Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [354,8,Mod(1,354)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(354, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("354.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 354 = 2 \cdot 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 354.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: | \(110.584299021\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 6162x^{3} - 12837x^{2} + 3760259x - 17264060 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(76.1395\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 354.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.00000 | 0.707107 | ||||||||
\(3\) | 27.0000 | 0.577350 | ||||||||
\(4\) | 64.0000 | 0.500000 | ||||||||
\(5\) | 322.557 | 1.15402 | 0.577008 | − | 0.816738i | \(-0.304220\pi\) | ||||
0.577008 | + | 0.816738i | \(0.304220\pi\) | |||||||
\(6\) | 216.000 | 0.408248 | ||||||||
\(7\) | −1226.16 | −1.35115 | −0.675573 | − | 0.737293i | \(-0.736104\pi\) | ||||
−0.675573 | + | 0.737293i | \(0.736104\pi\) | |||||||
\(8\) | 512.000 | 0.353553 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 2580.46 | 0.816013 | ||||||||
\(11\) | −5358.18 | −1.21379 | −0.606895 | − | 0.794782i | \(-0.707585\pi\) | ||||
−0.606895 | + | 0.794782i | \(0.707585\pi\) | |||||||
\(12\) | 1728.00 | 0.288675 | ||||||||
\(13\) | −10351.4 | −1.30677 | −0.653384 | − | 0.757027i | \(-0.726651\pi\) | ||||
−0.653384 | + | 0.757027i | \(0.726651\pi\) | |||||||
\(14\) | −9809.25 | −0.955405 | ||||||||
\(15\) | 8709.05 | 0.666272 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | 20353.6 | 1.00478 | 0.502389 | − | 0.864642i | \(-0.332455\pi\) | ||||
0.502389 | + | 0.864642i | \(0.332455\pi\) | |||||||
\(18\) | 5832.00 | 0.235702 | ||||||||
\(19\) | 29921.3 | 1.00079 | 0.500394 | − | 0.865798i | \(-0.333188\pi\) | ||||
0.500394 | + | 0.865798i | \(0.333188\pi\) | |||||||
\(20\) | 20643.7 | 0.577008 | ||||||||
\(21\) | −33106.2 | −0.780085 | ||||||||
\(22\) | −42865.5 | −0.858279 | ||||||||
\(23\) | 9894.44 | 0.169568 | 0.0847839 | − | 0.996399i | \(-0.472980\pi\) | ||||
0.0847839 | + | 0.996399i | \(0.472980\pi\) | |||||||
\(24\) | 13824.0 | 0.204124 | ||||||||
\(25\) | 25918.3 | 0.331755 | ||||||||
\(26\) | −82811.4 | −0.924025 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | −78474.0 | −0.675573 | ||||||||
\(29\) | −110415. | −0.840686 | −0.420343 | − | 0.907365i | \(-0.638090\pi\) | ||||
−0.420343 | + | 0.907365i | \(0.638090\pi\) | |||||||
\(30\) | 69672.4 | 0.471125 | ||||||||
\(31\) | −186449. | −1.12407 | −0.562036 | − | 0.827113i | \(-0.689982\pi\) | ||||
−0.562036 | + | 0.827113i | \(0.689982\pi\) | |||||||
\(32\) | 32768.0 | 0.176777 | ||||||||
\(33\) | −144671. | −0.700782 | ||||||||
\(34\) | 162829. | 0.710485 | ||||||||
\(35\) | −395506. | −1.55925 | ||||||||
\(36\) | 46656.0 | 0.166667 | ||||||||
\(37\) | −394202. | −1.27942 | −0.639709 | − | 0.768617i | \(-0.720945\pi\) | ||||
−0.639709 | + | 0.768617i | \(0.720945\pi\) | |||||||
\(38\) | 239370. | 0.707664 | ||||||||
\(39\) | −279489. | −0.754463 | ||||||||
\(40\) | 165149. | 0.408007 | ||||||||
\(41\) | −474592. | −1.07542 | −0.537708 | − | 0.843131i | \(-0.680710\pi\) | ||||
−0.537708 | + | 0.843131i | \(0.680710\pi\) | |||||||
\(42\) | −264850. | −0.551603 | ||||||||
\(43\) | −423064. | −0.811459 | −0.405730 | − | 0.913993i | \(-0.632983\pi\) | ||||
−0.405730 | + | 0.913993i | \(0.632983\pi\) | |||||||
\(44\) | −342924. | −0.606895 | ||||||||
\(45\) | 235144. | 0.384672 | ||||||||
\(46\) | 79155.5 | 0.119903 | ||||||||
\(47\) | 382727. | 0.537707 | 0.268854 | − | 0.963181i | \(-0.413355\pi\) | ||||
0.268854 | + | 0.963181i | \(0.413355\pi\) | |||||||
\(48\) | 110592. | 0.144338 | ||||||||
\(49\) | 679915. | 0.825598 | ||||||||
\(50\) | 207347. | 0.234586 | ||||||||
\(51\) | 549547. | 0.580108 | ||||||||
\(52\) | −662491. | −0.653384 | ||||||||
\(53\) | −126831. | −0.117019 | −0.0585097 | − | 0.998287i | \(-0.518635\pi\) | ||||
−0.0585097 | + | 0.998287i | \(0.518635\pi\) | |||||||
\(54\) | 157464. | 0.136083 | ||||||||
\(55\) | −1.72832e6 | −1.40073 | ||||||||
\(56\) | −627792. | −0.477703 | ||||||||
\(57\) | 807874. | 0.577805 | ||||||||
\(58\) | −883318. | −0.594455 | ||||||||
\(59\) | 205379. | 0.130189 | ||||||||
\(60\) | 557379. | 0.333136 | ||||||||
\(61\) | −162477. | −0.0916510 | −0.0458255 | − | 0.998949i | \(-0.514592\pi\) | ||||
−0.0458255 | + | 0.998949i | \(0.514592\pi\) | |||||||
\(62\) | −1.49159e6 | −0.794838 | ||||||||
\(63\) | −893868. | −0.450382 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | −3.33893e6 | −1.50803 | ||||||||
\(66\) | −1.15737e6 | −0.495527 | ||||||||
\(67\) | 1.53838e6 | 0.624887 | 0.312444 | − | 0.949936i | \(-0.398852\pi\) | ||||
0.312444 | + | 0.949936i | \(0.398852\pi\) | |||||||
\(68\) | 1.30263e6 | 0.502389 | ||||||||
\(69\) | 267150. | 0.0979001 | ||||||||
\(70\) | −3.16405e6 | −1.10255 | ||||||||
\(71\) | −5.92431e6 | −1.96442 | −0.982208 | − | 0.187799i | \(-0.939865\pi\) | ||||
−0.982208 | + | 0.187799i | \(0.939865\pi\) | |||||||
\(72\) | 373248. | 0.117851 | ||||||||
\(73\) | −2.48019e6 | −0.746199 | −0.373099 | − | 0.927791i | \(-0.621705\pi\) | ||||
−0.373099 | + | 0.927791i | \(0.621705\pi\) | |||||||
\(74\) | −3.15361e6 | −0.904685 | ||||||||
\(75\) | 699795. | 0.191539 | ||||||||
\(76\) | 1.91496e6 | 0.500394 | ||||||||
\(77\) | 6.56997e6 | 1.64001 | ||||||||
\(78\) | −2.23591e6 | −0.533486 | ||||||||
\(79\) | 3.93508e6 | 0.897964 | 0.448982 | − | 0.893541i | \(-0.351787\pi\) | ||||
0.448982 | + | 0.893541i | \(0.351787\pi\) | |||||||
\(80\) | 1.32120e6 | 0.288504 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | −3.79673e6 | −0.760434 | ||||||||
\(83\) | −4.28658e6 | −0.822883 | −0.411441 | − | 0.911436i | \(-0.634974\pi\) | ||||
−0.411441 | + | 0.911436i | \(0.634974\pi\) | |||||||
\(84\) | −2.11880e6 | −0.390043 | ||||||||
\(85\) | 6.56520e6 | 1.15953 | ||||||||
\(86\) | −3.38451e6 | −0.573788 | ||||||||
\(87\) | −2.98120e6 | −0.485370 | ||||||||
\(88\) | −2.74339e6 | −0.429139 | ||||||||
\(89\) | −4.71156e6 | −0.708435 | −0.354217 | − | 0.935163i | \(-0.615253\pi\) | ||||
−0.354217 | + | 0.935163i | \(0.615253\pi\) | |||||||
\(90\) | 1.88116e6 | 0.272004 | ||||||||
\(91\) | 1.26925e7 | 1.76564 | ||||||||
\(92\) | 633244. | 0.0847839 | ||||||||
\(93\) | −5.03412e6 | −0.648983 | ||||||||
\(94\) | 3.06181e6 | 0.380217 | ||||||||
\(95\) | 9.65132e6 | 1.15493 | ||||||||
\(96\) | 884736. | 0.102062 | ||||||||
\(97\) | 1.26688e7 | 1.40940 | 0.704699 | − | 0.709506i | \(-0.251082\pi\) | ||||
0.704699 | + | 0.709506i | \(0.251082\pi\) | |||||||
\(98\) | 5.43932e6 | 0.583786 | ||||||||
\(99\) | −3.90612e6 | −0.404596 | ||||||||
\(100\) | 1.65877e6 | 0.165877 | ||||||||
\(101\) | 1.06235e7 | 1.02599 | 0.512994 | − | 0.858392i | \(-0.328536\pi\) | ||||
0.512994 | + | 0.858392i | \(0.328536\pi\) | |||||||
\(102\) | 4.39638e6 | 0.410199 | ||||||||
\(103\) | 6.29033e6 | 0.567209 | 0.283605 | − | 0.958941i | \(-0.408470\pi\) | ||||
0.283605 | + | 0.958941i | \(0.408470\pi\) | |||||||
\(104\) | −5.29993e6 | −0.462012 | ||||||||
\(105\) | −1.06787e7 | −0.900231 | ||||||||
\(106\) | −1.01464e6 | −0.0827453 | ||||||||
\(107\) | −8.52760e6 | −0.672951 | −0.336476 | − | 0.941692i | \(-0.609235\pi\) | ||||
−0.336476 | + | 0.941692i | \(0.609235\pi\) | |||||||
\(108\) | 1.25971e6 | 0.0962250 | ||||||||
\(109\) | −7.25070e6 | −0.536274 | −0.268137 | − | 0.963381i | \(-0.586408\pi\) | ||||
