Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [15,7,Mod(14,15)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15, 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("15.14");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.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: | \(3.45081125430\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 60x^{6} + 7774x^{4} + 206220x^{2} + 5736025 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3^{6}\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 14.1 | ||
Root | \(-2.84382 + 4.80492i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 15.14 |
Dual form | 15.7.d.c.14.2 |
$q$-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 \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(11\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −11.8944 | −1.48680 | −0.743399 | − | 0.668848i | \(-0.766787\pi\) | ||||
−0.743399 | + | 0.668848i | \(0.766787\pi\) | |||||||
\(3\) | 9.31012 | − | 25.3441i | 0.344819 | − | 0.938669i | ||||
\(4\) | 77.4763 | 1.21057 | ||||||||
\(5\) | −102.129 | + | 72.0738i | −0.817033 | + | 0.576591i | ||||
\(6\) | −110.738 | + | 301.452i | −0.512677 | + | 1.39561i | ||||
\(7\) | 553.145i | 1.61267i | 0.591461 | + | 0.806334i | \(0.298551\pi\) | ||||
−0.591461 | + | 0.806334i | \(0.701449\pi\) | |||||||
\(8\) | −160.292 | −0.313070 | ||||||||
\(9\) | −555.643 | − | 471.913i | −0.762199 | − | 0.647343i | ||||
\(10\) | 1214.76 | − | 857.274i | 1.21476 | − | 0.857274i | ||||
\(11\) | 799.678i | 0.600810i | 0.953812 | + | 0.300405i | \(0.0971218\pi\) | ||||
−0.953812 | + | 0.300405i | \(0.902878\pi\) | |||||||
\(12\) | 721.314 | − | 1963.56i | 0.417427 | − | 1.13632i | ||||
\(13\) | 1119.56i | 0.509587i | 0.966995 | + | 0.254794i | \(0.0820075\pi\) | ||||
−0.966995 | + | 0.254794i | \(0.917992\pi\) | |||||||
\(14\) | − | 6579.32i | − | 2.39771i | ||||||
\(15\) | 875.810 | + | 3259.38i | 0.259499 | + | 0.965743i | ||||
\(16\) | −3051.91 | −0.745095 | ||||||||
\(17\) | −2580.88 | −0.525316 | −0.262658 | − | 0.964889i | \(-0.584599\pi\) | ||||
−0.262658 | + | 0.964889i | \(0.584599\pi\) | |||||||
\(18\) | 6609.03 | + | 5613.11i | 1.13324 | + | 0.962467i | ||||
\(19\) | −3496.52 | −0.509772 | −0.254886 | − | 0.966971i | \(-0.582038\pi\) | ||||
−0.254886 | + | 0.966971i | \(0.582038\pi\) | |||||||
\(20\) | −7912.58 | + | 5584.01i | −0.989073 | + | 0.698002i | ||||
\(21\) | 14018.9 | + | 5149.85i | 1.51376 | + | 0.556079i | ||||
\(22\) | − | 9511.67i | − | 0.893282i | ||||||
\(23\) | −5050.73 | −0.415117 | −0.207558 | − | 0.978223i | \(-0.566552\pi\) | ||||
−0.207558 | + | 0.978223i | \(0.566552\pi\) | |||||||
\(24\) | −1492.34 | + | 4062.45i | −0.107953 | + | 0.293869i | ||||
\(25\) | 5235.72 | − | 14721.7i | 0.335086 | − | 0.942188i | ||||
\(26\) | − | 13316.5i | − | 0.757653i | ||||||
\(27\) | −17133.3 | + | 9688.69i | −0.870461 | + | 0.492237i | ||||
\(28\) | 42855.6i | 1.95224i | ||||||||
\(29\) | 25414.6i | 1.04205i | 0.853540 | + | 0.521027i | \(0.174451\pi\) | ||||
−0.853540 | + | 0.521027i | \(0.825549\pi\) | |||||||
\(30\) | −10417.2 | − | 38768.3i | −0.385823 | − | 1.43586i | ||||
\(31\) | −11931.1 | −0.400494 | −0.200247 | − | 0.979745i | \(-0.564174\pi\) | ||||
−0.200247 | + | 0.979745i | \(0.564174\pi\) | |||||||
\(32\) | 46559.2 | 1.42088 | ||||||||
\(33\) | 20267.1 | + | 7445.10i | 0.563961 | + | 0.207171i | ||||
\(34\) | 30697.9 | 0.781038 | ||||||||
\(35\) | −39867.3 | − | 56492.2i | −0.929849 | − | 1.31760i | ||||
\(36\) | −43049.2 | − | 36562.0i | −0.922693 | − | 0.783651i | ||||
\(37\) | − | 28772.8i | − | 0.568037i | −0.958819 | − | 0.284018i | \(-0.908332\pi\) | ||
0.958819 | − | 0.284018i | \(-0.0916677\pi\) | |||||||
\(38\) | 41589.0 | 0.757927 | ||||||||
\(39\) | 28374.3 | + | 10423.3i | 0.478334 | + | 0.175716i | ||||
\(40\) | 16370.5 | − | 11552.9i | 0.255789 | − | 0.180513i | ||||
\(41\) | 55623.9i | 0.807067i | 0.914965 | + | 0.403534i | \(0.132218\pi\) | ||||
−0.914965 | + | 0.403534i | \(0.867782\pi\) | |||||||
\(42\) | −166747. | − | 61254.2i | −2.25066 | − | 0.826777i | ||||
\(43\) | 38502.9i | 0.484270i | 0.970243 | + | 0.242135i | \(0.0778477\pi\) | ||||
−0.970243 | + | 0.242135i | \(0.922152\pi\) | |||||||
\(44\) | 61956.0i | 0.727320i | ||||||||
\(45\) | 90759.9 | + | 8148.69i | 0.995994 | + | 0.0894232i | ||||
\(46\) | 60075.3 | 0.617195 | ||||||||
\(47\) | 151747. | 1.46160 | 0.730798 | − | 0.682594i | \(-0.239148\pi\) | ||||
0.730798 | + | 0.682594i | \(0.239148\pi\) | |||||||
\(48\) | −28413.6 | + | 77347.8i | −0.256923 | + | 0.699397i | ||||
\(49\) | −188320. | −1.60070 | ||||||||
\(50\) | −62275.6 | + | 175105.i | −0.498205 | + | 1.40084i | ||||
\(51\) | −24028.3 | + | 65409.9i | −0.181139 | + | 0.493098i | ||||
\(52\) | 86739.6i | 0.616889i | ||||||||
\(53\) | −143854. | −0.966258 | −0.483129 | − | 0.875549i | \(-0.660500\pi\) | ||||
−0.483129 | + | 0.875549i | \(0.660500\pi\) | |||||||
\(54\) | 203790. | − | 115241.i | 1.29420 | − | 0.731856i | ||||
\(55\) | −57635.9 | − | 81670.4i | −0.346421 | − | 0.490881i | ||||
\(56\) | − | 88664.7i | − | 0.504878i | ||||||
\(57\) | −32553.1 | + | 88616.1i | −0.175779 | + | 0.478507i | ||||
\(58\) | − | 302291.i | − | 1.54932i | ||||||
\(59\) | − | 401125.i | − | 1.95310i | −0.215294 | − | 0.976549i | \(-0.569071\pi\) | ||
0.215294 | − | 0.976549i | \(-0.430929\pi\) | |||||||
\(60\) | 67854.5 | + | 252525.i | 0.314141 | + | 1.16910i | ||||
\(61\) | 309592. | 1.36396 | 0.681978 | − | 0.731373i | \(-0.261120\pi\) | ||||
0.681978 | + | 0.731373i | \(0.261120\pi\) | |||||||
\(62\) | 141913. | 0.595453 | ||||||||
\(63\) | 261036. | − | 307351.i | 1.04395 | − | 1.22917i | ||||
\(64\) | −358471. | −1.36746 | ||||||||
\(65\) | −80691.2 | − | 114340.i | −0.293823 | − | 0.416350i | ||||
\(66\) | −241064. | − | 88554.8i | −0.838497 | − | 0.308021i | ||||
\(67\) | 163390.i | 0.543252i | 0.962403 | + | 0.271626i | \(0.0875614\pi\) | ||||
−0.962403 | + | 0.271626i | \(0.912439\pi\) | |||||||
\(68\) | −199957. | −0.635930 | ||||||||
\(69\) | −47022.9 | + | 128006.i | −0.143140 | + | 0.389657i | ||||
\(70\) | 474197. | + | 671940.i | 1.38250 | + | 1.95901i | ||||
\(71\) | 151582.i | 0.423518i | 0.977322 | + | 0.211759i | \(0.0679192\pi\) | ||||
