Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [55,6,Mod(32,55)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(55, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 2]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("55.32");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 55 = 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 55.e (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.82111008971\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Relative dimension: | \(26\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 32.14 | ||
Character | \(\chi\) | \(=\) | 55.32 |
Dual form | 55.6.e.b.43.14 |
$q$-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 \(\left(\mathbb{Z}/55\mathbb{Z}\right)^\times\).
\(n\) | \(12\) | \(46\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.819850 | − | 0.819850i | 0.144930 | − | 0.144930i | −0.630919 | − | 0.775849i | \(-0.717322\pi\) |
0.775849 | + | 0.630919i | \(0.217322\pi\) | |||||||
\(3\) | −2.25487 | + | 2.25487i | −0.144650 | + | 0.144650i | −0.775723 | − | 0.631073i | \(-0.782615\pi\) |
0.631073 | + | 0.775723i | \(0.282615\pi\) | |||||||
\(4\) | 30.6557i | 0.957990i | ||||||||
\(5\) | 5.74279 | − | 55.6059i | 0.102730 | − | 0.994709i | ||||
\(6\) | 3.69731i | 0.0419284i | ||||||||
\(7\) | 88.0749 | − | 88.0749i | 0.679371 | − | 0.679371i | −0.280487 | − | 0.959858i | \(-0.590496\pi\) |
0.959858 | + | 0.280487i | \(0.0904958\pi\) | |||||||
\(8\) | 51.3683 | + | 51.3683i | 0.283772 | + | 0.283772i | ||||
\(9\) | 232.831i | 0.958153i | ||||||||
\(10\) | −40.8803 | − | 50.2967i | −0.129275 | − | 0.159052i | ||||
\(11\) | 68.0926 | + | 395.493i | 0.169675 | + | 0.985500i | ||||
\(12\) | −69.1247 | − | 69.1247i | −0.138573 | − | 0.138573i | ||||
\(13\) | 741.664 | + | 741.664i | 1.21716 | + | 1.21716i | 0.968621 | + | 0.248542i | \(0.0799515\pi\) |
0.248542 | + | 0.968621i | \(0.420049\pi\) | |||||||
\(14\) | − | 144.416i | − | 0.196923i | ||||||
\(15\) | 112.435 | + | 138.334i | 0.129025 | + | 0.158745i | ||||
\(16\) | −896.754 | −0.875736 | ||||||||
\(17\) | 805.641 | − | 805.641i | 0.676113 | − | 0.676113i | −0.283005 | − | 0.959118i | \(-0.591331\pi\) |
0.959118 | + | 0.283005i | \(0.0913314\pi\) | |||||||
\(18\) | 190.887 | + | 190.887i | 0.138865 | + | 0.138865i | ||||
\(19\) | 1851.56 | 1.17667 | 0.588334 | − | 0.808618i | \(-0.299784\pi\) | ||||
0.588334 | + | 0.808618i | \(0.299784\pi\) | |||||||
\(20\) | 1704.64 | + | 176.049i | 0.952922 | + | 0.0984145i | ||||
\(21\) | 397.196i | 0.196542i | ||||||||
\(22\) | 380.070 | + | 268.419i | 0.167420 | + | 0.118238i | ||||
\(23\) | −561.188 | + | 561.188i | −0.221202 | + | 0.221202i | −0.809004 | − | 0.587803i | \(-0.799993\pi\) |
0.587803 | + | 0.809004i | \(0.299993\pi\) | |||||||
\(24\) | −231.658 | −0.0820954 | ||||||||
\(25\) | −3059.04 | − | 638.666i | −0.978893 | − | 0.204373i | ||||
\(26\) | 1216.11 | 0.352808 | ||||||||
\(27\) | −1072.94 | − | 1072.94i | −0.283247 | − | 0.283247i | ||||
\(28\) | 2700.00 | + | 2700.00i | 0.650831 | + | 0.650831i | ||||
\(29\) | −3983.79 | −0.879632 | −0.439816 | − | 0.898088i | \(-0.644956\pi\) | ||||
−0.439816 | + | 0.898088i | \(0.644956\pi\) | |||||||
\(30\) | 205.593 | + | 21.2329i | 0.0417066 | + | 0.00430731i | ||||
\(31\) | 4011.45 | 0.749717 | 0.374859 | − | 0.927082i | \(-0.377691\pi\) | ||||
0.374859 | + | 0.927082i | \(0.377691\pi\) | |||||||
\(32\) | −2378.99 | + | 2378.99i | −0.410693 | + | 0.410693i | ||||
\(33\) | −1045.33 | − | 738.246i | −0.167096 | − | 0.118009i | ||||
\(34\) | − | 1321.01i | − | 0.195979i | ||||||
\(35\) | −4391.69 | − | 5403.28i | −0.605985 | − | 0.745569i | ||||
\(36\) | −7137.60 | −0.917901 | ||||||||
\(37\) | 5642.57 | + | 5642.57i | 0.677598 | + | 0.677598i | 0.959456 | − | 0.281858i | \(-0.0909507\pi\) |
−0.281858 | + | 0.959456i | \(0.590951\pi\) | |||||||
\(38\) | 1518.00 | − | 1518.00i | 0.170535 | − | 0.170535i | ||||
\(39\) | −3344.72 | −0.352126 | ||||||||
\(40\) | 3151.38 | − | 2561.38i | 0.311423 | − | 0.253119i | ||||
\(41\) | − | 14226.7i | − | 1.32174i | −0.750502 | − | 0.660868i | \(-0.770188\pi\) | ||
0.750502 | − | 0.660868i | \(-0.229812\pi\) | |||||||
\(42\) | 325.641 | + | 325.641i | 0.0284849 | + | 0.0284849i | ||||
\(43\) | −3129.47 | − | 3129.47i | −0.258107 | − | 0.258107i | 0.566177 | − | 0.824284i | \(-0.308422\pi\) |
−0.824284 | + | 0.566177i | \(0.808422\pi\) | |||||||
\(44\) | −12124.1 | + | 2087.42i | −0.944100 | + | 0.162547i | ||||
\(45\) | 12946.8 | + | 1337.10i | 0.953083 | + | 0.0984311i | ||||
\(46\) | 920.180i | 0.0641177i | ||||||||
\(47\) | −18434.0 | − | 18434.0i | −1.21724 | − | 1.21724i | −0.968595 | − | 0.248645i | \(-0.920015\pi\) |
−0.248645 | − | 0.968595i | \(-0.579985\pi\) | |||||||
\(48\) | 2022.07 | − | 2022.07i | 0.126675 | − | 0.126675i | ||||
\(49\) | 1292.61i | 0.0769093i | ||||||||
\(50\) | −3031.56 | + | 1984.34i | −0.171491 | + | 0.112251i | ||||
\(51\) | 3633.24i | 0.195600i | ||||||||
\(52\) | −22736.2 | + | 22736.2i | −1.16603 | + | 1.16603i | ||||
\(53\) | −2404.01 | + | 2404.01i | −0.117557 | + | 0.117557i | −0.763438 | − | 0.645881i | \(-0.776490\pi\) |
0.645881 | + | 0.763438i | \(0.276490\pi\) | |||||||
\(54\) | −1759.30 | −0.0821022 | ||||||||
\(55\) | 22382.8 | − | 1515.12i | 0.997717 | − | 0.0675368i | ||||
\(56\) | 9048.51 | 0.385573 | ||||||||
\(57\) | −4175.04 | + | 4175.04i | −0.170205 | + | 0.170205i | ||||
\(58\) | −3266.11 | + | 3266.11i | −0.127485 | + | 0.127485i | ||||
\(59\) | 22820.4i | 0.853479i | 0.904375 | + | 0.426739i | \(0.140338\pi\) | ||||
−0.904375 | + | 0.426739i | \(0.859662\pi\) | |||||||
\(60\) | −4240.71 | + | 3446.77i | −0.152076 | + | 0.123605i | ||||
\(61\) | − | 37872.4i | − | 1.30316i | −0.758579 | − | 0.651581i | \(-0.774106\pi\) | ||
0.758579 | − | 0.651581i | \(-0.225894\pi\) | |||||||
\(62\) | 3288.79 | − | 3288.79i | 0.108657 | − | 0.108657i | ||||
\(63\) | 20506.6 | + | 20506.6i | 0.650941 | + | 0.650941i | ||||
\(64\) | − | 24795.3i | − | 0.756692i | ||||||
\(65\) | 45500.1 | − | 36981.7i | 1.33576 | − | 1.08568i | ||||
\(66\) | −1462.26 | + | 251.760i | −0.0413204 | + | 0.00711420i | ||||
\(67\) | 5682.77 | + | 5682.77i | 0.154658 | + | 0.154658i | 0.780195 | − | 0.625537i | \(-0.215120\pi\) |
−0.625537 | + | 0.780195i | \(0.715120\pi\) | |||||||
\(68\) | 24697.5 | + | 24697.5i | 0.647710 | + | 0.647710i | ||||
\(69\) | − | 2530.82i | − | 0.0639938i | ||||||
\(70\) | −8030.41 | − | 829.353i | −0.195881 | − | 0.0202299i | ||||
\(71\) | −3271.14 | −0.0770111 | −0.0385056 | − | 0.999258i | \(-0.512260\pi\) | ||||
−0.0385056 | + | 0.999258i | \(0.512260\pi\) | |||||||
\(72\) | −11960.1 | + | 11960.1i | −0.271897 | + | 0.271897i | ||||
\(73\) | 25842.3 | + | 25842.3i | 0.567575 | + | 0.567575i | 0.931449 | − | 0.363873i | \(-0.118546\pi\) |
−0.363873 | + | 0.931449i | \(0.618546\pi\) | |||||||
\(74\) | 9252.11 | 0.196409 | ||||||||
\(75\) | 8337.86 | − | 5457.64i | 0.171160 | − | 0.112034i | ||||
\(76\) | 56760.9i | 1.12724i | ||||||||
\(77\) | 40830.2 | + | 28835.7i | 0.784793 | + | 0.554248i | ||||
\(78\) | −2742.16 | + | 2742.16i | −0.0510337 | + | 0.0510337i | ||||
\(79\) | −41319.9 | −0.744889 | −0.372445 | − | 0.928054i | \(-0.621480\pi\) | ||||
−0.372445 | + | 0.928054i | \(0.621480\pi\) | |||||||
\(80\) | −5149.87 | + | 49864.8i | −0.0899645 | + | 0.871103i | ||||
\(81\) | −51739.3 | −0.876209 | ||||||||
\(82\) | −11663.8 | − | 11663.8i | −0.191560 | − | 0.191560i | ||||
\(83\) | 67888.9 | + | 67888.9i | 1.08169 | + | 1.08169i | 0.996352 | + | 0.0853401i | \(0.0271977\pi\) |
0.0853401 | + | 0.996352i | \(0.472802\pi\) | |||||||
\(84\) | −12176.3 | −0.188286 | ||||||||
\(85\) | −40171.8 | − | 49425.0i | −0.603079 | − | 0.741993i | ||||
\(86\) | −5131.39 | −0.0748151 | ||||||||
\(87\) | 8982.93 | − | 8982.93i | 0.127239 | − | 0.127239i | ||||
\(88\) | −16818.0 | + | 23813.6i | −0.231508 | + | 0.327807i | ||||
\(89\) | − | 86508.1i | − | 1.15766i | −0.815447 | − | 0.578831i | \(-0.803509\pi\) | ||
0.815447 | − | 0.578831i | \(-0.196491\pi\) | |||||||
\(90\) | 11710.6 | − | 9518.20i | 0.152396 | − | 0.123865i | ||||
\(91\) | 130644. | 1.65381 | ||||||||
\(92\) | −17203.6 | − | 17203.6i | −0.211909 | − | 0.211909i | ||||
\(93\) | −9045.31 | + | 9045.31i | −0.108447 | + | 0.108447i | ||||
\(94\) | −30226.3 | −0.352830 | ||||||||
\(95\) | 10633.1 | − | 102958.i | 0.120879 | − | 1.17044i | ||||
\(96\) | − | 10728.6i | − | 0.118814i | ||||||
\(97\) | −24593.2 | − | 24593.2i | −0.265390 | − | 0.265390i | 0.561849 | − | 0.827240i | \(-0.310090\pi\) |
−0.827240 | + | 0.561849i | \(0.810090\pi\) | |||||||
\(98\) | 1059.75 | + | 1059.75i | 0.0111465 | + | 0.0111465i | ||||
\(99\) | −92083.0 | + | 15854.1i | −0.944260 | + | 0.162575i | ||||
\(100\) | 19578.8 | − | 93777.0i | 0.195788 | − | 0.937770i | ||||
\(101\) | − | 102376.i | − | 0.998606i | −0.866427 | − | 0.499303i | \(-0.833589\pi\) | ||
0.866427 | − | 0.499303i | \(-0.166411\pi\) | |||||||
\(102\) | 2978.71 | + | 2978.71i | 0.0283483 | + | 0.0283483i | ||||
\(103\) | −99062.9 | + | 99062.9i | −0.920064 | + | 0.920064i | −0.997033 | − | 0.0769694i | \(-0.975476\pi\) |
0.0769694 | + | 0.997033i | \(0.475476\pi\) | |||||||
\(104\) | 76196.0i | 0.690794i | ||||||||
\(105\) | 22086.4 | + | 2281.01i | 0.195502 | + | 0.0201908i | ||||
\(106\) | 3941.86i | 0.0340750i | ||||||||
\(107\) | −489.464 | + | 489.464i | −0.00413296 | + | 0.00413296i | −0.709170 | − | 0.705037i | \(-0.750930\pi\) |
0.705037 | + | 0.709170i | \(0.250930\pi\) | |||||||
\(108\) | 32891.7 | − | 32891.7i | 0.271348 | − | 0.271348i | ||||
\(109\) | −134140. | −1.08141 | −0.540706 | − | 0.841212i | \(-0.681843\pi\) | ||||
−0.540706 | + | 0.841212i | \(0.681843\pi\) | |||||||
\(110\) | 17108.3 | − | 19592.7i | 0.134811 | − | 0.154388i | ||||
