Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,6,Mod(6,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.6");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.c (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.89650425196\) |
Analytic rank: | \(0\) |
Dimension: | \(34\) |
Relative dimension: | \(17\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 6.5 | ||
Character | \(\chi\) | \(=\) | 43.6 |
Dual form | 43.6.c.a.36.5 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −6.28648 | −1.11130 | −0.555651 | − | 0.831415i | \(-0.687531\pi\) | ||||
−0.555651 | + | 0.831415i | \(0.687531\pi\) | |||||||
\(3\) | 10.0721 | − | 17.4453i | 0.646123 | − | 1.11912i | −0.337918 | − | 0.941175i | \(-0.609723\pi\) |
0.984041 | − | 0.177942i | \(-0.0569438\pi\) | |||||||
\(4\) | 7.51978 | 0.234993 | ||||||||
\(5\) | 38.9844 | − | 67.5229i | 0.697374 | − | 1.20789i | −0.272000 | − | 0.962297i | \(-0.587685\pi\) |
0.969374 | − | 0.245590i | \(-0.0789816\pi\) | |||||||
\(6\) | −63.3177 | + | 109.670i | −0.718038 | + | 1.24368i | ||||
\(7\) | 4.83274 | + | 8.37056i | 0.0372777 | + | 0.0645668i | 0.884062 | − | 0.467369i | \(-0.154798\pi\) |
−0.846785 | + | 0.531936i | \(0.821465\pi\) | |||||||
\(8\) | 153.894 | 0.850154 | ||||||||
\(9\) | −81.3925 | − | 140.976i | −0.334949 | − | 0.580148i | ||||
\(10\) | −245.074 | + | 424.481i | −0.774993 | + | 1.34233i | ||||
\(11\) | −186.774 | −0.465408 | −0.232704 | − | 0.972548i | \(-0.574757\pi\) | ||||
−0.232704 | + | 0.972548i | \(0.574757\pi\) | |||||||
\(12\) | 75.7397 | − | 131.185i | 0.151834 | − | 0.262985i | ||||
\(13\) | −333.447 | − | 577.548i | −0.547229 | − | 0.947828i | −0.998463 | − | 0.0554222i | \(-0.982350\pi\) |
0.451234 | − | 0.892405i | \(-0.350984\pi\) | |||||||
\(14\) | −30.3809 | − | 52.6213i | −0.0414267 | − | 0.0717532i | ||||
\(15\) | −785.306 | − | 1360.19i | −0.901178 | − | 1.56089i | ||||
\(16\) | −1208.09 | −1.17977 | ||||||||
\(17\) | −506.517 | − | 877.313i | −0.425081 | − | 0.736262i | 0.571347 | − | 0.820709i | \(-0.306421\pi\) |
−0.996428 | + | 0.0844468i | \(0.973088\pi\) | |||||||
\(18\) | 511.672 | + | 886.242i | 0.372229 | + | 0.644720i | ||||
\(19\) | −510.806 | + | 884.742i | −0.324618 | + | 0.562254i | −0.981435 | − | 0.191796i | \(-0.938569\pi\) |
0.656817 | + | 0.754050i | \(0.271902\pi\) | |||||||
\(20\) | 293.154 | − | 507.758i | 0.163878 | − | 0.283845i | ||||
\(21\) | 194.703 | 0.0963437 | ||||||||
\(22\) | 1174.15 | 0.517210 | ||||||||
\(23\) | −359.501 | + | 622.675i | −0.141704 | + | 0.245438i | −0.928138 | − | 0.372236i | \(-0.878591\pi\) |
0.786435 | + | 0.617674i | \(0.211925\pi\) | |||||||
\(24\) | 1550.03 | − | 2684.73i | 0.549304 | − | 0.951422i | ||||
\(25\) | −1477.07 | − | 2558.35i | −0.472661 | − | 0.818673i | ||||
\(26\) | 2096.21 | + | 3630.74i | 0.608136 | + | 1.05332i | ||||
\(27\) | 1615.86 | 0.426574 | ||||||||
\(28\) | 36.3412 | + | 62.9448i | 0.00876000 | + | 0.0151728i | ||||
\(29\) | 2473.93 | + | 4284.97i | 0.546251 | + | 0.946134i | 0.998527 | + | 0.0542563i | \(0.0172788\pi\) |
−0.452276 | + | 0.891878i | \(0.649388\pi\) | |||||||
\(30\) | 4936.81 | + | 8550.80i | 1.00148 | + | 1.73462i | ||||
\(31\) | −1884.73 | + | 3264.45i | −0.352245 | + | 0.610106i | −0.986642 | − | 0.162901i | \(-0.947915\pi\) |
0.634397 | + | 0.773007i | \(0.281248\pi\) | |||||||
\(32\) | 2669.99 | 0.460929 | ||||||||
\(33\) | −1881.20 | + | 3258.33i | −0.300711 | + | 0.520847i | ||||
\(34\) | 3184.21 | + | 5515.21i | 0.472393 | + | 0.818210i | ||||
\(35\) | 753.606 | 0.103986 | ||||||||
\(36\) | −612.054 | − | 1060.11i | −0.0787107 | − | 0.136331i | ||||
\(37\) | 7597.92 | − | 13160.0i | 0.912411 | − | 1.58034i | 0.101763 | − | 0.994809i | \(-0.467552\pi\) |
0.810648 | − | 0.585534i | \(-0.199115\pi\) | |||||||
\(38\) | 3211.17 | − | 5561.91i | 0.360748 | − | 0.624834i | ||||
\(39\) | −13434.0 | −1.41431 | ||||||||
\(40\) | 5999.48 | − | 10391.4i | 0.592875 | − | 1.02689i | ||||
\(41\) | −11668.9 | −1.08411 | −0.542053 | − | 0.840344i | \(-0.682353\pi\) | ||||
−0.542053 | + | 0.840344i | \(0.682353\pi\) | |||||||
\(42\) | −1223.99 | −0.107067 | ||||||||
\(43\) | 3015.80 | − | 11743.7i | 0.248732 | − | 0.968572i | ||||
\(44\) | −1404.50 | −0.109368 | ||||||||
\(45\) | −12692.2 | −0.934338 | ||||||||
\(46\) | 2260.00 | − | 3914.43i | 0.157476 | − | 0.272756i | ||||
\(47\) | 10416.6 | 0.687829 | 0.343914 | − | 0.939001i | \(-0.388247\pi\) | ||||
0.343914 | + | 0.939001i | \(0.388247\pi\) | |||||||
\(48\) | −12167.9 | + | 21075.4i | −0.762277 | + | 1.32030i | ||||
\(49\) | 8356.79 | − | 14474.4i | 0.497221 | − | 0.861212i | ||||
\(50\) | 9285.53 | + | 16083.0i | 0.525269 | + | 0.909793i | ||||
\(51\) | −20406.7 | −1.09862 | ||||||||
\(52\) | −2507.45 | − | 4343.03i | −0.128595 | − | 0.222733i | ||||
\(53\) | −11449.6 | + | 19831.2i | −0.559885 | + | 0.969749i | 0.437620 | + | 0.899160i | \(0.355821\pi\) |
−0.997505 | + | 0.0705896i | \(0.977512\pi\) | |||||||
\(54\) | −10158.1 | −0.474052 | ||||||||
\(55\) | −7281.26 | + | 12611.5i | −0.324564 | + | 0.562161i | ||||
\(56\) | 743.732 | + | 1288.18i | 0.0316917 | + | 0.0548917i | ||||
\(57\) | 10289.7 | + | 17822.3i | 0.419485 | + | 0.726570i | ||||
\(58\) | −15552.3 | − | 26937.4i | −0.607050 | − | 1.05144i | ||||
\(59\) | 37264.8 | 1.39370 | 0.696850 | − | 0.717217i | \(-0.254584\pi\) | ||||
0.696850 | + | 0.717217i | \(0.254584\pi\) | |||||||
\(60\) | −5905.33 | − | 10228.3i | −0.211771 | − | 0.366798i | ||||
\(61\) | −5923.36 | − | 10259.6i | −0.203819 | − | 0.353024i | 0.745937 | − | 0.666016i | \(-0.232002\pi\) |
−0.949756 | + | 0.312992i | \(0.898669\pi\) | |||||||
\(62\) | 11848.3 | − | 20521.9i | 0.391451 | − | 0.678013i | ||||
\(63\) | 786.698 | − | 1362.60i | 0.0249722 | − | 0.0432531i | ||||
\(64\) | 21873.9 | 0.667540 | ||||||||
\(65\) | −51996.9 | −1.52649 | ||||||||
\(66\) | 11826.1 | − | 20483.4i | 0.334181 | − | 0.578818i | ||||
\(67\) | 29789.5 | − | 51597.0i | 0.810731 | − | 1.40423i | −0.101623 | − | 0.994823i | \(-0.532403\pi\) |
0.912353 | − | 0.409404i | \(-0.134263\pi\) | |||||||
\(68\) | −3808.90 | − | 6597.20i | −0.0998911 | − | 0.173017i | ||||
\(69\) | 7241.84 | + | 12543.2i | 0.183116 | + | 0.317166i | ||||
\(70\) | −4737.53 | −0.115560 | ||||||||
\(71\) | 4851.06 | + | 8402.29i | 0.114207 | + | 0.197812i | 0.917462 | − | 0.397823i | \(-0.130234\pi\) |
−0.803256 | + | 0.595634i | \(0.796901\pi\) | |||||||
\(72\) | −12525.8 | − | 21695.4i | −0.284758 | − | 0.493215i | ||||
\(73\) | 38551.9 | + | 66773.8i | 0.846718 | + | 1.46656i | 0.884121 | + | 0.467258i | \(0.154758\pi\) |
−0.0374035 | + | 0.999300i | \(0.511909\pi\) | |||||||
\(74\) | −47764.2 | + | 82730.0i | −1.01396 | + | 1.75624i | ||||
\(75\) | −59508.3 | −1.22159 | ||||||||
\(76\) | −3841.15 | + | 6653.07i | −0.0762829 | + | 0.132126i | ||||
\(77\) | −902.630 | − | 1563.40i | −0.0173493 | − | 0.0300499i | ||||
\(78\) | 84452.5 | 1.57172 | ||||||||
\(79\) | −45037.2 | − | 78006.7i | −0.811902 | − | 1.40625i | −0.911532 | − | 0.411230i | \(-0.865099\pi\) |
0.0996300 | − | 0.995025i | \(-0.468234\pi\) | |||||||
\(80\) | −47096.5 | + | 81573.5i | −0.822742 | + | 1.42503i | ||||
\(81\) | 36053.4 | − | 62446.3i | 0.610567 | − | 1.05753i | ||||
\(82\) | 73356.6 | 1.20477 | ||||||||
\(83\) | 8003.23 | − | 13862.0i | 0.127518 | − | 0.220867i | −0.795197 | − | 0.606352i | \(-0.792632\pi\) |
0.922714 | + | 0.385485i | \(0.125966\pi\) | |||||||
\(84\) | 1464.12 | 0.0226401 | ||||||||
\(85\) | −78985.0 | −1.18576 | ||||||||
\(86\) | −18958.7 | + | 73826.2i | −0.276416 | + | 1.07638i | ||||
\(87\) | 99670.2 | 1.41178 | ||||||||
\(88\) | −28743.4 | −0.395669 | ||||||||
\(89\) | 37970.7 | − | 65767.2i | 0.508129 | − | 0.880105i | −0.491827 | − | 0.870693i | \(-0.663671\pi\) |
0.999956 | − | 0.00941217i | \(-0.00299603\pi\) | |||||||
\(90\) | 79788.9 | 1.03833 | ||||||||
\(91\) | 3222.93 | − | 5582.28i | 0.0407988 | − | 0.0706656i | ||||
\(92\) | −2703.37 | + | 4682.38i | −0.0332994 | + | 0.0576763i | ||||
\(93\) | 37966.2 | + | 65759.4i | 0.455187 | + | 0.788407i | ||||
\(94\) | −65483.5 | −0.764386 | ||||||||
\(95\) | 39826.9 | + | 68982.2i | 0.452760 | + | 0.784203i | ||||
\(96\) | 26892.2 | − | 46578.7i | 0.297817 | − | 0.515833i | ||||
\(97\) | −80908.6 | −0.873102 | −0.436551 | − | 0.899679i | \(-0.643800\pi\) | ||||
−0.436551 | + | 0.899679i | \(0.643800\pi\) | |||||||
\(98\) | −52534.8 | + | 90992.9i | −0.552563 | + | 0.957067i | ||||
\(99\) | 15202.0 | + | 26330.6i | 0.155888 | + | 0.270006i | ||||
\(100\) | −11107.2 | − | 19238.3i | −0.111072 | − | 0.192383i | ||||
\(101\) | 64204.3 | + | 111205.i | 0.626269 | + | 1.08473i | 0.988294 | + | 0.152561i | \(0.0487522\pi\) |
−0.362025 | + | 0.932168i | \(0.617914\pi\) | |||||||
\(102\) | 128286. | 1.22090 | ||||||||
\(103\) | 6137.06 | + | 10629.7i | 0.0569990 | + | 0.0987252i | 0.893117 | − | 0.449825i | \(-0.148513\pi\) |
−0.836118 | + | 0.548550i | \(0.815180\pi\) | |||||||
\(104\) | −51315.6 | − | 88881.3i | −0.465229 | − | 0.805799i | ||||
\(105\) | 7590.36 | − | 13146.9i | 0.0671876 | − | 0.116372i | ||||
\(106\) | 71977.4 | − | 124668.i | 0.622202 | − | 1.07768i | ||||
\(107\) | 34934.3 | 0.294980 | 0.147490 | − | 0.989064i | \(-0.452881\pi\) | ||||
0.147490 | + | 0.989064i | \(0.452881\pi\) | |||||||
\(108\) | 12150.9 | 0.100242 | ||||||||
\(109\) | −64772.6 | + | 112189.i | −0.522186 | + | 0.904452i | 0.477481 | + | 0.878642i | \(0.341550\pi\) |
−0.999667 | + | 0.0258101i | \(0.991783\pi\) | |||||||
\(110\) | 45773.5 | − | 79282.0i | 0.360688 | − | 0.624731i | ||||
\(111\) | −153053. | − | 265096.i | −1.17906 | − | 2.04219i | ||||
\(112\) | −5838.37 | − | 10112.4i | −0.0439791 | − | 0.0761741i | ||||
\(113\) | 35849.9 | 0.264114 | 0.132057 | − | 0.991242i | \(-0.457842\pi\) | ||||
