Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [14,7,Mod(13,14)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(14, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("14.13");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 14 = 2 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 14.b (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: | \(3.22075717068\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.211968.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 30x^{2} + 207 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 13.1 | ||
Root | \(-3.27984i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 14.13 |
Dual form | 14.7.b.a.13.2 |
$q$-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 \(\left(\mathbb{Z}/14\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.65685 | −0.707107 | ||||||||
\(3\) | − | 3.84257i | − | 0.142318i | −0.997465 | − | 0.0711588i | \(-0.977330\pi\) | ||
0.997465 | − | 0.0711588i | \(-0.0226697\pi\) | |||||||
\(4\) | 32.0000 | 0.500000 | ||||||||
\(5\) | 204.749i | 1.63799i | 0.573801 | + | 0.818995i | \(0.305468\pi\) | ||||
−0.573801 | + | 0.818995i | \(0.694532\pi\) | |||||||
\(6\) | 21.7369i | 0.100634i | ||||||||
\(7\) | −41.7939 | + | 340.444i | −0.121848 | + | 0.992549i | ||||
\(8\) | −181.019 | −0.353553 | ||||||||
\(9\) | 714.235 | 0.979746 | ||||||||
\(10\) | − | 1158.23i | − | 1.15823i | ||||||
\(11\) | −1177.88 | −0.884960 | −0.442480 | − | 0.896778i | \(-0.645901\pi\) | ||||
−0.442480 | + | 0.896778i | \(0.645901\pi\) | |||||||
\(12\) | − | 122.962i | − | 0.0711588i | ||||||
\(13\) | − | 1399.64i | − | 0.637067i | −0.947912 | − | 0.318534i | \(-0.896810\pi\) | ||
0.947912 | − | 0.318534i | \(-0.103190\pi\) | |||||||
\(14\) | 236.422 | − | 1925.84i | 0.0861597 | − | 0.701838i | ||||
\(15\) | 786.762 | 0.233115 | ||||||||
\(16\) | 1024.00 | 0.250000 | ||||||||
\(17\) | 6063.65i | 1.23421i | 0.786883 | + | 0.617103i | \(0.211694\pi\) | ||||
−0.786883 | + | 0.617103i | \(0.788306\pi\) | |||||||
\(18\) | −4040.32 | −0.692785 | ||||||||
\(19\) | − | 3134.94i | − | 0.457054i | −0.973538 | − | 0.228527i | \(-0.926609\pi\) | ||
0.973538 | − | 0.228527i | \(-0.0733910\pi\) | |||||||
\(20\) | 6551.96i | 0.818995i | ||||||||
\(21\) | 1308.18 | + | 160.596i | 0.141257 | + | 0.0173411i | ||||
\(22\) | 6663.11 | 0.625761 | ||||||||
\(23\) | 8652.59 | 0.711152 | 0.355576 | − | 0.934647i | \(-0.384285\pi\) | ||||
0.355576 | + | 0.934647i | \(0.384285\pi\) | |||||||
\(24\) | 695.580i | 0.0503168i | ||||||||
\(25\) | −26297.0 | −1.68301 | ||||||||
\(26\) | 7917.54i | 0.450475i | ||||||||
\(27\) | − | 5545.73i | − | 0.281753i | ||||||
\(28\) | −1337.41 | + | 10894.2i | −0.0609241 | + | 0.496274i | ||||
\(29\) | 32565.6 | 1.33526 | 0.667629 | − | 0.744494i | \(-0.267309\pi\) | ||||
0.667629 | + | 0.744494i | \(0.267309\pi\) | |||||||
\(30\) | −4450.60 | −0.164837 | ||||||||
\(31\) | − | 42298.3i | − | 1.41984i | −0.704284 | − | 0.709918i | \(-0.748732\pi\) | ||
0.704284 | − | 0.709918i | \(-0.251268\pi\) | |||||||
\(32\) | −5792.62 | −0.176777 | ||||||||
\(33\) | 4526.10i | 0.125945i | ||||||||
\(34\) | − | 34301.2i | − | 0.872715i | ||||||
\(35\) | −69705.5 | − | 8557.26i | −1.62578 | − | 0.199586i | ||||
\(36\) | 22855.5 | 0.489873 | ||||||||
\(37\) | 37578.8 | 0.741886 | 0.370943 | − | 0.928656i | \(-0.379034\pi\) | ||||
0.370943 | + | 0.928656i | \(0.379034\pi\) | |||||||
\(38\) | 17733.9i | 0.323186i | ||||||||
\(39\) | −5378.21 | −0.0906659 | ||||||||
\(40\) | − | 37063.5i | − | 0.579117i | ||||||
\(41\) | 93520.9i | 1.35693i | 0.734634 | + | 0.678464i | \(0.237354\pi\) | ||||
−0.734634 | + | 0.678464i | \(0.762646\pi\) | |||||||
\(42\) | −7400.19 | − | 908.470i | −0.0998838 | − | 0.0122620i | ||||
\(43\) | 92007.0 | 1.15722 | 0.578610 | − | 0.815605i | \(-0.303596\pi\) | ||||
0.578610 | + | 0.815605i | \(0.303596\pi\) | |||||||
\(44\) | −37692.2 | −0.442480 | ||||||||
\(45\) | 146239.i | 1.60481i | ||||||||
\(46\) | −48946.4 | −0.502861 | ||||||||
\(47\) | 24952.4i | 0.240336i | 0.992754 | + | 0.120168i | \(0.0383433\pi\) | ||||
−0.992754 | + | 0.120168i | \(0.961657\pi\) | |||||||
\(48\) | − | 3934.79i | − | 0.0355794i | ||||||
\(49\) | −114156. | − | 28457.0i | −0.970306 | − | 0.241881i | ||||
\(50\) | 148758. | 1.19007 | ||||||||
\(51\) | 23300.0 | 0.175649 | ||||||||
\(52\) | − | 44788.4i | − | 0.318534i | ||||||
\(53\) | 109.623 | 0.000736330 | 0.000368165 | − | 1.00000i | \(-0.499883\pi\) | ||||
0.000368165 | 1.00000i | \(0.499883\pi\) | ||||||||
\(54\) | 31371.4i | 0.199229i | ||||||||
\(55\) | − | 241170.i | − | 1.44956i | ||||||
\(56\) | 7565.51 | − | 61627.0i | 0.0430799 | − | 0.350919i | ||||
\(57\) | −12046.2 | −0.0650468 | ||||||||
\(58\) | −184219. | −0.944170 | ||||||||
\(59\) | − | 326590.i | − | 1.59018i | −0.606491 | − | 0.795091i | \(-0.707423\pi\) | ||
0.606491 | − | 0.795091i | \(-0.292577\pi\) | |||||||
\(60\) | 25176.4 | 0.116557 | ||||||||
\(61\) | − | 84599.8i | − | 0.372717i | −0.982482 | − | 0.186359i | \(-0.940331\pi\) | ||
0.982482 | − | 0.186359i | \(-0.0596687\pi\) | |||||||
\(62\) | 239276.i | 1.00398i | ||||||||
\(63\) | −29850.7 | + | 243157.i | −0.119380 | + | 0.972445i | ||||
\(64\) | 32768.0 | 0.125000 | ||||||||
\(65\) | 286574. | 1.04351 | ||||||||
\(66\) | − | 25603.5i | − | 0.0890568i | ||||||
\(67\) | −111002. | −0.369068 | −0.184534 | − | 0.982826i | \(-0.559078\pi\) | ||||
−0.184534 | + | 0.982826i | \(0.559078\pi\) | |||||||
\(68\) | 194037.i | 0.617103i | ||||||||
\(69\) | − | 33248.2i | − | 0.101209i | ||||||
\(70\) | 394314. | + | 48407.1i | 1.14960 | + | 0.141129i | ||||
\(71\) | −441825. | −1.23446 | −0.617228 | − | 0.786784i | \(-0.711744\pi\) | ||||
−0.617228 | + | 0.786784i | \(0.711744\pi\) | |||||||
\(72\) | −129290. | −0.346392 | ||||||||
\(73\) | 464201.i | 1.19327i | 0.802514 | + | 0.596633i | \(0.203495\pi\) | ||||
−0.802514 | + | 0.596633i | \(0.796505\pi\) | |||||||
\(74\) | −212578. | −0.524593 | ||||||||
\(75\) | 101048.i | 0.239522i | ||||||||
\(76\) | − | 100318.i | − | 0.228527i | ||||||
\(77\) | 49228.3 | − | 401003.i | 0.107831 | − | 0.878366i | ||||
\(78\) | 30423.7 | 0.0641104 | ||||||||
\(79\) | 595011. | 1.20682 | 0.603412 | − | 0.797429i | \(-0.293807\pi\) | ||||
0.603412 | + | 0.797429i | \(0.293807\pi\) | |||||||
\(80\) | 209663.i | 0.409497i | ||||||||
\(81\) | 499367. | 0.939647 | ||||||||
\(82\) | − | 529034.i | − | 0.959493i | ||||||
\(83\) | 654116.i | 1.14398i | 0.820259 | + | 0.571992i | \(0.193829\pi\) | ||||
−0.820259 | + | 0.571992i | \(0.806171\pi\) | |||||||
\(84\) | 41861.8 | + | 5139.08i | 0.0706285 | + | 0.00867057i | ||||
\(85\) | −1.24152e6 | −2.02162 | ||||||||
\(86\) | −520470. | −0.818277 | ||||||||
\(87\) | − | 125136.i | − | 0.190031i | ||||||
\(88\) | 213219. | 0.312881 | ||||||||
\(89\) | − | 298317.i | − | 0.423164i | −0.977360 | − | 0.211582i | \(-0.932139\pi\) | ||
0.977360 | − | 0.211582i | \(-0.0678615\pi\) | |||||||
\(90\) | − | 827251.i | − | 1.13477i | ||||||
\(91\) | 476498. | + | 58496.3i | 0.632320 | + | 0.0776255i | ||||
\(92\) | 276883. | 0.355576 | ||||||||
\(93\) | −162534. | −0.202068 | ||||||||
\(94\) | − | 141152.i | − | 0.169943i | ||||||
\(95\) | 641874. | 0.748650 | ||||||||
\(96\) | 22258.6i | 0.0251584i | ||||||||
\(97\) | − | 169894.i | − | 0.186150i | −0.995659 | − | 0.0930752i | \(-0.970330\pi\) | ||
0.995659 | − | 0.0930752i | \(-0.0296697\pi\) | |||||||
\(98\) | 645761. | + | 160977.i | 0.686110 | + | 0.171035i | ||||
\(99\) | −841284. | −0.867036 | ||||||||
\(100\) | −841505. | −0.841505 | ||||||||
\(101\) | − | 1.11818e6i | − | 1.08530i | −0.839960 | − | 0.542648i | \(-0.817422\pi\) | ||
0.839960 | − | 0.542648i | \(-0.182578\pi\) | |||||||
\(102\) | −131805. | −0.124203 | ||||||||
\(103\) | 1.20424e6i | 1.10205i | 0.834489 | + | 0.551025i | \(0.185763\pi\) | ||||
−0.834489 | + | 0.551025i | \(0.814237\pi\) | |||||||
\(104\) | 253361.i | 0.225237i | ||||||||
\(105\) | −32881.9 | + | 267849.i | −0.0284046 | + | 0.231378i | ||||
\(106\) | −620.119 | −0.000520664 | ||||||||
\(107\) | −122039. | −0.0996204 | −0.0498102 | − | 0.998759i | \(-0.515862\pi\) | ||||
−0.0498102 | + | 0.998759i | \(0.515862\pi\) | |||||||
\(108\) | − | 177464.i | − | 0.140876i | ||||||
\(109\) | 1.10612e6 | 0.854127 | 0.427063 | − | 0.904222i | \(-0.359548\pi\) | ||||
0.427063 | + | 0.904222i | \(0.359548\pi\) | |||||||
\(110\) | 1.36426e6i | 1.02499i | ||||||||
