Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [160,6,Mod(63,160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(160, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("160.63");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 160 = 2^{5} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 160.n (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: | \(25.6614111701\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 4 x^{13} + 8 x^{12} - 4626 x^{11} + 149441 x^{10} - 2113414 x^{9} + 17958066 x^{8} + \cdots + 69451154208 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{31}\cdot 5^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 127.7 | ||
Root | \(2.75256 - 2.75256i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 160.127 |
Dual form | 160.6.n.b.63.7 |
$q$-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 \(\left(\mathbb{Z}/160\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(97\) | \(101\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 18.9245 | + | 18.9245i | 1.21401 | + | 1.21401i | 0.969698 | + | 0.244308i | \(0.0785609\pi\) |
0.244308 | + | 0.969698i | \(0.421439\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −36.4318 | − | 42.3996i | −0.651712 | − | 0.758466i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 112.521 | − | 112.521i | 0.867941 | − | 0.867941i | −0.124303 | − | 0.992244i | \(-0.539670\pi\) |
0.992244 | + | 0.124303i | \(0.0396696\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 473.272i | 1.94762i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 269.371i | 0.671228i | 0.942000 | + | 0.335614i | \(0.108944\pi\) | ||||
−0.942000 | + | 0.335614i | \(0.891056\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −403.647 | + | 403.647i | −0.662436 | + | 0.662436i | −0.955954 | − | 0.293518i | \(-0.905174\pi\) |
0.293518 | + | 0.955954i | \(0.405174\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 112.936 | − | 1491.84i | 0.129600 | − | 1.71197i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1098.68 | + | 1098.68i | 0.922035 | + | 0.922035i | 0.997173 | − | 0.0751382i | \(-0.0239398\pi\) |
−0.0751382 | + | 0.997173i | \(0.523940\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1802.73 | 1.14564 | 0.572819 | − | 0.819682i | \(-0.305850\pi\) | ||||
0.572819 | + | 0.819682i | \(0.305850\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4258.82 | 2.10737 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2833.05 | + | 2833.05i | 1.11670 | + | 1.11670i | 0.992223 | + | 0.124474i | \(0.0397243\pi\) |
0.124474 | + | 0.992223i | \(0.460276\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −470.444 | + | 3089.39i | −0.150542 | + | 0.988604i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4357.78 | + | 4357.78i | −1.15042 | + | 1.15042i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 7856.77i | − | 1.73480i | −0.497612 | − | 0.867400i | \(-0.665790\pi\) | ||
0.497612 | − | 0.867400i | \(-0.334210\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4682.69i | 0.875167i | 0.899178 | + | 0.437584i | \(0.144166\pi\) | ||||
−0.899178 | + | 0.437584i | \(0.855834\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5097.71 | + | 5097.71i | −0.814874 | + | 0.814874i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8870.22 | − | 671.497i | −1.22395 | − | 0.0926561i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5157.30 | + | 5157.30i | 0.619324 | + | 0.619324i | 0.945358 | − | 0.326034i | \(-0.105712\pi\) |
−0.326034 | + | 0.945358i | \(0.605712\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −15277.6 | −1.60840 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1658.51 | 0.154084 | 0.0770421 | − | 0.997028i | \(-0.475452\pi\) | ||||
0.0770421 | + | 0.997028i | \(0.475452\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3231.92 | − | 3231.92i | −0.266557 | − | 0.266557i | 0.561154 | − | 0.827711i | \(-0.310357\pi\) |
−0.827711 | + | 0.561154i | \(0.810357\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 20066.5 | − | 17242.2i | 1.47720 | − | 1.26929i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6001.67 | + | 6001.67i | −0.396303 | + | 0.396303i | −0.876927 | − | 0.480624i | \(-0.840410\pi\) |
0.480624 | + | 0.876927i | \(0.340410\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 8515.15i | − | 0.506643i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 41583.7i | 2.23871i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6075.77 | + | 6075.77i | −0.297106 | + | 0.297106i | −0.839879 | − | 0.542773i | \(-0.817374\pi\) |
0.542773 | + | 0.839879i | \(0.317374\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11421.2 | − | 9813.69i | 0.509103 | − | 0.437447i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 34115.8 | + | 34115.8i | 1.39081 | + | 1.39081i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −39361.1 | −1.47210 | −0.736050 | − | 0.676927i | \(-0.763311\pi\) | ||||
−0.736050 | + | 0.676927i | \(0.763311\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11975.4 | −0.412063 | −0.206032 | − | 0.978545i | \(-0.566055\pi\) | ||||
−0.206032 | + | 0.978545i | \(0.566055\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 53253.2 | + | 53253.2i | 1.69042 | + | 1.69042i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 31820.1 | + | 2408.86i | 0.934153 | + | 0.0707176i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 43638.2 | − | 43638.2i | 1.18763 | − | 1.18763i | 0.209904 | − | 0.977722i | \(-0.432685\pi\) |
0.977722 | − | 0.209904i | \(-0.0673153\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 107228.i | 2.71135i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7043.28i | − | 0.165817i | −0.996557 | − | 0.0829086i | \(-0.973579\pi\) | ||
0.996557 | − | 0.0829086i | \(-0.0264209\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 24461.9 | − | 24461.9i | 0.537257 | − | 0.537257i | −0.385465 | − | 0.922722i | \(-0.625959\pi\) |
0.922722 | + | 0.385465i | \(0.125959\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −67367.9 | + | 49562.1i | −1.38293 | + | 1.01741i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 30310.1 | + | 30310.1i | 0.582586 | + | 0.582586i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 30620.5 | 0.552007 | 0.276003 | − | 0.961157i | \(-0.410990\pi\) | ||||
0.276003 | + | 0.961157i | \(0.410990\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −49932.2 | −0.845606 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −25676.6 | − | 25676.6i | −0.409112 | − | 0.409112i | 0.472317 | − | 0.881429i | \(-0.343418\pi\) |
−0.881429 | + | 0.472317i | \(0.843418\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6556.60 | − | 86610.2i | 0.0984309 | − | 1.30023i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 148685. | − | 148685.i | 2.10606 | − | 2.10606i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 137436.i | − | 1.83919i | −0.392868 | − | 0.919595i | \(-0.628517\pi\) | ||
0.392868 | − | 0.919595i | \(-0.371483\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 90838.0i | 1.14991i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −88617.5 | + | 88617.5i | −1.06246 | + | 1.06246i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −65676.9 | − | 76435.1i | −0.746627 | − | 0.868928i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 47906.2 | + | 47906.2i | 0.516967 | + | 0.516967i | 0.916652 | − | 0.399685i | \(-0.130881\pi\) |
−0.399685 | + | 0.916652i | \(0.630881\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −127486. | −1.30730 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −49807.9 | −0.485842 | −0.242921 | − | 0.970046i | \(-0.578106\pi\) | ||||
−0.242921 | + | 0.970046i | \(0.578106\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −76305.7 | − | 76305.7i | −0.708703 | − | 0.708703i | 0.257560 | − | 0.966262i | \(-0.417082\pi\) |