0.132057 | + | 0.991242i | \(0.457842\pi\) | |||||||
\(114\) | −64686.1 | − | 112040.i | −0.466175 | − | 0.807439i | ||||
\(115\) | 28029.9 | + | 48549.2i | 0.197641 | + | 0.342324i | ||||
\(116\) | 18603.4 | + | 32222.0i | 0.128365 | + | 0.222335i | ||||
\(117\) | −54280.2 | + | 94016.1i | −0.366587 | + | 0.634947i | ||||
\(118\) | −234264. | −1.54882 | ||||||||
\(119\) | 4895.73 | − | 8479.66i | 0.0316920 | − | 0.0548922i | ||||
\(120\) | −120854. | − | 209325.i | −0.766140 | − | 1.32699i | ||||
\(121\) | −126167. | −0.783395 | ||||||||
\(122\) | 37237.1 | + | 64496.5i | 0.226504 | + | 0.392317i | ||||
\(123\) | −117530. | + | 203568.i | −0.700466 | + | 1.21324i | ||||
\(124\) | −14172.8 | + | 24547.9i | −0.0827752 | + | 0.143371i | ||||
\(125\) | 13322.5 | 0.0762625 | ||||||||
\(126\) | −4945.56 | + | 8565.96i | −0.0277517 | + | 0.0480673i | ||||
\(127\) | 209120. | 1.15050 | 0.575251 | − | 0.817977i | \(-0.304904\pi\) | ||||
0.575251 | + | 0.817977i | \(0.304904\pi\) | |||||||
\(128\) | −222950. | −1.20277 | ||||||||
\(129\) | −174496. | − | 170894.i | −0.923235 | − | 0.904176i | ||||
\(130\) | 326878. | 1.69639 | ||||||||
\(131\) | 201333. | 1.02503 | 0.512516 | − | 0.858678i | \(-0.328714\pi\) | ||||
0.512516 | + | 0.858678i | \(0.328714\pi\) | |||||||
\(132\) | −14146.2 | + | 24501.9i | −0.0706650 | + | 0.122395i | ||||
\(133\) | −9874.37 | −0.0484039 | ||||||||
\(134\) | −187271. | + | 324363.i | −0.900967 | + | 1.56052i | ||||
\(135\) | 62993.3 | − | 109108.i | 0.297481 | − | 0.515253i | ||||
\(136\) | −77950.1 | − | 135013.i | −0.361384 | − | 0.625936i | ||||
\(137\) | −203841. | −0.927874 | −0.463937 | − | 0.885868i | \(-0.653564\pi\) | ||||
−0.463937 | + | 0.885868i | \(0.653564\pi\) | |||||||
\(138\) | −45525.6 | − | 78852.7i | −0.203497 | − | 0.352467i | ||||
\(139\) | −190224. | + | 329478.i | −0.835081 | + | 1.44640i | 0.0588841 | + | 0.998265i | \(0.481246\pi\) |
−0.893965 | + | 0.448137i | \(0.852088\pi\) | |||||||
\(140\) | 5666.95 | 0.0244360 | ||||||||
\(141\) | 104916. | − | 181720.i | 0.444422 | − | 0.769761i | ||||
\(142\) | −30496.1 | − | 52820.8i | −0.126918 | − | 0.219828i | ||||
\(143\) | 62279.2 | + | 107871.i | 0.254685 | + | 0.441127i | ||||
\(144\) | 98329.2 | + | 170311.i | 0.395163 | + | 0.684442i | ||||
\(145\) | 385778. | 1.52376 | ||||||||
\(146\) | −242356. | − | 419772.i | −0.940959 | − | 1.62979i | ||||
\(147\) | −168340. | − | 291574.i | −0.642531 | − | 1.11290i | ||||
\(148\) | 57134.7 | − | 98960.3i | 0.214410 | − | 0.371370i | ||||
\(149\) | 205344. | − | 355667.i | 0.757735 | − | 1.31244i | −0.186268 | − | 0.982499i | \(-0.559639\pi\) |
0.944003 | − | 0.329936i | \(-0.107027\pi\) | |||||||
\(150\) | 374098. | 1.35755 | ||||||||
\(151\) | 463067. | 1.65273 | 0.826363 | − | 0.563137i | \(-0.190406\pi\) | ||||
0.826363 | + | 0.563137i | \(0.190406\pi\) | |||||||
\(152\) | −78610.1 | + | 136157.i | −0.275975 | + | 0.478002i | ||||
\(153\) | −82453.4 | + | 142813.i | −0.284761 | + | 0.493220i | ||||
\(154\) | 5674.36 | + | 9828.28i | 0.0192804 | + | 0.0333946i | ||||
\(155\) | 146950. | + | 254525.i | 0.491293 | + | 0.850945i | ||||
\(156\) | −101021. | −0.332353 | ||||||||
\(157\) | −136272. | − | 236030.i | −0.441222 | − | 0.764219i | 0.556559 | − | 0.830808i | \(-0.312121\pi\) |
−0.997780 | + | 0.0665897i | \(0.978788\pi\) | |||||||
\(158\) | 283125. | + | 490387.i | 0.902268 | + | 1.56277i | ||||
\(159\) | 230641. | + | 399482.i | 0.723509 | + | 1.25315i | ||||
\(160\) | 104088. | − | 180285.i | 0.321440 | − | 0.556750i | ||||
\(161\) | −6949.51 | −0.0211295 | ||||||||
\(162\) | −226649. | + | 392567.i | −0.678525 | + | 1.17524i | ||||
\(163\) | 206480. | + | 357634.i | 0.608708 | + | 1.05431i | 0.991454 | + | 0.130459i | \(0.0416452\pi\) |
−0.382746 | + | 0.923854i | \(0.625021\pi\) | |||||||
\(164\) | −87748.0 | −0.254758 | ||||||||
\(165\) | 146675. | + | 254048.i | 0.419416 | + | 0.726450i | ||||
\(166\) | −50312.1 | + | 87143.2i | −0.141711 | + | 0.245450i | ||||
\(167\) | −86367.9 | + | 149594.i | −0.239641 | + | 0.415070i | −0.960611 | − | 0.277896i | \(-0.910363\pi\) |
0.720970 | + | 0.692966i | \(0.243696\pi\) | |||||||
\(168\) | 29963.6 | 0.0819070 | ||||||||
\(169\) | −36727.6 | + | 63614.1i | −0.0989182 | + | 0.171331i | ||||
\(170\) | 496537. | 1.31774 | ||||||||
\(171\) | 166303. | 0.434921 | ||||||||
\(172\) | 22678.1 | − | 88309.7i | 0.0584502 | − | 0.227608i | ||||
\(173\) | −313319. | −0.795924 | −0.397962 | − | 0.917402i | \(-0.630282\pi\) | ||||
−0.397962 | + | 0.917402i | \(0.630282\pi\) | |||||||
\(174\) | −626574. | −1.56891 | ||||||||
\(175\) | 14276.6 | − | 24727.7i | 0.0352394 | − | 0.0610364i | ||||
\(176\) | 225639. | 0.549076 | ||||||||
\(177\) | 375333. | − | 650096.i | 0.900501 | − | 1.55971i | ||||
\(178\) | −238702. | + | 413444.i | −0.564685 | + | 0.978063i | ||||
\(179\) | 171933. | + | 297797.i | 0.401077 | + | 0.694685i | 0.993856 | − | 0.110680i | \(-0.0353027\pi\) |
−0.592779 | + | 0.805365i | \(0.701969\pi\) | |||||||
\(180\) | −95442.2 | −0.219563 | ||||||||
\(181\) | −287968. | − | 498774.i | −0.653352 | − | 1.13164i | −0.982304 | − | 0.187292i | \(-0.940029\pi\) |
0.328953 | − | 0.944346i | \(-0.393304\pi\) | |||||||
\(182\) | −20260.9 | + | 35092.9i | −0.0453398 | + | 0.0785308i | ||||
\(183\) | −238642. | −0.526767 | ||||||||
\(184\) | −55325.2 | + | 95826.1i | −0.120470 | + | 0.208660i | ||||
\(185\) | −592401. | − | 1.02607e6i | −1.27258 | − | 2.20418i | ||||
\(186\) | −238674. | − | 413395.i | −0.505850 | − | 0.876159i | ||||
\(187\) | 94604.1 | + | 163859.i | 0.197836 | + | 0.342662i | ||||
\(188\) | 78330.4 | 0.161635 | ||||||||
\(189\) | 7809.03 | + | 13525.6i | 0.0159017 | + | 0.0275425i | ||||
\(190\) | −250371. | − | 433655.i | −0.503153 | − | 0.871486i | ||||
\(191\) | −22025.6 | + | 38149.5i | −0.0436862 | + | 0.0756667i | −0.887042 | − | 0.461689i | \(-0.847244\pi\) |
0.843356 | + | 0.537356i | \(0.180577\pi\) | |||||||
\(192\) | 220316. | − | 381598.i | 0.431313 | − | 0.747055i | ||||
\(193\) | 32365.8 | 0.0625451 | 0.0312726 | − | 0.999511i | \(-0.490044\pi\) | ||||
0.0312726 | + | 0.999511i | \(0.490044\pi\) | |||||||
\(194\) | 508630. | 0.970281 | ||||||||
\(195\) | −523716. | + | 907103.i | −0.986301 | + | 1.70832i | ||||
\(196\) | 62841.2 | − | 108844.i | 0.116844 | − | 0.202379i | ||||
\(197\) | 234644. | + | 406415.i | 0.430768 | + | 0.746112i | 0.996940 | − | 0.0781754i | \(-0.0249094\pi\) |
−0.566172 | + | 0.824287i | \(0.691576\pi\) | |||||||
\(198\) | −95567.0 | − | 165527.i | −0.173239 | − | 0.300058i | ||||
\(199\) | −931.548 | −0.00166753 | −0.000833763 | − | 1.00000i | \(-0.500265\pi\) | ||||
−0.000833763 | 1.00000i | \(0.500265\pi\) | ||||||||
\(200\) | −227312. | − | 393716.i | −0.401834 | − | 0.695998i | ||||
\(201\) | −600083. | − | 1.03937e6i | −1.04766 | − | 1.81460i | ||||
\(202\) | −403619. | − | 699089.i | −0.695974 | − | 1.20546i | ||||
\(203\) | −23911.7 | + | 41416.3i | −0.0407259 | + | 0.0705393i | ||||
\(204\) | −153454. | −0.258168 | ||||||||
\(205\) | −454907. | + | 787922.i | −0.756028 | + | 1.30948i | ||||
\(206\) | −38580.5 | − | 66823.3i | −0.0633431 | − | 0.109714i | ||||
\(207\) | 117043. | 0.189854 | ||||||||
\(208\) | 402833. | + | 697727.i | 0.645605 | + | 1.11822i | ||||
\(209\) | 95405.2 | − | 165247.i | 0.151080 | − | 0.261678i | ||||
\(210\) | −47716.6 | + | 82647.6i | −0.0746658 | + | 0.129325i | ||||
\(211\) | 286371. | 0.442816 | 0.221408 | − | 0.975181i | \(-0.428935\pi\) | ||||
0.221408 | + | 0.975181i | \(0.428935\pi\) | |||||||
\(212\) | −86098.2 | + | 149126.i | −0.131569 | + | 0.227885i | ||||
\(213\) | 195441. | 0.295166 | ||||||||
\(214\) | −219614. | −0.327812 | ||||||||
\(215\) | −675397. | − | 661455.i | −0.996467 | − | 0.975897i | ||||
\(216\) | 248671. | 0.362653 | ||||||||
\(217\) | −36433.7 | −0.0525235 | ||||||||
\(218\) | 407191. | − | 705276.i | 0.580306 | − | 1.00512i | ||||
\(219\) | 1.55319e6 | 2.18833 | ||||||||
\(220\) | −54753.5 | + | 94835.9i | −0.0762703 | + | 0.132104i | ||||
\(221\) | −337793. | + | 585075.i | −0.465233 | + | 0.805807i | ||||
\(222\) | 962166. | + | 1.66652e6i | 1.31029 | + | 2.26949i | ||||
\(223\) | −355591. | −0.478839 | −0.239419 | − | 0.970916i | \(-0.576957\pi\) | ||||
−0.239419 | + | 0.970916i | \(0.576957\pi\) | |||||||
\(224\) | 12903.4 | + | 22349.3i | 0.0171823 | + | 0.0297607i | ||||
\(225\) | −240444. | + | 416461.i | −0.316634 | + | 0.548427i | ||||
\(226\) | −225369. | −0.293511 | ||||||||
\(227\) | −515120. | + | 892214.i | −0.663504 | + | 1.14922i | 0.316184 | + | 0.948698i | \(0.397598\pi\) |
−0.979689 | + | 0.200525i | \(0.935735\pi\) | |||||||
\(228\) | 77376.5 | + | 134020.i | 0.0985762 | + | 0.170739i | ||||
\(229\) | −131043. | − | 226973.i | −0.165130 | − | 0.286013i | 0.771572 | − | 0.636142i | \(-0.219471\pi\) |
−0.936701 | + | 0.350130i | \(0.886138\pi\) | |||||||
\(230\) | −176209. | − | 305203.i | −0.219639 | − | 0.380426i | ||||
\(231\) | −36365.3 | −0.0448392 | ||||||||
\(232\) | 380723. | + | 659432.i | 0.464397 | + | 0.804360i | ||||
\(233\) | 288976. | + | 500521.i | 0.348716 | + | 0.603993i | 0.986022 | − | 0.166618i | \(-0.0532846\pi\) |
−0.637306 | + | 0.770611i | \(0.719951\pi\) | |||||||
\(234\) | 341231. | − | 591030.i | 0.407389 | − | 0.705618i | ||||
\(235\) | 406084. | − | 703358.i | 0.479674 | − | 0.830819i | ||||
\(236\) | 280223. | 0.327510 | ||||||||
\(237\) | −1.81447e6 | −2.09835 | ||||||||
\(238\) | −30776.9 | + | 53307.2i | −0.0352194 | + | 0.0610019i | ||||
\(239\) | 326647. | − | 565769.i | 0.369899 | − | 0.640685i | −0.619650 | − | 0.784878i | \(-0.712725\pi\) |
0.989550 | + | 0.144194i | \(0.0460588\pi\) | |||||||
