Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,7,Mod(13,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.13");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.j (of order \(18\), degree \(6\), 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: | \(17.4841103551\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 13.6 | ||
Character | \(\chi\) | \(=\) | 76.13 |
Dual form | 76.7.j.a.41.6 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{5}{18}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.48422 | + | 4.07785i | −0.0549710 | + | 0.151032i | −0.964139 | − | 0.265398i | \(-0.914497\pi\) |
0.909168 | + | 0.416430i | \(0.136719\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −10.2967 | − | 58.3955i | −0.0823737 | − | 0.467164i | −0.997892 | − | 0.0648891i | \(-0.979331\pi\) |
0.915519 | − | 0.402275i | \(-0.131780\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −54.2532 | + | 93.9692i | −0.158173 | + | 0.273963i | −0.934210 | − | 0.356724i | \(-0.883894\pi\) |
0.776037 | + | 0.630687i | \(0.217227\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 544.020 | + | 456.487i | 0.746256 | + | 0.626183i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −149.837 | − | 259.525i | −0.112575 | − | 0.194985i | 0.804233 | − | 0.594314i | \(-0.202576\pi\) |
−0.916808 | + | 0.399329i | \(0.869243\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1260.56 | − | 3463.37i | −0.573766 | − | 1.57641i | −0.798503 | − | 0.601991i | \(-0.794374\pi\) |
0.224737 | − | 0.974420i | \(-0.427848\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 253.411 | + | 44.6832i | 0.0750847 | + | 0.0132395i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 322.518 | − | 270.624i | 0.0656458 | − | 0.0550833i | −0.609374 | − | 0.792883i | \(-0.708579\pi\) |
0.675020 | + | 0.737799i | \(0.264135\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6488.04 | + | 2225.15i | 0.945916 | + | 0.324413i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −302.669 | − | 360.707i | −0.0326821 | − | 0.0389490i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3117.50 | − | 17680.2i | 0.256226 | − | 1.45313i | −0.536679 | − | 0.843786i | \(-0.680322\pi\) |
0.792906 | − | 0.609345i | \(-0.208567\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11378.7 | − | 4141.50i | 0.728236 | − | 0.265056i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5408.64 | + | 3122.68i | −0.274787 | + | 0.158648i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 26902.0 | − | 32060.6i | 1.10304 | − | 1.31455i | 0.158056 | − | 0.987430i | \(-0.449477\pi\) |
0.944983 | − | 0.327120i | \(-0.106078\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7950.76 | − | 4590.37i | −0.266885 | − | 0.154086i | 0.360586 | − | 0.932726i | \(-0.382577\pi\) |
−0.627471 | + | 0.778640i | \(0.715910\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1280.69 | − | 225.821i | 0.0356372 | − | 0.00628380i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6046.01 | + | 2200.57i | 0.141015 | + | 0.0513252i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 62989.0i | − | 1.24354i | −0.783200 | − | 0.621770i | \(-0.786414\pi\) | ||
0.783200 | − | 0.621770i | \(-0.213586\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 15994.1 | 0.269628 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −14106.7 | + | 38757.7i | −0.204679 | + | 0.562350i | −0.998979 | − | 0.0451752i | \(-0.985615\pi\) |
0.794300 | + | 0.607525i | \(0.207838\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −21681.5 | − | 122962.i | −0.272699 | − | 1.54655i | −0.746178 | − | 0.665747i | \(-0.768113\pi\) |
0.473479 | − | 0.880805i | \(-0.342998\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 21055.2 | − | 36468.7i | 0.231058 | − | 0.400205i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 118432. | + | 99376.6i | 1.14071 | + | 0.957173i | 0.999462 | − | 0.0328000i | \(-0.0104425\pi\) |
0.141253 | + | 0.989974i | \(0.454887\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 52937.7 | + | 91690.8i | 0.449963 | + | 0.779359i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 624.880 | + | 1716.84i | 0.00471071 | + | 0.0129426i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −259093. | − | 45685.0i | −1.74031 | − | 0.306864i | −0.788841 | − | 0.614598i | \(-0.789318\pi\) |
−0.951473 | + | 0.307734i | \(0.900429\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −13612.3 | + | 11422.0i | −0.0818168 | + | 0.0686524i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −18703.5 | + | 23154.6i | −0.100994 | + | 0.125030i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 137971. | + | 164428.i | 0.671789 | + | 0.800607i | 0.989026 | − | 0.147739i | \(-0.0471995\pi\) |
−0.317237 | + | 0.948346i | \(0.602755\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3689.15 | − | 20922.2i | 0.0162531 | − | 0.0921760i | −0.975602 | − | 0.219546i | \(-0.929542\pi\) |
0.991855 | + | 0.127370i | \(0.0406535\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −72410.6 | + | 26355.3i | −0.289588 | + | 0.105401i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −189266. | + | 109273.i | −0.689179 | + | 0.397898i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −153564. | + | 183011.i | −0.510582 | + | 0.608488i | −0.958327 | − | 0.285673i | \(-0.907783\pi\) |
0.447745 | + | 0.894161i | \(0.352227\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 67470.3 | + | 38954.0i | 0.205384 | + | 0.118578i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14721.9 | + | 2595.87i | −0.0411328 | + | 0.00725283i | −0.194177 | − | 0.980967i | \(-0.562204\pi\) |
0.153044 | + | 0.988219i | \(0.451092\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −142653. | − | 51921.6i | −0.366702 | − | 0.133469i | 0.152095 | − | 0.988366i | \(-0.451398\pi\) |
−0.518797 | + | 0.854897i | \(0.673620\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 52547.4i | 0.124557i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 32516.5 | 0.0712248 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −213385. | + | 586271.i | −0.432796 | + | 1.18910i | 0.511293 | + | 0.859406i | \(0.329167\pi\) |
−0.944089 | + | 0.329691i | \(0.893056\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 85193.6 | + | 483157.i | 0.160307 | + | 0.909145i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −113121. | + | 195931.i | −0.197837 | + | 0.342665i | −0.947827 | − | 0.318785i | \(-0.896725\pi\) |
0.749990 | + | 0.661450i | \(0.230058\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −19124.1 | − | 16047.1i | −0.0311405 | − | 0.0261299i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 90809.8 | + | 157287.i | 0.137903 | + | 0.238856i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −343455. | − | 943634.i | −0.487191 | − | 1.33855i | −0.903213 | − | 0.429192i | \(-0.858798\pi\) |
0.416022 | − | 0.909355i | \(-0.363424\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 393840. | + | 69444.7i | 0.522632 | + | 0.0921541i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 30519.5 | − | 25608.9i | 0.0379427 | − | 0.0318377i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 63133.3 | − | 401784.i | 0.0736355 | − | 0.468621i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −405161. | − | 482852.i | −0.443928 | − | 0.529052i | 0.496959 | − | 0.867774i | \(-0.334450\pi\) |
−0.940887 | + | 0.338722i | \(0.890005\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 36955.5 | − | 209585.i | 0.0380868 | − | 0.216001i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.18740e6 | + | 432180.i | −1.15248 | + | 0.419469i | −0.846406 | − | 0.532538i | \(-0.821238\pi\) |
−0.306076 | + | 0.952007i | \(0.599016\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.70465e6 | − | 984180.i | 1.56000 | − | 0.900664i | 0.562740 | − | 0.826634i | \(-0.309747\pi\) |
0.997256 | − | 0.0740299i | \(-0.0235860\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −17947.2 | + | 21388.6i | −0.0155035 | + | 0.0184763i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.57988e6 | + | 912142.i | 1.28965 | + | 0.744579i | 0.978592 | − | 0.205812i | \(-0.0659834\pi\) |
0.311058 | + | 0.950391i | \(0.399317\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 169505. | − | 29888.3i | 0.130889 | − | 0.0230792i | −0.107820 | − | 0.994170i | \(-0.534387\pi\) |
