Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,5,Mod(19,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.19");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.f (of order \(6\), degree \(2\), not 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: | \(11.1639560131\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 19.15 | ||
Character | \(\chi\) | \(=\) | 108.19 |
Dual form | 108.5.f.a.91.15 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.14060 | − | 3.37903i | 0.535150 | − | 0.844757i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −6.83568 | − | 14.4663i | −0.427230 | − | 0.904143i | ||||
\(5\) | 14.8847 | + | 25.7811i | 0.595388 | + | 1.03124i | 0.993492 | + | 0.113902i | \(0.0363350\pi\) |
−0.398104 | + | 0.917340i | \(0.630332\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 51.8739 | + | 29.9494i | 1.05865 | + | 0.611212i | 0.925059 | − | 0.379824i | \(-0.124016\pi\) |
0.133592 | + | 0.991036i | \(0.457349\pi\) | |||||||
\(8\) | −63.5145 | − | 7.86857i | −0.992413 | − | 0.122946i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 118.977 | + | 4.89106i | 1.18977 | + | 0.0489106i | ||||
\(11\) | 195.278 | + | 112.744i | 1.61387 | + | 0.931767i | 0.988462 | + | 0.151467i | \(0.0483998\pi\) |
0.625406 | + | 0.780300i | \(0.284934\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −85.8824 | − | 148.753i | −0.508180 | − | 0.880194i | −0.999955 | − | 0.00947137i | \(-0.996985\pi\) |
0.491775 | − | 0.870722i | \(-0.336348\pi\) | |||||||
\(14\) | 212.241 | − | 111.174i | 1.08286 | − | 0.567213i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −162.547 | + | 197.774i | −0.634949 | + | 0.772554i | ||||
\(17\) | 99.0725 | 0.342812 | 0.171406 | − | 0.985201i | \(-0.445169\pi\) | ||||
0.171406 | + | 0.985201i | \(0.445169\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 169.267i | − | 0.468884i | −0.972130 | − | 0.234442i | \(-0.924674\pi\) | ||
0.972130 | − | 0.234442i | \(-0.0753262\pi\) | |||||||
\(20\) | 271.209 | − | 391.557i | 0.678023 | − | 0.978893i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 798.976 | − | 418.511i | 1.65078 | − | 0.864692i | ||||
\(23\) | 310.777 | − | 179.427i | 0.587480 | − | 0.339182i | −0.176620 | − | 0.984279i | \(-0.556516\pi\) |
0.764101 | + | 0.645097i | \(0.223183\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −130.609 | + | 226.221i | −0.208974 | + | 0.361953i | ||||
\(26\) | −686.480 | − | 28.2206i | −1.01550 | − | 0.0417465i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 78.6636 | − | 955.147i | 0.100336 | − | 1.21830i | ||||
\(29\) | −9.01635 | + | 15.6168i | −0.0107210 | + | 0.0185693i | −0.871336 | − | 0.490687i | \(-0.836746\pi\) |
0.860615 | + | 0.509256i | \(0.170079\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −671.898 | + | 387.920i | −0.699165 | + | 0.403663i | −0.807036 | − | 0.590502i | \(-0.798930\pi\) |
0.107871 | + | 0.994165i | \(0.465597\pi\) | |||||||
\(32\) | 320.335 | + | 972.605i | 0.312827 | + | 0.949810i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 212.075 | − | 334.769i | 0.183455 | − | 0.289593i | ||||
\(35\) | 1783.15i | 1.45563i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 609.762 | 0.445407 | 0.222703 | − | 0.974886i | \(-0.428512\pi\) | ||||
0.222703 | + | 0.974886i | \(0.428512\pi\) | |||||||
\(38\) | −571.958 | − | 362.333i | −0.396093 | − | 0.250923i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −742.534 | − | 1754.59i | −0.464083 | − | 1.09662i | ||||
\(41\) | −206.545 | − | 357.747i | −0.122871 | − | 0.212818i | 0.798028 | − | 0.602620i | \(-0.205877\pi\) |
−0.920899 | + | 0.389802i | \(0.872543\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −265.498 | − | 153.286i | −0.143590 | − | 0.0829019i | 0.426484 | − | 0.904495i | \(-0.359752\pi\) |
−0.570074 | + | 0.821593i | \(0.693085\pi\) | |||||||
\(44\) | 296.127 | − | 3595.63i | 0.152958 | − | 1.85725i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 58.9591 | − | 1434.21i | 0.0278635 | − | 0.677791i | ||||
\(47\) | 2270.59 | + | 1310.93i | 1.02788 | + | 0.593447i | 0.916377 | − | 0.400317i | \(-0.131100\pi\) |
0.111504 | + | 0.993764i | \(0.464433\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 593.432 | + | 1027.85i | 0.247160 | + | 0.428094i | ||||
\(50\) | 484.826 | + | 925.578i | 0.193930 | + | 0.370231i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1564.84 | + | 2259.23i | −0.578711 | + | 0.835512i | ||||
\(53\) | −2034.30 | −0.724209 | −0.362104 | − | 0.932138i | \(-0.617942\pi\) | ||||
−0.362104 | + | 0.932138i | \(0.617942\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6712.63i | 2.21905i | ||||||||
\(56\) | −3059.08 | − | 2310.39i | −0.975472 | − | 0.736732i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 33.4692 | + | 63.8958i | 0.00994922 | + | 0.0189940i | ||||
\(59\) | −2250.48 | + | 1299.32i | −0.646505 | + | 0.373260i | −0.787116 | − | 0.616805i | \(-0.788427\pi\) |
0.140611 | + | 0.990065i | \(0.455093\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 708.681 | − | 1227.47i | 0.190455 | − | 0.329877i | −0.754946 | − | 0.655786i | \(-0.772337\pi\) |
0.945401 | + | 0.325910i | \(0.105670\pi\) | |||||||
\(62\) | −127.469 | + | 3100.74i | −0.0331606 | + | 0.806645i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3972.17 | + | 999.536i | 0.969768 | + | 0.244027i | ||||
\(65\) | 2556.67 | − | 4428.28i | 0.605129 | − | 1.04811i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5191.93 | + | 2997.56i | −1.15659 | + | 0.667758i | −0.950485 | − | 0.310772i | \(-0.899412\pi\) |
−0.206106 | + | 0.978530i | \(0.566079\pi\) | |||||||
\(68\) | −677.228 | − | 1433.21i | −0.146459 | − | 0.309951i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6025.32 | + | 3817.01i | 1.22966 | + | 0.778982i | ||||
\(71\) | 1239.44i | 0.245872i | 0.992415 | + | 0.122936i | \(0.0392310\pi\) | ||||
−0.992415 | + | 0.122936i | \(0.960769\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5060.60 | −0.949633 | −0.474817 | − | 0.880085i | \(-0.657486\pi\) | ||||
−0.474817 | + | 0.880085i | \(0.657486\pi\) | |||||||
\(74\) | 1305.25 | − | 2060.40i | 0.238359 | − | 0.376260i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2448.66 | + | 1157.05i | −0.423938 | + | 0.200321i | ||||
\(77\) | 6753.22 | + | 11696.9i | 1.13901 | + | 1.97283i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1635.99 | − | 944.538i | −0.262135 | − | 0.151344i | 0.363173 | − | 0.931722i | \(-0.381693\pi\) |
−0.625308 | + | 0.780378i | \(0.715027\pi\) | |||||||
\(80\) | −7518.28 | − | 1246.83i | −1.17473 | − | 0.194818i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1650.97 | − | 67.8700i | −0.245534 | − | 0.0100937i | ||||
\(83\) | −5831.54 | − | 3366.84i | −0.846500 | − | 0.488727i | 0.0129681 | − | 0.999916i | \(-0.495872\pi\) |
−0.859469 | + | 0.511189i | \(0.829205\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1474.66 | + | 2554.19i | 0.204106 | + | 0.353522i | ||||
\(86\) | −1086.28 | + | 569.004i | −0.146874 | + | 0.0769340i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −11515.8 | − | 8697.42i | −1.48707 | − | 1.12312i | ||||
\(89\) | −9436.67 | −1.19135 | −0.595674 | − | 0.803226i | \(-0.703115\pi\) | ||||
−0.595674 | + | 0.803226i | \(0.703115\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 10288.5i | − | 1.24242i | ||||||
\(92\) | −4720.02 | − | 3269.29i | −0.557658 | − | 0.386258i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9290.07 | − | 4866.22i | 1.05139 | − | 0.550727i | ||||
\(95\) | 4363.88 | − | 2519.49i | 0.483533 | − | 0.279168i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7297.91 | − | 12640.4i | 0.775631 | − | 1.34343i | −0.158808 | − | 0.987309i | \(-0.550765\pi\) |
0.934439 | − | 0.356123i | \(-0.115902\pi\) | |||||||
\(98\) | 4743.45 | + | 195.000i | 0.493904 | + | 0.0203040i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4165.37 | + | 343.050i | 0.416537 | + | 0.0343050i | ||||
\(101\) | 3230.71 | − | 5595.76i | 0.316705 | − | 0.548550i | −0.663093 | − | 0.748537i | \(-0.730757\pi\) |
0.979799 | + | 0.199987i | \(0.0640900\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13991.6 | − | 8078.04i | 1.31884 | − | 0.761432i | 0.335298 | − | 0.942112i | \(-0.391163\pi\) |
0.983542 | + | 0.180680i | \(0.0578298\pi\) | |||||||
\(104\) | 4284.30 | + | 10123.7i | 0.396108 | + | 0.935995i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4354.62 | + | 6873.97i | −0.387560 | + | 0.611780i | ||||
\(107\) | − | 3065.27i | − | 0.267732i | −0.990999 | − | 0.133866i | \(-0.957261\pi\) | ||
0.990999 | − | 0.133866i | \(-0.0427392\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17728.8 | −1.49220 | −0.746098 | − | 0.665836i | \(-0.768075\pi\) | ||||
−0.746098 | + | 0.665836i | \(0.768075\pi\) | |||||||
\(110\) | 22682.2 | + | 14369.0i | 1.87456 | + | 1.18752i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −14355.1 | + | 5391.10i | −1.14438 | + | 0.429775i | ||||