\(240\) | 948717. | + | 1.64323e6i | 1.06318 | + | 1.84149i | ||||
\(241\) | −603340. | − | 1.04501e6i | −0.669144 | − | 1.15899i | −0.978144 | − | 0.207929i | \(-0.933328\pi\) |
0.309000 | − | 0.951062i | \(-0.400006\pi\) | |||||||
\(242\) | 793143. | 0.870589 | ||||||||
\(243\) | −529937. | − | 917877.i | −0.575716 | − | 0.997169i | ||||
\(244\) | −44542.4 | − | 77149.7i | −0.0478960 | − | 0.0829583i | ||||
\(245\) | −651569. | − | 1.12855e6i | −0.693498 | − | 1.20117i | ||||
\(246\) | 738851. | − | 1.27973e6i | 0.778430 | − | 1.34828i | ||||
\(247\) | 681307. | 0.710560 | ||||||||
\(248\) | −290049. | + | 502380.i | −0.299463 | + | 0.518684i | ||||
\(249\) | −161218. | − | 279238.i | −0.164784 | − | 0.285414i | ||||
\(250\) | −83751.6 | −0.0847507 | ||||||||
\(251\) | 323082. | + | 559595.i | 0.323690 | + | 0.560647i | 0.981246 | − | 0.192758i | \(-0.0617433\pi\) |
−0.657557 | + | 0.753405i | \(0.728410\pi\) | |||||||
\(252\) | 5915.80 | − | 10246.5i | 0.00586830 | − | 0.0101642i | ||||
\(253\) | 67145.5 | − | 116299.i | 0.0659501 | − | 0.114229i | ||||
\(254\) | −1.31463e6 | −1.27856 | ||||||||
\(255\) | −795541. | + | 1.37792e6i | −0.766147 | + | 1.32701i | ||||
\(256\) | 701601. | 0.669099 | ||||||||
\(257\) | 1.60197e6 | 1.51294 | 0.756471 | − | 0.654027i | \(-0.226922\pi\) | ||||
0.756471 | + | 0.654027i | \(0.226922\pi\) | |||||||
\(258\) | 1.09697e6 | + | 1.07432e6i | 1.02599 | + | 1.00481i | ||||
\(259\) | 146875. | 0.136050 | ||||||||
\(260\) | −391006. | −0.358715 | ||||||||
\(261\) | 402719. | − | 697529.i | 0.365932 | − | 0.633813i | ||||
\(262\) | −1.26568e6 | −1.13912 | ||||||||
\(263\) | 430251. | − | 745216.i | 0.383559 | − | 0.664344i | −0.608009 | − | 0.793930i | \(-0.708032\pi\) |
0.991568 | + | 0.129586i | \(0.0413649\pi\) | |||||||
\(264\) | −289505. | + | 501438.i | −0.255651 | + | 0.442800i | ||||
\(265\) | 892708. | + | 1.54622e6i | 0.780899 | + | 1.35256i | ||||
\(266\) | 62075.0 | 0.0537914 | ||||||||
\(267\) | −764887. | − | 1.32482e6i | −0.656627 | − | 1.13731i | ||||
\(268\) | 224011. | − | 387998.i | 0.190516 | − | 0.329984i | ||||
\(269\) | −441247. | −0.371793 | −0.185896 | − | 0.982569i | \(-0.559519\pi\) | ||||
−0.185896 | + | 0.982569i | \(0.559519\pi\) | |||||||
\(270\) | −396006. | + | 685902.i | −0.330592 | + | 0.572602i | ||||
\(271\) | −1.17916e6 | − | 2.04237e6i | −0.975326 | − | 1.68931i | −0.678856 | − | 0.734271i | \(-0.737524\pi\) |
−0.296469 | − | 0.955042i | \(-0.595809\pi\) | |||||||
\(272\) | 611916. | + | 1.05987e6i | 0.501498 | + | 0.868621i | ||||
\(273\) | −64923.0 | − | 112450.i | −0.0527220 | − | 0.0913172i | ||||
\(274\) | 1.28144e6 | 1.03115 | ||||||||
\(275\) | 275877. | + | 477833.i | 0.219980 | + | 0.381017i | ||||
\(276\) | 54457.0 | + | 94322.3i | 0.0430310 | + | 0.0745319i | ||||
\(277\) | −856545. | + | 1.48358e6i | −0.670735 | + | 1.16175i | 0.306961 | + | 0.951722i | \(0.400688\pi\) |
−0.977696 | + | 0.210025i | \(0.932645\pi\) | |||||||
\(278\) | 1.19584e6 | − | 2.07125e6i | 0.928027 | − | 1.60739i | ||||
\(279\) | 613612. | 0.471936 | ||||||||
\(280\) | 115976. | 0.0884040 | ||||||||
\(281\) | −938419. | + | 1.62539e6i | −0.708975 | + | 1.22798i | 0.256263 | + | 0.966607i | \(0.417509\pi\) |
−0.965238 | + | 0.261374i | \(0.915825\pi\) | |||||||
\(282\) | −659554. | + | 1.14238e6i | −0.493887 | + | 0.855437i | ||||
\(283\) | 435133. | + | 753672.i | 0.322965 | + | 0.559392i | 0.981098 | − | 0.193510i | \(-0.0619870\pi\) |
−0.658133 | + | 0.752901i | \(0.728654\pi\) | |||||||
\(284\) | 36478.9 | + | 63183.4i | 0.0268378 | + | 0.0464844i | ||||
\(285\) | 1.60456e6 | 1.17015 | ||||||||
\(286\) | −391517. | − | 678127.i | −0.283032 | − | 0.490226i | ||||
\(287\) | −56393.0 | − | 97675.6i | −0.0404130 | − | 0.0699973i | ||||
\(288\) | −217317. | − | 376404.i | −0.154388 | − | 0.267407i | ||||
\(289\) | 196810. | − | 340885.i | 0.138612 | − | 0.240084i | ||||
\(290\) | −2.42519e6 | −1.69336 | ||||||||
\(291\) | −814915. | + | 1.41147e6i | −0.564131 | + | 0.977104i | ||||
\(292\) | 289902. | + | 502125.i | 0.198973 | + | 0.344631i | ||||
\(293\) | 216695. | 0.147462 | 0.0737311 | − | 0.997278i | \(-0.476509\pi\) | ||||
0.0737311 | + | 0.997278i | \(0.476509\pi\) | |||||||
\(294\) | 1.05827e6 | + | 1.83297e6i | 0.714046 | + | 1.23676i | ||||
\(295\) | 1.45275e6 | − | 2.51623e6i | 0.971930 | − | 1.68343i | ||||
\(296\) | 1.16928e6 | − | 2.02525e6i | 0.775690 | − | 1.34353i | ||||
\(297\) | −301800. | −0.198531 | ||||||||
\(298\) | −1.29089e6 | + | 2.23589e6i | −0.842073 | + | 1.45851i | ||||
\(299\) | 479499. | 0.310177 | ||||||||
\(300\) | −447490. | −0.287065 | ||||||||
\(301\) | 112875. | − | 31510.2i | 0.0718097 | − | 0.0200463i | ||||
\(302\) | −2.91106e6 | −1.83668 | ||||||||
\(303\) | 2.58668e6 | 1.61859 | ||||||||
\(304\) | 617097. | − | 1.06884e6i | 0.382974 | − | 0.663331i | ||||
\(305\) | −923675. | −0.568551 | ||||||||
\(306\) | 518341. | − | 897793.i | 0.316455 | − | 0.548116i | ||||
\(307\) | −92551.3 | + | 160304.i | −0.0560450 | + | 0.0970727i | −0.892687 | − | 0.450678i | \(-0.851182\pi\) |
0.836642 | + | 0.547750i | \(0.184516\pi\) | |||||||
\(308\) | −6787.58 | − | 11756.4i | −0.00407698 | − | 0.00706153i | ||||
\(309\) | 247251. | 0.147313 | ||||||||
\(310\) | −923798. | − | 1.60007e6i | −0.545975 | − | 0.945657i | ||||
\(311\) | 168546. | − | 291930.i | 0.0988136 | − | 0.171150i | −0.812380 | − | 0.583128i | \(-0.801829\pi\) |
0.911194 | + | 0.411978i | \(0.135162\pi\) | |||||||
\(312\) | −2.06742e6 | −1.20238 | ||||||||
\(313\) | −487742. | + | 844794.i | −0.281403 | + | 0.487405i | −0.971731 | − | 0.236092i | \(-0.924133\pi\) |
0.690327 | + | 0.723497i | \(0.257467\pi\) | |||||||
\(314\) | 856670. | + | 1.48380e6i | 0.490331 | + | 0.849278i | ||||
\(315\) | −61337.9 | − | 106240.i | −0.0348299 | − | 0.0603272i | ||||
\(316\) | −338670. | − | 586593.i | −0.190791 | − | 0.330460i | ||||
\(317\) | −1.24802e6 | −0.697548 | −0.348774 | − | 0.937207i | \(-0.613402\pi\) | ||||
−0.348774 | + | 0.937207i | \(0.613402\pi\) | |||||||
\(318\) | −1.44992e6 | − | 2.51133e6i | −0.804037 | − | 1.39263i | ||||
\(319\) | −462065. | − | 800320.i | −0.254230 | − | 0.440339i | ||||
\(320\) | 852742. | − | 1.47699e6i | 0.465525 | − | 0.806313i | ||||
\(321\) | 351860. | − | 609440.i | 0.190593 | − | 0.330117i | ||||
\(322\) | 43687.9 | 0.0234813 | ||||||||
\(323\) | 1.03493e6 | 0.551955 | ||||||||
\(324\) | 271114. | − | 469583.i | 0.143479 | − | 0.248513i | ||||
\(325\) | −985047. | + | 1.70615e6i | −0.517307 | + | 0.896002i | ||||
\(326\) | −1.29803e6 | − | 2.24826e6i | −0.676459 | − | 1.17166i | ||||
\(327\) | 1.30479e6 | + | 2.25996e6i | 0.674792 | + | 1.16877i | ||||
\(328\) | −1.79578e6 | −0.921658 | ||||||||
\(329\) | 50340.6 | + | 87192.5i | 0.0256406 | + | 0.0444109i | ||||
\(330\) | −922066. | − | 1.59707e6i | −0.466098 | − | 0.807305i | ||||
\(331\) | 1.91017e6 | + | 3.30851e6i | 0.958302 | + | 1.65983i | 0.726624 | + | 0.687035i | \(0.241088\pi\) |
0.231678 | + | 0.972793i | \(0.425579\pi\) | |||||||
\(332\) | 60182.6 | − | 104239.i | 0.0299658 | − | 0.0519022i | ||||
\(333\) | −2.47366e6 | −1.22244 | ||||||||
\(334\) | 542950. | − | 940416.i | 0.266314 | − | 0.461269i | ||||
\(335\) | −2.32265e6 | − | 4.02295e6i | −1.13076 | − | 1.95854i | ||||
\(336\) | −235217. | −0.113664 | ||||||||
\(337\) | 1.37266e6 | + | 2.37752e6i | 0.658397 | + | 1.14038i | 0.981031 | + | 0.193853i | \(0.0620986\pi\) |
−0.322633 | + | 0.946524i | \(0.604568\pi\) | |||||||
\(338\) | 230887. | − | 399909.i | 0.109928 | − | 0.190401i | ||||
\(339\) | 361082. | − | 625412.i | 0.170650 | − | 0.295575i | ||||
\(340\) | −593950. | −0.278646 | ||||||||
\(341\) | 352018. | − | 609713.i | 0.163938 | − | 0.283949i | ||||
\(342\) | −1.04546e6 | −0.483329 | ||||||||
\(343\) | 323993. | 0.148696 | ||||||||
\(344\) | 464114. | − | 1.80728e6i | 0.211460 | − | 0.823436i | ||||
\(345\) | 1.12927e6 | 0.510801 | ||||||||
\(346\) | 1.96967e6 | 0.884512 | ||||||||
\(347\) | −32149.3 | + | 55684.2i | −0.0143334 | + | 0.0248261i | −0.873103 | − | 0.487536i | \(-0.837896\pi\) |
0.858770 | + | 0.512362i | \(0.171229\pi\) | |||||||
\(348\) | 749498. | 0.331759 | ||||||||
\(349\) | −1.03543e6 | + | 1.79342e6i | −0.455048 | + | 0.788166i | −0.998691 | − | 0.0511505i | \(-0.983711\pi\) |
0.543643 | + | 0.839316i | \(0.317045\pi\) | |||||||
\(350\) | −89749.2 | + | 155450.i | −0.0391616 | + | 0.0678299i | ||||
\(351\) | −538804. | − | 933235.i | −0.233433 | − | 0.404318i | ||||
\(352\) | −498683. | −0.214520 | ||||||||
\(353\) | 514516. | + | 891167.i | 0.219767 | + | 0.380647i | 0.954737 | − | 0.297453i | \(-0.0961371\pi\) |
−0.734970 | + | 0.678100i | \(0.762804\pi\) | |||||||
\(354\) | −2.35952e6 | + | 4.08682e6i | −1.00073 | + | 1.73331i | ||||
\(355\) | 756463. | 0.318579 | ||||||||
\(356\) | 285532. | − | 494555.i | 0.119407 | − | 0.206819i | ||||
\(357\) | −98620.1 | − | 170815.i | −0.0409539 | − | 0.0709342i | ||||
\(358\) | −1.08085e6 | − | 1.87210e6i | −0.445718 | − | 0.772006i | ||||
\(359\) | 1.17412e6 | + | 2.03363e6i | 0.480811 | + | 0.832790i | 0.999758 | − | 0.0220172i | \(-0.00700886\pi\) |
−0.518946 | + | 0.854807i | \(0.673676\pi\) | |||||||
\(360\) | −1.95325e6 | −0.794331 | ||||||||
\(361\) | 716204. | + | 1.24050e6i | 0.289247 | + | 0.500990i | ||||
\(362\) | 1.81030e6 | + | 3.13553e6i | 0.726071 | + | 1.25759i | ||||
\(363\) | −1.27076e6 | + | 2.20101e6i | −0.506169 | + | 0.876711i | ||||
\(364\) | 24235.7 | − | 41977.5i | 0.00958744 | − | 0.0166059i | ||||
\(365\) | 6.01169e6 | 2.36192 | ||||||||
\(366\) | 1.50022e6 | 0.585398 | ||||||||
\(367\) | −1.38661e6 | + | 2.40169e6i | −0.537391 | + | 0.930789i | 0.461652 | + | 0.887061i | \(0.347257\pi\) |
−0.999043 | + | 0.0437281i | \(0.986076\pi\) | |||||||
