Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [165,6,Mod(131,165)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(165, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("165.131");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 165 = 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 165.f (of order \(2\), degree \(1\), 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: | \(26.4633302691\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 131.37 | ||
Character | \(\chi\) | \(=\) | 165.131 |
Dual form | 165.6.f.a.131.38 |
$q$-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 \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) | \(67\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.39738 | −0.247024 | −0.123512 | − | 0.992343i | \(-0.539416\pi\) | ||||
−0.123512 | + | 0.992343i | \(0.539416\pi\) | |||||||
\(3\) | −15.5493 | + | 1.10386i | −0.997490 | + | 0.0708124i | ||||
\(4\) | −30.0473 | −0.938979 | ||||||||
\(5\) | 25.0000i | 0.447214i | ||||||||
\(6\) | 21.7283 | − | 1.54251i | 0.246404 | − | 0.0174924i | ||||
\(7\) | − | 138.835i | − | 1.07091i | −0.844562 | − | 0.535457i | \(-0.820139\pi\) | ||
0.844562 | − | 0.535457i | \(-0.179861\pi\) | |||||||
\(8\) | 86.7037 | 0.478975 | ||||||||
\(9\) | 240.563 | − | 34.3284i | 0.989971 | − | 0.141269i | ||||
\(10\) | − | 34.9345i | − | 0.110473i | ||||||
\(11\) | −275.850 | + | 291.475i | −0.687372 | + | 0.726306i | ||||
\(12\) | 467.216 | − | 33.1679i | 0.936622 | − | 0.0664914i | ||||
\(13\) | − | 840.588i | − | 1.37951i | −0.724043 | − | 0.689755i | \(-0.757718\pi\) | ||
0.724043 | − | 0.689755i | \(-0.242282\pi\) | |||||||
\(14\) | 194.006i | 0.264542i | ||||||||
\(15\) | −27.5964 | − | 388.733i | −0.0316683 | − | 0.446091i | ||||
\(16\) | 840.357 | 0.820661 | ||||||||
\(17\) | 1960.61 | 1.64539 | 0.822696 | − | 0.568482i | \(-0.192469\pi\) | ||||
0.822696 | + | 0.568482i | \(0.192469\pi\) | |||||||
\(18\) | −336.158 | + | 47.9698i | −0.244547 | + | 0.0348969i | ||||
\(19\) | − | 523.450i | − | 0.332653i | −0.986071 | − | 0.166326i | \(-0.946810\pi\) | ||
0.986071 | − | 0.166326i | \(-0.0531905\pi\) | |||||||
\(20\) | − | 751.183i | − | 0.419924i | ||||||
\(21\) | 153.254 | + | 2158.80i | 0.0758340 | + | 1.06823i | ||||
\(22\) | 385.467 | − | 407.301i | 0.169797 | − | 0.179415i | ||||
\(23\) | − | 1436.21i | − | 0.566107i | −0.959104 | − | 0.283053i | \(-0.908653\pi\) | ||
0.959104 | − | 0.283053i | \(-0.0913473\pi\) | |||||||
\(24\) | −1348.18 | + | 95.7084i | −0.477772 | + | 0.0339173i | ||||
\(25\) | −625.000 | −0.200000 | ||||||||
\(26\) | 1174.62i | 0.340772i | ||||||||
\(27\) | −3702.70 | + | 799.331i | −0.977482 | + | 0.211017i | ||||
\(28\) | 4171.63i | 1.00557i | ||||||||
\(29\) | −2962.47 | −0.654123 | −0.327061 | − | 0.945003i | \(-0.606058\pi\) | ||||
−0.327061 | + | 0.945003i | \(0.606058\pi\) | |||||||
\(30\) | 38.5626 | + | 543.208i | 0.00782283 | + | 0.110195i | ||||
\(31\) | −5097.69 | −0.952728 | −0.476364 | − | 0.879248i | \(-0.658046\pi\) | ||||
−0.476364 | + | 0.879248i | \(0.658046\pi\) | |||||||
\(32\) | −3948.81 | −0.681698 | ||||||||
\(33\) | 3967.54 | − | 4836.74i | 0.634215 | − | 0.773157i | ||||
\(34\) | −2739.72 | −0.406451 | ||||||||
\(35\) | 3470.88 | 0.478928 | ||||||||
\(36\) | −7228.28 | + | 1031.48i | −0.929562 | + | 0.132649i | ||||
\(37\) | −7043.39 | −0.845819 | −0.422910 | − | 0.906172i | \(-0.638991\pi\) | ||||
−0.422910 | + | 0.906172i | \(0.638991\pi\) | |||||||
\(38\) | 731.458i | 0.0821732i | ||||||||
\(39\) | 927.888 | + | 13070.6i | 0.0976864 | + | 1.37605i | ||||
\(40\) | 2167.59i | 0.214204i | ||||||||
\(41\) | 434.057 | 0.0403262 | 0.0201631 | − | 0.999797i | \(-0.493581\pi\) | ||||
0.0201631 | + | 0.999797i | \(0.493581\pi\) | |||||||
\(42\) | −214.154 | − | 3016.66i | −0.0187328 | − | 0.263878i | ||||
\(43\) | 16663.2i | 1.37432i | 0.726507 | + | 0.687159i | \(0.241142\pi\) | ||||
−0.726507 | + | 0.687159i | \(0.758858\pi\) | |||||||
\(44\) | 8288.56 | − | 8758.05i | 0.645427 | − | 0.681986i | ||||
\(45\) | 858.211 | + | 6014.08i | 0.0631775 | + | 0.442729i | ||||
\(46\) | 2006.93i | 0.139842i | ||||||||
\(47\) | 22378.6i | 1.47771i | 0.673866 | + | 0.738854i | \(0.264633\pi\) | ||||
−0.673866 | + | 0.738854i | \(0.735367\pi\) | |||||||
\(48\) | −13067.0 | + | 927.633i | −0.818601 | + | 0.0581130i | ||||
\(49\) | −2468.25 | −0.146859 | ||||||||
\(50\) | 873.362 | 0.0494048 | ||||||||
\(51\) | −30486.2 | + | 2164.23i | −1.64126 | + | 0.116514i | ||||
\(52\) | 25257.4i | 1.29533i | ||||||||
\(53\) | − | 27604.6i | − | 1.34987i | −0.737878 | − | 0.674934i | \(-0.764172\pi\) | ||
0.737878 | − | 0.674934i | \(-0.235828\pi\) | |||||||
\(54\) | 5174.08 | − | 1116.97i | 0.241462 | − | 0.0521263i | ||||
\(55\) | −7286.88 | − | 6896.25i | −0.324814 | − | 0.307402i | ||||
\(56\) | − | 12037.5i | − | 0.512941i | ||||||
\(57\) | 577.813 | + | 8139.29i | 0.0235559 | + | 0.331817i | ||||
\(58\) | 4139.70 | 0.161584 | ||||||||
\(59\) | 19119.9i | 0.715082i | 0.933897 | + | 0.357541i | \(0.116385\pi\) | ||||
−0.933897 | + | 0.357541i | \(0.883615\pi\) | |||||||
\(60\) | 829.198 | + | 11680.4i | 0.0297358 | + | 0.418870i | ||||
\(61\) | − | 22975.3i | − | 0.790562i | −0.918560 | − | 0.395281i | \(-0.870647\pi\) | ||
0.918560 | − | 0.395281i | \(-0.129353\pi\) | |||||||
\(62\) | 7123.41 | 0.235347 | ||||||||
\(63\) | −4766.00 | − | 33398.6i | −0.151287 | − | 1.06017i | ||||
\(64\) | −21373.4 | −0.652265 | ||||||||
\(65\) | 21014.7 | 0.616936 | ||||||||
\(66\) | −5544.16 | + | 6758.76i | −0.156666 | + | 0.190988i | ||||
\(67\) | −4684.91 | −0.127501 | −0.0637506 | − | 0.997966i | \(-0.520306\pi\) | ||||
−0.0637506 | + | 0.997966i | \(0.520306\pi\) | |||||||
\(68\) | −58911.1 | −1.54499 | ||||||||
\(69\) | 1585.37 | + | 22332.1i | 0.0400874 | + | 0.564685i | ||||
\(70\) | −4850.14 | −0.118307 | ||||||||
\(71\) | − | 40174.4i | − | 0.945809i | −0.881114 | − | 0.472905i | \(-0.843205\pi\) | ||
0.881114 | − | 0.472905i | \(-0.156795\pi\) | |||||||
\(72\) | 20857.7 | − | 2976.40i | 0.474171 | − | 0.0676644i | ||||
\(73\) | 17831.2i | 0.391628i | 0.980641 | + | 0.195814i | \(0.0627348\pi\) | ||||
−0.980641 | + | 0.195814i | \(0.937265\pi\) | |||||||
\(74\) | 9842.29 | 0.208938 | ||||||||
\(75\) | 9718.33 | − | 689.910i | 0.199498 | − | 0.0141625i | ||||
\(76\) | 15728.3i | 0.312354i | ||||||||
\(77\) | 40467.0 | + | 38297.8i | 0.777812 | + | 0.736116i | ||||
\(78\) | −1296.61 | − | 18264.6i | −0.0241309 | − | 0.339917i | ||||
\(79\) | 50592.8i | 0.912055i | 0.889966 | + | 0.456027i | \(0.150728\pi\) | ||||
−0.889966 | + | 0.456027i | \(0.849272\pi\) | |||||||
\(80\) | 21008.9i | 0.367011i | ||||||||
\(81\) | 56692.1 | − | 16516.3i | 0.960086 | − | 0.279705i | ||||
\(82\) | −606.542 | −0.00996153 | ||||||||
\(83\) | −74818.7 | −1.19211 | −0.596053 | − | 0.802945i | \(-0.703265\pi\) | ||||
−0.596053 | + | 0.802945i | \(0.703265\pi\) | |||||||
\(84\) | −4604.88 | − | 64866.1i | −0.0712066 | − | 1.00304i | ||||
\(85\) | 49015.3i | 0.735841i | ||||||||
\(86\) | − | 23284.8i | − | 0.339490i | ||||||
\(87\) | 46064.5 | − | 3270.14i | 0.652481 | − | 0.0463200i | ||||
\(88\) | −23917.2 | + | 25272.0i | −0.329234 | + | 0.347882i | ||||
\(89\) | − | 18693.0i | − | 0.250152i | −0.992147 | − | 0.125076i | \(-0.960082\pi\) | ||
0.992147 | − | 0.125076i | \(-0.0399175\pi\) | |||||||
\(90\) | −1199.25 | − | 8403.95i | −0.0156064 | − | 0.109365i | ||||
\(91\) | −116703. | −1.47734 | ||||||||
\(92\) | 43154.3i | 0.531562i | ||||||||
\(93\) | 79265.6 | − | 5627.11i | 0.950337 | − | 0.0674650i | ||||
\(94\) | − | 31271.4i | − | 0.365030i | ||||||
\(95\) | 13086.2 | 0.148767 | ||||||||
\(96\) | 61401.4 | − | 4358.92i | 0.679986 | − | 0.0482726i | ||||
\(97\) | −46491.6 | −0.501702 | −0.250851 | − | 0.968026i | \(-0.580710\pi\) | ||||
−0.250851 | + | 0.968026i | \(0.580710\pi\) | |||||||
\(98\) | 3449.08 | 0.0362776 | ||||||||
\(99\) | −56353.5 | + | 79587.6i | −0.577873 | + | 0.816126i | ||||
\(100\) | 18779.6 | 0.187796 | ||||||||
\(101\) | −69872.9 | −0.681562 | −0.340781 | − | 0.940143i | \(-0.610691\pi\) | ||||
−0.340781 | + | 0.940143i | \(0.610691\pi\) | |||||||
\(102\) | 42600.8 | − | 3024.25i | 0.405431 | − | 0.0287818i | ||||
\(103\) | −35346.8 | −0.328289 | −0.164145 | − | 0.986436i | \(-0.552486\pi\) | ||||
−0.164145 | + | 0.986436i | \(0.552486\pi\) | |||||||
\(104\) | − | 72882.1i | − | 0.660750i | ||||||
\(105\) | −53969.9 | + | 3831.36i | −0.477725 | + | 0.0339140i | ||||
\(106\) | 38574.1i | 0.333450i | ||||||||
\(107\) | 196873. | 1.66236 | 0.831181 | − | 0.556001i | \(-0.187665\pi\) | ||||
0.831181 | + | 0.556001i | \(0.187665\pi\) | |||||||
\(108\) | 111256. | − | 24017.8i | 0.917836 | − | 0.198140i | ||||
\(109\) | − | 30375.0i | − | 0.244878i | −0.992476 | − | 0.122439i | \(-0.960928\pi\) | ||
0.992476 | − | 0.122439i | \(-0.0390716\pi\) | |||||||
\(110\) | 10182.5 | + | 9636.68i | 0.0802369 | + | 0.0759357i | ||||