\(111\) | −25446.5 | −0.196029 | ||||||||
\(112\) | −78981.5 | + | 78981.5i | −0.594950 | + | 0.594950i | ||||
\(113\) | 113964. | − | 113964.i | 0.839601 | − | 0.839601i | −0.149205 | − | 0.988806i | \(-0.547671\pi\) |
0.988806 | + | 0.149205i | \(0.0476715\pi\) | |||||||
\(114\) | 6845.80i | 0.0493358i | ||||||||
\(115\) | 27982.6 | + | 34428.2i | 0.197307 | + | 0.242756i | ||||
\(116\) | − | 122126.i | − | 0.842679i | ||||||
\(117\) | −172682. | + | 172682.i | −1.16623 | + | 1.16623i | ||||
\(118\) | 18709.3 | + | 18709.3i | 0.123695 | + | 0.123695i | ||||
\(119\) | − | 141914.i | − | 0.918663i | ||||||
\(120\) | −1330.36 | + | 12881.5i | −0.00843367 | + | 0.0816610i | ||||
\(121\) | −151778. | + | 53860.2i | −0.942421 | + | 0.334430i | ||||
\(122\) | −31049.7 | − | 31049.7i | −0.188868 | − | 0.188868i | ||||
\(123\) | 32079.4 | + | 32079.4i | 0.191189 | + | 0.191189i | ||||
\(124\) | 122974.i | 0.718222i | ||||||||
\(125\) | −53081.1 | + | 166433.i | −0.303854 | + | 0.952719i | ||||
\(126\) | 33624.6 | 0.188682 | ||||||||
\(127\) | 72970.4 | − | 72970.4i | 0.401455 | − | 0.401455i | −0.477290 | − | 0.878746i | \(-0.658381\pi\) |
0.878746 | + | 0.477290i | \(0.158381\pi\) | |||||||
\(128\) | −96456.0 | − | 96456.0i | −0.520361 | − | 0.520361i | ||||
\(129\) | 14113.1 | 0.0746704 | ||||||||
\(130\) | 6983.84 | − | 67622.7i | 0.0362440 | − | 0.350941i | ||||
\(131\) | − | 170832.i | − | 0.869741i | −0.900493 | − | 0.434871i | \(-0.856794\pi\) | ||
0.900493 | − | 0.434871i | \(-0.143206\pi\) | |||||||
\(132\) | 22631.4 | − | 32045.2i | 0.113052 | − | 0.160077i | ||||
\(133\) | 163076. | − | 163076.i | 0.799395 | − | 0.799395i | ||||
\(134\) | 9318.04 | 0.0448294 | ||||||||
\(135\) | −65823.4 | + | 53500.1i | −0.310847 | + | 0.252651i | ||||
\(136\) | 82768.7 | 0.383724 | ||||||||
\(137\) | 145269. | + | 145269.i | 0.661258 | + | 0.661258i | 0.955677 | − | 0.294418i | \(-0.0951259\pi\) |
−0.294418 | + | 0.955677i | \(0.595126\pi\) | |||||||
\(138\) | −2074.89 | − | 2074.89i | −0.00927464 | − | 0.00927464i | ||||
\(139\) | 361121. | 1.58532 | 0.792659 | − | 0.609665i | \(-0.208696\pi\) | ||||
0.792659 | + | 0.609665i | \(0.208696\pi\) | |||||||
\(140\) | 165641. | − | 134630.i | 0.714248 | − | 0.580528i | ||||
\(141\) | 83132.9 | 0.352148 | ||||||||
\(142\) | −2681.85 | + | 2681.85i | −0.0111613 | + | 0.0111613i | ||||
\(143\) | −242821. | + | 343824.i | −0.992992 | + | 1.40604i | ||||
\(144\) | − | 208792.i | − | 0.839089i | ||||||
\(145\) | −22878.0 | + | 221522.i | −0.0903647 | + | 0.874978i | ||||
\(146\) | 42373.6 | 0.164518 | ||||||||
\(147\) | −2914.68 | − | 2914.68i | −0.0111249 | − | 0.0111249i | ||||
\(148\) | −172977. | + | 172977.i | −0.649133 | + | 0.649133i | ||||
\(149\) | −157044. | −0.579505 | −0.289752 | − | 0.957102i | \(-0.593573\pi\) | ||||
−0.289752 | + | 0.957102i | \(0.593573\pi\) | |||||||
\(150\) | 2361.35 | − | 11310.2i | 0.00856904 | − | 0.0410434i | ||||
\(151\) | 406149.i | 1.44958i | 0.688968 | + | 0.724792i | \(0.258064\pi\) | ||||
−0.688968 | + | 0.724792i | \(0.741936\pi\) | |||||||
\(152\) | 95111.5 | + | 95111.5i | 0.333906 | + | 0.333906i | ||||
\(153\) | 187578. | + | 187578.i | 0.647819 | + | 0.647819i | ||||
\(154\) | 57115.6 | − | 9833.68i | 0.194068 | − | 0.0334129i | ||||
\(155\) | 23036.9 | − | 223061.i | 0.0770185 | − | 0.745750i | ||||
\(156\) | − | 102535.i | − | 0.337333i | ||||||
\(157\) | −294046. | − | 294046.i | −0.952063 | − | 0.952063i | 0.0468397 | − | 0.998902i | \(-0.485085\pi\) |
−0.998902 | + | 0.0468397i | \(0.985085\pi\) | |||||||
\(158\) | −33876.1 | + | 33876.1i | −0.107957 | + | 0.107957i | ||||
\(159\) | − | 10841.5i | − | 0.0340091i | ||||||
\(160\) | 118624. | + | 145948.i | 0.366330 | + | 0.450711i | ||||
\(161\) | 98853.2i | 0.300556i | ||||||||
\(162\) | −42418.4 | + | 42418.4i | −0.126989 | + | 0.126989i | ||||
\(163\) | 321782. | − | 321782.i | 0.948620 | − | 0.948620i | −0.0501226 | − | 0.998743i | \(-0.515961\pi\) |
0.998743 | + | 0.0501226i | \(0.0159612\pi\) | |||||||
\(164\) | 436130. | 1.26621 | ||||||||
\(165\) | −47053.9 | + | 53886.7i | −0.134551 | + | 0.154089i | ||||
\(166\) | 111317. | 0.313540 | ||||||||
\(167\) | 285860. | − | 285860.i | 0.793164 | − | 0.793164i | −0.188843 | − | 0.982007i | \(-0.560474\pi\) |
0.982007 | + | 0.188843i | \(0.0604739\pi\) | |||||||
\(168\) | −20403.2 | + | 20403.2i | −0.0557733 | + | 0.0557733i | ||||
\(169\) | 728838.i | 1.96297i | ||||||||
\(170\) | −73455.9 | − | 7586.28i | −0.194942 | − | 0.0201329i | ||||
\(171\) | 431101.i | 1.12743i | ||||||||
\(172\) | 95936.1 | − | 95936.1i | 0.247264 | − | 0.247264i | ||||
\(173\) | −427806. | − | 427806.i | −1.08675 | − | 1.08675i | −0.995861 | − | 0.0908942i | \(-0.971027\pi\) |
−0.0908942 | − | 0.995861i | \(-0.528973\pi\) | |||||||
\(174\) | − | 14729.3i | − | 0.0368815i | ||||||
\(175\) | −325675. | + | 213174.i | −0.803877 | + | 0.526187i | ||||
\(176\) | −61062.3 | − | 354659.i | −0.148591 | − | 0.863038i | ||||
\(177\) | −51457.0 | − | 51457.0i | −0.123456 | − | 0.123456i | ||||
\(178\) | −70923.7 | − | 70923.7i | −0.167780 | − | 0.167780i | ||||
\(179\) | − | 241635.i | − | 0.563672i | −0.959463 | − | 0.281836i | \(-0.909057\pi\) | ||
0.959463 | − | 0.281836i | \(-0.0909434\pi\) | |||||||
\(180\) | −40989.7 | + | 396893.i | −0.0942961 | + | 0.913045i | ||||
\(181\) | −632254. | −1.43448 | −0.717241 | − | 0.696825i | \(-0.754595\pi\) | ||||
−0.717241 | + | 0.696825i | \(0.754595\pi\) | |||||||
\(182\) | 107108. | − | 107108.i | 0.239687 | − | 0.239687i | ||||
\(183\) | 85397.4 | + | 85397.4i | 0.188503 | + | 0.188503i | ||||
\(184\) | −57654.5 | −0.125542 | ||||||||
\(185\) | 346164. | − | 281356.i | 0.743623 | − | 0.604404i | ||||
\(186\) | 14831.6i | 0.0314344i | ||||||||
\(187\) | 373483. | + | 263767.i | 0.781029 | + | 0.551590i | ||||
\(188\) | 565108. | − | 565108.i | 1.16610 | − | 1.16610i | ||||
\(189\) | −188998. | −0.384860 | ||||||||
\(190\) | −75692.4 | − | 93127.5i | −0.152114 | − | 0.187152i | ||||
\(191\) | −8107.14 | −0.0160799 | −0.00803997 | − | 0.999968i | \(-0.502559\pi\) | ||||
−0.00803997 | + | 0.999968i | \(0.502559\pi\) | |||||||
\(192\) | 55910.2 | + | 55910.2i | 0.109456 | + | 0.109456i | ||||
\(193\) | −422534. | − | 422534.i | −0.816522 | − | 0.816522i | 0.169080 | − | 0.985602i | \(-0.445920\pi\) |
−0.985602 | + | 0.169080i | \(0.945920\pi\) | |||||||
\(194\) | −40325.4 | −0.0769263 | ||||||||
\(195\) | −19208.0 | + | 185986.i | −0.0361739 | + | 0.350263i | ||||
\(196\) | −39626.0 | −0.0736783 | ||||||||
\(197\) | 96838.2 | − | 96838.2i | 0.177779 | − | 0.177779i | −0.612608 | − | 0.790387i | \(-0.709879\pi\) |
0.790387 | + | 0.612608i | \(0.209879\pi\) | |||||||
\(198\) | −62496.3 | + | 88492.2i | −0.113290 | + | 0.160414i | ||||
\(199\) | − | 377063.i | − | 0.674965i | −0.941332 | − | 0.337482i | \(-0.890425\pi\) | ||
0.941332 | − | 0.337482i | \(-0.109575\pi\) | |||||||
\(200\) | −124330. | − | 189945.i | −0.219787 | − | 0.335778i | ||||
\(201\) | −25627.9 | −0.0447427 | ||||||||
\(202\) | −83932.9 | − | 83932.9i | −0.144728 | − | 0.144728i | ||||
\(203\) | −350872. | + | 350872.i | −0.597597 | + | 0.597597i | ||||
\(204\) | −111379. | −0.187383 | ||||||||
\(205\) | −791090. | − | 81701.0i | −1.31474 | − | 0.135782i | ||||
\(206\) | 162433.i | 0.266690i | ||||||||
\(207\) | −130662. | − | 130662.i | −0.211945 | − | 0.211945i | ||||
\(208\) | −665090. | − | 665090.i | −1.06591 | − | 1.06591i | ||||
\(209\) | 126078. | + | 732279.i | 0.199651 | + | 1.15961i | ||||
\(210\) | 19977.6 | − | 16237.5i | 0.0312605 | − | 0.0254080i | ||||
\(211\) | 737422.i | 1.14028i | 0.821549 | + | 0.570138i | \(0.193110\pi\) | ||||
−0.821549 | + | 0.570138i | \(0.806890\pi\) | |||||||
\(212\) | −73696.6 | − | 73696.6i | −0.112618 | − | 0.112618i | ||||
\(213\) | 7376.01 | − | 7376.01i | 0.0111397 | − | 0.0111397i | ||||
\(214\) | 802.574i | 0.00119798i | ||||||||
\(215\) | −191989. | + | 156045.i | −0.283257 | + | 0.230226i | ||||
\(216\) | − | 110230.i | − | 0.160755i | ||||||
\(217\) | 353308. | − | 353308.i | 0.509336 | − | 0.509336i | ||||
\(218\) | −109974. | + | 109974.i | −0.156729 | + | 0.156729i | ||||
\(219\) | −116542. | −0.164200 | ||||||||
\(220\) | 46447.1 | + | 686160.i | 0.0646996 | + | 0.955803i | ||||
\(221\) | 1.19503e6 | 1.64588 | ||||||||
\(222\) | −20862.3 | + | 20862.3i | −0.0284106 | + | 0.0284106i | ||||
\(223\) | 16331.6 | − | 16331.6i | 0.0219921 | − | 0.0219921i | −0.696025 | − | 0.718017i | \(-0.745050\pi\) |
0.718017 | + | 0.696025i | \(0.245050\pi\) | |||||||
\(224\) | 419058.i | 0.558026i | ||||||||
\(225\) | 148701. | − | 712240.i | 0.195821 | − | 0.937929i | ||||
\(226\) | − | 186867.i | − | 0.243367i | ||||||
\(227\) | 355915. | − | 355915.i | 0.458439 | − | 0.458439i | −0.439704 | − | 0.898143i | \(-0.644917\pi\) |
0.898143 | + | 0.439704i | \(0.144917\pi\) | |||||||
\(228\) | −127989. | − | 127989.i | −0.163055 | − | 0.163055i | ||||
\(229\) | − | 1.50015e6i | − | 1.89036i | −0.326544 | − | 0.945182i | \(-0.605884\pi\) | ||
0.326544 | − | 0.945182i | \(-0.394116\pi\) | |||||||
\(230\) | 51167.5 | + | 5284.40i | 0.0637785 | + | 0.00658682i | ||||
\(231\) | −157088. | + | 27046.1i | −0.193692 | + | 0.0333483i | ||||
\(232\) | −204640. | − | 204640.i | −0.249615 | − | 0.249615i | ||||
\(233\) | −191449. | − | 191449.i | −0.231028 | − | 0.231028i | 0.582094 | − | 0.813122i | \(-0.302234\pi\) |
−0.813122 | + | 0.582094i | \(0.802234\pi\) | |||||||
\(234\) | 283147.i | 0.338044i | ||||||||
\(235\) | −1.13091e6 | + | 919180.i | −1.33585 | + | 1.08575i | ||||
\(236\) | −699574. | −0.817625 | ||||||||
\(237\) | 93171.1 | − | 93171.1i | 0.107748 | − | 0.107748i | ||||
\(238\) | −116348. | − | 116348.i | −0.133142 | − | 0.133142i | ||||