−0.966262 | + | 0.257560i | \(0.917082\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −155157. | − | 180572.i | −1.37340 | − | 1.59837i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −86325.0 | + | 86325.0i | −0.728916 | + | 0.728916i | −0.970404 | − | 0.241488i | \(-0.922365\pi\) |
0.241488 | + | 0.970404i | \(0.422365\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 85263.0i | − | 0.687376i | −0.939084 | − | 0.343688i | \(-0.888324\pi\) | ||
0.939084 | − | 0.343688i | \(-0.111676\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 195198.i | 1.50373i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −150561. | + | 150561.i | −1.10922 | + | 1.10922i | −0.115962 | + | 0.993254i | \(0.536995\pi\) |
−0.993254 | + | 0.115962i | \(0.963005\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16906.9 | − | 223334.i | 0.119212 | − | 1.57474i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −191035. | − | 191035.i | −1.29017 | − | 1.29017i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 247249. | 1.60054 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 88490.1 | 0.549454 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 31386.4 | + | 31386.4i | 0.187059 | + | 0.187059i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 148128. | − | 92605.4i | 0.847933 | − | 0.530104i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 61749.1 | − | 61749.1i | 0.339720 | − | 0.339720i | −0.516542 | − | 0.856262i | \(-0.672781\pi\) |
0.856262 | + | 0.516542i | \(0.172781\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 122325.i | − | 0.647203i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 228440.i | − | 1.16304i | −0.813532 | − | 0.581520i | \(-0.802458\pi\) | ||
0.813532 | − | 0.581520i | \(-0.197542\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 202846. | − | 202846.i | 0.994346 | − | 0.994346i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 343529. | + | 26006.0i | 1.62229 | + | 0.122812i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 201798. | + | 201798.i | 0.918579 | + | 0.918579i | 0.996926 | − | 0.0783472i | \(-0.0249643\pi\) |
−0.0783472 | + | 0.996926i | \(0.524964\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −122666. | −0.538503 | −0.269252 | − | 0.963070i | \(-0.586776\pi\) | ||||
−0.269252 | + | 0.963070i | \(0.586776\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −227157. | −0.962229 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −108731. | − | 108731.i | −0.444645 | − | 0.444645i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −333124. | + | 286237.i | −1.31579 | + | 1.13059i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 161145. | − | 161145.i | 0.615067 | − | 0.615067i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 385846.i | 1.42380i | 0.702281 | + | 0.711900i | \(0.252165\pi\) | ||||
−0.702281 | + | 0.711900i | \(0.747835\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 325566.i | − | 1.16198i | −0.813912 | − | 0.580988i | \(-0.802666\pi\) | ||
0.813912 | − | 0.580988i | \(-0.197334\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −519973. | + | 519973.i | −1.79577 | + | 1.79577i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 198544. | − | 170599.i | 0.663785 | − | 0.570357i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −217734. | − | 217734.i | −0.704981 | − | 0.704981i | 0.260495 | − | 0.965475i | \(-0.416114\pi\) |
−0.965475 | + | 0.260495i | \(0.916114\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −229962. | −0.721377 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 637559. | 1.93845 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 128681. | + | 128681.i | 0.379353 | + | 0.379353i | 0.870869 | − | 0.491515i | \(-0.163557\pi\) |
−0.491515 | + | 0.870869i | \(0.663557\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 401860. | + | 30421.8i | 1.14912 | + | 0.0869910i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 84402.8 | − | 84402.8i | 0.234189 | − | 0.234189i | −0.580250 | − | 0.814438i | \(-0.697045\pi\) |
0.814438 | + | 0.580250i | \(0.197045\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 45430.5i | 0.122358i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 853183.i | 2.23127i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 66342.8 | − | 66342.8i | 0.168530 | − | 0.168530i | −0.617803 | − | 0.786333i | \(-0.711977\pi\) |
0.786333 | + | 0.617803i | \(0.211977\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 294687. | + | 400557.i | 0.727388 | + | 0.988711i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −744888. | − | 744888.i | −1.78714 | − | 1.78714i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −393894. | −0.918855 | −0.459427 | − | 0.888215i | \(-0.651945\pi\) | ||||
−0.459427 | + | 0.888215i | \(0.651945\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 589531. | 1.33755 | 0.668775 | − | 0.743465i | \(-0.266819\pi\) | ||||
0.668775 | + | 0.743465i | \(0.266819\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −226627. | − | 226627.i | −0.500247 | − | 0.500247i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 30777.3 | − | 406557.i | 0.0661153 | − | 0.873357i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −295952. | + | 295952.i | −0.618895 | + | 0.618895i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 980686.i | 1.99699i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 146556.i | 0.290683i | 0.989382 | + | 0.145342i | \(0.0464281\pi\) | ||||
−0.989382 | + | 0.145342i | \(0.953572\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 649988. | − | 649988.i | 1.25606 | − | 1.25606i | 0.303109 | − | 0.952956i | \(-0.401975\pi\) |
0.952956 | − | 0.303109i | \(-0.0980246\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 556592. | + | 647765.i | 1.04822 | + | 1.21992i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −484881. | − | 484881.i | −0.890163 | − | 0.890163i | 0.104375 | − | 0.994538i | \(-0.466716\pi\) |
−0.994538 | + | 0.104375i | \(0.966716\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −728394. | −1.30387 | −0.651934 | − | 0.758275i | \(-0.726042\pi\) | ||||
−0.651934 | + | 0.758275i | \(0.726042\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.65166e6 | 2.88357 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −884055. | − | 884055.i | −1.50570 | − | 1.50570i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −60422.5 | − | 70320.0i | −0.100419 | − | 0.116868i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.34080e6 | + | 1.34080e6i | −2.17490 | + | 2.17490i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 485605.i | 0.768984i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 396241.i | − | 0.612708i | −0.951918 | − | 0.306354i | \(-0.900891\pi\) | ||
0.951918 | − | 0.306354i | \(-0.0991091\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 133290. | − | 133290.i | 0.201303 | − | 0.201303i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −19287.2 | + | 254777.i | −0.0284560 | + | 0.375893i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 526903. | + | 526903.i | 0.759593 | + | 0.759593i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 925856. | 1.30447 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −886956. | −1.22158 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −382870. | − | 382870.i | −0.515572 | − | 0.515572i | 0.400657 | − | 0.916228i | \(-0.368782\pi\) |
−0.916228 | + | 0.400657i | \(0.868782\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.46212e6 | − | 222648.i | −1.92543 | − | 0.293199i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 420420. | − | 420420.i | 0.541525 | − | 0.541525i | −0.382451 | − | 0.923976i | \(-0.624920\pi\) |
0.923976 | + | 0.382451i | \(0.124920\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 842886.i | 1.06214i | 0.847329 | + | 0.531068i | \(0.178209\pi\) | ||||
