Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,7,Mod(31,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.31");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.d (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: | \(17.0240021879\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(9\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 8470 x^{16} + 28007049 x^{14} + 45282701078 x^{12} + 36580026955844 x^{10} + \cdots + 65\!\cdots\!44 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10}\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.9 | ||
Root | \(48.2475i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 74.43 |
Dual form | 74.7.d.a.31.1 |
$q$-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 \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).
\(n\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000 | − | 4.00000i | 0.500000 | − | 0.500000i | ||||
\(3\) | 44.2475i | 1.63880i | 0.573224 | + | 0.819398i | \(0.305692\pi\) | ||||
−0.573224 | + | 0.819398i | \(0.694308\pi\) | |||||||
\(4\) | − | 32.0000i | − | 0.500000i | ||||||
\(5\) | 111.595 | + | 111.595i | 0.892760 | + | 0.892760i | 0.994782 | − | 0.102022i | \(-0.0325313\pi\) |
−0.102022 | + | 0.994782i | \(0.532531\pi\) | |||||||
\(6\) | 176.990 | + | 176.990i | 0.819398 | + | 0.819398i | ||||
\(7\) | 600.642 | 1.75114 | 0.875572 | − | 0.483088i | \(-0.160485\pi\) | ||||
0.875572 | + | 0.483088i | \(0.160485\pi\) | |||||||
\(8\) | −128.000 | − | 128.000i | −0.250000 | − | 0.250000i | ||||
\(9\) | −1228.84 | −1.68566 | ||||||||
\(10\) | 892.760 | 0.892760 | ||||||||
\(11\) | 246.334i | 0.185075i | 0.995709 | + | 0.0925373i | \(0.0294978\pi\) | ||||
−0.995709 | + | 0.0925373i | \(0.970502\pi\) | |||||||
\(12\) | 1415.92 | 0.819398 | ||||||||
\(13\) | −1561.93 | − | 1561.93i | −0.710937 | − | 0.710937i | 0.255794 | − | 0.966731i | \(-0.417663\pi\) |
−0.966731 | + | 0.255794i | \(0.917663\pi\) | |||||||
\(14\) | 2402.57 | − | 2402.57i | 0.875572 | − | 0.875572i | ||||
\(15\) | −4937.80 | + | 4937.80i | −1.46305 | + | 1.46305i | ||||
\(16\) | −1024.00 | −0.250000 | ||||||||
\(17\) | 4838.50 | + | 4838.50i | 0.984836 | + | 0.984836i | 0.999887 | − | 0.0150508i | \(-0.00479100\pi\) |
−0.0150508 | + | 0.999887i | \(0.504791\pi\) | |||||||
\(18\) | −4915.37 | + | 4915.37i | −0.842828 | + | 0.842828i | ||||
\(19\) | 4177.15 | + | 4177.15i | 0.609003 | + | 0.609003i | 0.942685 | − | 0.333683i | \(-0.108291\pi\) |
−0.333683 | + | 0.942685i | \(0.608291\pi\) | |||||||
\(20\) | 3571.04 | − | 3571.04i | 0.446380 | − | 0.446380i | ||||
\(21\) | 26576.9i | 2.86977i | ||||||||
\(22\) | 985.338 | + | 985.338i | 0.0925373 | + | 0.0925373i | ||||
\(23\) | −11586.6 | − | 11586.6i | −0.952293 | − | 0.952293i | 0.0466194 | − | 0.998913i | \(-0.485155\pi\) |
−0.998913 | + | 0.0466194i | \(0.985155\pi\) | |||||||
\(24\) | 5663.68 | − | 5663.68i | 0.409699 | − | 0.409699i | ||||
\(25\) | 9281.87i | 0.594040i | ||||||||
\(26\) | −12495.4 | −0.710937 | ||||||||
\(27\) | − | 22116.8i | − | 1.12365i | ||||||
\(28\) | − | 19220.6i | − | 0.875572i | ||||||
\(29\) | −27962.6 | + | 27962.6i | −1.14652 | + | 1.14652i | −0.159293 | + | 0.987231i | \(0.550921\pi\) |
−0.987231 | + | 0.159293i | \(0.949079\pi\) | |||||||
\(30\) | 39502.4i | 1.46305i | ||||||||
\(31\) | 7332.73 | − | 7332.73i | 0.246139 | − | 0.246139i | −0.573245 | − | 0.819384i | \(-0.694316\pi\) |
0.819384 | + | 0.573245i | \(0.194316\pi\) | |||||||
\(32\) | −4096.00 | + | 4096.00i | −0.125000 | + | 0.125000i | ||||
\(33\) | −10899.7 | −0.303300 | ||||||||
\(34\) | 38708.0 | 0.984836 | ||||||||
\(35\) | 67028.7 | + | 67028.7i | 1.56335 | + | 1.56335i | ||||
\(36\) | 39323.0i | 0.842828i | ||||||||
\(37\) | 6840.45 | − | 50189.0i | 0.135045 | − | 0.990839i | ||||
\(38\) | 33417.2 | 0.609003 | ||||||||
\(39\) | 69111.4 | − | 69111.4i | 1.16508 | − | 1.16508i | ||||
\(40\) | − | 28568.3i | − | 0.446380i | ||||||
\(41\) | 30316.2i | 0.439869i | 0.975515 | + | 0.219934i | \(0.0705844\pi\) | ||||
−0.975515 | + | 0.219934i | \(0.929416\pi\) | |||||||
\(42\) | 106308. | + | 106308.i | 1.43488 | + | 1.43488i | ||||
\(43\) | −32582.5 | − | 32582.5i | −0.409807 | − | 0.409807i | 0.471864 | − | 0.881671i | \(-0.343581\pi\) |
−0.881671 | + | 0.471864i | \(0.843581\pi\) | |||||||
\(44\) | 7882.70 | 0.0925373 | ||||||||
\(45\) | −137133. | − | 137133.i | −1.50488 | − | 1.50488i | ||||
\(46\) | −92692.4 | −0.952293 | ||||||||
\(47\) | 40324.0 | 0.388391 | 0.194196 | − | 0.980963i | \(-0.437790\pi\) | ||||
0.194196 | + | 0.980963i | \(0.437790\pi\) | |||||||
\(48\) | − | 45309.5i | − | 0.409699i | ||||||
\(49\) | 243122. | 2.06650 | ||||||||
\(50\) | 37127.5 | + | 37127.5i | 0.297020 | + | 0.297020i | ||||
\(51\) | −214092. | + | 214092.i | −1.61395 | + | 1.61395i | ||||
\(52\) | −49981.7 | + | 49981.7i | −0.355468 | + | 0.355468i | ||||
\(53\) | −42260.0 | −0.283859 | −0.141929 | − | 0.989877i | \(-0.545331\pi\) | ||||
−0.141929 | + | 0.989877i | \(0.545331\pi\) | |||||||
\(54\) | −88467.2 | − | 88467.2i | −0.561825 | − | 0.561825i | ||||
\(55\) | −27489.7 | + | 27489.7i | −0.165227 | + | 0.165227i | ||||
\(56\) | −76882.2 | − | 76882.2i | −0.437786 | − | 0.437786i | ||||
\(57\) | −184829. | + | 184829.i | −0.998032 | + | 0.998032i | ||||
\(58\) | 223701.i | 1.14652i | ||||||||
\(59\) | −244670. | − | 244670.i | −1.19131 | − | 1.19131i | −0.976700 | − | 0.214608i | \(-0.931153\pi\) |
−0.214608 | − | 0.976700i | \(-0.568847\pi\) | |||||||
\(60\) | 158010. | + | 158010.i | 0.731526 | + | 0.731526i | ||||
\(61\) | 178253. | − | 178253.i | 0.785321 | − | 0.785321i | −0.195402 | − | 0.980723i | \(-0.562601\pi\) |
0.980723 | + | 0.195402i | \(0.0626013\pi\) | |||||||
\(62\) | − | 58661.9i | − | 0.246139i | ||||||
\(63\) | −738095. | −2.95182 | ||||||||
\(64\) | 32768.0i | 0.125000i | ||||||||
\(65\) | − | 348607.i | − | 1.26939i | ||||||
\(66\) | −43598.7 | + | 43598.7i | −0.151650 | + | 0.151650i | ||||
\(67\) | − | 237792.i | − | 0.790629i | −0.918546 | − | 0.395315i | \(-0.870636\pi\) | ||
0.918546 | − | 0.395315i | \(-0.129364\pi\) | |||||||
\(68\) | 154832. | − | 154832.i | 0.492418 | − | 0.492418i | ||||
\(69\) | 512676. | − | 512676.i | 1.56062 | − | 1.56062i | ||||
\(70\) | 536229. | 1.56335 | ||||||||
\(71\) | −87512.0 | −0.244508 | −0.122254 | − | 0.992499i | \(-0.539012\pi\) | ||||
−0.122254 | + | 0.992499i | \(0.539012\pi\) | |||||||
\(72\) | 157292. | + | 157292.i | 0.421414 | + | 0.421414i | ||||
\(73\) | 4275.04i | 0.0109893i | 0.999985 | + | 0.00549467i | \(0.00174902\pi\) | ||||
−0.999985 | + | 0.00549467i | \(0.998251\pi\) | |||||||
\(74\) | −173394. | − | 228118.i | −0.427897 | − | 0.562942i | ||||
\(75\) | −410700. | −0.973510 | ||||||||
\(76\) | 133669. | − | 133669.i | 0.304501 | − | 0.304501i | ||||
\(77\) | 147959.i | 0.324092i | ||||||||
\(78\) | − | 552892.i | − | 1.16508i | ||||||
\(79\) | 692161. | + | 692161.i | 1.40387 | + | 1.40387i | 0.787313 | + | 0.616553i | \(0.211472\pi\) |
0.616553 | + | 0.787313i | \(0.288528\pi\) | |||||||
\(80\) | −114273. | − | 114273.i | −0.223190 | − | 0.223190i | ||||
\(81\) | 82786.8 | 0.155778 | ||||||||
\(82\) | 121265. | + | 121265.i | 0.219934 | + | 0.219934i | ||||
\(83\) | 1.05044e6 | 1.83712 | 0.918562 | − | 0.395277i | \(-0.129351\pi\) | ||||
0.918562 | + | 0.395277i | \(0.129351\pi\) | |||||||
\(84\) | 850462. | 1.43488 | ||||||||
\(85\) | 1.07990e6i | 1.75844i | ||||||||
\(86\) | −260660. | −0.409807 | ||||||||
\(87\) | −1.23727e6 | − | 1.23727e6i | −1.87892 | − | 1.87892i | ||||
\(88\) | 31530.8 | − | 31530.8i | 0.0462687 | − | 0.0462687i | ||||
\(89\) | 767566. | − | 767566.i | 1.08879 | − | 1.08879i | 0.0931410 | − | 0.995653i | \(-0.470309\pi\) |
0.995653 | − | 0.0931410i | \(-0.0296907\pi\) | |||||||
\(90\) | −1.09706e6 | −1.50488 | ||||||||
\(91\) | −938160. | − | 938160.i | −1.24495 | − | 1.24495i | ||||
\(92\) | −370770. | + | 370770.i | −0.476147 | + | 0.476147i | ||||
\(93\) | 324455. | + | 324455.i | 0.403372 | + | 0.403372i | ||||
\(94\) | 161296. | − | 161296.i | 0.194196 | − | 0.194196i | ||||
\(95\) | 932298.i | 1.08739i | ||||||||
\(96\) | −181238. | − | 181238.i | −0.204850 | − | 0.204850i | ||||
\(97\) | −375821. | − | 375821.i | −0.411781 | − | 0.411781i | 0.470578 | − | 0.882359i | \(-0.344046\pi\) |
−0.882359 | + | 0.470578i | \(0.844046\pi\) | |||||||
\(98\) | 972489. | − | 972489.i | 1.03325 | − | 1.03325i | ||||
\(99\) | − | 302706.i | − | 0.311972i | ||||||
\(100\) | 297020. | 0.297020 | ||||||||
\(101\) | 50410.5i | 0.0489279i | 0.999701 | + | 0.0244640i | \(0.00778790\pi\) | ||||
−0.999701 | + | 0.0244640i | \(0.992212\pi\) | |||||||
\(102\) | 1.71273e6i | 1.61395i | ||||||||
\(103\) | −251781. | + | 251781.i | −0.230416 | + | 0.230416i | −0.812866 | − | 0.582450i | \(-0.802094\pi\) |
0.582450 | + | 0.812866i | \(0.302094\pi\) | |||||||
\(104\) | 399854.i | 0.355468i | ||||||||
\(105\) | −2.96585e6 | + | 2.96585e6i | −2.56201 | + | 2.56201i | ||||
\(106\) | −169040. | + | 169040.i | −0.141929 | + | 0.141929i | ||||
\(107\) | −1.95336e6 | −1.59452 | −0.797262 | − | 0.603633i | \(-0.793719\pi\) | ||||
−0.797262 | + | 0.603633i | \(0.793719\pi\) | |||||||
\(108\) | −707737. | −0.561825 | ||||||||
\(109\) | 586869. | + | 586869.i | 0.453170 | + | 0.453170i | 0.896405 | − | 0.443235i | \(-0.146169\pi\) |
−0.443235 | + | 0.896405i | \(0.646169\pi\) | |||||||
\(110\) | 219917.i | 0.165227i | ||||||||