\(239\) | 972477. | 1.10125 | 0.550624 | − | 0.834754i | \(-0.314390\pi\) | ||||
0.550624 | + | 0.834754i | \(0.314390\pi\) | |||||||
\(240\) | −100827. | − | 124051.i | −0.112992 | − | 0.139019i | ||||
\(241\) | 169545.i | 0.188037i | 0.995570 | + | 0.0940186i | \(0.0299713\pi\) | ||||
−0.995570 | + | 0.0940186i | \(0.970029\pi\) | |||||||
\(242\) | −80277.7 | + | 168592.i | −0.0881164 | + | 0.185054i | ||||
\(243\) | 377390. | − | 377390.i | 0.409991 | − | 0.409991i | ||||
\(244\) | 1.16100e6 | 1.24842 | ||||||||
\(245\) | 71877.0 | + | 7423.21i | 0.0765024 | + | 0.00790090i | ||||
\(246\) | 52600.6 | 0.0554183 | ||||||||
\(247\) | 1.37324e6 | + | 1.37324e6i | 1.43220 | + | 1.43220i | ||||
\(248\) | 206061. | + | 206061.i | 0.212749 | + | 0.212749i | ||||
\(249\) | −306162. | −0.312934 | ||||||||
\(250\) | 92931.6 | + | 179969.i | 0.0940402 | + | 0.182115i | ||||
\(251\) | −550651. | −0.551686 | −0.275843 | − | 0.961203i | \(-0.588957\pi\) | ||||
−0.275843 | + | 0.961203i | \(0.588957\pi\) | |||||||
\(252\) | −628643. | + | 628643.i | −0.623596 | + | 0.623596i | ||||
\(253\) | −260158. | − | 183733.i | −0.255527 | − | 0.180462i | ||||
\(254\) | − | 119649.i | − | 0.116366i | ||||||
\(255\) | 202029. | + | 20864.9i | 0.194565 | + | 0.0200940i | ||||
\(256\) | 635291. | 0.605860 | ||||||||
\(257\) | −708471. | − | 708471.i | −0.669097 | − | 0.669097i | 0.288410 | − | 0.957507i | \(-0.406873\pi\) |
−0.957507 | + | 0.288410i | \(0.906873\pi\) | |||||||
\(258\) | 11570.6 | − | 11570.6i | 0.0108220 | − | 0.0108220i | ||||
\(259\) | 993937. | 0.920682 | ||||||||
\(260\) | 1.13370e6 | + | 1.39484e6i | 1.04008 | + | 1.27965i | ||||
\(261\) | − | 927549.i | − | 0.842822i | ||||||
\(262\) | −140056. | − | 140056.i | −0.126052 | − | 0.126052i | ||||
\(263\) | 463210. | + | 463210.i | 0.412942 | + | 0.412942i | 0.882762 | − | 0.469820i | \(-0.155681\pi\) |
−0.469820 | + | 0.882762i | \(0.655681\pi\) | |||||||
\(264\) | −15774.2 | − | 91618.9i | −0.0139295 | − | 0.0809050i | ||||
\(265\) | 119872. | + | 147483.i | 0.104858 | + | 0.129011i | ||||
\(266\) | − | 267396.i | − | 0.231713i | ||||||
\(267\) | 195065. | + | 195065.i | 0.167456 | + | 0.167456i | ||||
\(268\) | −174209. | + | 174209.i | −0.148161 | + | 0.148161i | ||||
\(269\) | 657951.i | 0.554387i | 0.960814 | + | 0.277193i | \(0.0894043\pi\) | ||||
−0.960814 | + | 0.277193i | \(0.910596\pi\) | |||||||
\(270\) | −10103.3 | + | 97827.4i | −0.00843437 | + | 0.0816678i | ||||
\(271\) | 162774.i | 0.134636i | 0.997732 | + | 0.0673181i | \(0.0214442\pi\) | ||||
−0.997732 | + | 0.0673181i | \(0.978556\pi\) | |||||||
\(272\) | −722461. | + | 722461.i | −0.592096 | + | 0.592096i | ||||
\(273\) | −294586. | + | 294586.i | −0.239224 | + | 0.239224i | ||||
\(274\) | 238197. | 0.191673 | ||||||||
\(275\) | 44289.9 | − | 1.25332e6i | 0.0353161 | − | 0.999376i | ||||
\(276\) | 77583.9 | 0.0613054 | ||||||||
\(277\) | 322956. | − | 322956.i | 0.252897 | − | 0.252897i | −0.569260 | − | 0.822157i | \(-0.692770\pi\) |
0.822157 | + | 0.569260i | \(0.192770\pi\) | |||||||
\(278\) | 296065. | − | 296065.i | 0.229761 | − | 0.229761i | ||||
\(279\) | 933991.i | 0.718343i | ||||||||
\(280\) | 51963.7 | − | 503151.i | 0.0396100 | − | 0.383533i | ||||
\(281\) | 135801.i | 0.102598i | 0.998683 | + | 0.0512988i | \(0.0163361\pi\) | ||||
−0.998683 | + | 0.0512988i | \(0.983664\pi\) | |||||||
\(282\) | 68156.5 | − | 68156.5i | 0.0510369 | − | 0.0510369i | ||||
\(283\) | 1.20597e6 | + | 1.20597e6i | 0.895099 | + | 0.895099i | 0.994998 | − | 0.0998984i | \(-0.0318518\pi\) |
−0.0998984 | + | 0.994998i | \(0.531852\pi\) | |||||||
\(284\) | − | 100279.i | − | 0.0737759i | ||||||
\(285\) | 208180. | + | 256133.i | 0.151820 | + | 0.186790i | ||||
\(286\) | 82807.8 | + | 480961.i | 0.0598627 | + | 0.347692i | ||||
\(287\) | −1.25302e6 | − | 1.25302e6i | −0.897950 | − | 0.897950i | ||||
\(288\) | −553902. | − | 553902.i | −0.393506 | − | 0.393506i | ||||
\(289\) | 121742.i | 0.0857427i | ||||||||
\(290\) | 162858. | + | 200371.i | 0.113714 | + | 0.139907i | ||||
\(291\) | 110909. | 0.0767776 | ||||||||
\(292\) | −792213. | + | 792213.i | −0.543732 | + | 0.543732i | ||||
\(293\) | −251556. | − | 251556.i | −0.171185 | − | 0.171185i | 0.616315 | − | 0.787500i | \(-0.288625\pi\) |
−0.787500 | + | 0.616315i | \(0.788625\pi\) | |||||||
\(294\) | −4779.20 | −0.00322468 | ||||||||
\(295\) | 1.26895e6 | + | 131053.i | 0.848963 | + | 0.0876780i | ||||
\(296\) | 579697.i | 0.384567i | ||||||||
\(297\) | 351280. | − | 497398.i | 0.231080 | − | 0.327200i | ||||
\(298\) | −128753. | + | 128753.i | −0.0839878 | + | 0.0839878i | ||||
\(299\) | −832426. | −0.538478 | ||||||||
\(300\) | 167308. | + | 255603.i | 0.107328 | + | 0.163969i | ||||
\(301\) | −551256. | −0.350701 | ||||||||
\(302\) | 332981. | + | 332981.i | 0.210089 | + | 0.210089i | ||||
\(303\) | 230845. | + | 230845.i | 0.144449 | + | 0.144449i | ||||
\(304\) | −1.66039e6 | −1.03045 | ||||||||
\(305\) | −2.10593e6 | − | 217493.i | −1.29627 | − | 0.133874i | ||||
\(306\) | 307572. | 0.187777 | ||||||||
\(307\) | 1.73184e6 | − | 1.73184e6i | 1.04873 | − | 1.04873i | 0.0499766 | − | 0.998750i | \(-0.484085\pi\) |
0.998750 | − | 0.0499766i | \(-0.0159147\pi\) | |||||||
\(308\) | −883979. | + | 1.25168e6i | −0.530964 | + | 0.751824i | ||||
\(309\) | − | 446749.i | − | 0.266175i | ||||||
\(310\) | −163989. | − | 201763.i | −0.0969195 | − | 0.119244i | ||||
\(311\) | 750807. | 0.440177 | 0.220088 | − | 0.975480i | \(-0.429365\pi\) | ||||
0.220088 | + | 0.975480i | \(0.429365\pi\) | |||||||
\(312\) | −171812. | − | 171812.i | −0.0999235 | − | 0.0999235i | ||||
\(313\) | −15556.4 | + | 15556.4i | −0.00897526 | + | 0.00897526i | −0.711580 | − | 0.702605i | \(-0.752020\pi\) |
0.702605 | + | 0.711580i | \(0.252020\pi\) | |||||||
\(314\) | −482146. | −0.275966 | ||||||||
\(315\) | 1.25805e6 | − | 1.02252e6i | 0.714369 | − | 0.580626i | ||||
\(316\) | − | 1.26669e6i | − | 0.713597i | ||||||
\(317\) | 1.39427e6 | + | 1.39427e6i | 0.779289 | + | 0.779289i | 0.979710 | − | 0.200421i | \(-0.0642308\pi\) |
−0.200421 | + | 0.979710i | \(0.564231\pi\) | |||||||
\(318\) | −8888.38 | − | 8888.38i | −0.00492896 | − | 0.00492896i | ||||
\(319\) | −271266. | − | 1.57556e6i | −0.149252 | − | 0.866877i | ||||
\(320\) | −1.37877e6 | − | 142394.i | −0.752689 | − | 0.0777351i | ||||
\(321\) | − | 2207.36i | − | 0.00119567i | ||||||
\(322\) | 81044.8 | + | 81044.8i | 0.0435597 | + | 0.0435597i | ||||
\(323\) | 1.49169e6 | − | 1.49169e6i | 0.795561 | − | 0.795561i | ||||
\(324\) | − | 1.58610e6i | − | 0.839400i | ||||||
\(325\) | −1.79510e6 | − | 2.74246e6i | −0.942717 | − | 1.44023i | ||||
\(326\) | − | 527626.i | − | 0.274968i | ||||||
\(327\) | 302468. | − | 302468.i | 0.156426 | − | 0.156426i | ||||
\(328\) | 730801. | − | 730801.i | 0.375072 | − | 0.375072i | ||||
\(329\) | −3.24715e6 | −1.65391 | ||||||||
\(330\) | 5601.88 | + | 82756.2i | 0.00283171 | + | 0.0418327i | ||||
\(331\) | −1.98487e6 | −0.995779 | −0.497889 | − | 0.867241i | \(-0.665891\pi\) | ||||
−0.497889 | + | 0.867241i | \(0.665891\pi\) | |||||||
\(332\) | −2.08118e6 | + | 2.08118e6i | −1.03625 | + | 1.03625i | ||||
\(333\) | −1.31376e6 | + | 1.31376e6i | −0.649243 | + | 0.649243i | ||||
\(334\) | − | 468725.i | − | 0.229907i | ||||||
\(335\) | 348631. | − | 283361.i | 0.169728 | − | 0.137952i | ||||
\(336\) | − | 356187.i | − | 0.172119i | ||||||
\(337\) | 120865. | − | 120865.i | 0.0579729 | − | 0.0579729i | −0.677526 | − | 0.735499i | \(-0.736948\pi\) |
0.735499 | + | 0.677526i | \(0.236948\pi\) | |||||||
\(338\) | 597538. | + | 597538.i | 0.284494 | + | 0.284494i | ||||
\(339\) | 513950.i | 0.242897i | ||||||||
\(340\) | 1.51516e6 | − | 1.23149e6i | 0.710822 | − | 0.577744i | ||||
\(341\) | 273150. | + | 1.58650e6i | 0.127208 | + | 0.738846i | ||||
\(342\) | 353438. | + | 353438.i | 0.163399 | + | 0.163399i | ||||
\(343\) | 1.59412e6 | + | 1.59412e6i | 0.731621 | + | 0.731621i | ||||
\(344\) | − | 321511.i | − | 0.146487i | ||||||
\(345\) | −140728. | − | 14533.9i | −0.0636552 | − | 0.00657409i | ||||
\(346\) | −701473. | −0.315007 | ||||||||
\(347\) | −1.39645e6 | + | 1.39645e6i | −0.622591 | + | 0.622591i | −0.946193 | − | 0.323602i | \(-0.895106\pi\) |
0.323602 | + | 0.946193i | \(0.395106\pi\) | |||||||
\(348\) | 275378. | + | 275378.i | 0.121894 | + | 0.121894i | ||||
\(349\) | −3.13019e6 | −1.37565 | −0.687824 | − | 0.725878i | \(-0.741434\pi\) | ||||
−0.687824 | + | 0.725878i | \(0.741434\pi\) | |||||||
\(350\) | −92233.9 | + | 441776.i | −0.0402458 | + | 0.192767i | ||||
\(351\) | − | 1.59152e6i | − | 0.689516i | ||||||
\(352\) | −1.10286e6 | − | 778881.i | −0.474422 | − | 0.335054i | ||||
\(353\) | −23224.5 | + | 23224.5i | −0.00991995 | + | 0.00991995i | −0.712049 | − | 0.702129i | \(-0.752233\pi\) |
0.702129 | + | 0.712049i | \(0.252233\pi\) | |||||||
\(354\) | −84374.1 | −0.0357850 | ||||||||
\(355\) | −18785.5 | + | 181895.i | −0.00791136 | + | 0.0766037i | ||||
\(356\) | 2.65197e6 | 1.10903 | ||||||||
\(357\) | 319997. | + | 319997.i | 0.132885 | + | 0.132885i | ||||
\(358\) | −198104. | − | 198104.i | −0.0816932 | − | 0.0816932i | ||||
\(359\) | −690277. | −0.282675 | −0.141338 | − | 0.989961i | \(-0.545140\pi\) | ||||
−0.141338 | + | 0.989961i | \(0.545140\pi\) | |||||||
\(360\) | 596370. | + | 733739.i | 0.242527 | + | 0.298391i | ||||
\(361\) | 952181. | 0.384549 | ||||||||
\(362\) | −518353. | + | 518353.i | −0.207900 | + | 0.207900i | ||||
\(363\) | 220792. | − | 463688.i | 0.0879460 | − | 0.184697i | ||||
\(364\) | 4.00498e6i | 1.58434i | ||||||||
\(365\) | 1.58539e6 | − | 1.28858e6i | 0.622880 | − | 0.506265i | ||||
\(366\) | 140026. | 0.0546395 | ||||||||