−0.847329 | + | 0.531068i | \(0.821791\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.14720e6i | 1.41453i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −36169.3 | + | 36169.3i | −0.0436466 | + | 0.0436466i | −0.728593 | − | 0.684947i | \(-0.759825\pi\) |
0.684947 | + | 0.728593i | \(0.259825\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 473120. | + | 35816.3i | 0.558858 | + | 0.0423069i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 579477. | + | 579477.i | 0.670139 | + | 0.670139i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 273532. | 0.309751 | 0.154876 | − | 0.987934i | \(-0.450502\pi\) | ||||
0.154876 | + | 0.987934i | \(0.450502\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 901321. | 0.999624 | 0.499812 | − | 0.866134i | \(-0.333402\pi\) | ||||
0.499812 | + | 0.866134i | \(0.333402\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 113998. | + | 113998.i | 0.123846 | + | 0.123846i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −361038. | + | 310222.i | −0.384272 | + | 0.330185i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −727669. | + | 727669.i | −0.758912 | + | 0.758912i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 971832.i | − | 0.993329i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.31819e6i | 1.32067i | 0.750973 | + | 0.660333i | \(0.229585\pi\) | ||||
−0.750973 | + | 0.660333i | \(0.770415\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −763144. | + | 763144.i | −0.749558 | + | 0.749558i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.76313e6 | − | 1.51497e6i | 1.69799 | − | 1.45900i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 684108. | + | 684108.i | 0.646088 | + | 0.646088i | 0.952045 | − | 0.305957i | \(-0.0989764\pi\) |
−0.305957 | + | 0.952045i | \(0.598976\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.16061e6 | 1.07507 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.71839e6 | 3.37873 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −974703. | − | 974703.i | −0.868926 | − | 0.868926i | 0.123427 | − | 0.992354i | \(-0.460611\pi\) |
−0.992354 | + | 0.123427i | \(0.960611\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 478961. | + | 36258.5i | 0.418973 | + | 0.0317173i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.60091e6 | − | 2.60091e6i | 2.23279 | − | 2.23279i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 775071.i | 0.653072i | 0.945185 | + | 0.326536i | \(0.105881\pi\) | ||||
−0.945185 | + | 0.326536i | \(0.894119\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 102988.i | − | 0.0851848i | −0.999093 | − | 0.0425924i | \(-0.986438\pi\) | ||
0.999093 | − | 0.0425924i | \(-0.0135617\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.71906e6 | + | 1.71906e6i | −1.39600 | + | 1.39600i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −832192. | − | 126724.i | −0.663578 | − | 0.101048i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.46313e6 | − | 1.46313e6i | −1.14573 | − | 1.14573i | −0.987384 | − | 0.158347i | \(-0.949384\pi\) |
−0.158347 | − | 0.987384i | \(-0.550616\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.21619e6 | −1.70449 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.69321e6 | −1.27922 | −0.639611 | − | 0.768699i | \(-0.720905\pi\) | ||||
−0.639611 | + | 0.768699i | \(0.720905\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 67338.9 | + | 67338.9i | 0.0499804 | + | 0.0499804i | 0.731655 | − | 0.681675i | \(-0.238748\pi\) |
−0.681675 | + | 0.731655i | \(0.738748\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 203594. | − | 2.68940e6i | 0.148475 | − | 1.96129i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 186618. | − | 186618.i | 0.133736 | − | 0.133736i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 994321.i | 0.700297i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.81320e6i | 1.25520i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 342591. | − | 342591.i | 0.233135 | − | 0.233135i | −0.580865 | − | 0.814000i | \(-0.697286\pi\) |
0.814000 | + | 0.580865i | \(0.197286\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.43400e6 | + | 1.66889e6i | 0.959385 | + | 1.11654i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.17386e6 | − | 1.17386e6i | −0.772192 | − | 0.772192i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.28711e6 | −1.47948 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −727321. | −0.462711 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −942588. | − | 942588.i | −0.589815 | − | 0.589815i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 436284. | + | 507750.i | 0.268547 | + | 0.312536i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8371.33 | − | 8371.33i | 0.00506931 | − | 0.00506931i | −0.704568 | − | 0.709637i | \(-0.748859\pi\) |
0.709637 | + | 0.704568i | \(0.248859\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 2.88809e6i | − | 1.72074i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 112470.i | − | 0.0659383i | −0.999456 | − | 0.0329691i | \(-0.989504\pi\) | ||
0.999456 | − | 0.0329691i | \(-0.0104963\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 932889. | − | 932889.i | 0.538232 | − | 0.538232i | −0.384778 | − | 0.923009i | \(-0.625722\pi\) |
0.923009 | + | 0.384778i | \(0.125722\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 317801. | − | 4.19803e6i | 0.180459 | − | 2.38379i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.24528e6 | − | 1.24528e6i | −0.696018 | − | 0.696018i | 0.267531 | − | 0.963549i | \(-0.413792\pi\) |
−0.963549 | + | 0.267531i | \(0.913792\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.11639e6 | 1.16445 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.26731e6 | −1.76982 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.98062e6 | + | 1.98062e6i | 1.05632 | + | 1.05632i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.05713e6 | − | 1.43692e6i | −0.555162 | − | 0.754611i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.61356e6 | − | 1.61356e6i | 0.834478 | − | 0.834478i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.35063e6i | 0.687936i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 558197.i | − | 0.280038i | −0.990149 | − | 0.140019i | \(-0.955284\pi\) | ||
0.990149 | − | 0.140019i | \(-0.0447164\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.44080e6 | + | 2.44080e6i | −1.20621 | + | 1.20621i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.44006e6 | − | 260421.i | −1.67477 | − | 0.126784i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.10837e6 | − | 2.10837e6i | −1.01128 | − | 1.01128i | −0.999936 | − | 0.0113470i | \(-0.996388\pi\) |
−0.0113470 | − | 0.999936i | \(-0.503612\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.69857e6 | −2.69319 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.26138e6 | −0.587436 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 933011. | + | 933011.i | 0.428205 | + | 0.428205i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.54643e6 | − | 3.90652e6i | 2.05647 | − | 1.76702i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.22415e6 | − | 1.22415e6i | 0.545773 | − | 0.545773i | −0.379442 | − | 0.925215i | \(-0.623884\pi\) |
0.925215 | + | 0.379442i | \(0.123884\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 1.81586e6i | − | 0.798027i | −0.916945 | − | 0.399014i | \(-0.869353\pi\) | ||
0.916945 | − | 0.399014i | \(-0.130647\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 3.51801e6i | − | 1.52416i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.92561e6 | + | 2.92561e6i | −1.24963 | + | 1.24963i | −0.293740 | + | 0.955885i | \(0.594900\pi\) |
−0.955885 | + | 0.293740i | \(0.905100\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −298632. | + | 256600.i | −0.125767 | + | 0.108065i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.67906e6 | + | 4.67906e6i | 1.94307 | + | 1.94307i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.12540e6 | −0.870372 | −0.435186 | − | 0.900341i | \(-0.643317\pi\) | ||||