\(111\) | 109520. | − | 7774.89i | 0.843696 | − | 0.0598945i | ||||
\(112\) | − | 116671.i | − | 0.878858i | ||||||
\(113\) | 76118.7i | 0.560783i | 0.959886 | + | 0.280392i | \(0.0904643\pi\) | ||||
−0.959886 | + | 0.280392i | \(0.909536\pi\) | |||||||
\(114\) | −807.424 | − | 11373.7i | −0.00581888 | − | 0.0819669i | ||||
\(115\) | 35905.2 | 0.253171 | ||||||||
\(116\) | 89014.4 | 0.614208 | ||||||||
\(117\) | −28856.1 | − | 202214.i | −0.194882 | − | 1.36568i | ||||
\(118\) | − | 26717.8i | − | 0.176643i | ||||||
\(119\) | − | 272202.i | − | 1.76207i | ||||||
\(120\) | −2392.71 | − | 33704.6i | −0.0151683 | − | 0.213666i | ||||
\(121\) | −8864.36 | − | 160807.i | −0.0550407 | − | 0.998484i | ||||
\(122\) | 32105.2i | 0.195288i | ||||||||
\(123\) | −6749.29 | + | 479.136i | −0.0402249 | + | 0.00285559i | ||||
\(124\) | 153172. | 0.894592 | ||||||||
\(125\) | − | 15625.0i | − | 0.0894427i | ||||||
\(126\) | 6659.91 | + | 46670.6i | 0.0373716 | + | 0.261889i | ||||
\(127\) | 215773.i | 1.18710i | 0.804797 | + | 0.593551i | \(0.202274\pi\) | ||||
−0.804797 | + | 0.593551i | \(0.797726\pi\) | |||||||
\(128\) | 156229. | 0.842823 | ||||||||
\(129\) | −18393.8 | − | 259101.i | −0.0973187 | − | 1.37087i | ||||
\(130\) | −29365.5 | −0.152398 | ||||||||
\(131\) | −337322. | −1.71738 | −0.858690 | − | 0.512496i | \(-0.828721\pi\) | ||||
−0.858690 | + | 0.512496i | \(0.828721\pi\) | |||||||
\(132\) | −119214. | + | 145331.i | −0.595514 | + | 0.725978i | ||||
\(133\) | −72673.3 | −0.356243 | ||||||||
\(134\) | 6546.59 | 0.0314959 | ||||||||
\(135\) | −19983.3 | − | 92567.5i | −0.0943696 | − | 0.437143i | ||||
\(136\) | 169992. | 0.788101 | ||||||||
\(137\) | 352292.i | 1.60362i | 0.597578 | + | 0.801811i | \(0.296130\pi\) | ||||
−0.597578 | + | 0.801811i | \(0.703870\pi\) | |||||||
\(138\) | −2215.36 | − | 31206.4i | −0.00990255 | − | 0.139491i | ||||
\(139\) | 287525.i | 1.26223i | 0.775690 | + | 0.631115i | \(0.217402\pi\) | ||||
−0.775690 | + | 0.631115i | \(0.782598\pi\) | |||||||
\(140\) | −104291. | −0.449703 | ||||||||
\(141\) | −24702.8 | − | 347972.i | −0.104640 | − | 1.47400i | ||||
\(142\) | 56138.9i | 0.233638i | ||||||||
\(143\) | 245010. | + | 231876.i | 1.00195 | + | 0.948236i | ||||
\(144\) | 202159. | − | 28848.1i | 0.812431 | − | 0.115934i | ||||
\(145\) | − | 74061.8i | − | 0.292533i | ||||||
\(146\) | − | 24916.9i | − | 0.0967415i | ||||||
\(147\) | 38379.6 | − | 2724.59i | 0.146490 | − | 0.0103994i | ||||
\(148\) | 211635. | 0.794207 | ||||||||
\(149\) | −73103.7 | −0.269758 | −0.134879 | − | 0.990862i | \(-0.543065\pi\) | ||||
−0.134879 | + | 0.990862i | \(0.543065\pi\) | |||||||
\(150\) | −13580.2 | + | 964.066i | −0.0492808 | + | 0.00349847i | ||||
\(151\) | 74060.0i | 0.264327i | 0.991228 | + | 0.132163i | \(0.0421924\pi\) | ||||
−0.991228 | + | 0.132163i | \(0.957808\pi\) | |||||||
\(152\) | − | 45385.0i | − | 0.159332i | ||||||
\(153\) | 471651. | − | 67304.7i | 1.62889 | − | 0.232443i | ||||
\(154\) | −56547.8 | − | 53516.5i | −0.192138 | − | 0.181839i | ||||
\(155\) | − | 127442.i | − | 0.426073i | ||||||
\(156\) | −27880.6 | − | 392736.i | −0.0917255 | − | 1.29208i | ||||
\(157\) | 72104.8 | 0.233461 | 0.116731 | − | 0.993164i | \(-0.462759\pi\) | ||||
0.116731 | + | 0.993164i | \(0.462759\pi\) | |||||||
\(158\) | − | 70697.3i | − | 0.225300i | ||||||
\(159\) | 30471.5 | + | 429232.i | 0.0955874 | + | 1.34648i | ||||
\(160\) | − | 98720.4i | − | 0.304864i | ||||||
\(161\) | −199397. | −0.606252 | ||||||||
\(162\) | −79220.4 | + | 23079.5i | −0.237164 | + | 0.0690939i | ||||
\(163\) | 18749.8 | 0.0552748 | 0.0276374 | − | 0.999618i | \(-0.491202\pi\) | ||||
0.0276374 | + | 0.999618i | \(0.491202\pi\) | |||||||
\(164\) | −13042.2 | −0.0378654 | ||||||||
\(165\) | 120918. | + | 99188.4i | 0.345766 | + | 0.283629i | ||||
\(166\) | 104550. | 0.294479 | ||||||||
\(167\) | 550753. | 1.52815 | 0.764075 | − | 0.645128i | \(-0.223196\pi\) | ||||
0.764075 | + | 0.645128i | \(0.223196\pi\) | |||||||
\(168\) | 13287.7 | + | 187176.i | 0.0363226 | + | 0.511653i | ||||
\(169\) | −335295. | −0.903048 | ||||||||
\(170\) | − | 68493.0i | − | 0.181771i | ||||||
\(171\) | −17969.2 | − | 125923.i | −0.0469936 | − | 0.329316i | ||||
\(172\) | − | 500685.i | − | 1.29046i | ||||||
\(173\) | −603362. | −1.53272 | −0.766360 | − | 0.642412i | \(-0.777934\pi\) | ||||
−0.766360 | + | 0.642412i | \(0.777934\pi\) | |||||||
\(174\) | −64369.5 | + | 4569.63i | −0.161179 | + | 0.0114422i | ||||
\(175\) | 86772.1i | 0.214183i | ||||||||
\(176\) | −231813. | + | 244943.i | −0.564099 | + | 0.596051i | ||||
\(177\) | −21105.6 | − | 297302.i | −0.0506367 | − | 0.713287i | ||||
\(178\) | 26121.2i | 0.0617936i | ||||||||
\(179\) | 402941.i | 0.939959i | 0.882677 | + | 0.469979i | \(0.155739\pi\) | ||||
−0.882677 | + | 0.469979i | \(0.844261\pi\) | |||||||
\(180\) | −25786.9 | − | 180707.i | −0.0593224 | − | 0.415713i | ||||
\(181\) | −806318. | −1.82941 | −0.914703 | − | 0.404127i | \(-0.867575\pi\) | ||||
−0.914703 | + | 0.404127i | \(0.867575\pi\) | |||||||
\(182\) | 163079. | 0.364938 | ||||||||
\(183\) | 25361.4 | + | 357250.i | 0.0559816 | + | 0.788577i | ||||
\(184\) | − | 124525.i | − | 0.271151i | ||||||
\(185\) | − | 176085.i | − | 0.378262i | ||||||
\(186\) | −110764. | + | 7863.21i | −0.234756 | + | 0.0166655i | ||||
\(187\) | −540835. | + | 571469.i | −1.13100 | + | 1.19506i | ||||
\(188\) | − | 672418.i | − | 1.38754i | ||||||
\(189\) | 110975. | + | 514065.i | 0.225981 | + | 1.04680i | ||||
\(190\) | −18286.4 | −0.0367490 | ||||||||
\(191\) | − | 220023.i | − | 0.436400i | −0.975904 | − | 0.218200i | \(-0.929982\pi\) | ||
0.975904 | − | 0.218200i | \(-0.0700185\pi\) | |||||||
\(192\) | 332342. | − | 23593.2i | 0.650628 | − | 0.0461884i | ||||
\(193\) | 697297.i | 1.34749i | 0.738965 | + | 0.673744i | \(0.235315\pi\) | ||||
−0.738965 | + | 0.673744i | \(0.764685\pi\) | |||||||
\(194\) | 64966.5 | 0.123932 | ||||||||
\(195\) | −326764. | + | 23197.2i | −0.615387 | + | 0.0436867i | ||||
\(196\) | 74164.4 | 0.137897 | ||||||||
\(197\) | −389876. | −0.715749 | −0.357874 | − | 0.933770i | \(-0.616498\pi\) | ||||
−0.357874 | + | 0.933770i | \(0.616498\pi\) | |||||||
\(198\) | 78747.2 | − | 111214.i | 0.142749 | − | 0.201603i | ||||
\(199\) | −161225. | −0.288602 | −0.144301 | − | 0.989534i | \(-0.546093\pi\) | ||||
−0.144301 | + | 0.989534i | \(0.546093\pi\) | |||||||
\(200\) | −54189.8 | −0.0957949 | ||||||||
\(201\) | 72847.2 | − | 5171.46i | 0.127181 | − | 0.00902866i | ||||
\(202\) | 97638.9 | 0.168362 | ||||||||
\(203\) | 411296.i | 0.700510i | ||||||||
\(204\) | 916029. | − | 65029.4i | 1.54111 | − | 0.109404i | ||||
\(205\) | 10851.4i | 0.0180344i | ||||||||
\(206\) | 49392.8 | 0.0810954 | ||||||||
\(207\) | −49302.8 | − | 345499.i | −0.0799735 | − | 0.560429i | ||||
\(208\) | − | 706394.i | − | 1.13211i | ||||||
\(209\) | 152572. | + | 144394.i | 0.241608 | + | 0.228656i | ||||
\(210\) | 75416.4 | − | 5353.86i | 0.118010 | − | 0.00837758i | ||||
\(211\) | 1.26540e6i | 1.95669i | 0.206984 | + | 0.978344i | \(0.433635\pi\) | ||||
−0.206984 | + | 0.978344i | \(0.566365\pi\) | |||||||
\(212\) | 829444.i | 1.26750i | ||||||||
\(213\) | 44346.8 | + | 624685.i | 0.0669750 | + | 0.943435i | ||||
\(214\) | −275106. | −0.410644 | ||||||||
\(215\) | −416580. | −0.614614 | ||||||||
\(216\) | −321038. | + | 69304.9i | −0.468189 | + | 0.101072i | ||||
\(217\) | 707739.i | 1.02029i | ||||||||
\(218\) | 42445.4i | 0.0604908i | ||||||||
\(219\) | −19683.1 | − | 277263.i | −0.0277321 | − | 0.390644i | ||||
\(220\) | 218951. | + | 207214.i | 0.304993 | + | 0.288644i | ||||
\(221\) | − | 1.64807e6i | − | 2.26983i | ||||||
\(222\) | −153041. | + | 10864.5i | −0.208413 | + | 0.0147954i | ||||
\(223\) | −1.46934e6 | −1.97861 | −0.989305 | − | 0.145860i | \(-0.953405\pi\) | ||||
−0.989305 | + | 0.145860i | \(0.953405\pi\) | |||||||
\(224\) | 548235.i | 0.730040i | ||||||||
\(225\) | −150352. | + | 21455.3i | −0.197994 | + | 0.0282538i | ||||
\(226\) | − | 106367.i | − | 0.138527i | ||||||
\(227\) | 477669. | 0.615265 | 0.307633 | − | 0.951505i | \(-0.400463\pi\) | ||||
0.307633 | + | 0.951505i | \(0.400463\pi\) | |||||||
\(228\) | −17361.7 | − | 244564.i | −0.0221185 | − | 0.311570i | ||||
\(229\) | −354213. | −0.446351 | −0.223175 | − | 0.974778i | \(-0.571642\pi\) | ||||
−0.223175 | + | 0.974778i | \(0.571642\pi\) | |||||||
\(230\) | −50173.2 | −0.0625392 | ||||||||
\(231\) | −671510. | − | 550834.i | −0.827985 | − | 0.679190i | ||||
\(232\) | −256857. | −0.313308 | ||||||||
\(233\) | 677802. | 0.817924 | 0.408962 | − | 0.912551i | \(-0.365891\pi\) | ||||
0.408962 | + | 0.912551i | \(0.365891\pi\) | |||||||
\(234\) | 40322.9 | + | 282570.i | 0.0481406 | + | 0.337355i | ||||
\(235\) | −559465. | −0.660851 | ||||||||
\(236\) | − | 574502.i | − | 0.671447i | ||||||
\(237\) | −55847.1 | − | 786684.i | −0.0645848 | − | 0.909765i | ||||
\(238\) | 380370.i | 0.435275i | ||||||||
