Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [70,6,Mod(1,70)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(70, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("70.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 70 = 2 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 70.a (trivial) |
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: | yes |
Analytic conductor: | \(11.2268673869\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 70.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | −0.707107 | ||||||||
\(3\) | −23.0000 | −1.47545 | −0.737725 | − | 0.675101i | \(-0.764100\pi\) | ||||
−0.737725 | + | 0.675101i | \(0.764100\pi\) | |||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 92.0000 | 1.04330 | ||||||||
\(7\) | 49.0000 | 0.377964 | ||||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 286.000 | 1.17695 | ||||||||
\(10\) | −100.000 | −0.316228 | ||||||||
\(11\) | 555.000 | 1.38297 | 0.691483 | − | 0.722393i | \(-0.256958\pi\) | ||||
0.691483 | + | 0.722393i | \(0.256958\pi\) | |||||||
\(12\) | −368.000 | −0.737725 | ||||||||
\(13\) | −241.000 | −0.395511 | −0.197756 | − | 0.980251i | \(-0.563365\pi\) | ||||
−0.197756 | + | 0.980251i | \(0.563365\pi\) | |||||||
\(14\) | −196.000 | −0.267261 | ||||||||
\(15\) | −575.000 | −0.659842 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −1491.00 | −1.25128 | −0.625641 | − | 0.780111i | \(-0.715163\pi\) | ||||
−0.625641 | + | 0.780111i | \(0.715163\pi\) | |||||||
\(18\) | −1144.00 | −0.832233 | ||||||||
\(19\) | −2038.00 | −1.29515 | −0.647575 | − | 0.762002i | \(-0.724217\pi\) | ||||
−0.647575 | + | 0.762002i | \(0.724217\pi\) | |||||||
\(20\) | 400.000 | 0.223607 | ||||||||
\(21\) | −1127.00 | −0.557668 | ||||||||
\(22\) | −2220.00 | −0.977904 | ||||||||
\(23\) | −1230.00 | −0.484826 | −0.242413 | − | 0.970173i | \(-0.577939\pi\) | ||||
−0.242413 | + | 0.970173i | \(0.577939\pi\) | |||||||
\(24\) | 1472.00 | 0.521651 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 964.000 | 0.279669 | ||||||||
\(27\) | −989.000 | −0.261088 | ||||||||
\(28\) | 784.000 | 0.188982 | ||||||||
\(29\) | −5001.00 | −1.10424 | −0.552118 | − | 0.833766i | \(-0.686180\pi\) | ||||
−0.552118 | + | 0.833766i | \(0.686180\pi\) | |||||||
\(30\) | 2300.00 | 0.466578 | ||||||||
\(31\) | 5696.00 | 1.06455 | 0.532275 | − | 0.846572i | \(-0.321337\pi\) | ||||
0.532275 | + | 0.846572i | \(0.321337\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | −12765.0 | −2.04050 | ||||||||
\(34\) | 5964.00 | 0.884790 | ||||||||
\(35\) | 1225.00 | 0.169031 | ||||||||
\(36\) | 4576.00 | 0.588477 | ||||||||
\(37\) | −5602.00 | −0.672727 | −0.336363 | − | 0.941732i | \(-0.609197\pi\) | ||||
−0.336363 | + | 0.941732i | \(0.609197\pi\) | |||||||
\(38\) | 8152.00 | 0.915810 | ||||||||
\(39\) | 5543.00 | 0.583557 | ||||||||
\(40\) | −1600.00 | −0.158114 | ||||||||
\(41\) | −2424.00 | −0.225202 | −0.112601 | − | 0.993640i | \(-0.535918\pi\) | ||||
−0.112601 | + | 0.993640i | \(0.535918\pi\) | |||||||
\(42\) | 4508.00 | 0.394331 | ||||||||
\(43\) | 602.000 | 0.0496507 | 0.0248253 | − | 0.999692i | \(-0.492097\pi\) | ||||
0.0248253 | + | 0.999692i | \(0.492097\pi\) | |||||||
\(44\) | 8880.00 | 0.691483 | ||||||||
\(45\) | 7150.00 | 0.526350 | ||||||||
\(46\) | 4920.00 | 0.342823 | ||||||||
\(47\) | −23163.0 | −1.52950 | −0.764751 | − | 0.644326i | \(-0.777138\pi\) | ||||
−0.764751 | + | 0.644326i | \(0.777138\pi\) | |||||||
\(48\) | −5888.00 | −0.368863 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | −2500.00 | −0.141421 | ||||||||
\(51\) | 34293.0 | 1.84621 | ||||||||
\(52\) | −3856.00 | −0.197756 | ||||||||
\(53\) | −25296.0 | −1.23698 | −0.618489 | − | 0.785793i | \(-0.712255\pi\) | ||||
−0.618489 | + | 0.785793i | \(0.712255\pi\) | |||||||
\(54\) | 3956.00 | 0.184617 | ||||||||
\(55\) | 13875.0 | 0.618481 | ||||||||
\(56\) | −3136.00 | −0.133631 | ||||||||
\(57\) | 46874.0 | 1.91093 | ||||||||
\(58\) | 20004.0 | 0.780813 | ||||||||
\(59\) | 5724.00 | 0.214077 | 0.107038 | − | 0.994255i | \(-0.465863\pi\) | ||||
0.107038 | + | 0.994255i | \(0.465863\pi\) | |||||||
\(60\) | −9200.00 | −0.329921 | ||||||||
\(61\) | −36112.0 | −1.24259 | −0.621294 | − | 0.783578i | \(-0.713393\pi\) | ||||
−0.621294 | + | 0.783578i | \(0.713393\pi\) | |||||||
\(62\) | −22784.0 | −0.752750 | ||||||||
\(63\) | 14014.0 | 0.444847 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | −6025.00 | −0.176878 | ||||||||
\(66\) | 51060.0 | 1.44285 | ||||||||
\(67\) | 66104.0 | 1.79904 | 0.899520 | − | 0.436880i | \(-0.143917\pi\) | ||||
0.899520 | + | 0.436880i | \(0.143917\pi\) | |||||||
\(68\) | −23856.0 | −0.625641 | ||||||||
\(69\) | 28290.0 | 0.715336 | ||||||||
\(70\) | −4900.00 | −0.119523 | ||||||||
\(71\) | 16080.0 | 0.378565 | 0.189282 | − | 0.981923i | \(-0.439384\pi\) | ||||
0.189282 | + | 0.981923i | \(0.439384\pi\) | |||||||
\(72\) | −18304.0 | −0.416116 | ||||||||
\(73\) | −80482.0 | −1.76763 | −0.883816 | − | 0.467836i | \(-0.845034\pi\) | ||||
−0.883816 | + | 0.467836i | \(0.845034\pi\) | |||||||
\(74\) | 22408.0 | 0.475690 | ||||||||
\(75\) | −14375.0 | −0.295090 | ||||||||
\(76\) | −32608.0 | −0.647575 | ||||||||
\(77\) | 27195.0 | 0.522712 | ||||||||
\(78\) | −22172.0 | −0.412637 | ||||||||
\(79\) | −64147.0 | −1.15640 | −0.578201 | − | 0.815895i | \(-0.696245\pi\) | ||||
−0.578201 | + | 0.815895i | \(0.696245\pi\) | |||||||
\(80\) | 6400.00 | 0.111803 | ||||||||
\(81\) | −46751.0 | −0.791732 | ||||||||
\(82\) | 9696.00 | 0.159242 | ||||||||
\(83\) | −106284. | −1.69345 | −0.846726 | − | 0.532030i | \(-0.821429\pi\) | ||||
−0.846726 | + | 0.532030i | \(0.821429\pi\) | |||||||
\(84\) | −18032.0 | −0.278834 | ||||||||
\(85\) | −37275.0 | −0.559591 | ||||||||
\(86\) | −2408.00 | −0.0351083 | ||||||||
\(87\) | 115023. | 1.62925 | ||||||||
\(88\) | −35520.0 | −0.488952 | ||||||||
\(89\) | −71676.0 | −0.959177 | −0.479588 | − | 0.877494i | \(-0.659214\pi\) | ||||
−0.479588 | + | 0.877494i | \(0.659214\pi\) | |||||||
\(90\) | −28600.0 | −0.372186 | ||||||||
\(91\) | −11809.0 | −0.149489 | ||||||||
\(92\) | −19680.0 | −0.242413 | ||||||||
\(93\) | −131008. | −1.57069 | ||||||||
\(94\) | 92652.0 | 1.08152 | ||||||||
\(95\) | −50950.0 | −0.579209 | ||||||||
\(96\) | 23552.0 | 0.260825 | ||||||||
\(97\) | 151025. | 1.62974 | 0.814872 | − | 0.579641i | \(-0.196807\pi\) | ||||
0.814872 | + | 0.579641i | \(0.196807\pi\) | |||||||
\(98\) | −9604.00 | −0.101015 | ||||||||
\(99\) | 158730. | 1.62769 | ||||||||
\(100\) | 10000.0 | 0.100000 | ||||||||
\(101\) | −57150.0 | −0.557459 | −0.278729 | − | 0.960370i | \(-0.589913\pi\) | ||||
−0.278729 | + | 0.960370i | \(0.589913\pi\) | |||||||
\(102\) | −137172. | −1.30546 | ||||||||
\(103\) | 115889. | 1.07634 | 0.538170 | − | 0.842837i | \(-0.319116\pi\) | ||||
0.538170 | + | 0.842837i | \(0.319116\pi\) | |||||||
\(104\) | 15424.0 | 0.139834 | ||||||||
\(105\) | −28175.0 | −0.249397 | ||||||||
\(106\) | 101184. | 0.874676 | ||||||||
\(107\) | −137862. | −1.16409 | −0.582043 | − | 0.813158i | \(-0.697747\pi\) | ||||
−0.582043 | + | 0.813158i | \(0.697747\pi\) | |||||||
\(108\) | −15824.0 | −0.130544 | ||||||||
\(109\) | 88397.0 | 0.712642 | 0.356321 | − | 0.934364i | \(-0.384031\pi\) | ||||
0.356321 | + | 0.934364i | \(0.384031\pi\) | |||||||
\(110\) | −55500.0 | −0.437332 | ||||||||
\(111\) | 128846. | 0.992575 | ||||||||
\(112\) | 12544.0 | 0.0944911 | ||||||||