\(111\) | 2.22074e6 | + | 302673.i | 1.62378 | + | 0.221312i | ||||
\(112\) | −615058. | −0.437786 | ||||||||
\(113\) | 1.17936e6 | − | 1.17936e6i | 0.817355 | − | 0.817355i | −0.168369 | − | 0.985724i | \(-0.553850\pi\) |
0.985724 | + | 0.168369i | \(0.0538501\pi\) | |||||||
\(114\) | 1.47863e6i | 0.998032i | ||||||||
\(115\) | − | 2.58600e6i | − | 1.70034i | ||||||
\(116\) | 894802. | + | 894802.i | 0.573262 | + | 0.573262i | ||||
\(117\) | 1.91936e6 | + | 1.91936e6i | 1.19839 | + | 1.19839i | ||||
\(118\) | −1.95736e6 | −1.19131 | ||||||||
\(119\) | 2.90621e6 | + | 2.90621e6i | 1.72459 | + | 1.72459i | ||||
\(120\) | 1.26408e6 | 0.731526 | ||||||||
\(121\) | 1.71088e6 | 0.965747 | ||||||||
\(122\) | − | 1.42602e6i | − | 0.785321i | ||||||
\(123\) | −1.34142e6 | −0.720856 | ||||||||
\(124\) | −234647. | − | 234647.i | −0.123070 | − | 0.123070i | ||||
\(125\) | 707861. | − | 707861.i | 0.362425 | − | 0.362425i | ||||
\(126\) | −2.95238e6 | + | 2.95238e6i | −1.47591 | + | 1.47591i | ||||
\(127\) | 21725.6 | 0.0106062 | 0.00530312 | − | 0.999986i | \(-0.498312\pi\) | ||||
0.00530312 | + | 0.999986i | \(0.498312\pi\) | |||||||
\(128\) | 131072. | + | 131072.i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 1.44170e6 | − | 1.44170e6i | 0.671590 | − | 0.671590i | ||||
\(130\) | −1.39443e6 | − | 1.39443e6i | −0.634696 | − | 0.634696i | ||||
\(131\) | −2.29399e6 | + | 2.29399e6i | −1.02042 | + | 1.02042i | −0.0206316 | + | 0.999787i | \(0.506568\pi\) |
−0.999787 | + | 0.0206316i | \(0.993432\pi\) | |||||||
\(132\) | 348790.i | 0.151650i | ||||||||
\(133\) | 2.50897e6 | + | 2.50897e6i | 1.06645 | + | 1.06645i | ||||
\(134\) | −951168. | − | 951168.i | −0.395315 | − | 0.395315i | ||||
\(135\) | 2.46812e6 | − | 2.46812e6i | 1.00315 | − | 1.00315i | ||||
\(136\) | − | 1.23866e6i | − | 0.492418i | ||||||
\(137\) | 3.41062e6 | 1.32639 | 0.663196 | − | 0.748446i | \(-0.269200\pi\) | ||||
0.663196 | + | 0.748446i | \(0.269200\pi\) | |||||||
\(138\) | − | 4.10141e6i | − | 1.56062i | ||||||
\(139\) | − | 2.10396e6i | − | 0.783417i | −0.920089 | − | 0.391708i | \(-0.871884\pi\) | ||
0.920089 | − | 0.391708i | \(-0.128116\pi\) | |||||||
\(140\) | 2.14492e6 | − | 2.14492e6i | 0.781675 | − | 0.781675i | ||||
\(141\) | 1.78424e6i | 0.636495i | ||||||||
\(142\) | −350048. | + | 350048.i | −0.122254 | + | 0.122254i | ||||
\(143\) | 384757. | − | 384757.i | 0.131576 | − | 0.131576i | ||||
\(144\) | 1.25833e6 | 0.421414 | ||||||||
\(145\) | −6.24097e6 | −2.04714 | ||||||||
\(146\) | 17100.2 | + | 17100.2i | 0.00549467 | + | 0.00549467i | ||||
\(147\) | 1.07576e7i | 3.38658i | ||||||||
\(148\) | −1.60605e6 | − | 218894.i | −0.495420 | − | 0.0675227i | ||||
\(149\) | −336960. | −0.101864 | −0.0509318 | − | 0.998702i | \(-0.516219\pi\) | ||||
−0.0509318 | + | 0.998702i | \(0.516219\pi\) | |||||||
\(150\) | −1.64280e6 | + | 1.64280e6i | −0.486755 | + | 0.486755i | ||||
\(151\) | − | 4.04920e6i | − | 1.17608i | −0.808830 | − | 0.588042i | \(-0.799899\pi\) | ||
0.808830 | − | 0.588042i | \(-0.200101\pi\) | |||||||
\(152\) | − | 1.06935e6i | − | 0.304501i | ||||||
\(153\) | −5.94575e6 | − | 5.94575e6i | −1.66009 | − | 1.66009i | ||||
\(154\) | 591835. | + | 591835.i | 0.162046 | + | 0.162046i | ||||
\(155\) | 1.63659e6 | 0.439486 | ||||||||
\(156\) | −2.21157e6 | − | 2.21157e6i | −0.582541 | − | 0.582541i | ||||
\(157\) | 98709.9 | 0.0255071 | 0.0127536 | − | 0.999919i | \(-0.495940\pi\) | ||||
0.0127536 | + | 0.999919i | \(0.495940\pi\) | |||||||
\(158\) | 5.53729e6 | 1.40387 | ||||||||
\(159\) | − | 1.86990e6i | − | 0.465187i | ||||||
\(160\) | −914186. | −0.223190 | ||||||||
\(161\) | −6.95937e6 | − | 6.95937e6i | −1.66760 | − | 1.66760i | ||||
\(162\) | 331147. | − | 331147.i | 0.0778889 | − | 0.0778889i | ||||
\(163\) | −2.31873e6 | + | 2.31873e6i | −0.535410 | + | 0.535410i | −0.922177 | − | 0.386767i | \(-0.873592\pi\) |
0.386767 | + | 0.922177i | \(0.373592\pi\) | |||||||
\(164\) | 970119. | 0.219934 | ||||||||
\(165\) | −1.21635e6 | − | 1.21635e6i | −0.270774 | − | 0.270774i | ||||
\(166\) | 4.20177e6 | − | 4.20177e6i | 0.918562 | − | 0.918562i | ||||
\(167\) | 5.08220e6 | + | 5.08220e6i | 1.09119 | + | 1.09119i | 0.995401 | + | 0.0957928i | \(0.0305386\pi\) |
0.0957928 | + | 0.995401i | \(0.469461\pi\) | |||||||
\(168\) | 3.40185e6 | − | 3.40185e6i | 0.717442 | − | 0.717442i | ||||
\(169\) | 52430.7i | 0.0108624i | ||||||||
\(170\) | 4.31962e6 | + | 4.31962e6i | 0.879222 | + | 0.879222i | ||||
\(171\) | −5.13306e6 | − | 5.13306e6i | −1.02657 | − | 1.02657i | ||||
\(172\) | −1.04264e6 | + | 1.04264e6i | −0.204903 | + | 0.204903i | ||||
\(173\) | 3.50636e6i | 0.677203i | 0.940930 | + | 0.338601i | \(0.109954\pi\) | ||||
−0.940930 | + | 0.338601i | \(0.890046\pi\) | |||||||
\(174\) | −9.89820e6 | −1.87892 | ||||||||
\(175\) | 5.57508e6i | 1.04025i | ||||||||
\(176\) | − | 252246.i | − | 0.0462687i | ||||||
\(177\) | 1.08260e7 | − | 1.08260e7i | 1.95231 | − | 1.95231i | ||||
\(178\) | − | 6.14053e6i | − | 1.08879i | ||||||
\(179\) | −4.57026e6 | + | 4.57026e6i | −0.796860 | + | 0.796860i | −0.982599 | − | 0.185739i | \(-0.940532\pi\) |
0.185739 | + | 0.982599i | \(0.440532\pi\) | |||||||
\(180\) | −4.38824e6 | + | 4.38824e6i | −0.752442 | + | 0.752442i | ||||
\(181\) | 2.39962e6 | 0.404675 | 0.202337 | − | 0.979316i | \(-0.435146\pi\) | ||||
0.202337 | + | 0.979316i | \(0.435146\pi\) | |||||||
\(182\) | −7.50528e6 | −1.24495 | ||||||||
\(183\) | 7.88725e6 | + | 7.88725e6i | 1.28698 | + | 1.28698i | ||||
\(184\) | 2.96616e6i | 0.476147i | ||||||||
\(185\) | 6.36420e6 | − | 4.83748e6i | 1.00514 | − | 0.764018i | ||||
\(186\) | 2.59564e6 | 0.403372 | ||||||||
\(187\) | −1.19189e6 | + | 1.19189e6i | −0.182268 | + | 0.182268i | ||||
\(188\) | − | 1.29037e6i | − | 0.194196i | ||||||
\(189\) | − | 1.32843e7i | − | 1.96767i | ||||||
\(190\) | 3.72919e6 | + | 3.72919e6i | 0.543693 | + | 0.543693i | ||||
\(191\) | −7.14407e6 | − | 7.14407e6i | −1.02529 | − | 1.02529i | −0.999672 | − | 0.0256150i | \(-0.991846\pi\) |
−0.0256150 | − | 0.999672i | \(-0.508154\pi\) | |||||||
\(192\) | −1.44990e6 | −0.204850 | ||||||||
\(193\) | −6.02695e6 | − | 6.02695e6i | −0.838350 | − | 0.838350i | 0.150291 | − | 0.988642i | \(-0.451979\pi\) |
−0.988642 | + | 0.150291i | \(0.951979\pi\) | |||||||
\(194\) | −3.00657e6 | −0.411781 | ||||||||
\(195\) | 1.54250e7 | 2.08027 | ||||||||
\(196\) | − | 7.77991e6i | − | 1.03325i | ||||||
\(197\) | −8.81944e6 | −1.15357 | −0.576783 | − | 0.816897i | \(-0.695692\pi\) | ||||
−0.576783 | + | 0.816897i | \(0.695692\pi\) | |||||||
\(198\) | −1.21082e6 | − | 1.21082e6i | −0.155986 | − | 0.155986i | ||||
\(199\) | 839951. | − | 839951.i | 0.106585 | − | 0.106585i | −0.651803 | − | 0.758388i | \(-0.725987\pi\) |
0.758388 | + | 0.651803i | \(0.225987\pi\) | |||||||
\(200\) | 1.18808e6 | − | 1.18808e6i | 0.148510 | − | 0.148510i | ||||
\(201\) | 1.05217e7 | 1.29568 | ||||||||
\(202\) | 201642. | + | 201642.i | 0.0244640 | + | 0.0244640i | ||||
\(203\) | −1.67955e7 | + | 1.67955e7i | −2.00773 | + | 2.00773i | ||||
\(204\) | 6.85093e6 | + | 6.85093e6i | 0.806973 | + | 0.806973i | ||||
\(205\) | −3.38314e6 | + | 3.38314e6i | −0.392697 | + | 0.392697i | ||||
\(206\) | 2.01425e6i | 0.230416i | ||||||||
\(207\) | 1.42380e7 | + | 1.42380e7i | 1.60524 | + | 1.60524i | ||||
\(208\) | 1.59941e6 | + | 1.59941e6i | 0.177734 | + | 0.177734i | ||||
\(209\) | −1.02898e6 | + | 1.02898e6i | −0.112711 | + | 0.112711i | ||||
\(210\) | 2.37268e7i | 2.56201i | ||||||||
\(211\) | −5.22570e6 | −0.556285 | −0.278143 | − | 0.960540i | \(-0.589719\pi\) | ||||
−0.278143 | + | 0.960540i | \(0.589719\pi\) | |||||||
\(212\) | 1.35232e6i | 0.141929i | ||||||||
\(213\) | − | 3.87219e6i | − | 0.400699i | ||||||
\(214\) | −7.81345e6 | + | 7.81345e6i | −0.797262 | + | 0.797262i | ||||
\(215\) | − | 7.27209e6i | − | 0.731718i | ||||||
\(216\) | −2.83095e6 | + | 2.83095e6i | −0.280912 | + | 0.280912i | ||||
\(217\) | 4.40435e6 | − | 4.40435e6i | 0.431025 | − | 0.431025i | ||||
\(218\) | 4.69495e6 | 0.453170 | ||||||||
\(219\) | −189160. | −0.0180093 | ||||||||
\(220\) | 879670. | + | 879670.i | 0.0826136 | + | 0.0826136i | ||||
\(221\) | − | 1.51148e7i | − | 1.40031i | ||||||
\(222\) | 1.00936e7 | − | 7.67226e6i | 0.922548 | − | 0.701236i | ||||
\(223\) | −1.24614e7 | −1.12370 | −0.561852 | − | 0.827238i | \(-0.689911\pi\) | ||||
−0.561852 | + | 0.827238i | \(0.689911\pi\) | |||||||
\(224\) | −2.46023e6 | + | 2.46023e6i | −0.218893 | + | 0.218893i | ||||
\(225\) | − | 1.14060e7i | − | 1.00135i | ||||||
\(226\) | − | 9.43487e6i | − | 0.817355i | ||||||
\(227\) | 7.73573e6 | + | 7.73573e6i | 0.661339 | + | 0.661339i | 0.955696 | − | 0.294357i | \(-0.0951055\pi\) |
−0.294357 | + | 0.955696i | \(0.595105\pi\) | |||||||
\(228\) | 5.91451e6 | + | 5.91451e6i | 0.499016 | + | 0.499016i | ||||
\(229\) | −1.09121e7 | −0.908663 | −0.454332 | − | 0.890833i | \(-0.650122\pi\) | ||||
−0.454332 | + | 0.890833i | \(0.650122\pi\) | |||||||
\(230\) | −1.03440e7 | − | 1.03440e7i | −0.850169 | − | 0.850169i | ||||
\(231\) | −6.54681e6 | −0.531121 | ||||||||
\(232\) | 7.15842e6 | 0.573262 | ||||||||
\(233\) | 2.31412e6i | 0.182944i | 0.995808 | + | 0.0914722i | \(0.0291573\pi\) | ||||
−0.995808 | + | 0.0914722i | \(0.970843\pi\) | |||||||
\(234\) | 1.53549e7 | 1.19839 | ||||||||
\(235\) | 4.49995e6 | + | 4.49995e6i | 0.346740 | + | 0.346740i | ||||
\(236\) | −7.82943e6 | + | 7.82943e6i | −0.595654 | + | 0.595654i | ||||
