Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [20,7,Mod(19,20)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(20, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("20.19");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 20 = 2^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 20.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: | \(4.60108167240\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 16x^{10} - 10x^{8} - 1775x^{6} - 1000x^{4} + 160000x^{2} + 1000000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{2}\cdot 5^{2}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 19.10 | ||
Root | \(0.954985 + 3.01463i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 20.19 |
Dual form | 20.7.d.d.19.9 |
$q$-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 \(\left(\mathbb{Z}/20\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(17\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.94356 | + | 5.35482i | 0.742945 | + | 0.669352i | ||||
\(3\) | −40.3729 | −1.49529 | −0.747646 | − | 0.664098i | \(-0.768816\pi\) | ||||
−0.747646 | + | 0.664098i | \(0.768816\pi\) | |||||||
\(4\) | 6.65182 | + | 63.6534i | 0.103935 | + | 0.994584i | ||||
\(5\) | −32.9271 | − | 120.585i | −0.263417 | − | 0.964682i | ||||
\(6\) | −239.959 | − | 216.189i | −1.11092 | − | 1.00088i | ||||
\(7\) | −450.705 | −1.31401 | −0.657004 | − | 0.753887i | \(-0.728176\pi\) | ||||
−0.657004 | + | 0.753887i | \(0.728176\pi\) | |||||||
\(8\) | −301.317 | + | 413.947i | −0.588510 | + | 0.808490i | ||||
\(9\) | 900.969 | 1.23590 | ||||||||
\(10\) | 450.008 | − | 893.024i | 0.450008 | − | 0.893024i | ||||
\(11\) | 390.888i | 0.293680i | 0.989160 | + | 0.146840i | \(0.0469103\pi\) | ||||
−0.989160 | + | 0.146840i | \(0.953090\pi\) | |||||||
\(12\) | −268.553 | − | 2569.87i | −0.155413 | − | 1.48719i | ||||
\(13\) | 3234.51i | 1.47224i | 0.676852 | + | 0.736119i | \(0.263344\pi\) | ||||
−0.676852 | + | 0.736119i | \(0.736656\pi\) | |||||||
\(14\) | −2678.79 | − | 2413.44i | −0.976235 | − | 0.879534i | ||||
\(15\) | 1329.36 | + | 4868.37i | 0.393885 | + | 1.44248i | ||||
\(16\) | −4007.51 | + | 846.821i | −0.978395 | + | 0.206744i | ||||
\(17\) | − | 4937.20i | − | 1.00493i | −0.864599 | − | 0.502463i | \(-0.832427\pi\) | ||
0.864599 | − | 0.502463i | \(-0.167573\pi\) | |||||||
\(18\) | 5354.96 | + | 4824.53i | 0.918204 | + | 0.827251i | ||||
\(19\) | 1980.00i | 0.288672i | 0.989529 | + | 0.144336i | \(0.0461047\pi\) | ||||
−0.989529 | + | 0.144336i | \(0.953895\pi\) | |||||||
\(20\) | 7456.64 | − | 2898.03i | 0.932079 | − | 0.362254i | ||||
\(21\) | 18196.2 | 1.96482 | ||||||||
\(22\) | −2093.14 | + | 2323.27i | −0.196576 | + | 0.218188i | ||||
\(23\) | −1077.32 | −0.0885446 | −0.0442723 | − | 0.999020i | \(-0.514097\pi\) | ||||
−0.0442723 | + | 0.999020i | \(0.514097\pi\) | |||||||
\(24\) | 12165.0 | − | 16712.2i | 0.879993 | − | 1.20893i | ||||
\(25\) | −13456.6 | + | 7941.04i | −0.861223 | + | 0.508227i | ||||
\(26\) | −17320.2 | + | 19224.5i | −0.985447 | + | 1.09379i | ||||
\(27\) | −6942.88 | −0.352735 | ||||||||
\(28\) | −2998.00 | − | 28688.9i | −0.136571 | − | 1.30689i | ||||
\(29\) | −21158.1 | −0.867528 | −0.433764 | − | 0.901027i | \(-0.642815\pi\) | ||||
−0.433764 | + | 0.901027i | \(0.642815\pi\) | |||||||
\(30\) | −18168.1 | + | 36054.0i | −0.672894 | + | 1.33533i | ||||
\(31\) | − | 33221.4i | − | 1.11515i | −0.830127 | − | 0.557574i | \(-0.811732\pi\) | ||
0.830127 | − | 0.557574i | \(-0.188268\pi\) | |||||||
\(32\) | −28353.4 | − | 16426.3i | −0.865278 | − | 0.501292i | ||||
\(33\) | − | 15781.3i | − | 0.439138i | ||||||
\(34\) | 26437.8 | − | 29344.6i | 0.672650 | − | 0.746605i | ||||
\(35\) | 14840.4 | + | 54348.3i | 0.346132 | + | 1.26760i | ||||
\(36\) | 5993.08 | + | 57349.7i | 0.128453 | + | 1.22920i | ||||
\(37\) | 14159.5i | 0.279539i | 0.990184 | + | 0.139769i | \(0.0446362\pi\) | ||||
−0.990184 | + | 0.139769i | \(0.955364\pi\) | |||||||
\(38\) | −10602.6 | + | 11768.3i | −0.193223 | + | 0.214468i | ||||
\(39\) | − | 130586.i | − | 2.20143i | ||||||
\(40\) | 59837.4 | + | 22704.3i | 0.934959 | + | 0.354755i | ||||
\(41\) | −42870.4 | −0.622023 | −0.311011 | − | 0.950406i | \(-0.600668\pi\) | ||||
−0.311011 | + | 0.950406i | \(0.600668\pi\) | |||||||
\(42\) | 108150. | + | 97437.6i | 1.45976 | + | 1.31516i | ||||
\(43\) | −57775.6 | −0.726673 | −0.363337 | − | 0.931658i | \(-0.618363\pi\) | ||||
−0.363337 | + | 0.931658i | \(0.618363\pi\) | |||||||
\(44\) | −24881.4 | + | 2600.12i | −0.292090 | + | 0.0305236i | ||||
\(45\) | −29666.3 | − | 108644.i | −0.325556 | − | 1.19225i | ||||
\(46\) | −6403.13 | − | 5768.87i | −0.0657838 | − | 0.0592676i | ||||
\(47\) | 138151. | 1.33064 | 0.665320 | − | 0.746558i | \(-0.268295\pi\) | ||||
0.665320 | + | 0.746558i | \(0.268295\pi\) | |||||||
\(48\) | 161795. | − | 34188.6i | 1.46299 | − | 0.309142i | ||||
\(49\) | 85485.6 | 0.726616 | ||||||||
\(50\) | −122503. | − | 24859.7i | −0.980024 | − | 0.198877i | ||||
\(51\) | 199329.i | 1.50266i | ||||||||
\(52\) | −205887. | + | 21515.4i | −1.46427 | + | 0.153017i | ||||
\(53\) | 277123.i | 1.86142i | 0.365756 | + | 0.930711i | \(0.380811\pi\) | ||||
−0.365756 | + | 0.930711i | \(0.619189\pi\) | |||||||
\(54\) | −41265.4 | − | 37177.9i | −0.262063 | − | 0.236104i | ||||
\(55\) | 47135.4 | − | 12870.8i | 0.283308 | − | 0.0773603i | ||||
\(56\) | 135805. | − | 186568.i | 0.773306 | − | 1.06236i | ||||
\(57\) | − | 79938.4i | − | 0.431649i | ||||||
\(58\) | −125755. | − | 113298.i | −0.644525 | − | 0.580682i | ||||
\(59\) | 28176.1i | 0.137191i | 0.997645 | + | 0.0685954i | \(0.0218518\pi\) | ||||
−0.997645 | + | 0.0685954i | \(0.978148\pi\) | |||||||
\(60\) | −301046. | + | 117002.i | −1.39373 | + | 0.541675i | ||||
\(61\) | −34082.0 | −0.150154 | −0.0750769 | − | 0.997178i | \(-0.523920\pi\) | ||||
−0.0750769 | + | 0.997178i | \(0.523920\pi\) | |||||||
\(62\) | 177894. | − | 197453.i | 0.746427 | − | 0.828494i | ||||
\(63\) | −406071. | −1.62398 | ||||||||
\(64\) | −80560.3 | − | 249458.i | −0.307313 | − | 0.951608i | ||||
\(65\) | 390034. | − | 106503.i | 1.42024 | − | 0.387812i | ||||
\(66\) | 84506.0 | − | 93797.1i | 0.293938 | − | 0.326255i | ||||
\(67\) | −230002. | −0.764730 | −0.382365 | − | 0.924011i | \(-0.624890\pi\) | ||||
−0.382365 | + | 0.924011i | \(0.624890\pi\) | |||||||
\(68\) | 314270. | − | 32841.4i | 0.999484 | − | 0.104447i | ||||
\(69\) | 43494.6 | 0.132400 | ||||||||
\(70\) | −202821. | + | 402490.i | −0.591314 | + | 1.17344i | ||||
\(71\) | 214659.i | 0.599757i | 0.953977 | + | 0.299878i | \(0.0969461\pi\) | ||||
−0.953977 | + | 0.299878i | \(0.903054\pi\) | |||||||
\(72\) | −271477. | + | 372953.i | −0.727337 | + | 0.999211i | ||||
\(73\) | 21193.6i | 0.0544800i | 0.999629 | + | 0.0272400i | \(0.00867183\pi\) | ||||
−0.999629 | + | 0.0272400i | \(0.991328\pi\) | |||||||
\(74\) | −75821.5 | + | 84157.8i | −0.187110 | + | 0.207682i | ||||
\(75\) | 543282. | − | 320603.i | 1.28778 | − | 0.759947i | ||||
\(76\) | −126034. | + | 13170.6i | −0.287109 | + | 0.0300030i | ||||
\(77\) | − | 176175.i | − | 0.385898i | ||||||
\(78\) | 699267. | − | 776148.i | 1.47353 | − | 1.63554i | ||||
\(79\) | 365752.i | 0.741832i | 0.928666 | + | 0.370916i | \(0.120956\pi\) | ||||
−0.928666 | + | 0.370916i | \(0.879044\pi\) | |||||||
\(80\) | 234070. | + | 455363.i | 0.457167 | + | 0.889381i | ||||
\(81\) | −376502. | −0.708456 | ||||||||
\(82\) | −254803. | − | 229563.i | −0.462129 | − | 0.416352i | ||||
\(83\) | −50231.1 | −0.0878493 | −0.0439247 | − | 0.999035i | \(-0.513986\pi\) | ||||
−0.0439247 | + | 0.999035i | \(0.513986\pi\) | |||||||
\(84\) | 121038. | + | 1.15825e6i | 0.204213 | + | 1.95418i | ||||
\(85\) | −595354. | + | 162568.i | −0.969435 | + | 0.264714i | ||||
\(86\) | −343393. | − | 309378.i | −0.539878 | − | 0.486401i | ||||
\(87\) | 854215. | 1.29721 | ||||||||
\(88\) | −161807. | − | 117781.i | −0.237438 | − | 0.172834i | ||||
\(89\) | −177274. | −0.251463 | −0.125731 | − | 0.992064i | \(-0.540128\pi\) | ||||
−0.125731 | + | 0.992064i | \(0.540128\pi\) | |||||||
\(90\) | 405443. | − | 804587.i | 0.556164 | − | 1.10369i | ||||
\(91\) | − | 1.45781e6i | − | 1.93453i | ||||||
\(92\) | −7166.15 | − | 68575.2i | −0.00920286 | − | 0.0880651i | ||||
\(93\) | 1.34124e6i | 1.66747i | ||||||||
\(94\) | 821109. | + | 739774.i | 0.988592 | + | 0.890667i | ||||
\(95\) | 238759. | − | 65195.7i | 0.278477 | − | 0.0760411i | ||||
\(96\) | 1.14471e6 | + | 663179.i | 1.29384 | + | 0.749578i | ||||
\(97\) | − | 1.15267e6i | − | 1.26296i | −0.775393 | − | 0.631479i | \(-0.782448\pi\) | ||
0.775393 | − | 0.631479i | \(-0.217552\pi\) | |||||||
\(98\) | 508089. | + | 457760.i | 0.539836 | + | 0.486362i | ||||
\(99\) | 352178.i | 0.362959i | ||||||||
\(100\) | −594985. | − | 803737.i | −0.594985 | − | 0.803737i | ||||
\(101\) | 1.27960e6 | 1.24197 | 0.620985 | − | 0.783822i | \(-0.286733\pi\) | ||||
0.620985 | + | 0.783822i | \(0.286733\pi\) | |||||||
\(102\) | −1.06737e6 | + | 1.18472e6i | −1.00581 | + | 1.11639i | ||||
\(103\) | −2.08267e6 | −1.90593 | −0.952967 | − | 0.303074i | \(-0.901987\pi\) | ||||
−0.952967 | + | 0.303074i | \(0.901987\pi\) | |||||||
\(104\) | −1.33892e6 | − | 974612.i | −1.19029 | − | 0.866427i | ||||
\(105\) | −599149. | − | 2.19420e6i | −0.517568 | − | 1.89543i | ||||
\(106\) | −1.48394e6 | + | 1.64710e6i | −1.24595 | + | 1.38293i | ||||
\(107\) | −512122. | −0.418044 | −0.209022 | − | 0.977911i | \(-0.567028\pi\) | ||||
−0.209022 | + | 0.977911i | \(0.567028\pi\) | |||||||
\(108\) | −46182.8 | − | 441938.i | −0.0366614 | − | 0.350824i | ||||
\(109\) | −1.32906e6 | −1.02628 | −0.513141 | − | 0.858305i | \(-0.671518\pi\) | ||||
−0.513141 | + | 0.858305i | \(0.671518\pi\) | |||||||
\(110\) | 349073. | + | 175903.i | 0.262264 | + | 0.132159i | ||||
\(111\) | − | 571659.i | − | 0.417992i | ||||||
\(112\) | 1.80620e6 | − | 381666.i | 1.28562 | − | 0.271663i | ||||