\(239\) | 514240. | 0.582332 | 0.291166 | − | 0.956672i | \(-0.405957\pi\) | ||||
0.291166 | + | 0.956672i | \(0.405957\pi\) | |||||||
\(240\) | −23190.8 | − | 326674.i | −0.0259889 | − | 0.366089i | ||||
\(241\) | 417830.i | 0.463401i | 0.972787 | + | 0.231700i | \(0.0744289\pi\) | ||||
−0.972787 | + | 0.231700i | \(0.925571\pi\) | |||||||
\(242\) | 12386.9 | + | 224708.i | 0.0135964 | + | 0.246650i | ||||
\(243\) | −863293. | + | 319397.i | −0.937869 | + | 0.346989i | ||||
\(244\) | 690345.i | 0.742321i | ||||||||
\(245\) | − | 61706.3i | − | 0.0656771i | ||||||
\(246\) | 9431.32 | − | 669.535i | 0.00993653 | − | 0.000705400i | ||||
\(247\) | −440005. | −0.458898 | ||||||||
\(248\) | −441988. | −0.456333 | ||||||||
\(249\) | 1.16338e6 | − | 82589.0i | 1.18911 | − | 0.0844158i | ||||
\(250\) | 21834.1i | 0.0220945i | ||||||||
\(251\) | − | 549499.i | − | 0.550532i | −0.961368 | − | 0.275266i | \(-0.911234\pi\) | ||
0.961368 | − | 0.275266i | \(-0.0887660\pi\) | |||||||
\(252\) | 143206. | + | 1.00354e6i | 0.142056 | + | 0.995482i | ||||
\(253\) | 418619. | + | 396179.i | 0.411167 | + | 0.389126i | ||||
\(254\) | − | 301517.i | − | 0.293243i | ||||||
\(255\) | −54105.8 | − | 762155.i | −0.0521067 | − | 0.733994i | ||||
\(256\) | 465638. | 0.444067 | ||||||||
\(257\) | 836092.i | 0.789625i | 0.918762 | + | 0.394813i | \(0.129191\pi\) | ||||
−0.918762 | + | 0.394813i | \(0.870809\pi\) | |||||||
\(258\) | 25703.1 | + | 362063.i | 0.0240401 | + | 0.338637i | ||||
\(259\) | 977872.i | 0.905801i | ||||||||
\(260\) | −631436. | −0.579290 | ||||||||
\(261\) | −712661. | + | 101697.i | −0.647563 | + | 0.0924075i | ||||
\(262\) | 471367. | 0.424234 | ||||||||
\(263\) | 94258.7 | 0.0840295 | 0.0420148 | − | 0.999117i | \(-0.486622\pi\) | ||||
0.0420148 | + | 0.999117i | \(0.486622\pi\) | |||||||
\(264\) | 344000. | − | 419363.i | 0.303773 | − | 0.370323i | ||||
\(265\) | 690114. | 0.603679 | ||||||||
\(266\) | 101552. | 0.0880005 | ||||||||
\(267\) | 20634.4 | + | 290664.i | 0.0177139 | + | 0.249524i | ||||
\(268\) | 140769. | 0.119721 | ||||||||
\(269\) | 877258.i | 0.739174i | 0.929196 | + | 0.369587i | \(0.120501\pi\) | ||||
−0.929196 | + | 0.369587i | \(0.879499\pi\) | |||||||
\(270\) | 27924.2 | + | 129352.i | 0.0233116 | + | 0.107985i | ||||
\(271\) | − | 1.92473e6i | − | 1.59201i | −0.605287 | − | 0.796007i | \(-0.706942\pi\) | ||
0.605287 | − | 0.796007i | \(-0.293058\pi\) | |||||||
\(272\) | 1.64761e6 | 1.35031 | ||||||||
\(273\) | 1.81466e6 | − | 128824.i | 1.47363 | − | 0.104614i | ||||
\(274\) | − | 492286.i | − | 0.396133i | ||||||
\(275\) | 172406. | − | 182172.i | 0.137474 | − | 0.145261i | ||||
\(276\) | −47636.1 | − | 671020.i | −0.0376412 | − | 0.530228i | ||||
\(277\) | − | 1.65035e6i | − | 1.29234i | −0.763194 | − | 0.646170i | \(-0.776370\pi\) | ||
0.763194 | − | 0.646170i | \(-0.223630\pi\) | |||||||
\(278\) | − | 401781.i | − | 0.311801i | ||||||
\(279\) | −1.22632e6 | + | 174996.i | −0.943174 | + | 0.134591i | ||||
\(280\) | 300938. | 0.229394 | ||||||||
\(281\) | −1.85767e6 | −1.40347 | −0.701735 | − | 0.712438i | \(-0.747591\pi\) | ||||
−0.701735 | + | 0.712438i | \(0.747591\pi\) | |||||||
\(282\) | 34519.1 | + | 486250.i | 0.0258486 | + | 0.364113i | ||||
\(283\) | − | 954831.i | − | 0.708697i | −0.935113 | − | 0.354349i | \(-0.884703\pi\) | ||
0.935113 | − | 0.354349i | \(-0.115297\pi\) | |||||||
\(284\) | 1.20713e6i | 0.888095i | ||||||||
\(285\) | −203482. | + | 14445.3i | −0.148393 | + | 0.0105345i | ||||
\(286\) | −342373. | − | 324019.i | −0.247505 | − | 0.234237i | ||||
\(287\) | − | 60262.4i | − | 0.0431859i | ||||||
\(288\) | −949939. | + | 135557.i | −0.674861 | + | 0.0963029i | ||||
\(289\) | 2.42414e6 | 1.70731 | ||||||||
\(290\) | 103492.i | 0.0722626i | ||||||||
\(291\) | 722913. | − | 51320.1i | 0.500442 | − | 0.0355267i | ||||
\(292\) | − | 535780.i | − | 0.367730i | ||||||
\(293\) | 234905. | 0.159854 | 0.0799268 | − | 0.996801i | \(-0.474531\pi\) | ||||
0.0799268 | + | 0.996801i | \(0.474531\pi\) | |||||||
\(294\) | −53630.9 | + | 3807.29i | −0.0361865 | + | 0.00256890i | ||||
\(295\) | −477998. | −0.319794 | ||||||||
\(296\) | −610688. | −0.405126 | ||||||||
\(297\) | 788405. | − | 1.29974e6i | 0.518631 | − | 0.854998i | ||||
\(298\) | 102154. | 0.0666366 | ||||||||
\(299\) | −1.20726e6 | −0.780950 | ||||||||
\(300\) | −292010. | + | 20730.0i | −0.187324 | + | 0.0132983i | ||||
\(301\) | 2.31344e6 | 1.47178 | ||||||||
\(302\) | − | 103490.i | − | 0.0652951i | ||||||
\(303\) | 1.08648e6 | − | 77129.6i | 0.679851 | − | 0.0482630i | ||||
\(304\) | − | 439884.i | − | 0.272995i | ||||||
\(305\) | 574382. | 0.353550 | ||||||||
\(306\) | −659075. | + | 94050.2i | −0.402375 | + | 0.0574191i | ||||
\(307\) | 1.40308e6i | 0.849641i | 0.905278 | + | 0.424820i | \(0.139663\pi\) | ||||
−0.905278 | + | 0.424820i | \(0.860337\pi\) | |||||||
\(308\) | −1.21593e6 | − | 1.15075e6i | −0.730349 | − | 0.691198i | ||||
\(309\) | 549618. | − | 39017.7i | 0.327465 | − | 0.0232469i | ||||
\(310\) | 178085.i | 0.105250i | ||||||||
\(311\) | − | 436429.i | − | 0.255866i | −0.991783 | − | 0.127933i | \(-0.959166\pi\) | ||
0.991783 | − | 0.127933i | \(-0.0408342\pi\) | |||||||
\(312\) | 80451.3 | + | 1.13327e6i | 0.0467893 | + | 0.659092i | ||||
\(313\) | 513930. | 0.296513 | 0.148256 | − | 0.988949i | \(-0.452634\pi\) | ||||
0.148256 | + | 0.988949i | \(0.452634\pi\) | |||||||
\(314\) | −100758. | −0.0576706 | ||||||||
\(315\) | 834966. | − | 119150.i | 0.474125 | − | 0.0676578i | ||||
\(316\) | − | 1.52018e6i | − | 0.856400i | ||||||
\(317\) | 3.22326e6i | 1.80155i | 0.434282 | + | 0.900777i | \(0.357002\pi\) | ||||
−0.434282 | + | 0.900777i | \(0.642998\pi\) | |||||||
\(318\) | −42580.2 | − | 599801.i | −0.0236124 | − | 0.332613i | ||||
\(319\) | 817199. | − | 863487.i | 0.449626 | − | 0.475093i | ||||
\(320\) | − | 534336.i | − | 0.291702i | ||||||
\(321\) | −3.06124e6 | + | 217319.i | −1.65819 | + | 0.117716i | ||||
\(322\) | 278633. | 0.149759 | ||||||||
\(323\) | − | 1.02628e6i | − | 0.547344i | ||||||
\(324\) | −1.70345e6 | + | 496271.i | −0.901501 | + | 0.262637i | ||||
\(325\) | 525368.i | 0.275902i | ||||||||
\(326\) | −26200.5 | −0.0136542 | ||||||||
\(327\) | 33529.6 | + | 472311.i | 0.0173404 | + | 0.244263i | ||||
\(328\) | 37634.3 | 0.0193152 | ||||||||
\(329\) | 3.10694e6 | 1.58250 | ||||||||
\(330\) | −168969. | − | 138604.i | −0.0854126 | − | 0.0700633i | ||||
\(331\) | −1.55711e6 | −0.781178 | −0.390589 | − | 0.920565i | \(-0.627729\pi\) | ||||
−0.390589 | + | 0.920565i | \(0.627729\pi\) | |||||||
\(332\) | 2.24810e6 | 1.11936 | ||||||||
\(333\) | −1.69438e6 | + | 241789.i | −0.837337 | + | 0.119488i | ||||
\(334\) | −769611. | −0.377490 | ||||||||
\(335\) | − | 117123.i | − | 0.0570202i | ||||||
\(336\) | 128788. | + | 1.81416e6i | 0.0622340 | + | 0.876652i | ||||
\(337\) | − | 1.46323e6i | − | 0.701839i | −0.936406 | − | 0.350919i | \(-0.885869\pi\) | ||
0.936406 | − | 0.350919i | \(-0.114131\pi\) | |||||||
\(338\) | 468535. | 0.223075 | ||||||||
\(339\) | −84024.0 | − | 1.18359e6i | −0.0397104 | − | 0.559375i | ||||
\(340\) | − | 1.47278e6i | − | 0.690940i | ||||||
\(341\) | 1.40620e6 | − | 1.48585e6i | 0.654878 | − | 0.691972i | ||||
\(342\) | 25109.8 | + | 175962.i | 0.0116085 | + | 0.0813491i | ||||
\(343\) | − | 1.99072e6i | − | 0.913642i | ||||||
\(344\) | 1.44476e6i | 0.658263i | ||||||||
\(345\) | −558302. | + | 39634.2i | −0.252535 | + | 0.0179276i | ||||
\(346\) | 843126. | 0.378619 | ||||||||
\(347\) | 293544. | 0.130873 | 0.0654364 | − | 0.997857i | \(-0.479156\pi\) | ||||
0.0654364 | + | 0.997857i | \(0.479156\pi\) | |||||||
\(348\) | −1.38411e6 | + | 98259.1i | −0.612666 | + | 0.0434935i | ||||
\(349\) | − | 455937.i | − | 0.200374i | −0.994969 | − | 0.100187i | \(-0.968056\pi\) | ||
0.994969 | − | 0.100187i | \(-0.0319441\pi\) | |||||||
\(350\) | − | 121254.i | − | 0.0529084i | ||||||
\(351\) | 671908. | + | 3.11244e6i | 0.291100 | + | 1.34845i | ||||
\(352\) | 1.08928e6 | − | 1.15098e6i | 0.468580 | − | 0.495121i | ||||
\(353\) | − | 3.10592e6i | − | 1.32664i | −0.748334 | − | 0.663322i | \(-0.769146\pi\) | ||
0.748334 | − | 0.663322i | \(-0.230854\pi\) | |||||||
\(354\) | 29492.6 | + | 415443.i | 0.0125085 | + | 0.176199i | ||||
\(355\) | 1.00436e6 | 0.422979 | ||||||||
\(356\) | 561675.i | 0.234888i | ||||||||
\(357\) | 300472. | + | 4.23256e6i | 0.124777 | + | 1.75765i | ||||
\(358\) | − | 563062.i | − | 0.232193i | ||||||
\(359\) | −3.80076e6 | −1.55645 | −0.778224 | − | 0.627987i | \(-0.783879\pi\) | ||||
−0.778224 | + | 0.627987i | \(0.783879\pi\) | |||||||
\(360\) | 74410.0 | + | 521442.i | 0.0302604 | + | 0.212056i | ||||
\(361\) | 2.20210e6 | 0.889342 | ||||||||
\(362\) | 1.12673e6 | 0.451907 | ||||||||
\(363\) | 315342. | + | 2.49065e6i | 0.125608 | + | 0.992080i | ||||
\(364\) | 3.50662e6 | 1.38719 | ||||||||
\(365\) | −445780. | −0.175141 | ||||||||
\(366\) | −35439.5 | − | 499214.i | −0.0138288 | − | 0.194798i | ||||