\(237\) | −3.06264e7 | + | 3.06264e7i | −2.30065 | + | 2.30065i | ||||
\(238\) | 2.32497e7 | 1.72459 | ||||||||
\(239\) | −3.56646e6 | − | 3.56646e6i | −0.261242 | − | 0.261242i | 0.564316 | − | 0.825559i | \(-0.309140\pi\) |
−0.825559 | + | 0.564316i | \(0.809140\pi\) | |||||||
\(240\) | 5.05631e6 | − | 5.05631e6i | 0.365763 | − | 0.365763i | ||||
\(241\) | −3.14478e6 | − | 3.14478e6i | −0.224667 | − | 0.224667i | 0.585793 | − | 0.810460i | \(-0.300783\pi\) |
−0.810460 | + | 0.585793i | \(0.800783\pi\) | |||||||
\(242\) | 6.84352e6 | − | 6.84352e6i | 0.482874 | − | 0.482874i | ||||
\(243\) | − | 1.24600e7i | − | 0.868361i | ||||||
\(244\) | −5.70409e6 | − | 5.70409e6i | −0.392660 | − | 0.392660i | ||||
\(245\) | 2.71312e7 | + | 2.71312e7i | 1.84489 | + | 1.84489i | ||||
\(246\) | −5.36567e6 | + | 5.36567e6i | −0.360428 | + | 0.360428i | ||||
\(247\) | − | 1.30488e7i | − | 0.865925i | ||||||
\(248\) | −1.87718e6 | −0.123070 | ||||||||
\(249\) | 4.64795e7i | 3.01067i | ||||||||
\(250\) | − | 5.66289e6i | − | 0.362425i | ||||||
\(251\) | −982226. | + | 982226.i | −0.0621141 | + | 0.0621141i | −0.737481 | − | 0.675367i | \(-0.763985\pi\) |
0.675367 | + | 0.737481i | \(0.263985\pi\) | |||||||
\(252\) | 2.36190e7i | 1.47591i | ||||||||
\(253\) | 2.85417e6 | − | 2.85417e6i | 0.176245 | − | 0.176245i | ||||
\(254\) | 86902.5 | − | 86902.5i | 0.00530312 | − | 0.00530312i | ||||
\(255\) | −4.77831e7 | −2.88173 | ||||||||
\(256\) | 1.04858e6 | 0.0625000 | ||||||||
\(257\) | −9.18658e6 | − | 9.18658e6i | −0.541196 | − | 0.541196i | 0.382684 | − | 0.923879i | \(-0.375000\pi\) |
−0.923879 | + | 0.382684i | \(0.875000\pi\) | |||||||
\(258\) | − | 1.15336e7i | − | 0.671590i | ||||||
\(259\) | 4.10866e6 | − | 3.01456e7i | 0.236484 | − | 1.73510i | ||||
\(260\) | −1.11554e7 | −0.634696 | ||||||||
\(261\) | 3.43616e7 | − | 3.43616e7i | 1.93264 | − | 1.93264i | ||||
\(262\) | 1.83520e7i | 1.02042i | ||||||||
\(263\) | 8.68981e6i | 0.477687i | 0.971058 | + | 0.238843i | \(0.0767682\pi\) | ||||
−0.971058 | + | 0.238843i | \(0.923232\pi\) | |||||||
\(264\) | 1.39516e6 | + | 1.39516e6i | 0.0758249 | + | 0.0758249i | ||||
\(265\) | −4.71601e6 | − | 4.71601e6i | −0.253418 | − | 0.253418i | ||||
\(266\) | 2.00718e7 | 1.06645 | ||||||||
\(267\) | 3.39629e7 | + | 3.39629e7i | 1.78431 | + | 1.78431i | ||||
\(268\) | −7.60934e6 | −0.395315 | ||||||||
\(269\) | −6.14540e6 | −0.315714 | −0.157857 | − | 0.987462i | \(-0.550458\pi\) | ||||
−0.157857 | + | 0.987462i | \(0.550458\pi\) | |||||||
\(270\) | − | 1.97450e7i | − | 1.00315i | ||||||
\(271\) | −3.49852e6 | −0.175783 | −0.0878914 | − | 0.996130i | \(-0.528013\pi\) | ||||
−0.0878914 | + | 0.996130i | \(0.528013\pi\) | |||||||
\(272\) | −4.95462e6 | − | 4.95462e6i | −0.246209 | − | 0.246209i | ||||
\(273\) | 4.15113e7 | − | 4.15113e7i | 2.04022 | − | 2.04022i | ||||
\(274\) | 1.36425e7 | − | 1.36425e7i | 0.663196 | − | 0.663196i | ||||
\(275\) | −2.28644e6 | −0.109942 | ||||||||
\(276\) | −1.64056e7 | − | 1.64056e7i | −0.780308 | − | 0.780308i | ||||
\(277\) | 9.98601e6 | − | 9.98601e6i | 0.469843 | − | 0.469843i | −0.432021 | − | 0.901864i | \(-0.642199\pi\) |
0.901864 | + | 0.432021i | \(0.142199\pi\) | |||||||
\(278\) | −8.41584e6 | − | 8.41584e6i | −0.391708 | − | 0.391708i | ||||
\(279\) | −9.01077e6 | + | 9.01077e6i | −0.414906 | + | 0.414906i | ||||
\(280\) | − | 1.71593e7i | − | 0.781675i | ||||||
\(281\) | 2.73302e7 | + | 2.73302e7i | 1.23175 | + | 1.23175i | 0.963290 | + | 0.268461i | \(0.0865152\pi\) |
0.268461 | + | 0.963290i | \(0.413485\pi\) | |||||||
\(282\) | 7.13694e6 | + | 7.13694e6i | 0.318247 | + | 0.318247i | ||||
\(283\) | −2.70268e7 | + | 2.70268e7i | −1.19244 | + | 1.19244i | −0.216054 | + | 0.976381i | \(0.569319\pi\) |
−0.976381 | + | 0.216054i | \(0.930681\pi\) | |||||||
\(284\) | 2.80039e6i | 0.122254i | ||||||||
\(285\) | −4.12519e7 | −1.78201 | ||||||||
\(286\) | − | 3.07805e6i | − | 0.131576i | ||||||
\(287\) | 1.82092e7i | 0.770274i | ||||||||
\(288\) | 5.03334e6 | − | 5.03334e6i | 0.210707 | − | 0.210707i | ||||
\(289\) | 2.26846e7i | 0.939804i | ||||||||
\(290\) | −2.49639e7 | + | 2.49639e7i | −1.02357 | + | 1.02357i | ||||
\(291\) | 1.66292e7 | − | 1.66292e7i | 0.674826 | − | 0.674826i | ||||
\(292\) | 136801. | 0.00549467 | ||||||||
\(293\) | 5.04915e6 | 0.200731 | 0.100366 | − | 0.994951i | \(-0.467999\pi\) | ||||
0.100366 | + | 0.994951i | \(0.467999\pi\) | |||||||
\(294\) | 4.30302e7 | + | 4.30302e7i | 1.69329 | + | 1.69329i | ||||
\(295\) | − | 5.46078e7i | − | 2.12710i | ||||||
\(296\) | −7.29977e6 | + | 5.54861e6i | −0.281471 | + | 0.213949i | ||||
\(297\) | 5.44813e6 | 0.207959 | ||||||||
\(298\) | −1.34784e6 | + | 1.34784e6i | −0.0509318 | + | 0.0509318i | ||||
\(299\) | 3.61947e7i | 1.35404i | ||||||||
\(300\) | 1.31424e7i | 0.486755i | ||||||||
\(301\) | −1.95704e7 | − | 1.95704e7i | −0.717631 | − | 0.717631i | ||||
\(302\) | −1.61968e7 | − | 1.61968e7i | −0.588042 | − | 0.588042i | ||||
\(303\) | −2.23054e6 | −0.0801830 | ||||||||
\(304\) | −4.27740e6 | − | 4.27740e6i | −0.152251 | − | 0.152251i | ||||
\(305\) | 3.97842e7 | 1.40221 | ||||||||
\(306\) | −4.75660e7 | −1.66009 | ||||||||
\(307\) | − | 3.08824e7i | − | 1.06732i | −0.845698 | − | 0.533662i | \(-0.820816\pi\) | ||
0.845698 | − | 0.533662i | \(-0.179184\pi\) | |||||||
\(308\) | 4.73468e6 | 0.162046 | ||||||||
\(309\) | −1.11407e7 | − | 1.11407e7i | −0.377605 | − | 0.377605i | ||||
\(310\) | 6.54637e6 | − | 6.54637e6i | 0.219743 | − | 0.219743i | ||||
\(311\) | −2.05072e7 | + | 2.05072e7i | −0.681750 | + | 0.681750i | −0.960394 | − | 0.278644i | \(-0.910115\pi\) |
0.278644 | + | 0.960394i | \(0.410115\pi\) | |||||||
\(312\) | −1.76925e7 | −0.582541 | ||||||||
\(313\) | −3.53619e6 | − | 3.53619e6i | −0.115319 | − | 0.115319i | 0.647092 | − | 0.762412i | \(-0.275985\pi\) |
−0.762412 | + | 0.647092i | \(0.775985\pi\) | |||||||
\(314\) | 394839. | − | 394839.i | 0.0127536 | − | 0.0127536i | ||||
\(315\) | −8.23677e7 | − | 8.23677e7i | −2.63527 | − | 2.63527i | ||||
\(316\) | 2.21491e7 | − | 2.21491e7i | 0.701933 | − | 0.701933i | ||||
\(317\) | 3.88691e7i | 1.22019i | 0.792330 | + | 0.610093i | \(0.208868\pi\) | ||||
−0.792330 | + | 0.610093i | \(0.791132\pi\) | |||||||
\(318\) | −7.47960e6 | − | 7.47960e6i | −0.232593 | − | 0.232593i | ||||
\(319\) | −6.88814e6 | − | 6.88814e6i | −0.212193 | − | 0.212193i | ||||
\(320\) | −3.65674e6 | + | 3.65674e6i | −0.111595 | + | 0.111595i | ||||
\(321\) | − | 8.64314e7i | − | 2.61310i | ||||||
\(322\) | −5.56750e7 | −1.66760 | ||||||||
\(323\) | 4.04223e7i | 1.19954i | ||||||||
\(324\) | − | 2.64918e6i | − | 0.0778889i | ||||||
\(325\) | 1.44976e7 | − | 1.44976e7i | 0.422325 | − | 0.422325i | ||||
\(326\) | 1.85498e7i | 0.535410i | ||||||||
\(327\) | −2.59675e7 | + | 2.59675e7i | −0.742654 | + | 0.742654i | ||||
\(328\) | 3.88047e6 | − | 3.88047e6i | 0.109967 | − | 0.109967i | ||||
\(329\) | 2.42203e7 | 0.680129 | ||||||||
\(330\) | −9.73080e6 | −0.270774 | ||||||||
\(331\) | −4.45773e7 | − | 4.45773e7i | −1.22922 | − | 1.22922i | −0.964259 | − | 0.264961i | \(-0.914641\pi\) |
−0.264961 | − | 0.964259i | \(-0.585359\pi\) | |||||||
\(332\) | − | 3.36142e7i | − | 0.918562i | ||||||
\(333\) | −8.40584e6 | + | 6.16744e7i | −0.227640 | + | 1.67021i | ||||
\(334\) | 4.06576e7 | 1.09119 | ||||||||
\(335\) | 2.65364e7 | − | 2.65364e7i | 0.705842 | − | 0.705842i | ||||
\(336\) | − | 2.72148e7i | − | 0.717442i | ||||||
\(337\) | − | 4.43359e7i | − | 1.15842i | −0.815179 | − | 0.579209i | \(-0.803361\pi\) | ||
0.815179 | − | 0.579209i | \(-0.196639\pi\) | |||||||
\(338\) | 209723. | + | 209723.i | 0.00543120 | + | 0.00543120i | ||||
\(339\) | 5.21837e7 | + | 5.21837e7i | 1.33948 | + | 1.33948i | ||||
\(340\) | 3.45569e7 | 0.879222 | ||||||||
\(341\) | 1.80630e6 | + | 1.80630e6i | 0.0455541 | + | 0.0455541i | ||||
\(342\) | −4.10645e7 | −1.02657 | ||||||||
\(343\) | 7.53645e7 | 1.86760 | ||||||||
\(344\) | 8.34113e6i | 0.204903i | ||||||||
\(345\) | 1.14424e8 | 2.78651 | ||||||||
\(346\) | 1.40255e7 | + | 1.40255e7i | 0.338601 | + | 0.338601i | ||||
\(347\) | 2.32138e7 | − | 2.32138e7i | 0.555594 | − | 0.555594i | −0.372456 | − | 0.928050i | \(-0.621484\pi\) |
0.928050 | + | 0.372456i | \(0.121484\pi\) | |||||||
\(348\) | −3.95928e7 | + | 3.95928e7i | −0.939460 | + | 0.939460i | ||||
\(349\) | 6.82932e7 | 1.60657 | 0.803287 | − | 0.595592i | \(-0.203082\pi\) | ||||
0.803287 | + | 0.595592i | \(0.203082\pi\) | |||||||
\(350\) | 2.23003e7 | + | 2.23003e7i | 0.520124 | + | 0.520124i | ||||
\(351\) | −3.45448e7 | + | 3.45448e7i | −0.798844 | + | 0.798844i | ||||
\(352\) | −1.00899e6 | − | 1.00899e6i | −0.0231343 | − | 0.0231343i | ||||
\(353\) | 1.97626e7 | − | 1.97626e7i | 0.449284 | − | 0.449284i | −0.445832 | − | 0.895116i | \(-0.647092\pi\) |
0.895116 | + | 0.445832i | \(0.147092\pi\) | |||||||
\(354\) | − | 8.66082e7i | − | 1.95231i | ||||||
\(355\) | −9.76590e6 | − | 9.76590e6i | −0.218287 | − | 0.218287i | ||||
\(356\) | −2.45621e7 | − | 2.45621e7i | −0.544397 | − | 0.544397i | ||||
\(357\) | −1.28592e8 | + | 1.28592e8i | −2.82625 | + | 2.82625i | ||||
\(358\) | 3.65621e7i | 0.796860i | ||||||||
\(359\) | 7.16098e7 | 1.54771 | 0.773855 | − | 0.633363i | \(-0.218326\pi\) | ||||
0.773855 | + | 0.633363i | \(0.218326\pi\) | |||||||
\(360\) | 3.51060e7i | 0.752442i | ||||||||
\(361\) | − | 1.21487e7i | − | 0.258231i | ||||||