−0.977322 | + | 0.211759i | \(0.932081\pi\) | |||||||
\(72\) | 89065.1 | + | 75643.8i | 0.238622 | + | 0.202664i | ||||
\(73\) | − | 70173.6i | − | 0.180387i | −0.995924 | − | 0.0901935i | \(-0.971251\pi\) | ||
0.995924 | − | 0.0901935i | \(-0.0287485\pi\) | |||||||
\(74\) | 342234.i | 0.844556i | ||||||||
\(75\) | −324362. | − | 269755.i | −0.768858 | − | 0.639419i | ||||
\(76\) | −270898. | −0.617113 | ||||||||
\(77\) | −442338. | −0.968906 | ||||||||
\(78\) | −337495. | − | 123978.i | −0.711186 | − | 0.261253i | ||||
\(79\) | 437071. | 0.886484 | 0.443242 | − | 0.896402i | \(-0.353828\pi\) | ||||
0.443242 | + | 0.896402i | \(0.353828\pi\) | |||||||
\(80\) | 311689. | − | 219963.i | 0.608767 | − | 0.429615i | ||||
\(81\) | 86037.8 | + | 524430.i | 0.161895 | + | 0.986808i | ||||
\(82\) | − | 661612.i | − | 1.19995i | ||||||
\(83\) | −342935. | −0.599761 | −0.299880 | − | 0.953977i | \(-0.596947\pi\) | ||||
−0.299880 | + | 0.953977i | \(0.596947\pi\) | |||||||
\(84\) | 1.08614e6 | + | 398991.i | 1.83251 | + | 0.673171i | ||||
\(85\) | 263583. | − | 186014.i | 0.429200 | − | 0.302892i | ||||
\(86\) | − | 457968.i | − | 0.720012i | ||||||
\(87\) | 644110. | + | 236613.i | 0.978143 | + | 0.359320i | ||||
\(88\) | − | 128182.i | − | 0.188096i | ||||||
\(89\) | 631196.i | 0.895352i | 0.894196 | + | 0.447676i | \(0.147748\pi\) | ||||
−0.894196 | + | 0.447676i | \(0.852252\pi\) | |||||||
\(90\) | −1.07953e6 | − | 96923.6i | −1.48084 | − | 0.132954i | ||||
\(91\) | −619281. | −0.821795 | ||||||||
\(92\) | −391311. | −0.502527 | ||||||||
\(93\) | −111080. | + | 302383.i | −0.138098 | + | 0.375931i | ||||
\(94\) | −1.80494e6 | −2.17310 | ||||||||
\(95\) | 357097. | − | 252008.i | 0.416500 | − | 0.293930i | ||||
\(96\) | 433472. | − | 1.18000e6i | 0.489945 | − | 1.33373i | ||||
\(97\) | 1.55901e6i | 1.70818i | 0.520129 | + | 0.854088i | \(0.325884\pi\) | ||||
−0.520129 | + | 0.854088i | \(0.674116\pi\) | |||||||
\(98\) | 2.23995e6 | 2.37991 | ||||||||
\(99\) | 377378. | − | 444336.i | 0.388930 | − | 0.457937i | ||||
\(100\) | 405644. | − | 1.14058e6i | 0.405644 | − | 1.14058i | ||||
\(101\) | 96149.6i | 0.0933218i | 0.998911 | + | 0.0466609i | \(0.0148580\pi\) | ||||
−0.998911 | + | 0.0466609i | \(0.985142\pi\) | |||||||
\(102\) | 285801. | − | 778010.i | 0.269317 | − | 0.733136i | ||||
\(103\) | − | 364316.i | − | 0.333401i | −0.986008 | − | 0.166701i | \(-0.946689\pi\) | ||
0.986008 | − | 0.166701i | \(-0.0533113\pi\) | |||||||
\(104\) | − | 179457.i | − | 0.159537i | ||||||
\(105\) | −1.80291e6 | + | 484450.i | −1.55742 | + | 0.418486i | ||||
\(106\) | 1.71105e6 | 1.43663 | ||||||||
\(107\) | 43747.4 | 0.0357109 | 0.0178555 | − | 0.999841i | \(-0.494316\pi\) | ||||
0.0178555 | + | 0.999841i | \(0.494316\pi\) | |||||||
\(108\) | −1.32742e6 | + | 750644.i | −1.05375 | + | 0.595885i | ||||
\(109\) | −157763. | −0.121822 | −0.0609109 | − | 0.998143i | \(-0.519401\pi\) | ||||
−0.0609109 | + | 0.998143i | \(0.519401\pi\) | |||||||
\(110\) | 685543. | + | 971419.i | 0.515058 | + | 0.729841i | ||||
\(111\) | −729219. | − | 267878.i | −0.533199 | − | 0.195870i | ||||
\(112\) | − | 1.68815e6i | − | 1.20159i | ||||||
\(113\) | −811828. | −0.562637 | −0.281319 | − | 0.959614i | \(-0.590772\pi\) | ||||
−0.281319 | + | 0.959614i | \(0.590772\pi\) | |||||||
\(114\) | 387199. | − | 1.05403e6i | 0.261348 | − | 0.711443i | ||||
\(115\) | 515826. | − | 364025.i | 0.339164 | − | 0.239353i | ||||
\(116\) | 1.96903e6i | 1.26147i | ||||||||
\(117\) | 528336. | − | 622078.i | 0.329878 | − | 0.388407i | ||||
\(118\) | 4.77114e6i | 2.90386i | ||||||||
\(119\) | − | 1.42760e6i | − | 0.847160i | ||||||
\(120\) | −140385. | − | 522453.i | −0.0812414 | − | 0.302345i | ||||
\(121\) | 1.13208e6 | 0.639028 | ||||||||
\(122\) | −3.68240e6 | −2.02793 | ||||||||
\(123\) | 1.40974e6 | + | 517865.i | 0.757569 | + | 0.278292i | ||||
\(124\) | −924378. | −0.484824 | ||||||||
\(125\) | 526329. | + | 1.88087e6i | 0.269480 | + | 0.963006i | ||||
\(126\) | −3.10486e6 | + | 3.65575e6i | −1.55214 | + | 1.82753i | ||||
\(127\) | − | 705580.i | − | 0.344457i | −0.985057 | − | 0.172229i | \(-0.944903\pi\) | ||
0.985057 | − | 0.172229i | \(-0.0550968\pi\) | |||||||
\(128\) | 1.28400e6 | 0.612259 | ||||||||
\(129\) | 975819. | + | 358466.i | 0.454570 | + | 0.166986i | ||||
\(130\) | 959772. | + | 1.36000e6i | 0.436856 | + | 0.619028i | ||||
\(131\) | − | 2.35922e6i | − | 1.04943i | −0.851277 | − | 0.524716i | \(-0.824171\pi\) | ||
0.851277 | − | 0.524716i | \(-0.175829\pi\) | |||||||
\(132\) | 1.57022e6 | + | 576818.i | 0.682713 | + | 0.250794i | ||||
\(133\) | − | 1.93408e6i | − | 0.822092i | ||||||
\(134\) | − | 1.94342e6i | − | 0.807706i | ||||||
\(135\) | 1.05151e6 | − | 2.22436e6i | 0.427377 | − | 0.904074i | ||||
\(136\) | 413694. | 0.164461 | ||||||||
\(137\) | 2.73309e6 | 1.06290 | 0.531450 | − | 0.847090i | \(-0.321647\pi\) | ||||
0.531450 | + | 0.847090i | \(0.321647\pi\) | |||||||
\(138\) | 559308. | − | 1.52255e6i | 0.212821 | − | 0.579341i | ||||
\(139\) | −2.86791e6 | −1.06788 | −0.533939 | − | 0.845523i | \(-0.679289\pi\) | ||||
−0.533939 | + | 0.845523i | \(0.679289\pi\) | |||||||
\(140\) | −3.08877e6 | − | 4.37681e6i | −1.12564 | − | 1.59505i | ||||
\(141\) | 1.41279e6 | − | 3.84589e6i | 0.503986 | − | 1.37195i | ||||
\(142\) | − | 1.80297e6i | − | 0.629686i | ||||||
\(143\) | −895290. | −0.306165 | ||||||||
\(144\) | 1.69577e6 | + | 1.44023e6i | 0.567911 | + | 0.482332i | ||||
\(145\) | −1.83173e6 | − | 2.59557e6i | −0.600838 | − | 0.851392i | ||||
\(146\) | 834671.i | 0.268199i | ||||||||
\(147\) | −1.75329e6 | + | 4.77280e6i | −0.551951 | + | 1.50252i | ||||
\(148\) | − | 2.22921e6i | − | 0.687647i | ||||||
\(149\) | 3.71980e6i | 1.12450i | 0.826966 | + | 0.562252i | \(0.190065\pi\) | ||||
−0.826966 | + | 0.562252i | \(0.809935\pi\) | |||||||
\(150\) | 3.85808e6 | + | 3.20857e6i | 1.14314 | + | 0.950687i | ||||
\(151\) | −4.26236e6 | −1.23800 | −0.618998 | − | 0.785392i | \(-0.712461\pi\) | ||||
−0.618998 | + | 0.785392i | \(0.712461\pi\) | |||||||
\(152\) | 560464. | 0.159594 | ||||||||
\(153\) | 1.43405e6 | + | 1.21795e6i | 0.400395 | + | 0.340059i | ||||
\(154\) | 5.26133e6 | 1.44057 | ||||||||
\(155\) | 1.21851e6 | − | 859921.i | 0.327217 | − | 0.230921i | ||||
