Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,6,Mod(37,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.37");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.e (of order \(3\), 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: | \(10.1041806482\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 98x^{6} + 83x^{5} + 9122x^{4} - 91x^{3} + 28567x^{2} + 2058x + 86436 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 46.2 | ||
Root | \(0.895402 + 1.55088i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 63.46 |
Dual form | 63.6.e.e.37.2 |
$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.395402 | − | 0.684857i | −0.0698979 | − | 0.121067i | 0.828958 | − | 0.559310i | \(-0.188934\pi\) |
−0.898856 | + | 0.438244i | \(0.855601\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 15.6873 | − | 27.1712i | 0.490229 | − | 0.849101i | ||||
\(5\) | −52.0958 | − | 90.2327i | −0.931919 | − | 1.61413i | −0.780038 | − | 0.625732i | \(-0.784800\pi\) |
−0.151881 | − | 0.988399i | \(-0.548533\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.12980 | + | 129.446i | −0.0549961 | + | 0.998487i | ||||
\(8\) | −50.1170 | −0.276860 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −41.1977 | + | 71.3564i | −0.130278 | + | 0.225649i | ||||
\(11\) | −248.830 | + | 430.986i | −0.620041 | + | 1.07394i | 0.369436 | + | 0.929256i | \(0.379551\pi\) |
−0.989477 | + | 0.144687i | \(0.953782\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −206.551 | −0.338977 | −0.169488 | − | 0.985532i | \(-0.554211\pi\) | ||||
−0.169488 | + | 0.985532i | \(0.554211\pi\) | |||||||
\(14\) | 91.4709 | − | 46.3002i | 0.124728 | − | 0.0631340i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −482.178 | − | 835.156i | −0.470877 | − | 0.815582i | ||||
\(17\) | 31.5793 | − | 54.6969i | 0.0265021 | − | 0.0459030i | −0.852470 | − | 0.522776i | \(-0.824896\pi\) |
0.878972 | + | 0.476873i | \(0.158230\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −661.977 | − | 1146.58i | −0.420687 | − | 0.728651i | 0.575320 | − | 0.817929i | \(-0.304878\pi\) |
−0.996007 | + | 0.0892772i | \(0.971544\pi\) | |||||||
\(20\) | −3268.98 | −1.82741 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 393.552 | 0.173358 | ||||||||
\(23\) | −97.2187 | − | 168.388i | −0.0383204 | − | 0.0663729i | 0.846229 | − | 0.532819i | \(-0.178867\pi\) |
−0.884550 | + | 0.466446i | \(0.845534\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3865.45 | + | 6695.16i | −1.23695 | + | 2.14245i | ||||
\(26\) | 81.6709 | + | 141.458i | 0.0236938 | + | 0.0410388i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3405.35 | + | 2224.38i | 0.820855 | + | 0.536184i | ||||
\(29\) | −4323.14 | −0.954562 | −0.477281 | − | 0.878751i | \(-0.658378\pi\) | ||||
−0.477281 | + | 0.878751i | \(0.658378\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3762.66 | − | 6517.11i | 0.703219 | − | 1.21801i | −0.264112 | − | 0.964492i | \(-0.585079\pi\) |
0.967331 | − | 0.253518i | \(-0.0815879\pi\) | |||||||
\(32\) | −1183.18 | + | 2049.33i | −0.204256 | + | 0.353783i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −49.9461 | −0.00740977 | ||||||||
\(35\) | 12051.7 | − | 6100.24i | 1.66294 | − | 0.841738i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5177.82 | − | 8968.25i | −0.621789 | − | 1.07697i | −0.989152 | − | 0.146892i | \(-0.953073\pi\) |
0.367364 | − | 0.930077i | \(-0.380260\pi\) | |||||||
\(38\) | −523.495 | + | 906.720i | −0.0588103 | + | 0.101862i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2610.89 | + | 4522.19i | 0.258011 | + | 0.446888i | ||||
\(41\) | 4180.92 | 0.388429 | 0.194215 | − | 0.980959i | \(-0.437784\pi\) | ||||
0.194215 | + | 0.980959i | \(0.437784\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5960.87 | 0.491630 | 0.245815 | − | 0.969317i | \(-0.420944\pi\) | ||||
0.245815 | + | 0.969317i | \(0.420944\pi\) | |||||||
\(44\) | 7806.94 | + | 13522.0i | 0.607924 | + | 1.05296i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −76.8810 | + | 133.162i | −0.00535703 | + | 0.00927866i | ||||
\(47\) | −2194.87 | − | 3801.62i | −0.144932 | − | 0.251029i | 0.784416 | − | 0.620236i | \(-0.212963\pi\) |
−0.929348 | + | 0.369206i | \(0.879630\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −16705.3 | − | 1845.84i | −0.993951 | − | 0.109826i | ||||
\(50\) | 6113.64 | 0.345840 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3240.24 | + | 5612.25i | −0.166176 | + | 0.287825i | ||||
\(53\) | 8892.39 | − | 15402.1i | 0.434839 | − | 0.753164i | −0.562443 | − | 0.826836i | \(-0.690138\pi\) |
0.997283 | + | 0.0736720i | \(0.0234718\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 51852.0 | 2.31131 | ||||||||
\(56\) | 357.324 | − | 6487.42i | 0.0152262 | − | 0.276441i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1709.38 | + | 2960.73i | 0.0667219 | + | 0.115566i | ||||
\(59\) | 1750.23 | − | 3031.49i | 0.0654585 | − | 0.113377i | −0.831439 | − | 0.555616i | \(-0.812482\pi\) |
0.896897 | + | 0.442239i | \(0.145816\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5316.23 | + | 9207.98i | 0.182928 | + | 0.316840i | 0.942876 | − | 0.333143i | \(-0.108109\pi\) |
−0.759949 | + | 0.649983i | \(0.774776\pi\) | |||||||
\(62\) | −5951.06 | −0.196614 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −28988.0 | −0.884645 | ||||||||
\(65\) | 10760.5 | + | 18637.7i | 0.315899 | + | 0.547153i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6637.37 | − | 11496.3i | 0.180638 | − | 0.312874i | −0.761460 | − | 0.648212i | \(-0.775517\pi\) |
0.942098 | + | 0.335338i | \(0.108850\pi\) | |||||||
\(68\) | −990.789 | − | 1716.10i | −0.0259842 | − | 0.0450059i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −8943.05 | − | 5841.61i | −0.218143 | − | 0.142491i | ||||
\(71\) | −38811.1 | −0.913713 | −0.456857 | − | 0.889540i | \(-0.651025\pi\) | ||||
−0.456857 | + | 0.889540i | \(0.651025\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15687.8 | + | 27172.1i | −0.344552 | + | 0.596782i | −0.985272 | − | 0.170992i | \(-0.945303\pi\) |
0.640720 | + | 0.767775i | \(0.278636\pi\) | |||||||
\(74\) | −4094.65 | + | 7092.14i | −0.0869235 | + | 0.150556i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −41538.6 | −0.824931 | ||||||||
\(77\) | −54015.1 | − | 35282.8i | −1.03822 | − | 0.678166i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −19745.7 | − | 34200.6i | −0.355964 | − | 0.616547i | 0.631319 | − | 0.775523i | \(-0.282514\pi\) |
−0.987282 | + | 0.158976i | \(0.949181\pi\) | |||||||
\(80\) | −50238.9 | + | 87016.3i | −0.877638 | + | 1.52011i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1653.14 | − | 2863.33i | −0.0271504 | − | 0.0470259i | ||||
\(83\) | 102372. | 1.63112 | 0.815559 | − | 0.578675i | \(-0.196430\pi\) | ||||
0.815559 | + | 0.578675i | \(0.196430\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6580.60 | −0.0987912 | ||||||||
\(86\) | −2356.94 | − | 4082.34i | −0.0343639 | − | 0.0595201i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 12470.6 | − | 21599.7i | 0.171665 | − | 0.297332i | ||||
\(89\) | −56410.5 | − | 97705.8i | −0.754892 | − | 1.30751i | −0.945428 | − | 0.325831i | \(-0.894356\pi\) |
0.190536 | − | 0.981680i | \(-0.438977\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1472.67 | − | 26737.2i | 0.0186424 | − | 0.338464i | ||||
\(92\) | −6100.40 | −0.0751430 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1735.71 | + | 3006.34i | −0.0202609 | + | 0.0350929i | ||||
\(95\) | −68972.6 | + | 119464.i | −0.784092 | + | 1.35809i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 30334.3 | 0.327345 | 0.163672 | − | 0.986515i | \(-0.447666\pi\) | ||||
0.163672 | + | 0.986515i | \(0.447666\pi\) | |||||||
\(98\) | 5341.19 | + | 12170.6i | 0.0561789 | + | 0.128011i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 121277. | + | 210058.i | 1.21277 | + | 2.10058i | ||||
\(101\) | 53398.2 | − | 92488.4i | 0.520862 | − | 0.902160i | −0.478843 | − | 0.877900i | \(-0.658944\pi\) |
0.999706 | − | 0.0242599i | \(-0.00772291\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −78767.8 | − | 136430.i | −0.731570 | − | 1.26712i | −0.956212 | − | 0.292674i | \(-0.905455\pi\) |
0.224643 | − | 0.974441i | \(-0.427879\pi\) | |||||||
\(104\) | 10351.7 | 0.0938490 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14064.3 | −0.121578 | ||||||||
\(107\) | −44662.2 | − | 77357.1i | −0.377121 | − | 0.653192i | 0.613521 | − | 0.789678i | \(-0.289752\pi\) |
−0.990642 | + | 0.136486i | \(0.956419\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −83802.3 | + | 145150.i | −0.675600 | + | 1.17017i | 0.300693 | + | 0.953721i | \(0.402782\pi\) |
−0.976293 | + | 0.216452i | \(0.930551\pi\) | |||||||
