Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [150,7,Mod(101,150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("150.101");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 150 = 2 \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 150.d (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: | \(34.5081125430\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-2}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 6) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 101.2 | ||
Root | \(-1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 150.101 |
Dual form | 150.7.d.a.101.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.65685i | 0.707107i | ||||||||
\(3\) | −21.0000 | + | 16.9706i | −0.777778 | + | 0.628539i | ||||
\(4\) | −32.0000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −96.0000 | − | 118.794i | −0.444444 | − | 0.549972i | ||||
\(7\) | −2.00000 | −0.00583090 | −0.00291545 | − | 0.999996i | \(-0.500928\pi\) | ||||
−0.00291545 | + | 0.999996i | \(0.500928\pi\) | |||||||
\(8\) | − | 181.019i | − | 0.353553i | ||||||
\(9\) | 153.000 | − | 712.764i | 0.209877 | − | 0.977728i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 33.9411i | 0.0255005i | 0.999919 | + | 0.0127502i | \(0.00405864\pi\) | ||||
−0.999919 | + | 0.0127502i | \(0.995941\pi\) | |||||||
\(12\) | 672.000 | − | 543.058i | 0.388889 | − | 0.314270i | ||||
\(13\) | 2950.00 | 1.34274 | 0.671370 | − | 0.741122i | \(-0.265706\pi\) | ||||
0.671370 | + | 0.741122i | \(0.265706\pi\) | |||||||
\(14\) | − | 11.3137i | − | 0.00412307i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1024.00 | 0.250000 | ||||||||
\(17\) | 4480.23i | 0.911913i | 0.890002 | + | 0.455956i | \(0.150703\pi\) | ||||
−0.890002 | + | 0.455956i | \(0.849297\pi\) | |||||||
\(18\) | 4032.00 | + | 865.499i | 0.691358 | + | 0.148405i | ||||
\(19\) | 5258.00 | 0.766584 | 0.383292 | − | 0.923627i | \(-0.374790\pi\) | ||||
0.383292 | + | 0.923627i | \(0.374790\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 42.0000 | − | 33.9411i | 0.00453515 | − | 0.00366495i | ||||
\(22\) | −192.000 | −0.0180316 | ||||||||
\(23\) | − | 10250.2i | − | 0.842461i | −0.906954 | − | 0.421230i | \(-0.861598\pi\) | ||
0.906954 | − | 0.421230i | \(-0.138402\pi\) | |||||||
\(24\) | 3072.00 | + | 3801.41i | 0.222222 | + | 0.274986i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 16687.7i | 0.949461i | ||||||||
\(27\) | 8883.00 | + | 17564.5i | 0.451303 | + | 0.892371i | ||||
\(28\) | 64.0000 | 0.00291545 | ||||||||
\(29\) | − | 2206.17i | − | 0.0904577i | −0.998977 | − | 0.0452289i | \(-0.985598\pi\) | ||
0.998977 | − | 0.0452289i | \(-0.0144017\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 22898.0 | 0.768621 | 0.384311 | − | 0.923204i | \(-0.374439\pi\) | ||||
0.384311 | + | 0.923204i | \(0.374439\pi\) | |||||||
\(32\) | 5792.62i | 0.176777i | ||||||||
\(33\) | −576.000 | − | 712.764i | −0.0160280 | − | 0.0198337i | ||||
\(34\) | −25344.0 | −0.644820 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4896.00 | + | 22808.4i | −0.104938 | + | 0.488864i | ||||
\(37\) | −34058.0 | −0.672379 | −0.336189 | − | 0.941794i | \(-0.609138\pi\) | ||||
−0.336189 | + | 0.941794i | \(0.609138\pi\) | |||||||
\(38\) | 29743.7i | 0.542057i | ||||||||
\(39\) | −61950.0 | + | 50063.2i | −1.04435 | + | 0.843965i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 16766.9i | 0.243277i | 0.992574 | + | 0.121639i | \(0.0388149\pi\) | ||||
−0.992574 | + | 0.121639i | \(0.961185\pi\) | |||||||
\(42\) | 192.000 | + | 237.588i | 0.00259151 | + | 0.00320683i | ||||
\(43\) | 6406.00 | 0.0805715 | 0.0402858 | − | 0.999188i | \(-0.487173\pi\) | ||||
0.0402858 | + | 0.999188i | \(0.487173\pi\) | |||||||
\(44\) | − | 1086.12i | − | 0.0127502i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 57984.0 | 0.595710 | ||||||||
\(47\) | 179888.i | 1.73264i | 0.499489 | + | 0.866320i | \(0.333521\pi\) | ||||
−0.499489 | + | 0.866320i | \(0.666479\pi\) | |||||||
\(48\) | −21504.0 | + | 17377.9i | −0.194444 | + | 0.157135i | ||||
\(49\) | −117645. | −0.999966 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −76032.0 | − | 94084.8i | −0.573173 | − | 0.709266i | ||||
\(52\) | −94400.0 | −0.671370 | ||||||||
\(53\) | − | 192548.i | − | 1.29334i | −0.762772 | − | 0.646668i | \(-0.776162\pi\) | ||
0.762772 | − | 0.646668i | \(-0.223838\pi\) | |||||||
\(54\) | −99360.0 | + | 50249.8i | −0.631001 | + | 0.319120i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 362.039i | 0.00206154i | ||||||||
\(57\) | −110418. | + | 89231.2i | −0.596232 | + | 0.481828i | ||||
\(58\) | 12480.0 | 0.0639633 | ||||||||
\(59\) | 326819.i | 1.59130i | 0.605758 | + | 0.795649i | \(0.292870\pi\) | ||||
−0.605758 | + | 0.795649i | \(0.707130\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −62566.0 | −0.275644 | −0.137822 | − | 0.990457i | \(-0.544010\pi\) | ||||
−0.137822 | + | 0.990457i | \(0.544010\pi\) | |||||||
\(62\) | 129531.i | 0.543497i | ||||||||
\(63\) | −306.000 | + | 1425.53i | −0.00122377 | + | 0.00570104i | ||||
\(64\) | −32768.0 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4032.00 | − | 3258.35i | 0.0140245 | − | 0.0113335i | ||||
\(67\) | −438698. | −1.45862 | −0.729308 | − | 0.684185i | \(-0.760158\pi\) | ||||
−0.729308 | + | 0.684185i | \(0.760158\pi\) | |||||||
\(68\) | − | 143367.i | − | 0.455956i | ||||||
\(69\) | 173952. | + | 215255.i | 0.529520 | + | 0.655247i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 68221.7i | 0.190611i | 0.995448 | + | 0.0953053i | \(0.0303827\pi\) | ||||
−0.995448 | + | 0.0953053i | \(0.969617\pi\) | |||||||
\(72\) | −129024. | − | 27696.0i | −0.345679 | − | 0.0742026i | ||||
\(73\) | 730510. | 1.87784 | 0.938918 | − | 0.344141i | \(-0.111830\pi\) | ||||
0.938918 | + | 0.344141i | \(0.111830\pi\) | |||||||
\(74\) | − | 192661.i | − | 0.475444i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −168256. | −0.383292 | ||||||||
\(77\) | − | 67.8823i | − | 0.000148691i | ||||||
\(78\) | −283200. | − | 350442.i | −0.596773 | − | 0.738469i | ||||
\(79\) | 340562. | 0.690740 | 0.345370 | − | 0.938467i | \(-0.387753\pi\) | ||||
0.345370 | + | 0.938467i | \(0.387753\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −484623. | − | 218106.i | −0.911904 | − | 0.410404i | ||||
\(82\) | −94848.0 | −0.172023 | ||||||||
\(83\) | 496253.i | 0.867899i | 0.900937 | + | 0.433949i | \(0.142880\pi\) | ||||
−0.900937 | + | 0.433949i | \(0.857120\pi\) | |||||||
\(84\) | −1344.00 | + | 1086.12i | −0.00226757 | + | 0.00183248i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 36237.8i | 0.0569727i | ||||||||
\(87\) | 37440.0 | + | 46329.6i | 0.0568562 | + | 0.0703560i | ||||
\(88\) | 6144.00 | 0.00901578 | ||||||||
\(89\) | 386725.i | 0.548570i | 0.961648 | + | 0.274285i | \(0.0884412\pi\) | ||||
−0.961648 | + | 0.274285i | \(0.911559\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5900.00 | −0.00782939 | ||||||||
\(92\) | 328007.i | 0.421230i | ||||||||
\(93\) | −480858. | + | 388592.i | −0.597817 | + | 0.483109i | ||||
\(94\) | −1.01760e6 | −1.22516 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −98304.0 | − | 121645.i | −0.111111 | − | 0.137493i | ||||
\(97\) | 281086. | 0.307981 | 0.153991 | − | 0.988072i | \(-0.450787\pi\) | ||||
0.153991 | + | 0.988072i | \(0.450787\pi\) | |||||||
\(98\) | − | 665501.i | − | 0.707083i | ||||||
\(99\) | 24192.0 | + | 5192.99i | 0.0249325 | + | 0.00535195i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 945362.i | 0.917559i | 0.888550 | + | 0.458780i | \(0.151713\pi\) | ||||
−0.888550 | + | 0.458780i | \(0.848287\pi\) | |||||||
\(102\) | 532224. | − | 430102.i | 0.501527 | − | 0.405295i | ||||
\(103\) | 865726. | 0.792262 | 0.396131 | − | 0.918194i | \(-0.370353\pi\) | ||||
0.396131 | + | 0.918194i | \(0.370353\pi\) | |||||||
\(104\) | − | 534007.i | − | 0.474730i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.08922e6 | 0.914527 | ||||||||
\(107\) | 1.47410e6i | 1.20330i | 0.798759 | + | 0.601651i | \(0.205490\pi\) | ||||
−0.798759 | + | 0.601651i | \(0.794510\pi\) | |||||||
\(108\) | −284256. | − | 562065.i | −0.225652 | − | 0.446185i | ||||
\(109\) | 650810. | 0.502545 | 0.251272 | − | 0.967916i | \(-0.419151\pi\) | ||||
0.251272 | + | 0.967916i | \(0.419151\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 715218. | − | 577983.i | 0.522961 | − | 0.422616i | ||||
\(112\) | −2048.00 | −0.00145773 | ||||||||
\(113\) | 1.74417e6i | 1.20879i | 0.796683 | + | 0.604397i | \(0.206586\pi\) | ||||
