Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [15,5,Mod(7,15)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("15.7");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.f (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.55054944626\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 60x^{5} + 1973x^{4} - 3300x^{3} + 1800x^{2} + 31560x + 276676 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 7.1 | ||
Root | \(-5.02811 - 5.02811i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 15.7 |
Dual form | 15.5.f.a.13.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(11\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.02811 | − | 5.02811i | −1.25703 | − | 1.25703i | −0.952505 | − | 0.304522i | \(-0.901503\pi\) |
−0.304522 | − | 0.952505i | \(-0.598497\pi\) | |||||||
\(3\) | −3.67423 | + | 3.67423i | −0.408248 | + | 0.408248i | ||||
\(4\) | 34.5637i | 2.16023i | ||||||||
\(5\) | −23.8949 | − | 7.35070i | −0.955797 | − | 0.294028i | ||||
\(6\) | 36.9489 | 1.02636 | ||||||||
\(7\) | −38.5593 | − | 38.5593i | −0.786924 | − | 0.786924i | 0.194065 | − | 0.980989i | \(-0.437833\pi\) |
−0.980989 | + | 0.194065i | \(0.937833\pi\) | |||||||
\(8\) | 93.3405 | − | 93.3405i | 1.45845 | − | 1.45845i | ||||
\(9\) | − | 27.0000i | − | 0.333333i | ||||||
\(10\) | 83.1861 | + | 157.106i | 0.831861 | + | 1.57106i | ||||
\(11\) | −40.4333 | −0.334160 | −0.167080 | − | 0.985943i | \(-0.553434\pi\) | ||||
−0.167080 | + | 0.985943i | \(0.553434\pi\) | |||||||
\(12\) | −126.995 | − | 126.995i | −0.881912 | − | 0.881912i | ||||
\(13\) | 20.8688 | − | 20.8688i | 0.123484 | − | 0.123484i | −0.642664 | − | 0.766148i | \(-0.722171\pi\) |
0.766148 | + | 0.642664i | \(0.222171\pi\) | |||||||
\(14\) | 387.760i | 1.97837i | ||||||||
\(15\) | 114.804 | − | 60.7873i | 0.510239 | − | 0.270166i | ||||
\(16\) | −385.633 | −1.50638 | ||||||||
\(17\) | 15.8713 | + | 15.8713i | 0.0549181 | + | 0.0549181i | 0.734032 | − | 0.679114i | \(-0.237636\pi\) |
−0.679114 | + | 0.734032i | \(0.737636\pi\) | |||||||
\(18\) | −135.759 | + | 135.759i | −0.419009 | + | 0.419009i | ||||
\(19\) | − | 314.926i | − | 0.872371i | −0.899857 | − | 0.436185i | \(-0.856329\pi\) | ||
0.899857 | − | 0.436185i | \(-0.143671\pi\) | |||||||
\(20\) | 254.068 | − | 825.898i | 0.635170 | − | 2.06474i | ||||
\(21\) | 283.352 | 0.642521 | ||||||||
\(22\) | 203.303 | + | 203.303i | 0.420048 | + | 0.420048i | ||||
\(23\) | −572.869 | + | 572.869i | −1.08293 | + | 1.08293i | −0.0866935 | + | 0.996235i | \(0.527630\pi\) |
−0.996235 | + | 0.0866935i | \(0.972370\pi\) | |||||||
\(24\) | 685.910i | 1.19082i | ||||||||
\(25\) | 516.934 | + | 351.289i | 0.827095 | + | 0.562062i | ||||
\(26\) | −209.862 | −0.310446 | ||||||||
\(27\) | 99.2043 | + | 99.2043i | 0.136083 | + | 0.136083i | ||||
\(28\) | 1332.75 | − | 1332.75i | 1.69994 | − | 1.69994i | ||||
\(29\) | − | 824.433i | − | 0.980301i | −0.871638 | − | 0.490151i | \(-0.836942\pi\) | ||
0.871638 | − | 0.490151i | \(-0.163058\pi\) | |||||||
\(30\) | −882.891 | − | 271.600i | −0.980990 | − | 0.301778i | ||||
\(31\) | −1347.19 | −1.40186 | −0.700931 | − | 0.713229i | \(-0.747232\pi\) | ||||
−0.700931 | + | 0.713229i | \(0.747232\pi\) | |||||||
\(32\) | 445.555 | + | 445.555i | 0.435112 | + | 0.435112i | ||||
\(33\) | 148.561 | − | 148.561i | 0.136420 | − | 0.136420i | ||||
\(34\) | − | 159.606i | − | 0.138067i | ||||||
\(35\) | 637.933 | + | 1204.81i | 0.520762 | + | 0.983517i | ||||
\(36\) | 933.221 | 0.720078 | ||||||||
\(37\) | −589.843 | − | 589.843i | −0.430857 | − | 0.430857i | 0.458063 | − | 0.888920i | \(-0.348543\pi\) |
−0.888920 | + | 0.458063i | \(0.848543\pi\) | |||||||
\(38\) | −1583.48 | + | 1583.48i | −1.09659 | + | 1.09659i | ||||
\(39\) | 153.354i | 0.100824i | ||||||||
\(40\) | −2916.48 | + | 1544.25i | −1.82280 | + | 0.965154i | ||||
\(41\) | 1856.55 | 1.10443 | 0.552215 | − | 0.833702i | \(-0.313783\pi\) | ||||
0.552215 | + | 0.833702i | \(0.313783\pi\) | |||||||
\(42\) | −1424.72 | − | 1424.72i | −0.807666 | − | 0.807666i | ||||
\(43\) | −671.078 | + | 671.078i | −0.362941 | + | 0.362941i | −0.864894 | − | 0.501954i | \(-0.832615\pi\) |
0.501954 | + | 0.864894i | \(0.332615\pi\) | |||||||
\(44\) | − | 1397.53i | − | 0.721863i | ||||||
\(45\) | −198.469 | + | 645.163i | −0.0980094 | + | 0.318599i | ||||
\(46\) | 5760.90 | 2.72254 | ||||||||
\(47\) | 504.865 | + | 504.865i | 0.228549 | + | 0.228549i | 0.812086 | − | 0.583537i | \(-0.198332\pi\) |
−0.583537 | + | 0.812086i | \(0.698332\pi\) | |||||||
\(48\) | 1416.91 | − | 1416.91i | 0.614976 | − | 0.614976i | ||||
\(49\) | 572.636i | 0.238499i | ||||||||
\(50\) | −832.883 | − | 4365.52i | −0.333153 | − | 1.74621i | ||||
\(51\) | −116.630 | −0.0448405 | ||||||||
\(52\) | 721.305 | + | 721.305i | 0.266755 | + | 0.266755i | ||||
\(53\) | 2251.32 | − | 2251.32i | 0.801468 | − | 0.801468i | −0.181857 | − | 0.983325i | \(-0.558211\pi\) |
0.983325 | + | 0.181857i | \(0.0582107\pi\) | |||||||
\(54\) | − | 997.620i | − | 0.342119i | ||||||
\(55\) | 966.151 | + | 297.213i | 0.319389 | + | 0.0982523i | ||||
\(56\) | −7198.29 | −2.29537 | ||||||||
\(57\) | 1157.11 | + | 1157.11i | 0.356144 | + | 0.356144i | ||||
\(58\) | −4145.34 | + | 4145.34i | −1.23227 | + | 1.23227i | ||||
\(59\) | − | 2585.03i | − | 0.742610i | −0.928511 | − | 0.371305i | \(-0.878910\pi\) | ||
0.928511 | − | 0.371305i | \(-0.121090\pi\) | |||||||
\(60\) | 2101.04 | + | 3968.05i | 0.583622 | + | 1.10224i | ||||
\(61\) | −3276.74 | −0.880607 | −0.440304 | − | 0.897849i | \(-0.645129\pi\) | ||||
−0.440304 | + | 0.897849i | \(0.645129\pi\) | |||||||
\(62\) | 6773.81 | + | 6773.81i | 1.76218 | + | 1.76218i | ||||
\(63\) | −1041.10 | + | 1041.10i | −0.262308 | + | 0.262308i | ||||
\(64\) | 1689.53i | 0.412483i | ||||||||
\(65\) | −652.060 | + | 345.259i | −0.154334 | + | 0.0817180i | ||||
\(66\) | −1493.97 | −0.342967 | ||||||||
\(67\) | −3428.94 | − | 3428.94i | −0.763854 | − | 0.763854i | 0.213163 | − | 0.977017i | \(-0.431624\pi\) |
−0.977017 | + | 0.213163i | \(0.931624\pi\) | |||||||
\(68\) | −548.573 | + | 548.573i | −0.118636 | + | 0.118636i | ||||
\(69\) | − | 4209.71i | − | 0.884207i | ||||||
\(70\) | 2850.31 | − | 9265.50i | 0.581696 | − | 1.89092i | ||||
\(71\) | −5679.51 | −1.12666 | −0.563331 | − | 0.826231i | \(-0.690481\pi\) | ||||
−0.563331 | + | 0.826231i | \(0.690481\pi\) | |||||||
\(72\) | −2520.19 | − | 2520.19i | −0.486149 | − | 0.486149i | ||||
\(73\) | 4450.06 | − | 4450.06i | 0.835065 | − | 0.835065i | −0.153140 | − | 0.988205i | \(-0.548939\pi\) |
0.988205 | + | 0.153140i | \(0.0489385\pi\) | |||||||
\(74\) | 5931.59i | 1.08320i | ||||||||
\(75\) | −3190.06 | + | 608.620i | −0.567121 | + | 0.108199i | ||||
\(76\) | 10885.0 | 1.88453 | ||||||||
\(77\) | 1559.08 | + | 1559.08i | 0.262958 | + | 0.262958i | ||||
\(78\) | 771.081 | − | 771.081i | 0.126739 | − | 0.126739i | ||||
\(79\) | 6465.77i | 1.03602i | 0.855376 | + | 0.518008i | \(0.173326\pi\) | ||||
−0.855376 | + | 0.518008i | \(0.826674\pi\) | |||||||
\(80\) | 9214.66 | + | 2834.67i | 1.43979 | + | 0.442918i | ||||
\(81\) | −729.000 | −0.111111 | ||||||||
\(82\) | −9334.92 | − | 9334.92i | −1.38830 | − | 1.38830i | ||||
\(83\) | −621.380 | + | 621.380i | −0.0901988 | + | 0.0901988i | −0.750766 | − | 0.660568i | \(-0.770316\pi\) |
0.660568 | + | 0.750766i | \(0.270316\pi\) | |||||||
\(84\) | 9793.70i | 1.38800i | ||||||||
\(85\) | −262.579 | − | 495.910i | −0.0363431 | − | 0.0686380i | ||||
\(86\) | 6748.50 | 0.912453 | ||||||||
\(87\) | 3029.16 | + | 3029.16i | 0.400206 | + | 0.400206i | ||||
\(88\) | −3774.07 | + | 3774.07i | −0.487354 | + | 0.487354i | ||||
\(89\) | − | 1856.76i | − | 0.234410i | −0.993108 | − | 0.117205i | \(-0.962606\pi\) | ||
0.993108 | − | 0.117205i | \(-0.0373935\pi\) | |||||||
\(90\) | 4241.87 | − | 2246.02i | 0.523688 | − | 0.277287i | ||||
\(91\) | −1609.37 | −0.194345 | ||||||||
\(92\) | −19800.5 | − | 19800.5i | −2.33938 | − | 2.33938i | ||||
\(93\) | 4949.89 | − | 4949.89i | 0.572308 | − | 0.572308i | ||||
\(94\) | − | 5077.03i | − | 0.574585i | ||||||
\(95\) | −2314.93 | + | 7525.13i | −0.256502 | + | 0.833809i | ||||
\(96\) | −3274.14 | −0.355267 | ||||||||
\(97\) | 12383.5 | + | 12383.5i | 1.31614 | + | 1.31614i | 0.916806 | + | 0.399332i | \(0.130758\pi\) |
0.399332 | + | 0.916806i | \(0.369242\pi\) | |||||||
\(98\) | 2879.27 | − | 2879.27i | 0.299800 | − | 0.299800i | ||||
\(99\) | 1091.70i | 0.111387i | ||||||||
\(100\) | −12141.9 | + | 17867.2i | −1.21419 | + | 1.78672i | ||||
\(101\) | −189.344 | −0.0185613 | −0.00928067 | − | 0.999957i | \(-0.502954\pi\) | ||||
−0.00928067 | + | 0.999957i | \(0.502954\pi\) | |||||||
\(102\) | 586.428 | + | 586.428i | 0.0563657 | + | 0.0563657i | ||||
\(103\) | 14330.9 | − | 14330.9i | 1.35083 | − | 1.35083i | 0.466092 | − | 0.884736i | \(-0.345662\pi\) |
0.884736 | − | 0.466092i | \(-0.154338\pi\) | |||||||
\(104\) | − | 3895.82i | − | 0.360190i | ||||||
\(105\) | −6770.67 | − | 2082.83i | −0.614119 | − | 0.188919i | ||||
\(106\) | −22639.8 | −2.01493 | ||||||||
\(107\) | −384.065 | − | 384.065i | −0.0335457 | − | 0.0335457i | 0.690135 | − | 0.723681i | \(-0.257551\pi\) |
−0.723681 | + | 0.690135i | \(0.757551\pi\) | |||||||
\(108\) | −3428.87 | + | 3428.87i | −0.293971 | + | 0.293971i | ||||
\(109\) | 14104.7i | 1.18717i | 0.804773 | + | 0.593583i | \(0.202287\pi\) | ||||
−0.804773 | + | 0.593583i | \(0.797713\pi\) | |||||||
\(110\) | −3363.49 | − | 6352.33i | −0.277974 | − | 0.524986i | ||||
