Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,6,Mod(20,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.20");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.c (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: | \(3.36806021607\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 484x^{10} + 194194x^{8} - 39867800x^{6} + 5398720873x^{4} - 310089434788x^{2} + 9371104623076 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 20.9 | ||
Root | \(-12.2117 - 5.57294i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.20 |
Dual form | 21.6.c.a.20.3 |
$q$-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 \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.57294i | 0.985166i | 0.870265 | + | 0.492583i | \(0.163947\pi\) | ||||
−0.870265 | + | 0.492583i | \(0.836053\pi\) | |||||||
\(3\) | −13.5283 | + | 7.74498i | −0.867842 | + | 0.496840i | ||||
\(4\) | 0.942331 | 0.0294478 | ||||||||
\(5\) | −46.2136 | −0.826693 | −0.413347 | − | 0.910574i | \(-0.635640\pi\) | ||||
−0.413347 | + | 0.910574i | \(0.635640\pi\) | |||||||
\(6\) | −43.1623 | − | 75.3925i | −0.489470 | − | 0.854968i | ||||
\(7\) | −120.146 | − | 48.7024i | −0.926754 | − | 0.375669i | ||||
\(8\) | 183.586i | 1.01418i | ||||||||
\(9\) | 123.031 | − | 209.553i | 0.506299 | − | 0.862358i | ||||
\(10\) | − | 257.545i | − | 0.814430i | ||||||
\(11\) | 285.677i | 0.711858i | 0.934513 | + | 0.355929i | \(0.115835\pi\) | ||||
−0.934513 | + | 0.355929i | \(0.884165\pi\) | |||||||
\(12\) | −12.7482 | + | 7.29833i | −0.0255561 | + | 0.0146309i | ||||
\(13\) | 1141.52i | 1.87338i | 0.350154 | + | 0.936692i | \(0.386129\pi\) | ||||
−0.350154 | + | 0.936692i | \(0.613871\pi\) | |||||||
\(14\) | 271.416 | − | 669.567i | 0.370096 | − | 0.913006i | ||||
\(15\) | 625.192 | − | 357.923i | 0.717439 | − | 0.410735i | ||||
\(16\) | −992.957 | −0.969685 | ||||||||
\(17\) | 967.641 | 0.812067 | 0.406034 | − | 0.913858i | \(-0.366912\pi\) | ||||
0.406034 | + | 0.913858i | \(0.366912\pi\) | |||||||
\(18\) | 1167.83 | + | 685.643i | 0.849566 | + | 0.498789i | ||||
\(19\) | − | 112.619i | − | 0.0715693i | −0.999360 | − | 0.0357847i | \(-0.988607\pi\) | ||
0.999360 | − | 0.0357847i | \(-0.0113930\pi\) | |||||||
\(20\) | −43.5485 | −0.0243443 | ||||||||
\(21\) | 2002.57 | − | 271.667i | 0.990923 | − | 0.134427i | ||||
\(22\) | −1592.06 | −0.701298 | ||||||||
\(23\) | − | 1262.08i | − | 0.497469i | −0.968572 | − | 0.248735i | \(-0.919985\pi\) | ||
0.968572 | − | 0.248735i | \(-0.0800147\pi\) | |||||||
\(24\) | −1421.87 | − | 2483.61i | −0.503884 | − | 0.880145i | ||||
\(25\) | −989.307 | −0.316578 | ||||||||
\(26\) | −6361.65 | −1.84559 | ||||||||
\(27\) | −41.4161 | + | 3787.77i | −0.0109335 | + | 0.999940i | ||||
\(28\) | −113.217 | − | 45.8938i | −0.0272909 | − | 0.0110626i | ||||
\(29\) | 598.083i | 0.132058i | 0.997818 | + | 0.0660292i | \(0.0210331\pi\) | ||||
−0.997818 | + | 0.0660292i | \(0.978967\pi\) | |||||||
\(30\) | 1994.68 | + | 3484.16i | 0.404642 | + | 0.706797i | ||||
\(31\) | − | 2465.55i | − | 0.460797i | −0.973096 | − | 0.230398i | \(-0.925997\pi\) | ||
0.973096 | − | 0.230398i | \(-0.0740029\pi\) | |||||||
\(32\) | 341.048i | 0.0588764i | ||||||||
\(33\) | −2212.56 | − | 3864.73i | −0.353680 | − | 0.617780i | ||||
\(34\) | 5392.61i | 0.800021i | ||||||||
\(35\) | 5552.38 | + | 2250.71i | 0.766141 | + | 0.310563i | ||||
\(36\) | 115.936 | − | 197.468i | 0.0149094 | − | 0.0253946i | ||||
\(37\) | 4150.91 | 0.498471 | 0.249235 | − | 0.968443i | \(-0.419821\pi\) | ||||
0.249235 | + | 0.968443i | \(0.419821\pi\) | |||||||
\(38\) | 627.618 | 0.0705077 | ||||||||
\(39\) | −8841.08 | − | 15442.9i | −0.930773 | − | 1.62580i | ||||
\(40\) | − | 8484.15i | − | 0.838413i | ||||||
\(41\) | 16491.1 | 1.53211 | 0.766056 | − | 0.642774i | \(-0.222216\pi\) | ||||
0.766056 | + | 0.642774i | \(0.222216\pi\) | |||||||
\(42\) | 1513.98 | + | 11160.2i | 0.132433 | + | 0.976224i | ||||
\(43\) | 5104.06 | 0.420963 | 0.210482 | − | 0.977598i | \(-0.432497\pi\) | ||||
0.210482 | + | 0.977598i | \(0.432497\pi\) | |||||||
\(44\) | 269.202i | 0.0209627i | ||||||||
\(45\) | −5685.69 | + | 9684.19i | −0.418554 | + | 0.712905i | ||||
\(46\) | 7033.48 | 0.490090 | ||||||||
\(47\) | −17722.5 | −1.17026 | −0.585128 | − | 0.810941i | \(-0.698956\pi\) | ||||
−0.585128 | + | 0.810941i | \(0.698956\pi\) | |||||||
\(48\) | 13433.0 | − | 7690.43i | 0.841533 | − | 0.481779i | ||||
\(49\) | 12063.2 | + | 11702.8i | 0.717746 | + | 0.696305i | ||||
\(50\) | − | 5513.35i | − | 0.311882i | ||||||
\(51\) | −13090.6 | + | 7494.36i | −0.704746 | + | 0.403468i | ||||
\(52\) | 1075.69i | 0.0551671i | ||||||||
\(53\) | 30085.8i | 1.47120i | 0.677415 | + | 0.735601i | \(0.263100\pi\) | ||||
−0.677415 | + | 0.735601i | \(0.736900\pi\) | |||||||
\(54\) | −21109.0 | − | 230.810i | −0.985107 | − | 0.0107713i | ||||
\(55\) | − | 13202.1i | − | 0.588488i | ||||||
\(56\) | 8941.06 | − | 22057.1i | 0.380995 | − | 0.939893i | ||||
\(57\) | 872.230 | + | 1523.54i | 0.0355585 | + | 0.0621109i | ||||
\(58\) | −3333.08 | −0.130100 | ||||||||
\(59\) | −39985.0 | −1.49543 | −0.747717 | − | 0.664017i | \(-0.768850\pi\) | ||||
−0.747717 | + | 0.664017i | \(0.768850\pi\) | |||||||
\(60\) | 589.138 | − | 337.282i | 0.0211270 | − | 0.0120952i | ||||
\(61\) | − | 36958.1i | − | 1.27170i | −0.771812 | − | 0.635851i | \(-0.780649\pi\) | ||
0.771812 | − | 0.635851i | \(-0.219351\pi\) | |||||||
\(62\) | 13740.4 | 0.453961 | ||||||||
\(63\) | −24987.4 | + | 19185.1i | −0.793176 | + | 0.608993i | ||||
\(64\) | −33675.3 | −1.02769 | ||||||||
\(65\) | − | 52753.9i | − | 1.54871i | ||||||
\(66\) | 21537.9 | − | 12330.5i | 0.608616 | − | 0.348433i | ||||
\(67\) | 34620.1 | 0.942196 | 0.471098 | − | 0.882081i | \(-0.343858\pi\) | ||||
0.471098 | + | 0.882081i | \(0.343858\pi\) | |||||||
\(68\) | 911.838 | 0.0239136 | ||||||||
\(69\) | 9774.75 | + | 17073.8i | 0.247163 | + | 0.431725i | ||||
\(70\) | −12543.1 | + | 30943.1i | −0.305956 | + | 0.754776i | ||||
\(71\) | 43606.5i | 1.02661i | 0.858206 | + | 0.513305i | \(0.171579\pi\) | ||||
−0.858206 | + | 0.513305i | \(0.828421\pi\) | |||||||
\(72\) | 38470.9 | + | 22586.7i | 0.874584 | + | 0.513477i | ||||
\(73\) | 31725.9i | 0.696798i | 0.937346 | + | 0.348399i | \(0.113275\pi\) | ||||
−0.937346 | + | 0.348399i | \(0.886725\pi\) | |||||||
\(74\) | 23132.8i | 0.491076i | ||||||||
\(75\) | 13383.7 | − | 7662.16i | 0.274740 | − | 0.157289i | ||||
\(76\) | − | 106.124i | − | 0.00210756i | ||||||
\(77\) | 13913.1 | − | 34322.9i | 0.267423 | − | 0.659717i | ||||
\(78\) | 86062.4 | − | 49270.8i | 1.60168 | − | 0.916966i | ||||
\(79\) | −39763.9 | −0.716839 | −0.358420 | − | 0.933561i | \(-0.616684\pi\) | ||||
−0.358420 | + | 0.933561i | \(0.616684\pi\) | |||||||
\(80\) | 45888.1 | 0.801632 | ||||||||
\(81\) | −28775.9 | − | 51562.9i | −0.487322 | − | 0.873222i | ||||
\(82\) | 91904.0i | 1.50938i | ||||||||
\(83\) | −22963.5 | −0.365884 | −0.182942 | − | 0.983124i | \(-0.558562\pi\) | ||||
−0.182942 | + | 0.983124i | \(0.558562\pi\) | |||||||
\(84\) | 1887.09 | − | 256.000i | 0.0291806 | − | 0.00395860i | ||||
\(85\) | −44718.1 | −0.671331 | ||||||||
\(86\) | 28444.6i | 0.414719i | ||||||||
\(87\) | −4632.14 | − | 8091.05i | −0.0656120 | − | 0.114606i | ||||
\(88\) | −52446.1 | −0.721950 | ||||||||
\(89\) | 63601.9 | 0.851128 | 0.425564 | − | 0.904928i | \(-0.360076\pi\) | ||||
0.425564 | + | 0.904928i | \(0.360076\pi\) | |||||||
\(90\) | −53969.4 | − | 31686.0i | −0.702330 | − | 0.412345i | ||||
\(91\) | 55595.0 | − | 137150.i | 0.703772 | − | 1.73617i | ||||
\(92\) | − | 1189.29i | − | 0.0146494i | ||||||
\(93\) | 19095.6 | + | 33354.7i | 0.228942 | + | 0.399899i | ||||
\(94\) | − | 98766.6i | − | 1.15290i | ||||||
\(95\) | 5204.52i | 0.0591659i | ||||||||
\(96\) | −2641.41 | − | 4613.81i | −0.0292521 | − | 0.0510954i | ||||
\(97\) | 112394.i | 1.21286i | 0.795135 | + | 0.606432i | \(0.207400\pi\) | ||||
−0.795135 | + | 0.606432i | \(0.792600\pi\) | |||||||
\(98\) | −65219.0 | + | 67227.2i | −0.685976 | + | 0.707099i | ||||
\(99\) | 59864.4 | + | 35147.0i | 0.613876 | + | 0.360413i | ||||
\(100\) | −932.255 | −0.00932255 | ||||||||
\(101\) | 18851.6 | 0.183884 | 0.0919421 | − | 0.995764i | \(-0.470693\pi\) | ||||
0.0919421 | + | 0.995764i | \(0.470693\pi\) | |||||||
\(102\) | −41765.6 | − | 72952.9i | −0.397483 | − | 0.694292i | ||||
\(103\) | 34021.1i | 0.315976i | 0.987441 | + | 0.157988i | \(0.0505008\pi\) | ||||
−0.987441 | + | 0.157988i | \(0.949499\pi\) | |||||||
\(104\) | −209568. | −1.89994 | ||||||||
\(105\) | −92546.0 | + | 12554.7i | −0.819190 | + | 0.111130i | ||||
\(106\) | −167667. | −1.44938 | ||||||||
\(107\) | 24776.5i | 0.209209i | 0.994514 | + | 0.104605i | \(0.0333577\pi\) | ||||
−0.994514 | + | 0.104605i | \(0.966642\pi\) | |||||||
\(108\) | −39.0277 | + | 3569.33i | −0.000321969 | + | 0.0294461i | ||||
\(109\) | 152937. | 1.23295 | 0.616476 | − | 0.787374i | \(-0.288560\pi\) | ||||
0.616476 | + | 0.787374i | \(0.288560\pi\) | |||||||
\(110\) | 73574.7 | 0.579758 | ||||||||
\(111\) | −56154.9 | + | 32148.7i | −0.432594 | + | 0.247660i | ||||
