e7i | 1.31208 | + | 0.447395i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.90057e7 | 0.596631 | 0.298316 | − | 0.954467i | \(-0.403575\pi\) | ||||
0.298316 | + | 0.954467i | \(0.403575\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.66480e6 | 0.297729 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.53638e6 | − | 3.33912e7i | 0.167383 | − | 1.00952i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.45821e7 | −0.432726 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 182773.i | − | 0.00532429i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.81709e7 | − | 9.64496e6i | −1.66365 | − | 0.275840i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 7.46543e7i | − | 2.09637i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.96231e7i | 0.541107i | 0.962705 | + | 0.270554i | \(0.0872068\pi\) | ||||
−0.962705 | + | 0.270554i | \(0.912793\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.86856e7 | + | 5.47996e7i | −0.506029 | + | 1.48404i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 2.57107e7i | − | 0.683878i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.08566e7 | −0.283665 | −0.141833 | − | 0.989891i | \(-0.545299\pi\) | ||||
−0.141833 | + | 0.989891i | \(0.545299\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.80775e7 | + | 9.62947e6i | 1.49076 | + | 0.247174i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.46027e6 | −0.112486 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.66355e6 | −0.189910 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.90238e7 | − | 9.78636e6i | −1.43737 | − | 0.238322i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.40929e7 | −1.29465 | −0.647325 | − | 0.762214i | \(-0.724112\pi\) | ||||
−0.647325 | + | 0.762214i | \(0.724112\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.03836e7i | 0.244272i | 0.992513 | + | 0.122136i | \(0.0389743\pi\) | ||||
−0.992513 | + | 0.122136i | \(0.961026\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.19408e6 | + | 3.32717e6i | 0.143237 | + | 0.0769404i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 7.61934e7i | − | 1.73218i | −0.499887 | − | 0.866091i | \(-0.666625\pi\) | ||
0.499887 | − | 0.866091i | \(-0.333375\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 4.60199e7i | − | 1.02863i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.60269e7 | − | 9.28947e6i | −1.23138 | − | 0.204167i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 6.26465e7i | − | 1.35398i | −0.735990 | − | 0.676992i | \(-0.763283\pi\) | ||
0.735990 | − | 0.676992i | \(-0.236717\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.65243e7 | 0.776355 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.46442e6 | + | 3.89884e7i | −0.135148 | + | 0.815108i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.44262e7 | 0.913609 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.47119e7 | 0.297627 | 0.148813 | − | 0.988865i | \(-0.452455\pi\) | ||||
0.148813 | + | 0.988865i | \(0.452455\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.45416e7 | − | 4.26462e7i | 0.289422 | − | 0.848792i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.93233e7 | −1.74921 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 4.99644e7i | − | 0.962796i | −0.876502 | − | 0.481398i | \(-0.840129\pi\) | ||
0.876502 | − | 0.481398i | \(-0.159871\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.47884e6 | − | 5.11378e7i | 0.160784 | − | 0.969724i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.22256e6i | 0.116130i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.82580e7i | 0.519068i | 0.965734 | + | 0.259534i | \(0.0835690\pi\) | ||||
−0.965734 | + | 0.259534i | \(0.916431\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.18080e7 | − | 7.12169e7i | 0.213502 | − | 1.28768i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.93333e7i | 0.700106i | 0.936730 | + | 0.350053i | \(0.113836\pi\) | ||||
−0.936730 | + | 0.350053i | \(0.886164\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.29766e7 | 0.577861 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.06920e7 | − | 3.13566e7i | 0.184470 | − | 0.540998i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.93800e7 | 1.68830 | 0.844151 | − | 0.536105i | \(-0.180105\pi\) | ||||
0.844151 | + | 0.536105i | \(0.180105\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.84198e7 | 1.31188 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.06355e6 | − | 3.65706e7i | 0.0998962 | − | 0.602497i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.12305e7 | −1.48030 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.72756e7i | 0.276098i | 0.990425 | + | 0.138049i | \(0.0440831\pi\) | ||||
−0.990425 | + | 0.138049i | \(0.955917\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.04256e7 | − | 6.70272e6i | −0.636412 | − | 0.105519i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 2.51779e7i | − | 0.390469i | −0.980757 | − | 0.195235i | \(-0.937453\pi\) | ||