−0.268137 | + | 0.963381i | \(0.586408\pi\) | |||||||
\(110\) | −1.38266e7 | −0.990468 | ||||||||
\(111\) | −1.06434e7 | −0.738672 | ||||||||
\(112\) | −5.02233e6 | −0.337787 | ||||||||
\(113\) | −2.35877e7 | −1.53784 | −0.768920 | − | 0.639345i | \(-0.779206\pi\) | ||||
−0.768920 | + | 0.639345i | \(0.779206\pi\) | |||||||
\(114\) | 6.46299e6 | 0.408570 | ||||||||
\(115\) | 3.19152e6 | 0.195684 | ||||||||
\(116\) | −7.06654e6 | −0.420343 | ||||||||
\(117\) | −7.54619e6 | −0.435589 | ||||||||
\(118\) | 1.64303e6 | 0.0920575 | ||||||||
\(119\) | −2.49567e7 | −1.35760 | ||||||||
\(120\) | 4.45903e6 | 0.235563 | ||||||||
\(121\) | 9.22297e6 | 0.473284 | ||||||||
\(122\) | −1.29982e6 | −0.0648070 | ||||||||
\(123\) | −1.28140e7 | −0.620892 | ||||||||
\(124\) | −1.19327e7 | −0.562036 | ||||||||
\(125\) | −1.68397e7 | −0.771166 | ||||||||
\(126\) | −7.15094e6 | −0.318468 | ||||||||
\(127\) | 1.27104e7 | 0.550613 | 0.275306 | − | 0.961357i | \(-0.411221\pi\) | ||||
0.275306 | + | 0.961357i | \(0.411221\pi\) | |||||||
\(128\) | 2.09715e6 | 0.0883883 | ||||||||
\(129\) | −1.14227e7 | −0.468496 | ||||||||
\(130\) | −2.67114e7 | −1.06634 | ||||||||
\(131\) | −1.26929e6 | −0.0493301 | −0.0246651 | − | 0.999696i | \(-0.507852\pi\) | ||||
−0.0246651 | + | 0.999696i | \(0.507852\pi\) | |||||||
\(132\) | −9.25894e6 | −0.350391 | ||||||||
\(133\) | −3.66881e7 | −1.35221 | ||||||||
\(134\) | 1.23070e7 | 0.441862 | ||||||||
\(135\) | 6.34890e6 | 0.222091 | ||||||||
\(136\) | 1.04210e7 | 0.355242 | ||||||||
\(137\) | −1.04727e7 | −0.347965 | −0.173982 | − | 0.984749i | \(-0.555664\pi\) | ||||
−0.173982 | + | 0.984749i | \(0.555664\pi\) | |||||||
\(138\) | 2.13720e6 | 0.0692258 | ||||||||
\(139\) | −7.35998e6 | −0.232447 | −0.116224 | − | 0.993223i | \(-0.537079\pi\) | ||||
−0.116224 | + | 0.993223i | \(0.537079\pi\) | |||||||
\(140\) | −2.53124e7 | −0.779623 | ||||||||
\(141\) | 1.03336e7 | 0.310446 | ||||||||
\(142\) | −4.73944e7 | −1.38905 | ||||||||
\(143\) | 5.54649e7 | 1.58614 | ||||||||
\(144\) | 2.98598e6 | 0.0833333 | ||||||||
\(145\) | −3.56151e7 | −0.970166 | ||||||||
\(146\) | −1.98415e7 | −0.527642 | ||||||||
\(147\) | 1.83577e7 | 0.476659 | ||||||||
\(148\) | −2.52289e7 | −0.639709 | ||||||||
\(149\) | −5.23831e6 | −0.129730 | −0.0648648 | − | 0.997894i | \(-0.520662\pi\) | ||||
−0.0648648 | + | 0.997894i | \(0.520662\pi\) | |||||||
\(150\) | 5.59836e6 | 0.135438 | ||||||||
\(151\) | 2.69252e7 | 0.636415 | 0.318207 | − | 0.948021i | \(-0.396919\pi\) | ||||
0.318207 | + | 0.948021i | \(0.396919\pi\) | |||||||
\(152\) | 1.53197e7 | 0.353832 | ||||||||
\(153\) | 1.48378e7 | 0.334926 | ||||||||
\(154\) | 5.25598e7 | 1.15966 | ||||||||
\(155\) | −6.01405e7 | −1.29720 | ||||||||
\(156\) | −1.78873e7 | −0.377231 | ||||||||
\(157\) | −4.63248e6 | −0.0955355 | −0.0477677 | − | 0.998858i | \(-0.515211\pi\) | ||||
−0.0477677 | + | 0.998858i | \(0.515211\pi\) | |||||||
\(158\) | 3.14807e7 | 0.634957 | ||||||||
\(159\) | −3.42442e6 | −0.0675612 | ||||||||
\(160\) | 1.05696e7 | 0.204003 | ||||||||
\(161\) | −1.21321e7 | −0.229111 | ||||||||
\(162\) | 4.25153e6 | 0.0785674 | ||||||||
\(163\) | 4.98385e6 | 0.0901381 | 0.0450690 | − | 0.998984i | \(-0.485649\pi\) | ||||
0.0450690 | + | 0.998984i | \(0.485649\pi\) | |||||||
\(164\) | −3.03739e7 | −0.537708 | ||||||||
\(165\) | −4.66647e7 | −0.808714 | ||||||||
\(166\) | −3.42927e7 | −0.581866 | ||||||||
\(167\) | 8.87363e7 | 1.47433 | 0.737163 | − | 0.675715i | \(-0.236165\pi\) | ||||
0.737163 | + | 0.675715i | \(0.236165\pi\) | |||||||
\(168\) | −1.69504e7 | −0.275802 | ||||||||
\(169\) | 4.44035e7 | 0.707643 | ||||||||
\(170\) | 5.25216e7 | 0.819911 | ||||||||
\(171\) | 2.18126e7 | 0.333596 | ||||||||
\(172\) | −2.70761e7 | −0.405730 | ||||||||
\(173\) | −2.76291e7 | −0.405700 | −0.202850 | − | 0.979210i | \(-0.565020\pi\) | ||||
−0.202850 | + | 0.979210i | \(0.565020\pi\) | |||||||
\(174\) | −2.38496e7 | −0.343209 | ||||||||
\(175\) | −3.17799e7 | −0.448249 | ||||||||
\(176\) | −2.19471e7 | −0.303447 | ||||||||
\(177\) | 5.54523e6 | 0.0751646 | ||||||||
\(178\) | −3.76925e7 | −0.500939 | ||||||||
\(179\) | 3.52061e7 | 0.458809 | 0.229405 | − | 0.973331i | \(-0.426322\pi\) | ||||
0.229405 | + | 0.973331i | \(0.426322\pi\) | |||||||
\(180\) | 1.50492e7 | 0.192336 | ||||||||
\(181\) | 1.78616e7 | 0.223895 | 0.111948 | − | 0.993714i | \(-0.464291\pi\) | ||||
0.111948 | + | 0.993714i | \(0.464291\pi\) | |||||||
\(182\) | 1.01540e8 | 1.24849 | ||||||||
\(183\) | −4.38688e6 | −0.0529147 | ||||||||
\(184\) | 5.06595e6 | 0.0599513 | ||||||||
\(185\) | −1.27153e8 | −1.47647 | ||||||||
\(186\) | −4.02730e7 | −0.458900 | ||||||||
\(187\) | −1.09058e8 | −1.21959 | ||||||||
\(188\) | 2.44945e7 | 0.268854 | ||||||||
\(189\) | −2.41344e7 | −0.260028 | ||||||||
\(190\) | 7.72106e7 | 0.816656 | ||||||||
\(191\) | 1.81334e8 | 1.88305 | 0.941525 | − | 0.336943i | \(-0.109393\pi\) | ||||
0.941525 | + | 0.336943i | \(0.109393\pi\) | |||||||
\(192\) | 7.07789e6 | 0.0721688 | ||||||||
\(193\) | −1.03710e8 | −1.03842 | −0.519208 | − | 0.854648i | \(-0.673773\pi\) | ||||
−0.519208 | + | 0.854648i | \(0.673773\pi\) | |||||||
\(194\) | 1.01350e8 | 0.996595 | ||||||||
\(195\) | −9.01511e7 | −0.870663 | ||||||||
\(196\) | 4.35146e7 | 0.412799 | ||||||||
\(197\) | −3.56650e7 | −0.332361 | −0.166180 | − | 0.986095i | \(-0.553143\pi\) | ||||
−0.166180 | + | 0.986095i | \(0.553143\pi\) | |||||||
\(198\) | −3.12489e7 | −0.286093 | ||||||||
\(199\) | 1.41306e8 | 1.27108 | 0.635542 | − | 0.772066i | \(-0.280777\pi\) | ||||
0.635542 | + | 0.772066i | \(0.280777\pi\) | |||||||
\(200\) | 1.32702e7 | 0.117293 | ||||||||
\(201\) | 4.15363e7 | 0.360779 | ||||||||
\(202\) | 8.49878e7 | 0.725483 | ||||||||
\(203\) | 1.35386e8 | 1.13589 | ||||||||
\(204\) | 3.51710e7 | 0.290054 | ||||||||
\(205\) | −1.53083e8 | −1.24105 | ||||||||
\(206\) | 5.03227e7 | 0.401078 | ||||||||
\(207\) | 7.21304e6 | 0.0565226 | ||||||||
\(208\) | −4.23994e7 | −0.326692 | ||||||||
\(209\) | −1.60324e8 | −1.21475 | ||||||||
\(210\) | −8.54292e7 | −0.636560 | ||||||||
\(211\) | −7.74278e7 | −0.567425 | −0.283712 | − | 0.958909i | \(-0.591566\pi\) | ||||
−0.283712 | + | 0.958909i | \(0.591566\pi\) | |||||||
\(212\) | −8.11715e6 | −0.0585097 | ||||||||
\(213\) | −1.59956e8 | −1.13416 | ||||||||
\(214\) | −6.82208e7 | −0.475848 | ||||||||
\(215\) | −1.36463e8 | −0.936438 | ||||||||
\(216\) | 1.00777e7 | 0.0680414 | ||||||||
\(217\) | 2.28615e8 | 1.51879 | ||||||||
\(218\) | −5.80056e7 | −0.379203 | ||||||||
\(219\) | −6.69651e7 | −0.430818 | ||||||||
\(220\) | −1.10613e8 | −0.700367 | ||||||||
\(221\) | −2.10689e8 | −1.31301 | ||||||||
\(222\) | −8.51475e7 | −0.522320 | ||||||||
\(223\) | −1.17128e8 | −0.707286 | −0.353643 | − | 0.935381i | \(-0.615057\pi\) | ||||
−0.353643 | + | 0.935381i | \(0.615057\pi\) | |||||||
\(224\) | −4.01787e7 | −0.238851 | ||||||||
\(225\) | 1.88945e7 | 0.110585 | ||||||||
\(226\) | −1.88702e8 | −1.08742 | ||||||||
\(227\) | 1.23610e8 | 0.701396 | 0.350698 | − | 0.936489i | \(-0.385944\pi\) | ||||
0.350698 | + | 0.936489i | \(0.385944\pi\) | |||||||
\(228\) | 5.17039e7 | 0.288903 | ||||||||
\(229\) | −6.88315e6 | −0.0378759 | −0.0189380 | − | 0.999821i | \(-0.506029\pi\) | ||||
−0.0189380 | + | 0.999821i | \(0.506029\pi\) | |||||||
\(230\) | 2.55322e7 | 0.138370 | ||||||||
\(231\) | 1.77389e8 | 0.946859 | ||||||||
\(232\) | −5.65323e7 | −0.297227 | ||||||||