\(111\) | 4334.44 | 0.351793 | ||||||||
\(112\) | 14869.7 | + | 14869.7i | 1.18540 | + | 1.18540i | ||||
\(113\) | −12599.1 | + | 12599.1i | −0.986693 | + | 0.986693i | −0.999913 | − | 0.0132199i | \(-0.995792\pi\) |
0.0132199 | + | 0.999913i | \(0.495792\pi\) | |||||||
\(114\) | − | 11636.2i | − | 0.895365i | ||||||
\(115\) | 17899.7 | − | 9477.67i | 1.35347 | − | 0.716648i | ||||
\(116\) | 28495.5 | 2.11768 | ||||||||
\(117\) | −563.459 | − | 563.459i | −0.0411614 | − | 0.0411614i | ||||
\(118\) | −12997.8 | + | 12997.8i | −0.933481 | + | 0.933481i | ||||
\(119\) | − | 1223.97i | − | 0.0864328i | ||||||
\(120\) | 5041.92 | − | 16389.8i | 0.350134 | − | 1.13818i | ||||
\(121\) | −13006.1 | −0.888337 | ||||||||
\(122\) | 16475.8 | + | 16475.8i | 1.10695 | + | 1.10695i | ||||
\(123\) | −6821.39 | + | 6821.39i | −0.450882 | + | 0.450882i | ||||
\(124\) | − | 46563.9i | − | 3.02835i | ||||||
\(125\) | −9769.88 | − | 12193.9i | −0.625272 | − | 0.780407i | ||||
\(126\) | 10469.5 | 0.659457 | ||||||||
\(127\) | −10957.5 | − | 10957.5i | −0.679367 | − | 0.679367i | 0.280490 | − | 0.959857i | \(-0.409503\pi\) |
−0.959857 | + | 0.280490i | \(0.909503\pi\) | |||||||
\(128\) | 15624.0 | − | 15624.0i | 0.953614 | − | 0.953614i | ||||
\(129\) | − | 4931.39i | − | 0.296340i | ||||||
\(130\) | 5014.63 | + | 1542.63i | 0.296723 | + | 0.0912799i | ||||
\(131\) | 10872.8 | 0.633579 | 0.316789 | − | 0.948496i | \(-0.397395\pi\) | ||||
0.316789 | + | 0.948496i | \(0.397395\pi\) | |||||||
\(132\) | 5134.84 | + | 5134.84i | 0.294699 | + | 0.294699i | ||||
\(133\) | −12143.3 | + | 12143.3i | −0.686489 | + | 0.686489i | ||||
\(134\) | 34482.2i | 1.92037i | ||||||||
\(135\) | −1641.26 | − | 3099.70i | −0.0900553 | − | 0.170080i | ||||
\(136\) | 2962.88 | 0.160190 | ||||||||
\(137\) | −3387.27 | − | 3387.27i | −0.180471 | − | 0.180471i | 0.611090 | − | 0.791561i | \(-0.290731\pi\) |
−0.791561 | + | 0.611090i | \(0.790731\pi\) | |||||||
\(138\) | −21166.9 | + | 21166.9i | −1.11147 | + | 1.11147i | ||||
\(139\) | − | 6096.09i | − | 0.315516i | −0.987478 | − | 0.157758i | \(-0.949573\pi\) | ||
0.987478 | − | 0.157758i | \(-0.0504266\pi\) | |||||||
\(140\) | −41642.7 | + | 22049.4i | −2.12463 | + | 1.12497i | ||||
\(141\) | −3709.98 | −0.186610 | ||||||||
\(142\) | 28557.2 | + | 28557.2i | 1.41625 | + | 1.41625i | ||||
\(143\) | −843.796 | + | 843.796i | −0.0412634 | + | 0.0412634i | ||||
\(144\) | 10412.1i | 0.502126i | ||||||||
\(145\) | −6060.17 | + | 19699.8i | −0.288236 | + | 0.936969i | ||||
\(146\) | −44750.8 | −2.09940 | ||||||||
\(147\) | −2104.00 | − | 2104.00i | −0.0973668 | − | 0.0973668i | ||||
\(148\) | 20387.2 | − | 20387.2i | 0.930752 | − | 0.930752i | ||||
\(149\) | − | 41060.3i | − | 1.84948i | −0.380600 | − | 0.924740i | \(-0.624282\pi\) | ||
0.380600 | − | 0.924740i | \(-0.375718\pi\) | |||||||
\(150\) | 19100.2 | + | 12979.7i | 0.848896 | + | 0.576877i | ||||
\(151\) | 12096.5 | 0.530523 | 0.265262 | − | 0.964176i | \(-0.414542\pi\) | ||||
0.265262 | + | 0.964176i | \(0.414542\pi\) | |||||||
\(152\) | −29395.3 | − | 29395.3i | −1.27231 | − | 1.27231i | ||||
\(153\) | 428.526 | − | 428.526i | 0.0183060 | − | 0.0183060i | ||||
\(154\) | − | 15678.4i | − | 0.661091i | ||||||
\(155\) | 32191.0 | + | 9902.79i | 1.33989 | + | 0.412187i | ||||
\(156\) | −5300.49 | −0.217804 | ||||||||
\(157\) | −21184.3 | − | 21184.3i | −0.859440 | − | 0.859440i | 0.131832 | − | 0.991272i | \(-0.457914\pi\) |
−0.991272 | + | 0.131832i | \(0.957914\pi\) | |||||||
\(158\) | 32510.6 | − | 32510.6i | 1.30230 | − | 1.30230i | ||||
\(159\) | 16543.8i | 0.654396i | ||||||||
\(160\) | −7371.35 | − | 13921.6i | −0.287943 | − | 0.543814i | ||||
\(161\) | 44178.8 | 1.70436 | ||||||||
\(162\) | 3665.49 | + | 3665.49i | 0.139670 | + | 0.139670i | ||||
\(163\) | 3953.29 | − | 3953.29i | 0.148793 | − | 0.148793i | −0.628786 | − | 0.777579i | \(-0.716448\pi\) |
0.777579 | + | 0.628786i | \(0.216448\pi\) | |||||||
\(164\) | 64169.2i | 2.38583i | ||||||||
\(165\) | −4641.90 | + | 2457.83i | −0.170501 | + | 0.0902785i | ||||
\(166\) | 6248.73 | 0.226765 | ||||||||
\(167\) | −7863.94 | − | 7863.94i | −0.281973 | − | 0.281973i | 0.551922 | − | 0.833895i | \(-0.313894\pi\) |
−0.833895 | + | 0.551922i | \(0.813894\pi\) | |||||||
\(168\) | 26448.2 | − | 26448.2i | 0.937082 | − | 0.937082i | ||||
\(169\) | 27690.0i | 0.969503i | ||||||||
\(170\) | −1173.21 | + | 3813.76i | −0.0405956 | + | 0.131964i | ||||
\(171\) | −8503.00 | −0.290790 | ||||||||
\(172\) | −23195.0 | − | 23195.0i | −0.784037 | − | 0.784037i | ||||
\(173\) | −20563.0 | + | 20563.0i | −0.687059 | + | 0.687059i | −0.961581 | − | 0.274522i | \(-0.911480\pi\) |
0.274522 | + | 0.961581i | \(0.411480\pi\) | |||||||
\(174\) | − | 30461.9i | − | 1.00614i | ||||||
\(175\) | −6387.16 | − | 33478.1i | −0.208560 | − | 1.09316i | ||||
\(176\) | 15592.4 | 0.503371 | ||||||||
\(177\) | 9498.00 | + | 9498.00i | 0.303169 | + | 0.303169i | ||||
\(178\) | −9336.01 | + | 9336.01i | −0.294660 | + | 0.294660i | ||||
\(179\) | 11578.3i | 0.361360i | 0.983542 | + | 0.180680i | \(0.0578298\pi\) | ||||
−0.983542 | + | 0.180680i | \(0.942170\pi\) | |||||||
\(180\) | −22299.2 | − | 6859.83i | −0.688248 | − | 0.211723i | ||||
\(181\) | 15410.3 | 0.470385 | 0.235193 | − | 0.971949i | \(-0.424428\pi\) | ||||
0.235193 | + | 0.971949i | \(0.424428\pi\) | |||||||
\(182\) | 8092.11 | + | 8092.11i | 0.244298 | + | 0.244298i | ||||
\(183\) | 12039.5 | − | 12039.5i | 0.359506 | − | 0.359506i | ||||
\(184\) | 106944.i | 3.15879i | ||||||||
\(185\) | 9758.49 | + | 18430.0i | 0.285128 | + | 0.538496i | ||||
\(186\) | −49777.1 | −1.43881 | ||||||||
\(187\) | −641.731 | − | 641.731i | −0.0183514 | − | 0.0183514i | ||||
\(188\) | −17450.0 | + | 17450.0i | −0.493720 | + | 0.493720i | ||||
\(189\) | − | 7650.49i | − | 0.214174i | ||||||
\(190\) | 49476.9 | − | 26197.5i | 1.37055 | − | 0.725691i | ||||
\(191\) | −8129.00 | −0.222828 | −0.111414 | − | 0.993774i | \(-0.535538\pi\) | ||||
−0.111414 | + | 0.993774i | \(0.535538\pi\) | |||||||
\(192\) | −6207.73 | − | 6207.73i | −0.168395 | − | 0.168395i | ||||
\(193\) | −28495.5 | + | 28495.5i | −0.765001 | + | 0.765001i | −0.977222 | − | 0.212220i | \(-0.931931\pi\) |
0.212220 | + | 0.977222i | \(0.431931\pi\) | |||||||
\(194\) | − | 124532.i | − | 3.30884i | ||||||
\(195\) | 1127.26 | − | 3664.38i | 0.0296452 | − | 0.0963677i | ||||
\(196\) | −19792.4 | −0.515213 | ||||||||
\(197\) | −14908.5 | − | 14908.5i | −0.384150 | − | 0.384150i | 0.488445 | − | 0.872595i | \(-0.337564\pi\) |
−0.872595 | + | 0.488445i | \(0.837564\pi\) | |||||||
\(198\) | 5489.18 | − | 5489.18i | 0.140016 | − | 0.140016i | ||||
\(199\) | − | 3870.42i | − | 0.0977353i | −0.998805 | − | 0.0488677i | \(-0.984439\pi\) | ||
0.998805 | − | 0.0488677i | \(-0.0155613\pi\) | |||||||
\(200\) | 81040.4 | − | 15461.4i | 2.02601 | − | 0.386536i | ||||
\(201\) | 25197.5 | 0.623684 | ||||||||
\(202\) | 952.043 | + | 952.043i | 0.0233321 | + | 0.0233321i | ||||
\(203\) | −31789.6 | + | 31789.6i | −0.771423 | + | 0.771423i | ||||
\(204\) | − | 4031.17i | − | 0.0968659i | ||||||
\(205\) | −44362.1 | − | 13646.9i | −1.05561 | − | 0.324734i | ||||
\(206\) | −144115. | −3.39606 | ||||||||
\(207\) | 15467.5 | + | 15467.5i | 0.360976 | + | 0.360976i | ||||
\(208\) | −8047.71 | + | 8047.71i | −0.186014 | + | 0.186014i | ||||
\(209\) | 12733.5i | 0.291511i | ||||||||
\(210\) | 23570.9 | + | 44516.4i | 0.534488 | + | 1.00944i | ||||
\(211\) | −17666.9 | −0.396822 | −0.198411 | − | 0.980119i | \(-0.563578\pi\) | ||||
−0.198411 | + | 0.980119i | \(0.563578\pi\) | |||||||
\(212\) | 77814.2 | + | 77814.2i | 1.73136 | + | 1.73136i | ||||
\(213\) | 20867.8 | − | 20867.8i | 0.459958 | − | 0.459958i | ||||
\(214\) | 3862.24i | 0.0843358i | ||||||||
\(215\) | 20968.2 | − | 11102.4i | 0.453612 | − | 0.240183i | ||||
\(216\) | 18519.6 | 0.396939 | ||||||||
\(217\) | 51946.6 | + | 51946.6i | 1.10316 | + | 1.10316i | ||||
\(218\) | 70920.0 | − | 70920.0i | 1.49230 | − | 1.49230i | ||||
\(219\) | 32701.1i | 0.681827i | ||||||||
\(220\) | −10272.8 | + | 33393.8i | −0.212248 | + | 0.689954i | ||||
\(221\) | 662.433 | 0.0135630 | ||||||||
\(222\) | −21794.1 | − | 21794.1i | −0.442214 | − | 0.442214i | ||||
\(223\) | 10730.0 | − | 10730.0i | 0.215768 | − | 0.215768i | −0.590944 | − | 0.806713i | \(-0.701245\pi\) |
0.806713 | + | 0.590944i | \(0.201245\pi\) | |||||||
\(224\) | − | 34360.5i | − | 0.684800i | ||||||
\(225\) | 9484.80 | − | 13957.2i | 0.187354 | − | 0.275698i | ||||
\(226\) | 126699. | 2.48060 | ||||||||
\(227\) | −34199.9 | − | 34199.9i | −0.663703 | − | 0.663703i | 0.292548 | − | 0.956251i | \(-0.405497\pi\) |
−0.956251 | + | 0.292548i | \(0.905497\pi\) | |||||||
\(228\) | −39994.1 | + | 39994.1i | −0.769354 | + | 0.769354i | ||||
\(229\) | − | 73430.0i | − | 1.40024i | −0.714026 | − | 0.700120i | \(-0.753130\pi\) | ||
0.714026 | − | 0.700120i | \(-0.246870\pi\) | |||||||
\(230\) | −137656. | − | 42346.7i | −2.60220 | − | 0.800504i | ||||
\(231\) | −11456.8 | −0.214704 | ||||||||
\(232\) | −76953.1 | − | 76953.1i | −1.42972 | − | 1.42972i | ||||
\(233\) | 18203.1 | − | 18203.1i | 0.335300 | − | 0.335300i | −0.519295 | − | 0.854595i | \(-0.673805\pi\) |
0.854595 | + | 0.519295i | \(0.173805\pi\) | |||||||
\(234\) | 5666.26i | 0.103482i | ||||||||
\(235\) | −8352.59 | − | 15774.8i | −0.151247 | − | 0.285646i | ||||
\(236\) | 89348.2 | 1.60421 | ||||||||