\(113\) | 205554. | 1.51436 | 0.757181 | − | 0.653205i | \(-0.226576\pi\) | ||||
0.757181 | + | 0.653205i | \(0.226576\pi\) | |||||||
\(114\) | −187496. | −1.35123 | ||||||||
\(115\) | −30750.0 | −0.216821 | ||||||||
\(116\) | −80016.0 | −0.552118 | ||||||||
\(117\) | −68926.0 | −0.465499 | ||||||||
\(118\) | −22896.0 | −0.151375 | ||||||||
\(119\) | −73059.0 | −0.472940 | ||||||||
\(120\) | 36800.0 | 0.233289 | ||||||||
\(121\) | 146974. | 0.912593 | ||||||||
\(122\) | 144448. | 0.878642 | ||||||||
\(123\) | 55752.0 | 0.332275 | ||||||||
\(124\) | 91136.0 | 0.532275 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | −56056.0 | −0.314554 | ||||||||
\(127\) | 250916. | 1.38044 | 0.690222 | − | 0.723597i | \(-0.257513\pi\) | ||||
0.690222 | + | 0.723597i | \(0.257513\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | −13846.0 | −0.0732572 | ||||||||
\(130\) | 24100.0 | 0.125072 | ||||||||
\(131\) | −52122.0 | −0.265365 | −0.132682 | − | 0.991159i | \(-0.542359\pi\) | ||||
−0.132682 | + | 0.991159i | \(0.542359\pi\) | |||||||
\(132\) | −204240. | −1.02025 | ||||||||
\(133\) | −99862.0 | −0.489521 | ||||||||
\(134\) | −264416. | −1.27211 | ||||||||
\(135\) | −24725.0 | −0.116762 | ||||||||
\(136\) | 95424.0 | 0.442395 | ||||||||
\(137\) | −135468. | −0.616645 | −0.308323 | − | 0.951282i | \(-0.599768\pi\) | ||||
−0.308323 | + | 0.951282i | \(0.599768\pi\) | |||||||
\(138\) | −113160. | −0.505819 | ||||||||
\(139\) | −349486. | −1.53424 | −0.767119 | − | 0.641505i | \(-0.778310\pi\) | ||||
−0.767119 | + | 0.641505i | \(0.778310\pi\) | |||||||
\(140\) | 19600.0 | 0.0845154 | ||||||||
\(141\) | 532749. | 2.25671 | ||||||||
\(142\) | −64320.0 | −0.267686 | ||||||||
\(143\) | −133755. | −0.546978 | ||||||||
\(144\) | 73216.0 | 0.294239 | ||||||||
\(145\) | −125025. | −0.493829 | ||||||||
\(146\) | 321928. | 1.24990 | ||||||||
\(147\) | −55223.0 | −0.210779 | ||||||||
\(148\) | −89632.0 | −0.336363 | ||||||||
\(149\) | 176082. | 0.649754 | 0.324877 | − | 0.945756i | \(-0.394677\pi\) | ||||
0.324877 | + | 0.945756i | \(0.394677\pi\) | |||||||
\(150\) | 57500.0 | 0.208660 | ||||||||
\(151\) | 383333. | 1.36815 | 0.684075 | − | 0.729411i | \(-0.260206\pi\) | ||||
0.684075 | + | 0.729411i | \(0.260206\pi\) | |||||||
\(152\) | 130432. | 0.457905 | ||||||||
\(153\) | −426426. | −1.47270 | ||||||||
\(154\) | −108780. | −0.369613 | ||||||||
\(155\) | 142400. | 0.476081 | ||||||||
\(156\) | 88688.0 | 0.291779 | ||||||||
\(157\) | 345914. | 1.12000 | 0.560001 | − | 0.828492i | \(-0.310801\pi\) | ||||
0.560001 | + | 0.828492i | \(0.310801\pi\) | |||||||
\(158\) | 256588. | 0.817699 | ||||||||
\(159\) | 581808. | 1.82510 | ||||||||
\(160\) | −25600.0 | −0.0790569 | ||||||||
\(161\) | −60270.0 | −0.183247 | ||||||||
\(162\) | 187004. | 0.559839 | ||||||||
\(163\) | 91586.0 | 0.269998 | 0.134999 | − | 0.990846i | \(-0.456897\pi\) | ||||
0.134999 | + | 0.990846i | \(0.456897\pi\) | |||||||
\(164\) | −38784.0 | −0.112601 | ||||||||
\(165\) | −319125. | −0.912538 | ||||||||
\(166\) | 425136. | 1.19745 | ||||||||
\(167\) | 38097.0 | 0.105706 | 0.0528530 | − | 0.998602i | \(-0.483169\pi\) | ||||
0.0528530 | + | 0.998602i | \(0.483169\pi\) | |||||||
\(168\) | 72128.0 | 0.197165 | ||||||||
\(169\) | −313212. | −0.843571 | ||||||||
\(170\) | 149100. | 0.395690 | ||||||||
\(171\) | −582868. | −1.52433 | ||||||||
\(172\) | 9632.00 | 0.0248253 | ||||||||
\(173\) | −541443. | −1.37543 | −0.687713 | − | 0.725982i | \(-0.741385\pi\) | ||||
−0.687713 | + | 0.725982i | \(0.741385\pi\) | |||||||
\(174\) | −460092. | −1.15205 | ||||||||
\(175\) | 30625.0 | 0.0755929 | ||||||||
\(176\) | 142080. | 0.345741 | ||||||||
\(177\) | −131652. | −0.315860 | ||||||||
\(178\) | 286704. | 0.678241 | ||||||||
\(179\) | 166188. | 0.387674 | 0.193837 | − | 0.981034i | \(-0.437907\pi\) | ||||
0.193837 | + | 0.981034i | \(0.437907\pi\) | |||||||
\(180\) | 114400. | 0.263175 | ||||||||
\(181\) | −197320. | −0.447687 | −0.223844 | − | 0.974625i | \(-0.571860\pi\) | ||||
−0.223844 | + | 0.974625i | \(0.571860\pi\) | |||||||
\(182\) | 47236.0 | 0.105705 | ||||||||
\(183\) | 830576. | 1.83338 | ||||||||
\(184\) | 78720.0 | 0.171412 | ||||||||
\(185\) | −140050. | −0.300853 | ||||||||
\(186\) | 524032. | 1.11065 | ||||||||
\(187\) | −827505. | −1.73048 | ||||||||
\(188\) | −370608. | −0.764751 | ||||||||
\(189\) | −48461.0 | −0.0986820 | ||||||||
\(190\) | 203800. | 0.409562 | ||||||||
\(191\) | −337221. | −0.668854 | −0.334427 | − | 0.942422i | \(-0.608543\pi\) | ||||
−0.334427 | + | 0.942422i | \(0.608543\pi\) | |||||||
\(192\) | −94208.0 | −0.184431 | ||||||||
\(193\) | 260516. | 0.503432 | 0.251716 | − | 0.967801i | \(-0.419005\pi\) | ||||
0.251716 | + | 0.967801i | \(0.419005\pi\) | |||||||
\(194\) | −604100. | −1.15240 | ||||||||
\(195\) | 138575. | 0.260975 | ||||||||
\(196\) | 38416.0 | 0.0714286 | ||||||||
\(197\) | −409212. | −0.751247 | −0.375624 | − | 0.926772i | \(-0.622571\pi\) | ||||
−0.375624 | + | 0.926772i | \(0.622571\pi\) | |||||||
\(198\) | −634920. | −1.15095 | ||||||||
\(199\) | 300980. | 0.538772 | 0.269386 | − | 0.963032i | \(-0.413179\pi\) | ||||
0.269386 | + | 0.963032i | \(0.413179\pi\) | |||||||
\(200\) | −40000.0 | −0.0707107 | ||||||||
\(201\) | −1.52039e6 | −2.65439 | ||||||||
\(202\) | 228600. | 0.394183 | ||||||||
\(203\) | −245049. | −0.417362 | ||||||||
\(204\) | 548688. | 0.923103 | ||||||||
\(205\) | −60600.0 | −0.100714 | ||||||||
\(206\) | −463556. | −0.761087 | ||||||||
\(207\) | −351780. | −0.570618 | ||||||||
\(208\) | −61696.0 | −0.0988778 | ||||||||
\(209\) | −1.13109e6 | −1.79115 | ||||||||
\(210\) | 112700. | 0.176350 | ||||||||
\(211\) | −1.22618e6 | −1.89604 | −0.948021 | − | 0.318209i | \(-0.896919\pi\) | ||||
−0.948021 | + | 0.318209i | \(0.896919\pi\) | |||||||
\(212\) | −404736. | −0.618489 | ||||||||
\(213\) | −369840. | −0.558554 | ||||||||
\(214\) | 551448. | 0.823133 | ||||||||
\(215\) | 15050.0 | 0.0222045 | ||||||||
\(216\) | 63296.0 | 0.0923085 | ||||||||
\(217\) | 279104. | 0.402362 | ||||||||
\(218\) | −353588. | −0.503914 | ||||||||
\(219\) | 1.85109e6 | 2.60805 | ||||||||
\(220\) | 222000. | 0.309240 | ||||||||
\(221\) | 359331. | 0.494896 | ||||||||
\(222\) | −515384. | −0.701857 | ||||||||
\(223\) | 621257. | 0.836583 | 0.418292 | − | 0.908313i | \(-0.362629\pi\) | ||||
0.418292 | + | 0.908313i | \(0.362629\pi\) | |||||||
\(224\) | −50176.0 | −0.0668153 | ||||||||
\(225\) | 178750. | 0.235391 | ||||||||
\(226\) | −822216. | −1.07082 | ||||||||
\(227\) | 1.29768e6 | 1.67148 | 0.835742 | − | 0.549123i | \(-0.185038\pi\) | ||||
0.835742 | + | 0.549123i | \(0.185038\pi\) | |||||||
\(228\) | 749984. | 0.955465 | ||||||||
\(229\) | −124264. | −0.156587 | −0.0782937 | − | 0.996930i | \(-0.524947\pi\) | ||||
−0.0782937 | + | 0.996930i | \(0.524947\pi\) | |||||||
\(230\) | 123000. | 0.153315 | ||||||||
\(231\) | −625485. | −0.771235 | ||||||||
\(232\) | 320064. | 0.390406 | ||||||||
\(233\) | 1.08742e6 | 1.31222 | 0.656109 | − | 0.754666i | \(-0.272201\pi\) | ||||
0.656109 | + | 0.754666i | \(0.272201\pi\) | |||||||
\(234\) | 275704. | 0.329157 | ||||||||
\(235\) | −579075. | −0.684014 | ||||||||
\(236\) | 91584.0 | 0.107038 | ||||||||
\(237\) | 1.47538e6 | 1.70621 | ||||||||
\(238\) | 292236. | 0.334419 | ||||||||
\(239\) | −545631. | −0.617880 | −0.308940 | − | 0.951081i | \(-0.599974\pi\) | ||||