0.980757 | − | 0.195235i | \(-0.0625468\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 2.87169e6i | − | 0.0438756i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.34458e7 | − | 4.12434e7i | −0.804542 | − | 0.620853i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.40648e7i | 0.653594i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.22633e8 | −1.79241 | −0.896207 | − | 0.443637i | \(-0.853688\pi\) | ||||
−0.896207 | + | 0.443637i | \(0.853688\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.04930e8 | + | 1.73977e7i | 1.51138 | + | 0.250592i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.43430e8 | −2.03606 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.76211e7 | −0.246541 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.17507e7 | + | 1.35546e7i | 1.12741 | + | 0.186929i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.16934e8 | −1.58964 | −0.794822 | − | 0.606843i | \(-0.792436\pi\) | ||||
−0.794822 | + | 0.606843i | \(0.792436\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.29549e7i | 0.307631i | 0.988100 | + | 0.153815i | \(0.0491561\pi\) | ||||
−0.988100 | + | 0.153815i | \(0.950844\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.75394e7 | + | 1.10092e8i | −0.495982 | + | 1.45457i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 2.30016e6i | − | 0.0299635i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.17831e8i | 1.51348i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.27917e6 | + | 875306.i | 0.0668642 | + | 0.0110863i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.18511e7i | 0.897432i | 0.893674 | + | 0.448716i | \(0.148119\pi\) | ||||
−0.893674 | + | 0.448716i | \(0.851881\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.34813e7 | −0.289240 | −0.144620 | − | 0.989487i | \(-0.546196\pi\) | ||||
−0.144620 | + | 0.989487i | \(0.546196\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.77263e6 | − | 5.89409e7i | 0.118725 | − | 0.716060i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.65830e7 | 0.678018 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.93662e7 | −1.17448 | −0.587239 | − | 0.809413i | \(-0.699785\pi\) | ||||
−0.587239 | + | 0.809413i | \(0.699785\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.98753e7 | − | 2.38262e7i | −0.814720 | − | 0.277804i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.63633e7 | −0.993386 | −0.496693 | − | 0.867926i | \(-0.665453\pi\) | ||||
−0.496693 | + | 0.867926i | \(0.665453\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 1.55045e8i | − | 1.75946i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.61687e6 | − | 2.78454e7i | 0.0516922 | − | 0.311768i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 1.10266e8i | − | 1.21816i | −0.793110 | − | 0.609079i | \(-0.791539\pi\) | ||
0.793110 | − | 0.609079i | \(-0.208461\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 3.42921e7i | − | 0.373822i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.67109e7 | + | 1.00787e8i | −0.179765 | + | 1.08421i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.12316e7i | 0.225397i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.86668e7 | 0.928993 | 0.464496 | − | 0.885575i | \(-0.346235\pi\) | ||||
0.464496 | + | 0.885575i | \(0.346235\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.79513e7 | + | 4.18719e7i | 0.806094 | + | 0.432996i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.99786e7 | 0.714270 | 0.357135 | − | 0.934053i | \(-0.383754\pi\) | ||||
0.357135 | + | 0.934053i | \(0.383754\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.27134e8 | 1.28091 | 0.640455 | − | 0.767996i | \(-0.278746\pi\) | ||||
0.640455 | + | 0.767996i | \(0.278746\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.51004e6 | + | 2.72011e7i | −0.0448561 | + | 0.270537i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.45390e7 | −0.928240 | −0.464120 | − | 0.885772i | \(-0.653629\pi\) | ||||
−0.464120 | + | 0.885772i | \(0.653629\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.46996e7i | 0.917973i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.91976e8 | + | 3.18303e7i | 1.83731 | + | 0.304634i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 2.52140e7i | − | 0.238264i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 1.65966e6i | − | 0.0154860i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.31724e8 | + | 4.49156e7i | 1.21370 | + | 0.413849i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 2.12756e8i | − | 1.93586i | −0.251217 | − | 0.967931i | \(-0.580831\pi\) | ||
0.251217 | − | 0.967931i | \(-0.419169\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.83706e7 | −0.254937 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.17401e8 | + | 3.60459e7i | 1.92939 | + | 0.319900i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.47286e8 | −1.29103 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.59613e7 | −0.744246 | −0.372123 | − | 0.928183i | \(-0.621370\pi\) | ||||