\(111\) | − | 144399.i | − | 0.105583i | ||||||
\(112\) | −42797.0 | + | 348615.i | −0.0304621 | + | 0.248137i | ||||
\(113\) | 266739. | 0.184864 | 0.0924318 | − | 0.995719i | \(-0.470536\pi\) | ||||
0.0924318 | + | 0.995719i | \(0.470536\pi\) | |||||||
\(114\) | 68143.7 | 0.0459951 | ||||||||
\(115\) | 1.77161e6i | 1.16486i | ||||||||
\(116\) | 1.04210e6 | 0.667629 | ||||||||
\(117\) | − | 999669.i | − | 0.624164i | ||||||
\(118\) | 1.84747e6i | 1.12443i | ||||||||
\(119\) | −2.06434e6 | − | 253424.i | −1.22501 | − | 0.150386i | ||||
\(120\) | −142419. | −0.0824185 | ||||||||
\(121\) | −384154. | −0.216845 | ||||||||
\(122\) | 478569.i | 0.263551i | ||||||||
\(123\) | 359361. | 0.193115 | ||||||||
\(124\) | − | 1.35355e6i | − | 0.709918i | ||||||
\(125\) | − | 2.18509e6i | − | 1.11876i | ||||||
\(126\) | 168861. | − | 1.37550e6i | 0.0844146 | − | 0.687623i | ||||
\(127\) | 1.34435e6 | 0.656297 | 0.328149 | − | 0.944626i | \(-0.393575\pi\) | ||||
0.328149 | + | 0.944626i | \(0.393575\pi\) | |||||||
\(128\) | −185364. | −0.0883883 | ||||||||
\(129\) | − | 353544.i | − | 0.164693i | ||||||
\(130\) | −1.62111e6 | −0.737873 | ||||||||
\(131\) | − | 3.66483e6i | − | 1.63019i | −0.579324 | − | 0.815097i | \(-0.696684\pi\) | ||
0.579324 | − | 0.815097i | \(-0.303316\pi\) | |||||||
\(132\) | 144835.i | 0.0629727i | ||||||||
\(133\) | 1.06727e6 | + | 131021.i | 0.453649 | + | 0.0556913i | ||||
\(134\) | 627922. | 0.260970 | ||||||||
\(135\) | 1.13548e6 | 0.461508 | ||||||||
\(136\) | − | 1.09764e6i | − | 0.436358i | ||||||
\(137\) | −3.33009e6 | −1.29507 | −0.647537 | − | 0.762034i | \(-0.724201\pi\) | ||||
−0.647537 | + | 0.762034i | \(0.724201\pi\) | |||||||
\(138\) | 188080.i | 0.0715659i | ||||||||
\(139\) | 1.18963e6i | 0.442962i | 0.975165 | + | 0.221481i | \(0.0710890\pi\) | ||||
−0.975165 | + | 0.221481i | \(0.928911\pi\) | |||||||
\(140\) | −2.23058e6 | − | 273832.i | −0.812892 | − | 0.0997931i | ||||
\(141\) | 95881.3 | 0.0342040 | ||||||||
\(142\) | 2.49934e6 | 0.872892 | ||||||||
\(143\) | 1.64861e6i | 0.563779i | ||||||||
\(144\) | 731376. | 0.244936 | ||||||||
\(145\) | 6.66776e6i | 2.18714i | ||||||||
\(146\) | − | 2.62592e6i | − | 0.843766i | ||||||
\(147\) | −109348. | + | 438651.i | −0.0344238 | + | 0.138092i | ||||
\(148\) | 1.20252e6 | 0.370943 | ||||||||
\(149\) | 1.62144e6 | 0.490166 | 0.245083 | − | 0.969502i | \(-0.421185\pi\) | ||||
0.245083 | + | 0.969502i | \(0.421185\pi\) | |||||||
\(150\) | − | 571615.i | − | 0.169368i | ||||||
\(151\) | −4.35030e6 | −1.26354 | −0.631770 | − | 0.775156i | \(-0.717671\pi\) | ||||
−0.631770 | + | 0.775156i | \(0.717671\pi\) | |||||||
\(152\) | 567484.i | 0.161593i | ||||||||
\(153\) | 4.33087e6i | 1.20921i | ||||||||
\(154\) | −278478. | + | 2.26842e6i | −0.0762479 | + | 0.621099i | ||||
\(155\) | 8.66053e6 | 2.32568 | ||||||||
\(156\) | −172103. | −0.0453329 | ||||||||
\(157\) | − | 4.64090e6i | − | 1.19923i | −0.800288 | − | 0.599616i | \(-0.795320\pi\) | ||
0.800288 | − | 0.599616i | \(-0.204680\pi\) | |||||||
\(158\) | −3.36589e6 | −0.853354 | ||||||||
\(159\) | − | 421.233i | − | 0.000104793i | ||||||
\(160\) | − | 1.18603e6i | − | 0.289558i | ||||||
\(161\) | −361626. | + | 2.94572e6i | −0.0866526 | + | 0.705853i | ||||
\(162\) | −2.82485e6 | −0.664431 | ||||||||
\(163\) | −5.26597e6 | −1.21595 | −0.607975 | − | 0.793956i | \(-0.708018\pi\) | ||||
−0.607975 | + | 0.793956i | \(0.708018\pi\) | |||||||
\(164\) | 2.99267e6i | 0.678464i | ||||||||
\(165\) | −926713. | −0.206297 | ||||||||
\(166\) | − | 3.70024e6i | − | 0.808920i | ||||||
\(167\) | − | 1.99529e6i | − | 0.428406i | −0.976789 | − | 0.214203i | \(-0.931285\pi\) | ||
0.976789 | − | 0.214203i | \(-0.0687154\pi\) | |||||||
\(168\) | −236806. | − | 29071.0i | −0.0499419 | − | 0.00613102i | ||||
\(169\) | 2.86783e6 | 0.594145 | ||||||||
\(170\) | 7.02312e6 | 1.42950 | ||||||||
\(171\) | − | 2.23908e6i | − | 0.447797i | ||||||
\(172\) | 2.94422e6 | 0.578610 | ||||||||
\(173\) | − | 1.97345e6i | − | 0.381142i | −0.981673 | − | 0.190571i | \(-0.938966\pi\) | ||
0.981673 | − | 0.190571i | \(-0.0610340\pi\) | |||||||
\(174\) | 707874.i | 0.134372i | ||||||||
\(175\) | 1.09906e6 | − | 8.95267e6i | 0.205072 | − | 1.67047i | ||||
\(176\) | −1.20615e6 | −0.221240 | ||||||||
\(177\) | −1.25495e6 | −0.226311 | ||||||||
\(178\) | 1.68754e6i | 0.299222i | ||||||||
\(179\) | −6.59325e6 | −1.14958 | −0.574791 | − | 0.818300i | \(-0.694917\pi\) | ||||
−0.574791 | + | 0.818300i | \(0.694917\pi\) | |||||||
\(180\) | 4.67964e6i | 0.802407i | ||||||||
\(181\) | − | 2.60968e6i | − | 0.440100i | −0.975489 | − | 0.220050i | \(-0.929378\pi\) | ||
0.975489 | − | 0.220050i | \(-0.0706220\pi\) | |||||||
\(182\) | −2.69548e6 | − | 330905.i | −0.447118 | − | 0.0548895i | ||||
\(183\) | −325081. | −0.0530442 | ||||||||
\(184\) | −1.56629e6 | −0.251430 | ||||||||
\(185\) | 7.69420e6i | 1.21520i | ||||||||
\(186\) | 919434. | 0.142883 | ||||||||
\(187\) | − | 7.14227e6i | − | 1.09222i | ||||||
\(188\) | 798475.i | 0.120168i | ||||||||
\(189\) | 1.88801e6 | + | 231778.i | 0.279653 | + | 0.0343310i | ||||
\(190\) | −3.63099e6 | −0.529376 | ||||||||
\(191\) | 1.99290e6 | 0.286012 | 0.143006 | − | 0.989722i | \(-0.454323\pi\) | ||||
0.143006 | + | 0.989722i | \(0.454323\pi\) | |||||||
\(192\) | − | 125913.i | − | 0.0177897i | ||||||
\(193\) | 1.24013e7 | 1.72503 | 0.862513 | − | 0.506036i | \(-0.168890\pi\) | ||||
0.862513 | + | 0.506036i | \(0.168890\pi\) | |||||||
\(194\) | 961068.i | 0.131628i | ||||||||
\(195\) | − | 1.10118e6i | − | 0.148510i | ||||||
\(196\) | −3.65298e6 | − | 910624.i | −0.485153 | − | 0.120940i | ||||
\(197\) | −5.13349e6 | −0.671450 | −0.335725 | − | 0.941960i | \(-0.608981\pi\) | ||||
−0.335725 | + | 0.941960i | \(0.608981\pi\) | |||||||
\(198\) | 4.75902e6 | 0.613087 | ||||||||
\(199\) | − | 615146.i | − | 0.0780582i | −0.999238 | − | 0.0390291i | \(-0.987573\pi\) | ||
0.999238 | − | 0.0390291i | \(-0.0124265\pi\) | |||||||
\(200\) | 4.76027e6 | 0.595034 | ||||||||
\(201\) | 426533.i | 0.0525248i | ||||||||
\(202\) | 6.32539e6i | 0.767420i | ||||||||
\(203\) | −1.36104e6 | + | 1.10868e7i | −0.162699 | + | 1.32531i | ||||
\(204\) | 745601. | 0.0878245 | ||||||||
\(205\) | −1.91483e7 | −2.22263 | ||||||||
\(206\) | − | 6.81221e6i | − | 0.779267i | ||||||
\(207\) | 6.17998e6 | 0.696748 | ||||||||
\(208\) | − | 1.43323e6i | − | 0.159267i | ||||||
\(209\) | 3.69258e6i | 0.404475i | ||||||||
\(210\) | 186008. | − | 1.51518e6i | 0.0200851 | − | 0.163609i | ||||
\(211\) | 2.56281e6 | 0.272815 | 0.136408 | − | 0.990653i | \(-0.456444\pi\) | ||||
0.136408 | + | 0.990653i | \(0.456444\pi\) | |||||||
\(212\) | 3507.92 | 0.000368165 | ||||||||
\(213\) | 1.69775e6i | 0.175685i | ||||||||
\(214\) | 690358. | 0.0704422 | ||||||||
\(215\) | 1.88383e7i | 1.89551i | ||||||||
\(216\) | 1.00389e6i | 0.0996146i | ||||||||
\(217\) | 1.44002e7 | + | 1.76781e6i | 1.40926 | + | 0.173004i | ||||
\(218\) | −6.25716e6 | −0.603959 | ||||||||
\(219\) | 1.78373e6 | 0.169823 | ||||||||
\(220\) | − | 7.71744e6i | − | 0.724778i | ||||||
\(221\) | 8.48691e6 | 0.786272 | ||||||||
\(222\) | 816845.i | 0.0746587i | ||||||||
\(223\) | − | 7.82377e6i | − | 0.705507i | −0.935716 | − | 0.352753i | \(-0.885245\pi\) | ||
0.935716 | − | 0.352753i | \(-0.114755\pi\) | |||||||
\(224\) | 242096. | − | 1.97206e6i | 0.0215399 | − | 0.175459i | ||||
\(225\) | −1.87823e7 | −1.64892 | ||||||||
\(226\) | −1.50890e6 | −0.130718 | ||||||||
\(227\) | − | 8.19085e6i | − | 0.700247i | −0.936704 | − | 0.350124i | \(-0.886140\pi\) | ||
0.936704 | − | 0.350124i | \(-0.113860\pi\) | |||||||
\(228\) | −385479. | −0.0325234 | ||||||||
\(229\) | − | 1.30526e7i | − | 1.08690i | −0.839442 | − | 0.543449i | \(-0.817118\pi\) | ||
0.839442 | − | 0.543449i | \(-0.182882\pi\) | |||||||
\(230\) | − | 1.00217e7i | − | 0.823681i | ||||||
\(231\) | −1.54088e6 | − | 189163.i | −0.125007 | − | 0.0153462i | ||||
\(232\) | −5.89500e6 | −0.472085 | ||||||||
\(233\) | 1.38499e6 | 0.109491 | 0.0547456 | − | 0.998500i | \(-0.482565\pi\) | ||||
0.0547456 | + | 0.998500i | \(0.482565\pi\) | |||||||
\(234\) | 5.65498e6i | 0.441351i | ||||||||
\(235\) | −5.10896e6 | −0.393667 | ||||||||
\(236\) | − | 1.04509e7i | − | 0.795091i | ||||||
\(237\) | − | 2.28638e6i | − | 0.171752i | ||||||
\(238\) | 1.16776e7 | + | 1.43358e6i | 0.866212 | + | 0.106339i | ||||
\(239\) | 4.37563e6 | 0.320514 | 0.160257 | − | 0.987075i | \(-0.448768\pi\) | ||||