−0.796683 | + | 0.604397i | \(0.793414\pi\) | |||||||
\(114\) | −504768. | − | 624619.i | −0.340704 | − | 0.421600i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 70597.5i | 0.0452289i | ||||||||
\(117\) | 451350. | − | 2.10265e6i | 0.281810 | − | 1.31283i | ||||
\(118\) | −1.84877e6 | −1.12522 | ||||||||
\(119\) | − | 8960.46i | − | 0.00531728i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.77041e6 | 0.999350 | ||||||||
\(122\) | − | 353927.i | − | 0.194910i | ||||||
\(123\) | −284544. | − | 352105.i | −0.152909 | − | 0.189216i | ||||
\(124\) | −732736. | −0.384311 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −8064.00 | − | 1731.00i | −0.00403124 | − | 0.000865336i | ||||
\(127\) | 2.28053e6 | 1.11333 | 0.556665 | − | 0.830737i | \(-0.312081\pi\) | ||||
0.556665 | + | 0.830737i | \(0.312081\pi\) | |||||||
\(128\) | − | 185364.i | − | 0.0883883i | ||||||
\(129\) | −134526. | + | 108713.i | −0.0626667 | + | 0.0506424i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.07196e6i | 0.476832i | 0.971163 | + | 0.238416i | \(0.0766282\pi\) | ||||
−0.971163 | + | 0.238416i | \(0.923372\pi\) | |||||||
\(132\) | 18432.0 | + | 22808.4i | 0.00801402 | + | 0.00991685i | ||||
\(133\) | −10516.0 | −0.00446988 | ||||||||
\(134\) | − | 2.48165e6i | − | 1.03140i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 811008. | 0.322410 | ||||||||
\(137\) | − | 2.78338e6i | − | 1.08246i | −0.840876 | − | 0.541228i | \(-0.817960\pi\) | ||
0.840876 | − | 0.541228i | \(-0.182040\pi\) | |||||||
\(138\) | −1.21766e6 | + | 984021.i | −0.463330 | + | 0.374427i | ||||
\(139\) | 4.57395e6 | 1.70313 | 0.851563 | − | 0.524253i | \(-0.175655\pi\) | ||||
0.851563 | + | 0.524253i | \(0.175655\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.05280e6 | − | 3.77765e6i | −1.08903 | − | 1.34761i | ||||
\(142\) | −385920. | −0.134782 | ||||||||
\(143\) | 100126.i | 0.0342405i | ||||||||
\(144\) | 156672. | − | 729870.i | 0.0524691 | − | 0.244432i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.13239e6i | 1.32783i | ||||||||
\(147\) | 2.47054e6 | − | 1.99650e6i | 0.777751 | − | 0.628518i | ||||
\(148\) | 1.08986e6 | 0.336189 | ||||||||
\(149\) | − | 4.46010e6i | − | 1.34830i | −0.738595 | − | 0.674149i | \(-0.764511\pi\) | ||
0.738595 | − | 0.674149i | \(-0.235489\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.20809e6 | −0.641338 | −0.320669 | − | 0.947191i | \(-0.603908\pi\) | ||||
−0.320669 | + | 0.947191i | \(0.603908\pi\) | |||||||
\(152\) | − | 951800.i | − | 0.271028i | ||||||
\(153\) | 3.19334e6 | + | 685475.i | 0.891603 | + | 0.191389i | ||||
\(154\) | 384.000 | 0.000105140 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.98240e6 | − | 1.60202e6i | 0.522177 | − | 0.421983i | ||||
\(157\) | 1.28887e6 | 0.333051 | 0.166525 | − | 0.986037i | \(-0.446745\pi\) | ||||
0.166525 | + | 0.986037i | \(0.446745\pi\) | |||||||
\(158\) | 1.92651e6i | 0.488427i | ||||||||
\(159\) | 3.26765e6 | + | 4.04351e6i | 0.812913 | + | 1.00593i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20500.4i | 0.00491231i | ||||||||
\(162\) | 1.23379e6 | − | 2.74144e6i | 0.290200 | − | 0.644813i | ||||
\(163\) | −879914. | −0.203178 | −0.101589 | − | 0.994826i | \(-0.532393\pi\) | ||||
−0.101589 | + | 0.994826i | \(0.532393\pi\) | |||||||
\(164\) | − | 536541.i | − | 0.121639i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.80723e6 | −0.613697 | ||||||||
\(167\) | 5.96760e6i | 1.28130i | 0.767834 | + | 0.640649i | \(0.221335\pi\) | ||||
−0.767834 | + | 0.640649i | \(0.778665\pi\) | |||||||
\(168\) | −6144.00 | − | 7602.81i | −0.00129576 | − | 0.00160342i | ||||
\(169\) | 3.87569e6 | 0.802951 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 804474. | − | 3.74771e6i | 0.160888 | − | 0.749511i | ||||
\(172\) | −204992. | −0.0402858 | ||||||||
\(173\) | 418867.i | 0.0808981i | 0.999182 | + | 0.0404490i | \(0.0128788\pi\) | ||||
−0.999182 | + | 0.0404490i | \(0.987121\pi\) | |||||||
\(174\) | −262080. | + | 211793.i | −0.0497492 | + | 0.0402034i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 34755.7i | 0.00637512i | ||||||||
\(177\) | −5.54630e6 | − | 6.86320e6i | −1.00019 | − | 1.23768i | ||||
\(178\) | −2.18765e6 | −0.387898 | ||||||||
\(179\) | − | 302110.i | − | 0.0526752i | −0.999653 | − | 0.0263376i | \(-0.991616\pi\) | ||
0.999653 | − | 0.0263376i | \(-0.00838448\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.47618e6 | −1.09215 | −0.546076 | − | 0.837735i | \(-0.683879\pi\) | ||||
−0.546076 | + | 0.837735i | \(0.683879\pi\) | |||||||
\(182\) | − | 33375.4i | − | 0.00553621i | ||||||
\(183\) | 1.31389e6 | − | 1.06178e6i | 0.214390 | − | 0.173253i | ||||
\(184\) | −1.85549e6 | −0.297855 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.19821e6 | − | 2.72014e6i | −0.341610 | − | 0.422720i | ||||
\(187\) | −152064. | −0.0232542 | ||||||||
\(188\) | − | 5.75641e6i | − | 0.866320i | ||||||
\(189\) | −17766.0 | − | 35129.1i | −0.00263151 | − | 0.00520333i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.02166e6i | 0.720687i | 0.932820 | + | 0.360344i | \(0.117341\pi\) | ||||
−0.932820 | + | 0.360344i | \(0.882659\pi\) | |||||||
\(192\) | 688128. | − | 556091.i | 0.0972222 | − | 0.0785674i | ||||
\(193\) | −3.50093e6 | −0.486980 | −0.243490 | − | 0.969903i | \(-0.578292\pi\) | ||||
−0.243490 | + | 0.969903i | \(0.578292\pi\) | |||||||
\(194\) | 1.59006e6i | 0.217775i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.76464e6 | 0.499983 | ||||||||
\(197\) | 4.85423e6i | 0.634923i | 0.948271 | + | 0.317462i | \(0.102830\pi\) | ||||
−0.948271 | + | 0.317462i | \(0.897170\pi\) | |||||||
\(198\) | −29376.0 | + | 136851.i | −0.00378440 | + | 0.0176300i | ||||
\(199\) | −9.50976e6 | −1.20673 | −0.603365 | − | 0.797465i | \(-0.706174\pi\) | ||||
−0.603365 | + | 0.797465i | \(0.706174\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.21266e6 | − | 7.44495e6i | 1.13448 | − | 0.916798i | ||||
\(202\) | −5.34778e6 | −0.648812 | ||||||||
\(203\) | 4412.35i | 0.000527450i | ||||||||
\(204\) | 2.43302e6 | + | 3.01071e6i | 0.286587 | + | 0.354633i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.89729e6i | 0.560214i | ||||||||
\(207\) | −7.30598e6 | − | 1.56828e6i | −0.823697 | − | 0.176813i | ||||
\(208\) | 3.02080e6 | 0.335685 | ||||||||
\(209\) | 178462.i | 0.0195483i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.06414e6 | 0.751990 | 0.375995 | − | 0.926622i | \(-0.377301\pi\) | ||||
0.375995 | + | 0.926622i | \(0.377301\pi\) | |||||||
\(212\) | 6.16154e6i | 0.646668i | ||||||||
\(213\) | −1.15776e6 | − | 1.43265e6i | −0.119806 | − | 0.148253i | ||||
\(214\) | −8.33875e6 | −0.850863 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.17952e6 | − | 1.60799e6i | 0.315501 | − | 0.159560i | ||||
\(217\) | −45796.0 | −0.00448176 | ||||||||
\(218\) | 3.68154e6i | 0.355353i | ||||||||
\(219\) | −1.53407e7 | + | 1.23972e7i | −1.46054 | + | 1.18029i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.32167e7i | 1.22446i | ||||||||
\(222\) | 3.26957e6 | + | 4.04588e6i | 0.298835 | + | 0.369789i | ||||
\(223\) | −4.66891e6 | −0.421019 | −0.210509 | − | 0.977592i | \(-0.567512\pi\) | ||||
−0.210509 | + | 0.977592i | \(0.567512\pi\) | |||||||
\(224\) | − | 11585.2i | − | 0.00103077i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.86650e6 | −0.854747 | ||||||||
\(227\) | 1.96525e7i | 1.68012i | 0.542494 | + | 0.840059i | \(0.317480\pi\) | ||||
−0.542494 | + | 0.840059i | \(0.682520\pi\) | |||||||
\(228\) | 3.53338e6 | − | 2.85540e6i | 0.298116 | − | 0.240914i | ||||
\(229\) | −4.48178e6 | −0.373202 | −0.186601 | − | 0.982436i | \(-0.559747\pi\) | ||||
−0.186601 | + | 0.982436i | \(0.559747\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1152.00 | + | 1425.53i | 9.34580e−5 | + | 0.000115648i | ||||
\(232\) | −399360. | −0.0319816 | ||||||||
\(233\) | 2.29286e6i | 0.181263i | 0.995884 | + | 0.0906316i | \(0.0288886\pi\) | ||||
−0.995884 | + | 0.0906316i | \(0.971111\pi\) | |||||||
\(234\) | 1.18944e7 | + | 2.55322e6i | 0.928314 | + | 0.199270i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 1.04582e7i | − | 0.795649i | ||||||
\(237\) | −7.15180e6 | + | 5.77953e6i | −0.537243 | + | 0.434158i | ||||
\(238\) | 50688.0 | 0.00375988 | ||||||||
\(239\) | 2.64564e6i | 0.193793i | 0.995294 | + | 0.0968964i | \(0.0308915\pi\) | ||||
−0.995294 | + | 0.0968964i | \(0.969108\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.99581e6 | −0.499789 | −0.249894 | − | 0.968273i | \(-0.580396\pi\) | ||||
