Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [550,6,Mod(199,550)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(550, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("550.199");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 550 = 2 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 550.b (of order \(2\), degree \(1\), 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: | \(88.2111008971\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 22) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 550.199 |
Dual form | 550.6.b.a.199.2 |
$q$-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 \(\left(\mathbb{Z}/550\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 4.00000i | − 0.707107i | ||||||||
\(3\) | − 29.0000i | − 1.86035i | −0.367115 | − | 0.930175i | \(-0.619655\pi\) | ||||
0.367115 | − | 0.930175i | \(-0.380345\pi\) | |||||||
\(4\) | −16.0000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −116.000 | −1.31547 | ||||||||
\(7\) | 230.000i | 1.77412i | 0.461655 | + | 0.887059i | \(0.347256\pi\) | ||||
−0.461655 | + | 0.887059i | \(0.652744\pi\) | |||||||
\(8\) | 64.0000i | 0.353553i | ||||||||
\(9\) | −598.000 | −2.46091 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | 464.000i | 0.930175i | ||||||||
\(13\) | 112.000i | 0.183806i | 0.995768 | + | 0.0919030i | \(0.0292950\pi\) | ||||
−0.995768 | + | 0.0919030i | \(0.970705\pi\) | |||||||
\(14\) | 920.000 | 1.25449 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 1142.00i | 0.958393i | 0.877708 | + | 0.479197i | \(0.159072\pi\) | ||||
−0.877708 | + | 0.479197i | \(0.840928\pi\) | |||||||
\(18\) | 2392.00i | 1.74012i | ||||||||
\(19\) | 612.000 | 0.388926 | 0.194463 | − | 0.980910i | \(-0.437704\pi\) | ||||
0.194463 | + | 0.980910i | \(0.437704\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6670.00 | 3.30048 | ||||||||
\(22\) | − 484.000i | − 0.213201i | ||||||||
\(23\) | − 1941.00i | − 0.765078i | −0.923939 | − | 0.382539i | \(-0.875050\pi\) | ||||
0.923939 | − | 0.382539i | \(-0.124950\pi\) | |||||||
\(24\) | 1856.00 | 0.657733 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 448.000 | 0.129970 | ||||||||
\(27\) | 10295.0i | 2.71780i | ||||||||
\(28\) | − 3680.00i | − 0.887059i | ||||||||
\(29\) | −1192.00 | −0.263197 | −0.131599 | − | 0.991303i | \(-0.542011\pi\) | ||||
−0.131599 | + | 0.991303i | \(0.542011\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1037.00 | −0.193809 | −0.0969046 | − | 0.995294i | \(-0.530894\pi\) | ||||
−0.0969046 | + | 0.995294i | \(0.530894\pi\) | |||||||
\(32\) | − 1024.00i | − 0.176777i | ||||||||
\(33\) | − 3509.00i | − 0.560917i | ||||||||
\(34\) | 4568.00 | 0.677686 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 9568.00 | 1.23045 | ||||||||
\(37\) | − 8083.00i | − 0.970663i | −0.874330 | − | 0.485331i | \(-0.838699\pi\) | ||||
0.874330 | − | 0.485331i | \(-0.161301\pi\) | |||||||
\(38\) | − 2448.00i | − 0.275012i | ||||||||
\(39\) | 3248.00 | 0.341944 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10444.0 | −0.970303 | −0.485151 | − | 0.874430i | \(-0.661235\pi\) | ||||
−0.485151 | + | 0.874430i | \(0.661235\pi\) | |||||||
\(42\) | − 26680.0i | − 2.33379i | ||||||||
\(43\) | 58.0000i | 0.00478362i | 0.999997 | + | 0.00239181i | \(0.000761338\pi\) | ||||
−0.999997 | + | 0.00239181i | \(0.999239\pi\) | |||||||
\(44\) | −1936.00 | −0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7764.00 | −0.540992 | ||||||||
\(47\) | − 8656.00i | − 0.571574i | −0.958293 | − | 0.285787i | \(-0.907745\pi\) | ||||
0.958293 | − | 0.285787i | \(-0.0922550\pi\) | |||||||
\(48\) | − 7424.00i | − 0.465088i | ||||||||
\(49\) | −36093.0 | −2.14750 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 33118.0 | 1.78295 | ||||||||
\(52\) | − 1792.00i | − 0.0919030i | ||||||||
\(53\) | − 20318.0i | − 0.993554i | −0.867878 | − | 0.496777i | \(-0.834517\pi\) | ||||
0.867878 | − | 0.496777i | \(-0.165483\pi\) | |||||||
\(54\) | 41180.0 | 1.92177 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −14720.0 | −0.627246 | ||||||||
\(57\) | − 17748.0i | − 0.723540i | ||||||||
\(58\) | 4768.00i | 0.186109i | ||||||||
\(59\) | 21351.0 | 0.798524 | 0.399262 | − | 0.916837i | \(-0.369266\pi\) | ||||
0.399262 | + | 0.916837i | \(0.369266\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 47044.0 | 1.61875 | 0.809375 | − | 0.587293i | \(-0.199806\pi\) | ||||
0.809375 | + | 0.587293i | \(0.199806\pi\) | |||||||
\(62\) | 4148.00i | 0.137044i | ||||||||
\(63\) | − 137540.i | − 4.36594i | ||||||||
\(64\) | −4096.00 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −14036.0 | −0.396628 | ||||||||
\(67\) | − 48093.0i | − 1.30887i | −0.756120 | − | 0.654433i | \(-0.772908\pi\) | ||||
0.756120 | − | 0.654433i | \(-0.227092\pi\) | |||||||
\(68\) | − 18272.0i | − 0.479197i | ||||||||
\(69\) | −56289.0 | −1.42331 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −24967.0 | −0.587788 | −0.293894 | − | 0.955838i | \(-0.594951\pi\) | ||||
−0.293894 | + | 0.955838i | \(0.594951\pi\) | |||||||
\(72\) | − 38272.0i | − 0.870061i | ||||||||
\(73\) | − 42288.0i | − 0.928774i | −0.885632 | − | 0.464387i | \(-0.846275\pi\) | ||||
0.885632 | − | 0.464387i | \(-0.153725\pi\) | |||||||
\(74\) | −32332.0 | −0.686362 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −9792.00 | −0.194463 | ||||||||
\(77\) | 27830.0i | 0.534917i | ||||||||
\(78\) | − 12992.0i | − 0.241791i | ||||||||
\(79\) | 72410.0 | 1.30536 | 0.652681 | − | 0.757633i | \(-0.273644\pi\) | ||||
0.652681 | + | 0.757633i | \(0.273644\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 153241. | 2.59515 | ||||||||
\(82\) | 41776.0i | 0.686108i | ||||||||
\(83\) | − 15806.0i | − 0.251841i | −0.992040 | − | 0.125921i | \(-0.959812\pi\) | ||||
0.992040 | − | 0.125921i | \(-0.0401885\pi\) | |||||||
\(84\) | −106720. | −1.65024 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 232.000 | 0.00338253 | ||||||||
\(87\) | 34568.0i | 0.489639i | ||||||||
\(88\) | 7744.00i | 0.106600i | ||||||||
\(89\) | 114761. | 1.53575 | 0.767873 | − | 0.640602i | \(-0.221315\pi\) | ||||
0.767873 | + | 0.640602i | \(0.221315\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −25760.0 | −0.326094 | ||||||||
\(92\) | 31056.0i | 0.382539i | ||||||||
\(93\) | 30073.0i | 0.360553i | ||||||||
\(94\) | −34624.0 | −0.404164 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −29696.0 | −0.328867 | ||||||||
\(97\) | 5159.00i | 0.0556719i | 0.999613 | + | 0.0278360i | \(0.00886161\pi\) | ||||
−0.999613 | + | 0.0278360i | \(0.991138\pi\) | |||||||
\(98\) | 144372.i | 1.51851i | ||||||||
\(99\) | −72358.0 | −0.741991 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −61426.0 | −0.599168 | −0.299584 | − | 0.954070i | \(-0.596848\pi\) | ||||
−0.299584 | + | 0.954070i | \(0.596848\pi\) | |||||||
\(102\) | − 132472.i | − 1.26073i | ||||||||
\(103\) | 185896.i | 1.72654i | 0.504741 | + | 0.863271i | \(0.331588\pi\) | ||||
−0.504741 | + | 0.863271i | \(0.668412\pi\) | |||||||
\(104\) | −7168.00 | −0.0649852 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −81272.0 | −0.702548 | ||||||||
\(107\) | 23970.0i | 0.202399i | 0.994866 | + | 0.101200i | \(0.0322681\pi\) | ||||
−0.994866 | + | 0.101200i | \(0.967732\pi\) | |||||||
\(108\) | − 164720.i | − 1.35890i | ||||||||