\(156\) | 2.19833e6 | + | 807556.i | 0.579055 | + | 0.212715i | ||||
\(157\) | 5.22753e6i | 1.35082i | 0.737442 | + | 0.675410i | \(0.236034\pi\) | ||||
−0.737442 | + | 0.675410i | \(0.763966\pi\) | |||||||
\(158\) | −5.19869e6 | −1.31802 | ||||||||
\(159\) | −1.33929e6 | + | 3.64584e6i | −0.333185 | + | 0.906997i | ||||
\(160\) | −4.75506e6 | + | 3.35570e6i | −1.16090 | + | 0.819264i | ||||
\(161\) | − | 2.79378e6i | − | 0.669445i | ||||||
\(162\) | −1.02337e6 | − | 6.23777e6i | −0.240706 | − | 1.46718i | ||||
\(163\) | − | 1.86579e6i | − | 0.430825i | −0.976523 | − | 0.215413i | \(-0.930890\pi\) | ||
0.976523 | − | 0.215413i | \(-0.0691096\pi\) | |||||||
\(164\) | 4.30953e6i | 0.977009i | ||||||||
\(165\) | −2.60646e6 | + | 700365.i | −0.580228 | + | 0.155910i | ||||
\(166\) | 4.07900e6 | 0.891723 | ||||||||
\(167\) | 3.82949e6 | 0.822227 | 0.411114 | − | 0.911584i | \(-0.365140\pi\) | ||||
0.411114 | + | 0.911584i | \(0.365140\pi\) | |||||||
\(168\) | −2.24712e6 | − | 825479.i | −0.473913 | − | 0.174092i | ||||
\(169\) | 3.57339e6 | 0.740321 | ||||||||
\(170\) | −3.13515e6 | + | 2.21252e6i | −0.638134 | + | 0.450339i | ||||
\(171\) | 1.94282e6 | + | 1.65005e6i | 0.388548 | + | 0.329997i | ||||
\(172\) | 2.98306e6i | 0.586241i | ||||||||
\(173\) | −3.03786e6 | −0.586717 | −0.293359 | − | 0.956002i | \(-0.594773\pi\) | ||||
−0.293359 | + | 0.956002i | \(0.594773\pi\) | |||||||
\(174\) | −7.66129e6 | − | 2.81437e6i | −1.45430 | − | 0.534236i | ||||
\(175\) | 8.14322e6 | + | 2.89611e6i | 1.51944 | + | 0.540382i | ||||
\(176\) | − | 2.44054e6i | − | 0.447660i | ||||||
\(177\) | −1.01661e7 | − | 3.73453e6i | −1.83331 | − | 0.673466i | ||||
\(178\) | − | 7.50768e6i | − | 1.33121i | ||||||
\(179\) | 2.06795e6i | 0.360563i | 0.983615 | + | 0.180282i | \(0.0577009\pi\) | ||||
−0.983615 | + | 0.180282i | \(0.942299\pi\) | |||||||
\(180\) | 7.03174e6 | + | 631330.i | 1.20572 | + | 0.108253i | ||||
\(181\) | −2.88344e6 | −0.486267 | −0.243133 | − | 0.969993i | \(-0.578175\pi\) | ||||
−0.243133 | + | 0.969993i | \(0.578175\pi\) | |||||||
\(182\) | 7.36596e6 | 1.22184 | ||||||||
\(183\) | 2.88234e6 | − | 7.84632e6i | 0.470318 | − | 1.28030i | ||||
\(184\) | 809591. | 0.129961 | ||||||||
\(185\) | 2.07376e6 | + | 2.93854e6i | 0.327525 | + | 0.464105i | ||||
\(186\) | 1.32123e6 | − | 3.59666e6i | 0.205324 | − | 0.558933i | ||||
\(187\) | − | 2.06387e6i | − | 0.315615i | ||||||
\(188\) | 1.17568e7 | 1.76936 | ||||||||
\(189\) | −5.35925e6 | − | 9.47719e6i | −0.793814 | − | 1.40376i | ||||
\(190\) | −4.24745e6 | + | 2.99748e6i | −0.619252 | + | 0.437014i | ||||
\(191\) | 1.15389e7i | 1.65601i | 0.560720 | + | 0.828005i | \(0.310524\pi\) | ||||
−0.560720 | + | 0.828005i | \(0.689476\pi\) | |||||||
\(192\) | −3.33741e6 | + | 9.08512e6i | −0.471526 | + | 1.28359i | ||||
\(193\) | 5.52092e6i | 0.767961i | 0.923341 | + | 0.383981i | \(0.125447\pi\) | ||||
−0.923341 | + | 0.383981i | \(0.874553\pi\) | |||||||
\(194\) | − | 1.85434e7i | − | 2.53971i | ||||||
\(195\) | −3.64909e6 | + | 980524.i | −0.492131 | + | 0.132237i | ||||
\(196\) | −1.45904e7 | −1.93775 | ||||||||
\(197\) | 9.94059e6 | 1.30021 | 0.650105 | − | 0.759844i | \(-0.274725\pi\) | ||||
0.650105 | + | 0.759844i | \(0.274725\pi\) | |||||||
\(198\) | −4.48868e6 | + | 5.28510e6i | −0.578260 | + | 0.680859i | ||||
\(199\) | 8.27123e6 | 1.04957 | 0.524785 | − | 0.851235i | \(-0.324146\pi\) | ||||
0.524785 | + | 0.851235i | \(0.324146\pi\) | |||||||
\(200\) | −839244. | + | 2.35977e6i | −0.104905 | + | 0.294971i | ||||
\(201\) | 4.14097e6 | + | 1.52118e6i | 0.509934 | + | 0.187324i | ||||
\(202\) | − | 1.14364e6i | − | 0.138751i | ||||||
\(203\) | −1.40580e7 | −1.68049 | ||||||||
\(204\) | −1.86162e6 | + | 5.06772e6i | −0.219281 | + | 0.596928i | ||||
\(205\) | −4.00903e6 | − | 5.68082e6i | −0.465348 | − | 0.659401i | ||||
\(206\) | 4.33332e6i | 0.495700i | ||||||||
\(207\) | 2.80640e6 | + | 2.38350e6i | 0.316402 | + | 0.268723i | ||||
\(208\) | − | 3.41680e6i | − | 0.379691i | ||||||
\(209\) | − | 2.79609e6i | − | 0.306276i | ||||||
\(210\) | 2.14445e7 | − | 5.76223e6i | 2.31557 | − | 0.622204i | ||||
\(211\) | 6.31824e6 | 0.672587 | 0.336294 | − | 0.941757i | \(-0.390827\pi\) | ||||
0.336294 | + | 0.941757i | \(0.390827\pi\) | |||||||
\(212\) | −1.11452e7 | −1.16972 | ||||||||
\(213\) | 3.84170e6 | + | 1.41125e6i | 0.397544 | + | 0.146037i | ||||
\(214\) | −520349. | −0.0530950 | ||||||||
\(215\) | −2.77505e6 | − | 3.93227e6i | −0.279226 | − | 0.395665i | ||||
\(216\) | 2.74633e6 | − | 1.55302e6i | 0.272515 | − | 0.154105i | ||||
\(217\) | − | 6.59963e6i | − | 0.645863i | ||||||
\(218\) | 1.87649e6 | 0.181124 | ||||||||
\(219\) | −1.77848e6 | − | 653325.i | −0.169324 | − | 0.0622009i | ||||
\(220\) | −4.46541e6 | − | 6.32752e6i | −0.419366 | − | 0.594245i | ||||
\(221\) | − | 2.88945e6i | − | 0.267694i | ||||||
\(222\) | 8.67361e6 | + | 3.18624e6i | 0.792758 | + | 0.291219i | ||||
\(223\) | 1.15621e7i | 1.04261i | 0.853369 | + | 0.521307i | \(0.174555\pi\) | ||||
−0.853369 | + | 0.521307i | \(0.825445\pi\) | |||||||
\(224\) | 2.57540e7i | 2.29140i | ||||||||
\(225\) | −9.85654e6 | + | 5.70920e6i | −0.865320 | + | 0.501219i | ||||
\(226\) | 9.65619e6 | 0.836528 | ||||||||
\(227\) | −1.37437e7 | −1.17497 | −0.587484 | − | 0.809236i | \(-0.699882\pi\) | ||||
−0.587484 | + | 0.809236i | \(0.699882\pi\) | |||||||
\(228\) | −2.52209e6 | + | 6.86565e6i | −0.212792 | + | 0.579265i | ||||
\(229\) | −4.67634e6 | −0.389404 | −0.194702 | − | 0.980862i | \(-0.562374\pi\) | ||||
−0.194702 | + | 0.980862i | \(0.562374\pi\) | |||||||
\(230\) | −6.13543e6 | + | 4.32985e6i | −0.504268 | + | 0.355869i | ||||
\(231\) | −4.11822e6 | + | 1.12106e7i | −0.334098 | + | 0.909482i | ||||
\(232\) | − | 4.07376e6i | − | 0.326236i | ||||||
\(233\) | 1.90985e7 | 1.50984 | 0.754920 | − | 0.655817i | \(-0.227676\pi\) | ||||
0.754920 | + | 0.655817i | \(0.227676\pi\) | |||||||
\(234\) | −6.28423e6 | + | 7.39923e6i | −0.490461 | + | 0.577483i | ||||
\(235\) | −1.54978e7 | + | 1.09370e7i | −1.19417 | + | 0.842742i | ||||
\(236\) | − | 3.10777e7i | − | 2.36436i | ||||||
\(237\) | 4.06919e6 | − | 1.10772e7i | 0.305677 | − | 0.832115i | ||||
\(238\) | 1.69804e7i | 1.25955i | ||||||||