−0.249894 | + | 0.968273i | \(0.580396\pi\) | |||||||
\(242\) | 1.00149e7i | 0.706647i | ||||||||
\(243\) | 1.38785e7 | − | 3.64411e6i | 0.967214 | − | 0.253964i | ||||
\(244\) | 2.00211e6 | 0.137822 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.99181e6 | − | 1.60962e6i | 0.133796 | − | 0.108123i | ||||
\(247\) | 1.55111e7 | 1.02932 | ||||||||
\(248\) | − | 4.14498e6i | − | 0.271749i | ||||||
\(249\) | −8.42170e6 | − | 1.04213e7i | −0.545508 | − | 0.675032i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.84990e7i | 1.80223i | 0.433585 | + | 0.901113i | \(0.357248\pi\) | ||||
−0.433585 | + | 0.901113i | \(0.642752\pi\) | |||||||
\(252\) | 9792.00 | − | 45616.9i | 0.000611885 | − | 0.00285052i | ||||
\(253\) | 347904. | 0.0214831 | ||||||||
\(254\) | 1.29006e7i | 0.787243i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.04858e6 | 0.0625000 | ||||||||
\(257\) | − | 186812.i | − | 0.0110054i | −0.999985 | − | 0.00550269i | \(-0.998248\pi\) | ||
0.999985 | − | 0.00550269i | \(-0.00175157\pi\) | |||||||
\(258\) | −614976. | − | 760994.i | −0.0358096 | − | 0.0443121i | ||||
\(259\) | 68116.0 | 0.00392058 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.57248e6 | − | 337544.i | −0.0884430 | − | 0.0189850i | ||||
\(262\) | −6.06394e6 | −0.337171 | ||||||||
\(263\) | − | 8.61541e6i | − | 0.473597i | −0.971559 | − | 0.236798i | \(-0.923902\pi\) | ||
0.971559 | − | 0.236798i | \(-0.0760981\pi\) | |||||||
\(264\) | −129024. | + | 104267.i | −0.00701227 | + | 0.00566677i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 59487.5i | − | 0.00316068i | ||||||
\(267\) | −6.56294e6 | − | 8.12123e6i | −0.344798 | − | 0.426666i | ||||
\(268\) | 1.40383e7 | 0.729308 | ||||||||
\(269\) | 7.55132e6i | 0.387941i | 0.981007 | + | 0.193971i | \(0.0621367\pi\) | ||||
−0.981007 | + | 0.193971i | \(0.937863\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.39445e7 | 0.700642 | 0.350321 | − | 0.936630i | \(-0.386073\pi\) | ||||
0.350321 | + | 0.936630i | \(0.386073\pi\) | |||||||
\(272\) | 4.58775e6i | 0.227978i | ||||||||
\(273\) | 123900. | − | 100126.i | 0.00608952 | − | 0.00492108i | ||||
\(274\) | 1.57452e7 | 0.765412 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5.56646e6 | − | 6.88815e6i | −0.264760 | − | 0.327624i | ||||
\(277\) | −2.81293e7 | −1.32349 | −0.661744 | − | 0.749730i | \(-0.730183\pi\) | ||||
−0.661744 | + | 0.749730i | \(0.730183\pi\) | |||||||
\(278\) | 2.58741e7i | 1.20429i | ||||||||
\(279\) | 3.50339e6 | − | 1.63209e7i | 0.161316 | − | 0.751503i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 2.23430e7i | − | 1.00698i | −0.864000 | − | 0.503491i | \(-0.832049\pi\) | ||
0.864000 | − | 0.503491i | \(-0.167951\pi\) | |||||||
\(282\) | 2.13696e7 | − | 1.72692e7i | 0.952904 | − | 0.770063i | ||||
\(283\) | −1.01418e7 | −0.447464 | −0.223732 | − | 0.974651i | \(-0.571824\pi\) | ||||
−0.223732 | + | 0.974651i | \(0.571824\pi\) | |||||||
\(284\) | − | 2.18309e6i | − | 0.0953053i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −566400. | −0.0242117 | ||||||||
\(287\) | − | 33533.8i | − | 0.00141853i | ||||||
\(288\) | 4.12877e6 | + | 886271.i | 0.172840 | + | 0.0371013i | ||||
\(289\) | 4.06512e6 | 0.168415 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.90281e6 | + | 4.77019e6i | −0.239541 | + | 0.193578i | ||||
\(292\) | −2.33763e7 | −0.938918 | ||||||||
\(293\) | − | 2.78468e7i | − | 1.10706i | −0.832828 | − | 0.553532i | \(-0.813280\pi\) | ||
0.832828 | − | 0.553532i | \(-0.186720\pi\) | |||||||
\(294\) | 1.12939e7 | + | 1.39755e7i | 0.444429 | + | 0.549953i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.16516e6i | 0.237722i | ||||||||
\(297\) | −596160. | + | 301499.i | −0.0227559 | + | 0.0115084i | ||||
\(298\) | 2.52301e7 | 0.953391 | ||||||||
\(299\) | − | 3.02381e7i | − | 1.13121i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12812.0 | −0.000469805 | ||||||||
\(302\) | − | 1.24909e7i | − | 0.453494i | ||||||
\(303\) | −1.60433e7 | − | 1.98526e7i | −0.576722 | − | 0.713657i | ||||
\(304\) | 5.38419e6 | 0.191646 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.87763e6 | + | 1.80643e7i | −0.135333 | + | 0.630458i | ||||
\(307\) | 3.63254e7 | 1.25544 | 0.627718 | − | 0.778440i | \(-0.283989\pi\) | ||||
0.627718 | + | 0.778440i | \(0.283989\pi\) | |||||||
\(308\) | 2172.23i | 7.43454e-5i | ||||||||
\(309\) | −1.81802e7 | + | 1.46919e7i | −0.616204 | + | 0.497968i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 3.59921e7i | − | 1.19654i | −0.801296 | − | 0.598268i | \(-0.795856\pi\) | ||
0.801296 | − | 0.598268i | \(-0.204144\pi\) | |||||||
\(312\) | 9.06240e6 | + | 1.12141e7i | 0.298387 | + | 0.369235i | ||||
\(313\) | −4.01099e7 | −1.30803 | −0.654016 | − | 0.756480i | \(-0.726917\pi\) | ||||
−0.654016 | + | 0.756480i | \(0.726917\pi\) | |||||||
\(314\) | 7.29095e6i | 0.235502i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.08980e7 | −0.345370 | ||||||||
\(317\) | − | 3.94377e7i | − | 1.23804i | −0.785377 | − | 0.619018i | \(-0.787531\pi\) | ||
0.785377 | − | 0.619018i | \(-0.212469\pi\) | |||||||
\(318\) | −2.28735e7 | + | 1.84846e7i | −0.711299 | + | 0.574816i | ||||
\(319\) | 74880.0 | 0.00230671 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.50163e7 | − | 3.09560e7i | −0.756323 | − | 0.935902i | ||||
\(322\) | −115968. | −0.00347353 | ||||||||
\(323\) | 2.35570e7i | 0.699058i | ||||||||
\(324\) | 1.55079e7 | + | 6.97938e6i | 0.455952 | + | 0.205202i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 4.97755e6i | − | 0.143669i | ||||||
\(327\) | −1.36670e7 | + | 1.10446e7i | −0.390868 | + | 0.315869i | ||||
\(328\) | 3.03514e6 | 0.0860115 | ||||||||
\(329\) | − | 359776.i | − | 0.0101029i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.78363e7 | 0.767586 | 0.383793 | − | 0.923419i | \(-0.374618\pi\) | ||||
0.383793 | + | 0.923419i | \(0.374618\pi\) | |||||||
\(332\) | − | 1.58801e7i | − | 0.433949i | ||||||
\(333\) | −5.21087e6 | + | 2.42753e7i | −0.141117 | + | 0.657403i | ||||
\(334\) | −3.37578e7 | −0.906014 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 43008.0 | − | 34755.7i | 0.00113379 | − | 0.000916238i | ||||
\(337\) | 2.37897e7 | 0.621582 | 0.310791 | − | 0.950478i | \(-0.399406\pi\) | ||||
0.310791 | + | 0.950478i | \(0.399406\pi\) | |||||||
\(338\) | 2.19242e7i | 0.567772i | ||||||||
\(339\) | −2.95995e7 | − | 3.66275e7i | −0.759775 | − | 0.940174i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 777184.i | 0.0196002i | ||||||||
\(342\) | 2.12003e7 | + | 4.55079e6i | 0.529984 | + | 0.113765i | ||||
\(343\) | 470588. | 0.0116616 | ||||||||
\(344\) | − | 1.15961e6i | − | 0.0284863i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.36947e6 | −0.0572036 | ||||||||
\(347\) | − | 5.34078e7i | − | 1.27825i | −0.769103 | − | 0.639125i | \(-0.779297\pi\) | ||
0.769103 | − | 0.639125i | \(-0.220703\pi\) | |||||||
\(348\) | −1.19808e6 | − | 1.48255e6i | −0.0284281 | − | 0.0351780i | ||||
\(349\) | 4.71677e7 | 1.10961 | 0.554803 | − | 0.831982i | \(-0.312794\pi\) | ||||
0.554803 | + | 0.831982i | \(0.312794\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.62048e7 | + | 5.18154e7i | 0.605983 | + | 1.19822i | ||||
\(352\) | −196608. | −0.00450789 | ||||||||
\(353\) | − | 1.75443e7i | − | 0.398852i | −0.979913 | − | 0.199426i | \(-0.936092\pi\) | ||
0.979913 | − | 0.199426i | \(-0.0639078\pi\) | |||||||
\(354\) | 3.88241e7 | − | 3.13746e7i | 0.875169 | − | 0.707243i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 1.23752e7i | − | 0.274285i | ||||||
\(357\) | 152064. | + | 188170.i | 0.00334212 | + | 0.00413566i | ||||
\(358\) | 1.70899e6 | 0.0372470 | ||||||||
\(359\) | − | 6.18249e7i | − | 1.33623i | −0.744059 | − | 0.668113i | \(-0.767102\pi\) | ||
0.744059 | − | 0.668113i | \(-0.232898\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.93993e7 | −0.412349 | ||||||||
\(362\) | − | 3.66348e7i | − | 0.772269i | ||||||
\(363\) | −3.71786e7 | + | 3.00448e7i | −0.777272 | + | 0.628131i | ||||
\(364\) | 188800. | 0.00391469 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6.00634e6 | + | 7.43246e6i | 0.122509 | + | 0.151597i | ||||
\(367\) | 3.40461e7 | 0.688761 | 0.344381 | − | 0.938830i | \(-0.388089\pi\) | ||||
0.344381 | + | 0.938830i | \(0.388089\pi\) | |||||||
\(368\) | − | 1.04962e7i | − | 0.210615i | ||||||
\(369\) | 1.19508e7 | + | 2.56534e6i | 0.237859 | + | 0.0510582i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 385096.i | 0.00754132i | ||||||||