\(113\) | 160172.i | 0.111007i | 0.998458 | + | 0.0555035i | \(0.0176764\pi\) | ||||
−0.998458 | + | 0.0555035i | \(0.982324\pi\) | |||||||
\(114\) | 428056. | − | 475119.i | 0.288925 | − | 0.320692i | ||||
\(115\) | 35473.1 | + | 129909.i | 0.0233241 | + | 0.0854174i | ||||
\(116\) | −140740. | − | 1.34679e6i | −0.0901662 | − | 0.862829i | ||||
\(117\) | 2.91419e6i | 1.81954i | ||||||||
\(118\) | −150878. | + | 167466.i | −0.0918290 | + | 0.101925i | ||||
\(119\) | 2.22522e6i | 1.32048i | ||||||||
\(120\) | −2.41581e6 | − | 916638.i | −1.39804 | − | 0.530462i | ||||
\(121\) | 1.61877e6 | 0.913752 | ||||||||
\(122\) | −202569. | − | 182503.i | −0.111556 | − | 0.100506i | ||||
\(123\) | 1.73080e6 | 0.930105 | ||||||||
\(124\) | 2.11465e6 | − | 220982.i | 1.10911 | − | 0.115903i | ||||
\(125\) | 1.40066e6 | + | 1.36119e6i | 0.717138 | + | 0.696931i | ||||
\(126\) | −2.41351e6 | − | 2.17444e6i | −1.20653 | − | 1.08701i | ||||
\(127\) | 1.90105e6 | 0.928071 | 0.464036 | − | 0.885816i | \(-0.346401\pi\) | ||||
0.464036 | + | 0.885816i | \(0.346401\pi\) | |||||||
\(128\) | 856990. | − | 1.91406e6i | 0.408645 | − | 0.912693i | ||||
\(129\) | 2.33257e6 | 1.08659 | ||||||||
\(130\) | 2.88850e6 | + | 1.45556e6i | 1.31475 | + | 0.662520i | ||||
\(131\) | 2.76248e6i | 1.22881i | 0.788990 | + | 0.614407i | \(0.210605\pi\) | ||||
−0.788990 | + | 0.614407i | \(0.789395\pi\) | |||||||
\(132\) | 1.00453e6 | − | 104974.i | 0.436759 | − | 0.0456416i | ||||
\(133\) | − | 892396.i | − | 0.379317i | ||||||
\(134\) | −1.36703e6 | − | 1.23162e6i | −0.568152 | − | 0.511874i | ||||
\(135\) | 228609. | + | 837209.i | 0.0929162 | + | 0.340277i | ||||
\(136\) | 2.04374e6 | + | 1.48766e6i | 0.812473 | + | 0.591409i | ||||
\(137\) | − | 2.60078e6i | − | 1.01144i | −0.862696 | − | 0.505722i | \(-0.831226\pi\) | ||
0.862696 | − | 0.505722i | \(-0.168774\pi\) | |||||||
\(138\) | 258513. | + | 232906.i | 0.0983660 | + | 0.0886223i | ||||
\(139\) | − | 3.07350e6i | − | 1.14443i | −0.820104 | − | 0.572214i | \(-0.806085\pi\) | ||
0.820104 | − | 0.572214i | \(-0.193915\pi\) | |||||||
\(140\) | −3.36074e6 | + | 1.30616e6i | −1.22476 | + | 0.476004i | ||||
\(141\) | −5.57755e6 | −1.98969 | ||||||||
\(142\) | −1.14946e6 | + | 1.27584e6i | −0.401448 | + | 0.445586i | ||||
\(143\) | −1.26433e6 | −0.432368 | ||||||||
\(144\) | −3.61064e6 | + | 762960.i | −1.20920 | + | 0.255514i | ||||
\(145\) | 696676. | + | 2.55136e6i | 0.228521 | + | 0.836889i | ||||
\(146\) | −113488. | + | 125966.i | −0.0364663 | + | 0.0404756i | ||||
\(147\) | −3.45130e6 | −1.08650 | ||||||||
\(148\) | −901299. | + | 94186.3i | −0.278025 | + | 0.0290538i | ||||
\(149\) | 2.10750e6 | 0.637102 | 0.318551 | − | 0.947906i | \(-0.396804\pi\) | ||||
0.318551 | + | 0.947906i | \(0.396804\pi\) | |||||||
\(150\) | 4.94580e6 | + | 1.00366e6i | 1.46542 | + | 0.297380i | ||||
\(151\) | 2.20804e6i | 0.641323i | 0.947194 | + | 0.320662i | \(0.103905\pi\) | ||||
−0.947194 | + | 0.320662i | \(0.896095\pi\) | |||||||
\(152\) | −819616. | − | 596608.i | −0.233389 | − | 0.169886i | ||||
\(153\) | − | 4.44827e6i | − | 1.24199i | ||||||
\(154\) | 943387. | − | 1.04711e6i | 0.258302 | − | 0.286701i | ||||
\(155\) | −4.00601e6 | + | 1.09388e6i | −1.07576 | + | 0.293749i | ||||
\(156\) | 8.31227e6 | − | 868637.i | 2.18950 | − | 0.228805i | ||||
\(157\) | 821139.i | 0.212187i | 0.994356 | + | 0.106093i | \(0.0338342\pi\) | ||||
−0.994356 | + | 0.106093i | \(0.966166\pi\) | |||||||
\(158\) | −1.95854e6 | + | 2.17387e6i | −0.496547 | + | 0.551140i | ||||
\(159\) | − | 1.11882e7i | − | 2.78337i | ||||||
\(160\) | −1.04718e6 | + | 3.95988e6i | −0.255659 | + | 0.966767i | ||||
\(161\) | 485554. | 0.116348 | ||||||||
\(162\) | −2.23776e6 | − | 2.01610e6i | −0.526344 | − | 0.474206i | ||||
\(163\) | 7.70810e6 | 1.77985 | 0.889927 | − | 0.456103i | \(-0.150755\pi\) | ||||
0.889927 | + | 0.456103i | \(0.150755\pi\) | |||||||
\(164\) | −285166. | − | 2.72885e6i | −0.0646497 | − | 0.618654i | ||||
\(165\) | −1.90299e6 | + | 519632.i | −0.423628 | + | 0.115676i | ||||
\(166\) | −298552. | − | 268979.i | −0.0652672 | − | 0.0588022i | ||||
\(167\) | −2.37157e6 | −0.509197 | −0.254599 | − | 0.967047i | \(-0.581943\pi\) | ||||
−0.254599 | + | 0.967047i | \(0.581943\pi\) | |||||||
\(168\) | −5.48283e6 | + | 7.53228e6i | −1.15632 | + | 1.58854i | ||||
\(169\) | −5.63524e6 | −1.16749 | ||||||||
\(170\) | −4.40904e6 | − | 2.22178e6i | −0.897424 | − | 0.452225i | ||||
\(171\) | 1.78392e6i | 0.356769i | ||||||||
\(172\) | −384313. | − | 3.67761e6i | −0.0755266 | − | 0.722738i | ||||
\(173\) | 5.22589e6i | 1.00930i | 0.863323 | + | 0.504652i | \(0.168379\pi\) | ||||
−0.863323 | + | 0.504652i | \(0.831621\pi\) | |||||||
\(174\) | 5.07708e6 | + | 4.57417e6i | 0.963753 | + | 0.868289i | ||||
\(175\) | 6.06496e6 | − | 3.57906e6i | 1.13165 | − | 0.667814i | ||||
\(176\) | −331013. | − | 1.56649e6i | −0.0607165 | − | 0.287335i | ||||
\(177\) | − | 1.13755e6i | − | 0.205140i | ||||||
\(178\) | −1.05364e6 | − | 949268.i | −0.186823 | − | 0.168317i | ||||
\(179\) | 6.41696e6i | 1.11885i | 0.828882 | + | 0.559423i | \(0.188977\pi\) | ||||
−0.828882 | + | 0.559423i | \(0.811023\pi\) | |||||||
\(180\) | 6.71820e6 | − | 2.61104e6i | 1.15195 | − | 0.447709i | ||||
\(181\) | −2.74959e6 | −0.463694 | −0.231847 | − | 0.972752i | \(-0.574477\pi\) | ||||
−0.231847 | + | 0.972752i | \(0.574477\pi\) | |||||||
\(182\) | 7.80630e6 | − | 8.66457e6i | 1.29488 | − | 1.43725i | ||||
\(183\) | 1.37599e6 | 0.224524 | ||||||||
\(184\) | 324615. | − | 445954.i | 0.0521094 | − | 0.0715875i | ||||
\(185\) | 1.70743e6 | − | 466231.i | 0.269666 | − | 0.0736352i | ||||
\(186\) | −7.18211e6 | + | 7.97175e6i | −1.11613 | + | 1.23884i | ||||
\(187\) | 1.92990e6 | 0.295127 | ||||||||
\(188\) | 918955. | + | 8.79378e6i | 0.138300 | + | 1.32343i | ||||
\(189\) | 3.12919e6 | 0.463496 | ||||||||
\(190\) | 1.76819e6 | + | 891018.i | 0.257791 | + | 0.129905i | ||||
\(191\) | − | 7.97496e6i | − | 1.14453i | −0.820068 | − | 0.572267i | \(-0.806064\pi\) | ||
0.820068 | − | 0.572267i | \(-0.193936\pi\) | |||||||
\(192\) | 3.25245e6 | + | 1.00714e7i | 0.459523 | + | 1.42293i | ||||
\(193\) | − | 1.21860e7i | − | 1.69508i | −0.530734 | − | 0.847539i | \(-0.678084\pi\) | ||
0.530734 | − | 0.847539i | \(-0.321916\pi\) | |||||||
\(194\) | 6.17233e6 | − | 6.85095e6i | 0.845364 | − | 0.938308i | ||||
\(195\) | −1.57468e7 | + | 4.29983e6i | −2.12368 | + | 0.579893i | ||||
\(196\) | 568635. | + | 5.44145e6i | 0.0755206 | + | 0.722681i | ||||
\(197\) | 5.27192e6i | 0.689557i | 0.938684 | + | 0.344778i | \(0.112046\pi\) | ||||
−0.938684 | + | 0.344778i | \(0.887954\pi\) | |||||||
\(198\) | −1.88585e6 | + | 2.09319e6i | −0.242947 | + | 0.269658i | ||||
\(199\) | 1.14435e7i | 1.45210i | 0.687639 | + | 0.726052i | \(0.258647\pi\) | ||||
−0.687639 | + | 0.726052i | \(0.741353\pi\) | |||||||
\(200\) | 767534. | − | 7.96310e6i | 0.0959418 | − | 0.995387i | ||||
\(201\) | 9.28586e6 | 1.14349 | ||||||||
\(202\) | 7.60540e6 | + | 6.85205e6i | 0.922716 | + | 0.831316i | ||||
\(203\) | 9.53607e6 | 1.13994 | ||||||||
\(204\) | −1.26880e7 | + | 1.32590e6i | −1.49452 | + | 0.156178i | ||||
\(205\) | 1.41160e6 | + | 5.16954e6i | 0.163851 | + | 0.600054i | ||||
\(206\) | −1.23785e7 | − | 1.11523e7i | −1.41600 | − | 1.27574i | ||||
\(207\) | −970634. | −0.109432 | ||||||||
\(208\) | −2.73905e6 | − | 1.29623e7i | −0.304376 | − | 1.44043i | ||||
\(209\) | −773960. | −0.0847773 | ||||||||
\(210\) | 8.18846e6 | − | 1.62497e7i | 0.884187 | − | 1.75464i | ||||
\(211\) | − | 3.30342e6i | − | 0.351655i | −0.984421 | − | 0.175828i | \(-0.943740\pi\) | ||
0.984421 | − | 0.175828i | \(-0.0562601\pi\) | |||||||
\(212\) | −1.76398e7 | + | 1.84337e6i | −1.85134 | + | 0.193466i | ||||
\(213\) | − | 8.66642e6i | − | 0.896811i | ||||||
\(214\) | −3.04383e6 | − | 2.74232e6i | −0.310584 | − | 0.279819i | ||||
\(215\) | 1.90238e6 | + | 6.96689e6i | 0.191418 | + | 0.701009i | ||||
\(216\) | 2.09201e6 | − | 2.87398e6i | 0.207588 | − | 0.285183i | ||||
\(217\) | 1.49730e7i | 1.46531i | ||||||||
\(218\) | −7.89937e6 | − | 7.11690e6i | −0.762471 | − | 0.686944i | ||||
\(219\) | − | 855648.i | − | 0.0814634i | ||||||
\(220\) | 1.13281e6 | + | 2.91471e6i | 0.106387 | + | 0.273733i | ||||
\(221\) | 1.59694e7 | 1.47949 | ||||||||
\(222\) | 3.06113e6 | − | 3.39769e6i | 0.279784 | − | 0.310545i | ||||
\(223\) | −1.43034e7 | −1.28981 | −0.644903 | − | 0.764265i | \(-0.723102\pi\) | ||||
−0.644903 | + | 0.764265i | \(0.723102\pi\) | |||||||
\(224\) | 1.27790e7 | + | 7.40343e6i | 1.13698 | + | 0.658702i | ||||
\(225\) | −1.21240e7 | + | 7.15463e6i | −1.06438 | + | 0.628116i | ||||
\(226\) | −857690. | + | 951990.i | −0.0743028 | + | 0.0824721i | ||||
\(227\) | −879277. | −0.0751706 | −0.0375853 | − | 0.999293i | \(-0.511967\pi\) | ||||
−0.0375853 | + | 0.999293i | \(0.511967\pi\) | |||||||
\(228\) | 5.08835e6 | − | 531736.i | 0.429311 | − | 0.0448633i | ||||
\(229\) | −363899. | −0.0303022 | −0.0151511 | − | 0.999885i | \(-0.504823\pi\) | ||||
−0.0151511 | + | 0.999885i | \(0.504823\pi\) | |||||||
\(230\) | −484804. | + | 962075.i | −0.0398458 | + | 0.0790725i | ||||
\(231\) | 7.11270e6i | 0.577030i | ||||||||
\(232\) | 6.37530e6 | − | 8.75835e6i | 0.510548 | − | 0.701388i | ||||
\(233\) | 3.19027e6i | 0.252208i | 0.992017 | + | 0.126104i | \(0.0402474\pi\) | ||||
−0.992017 | + | 0.126104i | \(0.959753\pi\) | |||||||
\(234\) | −1.56050e7 | + | 1.73207e7i | −1.21791 | + | 1.35182i | ||||
\(235\) | −4.54891e6 | − | 1.66590e7i | −0.350513 | − | 1.28364i | ||||
\(236\) | −1.79350e6 | + | 187422.i | −0.136448 | + | 0.0142589i | ||||
\(237\) | − | 1.47665e7i | − | 1.10926i | ||||||
\(238\) | −1.19157e7 | + | 1.32257e7i | −0.883867 | + | 0.981045i | ||||
\(239\) | 1.72090e7i | 1.26056i | 0.776368 | + | 0.630279i | \(0.217060\pi\) | ||||
−0.776368 | + | 0.630279i | \(0.782940\pi\) | |||||||