\(367\) | −84271.0 | − | 84271.0i | −0.0326597 | − | 0.0326597i | 0.690588 | − | 0.723248i | \(-0.257352\pi\) |
−0.723248 | + | 0.690588i | \(0.757352\pi\) | |||||||
\(368\) | 503247. | − | 503247.i | 0.193714 | − | 0.193714i | ||||
\(369\) | 3.31242e6 | 1.26643 | ||||||||
\(370\) | 53132.9 | − | 514472.i | 0.0201771 | − | 0.195370i | ||||
\(371\) | 423466.i | 0.159729i | ||||||||
\(372\) | −277290. | − | 277290.i | −0.103891 | − | 0.103891i | ||||
\(373\) | 1.52634e6 | + | 1.52634e6i | 0.568042 | + | 0.568042i | 0.931579 | − | 0.363538i | \(-0.118431\pi\) |
−0.363538 | + | 0.931579i | \(0.618431\pi\) | |||||||
\(374\) | 522449. | − | 89950.9i | 0.193137 | − | 0.0332527i | ||||
\(375\) | −255594. | − | 494977.i | −0.0938584 | − | 0.181763i | ||||
\(376\) | − | 1.89385e6i | − | 0.690837i | ||||||
\(377\) | −2.95463e6 | − | 2.95463e6i | −1.07066 | − | 1.07066i | ||||
\(378\) | −154950. | + | 154950.i | −0.0557779 | + | 0.0557779i | ||||
\(379\) | 2.00045e6i | 0.715368i | 0.933843 | + | 0.357684i | \(0.116433\pi\) | ||||
−0.933843 | + | 0.357684i | \(0.883567\pi\) | |||||||
\(380\) | 3.15624e6 | + | 325966.i | 1.12127 | + | 0.115801i | ||||
\(381\) | 329078.i | 0.116141i | ||||||||
\(382\) | −6646.64 | + | 6646.64i | −0.00233047 | + | 0.00233047i | ||||
\(383\) | −3.76908e6 | + | 3.76908e6i | −1.31292 | + | 1.31292i | −0.393665 | + | 0.919254i | \(0.628793\pi\) |
−0.919254 | + | 0.393665i | \(0.871207\pi\) | |||||||
\(384\) | 434992. | 0.150540 | ||||||||
\(385\) | 1.83792e6 | − | 2.10481e6i | 0.631938 | − | 0.723703i | ||||
\(386\) | −692828. | −0.236678 | ||||||||
\(387\) | 728638. | − | 728638.i | 0.247306 | − | 0.247306i | ||||
\(388\) | 753921. | − | 753921.i | 0.254242 | − | 0.254242i | ||||
\(389\) | − | 4.53726e6i | − | 1.52026i | −0.649768 | − | 0.760132i | \(-0.725134\pi\) | ||
0.649768 | − | 0.760132i | \(-0.274866\pi\) | |||||||
\(390\) | 136733. | + | 168228.i | 0.0455210 | + | 0.0560064i | ||||
\(391\) | 904232.i | 0.299115i | ||||||||
\(392\) | −66399.3 | + | 66399.3i | −0.0218247 | + | 0.0218247i | ||||
\(393\) | 385204. | + | 385204.i | 0.125808 | + | 0.125808i | ||||
\(394\) | − | 158786.i | − | 0.0515312i | ||||||
\(395\) | −237291. | + | 2.29763e6i | −0.0765225 | + | 0.740948i | ||||
\(396\) | −486017. | − | 2.82287e6i | −0.155745 | − | 0.904592i | ||||
\(397\) | 3.97395e6 | + | 3.97395e6i | 1.26545 | + | 1.26545i | 0.948412 | + | 0.317041i | \(0.102689\pi\) |
0.317041 | + | 0.948412i | \(0.397311\pi\) | |||||||
\(398\) | −309135. | − | 309135.i | −0.0978228 | − | 0.0978228i | ||||
\(399\) | 735432.i | 0.231265i | ||||||||
\(400\) | 2.74321e6 | + | 572726.i | 0.857252 | + | 0.178977i | ||||
\(401\) | 185273. | 0.0575374 | 0.0287687 | − | 0.999586i | \(-0.490841\pi\) | ||||
0.0287687 | + | 0.999586i | \(0.490841\pi\) | |||||||
\(402\) | −21011.0 | + | 21011.0i | −0.00648457 | + | 0.00648457i | ||||
\(403\) | 2.97515e6 | + | 2.97515e6i | 0.912528 | + | 0.912528i | ||||
\(404\) | 3.13840e6 | 0.956655 | ||||||||
\(405\) | −297128. | + | 2.87701e6i | −0.0900131 | + | 0.871573i | ||||
\(406\) | 575324.i | 0.173220i | ||||||||
\(407\) | −1.84738e6 | + | 2.61581e6i | −0.552802 | + | 0.782745i | ||||
\(408\) | −186633. | + | 186633.i | −0.0555058 | + | 0.0555058i | ||||
\(409\) | −2.72097e6 | −0.804295 | −0.402148 | − | 0.915575i | \(-0.631736\pi\) | ||||
−0.402148 | + | 0.915575i | \(0.631736\pi\) | |||||||
\(410\) | −715557. | + | 581592.i | −0.210225 | + | 0.170867i | ||||
\(411\) | −655126. | −0.191302 | ||||||||
\(412\) | −3.03684e6 | − | 3.03684e6i | −0.881413 | − | 0.881413i | ||||
\(413\) | 2.00990e6 | + | 2.00990e6i | 0.579829 | + | 0.579829i | ||||
\(414\) | −214246. | −0.0614346 | ||||||||
\(415\) | 4.16490e6 | − | 3.38515e6i | 1.18709 | − | 0.964847i | ||||
\(416\) | −3.52882e6 | −0.999761 | ||||||||
\(417\) | −814283. | + | 814283.i | −0.229316 | + | 0.229316i | ||||
\(418\) | 703723. | + | 496994.i | 0.196998 | + | 0.139127i | ||||
\(419\) | 3.36223e6i | 0.935604i | 0.883833 | + | 0.467802i | \(0.154954\pi\) | ||||
−0.883833 | + | 0.467802i | \(0.845046\pi\) | |||||||
\(420\) | −69925.9 | + | 677075.i | −0.0193426 | + | 0.187290i | ||||
\(421\) | −798459. | −0.219557 | −0.109778 | − | 0.993956i | \(-0.535014\pi\) | ||||
−0.109778 | + | 0.993956i | \(0.535014\pi\) | |||||||
\(422\) | 604576. | + | 604576.i | 0.165261 | + | 0.165261i | ||||
\(423\) | 4.29202e6 | − | 4.29202e6i | 1.16630 | − | 1.16630i | ||||
\(424\) | −246980. | −0.0667186 | ||||||||
\(425\) | −2.97902e6 | + | 1.94995e6i | −0.800022 | + | 0.523663i | ||||
\(426\) | − | 12094.4i | − | 0.00322895i | ||||||
\(427\) | −3.33561e6 | − | 3.33561e6i | −0.885330 | − | 0.885330i | ||||
\(428\) | −15004.9 | − | 15004.9i | −0.00395934 | − | 0.00395934i | ||||
\(429\) | −227750. | − | 1.32281e6i | −0.0597469 | − | 0.347020i | ||||
\(430\) | −29468.5 | + | 285336.i | −0.00768576 | + | 0.0744192i | ||||
\(431\) | 3.94706e6i | 1.02348i | 0.859139 | + | 0.511742i | \(0.171000\pi\) | ||||
−0.859139 | + | 0.511742i | \(0.829000\pi\) | |||||||
\(432\) | 962162. | + | 962162.i | 0.248050 | + | 0.248050i | ||||
\(433\) | 1.70841e6 | − | 1.70841e6i | 0.437897 | − | 0.437897i | −0.453407 | − | 0.891304i | \(-0.649792\pi\) |
0.891304 | + | 0.453407i | \(0.149792\pi\) | |||||||
\(434\) | − | 579320.i | − | 0.147637i | ||||||
\(435\) | −447917. | − | 551091.i | −0.113494 | − | 0.139637i | ||||
\(436\) | − | 4.11214e6i | − | 1.03598i | ||||||
\(437\) | −1.03907e6 | + | 1.03907e6i | −0.260281 | + | 0.260281i | ||||
\(438\) | −95547.0 | + | 95547.0i | −0.0237975 | + | 0.0237975i | ||||
\(439\) | 678707. | 0.168082 | 0.0840409 | − | 0.996462i | \(-0.473217\pi\) | ||||
0.0840409 | + | 0.996462i | \(0.473217\pi\) | |||||||
\(440\) | 1.22759e6 | + | 1.07194e6i | 0.302289 | + | 0.263959i | ||||
\(441\) | −300961. | −0.0736908 | ||||||||
\(442\) | 979745. | − | 979745.i | 0.238538 | − | 0.238538i | ||||
\(443\) | −1.67407e6 | + | 1.67407e6i | −0.405289 | + | 0.405289i | −0.880092 | − | 0.474803i | \(-0.842519\pi\) |
0.474803 | + | 0.880092i | \(0.342519\pi\) | |||||||
\(444\) | − | 780081.i | − | 0.187794i | ||||||
\(445\) | −4.81036e6 | − | 496798.i | −1.15154 | − | 0.118927i | ||||
\(446\) | − | 26779.0i | − | 0.00637466i | ||||||
\(447\) | 354115. | − | 354115.i | 0.0838255 | − | 0.0838255i | ||||
\(448\) | −2.18384e6 | − | 2.18384e6i | −0.514075 | − | 0.514075i | ||||
\(449\) | 1.54007e6i | 0.360515i | 0.983619 | + | 0.180258i | \(0.0576931\pi\) | ||||
−0.983619 | + | 0.180258i | \(0.942307\pi\) | |||||||
\(450\) | −462017. | − | 705842.i | −0.107554 | − | 0.164315i | ||||
\(451\) | 5.62656e6 | − | 968733.i | 1.30257 | − | 0.224266i | ||||
\(452\) | 3.49366e6 | + | 3.49366e6i | 0.804330 | + | 0.804330i | ||||
\(453\) | −915815. | − | 915815.i | −0.209683 | − | 0.209683i | ||||
\(454\) | − | 583594.i | − | 0.132884i | ||||||
\(455\) | 750261. | − | 7.26458e6i | 0.169896 | − | 1.64506i | ||||
\(456\) | −428929. | −0.0965991 | ||||||||
\(457\) | 2.37478e6 | − | 2.37478e6i | 0.531904 | − | 0.531904i | −0.389235 | − | 0.921139i | \(-0.627261\pi\) |
0.921139 | + | 0.389235i | \(0.127261\pi\) | |||||||
\(458\) | −1.22990e6 | − | 1.22990e6i | −0.273971 | − | 0.273971i | ||||
\(459\) | −1.72881e6 | −0.383014 | ||||||||
\(460\) | −1.05542e6 | + | 857826.i | −0.232558 | + | 0.189019i | ||||
\(461\) | − | 4.89233e6i | − | 1.07217i | −0.844164 | − | 0.536084i | \(-0.819903\pi\) | ||
0.844164 | − | 0.536084i | \(-0.180097\pi\) | |||||||
\(462\) | −106615. | + | 150962.i | −0.0232387 | + | 0.0329051i | ||||
\(463\) | −5.39140e6 | + | 5.39140e6i | −1.16882 | + | 1.16882i | −0.186338 | + | 0.982486i | \(0.559662\pi\) |
−0.982486 | + | 0.186338i | \(0.940338\pi\) | |||||||
\(464\) | 3.57247e6 | 0.770325 | ||||||||
\(465\) | 451028. | + | 554919.i | 0.0967322 | + | 0.119014i | ||||
\(466\) | −313919. | −0.0669659 | ||||||||
\(467\) | 692307. | + | 692307.i | 0.146895 | + | 0.146895i | 0.776729 | − | 0.629835i | \(-0.216877\pi\) |
−0.629835 | + | 0.776729i | \(0.716877\pi\) | |||||||
\(468\) | −5.29370e6 | − | 5.29370e6i | −1.11724 | − | 1.11724i | ||||
\(469\) | 1.00102e6 | 0.210141 | ||||||||
\(470\) | −173583. | + | 1.68076e6i | −0.0362462 | + | 0.350963i | ||||
\(471\) | 1.32607e6 | 0.275432 | ||||||||
\(472\) | −1.17224e6 | + | 1.17224e6i | −0.242194 | + | 0.242194i | ||||
\(473\) | 1.02459e6 | − | 1.45078e6i | 0.210570 | − | 0.298159i | ||||
\(474\) | − | 152773.i | − | 0.0312320i | ||||||
\(475\) | −5.66400e6 | − | 1.18253e6i | −1.15183 | − | 0.240480i | ||||
\(476\) | 4.35046e6 | 0.880071 | ||||||||
\(477\) | −559729. | − | 559729.i | −0.112637 | − | 0.112637i | ||||
\(478\) | 797285. | − | 797285.i | 0.159604 | − | 0.159604i | ||||
\(479\) | −6.45641e6 | −1.28574 | −0.642869 | − | 0.765976i | \(-0.722256\pi\) | ||||
−0.642869 | + | 0.765976i | \(0.722256\pi\) | |||||||
\(480\) | −596575. | − | 61612.2i | −0.118185 | − | 0.0122057i | ||||
\(481\) | 8.36978e6i | 1.64950i | ||||||||
\(482\) | 139002. | + | 139002.i | 0.0272523 | + | 0.0272523i | ||||
\(483\) | −222901. | − | 222901.i | −0.0434755 | − | 0.0434755i | ||||
\(484\) | −1.65112e6 | − | 4.65285e6i | −0.320380 | − | 0.902830i | ||||
\(485\) | −1.50876e6 | + | 1.22629e6i | −0.291250 | + | 0.236723i | ||||
\(486\) | − | 618806.i | − | 0.118840i | ||||||
\(487\) | 1.03959e6 | + | 1.03959e6i | 0.198627 | + | 0.198627i | 0.799411 | − | 0.600784i | \(-0.205145\pi\) |
−0.600784 | + | 0.799411i | \(0.705145\pi\) | |||||||
\(488\) | 1.94544e6 | − | 1.94544e6i | 0.369801 | − | 0.369801i | ||||
\(489\) | 1.45115e6i | 0.274436i | ||||||||
\(490\) | 65014.3 | − | 52842.4i | 0.0122326 | − | 0.00994243i | ||||
\(491\) | 2.84028e6i | 0.531689i | 0.964016 | + | 0.265844i | \(0.0856507\pi\) | ||||
−0.964016 | + | 0.265844i | \(0.914349\pi\) | |||||||
\(492\) | −983417. | + | 983417.i | −0.183158 | + | 0.183158i | ||||