−0.372123 | + | 0.928183i | \(0.621370\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.73226e7 | − | 2.87215e6i | −0.148145 | − | 0.0245630i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.52056e7 | 0.297418 | 0.148709 | − | 0.988881i | \(-0.452488\pi\) | ||||
0.148709 | + | 0.988881i | \(0.452488\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.83097e7i | 0.653544i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.86303e7 | − | 1.65820e7i | −0.400951 | − | 0.136717i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.69504e8i | 1.38074i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 1.07651e8i | − | 0.866398i | −0.901298 | − | 0.433199i | \(-0.857385\pi\) | ||
0.901298 | − | 0.433199i | \(-0.142615\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.95716e7 | + | 1.48513e7i | 0.712290 | + | 0.118100i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.75253e7i | 0.373440i | 0.982413 | + | 0.186720i | \(0.0597857\pi\) | ||||
−0.982413 | + | 0.186720i | \(0.940214\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.77268e7 | 0.525880 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.07536e7 | − | 1.25170e8i | 0.159246 | − | 0.960451i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.93663e7 | −0.753504 | −0.376752 | − | 0.926314i | \(-0.622959\pi\) | ||||
−0.376752 | + | 0.926314i | \(0.622959\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.63634e8 | −1.22634 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.62450e7 | + | 3.02122e7i | 0.416612 | + | 0.223785i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 249763. | 0.00182855 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.85259e7i | 0.640617i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.36678e7 | − | 2.03058e8i | 0.240831 | − | 1.45251i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.28148e8i | 0.906144i | 0.891474 | + | 0.453072i | \(0.149672\pi\) | ||||
−0.891474 | + | 0.453072i | \(0.850328\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 9.82990e7i | − | 0.687138i | −0.939127 | − | 0.343569i | \(-0.888364\pi\) | ||
0.939127 | − | 0.343569i | \(-0.111636\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.05728e6 | − | 6.37668e6i | 0.00730653 | − | 0.0440673i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 3.61397e7i | − | 0.246918i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.56256e8 | −1.05553 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.11516e8 | + | 7.21229e7i | 1.41273 | + | 0.481715i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.20785e7 | 0.145811 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.59244e8 | −1.03993 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.11086e7 | + | 2.47935e8i | −0.265466 | + | 1.60109i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.61873e7 | −0.358816 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.70819e8i | 1.07881i | 0.842047 | + | 0.539404i | \(0.181350\pi\) | ||||
−0.842047 | + | 0.539404i | \(0.818650\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.47044e7 | + | 7.41216e6i | 0.279223 | + | 0.0462962i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.77420e8i | 1.71375i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.63277e8i | 0.997614i | 0.866713 | + | 0.498807i | \(0.166228\pi\) | ||||
−0.866713 | + | 0.498807i | \(0.833772\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.92506e7 | − | 1.73765e8i | 0.358077 | − | 1.05013i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.65036e7i | 0.337770i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.36028e8 | 1.98701 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.68730e8 | + | 4.45564e7i | 1.57194 | + | 0.260634i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.70053e8 | −0.984056 | −0.492028 | − | 0.870579i | \(-0.663744\pi\) | ||||
−0.492028 | + | 0.870579i | \(0.663744\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.62338e7 | 0.0929359 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.64374e7 | + | 1.10156e7i | 0.376291 | + | 0.0623905i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.19497e7 | −0.122999 | −0.0614997 | − | 0.998107i | \(-0.519588\pi\) | ||||
−0.0614997 | + | 0.998107i | \(0.519588\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 2.76975e8i | − | 1.53566i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.96856e8 | + | 1.51911e8i | 1.07994 | + | 0.833373i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.00451e8i | 1.08811i | 0.839051 | + | 0.544053i | \(0.183111\pi\) | ||||
−0.839051 | + | 0.544053i | \(0.816889\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 3.51719e8i | − | 1.88924i | −0.328161 | − | 0.944622i | \(-0.606429\pi\) | ||
0.328161 | − | 0.944622i | \(-0.393571\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.02111e8 | + | 1.69304e7i | 0.542761 | + | 0.0899918i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.92532e6i | 0.0469483i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.02762e7 | −0.469944 | −0.234972 | − | 0.972002i | \(-0.575500\pi\) | ||||
