Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,9,Mod(26,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.26");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(30.5533957546\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 64 x^{10} + 385774 x^{8} - 323639784 x^{6} - 48708595080 x^{4} + 21531002169600 x^{2} + 82\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{16}\cdot 3^{18}\cdot 5^{8} \) |
Twist minimal: | no (minimal twist has level 15) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 26.8 | ||
Root | \(17.1763 - 23.2266i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.26 |
Dual form | 75.9.c.h.26.6 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.66585i | 0.354116i | 0.984200 | + | 0.177058i | \(0.0566579\pi\) | ||||
−0.984200 | + | 0.177058i | \(0.943342\pi\) | |||||||
\(3\) | 72.8768 | − | 35.3550i | 0.899713 | − | 0.436481i | ||||
\(4\) | 223.898 | 0.874602 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 200.316 | + | 412.909i | 0.154565 | + | 0.318602i | ||||
\(7\) | 1674.62 | 0.697469 | 0.348734 | − | 0.937222i | \(-0.386612\pi\) | ||||
0.348734 | + | 0.937222i | \(0.386612\pi\) | |||||||
\(8\) | 2719.03i | 0.663826i | ||||||||
\(9\) | 4061.05 | − | 5153.12i | 0.618968 | − | 0.785416i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 21417.9i | 1.46287i | 0.681910 | + | 0.731436i | \(0.261150\pi\) | ||||
−0.681910 | + | 0.731436i | \(0.738850\pi\) | |||||||
\(12\) | 16317.0 | − | 7915.92i | 0.786891 | − | 0.381748i | ||||
\(13\) | 5980.82 | 0.209405 | 0.104703 | − | 0.994504i | \(-0.466611\pi\) | ||||
0.104703 | + | 0.994504i | \(0.466611\pi\) | |||||||
\(14\) | 9488.16i | 0.246985i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 41912.3 | 0.639531 | ||||||||
\(17\) | 69210.3i | 0.828657i | 0.910127 | + | 0.414329i | \(0.135984\pi\) | ||||
−0.910127 | + | 0.414329i | \(0.864016\pi\) | |||||||
\(18\) | 29196.8 | + | 23009.3i | 0.278128 | + | 0.219186i | ||||
\(19\) | 18044.8 | 0.138464 | 0.0692320 | − | 0.997601i | \(-0.477945\pi\) | ||||
0.0692320 | + | 0.997601i | \(0.477945\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 122041. | − | 59206.3i | 0.627522 | − | 0.304432i | ||||
\(22\) | −121351. | −0.518026 | ||||||||
\(23\) | − | 91800.0i | − | 0.328043i | −0.986457 | − | 0.164022i | \(-0.947553\pi\) | ||
0.986457 | − | 0.164022i | \(-0.0524467\pi\) | |||||||
\(24\) | 96131.3 | + | 198154.i | 0.289748 | + | 0.597253i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 33886.4i | 0.0741536i | ||||||||
\(27\) | 113768. | − | 519121.i | 0.214074 | − | 0.976817i | ||||
\(28\) | 374945. | 0.610008 | ||||||||
\(29\) | − | 1.12754e6i | − | 1.59419i | −0.603854 | − | 0.797095i | \(-0.706369\pi\) | ||
0.603854 | − | 0.797095i | \(-0.293631\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.27927e6 | −1.38521 | −0.692607 | − | 0.721316i | \(-0.743538\pi\) | ||||
−0.692607 | + | 0.721316i | \(0.743538\pi\) | |||||||
\(32\) | 933541.i | 0.890294i | ||||||||
\(33\) | 757230. | + | 1.56087e6i | 0.638517 | + | 1.31617i | ||||
\(34\) | −392135. | −0.293440 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 909261. | − | 1.15377e6i | 0.541351 | − | 0.686927i | ||||
\(37\) | 2.19804e6 | 1.17281 | 0.586405 | − | 0.810018i | \(-0.300543\pi\) | ||||
0.586405 | + | 0.810018i | \(0.300543\pi\) | |||||||
\(38\) | 102239.i | 0.0490322i | ||||||||
\(39\) | 435863. | − | 211452.i | 0.188404 | − | 0.0914014i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 29007.4i | − | 0.0102653i | −0.999987 | − | 0.00513267i | \(-0.998366\pi\) | ||
0.999987 | − | 0.00513267i | \(-0.00163379\pi\) | |||||||
\(42\) | 335454. | + | 691466.i | 0.107804 | + | 0.222215i | ||||
\(43\) | 6.78169e6 | 1.98365 | 0.991823 | − | 0.127625i | \(-0.0407354\pi\) | ||||
0.991823 | + | 0.127625i | \(0.0407354\pi\) | |||||||
\(44\) | 4.79543e6i | 1.27943i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 520125. | 0.116165 | ||||||||
\(47\) | 1.96089e6i | 0.401847i | 0.979607 | + | 0.200924i | \(0.0643943\pi\) | ||||
−0.979607 | + | 0.200924i | \(0.935606\pi\) | |||||||
\(48\) | 3.05443e6 | − | 1.48181e6i | 0.575395 | − | 0.279143i | ||||
\(49\) | −2.96044e6 | −0.513537 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.44693e6 | + | 5.04382e6i | 0.361694 | + | 0.745554i | ||||
\(52\) | 1.33909e6 | 0.183146 | ||||||||
\(53\) | 1.23039e7i | 1.55933i | 0.626198 | + | 0.779664i | \(0.284610\pi\) | ||||
−0.626198 | + | 0.779664i | \(0.715390\pi\) | |||||||
\(54\) | 2.94126e6 | + | 644591.i | 0.345906 | + | 0.0758070i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.55335e6i | 0.462998i | ||||||||
\(57\) | 1.31504e6 | − | 637973.i | 0.124578 | − | 0.0604370i | ||||
\(58\) | 6.38847e6 | 0.564527 | ||||||||
\(59\) | − | 5.58621e6i | − | 0.461009i | −0.973071 | − | 0.230504i | \(-0.925962\pi\) | ||
0.973071 | − | 0.230504i | \(-0.0740376\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 312034. | 0.0225363 | 0.0112681 | − | 0.999937i | \(-0.496413\pi\) | ||||
0.0112681 | + | 0.999937i | \(0.496413\pi\) | |||||||
\(62\) | − | 7.24817e6i | − | 0.490525i | ||||||
\(63\) | 6.80073e6 | − | 8.62953e6i | 0.431711 | − | 0.547803i | ||||
\(64\) | 5.44025e6 | 0.324264 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −8.84365e6 | + | 4.29035e6i | −0.466075 | + | 0.226109i | ||||
\(67\) | 853503. | 0.0423551 | 0.0211775 | − | 0.999776i | \(-0.493258\pi\) | ||||
0.0211775 | + | 0.999776i | \(0.493258\pi\) | |||||||
\(68\) | 1.54961e7i | 0.724746i | ||||||||
\(69\) | −3.24559e6 | − | 6.69009e6i | −0.143185 | − | 0.295145i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.18282e7i | − | 1.25250i | −0.779621 | − | 0.626252i | \(-0.784588\pi\) | ||
0.779621 | − | 0.626252i | \(-0.215412\pi\) | |||||||
\(72\) | 1.40115e7 | + | 1.10421e7i | 0.521379 | + | 0.410887i | ||||
\(73\) | 2.36800e6 | 0.0833855 | 0.0416927 | − | 0.999130i | \(-0.486725\pi\) | ||||
0.0416927 | + | 0.999130i | \(0.486725\pi\) | |||||||
\(74\) | 1.24537e7i | 0.415310i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.04019e6 | 0.121101 | ||||||||
\(77\) | 3.58669e7i | 1.02031i | ||||||||
\(78\) | 1.19805e6 | + | 2.46953e6i | 0.0323667 | + | 0.0667170i | ||||
\(79\) | −2.92328e7 | −0.750520 | −0.375260 | − | 0.926920i | \(-0.622447\pi\) | ||||
−0.375260 | + | 0.926920i | \(0.622447\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00625e7 | − | 4.18541e7i | −0.233757 | − | 0.972295i | ||||
\(82\) | 164351. | 0.00363512 | ||||||||
\(83\) | − | 6.73076e7i | − | 1.41825i | −0.705084 | − | 0.709124i | \(-0.749091\pi\) | ||
0.705084 | − | 0.709124i | \(-0.250909\pi\) | |||||||
\(84\) | 2.73248e7 | − | 1.32562e7i | 0.548832 | − | 0.266257i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.84240e7i | 0.702439i | ||||||||
\(87\) | −3.98642e7 | − | 8.21715e7i | −0.695834 | − | 1.43431i | ||||
\(88\) | −5.82360e7 | −0.971093 | ||||||||
\(89\) | − | 4.90240e7i | − | 0.781355i | −0.920528 | − | 0.390678i | \(-0.872241\pi\) | ||
0.920528 | − | 0.390678i | \(-0.127759\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00156e7 | 0.146054 | ||||||||
\(92\) | − | 2.05539e7i | − | 0.286908i | ||||||
\(93\) | −9.32293e7 | + | 4.52287e7i | −1.24629 | + | 0.604620i | ||||
\(94\) | −1.11101e7 | −0.142300 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.30053e7 | + | 6.80334e7i | 0.388597 | + | 0.801009i | ||||
\(97\) | −7.18400e7 | −0.811483 | −0.405741 | − | 0.913988i | \(-0.632987\pi\) | ||||
−0.405741 | + | 0.913988i | \(0.632987\pi\) | |||||||
\(98\) | − | 1.67734e7i | − | 0.181851i | ||||||
\(99\) | 1.10369e8 | + | 8.69792e7i | 1.14896 | + | 0.905471i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.12197e8i | 1.07819i | 0.842244 | + | 0.539097i | \(0.181234\pi\) | ||||
−0.842244 | + | 0.539097i | \(0.818766\pi\) | |||||||
\(102\) | −2.85775e7 | + | 1.38639e7i | −0.264012 | + | 0.128081i | ||||
\(103\) | −1.33889e8 | −1.18959 | −0.594795 | − | 0.803877i | \(-0.702767\pi\) | ||||
−0.594795 | + | 0.803877i | \(0.702767\pi\) | |||||||
\(104\) | 1.62620e7i | 0.139008i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.97118e7 | −0.552183 | ||||||||
\(107\) | 3.67153e7i | 0.280100i | 0.990144 | + | 0.140050i | \(0.0447263\pi\) | ||||
−0.990144 | + | 0.140050i | \(0.955274\pi\) | |||||||
\(108\) | 2.54724e7 | − | 1.16230e8i | 0.187230 | − | 0.854327i | ||||
\(109\) | −1.68006e8 | −1.19020 | −0.595099 | − | 0.803652i | \(-0.702887\pi\) | ||||