\(113\) | −7396.56 | − | 12811.2i | −0.579259 | − | 1.00331i | −0.995565 | − | 0.0940814i | \(-0.970009\pi\) |
0.416305 | − | 0.909225i | \(-0.363325\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9251.65 | + | 5341.44i | 0.699558 | + | 0.403890i | ||||
\(116\) | 287.550 | + | 23.6819i | 0.0213696 | + | 0.00175995i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −426.951 | + | 10385.8i | −0.0306629 | + | 0.745890i | ||||
\(119\) | 5139.28 | + | 2967.16i | 0.362918 | + | 0.209531i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18101.8 | + | 31353.3i | 1.23638 | + | 2.14147i | ||||
\(122\) | −2630.66 | − | 5022.18i | −0.176744 | − | 0.337421i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 10204.6 | + | 7068.17i | 0.663673 | + | 0.459688i | ||||
\(125\) | 10829.6 | 0.693094 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 18478.7i | − | 1.14568i | −0.819667 | − | 0.572841i | \(-0.805841\pi\) | ||
0.819667 | − | 0.572841i | \(-0.194159\pi\) | |||||||
\(128\) | 11880.3 | − | 11282.5i | 0.725115 | − | 0.688628i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −9490.49 | − | 18118.2i | −0.561567 | − | 1.07208i | ||||
\(131\) | 7205.95 | − | 4160.35i | 0.419902 | − | 0.242431i | −0.275133 | − | 0.961406i | \(-0.588722\pi\) |
0.695036 | + | 0.718975i | \(0.255389\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5069.44 | − | 8780.53i | 0.286587 | − | 0.496384i | ||||
\(134\) | −984.989 | + | 23960.3i | −0.0548557 | + | 1.33439i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6292.54 | − | 779.559i | −0.340211 | − | 0.0421474i | ||||
\(137\) | −10703.4 | + | 18538.7i | −0.570268 | + | 0.987732i | 0.426271 | + | 0.904596i | \(0.359827\pi\) |
−0.996538 | + | 0.0831367i | \(0.973506\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15783.6 | − | 9112.67i | 0.816915 | − | 0.471646i | −0.0324367 | − | 0.999474i | \(-0.510327\pi\) |
0.849351 | + | 0.527828i | \(0.176993\pi\) | |||||||
\(140\) | 25795.6 | − | 12189.0i | 1.31610 | − | 0.621890i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4188.11 | + | 2653.15i | 0.207702 | + | 0.131578i | ||||
\(143\) | − | 38730.8i | − | 1.89402i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −536.823 | −0.0255326 | ||||||||
\(146\) | −10832.7 | + | 17099.9i | −0.508196 | + | 0.802210i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4168.13 | − | 8820.99i | −0.190291 | − | 0.402711i | ||||
\(149\) | −8119.72 | − | 14063.8i | −0.365736 | − | 0.633474i | 0.623158 | − | 0.782096i | \(-0.285850\pi\) |
−0.988894 | + | 0.148622i | \(0.952516\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21240.4 | − | 12263.2i | −0.931557 | − | 0.537835i | −0.0442533 | − | 0.999020i | \(-0.514091\pi\) |
−0.887304 | + | 0.461186i | \(0.847424\pi\) | |||||||
\(152\) | −1331.89 | + | 10750.9i | −0.0576476 | + | 0.465326i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 53980.1 | + | 2219.08i | 2.27611 | + | 0.0935690i | ||||
\(155\) | −20002.0 | − | 11548.2i | −0.832549 | − | 0.480672i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19827.0 | − | 34341.4i | −0.804375 | − | 1.39322i | −0.916712 | − | 0.399548i | \(-0.869167\pi\) |
0.112337 | − | 0.993670i | \(-0.464166\pi\) | |||||||
\(158\) | −6693.61 | + | 3506.17i | −0.268131 | + | 0.140449i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −20306.7 | + | 22735.5i | −0.793231 | + | 0.888106i | ||||
\(161\) | 21494.9 | 0.829248 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 25324.6i | 0.953162i | 0.879130 | + | 0.476581i | \(0.158124\pi\) | ||||
−0.879130 | + | 0.476581i | \(0.841876\pi\) | |||||||
\(164\) | −3763.40 | + | 5433.39i | −0.139924 | + | 0.202015i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −23859.6 | + | 12497.9i | −0.865860 | + | 0.453545i | ||||
\(167\) | −24109.7 | + | 13919.8i | −0.864490 | + | 0.499113i | −0.865513 | − | 0.500886i | \(-0.833008\pi\) |
0.00102363 | + | 0.999999i | \(0.499674\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −471.081 | + | 815.937i | −0.0164939 | + | 0.0285682i | ||||
\(170\) | 11787.4 | + | 484.569i | 0.407867 | + | 0.0167671i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −402.612 | + | 4888.59i | −0.0136091 | + | 0.165244i | ||||
\(173\) | −11027.3 | + | 19099.8i | −0.368448 | + | 0.638170i | −0.989323 | − | 0.145739i | \(-0.953444\pi\) |
0.620875 | + | 0.783909i | \(0.286777\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13550.4 | + | 7823.30i | −0.442461 | + | 0.255455i | ||||
\(176\) | −54039.6 | + | 20294.7i | −1.74456 | + | 0.655174i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −20200.1 | + | 31886.8i | −0.637550 | + | 1.00640i | ||||
\(179\) | 52513.4i | 1.63895i | 0.573118 | + | 0.819473i | \(0.305734\pi\) | ||||
−0.573118 | + | 0.819473i | \(0.694266\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7223.25 | −0.220483 | −0.110242 | − | 0.993905i | \(-0.535162\pi\) | ||||
−0.110242 | + | 0.993905i | \(0.535162\pi\) | |||||||
\(182\) | −34765.2 | − | 22023.6i | −1.04955 | − | 0.664882i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −21150.7 | + | 8950.85i | −0.624725 | + | 0.264380i | ||||
\(185\) | 9076.12 | + | 15720.3i | 0.265190 | + | 0.459322i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 19346.7 | + | 11169.8i | 0.553252 | + | 0.319420i | ||||
\(188\) | 3443.21 | − | 41808.1i | 0.0974200 | − | 1.18289i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 827.894 | − | 20138.9i | 0.0229334 | − | 0.557864i | ||||
\(191\) | −9164.94 | − | 5291.38i | −0.251225 | − | 0.145045i | 0.369100 | − | 0.929390i | \(-0.379666\pi\) |
−0.620325 | + | 0.784345i | \(0.712999\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19543.2 | + | 33849.9i | 0.524665 | + | 0.908746i | 0.999588 | + | 0.0287188i | \(0.00914273\pi\) |
−0.474923 | + | 0.880028i | \(0.657524\pi\) | |||||||
\(194\) | −27090.2 | − | 51717.8i | −0.719796 | − | 1.37416i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10812.7 | − | 15610.8i | 0.281464 | − | 0.406363i | ||||
\(197\) | 10820.0 | 0.278802 | 0.139401 | − | 0.990236i | \(-0.455482\pi\) | ||||
0.139401 | + | 0.990236i | \(0.455482\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 807.389i | − | 0.0203881i | −0.999948 | − | 0.0101940i | \(-0.996755\pi\) | ||
0.999948 | − | 0.0101940i | \(-0.00324492\pi\) | |||||||
\(200\) | 10075.6 | − | 13340.6i | 0.251889 | − | 0.333515i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −11992.6 | − | 22894.9i | −0.293907 | − | 0.561095i | ||||
\(203\) | −935.426 | + | 540.068i | −0.0226996 | + | 0.0131056i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6148.73 | − | 10649.9i | 0.146311 | − | 0.253419i | ||||
\(206\) | 2654.41 | − | 64569.8i | 0.0625510 | − | 1.52158i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 43379.3 | + | 7194.03i | 1.00267 | + | 0.166282i | ||||
\(209\) | 19083.8 | − | 33054.1i | 0.436890 | − | 0.756716i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −52683.9 | + | 30417.0i | −1.18335 | + | 0.683207i | −0.956787 | − | 0.290790i | \(-0.906082\pi\) |
−0.226562 | + | 0.973997i | \(0.572749\pi\) | |||||||
\(212\) | 13905.8 | + | 29428.8i | 0.309403 | + | 0.654788i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −10357.6 | − | 6561.51i | −0.226169 | − | 0.143277i | ||||
\(215\) | − | 9126.44i | − | 0.197435i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −46471.9 | −0.986895 | ||||||||
\(218\) | −37950.2 | + | 59906.1i | −0.798549 | + | 1.26054i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 97106.9 | − | 45885.4i | 2.00634 | − | 0.948045i | ||||
\(221\) | −8508.59 | − | 14737.3i | −0.174210 | − | 0.301741i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9292.11 | − | 5364.80i | −0.186855 | − | 0.107881i | 0.403654 | − | 0.914912i | \(-0.367740\pi\) |
−0.590509 | + | 0.807031i | \(0.701073\pi\) | |||||||
\(224\) | −12511.9 | + | 60046.6i | −0.249361 | + | 1.19672i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −59122.5 | − | 2430.48i | −1.15754 | − | 0.0475856i | ||||
\(227\) | 65585.2 | + | 37865.7i | 1.27278 | + | 0.734842i | 0.975511 | − | 0.219951i | \(-0.0705898\pi\) |
0.297272 | + | 0.954793i | \(0.403923\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26683.3 | + | 46216.8i | 0.508825 | + | 0.881311i | 0.999948 | + | 0.0102204i | \(0.00325330\pi\) |
−0.491123 | + | 0.871090i | \(0.663413\pi\) | |||||||
\(230\) | 37853.0 | − | 19827.7i | 0.715557 | − | 0.374815i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 695.550 | − | 920.945i | 0.0129227 | − | 0.0171103i | ||||
\(233\) | −56485.5 | −1.04046 | −0.520230 | − | 0.854026i | \(-0.674154\pi\) | ||||
−0.520230 | + | 0.854026i | \(0.674154\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 78050.9i | 1.41333i | ||||||||
\(236\) | 34179.9 | + | 23674.4i | 0.613686 | + | 0.425065i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 21027.3 | − | 11014.3i | 0.371218 | − | 0.194447i | ||||