\(237\) | −23756.8 | − | 23756.8i | −0.422952 | − | 0.422952i | ||||
\(238\) | −6154.28 | + | 6154.28i | −0.108648 | + | 0.108648i | ||||
\(239\) | 102775.i | 1.79925i | 0.436661 | + | 0.899626i | \(0.356161\pi\) | ||||
−0.436661 | + | 0.899626i | \(0.643839\pi\) | |||||||
\(240\) | −44272.1 | + | 23441.6i | −0.768613 | + | 0.406972i | ||||
\(241\) | 69403.6 | 1.19495 | 0.597473 | − | 0.801889i | \(-0.296172\pi\) | ||||
0.597473 | + | 0.801889i | \(0.296172\pi\) | |||||||
\(242\) | 65396.3 | + | 65396.3i | 1.11666 | + | 1.11666i | ||||
\(243\) | 2678.52 | − | 2678.52i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | − | 113256.i | − | 1.90232i | ||||||
\(245\) | 4209.28 | − | 13683.1i | 0.0701254 | − | 0.227956i | ||||
\(246\) | 68597.4 | 1.13354 | ||||||||
\(247\) | −6572.14 | − | 6572.14i | −0.107724 | − | 0.107724i | ||||
\(248\) | −125747. | + | 125747.i | −2.04454 | + | 2.04454i | ||||
\(249\) | − | 4566.19i | − | 0.0736470i | ||||||
\(250\) | −12188.0 | + | 110436.i | −0.195008 | + | 1.76698i | ||||
\(251\) | −40858.0 | −0.648530 | −0.324265 | − | 0.945966i | \(-0.605117\pi\) | ||||
−0.324265 | + | 0.945966i | \(0.605117\pi\) | |||||||
\(252\) | −35984.3 | − | 35984.3i | −0.566647 | − | 0.566647i | ||||
\(253\) | 23163.0 | − | 23163.0i | 0.361871 | − | 0.361871i | ||||
\(254\) | 110191.i | 1.70796i | ||||||||
\(255\) | 2786.87 | + | 857.313i | 0.0428584 | + | 0.0131844i | ||||
\(256\) | −130086. | −1.98495 | ||||||||
\(257\) | 53271.7 | + | 53271.7i | 0.806548 | + | 0.806548i | 0.984110 | − | 0.177562i | \(-0.0568211\pi\) |
−0.177562 | + | 0.984110i | \(0.556821\pi\) | |||||||
\(258\) | −24795.6 | + | 24795.6i | −0.372507 | + | 0.372507i | ||||
\(259\) | 45487.9i | 0.678103i | ||||||||
\(260\) | −11933.4 | − | 22537.6i | −0.176530 | − | 0.333397i | ||||
\(261\) | −22259.7 | −0.326767 | ||||||||
\(262\) | −54669.8 | − | 54669.8i | −0.796425 | − | 0.796425i | ||||
\(263\) | 47788.6 | − | 47788.6i | 0.690896 | − | 0.690896i | −0.271533 | − | 0.962429i | \(-0.587531\pi\) |
0.962429 | + | 0.271533i | \(0.0875306\pi\) | |||||||
\(264\) | − | 27733.6i | − | 0.397923i | ||||||
\(265\) | −70344.0 | + | 37246.4i | −1.00170 | + | 0.530387i | ||||
\(266\) | 122116. | 1.72587 | ||||||||
\(267\) | 6822.19 | + | 6822.19i | 0.0956976 | + | 0.0956976i | ||||
\(268\) | 118517. | − | 118517.i | 1.65010 | − | 1.65010i | ||||
\(269\) | − | 130832.i | − | 1.80805i | −0.427483 | − | 0.904023i | \(-0.640600\pi\) | ||
0.427483 | − | 0.904023i | \(-0.359400\pi\) | |||||||
\(270\) | −7333.21 | + | 23838.1i | −0.100593 | + | 0.326997i | ||||
\(271\) | −116029. | −1.57989 | −0.789945 | − | 0.613178i | \(-0.789891\pi\) | ||||
−0.789945 | + | 0.613178i | \(0.789891\pi\) | |||||||
\(272\) | −6120.51 | − | 6120.51i | −0.0827274 | − | 0.0827274i | ||||
\(273\) | 5913.22 | − | 5913.22i | 0.0793412 | − | 0.0793412i | ||||
\(274\) | 34063.1i | 0.453715i | ||||||||
\(275\) | −20901.4 | − | 14203.8i | −0.276382 | − | 0.187819i | ||||
\(276\) | 145503. | 1.91010 | ||||||||
\(277\) | 41111.1 | + | 41111.1i | 0.535796 | + | 0.535796i | 0.922291 | − | 0.386495i | \(-0.126314\pi\) |
−0.386495 | + | 0.922291i | \(0.626314\pi\) | |||||||
\(278\) | −30651.8 | + | 30651.8i | −0.396613 | + | 0.396613i | ||||
\(279\) | 36374.1i | 0.467287i | ||||||||
\(280\) | 172003. | + | 52912.5i | 2.19391 | + | 0.674904i | ||||
\(281\) | −61086.4 | −0.773627 | −0.386814 | − | 0.922158i | \(-0.626424\pi\) | ||||
−0.386814 | + | 0.922158i | \(0.626424\pi\) | |||||||
\(282\) | 18654.2 | + | 18654.2i | 0.234573 | + | 0.234573i | ||||
\(283\) | 54739.9 | − | 54739.9i | 0.683489 | − | 0.683489i | −0.277296 | − | 0.960785i | \(-0.589438\pi\) |
0.960785 | + | 0.277296i | \(0.0894382\pi\) | |||||||
\(284\) | − | 196305.i | − | 2.43386i | ||||||
\(285\) | −19143.5 | − | 36154.7i | −0.235685 | − | 0.445117i | ||||
\(286\) | 8485.40 | 0.103739 | ||||||||
\(287\) | −71587.1 | − | 71587.1i | −0.869103 | − | 0.869103i | ||||
\(288\) | 12030.0 | − | 12030.0i | 0.145037 | − | 0.145037i | ||||
\(289\) | − | 83017.2i | − | 0.993968i | ||||||
\(290\) | 129524. | − | 68581.4i | 1.54012 | − | 0.815474i | ||||
\(291\) | −91000.1 | −1.07462 | ||||||||
\(292\) | 153811. | + | 153811.i | 1.80394 | + | 1.80394i | ||||
\(293\) | −33601.9 | + | 33601.9i | −0.391406 | + | 0.391406i | −0.875189 | − | 0.483782i | \(-0.839263\pi\) |
0.483782 | + | 0.875189i | \(0.339263\pi\) | |||||||
\(294\) | 21158.3i | 0.244785i | ||||||||
\(295\) | −19001.8 | + | 61769.0i | −0.218348 | + | 0.709785i | ||||
\(296\) | −110113. | −1.25676 | ||||||||
\(297\) | −4011.16 | − | 4011.16i | −0.0454734 | − | 0.0454734i | ||||
\(298\) | −206456. | + | 206456.i | −2.32485 | + | 2.32485i | ||||
\(299\) | 23910.2i | 0.267449i | ||||||||
\(300\) | −21036.2 | − | 110260.i | −0.233735 | − | 1.22511i | ||||
\(301\) | 51752.5 | 0.571214 | ||||||||
\(302\) | −60822.3 | − | 60822.3i | −0.666882 | − | 0.666882i | ||||
\(303\) | 695.695 | − | 695.695i | 0.00757763 | − | 0.00757763i | ||||
\(304\) | 121446.i | 1.31412i | ||||||||
\(305\) | 78297.4 | + | 24086.3i | 0.841681 | + | 0.258923i | ||||
\(306\) | −4309.35 | −0.0460224 | ||||||||
\(307\) | 84437.4 | + | 84437.4i | 0.895897 | + | 0.895897i | 0.995070 | − | 0.0991732i | \(-0.0316198\pi\) |
−0.0991732 | + | 0.995070i | \(0.531620\pi\) | |||||||
\(308\) | −53887.6 | + | 53887.6i | −0.568051 | + | 0.568051i | ||||
\(309\) | 105310.i | 1.10295i | ||||||||
\(310\) | −112067. | − | 211652.i | −1.16615 | − | 2.20241i | ||||
\(311\) | 93477.0 | 0.966460 | 0.483230 | − | 0.875493i | \(-0.339463\pi\) | ||||
0.483230 | + | 0.875493i | \(0.339463\pi\) | |||||||
\(312\) | 14314.1 | + | 14314.1i | 0.147047 | + | 0.147047i | ||||
\(313\) | −6979.59 | + | 6979.59i | −0.0712429 | + | 0.0712429i | −0.741830 | − | 0.670588i | \(-0.766042\pi\) |
0.670588 | + | 0.741830i | \(0.266042\pi\) | |||||||
\(314\) | 213034.i | 2.16068i | ||||||||
\(315\) | 32529.8 | − | 17224.2i | 0.327839 | − | 0.173587i | ||||
\(316\) | −223481. | −2.23804 | ||||||||
\(317\) | 41396.6 | + | 41396.6i | 0.411951 | + | 0.411951i | 0.882418 | − | 0.470467i | \(-0.155914\pi\) |
−0.470467 | + | 0.882418i | \(0.655914\pi\) | |||||||
\(318\) | 83184.0 | − | 83184.0i | 0.822594 | − | 0.822594i | ||||
\(319\) | 33334.6i | 0.327577i | ||||||||
\(320\) | 12419.2 | − | 40371.2i | 0.121282 | − | 0.394250i | ||||
\(321\) | 2822.29 | 0.0273900 | ||||||||
\(322\) | −222136. | − | 222136.i | −2.14243 | − | 2.14243i | ||||
\(323\) | 4998.29 | − | 4998.29i | 0.0479090 | − | 0.0479090i | ||||
\(324\) | − | 25197.0i | − | 0.240026i | ||||||
\(325\) | 18118.8 | − | 3456.82i | 0.171539 | − | 0.0327273i | ||||
\(326\) | −39755.1 | −0.374074 | ||||||||
\(327\) | −51824.0 | − | 51824.0i | −0.484658 | − | 0.484658i | ||||
\(328\) | 173291. | − | 173291.i | 1.61075 | − | 1.61075i | ||||
\(329\) | − | 38934.5i | − | 0.359702i | ||||||
\(330\) | 35698.2 | + | 10981.7i | 0.327807 | + | 0.100842i | ||||
\(331\) | 65879.3 | 0.601303 | 0.300651 | − | 0.953734i | \(-0.402796\pi\) | ||||
0.300651 | + | 0.953734i | \(0.402796\pi\) | |||||||
\(332\) | −21477.2 | − | 21477.2i | −0.194851 | − | 0.194851i | ||||
\(333\) | −15925.8 | + | 15925.8i | −0.143619 | + | 0.143619i | ||||
\(334\) | 79081.5i | 0.708895i | ||||||||
\(335\) | 56729.1 | + | 107139.i | 0.505495 | + | 0.954684i | ||||
\(336\) | −109270. | −0.967879 | ||||||||
\(337\) | 18022.9 | + | 18022.9i | 0.158696 | + | 0.158696i | 0.781989 | − | 0.623293i | \(-0.214205\pi\) |
−0.623293 | + | 0.781989i | \(0.714205\pi\) | |||||||
\(338\) | 139228. | − | 139228.i | 1.21869 | − | 1.21869i | ||||
\(339\) | − | 92583.9i | − | 0.805631i | ||||||
\(340\) | 17140.5 | − | 9075.71i | 0.148274 | − | 0.0785096i | ||||
\(341\) | 54471.3 | 0.468445 | ||||||||
\(342\) | 42754.0 | + | 42754.0i | 0.365531 | + | 0.365531i | ||||
\(343\) | −70500.4 | + | 70500.4i | −0.599244 | + | 0.599244i | ||||
\(344\) | 125277.i | 1.05866i | ||||||||
\(345\) | −30944.3 | + | 100591.i | −0.259982 | + | 0.845123i | ||||
\(346\) | 206786. | 1.72730 | ||||||||
\(347\) | −32583.8 | − | 32583.8i | −0.270610 | − | 0.270610i | 0.558736 | − | 0.829346i | \(-0.311287\pi\) |
−0.829346 | + | 0.558736i | \(0.811287\pi\) | |||||||
\(348\) | −104699. | + | 104699.i | −0.864539 | + | 0.864539i | ||||
\(349\) | − | 54340.9i | − | 0.446145i | −0.974802 | − | 0.223072i | \(-0.928391\pi\) | ||
0.974802 | − | 0.223072i | \(-0.0716086\pi\) | |||||||
\(350\) | −136216. | + | 200447.i | −1.11197 | + | 1.63630i | ||||
\(351\) | 4140.56 | 0.0336082 | ||||||||
\(352\) | −18015.2 | − | 18015.2i | −0.145397 | − | 0.145397i | ||||
\(353\) | −11345.9 | + | 11345.9i | −0.0910524 | + | 0.0910524i | −0.751166 | − | 0.660114i | \(-0.770508\pi\) |
0.660114 | + | 0.751166i | \(0.270508\pi\) | |||||||
\(354\) | − | 95513.9i | − | 0.762184i | ||||||
\(355\) | 135711. | + | 41748.4i | 1.07686 | + | 0.331271i | ||||
\(356\) | 64176.7 | 0.506381 | ||||||||
\(357\) | 4497.17 | + | 4497.17i | 0.0352860 | + | 0.0352860i | ||||
\(358\) | 58217.1 | − | 58217.1i | 0.454239 | − | 0.454239i | ||||
\(359\) | − | 26830.8i | − | 0.208183i | −0.994568 | − | 0.104091i | \(-0.966807\pi\) | ||
0.994568 | − | 0.104091i | \(-0.0331934\pi\) | |||||||
\(360\) | 41694.6 | + | 78745.1i | 0.321718 | + | 0.607601i | ||||
\(361\) | 31142.7 | 0.238969 | ||||||||
\(362\) | −77484.6 | − | 77484.6i | −0.591287 | − | 0.591287i | ||||
\(363\) | 47787.6 | − | 47787.6i | 0.362662 | − | 0.362662i | ||||