\(362\) | 9.59847e6 | − | 9.59847e6i | 0.202337 | − | 0.202337i | ||||
\(363\) | 7.57022e7i | 1.58266i | ||||||||
\(364\) | −3.00211e7 | + | 3.00211e7i | −0.622476 | + | 0.622476i | ||||
\(365\) | −477073. | + | 477073.i | −0.00981084 | + | 0.00981084i | ||||
\(366\) | 6.30980e7 | 1.28698 | ||||||||
\(367\) | 1.22255e6 | 0.0247326 | 0.0123663 | − | 0.999924i | \(-0.496064\pi\) | ||||
0.0123663 | + | 0.999924i | \(0.496064\pi\) | |||||||
\(368\) | 1.18646e7 | + | 1.18646e7i | 0.238073 | + | 0.238073i | ||||
\(369\) | − | 3.72538e7i | − | 0.741467i | ||||||
\(370\) | 6.10688e6 | − | 4.48067e7i | 0.120563 | − | 0.884581i | ||||
\(371\) | −2.53832e7 | −0.497077 | ||||||||
\(372\) | 1.03826e7 | − | 1.03826e7i | 0.201686 | − | 0.201686i | ||||
\(373\) | 7.35725e6i | 0.141772i | 0.997484 | + | 0.0708858i | \(0.0225826\pi\) | ||||
−0.997484 | + | 0.0708858i | \(0.977417\pi\) | |||||||
\(374\) | 9.53511e6i | 0.182268i | ||||||||
\(375\) | 3.13211e7 | + | 3.13211e7i | 0.593941 | + | 0.593941i | ||||
\(376\) | −5.16147e6 | − | 5.16147e6i | −0.0970979 | − | 0.0970979i | ||||
\(377\) | 8.73511e7 | 1.63021 | ||||||||
\(378\) | −5.31371e7 | − | 5.31371e7i | −0.983836 | − | 0.983836i | ||||
\(379\) | 1.63969e7 | 0.301193 | 0.150596 | − | 0.988595i | \(-0.451881\pi\) | ||||
0.150596 | + | 0.988595i | \(0.451881\pi\) | |||||||
\(380\) | 2.98335e7 | 0.543693 | ||||||||
\(381\) | 961305.i | 0.0173815i | ||||||||
\(382\) | −5.71525e7 | −1.02529 | ||||||||
\(383\) | −3.32822e7 | − | 3.32822e7i | −0.592400 | − | 0.592400i | 0.345879 | − | 0.938279i | \(-0.387581\pi\) |
−0.938279 | + | 0.345879i | \(0.887581\pi\) | |||||||
\(384\) | −5.79961e6 | + | 5.79961e6i | −0.102425 | + | 0.102425i | ||||
\(385\) | −1.65115e7 | + | 1.65115e7i | −0.289337 | + | 0.289337i | ||||
\(386\) | −4.82156e7 | −0.838350 | ||||||||
\(387\) | 4.00388e7 | + | 4.00388e7i | 0.690793 | + | 0.690793i | ||||
\(388\) | −1.20263e7 | + | 1.20263e7i | −0.205891 | + | 0.205891i | ||||
\(389\) | −4.42434e7 | − | 4.42434e7i | −0.751623 | − | 0.751623i | 0.223159 | − | 0.974782i | \(-0.428363\pi\) |
−0.974782 | + | 0.223159i | \(0.928363\pi\) | |||||||
\(390\) | 6.16999e7 | − | 6.16999e7i | 1.04014 | − | 1.04014i | ||||
\(391\) | − | 1.12123e8i | − | 1.87571i | ||||||
\(392\) | −3.11196e7 | − | 3.11196e7i | −0.516626 | − | 0.516626i | ||||
\(393\) | −1.01504e8 | − | 1.01504e8i | −1.67226 | − | 1.67226i | ||||
\(394\) | −3.52778e7 | + | 3.52778e7i | −0.576783 | + | 0.576783i | ||||
\(395\) | 1.54483e8i | 2.50663i | ||||||||
\(396\) | −9.68660e6 | −0.155986 | ||||||||
\(397\) | 8.78508e7i | 1.40402i | 0.712165 | + | 0.702012i | \(0.247715\pi\) | ||||
−0.712165 | + | 0.702012i | \(0.752285\pi\) | |||||||
\(398\) | − | 6.71961e6i | − | 0.106585i | ||||||
\(399\) | −1.11016e8 | + | 1.11016e8i | −1.74770 | + | 1.74770i | ||||
\(400\) | − | 9.50464e6i | − | 0.148510i | ||||||
\(401\) | 2.12803e7 | − | 2.12803e7i | 0.330023 | − | 0.330023i | −0.522572 | − | 0.852595i | \(-0.675027\pi\) |
0.852595 | + | 0.522572i | \(0.175027\pi\) | |||||||
\(402\) | 4.20868e7 | − | 4.20868e7i | 0.647840 | − | 0.647840i | ||||
\(403\) | −2.29064e7 | −0.349979 | ||||||||
\(404\) | 1.61314e6 | 0.0244640 | ||||||||
\(405\) | 9.23858e6 | + | 9.23858e6i | 0.139072 | + | 0.139072i | ||||
\(406\) | 1.34364e8i | 2.00773i | ||||||||
\(407\) | 1.23633e7 | + | 1.68504e6i | 0.183379 | + | 0.0249935i | ||||
\(408\) | 5.48074e7 | 0.806973 | ||||||||
\(409\) | −8.71985e7 | + | 8.71985e7i | −1.27450 | + | 1.27450i | −0.330796 | + | 0.943702i | \(0.607317\pi\) |
−0.943702 | + | 0.330796i | \(0.892683\pi\) | |||||||
\(410\) | 2.70651e7i | 0.392697i | ||||||||
\(411\) | 1.50911e8i | 2.17369i | ||||||||
\(412\) | 8.05701e6 | + | 8.05701e6i | 0.115208 | + | 0.115208i | ||||
\(413\) | −1.46959e8 | − | 1.46959e8i | −2.08615 | − | 2.08615i | ||||
\(414\) | 1.13904e8 | 1.60524 | ||||||||
\(415\) | 1.17224e8 | + | 1.17224e8i | 1.64011 | + | 1.64011i | ||||
\(416\) | 1.27953e7 | 0.177734 | ||||||||
\(417\) | 9.30950e7 | 1.28386 | ||||||||
\(418\) | 8.23181e6i | 0.112711i | ||||||||
\(419\) | 1.42045e7 | 0.193101 | 0.0965506 | − | 0.995328i | \(-0.469219\pi\) | ||||
0.0965506 | + | 0.995328i | \(0.469219\pi\) | |||||||
\(420\) | 9.49072e7 | + | 9.49072e7i | 1.28101 | + | 1.28101i | ||||
\(421\) | −1.01034e8 | + | 1.01034e8i | −1.35401 | + | 1.35401i | −0.472884 | + | 0.881124i | \(0.656787\pi\) |
−0.881124 | + | 0.472884i | \(0.843213\pi\) | |||||||
\(422\) | −2.09028e7 | + | 2.09028e7i | −0.278143 | + | 0.278143i | ||||
\(423\) | −4.95518e7 | −0.654694 | ||||||||
\(424\) | 5.40928e6 | + | 5.40928e6i | 0.0709647 | + | 0.0709647i | ||||
\(425\) | −4.49103e7 | + | 4.49103e7i | −0.585032 | + | 0.585032i | ||||
\(426\) | −1.54888e7 | − | 1.54888e7i | −0.200349 | − | 0.200349i | ||||
\(427\) | 1.07066e8 | − | 1.07066e8i | 1.37521 | − | 1.37521i | ||||
\(428\) | 6.25076e7i | 0.797262i | ||||||||
\(429\) | 1.70245e7 | + | 1.70245e7i | 0.215627 | + | 0.215627i | ||||
\(430\) | −2.90884e7 | − | 2.90884e7i | −0.365859 | − | 0.365859i | ||||
\(431\) | −8.31140e7 | + | 8.31140e7i | −1.03811 | + | 1.03811i | −0.0388629 | + | 0.999245i | \(0.512374\pi\) |
−0.999245 | + | 0.0388629i | \(0.987626\pi\) | |||||||
\(432\) | 2.26476e7i | 0.280912i | ||||||||
\(433\) | 1.30194e8 | 1.60372 | 0.801859 | − | 0.597514i | \(-0.203845\pi\) | ||||
0.801859 | + | 0.597514i | \(0.203845\pi\) | |||||||
\(434\) | − | 3.52348e7i | − | 0.431025i | ||||||
\(435\) | − | 2.76147e8i | − | 3.35485i | ||||||
\(436\) | 1.87798e7 | − | 1.87798e7i | 0.226585 | − | 0.226585i | ||||
\(437\) | − | 9.67976e7i | − | 1.15990i | ||||||
\(438\) | −756640. | + | 756640.i | −0.00900465 | + | 0.00900465i | ||||
\(439\) | 4819.45 | − | 4819.45i | 5.69644e−5 | − | 5.69644e-5i | −0.707078 | − | 0.707135i | \(-0.749987\pi\) |
0.707135 | + | 0.707078i | \(0.249987\pi\) | |||||||
\(440\) | 7.03736e6 | 0.0826136 | ||||||||
\(441\) | −2.98759e8 | −3.48341 | ||||||||
\(442\) | −6.04591e7 | − | 6.04591e7i | −0.700156 | − | 0.700156i | ||||
\(443\) | − | 4.41724e7i | − | 0.508090i | −0.967192 | − | 0.254045i | \(-0.918239\pi\) | ||
0.967192 | − | 0.254045i | \(-0.0817611\pi\) | |||||||
\(444\) | 9.68553e6 | − | 7.10636e7i | 0.110656 | − | 0.811892i | ||||
\(445\) | 1.71313e8 | 1.94406 | ||||||||
\(446\) | −4.98456e7 | + | 4.98456e7i | −0.561852 | + | 0.561852i | ||||
\(447\) | − | 1.49096e7i | − | 0.166934i | ||||||
\(448\) | 1.96818e7i | 0.218893i | ||||||||
\(449\) | −2.61301e7 | − | 2.61301e7i | −0.288670 | − | 0.288670i | 0.547884 | − | 0.836554i | \(-0.315433\pi\) |
−0.836554 | + | 0.547884i | \(0.815433\pi\) | |||||||
\(450\) | −4.56238e7 | − | 4.56238e7i | −0.500673 | − | 0.500673i | ||||
\(451\) | −7.46792e6 | −0.0814086 | ||||||||
\(452\) | −3.77395e7 | − | 3.77395e7i | −0.408677 | − | 0.408677i | ||||
\(453\) | 1.79167e8 | 1.92736 | ||||||||
\(454\) | 6.18859e7 | 0.661339 | ||||||||
\(455\) | − | 2.09388e8i | − | 2.22289i | ||||||
\(456\) | 4.73161e7 | 0.499016 | ||||||||
\(457\) | −6.76262e7 | − | 6.76262e7i | −0.708543 | − | 0.708543i | 0.257686 | − | 0.966229i | \(-0.417040\pi\) |
−0.966229 | + | 0.257686i | \(0.917040\pi\) | |||||||
\(458\) | −4.36485e7 | + | 4.36485e7i | −0.454332 | + | 0.454332i | ||||
\(459\) | 1.07012e8 | − | 1.07012e8i | 1.10661 | − | 1.10661i | ||||
\(460\) | −8.27521e7 | −0.850169 | ||||||||
\(461\) | 1.17549e8 | + | 1.17549e8i | 1.19982 | + | 1.19982i | 0.974219 | + | 0.225605i | \(0.0724360\pi\) |
0.225605 | + | 0.974219i | \(0.427564\pi\) | |||||||
\(462\) | −2.61872e7 | + | 2.61872e7i | −0.265561 | + | 0.265561i | ||||
\(463\) | −8.83216e7 | − | 8.83216e7i | −0.889865 | − | 0.889865i | 0.104645 | − | 0.994510i | \(-0.466629\pi\) |
−0.994510 | + | 0.104645i | \(0.966629\pi\) | |||||||
\(464\) | 2.86337e7 | − | 2.86337e7i | 0.286631 | − | 0.286631i | ||||
\(465\) | 7.24151e7i | 0.720229i | ||||||||
\(466\) | 9.25650e6 | + | 9.25650e6i | 0.0914722 | + | 0.0914722i | ||||
\(467\) | −1.59777e7 | − | 1.59777e7i | −0.156879 | − | 0.156879i | 0.624303 | − | 0.781182i | \(-0.285383\pi\) |
−0.781182 | + | 0.624303i | \(0.785383\pi\) | |||||||
\(468\) | 6.14196e7 | − | 6.14196e7i | 0.599197 | − | 0.599197i | ||||
\(469\) | − | 1.42828e8i | − | 1.38451i | ||||||
\(470\) | 3.59996e7 | 0.346740 | ||||||||
\(471\) | 4.36767e6i | 0.0418010i | ||||||||
\(472\) | 6.26354e7i | 0.595654i | ||||||||
\(473\) | 8.02620e6 | − | 8.02620e6i | 0.0758449 | − | 0.0758449i | ||||
\(474\) | 2.45011e8i | 2.30065i | ||||||||
\(475\) | −3.87718e7 | + | 3.87718e7i | −0.361772 | + | 0.361772i | ||||
\(476\) | 9.29986e7 | − | 9.29986e7i | 0.862295 | − | 0.862295i | ||||
\(477\) | 5.19309e7 | 0.478488 | ||||||||
\(478\) | −2.85317e7 | −0.261242 | ||||||||
\(479\) | 5.97333e7 | + | 5.97333e7i | 0.543513 | + | 0.543513i | 0.924557 | − | 0.381044i | \(-0.124435\pi\) |
−0.381044 | + | 0.924557i | \(0.624435\pi\) | |||||||
\(480\) | − | 4.04505e7i | − | 0.365763i | ||||||
\(481\) | −8.90759e7 | + | 6.77073e7i | −0.800433 | + | 0.608416i | ||||
\(482\) | −2.51583e7 | −0.224667 | ||||||||
\(483\) | 3.07935e8 | − | 3.07935e8i | 2.73286 | − | 2.73286i | ||||
\(484\) | − | 5.47482e7i | − | 0.482874i | ||||||
\(485\) | − | 8.38796e7i | − | 0.735243i | ||||||
\(486\) | −4.98401e7 | − | 4.98401e7i | −0.434181 | − | 0.434181i | ||||
\(487\) | −4.58606e7 | − | 4.58606e7i | −0.397057 | − | 0.397057i | 0.480137 | − | 0.877194i | \(-0.340587\pi\) |
−0.877194 | + | 0.480137i | \(0.840587\pi\) | |||||||