\(367\) | 1.87699e6 | 0.727438 | 0.363719 | − | 0.931509i | \(-0.381507\pi\) | ||||
0.363719 | + | 0.931509i | \(0.381507\pi\) | |||||||
\(368\) | − | 1.20693e6i | − | 0.464581i | ||||||
\(369\) | 104418. | − | 14900.5i | 0.0399217 | − | 0.00569685i | ||||
\(370\) | 246057.i | 0.0934398i | ||||||||
\(371\) | −3.83249e6 | −1.44559 | ||||||||
\(372\) | −2.38172e6 | + | 169080.i | −0.892346 | + | 0.0633482i | ||||
\(373\) | − | 4.12896e6i | − | 1.53663i | −0.640073 | − | 0.768314i | \(-0.721096\pi\) | ||
0.640073 | − | 0.768314i | \(-0.278904\pi\) | |||||||
\(374\) | 755752. | − | 798560.i | 0.279383 | − | 0.295208i | ||||
\(375\) | 17247.7 | + | 242958.i | 0.00633365 | + | 0.0892182i | ||||
\(376\) | 1.94031e6i | 0.707785i | ||||||||
\(377\) | 2.49022e6i | 0.902369i | ||||||||
\(378\) | −155075. | − | 718344.i | −0.0558228 | − | 0.258585i | ||||
\(379\) | −2.43886e6 | −0.872147 | −0.436073 | − | 0.899911i | \(-0.643631\pi\) | ||||
−0.436073 | + | 0.899911i | \(0.643631\pi\) | |||||||
\(380\) | −393207. | −0.139689 | ||||||||
\(381\) | −238182. | − | 3.35512e6i | −0.0840615 | − | 1.18412i | ||||
\(382\) | 307456.i | 0.107801i | ||||||||
\(383\) | 4.81751e6i | 1.67813i | 0.544032 | + | 0.839065i | \(0.316897\pi\) | ||||
−0.544032 | + | 0.839065i | \(0.683103\pi\) | |||||||
\(384\) | −2.42925e6 | + | 172454.i | −0.840707 | + | 0.0596823i | ||||
\(385\) | −957444. | + | 1.01168e6i | −0.329201 | + | 0.347848i | ||||
\(386\) | − | 974389.i | − | 0.332862i | ||||||
\(387\) | 572021. | + | 4.00855e6i | 0.194149 | + | 1.36054i | ||||
\(388\) | 1.39695e6 | 0.471087 | ||||||||
\(389\) | − | 5.52977e6i | − | 1.85282i | −0.376518 | − | 0.926409i | \(-0.622879\pi\) | ||
0.376518 | − | 0.926409i | \(-0.377121\pi\) | |||||||
\(390\) | 456614. | − | 32415.3i | 0.152015 | − | 0.0107917i | ||||
\(391\) | − | 2.81585e6i | − | 0.931467i | ||||||
\(392\) | −214006. | −0.0703415 | ||||||||
\(393\) | 5.24513e6 | − | 372355.i | 1.71307 | − | 0.121612i | ||||
\(394\) | 544804. | 0.176807 | ||||||||
\(395\) | −1.26482e6 | −0.407883 | ||||||||
\(396\) | 1.69327e6 | − | 2.39140e6i | 0.542611 | − | 0.766326i | ||||
\(397\) | 2.45580e6 | 0.782018 | 0.391009 | − | 0.920387i | \(-0.372126\pi\) | ||||
0.391009 | + | 0.920387i | \(0.372126\pi\) | |||||||
\(398\) | 225292. | 0.0712916 | ||||||||
\(399\) | 1.13002e6 | − | 80220.9i | 0.355348 | − | 0.0252264i | ||||
\(400\) | −525223. | −0.164132 | ||||||||
\(401\) | 3.23210e6i | 1.00375i | 0.864942 | + | 0.501873i | \(0.167355\pi\) | ||||
−0.864942 | + | 0.501873i | \(0.832645\pi\) | |||||||
\(402\) | −101795. | + | 7226.50i | −0.0314168 | + | 0.00223030i | ||||
\(403\) | 4.28506e6i | 1.31430i | ||||||||
\(404\) | 2.09949e6 | 0.639972 | ||||||||
\(405\) | 412907. | + | 1.41730e6i | 0.125088 | + | 0.429364i | ||||
\(406\) | − | 574737.i | − | 0.173043i | ||||||
\(407\) | 1.94292e6 | − | 2.05297e6i | 0.581392 | − | 0.614324i | ||||
\(408\) | −2.64326e6 | + | 187647.i | −0.786122 | + | 0.0558073i | ||||
\(409\) | − | 4.07843e6i | − | 1.20555i | −0.797912 | − | 0.602774i | \(-0.794062\pi\) | ||
0.797912 | − | 0.602774i | \(-0.205938\pi\) | |||||||
\(410\) | − | 15163.5i | − | 0.00445493i | ||||||
\(411\) | −388880. | − | 5.47791e6i | −0.113556 | − | 1.59960i | ||||
\(412\) | 1.06208e6 | 0.308257 | ||||||||
\(413\) | 2.65452e6 | 0.765792 | ||||||||
\(414\) | 68894.7 | + | 482793.i | 0.0197554 | + | 0.138440i | ||||
\(415\) | − | 1.87047e6i | − | 0.533126i | ||||||
\(416\) | 3.31933e6i | 0.940409i | ||||||||
\(417\) | −317386. | − | 4.47081e6i | −0.0893815 | − | 1.25906i | ||||
\(418\) | −213202. | − | 201773.i | −0.0596829 | − | 0.0564835i | ||||
\(419\) | − | 4.08003e6i | − | 1.13535i | −0.823254 | − | 0.567673i | \(-0.807844\pi\) | ||
0.823254 | − | 0.567673i | \(-0.192156\pi\) | |||||||
\(420\) | 1.62165e6 | − | 115122.i | 0.448574 | − | 0.0318445i | ||||
\(421\) | −2.92970e6 | −0.805598 | −0.402799 | − | 0.915288i | \(-0.631963\pi\) | ||||
−0.402799 | + | 0.915288i | \(0.631963\pi\) | |||||||
\(422\) | − | 1.76824e6i | − | 0.483349i | ||||||
\(423\) | 768223. | + | 5.38347e6i | 0.208755 | + | 1.46289i | ||||
\(424\) | − | 2.39342e6i | − | 0.646552i | ||||||
\(425\) | −1.22538e6 | −0.329078 | ||||||||
\(426\) | −61969.3 | − | 872922.i | −0.0165444 | − | 0.233051i | ||||
\(427\) | −3.18978e6 | −0.846625 | ||||||||
\(428\) | −5.91550e6 | −1.56092 | ||||||||
\(429\) | −4.06570e6 | − | 3.33506e6i | −1.06658 | − | 0.874905i | ||||
\(430\) | 582120. | 0.151824 | ||||||||
\(431\) | 1.75639e6 | 0.455437 | 0.227718 | − | 0.973727i | \(-0.426873\pi\) | ||||
0.227718 | + | 0.973727i | \(0.426873\pi\) | |||||||
\(432\) | −3.11159e6 | + | 671723.i | −0.802181 | + | 0.173173i | ||||
\(433\) | 5.00535e6 | 1.28297 | 0.641483 | − | 0.767137i | \(-0.278320\pi\) | ||||
0.641483 | + | 0.767137i | \(0.278320\pi\) | |||||||
\(434\) | − | 988981.i | − | 0.252037i | ||||||
\(435\) | 81753.6 | + | 1.15161e6i | 0.0207149 | + | 0.291798i | ||||
\(436\) | 912687.i | 0.229935i | ||||||||
\(437\) | −751783. | −0.188317 | ||||||||
\(438\) | 27504.7 | + | 387442.i | 0.00685049 | + | 0.0964986i | ||||
\(439\) | 7.01591e6i | 1.73749i | 0.495257 | + | 0.868746i | \(0.335074\pi\) | ||||
−0.495257 | + | 0.868746i | \(0.664926\pi\) | |||||||
\(440\) | −631799. | − | 597931.i | −0.155578 | − | 0.147238i | ||||
\(441\) | −593770. | + | 84731.2i | −0.145386 | + | 0.0207466i | ||||
\(442\) | 2.30297e6i | 0.560704i | ||||||||
\(443\) | 6.53003e6i | 1.58091i | 0.612523 | + | 0.790453i | \(0.290155\pi\) | ||||
−0.612523 | + | 0.790453i | \(0.709845\pi\) | |||||||
\(444\) | −3.29078e6 | + | 233615.i | −0.792213 | + | 0.0562397i | ||||
\(445\) | 467325. | 0.111871 | ||||||||
\(446\) | 2.05323e6 | 0.488765 | ||||||||
\(447\) | 1.13671e6 | − | 80696.0i | 0.269080 | − | 0.0191022i | ||||
\(448\) | 2.96739e6i | 0.698520i | ||||||||
\(449\) | 6.61450e6i | 1.54839i | 0.632945 | + | 0.774197i | \(0.281846\pi\) | ||||
−0.632945 | + | 0.774197i | \(0.718154\pi\) | |||||||
\(450\) | 210099. | − | 29981.2i | 0.0489094 | − | 0.00697938i | ||||
\(451\) | −119735. | + | 126517.i | −0.0277190 | + | 0.0292891i | ||||
\(452\) | − | 2.28716e6i | − | 0.526564i | ||||||
\(453\) | −81751.5 | − | 1.15158e6i | −0.0187176 | − | 0.263663i | ||||
\(454\) | −667485. | −0.151985 | ||||||||
\(455\) | − | 2.91758e6i | − | 0.660685i | ||||||
\(456\) | 50098.5 | + | 705706.i | 0.0112827 | + | 0.158932i | ||||
\(457\) | 5.03908e6i | 1.12865i | 0.825551 | + | 0.564327i | \(0.190864\pi\) | ||||
−0.825551 | + | 0.564327i | \(0.809136\pi\) | |||||||
\(458\) | 494970. | 0.110259 | ||||||||
\(459\) | −7.25955e6 | + | 1.56718e6i | −1.60834 | + | 0.347205i | ||||
\(460\) | −1.07886e6 | −0.237722 | ||||||||
\(461\) | 6.76448e6 | 1.48246 | 0.741229 | − | 0.671252i | \(-0.234243\pi\) | ||||
0.741229 | + | 0.671252i | \(0.234243\pi\) | |||||||
\(462\) | 938355. | + | 769725.i | 0.204532 | + | 0.167776i | ||||
\(463\) | −6.63151e6 | −1.43767 | −0.718837 | − | 0.695179i | \(-0.755325\pi\) | ||||
−0.718837 | + | 0.695179i | \(0.755325\pi\) | |||||||
\(464\) | −2.48953e6 | −0.536813 | ||||||||
\(465\) | 140678. | + | 1.98164e6i | 0.0301713 | + | 0.425004i | ||||
\(466\) | −947146. | −0.202047 | ||||||||
\(467\) | − | 1.23427e6i | − | 0.261890i | −0.991390 | − | 0.130945i | \(-0.958199\pi\) | ||
0.991390 | − | 0.130945i | \(-0.0418012\pi\) | |||||||
\(468\) | 867048. | + | 6.07600e6i | 0.182990 | + | 1.28234i | ||||
\(469\) | 650431.i | 0.136543i | ||||||||
\(470\) | 781786. | 0.163246 | ||||||||
\(471\) | −1.12118e6 | + | 79593.3i | −0.232875 | + | 0.0165320i | ||||
\(472\) | 1.65777e6i | 0.342506i | ||||||||
\(473\) | −4.85691e6 | − | 4.59655e6i | −0.998175 | − | 0.944667i | ||||
\(474\) | 78039.7 | + | 1.09930e6i | 0.0159540 | + | 0.224734i | ||||
\(475\) | 327156.i | 0.0665305i | ||||||||
\(476\) | 8.17895e6i | 1.65455i | ||||||||
\(477\) | −947621. | − | 6.64064e6i | −0.190695 | − | 1.33633i | ||||
\(478\) | −718588. | −0.143850 | ||||||||
\(479\) | 1.55344e6 | 0.309354 | 0.154677 | − | 0.987965i | \(-0.450566\pi\) | ||||
0.154677 | + | 0.987965i | \(0.450566\pi\) | |||||||
\(480\) | 108973. | + | 1.53504e6i | 0.0215882 | + | 0.304099i | ||||
\(481\) | 5.92059e6i | 1.16682i | ||||||||
\(482\) | − | 583867.i | − | 0.114471i | ||||||
\(483\) | 3.10048e6 | − | 220105.i | 0.604730 | − | 0.0429301i | ||||
\(484\) | 266350. | + | 4.83182e6i | 0.0516821 | + | 0.937556i | ||||
\(485\) | − | 1.16229e6i | − | 0.224368i | ||||||
\(486\) | 1.20635e6 | − | 446319.i | 0.231676 | − | 0.0857146i | ||||
\(487\) | −6.15081e6 | −1.17519 | −0.587597 | − | 0.809153i | \(-0.699926\pi\) | ||||
−0.587597 | + | 0.809153i | \(0.699926\pi\) | |||||||
\(488\) | − | 1.99204e6i | − | 0.378659i | ||||||
\(489\) | −291546. | + | 20697.0i | −0.0551360 | + | 0.00391414i | ||||
\(490\) | 86227.1i | 0.0162238i | ||||||||
\(491\) | 7.02276e6 | 1.31463 | 0.657316 | − | 0.753615i | \(-0.271692\pi\) | ||||
0.657316 | + | 0.753615i | \(0.271692\pi\) | |||||||