0.160257 | + | 0.987075i | \(0.448768\pi\) | |||||||
\(240\) | 805644. | 0.0582787 | ||||||||
\(241\) | 8.69878e6i | 0.621451i | 0.950500 | + | 0.310726i | \(0.100572\pi\) | ||||
−0.950500 | + | 0.310726i | \(0.899428\pi\) | |||||||
\(242\) | 2.17311e6 | 0.153333 | ||||||||
\(243\) | − | 5.96170e6i | − | 0.415481i | ||||||
\(244\) | − | 2.70719e6i | − | 0.186359i | ||||||
\(245\) | 5.82654e6 | − | 2.33732e7i | 0.396198 | − | 1.58935i | ||||
\(246\) | −2.03285e6 | −0.136553 | ||||||||
\(247\) | −4.38777e6 | −0.291174 | ||||||||
\(248\) | 7.65682e6i | 0.501988i | ||||||||
\(249\) | 2.51349e6 | 0.162809 | ||||||||
\(250\) | 1.23607e7i | 0.791085i | ||||||||
\(251\) | 2.65980e7i | 1.68201i | 0.541031 | + | 0.841003i | \(0.318034\pi\) | ||||
−0.541031 | + | 0.841003i | \(0.681966\pi\) | |||||||
\(252\) | −955222. | + | 7.78103e6i | −0.0596901 | + | 0.486223i | ||||
\(253\) | −1.01917e7 | −0.629342 | ||||||||
\(254\) | −7.60478e6 | −0.464072 | ||||||||
\(255\) | 4.77065e6i | 0.287711i | ||||||||
\(256\) | 1.04858e6 | 0.0625000 | ||||||||
\(257\) | − | 7.54668e6i | − | 0.444587i | −0.974980 | − | 0.222293i | \(-0.928646\pi\) | ||
0.974980 | − | 0.222293i | \(-0.0713543\pi\) | |||||||
\(258\) | 1.99995e6i | 0.116455i | ||||||||
\(259\) | −1.57056e6 | + | 1.27935e7i | −0.0903975 | + | 0.736358i | ||||
\(260\) | 9.17036e6 | 0.521755 | ||||||||
\(261\) | 2.32595e7 | 1.30821 | ||||||||
\(262\) | 2.07314e7i | 1.15272i | ||||||||
\(263\) | −1.31684e7 | −0.723880 | −0.361940 | − | 0.932201i | \(-0.617885\pi\) | ||||
−0.361940 | + | 0.932201i | \(0.617885\pi\) | |||||||
\(264\) | − | 819311.i | − | 0.0445284i | ||||||
\(265\) | 22445.1i | 0.00120610i | ||||||||
\(266\) | −6.03739e6 | − | 741168.i | −0.320778 | − | 0.0393797i | ||||
\(267\) | −1.14631e6 | −0.0602236 | ||||||||
\(268\) | −3.55206e6 | −0.184534 | ||||||||
\(269\) | − | 1.82863e7i | − | 0.939439i | −0.882816 | − | 0.469719i | \(-0.844355\pi\) | ||
0.882816 | − | 0.469719i | \(-0.155645\pi\) | |||||||
\(270\) | −6.42326e6 | −0.326335 | ||||||||
\(271\) | 2.78109e7i | 1.39736i | 0.715435 | + | 0.698679i | \(0.246229\pi\) | ||||
−0.715435 | + | 0.698679i | \(0.753771\pi\) | |||||||
\(272\) | 6.20918e6i | 0.308551i | ||||||||
\(273\) | 224776. | − | 1.83098e6i | 0.0110475 | − | 0.0899903i | ||||
\(274\) | 1.88379e7 | 0.915756 | ||||||||
\(275\) | 3.09748e7 | 1.48940 | ||||||||
\(276\) | − | 1.06394e6i | − | 0.0506047i | ||||||
\(277\) | −5.25419e6 | −0.247210 | −0.123605 | − | 0.992331i | \(-0.539446\pi\) | ||||
−0.123605 | + | 0.992331i | \(0.539446\pi\) | |||||||
\(278\) | − | 6.72954e6i | − | 0.313221i | ||||||
\(279\) | − | 3.02109e7i | − | 1.39108i | ||||||
\(280\) | 1.26180e7 | + | 1.54903e6i | 0.574802 | + | 0.0705644i | ||||
\(281\) | −3.12195e7 | −1.40704 | −0.703522 | − | 0.710674i | \(-0.748390\pi\) | ||||
−0.703522 | + | 0.710674i | \(0.748390\pi\) | |||||||
\(282\) | −542386. | −0.0241859 | ||||||||
\(283\) | − | 1.81450e7i | − | 0.800569i | −0.916391 | − | 0.400284i | \(-0.868911\pi\) | ||
0.916391 | − | 0.400284i | \(-0.131089\pi\) | |||||||
\(284\) | −1.41384e7 | −0.617228 | ||||||||
\(285\) | − | 2.46645e6i | − | 0.106546i | ||||||
\(286\) | − | 9.32593e6i | − | 0.398652i | ||||||
\(287\) | −3.18386e7 | − | 3.90860e6i | −1.34682 | − | 0.165339i | ||||
\(288\) | −4.13729e6 | −0.173196 | ||||||||
\(289\) | −1.26303e7 | −0.523263 | ||||||||
\(290\) | − | 3.77186e7i | − | 1.54654i | ||||||
\(291\) | −652832. | −0.0264925 | ||||||||
\(292\) | 1.48544e7i | 0.596633i | ||||||||
\(293\) | − | 5.83393e6i | − | 0.231931i | −0.993253 | − | 0.115965i | \(-0.963004\pi\) | ||
0.993253 | − | 0.115965i | \(-0.0369962\pi\) | |||||||
\(294\) | 618567. | − | 2.48138e6i | 0.0243413 | − | 0.0976455i | ||||
\(295\) | 6.68689e7 | 2.60470 | ||||||||
\(296\) | −6.80248e6 | −0.262296 | ||||||||
\(297\) | 6.53222e6i | 0.249340i | ||||||||
\(298\) | −9.17227e6 | −0.346599 | ||||||||
\(299\) | − | 1.21105e7i | − | 0.453052i | ||||||
\(300\) | 3.23354e6i | 0.119761i | ||||||||
\(301\) | −3.84534e6 | + | 3.13233e7i | −0.141005 | + | 1.14860i | ||||
\(302\) | 2.46090e7 | 0.893457 | ||||||||
\(303\) | −4.29669e6 | −0.154457 | ||||||||
\(304\) | − | 3.21017e6i | − | 0.114264i | ||||||
\(305\) | 1.73217e7 | 0.610507 | ||||||||
\(306\) | − | 2.44991e7i | − | 0.855039i | ||||||
\(307\) | 2.26871e7i | 0.784087i | 0.919947 | + | 0.392043i | \(0.128232\pi\) | ||||
−0.919947 | + | 0.392043i | \(0.871768\pi\) | |||||||
\(308\) | 1.57531e6 | − | 1.28321e7i | 0.0539154 | − | 0.439183i | ||||
\(309\) | 4.62738e6 | 0.156841 | ||||||||
\(310\) | −4.89914e7 | −1.64450 | ||||||||
\(311\) | 3.96340e7i | 1.31761i | 0.752314 | + | 0.658805i | \(0.228938\pi\) | ||||
−0.752314 | + | 0.658805i | \(0.771062\pi\) | |||||||
\(312\) | 973560. | 0.0320552 | ||||||||
\(313\) | − | 1.00856e7i | − | 0.328905i | −0.986385 | − | 0.164452i | \(-0.947414\pi\) | ||
0.986385 | − | 0.164452i | \(-0.0525857\pi\) | |||||||
\(314\) | 2.62529e7i | 0.847986i | ||||||||
\(315\) | −4.97861e7 | − | 6.11189e6i | −1.59286 | − | 0.195544i | ||||
\(316\) | 1.90404e7 | 0.603412 | ||||||||
\(317\) | 2.98372e7 | 0.936657 | 0.468329 | − | 0.883554i | \(-0.344856\pi\) | ||||
0.468329 | + | 0.883554i | \(0.344856\pi\) | |||||||
\(318\) | 2382.85i | 7.40996e-5i | ||||||||
\(319\) | −3.83584e7 | −1.18165 | ||||||||
\(320\) | 6.70921e6i | 0.204749i | ||||||||
\(321\) | 468945.i | 0.0141777i | ||||||||
\(322\) | 2.04566e6 | − | 1.66635e7i | 0.0612727 | − | 0.499114i | ||||
\(323\) | 1.90092e7 | 0.564099 | ||||||||
\(324\) | 1.59797e7 | 0.469824 | ||||||||
\(325\) | 3.68063e7i | 1.07219i | ||||||||
\(326\) | 2.97888e7 | 0.859807 | ||||||||
\(327\) | − | 4.25034e6i | − | 0.121557i | ||||||
\(328\) | − | 1.69291e7i | − | 0.479747i | ||||||
\(329\) | −8.49489e6 | − | 1.04286e6i | −0.238545 | − | 0.0292845i | ||||
\(330\) | 5.24228e6 | 0.145874 | ||||||||
\(331\) | 1.79016e6 | 0.0493637 | 0.0246819 | − | 0.999695i | \(-0.492143\pi\) | ||||
0.0246819 | + | 0.999695i | \(0.492143\pi\) | |||||||
\(332\) | 2.09317e7i | 0.571992i | ||||||||
\(333\) | 2.68401e7 | 0.726860 | ||||||||
\(334\) | 1.12870e7i | 0.302929i | ||||||||
\(335\) | − | 2.27275e7i | − | 0.604530i | ||||||
\(336\) | 1.33958e6 | + | 164451.i | 0.0353143 | + | 0.00433528i | ||||
\(337\) | −1.30113e6 | −0.0339964 | −0.0169982 | − | 0.999856i | \(-0.505411\pi\) | ||||
−0.0169982 | + | 0.999856i | \(0.505411\pi\) | |||||||
\(338\) | −1.62229e7 | −0.420124 | ||||||||
\(339\) | − | 1.02496e6i | − | 0.0263093i | ||||||
\(340\) | −3.97288e7 | −1.01081 | ||||||||
\(341\) | 4.98225e7i | 1.25650i | ||||||||
\(342\) | 1.26661e7i | 0.316640i | ||||||||
\(343\) | 1.44590e7 | − | 3.76743e7i | 0.358308 | − | 0.933603i | ||||
\(344\) | −1.66550e7 | −0.409139 | ||||||||
\(345\) | 6.80753e6 | 0.165780 | ||||||||
\(346\) | 1.11635e7i | 0.269508i | ||||||||
\(347\) | −2.67141e7 | −0.639370 | −0.319685 | − | 0.947524i | \(-0.603577\pi\) | ||||
−0.319685 | + | 0.947524i | \(0.603577\pi\) | |||||||
\(348\) | − | 4.00434e6i | − | 0.0950153i | ||||||
\(349\) | 2.39729e7i | 0.563956i | 0.959421 | + | 0.281978i | \(0.0909904\pi\) | ||||
−0.959421 | + | 0.281978i | \(0.909010\pi\) | |||||||
\(350\) | −6.21720e6 | + | 5.06440e7i | −0.145008 | + | 1.18120i | ||||
\(351\) | −7.76202e6 | −0.179495 | ||||||||
\(352\) | 6.82302e6 | 0.156440 | ||||||||
\(353\) | − | 7.99792e7i | − | 1.81825i | −0.416528 | − | 0.909123i | \(-0.636753\pi\) | ||
0.416528 | − | 0.909123i | \(-0.363247\pi\) | |||||||
\(354\) | 7.09904e6 | 0.160026 | ||||||||
\(355\) | − | 9.04632e7i | − | 2.02203i | ||||||
\(356\) | − | 9.54615e6i | − | 0.211582i | ||||||
\(357\) | −973800. | + | 7.93236e6i | −0.0214025 | + | 0.174340i | ||||
\(358\) | 3.72970e7 | 0.812878 | ||||||||
\(359\) | 4.51314e7 | 0.975429 | 0.487714 | − | 0.873003i | \(-0.337831\pi\) | ||||
0.487714 | + | 0.873003i | \(0.337831\pi\) | |||||||
\(360\) | − | 2.64720e7i | − | 0.567387i | ||||||
\(361\) | 3.72181e7 | 0.791101 | ||||||||
\(362\) | 1.47626e7i | 0.311197i | ||||||||
\(363\) | 1.47614e6i | 0.0308609i | ||||||||
\(364\) | 1.52479e7 | + | 1.87188e6i | 0.316160 | + | 0.0388128i | ||||
\(365\) | −9.50445e7 | −1.95456 | ||||||||
\(366\) | 1.83893e6 | 0.0375079 | ||||||||
\(367\) | − | 6.07183e7i | − | 1.22835i | −0.789171 | − | 0.614174i | \(-0.789489\pi\) | ||
0.789171 | − | 0.614174i | \(-0.210511\pi\) | |||||||
\(368\) | 8.86025e6 | 0.177788 | ||||||||