\(239\) | 41561.8 | − | 23995.7i | 0.727610 | − | 0.420086i | −0.0899375 | − | 0.995947i | \(-0.528667\pi\) |
0.817547 | + | 0.575862i | \(0.195333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 32075.1 | − | 55555.6i | 0.552247 | − | 0.956520i | −0.445865 | − | 0.895100i | \(-0.647104\pi\) |
0.998112 | − | 0.0614196i | \(-0.0195628\pi\) | |||||||
\(242\) | 144692. | + | 5948.19i | 2.47067 | + | 0.101567i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −22601.3 | − | 1861.39i | −0.379624 | − | 0.0312649i | ||||
\(245\) | −17666.1 | + | 30598.6i | −0.294313 | + | 0.509764i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −25178.9 | + | 14537.1i | −0.412708 | + | 0.238277i | ||||
\(248\) | 45727.6 | − | 19351.7i | 0.743490 | − | 0.314641i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 23181.8 | − | 36593.5i | 0.370909 | − | 0.585496i | ||||
\(251\) | 65230.8i | 1.03539i | 0.855564 | + | 0.517696i | \(0.173210\pi\) | ||||
−0.855564 | + | 0.517696i | \(0.826790\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 80917.3 | 1.26415 | ||||||||
\(254\) | −62440.1 | − | 39555.5i | −0.967823 | − | 0.613111i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12692.9 | − | 64295.1i | −0.193678 | − | 0.981065i | ||||
\(257\) | −21657.9 | − | 37512.6i | −0.327907 | − | 0.567951i | 0.654190 | − | 0.756331i | \(-0.273010\pi\) |
−0.982096 | + | 0.188380i | \(0.939676\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 31630.7 | + | 18262.0i | 0.471530 | + | 0.272238i | ||||
\(260\) | −81537.3 | − | 6715.22i | −1.20617 | − | 0.0993376i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1367.08 | − | 33254.7i | 0.0199155 | − | 0.484452i | ||||
\(263\) | 73443.4 | + | 42402.6i | 1.06180 | + | 0.613029i | 0.925929 | − | 0.377698i | \(-0.123284\pi\) |
0.135868 | + | 0.990727i | \(0.456618\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −30280.0 | − | 52446.5i | −0.431185 | − | 0.746835i | ||||
\(266\) | −18818.0 | − | 35925.4i | −0.265957 | − | 0.507736i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 78854.0 | + | 54617.6i | 1.09788 | + | 0.760437i | ||||
\(269\) | 66685.5 | 0.921567 | 0.460784 | − | 0.887513i | \(-0.347568\pi\) | ||||
0.460784 | + | 0.887513i | \(0.347568\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 122426.i | − | 1.66700i | −0.552516 | − | 0.833502i | \(-0.686332\pi\) | ||
0.552516 | − | 0.833502i | \(-0.313668\pi\) | |||||||
\(272\) | −16103.9 | + | 19593.9i | −0.217668 | + | 0.264840i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 39731.4 | + | 75851.0i | 0.529216 | + | 1.01032i | ||||
\(275\) | −51010.0 | + | 29450.6i | −0.674512 | + | 0.389430i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −68726.1 | + | 119037.i | −0.895699 | + | 1.55140i | −0.0627613 | + | 0.998029i | \(0.519991\pi\) |
−0.832937 | + | 0.553367i | \(0.813343\pi\) | |||||||
\(278\) | 2994.39 | − | 72839.8i | 0.0387453 | − | 0.942496i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 14030.8 | − | 113256.i | 0.178965 | − | 1.44459i | ||||
\(281\) | 7001.61 | − | 12127.2i | 0.0886718 | − | 0.153584i | −0.818278 | − | 0.574822i | \(-0.805071\pi\) |
0.906950 | + | 0.421238i | \(0.138404\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 99634.2 | − | 57523.8i | 1.24404 | − | 0.718249i | 0.274129 | − | 0.961693i | \(-0.411611\pi\) |
0.969915 | + | 0.243444i | \(0.0782773\pi\) | |||||||
\(284\) | 17930.1 | − | 8472.43i | 0.222304 | − | 0.105044i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −130873. | − | 82907.2i | −1.59999 | − | 1.01358i | ||||
\(287\) | − | 24743.6i | − | 0.300400i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −73705.6 | −0.882480 | ||||||||
\(290\) | −1149.12 | + | 1813.94i | −0.0136638 | + | 0.0215688i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 34592.6 | + | 73208.0i | 0.405712 | + | 0.858604i | ||||
\(293\) | 14259.3 | + | 24697.8i | 0.166097 | + | 0.287689i | 0.937044 | − | 0.349210i | \(-0.113550\pi\) |
−0.770947 | + | 0.636899i | \(0.780217\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −66995.6 | − | 38679.9i | −0.769843 | − | 0.444469i | ||||
\(296\) | −38728.7 | − | 4797.95i | −0.442027 | − | 0.0547611i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −64902.9 | − | 2668.11i | −0.730856 | − | 0.0300449i | ||||
\(299\) | −53380.6 | − | 30819.3i | −0.597092 | − | 0.344731i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9181.62 | − | 15903.0i | −0.101341 | − | 0.175528i | ||||
\(302\) | −86904.8 | + | 45521.5i | −0.952862 | + | 0.499117i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 33476.6 | + | 27513.8i | 0.362238 | + | 0.297717i | ||||
\(305\) | 42194.0 | 0.453577 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 115338.i | 1.22376i | 0.790952 | + | 0.611879i | \(0.209586\pi\) | ||||
−0.790952 | + | 0.611879i | \(0.790414\pi\) | |||||||
\(308\) | 123048. | − | 177650.i | 1.29710 | − | 1.87268i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −81837.8 | + | 42867.4i | −0.851590 | + | 0.446070i | ||||
\(311\) | 85566.6 | − | 49401.9i | 0.884674 | − | 0.510767i | 0.0124776 | − | 0.999922i | \(-0.496028\pi\) |
0.872197 | + | 0.489155i | \(0.162695\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 37066.1 | − | 64200.3i | 0.378345 | − | 0.655313i | −0.612477 | − | 0.790489i | \(-0.709827\pi\) |
0.990822 | + | 0.135176i | \(0.0431600\pi\) | |||||||
\(314\) | −158482. | − | 6515.09i | −1.60739 | − | 0.0660786i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2480.88 | + | 30123.2i | −0.0248445 | + | 0.301667i | ||||
\(317\) | −1057.30 | + | 1831.29i | −0.0105215 | + | 0.0182238i | −0.871238 | − | 0.490860i | \(-0.836682\pi\) |
0.860717 | + | 0.509084i | \(0.170016\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3521.39 | + | 2033.08i | −0.0346045 | + | 0.0199789i | ||||
\(320\) | 33355.5 | + | 117285.i | 0.325737 | + | 1.14536i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 46012.1 | − | 72632.1i | 0.443772 | − | 0.700514i | ||||
\(323\) | − | 16769.7i | − | 0.160739i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 44868.0 | 0.424785 | ||||||||
\(326\) | 85572.5 | + | 54209.7i | 0.805191 | + | 0.510084i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 10303.7 | + | 24347.3i | 0.0957731 | + | 0.226310i | ||||
\(329\) | 78522.8 | + | 136006.i | 0.725444 | + | 1.25651i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12334.0 | − | 7121.02i | −0.112576 | − | 0.0649960i | 0.442655 | − | 0.896692i | \(-0.354037\pi\) |
−0.555231 | + | 0.831696i | \(0.687370\pi\) | |||||||
\(332\) | −8843.19 | + | 107375.i | −0.0802292 | + | 0.974156i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4573.98 | + | 111264.i | −0.0410017 | + | 0.997384i | ||||
\(335\) | −154561. | − | 89235.7i | −1.37724 | − | 0.795150i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −37711.8 | − | 65318.7i | −0.332061 | − | 0.575146i | 0.650855 | − | 0.759202i | \(-0.274411\pi\) |
−0.982916 | + | 0.184056i | \(0.941077\pi\) | |||||||
\(338\) | 1748.68 | + | 3338.39i | 0.0153065 | + | 0.0292216i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 26869.4 | − | 38792.6i | 0.232434 | − | 0.335576i | ||||
\(341\) | −174942. | −1.50448 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 72725.3i | − | 0.618155i | ||||||
\(344\) | 15656.8 | + | 11824.9i | 0.132308 | + | 0.0999268i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 40933.8 | + | 78146.5i | 0.341924 | + | 0.652765i | ||||
\(347\) | −128553. | + | 74220.2i | −1.06764 | + | 0.616401i | −0.927535 | − | 0.373736i | \(-0.878077\pi\) |
−0.140103 | + | 0.990137i | \(0.544743\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11665.4 | − | 20205.1i | 0.0957745 | − | 0.165886i | −0.814157 | − | 0.580645i | \(-0.802801\pi\) |
0.909932 | + | 0.414758i | \(0.136134\pi\) | |||||||
\(350\) | −2570.71 | + | 62533.6i | −0.0209854 | + | 0.510478i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −47100.8 | + | 226044.i | −0.380140 | + | 1.82435i | ||||
\(353\) | 9687.21 | − | 16778.7i | 0.0777409 | − | 0.134651i | −0.824534 | − | 0.565812i | \(-0.808563\pi\) |
0.902275 | + | 0.431161i | \(0.141896\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −31954.1 | + | 18448.7i | −0.253554 | + | 0.146389i | ||||
\(356\) | 64506.0 | + | 136514.i | 0.508980 | + | 1.07715i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 177444. | + | 112410.i | 1.38451 | + | 0.877081i | ||||
\(359\) | − | 139927.i | − | 1.08571i | −0.839827 | − | 0.542854i | \(-0.817344\pi\) | ||
0.839827 | − | 0.542854i | \(-0.182656\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 101670. | 0.780148 | ||||||||
\(362\) | −15462.1 | + | 24407.6i | −0.117992 | + | 0.186255i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −148836. | + | 70328.9i | −1.12333 | + | 0.530800i | ||||
\(365\) | −75325.5 | − | 130468.i | −0.565400 | − | 0.979302i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 79304.5 | + | 45786.5i | 0.588797 | + | 0.339942i | 0.764622 | − | 0.644479i | \(-0.222926\pi\) |