−0.595099 | + | 0.803652i | \(0.702887\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.60186e8 | − | 7.77115e7i | 1.05519 | − | 0.511910i | ||||
\(112\) | 7.01873e7 | 0.446053 | ||||||||
\(113\) | − | 9.78362e7i | − | 0.600048i | −0.953932 | − | 0.300024i | \(-0.903005\pi\) | ||
0.953932 | − | 0.300024i | \(-0.0969947\pi\) | |||||||
\(114\) | 3.61466e6 | + | 7.45084e6i | 0.0214017 | + | 0.0441150i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 2.52454e8i | − | 1.39428i | ||||||
\(117\) | 2.42884e7 | − | 3.08198e7i | 0.129615 | − | 0.164470i | ||||
\(118\) | 3.16506e7 | 0.163250 | ||||||||
\(119\) | 1.15901e8i | 0.577963i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.44368e8 | −1.14000 | ||||||||
\(122\) | 1.76793e6i | 0.00798044i | ||||||||
\(123\) | −1.02556e6 | − | 2.11397e6i | −0.00448063 | − | 0.00923586i | ||||
\(124\) | −2.86427e8 | −1.21151 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.88936e7 | + | 3.85319e7i | 0.193986 | + | 0.152876i | ||||
\(127\) | −1.37799e8 | −0.529701 | −0.264851 | − | 0.964289i | \(-0.585323\pi\) | ||||
−0.264851 | + | 0.964289i | \(0.585323\pi\) | |||||||
\(128\) | 2.69810e8i | 1.00512i | ||||||||
\(129\) | 4.94228e8 | − | 2.39767e8i | 1.78471 | − | 0.865824i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.11572e7i | 0.241620i | 0.992676 | + | 0.120810i | \(0.0385492\pi\) | ||||
−0.992676 | + | 0.120810i | \(0.961451\pi\) | |||||||
\(132\) | 1.69543e8 | + | 3.49476e8i | 0.558448 | + | 1.15112i | ||||
\(133\) | 3.02182e7 | 0.0965743 | ||||||||
\(134\) | 4.83582e6i | 0.0149986i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.88185e8 | −0.550084 | ||||||||
\(137\) | − | 5.04740e8i | − | 1.43280i | −0.697689 | − | 0.716400i | \(-0.745788\pi\) | ||
0.697689 | − | 0.716400i | \(-0.254212\pi\) | |||||||
\(138\) | 3.79050e7 | − | 1.83890e7i | 0.104515 | − | 0.0507040i | ||||
\(139\) | −2.09113e8 | −0.560171 | −0.280086 | − | 0.959975i | \(-0.590363\pi\) | ||||
−0.280086 | + | 0.959975i | \(0.590363\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.93271e7 | + | 1.42903e8i | 0.175399 | + | 0.361547i | ||||
\(142\) | 1.80334e8 | 0.443531 | ||||||||
\(143\) | 1.28097e8i | 0.306333i | ||||||||
\(144\) | 1.70208e8 | − | 2.15979e8i | 0.395849 | − | 0.502298i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.34167e7i | 0.0295281i | ||||||||
\(147\) | −2.15747e8 | + | 1.04666e8i | −0.462036 | + | 0.224149i | ||||
\(148\) | 4.92136e8 | 1.02574 | ||||||||
\(149\) | − | 2.19726e8i | − | 0.445796i | −0.974842 | − | 0.222898i | \(-0.928448\pi\) | ||
0.974842 | − | 0.222898i | \(-0.0715517\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.50620e8 | 0.674418 | 0.337209 | − | 0.941430i | \(-0.390517\pi\) | ||||
0.337209 | + | 0.941430i | \(0.390517\pi\) | |||||||
\(152\) | 4.90643e7i | 0.0919160i | ||||||||
\(153\) | 3.56649e8 | + | 2.81066e8i | 0.650841 | + | 0.512912i | ||||
\(154\) | −2.03217e8 | −0.361307 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 9.75889e7 | − | 4.73437e7i | 0.164779 | − | 0.0799399i | ||||
\(157\) | −7.08761e7 | −0.116654 | −0.0583272 | − | 0.998298i | \(-0.518577\pi\) | ||||
−0.0583272 | + | 0.998298i | \(0.518577\pi\) | |||||||
\(158\) | − | 1.65629e8i | − | 0.265771i | ||||||
\(159\) | 4.35003e8 | + | 8.96665e8i | 0.680618 | + | 1.40295i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1.53730e8i | − | 0.228800i | ||||||
\(162\) | 2.37139e8 | − | 5.70125e7i | 0.344305 | − | 0.0827771i | ||||
\(163\) | 7.30934e8 | 1.03545 | 0.517724 | − | 0.855548i | \(-0.326780\pi\) | ||||
0.517724 | + | 0.855548i | \(0.326780\pi\) | |||||||
\(164\) | − | 6.49470e6i | − | 0.00897809i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.81355e8 | 0.502223 | ||||||||
\(167\) | 1.02725e9i | 1.32072i | 0.750948 | + | 0.660361i | \(0.229597\pi\) | ||||
−0.750948 | + | 0.660361i | \(0.770403\pi\) | |||||||
\(168\) | 1.60984e8 | + | 3.31833e8i | 0.202090 | + | 0.416565i | ||||
\(169\) | −7.79961e8 | −0.956150 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.32807e7 | − | 9.29868e7i | 0.0857048 | − | 0.108752i | ||||
\(172\) | 1.51841e9 | 1.73490 | ||||||||
\(173\) | 1.07140e8i | 0.119610i | 0.998210 | + | 0.0598050i | \(0.0190479\pi\) | ||||
−0.998210 | + | 0.0598050i | \(0.980952\pi\) | |||||||
\(174\) | 4.65571e8 | − | 2.25864e8i | 0.507913 | − | 0.246406i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8.97675e8i | 0.935553i | ||||||||
\(177\) | −1.97500e8 | − | 4.07105e8i | −0.201222 | − | 0.414776i | ||||
\(178\) | 2.77763e8 | 0.276690 | ||||||||
\(179\) | 1.76590e8i | 0.172010i | 0.996295 | + | 0.0860051i | \(0.0274101\pi\) | ||||
−0.996295 | + | 0.0860051i | \(0.972590\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.03775e9 | −0.966896 | −0.483448 | − | 0.875373i | \(-0.660616\pi\) | ||||
−0.483448 | + | 0.875373i | \(0.660616\pi\) | |||||||
\(182\) | 5.67469e7i | 0.0517198i | ||||||||
\(183\) | 2.27400e7 | − | 1.10319e7i | 0.0202762 | − | 0.00983666i | ||||
\(184\) | 2.49607e8 | 0.217764 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.56259e8 | − | 5.28223e8i | −0.214105 | − | 0.441332i | ||||
\(187\) | −1.48234e9 | −1.21222 | ||||||||
\(188\) | 4.39039e8i | 0.351456i | ||||||||
\(189\) | 1.90518e8 | − | 8.69332e8i | 0.149310 | − | 0.681300i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 4.41653e8i | − | 0.331854i | −0.986138 | − | 0.165927i | \(-0.946938\pi\) | ||
0.986138 | − | 0.165927i | \(-0.0530617\pi\) | |||||||
\(192\) | 3.96468e8 | − | 1.92340e8i | 0.291745 | − | 0.141535i | ||||
\(193\) | −1.80470e9 | −1.30070 | −0.650349 | − | 0.759635i | \(-0.725377\pi\) | ||||
−0.650349 | + | 0.759635i | \(0.725377\pi\) | |||||||
\(194\) | − | 4.07034e8i | − | 0.287359i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.62837e8 | −0.449141 | ||||||||
\(197\) | − | 1.84458e9i | − | 1.22471i | −0.790583 | − | 0.612355i | \(-0.790222\pi\) | ||
0.790583 | − | 0.612355i | \(-0.209778\pi\) | |||||||
\(198\) | −4.92811e8 | + | 6.25334e8i | −0.320641 | + | 0.406866i | ||||
\(199\) | −1.80610e9 | −1.15167 | −0.575837 | − | 0.817564i | \(-0.695324\pi\) | ||||
−0.575837 | + | 0.817564i | \(0.695324\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.22005e7 | − | 3.01756e7i | 0.0381074 | − | 0.0184872i | ||||
\(202\) | −6.35693e8 | −0.381805 | ||||||||
\(203\) | − | 1.88820e9i | − | 1.11190i | ||||||
\(204\) | 5.47863e8 | + | 1.12930e9i | 0.316338 | + | 0.652063i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 7.58597e8i | − | 0.421253i | ||||||
\(207\) | −4.73056e8 | − | 3.72804e8i | −0.257651 | − | 0.203048i | ||||
\(208\) | 2.50670e8 | 0.133921 | ||||||||
\(209\) | 3.86481e8i | 0.202555i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.94285e8 | 0.148470 | 0.0742350 | − | 0.997241i | \(-0.476349\pi\) | ||||
0.0742350 | + | 0.997241i | \(0.476349\pi\) | |||||||
\(212\) | 2.75481e9i | 1.36379i | ||||||||
\(213\) | −1.12529e9 | − | 2.31954e9i | −0.546695 | − | 1.12689i | ||||
\(214\) | −2.08024e8 | −0.0991876 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.41151e9 | + | 3.09338e8i | 0.648437 | + | 0.142108i | ||||
\(217\) | −2.14230e9 | −0.966143 | ||||||||
\(218\) | − | 9.51897e8i | − | 0.421468i | ||||||
\(219\) | 1.72572e8 | − | 8.37207e7i | 0.0750230 | − | 0.0363962i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.13934e8i | 0.173525i | ||||||||
\(222\) | 4.40302e8 | + | 9.07588e8i | 0.181275 | + | 0.373660i | ||||
\(223\) | −3.54930e9 | −1.43523 | −0.717617 | − | 0.696438i | \(-0.754767\pi\) | ||||
−0.717617 | + | 0.696438i | \(0.754767\pi\) | |||||||
\(224\) | 1.56333e9i | 0.620952i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.54325e8 | 0.212486 | ||||||||
\(227\) | − | 3.07376e9i | − | 1.15762i | −0.815461 | − | 0.578811i | \(-0.803517\pi\) | ||
0.815461 | − | 0.578811i | \(-0.196483\pi\) | |||||||
\(228\) | 2.94436e8 | − | 1.42841e8i | 0.108956 | − | 0.0528583i | ||||
\(229\) | 2.58716e9 | 0.940767 | 0.470383 | − | 0.882462i | \(-0.344116\pi\) | ||||
0.470383 | + | 0.882462i | \(0.344116\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.26808e9 | + | 2.61387e9i | 0.445346 | + | 0.917985i | ||||
\(232\) | 3.06582e9 | 1.05826 | ||||||||
\(233\) | 4.46492e9i | 1.51492i | 0.652882 | + | 0.757460i | \(0.273560\pi\) | ||||
−0.652882 | + | 0.757460i | \(0.726440\pi\) | |||||||
\(234\) | 1.74621e8 | + | 1.37614e8i | 0.0582414 | + | 0.0458987i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 1.25074e9i | − | 0.403199i | ||||||
\(237\) | −2.13039e9 | + | 1.03353e9i | −0.675253 | + | 0.327588i | ||||