\(110\) | −20502.4 | − | 35511.2i | −0.161556 | − | 0.279823i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 111545. | − | 56461.3i | 0.840244 | − | 0.425310i | ||||
\(113\) | 115794. | 0.853079 | 0.426539 | − | 0.904469i | \(-0.359733\pi\) | ||||
0.426539 | + | 0.904469i | \(0.359733\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10129.4 | + | 17544.6i | −0.0714230 | + | 0.123708i | ||||
\(116\) | −67818.4 | + | 117465.i | −0.467954 | + | 0.810519i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2768.19 | −0.0183017 | ||||||||
\(119\) | 6855.13 | + | 4477.78i | 0.0443760 | + | 0.0289865i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −43307.1 | − | 75010.0i | −0.268903 | − | 0.465753i | ||||
\(122\) | 4204.10 | − | 7281.72i | 0.0255725 | − | 0.0442929i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −118052. | − | 204472.i | −0.689476 | − | 1.19421i | ||||
\(125\) | 479898. | 2.74709 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 201513. | 1.10865 | 0.554325 | − | 0.832300i | \(-0.312977\pi\) | ||||
0.554325 | + | 0.832300i | \(0.312977\pi\) | |||||||
\(128\) | 49323.7 | + | 85431.2i | 0.266091 | + | 0.460884i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8509.43 | − | 14738.8i | 0.0441613 | − | 0.0764897i | ||||
\(131\) | 19234.8 | + | 33315.6i | 0.0979285 | + | 0.169617i | 0.910827 | − | 0.412788i | \(-0.135445\pi\) |
−0.812899 | + | 0.582405i | \(0.802112\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 153139. | − | 77515.2i | 0.750685 | − | 0.379977i | ||||
\(134\) | −10497.7 | −0.0505049 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1582.66 | + | 2741.25i | −0.00733736 | + | 0.0127087i | ||||
\(137\) | −120861. | + | 209337.i | −0.550155 | + | 0.952896i | 0.448108 | + | 0.893979i | \(0.352098\pi\) |
−0.998263 | + | 0.0589167i | \(0.981235\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −53112.2 | −0.233162 | −0.116581 | − | 0.993181i | \(-0.537193\pi\) | ||||
−0.116581 | + | 0.993181i | \(0.537193\pi\) | |||||||
\(140\) | 23307.1 | − | 423155.i | 0.100501 | − | 1.82465i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 15346.0 | + | 26580.1i | 0.0638667 | + | 0.110620i | ||||
\(143\) | 51396.1 | − | 89020.7i | 0.210180 | − | 0.364042i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 225218. | + | 390088.i | 0.889574 | + | 1.54079i | ||||
\(146\) | 24812.0 | 0.0963340 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −324905. | −1.21927 | ||||||||
\(149\) | 64531.0 | + | 111771.i | 0.238124 | + | 0.412443i | 0.960176 | − | 0.279396i | \(-0.0901342\pi\) |
−0.722052 | + | 0.691839i | \(0.756801\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −76603.2 | + | 132681.i | −0.273404 | + | 0.473549i | −0.969731 | − | 0.244175i | \(-0.921483\pi\) |
0.696327 | + | 0.717724i | \(0.254816\pi\) | |||||||
\(152\) | 33176.3 | + | 57463.0i | 0.116471 | + | 0.201734i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2805.94 | + | 50943.5i | −0.00953405 | + | 0.173096i | ||||
\(155\) | −784075. | −2.62137 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 75593.9 | − | 130932.i | 0.244758 | − | 0.423934i | −0.717305 | − | 0.696759i | \(-0.754625\pi\) |
0.962064 | + | 0.272825i | \(0.0879581\pi\) | |||||||
\(158\) | −15615.0 | + | 27046.0i | −0.0497622 | + | 0.0861907i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 246555. | 0.761402 | ||||||||
\(161\) | 22490.2 | − | 11384.0i | 0.0683799 | − | 0.0346122i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16458.3 | + | 28506.7i | 0.0485196 | + | 0.0840384i | 0.889265 | − | 0.457392i | \(-0.151216\pi\) |
−0.840746 | + | 0.541430i | \(0.817883\pi\) | |||||||
\(164\) | 65587.3 | − | 113601.i | 0.190419 | − | 0.329816i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −40478.1 | − | 70110.1i | −0.114012 | − | 0.197474i | ||||
\(167\) | −217586. | −0.603725 | −0.301862 | − | 0.953352i | \(-0.597608\pi\) | ||||
−0.301862 | + | 0.953352i | \(0.597608\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −328630. | −0.885095 | ||||||||
\(170\) | 2601.99 | + | 4506.77i | 0.00690530 | + | 0.0119603i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 93510.0 | − | 161964.i | 0.241011 | − | 0.417443i | ||||
\(173\) | −210621. | − | 364807.i | −0.535041 | − | 0.926718i | −0.999161 | − | 0.0409458i | \(-0.986963\pi\) |
0.464121 | − | 0.885772i | \(-0.346370\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −839100. | − | 548101.i | −2.07118 | − | 1.35290i | ||||
\(176\) | 479921. | 1.16785 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −44609.7 | + | 77266.3i | −0.105531 | + | 0.182785i | ||||
\(179\) | 1747.03 | − | 3025.94i | 0.00407538 | − | 0.00705876i | −0.863981 | − | 0.503525i | \(-0.832036\pi\) |
0.868056 | + | 0.496466i | \(0.165369\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 594611. | 1.34908 | 0.674538 | − | 0.738240i | \(-0.264343\pi\) | ||||
0.674538 | + | 0.738240i | \(0.264343\pi\) | |||||||
\(182\) | −18893.4 | + | 9563.37i | −0.0422798 | + | 0.0214009i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4872.30 | + | 8439.08i | 0.0106094 | + | 0.0183760i | ||||
\(185\) | −539486. | + | 934418.i | −1.15891 | + | 2.00730i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15715.7 | + | 27220.5i | 0.0328648 | + | 0.0569235i | ||||
\(188\) | −137726. | −0.284199 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 109088. | 0.219226 | ||||||||
\(191\) | 414322. | + | 717627.i | 0.821778 | + | 1.42336i | 0.904357 | + | 0.426777i | \(0.140351\pi\) |
−0.0825782 | + | 0.996585i | \(0.526315\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −109869. | + | 190299.i | −0.212316 | + | 0.367743i | −0.952439 | − | 0.304729i | \(-0.901434\pi\) |
0.740123 | + | 0.672472i | \(0.234767\pi\) | |||||||
\(194\) | −11994.3 | − | 20774.7i | −0.0228807 | − | 0.0396306i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −312216. | + | 424948.i | −0.580516 | + | 0.790125i | ||||
\(197\) | −475612. | −0.873146 | −0.436573 | − | 0.899669i | \(-0.643808\pi\) | ||||
−0.436573 | + | 0.899669i | \(0.643808\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −313778. | + | 543479.i | −0.561681 | + | 0.972859i | 0.435669 | + | 0.900107i | \(0.356512\pi\) |
−0.997350 | + | 0.0727525i | \(0.976822\pi\) | |||||||
\(200\) | 193725. | − | 335541.i | 0.342460 | − | 0.593159i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −84455.1 | −0.145629 | ||||||||
\(203\) | 30823.1 | − | 559611.i | 0.0524972 | − | 0.953117i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −217808. | − | 377255.i | −0.361984 | − | 0.626975i | ||||
\(206\) | −62290.0 | + | 107889.i | −0.102270 | + | 0.177138i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 99594.5 | + | 172503.i | 0.159616 | + | 0.276463i | ||||
\(209\) | 658879. | 1.04337 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 570989. | 0.882920 | 0.441460 | − | 0.897281i | \(-0.354461\pi\) | ||||
0.441460 | + | 0.897281i | \(0.354461\pi\) | |||||||
\(212\) | −278995. | − | 483234.i | −0.426341 | − | 0.738445i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −35319.1 | + | 61174.4i | −0.0527199 | + | 0.0913136i | ||||
\(215\) | −310536. | − | 537865.i | −0.458159 | − | 0.793555i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 816785. | + | 533525.i | 1.17749 | + | 0.769140i | ||||
\(218\) | 132543. | 0.188892 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 813419. | − | 1.40888e6i | 1.13307 | − | 1.96254i | ||||
\(221\) | −6522.75 | + | 11297.7i | −0.00898359 | + | 0.0155600i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4233.11 | 0.00570029 | 0.00285015 | − | 0.999996i | \(-0.499093\pi\) | ||||
0.00285015 | + | 0.999996i | \(0.499093\pi\) | |||||||
\(224\) | −256841. | − | 167769.i | −0.342014 | − | 0.223404i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −45785.2 | − | 79302.2i | −0.0596285 | − | 0.103280i | ||||
\(227\) | 564931. | − | 978490.i | 0.727664 | − | 1.26035i | −0.230204 | − | 0.973142i | \(-0.573939\pi\) |
0.957868 | − | 0.287209i | \(-0.0927274\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −402322. | − | 696842.i | −0.506973 | − | 0.878103i | −0.999967 | − | 0.00807048i | \(-0.997431\pi\) |
0.492994 | − | 0.870032i | \(-0.335902\pi\) | |||||||
\(230\) | 16020.7 | 0.0199693 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 216663. | 0.264280 | ||||||||
\(233\) | 584636. | + | 1.01262e6i | 0.705498 | + | 1.22196i | 0.966511 | + | 0.256624i | \(0.0826101\pi\) |
−0.261013 | + | 0.965335i | \(0.584057\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −228687. | + | 396098.i | −0.270130 | + | 0.467878i | ||||
\(236\) | −54912.9 | − | 95112.0i | −0.0641792 | − | 0.111162i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 356.106 | − | 6465.31i | 0.000407508 | − | 0.00739855i | ||||