\(112\) | 119300. | + | 48359.4i | 0.898659 | + | 0.364281i | ||||
\(113\) | − | 165698.i | − | 1.22074i | −0.792118 | − | 0.610368i | \(-0.791022\pi\) | ||
0.792118 | − | 0.610368i | \(-0.208978\pi\) | |||||||
\(114\) | −8490.62 | + | 4860.89i | −0.0611895 | + | 0.0350311i | ||||
\(115\) | 58325.1i | 0.411254i | ||||||||
\(116\) | 563.592i | 0.00388884i | ||||||||
\(117\) | 239210. | + | 140443.i | 1.61553 | + | 0.948493i | ||||
\(118\) | − | 222834.i | − | 1.47325i | ||||||
\(119\) | −116258. | − | 47126.5i | −0.752587 | − | 0.305068i | ||||
\(120\) | 65709.5 | + | 114776.i | 0.416558 | + | 0.727610i | ||||
\(121\) | 79439.8 | 0.493259 | ||||||||
\(122\) | 205965. | 1.25284 | ||||||||
\(123\) | −223097. | + | 127723.i | −1.32963 | + | 0.761215i | ||||
\(124\) | − | 2323.36i | − | 0.0135695i | ||||||
\(125\) | 190137. | 1.08841 | ||||||||
\(126\) | −106917. | − | 139253.i | −0.599959 | − | 0.781410i | ||||
\(127\) | −29830.5 | −0.164116 | −0.0820582 | − | 0.996628i | \(-0.526149\pi\) | ||||
−0.0820582 | + | 0.996628i | \(0.526149\pi\) | |||||||
\(128\) | − | 176757.i | − | 0.953567i | ||||||
\(129\) | −69049.3 | + | 39530.8i | −0.365330 | + | 0.209152i | ||||
\(130\) | 293994. | 1.52574 | ||||||||
\(131\) | 75634.1 | 0.385070 | 0.192535 | − | 0.981290i | \(-0.438329\pi\) | ||||
0.192535 | + | 0.981290i | \(0.438329\pi\) | |||||||
\(132\) | −2084.96 | − | 3641.85i | −0.0104151 | − | 0.0181923i | ||||
\(133\) | −5484.81 | + | 13530.7i | −0.0268864 | + | 0.0663272i | ||||
\(134\) | 192936.i | 0.928219i | ||||||||
\(135\) | 1913.99 | − | 175046.i | 0.00903867 | − | 0.826644i | ||||
\(136\) | 177645.i | 0.823580i | ||||||||
\(137\) | − | 29779.1i | − | 0.135554i | −0.997701 | − | 0.0677768i | \(-0.978409\pi\) | ||
0.997701 | − | 0.0677768i | \(-0.0215906\pi\) | |||||||
\(138\) | −95151.1 | + | 54474.1i | −0.425320 | + | 0.243496i | ||||
\(139\) | − | 119702.i | − | 0.525492i | −0.964865 | − | 0.262746i | \(-0.915372\pi\) | ||
0.964865 | − | 0.262746i | \(-0.0846281\pi\) | |||||||
\(140\) | 5232.18 | + | 2120.92i | 0.0225612 | + | 0.00914541i | ||||
\(141\) | 239756. | − | 137261.i | 1.01560 | − | 0.581431i | ||||
\(142\) | −243017. | −1.01138 | ||||||||
\(143\) | −326107. | −1.33358 | ||||||||
\(144\) | −122164. | + | 208077.i | −0.490951 | + | 0.836215i | ||||
\(145\) | − | 27639.5i | − | 0.109172i | ||||||
\(146\) | −176807. | −0.686461 | ||||||||
\(147\) | −253832. | − | 64890.5i | −0.968842 | − | 0.247678i | ||||
\(148\) | 3911.54 | 0.0146789 | ||||||||
\(149\) | 478865.i | 1.76705i | 0.468388 | + | 0.883523i | \(0.344835\pi\) | ||||
−0.468388 | + | 0.883523i | \(0.655165\pi\) | |||||||
\(150\) | 42700.8 | + | 74586.4i | 0.154956 | + | 0.270664i | ||||
\(151\) | −51677.8 | −0.184443 | −0.0922214 | − | 0.995739i | \(-0.529397\pi\) | ||||
−0.0922214 | + | 0.995739i | \(0.529397\pi\) | |||||||
\(152\) | 20675.2 | 0.0725840 | ||||||||
\(153\) | 119050. | − | 202772.i | 0.411149 | − | 0.700293i | ||||
\(154\) | 191280. | + | 77537.1i | 0.649931 | + | 0.263456i | ||||
\(155\) | 113942.i | 0.380937i | ||||||||
\(156\) | −8331.22 | − | 14552.3i | −0.0274093 | − | 0.0478764i | ||||
\(157\) | − | 215791.i | − | 0.698690i | −0.936994 | − | 0.349345i | \(-0.886404\pi\) | ||
0.936994 | − | 0.349345i | \(-0.113596\pi\) | |||||||
\(158\) | − | 221602.i | − | 0.706206i | ||||||
\(159\) | −233014. | − | 407011.i | −0.730953 | − | 1.27677i | ||||
\(160\) | − | 15761.1i | − | 0.0486727i | ||||||
\(161\) | −61466.2 | + | 151634.i | −0.186884 | + | 0.461031i | ||||
\(162\) | 287357. | − | 160366.i | 0.860269 | − | 0.480093i | ||||
\(163\) | −43718.7 | −0.128884 | −0.0644419 | − | 0.997921i | \(-0.520527\pi\) | ||||
−0.0644419 | + | 0.997921i | \(0.520527\pi\) | |||||||
\(164\) | 15540.1 | 0.0451174 | ||||||||
\(165\) | 102250. | + | 178603.i | 0.292385 | + | 0.510714i | ||||
\(166\) | − | 127974.i | − | 0.360456i | ||||||
\(167\) | 467393. | 1.29685 | 0.648427 | − | 0.761277i | \(-0.275427\pi\) | ||||
0.648427 | + | 0.761277i | \(0.275427\pi\) | |||||||
\(168\) | 49874.1 | + | 367644.i | 0.136333 | + | 1.00497i | ||||
\(169\) | −931785. | −2.50957 | ||||||||
\(170\) | − | 249212.i | − | 0.661372i | ||||||
\(171\) | −23599.6 | − | 13855.6i | −0.0617184 | − | 0.0362355i | ||||
\(172\) | 4809.71 | 0.0123965 | ||||||||
\(173\) | −261040. | −0.663120 | −0.331560 | − | 0.943434i | \(-0.607575\pi\) | ||||
−0.331560 | + | 0.943434i | \(0.607575\pi\) | |||||||
\(174\) | 45091.0 | − | 25814.6i | 0.112906 | − | 0.0646387i | ||||
\(175\) | 118861. | + | 48181.6i | 0.293390 | + | 0.118929i | ||||
\(176\) | − | 283665.i | − | 0.690278i | ||||||
\(177\) | 540930. | − | 309683.i | 1.29780 | − | 0.742992i | ||||
\(178\) | 354450.i | 0.838503i | ||||||||
\(179\) | − | 565935.i | − | 1.32018i | −0.751186 | − | 0.660091i | \(-0.770518\pi\) | ||
0.751186 | − | 0.660091i | \(-0.229482\pi\) | |||||||
\(180\) | −5357.80 | + | 9125.71i | −0.0123255 | + | 0.0209935i | ||||
\(181\) | 615493.i | 1.39645i | 0.715877 | + | 0.698227i | \(0.246027\pi\) | ||||
−0.715877 | + | 0.698227i | \(0.753973\pi\) | |||||||
\(182\) | 764327. | + | 309828.i | 1.71041 | + | 0.693333i | ||||
\(183\) | 286240. | + | 499981.i | 0.631833 | + | 1.10364i | ||||
\(184\) | 231699. | 0.504522 | ||||||||
\(185\) | −191829. | −0.412082 | ||||||||
\(186\) | −185884. | + | 106419.i | −0.393967 | + | 0.225546i | ||||
\(187\) | 276433.i | 0.578076i | ||||||||
\(188\) | −16700.5 | −0.0344615 | ||||||||
\(189\) | 189449. | − | 453068.i | 0.385779 | − | 0.922591i | ||||
\(190\) | −29004.5 | −0.0582882 | ||||||||
\(191\) | 588646.i | 1.16754i | 0.811920 | + | 0.583769i | \(0.198422\pi\) | ||||
−0.811920 | + | 0.583769i | \(0.801578\pi\) | |||||||
\(192\) | 455570. | − | 260814.i | 0.891871 | − | 0.510597i | ||||
\(193\) | 102554. | 0.198179 | 0.0990896 | − | 0.995079i | \(-0.468407\pi\) | ||||
0.0990896 | + | 0.995079i | \(0.468407\pi\) | |||||||
\(194\) | −626363. | −1.19487 | ||||||||
\(195\) | 408578. | + | 713672.i | 0.769464 | + | 1.34404i | ||||
\(196\) | 11367.5 | + | 11027.9i | 0.0211361 | + | 0.0205047i | ||||
\(197\) | − | 662538.i | − | 1.21631i | −0.793818 | − | 0.608156i | \(-0.791910\pi\) | ||
0.793818 | − | 0.608156i | \(-0.208090\pi\) | |||||||
\(198\) | −195872. | + | 333621.i | −0.355067 | + | 0.604770i | ||||
\(199\) | − | 697611.i | − | 1.24877i | −0.781119 | − | 0.624383i | \(-0.785351\pi\) | ||
0.781119 | − | 0.624383i | \(-0.214649\pi\) | |||||||
\(200\) | − | 181623.i | − | 0.321066i | ||||||
\(201\) | −468352. | + | 268132.i | −0.817677 | + | 0.468121i | ||||
\(202\) | 105059.i | 0.181157i | ||||||||
\(203\) | 29128.1 | − | 71857.3i | 0.0496103 | − | 0.122386i | ||||
\(204\) | −12335.6 | + | 7062.17i | −0.0207533 | + | 0.0118813i | ||||
\(205\) | −762113. | −1.26659 | ||||||||
\(206\) | −189597. | −0.311289 | ||||||||
\(207\) | −264472. | − | 155274.i | −0.428996 | − | 0.251868i | ||||
\(208\) | − | 1.13349e6i | − | 1.81659i | ||||||
\(209\) | 32172.6 | 0.0509472 | ||||||||
\(210\) | −69966.5 | − | 515753.i | −0.109482 | − | 0.807038i | ||||
\(211\) | 743288. | 1.14935 | 0.574673 | − | 0.818383i | \(-0.305129\pi\) | ||||
0.574673 | + | 0.818383i | \(0.305129\pi\) | |||||||
\(212\) | 28350.8i | 0.0433237i | ||||||||
\(213\) | −337732. | − | 589923.i | −0.510062 | − | 0.890936i | ||||
\(214\) | −138078. | −0.206106 | ||||||||
\(215\) | −235877. | −0.348008 | ||||||||
\(216\) | −695380. | − | 7603.41i | −1.01412 | − | 0.0110885i | ||||
\(217\) | −120078. | + | 296226.i | −0.173107 | + | 0.427045i | ||||
\(218\) | 852309.i | 1.21466i | ||||||||
\(219\) | −245716. | − | 429198.i | −0.346197 | − | 0.604710i | ||||
\(220\) | − | 12440.8i | − | 0.0173297i | ||||||
\(221\) | 1.10459e6i | 1.52131i | ||||||||
\(222\) | −179163. | − | 312948.i | −0.243987 | − | 0.426177i | ||||
\(223\) | 337580.i | 0.454584i | 0.973827 | + | 0.227292i | \(0.0729872\pi\) | ||||
−0.973827 | + | 0.227292i | \(0.927013\pi\) | |||||||
\(224\) | 16609.9 | − | 40975.6i | 0.0221180 | − | 0.0545639i | ||||
\(225\) | −121715. | + | 207312.i | −0.160283 | + | 0.273004i | ||||
\(226\) | 923426. | 1.20263 | ||||||||
\(227\) | 714316. | 0.920081 | 0.460040 | − | 0.887898i | \(-0.347835\pi\) | ||||
0.460040 | + | 0.887898i | \(0.347835\pi\) | |||||||
\(228\) | 821.930 | + | 1435.68i | 0.00104712 | + | 0.00182903i | ||||
\(229\) | 195949.i | 0.246920i | 0.992350 | + | 0.123460i | \(0.0393990\pi\) | ||||
−0.992350 | + | 0.123460i | \(0.960601\pi\) | |||||||
\(230\) | −325042. | −0.405154 | ||||||||
\(231\) | 77608.8 | + | 572088.i | 0.0956932 | + | 0.705396i | ||||
\(232\) | −109799. | −0.133931 | ||||||||
\(233\) | − | 1.00472e6i | − | 1.21243i | −0.795302 | − | 0.606214i | \(-0.792688\pi\) | ||
0.795302 | − | 0.606214i | \(-0.207312\pi\) | |||||||
\(234\) | −782678. | + | 1.33310e6i | −0.934423 | + | 1.59156i | ||||
\(235\) | 819021. | 0.967443 | ||||||||
\(236\) | −37679.1 | −0.0440373 | ||||||||
\(237\) | 537939. | − | 307971.i | 0.622103 | − | 0.356155i | ||||
\(238\) | 262633. | − | 647900.i | 0.300543 | − | 0.741423i | ||||
\(239\) | 181636.i | 0.205687i | 0.994698 | + | 0.102843i | \(0.0327940\pi\) | ||||