\(369\) | 6.67958e7i | 1.32944i | ||||||||
\(370\) | − | 4.35250e7i | − | 0.859277i | ||||||
\(371\) | −4581.56 | + | 37320.4i | −8.97205e−5 | + | 0.000730843i | ||||
\(372\) | −5.20110e6 | −0.101034 | ||||||||
\(373\) | −9.31710e7 | −1.79537 | −0.897685 | − | 0.440637i | \(-0.854753\pi\) | ||||
−0.897685 | + | 0.440637i | \(0.854753\pi\) | |||||||
\(374\) | 4.04028e7i | 0.772318i | ||||||||
\(375\) | −8.39635e6 | −0.159220 | ||||||||
\(376\) | − | 4.51686e6i | − | 0.0849714i | ||||||
\(377\) | − | 4.55800e7i | − | 0.850649i | ||||||
\(378\) | −1.06802e7 | − | 1.31113e6i | −0.197745 | − | 0.0242757i | ||||
\(379\) | 2.78773e7 | 0.512075 | 0.256037 | − | 0.966667i | \(-0.417583\pi\) | ||||
0.256037 | + | 0.966667i | \(0.417583\pi\) | |||||||
\(380\) | 2.05400e7 | 0.374325 | ||||||||
\(381\) | − | 5.16575e6i | − | 0.0934026i | ||||||
\(382\) | −1.12735e7 | −0.202241 | ||||||||
\(383\) | − | 2.63822e6i | − | 0.0469586i | −0.999724 | − | 0.0234793i | \(-0.992526\pi\) | ||
0.999724 | − | 0.0234793i | \(-0.00747438\pi\) | |||||||
\(384\) | 712274.i | 0.0125792i | ||||||||
\(385\) | 8.21049e7 | + | 1.00794e7i | 1.43875 | + | 0.176626i | ||||
\(386\) | −7.01524e7 | −1.21978 | ||||||||
\(387\) | 6.57146e7 | 1.13378 | ||||||||
\(388\) | − | 5.43662e6i | − | 0.0930752i | ||||||
\(389\) | 3.12589e7 | 0.531037 | 0.265519 | − | 0.964106i | \(-0.414457\pi\) | ||||
0.265519 | + | 0.964106i | \(0.414457\pi\) | |||||||
\(390\) | 6.22922e6i | 0.105012i | ||||||||
\(391\) | 5.24663e7i | 0.877708i | ||||||||
\(392\) | 2.06644e7 | + | 5.15127e6i | 0.343055 | + | 0.0855177i | ||||
\(393\) | −1.40824e7 | −0.232005 | ||||||||
\(394\) | 2.90394e7 | 0.474787 | ||||||||
\(395\) | 1.21828e8i | 1.97677i | ||||||||
\(396\) | −2.69211e7 | −0.433518 | ||||||||
\(397\) | 3.33743e7i | 0.533385i | 0.963782 | + | 0.266693i | \(0.0859309\pi\) | ||||
−0.963782 | + | 0.266693i | \(0.914069\pi\) | |||||||
\(398\) | 3.47979e6i | 0.0551955i | ||||||||
\(399\) | 503459. | − | 4.10107e6i | 0.00792584 | − | 0.0645622i | ||||
\(400\) | −2.69282e7 | −0.420753 | ||||||||
\(401\) | −4.06798e6 | −0.0630878 | −0.0315439 | − | 0.999502i | \(-0.510042\pi\) | ||||
−0.0315439 | + | 0.999502i | \(0.510042\pi\) | |||||||
\(402\) | − | 2.41284e6i | − | 0.0371407i | ||||||
\(403\) | −5.92023e7 | −0.904531 | ||||||||
\(404\) | − | 3.57818e7i | − | 0.542648i | ||||||
\(405\) | 1.02245e8i | 1.53913i | ||||||||
\(406\) | 7.69923e6 | − | 6.27162e7i | 0.115045 | − | 0.937134i | ||||
\(407\) | −4.42634e7 | −0.656540 | ||||||||
\(408\) | −4.21775e6 | −0.0621013 | ||||||||
\(409\) | 3.79002e7i | 0.553952i | 0.960877 | + | 0.276976i | \(0.0893322\pi\) | ||||
−0.960877 | + | 0.276976i | \(0.910668\pi\) | |||||||
\(410\) | 1.08319e8 | 1.57164 | ||||||||
\(411\) | 1.27961e7i | 0.184312i | ||||||||
\(412\) | 3.85357e7i | 0.551025i | ||||||||
\(413\) | 1.11186e8 | + | 1.36495e7i | 1.57833 | + | 0.193761i | ||||
\(414\) | −3.49592e7 | −0.492676 | ||||||||
\(415\) | −1.33929e8 | −1.87384 | ||||||||
\(416\) | 8.10756e6i | 0.112619i | ||||||||
\(417\) | 4.57123e6 | 0.0630412 | ||||||||
\(418\) | − | 2.08884e7i | − | 0.286007i | ||||||
\(419\) | − | 7.34255e7i | − | 0.998171i | −0.866553 | − | 0.499085i | \(-0.833669\pi\) | ||
0.866553 | − | 0.499085i | \(-0.166331\pi\) | |||||||
\(420\) | −1.05222e6 | + | 8.57115e6i | −0.0142023 | + | 0.115689i | ||||
\(421\) | 5.94103e6 | 0.0796187 | 0.0398094 | − | 0.999207i | \(-0.487325\pi\) | ||||
0.0398094 | + | 0.999207i | \(0.487325\pi\) | |||||||
\(422\) | −1.44974e7 | −0.192910 | ||||||||
\(423\) | 1.78218e7i | 0.235468i | ||||||||
\(424\) | −19843.8 | −0.000260332 | ||||||||
\(425\) | − | 1.59456e8i | − | 2.07718i | ||||||
\(426\) | − | 9.60391e6i | − | 0.124228i | ||||||
\(427\) | 2.88015e7 | + | 3.53576e6i | 0.369940 | + | 0.0454149i | ||||
\(428\) | −3.90526e6 | −0.0498102 | ||||||||
\(429\) | 6.33490e6 | 0.0802357 | ||||||||
\(430\) | − | 1.06566e8i | − | 1.34033i | ||||||
\(431\) | 9.58811e7 | 1.19757 | 0.598785 | − | 0.800909i | \(-0.295650\pi\) | ||||
0.598785 | + | 0.800909i | \(0.295650\pi\) | |||||||
\(432\) | − | 5.67883e6i | − | 0.0704381i | ||||||
\(433\) | − | 1.23332e8i | − | 1.51919i | −0.650396 | − | 0.759595i | \(-0.725397\pi\) | ||
0.650396 | − | 0.759595i | \(-0.274603\pi\) | |||||||
\(434\) | −8.14600e7 | − | 1.00003e7i | −0.996495 | − | 0.122333i | ||||
\(435\) | 2.56214e7 | 0.311268 | ||||||||
\(436\) | 3.53958e7 | 0.427063 | ||||||||
\(437\) | − | 2.71253e7i | − | 0.325035i | ||||||
\(438\) | −1.00903e7 | −0.120083 | ||||||||
\(439\) | 6.41673e7i | 0.758438i | 0.925307 | + | 0.379219i | \(0.123807\pi\) | ||||
−0.925307 | + | 0.379219i | \(0.876193\pi\) | |||||||
\(440\) | 4.36564e7i | 0.512495i | ||||||||
\(441\) | −8.15338e7 | − | 2.03250e7i | −0.950653 | − | 0.236981i | ||||
\(442\) | −4.80092e7 | −0.555978 | ||||||||
\(443\) | −6.58726e7 | −0.757693 | −0.378847 | − | 0.925459i | \(-0.623679\pi\) | ||||
−0.378847 | + | 0.925459i | \(0.623679\pi\) | |||||||
\(444\) | − | 4.62077e6i | − | 0.0527917i | ||||||
\(445\) | 6.10801e7 | 0.693138 | ||||||||
\(446\) | 4.42579e7i | 0.498869i | ||||||||
\(447\) | − | 6.23051e6i | − | 0.0697592i | ||||||
\(448\) | −1.36950e6 | + | 1.11557e7i | −0.0152310 | + | 0.124069i | ||||
\(449\) | −1.02206e8 | −1.12911 | −0.564555 | − | 0.825395i | \(-0.690952\pi\) | ||||
−0.564555 | + | 0.825395i | \(0.690952\pi\) | |||||||
\(450\) | 1.06248e8 | 1.16596 | ||||||||
\(451\) | − | 1.10157e8i | − | 1.20083i | ||||||
\(452\) | 8.53565e6 | 0.0924318 | ||||||||
\(453\) | 1.67164e7i | 0.179824i | ||||||||
\(454\) | 4.63344e7i | 0.495150i | ||||||||
\(455\) | −1.19771e7 | + | 9.75624e7i | −0.127150 | + | 1.03573i | ||||
\(456\) | 2.18060e6 | 0.0229975 | ||||||||
\(457\) | −5.62382e7 | −0.589227 | −0.294613 | − | 0.955617i | \(-0.595191\pi\) | ||||
−0.294613 | + | 0.955617i | \(0.595191\pi\) | |||||||
\(458\) | 7.38364e7i | 0.768553i | ||||||||
\(459\) | 3.36274e7 | 0.347740 | ||||||||
\(460\) | 5.66914e7i | 0.582430i | ||||||||
\(461\) | − | 2.46600e7i | − | 0.251705i | −0.992049 | − | 0.125852i | \(-0.959833\pi\) | ||
0.992049 | − | 0.125852i | \(-0.0401665\pi\) | |||||||
\(462\) | 8.71656e6 | + | 1.07007e6i | 0.0883932 | + | 0.0108514i | ||||
\(463\) | 1.91959e8 | 1.93404 | 0.967018 | − | 0.254707i | \(-0.0819791\pi\) | ||||
0.967018 | + | 0.254707i | \(0.0819791\pi\) | |||||||
\(464\) | 3.33472e7 | 0.333814 | ||||||||
\(465\) | − | 3.32787e7i | − | 0.330985i | ||||||
\(466\) | −7.83469e6 | −0.0774219 | ||||||||
\(467\) | 1.50925e8i | 1.48187i | 0.671578 | + | 0.740934i | \(0.265617\pi\) | ||||
−0.671578 | + | 0.740934i | \(0.734383\pi\) | |||||||
\(468\) | − | 3.19894e7i | − | 0.312082i | ||||||
\(469\) | 4.63921e6 | − | 3.77900e7i | 0.0449703 | − | 0.366318i | ||||
\(470\) | 2.89007e7 | 0.278365 | ||||||||
\(471\) | −1.78330e7 | −0.170672 | ||||||||
\(472\) | 5.91191e7i | 0.562214i | ||||||||
\(473\) | −1.08373e8 | −1.02409 | ||||||||
\(474\) | 1.29337e7i | 0.121447i | ||||||||
\(475\) | 8.24395e7i | 0.769227i | ||||||||
\(476\) | −6.60587e7 | − | 8.10956e6i | −0.612505 | − | 0.0751929i | ||||
\(477\) | 78296.3 | 0.000721416 | ||||||||
\(478\) | −2.47523e7 | −0.226638 | ||||||||
\(479\) | − | 4.70415e7i | − | 0.428031i | −0.976830 | − | 0.214015i | \(-0.931346\pi\) | ||
0.976830 | − | 0.214015i | \(-0.0686542\pi\) | |||||||
\(480\) | −4.55741e6 | −0.0412092 | ||||||||
\(481\) | − | 5.25966e7i | − | 0.472631i | ||||||
\(482\) | − | 4.92077e7i | − | 0.439432i | ||||||
\(483\) | 1.13192e7 | + | 1.38957e6i | 0.100455 | + | 0.0123322i | ||||
\(484\) | −1.22929e7 | −0.108423 | ||||||||
\(485\) | 3.47857e7 | 0.304912 | ||||||||
\(486\) | 3.37244e7i | 0.293789i | ||||||||
\(487\) | −4.36014e7 | −0.377497 | −0.188748 | − | 0.982025i | \(-0.560443\pi\) | ||||
−0.188748 | + | 0.982025i | \(0.560443\pi\) | |||||||
\(488\) | 1.53142e7i | 0.131775i | ||||||||
\(489\) | 2.02349e7i | 0.173051i | ||||||||
\(490\) | −3.29599e7 | + | 1.32219e8i | −0.280154 | + | 1.12384i | ||||
\(491\) | 7.78280e7 | 0.657494 | 0.328747 | − | 0.944418i | \(-0.393374\pi\) | ||||
0.328747 | + | 0.944418i | \(0.393374\pi\) | |||||||
\(492\) | 1.14995e7 | 0.0965573 | ||||||||
\(493\) | 1.97466e8i | 1.64798i | ||||||||
\(494\) | 2.48210e7 | 0.205891 | ||||||||
\(495\) | − | 1.72252e8i | − | 1.42020i | ||||||
\(496\) | − | 4.33135e7i | − | 0.354959i | ||||||
\(497\) | 1.84656e7 | − | 1.50417e8i | 0.150416 | − | 1.22526i | ||||