−0.175825 | + | 0.984421i | \(0.556259\pi\) | |||||||
\(368\) | −15029.9 | + | 90628.9i | −0.110984 | + | 0.669224i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 72547.7 | + | 2982.38i | 0.529932 | + | 0.0217851i | ||||
\(371\) | −105527. | − | 60926.1i | −0.766684 | − | 0.442645i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −42790.4 | − | 74115.1i | −0.307559 | − | 0.532708i | 0.670269 | − | 0.742118i | \(-0.266179\pi\) |
−0.977828 | + | 0.209411i | \(0.932845\pi\) | |||||||
\(374\) | 79156.6 | − | 41462.9i | 0.565906 | − | 0.296426i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −133900. | − | 101129.i | −0.947120 | − | 0.715319i | ||||
\(377\) | 3097.38 | 0.0217928 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 39838.1i | − | 0.277345i | −0.990338 | − | 0.138672i | \(-0.955716\pi\) | ||
0.990338 | − | 0.138672i | \(-0.0442835\pi\) | |||||||
\(380\) | −66277.7 | − | 45906.8i | −0.458987 | − | 0.317914i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −37498.2 | + | 19641.9i | −0.256971 | + | 0.134603i | ||||
\(383\) | 147816. | − | 85341.8i | 1.00769 | − | 0.581787i | 0.0971722 | − | 0.995268i | \(-0.469020\pi\) |
0.910513 | + | 0.413480i | \(0.135687\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −201039. | + | 348210.i | −1.35631 | + | 2.34920i | ||||
\(386\) | 156214. | + | 6421.84i | 1.04844 | + | 0.0431007i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −232745. | − | 19168.3i | −1.54603 | − | 0.127327i | ||||
\(389\) | 107907. | − | 186901.i | 0.713103 | − | 1.23513i | −0.250583 | − | 0.968095i | \(-0.580622\pi\) |
0.963687 | − | 0.267036i | \(-0.0860443\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30789.5 | − | 17776.3i | 0.201395 | − | 0.116275i | ||||
\(392\) | −29603.8 | − | 69953.1i | −0.192653 | − | 0.455234i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 23161.3 | − | 36561.2i | 0.149201 | − | 0.235520i | ||||
\(395\) | − | 56236.6i | − | 0.360434i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 292553. | 1.85620 | 0.928098 | − | 0.372336i | \(-0.121443\pi\) | ||||
0.928098 | + | 0.372336i | \(0.121443\pi\) | |||||||
\(398\) | −2728.19 | − | 1728.30i | −0.0172230 | − | 0.0109107i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −23510.5 | − | 62602.5i | −0.146941 | − | 0.391266i | ||||
\(401\) | 102157. | + | 176941.i | 0.635300 | + | 1.10037i | 0.986452 | + | 0.164053i | \(0.0524567\pi\) |
−0.351152 | + | 0.936318i | \(0.614210\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 115408. | + | 66631.1i | 0.710604 | + | 0.410267i | ||||
\(404\) | −103034. | − | 8485.63i | −0.631274 | − | 0.0519902i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −177.464 | + | 4316.90i | −0.00107661 | + | 0.0261891i | ||||
\(407\) | 119073. | + | 68746.9i | 0.718827 | + | 0.415015i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17364.4 | − | 30076.0i | −0.103804 | − | 0.179793i | 0.809445 | − | 0.587196i | \(-0.199768\pi\) |
−0.913249 | + | 0.407402i | \(0.866435\pi\) | |||||||
\(410\) | −22824.4 | − | 43573.9i | −0.135779 | − | 0.259214i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −212501. | − | 147187.i | −1.25189 | − | 0.867113i | ||||
\(413\) | −155655. | −0.912564 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 200458.i | − | 1.16393i | ||||||
\(416\) | 117167. | − | 131180.i | 0.677044 | − | 0.758023i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −70840.1 | − | 135240.i | −0.405440 | − | 0.774023i | ||||
\(419\) | −277682. | + | 160320.i | −1.58169 | + | 0.913187i | −0.587073 | + | 0.809534i | \(0.699720\pi\) |
−0.994614 | + | 0.103653i | \(0.966947\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −67885.7 | + | 117582.i | −0.383014 | + | 0.663399i | −0.991491 | − | 0.130172i | \(-0.958447\pi\) |
0.608478 | + | 0.793571i | \(0.291780\pi\) | |||||||
\(422\) | −9994.93 | + | 243131.i | −0.0561248 | + | 1.36526i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 129208. | + | 16007.0i | 0.718714 | + | 0.0890388i | ||||
\(425\) | −12939.7 | + | 22412.3i | −0.0716386 | + | 0.124082i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 73524.1 | − | 42449.2i | 0.403250 | − | 0.232816i | ||||
\(428\) | −44343.0 | + | 20953.2i | −0.242068 | + | 0.114383i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −30838.5 | − | 19536.0i | −0.166785 | − | 0.105657i | ||||
\(431\) | − | 31343.0i | − | 0.168728i | −0.996435 | − | 0.0843638i | \(-0.973114\pi\) | ||
0.996435 | − | 0.0843638i | \(-0.0268858\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 101022. | 0.538815 | 0.269407 | − | 0.963026i | \(-0.413172\pi\) | ||||
0.269407 | + | 0.963026i | \(0.413172\pi\) | |||||||
\(434\) | −99477.7 | + | 157030.i | −0.528137 | + | 0.833687i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 121188. | + | 256470.i | 0.637511 | + | 1.34916i | ||||
\(437\) | −30371.1 | − | 52604.3i | −0.159037 | − | 0.275460i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −157593. | − | 90986.2i | −0.817724 | − | 0.472113i | 0.0319068 | − | 0.999491i | \(-0.489842\pi\) |
−0.849631 | + | 0.527378i | \(0.823175\pi\) | |||||||
\(440\) | 52818.8 | − | 426349.i | 0.272824 | − | 2.20222i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −68011.3 | − | 2795.89i | −0.348126 | − | 0.0143112i | ||||
\(443\) | 32206.4 | + | 18594.4i | 0.164110 | + | 0.0947490i | 0.579806 | − | 0.814755i | \(-0.303128\pi\) |
−0.415696 | + | 0.909504i | \(0.636462\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −140462. | − | 243287.i | −0.709315 | − | 1.22857i | ||||
\(446\) | −38018.5 | + | 19914.4i | −0.191128 | + | 0.100115i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 176116. | + | 170814.i | 0.877493 | + | 0.851074i | ||||
\(449\) | 20385.0 | 0.101115 | 0.0505577 | − | 0.998721i | \(-0.483900\pi\) | ||||
0.0505577 | + | 0.998721i | \(0.483900\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 93146.9i | − | 0.457947i | ||||||
\(452\) | −134770. | + | 194574.i | −0.659656 | + | 0.952375i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 268341. | − | 140559.i | 1.30189 | − | 0.681943i | ||||
\(455\) | 265249. | − | 153141.i | 1.28124 | − | 0.739724i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 139829. | − | 242191.i | 0.669521 | − | 1.15964i | −0.308517 | − | 0.951219i | \(-0.599833\pi\) |
0.978038 | − | 0.208426i | \(-0.0668340\pi\) | |||||||
\(458\) | 213286. | + | 8768.03i | 1.01679 | + | 0.0417995i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 14029.6 | − | 170349.i | 0.0663023 | − | 0.805054i | ||||
\(461\) | −80298.4 | + | 139081.i | −0.377838 | + | 0.654434i | −0.990747 | − | 0.135719i | \(-0.956666\pi\) |
0.612910 | + | 0.790153i | \(0.289999\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 85869.5 | − | 49576.8i | 0.400569 | − | 0.231268i | −0.286161 | − | 0.958182i | \(-0.592379\pi\) |
0.686729 | + | 0.726913i | \(0.259046\pi\) | |||||||
\(464\) | −1623.01 | − | 4321.66i | −0.00753849 | − | 0.0200731i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −120913. | + | 190866.i | −0.556802 | + | 0.878936i | ||||
\(467\) | 278790.i | 1.27833i | 0.769068 | + | 0.639167i | \(0.220721\pi\) | ||||
−0.769068 | + | 0.639167i | \(0.779279\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −359101. | −1.63257 | ||||||||
\(470\) | 263736. | + | 167076.i | 1.19392 | + | 0.756341i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 153162. | − | 64817.3i | 0.687491 | − | 0.290943i | ||||
\(473\) | −34564.0 | − | 59866.6i | −0.154490 | − | 0.267585i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 38291.7 | + | 22107.7i | 0.169714 | + | 0.0979844i | ||||
\(476\) | 7793.40 | − | 94628.8i | 0.0343964 | − | 0.417647i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7884.90 | − | 191804.i | 0.0345096 | − | 0.839462i | ||||
\(479\) | −27705.5 | − | 15995.8i | −0.120752 | − | 0.0697163i | 0.438407 | − | 0.898776i | \(-0.355543\pi\) |
−0.559160 | + | 0.829060i | \(0.688876\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −52367.8 | − | 90703.7i | −0.226347 | − | 0.392044i | ||||
\(482\) | −119064. | − | 227305.i | −0.512492 | − | 0.978396i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 329828. | − | 476187.i | 1.40798 | − | 2.03276i | ||||
\(485\) | 434509. | 1.84721 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 346823.i | 1.46235i | 0.682192 | + | 0.731173i | \(0.261027\pi\) | ||||
−0.682192 | + | 0.731173i | \(0.738973\pi\) | |||||||
\(488\) | −54670.0 | + | 72385.9i | −0.229567 | + | 0.303959i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 65577.5 | + | 125194.i | 0.273126 | + | 0.521423i | ||||
\(491\) | 207830. | − | 119991.i | 0.862076 | − | 0.497720i | −0.00263098 | − | 0.999997i | \(-0.500837\pi\) |
0.864707 | + | 0.502277i | \(0.167504\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −893.273 | + | 1547.19i | −0.00367528 | + | 0.00636577i | ||||