−0.308940 | + | 0.951081i | \(0.599974\pi\) | |||||||
\(240\) | −147200. | −0.164960 | ||||||||
\(241\) | 811310. | 0.899796 | 0.449898 | − | 0.893080i | \(-0.351460\pi\) | ||||
0.449898 | + | 0.893080i | \(0.351460\pi\) | |||||||
\(242\) | −587896. | −0.645301 | ||||||||
\(243\) | 1.31560e6 | 1.42925 | ||||||||
\(244\) | −577792. | −0.621294 | ||||||||
\(245\) | 60025.0 | 0.0638877 | ||||||||
\(246\) | −223008. | −0.234954 | ||||||||
\(247\) | 491158. | 0.512246 | ||||||||
\(248\) | −364544. | −0.376375 | ||||||||
\(249\) | 2.44453e6 | 2.49860 | ||||||||
\(250\) | −62500.0 | −0.0632456 | ||||||||
\(251\) | −897738. | −0.899426 | −0.449713 | − | 0.893173i | \(-0.648474\pi\) | ||||
−0.449713 | + | 0.893173i | \(0.648474\pi\) | |||||||
\(252\) | 224224. | 0.222424 | ||||||||
\(253\) | −682650. | −0.670497 | ||||||||
\(254\) | −1.00366e6 | −0.976122 | ||||||||
\(255\) | 857325. | 0.825648 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −594678. | −0.561628 | −0.280814 | − | 0.959762i | \(-0.590604\pi\) | ||||
−0.280814 | + | 0.959762i | \(0.590604\pi\) | |||||||
\(258\) | 55384.0 | 0.0518006 | ||||||||
\(259\) | −274498. | −0.254267 | ||||||||
\(260\) | −96400.0 | −0.0884390 | ||||||||
\(261\) | −1.43029e6 | −1.29964 | ||||||||
\(262\) | 208488. | 0.187641 | ||||||||
\(263\) | 1.02837e6 | 0.916769 | 0.458385 | − | 0.888754i | \(-0.348428\pi\) | ||||
0.458385 | + | 0.888754i | \(0.348428\pi\) | |||||||
\(264\) | 816960. | 0.721425 | ||||||||
\(265\) | −632400. | −0.553194 | ||||||||
\(266\) | 399448. | 0.346143 | ||||||||
\(267\) | 1.64855e6 | 1.41522 | ||||||||
\(268\) | 1.05766e6 | 0.899520 | ||||||||
\(269\) | −1.24390e6 | −1.04811 | −0.524053 | − | 0.851685i | \(-0.675581\pi\) | ||||
−0.524053 | + | 0.851685i | \(0.675581\pi\) | |||||||
\(270\) | 98900.0 | 0.0825633 | ||||||||
\(271\) | 737624. | 0.610115 | 0.305058 | − | 0.952334i | \(-0.401324\pi\) | ||||
0.305058 | + | 0.952334i | \(0.401324\pi\) | |||||||
\(272\) | −381696. | −0.312821 | ||||||||
\(273\) | 271607. | 0.220564 | ||||||||
\(274\) | 541872. | 0.436034 | ||||||||
\(275\) | 346875. | 0.276593 | ||||||||
\(276\) | 452640. | 0.357668 | ||||||||
\(277\) | −2.20063e6 | −1.72325 | −0.861624 | − | 0.507548i | \(-0.830552\pi\) | ||||
−0.861624 | + | 0.507548i | \(0.830552\pi\) | |||||||
\(278\) | 1.39794e6 | 1.08487 | ||||||||
\(279\) | 1.62906e6 | 1.25293 | ||||||||
\(280\) | −78400.0 | −0.0597614 | ||||||||
\(281\) | 173979. | 0.131441 | 0.0657205 | − | 0.997838i | \(-0.479065\pi\) | ||||
0.0657205 | + | 0.997838i | \(0.479065\pi\) | |||||||
\(282\) | −2.13100e6 | −1.59573 | ||||||||
\(283\) | −551053. | −0.409004 | −0.204502 | − | 0.978866i | \(-0.565557\pi\) | ||||
−0.204502 | + | 0.978866i | \(0.565557\pi\) | |||||||
\(284\) | 257280. | 0.189282 | ||||||||
\(285\) | 1.17185e6 | 0.854594 | ||||||||
\(286\) | 535020. | 0.386772 | ||||||||
\(287\) | −118776. | −0.0851185 | ||||||||
\(288\) | −292864. | −0.208058 | ||||||||
\(289\) | 803224. | 0.565708 | ||||||||
\(290\) | 500100. | 0.349190 | ||||||||
\(291\) | −3.47358e6 | −2.40461 | ||||||||
\(292\) | −1.28771e6 | −0.883816 | ||||||||
\(293\) | −1.67512e6 | −1.13993 | −0.569963 | − | 0.821670i | \(-0.693042\pi\) | ||||
−0.569963 | + | 0.821670i | \(0.693042\pi\) | |||||||
\(294\) | 220892. | 0.149043 | ||||||||
\(295\) | 143100. | 0.0957381 | ||||||||
\(296\) | 358528. | 0.237845 | ||||||||
\(297\) | −548895. | −0.361076 | ||||||||
\(298\) | −704328. | −0.459446 | ||||||||
\(299\) | 296430. | 0.191754 | ||||||||
\(300\) | −230000. | −0.147545 | ||||||||
\(301\) | 29498.0 | 0.0187662 | ||||||||
\(302\) | −1.53333e6 | −0.967428 | ||||||||
\(303\) | 1.31445e6 | 0.822503 | ||||||||
\(304\) | −521728. | −0.323788 | ||||||||
\(305\) | −902800. | −0.555702 | ||||||||
\(306\) | 1.70570e6 | 1.04136 | ||||||||
\(307\) | 2.33060e6 | 1.41131 | 0.705655 | − | 0.708556i | \(-0.250653\pi\) | ||||
0.705655 | + | 0.708556i | \(0.250653\pi\) | |||||||
\(308\) | 435120. | 0.261356 | ||||||||
\(309\) | −2.66545e6 | −1.58809 | ||||||||
\(310\) | −569600. | −0.336640 | ||||||||
\(311\) | 706266. | 0.414064 | 0.207032 | − | 0.978334i | \(-0.433620\pi\) | ||||
0.207032 | + | 0.978334i | \(0.433620\pi\) | |||||||
\(312\) | −354752. | −0.206319 | ||||||||
\(313\) | −183565. | −0.105908 | −0.0529540 | − | 0.998597i | \(-0.516864\pi\) | ||||
−0.0529540 | + | 0.998597i | \(0.516864\pi\) | |||||||
\(314\) | −1.38366e6 | −0.791961 | ||||||||
\(315\) | 350350. | 0.198942 | ||||||||
\(316\) | −1.02635e6 | −0.578201 | ||||||||
\(317\) | 2.70665e6 | 1.51281 | 0.756405 | − | 0.654103i | \(-0.226954\pi\) | ||||
0.756405 | + | 0.654103i | \(0.226954\pi\) | |||||||
\(318\) | −2.32723e6 | −1.29054 | ||||||||
\(319\) | −2.77556e6 | −1.52712 | ||||||||
\(320\) | 102400. | 0.0559017 | ||||||||
\(321\) | 3.17083e6 | 1.71755 | ||||||||
\(322\) | 241080. | 0.129575 | ||||||||
\(323\) | 3.03866e6 | 1.62060 | ||||||||
\(324\) | −748016. | −0.395866 | ||||||||
\(325\) | −150625. | −0.0791022 | ||||||||
\(326\) | −366344. | −0.190917 | ||||||||
\(327\) | −2.03313e6 | −1.05147 | ||||||||
\(328\) | 155136. | 0.0796211 | ||||||||
\(329\) | −1.13499e6 | −0.578098 | ||||||||
\(330\) | 1.27650e6 | 0.645262 | ||||||||
\(331\) | −2.14337e6 | −1.07529 | −0.537647 | − | 0.843170i | \(-0.680687\pi\) | ||||
−0.537647 | + | 0.843170i | \(0.680687\pi\) | |||||||
\(332\) | −1.70054e6 | −0.846726 | ||||||||
\(333\) | −1.60217e6 | −0.791769 | ||||||||
\(334\) | −152388. | −0.0747454 | ||||||||
\(335\) | 1.65260e6 | 0.804555 | ||||||||
\(336\) | −288512. | −0.139417 | ||||||||
\(337\) | 655346. | 0.314337 | 0.157169 | − | 0.987572i | \(-0.449763\pi\) | ||||
0.157169 | + | 0.987572i | \(0.449763\pi\) | |||||||
\(338\) | 1.25285e6 | 0.596495 | ||||||||
\(339\) | −4.72774e6 | −2.23437 | ||||||||
\(340\) | −596400. | −0.279795 | ||||||||
\(341\) | 3.16128e6 | 1.47223 | ||||||||
\(342\) | 2.33147e6 | 1.07787 | ||||||||
\(343\) | 117649. | 0.0539949 | ||||||||
\(344\) | −38528.0 | −0.0175542 | ||||||||
\(345\) | 707250. | 0.319908 | ||||||||
\(346\) | 2.16577e6 | 0.972574 | ||||||||
\(347\) | −4.22275e6 | −1.88266 | −0.941329 | − | 0.337491i | \(-0.890422\pi\) | ||||
−0.941329 | + | 0.337491i | \(0.890422\pi\) | |||||||
\(348\) | 1.84037e6 | 0.814623 | ||||||||
\(349\) | 3.01710e6 | 1.32595 | 0.662974 | − | 0.748643i | \(-0.269294\pi\) | ||||
0.662974 | + | 0.748643i | \(0.269294\pi\) | |||||||
\(350\) | −122500. | −0.0534522 | ||||||||
\(351\) | 238349. | 0.103263 | ||||||||
\(352\) | −568320. | −0.244476 | ||||||||
\(353\) | 2.25258e6 | 0.962150 | 0.481075 | − | 0.876679i | \(-0.340246\pi\) | ||||
0.481075 | + | 0.876679i | \(0.340246\pi\) | |||||||
\(354\) | 526608. | 0.223347 | ||||||||
\(355\) | 402000. | 0.169299 | ||||||||
\(356\) | −1.14682e6 | −0.479588 | ||||||||
\(357\) | 1.68036e6 | 0.697800 | ||||||||
\(358\) | −664752. | −0.274127 | ||||||||
\(359\) | −1.83950e6 | −0.753294 | −0.376647 | − | 0.926357i | \(-0.622923\pi\) | ||||
−0.376647 | + | 0.926357i | \(0.622923\pi\) | |||||||
\(360\) | −457600. | −0.186093 | ||||||||
\(361\) | 1.67735e6 | 0.677414 | ||||||||
\(362\) | 789280. | 0.316563 | ||||||||
\(363\) | −3.38040e6 | −1.34649 | ||||||||
\(364\) | −188944. | −0.0747446 | ||||||||
\(365\) | −2.01205e6 | −0.790509 | ||||||||
\(366\) | −3.32230e6 | −1.29639 | ||||||||
\(367\) | −1.68832e6 | −0.654320 | −0.327160 | − | 0.944969i | \(-0.606092\pi\) | ||||