\(488\) | −4.56327e7 | −0.392660 | ||||||||
\(489\) | −1.02598e8 | − | 1.02598e8i | −0.877429 | − | 0.877429i | ||||
\(490\) | 2.17050e8 | 1.84489 | ||||||||
\(491\) | 1.26998e8 | 1.07288 | 0.536440 | − | 0.843938i | \(-0.319769\pi\) | ||||
0.536440 | + | 0.843938i | \(0.319769\pi\) | |||||||
\(492\) | 4.29253e7i | 0.360428i | ||||||||
\(493\) | −2.70594e8 | −2.25828 | ||||||||
\(494\) | −5.21953e7 | − | 5.21953e7i | −0.432963 | − | 0.432963i | ||||
\(495\) | 3.37805e7 | − | 3.37805e7i | 0.278516 | − | 0.278516i | ||||
\(496\) | −7.50872e6 | + | 7.50872e6i | −0.0615348 | + | 0.0615348i | ||||
\(497\) | −5.25634e7 | −0.428168 | ||||||||
\(498\) | 1.85918e8 | + | 1.85918e8i | 1.50534 | + | 1.50534i | ||||
\(499\) | −1.10645e7 | + | 1.10645e7i | −0.0890494 | + | 0.0890494i | −0.750228 | − | 0.661179i | \(-0.770056\pi\) |
0.661179 | + | 0.750228i | \(0.270056\pi\) | |||||||
\(500\) | −2.26516e7 | − | 2.26516e7i | −0.181212 | − | 0.181212i | ||||
\(501\) | −2.24875e8 | + | 2.24875e8i | −1.78825 | + | 1.78825i | ||||
\(502\) | 7.85781e6i | 0.0621141i | ||||||||
\(503\) | 5.23567e7 | + | 5.23567e7i | 0.411404 | + | 0.411404i | 0.882227 | − | 0.470824i | \(-0.156043\pi\) |
−0.470824 | + | 0.882227i | \(0.656043\pi\) | |||||||
\(504\) | 9.44761e7 | + | 9.44761e7i | 0.737956 | + | 0.737956i | ||||
\(505\) | −5.62556e6 | + | 5.62556e6i | −0.0436809 | + | 0.0436809i | ||||
\(506\) | − | 2.28333e7i | − | 0.176245i | ||||||
\(507\) | −2.31993e6 | −0.0178013 | ||||||||
\(508\) | − | 695220.i | − | 0.00530312i | ||||||
\(509\) | 7.60753e7i | 0.576886i | 0.957497 | + | 0.288443i | \(0.0931376\pi\) | ||||
−0.957497 | + | 0.288443i | \(0.906862\pi\) | |||||||
\(510\) | −1.91132e8 | + | 1.91132e8i | −1.44087 | + | 1.44087i | ||||
\(511\) | 2.56777e6i | 0.0192439i | ||||||||
\(512\) | 4.19430e6 | − | 4.19430e6i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 9.23852e7 | − | 9.23852e7i | 0.684306 | − | 0.684306i | ||||
\(514\) | −7.34926e7 | −0.541196 | ||||||||
\(515\) | −5.61951e7 | −0.411412 | ||||||||
\(516\) | −4.61343e7 | − | 4.61343e7i | −0.335795 | − | 0.335795i | ||||
\(517\) | 9.93318e6i | 0.0718814i | ||||||||
\(518\) | −1.04148e8 | − | 1.37017e8i | −0.749309 | − | 0.985793i | ||||
\(519\) | −1.55148e8 | −1.10980 | ||||||||
\(520\) | −4.46217e7 | + | 4.46217e7i | −0.317348 | + | 0.317348i | ||||
\(521\) | 8.45653e7i | 0.597969i | 0.954258 | + | 0.298985i | \(0.0966479\pi\) | ||||
−0.954258 | + | 0.298985i | \(0.903352\pi\) | |||||||
\(522\) | − | 2.74893e8i | − | 1.93264i | ||||||
\(523\) | −1.78463e8 | − | 1.78463e8i | −1.24751 | − | 1.24751i | −0.956816 | − | 0.290694i | \(-0.906114\pi\) |
−0.290694 | − | 0.956816i | \(-0.593886\pi\) | |||||||
\(524\) | 7.34078e7 | + | 7.34078e7i | 0.510209 | + | 0.510209i | ||||
\(525\) | −2.46684e8 | −1.70476 | ||||||||
\(526\) | 3.47592e7 | + | 3.47592e7i | 0.238843 | + | 0.238843i | ||||
\(527\) | 7.09588e7 | 0.484813 | ||||||||
\(528\) | 1.11613e7 | 0.0758249 | ||||||||
\(529\) | 1.20461e8i | 0.813725i | ||||||||
\(530\) | −3.77280e7 | −0.253418 | ||||||||
\(531\) | 3.00661e8 | + | 3.00661e8i | 2.00813 | + | 2.00813i | ||||
\(532\) | 8.02872e7 | − | 8.02872e7i | 0.533226 | − | 0.533226i | ||||
\(533\) | 4.73517e7 | − | 4.73517e7i | 0.312719 | − | 0.312719i | ||||
\(534\) | 2.71703e8 | 1.78431 | ||||||||
\(535\) | −2.17985e8 | − | 2.17985e8i | −1.42353 | − | 1.42353i | ||||
\(536\) | −3.04374e7 | + | 3.04374e7i | −0.197657 | + | 0.197657i | ||||
\(537\) | −2.02223e8 | − | 2.02223e8i | −1.30589 | − | 1.30589i | ||||
\(538\) | −2.45816e7 | + | 2.45816e7i | −0.157857 | + | 0.157857i | ||||
\(539\) | 5.98893e7i | 0.382458i | ||||||||
\(540\) | −7.89799e7 | − | 7.89799e7i | −0.501574 | − | 0.501574i | ||||
\(541\) | 2.92559e7 | + | 2.92559e7i | 0.184766 | + | 0.184766i | 0.793429 | − | 0.608663i | \(-0.208294\pi\) |
−0.608663 | + | 0.793429i | \(0.708294\pi\) | |||||||
\(542\) | −1.39941e7 | + | 1.39941e7i | −0.0878914 | + | 0.0878914i | ||||
\(543\) | 1.06177e8i | 0.663180i | ||||||||
\(544\) | −3.96370e7 | −0.246209 | ||||||||
\(545\) | 1.30983e8i | 0.809145i | ||||||||
\(546\) | − | 3.32090e8i | − | 2.04022i | ||||||
\(547\) | −8.91641e7 | + | 8.91641e7i | −0.544789 | + | 0.544789i | −0.924929 | − | 0.380140i | \(-0.875876\pi\) |
0.380140 | + | 0.924929i | \(0.375876\pi\) | |||||||
\(548\) | − | 1.09140e8i | − | 0.663196i | ||||||
\(549\) | −2.19045e8 | + | 2.19045e8i | −1.32378 | + | 1.32378i | ||||
\(550\) | −9.14578e6 | + | 9.14578e6i | −0.0549709 | + | 0.0549709i | ||||
\(551\) | −2.33608e8 | −1.39647 | ||||||||
\(552\) | −1.31245e8 | −0.780308 | ||||||||
\(553\) | 4.15741e8 | + | 4.15741e8i | 2.45837 | + | 2.45837i | ||||
\(554\) | − | 7.98881e7i | − | 0.469843i | ||||||
\(555\) | 2.14046e8 | + | 2.81600e8i | 1.25207 | + | 1.64723i | ||||
\(556\) | −6.73267e7 | −0.391708 | ||||||||
\(557\) | −1.01266e7 | + | 1.01266e7i | −0.0586002 | + | 0.0586002i | −0.735800 | − | 0.677199i | \(-0.763193\pi\) |
0.677199 | + | 0.735800i | \(0.263193\pi\) | |||||||
\(558\) | 7.20862e7i | 0.414906i | ||||||||
\(559\) | 1.01783e8i | 0.582694i | ||||||||
\(560\) | −6.86373e7 | − | 6.86373e7i | −0.390838 | − | 0.390838i | ||||
\(561\) | −5.27381e7 | − | 5.27381e7i | −0.298701 | − | 0.298701i | ||||
\(562\) | 2.18641e8 | 1.23175 | ||||||||
\(563\) | −5.06100e7 | − | 5.06100e7i | −0.283603 | − | 0.283603i | 0.550941 | − | 0.834544i | \(-0.314269\pi\) |
−0.834544 | + | 0.550941i | \(0.814269\pi\) | |||||||
\(564\) | 5.70955e7 | 0.318247 | ||||||||
\(565\) | 2.63221e8 | 1.45940 | ||||||||
\(566\) | 2.16214e8i | 1.19244i | ||||||||
\(567\) | 4.97252e7 | 0.272789 | ||||||||
\(568\) | 1.12015e7 | + | 1.12015e7i | 0.0611270 | + | 0.0611270i | ||||
\(569\) | 5.14258e6 | − | 5.14258e6i | 0.0279154 | − | 0.0279154i | −0.693011 | − | 0.720927i | \(-0.743716\pi\) |
0.720927 | + | 0.693011i | \(0.243716\pi\) | |||||||
\(570\) | −1.65007e8 | + | 1.65007e8i | −0.891003 | + | 0.891003i | ||||
\(571\) | −2.36499e8 | −1.27034 | −0.635171 | − | 0.772372i | \(-0.719070\pi\) | ||||
−0.635171 | + | 0.772372i | \(0.719070\pi\) | |||||||
\(572\) | −1.23122e7 | − | 1.23122e7i | −0.0657882 | − | 0.0657882i | ||||
\(573\) | 3.16107e8 | − | 3.16107e8i | 1.68024 | − | 1.68024i | ||||
\(574\) | 7.28368e7 | + | 7.28368e7i | 0.385137 | + | 0.385137i | ||||
\(575\) | 1.07545e8 | − | 1.07545e8i | 0.565700 | − | 0.565700i | ||||
\(576\) | − | 4.02667e7i | − | 0.210707i | ||||||
\(577\) | 8.51919e7 | + | 8.51919e7i | 0.443477 | + | 0.443477i | 0.893179 | − | 0.449702i | \(-0.148470\pi\) |
−0.449702 | + | 0.893179i | \(0.648470\pi\) | |||||||
\(578\) | 9.07383e7 | + | 9.07383e7i | 0.469902 | + | 0.469902i | ||||
\(579\) | 2.66677e8 | − | 2.66677e8i | 1.37389 | − | 1.37389i | ||||
\(580\) | 1.99711e8i | 1.02357i | ||||||||
\(581\) | 6.30941e8 | 3.21707 | ||||||||
\(582\) | − | 1.33033e8i | − | 0.674826i | ||||||
\(583\) | − | 1.04101e7i | − | 0.0525350i | ||||||
\(584\) | 547205. | − | 547205.i | 0.00274734 | − | 0.00274734i | ||||
\(585\) | 4.28383e8i | 2.13976i | ||||||||
\(586\) | 2.01966e7 | − | 2.01966e7i | 0.100366 | − | 0.100366i | ||||
\(587\) | 3.56163e7 | − | 3.56163e7i | 0.176090 | − | 0.176090i | −0.613559 | − | 0.789649i | \(-0.710263\pi\) |
0.789649 | + | 0.613559i | \(0.210263\pi\) | |||||||
\(588\) | 3.44242e8 | 1.69329 | ||||||||
\(589\) | 6.12599e7 | 0.299799 | ||||||||
\(590\) | −2.18431e8 | − | 2.18431e8i | −1.06355 | − | 1.06355i | ||||
\(591\) | − | 3.90238e8i | − | 1.89046i | ||||||
\(592\) | −7.00462e6 | + | 5.13935e7i | −0.0337613 | + | 0.247710i | ||||
\(593\) | −1.38971e7 | −0.0666441 | −0.0333220 | − | 0.999445i | \(-0.510609\pi\) | ||||
−0.0333220 | + | 0.999445i | \(0.510609\pi\) | |||||||
\(594\) | 2.17925e7 | − | 2.17925e7i | 0.103980 | − | 0.103980i | ||||
\(595\) | 6.48636e8i | 3.07929i | ||||||||
\(596\) | 1.07827e7i | 0.0509318i | ||||||||
\(597\) | 3.71657e7 | + | 3.71657e7i | 0.174671 | + | 0.174671i | ||||
\(598\) | 1.44779e8 | + | 1.44779e8i | 0.677020 | + | 0.677020i | ||||
\(599\) | −1.49063e8 | −0.693567 | −0.346783 | − | 0.937945i | \(-0.612726\pi\) | ||||
−0.346783 | + | 0.937945i | \(0.612726\pi\) | |||||||
\(600\) | 5.25696e7 | + | 5.25696e7i | 0.243378 | + | 0.243378i | ||||
\(601\) | 4.67270e7 | 0.215251 | 0.107625 | − | 0.994192i | \(-0.465675\pi\) | ||||
0.107625 | + | 0.994192i | \(0.465675\pi\) | |||||||
\(602\) | −1.56564e8 | −0.717631 | ||||||||
\(603\) | 2.92209e8i | 1.33273i | ||||||||
\(604\) | −1.29574e8 | −0.588042 | ||||||||
\(605\) | 1.90926e8 | + | 1.90926e8i | 0.862180 | + | 0.862180i | ||||
\(606\) | −8.92216e6 | + | 8.92216e6i | −0.0400915 | + | 0.0400915i | ||||
\(607\) | −2.92860e7 | + | 2.92860e7i | −0.130947 | + | 0.130947i | −0.769542 | − | 0.638596i | \(-0.779516\pi\) |
0.638596 | + | 0.769542i | \(0.279516\pi\) | |||||||
\(608\) | −3.42192e7 | −0.152251 | ||||||||
\(609\) | −7.43159e8 | − | 7.43159e8i | −3.29026 | − | 3.29026i | ||||
\(610\) | 1.59137e8 | − | 1.59137e8i | 0.701103 | − | 0.701103i | ||||
\(611\) | −6.29831e7 | − | 6.29831e7i | −0.276122 | − | 0.276122i | ||||
\(612\) | −1.90264e8 | + | 1.90264e8i | −0.830047 | + | 0.830047i | ||||
\(613\) | 2.00531e8i | 0.870563i | 0.900294 | + | 0.435282i | \(0.143351\pi\) | ||||
−0.900294 | + | 0.435282i | \(0.856649\pi\) | |||||||
\(614\) | −1.23530e8 | − | 1.23530e8i | −0.533662 | − | 0.533662i | ||||
\(615\) | −1.49695e8 | − | 1.49695e8i | −0.643551 | − | 0.643551i | ||||
\(616\) | 1.89387e7 | − | 1.89387e7i | 0.0810231 | − | 0.0810231i | ||||