\(240\) | −9.45007e6 | − | 1.83843e7i | −0.683599 | − | 1.32988i | ||||
\(241\) | −1.26609e7 | −0.904508 | −0.452254 | − | 0.891889i | \(-0.649380\pi\) | ||||
−0.452254 | + | 0.891889i | \(0.649380\pi\) | |||||||
\(242\) | 9.62124e6 | + | 8.66821e6i | 0.678867 | + | 0.611622i | ||||
\(243\) | 2.02618e7 | 1.41208 | ||||||||
\(244\) | −226708. | − | 2.16944e6i | −0.0156062 | − | 0.149341i | ||||
\(245\) | −2.81479e6 | − | 1.03083e7i | −0.191403 | − | 0.700953i | ||||
\(246\) | 1.02871e7 | + | 9.26813e6i | 0.691017 | + | 0.622568i | ||||
\(247\) | −6.40434e6 | −0.424995 | ||||||||
\(248\) | 1.37519e7 | + | 1.00102e7i | 0.901586 | + | 0.656275i | ||||
\(249\) | 2.02797e6 | 0.131360 | ||||||||
\(250\) | 1.03596e6 | + | 1.55906e7i | 0.0663013 | + | 0.997800i | ||||
\(251\) | − | 2.69052e7i | − | 1.70143i | −0.525625 | − | 0.850716i | \(-0.676168\pi\) | ||
0.525625 | − | 0.850716i | \(-0.323832\pi\) | |||||||
\(252\) | −2.70111e6 | − | 2.58478e7i | −0.168788 | − | 1.61518i | ||||
\(253\) | − | 421113.i | − | 0.0260038i | ||||||
\(254\) | 1.12990e7 | + | 1.01798e7i | 0.689506 | + | 0.621207i | ||||
\(255\) | 2.40362e7 | − | 6.56333e6i | 1.44959 | − | 0.395825i | ||||
\(256\) | 1.53430e7 | − | 6.78729e6i | 0.914514 | − | 0.404554i | ||||
\(257\) | − | 7.81210e6i | − | 0.460223i | −0.973164 | − | 0.230112i | \(-0.926091\pi\) | ||
0.973164 | − | 0.230112i | \(-0.0739091\pi\) | |||||||
\(258\) | 1.38638e7 | + | 1.24905e7i | 0.807276 | + | 0.727311i | ||||
\(259\) | − | 6.38175e6i | − | 0.367316i | ||||||
\(260\) | 9.37371e6 | + | 2.41186e7i | 0.533324 | + | 1.37224i | ||||
\(261\) | −1.90628e7 | −1.07217 | ||||||||
\(262\) | −1.47926e7 | + | 1.64190e7i | −0.822509 | + | 0.912941i | ||||
\(263\) | −1.33139e7 | −0.731877 | −0.365938 | − | 0.930639i | \(-0.619252\pi\) | ||||
−0.365938 | + | 0.930639i | \(0.619252\pi\) | |||||||
\(264\) | 6.53262e6 | + | 4.75517e6i | 0.355039 | + | 0.258437i | ||||
\(265\) | 3.34169e7 | − | 9.12485e6i | 1.79568 | − | 0.490330i | ||||
\(266\) | 4.77862e6 | − | 5.30401e6i | 0.253897 | − | 0.281812i | ||||
\(267\) | 7.15704e6 | 0.376010 | ||||||||
\(268\) | −1.52993e6 | − | 1.46404e7i | −0.0794819 | − | 0.760588i | ||||
\(269\) | −1.73876e7 | −0.893271 | −0.446635 | − | 0.894716i | \(-0.647378\pi\) | ||||
−0.446635 | + | 0.894716i | \(0.647378\pi\) | |||||||
\(270\) | −3.12435e6 | + | 6.20016e6i | −0.158734 | + | 0.315001i | ||||
\(271\) | 2.13357e7i | 1.07201i | 0.844215 | + | 0.536005i | \(0.180067\pi\) | ||||
−0.844215 | + | 0.536005i | \(0.819933\pi\) | |||||||
\(272\) | 4.18093e6 | + | 1.97859e7i | 0.207762 | + | 0.983215i | ||||
\(273\) | 5.88559e7i | 2.89269i | ||||||||
\(274\) | 1.39267e7 | − | 1.54579e7i | 0.677013 | − | 0.751447i | ||||
\(275\) | −3.10406e6 | − | 5.26004e6i | −0.149256 | − | 0.252924i | ||||
\(276\) | 289318. | + | 2.76858e6i | 0.0137610 | + | 0.131683i | ||||
\(277\) | − | 1.72036e7i | − | 0.809431i | −0.914443 | − | 0.404716i | \(-0.867371\pi\) | ||
0.914443 | − | 0.404716i | \(-0.132629\pi\) | |||||||
\(278\) | 1.64580e7 | − | 1.82675e7i | 0.766025 | − | 0.850247i | ||||
\(279\) | − | 2.99314e7i | − | 1.37821i | ||||||
\(280\) | −2.69690e7 | − | 1.02329e7i | −1.22854 | − | 0.466151i | ||||
\(281\) | −2.56886e7 | −1.15777 | −0.578883 | − | 0.815411i | \(-0.696511\pi\) | ||||
−0.578883 | + | 0.815411i | \(0.696511\pi\) | |||||||
\(282\) | −3.31505e7 | − | 2.98668e7i | −1.47823 | − | 1.33181i | ||||
\(283\) | −1.39377e7 | −0.614937 | −0.307469 | − | 0.951558i | \(-0.599482\pi\) | ||||
−0.307469 | + | 0.951558i | \(0.599482\pi\) | |||||||
\(284\) | −1.36638e7 | + | 1.42788e6i | −0.596508 | + | 0.0623355i | ||||
\(285\) | −9.63939e6 | + | 2.63214e6i | −0.416404 | + | 0.113704i | ||||
\(286\) | −7.51464e6 | − | 6.77027e6i | −0.321225 | − | 0.289406i | ||||
\(287\) | 1.93219e7 | 0.817342 | ||||||||
\(288\) | −2.55456e7 | − | 1.47996e7i | −1.06939 | − | 0.619545i | ||||
\(289\) | −238417. | −0.00987743 | ||||||||
\(290\) | −9.52133e6 | + | 1.88947e7i | −0.390395 | + | 0.774723i | ||||
\(291\) | 4.65365e7i | 1.88849i | ||||||||
\(292\) | −1.34905e6 | + | 140976.i | −0.0541849 | + | 0.00566235i | ||||
\(293\) | − | 3.28329e7i | − | 1.30529i | −0.757665 | − | 0.652644i | \(-0.773660\pi\) | ||
0.757665 | − | 0.652644i | \(-0.226340\pi\) | |||||||
\(294\) | −2.05130e7 | − | 1.84811e7i | −0.807212 | − | 0.727253i | ||||
\(295\) | 3.39762e6 | − | 927757.i | 0.132345 | − | 0.0361383i | ||||
\(296\) | −5.86128e6 | − | 4.26649e6i | −0.226005 | − | 0.164511i | ||||
\(297\) | − | 2.71389e6i | − | 0.103591i | ||||||
\(298\) | 1.25261e7 | + | 1.12853e7i | 0.473332 | + | 0.426446i | ||||
\(299\) | − | 3.48461e6i | − | 0.130359i | ||||||
\(300\) | 2.40213e7 | + | 3.24492e7i | 0.889676 | + | 1.20182i | ||||
\(301\) | 2.60397e7 | 0.954854 | ||||||||
\(302\) | −1.18237e7 | + | 1.31236e7i | −0.429271 | + | 0.476468i | ||||
\(303\) | −5.16613e7 | −1.85711 | ||||||||
\(304\) | −1.67671e6 | − | 7.93487e6i | −0.0596811 | − | 0.282436i | ||||
\(305\) | 1.12222e6 | + | 4.10979e6i | 0.0395530 | + | 0.144851i | ||||
\(306\) | 2.38197e7 | − | 2.64385e7i | 0.831326 | − | 0.922727i | ||||
\(307\) | −3.20799e7 | −1.10871 | −0.554356 | − | 0.832280i | \(-0.687035\pi\) | ||||
−0.554356 | + | 0.832280i | \(0.687035\pi\) | |||||||
\(308\) | 1.12141e7 | − | 1.17189e6i | 0.383808 | − | 0.0401082i | ||||
\(309\) | 8.40832e7 | 2.84993 | ||||||||
\(310\) | −2.96675e7 | − | 1.49499e7i | −0.995854 | − | 0.501826i | ||||
\(311\) | − | 3.21955e7i | − | 1.07032i | −0.844751 | − | 0.535160i | \(-0.820251\pi\) | ||
0.844751 | − | 0.535160i | \(-0.179749\pi\) | |||||||
\(312\) | 5.40559e7 | + | 3.93479e7i | 1.77983 | + | 1.29556i | ||||
\(313\) | 3.62694e6i | 0.118279i | 0.998250 | + | 0.0591394i | \(0.0188357\pi\) | ||||
−0.998250 | + | 0.0591394i | \(0.981164\pi\) | |||||||
\(314\) | −4.39705e6 | + | 4.88049e6i | −0.142028 | + | 0.157643i | ||||
\(315\) | 1.33707e7 | + | 4.89662e7i | 0.427783 | + | 1.56662i | ||||
\(316\) | −2.32814e7 | + | 2.43292e6i | −0.737814 | + | 0.0771020i | ||||
\(317\) | 2.70689e7i | 0.849754i | 0.905251 | + | 0.424877i | \(0.139683\pi\) | ||||
−0.905251 | + | 0.424877i | \(0.860317\pi\) | |||||||
\(318\) | 5.99110e7 | − | 6.64980e7i | 1.86305 | − | 2.06789i | ||||
\(319\) | − | 8.27047e6i | − | 0.254776i | ||||||
\(320\) | −2.74284e7 | + | 1.79283e7i | −0.837048 | + | 0.547129i | ||||
\(321\) | 2.06758e7 | 0.625098 | ||||||||
\(322\) | 2.88592e6 | + | 2.60006e6i | 0.0864404 | + | 0.0778780i | ||||
\(323\) | 9.77568e6 | 0.290094 | ||||||||
\(324\) | −2.50443e6 | − | 2.39656e7i | −0.0736331 | − | 0.704619i | ||||
\(325\) | −2.56854e7 | − | 4.35255e7i | −0.748231 | − | 1.26793i | ||||
\(326\) | 4.58135e7 | + | 4.12755e7i | 1.32233 | + | 1.19135i | ||||
\(327\) | 5.36581e7 | 1.53459 | ||||||||
\(328\) | 1.29176e7 | − | 1.77461e7i | 0.366066 | − | 0.502899i | ||||
\(329\) | −6.22653e7 | −1.74847 | ||||||||
\(330\) | −1.40931e7 | − | 7.10171e6i | −0.392161 | − | 0.197616i | ||||
\(331\) | 3.35438e7i | 0.924972i | 0.886627 | + | 0.462486i | \(0.153042\pi\) | ||||
−0.886627 | + | 0.462486i | \(0.846958\pi\) | |||||||
\(332\) | −334128. | − | 3.19738e6i | −0.00913059 | − | 0.0873736i | ||||
\(333\) | 1.27573e7i | 0.345481i | ||||||||
\(334\) | −1.40955e7 | − | 1.26993e7i | −0.378305 | − | 0.340832i | ||||
\(335\) | 7.57331e6 | + | 2.77349e7i | 0.201443 | + | 0.737721i | ||||
\(336\) | −7.29215e7 | + | 1.54090e7i | −1.92237 | + | 0.406215i | ||||
\(337\) | 5.29894e7i | 1.38452i | 0.721648 | + | 0.692260i | \(0.243385\pi\) | ||||
−0.721648 | + | 0.692260i | \(0.756615\pi\) | |||||||
\(338\) | −3.34934e7 | − | 3.01757e7i | −0.867379 | − | 0.781461i | ||||
\(339\) | − | 6.46659e6i | − | 0.165988i | ||||||
\(340\) | −1.43082e7 | − | 3.68149e7i | −0.364039 | − | 0.936671i | ||||
\(341\) | 1.29859e7 | 0.327497 | ||||||||
\(342\) | −9.55257e6 | + | 1.06028e7i | −0.238804 | + | 0.265060i | ||||
\(343\) | 1.44962e7 | 0.359229 | ||||||||
\(344\) | 1.74088e7 | − | 2.39160e7i | 0.427654 | − | 0.587508i | ||||
\(345\) | −1.43215e6 | − | 5.24481e6i | −0.0348764 | − | 0.127724i | ||||
\(346\) | −2.79837e7 | + | 3.10604e7i | −0.675580 | + | 0.749858i | ||||
\(347\) | 1.30197e7 | 0.311611 | 0.155805 | − | 0.987788i | \(-0.450203\pi\) | ||||
0.155805 | + | 0.987788i | \(0.450203\pi\) | |||||||
\(348\) | 5.68208e6 | + | 5.43737e7i | 0.134825 | + | 1.29018i | ||||
\(349\) | −1.95421e7 | −0.459721 | −0.229860 | − | 0.973224i | \(-0.573827\pi\) | ||||
−0.229860 | + | 0.973224i | \(0.573827\pi\) | |||||||
\(350\) | 5.52127e7 | + | 1.12044e7i | 1.28776 | + | 0.261326i | ||||
\(351\) | − | 2.24568e7i | − | 0.519310i | ||||||
\(352\) | 6.42087e6 | − | 1.10830e7i | 0.147220 | − | 0.254115i | ||||
\(353\) | 4.20948e7i | 0.956984i | 0.878092 | + | 0.478492i | \(0.158816\pi\) | ||||
−0.878092 | + | 0.478492i | \(0.841184\pi\) | |||||||
\(354\) | 6.09138e6 | − | 6.76110e6i | 0.137311 | − | 0.152408i | ||||
\(355\) | 2.58848e7 | − | 7.06811e6i | 0.578574 | − | 0.157986i | ||||
\(356\) | −1.17919e6 | − | 1.12841e7i | −0.0261357 | − | 0.250101i | ||||
\(357\) | − | 8.98386e7i | − | 1.97450i | ||||||
\(358\) | −3.43617e7 | + | 3.81396e7i | −0.748902 | + | 0.831241i | ||||
\(359\) | − | 6.88488e6i | − | 0.148803i | −0.997228 | − | 0.0744017i | \(-0.976295\pi\) | ||
0.997228 | − | 0.0744017i | \(-0.0237047\pi\) | |||||||
\(360\) | 5.39116e7 | + | 2.04559e7i | 1.15551 | + | 0.438440i | ||||
\(361\) | 4.31255e7 | 0.916668 | ||||||||
\(362\) | −1.63423e7 | − | 1.47235e7i | −0.344499 | − | 0.310375i | ||||
\(363\) | −6.53543e7 | −1.36633 | ||||||||
\(364\) | 9.27944e7 | − | 9.69707e6i | 1.92406 | − | 0.201065i | ||||
\(365\) | 2.55564e6 | − | 697844.i | 0.0525558 | − | 0.0143509i | ||||
\(366\) | 8.17828e6 | + | 7.36818e6i | 0.166809 | + | 0.150285i | ||||
\(367\) | −1.25791e7 | −0.254480 | −0.127240 | − | 0.991872i | \(-0.540612\pi\) | ||||
−0.127240 | + | 0.991872i | \(0.540612\pi\) | |||||||