\(368\) | 434309. | − | 752245.i | 0.167178 | − | 0.289561i | ||||
\(369\) | 949765. | + | 1.64504e6i | 0.363120 | + | 0.628943i | ||||
\(370\) | 3.72411e6 | + | 6.45035e6i | 1.41423 | + | 2.44951i | ||||
\(371\) | −221331. | −0.0834848 | ||||||||
\(372\) | 285498. | + | 494496.i | 0.106966 | + | 0.185270i | ||||
\(373\) | −1.71280e6 | − | 2.96666e6i | −0.637434 | − | 1.10407i | −0.985994 | − | 0.166781i | \(-0.946663\pi\) |
0.348560 | − | 0.937286i | \(-0.386671\pi\) | |||||||
\(374\) | −594726. | − | 1.03010e6i | −0.219856 | − | 0.380802i | ||||
\(375\) | 134185. | − | 232415.i | 0.0492749 | − | 0.0853466i | ||||
\(376\) | 1.60305e6 | 0.584760 | ||||||||
\(377\) | 1.64985e6 | − | 2.85762e6i | 0.597848 | − | 1.03550i | ||||
\(378\) | −49091.3 | − | 85028.6i | −0.0176716 | − | 0.0306080i | ||||
\(379\) | −1.39653e6 | −0.499403 | −0.249702 | − | 0.968323i | \(-0.580333\pi\) | ||||
−0.249702 | + | 0.968323i | \(0.580333\pi\) | |||||||
\(380\) | 299490. | + | 518731.i | 0.106395 | + | 0.184282i | ||||
\(381\) | 2.10627e6 | − | 3.64817e6i | 0.743365 | − | 1.28755i | ||||
\(382\) | 138463. | − | 239826.i | 0.0485486 | − | 0.0840886i | ||||
\(383\) | 4.31485e6 | 1.50304 | 0.751518 | − | 0.659713i | \(-0.229322\pi\) | ||||
0.751518 | + | 0.659713i | \(0.229322\pi\) | |||||||
\(384\) | −2.24556e6 | + | 3.88942e6i | −0.777135 | + | 1.34604i | ||||
\(385\) | −140754. | −0.0483959 | ||||||||
\(386\) | −203467. | −0.0695066 | ||||||||
\(387\) | −1.90104e6 | + | 530691.i | −0.645228 | + | 0.180121i | ||||
\(388\) | −608415. | −0.205173 | ||||||||
\(389\) | 2.72557e6 | 0.913236 | 0.456618 | − | 0.889663i | \(-0.349061\pi\) | ||||
0.456618 | + | 0.889663i | \(0.349061\pi\) | |||||||
\(390\) | 3.29233e6 | − | 5.70248e6i | 1.09608 | − | 1.89846i | ||||
\(391\) | 728374. | 0.240942 | ||||||||
\(392\) | 1.28606e6 | − | 2.22753e6i | 0.422714 | − | 0.732162i | ||||
\(393\) | 2.02784e6 | − | 3.51232e6i | 0.662296 | − | 1.14713i | ||||
\(394\) | −1.47508e6 | − | 2.55492e6i | −0.478713 | − | 0.829156i | ||||
\(395\) | −7.02299e6 | −2.26480 | ||||||||
\(396\) | 114316. | + | 198001.i | 0.0366326 | + | 0.0634495i | ||||
\(397\) | 412186. | − | 713928.i | 0.131255 | − | 0.227341i | −0.792905 | − | 0.609345i | \(-0.791433\pi\) |
0.924161 | + | 0.382004i | \(0.124766\pi\) | |||||||
\(398\) | 5856.16 | 0.00185313 | ||||||||
\(399\) | −99455.2 | + | 172262.i | −0.0312749 | + | 0.0541697i | ||||
\(400\) | 1.78442e6 | + | 3.09071e6i | 0.557632 | + | 0.965847i | ||||
\(401\) | −519930. | − | 900546.i | −0.161467 | − | 0.279669i | 0.773928 | − | 0.633274i | \(-0.218289\pi\) |
−0.935395 | + | 0.353604i | \(0.884956\pi\) | |||||||
\(402\) | 3.77241e6 | + | 6.53401e6i | 1.16427 | + | 2.01658i | ||||
\(403\) | 2.51383e6 | 0.771034 | ||||||||
\(404\) | 482803. | + | 836239.i | 0.147169 | + | 0.254904i | ||||
\(405\) | −2.81104e6 | − | 4.86886e6i | −0.851588 | − | 1.47499i | ||||
\(406\) | 150320. | − | 260363.i | 0.0452588 | − | 0.0783905i | ||||
\(407\) | −1.41909e6 | + | 2.45794e6i | −0.424644 | + | 0.735505i | ||||
\(408\) | −3.14047e6 | −0.933994 | ||||||||
\(409\) | −4.98218e6 | −1.47269 | −0.736345 | − | 0.676606i | \(-0.763450\pi\) | ||||
−0.736345 | + | 0.676606i | \(0.763450\pi\) | |||||||
\(410\) | 2.85976e6 | − | 4.95325e6i | 0.840176 | − | 1.45523i | ||||
\(411\) | −2.05309e6 | + | 3.55606e6i | −0.599520 | + | 1.03840i | ||||
\(412\) | 46149.4 | + | 79933.0i | 0.0133944 | + | 0.0231997i | ||||
\(413\) | 180091. | + | 311927.i | 0.0519538 | + | 0.0899867i | ||||
\(414\) | −735788. | −0.210985 | ||||||||
\(415\) | −624002. | − | 1.08080e6i | −0.177855 | − | 0.308054i | ||||
\(416\) | −890299. | − | 1.54204e6i | −0.252233 | − | 0.436881i | ||||
\(417\) | 3.83189e6 | + | 6.63703e6i | 1.07913 | + | 1.86911i | ||||
\(418\) | −599762. | + | 1.03882e6i | −0.167895 | + | 0.290803i | ||||
\(419\) | −6.25082e6 | −1.73941 | −0.869705 | − | 0.493571i | \(-0.835691\pi\) | ||||
−0.869705 | + | 0.493571i | \(0.835691\pi\) | |||||||
\(420\) | 57077.9 | − | 98861.8i | 0.0157886 | − | 0.0273467i | ||||
\(421\) | −2.97298e6 | − | 5.14935e6i | −0.817497 | − | 1.41595i | −0.907521 | − | 0.420007i | \(-0.862028\pi\) |
0.0900234 | − | 0.995940i | \(-0.471306\pi\) | |||||||
\(422\) | −1.80027e6 | −0.492103 | ||||||||
\(423\) | −847831. | − | 1.46849e6i | −0.230387 | − | 0.399042i | ||||
\(424\) | −1.76202e6 | + | 3.05191e6i | −0.475989 | + | 0.824436i | ||||
\(425\) | −1.49632e6 | + | 2.59170e6i | −0.401838 | + | 0.696004i | ||||
\(426\) | −1.22863e6 | −0.328018 | ||||||||
\(427\) | 57252.2 | − | 99163.7i | 0.0151958 | − | 0.0263198i | ||||
\(428\) | 262698. | 0.0693183 | ||||||||
\(429\) | 2.50912e6 | 0.658230 | ||||||||
\(430\) | 4.24587e6 | + | 4.15822e6i | 1.10738 | + | 1.08452i | ||||
\(431\) | −578122. | −0.149909 | −0.0749543 | − | 0.997187i | \(-0.523881\pi\) | ||||
−0.0749543 | + | 0.997187i | \(0.523881\pi\) | |||||||
\(432\) | −1.95210e6 | −0.503259 | ||||||||
\(433\) | −523790. | + | 907231.i | −0.134257 | + | 0.232540i | −0.925313 | − | 0.379203i | \(-0.876198\pi\) |
0.791056 | + | 0.611743i | \(0.209532\pi\) | |||||||
\(434\) | 229039. | 0.0583695 | ||||||||
\(435\) | 3.88558e6 | − | 6.73002e6i | 0.984539 | − | 1.70527i | ||||
\(436\) | −487076. | + | 843640.i | −0.122710 | + | 0.212540i | ||||
\(437\) | −367271. | − | 636132.i | −0.0919990 | − | 0.159347i | ||||
\(438\) | −9.76407e6 | −2.43190 | ||||||||
\(439\) | 1.05066e6 | + | 1.81980e6i | 0.260197 | + | 0.450674i | 0.966294 | − | 0.257441i | \(-0.0828793\pi\) |
−0.706097 | + | 0.708115i | \(0.749546\pi\) | |||||||
\(440\) | −1.12054e6 | + | 1.94084e6i | −0.275929 | + | 0.477923i | ||||
\(441\) | −2.72072e6 | −0.666174 | ||||||||
\(442\) | 2.12353e6 | − | 3.67806e6i | 0.517014 | − | 0.895495i | ||||
\(443\) | 1.80645e6 | + | 3.12886e6i | 0.437338 | + | 0.757491i | 0.997483 | − | 0.0709033i | \(-0.0225882\pi\) |
−0.560146 | + | 0.828394i | \(0.689255\pi\) | |||||||
\(444\) | −1.15093e6 | − | 1.99347e6i | −0.277071 | − | 0.479901i | ||||
\(445\) | −2.96053e6 | − | 5.12779e6i | −0.708712 | − | 1.22753i | ||||
\(446\) | 2.23542e6 | 0.532135 | ||||||||
\(447\) | −4.13648e6 | − | 7.16459e6i | −0.979179 | − | 1.69599i | ||||
\(448\) | 105711. | + | 183097.i | 0.0248843 | + | 0.0431009i | ||||
\(449\) | −3.61136e6 | + | 6.25506e6i | −0.845386 | + | 1.46425i | 0.0399003 | + | 0.999204i | \(0.487296\pi\) |
−0.885286 | + | 0.465047i | \(0.846037\pi\) | |||||||
\(450\) | 1.51155e6 | − | 2.61807e6i | 0.351876 | − | 0.609468i | ||||
\(451\) | 2.17945e6 | 0.504553 | ||||||||
\(452\) | 269583. | 0.0620650 | ||||||||
\(453\) | 4.66403e6 | − | 8.07834e6i | 1.06786 | − | 1.84959i | ||||
\(454\) | 3.23829e6 | − | 5.60888e6i | 0.737354 | − | 1.27713i | ||||
\(455\) | −251288. | − | 435243.i | −0.0569040 | − | 0.0985607i | ||||
\(456\) | 1.58353e6 | + | 2.74276e6i | 0.356627 | + | 0.617696i | ||||
\(457\) | −2.01242e6 | −0.450743 | −0.225372 | − | 0.974273i | \(-0.572360\pi\) | ||||
−0.225372 | + | 0.974273i | \(0.572360\pi\) | |||||||
\(458\) | 823798. | + | 1.42686e6i | 0.183509 | + | 0.317847i | ||||
\(459\) | −818460. | − | 1.41761e6i | −0.181328 | − | 0.314070i | ||||
\(460\) | 210779. | + | 365079.i | 0.0464443 | + | 0.0804438i | ||||
\(461\) | −3.82299e6 | + | 6.62162e6i | −0.837821 | + | 1.45115i | 0.0538918 | + | 0.998547i | \(0.482837\pi\) |
−0.891713 | + | 0.452602i | \(0.850496\pi\) | |||||||
\(462\) | 228610. | 0.0498299 | ||||||||
\(463\) | 851580. | − | 1.47498e6i | 0.184618 | − | 0.319767i | −0.758830 | − | 0.651289i | \(-0.774229\pi\) |
0.943448 | + | 0.331522i | \(0.107562\pi\) | |||||||
\(464\) | −2.98872e6 | − | 5.17661e6i | −0.644451 | − | 1.11622i | ||||
\(465\) | 5.92036e6 | 1.26974 | ||||||||
\(466\) | −1.81664e6 | − | 3.14651e6i | −0.387529 | − | 0.671219i | ||||
\(467\) | 2.49201e6 | − | 4.31629e6i | 0.528758 | − | 0.915837i | −0.470679 | − | 0.882304i | \(-0.655991\pi\) |
0.999438 | − | 0.0335321i | \(-0.0106756\pi\) | |||||||
\(468\) | −408176. | + | 706981.i | −0.0861454 | + | 0.149208i | ||||
\(469\) | 575860. | 0.120889 | ||||||||
\(470\) | −2.55284e6 | + | 4.42164e6i | −0.533063 | + | 0.923292i | ||||
\(471\) | −5.49015e6 | −1.14033 | ||||||||
\(472\) | 5.73484e6 | 1.18486 | ||||||||
\(473\) | −563272. | + | 2.19341e6i | −0.115762 | + | 0.450782i | ||||
\(474\) | 1.14066e7 | 2.33190 | ||||||||
\(475\) | 3.01797e6 | 0.613736 | ||||||||
\(476\) | 36814.8 | − | 63765.2i | 0.00744741 | − | 0.0128993i | ||||
\(477\) | 3.72763e6 | 0.750131 | ||||||||
\(478\) | −2.05346e6 | + | 3.55669e6i | −0.411070 | + | 0.711994i | ||||
\(479\) | −3.69922e6 | + | 6.40724e6i | −0.736668 | + | 1.27595i | 0.217320 | + | 0.976100i | \(0.430268\pi\) |
−0.953988 | + | 0.299846i | \(0.903065\pi\) | |||||||
\(480\) | −2.09676e6 | − | 3.63169e6i | −0.415379 | − | 0.719458i | ||||
\(481\) | −1.01340e7 | −1.99719 | ||||||||
\(482\) | 3.79288e6 | + | 6.56946e6i | 0.743621 | + | 1.28799i | ||||
\(483\) | −69995.9 | + | 121236.i | −0.0136523 | + | 0.0236464i | ||||
\(484\) | −948745. | −0.184093 | ||||||||
\(485\) | −3.15417e6 | + | 5.46318e6i | −0.608879 | + | 1.05461i | ||||
\(486\) | 3.33143e6 | + | 5.77021e6i | 0.639795 | + | 1.10816i | ||||
\(487\) | −1.07418e6 | − | 1.86054e6i | −0.205237 | − | 0.355481i | 0.744971 | − | 0.667097i | \(-0.232463\pi\) |
−0.950208 | + | 0.311615i | \(0.899130\pi\) | |||||||
\(488\) | −911572. | − | 1.57889e6i | −0.173277 | − | 0.300125i | ||||
\(489\) | 8.31871e6 | 1.57320 | ||||||||
\(490\) | 4.09607e6 | + | 7.09460e6i | 0.770686 | + | 1.33487i | ||||
\(491\) | 5.08635e6 | + | 8.80982e6i | 0.952144 | + | 1.64916i | 0.740773 | + | 0.671755i | \(0.234459\pi\) |
0.211371 | + | 0.977406i | \(0.432207\pi\) | |||||||
\(492\) | −883802. | + | 1.53079e6i | −0.164605 | + | 0.285104i | ||||