\(238\) | −6.56678e8 | −0.204666 | ||||||||
\(239\) | − | 2.49405e9i | − | 0.764388i | −0.924082 | − | 0.382194i | \(-0.875169\pi\) | ||
0.924082 | − | 0.382194i | \(-0.124831\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.06935e9 | −0.316993 | −0.158497 | − | 0.987360i | \(-0.550665\pi\) | ||||
−0.158497 | + | 0.987360i | \(0.550665\pi\) | |||||||
\(242\) | − | 1.38455e9i | − | 0.403691i | ||||||
\(243\) | −2.21307e9 | − | 2.69443e9i | −0.634703 | − | 0.772756i | ||||
\(244\) | 6.98637e7 | 0.0197103 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.19774e7 | − | 5.81065e6i | 0.00327056 | − | 0.00158666i | ||||
\(247\) | 1.07922e8 | 0.0289951 | ||||||||
\(248\) | − | 3.47838e9i | − | 0.919540i | ||||||
\(249\) | −2.37966e9 | − | 4.90516e9i | −0.619039 | − | 1.27602i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.58790e9i | 0.652007i | 0.945369 | + | 0.326003i | \(0.105702\pi\) | ||||
−0.945369 | + | 0.326003i | \(0.894298\pi\) | |||||||
\(252\) | 1.52267e9 | − | 1.93214e9i | 0.377575 | − | 0.479110i | ||||
\(253\) | 1.96617e9 | 0.479886 | ||||||||
\(254\) | − | 7.80748e8i | − | 0.187575i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.35998e8 | −0.0316644 | ||||||||
\(257\) | 3.99995e9i | 0.916900i | 0.888720 | + | 0.458450i | \(0.151595\pi\) | ||||
−0.888720 | + | 0.458450i | \(0.848405\pi\) | |||||||
\(258\) | 1.35848e9 | + | 2.80022e9i | 0.306602 | + | 0.631994i | ||||
\(259\) | 3.68088e9 | 0.817999 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.81035e9 | − | 4.57900e9i | −1.25210 | − | 0.986753i | ||||
\(262\) | −4.03166e8 | −0.0855615 | ||||||||
\(263\) | 2.61772e9i | 0.547142i | 0.961852 | + | 0.273571i | \(0.0882048\pi\) | ||||
−0.961852 | + | 0.273571i | \(0.911795\pi\) | |||||||
\(264\) | −4.24405e9 | + | 2.05893e9i | −0.873705 | + | 0.423864i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.71212e8i | 0.0341985i | ||||||||
\(267\) | −1.73324e9 | − | 3.57271e9i | −0.341047 | − | 0.702996i | ||||
\(268\) | 1.91098e8 | 0.0370439 | ||||||||
\(269\) | 6.21608e9i | 1.18715i | 0.804777 | + | 0.593577i | \(0.202285\pi\) | ||||
−0.804777 | + | 0.593577i | \(0.797715\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.31021e9 | 0.984543 | 0.492271 | − | 0.870442i | \(-0.336167\pi\) | ||||
0.492271 | + | 0.870442i | \(0.336167\pi\) | |||||||
\(272\) | 2.90076e9i | 0.529952i | ||||||||
\(273\) | 7.29906e8 | − | 3.54102e8i | 0.131406 | − | 0.0637496i | ||||
\(274\) | 2.85978e9 | 0.507377 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −7.26681e8 | − | 1.49790e9i | −0.125230 | − | 0.258135i | ||||
\(277\) | −2.24918e9 | −0.382037 | −0.191018 | − | 0.981586i | \(-0.561179\pi\) | ||||
−0.191018 | + | 0.981586i | \(0.561179\pi\) | |||||||
\(278\) | − | 1.18480e9i | − | 0.198365i | ||||||
\(279\) | −5.19519e9 | + | 6.59224e9i | −0.857403 | + | 1.08797i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 7.68684e9i | − | 1.23289i | −0.787400 | − | 0.616443i | \(-0.788573\pi\) | ||
0.787400 | − | 0.616443i | \(-0.211427\pi\) | |||||||
\(282\) | −8.09667e8 | + | 3.92797e8i | −0.128029 | + | 0.0621114i | ||||
\(283\) | 7.20498e9 | 1.12328 | 0.561639 | − | 0.827382i | \(-0.310171\pi\) | ||||
0.561639 | + | 0.827382i | \(0.310171\pi\) | |||||||
\(284\) | − | 7.12628e9i | − | 1.09544i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.25776e8 | −0.108477 | ||||||||
\(287\) | − | 4.85765e7i | − | 0.00715976i | ||||||
\(288\) | 4.81064e9 | + | 3.79115e9i | 0.699251 | + | 0.551063i | ||||
\(289\) | 2.18569e9 | 0.313327 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.23547e9 | + | 2.53990e9i | −0.730102 | + | 0.354197i | ||||
\(292\) | 5.30191e8 | 0.0729291 | ||||||||
\(293\) | − | 3.98677e9i | − | 0.540942i | −0.962728 | − | 0.270471i | \(-0.912821\pi\) | ||
0.962728 | − | 0.270471i | \(-0.0871794\pi\) | |||||||
\(294\) | −5.93023e8 | − | 1.22239e9i | −0.0793748 | − | 0.163614i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.97653e9i | 0.778542i | ||||||||
\(297\) | 1.11185e10 | + | 2.43667e9i | 1.42896 | + | 0.313163i | ||||
\(298\) | 1.24493e9 | 0.157863 | ||||||||
\(299\) | − | 5.49039e8i | − | 0.0686940i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.13568e10 | 1.38353 | ||||||||
\(302\) | 1.98656e9i | 0.238822i | ||||||||
\(303\) | 3.96674e9 | + | 8.17658e9i | 0.470612 | + | 0.970066i | ||||
\(304\) | 7.56298e8 | 0.0885520 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.59248e9 | + | 2.02072e9i | −0.181630 | + | 0.230473i | ||||
\(307\) | 9.29130e9 | 1.04598 | 0.522990 | − | 0.852339i | \(-0.324817\pi\) | ||||
0.522990 | + | 0.852339i | \(0.324817\pi\) | |||||||
\(308\) | 8.03054e9i | 0.892364i | ||||||||
\(309\) | −9.75743e9 | + | 4.73366e9i | −1.07029 | + | 0.519234i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.12048e10i | 1.19774i | 0.800847 | + | 0.598869i | \(0.204383\pi\) | ||||
−0.800847 | + | 0.598869i | \(0.795617\pi\) | |||||||
\(312\) | 5.74944e8 | + | 1.18512e9i | 0.0606746 | + | 0.125068i | ||||
\(313\) | 9.45147e9 | 0.984741 | 0.492371 | − | 0.870386i | \(-0.336130\pi\) | ||||
0.492371 | + | 0.870386i | \(0.336130\pi\) | |||||||
\(314\) | − | 4.01573e8i | − | 0.0413092i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.54518e9 | −0.656407 | ||||||||
\(317\) | − | 8.48385e8i | − | 0.0840148i | −0.999117 | − | 0.0420074i | \(-0.986625\pi\) | ||
0.999117 | − | 0.0420074i | \(-0.0133753\pi\) | |||||||
\(318\) | −5.08037e9 | + | 2.46466e9i | −0.496806 | + | 0.241017i | ||||
\(319\) | 2.41496e10 | 2.33210 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.29807e9 | + | 2.67570e9i | 0.122258 | + | 0.252009i | ||||
\(322\) | 8.71013e8 | 0.0810217 | ||||||||
\(323\) | 1.24888e9i | 0.114739i | ||||||||
\(324\) | −2.25297e9 | − | 9.37106e9i | −0.204445 | − | 0.850371i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.14136e9i | 0.366668i | ||||||||
\(327\) | −1.22437e10 | + | 5.93986e9i | −1.07084 | + | 0.519499i | ||||
\(328\) | 7.88720e7 | 0.00681440 | ||||||||
\(329\) | 3.28374e9i | 0.280276i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.71539e9 | 0.392831 | 0.196415 | − | 0.980521i | \(-0.437070\pi\) | ||||
0.196415 | + | 0.980521i | \(0.437070\pi\) | |||||||
\(332\) | − | 1.50701e10i | − | 1.24040i | ||||||
\(333\) | 8.92633e9 | − | 1.13267e10i | 0.725932 | − | 0.921144i | ||||
\(334\) | −5.82026e9 | −0.467688 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 5.11503e9 | − | 2.48147e9i | 0.401320 | − | 0.194694i | ||||
\(337\) | 3.45801e8 | 0.0268106 | 0.0134053 | − | 0.999910i | \(-0.495733\pi\) | ||||
0.0134053 | + | 0.999910i | \(0.495733\pi\) | |||||||
\(338\) | − | 4.41914e9i | − | 0.338587i | ||||||
\(339\) | −3.45900e9 | − | 7.12999e9i | −0.261910 | − | 0.539871i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 2.73994e10i | − | 2.02639i | ||||||
\(342\) | 5.26849e8 | + | 4.15197e8i | 0.0385107 | + | 0.0303494i | ||||
\(343\) | −1.46115e10 | −1.05565 | ||||||||
\(344\) | 1.84396e10i | 1.31679i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.07040e8 | −0.0423558 | ||||||||
\(347\) | 3.52962e9i | 0.243450i | 0.992564 | + | 0.121725i | \(0.0388426\pi\) | ||||
−0.992564 | + | 0.121725i | \(0.961157\pi\) | |||||||
\(348\) | −8.92552e9 | − | 1.83980e10i | −0.608578 | − | 1.25445i | ||||
\(349\) | −8.25013e9 | −0.556108 | −0.278054 | − | 0.960565i | \(-0.589689\pi\) | ||||
−0.278054 | + | 0.960565i | \(0.589689\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.80424e8 | − | 3.10477e9i | 0.0448282 | − | 0.204550i | ||||
\(352\) | −1.99945e10 | −1.30239 | ||||||||
\(353\) | 1.08036e10i | 0.695776i | 0.937536 | + | 0.347888i | \(0.113101\pi\) | ||||
−0.937536 | + | 0.347888i | \(0.886899\pi\) | |||||||
\(354\) | 2.30659e9 | − | 1.11901e9i | 0.146878 | − | 0.0712557i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 1.09764e10i | − | 0.683375i | ||||||
\(357\) | 4.09768e9 | + | 8.44650e9i | 0.252270 | + | 0.520001i | ||||
\(358\) | −1.00053e9 | −0.0609115 | ||||||||
\(359\) | − | 1.78116e10i | − | 1.07232i | −0.844115 | − | 0.536162i | \(-0.819874\pi\) | ||
0.844115 | − | 0.536162i | \(-0.180126\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.66579e10 | −0.980828 | ||||||||
\(362\) | − | 5.87975e9i | − | 0.342393i | ||||||
\(363\) | −1.78088e10 | + | 8.63965e9i | −1.02567 | + | 0.497587i | ||||
\(364\) | 2.24248e9 | 0.127739 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6.25053e7 | + | 1.28841e8i | 0.00348331 | + | 0.00718011i | ||||
\(367\) | 7.25059e9 | 0.399677 | 0.199839 | − | 0.979829i | \(-0.435958\pi\) | ||||