\(239\) | − | 7.64223e6i | − | 0.559792i | −0.960030 | − | 0.279896i | \(-0.909700\pi\) | ||
0.960030 | − | 0.279896i | \(-0.0902999\pi\) | |||||||
\(240\) | −2.67289e6 | − | 9.94734e6i | −0.193351 | − | 0.719570i | ||||
\(241\) | 2.44181e6 | 0.174446 | 0.0872229 | − | 0.996189i | \(-0.472201\pi\) | ||||
0.0872229 | + | 0.996189i | \(0.472201\pi\) | |||||||
\(242\) | −1.34653e7 | −0.950105 | ||||||||
\(243\) | 1.40922e7 | + | 2.70196e6i | 0.982111 | + | 0.188304i | ||||
\(244\) | 2.39860e7 | 1.65116 | ||||||||
\(245\) | 1.92330e7 | − | 1.35730e7i | 1.30782 | − | 0.922947i | ||||
\(246\) | −1.67679e7 | − | 6.15969e6i | −1.12635 | − | 0.413764i | ||||
\(247\) | − | 3.91458e6i | − | 0.259773i | ||||||
\(248\) | 1.91246e6 | 0.125383 | ||||||||
\(249\) | −3.19277e6 | + | 8.69138e6i | −0.206809 | + | 0.562977i | ||||
\(250\) | −6.26035e6 | − | 2.23718e7i | −0.400662 | − | 1.43179i | ||||
\(251\) | 2.52632e6i | 0.159760i | 0.996805 | + | 0.0798798i | \(0.0254536\pi\) | ||||
−0.996805 | + | 0.0798798i | \(0.974546\pi\) | |||||||
\(252\) | 2.02241e7 | − | 2.38124e7i | 1.26377 | − | 1.48800i | ||||
\(253\) | − | 4.03895e6i | − | 0.249406i | ||||||
\(254\) | 8.39244e6i | 0.512138i | ||||||||
\(255\) | −2.26036e6 | − | 8.41207e6i | −0.136319 | − | 0.507320i | ||||
\(256\) | 7.66976e6 | 0.457153 | ||||||||
\(257\) | −9.70704e6 | −0.571857 | −0.285928 | − | 0.958251i | \(-0.592302\pi\) | ||||
−0.285928 | + | 0.958251i | \(0.592302\pi\) | |||||||
\(258\) | −1.16068e7 | − | 4.26374e6i | −0.675853 | − | 0.248274i | ||||
\(259\) | 1.59155e7 | 0.916055 | ||||||||
\(260\) | −6.25166e6 | − | 8.85864e6i | −0.355693 | − | 0.504019i | ||||
\(261\) | 1.19935e7 | − | 1.41215e7i | 0.674565 | − | 0.794252i | ||||
\(262\) | 2.80615e7i | 1.56029i | ||||||||
\(263\) | −2.50512e7 | −1.37709 | −0.688544 | − | 0.725195i | \(-0.741750\pi\) | ||||
−0.688544 | + | 0.725195i | \(0.741750\pi\) | |||||||
\(264\) | −3.24865e6 | − | 1.19339e6i | −0.176560 | − | 0.0648590i | ||||
\(265\) | 1.46916e7 | − | 1.03681e7i | 0.789465 | − | 0.557136i | ||||
\(266\) | 2.30047e7i | 1.22228i | ||||||||
\(267\) | 1.59971e7 | + | 5.87651e6i | 0.840439 | + | 0.308735i | ||||
\(268\) | 1.26589e7i | 0.657643i | ||||||||
\(269\) | − | 1.84000e7i | − | 0.945282i | −0.881255 | − | 0.472641i | \(-0.843301\pi\) | ||
0.881255 | − | 0.472641i | \(-0.156699\pi\) | |||||||
\(270\) | −1.25070e7 | + | 2.64574e7i | −0.635423 | + | 1.34417i | ||||
\(271\) | −3.59204e7 | −1.80482 | −0.902408 | − | 0.430883i | \(-0.858202\pi\) | ||||
−0.902408 | + | 0.430883i | \(0.858202\pi\) | |||||||
\(272\) | 7.87660e6 | 0.391410 | ||||||||
\(273\) | −5.76558e6 | + | 1.56951e7i | −0.283371 | + | 0.771393i | ||||
\(274\) | −3.25084e7 | −1.58032 | ||||||||
\(275\) | 1.17726e7 | + | 4.18689e6i | 0.566075 | + | 0.201323i | ||||
\(276\) | −3.64316e6 | + | 9.91742e6i | −0.173281 | + | 0.471706i | ||||
\(277\) | − | 9.87614e6i | − | 0.464673i | −0.972635 | − | 0.232337i | \(-0.925363\pi\) | ||
0.972635 | − | 0.232337i | \(-0.0746371\pi\) | |||||||
\(278\) | 3.41120e7 | 1.58772 | ||||||||
\(279\) | 6.62944e6 | + | 5.63044e6i | 0.305256 | + | 0.259257i | ||||
\(280\) | 6.39040e6 | + | 9.05525e6i | 0.291108 | + | 0.412502i | ||||
\(281\) | 2.31654e7i | 1.04405i | 0.852930 | + | 0.522025i | \(0.174823\pi\) | ||||
−0.852930 | + | 0.522025i | \(0.825177\pi\) | |||||||
\(282\) | −1.68042e7 | + | 4.57445e7i | −0.749326 | + | 2.03982i | ||||
\(283\) | − | 3.21328e7i | − | 1.41772i | −0.705351 | − | 0.708859i | \(-0.749210\pi\) | ||
0.705351 | − | 0.708859i | \(-0.250790\pi\) | |||||||
\(284\) | 1.17440e7i | 0.512697i | ||||||||
\(285\) | −3.06229e6 | − | 1.13965e7i | −0.132285 | − | 0.492309i | ||||
\(286\) | 1.06489e7 | 0.455205 | ||||||||
\(287\) | −3.07681e7 | −1.30153 | ||||||||
\(288\) | −2.58703e7 | − | 2.19719e7i | −1.08299 | − | 0.919793i | ||||
\(289\) | −1.74766e7 | −0.724043 | ||||||||
\(290\) | 2.17873e7 | + | 3.08727e7i | 0.893325 | + | 1.26585i | ||||
\(291\) | 3.95115e7 | + | 1.45145e7i | 1.60341 | + | 0.589012i | ||||
\(292\) | − | 5.43679e6i | − | 0.218370i | ||||||
\(293\) | 1.23376e7 | 0.490487 | 0.245244 | − | 0.969462i | \(-0.421132\pi\) | ||||
0.245244 | + | 0.969462i | \(0.421132\pi\) | |||||||
\(294\) | 2.08542e7 | − | 5.67695e7i | 0.820640 | − | 2.23395i | ||||
\(295\) | 2.89107e7 | + | 4.09666e7i | 1.12614 | + | 1.59575i | ||||
\(296\) | 4.61204e6i | 0.177835i | ||||||||
\(297\) | −7.74783e6 | − | 1.37011e7i | −0.295741 | − | 0.522982i | ||||
\(298\) | − | 4.42448e7i | − | 1.67191i | ||||||
\(299\) | − | 5.65461e6i | − | 0.211538i | ||||||
\(300\) | −2.51304e7 | − | 2.08996e7i | −0.930754 | − | 0.774060i | ||||
\(301\) | −2.12977e7 | −0.780967 | ||||||||
\(302\) | 5.06981e7 | 1.84065 | ||||||||
\(303\) | 2.43682e6 | + | 895164.i | 0.0875983 | + | 0.0321792i | ||||
\(304\) | 1.06711e7 | 0.379828 | ||||||||
\(305\) | −3.16184e7 | + | 2.23135e7i | −1.11440 | + | 0.786444i | ||||
\(306\) | −1.70571e7 | − | 1.44867e7i | −0.595307 | − | 0.505599i | ||||
\(307\) | − | 3.27655e7i | − | 1.13241i | −0.824266 | − | 0.566203i | \(-0.808412\pi\) | ||
0.824266 | − | 0.566203i | \(-0.191588\pi\) | |||||||
\(308\) | −3.42707e7 | −1.17293 | ||||||||
\(309\) | −9.23326e6 | − | 3.39183e6i | −0.312953 | − | 0.114963i | ||||
\(310\) | −1.44935e7 | + | 1.02282e7i | −0.486505 | + | 0.343333i | ||||
\(311\) | − | 5.29003e7i | − | 1.75864i | −0.476230 | − | 0.879321i | \(-0.657997\pi\) | ||
0.476230 | − | 0.879321i | \(-0.342003\pi\) | |||||||
\(312\) | −4.54817e6 | − | 1.67077e6i | −0.149752 | − | 0.0550113i | ||||
\(313\) | 4.25349e7i | 1.38712i | 0.720401 | + | 0.693558i | \(0.243958\pi\) | ||||
−0.720401 | + | 0.693558i | \(0.756042\pi\) | |||||||
\(314\) | − | 6.21783e7i | − | 2.00840i | ||||||
\(315\) | −4.50741e6 | + | 5.02034e7i | −0.144210 | + | 1.60621i | ||||
\(316\) | 3.38627e7 | 1.07315 | ||||||||
\(317\) | 1.94179e7 | 0.609571 | 0.304786 | − | 0.952421i | \(-0.401415\pi\) | ||||
0.304786 | + | 0.952421i | \(0.401415\pi\) | |||||||
\(318\) | 1.59301e7 | − | 4.33650e7i | 0.495378 | − | 1.34852i | ||||
\(319\) | −2.03235e7 | −0.626076 | ||||||||
\(320\) | 3.66104e7 | − | 2.58364e7i | 1.11726 | − | 0.788464i | ||||
\(321\) | 407294. | − | 1.10874e6i | 0.0123138 | − | 0.0335208i | ||||
\(322\) | 3.32303e7i | 0.995330i | ||||||||