\(494\) | −4776.82 | + | 116198.i | −0.0195743 | + | 0.476152i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 32494.6 | − | 195939.i | 0.132083 | − | 0.796448i | ||||
\(497\) | −37120.5 | + | 64294.7i | −0.150280 | + | 0.260293i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −295354. | + | 170523.i | −1.18616 | + | 0.684828i | −0.957431 | − | 0.288663i | \(-0.906789\pi\) |
−0.228726 | + | 0.973491i | \(0.573456\pi\) | |||||||
\(500\) | −74027.6 | − | 156664.i | −0.296110 | − | 0.626656i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 220417. | + | 139633.i | 0.874655 | + | 0.554090i | ||||
\(503\) | − | 3886.22i | − | 0.0153600i | −0.999971 | − | 0.00768001i | \(-0.997555\pi\) | ||
0.999971 | − | 0.00768001i | \(-0.00244465\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 192353. | 0.754250 | ||||||||
\(506\) | 173211. | − | 273422.i | 0.676512 | − | 1.06790i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −267318. | + | 126314.i | −1.03586 | + | 0.489469i | ||||
\(509\) | 98673.1 | + | 170907.i | 0.380858 | + | 0.659666i | 0.991185 | − | 0.132484i | \(-0.0422952\pi\) |
−0.610327 | + | 0.792150i | \(0.708962\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −262513. | − | 151562.i | −1.00533 | − | 0.580427i | ||||
\(512\) | −244425. | − | 94740.3i | −0.932409 | − | 0.361405i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −173117. | − | 7116.71i | −0.655260 | − | 0.0269372i | ||||
\(515\) | 416521. | + | 240478.i | 1.57044 | + | 0.906696i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 295597. | + | 511990.i | 1.10591 | + | 1.91549i | ||||
\(518\) | 129416. | − | 67789.5i | 0.482314 | − | 0.252640i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −197230. | + | 261142.i | −0.729399 | + | 0.965763i | ||||
\(521\) | −229165. | −0.844255 | −0.422127 | − | 0.906536i | \(-0.638717\pi\) | ||||
−0.422127 | + | 0.906536i | \(0.638717\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 346673.i | 1.26741i | 0.773575 | + | 0.633705i | \(0.218467\pi\) | ||||
−0.773575 | + | 0.633705i | \(0.781533\pi\) | |||||||
\(524\) | −109442. | − | 75804.5i | −0.398587 | − | 0.276078i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 300492. | − | 157401.i | 1.08608 | − | 0.568899i | ||||
\(527\) | −66566.6 | + | 38432.2i | −0.239682 | + | 0.138380i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −75532.2 | + | 130826.i | −0.269911 | + | 0.467500i | ||||
\(530\) | −242035. | − | 9949.89i | −0.861642 | − | 0.0354215i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −161675. | − | 13315.2i | −0.571241 | − | 0.0470460i | ||||
\(533\) | −35477.2 | + | 61448.4i | −0.124881 | + | 0.216300i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 79025.8 | − | 45625.6i | 0.276097 | − | 0.159405i | ||||
\(536\) | 353349. | − | 149536.i | 1.22991 | − | 0.520493i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 142747. | − | 225332.i | 0.493176 | − | 0.778500i | ||||
\(539\) | 267623.i | 0.921184i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −287354. | −0.981799 | −0.490900 | − | 0.871216i | \(-0.663332\pi\) | ||||
−0.490900 | + | 0.871216i | \(0.663332\pi\) | |||||||
\(542\) | −413683. | − | 262066.i | −1.40821 | − | 0.892097i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 31736.4 | + | 96358.5i | 0.107241 | + | 0.325606i | ||||
\(545\) | −263888. | − | 457067.i | −0.888436 | − | 1.53882i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 486589. | + | 280932.i | 1.62625 | + | 0.938917i | 0.985198 | + | 0.171421i | \(0.0548357\pi\) |
0.641054 | + | 0.767496i | \(0.278498\pi\) | |||||||
\(548\) | 341352. | + | 28112.9i | 1.13669 | + | 0.0936148i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −9677.37 | + | 235406.i | −0.0319913 | + | 0.778203i | ||||
\(551\) | 2643.40 | + | 1526.17i | 0.00870684 | + | 0.00502689i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −56576.7 | − | 97993.6i | −0.185006 | − | 0.320441i | ||||
\(554\) | 255115. | + | 487038.i | 0.831220 | + | 1.58688i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −239718. | − | 166039.i | −0.775446 | − | 0.537107i | ||||
\(557\) | 393303. | 1.26770 | 0.633850 | − | 0.773456i | \(-0.281474\pi\) | ||||
0.633850 | + | 0.773456i | \(0.281474\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 52658.1i | 0.168516i | ||||||||
\(560\) | −352660. | − | 289846.i | −1.12455 | − | 0.924254i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −25990.4 | − | 49618.0i | −0.0822886 | − | 0.157097i | ||||
\(563\) | −481867. | + | 278206.i | −1.52023 | + | 0.877707i | −0.520518 | + | 0.853851i | \(0.674261\pi\) |
−0.999715 | + | 0.0238561i | \(0.992406\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 220191. | − | 381382.i | 0.689768 | − | 1.19471i | ||||
\(566\) | 18902.1 | − | 459802.i | 0.0590035 | − | 1.43529i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9752.64 | − | 78722.5i | 0.0302291 | − | 0.244007i | ||||
\(569\) | 91030.8 | − | 157670.i | 0.281167 | − | 0.486995i | −0.690506 | − | 0.723327i | \(-0.742612\pi\) |
0.971672 | + | 0.236332i | \(0.0759453\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −190279. | + | 109858.i | −0.583604 | + | 0.336944i | −0.762565 | − | 0.646912i | \(-0.776060\pi\) |
0.178960 | + | 0.983856i | \(0.442727\pi\) | |||||||
\(572\) | −560292. | + | 264752.i | −1.71247 | + | 0.809182i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −83609.5 | − | 52966.2i | −0.253765 | − | 0.160759i | ||||
\(575\) | 93739.0i | 0.283521i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9527.81 | 0.0286181 | 0.0143091 | − | 0.999898i | \(-0.495445\pi\) | ||||
0.0143091 | + | 0.999898i | \(0.495445\pi\) | |||||||
\(578\) | −157774. | + | 249053.i | −0.472259 | + | 0.745482i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3669.55 | + | 7765.83i | 0.0109083 | + | 0.0230851i | ||||
\(581\) | −201670. | − | 349302.i | −0.597432 | − | 1.03478i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −397254. | − | 229355.i | −1.16878 | − | 0.674794i | ||||
\(584\) | 321421. | + | 39819.7i | 0.942429 | + | 0.116754i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 113978. | + | 4685.55i | 0.331914 | + | 0.0136447i | ||||
\(587\) | 8948.63 | + | 5166.49i | 0.0259705 | + | 0.0149941i | 0.512929 | − | 0.858431i | \(-0.328560\pi\) |
−0.486959 | + | 0.873425i | \(0.661894\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 65662.1 | + | 113730.i | 0.189271 | + | 0.327827i | ||||
\(590\) | −274111. | + | 143582.i | −0.787449 | + | 0.412473i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −99115.0 | + | 120595.i | −0.282811 | + | 0.344101i | ||||
\(593\) | −143639. | −0.408473 | −0.204236 | − | 0.978922i | \(-0.565471\pi\) | ||||
−0.204236 | + | 0.978922i | \(0.565471\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 176661.i | 0.499008i | ||||||||
\(596\) | −147947. | + | 213597.i | −0.416498 | + | 0.601317i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −218406. | + | 114403.i | −0.610747 | + | 0.319915i | ||||
\(599\) | −305650. | + | 176467.i | −0.851865 | + | 0.491824i | −0.861280 | − | 0.508131i | \(-0.830336\pi\) |
0.00941494 | + | 0.999956i | \(0.497003\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17733.8 | + | 30715.9i | −0.0490969 | + | 0.0850382i | −0.889529 | − | 0.456878i | \(-0.848968\pi\) |
0.840433 | + | 0.541916i | \(0.182301\pi\) | |||||||
\(602\) | −73390.9 | − | 3017.04i | −0.202511 | − | 0.00832509i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −32209.8 | + | 391097.i | −0.0882907 | + | 1.07204i | ||||
\(605\) | −538881. | + | 933369.i | −1.47225 | + | 2.55001i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −424309. | + | 244975.i | −1.15161 | + | 0.664881i | −0.949279 | − | 0.314436i | \(-0.898185\pi\) |
−0.202330 | + | 0.979317i | \(0.564851\pi\) | |||||||
\(608\) | 164630. | − | 54222.2i | 0.445350 | − | 0.146680i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 90320.5 | − | 142575.i | 0.242732 | − | 0.383163i | ||||
\(611\) | − | 450342.i | − | 1.20631i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 284390. | 0.756821 | 0.378410 | − | 0.925638i | \(-0.376471\pi\) | ||||
0.378410 | + | 0.925638i | \(0.376471\pi\) | |||||||
\(614\) | 389730. | + | 246892.i | 1.03378 | + | 0.654893i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −336889. | − | 796061.i | −0.887821 | − | 2.09790i | ||||
\(617\) | 98237.4 | + | 170152.i | 0.258052 | + | 0.446958i | 0.965720 | − | 0.259586i | \(-0.0835862\pi\) |
−0.707668 | + | 0.706545i | \(0.750253\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 58731.2 | + | 33908.5i | 0.153281 | + | 0.0884967i | 0.574679 | − | 0.818379i | \(-0.305127\pi\) |
−0.421398 | + | 0.906876i | \(0.638460\pi\) | |||||||
\(620\) | −30331.8 | + | 368294.i | −0.0789069 | + | 0.958101i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 16233.3 | − | 394882.i | 0.0419590 | − | 1.02067i | ||||