0.199839 | + | 0.979829i | \(0.435958\pi\) | |||||||
\(368\) | − | 3.84755e9i | − | 0.209794i | ||||||
\(369\) | −1.49478e8 | − | 1.17800e8i | −0.00806256 | − | 0.00635392i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.06043e10i | 1.08758i | ||||||||
\(372\) | −2.08739e10 | + | 1.01266e10i | −1.09001 | + | 0.528802i | ||||
\(373\) | −1.40594e10 | −0.726325 | −0.363163 | − | 0.931726i | \(-0.618303\pi\) | ||||
−0.363163 | + | 0.931726i | \(0.618303\pi\) | |||||||
\(374\) | − | 8.39872e9i | − | 0.429266i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.33171e9 | −0.266757 | ||||||||
\(377\) | − | 6.74361e9i | − | 0.333831i | ||||||
\(378\) | 4.92550e9 | + | 1.07945e9i | 0.241259 | + | 0.0528730i | ||||
\(379\) | −9.41156e9 | −0.456147 | −0.228073 | − | 0.973644i | \(-0.573243\pi\) | ||||
−0.228073 | + | 0.973644i | \(0.573243\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.00423e10 | + | 4.87188e9i | −0.476579 | + | 0.231205i | ||||
\(382\) | 2.50234e9 | 0.117515 | ||||||||
\(383\) | − | 2.22515e10i | − | 1.03410i | −0.855954 | − | 0.517052i | \(-0.827029\pi\) | ||
0.855954 | − | 0.517052i | \(-0.172971\pi\) | |||||||
\(384\) | 9.53913e9 | + | 1.96629e10i | 0.438716 | + | 0.904320i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 1.02252e10i | − | 0.460598i | ||||||
\(387\) | 2.75408e10 | − | 3.49468e10i | 1.22781 | − | 1.55799i | ||||
\(388\) | −1.60848e10 | −0.709725 | ||||||||
\(389\) | − | 1.67518e10i | − | 0.731582i | −0.930697 | − | 0.365791i | \(-0.880798\pi\) | ||
0.930697 | − | 0.365791i | \(-0.119202\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.35351e9 | 0.271836 | ||||||||
\(392\) | − | 8.04952e9i | − | 0.340899i | ||||||
\(393\) | 2.51576e9 | + | 5.18570e9i | 0.105463 | + | 0.217389i | ||||
\(394\) | 1.04511e10 | 0.433689 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.47114e10 | + | 1.94745e10i | 1.00489 | + | 0.791927i | ||||
\(397\) | 3.88428e9 | 0.156368 | 0.0781840 | − | 0.996939i | \(-0.475088\pi\) | ||||
0.0781840 | + | 0.996939i | \(0.475088\pi\) | |||||||
\(398\) | − | 1.02331e10i | − | 0.407826i | ||||||
\(399\) | 2.20220e9 | − | 1.06836e9i | 0.0868892 | − | 0.0421529i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.28950e10i | 1.27219i | 0.771610 | + | 0.636096i | \(0.219452\pi\) | ||||
−0.771610 | + | 0.636096i | \(0.780548\pi\) | |||||||
\(402\) | 1.70970e8 | + | 3.52419e8i | 0.00654661 | + | 0.0134944i | ||||
\(403\) | −7.65110e9 | −0.290071 | ||||||||
\(404\) | 2.51208e10i | 0.942991i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.06983e10 | 0.393740 | ||||||||
\(407\) | 4.70774e10i | 1.71567i | ||||||||
\(408\) | −1.37143e10 | + | 6.65327e9i | −0.494918 | + | 0.240101i | ||||
\(409\) | 1.08495e9 | 0.0387718 | 0.0193859 | − | 0.999812i | \(-0.493829\pi\) | ||||
0.0193859 | + | 0.999812i | \(0.493829\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.78451e10 | − | 3.67838e10i | −0.625391 | − | 1.28911i | ||||
\(412\) | −2.99776e10 | −1.04042 | ||||||||
\(413\) | − | 9.35479e9i | − | 0.321539i | ||||||
\(414\) | 2.11225e9 | − | 2.68026e9i | 0.0719026 | − | 0.0912381i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.58334e9i | 0.186432i | ||||||||
\(417\) | −1.52395e10 | + | 7.39317e9i | −0.503994 | + | 0.244504i | ||||
\(418\) | −2.18974e9 | −0.0717279 | ||||||||
\(419\) | 3.39202e10i | 1.10053i | 0.834990 | + | 0.550266i | \(0.185474\pi\) | ||||
−0.834990 | + | 0.550266i | \(0.814526\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.88554e10 | 0.918542 | 0.459271 | − | 0.888296i | \(-0.348111\pi\) | ||||
0.459271 | + | 0.888296i | \(0.348111\pi\) | |||||||
\(422\) | 1.66738e9i | 0.0525755i | ||||||||
\(423\) | 1.01047e10 | + | 7.96325e9i | 0.315617 | + | 0.248731i | ||||
\(424\) | −3.34546e10 | −1.03512 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.31422e10 | − | 6.37570e9i | 0.399051 | − | 0.193593i | ||||
\(427\) | 5.22539e8 | 0.0157183 | ||||||||
\(428\) | 8.22050e9i | 0.244976i | ||||||||
\(429\) | 4.52886e9 | + | 9.33527e9i | 0.133709 | + | 0.275612i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 7.99799e8i | − | 0.0231778i | −0.999933 | − | 0.0115889i | \(-0.996311\pi\) | ||
0.999933 | − | 0.0115889i | \(-0.00368894\pi\) | |||||||
\(432\) | 4.76827e9 | − | 2.17576e10i | 0.136907 | − | 0.624705i | ||||
\(433\) | 2.02420e10 | 0.575839 | 0.287920 | − | 0.957655i | \(-0.407036\pi\) | ||||
0.287920 | + | 0.957655i | \(0.407036\pi\) | |||||||
\(434\) | − | 1.21380e10i | − | 0.342126i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.76163e10 | −1.04095 | ||||||||
\(437\) | − | 1.65651e9i | − | 0.0454222i | ||||||
\(438\) | 4.74349e8 | + | 9.77768e8i | 0.0128885 | + | 0.0265668i | ||||
\(439\) | −4.16160e10 | −1.12048 | −0.560238 | − | 0.828332i | \(-0.689290\pi\) | ||||
−0.560238 | + | 0.828332i | \(0.689290\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.20225e10 | + | 1.52555e10i | −0.317863 | + | 0.403340i | ||||
\(442\) | −2.34529e9 | −0.0614479 | ||||||||
\(443\) | − | 1.00330e10i | − | 0.260504i | −0.991481 | − | 0.130252i | \(-0.958421\pi\) | ||
0.991481 | − | 0.130252i | \(-0.0415787\pi\) | |||||||
\(444\) | 3.58653e10 | − | 1.73995e10i | 0.922874 | − | 0.447718i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 2.01098e10i | − | 0.508239i | ||||||
\(447\) | −7.76841e9 | − | 1.60129e10i | −0.194582 | − | 0.401088i | ||||
\(448\) | 9.11037e9 | 0.226164 | ||||||||
\(449\) | − | 2.59211e10i | − | 0.637775i | −0.947793 | − | 0.318888i | \(-0.896691\pi\) | ||
0.947793 | − | 0.318888i | \(-0.103309\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.21278e8 | 0.0150169 | ||||||||
\(452\) | − | 2.19054e10i | − | 0.524803i | ||||||
\(453\) | 2.55521e10 | − | 1.23962e10i | 0.606783 | − | 0.294371i | ||||
\(454\) | 1.74155e10 | 0.409932 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.73467e9 | + | 3.57565e9i | 0.0401196 | + | 0.0826980i | ||||
\(457\) | 5.83258e10 | 1.33720 | 0.668599 | − | 0.743623i | \(-0.266894\pi\) | ||||
0.668599 | + | 0.743623i | \(0.266894\pi\) | |||||||
\(458\) | 1.46585e10i | 0.333140i | ||||||||
\(459\) | 3.59285e10 | + | 7.87390e9i | 0.809447 | + | 0.177394i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 2.73170e10i | − | 0.604825i | −0.953177 | − | 0.302412i | \(-0.902208\pi\) | ||
0.953177 | − | 0.302412i | \(-0.0977920\pi\) | |||||||
\(462\) | −1.48098e10 | + | 7.18472e9i | −0.325073 | + | 0.157704i | ||||
\(463\) | 5.50831e10 | 1.19866 | 0.599328 | − | 0.800504i | \(-0.295435\pi\) | ||||
0.599328 | + | 0.800504i | \(0.295435\pi\) | |||||||
\(464\) | − | 4.72578e10i | − | 1.01953i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.52975e10 | −0.536456 | ||||||||
\(467\) | 4.06476e10i | 0.854610i | 0.904108 | + | 0.427305i | \(0.140537\pi\) | ||||
−0.904108 | + | 0.427305i | \(0.859463\pi\) | |||||||
\(468\) | 5.43813e9 | − | 6.90051e9i | 0.113362 | − | 0.143846i | ||||
\(469\) | 1.42929e9 | 0.0295414 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.16522e9 | + | 2.50582e9i | −0.104956 | + | 0.0509175i | ||||
\(472\) | 1.51891e10 | 0.306029 | ||||||||
\(473\) | 1.45250e11i | 2.90182i | ||||||||
\(474\) | −5.85580e9 | − | 1.20705e10i | −0.116004 | − | 0.239118i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.59501e10i | 0.505488i | ||||||||
\(477\) | 6.34032e10 | + | 4.99666e10i | 1.22472 | + | 0.965175i | ||||
\(478\) | 1.41309e10 | 0.270682 | ||||||||
\(479\) | 1.08547e10i | 0.206194i | 0.994671 | + | 0.103097i | \(0.0328752\pi\) | ||||
−0.994671 | + | 0.103097i | \(0.967125\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.31460e10 | 0.245592 | ||||||||
\(482\) | − | 6.05876e9i | − | 0.112252i | ||||||
\(483\) | −5.43514e9 | − | 1.12034e10i | −0.0998670 | − | 0.205855i | ||||
\(484\) | −5.47137e10 | −0.997044 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.52663e10 | − | 1.25389e10i | 0.273645 | − | 0.224758i | ||||
\(487\) | 1.77991e10 | 0.316433 | 0.158216 | − | 0.987404i | \(-0.449426\pi\) | ||||
0.158216 | + | 0.987404i | \(0.449426\pi\) | |||||||
\(488\) | 8.48429e8i | 0.0149602i | ||||||||
\(489\) | 5.32681e10 | − | 2.58422e10i | 0.931606 | − | 0.451953i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 7.93615e10i | − | 1.36547i | −0.730664 | − | 0.682737i | \(-0.760789\pi\) | ||
0.730664 | − | 0.682737i | \(-0.239211\pi\) | |||||||
\(492\) | −2.29620e8 | − | 4.73313e8i | −0.00391877 | − | 0.00807771i | ||||
\(493\) | 7.80374e10 | 1.32104 | ||||||||