\(239\) | 1.70554e6 | 1.93138 | 0.965689 | − | 0.259700i | \(-0.0836238\pi\) | ||||
0.965689 | + | 0.259700i | \(0.0836238\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −475598. | + | 823760.i | −0.527470 | + | 0.913604i | 0.472018 | + | 0.881589i | \(0.343526\pi\) |
−0.999487 | + | 0.0320153i | \(0.989807\pi\) | |||||||
\(242\) | −34247.4 | + | 59318.3i | −0.0375915 | + | 0.0651104i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 333590. | 0.358705 | ||||||||
\(245\) | 703723. | + | 1.60353e6i | 0.749008 | + | 1.70672i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 136732. | + | 236827.i | 0.142603 | + | 0.246996i | ||||
\(248\) | −188573. | + | 326618.i | −0.194693 | + | 0.337218i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −189753. | − | 328661.i | −0.192016 | − | 0.332582i | ||||
\(251\) | −1.14498e6 | −1.14713 | −0.573566 | − | 0.819159i | \(-0.694440\pi\) | ||||
−0.573566 | + | 0.819159i | \(0.694440\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 96763.6 | 0.0950409 | ||||||||
\(254\) | −79678.8 | − | 138008.i | −0.0774923 | − | 0.134221i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −424803. | + | 735781.i | −0.405124 | + | 0.701695i | ||||
\(257\) | 591869. | + | 1.02515e6i | 0.558976 | + | 0.968175i | 0.997582 | + | 0.0694955i | \(0.0221389\pi\) |
−0.438606 | + | 0.898679i | \(0.644528\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.19782e6 | − | 606305.i | 1.10954 | − | 0.561619i | ||||
\(260\) | 675211. | 0.619450 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 15211.0 | − | 26346.2i | 0.0136900 | − | 0.0237118i | ||||
\(263\) | 224158. | − | 388253.i | 0.199832 | − | 0.346119i | −0.748642 | − | 0.662975i | \(-0.769294\pi\) |
0.948474 | + | 0.316856i | \(0.102627\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.85303e6 | −1.62094 | ||||||||
\(266\) | −113639. | − | 74228.9i | −0.0984740 | − | 0.0643234i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −208245. | − | 360691.i | −0.177108 | − | 0.306760i | ||||
\(269\) | 373737. | − | 647332.i | 0.314909 | − | 0.545439i | −0.664509 | − | 0.747280i | \(-0.731359\pi\) |
0.979418 | + | 0.201841i | \(0.0646925\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 116319. | + | 201470.i | 0.0962114 | + | 0.166643i | 0.910114 | − | 0.414359i | \(-0.135994\pi\) |
−0.813902 | + | 0.581002i | \(0.802661\pi\) | |||||||
\(272\) | −60907.3 | −0.0499169 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 191155. | 0.153819 | ||||||||
\(275\) | −1.92368e6 | − | 3.33191e6i | −1.53391 | − | 2.65682i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.21462e6 | − | 2.10379e6i | 0.951134 | − | 1.64741i | 0.208157 | − | 0.978095i | \(-0.433253\pi\) |
0.742977 | − | 0.669317i | \(-0.233413\pi\) | |||||||
\(278\) | 21000.7 | + | 36374.3i | 0.0162975 | + | 0.0282282i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −603992. | + | 305725.i | −0.460401 | + | 0.233043i | ||||
\(281\) | −2.51704e6 | −1.90163 | −0.950813 | − | 0.309766i | \(-0.899749\pi\) | ||||
−0.950813 | + | 0.309766i | \(0.899749\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −130497. | + | 226028.i | −0.0968579 | + | 0.167763i | −0.910382 | − | 0.413768i | \(-0.864213\pi\) |
0.813525 | + | 0.581530i | \(0.197546\pi\) | |||||||
\(284\) | −608842. | + | 1.05454e6i | −0.447928 | + | 0.775835i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −81288.6 | −0.0587645 | ||||||||
\(287\) | −29809.1 | + | 541201.i | −0.0213621 | + | 0.387841i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 707934. | + | 1.22618e6i | 0.498595 | + | 0.863592i | ||||
\(290\) | 178103. | − | 308484.i | 0.124359 | − | 0.215396i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 492199. | + | 852514.i | 0.337819 | + | 0.585119i | ||||
\(293\) | −65011.7 | −0.0442408 | −0.0221204 | − | 0.999755i | \(-0.507042\pi\) | ||||
−0.0221204 | + | 0.999755i | \(0.507042\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −364720. | −0.244008 | ||||||||
\(296\) | 259497. | + | 449462.i | 0.172148 | + | 0.298170i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 51031.5 | − | 88389.1i | 0.0332887 | − | 0.0576578i | ||||
\(299\) | 20080.6 | + | 34780.7i | 0.0129897 | + | 0.0224989i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −42499.8 | + | 771608.i | −0.0270377 | + | 0.490886i | ||||
\(302\) | 121156. | 0.0764414 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −638381. | + | 1.10571e6i | −0.396183 | + | 0.686210i | ||||
\(305\) | 553907. | − | 959395.i | 0.340947 | − | 0.590538i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.35599e6 | −1.42668 | −0.713342 | − | 0.700816i | \(-0.752819\pi\) | ||||
−0.713342 | + | 0.700816i | \(0.752819\pi\) | |||||||
\(308\) | −1.80603e6 | + | 914165.i | −1.08480 | + | 0.549096i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 310025. | + | 536980.i | 0.183228 | + | 0.317361i | ||||
\(311\) | −1.05903e6 | + | 1.83429e6i | −0.620878 | + | 1.07539i | 0.368445 | + | 0.929650i | \(0.379890\pi\) |
−0.989323 | + | 0.145742i | \(0.953443\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 93756.8 | + | 162392.i | 0.0540931 | + | 0.0936920i | 0.891804 | − | 0.452422i | \(-0.149440\pi\) |
−0.837711 | + | 0.546114i | \(0.816107\pi\) | |||||||
\(314\) | −119560. | −0.0684324 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.23903e6 | −0.698014 | ||||||||
\(317\) | −502705. | − | 870711.i | −0.280974 | − | 0.486661i | 0.690651 | − | 0.723188i | \(-0.257324\pi\) |
−0.971625 | + | 0.236527i | \(0.923991\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.07573e6 | − | 1.86321e6i | 0.591868 | − | 1.02515i | ||||
\(320\) | 1.51016e6 | + | 2.61567e6i | 0.824417 | + | 1.42793i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −16689.1 | − | 10901.3i | −0.00897000 | − | 0.00585922i | ||||
\(323\) | −83619.1 | −0.0445964 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 798415. | − | 1.38290e6i | 0.419296 | − | 0.726241i | ||||
\(326\) | 13015.3 | − | 22543.2i | 0.00678284 | − | 0.0117482i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −209535. | −0.107540 | ||||||||
\(329\) | 507753. | − | 257011.i | 0.258620 | − | 0.130907i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −839920. | − | 1.45478e6i | −0.421374 | − | 0.729841i | 0.574700 | − | 0.818364i | \(-0.305119\pi\) |
−0.996074 | + | 0.0885229i | \(0.971785\pi\) | |||||||
\(332\) | 1.60594e6 | − | 2.78157e6i | 0.799620 | − | 1.38498i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 86033.9 | + | 149015.i | 0.0421991 | + | 0.0730910i | ||||
\(335\) | −1.38312e6 | −0.673360 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −995036. | −0.477270 | −0.238635 | − | 0.971109i | \(-0.576700\pi\) | ||||
−0.238635 | + | 0.971109i | \(0.576700\pi\) | |||||||
\(338\) | 129941. | + | 225064.i | 0.0618663 | + | 0.107156i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −103232. | + | 178803.i | −0.0484303 | + | 0.0838837i | ||||
\(341\) | 1.87252e6 | + | 3.24330e6i | 0.872049 | + | 1.51043i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 358042. | − | 2.14927e6i | 0.164323 | − | 0.986407i | ||||
\(344\) | −298741. | −0.136113 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −166560. | + | 288491.i | −0.0747965 | + | 0.129551i | ||||
\(347\) | 2.02833e6 | − | 3.51317e6i | 0.904304 | − | 1.56630i | 0.0824546 | − | 0.996595i | \(-0.473724\pi\) |
0.821849 | − | 0.569705i | \(-0.192943\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.86202e6 | 1.25779 | 0.628897 | − | 0.777488i | \(-0.283507\pi\) | ||||
0.628897 | + | 0.777488i | \(0.283507\pi\) | |||||||
\(350\) | −43589.0 | + | 791384.i | −0.0190198 | + | 0.345316i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −588821. | − | 1.01987e6i | −0.253295 | − | 0.438720i | ||||
\(353\) | 416343. | − | 721126.i | 0.177834 | − | 0.308017i | −0.763305 | − | 0.646039i | \(-0.776424\pi\) |
0.941138 | + | 0.338022i | \(0.109758\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.02190e6 | + | 3.50203e6i | 0.851507 | + | 1.47485i | ||||
\(356\) | −3.53972e6 | −1.48028 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2763.12 | −0.00113944 | ||||||||
\(359\) | −1.34875e6 | − | 2.33611e6i | −0.552327 | − | 0.956659i | −0.998106 | − | 0.0615157i | \(-0.980407\pi\) |
0.445779 | − | 0.895143i | \(-0.352927\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 361621. | − | 626346.i | 0.146045 | − | 0.252957i | ||||
\(362\) | −235110. | − | 407223.i | −0.0942976 | − | 0.163328i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −703379. | − | 459449.i | −0.278251 | − | 0.181754i | ||||
\(365\) | 3.26908e6 | 1.28438 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −727411. | + | 1.25991e6i | −0.281913 | + | 0.488287i | −0.971856 | − | 0.235576i | \(-0.924302\pi\) |