\(323\) | 9.02410e6 | 0.267791 | ||||||||
\(324\) | 6.66589e6 | + | 4.06309e7i | 0.195985 | + | 1.19460i | ||||
\(325\) | 1.64819e7 | + | 5.86172e6i | 0.480127 | + | 0.170756i | ||||
\(326\) | 2.21925e7i | 0.640550i | ||||||||
\(327\) | −1.46879e6 | + | 3.99835e6i | −0.0420065 | + | 0.114350i | ||||
\(328\) | − | 8.91606e6i | − | 0.252669i | ||||||
\(329\) | 8.39382e7i | 2.35707i | ||||||||
\(330\) | 3.10022e7 | − | 8.33041e6i | 0.862681 | − | 0.231806i | ||||
\(331\) | 2.37685e7 | 0.655417 | 0.327709 | − | 0.944779i | \(-0.393724\pi\) | ||||
0.327709 | + | 0.944779i | \(0.393724\pi\) | |||||||
\(332\) | −2.65694e7 | −0.726050 | ||||||||
\(333\) | −1.35782e7 | + | 1.59874e7i | −0.367714 | + | 0.432957i | ||||
\(334\) | −4.55494e7 | −1.22249 | ||||||||
\(335\) | −1.17762e7 | − | 1.66869e7i | −0.313234 | − | 0.443855i | ||||
\(336\) | −4.27845e7 | − | 1.57169e7i | −1.12790 | − | 0.414332i | ||||
\(337\) | 2.12188e7i | 0.554411i | 0.960811 | + | 0.277205i | \(0.0894082\pi\) | ||||
−0.960811 | + | 0.277205i | \(0.910592\pi\) | |||||||
\(338\) | −4.25032e7 | −1.10071 | ||||||||
\(339\) | −7.55822e6 | + | 2.05750e7i | −0.194008 | + | 0.528130i | ||||
\(340\) | 2.04214e7 | − | 1.44116e7i | 0.519576 | − | 0.366671i | ||||
\(341\) | − | 9.54104e6i | − | 0.240621i | ||||||
\(342\) | −2.31086e7 | − | 1.96264e7i | −0.577692 | − | 0.490639i | ||||
\(343\) | − | 3.90915e7i | − | 0.968724i | ||||||
\(344\) | − | 6.17170e6i | − | 0.151611i | ||||||
\(345\) | −4.42347e6 | − | 1.64623e7i | −0.107722 | − | 0.400896i | ||||
\(346\) | 3.61334e7 | 0.872330 | ||||||||
\(347\) | 4.05537e7 | 0.970604 | 0.485302 | − | 0.874347i | \(-0.338710\pi\) | ||||
0.485302 | + | 0.874347i | \(0.338710\pi\) | |||||||
\(348\) | 4.99032e7 | + | 1.83319e7i | 1.18411 | + | 0.434981i | ||||
\(349\) | 5.02250e7 | 1.18153 | 0.590763 | − | 0.806845i | \(-0.298827\pi\) | ||||
0.590763 | + | 0.806845i | \(0.298827\pi\) | |||||||
\(350\) | −9.68586e7 | − | 3.44475e7i | −2.25909 | − | 0.803439i | ||||
\(351\) | −1.08471e7 | − | 1.91818e7i | −0.250838 | − | 0.443576i | ||||
\(352\) | 3.72324e7i | 0.853676i | ||||||||
\(353\) | −3.52598e7 | −0.801596 | −0.400798 | − | 0.916166i | \(-0.631267\pi\) | ||||
−0.400798 | + | 0.916166i | \(0.631267\pi\) | |||||||
\(354\) | 1.20920e8 | + | 4.44199e7i | 2.72577 | + | 1.00131i | ||||
\(355\) | −1.09251e7 | − | 1.54809e7i | −0.244197 | − | 0.346028i | ||||
\(356\) | 4.89027e7i | 1.08388i | ||||||||
\(357\) | −3.61812e7 | − | 1.32911e7i | −0.795203 | − | 0.292117i | ||||
\(358\) | − | 2.45970e7i | − | 0.536084i | ||||||
\(359\) | 1.68991e7i | 0.365241i | 0.983184 | + | 0.182620i | \(0.0584579\pi\) | ||||
−0.983184 | + | 0.182620i | \(0.941542\pi\) | |||||||
\(360\) | −1.45481e7 | − | 1.30617e6i | −0.311816 | − | 0.0279957i | ||||
\(361\) | −3.48202e7 | −0.740133 | ||||||||
\(362\) | 3.42967e7 | 0.722980 | ||||||||
\(363\) | 1.05398e7 | − | 2.86914e7i | 0.220349 | − | 0.599836i | ||||
\(364\) | −4.79796e7 | −0.994838 | ||||||||
\(365\) | 5.05768e6 | + | 7.16677e6i | 0.104009 | + | 0.147382i | ||||
\(366\) | −3.42836e7 | + | 9.33271e7i | −0.699268 | + | 1.90355i | ||||
\(367\) | 3.38754e7i | 0.685308i | 0.939462 | + | 0.342654i | \(0.111326\pi\) | ||||
−0.939462 | + | 0.342654i | \(0.888674\pi\) | |||||||
\(368\) | 1.54144e7 | 0.309301 | ||||||||
\(369\) | 2.62496e7 | − | 3.09070e7i | 0.522449 | − | 0.615146i | ||||
\(370\) | −2.46661e7 | − | 3.49521e7i | −0.486963 | − | 0.690030i | ||||
\(371\) | − | 7.95719e7i | − | 1.55825i | ||||||
\(372\) | −8.60607e6 | + | 2.34275e7i | −0.167177 | + | 0.455090i | ||||
\(373\) | 4.90621e7i | 0.945409i | 0.881221 | + | 0.472704i | \(0.156722\pi\) | ||||
−0.881221 | + | 0.472704i | \(0.843278\pi\) | |||||||
\(374\) | 2.45484e7i | 0.469255i | ||||||||
\(375\) | 5.25691e7 | + | 4.17184e6i | 0.996866 | + | 0.0791104i | ||||
\(376\) | −2.43239e7 | −0.457582 | ||||||||
\(377\) | −2.84533e7 | −0.531017 | ||||||||
\(378\) | 6.37450e7 | + | 1.12725e8i | 1.18024 | + | 2.08711i | ||||
\(379\) | −4.36223e7 | −0.801293 | −0.400646 | − | 0.916233i | \(-0.631214\pi\) | ||||
−0.400646 | + | 0.916233i | \(0.631214\pi\) | |||||||
\(380\) | 2.76665e7 | − | 1.95246e7i | 0.504201 | − | 0.355821i | ||||
\(381\) | −1.78823e7 | − | 6.56904e6i | −0.323331 | − | 0.118775i | ||||
\(382\) | − | 1.37248e8i | − | 2.46215i | ||||||
\(383\) | 4.69624e7 | 0.835900 | 0.417950 | − | 0.908470i | \(-0.362749\pi\) | ||||
0.417950 | + | 0.908470i | \(0.362749\pi\) | |||||||
\(384\) | 1.19542e7 | − | 3.25418e7i | 0.211119 | − | 0.574709i | ||||
\(385\) | 4.51756e7 | − | 3.18810e7i | 0.791629 | − | 0.558662i | ||||
\(386\) | − | 6.56679e7i | − | 1.14180i | ||||||
\(387\) | 1.81700e7 | − | 2.13939e7i | 0.313489 | − | 0.369110i | ||||
\(388\) | 1.20786e8i | 2.06786i | ||||||||
\(389\) | − | 8.46600e7i | − | 1.43823i | −0.694889 | − | 0.719117i | \(-0.744547\pi\) | ||
0.694889 | − | 0.719117i | \(-0.255453\pi\) | |||||||
\(390\) | 4.34036e7 | − | 1.16627e7i | 0.731698 | − | 0.196610i | ||||
\(391\) | 1.30353e7 | 0.218067 | ||||||||
\(392\) | 3.01862e7 | 0.501130 | ||||||||
\(393\) | −5.97922e7 | − | 2.19646e7i | −0.985070 | − | 0.361865i | ||||
\(394\) | −1.18237e8 | −1.93315 | ||||||||
\(395\) | −4.46377e7 | + | 3.15014e7i | −0.724287 | + | 0.511139i | ||||
\(396\) | 2.92378e7 | − | 3.44255e7i | 0.470825 | − | 0.554363i | ||||
\(397\) | − | 6.77384e7i | − | 1.08259i | −0.840833 | − | 0.541294i | \(-0.817935\pi\) | ||
0.840833 | − | 0.541294i | \(-0.182065\pi\) | |||||||
\(398\) | −9.83812e7 | −1.56050 | ||||||||
\(399\) | −4.90176e7 | − | 1.80066e7i | −0.771673 | − | 0.283473i | ||||
\(400\) | −1.59789e7 | + | 4.49292e7i | −0.249671 | + | 0.702019i | ||||
\(401\) | 1.25256e8i | 1.94252i | 0.238015 | + | 0.971262i | \(0.423503\pi\) | ||||
−0.238015 | + | 0.971262i | \(0.576497\pi\) | |||||||
\(402\) | −4.92543e7 | − | 1.80935e7i | −0.758169 | − | 0.278513i | ||||
\(403\) | − | 1.33576e7i | − | 0.204087i | ||||||
\(404\) | 7.44931e6i | 0.112972i | ||||||||
\(405\) | −4.65847e7 | − | 4.73585e7i | −0.701258 | − | 0.712907i | ||||
\(406\) | 1.67211e8 | 2.49854 | ||||||||
\(407\) | 2.30089e7 | 0.341282 | ||||||||
\(408\) | 3.85154e6 | − | 1.04847e7i | 0.0567092 | − | 0.154374i | ||||
\(409\) | 1.16966e8 | 1.70958 | 0.854791 | − | 0.518972i | \(-0.173685\pi\) | ||||