\(617\) | 1.10584e8i | 0.470802i | 0.971898 | + | 0.235401i | \(0.0756404\pi\) | ||||
−0.971898 | + | 0.235401i | \(0.924360\pi\) | |||||||
\(618\) | −8.91256e7 | −0.377605 | ||||||||
\(619\) | − | 2.02631e8i | − | 0.854348i | −0.904169 | − | 0.427174i | \(-0.859509\pi\) | ||
0.904169 | − | 0.427174i | \(-0.140491\pi\) | |||||||
\(620\) | − | 5.23709e7i | − | 0.219743i | ||||||
\(621\) | −2.56257e8 | + | 2.56257e8i | −1.07004 | + | 1.07004i | ||||
\(622\) | 1.64058e8i | 0.681750i | ||||||||
\(623\) | 4.61033e8 | − | 4.61033e8i | 1.90663 | − | 1.90663i | ||||
\(624\) | −7.07701e7 | + | 7.07701e7i | −0.291270 | + | 0.291270i | ||||
\(625\) | 3.03017e8 | 1.24116 | ||||||||
\(626\) | −2.82895e7 | −0.115319 | ||||||||
\(627\) | −4.55296e7 | − | 4.55296e7i | −0.184710 | − | 0.184710i | ||||
\(628\) | − | 3.15872e6i | − | 0.0127536i | ||||||
\(629\) | 2.75937e8 | − | 2.09742e8i | 1.10881 | − | 0.842817i | ||||
\(630\) | −6.58941e8 | −2.63527 | ||||||||
\(631\) | −1.22295e8 | + | 1.22295e8i | −0.486768 | + | 0.486768i | −0.907285 | − | 0.420517i | \(-0.861849\pi\) |
0.420517 | + | 0.907285i | \(0.361849\pi\) | |||||||
\(632\) | − | 1.77193e8i | − | 0.701933i | ||||||
\(633\) | − | 2.31224e8i | − | 0.911638i | ||||||
\(634\) | 1.55476e8 | + | 1.55476e8i | 0.610093 | + | 0.610093i | ||||
\(635\) | 2.42447e6 | + | 2.42447e6i | 0.00946882 | + | 0.00946882i | ||||
\(636\) | −5.98368e7 | −0.232593 | ||||||||
\(637\) | −3.79739e8 | − | 3.79739e8i | −1.46915 | − | 1.46915i | ||||
\(638\) | −5.51052e7 | −0.212193 | ||||||||
\(639\) | 1.07539e8 | 0.412156 | ||||||||
\(640\) | 2.92539e7i | 0.111595i | ||||||||
\(641\) | 6.86101e7 | 0.260504 | 0.130252 | − | 0.991481i | \(-0.458421\pi\) | ||||
0.130252 | + | 0.991481i | \(0.458421\pi\) | |||||||
\(642\) | −3.45726e8 | − | 3.45726e8i | −1.30655 | − | 1.30655i | ||||
\(643\) | −1.49047e8 | + | 1.49047e8i | −0.560648 | + | 0.560648i | −0.929492 | − | 0.368843i | \(-0.879754\pi\) |
0.368843 | + | 0.929492i | \(0.379754\pi\) | |||||||
\(644\) | −2.22700e8 | + | 2.22700e8i | −0.833801 | + | 0.833801i | ||||
\(645\) | 3.21772e8 | 1.19914 | ||||||||
\(646\) | 1.61689e8 | + | 1.61689e8i | 0.599768 | + | 0.599768i | ||||
\(647\) | −1.49330e8 | + | 1.49330e8i | −0.551358 | + | 0.551358i | −0.926833 | − | 0.375474i | \(-0.877480\pi\) |
0.375474 | + | 0.926833i | \(0.377480\pi\) | |||||||
\(648\) | −1.05967e7 | − | 1.05967e7i | −0.0389445 | − | 0.0389445i | ||||
\(649\) | 6.02706e7 | − | 6.02706e7i | 0.220481 | − | 0.220481i | ||||
\(650\) | − | 1.15981e8i | − | 0.422325i | ||||||
\(651\) | 1.94881e8 | + | 1.94881e8i | 0.706362 | + | 0.706362i | ||||
\(652\) | 7.41992e7 | + | 7.41992e7i | 0.267705 | + | 0.267705i | ||||
\(653\) | −1.47226e8 | + | 1.47226e8i | −0.528743 | + | 0.528743i | −0.920197 | − | 0.391455i | \(-0.871972\pi\) |
0.391455 | + | 0.920197i | \(0.371972\pi\) | |||||||
\(654\) | 2.07740e8i | 0.742654i | ||||||||
\(655\) | −5.11996e8 | −1.82198 | ||||||||
\(656\) | − | 3.10438e7i | − | 0.109967i | ||||||
\(657\) | − | 5.25335e6i | − | 0.0185242i | ||||||
\(658\) | 9.68811e7 | − | 9.68811e7i | 0.340065 | − | 0.340065i | ||||
\(659\) | − | 8.98408e7i | − | 0.313919i | −0.987605 | − | 0.156959i | \(-0.949831\pi\) | ||
0.987605 | − | 0.156959i | \(-0.0501692\pi\) | |||||||
\(660\) | −3.89232e7 | + | 3.89232e7i | −0.135387 | + | 0.135387i | ||||
\(661\) | −3.52940e8 | + | 3.52940e8i | −1.22207 | + | 1.22207i | −0.255175 | + | 0.966895i | \(0.582133\pi\) |
−0.966895 | + | 0.255175i | \(0.917867\pi\) | |||||||
\(662\) | −3.56618e8 | −1.22922 | ||||||||
\(663\) | 6.68791e8 | 2.29483 | ||||||||
\(664\) | −1.34457e8 | − | 1.34457e8i | −0.459281 | − | 0.459281i | ||||
\(665\) | 5.59978e8i | 1.90417i | ||||||||
\(666\) | 2.13074e8 | + | 2.80321e8i | 0.721287 | + | 0.948927i | ||||
\(667\) | 6.47980e8 | 2.18365 | ||||||||
\(668\) | 1.62630e8 | − | 1.62630e8i | 0.545597 | − | 0.545597i | ||||
\(669\) | − | 5.51385e8i | − | 1.84152i | ||||||
\(670\) | − | 2.12291e8i | − | 0.705842i | ||||||
\(671\) | 4.39098e7 | + | 4.39098e7i | 0.145343 | + | 0.145343i | ||||
\(672\) | −1.08859e8 | − | 1.08859e8i | −0.358721 | − | 0.358721i | ||||
\(673\) | −1.07584e8 | −0.352941 | −0.176470 | − | 0.984306i | \(-0.556468\pi\) | ||||
−0.176470 | + | 0.984306i | \(0.556468\pi\) | |||||||
\(674\) | −1.77343e8 | − | 1.77343e8i | −0.579209 | − | 0.579209i | ||||
\(675\) | 2.05285e8 | 0.667492 | ||||||||
\(676\) | 1.67778e6 | 0.00543120 | ||||||||
\(677\) | 1.88022e8i | 0.605959i | 0.952997 | + | 0.302980i | \(0.0979814\pi\) | ||||
−0.952997 | + | 0.302980i | \(0.902019\pi\) | |||||||
\(678\) | 4.17469e8 | 1.33948 | ||||||||
\(679\) | −2.25734e8 | − | 2.25734e8i | −0.721088 | − | 0.721088i | ||||
\(680\) | 1.38228e8 | − | 1.38228e8i | 0.439611 | − | 0.439611i | ||||
\(681\) | −3.42287e8 | + | 3.42287e8i | −1.08380 | + | 1.08380i | ||||
\(682\) | 1.44504e7 | 0.0455541 | ||||||||
\(683\) | −2.35728e8 | − | 2.35728e8i | −0.739860 | − | 0.739860i | 0.232691 | − | 0.972551i | \(-0.425247\pi\) |
−0.972551 | + | 0.232691i | \(0.925247\pi\) | |||||||
\(684\) | −1.64258e8 | + | 1.64258e8i | −0.513284 | + | 0.513284i | ||||
\(685\) | 3.80608e8 | + | 3.80608e8i | 1.18415 | + | 1.18415i | ||||
\(686\) | 3.01458e8 | − | 3.01458e8i | 0.933801 | − | 0.933801i | ||||
\(687\) | − | 4.82834e8i | − | 1.48911i | ||||||
\(688\) | 3.33645e7 | + | 3.33645e7i | 0.102452 | + | 0.102452i | ||||
\(689\) | 6.60071e7 | + | 6.60071e7i | 0.201806 | + | 0.201806i | ||||
\(690\) | 4.57697e8 | − | 4.57697e8i | 1.39325 | − | 1.39325i | ||||
\(691\) | − | 1.69059e7i | − | 0.0512395i | −0.999672 | − | 0.0256197i | \(-0.991844\pi\) | ||
0.999672 | − | 0.0256197i | \(-0.00815591\pi\) | |||||||
\(692\) | 1.12204e8 | 0.338601 | ||||||||
\(693\) | − | 1.81818e8i | − | 0.546308i | ||||||
\(694\) | − | 1.85710e8i | − | 0.555594i | ||||||
\(695\) | 2.34791e8 | − | 2.34791e8i | 0.699403 | − | 0.699403i | ||||
\(696\) | 3.16742e8i | 0.939460i | ||||||||
\(697\) | −1.46685e8 | + | 1.46685e8i | −0.433199 | + | 0.433199i | ||||
\(698\) | 2.73173e8 | − | 2.73173e8i | 0.803287 | − | 0.803287i | ||||
\(699\) | −1.02394e8 | −0.299809 | ||||||||
\(700\) | 1.78403e8 | 0.520124 | ||||||||
\(701\) | −1.08170e8 | − | 1.08170e8i | −0.314017 | − | 0.314017i | 0.532447 | − | 0.846464i | \(-0.321273\pi\) |
−0.846464 | + | 0.532447i | \(0.821273\pi\) | |||||||
\(702\) | 2.76359e8i | 0.798844i | ||||||||
\(703\) | 2.38221e8 | − | 1.81073e8i | 0.685667 | − | 0.521181i | ||||
\(704\) | −8.07189e6 | −0.0231343 | ||||||||
\(705\) | −1.99112e8 | + | 1.99112e8i | −0.568237 | + | 0.568237i | ||||
\(706\) | − | 1.58101e8i | − | 0.449284i | ||||||
\(707\) | 3.02787e7i | 0.0856799i | ||||||||
\(708\) | −3.46433e8 | − | 3.46433e8i | −0.976156 | − | 0.976156i | ||||
\(709\) | 2.12594e7 | + | 2.12594e7i | 0.0596501 | + | 0.0596501i | 0.736303 | − | 0.676652i | \(-0.236570\pi\) |
−0.676652 | + | 0.736303i | \(0.736570\pi\) | |||||||
\(710\) | −7.81272e7 | −0.218287 | ||||||||
\(711\) | −8.50557e8 | − | 8.50557e8i | −2.36643 | − | 2.36643i | ||||
\(712\) | −1.96497e8 | −0.544397 | ||||||||
\(713\) | −1.69922e8 | −0.468793 | ||||||||
\(714\) | 1.02874e9i | 2.82625i | ||||||||
\(715\) | 8.58738e7 | 0.234932 | ||||||||
\(716\) | 1.46248e8 | + | 1.46248e8i | 0.398430 | + | 0.398430i | ||||
\(717\) | 1.57807e8 | − | 1.57807e8i | 0.428123 | − | 0.428123i | ||||
\(718\) | 2.86439e8 | − | 2.86439e8i | 0.773855 | − | 0.773855i | ||||
\(719\) | −9.23207e7 | −0.248378 | −0.124189 | − | 0.992259i | \(-0.539633\pi\) | ||||
−0.124189 | + | 0.992259i | \(0.539633\pi\) | |||||||
\(720\) | 1.40424e8 | + | 1.40424e8i | 0.376221 | + | 0.376221i | ||||
\(721\) | −1.51231e8 | + | 1.51231e8i | −0.403491 | + | 0.403491i | ||||
\(722\) | −4.85948e7 | − | 4.85948e7i | −0.129115 | − | 0.129115i | ||||
\(723\) | 1.39149e8 | − | 1.39149e8i | 0.368184 | − | 0.368184i | ||||
\(724\) | − | 7.67877e7i | − | 0.202337i | ||||||
\(725\) | −2.59545e8 | − | 2.59545e8i | −0.681081 | − | 0.681081i | ||||
\(726\) | 3.02809e8 | + | 3.02809e8i | 0.791332 | + | 0.791332i | ||||
\(727\) | 1.14944e8 | − | 1.14944e8i | 0.299146 | − | 0.299146i | −0.541534 | − | 0.840679i | \(-0.682156\pi\) |
0.840679 | + | 0.541534i | \(0.182156\pi\) | |||||||
\(728\) | 2.40169e8i | 0.622476i | ||||||||
\(729\) | 6.11677e8 | 1.57885 | ||||||||
\(730\) | 3.81658e6i | 0.00981084i | ||||||||
\(731\) | − | 3.15301e8i | − | 0.807185i | ||||||
\(732\) | 2.52392e8 | − | 2.52392e8i | 0.643491 | − | 0.643491i | ||||
\(733\) | − | 2.63841e8i | − | 0.669931i | −0.942230 | − | 0.334965i | \(-0.891275\pi\) | ||
0.942230 | − | 0.334965i | \(-0.108725\pi\) | |||||||
\(734\) | 4.89022e6 | − | 4.89022e6i | 0.0123663 | − | 0.0123663i | ||||
\(735\) | −1.20049e9 | + | 1.20049e9i | −3.02340 | + | 3.02340i | ||||
\(736\) | 9.49170e7 | 0.238073 | ||||||||
\(737\) | 5.85763e7 | 0.146325 | ||||||||
\(738\) | −1.49015e8 | − | 1.49015e8i | −0.370734 | − | 0.370734i | ||||
\(739\) | − | 9.46158e7i | − | 0.234439i | −0.993106 | − | 0.117220i | \(-0.962602\pi\) | ||
0.993106 | − | 0.117220i | \(-0.0373981\pi\) | |||||||
\(740\) | −1.54799e8 | − | 2.03654e8i | −0.382009 | − | 0.502572i | ||||
\(741\) | 5.77378e8 | 1.41908 | ||||||||
\(742\) | −1.01533e8 | + | 1.01533e8i | −0.248539 | + | 0.248539i | ||||
\(743\) | 7.09886e8i | 1.73070i | 0.501166 | + | 0.865351i | \(0.332904\pi\) | ||||
−0.501166 | + | 0.865351i | \(0.667096\pi\) | |||||||