\(493\) | −3.20950e6 | + | 3.20950e6i | −0.594730 | + | 0.594730i | ||||
\(494\) | 2.25170e6 | 0.415138 | ||||||||
\(495\) | 352767. | + | 5.21141e6i | 0.0647106 | + | 0.955965i | ||||
\(496\) | −3.59728e6 | −0.656554 | ||||||||
\(497\) | −288106. | + | 288106.i | −0.0523192 | + | 0.0523192i | ||||
\(498\) | −251007. | + | 251007.i | −0.0453536 | + | 0.0453536i | ||||
\(499\) | − | 3.97737e6i | − | 0.715064i | −0.933901 | − | 0.357532i | \(-0.883618\pi\) | ||
0.933901 | − | 0.357532i | \(-0.116382\pi\) | |||||||
\(500\) | −5.10212e6 | − | 1.62724e6i | −0.912695 | − | 0.291089i | ||||
\(501\) | 1.28916e6i | 0.229463i | ||||||||
\(502\) | −451451. | + | 451451.i | −0.0799560 | + | 0.0799560i | ||||
\(503\) | −6.10079e6 | − | 6.10079e6i | −1.07514 | − | 1.07514i | −0.996937 | − | 0.0782056i | \(-0.975081\pi\) |
−0.0782056 | − | 0.996937i | \(-0.524919\pi\) | |||||||
\(504\) | 2.10677e6i | 0.369438i | ||||||||
\(505\) | −5.69271e6 | − | 587923.i | −0.993323 | − | 0.102587i | ||||
\(506\) | −363924. | + | 62657.4i | −0.0631880 | + | 0.0108792i | ||||
\(507\) | −1.64344e6 | − | 1.64344e6i | −0.283944 | − | 0.283944i | ||||
\(508\) | 2.23696e6 | + | 2.23696e6i | 0.384590 | + | 0.384590i | ||||
\(509\) | − | 1.28443e6i | − | 0.219743i | −0.993946 | − | 0.109871i | \(-0.964956\pi\) | ||
0.993946 | − | 0.109871i | \(-0.0350439\pi\) | |||||||
\(510\) | 182740. | − | 148528.i | 0.0311106 | − | 0.0252861i | ||||
\(511\) | 4.55211e6 | 0.771189 | ||||||||
\(512\) | 3.60744e6 | − | 3.60744e6i | 0.608168 | − | 0.608168i | ||||
\(513\) | −1.98661e6 | − | 1.98661e6i | −0.333288 | − | 0.333288i | ||||
\(514\) | −1.16168e6 | −0.193945 | ||||||||
\(515\) | 4.93959e6 | + | 6.07738e6i | 0.820678 | + | 1.00971i | ||||
\(516\) | 432647.i | 0.0715336i | ||||||||
\(517\) | 6.03531e6 | − | 8.54575e6i | 0.993054 | − | 1.40612i | ||||
\(518\) | 814879. | − | 814879.i | 0.133435 | − | 0.133435i | ||||
\(519\) | 1.92930e6 | 0.314399 | ||||||||
\(520\) | 4.23695e6 | + | 437577.i | 0.687139 | + | 0.0709654i | ||||
\(521\) | −6.78721e6 | −1.09546 | −0.547731 | − | 0.836655i | \(-0.684508\pi\) | ||||
−0.547731 | + | 0.836655i | \(0.684508\pi\) | |||||||
\(522\) | −760451. | − | 760451.i | −0.122150 | − | 0.122150i | ||||
\(523\) | 2.29263e6 | + | 2.29263e6i | 0.366506 | + | 0.366506i | 0.866201 | − | 0.499695i | \(-0.166555\pi\) |
−0.499695 | + | 0.866201i | \(0.666555\pi\) | |||||||
\(524\) | 5.23696e6 | 0.833204 | ||||||||
\(525\) | 253675. | − | 1.21504e6i | 0.0401680 | − | 0.192394i | ||||
\(526\) | 759526. | 0.119696 | ||||||||
\(527\) | 3.23179e6 | − | 3.23179e6i | 0.506893 | − | 0.506893i | ||||
\(528\) | 937400. | + | 662024.i | 0.146332 | + | 0.103345i | ||||
\(529\) | 5.80648e6i | 0.902139i | ||||||||
\(530\) | 219191. | + | 22637.2i | 0.0338947 | + | 0.00350053i | ||||
\(531\) | −5.31329e6 | −0.817763 | ||||||||
\(532\) | 4.99921e6 | + | 4.99921e6i | 0.765813 | + | 0.765813i | ||||
\(533\) | 1.05514e7 | − | 1.05514e7i | 1.60877 | − | 1.60877i | ||||
\(534\) | 319848. | 0.0485389 | ||||||||
\(535\) | 24406.2 | + | 30028.0i | 0.00368652 | + | 0.00453568i | ||||
\(536\) | 583828.i | 0.0877755i | ||||||||
\(537\) | 544855. | + | 544855.i | 0.0815353 | + | 0.0815353i | ||||
\(538\) | 539421. | + | 539421.i | 0.0803475 | + | 0.0803475i | ||||
\(539\) | −511219. | + | 88017.4i | −0.0757941 | + | 0.0130496i | ||||
\(540\) | −1.64008e6 | − | 2.01786e6i | −0.242037 | − | 0.297788i | ||||
\(541\) | − | 2.13626e6i | − | 0.313805i | −0.987614 | − | 0.156903i | \(-0.949849\pi\) | ||
0.987614 | − | 0.156903i | \(-0.0501509\pi\) | |||||||
\(542\) | 133450. | + | 133450.i | 0.0195129 | + | 0.0195129i | ||||
\(543\) | 1.42565e6 | − | 1.42565e6i | 0.207498 | − | 0.207498i | ||||
\(544\) | 3.83322e6i | 0.555350i | ||||||||
\(545\) | −770336. | + | 7.45896e6i | −0.111094 | + | 1.07569i | ||||
\(546\) | 483032.i | 0.0693417i | ||||||||
\(547\) | 3.51247e6 | − | 3.51247e6i | 0.501932 | − | 0.501932i | −0.410106 | − | 0.912038i | \(-0.634508\pi\) |
0.912038 | + | 0.410106i | \(0.134508\pi\) | |||||||
\(548\) | −4.45332e6 | + | 4.45332e6i | −0.633479 | + | 0.633479i | ||||
\(549\) | 8.81787e6 | 1.24863 | ||||||||
\(550\) | −991220. | − | 1.06384e6i | −0.139722 | − | 0.149958i | ||||
\(551\) | −7.37622e6 | −1.03504 | ||||||||
\(552\) | 130004. | − | 130004.i | 0.0181597 | − | 0.0181597i | ||||
\(553\) | −3.63925e6 | + | 3.63925e6i | −0.506056 | + | 0.506056i | ||||
\(554\) | − | 529550.i | − | 0.0733049i | ||||||
\(555\) | −146134. | + | 1.41498e6i | −0.0201381 | + | 0.194992i | ||||
\(556\) | 1.10704e7i | 1.51872i | ||||||||
\(557\) | 1.23335e6 | − | 1.23335e6i | 0.168442 | − | 0.168442i | −0.617852 | − | 0.786294i | \(-0.711997\pi\) |
0.786294 | + | 0.617852i | \(0.211997\pi\) | |||||||
\(558\) | 765732. | + | 765732.i | 0.104110 | + | 0.104110i | ||||
\(559\) | − | 4.64203e6i | − | 0.628317i | ||||||
\(560\) | 3.93827e6 | + | 4.84542e6i | 0.530683 | + | 0.652921i | ||||
\(561\) | −1.43692e6 | + | 247396.i | −0.192764 | + | 0.0331884i | ||||
\(562\) | 111336. | + | 111336.i | 0.0148695 | + | 0.0148695i | ||||
\(563\) | −4.59650e6 | − | 4.59650e6i | −0.611161 | − | 0.611161i | 0.332087 | − | 0.943249i | \(-0.392247\pi\) |
−0.943249 | + | 0.332087i | \(0.892247\pi\) | |||||||
\(564\) | 2.54850e6i | 0.337354i | ||||||||
\(565\) | −5.68262e6 | − | 6.99157e6i | −0.748907 | − | 0.921411i | ||||
\(566\) | 1.97743e6 | 0.259454 | ||||||||
\(567\) | −4.55693e6 | + | 4.55693e6i | −0.595271 | + | 0.595271i | ||||
\(568\) | −168033. | − | 168033.i | −0.0218536 | − | 0.0218536i | ||||
\(569\) | 1.33573e7 | 1.72957 | 0.864785 | − | 0.502143i | \(-0.167455\pi\) | ||||
0.864785 | + | 0.502143i | \(0.167455\pi\) | |||||||
\(570\) | 380667. | + | 39314.0i | 0.0490748 | + | 0.00506828i | ||||
\(571\) | 9.47840e6i | 1.21659i | 0.793711 | + | 0.608296i | \(0.208146\pi\) | ||||
−0.793711 | + | 0.608296i | \(0.791854\pi\) | |||||||
\(572\) | −1.05402e7 | − | 7.44384e6i | −1.34697 | − | 0.951277i | ||||
\(573\) | 18280.6 | − | 18280.6i | 0.00232597 | − | 0.00232597i | ||||
\(574\) | −2.05457e6 | −0.260280 | ||||||||
\(575\) | 2.07511e6 | − | 1.35829e6i | 0.261741 | − | 0.171325i | ||||
\(576\) | 5.77312e6 | 0.725027 | ||||||||
\(577\) | 6.28321e6 | + | 6.28321e6i | 0.785674 | + | 0.785674i | 0.980782 | − | 0.195108i | \(-0.0625057\pi\) |
−0.195108 | + | 0.980782i | \(0.562506\pi\) | |||||||
\(578\) | 99810.5 | + | 99810.5i | 0.0124267 | + | 0.0124267i | ||||
\(579\) | 1.90552e6 | 0.236220 | ||||||||
\(580\) | −6.79091e6 | − | 701342.i | −0.838220 | − | 0.0865685i | ||||
\(581\) | 1.19586e7 | 1.46974 | ||||||||
\(582\) | 90928.7 | − | 90928.7i | 0.0111274 | − | 0.0111274i | ||||
\(583\) | −1.11446e6 | − | 787073.i | −0.135798 | − | 0.0959056i | ||||
\(584\) | 2.65494e6i | 0.322124i | ||||||||
\(585\) | 8.61049e6 | + | 1.05938e7i | 1.04025 | + | 1.27986i | ||||
\(586\) | −412476. | −0.0496198 | ||||||||
\(587\) | 4.86606e6 | + | 4.86606e6i | 0.582884 | + | 0.582884i | 0.935695 | − | 0.352811i | \(-0.114774\pi\) |
−0.352811 | + | 0.935695i | \(0.614774\pi\) | |||||||
\(588\) | 89351.6 | − | 89351.6i | 0.0106576 | − | 0.0106576i | ||||
\(589\) | 7.42745e6 | 0.882168 | ||||||||
\(590\) | 1.14779e6 | − | 932904.i | 0.135748 | − | 0.110333i | ||||
\(591\) | 436716.i | 0.0514316i | ||||||||
\(592\) | −5.05999e6 | − | 5.05999e6i | −0.593397 | − | 0.593397i | ||||
\(593\) | −6.68231e6 | − | 6.68231e6i | −0.780351 | − | 0.780351i | 0.199539 | − | 0.979890i | \(-0.436055\pi\) |
−0.979890 | + | 0.199539i | \(0.936055\pi\) | |||||||
\(594\) | −119795. | − | 695789.i | −0.0139307 | − | 0.0809117i | ||||
\(595\) | −7.89124e6 | − | 814979.i | −0.913803 | − | 0.0943744i | ||||
\(596\) | − | 4.81431e6i | − | 0.555160i | ||||||
\(597\) | 850229. | + | 850229.i | 0.0976337 | + | 0.0976337i | ||||
\(598\) | −682464. | + | 682464.i | −0.0780417 | + | 0.0780417i | ||||
\(599\) | 9.73065e6i | 1.10809i | 0.832487 | + | 0.554045i | \(0.186916\pi\) | ||||
−0.832487 | + | 0.554045i | \(0.813084\pi\) | |||||||
\(600\) | 708651. | + | 147952.i | 0.0803626 | + | 0.0167781i | ||||
\(601\) | 1.28500e6i | 0.145117i | 0.997364 | + | 0.0725584i | \(0.0231164\pi\) | ||||
−0.997364 | + | 0.0725584i | \(0.976884\pi\) | |||||||
\(602\) | −451947. | + | 451947.i | −0.0508272 | + | 0.0508272i | ||||
\(603\) | −1.32313e6 | + | 1.32313e6i | −0.148186 | + | 0.148186i | ||||
\(604\) | −1.24508e7 | −1.38869 | ||||||||
\(605\) | 2.12332e6 | + | 8.74906e6i | 0.235845 | + | 0.971791i | ||||
\(606\) | 378516. | 0.0418700 | ||||||||
\(607\) | 2.93816e6 | − | 2.93816e6i | 0.323671 | − | 0.323671i | −0.526502 | − | 0.850174i | \(-0.676497\pi\) |
0.850174 | + | 0.526502i | \(0.176497\pi\) | |||||||
\(608\) | −4.40484e6 | + | 4.40484e6i | −0.483249 | + | 0.483249i | ||||
\(609\) | − | 1.58234e6i | − | 0.172885i | ||||||
\(610\) | −1.90486e6 | + | 1.54823e6i | −0.207271 | + | 0.168466i | ||||
\(611\) | − | 2.73437e7i | − | 2.96316i | ||||||
\(612\) | −5.75034e6 | + | 5.75034e6i | −0.620605 | + | 0.620605i | ||||
\(613\) | 2.21322e6 | + | 2.21322e6i | 0.237889 | + | 0.237889i | 0.815975 | − | 0.578087i | \(-0.196200\pi\) |
−0.578087 | + | 0.815975i | \(0.696200\pi\) | |||||||
\(614\) | − | 2.83970e6i | − | 0.303985i | ||||||
\(615\) | 1.96803e6 | − | 1.59958e6i | 0.209819 | − | 0.170537i | ||||
\(616\) | 616136. | + | 3.57862e6i | 0.0654222 | + | 0.379983i | ||||
\(617\) | 1.25927e6 | + | 1.25927e6i | 0.133170 | + | 0.133170i | 0.770550 | − | 0.637380i | \(-0.219982\pi\) |
−0.637380 | + | 0.770550i | \(0.719982\pi\) | |||||||
\(618\) | −366267. | − | 366267.i | −0.0385768 | − | 0.0385768i | ||||
\(619\) | − | 1.33220e7i | − | 1.39747i | −0.715380 | − | 0.698735i | \(-0.753746\pi\) | ||
0.715380 | − | 0.698735i | \(-0.246254\pi\) | |||||||