\(233\) | −3.18340e8 | −1.64872 | −0.824358 | − | 0.566068i | \(-0.808464\pi\) | ||||
−0.824358 | + | 0.566068i | \(0.808464\pi\) | |||||||
\(234\) | −6.03695e7 | −0.308008 | ||||||||
\(235\) | 1.23451e8 | 0.620523 | ||||||||
\(236\) | 1.31443e7 | 0.0650945 | ||||||||
\(237\) | 1.06247e8 | 0.518440 | ||||||||
\(238\) | −1.99653e8 | −0.959969 | ||||||||
\(239\) | 9.13265e7 | 0.432717 | 0.216359 | − | 0.976314i | \(-0.430582\pi\) | ||||
0.216359 | + | 0.976314i | \(0.430582\pi\) | |||||||
\(240\) | 3.56723e7 | 0.166568 | ||||||||
\(241\) | 3.27837e8 | 1.50868 | 0.754342 | − | 0.656482i | \(-0.227956\pi\) | ||||
0.754342 | + | 0.656482i | \(0.227956\pi\) | |||||||
\(242\) | 7.37838e7 | 0.334663 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | −1.03985e7 | −0.0458255 | ||||||||
\(245\) | 2.19312e8 | 0.952754 | ||||||||
\(246\) | −1.02512e8 | −0.439037 | ||||||||
\(247\) | −3.09728e8 | −1.30780 | ||||||||
\(248\) | −9.54618e7 | −0.397419 | ||||||||
\(249\) | −1.15738e8 | −0.475091 | ||||||||
\(250\) | −1.34717e8 | −0.545297 | ||||||||
\(251\) | −4.81502e8 | −1.92194 | −0.960970 | − | 0.276652i | \(-0.910775\pi\) | ||||
−0.960970 | + | 0.276652i | \(0.910775\pi\) | |||||||
\(252\) | −5.72075e7 | −0.225191 | ||||||||
\(253\) | −5.30162e7 | −0.205820 | ||||||||
\(254\) | 1.01683e8 | 0.389342 | ||||||||
\(255\) | 1.77260e8 | 0.669455 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | −6.16203e7 | −0.226442 | −0.113221 | − | 0.993570i | \(-0.536117\pi\) | ||||
−0.113221 | + | 0.993570i | \(0.536117\pi\) | |||||||
\(258\) | −9.13819e7 | −0.331277 | ||||||||
\(259\) | 4.83353e8 | 1.72868 | ||||||||
\(260\) | −2.13692e8 | −0.754016 | ||||||||
\(261\) | −8.04923e7 | −0.280229 | ||||||||
\(262\) | −1.01543e7 | −0.0348817 | ||||||||
\(263\) | 1.61880e8 | 0.548718 | 0.274359 | − | 0.961627i | \(-0.411534\pi\) | ||||
0.274359 | + | 0.961627i | \(0.411534\pi\) | |||||||
\(264\) | −7.40715e7 | −0.247764 | ||||||||
\(265\) | −4.09101e7 | −0.135042 | ||||||||
\(266\) | −2.93505e8 | −0.956158 | ||||||||
\(267\) | −1.27212e8 | −0.409015 | ||||||||
\(268\) | 9.84563e7 | 0.312444 | ||||||||
\(269\) | 1.19284e8 | 0.373638 | 0.186819 | − | 0.982394i | \(-0.440182\pi\) | ||||
0.186819 | + | 0.982394i | \(0.440182\pi\) | |||||||
\(270\) | 5.07912e7 | 0.157042 | ||||||||
\(271\) | 4.65783e8 | 1.42164 | 0.710822 | − | 0.703372i | \(-0.248323\pi\) | ||||
0.710822 | + | 0.703372i | \(0.248323\pi\) | |||||||
\(272\) | 8.33683e7 | 0.251194 | ||||||||
\(273\) | 3.42697e8 | 1.01939 | ||||||||
\(274\) | −8.37814e7 | −0.246048 | ||||||||
\(275\) | −1.38875e8 | −0.402680 | ||||||||
\(276\) | 1.70976e7 | 0.0489500 | ||||||||
\(277\) | 2.02046e7 | 0.0571176 | 0.0285588 | − | 0.999592i | \(-0.490908\pi\) | ||||
0.0285588 | + | 0.999592i | \(0.490908\pi\) | |||||||
\(278\) | −5.88798e7 | −0.164365 | ||||||||
\(279\) | −1.35921e8 | −0.374690 | ||||||||
\(280\) | −2.02499e8 | −0.551277 | ||||||||
\(281\) | −4.07044e8 | −1.09438 | −0.547192 | − | 0.837007i | \(-0.684303\pi\) | ||||
−0.547192 | + | 0.837007i | \(0.684303\pi\) | |||||||
\(282\) | 8.26689e7 | 0.219518 | ||||||||
\(283\) | −2.22689e8 | −0.584045 | −0.292022 | − | 0.956411i | \(-0.594328\pi\) | ||||
−0.292022 | + | 0.956411i | \(0.594328\pi\) | |||||||
\(284\) | −3.79156e8 | −0.982208 | ||||||||
\(285\) | 2.60586e8 | 0.666797 | ||||||||
\(286\) | 4.43719e8 | 1.12157 | ||||||||
\(287\) | 5.81924e8 | 1.45305 | ||||||||
\(288\) | 2.38879e7 | 0.0589256 | ||||||||
\(289\) | 3.92990e6 | 0.00957722 | ||||||||
\(290\) | −2.84921e8 | −0.686011 | ||||||||
\(291\) | 3.42057e8 | 0.813716 | ||||||||
\(292\) | −1.58732e8 | −0.373099 | ||||||||
\(293\) | −4.37450e8 | −1.01600 | −0.507998 | − | 0.861358i | \(-0.669614\pi\) | ||||
−0.507998 | + | 0.861358i | \(0.669614\pi\) | |||||||
\(294\) | 1.46862e8 | 0.337049 | ||||||||
\(295\) | 6.62465e7 | 0.150240 | ||||||||
\(296\) | −2.01831e8 | −0.452342 | ||||||||
\(297\) | −1.05465e8 | −0.233594 | ||||||||
\(298\) | −4.19065e7 | −0.0917327 | ||||||||
\(299\) | −1.02422e8 | −0.221586 | ||||||||
\(300\) | 4.47869e7 | 0.0957693 | ||||||||
\(301\) | 5.18743e8 | 1.09640 | ||||||||
\(302\) | 2.15402e8 | 0.450013 | ||||||||
\(303\) | 2.86834e8 | 0.592354 | ||||||||
\(304\) | 1.22557e8 | 0.250197 | ||||||||
\(305\) | −5.24081e7 | −0.105767 | ||||||||
\(306\) | 1.18702e8 | 0.236828 | ||||||||
\(307\) | 8.33109e8 | 1.64330 | 0.821651 | − | 0.569990i | \(-0.193053\pi\) | ||||
0.821651 | + | 0.569990i | \(0.193053\pi\) | |||||||
\(308\) | 4.20478e8 | 0.820004 | ||||||||
\(309\) | 1.69839e8 | 0.327478 | ||||||||
\(310\) | −4.81124e8 | −0.917257 | ||||||||
\(311\) | −3.29748e8 | −0.621614 | −0.310807 | − | 0.950473i | \(-0.600599\pi\) | ||||
−0.310807 | + | 0.950473i | \(0.600599\pi\) | |||||||
\(312\) | −1.43098e8 | −0.266743 | ||||||||
\(313\) | 2.41712e8 | 0.445547 | 0.222773 | − | 0.974870i | \(-0.428489\pi\) | ||||
0.222773 | + | 0.974870i | \(0.428489\pi\) | |||||||
\(314\) | −3.70598e7 | −0.0675538 | ||||||||
\(315\) | −2.88324e8 | −0.519749 | ||||||||
\(316\) | 2.51845e8 | 0.448982 | ||||||||
\(317\) | 5.09923e8 | 0.899078 | 0.449539 | − | 0.893261i | \(-0.351588\pi\) | ||||
0.449539 | + | 0.893261i | \(0.351588\pi\) | |||||||
\(318\) | −2.73954e7 | −0.0477730 | ||||||||
\(319\) | 5.91622e8 | 1.02042 | ||||||||
\(320\) | 8.45565e7 | 0.144252 | ||||||||
\(321\) | −2.30245e8 | −0.388529 | ||||||||
\(322\) | −9.70570e7 | −0.162006 | ||||||||
\(323\) | 6.09005e8 | 1.00557 | ||||||||
\(324\) | 3.40122e7 | 0.0555556 | ||||||||
\(325\) | −2.68292e8 | −0.433526 | ||||||||
\(326\) | 3.98708e7 | 0.0637372 | ||||||||
\(327\) | −1.95769e8 | −0.309618 | ||||||||
\(328\) | −2.42991e8 | −0.380217 | ||||||||
\(329\) | −4.69282e8 | −0.726522 | ||||||||
\(330\) | −3.73318e8 | −0.571847 | ||||||||
\(331\) | −8.63343e8 | −1.30854 | −0.654268 | − | 0.756263i | \(-0.727023\pi\) | ||||
−0.654268 | + | 0.756263i | \(0.727023\pi\) | |||||||
\(332\) | −2.74341e8 | −0.411441 | ||||||||
\(333\) | −2.87373e8 | −0.426472 | ||||||||
\(334\) | 7.09890e8 | 1.04251 | ||||||||
\(335\) | 4.96216e8 | 0.721130 | ||||||||
\(336\) | −1.35603e8 | −0.195021 | ||||||||
\(337\) | −7.48761e8 | −1.06571 | −0.532854 | − | 0.846207i | \(-0.678881\pi\) | ||||
−0.532854 | + | 0.846207i | \(0.678881\pi\) | |||||||
\(338\) | 3.55228e8 | 0.500379 | ||||||||
\(339\) | −6.36868e8 | −0.887872 | ||||||||
\(340\) | 4.20173e8 | 0.579765 | ||||||||
\(341\) | 9.99028e8 | 1.36439 | ||||||||
\(342\) | 1.74501e8 | 0.235888 | ||||||||
\(343\) | 1.76110e8 | 0.235643 | ||||||||
\(344\) | −2.16609e8 | −0.286894 | ||||||||
\(345\) | 8.61712e7 | 0.112978 | ||||||||
\(346\) | −2.21033e8 | −0.286873 | ||||||||
\(347\) | 4.18560e7 | 0.0537780 | 0.0268890 | − | 0.999638i | \(-0.491440\pi\) | ||||
0.0268890 | + | 0.999638i | \(0.491440\pi\) | |||||||
\(348\) | −1.90797e8 | −0.242685 | ||||||||
\(349\) | 1.12818e9 | 1.42065 | 0.710327 | − | 0.703872i | \(-0.248547\pi\) | ||||
0.710327 | + | 0.703872i | \(0.248547\pi\) | |||||||
\(350\) | −2.54239e8 | −0.316960 | ||||||||
\(351\) | −2.03747e8 | −0.251488 | ||||||||
\(352\) | −1.75577e8 | −0.214570 | ||||||||
\(353\) | 6.63700e8 | 0.803083 | 0.401542 | − | 0.915841i | \(-0.368475\pi\) | ||||
0.401542 | + | 0.915841i | \(0.368475\pi\) | |||||||
\(354\) | 4.43619e7 | 0.0531494 | ||||||||
\(355\) | −1.91093e9 | −2.26697 | ||||||||
\(356\) | −3.01540e8 | −0.354217 | ||||||||
\(357\) | −6.73830e8 | −0.783812 | ||||||||
\(358\) | 2.81649e8 | 0.324427 | ||||||||