−0.994698 | + | 0.102843i | \(0.967206\pi\) | |||||||
\(240\) | −620789. | + | 355402.i | −0.695690 | + | 0.398283i | ||||
\(241\) | − | 194274.i | − | 0.215463i | −0.994180 | − | 0.107731i | \(-0.965641\pi\) | ||
0.994180 | − | 0.107731i | \(-0.0343587\pi\) | |||||||
\(242\) | 442713.i | 0.485942i | ||||||||
\(243\) | 788643. | + | 474691.i | 0.856771 | + | 0.515698i | ||||
\(244\) | − | 34826.8i | − | 0.0374489i | ||||||
\(245\) | −557481. | − | 540828.i | −0.593355 | − | 0.575631i | ||||
\(246\) | −711794. | − | 1.24331e6i | −0.749923 | − | 1.30991i | ||||
\(247\) | 128557. | 0.134077 | ||||||||
\(248\) | 452639. | 0.467329 | ||||||||
\(249\) | 310658. | − | 177852.i | 0.317529 | − | 0.181786i | ||||
\(250\) | 1.05962e6i | 1.07226i | ||||||||
\(251\) | 1.15023e6 | 1.15239 | 0.576195 | − | 0.817313i | \(-0.304537\pi\) | ||||
0.576195 | + | 0.817313i | \(0.304537\pi\) | |||||||
\(252\) | −23546.4 | + | 18078.7i | −0.0233573 | + | 0.0179335i | ||||
\(253\) | 360546. | 0.354127 | ||||||||
\(254\) | − | 166244.i | − | 0.161682i | ||||||
\(255\) | 604961. | − | 346341.i | 0.582609 | − | 0.333544i | ||||
\(256\) | −92553.8 | −0.0882662 | ||||||||
\(257\) | 753698. | 0.711810 | 0.355905 | − | 0.934522i | \(-0.384173\pi\) | ||||
0.355905 | + | 0.934522i | \(0.384173\pi\) | |||||||
\(258\) | −220303. | − | 384808.i | −0.206049 | − | 0.359910i | ||||
\(259\) | −498716. | − | 202160.i | −0.461960 | − | 0.187260i | ||||
\(260\) | − | 49711.6i | − | 0.0456063i | ||||||
\(261\) | 125330. | + | 73582.6i | 0.113882 | + | 0.0668611i | ||||
\(262\) | 421504.i | 0.379358i | ||||||||
\(263\) | − | 636200.i | − | 0.567158i | −0.958949 | − | 0.283579i | \(-0.908478\pi\) | ||
0.958949 | − | 0.283579i | \(-0.0915219\pi\) | |||||||
\(264\) | 709508. | − | 406194.i | 0.626538 | − | 0.358694i | ||||
\(265\) | − | 1.39037e6i | − | 1.21623i | ||||||
\(266\) | −75405.8 | − | 30566.5i | −0.0653433 | − | 0.0264876i | ||||
\(267\) | −860426. | + | 492595.i | −0.738645 | + | 0.422875i | ||||
\(268\) | 32623.6 | 0.0277456 | ||||||||
\(269\) | −906619. | −0.763914 | −0.381957 | − | 0.924180i | \(-0.624750\pi\) | ||||
−0.381957 | + | 0.924180i | \(0.624750\pi\) | |||||||
\(270\) | 975522. | + | 10666.5i | 0.814381 | + | 0.00890459i | ||||
\(271\) | 64809.8i | 0.0536065i | 0.999641 | + | 0.0268032i | \(0.00853276\pi\) | ||||
−0.999641 | + | 0.0268032i | \(0.991467\pi\) | |||||||
\(272\) | −960826. | −0.787449 | ||||||||
\(273\) | 310114. | + | 2.28599e6i | 0.251834 | + | 1.85638i | ||||
\(274\) | 165957. | 0.133543 | ||||||||
\(275\) | − | 282622.i | − | 0.225359i | ||||||
\(276\) | 9211.05 | + | 16089.1i | 0.00727841 | + | 0.0127134i | ||||
\(277\) | −1.20323e6 | −0.942215 | −0.471108 | − | 0.882076i | \(-0.656146\pi\) | ||||
−0.471108 | + | 0.882076i | \(0.656146\pi\) | |||||||
\(278\) | 667095. | 0.517697 | ||||||||
\(279\) | −516663. | − | 303338.i | −0.397372 | − | 0.233301i | ||||
\(280\) | −413198. | + | 1.01934e6i | −0.314966 | + | 0.777003i | ||||
\(281\) | 199614.i | 0.150808i | 0.997153 | + | 0.0754040i | \(0.0240246\pi\) | ||||
−0.997153 | + | 0.0754040i | \(0.975975\pi\) | |||||||
\(282\) | 764945. | + | 1.33615e6i | 0.572806 | + | 1.00053i | ||||
\(283\) | 1.72910e6i | 1.28338i | 0.766966 | + | 0.641688i | \(0.221766\pi\) | ||||
−0.766966 | + | 0.641688i | \(0.778234\pi\) | |||||||
\(284\) | 41091.8i | 0.0302315i | ||||||||
\(285\) | −40308.9 | − | 70408.4i | −0.0293960 | − | 0.0513466i | ||||
\(286\) | − | 1.81737e6i | − | 1.31380i | ||||||
\(287\) | −1.98134e6 | − | 803157.i | −1.41989 | − | 0.575567i | ||||
\(288\) | 71467.7 | + | 41959.4i | 0.0507725 | + | 0.0298091i | ||||
\(289\) | −483528. | −0.340547 | ||||||||
\(290\) | 154033. | 0.107552 | ||||||||
\(291\) | −870486. | − | 1.52050e6i | −0.602600 | − | 1.05257i | ||||
\(292\) | 29896.3i | 0.0205192i | ||||||||
\(293\) | −1.91518e6 | −1.30329 | −0.651645 | − | 0.758524i | \(-0.725921\pi\) | ||||
−0.651645 | + | 0.758524i | \(0.725921\pi\) | |||||||
\(294\) | 361631. | − | 1.41459e6i | 0.244004 | − | 0.954471i | ||||
\(295\) | 1.84785e6 | 1.23627 | ||||||||
\(296\) | 762048.i | 0.505537i | ||||||||
\(297\) | −1.08208e6 | − | 11831.6i | −0.711815 | − | 0.00778311i | ||||
\(298\) | −2.66869e6 | −1.74083 | ||||||||
\(299\) | 1.44069e6 | 0.931951 | ||||||||
\(300\) | 12611.8 | − | 7220.29i | 0.00809050 | − | 0.00463182i | ||||
\(301\) | −613232. | − | 248580.i | −0.390130 | − | 0.158143i | ||||
\(302\) | − | 287997.i | − | 0.181707i | ||||||
\(303\) | −255030. | + | 146005.i | −0.159582 | + | 0.0913611i | ||||
\(304\) | 111826.i | 0.0693997i | ||||||||
\(305\) | 1.70797e6i | 1.05131i | ||||||||
\(306\) | 1.13004e6 | + | 663456.i | 0.689904 | + | 0.405050i | ||||
\(307\) | − | 131454.i | − | 0.0796030i | −0.999208 | − | 0.0398015i | \(-0.987327\pi\) | ||
0.999208 | − | 0.0398015i | \(-0.0126726\pi\) | |||||||
\(308\) | 13110.8 | − | 32343.6i | 0.00787503 | − | 0.0194272i | ||||
\(309\) | −263492. | − | 460248.i | −0.156990 | − | 0.274218i | ||||
\(310\) | −634991. | −0.375287 | ||||||||
\(311\) | 447026. | 0.262079 | 0.131039 | − | 0.991377i | \(-0.458169\pi\) | ||||
0.131039 | + | 0.991377i | \(0.458169\pi\) | |||||||
\(312\) | 2.83510e6 | − | 1.62310e6i | 1.64885 | − | 0.943969i | ||||
\(313\) | 211680.i | 0.122129i | 0.998134 | + | 0.0610645i | \(0.0194495\pi\) | ||||
−0.998134 | + | 0.0610645i | \(0.980550\pi\) | |||||||
\(314\) | 1.20259e6 | 0.688325 | ||||||||
\(315\) | 1.15476e6 | − | 886610.i | 0.655713 | − | 0.503450i | ||||
\(316\) | −37470.8 | −0.0211094 | ||||||||
\(317\) | 920013.i | 0.514216i | 0.966383 | + | 0.257108i | \(0.0827697\pi\) | ||||
−0.966383 | + | 0.257108i | \(0.917230\pi\) | |||||||
\(318\) | 2.26825e6 | − | 1.29857e6i | 1.25783 | − | 0.720110i | ||||
\(319\) | −170858. | −0.0940068 | ||||||||
\(320\) | 1.55625e6 | 0.849583 | ||||||||
\(321\) | −191893. | − | 335184.i | −0.103944 | − | 0.181560i | ||||
\(322\) | −845045. | − | 342547.i | −0.454193 | − | 0.184112i | ||||
\(323\) | − | 108975.i | − | 0.0581191i | ||||||
\(324\) | −27116.4 | − | 48589.3i | −0.0143506 | − | 0.0257145i | ||||
\(325\) | − | 1.12932e6i | − | 0.593073i | ||||||
\(326\) | − | 243642.i | − | 0.126972i | ||||||
\(327\) | −2.06898e6 | + | 1.18449e6i | −1.07001 | + | 0.612580i | ||||
\(328\) | 3.02753e6i | 1.55383i | ||||||||
\(329\) | 2.12929e6 | + | 863130.i | 1.08454 | + | 0.439629i | ||||
\(330\) | −995342. | + | 569834.i | −0.503139 | + | 0.288047i | ||||
\(331\) | 2.59767e6 | 1.30321 | 0.651605 | − | 0.758559i | \(-0.274096\pi\) | ||||
0.651605 | + | 0.758559i | \(0.274096\pi\) | |||||||
\(332\) | −21639.2 | −0.0107745 | ||||||||
\(333\) | 510690. | − | 869836.i | 0.252375 | − | 0.429860i | ||||
\(334\) | 2.60475e6i | 1.27762i | ||||||||
\(335\) | −1.59992e6 | −0.778907 | ||||||||
\(336\) | −1.98847e6 | + | 269753.i | −0.960884 | + | 0.130352i | ||||
\(337\) | 259510. | 0.124474 | 0.0622372 | − | 0.998061i | \(-0.480176\pi\) | ||||
0.0622372 | + | 0.998061i | \(0.480176\pi\) | |||||||
\(338\) | − | 5.19278e6i | − | 2.47234i | ||||||
\(339\) | 1.28333e6 | + | 2.24162e6i | 0.606510 | + | 1.05941i | ||||
\(340\) | −42139.3 | −0.0197692 | ||||||||
\(341\) | 704350. | 0.328022 | ||||||||
\(342\) | 77216.3 | − | 131519.i | 0.0356980 | − | 0.0608029i | ||||
\(343\) | −879385. | − | 1.99355e6i | −0.403593 | − | 0.914939i | ||||
\(344\) | 937032.i | 0.426931i | ||||||||
\(345\) | −451726. | − | 789040.i | −0.204328 | − | 0.356904i | ||||
\(346\) | − | 1.45476e6i | − | 0.653284i | ||||||
\(347\) | 2.10380e6i | 0.937951i | 0.883211 | + | 0.468975i | \(0.155377\pi\) | ||||
−0.883211 | + | 0.468975i | \(0.844623\pi\) | |||||||
\(348\) | −4365.01 | − | 7624.45i | −0.00193213 | − | 0.00337490i | ||||
\(349\) | 2.10644e6i | 0.925732i | 0.886428 | + | 0.462866i | \(0.153179\pi\) | ||||
−0.886428 | + | 0.462866i | \(0.846821\pi\) | |||||||
\(350\) | −268513. | + | 662407.i | −0.117164 | + | 0.289038i | ||||
\(351\) | −4.32383e6 | − | 47277.5i | −1.87327 | − | 0.0204827i | ||||
\(352\) | −97429.5 | −0.0419116 | ||||||||
\(353\) | −106417. | −0.0454541 | −0.0227271 | − | 0.999742i | \(-0.507235\pi\) | ||||
−0.0227271 | + | 0.999742i | \(0.507235\pi\) | |||||||
\(354\) | 1.72585e6 | + | 3.01457e6i | 0.731971 | + | 1.27855i | ||||
\(355\) | − | 2.01521e6i | − | 0.848692i | ||||||
\(356\) | 59934.0 | 0.0250639 | ||||||||
\(357\) | 1.93777e6 | − | 262876.i | 0.804696 | − | 0.109164i | ||||
\(358\) | 3.15392e6 | 1.30060 | ||||||||
\(359\) | 2.24142e6i | 0.917882i | 0.888467 | + | 0.458941i | \(0.151771\pi\) | ||||
−0.888467 | + | 0.458941i | \(0.848229\pi\) | |||||||
\(360\) | −1.77788e6 | − | 1.04381e6i | −0.723012 | − | 0.424488i | ||||
\(361\) | 2.46342e6 | 0.994878 | ||||||||
\(362\) | −3.43010e6 | −1.37574 | ||||||||
\(363\) | −1.07469e6 | + | 615259.i | −0.428071 | + | 0.245071i | ||||
\(364\) | 52388.9 | − | 129240.i | 0.0207246 | − | 0.0511264i | ||||
\(365\) | − | 1.46617e6i | − | 0.576038i | ||||||
\(366\) | −2.78637e6 | + | 1.59520e6i | −1.08726 | + | 0.622460i | ||||
\(367\) | − | 1.72877e6i | − | 0.669995i | −0.942219 | − | 0.334997i | \(-0.891265\pi\) | ||
0.942219 | − | 0.334997i | \(-0.108735\pi\) | |||||||