\(494\) | 6.11472e8i | 0.0102676i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.36173e10 | −0.885887 | ||||||||
\(497\) | − | 5.33003e10i | − | 0.873582i | ||||||
\(498\) | 2.77919e10 | − | 1.34828e10i | 0.451857 | − | 0.219211i | ||||
\(499\) | −6.54034e10 | −1.05487 | −0.527434 | − | 0.849596i | \(-0.676846\pi\) | ||||
−0.527434 | + | 0.849596i | \(0.676846\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.63185e10 | + | 7.48629e10i | 0.576471 | + | 1.18827i | ||||
\(502\) | −1.46626e10 | −0.230886 | ||||||||
\(503\) | − | 1.01074e11i | − | 1.57894i | −0.613788 | − | 0.789471i | \(-0.710355\pi\) | ||
0.613788 | − | 0.789471i | \(-0.289645\pi\) | |||||||
\(504\) | 2.34639e10 | + | 1.84914e10i | 0.363646 | + | 0.286581i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.11400e10i | 0.169935i | ||||||||
\(507\) | −5.68410e10 | + | 2.75755e10i | −0.860260 | + | 0.417341i | ||||
\(508\) | −3.08529e10 | −0.463278 | ||||||||
\(509\) | 1.19907e11i | 1.78638i | 0.449681 | + | 0.893189i | \(0.351538\pi\) | ||||
−0.449681 | + | 0.893189i | \(0.648462\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.96551e9 | 0.0581588 | ||||||||
\(512\) | 6.83008e10i | 0.993908i | ||||||||
\(513\) | 2.05291e9 | − | 9.36741e9i | 0.0296416 | − | 0.135254i | ||||
\(514\) | −2.26631e10 | −0.324689 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.10657e11 | − | 5.36833e10i | 1.56091 | − | 0.757252i | ||||
\(517\) | −4.19981e10 | −0.587851 | ||||||||
\(518\) | 2.08553e10i | 0.289666i | ||||||||
\(519\) | 3.78794e9 | + | 7.80802e9i | 0.0522076 | + | 0.107615i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.21461e11i | 1.64849i | 0.566230 | + | 0.824247i | \(0.308401\pi\) | ||||
−0.566230 | + | 0.824247i | \(0.691599\pi\) | |||||||
\(522\) | 2.59439e10 | − | 3.29205e10i | 0.349424 | − | 0.443389i | ||||
\(523\) | −8.02894e10 | −1.07313 | −0.536564 | − | 0.843860i | \(-0.680278\pi\) | ||||
−0.536564 | + | 0.843860i | \(0.680278\pi\) | |||||||
\(524\) | 1.59320e10i | 0.211322i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.48316e10 | −0.193751 | ||||||||
\(527\) | − | 8.85389e10i | − | 1.14787i | ||||||
\(528\) | 3.17373e10 | + | 6.54196e10i | 0.408351 | + | 0.841729i | ||||
\(529\) | 6.98837e10 | 0.892387 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.87864e10 | − | 2.26859e10i | −0.362084 | − | 0.285350i | ||||
\(532\) | 6.76580e9 | 0.0844641 | ||||||||
\(533\) | − | 1.73488e8i | − | 0.00214961i | ||||||
\(534\) | 2.02424e10 | − | 9.82029e9i | 0.248942 | − | 0.120770i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.32070e9i | 0.0281164i | ||||||||
\(537\) | 6.24334e9 | + | 1.28693e10i | 0.0750793 | + | 0.154760i | ||||
\(538\) | −3.52193e10 | −0.420390 | ||||||||
\(539\) | − | 6.34064e10i | − | 0.751239i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.31499e10 | 0.270246 | 0.135123 | − | 0.990829i | \(-0.456857\pi\) | ||||
0.135123 | + | 0.990829i | \(0.456857\pi\) | |||||||
\(542\) | 3.00868e10i | 0.348642i | ||||||||
\(543\) | −7.56281e10 | + | 3.66897e10i | −0.869929 | + | 0.422032i | ||||
\(544\) | −6.46106e10 | −0.737748 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.00629e9 | + | 4.13553e9i | 0.0225747 | + | 0.0465330i | ||||
\(547\) | −1.06905e11 | −1.19412 | −0.597061 | − | 0.802196i | \(-0.703665\pi\) | ||||
−0.597061 | + | 0.802196i | \(0.703665\pi\) | |||||||
\(548\) | − | 1.13010e11i | − | 1.25313i | ||||||
\(549\) | 1.26718e9 | − | 1.60794e9i | 0.0139492 | − | 0.0177003i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 2.03462e10i | − | 0.220738i | ||||||
\(552\) | 1.81906e10 | − | 8.82485e9i | 0.195925 | − | 0.0950498i | ||||
\(553\) | −4.89540e10 | −0.523465 | ||||||||
\(554\) | − | 1.27435e10i | − | 0.135285i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.68199e10 | −0.489927 | ||||||||
\(557\) | − | 3.49063e10i | − | 0.362646i | −0.983424 | − | 0.181323i | \(-0.941962\pi\) | ||
0.983424 | − | 0.181323i | \(-0.0580379\pi\) | |||||||
\(558\) | −3.73507e10 | − | 2.94352e10i | −0.385267 | − | 0.303620i | ||||
\(559\) | 4.05600e10 | 0.415385 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.08028e11 | + | 5.24081e10i | −1.09065 | + | 0.529112i | ||||
\(562\) | 4.35525e10 | 0.436584 | ||||||||
\(563\) | − | 1.11294e10i | − | 0.110775i | −0.998465 | − | 0.0553873i | \(-0.982361\pi\) | ||
0.998465 | − | 0.0553873i | \(-0.0176393\pi\) | |||||||
\(564\) | 1.55222e10 | + | 3.19957e10i | 0.153404 | + | 0.316210i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4.08223e10i | 0.397770i | ||||||||
\(567\) | −1.68509e10 | − | 7.00899e10i | −0.163038 | − | 0.678146i | ||||
\(568\) | 8.65419e10 | 0.831444 | ||||||||
\(569\) | − | 1.10613e11i | − | 1.05526i | −0.849475 | − | 0.527629i | \(-0.823081\pi\) | ||
0.849475 | − | 0.527629i | \(-0.176919\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.15777e10 | −0.297055 | −0.148527 | − | 0.988908i | \(-0.547453\pi\) | ||||
−0.148527 | + | 0.988908i | \(0.547453\pi\) | |||||||
\(572\) | 2.86806e10i | 0.267919i | ||||||||
\(573\) | −1.56146e10 | − | 3.21862e10i | −0.144848 | − | 0.298574i | ||||
\(574\) | 2.75227e8 | 0.00253538 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.20931e10 | − | 2.80343e10i | 0.200709 | − | 0.254683i | ||||
\(577\) | 3.66049e10 | 0.330245 | 0.165123 | − | 0.986273i | \(-0.447198\pi\) | ||||
0.165123 | + | 0.986273i | \(0.447198\pi\) | |||||||
\(578\) | 1.23838e10i | 0.110954i | ||||||||
\(579\) | −1.31521e11 | + | 6.38053e10i | −1.17026 | + | 0.567731i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 1.12715e11i | − | 0.989184i | ||||||
\(582\) | −1.43907e10 | − | 2.96634e10i | −0.125427 | − | 0.258540i | ||||
\(583\) | −2.63523e11 | −2.28110 | ||||||||
\(584\) | 6.43867e9i | 0.0553534i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.25884e10 | 0.191556 | ||||||||
\(587\) | 5.45783e10i | 0.459693i | 0.973227 | + | 0.229846i | \(0.0738223\pi\) | ||||
−0.973227 | + | 0.229846i | \(0.926178\pi\) | |||||||
\(588\) | −4.83054e10 | + | 2.34346e10i | −0.404098 | + | 0.196042i | ||||
\(589\) | −2.30842e10 | −0.191802 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.52152e10 | − | 1.34427e11i | −0.534563 | − | 1.10189i | ||||
\(592\) | 9.21248e10 | 0.750049 | ||||||||
\(593\) | − | 8.35997e10i | − | 0.676061i | −0.941135 | − | 0.338031i | \(-0.890239\pi\) | ||
0.941135 | − | 0.338031i | \(-0.109761\pi\) | |||||||
\(594\) | −1.38058e10 | + | 6.29957e10i | −0.110896 | + | 0.506017i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 4.91962e10i | − | 0.389894i | ||||||
\(597\) | −1.31623e11 | + | 6.38547e10i | −1.03618 | + | 0.502684i | ||||
\(598\) | 3.11077e9 | 0.0243256 | ||||||||
\(599\) | − | 1.39529e10i | − | 0.108382i | −0.998531 | − | 0.0541909i | \(-0.982742\pi\) | ||
0.998531 | − | 0.0541909i | \(-0.0172579\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.42138e11 | 1.85595 | 0.927974 | − | 0.372645i | \(-0.121549\pi\) | ||||
0.927974 | + | 0.372645i | \(0.121549\pi\) | |||||||
\(602\) | 6.43457e10i | 0.489930i | ||||||||
\(603\) | 3.46612e9 | − | 4.39820e9i | 0.0262164 | − | 0.0332664i | ||||
\(604\) | 7.85032e10 | 0.589847 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −4.63273e10 | + | 2.24749e10i | −0.343515 | + | 0.166651i | ||||
\(607\) | −1.24176e11 | −0.914712 | −0.457356 | − | 0.889284i | \(-0.651203\pi\) | ||||
−0.457356 | + | 0.889284i | \(0.651203\pi\) | |||||||
\(608\) | 1.68455e10i | 0.123274i | ||||||||
\(609\) | −6.67575e10 | − | 1.37606e11i | −0.485323 | − | 1.00039i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.17277e10i | 0.0841488i | ||||||||
\(612\) | 7.98530e10 | + | 6.29302e10i | 0.569227 | + | 0.448594i | ||||
\(613\) | 1.73317e11 | 1.22743 | 0.613717 | − | 0.789526i | \(-0.289673\pi\) | ||||
0.613717 | + | 0.789526i | \(0.289673\pi\) | |||||||
\(614\) | 5.26431e10i | 0.370397i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.75233e10 | −0.677307 | ||||||||
\(617\) | − | 1.52659e11i | − | 1.05337i | −0.850060 | − | 0.526687i | \(-0.823434\pi\) | ||
0.850060 | − | 0.526687i | \(-0.176566\pi\) | |||||||
\(618\) | −2.68202e10 | − | 5.52841e10i | −0.183869 | − | 0.379006i | ||||
\(619\) | 2.41342e11 | 1.64388 | 0.821942 | − | 0.569571i | \(-0.192891\pi\) | ||||
0.821942 | + | 0.569571i | \(0.192891\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.76553e10 | − | 1.04439e10i | −0.320439 | − | 0.0702256i | ||||
\(622\) | −6.34846e10 | −0.424137 | ||||||||
\(623\) | − | 8.20967e10i | − | 0.544971i | ||||||