\(372\) | 1.53875e7 | − | 1.24349e7i | 0.298908 | − | 0.241554i | ||||
\(373\) | 5.15781e7 | 0.993892 | 0.496946 | − | 0.867782i | \(-0.334455\pi\) | ||||
0.496946 | + | 0.867782i | \(0.334455\pi\) | |||||||
\(374\) | − | 860204.i | − | 0.0164432i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.25632e7 | 0.612581 | ||||||||
\(377\) | − | 6.50821e6i | − | 0.121461i | ||||||
\(378\) | 198720. | − | 100500.i | 0.00367931 | − | 0.00186076i | ||||
\(379\) | 4.28828e7 | 0.787709 | 0.393855 | − | 0.919173i | \(-0.371141\pi\) | ||||
0.393855 | + | 0.919173i | \(0.371141\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.78910e7 | + | 3.87018e7i | −0.865923 | + | 0.699772i | ||||
\(382\) | −2.84068e7 | −0.509603 | ||||||||
\(383\) | 1.51307e7i | 0.269316i | 0.990892 | + | 0.134658i | \(0.0429936\pi\) | ||||
−0.990892 | + | 0.134658i | \(0.957006\pi\) | |||||||
\(384\) | 3.14573e6 | + | 3.89264e6i | 0.0555556 | + | 0.0687465i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 1.98043e7i | − | 0.344347i | ||||||
\(387\) | 980118. | − | 4.56596e6i | 0.0169101 | − | 0.0787770i | ||||
\(388\) | −8.99475e6 | −0.153991 | ||||||||
\(389\) | 6.15319e7i | 1.04533i | 0.852540 | + | 0.522663i | \(0.175061\pi\) | ||||
−0.852540 | + | 0.522663i | \(0.824939\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.59233e7 | 0.768251 | ||||||||
\(392\) | 2.12960e7i | 0.353541i | ||||||||
\(393\) | −1.81918e7 | − | 2.25112e7i | −0.299708 | − | 0.370870i | ||||
\(394\) | −2.74596e7 | −0.448959 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −774144. | − | 166176.i | −0.0124663 | − | 0.00267598i | ||||
\(397\) | 8.55816e7 | 1.36776 | 0.683878 | − | 0.729596i | \(-0.260292\pi\) | ||||
0.683878 | + | 0.729596i | \(0.260292\pi\) | |||||||
\(398\) | − | 5.37953e7i | − | 0.853287i | ||||||
\(399\) | 220836. | − | 178462.i | 0.00347657 | − | 0.00280949i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 4.09739e7i | − | 0.635439i | −0.948185 | − | 0.317719i | \(-0.897083\pi\) | ||
0.948185 | − | 0.317719i | \(-0.102917\pi\) | |||||||
\(402\) | 4.21150e7 | + | 5.21147e7i | 0.648274 | + | 0.802198i | ||||
\(403\) | 6.75491e7 | 1.03206 | ||||||||
\(404\) | − | 3.02516e7i | − | 0.458780i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −24960.0 | −0.000372964 | ||||||||
\(407\) | − | 1.15597e6i | − | 0.0171460i | ||||||
\(408\) | −1.70312e7 | + | 1.37633e7i | −0.250763 | + | 0.202647i | ||||
\(409\) | 6.10556e7 | 0.892391 | 0.446196 | − | 0.894935i | \(-0.352779\pi\) | ||||
0.446196 | + | 0.894935i | \(0.352779\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.72355e7 | + | 5.84509e7i | 0.680366 | + | 0.841910i | ||||
\(412\) | −2.77032e7 | −0.396131 | ||||||||
\(413\) | − | 653638.i | − | 0.00927870i | ||||||
\(414\) | 8.87155e6 | − | 4.13289e7i | 0.125025 | − | 0.582442i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.70882e7i | 0.237365i | ||||||||
\(417\) | −9.60529e7 | + | 7.76224e7i | −1.32465 | + | 1.07048i | ||||
\(418\) | −1.00954e6 | −0.0138227 | ||||||||
\(419\) | 3.38860e7i | 0.460657i | 0.973113 | + | 0.230329i | \(0.0739801\pi\) | ||||
−0.973113 | + | 0.230329i | \(0.926020\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.96156e7 | −0.262879 | −0.131439 | − | 0.991324i | \(-0.541960\pi\) | ||||
−0.131439 | + | 0.991324i | \(0.541960\pi\) | |||||||
\(422\) | 3.99608e7i | 0.531737i | ||||||||
\(423\) | 1.28218e8 | + | 2.75229e7i | 1.69405 | + | 0.363641i | ||||
\(424\) | −3.48549e7 | −0.457263 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 8.10432e6 | − | 6.54928e6i | 0.104831 | − | 0.0847159i | ||||
\(427\) | 125132. | 0.00160725 | ||||||||
\(428\) | − | 4.71711e7i | − | 0.601651i | ||||||
\(429\) | −1.69920e6 | − | 2.10265e6i | −0.0215215 | − | 0.0266315i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 4.01587e7i | − | 0.501589i | −0.968040 | − | 0.250795i | \(-0.919308\pi\) | ||
0.968040 | − | 0.250795i | \(-0.0806919\pi\) | |||||||
\(432\) | 9.09619e6 | + | 1.79861e7i | 0.112826 | + | 0.223093i | ||||
\(433\) | 845854. | 0.0104191 | 0.00520957 | − | 0.999986i | \(-0.498342\pi\) | ||||
0.00520957 | + | 0.999986i | \(0.498342\pi\) | |||||||
\(434\) | − | 259061.i | − | 0.00316908i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.08259e7 | −0.251272 | ||||||||
\(437\) | − | 5.38957e7i | − | 0.645817i | ||||||
\(438\) | −7.01290e7 | − | 8.67802e7i | −0.834594 | − | 1.03276i | ||||
\(439\) | −7.48204e7 | −0.884354 | −0.442177 | − | 0.896928i | \(-0.645794\pi\) | ||||
−0.442177 | + | 0.896928i | \(0.645794\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.79997e7 | + | 8.38531e7i | −0.209869 | + | 0.977695i | ||||
\(442\) | −7.47648e7 | −0.865825 | ||||||||
\(443\) | 1.25246e8i | 1.44063i | 0.693649 | + | 0.720313i | \(0.256002\pi\) | ||||
−0.693649 | + | 0.720313i | \(0.743998\pi\) | |||||||
\(444\) | −2.28870e7 | + | 1.84955e7i | −0.261481 | + | 0.211308i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 2.64114e7i | − | 0.297705i | ||||||
\(447\) | 7.56904e7 | + | 9.36621e7i | 0.847458 | + | 1.04868i | ||||
\(448\) | 65536.0 | 0.000728863 | ||||||||
\(449\) | 1.12812e8i | 1.24628i | 0.782109 | + | 0.623142i | \(0.214144\pi\) | ||||
−0.782109 | + | 0.623142i | \(0.785856\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −569088. | −0.00620369 | ||||||||
\(452\) | − | 5.58133e7i | − | 0.604397i | ||||||
\(453\) | 4.63700e7 | − | 3.74726e7i | 0.498818 | − | 0.403106i | ||||
\(454\) | −1.11171e8 | −1.18802 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.61526e7 | + | 1.99878e7i | 0.170352 | + | 0.210800i | ||||
\(457\) | −1.57358e8 | −1.64870 | −0.824350 | − | 0.566081i | \(-0.808459\pi\) | ||||
−0.824350 | + | 0.566081i | \(0.808459\pi\) | |||||||
\(458\) | − | 2.53528e7i | − | 0.263894i | ||||||
\(459\) | −7.86931e7 | + | 3.97979e7i | −0.813764 | + | 0.411549i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 1.83107e8i | − | 1.86897i | −0.356002 | − | 0.934485i | \(-0.615860\pi\) | ||
0.356002 | − | 0.934485i | \(-0.384140\pi\) | |||||||
\(462\) | −8064.00 | + | 6516.70i | −8.17758e−5 | + | 6.60848e-5i | ||||
\(463\) | −1.77978e8 | −1.79318 | −0.896588 | − | 0.442866i | \(-0.853962\pi\) | ||||
−0.896588 | + | 0.442866i | \(0.853962\pi\) | |||||||
\(464\) | − | 2.25912e6i | − | 0.0226144i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.29704e7 | −0.128172 | ||||||||
\(467\) | 9.35797e7i | 0.918821i | 0.888224 | + | 0.459410i | \(0.151939\pi\) | ||||
−0.888224 | + | 0.459410i | \(0.848061\pi\) | |||||||
\(468\) | −1.44432e7 | + | 6.72849e7i | −0.140905 | + | 0.656417i | ||||
\(469\) | 877396. | 0.00850505 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.70663e7 | + | 2.18728e7i | −0.259039 | + | 0.209335i | ||||
\(472\) | 5.91606e7 | 0.562609 | ||||||||
\(473\) | 217427.i | 0.00205461i | ||||||||
\(474\) | −3.26940e7 | − | 4.04567e7i | −0.306996 | − | 0.379888i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 286735.i | 0.00265864i | ||||||||
\(477\) | −1.37241e8 | − | 2.94598e7i | −1.26453 | − | 0.271441i | ||||
\(478\) | −1.49660e7 | −0.137032 | ||||||||
\(479\) | 1.07662e8i | 0.979617i | 0.871830 | + | 0.489808i | \(0.162933\pi\) | ||||
−0.871830 | + | 0.489808i | \(0.837067\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.00471e8 | −0.902830 | ||||||||
\(482\) | − | 3.95743e7i | − | 0.353404i | ||||||
\(483\) | −347904. | − | 430509.i | −0.00308758 | − | 0.00382068i | ||||
\(484\) | −5.66531e7 | −0.499675 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.06142e7 | + | 7.85084e7i | 0.179580 | + | 0.683923i | ||||
\(487\) | 4.14432e6 | 0.0358811 | 0.0179406 | − | 0.999839i | \(-0.494289\pi\) | ||||
0.0179406 | + | 0.999839i | \(0.494289\pi\) | |||||||
\(488\) | 1.13257e7i | 0.0974549i | ||||||||
\(489\) | 1.84782e7 | − | 1.49326e7i | 0.158028 | − | 0.127706i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.19347e8i | 1.00824i | 0.863633 | + | 0.504122i | \(0.168184\pi\) | ||||
−0.863633 | + | 0.504122i | \(0.831816\pi\) | |||||||
\(492\) | 9.10541e6 | + | 1.12674e7i | 0.0764547 | + | 0.0946078i | ||||
\(493\) | 9.88416e6 | 0.0824896 | ||||||||
\(494\) | 8.77440e7i | 0.727841i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.34476e7 | 0.192155 | ||||||||
\(497\) | − | 136443.i | − | 0.00111143i | ||||||
\(498\) | 5.89519e7 | − | 4.76403e7i | 0.477320 | − | 0.385733i | ||||
\(499\) | 1.17436e8 | 0.945144 | 0.472572 | − | 0.881292i | \(-0.343326\pi\) | ||||