\(368\) | 1.25319e6i | 0.482388i | ||||||||
\(369\) | 2.02891e6 | − | 3.45576e6i | 0.775707 | − | 1.32123i | ||||
\(370\) | − | 1.06905e6i | − | 0.405969i | ||||||
\(371\) | 1.46525e6 | − | 3.61469e6i | 0.552685 | − | 1.36344i | ||||
\(372\) | 17994.4 | + | 31431.2i | 0.00674186 | + | 0.0117762i | ||||
\(373\) | −2.66469e6 | −0.991687 | −0.495844 | − | 0.868412i | \(-0.665141\pi\) | ||||
−0.495844 | + | 0.868412i | \(0.665141\pi\) | |||||||
\(374\) | −1.54054e6 | −0.569501 | ||||||||
\(375\) | −2.57223e6 | + | 1.47260e6i | −0.944565 | + | 0.540764i | ||||
\(376\) | − | 3.25360e6i | − | 1.18685i | ||||||
\(377\) | −682726. | −0.247396 | ||||||||
\(378\) | 2.52492e6 | + | 1.05579e6i | 0.908905 | + | 0.380057i | ||||
\(379\) | 2.31059e6 | 0.826274 | 0.413137 | − | 0.910669i | \(-0.364433\pi\) | ||||
0.413137 | + | 0.910669i | \(0.364433\pi\) | |||||||
\(380\) | 4904.38i | 0.00174231i | ||||||||
\(381\) | 403557. | − | 231037.i | 0.142427 | − | 0.0815396i | ||||
\(382\) | −3.28049e6 | −1.15022 | ||||||||
\(383\) | −3.80041e6 | −1.32384 | −0.661918 | − | 0.749577i | \(-0.730257\pi\) | ||||
−0.661918 | + | 0.749577i | \(0.730257\pi\) | |||||||
\(384\) | 1.36898e6 | + | 2.39122e6i | 0.473771 | + | 0.827545i | ||||
\(385\) | −642976. | + | 1.58618e6i | −0.221077 | + | 0.545383i | ||||
\(386\) | 571526.i | 0.195239i | ||||||||
\(387\) | 627956. | − | 1.06957e6i | 0.213133 | − | 0.363021i | ||||
\(388\) | 105912.i | 0.0357162i | ||||||||
\(389\) | − | 5.17147e6i | − | 1.73277i | −0.499380 | − | 0.866383i | \(-0.666439\pi\) | ||
0.499380 | − | 0.866383i | \(-0.333561\pi\) | |||||||
\(390\) | −3.97725e6 | + | 2.27698e6i | −1.32410 | + | 0.758049i | ||||
\(391\) | − | 1.22124e6i | − | 0.403978i | ||||||
\(392\) | −2.14847e6 | + | 2.21462e6i | −0.706177 | + | 0.727921i | ||||
\(393\) | −1.02320e6 | + | 585784.i | −0.334180 | + | 0.191318i | ||||
\(394\) | 3.69228e6 | 1.19827 | ||||||||
\(395\) | 1.83763e6 | 0.592606 | ||||||||
\(396\) | 56412.1 | + | 33120.1i | 0.0180773 | + | 0.0106134i | ||||
\(397\) | 2.02589e6i | 0.645119i | 0.946549 | + | 0.322559i | \(0.104543\pi\) | ||||
−0.946549 | + | 0.322559i | \(0.895457\pi\) | |||||||
\(398\) | 3.88775e6 | 1.23024 | ||||||||
\(399\) | −30594.8 | − | 225527.i | −0.00962088 | − | 0.0709197i | ||||
\(400\) | 982340. | 0.306981 | ||||||||
\(401\) | 2.60526e6i | 0.809079i | 0.914521 | + | 0.404539i | \(0.132568\pi\) | ||||
−0.914521 | + | 0.404539i | \(0.867432\pi\) | |||||||
\(402\) | −1.49428e6 | − | 2.61010e6i | −0.461177 | − | 0.805548i | ||||
\(403\) | 2.81448e6 | 0.863249 | ||||||||
\(404\) | 17764.4 | 0.00541500 | ||||||||
\(405\) | 1.32984e6 | + | 2.38291e6i | 0.402866 | + | 0.721887i | ||||
\(406\) | 400456. | + | 162329.i | 0.120570 | + | 0.0488744i | ||||
\(407\) | 1.18582e6i | 0.354840i | ||||||||
\(408\) | −1.37586e6 | − | 2.40324e6i | −0.409188 | − | 0.714737i | ||||
\(409\) | 4.09861e6i | 1.21151i | 0.795650 | + | 0.605756i | \(0.207129\pi\) | ||||
−0.795650 | + | 0.605756i | \(0.792871\pi\) | |||||||
\(410\) | − | 4.24721e6i | − | 1.24780i | ||||||
\(411\) | 230639. | + | 402862.i | 0.0673485 | + | 0.117639i | ||||
\(412\) | 32059.1i | 0.00930483i | ||||||||
\(413\) | 4.80404e6 | + | 1.94737e6i | 1.38590 | + | 0.561788i | ||||
\(414\) | 865334. | − | 1.47389e6i | 0.248132 | − | 0.422633i | ||||
\(415\) | 1.06123e6 | 0.302474 | ||||||||
\(416\) | −389315. | −0.110298 | ||||||||
\(417\) | 927092. | + | 1.61937e6i | 0.261086 | + | 0.456044i | ||||
\(418\) | 179296.i | 0.0501914i | ||||||||
\(419\) | 4.44364e6 | 1.23653 | 0.618264 | − | 0.785971i | \(-0.287836\pi\) | ||||
0.618264 | + | 0.785971i | \(0.287836\pi\) | |||||||
\(420\) | −87209.0 | + | 11830.7i | −0.0241234 | + | 0.00327255i | ||||
\(421\) | 518872. | 0.142677 | 0.0713387 | − | 0.997452i | \(-0.477273\pi\) | ||||
0.0713387 | + | 0.997452i | \(0.477273\pi\) | |||||||
\(422\) | 4.14230e6i | 1.13230i | ||||||||
\(423\) | −2.18042e6 | + | 3.71381e6i | −0.592500 | + | 1.00918i | ||||
\(424\) | −5.52333e6 | −1.49206 | ||||||||
\(425\) | −957294. | −0.257083 | ||||||||
\(426\) | 3.28761e6 | − | 1.88216e6i | 0.877720 | − | 0.502495i | ||||
\(427\) | −1.79995e6 | + | 4.44037e6i | −0.477739 | + | 1.17855i | ||||
\(428\) | 23347.7i | 0.00616076i | ||||||||
\(429\) | 4.41168e6 | − | 2.52569e6i | 1.15734 | − | 0.662578i | ||||
\(430\) | − | 1.31453e6i | − | 0.342845i | ||||||
\(431\) | − | 851882.i | − | 0.220895i | −0.993882 | − | 0.110448i | \(-0.964772\pi\) | ||
0.993882 | − | 0.110448i | \(-0.0352284\pi\) | |||||||
\(432\) | 41124.5 | − | 3.76109e6i | 0.0106021 | − | 0.969627i | ||||
\(433\) | − | 2.57351e6i | − | 0.659639i | −0.944044 | − | 0.329820i | \(-0.893012\pi\) | ||
0.944044 | − | 0.329820i | \(-0.106988\pi\) | |||||||
\(434\) | −1.65085e6 | − | 669188.i | −0.420710 | − | 0.170539i | ||||
\(435\) | 214067. | + | 373916.i | 0.0542410 | + | 0.0947439i | ||||
\(436\) | 144117. | 0.0363078 | ||||||||
\(437\) | −142134. | −0.0356035 | ||||||||
\(438\) | 2.39189e6 | − | 1.36936e6i | 0.595740 | − | 0.341062i | ||||
\(439\) | − | 7.33839e6i | − | 1.81735i | −0.417500 | − | 0.908677i | \(-0.637094\pi\) | ||
0.417500 | − | 0.908677i | \(-0.362906\pi\) | |||||||
\(440\) | 2.42372e6 | 0.596831 | ||||||||
\(441\) | 3.93650e6 | − | 1.08806e6i | 0.963859 | − | 0.266415i | ||||
\(442\) | −6.15579e6 | −1.49875 | ||||||||
\(443\) | 891340.i | 0.215791i | 0.994162 | + | 0.107896i | \(0.0344113\pi\) | ||||
−0.994162 | + | 0.107896i | \(0.965589\pi\) | |||||||
\(444\) | −52916.5 | + | 30294.8i | −0.0127390 | + | 0.00729306i | ||||
\(445\) | −2.93927e6 | −0.703622 | ||||||||
\(446\) | −1.88131e6 | −0.447841 | ||||||||
\(447\) | −3.70880e6 | − | 6.47824e6i | −0.877939 | − | 1.53352i | ||||
\(448\) | 4.04595e6 | + | 1.64007e6i | 0.952414 | + | 0.386071i | ||||
\(449\) | − | 4.74883e6i | − | 1.11166i | −0.831297 | − | 0.555829i | \(-0.812401\pi\) | ||
0.831297 | − | 0.555829i | \(-0.187599\pi\) | |||||||
\(450\) | −1.15534e6 | − | 678311.i | −0.268954 | − | 0.157906i | ||||
\(451\) | 4.71113e6i | 1.09065i | ||||||||
\(452\) | − | 156142.i | − | 0.0359480i | ||||||
\(453\) | 699113. | − | 400243.i | 0.160067 | − | 0.0916386i | ||||
\(454\) | 3.98084e6i | 0.906432i | ||||||||
\(455\) | −2.56924e6 | + | 6.33817e6i | −0.581804 | + | 1.43528i | ||||
\(456\) | −279701. | + | 160129.i | −0.0629914 | + | 0.0360627i | ||||
\(457\) | −3.14654e6 | −0.704762 | −0.352381 | − | 0.935857i | \(-0.614628\pi\) | ||||
−0.352381 | + | 0.935857i | \(0.614628\pi\) | |||||||
\(458\) | −1.09201e6 | −0.243257 | ||||||||
\(459\) | −40076.0 | + | 3.66520e6i | −0.00887876 | + | 0.812019i | ||||
\(460\) | 54961.5i | 0.0121106i | ||||||||
\(461\) | −2.98519e6 | −0.654213 | −0.327107 | − | 0.944987i | \(-0.606074\pi\) | ||||
−0.327107 | + | 0.944987i | \(0.606074\pi\) | |||||||
\(462\) | −3.18822e6 | + | 432509.i | −0.694933 | + | 0.0942737i | ||||
\(463\) | −2.38242e6 | −0.516495 | −0.258248 | − | 0.966079i | \(-0.583145\pi\) | ||||
−0.258248 | + | 0.966079i | \(0.583145\pi\) | |||||||
\(464\) | − | 593871.i | − | 0.128055i | ||||||
\(465\) | −882476. | − | 1.54144e6i | −0.189265 | − | 0.330594i | ||||
\(466\) | 5.59925e6 | 1.19444 | ||||||||
\(467\) | −5.36944e6 | −1.13930 | −0.569648 | − | 0.821889i | \(-0.692921\pi\) | ||||
−0.569648 | + | 0.821889i | \(0.692921\pi\) | |||||||
\(468\) | 225415. | + | 132343.i | 0.0475738 | + | 0.0279311i | ||||
\(469\) | −4.15947e6 | − | 1.68608e6i | −0.873184 | − | 0.353954i | ||||
\(470\) | 4.56436e6i | 0.953092i | ||||||||
\(471\) | 1.67130e6 | + | 2.91929e6i | 0.347137 | + | 0.606352i | ||||
\(472\) | − | 7.34068e6i | − | 1.51664i | ||||||
\(473\) | 1.45811e6i | 0.299666i | ||||||||
\(474\) | 1.71630e6 | + | 2.99790e6i | 0.350871 | + | 0.612875i | ||||
\(475\) | 111415.i | 0.0226573i | ||||||||
\(476\) | −109554. | − | 44408.7i | −0.0221621 | − | 0.00898361i | ||||
\(477\) | 6.30458e6 | + | 3.70148e6i | 1.26870 | + | 0.744869i | ||||
\(478\) | −1.01224e6 | −0.202636 | ||||||||
\(479\) | −1.33255e6 | −0.265366 | −0.132683 | − | 0.991158i | \(-0.542359\pi\) | ||||
−0.132683 | + | 0.991158i | \(0.542359\pi\) | |||||||
\(480\) | 122069. | + | 213221.i | 0.0241826 | + | 0.0422402i | ||||
\(481\) | 4.73837e6i | 0.933827i | ||||||||
\(482\) | 1.08268e6 | 0.212267 | ||||||||
\(483\) | −342864. | − | 2.52740e6i | −0.0668735 | − | 0.492954i | ||||
\(484\) | 74858.6 | 0.0145254 | ||||||||
\(485\) | − | 5.19411e6i | − | 1.00267i | ||||||
\(486\) | −2.64542e6 | + | 4.39506e6i | −0.508048 | + | 0.844061i | ||||
\(487\) | 3.86580e6 | 0.738612 | 0.369306 | − | 0.929308i | \(-0.379595\pi\) | ||||
0.369306 | + | 0.929308i | \(0.379595\pi\) | |||||||
\(488\) | 6.78498e6 | 1.28973 | ||||||||
\(489\) | 591440. | − | 338600.i | 0.111851 | − | 0.0640346i | ||||
\(490\) | 3.01400e6 | − | 3.10681e6i | 0.567092 | − | 0.584554i | ||||
\(491\) | − | 5.61830e6i | − | 1.05172i | −0.850571 | − | 0.525861i | \(-0.823743\pi\) | ||
0.850571 | − | 0.525861i | \(-0.176257\pi\) | |||||||
\(492\) | −210231. | + | 120358.i | −0.0391548 | + | 0.0224161i | ||||
\(493\) | 578729.i | 0.107240i | ||||||||
\(494\) | 716441.i | 0.132088i | ||||||||