−0.234972 | + | 0.972002i | \(0.575500\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.92536e6 | + | 5.98621e7i | −0.0511341 | + | 0.308401i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.49035e7 | 0.330933 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.05921e8 | 0.534533 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.06761e7 | − | 3.13100e7i | 0.0533270 | − | 0.156393i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.80510e8 | −0.892454 | −0.446227 | − | 0.894920i | \(-0.647233\pi\) | ||||
−0.446227 | + | 0.894920i | \(0.647233\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 2.60762e7i | − | 0.127614i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.24832e7 | + | 1.95914e8i | −0.157361 | + | 0.949079i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.01357e8i | 0.965612i | 0.875727 | + | 0.482806i | \(0.160382\pi\) | ||||
−0.875727 | + | 0.482806i | \(0.839618\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.67195e8i | 1.26846i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.64249e7 | + | 9.90624e7i | −0.0771934 | + | 0.465571i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 7.43194e7i | − | 0.345798i | −0.984940 | − | 0.172899i | \(-0.944687\pi\) | ||
0.984940 | − | 0.172899i | \(-0.0553134\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.71387e8 | 0.789503 | 0.394751 | − | 0.918788i | \(-0.370831\pi\) | ||||
0.394751 | + | 0.918788i | \(0.370831\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.76190e7 | − | 1.39653e8i | 0.217184 | − | 0.636939i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.85938e8 | 0.839656 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.37495e8 | 1.06191 | 0.530955 | − | 0.847400i | \(-0.321833\pi\) | ||||
0.530955 | + | 0.847400i | \(0.321833\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.59953e7 | + | 2.17096e8i | −0.159366 | + | 0.961169i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.69963e7 | −0.249875 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 3.27675e8i | − | 1.42253i | −0.702923 | − | 0.711266i | \(-0.748122\pi\) | ||
0.702923 | − | 0.711266i | \(-0.251878\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.09131e8 | − | 3.46747e7i | −0.899069 | − | 0.149069i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.80045e7i | 0.0766525i | 0.999265 | + | 0.0383262i | \(0.0122026\pi\) | ||||
−0.999265 | + | 0.0383262i | \(0.987797\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.50189e8i | 0.633236i | 0.948553 | + | 0.316618i | \(0.102547\pi\) | ||||
−0.948553 | + | 0.316618i | \(0.897453\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.02474e8 | − | 1.62475e8i | −1.26303 | − | 0.678442i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.71075e8i | 2.36172i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.51873e8 | −1.03167 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.79372e7 | + | 7.94816e6i | 0.194478 | + | 0.0322451i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.57038e8 | −1.43470 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.58819e8 | −1.03017 | −0.515085 | − | 0.857139i | \(-0.672240\pi\) | ||||
−0.515085 | + | 0.857139i | \(0.672240\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.76330e8 | − | 2.92362e7i | −0.695209 | − | 0.115268i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.39637e8 | −1.32646 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 3.61755e7i | − | 0.139957i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.52341e7 | − | 2.49967e8i | 0.326671 | − | 0.958032i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.39494e8i | 0.529643i | 0.964297 | + | 0.264821i | \(0.0853130\pi\) | ||||
−0.964297 | + | 0.264821i | \(0.914687\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.32870e8i | 0.499799i | 0.968272 | + | 0.249900i | \(0.0803976\pi\) | ||||
−0.968272 | + | 0.249900i | \(0.919602\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.53768e8 | − | 2.54954e7i | −0.573044 | − | 0.0950128i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 2.12047e8i | − | 0.782923i | −0.920195 | − | 0.391461i | \(-0.871970\pi\) | ||
0.920195 | − | 0.391461i | \(-0.128030\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.70081e8 | 0.622189 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.66117e7 | − | 1.00189e8i | 0.0602105 | − | 0.363143i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.44308e8 | 1.95481 | 0.977406 | − | 0.211371i | \(-0.0677928\pi\) | ||||
0.977406 | + | 0.211371i | \(0.0677928\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.74407e8 | −0.620641 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.41310e8 | + | 8.22822e7i | 0.850901 | + | 0.290142i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.74809e8 | −0.960229 | −0.480115 | − | 0.877206i | \(-0.659405\pi\) | ||||
−0.480115 | + | 0.877206i | \(0.659405\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.26671e8i | 1.47737i | 0.674052 | + | 0.738684i | \(0.264552\pi\) | ||||