\(109\) | 56326.0 | 0.454091 | 0.227045 | − | 0.973884i | \(-0.427093\pi\) | ||||
0.227045 | + | 0.973884i | \(0.427093\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −234407. | −1.80577 | ||||||||
\(112\) | 58880.0i | 0.443530i | ||||||||
\(113\) | − 261903.i | − 1.92950i | −0.263171 | − | 0.964749i | \(-0.584769\pi\) | ||||
0.263171 | − | 0.964749i | \(-0.415231\pi\) | |||||||
\(114\) | −70992.0 | −0.511620 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 19072.0 | 0.131599 | ||||||||
\(117\) | − 66976.0i | − 0.452329i | ||||||||
\(118\) | − 85404.0i | − 0.564642i | ||||||||
\(119\) | −262660. | −1.70030 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | − 188176.i | − 1.14463i | ||||||||
\(123\) | 302876.i | 1.80510i | ||||||||
\(124\) | 16592.0 | 0.0969046 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −550160. | −3.08718 | ||||||||
\(127\) | − 87404.0i | − 0.480864i | −0.970666 | − | 0.240432i | \(-0.922711\pi\) | ||||
0.970666 | − | 0.240432i | \(-0.0772891\pi\) | |||||||
\(128\) | 16384.0i | 0.0883883i | ||||||||
\(129\) | 1682.00 | 0.00889922 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 265122. | 1.34979 | 0.674897 | − | 0.737912i | \(-0.264188\pi\) | ||||
0.674897 | + | 0.737912i | \(0.264188\pi\) | |||||||
\(132\) | 56144.0i | 0.280458i | ||||||||
\(133\) | 140760.i | 0.690002i | ||||||||
\(134\) | −192372. | −0.925507 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −73088.0 | −0.338843 | ||||||||
\(137\) | − 245857.i | − 1.11913i | −0.828786 | − | 0.559566i | \(-0.810968\pi\) | ||||
0.828786 | − | 0.559566i | \(-0.189032\pi\) | |||||||
\(138\) | 225156.i | 1.00644i | ||||||||
\(139\) | 363594. | 1.59617 | 0.798086 | − | 0.602544i | \(-0.205846\pi\) | ||||
0.798086 | + | 0.602544i | \(0.205846\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −251024. | −1.06333 | ||||||||
\(142\) | 99868.0i | 0.415629i | ||||||||
\(143\) | 13552.0i | 0.0554196i | ||||||||
\(144\) | −153088. | −0.615226 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −169152. | −0.656742 | ||||||||
\(147\) | 1.04670e6i | 3.99510i | ||||||||
\(148\) | 129328.i | 0.485331i | ||||||||
\(149\) | 55750.0 | 0.205721 | 0.102861 | − | 0.994696i | \(-0.467200\pi\) | ||||
0.102861 | + | 0.994696i | \(0.467200\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 65642.0 | 0.234282 | 0.117141 | − | 0.993115i | \(-0.462627\pi\) | ||||
0.117141 | + | 0.993115i | \(0.462627\pi\) | |||||||
\(152\) | 39168.0i | 0.137506i | ||||||||
\(153\) | − 682916.i | − 2.35852i | ||||||||
\(154\) | 111320. | 0.378243 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −51968.0 | −0.170972 | ||||||||
\(157\) | 275367.i | 0.891585i | 0.895136 | + | 0.445793i | \(0.147078\pi\) | ||||
−0.895136 | + | 0.445793i | \(0.852922\pi\) | |||||||
\(158\) | − 289640.i | − 0.923030i | ||||||||
\(159\) | −589222. | −1.84836 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 446430. | 1.35734 | ||||||||
\(162\) | − 612964.i | − 1.83505i | ||||||||
\(163\) | 291940.i | 0.860646i | 0.902675 | + | 0.430323i | \(0.141600\pi\) | ||||
−0.902675 | + | 0.430323i | \(0.858400\pi\) | |||||||
\(164\) | 167104. | 0.485151 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −63224.0 | −0.178079 | ||||||||
\(167\) | 337344.i | 0.936013i | 0.883725 | + | 0.468006i | \(0.155028\pi\) | ||||
−0.883725 | + | 0.468006i | \(0.844972\pi\) | |||||||
\(168\) | 426880.i | 1.16690i | ||||||||
\(169\) | 358749. | 0.966215 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −365976. | −0.957111 | ||||||||
\(172\) | − 928.000i | − 0.00239181i | ||||||||
\(173\) | − 116742.i | − 0.296560i | −0.988945 | − | 0.148280i | \(-0.952626\pi\) | ||||
0.988945 | − | 0.148280i | \(-0.0473736\pi\) | |||||||
\(174\) | 138272. | 0.346227 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 30976.0 | 0.0753778 | ||||||||
\(177\) | − 619179.i | − 1.48554i | ||||||||
\(178\) | − 459044.i | − 1.08594i | ||||||||
\(179\) | 19107.0 | 0.0445718 | 0.0222859 | − | 0.999752i | \(-0.492906\pi\) | ||||
0.0222859 | + | 0.999752i | \(0.492906\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16177.0 | −0.0367030 | −0.0183515 | − | 0.999832i | \(-0.505842\pi\) | ||||
−0.0183515 | + | 0.999832i | \(0.505842\pi\) | |||||||
\(182\) | 103040.i | 0.230583i | ||||||||
\(183\) | − 1.36428e6i | − 3.01144i | ||||||||
\(184\) | 124224. | 0.270496 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 120292. | 0.254950 | ||||||||
\(187\) | 138182.i | 0.288966i | ||||||||
\(188\) | 138496.i | 0.285787i | ||||||||
\(189\) | −2.36785e6 | −4.82169 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 685333. | 1.35931 | 0.679655 | − | 0.733532i | \(-0.262130\pi\) | ||||
0.679655 | + | 0.733532i | \(0.262130\pi\) | |||||||
\(192\) | 118784.i | 0.232544i | ||||||||
\(193\) | − 309292.i | − 0.597689i | −0.954302 | − | 0.298845i | \(-0.903399\pi\) | ||||
0.954302 | − | 0.298845i | \(-0.0966012\pi\) | |||||||
\(194\) | 20636.0 | 0.0393660 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 577488. | 1.07375 | ||||||||
\(197\) | 120930.i | 0.222008i | 0.993820 | + | 0.111004i | \(0.0354066\pi\) | ||||
−0.993820 | + | 0.111004i | \(0.964593\pi\) | |||||||
\(198\) | 289432.i | 0.524667i | ||||||||
\(199\) | −915536. | −1.63886 | −0.819432 | − | 0.573177i | \(-0.805711\pi\) | ||||
−0.819432 | + | 0.573177i | \(0.805711\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.39470e6 | −2.43495 | ||||||||
\(202\) | 245704.i | 0.423676i | ||||||||
\(203\) | − 274160.i | − 0.466943i | ||||||||
\(204\) | −529888. | −0.891474 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 743584. | 1.22085 | ||||||||
\(207\) | 1.16072e6i | 1.88279i | ||||||||
\(208\) | 28672.0i | 0.0459515i | ||||||||
\(209\) | 74052.0 | 0.117266 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −134580. | −0.208101 | −0.104051 | − | 0.994572i | \(-0.533180\pi\) | ||||
−0.104051 | + | 0.994572i | \(0.533180\pi\) | |||||||
\(212\) | 325088.i | 0.496777i | ||||||||
\(213\) | 724043.i | 1.09349i | ||||||||
\(214\) | 95880.0 | 0.143118 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −658880. | −0.960886 | ||||||||
\(217\) | − 238510.i | − 0.343841i | ||||||||
\(218\) | − 225304.i | − 0.321091i | ||||||||
\(219\) | −1.22635e6 | −1.72785 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −127904. | −0.176158 | ||||||||
\(222\) | 937628.i | 1.27687i | ||||||||
\(223\) | 468839.i | 0.631337i | 0.948869 | + | 0.315669i | \(0.102229\pi\) | ||||
−0.948869 | + | 0.315669i | \(0.897771\pi\) | |||||||
\(224\) | 235520. | 0.313623 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.04761e6 | −1.36436 | ||||||||
\(227\) | − 275022.i | − 0.354244i | −0.984189 | − | 0.177122i | \(-0.943321\pi\) | ||||
0.984189 | − | 0.177122i | \(-0.0566788\pi\) | |||||||
\(228\) | 283968.i | 0.361770i | ||||||||
\(229\) | 642281. | 0.809350 | 0.404675 | − | 0.914461i | \(-0.367385\pi\) | ||||
0.404675 | + | 0.914461i | \(0.367385\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 807070. | 0.995133 | ||||||||
\(232\) | − 76288.0i | − 0.0930543i | ||||||||
\(233\) | − 1.50485e6i | − 1.81595i | −0.419029 | − | 0.907973i | \(-0.637629\pi\) | ||||
0.419029 | − | 0.907973i | \(-0.362371\pi\) | |||||||
\(234\) | −267904. | −0.319845 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −341616. | −0.399262 | ||||||||