\(623\) | −489517. | − | 282623.i | −1.26122 | − | 0.728167i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 242826. | + | 420586.i | 0.621634 | + | 1.07670i | ||||
\(626\) | −137591. | − | 262674.i | −0.351109 | − | 0.670300i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −361262. | + | 521571.i | −0.916016 | + | 1.32249i | ||||
\(629\) | 60410.6 | 0.152691 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 716972.i | − | 1.80071i | −0.435158 | − | 0.900354i | \(-0.643308\pi\) | ||
0.435158 | − | 0.900354i | \(-0.356692\pi\) | |||||||
\(632\) | 96476.7 | + | 72864.7i | 0.241539 | + | 0.182424i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3924.74 | + | 7492.69i | 0.00976409 | + | 0.0186406i | ||||
\(635\) | 476401. | − | 275050.i | 1.18148 | − | 0.682125i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 101931. | − | 176549.i | 0.251204 | − | 0.435098i | ||||
\(638\) | −668.061 | + | 16250.9i | −0.00164125 | + | 0.0399241i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 467709. | + | 138350.i | 1.14187 | + | 0.337769i | ||||
\(641\) | 321445. | − | 556760.i | 0.782332 | − | 1.35504i | −0.148248 | − | 0.988950i | \(-0.547363\pi\) |
0.930580 | − | 0.366089i | \(-0.119303\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1326.59 | + | 765.910i | −0.00320861 | + | 0.00185249i | −0.501603 | − | 0.865098i | \(-0.667256\pi\) |
0.498395 | + | 0.866950i | \(0.333923\pi\) | |||||||
\(644\) | −146933. | − | 310952.i | −0.354280 | − | 0.749759i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −56665.3 | − | 35897.2i | −0.135785 | − | 0.0860192i | ||||
\(647\) | − | 106720.i | − | 0.254938i | −0.991843 | − | 0.127469i | \(-0.959315\pi\) | ||
0.991843 | − | 0.127469i | \(-0.0406854\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −585960. | −1.39116 | ||||||||
\(650\) | 96044.3 | − | 151610.i | 0.227324 | − | 0.358841i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 366353. | − | 173111.i | 0.861795 | − | 0.407219i | ||||
\(653\) | 114833. | + | 198896.i | 0.269301 | + | 0.466444i | 0.968682 | − | 0.248306i | \(-0.0798739\pi\) |
−0.699380 | + | 0.714750i | \(0.746541\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 214517. | + | 123851.i | 0.500010 | + | 0.288681i | ||||
\(656\) | 104326. | + | 17301.5i | 0.242430 | + | 0.0402046i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 627652. | + | 25802.3i | 1.44966 | + | 0.0595946i | ||||
\(659\) | −337909. | − | 195092.i | −0.778089 | − | 0.449230i | 0.0576633 | − | 0.998336i | \(-0.481635\pi\) |
−0.835753 | + | 0.549106i | \(0.814968\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −223443. | − | 387014.i | −0.511403 | − | 0.885776i | −0.999913 | − | 0.0132177i | \(-0.995793\pi\) |
0.488509 | − | 0.872559i | \(-0.337541\pi\) | |||||||
\(662\) | −50464.2 | + | 26433.6i | −0.115151 | + | 0.0603171i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 343895. | + | 259729.i | 0.779991 | + | 0.589094i | ||||
\(665\) | 301829. | 0.682523 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6471.12i | 0.0145455i | ||||||||
\(668\) | 366174. | + | 253628.i | 0.820605 | + | 0.568386i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −632383. | + | 331248.i | −1.40874 | + | 0.737909i | ||||
\(671\) | 276780. | − | 159799.i | 0.614737 | − | 0.354919i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −169746. | + | 294009.i | −0.374774 | + | 0.649128i | −0.990293 | − | 0.138994i | \(-0.955613\pi\) |
0.615519 | + | 0.788122i | \(0.288946\pi\) | |||||||
\(674\) | −301440. | − | 12392.0i | −0.663561 | − | 0.0272785i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15023.7 | + | 1237.32i | 0.0328764 | + | 0.00270762i | ||||
\(677\) | 266702. | − | 461941.i | 0.581900 | − | 1.00788i | −0.413354 | − | 0.910570i | \(-0.635643\pi\) |
0.995254 | − | 0.0973098i | \(-0.0310238\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 757142. | − | 437136.i | 1.64224 | − | 0.948150i | ||||
\(680\) | −73564.7 | − | 173832.i | −0.159093 | − | 0.375934i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −374482. | + | 591136.i | −0.805122 | + | 1.27092i | ||||
\(683\) | 175866.i | 0.376999i | 0.982073 | + | 0.188500i | \(0.0603624\pi\) | ||||
−0.982073 | + | 0.188500i | \(0.939638\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −637265. | −1.35812 | ||||||||
\(686\) | −245741. | − | 155676.i | −0.522191 | − | 0.330805i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 73471.8 | − | 27592.5i | 0.155219 | − | 0.0582927i | ||||
\(689\) | 174711. | + | 302608.i | 0.368028 | + | 0.637444i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −203114. | − | 117268.i | −0.425386 | − | 0.245597i | 0.271993 | − | 0.962299i | \(-0.412317\pi\) |
−0.697379 | + | 0.716702i | \(0.745651\pi\) | |||||||
\(692\) | 351682. | + | 28963.7i | 0.734409 | + | 0.0604842i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −24388.5 | + | 593261.i | −0.0506368 | + | 1.23176i | ||||
\(695\) | 469869. | + | 271279.i | 0.972762 | + | 0.561625i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20463.0 | − | 35442.9i | −0.0421214 | − | 0.0729565i | ||||
\(698\) | −43302.7 | − | 82668.8i | −0.0888799 | − | 0.169680i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 205800. | + | 142546.i | 0.420000 | + | 0.290910i | ||||
\(701\) | −192485. | −0.391707 | −0.195853 | − | 0.980633i | \(-0.562748\pi\) | ||||
−0.195853 | + | 0.980633i | \(0.562748\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 103213.i | − | 0.208844i | ||||||
\(704\) | 662986. | + | 643025.i | 1.33770 | + | 1.29743i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −35959.4 | − | 68649.9i | −0.0721445 | − | 0.137731i | ||||
\(707\) | 335179. | − | 193516.i | 0.670561 | − | 0.387148i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 300439. | − | 520376.i | 0.597674 | − | 1.03520i | −0.395489 | − | 0.918471i | \(-0.629425\pi\) |
0.993164 | − | 0.116731i | \(-0.0372417\pi\) | |||||||
\(710\) | −6062.18 | + | 147465.i | −0.0120258 | + | 0.292532i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 599365. | + | 74253.1i | 1.18231 | + | 0.146472i | ||||
\(713\) | −139207. | + | 241114.i | −0.273831 | + | 0.474288i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 998522. | − | 576497.i | 1.95320 | − | 1.12768i | ||||
\(716\) | 759675. | − | 358965.i | 1.48184 | − | 0.700206i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −472818. | − | 299528.i | −0.917160 | − | 0.581016i | ||||
\(719\) | − | 37302.4i | − | 0.0721571i | −0.999349 | − | 0.0360786i | \(-0.988513\pi\) | ||
0.999349 | − | 0.0360786i | \(-0.0114867\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 967729. | 1.86159 | ||||||||
\(722\) | 217634. | − | 343545.i | 0.417496 | − | 0.659036i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 49375.8 | + | 104494.i | 0.0941970 | + | 0.199348i | ||||
\(725\) | −2355.23 | − | 4079.37i | −0.00448081 | − | 0.00776099i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 647844. | + | 374033.i | 1.22575 | + | 0.707686i | 0.966138 | − | 0.258027i | \(-0.0830723\pi\) |
0.259611 | + | 0.965713i | \(0.416406\pi\) | |||||||
\(728\) | −80955.8 | + | 653469.i | −0.152751 | + | 1.23300i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −602095. | − | 24751.7i | −1.12985 | − | 0.0464471i | ||||
\(731\) | −26303.6 | − | 15186.4i | −0.0492244 | − | 0.0284197i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 131709. | + | 228126.i | 0.245136 | + | 0.424588i | 0.962170 | − | 0.272450i | \(-0.0878341\pi\) |
−0.717034 | + | 0.697038i | \(0.754501\pi\) | |||||||
\(734\) | 324473. | − | 169962.i | 0.602263 | − | 0.315471i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 274065. | + | 244787.i | 0.505938 | + | 0.451889i | ||||
\(737\) | −1.35183e6 | −2.48878 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 288908.i | − | 0.529018i | −0.964383 | − | 0.264509i | \(-0.914790\pi\) | ||
0.964383 | − | 0.264509i | \(-0.0852099\pi\) | |||||||
\(740\) | 165373. | − | 238757.i | 0.301996 | − | 0.436006i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −431762. | + | 226161.i | −0.784218 | + | 0.410780i | ||||
\(743\) | −271416. | + | 156702.i | −0.491651 | + | 0.283855i | −0.725259 | − | 0.688476i | \(-0.758280\pi\) |
0.233608 | + | 0.972331i | \(0.424947\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 241719. | − | 418670.i | 0.435510 | − | 0.754326i | ||||
\(746\) | −342034. | − | 14060.8i | −0.614599 | − | 0.0252657i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 29338.1 | − | 356228.i | 0.0524359 | − | 0.636685i | ||||
\(749\) | 91802.9 | − | 159007.i | 0.163641 | − | 0.283435i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −204539. | + | 118091.i | −0.362658 | + | 0.209381i | −0.670246 | − | 0.742139i | \(-0.733811\pi\) |
0.307588 | + | 0.951520i | \(0.400478\pi\) | |||||||
\(752\) | −628344. | + | 235976.i | −1.11112 | + | 0.417284i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6630.26 | − | 10466.2i | 0.0116624 | − | 0.0184096i | ||||