0.238709 | + | 0.971091i | \(0.423276\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 256860. | + | 93489.4i | 0.187814 | + | 0.0683586i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 466113.i | − | 0.323039i | −0.986869 | − | 0.161520i | \(-0.948360\pi\) | ||
0.986869 | − | 0.161520i | \(-0.0516395\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.06455e6 | −0.699957 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 895213. | − | 2.45958e6i | 0.558945 | − | 1.53569i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7932.77 | + | 44989.0i | 0.00470743 | + | 0.0266972i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 840878. | − | 1.45644e6i | 0.474654 | − | 0.822125i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −137111. | − | 115050.i | −0.0736812 | − | 0.0618259i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −822261. | − | 1.42420e6i | −0.420998 | − | 0.729189i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 318866. | + | 876078.i | 0.155667 | + | 0.427693i | 0.992870 | − | 0.119200i | \(-0.0380329\pi\) |
−0.837203 | + | 0.546892i | \(0.815811\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 533600. | + | 94088.0i | 0.248569 | + | 0.0438294i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 552365. | − | 463490.i | 0.245704 | − | 0.206170i | −0.511616 | − | 0.859214i | \(-0.670953\pi\) |
0.757320 | + | 0.653044i | \(0.226508\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −561092. | + | 488954.i | −0.238495 | + | 0.207833i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 238042. | + | 283687.i | 0.0967501 | + | 0.115302i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −194518. | + | 1.10317e6i | −0.0756483 | + | 0.429023i | 0.923337 | + | 0.383990i | \(0.125450\pi\) |
−0.998986 | + | 0.0450326i | \(0.985661\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.65679e6 | − | 1.33096e6i | 1.36162 | − | 0.495589i | 0.445065 | − | 0.895498i | \(-0.353181\pi\) |
0.916555 | + | 0.399909i | \(0.130958\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −581022. | + | 335453.i | −0.207270 | + | 0.119667i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −709952. | + | 846088.i | −0.242785 | + | 0.289339i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.14920e6 | − | 1.24084e6i | −0.704972 | − | 0.407016i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −452472. | + | 79783.1i | −0.142443 | + | 0.0251165i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.61390e6 | − | 1.31535e6i | −1.09249 | − | 0.397634i | −0.267947 | − | 0.963434i | \(-0.586345\pi\) |
−0.824543 | + | 0.565800i | \(0.808567\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.78755e6i | 0.809640i | 0.914396 | + | 0.404820i | \(0.132666\pi\) | ||||
−0.914396 | + | 0.404820i | \(0.867334\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 298993. | 0.0834808 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −186191. | + | 511555.i | −0.0499992 | + | 0.137372i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −138418. | − | 785010.i | −0.0357680 | − | 0.202851i | 0.961687 | − | 0.274150i | \(-0.0883965\pi\) |
−0.997455 | + | 0.0712995i | \(0.977285\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 570846. | − | 988735.i | 0.142013 | − | 0.245974i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.49226e6 | + | 1.25216e6i | 0.357576 | + | 0.300042i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.24002e6 | + | 3.87983e6i | 0.517236 | + | 0.895879i | 0.999800 | + | 0.0200184i | \(0.00637248\pi\) |
−0.482563 | + | 0.875861i | \(0.660294\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −26373.8 | − | 72461.6i | −0.00587113 | − | 0.0161308i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.17988e6 | − | 384372.i | −0.468040 | − | 0.0825281i | −0.0653460 | − | 0.997863i | \(-0.520815\pi\) |
−0.402694 | + | 0.915335i | \(0.631926\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.70838e6 | + | 5.62900e6i | −1.38982 | + | 1.16620i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.51387e6 | + | 4.17223e6i | 0.502753 | + | 0.834411i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.48614e6 | + | 2.96286e6i | 0.480161 | + | 0.572233i | 0.950687 | − | 0.310153i | \(-0.100380\pi\) |
−0.470526 | + | 0.882386i | \(0.655936\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −228156. | + | 1.29394e6i | −0.0425713 | + | 0.241434i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −875292. | + | 318580.i | −0.157846 | + | 0.0574512i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.57104e6 | + | 2.63909e6i | −0.796996 | + | 0.460146i | −0.842420 | − | 0.538822i | \(-0.818870\pi\) |
0.0454235 | + | 0.998968i | \(0.485536\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.48919e6 | − | 5.35000e6i | 0.757063 | − | 0.902232i | −0.240596 | − | 0.970625i | \(-0.577343\pi\) |
0.997658 | + | 0.0683930i | \(0.0217872\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 79842.1 | + | 46096.8i | 0.0130280 | + | 0.00752173i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.67828e6 | + | 648580.i | −0.580938 | + | 0.102435i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −118559. | − | 43151.8i | −0.0181305 | − | 0.00659895i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 677661.i | − | 0.100375i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.79183e6 | −1.26177 | −0.630884 | − | 0.775878i | \(-0.717307\pi\) | ||||
−0.630884 | + | 0.775878i | \(0.717307\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.53063e6 | − | 4.20537e6i | 0.212911 | − | 0.584968i | −0.786559 | − | 0.617515i | \(-0.788139\pi\) |
0.999470 | + | 0.0325465i | \(0.0103617\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −164686. | − | 933982.i | −0.0222103 | − | 0.125961i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.51408e6 | + | 7.81861e6i | −0.590433 | + | 1.02266i | 0.403742 | + | 0.914873i | \(0.367710\pi\) |
−0.994174 | + | 0.107786i | \(0.965624\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.48531e6 | + | 3.76362e6i | 0.569158 | + | 0.477580i | 0.881366 | − | 0.472433i | \(-0.156624\pi\) |
−0.312208 | + | 0.950014i | \(0.601069\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −518368. | − | 897839.i | −0.0638337 | − | 0.110563i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.55319e6 | + | 4.26735e6i | 0.185668 | + | 0.510117i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.40853e6 | + | 424689.i | 0.279570 | + | 0.0492957i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.76679e6 | − | 8.19531e6i | 1.10114 | − | 0.923963i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −394665. | − | 2.01721e6i | −0.0432304 | − | 0.220960i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.78955e6 | − | 9.28322e6i | −0.829211 | − | 0.988215i | −0.999996 | − | 0.00290652i | \(-0.999075\pi\) |
0.170785 | − | 0.985308i | \(-0.445370\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11264.9 | − | 63886.5i | 0.00116571 | − | 0.00661105i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.95717e6 | + | 2.53220e6i | −0.700031 | + | 0.254790i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 862708. | − | 498085.i | 0.0844276 | − | 0.0487443i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 423457. | − | 504656.i | 0.0403159 | − | 0.0480467i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.34383e6 | − | 775860.i | −0.124499 | − | 0.0718797i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.01101e6 | − | 1.23623e6i | 0.632217 | − | 0.111477i | 0.151649 | − | 0.988434i | \(-0.451542\pi\) |
0.480568 | + | 0.876958i | \(0.340431\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.08078e6 | + | 2.94116e6i | 0.709424 | + | 0.258209i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 4.73355e6i | − | 0.404678i | −0.979316 | − | 0.202339i | \(-0.935146\pi\) | ||
0.979316 | − | 0.202339i | \(-0.0648542\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.12959e7 | 1.77333 | 0.886664 | − | 0.462414i | \(-0.153017\pi\) | ||||
0.886664 | + | 0.462414i | \(0.153017\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −48261.5 | + | 132597.i | −0.00391530 | + | 0.0107572i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 265231. | + | 1.50420e6i | 0.0209679 | + | 0.118915i | 0.993495 | − | 0.113874i | \(-0.0363260\pi\) |