\(368\) | 4.31738e6 | − | 912300.i | 0.0866316 | − | 0.0183060i | ||||
\(369\) | −3.86249e7 | −0.768756 | ||||||||
\(370\) | 1.26448e7 | + | 6.37189e6i | 0.249635 | + | 0.125795i | ||||
\(371\) | − | 1.24901e8i | − | 2.44592i | ||||||
\(372\) | −8.53746e7 | + | 8.92170e6i | −1.65844 | + | 0.173308i | ||||
\(373\) | 5.80469e7i | 1.11854i | 0.828984 | + | 0.559272i | \(0.188919\pi\) | ||||
−0.828984 | + | 0.559272i | \(0.811081\pi\) | |||||||
\(374\) | 1.14705e7 | + | 1.03342e7i | 0.219263 | + | 0.197544i | ||||
\(375\) | −5.65487e7 | − | 5.49553e7i | −1.07233 | − | 1.04212i | ||||
\(376\) | −4.16272e7 | + | 5.71872e7i | −0.783094 | + | 1.07581i | ||||
\(377\) | − | 6.84362e7i | − | 1.27721i | ||||||
\(378\) | 1.85985e7 | + | 1.67562e7i | 0.344352 | + | 0.310242i | ||||
\(379\) | 4.35438e7i | 0.799850i | 0.916548 | + | 0.399925i | \(0.130964\pi\) | ||||
−0.916548 | + | 0.399925i | \(0.869036\pi\) | |||||||
\(380\) | 5.73811e6 | + | 1.47642e7i | 0.104573 | + | 0.269065i | ||||
\(381\) | −7.67507e7 | −1.38774 | ||||||||
\(382\) | 4.27045e7 | − | 4.73997e7i | 0.766096 | − | 0.850325i | ||||
\(383\) | 2.94725e6 | 0.0524591 | 0.0262296 | − | 0.999656i | \(-0.491650\pi\) | ||||
0.0262296 | + | 0.999656i | \(0.491650\pi\) | |||||||
\(384\) | −3.45992e7 | + | 7.72760e7i | −0.611043 | + | 1.36474i | ||||
\(385\) | −2.12441e7 | + | 5.80094e6i | −0.372269 | + | 0.101652i | ||||
\(386\) | 6.52539e7 | − | 7.24283e7i | 1.13460 | − | 1.25935i | ||||
\(387\) | −5.20540e7 | −0.898094 | ||||||||
\(388\) | 7.33712e7 | − | 7.66733e6i | 1.25612 | − | 0.131265i | ||||
\(389\) | 1.87700e7 | 0.318871 | 0.159436 | − | 0.987208i | \(-0.449033\pi\) | ||||
0.159436 | + | 0.987208i | \(0.449033\pi\) | |||||||
\(390\) | −1.16617e8 | − | 5.87650e7i | −1.96593 | − | 0.990660i | ||||
\(391\) | 5.31896e6i | 0.0889809i | ||||||||
\(392\) | −2.57583e7 | + | 3.53865e7i | −0.427620 | + | 0.587462i | ||||
\(393\) | − | 1.11529e8i | − | 1.83743i | ||||||
\(394\) | −2.82302e7 | + | 3.13340e7i | −0.461556 | + | 0.512303i | ||||
\(395\) | 4.41043e7 | − | 1.20432e7i | 0.715632 | − | 0.195411i | ||||
\(396\) | −2.24173e7 | + | 2.34263e6i | −0.360993 | + | 0.0377240i | ||||
\(397\) | 3.99848e7i | 0.639033i | 0.947581 | + | 0.319517i | \(0.103521\pi\) | ||||
−0.947581 | + | 0.319517i | \(0.896479\pi\) | |||||||
\(398\) | −6.12776e7 | + | 6.80149e7i | −0.971970 | + | 1.07883i | ||||
\(399\) | 3.60286e7i | 0.567190i | ||||||||
\(400\) | 4.72028e7 | − | 4.32191e7i | 0.737544 | − | 0.675299i | ||||
\(401\) | 6.49364e6 | 0.100706 | 0.0503530 | − | 0.998731i | \(-0.483965\pi\) | ||||
0.0503530 | + | 0.998731i | \(0.483965\pi\) | |||||||
\(402\) | 5.51911e7 | + | 4.97241e7i | 0.849553 | + | 0.765401i | ||||
\(403\) | 1.07455e8 | 1.64176 | ||||||||
\(404\) | 8.51169e6 | + | 8.14511e7i | 0.129084 | + | 1.23524i | ||||
\(405\) | 1.23971e7 | + | 4.54006e7i | 0.186619 | + | 0.683434i | ||||
\(406\) | 5.66782e7 | + | 5.10639e7i | 0.846911 | + | 0.763020i | ||||
\(407\) | −5.53478e6 | −0.0820951 | ||||||||
\(408\) | −8.25117e7 | − | 6.00612e7i | −1.21488 | − | 0.884329i | ||||
\(409\) | 2.76062e7 | 0.403494 | 0.201747 | − | 0.979438i | \(-0.435338\pi\) | ||||
0.201747 | + | 0.979438i | \(0.435338\pi\) | |||||||
\(410\) | −1.92920e7 | + | 3.82843e7i | −0.279915 | + | 0.555481i | ||||
\(411\) | 1.05001e8i | 1.51240i | ||||||||
\(412\) | −1.38535e7 | − | 1.32569e8i | −0.198093 | − | 1.89561i | ||||
\(413\) | − | 1.26991e7i | − | 0.180270i | ||||||
\(414\) | −5.76902e6 | − | 5.19757e6i | −0.0813020 | − | 0.0732486i | ||||
\(415\) | 1.65396e6 | + | 6.05713e6i | 0.0231410 | + | 0.0847467i | ||||
\(416\) | 5.31311e7 | − | 9.17094e7i | 0.738022 | − | 1.27390i | ||||
\(417\) | 1.24086e8i | 1.71125i | ||||||||
\(418\) | −4.60008e6 | − | 4.14442e6i | −0.0629849 | − | 0.0567459i | ||||
\(419\) | − | 1.47995e7i | − | 0.201190i | −0.994927 | − | 0.100595i | \(-0.967925\pi\) | ||
0.994927 | − | 0.100595i | \(-0.0320746\pi\) | |||||||
\(420\) | 1.35683e8 | − | 5.27333e7i | 1.83137 | − | 0.711765i | ||||
\(421\) | −3.29248e7 | −0.441242 | −0.220621 | − | 0.975360i | \(-0.570808\pi\) | ||||
−0.220621 | + | 0.975360i | \(0.570808\pi\) | |||||||
\(422\) | 1.76892e7 | − | 1.96341e7i | 0.235381 | − | 0.261260i | ||||
\(423\) | 1.24470e8 | 1.64453 | ||||||||
\(424\) | −1.14714e8 | − | 8.35018e7i | −1.50494 | − | 1.09546i | ||||
\(425\) | 3.92066e7 | + | 6.64381e7i | 0.510731 | + | 0.865466i | ||||
\(426\) | 4.64071e7 | − | 5.15094e7i | 0.600283 | − | 0.666281i | ||||
\(427\) | 1.53609e7 | 0.197303 | ||||||||
\(428\) | −3.40654e6 | − | 3.25983e7i | −0.0434493 | − | 0.415780i | ||||
\(429\) | 5.10447e7 | 0.646516 | ||||||||
\(430\) | −2.59995e7 | + | 5.15950e7i | −0.327009 | + | 0.648937i | ||||
\(431\) | 9.46095e7i | 1.18169i | 0.806786 | + | 0.590844i | \(0.201205\pi\) | ||||
−0.806786 | + | 0.590844i | \(0.798795\pi\) | |||||||
\(432\) | 2.78236e7 | − | 5.87938e6i | 0.345114 | − | 0.0729256i | ||||
\(433\) | − | 6.50578e7i | − | 0.801375i | −0.916215 | − | 0.400687i | \(-0.868771\pi\) | ||
0.916215 | − | 0.400687i | \(-0.131229\pi\) | |||||||
\(434\) | −8.01778e7 | + | 8.89931e7i | −0.980811 | + | 1.08865i | ||||
\(435\) | −2.81268e7 | − | 1.03006e8i | −0.341706 | − | 1.25139i | ||||
\(436\) | −8.84069e6 | − | 8.45994e7i | −0.106666 | − | 1.02072i | ||||
\(437\) | − | 2.13310e6i | − | 0.0255604i | ||||||
\(438\) | 4.58184e6 | − | 5.08559e6i | 0.0545277 | − | 0.0605228i | ||||
\(439\) | 5.30694e7i | 0.627264i | 0.949545 | + | 0.313632i | \(0.101546\pi\) | ||||
−0.949545 | + | 0.313632i | \(0.898454\pi\) | |||||||
\(440\) | −8.87485e6 | + | 2.33898e7i | −0.104185 | + | 0.274579i | ||||
\(441\) | 7.70199e7 | 0.898022 | ||||||||
\(442\) | 9.49153e7 | + | 8.55134e7i | 1.09918 | + | 0.990302i | ||||
\(443\) | −1.37420e8 | −1.58066 | −0.790328 | − | 0.612684i | \(-0.790090\pi\) | ||||
−0.790328 | + | 0.612684i | \(0.790090\pi\) | |||||||
\(444\) | 3.63880e7 | − | 3.80257e6i | 0.415729 | − | 0.0434439i | ||||
\(445\) | 5.83710e6 | + | 2.13766e7i | 0.0662395 | + | 0.242582i | ||||
\(446\) | −8.50130e7 | − | 7.65921e7i | −0.958255 | − | 0.863335i | ||||
\(447\) | −8.50859e7 | −0.952654 | ||||||||
\(448\) | 3.63089e7 | + | 1.12432e8i | 0.403812 | + | 1.25042i | ||||
\(449\) | 1.37603e6 | 0.0152016 | 0.00760078 | − | 0.999971i | \(-0.497581\pi\) | ||||
0.00760078 | + | 0.999971i | \(0.497581\pi\) | |||||||
\(450\) | −1.10371e8 | − | 2.23978e7i | −1.21121 | − | 0.245792i | ||||
\(451\) | − | 1.67576e7i | − | 0.182676i | ||||||
\(452\) | −1.01955e7 | + | 1.06543e6i | −0.110406 | + | 0.0115375i | ||||
\(453\) | − | 8.91451e7i | − | 0.958965i | ||||||
\(454\) | −5.22603e6 | − | 4.70837e6i | −0.0558476 | − | 0.0503156i | ||||
\(455\) | −1.75790e8 | + | 4.80014e7i | −1.86621 | + | 0.509588i | ||||
\(456\) | 3.30903e7 | + | 2.40868e7i | 0.348984 | + | 0.254030i | ||||
\(457\) | − | 1.19484e8i | − | 1.25187i | −0.779873 | − | 0.625937i | \(-0.784717\pi\) | ||
0.779873 | − | 0.625937i | \(-0.215283\pi\) | |||||||
\(458\) | −2.16285e6 | − | 1.94861e6i | −0.0225129 | − | 0.0202828i | ||||
\(459\) | 3.42784e7i | 0.354473i | ||||||||
\(460\) | −8.03320e6 | + | 3.12211e6i | −0.0825306 | + | 0.0320756i | ||||
\(461\) | −1.26030e8 | −1.28639 | −0.643194 | − | 0.765703i | \(-0.722391\pi\) | ||||
−0.643194 | + | 0.765703i | \(0.722391\pi\) | |||||||
\(462\) | −3.80872e7 | + | 4.22748e7i | −0.386237 | + | 0.428702i | ||||
\(463\) | 1.01206e8 | 1.01968 | 0.509839 | − | 0.860270i | \(-0.329705\pi\) | ||||
0.509839 | + | 0.860270i | \(0.329705\pi\) | |||||||
\(464\) | 8.47914e7 | − | 1.79172e7i | 0.848785 | − | 0.179356i | ||||
\(465\) | 1.61734e8 | − | 4.41632e7i | 1.60858 | − | 0.439240i | ||||
\(466\) | −1.70833e7 | + | 1.89616e7i | −0.168816 | + | 0.187377i | ||||
\(467\) | 9.72528e7 | 0.954886 | 0.477443 | − | 0.878663i | \(-0.341564\pi\) | ||||
0.477443 | + | 0.878663i | \(0.341564\pi\) | |||||||
\(468\) | −1.85498e8 | + | 1.93847e7i | −1.80968 | + | 0.189113i | ||||
\(469\) | 1.03663e8 | 1.00486 | ||||||||
\(470\) | 6.21691e7 | − | 1.23372e8i | 0.598799 | − | 1.18829i | ||||
\(471\) | − | 3.31517e7i | − | 0.317281i | ||||||
\(472\) | −1.16634e7 | − | 8.48994e6i | −0.110917 | − | 0.0807381i | ||||
\(473\) | − | 2.25838e7i | − | 0.213410i | ||||||
\(474\) | 7.90717e7 | − | 8.77654e7i | 0.742483 | − | 0.824116i | ||||
\(475\) | −1.57233e7 | − | 2.66441e7i | −0.146711 | − | 0.248611i | ||||
\(476\) | −1.41643e8 | + | 1.48018e7i | −1.31333 | + | 0.137244i | ||||
\(477\) | 2.49679e8i | 2.30053i | ||||||||
\(478\) | −9.21513e7 | + | 1.02283e8i | −0.843758 | + | 0.936526i | ||||
\(479\) | 6.06291e7i | 0.551664i | 0.961206 | + | 0.275832i | \(0.0889533\pi\) | ||||
−0.961206 | + | 0.275832i | \(0.911047\pi\) | |||||||
\(480\) | 4.22776e7 | − | 1.59872e8i | 0.382285 | − | 1.44560i | ||||
\(481\) | −4.57990e7 | −0.411548 | ||||||||
\(482\) | −7.52506e7 | − | 6.77967e7i | −0.672000 | − | 0.605435i | ||||
\(483\) | −1.96032e7 | −0.173975 | ||||||||
\(484\) | 1.07677e7 | + | 1.03040e8i | 0.0949705 | + | 0.908803i | ||||
\(485\) | −1.38995e8 | + | 3.79540e7i | −1.21835 | + | 0.332684i | ||||
\(486\) | 1.20427e8 | + | 1.08498e8i | 1.04910 | + | 0.945181i | ||||
\(487\) | −1.20117e8 | −1.03996 | −0.519979 | − | 0.854179i | \(-0.674060\pi\) | ||||
−0.519979 | + | 0.854179i | \(0.674060\pi\) | |||||||
\(488\) | 1.02695e7 | − | 1.41082e7i | 0.0883669 | − | 0.121398i | ||||
\(489\) | −3.11198e8 | −2.66140 | ||||||||
\(490\) | 3.84692e7 | − | 7.63408e7i | 0.326983 | − | 0.648886i | ||||
\(491\) | − | 1.17425e8i | − | 0.992011i | −0.868319 | − | 0.496005i | \(-0.834800\pi\) | ||
0.868319 | − | 0.496005i | \(-0.165200\pi\) | |||||||
\(492\) | 1.15130e7 | + | 1.10171e8i | 0.0966701 | + | 0.925068i | ||||
\(493\) | 1.04462e8i | 0.871802i | ||||||||
\(494\) | −3.80646e7 | − | 3.42941e7i | −0.315748 | − | 0.284471i | ||||
\(495\) | 4.24675e7 | − | 1.15962e7i | 0.350140 | − | 0.0956094i | ||||