\(498\) | −1.42184e7 | −0.115123 | ||||||||
\(499\) | −6.33741e7 | −0.510047 | −0.255024 | − | 0.966935i | \(-0.582083\pi\) | ||||
−0.255024 | + | 0.966935i | \(0.582083\pi\) | |||||||
\(500\) | − | 6.99227e7i | − | 0.559382i | ||||||
\(501\) | −7.66703e6 | −0.0609697 | ||||||||
\(502\) | − | 1.50461e8i | − | 1.18936i | ||||||
\(503\) | 1.88800e8i | 1.48354i | 0.670657 | + | 0.741768i | \(0.266012\pi\) | ||||
−0.670657 | + | 0.741768i | \(0.733988\pi\) | |||||||
\(504\) | 5.40355e6 | − | 4.40161e7i | 0.0422073 | − | 0.343811i | ||||
\(505\) | 2.28946e8 | 1.77770 | ||||||||
\(506\) | 5.76531e7 | 0.445012 | ||||||||
\(507\) | − | 1.10198e7i | − | 0.0845573i | ||||||
\(508\) | 4.30191e7 | 0.328149 | ||||||||
\(509\) | − | 5.84845e7i | − | 0.443493i | −0.975104 | − | 0.221747i | \(-0.928824\pi\) | ||
0.975104 | − | 0.221747i | \(-0.0711758\pi\) | |||||||
\(510\) | − | 2.69869e7i | − | 0.203443i | ||||||
\(511\) | −1.58034e8 | − | 1.94008e7i | −1.18437 | − | 0.145397i | ||||
\(512\) | −5.93164e6 | −0.0441942 | ||||||||
\(513\) | −1.73855e7 | −0.128776 | ||||||||
\(514\) | 4.26905e7i | 0.314370i | ||||||||
\(515\) | −2.46566e8 | −1.80515 | ||||||||
\(516\) | − | 1.13134e7i | − | 0.0823463i | ||||||
\(517\) | − | 2.93909e7i | − | 0.212687i | ||||||
\(518\) | 8.88445e6 | − | 7.23708e7i | 0.0639207 | − | 0.520684i | ||||
\(519\) | −7.58311e6 | −0.0542432 | ||||||||
\(520\) | −5.18754e7 | −0.368936 | ||||||||
\(521\) | − | 1.51011e7i | − | 0.106781i | −0.998574 | − | 0.0533907i | \(-0.982997\pi\) | ||
0.998574 | − | 0.0533907i | \(-0.0170029\pi\) | |||||||
\(522\) | −1.31575e8 | −0.925046 | ||||||||
\(523\) | 2.31852e8i | 1.62071i | 0.585939 | + | 0.810355i | \(0.300726\pi\) | ||||
−0.585939 | + | 0.810355i | \(0.699274\pi\) | |||||||
\(524\) | − | 1.17274e8i | − | 0.815097i | ||||||
\(525\) | −3.44013e7 | − | 4.22321e6i | −0.237737 | − | 0.0291853i | ||||
\(526\) | 7.44918e7 | 0.511860 | ||||||||
\(527\) | 2.56482e8 | 1.75237 | ||||||||
\(528\) | 4.63473e6i | 0.0314863i | ||||||||
\(529\) | −7.31686e7 | −0.494262 | ||||||||
\(530\) | − | 126969.i | − | 0.000852842i | ||||||
\(531\) | − | 2.33262e8i | − | 1.55797i | ||||||
\(532\) | 3.41527e7 | + | 4.19268e6i | 0.226824 | + | 0.0278456i | ||||
\(533\) | 1.30895e8 | 0.864455 | ||||||||
\(534\) | 6.48448e6 | 0.0425845 | ||||||||
\(535\) | − | 2.49874e7i | − | 0.163177i | ||||||
\(536\) | 2.00935e7 | 0.130485 | ||||||||
\(537\) | 2.53350e7i | 0.163606i | ||||||||
\(538\) | 1.03443e8i | 0.664284i | ||||||||
\(539\) | 1.34462e8 | + | 3.35190e7i | 0.858682 | + | 0.214055i | ||||
\(540\) | 3.63354e7 | 0.230754 | ||||||||
\(541\) | −1.16913e7 | −0.0738363 | −0.0369181 | − | 0.999318i | \(-0.511754\pi\) | ||||
−0.0369181 | + | 0.999318i | \(0.511754\pi\) | |||||||
\(542\) | − | 1.57322e8i | − | 0.988082i | ||||||
\(543\) | −1.00279e7 | −0.0626339 | ||||||||
\(544\) | − | 3.51244e7i | − | 0.218179i | ||||||
\(545\) | 2.26476e8i | 1.39905i | ||||||||
\(546\) | −1.27153e6 | + | 1.03576e7i | −0.00781174 | + | 0.0636327i | ||||
\(547\) | −1.11900e8 | −0.683704 | −0.341852 | − | 0.939754i | \(-0.611054\pi\) | ||||
−0.341852 | + | 0.939754i | \(0.611054\pi\) | |||||||
\(548\) | −1.06563e8 | −0.647537 | ||||||||
\(549\) | − | 6.04241e7i | − | 0.365168i | ||||||
\(550\) | −1.75220e8 | −1.05316 | ||||||||
\(551\) | − | 1.02091e8i | − | 0.610285i | ||||||
\(552\) | 6.01857e6i | 0.0357829i | ||||||||
\(553\) | −2.48679e7 | + | 2.02568e8i | −0.147049 | + | 1.19783i | ||||
\(554\) | 2.97222e7 | 0.174804 | ||||||||
\(555\) | 2.95655e7 | 0.172945 | ||||||||
\(556\) | 3.80680e7i | 0.221481i | ||||||||
\(557\) | −1.37837e8 | −0.797629 | −0.398815 | − | 0.917032i | \(-0.630578\pi\) | ||||
−0.398815 | + | 0.917032i | \(0.630578\pi\) | |||||||
\(558\) | 1.70899e8i | 0.983641i | ||||||||
\(559\) | − | 1.28776e8i | − | 0.737227i | ||||||
\(560\) | −7.13784e7 | − | 8.76263e6i | −0.406446 | − | 0.0498965i | ||||
\(561\) | −2.74447e7 | −0.155442 | ||||||||
\(562\) | 1.76604e8 | 0.994930 | ||||||||
\(563\) | − | 3.73228e7i | − | 0.209146i | −0.994517 | − | 0.104573i | \(-0.966652\pi\) | ||
0.994517 | − | 0.104573i | \(-0.0333476\pi\) | |||||||
\(564\) | 3.06820e6 | 0.0171020 | ||||||||
\(565\) | 5.46145e7i | 0.302805i | ||||||||
\(566\) | 1.02644e8i | 0.566088i | ||||||||
\(567\) | −2.08705e7 | + | 1.70007e8i | −0.114494 | + | 0.932646i | ||||
\(568\) | 7.99789e7 | 0.436446 | ||||||||
\(569\) | 1.41857e8 | 0.770042 | 0.385021 | − | 0.922908i | \(-0.374194\pi\) | ||||
0.385021 | + | 0.922908i | \(0.374194\pi\) | |||||||
\(570\) | 1.39523e7i | 0.0753394i | ||||||||
\(571\) | 2.47829e8 | 1.33120 | 0.665600 | − | 0.746308i | \(-0.268176\pi\) | ||||
0.665600 | + | 0.746308i | \(0.268176\pi\) | |||||||
\(572\) | 5.27554e7i | 0.281890i | ||||||||
\(573\) | − | 7.65786e6i | − | 0.0407046i | ||||||
\(574\) | 1.80107e8 | + | 2.21104e7i | 0.952344 | + | 0.116913i | ||||
\(575\) | −2.27537e8 | −1.19688 | ||||||||
\(576\) | 2.34040e7 | 0.122468 | ||||||||
\(577\) | 1.43601e8i | 0.747531i | 0.927523 | + | 0.373766i | \(0.121934\pi\) | ||||
−0.927523 | + | 0.373766i | \(0.878066\pi\) | |||||||
\(578\) | 7.14478e7 | 0.370003 | ||||||||
\(579\) | − | 4.76529e7i | − | 0.245501i | ||||||
\(580\) | 2.13368e8i | 1.09357i | ||||||||
\(581\) | −2.22690e8 | − | 2.73381e7i | −1.13546 | − | 0.139393i | ||||
\(582\) | 3.69297e6 | 0.0187330 | ||||||||
\(583\) | −129123. | −0.000651623 | ||||||||
\(584\) | − | 8.40293e7i | − | 0.421883i | ||||||
\(585\) | 2.04681e8 | 1.02237 | ||||||||
\(586\) | 3.30017e7i | 0.164000i | ||||||||
\(587\) | − | 1.55774e8i | − | 0.770160i | −0.922883 | − | 0.385080i | \(-0.874174\pi\) | ||
0.922883 | − | 0.385080i | \(-0.125826\pi\) | |||||||
\(588\) | −3.49914e6 | + | 1.40368e7i | −0.0172119 | + | 0.0690458i | ||||
\(589\) | −1.32603e8 | −0.648942 | ||||||||
\(590\) | −3.78267e8 | −1.84180 | ||||||||
\(591\) | 1.97258e7i | 0.0955591i | ||||||||
\(592\) | 3.84806e7 | 0.185472 | ||||||||
\(593\) | 6.85593e7i | 0.328777i | 0.986396 | + | 0.164389i | \(0.0525651\pi\) | ||||
−0.986396 | + | 0.164389i | \(0.947435\pi\) | |||||||
\(594\) | − | 3.69518e7i | − | 0.176310i | ||||||
\(595\) | 5.18882e7 | − | 4.22670e8i | 0.246330 | − | 2.00655i | ||||
\(596\) | 5.18862e7 | 0.245083 | ||||||||
\(597\) | −2.36374e6 | −0.0111091 | ||||||||
\(598\) | 6.85073e7i | 0.320356i | ||||||||
\(599\) | 6.44816e7 | 0.300024 | 0.150012 | − | 0.988684i | \(-0.452069\pi\) | ||||
0.150012 | + | 0.988684i | \(0.452069\pi\) | |||||||
\(600\) | − | 1.82917e7i | − | 0.0846838i | ||||||
\(601\) | − | 2.18773e8i | − | 1.00779i | −0.863765 | − | 0.503895i | \(-0.831900\pi\) | ||
0.863765 | − | 0.503895i | \(-0.168100\pi\) | |||||||
\(602\) | 2.17525e7 | − | 1.77191e8i | 0.0997057 | − | 0.812180i | ||||
\(603\) | −7.92815e7 | −0.361593 | ||||||||
\(604\) | −1.39210e8 | −0.631770 | ||||||||
\(605\) | − | 7.86551e7i | − | 0.355190i | ||||||
\(606\) | 2.43058e7 | 0.109217 | ||||||||
\(607\) | − | 3.55798e8i | − | 1.59088i | −0.606032 | − | 0.795441i | \(-0.707240\pi\) | ||
0.606032 | − | 0.795441i | \(-0.292760\pi\) | |||||||
\(608\) | 1.81595e7i | 0.0807965i | ||||||||
\(609\) | 4.26017e7 | + | 5.22991e6i | 0.188615 | + | 0.0231549i | ||||
\(610\) | −9.79863e7 | −0.431694 | ||||||||
\(611\) | 3.49242e7 | 0.153110 | ||||||||
\(612\) | 1.38588e8i | 0.604604i | ||||||||
\(613\) | 1.50352e7 | 0.0652719 | 0.0326360 | − | 0.999467i | \(-0.489610\pi\) | ||||
0.0326360 | + | 0.999467i | \(0.489610\pi\) | |||||||
\(614\) | − | 1.28338e8i | − | 0.554433i | ||||||
\(615\) | 7.35786e7i | 0.316320i | ||||||||
\(616\) | −8.91128e6 | + | 7.25893e7i | −0.0381240 | + | 0.310549i | ||||
\(617\) | 4.45354e7 | 0.189605 | 0.0948025 | − | 0.995496i | \(-0.469778\pi\) | ||||
0.0948025 | + | 0.995496i | \(0.469778\pi\) | |||||||
\(618\) | −2.61764e7 | −0.110903 | ||||||||
\(619\) | 3.58045e7i | 0.150962i | 0.997147 | + | 0.0754808i | \(0.0240491\pi\) | ||||
−0.997147 | + | 0.0754808i | \(0.975951\pi\) | |||||||
\(620\) | 2.77137e8 | 1.16284 | ||||||||
\(621\) | − | 4.79850e7i | − | 0.200369i | ||||||
\(622\) | − | 2.24204e8i | − | 0.931691i | ||||||
\(623\) | 1.01560e8 | + | 1.24679e7i | 0.420011 | + | 0.0515617i | ||||
\(624\) | −5.50728e6 | −0.0226665 | ||||||||
\(625\) | 3.65022e7 | 0.149513 | ||||||||
\(626\) | 5.70530e7i | 0.232571i | ||||||||
\(627\) | 1.41890e7 | 0.0575639 | ||||||||
\(628\) | − | 1.48509e8i | − | 0.599616i | ||||||
\(629\) | 2.27864e8i | 0.915640i | ||||||||