0.472572 | + | 0.881292i | \(0.343326\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.01273e8 | − | 1.25320e8i | −0.805346 | − | 0.996565i | ||||
\(502\) | −1.61215e8 | −1.27437 | ||||||||
\(503\) | − | 1.99753e8i | − | 1.56960i | −0.619747 | − | 0.784802i | \(-0.712765\pi\) | ||
0.619747 | − | 0.784802i | \(-0.287235\pi\) | |||||||
\(504\) | 258048. | + | 55391.9i | 0.00201562 | + | 0.000432668i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.96804e6i | 0.0151909i | ||||||||
\(507\) | −8.13895e7 | + | 6.57727e7i | −0.624517 | + | 0.504686i | ||||
\(508\) | −7.29768e7 | −0.556665 | ||||||||
\(509\) | 1.12725e8i | 0.854804i | 0.904062 | + | 0.427402i | \(0.140571\pi\) | ||||
−0.904062 | + | 0.427402i | \(0.859429\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.46102e6 | −0.0109495 | ||||||||
\(512\) | 5.93164e6i | 0.0441942i | ||||||||
\(513\) | 4.67068e7 | + | 9.23543e7i | 0.345962 | + | 0.684077i | ||||
\(514\) | 1.05677e6 | 0.00778198 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4.30483e6 | − | 3.47883e6i | 0.0313334 | − | 0.0253212i | ||||
\(517\) | −6.10560e6 | −0.0441832 | ||||||||
\(518\) | 385322.i | 0.00277227i | ||||||||
\(519\) | −7.10842e6 | − | 8.79622e6i | −0.0508476 | − | 0.0629207i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 1.14581e8i | − | 0.810215i | −0.914269 | − | 0.405108i | \(-0.867234\pi\) | ||
0.914269 | − | 0.405108i | \(-0.132766\pi\) | |||||||
\(522\) | 1.90944e6 | − | 8.89529e6i | 0.0134244 | − | 0.0625387i | ||||
\(523\) | 1.49806e8 | 1.04719 | 0.523594 | − | 0.851968i | \(-0.324591\pi\) | ||||
0.523594 | + | 0.851968i | \(0.324591\pi\) | |||||||
\(524\) | − | 3.43028e7i | − | 0.238416i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.87361e7 | 0.334884 | ||||||||
\(527\) | 1.02588e8i | 0.700916i | ||||||||
\(528\) | −589824. | − | 729870.i | −0.00400701 | − | 0.00495842i | ||||
\(529\) | 4.29689e7 | 0.290260 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.32945e8 | + | 5.00033e7i | 1.55586 | + | 0.333976i | ||||
\(532\) | 336512. | 0.00223494 | ||||||||
\(533\) | 4.94624e7i | 0.326658i | ||||||||
\(534\) | 4.59406e7 | − | 3.71256e7i | 0.301698 | − | 0.243809i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 7.94128e7i | 0.515699i | ||||||||
\(537\) | 5.12698e6 | + | 6.34431e6i | 0.0331084 | + | 0.0409696i | ||||
\(538\) | −4.27167e7 | −0.274316 | ||||||||
\(539\) | − | 3.99300e6i | − | 0.0254996i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.57017e8 | −0.991644 | −0.495822 | − | 0.868424i | \(-0.665133\pi\) | ||||
−0.495822 | + | 0.868424i | \(0.665133\pi\) | |||||||
\(542\) | 7.88822e7i | 0.495429i | ||||||||
\(543\) | 1.36000e8 | − | 1.09904e8i | 0.849452 | − | 0.686461i | ||||
\(544\) | −2.59523e7 | −0.161205 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 566400. | + | 700884.i | 0.00347973 | + | 0.00430594i | ||||
\(547\) | 2.79469e8 | 1.70754 | 0.853770 | − | 0.520650i | \(-0.174310\pi\) | ||||
0.853770 | + | 0.520650i | \(0.174310\pi\) | |||||||
\(548\) | 8.90680e7i | 0.541228i | ||||||||
\(549\) | −9.57260e6 | + | 4.45948e7i | −0.0578513 | + | 0.269505i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 1.16001e7i | − | 0.0693434i | ||||||
\(552\) | 3.89652e7 | − | 3.14887e7i | 0.231665 | − | 0.187213i | ||||
\(553\) | −681124. | −0.00402764 | ||||||||
\(554\) | − | 1.59123e8i | − | 0.935847i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.46366e8 | −0.851563 | ||||||||
\(557\) | − | 1.50294e8i | − | 0.869712i | −0.900500 | − | 0.434856i | \(-0.856799\pi\) | ||
0.900500 | − | 0.434856i | \(-0.143201\pi\) | |||||||
\(558\) | 9.23247e7 | + | 1.98182e7i | 0.531393 | + | 0.114067i | ||||
\(559\) | 1.88977e7 | 0.108187 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.19334e6 | − | 2.58061e6i | 0.0180866 | − | 0.0146162i | ||||
\(562\) | 1.26391e8 | 0.712044 | ||||||||
\(563\) | − | 8.27836e7i | − | 0.463894i | −0.972728 | − | 0.231947i | \(-0.925490\pi\) | ||
0.972728 | − | 0.231947i | \(-0.0745097\pi\) | |||||||
\(564\) | 9.76896e7 | + | 1.20885e8i | 0.544516 | + | 0.673805i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 5.73710e7i | − | 0.316405i | ||||||
\(567\) | 969246. | + | 436211.i | 0.00531722 | + | 0.00239303i | ||||
\(568\) | 1.23494e7 | 0.0673911 | ||||||||
\(569\) | − | 2.57230e8i | − | 1.39632i | −0.715942 | − | 0.698160i | \(-0.754003\pi\) | ||
0.715942 | − | 0.698160i | \(-0.245997\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.84039e7 | 0.152570 | 0.0762852 | − | 0.997086i | \(-0.475694\pi\) | ||||
0.0762852 | + | 0.997086i | \(0.475694\pi\) | |||||||
\(572\) | − | 3.20404e6i | − | 0.0171203i | ||||||
\(573\) | −8.52204e7 | − | 1.05455e8i | −0.452980 | − | 0.560535i | ||||
\(574\) | 189696. | 0.00100305 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −5.01350e6 | + | 2.33558e7i | −0.0262346 | + | 0.122216i | ||||
\(577\) | −6.52476e7 | −0.339654 | −0.169827 | − | 0.985474i | \(-0.554321\pi\) | ||||
−0.169827 | + | 0.985474i | \(0.554321\pi\) | |||||||
\(578\) | 2.29958e7i | 0.119087i | ||||||||
\(579\) | 7.35195e7 | − | 5.94128e7i | 0.378763 | − | 0.306086i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 992506.i | − | 0.00506063i | ||||||
\(582\) | −2.69843e7 | − | 3.33913e7i | −0.136880 | − | 0.169381i | ||||
\(583\) | 6.53530e6 | 0.0329807 | ||||||||
\(584\) | − | 1.32236e8i | − | 0.663915i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.57525e8 | 0.782813 | ||||||||
\(587\) | − | 6.66740e7i | − | 0.329642i | −0.986324 | − | 0.164821i | \(-0.947295\pi\) | ||
0.986324 | − | 0.164821i | \(-0.0527046\pi\) | |||||||
\(588\) | −7.90574e7 | + | 6.38881e7i | −0.388876 | + | 0.314259i | ||||
\(589\) | 1.20398e8 | 0.589213 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.23789e7 | − | 1.01939e8i | −0.399074 | − | 0.493829i | ||||
\(592\) | −3.48754e7 | −0.168095 | ||||||||
\(593\) | 1.53324e8i | 0.735271i | 0.929970 | + | 0.367635i | \(0.119833\pi\) | ||||
−0.929970 | + | 0.367635i | \(0.880167\pi\) | |||||||
\(594\) | −1.70554e6 | − | 3.37239e6i | −0.00813770 | − | 0.0160908i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.42723e8i | 0.674149i | ||||||||
\(597\) | 1.99705e8 | − | 1.61386e8i | 0.938568 | − | 0.758478i | ||||
\(598\) | 1.71053e8 | 0.799883 | ||||||||
\(599\) | − | 2.18294e8i | − | 1.01569i | −0.861448 | − | 0.507846i | \(-0.830442\pi\) | ||
0.861448 | − | 0.507846i | \(-0.169558\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.08478e8 | 0.499709 | 0.249854 | − | 0.968283i | \(-0.419617\pi\) | ||||
0.249854 | + | 0.968283i | \(0.419617\pi\) | |||||||
\(602\) | − | 72475.6i | − | 0.000332202i | ||||||
\(603\) | −6.71208e7 | + | 3.12688e8i | −0.306129 | + | 1.42613i | ||||
\(604\) | 7.06590e7 | 0.320669 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.12303e8 | − | 9.07548e7i | 0.504632 | − | 0.407804i | ||||
\(607\) | 3.43321e8 | 1.53509 | 0.767547 | − | 0.640993i | \(-0.221477\pi\) | ||||
0.767547 | + | 0.640993i | \(0.221477\pi\) | |||||||
\(608\) | 3.04576e7i | 0.135514i | ||||||||
\(609\) | −74880.0 | − | 92659.3i | −0.000331523 | − | 0.000410239i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.30669e8i | 2.32649i | ||||||||
\(612\) | −1.02187e8 | − | 2.19352e7i | −0.445801 | − | 0.0956946i | ||||
\(613\) | −2.96325e8 | −1.28643 | −0.643216 | − | 0.765685i | \(-0.722400\pi\) | ||||
−0.643216 | + | 0.765685i | \(0.722400\pi\) | |||||||
\(614\) | 2.05487e8i | 0.887728i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12288.0 | −5.25701e−5 | ||||||||
\(617\) | − | 1.32676e8i | − | 0.564853i | −0.959289 | − | 0.282426i | \(-0.908861\pi\) | ||
0.959289 | − | 0.282426i | \(-0.0911393\pi\) | |||||||
\(618\) | −8.31097e7 | − | 1.02843e8i | −0.352116 | − | 0.435722i | ||||
\(619\) | −4.14773e8 | −1.74879 | −0.874397 | − | 0.485211i | \(-0.838743\pi\) | ||||
−0.874397 | + | 0.485211i | \(0.838743\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.80040e8 | − | 9.10527e7i | 0.751787 | − | 0.380205i | ||||
\(622\) | 2.03602e8 | 0.846078 | ||||||||
\(623\) | − | 773450.i | − | 0.00319866i | ||||||
\(624\) | −6.34368e7 | + | 5.12647e7i | −0.261088 | + | 0.210991i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 2.26896e8i | − | 0.924919i | ||||||
\(627\) | −3.02861e6 | − | 3.74771e6i | −0.0122868 | − | 0.0152042i | ||||
\(628\) | −4.12438e7 | −0.166525 | ||||||||
\(629\) | − | 1.52588e8i | − | 0.613151i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.03858e8 | 1.20944 | 0.604718 | − | 0.796440i | \(-0.293286\pi\) | ||||