\(359\) | 1.27993e9 | 1.46001 | 0.730005 | − | 0.683441i | \(-0.239517\pi\) | ||||
0.730005 | + | 0.683441i | \(0.239517\pi\) | |||||||
\(360\) | 1.20394e8 | 0.136002 | ||||||||
\(361\) | 1.40957e6 | 0.00157693 | ||||||||
\(362\) | 1.42893e8 | 0.158318 | ||||||||
\(363\) | 2.49020e8 | 0.273251 | ||||||||
\(364\) | 8.12318e8 | 0.882818 | ||||||||
\(365\) | −8.00003e8 | −0.861126 | ||||||||
\(366\) | −3.50950e7 | −0.0374164 | ||||||||
\(367\) | −7.43725e8 | −0.785382 | −0.392691 | − | 0.919670i | \(-0.628456\pi\) | ||||
−0.392691 | + | 0.919670i | \(0.628456\pi\) | |||||||
\(368\) | 4.05276e7 | 0.0423920 | ||||||||
\(369\) | −3.45977e8 | −0.358472 | ||||||||
\(370\) | −1.01722e9 | −1.04402 | ||||||||
\(371\) | 1.55514e8 | 0.158111 | ||||||||
\(372\) | −3.22184e8 | −0.324491 | ||||||||
\(373\) | −7.18516e8 | −0.716895 | −0.358448 | − | 0.933550i | \(-0.616694\pi\) | ||||
−0.358448 | + | 0.933550i | \(0.616694\pi\) | |||||||
\(374\) | −8.72466e8 | −0.862379 | ||||||||
\(375\) | −4.54671e8 | −0.445233 | ||||||||
\(376\) | 1.95956e8 | 0.190108 | ||||||||
\(377\) | 1.14295e9 | 1.09858 | ||||||||
\(378\) | −1.93075e8 | −0.183868 | ||||||||
\(379\) | −2.01382e9 | −1.90013 | −0.950066 | − | 0.312050i | \(-0.898984\pi\) | ||||
−0.950066 | + | 0.312050i | \(0.898984\pi\) | |||||||
\(380\) | 6.17685e8 | 0.577463 | ||||||||
\(381\) | 3.43181e8 | 0.317897 | ||||||||
\(382\) | 1.45067e9 | 1.33152 | ||||||||
\(383\) | 1.25647e9 | 1.14276 | 0.571380 | − | 0.820686i | \(-0.306408\pi\) | ||||
0.571380 | + | 0.820686i | \(0.306408\pi\) | |||||||
\(384\) | 5.66231e7 | 0.0510310 | ||||||||
\(385\) | 2.11919e9 | 1.89260 | ||||||||
\(386\) | −8.29683e8 | −0.734271 | ||||||||
\(387\) | −3.08414e8 | −0.270486 | ||||||||
\(388\) | 8.10802e8 | 0.704699 | ||||||||
\(389\) | 8.28001e8 | 0.713193 | 0.356597 | − | 0.934258i | \(-0.383937\pi\) | ||||
0.356597 | + | 0.934258i | \(0.383937\pi\) | |||||||
\(390\) | −7.21209e8 | −0.615652 | ||||||||
\(391\) | 2.01387e8 | 0.170378 | ||||||||
\(392\) | 3.48117e8 | 0.291893 | ||||||||
\(393\) | −3.42709e7 | −0.0284808 | ||||||||
\(394\) | −2.85320e8 | −0.235015 | ||||||||
\(395\) | 1.26929e9 | 1.03627 | ||||||||
\(396\) | −2.49991e8 | −0.202298 | ||||||||
\(397\) | 8.08343e8 | 0.648379 | 0.324190 | − | 0.945992i | \(-0.394908\pi\) | ||||
0.324190 | + | 0.945992i | \(0.394908\pi\) | |||||||
\(398\) | 1.13045e9 | 0.898792 | ||||||||
\(399\) | −9.90579e8 | −0.780700 | ||||||||
\(400\) | 1.06161e8 | 0.0829387 | ||||||||
\(401\) | 2.78432e8 | 0.215632 | 0.107816 | − | 0.994171i | \(-0.465614\pi\) | ||||
0.107816 | + | 0.994171i | \(0.465614\pi\) | |||||||
\(402\) | 3.32290e8 | 0.255109 | ||||||||
\(403\) | 1.93001e9 | 1.46890 | ||||||||
\(404\) | 6.79903e8 | 0.512994 | ||||||||
\(405\) | 1.71420e8 | 0.128224 | ||||||||
\(406\) | 1.08309e9 | 0.803196 | ||||||||
\(407\) | 2.11220e9 | 1.55294 | ||||||||
\(408\) | 2.81368e8 | 0.205099 | ||||||||
\(409\) | 4.22442e8 | 0.305306 | 0.152653 | − | 0.988280i | \(-0.451218\pi\) | ||||
0.152653 | + | 0.988280i | \(0.451218\pi\) | |||||||
\(410\) | −1.22467e9 | −0.877554 | ||||||||
\(411\) | −2.82762e8 | −0.200898 | ||||||||
\(412\) | 4.02581e8 | 0.283605 | ||||||||
\(413\) | −2.51827e8 | −0.175904 | ||||||||
\(414\) | 5.77043e7 | 0.0399675 | ||||||||
\(415\) | −1.38267e9 | −0.949620 | ||||||||
\(416\) | −3.39196e8 | −0.231006 | ||||||||
\(417\) | −1.98719e8 | −0.134204 | ||||||||
\(418\) | −1.28259e9 | −0.858955 | ||||||||
\(419\) | 2.24349e8 | 0.148996 | 0.0744982 | − | 0.997221i | \(-0.476265\pi\) | ||||
0.0744982 | + | 0.997221i | \(0.476265\pi\) | |||||||
\(420\) | −6.83434e8 | −0.450116 | ||||||||
\(421\) | 1.77468e9 | 1.15913 | 0.579565 | − | 0.814926i | \(-0.303222\pi\) | ||||
0.579565 | + | 0.814926i | \(0.303222\pi\) | |||||||
\(422\) | −6.19422e8 | −0.401230 | ||||||||
\(423\) | 2.79008e8 | 0.179236 | ||||||||
\(424\) | −6.49372e7 | −0.0413726 | ||||||||
\(425\) | 5.27531e8 | 0.333340 | ||||||||
\(426\) | −1.27965e9 | −0.801969 | ||||||||
\(427\) | 1.99222e8 | 0.123834 | ||||||||
\(428\) | −5.45766e8 | −0.336476 | ||||||||
\(429\) | 1.49755e9 | 0.915759 | ||||||||
\(430\) | −1.09170e9 | −0.662161 | ||||||||
\(431\) | 3.12710e9 | 1.88136 | 0.940679 | − | 0.339297i | \(-0.110189\pi\) | ||||
0.940679 | + | 0.339297i | \(0.110189\pi\) | |||||||
\(432\) | 8.06216e7 | 0.0481125 | ||||||||
\(433\) | 4.54242e8 | 0.268893 | 0.134446 | − | 0.990921i | \(-0.457074\pi\) | ||||
0.134446 | + | 0.990921i | \(0.457074\pi\) | |||||||
\(434\) | 1.82892e9 | 1.07394 | ||||||||
\(435\) | −9.61607e8 | −0.560126 | ||||||||
\(436\) | −4.64045e8 | −0.268137 | ||||||||
\(437\) | 2.96054e8 | 0.169702 | ||||||||
\(438\) | −5.35720e8 | −0.304634 | ||||||||
\(439\) | 6.63917e8 | 0.374531 | 0.187266 | − | 0.982309i | \(-0.440037\pi\) | ||||
0.187266 | + | 0.982309i | \(0.440037\pi\) | |||||||
\(440\) | −8.84901e8 | −0.495234 | ||||||||
\(441\) | 4.95658e8 | 0.275199 | ||||||||
\(442\) | −1.68551e9 | −0.928439 | ||||||||
\(443\) | −3.29437e9 | −1.80036 | −0.900180 | − | 0.435517i | \(-0.856565\pi\) | ||||
−0.900180 | + | 0.435517i | \(0.856565\pi\) | |||||||
\(444\) | −6.81180e8 | −0.369336 | ||||||||
\(445\) | −1.51975e9 | −0.817546 | ||||||||
\(446\) | −9.37026e8 | −0.500126 | ||||||||
\(447\) | −1.41434e8 | −0.0748994 | ||||||||
\(448\) | −3.21429e8 | −0.168893 | ||||||||
\(449\) | 1.96325e9 | 1.02356 | 0.511779 | − | 0.859117i | \(-0.328987\pi\) | ||||
0.511779 | + | 0.859117i | \(0.328987\pi\) | |||||||
\(450\) | 1.51156e8 | 0.0781953 | ||||||||
\(451\) | 2.54295e9 | 1.30533 | ||||||||
\(452\) | −1.50961e9 | −0.768920 | ||||||||
\(453\) | 7.26981e8 | 0.367434 | ||||||||
\(454\) | 9.88880e8 | 0.495962 | ||||||||
\(455\) | 4.09405e9 | 2.03757 | ||||||||
\(456\) | 4.13631e8 | 0.204285 | ||||||||
\(457\) | 1.93867e9 | 0.950160 | 0.475080 | − | 0.879943i | \(-0.342419\pi\) | ||||
0.475080 | + | 0.879943i | \(0.342419\pi\) | |||||||
\(458\) | −5.50652e7 | −0.0267823 | ||||||||
\(459\) | 4.00620e8 | 0.193369 | ||||||||
\(460\) | 2.04258e8 | 0.0978421 | ||||||||
\(461\) | −1.69548e9 | −0.806009 | −0.403005 | − | 0.915198i | \(-0.632034\pi\) | ||||
−0.403005 | + | 0.915198i | \(0.632034\pi\) | |||||||
\(462\) | 1.41911e9 | 0.669530 | ||||||||
\(463\) | −5.76366e8 | −0.269876 | −0.134938 | − | 0.990854i | \(-0.543084\pi\) | ||||
−0.134938 | + | 0.990854i | \(0.543084\pi\) | |||||||
\(464\) | −4.52259e8 | −0.210172 | ||||||||
\(465\) | −1.62379e9 | −0.748937 | ||||||||
\(466\) | −2.54672e9 | −1.16582 | ||||||||
\(467\) | −1.46753e9 | −0.666771 | −0.333385 | − | 0.942791i | \(-0.608191\pi\) | ||||
−0.333385 | + | 0.942791i | \(0.608191\pi\) | |||||||
\(468\) | −4.82956e8 | −0.217795 | ||||||||
\(469\) | −1.88629e9 | −0.844315 | ||||||||
\(470\) | 9.87610e8 | 0.438776 | ||||||||
\(471\) | −1.25077e8 | −0.0551574 | ||||||||
\(472\) | 1.05154e8 | 0.0460287 | ||||||||
\(473\) | 2.26686e9 | 0.984941 | ||||||||
\(474\) | 8.49978e8 | 0.366592 | ||||||||
\(475\) | 7.75509e8 | 0.332016 | ||||||||
\(476\) | −1.59723e9 | −0.678801 | ||||||||
\(477\) | −9.24594e7 | −0.0390065 | ||||||||
\(478\) | 7.30612e8 | 0.305977 | ||||||||
\(479\) | 3.66657e9 | 1.52435 | 0.762177 | − | 0.647369i | \(-0.224131\pi\) | ||||
0.762177 | + | 0.647369i | \(0.224131\pi\) | |||||||
\(480\) | 2.85378e8 | 0.117781 | ||||||||
\(481\) | 4.08055e9 | 1.67190 | ||||||||
\(482\) | 2.62270e9 | 1.06680 | ||||||||
\(483\) | −3.27567e8 | −0.132277 | ||||||||
\(484\) | 5.90270e8 | 0.236642 | ||||||||
\(485\) | 4.08641e9 | 1.62647 | ||||||||