−0.972527 | + | 0.232789i | \(0.925215\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.58369e6 | − | 7.93918e6i | 0.353192 | − | 0.611747i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.07402e6 | − | 1.74031e6i | −0.155800 | − | 0.130732i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 761473. | + | 1.31891e6i | 0.0557777 | + | 0.0966099i | 0.892566 | − | 0.450917i | \(-0.148903\pi\) |
−0.836788 | + | 0.547527i | \(0.815570\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.25763e6 | − | 1.16977e7i | −0.304170 | − | 0.835701i | −0.993764 | − | 0.111505i | \(-0.964433\pi\) |
0.689593 | − | 0.724197i | \(-0.257789\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.58038e6 | − | 1.16030e6i | −0.458598 | − | 0.0808632i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.80925e6 | − | 4.03544e6i | 0.327023 | − | 0.274405i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −472072. | − | 2.52754e7i | −0.0313269 | − | 1.67729i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −631082. | − | 752094.i | −0.0408778 | − | 0.0487163i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.34991e6 | − | 7.65573e6i | 0.0853659 | − | 0.484134i | −0.911911 | − | 0.410388i | \(-0.865393\pi\) |
0.997277 | − | 0.0737463i | \(-0.0234955\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.05558e6 | + | 1.84008e6i | −0.312183 | + | 0.113625i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 93821.8 | − | 54168.1i | 0.00565827 | − | 0.00326680i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.79997e6 | + | 1.16791e7i | −0.577332 | + | 0.688037i | −0.973118 | − | 0.230305i | \(-0.926027\pi\) |
0.395787 | + | 0.918342i | \(0.370472\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.91903e6 | + | 3.41736e6i | 0.340684 | + | 0.196694i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.92705e7 | − | 5.16118e6i | 1.64630 | − | 0.290287i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.47547e7 | − | 9.00998e6i | −1.36079 | − | 0.495286i | −0.444490 | − | 0.895784i | \(-0.646615\pi\) |
−0.916298 | + | 0.400497i | \(0.868837\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.56003e7i | 0.838290i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.35776e6 | 0.228944 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.11105e6 | − | 8.54754e6i | 0.159827 | − | 0.439121i | −0.833769 | − | 0.552114i | \(-0.813821\pi\) |
0.993596 | + | 0.112992i | \(0.0360436\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.36924e6 | + | 2.47792e7i | 0.219532 | + | 1.24503i | 0.872866 | + | 0.487959i | \(0.162259\pi\) |
−0.653334 | + | 0.757070i | \(0.726630\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −867729. | + | 1.50295e6i | −0.0426478 | + | 0.0738681i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.77977e6 | − | 2.33250e6i | −0.133663 | − | 0.112156i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.24592e6 | + | 2.15800e6i | 0.0586207 | + | 0.101534i | 0.893846 | − | 0.448373i | \(-0.147996\pi\) |
−0.835226 | + | 0.549907i | \(0.814663\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.22993e6 | − | 6.12668e6i | −0.102678 | − | 0.282106i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −274478. | − | 48397.9i | −0.0123705 | − | 0.00218126i | 0.167459 | − | 0.985879i | \(-0.446444\pi\) |
−0.179830 | + | 0.983698i | \(0.557555\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.26563e7 | − | 1.06199e7i | 0.558405 | − | 0.468557i | −0.319371 | − | 0.947630i | \(-0.603471\pi\) |
0.877775 | + | 0.479073i | \(0.159027\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.54471e6 | + | 853782.i | 0.0667287 | + | 0.0368818i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.87670e6 | − | 3.42832e6i | −0.121688 | − | 0.145023i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.16066e6 | + | 2.35963e7i | −0.172373 | + | 0.977576i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.57034e6 | − | 935529.i | 0.104307 | − | 0.0379645i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.06958e7 | + | 1.19488e7i | −0.822773 | + | 0.475028i | −0.851372 | − | 0.524563i | \(-0.824229\pi\) |
0.0285985 | + | 0.999591i | \(0.490896\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.18121e6 | − | 9.74998e6i | 0.318677 | − | 0.379785i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.62082e6 | + | 935783.i | 0.0618681 | + | 0.0357195i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.51631e7 | + | 1.14900e7i | −2.43774 | + | 0.429840i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.27309e7 | + | 4.63367e6i | 0.466831 | + | 0.169913i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 5.48350e6i | − | 0.197120i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.25975e6 | −0.0444001 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21067.7 | + | 57882.9i | −0.000728117 | + | 0.00200049i | −0.940056 | − | 0.341020i | \(-0.889228\pi\) |
0.939328 | + | 0.343020i | \(0.111450\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.48327e6 | + | 8.41204e6i | 0.0502742 | + | 0.285119i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.48987e7 | + | 2.58052e7i | −0.495297 | + | 0.857880i | −0.999985 | − | 0.00542175i | \(-0.998274\pi\) |
0.504688 | + | 0.863302i | \(0.331608\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.98192e7 | + | 2.50213e7i | 0.972441 | + | 0.815975i | 0.982932 | − | 0.183970i | \(-0.0588949\pi\) |
−0.0104907 | + | 0.999945i | \(0.503339\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.28462e6 | + | 3.95708e6i | 0.0730942 | + | 0.126603i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.69511e7 | + | 4.65728e7i | 0.532133 | + | 1.46202i | 0.856527 | + | 0.516102i | \(0.172617\pi\) |
−0.324394 | + | 0.945922i | \(0.605160\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.23514e7 | − | 2.17789e6i | −0.380491 | − | 0.0670909i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.06446e6 | + | 5.08868e6i | −0.183348 | + | 0.153847i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.69469e6 | − | 1.03817e6i | 0.0799651 | − | 0.0308079i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.86871e7 | − | 3.41880e7i | −0.835674 | − | 0.995918i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −129702. | + | 735576.i | −0.00370939 | + | 0.0210370i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.57637e7 | + | 5.73751e6i | −0.442660 | + | 0.161115i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.06311e7 | + | 2.34584e7i | −1.12040 | + | 0.646865i | −0.941504 | − | 0.337002i | \(-0.890587\pi\) |
−0.178900 | + | 0.983867i | \(0.557254\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.87537e7 | − | 3.42673e7i | 0.778684 | − | 0.927999i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.22682e7 | + | 7.08305e6i | 0.326322 | + | 0.188402i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.60320e6 | + | 459015.i | −0.0680171 | + | 0.0119932i | −0.207553 | − | 0.978224i | \(-0.566550\pi\) |
0.139536 | + | 0.990217i | \(0.455439\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.90074e6 | + | 691812.i | 0.0487891 | + | 0.0177578i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.75123e6i | 0.0693846i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.42538e7 | −0.601032 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.58002e6 | − | 4.34107e6i | 0.0384773 | − | 0.105716i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −690013. | − | 3.91326e6i | −0.0165146 | − | 0.0936592i | 0.975436 | − | 0.220281i | \(-0.0706975\pi\) |
−0.991951 | + | 0.126622i | \(0.959586\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.54666e7 | − | 4.41094e7i | 0.599093 | − | 1.03766i | −0.393863 | − | 0.919169i | \(-0.628861\pi\) |
0.992955 | − | 0.118490i | \(-0.0378053\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.76329e7 | + | 1.47958e7i | 0.407759 | + | 0.342150i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.27843e7 | + | 2.21431e7i | 0.290639 | + | 0.503401i | 0.973961 | − | 0.226716i | \(-0.0727990\pi\) |
−0.683322 | + | 0.730117i | \(0.739466\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 303174. | + | 832964.i | 0.00677652 | + | 0.0186183i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −195232. | − | 34424.7i | −0.00429089 | − | 0.000756599i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.51661e7 | + | 2.95078e7i | −0.760047 | + | 0.637755i | −0.938139 | − | 0.346259i | \(-0.887452\pi\) |