0.604718 | + | 0.796440i | \(0.293286\pi\) | |||||||
\(632\) | − | 6.16483e7i | − | 0.244214i | ||||||
\(633\) | −1.48347e8 | + | 1.19882e8i | −0.584881 | + | 0.472655i | ||||
\(634\) | 2.23093e8 | 0.875424 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.04565e8 | − | 1.29392e8i | −0.406456 | − | 0.502964i | ||||
\(637\) | −3.47053e8 | −1.34269 | ||||||||
\(638\) | 423585.i | 0.00163109i | ||||||||
\(639\) | 4.86259e7 | + | 1.04379e7i | 0.186365 | + | 0.0400047i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.81629e8i | 0.689622i | 0.938672 | + | 0.344811i | \(0.112057\pi\) | ||||
−0.938672 | + | 0.344811i | \(0.887943\pi\) | |||||||
\(642\) | 1.75114e8 | − | 1.41513e8i | 0.661782 | − | 0.534801i | ||||
\(643\) | −1.73811e8 | −0.653798 | −0.326899 | − | 0.945059i | \(-0.606004\pi\) | ||||
−0.326899 | + | 0.945059i | \(0.606004\pi\) | |||||||
\(644\) | − | 656014.i | − | 0.00245615i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.33259e8 | −0.494309 | ||||||||
\(647\) | 2.43137e8i | 0.897713i | 0.893604 | + | 0.448856i | \(0.148168\pi\) | ||||
−0.893604 | + | 0.448856i | \(0.851832\pi\) | |||||||
\(648\) | −3.94813e7 | + | 8.77261e7i | −0.145100 | + | 0.322407i | ||||
\(649\) | −1.10926e7 | −0.0405788 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 961716. | − | 777184.i | 0.00348581 | − | 0.00281696i | ||||
\(652\) | 2.81572e7 | 0.101589 | ||||||||
\(653\) | − | 4.47562e7i | − | 0.160736i | −0.996765 | − | 0.0803681i | \(-0.974390\pi\) | ||
0.996765 | − | 0.0803681i | \(-0.0256096\pi\) | |||||||
\(654\) | −6.24778e7 | − | 7.73123e7i | −0.223353 | − | 0.276386i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.71693e7i | 0.0608193i | ||||||||
\(657\) | 1.11768e8 | − | 5.20681e8i | 0.394114 | − | 1.83601i | ||||
\(658\) | 2.03520e6 | 0.00714380 | ||||||||
\(659\) | 1.13574e8i | 0.396845i | 0.980117 | + | 0.198423i | \(0.0635819\pi\) | ||||
−0.980117 | + | 0.198423i | \(0.936418\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.93464e7 | −0.343992 | −0.171996 | − | 0.985098i | \(-0.555022\pi\) | ||||
−0.171996 | + | 0.985098i | \(0.555022\pi\) | |||||||
\(662\) | 1.57466e8i | 0.542766i | ||||||||
\(663\) | −2.24294e8 | − | 2.77550e8i | −0.769623 | − | 0.952359i | ||||
\(664\) | 8.98314e7 | 0.306849 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.37322e8 | − | 2.94772e7i | −0.464854 | − | 0.0997845i | ||||
\(667\) | −2.26138e7 | −0.0762071 | ||||||||
\(668\) | − | 1.90963e8i | − | 0.640649i | ||||||
\(669\) | 9.80472e7 | − | 7.92341e7i | 0.327459 | − | 0.264627i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 2.12356e6i | − | 0.00702906i | ||||||
\(672\) | 196608. | + | 243290.i | 0.000647878 | + | 0.000801708i | ||||
\(673\) | 2.79412e8 | 0.916642 | 0.458321 | − | 0.888787i | \(-0.348451\pi\) | ||||
0.458321 | + | 0.888787i | \(0.348451\pi\) | |||||||
\(674\) | 1.34575e8i | 0.439525i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.24022e8 | −0.401475 | ||||||||
\(677\) | 4.09293e7i | 0.131907i | 0.997823 | + | 0.0659536i | \(0.0210089\pi\) | ||||
−0.997823 | + | 0.0659536i | \(0.978991\pi\) | |||||||
\(678\) | 2.07196e8 | − | 1.67440e8i | 0.664803 | − | 0.537242i | ||||
\(679\) | −562172. | −0.00179581 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.33514e8 | − | 4.12702e8i | −1.05602 | − | 1.30676i | ||||
\(682\) | −4.39642e6 | −0.0138594 | ||||||||
\(683\) | 3.74260e8i | 1.17466i | 0.809348 | + | 0.587329i | \(0.199820\pi\) | ||||
−0.809348 | + | 0.587329i | \(0.800180\pi\) | |||||||
\(684\) | −2.57432e7 | + | 1.19927e8i | −0.0804440 | + | 0.374755i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.66205e6i | 0.00824600i | ||||||||
\(687\) | 9.41174e7 | − | 7.60584e7i | 0.290268 | − | 0.234572i | ||||
\(688\) | 6.55974e6 | 0.0201429 | ||||||||
\(689\) | − | 5.68017e8i | − | 1.73661i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.15164e8 | 0.349047 | 0.174524 | − | 0.984653i | \(-0.444161\pi\) | ||||
0.174524 | + | 0.984653i | \(0.444161\pi\) | |||||||
\(692\) | − | 1.34038e7i | − | 0.0404490i | ||||||
\(693\) | −48384.0 | − | 10386.0i | −0.000145379 | − | 3.12067e-5i | ||||
\(694\) | 3.02120e8 | 0.903859 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 8.38656e6 | − | 6.77736e6i | 0.0248746 | − | 0.0201017i | ||||
\(697\) | −7.51196e7 | −0.221848 | ||||||||
\(698\) | 2.66821e8i | 0.784609i | ||||||||
\(699\) | −3.89111e7 | − | 4.81500e7i | −0.113931 | − | 0.140982i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 5.65717e7i | − | 0.164227i | −0.996623 | − | 0.0821137i | \(-0.973833\pi\) | ||
0.996623 | − | 0.0821137i | \(-0.0261671\pi\) | |||||||
\(702\) | −2.93112e8 | + | 1.48237e8i | −0.847271 | + | 0.428495i | ||||
\(703\) | −1.79077e8 | −0.515435 | ||||||||
\(704\) | − | 1.11218e6i | − | 0.00318756i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.92456e7 | 0.282031 | ||||||||
\(707\) | − | 1.89072e6i | − | 0.00535020i | ||||||
\(708\) | 1.77482e8 | + | 2.19622e8i | 0.500097 | + | 0.618838i | ||||
\(709\) | −1.28652e8 | −0.360975 | −0.180488 | − | 0.983577i | \(-0.557768\pi\) | ||||
−0.180488 | + | 0.983577i | \(0.557768\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.21060e7 | − | 2.42740e8i | 0.144970 | − | 0.675356i | ||||
\(712\) | 7.00047e7 | 0.193949 | ||||||||
\(713\) | − | 2.34710e8i | − | 0.647533i | ||||||
\(714\) | −1.06445e6 | + | 860204.i | −0.00292435 | + | 0.00236323i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.66752e6i | 0.0263376i | ||||||||
\(717\) | −4.48980e7 | − | 5.55585e7i | −0.121806 | − | 0.150728i | ||||
\(718\) | 3.49735e8 | 0.944855 | ||||||||
\(719\) | 2.01053e8i | 0.540908i | 0.962733 | + | 0.270454i | \(0.0871738\pi\) | ||||
−0.962733 | + | 0.270454i | \(0.912826\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.73145e6 | −0.00461960 | ||||||||
\(722\) | − | 1.09739e8i | − | 0.291575i | ||||||
\(723\) | 1.46912e8 | − | 1.18723e8i | 0.388725 | − | 0.314137i | ||||
\(724\) | 2.07238e8 | 0.546076 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.69959e8 | − | 2.10314e8i | −0.444155 | − | 0.549614i | ||||
\(727\) | −5.23208e8 | −1.36167 | −0.680833 | − | 0.732438i | \(-0.738382\pi\) | ||||
−0.680833 | + | 0.732438i | \(0.738382\pi\) | |||||||
\(728\) | 1.06801e6i | 0.00276811i | ||||||||
\(729\) | −2.29605e8 | + | 3.12051e8i | −0.592651 | + | 0.805459i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.87003e7i | 0.0734742i | ||||||||
\(732\) | −4.20444e7 | + | 3.39770e7i | −0.107195 | + | 0.0866266i | ||||
\(733\) | 6.57372e8 | 1.66917 | 0.834583 | − | 0.550882i | \(-0.185709\pi\) | ||||
0.834583 | + | 0.550882i | \(0.185709\pi\) | |||||||
\(734\) | 1.92594e8i | 0.487028i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.93756e7 | 0.148927 | ||||||||
\(737\) | − | 1.48899e7i | − | 0.0371954i | ||||||
\(738\) | −1.45117e7 | + | 6.76042e7i | −0.0361036 | + | 0.168192i | ||||
\(739\) | 3.50495e8 | 0.868458 | 0.434229 | − | 0.900803i | \(-0.357021\pi\) | ||||
0.434229 | + | 0.900803i | \(0.357021\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.25733e8 | + | 2.63232e8i | −0.800585 | + | 0.646970i | ||||
\(742\) | −2.17843e6 | −0.00533252 | ||||||||
\(743\) | − | 4.66667e8i | − | 1.13773i | −0.822429 | − | 0.568867i | \(-0.807382\pi\) | ||
0.822429 | − | 0.568867i | \(-0.192618\pi\) | |||||||
\(744\) | 7.03427e7 | + | 8.70446e7i | 0.170805 | + | 0.211360i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.91770e8i | 0.702788i | ||||||||
\(747\) | 3.53711e8 | + | 7.59267e7i | 0.848569 | + | 0.182152i | ||||
\(748\) | 4.86605e6 | 0.0116271 | ||||||||
\(749\) | − | 2.94819e6i | − | 0.00701634i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.36993e7 | −0.0795612 | −0.0397806 | − | 0.999208i | \(-0.512666\pi\) | ||||
−0.0397806 | + | 0.999208i | \(0.512666\pi\) | |||||||
\(752\) | 1.84205e8i | 0.433160i | ||||||||
\(753\) | −4.83645e8 | − | 5.98480e8i | −1.13277 | − | 1.40173i | ||||
\(754\) | 3.68160e7 | 0.0858860 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 568512. | + | 1.12413e6i | 0.00131575 | + | 0.00260166i | ||||
\(757\) | −2.98552e8 | −0.688227 | −0.344113 | − | 0.938928i | \(-0.611820\pi\) | ||||
−0.344113 | + | 0.938928i | \(0.611820\pi\) | |||||||
\(758\) | 2.42582e8i | 0.556995i | ||||||||
\(759\) | −7.30598e6 | + | 5.90413e6i | −0.0167091 | + | 0.0135030i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.98702e8i | 0.904679i | 0.891846 | + | 0.452340i | \(0.149410\pi\) | ||||
−0.891846 | + | 0.452340i | \(0.850590\pi\) | |||||||