0.689943 | + | 0.723864i | \(0.257636\pi\) | |||||||
\(368\) | −93753.3 | + | 162386.i | −0.0360884 | + | 0.0625069i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 853257. | 0.324023 | ||||||||
\(371\) | 1.93033e6 | + | 1.26089e6i | 0.728110 | + | 0.475602i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.02344e6 | + | 1.77265e6i | 0.380883 | + | 0.659708i | 0.991189 | − | 0.132457i | \(-0.0422868\pi\) |
−0.610306 | + | 0.792166i | \(0.708953\pi\) | |||||||
\(374\) | 12428.1 | − | 21526.1i | 0.00459436 | − | 0.00795767i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 110000. | + | 190526.i | 0.0401258 | + | 0.0694999i | ||||
\(377\) | 892950. | 0.323574 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −416898. | −0.149084 | −0.0745421 | − | 0.997218i | \(-0.523750\pi\) | ||||
−0.0745421 | + | 0.997218i | \(0.523750\pi\) | |||||||
\(380\) | 2.16399e6 | + | 3.74814e6i | 0.768769 | + | 1.33155i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 327648. | − | 567503.i | 0.114881 | − | 0.198980i | ||||
\(383\) | −1.93813e6 | − | 3.35694e6i | −0.675127 | − | 1.16935i | −0.976432 | − | 0.215827i | \(-0.930755\pi\) |
0.301305 | − | 0.953528i | \(-0.402578\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −369694. | + | 6.71201e6i | −0.127113 | + | 2.30782i | ||||
\(386\) | 173771. | 0.0593619 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 475864. | − | 824221.i | 0.160474 | − | 0.277949i | ||||
\(389\) | 1.41901e6 | − | 2.45780e6i | 0.475458 | − | 0.823517i | −0.524147 | − | 0.851628i | \(-0.675616\pi\) |
0.999605 | + | 0.0281111i | \(0.00894921\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12280.4 | −0.00406228 | ||||||||
\(392\) | 837221. | + | 92508.0i | 0.275185 | + | 0.0304063i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 188058. | + | 325726.i | 0.0610311 | + | 0.105709i | ||||
\(395\) | −2.05734e6 | + | 3.56342e6i | −0.663458 | + | 1.14914i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.17133e6 | − | 3.76085e6i | −0.691432 | − | 1.19760i | −0.971369 | − | 0.237577i | \(-0.923647\pi\) |
0.279937 | − | 0.960018i | \(-0.409686\pi\) | |||||||
\(398\) | 496274. | 0.157041 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.45534e6 | 2.32979 | ||||||||
\(401\) | 1.70152e6 | + | 2.94712e6i | 0.528417 | + | 0.915244i | 0.999451 | + | 0.0331296i | \(0.0105474\pi\) |
−0.471034 | + | 0.882115i | \(0.656119\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −777182. | + | 1.34612e6i | −0.238375 | + | 0.412877i | ||||
\(404\) | −1.67535e6 | − | 2.90179e6i | −0.510683 | − | 0.884529i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −395441. | + | 200162.i | −0.119060 | + | 0.0602653i | ||||
\(407\) | 5.15359e6 | 1.54214 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.64716e6 | − | 4.58501e6i | 0.782477 | − | 1.35529i | −0.148018 | − | 0.988985i | \(-0.547289\pi\) |
0.930495 | − | 0.366305i | \(-0.119377\pi\) | |||||||
\(410\) | −172244. | + | 298335.i | −0.0506039 | + | 0.0876486i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.94262e6 | −1.43455 | ||||||||
\(413\) | 379935. | + | 248174.i | 0.109606 | + | 0.0715947i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.33315e6 | − | 9.23728e6i | −1.52007 | − | 2.63284i | ||||
\(416\) | 244387. | − | 423291.i | 0.0692382 | − | 0.119924i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −260522. | − | 451238.i | −0.0729297 | − | 0.126318i | ||||
\(419\) | −2.87267e6 | −0.799376 | −0.399688 | − | 0.916651i | \(-0.630881\pi\) | ||||
−0.399688 | + | 0.916651i | \(0.630881\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.08688e6 | 0.573843 | 0.286921 | − | 0.957954i | \(-0.407368\pi\) | ||||
0.286921 | + | 0.957954i | \(0.407368\pi\) | |||||||
\(422\) | −225770. | − | 391046.i | −0.0617143 | − | 0.106892i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −445660. | + | 771905.i | −0.120390 | + | 0.208521i | ||||
\(425\) | 244137. | + | 422857.i | 0.0655633 | + | 0.113559i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.22984e6 | + | 622512.i | −0.326421 | + | 0.165226i | ||||
\(428\) | −2.80252e6 | −0.739501 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −245574. | + | 425346.i | −0.0640488 | + | 0.110936i | ||||
\(431\) | −1.21432e6 | + | 2.10326e6i | −0.314876 | + | 0.545380i | −0.979411 | − | 0.201876i | \(-0.935296\pi\) |
0.664535 | + | 0.747257i | \(0.268629\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 956219. | 0.245097 | 0.122548 | − | 0.992463i | \(-0.460893\pi\) | ||||
0.122548 | + | 0.992463i | \(0.460893\pi\) | |||||||
\(434\) | 42429.8 | − | 770338.i | 0.0108130 | − | 0.196317i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.62927e6 | + | 4.55402e6i | 0.662397 | + | 1.14730i | ||||
\(437\) | −128713. | + | 222938.i | −0.0322418 | + | 0.0558444i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.32102e6 | − | 2.28808e6i | −0.327152 | − | 0.566644i | 0.654794 | − | 0.755808i | \(-0.272756\pi\) |
−0.981946 | + | 0.189164i | \(0.939422\pi\) | |||||||
\(440\) | −2.59867e6 | −0.639910 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 10316.4 | 0.00251174 | ||||||||
\(443\) | −1.71983e6 | − | 2.97883e6i | −0.416366 | − | 0.721168i | 0.579205 | − | 0.815182i | \(-0.303363\pi\) |
−0.995571 | + | 0.0940147i | \(0.970030\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.87750e6 | + | 1.01801e7i | −1.40700 | + | 2.43699i | ||||
\(446\) | −1673.78 | − | 2899.07i | −0.000398439 | − | 0.000690116i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 206679. | − | 3.75237e6i | 0.0486520 | − | 0.883306i | ||||
\(449\) | −4.39903e6 | −1.02977 | −0.514886 | − | 0.857259i | \(-0.672166\pi\) | ||||
−0.514886 | + | 0.857259i | \(0.672166\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.04034e6 | + | 1.80192e6i | −0.240842 | + | 0.417151i | ||||
\(452\) | 1.81649e6 | − | 3.14626e6i | 0.418204 | − | 0.724350i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −893501. | −0.203449 | ||||||||
\(455\) | −2.48929e6 | + | 1.26001e6i | −0.563698 | + | 0.285329i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.12555e6 | + | 1.94951e6i | 0.252101 | + | 0.436652i | 0.964104 | − | 0.265524i | \(-0.0855451\pi\) |
−0.712003 | + | 0.702176i | \(0.752212\pi\) | |||||||
\(458\) | −318158. | + | 551066.i | −0.0708727 | + | 0.122755i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 317805. | + | 550455.i | 0.0700272 | + | 0.121291i | ||||
\(461\) | −1.85307e6 | −0.406107 | −0.203053 | − | 0.979168i | \(-0.565087\pi\) | ||||
−0.203053 | + | 0.979168i | \(0.565087\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.01089e6 | −0.652744 | −0.326372 | − | 0.945241i | \(-0.605826\pi\) | ||||
−0.326372 | + | 0.945241i | \(0.605826\pi\) | |||||||
\(464\) | 2.08452e6 | + | 3.61050e6i | 0.449481 | + | 0.778524i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 462333. | − | 800785.i | 0.0986258 | − | 0.170825i | ||||
\(467\) | −533627. | − | 924270.i | −0.113226 | − | 0.196113i | 0.803843 | − | 0.594841i | \(-0.202785\pi\) |
−0.917069 | + | 0.398728i | \(0.869452\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.44082e6 | + | 941145.i | 0.302466 | + | 0.197572i | ||||
\(470\) | 361694. | 0.0755260 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −87716.4 | + | 151929.i | −0.0181228 | + | 0.0313896i | ||||
\(473\) | −1.48324e6 | + | 2.56905e6i | −0.304831 | + | 0.527983i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.02354e7 | 2.08147 | ||||||||
\(476\) | 229205. | − | 116018.i | 0.0463668 | − | 0.0234697i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −674375. | − | 1.16805e6i | −0.134999 | − | 0.233826i | ||||
\(479\) | −2.84394e6 | + | 4.92585e6i | −0.566346 | + | 0.980939i | 0.430577 | + | 0.902554i | \(0.358310\pi\) |
−0.996923 | + | 0.0783858i | \(0.975023\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.06949e6 | + | 1.85240e6i | 0.210772 | + | 0.365068i | ||||
\(482\) | 752211. | 0.147476 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.71749e6 | −0.527295 | ||||||||
\(485\) | −1.58029e6 | − | 2.73715e6i | −0.305059 | − | 0.528377i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.42239e6 | − | 5.92775e6i | 0.653893 | − | 1.13258i | −0.328277 | − | 0.944582i | \(-0.606468\pi\) |
0.982170 | − | 0.187995i | \(-0.0601987\pi\) | |||||||
\(488\) | −266433. | − | 461476.i | −0.0506453 | − | 0.0877202i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 819933. | − | 1.11599e6i | 0.154272 | − | 0.209976i | ||||
\(491\) | −5.60132e6 | −1.04854 | −0.524272 | − | 0.851551i | \(-0.675662\pi\) | ||||
−0.524272 | + | 0.851551i | \(0.675662\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −136522. | + | 236462.i | −0.0252979 | + | 0.0438172i | ||||