−0.435186 | + | 0.900341i | \(0.643317\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 773749. | 0.312487 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.67463e6 | + | 1.67463e6i | 0.667040 | + | 0.667040i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.92836e6 | − | 145982.i | −0.757629 | − | 0.0573544i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.48776e6 | − | 2.48776e6i | 0.964149 | − | 0.964149i | −0.0352305 | − | 0.999379i | \(-0.511217\pi\) |
0.999379 | + | 0.0352305i | \(0.0112165\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 784925.i | 0.300097i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.36731e6i | 0.515741i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.03845e6 | + | 1.03845e6i | −0.386469 | + | 0.386469i | −0.873426 | − | 0.486957i | \(-0.838107\pi\) |
0.486957 | + | 0.873426i | \(0.338107\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.55575e6 | + | 1.05073e6i | 1.67294 | + | 0.385846i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.17137e6 | + | 3.17137e6i | 1.14919 | + | 1.14919i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.06631e6 | 0.738921 | 0.369461 | − | 0.929246i | \(-0.379542\pi\) | ||||
0.369461 | + | 0.929246i | \(0.379542\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.33714e6 | 0.824845 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −413143. | − | 413143.i | −0.143914 | − | 0.143914i | 0.631479 | − | 0.775393i | \(-0.282448\pi\) |
−0.775393 | + | 0.631479i | \(0.782448\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 180882. | − | 2.38938e6i | 0.0621933 | − | 0.821550i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.52958e6 | − | 1.52958e6i | 0.519152 | − | 0.519152i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.20146e6i | 0.737628i | 0.929503 | + | 0.368814i | \(0.120236\pi\) | ||||
−0.929503 | + | 0.368814i | \(0.879764\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.22522e6i | 2.05927i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.32312e6 | − | 4.32312e6i | 1.41194 | − | 1.41194i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.11556e6 | − | 1.29829e6i | −0.359749 | − | 0.418678i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.35037e6 | + | 1.35037e6i | 0.430007 | + | 0.430007i | 0.888630 | − | 0.458624i | \(-0.151657\pi\) |
−0.458624 | + | 0.888630i | \(0.651657\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.67752e6 | 2.41428 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −478159. | −0.148495 | −0.0742474 | − | 0.997240i | \(-0.523655\pi\) | ||||
−0.0742474 | + | 0.997240i | \(0.523655\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.89016e6 | − | 1.89016e6i | −0.579742 | − | 0.579742i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.81912e6 | + | 2.11710e6i | 0.551092 | + | 0.641364i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.38923e6 | + | 1.38923e6i | −0.415707 | + | 0.415707i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.52948e6i | 0.452101i | 0.974116 | + | 0.226051i | \(0.0725815\pi\) | ||||
−0.974116 | + | 0.226051i | \(0.927419\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.63786e6i | 2.23032i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.42897e6 | + | 4.42897e6i | −1.27770 | + | 1.27770i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −153231. | + | 2.02412e6i | −0.0436743 | + | 0.576921i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.32140e6 | − | 2.32140e6i | −0.653746 | − | 0.653746i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −430992. | −0.119932 | −0.0599658 | − | 0.998200i | \(-0.519099\pi\) | ||||
−0.0599658 | + | 0.998200i | \(0.519099\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 532919. | 0.146540 | 0.0732700 | − | 0.997312i | \(-0.476657\pi\) | ||||
0.0732700 | + | 0.997312i | \(0.476657\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.84042e6 | − | 2.84042e6i | −0.771849 | − | 0.771849i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.91110e6 | + | 2.87737e6i | −1.05033 | + | 0.772722i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.34748e6 | + | 1.34748e6i | −0.357647 | + | 0.357647i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 4.11536e6i | − | 1.07960i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 2.91761e6i | − | 0.756544i | −0.925695 | − | 0.378272i | \(-0.876518\pi\) | ||
0.925695 | − | 0.378272i | \(-0.123482\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.83132e6 | − | 2.83132e6i | 0.725719 | − | 0.725719i | −0.244045 | − | 0.969764i | \(-0.578474\pi\) |
0.969764 | + | 0.244045i | \(0.0784744\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.17211e7 | − | 887314.i | −2.96992 | − | 0.224830i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.10724e6 | + | 5.10724e6i | 1.27933 | + | 1.27933i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.88608e6 | 0.962389 | 0.481195 | − | 0.876614i | \(-0.340203\pi\) | ||||
0.481195 | + | 0.876614i | \(0.340203\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.02998e6 | 0.986748 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.65811e6 | − | 2.65811e6i | −0.643523 | − | 0.643523i | 0.307897 | − | 0.951420i | \(-0.400375\pi\) |
−0.951420 | + | 0.307897i | \(0.900375\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.82724e6 | + | 5.00706e6i | −1.39496 | + | 1.19862i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.30194e6 | + | 7.30194e6i | −1.72850 | + | 1.72850i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.36957e6i | 0.554695i | 0.960770 | + | 0.277347i | \(0.0894553\pi\) | ||||
−0.960770 | + | 0.277347i | \(0.910545\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 446755.i | 0.103425i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.16117e6 | − | 6.16117e6i | 1.41065 | − | 1.41065i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.85149e6 | − | 3.30939e6i | 0.872168 | − | 0.749411i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −522790. | − | 522790.i | −0.117095 | − | 0.117095i | 0.646132 | − | 0.763226i | \(-0.276386\pi\) |
−0.763226 | + | 0.646132i | \(0.776386\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −9.57557e6 | −2.12145 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.50003e6 | −0.547890 | −0.273945 | − | 0.961745i | \(-0.588329\pi\) | ||||
−0.273945 | + | 0.961745i | \(0.588329\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.66673e6 | + | 1.66673e6i | 0.361338 | + | 0.361338i | 0.864306 | − | 0.502967i | \(-0.167758\pi\) |
−0.502967 | + | 0.864306i | \(0.667758\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.98584e6 | + | 528845.i | 1.49826 | + | 0.113422i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −694126. | + | 694126.i | −0.147281 | + | 0.147281i | −0.776902 | − | 0.629621i | \(-0.783210\pi\) |
0.629621 | + | 0.776902i | \(0.283210\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 9.82047e6i | − | 2.06158i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 8.24101e6i | − | 1.71170i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 870588. | − | 870588.i | 0.178920 | − | 0.178920i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −848085. | + | 5.56934e6i | −0.172467 | + | 1.13258i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.87549e6 | − | 2.87549e6i | −0.578650 | − | 0.578650i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.67104e6 | −0.531914 | −0.265957 | − | 0.963985i | \(-0.585688\pi\) | ||||
−0.265957 | + | 0.963985i | \(0.585688\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.16346e6 | −0.820525 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.20655e7 | + | 1.20655e7i | 2.35329 | + | 2.35329i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 285891. | − | 3.77652e6i | 0.0551883 | − | 0.729016i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.46493e6 | + | 3.46493e6i | −0.662021 | + | 0.662021i | −0.955856 | − | 0.293835i | \(-0.905068\pi\) |