\(762\) | −2.18930e8 | − | 2.70913e8i | −0.494813 | − | 0.612300i | ||||
\(763\) | −1.30162e6 | −0.00293029 | ||||||||
\(764\) | − | 1.60693e8i | − | 0.360344i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.55921e7 | −0.190435 | ||||||||
\(767\) | 9.64116e8i | 2.13670i | ||||||||
\(768\) | −2.20201e7 | + | 1.77949e7i | −0.0486111 | + | 0.0392837i | ||||
\(769\) | −5.17372e8 | −1.13769 | −0.568845 | − | 0.822444i | \(-0.692610\pi\) | ||||
−0.568845 | + | 0.822444i | \(0.692610\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.17030e6 | + | 3.92305e6i | 0.00691732 | + | 0.00855974i | ||||
\(772\) | 1.12030e8 | 0.243490 | ||||||||
\(773\) | 1.83241e8i | 0.396719i | 0.980129 | + | 0.198360i | \(0.0635614\pi\) | ||||
−0.980129 | + | 0.198360i | \(0.936439\pi\) | |||||||
\(774\) | 2.58290e7 | + | 5.54438e6i | 0.0557038 | + | 0.0119572i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 5.08820e7i | − | 0.108888i | ||||||
\(777\) | −1.43044e6 | + | 1.15597e6i | −0.00304934 | + | 0.00246424i | ||||
\(778\) | −3.48077e8 | −0.739157 | ||||||||
\(779\) | 8.81604e7i | 0.186493i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.31552e6 | −0.00486066 | ||||||||
\(782\) | 2.59782e8i | 0.543235i | ||||||||
\(783\) | 3.87504e7 | − | 1.95974e7i | 0.0807218 | − | 0.0408239i | ||||
\(784\) | −1.20468e8 | −0.249992 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.27343e8 | − | 1.02908e8i | 0.262244 | − | 0.211925i | ||||
\(787\) | −3.14718e8 | −0.645650 | −0.322825 | − | 0.946459i | \(-0.604633\pi\) | ||||
−0.322825 | + | 0.946459i | \(0.604633\pi\) | |||||||
\(788\) | − | 1.55335e8i | − | 0.317462i | ||||||
\(789\) | 1.46208e8 | + | 1.80924e8i | 0.297674 | + | 0.368353i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 3.48833e6i | − | 0.00704837i | ||||||
\(792\) | 940032. | − | 4.37922e6i | 0.00189220 | − | 0.00881498i | ||||
\(793\) | −1.84570e8 | −0.370119 | ||||||||
\(794\) | 4.84122e8i | 0.967150i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.04312e8 | 0.603365 | ||||||||
\(797\) | 7.88168e8i | 1.55684i | 0.627744 | + | 0.778420i | \(0.283979\pi\) | ||||
−0.627744 | + | 0.778420i | \(0.716021\pi\) | |||||||
\(798\) | 1.00954e6 | + | 1.24924e6i | 0.00198661 | + | 0.00245831i | ||||
\(799\) | −8.05939e8 | −1.58002 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.75644e8 | + | 5.91690e7i | 0.536353 | + | 0.115132i | ||||
\(802\) | 2.31783e8 | 0.449323 | ||||||||
\(803\) | 2.47943e7i | 0.0478857i | ||||||||
\(804\) | −2.94805e8 | + | 2.38238e8i | −0.567240 | + | 0.458399i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.82115e8i | 0.729776i | ||||||||
\(807\) | −1.28150e8 | − | 1.58578e8i | −0.243836 | − | 0.301732i | ||||
\(808\) | 1.71129e8 | 0.324406 | ||||||||
\(809\) | 1.04745e9i | 1.97828i | 0.146993 | + | 0.989138i | \(0.453041\pi\) | ||||
−0.146993 | + | 0.989138i | \(0.546959\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.17930e8 | −0.221086 | −0.110543 | − | 0.993871i | \(-0.535259\pi\) | ||||
−0.110543 | + | 0.993871i | \(0.535259\pi\) | |||||||
\(812\) | − | 141195.i | − | 0.000263725i | ||||||
\(813\) | −2.92835e8 | + | 2.36647e8i | −0.544944 | + | 0.440381i | ||||
\(814\) | 6.53914e6 | 0.0121240 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −7.78568e7 | − | 9.63428e7i | −0.143293 | − | 0.177316i | ||||
\(817\) | 3.36827e7 | 0.0617648 | ||||||||
\(818\) | 3.45382e8i | 0.631016i | ||||||||
\(819\) | −902700. | + | 4.20531e6i | −0.00164320 | + | 0.00765501i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.01939e7i | 0.108774i | 0.998520 | + | 0.0543868i | \(0.0173204\pi\) | ||||
−0.998520 | + | 0.0543868i | \(0.982680\pi\) | |||||||
\(822\) | −3.30648e8 | + | 2.67204e8i | −0.595320 | + | 0.481091i | ||||
\(823\) | −1.60620e7 | −0.0288139 | −0.0144069 | − | 0.999896i | \(-0.504586\pi\) | ||||
−0.0144069 | + | 0.999896i | \(0.504586\pi\) | |||||||
\(824\) | − | 1.56713e8i | − | 0.280107i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.69754e6 | 0.00656103 | ||||||||
\(827\) | − | 3.66665e8i | − | 0.648266i | −0.946012 | − | 0.324133i | \(-0.894928\pi\) | ||
0.946012 | − | 0.324133i | \(-0.105072\pi\) | |||||||
\(828\) | 2.33791e8 | + | 5.01851e7i | 0.411849 | + | 0.0884064i | ||||
\(829\) | −3.63153e8 | −0.637421 | −0.318711 | − | 0.947852i | \(-0.603250\pi\) | ||||
−0.318711 | + | 0.947852i | \(0.603250\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.90716e8 | − | 4.77370e8i | 1.02938 | − | 0.831864i | ||||
\(832\) | −9.66656e7 | −0.167843 | ||||||||
\(833\) | − | 5.27076e8i | − | 0.911882i | ||||||
\(834\) | −4.39099e8 | − | 5.43357e8i | −0.756945 | − | 0.936671i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 5.71080e6i | − | 0.00977413i | ||||||
\(837\) | 2.03403e8 | + | 4.02193e8i | 0.346881 | + | 0.685895i | ||||
\(838\) | −1.91688e8 | −0.325734 | ||||||||
\(839\) | − | 8.80700e8i | − | 1.49122i | −0.666382 | − | 0.745611i | \(-0.732158\pi\) | ||
0.666382 | − | 0.745611i | \(-0.267842\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.89956e8 | 0.991817 | ||||||||
\(842\) | − | 1.10963e8i | − | 0.185883i | ||||||
\(843\) | 3.79173e8 | + | 4.69202e8i | 0.632928 | + | 0.783209i | ||||
\(844\) | −2.26052e8 | −0.375995 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.55693e8 | + | 7.25308e8i | −0.257133 | + | 1.19788i | ||||
\(847\) | −3.54082e6 | −0.00582711 | ||||||||
\(848\) | − | 1.97169e8i | − | 0.323334i | ||||||
\(849\) | 2.12979e8 | − | 1.72113e8i | 0.348027 | − | 0.281249i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.49102e8i | 0.566453i | ||||||||
\(852\) | 3.70483e7 | + | 4.58450e7i | 0.0599032 | + | 0.0741264i | ||||
\(853\) | 3.84724e8 | 0.619873 | 0.309936 | − | 0.950757i | \(-0.399692\pi\) | ||||
0.309936 | + | 0.950757i | \(0.399692\pi\) | |||||||
\(854\) | 707853.i | 0.00113650i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.66840e8 | 0.425432 | ||||||||
\(857\) | 3.42647e8i | 0.544382i | 0.962243 | + | 0.272191i | \(0.0877483\pi\) | ||||
−0.962243 | + | 0.272191i | \(0.912252\pi\) | |||||||
\(858\) | 1.18944e7 | − | 9.61213e6i | 0.0188313 | − | 0.0152180i | ||||
\(859\) | −3.87443e8 | −0.611263 | −0.305631 | − | 0.952150i | \(-0.598868\pi\) | ||||
−0.305631 | + | 0.952150i | \(0.598868\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 569088. | + | 704210.i | 0.000891600 | + | 0.00110330i | ||||
\(862\) | 2.27172e8 | 0.354677 | ||||||||
\(863\) | − | 6.46530e7i | − | 0.100590i | −0.998734 | − | 0.0502951i | \(-0.983984\pi\) | ||
0.998734 | − | 0.0502951i | \(-0.0160162\pi\) | |||||||
\(864\) | −1.01745e8 | + | 5.14558e7i | −0.157750 | + | 0.0797799i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.78487e6i | 0.00736744i | ||||||||
\(867\) | −8.53675e7 | + | 6.89874e7i | −0.130989 | + | 0.105855i | ||||
\(868\) | 1.46547e6 | 0.00224088 | ||||||||
\(869\) | 1.15591e7i | 0.0176142i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.29416e9 | −1.95854 | ||||||||
\(872\) | − | 1.17809e8i | − | 0.177676i | ||||||
\(873\) | 4.30062e7 | − | 2.00348e8i | 0.0646380 | − | 0.301122i | ||||
\(874\) | 3.04880e8 | 0.456662 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.90903e8 | − | 3.96709e8i | 0.730269 | − | 0.590147i | ||||
\(877\) | 4.99281e8 | 0.740196 | 0.370098 | − | 0.928993i | \(-0.379324\pi\) | ||||
0.370098 | + | 0.928993i | \(0.379324\pi\) | |||||||
\(878\) | − | 4.23248e8i | − | 0.625333i | ||||||
\(879\) | 4.72576e8 | + | 5.84783e8i | 0.695833 | + | 0.861050i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 9.14796e8i | − | 1.33782i | −0.743345 | − | 0.668908i | \(-0.766762\pi\) | ||
0.743345 | − | 0.668908i | \(-0.233238\pi\) | |||||||
\(882\) | −4.74345e8 | − | 1.01822e8i | −0.691335 | − | 0.148400i | ||||
\(883\) | −7.85211e6 | −0.0114052 | −0.00570261 | − | 0.999984i | \(-0.501815\pi\) | ||||
−0.00570261 | + | 0.999984i | \(0.501815\pi\) | |||||||
\(884\) | − | 4.22934e8i | − | 0.612231i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.08496e8 | −1.01868 | ||||||||
\(887\) | − | 1.10737e9i | − | 1.58679i | −0.608704 | − | 0.793397i | \(-0.708310\pi\) | ||
0.608704 | − | 0.793397i | \(-0.291690\pi\) | |||||||
\(888\) | −1.04626e8 | − | 1.29468e8i | −0.149417 | − | 0.184895i | ||||
\(889\) | −4.56105e6 | −0.00649172 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.40275e6 | − | 1.64487e7i | 0.0104655 | − | 0.0232540i | ||||
\(892\) | 1.49405e8 | 0.210509 | ||||||||
\(893\) | 9.45851e8i | 1.32821i | ||||||||