\(492\) | 202798. | − | 14396.8i | 0.0377704 | − | 0.00268134i | ||||
\(493\) | −5.80826e6 | −1.07629 | ||||||||
\(494\) | 614855. | 0.113359 | ||||||||
\(495\) | −1.98969e6 | − | 1.40884e6i | −0.364983 | − | 0.258433i | ||||
\(496\) | −4.28388e6 | −0.781867 | ||||||||
\(497\) | −5.57763e6 | −1.01288 | ||||||||
\(498\) | −1.62568e6 | + | 115408.i | −0.293740 | + | 0.0208527i | ||||
\(499\) | −4.29161e6 | −0.771559 | −0.385780 | − | 0.922591i | \(-0.626067\pi\) | ||||
−0.385780 | + | 0.922591i | \(0.626067\pi\) | |||||||
\(500\) | 469490.i | 0.0839848i | ||||||||
\(501\) | −8.56384e6 | + | 607952.i | −1.52431 | + | 0.108212i | ||||
\(502\) | 767859.i | 0.135995i | ||||||||
\(503\) | −5.99556e6 | −1.05660 | −0.528299 | − | 0.849058i | \(-0.677170\pi\) | ||||
−0.528299 | + | 0.849058i | \(0.677170\pi\) | |||||||
\(504\) | −413230. | − | 2.89579e6i | −0.0724628 | − | 0.507797i | ||||
\(505\) | − | 1.74682e6i | − | 0.304804i | ||||||
\(506\) | −584970. | − | 553612.i | −0.101568 | − | 0.0961234i | ||||
\(507\) | 5.21362e6 | − | 370118.i | 0.900781 | − | 0.0639470i | ||||
\(508\) | − | 6.48340e6i | − | 1.11466i | ||||||
\(509\) | 6.95131e6i | 1.18925i | 0.804004 | + | 0.594624i | \(0.202699\pi\) | ||||
−0.804004 | + | 0.594624i | \(0.797301\pi\) | |||||||
\(510\) | 75606.4 | + | 1.06502e6i | 0.0128716 | + | 0.181314i | ||||
\(511\) | 2.47560e6 | 0.419400 | ||||||||
\(512\) | −5.65000e6 | −0.952518 | ||||||||
\(513\) | 418409. | + | 1.93818e6i | 0.0701953 | + | 0.325162i | ||||
\(514\) | − | 1.16834e6i | − | 0.195057i | ||||||
\(515\) | − | 883669.i | − | 0.146815i | ||||||
\(516\) | 552684. | + | 7.78531e6i | 0.0913803 | + | 1.28722i | ||||
\(517\) | −6.52281e6 | − | 6.17315e6i | −1.07327 | − | 1.01573i | ||||
\(518\) | − | 1.36646e6i | − | 0.223755i | ||||||
\(519\) | 9.38187e6 | − | 666025.i | 1.52887 | − | 0.108536i | ||||
\(520\) | 1.82205e6 | 0.295497 | ||||||||
\(521\) | 204305.i | 0.0329750i | 0.999864 | + | 0.0164875i | \(0.00524837\pi\) | ||||
−0.999864 | + | 0.0164875i | \(0.994752\pi\) | |||||||
\(522\) | 995858. | − | 142109.i | 0.159964 | − | 0.0228269i | ||||
\(523\) | 2.38745e6i | 0.381662i | 0.981623 | + | 0.190831i | \(0.0611183\pi\) | ||||
−0.981623 | + | 0.190831i | \(0.938882\pi\) | |||||||
\(524\) | 1.01356e7 | 1.61258 | ||||||||
\(525\) | −95783.9 | − | 1.34925e6i | −0.0151668 | − | 0.213645i | ||||
\(526\) | −131715. | −0.0207573 | ||||||||
\(527\) | −9.99459e6 | −1.56761 | ||||||||
\(528\) | 3.33415e6 | − | 4.06459e6i | 0.520475 | − | 0.634500i | ||||
\(529\) | 4.37365e6 | 0.679523 | ||||||||
\(530\) | −964351. | −0.149123 | ||||||||
\(531\) | 656357. | + | 4.59954e6i | 0.101019 | + | 0.707911i | ||||
\(532\) | 2.18364e6 | 0.334504 | ||||||||
\(533\) | − | 364863.i | − | 0.0556303i | ||||||
\(534\) | −28834.1 | − | 406168.i | −0.00437575 | − | 0.0616385i | ||||
\(535\) | 4.92181e6i | 0.743431i | ||||||||
\(536\) | −406199. | −0.0610698 | ||||||||
\(537\) | −444789. | − | 6.26546e6i | −0.0665607 | − | 0.937599i | ||||
\(538\) | − | 1.22586e6i | − | 0.182594i | ||||||
\(539\) | 680868. | − | 719434.i | 0.100946 | − | 0.106664i | ||||
\(540\) | 600444. | + | 2.78141e6i | 0.0886111 | + | 0.410469i | ||||
\(541\) | 2.50628e6i | 0.368159i | 0.982911 | + | 0.184080i | \(0.0589304\pi\) | ||||
−0.982911 | + | 0.184080i | \(0.941070\pi\) | |||||||
\(542\) | 2.68958e6i | 0.393266i | ||||||||
\(543\) | 1.25377e7 | − | 890059.i | 1.82481 | − | 0.129545i | ||||
\(544\) | −7.74209e6 | −1.12166 | ||||||||
\(545\) | 759375. | 0.109513 | ||||||||
\(546\) | −2.53577e6 | + | 180016.i | −0.364022 | + | 0.0258421i | ||||
\(547\) | − | 1.27903e7i | − | 1.82773i | −0.406020 | − | 0.913864i | \(-0.633084\pi\) | ||
0.406020 | − | 0.913864i | \(-0.366916\pi\) | |||||||
\(548\) | − | 1.05854e7i | − | 1.50577i | ||||||
\(549\) | −788705. | − | 5.52700e6i | −0.111682 | − | 0.782634i | ||||
\(550\) | −240917. | + | 254563.i | −0.0339595 | + | 0.0358830i | ||||
\(551\) | 1.55071e6i | 0.217596i | ||||||||
\(552\) | 137457. | + | 1.93627e6i | 0.0192008 | + | 0.270470i | ||||
\(553\) | 7.02407e6 | 0.976733 | ||||||||
\(554\) | 2.30617e6i | 0.319239i | ||||||||
\(555\) | 194372. | + | 2.73800e6i | 0.0267856 | + | 0.377312i | ||||
\(556\) | − | 8.63935e6i | − | 1.18521i | ||||||
\(557\) | 741557. | 0.101276 | 0.0506380 | − | 0.998717i | \(-0.483875\pi\) | ||||
0.0506380 | + | 0.998717i | \(0.483875\pi\) | |||||||
\(558\) | 1.71363e6 | − | 244535.i | 0.232987 | − | 0.0332473i | ||||
\(559\) | 1.40069e7 | 1.89589 | ||||||||
\(560\) | 2.91678e6 | 0.393037 | ||||||||
\(561\) | 7.77880e6 | − | 9.48297e6i | 1.04353 | − | 1.27215i | ||||
\(562\) | 2.59587e6 | 0.346691 | ||||||||
\(563\) | 4.67593e6 | 0.621723 | 0.310861 | − | 0.950455i | \(-0.399382\pi\) | ||||
0.310861 | + | 0.950455i | \(0.399382\pi\) | |||||||
\(564\) | 742252. | + | 1.04556e7i | 0.0982548 | + | 1.38405i | ||||
\(565\) | −1.90297e6 | −0.250790 | ||||||||
\(566\) | 1.33426e6i | 0.175065i | ||||||||
\(567\) | −2.29305e6 | − | 7.87087e6i | −0.299540 | − | 1.02817i | ||||
\(568\) | − | 3.48327e6i | − | 0.453019i | ||||||
\(569\) | 6.02363e6 | 0.779970 | 0.389985 | − | 0.920821i | \(-0.372480\pi\) | ||||
0.389985 | + | 0.920821i | \(0.372480\pi\) | |||||||
\(570\) | 284342. | − | 20185.6i | 0.0366567 | − | 0.00260228i | ||||
\(571\) | − | 4.58256e6i | − | 0.588190i | −0.955776 | − | 0.294095i | \(-0.904982\pi\) | ||
0.955776 | − | 0.294095i | \(-0.0950183\pi\) | |||||||
\(572\) | −7.36191e6 | − | 6.96727e6i | −0.940807 | − | 0.890374i | ||||
\(573\) | 242874. | + | 3.42121e6i | 0.0309025 | + | 0.435304i | ||||
\(574\) | 84209.5i | 0.0106680i | ||||||||
\(575\) | 897631.i | 0.113221i | ||||||||
\(576\) | −5.14165e6 | + | 733716.i | −0.645724 | + | 0.0921450i | ||||
\(577\) | 1.48538e7 | 1.85737 | 0.928684 | − | 0.370871i | \(-0.120941\pi\) | ||||
0.928684 | + | 0.370871i | \(0.120941\pi\) | |||||||
\(578\) | −3.38745e6 | −0.421748 | ||||||||
\(579\) | −769716. | − | 1.08425e7i | −0.0954188 | − | 1.34410i | ||||
\(580\) | 2.22536e6i | 0.274682i | ||||||||
\(581\) | 1.03875e7i | 1.27664i | ||||||||
\(582\) | −1.01018e6 | + | 71713.6i | −0.123621 | + | 0.00877595i | ||||
\(583\) | 8.04604e6 | + | 7.61472e6i | 0.980417 | + | 0.927861i | ||||
\(584\) | 1.54603e6i | 0.187580i | ||||||||
\(585\) | 5.05536e6 | − | 721402.i | 0.610749 | − | 0.0871540i | ||||
\(586\) | −328251. | −0.0394877 | ||||||||
\(587\) | − | 1.13235e7i | − | 1.35639i | −0.734880 | − | 0.678197i | \(-0.762762\pi\) | ||
0.734880 | − | 0.678197i | \(-0.237238\pi\) | |||||||
\(588\) | −1.15321e6 | + | 81866.8i | −0.137551 | + | 0.00976482i | ||||
\(589\) | 2.66838e6i | 0.316928i | ||||||||
\(590\) | 667944. | 0.0789969 | ||||||||
\(591\) | 6.06230e6 | − | 430367.i | 0.713952 | − | 0.0506839i | ||||
\(592\) | −5.91896e6 | −0.694131 | ||||||||
\(593\) | 2.42922e6 | 0.283681 | 0.141840 | − | 0.989890i | \(-0.454698\pi\) | ||||
0.141840 | + | 0.989890i | \(0.454698\pi\) | |||||||
\(594\) | −1.10170e6 | + | 1.81623e6i | −0.128114 | + | 0.211205i | ||||
\(595\) | 6.80505e6 | 0.788024 | ||||||||
\(596\) | 2.19657e6 | 0.253297 | ||||||||
\(597\) | 2.50694e6 | − | 177969.i | 0.287877 | − | 0.0204366i | ||||
\(598\) | 1.68700e6 | 0.192913 | ||||||||
\(599\) | 3.45814e6i | 0.393799i | 0.980424 | + | 0.196900i | \(0.0630873\pi\) | ||||
−0.980424 | + | 0.196900i | \(0.936913\pi\) | |||||||
\(600\) | 842615. | − | 59817.7i | 0.0955544 | − | 0.00678347i | ||||
\(601\) | − | 423984.i | − | 0.0478810i | −0.999713 | − | 0.0239405i | \(-0.992379\pi\) | ||
0.999713 | − | 0.0239405i | \(-0.00762123\pi\) | |||||||
\(602\) | −3.23275e6 | −0.363565 | ||||||||
\(603\) | −1.12702e6 | + | 160826.i | −0.126222 | + | 0.0180120i | ||||
\(604\) | − | 2.22530e6i | − | 0.248197i | ||||||
\(605\) | 4.02017e6 | − | 221609.i | 0.446536 | − | 0.0246150i | ||||
\(606\) | −1.51822e6 | + | 107779.i | −0.167940 | + | 0.0119221i | ||||
\(607\) | 6.40194e6i | 0.705245i | 0.935766 | + | 0.352622i | \(0.114710\pi\) | ||||
−0.935766 | + | 0.352622i | \(0.885290\pi\) | |||||||
\(608\) | 2.06701e6i | 0.226768i | ||||||||
\(609\) | −454011. | − | 6.39537e6i | −0.0496048 | − | 0.698751i | ||||
\(610\) | −802629. | −0.0873354 | ||||||||
\(611\) | 1.88112e7 | 2.03851 | ||||||||
\(612\) | −1.41718e7 | + | 2.02233e6i | −1.52949 | + | 0.218259i | ||||
\(613\) | 675340.i | 0.0725891i | 0.999341 | + | 0.0362946i | \(0.0115555\pi\) | ||||
−0.999341 | + | 0.0362946i | \(0.988445\pi\) | |||||||
\(614\) | − | 1.96063e6i | − | 0.209882i | ||||||
\(615\) | −11978.4 | − | 168732.i | −0.00127706 | − | 0.0179891i | ||||
\(616\) | 3.50864e6 | + | 3.32056e6i | 0.372552 | + | 0.352581i | ||||
\(617\) | − | 1.23886e7i | − | 1.31011i | −0.755580 | − | 0.655057i | \(-0.772645\pi\) | ||
0.755580 | − | 0.655057i | \(-0.227355\pi\) | |||||||
\(618\) | −768025. | + | 54522.6i | −0.0808918 | + | 0.00574256i | ||||
\(619\) | −2.48834e6 | −0.261026 | −0.130513 | − | 0.991447i | \(-0.541662\pi\) | ||||
−0.130513 | + | 0.991447i | \(0.541662\pi\) | |||||||