\(493\) | 2.50617e6 | − | 4.34082e6i | 0.464402 | − | 0.804367i | ||||
\(494\) | −4.28302e6 | −0.789647 | ||||||||
\(495\) | 2.37056e6 | 0.434849 | ||||||||
\(496\) | 2.27692e6 | − | 3.94373e6i | 0.415569 | − | 0.719786i | ||||
\(497\) | −46887.9 | + | 81212.2i | −0.00851470 | + | 0.0147479i | ||||
\(498\) | 1.01349e6 | + | 1.75542e6i | 0.183125 | + | 0.317182i | ||||
\(499\) | −1.95088e6 | − | 3.37902e6i | −0.350734 | − | 0.607490i | 0.635644 | − | 0.771982i | \(-0.280735\pi\) |
−0.986378 | + | 0.164493i | \(0.947401\pi\) | |||||||
\(500\) | 100182. | 0.0179212 | ||||||||
\(501\) | 1.73980e6 | + | 3.01343e6i | 0.309675 | + | 0.536373i | ||||
\(502\) | −2.03105e6 | − | 3.51788e6i | −0.359717 | − | 0.623048i | ||||
\(503\) | −1.88506e6 | − | 3.26502e6i | −0.332205 | − | 0.575395i | 0.650739 | − | 0.759301i | \(-0.274459\pi\) |
−0.982944 | + | 0.183906i | \(0.941126\pi\) | |||||||
\(504\) | 121068. | − | 209697.i | 0.0212302 | − | 0.0367718i | ||||
\(505\) | 1.00119e7 | 1.74697 | ||||||||
\(506\) | −422108. | + | 731113.i | −0.0732905 | + | 0.126943i | ||||
\(507\) | 739845. | + | 1.28145e6i | 0.127827 | + | 0.221402i | ||||
\(508\) | 1.57254e6 | 0.270360 | ||||||||
\(509\) | −1.41272e6 | − | 2.44690e6i | −0.241692 | − | 0.418622i | 0.719505 | − | 0.694488i | \(-0.244369\pi\) |
−0.961196 | + | 0.275865i | \(0.911036\pi\) | |||||||
\(510\) | 5.00115e6 | − | 8.66225e6i | 0.851421 | − | 1.47470i | ||||
\(511\) | −372623. | + | 645402.i | −0.0631273 | + | 0.109340i | ||||
\(512\) | 2.72379e6 | 0.459197 | ||||||||
\(513\) | −825390. | + | 1.42962e6i | −0.138473 | + | 0.239843i | ||||
\(514\) | −1.00708e7 | −1.68134 | ||||||||
\(515\) | 956998. | 0.158998 | ||||||||
\(516\) | −1.31218e6 | − | 1.28509e6i | −0.216954 | − | 0.212475i | ||||
\(517\) | −1.94554e6 | −0.320121 | ||||||||
\(518\) | −923328. | −0.151193 | ||||||||
\(519\) | −3.15577e6 | + | 5.46595e6i | −0.514264 | + | 0.890732i | ||||
\(520\) | −8.00203e6 | −1.29775 | ||||||||
\(521\) | 825108. | − | 1.42913e6i | 0.133173 | − | 0.230663i | −0.791725 | − | 0.610878i | \(-0.790817\pi\) |
0.924898 | + | 0.380215i | \(0.124150\pi\) | |||||||
\(522\) | −2.53168e6 | + | 4.38500e6i | −0.406661 | + | 0.704358i | ||||
\(523\) | −1.87718e6 | − | 3.25137e6i | −0.300090 | − | 0.519771i | 0.676066 | − | 0.736841i | \(-0.263683\pi\) |
−0.976156 | + | 0.217070i | \(0.930350\pi\) | |||||||
\(524\) | 1.51398e6 | 0.240875 | ||||||||
\(525\) | −287588. | − | 498118.i | −0.0455379 | − | 0.0788740i | ||||
\(526\) | −2.70476e6 | + | 4.68479e6i | −0.426250 | + | 0.738287i | ||||
\(527\) | 3.81859e6 | 0.598931 | ||||||||
\(528\) | 2.27265e6 | − | 3.93634e6i | 0.354770 | − | 0.614480i | ||||
\(529\) | 2.95969e6 | + | 5.12633e6i | 0.459840 | + | 0.796466i | ||||
\(530\) | −5.61199e6 | − | 9.72025e6i | −0.867815 | − | 1.50310i | ||||
\(531\) | −3.03308e6 | − | 5.25345e6i | −0.466818 | − | 0.808552i | ||||
\(532\) | −74253.2 | −0.0113746 | ||||||||
\(533\) | 3.89098e6 | + | 6.73937e6i | 0.593254 | + | 1.02755i | ||||
\(534\) | 4.80844e6 | + | 8.32846e6i | 0.729711 | + | 1.26390i | ||||
\(535\) | 1.36189e6 | − | 2.35887e6i | 0.205711 | − | 0.356302i | ||||
\(536\) | 4.58444e6 | − | 7.94048e6i | 0.689246 | − | 1.19381i | ||||
\(537\) | 6.92689e6 | 1.03658 | ||||||||
\(538\) | 2.77389e6 | 0.413174 | ||||||||
\(539\) | −1.56083e6 | + | 2.70344e6i | −0.231411 | + | 0.400815i | ||||
\(540\) | 473696. | − | 820465.i | 0.0699061 | − | 0.121081i | ||||
\(541\) | 1.49350e6 | + | 2.58682e6i | 0.219388 | + | 0.379991i | 0.954621 | − | 0.297823i | \(-0.0962607\pi\) |
−0.735233 | + | 0.677814i | \(0.762927\pi\) | |||||||
\(542\) | 7.41276e6 | + | 1.28393e7i | 1.08388 | + | 1.87734i | ||||
\(543\) | −1.16017e7 | −1.68858 | ||||||||
\(544\) | −1.35239e6 | − | 2.34241e6i | −0.195932 | − | 0.339364i | ||||
\(545\) | 5.05024e6 | + | 8.74727e6i | 0.728317 | + | 1.26148i | ||||
\(546\) | 408137. | + | 706914.i | 0.0585901 | + | 0.101481i | ||||
\(547\) | 4.45149e6 | − | 7.71020e6i | 0.636117 | − | 1.10179i | −0.350161 | − | 0.936690i | \(-0.613873\pi\) |
0.986277 | − | 0.165097i | \(-0.0527936\pi\) | |||||||
\(548\) | −1.53284e6 | −0.218044 | ||||||||
\(549\) | −964235. | + | 1.67010e6i | −0.136538 | + | 0.236490i | ||||
\(550\) | −1.73429e6 | − | 3.00389e6i | −0.244465 | − | 0.423425i | ||||
\(551\) | −5.05479e6 | −0.709290 | ||||||||
\(552\) | 1.11448e6 | + | 1.93033e6i | 0.155677 | + | 0.269640i | ||||
\(553\) | 435306. | − | 753972.i | 0.0605316 | − | 0.104844i | ||||
\(554\) | 5.38465e6 | − | 9.32649e6i | 0.745389 | − | 1.29105i | ||||
\(555\) | −2.38668e7 | −3.28898 | ||||||||
\(556\) | −1.43044e6 | + | 2.47760e6i | −0.196238 | + | 0.339895i | ||||
\(557\) | −9.53108e6 | −1.30168 | −0.650840 | − | 0.759215i | \(-0.725583\pi\) | ||||
−0.650840 | + | 0.759215i | \(0.725583\pi\) | |||||||
\(558\) | −3.85746e6 | −0.524464 | ||||||||
\(559\) | −7.78813e6 | + | 2.17412e6i | −1.05415 | + | 0.294276i | ||||
\(560\) | −910421. | −0.122680 | ||||||||
\(561\) | 3.81143e6 | 0.511306 | ||||||||
\(562\) | 5.89935e6 | − | 1.02180e7i | 0.787886 | − | 1.36466i | ||||
\(563\) | 1.08614e7 | 1.44416 | 0.722080 | − | 0.691809i | \(-0.243186\pi\) | ||||
0.722080 | + | 0.691809i | \(0.243186\pi\) | |||||||
\(564\) | 788948. | − | 1.36650e6i | 0.104436 | − | 0.180889i | ||||
\(565\) | 1.39759e6 | − | 2.42069e6i | 0.184186 | − | 0.319020i | ||||
\(566\) | −2.73545e6 | − | 4.73794e6i | −0.358912 | − | 0.621654i | ||||
\(567\) | 696947. | 0.0910421 | ||||||||
\(568\) | 746551. | + | 1.29306e6i | 0.0970931 | + | 0.168170i | ||||
\(569\) | 5.76350e6 | − | 9.98268e6i | 0.746287 | − | 1.29261i | −0.203304 | − | 0.979116i | \(-0.565168\pi\) |
0.949591 | − | 0.313491i | \(-0.101499\pi\) | |||||||
\(570\) | −1.00870e7 | −1.30039 | ||||||||
\(571\) | 4.76988e6 | − | 8.26167e6i | 0.612233 | − | 1.06042i | −0.378630 | − | 0.925548i | \(-0.623605\pi\) |
0.990863 | − | 0.134871i | \(-0.0430619\pi\) | |||||||
\(572\) | 468326. | + | 811165.i | 0.0598492 | + | 0.103662i | ||||
\(573\) | 443686. | + | 768487.i | 0.0564533 | + | 0.0977800i | ||||
\(574\) | 354513. | + | 614035.i | 0.0449110 | + | 0.0777882i | ||||
\(575\) | 2.12403e6 | 0.267911 | ||||||||
\(576\) | −1.78038e6 | − | 3.08370e6i | −0.223592 | − | 0.387272i | ||||
\(577\) | −3.15504e6 | − | 5.46468e6i | −0.394516 | − | 0.683322i | 0.598523 | − | 0.801106i | \(-0.295754\pi\) |
−0.993039 | + | 0.117783i | \(0.962421\pi\) | |||||||
\(578\) | −1.23724e6 | + | 2.14296e6i | −0.154040 | + | 0.266806i | ||||
\(579\) | 325990. | − | 564632.i | 0.0404118 | − | 0.0699953i | ||||
\(580\) | 2.90097e6 | 0.358074 | ||||||||
\(581\) | 154710. | 0.0190142 | ||||||||
\(582\) | 5.12295e6 | − | 8.87320e6i | 0.626920 | − | 1.08586i | ||||
\(583\) | 2.13848e6 | − | 3.70395e6i | 0.260575 | − | 0.451330i | ||||
\(584\) | 5.93292e6 | + | 1.02761e7i | 0.719840 | + | 1.24680i | ||||
\(585\) | 4.23216e6 | + | 7.33032e6i | 0.511296 | + | 0.885591i | ||||
\(586\) | −1.36225e6 | −0.163875 | ||||||||
\(587\) | 75965.6 | + | 131576.i | 0.00909958 | + | 0.0157609i | 0.870539 | − | 0.492099i | \(-0.163770\pi\) |
−0.861440 | + | 0.507860i | \(0.830437\pi\) | |||||||
\(588\) | −1.26588e6 | − | 2.19257e6i | −0.150990 | − | 0.261523i | ||||
\(589\) | −1.92546e6 | − | 3.33500e6i | −0.228690 | − | 0.396102i | ||||
\(590\) | −9.13266e6 | + | 1.58182e7i | −1.08011 | + | 1.87080i | ||||
\(591\) | 9.45338e6 | 1.11332 | ||||||||
\(592\) | −9.17894e6 | + | 1.58984e7i | −1.07644 | + | 1.86444i | ||||
\(593\) | 3.41518e6 | + | 5.91527e6i | 0.398820 | + | 0.690777i | 0.993581 | − | 0.113126i | \(-0.0360865\pi\) |
−0.594761 | + | 0.803903i | \(0.702753\pi\) | |||||||
\(594\) | 1.89726e6 | 0.220628 | ||||||||
\(595\) | −381714. | − | 661148.i | −0.0442024 | − | 0.0765608i | ||||
\(596\) | 1.54415e6 | − | 2.67454e6i | 0.178063 | − | 0.308413i | ||||
\(597\) | −9382.60 | + | 16251.1i | −0.00107743 | + | 0.00186616i | ||||
\(598\) | −3.01436e6 | −0.344701 | ||||||||
\(599\) | −826832. | + | 1.43211e6i | −0.0941565 | + | 0.163084i | −0.909256 | − | 0.416237i | \(-0.863349\pi\) |
0.815100 | + | 0.579321i | \(0.196682\pi\) | |||||||
\(600\) | −9.15799e6 | −1.03854 | ||||||||
\(601\) | 1.30843e7 | 1.47762 | 0.738811 | − | 0.673912i | \(-0.235387\pi\) | ||||
0.738811 | + | 0.673912i | \(0.235387\pi\) | |||||||
\(602\) | −709589. | + | 198088.i | −0.0798023 | + | 0.0222775i | ||||
\(603\) | −9.69858e6 | −1.08621 | ||||||||
\(604\) | 3.48216e6 | 0.388380 | ||||||||
\(605\) | −4.91853e6 | + | 8.51914e6i | −0.546319 | + | 0.946253i | ||||
\(606\) | −1.62611e7 | −1.79874 | ||||||||
\(607\) | 2.91479e6 | − | 5.04857e6i | 0.321097 | − | 0.556156i | −0.659618 | − | 0.751601i | \(-0.729282\pi\) |
0.980715 | + | 0.195445i | \(0.0626152\pi\) | |||||||
\(608\) | −1.36384e6 | + | 2.36225e6i | −0.149626 | + | 0.259159i | ||||
\(609\) | 481680. | + | 834295.i | 0.0526278 | + | 0.0911541i | ||||
\(610\) | 5.80666e6 | 0.631832 | ||||||||
\(611\) | −3.47338e6 | − | 6.01607e6i | −0.376399 | − | 0.651943i | ||||
\(612\) | −620032. | + | 1.07393e6i | −0.0669168 | + | 0.115903i | ||||
\(613\) | −9.95179e6 | −1.06967 | −0.534835 | − | 0.844956i | \(-0.679626\pi\) | ||||
−0.534835 | + | 0.844956i | \(0.679626\pi\) | |||||||
\(614\) | 581822. | − | 1.00774e6i | 0.0622829 | − | 0.107877i | ||||
\(615\) | 9.16369e6 | + | 1.58720e7i | 0.976973 | + | 1.69217i | ||||
\(616\) | −138910. | − | 240598.i | −0.0147496 | − | 0.0255471i | ||||
\(617\) | −1.07920e6 | − | 1.86923e6i | −0.114127 | − | 0.197674i | 0.803303 | − | 0.595570i | \(-0.203074\pi\) |
−0.917431 | + | 0.397896i | \(0.869741\pi\) | |||||||
\(618\) | −1.55434e6 | −0.163710 | ||||||||
\(619\) | −1.74394e6 | − | 3.02059e6i | −0.182938 | − | 0.316858i | 0.759942 | − | 0.649991i | \(-0.225227\pi\) |
−0.942880 | + | 0.333133i | \(0.891894\pi\) | |||||||