\(496\) | 2.81326e7 | + | 1.33135e8i | 0.230550 | + | 1.09106i | ||||
\(497\) | − | 9.67480e7i | − | 0.788085i | ||||||
\(498\) | 1.20534e7 | + | 1.08594e7i | 0.0975935 | + | 0.0879264i | ||||
\(499\) | − | 2.08663e8i | − | 1.67936i | −0.543083 | − | 0.839679i | \(-0.682743\pi\) | ||
0.543083 | − | 0.839679i | \(-0.317257\pi\) | |||||||
\(500\) | −7.73277e7 | + | 9.82112e7i | −0.618621 | + | 0.785689i | ||||
\(501\) | 9.57470e7 | 0.761398 | ||||||||
\(502\) | 1.44072e8 | − | 1.59913e8i | 1.13886 | − | 1.26407i | ||||
\(503\) | 2.10295e8 | 1.65244 | 0.826220 | − | 0.563348i | \(-0.190487\pi\) | ||||
0.826220 | + | 0.563348i | \(0.190487\pi\) | |||||||
\(504\) | 1.22356e8 | − | 1.68092e8i | 0.955727 | − | 1.31297i | ||||
\(505\) | −4.21336e7 | − | 1.54301e8i | −0.327156 | − | 1.19811i | ||||
\(506\) | 2.25498e6 | − | 2.50291e6i | 0.0174057 | − | 0.0193194i | ||||
\(507\) | 2.27511e8 | 1.74573 | ||||||||
\(508\) | 1.26454e7 | + | 1.21008e8i | 0.0964588 | + | 0.923045i | ||||
\(509\) | 1.78286e8 | 1.35196 | 0.675980 | − | 0.736920i | \(-0.263721\pi\) | ||||
0.675980 | + | 0.736920i | \(0.263721\pi\) | |||||||
\(510\) | 1.78006e8 | + | 8.96997e7i | 1.34191 | + | 0.676209i | ||||
\(511\) | − | 9.55206e6i | − | 0.0715871i | ||||||
\(512\) | 1.27537e8 | + | 4.18184e7i | 0.950223 | + | 0.311571i | ||||
\(513\) | − | 1.37469e7i | − | 0.101825i | ||||||
\(514\) | 4.18324e7 | − | 4.64317e7i | 0.308052 | − | 0.341921i | ||||
\(515\) | 6.85761e7 | + | 2.51139e8i | 0.502055 | + | 1.83862i | ||||
\(516\) | 1.55158e7 | + | 1.48476e8i | 0.112934 | + | 1.08070i | ||||
\(517\) | 5.40016e7i | 0.390783i | ||||||||
\(518\) | 3.41731e7 | − | 3.79303e7i | 0.245864 | − | 0.272896i | ||||
\(519\) | − | 2.10984e8i | − | 1.50920i | ||||||
\(520\) | −7.34373e7 | + | 1.93545e8i | −0.522284 | + | 1.37648i | ||||
\(521\) | 2.05210e8 | 1.45106 | 0.725531 | − | 0.688189i | \(-0.241594\pi\) | ||||
0.725531 | + | 0.688189i | \(0.241594\pi\) | |||||||
\(522\) | −1.13301e8 | − | 1.02078e8i | −0.796567 | − | 0.717663i | ||||
\(523\) | −7.21180e7 | −0.504125 | −0.252063 | − | 0.967711i | \(-0.581109\pi\) | ||||
−0.252063 | + | 0.967711i | \(0.581109\pi\) | |||||||
\(524\) | −1.75841e8 | + | 1.83755e7i | −1.22216 | + | 0.127716i | ||||
\(525\) | −2.44860e8 | + | 1.44497e8i | −1.69215 | + | 0.998576i | ||||
\(526\) | −7.91320e7 | − | 7.12935e7i | −0.543744 | − | 0.489884i | ||||
\(527\) | −1.64021e8 | −1.12064 | ||||||||
\(528\) | 1.33639e7 | + | 6.32436e7i | 0.0907889 | + | 0.429650i | ||||
\(529\) | −1.46875e8 | −0.992160 | ||||||||
\(530\) | 2.47477e8 | + | 1.24708e8i | 1.66229 | + | 0.837655i | ||||
\(531\) | 2.53858e7i | 0.169554i | ||||||||
\(532\) | 5.68040e7 | − | 5.93606e6i | 0.377263 | − | 0.0394242i | ||||
\(533\) | − | 1.38665e8i | − | 0.915766i | ||||||
\(534\) | 4.25383e7 | + | 3.83247e7i | 0.279355 | + | 0.251683i | ||||
\(535\) | 1.68627e7 | + | 6.17544e7i | 0.110120 | + | 0.403280i | ||||
\(536\) | 6.93036e7 | − | 9.52088e7i | 0.450051 | − | 0.618277i | ||||
\(537\) | − | 2.59071e8i | − | 1.67300i | ||||||
\(538\) | −1.03344e8 | − | 9.31075e7i | −0.663651 | − | 0.597913i | ||||
\(539\) | 3.34153e7i | 0.213393i | ||||||||
\(540\) | −5.17705e7 | + | 2.01207e7i | −0.328777 | + | 0.127780i | ||||
\(541\) | −1.48242e7 | −0.0936225 | −0.0468112 | − | 0.998904i | \(-0.514906\pi\) | ||||
−0.0468112 | + | 0.998904i | \(0.514906\pi\) | |||||||
\(542\) | −1.14249e8 | + | 1.26810e8i | −0.717552 | + | 0.796444i | ||||
\(543\) | 1.11009e8 | 0.693358 | ||||||||
\(544\) | −8.11002e7 | + | 1.39987e8i | −0.503762 | + | 0.869541i | ||||
\(545\) | 4.37622e7 | + | 1.60266e8i | 0.270340 | + | 0.990035i | ||||
\(546\) | −3.15163e8 | + | 3.49814e8i | −1.93623 | + | 2.14911i | ||||
\(547\) | −2.59533e8 | −1.58574 | −0.792869 | − | 0.609392i | \(-0.791413\pi\) | ||||
−0.792869 | + | 0.609392i | \(0.791413\pi\) | |||||||
\(548\) | 1.65548e8 | − | 1.72999e7i | 1.00597 | − | 0.105124i | ||||
\(549\) | −3.07069e7 | −0.185575 | ||||||||
\(550\) | 9.71736e6 | − | 4.78850e7i | 0.0584064 | − | 0.287814i | ||||
\(551\) | − | 4.18932e7i | − | 0.250431i | ||||||
\(552\) | −1.31057e7 | + | 1.80045e7i | −0.0779187 | + | 0.107044i | ||||
\(553\) | − | 1.64846e8i | − | 0.974773i | ||||||
\(554\) | 9.21221e7 | − | 1.02251e8i | 0.541795 | − | 0.601363i | ||||
\(555\) | −6.89337e7 | + | 1.88231e7i | −0.403230 | + | 0.110106i | ||||
\(556\) | 1.95638e8 | − | 2.04443e7i | 1.13823 | − | 0.118946i | ||||
\(557\) | 3.21717e7i | 0.186169i | 0.995658 | + | 0.0930847i | \(0.0296727\pi\) | ||||
−0.995658 | + | 0.0930847i | \(0.970327\pi\) | |||||||
\(558\) | 1.60277e8 | − | 1.77899e8i | 0.922507 | − | 1.02393i | ||||
\(559\) | − | 1.86876e8i | − | 1.06984i | ||||||
\(560\) | −1.05496e8 | − | 2.05234e8i | −0.600721 | − | 1.16865i | ||||
\(561\) | −7.79155e7 | −0.441301 | ||||||||
\(562\) | −1.52681e8 | − | 1.37558e8i | −0.860156 | − | 0.774953i | ||||
\(563\) | −2.80885e8 | −1.57400 | −0.786999 | − | 0.616955i | \(-0.788366\pi\) | ||||
−0.786999 | + | 0.616955i | \(0.788366\pi\) | |||||||
\(564\) | −3.71009e7 | − | 3.55030e8i | −0.206798 | − | 1.97892i | ||||
\(565\) | 1.93143e7 | − | 5.27398e6i | 0.107086 | − | 0.0292411i | ||||
\(566\) | −8.28394e7 | − | 7.46337e7i | −0.456865 | − | 0.411610i | ||||
\(567\) | 1.69691e8 | 0.930916 | ||||||||
\(568\) | −8.88576e7 | − | 6.46805e7i | −0.484897 | − | 0.352962i | ||||
\(569\) | 3.50834e8 | 1.90443 | 0.952216 | − | 0.305426i | \(-0.0987987\pi\) | ||||
0.952216 | + | 0.305426i | \(0.0987987\pi\) | |||||||
\(570\) | −7.13869e7 | − | 3.59729e7i | −0.385473 | − | 0.194246i | ||||
\(571\) | 1.49375e8i | 0.802360i | 0.915999 | + | 0.401180i | \(0.131400\pi\) | ||||
−0.915999 | + | 0.401180i | \(0.868600\pi\) | |||||||
\(572\) | −8.41011e6 | − | 8.04790e7i | −0.0449380 | − | 0.430026i | ||||
\(573\) | 3.21972e8i | 1.71141i | ||||||||
\(574\) | 1.14841e8 | + | 1.03465e8i | 0.607240 | + | 0.547090i | ||||
\(575\) | 1.44971e7 | − | 8.55506e6i | 0.0762567 | − | 0.0450008i | ||||
\(576\) | −7.25823e7 | − | 2.24754e8i | −0.379807 | − | 1.17609i | ||||
\(577\) | 3.18308e8i | 1.65699i | 0.559996 | + | 0.828496i | \(0.310803\pi\) | ||||
−0.559996 | + | 0.828496i | \(0.689197\pi\) | |||||||
\(578\) | −1.41705e6 | − | 1.27668e6i | −0.00733839 | − | 0.00661148i | ||||
\(579\) | 4.91984e8i | 2.53463i | ||||||||
\(580\) | −1.57768e8 | + | 6.13169e7i | −0.808605 | + | 0.314265i | ||||
\(581\) | 2.26394e7 | 0.115435 | ||||||||
\(582\) | −2.49195e8 | + | 2.76592e8i | −1.26407 | + | 1.40304i | ||||
\(583\) | −1.08324e8 | −0.546663 | ||||||||
\(584\) | −8.77304e6 | − | 6.38600e6i | −0.0440465 | − | 0.0320620i | ||||
\(585\) | 3.51409e8 | − | 9.59559e7i | 1.75527 | − | 0.479296i | ||||
\(586\) | 1.75814e8 | − | 1.95144e8i | 0.873697 | − | 0.969757i | ||||
\(587\) | 3.05295e8 | 1.50940 | 0.754702 | − | 0.656068i | \(-0.227782\pi\) | ||||
0.754702 | + | 0.656068i | \(0.227782\pi\) | |||||||
\(588\) | −2.29574e7 | − | 2.19687e8i | −0.112925 | − | 1.08062i | ||||
\(589\) | 6.57784e7 | 0.321912 | ||||||||
\(590\) | 2.51619e7 | + | 1.26795e7i | 0.122515 | + | 0.0617370i | ||||
\(591\) | − | 2.12842e8i | − | 1.03109i | ||||||
\(592\) | −1.19906e7 | − | 5.67442e7i | −0.0577929 | − | 0.273500i | ||||
\(593\) | 3.16115e8i | 1.51594i | 0.652292 | + | 0.757968i | \(0.273808\pi\) | ||||
−0.652292 | + | 0.757968i | \(0.726192\pi\) | |||||||
\(594\) | 1.45324e7 | − | 1.61302e7i | 0.0693391 | − | 0.0769626i | ||||
\(595\) | 2.68329e8 | − | 7.32700e7i | 1.27384 | − | 0.347837i | ||||
\(596\) | 1.40187e7 | + | 1.34150e8i | 0.0662170 | + | 0.633652i | ||||
\(597\) | − | 4.62005e8i | − | 2.17132i | ||||||
\(598\) | 1.86595e7 | − | 2.07110e7i | 0.0872560 | − | 0.0968495i | ||||
\(599\) | 1.45523e8i | 0.677097i | 0.940949 | + | 0.338549i | \(0.109936\pi\) | ||||
−0.940949 | + | 0.338549i | \(0.890064\pi\) | |||||||
\(600\) | −3.09876e7 | + | 3.21493e8i | −0.143461 | + | 1.48839i | ||||
\(601\) | −1.38073e8 | −0.636040 | −0.318020 | − | 0.948084i | \(-0.603018\pi\) | ||||
−0.318020 | + | 0.948084i | \(0.603018\pi\) | |||||||
\(602\) | 1.54769e8 | + | 1.39438e8i | 0.709404 | + | 0.639134i | ||||
\(603\) | −2.07225e8 | −0.945128 | ||||||||
\(604\) | −1.40550e8 | + | 1.46875e7i | −0.637850 | + | 0.0666557i | ||||
\(605\) | −5.33013e7 | − | 1.95199e8i | −0.240697 | − | 0.881480i | ||||
\(606\) | −3.07052e8 | − | 2.76637e8i | −1.37973 | − | 1.24306i | ||||
\(607\) | −2.20855e8 | −0.987510 | −0.493755 | − | 0.869601i | \(-0.664376\pi\) | ||||
−0.493755 | + | 0.869601i | \(0.664376\pi\) | |||||||
\(608\) | 3.25242e7 | − | 5.61399e7i | 0.144709 | − | 0.249782i | ||||
\(609\) | −3.84998e8 | −1.70454 | ||||||||
\(610\) | −1.53372e7 | + | 3.04361e7i | −0.0675704 | + | 0.134091i | ||||
\(611\) | 4.46851e8i | 1.95902i | ||||||||
\(612\) | 2.83147e8 | − | 2.95891e7i | 1.23526 | − | 0.129085i | ||||
\(613\) | − | 6.60483e7i | − | 0.286735i | −0.989670 | − | 0.143367i | \(-0.954207\pi\) | ||
0.989670 | − | 0.143367i | \(-0.0457931\pi\) | |||||||
\(614\) | −1.90669e8 | − | 1.71782e8i | −0.823712 | − | 0.742119i | ||||
\(615\) | −5.69903e7 | − | 2.08709e8i | −0.245005 | − | 0.897256i | ||||
\(616\) | 7.29272e7 | + | 5.30846e7i | 0.311995 | + | 0.227105i | ||||
\(617\) | 9.38189e6i | 0.0399425i | 0.999801 | + | 0.0199712i | \(0.00635746\pi\) | ||||
−0.999801 | + | 0.0199712i | \(0.993643\pi\) | |||||||
\(618\) | 4.99754e8 | + | 4.50250e8i | 2.11734 | + | 1.90761i | ||||
\(619\) | − | 3.27827e8i | − | 1.38221i | −0.722756 | − | 0.691103i | \(-0.757125\pi\) | ||
0.722756 | − | 0.691103i | \(-0.242875\pi\) | |||||||
\(620\) | −9.62766e7 | − | 2.47720e8i | −0.403967 | − | 1.03941i | ||||
\(621\) | 7.47972e6 | 0.0312328 | ||||||||
\(622\) | 1.72401e8 | − | 1.91356e8i | 0.716421 | − | 0.795188i | ||||
\(623\) | 7.98980e7 | 0.330424 | ||||||||
\(624\) | 1.10583e8 | + | 5.23326e8i | 0.455131 | + | 2.15387i | ||||
\(625\) | 1.18020e8 | − | 2.13719e8i | 0.483411 | − | 0.875393i | ||||