\(237\) | − 2.09989e6i | − 2.42843i | ||||||||
\(238\) | 1.05064e6i | 1.20230i | ||||||||
\(239\) | 304694. | 0.345040 | 0.172520 | − | 0.985006i | \(-0.444809\pi\) | ||||
0.172520 | + | 0.985006i | \(0.444809\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.27181e6 | 1.41052 | 0.705260 | − | 0.708949i | \(-0.250830\pi\) | ||||
0.705260 | + | 0.708949i | \(0.250830\pi\) | |||||||
\(242\) | − 58564.0i | − 0.0642824i | ||||||||
\(243\) | − 1.94230e6i | − 2.11009i | ||||||||
\(244\) | −752704. | −0.809375 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.21150e6 | 1.27640 | ||||||||
\(247\) | 68544.0i | 0.0714870i | ||||||||
\(248\) | − 66368.0i | − 0.0685219i | ||||||||
\(249\) | −458374. | −0.468513 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 629965. | 0.631149 | 0.315575 | − | 0.948901i | \(-0.397803\pi\) | ||||
0.315575 | + | 0.948901i | \(0.397803\pi\) | |||||||
\(252\) | 2.20064e6i | 2.18297i | ||||||||
\(253\) | − 234861.i | − 0.230680i | ||||||||
\(254\) | −349616. | −0.340022 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | − 544086.i | − 0.513848i | −0.966432 | − | 0.256924i | \(-0.917291\pi\) | ||||
0.966432 | − | 0.256924i | \(-0.0827090\pi\) | |||||||
\(258\) | − 6728.00i | − 0.00629270i | ||||||||
\(259\) | 1.85909e6 | 1.72207 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 712816. | 0.647703 | ||||||||
\(262\) | − 1.06049e6i | − 0.954449i | ||||||||
\(263\) | − 1.98933e6i | − 1.77345i | −0.462300 | − | 0.886724i | \(-0.652976\pi\) | ||||
0.462300 | − | 0.886724i | \(-0.347024\pi\) | |||||||
\(264\) | 224576. | 0.198314 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 563040. | 0.487905 | ||||||||
\(267\) | − 3.32807e6i | − 2.85703i | ||||||||
\(268\) | 769488.i | 0.654433i | ||||||||
\(269\) | −1.75446e6 | −1.47830 | −0.739149 | − | 0.673541i | \(-0.764772\pi\) | ||||
−0.739149 | + | 0.673541i | \(0.764772\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.65824e6 | −1.37159 | −0.685795 | − | 0.727795i | \(-0.740545\pi\) | ||||
−0.685795 | + | 0.727795i | \(0.740545\pi\) | |||||||
\(272\) | 292352.i | 0.239598i | ||||||||
\(273\) | 747040.i | 0.606649i | ||||||||
\(274\) | −983428. | −0.791346 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 900624. | 0.711657 | ||||||||
\(277\) | 42634.0i | 0.0333854i | 0.999861 | + | 0.0166927i | \(0.00531370\pi\) | ||||
−0.999861 | + | 0.0166927i | \(0.994686\pi\) | |||||||
\(278\) | − 1.45438e6i | − 1.12866i | ||||||||
\(279\) | 620126. | 0.476946 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 319510. | 0.241390 | 0.120695 | − | 0.992690i | \(-0.461488\pi\) | ||||
0.120695 | + | 0.992690i | \(0.461488\pi\) | |||||||
\(282\) | 1.00410e6i | 0.751887i | ||||||||
\(283\) | − 2.02735e6i | − 1.50474i | −0.658739 | − | 0.752371i | \(-0.728910\pi\) | ||||
0.658739 | − | 0.752371i | \(-0.271090\pi\) | |||||||
\(284\) | 399472. | 0.293894 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 54208.0 | 0.0391876 | ||||||||
\(287\) | − 2.40212e6i | − 1.72143i | ||||||||
\(288\) | 612352.i | 0.435031i | ||||||||
\(289\) | 115693. | 0.0814821 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 149611. | 0.103569 | ||||||||
\(292\) | 676608.i | 0.464387i | ||||||||
\(293\) | 718844.i | 0.489177i | 0.969627 | + | 0.244588i | \(0.0786528\pi\) | ||||
−0.969627 | + | 0.244588i | \(0.921347\pi\) | |||||||
\(294\) | 4.18679e6 | 2.82496 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 517312. | 0.343181 | ||||||||
\(297\) | 1.24570e6i | 0.819446i | ||||||||
\(298\) | − 223000.i | − 0.145467i | ||||||||
\(299\) | 217392. | 0.140626 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13340.0 | −0.00848671 | ||||||||
\(302\) | − 262568.i | − 0.165663i | ||||||||
\(303\) | 1.78135e6i | 1.11466i | ||||||||
\(304\) | 156672. | 0.0972316 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.73166e6 | −1.66772 | ||||||||
\(307\) | 1.98142e6i | 1.19986i | 0.800052 | + | 0.599930i | \(0.204805\pi\) | ||||
−0.800052 | + | 0.599930i | \(0.795195\pi\) | |||||||
\(308\) | − 445280.i | − 0.267458i | ||||||||
\(309\) | 5.39098e6 | 3.21197 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.51030e6 | −0.885446 | −0.442723 | − | 0.896658i | \(-0.645988\pi\) | ||||
−0.442723 | + | 0.896658i | \(0.645988\pi\) | |||||||
\(312\) | 207872.i | 0.120895i | ||||||||
\(313\) | 2.00092e6i | 1.15443i | 0.816591 | + | 0.577216i | \(0.195861\pi\) | ||||
−0.816591 | + | 0.577216i | \(0.804139\pi\) | |||||||
\(314\) | 1.10147e6 | 0.630446 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.15856e6 | −0.652681 | ||||||||
\(317\) | 259331.i | 0.144946i | 0.997370 | + | 0.0724730i | \(0.0230891\pi\) | ||||
−0.997370 | + | 0.0724730i | \(0.976911\pi\) | |||||||
\(318\) | 2.35689e6i | 1.30699i | ||||||||
\(319\) | −144232. | −0.0793569 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 695130. | 0.376533 | ||||||||
\(322\) | − 1.78572e6i | − 0.959784i | ||||||||
\(323\) | 698904.i | 0.372744i | ||||||||
\(324\) | −2.45186e6 | −1.29757 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.16776e6 | 0.608569 | ||||||||
\(327\) | − 1.63345e6i | − 0.844768i | ||||||||
\(328\) | − 668416.i | − 0.343054i | ||||||||
\(329\) | 1.99088e6 | 1.01404 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 51203.0 | 0.0256877 | 0.0128439 | − | 0.999918i | \(-0.495912\pi\) | ||||
0.0128439 | + | 0.999918i | \(0.495912\pi\) | |||||||
\(332\) | 252896.i | 0.125921i | ||||||||
\(333\) | 4.83363e6i | 2.38871i | ||||||||
\(334\) | 1.34938e6 | 0.661861 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.70752e6 | 0.825121 | ||||||||
\(337\) | − 266870.i | − 0.128004i | −0.997950 | − | 0.0640022i | \(-0.979614\pi\) | ||||
0.997950 | − | 0.0640022i | \(-0.0203865\pi\) | |||||||
\(338\) | − 1.43500e6i | − 0.683217i | ||||||||
\(339\) | −7.59519e6 | −3.58954 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −125477. | −0.0584357 | ||||||||
\(342\) | 1.46390e6i | 0.676780i | ||||||||
\(343\) | − 4.43578e6i | − 2.03580i | ||||||||
\(344\) | −3712.00 | −0.00169127 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −466968. | −0.209699 | ||||||||
\(347\) | − 622800.i | − 0.277667i | −0.990316 | − | 0.138834i | \(-0.955665\pi\) | ||||
0.990316 | − | 0.138834i | \(-0.0443354\pi\) | |||||||
\(348\) | − 553088.i | − 0.244820i | ||||||||
\(349\) | −2.43649e6 | −1.07078 | −0.535391 | − | 0.844604i | \(-0.679836\pi\) | ||||
−0.535391 | + | 0.844604i | \(0.679836\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.15304e6 | −0.499547 | ||||||||
\(352\) | − 123904.i | − 0.0533002i | ||||||||
\(353\) | 1.55957e6i | 0.666144i | 0.942901 | + | 0.333072i | \(0.108085\pi\) | ||||
−0.942901 | + | 0.333072i | \(0.891915\pi\) | |||||||
\(354\) | −2.47672e6 | −1.05043 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.83618e6 | −0.767873 | ||||||||
\(357\) | 7.61714e6i | 3.16316i | ||||||||
\(358\) | − 76428.0i | − 0.0315170i | ||||||||
\(359\) | −1.91961e6 | −0.786098 | −0.393049 | − | 0.919518i | \(-0.628580\pi\) | ||||
−0.393049 | + | 0.919518i | \(0.628580\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.10156e6 | −0.848736 | ||||||||
\(362\) | 64708.0i | 0.0259529i | ||||||||
\(363\) | − 424589.i | − 0.169123i | ||||||||
\(364\) | 412160. | 0.163047 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5.45710e6 | −2.12941 | ||||||||