\(624\) | 1.82680e10 | − | 8.86243e9i | 0.120491 | − | 0.0584541i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 5.35506e10i | 0.348712i | ||||||||
\(627\) | 1.36640e10 | + | 2.81655e10i | 0.0884116 | + | 0.182242i | ||||
\(628\) | −1.58690e10 | −0.102026 | ||||||||
\(629\) | 1.52127e11i | 0.971858i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.68033e11 | 1.05993 | 0.529966 | − | 0.848019i | \(-0.322205\pi\) | ||||
0.529966 | + | 0.848019i | \(0.322205\pi\) | |||||||
\(632\) | − | 7.94849e10i | − | 0.498215i | ||||||
\(633\) | 2.14466e10 | − | 1.04045e10i | 0.133580 | − | 0.0648044i | ||||
\(634\) | 4.80682e9 | 0.0297510 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 9.73963e10 | + | 2.00762e11i | 0.595270 | + | 1.22702i | ||||
\(637\) | −1.77058e10 | −0.107537 | ||||||||
\(638\) | 1.36828e11i | 0.825832i | ||||||||
\(639\) | −1.64015e11 | − | 1.29256e11i | −0.983737 | − | 0.775260i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.07087e11i | 0.634313i | 0.948373 | + | 0.317156i | \(0.102728\pi\) | ||||
−0.948373 | + | 0.317156i | \(0.897272\pi\) | |||||||
\(642\) | −1.51601e10 | + | 7.35467e9i | −0.0892404 | + | 0.0432935i | ||||
\(643\) | −1.21734e11 | −0.712142 | −0.356071 | − | 0.934459i | \(-0.615884\pi\) | ||||
−0.356071 | + | 0.934459i | \(0.615884\pi\) | |||||||
\(644\) | − | 3.44200e10i | − | 0.200109i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.07598e9 | −0.0406309 | ||||||||
\(647\) | − | 1.91646e11i | − | 1.09366i | −0.837244 | − | 0.546829i | \(-0.815835\pi\) | ||
0.837244 | − | 0.546829i | \(-0.184165\pi\) | |||||||
\(648\) | 1.13803e11 | − | 2.73602e10i | 0.645434 | − | 0.155174i | ||||
\(649\) | 1.19645e11 | 0.674397 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.56124e11 | + | 7.57410e10i | −0.869252 | + | 0.421704i | ||||
\(652\) | 1.63655e11 | 0.905604 | ||||||||
\(653\) | 1.71426e11i | 0.942811i | 0.881917 | + | 0.471406i | \(0.156253\pi\) | ||||
−0.881917 | + | 0.471406i | \(0.843747\pi\) | |||||||
\(654\) | −3.36543e10 | − | 6.93712e10i | −0.183963 | − | 0.379200i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 1.21577e9i | − | 0.00656500i | ||||||
\(657\) | 9.61657e9 | − | 1.22026e10i | 0.0516129 | − | 0.0654923i | ||||
\(658\) | −1.86052e10 | −0.0992501 | ||||||||
\(659\) | − | 6.16692e10i | − | 0.326984i | −0.986545 | − | 0.163492i | \(-0.947724\pi\) | ||
0.986545 | − | 0.163492i | \(-0.0522758\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.25974e10 | 0.118373 | 0.0591864 | − | 0.998247i | \(-0.481149\pi\) | ||||
0.0591864 | + | 0.998247i | \(0.481149\pi\) | |||||||
\(662\) | 2.67167e10i | 0.139107i | ||||||||
\(663\) | 1.46346e10 | + | 3.01662e10i | 0.0757404 | + | 0.156123i | ||||
\(664\) | 1.83012e11 | 0.941469 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.41755e10 | + | 5.05752e10i | 0.326192 | + | 0.257064i | ||||
\(667\) | −1.03508e11 | −0.522964 | ||||||||
\(668\) | 2.30000e11i | 1.15511i | ||||||||
\(669\) | −2.58661e11 | + | 1.25485e11i | −1.29130 | + | 0.626453i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.68311e9i | 0.0329677i | ||||||||
\(672\) | 5.52715e10 | + | 1.13930e11i | 0.271034 | + | 0.558679i | ||||
\(673\) | 3.18816e11 | 1.55410 | 0.777051 | − | 0.629437i | \(-0.216715\pi\) | ||||
0.777051 | + | 0.629437i | \(0.216715\pi\) | |||||||
\(674\) | 1.95925e9i | 0.00949404i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.74632e11 | −0.836250 | ||||||||
\(677\) | 3.75454e11i | 1.78732i | 0.448745 | + | 0.893660i | \(0.351871\pi\) | ||||
−0.448745 | + | 0.893660i | \(0.648129\pi\) | |||||||
\(678\) | 4.03974e10 | − | 1.95982e10i | 0.191177 | − | 0.0927463i | ||||
\(679\) | −1.20305e11 | −0.565984 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.08673e11 | − | 2.24006e11i | −0.505281 | − | 1.04153i | ||||
\(682\) | 1.55241e11 | 0.717576 | ||||||||
\(683\) | − | 1.83700e11i | − | 0.844162i | −0.906558 | − | 0.422081i | \(-0.861300\pi\) | ||
0.906558 | − | 0.422081i | \(-0.138700\pi\) | |||||||
\(684\) | 1.64074e10 | − | 2.08196e10i | 0.0749576 | − | 0.0951146i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 8.27865e10i | − | 0.373820i | ||||||
\(687\) | 1.88544e11 | − | 9.14692e10i | 0.846420 | − | 0.410627i | ||||
\(688\) | 2.84236e11 | 1.26860 | ||||||||
\(689\) | 7.35871e10i | 0.326531i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.46577e11 | 0.642916 | 0.321458 | − | 0.946924i | \(-0.395827\pi\) | ||||
0.321458 | + | 0.946924i | \(0.395827\pi\) | |||||||
\(692\) | 2.39885e10i | 0.104611i | ||||||||
\(693\) | 1.84827e11 | + | 1.45657e11i | 0.801367 | + | 0.631538i | ||||
\(694\) | −1.99983e10 | −0.0862095 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.23427e11 | − | 1.08392e11i | 0.952134 | − | 0.461913i | ||||
\(697\) | 2.00761e9 | 0.00850645 | ||||||||
\(698\) | − | 4.67440e10i | − | 0.196926i | ||||||
\(699\) | 1.57857e11 | + | 3.25389e11i | 0.661234 | + | 1.36299i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 3.90726e11i | − | 1.61808i | −0.587753 | − | 0.809041i | \(-0.699987\pi\) | ||
0.587753 | − | 0.809041i | \(-0.300013\pi\) | |||||||
\(702\) | 1.75911e10 | + | 3.85518e9i | 0.0724345 | + | 0.0158744i | ||||
\(703\) | 3.96630e10 | 0.162392 | ||||||||
\(704\) | 1.16519e11i | 0.474358i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.12115e10 | −0.246385 | ||||||||
\(707\) | 1.87888e11i | 0.752007i | ||||||||
\(708\) | −4.42200e10 | − | 9.11500e10i | −0.175989 | − | 0.362764i | ||||
\(709\) | 3.36760e10 | 0.133271 | 0.0666354 | − | 0.997777i | \(-0.478774\pi\) | ||||
0.0666354 | + | 0.997777i | \(0.478774\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.18716e11 | + | 1.50640e11i | −0.464548 | + | 0.589471i | ||||
\(712\) | 1.33298e11 | 0.518684 | ||||||||
\(713\) | 1.17437e11i | 0.454410i | ||||||||
\(714\) | −4.78566e10 | + | 2.32169e10i | −0.184140 | + | 0.0893327i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.95382e10i | 0.150441i | ||||||||
\(717\) | −8.81772e10 | − | 1.81758e11i | −0.333641 | − | 0.687730i | ||||
\(718\) | 1.00918e11 | 0.379726 | ||||||||
\(719\) | − | 3.34576e11i | − | 1.25193i | −0.779852 | − | 0.625964i | \(-0.784706\pi\) | ||
0.779852 | − | 0.625964i | \(-0.215294\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.24214e11 | −0.829703 | ||||||||
\(722\) | − | 9.43814e10i | − | 0.347326i | ||||||
\(723\) | −7.79305e10 | + | 3.78067e10i | −0.285203 | + | 0.138362i | ||||
\(724\) | −2.32351e11 | −0.845649 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −4.89509e10 | − | 1.00902e11i | −0.176203 | − | 0.363206i | ||||
\(727\) | −7.75537e10 | −0.277629 | −0.138815 | − | 0.990318i | \(-0.544329\pi\) | ||||
−0.138815 | + | 0.990318i | \(0.544329\pi\) | |||||||
\(728\) | 2.72328e10i | 0.0969541i | ||||||||
\(729\) | −2.56543e11 | − | 1.18118e11i | −0.908345 | − | 0.418223i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.69363e11i | 1.64376i | ||||||||
\(732\) | 5.09144e9 | − | 2.47003e9i | 0.0177336 | − | 0.00860316i | ||||
\(733\) | −1.83371e10 | −0.0635205 | −0.0317603 | − | 0.999496i | \(-0.510111\pi\) | ||||
−0.0317603 | + | 0.999496i | \(0.510111\pi\) | |||||||
\(734\) | 4.10808e10i | 0.141532i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.56990e10 | 0.292055 | ||||||||
\(737\) | 1.82803e10i | 0.0619601i | ||||||||
\(738\) | 6.67439e8 | − | 8.46922e8i | 0.00225002 | − | 0.00285508i | ||||
\(739\) | 4.44324e11 | 1.48978 | 0.744890 | − | 0.667187i | \(-0.232502\pi\) | ||||
0.744890 | + | 0.667187i | \(0.232502\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.86504e9 | − | 3.81560e9i | 0.0260872 | − | 0.0126558i | ||||
\(742\) | −1.16741e11 | −0.385130 | ||||||||
\(743\) | − | 5.92783e10i | − | 0.194509i | −0.995260 | − | 0.0972547i | \(-0.968994\pi\) | ||
0.995260 | − | 0.0972547i | \(-0.0310061\pi\) | |||||||
\(744\) | −1.22978e11 | − | 2.53493e11i | −0.401362 | − | 0.827323i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 7.96584e10i | − | 0.257203i | ||||||
\(747\) | −3.46844e11 | − | 2.73340e11i | −1.11391 | − | 0.877850i | ||||
\(748\) | −3.31893e11 | −1.06021 | ||||||||
\(749\) | 6.14843e10i | 0.195361i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.35059e11 | −0.424585 | −0.212292 | − | 0.977206i | \(-0.568093\pi\) | ||||
−0.212292 | + | 0.977206i | \(0.568093\pi\) | |||||||
\(752\) | 8.21853e10i | 0.256994i | ||||||||
\(753\) | 9.14950e10 | + | 1.88598e11i | 0.284589 | + | 0.586619i | ||||
\(754\) | 3.82083e10 | 0.118215 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.26567e10 | − | 1.94642e11i | 0.130587 | − | 0.595866i | ||||