−0.327160 | + | 0.944969i | \(0.606092\pi\) | |||||||
\(368\) | −314880. | −0.121206 | ||||||||
\(369\) | −693264. | −0.265053 | ||||||||
\(370\) | 560200. | 0.212735 | ||||||||
\(371\) | −1.23950e6 | −0.467534 | ||||||||
\(372\) | −2.09613e6 | −0.785345 | ||||||||
\(373\) | 1.81212e6 | 0.674394 | 0.337197 | − | 0.941434i | \(-0.390521\pi\) | ||||
0.337197 | + | 0.941434i | \(0.390521\pi\) | |||||||
\(374\) | 3.31002e6 | 1.22363 | ||||||||
\(375\) | −359375. | −0.131968 | ||||||||
\(376\) | 1.48243e6 | 0.540761 | ||||||||
\(377\) | 1.20524e6 | 0.436738 | ||||||||
\(378\) | 193844. | 0.0697787 | ||||||||
\(379\) | −4.76708e6 | −1.70472 | −0.852362 | − | 0.522952i | \(-0.824831\pi\) | ||||
−0.852362 | + | 0.522952i | \(0.824831\pi\) | |||||||
\(380\) | −815200. | −0.289604 | ||||||||
\(381\) | −5.77107e6 | −2.03678 | ||||||||
\(382\) | 1.34888e6 | 0.472951 | ||||||||
\(383\) | −69996.0 | −0.0243824 | −0.0121912 | − | 0.999926i | \(-0.503881\pi\) | ||||
−0.0121912 | + | 0.999926i | \(0.503881\pi\) | |||||||
\(384\) | 376832. | 0.130413 | ||||||||
\(385\) | 679875. | 0.233764 | ||||||||
\(386\) | −1.04206e6 | −0.355980 | ||||||||
\(387\) | 172172. | 0.0584366 | ||||||||
\(388\) | 2.41640e6 | 0.814872 | ||||||||
\(389\) | 3.98895e6 | 1.33655 | 0.668275 | − | 0.743915i | \(-0.267033\pi\) | ||||
0.668275 | + | 0.743915i | \(0.267033\pi\) | |||||||
\(390\) | −554300. | −0.184537 | ||||||||
\(391\) | 1.83393e6 | 0.606654 | ||||||||
\(392\) | −153664. | −0.0505076 | ||||||||
\(393\) | 1.19881e6 | 0.391532 | ||||||||
\(394\) | 1.63685e6 | 0.531212 | ||||||||
\(395\) | −1.60367e6 | −0.517158 | ||||||||
\(396\) | 2.53968e6 | 0.813844 | ||||||||
\(397\) | −3.05904e6 | −0.974110 | −0.487055 | − | 0.873371i | \(-0.661929\pi\) | ||||
−0.487055 | + | 0.873371i | \(0.661929\pi\) | |||||||
\(398\) | −1.20392e6 | −0.380969 | ||||||||
\(399\) | 2.29683e6 | 0.722264 | ||||||||
\(400\) | 160000. | 0.0500000 | ||||||||
\(401\) | 4.30794e6 | 1.33785 | 0.668927 | − | 0.743329i | \(-0.266754\pi\) | ||||
0.668927 | + | 0.743329i | \(0.266754\pi\) | |||||||
\(402\) | 6.08157e6 | 1.87694 | ||||||||
\(403\) | −1.37274e6 | −0.421041 | ||||||||
\(404\) | −914400. | −0.278729 | ||||||||
\(405\) | −1.16878e6 | −0.354073 | ||||||||
\(406\) | 980196. | 0.295119 | ||||||||
\(407\) | −3.10911e6 | −0.930358 | ||||||||
\(408\) | −2.19475e6 | −0.652732 | ||||||||
\(409\) | −239206. | −0.0707072 | −0.0353536 | − | 0.999375i | \(-0.511256\pi\) | ||||
−0.0353536 | + | 0.999375i | \(0.511256\pi\) | |||||||
\(410\) | 242400. | 0.0712152 | ||||||||
\(411\) | 3.11576e6 | 0.909829 | ||||||||
\(412\) | 1.85422e6 | 0.538170 | ||||||||
\(413\) | 280476. | 0.0809134 | ||||||||
\(414\) | 1.40712e6 | 0.403488 | ||||||||
\(415\) | −2.65710e6 | −0.757334 | ||||||||
\(416\) | 246784. | 0.0699171 | ||||||||
\(417\) | 8.03818e6 | 2.26369 | ||||||||
\(418\) | 4.52436e6 | 1.26653 | ||||||||
\(419\) | 4.63462e6 | 1.28967 | 0.644835 | − | 0.764322i | \(-0.276926\pi\) | ||||
0.644835 | + | 0.764322i | \(0.276926\pi\) | |||||||
\(420\) | −450800. | −0.124698 | ||||||||
\(421\) | −2.10108e6 | −0.577745 | −0.288873 | − | 0.957368i | \(-0.593280\pi\) | ||||
−0.288873 | + | 0.957368i | \(0.593280\pi\) | |||||||
\(422\) | 4.90472e6 | 1.34070 | ||||||||
\(423\) | −6.62462e6 | −1.80016 | ||||||||
\(424\) | 1.61894e6 | 0.437338 | ||||||||
\(425\) | −931875. | −0.250256 | ||||||||
\(426\) | 1.47936e6 | 0.394957 | ||||||||
\(427\) | −1.76949e6 | −0.469654 | ||||||||
\(428\) | −2.20579e6 | −0.582043 | ||||||||
\(429\) | 3.07636e6 | 0.807039 | ||||||||
\(430\) | −60200.0 | −0.0157009 | ||||||||
\(431\) | 1.65484e6 | 0.429104 | 0.214552 | − | 0.976713i | \(-0.431171\pi\) | ||||
0.214552 | + | 0.976713i | \(0.431171\pi\) | |||||||
\(432\) | −253184. | −0.0652720 | ||||||||
\(433\) | −1.84031e6 | −0.471705 | −0.235852 | − | 0.971789i | \(-0.575788\pi\) | ||||
−0.235852 | + | 0.971789i | \(0.575788\pi\) | |||||||
\(434\) | −1.11642e6 | −0.284513 | ||||||||
\(435\) | 2.87558e6 | 0.728621 | ||||||||
\(436\) | 1.41435e6 | 0.356321 | ||||||||
\(437\) | 2.50674e6 | 0.627922 | ||||||||
\(438\) | −7.40434e6 | −1.84417 | ||||||||
\(439\) | 5.83684e6 | 1.44549 | 0.722747 | − | 0.691113i | \(-0.242879\pi\) | ||||
0.722747 | + | 0.691113i | \(0.242879\pi\) | |||||||
\(440\) | −888000. | −0.218666 | ||||||||
\(441\) | 686686. | 0.168136 | ||||||||
\(442\) | −1.43732e6 | −0.349944 | ||||||||
\(443\) | 1.19704e6 | 0.289801 | 0.144901 | − | 0.989446i | \(-0.453714\pi\) | ||||
0.144901 | + | 0.989446i | \(0.453714\pi\) | |||||||
\(444\) | 2.06154e6 | 0.496288 | ||||||||
\(445\) | −1.79190e6 | −0.428957 | ||||||||
\(446\) | −2.48503e6 | −0.591554 | ||||||||
\(447\) | −4.04989e6 | −0.958681 | ||||||||
\(448\) | 200704. | 0.0472456 | ||||||||
\(449\) | −3.42570e6 | −0.801924 | −0.400962 | − | 0.916095i | \(-0.631324\pi\) | ||||
−0.400962 | + | 0.916095i | \(0.631324\pi\) | |||||||
\(450\) | −715000. | −0.166447 | ||||||||
\(451\) | −1.34532e6 | −0.311447 | ||||||||
\(452\) | 3.28886e6 | 0.757181 | ||||||||
\(453\) | −8.81666e6 | −2.01864 | ||||||||
\(454\) | −5.19071e6 | −1.18192 | ||||||||
\(455\) | −295225. | −0.0668536 | ||||||||
\(456\) | −2.99994e6 | −0.675616 | ||||||||
\(457\) | 5.29742e6 | 1.18652 | 0.593258 | − | 0.805012i | \(-0.297841\pi\) | ||||
0.593258 | + | 0.805012i | \(0.297841\pi\) | |||||||
\(458\) | 497056. | 0.110724 | ||||||||
\(459\) | 1.47460e6 | 0.326695 | ||||||||
\(460\) | −492000. | −0.108410 | ||||||||
\(461\) | 8.87731e6 | 1.94549 | 0.972745 | − | 0.231876i | \(-0.0744863\pi\) | ||||
0.972745 | + | 0.231876i | \(0.0744863\pi\) | |||||||
\(462\) | 2.50194e6 | 0.545346 | ||||||||
\(463\) | −2.17475e6 | −0.471473 | −0.235737 | − | 0.971817i | \(-0.575750\pi\) | ||||
−0.235737 | + | 0.971817i | \(0.575750\pi\) | |||||||
\(464\) | −1.28026e6 | −0.276059 | ||||||||
\(465\) | −3.27520e6 | −0.702434 | ||||||||
\(466\) | −4.34966e6 | −0.927878 | ||||||||
\(467\) | −378969. | −0.0804103 | −0.0402051 | − | 0.999191i | \(-0.512801\pi\) | ||||
−0.0402051 | + | 0.999191i | \(0.512801\pi\) | |||||||
\(468\) | −1.10282e6 | −0.232749 | ||||||||
\(469\) | 3.23910e6 | 0.679973 | ||||||||
\(470\) | 2.31630e6 | 0.483671 | ||||||||
\(471\) | −7.95602e6 | −1.65251 | ||||||||
\(472\) | −366336. | −0.0756876 | ||||||||
\(473\) | 334110. | 0.0686652 | ||||||||
\(474\) | −5.90152e6 | −1.20647 | ||||||||
\(475\) | −1.27375e6 | −0.259030 | ||||||||
\(476\) | −1.16894e6 | −0.236470 | ||||||||
\(477\) | −7.23466e6 | −1.45587 | ||||||||
\(478\) | 2.18252e6 | 0.436907 | ||||||||
\(479\) | 1.88489e6 | 0.375360 | 0.187680 | − | 0.982230i | \(-0.439903\pi\) | ||||
0.187680 | + | 0.982230i | \(0.439903\pi\) | |||||||
\(480\) | 588800. | 0.116645 | ||||||||
\(481\) | 1.35008e6 | 0.266071 | ||||||||
\(482\) | −3.24524e6 | −0.636252 | ||||||||
\(483\) | 1.38621e6 | 0.270372 | ||||||||
\(484\) | 2.35158e6 | 0.456296 | ||||||||
\(485\) | 3.77562e6 | 0.728844 | ||||||||
\(486\) | −5.26240e6 | −1.01063 | ||||||||
\(487\) | 3.67689e6 | 0.702518 | 0.351259 | − | 0.936278i | \(-0.385754\pi\) | ||||
0.351259 | + | 0.936278i | \(0.385754\pi\) | |||||||
\(488\) | 2.31117e6 | 0.439321 | ||||||||
\(489\) | −2.10648e6 | −0.398368 | ||||||||
\(490\) | −240100. | −0.0451754 | ||||||||
\(491\) | 9.54015e6 | 1.78588 | 0.892939 | − | 0.450178i | \(-0.148640\pi\) | ||||
0.892939 | + | 0.450178i | \(0.148640\pi\) | |||||||
\(492\) | 892032. | 0.166138 | ||||||||