\(620\) | 6.83808e6 | + | 706213.i | 0.714422 | + | 0.0737830i | ||||
\(621\) | 1.20424e6 | 0.125310 | ||||||||
\(622\) | 615549. | − | 615549.i | 0.0637950 | − | 0.0637950i | ||||
\(623\) | −7.61920e6 | − | 7.61920e6i | −0.786482 | − | 0.786482i | ||||
\(624\) | 2.99939e6 | 0.308369 | ||||||||
\(625\) | 8.94984e6 | + | 3.90741e6i | 0.916463 | + | 0.400119i | ||||
\(626\) | 25507.8i | 0.00260158i | ||||||||
\(627\) | −1.93548e6 | − | 1.36691e6i | −0.196617 | − | 0.138858i | ||||
\(628\) | 9.01417e6 | − | 9.01417e6i | 0.912067 | − | 0.912067i | ||||
\(629\) | 9.09176e6 | 0.916266 | ||||||||
\(630\) | 193099. | − | 1.86973e6i | 0.0193834 | − | 0.187684i | ||||
\(631\) | −9.67806e6 | −0.967642 | −0.483821 | − | 0.875167i | \(-0.660751\pi\) | ||||
−0.483821 | + | 0.875167i | \(0.660751\pi\) | |||||||
\(632\) | −2.12253e6 | − | 2.12253e6i | −0.211379 | − | 0.211379i | ||||
\(633\) | −1.66279e6 | − | 1.66279e6i | −0.164941 | − | 0.164941i | ||||
\(634\) | 2.28618e6 | 0.225885 | ||||||||
\(635\) | −3.63853e6 | − | 4.47664e6i | −0.358090 | − | 0.440573i | ||||
\(636\) | 332353. | 0.0325804 | ||||||||
\(637\) | −958685. | + | 958685.i | −0.0936111 | + | 0.0936111i | ||||
\(638\) | −1.51412e6 | − | 1.06932e6i | −0.147268 | − | 0.104006i | ||||
\(639\) | − | 761624.i | − | 0.0737884i | ||||||
\(640\) | −5.91745e6 | + | 4.80960e6i | −0.571064 | + | 0.464151i | ||||
\(641\) | −4.75399e6 | −0.456997 | −0.228498 | − | 0.973544i | \(-0.573382\pi\) | ||||
−0.228498 | + | 0.973544i | \(0.573382\pi\) | |||||||
\(642\) | −1809.70 | − | 1809.70i | −0.000173288 | − | 0.000173288i | ||||
\(643\) | 8.80966e6 | − | 8.80966e6i | 0.840295 | − | 0.840295i | −0.148602 | − | 0.988897i | \(-0.547477\pi\) |
0.988897 | + | 0.148602i | \(0.0474774\pi\) | |||||||
\(644\) | −3.03041e6 | −0.287930 | ||||||||
\(645\) | 81048.7 | − | 784773.i | 0.00767090 | − | 0.0742754i | ||||
\(646\) | − | 2.44593e6i | − | 0.230602i | ||||||
\(647\) | −4.90324e6 | − | 4.90324e6i | −0.460492 | − | 0.460492i | 0.438325 | − | 0.898817i | \(-0.355572\pi\) |
−0.898817 | + | 0.438325i | \(0.855572\pi\) | |||||||
\(648\) | −2.65776e6 | − | 2.65776e6i | −0.248644 | − | 0.248644i | ||||
\(649\) | −9.02529e6 | + | 1.55390e6i | −0.841103 | + | 0.144814i | ||||
\(650\) | −3.72012e6 | − | 776686.i | −0.345361 | − | 0.0721045i | ||||
\(651\) | 1.59333e6i | 0.147351i | ||||||||
\(652\) | 9.86444e6 | + | 9.86444e6i | 0.908769 | + | 0.908769i | ||||
\(653\) | −9.36700e6 | + | 9.36700e6i | −0.859642 | + | 0.859642i | −0.991296 | − | 0.131653i | \(-0.957971\pi\) |
0.131653 | + | 0.991296i | \(0.457971\pi\) | |||||||
\(654\) | − | 495957.i | − | 0.0453419i | ||||||
\(655\) | −9.49925e6 | − | 981050.i | −0.865140 | − | 0.0893486i | ||||
\(656\) | 1.27579e7i | 1.15749i | ||||||||
\(657\) | −6.01688e6 | + | 6.01688e6i | −0.543824 | + | 0.543824i | ||||
\(658\) | −2.66218e6 | + | 2.66218e6i | −0.239702 | + | 0.239702i | ||||
\(659\) | −1.65001e7 | −1.48004 | −0.740020 | − | 0.672585i | \(-0.765184\pi\) | ||||
−0.740020 | + | 0.672585i | \(0.765184\pi\) | |||||||
\(660\) | −1.65193e6 | − | 1.44247e6i | −0.147616 | − | 0.128898i | ||||
\(661\) | 3.06152e6 | 0.272542 | 0.136271 | − | 0.990672i | \(-0.456488\pi\) | ||||
0.136271 | + | 0.990672i | \(0.456488\pi\) | |||||||
\(662\) | −1.62730e6 | + | 1.62730e6i | −0.144319 | + | 0.144319i | ||||
\(663\) | −2.69464e6 | + | 2.69464e6i | −0.238077 | + | 0.238077i | ||||
\(664\) | 6.97467e6i | 0.613908i | ||||||||
\(665\) | −8.13149e6 | − | 1.00045e7i | −0.713044 | − | 0.877287i | ||||
\(666\) | 2.15418e6i | 0.188190i | ||||||||
\(667\) | 2.23565e6 | − | 2.23565e6i | 0.194576 | − | 0.194576i | ||||
\(668\) | 8.76325e6 | + | 8.76325e6i | 0.759843 | + | 0.759843i | ||||
\(669\) | 73651.5i | 0.00636233i | ||||||||
\(670\) | 53511.5 | − | 518138.i | 0.00460533 | − | 0.0445922i | ||||
\(671\) | 1.49783e7 | − | 2.57883e6i | 1.28427 | − | 0.221114i | ||||
\(672\) | −944923. | − | 944923.i | −0.0807185 | − | 0.0807185i | ||||
\(673\) | 1.46489e6 | + | 1.46489e6i | 0.124672 | + | 0.124672i | 0.766690 | − | 0.642018i | \(-0.221902\pi\) |
−0.642018 | + | 0.766690i | \(0.721902\pi\) | |||||||
\(674\) | − | 198182.i | − | 0.0168041i | ||||||
\(675\) | 2.59691e6 | + | 3.96741e6i | 0.219381 | + | 0.335157i | ||||
\(676\) | −2.23430e7 | −1.88051 | ||||||||
\(677\) | −1.01776e6 | + | 1.01776e6i | −0.0853441 | + | 0.0853441i | −0.748490 | − | 0.663146i | \(-0.769221\pi\) |
0.663146 | + | 0.748490i | \(0.269221\pi\) | |||||||
\(678\) | 421362. | + | 421362.i | 0.0352031 | + | 0.0352031i | ||||
\(679\) | −4.33208e6 | −0.360597 | ||||||||
\(680\) | 475323. | − | 4.60243e6i | 0.0394200 | − | 0.381694i | ||||
\(681\) | 1.60509e6i | 0.132627i | ||||||||
\(682\) | 1.52463e6 | + | 1.07675e6i | 0.125518 | + | 0.0886449i | ||||
\(683\) | 1.70844e7 | − | 1.70844e7i | 1.40136 | − | 1.40136i | 0.605548 | − | 0.795809i | \(-0.292954\pi\) |
0.795809 | − | 0.605548i | \(-0.207046\pi\) | |||||||
\(684\) | −1.32157e7 | −1.08007 | ||||||||
\(685\) | 8.91206e6 | − | 7.24357e6i | 0.725691 | − | 0.589829i | ||||
\(686\) | 2.61388e6 | 0.212068 | ||||||||
\(687\) | 3.38264e6 | + | 3.38264e6i | 0.273441 | + | 0.273441i | ||||
\(688\) | 2.80636e6 | + | 2.80636e6i | 0.226034 | + | 0.226034i | ||||
\(689\) | −3.56594e6 | −0.286171 | ||||||||
\(690\) | −127292. | + | 103460.i | −0.0101784 | + | 0.00827279i | ||||
\(691\) | 1.82141e6 | 0.145115 | 0.0725577 | − | 0.997364i | \(-0.476884\pi\) | ||||
0.0725577 | + | 0.997364i | \(0.476884\pi\) | |||||||
\(692\) | 1.31147e7 | − | 1.31147e7i | 1.04110 | − | 1.04110i | ||||
\(693\) | −6.71386e6 | + | 9.50655e6i | −0.531054 | + | 0.751951i | ||||
\(694\) | 2.28977e6i | 0.180465i | ||||||||
\(695\) | 2.07384e6 | − | 2.00805e7i | 0.162860 | − | 1.57693i | ||||
\(696\) | 922875. | 0.0722137 | ||||||||
\(697\) | −1.14616e7 | − | 1.14616e7i | −0.893643 | − | 0.893643i | ||||
\(698\) | −2.56629e6 | + | 2.56629e6i | −0.199373 | + | 0.199373i | ||||
\(699\) | 863388. | 0.0668364 | ||||||||
\(700\) | −6.53501e6 | − | 9.98380e6i | −0.504082 | − | 0.770107i | ||||
\(701\) | − | 1.47651e7i | − | 1.13486i | −0.823422 | − | 0.567429i | \(-0.807938\pi\) | ||
0.823422 | − | 0.567429i | \(-0.192062\pi\) | |||||||
\(702\) | −1.30481e6 | − | 1.30481e6i | −0.0999318 | − | 0.0999318i | ||||
\(703\) | 1.04476e7 | + | 1.04476e7i | 0.797309 | + | 0.797309i | ||||
\(704\) | 9.80636e6 | − | 1.68838e6i | 0.745720 | − | 0.128392i | ||||
\(705\) | 477414. | − | 4.62268e6i | 0.0361762 | − | 0.350285i | ||||
\(706\) | 38081.2i | 0.00287540i | ||||||||
\(707\) | −9.01675e6 | − | 9.01675e6i | −0.678425 | − | 0.678425i | ||||
\(708\) | 1.57745e6 | − | 1.57745e6i | 0.118270 | − | 0.118270i | ||||
\(709\) | 1.67676e7i | 1.25273i | 0.779532 | + | 0.626363i | \(0.215457\pi\) | ||||
−0.779532 | + | 0.626363i | \(0.784543\pi\) | |||||||
\(710\) | 133725. | + | 164528.i | 0.00995560 | + | 0.0122488i | ||||
\(711\) | − | 9.62056e6i | − | 0.713717i | ||||||
\(712\) | 4.44377e6 | − | 4.44377e6i | 0.328512 | − | 0.328512i | ||||
\(713\) | −2.25118e6 | + | 2.25118e6i | −0.165839 | + | 0.165839i | ||||
\(714\) | 524699. | 0.0385181 | ||||||||
\(715\) | 1.77242e7 | + | 1.54768e7i | 1.29659 | + | 1.13218i | ||||
\(716\) | 7.40748e6 | 0.539993 | ||||||||
\(717\) | −2.19281e6 | + | 2.19281e6i | −0.159296 | + | 0.159296i | ||||
\(718\) | −565924. | + | 565924.i | −0.0409682 | + | 0.0409682i | ||||
\(719\) | 1.39297e7i | 1.00489i | 0.864609 | + | 0.502445i | \(0.167566\pi\) | ||||
−0.864609 | + | 0.502445i | \(0.832434\pi\) | |||||||
\(720\) | −1.16101e7 | − | 1.19905e6i | −0.834649 | − | 0.0861997i | ||||
\(721\) | 1.74499e7i | 1.25013i | ||||||||
\(722\) | 780646. | − | 780646.i | 0.0557328 | − | 0.0557328i | ||||
\(723\) | −382304. | − | 382304.i | −0.0271996 | − | 0.0271996i | ||||
\(724\) | − | 1.93822e7i | − | 1.37422i | ||||||
\(725\) | 1.21866e7 | + | 2.54431e6i | 0.861065 | + | 0.179773i | ||||
\(726\) | −199138. | − | 561170.i | −0.0140221 | − | 0.0395142i | ||||
\(727\) | 8.02094e6 | + | 8.02094e6i | 0.562846 | + | 0.562846i | 0.930115 | − | 0.367269i | \(-0.119707\pi\) |
−0.367269 | + | 0.930115i | \(0.619707\pi\) | |||||||
\(728\) | 6.71095e6 | + | 6.71095e6i | 0.469306 | + | 0.469306i | ||||
\(729\) | − | 1.08707e7i | − | 0.757599i | ||||||
\(730\) | 243342. | − | 2.35622e6i | 0.0169009 | − | 0.163647i | ||||
\(731\) | −5.04246e6 | −0.349019 | ||||||||
\(732\) | −2.61792e6 | + | 2.61792e6i | −0.180584 | + | 0.180584i | ||||
\(733\) | 1.26801e7 | + | 1.26801e7i | 0.871691 | + | 0.871691i | 0.992657 | − | 0.120966i | \(-0.0385991\pi\) |
−0.120966 | + | 0.992657i | \(0.538599\pi\) | |||||||
\(734\) | −138179. | −0.00946677 | ||||||||
\(735\) | −178812. | + | 145335.i | −0.0122089 | + | 0.00992321i | ||||
\(736\) | − | 2.67012e6i | − | 0.181692i | ||||||
\(737\) | −1.86054e6 | + | 2.63445e6i | −0.126174 | + | 0.178657i | ||||
\(738\) | 2.71569e6 | − | 2.71569e6i | 0.183543 | − | 0.183543i | ||||
\(739\) | −8.77406e6 | −0.591002 | −0.295501 | − | 0.955342i | \(-0.595487\pi\) | ||||
−0.295501 | + | 0.955342i | \(0.595487\pi\) | |||||||
\(740\) | 8.62517e6 | + | 1.06119e7i | 0.579013 | + | 0.712384i | ||||
\(741\) | −6.19295e6 | −0.414335 | ||||||||
\(742\) | 347179. | + | 347179.i | 0.0231496 | + | 0.0231496i | ||||
\(743\) | 9.85338e6 | + | 9.85338e6i | 0.654807 | + | 0.654807i | 0.954147 | − | 0.299340i | \(-0.0967664\pi\) |
−0.299340 | + | 0.954147i | \(0.596766\pi\) | |||||||
\(744\) | −929284. | −0.0615483 | ||||||||
\(745\) | −901873. | + | 8.73261e6i | −0.0595326 | + | 0.576439i | ||||
\(746\) | 2.50275e6 | 0.164653 | ||||||||
\(747\) | −1.58066e7 | + | 1.58066e7i | −1.03643 | + | 1.03643i | ||||
\(748\) | −8.08596e6 | + | 1.14494e7i | −0.528418 | + | 0.748218i | ||||
\(749\) | 86219.0i | 0.00561563i | ||||||||