0.178092 | + | 0.984014i | \(0.443008\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.71433e7 | + | 2.88737e7i | 0.789513 | + | 0.613734i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.69112e6 | + | 5.59065e6i | 0.0980746 | + | 0.116881i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.56313e6 | + | 8.86494e6i | −0.0321452 | + | 0.182304i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.63021e7 | − | 2.04923e7i | 1.13901 | − | 0.414564i | 0.297452 | − | 0.954737i | \(-0.403863\pi\) |
0.841554 | + | 0.540172i | \(0.181641\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.53667e7 | + | 1.46455e7i | −0.504877 | + | 0.291491i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.83496e7 | − | 2.18682e7i | 0.359339 | − | 0.428244i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.14080e7 | + | 6.58643e6i | 0.219829 | + | 0.126918i | 0.605871 | − | 0.795563i | \(-0.292825\pi\) |
−0.386042 | + | 0.922481i | \(0.626158\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.02808e6 | − | 1.23924e6i | 0.133273 | − | 0.0234997i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.44949e8 | − | 5.27573e7i | −2.70516 | − | 0.984597i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1.51006e7i | − | 0.277381i | −0.990336 | − | 0.138690i | \(-0.955711\pi\) | ||
0.990336 | − | 0.138690i | \(-0.0442893\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.04578e6 | −0.0731523 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.20701e7 | − | 8.81120e7i | 0.570827 | − | 1.56833i | −0.232374 | − | 0.972626i | \(-0.574649\pi\) |
0.803201 | − | 0.595708i | \(-0.203128\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −334813. | − | 1.89882e6i | −0.00586705 | − | 0.0332737i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.43353e7 | − | 7.67910e7i | 0.764921 | − | 1.32488i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.06225e7 | + | 1.73043e7i | 0.350341 | + | 0.293971i | 0.800927 | − | 0.598762i | \(-0.204340\pi\) |
−0.450586 | + | 0.892733i | \(0.648785\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.77926e6 | − | 6.54586e6i | −0.0632231 | − | 0.109506i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.07021e6 | + | 2.94038e6i | 0.0176316 | + | 0.0484425i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.64328e7 | + | 6.42408e6i | 0.591155 | + | 0.104237i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.01633e7 | − | 6.72650e7i | 1.28116 | − | 1.07502i | 0.288080 | − | 0.957606i | \(-0.406983\pi\) |
0.993083 | − | 0.117416i | \(-0.0374612\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.16110e6 | − | 3.01376e6i | −0.0182790 | − | 0.0474450i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.43339e7 | − | 4.09176e7i | −0.532464 | − | 0.634566i | 0.431016 | − | 0.902344i | \(-0.358155\pi\) |
−0.963481 | + | 0.267778i | \(0.913711\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.87573e6 | + | 3.33229e7i | −0.0897732 | + | 0.509129i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.73370e7 | − | 9.94986e6i | 0.411515 | − | 0.149779i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.63472e7 | + | 9.43807e6i | −0.242471 | + | 0.139991i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.53764e7 | + | 3.02424e7i | −0.370902 | + | 0.442024i | −0.918921 | − | 0.394442i | \(-0.870938\pi\) |
0.548019 | + | 0.836466i | \(0.315382\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.20985e6 | − | 2.43056e6i | −0.0606375 | − | 0.0350091i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.29366e7 | + | 4.04433e6i | −0.325595 | + | 0.0574112i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.26063e7 | + | 4.58831e6i | 0.176377 | + | 0.0641961i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.68873e7i | 0.232890i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.11380e8 | 1.51413 | 0.757067 | − | 0.653337i | \(-0.226631\pi\) | ||||
0.757067 | + | 0.653337i | \(0.226631\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.82929e7 | − | 1.05209e8i | 0.513182 | − | 1.40996i | −0.364720 | − | 0.931117i | \(-0.618835\pi\) |
0.877902 | − | 0.478840i | \(-0.158943\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.90655e7 | + | 1.08126e8i | 0.251899 | + | 1.42859i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.54903e6 | − | 4.41506e6i | 0.0332054 | − | 0.0575135i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.76589e6 | + | 1.48176e6i | 0.0226820 | + | 0.0190324i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.39650e6 | − | 4.15086e6i | −0.0303533 | − | 0.0525734i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.77277e7 | − | 4.87066e7i | −0.221422 | − | 0.608353i | 0.778389 | − | 0.627782i | \(-0.216037\pi\) |
−0.999811 | + | 0.0194295i | \(0.993815\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.73042e7 | − | 1.01043e7i | −0.705867 | − | 0.124463i | −0.190820 | − | 0.981625i | \(-0.561115\pi\) |
−0.515047 | + | 0.857162i | \(0.672226\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.24983e6 | − | 6.92243e6i | 0.100225 | − | 0.0840990i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.95676e7 | − | 1.07773e8i | 0.713783 | − | 1.29142i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.89507e6 | − | 1.17925e7i | −0.116957 | − | 0.139384i | 0.704389 | − | 0.709814i | \(-0.251221\pi\) |
−0.821346 | + | 0.570430i | \(0.806777\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.30565e7 | + | 7.40470e7i | −0.152234 | + | 0.863360i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.52760e8 | + | 5.56000e7i | −1.75711 | + | 0.639534i | −0.999907 | − | 0.0136513i | \(-0.995655\pi\) |
−0.757198 | + | 0.653185i | \(0.773432\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.15676e7 | + | 2.97726e7i | −0.585190 | + | 0.337859i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.07276e7 | − | 1.27847e7i | 0.120110 | − | 0.143142i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.37310e8 | + | 7.92762e7i | 1.51693 | + | 0.875798i | 0.999802 | + | 0.0198880i | \(0.00633096\pi\) |
0.517125 | + | 0.855910i | \(0.327002\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.21723e7 | − | 2.14630e6i | 0.132691 | − | 0.0233971i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.13672e7 | − | 4.13733e6i | −0.122281 | − | 0.0445067i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 2.37136e7i | − | 0.251746i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.72003e7 | −0.599307 | −0.299654 | − | 0.954048i | \(-0.596871\pi\) | ||||
−0.299654 | + | 0.954048i | \(0.596871\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −899308. | + | 2.47083e6i | −0.00929973 | + | 0.0255508i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.20370e6 | − | 2.95116e7i | −0.0531140 | − | 0.301225i | 0.946666 | − | 0.322218i | \(-0.104428\pi\) |
−0.999780 | + | 0.0209931i | \(0.993317\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.30767e6 | + | 2.26496e6i | −0.0131752 | + | 0.0228201i | −0.872538 | − | 0.488547i | \(-0.837527\pi\) |
0.859363 | + | 0.511367i | \(0.170861\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.80970e6 | − | 1.51852e6i | −0.0179989 | − | 0.0151029i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.36187e7 | + | 1.10191e8i | 0.624647 | + | 1.08192i | 0.988609 | + | 0.150506i | \(0.0480903\pi\) |
−0.363962 | + | 0.931414i | \(0.618576\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.86603e6 | − | 2.43592e7i | −0.0859430 | − | 0.236127i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.40660e6 | + | 600675.i | 0.0326030 | + | 0.00574879i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.86629e7 | + | 2.40511e7i | −0.270855 | + | 0.227275i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.30407e7 | − | 1.55096e6i | 0.774837 | − | 0.0144717i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.20097e8 | − | 1.43126e8i | −1.10657 | − | 1.31875i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.99238e7 | + | 1.69706e8i | −0.272276 | + | 1.54415i | 0.475207 | + | 0.879874i | \(0.342373\pi\) |
−0.747483 | + | 0.664281i | \(0.768738\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.18155e8 | + | 7.94018e7i | −1.96033 | + | 0.713502i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.32096e6 | + | 4.22676e6i | −0.0649721 | + | 0.0375116i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.40246e7 | + | 2.86314e7i | −0.210586 | + | 0.250967i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.67561e7 | + | 3.27681e7i | 0.491389 | + | 0.283704i | 0.725151 | − | 0.688590i | \(-0.241770\pi\) |