\(367\) | − 3.61225e6i | − 1.39995i | −0.714167 | − | 0.699975i | \(-0.753194\pi\) | ||||
0.714167 | − | 0.699975i | \(-0.246806\pi\) | |||||||
\(368\) | − 496896.i | − 0.191270i | ||||||||
\(369\) | 6.24551e6 | 2.38782 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.67314e6 | 1.76268 | ||||||||
\(372\) | − 481168.i | − 0.180277i | ||||||||
\(373\) | 3.93968e6i | 1.46619i | 0.680128 | + | 0.733093i | \(0.261924\pi\) | ||||
−0.680128 | + | 0.733093i | \(0.738076\pi\) | |||||||
\(374\) | 552728. | 0.204330 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 553984. | 0.202082 | ||||||||
\(377\) | − 133504.i | − 0.0483772i | ||||||||
\(378\) | 9.47140e6i | 3.40945i | ||||||||
\(379\) | 2.18829e6 | 0.782540 | 0.391270 | − | 0.920276i | \(-0.372036\pi\) | ||||
0.391270 | + | 0.920276i | \(0.372036\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.53472e6 | −0.894575 | ||||||||
\(382\) | − 2.74133e6i | − 0.961177i | ||||||||
\(383\) | 768387.i | 0.267660i | 0.991004 | + | 0.133830i | \(0.0427276\pi\) | ||||
−0.991004 | + | 0.133830i | \(0.957272\pi\) | |||||||
\(384\) | 475136. | 0.164433 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.23717e6 | −0.422630 | ||||||||
\(387\) | − 34684.0i | − 0.0117720i | ||||||||
\(388\) | − 82544.0i | − 0.0278360i | ||||||||
\(389\) | −324313. | −0.108665 | −0.0543326 | − | 0.998523i | \(-0.517303\pi\) | ||||
−0.0543326 | + | 0.998523i | \(0.517303\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.21662e6 | 0.733246 | ||||||||
\(392\) | − 2.30995e6i | − 0.759255i | ||||||||
\(393\) | − 7.68854e6i | − 2.51109i | ||||||||
\(394\) | 483720. | 0.156983 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.15773e6 | 0.370995 | ||||||||
\(397\) | − 334758.i | − 0.106599i | −0.998579 | − | 0.0532997i | \(-0.983026\pi\) | ||||
0.998579 | − | 0.0532997i | \(-0.0169739\pi\) | |||||||
\(398\) | 3.66214e6i | 1.15885i | ||||||||
\(399\) | 4.08204e6 | 1.28365 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −902022. | −0.280128 | −0.140064 | − | 0.990142i | \(-0.544731\pi\) | ||||
−0.140064 | + | 0.990142i | \(0.544731\pi\) | |||||||
\(402\) | 5.57879e6i | 1.72177i | ||||||||
\(403\) | − 116144.i | − 0.0356233i | ||||||||
\(404\) | 982816. | 0.299584 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.09664e6 | −0.330179 | ||||||||
\(407\) | − 978043.i | − 0.292666i | ||||||||
\(408\) | 2.11955e6i | 0.630367i | ||||||||
\(409\) | 5.00457e6 | 1.47931 | 0.739654 | − | 0.672987i | \(-0.234989\pi\) | ||||
0.739654 | + | 0.672987i | \(0.234989\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.12985e6 | −2.08198 | ||||||||
\(412\) | − 2.97434e6i | − 0.863271i | ||||||||
\(413\) | 4.91073e6i | 1.41668i | ||||||||
\(414\) | 4.64287e6 | 1.33133 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 114688. | 0.0324926 | ||||||||
\(417\) | − 1.05442e7i | − 2.96944i | ||||||||
\(418\) | − 296208.i | − 0.0829194i | ||||||||
\(419\) | 3.00124e6 | 0.835151 | 0.417576 | − | 0.908642i | \(-0.362880\pi\) | ||||
0.417576 | + | 0.908642i | \(0.362880\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.56224e6 | 1.25451 | 0.627253 | − | 0.778816i | \(-0.284179\pi\) | ||||
0.627253 | + | 0.778816i | \(0.284179\pi\) | |||||||
\(422\) | 538320.i | 0.147150i | ||||||||
\(423\) | 5.17629e6i | 1.40659i | ||||||||
\(424\) | 1.30035e6 | 0.351274 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.89617e6 | 0.773215 | ||||||||
\(427\) | 1.08201e7i | 2.87185i | ||||||||
\(428\) | − 383520.i | − 0.101200i | ||||||||
\(429\) | 393008. | 0.103100 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.89783e6 | 1.27002 | 0.635009 | − | 0.772504i | \(-0.280996\pi\) | ||||
0.635009 | + | 0.772504i | \(0.280996\pi\) | |||||||
\(432\) | 2.63552e6i | 0.679449i | ||||||||
\(433\) | 6.72876e6i | 1.72471i | 0.506307 | + | 0.862353i | \(0.331010\pi\) | ||||
−0.506307 | + | 0.862353i | \(0.668990\pi\) | |||||||
\(434\) | −954040. | −0.243132 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −901216. | −0.227045 | ||||||||
\(437\) | − 1.18789e6i | − 0.297559i | ||||||||
\(438\) | 4.90541e6i | 1.22177i | ||||||||
\(439\) | 3.35034e6 | 0.829711 | 0.414856 | − | 0.909887i | \(-0.363832\pi\) | ||||
0.414856 | + | 0.909887i | \(0.363832\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.15836e7 | 5.28479 | ||||||||
\(442\) | 511616.i | 0.124563i | ||||||||
\(443\) | − 7.12434e6i | − 1.72479i | −0.506238 | − | 0.862394i | \(-0.668964\pi\) | ||||
0.506238 | − | 0.862394i | \(-0.331036\pi\) | |||||||
\(444\) | 3.75051e6 | 0.902886 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.87536e6 | 0.446423 | ||||||||
\(447\) | − 1.61675e6i | − 0.382714i | ||||||||
\(448\) | − 942080.i | − 0.221765i | ||||||||
\(449\) | 2.70928e6 | 0.634218 | 0.317109 | − | 0.948389i | \(-0.397288\pi\) | ||||
0.317109 | + | 0.948389i | \(0.397288\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.26372e6 | −0.292557 | ||||||||
\(452\) | 4.19045e6i | 0.964749i | ||||||||
\(453\) | − 1.90362e6i | − 0.435847i | ||||||||
\(454\) | −1.10009e6 | −0.250489 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.13587e6 | 0.255810 | ||||||||
\(457\) | − 2.41361e6i | − 0.540601i | −0.962776 | − | 0.270301i | \(-0.912877\pi\) | ||||
0.962776 | − | 0.270301i | \(-0.0871231\pi\) | |||||||
\(458\) | − 2.56912e6i | − 0.572297i | ||||||||
\(459\) | −1.17569e7 | −2.60472 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.56065e6 | −1.43779 | −0.718894 | − | 0.695120i | \(-0.755351\pi\) | ||||
−0.718894 | + | 0.695120i | \(0.755351\pi\) | |||||||
\(462\) | − 3.22828e6i | − 0.703665i | ||||||||
\(463\) | − 4.72421e6i | − 1.02418i | −0.858932 | − | 0.512090i | \(-0.828871\pi\) | ||||
0.858932 | − | 0.512090i | \(-0.171129\pi\) | |||||||
\(464\) | −305152. | −0.0657993 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.01939e6 | −1.28407 | ||||||||
\(467\) | 2.28444e6i | 0.484716i | 0.970187 | + | 0.242358i | \(0.0779209\pi\) | ||||
−0.970187 | + | 0.242358i | \(0.922079\pi\) | |||||||
\(468\) | 1.07162e6i | 0.226165i | ||||||||
\(469\) | 1.10614e7 | 2.32208 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.98564e6 | 1.65866 | ||||||||
\(472\) | 1.36646e6i | 0.282321i | ||||||||
\(473\) | 7018.00i | 0.00144232i | ||||||||
\(474\) | −8.39956e6 | −1.71716 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.20256e6 | 0.850152 | ||||||||
\(477\) | 1.21502e7i | 2.44504i | ||||||||
\(478\) | − 1.21878e6i | − 0.243980i | ||||||||
\(479\) | −951544. | −0.189492 | −0.0947458 | − | 0.995501i | \(-0.530204\pi\) | ||||
−0.0947458 | + | 0.995501i | \(0.530204\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 905296. | 0.178414 | ||||||||
\(482\) | − 5.08723e6i | − 0.997388i | ||||||||
\(483\) | − 1.29465e7i | − 2.52513i | ||||||||
\(484\) | −234256. | −0.0454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −7.76922e6 | −1.49206 | ||||||||
\(487\) | − 3.51484e6i | − 0.671558i | −0.941941 | − | 0.335779i | \(-0.891000\pi\) | ||||
0.941941 | − | 0.335779i | \(-0.109000\pi\) | |||||||
\(488\) | 3.01082e6i | 0.572314i | ||||||||
\(489\) | 8.46626e6 | 1.60110 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.78719e6 | −1.08334 | −0.541669 | − | 0.840592i | \(-0.682207\pi\) | ||||
−0.541669 | + | 0.840592i | \(0.682207\pi\) | |||||||
\(492\) | − 4.84602e6i | − 0.902552i | ||||||||