\(620\) | 3.82930e6i | 0.400074i | ||||||||
\(621\) | 1.14801e6 | + | 5.31785e6i | 0.119458 | + | 0.553359i | ||||
\(622\) | 609857.i | 0.0632050i | ||||||||
\(623\) | −2.59525e6 | −0.267892 | ||||||||
\(624\) | 779757. | + | 1.09839e7i | 0.0801674 | + | 1.12927i | ||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | −718155. | −0.0732458 | ||||||||
\(627\) | −2.53179e6 | − | 2.07681e6i | −0.257193 | − | 0.210973i | ||||
\(628\) | −2.16656e6 | −0.219215 | ||||||||
\(629\) | −1.38094e7 | −1.39170 | ||||||||
\(630\) | −1.16676e6 | + | 166498.i | −0.117120 | + | 0.0167131i | ||||
\(631\) | −3.88805e6 | −0.388739 | −0.194369 | − | 0.980928i | \(-0.562266\pi\) | ||||
−0.194369 | + | 0.980928i | \(0.562266\pi\) | |||||||
\(632\) | 4.38658e6i | 0.436851i | ||||||||
\(633\) | −1.39682e6 | − | 1.96761e7i | −0.138558 | − | 1.95178i | ||||
\(634\) | − | 4.50412e6i | − | 0.445027i | ||||||
\(635\) | −5.39432e6 | −0.530888 | ||||||||
\(636\) | −915586. | − | 1.28973e7i | −0.0897545 | − | 1.26432i | ||||
\(637\) | 2.07478e6i | 0.202593i | ||||||||
\(638\) | −1.14194e6 | + | 1.20662e6i | −0.111068 | + | 0.117360i | ||||
\(639\) | −1.37912e6 | − | 9.66448e6i | −0.133614 | − | 0.936324i | ||||
\(640\) | 3.90572e6i | 0.376922i | ||||||||
\(641\) | 1.83757e7i | 1.76644i | 0.468963 | + | 0.883218i | \(0.344628\pi\) | ||||
−0.468963 | + | 0.883218i | \(0.655372\pi\) | |||||||
\(642\) | 4.27771e6 | − | 303677.i | 0.409613 | − | 0.0290787i | ||||
\(643\) | −1.32875e7 | −1.26740 | −0.633702 | − | 0.773577i | \(-0.718466\pi\) | ||||
−0.633702 | + | 0.773577i | \(0.718466\pi\) | |||||||
\(644\) | 5.99134e6 | 0.569258 | ||||||||
\(645\) | 6.47754e6 | − | 459844.i | 0.613071 | − | 0.0435223i | ||||
\(646\) | 1.43410e6i | 0.135207i | ||||||||
\(647\) | − | 94897.1i | − | 0.00891235i | −0.999990 | − | 0.00445618i | \(-0.998582\pi\) | ||
0.999990 | − | 0.00445618i | \(-0.00141845\pi\) | |||||||
\(648\) | 4.91541e6 | − | 1.43202e6i | 0.459857 | − | 0.133972i | ||||
\(649\) | −5.57298e6 | − | 5.27423e6i | −0.519368 | − | 0.491527i | ||||
\(650\) | − | 734138.i | − | 0.0681545i | ||||||
\(651\) | −781242. | − | 1.10049e7i | −0.0722492 | − | 1.01773i | ||||
\(652\) | −563380. | −0.0519018 | ||||||||
\(653\) | − | 1.28910e7i | − | 1.18305i | −0.806285 | − | 0.591527i | \(-0.798525\pi\) | ||
0.806285 | − | 0.591527i | \(-0.201475\pi\) | |||||||
\(654\) | −46853.6 | − | 659997.i | −0.00428350 | − | 0.0603389i | ||||
\(655\) | − | 8.43305e6i | − | 0.768035i | ||||||
\(656\) | 364762. | 0.0330941 | ||||||||
\(657\) | 612117. | + | 4.28953e6i | 0.0553249 | + | 0.387700i | ||||
\(658\) | −4.34158e6 | −0.390916 | ||||||||
\(659\) | −8.08015e6 | −0.724780 | −0.362390 | − | 0.932027i | \(-0.618039\pi\) | ||||
−0.362390 | + | 0.932027i | \(0.618039\pi\) | |||||||
\(660\) | −3.63328e6 | − | 2.98035e6i | −0.324667 | − | 0.266322i | ||||
\(661\) | −1.49581e6 | −0.133160 | −0.0665799 | − | 0.997781i | \(-0.521209\pi\) | ||||
−0.0665799 | + | 0.997781i | \(0.521209\pi\) | |||||||
\(662\) | 2.17588e6 | 0.192970 | ||||||||
\(663\) | 1.81923e6 | + | 2.56263e7i | 0.160732 | + | 2.26414i | ||||
\(664\) | −6.48705e6 | −0.570988 | ||||||||
\(665\) | − | 1.81683e6i | − | 0.159317i | ||||||
\(666\) | 2.36769e6 | − | 337870.i | 0.206842 | − | 0.0295165i | ||||
\(667\) | 4.25473e6i | 0.370303i | ||||||||
\(668\) | −1.65487e7 | −1.43490 | ||||||||
\(669\) | 2.28473e7 | − | 1.62194e6i | 1.97364 | − | 0.140110i | ||||
\(670\) | 163665.i | 0.0140854i | ||||||||
\(671\) | 6.69672e6 | + | 6.33773e6i | 0.574190 | + | 0.543410i | ||||
\(672\) | −605172. | − | 8.52468e6i | −0.0516959 | − | 0.728207i | ||||
\(673\) | 5.41721e6i | 0.461040i | 0.973068 | + | 0.230520i | \(0.0740427\pi\) | ||||
−0.973068 | + | 0.230520i | \(0.925957\pi\) | |||||||
\(674\) | 2.04468e6i | 0.173371i | ||||||||
\(675\) | 2.31419e6 | − | 499582.i | 0.195496 | − | 0.0422034i | ||||
\(676\) | 1.00747e7 | 0.847943 | ||||||||
\(677\) | 1.02950e7 | 0.863283 | 0.431642 | − | 0.902045i | \(-0.357935\pi\) | ||||
0.431642 | + | 0.902045i | \(0.357935\pi\) | |||||||
\(678\) | 117413. | + | 1.65393e6i | 0.00980943 | + | 0.138179i | ||||
\(679\) | 6.45468e6i | 0.537280i | ||||||||
\(680\) | 4.24981e6i | 0.352449i | ||||||||
\(681\) | −7.42743e6 | + | 527278.i | −0.613721 | + | 0.0435684i | ||||
\(682\) | −1.96499e6 | + | 2.07630e6i | −0.161771 | + | 0.170934i | ||||
\(683\) | − | 2.35514e7i | − | 1.93182i | −0.258887 | − | 0.965908i | \(-0.583356\pi\) | ||
0.258887 | − | 0.965908i | \(-0.416644\pi\) | |||||||
\(684\) | 539927. | + | 3.78364e6i | 0.0441260 | + | 0.309221i | ||||
\(685\) | −8.80731e6 | −0.717161 | ||||||||
\(686\) | 2.78180e6i | 0.225692i | ||||||||
\(687\) | 5.50778e6 | − | 391000.i | 0.445230 | − | 0.0316071i | ||||
\(688\) | 1.40030e7i | 1.12785i | ||||||||
\(689\) | −2.32041e7 | −1.86216 | ||||||||
\(690\) | 780160. | − | 55384.0i | 0.0623822 | − | 0.00442855i | ||||
\(691\) | −8.87036e6 | −0.706718 | −0.353359 | − | 0.935488i | \(-0.614961\pi\) | ||||
−0.353359 | + | 0.935488i | \(0.614961\pi\) | |||||||
\(692\) | 1.81294e7 | 1.43919 | ||||||||
\(693\) | 1.10496e7 | + | 7.82385e6i | 0.874002 | + | 0.618853i | ||||
\(694\) | −410192. | −0.0323287 | ||||||||
\(695\) | −7.18812e6 | −0.564486 | ||||||||
\(696\) | 3.99396e6 | − | 283533.i | 0.312522 | − | 0.0221861i | ||||
\(697\) | 851017. | 0.0663523 | ||||||||
\(698\) | 637117.i | 0.0494972i | ||||||||
\(699\) | −1.05394e7 | + | 748195.i | −0.815871 | + | 0.0579191i | ||||
\(700\) | − | 2.60727e6i | − | 0.201113i | ||||||
\(701\) | 2.46502e7 | 1.89463 | 0.947317 | − | 0.320297i | \(-0.103783\pi\) | ||||
0.947317 | + | 0.320297i | \(0.103783\pi\) | |||||||
\(702\) | −938910. | − | 4.34927e6i | −0.0719087 | − | 0.333099i | ||||
\(703\) | 3.68686e6i | 0.281364i | ||||||||
\(704\) | 5.89586e6 | − | 6.22982e6i | 0.448348 | − | 0.473744i | ||||
\(705\) | 8.69931e6 | − | 617569.i | 0.659192 | − | 0.0467964i | ||||
\(706\) | 4.34016e6i | 0.327713i | ||||||||
\(707\) | 9.70082e6i | 0.729895i | ||||||||
\(708\) | 634168. | + | 8.93312e6i | 0.0475468 | + | 0.669762i | ||||
\(709\) | −2.60825e7 | −1.94865 | −0.974326 | − | 0.225141i | \(-0.927716\pi\) | ||||
−0.974326 | + | 0.225141i | \(0.927716\pi\) | |||||||
\(710\) | −1.40347e6 | −0.104486 | ||||||||
\(711\) | 1.73677e6 | + | 1.21708e7i | 0.128845 | + | 0.902908i | ||||
\(712\) | − | 1.62075e6i | − | 0.119817i | ||||||
\(713\) | 7.32135e6i | 0.539346i | ||||||||
\(714\) | −419873. | − | 5.91449e6i | −0.0308229 | − | 0.434182i | ||||
\(715\) | −5.79691e6 | + | 6.12526e6i | −0.424064 | + | 0.448084i | ||||
\(716\) | − | 1.21073e7i | − | 0.882602i | ||||||
\(717\) | −7.99608e6 | + | 567647.i | −0.580871 | + | 0.0412364i | ||||
\(718\) | 5.31111e6 | 0.384480 | ||||||||
\(719\) | − | 1.34835e7i | − | 0.972700i | −0.873764 | − | 0.486350i | \(-0.838328\pi\) | ||
0.873764 | − | 0.486350i | \(-0.161672\pi\) | |||||||
\(720\) | 721203. | + | 5.05397e6i | 0.0518473 | + | 0.363330i | ||||
\(721\) | 4.90738e6i | 0.351570i | ||||||||
\(722\) | −3.07717e6 | −0.219689 | ||||||||
\(723\) | −461224. | − | 6.49697e6i | −0.0328145 | − | 0.462238i | ||||
\(724\) | 2.42277e7 | 1.71777 | ||||||||
\(725\) | 1.85155e6 | 0.130825 | ||||||||
\(726\) | −440653. | − | 3.48039e6i | −0.0310281 | − | 0.245068i | ||||
\(727\) | −1.07470e7 | −0.754135 | −0.377068 | − | 0.926186i | \(-0.623068\pi\) | ||||
−0.377068 | + | 0.926186i | \(0.623068\pi\) | |||||||
\(728\) | −1.01186e7 | −0.707607 | ||||||||
\(729\) | 1.30710e7 | − | 5.91936e6i | 0.910944 | − | 0.412531i | ||||
\(730\) | 622924. | 0.0432641 | ||||||||
\(731\) | 3.26701e7i | 2.26129i | ||||||||
\(732\) | −762042. | − | 1.07344e7i | −0.0525655 | − | 0.740458i | ||||
\(733\) | 1.57510e6i | 0.108280i | 0.998533 | + | 0.0541399i | \(0.0172417\pi\) | ||||
−0.998533 | + | 0.0541399i | \(0.982758\pi\) | |||||||
\(734\) | −2.62286e6 | −0.179695 | ||||||||
\(735\) | 68114.9 | + | 959491.i | 0.00465076 | + | 0.0655123i | ||||
\(736\) | 5.67133e6i | 0.385914i | ||||||||
\(737\) | 1.29233e6 | − | 1.36553e6i | 0.0876407 | − | 0.0926048i | ||||
\(738\) | −145912. | + | 20821.6i | −0.00986163 | + | 0.00140726i | ||||
\(739\) | − | 9.91755e6i | − | 0.668026i | −0.942568 | − | 0.334013i | \(-0.891597\pi\) | ||
0.942568 | − | 0.334013i | \(-0.108403\pi\) | |||||||
\(740\) | 5.29088e6i | 0.355180i | ||||||||
\(741\) | 6.84179e6 | − | 485703.i | 0.457746 | − | 0.0324956i | ||||
\(742\) | 5.35544e6 | 0.357096 | ||||||||
\(743\) | −1.35817e7 | −0.902571 | −0.451286 | − | 0.892380i | \(-0.649034\pi\) | ||||
−0.451286 | + | 0.892380i | \(0.649034\pi\) | |||||||
\(744\) | 6.87262e6 | − | 487891.i | 0.455187 | − | 0.0323140i | ||||
\(745\) | − | 1.82759e6i | − | 0.120639i | ||||||
\(746\) | 5.76973e6i | 0.379584i | ||||||||
\(747\) | −1.79986e7 | + | 2.56841e6i | −1.18015 | + | 0.168408i | ||||
\(748\) | 1.62507e7 | − | 1.71711e7i | 1.06198 | − | 1.12213i | ||||
\(749\) | − | 2.73329e7i | − | 1.78025i | ||||||