−0.233761 | + | 0.972294i | \(0.575103\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.91460e7 | + | 3.37596e6i | −0.163739 | + | 0.0288716i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.58041e7 | − | 3.48699e7i | −0.809356 | − | 0.294582i | −0.0959984 | − | 0.995381i | \(-0.530604\pi\) |
−0.713358 | + | 0.700800i | \(0.752827\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 1.76204e7i | − | 0.147054i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.26194e7 | −0.104045 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 554778. | − | 1.52424e6i | 0.00451908 | − | 0.0124161i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.84358e7 | + | 2.17980e8i | 0.309338 | + | 1.75435i | 0.602345 | + | 0.798235i | \(0.294233\pi\) |
−0.293007 | + | 0.956110i | \(0.594656\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.80282e6 | − | 8.31874e6i | 0.0381930 | − | 0.0661522i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.37967e8 | + | 1.15768e8i | 1.08410 | + | 0.909669i | 0.996255 | − | 0.0864653i | \(-0.0275572\pi\) |
0.0878461 | + | 0.996134i | \(0.472002\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.74637e7 | + | 6.48890e7i | 0.290895 | + | 0.503845i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.29975e7 | − | 3.57104e7i | −0.0997326 | − | 0.274013i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.65120e7 | + | 9.96459e6i | 0.428536 | + | 0.0755625i | 0.383756 | − | 0.923434i | \(-0.374630\pi\) |
0.0447797 | + | 0.998997i | \(0.485741\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.26184e7 | − | 1.05881e7i | 0.0945676 | − | 0.0793516i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.20398e7 | + | 8.22503e6i | −0.311393 | + | 0.0609236i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.50240e7 | − | 8.94101e7i | −0.549261 | − | 0.654583i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.04517e6 | − | 4.56264e7i | 0.0582188 | − | 0.330175i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.57721e7 | + | 5.74056e6i | −0.112820 | + | 0.0410632i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.49649e8 | + | 8.64000e7i | −1.05818 | + | 0.610943i | −0.924929 | − | 0.380139i | \(-0.875876\pi\) |
−0.133254 | + | 0.991082i | \(0.542543\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.02460e7 | − | 5.98809e7i | 0.351234 | − | 0.418584i | −0.561282 | − | 0.827624i | \(-0.689692\pi\) |
0.912517 | + | 0.409040i | \(0.134136\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.93784e6 | − | 2.85087e6i | −0.0341240 | − | 0.0197015i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.80653e6 | + | 671194.i | −0.0260074 | + | 0.00458581i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.63764e8 | − | 5.96052e7i | −1.10624 | − | 0.402640i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.52434e8i | 1.01812i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.52015e8 | 1.00393 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.69975e7 | − | 1.01650e8i | 0.241608 | − | 0.663812i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.97741e6 | − | 2.25570e7i | −0.0256849 | − | 0.145666i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.58640e7 | − | 2.74773e7i | 0.101309 | − | 0.175472i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.81326e8 | + | 1.52151e8i | 1.14517 | + | 0.960910i | 0.999596 | − | 0.0284382i | \(-0.00905337\pi\) |
0.145572 | + | 0.989348i | \(0.453498\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.51536e7 | + | 2.62468e7i | 0.0946490 | + | 0.163937i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.49068e6 | − | 9.59057e6i | −0.0215636 | − | 0.0592454i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.14136e8 | − | 3.77580e7i | −1.30836 | − | 0.230700i | −0.524381 | − | 0.851484i | \(-0.675703\pi\) |
−0.783982 | + | 0.620784i | \(0.786814\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.15577e7 | − | 9.69805e6i | 0.0698480 | − | 0.0586094i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.45881e8 | − | 1.48149e8i | 1.46984 | − | 0.885614i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.35146e7 | − | 5.18587e7i | −0.257312 | − | 0.306652i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.81455e6 | − | 1.59621e7i | 0.0164638 | − | 0.0933708i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.22017e8 | − | 8.08077e7i | 1.28476 | − | 0.467614i | 0.392755 | − | 0.919643i | \(-0.371522\pi\) |
0.892003 | + | 0.452030i | \(0.149300\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.98531e8 | + | 2.30092e8i | −2.28154 | + | 1.31725i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 351934. | − | 419418.i | 0.00199330 | − | 0.00237552i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.65704e7 | + | 2.68875e7i | 0.260967 | + | 0.150669i | 0.624775 | − | 0.780804i | \(-0.285191\pi\) |
−0.363809 | + | 0.931474i | \(0.618524\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.72189e7 | + | 4.79943e6i | −0.150912 | + | 0.0266099i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.00239e7 | − | 1.82072e7i | −0.274428 | − | 0.0998837i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 7.26953e7i | − | 0.394611i | −0.980342 | − | 0.197306i | \(-0.936781\pi\) | ||
0.980342 | − | 0.197306i | \(-0.0632192\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.04269e8 | 1.09722 | 0.548610 | − | 0.836078i | \(-0.315157\pi\) | ||||
0.548610 | + | 0.836078i | \(0.315157\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.30490e7 | − | 3.58518e7i | 0.0693606 | − | 0.190567i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.77497e7 | − | 2.14089e8i | −0.198568 | − | 1.12614i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.42587e8 | − | 2.46968e8i | 0.742253 | − | 1.28562i | −0.209215 | − | 0.977870i | \(-0.567091\pi\) |
0.951467 | − | 0.307750i | \(-0.0995760\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.48771e7 | + | 1.24834e7i | 0.0766447 | + | 0.0643126i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.22743e7 | − | 2.12598e7i | −0.0625849 | − | 0.108400i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.69652e7 | + | 7.40862e7i | 0.136081 | + | 0.373880i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.52846e8 | − | 2.69509e7i | −0.763461 | − | 0.134619i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.63730e8 | − | 1.37386e8i | 0.809495 | − | 0.679247i | −0.140992 | − | 0.990011i | \(-0.545029\pi\) |
0.950487 | + | 0.310764i | \(0.100585\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.13706e7 | − | 4.74741e7i | −0.202463 | − | 0.232333i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.51833e7 | − | 3.00122e7i | −0.121997 | − | 0.145391i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.43121e7 | + | 8.11682e7i | −0.0686342 | + | 0.389244i | 0.931068 | + | 0.364845i | \(0.118878\pi\) |
−0.999702 | + | 0.0243985i | \(0.992233\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.54547e6 | − | 926477.i | 0.0120842 | − | 0.00439829i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.20046e7 | + | 1.27044e7i | −0.103417 | + | 0.0597078i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.82445e8 | − | 2.17429e8i | 0.848890 | − | 1.01167i | −0.150843 | − | 0.988558i | \(-0.548199\pi\) |
0.999733 | − | 0.0231098i | \(-0.00735673\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.83689e7 | − | 1.63788e7i | −0.130683 | − | 0.0754498i | 0.433233 | − | 0.901282i | \(-0.357373\pi\) |
−0.563916 | + | 0.825832i | \(0.690706\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.67084e8 | + | 2.94614e7i | −0.762049 | + | 0.134370i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.37081e7 | − | 3.41070e7i | −0.423166 | − | 0.154020i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1.72002e8i | − | 0.769073i | −0.923110 | − | 0.384536i | \(-0.874361\pi\) | ||
0.923110 | − | 0.384536i | \(-0.125639\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.97069e7 | −0.0872501 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.94887e8 | − | 5.35446e8i | 0.854394 | − | 2.34743i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.34637e7 | + | 3.03208e8i | 0.232101 | + | 1.31631i | 0.848633 | + | 0.528982i | \(0.177426\pi\) |
−0.616532 | + | 0.787330i | \(0.711463\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.30660e6 | + | 9.19130e6i | −0.0228134 | + | 0.0395140i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.22119e8 | + | 1.86380e8i | 0.945648 | + | 0.793493i | 0.978559 | − | 0.205965i | \(-0.0660334\pi\) |