\(757\) | 3.52798e11 | 1.07434 | 0.537171 | − | 0.843473i | \(-0.319493\pi\) | ||||
0.537171 | + | 0.843473i | \(0.319493\pi\) | |||||||
\(758\) | − | 5.33245e10i | − | 0.161529i | ||||||
\(759\) | 1.43288e11 | − | 6.95138e10i | 0.431760 | − | 0.209461i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.67185e11i | 1.39300i | 0.717558 | + | 0.696499i | \(0.245260\pi\) | ||||
−0.717558 | + | 0.696499i | \(0.754740\pi\) | |||||||
\(762\) | −2.76033e10 | − | 5.68984e10i | −0.0818732 | − | 0.168764i | ||||
\(763\) | −2.81347e11 | −0.830126 | ||||||||
\(764\) | − | 9.88853e10i | − | 0.290241i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.26074e11 | 0.366193 | ||||||||
\(767\) | − | 3.34101e10i | − | 0.0965375i | ||||||
\(768\) | −9.91106e9 | + | 4.80819e9i | −0.0284889 | + | 0.0138209i | ||||
\(769\) | 1.44792e11 | 0.414038 | 0.207019 | − | 0.978337i | \(-0.433624\pi\) | ||||
0.207019 | + | 0.978337i | \(0.433624\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.41418e11 | + | 2.91503e11i | 0.400210 | + | 0.824947i | ||||
\(772\) | −4.04070e11 | −1.13759 | ||||||||
\(773\) | − | 1.13132e11i | − | 0.316860i | −0.987370 | − | 0.158430i | \(-0.949357\pi\) | ||
0.987370 | − | 0.158430i | \(-0.0506433\pi\) | |||||||
\(774\) | 1.98003e11 | + | 1.56042e11i | 0.551707 | + | 0.434788i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 1.95335e11i | − | 0.538683i | ||||||
\(777\) | 2.68251e11 | − | 1.30138e11i | 0.735964 | − | 0.357041i | ||||
\(778\) | 9.49132e10 | 0.259065 | ||||||||
\(779\) | − | 5.23432e8i | − | 0.00142138i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.81694e11 | 1.83225 | ||||||||
\(782\) | 3.59980e10i | 0.0962612i | ||||||||
\(783\) | −5.85330e11 | − | 1.28278e11i | −1.55723 | − | 0.341275i | ||||
\(784\) | −1.24079e11 | −0.328423 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −2.93814e10 | + | 1.42539e10i | −0.0769808 | + | 0.0373460i | ||||
\(787\) | −4.10788e10 | −0.107083 | −0.0535413 | − | 0.998566i | \(-0.517051\pi\) | ||||
−0.0535413 | + | 0.998566i | \(0.517051\pi\) | |||||||
\(788\) | − | 4.12999e11i | − | 1.07113i | ||||||
\(789\) | 9.25494e10 | + | 1.90771e11i | 0.238817 | + | 0.492271i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1.63839e11i | − | 0.418515i | ||||||
\(792\) | −2.36499e11 | + | 3.00097e11i | −0.601075 | + | 0.762712i | ||||
\(793\) | 1.86622e9 | 0.00471921 | ||||||||
\(794\) | 2.20077e10i | 0.0553723i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.04383e11 | −1.00726 | ||||||||
\(797\) | 1.01477e11i | 0.251498i | 0.992062 | + | 0.125749i | \(0.0401334\pi\) | ||||
−0.992062 | + | 0.125749i | \(0.959867\pi\) | |||||||
\(798\) | 6.05319e9 | + | 1.24774e10i | 0.0149270 | + | 0.0307688i | ||||
\(799\) | −1.35713e11 | −0.332994 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.52626e11 | − | 1.99089e11i | −0.613689 | − | 0.483634i | ||||
\(802\) | −1.86378e11 | −0.450503 | ||||||||
\(803\) | 5.07177e10i | 0.121982i | ||||||||
\(804\) | 1.39266e10 | − | 6.75626e9i | 0.0333288 | − | 0.0161690i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 4.33500e10i | − | 0.102719i | ||||||
\(807\) | 2.19769e11 | + | 4.53008e11i | 0.518171 | + | 1.06810i | ||||
\(808\) | −3.05068e11 | −0.715733 | ||||||||
\(809\) | 2.81290e11i | 0.656689i | 0.944558 | + | 0.328344i | \(0.106491\pi\) | ||||
−0.944558 | + | 0.328344i | \(0.893509\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.06605e11 | 0.708754 | 0.354377 | − | 0.935103i | \(-0.384693\pi\) | ||||
0.354377 | + | 0.935103i | \(0.384693\pi\) | |||||||
\(812\) | − | 4.22766e11i | − | 0.972468i | ||||||
\(813\) | 3.86991e11 | − | 1.87742e11i | 0.885806 | − | 0.429735i | ||||
\(814\) | −2.66733e11 | −0.607546 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.02556e11 | + | 2.11398e11i | 0.231314 | + | 0.476805i | ||||
\(817\) | 1.22374e11 | 0.274663 | ||||||||
\(818\) | 6.14716e9i | 0.0137297i | ||||||||
\(819\) | 4.06739e10 | − | 5.16116e10i | 0.0904024 | − | 0.114713i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 5.33533e11i | − | 1.17433i | −0.809469 | − | 0.587163i | \(-0.800245\pi\) | ||
0.809469 | − | 0.587163i | \(-0.199755\pi\) | |||||||
\(822\) | 2.08412e11 | − | 1.01108e11i | 0.456494 | − | 0.221461i | ||||
\(823\) | −5.45096e11 | −1.18816 | −0.594078 | − | 0.804407i | \(-0.702483\pi\) | ||||
−0.594078 | + | 0.804407i | \(0.702483\pi\) | |||||||
\(824\) | − | 3.64050e11i | − | 0.789681i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.30028e10 | 0.113862 | ||||||||
\(827\) | − | 7.10494e11i | − | 1.51893i | −0.650547 | − | 0.759466i | \(-0.725460\pi\) | ||
0.650547 | − | 0.759466i | \(-0.274540\pi\) | |||||||
\(828\) | −1.05916e11 | − | 8.34702e10i | −0.225342 | − | 0.177587i | ||||
\(829\) | −3.64341e11 | −0.771419 | −0.385710 | − | 0.922620i | \(-0.626043\pi\) | ||||
−0.385710 | + | 0.922620i | \(0.626043\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.63913e11 | + | 7.95198e10i | −0.343724 | + | 0.166752i | ||||
\(832\) | 3.25372e10 | 0.0679026 | ||||||||
\(833\) | − | 2.04893e11i | − | 0.425546i | ||||||
\(834\) | −4.18886e10 | − | 8.63444e10i | −0.0865828 | − | 0.178472i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 8.65325e10i | 0.177155i | ||||||||
\(837\) | −1.45540e11 | + | 6.64098e11i | −0.296538 | + | 1.35310i | ||||
\(838\) | −1.92187e11 | −0.389715 | ||||||||
\(839\) | 3.80877e11i | 0.768665i | 0.923195 | + | 0.384333i | \(0.125568\pi\) | ||||
−0.923195 | + | 0.384333i | \(0.874432\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.71101e11 | −1.54144 | ||||||||
\(842\) | 1.63490e11i | 0.325270i | ||||||||
\(843\) | −2.71768e11 | − | 5.60192e11i | −0.538132 | − | 1.10924i | ||||
\(844\) | 6.58899e10 | 0.129852 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.51186e10 | + | 5.72515e10i | −0.0880793 | + | 0.111765i | ||||
\(847\) | −4.09225e11 | −0.795112 | ||||||||
\(848\) | 5.15683e11i | 0.997240i | ||||||||
\(849\) | 5.25076e11 | − | 2.54732e11i | 1.01063 | − | 0.490290i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 2.01780e11i | − | 0.384733i | ||||||
\(852\) | −2.51950e11 | − | 5.19340e11i | −0.478140 | − | 0.985584i | ||||
\(853\) | 8.33398e11 | 1.57419 | 0.787093 | − | 0.616834i | \(-0.211585\pi\) | ||||
0.787093 | + | 0.616834i | \(0.211585\pi\) | |||||||
\(854\) | 2.96062e9i | 0.00556611i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.98301e10 | −0.185937 | ||||||||
\(857\) | 2.81549e11i | 0.521952i | 0.965345 | + | 0.260976i | \(0.0840444\pi\) | ||||
−0.965345 | + | 0.260976i | \(0.915956\pi\) | |||||||
\(858\) | −5.28922e10 | + | 2.56598e10i | −0.0975984 | + | 0.0473483i | ||||
\(859\) | −6.11769e11 | −1.12361 | −0.561804 | − | 0.827271i | \(-0.689892\pi\) | ||||
−0.561804 | + | 0.827271i | \(0.689892\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.71742e9 | − | 3.54010e9i | −0.00312510 | − | 0.00644173i | ||||
\(862\) | 4.53154e9 | 0.00820761 | ||||||||
\(863\) | 4.91320e11i | 0.885771i | 0.896578 | + | 0.442886i | \(0.146045\pi\) | ||||
−0.896578 | + | 0.442886i | \(0.853955\pi\) | |||||||
\(864\) | 4.84620e11 | + | 1.06207e11i | 0.869654 | + | 0.190589i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.14688e11i | 0.203914i | ||||||||
\(867\) | 1.59286e11 | − | 7.72752e10i | 0.281904 | − | 0.136761i | ||||
\(868\) | −4.79657e11 | −0.844991 | ||||||||
\(869\) | − | 6.26106e11i | − | 1.09792i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.10464e9 | 0.00886937 | ||||||||
\(872\) | − | 4.56814e11i | − | 0.790084i | ||||||
\(873\) | −2.91746e11 | + | 3.70200e11i | −0.502282 | + | 0.637352i | ||||
\(874\) | 9.38553e9 | 0.0160847 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.86386e10 | − | 1.87449e10i | 0.0656153 | − | 0.0318322i | ||||
\(877\) | 2.91940e11 | 0.493509 | 0.246755 | − | 0.969078i | \(-0.420636\pi\) | ||||
0.246755 | + | 0.969078i | \(0.420636\pi\) | |||||||
\(878\) | − | 2.35790e11i | − | 0.396778i | ||||||
\(879\) | −1.40952e11 | − | 2.90543e11i | −0.236111 | − | 0.486693i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.04364e11i | 0.505230i | 0.967567 | + | 0.252615i | \(0.0812906\pi\) | ||||
−0.967567 | + | 0.252615i | \(0.918709\pi\) | |||||||
\(882\) | −8.64353e10 | − | 6.81176e10i | −0.142829 | − | 0.112560i | ||||
\(883\) | −4.35514e11 | −0.716407 | −0.358203 | − | 0.933644i | \(-0.616611\pi\) | ||||
−0.358203 | + | 0.933644i | \(0.616611\pi\) | |||||||