\(750\) | −24101.7 | − | 339505.i | −0.00156457 | − | 0.0220390i | ||||
\(751\) | −2.10798e7 | −1.36385 | −0.681924 | − | 0.731423i | \(-0.738856\pi\) | ||||
−0.681924 | + | 0.731423i | \(0.738856\pi\) | |||||||
\(752\) | 1.88060e7i | 1.21270i | ||||||||
\(753\) | 606568. | + | 8.54434e6i | 0.0389845 | + | 0.549150i | ||||
\(754\) | − | 3.47978e6i | − | 0.222907i | ||||||
\(755\) | −1.85150e6 | −0.118211 | ||||||||
\(756\) | −3.33451e6 | − | 1.54463e7i | −0.212191 | − | 0.982924i | ||||
\(757\) | −1.95414e7 | −1.23941 | −0.619706 | − | 0.784834i | \(-0.712748\pi\) | ||||
−0.619706 | + | 0.784834i | \(0.712748\pi\) | |||||||
\(758\) | 3.40802e6 | 0.215441 | ||||||||
\(759\) | −6.94657e6 | − | 5.69822e6i | −0.437689 | − | 0.359033i | ||||
\(760\) | 1.13463e6 | 0.0712555 | ||||||||
\(761\) | 1.73938e7 | 1.08876 | 0.544380 | − | 0.838839i | \(-0.316765\pi\) | ||||
0.544380 | + | 0.838839i | \(0.316765\pi\) | |||||||
\(762\) | 332831. | + | 4.68838e6i | 0.0207652 | + | 0.292506i | ||||
\(763\) | −4.21712e6 | −0.262244 | ||||||||
\(764\) | 6.61110e6i | 0.409770i | ||||||||
\(765\) | 1.68262e6 | + | 1.17913e7i | 0.103952 | + | 0.728462i | ||||
\(766\) | − | 6.73189e6i | − | 0.414538i | ||||||
\(767\) | 1.60720e7 | 0.986463 | ||||||||
\(768\) | −7.24036e6 | + | 513998.i | −0.442953 | + | 0.0314455i | ||||
\(769\) | 7.80032e6i | 0.475660i | 0.971307 | + | 0.237830i | \(0.0764361\pi\) | ||||
−0.971307 | + | 0.237830i | \(0.923564\pi\) | |||||||
\(770\) | 1.33791e6 | − | 1.41370e6i | 0.0813207 | − | 0.0859269i | ||||
\(771\) | −922925. | − | 1.30007e7i | −0.0559153 | − | 0.787643i | ||||
\(772\) | − | 2.09519e7i | − | 1.26526i | ||||||
\(773\) | − | 2.80638e7i | − | 1.68927i | −0.535346 | − | 0.844633i | \(-0.679819\pi\) | ||
0.535346 | − | 0.844633i | \(-0.320181\pi\) | |||||||
\(774\) | −799331. | − | 5.60146e6i | −0.0479595 | − | 0.336085i | ||||
\(775\) | 3.18606e6 | 0.190546 | ||||||||
\(776\) | −4.03099e6 | −0.240302 | ||||||||
\(777\) | −1.07943e6 | − | 1.52052e7i | −0.0641419 | − | 0.903527i | ||||
\(778\) | 7.72719e6i | 0.457691i | ||||||||
\(779\) | − | 227207.i | − | 0.0134146i | ||||||
\(780\) | 9.81840e6 | − | 697014.i | 0.577835 | − | 0.0410209i | ||||
\(781\) | 1.17098e7 | + | 1.10821e7i | 0.686947 | + | 0.650122i | ||||
\(782\) | 3.93481e6i | 0.230095i | ||||||||
\(783\) | 1.09691e7 | − | 2.36800e6i | 0.639394 | − | 0.138031i | ||||
\(784\) | −2.07421e6 | −0.120521 | ||||||||
\(785\) | 1.80262e6i | 0.104407i | ||||||||
\(786\) | −7.32943e6 | + | 520321.i | −0.423169 | + | 0.0300410i | ||||
\(787\) | 2.41883e7i | 1.39209i | 0.717996 | + | 0.696047i | \(0.245059\pi\) | ||||
−0.717996 | + | 0.696047i | \(0.754941\pi\) | |||||||
\(788\) | 1.17147e7 | 0.672073 | ||||||||
\(789\) | −1.46566e6 | + | 104048.i | −0.0838186 | + | 0.00595033i | ||||
\(790\) | 1.76743e6 | 0.100757 | ||||||||
\(791\) | 1.05680e7 | 0.600551 | ||||||||
\(792\) | −4.88605e6 | + | 6.90054e6i | −0.276787 | + | 0.390904i | ||||
\(793\) | −1.93127e7 | −1.09059 | ||||||||
\(794\) | −3.43169e6 | −0.193177 | ||||||||
\(795\) | −1.07308e7 | + | 761787.i | −0.602164 | + | 0.0427480i | ||||
\(796\) | 4.84437e6 | 0.270991 | ||||||||
\(797\) | 3.01945e7i | 1.68377i | 0.539659 | + | 0.841884i | \(0.318553\pi\) | ||||
−0.539659 | + | 0.841884i | \(0.681447\pi\) | |||||||
\(798\) | −1.57907e6 | + | 112099.i | −0.0877796 | + | 0.00623153i | ||||
\(799\) | 4.38758e7i | 2.43141i | ||||||||
\(800\) | 2.46801e6 | 0.136340 | ||||||||
\(801\) | −641702. | − | 4.49685e6i | −0.0353388 | − | 0.247643i | ||||
\(802\) | − | 4.51647e6i | − | 0.247949i | ||||||
\(803\) | −5.19735e6 | − | 4.91874e6i | −0.284441 | − | 0.269194i | ||||
\(804\) | −2.18886e6 | + | 155389.i | −0.119420 | + | 0.00847772i | ||||
\(805\) | − | 4.98492e6i | − | 0.271124i | ||||||
\(806\) | − | 5.98785e6i | − | 0.324663i | ||||||
\(807\) | −968366. | − | 1.36408e7i | −0.0523427 | − | 0.737318i | ||||
\(808\) | −6.05823e6 | −0.326451 | ||||||||
\(809\) | −2.41414e7 | −1.29685 | −0.648427 | − | 0.761277i | \(-0.724573\pi\) | ||||
−0.648427 | + | 0.761277i | \(0.724573\pi\) | |||||||
\(810\) | −576988. | − | 1.98051e6i | −0.0308997 | − | 0.106063i | ||||
\(811\) | 2.59455e7i | 1.38519i | 0.721326 | + | 0.692596i | \(0.243533\pi\) | ||||
−0.721326 | + | 0.692596i | \(0.756467\pi\) | |||||||
\(812\) | − | 1.23583e7i | − | 0.657764i | ||||||
\(813\) | 2.12463e6 | + | 2.99283e7i | 0.112734 | + | 1.58802i | ||||
\(814\) | −2.71500e6 | + | 2.86878e6i | −0.143618 | + | 0.151753i | ||||
\(815\) | 468744.i | 0.0247196i | ||||||||
\(816\) | −2.56193e7 | + | 1.81873e6i | −1.34692 | + | 0.0956186i | ||||
\(817\) | 8.72234e6 | 0.457170 | ||||||||
\(818\) | 5.69911e6i | 0.297799i | ||||||||
\(819\) | −2.80745e7 | + | 4.00624e6i | −1.46252 | + | 0.208702i | ||||
\(820\) | − | 326056.i | − | 0.0169339i | ||||||
\(821\) | −1.80459e7 | −0.934375 | −0.467188 | − | 0.884158i | \(-0.654733\pi\) | ||||
−0.467188 | + | 0.884158i | \(0.654733\pi\) | |||||||
\(822\) | 543413. | + | 7.65472e6i | 0.0280511 | + | 0.395139i | ||||
\(823\) | −1.21944e7 | −0.627568 | −0.313784 | − | 0.949494i | \(-0.601597\pi\) | ||||
−0.313784 | + | 0.949494i | \(0.601597\pi\) | |||||||
\(824\) | −3.06469e6 | −0.157242 | ||||||||
\(825\) | −2.47971e6 | + | 3.02296e6i | −0.126843 | + | 0.154631i | ||||
\(826\) | −3.70937e6 | −0.189169 | ||||||||
\(827\) | −1.17300e7 | −0.596396 | −0.298198 | − | 0.954504i | \(-0.596386\pi\) | ||||
−0.298198 | + | 0.954504i | \(0.596386\pi\) | |||||||
\(828\) | 1.48142e6 | + | 1.03813e7i | 0.0750934 | + | 0.526231i | ||||
\(829\) | −1.10261e7 | −0.557231 | −0.278616 | − | 0.960403i | \(-0.589876\pi\) | ||||
−0.278616 | + | 0.960403i | \(0.589876\pi\) | |||||||
\(830\) | 2.61375e6i | 0.131695i | ||||||||
\(831\) | 1.82175e6 | + | 2.56618e7i | 0.0915137 | + | 1.28910i | ||||
\(832\) | 1.79662e7i | 0.899806i | ||||||||
\(833\) | −4.83928e6 | −0.241640 | ||||||||
\(834\) | 443508. | + | 6.24743e6i | 0.0220794 | + | 0.311018i | ||||
\(835\) | 1.37688e7i | 0.683409i | ||||||||
\(836\) | −4.58440e6 | − | 4.33864e6i | −0.226864 | − | 0.214703i | ||||
\(837\) | 1.88752e7 | − | 4.07474e6i | 0.931275 | − | 0.201042i | ||||
\(838\) | 5.70135e6i | 0.280458i | ||||||||
\(839\) | − | 1.88733e7i | − | 0.925641i | −0.886452 | − | 0.462821i | \(-0.846837\pi\) | ||
0.886452 | − | 0.462821i | \(-0.153163\pi\) | |||||||
\(840\) | −4.67939e6 | + | 332193.i | −0.228818 | + | 0.0162440i | ||||
\(841\) | −1.17349e7 | −0.572123 | ||||||||
\(842\) | 4.09391e6 | 0.199002 | ||||||||
\(843\) | 2.88855e7 | − | 2.05060e6i | 1.39995 | − | 0.0993831i | ||||
\(844\) | − | 3.80219e7i | − | 1.83729i | ||||||
\(845\) | − | 8.38238e6i | − | 0.403855i | ||||||
\(846\) | −1.07350e6 | − | 7.52275e6i | −0.0515675 | − | 0.361369i | ||||
\(847\) | −2.23257e7 | + | 1.23069e6i | −1.06929 | + | 0.0589439i | ||||
\(848\) | − | 2.31977e7i | − | 1.10778i | ||||||
\(849\) | 1.05400e6 | + | 1.48470e7i | 0.0501845 | + | 0.706918i | ||||
\(850\) | 1.71232e6 | 0.0812903 | ||||||||
\(851\) | 1.01158e7i | 0.478824i | ||||||||
\(852\) | −1.33250e6 | − | 1.87701e7i | −0.0628881 | − | 0.885866i | ||||
\(853\) | − | 1.21410e7i | − | 0.571324i | −0.958330 | − | 0.285662i | \(-0.907786\pi\) | ||
0.958330 | − | 0.285662i | \(-0.0922135\pi\) | |||||||
\(854\) | 4.45733e6 | 0.209137 | ||||||||
\(855\) | 3.14807e6 | − | 449230.i | 0.147275 | − | 0.0210162i | ||||
\(856\) | 1.70696e7 | 0.796230 | ||||||||
\(857\) | 1.39003e7 | 0.646504 | 0.323252 | − | 0.946313i | \(-0.395224\pi\) | ||||
0.323252 | + | 0.946313i | \(0.395224\pi\) | |||||||
\(858\) | 5.68133e6 | + | 4.66035e6i | 0.263470 | + | 0.216123i | ||||
\(859\) | 3.57507e6 | 0.165311 | 0.0826555 | − | 0.996578i | \(-0.473660\pi\) | ||||
0.0826555 | + | 0.996578i | \(0.473660\pi\) | |||||||
\(860\) | 1.25171e7 | 0.577109 | ||||||||
\(861\) | 66521.0 | + | 937040.i | 0.00305809 | + | 0.0430775i | ||||
\(862\) | −2.45435e6 | −0.112504 | ||||||||
\(863\) | 1.01838e7i | 0.465458i | 0.972542 | + | 0.232729i | \(0.0747656\pi\) | ||||
−0.972542 | + | 0.232729i | \(0.925234\pi\) | |||||||
\(864\) | 1.46213e7 | − | 3.15641e6i | 0.666347 | − | 0.143850i | ||||
\(865\) | − | 1.50840e7i | − | 0.685453i | ||||||
\(866\) | −6.99438e6 | −0.316923 | ||||||||
\(867\) | −3.76938e7 | + | 2.67590e6i | −1.70303 | + | 0.120899i | ||||
\(868\) | − | 2.12657e7i | − | 0.958032i | ||||||
\(869\) | −1.47465e7 | − | 1.39560e7i | −0.662431 | − | 0.626920i | ||||
\(870\) | −114241. | − | 1.60924e6i | −0.00511709 | − | 0.0720812i | ||||
\(871\) | 3.93808e6i | 0.175889i | ||||||||
\(872\) | − | 2.63362e6i | − | 0.117290i | ||||||
\(873\) | −1.11842e7 | + | 1.59598e6i | −0.496670 | + | 0.0708750i | ||||
\(874\) | 1.05053e6 | 0.0465188 | ||||||||
\(875\) | −2.16930e6 | −0.0957855 | ||||||||
\(876\) | 591424. | + | 8.33101e6i | 0.0260398 | + | 0.366807i | ||||
\(877\) | 3.85273e7i | 1.69149i | 0.533585 | + | 0.845746i | \(0.320844\pi\) | ||||
−0.533585 | + | 0.845746i | \(0.679156\pi\) | |||||||