\(620\) | 1.10503e6 | + | 1.91397e6i | 0.115451 | + | 0.199966i | ||||
\(621\) | −580903. | + | 1.00615e6i | −0.0604470 | + | 0.104697i | ||||
\(622\) | −1.05956e6 | + | 1.83521e6i | −0.109812 | + | 0.190200i | ||||
\(623\) | 734011. | 0.0757674 | ||||||||
\(624\) | 1.62294e7 | 1.66856 | ||||||||
\(625\) | 5.13520e6 | − | 8.89442e6i | 0.525844 | − | 0.910789i | ||||
\(626\) | 3.06618e6 | − | 5.31078e6i | 0.312724 | − | 0.541654i | ||||
\(627\) | −1.92185e6 | − | 3.32875e6i | −0.195232 | − | 0.338152i | ||||
\(628\) | −1.02473e6 | − | 1.77489e6i | −0.103684 | − | 0.179586i | ||||
\(629\) | −1.53939e7 | −1.55139 | ||||||||
\(630\) | 385599. | + | 667878.i | 0.0387066 | + | 0.0670418i | ||||
\(631\) | −3.18552e6 | − | 5.51747e6i | −0.318498 | − | 0.551654i | 0.661677 | − | 0.749789i | \(-0.269845\pi\) |
−0.980175 | + | 0.198135i | \(0.936512\pi\) | |||||||
\(632\) | −6.93096e6 | − | 1.20048e7i | −0.690241 | − | 1.19553i | ||||
\(633\) | 2.88435e6 | − | 4.99584e6i | 0.286114 | − | 0.495563i | ||||
\(634\) | 7.84566e6 | 0.775187 | ||||||||
\(635\) | 8.15243e6 | − | 1.41204e7i | 0.802330 | − | 1.38968i | ||||
\(636\) | 1.73437e6 | + | 3.00402e6i | 0.170020 | + | 0.294483i | ||||
\(637\) | −1.11462e7 | −1.08837 | ||||||||
\(638\) | 2.90476e6 | + | 5.03119e6i | 0.282526 | + | 0.489350i | ||||
\(639\) | 789680. | − | 1.36777e6i | 0.0765067 | − | 0.132513i | ||||
\(640\) | −8.69155e6 | + | 1.50542e7i | −0.838779 | + | 1.45281i | ||||
\(641\) | −8.19576e6 | −0.787851 | −0.393926 | − | 0.919142i | \(-0.628883\pi\) | ||||
−0.393926 | + | 0.919142i | \(0.628883\pi\) | |||||||
\(642\) | −2.21196e6 | + | 3.83123e6i | −0.211807 | + | 0.366860i | ||||
\(643\) | 1.13866e7 | 1.08609 | 0.543044 | − | 0.839704i | \(-0.317272\pi\) | ||||
0.543044 | + | 0.839704i | \(0.317272\pi\) | |||||||
\(644\) | −52258.8 | −0.00496529 | ||||||||
\(645\) | −1.83419e7 | + | 5.12030e6i | −1.73598 | + | 0.484615i | ||||
\(646\) | −6.50605e6 | −0.613389 | ||||||||
\(647\) | −7.13106e6 | −0.669720 | −0.334860 | − | 0.942268i | \(-0.608689\pi\) | ||||
−0.334860 | + | 0.942268i | \(0.608689\pi\) | |||||||
\(648\) | 5.54841e6 | − | 9.61013e6i | 0.519076 | − | 0.899067i | ||||
\(649\) | −6.96009e6 | −0.648639 | ||||||||
\(650\) | 6.19247e6 | − | 1.07257e7i | 0.574885 | − | 0.995729i | ||||
\(651\) | −366962. | + | 635597.i | −0.0339366 | + | 0.0587799i | ||||
\(652\) | 1.55268e6 | + | 2.68933e6i | 0.143042 | + | 0.247756i | ||||
\(653\) | 1.50871e7 | 1.38459 | 0.692297 | − | 0.721612i | \(-0.256599\pi\) | ||||
0.692297 | + | 0.721612i | \(0.256599\pi\) | |||||||
\(654\) | −8.20250e6 | − | 1.42072e7i | −0.749898 | − | 1.29886i | ||||
\(655\) | 7.84885e6 | − | 1.35946e7i | 0.714830 | − | 1.23812i | ||||
\(656\) | 1.40971e7 | 1.27900 | ||||||||
\(657\) | 6.27567e6 | − | 1.08698e7i | 0.567214 | − | 0.982443i | ||||
\(658\) | −316465. | − | 548134.i | −0.0284945 | − | 0.0493539i | ||||
\(659\) | 3.44954e6 | + | 5.97477e6i | 0.309419 | + | 0.535930i | 0.978235 | − | 0.207498i | \(-0.0665320\pi\) |
−0.668816 | + | 0.743428i | \(0.733199\pi\) | |||||||
\(660\) | 1.10296e6 | + | 1.91038e6i | 0.0985599 | + | 0.170711i | ||||
\(661\) | 1.10554e7 | 0.984174 | 0.492087 | − | 0.870546i | \(-0.336234\pi\) | ||||
0.492087 | + | 0.870546i | \(0.336234\pi\) | |||||||
\(662\) | −1.20082e7 | − | 2.07989e7i | −1.06496 | − | 1.84457i | ||||
\(663\) | 6.80454e6 | + | 1.17858e7i | 0.601195 | + | 1.04130i | ||||
\(664\) | 1.23165e6 | − | 2.13328e6i | 0.108410 | − | 0.187771i | ||||
\(665\) | −384946. | + | 666747.i | −0.0337556 | + | 0.0584665i | ||||
\(666\) | 1.55506e7 | 1.35850 | ||||||||
\(667\) | −3.55752e6 | −0.309623 | ||||||||
\(668\) | −649468. | + | 1.12491e6i | −0.0563140 | + | 0.0975387i | ||||
\(669\) | −3.58154e6 | + | 6.20340e6i | −0.309388 | + | 0.535876i | ||||
\(670\) | 1.46013e7 | + | 2.52902e7i | 1.25662 | + | 2.17653i | ||||
\(671\) | 1.10633e6 | + | 1.91622e6i | 0.0948589 | + | 0.164300i | ||||
\(672\) | 519853. | 0.0444076 | ||||||||
\(673\) | 1.14107e7 | + | 1.97639e7i | 0.971121 | + | 1.68203i | 0.692183 | + | 0.721722i | \(0.256649\pi\) |
0.278938 | + | 0.960309i | \(0.410018\pi\) | |||||||
\(674\) | −8.62919e6 | − | 1.49462e7i | −0.731678 | − | 1.26730i | ||||
\(675\) | −2.38673e6 | − | 4.13393e6i | −0.201625 | − | 0.349224i | ||||
\(676\) | −276184. | + | 478364.i | −0.0232451 | + | 0.0402617i | ||||
\(677\) | 974569. | 0.0817224 | 0.0408612 | − | 0.999165i | \(-0.486990\pi\) | ||||
0.0408612 | + | 0.999165i | \(0.486990\pi\) | |||||||
\(678\) | −2.26993e6 | + | 3.93164e6i | −0.189644 | + | 0.328473i | ||||
\(679\) | −391010. | − | 677250.i | −0.0325472 | − | 0.0563734i | ||||
\(680\) | −1.21553e7 | −1.00808 | ||||||||
\(681\) | 1.03766e7 | + | 1.79728e7i | 0.857410 | + | 1.48508i | ||||
\(682\) | −2.21295e6 | + | 3.83295e6i | −0.182185 | + | 0.315553i | ||||
\(683\) | −7.34365e6 | + | 1.27196e7i | −0.602366 | + | 1.04333i | 0.390096 | + | 0.920774i | \(0.372442\pi\) |
−0.992462 | + | 0.122554i | \(0.960891\pi\) | |||||||
\(684\) | 1.25056e6 | 0.102203 | ||||||||
\(685\) | −7.94660e6 | + | 1.37639e7i | −0.647075 | + | 1.12077i | ||||
\(686\) | −2.03677e6 | −0.165246 | ||||||||
\(687\) | −5.27949e6 | −0.426776 | ||||||||
\(688\) | −3.64334e6 | + | 1.41873e7i | −0.293446 | + | 1.14269i | ||||
\(689\) | 1.52713e7 | 1.22554 | ||||||||
\(690\) | −7.09916e6 | −0.567654 | ||||||||
\(691\) | −4.32305e6 | + | 7.48774e6i | −0.344425 | + | 0.596562i | −0.985249 | − | 0.171126i | \(-0.945260\pi\) |
0.640824 | + | 0.767688i | \(0.278593\pi\) | |||||||
\(692\) | −2.35609e6 | −0.187037 | ||||||||
\(693\) | −146935. | + | 254498.i | −0.0116223 | + | 0.0201304i | ||||
\(694\) | 202106. | − | 350058.i | 0.0159287 | − | 0.0275893i | ||||
\(695\) | 1.48315e7 | + | 2.56890e7i | 1.16473 | + | 2.01737i | ||||
\(696\) | 1.53387e7 | 1.20023 | ||||||||
\(697\) | 5.91052e6 | + | 1.02373e7i | 0.460833 | + | 0.798187i | ||||
\(698\) | 6.50920e6 | − | 1.12743e7i | 0.505696 | − | 0.875891i | ||||
\(699\) | 1.16423e7 | 0.901252 | ||||||||
\(700\) | 107357. | − | 185947.i | 0.00828101 | − | 0.0143431i | ||||
\(701\) | 2.72120e6 | + | 4.71326e6i | 0.209154 | + | 0.362265i | 0.951448 | − | 0.307809i | \(-0.0995957\pi\) |
−0.742294 | + | 0.670074i | \(0.766262\pi\) | |||||||
\(702\) | 3.38718e6 | + | 5.86676e6i | 0.259415 | + | 0.449320i | ||||
\(703\) | 7.76213e6 | + | 1.34444e7i | 0.592369 | + | 1.02601i | ||||
\(704\) | −4.08548e6 | −0.310679 | ||||||||
\(705\) | −8.18019e6 | − | 1.41685e7i | −0.619856 | − | 1.07362i | ||||
\(706\) | −3.23449e6 | − | 5.60230e6i | −0.244227 | − | 0.423014i | ||||
\(707\) | −620566. | + | 1.07485e6i | −0.0466917 | + | 0.0808724i | ||||
\(708\) | 2.82243e6 | − | 4.88858e6i | 0.211612 | − | 0.366522i | ||||
\(709\) | 1.17367e7 | 0.876863 | 0.438431 | − | 0.898765i | \(-0.355534\pi\) | ||||
0.438431 | + | 0.898765i | \(0.355534\pi\) | |||||||
\(710\) | −4.75548e6 | −0.354037 | ||||||||
\(711\) | −7.33138e6 | + | 1.26983e7i | −0.543891 | + | 0.942046i | ||||
\(712\) | 5.84348e6 | − | 1.01212e7i | 0.431988 | − | 0.748225i | ||||
\(713\) | −1.35513e6 | − | 2.34715e6i | −0.0998288 | − | 0.172909i | ||||
\(714\) | 619973. | + | 1.07382e6i | 0.0455122 | + | 0.0788294i | ||||
\(715\) | 9.71167e6 | 0.710442 | ||||||||
\(716\) | 1.29290e6 | + | 2.23937e6i | 0.0942503 | + | 0.163246i | ||||
\(717\) | −6.58001e6 | − | 1.13969e7i | −0.478001 | − | 0.827922i | ||||
\(718\) | −7.38105e6 | − | 1.27844e7i | −0.534327 | − | 0.925481i | ||||
\(719\) | 1.33219e7 | − | 2.30742e7i | 0.961046 | − | 1.66458i | 0.241162 | − | 0.970485i | \(-0.422471\pi\) |
0.719883 | − | 0.694095i | \(-0.244195\pi\) | |||||||
\(720\) | 1.53332e7 | 1.10231 | ||||||||
\(721\) | −59317.7 | + | 102741.i | −0.00424958 | + | 0.00736049i | ||||
\(722\) | −4.50240e6 | − | 7.79838e6i | −0.321441 | − | 0.556752i | ||||
\(723\) | −2.43075e7 | −1.72939 | ||||||||
\(724\) | −2.16545e6 | − | 3.75067e6i | −0.153533 | − | 0.265927i | ||||
\(725\) | 7.30831e6 | − | 1.26584e7i | 0.516383 | − | 0.894401i | ||||
\(726\) | 7.98858e6 | − | 1.38366e7i | 0.562507 | − | 0.974291i | ||||
\(727\) | 9.11930e6 | 0.639920 | 0.319960 | − | 0.947431i | \(-0.396331\pi\) | ||||
0.319960 | + | 0.947431i | \(0.396331\pi\) | |||||||
\(728\) | 495990. | − | 859081.i | 0.0346853 | − | 0.0600766i | ||||
\(729\) | −3.82825e6 | −0.266797 | ||||||||
\(730\) | −3.77923e7 | −2.62480 | ||||||||
\(731\) | −1.18304e7 | + | 3.30256e6i | −0.818854 | + | 0.228590i | ||||
\(732\) | −1.79453e6 | −0.123787 | ||||||||
\(733\) | 1.63605e7 | 1.12470 | 0.562350 | − | 0.826900i | \(-0.309898\pi\) | ||||
0.562350 | + | 0.826900i | \(0.309898\pi\) | |||||||
\(734\) | 8.71692e6 | − | 1.50981e7i | 0.597204 | − | 1.03439i | ||||
\(735\) | −2.62505e7 | −1.79234 | ||||||||
\(736\) | −959864. | + | 1.66253e6i | −0.0653153 | + | 0.113129i | ||||
\(737\) | −5.56390e6 | + | 9.63696e6i | −0.377321 | + | 0.653539i | ||||
\(738\) | −5.97068e6 | − | 1.03415e7i | −0.403536 | − | 0.698945i | ||||
\(739\) | −1.57284e7 | −1.05943 | −0.529717 | − | 0.848175i | \(-0.677702\pi\) | ||||
−0.529717 | + | 0.848175i | \(0.677702\pi\) | |||||||
\(740\) | −4.45473e6 | − | 7.71581e6i | −0.299048 | − | 0.517967i | ||||
\(741\) | 6.86216e6 | − | 1.18856e7i | 0.459109 | − | 0.795200i | ||||
\(742\) | 1.39139e6 | 0.0927769 | ||||||||
\(743\) | −1.01691e7 | + | 1.76135e7i | −0.675790 | + | 1.17050i | 0.300447 | + | 0.953799i | \(0.402864\pi\) |
−0.976237 | + | 0.216705i | \(0.930469\pi\) | |||||||
\(744\) | 5.84278e6 | + | 1.01200e7i | 0.386979 | + | 0.670267i | ||||
\(745\) | −1.60105e7 | − | 2.77309e7i | −1.05685 | − | 1.83052i | ||||
\(746\) | 1.07675e7 | + | 1.86498e7i | 0.708382 | + | 1.22695i | ||||
\(747\) | −2.60561e6 | −0.170847 | ||||||||