−0.674052 | + | 0.738684i | \(0.735448\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.09223e6 | + | 4.27749e7i | −0.0243356 | + | 0.146774i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.92792e8i | 0.655577i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 3.03865e8i | − | 1.02401i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.87793e7 | + | 2.94199e8i | −0.162913 | + | 0.982568i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1.39726e8i | − | 0.462497i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.68141e8 | −0.879668 | −0.439834 | − | 0.898079i | \(-0.644963\pi\) | ||||
−0.439834 | + | 0.898079i | \(0.644963\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.76563e6 | + | 8.87200e6i | −0.0154956 | + | 0.0288476i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.37500e8 | 1.40998 | 0.704989 | − | 0.709218i | \(-0.250952\pi\) | ||||
0.704989 | + | 0.709218i | \(0.250952\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.42495e8 | 1.73295 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.99451e7 | + | 3.01230e8i | −0.158144 | + | 0.953800i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.13239e8 | −0.983136 | −0.491568 | − | 0.870839i | \(-0.663576\pi\) | ||||
−0.491568 | + | 0.870839i | \(0.663576\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 5.00415e8i | − | 1.55689i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.04520e7 | − | 1.16812e7i | −0.217282 | − | 0.0360261i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.81957e7i | 0.208497i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.18941e8i | 1.26975i | 0.772614 | + | 0.634876i | \(0.218949\pi\) | ||||
−0.772614 | + | 0.634876i | \(0.781051\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.79119e8 | + | 6.10763e7i | 0.538199 | + | 0.183516i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 3.89873e8i | − | 1.16137i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.77854e8 | 0.820576 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.92743e7 | − | 1.31440e7i | −0.232114 | − | 0.0384853i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.49924e8 | −1.01583 | −0.507913 | − | 0.861408i | \(-0.669583\pi\) | ||||
−0.507913 | + | 0.861408i | \(0.669583\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.57617e8 | −0.741496 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.39877e8 | + | 8.95136e7i | 1.54073 | + | 0.255459i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.49457e8 | −0.705891 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.25354e8i | 1.47405i | 0.675863 | + | 0.737027i | \(0.263771\pi\) | ||||
−0.675863 | + | 0.737027i | \(0.736229\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.95538e8 | − | 1.68969e8i | −1.37869 | − | 0.470109i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.40233e8i | 0.386884i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 2.51766e7i | − | 0.0688778i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.59464e8 | − | 9.27612e7i | −1.51780 | − | 0.251657i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 5.20947e8i | − | 1.40154i | −0.713385 | − | 0.700772i | \(-0.752839\pi\) | ||
0.713385 | − | 0.700772i | \(-0.247161\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −919948. | −0.00245447 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.05589e7 | + | 5.46181e8i | −0.239616 | + | 1.44518i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.91279e6 | −0.0233884 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.30045e8 | 0.858954 | 0.429477 | − | 0.903078i | \(-0.358698\pi\) | ||||
0.429477 | + | 0.903078i | \(0.358698\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.13915e8 | − | 3.23009e8i | −0.552151 | − | 0.833744i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.04299e8 | 0.523014 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.53999e8i | 1.66060i | 0.557316 | + | 0.830301i | \(0.311831\pi\) | ||||
−0.557316 | + | 0.830301i | \(0.688169\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.68142e7 | + | 3.42659e8i | −0.143085 | + | 0.862979i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.12296e8i | − | 0.280518i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 4.59389e7i | − | 0.113828i | −0.998379 | − | 0.0569138i | \(-0.981874\pi\) | ||
0.998379 | − | 0.0569138i | \(-0.0181260\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.11733e6 | + | 3.08638e7i | −0.0125773 | + | 0.0758567i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.05609e8i | 0.988873i | 0.869214 | + | 0.494437i | \(0.164626\pi\) | ||||
−0.869214 | + | 0.494437i | \(0.835374\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.32796e8 | −0.321157 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.57127e7 | − | 3.26362e7i | −0.229619 | − | 0.0782958i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.86542e8 | 1.39590 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.97506e8 | 1.64675 | 0.823375 | − | 0.567497i | \(-0.192088\pi\) | ||||