\(878\) | − | 9.80389e6i | − | 0.429203i | ||||||
\(879\) | −3.65261e6 | + | 259301.i | −0.159452 | + | 0.0113196i | ||||
\(880\) | −6.12357e6 | − | 5.79531e6i | −0.266562 | − | 0.252273i | ||||
\(881\) | 9.15303e6i | 0.397306i | 0.980070 | + | 0.198653i | \(0.0636567\pi\) | ||||
−0.980070 | + | 0.198653i | \(0.936343\pi\) | |||||||
\(882\) | 829722. | − | 118402.i | 0.0359138 | − | 0.00512491i | ||||
\(883\) | 4.56227e6 | 0.196915 | 0.0984575 | − | 0.995141i | \(-0.468609\pi\) | ||||
0.0984575 | + | 0.995141i | \(0.468609\pi\) | |||||||
\(884\) | 4.95200e7i | 2.13133i | ||||||||
\(885\) | 7.43254e6 | − | 527641.i | 0.318992 | − | 0.0226454i | ||||
\(886\) | − | 9.12493e6i | − | 0.390522i | ||||||
\(887\) | 2.66298e7 | 1.13647 | 0.568236 | − | 0.822866i | \(-0.307626\pi\) | ||||
0.568236 | + | 0.822866i | \(0.307626\pi\) | |||||||
\(888\) | 9.49579e6 | − | 674112.i | 0.404109 | − | 0.0286879i | ||||
\(889\) | 2.99569e7 | 1.27128 | ||||||||
\(890\) | −653031. | −0.0276350 | ||||||||
\(891\) | −1.08244e7 | + | 2.10804e7i | −0.456784 | + | 0.889577i | ||||
\(892\) | 4.41498e7 | 1.85787 | ||||||||
\(893\) | 1.17141e7 | 0.491563 | ||||||||
\(894\) | −1.58842e6 | + | 112763.i | −0.0664694 | + | 0.00471870i | ||||
\(895\) | −1.00735e7 | −0.420362 | ||||||||
\(896\) | − | 2.16901e7i | − | 0.902591i | ||||||
\(897\) | 1.87721e7 | − | 1.33264e6i | 0.778989 | − | 0.0553009i | ||||
\(898\) | − | 9.24297e6i | − | 0.382490i | ||||||
\(899\) | 1.51018e7 | 0.623202 | ||||||||
\(900\) | 4.51767e6 | − | 644674.i | 0.185912 | − | 0.0265298i | ||||
\(901\) | − | 5.41218e7i | − | 2.22106i | ||||||
\(902\) | 167315. | − | 176792.i | 0.00684727 | − | 0.00723512i | ||||
\(903\) | −3.59724e7 | + | 2.55371e6i | −1.46808 | + | 0.104220i | ||||
\(904\) | 6.59977e6i | 0.268601i | ||||||||
\(905\) | − | 2.01580e7i | − | 0.818135i | ||||||
\(906\) | 114238. | + | 1.60920e6i | 0.00462370 | + | 0.0651312i | ||||
\(907\) | 4.08806e7 | 1.65006 | 0.825029 | − | 0.565091i | \(-0.191159\pi\) | ||||
0.825029 | + | 0.565091i | \(0.191159\pi\) | |||||||
\(908\) | −1.43527e7 | −0.577721 | ||||||||
\(909\) | −1.68088e7 | + | 2.39863e6i | −0.674726 | + | 0.0962837i | ||||
\(910\) | 4.07697e6i | 0.163205i | ||||||||
\(911\) | 1.44844e7i | 0.578237i | 0.957293 | + | 0.289118i | \(0.0933621\pi\) | ||||
−0.957293 | + | 0.289118i | \(0.906638\pi\) | |||||||
\(912\) | 485569. | + | 6.83990e6i | 0.0193314 | + | 0.272310i | ||||
\(913\) | 2.06387e7 | − | 2.18078e7i | 0.819419 | − | 0.865833i | ||||
\(914\) | − | 7.04151e6i | − | 0.278805i | ||||||
\(915\) | −8.93125e6 | + | 634035.i | −0.352663 | + | 0.0250357i | ||||
\(916\) | 1.06432e7 | 0.419114 | ||||||||
\(917\) | 4.68322e7i | 1.83917i | ||||||||
\(918\) | 1.01444e7 | − | 2.18994e6i | 0.397299 | − | 0.0857681i | ||||
\(919\) | − | 2.32892e7i | − | 0.909634i | −0.890585 | − | 0.454817i | \(-0.849705\pi\) | ||
0.890585 | − | 0.454817i | \(-0.150295\pi\) | |||||||
\(920\) | 3.11312e6 | 0.121262 | ||||||||
\(921\) | −1.54879e6 | − | 2.18169e7i | −0.0601651 | − | 0.847508i | ||||
\(922\) | −9.45255e6 | −0.366203 | ||||||||
\(923\) | −3.37701e7 | −1.30475 | ||||||||
\(924\) | 2.01771e7 | + | 1.65511e7i | 0.777461 | + | 0.637745i | ||||
\(925\) | 4.40212e6 | 0.169164 | ||||||||
\(926\) | 9.26674e6 | 0.355140 | ||||||||
\(927\) | −8.50312e6 | + | 1.21340e6i | −0.324997 | + | 0.0463772i | ||||
\(928\) | 1.16983e7 | 0.445914 | ||||||||
\(929\) | 3.26942e6i | 0.124289i | 0.998067 | + | 0.0621443i | \(0.0197939\pi\) | ||||
−0.998067 | + | 0.0621443i | \(0.980206\pi\) | |||||||
\(930\) | −196580. | − | 2.76910e6i | −0.00745303 | − | 0.104986i | ||||
\(931\) | 1.29201e6i | 0.0488529i | ||||||||
\(932\) | −2.03661e7 | −0.768013 | ||||||||
\(933\) | 481754. | + | 6.78617e6i | 0.0181185 | + | 0.255224i | ||||
\(934\) | 1.72475e6i | 0.0646933i | ||||||||
\(935\) | −1.42867e7 | − | 1.35209e7i | −0.534446 | − | 0.505797i | ||||
\(936\) | −2.50193e6 | − | 1.75327e7i | −0.0933437 | − | 0.654124i | ||||
\(937\) | − | 4.66482e7i | − | 1.73574i | −0.496787 | − | 0.867872i | \(-0.665487\pi\) | ||
0.496787 | − | 0.867872i | \(-0.334513\pi\) | |||||||
\(938\) | − | 908899.i | − | 0.0337294i | ||||||
\(939\) | −7.99127e6 | + | 567305.i | −0.295768 | + | 0.0209968i | ||||
\(940\) | 1.68104e7 | 0.620525 | ||||||||
\(941\) | −5.01997e6 | −0.184811 | −0.0924054 | − | 0.995721i | \(-0.529456\pi\) | ||||
−0.0924054 | + | 0.995721i | \(0.529456\pi\) | |||||||
\(942\) | 1.56672e6 | − | 111222.i | 0.0575258 | − | 0.00408379i | ||||
\(943\) | − | 623396.i | − | 0.0228289i | ||||||
\(944\) | 1.60675e7i | 0.586840i | ||||||||
\(945\) | −1.28516e7 | + | 2.77438e6i | −0.468143 | + | 0.101062i | ||||
\(946\) | 6.78694e6 | + | 6.42312e6i | 0.246573 | + | 0.233356i | ||||
\(947\) | − | 1.94472e6i | − | 0.0704663i | −0.999379 | − | 0.0352332i | \(-0.988783\pi\) | ||
0.999379 | − | 0.0352332i | \(-0.0112174\pi\) | |||||||
\(948\) | 1.67806e6 | + | 2.36377e7i | 0.0606438 | + | 0.854250i | ||||
\(949\) | 1.49887e7 | 0.540254 | ||||||||
\(950\) | − | 457161.i | − | 0.0164346i | ||||||
\(951\) | −3.55801e6 | − | 5.01195e7i | −0.127572 | − | 1.79703i | ||||
\(952\) | − | 2.36009e7i | − | 0.843989i | ||||||
\(953\) | −3.60789e7 | −1.28683 | −0.643415 | − | 0.765517i | \(-0.722483\pi\) | ||||
−0.643415 | + | 0.765517i | \(0.722483\pi\) | |||||||
\(954\) | 1.32419e6 | + | 9.27949e6i | 0.0471062 | + | 0.330106i | ||||
\(955\) | 5.50057e6 | 0.195164 | ||||||||
\(956\) | −1.54515e7 | −0.546798 | ||||||||
\(957\) | −1.17537e7 | + | 1.43287e7i | −0.414854 | + | 0.505740i | ||||
\(958\) | −2.17075e6 | −0.0764180 | ||||||||
\(959\) | 4.89106e7 | 1.71734 | ||||||||
\(960\) | 589829. | + | 8.30856e6i | 0.0206561 | + | 0.290970i | ||||
\(961\) | −2.64271e6 | −0.0923085 | ||||||||
\(962\) | − | 8.27331e6i | − | 0.288232i | ||||||
\(963\) | 4.73603e7 | − | 6.75833e6i | 1.64569 | − | 0.234841i | ||||
\(964\) | − | 1.25547e7i | − | 0.435124i | ||||||
\(965\) | −1.74324e7 | −0.602615 | ||||||||
\(966\) | −4.33255e6 | + | 307570.i | −0.149383 | + | 0.0106048i | ||||
\(967\) | − | 2.09471e7i | − | 0.720372i | −0.932880 | − | 0.360186i | \(-0.882713\pi\) | ||
0.932880 | − | 0.360186i | \(-0.117287\pi\) | |||||||
\(968\) | −768573. | − | 1.39425e7i | −0.0263631 | − | 0.478249i | ||||
\(969\) | 1.13287e6 | + | 1.59580e7i | 0.0387587 | + | 0.545970i | ||||
\(970\) | 1.62416e6i | 0.0554243i | ||||||||
\(971\) | − | 2.80807e7i | − | 0.955785i | −0.878418 | − | 0.477893i | \(-0.841401\pi\) | ||
0.878418 | − | 0.477893i | \(-0.158599\pi\) | |||||||
\(972\) | 2.59396e7 | − | 9.59703e6i | 0.880640 | − | 0.325815i | ||||
\(973\) | 3.99186e7 | 1.35174 | ||||||||
\(974\) | 8.59502e6 | 0.290301 | ||||||||
\(975\) | −579930. | − | 8.16911e6i | −0.0195373 | − | 0.275209i | ||||
\(976\) | − | 1.93074e7i | − | 0.648783i | ||||||
\(977\) | 4.09204e7i | 1.37153i | 0.727825 | + | 0.685763i | \(0.240531\pi\) | ||||
−0.727825 | + | 0.685763i | \(0.759469\pi\) | |||||||
\(978\) | 407401. | − | 28921.6i | 0.0136199 | − | 0.000966887i | ||||
\(979\) | 5.44855e6 | + | 5.15647e6i | 0.181687 | + | 0.171948i | ||||
\(980\) | 1.85411e6i | 0.0616695i | ||||||||
\(981\) | −1.04273e6 | − | 7.30710e6i | −0.0345937 | − | 0.242422i | ||||
\(982\) | −9.81346e6 | −0.324746 | ||||||||
\(983\) | 1.12318e7i | 0.370736i | 0.982669 | + | 0.185368i | \(0.0593478\pi\) | ||||
−0.982669 | + | 0.185368i | \(0.940652\pi\) | |||||||
\(984\) | −585188. | + | 41542.8i | −0.0192667 | + | 0.00136776i | ||||
\(985\) | − | 9.74689e6i | − | 0.320093i | ||||||
\(986\) | 8.11634e6 | 0.265869 | ||||||||
\(987\) | −4.83109e7 | + | 3.42962e6i | −1.57853 | + | 0.112061i | ||||
\(988\) | 1.32210e7 | 0.430895 | ||||||||
\(989\) | 2.39318e7 | 0.778011 | ||||||||
\(990\) | 2.78035e6 | + | 1.96868e6i | 0.0901596 | + | 0.0638391i | ||||
\(991\) | 2.65187e7 | 0.857764 | 0.428882 | − | 0.903360i | \(-0.358908\pi\) | ||||
0.428882 | + | 0.903360i | \(0.358908\pi\) | |||||||
\(992\) | 2.01298e7 | 0.649473 | ||||||||
\(993\) | 2.42120e7 | − | 1.71883e6i | 0.779217 | − | 0.0553171i | ||||
\(994\) | 7.79406e6 | 0.250206 | ||||||||
\(995\) | − | 4.03062e6i | − | 0.129067i | ||||||
\(996\) | −3.49564e7 | + | 2.48158e6i | −1.11655 | + | 0.0792647i | ||||
\(997\) | − | 8.63647e6i | − | 0.275168i | −0.990490 | − | 0.137584i | \(-0.956066\pi\) | ||
0.990490 | − | 0.137584i | \(-0.0439338\pi\) | |||||||
\(998\) | 5.99701e6 | 0.190594 | ||||||||
\(999\) | 2.60796e7 | − | 5.63000e6i | 0.826774 | − | 0.178482i |
(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 | 165.6.f.a.131.37 | ✓ | 80 | |
3.2 | odd | 2 | inner | 165.6.f.a.131.43 | yes | 80 | |
11.10 | odd | 2 | inner | 165.6.f.a.131.44 | yes | 80 | |
33.32 | even | 2 | inner | 165.6.f.a.131.38 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.6.f.a.131.37 | ✓ | 80 | 1.1 | even | 1 | trivial | |
165.6.f.a.131.38 | yes | 80 | 33.32 | even | 2 | inner | |
165.6.f.a.131.43 | yes | 80 | 3.2 | odd | 2 | inner | |
165.6.f.a.131.44 | yes | 80 | 11.10 | odd | 2 | inner |