\(493\) | 7.45649e6 | 1.38171 | ||||||||
\(494\) | −1.96463e6 | −0.362213 | ||||||||
\(495\) | 3.96825e6 | 0.727924 | ||||||||
\(496\) | 1.45818e6 | 0.266137 | ||||||||
\(497\) | 787920. | 0.143084 | ||||||||
\(498\) | −9.77813e6 | −1.76678 | ||||||||
\(499\) | 4.78243e6 | 0.859800 | 0.429900 | − | 0.902877i | \(-0.358549\pi\) | ||||
0.429900 | + | 0.902877i | \(0.358549\pi\) | |||||||
\(500\) | 250000. | 0.0447214 | ||||||||
\(501\) | −876231. | −0.155964 | ||||||||
\(502\) | 3.59095e6 | 0.635990 | ||||||||
\(503\) | −1.08395e7 | −1.91024 | −0.955120 | − | 0.296220i | \(-0.904274\pi\) | ||||
−0.955120 | + | 0.296220i | \(0.904274\pi\) | |||||||
\(504\) | −896896. | −0.157277 | ||||||||
\(505\) | −1.42875e6 | −0.249303 | ||||||||
\(506\) | 2.73060e6 | 0.474113 | ||||||||
\(507\) | 7.20388e6 | 1.24465 | ||||||||
\(508\) | 4.01466e6 | 0.690222 | ||||||||
\(509\) | −7.64177e6 | −1.30737 | −0.653687 | − | 0.756765i | \(-0.726779\pi\) | ||||
−0.653687 | + | 0.756765i | \(0.726779\pi\) | |||||||
\(510\) | −3.42930e6 | −0.583821 | ||||||||
\(511\) | −3.94362e6 | −0.668102 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | 2.01558e6 | 0.338148 | ||||||||
\(514\) | 2.37871e6 | 0.397131 | ||||||||
\(515\) | 2.89723e6 | 0.481354 | ||||||||
\(516\) | −221536. | −0.0366286 | ||||||||
\(517\) | −1.28555e7 | −2.11525 | ||||||||
\(518\) | 1.09799e6 | 0.179794 | ||||||||
\(519\) | 1.24532e7 | 2.02937 | ||||||||
\(520\) | 385600. | 0.0625358 | ||||||||
\(521\) | 6.44011e6 | 1.03944 | 0.519719 | − | 0.854337i | \(-0.326037\pi\) | ||||
0.519719 | + | 0.854337i | \(0.326037\pi\) | |||||||
\(522\) | 5.72114e6 | 0.918981 | ||||||||
\(523\) | −4.77929e6 | −0.764028 | −0.382014 | − | 0.924157i | \(-0.624769\pi\) | ||||
−0.382014 | + | 0.924157i | \(0.624769\pi\) | |||||||
\(524\) | −833952. | −0.132682 | ||||||||
\(525\) | −704375. | −0.111534 | ||||||||
\(526\) | −4.11348e6 | −0.648254 | ||||||||
\(527\) | −8.49274e6 | −1.33205 | ||||||||
\(528\) | −3.26784e6 | −0.510124 | ||||||||
\(529\) | −4.92344e6 | −0.764944 | ||||||||
\(530\) | 2.52960e6 | 0.391167 | ||||||||
\(531\) | 1.63706e6 | 0.251959 | ||||||||
\(532\) | −1.59779e6 | −0.244760 | ||||||||
\(533\) | 584184. | 0.0890700 | ||||||||
\(534\) | −6.59419e6 | −1.00071 | ||||||||
\(535\) | −3.44655e6 | −0.520595 | ||||||||
\(536\) | −4.23066e6 | −0.636057 | ||||||||
\(537\) | −3.82232e6 | −0.571994 | ||||||||
\(538\) | 4.97561e6 | 0.741123 | ||||||||
\(539\) | 1.33256e6 | 0.197566 | ||||||||
\(540\) | −395600. | −0.0583810 | ||||||||
\(541\) | −2.05678e6 | −0.302130 | −0.151065 | − | 0.988524i | \(-0.548270\pi\) | ||||
−0.151065 | + | 0.988524i | \(0.548270\pi\) | |||||||
\(542\) | −2.95050e6 | −0.431417 | ||||||||
\(543\) | 4.53836e6 | 0.660540 | ||||||||
\(544\) | 1.52678e6 | 0.221198 | ||||||||
\(545\) | 2.20992e6 | 0.318703 | ||||||||
\(546\) | −1.08643e6 | −0.155962 | ||||||||
\(547\) | −1.20189e7 | −1.71750 | −0.858751 | − | 0.512393i | \(-0.828759\pi\) | ||||
−0.858751 | + | 0.512393i | \(0.828759\pi\) | |||||||
\(548\) | −2.16749e6 | −0.308323 | ||||||||
\(549\) | −1.03280e7 | −1.46247 | ||||||||
\(550\) | −1.38750e6 | −0.195581 | ||||||||
\(551\) | 1.01920e7 | 1.43015 | ||||||||
\(552\) | −1.81056e6 | −0.252910 | ||||||||
\(553\) | −3.14320e6 | −0.437079 | ||||||||
\(554\) | 8.80252e6 | 1.21852 | ||||||||
\(555\) | 3.22115e6 | 0.443893 | ||||||||
\(556\) | −5.59178e6 | −0.767119 | ||||||||
\(557\) | 8.69942e6 | 1.18810 | 0.594049 | − | 0.804429i | \(-0.297528\pi\) | ||||
0.594049 | + | 0.804429i | \(0.297528\pi\) | |||||||
\(558\) | −6.51622e6 | −0.885953 | ||||||||
\(559\) | −145082. | −0.0196374 | ||||||||
\(560\) | 313600. | 0.0422577 | ||||||||
\(561\) | 1.90326e7 | 2.55324 | ||||||||
\(562\) | −695916. | −0.0929429 | ||||||||
\(563\) | −7.35942e6 | −0.978527 | −0.489263 | − | 0.872136i | \(-0.662734\pi\) | ||||
−0.489263 | + | 0.872136i | \(0.662734\pi\) | |||||||
\(564\) | 8.52398e6 | 1.12835 | ||||||||
\(565\) | 5.13885e6 | 0.677243 | ||||||||
\(566\) | 2.20421e6 | 0.289209 | ||||||||
\(567\) | −2.29080e6 | −0.299247 | ||||||||
\(568\) | −1.02912e6 | −0.133843 | ||||||||
\(569\) | −7.50029e6 | −0.971175 | −0.485588 | − | 0.874188i | \(-0.661394\pi\) | ||||
−0.485588 | + | 0.874188i | \(0.661394\pi\) | |||||||
\(570\) | −4.68740e6 | −0.604289 | ||||||||
\(571\) | −2.22879e6 | −0.286074 | −0.143037 | − | 0.989717i | \(-0.545687\pi\) | ||||
−0.143037 | + | 0.989717i | \(0.545687\pi\) | |||||||
\(572\) | −2.14008e6 | −0.273489 | ||||||||
\(573\) | 7.75608e6 | 0.986861 | ||||||||
\(574\) | 475104. | 0.0601879 | ||||||||
\(575\) | −768750. | −0.0969651 | ||||||||
\(576\) | 1.17146e6 | 0.147119 | ||||||||
\(577\) | −5.10946e6 | −0.638903 | −0.319452 | − | 0.947603i | \(-0.603499\pi\) | ||||
−0.319452 | + | 0.947603i | \(0.603499\pi\) | |||||||
\(578\) | −3.21290e6 | −0.400016 | ||||||||
\(579\) | −5.99187e6 | −0.742790 | ||||||||
\(580\) | −2.00040e6 | −0.246915 | ||||||||
\(581\) | −5.20792e6 | −0.640064 | ||||||||
\(582\) | 1.38943e7 | 1.70031 | ||||||||
\(583\) | −1.40393e7 | −1.71070 | ||||||||
\(584\) | 5.15085e6 | 0.624952 | ||||||||
\(585\) | −1.72315e6 | −0.208177 | ||||||||
\(586\) | 6.70048e6 | 0.806049 | ||||||||
\(587\) | 1.10646e7 | 1.32537 | 0.662687 | − | 0.748896i | \(-0.269416\pi\) | ||||
0.662687 | + | 0.748896i | \(0.269416\pi\) | |||||||
\(588\) | −883568. | −0.105389 | ||||||||
\(589\) | −1.16084e7 | −1.37875 | ||||||||
\(590\) | −572400. | −0.0676970 | ||||||||
\(591\) | 9.41188e6 | 1.10843 | ||||||||
\(592\) | −1.43411e6 | −0.168182 | ||||||||
\(593\) | 9.10043e6 | 1.06274 | 0.531368 | − | 0.847141i | \(-0.321678\pi\) | ||||
0.531368 | + | 0.847141i | \(0.321678\pi\) | |||||||
\(594\) | 2.19558e6 | 0.255319 | ||||||||
\(595\) | −1.82648e6 | −0.211505 | ||||||||
\(596\) | 2.81731e6 | 0.324877 | ||||||||
\(597\) | −6.92254e6 | −0.794931 | ||||||||
\(598\) | −1.18572e6 | −0.135590 | ||||||||
\(599\) | −1.28615e7 | −1.46462 | −0.732309 | − | 0.680973i | \(-0.761557\pi\) | ||||
−0.732309 | + | 0.680973i | \(0.761557\pi\) | |||||||
\(600\) | 920000. | 0.104330 | ||||||||
\(601\) | 1.58163e6 | 0.178615 | 0.0893074 | − | 0.996004i | \(-0.471535\pi\) | ||||
0.0893074 | + | 0.996004i | \(0.471535\pi\) | |||||||
\(602\) | −117992. | −0.0132697 | ||||||||
\(603\) | 1.89057e7 | 2.11739 | ||||||||
\(604\) | 6.13333e6 | 0.684075 | ||||||||
\(605\) | 3.67435e6 | 0.408124 | ||||||||
\(606\) | −5.25780e6 | −0.581597 | ||||||||
\(607\) | −688297. | −0.0758236 | −0.0379118 | − | 0.999281i | \(-0.512071\pi\) | ||||
−0.0379118 | + | 0.999281i | \(0.512071\pi\) | |||||||
\(608\) | 2.08691e6 | 0.228952 | ||||||||
\(609\) | 5.63613e6 | 0.615797 | ||||||||
\(610\) | 3.61120e6 | 0.392941 | ||||||||
\(611\) | 5.58228e6 | 0.604935 | ||||||||
\(612\) | −6.82282e6 | −0.736351 | ||||||||
\(613\) | −6.02150e6 | −0.647223 | −0.323611 | − | 0.946190i | \(-0.604897\pi\) | ||||
−0.323611 | + | 0.946190i | \(0.604897\pi\) | |||||||
\(614\) | −9.32241e6 | −0.997947 | ||||||||
\(615\) | 1.39380e6 | 0.148598 | ||||||||
\(616\) | −1.74048e6 | −0.184807 | ||||||||
\(617\) | 3.36137e6 | 0.355471 | 0.177735 | − | 0.984078i | \(-0.443123\pi\) | ||||
0.177735 | + | 0.984078i | \(0.443123\pi\) | |||||||
\(618\) | 1.06618e7 | 1.12295 | ||||||||
\(619\) | 1.31769e7 | 1.38225 | 0.691126 | − | 0.722734i | \(-0.257115\pi\) | ||||
0.691126 | + | 0.722734i | \(0.257115\pi\) | |||||||
\(620\) | 2.27840e6 | 0.238040 | ||||||||