\(493\) | − 1.36126e6i | − 0.252246i | ||||||||
\(494\) | 274176. | 0.0505489 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −265472. | −0.0484523 | ||||||||
\(497\) | − 5.74241e6i | − 1.04281i | ||||||||
\(498\) | 1.83350e6i | 0.331289i | ||||||||
\(499\) | −1.02912e6 | −0.185019 | −0.0925095 | − | 0.995712i | \(-0.529489\pi\) | ||||
−0.0925095 | + | 0.995712i | \(0.529489\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.78298e6 | 1.74131 | ||||||||
\(502\) | − 2.51986e6i | − 0.446290i | ||||||||
\(503\) | − 727370.i | − 0.128184i | −0.997944 | − | 0.0640922i | \(-0.979585\pi\) | ||||
0.997944 | − | 0.0640922i | \(-0.0204152\pi\) | |||||||
\(504\) | 8.80256e6 | 1.54359 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −939444. | −0.163115 | ||||||||
\(507\) | − 1.04037e7i | − 1.79750i | ||||||||
\(508\) | 1.39846e6i | 0.240432i | ||||||||
\(509\) | 1.94630e6 | 0.332977 | 0.166489 | − | 0.986043i | \(-0.446757\pi\) | ||||
0.166489 | + | 0.986043i | \(0.446757\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.72624e6 | 1.64776 | ||||||||
\(512\) | − 262144.i | − 0.0441942i | ||||||||
\(513\) | 6.30054e6i | 1.05702i | ||||||||
\(514\) | −2.17634e6 | −0.363345 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −26912.0 | −0.00444961 | ||||||||
\(517\) | − 1.04738e6i | − 0.172336i | ||||||||
\(518\) | − 7.43636e6i | − 1.21769i | ||||||||
\(519\) | −3.38552e6 | −0.551705 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.03133e7 | −1.66457 | −0.832286 | − | 0.554346i | \(-0.812968\pi\) | ||||
−0.832286 | + | 0.554346i | \(0.812968\pi\) | |||||||
\(522\) | − 2.85126e6i | − 0.457995i | ||||||||
\(523\) | − 6.86840e6i | − 1.09800i | −0.835823 | − | 0.548998i | \(-0.815009\pi\) | ||||
0.835823 | − | 0.548998i | \(-0.184991\pi\) | |||||||
\(524\) | −4.24195e6 | −0.674897 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.95734e6 | −1.25402 | ||||||||
\(527\) | − 1.18425e6i | − 0.185746i | ||||||||
\(528\) | − 898304.i | − 0.140229i | ||||||||
\(529\) | 2.66886e6 | 0.414655 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.27679e7 | −1.96509 | ||||||||
\(532\) | − 2.25216e6i | − 0.345001i | ||||||||
\(533\) | − 1.16973e6i | − 0.178347i | ||||||||
\(534\) | −1.33123e7 | −2.02022 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.07795e6 | 0.462754 | ||||||||
\(537\) | − 554103.i | − 0.0829191i | ||||||||
\(538\) | 7.01783e6i | 1.04532i | ||||||||
\(539\) | −4.36725e6 | −0.647495 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.00545e7 | 1.47695 | 0.738476 | − | 0.674280i | \(-0.235546\pi\) | ||||
0.738476 | + | 0.674280i | \(0.235546\pi\) | |||||||
\(542\) | 6.63296e6i | 0.969860i | ||||||||
\(543\) | 469133.i | 0.0682805i | ||||||||
\(544\) | 1.16941e6 | 0.169422 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.98816e6 | 0.428965 | ||||||||
\(547\) | − 9.85725e6i | − 1.40860i | −0.709903 | − | 0.704299i | \(-0.751261\pi\) | ||||
0.709903 | − | 0.704299i | \(-0.248739\pi\) | |||||||
\(548\) | 3.93371e6i | 0.559566i | ||||||||
\(549\) | −2.81323e7 | −3.98359 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −729504. | −0.102364 | ||||||||
\(552\) | − 3.60250e6i | − 0.503218i | ||||||||
\(553\) | 1.66543e7i | 2.31587i | ||||||||
\(554\) | 170536. | 0.0236070 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.81750e6 | −0.798086 | ||||||||
\(557\) | 1.45892e7i | 1.99247i | 0.0866757 | + | 0.996237i | \(0.472376\pi\) | ||||
−0.0866757 | + | 0.996237i | \(0.527624\pi\) | |||||||
\(558\) | − 2.48050e6i | − 0.337252i | ||||||||
\(559\) | −6496.00 | −0.000879258 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.00728e6 | 0.537579 | ||||||||
\(562\) | − 1.27804e6i | − 0.170688i | ||||||||
\(563\) | − 1.02413e7i | − 1.36171i | −0.732418 | − | 0.680855i | \(-0.761608\pi\) | ||||
0.732418 | − | 0.680855i | \(-0.238392\pi\) | |||||||
\(564\) | 4.01638e6 | 0.531664 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −8.10939e6 | −1.06401 | ||||||||
\(567\) | 3.52454e7i | 4.60410i | ||||||||
\(568\) | − 1.59789e6i | − 0.207814i | ||||||||
\(569\) | 751816. | 0.0973489 | 0.0486744 | − | 0.998815i | \(-0.484500\pi\) | ||||
0.0486744 | + | 0.998815i | \(0.484500\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.01854e6 | −0.900858 | −0.450429 | − | 0.892812i | \(-0.648729\pi\) | ||||
−0.450429 | + | 0.892812i | \(0.648729\pi\) | |||||||
\(572\) | − 216832.i | − 0.0277098i | ||||||||
\(573\) | − 1.98747e7i | − 2.52879i | ||||||||
\(574\) | −9.60848e6 | −1.21724 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.44941e6 | 0.307613 | ||||||||
\(577\) | 3.36377e6i | 0.420617i | 0.977635 | + | 0.210308i | \(0.0674468\pi\) | ||||
−0.977635 | + | 0.210308i | \(0.932553\pi\) | |||||||
\(578\) | − 462772.i | − 0.0576166i | ||||||||
\(579\) | −8.96947e6 | −1.11191 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.63538e6 | 0.446796 | ||||||||
\(582\) | − 598444.i | − 0.0732346i | ||||||||
\(583\) | − 2.45848e6i | − 0.299568i | ||||||||
\(584\) | 2.70643e6 | 0.328371 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.87538e6 | 0.345900 | ||||||||
\(587\) | − 1.40585e7i | − 1.68401i | −0.539468 | − | 0.842006i | \(-0.681375\pi\) | ||||
0.539468 | − | 0.842006i | \(-0.318625\pi\) | |||||||
\(588\) | − 1.67472e7i | − 1.99755i | ||||||||
\(589\) | −634644. | −0.0753775 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.50697e6 | 0.413013 | ||||||||
\(592\) | − 2.06925e6i | − 0.242666i | ||||||||
\(593\) | − 5.39420e6i | − 0.629927i | −0.949104 | − | 0.314963i | \(-0.898008\pi\) | ||||
0.949104 | − | 0.314963i | \(-0.101992\pi\) | |||||||
\(594\) | 4.98278e6 | 0.579436 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −892000. | −0.102861 | ||||||||
\(597\) | 2.65505e7i | 3.04886i | ||||||||
\(598\) | − 869568.i | − 0.0994376i | ||||||||
\(599\) | 1.20204e7 | 1.36883 | 0.684417 | − | 0.729090i | \(-0.260057\pi\) | ||||
0.684417 | + | 0.729090i | \(0.260057\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.64636e6 | 0.185925 | 0.0929626 | − | 0.995670i | \(-0.470366\pi\) | ||||
0.0929626 | + | 0.995670i | \(0.470366\pi\) | |||||||
\(602\) | 53360.0i | 0.00600101i | ||||||||
\(603\) | 2.87596e7i | 3.22099i | ||||||||
\(604\) | −1.05027e6 | −0.117141 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 7.12542e6 | 0.788186 | ||||||||
\(607\) | − 4.88451e6i | − 0.538083i | −0.963129 | − | 0.269041i | \(-0.913293\pi\) | ||||
0.963129 | − | 0.269041i | \(-0.0867068\pi\) | |||||||
\(608\) | − 626688.i | − 0.0687531i | ||||||||
\(609\) | −7.95064e6 | −0.868678 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 969472. | 0.105059 | ||||||||
\(612\) | 1.09267e7i | 1.17926i | ||||||||
\(613\) | 3.49011e6i | 0.375136i | 0.982252 | + | 0.187568i | \(0.0600604\pi\) | ||||
−0.982252 | + | 0.187568i | \(0.939940\pi\) | |||||||
\(614\) | 7.92568e6 | 0.848429 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.78112e6 | −0.189122 | ||||||||
\(617\) | − 9.12072e6i | − 0.964531i | −0.876025 | − | 0.482266i | \(-0.839814\pi\) | ||||
0.876025 | − | 0.482266i | \(-0.160186\pi\) | |||||||
\(618\) | − 2.15639e7i | − 2.27121i | ||||||||
\(619\) | −1.46635e7 | −1.53820 | −0.769098 | − | 0.639131i | \(-0.779294\pi\) | ||||
−0.769098 | + | 0.639131i | \(0.779294\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.99826e7 | 2.07933 | ||||||||