\(494\) | 108129. | − | 187284.i | 0.0199353 | − | 0.0345290i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.25708e6 | −1.32452 | ||||||||
\(497\) | 276715. | − | 5.02392e6i | 0.0502507 | − | 0.912330i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.16764e6 | + | 2.02242e6i | 0.209923 | + | 0.363596i | 0.951690 | − | 0.307061i | \(-0.0993455\pi\) |
−0.741767 | + | 0.670657i | \(0.766012\pi\) | |||||||
\(500\) | 7.52830e6 | − | 1.30394e7i | 1.34670 | − | 2.33256i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 452728. | + | 784147.i | 0.0801822 | + | 0.138880i | ||||
\(503\) | 1.08278e7 | 1.90819 | 0.954093 | − | 0.299510i | \(-0.0968233\pi\) | ||||
0.954093 | + | 0.299510i | \(0.0968233\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.11273e7 | −1.94161 | ||||||||
\(506\) | −38260.6 | − | 66269.3i | −0.00664317 | − | 0.0115063i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.16120e6 | − | 5.47536e6i | 0.543492 | − | 0.941355i | ||||
\(509\) | 1.58924e6 | + | 2.75264e6i | 0.271890 | + | 0.470928i | 0.969346 | − | 0.245700i | \(-0.0790178\pi\) |
−0.697455 | + | 0.716628i | \(0.745684\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.40546e6 | − | 2.22445e6i | −0.576930 | − | 0.376852i | ||||
\(512\) | 3.82859e6 | 0.645452 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 468053. | − | 810692.i | 0.0781425 | − | 0.135347i | ||||
\(515\) | −8.20695e6 | + | 1.42149e7i | −1.36353 | + | 2.36170i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.18460e6 | 0.359455 | ||||||||
\(518\) | −888852. | − | 580600.i | −0.145548 | − | 0.0950720i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −539282. | − | 934064.i | −0.0874596 | − | 0.151485i | ||||
\(521\) | −3.17918e6 | + | 5.50651e6i | −0.513123 | + | 0.888755i | 0.486761 | + | 0.873535i | \(0.338178\pi\) |
−0.999884 | + | 0.0152197i | \(0.995155\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.61094e6 | + | 6.25433e6i | 0.577252 | + | 0.999830i | 0.995793 | + | 0.0916321i | \(0.0292084\pi\) |
−0.418541 | + | 0.908198i | \(0.637458\pi\) | |||||||
\(524\) | 1.20697e6 | 0.192029 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −354531. | −0.0558714 | ||||||||
\(527\) | −237644. | − | 411612.i | −0.0372735 | − | 0.0645597i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.19927e6 | − | 5.54130e6i | 0.497063 | − | 0.860939i | ||||
\(530\) | 732691. | + | 1.26906e6i | 0.113300 | + | 0.196242i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 296162. | − | 5.37699e6i | 0.0453680 | − | 0.823683i | ||||
\(533\) | −863574. | −0.131668 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.65343e6 | + | 8.05997e6i | −0.702892 | + | 1.21744i | ||||
\(536\) | −332645. | + | 576158.i | −0.0500114 | + | 0.0866223i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −591106. | −0.0880461 | ||||||||
\(539\) | 4.95232e6 | − | 6.74046e6i | 0.734237 | − | 0.999350i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.71583e6 | + | 8.16805e6i | 0.692731 | + | 1.19985i | 0.970940 | + | 0.239325i | \(0.0769260\pi\) |
−0.278209 | + | 0.960521i | \(0.589741\pi\) | |||||||
\(542\) | 91985.4 | − | 159323.i | 0.0134500 | − | 0.0232960i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 74728.0 | + | 129433.i | 0.0108264 | + | 0.0187520i | ||||
\(545\) | 1.74630e7 | 2.51842 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.91568e6 | 1.41695 | 0.708474 | − | 0.705737i | \(-0.249384\pi\) | ||||
0.708474 | + | 0.705737i | \(0.249384\pi\) | |||||||
\(548\) | 3.79197e6 | + | 6.56788e6i | 0.539403 | + | 0.934274i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.52126e6 | + | 2.63489e6i | −0.214435 | + | 0.371412i | ||||
\(551\) | 2.86182e6 | + | 4.95682e6i | 0.401572 | + | 0.695543i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.56790e6 | − | 2.31216e6i | 0.635191 | − | 0.321517i | ||||
\(554\) | −1.92106e6 | −0.265929 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −833188. | + | 1.44312e6i | −0.114303 | + | 0.197978i | ||||
\(557\) | 4.82306e6 | − | 8.35379e6i | 0.658696 | − | 1.14089i | −0.322258 | − | 0.946652i | \(-0.604442\pi\) |
0.980953 | − | 0.194243i | \(-0.0622249\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.23123e6 | −0.166651 | ||||||||
\(560\) | −1.09057e7 | − | 7.12362e6i | −1.46955 | − | 0.959910i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 995245. | + | 1.72382e6i | 0.132920 | + | 0.230224i | ||||
\(563\) | 1.54752e6 | − | 2.68038e6i | 0.205762 | − | 0.356390i | −0.744613 | − | 0.667496i | \(-0.767366\pi\) |
0.950375 | + | 0.311106i | \(0.100699\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.03238e6 | − | 1.04484e7i | −0.795000 | − | 1.37698i | ||||
\(566\) | 206396. | 0.0270807 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.94509e6 | 0.252970 | ||||||||
\(569\) | −6.15927e6 | − | 1.06682e7i | −0.797533 | − | 1.38137i | −0.921218 | − | 0.389046i | \(-0.872805\pi\) |
0.123685 | − | 0.992322i | \(-0.460529\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.61755e6 | − | 2.80168e6i | 0.207619 | − | 0.359607i | −0.743345 | − | 0.668908i | \(-0.766762\pi\) |
0.950964 | + | 0.309302i | \(0.100095\pi\) | |||||||
\(572\) | −1.61253e6 | − | 2.79299e6i | −0.206072 | − | 0.356927i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 382432. | − | 193577.i | 0.0484479 | − | 0.0245231i | ||||
\(575\) | 1.50318e6 | 0.189601 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.52525e6 | − | 7.83796e6i | 0.565852 | − | 0.980084i | −0.431118 | − | 0.902296i | \(-0.641881\pi\) |
0.996970 | − | 0.0777887i | \(-0.0247859\pi\) | |||||||
\(578\) | 559838. | − | 969667.i | 0.0697016 | − | 0.120727i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.41322e7 | 1.74438 | ||||||||
\(581\) | −729890. | + | 1.32516e7i | −0.0897051 | + | 1.62865i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.42538e6 | + | 7.66499e6i | 0.539237 | + | 0.933986i | ||||
\(584\) | 786226. | − | 1.36178e6i | 0.0953927 | − | 0.165225i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 25705.8 | + | 44523.8i | 0.00309234 | + | 0.00535609i | ||||
\(587\) | 2.13170e6 | 0.255347 | 0.127673 | − | 0.991816i | \(-0.459249\pi\) | ||||
0.127673 | + | 0.991816i | \(0.459249\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.96318e6 | −1.18334 | ||||||||
\(590\) | 144211. | + | 249781.i | 0.0170557 | + | 0.0295413i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.99326e6 | + | 8.64858e6i | −0.585572 | + | 1.01424i | ||||
\(593\) | −3.63467e6 | − | 6.29543e6i | −0.424451 | − | 0.735171i | 0.571918 | − | 0.820311i | \(-0.306200\pi\) |
−0.996369 | + | 0.0851397i | \(0.972866\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 46918.4 | − | 851830.i | 0.00543313 | − | 0.0986417i | ||||
\(596\) | 4.04927e6 | 0.466941 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 15879.9 | − | 27504.8i | 0.00181591 | − | 0.00314525i | ||||
\(599\) | −1.10282e6 | + | 1.91015e6i | −0.125585 | + | 0.217520i | −0.921962 | − | 0.387281i | \(-0.873414\pi\) |
0.796376 | + | 0.604802i | \(0.206748\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.00121e7 | −1.13067 | −0.565336 | − | 0.824860i | \(-0.691254\pi\) | ||||
−0.565336 | + | 0.824860i | \(0.691254\pi\) | |||||||
\(602\) | 545246. | − | 275990.i | 0.0613199 | − | 0.0310385i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.40340e6 | + | 4.16280e6i | 0.268061 | + | 0.464295i | ||||
\(605\) | −4.51224e6 | + | 7.81542e6i | −0.501191 | + | 0.868088i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.16069e6 | − | 5.47448e6i | −0.348185 | − | 0.603075i | 0.637742 | − | 0.770250i | \(-0.279869\pi\) |
−0.985927 | + | 0.167175i | \(0.946535\pi\) | |||||||
\(608\) | 3.13295e6 | 0.343712 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −876065. | −0.0953261 | ||||||||
\(611\) | 453353. | + | 785231.i | 0.0491285 | + | 0.0850931i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.15392e6 | + | 1.23910e7i | −0.768941 | + | 1.33185i | 0.169196 | + | 0.985582i | \(0.445883\pi\) |
−0.938138 | + | 0.346263i | \(0.887451\pi\) | |||||||
\(614\) | 931565. | + | 1.61352e6i | 0.0997223 | + | 0.172724i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.70707e6 | + | 1.76827e6i | 0.287441 | + | 0.187757i | ||||
\(617\) | −1.73991e7 | −1.83999 | −0.919993 | − | 0.391936i | \(-0.871806\pi\) | ||||
−0.919993 | + | 0.391936i | \(0.871806\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.13368e6 | + | 7.15975e6i | −0.433621 | + | 0.751054i | −0.997182 | − | 0.0750208i | \(-0.976098\pi\) |
0.563561 | + | 0.826074i | \(0.309431\pi\) | |||||||
\(620\) | −1.23000e7 | + | 2.13043e7i | −1.28507 | + | 2.22581i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.67497e6 | 0.173592 | ||||||||