\(884\) | 9.26791e10i | 0.151765i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.68453e10 | 0.0922486 | ||||||||
\(887\) | 1.80753e11i | 0.292006i | 0.989284 | + | 0.146003i | \(0.0466409\pi\) | ||||
−0.989284 | + | 0.146003i | \(0.953359\pi\) | |||||||
\(888\) | 2.11300e11 | + | 4.35550e11i | 0.339819 | + | 0.700464i | ||||
\(889\) | −2.30761e11 | −0.369450 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.96428e11 | − | 2.15518e11i | 1.42234 | − | 0.341957i | ||||
\(892\) | −7.94681e11 | −1.25526 | ||||||||
\(893\) | 3.53837e10i | 0.0556414i | ||||||||
\(894\) | 9.07267e10 | − | 4.40146e10i | 0.142032 | − | 0.0689044i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.51830e11i | 0.701040i | ||||||||
\(897\) | −1.94113e10 | − | 4.00122e10i | −0.0299836 | − | 0.0618049i | ||||
\(898\) | 1.46865e11 | 0.225846 | ||||||||
\(899\) | 1.44243e12i | 2.20829i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.51553e11 | −1.29215 | ||||||||
\(902\) | 3.52007e9i | 0.00531771i | ||||||||
\(903\) | 8.27645e11 | − | 4.01519e11i | 1.24478 | − | 0.603885i | ||||
\(904\) | 2.66020e11 | 0.398327 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 7.02348e10 | + | 1.44774e11i | 0.104241 | + | 0.214871i | ||||
\(907\) | 1.24264e12 | 1.83618 | 0.918089 | − | 0.396374i | \(-0.129732\pi\) | ||||
0.918089 | + | 0.396374i | \(0.129732\pi\) | |||||||
\(908\) | − | 6.88210e11i | − | 1.01246i | ||||||
\(909\) | 5.78166e11 | + | 4.55639e11i | 0.846832 | + | 0.667368i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 3.34146e10i | − | 0.0485135i | −0.999706 | − | 0.0242568i | \(-0.992278\pi\) | ||
0.999706 | − | 0.0242568i | \(-0.00772193\pi\) | |||||||
\(912\) | 5.51166e10 | − | 2.67389e10i | 0.0796715 | − | 0.0386513i | ||||
\(913\) | 1.44159e12 | 2.07472 | ||||||||
\(914\) | 3.30465e11i | 0.473523i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.79261e11 | 0.822797 | ||||||||
\(917\) | 1.19161e11i | 0.168523i | ||||||||
\(918\) | −4.46123e10 | + | 2.03565e11i | −0.0628180 | + | 0.286638i | ||||
\(919\) | −1.22601e12 | −1.71882 | −0.859412 | − | 0.511283i | \(-0.829170\pi\) | ||||
−0.859412 | + | 0.511283i | \(0.829170\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.77120e11 | − | 3.28494e11i | 0.941081 | − | 0.456550i | ||||
\(922\) | 1.54774e11 | 0.214178 | ||||||||
\(923\) | − | 1.90359e11i | − | 0.262281i | ||||||
\(924\) | 2.83920e11 | + | 5.85240e11i | 0.389500 | + | 0.802872i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.12093e11i | 0.424463i | ||||||||
\(927\) | −5.43732e11 | + | 6.89948e11i | −0.736319 | + | 0.934324i | ||||
\(928\) | 1.05260e12 | 1.41930 | ||||||||
\(929\) | − | 1.46087e12i | − | 1.96133i | −0.195701 | − | 0.980664i | \(-0.562698\pi\) | ||
0.195701 | − | 0.980664i | \(-0.437302\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.34204e10 | −0.0711064 | ||||||||
\(932\) | 9.99686e11i | 1.32495i | ||||||||
\(933\) | 3.96145e11 | + | 8.16568e11i | 0.522790 | + | 1.07762i | ||||
\(934\) | −2.30303e11 | −0.302631 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 8.38001e10 | + | 6.60409e10i | 0.109179 | + | 0.0860418i | ||||
\(937\) | 1.02495e12 | 1.32968 | 0.664838 | − | 0.746987i | \(-0.268500\pi\) | ||||
0.664838 | + | 0.746987i | \(0.268500\pi\) | |||||||
\(938\) | 8.09817e9i | 0.0104611i | ||||||||
\(939\) | 6.88793e11 | − | 3.34157e11i | 0.885985 | − | 0.429821i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1.83735e11i | − | 0.234333i | −0.993112 | − | 0.117166i | \(-0.962619\pi\) | ||
0.993112 | − | 0.117166i | \(-0.0373811\pi\) | |||||||
\(942\) | −1.41976e10 | − | 2.92654e10i | −0.0180307 | − | 0.0371664i | ||||
\(943\) | −2.66288e9 | −0.00336748 | ||||||||
\(944\) | − | 2.34131e11i | − | 0.294829i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.22962e11 | −1.02758 | ||||||||
\(947\) | 2.26053e11i | 0.281067i | 0.990076 | + | 0.140533i | \(0.0448817\pi\) | ||||
−0.990076 | + | 0.140533i | \(0.955118\pi\) | |||||||
\(948\) | −4.76991e11 | + | 2.31405e11i | −0.590578 | + | 0.286509i | ||||
\(949\) | 1.41626e10 | 0.0174613 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.99946e10 | − | 6.18276e10i | −0.0366709 | − | 0.0755893i | ||||
\(952\) | −3.15139e11 | −0.383667 | ||||||||
\(953\) | 1.49255e12i | 1.80949i | 0.425953 | + | 0.904745i | \(0.359939\pi\) | ||||
−0.425953 | + | 0.904745i | \(0.640061\pi\) | |||||||
\(954\) | −2.83103e11 | + | 3.59233e11i | −0.341783 | + | 0.433693i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 5.58414e11i | − | 0.668535i | ||||||
\(957\) | 1.75994e12 | − | 8.53808e11i | 2.09822 | − | 1.01792i | ||||
\(958\) | −6.15012e10 | −0.0730166 | ||||||||
\(959\) | − | 8.45250e11i | − | 0.999334i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.83650e11 | 0.918816 | ||||||||
\(962\) | 7.44835e10i | 0.0869681i | ||||||||
\(963\) | 1.89198e11 | + | 1.49103e11i | 0.219995 | + | 0.173373i | ||||
\(964\) | −2.39425e11 | −0.277243 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 6.34766e10 | − | 3.07947e10i | 0.0728963 | − | 0.0353645i | ||||
\(967\) | −7.94256e11 | −0.908352 | −0.454176 | − | 0.890912i | \(-0.650066\pi\) | ||||
−0.454176 | + | 0.890912i | \(0.650066\pi\) | |||||||
\(968\) | − | 6.64445e11i | − | 0.756759i | ||||||
\(969\) | 4.41543e10 | + | 9.10146e10i | 0.0500815 | + | 0.103232i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.55855e10i | 0.0850279i | 0.999096 | + | 0.0425139i | \(0.0135367\pi\) | ||||
−0.999096 | + | 0.0425139i | \(0.986463\pi\) | |||||||
\(972\) | −4.95503e11 | − | 6.03279e11i | −0.555113 | − | 0.675854i | ||||
\(973\) | −3.50185e11 | −0.390702 | ||||||||
\(974\) | 1.00847e11i | 0.112054i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.30780e10 | 0.0144126 | ||||||||
\(977\) | 1.31247e11i | 0.144049i | 0.997403 | + | 0.0720244i | \(0.0229460\pi\) | ||||
−0.997403 | + | 0.0720244i | \(0.977054\pi\) | |||||||
\(978\) | 1.46418e11 | + | 3.01809e11i | 0.160044 | + | 0.329896i | ||||
\(979\) | 1.04999e12 | 1.14302 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.82281e11 | + | 8.65755e11i | −0.736694 | + | 0.934801i | ||||
\(982\) | 4.49650e11 | 0.483536 | ||||||||
\(983\) | − | 2.55150e11i | − | 0.273264i | −0.990622 | − | 0.136632i | \(-0.956372\pi\) | ||
0.990622 | − | 0.136632i | \(-0.0436277\pi\) | |||||||
\(984\) | 5.74794e9 | − | 2.78852e9i | 0.00613100 | − | 0.00297436i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 4.42148e11i | 0.467800i | ||||||||
\(987\) | 1.16097e11 | + | 2.39309e11i | 0.122335 | + | 0.252168i | ||||
\(988\) | 2.41636e10 | 0.0253591 | ||||||||
\(989\) | − | 6.22559e11i | − | 0.650722i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.00441e12 | −1.04139 | −0.520697 | − | 0.853742i | \(-0.674328\pi\) | ||||
−0.520697 | + | 0.853742i | \(0.674328\pi\) | |||||||
\(992\) | − | 1.19425e12i | − | 1.23325i | ||||||
\(993\) | 3.43642e11 | − | 1.66713e11i | 0.353435 | − | 0.171463i | ||||
\(994\) | 3.01991e11 | 0.309349 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −5.32802e11 | − | 1.09826e12i | −0.541413 | − | 1.11601i | ||||
\(997\) | −1.22258e12 | −1.23737 | −0.618683 | − | 0.785641i | \(-0.712333\pi\) | ||||
−0.618683 | + | 0.785641i | \(0.712333\pi\) | |||||||
\(998\) | − | 3.70566e11i | − | 0.373545i | ||||||
\(999\) | 2.50066e11 | − | 1.14105e12i | 0.251068 | − | 1.14562i |
(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 | 75.9.c.h.26.8 | 12 | ||
3.2 | odd | 2 | inner | 75.9.c.h.26.6 | 12 | ||
5.2 | odd | 4 | 15.9.d.c.14.5 | ✓ | 12 | ||
5.3 | odd | 4 | 15.9.d.c.14.8 | yes | 12 | ||
5.4 | even | 2 | inner | 75.9.c.h.26.5 | 12 | ||
15.2 | even | 4 | 15.9.d.c.14.7 | yes | 12 | ||
15.8 | even | 4 | 15.9.d.c.14.6 | yes | 12 | ||
15.14 | odd | 2 | inner | 75.9.c.h.26.7 | 12 | ||
20.3 | even | 4 | 240.9.c.c.209.3 | 12 | |||
20.7 | even | 4 | 240.9.c.c.209.10 | 12 | |||
60.23 | odd | 4 | 240.9.c.c.209.9 | 12 | |||
60.47 | odd | 4 | 240.9.c.c.209.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.9.d.c.14.5 | ✓ | 12 | 5.2 | odd | 4 | ||
15.9.d.c.14.6 | yes | 12 | 15.8 | even | 4 | ||
15.9.d.c.14.7 | yes | 12 | 15.2 | even | 4 | ||
15.9.d.c.14.8 | yes | 12 | 5.3 | odd | 4 | ||
75.9.c.h.26.5 | 12 | 5.4 | even | 2 | inner | ||
75.9.c.h.26.6 | 12 | 3.2 | odd | 2 | inner | ||
75.9.c.h.26.7 | 12 | 15.14 | odd | 2 | inner | ||
75.9.c.h.26.8 | 12 | 1.1 | even | 1 | trivial | ||
240.9.c.c.209.3 | 12 | 20.3 | even | 4 | |||
240.9.c.c.209.4 | 12 | 60.47 | odd | 4 | |||
240.9.c.c.209.9 | 12 | 60.23 | odd | 4 | |||
240.9.c.c.209.10 | 12 | 20.7 | even | 4 |