\(626\) | −1.94216e7 | + | 2.15569e7i | −0.0791702 | + | 0.0878747i | ||||
\(627\) | 3.12470e7 | 0.126767 | ||||||||
\(628\) | −5.22683e7 | + | 5.46207e6i | −0.211037 | + | 0.0220535i | ||||
\(629\) | 6.99083e7 | 0.280916 | ||||||||
\(630\) | −1.82735e8 | + | 3.62631e8i | −0.730803 | + | 1.45025i | ||||
\(631\) | 2.66189e8i | 1.05950i | 0.848153 | + | 0.529751i | \(0.177715\pi\) | ||||
−0.848153 | + | 0.529751i | \(0.822285\pi\) | |||||||
\(632\) | −1.51402e8 | − | 1.10207e8i | −0.599764 | − | 0.436575i | ||||
\(633\) | 1.33369e8i | 0.525827i | ||||||||
\(634\) | −1.44949e8 | + | 1.60886e8i | −0.568785 | + | 0.631320i | ||||
\(635\) | −6.25959e7 | − | 2.29238e8i | −0.244470 | − | 0.895294i | ||||
\(636\) | 7.12170e8 | − | 7.44222e7i | 2.76829 | − | 0.289288i | ||||
\(637\) | 2.76504e8i | 1.06975i | ||||||||
\(638\) | 4.42869e7 | − | 4.91560e7i | 0.170535 | − | 0.189284i | ||||
\(639\) | 1.93401e8i | 0.741237i | ||||||||
\(640\) | −2.59025e8 | − | 4.03161e7i | −0.988103 | − | 0.153794i | ||||
\(641\) | 4.00719e7 | 0.152148 | 0.0760739 | − | 0.997102i | \(-0.475762\pi\) | ||||
0.0760739 | + | 0.997102i | \(0.475762\pi\) | |||||||
\(642\) | 1.22888e8 | + | 1.10715e8i | 0.464413 | + | 0.418411i | ||||
\(643\) | 7.15926e7 | 0.269299 | 0.134650 | − | 0.990893i | \(-0.457009\pi\) | ||||
0.134650 | + | 0.990893i | \(0.457009\pi\) | |||||||
\(644\) | 3.22982e6 | + | 3.09072e7i | 0.0120926 | + | 0.115718i | ||||
\(645\) | −7.68047e7 | − | 2.81273e8i | −0.286226 | − | 1.04821i | ||||
\(646\) | 5.81023e7 | + | 5.23470e7i | 0.215524 | + | 0.194175i | ||||
\(647\) | 4.24659e8 | 1.56793 | 0.783966 | − | 0.620803i | \(-0.213193\pi\) | ||||
0.783966 | + | 0.620803i | \(0.213193\pi\) | |||||||
\(648\) | 1.13447e8 | − | 1.55852e8i | 0.416933 | − | 0.572779i | ||||
\(649\) | −1.10137e7 | −0.0402902 | ||||||||
\(650\) | 8.04088e7 | − | 3.96237e8i | 0.292795 | − | 1.44283i | ||||
\(651\) | − | 6.04504e8i | − | 2.19107i | ||||||
\(652\) | 5.12728e7 | + | 4.90646e8i | 0.184988 | + | 1.77021i | ||||
\(653\) | 3.37874e8i | 1.21343i | 0.794918 | + | 0.606716i | \(0.207514\pi\) | ||||
−0.794918 | + | 0.606716i | \(0.792486\pi\) | |||||||
\(654\) | 3.18920e8 | + | 2.87330e8i | 1.14012 | + | 1.02718i | ||||
\(655\) | 3.33115e8 | − | 9.09606e7i | 1.18541 | − | 0.323690i | ||||
\(656\) | 1.71803e8 | − | 3.63036e7i | 0.608584 | − | 0.128599i | ||||
\(657\) | 1.90948e7i | 0.0673316i | ||||||||
\(658\) | −3.70077e8 | − | 3.33419e8i | −1.29902 | − | 1.17034i | ||||
\(659\) | − | 2.03482e8i | − | 0.711001i | −0.934676 | − | 0.355501i | \(-0.884310\pi\) | ||
0.934676 | − | 0.355501i | \(-0.115690\pi\) | |||||||
\(660\) | −4.57347e7 | − | 1.17675e8i | −0.159079 | − | 0.409311i | ||||
\(661\) | −5.04157e8 | −1.74567 | −0.872833 | − | 0.488019i | \(-0.837720\pi\) | ||||
−0.872833 | + | 0.488019i | \(0.837720\pi\) | |||||||
\(662\) | −1.79621e8 | + | 1.99370e8i | −0.619132 | + | 0.687203i | ||||
\(663\) | −6.44732e8 | −2.21227 | ||||||||
\(664\) | 1.51355e7 | − | 2.07930e7i | 0.0517002 | − | 0.0710253i | ||||
\(665\) | −1.07610e8 | + | 2.93840e7i | −0.365921 | + | 0.0999186i | ||||
\(666\) | −6.83128e7 | + | 7.58235e7i | −0.231249 | + | 0.256674i | ||||
\(667\) | 2.27941e7 | 0.0768149 | ||||||||
\(668\) | −1.57752e7 | − | 1.50958e8i | −0.0529232 | − | 0.506439i | ||||
\(669\) | 5.77469e8 | 1.92864 | ||||||||
\(670\) | −1.03503e8 | + | 2.05398e8i | −0.344135 | + | 0.682923i | ||||
\(671\) | − | 1.33223e7i | − | 0.0440972i | ||||||
\(672\) | −5.15926e8 | − | 2.98898e8i | −1.70012 | − | 0.984951i | ||||
\(673\) | − | 2.63250e8i | − | 0.863621i | −0.901964 | − | 0.431810i | \(-0.857875\pi\) | ||
0.901964 | − | 0.431810i | \(-0.142125\pi\) | |||||||
\(674\) | −2.83749e8 | + | 3.14946e8i | −0.926732 | + | 1.02862i | ||||
\(675\) | 9.34276e7 | − | 5.51337e7i | 0.303783 | − | 0.179269i | ||||
\(676\) | −3.74846e7 | − | 3.58702e8i | −0.121342 | − | 1.16116i | ||||
\(677\) | − | 2.04498e8i | − | 0.659056i | −0.944146 | − | 0.329528i | \(-0.893110\pi\) | ||
0.944146 | − | 0.329528i | \(-0.106890\pi\) | |||||||
\(678\) | 3.46274e7 | − | 3.84346e7i | 0.111104 | − | 0.123320i | ||||
\(679\) | 5.19513e8i | 1.65954i | ||||||||
\(680\) | 1.12096e8 | − | 2.95429e8i | 0.356503 | − | 0.939566i | ||||
\(681\) | 3.54989e7 | 0.112402 | ||||||||
\(682\) | 7.71822e7 | + | 6.95369e7i | 0.243312 | + | 0.219211i | ||||
\(683\) | 9.73212e7 | 0.305454 | 0.152727 | − | 0.988268i | \(-0.451195\pi\) | ||||
0.152727 | + | 0.988268i | \(0.451195\pi\) | |||||||
\(684\) | −1.13553e8 | + | 1.18663e7i | −0.354837 | + | 0.0370807i | ||||
\(685\) | −3.13616e8 | + | 8.56361e7i | −0.975722 | + | 0.266431i | ||||
\(686\) | 8.61589e7 | + | 7.76244e7i | 0.266887 | + | 0.240451i | ||||
\(687\) | 1.46916e7 | 0.0453106 | ||||||||
\(688\) | 2.31536e8 | − | 4.89256e7i | 0.710974 | − | 0.150235i | ||||
\(689\) | −8.96356e8 | −2.74046 | ||||||||
\(690\) | 1.95729e7 | − | 3.88417e7i | 0.0595811 | − | 0.118236i | ||||
\(691\) | − | 4.93368e8i | − | 1.49533i | −0.664076 | − | 0.747665i | \(-0.731175\pi\) | ||
0.664076 | − | 0.747665i | \(-0.268825\pi\) | |||||||
\(692\) | −3.32646e8 | + | 3.47617e7i | −1.00384 | + | 0.104902i | ||||
\(693\) | − | 1.58728e8i | − | 0.476930i | ||||||
\(694\) | 7.73833e7 | + | 6.97181e7i | 0.231510 | + | 0.208577i | ||||
\(695\) | −3.70618e8 | + | 1.01201e8i | −1.10401 | + | 0.301461i | ||||
\(696\) | −2.57389e8 | + | 3.53600e8i | −0.763419 | + | 1.04878i | ||||
\(697\) | 2.11660e8i | 0.625087i | ||||||||
\(698\) | −1.16149e8 | − | 1.04644e8i | −0.341547 | − | 0.307715i | ||||
\(699\) | − | 1.28800e8i | − | 0.377125i | ||||||
\(700\) | 2.68163e8 | + | 3.62248e8i | 0.781815 | + | 1.05612i | ||||
\(701\) | −1.60818e6 | −0.00466855 | −0.00233427 | − | 0.999997i | \(-0.500743\pi\) | ||||
−0.00233427 | + | 0.999997i | \(0.500743\pi\) | |||||||
\(702\) | 1.20252e8 | − | 1.33473e8i | 0.347601 | − | 0.385819i | ||||
\(703\) | −2.80358e7 | −0.0806951 | ||||||||
\(704\) | 9.75104e7 | − | 3.14901e7i | 0.279469 | − | 0.0902518i | ||||
\(705\) | 1.83653e8 | + | 6.72571e8i | 0.524119 | + | 1.91942i | ||||
\(706\) | −2.25410e8 | + | 2.50193e8i | −0.640559 | + | 0.710986i | ||||
\(707\) | −5.76723e8 | −1.63196 | ||||||||
\(708\) | 7.24089e7 | − | 7.56678e6i | 0.204029 | − | 0.0213212i | ||||
\(709\) | 5.27495e8 | 1.48006 | 0.740031 | − | 0.672573i | \(-0.234811\pi\) | ||||
0.740031 | + | 0.672573i | \(0.234811\pi\) | |||||||
\(710\) | 1.91696e8 | + | 9.65985e7i | 0.535597 | + | 0.269895i | ||||
\(711\) | 3.29531e8i | 0.916828i | ||||||||
\(712\) | 5.34155e7 | − | 7.33819e7i | 0.147988 | − | 0.203305i | ||||
\(713\) | 3.57901e7i | 0.0987404i | ||||||||
\(714\) | 4.81069e8 | − | 5.33961e8i | 1.32164 | − | 1.46695i | ||||
\(715\) | 4.16308e7 | + | 1.52460e8i | 0.113893 | + | 0.417097i | ||||
\(716\) | −4.08461e8 | + | 4.26845e7i | −1.11279 | + | 0.116287i | ||||
\(717\) | − | 6.94779e8i | − | 1.88490i | ||||||
\(718\) | 3.68673e7 | − | 4.09207e7i | 0.0996020 | − | 0.110553i | ||||
\(719\) | − | 3.85369e8i | − | 1.03679i | −0.855142 | − | 0.518394i | \(-0.826530\pi\) | ||
0.855142 | − | 0.518394i | \(-0.173470\pi\) | |||||||
\(720\) | 2.10890e8 | + | 4.10268e8i | 0.565012 | + | 1.09918i | ||||
\(721\) | 9.38667e8 | 2.50441 | ||||||||
\(722\) | 2.56319e8 | + | 2.30929e8i | 0.681034 | + | 0.613574i | ||||
\(723\) | 5.11156e8 | 1.35250 | ||||||||
\(724\) | −1.82898e7 | − | 1.75021e8i | −0.0481939 | − | 0.461183i | ||||
\(725\) | 2.84717e8 | − | 1.68018e8i | 0.747135 | − | 0.440901i | ||||
\(726\) | −3.88437e8 | − | 3.49960e8i | −1.01510 | − | 0.914553i | ||||
\(727\) | 2.91515e8 | 0.758679 | 0.379339 | − | 0.925258i | \(-0.376151\pi\) | ||||
0.379339 | + | 0.925258i | \(0.376151\pi\) | |||||||
\(728\) | 6.03455e8 | + | 4.39262e8i | 1.56405 | + | 1.13849i | ||||
\(729\) | −5.43559e8 | −1.40302 | ||||||||
\(730\) | 1.89264e7 | + | 9.53731e6i | 0.0486519 | + | 0.0245164i | ||||
\(731\) | 2.85250e8i | 0.730254i | ||||||||
\(732\) | 9.15283e6 | + | 8.75864e7i | 0.0233358 | + | 0.223308i | ||||
\(733\) | − | 4.31296e8i | − | 1.09512i | −0.836765 | − | 0.547562i | \(-0.815556\pi\) | ||
0.836765 | − | 0.547562i | \(-0.184444\pi\) | |||||||
\(734\) | −7.47649e7 | − | 6.73591e7i | −0.189064 | − | 0.170337i | ||||
\(735\) | 1.13641e8 | + | 4.16176e8i | 0.286203 | + | 1.04813i | ||||
\(736\) | 3.05458e7 | + | 1.76965e7i | 0.0766157 | + | 0.0443867i | ||||
\(737\) | − | 8.99053e7i | − | 0.224586i | ||||||
\(738\) | −2.29569e8 | − | 2.06829e8i | −0.571143 | − | 0.514569i | ||||
\(739\) | 6.53807e8i | 1.62000i | 0.586427 | + | 0.810002i | \(0.300534\pi\) | ||||
−0.586427 | + | 0.810002i | \(0.699466\pi\) | |||||||
\(740\) | 4.10346e7 | + | 1.05582e8i | 0.101264 | + | 0.260553i | ||||
\(741\) | 2.58561e8 | 0.635491 | ||||||||
\(742\) | 6.68820e8 | − | 7.42354e8i | 1.63718 | − | 1.81719i | ||||
\(743\) | −3.07461e8 | −0.749589 | −0.374794 | − | 0.927108i | \(-0.622287\pi\) | ||||
−0.374794 | + | 0.927108i | \(0.622287\pi\) | |||||||
\(744\) | −5.55203e8 | − | 4.04139e8i | −1.34813 | − | 0.981323i | ||||
\(745\) | −6.93939e7 | − | 2.54134e8i | −0.167823 | − | 0.614601i | ||||
\(746\) | −3.10831e8 | + | 3.45005e8i | −0.748700 | + | 0.831016i | ||||
\(747\) | −4.52567e7 | −0.108573 | ||||||||
\(748\) | 1.28373e7 | + | 1.22844e8i | 0.0306739 | + | 0.293529i | ||||
\(749\) | 2.30816e8 | 0.549313 | ||||||||
\(750\) | −4.18246e7 | − | 6.29438e8i | −0.0991399 | − | 1.49200i | ||||
\(751\) | − | 4.94845e8i | − | 1.16829i | −0.811650 | − | 0.584143i | \(-0.801431\pi\) | ||
0.811650 | − | 0.584143i | \(-0.198569\pi\) | |||||||
\(752\) | −5.53641e8 | + | 1.16989e8i | −1.30189 | + | 0.275101i | ||||
\(753\) | 1.08624e9i | 2.54414i | ||||||||
\(754\) | 3.66463e8 | − | 4.06755e8i | 0.854902 | − | 0.948895i | ||||
\(755\) | 2.66258e8 | − | 7.27045e7i | 0.618673 | − | 0.168935i | ||||
\(756\) | 2.08148e7 | + | 1.99183e8i | 0.0481733 | + | 0.460986i | ||||
\(757\) | 8.18948e8i | 1.88786i | 0.330152 | + | 0.943928i | \(0.392900\pi\) | ||||