\(744\) | − | 8.30605e7i | − | 0.201686i | ||||||
\(745\) | −3.76030e7 | − | 3.76030e7i | −0.0909397 | − | 0.0909397i | ||||
\(746\) | 2.94290e7 | + | 2.94290e7i | 0.0708858 | + | 0.0708858i | ||||
\(747\) | −1.29083e9 | −3.09676 | ||||||||
\(748\) | 3.81404e7 | + | 3.81404e7i | 0.0911341 | + | 0.0911341i | ||||
\(749\) | −1.17327e9 | −2.79224 | ||||||||
\(750\) | 2.50569e8 | 0.593941 | ||||||||
\(751\) | − | 4.67753e7i | − | 0.110432i | −0.998474 | − | 0.0552162i | \(-0.982415\pi\) | ||
0.998474 | − | 0.0552162i | \(-0.0175848\pi\) | |||||||
\(752\) | −4.12917e7 | −0.0970979 | ||||||||
\(753\) | −4.34611e7 | − | 4.34611e7i | −0.101792 | − | 0.101792i | ||||
\(754\) | 3.49404e8 | − | 3.49404e8i | 0.815106 | − | 0.815106i | ||||
\(755\) | 4.51870e8 | − | 4.51870e8i | 1.04996 | − | 1.04996i | ||||
\(756\) | −4.25097e8 | −0.983836 | ||||||||
\(757\) | 3.67066e8 | + | 3.67066e8i | 0.846168 | + | 0.846168i | 0.989653 | − | 0.143485i | \(-0.0458309\pi\) |
−0.143485 | + | 0.989653i | \(0.545831\pi\) | |||||||
\(758\) | 6.55877e7 | − | 6.55877e7i | 0.150596 | − | 0.150596i | ||||
\(759\) | 1.26290e8 | + | 1.26290e8i | 0.288830 | + | 0.288830i | ||||
\(760\) | 1.19334e8 | − | 1.19334e8i | 0.271847 | − | 0.271847i | ||||
\(761\) | 4.61005e8i | 1.04605i | 0.852318 | + | 0.523025i | \(0.175196\pi\) | ||||
−0.852318 | + | 0.523025i | \(0.824804\pi\) | |||||||
\(762\) | 3.84522e6 | + | 3.84522e6i | 0.00869073 | + | 0.00869073i | ||||
\(763\) | 3.52498e8 | + | 3.52498e8i | 0.793567 | + | 0.793567i | ||||
\(764\) | −2.28610e8 | + | 2.28610e8i | −0.512643 | + | 0.512643i | ||||
\(765\) | − | 1.32703e9i | − | 2.96413i | ||||||
\(766\) | −2.66257e8 | −0.592400 | ||||||||
\(767\) | 7.64313e8i | 1.69389i | ||||||||
\(768\) | 4.63969e7i | 0.102425i | ||||||||
\(769\) | 1.61970e8 | − | 1.61970e8i | 0.356168 | − | 0.356168i | −0.506230 | − | 0.862398i | \(-0.668961\pi\) |
0.862398 | + | 0.506230i | \(0.168961\pi\) | |||||||
\(770\) | 1.32092e8i | 0.289337i | ||||||||
\(771\) | 4.06483e8 | − | 4.06483e8i | 0.886910 | − | 0.886910i | ||||
\(772\) | −1.92862e8 | + | 1.92862e8i | −0.419175 | + | 0.419175i | ||||
\(773\) | −3.85167e8 | −0.833893 | −0.416947 | − | 0.908931i | \(-0.636900\pi\) | ||||
−0.416947 | + | 0.908931i | \(0.636900\pi\) | |||||||
\(774\) | 3.20310e8 | 0.690793 | ||||||||
\(775\) | 6.80615e7 | + | 6.80615e7i | 0.146216 | + | 0.146216i | ||||
\(776\) | 9.62103e7i | 0.205891i | ||||||||
\(777\) | 1.33387e9 | + | 1.81798e8i | 2.84348 | + | 0.387549i | ||||
\(778\) | −3.53948e8 | −0.751623 | ||||||||
\(779\) | −1.26635e8 | + | 1.26635e8i | −0.267881 | + | 0.267881i | ||||
\(780\) | − | 4.93599e8i | − | 1.04014i | ||||||
\(781\) | − | 2.15572e7i | − | 0.0452522i | ||||||
\(782\) | −4.48492e8 | − | 4.48492e8i | −0.937853 | − | 0.937853i | ||||
\(783\) | 6.18442e8 | + | 6.18442e8i | 1.28829 | + | 1.28829i | ||||
\(784\) | −2.48957e8 | −0.516626 | ||||||||
\(785\) | 1.10155e7 | + | 1.10155e7i | 0.0227717 | + | 0.0227717i | ||||
\(786\) | −8.12028e8 | −1.67226 | ||||||||
\(787\) | −4.83332e7 | −0.0991566 | −0.0495783 | − | 0.998770i | \(-0.515788\pi\) | ||||
−0.0495783 | + | 0.998770i | \(0.515788\pi\) | |||||||
\(788\) | 2.82222e8i | 0.576783i | ||||||||
\(789\) | −3.84503e8 | −0.782831 | ||||||||
\(790\) | 6.17933e8 | + | 6.17933e8i | 1.25332 | + | 1.25332i | ||||
\(791\) | 7.08373e8 | − | 7.08373e8i | 1.43131 | − | 1.43131i | ||||
\(792\) | −3.87464e7 | + | 3.87464e7i | −0.0779930 | + | 0.0779930i | ||||
\(793\) | −5.56836e8 | −1.11663 | ||||||||
\(794\) | 3.51403e8 | + | 3.51403e8i | 0.702012 | + | 0.702012i | ||||
\(795\) | 2.08672e8 | − | 2.08672e8i | 0.415300 | − | 0.415300i | ||||
\(796\) | −2.68784e7 | − | 2.68784e7i | −0.0532923 | − | 0.0532923i | ||||
\(797\) | 3.86346e8 | − | 3.86346e8i | 0.763134 | − | 0.763134i | −0.213753 | − | 0.976888i | \(-0.568569\pi\) |
0.976888 | + | 0.213753i | \(0.0685689\pi\) | |||||||
\(798\) | 8.88127e8i | 1.74770i | ||||||||
\(799\) | 1.95107e8 | + | 1.95107e8i | 0.382502 | + | 0.382502i | ||||
\(800\) | −3.80185e7 | − | 3.80185e7i | −0.0742550 | − | 0.0742550i | ||||
\(801\) | −9.43218e8 | + | 9.43218e8i | −1.83533 | + | 1.83533i | ||||
\(802\) | − | 1.70242e8i | − | 0.330023i | ||||||
\(803\) | −1.05309e6 | −0.00203385 | ||||||||
\(804\) | − | 3.36695e8i | − | 0.647840i | ||||||
\(805\) | − | 1.55326e9i | − | 2.97754i | ||||||
\(806\) | −9.16256e7 | + | 9.16256e7i | −0.174989 | + | 0.174989i | ||||
\(807\) | − | 2.71919e8i | − | 0.517391i | ||||||
\(808\) | 6.45255e6 | − | 6.45255e6i | 0.0122320 | − | 0.0122320i | ||||
\(809\) | −2.96742e6 | + | 2.96742e6i | −0.00560445 | + | 0.00560445i | −0.709903 | − | 0.704299i | \(-0.751261\pi\) |
0.704299 | + | 0.709903i | \(0.251261\pi\) | |||||||
\(810\) | 7.39087e7 | 0.139072 | ||||||||
\(811\) | −1.01026e9 | −1.89396 | −0.946979 | − | 0.321296i | \(-0.895882\pi\) | ||||
−0.946979 | + | 0.321296i | \(0.895882\pi\) | |||||||
\(812\) | 5.37456e8 | + | 5.37456e8i | 1.00386 | + | 1.00386i | ||||
\(813\) | − | 1.54801e8i | − | 0.288072i | ||||||
\(814\) | 5.61932e7 | − | 4.27129e7i | 0.104186 | − | 0.0791929i | ||||
\(815\) | −5.17516e8 | −0.955985 | ||||||||
\(816\) | 2.19230e8 | − | 2.19230e8i | 0.403486 | − | 0.403486i | ||||
\(817\) | − | 2.72204e8i | − | 0.499147i | ||||||
\(818\) | 6.97588e8i | 1.27450i | ||||||||
\(819\) | 1.15285e9 | + | 1.15285e9i | 2.09856 | + | 2.09856i | ||||
\(820\) | 1.08260e8 | + | 1.08260e8i | 0.196349 | + | 0.196349i | ||||
\(821\) | −6.31182e8 | −1.14058 | −0.570290 | − | 0.821444i | \(-0.693169\pi\) | ||||
−0.570290 | + | 0.821444i | \(0.693169\pi\) | |||||||
\(822\) | 6.03646e8 | + | 6.03646e8i | 1.08684 | + | 1.08684i | ||||
\(823\) | 2.23279e8 | 0.400542 | 0.200271 | − | 0.979741i | \(-0.435818\pi\) | ||||
0.200271 | + | 0.979741i | \(0.435818\pi\) | |||||||
\(824\) | 6.44561e7 | 0.115208 | ||||||||
\(825\) | − | 1.01169e8i | − | 0.180172i | ||||||
\(826\) | −1.17567e9 | −2.08615 | ||||||||
\(827\) | −6.52598e7 | − | 6.52598e7i | −0.115380 | − | 0.115380i | 0.647060 | − | 0.762439i | \(-0.275998\pi\) |
−0.762439 | + | 0.647060i | \(0.775998\pi\) | |||||||
\(828\) | 4.55618e8 | − | 4.55618e8i | 0.802619 | − | 0.802619i | ||||
\(829\) | 4.57143e8 | − | 4.57143e8i | 0.802395 | − | 0.802395i | −0.181074 | − | 0.983469i | \(-0.557957\pi\) |
0.983469 | + | 0.181074i | \(0.0579575\pi\) | |||||||
\(830\) | 9.37794e8 | 1.64011 | ||||||||
\(831\) | 4.41856e8 | + | 4.41856e8i | 0.769977 | + | 0.769977i | ||||
\(832\) | 5.11813e7 | − | 5.11813e7i | 0.0888671 | − | 0.0888671i | ||||
\(833\) | 1.17635e9 | + | 1.17635e9i | 2.03517 | + | 2.03517i | ||||
\(834\) | 3.72380e8 | − | 3.72380e8i | 0.641931 | − | 0.641931i | ||||
\(835\) | 1.13429e9i | 1.94835i | ||||||||
\(836\) | 3.29272e7 | + | 3.29272e7i | 0.0563555 | + | 0.0563555i | ||||
\(837\) | −1.62176e8 | − | 1.62176e8i | −0.276574 | − | 0.276574i | ||||
\(838\) | 5.68182e7 | − | 5.68182e7i | 0.0965506 | − | 0.0965506i | ||||
\(839\) | − | 3.29453e8i | − | 0.557837i | −0.960315 | − | 0.278918i | \(-0.910024\pi\) | ||
0.960315 | − | 0.278918i | \(-0.0899759\pi\) | |||||||
\(840\) | 7.59258e8 | 1.28101 | ||||||||
\(841\) | − | 9.68988e8i | − | 1.62904i | ||||||
\(842\) | 8.08272e8i | 1.35401i | ||||||||
\(843\) | −1.20929e9 | + | 1.20929e9i | −2.01859 | + | 2.01859i | ||||
\(844\) | 1.67223e8i | 0.278143i | ||||||||
\(845\) | −5.85100e6 | + | 5.85100e6i | −0.00969751 | + | 0.00969751i | ||||
\(846\) | −1.98207e8 | + | 1.98207e8i | −0.327347 | + | 0.327347i | ||||
\(847\) | 1.02763e9 | 1.69116 | ||||||||
\(848\) | 4.32743e7 | 0.0709647 | ||||||||
\(849\) | −1.19587e9 | − | 1.19587e9i | −1.95416 | − | 1.95416i | ||||
\(850\) | 3.59283e8i | 0.585032i | ||||||||
\(851\) | −6.60775e8 | + | 5.02260e8i | −1.07217 | + | 0.814967i | ||||
\(852\) | −1.23910e8 | −0.200349 | ||||||||
\(853\) | −3.32297e7 | + | 3.32297e7i | −0.0535402 | + | 0.0535402i | −0.733370 | − | 0.679830i | \(-0.762054\pi\) |
0.679830 | + | 0.733370i | \(0.262054\pi\) | |||||||
\(854\) | − | 8.56530e8i | − | 1.37521i | ||||||
\(855\) | − | 1.14565e9i | − | 1.83296i | ||||||
\(856\) | 2.50030e8 | + | 2.50030e8i | 0.398631 | + | 0.398631i | ||||
\(857\) | 3.81758e8 | + | 3.81758e8i | 0.606520 | + | 0.606520i | 0.942035 | − | 0.335515i | \(-0.108910\pi\) |
−0.335515 | + | 0.942035i | \(0.608910\pi\) | |||||||
\(858\) | 1.36196e8 | 0.215627 | ||||||||
\(859\) | 4.91969e8 | + | 4.91969e8i | 0.776172 | + | 0.776172i | 0.979178 | − | 0.203005i | \(-0.0650709\pi\) |
−0.203005 | + | 0.979178i | \(0.565071\pi\) | |||||||
\(860\) | −2.32707e8 | −0.365859 | ||||||||
\(861\) | −8.05712e8 | −1.26232 | ||||||||
\(862\) | 6.64912e8i | 1.03811i | ||||||||
\(863\) | −5.75659e8 | −0.895639 | −0.447819 | − | 0.894124i | \(-0.647799\pi\) | ||||
−0.447819 | + | 0.894124i | \(0.647799\pi\) | |||||||
\(864\) | 9.05904e7 | + | 9.05904e7i | 0.140456 | + | 0.140456i | ||||
\(865\) | −3.91292e8 | + | 3.91292e8i | −0.604579 | + | 0.604579i | ||||
\(866\) | 5.20777e8 | − | 5.20777e8i | 0.801859 | − | 0.801859i | ||||
\(867\) | −1.00374e9 | −1.54015 | ||||||||
\(868\) | −1.40939e8 | − | 1.40939e8i | −0.215513 | − | 0.215513i | ||||
\(869\) | −1.70503e8 | + | 1.70503e8i | −0.259820 | + | 0.259820i | ||||
\(870\) | −1.10459e9 | − | 1.10459e9i | −1.67742 | − | 1.67742i | ||||
\(871\) | −3.71414e8 | + | 3.71414e8i | −0.562087 | + | 0.562087i | ||||
\(872\) | − | 1.50238e8i | − | 0.226585i | ||||||
\(873\) | 4.61825e8 | + | 4.61825e8i | 0.694121 | + | 0.694121i | ||||