\(364\) | − | 55626.0i | − | 0.419832i | ||||||
\(365\) | −139045. | + | 73622.7i | −1.04368 | + | 0.552620i | ||||
\(366\) | −121072. | −0.903818 | ||||||||
\(367\) | −112367. | − | 112367.i | −0.834267 | − | 0.834267i | 0.153830 | − | 0.988097i | \(-0.450839\pi\) |
−0.988097 | + | 0.153830i | \(0.950839\pi\) | |||||||
\(368\) | 220917. | − | 220917.i | 1.63130 | − | 1.63130i | ||||
\(369\) | − | 50126.8i | − | 0.368143i | ||||||
\(370\) | 43601.4 | − | 141735.i | 0.318491 | − | 1.03532i | ||||
\(371\) | −173619. | −1.26139 | ||||||||
\(372\) | 171087. | + | 171087.i | 1.23632 | + | 1.23632i | ||||
\(373\) | −16877.0 | + | 16877.0i | −0.121305 | + | 0.121305i | −0.765153 | − | 0.643848i | \(-0.777337\pi\) |
0.643848 | + | 0.765153i | \(0.277337\pi\) | |||||||
\(374\) | 6453.38i | 0.0461364i | ||||||||
\(375\) | 80699.9 | + | 8906.24i | 0.573866 | + | 0.0633333i | ||||
\(376\) | 94248.7 | 0.666653 | ||||||||
\(377\) | −17205.0 | − | 17205.0i | −0.121052 | − | 0.121052i | ||||
\(378\) | −38467.5 | + | 38467.5i | −0.269222 | + | 0.269222i | ||||
\(379\) | − | 50523.2i | − | 0.351733i | −0.984414 | − | 0.175866i | \(-0.943727\pi\) | ||
0.984414 | − | 0.175866i | \(-0.0562726\pi\) | |||||||
\(380\) | −260097. | − | 80012.5i | −1.80122 | − | 0.554104i | ||||
\(381\) | 80520.9 | 0.554700 | ||||||||
\(382\) | 40873.5 | + | 40873.5i | 0.280101 | + | 0.280101i | ||||
\(383\) | 17592.0 | − | 17592.0i | 0.119927 | − | 0.119927i | −0.644596 | − | 0.764523i | \(-0.722974\pi\) |
0.764523 | + | 0.644596i | \(0.222974\pi\) | |||||||
\(384\) | 114813.i | 0.778623i | ||||||||
\(385\) | −25793.7 | − | 48714.4i | −0.174017 | − | 0.328652i | ||||
\(386\) | 286557. | 1.92325 | ||||||||
\(387\) | 18119.1 | + | 18119.1i | 0.120980 | + | 0.120980i | ||||
\(388\) | −428022. | + | 428022.i | −2.84317 | + | 2.84317i | ||||
\(389\) | − | 6343.53i | − | 0.0419210i | −0.999780 | − | 0.0209605i | \(-0.993328\pi\) | ||
0.999780 | − | 0.0209605i | \(-0.00667242\pi\) | |||||||
\(390\) | −24092.9 | + | 12756.9i | −0.158402 | + | 0.0838719i | ||||
\(391\) | −18184.4 | −0.118945 | ||||||||
\(392\) | 53450.1 | + | 53450.1i | 0.347838 | + | 0.347838i | ||||
\(393\) | −39949.4 | + | 39949.4i | −0.258657 | + | 0.258657i | ||||
\(394\) | 149923.i | 0.965773i | ||||||||
\(395\) | 47528.0 | − | 154499.i | 0.304618 | − | 0.990221i | ||||
\(396\) | −37733.2 | −0.240621 | ||||||||
\(397\) | −145003. | − | 145003.i | −0.920018 | − | 0.920018i | 0.0770121 | − | 0.997030i | \(-0.475462\pi\) |
−0.997030 | + | 0.0770121i | \(0.975462\pi\) | |||||||
\(398\) | −19460.9 | + | 19460.9i | −0.122856 | + | 0.122856i | ||||
\(399\) | − | 89234.8i | − | 0.560516i | ||||||
\(400\) | −199347. | − | 135469.i | −1.24592 | − | 0.846678i | ||||
\(401\) | −299021. | −1.85957 | −0.929786 | − | 0.368100i | \(-0.880008\pi\) | ||||
−0.929786 | + | 0.368100i | \(0.880008\pi\) | |||||||
\(402\) | −126696. | − | 126696.i | −0.783988 | − | 0.783988i | ||||
\(403\) | −28114.3 | + | 28114.3i | −0.173108 | + | 0.173108i | ||||
\(404\) | − | 6544.44i | − | 0.0400968i | ||||||
\(405\) | 17419.4 | + | 5358.66i | 0.106200 | + | 0.0326698i | ||||
\(406\) | 319683. | 1.93940 | ||||||||
\(407\) | 23849.3 | + | 23849.3i | 0.143975 | + | 0.143975i | ||||
\(408\) | −10886.3 | + | 10886.3i | −0.0653974 | + | 0.0653974i | ||||
\(409\) | − | 17363.2i | − | 0.103796i | −0.998652 | − | 0.0518982i | \(-0.983473\pi\) | ||
0.998652 | − | 0.0518982i | \(-0.0165271\pi\) | |||||||
\(410\) | 154439. | + | 291675.i | 0.918733 | + | 1.73513i | ||||
\(411\) | 24891.2 | 0.147354 | ||||||||
\(412\) | 495331. | + | 495331.i | 2.91811 | + | 2.91811i | ||||
\(413\) | −99676.8 | + | 99676.8i | −0.584378 | + | 0.584378i | ||||
\(414\) | − | 155544.i | − | 0.907514i | ||||||
\(415\) | 19415.4 | − | 10280.2i | 0.112733 | − | 0.0596907i | ||||
\(416\) | 18596.4 | 0.107459 | ||||||||
\(417\) | 22398.5 | + | 22398.5i | 0.128809 | + | 0.128809i | ||||
\(418\) | 64025.4 | − | 64025.4i | 0.366437 | − | 0.366437i | ||||
\(419\) | 36236.3i | 0.206403i | 0.994660 | + | 0.103201i | \(0.0329086\pi\) | ||||
−0.994660 | + | 0.103201i | \(0.967091\pi\) | |||||||
\(420\) | 71990.6 | − | 234020.i | 0.408110 | − | 1.32664i | ||||
\(421\) | −121899. | −0.687761 | −0.343881 | − | 0.939013i | \(-0.611742\pi\) | ||||
−0.343881 | + | 0.939013i | \(0.611742\pi\) | |||||||
\(422\) | 88831.2 | + | 88831.2i | 0.498817 | + | 0.498817i | ||||
\(423\) | 13631.4 | − | 13631.4i | 0.0761830 | − | 0.0761830i | ||||
\(424\) | − | 420280.i | − | 2.33780i | ||||||
\(425\) | 2629.01 | + | 13779.9i | 0.0145551 | + | 0.0762899i | ||||
\(426\) | −209852. | −1.15636 | ||||||||
\(427\) | 126349. | + | 126349.i | 0.692971 | + | 0.692971i | ||||
\(428\) | 13274.7 | − | 13274.7i | 0.0724666 | − | 0.0724666i | ||||
\(429\) | − | 6200.61i | − | 0.0336915i | ||||||
\(430\) | −161255. | − | 49606.2i | −0.872119 | − | 0.268287i | ||||
\(431\) | 330169. | 1.77739 | 0.888693 | − | 0.458504i | \(-0.151614\pi\) | ||||
0.888693 | + | 0.458504i | \(0.151614\pi\) | |||||||
\(432\) | −38256.4 | − | 38256.4i | −0.204992 | − | 0.204992i | ||||
\(433\) | 140458. | − | 140458.i | 0.749151 | − | 0.749151i | −0.225169 | − | 0.974320i | \(-0.572293\pi\) |
0.974320 | + | 0.225169i | \(0.0722934\pi\) | |||||||
\(434\) | − | 522387.i | − | 2.77340i | ||||||
\(435\) | −50115.1 | − | 94648.0i | −0.264844 | − | 0.500188i | ||||
\(436\) | −487512. | −2.56455 | ||||||||
\(437\) | 180411. | + | 180411.i | 0.944715 | + | 0.944715i | ||||
\(438\) | 164425. | − | 164425.i | 0.857076 | − | 0.857076i | ||||
\(439\) | 25797.9i | 0.133861i | 0.997758 | + | 0.0669306i | \(0.0213206\pi\) | ||||
−0.997758 | + | 0.0669306i | \(0.978679\pi\) | |||||||
\(440\) | 117923. | − | 62439.0i | 0.609107 | − | 0.322515i | ||||
\(441\) | 15461.2 | 0.0794996 | ||||||||
\(442\) | −3330.78 | − | 3330.78i | −0.0170491 | − | 0.0170491i | ||||
\(443\) | 131776. | − | 131776.i | 0.671473 | − | 0.671473i | −0.286583 | − | 0.958056i | \(-0.592519\pi\) |
0.958056 | + | 0.286583i | \(0.0925193\pi\) | |||||||
\(444\) | 149815.i | 0.759956i | ||||||||
\(445\) | −13648.5 | + | 44367.2i | −0.0689232 | + | 0.224049i | ||||
\(446\) | −107903. | −0.542454 | ||||||||
\(447\) | 150865. | + | 150865.i | 0.755047 | + | 0.755047i | ||||
\(448\) | 65147.1 | − | 65147.1i | 0.324593 | − | 0.324593i | ||||
\(449\) | 133600.i | 0.662697i | 0.943508 | + | 0.331349i | \(0.107504\pi\) | ||||
−0.943508 | + | 0.331349i | \(0.892496\pi\) | |||||||
\(450\) | −117869. | + | 22487.8i | −0.582069 | + | 0.111051i | ||||
\(451\) | −75066.4 | −0.369056 | ||||||||
\(452\) | −435471. | − | 435471.i | −2.13149 | − | 2.13149i | ||||
\(453\) | −44445.3 | + | 44445.3i | −0.216585 | + | 0.216585i | ||||
\(454\) | 343922.i | 1.66858i | ||||||||
\(455\) | 38455.9 | + | 11830.0i | 0.185755 | + | 0.0571430i | ||||
\(456\) | 216011. | 1.03883 | ||||||||
\(457\) | −147483. | − | 147483.i | −0.706170 | − | 0.706170i | 0.259558 | − | 0.965728i | \(-0.416423\pi\) |
−0.965728 | + | 0.259558i | \(0.916423\pi\) | |||||||
\(458\) | −369214. | + | 369214.i | −1.76014 | + | 1.76014i | ||||
\(459\) | 3149.01i | 0.0149468i | ||||||||
\(460\) | 327584. | + | 618679.i | 1.54813 | + | 2.92381i | ||||
\(461\) | 206578. | 0.972034 | 0.486017 | − | 0.873949i | \(-0.338449\pi\) | ||||
0.486017 | + | 0.873949i | \(0.338449\pi\) | |||||||
\(462\) | 57606.3 | + | 57606.3i | 0.269889 | + | 0.269889i | ||||
\(463\) | −156702. | + | 156702.i | −0.730990 | + | 0.730990i | −0.970816 | − | 0.239826i | \(-0.922910\pi\) |
0.239826 | + | 0.970816i | \(0.422910\pi\) | |||||||
\(464\) | 317928.i | 1.47670i | ||||||||
\(465\) | −154662. | + | 81892.0i | −0.715284 | + | 0.378735i | ||||
\(466\) | −183055. | −0.842963 | ||||||||
\(467\) | −100008. | − | 100008.i | −0.458566 | − | 0.458566i | 0.439619 | − | 0.898184i | \(-0.355114\pi\) |
−0.898184 | + | 0.439619i | \(0.855114\pi\) | |||||||
\(468\) | 19475.2 | − | 19475.2i | 0.0889183 | − | 0.0889183i | ||||
\(469\) | 264435.i | 1.20219i | ||||||||
\(470\) | −37319.8 | + | 121315.i | −0.168944 | + | 0.549186i | ||||
\(471\) | 155672. | 0.701730 | ||||||||
\(472\) | −241288. | − | 241288.i | −1.08306 | − | 1.08306i | ||||
\(473\) | 27133.9 | − | 27133.9i | 0.121280 | − | 0.121280i | ||||
\(474\) | 238903.i | 1.06332i | ||||||||
\(475\) | 110630. | − | 162796.i | 0.490327 | − | 0.721533i | ||||
\(476\) | 42305.1 | 0.186715 | ||||||||
\(477\) | −60785.8 | − | 60785.8i | −0.267156 | − | 0.267156i | ||||
\(478\) | 516764. | − | 516764.i | 2.26171 | − | 2.26171i | ||||
\(479\) | − | 124818.i | − | 0.544010i | −0.962296 | − | 0.272005i | \(-0.912313\pi\) | ||
0.962296 | − | 0.272005i | \(-0.0876867\pi\) | |||||||
\(480\) | 78235.4 | + | 24067.3i | 0.339563 | + | 0.104459i | ||||
\(481\) | −24618.7 | −0.106408 | ||||||||
\(482\) | −348969. | − | 348969.i | −1.50208 | − | 1.50208i | ||||
\(483\) | −162323. | + | 162323.i | −0.695804 | + | 0.695804i | ||||
\(484\) | − | 449541.i | − | 1.91902i | ||||||
\(485\) | −204876. | − | 386932.i | −0.870979 | − | 1.64494i | ||||
\(486\) | −26935.7 | −0.114040 | ||||||||
\(487\) | −106165. | − | 106165.i | −0.447635 | − | 0.447635i | 0.446932 | − | 0.894568i | \(-0.352516\pi\) |
−0.894568 | + | 0.446932i | \(0.852516\pi\) | |||||||
\(488\) | −305853. | + | 305853.i | −1.28432 | + | 1.28432i | ||||
\(489\) | 29050.6i | 0.121489i | ||||||||
\(490\) | −89964.7 | + | 47635.3i | −0.374697 | + | 0.198398i | ||||
\(491\) | 185092. | 0.767758 | 0.383879 | − | 0.923383i | \(-0.374588\pi\) | ||||