\(495\) | −2.76655e6 | − | 1.62427e6i | −0.507487 | − | 0.297951i | ||||
\(496\) | 2.44818e6i | 0.446828i | ||||||||
\(497\) | 2.12374e6 | − | 5.23915e6i | 0.385666 | − | 0.951415i | ||||
\(498\) | 991158. | + | 1.73128e6i | 0.179089 | + | 0.312819i | ||||
\(499\) | −1.06142e7 | −1.90826 | −0.954130 | − | 0.299394i | \(-0.903216\pi\) | ||||
−0.954130 | + | 0.299394i | \(0.903216\pi\) | |||||||
\(500\) | 179172. | 0.0320512 | ||||||||
\(501\) | −6.32304e6 | + | 3.61995e6i | −1.12546 | + | 0.644329i | ||||
\(502\) | 6.41015e6i | 1.13529i | ||||||||
\(503\) | −8.14783e6 | −1.43589 | −0.717946 | − | 0.696098i | \(-0.754918\pi\) | ||||
−0.717946 | + | 0.696098i | \(0.754918\pi\) | |||||||
\(504\) | −3.52210e6 | − | 4.58733e6i | −0.617626 | − | 0.804421i | ||||
\(505\) | −871199. | −0.152016 | ||||||||
\(506\) | 2.00930e6i | 0.348874i | ||||||||
\(507\) | 1.26055e7 | − | 7.21665e6i | 2.17791 | − | 1.24685i | ||||
\(508\) | −28110.2 | −0.00483287 | ||||||||
\(509\) | 7.27954e6 | 1.24540 | 0.622701 | − | 0.782460i | \(-0.286035\pi\) | ||||
0.622701 | + | 0.782460i | \(0.286035\pi\) | |||||||
\(510\) | 1.93014e6 | + | 3.37141e6i | 0.328596 | + | 0.573966i | ||||
\(511\) | 1.54513e6 | − | 3.81174e6i | 0.261765 | − | 0.645760i | ||||
\(512\) | − | 6.17201e6i | − | 1.04052i | ||||||
\(513\) | 426574. | + | 4664.24i | 0.0715651 | + | 0.000782505i | ||||
\(514\) | 4.20031e6i | 0.701251i | ||||||||
\(515\) | − | 1.57223e6i | − | 0.261216i | ||||||
\(516\) | −65067.3 | + | 37251.1i | −0.0107582 | + | 0.00615907i | ||||
\(517\) | − | 5.06291e6i | − | 0.833056i | ||||||
\(518\) | 1.12662e6 | − | 2.77931e6i | 0.184482 | − | 0.455107i | ||||
\(519\) | 3.53144e6 | − | 2.02175e6i | 0.575484 | − | 0.329465i | ||||
\(520\) | 9.68486e6 | 1.57067 | ||||||||
\(521\) | 2.38061e6 | 0.384232 | 0.192116 | − | 0.981372i | \(-0.438465\pi\) | ||||
0.192116 | + | 0.981372i | \(0.438465\pi\) | |||||||
\(522\) | −410071. | + | 698457.i | −0.0658693 | + | 0.112192i | ||||
\(523\) | − | 1.14144e6i | − | 0.182473i | −0.995829 | − | 0.0912363i | \(-0.970918\pi\) | ||
0.995829 | − | 0.0912363i | \(-0.0290818\pi\) | |||||||
\(524\) | 71272.4 | 0.0113395 | ||||||||
\(525\) | −1.98116e6 | + | 268762.i | −0.313705 | + | 0.0425568i | ||||
\(526\) | 3.54550e6 | 0.558745 | ||||||||
\(527\) | − | 2.38577e6i | − | 0.374198i | ||||||
\(528\) | 2.19698e6 | + | 3.83751e6i | 0.342958 | + | 0.599052i | ||||
\(529\) | 4.84351e6 | 0.752524 | ||||||||
\(530\) | 7.74847e6 | 1.19819 | ||||||||
\(531\) | −4.91939e6 | + | 8.37898e6i | −0.757137 | + | 1.28960i | ||||
\(532\) | −5168.51 | + | 12750.4i | −0.000791746 | + | 0.00195319i | ||||
\(533\) | 1.88250e7i | 2.87023i | ||||||||
\(534\) | −2.74520e6 | − | 4.79511e6i | −0.416602 | − | 0.727688i | ||||
\(535\) | − | 1.14501e6i | − | 0.172952i | ||||||
\(536\) | 6.35575e6i | 0.955553i | ||||||||
\(537\) | 4.38315e6 | + | 7.65614e6i | 0.655920 | + | 1.14571i | ||||
\(538\) | − | 5.05254e6i | − | 0.752582i | ||||||
\(539\) | −3.34322e6 | + | 3.44616e6i | −0.495670 | + | 0.510933i | ||||
\(540\) | 1803.61 | − | 164952.i | 0.000266169 | − | 0.0243429i | ||||
\(541\) | 7.55281e6 | 1.10947 | 0.554735 | − | 0.832027i | \(-0.312820\pi\) | ||||
0.554735 | + | 0.832027i | \(0.312820\pi\) | |||||||
\(542\) | −361181. | −0.0528113 | ||||||||
\(543\) | −4.76698e6 | − | 8.32658e6i | −0.693814 | − | 1.21190i | ||||
\(544\) | 330012.i | 0.0478116i | ||||||||
\(545\) | −7.06776e6 | −1.01927 | ||||||||
\(546\) | −1.27397e7 | + | 1.72825e6i | −1.82884 | + | 0.248099i | ||||
\(547\) | −7.39779e6 | −1.05714 | −0.528571 | − | 0.848889i | \(-0.677272\pi\) | ||||
−0.528571 | + | 0.848889i | \(0.677272\pi\) | |||||||
\(548\) | − | 28061.8i | − | 0.00399176i | ||||||
\(549\) | −7.74468e6 | − | 4.54698e6i | −1.09666 | − | 0.643862i | ||||
\(550\) | 1.57504e6 | 0.222016 | ||||||||
\(551\) | 67355.4 | 0.00945134 | ||||||||
\(552\) | −3.13450e6 | + | 1.79450e6i | −0.437845 | + | 0.250667i | ||||
\(553\) | 4.77748e6 | + | 1.93660e6i | 0.664334 | + | 0.269294i | ||||
\(554\) | − | 6.70554e6i | − | 0.928239i | ||||||
\(555\) | 2.59512e6 | − | 1.48571e6i | 0.357622 | − | 0.204739i | ||||
\(556\) | − | 112799.i | − | 0.0154746i | ||||||
\(557\) | − | 3.17885e6i | − | 0.434143i | −0.976156 | − | 0.217071i | \(-0.930350\pi\) | ||
0.976156 | − | 0.217071i | \(-0.0696505\pi\) | |||||||
\(558\) | 1.69049e6 | − | 2.87933e6i | 0.229840 | − | 0.391477i | ||||
\(559\) | 5.82641e6i | 0.788626i | ||||||||
\(560\) | −5.51327e6 | − | 2.23486e6i | −0.742916 | − | 0.301148i | ||||
\(561\) | −2.14096e6 | − | 3.73967e6i | −0.287212 | − | 0.501679i | ||||
\(562\) | −1.11243e6 | −0.148571 | ||||||||
\(563\) | 7.56588e6 | 1.00598 | 0.502989 | − | 0.864293i | \(-0.332234\pi\) | ||||
0.502989 | + | 0.864293i | \(0.332234\pi\) | |||||||
\(564\) | 225929. | − | 129345.i | 0.0299072 | − | 0.0171219i | ||||
\(565\) | 7.65750e6i | 1.00917i | ||||||||
\(566\) | −9.63617e6 | −1.26434 | ||||||||
\(567\) | 946071. | + | 7.59653e6i | 0.123585 | + | 0.992334i | ||||
\(568\) | −8.00554e6 | −1.04116 | ||||||||
\(569\) | 4.34836e6i | 0.563047i | 0.959554 | + | 0.281524i | \(0.0908397\pi\) | ||||
−0.959554 | + | 0.281524i | \(0.909160\pi\) | |||||||
\(570\) | 392382. | − | 224639.i | 0.0505850 | − | 0.0289599i | ||||
\(571\) | 5.84474e6 | 0.750196 | 0.375098 | − | 0.926985i | \(-0.377609\pi\) | ||||
0.375098 | + | 0.926985i | \(0.377609\pi\) | |||||||
\(572\) | −307301. | −0.0392711 | ||||||||
\(573\) | −4.55905e6 | − | 7.96339e6i | −0.580080 | − | 1.01324i | ||||
\(574\) | 4.47595e6 | − | 1.10419e7i | 0.567029 | − | 1.39883i | ||||
\(575\) | 1.24858e6i | 0.157488i | ||||||||
\(576\) | −4.14309e6 | + | 7.05675e6i | −0.520318 | + | 0.886235i | ||||
\(577\) | − | 1.37469e7i | − | 1.71896i | −0.511173 | − | 0.859478i | \(-0.670789\pi\) | ||
0.511173 | − | 0.859478i | \(-0.329211\pi\) | |||||||
\(578\) | − | 2.69467e6i | − | 0.335495i | ||||||
\(579\) | −1.38738e6 | + | 794276.i | −0.171988 | + | 0.0984635i | ||||
\(580\) | − | 26045.6i | − | 0.00321488i | ||||||
\(581\) | 2.75898e6 | + | 1.11838e6i | 0.339084 | + | 0.137451i | ||||
\(582\) | 8.47364e6 | − | 4.85116e6i | 1.03696 | − | 0.593661i | ||||
\(583\) | −8.59482e6 | −1.04729 | ||||||||
\(584\) | −5.82442e6 | −0.706676 | ||||||||
\(585\) | −1.10547e7 | − | 6.49035e6i | −1.33555 | − | 0.784113i | ||||
\(586\) | − | 1.06732e7i | − | 1.28396i | ||||||
\(587\) | 1.10150e7 | 1.31944 | 0.659721 | − | 0.751511i | \(-0.270675\pi\) | ||||
0.659721 | + | 0.751511i | \(0.270675\pi\) | |||||||
\(588\) | −239194. | − | 61148.3i | −0.0285303 | − | 0.00729359i | ||||
\(589\) | −277667. | −0.0329789 | ||||||||
\(590\) | 1.02980e7i | 1.21793i | ||||||||
\(591\) | 5.13134e6 | + | 8.96302e6i | 0.604313 | + | 1.05557i | ||||
\(592\) | −4.12168e6 | −0.483359 | ||||||||
\(593\) | 832174. | 0.0971802 | 0.0485901 | − | 0.998819i | \(-0.484527\pi\) | ||||
0.0485901 | + | 0.998819i | \(0.484527\pi\) | |||||||
\(594\) | 65936.9 | − | 6.03035e6i | 0.00766766 | − | 0.701256i | ||||
\(595\) | 5.37271e6 | + | 2.17788e6i | 0.622158 | + | 0.252198i | ||||
\(596\) | 451250.i | 0.0520357i | ||||||||
\(597\) | 5.40298e6 | + | 9.43751e6i | 0.620437 | + | 1.08373i | ||||
\(598\) | 8.02889e6i | 0.918126i | ||||||||
\(599\) | 9.00401e6i | 1.02534i | 0.858585 | + | 0.512671i | \(0.171344\pi\) | ||||
−0.858585 | + | 0.512671i | \(0.828656\pi\) | |||||||
\(600\) | 1.40666e6 | + | 2.45705e6i | 0.159519 | + | 0.278635i | ||||
\(601\) | − | 1.57084e6i | − | 0.177397i | −0.996059 | − | 0.0886984i | \(-0.971729\pi\) | ||
0.996059 | − | 0.0886984i | \(-0.0282707\pi\) | |||||||
\(602\) | 1.38532e6 | − | 3.41751e6i | 0.155797 | − | 0.384342i | ||||
\(603\) | 4.25933e6 | − | 7.25474e6i | 0.477033 | − | 0.812510i | ||||
\(604\) | −48697.6 | −0.00543144 | ||||||||
\(605\) | −3.67120e6 | −0.407774 | ||||||||
\(606\) | −813678. | − | 1.42127e6i | −0.0900059 | − | 0.157215i | ||||
\(607\) | 9.46468e6i | 1.04264i | 0.853361 | + | 0.521320i | \(0.174560\pi\) | ||||
−0.853361 | + | 0.521320i | \(0.825440\pi\) | |||||||
\(608\) | 38408.5 | 0.00421374 | ||||||||
\(609\) | 162479. | + | 1.19770e6i | 0.0177523 | + | 0.130860i | ||||
\(610\) | −9.51839e6 | −1.03571 | ||||||||
\(611\) | − | 2.02307e7i | − | 2.19234i | ||||||
\(612\) | 112184. | − | 191078.i | 0.0121075 | − | 0.0206221i | ||||
\(613\) | 9.55862e6 | 1.02741 | 0.513705 | − | 0.857967i | \(-0.328273\pi\) | ||||
0.513705 | + | 0.857967i | \(0.328273\pi\) | |||||||
\(614\) | 732588. | 0.0784222 | ||||||||
\(615\) | 1.03101e7 | − | 5.90255e6i | 1.09920 | − | 0.629291i | ||||
\(616\) | 6.30120e6 | + | 2.55425e6i | 0.669070 | + | 0.271214i | ||||
\(617\) | − | 4.88602e6i | − | 0.516704i | −0.966051 | − | 0.258352i | \(-0.916821\pi\) | ||
0.966051 | − | 0.258352i | \(-0.0831795\pi\) | |||||||
\(618\) | 2.56493e6 | − | 1.46843e6i | 0.270150 | − | 0.154661i | ||||
\(619\) | 9.76741e6i | 1.02460i | 0.858808 | + | 0.512298i | \(0.171206\pi\) | ||||
−0.858808 | + | 0.512298i | \(0.828794\pi\) | |||||||
\(620\) | 107371.i | 0.0112178i | ||||||||
\(621\) | 4.78045e6 | + | 52270.3i | 0.497439 | + | 0.00543909i | ||||
\(622\) | 2.49125e6i | 0.258191i | ||||||||