0.293835 | + | 0.955856i | \(0.405068\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.87043e6i | 0.921075i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.65929e6i | 0.872199i | 0.899898 | + | 0.436100i | \(0.143640\pi\) | ||||
−0.899898 | + | 0.436100i | \(0.856360\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.63205e6 | − | 8.63205e6i | 1.59955 | − | 1.59955i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.64454e6 | + | 5.40535e6i | 0.851981 | + | 0.991541i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −792520. | − | 792520.i | −0.143919 | − | 0.143919i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.22603e6 | 0.939551 | 0.469776 | − | 0.882786i | \(-0.344335\pi\) | ||||
0.469776 | + | 0.882786i | \(0.344335\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.19456e6 | 0.568613 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.92987e6 | − | 3.92987e6i | −0.692561 | − | 0.692561i | 0.270234 | − | 0.962795i | \(-0.412899\pi\) |
−0.962795 | + | 0.270234i | \(0.912899\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.81459e6 | + | 2.11183e6i | 0.316629 | + | 0.368494i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −859749. | + | 859749.i | −0.148543 | + | 0.148543i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.30782e6i | 1.25024i | 0.780529 | + | 0.625120i | \(0.214950\pi\) | ||||
−0.780529 | + | 0.625120i | \(0.785050\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 5.50497e6i | − | 0.932615i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.85591e6 | + | 7.85591e6i | −1.31796 | + | 1.31796i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −455372. | + | 6.01529e6i | −0.0756568 | + | 0.999398i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.61668e6 | − | 1.61668e6i | −0.266010 | − | 0.266010i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.51100e6 | 0.409194 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.41968e6 | 0.551940 | 0.275970 | − | 0.961166i | \(-0.411001\pi\) | ||||
0.275970 | + | 0.961166i | \(0.411001\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.89585e6 | − | 7.89585e6i | −1.26225 | − | 1.26225i | −0.950001 | − | 0.312248i | \(-0.898918\pi\) |
−0.312248 | − | 0.950001i | \(-0.601082\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.00354e6 | + | 1.31571e7i | −0.317248 | + | 2.08335i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.14476e6 | + | 5.14476e6i | −0.806935 | + | 0.806935i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.61605e6i | 1.49402i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 1.86285e7i | − | 2.86709i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −669452. | + | 669452.i | −0.102071 | + | 0.102071i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.80512e6 | + | 515164.i | 1.02790 | + | 0.0778146i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.45424e6 | − | 7.45424e6i | −1.11550 | − | 1.11550i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.29374e6 | 0.340073 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.77154e6 | 0.554020 | 0.277010 | − | 0.960867i | \(-0.410656\pi\) | ||||
0.277010 | + | 0.960867i | \(0.410656\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.11566e7 | + | 1.11566e7i | 1.62379 | + | 1.62379i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.61511e6 | + | 3.10629e6i | −0.521351 | + | 0.447971i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.30474e6 | − | 8.30474e6i | 1.18675 | − | 1.18675i | 0.208783 | − | 0.977962i | \(-0.433050\pi\) |
0.977962 | − | 0.208783i | \(-0.0669503\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 5.66760e6i | − | 0.802543i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 1.41637e7i | − | 1.98745i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.44546e6 | − | 3.44546e6i | 0.479109 | − | 0.479109i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.27632e6 | − | 7.11143e6i | 1.14053 | − | 0.979996i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.82357e6 | − | 3.82357e6i | −0.522193 | − | 0.522193i | 0.396040 | − | 0.918233i | \(-0.370384\pi\) |
−0.918233 | + | 0.396040i | \(0.870384\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.60912e6 | 0.353154 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.12015e7 | −1.50269 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.83668e6 | − | 7.83668e6i | −1.04198 | − | 1.04198i | −0.999079 | − | 0.0429050i | \(-0.986339\pi\) |
−0.0429050 | − | 0.999079i | \(-0.513661\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.18689e7 | + | 898506.i | 1.56419 | + | 0.118413i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.61844e6 | + | 5.61844e6i | −0.733936 | + | 0.733936i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 1.06662e7i | − | 1.38111i | −0.723280 | − | 0.690555i | \(-0.757366\pi\) | ||
0.723280 | − | 0.690555i | \(-0.242634\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 103844.i | 0.0133288i | 0.999978 | + | 0.00666439i | \(0.00212136\pi\) | ||||
−0.999978 | + | 0.00666439i | \(0.997879\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.77349e6 | + | 2.77349e6i | −0.352891 | + | 0.352891i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.00852e7 | + | 7.41960e6i | −1.27208 | + | 0.935861i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.35378e6 | + | 5.35378e6i | 0.669455 | + | 0.669455i | 0.957590 | − | 0.288135i | \(-0.0930352\pi\) |
−0.288135 | + | 0.957590i | \(0.593035\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.46014e7 | 3.04974 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.77833e6 | −0.710170 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.63664e6 | − | 1.63664e6i | −0.199426 | − | 0.199426i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.14004e6 | + | 1.50596e7i | −0.137731 | + | 1.81938i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.02584e6 | − | 3.02584e6i | 0.362453 | − | 0.362453i | −0.502263 | − | 0.864715i | \(-0.667499\pi\) |
0.864715 | + | 0.502263i | \(0.167499\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.44164e6i | 1.00263i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 1.83522e7i | − | 2.16133i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.77341e6 | − | 7.77341e6i | 0.907768 | − | 0.907768i | −0.0883240 | − | 0.996092i | \(-0.528151\pi\) |
0.996092 | + | 0.0883240i | \(0.0281511\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.00774e6 | − | 1.04833e7i | −1.04309 | − | 1.21396i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.37845e7 | − | 1.37845e7i | −1.58290 | − | 1.58290i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −396440. | −0.0451451 | −0.0225726 | − | 0.999745i | \(-0.507186\pi\) | ||||
−0.0225726 | + | 0.999745i | \(0.507186\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.27167e6 | −0.369474 | −0.184737 | − | 0.982788i | \(-0.559143\pi\) | ||||
−0.184737 | + | 0.982788i | \(0.559143\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.06527e7 | + | 2.06527e7i | 2.31305 | + | 2.31305i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.22385e6 | − | 3.75194e6i | −0.358086 | − | 0.416742i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.39370e6 | + | 7.39370e6i | −0.814498 | + | 0.814498i | −0.985305 | − | 0.170807i | \(-0.945363\pi\) |
0.170807 | + | 0.985305i | \(0.445363\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 3.34606e7i | − | 3.65587i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 4.84512e6i | − | 0.525051i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.55531e6 | + | 3.55531e6i | −0.382143 | + | 0.382143i | −0.871874 | − | 0.489730i | \(-0.837095\pi\) |