\(748\) | 711402. | + | 1.23218e6i | 0.0464902 | + | 0.0805233i | ||||
\(749\) | 168828. | + | 292419.i | 0.0109962 | + | 0.0190459i | ||||
\(750\) | −843551. | + | 1.46107e6i | −0.0547593 | + | 0.0948459i | ||||
\(751\) | −4.36602e6 | + | 7.56217e6i | −0.282479 | + | 0.489268i | −0.971995 | − | 0.235003i | \(-0.924490\pi\) |
0.689516 | + | 0.724271i | \(0.257823\pi\) | |||||||
\(752\) | −1.25841e7 | −0.811481 | ||||||||
\(753\) | 1.30164e7 | 0.836573 | ||||||||
\(754\) | −1.03717e7 | + | 1.79644e7i | −0.664390 | + | 1.15076i | ||||
\(755\) | 1.80524e7 | − | 3.12676e7i | 1.15257 | − | 1.99631i | ||||
\(756\) | 58722.2 | + | 101710.i | 0.00373678 | + | 0.00647230i | ||||
\(757\) | −4.42807e6 | − | 7.66964e6i | −0.280850 | − | 0.486447i | 0.690744 | − | 0.723099i | \(-0.257283\pi\) |
−0.971594 | + | 0.236652i | \(0.923950\pi\) | |||||||
\(758\) | 8.77924e6 | 0.554988 | ||||||||
\(759\) | −1.35259e6 | − | 2.34275e6i | −0.0852237 | − | 0.147612i | ||||
\(760\) | 6.12914e6 | + | 1.06160e7i | 0.384915 | + | 0.666693i | ||||
\(761\) | −5.86909e6 | − | 1.01656e7i | −0.367374 | − | 0.636311i | 0.621780 | − | 0.783192i | \(-0.286410\pi\) |
−0.989154 | + | 0.146881i | \(0.953077\pi\) | |||||||
\(762\) | −1.32410e7 | + | 2.29341e7i | −0.826103 | + | 1.43085i | ||||
\(763\) | −1.25212e6 | −0.0778634 | ||||||||
\(764\) | −165628. | + | 286876.i | −0.0102660 | + | 0.0177812i | ||||
\(765\) | 6.42879e6 | + | 1.11350e7i | 0.397169 | + | 0.687917i | ||||
\(766\) | −2.71252e7 | −1.67033 | ||||||||
\(767\) | −1.24259e7 | − | 2.15222e7i | −0.762672 | − | 1.32099i | ||||
\(768\) | 7.06656e6 | − | 1.22396e7i | 0.432320 | − | 0.748800i | ||||
\(769\) | −1.61087e6 | + | 2.79010e6i | −0.0982300 | + | 0.170139i | −0.910952 | − | 0.412512i | \(-0.864651\pi\) |
0.812722 | + | 0.582652i | \(0.197985\pi\) | |||||||
\(770\) | 884846. | 0.0537825 | ||||||||
\(771\) | 1.61352e7 | − | 2.79469e7i | 0.977546 | − | 1.69316i | ||||
\(772\) | 243384. | 0.0146977 | ||||||||
\(773\) | −1.79989e7 | −1.08342 | −0.541710 | − | 0.840565i | \(-0.682223\pi\) | ||||
−0.541710 | + | 0.840565i | \(0.682223\pi\) | |||||||
\(774\) | 1.19508e7 | − | 3.33618e6i | 0.717043 | − | 0.200169i | ||||
\(775\) | 1.11355e7 | 0.665970 | ||||||||
\(776\) | −1.24514e7 | −0.742271 | ||||||||
\(777\) | 1.47934e6 | − | 2.56228e6i | 0.0879051 | − | 0.152256i | ||||
\(778\) | −1.71342e7 | −1.01488 | ||||||||
\(779\) | 5.96057e6 | − | 1.03240e7i | 0.351920 | − | 0.609544i | ||||
\(780\) | −3.93823e6 | + | 6.82122e6i | −0.231774 | + | 0.401444i | ||||
\(781\) | −906051. | − | 1.56933e6i | −0.0531527 | − | 0.0920631i | ||||
\(782\) | −4.57891e6 | −0.267760 | ||||||||
\(783\) | 3.99752e6 | + | 6.92390e6i | 0.233016 | + | 0.403596i | ||||
\(784\) | −1.00957e7 | + | 1.74863e7i | −0.586607 | + | 1.01603i | ||||
\(785\) | −2.12499e7 | −1.23079 | ||||||||
\(786\) | −1.27480e7 | + | 2.20801e7i | −0.736011 | + | 1.27481i | ||||
\(787\) | −3.62125e6 | − | 6.27220e6i | −0.208412 | − | 0.360980i | 0.742803 | − | 0.669510i | \(-0.233496\pi\) |
−0.951214 | + | 0.308531i | \(0.900163\pi\) | |||||||
\(788\) | 1.76447e6 | + | 3.05615e6i | 0.101228 | + | 0.175331i | ||||
\(789\) | −8.66702e6 | − | 1.50117e7i | −0.495653 | − | 0.858495i | ||||
\(790\) | 4.41498e7 | 2.51687 | ||||||||
\(791\) | 173253. | + | 300083.i | 0.00984556 | + | 0.0170530i | ||||
\(792\) | 2.33950e6 | + | 4.05213e6i | 0.132529 | + | 0.229547i | ||||
\(793\) | −3.95026e6 | + | 6.84205e6i | −0.223071 | + | 0.386370i | ||||
\(794\) | −2.59120e6 | + | 4.48809e6i | −0.145865 | + | 0.252645i | ||||
\(795\) | 3.59656e7 | 2.01822 | ||||||||
\(796\) | −7005.04 | −0.000391857 | ||||||||
\(797\) | 3.05114e6 | − | 5.28474e6i | 0.170144 | − | 0.294698i | −0.768326 | − | 0.640059i | \(-0.778910\pi\) |
0.938470 | + | 0.345360i | \(0.112243\pi\) | |||||||
\(798\) | 625223. | − | 1.08292e6i | 0.0347558 | − | 0.0601989i | ||||
\(799\) | −5.27617e6 | − | 9.13860e6i | −0.292383 | − | 0.506422i | ||||
\(800\) | −3.94374e6 | − | 6.83076e6i | −0.217863 | − | 0.377350i | ||||
\(801\) | −1.23621e7 | −0.680789 | ||||||||
\(802\) | 3.26853e6 | + | 5.66126e6i | 0.179439 | + | 0.310797i | ||||
\(803\) | −7.20048e6 | − | 1.24716e7i | −0.394070 | − | 0.682548i | ||||
\(804\) | −4.51250e6 | − | 7.81587e6i | −0.246194 | − | 0.426420i | ||||
\(805\) | −270922. | + | 469251.i | −0.0147352 | + | 0.0255221i | ||||
\(806\) | −1.58031e7 | −0.856852 | ||||||||
\(807\) | −4.44426e6 | + | 7.69768e6i | −0.240224 | + | 0.416079i | ||||
\(808\) | 9.88068e6 | + | 1.71138e7i | 0.532425 | + | 0.922187i | ||||
\(809\) | 1.45291e7 | 0.780489 | 0.390244 | − | 0.920711i | \(-0.372390\pi\) | ||||
0.390244 | + | 0.920711i | \(0.372390\pi\) | |||||||
\(810\) | 1.76715e7 | + | 3.06080e7i | 0.946371 | + | 1.63916i | ||||
\(811\) | −1.37895e7 | + | 2.38842e7i | −0.736203 | + | 1.27514i | 0.217991 | + | 0.975951i | \(0.430050\pi\) |
−0.954194 | + | 0.299190i | \(0.903284\pi\) | |||||||
\(812\) | −179811. | + | 311442.i | −0.00957031 | + | 0.0165763i | ||||
\(813\) | −4.75063e7 | −2.52072 | ||||||||
\(814\) | 8.92109e6 | − | 1.54518e7i | 0.471908 | − | 0.817368i | ||||
\(815\) | 3.21980e7 | 1.69799 | ||||||||
\(816\) | 2.46530e7 | 1.29612 | ||||||||
\(817\) | 8.84962e6 | + | 8.66693e6i | 0.463841 | + | 0.454266i | ||||
\(818\) | 3.13204e7 | 1.63660 | ||||||||
\(819\) | −1.04929e6 | −0.0546620 | ||||||||
\(820\) | −3.42080e6 | + | 5.92500e6i | −0.177661 | + | 0.307719i | ||||
\(821\) | −1.82624e7 | −0.945584 | −0.472792 | − | 0.881174i | \(-0.656754\pi\) | ||||
−0.472792 | + | 0.881174i | \(0.656754\pi\) | |||||||
\(822\) | 1.29067e7 | − | 2.23551e7i | 0.666248 | − | 1.15398i | ||||
\(823\) | −1.72786e7 | + | 2.99274e7i | −0.889218 | + | 1.54017i | −0.0484164 | + | 0.998827i | \(0.515417\pi\) |
−0.840802 | + | 0.541343i | \(0.817916\pi\) | |||||||
\(824\) | 944458. | + | 1.63585e6i | 0.0484579 | + | 0.0839316i | ||||
\(825\) | 1.11146e7 | 0.568537 | ||||||||
\(826\) | −1.13214e6 | − | 1.96092e6i | −0.0577364 | − | 0.100002i | ||||
\(827\) | 9.68067e6 | − | 1.67674e7i | 0.492200 | − | 0.852515i | −0.507760 | − | 0.861499i | \(-0.669526\pi\) |
0.999960 | + | 0.00898342i | \(0.00285955\pi\) | |||||||
\(828\) | 880137. | 0.0446144 | ||||||||
\(829\) | 996101. | − | 1.72530e6i | 0.0503405 | − | 0.0871922i | −0.839757 | − | 0.542962i | \(-0.817303\pi\) |
0.890098 | + | 0.455770i | \(0.150636\pi\) | |||||||
\(830\) | 3.92277e6 | + | 6.79445e6i | 0.197651 | + | 0.342341i | ||||
\(831\) | 1.72543e7 | + | 2.98854e7i | 0.866754 | + | 1.50126i | ||||
\(832\) | −7.29381e6 | − | 1.26332e7i | −0.365297 | − | 0.632713i | ||||
\(833\) | −1.69314e7 | −0.845436 | ||||||||
\(834\) | −2.40891e7 | − | 4.17236e7i | −1.19924 | − | 2.07714i | ||||
\(835\) | 6.73400e6 | + | 1.16636e7i | 0.334239 | + | 0.578919i | ||||
\(836\) | 717426. | − | 1.24262e6i | 0.0355027 | − | 0.0614925i | ||||
\(837\) | −3.04546e6 | + | 5.27489e6i | −0.150258 | + | 0.260255i | ||||
\(838\) | 3.92957e7 | 1.93301 | ||||||||
\(839\) | 2.77268e6 | 0.135986 | 0.0679931 | − | 0.997686i | \(-0.478340\pi\) | ||||
0.0679931 | + | 0.997686i | \(0.478340\pi\) | |||||||
\(840\) | 1.16811e6 | − | 2.02323e6i | 0.0571198 | − | 0.0989344i | ||||
\(841\) | −1.98507e6 | + | 3.43824e6i | −0.0967799 | + | 0.167628i | ||||
\(842\) | 1.86896e7 | + | 3.23713e7i | 0.908487 | + | 1.57355i | ||||
\(843\) | 1.89036e7 | + | 3.27420e7i | 0.916170 | + | 1.58685i | ||||
\(844\) | 2.15345e6 | 0.104059 | ||||||||
\(845\) | 2.86361e6 | + | 4.95992e6i | 0.137966 | + | 0.238964i | ||||
\(846\) | 5.32987e6 | + | 9.23161e6i | 0.256030 | + | 0.443457i | ||||
\(847\) | −609730. | − | 1.05608e6i | −0.0292031 | − | 0.0505813i | ||||
\(848\) | 1.38320e7 | − | 2.39578e7i | 0.660536 | − | 1.14408i | ||||
\(849\) | 1.75307e7 | 0.834700 | ||||||||
\(850\) | 9.40656e6 | − | 1.62926e7i | 0.446564 | − | 0.773471i | ||||
\(851\) | 5.46293e6 | + | 9.46207e6i | 0.258584 | + | 0.447881i | ||||
\(852\) | 1.46967e6 | 0.0693619 | ||||||||
\(853\) | −1.11000e7 | − | 1.92258e7i | −0.522337 | − | 0.904715i | −0.999662 | − | 0.0259878i | \(-0.991727\pi\) |
0.477325 | − | 0.878727i | \(-0.341606\pi\) | |||||||
\(854\) | −359915. | + | 623390.i | −0.0168871 | + | 0.0292493i | ||||
\(855\) | 6.48323e6 | − | 1.12293e7i | 0.303302 | − | 0.525335i | ||||
\(856\) | 5.37619e6 | 0.250778 | ||||||||
\(857\) | 1.29882e7 | − | 2.24962e7i | 0.604082 | − | 1.04630i | −0.388114 | − | 0.921611i | \(-0.626873\pi\) |
0.992196 | − | 0.124689i | \(-0.0397933\pi\) | |||||||
\(858\) | −1.57735e7 | −0.731493 | ||||||||
\(859\) | −1.51852e7 | −0.702161 | −0.351080 | − | 0.936345i | \(-0.614186\pi\) | ||||
−0.351080 | + | 0.936345i | \(0.614186\pi\) | |||||||
\(860\) | −5.07884e6 | − | 4.97400e6i | −0.234163 | − | 0.229329i | ||||
\(861\) | −2.27197e6 | −0.104447 | ||||||||
\(862\) | 3.63435e6 | 0.166594 | ||||||||
\(863\) | 9.09307e6 | − | 1.57497e7i | 0.415607 | − | 0.719853i | −0.579885 | − | 0.814699i | \(-0.696902\pi\) |
0.995492 | + | 0.0948455i | \(0.0302357\pi\) | |||||||
\(864\) | 4.31432e6 | 0.196620 | ||||||||
\(865\) | −1.22146e7 | + | 2.11562e7i | −0.555057 | + | 0.961386i | ||||
\(866\) | 3.29280e6 | − | 5.70329e6i | 0.149200 | − | 0.258423i | ||||
\(867\) | −3.96456e6 | − | 6.86682e6i | −0.179121 | − | 0.310247i | ||||
\(868\) | −273973. | −0.0123427 | ||||||||
\(869\) | 8.41176e6 | + | 1.45696e7i | 0.377866 | + | 0.654483i | ||||
\(870\) | −2.44266e7 | + | 4.23081e7i | −1.09412 | + | 1.89507i | ||||
\(871\) | −3.97329e7 | −1.77462 | ||||||||
\(872\) | −9.96813e6 | + | 1.72653e7i | −0.443938 | + | 0.768924i | ||||
\(873\) | 6.58535e6 | + | 1.14062e7i | 0.292444 | + | 0.506529i | ||||
\(874\) | 2.30884e6 | + | 3.99903e6i | 0.102239 | + | 0.177083i | ||||
\(875\) | 64384.3 | + | 111517.i | 0.00284289 | + | 0.00492402i | ||||