\(621\) | 1.21647e6 | 0.126582 | ||||||||
\(622\) | −2.82506e6 | −0.292787 | ||||||||
\(623\) | −3.51212e6 | −0.362535 | ||||||||
\(624\) | 1.41901e6 | 0.145889 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 734260. | 0.0748883 | ||||||||
\(627\) | 2.60151e7 | 2.64275 | ||||||||
\(628\) | 5.53462e6 | 0.560001 | ||||||||
\(629\) | 8.35258e6 | 0.841771 | ||||||||
\(630\) | −1.40140e6 | −0.140673 | ||||||||
\(631\) | 1.26264e6 | 0.126243 | 0.0631213 | − | 0.998006i | \(-0.479895\pi\) | ||||
0.0631213 | + | 0.998006i | \(0.479895\pi\) | |||||||
\(632\) | 4.10541e6 | 0.408850 | ||||||||
\(633\) | 2.82021e7 | 2.79752 | ||||||||
\(634\) | −1.08266e7 | −1.06972 | ||||||||
\(635\) | 6.27290e6 | 0.617354 | ||||||||
\(636\) | 9.30893e6 | 0.912550 | ||||||||
\(637\) | −578641. | −0.0565016 | ||||||||
\(638\) | 1.11022e7 | 1.07984 | ||||||||
\(639\) | 4.59888e6 | 0.445554 | ||||||||
\(640\) | −409600. | −0.0395285 | ||||||||
\(641\) | −1.58859e7 | −1.52710 | −0.763550 | − | 0.645749i | \(-0.776545\pi\) | ||||
−0.763550 | + | 0.645749i | \(0.776545\pi\) | |||||||
\(642\) | −1.26833e7 | −1.21449 | ||||||||
\(643\) | 1.80880e6 | 0.172529 | 0.0862647 | − | 0.996272i | \(-0.472507\pi\) | ||||
0.0862647 | + | 0.996272i | \(0.472507\pi\) | |||||||
\(644\) | −964320. | −0.0916234 | ||||||||
\(645\) | −346150. | −0.0327616 | ||||||||
\(646\) | −1.21546e7 | −1.14594 | ||||||||
\(647\) | 95712.0 | 0.00898888 | 0.00449444 | − | 0.999990i | \(-0.498569\pi\) | ||||
0.00449444 | + | 0.999990i | \(0.498569\pi\) | |||||||
\(648\) | 2.99206e6 | 0.279920 | ||||||||
\(649\) | 3.17682e6 | 0.296061 | ||||||||
\(650\) | 602500. | 0.0559337 | ||||||||
\(651\) | −6.41939e6 | −0.593665 | ||||||||
\(652\) | 1.46538e6 | 0.134999 | ||||||||
\(653\) | 3.06736e6 | 0.281502 | 0.140751 | − | 0.990045i | \(-0.455048\pi\) | ||||
0.140751 | + | 0.990045i | \(0.455048\pi\) | |||||||
\(654\) | 8.13252e6 | 0.743500 | ||||||||
\(655\) | −1.30305e6 | −0.118675 | ||||||||
\(656\) | −620544. | −0.0563006 | ||||||||
\(657\) | −2.30179e7 | −2.08042 | ||||||||
\(658\) | 4.53995e6 | 0.408777 | ||||||||
\(659\) | −1.32961e6 | −0.119264 | −0.0596321 | − | 0.998220i | \(-0.518993\pi\) | ||||
−0.0596321 | + | 0.998220i | \(0.518993\pi\) | |||||||
\(660\) | −5.10600e6 | −0.456269 | ||||||||
\(661\) | −7.37188e6 | −0.656258 | −0.328129 | − | 0.944633i | \(-0.606418\pi\) | ||||
−0.328129 | + | 0.944633i | \(0.606418\pi\) | |||||||
\(662\) | 8.57349e6 | 0.760348 | ||||||||
\(663\) | −8.26461e6 | −0.730195 | ||||||||
\(664\) | 6.80218e6 | 0.598725 | ||||||||
\(665\) | −2.49655e6 | −0.218920 | ||||||||
\(666\) | 6.40869e6 | 0.559865 | ||||||||
\(667\) | 6.15123e6 | 0.535362 | ||||||||
\(668\) | 609552. | 0.0528530 | ||||||||
\(669\) | −1.42889e7 | −1.23434 | ||||||||
\(670\) | −6.61040e6 | −0.568906 | ||||||||
\(671\) | −2.00422e7 | −1.71846 | ||||||||
\(672\) | 1.15405e6 | 0.0985827 | ||||||||
\(673\) | 8.48476e6 | 0.722108 | 0.361054 | − | 0.932545i | \(-0.382417\pi\) | ||||
0.361054 | + | 0.932545i | \(0.382417\pi\) | |||||||
\(674\) | −2.62138e6 | −0.222270 | ||||||||
\(675\) | −618125. | −0.0522176 | ||||||||
\(676\) | −5.01139e6 | −0.421785 | ||||||||
\(677\) | −4.35891e6 | −0.365516 | −0.182758 | − | 0.983158i | \(-0.558503\pi\) | ||||
−0.182758 | + | 0.983158i | \(0.558503\pi\) | |||||||
\(678\) | 1.89110e7 | 1.57994 | ||||||||
\(679\) | 7.40022e6 | 0.615985 | ||||||||
\(680\) | 2.38560e6 | 0.197845 | ||||||||
\(681\) | −2.98466e7 | −2.46619 | ||||||||
\(682\) | −1.26451e7 | −1.04103 | ||||||||
\(683\) | −1.58732e7 | −1.30200 | −0.651001 | − | 0.759077i | \(-0.725651\pi\) | ||||
−0.651001 | + | 0.759077i | \(0.725651\pi\) | |||||||
\(684\) | −9.32589e6 | −0.762167 | ||||||||
\(685\) | −3.38670e6 | −0.275772 | ||||||||
\(686\) | −470596. | −0.0381802 | ||||||||
\(687\) | 2.85807e6 | 0.231037 | ||||||||
\(688\) | 154112. | 0.0124127 | ||||||||
\(689\) | 6.09634e6 | 0.489239 | ||||||||
\(690\) | −2.82900e6 | −0.226209 | ||||||||
\(691\) | −554956. | −0.0442144 | −0.0221072 | − | 0.999756i | \(-0.507038\pi\) | ||||
−0.0221072 | + | 0.999756i | \(0.507038\pi\) | |||||||
\(692\) | −8.66309e6 | −0.687713 | ||||||||
\(693\) | 7.77777e6 | 0.615208 | ||||||||
\(694\) | 1.68910e7 | 1.33124 | ||||||||
\(695\) | −8.73715e6 | −0.686132 | ||||||||
\(696\) | −7.36147e6 | −0.576025 | ||||||||
\(697\) | 3.61418e6 | 0.281792 | ||||||||
\(698\) | −1.20684e7 | −0.937587 | ||||||||
\(699\) | −2.50106e7 | −1.93611 | ||||||||
\(700\) | 490000. | 0.0377964 | ||||||||
\(701\) | −7.74720e6 | −0.595456 | −0.297728 | − | 0.954651i | \(-0.596229\pi\) | ||||
−0.297728 | + | 0.954651i | \(0.596229\pi\) | |||||||
\(702\) | −953396. | −0.0730181 | ||||||||
\(703\) | 1.14169e7 | 0.871282 | ||||||||
\(704\) | 2.27328e6 | 0.172871 | ||||||||
\(705\) | 1.33187e7 | 1.00923 | ||||||||
\(706\) | −9.01031e6 | −0.680343 | ||||||||
\(707\) | −2.80035e6 | −0.210700 | ||||||||
\(708\) | −2.10643e6 | −0.157930 | ||||||||
\(709\) | −1.89055e7 | −1.41245 | −0.706225 | − | 0.707987i | \(-0.749603\pi\) | ||||
−0.706225 | + | 0.707987i | \(0.749603\pi\) | |||||||
\(710\) | −1.60800e6 | −0.119713 | ||||||||
\(711\) | −1.83460e7 | −1.36103 | ||||||||
\(712\) | 4.58726e6 | 0.339120 | ||||||||
\(713\) | −7.00608e6 | −0.516121 | ||||||||
\(714\) | −6.72143e6 | −0.493419 | ||||||||
\(715\) | −3.34388e6 | −0.244616 | ||||||||
\(716\) | 2.65901e6 | 0.193837 | ||||||||
\(717\) | 1.25495e7 | 0.911652 | ||||||||
\(718\) | 7.35802e6 | 0.532659 | ||||||||
\(719\) | −1.83928e7 | −1.32686 | −0.663430 | − | 0.748238i | \(-0.730900\pi\) | ||||
−0.663430 | + | 0.748238i | \(0.730900\pi\) | |||||||
\(720\) | 1.83040e6 | 0.131588 | ||||||||
\(721\) | 5.67856e6 | 0.406818 | ||||||||
\(722\) | −6.70938e6 | −0.479004 | ||||||||
\(723\) | −1.86601e7 | −1.32761 | ||||||||
\(724\) | −3.15712e6 | −0.223844 | ||||||||
\(725\) | −3.12562e6 | −0.220847 | ||||||||
\(726\) | 1.35216e7 | 0.952109 | ||||||||
\(727\) | −1.34259e7 | −0.942123 | −0.471061 | − | 0.882100i | \(-0.656129\pi\) | ||||
−0.471061 | + | 0.882100i | \(0.656129\pi\) | |||||||
\(728\) | 755776. | 0.0528524 | ||||||||
\(729\) | −1.88983e7 | −1.31706 | ||||||||
\(730\) | 8.04820e6 | 0.558974 | ||||||||
\(731\) | −897582. | −0.0621270 | ||||||||
\(732\) | 1.32892e7 | 0.916688 | ||||||||
\(733\) | 1.08473e7 | 0.745697 | 0.372848 | − | 0.927892i | \(-0.378381\pi\) | ||||
0.372848 | + | 0.927892i | \(0.378381\pi\) | |||||||
\(734\) | 6.75329e6 | 0.462674 | ||||||||
\(735\) | −1.38058e6 | −0.0942631 | ||||||||
\(736\) | 1.25952e6 | 0.0857059 | ||||||||
\(737\) | 3.66877e7 | 2.48801 | ||||||||
\(738\) | 2.77306e6 | 0.187421 | ||||||||
\(739\) | 2.64323e7 | 1.78043 | 0.890214 | − | 0.455542i | \(-0.150555\pi\) | ||||
0.890214 | + | 0.455542i | \(0.150555\pi\) | |||||||
\(740\) | −2.24080e6 | −0.150426 | ||||||||
\(741\) | −1.12966e7 | −0.755794 | ||||||||
\(742\) | 4.95802e6 | 0.330596 | ||||||||
\(743\) | 2.03120e7 | 1.34984 | 0.674918 | − | 0.737893i | \(-0.264179\pi\) | ||||
0.674918 | + | 0.737893i | \(0.264179\pi\) | |||||||
\(744\) | 8.38451e6 | 0.555323 | ||||||||
\(745\) | 4.40205e6 | 0.290579 | ||||||||
\(746\) | −7.24846e6 | −0.476869 | ||||||||
\(747\) | −3.03972e7 | −1.99312 | ||||||||
\(748\) | −1.32401e7 | −0.865240 | ||||||||
\(749\) | −6.75524e6 | −0.439983 | ||||||||
\(750\) | 1.43750e6 | 0.0933157 | ||||||||
\(751\) | −3.95388e6 | −0.255813 | −0.127907 | − | 0.991786i | \(-0.540826\pi\) | ||||