\(623\) | 1.30498e7 | − | 6.60547e6i | 1.34705 | − | 0.681841i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.29211e7 | − | 2.23800e7i | −1.32312 | − | 2.29172i | ||||
\(626\) | 74143.4 | − | 128420.i | 0.00756200 | − | 0.0130978i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.37173e6 | − | 4.10796e6i | −0.239975 | − | 0.415649i | ||||
\(629\) | −654048. | −0.0659148 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.83238e6 | 0.283190 | 0.141595 | − | 0.989925i | \(-0.454777\pi\) | ||||
0.141595 | + | 0.989925i | \(0.454777\pi\) | |||||||
\(632\) | 989596. | + | 1.71403e6i | 0.0985520 | + | 0.170697i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −397542. | + | 688563.i | −0.0392790 | + | 0.0680331i | ||||
\(635\) | −1.04980e7 | − | 1.81831e7i | −1.03317 | − | 1.78951i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.45051e6 | + | 381261.i | 0.336926 | + | 0.0372284i | ||||
\(638\) | −1.70138e6 | −0.165481 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 5.13912e6 | − | 8.90122e6i | 0.495951 | − | 0.859012i | ||||
\(641\) | −1.78588e6 | + | 3.09324e6i | −0.171675 | + | 0.297350i | −0.939006 | − | 0.343902i | \(-0.888251\pi\) |
0.767330 | + | 0.641252i | \(0.221585\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.96911e6 | −0.569354 | −0.284677 | − | 0.958624i | \(-0.591886\pi\) | ||||
−0.284677 | + | 0.958624i | \(0.591886\pi\) | |||||||
\(644\) | 43494.6 | − | 789670.i | 0.00413258 | − | 0.0750293i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 33063.2 | + | 57267.2i | 0.00311719 | + | 0.00539914i | ||||
\(647\) | −841379. | + | 1.45731e6i | −0.0790189 | + | 0.136865i | −0.902827 | − | 0.430004i | \(-0.858512\pi\) |
0.823808 | + | 0.566869i | \(0.191845\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 871021. | + | 1.50865e6i | 0.0811739 | + | 0.140597i | ||||
\(650\) | −1.26278e6 | −0.117232 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.03275e6 | 0.0951427 | ||||||||
\(653\) | 8.51526e6 | + | 1.47489e7i | 0.781475 | + | 1.35355i | 0.931082 | + | 0.364809i | \(0.118866\pi\) |
−0.149608 | + | 0.988745i | \(0.547801\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.00411e6 | − | 3.47121e6i | 0.182523 | − | 0.316139i | ||||
\(656\) | −2.01594e6 | − | 3.49172e6i | −0.182902 | − | 0.316796i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −376783. | − | 246115.i | −0.0339255 | − | 0.0221602i | ||||
\(659\) | 1.99303e7 | 1.78772 | 0.893862 | − | 0.448342i | \(-0.147985\pi\) | ||||
0.893862 | + | 0.448342i | \(0.147985\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.77867e6 | + | 8.27691e6i | −0.425406 | + | 0.736825i | −0.996458 | − | 0.0840888i | \(-0.973202\pi\) |
0.571052 | + | 0.820914i | \(0.306535\pi\) | |||||||
\(662\) | −664213. | + | 1.15045e6i | −0.0589064 | + | 0.102029i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.13056e6 | −0.451591 | ||||||||
\(665\) | −1.49723e7 | − | 9.77995e6i | −1.31291 | − | 0.857595i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 420290. | + | 727963.i | 0.0365792 | + | 0.0633570i | ||||
\(668\) | −3.41333e6 | + | 5.91207e6i | −0.295963 | + | 0.512623i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 546889. | + | 947239.i | 0.0470665 | + | 0.0815216i | ||||
\(671\) | −5.29135e6 | −0.453691 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.80397e7 | 1.53530 | 0.767648 | − | 0.640872i | \(-0.221427\pi\) | ||||
0.767648 | + | 0.640872i | \(0.221427\pi\) | |||||||
\(674\) | 393440. | + | 681457.i | 0.0333602 | + | 0.0577815i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.15531e6 | + | 8.92927e6i | −0.433899 | + | 0.751535i | ||||
\(677\) | −7.23704e6 | − | 1.25349e7i | −0.606861 | − | 1.05111i | −0.991754 | − | 0.128153i | \(-0.959095\pi\) |
0.384894 | − | 0.922961i | \(-0.374238\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −216278. | + | 3.92665e6i | −0.0180027 | + | 0.326849i | ||||
\(680\) | 329800. | 0.0273513 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.48080e6 | − | 2.56482e6i | 0.121909 | − | 0.211152i | ||||
\(683\) | 1.34392e6 | − | 2.32774e6i | 0.110236 | − | 0.190934i | −0.805629 | − | 0.592420i | \(-0.798173\pi\) |
0.915865 | + | 0.401486i | \(0.131506\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.51854e7 | 2.05080 | ||||||||
\(686\) | −1.61351e6 | + | 604620.i | −0.130907 | + | 0.0490537i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.87420e6 | − | 4.97826e6i | −0.231497 | − | 0.400965i | ||||
\(689\) | −1.83674e6 | + | 3.18132e6i | −0.147400 | + | 0.255305i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.33814e6 | − | 4.04977e6i | −0.186284 | − | 0.322653i | 0.757725 | − | 0.652574i | \(-0.226311\pi\) |
−0.944008 | + | 0.329922i | \(0.892978\pi\) | |||||||
\(692\) | −1.32163e7 | −1.04917 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.20802e6 | −0.252836 | ||||||||
\(695\) | 2.76693e6 | + | 4.79246e6i | 0.217288 | + | 0.376354i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 132030. | − | 228683.i | 0.0102942 | − | 0.0178301i | ||||
\(698\) | −1.13165e6 | − | 1.96008e6i | −0.0879172 | − | 0.152277i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.80558e7 | + | 1.42011e7i | −2.16410 | + | 1.09541i | ||||
\(701\) | −6.34801e6 | −0.487913 | −0.243957 | − | 0.969786i | \(-0.578445\pi\) | ||||
−0.243957 | + | 0.969786i | \(0.578445\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.85520e6 | + | 1.18736e7i | −0.523157 | + | 0.906135i | ||||
\(704\) | 7.21309e6 | − | 1.24934e7i | 0.548516 | − | 0.950058i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −658492. | −0.0497208 | ||||||||
\(707\) | 1.15915e7 | + | 7.57158e6i | 0.872150 | + | 0.569690i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.20526e6 | + | 5.55168e6i | 0.239468 | + | 0.414771i | 0.960562 | − | 0.278067i | \(-0.0896936\pi\) |
−0.721094 | + | 0.692838i | \(0.756360\pi\) | |||||||
\(710\) | 1.59893e6 | − | 2.76942e6i | 0.119037 | − | 0.206178i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.82712e6 | + | 4.89672e6i | 0.208999 | + | 0.361997i | ||||
\(713\) | −1.46320e6 | −0.107790 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.07101e7 | −0.783481 | ||||||||
\(716\) | −54812.4 | − | 94937.9i | −0.00399573 | − | 0.00692081i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.06660e6 | + | 1.84741e6i | −0.0772131 | + | 0.133737i | ||||
\(719\) | 3.67253e6 | + | 6.36100e6i | 0.264937 | + | 0.458885i | 0.967547 | − | 0.252691i | \(-0.0813155\pi\) |
−0.702610 | + | 0.711575i | \(0.747982\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.82218e7 | − | 9.22343e6i | 1.30543 | − | 0.660776i | ||||
\(722\) | −571944. | −0.0408329 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.32784e6 | − | 1.61563e7i | 0.661355 | − | 1.14550i | ||||
\(725\) | 1.67109e7 | − | 2.89441e7i | 1.18074 | − | 2.04510i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.57839e7 | 1.10759 | 0.553793 | − | 0.832655i | \(-0.313180\pi\) | ||||
0.553793 | + | 0.832655i | \(0.313180\pi\) | |||||||
\(728\) | −73805.7 | + | 1.33999e6i | −0.00516133 | + | 0.0937069i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.29260e6 | − | 2.23885e6i | −0.0897755 | − | 0.155496i | ||||
\(731\) | 188240. | − | 326041.i | 0.0130292 | − | 0.0225673i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.76835e6 | − | 1.17231e7i | −0.465289 | − | 0.805905i | 0.533925 | − | 0.845532i | \(-0.320716\pi\) |
−0.999215 | + | 0.0396269i | \(0.987383\pi\) | |||||||
\(734\) | 1.15048e6 | 0.0788205 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 460109. | 0.0313088 | ||||||||
\(737\) | 3.30315e6 | + | 5.72123e6i | 0.224006 | + | 0.387990i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.66851e6 | − | 6.35405e6i | 0.247103 | − | 0.427996i | −0.715617 | − | 0.698492i | \(-0.753855\pi\) |
0.962721 | + | 0.270497i | \(0.0871879\pi\) | |||||||
\(740\) | 1.69262e7 | + | 2.93170e7i | 1.13626 | + | 1.96807i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 100276. | − | 1.82056e6i | 0.00668629 | − | 0.121394i | ||||
\(743\) | −1.20844e7 | −0.803068 | −0.401534 | − | 0.915844i | \(-0.631523\pi\) | ||||
−0.401534 | + | 0.915844i | \(0.631523\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.72360e6 | − | 1.16456e7i | 0.443824 | − | 0.768726i | ||||
\(746\) | 809343. | − | 1.40182e6i | 0.0532459 | − | 0.0922245i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 986151. | 0.0644450 | ||||||||
\(749\) | 1.03320e7 | − | 5.22978e6i | 0.672944 | − | 0.340627i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.39088e6 | − | 7.60523e6i | −0.284087 | − | 0.492054i | 0.688300 | − | 0.725426i | \(-0.258357\pi\) |
−0.972387 | + | 0.233372i | \(0.925024\pi\) | |||||||
\(752\) | −2.11663e6 | + | 3.66612e6i | −0.136490 | + | 0.236408i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −353075. | − | 611543.i | −0.0226172 | − | 0.0391741i | ||||