\(622\) | 6.04120e6i | 0.626105i | ||||||||
\(623\) | 2.63950e7i | 2.72460i | ||||||||
\(624\) | 831488. | 0.0854859 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 8.00368e6 | 0.816307 | ||||||||
\(627\) | − 2.14751e6i | − 0.218155i | ||||||||
\(628\) | − 4.40587e6i | − 0.445793i | ||||||||
\(629\) | 9.23079e6 | 0.930277 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.63870e7 | −1.63842 | −0.819212 | − | 0.573491i | \(-0.805589\pi\) | ||||
−0.819212 | + | 0.573491i | \(0.805589\pi\) | |||||||
\(632\) | 4.63424e6i | 0.461515i | ||||||||
\(633\) | 3.90282e6i | 0.387141i | ||||||||
\(634\) | 1.03732e6 | 0.102492 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 9.42755e6 | 0.924179 | ||||||||
\(637\) | − 4.04242e6i | − 0.394723i | ||||||||
\(638\) | 576928.i | 0.0561138i | ||||||||
\(639\) | 1.49303e7 | 1.44649 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.26835e6 | −0.314184 | −0.157092 | − | 0.987584i | \(-0.550212\pi\) | ||||
−0.157092 | + | 0.987584i | \(0.550212\pi\) | |||||||
\(642\) | − 2.78052e6i | − 0.266249i | ||||||||
\(643\) | 8.32842e6i | 0.794393i | 0.917734 | + | 0.397197i | \(0.130017\pi\) | ||||
−0.917734 | + | 0.397197i | \(0.869983\pi\) | |||||||
\(644\) | −7.14288e6 | −0.678670 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.79562e6 | 0.263570 | ||||||||
\(647\) | − 2.49694e6i | − 0.234503i | −0.993102 | − | 0.117251i | \(-0.962592\pi\) | ||||
0.993102 | − | 0.117251i | \(-0.0374083\pi\) | |||||||
\(648\) | 9.80742e6i | 0.917524i | ||||||||
\(649\) | 2.58347e6 | 0.240764 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.91679e6 | −0.639664 | ||||||||
\(652\) | − 4.67104e6i | − 0.430323i | ||||||||
\(653\) | − 789105.i | − 0.0724189i | −0.999344 | − | 0.0362094i | \(-0.988472\pi\) | ||||
0.999344 | − | 0.0362094i | \(-0.0115283\pi\) | |||||||
\(654\) | −6.53382e6 | −0.597341 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.67366e6 | −0.242576 | ||||||||
\(657\) | 2.52882e7i | 2.28562i | ||||||||
\(658\) | − 7.96352e6i | − 0.717035i | ||||||||
\(659\) | 8.31393e6 | 0.745749 | 0.372874 | − | 0.927882i | \(-0.378372\pi\) | ||||
0.372874 | + | 0.927882i | \(0.378372\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.33517e6 | −0.385925 | −0.192962 | − | 0.981206i | \(-0.561810\pi\) | ||||
−0.192962 | + | 0.981206i | \(0.561810\pi\) | |||||||
\(662\) | − 204812.i | − 0.0181640i | ||||||||
\(663\) | 3.70922e6i | 0.327716i | ||||||||
\(664\) | 1.01158e6 | 0.0890393 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.93345e7 | 1.68907 | ||||||||
\(667\) | 2.31367e6i | 0.201366i | ||||||||
\(668\) | − 5.39750e6i | − 0.468006i | ||||||||
\(669\) | 1.35963e7 | 1.17451 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.69232e6 | 0.488071 | ||||||||
\(672\) | − 6.83008e6i | − 0.583449i | ||||||||
\(673\) | 7.29313e6i | 0.620693i | 0.950624 | + | 0.310346i | \(0.100445\pi\) | ||||
−0.950624 | + | 0.310346i | \(0.899555\pi\) | |||||||
\(674\) | −1.06748e6 | −0.0905128 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.73998e6 | −0.483108 | ||||||||
\(677\) | − 1.55814e7i | − 1.30658i | −0.757109 | − | 0.653288i | \(-0.773389\pi\) | ||||
0.757109 | − | 0.653288i | \(-0.226611\pi\) | |||||||
\(678\) | 3.03807e7i | 2.53819i | ||||||||
\(679\) | −1.18657e6 | −0.0987686 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.97564e6 | −0.659019 | ||||||||
\(682\) | 501908.i | 0.0413203i | ||||||||
\(683\) | − 2.16930e6i | − 0.177938i | −0.996034 | − | 0.0889690i | \(-0.971643\pi\) | ||||
0.996034 | − | 0.0889690i | \(-0.0283572\pi\) | |||||||
\(684\) | 5.85562e6 | 0.478556 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.77431e7 | −1.43953 | ||||||||
\(687\) | − 1.86261e7i | − 1.50567i | ||||||||
\(688\) | 14848.0i | 0.00119591i | ||||||||
\(689\) | 2.27562e6 | 0.182621 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.32195e7 | −1.05322 | −0.526610 | − | 0.850107i | \(-0.676537\pi\) | ||||
−0.526610 | + | 0.850107i | \(0.676537\pi\) | |||||||
\(692\) | 1.86787e6i | 0.148280i | ||||||||
\(693\) | − 1.66423e7i | − 1.31638i | ||||||||
\(694\) | −2.49120e6 | −0.196341 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.21235e6 | −0.173114 | ||||||||
\(697\) | − 1.19270e7i | − 0.929932i | ||||||||
\(698\) | 9.74596e6i | 0.757157i | ||||||||
\(699\) | −4.36406e7 | −3.37830 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.59395e7 | −1.99373 | −0.996866 | − | 0.0791122i | \(-0.974791\pi\) | ||||
−0.996866 | + | 0.0791122i | \(0.974791\pi\) | |||||||
\(702\) | 4.61216e6i | 0.353233i | ||||||||
\(703\) | − 4.94680e6i | − 0.377516i | ||||||||
\(704\) | −495616. | −0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.23828e6 | 0.471035 | ||||||||
\(707\) | − 1.41280e7i | − 1.06300i | ||||||||
\(708\) | 9.90686e6i | 0.742768i | ||||||||
\(709\) | −3.57531e6 | −0.267115 | −0.133557 | − | 0.991041i | \(-0.542640\pi\) | ||||
−0.133557 | + | 0.991041i | \(0.542640\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.33012e7 | −3.21237 | ||||||||
\(712\) | 7.34470e6i | 0.542968i | ||||||||
\(713\) | 2.01282e6i | 0.148279i | ||||||||
\(714\) | 3.04686e7 | 2.23669 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −305712. | −0.0222859 | ||||||||
\(717\) | − 8.83613e6i | − 0.641895i | ||||||||
\(718\) | 7.67843e6i | 0.555855i | ||||||||
\(719\) | 1.95814e6 | 0.141261 | 0.0706304 | − | 0.997503i | \(-0.477499\pi\) | ||||
0.0706304 | + | 0.997503i | \(0.477499\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.27561e7 | −3.06309 | ||||||||
\(722\) | 8.40622e6i | 0.600147i | ||||||||
\(723\) | − 3.68824e7i | − 2.62406i | ||||||||
\(724\) | 258832. | 0.0183515 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.69836e6 | −0.119588 | ||||||||
\(727\) | − 1.55360e7i | − 1.09019i | −0.838374 | − | 0.545095i | \(-0.816493\pi\) | ||||
0.838374 | − | 0.545095i | \(-0.183507\pi\) | |||||||
\(728\) | − 1.64864e6i | − 0.115292i | ||||||||
\(729\) | −1.90893e7 | −1.33036 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −66236.0 | −0.00458459 | ||||||||
\(732\) | 2.18284e7i | 1.50572i | ||||||||
\(733\) | − 1.46002e7i | − 1.00369i | −0.864958 | − | 0.501844i | \(-0.832655\pi\) | ||||
0.864958 | − | 0.501844i | \(-0.167345\pi\) | |||||||
\(734\) | −1.44490e7 | −0.989915 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.98758e6 | −0.135248 | ||||||||
\(737\) | − 5.81925e6i | − 0.394638i | ||||||||
\(738\) | − 2.49820e7i | − 1.68845i | ||||||||
\(739\) | 2.06682e7 | 1.39217 | 0.696085 | − | 0.717959i | \(-0.254923\pi\) | ||||
0.696085 | + | 0.717959i | \(0.254923\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.98778e6 | 0.132991 | ||||||||
\(742\) | − 1.86926e7i | − 1.24640i | ||||||||
\(743\) | 1.17065e7i | 0.777953i | 0.921248 | + | 0.388976i | \(0.127171\pi\) | ||||
−0.921248 | + | 0.388976i | \(0.872829\pi\) | |||||||
\(744\) | −1.92467e6 | −0.127475 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.57587e7 | 1.03675 | ||||||||
\(747\) | 9.45199e6i | 0.619757i | ||||||||
\(748\) | − 2.21091e6i | − 0.144483i | ||||||||
\(749\) | −5.51310e6 | −0.359080 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.27607e7 | −0.825610 | −0.412805 | − | 0.910819i | \(-0.635451\pi\) | ||||
−0.412805 | + | 0.910819i | \(0.635451\pi\) | |||||||
\(752\) | − 2.21594e6i | − 0.142894i | ||||||||