\(874\) | −3.87190e8 | − | 3.87190e8i | −0.579949 | − | 0.579949i | ||||
\(875\) | 4.25171e8 | − | 4.25171e8i | 0.634658 | − | 0.634658i | ||||
\(876\) | 6.05312e6i | 0.00900465i | ||||||||
\(877\) | 8.64610e8 | 1.28180 | 0.640902 | − | 0.767623i | \(-0.278561\pi\) | ||||
0.640902 | + | 0.767623i | \(0.278561\pi\) | |||||||
\(878\) | − | 38555.6i | − | 5.69644e-5i | ||||||
\(879\) | 2.23412e8i | 0.328958i | ||||||||
\(880\) | 2.81494e7 | − | 2.81494e7i | 0.0413068 | − | 0.0413068i | ||||
\(881\) | − | 8.04062e8i | − | 1.17588i | −0.808906 | − | 0.587938i | \(-0.799940\pi\) | ||
0.808906 | − | 0.587938i | \(-0.200060\pi\) | |||||||
\(882\) | −1.19504e9 | + | 1.19504e9i | −1.74171 | + | 1.74171i | ||||
\(883\) | 6.47858e8 | − | 6.47858e8i | 0.941017 | − | 0.941017i | −0.0573378 | − | 0.998355i | \(-0.518261\pi\) |
0.998355 | + | 0.0573378i | \(0.0182612\pi\) | |||||||
\(884\) | −4.83673e8 | −0.700156 | ||||||||
\(885\) | 2.41626e9 | 3.48589 | ||||||||
\(886\) | −1.76690e8 | − | 1.76690e8i | −0.254045 | − | 0.254045i | ||||
\(887\) | − | 4.90984e8i | − | 0.703552i | −0.936084 | − | 0.351776i | \(-0.885578\pi\) | ||
0.936084 | − | 0.351776i | \(-0.114422\pi\) | |||||||
\(888\) | −2.45512e8 | − | 3.22997e8i | −0.350618 | − | 0.461274i | ||||
\(889\) | 1.30493e7 | 0.0185730 | ||||||||
\(890\) | 6.85252e8 | − | 6.85252e8i | 0.972031 | − | 0.972031i | ||||
\(891\) | 2.03932e7i | 0.0288305i | ||||||||
\(892\) | 3.98764e8i | 0.561852i | ||||||||
\(893\) | 1.68439e8 | + | 1.68439e8i | 0.236532 | + | 0.236532i | ||||
\(894\) | −5.96385e7 | − | 5.96385e7i | −0.0834669 | − | 0.0834669i | ||||
\(895\) | −1.02004e9 | −1.42281 | ||||||||
\(896\) | 7.87274e7 | + | 7.87274e7i | 0.109446 | + | 0.109446i | ||||
\(897\) | −1.60153e9 | −2.21900 | ||||||||
\(898\) | −2.09041e8 | −0.288670 | ||||||||
\(899\) | 4.10084e8i | 0.564409i | ||||||||
\(900\) | −3.64991e8 | −0.500673 | ||||||||
\(901\) | −2.04475e8 | − | 2.04475e8i | −0.279554 | − | 0.279554i | ||||
\(902\) | −2.98717e7 | + | 2.98717e7i | −0.0407043 | + | 0.0407043i | ||||
\(903\) | 8.65943e8 | − | 8.65943e8i | 1.17605 | − | 1.17605i | ||||
\(904\) | −3.01916e8 | −0.408677 | ||||||||
\(905\) | 2.67785e8 | + | 2.67785e8i | 0.361277 | + | 0.361277i | ||||
\(906\) | 7.16668e8 | − | 7.16668e8i | 0.963681 | − | 0.963681i | ||||
\(907\) | −1.46791e8 | − | 1.46791e8i | −0.196733 | − | 0.196733i | 0.601865 | − | 0.798598i | \(-0.294425\pi\) |
−0.798598 | + | 0.601865i | \(0.794425\pi\) | |||||||
\(908\) | 2.47543e8 | − | 2.47543e8i | 0.330669 | − | 0.330669i | ||||
\(909\) | − | 6.19466e7i | − | 0.0824756i | ||||||
\(910\) | −8.37552e8 | − | 8.37552e8i | −1.11144 | − | 1.11144i | ||||
\(911\) | −5.58937e8 | − | 5.58937e8i | −0.739277 | − | 0.739277i | 0.233161 | − | 0.972438i | \(-0.425093\pi\) |
−0.972438 | + | 0.233161i | \(0.925093\pi\) | |||||||
\(912\) | 1.89264e8 | − | 1.89264e8i | 0.249508 | − | 0.249508i | ||||
\(913\) | 2.58760e8i | 0.340005i | ||||||||
\(914\) | −5.41009e8 | −0.708543 | ||||||||
\(915\) | 1.76035e9i | 2.29793i | ||||||||
\(916\) | 3.49188e8i | 0.454332i | ||||||||
\(917\) | −1.37787e9 | + | 1.37787e9i | −1.78690 | + | 1.78690i | ||||
\(918\) | − | 8.56096e8i | − | 1.10661i | ||||||
\(919\) | −8.40968e8 | + | 8.40968e8i | −1.08351 | + | 1.08351i | −0.0873309 | + | 0.996179i | \(0.527834\pi\) |
−0.996179 | + | 0.0873309i | \(0.972166\pi\) | |||||||
\(920\) | −3.31008e8 | + | 3.31008e8i | −0.425085 | + | 0.425085i | ||||
\(921\) | 1.36647e9 | 1.74913 | ||||||||
\(922\) | 9.40395e8 | 1.19982 | ||||||||
\(923\) | 1.36688e8 | + | 1.36688e8i | 0.173830 | + | 0.173830i | ||||
\(924\) | 2.09498e8i | 0.265561i | ||||||||
\(925\) | 4.65848e8 | + | 6.34922e7i | 0.588598 | + | 0.0802223i | ||||
\(926\) | −7.06573e8 | −0.889865 | ||||||||
\(927\) | 3.09400e8 | − | 3.09400e8i | 0.388401 | − | 0.388401i | ||||
\(928\) | − | 2.29069e8i | − | 0.286631i | ||||||
\(929\) | 2.82257e8i | 0.352044i | 0.984386 | + | 0.176022i | \(0.0563230\pi\) | ||||
−0.984386 | + | 0.176022i | \(0.943677\pi\) | |||||||
\(930\) | 2.89660e8 | + | 2.89660e8i | 0.360114 | + | 0.360114i | ||||
\(931\) | 1.01556e9 | + | 1.01556e9i | 1.25851 | + | 1.25851i | ||||
\(932\) | 7.40520e7 | 0.0914722 | ||||||||
\(933\) | −9.07392e8 | − | 9.07392e8i | −1.11725 | − | 1.11725i | ||||
\(934\) | −1.27822e8 | −0.156879 | ||||||||
\(935\) | −2.66018e8 | −0.325443 | ||||||||
\(936\) | − | 4.91357e8i | − | 0.599197i | ||||||
\(937\) | −8.83005e8 | −1.07336 | −0.536678 | − | 0.843787i | \(-0.680321\pi\) | ||||
−0.536678 | + | 0.843787i | \(0.680321\pi\) | |||||||
\(938\) | −5.71312e8 | − | 5.71312e8i | −0.692253 | − | 0.692253i | ||||
\(939\) | 1.56468e8 | − | 1.56468e8i | 0.188985 | − | 0.188985i | ||||
\(940\) | 1.43998e8 | − | 1.43998e8i | 0.173370 | − | 0.173370i | ||||
\(941\) | 3.11294e8 | 0.373595 | 0.186798 | − | 0.982398i | \(-0.440189\pi\) | ||||
0.186798 | + | 0.982398i | \(0.440189\pi\) | |||||||
\(942\) | 1.74707e7 | + | 1.74707e7i | 0.0209005 | + | 0.0209005i | ||||
\(943\) | 3.51260e8 | − | 3.51260e8i | 0.418884 | − | 0.418884i | ||||
\(944\) | 2.50542e8 | + | 2.50542e8i | 0.297827 | + | 0.297827i | ||||
\(945\) | 1.48246e9 | − | 1.48246e9i | 1.75666 | − | 1.75666i | ||||
\(946\) | − | 6.42096e7i | − | 0.0758449i | ||||||
\(947\) | −6.02686e8 | − | 6.02686e8i | −0.709645 | − | 0.709645i | 0.256816 | − | 0.966460i | \(-0.417327\pi\) |
−0.966460 | + | 0.256816i | \(0.917327\pi\) | |||||||
\(948\) | 9.80045e8 | + | 9.80045e8i | 1.15033 | + | 1.15033i | ||||
\(949\) | 6.67731e6 | − | 6.67731e6i | 0.00781273 | − | 0.00781273i | ||||
\(950\) | 3.10174e8i | 0.361772i | ||||||||
\(951\) | −1.71986e9 | −1.99964 | ||||||||
\(952\) | − | 7.43989e8i | − | 0.862295i | ||||||
\(953\) | − | 2.53838e7i | − | 0.0293277i | −0.999892 | − | 0.0146638i | \(-0.995332\pi\) | ||
0.999892 | − | 0.0146638i | \(-0.00466781\pi\) | |||||||
\(954\) | 2.07724e8 | − | 2.07724e8i | 0.239244 | − | 0.239244i | ||||
\(955\) | − | 1.59448e9i | − | 1.83067i | ||||||
\(956\) | −1.14127e8 | + | 1.14127e8i | −0.130621 | + | 0.130621i | ||||
\(957\) | 3.04783e8 | − | 3.04783e8i | 0.347741 | − | 0.347741i | ||||
\(958\) | 4.77866e8 | 0.543513 | ||||||||
\(959\) | 2.04856e9 | 2.32270 | ||||||||
\(960\) | −1.61802e8 | − | 1.61802e8i | −0.182881 | − | 0.182881i | ||||
\(961\) | 7.79966e8i | 0.878831i | ||||||||
\(962\) | −8.54743e7 | + | 6.27133e8i | −0.0960087 | + | 0.704424i | ||||
\(963\) | 2.40037e9 | 2.68782 | ||||||||
\(964\) | −1.00633e8 | + | 1.00633e8i | −0.112334 | + | 0.112334i | ||||
\(965\) | − | 1.34515e9i | − | 1.49689i | ||||||
\(966\) | − | 2.46348e9i | − | 2.73286i | ||||||
\(967\) | −8.11671e8 | − | 8.11671e8i | −0.897637 | − | 0.897637i | 0.0975900 | − | 0.995227i | \(-0.468887\pi\) |
−0.995227 | + | 0.0975900i | \(0.968887\pi\) | |||||||
\(968\) | −2.18993e8 | − | 2.18993e8i | −0.241437 | − | 0.241437i | ||||
\(969\) | −1.78859e9 | −1.96580 | ||||||||
\(970\) | −3.35518e8 | − | 3.35518e8i | −0.367622 | − | 0.367622i | ||||
\(971\) | 5.17035e8 | 0.564758 | 0.282379 | − | 0.959303i | \(-0.408876\pi\) | ||||
0.282379 | + | 0.959303i | \(0.408876\pi\) | |||||||
\(972\) | −3.98721e8 | −0.434181 | ||||||||
\(973\) | − | 1.26373e9i | − | 1.37188i | ||||||
\(974\) | −3.66885e8 | −0.397057 | ||||||||
\(975\) | 6.41483e8 | + | 6.41483e8i | 0.692104 | + | 0.692104i | ||||
\(976\) | −1.82531e8 | + | 1.82531e8i | −0.196330 | + | 0.196330i | ||||
\(977\) | −8.57304e7 | + | 8.57304e7i | −0.0919287 | + | 0.0919287i | −0.751576 | − | 0.659647i | \(-0.770706\pi\) |
0.659647 | + | 0.751576i | \(0.270706\pi\) | |||||||
\(978\) | −8.20783e8 | −0.877429 | ||||||||
\(979\) | 1.89078e8 | + | 1.89078e8i | 0.201508 | + | 0.201508i | ||||
\(980\) | 8.68199e8 | − | 8.68199e8i | 0.922446 | − | 0.922446i | ||||
\(981\) | −7.21169e8 | − | 7.21169e8i | −0.763889 | − | 0.763889i | ||||
\(982\) | 5.07990e8 | − | 5.07990e8i | 0.536440 | − | 0.536440i | ||||
\(983\) | 9.48208e8i | 0.998259i | 0.866527 | + | 0.499130i | \(0.166347\pi\) | ||||
−0.866527 | + | 0.499130i | \(0.833653\pi\) | |||||||
\(984\) | 1.71701e8 | + | 1.71701e8i | 0.180214 | + | 0.180214i | ||||
\(985\) | −9.84206e8 | − | 9.84206e8i | −1.02986 | − | 1.02986i | ||||
\(986\) | −1.08238e9 | + | 1.08238e9i | −1.12914 | + | 1.12914i | ||||
\(987\) | 1.07169e9i | 1.11459i | ||||||||
\(988\) | −4.17562e8 | −0.432963 | ||||||||
\(989\) | 7.55038e8i | 0.780513i | ||||||||
\(990\) | − | 2.70244e8i | − | 0.278516i | ||||||
\(991\) | −1.07229e9 | + | 1.07229e9i | −1.10177 | + | 1.10177i | −0.107577 | + | 0.994197i | \(0.534309\pi\) |
−0.994197 | + | 0.107577i | \(0.965691\pi\) | |||||||
\(992\) | 6.00697e7i | 0.0615348i | ||||||||
\(993\) | 1.97243e9 | − | 1.97243e9i | 2.01444 | − | 2.01444i | ||||
\(994\) | −2.10254e8 | + | 2.10254e8i | −0.214084 | + | 0.214084i | ||||
\(995\) | 1.87469e8 | 0.190309 | ||||||||
\(996\) | 1.48734e9 | 1.50534 | ||||||||
\(997\) | 1.01415e9 | + | 1.01415e9i | 1.02334 | + | 1.02334i | 0.999721 | + | 0.0236141i | \(0.00751729\pi\) |
0.0236141 | + | 0.999721i | \(0.492483\pi\) | |||||||
\(998\) | 8.85162e7i | 0.0890494i | ||||||||
\(999\) | −1.11002e9 | − | 1.51289e8i | −1.11336 | − | 0.151744i |
(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 | 74.7.d.a.43.9 | yes | 18 | |
37.31 | odd | 4 | inner | 74.7.d.a.31.1 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.7.d.a.31.1 | ✓ | 18 | 37.31 | odd | 4 | inner | |
74.7.d.a.43.9 | yes | 18 | 1.1 | even | 1 | trivial |