\(755\) | − | 730134.i | − | 1.28088i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.00219e6 | −1.74888 | −0.874438 | − | 0.485137i | \(-0.838770\pi\) | ||||
−0.874438 | + | 0.485137i | \(0.838770\pi\) | |||||||
\(758\) | −134614. | − | 85277.4i | −0.234289 | − | 0.148421i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −296994. | + | 125686.i | −0.514187 | + | 0.217601i | ||||
\(761\) | 456412. | + | 790529.i | 0.788112 | + | 1.36505i | 0.927122 | + | 0.374759i | \(0.122275\pi\) |
−0.139010 | + | 0.990291i | \(0.544392\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −919661. | − | 530967.i | −1.57971 | − | 0.912049i | ||||
\(764\) | −13898.1 | + | 168753.i | −0.0238105 | + | 0.289111i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 28043.0 | − | 682158.i | 0.0477933 | − | 1.16259i | ||||
\(767\) | 386554. | + | 223177.i | 0.657082 | + | 0.379366i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 104325. | + | 180697.i | 0.176416 | + | 0.305561i | 0.940650 | − | 0.339378i | \(-0.110216\pi\) |
−0.764235 | + | 0.644938i | \(0.776883\pi\) | |||||||
\(770\) | 746268. | + | 1.42470e6i | 1.25867 | + | 2.40293i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 356091. | − | 514105.i | 0.597484 | − | 0.862616i | ||||
\(773\) | 661279. | 1.10669 | 0.553345 | − | 0.832952i | \(-0.313351\pi\) | ||||
0.553345 | + | 0.832952i | \(0.313351\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 202663.i | − | 0.337420i | ||||||
\(776\) | −562984. | + | 745421.i | −0.934917 | + | 1.23788i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −400558. | − | 764703.i | −0.661769 | − | 1.26338i | ||||
\(779\) | −60554.8 | + | 34961.3i | −0.0997869 | + | 0.0576120i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −139739. | + | 242036.i | −0.229096 | + | 0.396805i | ||||
\(782\) | 5841.23 | − | 142090.i | 0.00955192 | − | 0.232355i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −299743. | − | 49709.5i | −0.487660 | − | 0.0808736i | ||||
\(785\) | 590239. | − | 1.02232e6i | 0.957830 | − | 1.65901i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33656.2 | − | 19431.4i | 0.0543395 | − | 0.0313729i | −0.472584 | − | 0.881286i | \(-0.656679\pi\) |
0.526924 | + | 0.849913i | \(0.323345\pi\) | |||||||
\(788\) | −73962.2 | − | 156526.i | −0.119113 | − | 0.252077i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −190025. | − | 120380.i | −0.304479 | − | 0.192886i | ||||
\(791\) | − | 886090.i | − | 1.41620i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −243453. | −0.387141 | ||||||||
\(794\) | 626239. | − | 988546.i | 0.993343 | − | 1.56804i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11679.9 | + | 5519.05i | −0.0184338 | + | 0.00871040i | ||||
\(797\) | −321301. | − | 556510.i | −0.505820 | − | 0.876105i | −0.999977 | − | 0.00673297i | \(-0.997857\pi\) |
0.494158 | − | 0.869372i | \(-0.335477\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 224953. | + | 129877.i | 0.352369 | + | 0.203441i | ||||
\(800\) | −261862. | − | 54564.2i | −0.409160 | − | 0.0852566i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 816565. | + | 33568.3i | 1.26953 | + | 0.0521893i | ||||
\(803\) | −988223. | − | 570551.i | −1.53258 | − | 0.884837i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 319946. | + | 554163.i | 0.493725 | + | 0.855156i | ||||
\(806\) | 472191. | − | 247338.i | 0.726855 | − | 0.380733i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −249228. | + | 329990.i | −0.381745 | + | 0.505450i | ||||
\(809\) | −737297. | −1.12654 | −0.563269 | − | 0.826274i | \(-0.690456\pi\) | ||||
−0.563269 | + | 0.826274i | \(0.690456\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 823394.i | − | 1.25189i | −0.779867 | − | 0.625945i | \(-0.784714\pi\) | ||
0.779867 | − | 0.625945i | \(-0.215286\pi\) | |||||||
\(812\) | 14207.1 | + | 9840.41i | 0.0215473 | + | 0.0149245i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 487185. | − | 255192.i | 0.735267 | − | 0.385139i | ||||
\(815\) | −652894. | + | 376949.i | −0.982941 | + | 0.567501i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −25946.2 | + | 44940.1i | −0.0388713 | + | 0.0673271i | ||||
\(818\) | −138798. | − | 5705.87i | −0.207432 | − | 0.00852738i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −196096. | − | 16150.0i | −0.291635 | − | 0.0240184i | ||||
\(821\) | −290123. | + | 502508.i | −0.430424 | + | 0.745516i | −0.996910 | − | 0.0785556i | \(-0.974969\pi\) |
0.566486 | + | 0.824071i | \(0.308303\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −400074. | + | 230983.i | −0.590664 | + | 0.341020i | −0.765360 | − | 0.643602i | \(-0.777439\pi\) |
0.174696 | + | 0.984622i | \(0.444106\pi\) | |||||||
\(824\) | −952230. | + | 402978.i | −1.40245 | + | 0.593509i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −333195. | + | 525963.i | −0.488358 | + | 0.770895i | ||||
\(827\) | 1.11437e6i | 1.62936i | 0.579912 | + | 0.814679i | \(0.303087\pi\) | ||||
−0.579912 | + | 0.814679i | \(0.696913\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 915553. | 1.33222 | 0.666108 | − | 0.745856i | \(-0.267959\pi\) | ||||
0.666108 | + | 0.745856i | \(0.267959\pi\) | |||||||
\(830\) | −677353. | − | 429100.i | −0.983238 | − | 0.622876i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −192456. | − | 676714.i | −0.278026 | − | 0.977594i | ||||
\(833\) | 58792.8 | + | 101832.i | 0.0847294 | + | 0.146756i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −717733. | − | 414383.i | −1.02941 | − | 0.594332i | ||||
\(836\) | −608621. | − | 50124.6i | −0.870832 | − | 0.0717197i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −52680.6 | + | 1.28148e6i | −0.0750175 | + | 1.82483i | ||||
\(839\) | −489653. | − | 282701.i | −0.695608 | − | 0.401610i | 0.110101 | − | 0.993920i | \(-0.464882\pi\) |
−0.805710 | + | 0.592311i | \(0.798216\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 353478. | + | 612242.i | 0.499770 | + | 0.865627i | ||||
\(842\) | 251995. | + | 481083.i | 0.355442 | + | 0.678572i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 800152. | + | 554219.i | 1.12328 | + | 0.778030i | ||||
\(845\) | −28047.6 | −0.0392810 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.16856e6i | 3.02276i | ||||||||
\(848\) | 330670. | − | 402331.i | 0.459836 | − | 0.559490i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 48032.9 | + | 91699.4i | 0.0664816 | + | 0.126920i | ||||
\(851\) | 189500. | − | 109408.i | 0.261668 | − | 0.151074i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −100990. | + | 174919.i | −0.138796 | + | 0.240402i | −0.927041 | − | 0.374959i | \(-0.877657\pi\) |
0.788245 | + | 0.615362i | \(0.210990\pi\) | |||||||
\(854\) | 13948.6 | − | 339307.i | 0.0191256 | − | 0.465240i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −24119.3 | + | 194689.i | −0.0329167 | + | 0.265701i | ||||
\(857\) | −252164. | + | 436762.i | −0.343338 | + | 0.594679i | −0.985050 | − | 0.172266i | \(-0.944891\pi\) |
0.641712 | + | 0.766946i | \(0.278224\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −662245. | + | 382348.i | −0.897496 | + | 0.518170i | −0.876387 | − | 0.481608i | \(-0.840053\pi\) |
−0.0211092 | + | 0.999777i | \(0.506720\pi\) | |||||||
\(860\) | −132026. | + | 62385.4i | −0.178510 | + | 0.0843501i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −105909. | − | 67092.8i | −0.142534 | − | 0.0902946i | ||||
\(863\) | 1.21817e6i | 1.63564i | 0.575477 | + | 0.817818i | \(0.304817\pi\) | ||||
−0.575477 | + | 0.817818i | \(0.695183\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −656551. | −0.877477 | ||||||||
\(866\) | 216247. | − | 341356.i | 0.288346 | − | 0.455168i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 317667. | + | 672276.i | 0.421631 | + | 0.892295i | ||||
\(869\) | −212982. | − | 368895.i | −0.282035 | − | 0.488498i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 891792. | + | 514876.i | 1.17551 | + | 0.678682i | ||||
\(872\) | 1.12603e6 | + | 139500.i | 1.48088 | + | 0.183460i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −242764. | − | 9979.83i | −0.317805 | − | 0.0130647i | ||||
\(875\) | 561773. | + | 324340.i | 0.733744 | + | 0.423627i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −225455. | − | 390499.i | −0.293130 | − | 0.507716i | 0.681418 | − | 0.731894i | \(-0.261364\pi\) |
−0.974548 | + | 0.224178i | \(0.928030\pi\) | |||||||
\(878\) | −644787. | + | 337745.i | −0.836426 | + | 0.438127i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.32758e6 | − | 1.09112e6i | −1.71434 | − | 1.40899i | ||||
\(881\) | 1.04312e6 | 1.34395 | 0.671974 | − | 0.740575i | \(-0.265447\pi\) | ||||
0.671974 | + | 0.740575i | \(0.265447\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 303710.i | 0.389527i | 0.980850 | + | 0.194763i | \(0.0623939\pi\) | ||||
−0.980850 | + | 0.194763i | \(0.937606\pi\) | |||||||