\(753\) | − 1.82690e7i | − 1.17416i | ||||||||
\(754\) | −534016. | −0.0342079 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3.78856e7 | 2.41085 | ||||||||
\(757\) | 1.40869e7i | 0.893458i | 0.894669 | + | 0.446729i | \(0.147411\pi\) | ||||
−0.894669 | + | 0.446729i | \(0.852589\pi\) | |||||||
\(758\) | − 8.75316e6i | − 0.553339i | ||||||||
\(759\) | −6.81097e6 | −0.429145 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.33822e7 | 1.46360 | 0.731801 | − | 0.681518i | \(-0.238680\pi\) | ||||
0.731801 | + | 0.681518i | \(0.238680\pi\) | |||||||
\(762\) | 1.01389e7i | 0.632560i | ||||||||
\(763\) | 1.29550e7i | 0.805611i | ||||||||
\(764\) | −1.09653e7 | −0.679655 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.07355e6 | 0.189264 | ||||||||
\(767\) | 2.39131e6i | 0.146774i | ||||||||
\(768\) | − 1.90054e6i | − 0.116272i | ||||||||
\(769\) | 1.09575e7 | 0.668185 | 0.334092 | − | 0.942540i | \(-0.391570\pi\) | ||||
0.334092 | + | 0.942540i | \(0.391570\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.57785e7 | −0.955938 | ||||||||
\(772\) | 4.94867e6i | 0.298845i | ||||||||
\(773\) | 1.69336e7i | 1.01930i | 0.860383 | + | 0.509648i | \(0.170224\pi\) | ||||
−0.860383 | + | 0.509648i | \(0.829776\pi\) | |||||||
\(774\) | −138736. | −0.00832409 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −330176. | −0.0196830 | ||||||||
\(777\) | − 5.39136e7i | − 3.20366i | ||||||||
\(778\) | 1.29725e6i | 0.0768379i | ||||||||
\(779\) | −6.39173e6 | −0.377376 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.02101e6 | −0.177225 | ||||||||
\(782\) | − 8.86649e6i | − 0.518483i | ||||||||
\(783\) | − 1.22716e7i | − 0.715316i | ||||||||
\(784\) | −9.23981e6 | −0.536875 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.07542e7 | −1.77561 | ||||||||
\(787\) | 7.51655e6i | 0.432595i | 0.976327 | + | 0.216298i | \(0.0693982\pi\) | ||||
−0.976327 | + | 0.216298i | \(0.930602\pi\) | |||||||
\(788\) | − 1.93488e6i | − 0.111004i | ||||||||
\(789\) | −5.76907e7 | −3.29923 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.02377e7 | 3.42316 | ||||||||
\(792\) | − 4.63091e6i | − 0.262333i | ||||||||
\(793\) | 5.26893e6i | 0.297536i | ||||||||
\(794\) | −1.33903e6 | −0.0753771 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.46486e7 | 0.819432 | ||||||||
\(797\) | − 3.93788e6i | − 0.219592i | −0.993954 | − | 0.109796i | \(-0.964980\pi\) | ||||
0.993954 | − | 0.109796i | \(-0.0350198\pi\) | |||||||
\(798\) | − 1.63282e7i | − 0.907674i | ||||||||
\(799\) | 9.88515e6 | 0.547793 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.86271e7 | −3.77932 | ||||||||
\(802\) | 3.60809e6i | 0.198080i | ||||||||
\(803\) | − 5.11685e6i | − 0.280036i | ||||||||
\(804\) | 2.23152e7 | 1.21747 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −464576. | −0.0251895 | ||||||||
\(807\) | 5.08793e7i | 2.75015i | ||||||||
\(808\) | − 3.93126e6i | − 0.211838i | ||||||||
\(809\) | 1.73609e7 | 0.932612 | 0.466306 | − | 0.884624i | \(-0.345585\pi\) | ||||
0.466306 | + | 0.884624i | \(0.345585\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.70850e7 | 1.44603 | 0.723014 | − | 0.690833i | \(-0.242756\pi\) | ||||
0.723014 | + | 0.690833i | \(0.242756\pi\) | |||||||
\(812\) | 4.38656e6i | 0.233472i | ||||||||
\(813\) | 4.80890e7i | 2.55164i | ||||||||
\(814\) | −3.91217e6 | −0.206946 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 8.47821e6 | 0.445737 | ||||||||
\(817\) | 35496.0i | 0.00186048i | ||||||||
\(818\) | − 2.00183e7i | − 1.04603i | ||||||||
\(819\) | 1.54045e7 | 0.802486 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.59384e7 | 1.86080 | 0.930402 | − | 0.366540i | \(-0.119458\pi\) | ||||
0.930402 | + | 0.366540i | \(0.119458\pi\) | |||||||
\(822\) | 2.85194e7i | 1.47218i | ||||||||
\(823\) | − 505509.i | − 0.0260153i | −0.999915 | − | 0.0130077i | \(-0.995859\pi\) | ||||
0.999915 | − | 0.0130077i | \(-0.00414058\pi\) | |||||||
\(824\) | −1.18973e7 | −0.610425 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.96429e7 | 1.00174 | ||||||||
\(827\) | 2.99955e7i | 1.52508i | 0.646942 | + | 0.762539i | \(0.276048\pi\) | ||||
−0.646942 | + | 0.762539i | \(0.723952\pi\) | |||||||
\(828\) | − 1.85715e7i | − 0.941393i | ||||||||
\(829\) | −2.96942e7 | −1.50067 | −0.750334 | − | 0.661059i | \(-0.770107\pi\) | ||||
−0.750334 | + | 0.661059i | \(0.770107\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.23639e6 | 0.0621086 | ||||||||
\(832\) | − 458752.i | − 0.0229757i | ||||||||
\(833\) | − 4.12182e7i | − 2.05815i | ||||||||
\(834\) | −4.21769e7 | −2.09971 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.18483e6 | −0.0586329 | ||||||||
\(837\) | − 1.06759e7i | − 0.526734i | ||||||||
\(838\) | − 1.20049e7i | − 0.590541i | ||||||||
\(839\) | 1.41371e7 | 0.693356 | 0.346678 | − | 0.937984i | \(-0.387310\pi\) | ||||
0.346678 | + | 0.937984i | \(0.387310\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.90903e7 | −0.930727 | ||||||||
\(842\) | − 1.82490e7i | − 0.887070i | ||||||||
\(843\) | − 9.26579e6i | − 0.449069i | ||||||||
\(844\) | 2.15328e6 | 0.104051 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.07052e7 | 0.994609 | ||||||||
\(847\) | 3.36743e6i | 0.161284i | ||||||||
\(848\) | − 5.20141e6i | − 0.248388i | ||||||||
\(849\) | −5.87931e7 | −2.79935 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.56891e7 | −0.742633 | ||||||||
\(852\) | − 1.15847e7i | − 0.546746i | ||||||||
\(853\) | − 4.68539e6i | − 0.220482i | −0.993905 | − | 0.110241i | \(-0.964838\pi\) | ||||
0.993905 | − | 0.110241i | \(-0.0351623\pi\) | |||||||
\(854\) | 4.32805e7 | 2.03071 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.53408e6 | −0.0715589 | ||||||||
\(857\) | 4.12846e7i | 1.92015i | 0.279740 | + | 0.960076i | \(0.409752\pi\) | ||||
−0.279740 | + | 0.960076i | \(0.590248\pi\) | |||||||
\(858\) | − 1.57203e6i | − 0.0729026i | ||||||||
\(859\) | 3.54805e6 | 0.164062 | 0.0820308 | − | 0.996630i | \(-0.473859\pi\) | ||||
0.0820308 | + | 0.996630i | \(0.473859\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.96615e7 | −3.20247 | ||||||||
\(862\) | − 1.95913e7i | − 0.898039i | ||||||||
\(863\) | − 3.07605e7i | − 1.40594i | −0.711219 | − | 0.702970i | \(-0.751857\pi\) | ||||
0.711219 | − | 0.702970i | \(-0.248143\pi\) | |||||||
\(864\) | 1.05421e7 | 0.480443 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.69150e7 | 1.21955 | ||||||||
\(867\) | − 3.35510e6i | − 0.151585i | ||||||||
\(868\) | 3.81616e6i | 0.171920i | ||||||||
\(869\) | 8.76161e6 | 0.393581 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.38642e6 | 0.240577 | ||||||||
\(872\) | 3.60486e6i | 0.160545i | ||||||||
\(873\) | − 3.08508e6i | − 0.137003i | ||||||||
\(874\) | −4.75157e6 | −0.210406 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.96216e7 | 0.863923 | ||||||||
\(877\) | − 3.05535e7i | − 1.34141i | −0.741723 | − | 0.670706i | \(-0.765991\pi\) | ||||
0.741723 | − | 0.670706i | \(-0.234009\pi\) | |||||||
\(878\) | − 1.34013e7i | − 0.586695i | ||||||||
\(879\) | 2.08465e7 | 0.910040 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.21018e7 | 1.82751 | 0.913757 | − | 0.406262i | \(-0.133168\pi\) | ||||
0.913757 | + | 0.406262i | \(0.133168\pi\) | |||||||
\(882\) | − 8.63345e7i | − 3.73691i | ||||||||
\(883\) | 57164.0i | 0.00246729i | 0.999999 | + | 0.00123365i | \(0.000392682\pi\) | ||||