−0.0329113 | + | 0.999458i | \(0.510478\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.55810e8 | + | 2.69871e8i | 0.656937 | + | 1.13785i | 0.981404 | + | 0.191952i | \(0.0614817\pi\) |
−0.324467 | + | 0.945897i | \(0.605185\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.83483e7 | + | 1.05361e8i | 0.160129 | + | 0.439952i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.07306e8 | + | 1.89210e7i | 0.443772 | + | 0.0782490i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.02370e7 | − | 5.89359e7i | 0.287691 | − | 0.241401i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.81167e6 | + | 1.38460e6i | 0.0357483 | + | 0.00561722i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.70464e7 | − | 2.03151e7i | −0.0684984 | − | 0.0816332i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.71437e7 | + | 3.24078e8i | −0.227447 | + | 1.28992i | 0.630505 | + | 0.776186i | \(0.282848\pi\) |
−0.857952 | + | 0.513731i | \(0.828263\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.94170e7 | − | 1.79863e7i | 0.194834 | − | 0.0709138i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.78758e7 | − | 2.76411e7i | 0.186980 | − | 0.107953i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.50828e8 | − | 2.98925e8i | 0.970415 | − | 1.15650i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.19399e6 | − | 5.30815e6i | −0.0352372 | − | 0.0203442i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.80113e8 | + | 3.17588e7i | −0.683867 | + | 0.120584i | −0.504779 | − | 0.863249i | \(-0.668426\pi\) |
−0.179088 | + | 0.983833i | \(0.557315\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.85399e8 | − | 1.40274e8i | −1.44970 | − | 0.527647i | −0.507192 | − | 0.861833i | \(-0.669317\pi\) |
−0.942507 | + | 0.334185i | \(0.891539\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 3.21286e7i | − | 0.119733i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.00921e8 | −1.11107 | −0.555533 | − | 0.831495i | \(-0.687486\pi\) | ||||
−0.555533 | + | 0.831495i | \(0.687486\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.19999e7 | − | 6.04443e7i | 0.0804799 | − | 0.221117i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 750670. | + | 4.25726e6i | 0.00272086 | + | 0.0154308i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.02171e8 | − | 1.76965e8i | 0.366933 | − | 0.635547i | −0.622151 | − | 0.782897i | \(-0.713741\pi\) |
0.989084 | + | 0.147350i | \(0.0470743\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.27533e7 | − | 2.74833e7i | −0.116555 | − | 0.0978012i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.39048e7 | − | 9.33658e7i | −0.190078 | − | 0.329224i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.67943e7 | + | 2.65940e8i | 0.338215 | + | 0.929239i | 0.985901 | + | 0.167331i | \(0.0535149\pi\) |
−0.647685 | + | 0.761908i | \(0.724263\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.66901e8 | + | 2.94292e7i | 0.577903 | + | 0.101900i | 0.454957 | − | 0.890513i | \(-0.349655\pi\) |
0.122946 | + | 0.992413i | \(0.460766\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.15837e6 | − | 4.32839e6i | 0.0176999 | − | 0.0148520i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.43302e7 | + | 2.77306e7i | 0.116738 | + | 0.0942964i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.82972e8 | − | 5.75583e8i | −1.62759 | − | 1.93968i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.36469e6 | + | 3.04247e7i | −0.0179171 | + | 0.101613i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.98260e6 | + | 2.17749e6i | −0.0198026 | + | 0.00720755i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.38823e8 | + | 1.95619e8i | −1.11155 | + | 0.641751i | −0.939229 | − | 0.343291i | \(-0.888458\pi\) |
−0.172316 | + | 0.985042i | \(0.555125\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.86106e7 | + | 5.79318e7i | −0.158059 | + | 0.188367i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.44170e8 | + | 1.98707e8i | 1.10919 | + | 0.640393i | 0.938620 | − | 0.344952i | \(-0.112105\pi\) |
0.170573 | + | 0.985345i | \(0.445438\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.73545e7 | − | 1.18764e7i | 0.215158 | − | 0.0379381i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.93027e7 | + | 7.02561e6i | 0.0611191 | + | 0.0222455i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.57229e8i | 1.43506i | 0.696525 | + | 0.717532i | \(0.254728\pi\) | ||||
−0.696525 | + | 0.717532i | \(0.745272\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.64230e7 | 0.206655 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.16077e7 | + | 8.68414e7i | −0.0974816 | + | 0.267828i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.68379e8 | + | 9.54923e8i | 0.514789 | + | 2.91952i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.05612e8 | + | 3.56130e8i | −0.623181 | + | 1.07938i | 0.365709 | + | 0.930729i | \(0.380827\pi\) |
−0.988890 | + | 0.148652i | \(0.952507\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.76896e7 | + | 1.48434e7i | 0.0531519 | + | 0.0445997i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.15375e8 | − | 1.99836e8i | −0.343683 | − | 0.595277i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.93914e6 | + | 1.63177e7i | 0.0175398 | + | 0.0481903i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.52755e6 | − | 1.15098e6i | −0.0191126 | − | 0.00337006i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.59937e8 | − | 1.34203e8i | 0.464297 | − | 0.389591i | −0.380412 | − | 0.924817i | \(-0.624218\pi\) |
0.844709 | + | 0.535226i | \(0.179773\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.40160e8 | − | 4.08675e8i | 0.403420 | − | 1.17628i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.55716e7 | + | 3.04750e7i | 0.0729778 | + | 0.0869715i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.38088e7 | − | 1.35027e8i | 0.0673720 | − | 0.382086i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.28921e8 | + | 1.56115e8i | −1.20348 | + | 0.438031i | −0.864438 | − | 0.502740i | \(-0.832325\pi\) |
−0.339043 | + | 0.940771i | \(0.610103\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.83711e8 | + | 2.21536e8i | −1.06757 | + | 0.616361i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.05945e8 | + | 1.26261e8i | −0.292290 | + | 0.348337i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.67179e7 | + | 3.27461e7i | 0.155168 | + | 0.0895863i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.50851e6 | + | 1.14763e6i | −0.0176573 | + | 0.00311346i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.59270e8 | − | 5.79694e7i | −0.428496 | − | 0.155960i | 0.118764 | − | 0.992922i | \(-0.462107\pi\) |
−0.547260 | + | 0.836963i | \(0.684329\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.13580e8i | 0.569841i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.40209e7 | 0.142938 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.73331e8 | − | 4.76222e8i | 0.454842 | − | 1.24967i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.89960e7 | + | 1.07732e8i | 0.0494379 | + | 0.280376i | 0.999498 | − | 0.0316918i | \(-0.0100895\pi\) |
−0.950060 | + | 0.312068i | \(0.898978\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.64329e8 | + | 2.84627e8i | −0.424163 | + | 0.734671i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.02691e7 | − | 3.37898e7i | −0.103091 | − | 0.0865035i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.90834e7 | + | 1.71617e8i | 0.251587 | + | 0.435762i | 0.963963 | − | 0.266036i | \(-0.0857141\pi\) |
−0.712376 | + | 0.701798i | \(0.752381\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.31795e6 | + | 2.56009e7i | 0.0234670 | + | 0.0644752i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.05053e7 | + | 1.24320e7i | 0.176124 | + | 0.0310555i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.03985e8 | − | 8.72537e7i | 0.257654 | − | 0.216197i | −0.504806 | − | 0.863233i | \(-0.668436\pi\) |
0.762460 | + | 0.647035i | \(0.223991\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.03770e8 | + | 3.55892e7i | 0.255045 | + | 0.0874708i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.54725e8 | − | 1.84394e8i | −0.377219 | − | 0.449553i | 0.543715 | − | 0.839270i | \(-0.317017\pi\) |