\(623\) | −7.64152e6 | − | 3.09756e6i | −0.788786 | − | 0.319742i | ||||
\(624\) | 8.77881e6 | + | 1.53341e7i | 0.902557 | + | 1.57652i | ||||
\(625\) | −5.69531e6 | −0.583200 | ||||||||
\(626\) | −1.17968e6 | −0.120317 | ||||||||
\(627\) | −435241. | + | 249176.i | −0.0442141 | + | 0.0253126i | ||||
\(628\) | − | 203347.i | − | 0.0205749i | ||||||
\(629\) | 4.01660e6 | 0.404792 | ||||||||
\(630\) | 4.94103e6 | + | 6.43539e6i | 0.495982 | + | 0.645986i | ||||
\(631\) | −899670. | −0.0899518 | −0.0449759 | − | 0.998988i | \(-0.514321\pi\) | ||||
−0.0449759 | + | 0.998988i | \(0.514321\pi\) | |||||||
\(632\) | − | 7.30009e6i | − | 0.727002i | ||||||
\(633\) | −1.00554e7 | + | 5.75675e6i | −0.997451 | + | 0.571042i | ||||
\(634\) | −5.12718e6 | −0.506588 | ||||||||
\(635\) | 1.37858e6 | 0.135674 | ||||||||
\(636\) | −219576. | − | 383539.i | −0.0215250 | − | 0.0375982i | ||||
\(637\) | −1.33590e7 | + | 1.37704e7i | −1.30445 | + | 1.34461i | ||||
\(638\) | − | 952183.i | − | 0.0926123i | ||||||
\(639\) | 9.13788e6 | + | 5.36494e6i | 0.885306 | + | 0.519772i | ||||
\(640\) | 8.16856e6i | 0.788307i | ||||||||
\(641\) | − | 4.01387e6i | − | 0.385850i | −0.981214 | − | 0.192925i | \(-0.938203\pi\) | ||
0.981214 | − | 0.192925i | \(-0.0617974\pi\) | |||||||
\(642\) | 1.86796e6 | − | 1.06941e6i | 0.178867 | − | 0.102402i | ||||
\(643\) | − | 7.33239e6i | − | 0.699388i | −0.936864 | − | 0.349694i | \(-0.886286\pi\) | ||
0.936864 | − | 0.349694i | \(-0.113714\pi\) | |||||||
\(644\) | −57921.5 | + | 142889.i | −0.00550332 | + | 0.0135764i | ||||
\(645\) | 3.19101e6 | − | 1.82686e6i | 0.302016 | − | 0.172904i | ||||
\(646\) | 607309. | 0.0572570 | ||||||||
\(647\) | 1.70332e7 | 1.59969 | 0.799846 | − | 0.600205i | \(-0.204915\pi\) | ||||
0.799846 | + | 0.600205i | \(0.204915\pi\) | |||||||
\(648\) | 9.46621e6 | − | 5.28284e6i | 0.885602 | − | 0.494231i | ||||
\(649\) | − | 1.14228e7i | − | 1.06454i | ||||||
\(650\) | 6.29362e6 | 0.584275 | ||||||||
\(651\) | −669807. | − | 4.93744e6i | −0.0619437 | − | 0.456614i | ||||
\(652\) | −41197.5 | −0.00379535 | ||||||||
\(653\) | − | 4.19237e6i | − | 0.384748i | −0.981322 | − | 0.192374i | \(-0.938381\pi\) | ||
0.981322 | − | 0.192374i | \(-0.0616186\pi\) | |||||||
\(654\) | −6.60111e6 | − | 1.15303e7i | −0.603493 | − | 1.05414i | ||||
\(655\) | −3.49532e6 | −0.318335 | ||||||||
\(656\) | −1.63750e7 | −1.48567 | ||||||||
\(657\) | 6.64825e6 | + | 3.90326e6i | 0.600889 | + | 0.352788i | ||||
\(658\) | −4.81017e6 | + | 1.18664e7i | −0.433108 | + | 1.06845i | ||||
\(659\) | 1.07708e7i | 0.966131i | 0.875584 | + | 0.483065i | \(0.160477\pi\) | ||||
−0.875584 | + | 0.483065i | \(0.839523\pi\) | |||||||
\(660\) | 96353.6 | + | 168303.i | 0.00861010 | + | 0.0150394i | ||||
\(661\) | − | 9.47459e6i | − | 0.843445i | −0.906725 | − | 0.421723i | \(-0.861426\pi\) | ||
0.906725 | − | 0.421723i | \(-0.138574\pi\) | |||||||
\(662\) | 1.44767e7i | 1.28388i | ||||||||
\(663\) | −8.55499e6 | − | 1.49432e7i | −0.755850 | − | 1.32026i | ||||
\(664\) | − | 4.21577e6i | − | 0.371071i | ||||||
\(665\) | 253473. | − | 625302.i | 0.0222268 | − | 0.0548322i | ||||
\(666\) | 4.84755e6 | + | 2.84605e6i | 0.423483 | + | 0.248632i | ||||
\(667\) | 754826. | 0.0656950 | ||||||||
\(668\) | 440439. | 0.0381895 | ||||||||
\(669\) | −2.61455e6 | − | 4.56689e6i | −0.225856 | − | 0.394507i | ||||
\(670\) | − | 8.91625e6i | − | 0.767353i | ||||||
\(671\) | 1.05581e7 | 0.905270 | ||||||||
\(672\) | 92651.4 | + | 682974.i | 0.00791460 | + | 0.0583420i | ||||
\(673\) | −2.97586e6 | −0.253265 | −0.126632 | − | 0.991950i | \(-0.540417\pi\) | ||||
−0.126632 | + | 0.991950i | \(0.540417\pi\) | |||||||
\(674\) | 1.44624e6i | 0.122628i | ||||||||
\(675\) | 40973.3 | − | 3.74727e6i | 0.00346132 | − | 0.316559i | ||||
\(676\) | −878050. | −0.0739014 | ||||||||
\(677\) | −5.53094e6 | −0.463796 | −0.231898 | − | 0.972740i | \(-0.574494\pi\) | ||||
−0.231898 | + | 0.972740i | \(0.574494\pi\) | |||||||
\(678\) | −1.24924e7 | + | 7.15191e6i | −1.04369 | + | 0.597514i | ||||
\(679\) | 5.47384e6 | − | 1.35036e7i | 0.455636 | − | 1.12403i | ||||
\(680\) | − | 8.20961e6i | − | 0.680848i | ||||||
\(681\) | −9.66350e6 | + | 5.53236e6i | −0.798485 | + | 0.457133i | ||||
\(682\) | 3.92530e6i | 0.323156i | ||||||||
\(683\) | 2.08889e7i | 1.71342i | 0.515796 | + | 0.856712i | \(0.327496\pi\) | ||||
−0.515796 | + | 0.856712i | \(0.672504\pi\) | |||||||
\(684\) | −22238.6 | − | 13056.5i | −0.00181747 | − | 0.00106706i | ||||
\(685\) | 1.37620e6i | 0.112061i | ||||||||
\(686\) | 1.11099e7 | − | 4.90076e6i | 0.901366 | − | 0.397606i | ||||
\(687\) | −1.51762e6 | − | 2.65087e6i | −0.122680 | − | 0.214287i | ||||
\(688\) | −5.06811e6 | −0.408202 | ||||||||
\(689\) | −3.43437e7 | −2.75613 | ||||||||
\(690\) | 4.39727e6 | − | 2.51744e6i | 0.351610 | − | 0.201297i | ||||
\(691\) | 2.76828e6i | 0.220554i | 0.993901 | + | 0.110277i | \(0.0351738\pi\) | ||||
−0.993901 | + | 0.110277i | \(0.964826\pi\) | |||||||
\(692\) | −245986. | −0.0195275 | ||||||||
\(693\) | −5.48073e6 | − | 7.13832e6i | −0.433516 | − | 0.564628i | ||||
\(694\) | −1.17243e7 | −0.924037 | ||||||||
\(695\) | 5.53188e6i | 0.434421i | ||||||||
\(696\) | 1.48540e6 | − | 850394.i | 0.116231 | − | 0.0665422i | ||||
\(697\) | 1.59575e7 | 1.24418 | ||||||||
\(698\) | −1.17391e7 | −0.912000 | ||||||||
\(699\) | 7.78154e6 | + | 1.35922e7i | 0.602383 | + | 1.05220i | ||||
\(700\) | 112007. | + | 45403.1i | 0.00863971 | + | 0.00350219i | ||||
\(701\) | 2.86133e6i | 0.219924i | 0.993936 | + | 0.109962i | \(0.0350729\pi\) | ||||
−0.993936 | + | 0.109962i | \(0.964927\pi\) | |||||||
\(702\) | 263475. | − | 2.40965e7i | 0.0201789 | − | 1.84548i | ||||
\(703\) | − | 467471.i | − | 0.0356752i | ||||||
\(704\) | − | 9.62024e6i | − | 0.731568i | ||||||
\(705\) | −1.10800e7 | + | 6.34330e6i | −0.839588 | + | 0.480665i | ||||
\(706\) | − | 593054.i | − | 0.0447798i | ||||||
\(707\) | −2.26494e6 | − | 918118.i | −0.170415 | − | 0.0690796i | ||||
\(708\) | 509735. | − | 291824.i | 0.0382174 | − | 0.0218795i | ||||
\(709\) | 3.16019e6 | 0.236101 | 0.118050 | − | 0.993008i | \(-0.462336\pi\) | ||||
0.118050 | + | 0.993008i | \(0.462336\pi\) | |||||||
\(710\) | 1.12307e7 | 0.836103 | ||||||||
\(711\) | −4.89219e6 | + | 8.33265e6i | −0.362935 | + | 0.618172i | ||||
\(712\) | 1.16764e7i | 0.863195i | ||||||||
\(713\) | −3.11171e6 | −0.229232 | ||||||||
\(714\) | 1.46499e6 | + | 1.07991e7i | 0.107545 | + | 0.792760i | ||||
\(715\) | 1.50706e7 | 1.10246 | ||||||||
\(716\) | − | 533298.i | − | 0.0388765i | ||||||
\(717\) | −1.40676e6 | − | 2.45722e6i | −0.102193 | − | 0.178504i | ||||
\(718\) | −1.24913e7 | −0.904266 | ||||||||
\(719\) | −7.16590e6 | −0.516950 | −0.258475 | − | 0.966018i | \(-0.583220\pi\) | ||||
−0.258475 | + | 0.966018i | \(0.583220\pi\) | |||||||
\(720\) | 5.64565e6 | − | 9.61599e6i | 0.405866 | − | 0.691294i | ||||
\(721\) | 1.65691e6 | − | 4.08750e6i | 0.118703 | − | 0.292832i | ||||
\(722\) | 1.37285e7i | 0.980120i | ||||||||
\(723\) | 1.50465e6 | + | 2.62820e6i | 0.107051 | + | 0.186988i | ||||
\(724\) | 579998.i | 0.0411225i | ||||||||
\(725\) | − | 591688.i | − | 0.0418069i | ||||||
\(726\) | −3.42880e6 | − | 5.98917e6i | −0.241435 | − | 0.421721i | ||||
\(727\) | 2.11535e7i | 1.48439i | 0.670186 | + | 0.742194i | \(0.266215\pi\) | ||||
−0.670186 | + | 0.742194i | \(0.733785\pi\) | |||||||
\(728\) | 2.51787e7 | + | 1.02064e7i | 1.76078 | + | 0.713750i | ||||
\(729\) | −1.43455e7 | − | 313749.i | −0.999761 | − | 0.0218657i | ||||
\(730\) | 8.17086e6 | 0.567493 | ||||||||
\(731\) | 4.93890e6 | 0.341851 | ||||||||
\(732\) | 269733. | + | 471148.i | 0.0186061 | + | 0.0324997i | ||||
\(733\) | − | 1.58013e7i | − | 1.08626i | −0.839648 | − | 0.543130i | \(-0.817239\pi\) | ||
0.839648 | − | 0.543130i | \(-0.182761\pi\) | |||||||
\(734\) | 9.63431e6 | 0.660056 | ||||||||
\(735\) | 1.17305e7 | + | 2.99882e6i | 0.800935 | + | 0.204754i | ||||
\(736\) | 430429. | 0.0292892 | ||||||||
\(737\) | 9.89015e6i | 0.670709i | ||||||||
\(738\) | 1.92588e7 | + | 1.13070e7i | 1.30163 | + | 0.764200i | ||||
\(739\) | 1.13985e7 | 0.767781 | 0.383890 | − | 0.923379i | \(-0.374584\pi\) | ||||
0.383890 | + | 0.923379i | \(0.374584\pi\) | |||||||
\(740\) | −180766. | −0.0121349 | ||||||||
\(741\) | −1.73916e6 | + | 995672.i | −0.116358 | + | 0.0666148i | ||||
\(742\) | 2.01445e7 | + | 8.16577e6i | 1.34322 | + | 0.544487i | ||||
\(743\) | − | 2.74896e7i | − | 1.82683i | −0.407035 | − | 0.913413i | \(-0.633437\pi\) | ||
0.407035 | − | 0.913413i | \(-0.366563\pi\) | |||||||
\(744\) | −6.12345e6 | + | 3.50568e6i | −0.405568 | + | 0.232188i | ||||
\(745\) | − | 2.21301e7i | − | 1.46080i | ||||||
\(746\) | − | 1.48502e7i | − | 0.976977i | ||||||
\(747\) | −2.82522e6 | + | 4.81207e6i | −0.185247 | + | 0.315523i | ||||
\(748\) | 260491.i | 0.0170231i | ||||||||
\(749\) | 1.20668e6 | − | 2.97680e6i | 0.0785934 | − | 0.193885i | ||||
\(750\) | −8.20674e6 | − | 1.43349e7i | −0.532743 | − | 0.930553i | ||||
\(751\) | −7.32522e6 | −0.473937 | −0.236969 | − | 0.971517i | \(-0.576154\pi\) | ||||
−0.236969 | + | 0.971517i | \(0.576154\pi\) | |||||||
\(752\) | 1.75977e7 | 1.13478 | ||||||||