−0.999999 | + | 0.00123365i | \(0.999607\pi\) | |||||||
\(884\) | 2.04646e6 | 0.0880792 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.84974e7 | −1.21961 | ||||||||
\(887\) | 1.16106e7i | 0.495504i | 0.968824 | + | 0.247752i | \(0.0796917\pi\) | ||||
−0.968824 | + | 0.247752i | \(0.920308\pi\) | |||||||
\(888\) | − 1.50020e7i | − 0.638437i | ||||||||
\(889\) | 2.01029e7 | 0.853109 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.85422e7 | 0.782467 | ||||||||
\(892\) | − 7.50142e6i | − 0.315669i | ||||||||
\(893\) | − 5.29747e6i | − 0.222300i | ||||||||
\(894\) | −6.46700e6 | −0.270619 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.76832e6 | −0.156811 | ||||||||
\(897\) | − 6.30437e6i | − 0.261614i | ||||||||
\(898\) | − 1.08371e7i | − 0.448460i | ||||||||
\(899\) | 1.23610e6 | 0.0510101 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.32032e7 | 0.952215 | ||||||||
\(902\) | 5.05490e6i | 0.206869i | ||||||||
\(903\) | 386860.i | 0.0157883i | ||||||||
\(904\) | 1.67618e7 | 0.682181 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −7.61447e6 | −0.308191 | ||||||||
\(907\) | − 2.09855e7i | − 0.847034i | −0.905888 | − | 0.423517i | \(-0.860795\pi\) | ||||
0.905888 | − | 0.423517i | \(-0.139205\pi\) | |||||||
\(908\) | 4.40035e6i | 0.177122i | ||||||||
\(909\) | 3.67327e7 | 1.47450 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.74125e7 | 1.89277 | 0.946383 | − | 0.323047i | \(-0.104707\pi\) | ||||
0.946383 | + | 0.323047i | \(0.104707\pi\) | |||||||
\(912\) | − 4.54349e6i | − 0.180885i | ||||||||
\(913\) | − 1.91253e6i | − 0.0759330i | ||||||||
\(914\) | −9.65445e6 | −0.382263 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.02765e7 | −0.404675 | ||||||||
\(917\) | 6.09781e7i | 2.39470i | ||||||||
\(918\) | 4.70276e7i | 1.84181i | ||||||||
\(919\) | −4.04326e7 | −1.57922 | −0.789610 | − | 0.613609i | \(-0.789717\pi\) | ||||
−0.789610 | + | 0.613609i | \(0.789717\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.74612e7 | 2.23216 | ||||||||
\(922\) | 2.62426e7i | 1.01667i | ||||||||
\(923\) | − 2.79630e6i | − 0.108039i | ||||||||
\(924\) | −1.29131e7 | −0.497567 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.88968e7 | −0.724205 | ||||||||
\(927\) | − 1.11166e8i | − 4.24885i | ||||||||
\(928\) | 1.22061e6i | 0.0465271i | ||||||||
\(929\) | −3.30757e7 | −1.25739 | −0.628694 | − | 0.777652i | \(-0.716410\pi\) | ||||
−0.628694 | + | 0.777652i | \(0.716410\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.20889e7 | −0.835219 | ||||||||
\(932\) | 2.40776e7i | 0.907973i | ||||||||
\(933\) | 4.37987e7i | 1.64724i | ||||||||
\(934\) | 9.13776e6 | 0.342746 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.28646e6 | 0.159922 | ||||||||
\(937\) | 3.15132e7i | 1.17258i | 0.810100 | + | 0.586292i | \(0.199413\pi\) | ||||
−0.810100 | + | 0.586292i | \(0.800587\pi\) | |||||||
\(938\) | − 4.42456e7i | − 1.64196i | ||||||||
\(939\) | 5.80267e7 | 2.14765 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.54147e6 | −0.351270 | −0.175635 | − | 0.984455i | \(-0.556198\pi\) | ||||
−0.175635 | + | 0.984455i | \(0.556198\pi\) | |||||||
\(942\) | − 3.19426e7i | − 1.17285i | ||||||||
\(943\) | 2.02718e7i | 0.742358i | ||||||||
\(944\) | 5.46586e6 | 0.199631 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 28072.0 | 0.00101987 | ||||||||
\(947\) | − 2.24208e7i | − 0.812410i | −0.913782 | − | 0.406205i | \(-0.866852\pi\) | ||||
0.913782 | − | 0.406205i | \(-0.133148\pi\) | |||||||
\(948\) | 3.35982e7i | 1.21422i | ||||||||
\(949\) | 4.73626e6 | 0.170714 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.52060e6 | 0.269650 | ||||||||
\(952\) | − 1.68102e7i | − 0.601148i | ||||||||
\(953\) | 1.68985e7i | 0.602720i | 0.953510 | + | 0.301360i | \(0.0974405\pi\) | ||||
−0.953510 | + | 0.301360i | \(0.902559\pi\) | |||||||
\(954\) | 4.86007e7 | 1.72891 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −4.87510e6 | −0.172520 | ||||||||
\(957\) | 4.18273e6i | 0.147632i | ||||||||
\(958\) | 3.80618e6i | 0.133991i | ||||||||
\(959\) | 5.65471e7 | 1.98547 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.75538e7 | −0.962438 | ||||||||
\(962\) | − 3.62118e6i | − 0.126157i | ||||||||
\(963\) | − 1.43341e7i | − 0.498085i | ||||||||
\(964\) | −2.03489e7 | −0.705260 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −5.17859e7 | −1.78554 | ||||||||
\(967\) | 3.06946e7i | 1.05559i | 0.849371 | + | 0.527796i | \(0.176982\pi\) | ||||
−0.849371 | + | 0.527796i | \(0.823018\pi\) | |||||||
\(968\) | 937024.i | 0.0321412i | ||||||||
\(969\) | 2.02682e7 | 0.693436 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.35664e7 | 1.14250 | 0.571251 | − | 0.820776i | \(-0.306458\pi\) | ||||
0.571251 | + | 0.820776i | \(0.306458\pi\) | |||||||
\(972\) | 3.10769e7i | 1.05505i | ||||||||
\(973\) | 8.36266e7i | 2.83180i | ||||||||
\(974\) | −1.40594e7 | −0.474863 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.20433e7 | 0.404687 | ||||||||
\(977\) | − 2.47897e7i | − 0.830873i | −0.909622 | − | 0.415436i | \(-0.863629\pi\) | ||||
0.909622 | − | 0.415436i | \(-0.136371\pi\) | |||||||
\(978\) | − 3.38650e7i | − 1.13215i | ||||||||
\(979\) | 1.38861e7 | 0.463045 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.36829e7 | −1.11747 | ||||||||
\(982\) | 2.31488e7i | 0.766036i | ||||||||
\(983\) | 5.22606e6i | 0.172501i | 0.996274 | + | 0.0862503i | \(0.0274885\pi\) | ||||
−0.996274 | + | 0.0862503i | \(0.972512\pi\) | |||||||
\(984\) | −1.93841e7 | −0.638200 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −5.44506e6 | −0.178365 | ||||||||
\(987\) | − 5.77355e7i | − 1.88647i | ||||||||
\(988\) | − 1.09670e6i | − 0.0357435i | ||||||||
\(989\) | 112578. | 0.00365985 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.40826e7 | 0.778967 | 0.389484 | − | 0.921033i | \(-0.372653\pi\) | ||||
0.389484 | + | 0.921033i | \(0.372653\pi\) | |||||||
\(992\) | 1.06189e6i | 0.0342610i | ||||||||
\(993\) | − 1.48489e6i | − 0.0477882i | ||||||||
\(994\) | −2.29696e7 | −0.737375 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 7.33398e6 | 0.234256 | ||||||||
\(997\) | 1.32606e7i | 0.422499i | 0.977432 | + | 0.211249i | \(0.0677532\pi\) | ||||
−0.977432 | + | 0.211249i | \(0.932247\pi\) | |||||||
\(998\) | 4.11650e6i | 0.130828i | ||||||||
\(999\) | 8.32145e7 | 2.63806 |
(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 | 550.6.b.a.199.1 | 2 | ||
5.2 | odd | 4 | 22.6.a.c.1.1 | ✓ | 1 | ||
5.3 | odd | 4 | 550.6.a.c.1.1 | 1 | |||
5.4 | even | 2 | inner | 550.6.b.a.199.2 | 2 | ||
15.2 | even | 4 | 198.6.a.b.1.1 | 1 | |||
20.7 | even | 4 | 176.6.a.e.1.1 | 1 | |||
35.27 | even | 4 | 1078.6.a.f.1.1 | 1 | |||
40.27 | even | 4 | 704.6.a.a.1.1 | 1 | |||
40.37 | odd | 4 | 704.6.a.j.1.1 | 1 | |||
55.32 | even | 4 | 242.6.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
22.6.a.c.1.1 | ✓ | 1 | 5.2 | odd | 4 | ||
176.6.a.e.1.1 | 1 | 20.7 | even | 4 | |||
198.6.a.b.1.1 | 1 | 15.2 | even | 4 | |||
242.6.a.a.1.1 | 1 | 55.32 | even | 4 | |||
550.6.a.c.1.1 | 1 | 5.3 | odd | 4 | |||
550.6.b.a.199.1 | 2 | 1.1 | even | 1 | trivial | ||
550.6.b.a.199.2 | 2 | 5.4 | even | 2 | inner | ||
704.6.a.a.1.1 | 1 | 40.27 | even | 4 | |||
704.6.a.j.1.1 | 1 | 40.37 | odd | 4 | |||
1078.6.a.f.1.1 | 1 | 35.27 | even | 4 |