0.383879 | + | 0.923383i | \(0.374588\pi\) | |||||||
\(492\) | −235773. | − | 235773.i | −0.974010 | − | 0.974010i | ||||
\(493\) | 13084.9 | − | 13084.9i | 0.0538363 | − | 0.0538363i | ||||
\(494\) | 66090.8i | 0.270824i | ||||||||
\(495\) | 8024.76 | − | 26086.1i | 0.0327508 | − | 0.106463i | ||||
\(496\) | 519520. | 2.11173 | ||||||||
\(497\) | 218998. | + | 218998.i | 0.886598 | + | 0.886598i | ||||
\(498\) | −22959.3 | + | 22959.3i | −0.0925763 | + | 0.0925763i | ||||
\(499\) | 482480.i | 1.93766i | 0.247723 | + | 0.968831i | \(0.420318\pi\) | ||||
−0.247723 | + | 0.968831i | \(0.579682\pi\) | |||||||
\(500\) | 421465. | − | 337684.i | 1.68586 | − | 1.35073i | ||||
\(501\) | 57787.9 | 0.230230 | ||||||||
\(502\) | 205439. | + | 205439.i | 0.815220 | + | 0.815220i | ||||
\(503\) | 224311. | − | 224311.i | 0.886572 | − | 0.886572i | −0.107620 | − | 0.994192i | \(-0.534323\pi\) |
0.994192 | + | 0.107620i | \(0.0343230\pi\) | |||||||
\(504\) | 194354.i | 0.765124i | ||||||||
\(505\) | 4524.36 | + | 1391.81i | 0.0177409 | + | 0.00545756i | ||||
\(506\) | −232932. | −0.909763 | ||||||||
\(507\) | −101739. | − | 101739.i | −0.395798 | − | 0.395798i | ||||
\(508\) | 378732. | − | 378732.i | 1.46759 | − | 1.46759i | ||||
\(509\) | 390482.i | 1.50718i | 0.657344 | + | 0.753591i | \(0.271680\pi\) | ||||
−0.657344 | + | 0.753591i | \(0.728320\pi\) | |||||||
\(510\) | −9702.00 | − | 18323.3i | −0.0373010 | − | 0.0704472i | ||||
\(511\) | −343182. | −1.31426 | ||||||||
\(512\) | 404102. | + | 404102.i | 1.54153 | + | 1.54153i | ||||
\(513\) | 31242.0 | − | 31242.0i | 0.118715 | − | 0.118715i | ||||
\(514\) | − | 535711.i | − | 2.02770i | ||||||
\(515\) | −447779. | + | 237094.i | −1.68830 | + | 0.893936i | ||||
\(516\) | 170447. | 0.640164 | ||||||||
\(517\) | −20413.4 | − | 20413.4i | −0.0763719 | − | 0.0763719i | ||||
\(518\) | 228718. | − | 228718.i | 0.852394 | − | 0.852394i | ||||
\(519\) | − | 151107.i | − | 0.560981i | ||||||
\(520\) | −28637.0 | + | 93090.2i | −0.105906 | + | 0.344269i | ||||
\(521\) | −71234.7 | −0.262432 | −0.131216 | − | 0.991354i | \(-0.541888\pi\) | ||||
−0.131216 | + | 0.991354i | \(0.541888\pi\) | |||||||
\(522\) | 111924. | + | 111924.i | 0.410755 | + | 0.410755i | ||||
\(523\) | −26895.3 | + | 26895.3i | −0.0983272 | + | 0.0983272i | −0.754559 | − | 0.656232i | \(-0.772149\pi\) |
0.656232 | + | 0.754559i | \(0.272149\pi\) | |||||||
\(524\) | 375806.i | 1.36868i | ||||||||
\(525\) | 146474. | + | 99538.3i | 0.531426 | + | 0.361137i | ||||
\(526\) | −480573. | −1.73695 | ||||||||
\(527\) | −21381.7 | − | 21381.7i | −0.0769876 | − | 0.0769876i | ||||
\(528\) | −57290.2 | + | 57290.2i | −0.205500 | + | 0.205500i | ||||
\(529\) | − | 376517.i | − | 1.34547i | ||||||
\(530\) | 540976. | + | 166419.i | 1.92587 | + | 0.592448i | ||||
\(531\) | −69795.7 | −0.247537 | ||||||||
\(532\) | −419718. | − | 419718.i | −1.48298 | − | 1.48298i | ||||
\(533\) | 38744.0 | − | 38744.0i | 0.136380 | − | 0.136380i | ||||
\(534\) | − | 68605.4i | − | 0.240589i | ||||||
\(535\) | 6354.05 | + | 12000.3i | 0.0221995 | + | 0.0419263i | ||||
\(536\) | −640119. | −2.22808 | ||||||||
\(537\) | −42541.5 | − | 42541.5i | −0.147525 | − | 0.147525i | ||||
\(538\) | −657838. | + | 657838.i | −2.27276 | + | 2.27276i | ||||
\(539\) | − | 23153.6i | − | 0.0796967i | ||||||
\(540\) | 107137. | − | 56728.0i | 0.367412 | − | 0.194541i | ||||
\(541\) | 293490. | 1.00276 | 0.501382 | − | 0.865226i | \(-0.332825\pi\) | ||||
0.501382 | + | 0.865226i | \(0.332825\pi\) | |||||||
\(542\) | 583405. | + | 583405.i | 1.98596 | + | 1.98596i | ||||
\(543\) | −56621.0 | + | 56621.0i | −0.192034 | + | 0.192034i | ||||
\(544\) | 14143.1i | 0.0477911i | ||||||||
\(545\) | 103680. | − | 337031.i | 0.349060 | − | 1.13469i | ||||
\(546\) | −59464.6 | −0.199468 | ||||||||
\(547\) | 178128. | + | 178128.i | 0.595330 | + | 0.595330i | 0.939066 | − | 0.343736i | \(-0.111693\pi\) |
−0.343736 | + | 0.939066i | \(0.611693\pi\) | |||||||
\(548\) | 117077. | − | 117077.i | 0.389860 | − | 0.389860i | ||||
\(549\) | 88471.9i | 0.293536i | ||||||||
\(550\) | 33676.2 | + | 176512.i | 0.111326 | + | 0.583512i | ||||
\(551\) | −259635. | −0.855186 | ||||||||
\(552\) | −392937. | − | 392937.i | −1.28957 | − | 1.28957i | ||||
\(553\) | 249316. | − | 249316.i | 0.815266 | − | 0.815266i | ||||
\(554\) | − | 413422.i | − | 1.34702i | ||||||
\(555\) | −103571. | − | 31861.2i | −0.336243 | − | 0.103437i | ||||
\(556\) | 210704. | 0.681589 | ||||||||
\(557\) | 122805. | + | 122805.i | 0.395827 | + | 0.395827i | 0.876758 | − | 0.480931i | \(-0.159701\pi\) |
−0.480931 | + | 0.876758i | \(0.659701\pi\) | |||||||
\(558\) | 182893. | − | 182893.i | 0.587393 | − | 0.587393i | ||||
\(559\) | 28009.2i | 0.0896349i | ||||||||
\(560\) | −246008. | − | 464614.i | −0.784464 | − | 1.48155i | ||||
\(561\) | 4715.74 | 0.0149839 | ||||||||
\(562\) | 307149. | + | 307149.i | 0.972470 | + | 0.972470i | ||||
\(563\) | −86662.0 | + | 86662.0i | −0.273408 | + | 0.273408i | −0.830471 | − | 0.557062i | \(-0.811928\pi\) |
0.557062 | + | 0.830471i | \(0.311928\pi\) | |||||||
\(564\) | − | 128231.i | − | 0.403120i | ||||||
\(565\) | 393666. | − | 208442.i | 1.23319 | − | 0.652962i | ||||
\(566\) | −550477. | −1.71833 | ||||||||
\(567\) | 28109.7 | + | 28109.7i | 0.0874360 | + | 0.0874360i | ||||
\(568\) | −530128. | + | 530128.i | −1.64318 | + | 1.64318i | ||||
\(569\) | − | 358179.i | − | 1.10631i | −0.833080 | − | 0.553153i | \(-0.813425\pi\) | ||
0.833080 | − | 0.553153i | \(-0.186575\pi\) | |||||||
\(570\) | −85534.0 | + | 278045.i | −0.263263 | + | 0.855787i | ||||
\(571\) | 420094. | 1.28847 | 0.644234 | − | 0.764828i | \(-0.277176\pi\) | ||||
0.644234 | + | 0.764828i | \(0.277176\pi\) | |||||||
\(572\) | −29164.8 | − | 29164.8i | −0.0891387 | − | 0.0891387i | ||||
\(573\) | 29867.9 | − | 29867.9i | 0.0909693 | − | 0.0909693i | ||||
\(574\) | 719896.i | 2.18497i | ||||||||
\(575\) | −497378. | + | 94893.1i | −1.50436 | + | 0.287011i | ||||
\(576\) | 45617.3 | 0.137494 | ||||||||
\(577\) | −167153. | − | 167153.i | −0.502068 | − | 0.502068i | 0.410012 | − | 0.912080i | \(-0.365524\pi\) |
−0.912080 | + | 0.410012i | \(0.865524\pi\) | |||||||
\(578\) | −417419. | + | 417419.i | −1.24944 | + | 1.24944i | ||||
\(579\) | − | 209399.i | − | 0.624621i | ||||||
\(580\) | −680898. | − | 209462.i | −2.02407 | − | 0.622658i | ||||
\(581\) | 47919.9 | 0.141959 | ||||||||
\(582\) | 457558. | + | 457558.i | 1.35083 | + | 1.35083i | ||||
\(583\) | −91028.5 | + | 91028.5i | −0.267818 | + | 0.267818i | ||||
\(584\) | − | 830742.i | − | 2.43579i | ||||||
\(585\) | 9321.98 | + | 17605.6i | 0.0272393 | + | 0.0514446i | ||||
\(586\) | 337908. | 0.984017 | ||||||||
\(587\) | −43094.6 | − | 43094.6i | −0.125068 | − | 0.125068i | 0.641802 | − | 0.766870i | \(-0.278187\pi\) |
−0.766870 | + | 0.641802i | \(0.778187\pi\) | |||||||
\(588\) | 72722.1 | − | 72722.1i | 0.210335 | − | 0.210335i | ||||
\(589\) | 424265.i | 1.22294i | ||||||||
\(590\) | 406124. | − | 215038.i | 1.16669 | − | 0.617749i | ||||
\(591\) | 109554. | 0.313657 | ||||||||
\(592\) | 227463. | + | 227463.i | 0.649033 | + | 0.649033i | ||||
\(593\) | −114499. | + | 114499.i | −0.325605 | + | 0.325605i | −0.850912 | − | 0.525307i | \(-0.823950\pi\) |
0.525307 | + | 0.850912i | \(0.323950\pi\) | |||||||
\(594\) | 40337.1i | 0.114322i | ||||||||
\(595\) | −8997.08 | + | 29246.8i | −0.0254137 | + | 0.0826122i | ||||
\(596\) | 1.41920e6 | 3.99531 | ||||||||
\(597\) | 14220.8 | + | 14220.8i | 0.0399003 | + | 0.0399003i | ||||
\(598\) | 120223. | − | 120223.i | 0.336191 | − | 0.336191i | ||||
\(599\) | 282109.i | 0.786254i | 0.919484 | + | 0.393127i | \(0.128607\pi\) | ||||
−0.919484 | + | 0.393127i | \(0.871393\pi\) | |||||||
\(600\) | −240953. | + | 354570.i | −0.669313 | + | 0.984918i | ||||
\(601\) | −155225. | −0.429747 | −0.214874 | − | 0.976642i | \(-0.568934\pi\) | ||||
−0.214874 | + | 0.976642i | \(0.568934\pi\) | |||||||
\(602\) | −260217. | − | 260217.i | −0.718031 | − | 0.718031i | ||||
\(603\) | −92581.4 | + | 92581.4i | −0.254618 | + | 0.254618i | ||||
\(604\) | 418099.i | 1.14605i | ||||||||
\(605\) | 310781. | + | 95604.4i | 0.849070 | + | 0.261196i | ||||
\(606\) | −6996.06 | −0.0190506 | ||||||||
\(607\) | −262539. | − | 262539.i | −0.712553 | − | 0.712553i | 0.254516 | − | 0.967069i | \(-0.418084\pi\) |
−0.967069 | + | 0.254516i | \(0.918084\pi\) | |||||||
\(608\) | 140317. | − | 140317.i | 0.379579 | − | 0.379579i | ||||
\(609\) | − | 233605.i | − | 0.629864i | ||||||
\(610\) | −272579. | − | 514797.i | −0.732543 | − | 1.38349i | ||||
\(611\) | 21071.9 | 0.0564444 | ||||||||
\(612\) | 14811.5 | + | 14811.5i | 0.0395453 | + | 0.0395453i | ||||
\(613\) | −98919.2 | + | 98919.2i | −0.263245 | + | 0.263245i | −0.826371 | − | 0.563126i | \(-0.809598\pi\) |
0.563126 | + | 0.826371i | \(0.309598\pi\) | |||||||
\(614\) | − | 849121.i | − | 2.25233i | ||||||
\(615\) | 213139. | − | 112855.i | 0.563523 | − | 0.298379i | ||||
\(616\) | 291051. | 0.767021 | ||||||||
\(617\) | −440524. | − | 440524.i | −1.15717 | − | 1.15717i | −0.985080 | − | 0.172095i | \(-0.944947\pi\) |
−0.172095 | − | 0.985080i | \(-0.555053\pi\) | |||||||
\(618\) | 529512. | − | 529512.i | 1.38643 | − | 1.38643i | ||||
\(619\) | − | 468975.i | − | 1.22396i | −0.790871 | − | 0.611982i | \(-0.790372\pi\) | ||
0.790871 | − | 0.611982i | \(-0.209628\pi\) | |||||||