\(486\) | 1.14791e8 | 0.0453609 | ||||||||
\(487\) | −3.75489e9 | −1.47315 | −0.736573 | − | 0.676358i | \(-0.763557\pi\) | ||||
−0.736573 | + | 0.676358i | \(0.763557\pi\) | |||||||
\(488\) | −8.31882e7 | −0.0324035 | ||||||||
\(489\) | 1.34564e8 | 0.0520412 | ||||||||
\(490\) | 1.75449e9 | 0.673699 | ||||||||
\(491\) | 4.00343e9 | 1.52633 | 0.763163 | − | 0.646206i | \(-0.223645\pi\) | ||||
0.763163 | + | 0.646206i | \(0.223645\pi\) | |||||||
\(492\) | −8.20095e8 | −0.310446 | ||||||||
\(493\) | −2.24734e9 | −0.844702 | ||||||||
\(494\) | −2.47782e9 | −0.924753 | ||||||||
\(495\) | −1.25995e9 | −0.466911 | ||||||||
\(496\) | −7.63695e8 | −0.281018 | ||||||||
\(497\) | 7.26412e9 | 2.65421 | ||||||||
\(498\) | −9.25902e8 | −0.335940 | ||||||||
\(499\) | −3.91834e9 | −1.41173 | −0.705863 | − | 0.708348i | \(-0.749441\pi\) | ||||
−0.705863 | + | 0.708348i | \(0.749441\pi\) | |||||||
\(500\) | −1.07774e9 | −0.385583 | ||||||||
\(501\) | 2.39588e9 | 0.851202 | ||||||||
\(502\) | −3.85201e9 | −1.35902 | ||||||||
\(503\) | −3.88903e9 | −1.36255 | −0.681276 | − | 0.732027i | \(-0.738575\pi\) | ||||
−0.681276 | + | 0.732027i | \(0.738575\pi\) | |||||||
\(504\) | −4.57660e8 | −0.159234 | ||||||||
\(505\) | 3.42668e9 | 1.18401 | ||||||||
\(506\) | −4.24130e8 | −0.145536 | ||||||||
\(507\) | 1.19890e9 | 0.408558 | ||||||||
\(508\) | 8.13466e8 | 0.275306 | ||||||||
\(509\) | −3.25729e9 | −1.09482 | −0.547411 | − | 0.836864i | \(-0.684387\pi\) | ||||
−0.547411 | + | 0.836864i | \(0.684387\pi\) | |||||||
\(510\) | 1.41808e9 | 0.473376 | ||||||||
\(511\) | 3.04110e9 | 1.00822 | ||||||||
\(512\) | 1.34218e8 | 0.0441942 | ||||||||
\(513\) | 5.88940e8 | 0.192602 | ||||||||
\(514\) | −4.92962e8 | −0.160119 | ||||||||
\(515\) | 2.02899e9 | 0.654569 | ||||||||
\(516\) | −7.31055e8 | −0.234248 | ||||||||
\(517\) | −2.05072e9 | −0.652664 | ||||||||
\(518\) | 3.86682e9 | 1.22236 | ||||||||
\(519\) | −7.45985e8 | −0.234231 | ||||||||
\(520\) | −1.70953e9 | −0.533170 | ||||||||
\(521\) | −2.44271e9 | −0.756727 | −0.378363 | − | 0.925657i | \(-0.623513\pi\) | ||||
−0.378363 | + | 0.925657i | \(0.623513\pi\) | |||||||
\(522\) | −6.43939e8 | −0.198152 | ||||||||
\(523\) | 4.46703e9 | 1.36541 | 0.682705 | − | 0.730695i | \(-0.260804\pi\) | ||||
0.682705 | + | 0.730695i | \(0.260804\pi\) | |||||||
\(524\) | −8.12348e7 | −0.0246651 | ||||||||
\(525\) | −8.58058e8 | −0.258797 | ||||||||
\(526\) | 1.29504e9 | 0.388002 | ||||||||
\(527\) | −3.79490e9 | −1.12944 | ||||||||
\(528\) | −5.92572e8 | −0.175195 | ||||||||
\(529\) | −3.30693e9 | −0.971247 | ||||||||
\(530\) | −3.27281e8 | −0.0954894 | ||||||||
\(531\) | 1.49721e8 | 0.0433963 | ||||||||
\(532\) | −2.34804e9 | −0.676106 | ||||||||
\(533\) | 4.91270e9 | 1.40532 | ||||||||
\(534\) | −1.01770e9 | −0.289217 | ||||||||
\(535\) | −2.75064e9 | −0.776597 | ||||||||
\(536\) | 7.87650e8 | 0.220931 | ||||||||
\(537\) | 9.50564e8 | 0.264894 | ||||||||
\(538\) | 9.54276e8 | 0.264202 | ||||||||
\(539\) | −3.64311e9 | −1.00210 | ||||||||
\(540\) | 4.06330e8 | 0.111045 | ||||||||
\(541\) | −2.69368e9 | −0.731402 | −0.365701 | − | 0.930732i | \(-0.619171\pi\) | ||||
−0.365701 | + | 0.930732i | \(0.619171\pi\) | |||||||
\(542\) | 3.72626e9 | 1.00525 | ||||||||
\(543\) | 4.82263e8 | 0.129266 | ||||||||
\(544\) | 6.66946e8 | 0.177621 | ||||||||
\(545\) | −2.33877e9 | −0.618870 | ||||||||
\(546\) | 2.74157e9 | 0.720818 | ||||||||
\(547\) | 5.19290e9 | 1.35661 | 0.678304 | − | 0.734782i | \(-0.262715\pi\) | ||||
0.678304 | + | 0.734782i | \(0.262715\pi\) | |||||||
\(548\) | −6.70251e8 | −0.173982 | ||||||||
\(549\) | −1.18446e8 | −0.0305503 | ||||||||
\(550\) | −1.11100e9 | −0.284738 | ||||||||
\(551\) | −3.30375e9 | −0.841349 | ||||||||
\(552\) | 1.36781e8 | 0.0346129 | ||||||||
\(553\) | −4.82502e9 | −1.21328 | ||||||||
\(554\) | 1.61636e8 | 0.0403882 | ||||||||
\(555\) | −3.43312e9 | −0.852440 | ||||||||
\(556\) | −4.71039e8 | −0.116224 | ||||||||
\(557\) | 1.72219e9 | 0.422269 | 0.211134 | − | 0.977457i | \(-0.432284\pi\) | ||||
0.211134 | + | 0.977457i | \(0.432284\pi\) | |||||||
\(558\) | −1.08737e9 | −0.264946 | ||||||||
\(559\) | 4.37932e9 | 1.06039 | ||||||||
\(560\) | −1.61999e9 | −0.389812 | ||||||||
\(561\) | −2.94457e9 | −0.704129 | ||||||||
\(562\) | −3.25635e9 | −0.773846 | ||||||||
\(563\) | 1.40294e9 | 0.331329 | 0.165664 | − | 0.986182i | \(-0.447023\pi\) | ||||
0.165664 | + | 0.986182i | \(0.447023\pi\) | |||||||
\(564\) | 6.61351e8 | 0.155223 | ||||||||
\(565\) | −7.60839e9 | −1.77469 | ||||||||
\(566\) | −1.78151e9 | −0.412982 | ||||||||
\(567\) | −6.51630e8 | −0.150127 | ||||||||
\(568\) | −3.03324e9 | −0.694526 | ||||||||
\(569\) | −4.92673e9 | −1.12115 | −0.560577 | − | 0.828102i | \(-0.689421\pi\) | ||||
−0.560577 | + | 0.828102i | \(0.689421\pi\) | |||||||
\(570\) | 2.08469e9 | 0.471497 | ||||||||
\(571\) | 4.78084e8 | 0.107468 | 0.0537338 | − | 0.998555i | \(-0.482888\pi\) | ||||
0.0537338 | + | 0.998555i | \(0.482888\pi\) | |||||||
\(572\) | 3.54975e9 | 0.793071 | ||||||||
\(573\) | 4.89601e9 | 1.08718 | ||||||||
\(574\) | 4.65539e9 | 1.02746 | ||||||||
\(575\) | 2.56447e8 | 0.0562549 | ||||||||
\(576\) | 1.91103e8 | 0.0416667 | ||||||||
\(577\) | −3.05951e9 | −0.663034 | −0.331517 | − | 0.943449i | \(-0.607560\pi\) | ||||
−0.331517 | + | 0.943449i | \(0.607560\pi\) | |||||||
\(578\) | 3.14392e7 | 0.00677212 | ||||||||
\(579\) | −2.80018e9 | −0.599530 | ||||||||
\(580\) | −2.27937e9 | −0.485083 | ||||||||
\(581\) | 5.25602e9 | 1.11184 | ||||||||
\(582\) | 2.73646e9 | 0.575384 | ||||||||
\(583\) | 6.79581e8 | 0.142037 | ||||||||
\(584\) | −1.26986e9 | −0.263821 | ||||||||
\(585\) | −2.43408e9 | −0.502677 | ||||||||
\(586\) | −3.49960e9 | −0.718417 | ||||||||
\(587\) | 6.44785e8 | 0.131578 | 0.0657888 | − | 0.997834i | \(-0.479044\pi\) | ||||
0.0657888 | + | 0.997834i | \(0.479044\pi\) | |||||||
\(588\) | 1.17489e9 | 0.238330 | ||||||||
\(589\) | −5.57878e9 | −1.12496 | ||||||||
\(590\) | 5.29972e8 | 0.106236 | ||||||||
\(591\) | −9.62954e8 | −0.191889 | ||||||||
\(592\) | −1.61465e9 | −0.319854 | ||||||||
\(593\) | 6.38051e9 | 1.25650 | 0.628252 | − | 0.778010i | \(-0.283771\pi\) | ||||
0.628252 | + | 0.778010i | \(0.283771\pi\) | |||||||
\(594\) | −8.43721e8 | −0.165176 | ||||||||
\(595\) | −8.04996e9 | −1.56669 | ||||||||
\(596\) | −3.35252e8 | −0.0648648 | ||||||||
\(597\) | 3.81526e9 | 0.733861 | ||||||||
\(598\) | −8.19372e8 | −0.156685 | ||||||||
\(599\) | −2.32167e9 | −0.441373 | −0.220687 | − | 0.975345i | \(-0.570830\pi\) | ||||
−0.220687 | + | 0.975345i | \(0.570830\pi\) | |||||||
\(600\) | 3.58295e8 | 0.0677191 | ||||||||
\(601\) | −5.96090e9 | −1.12009 | −0.560043 | − | 0.828464i | \(-0.689215\pi\) | ||||
−0.560043 | + | 0.828464i | \(0.689215\pi\) | |||||||
\(602\) | 4.14994e9 | 0.775272 | ||||||||
\(603\) | 1.12148e9 | 0.208296 | ||||||||
\(604\) | 1.72321e9 | 0.318207 | ||||||||
\(605\) | 2.97494e9 | 0.546178 | ||||||||
\(606\) | 2.29467e9 | 0.418858 | ||||||||
\(607\) | −7.59139e9 | −1.37772 | −0.688860 | − | 0.724895i | \(-0.741888\pi\) | ||||
−0.688860 | + | 0.724895i | \(0.741888\pi\) | |||||||
\(608\) | 9.80460e8 | 0.176916 | ||||||||
\(609\) | 3.65541e9 | 0.655807 | ||||||||
\(610\) | −4.19265e8 | −0.0747884 | ||||||||
\(611\) | −3.96177e9 | −0.702659 | ||||||||
\(612\) | 9.49617e8 | 0.167463 | ||||||||
\(613\) | −6.19336e9 | −1.08596 | −0.542981 | − | 0.839745i | \(-0.682704\pi\) | ||||
−0.542981 | + | 0.839745i | \(0.682704\pi\) | |||||||