\(750\) | −615355. | − | 196257.i | −0.0399460 | − | 0.0127401i | ||||
\(751\) | −3.38585e6 | −0.219063 | −0.109531 | − | 0.993983i | \(-0.534935\pi\) | ||||
−0.109531 | + | 0.993983i | \(0.534935\pi\) | |||||||
\(752\) | 1.65308e7 | + | 1.65308e7i | 1.06598 | + | 1.06598i | ||||
\(753\) | 1.24165e6 | − | 1.24165e6i | 0.0798015 | − | 0.0798015i | ||||
\(754\) | −4.84471e6 | −0.310341 | ||||||||
\(755\) | 2.25843e7 | + | 2.33243e6i | 1.44191 | + | 0.148916i | ||||
\(756\) | − | 5.79386e6i | − | 0.368692i | ||||||
\(757\) | −1.13440e7 | − | 1.13440e7i | −0.719494 | − | 0.719494i | 0.249007 | − | 0.968502i | \(-0.419896\pi\) |
−0.968502 | + | 0.249007i | \(0.919896\pi\) | |||||||
\(758\) | 1.64007e6 | + | 1.64007e6i | 0.103678 | + | 0.103678i | ||||
\(759\) | 1.00092e6 | − | 172330.i | 0.0630659 | − | 0.0108581i | ||||
\(760\) | 5.83497e6 | − | 4.74256e6i | 0.366441 | − | 0.297837i | ||||
\(761\) | 1.02068e7i | 0.638891i | 0.947605 | + | 0.319446i | \(0.103497\pi\) | ||||
−0.947605 | + | 0.319446i | \(0.896503\pi\) | |||||||
\(762\) | 269794. | + | 269794.i | 0.0168324 | + | 0.0168324i | ||||
\(763\) | −1.18143e7 | + | 1.18143e7i | −0.734680 | + | 0.734680i | ||||
\(764\) | − | 248530.i | − | 0.0154044i | ||||||
\(765\) | 1.15077e7 | − | 9.35324e6i | 0.710942 | − | 0.577841i | ||||
\(766\) | 6.18015e6i | 0.380563i | ||||||||
\(767\) | −1.69251e7 | + | 1.69251e7i | −1.03882 | + | 1.03882i | ||||
\(768\) | −1.43250e6 | + | 1.43250e6i | −0.0876378 | + | 0.0876378i | ||||
\(769\) | 3.02499e7 | 1.84462 | 0.922312 | − | 0.386447i | \(-0.126298\pi\) | ||||
0.922312 | + | 0.386447i | \(0.126298\pi\) | |||||||
\(770\) | −218808. | − | 3.23244e6i | −0.0132995 | − | 0.196473i | ||||
\(771\) | 3.19502e6 | 0.193570 | ||||||||
\(772\) | 1.29531e7 | − | 1.29531e7i | 0.782220 | − | 0.782220i | ||||
\(773\) | −6.66230e6 | + | 6.66230e6i | −0.401028 | + | 0.401028i | −0.878595 | − | 0.477567i | \(-0.841519\pi\) |
0.477567 | + | 0.878595i | \(0.341519\pi\) | |||||||
\(774\) | − | 1.19475e6i | − | 0.0716843i | ||||||
\(775\) | −1.22712e7 | − | 2.56198e6i | −0.733893 | − | 0.153222i | ||||
\(776\) | − | 2.52662e6i | − | 0.150621i | ||||||
\(777\) | −2.24120e6 | + | 2.24120e6i | −0.133177 | + | 0.133177i | ||||
\(778\) | −3.71987e6 | − | 3.71987e6i | −0.220333 | − | 0.220333i | ||||
\(779\) | − | 2.63416e7i | − | 1.55525i | ||||||
\(780\) | −5.70153e6 | − | 588834.i | −0.335548 | − | 0.0346543i | ||||
\(781\) | −222740. | − | 1.29371e6i | −0.0130669 | − | 0.0758945i | ||||
\(782\) | 741335. | + | 741335.i | 0.0433508 | + | 0.0433508i | ||||
\(783\) | 4.27436e6 | + | 4.27436e6i | 0.249153 | + | 0.249153i | ||||
\(784\) | − | 1.15916e6i | − | 0.0673522i | ||||||
\(785\) | −1.80393e7 | + | 1.46620e7i | −1.04483 | + | 0.849220i | ||||
\(786\) | 631618. | 0.0364669 | ||||||||
\(787\) | −1.23587e6 | + | 1.23587e6i | −0.0711273 | + | 0.0711273i | −0.741776 | − | 0.670648i | \(-0.766016\pi\) |
0.670648 | + | 0.741776i | \(0.266016\pi\) | |||||||
\(788\) | 2.96864e6 | + | 2.96864e6i | 0.170311 | + | 0.170311i | ||||
\(789\) | −2.08896e6 | −0.119464 | ||||||||
\(790\) | 1.68917e6 | + | 2.07826e6i | 0.0962954 | + | 0.118476i | ||||
\(791\) | − | 2.00748e7i | − | 1.14080i | ||||||
\(792\) | −5.54454e6 | − | 3.91575e6i | −0.314089 | − | 0.221820i | ||||
\(793\) | 2.80886e7 | − | 2.80886e7i | 1.58616 | − | 1.58616i | ||||
\(794\) | 6.51608e6 | 0.366805 | ||||||||
\(795\) | −602851. | − | 62260.3i | −0.0338292 | − | 0.00349376i | ||||
\(796\) | 1.15591e7 | 0.646610 | ||||||||
\(797\) | 1.75174e7 | + | 1.75174e7i | 0.976840 | + | 0.976840i | 0.999738 | − | 0.0228981i | \(-0.00728933\pi\) |
−0.0228981 | + | 0.999738i | \(0.507289\pi\) | |||||||
\(798\) | 602944. | + | 602944.i | 0.0335173 | + | 0.0335173i | ||||
\(799\) | −2.97024e7 | −1.64598 | ||||||||
\(800\) | 8.79680e6 | − | 5.75804e6i | 0.485959 | − | 0.318090i | ||||
\(801\) | 2.01418e7 | 1.10922 | ||||||||
\(802\) | 151896. | − | 151896.i | 0.00833891 | − | 0.00833891i | ||||
\(803\) | −8.46076e6 | + | 1.19801e7i | −0.463042 | + | 0.655649i | ||||
\(804\) | − | 785640.i | − | 0.0428631i | ||||||
\(805\) | 5.49682e6 | + | 567693.i | 0.298966 | + | 0.0308762i | ||||
\(806\) | 4.87835e6 | 0.264506 | ||||||||
\(807\) | −1.48360e6 | − | 1.48360e6i | −0.0801922 | − | 0.0801922i | ||||
\(808\) | 5.25887e6 | − | 5.25887e6i | 0.283377 | − | 0.283377i | ||||
\(809\) | −3.44189e6 | −0.184895 | −0.0924477 | − | 0.995718i | \(-0.529469\pi\) | ||||
−0.0924477 | + | 0.995718i | \(0.529469\pi\) | |||||||
\(810\) | 2.11512e6 | + | 2.60232e6i | 0.113272 | + | 0.139363i | ||||
\(811\) | 1.27797e7i | 0.682291i | 0.940010 | + | 0.341146i | \(0.110815\pi\) | ||||
−0.940010 | + | 0.341146i | \(0.889185\pi\) | |||||||
\(812\) | −1.07562e7 | − | 1.07562e7i | −0.572492 | − | 0.572492i | ||||
\(813\) | −367035. | − | 367035.i | −0.0194752 | − | 0.0194752i | ||||
\(814\) | 630000. | + | 3.65914e6i | 0.0333257 | + | 0.193561i | ||||
\(815\) | −1.60451e7 | − | 1.97409e7i | −0.846150 | − | 1.04105i | ||||
\(816\) | − | 3.25812e6i | − | 0.171294i | ||||||
\(817\) | −5.79441e6 | − | 5.79441e6i | −0.303706 | − | 0.303706i | ||||
\(818\) | −2.23079e6 | + | 2.23079e6i | −0.116567 | + | 0.116567i | ||||
\(819\) | 3.04180e7i | 1.58460i | ||||||||
\(820\) | 2.50460e6 | − | 2.42514e7i | 0.130078 | − | 1.25951i | ||||
\(821\) | − | 2.66295e7i | − | 1.37881i | −0.724374 | − | 0.689407i | \(-0.757871\pi\) | ||
0.724374 | − | 0.689407i | \(-0.242129\pi\) | |||||||
\(822\) | −537105. | + | 537105.i | −0.0277255 | + | 0.0277255i | ||||
\(823\) | −1.61359e7 | + | 1.61359e7i | −0.830410 | + | 0.830410i | −0.987573 | − | 0.157163i | \(-0.949765\pi\) |
0.157163 | + | 0.987573i | \(0.449765\pi\) | |||||||
\(824\) | −1.01774e7 | −0.522177 | ||||||||
\(825\) | 2.72620e6 | + | 2.92594e6i | 0.139451 | + | 0.149668i | ||||
\(826\) | 3.29564e6 | 0.168070 | ||||||||
\(827\) | −2.40113e7 | + | 2.40113e7i | −1.22082 | + | 1.22082i | −0.253478 | + | 0.967341i | \(0.581574\pi\) |
−0.967341 | + | 0.253478i | \(0.918426\pi\) | |||||||
\(828\) | 4.00554e6 | − | 4.00554e6i | 0.203041 | − | 0.203041i | ||||
\(829\) | 7.97873e6i | 0.403225i | 0.979465 | + | 0.201612i | \(0.0646181\pi\) | ||||
−0.979465 | + | 0.201612i | \(0.935382\pi\) | |||||||
\(830\) | 639272. | − | 6.18991e6i | 0.0322100 | − | 0.311881i | ||||
\(831\) | 1.45645e6i | 0.0731631i | ||||||||
\(832\) | 1.83898e7 | − | 1.83898e7i | 0.921018 | − | 0.921018i | ||||
\(833\) | 1.04138e6 | + | 1.04138e6i | 0.0519994 | + | 0.0519994i | ||||
\(834\) | 1.33518e6i | 0.0664698i | ||||||||
\(835\) | −1.42539e7 | − | 1.75372e7i | −0.707485 | − | 0.870449i | ||||
\(836\) | −2.24485e7 | + | 3.86500e6i | −1.11089 | + | 0.191264i | ||||
\(837\) | −4.30404e6 | − | 4.30404e6i | −0.212355 | − | 0.212355i | ||||
\(838\) | 2.75652e6 | + | 2.75652e6i | 0.135597 | + | 0.135597i | ||||
\(839\) | − | 1.69830e7i | − | 0.832931i | −0.909152 | − | 0.416465i | \(-0.863269\pi\) | ||
0.909152 | − | 0.416465i | \(-0.136731\pi\) | |||||||
\(840\) | 1.01737e6 | + | 1.25171e6i | 0.0497486 | + | 0.0612078i | ||||
\(841\) | −4.64060e6 | −0.226248 | ||||||||
\(842\) | −654616. | + | 654616.i | −0.0318205 | + | 0.0318205i | ||||
\(843\) | −306214. | − | 306214.i | −0.0148408 | − | 0.0148408i | ||||
\(844\) | −2.26062e7 | −1.09237 | ||||||||
\(845\) | 4.05277e7 | + | 4.18556e6i | 1.95259 | + | 0.201656i | ||||
\(846\) | − | 7.03762e6i | − | 0.338065i | ||||||
\(847\) | −8.62409e6 | + | 1.81116e7i | −0.413052 | + | 0.867455i | ||||
\(848\) | 2.15581e6 | − | 2.15581e6i | 0.102948 | − | 0.102948i | ||||
\(849\) | −5.43863e6 | −0.258953 | ||||||||
\(850\) | −843684. | + | 4.04102e6i | −0.0400528 | + | 0.191842i | ||||
\(851\) | −6.33308e6 | −0.299772 | ||||||||
\(852\) | 226117. | + | 226117.i | 0.0106717 | + | 0.0106717i | ||||
\(853\) | −2.49281e7 | − | 2.49281e7i | −1.17305 | − | 1.17305i | −0.981479 | − | 0.191569i | \(-0.938642\pi\) |
−0.191569 | − | 0.981479i | \(-0.561358\pi\) | |||||||
\(854\) | −5.46940e6 | −0.256622 | ||||||||
\(855\) | 2.39718e7 | + | 2.47572e6i | 1.12146 | + | 0.115821i | ||||
\(856\) | −50285.8 | −0.00234564 | ||||||||
\(857\) | −1.77081e7 | + | 1.77081e7i | −0.823609 | + | 0.823609i | −0.986624 | − | 0.163015i | \(-0.947878\pi\) |
0.163015 | + | 0.986624i | \(0.447878\pi\) | |||||||
\(858\) | −1.27123e6 | − | 897785.i | −0.0589529 | − | 0.0416346i | ||||
\(859\) | − | 2.11987e7i | − | 0.980225i | −0.871659 | − | 0.490113i | \(-0.836956\pi\) | ||
0.871659 | − | 0.490113i | \(-0.163044\pi\) | |||||||
\(860\) | −4.78368e6 | − | 5.88556e6i | −0.220554 | − | 0.271357i | ||||
\(861\) | 5.65079e6 | 0.259777 | ||||||||
\(862\) | 3.23600e6 | + | 3.23600e6i | 0.148334 | + | 0.148334i | ||||
\(863\) | 1.53434e7 | − | 1.53434e7i | 0.701286 | − | 0.701286i | −0.263400 | − | 0.964687i | \(-0.584844\pi\) |
0.964687 | + | 0.263400i | \(0.0848440\pi\) | |||||||
\(864\) | 5.10502e6 | 0.232655 | ||||||||
\(865\) | −2.62454e7 | + | 2.13318e7i | −1.19265 | + | 0.969363i | ||||
\(866\) | − | 2.80127e6i | − | 0.126929i | ||||||
\(867\) | −274514. | − | 274514.i | −0.0124027 | − | 0.0124027i | ||||
\(868\) | 1.08309e7 | + | 1.08309e7i | 0.487939 | + | 0.487939i | ||||
\(869\) | −2.81358e6 | − | 1.63417e7i | −0.126389 | − | 0.734088i | ||||
\(870\) | −819037. | − | 84587.3i | −0.0366864 | − | 0.00378885i | ||||
\(871\) | 8.42942e6i | 0.376489i | ||||||||
\(872\) | −6.89052e6 | − | 6.89052e6i | −0.306875 | − | 0.306875i | ||||
\(873\) | 5.72606e6 | − | 5.72606e6i | 0.254285 | − | 0.254285i | ||||
\(874\) | 1.70377e6i | 0.0754453i | ||||||||
\(875\) | 9.98347e6 | + | 1.93337e7i | 0.440820 | + | 0.853679i | ||||
\(876\) | − | 3.57268e6i | − | 0.157302i | ||||||
\(877\) | 3.15258e7 | − | 3.15258e7i | 1.38410 | − | 1.38410i | 0.546907 | − | 0.837193i | \(-0.315805\pi\) |