\(620\) | −342277. | + | 1.11264e6i | −0.890420 | + | 2.89449i | ||||
\(621\) | −113662. | −0.294736 | ||||||||
\(622\) | −470012. | − | 470012.i | −1.21487 | − | 1.21487i | ||||
\(623\) | −71595.5 | + | 71595.5i | −0.184463 | + | 0.184463i | ||||
\(624\) | − | 59138.3i | − | 0.151880i | ||||||
\(625\) | 143817. | + | 363187.i | 0.368172 | + | 0.929758i | ||||
\(626\) | 70188.3 | 0.179108 | ||||||||
\(627\) | −46785.8 | − | 46785.8i | −0.119009 | − | 0.119009i | ||||
\(628\) | 732210. | − | 732210.i | 1.85659 | − | 1.85659i | ||||
\(629\) | − | 18723.2i | − | 0.0473237i | ||||||
\(630\) | −250169. | − | 76958.4i | −0.630306 | − | 0.193899i | ||||
\(631\) | 327190. | 0.821752 | 0.410876 | − | 0.911691i | \(-0.365223\pi\) | ||||
0.410876 | + | 0.911691i | \(0.365223\pi\) | |||||||
\(632\) | 603519. | + | 603519.i | 1.51097 | + | 1.51097i | ||||
\(633\) | 64912.4 | − | 64912.4i | 0.162002 | − | 0.162002i | ||||
\(634\) | − | 416293.i | − | 1.03567i | ||||||
\(635\) | 181283. | + | 342374.i | 0.449583 | + | 0.849089i | ||||
\(636\) | −571815. | −1.41365 | ||||||||
\(637\) | 11950.2 | + | 11950.2i | 0.0294509 | + | 0.0294509i | ||||
\(638\) | 167610. | − | 167610.i | 0.411773 | − | 0.411773i | ||||
\(639\) | 153347.i | 0.375554i | ||||||||
\(640\) | −488182. | + | 258487.i | −1.19185 | + | 0.631072i | ||||
\(641\) | −584738. | −1.42313 | −0.711567 | − | 0.702619i | \(-0.752014\pi\) | ||||
−0.711567 | + | 0.702619i | \(0.752014\pi\) | |||||||
\(642\) | −14190.8 | − | 14190.8i | −0.0344299 | − | 0.0344299i | ||||
\(643\) | −202062. | + | 202062.i | −0.488723 | + | 0.488723i | −0.907903 | − | 0.419180i | \(-0.862318\pi\) |
0.419180 | + | 0.907903i | \(0.362318\pi\) | |||||||
\(644\) | 1.52699e6i | 3.68183i | ||||||||
\(645\) | −36249.2 | + | 117835.i | −0.0871323 | + | 0.283241i | ||||
\(646\) | −50263.9 | −0.120446 | ||||||||
\(647\) | 119543. | + | 119543.i | 0.285573 | + | 0.285573i | 0.835327 | − | 0.549754i | \(-0.185278\pi\) |
−0.549754 | + | 0.835327i | \(0.685278\pi\) | |||||||
\(648\) | −68045.3 | + | 68045.3i | −0.162050 | + | 0.162050i | ||||
\(649\) | 104521.i | 0.248150i | ||||||||
\(650\) | −108485. | − | 73722.1i | −0.256768 | − | 0.174490i | ||||
\(651\) | −381728. | −0.900725 | ||||||||
\(652\) | 136640. | + | 136640.i | 0.321428 | + | 0.321428i | ||||
\(653\) | −279985. | + | 279985.i | −0.656611 | + | 0.656611i | −0.954577 | − | 0.297965i | \(-0.903692\pi\) |
0.297965 | + | 0.954577i | \(0.403692\pi\) | |||||||
\(654\) | 521153.i | 1.21846i | ||||||||
\(655\) | −259806. | − | 79923.0i | −0.605572 | − | 0.186290i | ||||
\(656\) | −715946. | −1.66369 | ||||||||
\(657\) | −120152. | − | 120152.i | −0.278355 | − | 0.278355i | ||||
\(658\) | −195767. | + | 195767.i | −0.452155 | + | 0.452155i | ||||
\(659\) | − | 171782.i | − | 0.395555i | −0.980247 | − | 0.197778i | \(-0.936628\pi\) | ||
0.980247 | − | 0.197778i | \(-0.0633724\pi\) | |||||||
\(660\) | −84951.9 | − | 160441.i | −0.195023 | − | 0.368323i | ||||
\(661\) | 566188. | 1.29586 | 0.647929 | − | 0.761701i | \(-0.275635\pi\) | ||||
0.647929 | + | 0.761701i | \(0.275635\pi\) | |||||||
\(662\) | −331248. | − | 331248.i | −0.755854 | − | 0.755854i | ||||
\(663\) | −2433.93 | + | 2433.93i | −0.00553709 | + | 0.00553709i | ||||
\(664\) | 116000.i | 0.263100i | ||||||||
\(665\) | 379425. | − | 200902.i | 0.857992 | − | 0.454297i | ||||
\(666\) | 160153. | 0.361066 | ||||||||
\(667\) | 472292. | + | 472292.i | 1.06160 | + | 1.06160i | ||||
\(668\) | 271807. | − | 271807.i | 0.609128 | − | 0.609128i | ||||
\(669\) | 78848.7i | 0.176174i | ||||||||
\(670\) | 253468. | − | 823949.i | 0.564643 | − | 1.83548i | ||||
\(671\) | 132489. | 0.294263 | ||||||||
\(672\) | 126249. | + | 126249.i | 0.279568 | + | 0.279568i | ||||
\(673\) | −115466. | + | 115466.i | −0.254932 | + | 0.254932i | −0.822989 | − | 0.568057i | \(-0.807695\pi\) |
0.568057 | + | 0.822989i | \(0.307695\pi\) | |||||||
\(674\) | − | 181243.i | − | 0.398970i | ||||||
\(675\) | 16432.7 | + | 86131.5i | 0.0360664 | + | 0.189040i | ||||
\(676\) | −957070. | −2.09435 | ||||||||
\(677\) | 255557. | + | 255557.i | 0.557584 | + | 0.557584i | 0.928619 | − | 0.371035i | \(-0.120997\pi\) |
−0.371035 | + | 0.928619i | \(0.620997\pi\) | |||||||
\(678\) | −465522. | + | 465522.i | −1.01270 | + | 1.01270i | ||||
\(679\) | − | 955001.i | − | 2.07140i | ||||||
\(680\) | −70797.7 | − | 21779.2i | −0.153109 | − | 0.0471004i | ||||
\(681\) | 251317. | 0.541911 | ||||||||
\(682\) | −273888. | − | 273888.i | −0.588849 | − | 0.588849i | ||||
\(683\) | 97131.8 | − | 97131.8i | 0.208219 | − | 0.208219i | −0.595291 | − | 0.803510i | \(-0.702963\pi\) |
0.803510 | + | 0.595291i | \(0.202963\pi\) | |||||||
\(684\) | − | 293895.i | − | 0.628175i | ||||||
\(685\) | 56039.6 | + | 105837.i | 0.119430 | + | 0.225558i | ||||
\(686\) | 708967. | 1.50653 | ||||||||
\(687\) | 269799. | + | 269799.i | 0.571645 | + | 0.571645i | ||||
\(688\) | 258789. | − | 258789.i | 0.546726 | − | 0.546726i | ||||
\(689\) | − | 93965.1i | − | 0.197937i | ||||||
\(690\) | 661373. | − | 350189.i | 1.38915 | − | 0.735538i | ||||
\(691\) | −40145.6 | −0.0840778 | −0.0420389 | − | 0.999116i | \(-0.513385\pi\) | ||||
−0.0420389 | + | 0.999116i | \(0.513385\pi\) | |||||||
\(692\) | −710734. | − | 710734.i | −1.48421 | − | 1.48421i | ||||
\(693\) | 42095.1 | − | 42095.1i | 0.0876527 | − | 0.0876527i | ||||
\(694\) | 327670.i | 0.680327i | ||||||||
\(695\) | −44810.6 | + | 145666.i | −0.0927707 | + | 0.301569i | ||||
\(696\) | 565487. | 1.16736 | ||||||||
\(697\) | 29465.9 | + | 29465.9i | 0.0606532 | + | 0.0606532i | ||||
\(698\) | −273232. | + | 273232.i | −0.560816 | + | 0.560816i | ||||
\(699\) | 133765.i | 0.273772i | ||||||||
\(700\) | 1.15713e6 | − | 220764.i | 2.36148 | − | 0.450539i | ||||
\(701\) | 225909. | 0.459724 | 0.229862 | − | 0.973223i | \(-0.426172\pi\) | ||||
0.229862 | + | 0.973223i | \(0.426172\pi\) | |||||||
\(702\) | −20819.2 | − | 20819.2i | −0.0422464 | − | 0.0422464i | ||||
\(703\) | −185757. | + | 185757.i | −0.375867 | + | 0.375867i | ||||
\(704\) | − | 68313.3i | − | 0.137835i | ||||||
\(705\) | 88649.8 | + | 27271.0i | 0.178361 | + | 0.0548685i | ||||
\(706\) | 114097. | 0.228911 | ||||||||
\(707\) | 7300.97 | + | 7300.97i | 0.0146064 | + | 0.0146064i | ||||
\(708\) | −328286. | + | 328286.i | −0.654917 | + | 0.654917i | ||||
\(709\) | 459779.i | 0.914654i | 0.889299 | + | 0.457327i | \(0.151193\pi\) | ||||
−0.889299 | + | 0.457327i | \(0.848807\pi\) | |||||||
\(710\) | −472456. | − | 892287.i | −0.937227 | − | 1.77006i | ||||
\(711\) | 174576. | 0.345339 | ||||||||
\(712\) | −173311. | − | 173311.i | −0.341875 | − | 0.341875i | ||||
\(713\) | 771763. | − | 771763.i | 1.51812 | − | 1.51812i | ||||
\(714\) | − | 45224.5i | − | 0.0887110i | ||||||
\(715\) | 26364.9 | − | 13959.9i | 0.0515721 | − | 0.0273068i | ||||
\(716\) | −400191. | −0.780622 | ||||||||
\(717\) | −377620. | − | 377620.i | −0.734542 | − | 0.734542i | ||||
\(718\) | −134908. | + | 134908.i | −0.261691 | + | 0.261691i | ||||
\(719\) | 633365.i | 1.22517i | 0.790405 | + | 0.612585i | \(0.209870\pi\) | ||||
−0.790405 | + | 0.612585i | \(0.790130\pi\) | |||||||
\(720\) | 76536.2 | − | 248796.i | 0.147639 | − | 0.479930i | ||||
\(721\) | −1.10518e6 | −2.12600 | ||||||||
\(722\) | −156589. | − | 156589.i | −0.300391 | − | 0.300391i | ||||
\(723\) | −255005. | + | 255005.i | −0.487835 | + | 0.487835i | ||||
\(724\) | 532637.i | 1.01614i | ||||||||
\(725\) | 289614. | − | 426178.i | 0.550990 | − | 0.810802i | ||||
\(726\) | −480563. | −0.911752 | ||||||||
\(727\) | 483916. | + | 483916.i | 0.915590 | + | 0.915590i | 0.996705 | − | 0.0811152i | \(-0.0258482\pi\) |
−0.0811152 | + | 0.996705i | \(0.525848\pi\) | |||||||
\(728\) | −150220. | + | 150220.i | −0.283442 | + | 0.283442i | ||||
\(729\) | 19683.0i | 0.0370370i | ||||||||
\(730\) | 1.06932e6 | + | 328950.i | 2.00660 | + | 0.617282i | ||||
\(731\) | −21301.8 | −0.0398641 | ||||||||
\(732\) | 416130. | + | 416130.i | 0.776618 | + | 0.776618i | ||||
\(733\) | −79446.4 | + | 79446.4i | −0.147865 | + | 0.147865i | −0.777164 | − | 0.629298i | \(-0.783342\pi\) |
0.629298 | + | 0.777164i | \(0.283342\pi\) | |||||||
\(734\) | 1.12998e6i | 2.09739i | ||||||||
\(735\) | 34809.0 | + | 65740.7i | 0.0644343 | + | 0.121691i | ||||
\(736\) | −510489. | −0.942390 | ||||||||
\(737\) | 138643. | + | 138643.i | 0.255249 | + | 0.255249i | ||||
\(738\) | −252043. | + | 252043.i | −0.462766 | + | 0.462766i | ||||
\(739\) | − | 885328.i | − | 1.62112i | −0.585655 | − | 0.810561i | \(-0.699163\pi\) | ||
0.585655 | − | 0.810561i | \(-0.300837\pi\) | |||||||
\(740\) | −637010. | + | 337290.i | −1.16328 | + | 0.615942i | ||||
\(741\) | 48295.1 | 0.0879563 | ||||||||
\(742\) | 872975. | + | 872975.i | 1.58560 | + | 1.58560i | ||||
\(743\) | 693877. | − | 693877.i | 1.25691 | − | 1.25691i | 0.304352 | − | 0.952560i | \(-0.401560\pi\) |
0.952560 | − | 0.304352i | \(-0.0984400\pi\) | |||||||
\(744\) | − | 924050.i | − | 1.66936i | ||||||
\(745\) | −301822. | + | 981133.i | −0.543799 | + | 1.76773i | ||||
\(746\) | 169719. | 0.304967 | ||||||||
\(747\) | 16777.2 | + | 16777.2i | 0.0300663 | + | 0.0300663i | ||||
\(748\) | 22180.6 | − | 22180.6i | 0.0396434 | − | 0.0396434i | ||||
\(749\) | 29618.5i | 0.0527959i | ||||||||
\(750\) | −360986. | − | 450549.i | −0.641754 | − | 0.800977i | ||||
\(751\) | −1.03267e6 | −1.83097 | −0.915487 | − | 0.402347i | \(-0.868194\pi\) | ||||