\(614\) | 6.66487e9 | 1.16199 | ||||||||
\(615\) | −4.13324e9 | −0.716520 | ||||||||
\(616\) | 3.36382e9 | 0.579830 | ||||||||
\(617\) | 9.17538e9 | 1.57263 | 0.786314 | − | 0.617827i | \(-0.211987\pi\) | ||||
0.786314 | + | 0.617827i | \(0.211987\pi\) | |||||||
\(618\) | 1.35871e9 | 0.231562 | ||||||||
\(619\) | 1.05282e9 | 0.178417 | 0.0892084 | − | 0.996013i | \(-0.471566\pi\) | ||||
0.0892084 | + | 0.996013i | \(0.471566\pi\) | |||||||
\(620\) | −3.84899e9 | −0.648599 | ||||||||
\(621\) | 1.94752e8 | 0.0326334 | ||||||||
\(622\) | −2.63798e9 | −0.439548 | ||||||||
\(623\) | 5.77711e9 | 0.957200 | ||||||||
\(624\) | −1.14479e9 | −0.188616 | ||||||||
\(625\) | −7.45663e9 | −1.22169 | ||||||||
\(626\) | 1.93370e9 | 0.315049 | ||||||||
\(627\) | −4.32874e9 | −0.701334 | ||||||||
\(628\) | −2.96479e8 | −0.0477677 | ||||||||
\(629\) | −8.02342e9 | −1.28553 | ||||||||
\(630\) | −2.30659e9 | −0.367518 | ||||||||
\(631\) | −7.36983e9 | −1.16776 | −0.583882 | − | 0.811839i | \(-0.698467\pi\) | ||||
−0.583882 | + | 0.811839i | \(0.698467\pi\) | |||||||
\(632\) | 2.01476e9 | 0.317478 | ||||||||
\(633\) | −2.09055e9 | −0.327603 | ||||||||
\(634\) | 4.07939e9 | 0.635744 | ||||||||
\(635\) | 4.09984e9 | 0.635417 | ||||||||
\(636\) | −2.19163e8 | −0.0337806 | ||||||||
\(637\) | −7.03810e9 | −1.07887 | ||||||||
\(638\) | 4.73298e9 | 0.721543 | ||||||||
\(639\) | −4.31882e9 | −0.654805 | ||||||||
\(640\) | 6.76452e8 | 0.102002 | ||||||||
\(641\) | 1.57655e9 | 0.236431 | 0.118216 | − | 0.992988i | \(-0.462283\pi\) | ||||
0.118216 | + | 0.992988i | \(0.462283\pi\) | |||||||
\(642\) | −1.84196e9 | −0.274731 | ||||||||
\(643\) | −8.94286e9 | −1.32659 | −0.663297 | − | 0.748356i | \(-0.730843\pi\) | ||||
−0.663297 | + | 0.748356i | \(0.730843\pi\) | |||||||
\(644\) | −7.76456e8 | −0.114556 | ||||||||
\(645\) | −3.68449e9 | −0.540652 | ||||||||
\(646\) | 4.87204e9 | 0.711045 | ||||||||
\(647\) | 1.24615e10 | 1.80886 | 0.904432 | − | 0.426617i | \(-0.140295\pi\) | ||||
0.904432 | + | 0.426617i | \(0.140295\pi\) | |||||||
\(648\) | 2.72098e8 | 0.0392837 | ||||||||
\(649\) | −1.10046e9 | −0.158022 | ||||||||
\(650\) | −2.14633e9 | −0.306549 | ||||||||
\(651\) | 6.17262e9 | 0.876871 | ||||||||
\(652\) | 3.18966e8 | 0.0450690 | ||||||||
\(653\) | −2.44833e9 | −0.344091 | −0.172045 | − | 0.985089i | \(-0.555038\pi\) | ||||
−0.172045 | + | 0.985089i | \(0.555038\pi\) | |||||||
\(654\) | −1.56615e9 | −0.218933 | ||||||||
\(655\) | −4.09420e8 | −0.0569278 | ||||||||
\(656\) | −1.94393e9 | −0.268854 | ||||||||
\(657\) | −1.80806e9 | −0.248733 | ||||||||
\(658\) | −3.75426e9 | −0.513728 | ||||||||
\(659\) | −1.99119e8 | −0.0271028 | −0.0135514 | − | 0.999908i | \(-0.504314\pi\) | ||||
−0.0135514 | + | 0.999908i | \(0.504314\pi\) | |||||||
\(660\) | −2.98654e9 | −0.404357 | ||||||||
\(661\) | 1.28846e10 | 1.73526 | 0.867630 | − | 0.497211i | \(-0.165642\pi\) | ||||
0.867630 | + | 0.497211i | \(0.165642\pi\) | |||||||
\(662\) | −6.90674e9 | −0.925274 | ||||||||
\(663\) | −5.68860e9 | −0.758067 | ||||||||
\(664\) | −2.19473e9 | −0.290933 | ||||||||
\(665\) | −1.18340e10 | −1.56048 | ||||||||
\(666\) | −2.29898e9 | −0.301562 | ||||||||
\(667\) | −1.09249e9 | −0.142553 | ||||||||
\(668\) | 5.67912e9 | 0.737163 | ||||||||
\(669\) | −3.16246e9 | −0.408352 | ||||||||
\(670\) | 3.96973e9 | 0.509916 | ||||||||
\(671\) | 8.70581e8 | 0.111245 | ||||||||
\(672\) | −1.08482e9 | −0.137901 | ||||||||
\(673\) | −3.87189e8 | −0.0489633 | −0.0244816 | − | 0.999700i | \(-0.507794\pi\) | ||||
−0.0244816 | + | 0.999700i | \(0.507794\pi\) | |||||||
\(674\) | −5.99009e9 | −0.753570 | ||||||||
\(675\) | 5.10151e8 | 0.0638462 | ||||||||
\(676\) | 2.84183e9 | 0.353821 | ||||||||
\(677\) | 4.34195e8 | 0.0537805 | 0.0268902 | − | 0.999638i | \(-0.491440\pi\) | ||||
0.0268902 | + | 0.999638i | \(0.491440\pi\) | |||||||
\(678\) | −5.09494e9 | −0.627820 | ||||||||
\(679\) | −1.55339e10 | −1.90430 | ||||||||
\(680\) | 3.36138e9 | 0.409956 | ||||||||
\(681\) | 3.33747e9 | 0.404951 | ||||||||
\(682\) | 7.99222e9 | 0.964766 | ||||||||
\(683\) | −1.36648e10 | −1.64109 | −0.820545 | − | 0.571582i | \(-0.806330\pi\) | ||||
−0.820545 | + | 0.571582i | \(0.806330\pi\) | |||||||
\(684\) | 1.39601e9 | 0.166798 | ||||||||
\(685\) | −3.37804e9 | −0.401557 | ||||||||
\(686\) | 1.40888e9 | 0.166625 | ||||||||
\(687\) | −1.85845e8 | −0.0218677 | ||||||||
\(688\) | −1.73287e9 | −0.202865 | ||||||||
\(689\) | 1.31288e9 | 0.152917 | ||||||||
\(690\) | 6.89369e8 | 0.0798877 | ||||||||
\(691\) | 7.90278e9 | 0.911185 | 0.455593 | − | 0.890188i | \(-0.349427\pi\) | ||||
0.455593 | + | 0.890188i | \(0.349427\pi\) | |||||||
\(692\) | −1.76826e9 | −0.202850 | ||||||||
\(693\) | 4.78951e9 | 0.546669 | ||||||||
\(694\) | 3.34848e8 | 0.0380268 | ||||||||
\(695\) | −2.37402e9 | −0.268248 | ||||||||
\(696\) | −1.52637e9 | −0.171604 | ||||||||
\(697\) | −9.65965e9 | −1.08055 | ||||||||
\(698\) | 9.02541e9 | 1.00455 | ||||||||
\(699\) | −8.59519e9 | −0.951887 | ||||||||
\(700\) | −2.03391e9 | −0.224125 | ||||||||
\(701\) | −1.58623e9 | −0.173922 | −0.0869610 | − | 0.996212i | \(-0.527716\pi\) | ||||
−0.0869610 | + | 0.996212i | \(0.527716\pi\) | |||||||
\(702\) | −1.62998e9 | −0.177829 | ||||||||
\(703\) | −1.17950e10 | −1.28043 | ||||||||
\(704\) | −1.40462e9 | −0.151724 | ||||||||
\(705\) | 3.33319e9 | 0.358259 | ||||||||
\(706\) | 5.30960e9 | 0.567866 | ||||||||
\(707\) | −1.30260e10 | −1.38626 | ||||||||
\(708\) | 3.54895e8 | 0.0375823 | ||||||||
\(709\) | −1.59906e10 | −1.68501 | −0.842505 | − | 0.538688i | \(-0.818920\pi\) | ||||
−0.842505 | + | 0.538688i | \(0.818920\pi\) | |||||||
\(710\) | −1.52874e10 | −1.60299 | ||||||||
\(711\) | 2.86868e9 | 0.299321 | ||||||||
\(712\) | −2.41232e9 | −0.250470 | ||||||||
\(713\) | −1.84481e9 | −0.190606 | ||||||||
\(714\) | −5.39064e9 | −0.554239 | ||||||||
\(715\) | 1.78906e10 | 1.83043 | ||||||||
\(716\) | 2.25319e9 | 0.229405 | ||||||||
\(717\) | 2.46581e9 | 0.249829 | ||||||||
\(718\) | 1.02395e10 | 1.03238 | ||||||||
\(719\) | −1.65500e10 | −1.66053 | −0.830264 | − | 0.557371i | \(-0.811810\pi\) | ||||
−0.830264 | + | 0.557371i | \(0.811810\pi\) | |||||||
\(720\) | 9.63151e8 | 0.0961681 | ||||||||
\(721\) | −7.71293e9 | −0.766383 | ||||||||
\(722\) | 1.12766e7 | 0.00111506 | ||||||||
\(723\) | 8.85160e9 | 0.871039 | ||||||||
\(724\) | 1.14314e9 | 0.111948 | ||||||||
\(725\) | −2.86176e9 | −0.278902 | ||||||||
\(726\) | 1.99216e9 | 0.193218 | ||||||||
\(727\) | 1.62431e10 | 1.56783 | 0.783915 | − | 0.620869i | \(-0.213220\pi\) | ||||
0.783915 | + | 0.620869i | \(0.213220\pi\) | |||||||
\(728\) | 6.49854e9 | 0.624246 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | −6.40002e9 | −0.608908 | ||||||||
\(731\) | −8.61088e9 | −0.815336 | ||||||||
\(732\) | −2.80760e8 | −0.0264574 | ||||||||
\(733\) | 1.38947e10 | 1.30312 | 0.651561 | − | 0.758596i | \(-0.274115\pi\) | ||||
0.651561 | + | 0.758596i | \(0.274115\pi\) | |||||||
\(734\) | −5.94980e9 | −0.555349 | ||||||||
\(735\) | 5.92142e9 | 0.550073 | ||||||||
\(736\) | 3.24221e8 | 0.0299756 | ||||||||
\(737\) | −8.24292e9 | −0.758482 | ||||||||
\(738\) | −2.76782e9 | −0.253478 | ||||||||
\(739\) | −8.35461e9 | −0.761501 | −0.380750 | − | 0.924678i | \(-0.624334\pi\) | ||||
−0.380750 | + | 0.924678i | \(0.624334\pi\) | |||||||
\(740\) | −8.13777e9 | −0.738235 | ||||||||
\(741\) | −8.36265e9 | −0.755058 | ||||||||
\(742\) | 1.24411e9 | 0.111801 | ||||||||