0.489730 | + | 0.871874i | \(0.337095\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 187305. | − | 2.47423e6i | 0.0199693 | − | 0.263787i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.25539e6 | + | 3.25539e6i | 0.344263 | + | 0.344263i | 0.857967 | − | 0.513704i | \(-0.171727\pi\) |
−0.513704 | + | 0.857967i | \(0.671727\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.78255e7 | −1.86989 | −0.934943 | − | 0.354798i | \(-0.884550\pi\) | ||||
−0.934943 | + | 0.354798i | \(0.884550\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.46916e7 | −2.56933 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.54645e7 | − | 1.54645e7i | −1.59631 | − | 1.59631i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.32299e6 | − | 2.90677e6i | −0.954674 | − | 0.297653i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.18982e6 | + | 9.18982e6i | −0.933551 | + | 0.933551i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.13324e7i | 1.14208i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.77949e7i | 1.77919i | 0.456754 | + | 0.889593i | \(0.349012\pi\) | ||||
−0.456754 | + | 0.889593i | \(0.650988\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.49866e6 | − | 7.49866e6i | 0.743831 | − | 0.743831i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.86777e6 | − | 368502.i | −0.479066 | − | 0.0362665i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.43712e6 | + | 3.43712e6i | 0.335618 | + | 0.335618i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.33339e6 | 0.322949 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.48962e6 | −0.335454 | −0.167727 | − | 0.985833i | \(-0.553643\pi\) | ||||
−0.167727 | + | 0.985833i | \(0.553643\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.79073e6 | + | 9.79073e6i | 0.933873 | + | 0.933873i | 0.997945 | − | 0.0640725i | \(-0.0204089\pi\) |
−0.0640725 | + | 0.997945i | \(0.520409\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.18652e6 | + | 4.45652e6i | −0.490882 | + | 0.421790i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.53507e6 | − | 9.53507e6i | 0.895495 | − | 0.895495i | −0.0995389 | − | 0.995034i | \(-0.531737\pi\) |
0.995034 | + | 0.0995389i | \(0.0317368\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1.06028e7i | − | 0.988114i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.99427e7i | 1.84430i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.15953e7 | − | 1.15953e7i | 1.06414 | − | 1.06414i | 0.0663484 | − | 0.997797i | \(-0.478865\pi\) |
0.997797 | − | 0.0663484i | \(-0.0211349\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.68577e6 | + | 8.32250e6i | −0.882127 | + | 0.757968i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.15771e7 | + | 1.15771e7i | 1.04637 | + | 1.04637i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.06117e6 | 0.543679 | 0.271840 | − | 0.962343i | \(-0.412368\pi\) | ||||
0.271840 | + | 0.962343i | \(0.412368\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.27293e6 | 0.380384 | 0.190192 | − | 0.981747i | \(-0.439089\pi\) | ||||
0.190192 | + | 0.981747i | \(0.439089\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.67852e7 | − | 1.67852e7i | −1.48300 | − | 1.48300i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.59906e7 | − | 1.21053e6i | −1.40221 | − | 0.106150i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.22587e7 | − | 2.22587e7i | 1.93724 | − | 1.93724i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 1.44912e7i | − | 1.25181i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 3.22582e6i | − | 0.276588i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.55486e6 | − | 5.55486e6i | 0.472755 | − | 0.472755i | −0.430050 | − | 0.902805i | \(-0.641504\pi\) |
0.902805 | + | 0.430050i | \(0.141504\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.14128e7 | − | 1.55129e7i | −0.964121 | − | 1.31049i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.30293e7 | + | 1.30293e7i | 1.09257 | + | 1.09257i | 0.995254 | + | 0.0973148i | \(0.0310253\pi\) |
0.0973148 | + | 0.995254i | \(0.468975\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.07810e7 | 0.897393 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.59124e7 | 1.31483 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 378888. | + | 378888.i | 0.0310784 | + | 0.0310784i | 0.722475 | − | 0.691397i | \(-0.243004\pi\) |
−0.691397 | + | 0.722475i | \(0.743004\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.20428e6 | − | 1.59081e7i | 0.0980619 | − | 1.29536i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.59512e7 | + | 1.59512e7i | −1.28944 | + | 1.28944i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 4.90494e6i | − | 0.393628i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 2.01178e7i | − | 1.60282i | −0.598113 | − | 0.801412i | \(-0.704083\pi\) | ||
0.598113 | − | 0.801412i | \(-0.295917\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.43449e7 | + | 1.43449e7i | −1.13466 | + | 1.13466i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.46896e6 | + | 5.20100e6i | 0.350949 | + | 0.408437i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.82216e6 | + | 1.82216e6i | 0.142071 | + | 0.142071i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.36897e6 | −0.105974 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 891657. | 0.0685335 | 0.0342667 | − | 0.999413i | \(-0.489090\pi\) | ||||
0.0342667 | + | 0.999413i | \(0.489090\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.29723e6 | + | 9.29723e6i | 0.709521 | + | 0.709521i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.27575e6 | + | 9.63136e6i | 0.627097 | + | 0.729818i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.60445e6 | + | 5.60445e6i | −0.421682 | + | 0.421682i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.98980e7i | 1.48660i | 0.668959 | + | 0.743299i | \(0.266740\pi\) | ||||
−0.668959 | + | 0.743299i | \(0.733260\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.44918e7i | 1.07510i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.32663e7 | + | 1.32663e7i | −0.977296 | + | 0.977296i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −648877. | + | 8.57142e6i | −0.0474676 | + | 0.627029i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.17644e6 | + | 5.17644e6i | 0.376040 | + | 0.376040i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.06358e7 | 0.767272 | 0.383636 | − | 0.923484i | \(-0.374672\pi\) | ||||
0.383636 | + | 0.923484i | \(0.374672\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.71721e7 | −1.23022 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.70570e7 | + | 1.70570e7i | 1.21355 | + | 1.21355i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.42726e7 | + | 3.69617e6i | 1.71503 | + | 0.261160i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.76230e6 | − | 3.76230e6i | 0.264008 | − | 0.264008i | −0.562672 | − | 0.826680i | \(-0.690227\pi\) |
0.826680 | + | 0.562672i | \(0.190227\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.64482e7i | 1.14631i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 7.10167e6i | − | 0.491550i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.16678e7 | − | 1.16678e7i | 0.802104 | − | 0.802104i | −0.181320 | − | 0.983424i | \(-0.558037\pi\) |
0.983424 | + | 0.181320i | \(0.0580369\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.27033e7 | − | 961668.i | −0.867355 | − | 0.0656609i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.17549e7 | + | 1.17549e7i | 0.797167 | + | 0.797167i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.52408e6 | 0.102659 | 0.0513296 | − | 0.998682i | \(-0.483654\pi\) | ||||
0.0513296 | + | 0.998682i | \(0.483654\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.75415e7 | −1.84265 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.92734e6 | + | 5.92734e6i | 0.393901 | + | 0.393901i | 0.876075 | − | 0.482174i | \(-0.160153\pi\) |