\(884\) | −155032. | + | 223827.i | −0.198389 | + | 0.286423i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 131772. | − | 69023.4i | 0.167863 | − | 0.0879283i | ||||
\(887\) | 587624. | − | 339265.i | 0.746882 | − | 0.431213i | −0.0776839 | − | 0.996978i | \(-0.524752\pi\) |
0.824566 | + | 0.565765i | \(0.191419\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 553426. | − | 958562.i | 0.700255 | − | 1.21288i | ||||
\(890\) | −1.12275e6 | − | 46155.3i | −1.41743 | − | 0.0582696i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −14090.9 | + | 171094.i | −0.0177097 | + | 0.215034i | ||||
\(893\) | 221896. | − | 384336.i | 0.278258 | − | 0.481956i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.35385e6 | + | 781647.i | −1.69015 | + | 0.975808i | ||||
\(896\) | 954180. | − | 229458.i | 1.18854 | − | 0.285817i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 43636.0 | − | 68881.4i | 0.0541119 | − | 0.0854179i | ||||
\(899\) | − | 13990.5i | − | 0.0173107i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −201543. | −0.248267 | ||||||||
\(902\) | −314746. | − | 199390.i | −0.386854 | − | 0.245070i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 368983. | + | 871898.i | 0.451512 | + | 1.06691i | ||||
\(905\) | −107516. | − | 186223.i | −0.131273 | − | 0.227372i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.02766e6 | + | 593322.i | 1.24921 | + | 0.721233i | 0.970952 | − | 0.239273i | \(-0.0769090\pi\) |
0.278260 | + | 0.960506i | \(0.410242\pi\) | |||||||
\(908\) | 99456.1 | − | 1.20761e6i | 0.120631 | − | 1.46472i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 50321.7 | − | 1.22410e6i | 0.0607676 | − | 1.47820i | ||||
\(911\) | 754071. | + | 435363.i | 0.908606 | + | 0.524584i | 0.879982 | − | 0.475007i | \(-0.157554\pi\) |
0.0286234 | + | 0.999590i | \(0.490888\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −759181. | − | 1.31494e6i | −0.910760 | − | 1.57748i | ||||
\(914\) | −519052. | − | 990919.i | −0.621324 | − | 1.18617i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 486188. | − | 701931.i | 0.579446 | − | 0.836573i | ||||
\(917\) | 498400. | 0.592706 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 60879.9i | − | 0.0720847i | −0.999350 | − | 0.0360423i | \(-0.988525\pi\) | ||
0.999350 | − | 0.0360423i | \(-0.0114751\pi\) | |||||||
\(920\) | −545584. | − | 412056.i | −0.644594 | − | 0.486834i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 298072. | + | 569047.i | 0.350638 | + | 0.669401i | ||||
\(923\) | 184370. | − | 106446.i | 0.216415 | − | 0.124947i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −79640.2 | + | 137941.i | −0.0930783 | + | 0.161216i | ||||
\(926\) | 16290.7 | − | 396280.i | 0.0189985 | − | 0.462147i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −18077.2 | − | 3766.75i | −0.0209911 | − | 0.00437392i | ||||
\(929\) | −470405. | + | 814765.i | −0.545055 | + | 0.944063i | 0.453548 | + | 0.891232i | \(0.350158\pi\) |
−0.998603 | + | 0.0528314i | \(0.983175\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 173982. | − | 100448.i | 0.200726 | − | 0.115889i | ||||
\(932\) | 386117. | + | 817136.i | 0.444516 | + | 0.940725i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 942041. | + | 596778.i | 1.07988 | + | 0.684100i | ||||
\(935\) | 665037.i | 0.760717i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −634530. | −0.722725 | −0.361362 | − | 0.932425i | \(-0.617688\pi\) | ||||
−0.361362 | + | 0.932425i | \(0.617688\pi\) | |||||||
\(938\) | −768691. | + | 1.21341e6i | −0.873667 | + | 1.37912i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.12911e6 | − | 533531.i | 1.27785 | − | 0.603815i | ||||
\(941\) | 34049.0 | + | 58974.5i | 0.0384525 | + | 0.0666017i | 0.884611 | − | 0.466329i | \(-0.154424\pi\) |
−0.846159 | + | 0.532931i | \(0.821091\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −128379. | − | 74119.7i | −0.144368 | − | 0.0833509i | ||||
\(944\) | 108839. | − | 656287.i | 0.122135 | − | 0.736461i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −276279. | − | 11357.6i | −0.308720 | − | 0.0126912i | ||||
\(947\) | 461349. | + | 266360.i | 0.514434 | + | 0.297009i | 0.734654 | − | 0.678442i | \(-0.237344\pi\) |
−0.220220 | + | 0.975450i | \(0.570678\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 434616. | + | 752777.i | 0.482585 | + | 0.835861i | ||||
\(950\) | 156670. | − | 82065.0i | 0.173595 | − | 0.0909308i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −303071. | − | 228896.i | −0.334403 | − | 0.252560i | ||||
\(953\) | −72542.5 | −0.0798742 | −0.0399371 | − | 0.999202i | \(-0.512716\pi\) | ||||
−0.0399371 | + | 0.999202i | \(0.512716\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 315042.i | − | 0.345432i | ||||||
\(956\) | −631232. | − | 437218.i | −0.690674 | − | 0.478390i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −113357. | + | 59377.1i | −0.123514 | + | 0.0646976i | ||||
\(959\) | −1.11045e6 | + | 641118.i | −1.20743 | + | 0.697109i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −160796. | + | 278507.i | −0.174112 | + | 0.301571i | ||||
\(962\) | −418589. | − | 17207.9i | −0.452311 | − | 0.0185942i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.02294e6 | − | 84246.8i | −1.10077 | − | 0.0906566i | ||||
\(965\) | −581791. | + | 1.00769e6i | −0.624759 | + | 1.08211i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 705768. | − | 407475.i | 0.754760 | − | 0.435761i | −0.0726511 | − | 0.997357i | \(-0.523146\pi\) |
0.827411 | + | 0.561596i | \(0.189813\pi\) | |||||||
\(968\) | −903022. | − | 2.13382e6i | −0.963713 | − | 2.27723i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 930109. | − | 1.46822e6i | 0.988532 | − | 1.56044i | ||||
\(971\) | − | 939538.i | − | 0.996496i | −0.867034 | − | 0.498248i | \(-0.833977\pi\) | ||
0.867034 | − | 0.498248i | \(-0.166023\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.09168e6 | 1.15310 | ||||||||
\(974\) | 1.17193e6 | + | 742409.i | 1.23533 | + | 0.782574i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 127568. | + | 339681.i | 0.133919 | + | 0.356592i | ||||
\(977\) | 870579. | + | 1.50789e6i | 0.912051 | + | 1.57972i | 0.811162 | + | 0.584821i | \(0.198835\pi\) |
0.100889 | + | 0.994898i | \(0.467831\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.84277e6 | − | 1.06393e6i | −1.92268 | − | 1.11006i | ||||
\(980\) | 563408. | + | 46401.0i | 0.586639 | + | 0.0483142i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 39428.5 | − | 959116.i | 0.0408872 | − | 0.994599i | ||||
\(983\) | 1.07730e6 | + | 621978.i | 1.11488 | + | 0.643677i | 0.940089 | − | 0.340929i | \(-0.110741\pi\) |
0.174792 | + | 0.984605i | \(0.444075\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 161053. | + | 278952.i | 0.165995 | + | 0.287513i | ||||
\(986\) | 3315.87 | + | 6330.31i | 0.00341071 | + | 0.00651136i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 382412. | + | 264875.i | 0.391758 | + | 0.271348i | ||||
\(989\) | −110014. | −0.112475 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 766088.i | 0.780066i | 0.920801 | + | 0.390033i | \(0.127536\pi\) | ||||
−0.920801 | + | 0.390033i | \(0.872464\pi\) | |||||||
\(992\) | −592526. | − | 529227.i | −0.602121 | − | 0.537797i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 137793. | + | 263060.i | 0.139462 | + | 0.266246i | ||||
\(995\) | 20815.3 | − | 12017.7i | 0.0210251 | − | 0.0121388i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −192679. | + | 333731.i | −0.193841 | + | 0.335742i | −0.946520 | − | 0.322645i | \(-0.895428\pi\) |
0.752679 | + | 0.658388i | \(0.228761\pi\) | |||||||
\(998\) | −56033.2 | + | 1.36303e6i | −0.0562580 | + | 1.36850i | ||||
\(999\) | 0 | 0 |
(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 | 108.5.f.a.19.15 | 44 | ||
3.2 | odd | 2 | 36.5.f.a.7.8 | ✓ | 44 | ||
4.3 | odd | 2 | inner | 108.5.f.a.19.14 | 44 | ||
9.2 | odd | 6 | 324.5.d.f.163.22 | 22 | |||
9.4 | even | 3 | inner | 108.5.f.a.91.14 | 44 | ||
9.5 | odd | 6 | 36.5.f.a.31.9 | yes | 44 | ||
9.7 | even | 3 | 324.5.d.e.163.1 | 22 | |||
12.11 | even | 2 | 36.5.f.a.7.9 | yes | 44 | ||
36.7 | odd | 6 | 324.5.d.e.163.2 | 22 | |||
36.11 | even | 6 | 324.5.d.f.163.21 | 22 | |||
36.23 | even | 6 | 36.5.f.a.31.8 | yes | 44 | ||
36.31 | odd | 6 | inner | 108.5.f.a.91.15 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.5.f.a.7.8 | ✓ | 44 | 3.2 | odd | 2 | ||
36.5.f.a.7.9 | yes | 44 | 12.11 | even | 2 | ||
36.5.f.a.31.8 | yes | 44 | 36.23 | even | 6 | ||
36.5.f.a.31.9 | yes | 44 | 9.5 | odd | 6 | ||
108.5.f.a.19.14 | 44 | 4.3 | odd | 2 | inner | ||
108.5.f.a.19.15 | 44 | 1.1 | even | 1 | trivial | ||
108.5.f.a.91.14 | 44 | 9.4 | even | 3 | inner | ||
108.5.f.a.91.15 | 44 | 36.31 | odd | 6 | inner | ||
324.5.d.e.163.1 | 22 | 9.7 | even | 3 | |||
324.5.d.e.163.2 | 22 | 36.7 | odd | 6 | |||
324.5.d.f.163.21 | 22 | 36.11 | even | 6 | |||
324.5.d.f.163.22 | 22 | 9.2 | odd | 6 |