\(753\) | −1.55606e7 | + | 8.90848e6i | −1.00009 | + | 0.572554i | ||||
\(754\) | − | 3.80479e6i | − | 0.243726i | ||||||
\(755\) | 2.38821e6 | 0.152478 | ||||||||
\(756\) | 178524. | − | 426940.i | 0.0113604 | − | 0.0271683i | ||||
\(757\) | 1.29529e7 | 0.821536 | 0.410768 | − | 0.911740i | \(-0.365261\pi\) | ||||
0.410768 | + | 0.911740i | \(0.365261\pi\) | |||||||
\(758\) | 1.28768e7i | 0.814017i | ||||||||
\(759\) | −4.87758e6 | + | 2.79242e6i | −0.307326 | + | 0.175945i | ||||
\(760\) | −955475. | −0.0600047 | ||||||||
\(761\) | 1.43097e7 | 0.895714 | 0.447857 | − | 0.894105i | \(-0.352187\pi\) | ||||
0.447857 | + | 0.894105i | \(0.352187\pi\) | |||||||
\(762\) | 1.28755e6 | + | 2.24900e6i | 0.0803301 | + | 0.140314i | ||||
\(763\) | −1.83748e7 | − | 7.44840e6i | −1.14264 | − | 0.463182i | ||||
\(764\) | 554699.i | 0.0343815i | ||||||||
\(765\) | −5.50170e6 | + | 9.37082e6i | −0.339894 | + | 0.578927i | ||||
\(766\) | − | 2.11795e7i | − | 1.30420i | ||||||
\(767\) | − | 4.56439e7i | − | 2.80152i | ||||||
\(768\) | 1.25210e6 | − | 716827.i | 0.0766011 | − | 0.0438542i | ||||
\(769\) | 2.84449e7i | 1.73456i | 0.497822 | + | 0.867279i | \(0.334133\pi\) | ||||
−0.497822 | + | 0.867279i | \(0.665867\pi\) | |||||||
\(770\) | −8.83971e6 | − | 3.58327e6i | −0.537293 | − | 0.217797i | ||||
\(771\) | −1.01963e7 | + | 5.83737e6i | −0.617739 | + | 0.353656i | ||||
\(772\) | 96639.6 | 0.00583595 | ||||||||
\(773\) | −1.79858e7 | −1.08263 | −0.541316 | − | 0.840819i | \(-0.682074\pi\) | ||||
−0.541316 | + | 0.840819i | \(0.682074\pi\) | |||||||
\(774\) | 5.96065e6 | + | 3.49956e6i | 0.357636 | + | 0.209972i | ||||
\(775\) | 2.43918e6i | 0.145878i | ||||||||
\(776\) | −2.06339e7 | −1.23006 | ||||||||
\(777\) | 8.31251e6 | − | 1.12766e6i | 0.493946 | − | 0.0670081i | ||||
\(778\) | 2.88203e7 | 1.70706 | ||||||||
\(779\) | − | 1.85721e6i | − | 0.109652i | ||||||
\(780\) | 385015. | + | 672515.i | 0.0226590 | + | 0.0395791i | ||||
\(781\) | −1.24574e7 | −0.730801 | ||||||||
\(782\) | 6.80588e6 | 0.397986 | ||||||||
\(783\) | −2.26540e6 | − | 24770.3i | −0.132051 | − | 0.00144386i | ||||
\(784\) | −1.19782e7 | − | 1.16204e7i | −0.695987 | − | 0.675197i | ||||
\(785\) | 9.97247e6i | 0.577602i | ||||||||
\(786\) | −3.26454e6 | − | 5.70224e6i | −0.188480 | − | 0.329222i | ||||
\(787\) | 1.53079e7i | 0.881003i | 0.897752 | + | 0.440502i | \(0.145199\pi\) | ||||
−0.897752 | + | 0.440502i | \(0.854801\pi\) | |||||||
\(788\) | − | 624330.i | − | 0.0358178i | ||||||
\(789\) | 4.92735e6 | + | 8.60671e6i | 0.281787 | + | 0.492204i | ||||
\(790\) | 1.02410e7i | 0.583815i | ||||||||
\(791\) | −8.06990e6 | + | 1.99080e7i | −0.458592 | + | 1.13132i | ||||
\(792\) | −6.45249e6 | + | 1.09902e7i | −0.365523 | + | 0.622579i | ||||
\(793\) | 4.21886e7 | 2.38239 | ||||||||
\(794\) | −1.12902e7 | −0.635549 | ||||||||
\(795\) | 1.07684e7 | + | 1.88094e7i | 0.604274 | + | 1.05550i | ||||
\(796\) | − | 657381.i | − | 0.0367735i | ||||||
\(797\) | −5.35963e6 | −0.298875 | −0.149437 | − | 0.988771i | \(-0.547746\pi\) | ||||
−0.149437 | + | 0.988771i | \(0.547746\pi\) | |||||||
\(798\) | 1.25685e6 | − | 170503.i | 0.0698677 | − | 0.00947817i | ||||
\(799\) | −1.71490e7 | −0.950327 | ||||||||
\(800\) | − | 337401.i | − | 0.0186390i | ||||||
\(801\) | 7.82499e6 | − | 1.33280e7i | 0.430926 | − | 0.733977i | ||||
\(802\) | −1.45190e7 | −0.797077 | ||||||||
\(803\) | −9.06335e6 | −0.496021 | ||||||||
\(804\) | −441342. | + | 252669.i | −0.0240788 | + | 0.0137852i | ||||
\(805\) | 2.84057e6 | − | 7.00753e6i | 0.154496 | − | 0.381132i | ||||
\(806\) | 1.56850e7i | 0.850444i | ||||||||
\(807\) | 1.22650e7 | − | 7.02175e6i | 0.662956 | − | 0.379543i | ||||
\(808\) | 3.46088e6i | 0.186491i | ||||||||
\(809\) | 9.70495e6i | 0.521341i | 0.965428 | + | 0.260671i | \(0.0839436\pi\) | ||||
−0.965428 | + | 0.260671i | \(0.916056\pi\) | |||||||
\(810\) | −1.32798e7 | + | 7.41110e6i | −0.711179 | + | 0.396890i | ||||
\(811\) | − | 3.08898e7i | − | 1.64916i | −0.565746 | − | 0.824579i | \(-0.691412\pi\) | ||
0.565746 | − | 0.824579i | \(-0.308588\pi\) | |||||||
\(812\) | 27448.3 | − | 67713.4i | 0.00146092 | − | 0.00360400i | ||||
\(813\) | −501950. | − | 876767.i | −0.0266339 | − | 0.0465220i | ||||
\(814\) | −6.60850e6 | −0.349576 | ||||||||
\(815\) | 2.02040e6 | 0.106547 | ||||||||
\(816\) | 1.29984e7 | − | 7.44158e6i | 0.683382 | − | 0.391237i | ||||
\(817\) | − | 574813.i | − | 0.0301281i | ||||||
\(818\) | −2.28413e7 | −1.19354 | ||||||||
\(819\) | −2.19002e7 | − | 2.85237e7i | −1.14088 | − | 1.48592i | ||||
\(820\) | −718163. | −0.0372982 | ||||||||
\(821\) | − | 8.98419e6i | − | 0.465180i | −0.972575 | − | 0.232590i | \(-0.925280\pi\) | ||
0.972575 | − | 0.232590i | \(-0.0747200\pi\) | |||||||
\(822\) | −2.24512e6 | + | 1.28534e6i | −0.115894 | + | 0.0663494i | ||||
\(823\) | −2.18846e7 | −1.12626 | −0.563132 | − | 0.826367i | \(-0.690404\pi\) | ||||
−0.563132 | + | 0.826367i | \(0.690404\pi\) | |||||||
\(824\) | −6.24578e6 | −0.320456 | ||||||||
\(825\) | 2.18890e6 | + | 3.82340e6i | 0.111967 | + | 0.195576i | ||||
\(826\) | −1.08526e7 | + | 2.67727e7i | −0.553455 | + | 1.36534i | ||||
\(827\) | 3.72199e6i | 0.189239i | 0.995514 | + | 0.0946196i | \(0.0301635\pi\) | ||||
−0.995514 | + | 0.0946196i | \(0.969837\pi\) | |||||||
\(828\) | −249220. | − | 146320.i | −0.0126330 | − | 0.00741698i | ||||
\(829\) | 2.09659e7i | 1.05956i | 0.848135 | + | 0.529781i | \(0.177726\pi\) | ||||
−0.848135 | + | 0.529781i | \(0.822274\pi\) | |||||||
\(830\) | 5.91415e6i | 0.297987i | ||||||||
\(831\) | 1.62777e7 | − | 9.31901e6i | 0.817694 | − | 0.468131i | ||||
\(832\) | − | 3.84412e7i | − | 1.92525i | ||||||
\(833\) | 1.16728e7 | + | 1.13241e7i | 0.582858 | + | 0.565447i | ||||
\(834\) | −9.02467e6 | + | 5.16663e6i | −0.449279 | + | 0.257213i | ||||
\(835\) | −2.15999e7 | −1.07210 | ||||||||
\(836\) | 30317.2 | 0.00150028 | ||||||||
\(837\) | 9.33893e6 | + | 102113.i | 0.460769 | + | 0.00503813i | ||||
\(838\) | 2.47641e7i | 1.21818i | ||||||||
\(839\) | 2.54324e7 | 1.24733 | 0.623666 | − | 0.781691i | \(-0.285643\pi\) | ||||
0.623666 | + | 0.781691i | \(0.285643\pi\) | |||||||
\(840\) | −2.30486e6 | − | 1.69901e7i | −0.112706 | − | 0.830803i | ||||
\(841\) | 2.01534e7 | 0.982561 | ||||||||
\(842\) | 2.89165e6i | 0.140561i | ||||||||
\(843\) | −1.54600e6 | − | 2.70044e6i | −0.0749275 | − | 0.130877i | ||||
\(844\) | 700423. | 0.0338458 | ||||||||
\(845\) | 4.30611e7 | 2.07464 | ||||||||
\(846\) | −2.06968e7 | − | 1.21513e7i | −0.994210 | − | 0.583711i | ||||
\(847\) | −9.54438e6 | − | 3.86891e6i | −0.457129 | − | 0.185302i | ||||
\(848\) | − | 2.98740e7i | − | 1.42660i | ||||||
\(849\) | −1.33918e7 | − | 2.33918e7i | −0.637633 | − | 1.11377i | ||||
\(850\) | − | 5.33494e6i | − | 0.253269i | ||||||
\(851\) | − | 5.23877e6i | − | 0.247974i | ||||||
\(852\) | −318255. | − | 555903.i | −0.0150202 | − | 0.0262361i | ||||
\(853\) | − | 1.95954e7i | − | 0.922110i | −0.887372 | − | 0.461055i | \(-0.847471\pi\) | ||
0.887372 | − | 0.461055i | \(-0.152529\pi\) | |||||||
\(854\) | −2.47459e7 | − | 1.00310e7i | −1.16107 | − | 0.470652i | ||||
\(855\) | 1.09062e6 | + | 640315.i | 0.0510222 | + | 0.0299556i | ||||
\(856\) | −4.54861e6 | −0.212175 | ||||||||
\(857\) | 384054. | 0.0178624 | 0.00893120 | − | 0.999960i | \(-0.497157\pi\) | ||||
0.00893120 | + | 0.999960i | \(0.497157\pi\) | |||||||
\(858\) | 1.40755e7 | + | 2.45860e7i | 0.652749 | + | 1.14017i | ||||
\(859\) | − | 4.78621e6i | − | 0.221314i | −0.993859 | − | 0.110657i | \(-0.964705\pi\) | ||
0.993859 | − | 0.110657i | \(-0.0352955\pi\) | |||||||
\(860\) | −222274. | −0.0102481 | ||||||||
\(861\) | 3.30247e7 | − | 4.48009e6i | 1.51821 | − | 0.205958i | ||||
\(862\) | 4.74749e6 | 0.217618 | ||||||||
\(863\) | 3.11656e7i | 1.42445i | 0.701950 | + | 0.712227i | \(0.252313\pi\) | ||||
−0.701950 | + | 0.712227i | \(0.747687\pi\) | |||||||
\(864\) | −1.29181e6 | − | 14124.9i | −0.0588728 | − | 0.000643726i | ||||
\(865\) | 1.20636e7 | 0.548197 | ||||||||
\(866\) | 1.43420e7 | 0.649854 | ||||||||
\(867\) | 6.54132e6 | − | 3.74491e6i | 0.295541 | − | 0.169197i | ||||
\(868\) | −113153. | + | 279143.i | −0.00509763 | + | 0.0125756i | ||||
\(869\) | − | 1.13596e7i | − | 0.510287i | ||||||
\(870\) | −2.08381e6 | + | 1.19299e6i | −0.0933385 | + | 0.0534364i | ||||
\(871\) | 3.95197e7i | 1.76509i | ||||||||
\(872\) | 2.80770e7i | 1.25043i | ||||||||
\(873\) | 2.35524e7 | + | 1.38279e7i | 1.04592 | + | 0.614072i | ||||
\(874\) | − | 792102.i | − | 0.0350754i | ||||||
\(875\) | −2.28442e7 | − | 9.26012e6i | −1.00868 | − | 0.408881i | ||||
\(876\) | −231546. | − | 404447.i | −0.0101948 | − | 0.0178074i | ||||
\(877\) | −4.19059e7 | −1.83982 | −0.919912 | − | 0.392125i | \(-0.871740\pi\) | ||||
−0.919912 | + | 0.392125i | \(0.871740\pi\) | |||||||
\(878\) | 4.08964e7 | 1.79040 | ||||||||
\(879\) | 2.59092e7 | − | 1.48330e7i | 1.13105 | − | 0.647527i | ||||
\(880\) | 1.31092e7i | 0.570648i | ||||||||
\(881\) | 2.28985e7 | 0.993955 | 0.496977 | − | 0.867764i | \(-0.334443\pi\) | ||||
0.496977 | + | 0.867764i | \(0.334443\pi\) | |||||||