−0.915487 | + | 0.402347i | \(0.868194\pi\) | |||||||
\(752\) | −194692. | − | 194692.i | −0.344281 | − | 0.344281i | ||||
\(753\) | 150122. | − | 150122.i | 0.264761 | − | 0.264761i | ||||
\(754\) | 173017.i | 0.304331i | ||||||||
\(755\) | −289044. | − | 88917.5i | −0.507073 | − | 0.155989i | ||||
\(756\) | 264430. | 0.462665 | ||||||||
\(757\) | −366937. | − | 366937.i | −0.640323 | − | 0.640323i | 0.310312 | − | 0.950635i | \(-0.399567\pi\) |
−0.950635 | + | 0.310312i | \(0.899567\pi\) | |||||||
\(758\) | −254036. | + | 254036.i | −0.442137 | + | 0.442137i | ||||
\(759\) | 170213.i | 0.295466i | ||||||||
\(760\) | 486323. | + | 918476.i | 0.841972 | + | 1.59016i | ||||
\(761\) | −721432. | −1.24574 | −0.622868 | − | 0.782327i | \(-0.714033\pi\) | ||||
−0.622868 | + | 0.782327i | \(0.714033\pi\) | |||||||
\(762\) | −404868. | − | 404868.i | −0.697274 | − | 0.697274i | ||||
\(763\) | 543867. | − | 543867.i | 0.934209 | − | 0.934209i | ||||
\(764\) | − | 280969.i | − | 0.481361i | ||||||
\(765\) | −13389.6 | + | 7089.63i | −0.0228793 | + | 0.0121144i | ||||
\(766\) | −176909. | −0.301504 | ||||||||
\(767\) | −53946.5 | − | 53946.5i | −0.0917007 | − | 0.0917007i | ||||
\(768\) | 477966. | − | 477966.i | 0.810354 | − | 0.810354i | ||||
\(769\) | − | 543034.i | − | 0.918279i | −0.888364 | − | 0.459139i | \(-0.848158\pi\) | ||
0.888364 | − | 0.459139i | \(-0.151842\pi\) | |||||||
\(770\) | −115248. | + | 374635.i | −0.194379 | + | 0.631869i | ||||
\(771\) | −391465. | −0.658543 | ||||||||
\(772\) | −984913. | − | 984913.i | −1.65258 | − | 1.65258i | ||||
\(773\) | −501793. | + | 501793.i | −0.839780 | + | 0.839780i | −0.988830 | − | 0.149050i | \(-0.952378\pi\) |
0.149050 | + | 0.988830i | \(0.452378\pi\) | |||||||
\(774\) | − | 182210.i | − | 0.304151i | ||||||
\(775\) | −696408. | − | 473253.i | −1.15947 | − | 0.787934i | ||||
\(776\) | 2.31177e6 | 3.83903 | ||||||||
\(777\) | −167133. | − | 167133.i | −0.276835 | − | 0.276835i | ||||
\(778\) | −31895.9 | + | 31895.9i | −0.0526958 | + | 0.0526958i | ||||
\(779\) | − | 584675.i | − | 0.963473i | ||||||
\(780\) | 126655. | + | 38962.3i | 0.208177 | + | 0.0640407i | ||||
\(781\) | 229641. | 0.376485 | ||||||||
\(782\) | 91433.1 | + | 91433.1i | 0.149517 | + | 0.149517i | ||||
\(783\) | 81787.4 | − | 81787.4i | 0.133402 | − | 0.133402i | ||||
\(784\) | − | 220827.i | − | 0.359269i | ||||||
\(785\) | 350478. | + | 661918.i | 0.568750 | + | 1.07415i | ||||
\(786\) | 401740. | 0.650279 | ||||||||
\(787\) | −219605. | − | 219605.i | −0.354562 | − | 0.354562i | 0.507242 | − | 0.861804i | \(-0.330665\pi\) |
−0.861804 | + | 0.507242i | \(0.830665\pi\) | |||||||
\(788\) | 515293. | − | 515293.i | 0.829854 | − | 0.829854i | ||||
\(789\) | 351173.i | 0.564115i | ||||||||
\(790\) | −1.01581e6 | + | 537863.i | −1.62765 | + | 0.861821i | ||||
\(791\) | 971623. | 1.55290 | ||||||||
\(792\) | 101900. | + | 101900.i | 0.162451 | + | 0.162451i | ||||
\(793\) | −68381.7 | + | 68381.7i | −0.108741 | + | 0.108741i | ||||
\(794\) | 1.45818e6i | 2.31298i | ||||||||
\(795\) | 121609. | − | 395312.i | 0.192411 | − | 0.625470i | ||||
\(796\) | 133776. | 0.211131 | ||||||||
\(797\) | −311150. | − | 311150.i | −0.489839 | − | 0.489839i | 0.418416 | − | 0.908255i | \(-0.362585\pi\) |
−0.908255 | + | 0.418416i | \(0.862585\pi\) | |||||||
\(798\) | −448682. | + | 448682.i | −0.704584 | + | 0.704584i | ||||
\(799\) | 16025.8i | 0.0251030i | ||||||||
\(800\) | 73804.0 | + | 386841.i | 0.115319 | + | 0.604439i | ||||
\(801\) | −50132.6 | −0.0781368 | ||||||||
\(802\) | 1.50351e6 | + | 1.50351e6i | 2.33753 | + | 2.33753i | ||||
\(803\) | −179931. | + | 179931.i | −0.279045 | + | 0.279045i | ||||
\(804\) | 870919.i | 1.34730i | ||||||||
\(805\) | −1.05565e6 | − | 324746.i | −1.62903 | − | 0.501131i | ||||
\(806\) | 282723. | 0.435202 | ||||||||
\(807\) | 480708. | + | 480708.i | 0.738132 | + | 0.738132i | ||||
\(808\) | −17673.5 | + | 17673.5i | −0.0270707 | + | 0.0270707i | ||||
\(809\) | 827176.i | 1.26387i | 0.775023 | + | 0.631933i | \(0.217738\pi\) | ||||
−0.775023 | + | 0.631933i | \(0.782262\pi\) | |||||||
\(810\) | −60642.7 | − | 114531.i | −0.0924290 | − | 0.174563i | ||||
\(811\) | 1.22035e6 | 1.85542 | 0.927711 | − | 0.373300i | \(-0.121774\pi\) | ||||
0.927711 | + | 0.373300i | \(0.121774\pi\) | |||||||
\(812\) | −1.09877e6 | − | 1.09877e6i | −1.66645 | − | 1.66645i | ||||
\(813\) | 426317. | − | 426317.i | 0.644987 | − | 0.644987i | ||||
\(814\) | − | 239834.i | − | 0.361961i | ||||||
\(815\) | −123523. | + | 65404.0i | −0.185966 | + | 0.0984667i | ||||
\(816\) | 44976.4 | 0.0675467 | ||||||||
\(817\) | 211340. | + | 211340.i | 0.316619 | + | 0.316619i | ||||
\(818\) | −87303.8 | + | 87303.8i | −0.130475 | + | 0.130475i | ||||
\(819\) | 43453.1i | 0.0647818i | ||||||||
\(820\) | 471689. | − | 1.53332e6i | 0.701501 | − | 2.28037i | ||||
\(821\) | −1.13223e6 | −1.67977 | −0.839884 | − | 0.542766i | \(-0.817377\pi\) | ||||
−0.839884 | + | 0.542766i | \(0.817377\pi\) | |||||||
\(822\) | −125156. | − | 125156.i | −0.185228 | − | 0.185228i | ||||
\(823\) | 504583. | − | 504583.i | 0.744961 | − | 0.744961i | −0.228567 | − | 0.973528i | \(-0.573404\pi\) |
0.973528 | + | 0.228567i | \(0.0734041\pi\) | |||||||
\(824\) | − | 2.67531e6i | − | 3.94022i | ||||||
\(825\) | 128985. | − | 24608.5i | 0.189509 | − | 0.0361557i | ||||
\(826\) | 1.00237e6 | 1.46916 | ||||||||
\(827\) | −707633. | − | 707633.i | −1.03466 | − | 1.03466i | −0.999377 | − | 0.0352807i | \(-0.988767\pi\) |
−0.0352807 | − | 0.999377i | \(-0.511233\pi\) | |||||||
\(828\) | −534614. | + | 534614.i | −0.779793 | + | 0.779793i | ||||
\(829\) | 846141.i | 1.23121i | 0.788053 | + | 0.615607i | \(0.211089\pi\) | ||||
−0.788053 | + | 0.615607i | \(0.788911\pi\) | |||||||
\(830\) | −149313. | − | 45932.6i | −0.216741 | − | 0.0666752i | ||||
\(831\) | −302104. | −0.437476 | ||||||||
\(832\) | 35258.5 | + | 35258.5i | 0.0509352 | + | 0.0509352i | ||||
\(833\) | −9088.50 | + | 9088.50i | −0.0130979 | + | 0.0130979i | ||||
\(834\) | − | 225244.i | − | 0.323833i | ||||||
\(835\) | 130103. | + | 245714.i | 0.186601 | + | 0.352417i | ||||
\(836\) | −440117. | −0.629732 | ||||||||
\(837\) | −133647. | − | 133647.i | −0.190769 | − | 0.190769i | ||||
\(838\) | 182200. | − | 182200.i | 0.259454 | − | 0.259454i | ||||
\(839\) | − | 499671.i | − | 0.709839i | −0.934897 | − | 0.354920i | \(-0.884508\pi\) | ||
0.934897 | − | 0.354920i | \(-0.115492\pi\) | |||||||
\(840\) | −826390. | + | 437565.i | −1.17119 | + | 0.620131i | ||||
\(841\) | 27590.7 | 0.0390096 | ||||||||
\(842\) | 612924. | + | 612924.i | 0.864534 | + | 0.864534i | ||||
\(843\) | 224446. | − | 224446.i | 0.315832 | − | 0.315832i | ||||
\(844\) | − | 610635.i | − | 0.857229i | ||||||
\(845\) | 203541. | − | 661650.i | 0.285061 | − | 0.926648i | ||||
\(846\) | −137080. | −0.191528 | ||||||||
\(847\) | 501508. | + | 501508.i | 0.699054 | + | 0.699054i | ||||
\(848\) | −868184. | + | 868184.i | −1.20731 | + | 1.20731i | ||||
\(849\) | 402255.i | 0.558066i | ||||||||
\(850\) | 56067.7 | − | 82505.6i | 0.0776023 | − | 0.114195i | ||||
\(851\) | 675806. | 0.933175 | ||||||||
\(852\) | 721271. | + | 721271.i | 0.993617 | + | 0.993617i | ||||
\(853\) | −175495. | + | 175495.i | −0.241194 | + | 0.241194i | −0.817344 | − | 0.576150i | \(-0.804554\pi\) |
0.576150 | + | 0.817344i | \(0.304554\pi\) | |||||||
\(854\) | − | 1.27059e6i | − | 1.74217i | ||||||
\(855\) | 203178. | + | 62503.0i | 0.277936 | + | 0.0855005i | ||||
\(856\) | −71697.7 | −0.0978492 | ||||||||
\(857\) | 932907. | + | 932907.i | 1.27021 | + | 1.27021i | 0.945976 | + | 0.324237i | \(0.105108\pi\) |
0.324237 | + | 0.945976i | \(0.394892\pi\) | |||||||
\(858\) | −31177.3 | + | 31177.3i | −0.0423511 | + | 0.0423511i | ||||
\(859\) | 318689.i | 0.431897i | 0.976405 | + | 0.215948i | \(0.0692843\pi\) | ||||
−0.976405 | + | 0.215948i | \(0.930716\pi\) | |||||||
\(860\) | 383742. | + | 724741.i | 0.518851 | + | 0.979909i | ||||
\(861\) | 526056. | 0.709619 | ||||||||
\(862\) | −1.66012e6 | − | 1.66012e6i | −2.23422 | − | 2.23422i | ||||
\(863\) | −834366. | + | 834366.i | −1.12030 | + | 1.12030i | −0.128606 | + | 0.991696i | \(0.541050\pi\) |
−0.991696 | + | 0.128606i | \(0.958950\pi\) | |||||||
\(864\) | 88401.9i | 0.118422i | ||||||||
\(865\) | 642504. | − | 340199.i | 0.858704 | − | 0.454674i | ||||
\(866\) | −1.41247e6 | −1.88341 | ||||||||
\(867\) | 305025. | + | 305025.i | 0.405786 | + | 0.405786i | ||||
\(868\) | −1.79547e6 | + | 1.79547e6i | −2.38308 | + | 2.38308i | ||||
\(869\) | − | 261433.i | − | 0.346195i | ||||||
\(870\) | −223916. | + | 727885.i | −0.295834 | + | 0.961666i | ||||
\(871\) | −143116. | −0.188648 | ||||||||
\(872\) | 1.31654e6 | + | 1.31654e6i | 1.73142 | + | 1.73142i | ||||
\(873\) | 334356. | − | 334356.i | 0.438713 | − | 0.438713i | ||||
\(874\) | − | 1.81426e6i | − | 2.37507i | ||||||
\(875\) | −93466.6 | + | 846906.i | −0.122079 | + | 1.10616i | ||||
\(876\) | −1.13027e6 | −1.47291 | ||||||||
\(877\) | −218162. | − | 218162.i | −0.283648 | − | 0.283648i | 0.550914 | − | 0.834562i | \(-0.314279\pi\) |
−0.834562 | + | 0.550914i | \(0.814279\pi\) | |||||||
\(878\) | 129714. | − | 129714.i | 0.168267 | − | 0.168267i | ||||
\(879\) | − | 246922.i | − | 0.319582i | ||||||
\(880\) | −372579. | − | 114615.i | −0.481120 | − | 0.148005i | ||||
\(881\) | −279844. | −0.360549 | −0.180274 | − | 0.983616i | \(-0.557699\pi\) | ||||