−0.330152 | + | 0.943928i | \(0.607100\pi\) | |||||||
\(758\) | −2.33169e8 | + | 2.58805e8i | −0.535382 | + | 0.594245i | ||||
\(759\) | 1.70015e7i | 0.0388833i | ||||||||
\(760\) | −4.49546e7 | + | 1.18478e8i | −0.102408 | + | 0.269897i | ||||
\(761\) | −4.68400e7 | −0.106283 | −0.0531414 | − | 0.998587i | \(-0.516923\pi\) | ||||
−0.0531414 | + | 0.998587i | \(0.516923\pi\) | |||||||
\(762\) | −4.56172e8 | − | 4.10986e8i | −1.03101 | − | 0.928885i | ||||
\(763\) | 5.99015e8 | 1.34854 | ||||||||
\(764\) | 5.07633e8 | − | 5.30480e7i | 1.13833 | − | 0.118957i | ||||
\(765\) | −5.36396e8 | + | 1.46468e8i | −1.19812 | + | 0.327160i | ||||
\(766\) | 1.75172e7 | + | 1.57820e7i | 0.0389742 | + | 0.0351136i | ||||
\(767\) | −9.11359e7 | −0.201978 | ||||||||
\(768\) | −6.19441e8 | + | 2.74022e8i | −1.36747 | + | 0.604926i | ||||
\(769\) | −5.79761e6 | −0.0127488 | −0.00637441 | − | 0.999980i | \(-0.502029\pi\) | ||||
−0.00637441 | + | 0.999980i | \(0.502029\pi\) | |||||||
\(770\) | −1.57329e8 | − | 7.92803e7i | −0.344616 | − | 0.173657i | ||||
\(771\) | 3.15397e8i | 0.688168i | ||||||||
\(772\) | 7.75681e8 | − | 8.10591e7i | 1.68590 | − | 0.176177i | ||||
\(773\) | − | 4.58350e8i | − | 0.992335i | −0.868227 | − | 0.496168i | \(-0.834740\pi\) | ||
0.868227 | − | 0.496168i | \(-0.165260\pi\) | |||||||
\(774\) | −3.09386e8 | − | 2.78740e8i | −0.667234 | − | 0.601141i | ||||
\(775\) | 2.63812e8 | + | 4.47047e8i | 0.566748 | + | 0.960391i | ||||
\(776\) | 4.77143e8 | + | 3.47318e8i | 1.02109 | + | 0.743263i | ||||
\(777\) | 2.57649e8i | 0.549245i | ||||||||
\(778\) | 1.11561e8 | + | 1.00510e8i | 0.236904 | + | 0.213437i | ||||
\(779\) | − | 8.48835e7i | − | 0.179561i | ||||||
\(780\) | −3.78444e8 | − | 9.73735e8i | −0.797476 | − | 2.05190i | ||||
\(781\) | −8.39079e7 | −0.176137 | ||||||||
\(782\) | −2.84821e7 | + | 3.16136e7i | −0.0595595 | + | 0.0661079i | ||||
\(783\) | 1.46898e8 | 0.306007 | ||||||||
\(784\) | −3.42584e8 | + | 7.23911e7i | −0.710917 | + | 0.150223i | ||||
\(785\) | 9.90173e7 | − | 2.70377e7i | 0.204693 | − | 0.0558935i | ||||
\(786\) | 5.97220e8 | − | 6.62882e8i | 1.22989 | − | 1.36511i | ||||
\(787\) | −8.86461e8 | −1.81859 | −0.909297 | − | 0.416149i | \(-0.863380\pi\) | ||||
−0.909297 | + | 0.416149i | \(0.863380\pi\) | |||||||
\(788\) | −3.35575e8 | + | 3.50678e7i | −0.685822 | + | 0.0716688i | ||||
\(789\) | 5.37520e8 | 1.09437 | ||||||||
\(790\) | 3.26626e8 | + | 1.64591e8i | 0.662474 | + | 0.333830i | ||||
\(791\) | − | 7.21901e7i | − | 0.145864i | ||||||
\(792\) | −1.45783e8 | − | 1.06117e8i | −0.293448 | − | 0.213605i | ||||
\(793\) | − | 1.10239e8i | − | 0.221062i | ||||||
\(794\) | −2.14111e8 | + | 2.37652e8i | −0.427739 | + | 0.474767i | ||||
\(795\) | −1.34914e9 | + | 3.68396e8i | −2.68507 | + | 0.733186i | ||||
\(796\) | −7.28415e8 | + | 7.61198e7i | −1.44424 | + | 0.150924i | ||||
\(797\) | − | 5.08284e8i | − | 1.00400i | −0.864869 | − | 0.501998i | \(-0.832599\pi\) | ||
0.864869 | − | 0.501998i | \(-0.167401\pi\) | |||||||
\(798\) | −1.92927e8 | + | 2.14138e8i | −0.379650 | + | 0.421391i | ||||
\(799\) | − | 6.82080e8i | − | 1.33720i | ||||||
\(800\) | 5.11983e8 | − | 4.11292e6i | 0.999968 | − | 0.00803304i | ||||
\(801\) | −1.59718e8 | −0.310782 | ||||||||
\(802\) | 3.85954e7 | + | 3.47723e7i | 0.0748190 | + | 0.0674078i | ||||
\(803\) | −8.28434e6 | −0.0159997 | ||||||||
\(804\) | 6.17679e7 | + | 5.91077e8i | 0.118849 | + | 1.13730i | ||||
\(805\) | −1.59879e7 | − | 5.85507e7i | −0.0306481 | − | 0.112239i | ||||
\(806\) | 6.38664e8 | + | 5.75401e8i | 1.21974 | + | 1.09892i | ||||
\(807\) | 7.01988e8 | 1.33570 | ||||||||
\(808\) | −3.85566e8 | + | 5.29688e8i | −0.730912 | + | 1.00412i | ||||
\(809\) | −3.14322e6 | −0.00593648 | −0.00296824 | − | 0.999996i | \(-0.500945\pi\) | ||||
−0.00296824 | + | 0.999996i | \(0.500945\pi\) | |||||||
\(810\) | −1.69429e8 | + | 3.36226e8i | −0.318811 | + | 0.632668i | ||||
\(811\) | 3.62482e8i | 0.679553i | 0.940506 | + | 0.339777i | \(0.110352\pi\) | ||||
−0.940506 | + | 0.339777i | \(0.889648\pi\) | |||||||
\(812\) | 6.34322e7 | + | 6.07003e8i | 0.118479 | + | 1.13376i | ||||
\(813\) | − | 8.61382e8i | − | 1.60297i | ||||||
\(814\) | −3.28963e7 | − | 2.96378e7i | −0.0609921 | − | 0.0549506i | ||||
\(815\) | −2.53805e8 | − | 9.29483e8i | −0.468843 | − | 1.71699i | ||||
\(816\) | −1.68796e8 | − | 7.98813e8i | −0.310665 | − | 1.47019i | ||||
\(817\) | − | 1.14396e8i | − | 0.209770i | ||||||
\(818\) | 1.64079e8 | + | 1.47826e8i | 0.299774 | + | 0.270080i | ||||
\(819\) | − | 1.31344e9i | − | 2.39088i | ||||||
\(820\) | −3.19669e8 | + | 1.24240e8i | −0.579774 | + | 0.225330i | ||||
\(821\) | −7.24735e8 | −1.30963 | −0.654816 | − | 0.755788i | \(-0.727254\pi\) | ||||
−0.654816 | + | 0.755788i | \(0.727254\pi\) | |||||||
\(822\) | −5.62261e8 | + | 6.24080e8i | −1.01233 | + | 1.12363i | ||||
\(823\) | −5.63218e8 | −1.01036 | −0.505181 | − | 0.863013i | \(-0.668574\pi\) | ||||
−0.505181 | + | 0.863013i | \(0.668574\pi\) | |||||||
\(824\) | 6.27542e8 | − | 8.62113e8i | 1.12166 | − | 1.54093i | ||||
\(825\) | 1.25320e8 | + | 2.12363e8i | 0.223182 | + | 0.378196i | ||||
\(826\) | 6.80014e7 | − | 7.54779e7i | 0.120664 | − | 0.133930i | ||||
\(827\) | 6.66821e8 | 1.17894 | 0.589471 | − | 0.807789i | \(-0.299336\pi\) | ||||
0.589471 | + | 0.807789i | \(0.299336\pi\) | |||||||
\(828\) | −6.45648e6 | − | 6.17841e7i | −0.0113738 | − | 0.108839i | ||||
\(829\) | −5.69391e8 | −0.999418 | −0.499709 | − | 0.866193i | \(-0.666560\pi\) | ||||
−0.499709 | + | 0.866193i | \(0.666560\pi\) | |||||||
\(830\) | −2.26044e7 | + | 4.48576e7i | −0.0395329 | + | 0.0784516i | ||||
\(831\) | 6.94558e8i | 1.21034i | ||||||||
\(832\) | 8.06876e8 | − | 2.60573e8i | 1.40100 | − | 0.452438i | ||||
\(833\) | − | 4.22060e8i | − | 0.730196i | ||||||
\(834\) | −6.64458e8 | + | 7.37512e8i | −1.14543 | + | 1.27137i | ||||
\(835\) | 7.80888e7 | + | 2.85976e8i | 0.134131 | + | 0.491213i | ||||
\(836\) | −5.14824e6 | − | 4.92652e7i | −0.00881130 | − | 0.0843182i | ||||
\(837\) | 2.30652e8i | 0.393351i | ||||||||
\(838\) | 7.92488e7 | − | 8.79619e7i | 0.134667 | − | 0.149473i | ||||
\(839\) | − | 9.23641e8i | − | 1.56393i | −0.623322 | − | 0.781965i | \(-0.714217\pi\) | ||
0.623322 | − | 0.781965i | \(-0.285783\pi\) | |||||||
\(840\) | 1.08882e9 | + | 4.13133e8i | 1.83703 | + | 0.697031i | ||||
\(841\) | −1.47157e8 | −0.247396 | ||||||||
\(842\) | −1.95691e8 | − | 1.76306e8i | −0.327819 | − | 0.295346i | ||||
\(843\) | 1.03712e9 | 1.73120 | ||||||||
\(844\) | 2.10274e8 | − | 2.19738e7i | 0.349751 | − | 0.0365492i | ||||
\(845\) | 1.85552e8 | + | 6.79527e8i | 0.307536 | + | 1.12625i | ||||
\(846\) | 7.39793e8 | + | 6.66513e8i | 1.22180 | + | 1.10077i | ||||
\(847\) | −7.29586e8 | −1.20068 | ||||||||
\(848\) | −2.34674e8 | − | 1.11057e9i | −0.384837 | − | 1.82121i | ||||
\(849\) | 5.62704e8 | 0.919511 | ||||||||
\(850\) | −1.22737e8 | + | 6.04823e8i | −0.199857 | + | 0.984853i | ||||
\(851\) | − | 1.52543e7i | − | 0.0247517i | ||||||
\(852\) | 5.51647e8 | − | 5.76474e7i | 0.891954 | − | 0.0932097i | ||||
\(853\) | − | 7.92638e7i | − | 0.127711i | −0.997959 | − | 0.0638555i | \(-0.979660\pi\) | ||
0.997959 | − | 0.0638555i | \(-0.0203397\pi\) | |||||||
\(854\) | 9.12986e7 | + | 8.22550e7i | 0.146585 | + | 0.132065i | ||||
\(855\) | 2.15115e8 | − | 5.87393e7i | 0.344169 | − | 0.0939789i | ||||
\(856\) | 1.54311e8 | − | 2.11991e8i | 0.246023 | − | 0.337985i | ||||
\(857\) | 8.08687e8i | 1.28481i | 0.766366 | + | 0.642404i | \(0.222063\pi\) | ||||
−0.766366 | + | 0.642404i | \(0.777937\pi\) | |||||||
\(858\) | 3.03387e8 | + | 2.73335e8i | 0.480326 | + | 0.432747i | ||||
\(859\) | 1.08418e9i | 1.71049i | 0.518225 | + | 0.855244i | \(0.326593\pi\) | ||||
−0.518225 | + | 0.855244i | \(0.673407\pi\) | |||||||
\(860\) | −4.30812e8 | + | 1.67436e8i | −0.677317 | + | 0.263240i | ||||
\(861\) | −7.80080e8 | −1.22217 | ||||||||
\(862\) | −5.06617e8 | + | 5.62317e8i | −0.790966 | + | 0.877929i | ||||
\(863\) | 8.65764e8 | 1.34700 | 0.673499 | − | 0.739188i | \(-0.264790\pi\) | ||||
0.673499 | + | 0.739188i | \(0.264790\pi\) | |||||||
\(864\) | 1.96854e8 | + | 1.14046e8i | 0.305214 | + | 0.176823i | ||||
\(865\) | 6.30166e8 | − | 1.72073e8i | 0.973658 | − | 0.265868i | ||||
\(866\) | 3.48373e8 | − | 3.86675e8i | 0.536402 | − | 0.595377i | ||||
\(867\) | 9.62558e6 | 0.0147696 | ||||||||
\(868\) | −9.53084e8 | + | 9.95978e7i | −1.45738 | + | 0.152297i | ||||
\(869\) | −1.42968e8 | −0.217861 | ||||||||
\(870\) | 3.84404e8 | − | 7.62835e8i | 0.583754 | − | 1.15844i | ||||
\(871\) | − | 7.43945e8i | − | 1.12587i | ||||||
\(872\) | 4.00469e8 | − | 5.50162e8i | 0.603976 | − | 0.829738i | ||||
\(873\) | − | 1.03852e9i | − | 1.56089i | ||||||
\(874\) | 1.14224e7 | − | 1.26782e7i | 0.0171089 | − | 0.0189900i | ||||
\(875\) | −6.31284e8 | − | 6.13496e8i | −0.942325 | − | 0.915773i | ||||
\(876\) | 5.44649e7 | − | 5.69161e6i | 0.0810222 | − | 0.00846687i | ||||
\(877\) | 6.80856e8i | 1.00938i | 0.863299 | + | 0.504692i | \(0.168394\pi\) | ||||
−0.863299 | + | 0.504692i | \(0.831606\pi\) | |||||||
\(878\) | −2.84177e8 | + | 3.15421e8i | −0.419861 | + | 0.466023i | ||||
\(879\) | 1.32556e9i | 1.95179i | ||||||||
\(880\) | −1.77996e8 | + | 9.14952e7i | −0.261194 | + | 0.134261i | ||||
\(881\) | −1.01305e9 | −1.48150 | −0.740750 | − | 0.671780i | \(-0.765530\pi\) | ||||
−0.740750 | + | 0.671780i | \(0.765530\pi\) | |||||||
\(882\) | 4.57772e8 | + | 4.12428e8i | 0.667181 | + | 0.601093i | ||||
\(883\) | 7.97017e8 | 1.15767 | 0.578836 | − | 0.815444i | \(-0.303507\pi\) | ||||
0.578836 | + | 0.815444i | \(0.303507\pi\) | |||||||
\(884\) | 1.06226e8 | + | 1.01651e9i | 0.153770 | + | 1.47148i | ||||
\(885\) | −1.37172e8 | + | 3.74562e7i | −0.197895 | + | 0.0540374i | ||||
\(886\) | −8.16761e8 | − | 7.35857e8i | −1.17434 | − | 1.05802i | ||||