−0.920935 | + | 0.389717i | \(0.872573\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.95994e7 | + | 2.24579e8i | −0.0957679 | + | 0.543127i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.50980e8 | + | 5.49523e7i | −0.362208 | + | 0.131833i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.71427e8 | + | 9.89732e7i | −0.407974 | + | 0.235544i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.95147e8 | + | 3.51742e8i | −0.696817 | + | 0.830434i | −0.992162 | − | 0.124957i | \(-0.960121\pi\) |
0.295345 | + | 0.955391i | \(0.404565\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.92154e7 | + | 1.68675e7i | 0.0684269 | + | 0.0395063i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.62780e8 | − | 2.87026e7i | 0.378235 | − | 0.0666930i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.49888e8 | − | 1.63746e8i | −1.03709 | − | 0.377470i | −0.233314 | − | 0.972401i | \(-0.574957\pi\) |
−0.803777 | + | 0.594931i | \(0.797179\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 2.33470e7i | − | 0.0533956i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.83137e8 | 0.642456 | 0.321228 | − | 0.947002i | \(-0.395904\pi\) | ||||
0.321228 | + | 0.947002i | \(0.395904\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.38759e6 | + | 1.75498e7i | −0.0143802 | + | 0.0395092i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.07864e6 | − | 1.74598e7i | −0.00687662 | − | 0.0389992i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.95553e8 | − | 6.85119e8i | 0.876636 | − | 1.51838i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.34186e8 | + | 2.80416e8i | 0.734868 | + | 0.616628i | 0.931454 | − | 0.363859i | \(-0.118541\pi\) |
−0.196586 | + | 0.980487i | \(0.562985\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.30805e7 | − | 5.72972e7i | −0.0721788 | − | 0.125017i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.08240e8 | − | 2.97387e8i | −0.234342 | − | 0.643849i | −1.00000 | 0.000600907i | \(-0.999809\pi\) | |
0.765658 | − | 0.643248i | \(-0.222413\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.09480e8 | − | 1.93043e7i | −0.235196 | − | 0.0414715i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.27206e7 | + | 1.90648e7i | −0.0484347 | + | 0.0406415i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.77766e8 | + | 2.20072e8i | −0.376042 | + | 0.465535i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.87957e6 | + | 3.43174e6i | 0.00604470 | + | 0.00720379i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.53884e7 | + | 2.57410e8i | −0.0945495 | + | 0.536217i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.44158e7 | + | 1.61660e7i | −0.0918182 | + | 0.0334191i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.85266e8 | − | 2.22433e8i | 0.790380 | − | 0.456326i | −0.0497160 | − | 0.998763i | \(-0.515832\pi\) |
0.840096 | + | 0.542437i | \(0.182498\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.34827e7 | − | 8.75733e7i | 0.149608 | − | 0.178296i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.38003e7 | + | 2.52881e7i | 0.0885008 | + | 0.0510960i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.71118e7 | + | 1.35969e7i | −0.154633 | + | 0.0272659i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.36155e7 | − | 2.31542e7i | −0.126608 | − | 0.0460816i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 3.80132e8i | − | 0.750861i | −0.926851 | − | 0.375430i | \(-0.877495\pi\) | ||
0.926851 | − | 0.375430i | \(-0.122505\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.50903e7 | 0.127607 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.43911e8 | − | 6.70139e8i | 0.474606 | − | 1.30397i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.89977e6 | + | 4.48018e7i | 0.0152570 | + | 0.0865265i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.77551e7 | − | 1.00035e8i | 0.110714 | − | 0.191762i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.02381e7 | + | 2.53728e7i | 0.0575353 | + | 0.0482779i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.62284e8 | + | 6.27493e8i | 0.684231 | + | 1.18512i | 0.973678 | + | 0.227929i | \(0.0731955\pi\) |
−0.289446 | + | 0.957194i | \(0.593471\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.92391e7 | − | 8.03337e7i | −0.0548152 | − | 0.150604i | 0.909263 | − | 0.416222i | \(-0.136646\pi\) |
−0.964078 | + | 0.265618i | \(0.914424\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.07531e8 | − | 1.89606e7i | −0.200106 | − | 0.0352842i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.03500e8 | − | 1.70757e8i | 0.375916 | − | 0.315431i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.32938e8 | − | 8.46024e8i | 0.243771 | − | 1.55137i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.82557e8 | + | 2.17562e8i | 0.332312 | + | 0.396034i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.03681e7 | + | 3.99077e8i | −0.127159 | + | 0.721153i | 0.852844 | + | 0.522167i | \(0.174876\pi\) |
−0.980002 | + | 0.198986i | \(0.936235\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.14296e8 | − | 7.79973e7i | 0.384427 | − | 0.139920i | −0.142575 | − | 0.989784i | \(-0.545538\pi\) |
0.527002 | + | 0.849864i | \(0.323316\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.36374e7 | − | 7.87353e6i | 0.0242867 | − | 0.0140219i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.07627e8 | − | 8.43317e8i | 1.25109 | − | 1.49099i | 0.449298 | − | 0.893382i | \(-0.351674\pi\) |
0.801790 | − | 0.597606i | \(-0.203881\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.54920e7 | + | 1.47178e7i | 0.0447445 | + | 0.0258333i | 0.522205 | − | 0.852820i | \(-0.325109\pi\) |
−0.477461 | + | 0.878653i | \(0.658443\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.06492e7 | + | 1.87774e6i | −0.0185573 | + | 0.00327215i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.18871e7 | + | 1.52457e7i | 0.0724678 | + | 0.0263761i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.31253e8i | 0.225450i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.73370e7 | 0.0977820 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.05496e8 | + | 2.89849e8i | −0.178629 | + | 0.490779i | −0.996401 | − | 0.0847632i | \(-0.972987\pi\) |
0.817772 | + | 0.575542i | \(0.195209\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.00872e8 | − | 1.13920e9i | −0.337700 | − | 1.91519i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 604744. | − | 1.04745e6i | 0.00100946 | − | 0.00174843i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.97783e8 | + | 3.33779e8i | 0.659289 | + | 0.553209i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.12406e7 | + | 1.58033e8i | 0.150154 | + | 0.260075i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.45218e7 | + | 6.73730e7i | 0.0400708 | + | 0.110094i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.11366e9 | − | 1.96369e8i | −1.80703 | − | 0.318628i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.99545e8 | + | 2.51348e8i | −0.482631 | + | 0.404975i | −0.851377 | − | 0.524555i | \(-0.824232\pi\) |
0.368746 | + | 0.929530i | \(0.379787\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.17755e8 | − | 1.89759e8i | 0.348393 | − | 0.303602i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.24517e8 | − | 5.05920e8i | −0.674455 | − | 0.803784i | 0.314928 | − | 0.949116i | \(-0.398020\pi\) |
−0.989383 | + | 0.145331i | \(0.953575\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.69923e7 | − | 4.93358e8i | 0.137246 | − | 0.778363i | −0.836023 | − | 0.548695i | \(-0.815125\pi\) |
0.973269 | − | 0.229668i | \(-0.0737641\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.82498e7 | − | 6.64240e6i | 0.0285923 | − | 0.0104068i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.22220e8 | + | 3.59239e8i | −0.968081 | + | 0.558922i | −0.898651 | − | 0.438665i | \(-0.855451\pi\) |
−0.0694301 | + | 0.997587i | \(0.522118\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.47419e8 | − | 1.75687e8i | 0.227774 | − | 0.271451i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.00469e7 | − | 5.19886e7i | −0.138169 | − | 0.0797720i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.84125e8 | − | 3.24662e7i | 0.280578 | − | 0.0494734i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.27412e8 | + | 3.01153e8i | 1.25218 | + | 0.455757i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 4.47632e8i | − | 0.672788i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.78441e8 | 0.266361 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.31784e7 | + | 2.56006e8i | −0.138139 | + | 0.379534i | −0.989401 | − | 0.145206i | \(-0.953615\pi\) |