\(882\) | 6.06372e6 | + | 2.19379e7i | 0.262463 | + | 0.949561i | ||||
\(883\) | −5.01973e6 | −0.216660 | −0.108330 | − | 0.994115i | \(-0.534550\pi\) | ||||
−0.108330 | + | 0.994115i | \(0.534550\pi\) | |||||||
\(884\) | 1.04089e6i | 0.0447994i | ||||||||
\(885\) | −2.49983e7 | + | 1.43116e7i | −1.07288 | + | 0.614227i | ||||
\(886\) | −4.96739e6 | −0.212590 | ||||||||
\(887\) | −1.26497e6 | −0.0539846 | −0.0269923 | − | 0.999636i | \(-0.508593\pi\) | ||||
−0.0269923 | + | 0.999636i | \(0.508593\pi\) | |||||||
\(888\) | −5.90205e6 | − | 1.03092e7i | −0.251171 | − | 0.438727i | ||||
\(889\) | 3.58402e6 | + | 1.45282e6i | 0.152095 | + | 0.0616534i | ||||
\(890\) | − | 1.63804e7i | − | 0.693184i | ||||||
\(891\) | 1.47303e7 | − | 8.22060e6i | 0.621610 | − | 0.346904i | ||||
\(892\) | 318112.i | 0.0133865i | ||||||||
\(893\) | 1.99589e6i | 0.0837545i | ||||||||
\(894\) | 3.61029e7 | − | 2.06689e7i | 1.51077 | − | 0.864916i | ||||
\(895\) | 2.61539e7i | 1.09139i | ||||||||
\(896\) | −8.60848e6 | + | 2.12366e7i | −0.358226 | + | 0.883722i | ||||
\(897\) | −1.94901e7 | + | 1.11581e7i | −0.808786 | + | 0.463031i | ||||
\(898\) | 2.64650e7 | 1.09517 | ||||||||
\(899\) | 1.47460e6 | 0.0608521 | ||||||||
\(900\) | −114696. | + | 195357.i | −0.00472000 | + | 0.00803937i | ||||
\(901\) | 2.91123e7i | 1.19472i | ||||||||
\(902\) | −2.62548e7 | −1.07447 | ||||||||
\(903\) | 1.02212e7 | − | 1.38660e6i | 0.417143 | − | 0.0565890i | ||||
\(904\) | 3.04198e7 | 1.23804 | ||||||||
\(905\) | − | 2.84441e7i | − | 1.15444i | ||||||
\(906\) | 2.23053e6 | + | 3.89612e6i | 0.0902792 | + | 0.157693i | ||||
\(907\) | −1.39026e7 | −0.561148 | −0.280574 | − | 0.959832i | \(-0.590525\pi\) | ||||
−0.280574 | + | 0.959832i | \(0.590525\pi\) | |||||||
\(908\) | 673123. | 0.0270944 | ||||||||
\(909\) | 2.31932e6 | − | 3.95041e6i | 0.0931005 | − | 0.158574i | ||||
\(910\) | −3.53223e7 | − | 1.43182e7i | −1.41399 | − | 0.573173i | ||||
\(911\) | 3.48951e7i | 1.39306i | 0.717530 | + | 0.696528i | \(0.245273\pi\) | ||||
−0.717530 | + | 0.696528i | \(0.754727\pi\) | |||||||
\(912\) | −866087. | − | 1.51281e6i | −0.0344806 | − | 0.0602280i | ||||
\(913\) | − | 6.56014e6i | − | 0.260457i | ||||||
\(914\) | − | 1.75355e7i | − | 0.694308i | ||||||
\(915\) | −1.32282e7 | − | 2.31059e7i | −0.522332 | − | 0.912368i | ||||
\(916\) | 184649.i | 0.00727125i | ||||||||
\(917\) | −9.08714e6 | − | 3.68356e6i | −0.356865 | − | 0.144659i | ||||
\(918\) | −2.04259e7 | − | 223341.i | −0.799973 | − | 0.00874705i | ||||
\(919\) | 2.31882e7 | 0.905686 | 0.452843 | − | 0.891590i | \(-0.350410\pi\) | ||||
0.452843 | + | 0.891590i | \(0.350410\pi\) | |||||||
\(920\) | −1.07076e7 | −0.417085 | ||||||||
\(921\) | 1.01811e6 | + | 1.77836e6i | 0.0395500 | + | 0.0690828i | ||||
\(922\) | − | 1.66363e7i | − | 0.644509i | ||||||
\(923\) | −4.97779e7 | −1.92324 | ||||||||
\(924\) | 73133.2 | + | 539097.i | 0.00281796 | + | 0.0207724i | ||||
\(925\) | −4.10653e6 | −0.157805 | ||||||||
\(926\) | − | 1.32771e7i | − | 0.508834i | ||||||
\(927\) | 7.12921e6 | + | 4.18563e6i | 0.272485 | + | 0.159979i | ||||
\(928\) | −203975. | −0.00777512 | ||||||||
\(929\) | 1.35101e7 | 0.513595 | 0.256797 | − | 0.966465i | \(-0.417333\pi\) | ||||
0.256797 | + | 0.966465i | \(0.417333\pi\) | |||||||
\(930\) | 8.59036e6 | − | 4.91799e6i | 0.325690 | − | 0.186458i | ||||
\(931\) | 1.31796e6 | − | 1.35854e6i | 0.0498341 | − | 0.0513686i | ||||
\(932\) | − | 946780.i | − | 0.0357034i | ||||||
\(933\) | −6.04751e6 | + | 3.46221e6i | −0.227443 | + | 0.130211i | ||||
\(934\) | − | 2.99236e7i | − | 1.12240i | ||||||
\(935\) | − | 1.27749e7i | − | 0.477892i | ||||||
\(936\) | −2.57832e7 | + | 4.39155e7i | −0.961940 | + | 1.63843i | ||||
\(937\) | − | 1.67971e7i | − | 0.625008i | −0.949916 | − | 0.312504i | \(-0.898832\pi\) | ||
0.949916 | − | 0.312504i | \(-0.101168\pi\) | |||||||
\(938\) | 9.39643e6 | − | 2.31805e7i | 0.348703 | − | 0.860231i | ||||
\(939\) | −1.63946e6 | − | 2.86367e6i | −0.0606786 | − | 0.105989i | ||||
\(940\) | 771789. | 0.0284891 | ||||||||
\(941\) | −1.19282e7 | −0.439136 | −0.219568 | − | 0.975597i | \(-0.570465\pi\) | ||||
−0.219568 | + | 0.975597i | \(0.570465\pi\) | |||||||
\(942\) | −1.62690e7 | + | 9.31404e6i | −0.597358 | + | 0.341988i | ||||
\(943\) | − | 2.08131e7i | − | 0.762178i | ||||||
\(944\) | 3.97034e7 | 1.45010 | ||||||||
\(945\) | −8.75513e6 | + | 2.09379e7i | −0.318921 | + | 0.762700i | ||||
\(946\) | −8.12596e6 | −0.295221 | ||||||||
\(947\) | 1.48015e7i | 0.536329i | 0.963373 | + | 0.268164i | \(0.0864170\pi\) | ||||
−0.963373 | + | 0.268164i | \(0.913583\pi\) | |||||||
\(948\) | 506917. | − | 290210.i | 0.0183196 | − | 0.0104880i | ||||
\(949\) | −3.62159e7 | −1.30537 | ||||||||
\(950\) | −620907. | −0.0223212 | ||||||||
\(951\) | −7.12548e6 | − | 1.24462e7i | −0.255483 | − | 0.446258i | ||||
\(952\) | 8.65174e6 | − | 2.13433e7i | 0.309393 | − | 0.763256i | ||||
\(953\) | − | 1.39997e7i | − | 0.499327i | −0.968333 | − | 0.249664i | \(-0.919680\pi\) | ||
0.968333 | − | 0.249664i | \(-0.0803201\pi\) | |||||||
\(954\) | −2.06281e7 | + | 3.51350e7i | −0.733819 | + | 1.24988i | ||||
\(955\) | − | 2.72034e7i | − | 0.965195i | ||||||
\(956\) | 171161.i | 0.00605703i | ||||||||
\(957\) | 2.31143e6 | − | 1.32329e6i | 0.0815831 | − | 0.0467064i | ||||
\(958\) | − | 7.42624e6i | − | 0.261430i | ||||||
\(959\) | −1.45032e6 | + | 3.57785e6i | −0.0509233 | + | 0.125625i | ||||
\(960\) | −2.10535e7 | + | 1.20532e7i | −0.737303 | + | 0.422107i | ||||
\(961\) | 2.25502e7 | 0.787666 | ||||||||
\(962\) | −2.64067e7 | −0.919975 | ||||||||
\(963\) | 5.19199e6 | + | 3.04827e6i | 0.180413 | + | 0.105922i | ||||
\(964\) | − | 183071.i | − | 0.00634492i | ||||||
\(965\) | −4.73937e6 | −0.163833 | ||||||||
\(966\) | 1.40851e7 | − | 1.91076e6i | 0.485641 | − | 0.0658815i | ||||
\(967\) | 4.96805e7 | 1.70852 | 0.854260 | − | 0.519846i | \(-0.174011\pi\) | ||||
0.854260 | + | 0.519846i | \(0.174011\pi\) | |||||||
\(968\) | 1.45840e7i | 0.500252i | ||||||||
\(969\) | 844006. | + | 1.47424e6i | 0.0288759 | + | 0.0504382i | ||||
\(970\) | 2.89465e7 | 0.987793 | ||||||||
\(971\) | −4.52830e7 | −1.54130 | −0.770649 | − | 0.637260i | \(-0.780068\pi\) | ||||
−0.770649 | + | 0.637260i | \(0.780068\pi\) | |||||||
\(972\) | 743163. | + | 447316.i | 0.0252301 | + | 0.0151862i | ||||
\(973\) | −5.82980e6 | + | 1.43818e7i | −0.197411 | + | 0.487002i | ||||
\(974\) | 2.15438e7i | 0.727656i | ||||||||
\(975\) | 8.74654e6 | + | 1.52778e7i | 0.294663 | + | 0.514693i | ||||
\(976\) | 3.66978e7i | 1.23315i | ||||||||
\(977\) | − | 349146.i | − | 0.0117023i | −0.999983 | − | 0.00585114i | \(-0.998138\pi\) | ||
0.999983 | − | 0.00585114i | \(-0.00186249\pi\) | |||||||
\(978\) | 1.88700e6 | + | 3.29606e6i | 0.0630848 | + | 0.110192i | ||||
\(979\) | 1.81696e7i | 0.605882i | ||||||||
\(980\) | −525332. | − | 509639.i | −0.0174730 | − | 0.0169511i | ||||
\(981\) | 1.88159e7 | − | 3.20484e7i | 0.624243 | − | 1.06325i | ||||
\(982\) | 3.13104e7 | 1.03612 | ||||||||
\(983\) | 4.78815e7 | 1.58046 | 0.790231 | − | 0.612809i | \(-0.209961\pi\) | ||||
0.790231 | + | 0.612809i | \(0.209961\pi\) | |||||||
\(984\) | −2.34482e7 | − | 4.09574e7i | −0.772007 | − | 1.34848i | ||||
\(985\) | 3.06182e7i | 1.00552i | ||||||||
\(986\) | −3.22523e6 | −0.105650 | ||||||||
\(987\) | −3.54907e7 | + | 4.81462e6i | −1.15963 | + | 0.157315i | ||||
\(988\) | 121143. | 0.00394828 | ||||||||
\(989\) | − | 6.44171e6i | − | 0.209416i | ||||||
\(990\) | 9.05195e6 | − | 1.54178e7i | 0.293531 | − | 0.499959i | ||||
\(991\) | −2.48785e7 | −0.804711 | −0.402356 | − | 0.915483i | \(-0.631808\pi\) | ||||
−0.402356 | + | 0.915483i | \(0.631808\pi\) | |||||||
\(992\) | 840871. | 0.0271300 | ||||||||
\(993\) | −3.51421e7 | + | 2.01189e7i | −1.13098 | + | 0.647487i | ||||
\(994\) | 2.91975e7 | + | 1.18355e7i | 0.937302 | + | 0.379945i | ||||
\(995\) | 3.22391e7i | 1.03235i | ||||||||
\(996\) | 292743. | − | 167595.i | 0.00935056 | − | 0.00535320i | ||||
\(997\) | − | 2.95568e7i | − | 0.941714i | −0.882209 | − | 0.470857i | \(-0.843945\pi\) | ||
0.882209 | − | 0.470857i | \(-0.156055\pi\) | |||||||
\(998\) | − | 5.91525e7i | − | 1.87995i | ||||||
\(999\) | −171915. | + | 1.57227e7i | −0.00545004 | + | 0.498441i |
(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 | 21.6.c.a.20.9 | yes | 12 | |
3.2 | odd | 2 | inner | 21.6.c.a.20.4 | yes | 12 | |
4.3 | odd | 2 | 336.6.k.d.209.11 | 12 | |||
7.6 | odd | 2 | inner | 21.6.c.a.20.10 | yes | 12 | |
12.11 | even | 2 | 336.6.k.d.209.1 | 12 | |||
21.20 | even | 2 | inner | 21.6.c.a.20.3 | ✓ | 12 | |
28.27 | even | 2 | 336.6.k.d.209.2 | 12 | |||
84.83 | odd | 2 | 336.6.k.d.209.12 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.6.c.a.20.3 | ✓ | 12 | 21.20 | even | 2 | inner | |
21.6.c.a.20.4 | yes | 12 | 3.2 | odd | 2 | inner | |
21.6.c.a.20.9 | yes | 12 | 1.1 | even | 1 | trivial | |
21.6.c.a.20.10 | yes | 12 | 7.6 | odd | 2 | inner | |
336.6.k.d.209.1 | 12 | 12.11 | even | 2 | |||
336.6.k.d.209.2 | 12 | 28.27 | even | 2 | |||
336.6.k.d.209.11 | 12 | 4.3 | odd | 2 | |||
336.6.k.d.209.12 | 12 | 84.83 | odd | 2 |