\(630\) | 2.81633e8 | + | 3.45741e7i | 1.12632 | + | 0.138270i | ||||
\(631\) | −4.30383e8 | −1.71304 | −0.856520 | − | 0.516115i | \(-0.827378\pi\) | ||||
−0.856520 | + | 0.516115i | \(0.827378\pi\) | |||||||
\(632\) | −1.07709e8 | −0.426677 | ||||||||
\(633\) | − | 9.84778e6i | − | 0.0388264i | ||||||
\(634\) | −1.68785e8 | −0.662317 | ||||||||
\(635\) | 2.75253e8i | 1.07501i | ||||||||
\(636\) | − | 13479.5i | − | 5.23963e-5i | ||||||
\(637\) | −3.98295e7 | + | 1.59776e8i | −0.154094 | + | 0.618150i | ||||
\(638\) | 2.16988e8 | 0.835553 | ||||||||
\(639\) | −3.15567e8 | −1.20945 | ||||||||
\(640\) | − | 3.79530e7i | − | 0.144779i | ||||||
\(641\) | 1.87109e8 | 0.710429 | 0.355215 | − | 0.934785i | \(-0.384408\pi\) | ||||
0.355215 | + | 0.934785i | \(0.384408\pi\) | |||||||
\(642\) | − | 2.65275e6i | − | 0.0100252i | ||||||
\(643\) | 2.52905e8i | 0.951314i | 0.879631 | + | 0.475657i | \(0.157790\pi\) | ||||
−0.879631 | + | 0.475657i | \(0.842210\pi\) | |||||||
\(644\) | −1.15720e7 | + | 9.42632e7i | −0.0433263 | + | 0.352927i | ||||
\(645\) | 7.23876e7 | 0.269765 | ||||||||
\(646\) | −1.07532e8 | −0.398878 | ||||||||
\(647\) | 1.95969e8i | 0.723560i | 0.932263 | + | 0.361780i | \(0.117831\pi\) | ||||
−0.932263 | + | 0.361780i | \(0.882169\pi\) | |||||||
\(648\) | −9.03951e7 | −0.332216 | ||||||||
\(649\) | 3.84684e8i | 1.40725i | ||||||||
\(650\) | − | 2.08208e8i | − | 0.758153i | ||||||
\(651\) | 6.79295e6 | − | 5.53339e7i | 0.0246216 | − | 0.200562i | ||||
\(652\) | −1.68511e8 | −0.607975 | ||||||||
\(653\) | 1.11109e8 | 0.399033 | 0.199516 | − | 0.979894i | \(-0.436063\pi\) | ||||
0.199516 | + | 0.979894i | \(0.436063\pi\) | |||||||
\(654\) | 2.40436e7i | 0.0859539i | ||||||||
\(655\) | 7.50368e8 | 2.67024 | ||||||||
\(656\) | 9.57654e7i | 0.339232i | ||||||||
\(657\) | 3.31548e8i | 1.16910i | ||||||||
\(658\) | 4.80543e7 | + | 5.89929e6i | 0.168677 | + | 0.0207072i | ||||
\(659\) | −2.24885e8 | −0.785786 | −0.392893 | − | 0.919584i | \(-0.628526\pi\) | ||||
−0.392893 | + | 0.919584i | \(0.628526\pi\) | |||||||
\(660\) | −2.96548e7 | −0.103149 | ||||||||
\(661\) | − | 5.19969e8i | − | 1.80042i | −0.435458 | − | 0.900209i | \(-0.643414\pi\) | ||
0.435458 | − | 0.900209i | \(-0.356586\pi\) | |||||||
\(662\) | −1.01267e7 | −0.0349054 | ||||||||
\(663\) | − | 3.26116e7i | − | 0.111900i | ||||||
\(664\) | − | 1.18408e8i | − | 0.404460i | ||||||
\(665\) | −2.68264e7 | + | 2.18522e8i | −0.0912217 | + | 0.743072i | ||||
\(666\) | −1.51830e8 | −0.513967 | ||||||||
\(667\) | 2.81777e8 | 0.949571 | ||||||||
\(668\) | − | 6.38491e7i | − | 0.214203i | ||||||
\(669\) | −3.00634e7 | −0.100406 | ||||||||
\(670\) | 1.28566e8i | 0.427467i | ||||||||
\(671\) | 9.96486e7i | 0.329840i | ||||||||
\(672\) | −7.57780e6 | − | 930273.i | −0.0249710 | − | 0.00306551i | ||||
\(673\) | −3.68354e8 | −1.20842 | −0.604212 | − | 0.796823i | \(-0.706512\pi\) | ||||
−0.604212 | + | 0.796823i | \(0.706512\pi\) | |||||||
\(674\) | 7.36033e6 | 0.0240391 | ||||||||
\(675\) | 1.45836e8i | 0.474192i | ||||||||
\(676\) | 9.17704e7 | 0.297073 | ||||||||
\(677\) | 1.91687e7i | 0.0617770i | 0.999523 | + | 0.0308885i | \(0.00983367\pi\) | ||||
−0.999523 | + | 0.0308885i | \(0.990166\pi\) | |||||||
\(678\) | 5.79808e6i | 0.0186035i | ||||||||
\(679\) | 5.78396e7 | + | 7.10056e6i | 0.184763 | + | 0.0226821i | ||||
\(680\) | 2.24740e8 | 0.714749 | ||||||||
\(681\) | −3.14739e7 | −0.0996574 | ||||||||
\(682\) | − | 2.81838e8i | − | 0.888479i | ||||||
\(683\) | −3.28267e8 | −1.03030 | −0.515152 | − | 0.857099i | \(-0.672264\pi\) | ||||
−0.515152 | + | 0.857099i | \(0.672264\pi\) | |||||||
\(684\) | − | 7.16505e7i | − | 0.223898i | ||||||
\(685\) | − | 6.81833e8i | − | 2.12132i | ||||||
\(686\) | −8.17926e7 | + | 2.13118e8i | −0.253362 | + | 0.660157i | ||||
\(687\) | −5.01554e7 | −0.154685 | ||||||||
\(688\) | 9.42152e7 | 0.289305 | ||||||||
\(689\) | − | 153432.i | − | 0.000469092i | ||||||
\(690\) | −3.85092e7 | −0.117224 | ||||||||
\(691\) | − | 1.96349e8i | − | 0.595107i | −0.954705 | − | 0.297554i | \(-0.903829\pi\) | ||
0.954705 | − | 0.297554i | \(-0.0961707\pi\) | |||||||
\(692\) | − | 6.31503e7i | − | 0.190571i | ||||||
\(693\) | 3.51606e7 | − | 2.86410e8i | 0.105647 | − | 0.860576i | ||||
\(694\) | 1.51118e8 | 0.452103 | ||||||||
\(695\) | −2.43574e8 | −0.725567 | ||||||||
\(696\) | 2.26520e7i | 0.0671859i | ||||||||
\(697\) | −5.67078e8 | −1.67473 | ||||||||
\(698\) | − | 1.35611e8i | − | 0.398777i | ||||||
\(699\) | − | 5.32193e6i | − | 0.0155825i | ||||||
\(700\) | 3.51698e7 | − | 2.86486e8i | 0.102536 | − | 0.835235i | ||||
\(701\) | 4.19696e8 | 1.21837 | 0.609187 | − | 0.793026i | \(-0.291496\pi\) | ||||
0.609187 | + | 0.793026i | \(0.291496\pi\) | |||||||
\(702\) | 4.39086e7 | 0.126922 | ||||||||
\(703\) | − | 1.17807e8i | − | 0.339082i | ||||||
\(704\) | −3.85968e7 | −0.110620 | ||||||||
\(705\) | 1.96316e7i | 0.0560257i | ||||||||
\(706\) | 4.52430e8i | 1.28569i | ||||||||
\(707\) | 3.80678e8 | + | 4.67332e7i | 1.07721 | + | 0.132241i | ||||
\(708\) | −4.01583e7 | −0.113155 | ||||||||
\(709\) | 6.46327e8 | 1.81348 | 0.906742 | − | 0.421686i | \(-0.138562\pi\) | ||||
0.906742 | + | 0.421686i | \(0.138562\pi\) | |||||||
\(710\) | 5.11737e8i | 1.42979i | ||||||||
\(711\) | 4.24978e8 | 1.18238 | ||||||||
\(712\) | 5.40012e7i | 0.149611i | ||||||||
\(713\) | − | 3.65990e8i | − | 1.00972i | ||||||
\(714\) | 5.50864e6 | − | 4.48722e7i | 0.0151339 | − | 0.123277i | ||||
\(715\) | −3.37550e8 | −0.923465 | ||||||||
\(716\) | −2.10984e8 | −0.574791 | ||||||||
\(717\) | − | 1.68137e7i | − | 0.0456148i | ||||||
\(718\) | −2.55302e8 | −0.689732 | ||||||||
\(719\) | − | 3.24953e8i | − | 0.874246i | −0.899402 | − | 0.437123i | \(-0.855998\pi\) | ||
0.899402 | − | 0.437123i | \(-0.144002\pi\) | |||||||
\(720\) | 1.49748e8i | 0.401203i | ||||||||
\(721\) | −4.09976e8 | − | 5.03299e7i | −1.09384 | − | 0.134283i | ||||
\(722\) | −2.10537e8 | −0.559393 | ||||||||
\(723\) | 3.34257e7 | 0.0884434 | ||||||||
\(724\) | − | 8.35097e7i | − | 0.220050i | ||||||
\(725\) | −8.56378e8 | −2.24725 | ||||||||
\(726\) | − | 8.35032e6i | − | 0.0218219i | ||||||
\(727\) | 5.08659e8i | 1.32380i | 0.749591 | + | 0.661902i | \(0.230250\pi\) | ||||
−0.749591 | + | 0.661902i | \(0.769750\pi\) | |||||||
\(728\) | −8.62554e7 | − | 1.05890e7i | −0.223559 | − | 0.0274448i | ||||
\(729\) | 3.41130e8 | 0.880517 | ||||||||
\(730\) | 5.37653e8 | 1.38208 | ||||||||
\(731\) | 5.57899e8i | 1.42825i | ||||||||
\(732\) | −1.04026e7 | −0.0265221 | ||||||||
\(733\) | − | 7.52837e8i | − | 1.91156i | −0.294075 | − | 0.955782i | \(-0.595011\pi\) | ||
0.294075 | − | 0.955782i | \(-0.404989\pi\) | |||||||
\(734\) | 3.43475e8i | 0.868573i | ||||||||
\(735\) | −8.98132e7 | − | 2.23889e7i | −0.226193 | − | 0.0563859i | ||||
\(736\) | −5.01212e7 | −0.125715 | ||||||||
\(737\) | 1.30747e8 | 0.326611 | ||||||||
\(738\) | − | 3.77854e8i | − | 0.940059i | ||||||
\(739\) | −1.58548e8 | −0.392850 | −0.196425 | − | 0.980519i | \(-0.562933\pi\) | ||||
−0.196425 | + | 0.980519i | \(0.562933\pi\) | |||||||
\(740\) | 2.46214e8i | 0.607601i | ||||||||
\(741\) | 1.68603e7i | 0.0414392i | ||||||||
\(742\) | 25917.2 | − | 211116.i | 6.34420e−5 | − | 0.000516784i | ||||
\(743\) | 5.89089e8 | 1.43620 | 0.718099 | − | 0.695941i | \(-0.245013\pi\) | ||||
0.718099 | + | 0.695941i | \(0.245013\pi\) | |||||||
\(744\) | 2.94219e7 | 0.0714417 | ||||||||
\(745\) | 3.31988e8i | 0.802886i | ||||||||
\(746\) | 5.27055e8 | 1.26952 | ||||||||
\(747\) | 4.67192e8i | 1.12081i | ||||||||
\(748\) | − | 2.28553e8i | − | 0.546111i | ||||||
\(749\) | 5.10050e6 | − | 4.15475e7i | 0.0121386 | − | 0.0988781i | ||||
\(750\) | 4.74969e7 | 0.112585 | ||||||||
\(751\) | −3.67603e8 | −0.867879 | −0.433939 | − | 0.900942i | \(-0.642877\pi\) | ||||
−0.433939 | + | 0.900942i | \(0.642877\pi\) | |||||||
\(752\) | 2.55512e7i | 0.0600839i | ||||||||
\(753\) | 1.02205e8 | 0.239379 | ||||||||
\(754\) | 2.57839e8i | 0.601500i | ||||||||
\(755\) | − | 8.90719e8i | − | 2.06966i | ||||||
\(756\) | 6.04164e7 | + | 7.41690e6i | 0.139827 | + | 0.0171655i | ||||
\(757\) | 6.54505e8 | 1.50878 | 0.754389 | − | 0.656427i | \(-0.227933\pi\) | ||||
0.754389 | + | 0.656427i | \(0.227933\pi\) | |||||||
\(758\) | −1.57698e8 | −0.362092 | ||||||||
\(759\) | 3.91625e7i | 0.0895663i | ||||||||
\(760\) | −1.16192e8 | −0.264688 | ||||||||
\(761\) | 6.48428e7i | 0.147132i | 0.997290 | + | 0.0735661i | \(0.0234380\pi\) | ||||