\(887\) | 8.37782e8 | 1.20049 | 0.600247 | − | 0.799815i | \(-0.295069\pi\) | ||||
0.600247 | + | 0.799815i | \(0.295069\pi\) | |||||||
\(888\) | 2.36637e8 | + | 1.72251e8i | 0.337943 | + | 0.245992i | ||||
\(889\) | −8.56810e8 | −1.21949 | ||||||||
\(890\) | −7.97746e7 | + | 1.58310e8i | −0.113160 | + | 0.224563i | ||||
\(891\) | − | 1.47170e8i | − | 0.208059i | ||||||
\(892\) | −9.51435e7 | − | 9.10459e8i | −0.134056 | − | 1.28282i | ||||
\(893\) | 2.73539e8i | 0.384119i | ||||||||
\(894\) | −5.05713e8 | − | 4.55620e8i | −0.707769 | − | 0.637661i | ||||
\(895\) | 7.73791e8 | − | 2.11292e8i | 1.07933 | − | 0.294723i | ||||
\(896\) | −3.86249e8 | + | 8.62674e8i | −0.536962 | + | 1.19929i | ||||
\(897\) | 1.40684e8i | 0.194924i | ||||||||
\(898\) | 8.17851e6 | + | 7.36838e6i | 0.0112939 | + | 0.0101752i | ||||
\(899\) | 7.02902e8i | 0.967422i | ||||||||
\(900\) | −5.36063e8 | − | 7.24142e8i | −0.735340 | − | 0.993336i | ||||
\(901\) | 1.36821e9 | 1.87059 | ||||||||
\(902\) | 8.97337e7 | − | 9.95995e7i | 0.122274 | − | 0.135718i | ||||
\(903\) | −1.05130e9 | −1.42779 | ||||||||
\(904\) | −6.63026e7 | − | 4.82624e7i | −0.0897481 | − | 0.0653287i | ||||
\(905\) | 9.05359e7 | + | 3.31560e8i | 0.122145 | + | 0.447318i | ||||
\(906\) | 4.77356e8 | − | 5.29839e8i | 0.641886 | − | 0.712458i | ||||
\(907\) | −8.35297e8 | −1.11949 | −0.559743 | − | 0.828666i | \(-0.689100\pi\) | ||||
−0.559743 | + | 0.828666i | \(0.689100\pi\) | |||||||
\(908\) | −5.84879e6 | − | 5.59689e7i | −0.00781283 | − | 0.0747635i | ||||
\(909\) | 1.15288e9 | 1.53495 | ||||||||
\(910\) | −1.30186e9 | − | 6.56026e8i | −1.72759 | − | 0.870556i | ||||
\(911\) | 5.22073e8i | 0.690519i | 0.938507 | + | 0.345260i | \(0.112209\pi\) | ||||
−0.938507 | + | 0.345260i | \(0.887791\pi\) | |||||||
\(912\) | 6.76936e7 | + | 3.20354e8i | 0.0892407 | + | 0.422323i | ||||
\(913\) | − | 1.96348e7i | − | 0.0257996i | ||||||
\(914\) | 6.39815e8 | − | 7.10160e8i | 0.837945 | − | 0.930074i | ||||
\(915\) | −4.53073e7 | − | 1.65924e8i | −0.0591433 | − | 0.216594i | ||||
\(916\) | −2.42059e6 | − | 2.31634e7i | −0.00314945 | − | 0.0301381i | ||||
\(917\) | − | 1.24506e9i | − | 1.61467i | ||||||
\(918\) | −1.83555e8 | + | 2.03736e8i | −0.237267 | + | 0.263354i | ||||
\(919\) | 7.05912e7i | 0.0909502i | 0.998965 | + | 0.0454751i | \(0.0144802\pi\) | ||||
−0.998965 | + | 0.0454751i | \(0.985520\pi\) | |||||||
\(920\) | −6.44642e7 | − | 2.44599e7i | −0.0827856 | − | 0.0314116i | ||||
\(921\) | 1.29516e9 | 1.65785 | ||||||||
\(922\) | −7.49069e8 | − | 6.74870e8i | −0.955716 | − | 0.861047i | ||||
\(923\) | −6.94318e8 | −0.882985 | ||||||||
\(924\) | −4.52747e8 | + | 4.73124e7i | −0.573905 | + | 0.0599734i | ||||
\(925\) | −1.12441e8 | − | 1.90539e8i | −0.142069 | − | 0.240745i | ||||
\(926\) | 6.01523e8 | + | 5.41939e8i | 0.757564 | + | 0.682524i | ||||
\(927\) | −1.87642e9 | −2.35554 | ||||||||
\(928\) | 5.99906e8 | + | 3.47551e8i | 0.750653 | + | 0.434885i | ||||
\(929\) | −3.30334e8 | −0.412008 | −0.206004 | − | 0.978551i | \(-0.566046\pi\) | ||||
−0.206004 | + | 0.978551i | \(0.566046\pi\) | |||||||
\(930\) | 1.19776e9 | + | 6.03570e8i | 1.48909 | + | 0.750376i | ||||
\(931\) | 1.69262e8i | 0.209754i | ||||||||
\(932\) | −2.03071e8 | + | 2.12211e7i | −0.250843 | + | 0.0262132i | ||||
\(933\) | 1.29982e9i | 1.60044i | ||||||||
\(934\) | 5.78028e8 | + | 5.20771e8i | 0.709428 | + | 0.639155i | ||||
\(935\) | −6.35459e7 | − | 2.32717e8i | −0.0777414 | − | 0.284704i | ||||
\(936\) | −1.20632e9 | − | 8.78095e8i | −1.47108 | − | 1.07081i | ||||
\(937\) | − | 1.37475e9i | − | 1.67111i | −0.549406 | − | 0.835556i | \(-0.685146\pi\) | ||
0.549406 | − | 0.835556i | \(-0.314854\pi\) | |||||||
\(938\) | 6.16128e8 | + | 5.55098e8i | 0.746557 | + | 0.672606i | ||||
\(939\) | − | 1.46430e8i | − | 0.176861i | ||||||
\(940\) | 1.03014e9 | − | 4.00366e8i | 1.24026 | − | 0.482029i | ||||
\(941\) | 1.35847e9 | 1.63035 | 0.815177 | − | 0.579211i | \(-0.196639\pi\) | ||||
0.815177 | + | 0.579211i | \(0.196639\pi\) | |||||||
\(942\) | 1.77522e8 | − | 1.97039e8i | 0.212373 | − | 0.235722i | ||||
\(943\) | 4.61853e7 | 0.0550768 | ||||||||
\(944\) | −2.38601e7 | − | 1.12916e8i | −0.0283633 | − | 0.134227i | ||||
\(945\) | −1.03035e8 | − | 3.77334e8i | −0.122093 | − | 0.447126i | ||||
\(946\) | 1.20932e8 | − | 1.34228e8i | 0.142846 | − | 0.158552i | ||||
\(947\) | 3.76294e8 | 0.443075 | 0.221537 | − | 0.975152i | \(-0.428892\pi\) | ||||
0.221537 | + | 0.975152i | \(0.428892\pi\) | |||||||
\(948\) | 9.39935e8 | − | 9.82238e7i | 1.10325 | − | 0.115290i | ||||
\(949\) | −6.85510e7 | −0.0802075 | ||||||||
\(950\) | 4.92222e7 | − | 2.42556e8i | 0.0574104 | − | 0.282906i | ||||
\(951\) | − | 1.09285e9i | − | 1.27063i | ||||||
\(952\) | −9.21123e8 | − | 6.70497e8i | −1.06760 | − | 0.777116i | ||||
\(953\) | 6.28773e8i | 0.726465i | 0.931698 | + | 0.363233i | \(0.118327\pi\) | ||||
−0.931698 | + | 0.363233i | \(0.881673\pi\) | |||||||
\(954\) | −1.33699e9 | + | 1.48398e9i | −1.53986 | + | 1.70916i | ||||
\(955\) | −9.61663e8 | + | 2.62592e8i | −1.10411 | + | 0.301489i | ||||
\(956\) | −1.09541e9 | + | 1.14471e8i | −1.25373 | + | 0.131016i | ||||
\(957\) | 3.33903e8i | 0.380964i | ||||||||
\(958\) | −3.24658e8 | + | 3.60353e8i | −0.369258 | + | 0.409856i | ||||
\(959\) | 1.17218e9i | 1.32905i | ||||||||
\(960\) | 1.10736e9 | − | 7.23818e8i | 1.25163 | − | 0.818117i | ||||
\(961\) | −2.16156e8 | −0.243555 | ||||||||
\(962\) | −2.72209e8 | − | 2.45245e8i | −0.305758 | − | 0.275471i | ||||
\(963\) | −4.61406e8 | −0.516660 | ||||||||
\(964\) | −8.42178e7 | − | 8.05907e8i | −0.0940097 | − | 0.899609i | ||||
\(965\) | −1.46945e9 | + | 4.01250e8i | −1.63521 | + | 0.446512i | ||||
\(966\) | −1.16513e8 | − | 1.04972e8i | −0.129254 | − | 0.116450i | ||||
\(967\) | 6.61713e8 | 0.731796 | 0.365898 | − | 0.930655i | \(-0.380762\pi\) | ||||
0.365898 | + | 0.930655i | \(0.380762\pi\) | |||||||
\(968\) | −4.87762e8 | + | 6.70084e8i | −0.537752 | + | 0.738759i | ||||
\(969\) | −3.94672e8 | −0.433776 | ||||||||
\(970\) | −1.02936e9 | − | 5.18710e8i | −1.12785 | − | 0.568341i | ||||
\(971\) | 8.80062e7i | 0.0961292i | 0.998844 | + | 0.0480646i | \(0.0153053\pi\) | ||||
−0.998844 | + | 0.0480646i | \(0.984695\pi\) | |||||||
\(972\) | 1.34778e8 | + | 1.28973e9i | 0.146764 | + | 1.40443i | ||||
\(973\) | 1.38524e9i | 1.50379i | ||||||||
\(974\) | −7.13920e8 | − | 6.43202e8i | −0.772632 | − | 0.696099i | ||||
\(975\) | 1.03699e9 | + | 1.75725e9i | 1.11882 | + | 1.89592i | ||||
\(976\) | 1.36584e8 | − | 2.88614e7i | 0.146910 | − | 0.0310433i | ||||
\(977\) | − | 7.15460e8i | − | 0.767188i | −0.923502 | − | 0.383594i | \(-0.874686\pi\) | ||
0.923502 | − | 0.383594i | \(-0.125314\pi\) | |||||||
\(978\) | −1.84962e9 | − | 1.66641e9i | −1.97727 | − | 1.78141i | ||||
\(979\) | − | 6.92942e7i | − | 0.0738497i | ||||||
\(980\) | 6.37435e8 | − | 2.47740e8i | 0.677264 | − | 0.263219i | ||||
\(981\) | −1.19745e9 | −1.26838 | ||||||||
\(982\) | 6.28790e8 | − | 6.97923e8i | 0.664005 | − | 0.737010i | ||||
\(983\) | 1.11848e8 | 0.117752 | 0.0588760 | − | 0.998265i | \(-0.481248\pi\) | ||||
0.0588760 | + | 0.998265i | \(0.481248\pi\) | |||||||
\(984\) | −5.21520e8 | + | 7.16460e8i | −0.547376 | + | 0.751981i | ||||
\(985\) | 6.35716e8 | − | 1.73589e8i | 0.665203 | − | 0.181641i | ||||
\(986\) | −5.59375e8 | + | 6.20876e8i | −0.583543 | + | 0.647701i | ||||
\(987\) | 2.51383e9 | 2.61447 | ||||||||
\(988\) | −4.26005e7 | − | 4.07658e8i | −0.0441717 | − | 0.422693i | ||||
\(989\) | 6.22430e7 | 0.0643430 | ||||||||
\(990\) | 3.14504e8 | + | 1.58483e8i | 0.324131 | + | 0.163334i | ||||
\(991\) | − | 1.31906e8i | − | 0.135532i | −0.997701 | − | 0.0677661i | \(-0.978413\pi\) | ||
0.997701 | − | 0.0677661i | \(-0.0215872\pi\) | |||||||
\(992\) | −5.45706e8 | + | 9.41940e8i | −0.559015 | + | 0.964913i | ||||
\(993\) | − | 1.35426e9i | − | 1.38310i | ||||||
\(994\) | 5.18068e8 | − | 5.75028e8i | 0.527506 | − | 0.585504i | ||||
\(995\) | 1.37991e9 | − | 3.76800e8i | 1.40082 | − | 0.382509i | ||||
\(996\) | 1.34897e7 | + | 1.29087e8i | 0.0136529 | + | 0.130649i | ||||
\(997\) | 1.67136e9i | 1.68649i | 0.537527 | + | 0.843246i | \(0.319359\pi\) | ||||
−0.537527 | + | 0.843246i | \(0.680641\pi\) | |||||||
\(998\) | 1.11735e9 | − | 1.24020e9i | 1.12408 | − | 1.24767i | ||||
\(999\) | − | 9.83076e7i | − | 0.0986031i |
(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 | 20.7.d.d.19.10 | yes | 12 | |
3.2 | odd | 2 | 180.7.f.e.19.3 | 12 | |||
4.3 | odd | 2 | inner | 20.7.d.d.19.4 | yes | 12 | |
5.2 | odd | 4 | 100.7.b.f.51.4 | 12 | |||
5.3 | odd | 4 | 100.7.b.f.51.9 | 12 | |||
5.4 | even | 2 | inner | 20.7.d.d.19.3 | ✓ | 12 | |
8.3 | odd | 2 | 320.7.h.f.319.2 | 12 | |||
8.5 | even | 2 | 320.7.h.f.319.12 | 12 | |||
12.11 | even | 2 | 180.7.f.e.19.9 | 12 | |||
15.14 | odd | 2 | 180.7.f.e.19.10 | 12 | |||
20.3 | even | 4 | 100.7.b.f.51.10 | 12 | |||
20.7 | even | 4 | 100.7.b.f.51.3 | 12 | |||
20.19 | odd | 2 | inner | 20.7.d.d.19.9 | yes | 12 | |
40.19 | odd | 2 | 320.7.h.f.319.11 | 12 | |||
40.29 | even | 2 | 320.7.h.f.319.1 | 12 | |||
60.59 | even | 2 | 180.7.f.e.19.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.7.d.d.19.3 | ✓ | 12 | 5.4 | even | 2 | inner | |
20.7.d.d.19.4 | yes | 12 | 4.3 | odd | 2 | inner | |
20.7.d.d.19.9 | yes | 12 | 20.19 | odd | 2 | inner | |
20.7.d.d.19.10 | yes | 12 | 1.1 | even | 1 | trivial | |
100.7.b.f.51.3 | 12 | 20.7 | even | 4 | |||
100.7.b.f.51.4 | 12 | 5.2 | odd | 4 | |||
100.7.b.f.51.9 | 12 | 5.3 | odd | 4 | |||
100.7.b.f.51.10 | 12 | 20.3 | even | 4 | |||
180.7.f.e.19.3 | 12 | 3.2 | odd | 2 | |||
180.7.f.e.19.4 | 12 | 60.59 | even | 2 | |||
180.7.f.e.19.9 | 12 | 12.11 | even | 2 | |||
180.7.f.e.19.10 | 12 | 15.14 | odd | 2 | |||
320.7.h.f.319.1 | 12 | 40.29 | even | 2 | |||
320.7.h.f.319.2 | 12 | 8.3 | odd | 2 | |||
320.7.h.f.319.11 | 12 | 40.19 | odd | 2 | |||
320.7.h.f.319.12 | 12 | 8.5 | even | 2 |