\(755\) | 1.59628e7 | 1.01916 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 465874. | 0.0295480 | 0.0147740 | − | 0.999891i | \(-0.495297\pi\) | ||||
0.0147740 | + | 0.999891i | \(0.495297\pi\) | |||||||
\(758\) | 164842. | + | 285516.i | 0.0104207 | + | 0.0180491i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.45670e6 | − | 5.98717e6i | 0.217084 | − | 0.376000i | ||||
\(761\) | 7.49891e6 | + | 1.29885e7i | 0.469393 | + | 0.813013i | 0.999388 | − | 0.0349882i | \(-0.0111394\pi\) |
−0.529995 | + | 0.848001i | \(0.677806\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.81915e7 | − | 1.18827e7i | −1.13125 | − | 0.738932i | ||||
\(764\) | 2.59984e7 | 1.61144 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.53268e6 | + | 2.65468e6i | −0.0943800 | + | 0.163471i | ||||
\(767\) | −361513. | + | 626159.i | −0.0221889 | + | 0.0384323i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.85606e7 | −1.13181 | −0.565907 | − | 0.824469i | \(-0.691474\pi\) | ||||
−0.565907 | + | 0.824469i | \(0.691474\pi\) | |||||||
\(770\) | 4.74295e6 | − | 2.40076e6i | 0.288285 | − | 0.145922i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.44711e6 | + | 5.97057e6i | 0.208167 | + | 0.360556i | ||||
\(773\) | 6.13802e6 | − | 1.06314e7i | 0.369470 | − | 0.639941i | −0.620013 | − | 0.784592i | \(-0.712872\pi\) |
0.989483 | + | 0.144651i | \(0.0462058\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.90888e7 | + | 5.03832e7i | 1.73969 | + | 3.01323i | ||||
\(776\) | −1.52027e6 | −0.0906286 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.24432e6 | −0.132934 | ||||||||
\(779\) | −2.76767e6 | − | 4.79375e6i | −0.163407 | − | 0.283029i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.65736e6 | − | 1.67270e7i | 0.566540 | − | 0.981276i | ||||
\(782\) | 4855.70 | + | 8410.31i | 0.000283945 | + | 0.000491808i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.51337e6 | + | 1.48416e7i | 0.378456 | + | 0.862363i | ||||
\(785\) | −1.57525e7 | −0.912380 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.63496e6 | + | 4.56388e6i | −0.151648 | + | 0.262662i | −0.931833 | − | 0.362886i | \(-0.881791\pi\) |
0.780185 | + | 0.625548i | \(0.215125\pi\) | |||||||
\(788\) | −7.46107e6 | + | 1.29230e7i | −0.428041 | + | 0.741389i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.25391e6 | 0.185497 | ||||||||
\(791\) | −825586. | + | 1.49890e7i | −0.0469160 | + | 0.851788i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.09807e6 | − | 1.90192e6i | −0.0620082 | − | 0.107401i | ||||
\(794\) | −1.71710e6 | + | 2.97410e6i | −0.0966593 | + | 0.167419i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.84466e6 | + | 1.70514e7i | 0.550704 | + | 0.953847i | ||||
\(797\) | −1.11889e7 | −0.623940 | −0.311970 | − | 0.950092i | \(-0.600989\pi\) | ||||
−0.311970 | + | 0.950092i | \(0.600989\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −277250. | −0.0153640 | ||||||||
\(800\) | −9.14706e6 | − | 1.58432e7i | −0.505308 | − | 0.875220i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.34557e6 | − | 2.33060e6i | 0.0738705 | − | 0.127947i | ||||
\(803\) | −7.80719e6 | − | 1.35225e7i | −0.427274 | − | 0.740059i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.19885e6 | − | 1.43629e6i | −0.119593 | − | 0.0781184i | ||||
\(806\) | 1.22920e6 | 0.0666476 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.67616e6 | + | 4.63524e6i | −0.144206 | + | 0.249772i | ||||
\(809\) | 3.52526e6 | − | 6.10592e6i | 0.189374 | − | 0.328005i | −0.755668 | − | 0.654955i | \(-0.772688\pi\) |
0.945042 | + | 0.326950i | \(0.106021\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.54873e7 | −1.36073 | −0.680364 | − | 0.732875i | \(-0.738178\pi\) | ||||
−0.680364 | + | 0.732875i | \(0.738178\pi\) | |||||||
\(812\) | −1.47218e7 | − | 9.61630e6i | −0.783557 | − | 0.511821i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.03774e6 | − | 3.52947e6i | −0.107792 | − | 0.186702i | ||||
\(815\) | 1.71482e6 | − | 2.97016e6i | 0.0904326 | − | 0.156634i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.94596e6 | − | 6.83460e6i | −0.206822 | − | 0.358227i | ||||
\(818\) | −4.18677e6 | −0.218774 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.36673e7 | −0.709820 | ||||||||
\(821\) | −1.17439e7 | − | 2.03411e7i | −0.608073 | − | 1.05321i | −0.991558 | − | 0.129666i | \(-0.958610\pi\) |
0.383485 | − | 0.923547i | \(-0.374724\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.04517e6 | − | 1.04705e7i | 0.311107 | − | 0.538852i | −0.667496 | − | 0.744614i | \(-0.732634\pi\) |
0.978602 | + | 0.205761i | \(0.0659671\pi\) | |||||||
\(824\) | 3.94760e6 | + | 6.83745e6i | 0.202542 | + | 0.350813i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 19736.6 | − | 358330.i | 0.00100652 | − | 0.0182740i | ||||
\(827\) | −3.33335e6 | −0.169480 | −0.0847398 | − | 0.996403i | \(-0.527006\pi\) | ||||
−0.0847398 | + | 0.996403i | \(0.527006\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.85267e6 | − | 6.67302e6i | 0.194704 | − | 0.337238i | −0.752099 | − | 0.659050i | \(-0.770959\pi\) |
0.946804 | + | 0.321812i | \(0.104292\pi\) | |||||||
\(830\) | −4.21748e6 | + | 7.30489e6i | −0.212499 | + | 0.368060i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.98752e6 | 0.299874 | ||||||||
\(833\) | −628505. | + | 855440.i | −0.0313831 | + | 0.0427147i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.13353e7 | + | 1.96333e7i | 0.562622 | + | 0.974490i | ||||
\(836\) | 1.03360e7 | − | 1.79025e7i | 0.511492 | − | 0.885929i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.13586e6 | + | 1.96737e6i | 0.0558747 | + | 0.0967779i | ||||
\(839\) | −2.40843e7 | −1.18121 | −0.590607 | − | 0.806959i | \(-0.701112\pi\) | ||||
−0.590607 | + | 0.806959i | \(0.701112\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.82163e6 | −0.0888116 | ||||||||
\(842\) | −825159. | − | 1.42922e6i | −0.0401104 | − | 0.0694733i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.95728e6 | − | 1.55145e7i | 0.432832 | − | 0.749688i | ||||
\(845\) | 1.71202e7 | + | 2.96531e7i | 0.824837 | + | 1.42866i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00185e7 | − | 5.07110e6i | 0.479837 | − | 0.242881i | ||||
\(848\) | −1.71509e7 | −0.819023 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 193064. | − | 334398.i | 0.00916548 | − | 0.0158751i | ||||
\(851\) | −1.00676e6 | + | 1.74376e6i | −0.0476544 | + | 0.0825398i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.82938e7 | −1.33143 | −0.665716 | − | 0.746206i | \(-0.731874\pi\) | ||||
−0.665716 | + | 0.746206i | \(0.731874\pi\) | |||||||
\(854\) | 912612. | + | 596120.i | 0.0428195 | + | 0.0279698i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.23833e6 | + | 3.87690e6i | 0.104410 | + | 0.180843i | ||||
\(857\) | 1.08088e7 | − | 1.87214e7i | 0.502719 | − | 0.870734i | −0.497276 | − | 0.867592i | \(-0.665666\pi\) |
0.999995 | − | 0.00314220i | \(-0.00100019\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.62691e7 | − | 2.81789e7i | −0.752282 | − | 1.30299i | −0.946714 | − | 0.322075i | \(-0.895620\pi\) |
0.194432 | − | 0.980916i | \(-0.437714\pi\) | |||||||
\(860\) | −1.94859e7 | −0.898411 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.92058e6 | 0.0880366 | ||||||||
\(863\) | 4.03192e6 | + | 6.98349e6i | 0.184283 | + | 0.319187i | 0.943335 | − | 0.331843i | \(-0.107670\pi\) |
−0.759052 | + | 0.651030i | \(0.774337\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.19450e7 | + | 3.80098e7i | −0.997229 | + | 1.72725i | ||||
\(866\) | −378091. | − | 654874.i | −0.0171318 | − | 0.0296731i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.73097e7 | − | 1.38235e7i | 1.23032 | − | 0.622756i | ||||
\(869\) | 1.96533e7 | 0.882849 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.37096e6 | + | 2.37457e6i | −0.0612321 | + | 0.106057i | ||||
\(872\) | 4.19992e6 | − | 7.27447e6i | 0.187046 | − | 0.323974i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 203574. | 0.00901454 | ||||||||
\(875\) | −3.42157e6 | + | 6.21206e7i | −0.151080 | + | 2.74294i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.51559e6 | − | 1.47494e7i | −0.373866 | − | 0.647555i | 0.616291 | − | 0.787519i | \(-0.288635\pi\) |
−0.990157 | + | 0.139964i | \(0.955301\pi\) | |||||||
\(878\) | −1.04467e6 | + | 1.80943e6i | −0.0457345 | + | 0.0792145i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.50019e7 | − | 4.33045e7i | −1.08834 | − | 1.88507i | ||||
\(881\) | −1.24740e7 | −0.541459 | −0.270729 | − | 0.962655i | \(-0.587265\pi\) | ||||
−0.270729 | + | 0.962655i | \(0.587265\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.28955e6 | 0.314629 | 0.157315 | − | 0.987549i | \(-0.449716\pi\) | ||||