0.851262 | + | 0.524740i | \(0.175838\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.80081e7 | − | 1.02129e8i | −0.0265156 | − | 0.150377i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.05577e7 | − | 1.56850e8i | 0.132433 | − | 0.229381i | −0.792181 | − | 0.610287i | \(-0.791054\pi\) |
0.924614 | + | 0.380905i | \(0.124388\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.79151e8 | + | 4.85966e8i | 0.841221 | + | 0.705868i | 0.957838 | − | 0.287309i | \(-0.0927607\pi\) |
−0.116617 | + | 0.993177i | \(0.537205\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.76163e7 | + | 4.78328e7i | 0.0398415 | + | 0.0690075i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.06055e8 | − | 5.66131e8i | −0.295265 | − | 0.811233i | −0.995275 | − | 0.0971002i | \(-0.969043\pi\) |
0.700010 | − | 0.714133i | \(-0.253179\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.96239e7 | − | 1.75664e7i | −0.141794 | − | 0.0250021i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.12626e8 | − | 9.45045e7i | 0.159223 | − | 0.133604i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.47266e8 | + | 9.08289e8i | 0.768501 | + | 1.27547i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.01178e8 | + | 2.39755e8i | 0.280615 | + | 0.334424i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.98616e7 | − | 2.82779e8i | 0.0690858 | − | 0.391805i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.61061e8 | + | 1.31416e8i | −0.496938 | + | 0.180871i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.59254e7 | + | 5.53826e7i | −0.131147 | + | 0.0757179i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.77908e7 | + | 4.50374e7i | −0.0513243 | + | 0.0611660i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.58640e8 | − | 2.07061e8i | −0.483853 | − | 0.279353i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.20686e8 | + | 5.65456e7i | −0.429792 | + | 0.0757839i | −0.384359 | − | 0.923184i | \(-0.625578\pi\) |
−0.0454323 | + | 0.998967i | \(0.514467\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.43256e8 | − | 3.06920e8i | −1.12271 | − | 0.408633i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.57033e7i | 0.0604494i | 0.999543 | + | 0.0302247i | \(0.00962229\pi\) | ||||
−0.999543 | + | 0.0302247i | \(0.990378\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.77986e7 | 0.0890858 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.86974e6 | − | 5.13707e6i | 0.00244072 | − | 0.00670582i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.35862e7 | + | 7.70511e7i | 0.0176193 | + | 0.0999243i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.63865e8 | + | 4.57028e8i | −0.339966 | + | 0.588839i | −0.984426 | − | 0.175800i | \(-0.943749\pi\) |
0.644460 | + | 0.764638i | \(0.277082\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −204769. | − | 171822.i | −0.000262111 | − | 0.000219937i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.75484e7 | + | 4.77152e7i | 0.0350341 | + | 0.0606808i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.60869e8 | − | 7.16732e8i | −0.329608 | − | 0.905590i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.37663e9 | + | 2.42737e8i | 1.72814 | + | 0.304717i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.04318e8 | + | 2.55353e8i | −0.379559 | + | 0.318488i | −0.812529 | − | 0.582920i | \(-0.801910\pi\) |
0.432970 | + | 0.901408i | \(0.357466\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.39436e8 | + | 7.12687e8i | 0.172793 | + | 0.883181i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.31170e7 | − | 9.90550e7i | −0.102340 | − | 0.121964i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.29911e6 | + | 7.36762e6i | −0.00158932 | + | 0.00901348i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.76206e8 | − | 6.41337e7i | 0.214191 | − | 0.0779592i | −0.232696 | − | 0.972550i | \(-0.574755\pi\) |
0.446887 | + | 0.894590i | \(0.352533\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.46291e8 | + | 8.44613e7i | −0.176694 | + | 0.102014i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.00902e8 | + | 9.54477e8i | −0.961192 | + | 1.14550i | 0.0281071 | + | 0.999605i | \(0.491052\pi\) |
−0.989299 | + | 0.145900i | \(0.953392\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.41269e8 | + | 3.70237e8i | 0.764724 | + | 0.441514i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.95723e7 | + | 6.97767e6i | −0.0468917 | + | 0.00826828i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.56153e8 | − | 2.38820e8i | −0.772601 | − | 0.281204i | −0.0745173 | − | 0.997220i | \(-0.523742\pi\) |
−0.698084 | + | 0.716016i | \(0.745964\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.59512e8i | 0.654653i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.15076e8 | −0.250064 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.63356e8 | + | 7.23566e8i | −0.304274 | + | 0.835986i | 0.689471 | + | 0.724313i | \(0.257843\pi\) |
−0.993745 | + | 0.111673i | \(0.964379\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.05269e7 | + | 5.13404e8i | 0.103936 | + | 0.589453i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.72133e7 | − | 4.71348e7i | 0.0310488 | − | 0.0537781i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.31107e7 | − | 7.81291e7i | −0.105571 | − | 0.0885844i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.01609e8 | − | 6.95607e8i | −0.452515 | − | 0.783779i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.43104e8 | + | 1.21742e9i | 0.496165 | + | 1.36320i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.61335e8 | − | 4.60805e7i | −0.290815 | − | 0.0512785i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.80410e8 | + | 6.54842e8i | −0.863065 | + | 0.724197i | −0.962626 | − | 0.270834i | \(-0.912700\pi\) |
0.0995614 | + | 0.995031i | \(0.468256\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 234013. | + | 1.25294e7i | 0.000257199 | + | 0.0137708i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.25110e8 | + | 2.68275e8i | 0.245888 | + | 0.293037i | 0.874846 | − | 0.484402i | \(-0.160963\pi\) |
−0.628958 | + | 0.777439i | \(0.716518\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.33229e7 | + | 4.15835e8i | −0.0795978 | + | 0.451422i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.81991e8 | − | 6.62395e7i | 0.196353 | − | 0.0714666i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.87732e8 | − | 4.54797e8i | 0.844685 | − | 0.487679i | −0.0141689 | − | 0.999900i | \(-0.504510\pi\) |
0.858854 | + | 0.512220i | \(0.171177\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.93434e8 | + | 2.30526e8i | −0.206151 | + | 0.245681i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.05858e8 | + | 6.11169e7i | 0.112128 | + | 0.0647373i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.47181e8 | − | 7.88500e7i | 0.470785 | − | 0.0830121i | 0.0667777 | − | 0.997768i | \(-0.478728\pi\) |
0.404007 | + | 0.914756i | \(0.367617\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.03052e8 | + | 1.83096e8i | 0.526386 | + | 0.191589i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 7.27976e7i | − | 0.0757122i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.24159e9 | −2.31722 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.53545e8 | − | 6.96609e8i | 0.260516 | − | 0.715761i | −0.738617 | − | 0.674125i | \(-0.764521\pi\) |
0.999133 | − | 0.0416359i | \(-0.0132569\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.53544e7 | − | 2.00505e8i | −0.0361074 | − | 0.204775i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.73595e8 | − | 3.00675e8i | 0.176225 | − | 0.305230i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.68788e8 | − | 7.29000e8i | −0.876654 | − | 0.735600i | 0.0888339 | − | 0.996046i | \(-0.471686\pi\) |
−0.965488 | + | 0.260446i | \(0.916130\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.96694e8 | + | 3.40685e8i | 0.197286 | + | 0.341709i |
(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 | 76.7.j.a.13.6 | ✓ | 60 | |
19.3 | odd | 18 | inner | 76.7.j.a.41.6 | yes | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.7.j.a.13.6 | ✓ | 60 | 1.1 | even | 1 | trivial | |
76.7.j.a.41.6 | yes | 60 | 19.3 | odd | 18 | inner |