0.823375 | + | 0.567497i | \(0.192088\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.87507e6 | − | 3.54339e7i | 0.0137603 | − | 0.0829915i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.80661e8 | 1.11686 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.78773e8i | 0.412111i | 0.978540 | + | 0.206056i | \(0.0660628\pi\) | ||||
−0.978540 | + | 0.206056i | \(0.933937\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.57797e8 | − | 4.27437e7i | −0.589593 | − | 0.0977567i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 6.37897e7i | − | 0.144743i | −0.997378 | − | 0.0723713i | \(-0.976943\pi\) | ||
0.997378 | − | 0.0723713i | \(-0.0230567\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1.02182e9i | − | 2.30038i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.34357e8 | − | 3.94031e8i | 0.300107 | − | 0.880128i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.09505e8i | 0.242687i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.87883e7 | −0.173254 | −0.0866269 | − | 0.996241i | \(-0.527609\pi\) | ||||
−0.0866269 | + | 0.996241i | \(0.527609\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.11697e8 | + | 3.51001e7i | 0.461903 | + | 0.0765852i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.67409e8 | −0.795447 | −0.397724 | − | 0.917505i | \(-0.630200\pi\) | ||||
−0.397724 | + | 0.917505i | \(0.630200\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.11323e6 | 0.00883644 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.89807e8 | − | 1.64114e8i | −2.11002 | − | 0.349850i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.00483e8 | 0.424097 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 2.01000e8i | − | 0.421933i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.62247e8 | − | 3.02050e8i | 0.337981 | − | 0.629207i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 9.15542e8i | − | 1.89265i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.70858e8i | 1.78658i | 0.449478 | + | 0.893291i | \(0.351610\pi\) | ||||
−0.449478 | + | 0.893291i | \(0.648390\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.03454e8 | + | 8.34746e7i | 1.02501 | + | 0.169951i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.02018e9i | 2.06132i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.99606e7 | 0.180399 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.07102e8 | − | 6.45959e8i | 0.213156 | − | 1.28559i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.64155e6 | −0.00719301 | −0.00359651 | − | 0.999994i | \(-0.501145\pi\) | ||||
−0.00359651 | + | 0.999994i | \(0.501145\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.17288e8 | −1.40622 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.87161e8 | − | 8.42160e8i | 0.558763 | − | 1.63869i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.94039e8 | 0.374751 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 1.03680e9i | − | 1.98750i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.27211e7 | + | 4.98909e8i | −0.157397 | + | 0.949295i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 4.45865e8i | − | 0.842089i | −0.907040 | − | 0.421044i | \(-0.861664\pi\) | ||
0.907040 | − | 0.421044i | \(-0.138336\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.14079e7i | 0.152617i | 0.997084 | + | 0.0763087i | \(0.0243134\pi\) | ||||
−0.997084 | + | 0.0763087i | \(0.975687\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.83349e7 | + | 3.51831e8i | −0.108557 | + | 0.654730i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.26124e7i | 0.152606i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.47410e8 | 0.270308 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.93232e7 | + | 1.15324e8i | −0.0715810 | + | 0.209926i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.59042e8 | −0.829512 | −0.414756 | − | 0.909933i | \(-0.636133\pi\) | ||||
−0.414756 | + | 0.909933i | \(0.636133\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.53343e8 | 0.813256 | 0.406628 | − | 0.913594i | \(-0.366704\pi\) | ||||
0.406628 | + | 0.913594i | \(0.366704\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.25373e6 | + | 7.56154e6i | −0.00223276 | + | 0.0134663i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.67719e8 | 0.296529 | 0.148264 | − | 0.988948i | \(-0.452631\pi\) | ||||
0.148264 | + | 0.988948i | \(0.452631\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 3.19622e8i | − | 0.561013i | −0.959852 | − | 0.280506i | \(-0.909498\pi\) | ||
0.959852 | − | 0.280506i | \(-0.0905023\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.58504e8 | + | 4.28609e7i | 0.450468 | + | 0.0746893i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 4.55262e8i | − | 0.787637i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 4.27171e8i | − | 0.733741i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.48766e7 | + | 1.39395e8i | −0.127694 | + | 0.237723i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1.92002e8i | − | 0.325103i | −0.986700 | − | 0.162551i | \(-0.948028\pi\) | ||