0.854791 | + | 0.518972i | \(0.173685\pi\) | |||||||
\(410\) | 4.76849e7 | + | 6.75698e7i | 0.691878 | + | 0.980395i | ||||
\(411\) | 2.54454e7 | − | 6.92676e7i | 0.366509 | − | 0.997711i | ||||
\(412\) | − | 2.82259e7i | − | 0.403604i | ||||||
\(413\) | 2.21881e8 | 3.14970 | ||||||||
\(414\) | −3.33804e7 | − | 2.83503e7i | −0.470425 | − | 0.399536i | ||||
\(415\) | 3.50237e7 | − | 2.47167e7i | 0.490024 | − | 0.345816i | ||||
\(416\) | 5.21260e7i | 0.724060i | ||||||||
\(417\) | −2.67006e7 | + | 7.26846e7i | −0.368225 | + | 1.00238i | ||||
\(418\) | 3.32578e7i | 0.455370i | ||||||||
\(419\) | − | 8.41723e7i | − | 1.14427i | −0.820161 | − | 0.572133i | \(-0.806116\pi\) | ||
0.820161 | − | 0.572133i | \(-0.193884\pi\) | |||||||
\(420\) | −1.39683e8 | + | 3.75334e7i | −1.88536 | + | 0.506605i | ||||
\(421\) | −1.05982e8 | −1.42032 | −0.710161 | − | 0.704039i | \(-0.751378\pi\) | ||||
−0.710161 | + | 0.704039i | \(0.751378\pi\) | |||||||
\(422\) | −7.51515e7 | −1.00000 | ||||||||
\(423\) | −8.43173e7 | − | 7.16114e7i | −1.11403 | − | 0.946153i | ||||
\(424\) | 2.30586e7 | 0.302507 | ||||||||
\(425\) | −1.35127e7 | + | 3.79948e7i | −0.176026 | + | 0.494946i | ||||
\(426\) | −4.56946e7 | − | 1.67859e7i | −0.591067 | − | 0.217128i | ||||
\(427\) | 1.71249e8i | 2.19961i | ||||||||
\(428\) | 3.38939e6 | 0.0432305 | ||||||||
\(429\) | −8.33526e6 | + | 2.26903e7i | −0.105572 | + | 0.287388i | ||||
\(430\) | 3.30075e7 | + | 4.67719e7i | 0.415152 | + | 0.588273i | ||||
\(431\) | 6.83902e7i | 0.854205i | 0.904203 | + | 0.427103i | \(0.140466\pi\) | ||||
−0.904203 | + | 0.427103i | \(0.859534\pi\) | |||||||
\(432\) | 5.22892e7 | − | 2.95690e7i | 0.648576 | − | 0.366763i | ||||
\(433\) | 1.01612e8i | 1.25165i | 0.779964 | + | 0.625825i | \(0.215238\pi\) | ||||
−0.779964 | + | 0.625825i | \(0.784762\pi\) | |||||||
\(434\) | 7.84986e7i | 0.960268i | ||||||||
\(435\) | −8.28360e7 | + | 2.22584e7i | −1.00636 | + | 0.270412i | ||||
\(436\) | −1.22229e7 | −0.147473 | ||||||||
\(437\) | 1.76600e7 | 0.211615 | ||||||||
\(438\) | 2.11540e7 | + | 7.77089e6i | 0.251750 | + | 0.0924801i | ||||
\(439\) | −3.82362e7 | −0.451940 | −0.225970 | − | 0.974134i | \(-0.572555\pi\) | ||||
−0.225970 | + | 0.974134i | \(0.572555\pi\) | |||||||
\(440\) | 9.23856e6 | + | 1.30911e7i | 0.108454 | + | 0.153680i | ||||
\(441\) | 1.04639e8 | + | 8.88708e7i | 1.22005 | + | 1.03620i | ||||
\(442\) | 3.43683e7i | 0.398007i | ||||||||
\(443\) | −1.20185e8 | −1.38242 | −0.691210 | − | 0.722654i | \(-0.742922\pi\) | ||||
−0.691210 | + | 0.722654i | \(0.742922\pi\) | |||||||
\(444\) | −5.64972e7 | − | 2.07542e7i | −0.645473 | − | 0.237114i | ||||
\(445\) | −4.54927e7 | − | 6.44635e7i | −0.516252 | − | 0.731532i | ||||
\(446\) | − | 1.37524e8i | − | 1.55015i | ||||||
\(447\) | 9.42750e7 | + | 3.46318e7i | 1.05554 | + | 0.387751i | ||||
\(448\) | − | 1.98287e8i | − | 2.20526i | ||||||
\(449\) | 6.41137e7i | 0.708292i | 0.935190 | + | 0.354146i | \(0.115228\pi\) | ||||
−0.935190 | + | 0.354146i | \(0.884772\pi\) | |||||||
\(450\) | 1.17237e8 | − | 6.79074e7i | 1.28656 | − | 0.745211i | ||||
\(451\) | −4.44812e7 | −0.484894 | ||||||||
\(452\) | −6.28974e7 | −0.681110 | ||||||||
\(453\) | −3.96831e7 | + | 1.08026e8i | −0.426885 | + | 1.16207i | ||||
\(454\) | 1.63473e8 | 1.74694 | ||||||||
\(455\) | 6.32466e7 | − | 4.46340e7i | 0.671434 | − | 0.473839i | ||||
\(456\) | 5.21799e6 | − | 1.42044e7i | 0.0550312 | − | 0.149806i | ||||
\(457\) | − | 1.07536e8i | − | 1.12670i | −0.826219 | − | 0.563348i | \(-0.809513\pi\) | ||
0.826219 | − | 0.563348i | \(-0.190487\pi\) | |||||||
\(458\) | 5.56222e7 | 0.578964 | ||||||||
\(459\) | 4.42189e7 | − | 2.50053e7i | 0.457267 | − | 0.258580i | ||||
\(460\) | 3.99643e7 | − | 2.82033e7i | 0.410581 | − | 0.289752i | ||||
\(461\) | − | 2.74690e7i | − | 0.280376i | −0.990125 | − | 0.140188i | \(-0.955229\pi\) | ||
0.990125 | − | 0.140188i | \(-0.0447707\pi\) | |||||||
\(462\) | 4.89837e7 | − | 1.33344e8i | 0.496736 | − | 1.35222i | ||||
\(463\) | − | 1.62428e8i | − | 1.63650i | −0.574860 | − | 0.818252i | \(-0.694943\pi\) | ||
0.574860 | − | 0.818252i | \(-0.305057\pi\) | |||||||
\(464\) | − | 7.75631e7i | − | 0.776428i | ||||||
\(465\) | −1.04494e7 | − | 3.88881e7i | −0.103928 | − | 0.386774i | ||||
\(466\) | −2.27165e8 | −2.24483 | ||||||||
\(467\) | −6.70106e7 | −0.657950 | −0.328975 | − | 0.944339i | \(-0.606703\pi\) | ||||
−0.328975 | + | 0.944339i | \(0.606703\pi\) | |||||||
\(468\) | 4.09335e7 | − | 4.81963e7i | 0.399339 | − | 0.470193i | ||||
\(469\) | −9.03785e7 | −0.876085 | ||||||||
\(470\) | 1.84337e8 | − | 1.30089e8i | 1.77549 | − | 1.25299i | ||||
\(471\) | 1.32487e8 | + | 4.86690e7i | 1.26797 | + | 0.465789i | ||||
\(472\) | 6.42972e7i | 0.611457i | ||||||||
\(473\) | −3.07899e7 | −0.290954 | ||||||||
\(474\) | −4.84005e7 | + | 1.31756e8i | −0.454480 | + | 1.23719i | ||||
\(475\) | −1.83068e7 | + | 5.14747e7i | −0.170817 | + | 0.480300i | ||||
\(476\) | − | 1.10605e8i | − | 1.02554i | ||||||
\(477\) | 7.99313e7 | + | 6.78864e7i | 0.736481 | + | 0.625500i | ||||
\(478\) | 9.08996e7i | 0.832297i | ||||||||
\(479\) | 1.39226e8i | 1.26681i | 0.773819 | + | 0.633407i | \(0.218344\pi\) | ||||
−0.773819 | + | 0.633407i | \(0.781656\pi\) | |||||||
\(480\) | 4.07770e7 | + | 1.51754e8i | 0.368716 | + | 1.37220i | ||||
\(481\) | 3.22129e7 | 0.289464 | ||||||||
\(482\) | −2.90438e7 | −0.259366 | ||||||||
\(483\) | −7.08058e7 | − | 2.60105e7i | −0.628388 | − | 0.230838i | ||||
\(484\) | 8.77091e7 | 0.773586 | ||||||||
\(485\) | −1.12364e8 | − | 1.59220e8i | −0.984918 | − | 1.39564i | ||||
\(486\) | −1.67618e8 | − | 3.21382e7i | −1.46020 | − | 0.279970i | ||||
\(487\) | 3.73851e7i | 0.323677i | 0.986817 | + | 0.161838i | \(0.0517423\pi\) | ||||
−0.986817 | + | 0.161838i | \(0.948258\pi\) | |||||||
\(488\) | −4.96251e7 | −0.427014 | ||||||||
\(489\) | −4.72868e7 | − | 1.73708e7i | −0.404402 | − | 0.148557i | ||||
\(490\) | −2.28765e8 | + | 1.61442e8i | −1.94447 | + | 1.37224i | ||||
\(491\) | 1.38323e8i | 1.16856i | 0.811553 | + | 0.584278i | \(0.198622\pi\) | ||||
−0.811553 | + | 0.584278i | \(0.801378\pi\) | |||||||
\(492\) | 1.09221e8 | + | 4.01223e7i | 0.917088 | + | 0.336892i | ||||
\(493\) | − | 6.55920e7i | − | 0.547407i | ||||||