−0.997290 | + | 0.0735661i | \(0.976562\pi\) | |||||||
\(762\) | 2.92219e7i | 0.0660456i | ||||||||
\(763\) | −4.62291e7 | + | 3.76572e8i | −0.104074 | + | 0.847763i | ||||
\(764\) | 6.37727e7 | 0.143006 | ||||||||
\(765\) | −8.86740e8 | −1.98067 | ||||||||
\(766\) | 1.49240e7i | 0.0332047i | ||||||||
\(767\) | −4.57107e8 | −1.01305 | ||||||||
\(768\) | − | 4.02923e6i | − | 0.00889485i | ||||||
\(769\) | 7.56321e8i | 1.66313i | 0.555425 | + | 0.831566i | \(0.312556\pi\) | ||||
−0.555425 | + | 0.831566i | \(0.687444\pi\) | |||||||
\(770\) | −4.64455e8 | − | 5.70179e7i | −1.01735 | − | 0.124893i | ||||
\(771\) | −2.89987e7 | −0.0632725 | ||||||||
\(772\) | 3.96842e8 | 0.862513 | ||||||||
\(773\) | − | 2.42896e8i | − | 0.525875i | −0.964813 | − | 0.262937i | \(-0.915309\pi\) | ||
0.964813 | − | 0.262937i | \(-0.0846913\pi\) | |||||||
\(774\) | −3.71738e8 | −0.801704 | ||||||||
\(775\) | 1.11232e9i | 2.38960i | ||||||||
\(776\) | 3.07542e7i | 0.0658141i | ||||||||
\(777\) | 4.91598e7 | + | 6.03501e6i | 0.104797 | + | 0.0128651i | ||||
\(778\) | −1.76827e8 | −0.375500 | ||||||||
\(779\) | 2.93182e8 | 0.620190 | ||||||||
\(780\) | − | 3.52378e7i | − | 0.0742549i | ||||||
\(781\) | 5.20418e8 | 1.09244 | ||||||||
\(782\) | − | 2.96794e8i | − | 0.620633i | ||||||
\(783\) | − | 1.80600e8i | − | 0.376212i | ||||||
\(784\) | −1.16895e8 | − | 2.91400e7i | −0.242577 | − | 0.0604701i | ||||
\(785\) | 9.50219e8 | 1.96433 | ||||||||
\(786\) | 7.96619e7 | 0.164052 | ||||||||
\(787\) | − | 4.68172e8i | − | 0.960465i | −0.877141 | − | 0.480232i | \(-0.840552\pi\) | ||
0.877141 | − | 0.480232i | \(-0.159448\pi\) | |||||||
\(788\) | −1.64272e8 | −0.335725 | ||||||||
\(789\) | 5.06006e7i | 0.103021i | ||||||||
\(790\) | − | 6.89162e8i | − | 1.39778i | ||||||
\(791\) | −1.11481e7 | + | 9.08098e7i | −0.0225253 | + | 0.183486i | ||||
\(792\) | 1.52289e8 | 0.306544 | ||||||||
\(793\) | −1.18409e8 | −0.237446 | ||||||||
\(794\) | − | 1.88794e8i | − | 0.377160i | ||||||
\(795\) | 86246.9 | 0.000171649 | ||||||||
\(796\) | − | 1.96847e7i | − | 0.0390291i | ||||||
\(797\) | − | 1.00075e8i | − | 0.197674i | −0.995104 | − | 0.0988370i | \(-0.968488\pi\) | ||
0.995104 | − | 0.0988370i | \(-0.0315122\pi\) | |||||||
\(798\) | −2.84799e6 | + | 2.31991e7i | −0.00560442 | + | 0.0456523i | ||||
\(799\) | −1.51302e8 | −0.296623 | ||||||||
\(800\) | 1.52329e8 | 0.297517 | ||||||||
\(801\) | − | 2.13068e8i | − | 0.414593i | ||||||
\(802\) | 2.30119e7 | 0.0446098 | ||||||||
\(803\) | − | 5.46774e8i | − | 1.05599i | ||||||
\(804\) | 1.36491e7i | 0.0262624i | ||||||||
\(805\) | −6.03133e8 | − | 7.40424e7i | −1.15618 | − | 0.141936i | ||||
\(806\) | 3.34899e8 | 0.639600 | ||||||||
\(807\) | −7.02664e7 | −0.133699 | ||||||||
\(808\) | 2.02412e8i | 0.383710i | ||||||||
\(809\) | −5.87217e8 | −1.10906 | −0.554528 | − | 0.832165i | \(-0.687101\pi\) | ||||
−0.554528 | + | 0.832165i | \(0.687101\pi\) | |||||||
\(810\) | − | 5.78384e8i | − | 1.08833i | ||||||
\(811\) | 8.86023e8i | 1.66105i | 0.556983 | + | 0.830524i | \(0.311959\pi\) | ||||
−0.556983 | + | 0.830524i | \(0.688041\pi\) | |||||||
\(812\) | −4.35534e7 | + | 3.54777e8i | −0.0813494 | + | 0.662654i | ||||
\(813\) | 1.06866e8 | 0.198869 | ||||||||
\(814\) | 2.50391e8 | 0.464244 | ||||||||
\(815\) | − | 1.07820e9i | − | 1.99171i | ||||||
\(816\) | 2.38592e7 | 0.0439123 | ||||||||
\(817\) | − | 2.88436e8i | − | 0.528912i | ||||||
\(818\) | − | 2.14396e8i | − | 0.391703i | ||||||
\(819\) | 3.40332e8 | + | 4.17801e7i | 0.619513 | + | 0.0760533i | ||||
\(820\) | −6.12745e8 | −1.11132 | ||||||||
\(821\) | −5.51065e8 | −0.995803 | −0.497902 | − | 0.867233i | \(-0.665896\pi\) | ||||
−0.497902 | + | 0.867233i | \(0.665896\pi\) | |||||||
\(822\) | − | 7.23858e7i | − | 0.130328i | ||||||
\(823\) | 5.33974e8 | 0.957901 | 0.478951 | − | 0.877842i | \(-0.341017\pi\) | ||||
0.478951 | + | 0.877842i | \(0.341017\pi\) | |||||||
\(824\) | − | 2.17991e8i | − | 0.389633i | ||||||
\(825\) | − | 1.19023e8i | − | 0.211967i | ||||||
\(826\) | −6.28961e8 | − | 7.72131e7i | −1.11605 | − | 0.137010i | ||||
\(827\) | −5.33590e8 | −0.943390 | −0.471695 | − | 0.881762i | \(-0.656358\pi\) | ||||
−0.471695 | + | 0.881762i | \(0.656358\pi\) | |||||||
\(828\) | 1.97759e8 | 0.348374 | ||||||||
\(829\) | 1.11584e9i | 1.95857i | 0.202476 | + | 0.979287i | \(0.435101\pi\) | ||||
−0.202476 | + | 0.979287i | \(0.564899\pi\) | |||||||
\(830\) | 7.57619e8 | 1.32500 | ||||||||
\(831\) | 2.01896e7i | 0.0351823i | ||||||||
\(832\) | − | 4.58633e7i | − | 0.0796334i | ||||||
\(833\) | 1.72553e8 | − | 6.92199e8i | 0.298530 | − | 1.19756i | ||||
\(834\) | −2.58588e7 | −0.0445769 | ||||||||
\(835\) | 4.08532e8 | 0.701725 | ||||||||
\(836\) | 1.18163e8i | 0.202237i | ||||||||
\(837\) | −2.34575e8 | −0.400042 | ||||||||
\(838\) | 4.15357e8i | 0.705813i | ||||||||
\(839\) | − | 2.23881e8i | − | 0.379081i | −0.981873 | − | 0.189540i | \(-0.939300\pi\) | ||
0.981873 | − | 0.189540i | \(-0.0606998\pi\) | |||||||
\(840\) | 5.95226e6 | − | 4.84858e7i | 0.0100425 | − | 0.0818043i | ||||
\(841\) | 4.65694e8 | 0.782912 | ||||||||
\(842\) | −3.36075e7 | −0.0562989 | ||||||||
\(843\) | 1.19963e8i | 0.200247i | ||||||||
\(844\) | 8.20098e7 | 0.136408 | ||||||||
\(845\) | 5.87184e8i | 0.973204i | ||||||||
\(846\) | − | 1.00816e8i | − | 0.166501i | ||||||
\(847\) | 1.60553e7 | − | 1.30783e8i | 0.0264222 | − | 0.215229i | ||||
\(848\) | 112254. | 0.000184082 | ||||||||
\(849\) | −6.97237e7 | −0.113935 | ||||||||
\(850\) | 9.02020e8i | 1.46879i | ||||||||
\(851\) | 3.25154e8 | 0.527594 | ||||||||
\(852\) | 5.43279e7i | 0.0878424i | ||||||||
\(853\) | 2.97785e8i | 0.479795i | 0.970798 | + | 0.239898i | \(0.0771139\pi\) | ||||
−0.970798 | + | 0.239898i | \(0.922886\pi\) | |||||||
\(854\) | −1.62926e8 | − | 2.00013e7i | −0.261587 | − | 0.0321132i | ||||
\(855\) | 4.58449e8 | 0.733487 | ||||||||
\(856\) | 2.20915e7 | 0.0352211 | ||||||||
\(857\) | 7.86923e8i | 1.25023i | 0.780533 | + | 0.625115i | \(0.214948\pi\) | ||||
−0.780533 | + | 0.625115i | \(0.785052\pi\) | |||||||
\(858\) | −3.58356e7 | −0.0567352 | ||||||||
\(859\) | − | 7.66256e8i | − | 1.20891i | −0.796639 | − | 0.604456i | \(-0.793391\pi\) | ||
0.796639 | − | 0.604456i | \(-0.206609\pi\) | |||||||
\(860\) | 6.02826e8i | 0.947757i | ||||||||
\(861\) | −1.50191e7 | + | 1.22342e8i | −0.0235307 | + | 0.191676i | ||||
\(862\) | −5.42385e8 | −0.846811 | ||||||||
\(863\) | −1.16650e9 | −1.81490 | −0.907452 | − | 0.420157i | \(-0.861975\pi\) | ||||
−0.907452 | + | 0.420157i | \(0.861975\pi\) | |||||||
\(864\) | 3.21243e7i | 0.0498073i | ||||||||
\(865\) | 4.04061e8 | 0.624307 | ||||||||
\(866\) | 6.97671e8i | 1.07423i | ||||||||
\(867\) | 4.85329e7i | 0.0744695i | ||||||||
\(868\) | 4.60807e8 | + | 5.65700e7i | 0.704628 | + | 0.0865022i | ||||
\(869\) | −7.00853e8 | −1.06799 | ||||||||
\(870\) | −1.44936e8 | −0.220100 | ||||||||
\(871\) | 1.55363e8i | 0.235121i | ||||||||
\(872\) | −2.00229e8 | −0.301979 | ||||||||
\(873\) | − | 1.21344e8i | − | 0.182380i | ||||||
\(874\) | 1.53444e8i | 0.229835i | ||||||||
\(875\) | 7.43900e8 | + | 9.13233e7i | 1.11043 | + | 0.136319i | ||||
\(876\) | 5.70792e7 | 0.0849113 | ||||||||
\(877\) | 7.56442e8 | 1.12144 | 0.560721 | − | 0.828005i | \(-0.310524\pi\) | ||||
0.560721 | + | 0.828005i | \(0.310524\pi\) | |||||||
\(878\) | − | 3.62985e8i | − | 0.536297i | ||||||
\(879\) | −2.24173e7 | −0.0330078 | ||||||||
\(880\) | − | 2.46958e8i | − | 0.362389i | ||||||
\(881\) | 3.69412e8i | 0.540235i | 0.962827 | + | 0.270118i | \(0.0870626\pi\) | ||||
−0.962827 | + | 0.270118i | \(0.912937\pi\) | |||||||
\(882\) | 4.61225e8 | + | 1.14975e8i | 0.672213 | + | 0.167571i | ||||
\(883\) | −5.87419e8 | −0.853230 | −0.426615 | − | 0.904433i | \(-0.640294\pi\) | ||||
−0.426615 | + | 0.904433i | \(0.640294\pi\) | |||||||
\(884\) | 2.71581e8 | 0.393136 | ||||||||
\(885\) | − | 2.56948e8i | − | 0.370695i | ||||||
\(886\) | 3.72632e8 | 0.535770 | ||||||||
\(887\) | − | 2.15522e7i | − | 0.0308831i | −0.999881 | − | 0.0154416i | \(-0.995085\pi\) | ||
0.999881 | − | 0.0154416i | \(-0.00491540\pi\) | |||||||
\(888\) | 2.61390e7i | 0.0373294i | ||||||||
\(889\) | −5.61856e7 | + | 4.57675e8i | −0.0799686 | + | 0.651407i | ||||
\(890\) | −3.45521e8 | −0.490122 | ||||||||
\(891\) | −5.88196e8 | −0.831551 | ||||||||
\(892\) | − | 2.50361e8i | − | 0.352753i | ||||||
\(893\) | 7.82240e7 | 0.109846 | ||||||||