0.157315 | + | 0.987549i | \(0.449716\pi\) | |||||||
\(884\) | 204649. | + | 354462.i | 0.00880802 | + | 0.0152559i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.36005e6 | + | 2.35567e6i | −0.0582063 | + | 0.100816i | ||||
\(887\) | 9.38377e6 | + | 1.62532e7i | 0.400469 | + | 0.693632i | 0.993782 | − | 0.111339i | \(-0.0355140\pi\) |
−0.593314 | + | 0.804971i | \(0.702181\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.43675e6 | + | 2.60850e7i | −0.0609714 | + | 1.10697i | ||||
\(890\) | 9.29592e6 | 0.393385 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 66406.1 | − | 115019.i | 0.00279445 | − | 0.00484012i | ||||
\(893\) | −2.90591e6 | + | 5.03318e6i | −0.121942 | + | 0.211210i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −364052. | −0.0151917 | ||||||||
\(896\) | −1.14104e7 | + | 5.77563e6i | −0.474820 | + | 0.240342i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.73939e6 | + | 3.01271e6i | 0.0719790 | + | 0.124671i | ||||
\(899\) | −1.62665e7 | + | 2.81744e7i | −0.671266 | + | 1.16267i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −561631. | − | 972773.i | −0.0230483 | − | 0.0399208i | ||||
\(902\) | 1.64541e6 | 0.0673375 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.80323e6 | −0.236183 | ||||||||
\(905\) | −3.09767e7 | − | 5.36533e7i | −1.25723 | − | 2.17758i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −631833. | + | 1.09437e6i | −0.0255026 | + | 0.0441718i | −0.878495 | − | 0.477751i | \(-0.841452\pi\) |
0.852992 | + | 0.521923i | \(0.174785\pi\) | |||||||
\(908\) | −1.77245e7 | − | 3.06998e7i | −0.713444 | − | 1.23572i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.84720e6 | + | 1.20659e6i | 0.0739452 | + | 0.0483011i | ||||
\(911\) | 2.47718e7 | 0.988921 | 0.494461 | − | 0.869200i | \(-0.335366\pi\) | ||||
0.494461 | + | 0.869200i | \(0.335366\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.54732e7 | + | 4.41208e7i | −1.01136 | + | 1.75173i | ||||
\(914\) | 890092. | − | 1.54168e6i | 0.0352427 | − | 0.0610422i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.52454e7 | −0.994130 | ||||||||
\(917\) | −4.44970e6 | + | 2.25233e6i | −0.174746 | + | 0.0884520i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.68338e6 | + | 8.11185e6i | 0.182924 | + | 0.316834i | 0.942875 | − | 0.333147i | \(-0.108110\pi\) |
−0.759951 | + | 0.649980i | \(0.774777\pi\) | |||||||
\(920\) | 507654. | − | 879282.i | 0.0197742 | − | 0.0342498i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 732710. | + | 1.26909e6i | 0.0283860 | + | 0.0491661i | ||||
\(923\) | 8.01648e6 | 0.309727 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.00586e7 | 3.07648 | ||||||||
\(926\) | 1.19051e6 | + | 2.06203e6i | 0.0456255 | + | 0.0790256i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.11505e6 | − | 8.85953e6i | 0.194975 | − | 0.337707i | ||||
\(929\) | −3.43675e6 | − | 5.95263e6i | −0.130650 | − | 0.226292i | 0.793277 | − | 0.608860i | \(-0.208373\pi\) |
−0.923927 | + | 0.382568i | \(0.875040\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.94215e6 | + | 2.03759e7i | 0.338118 | + | 0.770446i | ||||
\(932\) | 3.66855e7 | 1.38342 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −421995. | + | 730917.i | −0.0158285 | + | 0.0274158i | ||||
\(935\) | 1.63745e6 | − | 2.83615e6i | 0.0612546 | − | 0.106096i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.26197e7 | −1.58585 | −0.792923 | − | 0.609322i | \(-0.791442\pi\) | ||||
−0.792923 | + | 0.609322i | \(0.791442\pi\) | |||||||
\(938\) | 74846.7 | − | 1.35889e6i | 0.00277758 | − | 0.0504285i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 7.17497e6 | + | 1.24274e7i | 0.264850 | + | 0.458734i | ||||
\(941\) | 2.25113e6 | − | 3.89907e6i | 0.0828755 | − | 0.143545i | −0.821608 | − | 0.570052i | \(-0.806923\pi\) |
0.904484 | + | 0.426508i | \(0.140256\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −406463. | − | 704015.i | −0.0148848 | − | 0.0257812i | ||||
\(944\) | −3.37569e6 | −0.123291 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.34591e6 | 0.0852282 | ||||||||
\(947\) | 1.68863e7 | + | 2.92479e7i | 0.611870 | + | 1.05979i | 0.990925 | + | 0.134415i | \(0.0429156\pi\) |
−0.379055 | + | 0.925374i | \(0.623751\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.24034e6 | − | 5.61243e6i | 0.116795 | − | 0.202295i | ||||
\(950\) | −4.04709e6 | − | 7.00977e6i | −0.145490 | − | 0.251997i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −343558. | − | 224413.i | −0.0122859 | − | 0.00802519i | ||||
\(953\) | −4.81813e7 | −1.71849 | −0.859244 | − | 0.511566i | \(-0.829066\pi\) | ||||
−0.859244 | + | 0.511566i | \(0.829066\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.31689e7 | − | 7.47708e7i | 1.53166 | − | 2.65292i | ||||
\(956\) | 2.67554e7 | − | 4.63416e7i | 0.946817 | − | 1.63993i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.49800e6 | 0.158346 | ||||||||
\(959\) | −2.62361e7 | − | 1.71375e7i | −0.921198 | − | 0.601728i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.40006e7 | − | 2.42498e7i | −0.489033 | − | 0.847030i | ||||
\(962\) | 845755. | − | 1.46489e6i | 0.0294650 | − | 0.0510349i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.49217e7 | + | 2.58452e7i | 0.517161 | + | 0.895750i | ||||
\(965\) | 2.28950e7 | 0.791446 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.54640e7 | −1.21961 | −0.609805 | − | 0.792551i | \(-0.708752\pi\) | ||||
−0.609805 | + | 0.792551i | \(0.708752\pi\) | |||||||
\(968\) | 2.17042e6 | + | 3.75927e6i | 0.0744483 | + | 0.128948i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.24970e6 | + | 2.16455e6i | −0.0426459 | + | 0.0738649i | ||||
\(971\) | −3.92148e6 | − | 6.79221e6i | −0.133476 | − | 0.231187i | 0.791538 | − | 0.611119i | \(-0.209280\pi\) |
−0.925014 | + | 0.379933i | \(0.875947\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 378679. | − | 6.87514e6i | 0.0128230 | − | 0.232809i | ||||
\(974\) | −5.41288e6 | −0.182823 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.12674e6 | − | 8.87977e6i | 0.172273 | − | 0.298385i | ||||
\(977\) | −1.23767e7 | + | 2.14371e7i | −0.414829 | + | 0.718505i | −0.995410 | − | 0.0956975i | \(-0.969492\pi\) |
0.580582 | + | 0.814202i | \(0.302825\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.61464e7 | 1.87226 | ||||||||
\(980\) | 5.46093e7 | + | 6.03401e6i | 1.81636 | + | 0.200697i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.21477e6 | + | 3.83610e6i | 0.0732910 | + | 0.126944i | ||||
\(983\) | 2.26564e7 | − | 3.92421e7i | 0.747838 | − | 1.29529i | −0.201018 | − | 0.979587i | \(-0.564425\pi\) |
0.948857 | − | 0.315707i | \(-0.102242\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.47774e7 | + | 4.29157e7i | 0.813701 | + | 1.40937i | ||||
\(986\) | 215924. | 0.00707308 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.57985e6 | 0.279632 | ||||||||
\(989\) | −579508. | − | 1.00374e6i | −0.0188395 | − | 0.0326309i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.87071e7 | − | 3.24017e7i | 0.605095 | − | 1.04805i | −0.386942 | − | 0.922104i | \(-0.626469\pi\) |
0.992037 | − | 0.125951i | \(-0.0401981\pi\) | |||||||
\(992\) | 8.90380e6 | + | 1.54218e7i | 0.287274 | + | 0.497573i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.55008e6 | + | 1.79696e6i | −0.113965 | + | 0.0576863i | ||||
\(995\) | 6.53861e7 | 2.09376 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.32639e7 | + | 4.02943e7i | −0.741216 | + | 1.28382i | 0.210726 | + | 0.977545i | \(0.432417\pi\) |
−0.951942 | + | 0.306279i | \(0.900916\pi\) | |||||||
\(998\) | 923379. | − | 1.59934e6i | 0.0293463 | − | 0.0508293i | ||||
\(999\) | 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 | 63.6.e.e.46.2 | 8 | ||
3.2 | odd | 2 | 21.6.e.c.4.3 | ✓ | 8 | ||
7.2 | even | 3 | inner | 63.6.e.e.37.2 | 8 | ||
7.3 | odd | 6 | 441.6.a.v.1.3 | 4 | |||
7.4 | even | 3 | 441.6.a.w.1.3 | 4 | |||
12.11 | even | 2 | 336.6.q.j.193.4 | 8 | |||
21.2 | odd | 6 | 21.6.e.c.16.3 | yes | 8 | ||
21.5 | even | 6 | 147.6.e.o.79.3 | 8 | |||
21.11 | odd | 6 | 147.6.a.m.1.2 | 4 | |||
21.17 | even | 6 | 147.6.a.l.1.2 | 4 | |||
21.20 | even | 2 | 147.6.e.o.67.3 | 8 | |||
84.23 | even | 6 | 336.6.q.j.289.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.6.e.c.4.3 | ✓ | 8 | 3.2 | odd | 2 | ||
21.6.e.c.16.3 | yes | 8 | 21.2 | odd | 6 | ||
63.6.e.e.37.2 | 8 | 7.2 | even | 3 | inner | ||
63.6.e.e.46.2 | 8 | 1.1 | even | 1 | trivial | ||
147.6.a.l.1.2 | 4 | 21.17 | even | 6 | |||
147.6.a.m.1.2 | 4 | 21.11 | odd | 6 | |||
147.6.e.o.67.3 | 8 | 21.20 | even | 2 | |||
147.6.e.o.79.3 | 8 | 21.5 | even | 6 | |||
336.6.q.j.193.4 | 8 | 12.11 | even | 2 | |||
336.6.q.j.289.4 | 8 | 84.23 | even | 6 | |||
441.6.a.v.1.3 | 4 | 7.3 | odd | 6 | |||
441.6.a.w.1.3 | 4 | 7.4 | even | 3 |