0.986700 | − | 0.162551i | \(-0.0519723\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.91385e8 | −0.489868 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.16700e8 | − | 6.90904e7i | −0.695569 | − | 0.115328i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.96941e8 | −0.989375 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.84861e8 | −1.12707 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.38169e8 | + | 1.55552e8i | 1.53306 | + | 0.254186i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.38541e9 | 2.24797 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 6.72155e8i | − | 1.08299i | −0.840705 | − | 0.541493i | \(-0.817859\pi\) | ||
0.840705 | − | 0.541493i | \(-0.182141\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.69440e7 | − | 2.84309e8i | 0.155104 | − | 0.454875i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 9.87663e8i | − | 1.56916i | −0.620030 | − | 0.784578i | \(-0.712879\pi\) | ||
0.620030 | − | 0.784578i | \(-0.287121\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 5.32239e8i | − | 0.839706i | −0.907592 | − | 0.419853i | \(-0.862082\pi\) | ||
0.907592 | − | 0.419853i | \(-0.137918\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.70288e8 | + | 1.27717e8i | 1.20682 | + | 0.200096i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1.74543e8i | − | 0.271562i | −0.990739 | − | 0.135781i | \(-0.956646\pi\) | ||
0.990739 | − | 0.135781i | \(-0.0433543\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.68396e8 | −1.49625 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.73469e7 | − | 1.04623e8i | 0.0266174 | − | 0.160535i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.98465e8 | −0.607199 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.23003e7 | 0.109417 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.00013e8 | − | 2.72790e8i | −1.20242 | − | 0.410001i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.98274e8 | 1.34086 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.87256e8i | 0.574116i | 0.957913 | + | 0.287058i | \(0.0926772\pi\) | ||||
−0.957913 | + | 0.287058i | \(0.907323\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.19404e7 | − | 1.92640e8i | 0.0470299 | − | 0.283648i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1.53296e8i | − | 0.224184i | −0.993698 | − | 0.112092i | \(-0.964245\pi\) | ||
0.993698 | − | 0.112092i | \(-0.0357551\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.44238e8i | 0.645259i | 0.946525 | + | 0.322629i | \(0.104567\pi\) | ||||
−0.946525 | + | 0.322629i | \(0.895433\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.71979e8 | − | 1.03724e9i | 0.248111 | − | 1.49641i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 7.24788e8i | − | 1.03858i | −0.854598 | − | 0.519291i | \(-0.826196\pi\) | ||
0.854598 | − | 0.519291i | \(-0.173804\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.25098e9 | 1.78051 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.33434e8 | − | 1.80138e8i | −0.330013 | − | 0.254666i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.17551e8 | −0.726774 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.18241e9 | 1.64930 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.75200e7 | − | 1.65979e8i | 0.0381304 | − | 0.229973i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.40036e8 | −0.192735 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.58229e8i | 1.17335i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.66372e8 | + | 9.39066e7i | 0.769199 | + | 0.127536i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 2.13198e8i | − | 0.287632i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.84004e8i | 1.31879i | 0.751797 | + | 0.659394i | \(0.229187\pi\) | ||||
−0.751797 | + | 0.659394i | \(0.770813\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.67872e8 | + | 1.25438e8i | 0.489785 | + | 0.167008i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1.03637e9i | − | 1.37075i | −0.728188 | − | 0.685377i | \(-0.759637\pi\) | ||
0.728188 | − | 0.685377i | \(-0.240363\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.69633e7 | −0.101128 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.52119e8 | − | 1.41285e8i | −1.11234 | − | 0.184430i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.42391e8 | 0.833089 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.38166e9 | −1.78015 | −0.890074 | − | 0.455817i | \(-0.849347\pi\) | ||||
−0.890074 | + | 0.455817i | \(0.849347\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.41204e8 | − | 1.22894e8i | −0.948766 | − | 0.157309i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.29411e8 | 0.164576 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 4.06361e7i | − | 0.0513437i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.35664e6 | + | 462589.i | 0.00170304 | + | 0.000580706i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 3.15587e7i | − | 0.0393615i | −0.999806 | − | 0.0196807i | \(-0.993735\pi\) | ||