\(494\) | 4.65615e7i | 0.386230i | ||||||||
\(495\) | −6.51633e6 | + | 7.25787e7i | −0.0537263 | + | 0.598403i | ||||
\(496\) | 3.64127e7 | 0.298406 | ||||||||
\(497\) | −8.38467e7 | −0.682994 | ||||||||
\(498\) | 3.79760e7 | − | 1.03379e8i | 0.307483 | − | 0.837032i | ||||
\(499\) | 1.75601e8 | 1.41327 | 0.706634 | − | 0.707580i | \(-0.250213\pi\) | ||||
0.706634 | + | 0.707580i | \(0.250213\pi\) | |||||||
\(500\) | 4.07780e7 | + | 1.45723e8i | 0.326224 | + | 1.16578i | ||||
\(501\) | 3.56530e7 | − | 9.70549e7i | 0.283520 | − | 0.771799i | ||||
\(502\) | − | 3.00490e7i | − | 0.237530i | ||||||
\(503\) | 9.11890e7 | 0.716537 | 0.358268 | − | 0.933619i | \(-0.383367\pi\) | ||||
0.358268 | + | 0.933619i | \(0.383367\pi\) | |||||||
\(504\) | −4.18420e7 | + | 4.92659e7i | −0.326829 | + | 0.384818i | ||||
\(505\) | −6.92987e6 | − | 9.81967e6i | −0.0538085 | − | 0.0762470i | ||||
\(506\) | 4.80408e7i | 0.370817i | ||||||||
\(507\) | 3.32687e7 | − | 9.05642e7i | 0.255277 | − | 0.694916i | ||||
\(508\) | − | 5.46657e7i | − | 0.416988i | ||||||
\(509\) | − | 1.82953e7i | − | 0.138735i | −0.997591 | − | 0.0693675i | \(-0.977902\pi\) | ||
0.997591 | − | 0.0693675i | \(-0.0220981\pi\) | |||||||
\(510\) | 2.68855e7 | + | 1.00056e8i | 0.202679 | + | 0.754282i | ||||
\(511\) | 3.88162e7 | 0.290904 | ||||||||
\(512\) | −1.73403e8 | −1.29195 | ||||||||
\(513\) | 5.99070e7 | − | 3.38767e7i | 0.443737 | − | 0.250928i | ||||
\(514\) | 1.15459e8 | 0.850235 | ||||||||
\(515\) | 2.62577e7 | + | 3.72073e7i | 0.192236 | + | 0.272400i | ||||
\(516\) | 7.56028e7 | + | 2.77726e7i | 0.550287 | + | 0.202147i | ||||
\(517\) | 1.21349e8i | 0.878141i | ||||||||
\(518\) | −1.89305e8 | −1.36199 | ||||||||
\(519\) | −2.82828e7 | + | 7.69916e7i | −0.202311 | + | 0.550733i | ||||
\(520\) | 1.29342e7 | + | 1.83278e7i | 0.0919873 | + | 0.130347i | ||||
\(521\) | − | 1.08670e8i | − | 0.768416i | −0.923247 | − | 0.384208i | \(-0.874475\pi\) | ||
0.923247 | − | 0.384208i | \(-0.125525\pi\) | |||||||
\(522\) | −1.42655e8 | + | 1.67966e8i | −1.00294 | + | 1.18089i | ||||
\(523\) | − | 1.47334e8i | − | 1.02990i | −0.857219 | − | 0.514952i | \(-0.827810\pi\) | ||
0.857219 | − | 0.514952i | \(-0.172190\pi\) | |||||||
\(524\) | − | 1.82784e8i | − | 1.27041i | ||||||
\(525\) | 1.49214e8 | − | 1.79419e8i | 1.03117 | − | 1.23991i | ||||
\(526\) | 2.97969e8 | 2.04745 | ||||||||
\(527\) | 3.07927e7 | 0.210386 | ||||||||
\(528\) | −6.18533e7 | − | 2.27218e7i | −0.420205 | − | 0.154362i | ||||
\(529\) | −1.22526e8 | −0.827678 | ||||||||
\(530\) | −1.74748e8 | + | 1.23322e8i | −1.17377 | + | 0.828348i | ||||
\(531\) | −1.89296e8 | + | 2.22883e8i | −1.26432 | + | 1.48865i | ||||
\(532\) | − | 1.49846e8i | − | 0.995197i | ||||||
\(533\) | −6.22745e7 | −0.411271 | ||||||||
\(534\) | −1.90275e8 | − | 6.98974e7i | −1.24956 | − | 0.459026i | ||||
\(535\) | −4.46789e6 | + | 3.15305e6i | −0.0291770 | + | 0.0205906i | ||||
\(536\) | − | 2.61901e7i | − | 0.170076i | ||||||
\(537\) | 5.24103e7 | + | 1.92529e7i | 0.338449 | + | 0.124329i | ||||
\(538\) | 2.18857e8i | 1.40544i | ||||||||
\(539\) | − | 1.50596e8i | − | 0.961714i | ||||||
\(540\) | 8.14668e7 | − | 1.72335e8i | 0.517368 | − | 1.09444i | ||||
\(541\) | 9.02632e7 | 0.570058 | 0.285029 | − | 0.958519i | \(-0.407997\pi\) | ||||
0.285029 | + | 0.958519i | \(0.407997\pi\) | |||||||
\(542\) | 4.27250e8 | 2.68340 | ||||||||
\(543\) | −2.68451e7 | + | 7.30780e7i | −0.167674 | + | 0.456444i | ||||
\(544\) | −1.20164e8 | −0.746408 | ||||||||
\(545\) | 1.61122e7 | − | 1.13706e7i | 0.0995324 | − | 0.0702413i | ||||
\(546\) | 6.85780e7 | − | 1.86683e8i | 0.421315 | − | 1.14691i | ||||
\(547\) | 1.91691e8i | 1.17122i | 0.810592 | + | 0.585611i | \(0.199145\pi\) | ||||
−0.810592 | + | 0.585611i | \(0.800855\pi\) | |||||||
\(548\) | 2.11750e8 | 1.28671 | ||||||||
\(549\) | −1.72023e8 | − | 1.46100e8i | −1.03961 | − | 0.882946i | ||||
\(550\) | −1.40028e8 | − | 4.98004e7i | −0.841639 | − | 0.299327i | ||||
\(551\) | − | 8.88629e7i | − | 0.531209i | ||||||
\(552\) | 7.53739e6 | − | 2.05183e7i | 0.0448130 | − | 0.121990i | ||||
\(553\) | 2.41764e8i | 1.42960i | ||||||||
\(554\) | 1.17471e8i | 0.690875i | ||||||||
\(555\) | 9.37815e7 | − | 2.51995e7i | 0.548578 | − | 0.147405i | ||||
\(556\) | −2.22195e8 | −1.29274 | ||||||||
\(557\) | 1.22977e8 | 0.711634 | 0.355817 | − | 0.934556i | \(-0.384203\pi\) | ||||
0.355817 | + | 0.934556i | \(0.384203\pi\) | |||||||
\(558\) | −7.88531e7 | − | 6.69706e7i | −0.453854 | − | 0.385462i | ||||
\(559\) | −4.31064e7 | −0.246778 | ||||||||
\(560\) | 1.21671e8 | + | 1.72409e8i | 0.692826 | + | 0.981739i | ||||
\(561\) | −5.23068e7 | − | 1.92149e7i | −0.296258 | − | 0.108830i | ||||
\(562\) | − | 2.75538e8i | − | 1.55229i | ||||||
\(563\) | −1.42149e7 | −0.0796559 | −0.0398279 | − | 0.999207i | \(-0.512681\pi\) | ||||
−0.0398279 | + | 0.999207i | \(0.512681\pi\) | |||||||
\(564\) | 1.09457e8 | − | 2.97965e8i | 0.610109 | − | 1.66084i | ||||
\(565\) | 8.29113e7 | − | 5.85115e7i | 0.459693 | − | 0.324411i | ||||
\(566\) | 3.82200e8i | 2.10786i | ||||||||
\(567\) | −2.90086e8 | + | 4.75914e7i | −1.59139 | + | 0.261083i | ||||
\(568\) | − | 2.42973e7i | − | 0.132591i | ||||||
\(569\) | − | 1.16372e8i | − | 0.631699i | −0.948809 | − | 0.315849i | \(-0.897711\pi\) | ||
0.948809 | − | 0.315849i | \(-0.102289\pi\) | |||||||
\(570\) | 3.64240e7 | + | 1.35554e8i | 0.196681 | + | 0.731963i | ||||
\(571\) | −2.29444e8 | −1.23245 | −0.616225 | − | 0.787570i | \(-0.711339\pi\) | ||||
−0.616225 | + | 0.787570i | \(0.711339\pi\) | |||||||
\(572\) | −6.93637e7 | −0.370633 | ||||||||
\(573\) | 2.92442e8 | + | 1.07428e8i | 1.55445 | + | 0.571024i | ||||
\(574\) | 3.65967e8 | 1.93511 | ||||||||
\(575\) | −2.64442e7 | + | 7.43552e7i | −0.139100 | + | 0.391118i | ||||
\(576\) | 1.99182e8 | + | 1.69167e8i | 1.04228 | + | 0.885214i | ||||
\(577\) | − | 1.79763e8i | − | 0.935779i | −0.883787 | − | 0.467890i | \(-0.845014\pi\) | ||
0.883787 | − | 0.467890i | \(-0.154986\pi\) | |||||||
\(578\) | 2.07874e8 | 1.07651 | ||||||||
\(579\) | 1.39922e8 | + | 5.14004e7i | 0.720861 | + | 0.264808i | ||||
\(580\) | −1.41916e8 | − | 2.01095e8i | −0.727355 | − | 1.03067i | ||||
\(581\) | − | 1.89693e8i | − | 0.967214i | ||||||