−0.482174 | + | 0.876075i | \(0.660153\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.63597e7 | − | 1.40571e7i | 1.07990 | − | 0.927907i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.21520e7 | − | 1.21520e7i | 0.796795 | − | 0.796795i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.94268e7i | 1.26531i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1.28380e7i | − | 0.830614i | −0.909681 | − | 0.415307i | \(-0.863674\pi\) | ||
0.909681 | − | 0.415307i | \(-0.136326\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.49460e7 | + | 2.49460e7i | −1.60330 | + | 1.60330i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.38039e7 | + | 1.18610e7i | −0.881319 | + | 0.757274i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.71886e6 | + | 9.71886e6i | 0.616418 | + | 0.616418i | 0.944611 | − | 0.328192i | \(-0.106439\pi\) |
−0.328192 | + | 0.944611i | \(0.606439\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.88842e7 | −1.81993 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.02827e7 | −1.26959 | −0.634795 | − | 0.772680i | \(-0.718916\pi\) | ||||
−0.634795 | + | 0.772680i | \(0.718916\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.59391e6 | − | 9.59391e6i | −0.596602 | − | 0.596602i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.09902e7 | + | 3.10305e6i | 2.53236 | + | 0.191706i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.58880e7 | − | 1.58880e7i | 0.975171 | − | 0.975171i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 4.07161e6i | − | 0.248285i | −0.992264 | − | 0.124142i | \(-0.960382\pi\) | ||
0.992264 | − | 0.124142i | \(-0.0396180\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.58928e7i | 1.56871i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.88515e7 | − | 1.88515e7i | 1.13474 | − | 1.13474i | 0.145362 | − | 0.989378i | \(-0.453565\pi\) |
0.989378 | − | 0.145362i | \(-0.0464348\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.44666e7 | − | 2.20294e6i | −0.865194 | − | 0.131750i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.19640e7 | + | 2.19640e7i | 1.30514 | + | 1.30514i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.98985e6 | 0.176525 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.89726e6 | 0.111301 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.42381e7 | + | 3.42381e7i | 1.99574 | + | 1.99574i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.29938e6 | + | 1.71643e7i | −0.0752595 | + | 0.994148i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.81274e6 | + | 1.81274e6i | −0.104327 | + | 0.104327i | −0.757344 | − | 0.653016i | \(-0.773503\pi\) |
0.653016 | + | 0.757344i | \(0.273503\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 3.68915e7i | − | 2.10976i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.38826e7i | 1.92547i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.83382e6 | − | 4.83382e6i | 0.272966 | − | 0.272966i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.37792e6 | + | 9.75027e6i | 0.470130 | + | 0.547140i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.40418e7 | − | 1.40418e7i | −0.783027 | − | 0.783027i | 0.197313 | − | 0.980341i | \(-0.436778\pi\) |
−0.980341 | + | 0.197313i | \(0.936778\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.31878e7 | −0.730811 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.50448e7 | 3.58204 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.58933e6 | + | 6.58933e6i | 0.360622 | + | 0.360622i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.32274e7 | − | 2.70322e7i | −1.26331 | − | 1.47025i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.46678e7 | + | 1.46678e7i | −0.792833 | + | 0.792833i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 5.17254e6i | − | 0.277864i | −0.990302 | − | 0.138932i | \(-0.955633\pi\) | ||
0.990302 | − | 0.138932i | \(-0.0443670\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.42351e6i | 0.396330i | 0.980169 | + | 0.198165i | \(0.0634982\pi\) | ||||
−0.980169 | + | 0.198165i | \(0.936502\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.94899e6 | − | 1.94899e6i | 0.103415 | − | 0.103415i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 767931. | − | 1.01441e7i | 0.0404975 | − | 0.534956i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.82630e6 | − | 5.82630e6i | −0.305378 | − | 0.305378i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.29911e7 | −2.23959 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.07068e6 | 0.417881 | 0.208940 | − | 0.977928i | \(-0.432999\pi\) | ||||
0.208940 | + | 0.977928i | \(0.432999\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.89931e6 | + | 4.89931e6i | 0.252136 | + | 0.252136i | 0.821846 | − | 0.569710i | \(-0.192944\pi\) |
−0.569710 | + | 0.821846i | \(0.692944\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.33506e7 | − | 1.81470e7i | −0.682915 | − | 0.928260i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.10433e7 | + | 1.10433e7i | −0.561482 | + | 0.561482i | −0.929728 | − | 0.368247i | \(-0.879958\pi\) |
0.368247 | + | 0.929728i | \(0.379958\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.14531e6i | 0.462181i | 0.972932 | + | 0.231091i | \(0.0742294\pi\) | ||||
−0.972932 | + | 0.231091i | \(0.925771\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 5.53778e7i | − | 2.78185i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.35539e6 | − | 9.35539e6i | 0.467142 | − | 0.467142i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.65359e6 | − | 503693.i | −0.330248 | − | 0.0250005i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.04061e7 | − | 2.04061e7i | −1.00681 | − | 1.00681i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.10920e6 | −0.299626 | −0.149813 | − | 0.988714i | \(-0.547867\pi\) | ||||
−0.149813 | + | 0.988714i | \(0.547867\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.12177e7 | −2.00953 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.20432e7 | − | 3.20432e7i | −1.55298 | − | 1.55298i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.92623e6 | − | 1.65512e6i | 0.0928041 | − | 0.0797419i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.95703e6 | − | 9.95703e6i | 0.476893 | − | 0.476893i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.54871e6i | 0.121353i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.92218e7i | 1.38319i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.91716e7 | + | 1.91716e7i | −0.902162 | + | 0.902162i | −0.995623 | − | 0.0934606i | \(-0.970207\pi\) |
0.0934606 | + | 0.995623i | \(0.470207\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.61746e7 | − | 3.10830e7i | 1.69234 | − | 1.45415i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.93923e6 | − | 6.93923e6i | −0.322745 | − | 0.322745i | 0.527074 | − | 0.849819i | \(-0.323289\pi\) |
−0.849819 | + | 0.527074i | \(0.823289\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.45235e7 | −1.13396 | −0.566981 | − | 0.823731i | \(-0.691889\pi\) | ||||
−0.566981 | + | 0.823731i | \(0.691889\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.06328e6 | 0.324712 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.42655e6 | − | 6.42655e6i | −0.293732 | − | 0.293732i | 0.544821 | − | 0.838552i | \(-0.316598\pi\) |
−0.838552 | + | 0.544821i | \(0.816598\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.22989e6 | − | 395916.i | −0.237658 | − | 0.0179913i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.88170e7 | + | 1.88170e7i | −0.850165 | + | 0.850165i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.24828e6i | 0.370522i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.52289e7i | 1.57345i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.26727e7 | + | 2.26727e7i | −1.00686 | + | 1.00686i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.24746e6 | − | 2.70876e7i | 0.275856 | − | 1.19605i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.15276e7 | + | 2.15276e7i | 0.945142 | + | 0.945142i | 0.998572 | − | 0.0534292i | \(-0.0170151\pi\) |