\(743\) | 1.96752e10 | 1.75978 | 0.879889 | − | 0.475179i | \(-0.157617\pi\) | ||||
0.879889 | + | 0.475179i | \(0.157617\pi\) | |||||||
\(744\) | −2.57747e9 | −0.229450 | ||||||||
\(745\) | −1.68966e9 | −0.149710 | ||||||||
\(746\) | −5.74813e9 | −0.506922 | ||||||||
\(747\) | −3.12492e9 | −0.274294 | ||||||||
\(748\) | −6.97973e9 | −0.609794 | ||||||||
\(749\) | 1.04562e10 | 0.909256 | ||||||||
\(750\) | −3.63736e9 | −0.314827 | ||||||||
\(751\) | −7.23538e9 | −0.623335 | −0.311668 | − | 0.950191i | \(-0.600888\pi\) | ||||
−0.311668 | + | 0.950191i | \(0.600888\pi\) | |||||||
\(752\) | 1.56765e9 | 0.134427 | ||||||||
\(753\) | −1.30006e10 | −1.10963 | ||||||||
\(754\) | 9.14360e9 | 0.776815 | ||||||||
\(755\) | 8.68493e9 | 0.734433 | ||||||||
\(756\) | −1.54460e9 | −0.130014 | ||||||||
\(757\) | 5.60569e9 | 0.469671 | 0.234836 | − | 0.972035i | \(-0.424545\pi\) | ||||
0.234836 | + | 0.972035i | \(0.424545\pi\) | |||||||
\(758\) | −1.61106e10 | −1.34360 | ||||||||
\(759\) | −1.43144e9 | −0.118830 | ||||||||
\(760\) | 4.94148e9 | 0.408328 | ||||||||
\(761\) | 1.97229e10 | 1.62228 | 0.811139 | − | 0.584853i | \(-0.198848\pi\) | ||||
0.811139 | + | 0.584853i | \(0.198848\pi\) | |||||||
\(762\) | 2.74545e9 | 0.224787 | ||||||||
\(763\) | 8.89049e9 | 0.724586 | ||||||||
\(764\) | 1.16054e10 | 0.941525 | ||||||||
\(765\) | 4.78603e9 | 0.386510 | ||||||||
\(766\) | 1.00517e10 | 0.808053 | ||||||||
\(767\) | −2.12597e9 | −0.170127 | ||||||||
\(768\) | 4.52985e8 | 0.0360844 | ||||||||
\(769\) | −4.89997e8 | −0.0388554 | −0.0194277 | − | 0.999811i | \(-0.506184\pi\) | ||||
−0.0194277 | + | 0.999811i | \(0.506184\pi\) | |||||||
\(770\) | 1.69535e10 | 1.33827 | ||||||||
\(771\) | −1.66375e9 | −0.130737 | ||||||||
\(772\) | −6.63746e9 | −0.519208 | ||||||||
\(773\) | 2.14868e10 | 1.67319 | 0.836593 | − | 0.547825i | \(-0.184544\pi\) | ||||
0.836593 | + | 0.547825i | \(0.184544\pi\) | |||||||
\(774\) | −2.46731e9 | −0.191263 | ||||||||
\(775\) | −4.83244e9 | −0.372916 | ||||||||
\(776\) | 6.48642e9 | 0.498298 | ||||||||
\(777\) | 1.30505e10 | 0.998054 | ||||||||
\(778\) | 6.62401e9 | 0.504304 | ||||||||
\(779\) | −1.42004e10 | −1.07626 | ||||||||
\(780\) | −5.76967e9 | −0.435331 | ||||||||
\(781\) | 3.17435e10 | 2.38439 | ||||||||
\(782\) | 1.61110e9 | 0.120475 | ||||||||
\(783\) | −2.17329e9 | −0.161790 | ||||||||
\(784\) | 2.78493e9 | 0.206399 | ||||||||
\(785\) | −1.49424e9 | −0.110250 | ||||||||
\(786\) | −2.74167e8 | −0.0201389 | ||||||||
\(787\) | 1.39897e9 | 0.102305 | 0.0511524 | − | 0.998691i | \(-0.483711\pi\) | ||||
0.0511524 | + | 0.998691i | \(0.483711\pi\) | |||||||
\(788\) | −2.28256e9 | −0.166180 | ||||||||
\(789\) | 4.37077e9 | 0.316803 | ||||||||
\(790\) | 1.01543e10 | 0.732751 | ||||||||
\(791\) | 2.89222e10 | 2.07785 | ||||||||
\(792\) | −1.99993e9 | −0.143046 | ||||||||
\(793\) | 1.68187e9 | 0.119767 | ||||||||
\(794\) | 6.46675e9 | 0.458473 | ||||||||
\(795\) | −1.10457e9 | −0.0779668 | ||||||||
\(796\) | 9.04357e9 | 0.635542 | ||||||||
\(797\) | −1.79920e10 | −1.25885 | −0.629425 | − | 0.777061i | \(-0.716710\pi\) | ||||
−0.629425 | + | 0.777061i | \(0.716710\pi\) | |||||||
\(798\) | −7.92463e9 | −0.552038 | ||||||||
\(799\) | 7.78986e9 | 0.540276 | ||||||||
\(800\) | 8.49292e8 | 0.0586465 | ||||||||
\(801\) | −3.43473e9 | −0.236145 | ||||||||
\(802\) | 2.22745e9 | 0.152475 | ||||||||
\(803\) | 1.32893e10 | 0.905728 | ||||||||
\(804\) | 2.65832e9 | 0.180389 | ||||||||
\(805\) | −3.91331e9 | −0.264398 | ||||||||
\(806\) | 1.54401e10 | 1.03867 | ||||||||
\(807\) | 3.22068e9 | 0.215720 | ||||||||
\(808\) | 5.43922e9 | 0.362741 | ||||||||
\(809\) | −2.09906e10 | −1.39382 | −0.696909 | − | 0.717160i | \(-0.745442\pi\) | ||||
−0.696909 | + | 0.717160i | \(0.745442\pi\) | |||||||
\(810\) | 1.37136e9 | 0.0906681 | ||||||||
\(811\) | −9.94254e8 | −0.0654522 | −0.0327261 | − | 0.999464i | \(-0.510419\pi\) | ||||
−0.0327261 | + | 0.999464i | \(0.510419\pi\) | |||||||
\(812\) | 8.66468e9 | 0.567945 | ||||||||
\(813\) | 1.25761e10 | 0.820786 | ||||||||
\(814\) | 1.68976e10 | 1.09810 | ||||||||
\(815\) | 1.60758e9 | 0.104021 | ||||||||
\(816\) | 2.25094e9 | 0.145027 | ||||||||
\(817\) | −1.26586e10 | −0.812099 | ||||||||
\(818\) | 3.37954e9 | 0.215884 | ||||||||
\(819\) | 9.25281e9 | 0.588545 | ||||||||
\(820\) | −9.79732e9 | −0.620524 | ||||||||
\(821\) | −1.54313e10 | −0.973197 | −0.486598 | − | 0.873626i | \(-0.661762\pi\) | ||||
−0.486598 | + | 0.873626i | \(0.661762\pi\) | |||||||
\(822\) | −2.26210e9 | −0.142056 | ||||||||
\(823\) | −9.46903e9 | −0.592115 | −0.296057 | − | 0.955170i | \(-0.595672\pi\) | ||||
−0.296057 | + | 0.955170i | \(0.595672\pi\) | |||||||
\(824\) | 3.22065e9 | 0.200539 | ||||||||
\(825\) | −3.74963e9 | −0.232488 | ||||||||
\(826\) | −2.01461e9 | −0.124383 | ||||||||
\(827\) | 2.36563e10 | 1.45438 | 0.727190 | − | 0.686436i | \(-0.240826\pi\) | ||||
0.727190 | + | 0.686436i | \(0.240826\pi\) | |||||||
\(828\) | 4.61635e8 | 0.0282613 | ||||||||
\(829\) | −1.69387e10 | −1.03262 | −0.516308 | − | 0.856403i | \(-0.672694\pi\) | ||||
−0.516308 | + | 0.856403i | \(0.672694\pi\) | |||||||
\(830\) | −1.10614e10 | −0.671483 | ||||||||
\(831\) | 5.45523e8 | 0.0329769 | ||||||||
\(832\) | −2.71356e9 | −0.163346 | ||||||||
\(833\) | 1.38387e10 | 0.829542 | ||||||||
\(834\) | −1.58976e9 | −0.0948962 | ||||||||
\(835\) | 2.86225e10 | 1.70140 | ||||||||
\(836\) | −1.02607e10 | −0.607373 | ||||||||
\(837\) | −3.66987e9 | −0.216328 | ||||||||
\(838\) | 1.79479e9 | 0.105356 | ||||||||
\(839\) | −2.22357e10 | −1.29982 | −0.649912 | − | 0.760010i | \(-0.725194\pi\) | ||||
−0.649912 | + | 0.760010i | \(0.725194\pi\) | |||||||
\(840\) | −5.46747e9 | −0.318280 | ||||||||
\(841\) | −5.05847e9 | −0.293247 | ||||||||
\(842\) | 1.41974e10 | 0.819629 | ||||||||
\(843\) | −1.09902e10 | −0.631842 | ||||||||
\(844\) | −4.95538e9 | −0.283712 | ||||||||
\(845\) | 1.43227e10 | 0.816632 | ||||||||
\(846\) | 2.23206e9 | 0.126739 | ||||||||
\(847\) | −1.13088e10 | −0.639477 | ||||||||
\(848\) | −5.19498e8 | −0.0292549 | ||||||||
\(849\) | −6.01260e9 | −0.337198 | ||||||||
\(850\) | 4.22025e9 | 0.235707 | ||||||||
\(851\) | −3.90040e9 | −0.216948 | ||||||||
\(852\) | −1.02372e10 | −0.567078 | ||||||||
\(853\) | 1.84144e10 | 1.01587 | 0.507933 | − | 0.861397i | \(-0.330410\pi\) | ||||
0.507933 | + | 0.861397i | \(0.330410\pi\) | |||||||
\(854\) | 1.59378e9 | 0.0875638 | ||||||||
\(855\) | 7.03582e9 | 0.384975 | ||||||||
\(856\) | −4.36613e9 | −0.237924 | ||||||||
\(857\) | −2.00335e10 | −1.08723 | −0.543617 | − | 0.839333i | \(-0.682946\pi\) | ||||
−0.543617 | + | 0.839333i | \(0.682946\pi\) | |||||||
\(858\) | 1.19804e10 | 0.647539 | ||||||||
\(859\) | −1.92592e10 | −1.03672 | −0.518360 | − | 0.855162i | \(-0.673457\pi\) | ||||
−0.518360 | + | 0.855162i | \(0.673457\pi\) | |||||||
\(860\) | −8.73360e9 | −0.468219 | ||||||||
\(861\) | 1.57119e10 | 0.838916 | ||||||||
\(862\) | 2.50168e10 | 1.33032 | ||||||||
\(863\) | −2.49169e10 | −1.31964 | −0.659820 | − | 0.751424i | \(-0.729368\pi\) | ||||
−0.659820 | + | 0.751424i | \(0.729368\pi\) | |||||||
\(864\) | 6.44973e8 | 0.0340207 | ||||||||
\(865\) | −8.91197e9 | −0.468185 | ||||||||
\(866\) | 3.63393e9 | 0.190136 | ||||||||
\(867\) | 1.06107e8 | 0.00552941 | ||||||||
\(868\) | 1.46314e10 | 0.759393 | ||||||||
\(869\) | −2.10849e10 | −1.08994 | ||||||||
\(870\) | −7.69286e9 | −0.396069 | ||||||||
\(871\) | −1.59244e10 | −0.816583 | ||||||||
\(872\) | −3.71236e9 | −0.189602 | ||||||||