\(894\) | −5.29833e8 | + | 4.28170e8i | −0.741526 | + | 0.599244i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 370728.i | 0.000515384i | ||||||||
\(897\) | 5.13158e8 | + | 6.35001e8i | 0.711007 | + | 0.879827i | ||||
\(898\) | −6.38162e8 | −0.881256 | ||||||||
\(899\) | − | 5.05170e7i | − | 0.0695277i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.62659e8 | 1.17941 | ||||||||
\(902\) | − | 3.21925e6i | − | 0.00438667i | ||||||
\(903\) | 269052. | − | 217427.i | 0.000365404 | − | 0.000295291i | ||||
\(904\) | 3.15728e8 | 0.427374 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.11977e8 | + | 2.62308e8i | 0.285039 | + | 0.352718i | ||||
\(907\) | −1.16193e9 | −1.55725 | −0.778623 | − | 0.627492i | \(-0.784082\pi\) | ||||
−0.778623 | + | 0.627492i | \(0.784082\pi\) | |||||||
\(908\) | − | 6.28880e8i | − | 0.840059i | ||||||
\(909\) | 6.73820e8 | + | 1.44640e8i | 0.897123 | + | 0.192574i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 3.61439e8i | − | 0.478057i | −0.971013 | − | 0.239028i | \(-0.923171\pi\) | ||
0.971013 | − | 0.239028i | \(-0.0768289\pi\) | |||||||
\(912\) | −1.13068e8 | + | 9.13728e7i | −0.149058 | + | 0.120457i | ||||
\(913\) | −1.68434e7 | −0.0221318 | ||||||||
\(914\) | − | 8.90154e8i | − | 1.16581i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.43417e8 | 0.186601 | ||||||||
\(917\) | − | 2.14393e6i | − | 0.00278036i | ||||||
\(918\) | −2.25131e8 | − | 4.45156e8i | −0.291009 | − | 0.575418i | ||||
\(919\) | 1.20431e9 | 1.55164 | 0.775820 | − | 0.630954i | \(-0.217336\pi\) | ||||
0.775820 | + | 0.630954i | \(0.217336\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.62833e8 | + | 6.16462e8i | −0.976451 | + | 0.789091i | ||||
\(922\) | 1.03581e9 | 1.32156 | ||||||||
\(923\) | 2.01254e8i | 0.255941i | ||||||||
\(924\) | −36864.0 | − | 45616.9i | −4.67290e−5 | − | 5.78242e-5i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 1.00679e9i | − | 1.26797i | ||||||
\(927\) | 1.32456e8 | − | 6.17058e8i | 0.166277 | − | 0.774617i | ||||
\(928\) | 1.27795e7 | 0.0159908 | ||||||||
\(929\) | 6.33924e8i | 0.790661i | 0.918539 | + | 0.395330i | \(0.129370\pi\) | ||||
−0.918539 | + | 0.395330i | \(0.870630\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.18577e8 | −0.766558 | ||||||||
\(932\) | − | 7.33715e7i | − | 0.0906316i | ||||||
\(933\) | 6.10805e8 | + | 7.55833e8i | 0.752069 | + | 0.930638i | ||||
\(934\) | −5.29366e8 | −0.649704 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.80621e8 | − | 8.17031e7i | −0.464157 | − | 0.0996348i | ||||
\(937\) | 2.47138e8 | 0.300414 | 0.150207 | − | 0.988655i | \(-0.452006\pi\) | ||||
0.150207 | + | 0.988655i | \(0.452006\pi\) | |||||||
\(938\) | 4.96330e6i | 0.00601398i | ||||||||
\(939\) | 8.42308e8 | − | 6.80688e8i | 1.01736 | − | 0.822150i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.37355e8i | 1.12496i | 0.826812 | + | 0.562478i | \(0.190152\pi\) | ||||
−0.826812 | + | 0.562478i | \(0.809848\pi\) | |||||||
\(942\) | −1.23732e8 | − | 1.53110e8i | −0.148022 | − | 0.183168i | ||||
\(943\) | 1.71865e8 | 0.204952 | ||||||||
\(944\) | 3.34663e8i | 0.397824i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.22995e6 | −0.00145283 | ||||||||
\(947\) | − | 1.49756e9i | − | 1.76333i | −0.471877 | − | 0.881664i | \(-0.656424\pi\) | ||
0.471877 | − | 0.881664i | \(-0.343576\pi\) | |||||||
\(948\) | 2.28858e8 | − | 1.84945e8i | 0.268621 | − | 0.217079i | ||||
\(949\) | 2.15500e9 | 2.52145 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.69279e8 | + | 8.28191e8i | 0.778154 | + | 0.962917i | ||||
\(952\) | −1.62202e6 | −0.00187994 | ||||||||
\(953\) | 4.28296e7i | 0.0494840i | 0.999694 | + | 0.0247420i | \(0.00787643\pi\) | ||||
−0.999694 | + | 0.0247420i | \(0.992124\pi\) | |||||||
\(954\) | 1.66650e8 | − | 7.76354e8i | 0.191938 | − | 0.894158i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 8.46606e7i | − | 0.0968964i | ||||||
\(957\) | −1.57248e6 | + | 1.27076e6i | −0.00179411 | + | 0.00144986i | ||||
\(958\) | −6.09029e8 | −0.692694 | ||||||||
\(959\) | 5.56675e6i | 0.00631170i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.63185e8 | −0.409221 | ||||||||
\(962\) | − | 5.68350e8i | − | 0.638397i | ||||||
\(963\) | 1.05068e9 | + | 2.25537e8i | 1.17650 | + | 0.252545i | ||||
\(964\) | 2.23866e8 | 0.249894 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.43533e6 | − | 1.96804e6i | 0.00270163 | − | 0.00218325i | ||||
\(967\) | 1.16322e9 | 1.28642 | 0.643210 | − | 0.765690i | \(-0.277602\pi\) | ||||
0.643210 | + | 0.765690i | \(0.277602\pi\) | |||||||
\(968\) | − | 3.20478e8i | − | 0.353323i | ||||||
\(969\) | −3.99776e8 | − | 4.94698e8i | −0.439385 | − | 0.543712i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1.39293e9i | − | 1.52150i | −0.649045 | − | 0.760750i | \(-0.724831\pi\) | ||
0.649045 | − | 0.760750i | \(-0.275169\pi\) | |||||||
\(972\) | −4.44111e8 | + | 1.16611e8i | −0.483607 | + | 0.126982i | ||||
\(973\) | −9.14789e6 | −0.00993076 | ||||||||
\(974\) | 2.34438e7i | 0.0253718i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.40676e7 | −0.0689111 | ||||||||
\(977\) | − | 7.81956e8i | − | 0.838492i | −0.907873 | − | 0.419246i | \(-0.862295\pi\) | ||
0.907873 | − | 0.419246i | \(-0.137705\pi\) | |||||||
\(978\) | 8.44717e7 | + | 1.04528e8i | 0.0903015 | + | 0.111742i | ||||
\(979\) | −1.31259e7 | −0.0139888 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.95739e7 | − | 4.63874e8i | 0.105472 | − | 0.491352i | ||||
\(982\) | −6.75126e8 | −0.712936 | ||||||||
\(983\) | 8.80220e8i | 0.926682i | 0.886180 | + | 0.463341i | \(0.153349\pi\) | ||||
−0.886180 | + | 0.463341i | \(0.846651\pi\) | |||||||
\(984\) | −6.37379e7 | + | 5.15080e7i | −0.0668978 | + | 0.0540616i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.59133e7i | 0.0583289i | ||||||||
\(987\) | 6.10560e6 | + | 7.55529e6i | 0.00635005 | + | 0.00785778i | ||||
\(988\) | −4.96355e8 | −0.514662 | ||||||||
\(989\) | − | 6.56629e7i | − | 0.0678783i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.83915e9 | −1.88971 | −0.944857 | − | 0.327483i | \(-0.893800\pi\) | ||||
−0.944857 | + | 0.327483i | \(0.893800\pi\) | |||||||
\(992\) | 1.32639e8i | 0.135874i | ||||||||
\(993\) | −5.84562e8 | + | 4.72397e8i | −0.597012 | + | 0.482458i | ||||
\(994\) | 771840. | 0.000785902 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.69494e8 | + | 3.33482e8i | 0.272754 | + | 0.337516i | ||||
\(997\) | −5.69927e8 | −0.575088 | −0.287544 | − | 0.957767i | \(-0.592839\pi\) | ||||
−0.287544 | + | 0.957767i | \(0.592839\pi\) | |||||||
\(998\) | 6.64316e8i | 0.668318i | ||||||||
\(999\) | −3.02537e8 | − | 5.98213e8i | −0.303447 | − | 0.600011i |
(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 | 150.7.d.a.101.2 | 2 | ||
3.2 | odd | 2 | inner | 150.7.d.a.101.1 | 2 | ||
5.2 | odd | 4 | 150.7.b.a.149.2 | 4 | |||
5.3 | odd | 4 | 150.7.b.a.149.3 | 4 | |||
5.4 | even | 2 | 6.7.b.a.5.1 | ✓ | 2 | ||
15.2 | even | 4 | 150.7.b.a.149.4 | 4 | |||
15.8 | even | 4 | 150.7.b.a.149.1 | 4 | |||
15.14 | odd | 2 | 6.7.b.a.5.2 | yes | 2 | ||
20.19 | odd | 2 | 48.7.e.b.17.2 | 2 | |||
35.34 | odd | 2 | 294.7.b.a.197.1 | 2 | |||
40.19 | odd | 2 | 192.7.e.f.65.1 | 2 | |||
40.29 | even | 2 | 192.7.e.c.65.2 | 2 | |||
45.4 | even | 6 | 162.7.d.b.107.2 | 4 | |||
45.14 | odd | 6 | 162.7.d.b.107.1 | 4 | |||
45.29 | odd | 6 | 162.7.d.b.53.2 | 4 | |||
45.34 | even | 6 | 162.7.d.b.53.1 | 4 | |||
60.59 | even | 2 | 48.7.e.b.17.1 | 2 | |||
105.104 | even | 2 | 294.7.b.a.197.2 | 2 | |||
120.29 | odd | 2 | 192.7.e.c.65.1 | 2 | |||
120.59 | even | 2 | 192.7.e.f.65.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.7.b.a.5.1 | ✓ | 2 | 5.4 | even | 2 | ||
6.7.b.a.5.2 | yes | 2 | 15.14 | odd | 2 | ||
48.7.e.b.17.1 | 2 | 60.59 | even | 2 | |||
48.7.e.b.17.2 | 2 | 20.19 | odd | 2 | |||
150.7.b.a.149.1 | 4 | 15.8 | even | 4 | |||
150.7.b.a.149.2 | 4 | 5.2 | odd | 4 | |||
150.7.b.a.149.3 | 4 | 5.3 | odd | 4 | |||
150.7.b.a.149.4 | 4 | 15.2 | even | 4 | |||
150.7.d.a.101.1 | 2 | 3.2 | odd | 2 | inner | ||
150.7.d.a.101.2 | 2 | 1.1 | even | 1 | trivial | ||
162.7.d.b.53.1 | 4 | 45.34 | even | 6 | |||
162.7.d.b.53.2 | 4 | 45.29 | odd | 6 | |||
162.7.d.b.107.1 | 4 | 45.14 | odd | 6 | |||
162.7.d.b.107.2 | 4 | 45.4 | even | 6 | |||
192.7.e.c.65.1 | 2 | 120.29 | odd | 2 | |||
192.7.e.c.65.2 | 2 | 40.29 | even | 2 | |||
192.7.e.f.65.1 | 2 | 40.19 | odd | 2 | |||
192.7.e.f.65.2 | 2 | 120.59 | even | 2 | |||
294.7.b.a.197.1 | 2 | 35.34 | odd | 2 | |||
294.7.b.a.197.2 | 2 | 105.104 | even | 2 |