0.837193 | − | 0.546907i | \(-0.184195\pi\) | |||||||
\(878\) | 556438. | − | 556438.i | 0.0243602 | − | 0.0243602i | ||||
\(879\) | 1.13445e6 | 0.0495239 | ||||||||
\(880\) | −2.00718e7 | + | 1.35869e6i | −0.873737 | + | 0.0591444i | ||||
\(881\) | −2.91839e7 | −1.26679 | −0.633394 | − | 0.773829i | \(-0.718339\pi\) | ||||
−0.633394 | + | 0.773829i | \(0.718339\pi\) | |||||||
\(882\) | −246743. | + | 246743.i | −0.0106800 | + | 0.0106800i | ||||
\(883\) | −757927. | + | 757927.i | −0.0327134 | + | 0.0327134i | −0.723274 | − | 0.690561i | \(-0.757364\pi\) |
0.690561 | + | 0.723274i | \(0.257364\pi\) | |||||||
\(884\) | 3.66345e7i | 1.57674i | ||||||||
\(885\) | −3.15682e6 | + | 2.56581e6i | −0.135485 | + | 0.110120i | ||||
\(886\) | 2.74498e6i | 0.117477i | ||||||||
\(887\) | −1.51267e7 | + | 1.51267e7i | −0.645558 | + | 0.645558i | −0.951916 | − | 0.306358i | \(-0.900889\pi\) |
0.306358 | + | 0.951916i | \(0.400889\pi\) | |||||||
\(888\) | −1.30714e6 | − | 1.30714e6i | −0.0556277 | − | 0.0556277i | ||||
\(889\) | − | 1.28537e7i | − | 0.545475i | ||||||
\(890\) | −4.35108e6 | + | 3.53648e6i | −0.184129 | + | 0.149657i | ||||
\(891\) | −3.52306e6 | − | 2.04625e7i | −0.148671 | − | 0.863504i | ||||
\(892\) | 500658. | + | 500658.i | 0.0210683 | + | 0.0210683i | ||||
\(893\) | −3.41318e7 | − | 3.41318e7i | −1.43229 | − | 1.43229i | ||||
\(894\) | − | 580643.i | − | 0.0242977i | ||||||
\(895\) | −1.34363e7 | − | 1.38766e6i | −0.560690 | − | 0.0579061i | ||||
\(896\) | −1.69907e7 | −0.707036 | ||||||||
\(897\) | 1.87701e6 | − | 1.87701e6i | 0.0778909 | − | 0.0778909i | ||||
\(898\) | 1.26262e6 | + | 1.26262e6i | 0.0522496 | + | 0.0522496i | ||||
\(899\) | −1.59808e7 | −0.659475 | ||||||||
\(900\) | 2.18342e7 | + | 4.55854e6i | 0.898527 | + | 0.187594i | ||||
\(901\) | 3.87354e6i | 0.158963i | ||||||||
\(902\) | 3.81872e6 | − | 5.40715e6i | 0.156279 | − | 0.221285i | ||||
\(903\) | 1.24301e6 | − | 1.24301e6i | 0.0507290 | − | 0.0507290i | ||||
\(904\) | 1.17083e7 | 0.476511 | ||||||||
\(905\) | −3.63090e6 | + | 3.51571e7i | −0.147365 | + | 1.42689i | ||||
\(906\) | −1.50166e6 | −0.0607787 | ||||||||
\(907\) | 2.81619e7 | + | 2.81619e7i | 1.13670 | + | 1.13670i | 0.989039 | + | 0.147657i | \(0.0471731\pi\) |
0.147657 | + | 0.989039i | \(0.452827\pi\) | |||||||
\(908\) | 1.09108e7 | + | 1.09108e7i | 0.439180 | + | 0.439180i | ||||
\(909\) | 2.38363e7 | 0.956817 | ||||||||
\(910\) | −5.34077e6 | − | 6.57097e6i | −0.213796 | − | 0.263042i | ||||
\(911\) | 4.14771e7 | 1.65582 | 0.827908 | − | 0.560864i | \(-0.189531\pi\) | ||||
0.827908 | + | 0.560864i | \(0.189531\pi\) | |||||||
\(912\) | 3.74398e6 | − | 3.74398e6i | 0.149055 | − | 0.149055i | ||||
\(913\) | −2.22268e7 | + | 3.14723e7i | −0.882471 | + | 1.24954i | ||||
\(914\) | − | 3.89393e6i | − | 0.154178i | ||||||
\(915\) | 5.23902e6 | − | 4.25819e6i | 0.206870 | − | 0.168140i | ||||
\(916\) | 4.59881e7 | 1.81095 | ||||||||
\(917\) | −1.50460e7 | − | 1.50460e7i | −0.590877 | − | 0.590877i | ||||
\(918\) | −1.41736e6 | + | 1.41736e6i | −0.0555104 | + | 0.0555104i | ||||
\(919\) | 1.89628e7 | 0.740650 | 0.370325 | − | 0.928902i | \(-0.379246\pi\) | ||||
0.370325 | + | 0.928902i | \(0.379246\pi\) | |||||||
\(920\) | −331098. | + | 3.20593e6i | −0.0128969 | + | 0.124878i | ||||
\(921\) | 7.81017e6i | 0.303397i | ||||||||
\(922\) | −4.01097e6 | − | 4.01097e6i | −0.155390 | − | 0.155390i | ||||
\(923\) | −2.42609e6 | − | 2.42609e6i | −0.0937351 | − | 0.0937351i | ||||
\(924\) | −829116. | − | 4.81564e6i | −0.0319474 | − | 0.185556i | ||||
\(925\) | −1.36571e7 | − | 2.08646e7i | −0.524813 | − | 0.801779i | ||||
\(926\) | 8.84028e6i | 0.338796i | ||||||||
\(927\) | −2.30649e7 | − | 2.30649e7i | −0.881562 | − | 0.881562i | ||||
\(928\) | 9.47737e6 | − | 9.47737e6i | 0.361259 | − | 0.361259i | ||||
\(929\) | 1.78035e7i | 0.676810i | 0.941001 | + | 0.338405i | \(0.109887\pi\) | ||||
−0.941001 | + | 0.338405i | \(0.890113\pi\) | |||||||
\(930\) | 824725. | + | 85174.7i | 0.0312681 | + | 0.00322926i | ||||
\(931\) | 2.39335e6i | 0.0904967i | ||||||||
\(932\) | 5.86901e6 | − | 5.86901e6i | 0.221322 | − | 0.221322i | ||||
\(933\) | −1.69297e6 | + | 1.69297e6i | −0.0636716 | + | 0.0636716i | ||||
\(934\) | 1.13518e6 | 0.0425790 | ||||||||
\(935\) | 1.68118e7 | − | 1.92531e7i | 0.628907 | − | 0.720232i | ||||
\(936\) | −1.77408e7 | −0.661886 | ||||||||
\(937\) | 1.04846e7 | − | 1.04846e7i | 0.390123 | − | 0.390123i | −0.484608 | − | 0.874731i | \(-0.661038\pi\) |
0.874731 | + | 0.484608i | \(0.161038\pi\) | |||||||
\(938\) | 820686. | − | 820686.i | 0.0304558 | − | 0.0304558i | ||||
\(939\) | − | 70155.2i | − | 0.00259655i | ||||||
\(940\) | −2.81781e7 | − | 3.46687e7i | −1.04014 | − | 1.27973i | ||||
\(941\) | 1.69543e7i | 0.624173i | 0.950054 | + | 0.312086i | \(0.101028\pi\) | ||||
−0.950054 | + | 0.312086i | \(0.898972\pi\) | |||||||
\(942\) | 1.08718e6 | − | 1.08718e6i | 0.0399185 | − | 0.0399185i | ||||
\(943\) | 7.98386e6 | + | 7.98386e6i | 0.292371 | + | 0.292371i | ||||
\(944\) | − | 2.04643e7i | − | 0.747422i | ||||||
\(945\) | −1.08538e6 | + | 1.05094e7i | −0.0395367 | + | 0.382824i | ||||
\(946\) | −349410. | − | 2.02943e6i | −0.0126942 | − | 0.0737303i | ||||
\(947\) | 1.12252e7 | + | 1.12252e7i | 0.406741 | + | 0.406741i | 0.880600 | − | 0.473860i | \(-0.157140\pi\) |
−0.473860 | + | 0.880600i | \(0.657140\pi\) | |||||||
\(948\) | 2.85623e6 | + | 2.85623e6i | 0.103222 | + | 0.103222i | ||||
\(949\) | 3.83326e7i | 1.38166i | ||||||||
\(950\) | −5.61313e6 | + | 3.67413e6i | −0.201788 | + | 0.132083i | ||||
\(951\) | −6.28780e6 | −0.225449 | ||||||||
\(952\) | 7.28985e6 | − | 7.28985e6i | 0.260691 | − | 0.260691i | ||||
\(953\) | 1.49848e7 | + | 1.49848e7i | 0.534464 | + | 0.534464i | 0.921898 | − | 0.387434i | \(-0.126638\pi\) |
−0.387434 | + | 0.921898i | \(0.626638\pi\) | |||||||
\(954\) | −917787. | −0.0326491 | ||||||||
\(955\) | −46557.6 | + | 450805.i | −0.00165189 | + | 0.0159949i | ||||
\(956\) | 2.98120e7i | 1.05498i | ||||||||
\(957\) | 4.16435e6 | + | 2.94101e6i | 0.146983 | + | 0.103805i | ||||
\(958\) | −5.29329e6 | + | 5.29329e6i | −0.186342 | + | 0.186342i | ||||
\(959\) | 2.55891e7 | 0.898480 | ||||||||
\(960\) | 3.43002e6 | − | 2.78786e6i | 0.120121 | − | 0.0976322i | ||||
\(961\) | −1.25374e7 | −0.437924 | ||||||||
\(962\) | 6.86196e6 | + | 6.86196e6i | 0.239062 | + | 0.239062i | ||||
\(963\) | −113962. | − | 113962.i | −0.00396001 | − | 0.00396001i | ||||
\(964\) | −5.19753e6 | −0.180138 | ||||||||
\(965\) | −2.59219e7 | + | 2.10689e7i | −0.896083 | + | 0.728321i | ||||
\(966\) | −365491. | −0.0126018 | ||||||||
\(967\) | 3.17757e7 | − | 3.17757e7i | 1.09277 | − | 1.09277i | 0.0975384 | − | 0.995232i | \(-0.468903\pi\) |
0.995232 | − | 0.0975384i | \(-0.0310969\pi\) | |||||||
\(968\) | −1.05633e7 | − | 5.02986e6i | −0.362335 | − | 0.172531i | ||||
\(969\) | 6.72716e6i | 0.230156i | ||||||||
\(970\) | −231580. | + | 2.24233e6i | −0.00790264 | + | 0.0765193i | ||||
\(971\) | −9.35785e6 | −0.318514 | −0.159257 | − | 0.987237i | \(-0.550910\pi\) | ||||
−0.159257 | + | 0.987237i | \(0.550910\pi\) | |||||||
\(972\) | 1.15691e7 | + | 1.15691e7i | 0.392767 | + | 0.392767i | ||||
\(973\) | 3.18057e7 | − | 3.18057e7i | 1.07702 | − | 1.07702i | ||||
\(974\) | 1.70461e6 | 0.0575742 | ||||||||
\(975\) | 1.02316e7 | + | 2.13616e6i | 0.344693 | + | 0.0719651i | ||||
\(976\) | 3.39622e7i | 1.14123i | ||||||||
\(977\) | 1.40931e6 | + | 1.40931e6i | 0.0472355 | + | 0.0472355i | 0.730330 | − | 0.683094i | \(-0.239366\pi\) |
−0.683094 | + | 0.730330i | \(0.739366\pi\) | |||||||
\(978\) | 1.18973e6 | + | 1.18973e6i | 0.0397741 | + | 0.0397741i | ||||
\(979\) | 3.42133e7 | − | 5.89056e6i | 1.14088 | − | 0.196426i | ||||
\(980\) | −227564. | + | 2.20344e6i | −0.00756899 | + | 0.0732885i | ||||
\(981\) | − | 3.12319e7i | − | 1.03616i | ||||||
\(982\) | 2.32860e6 | + | 2.32860e6i | 0.0770578 | + | 0.0770578i | ||||
\(983\) | 2.12347e6 | − | 2.12347e6i | 0.0700910 | − | 0.0700910i | −0.671192 | − | 0.741283i | \(-0.734218\pi\) |
0.741283 | + | 0.671192i | \(0.234218\pi\) | |||||||
\(984\) | 3.29573e6i | 0.108508i | ||||||||
\(985\) | −4.82866e6 | − | 5.94090e6i | −0.158575 | − | 0.195102i | ||||
\(986\) | 5.26262e6i | 0.172389i | ||||||||
\(987\) | 7.32192e6 | − | 7.32192e6i | 0.239239 | − | 0.239239i | ||||
\(988\) | −4.20975e7 | + | 4.20975e7i | −1.37203 | + | 1.37203i | ||||
\(989\) | 3.51244e6 | 0.114188 | ||||||||
\(990\) | 4.56179e6 | + | 3.98335e6i | 0.147927 | + | 0.129170i | ||||
\(991\) | 7.24962e6 | 0.234494 | 0.117247 | − | 0.993103i | \(-0.462593\pi\) | ||||
0.117247 | + | 0.993103i | \(0.462593\pi\) | |||||||
\(992\) | −9.54319e6 | + | 9.54319e6i | −0.307903 | + | 0.307903i | ||||
\(993\) | 4.47564e6 | − | 4.47564e6i | 0.144040 | − | 0.144040i | ||||
\(994\) | 472407.i | 0.0151653i | ||||||||
\(995\) | −2.09669e7 | − | 2.16539e6i | −0.671394 | − | 0.0693392i | ||||
\(996\) | − | 9.38560e6i | − | 0.299788i | ||||||
\(997\) | 1.80710e7 | − | 1.80710e7i | 0.575764 | − | 0.575764i | −0.357970 | − | 0.933733i | \(-0.616531\pi\) |
0.933733 | + | 0.357970i | \(0.116531\pi\) | |||||||
\(998\) | −3.26085e6 | − | 3.26085e6i | −0.103634 | − | 0.103634i | ||||
\(999\) | − | 1.21083e7i | − | 0.383856i |
(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 | 55.6.e.b.32.14 | yes | 52 | |
5.3 | odd | 4 | inner | 55.6.e.b.43.13 | yes | 52 | |
11.10 | odd | 2 | inner | 55.6.e.b.32.13 | ✓ | 52 | |
55.43 | even | 4 | inner | 55.6.e.b.43.14 | yes | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
55.6.e.b.32.13 | ✓ | 52 | 11.10 | odd | 2 | inner | |
55.6.e.b.32.14 | yes | 52 | 1.1 | even | 1 | trivial | |
55.6.e.b.43.13 | yes | 52 | 5.3 | odd | 4 | inner | |
55.6.e.b.43.14 | yes | 52 | 55.43 | even | 4 | inner |