−0.127907 | + | 0.991786i | \(0.540826\pi\) | |||||||
\(752\) | −5.92973e6 | −0.382376 | ||||||||
\(753\) | 2.06480e7 | 1.32706 | ||||||||
\(754\) | −4.82096e6 | −0.308820 | ||||||||
\(755\) | 9.58332e6 | 0.611855 | ||||||||
\(756\) | −775376. | −0.0493410 | ||||||||
\(757\) | −2.62165e7 | −1.66278 | −0.831391 | − | 0.555688i | \(-0.812455\pi\) | ||||
−0.831391 | + | 0.555688i | \(0.812455\pi\) | |||||||
\(758\) | 1.90683e7 | 1.20542 | ||||||||
\(759\) | 1.57010e7 | 0.989285 | ||||||||
\(760\) | 3.26080e6 | 0.204781 | ||||||||
\(761\) | 1.14329e7 | 0.715638 | 0.357819 | − | 0.933791i | \(-0.383521\pi\) | ||||
0.357819 | + | 0.933791i | \(0.383521\pi\) | |||||||
\(762\) | 2.30843e7 | 1.44022 | ||||||||
\(763\) | 4.33145e6 | 0.269353 | ||||||||
\(764\) | −5.39554e6 | −0.334427 | ||||||||
\(765\) | −1.06606e7 | −0.658613 | ||||||||
\(766\) | 279984. | 0.0172410 | ||||||||
\(767\) | −1.37948e6 | −0.0846697 | ||||||||
\(768\) | −1.50733e6 | −0.0922157 | ||||||||
\(769\) | 2.37076e7 | 1.44568 | 0.722840 | − | 0.691015i | \(-0.242836\pi\) | ||||
0.722840 | + | 0.691015i | \(0.242836\pi\) | |||||||
\(770\) | −2.71950e6 | −0.165296 | ||||||||
\(771\) | 1.36776e7 | 0.828655 | ||||||||
\(772\) | 4.16826e6 | 0.251716 | ||||||||
\(773\) | −1.24180e7 | −0.747484 | −0.373742 | − | 0.927533i | \(-0.621925\pi\) | ||||
−0.373742 | + | 0.927533i | \(0.621925\pi\) | |||||||
\(774\) | −688688. | −0.0413209 | ||||||||
\(775\) | 3.56000e6 | 0.212910 | ||||||||
\(776\) | −9.66560e6 | −0.576202 | ||||||||
\(777\) | 6.31345e6 | 0.375158 | ||||||||
\(778\) | −1.59558e7 | −0.945083 | ||||||||
\(779\) | 4.94011e6 | 0.291671 | ||||||||
\(780\) | 2.21720e6 | 0.130487 | ||||||||
\(781\) | 8.92440e6 | 0.523542 | ||||||||
\(782\) | −7.33572e6 | −0.428969 | ||||||||
\(783\) | 4.94599e6 | 0.288303 | ||||||||
\(784\) | 614656. | 0.0357143 | ||||||||
\(785\) | 8.64785e6 | 0.500880 | ||||||||
\(786\) | −4.79522e6 | −0.276855 | ||||||||
\(787\) | 3.06553e7 | 1.76428 | 0.882142 | − | 0.470984i | \(-0.156101\pi\) | ||||
0.882142 | + | 0.470984i | \(0.156101\pi\) | |||||||
\(788\) | −6.54739e6 | −0.375624 | ||||||||
\(789\) | −2.36525e7 | −1.35265 | ||||||||
\(790\) | 6.41470e6 | 0.365686 | ||||||||
\(791\) | 1.00721e7 | 0.572375 | ||||||||
\(792\) | −1.01587e7 | −0.575474 | ||||||||
\(793\) | 8.70299e6 | 0.491457 | ||||||||
\(794\) | 1.22361e7 | 0.688800 | ||||||||
\(795\) | 1.45452e7 | 0.816210 | ||||||||
\(796\) | 4.81568e6 | 0.269386 | ||||||||
\(797\) | −1.51870e7 | −0.846886 | −0.423443 | − | 0.905923i | \(-0.639179\pi\) | ||||
−0.423443 | + | 0.905923i | \(0.639179\pi\) | |||||||
\(798\) | −9.18730e6 | −0.510718 | ||||||||
\(799\) | 3.45360e7 | 1.91384 | ||||||||
\(800\) | −640000. | −0.0353553 | ||||||||
\(801\) | −2.04993e7 | −1.12891 | ||||||||
\(802\) | −1.72317e7 | −0.946005 | ||||||||
\(803\) | −4.46675e7 | −2.44457 | ||||||||
\(804\) | −2.43263e7 | −1.32720 | ||||||||
\(805\) | −1.50675e6 | −0.0819505 | ||||||||
\(806\) | 5.49094e6 | 0.297721 | ||||||||
\(807\) | 2.86097e7 | 1.54643 | ||||||||
\(808\) | 3.65760e6 | 0.197091 | ||||||||
\(809\) | 539721. | 0.0289933 | 0.0144967 | − | 0.999895i | \(-0.495385\pi\) | ||||
0.0144967 | + | 0.999895i | \(0.495385\pi\) | |||||||
\(810\) | 4.67510e6 | 0.250368 | ||||||||
\(811\) | 1.39772e7 | 0.746221 | 0.373111 | − | 0.927787i | \(-0.378291\pi\) | ||||
0.373111 | + | 0.927787i | \(0.378291\pi\) | |||||||
\(812\) | −3.92078e6 | −0.208681 | ||||||||
\(813\) | −1.69654e7 | −0.900195 | ||||||||
\(814\) | 1.24364e7 | 0.657862 | ||||||||
\(815\) | 2.28965e6 | 0.120747 | ||||||||
\(816\) | 8.77901e6 | 0.461551 | ||||||||
\(817\) | −1.22688e6 | −0.0643051 | ||||||||
\(818\) | 956824. | 0.0499976 | ||||||||
\(819\) | −3.37737e6 | −0.175942 | ||||||||
\(820\) | −969600. | −0.0503568 | ||||||||
\(821\) | −1.78137e7 | −0.922350 | −0.461175 | − | 0.887309i | \(-0.652572\pi\) | ||||
−0.461175 | + | 0.887309i | \(0.652572\pi\) | |||||||
\(822\) | −1.24631e7 | −0.643347 | ||||||||
\(823\) | 1.91010e7 | 0.983005 | 0.491502 | − | 0.870876i | \(-0.336448\pi\) | ||||
0.491502 | + | 0.870876i | \(0.336448\pi\) | |||||||
\(824\) | −7.41690e6 | −0.380543 | ||||||||
\(825\) | −7.97813e6 | −0.408099 | ||||||||
\(826\) | −1.12190e6 | −0.0572144 | ||||||||
\(827\) | 3.19225e6 | 0.162305 | 0.0811526 | − | 0.996702i | \(-0.474140\pi\) | ||||
0.0811526 | + | 0.996702i | \(0.474140\pi\) | |||||||
\(828\) | −5.62848e6 | −0.285309 | ||||||||
\(829\) | 8.56842e6 | 0.433026 | 0.216513 | − | 0.976280i | \(-0.430532\pi\) | ||||
0.216513 | + | 0.976280i | \(0.430532\pi\) | |||||||
\(830\) | 1.06284e7 | 0.535516 | ||||||||
\(831\) | 5.06145e7 | 2.54257 | ||||||||
\(832\) | −987136. | −0.0494389 | ||||||||
\(833\) | −3.57989e6 | −0.178755 | ||||||||
\(834\) | −3.21527e7 | −1.60067 | ||||||||
\(835\) | 952425. | 0.0472732 | ||||||||
\(836\) | −1.80974e7 | −0.895574 | ||||||||
\(837\) | −5.63334e6 | −0.277941 | ||||||||
\(838\) | −1.85385e7 | −0.911935 | ||||||||
\(839\) | 3.56751e7 | 1.74969 | 0.874843 | − | 0.484407i | \(-0.160964\pi\) | ||||
0.874843 | + | 0.484407i | \(0.160964\pi\) | |||||||
\(840\) | 1.80320e6 | 0.0881750 | ||||||||
\(841\) | 4.49885e6 | 0.219337 | ||||||||
\(842\) | 8.40430e6 | 0.408528 | ||||||||
\(843\) | −4.00152e6 | −0.193935 | ||||||||
\(844\) | −1.96189e7 | −0.948021 | ||||||||
\(845\) | −7.83030e6 | −0.377256 | ||||||||
\(846\) | 2.64985e7 | 1.27290 | ||||||||
\(847\) | 7.20173e6 | 0.344928 | ||||||||
\(848\) | −6.47578e6 | −0.309245 | ||||||||
\(849\) | 1.26742e7 | 0.603465 | ||||||||
\(850\) | 3.72750e6 | 0.176958 | ||||||||
\(851\) | 6.89046e6 | 0.326155 | ||||||||
\(852\) | −5.91744e6 | −0.279277 | ||||||||
\(853\) | 3.06355e7 | 1.44163 | 0.720814 | − | 0.693129i | \(-0.243768\pi\) | ||||
0.720814 | + | 0.693129i | \(0.243768\pi\) | |||||||
\(854\) | 7.07795e6 | 0.332095 | ||||||||
\(855\) | −1.45717e7 | −0.681703 | ||||||||
\(856\) | 8.82317e6 | 0.411567 | ||||||||
\(857\) | −4.46188e6 | −0.207523 | −0.103761 | − | 0.994602i | \(-0.533088\pi\) | ||||
−0.103761 | + | 0.994602i | \(0.533088\pi\) | |||||||
\(858\) | −1.23055e7 | −0.570663 | ||||||||
\(859\) | 2.63974e7 | 1.22061 | 0.610307 | − | 0.792165i | \(-0.291046\pi\) | ||||
0.610307 | + | 0.792165i | \(0.291046\pi\) | |||||||
\(860\) | 240800. | 0.0111022 | ||||||||
\(861\) | 2.73185e6 | 0.125588 | ||||||||
\(862\) | −6.61936e6 | −0.303422 | ||||||||
\(863\) | −2.17530e7 | −0.994244 | −0.497122 | − | 0.867681i | \(-0.665610\pi\) | ||||
−0.497122 | + | 0.867681i | \(0.665610\pi\) | |||||||
\(864\) | 1.01274e6 | 0.0461543 | ||||||||
\(865\) | −1.35361e7 | −0.615110 | ||||||||
\(866\) | 7.36122e6 | 0.333546 | ||||||||
\(867\) | −1.84742e7 | −0.834674 | ||||||||
\(868\) | 4.46566e6 | 0.201181 | ||||||||
\(869\) | −3.56016e7 | −1.59926 | ||||||||
\(870\) | −1.15023e7 | −0.515213 | ||||||||
\(871\) | −1.59311e7 | −0.711540 | ||||||||
\(872\) | −5.65741e6 | −0.251957 | ||||||||
\(873\) | 4.31932e7 | 1.91814 | ||||||||
\(874\) | −1.00270e7 | −0.444008 | ||||||||
\(875\) | 765625. | 0.0338062 | ||||||||
\(876\) | 2.96174e7 | 1.30403 | ||||||||
\(877\) | −1.58383e7 | −0.695361 | −0.347680 | − | 0.937613i | \(-0.613031\pi\) | ||||
−0.347680 | + | 0.937613i | \(0.613031\pi\) | |||||||
\(878\) | −2.33474e7 | −1.02212 | ||||||||
\(879\) | 3.85277e7 | 1.68190 | ||||||||
\(880\) | 3.55200e6 | 0.154620 | ||||||||
\(881\) | 1.97427e7 | 0.856974 | 0.428487 | − | 0.903548i | \(-0.359047\pi\) | ||||