−0.180274 | + | 0.983616i | \(0.557699\pi\) | |||||||
\(882\) | −77740.4 | − | 77740.4i | −0.0999332 | − | 0.0999332i | ||||
\(883\) | 269641. | − | 269641.i | 0.345831 | − | 0.345831i | −0.512723 | − | 0.858554i | \(-0.671363\pi\) |
0.858554 | + | 0.512723i | \(0.171363\pi\) | |||||||
\(884\) | 22896.2i | 0.0292994i | ||||||||
\(885\) | −157137. | − | 296771.i | −0.200628 | − | 0.378909i | ||||
\(886\) | −1.32517e6 | −1.68812 | ||||||||
\(887\) | 566987. | + | 566987.i | 0.720653 | + | 0.720653i | 0.968738 | − | 0.248085i | \(-0.0798013\pi\) |
−0.248085 | + | 0.968738i | \(0.579801\pi\) | |||||||
\(888\) | 404579. | − | 404579.i | 0.513071 | − | 0.513071i | ||||
\(889\) | 845027.i | 1.06922i | ||||||||
\(890\) | 291710. | − | 154457.i | 0.368274 | − | 0.194997i | ||||
\(891\) | 29475.9 | 0.0371288 | ||||||||
\(892\) | 370867. | + | 370867.i | 0.466110 | + | 0.466110i | ||||
\(893\) | 158995. | − | 158995.i | 0.199380 | − | 0.199380i | ||||
\(894\) | − | 1.51713e6i | − | 1.89823i | ||||||
\(895\) | 85108.9 | − | 276663.i | 0.106250 | − | 0.345387i | ||||
\(896\) | −1.20490e6 | −1.50084 | ||||||||
\(897\) | −87851.8 | − | 87851.8i | −0.109186 | − | 0.109186i | ||||
\(898\) | 671758. | − | 671758.i | 0.833029 | − | 0.833029i | ||||
\(899\) | 1.11067e6i | 1.37425i | ||||||||
\(900\) | 482414. | + | 327830.i | 0.595573 | + | 0.404729i | ||||
\(901\) | 71463.1 | 0.0880303 | ||||||||
\(902\) | 377442. | + | 377442.i | 0.463913 | + | 0.463913i | ||||
\(903\) | −190151. | + | 190151.i | −0.233197 | + | 0.233197i | ||||
\(904\) | 2.35201e6i | 2.87808i | ||||||||
\(905\) | −368228. | − | 113276.i | −0.449593 | − | 0.138306i | ||||
\(906\) | 446951. | 0.544507 | ||||||||
\(907\) | 256644. | + | 256644.i | 0.311973 | + | 0.311973i | 0.845674 | − | 0.533700i | \(-0.179199\pi\) |
−0.533700 | + | 0.845674i | \(0.679199\pi\) | |||||||
\(908\) | 1.18208e6 | − | 1.18208e6i | 1.43375 | − | 1.43375i | ||||
\(909\) | 5112.29i | 0.00618711i | ||||||||
\(910\) | −133878. | − | 252843.i | −0.161668 | − | 0.305329i | ||||
\(911\) | −143826. | −0.173301 | −0.0866506 | − | 0.996239i | \(-0.527616\pi\) | ||||
−0.0866506 | + | 0.996239i | \(0.527616\pi\) | |||||||
\(912\) | −446220. | − | 446220.i | −0.536487 | − | 0.536487i | ||||
\(913\) | 25124.4 | − | 25124.4i | 0.0301408 | − | 0.0301408i | ||||
\(914\) | 1.48312e6i | 1.77535i | ||||||||
\(915\) | −376182. | + | 199184.i | −0.449320 | + | 0.237910i | ||||
\(916\) | 2.53801e6 | 3.02485 | ||||||||
\(917\) | −419249. | − | 419249.i | −0.498578 | − | 0.498578i | ||||
\(918\) | 15833.6 | − | 15833.6i | 0.0187886 | − | 0.0187886i | ||||
\(919\) | − | 993411.i | − | 1.17625i | −0.808772 | − | 0.588123i | \(-0.799867\pi\) | ||
0.808772 | − | 0.588123i | \(-0.200133\pi\) | |||||||
\(920\) | 786113. | − | 2.55541e6i | 0.928772 | − | 3.01916i | ||||
\(921\) | −620486. | −0.731497 | ||||||||
\(922\) | −1.03869e6 | − | 1.03869e6i | −1.22187 | − | 1.22187i | ||||
\(923\) | −118525. | + | 118525.i | −0.139125 | + | 0.139125i | ||||
\(924\) | − | 395991.i | − | 0.463812i | ||||||
\(925\) | −97704.7 | − | 512116.i | −0.114191 | − | 0.598528i | ||||
\(926\) | 1.57582e6 | 1.83775 | ||||||||
\(927\) | −386935. | − | 386935.i | −0.450276 | − | 0.450276i | ||||
\(928\) | 367330. | − | 367330.i | 0.426541 | − | 0.426541i | ||||
\(929\) | − | 1.39909e6i | − | 1.62112i | −0.585658 | − | 0.810558i | \(-0.699164\pi\) | ||
0.585658 | − | 0.810558i | \(-0.300836\pi\) | |||||||
\(930\) | 1.18942e6 | + | 365897.i | 1.37521 | + | 0.423051i | ||||
\(931\) | 180338. | 0.208059 | ||||||||
\(932\) | 629168. | + | 629168.i | 0.724327 | + | 0.724327i | ||||
\(933\) | −343456. | + | 343456.i | −0.394556 | + | 0.394556i | ||||
\(934\) | 1.00570e6i | 1.15286i | ||||||||
\(935\) | 10616.9 | + | 20051.3i | 0.0121444 | + | 0.0229361i | ||||
\(936\) | −105187. | −0.120063 | ||||||||
\(937\) | 482443. | + | 482443.i | 0.549499 | + | 0.549499i | 0.926296 | − | 0.376797i | \(-0.122975\pi\) |
−0.376797 | + | 0.926296i | \(0.622975\pi\) | |||||||
\(938\) | 1.32961e6 | − | 1.32961e6i | 1.51119 | − | 1.51119i | ||||
\(939\) | − | 51289.3i | − | 0.0581696i | ||||||
\(940\) | 545237. | − | 288697.i | 0.617063 | − | 0.326728i | ||||
\(941\) | 494897. | 0.558902 | 0.279451 | − | 0.960160i | \(-0.409848\pi\) | ||||
0.279451 | + | 0.960160i | \(0.409848\pi\) | |||||||
\(942\) | −782738. | − | 782738.i | −0.882094 | − | 0.882094i | ||||
\(943\) | −1.06356e6 | + | 1.06356e6i | −1.19602 | + | 1.19602i | ||||
\(944\) | 996871.i | 1.11865i | ||||||||
\(945\) | −56236.5 | + | 182808.i | −0.0629731 | + | 0.204706i | ||||
\(946\) | −272864. | −0.304905 | ||||||||
\(947\) | −1.05460e6 | − | 1.05460e6i | −1.17595 | − | 1.17595i | −0.980767 | − | 0.195183i | \(-0.937470\pi\) |
−0.195183 | − | 0.980767i | \(-0.562530\pi\) | |||||||
\(948\) | 821123. | − | 821123.i | 0.913675 | − | 0.913675i | ||||
\(949\) | − | 185735.i | − | 0.206235i | ||||||
\(950\) | −1.37482e6 | + | 262296.i | −1.52334 | + | 0.290633i | ||||
\(951\) | −304201. | −0.336357 | ||||||||
\(952\) | −114246. | − | 114246.i | −0.126058 | − | 0.126058i | ||||
\(953\) | −319054. | + | 319054.i | −0.351300 | + | 0.351300i | −0.860593 | − | 0.509293i | \(-0.829907\pi\) |
0.509293 | + | 0.860593i | \(0.329907\pi\) | |||||||
\(954\) | 611275.i | 0.671645i | ||||||||
\(955\) | 194242. | + | 59753.9i | 0.212979 | + | 0.0655178i | ||||
\(956\) | −3.55229e6 | −3.88681 | ||||||||
\(957\) | −122479. | − | 122479.i | −0.133733 | − | 0.133733i | ||||
\(958\) | −627599. | + | 627599.i | −0.683835 | + | 0.683835i | ||||
\(959\) | 261221.i | 0.284034i | ||||||||
\(960\) | 102702. | + | 193964.i | 0.111439 | + | 0.210465i | ||||
\(961\) | 891397. | 0.965216 | ||||||||
\(962\) | 123785. | + | 123785.i | 0.133758 | + | 0.133758i | ||||
\(963\) | −10369.8 | + | 10369.8i | −0.0111819 | + | 0.0111819i | ||||
\(964\) | 2.39885e6i | 2.58136i | ||||||||
\(965\) | 890361. | − | 471436.i | 0.956118 | − | 0.506254i | ||||
\(966\) | 1.63236e6 | 1.74929 | ||||||||
\(967\) | −1.01810e6 | − | 1.01810e6i | −1.08877 | − | 1.08877i | −0.995655 | − | 0.0931182i | \(-0.970317\pi\) |
−0.0931182 | − | 0.995655i | \(-0.529683\pi\) | |||||||
\(968\) | −1.21400e6 | + | 1.21400e6i | −1.29559 | + | 1.29559i | ||||
\(969\) | 36729.8i | 0.0391175i | ||||||||
\(970\) | −915395. | + | 2.97567e6i | −0.972893 | + | 3.16258i | ||||
\(971\) | 610675. | 0.647696 | 0.323848 | − | 0.946109i | \(-0.395023\pi\) | ||||
0.323848 | + | 0.946109i | \(0.395023\pi\) | |||||||
\(972\) | 92579.6 | + | 92579.6i | 0.0979902 | + | 0.0979902i | ||||
\(973\) | −235061. | + | 235061.i | −0.248287 | + | 0.248287i | ||||
\(974\) | 1.06762e6i | 1.12538i | ||||||||
\(975\) | −53871.6 | + | 79273.9i | −0.0566696 | + | 0.0833914i | ||||
\(976\) | 1.26362e6 | 1.32653 | ||||||||
\(977\) | −90031.7 | − | 90031.7i | −0.0943206 | − | 0.0943206i | 0.658372 | − | 0.752693i | \(-0.271245\pi\) |
−0.752693 | + | 0.658372i | \(0.771245\pi\) | |||||||
\(978\) | 146070. | − | 146070.i | 0.152715 | − | 0.152715i | ||||
\(979\) | 75075.1i | 0.0783305i | ||||||||
\(980\) | 472939. | + | 145488.i | 0.492439 | + | 0.151487i | ||||
\(981\) | 380827. | 0.395722 | ||||||||
\(982\) | −930662. | − | 930662.i | −0.965093 | − | 0.965093i | ||||
\(983\) | 406452. | − | 406452.i | 0.420632 | − | 0.420632i | −0.464790 | − | 0.885421i | \(-0.653870\pi\) |
0.885421 | + | 0.464790i | \(0.153870\pi\) | |||||||
\(984\) | 1.27342e6i | 1.31517i | ||||||||
\(985\) | 246649. | + | 465824.i | 0.254218 | + | 0.480120i | ||||
\(986\) | −131584. | −0.135347 | ||||||||
\(987\) | 143054. | + | 143054.i | 0.146848 | + | 0.146848i | ||||
\(988\) | 227158. | − | 227158.i | 0.232709 | − | 0.232709i | ||||
\(989\) | − | 768879.i | − | 0.786078i | ||||||
\(990\) | −171513. | + | 90814.2i | −0.174995 | + | 0.0926581i | ||||
\(991\) | −563990. | −0.574281 | −0.287140 | − | 0.957889i | \(-0.592705\pi\) | ||||
−0.287140 | + | 0.957889i | \(0.592705\pi\) | |||||||
\(992\) | −600246. | − | 600246.i | −0.609967 | − | 0.609967i | ||||
\(993\) | −242056. | + | 242056.i | −0.245481 | + | 0.245481i | ||||
\(994\) | − | 2.20229e6i | − | 2.22896i | ||||||
\(995\) | −28450.3 | + | 92483.3i | −0.0287369 | + | 0.0934151i | ||||
\(996\) | 157825. | 0.159095 | ||||||||
\(997\) | 49988.1 | + | 49988.1i | 0.0502894 | + | 0.0502894i | 0.731804 | − | 0.681515i | \(-0.238679\pi\) |
−0.681515 | + | 0.731804i | \(0.738679\pi\) | |||||||
\(998\) | 2.42596e6 | − | 2.42596e6i | 2.43569 | − | 2.43569i | ||||
\(999\) | − | 117030.i | − | 0.117264i |
(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 | 15.5.f.a.7.1 | ✓ | 8 | |
3.2 | odd | 2 | 45.5.g.e.37.4 | 8 | |||
4.3 | odd | 2 | 240.5.bg.c.97.3 | 8 | |||
5.2 | odd | 4 | 75.5.f.e.43.4 | 8 | |||
5.3 | odd | 4 | inner | 15.5.f.a.13.1 | yes | 8 | |
5.4 | even | 2 | 75.5.f.e.7.4 | 8 | |||
15.2 | even | 4 | 225.5.g.m.118.1 | 8 | |||
15.8 | even | 4 | 45.5.g.e.28.4 | 8 | |||
15.14 | odd | 2 | 225.5.g.m.82.1 | 8 | |||
20.3 | even | 4 | 240.5.bg.c.193.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.5.f.a.7.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
15.5.f.a.13.1 | yes | 8 | 5.3 | odd | 4 | inner | |
45.5.g.e.28.4 | 8 | 15.8 | even | 4 | |||
45.5.g.e.37.4 | 8 | 3.2 | odd | 2 | |||
75.5.f.e.7.4 | 8 | 5.4 | even | 2 | |||
75.5.f.e.43.4 | 8 | 5.2 | odd | 4 | |||
225.5.g.m.82.1 | 8 | 15.14 | odd | 2 | |||
225.5.g.m.118.1 | 8 | 15.2 | even | 4 | |||
240.5.bg.c.97.3 | 8 | 4.3 | odd | 2 | |||
240.5.bg.c.193.3 | 8 | 20.3 | even | 4 |