\(894\) | 3.52451e7i | 0.0493272i | ||||||||
\(895\) | − | 1.34996e9i | − | 1.88300i | ||||||
\(896\) | 7.74708e6 | − | 6.31060e7i | 0.0107700 | − | 0.0877297i | ||||
\(897\) | −4.65354e7 | −0.0644772 | ||||||||
\(898\) | 5.78163e8 | 0.798402 | ||||||||
\(899\) | − | 1.37747e9i | − | 1.89585i | ||||||
\(900\) | −6.01032e8 | −0.824461 | ||||||||
\(901\) | 664713.i | 0.000908782i | ||||||||
\(902\) | 6.23140e8i | 0.849113i | ||||||||
\(903\) | 1.20362e8 | + | 1.47760e7i | 0.163465 | + | 0.0200675i | ||||
\(904\) | −4.82849e7 | −0.0653591 | ||||||||
\(905\) | 5.34328e8 | 0.720879 | ||||||||
\(906\) | − | 9.45620e7i | − | 0.127155i | ||||||
\(907\) | −1.14115e9 | −1.52939 | −0.764697 | − | 0.644390i | \(-0.777111\pi\) | ||||
−0.764697 | + | 0.644390i | \(0.777111\pi\) | |||||||
\(908\) | − | 2.62107e8i | − | 0.350124i | ||||||
\(909\) | − | 7.98644e8i | − | 1.06331i | ||||||
\(910\) | 6.77524e7 | − | 5.51896e8i | 0.0899085 | − | 0.732375i | ||||
\(911\) | −3.29876e8 | −0.436310 | −0.218155 | − | 0.975914i | \(-0.570004\pi\) | ||||
−0.218155 | + | 0.975914i | \(0.570004\pi\) | |||||||
\(912\) | −1.23353e7 | −0.0162617 | ||||||||
\(913\) | − | 7.70471e8i | − | 1.01238i | ||||||
\(914\) | 3.18131e8 | 0.416646 | ||||||||
\(915\) | − | 6.65599e7i | − | 0.0868859i | ||||||
\(916\) | − | 4.17682e8i | − | 0.543449i | ||||||
\(917\) | 1.24767e9 | + | 1.53167e8i | 1.61805 | + | 0.198636i | ||||
\(918\) | −1.90225e8 | −0.245890 | ||||||||
\(919\) | −1.10236e8 | −0.142029 | −0.0710144 | − | 0.997475i | \(-0.522624\pi\) | ||||
−0.0710144 | + | 0.997475i | \(0.522624\pi\) | |||||||
\(920\) | − | 3.20695e8i | − | 0.411840i | ||||||
\(921\) | 8.71769e7 | 0.111589 | ||||||||
\(922\) | 1.39498e8i | 0.177982i | ||||||||
\(923\) | 6.18395e8i | 0.786432i | ||||||||
\(924\) | −4.93083e7 | − | 6.05323e6i | −0.0625035 | − | 0.00767311i | ||||
\(925\) | −9.88210e8 | −1.24860 | ||||||||
\(926\) | −1.08588e9 | −1.36757 | ||||||||
\(927\) | 8.60109e8i | 1.07973i | ||||||||
\(928\) | −1.88640e8 | −0.236042 | ||||||||
\(929\) | 4.58674e8i | 0.572081i | 0.958218 | + | 0.286040i | \(0.0923391\pi\) | ||||
−0.958218 | + | 0.286040i | \(0.907661\pi\) | |||||||
\(930\) | 1.88253e8i | 0.234041i | ||||||||
\(931\) | −8.92109e7 | + | 3.57870e8i | −0.110553 | + | 0.443483i | ||||
\(932\) | 4.43197e7 | 0.0547456 | ||||||||
\(933\) | 1.52297e8 | 0.187519 | ||||||||
\(934\) | − | 8.53759e8i | − | 1.04784i | ||||||
\(935\) | 1.46237e9 | 1.78905 | ||||||||
\(936\) | 1.80959e8i | 0.220675i | ||||||||
\(937\) | − | 9.98325e8i | − | 1.21354i | −0.794878 | − | 0.606769i | \(-0.792465\pi\) | ||
0.794878 | − | 0.606769i | \(-0.207535\pi\) | |||||||
\(938\) | −2.62433e7 | + | 2.13772e8i | −0.0317988 | + | 0.259026i | ||||
\(939\) | −3.87548e7 | −0.0468089 | ||||||||
\(940\) | −1.63487e8 | −0.196834 | ||||||||
\(941\) | 1.08263e9i | 1.29930i | 0.760231 | + | 0.649652i | \(0.225085\pi\) | ||||
−0.760231 | + | 0.649652i | \(0.774915\pi\) | |||||||
\(942\) | 1.00879e8 | 0.120683 | ||||||||
\(943\) | 8.09198e8i | 0.964983i | ||||||||
\(944\) | − | 3.34428e8i | − | 0.397545i | ||||||
\(945\) | −4.74563e7 | + | 3.86568e8i | −0.0562339 | + | 0.458069i | ||||
\(946\) | 6.13053e8 | 0.724143 | ||||||||
\(947\) | 7.97542e8 | 0.939082 | 0.469541 | − | 0.882911i | \(-0.344419\pi\) | ||||
0.469541 | + | 0.882911i | \(0.344419\pi\) | |||||||
\(948\) | − | 7.31640e7i | − | 0.0858761i | ||||||
\(949\) | 6.49713e8 | 0.760191 | ||||||||
\(950\) | − | 4.66348e8i | − | 0.543926i | ||||||
\(951\) | − | 1.14652e8i | − | 0.133303i | ||||||
\(952\) | 3.73685e8 | + | 4.58746e7i | 0.433106 | + | 0.0531694i | ||||
\(953\) | −1.15116e9 | −1.33002 | −0.665009 | − | 0.746836i | \(-0.731572\pi\) | ||||
−0.665009 | + | 0.746836i | \(0.731572\pi\) | |||||||
\(954\) | −442910. | −0.000510118 | ||||||||
\(955\) | 4.08043e8i | 0.468485i | ||||||||
\(956\) | 1.40020e8 | 0.160257 | ||||||||
\(957\) | 1.47395e8i | 0.168169i | ||||||||
\(958\) | 2.66107e8i | 0.302663i | ||||||||
\(959\) | 1.39178e8 | − | 1.13371e9i | 0.157803 | − | 1.28542i | ||||
\(960\) | 2.57806e7 | 0.0291393 | ||||||||
\(961\) | −9.01645e8 | −1.01593 | ||||||||
\(962\) | 2.97531e8i | 0.334201i | ||||||||
\(963\) | −8.71646e7 | −0.0976026 | ||||||||
\(964\) | 2.78361e8i | 0.310726i | ||||||||
\(965\) | 2.53915e9i | 2.82557i | ||||||||
\(966\) | −6.40308e7 | − | 7.86062e6i | −0.0710326 | − | 0.00872018i | ||||
\(967\) | −6.50101e8 | −0.718954 | −0.359477 | − | 0.933154i | \(-0.617045\pi\) | ||||
−0.359477 | + | 0.933154i | \(0.617045\pi\) | |||||||
\(968\) | 6.95394e7 | 0.0766663 | ||||||||
\(969\) | − | 7.30441e7i | − | 0.0802812i | ||||||
\(970\) | −1.96777e8 | −0.215606 | ||||||||
\(971\) | − | 4.14091e8i | − | 0.452312i | −0.974091 | − | 0.226156i | \(-0.927384\pi\) | ||
0.974091 | − | 0.226156i | \(-0.0726159\pi\) | |||||||
\(972\) | − | 1.90774e8i | − | 0.207740i | ||||||
\(973\) | −4.05001e8 | − | 4.97192e7i | −0.439661 | − | 0.0539741i | ||||
\(974\) | 2.46647e8 | 0.266931 | ||||||||
\(975\) | 1.41431e8 | 0.152592 | ||||||||
\(976\) | − | 8.66302e7i | − | 0.0931793i | ||||||
\(977\) | −1.24398e9 | −1.33392 | −0.666962 | − | 0.745091i | \(-0.732406\pi\) | ||||
−0.666962 | + | 0.745091i | \(0.732406\pi\) | |||||||
\(978\) | − | 1.14466e8i | − | 0.122366i | ||||||
\(979\) | 3.51383e8i | 0.374483i | ||||||||
\(980\) | 1.86449e8 | − | 7.47942e8i | 0.198099 | − | 0.794676i | ||||
\(981\) | 7.90029e8 | 0.836827 | ||||||||
\(982\) | −4.40262e8 | −0.464918 | ||||||||
\(983\) | 1.65067e9i | 1.73780i | 0.494986 | + | 0.868901i | \(0.335173\pi\) | ||||
−0.494986 | + | 0.868901i | \(0.664827\pi\) | |||||||
\(984\) | −6.50512e7 | −0.0682763 | ||||||||
\(985\) | − | 1.05107e9i | − | 1.09983i | ||||||
\(986\) | − | 1.11704e9i | − | 1.16530i | ||||||
\(987\) | −4.00726e6 | + | 3.26422e7i | −0.00416769 | + | 0.0339491i | ||||
\(988\) | −1.40409e8 | −0.145587 | ||||||||
\(989\) | 7.96099e8 | 0.822959 | ||||||||
\(990\) | 9.74404e8i | 1.00423i | ||||||||
\(991\) | 1.85734e9 | 1.90841 | 0.954203 | − | 0.299159i | \(-0.0967060\pi\) | ||||
0.954203 | + | 0.299159i | \(0.0967060\pi\) | |||||||
\(992\) | 2.45018e8i | 0.250994i | ||||||||
\(993\) | − | 6.87882e6i | − | 0.00702532i | ||||||
\(994\) | −1.04457e8 | + | 8.50887e8i | −0.106360 | + | 0.866388i | ||||
\(995\) | 1.25950e8 | 0.127859 | ||||||||
\(996\) | 8.04316e7 | 0.0814046 | ||||||||
\(997\) | − | 1.40620e9i | − | 1.41893i | −0.704740 | − | 0.709466i | \(-0.748936\pi\) | ||
0.704740 | − | 0.709466i | \(-0.251064\pi\) | |||||||
\(998\) | 3.58498e8 | 0.360658 | ||||||||
\(999\) | − | 2.08402e8i | − | 0.209028i |
(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 | 14.7.b.a.13.1 | ✓ | 4 | |
3.2 | odd | 2 | 126.7.c.a.55.3 | 4 | |||
4.3 | odd | 2 | 112.7.c.c.97.3 | 4 | |||
5.2 | odd | 4 | 350.7.d.a.349.2 | 8 | |||
5.3 | odd | 4 | 350.7.d.a.349.7 | 8 | |||
5.4 | even | 2 | 350.7.b.a.251.4 | 4 | |||
7.2 | even | 3 | 98.7.d.b.31.4 | 8 | |||
7.3 | odd | 6 | 98.7.d.b.19.4 | 8 | |||
7.4 | even | 3 | 98.7.d.b.19.3 | 8 | |||
7.5 | odd | 6 | 98.7.d.b.31.3 | 8 | |||
7.6 | odd | 2 | inner | 14.7.b.a.13.2 | yes | 4 | |
8.3 | odd | 2 | 448.7.c.e.321.2 | 4 | |||
8.5 | even | 2 | 448.7.c.h.321.3 | 4 | |||
21.20 | even | 2 | 126.7.c.a.55.4 | 4 | |||
28.27 | even | 2 | 112.7.c.c.97.2 | 4 | |||
35.13 | even | 4 | 350.7.d.a.349.6 | 8 | |||
35.27 | even | 4 | 350.7.d.a.349.3 | 8 | |||
35.34 | odd | 2 | 350.7.b.a.251.3 | 4 | |||
56.13 | odd | 2 | 448.7.c.h.321.2 | 4 | |||
56.27 | even | 2 | 448.7.c.e.321.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.7.b.a.13.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
14.7.b.a.13.2 | yes | 4 | 7.6 | odd | 2 | inner | |
98.7.d.b.19.3 | 8 | 7.4 | even | 3 | |||
98.7.d.b.19.4 | 8 | 7.3 | odd | 6 | |||
98.7.d.b.31.3 | 8 | 7.5 | odd | 6 | |||
98.7.d.b.31.4 | 8 | 7.2 | even | 3 | |||
112.7.c.c.97.2 | 4 | 28.27 | even | 2 | |||
112.7.c.c.97.3 | 4 | 4.3 | odd | 2 | |||
126.7.c.a.55.3 | 4 | 3.2 | odd | 2 | |||
126.7.c.a.55.4 | 4 | 21.20 | even | 2 | |||
350.7.b.a.251.3 | 4 | 35.34 | odd | 2 | |||
350.7.b.a.251.4 | 4 | 5.4 | even | 2 | |||
350.7.d.a.349.2 | 8 | 5.2 | odd | 4 | |||
350.7.d.a.349.3 | 8 | 35.27 | even | 4 | |||
350.7.d.a.349.6 | 8 | 35.13 | even | 4 | |||
350.7.d.a.349.7 | 8 | 5.3 | odd | 4 | |||
448.7.c.e.321.2 | 4 | 8.3 | odd | 2 | |||
448.7.c.e.321.3 | 4 | 56.27 | even | 2 | |||
448.7.c.h.321.2 | 4 | 56.13 | odd | 2 | |||
448.7.c.h.321.3 | 4 | 8.5 | even | 2 |