0.999806 | − | 0.0196807i | \(-0.00626498\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 3.28489e8i | − | 0.407073i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.29621e8 | − | 2.14917e7i | −0.159600 | − | 0.0264622i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 3.16843e8i | − | 0.387623i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.85838e8 | −0.347458 | −0.173729 | − | 0.984794i | \(-0.555582\pi\) | ||||
−0.173729 | + | 0.984794i | \(0.555582\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.67480e8 | + | 1.01011e9i | −0.202286 | + | 1.22003i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.48717e8 | 0.418508 | 0.209254 | − | 0.977861i | \(-0.432896\pi\) | ||||
0.209254 | + | 0.977861i | \(0.432896\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.07816e9 | −1.28572 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.53593e8 | − | 1.03060e9i | 0.655987 | − | 1.22123i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.21830e8 | −1.08543 | −0.542714 | − | 0.839918i | \(-0.682603\pi\) | ||||
−0.542714 | + | 0.839918i | \(0.682603\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.24930e8i | 0.146173i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.39369e7 | − | 5.06242e8i | 0.0975914 | − | 0.588596i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.07551e9i | − | 1.24261i | −0.783569 | − | 0.621305i | \(-0.786603\pi\) | ||
0.783569 | − | 0.621305i | \(-0.213397\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 4.86972e8i | − | 0.559106i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.26837e7 | − | 2.57435e8i | 0.0486997 | − | 0.293719i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.84317e9i | 2.08982i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.22877e8 | −0.927182 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.64969e8 | − | 2.94938e8i | −0.968549 | − | 0.330257i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.85485e8 | 0.317689 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.73910e8 | −1.07706 | −0.538529 | − | 0.842607i | \(-0.681020\pi\) | ||||
−0.538529 | + | 0.842607i | \(0.681020\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.44006e7 | + | 3.88414e8i | −0.0707813 | + | 0.426898i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.09930e9 | 1.20077 | 0.600384 | − | 0.799712i | \(-0.295014\pi\) | ||||
0.600384 | + | 0.799712i | \(0.295014\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.43601e9i | 1.55891i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.86841e6 | − | 807200.i | −0.00525258 | − | 0.000870898i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1.04074e9i | − | 1.11598i | −0.829847 | − | 0.557991i | \(-0.811572\pi\) | ||
0.829847 | − | 0.557991i | \(-0.188428\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 6.77187e8i | − | 0.721707i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.13813e8 | + | 1.50686e9i | −0.544250 | + | 1.59613i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1.57468e8i | − | 0.165780i | −0.996559 | − | 0.0828902i | \(-0.973585\pi\) | ||
0.996559 | − | 0.0828902i | \(-0.0264151\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.34323e8 | 0.977661 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.98852e9 | − | 3.29704e8i | −2.06813 | − | 0.342904i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.92740e8 | −0.819486 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.36854e8 | 0.448865 | 0.224432 | − | 0.974490i | \(-0.427947\pi\) | ||||
0.224432 | + | 0.974490i | \(0.427947\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.22688e8 | + | 8.66636e7i | 0.533819 | + | 0.0885093i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.72434e8 | 0.479592 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.98815e8i | 0.906953i | 0.891268 | + | 0.453477i | \(0.149816\pi\) | ||||
−0.891268 | + | 0.453477i | \(0.850184\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.37714e9 | + | 7.39735e8i | 1.38128 | + | 0.741958i |
(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 | 384.7.h.e.65.5 | ✓ | 8 | |
3.2 | odd | 2 | 384.7.h.f.65.2 | yes | 8 | ||
4.3 | odd | 2 | 384.7.h.f.65.3 | yes | 8 | ||
8.3 | odd | 2 | inner | 384.7.h.e.65.6 | yes | 8 | |
8.5 | even | 2 | 384.7.h.f.65.4 | yes | 8 | ||
12.11 | even | 2 | inner | 384.7.h.e.65.8 | yes | 8 | |
24.5 | odd | 2 | inner | 384.7.h.e.65.7 | yes | 8 | |
24.11 | even | 2 | 384.7.h.f.65.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.7.h.e.65.5 | ✓ | 8 | 1.1 | even | 1 | trivial | |
384.7.h.e.65.6 | yes | 8 | 8.3 | odd | 2 | inner | |
384.7.h.e.65.7 | yes | 8 | 24.5 | odd | 2 | inner | |
384.7.h.e.65.8 | yes | 8 | 12.11 | even | 2 | inner | |
384.7.h.f.65.1 | yes | 8 | 24.11 | even | 2 | ||
384.7.h.f.65.2 | yes | 8 | 3.2 | odd | 2 | ||
384.7.h.f.65.3 | yes | 8 | 4.3 | odd | 2 | ||
384.7.h.f.65.4 | yes | 8 | 8.5 | even | 2 |