−0.0534292 | + | 0.998572i | \(0.517015\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.29667e7 | 0.566055 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.72835e7 | 1.61836 | 0.809182 | − | 0.587558i | \(-0.199910\pi\) | ||||
0.809182 | + | 0.587558i | \(0.199910\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.55054e6 | − | 6.55054e6i | −0.282732 | − | 0.282732i | 0.551465 | − | 0.834198i | \(-0.314069\pi\) |
−0.834198 | + | 0.551465i | \(0.814069\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.44529e6 | + | 5.87206e7i | −0.190784 | + | 2.52018i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.51685e6 | + | 3.51685e6i | −0.150087 | + | 0.150087i | −0.778157 | − | 0.628070i | \(-0.783845\pi\) |
0.628070 | + | 0.778157i | \(0.283845\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1.38962e7i | − | 0.589714i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 1.34503e7i | − | 0.567594i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.08194e7 | + | 1.08194e7i | −0.454020 | + | 0.454020i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.43503e7 | + | 1.67009e7i | 0.598829 | + | 0.696920i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.32824e7 | − | 4.32824e7i | −1.79610 | − | 1.79610i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.67908e7 | 1.51824 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.33506e7 | −0.547884 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.37642e7 | − | 1.37642e7i | −0.561734 | − | 0.561734i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.14777e7 | − | 2.49958e7i | −0.871698 | − | 1.01449i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.47394e6 | − | 7.47394e6i | 0.301670 | − | 0.301670i | −0.539997 | − | 0.841667i | \(-0.681575\pi\) |
0.841667 | + | 0.539997i | \(0.181575\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 2.35727e7i | − | 0.946235i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 2.11403e6i | − | 0.0843949i | −0.999109 | − | 0.0421974i | \(-0.986564\pi\) | ||
0.999109 | − | 0.0421974i | \(-0.0134358\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.91654e6 | − | 6.91654e6i | 0.274607 | − | 0.274607i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.35245e6 | + | 1.78654e7i | −0.0534034 | + | 0.705438i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.57044e7 | − | 2.57044e7i | −1.00945 | − | 1.00945i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.25445e7 | 1.27113 | 0.635564 | − | 0.772049i | \(-0.280768\pi\) | ||||
0.635564 | + | 0.772049i | \(0.280768\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 316846. | 0.0123083 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.84300e6 | + | 2.84300e6i | 0.109843 | + | 0.109843i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.83591e7 | + | 1.35067e7i | −0.705500 | + | 0.519031i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.61134e7 | − | 3.61134e7i | 1.38028 | − | 1.38028i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 3.59514e6i | − | 0.136671i | −0.997662 | − | 0.0683354i | \(-0.978231\pi\) | ||
0.997662 | − | 0.0683354i | \(-0.0217688\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 1.53505e7i | − | 0.580430i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.12845e6 | − | 2.12845e6i | 0.0800494 | − | 0.0800494i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.33303e7 | + | 1.76616e6i | 0.872753 | + | 0.0660695i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.34165e7 | + | 2.34165e7i | 0.871312 | + | 0.871312i | 0.992616 | − | 0.121303i | \(-0.0387073\pi\) |
−0.121303 | + | 0.992616i | \(0.538707\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.53089e7 | 1.30683 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.41809e7 | 0.890221 | 0.445111 | − | 0.895476i | \(-0.353164\pi\) | ||||
0.445111 | + | 0.895476i | \(0.353164\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.69864e6 | + | 4.69864e6i | 0.172065 | + | 0.172065i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.15807e7 | − | 3.57282e7i | 1.51465 | − | 1.30146i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.13320e6 | + | 4.13320e6i | −0.149765 | + | 0.149765i | −0.778013 | − | 0.628248i | \(-0.783772\pi\) |
0.628248 | + | 0.778013i | \(0.283772\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.97479e7i | 0.711797i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 4.71327e7i | − | 1.68994i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.17837e7 | − | 2.17837e7i | 0.776961 | − | 0.776961i | −0.202352 | − | 0.979313i | \(-0.564858\pi\) |
0.979313 | + | 0.202352i | \(0.0648584\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.21390e6 | − | 5.33930e6i | 0.220473 | − | 0.189442i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.00516e7 | + | 4.00516e7i | 1.41364 | + | 1.41364i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.54133e7 | 1.59454 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.70158e6 | 0.234082 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.08552e7 | − | 4.08552e7i | −1.41965 | − | 1.41965i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.12394e7 | − | 3.87895e6i | −1.77128 | − | 0.134090i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.19376e7 | − | 1.19376e7i | 0.410537 | − | 0.410537i | −0.471389 | − | 0.881925i | \(-0.656247\pi\) |
0.881925 | + | 0.471389i | \(0.156247\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.49644e7i | 2.56475i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.44007e7i | 1.17090i | 0.810709 | + | 0.585449i | \(0.199082\pi\) | ||||
−0.810709 | + | 0.585449i | \(0.800918\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.38026e7 | + | 1.38026e7i | −0.467389 | + | 0.467389i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.18727e6 | − | 4.71985e7i | 0.242132 | − | 1.59007i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.17722e7 | − | 2.17722e7i | −0.729735 | − | 0.729735i | 0.240832 | − | 0.970567i | \(-0.422580\pi\) |
−0.970567 | + | 0.240832i | \(0.922580\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.70214e7 | 1.23451 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.03526e7 | 1.33875 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.19706e7 | − | 2.19706e7i | −0.725202 | − | 0.725202i | 0.244458 | − | 0.969660i | \(-0.421390\pi\) |
−0.969660 | + | 0.244458i | \(0.921390\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.89364e6 | + | 3.82238e7i | −0.0950284 | + | 1.25529i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.55600e7 | + | 2.55600e7i | −0.835158 | + | 0.835158i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 1.83124e7i | − | 0.595326i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.31203e7i | 1.39475i | 0.716704 | + | 0.697377i | \(0.245650\pi\) | ||||
−0.716704 | + | 0.697377i | \(0.754350\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.05636e7 | − | 1.05636e7i | 0.339968 | − | 0.339968i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.65367e7 | + | 3.08836e7i | 0.849747 | + | 0.988940i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.23176e7 | − | 2.23176e7i | −0.711065 | − | 0.711065i | 0.255693 | − | 0.966758i | \(-0.417696\pi\) |
−0.966758 | + | 0.255693i | \(0.917696\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.49487e7 | −1.42496 |
(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 | 160.6.n.b.127.7 | yes | 14 | |
4.3 | odd | 2 | 160.6.n.a.127.1 | yes | 14 | ||
5.3 | odd | 4 | 160.6.n.a.63.1 | ✓ | 14 | ||
20.3 | even | 4 | inner | 160.6.n.b.63.7 | yes | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.6.n.a.63.1 | ✓ | 14 | 5.3 | odd | 4 | ||
160.6.n.a.127.1 | yes | 14 | 4.3 | odd | 2 | ||
160.6.n.b.63.7 | yes | 14 | 20.3 | even | 4 | inner | |
160.6.n.b.127.7 | yes | 14 | 1.1 | even | 1 | trivial |