\(873\) | 9.23554e9 | 0.469799 | ||||||||
\(874\) | 2.36843e9 | 0.119997 | ||||||||
\(875\) | 2.06480e10 | 1.04196 | ||||||||
\(876\) | −4.28576e9 | −0.215409 | ||||||||
\(877\) | −7.87530e9 | −0.394247 | −0.197124 | − | 0.980379i | \(-0.563160\pi\) | ||||
−0.197124 | + | 0.980379i | \(0.563160\pi\) | |||||||
\(878\) | 5.31134e9 | 0.264834 | ||||||||
\(879\) | −1.18111e10 | −0.586585 | ||||||||
\(880\) | −7.07921e9 | −0.350183 | ||||||||
\(881\) | 1.25524e9 | 0.0618460 | 0.0309230 | − | 0.999522i | \(-0.490155\pi\) | ||||
0.0309230 | + | 0.999522i | \(0.490155\pi\) | |||||||
\(882\) | 3.96527e9 | 0.194595 | ||||||||
\(883\) | −1.18621e10 | −0.579826 | −0.289913 | − | 0.957053i | \(-0.593626\pi\) | ||||
−0.289913 | + | 0.957053i | \(0.593626\pi\) | |||||||
\(884\) | −1.34841e10 | −0.656505 | ||||||||
\(885\) | 1.78866e9 | 0.0867412 | ||||||||
\(886\) | −2.63550e10 | −1.27305 | ||||||||
\(887\) | 3.32958e10 | 1.60198 | 0.800988 | − | 0.598680i | \(-0.204308\pi\) | ||||
0.800988 | + | 0.598680i | \(0.204308\pi\) | |||||||
\(888\) | −5.44944e9 | −0.261160 | ||||||||
\(889\) | −1.55849e10 | −0.743959 | ||||||||
\(890\) | −1.21580e10 | −0.578092 | ||||||||
\(891\) | −2.84756e9 | −0.134865 | ||||||||
\(892\) | −7.49621e9 | −0.353643 | ||||||||
\(893\) | 1.14517e10 | 0.538131 | ||||||||
\(894\) | −1.13147e9 | −0.0529619 | ||||||||
\(895\) | 1.13560e10 | 0.529474 | ||||||||
\(896\) | −2.57144e9 | −0.119426 | ||||||||
\(897\) | −2.76538e9 | −0.127933 | ||||||||
\(898\) | 1.57060e10 | 0.723765 | ||||||||
\(899\) | 2.05867e10 | 0.944991 | ||||||||
\(900\) | 1.20925e9 | 0.0552924 | ||||||||
\(901\) | −2.58146e9 | −0.117579 | ||||||||
\(902\) | 2.03436e10 | 0.923007 | ||||||||
\(903\) | 1.40061e10 | 0.633007 | ||||||||
\(904\) | −1.20769e10 | −0.543708 | ||||||||
\(905\) | 5.76139e9 | 0.258379 | ||||||||
\(906\) | 5.81585e9 | 0.259815 | ||||||||
\(907\) | 3.41140e10 | 1.51813 | 0.759063 | − | 0.651017i | \(-0.225658\pi\) | ||||
0.759063 | + | 0.651017i | \(0.225658\pi\) | |||||||
\(908\) | 7.91104e9 | 0.350698 | ||||||||
\(909\) | 7.74452e9 | 0.341996 | ||||||||
\(910\) | 3.27524e10 | 1.44078 | ||||||||
\(911\) | −9.72303e9 | −0.426076 | −0.213038 | − | 0.977044i | \(-0.568336\pi\) | ||||
−0.213038 | + | 0.977044i | \(0.568336\pi\) | |||||||
\(912\) | 3.30905e9 | 0.144451 | ||||||||
\(913\) | 2.29683e10 | 0.998806 | ||||||||
\(914\) | 1.55093e10 | 0.671865 | ||||||||
\(915\) | −1.41502e9 | −0.0610645 | ||||||||
\(916\) | −4.40522e8 | −0.0189380 | ||||||||
\(917\) | 1.55635e9 | 0.0666523 | ||||||||
\(918\) | 3.20496e9 | 0.136733 | ||||||||
\(919\) | −2.18969e10 | −0.930632 | −0.465316 | − | 0.885145i | \(-0.654059\pi\) | ||||
−0.465316 | + | 0.885145i | \(0.654059\pi\) | |||||||
\(920\) | 1.63406e9 | 0.0691848 | ||||||||
\(921\) | 2.24939e10 | 0.948761 | ||||||||
\(922\) | −1.35639e10 | −0.569935 | ||||||||
\(923\) | 6.13250e10 | 2.56703 | ||||||||
\(924\) | 1.13529e10 | 0.473429 | ||||||||
\(925\) | −1.02170e10 | −0.424453 | ||||||||
\(926\) | −4.61093e9 | −0.190831 | ||||||||
\(927\) | 4.58565e9 | 0.189070 | ||||||||
\(928\) | −3.61807e9 | −0.148614 | ||||||||
\(929\) | 2.68885e9 | 0.110030 | 0.0550152 | − | 0.998486i | \(-0.482479\pi\) | ||||
0.0550152 | + | 0.998486i | \(0.482479\pi\) | |||||||
\(930\) | −1.29903e10 | −0.529579 | ||||||||
\(931\) | 2.03439e10 | 0.826249 | ||||||||
\(932\) | −2.03738e10 | −0.824358 | ||||||||
\(933\) | −8.90320e9 | −0.358889 | ||||||||
\(934\) | −1.17402e10 | −0.471478 | ||||||||
\(935\) | −3.51776e10 | −1.40742 | ||||||||
\(936\) | −3.86365e9 | −0.154004 | ||||||||
\(937\) | −3.69169e10 | −1.46601 | −0.733004 | − | 0.680224i | \(-0.761882\pi\) | ||||
−0.733004 | + | 0.680224i | \(0.761882\pi\) | |||||||
\(938\) | −1.50903e10 | −0.597021 | ||||||||
\(939\) | 6.52623e9 | 0.257237 | ||||||||
\(940\) | 7.90088e9 | 0.310262 | ||||||||
\(941\) | −2.24060e10 | −0.876597 | −0.438298 | − | 0.898830i | \(-0.644419\pi\) | ||||
−0.438298 | + | 0.898830i | \(0.644419\pi\) | |||||||
\(942\) | −1.00062e9 | −0.0390022 | ||||||||
\(943\) | −4.69582e9 | −0.182356 | ||||||||
\(944\) | 8.41232e8 | 0.0325472 | ||||||||
\(945\) | −7.78474e9 | −0.300077 | ||||||||
\(946\) | 1.81349e10 | 0.696458 | ||||||||
\(947\) | 3.09991e10 | 1.18611 | 0.593053 | − | 0.805163i | \(-0.297922\pi\) | ||||
0.593053 | + | 0.805163i | \(0.297922\pi\) | |||||||
\(948\) | 6.79982e9 | 0.259220 | ||||||||
\(949\) | 2.56735e10 | 0.975109 | ||||||||
\(950\) | 6.20407e9 | 0.234771 | ||||||||
\(951\) | 1.37679e10 | 0.519083 | ||||||||
\(952\) | −1.27778e10 | −0.479985 | ||||||||
\(953\) | −2.38381e10 | −0.892169 | −0.446084 | − | 0.894991i | \(-0.647182\pi\) | ||||
−0.446084 | + | 0.894991i | \(0.647182\pi\) | |||||||
\(954\) | −7.39676e8 | −0.0275818 | ||||||||
\(955\) | 5.84906e10 | 2.17307 | ||||||||
\(956\) | 5.84489e9 | 0.216359 | ||||||||
\(957\) | 1.59738e10 | 0.589137 | ||||||||
\(958\) | 2.93326e10 | 1.07788 | ||||||||
\(959\) | 1.28411e10 | 0.470152 | ||||||||
\(960\) | 2.28303e9 | 0.0832840 | ||||||||
\(961\) | 7.25057e9 | 0.263536 | ||||||||
\(962\) | 3.26444e10 | 1.18221 | ||||||||
\(963\) | −6.21662e9 | −0.224317 | ||||||||
\(964\) | 2.09816e10 | 0.754342 | ||||||||
\(965\) | −3.34525e10 | −1.19835 | ||||||||
\(966\) | −2.62054e9 | −0.0935342 | ||||||||
\(967\) | 2.26067e10 | 0.803980 | 0.401990 | − | 0.915644i | \(-0.368319\pi\) | ||||
0.401990 | + | 0.915644i | \(0.368319\pi\) | |||||||
\(968\) | 4.72216e9 | 0.167331 | ||||||||
\(969\) | 1.64431e10 | 0.580566 | ||||||||
\(970\) | 3.26913e10 | 1.15009 | ||||||||
\(971\) | 1.48779e10 | 0.521524 | 0.260762 | − | 0.965403i | \(-0.416026\pi\) | ||||
0.260762 | + | 0.965403i | \(0.416026\pi\) | |||||||
\(972\) | 9.18330e8 | 0.0320750 | ||||||||
\(973\) | 9.02448e9 | 0.314071 | ||||||||
\(974\) | −3.00391e10 | −1.04167 | ||||||||
\(975\) | −7.24388e9 | −0.250297 | ||||||||
\(976\) | −6.65505e8 | −0.0229127 | ||||||||
\(977\) | −5.80549e10 | −1.99163 | −0.995814 | − | 0.0914033i | \(-0.970865\pi\) | ||||
−0.995814 | + | 0.0914033i | \(0.970865\pi\) | |||||||
\(978\) | 1.07651e9 | 0.0367987 | ||||||||
\(979\) | 2.52454e10 | 0.859891 | ||||||||
\(980\) | 1.40360e10 | 0.476377 | ||||||||
\(981\) | −5.28576e9 | −0.178758 | ||||||||
\(982\) | 3.20275e10 | 1.07928 | ||||||||
\(983\) | 3.18931e10 | 1.07093 | 0.535463 | − | 0.844559i | \(-0.320137\pi\) | ||||
0.535463 | + | 0.844559i | \(0.320137\pi\) | |||||||
\(984\) | −6.56076e9 | −0.219519 | ||||||||
\(985\) | −1.15040e10 | −0.383550 | ||||||||
\(986\) | −1.79787e10 | −0.597295 | ||||||||
\(987\) | −1.26706e10 | −0.419458 | ||||||||
\(988\) | −1.98226e10 | −0.653899 | ||||||||
\(989\) | −4.18598e9 | −0.137597 | ||||||||
\(990\) | −1.00796e10 | −0.330156 | ||||||||
\(991\) | 3.64453e10 | 1.18955 | 0.594777 | − | 0.803891i | \(-0.297240\pi\) | ||||
0.594777 | + | 0.803891i | \(0.297240\pi\) | |||||||
\(992\) | −6.10956e9 | −0.198710 | ||||||||
\(993\) | −2.33103e10 | −0.755483 | ||||||||
\(994\) | 5.81130e10 | 1.87681 | ||||||||
\(995\) | 4.55793e10 | 1.46685 | ||||||||
\(996\) | −7.40721e9 | −0.237546 | ||||||||
\(997\) | −6.66993e9 | −0.213151 | −0.106576 | − | 0.994305i | \(-0.533989\pi\) | ||||
−0.106576 | + | 0.994305i | \(0.533989\pi\) | |||||||
\(998\) | −3.13467e10 | −0.998241 | ||||||||
\(999\) | −7.75907e9 | −0.246224 |
(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 | 354.8.a.b.1.5 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
354.8.a.b.1.5 | ✓ | 5 | 1.1 | even | 1 | trivial |