0.428487 | + | 0.903548i | \(0.359047\pi\) | |||||||
\(882\) | −2.74674e6 | −0.118890 | ||||||||
\(883\) | −1.72899e7 | −0.746263 | −0.373131 | − | 0.927779i | \(-0.621716\pi\) | ||||
−0.373131 | + | 0.927779i | \(0.621716\pi\) | |||||||
\(884\) | 5.74930e6 | 0.247448 | ||||||||
\(885\) | −3.29130e6 | −0.141257 | ||||||||
\(886\) | −4.78817e6 | −0.204920 | ||||||||
\(887\) | −4.44693e7 | −1.89780 | −0.948901 | − | 0.315574i | \(-0.897803\pi\) | ||||
−0.948901 | + | 0.315574i | \(0.897803\pi\) | |||||||
\(888\) | −8.24614e6 | −0.350928 | ||||||||
\(889\) | 1.22949e7 | 0.521759 | ||||||||
\(890\) | 7.16760e6 | 0.303318 | ||||||||
\(891\) | −2.59468e7 | −1.09494 | ||||||||
\(892\) | 9.94011e6 | 0.418292 | ||||||||
\(893\) | 4.72062e7 | 1.98094 | ||||||||
\(894\) | 1.61995e7 | 0.677890 | ||||||||
\(895\) | 4.15470e6 | 0.173373 | ||||||||
\(896\) | −802816. | −0.0334077 | ||||||||
\(897\) | −6.81789e6 | −0.282923 | ||||||||
\(898\) | 1.37028e7 | 0.567046 | ||||||||
\(899\) | −2.84857e7 | −1.17551 | ||||||||
\(900\) | 2.86000e6 | 0.117695 | ||||||||
\(901\) | 3.77163e7 | 1.54781 | ||||||||
\(902\) | 5.38128e6 | 0.220226 | ||||||||
\(903\) | −678454. | −0.0276886 | ||||||||
\(904\) | −1.31555e7 | −0.535408 | ||||||||
\(905\) | −4.93300e6 | −0.200212 | ||||||||
\(906\) | 3.52666e7 | 1.42739 | ||||||||
\(907\) | 2.56887e6 | 0.103687 | 0.0518434 | − | 0.998655i | \(-0.483490\pi\) | ||||
0.0518434 | + | 0.998655i | \(0.483490\pi\) | |||||||
\(908\) | 2.07628e7 | 0.835742 | ||||||||
\(909\) | −1.63449e7 | −0.656104 | ||||||||
\(910\) | 1.18090e6 | 0.0472726 | ||||||||
\(911\) | 1.12692e7 | 0.449882 | 0.224941 | − | 0.974372i | \(-0.427781\pi\) | ||||
0.224941 | + | 0.974372i | \(0.427781\pi\) | |||||||
\(912\) | 1.19997e7 | 0.477733 | ||||||||
\(913\) | −5.89876e7 | −2.34198 | ||||||||
\(914\) | −2.11897e7 | −0.838994 | ||||||||
\(915\) | 2.07644e7 | 0.819911 | ||||||||
\(916\) | −1.98822e6 | −0.0782937 | ||||||||
\(917\) | −2.55398e6 | −0.100298 | ||||||||
\(918\) | −5.89840e6 | −0.231008 | ||||||||
\(919\) | 3.18378e7 | 1.24353 | 0.621763 | − | 0.783205i | \(-0.286417\pi\) | ||||
0.621763 | + | 0.783205i | \(0.286417\pi\) | |||||||
\(920\) | 1.96800e6 | 0.0766577 | ||||||||
\(921\) | −5.36039e7 | −2.08232 | ||||||||
\(922\) | −3.55092e7 | −1.37567 | ||||||||
\(923\) | −3.87528e6 | −0.149727 | ||||||||
\(924\) | −1.00078e7 | −0.385618 | ||||||||
\(925\) | −3.50125e6 | −0.134545 | ||||||||
\(926\) | 8.69901e6 | 0.333382 | ||||||||
\(927\) | 3.31443e7 | 1.26680 | ||||||||
\(928\) | 5.12102e6 | 0.195203 | ||||||||
\(929\) | 1.88558e7 | 0.716813 | 0.358407 | − | 0.933566i | \(-0.383320\pi\) | ||||
0.358407 | + | 0.933566i | \(0.383320\pi\) | |||||||
\(930\) | 1.31008e7 | 0.496696 | ||||||||
\(931\) | −4.89324e6 | −0.185021 | ||||||||
\(932\) | 1.73987e7 | 0.656109 | ||||||||
\(933\) | −1.62441e7 | −0.610931 | ||||||||
\(934\) | 1.51588e6 | 0.0568586 | ||||||||
\(935\) | −2.06876e7 | −0.773894 | ||||||||
\(936\) | 4.41126e6 | 0.164579 | ||||||||
\(937\) | 1.12946e7 | 0.420265 | 0.210132 | − | 0.977673i | \(-0.432610\pi\) | ||||
0.210132 | + | 0.977673i | \(0.432610\pi\) | |||||||
\(938\) | −1.29564e7 | −0.480814 | ||||||||
\(939\) | 4.22200e6 | 0.156262 | ||||||||
\(940\) | −9.26520e6 | −0.342007 | ||||||||
\(941\) | −2.91941e7 | −1.07478 | −0.537392 | − | 0.843333i | \(-0.680590\pi\) | ||||
−0.537392 | + | 0.843333i | \(0.680590\pi\) | |||||||
\(942\) | 3.18241e7 | 1.16850 | ||||||||
\(943\) | 2.98152e6 | 0.109184 | ||||||||
\(944\) | 1.46534e6 | 0.0535192 | ||||||||
\(945\) | −1.21152e6 | −0.0441319 | ||||||||
\(946\) | −1.33644e6 | −0.0485536 | ||||||||
\(947\) | 1.05892e7 | 0.383697 | 0.191848 | − | 0.981425i | \(-0.438552\pi\) | ||||
0.191848 | + | 0.981425i | \(0.438552\pi\) | |||||||
\(948\) | 2.36061e7 | 0.853107 | ||||||||
\(949\) | 1.93962e7 | 0.699118 | ||||||||
\(950\) | 5.09500e6 | 0.183162 | ||||||||
\(951\) | −6.22530e7 | −2.23208 | ||||||||
\(952\) | 4.67578e6 | 0.167210 | ||||||||
\(953\) | −3.90317e7 | −1.39215 | −0.696074 | − | 0.717970i | \(-0.745071\pi\) | ||||
−0.696074 | + | 0.717970i | \(0.745071\pi\) | |||||||
\(954\) | 2.89386e7 | 1.02945 | ||||||||
\(955\) | −8.43052e6 | −0.299121 | ||||||||
\(956\) | −8.73010e6 | −0.308940 | ||||||||
\(957\) | 6.38378e7 | 2.25319 | ||||||||
\(958\) | −7.53958e6 | −0.265420 | ||||||||
\(959\) | −6.63793e6 | −0.233070 | ||||||||
\(960\) | −2.35520e6 | −0.0824802 | ||||||||
\(961\) | 3.81526e6 | 0.133265 | ||||||||
\(962\) | −5.40033e6 | −0.188141 | ||||||||
\(963\) | −3.94285e7 | −1.37008 | ||||||||
\(964\) | 1.29810e7 | 0.449898 | ||||||||
\(965\) | 6.51290e6 | 0.225142 | ||||||||
\(966\) | −5.54484e6 | −0.191182 | ||||||||
\(967\) | −3.43395e7 | −1.18094 | −0.590470 | − | 0.807059i | \(-0.701058\pi\) | ||||
−0.590470 | + | 0.807059i | \(0.701058\pi\) | |||||||
\(968\) | −9.40634e6 | −0.322650 | ||||||||
\(969\) | −6.98891e7 | −2.39111 | ||||||||
\(970\) | −1.51025e7 | −0.515370 | ||||||||
\(971\) | −1.81464e7 | −0.617651 | −0.308826 | − | 0.951119i | \(-0.599936\pi\) | ||||
−0.308826 | + | 0.951119i | \(0.599936\pi\) | |||||||
\(972\) | 2.10496e7 | 0.714625 | ||||||||
\(973\) | −1.71248e7 | −0.579888 | ||||||||
\(974\) | −1.47075e7 | −0.496756 | ||||||||
\(975\) | 3.46438e6 | 0.116711 | ||||||||
\(976\) | −9.24467e6 | −0.310647 | ||||||||
\(977\) | −1.05223e7 | −0.352675 | −0.176338 | − | 0.984330i | \(-0.556425\pi\) | ||||
−0.176338 | + | 0.984330i | \(0.556425\pi\) | |||||||
\(978\) | 8.42591e6 | 0.281689 | ||||||||
\(979\) | −3.97802e7 | −1.32651 | ||||||||
\(980\) | 960400. | 0.0319438 | ||||||||
\(981\) | 2.52815e7 | 0.838747 | ||||||||
\(982\) | −3.81606e7 | −1.26281 | ||||||||
\(983\) | −7.91353e6 | −0.261208 | −0.130604 | − | 0.991435i | \(-0.541692\pi\) | ||||
−0.130604 | + | 0.991435i | \(0.541692\pi\) | |||||||
\(984\) | −3.56813e6 | −0.117477 | ||||||||
\(985\) | −1.02303e7 | −0.335968 | ||||||||
\(986\) | −2.98260e7 | −0.977017 | ||||||||
\(987\) | 2.61047e7 | 0.852954 | ||||||||
\(988\) | 7.85853e6 | 0.256123 | ||||||||
\(989\) | −740460. | −0.0240719 | ||||||||
\(990\) | −1.58730e7 | −0.514720 | ||||||||
\(991\) | 4.01556e7 | 1.29886 | 0.649429 | − | 0.760422i | \(-0.275008\pi\) | ||||
0.649429 | + | 0.760422i | \(0.275008\pi\) | |||||||
\(992\) | −5.83270e6 | −0.188187 | ||||||||
\(993\) | 4.92976e7 | 1.58654 | ||||||||
\(994\) | −3.15168e6 | −0.101176 | ||||||||
\(995\) | 7.52450e6 | 0.240946 | ||||||||
\(996\) | 3.91125e7 | 1.24930 | ||||||||
\(997\) | −4.93478e7 | −1.57228 | −0.786140 | − | 0.618048i | \(-0.787924\pi\) | ||||
−0.786140 | + | 0.618048i | \(0.787924\pi\) | |||||||
\(998\) | −1.91297e7 | −0.607970 | ||||||||
\(999\) | 5.54038e6 | 0.175641 |
(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 | 70.6.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 630.6.a.j.1.1 | 1 | |||
4.3 | odd | 2 | 560.6.a.i.1.1 | 1 | |||
5.2 | odd | 4 | 350.6.c.h.99.1 | 2 | |||
5.3 | odd | 4 | 350.6.c.h.99.2 | 2 | |||
5.4 | even | 2 | 350.6.a.n.1.1 | 1 | |||
7.6 | odd | 2 | 490.6.a.i.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.6.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
350.6.a.n.1.1 | 1 | 5.4 | even | 2 | |||
350.6.c.h.99.1 | 2 | 5.2 | odd | 4 | |||
350.6.c.h.99.2 | 2 | 5.3 | odd | 4 | |||
490.6.a.i.1.1 | 1 | 7.6 | odd | 2 | |||
560.6.a.i.1.1 | 1 | 4.3 | odd | 2 | |||
630.6.a.j.1.1 | 1 | 3.2 | odd | 2 |