\(876\) | 1.16796e7 | 0.514244 | ||||||||
\(877\) | −6.80057e6 | − | 1.17789e7i | −0.298570 | − | 0.517139i | 0.677239 | − | 0.735763i | \(-0.263176\pi\) |
−0.975809 | + | 0.218624i | \(0.929843\pi\) | |||||||
\(878\) | −6.60496e6 | − | 1.14401e7i | −0.289157 | − | 0.500835i | ||||
\(879\) | 2.18257e6 | − | 3.78032e6i | 0.0952787 | − | 0.165027i | ||||
\(880\) | 8.79639e6 | − | 1.52358e7i | 0.382911 | − | 0.663221i | ||||
\(881\) | 1.65369e7 | 0.717818 | 0.358909 | − | 0.933373i | \(-0.383149\pi\) | ||||
0.358909 | + | 0.933373i | \(0.383149\pi\) | |||||||
\(882\) | 1.71037e7 | 0.740321 | ||||||||
\(883\) | −3.31723e6 | + | 5.74561e6i | −0.143177 | + | 0.247990i | −0.928691 | − | 0.370854i | \(-0.879065\pi\) |
0.785514 | + | 0.618844i | \(0.212399\pi\) | |||||||
\(884\) | −2.54013e6 | + | 4.39964e6i | −0.109327 | + | 0.189359i | ||||
\(885\) | −2.92643e7 | − | 5.06872e7i | −1.25597 | − | 2.17541i | ||||
\(886\) | −1.13562e7 | − | 1.96695e7i | −0.486014 | − | 0.841801i | ||||
\(887\) | 1.51238e6 | 0.0645435 | 0.0322718 | − | 0.999479i | \(-0.489726\pi\) | ||||
0.0322718 | + | 0.999479i | \(0.489726\pi\) | |||||||
\(888\) | −2.35540e7 | − | 4.07968e7i | −1.00238 | − | 1.73618i | ||||
\(889\) | 1.01063e6 | + | 1.75045e6i | 0.0428880 | + | 0.0742842i | ||||
\(890\) | 1.86113e7 | + | 3.22357e7i | 0.787593 | + | 1.36415i | ||||
\(891\) | −6.73383e6 | + | 1.16633e7i | −0.284163 | + | 0.492185i | ||||
\(892\) | −2.67397e6 | −0.112524 | ||||||||
\(893\) | −5.32085e6 | + | 9.21598e6i | −0.223281 | + | 0.386734i | ||||
\(894\) | 2.60039e7 | + | 4.50400e7i | 1.08816 | + | 1.88476i | ||||
\(895\) | 2.68109e7 | 1.11880 | ||||||||
\(896\) | −1.07746e6 | − | 1.86621e6i | −0.0448364 | − | 0.0776588i | ||||
\(897\) | 4.82954e6 | − | 8.36501e6i | 0.200412 | − | 0.347125i | ||||
\(898\) | 2.27027e7 | − | 3.93223e7i | 0.939479 | − | 1.62723i | ||||
\(899\) | −1.86507e7 | −0.769657 | ||||||||
\(900\) | −1.80809e6 | + | 3.13170e6i | −0.0744069 | + | 0.128877i | ||||
\(901\) | 2.31976e7 | 0.951986 | ||||||||
\(902\) | −1.37011e7 | −0.560710 | ||||||||
\(903\) | 587183. | − | 2.28652e6i | 0.0239637 | − | 0.0933159i | ||||
\(904\) | 5.51709e6 | 0.224538 | ||||||||
\(905\) | −4.49049e7 | −1.82252 | ||||||||
\(906\) | −2.93203e7 | + | 5.07843e7i | −1.18672 | + | 2.05546i | ||||
\(907\) | 3.44522e7 | 1.39059 | 0.695294 | − | 0.718725i | \(-0.255274\pi\) | ||||
0.695294 | + | 0.718725i | \(0.255274\pi\) | |||||||
\(908\) | −3.87359e6 | + | 6.70925e6i | −0.155919 | + | 0.270060i | ||||
\(909\) | 1.04515e7 | − | 1.81025e7i | 0.419536 | − | 0.726658i | ||||
\(910\) | 1.57972e6 | + | 2.73615e6i | 0.0632376 | + | 0.109531i | ||||
\(911\) | −4.93023e7 | −1.96821 | −0.984105 | − | 0.177587i | \(-0.943171\pi\) | ||||
−0.984105 | + | 0.177587i | \(0.943171\pi\) | |||||||
\(912\) | −1.24309e7 | − | 2.15309e7i | −0.494897 | − | 0.857187i | ||||
\(913\) | −1.49479e6 | + | 2.58906e6i | −0.0593478 | + | 0.102793i | ||||
\(914\) | 1.26511e7 | 0.500912 | ||||||||
\(915\) | −9.30330e6 | + | 1.61138e7i | −0.367354 | + | 0.636275i | ||||
\(916\) | −985414. | − | 1.70679e6i | −0.0388043 | − | 0.0672111i | ||||
\(917\) | 972991. | + | 1.68527e6i | 0.0382108 | + | 0.0661830i | ||||
\(918\) | 5.14523e6 | + | 8.91179e6i | 0.201511 | + | 0.349027i | ||||
\(919\) | −2.32795e7 | −0.909255 | −0.454627 | − | 0.890682i | \(-0.650228\pi\) | ||||
−0.454627 | + | 0.890682i | \(0.650228\pi\) | |||||||
\(920\) | 4.31364e6 | + | 7.47144e6i | 0.168025 | + | 0.291028i | ||||
\(921\) | 1.86436e6 | + | 3.22917e6i | 0.0724238 | + | 0.125442i | ||||
\(922\) | 2.40332e7 | − | 4.16266e7i | 0.931073 | − | 1.61266i | ||||
\(923\) | 3.23515e6 | − | 5.60344e6i | 0.124994 | − | 0.216496i | ||||
\(924\) | −273459. | −0.0105369 | ||||||||
\(925\) | −4.48905e7 | −1.72504 | ||||||||
\(926\) | −5.35344e6 | + | 9.27242e6i | −0.205166 | + | 0.355358i | ||||
\(927\) | 999022. | − | 1.73036e6i | 0.0381835 | − | 0.0661357i | ||||
\(928\) | 6.60535e6 | + | 1.14408e7i | 0.251783 | + | 0.436101i | ||||
\(929\) | −1.25748e6 | − | 2.17801e6i | −0.0478035 | − | 0.0827982i | 0.841134 | − | 0.540827i | \(-0.181889\pi\) |
−0.888937 | + | 0.458029i | \(0.848555\pi\) | |||||||
\(930\) | −3.72182e7 | −1.41107 | ||||||||
\(931\) | 8.53740e6 | + | 1.47872e7i | 0.322813 | + | 0.559129i | ||||
\(932\) | 2.17303e6 | + | 3.76381e6i | 0.0819458 | + | 0.141934i | ||||
\(933\) | −3.39520e6 | − | 5.88066e6i | −0.127691 | − | 0.221168i | ||||
\(934\) | −1.56660e7 | + | 2.71342e7i | −0.587611 | + | 1.01777i | ||||
\(935\) | 1.47523e7 | 0.551863 | ||||||||
\(936\) | −8.35342e6 | + | 1.44685e7i | −0.311655 | + | 0.539803i | ||||
\(937\) | −2.05774e7 | − | 3.56411e7i | −0.765669 | − | 1.32618i | −0.939892 | − | 0.341471i | \(-0.889075\pi\) |
0.174223 | − | 0.984706i | \(-0.444259\pi\) | |||||||
\(938\) | −3.62013e6 | −0.134344 | ||||||||
\(939\) | 9.82513e6 | + | 1.70176e7i | 0.363642 | + | 0.629847i | ||||
\(940\) | 3.05366e6 | − | 5.28910e6i | 0.112720 | − | 0.195237i | ||||
\(941\) | 5.95328e6 | − | 1.03114e7i | 0.219171 | − | 0.379614i | −0.735384 | − | 0.677651i | \(-0.762998\pi\) |
0.954555 | + | 0.298036i | \(0.0963316\pi\) | |||||||
\(942\) | 3.45137e7 | 1.26726 | ||||||||
\(943\) | 4.19500e6 | − | 7.26596e6i | 0.153622 | − | 0.266081i | ||||
\(944\) | −4.50191e7 | −1.64425 | ||||||||
\(945\) | 1.21772e6 | 0.0443576 | ||||||||
\(946\) | 3.54099e6 | − | 1.37888e7i | 0.128646 | − | 0.500955i | ||||
\(947\) | 3.84828e7 | 1.39441 | 0.697207 | − | 0.716870i | \(-0.254426\pi\) | ||||
0.697207 | + | 0.716870i | \(0.254426\pi\) | |||||||
\(948\) | −1.36444e7 | −0.493098 | ||||||||
\(949\) | 2.57100e7 | − | 4.45311e7i | 0.926696 | − | 1.60508i | ||||
\(950\) | −1.89724e7 | −0.682046 | ||||||||
\(951\) | −1.25702e7 | + | 2.17721e7i | −0.450702 | + | 0.780638i | ||||
\(952\) | 753425. | − | 1.30497e6i | 0.0269431 | − | 0.0466668i | ||||
\(953\) | 9.14494e6 | + | 1.58395e7i | 0.326173 | + | 0.564949i | 0.981749 | − | 0.190180i | \(-0.0609073\pi\) |
−0.655576 | + | 0.755129i | \(0.727574\pi\) | |||||||
\(954\) | −2.34337e7 | −0.833623 | ||||||||
\(955\) | 1.71731e6 | + | 2.97447e6i | 0.0609312 | + | 0.105536i | ||||
\(956\) | 2.45631e6 | − | 4.25446e6i | 0.0869239 | − | 0.150557i | ||||
\(957\) | −1.86158e7 | −0.657054 | ||||||||
\(958\) | 2.32551e7 | − | 4.02790e7i | 0.818661 | − | 1.41796i | ||||
\(959\) | −985109. | − | 1.70626e6i | −0.0345890 | − | 0.0599099i | ||||
\(960\) | −1.71777e7 | − | 2.97527e7i | −0.601572 | − | 1.04195i | ||||
\(961\) | 7.21016e6 | + | 1.24884e7i | 0.251847 | + | 0.436211i | ||||
\(962\) | 6.37073e7 | 2.21948 | ||||||||
\(963\) | −2.84339e6 | − | 4.92490e6i | −0.0988031 | − | 0.171132i | ||||
\(964\) | −4.53698e6 | − | 7.85829e6i | −0.157244 | − | 0.272355i | ||||
\(965\) | 1.26176e6 | − | 2.18544e6i | 0.0436174 | − | 0.0755475i | ||||
\(966\) | 440027. | − | 762150.i | 0.0151718 | − | 0.0262783i | ||||
\(967\) | 1.30722e7 | 0.449553 | 0.224777 | − | 0.974410i | \(-0.427835\pi\) | ||||
0.224777 | + | 0.974410i | \(0.427835\pi\) | |||||||
\(968\) | −1.94163e7 | −0.666006 | ||||||||
\(969\) | 1.04238e7 | − | 1.80546e7i | 0.356630 | − | 0.617702i | ||||
\(970\) | 1.98286e7 | − | 3.43442e7i | 0.676649 | − | 1.17199i | ||||
\(971\) | −2.04654e6 | − | 3.54472e6i | −0.0696583 | − | 0.120652i | 0.829093 | − | 0.559111i | \(-0.188858\pi\) |
−0.898751 | + | 0.438460i | \(0.855524\pi\) | |||||||
\(972\) | −3.98501e6 | − | 6.90224e6i | −0.135289 | − | 0.234328i | ||||
\(973\) | −3.67722e6 | −0.124519 | ||||||||
\(974\) | 6.75283e6 | + | 1.16962e7i | 0.228081 | + | 0.395047i | ||||
\(975\) | 1.98429e7 | + | 3.43689e7i | 0.668487 | + | 1.15785i | ||||
\(976\) | 7.15593e6 | + | 1.23944e7i | 0.240459 | + | 0.416488i | ||||
\(977\) | −8.95300e6 | + | 1.55070e7i | −0.300076 | + | 0.519748i | −0.976153 | − | 0.217084i | \(-0.930346\pi\) |
0.676076 | + | 0.736831i | \(0.263679\pi\) | |||||||
\(978\) | −5.22954e7 | −1.74830 | ||||||||
\(979\) | −7.09194e6 | + | 1.22836e7i | −0.236488 | + | 0.409608i | ||||
\(980\) | −4.89965e6 | − | 8.48645e6i | −0.162967 | − | 0.282268i | ||||
\(981\) | 2.10880e7 | 0.699622 | ||||||||
\(982\) | −3.19752e7 | − | 5.53827e7i | −1.05812 | − | 1.83272i | ||||
\(983\) | −9.40595e6 | + | 1.62916e7i | −0.310470 | + | 0.537749i | −0.978464 | − | 0.206417i | \(-0.933820\pi\) |
0.667994 | + | 0.744166i | \(0.267153\pi\) | |||||||
\(984\) | −1.80872e7 | + | 3.13280e7i | −0.595504 | + | 1.03144i | ||||
\(985\) | 3.65898e7 | 1.20163 | ||||||||
\(986\) | −1.57550e7 | + | 2.72885e7i | −0.516091 | + | 0.893895i | ||||
\(987\) | 2.02813e6 | 0.0662680 | ||||||||
\(988\) | 5.12328e6 | 0.166977 | ||||||||
\(989\) | 6.22829e6 | + | 6.09972e6i | 0.202478 | + | 0.198298i | ||||
\(990\) | −1.49025e7 | −0.483248 | ||||||||
\(991\) | 3.11542e7 | 1.00770 | 0.503851 | − | 0.863791i | \(-0.331916\pi\) | ||||
0.503851 | + | 0.863791i | \(0.331916\pi\) | |||||||
\(992\) | −5.03220e6 | + | 8.71603e6i | −0.162360 | + | 0.281216i | ||||
\(993\) | 7.69574e7 | 2.47672 | ||||||||
\(994\) | 294759. | − | 510538.i | 0.00946241 | − | 0.0163894i | ||||
\(995\) | −36315.8 | + | 62900.9i | −0.00116289 | + | 0.00201418i | ||||
\(996\) | −1.21232e6 | − | 2.09981e6i | −0.0387231 | − | 0.0670704i | ||||
\(997\) | 6.61845e6 | 0.210872 | 0.105436 | − | 0.994426i | \(-0.466376\pi\) | ||||
0.105436 | + | 0.994426i | \(0.466376\pi\) | |||||||
\(998\) | 1.22641e7 | + | 2.12421e7i | 0.389772 | + | 0.675105i | ||||
\(999\) | 1.22772e7 | − | 2.12647e7i | 0.389210 | − | 0.674132i |
(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 | 43.6.c.a.6.5 | ✓ | 34 | |
43.36 | even | 3 | inner | 43.6.c.a.36.5 | yes | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.6.c.a.6.5 | ✓ | 34 | 1.1 | even | 1 | trivial | |
43.6.c.a.36.5 | yes | 34 | 43.36 | even | 3 | inner |