\(582\) | −4.69965e8 | − | 1.72641e8i | −2.38395 | − | 0.875741i | ||||
\(583\) | − | 1.15037e8i | − | 0.580537i | ||||||
\(584\) | 1.12483e7i | 0.0564738i | ||||||||
\(585\) | −9.12297e6 | + | 1.01611e8i | −0.0455689 | + | 0.507546i | ||||
\(586\) | −1.46748e8 | −0.729255 | ||||||||
\(587\) | −2.09507e7 | −0.103582 | −0.0517911 | − | 0.998658i | \(-0.516493\pi\) | ||||
−0.0517911 | + | 0.998658i | \(0.516493\pi\) | |||||||
\(588\) | −1.35838e8 | + | 3.69779e8i | −0.668174 | + | 1.81891i | ||||
\(589\) | 4.17174e7 | 0.204160 | ||||||||
\(590\) | −3.43874e8 | − | 4.87272e8i | −1.67434 | − | 2.37255i | ||||
\(591\) | 9.25481e7 | − | 2.51935e8i | 0.448338 | − | 1.22047i | ||||
\(592\) | 8.78119e7i | 0.423241i | ||||||||
\(593\) | −7.12863e6 | −0.0341855 | −0.0170928 | − | 0.999854i | \(-0.505441\pi\) | ||||
−0.0170928 | + | 0.999854i | \(0.505441\pi\) | |||||||
\(594\) | 9.21557e7 | + | 1.62966e8i | 0.439706 | + | 0.777568i | ||||
\(595\) | 1.02893e8 | + | 1.45799e8i | 0.488465 | + | 0.692158i | ||||
\(596\) | 2.88197e8i | 1.36129i | ||||||||
\(597\) | 7.70062e7 | − | 2.09627e8i | 0.361912 | − | 0.985198i | ||||
\(598\) | 6.72580e7i | 0.314515i | ||||||||
\(599\) | 1.78170e8i | 0.829001i | 0.910049 | + | 0.414500i | \(0.136044\pi\) | ||||
−0.910049 | + | 0.414500i | \(0.863956\pi\) | |||||||
\(600\) | 5.19926e7 | + | 4.32396e7i | 0.240707 | + | 0.200183i | ||||
\(601\) | −5.30074e7 | −0.244182 | −0.122091 | − | 0.992519i | \(-0.538960\pi\) | ||||
−0.122091 | + | 0.992519i | \(0.538960\pi\) | |||||||
\(602\) | 2.53323e8 | 1.16114 | ||||||||
\(603\) | 7.71059e7 | − | 9.07866e7i | 0.351670 | − | 0.414066i | ||||
\(604\) | −3.30232e8 | −1.49868 | ||||||||
\(605\) | −1.15618e8 | + | 8.15931e7i | −0.522107 | + | 0.368457i | ||||
\(606\) | −2.89845e7 | − | 1.06474e7i | −0.130241 | − | 0.0478439i | ||||
\(607\) | − | 1.06802e8i | − | 0.477543i | −0.971076 | − | 0.238772i | \(-0.923255\pi\) | ||
0.971076 | − | 0.238772i | \(-0.0767447\pi\) | |||||||
\(608\) | −1.62795e8 | −0.724322 | ||||||||
\(609\) | −1.30881e8 | + | 3.56286e8i | −0.579464 | + | 1.57742i | ||||
\(610\) | 3.76081e8 | − | 2.65405e8i | 1.65688 | − | 1.16928i | ||||
\(611\) | 1.69891e8i | 0.744810i | ||||||||
\(612\) | 1.11105e8 | + | 9.43621e7i | 0.484705 | + | 0.411664i | ||||
\(613\) | 2.08653e8i | 0.905822i | 0.891556 | + | 0.452911i | \(0.149614\pi\) | ||||
−0.891556 | + | 0.452911i | \(0.850386\pi\) | |||||||
\(614\) | 3.89725e8i | 1.68366i | ||||||||
\(615\) | −1.81300e8 | + | 4.87159e7i | −0.779420 | + | 0.209433i | ||||
\(616\) | 7.09032e7 | 0.303336 | ||||||||
\(617\) | 5.25824e6 | 0.0223864 | 0.0111932 | − | 0.999937i | \(-0.496437\pi\) | ||||
0.0111932 | + | 0.999937i | \(0.496437\pi\) | |||||||
\(618\) | 1.09824e8 | + | 4.03437e7i | 0.465298 | + | 0.170927i | ||||
\(619\) | 2.96719e8 | 1.25105 | 0.625523 | − | 0.780205i | \(-0.284886\pi\) | ||||
0.625523 | + | 0.780205i | \(0.284886\pi\) | |||||||
\(620\) | 9.44059e7 | − | 6.66235e7i | 0.396118 | − | 0.279545i | ||||
\(621\) | 8.65356e7 | − | 4.89349e7i | 0.361343 | − | 0.204336i | ||||
\(622\) | 6.29217e8i | 2.61474i | ||||||||
\(623\) | −3.49143e8 | −1.44391 | ||||||||
\(624\) | −8.65957e7 | − | 3.18109e7i | −0.356404 | − | 0.130925i | ||||
\(625\) | −1.89315e8 | − | 1.54157e8i | −0.775435 | − | 0.631428i | ||||
\(626\) | − | 5.05927e8i | − | 2.06236i | ||||||
\(627\) | −7.08643e7 | − | 2.60320e7i | −0.287492 | − | 0.105610i | ||||
\(628\) | 4.05010e8i | 1.63526i | ||||||||
\(629\) | 7.42590e7i | 0.298399i | ||||||||
\(630\) | 5.36128e7 | − | 5.97138e8i | 0.214411 | − | 2.38810i | ||||
\(631\) | 2.08250e8 | 0.828891 | 0.414446 | − | 0.910074i | \(-0.363975\pi\) | ||||
0.414446 | + | 0.910074i | \(0.363975\pi\) | |||||||
\(632\) | −7.00590e7 | −0.277532 | ||||||||
\(633\) | 5.88236e7 | − | 1.60130e8i | 0.231921 | − | 0.631337i | ||||
\(634\) | −2.30964e8 | −0.906309 | ||||||||
\(635\) | 5.08539e7 | + | 7.20603e7i | 0.198611 | + | 0.281433i | ||||
\(636\) | −1.03764e8 | + | 2.82466e8i | −0.403342 | + | 1.09798i | ||||
\(637\) | − | 2.10837e8i | − | 0.815695i | ||||||
\(638\) | 2.41736e8 | 0.930848 | ||||||||
\(639\) | 7.15334e7 | − | 8.42254e7i | 0.274161 | − | 0.322805i | ||||
\(640\) | −1.31134e8 | + | 9.25429e7i | −0.500236 | + | 0.353023i | ||||
\(641\) | − | 4.68502e8i | − | 1.77884i | −0.457088 | − | 0.889421i | \(-0.651108\pi\) | ||
0.457088 | − | 0.889421i | \(-0.348892\pi\) | |||||||
\(642\) | −4.84451e6 | + | 1.31878e7i | −0.0183082 | + | 0.0498386i | ||||
\(643\) | − | 6.77858e7i | − | 0.254980i | −0.991840 | − | 0.127490i | \(-0.959308\pi\) | ||
0.991840 | − | 0.127490i | \(-0.0406921\pi\) | |||||||
\(644\) | − | 2.16452e8i | − | 0.810408i | ||||||
\(645\) | −1.25496e8 | + | 3.37212e7i | −0.467681 | + | 0.125668i | ||||
\(646\) | −1.07336e8 | −0.398151 | ||||||||
\(647\) | 3.49360e8 | 1.28991 | 0.644956 | − | 0.764220i | \(-0.276876\pi\) | ||||
0.644956 | + | 0.764220i | \(0.276876\pi\) | |||||||
\(648\) | −1.37912e7 | − | 8.40619e7i | −0.0506846 | − | 0.308940i | ||||
\(649\) | 3.20771e8 | 1.17344 | ||||||||
\(650\) | −1.96041e8 | − | 6.97215e7i | −0.713851 | − | 0.253879i | ||||
\(651\) | −1.67262e8 | − | 6.14434e7i | −0.606252 | − | 0.222706i | ||||
\(652\) | − | 1.44555e8i | − | 0.521543i | ||||||
\(653\) | −1.61388e8 | −0.579604 | −0.289802 | − | 0.957087i | \(-0.593589\pi\) | ||||
−0.289802 | + | 0.957087i | \(0.593589\pi\) | |||||||
\(654\) | 1.74704e7 | − | 4.75579e7i | 0.0624552 | − | 0.170016i | ||||
\(655\) | 1.70038e8 | + | 2.40945e8i | 0.605093 | + | 0.857421i | ||||
\(656\) | − | 1.69759e8i | − | 0.601342i | ||||||
\(657\) | −3.31158e7 | + | 3.89915e7i | −0.116772 | + | 0.137491i | ||||
\(658\) | − | 9.98393e8i | − | 3.50448i | ||||||
\(659\) | − | 9.59866e7i | − | 0.335393i | −0.985839 | − | 0.167697i | \(-0.946367\pi\) | ||
0.985839 | − | 0.167697i | \(-0.0536329\pi\) | |||||||
\(660\) | −2.01939e8 | + | 5.42617e7i | −0.702405 | + | 0.188739i | ||||
\(661\) | 1.66521e8 | 0.576586 | 0.288293 | − | 0.957542i | \(-0.406912\pi\) | ||||
0.288293 | + | 0.957542i | \(0.406912\pi\) | |||||||
\(662\) | −2.82712e8 | −0.974473 | ||||||||
\(663\) | −7.32305e7 | − | 2.69012e7i | −0.251276 | − | 0.0923062i | ||||
\(664\) | 5.49698e7 | 0.187767 | ||||||||
\(665\) | 1.39397e8 | + | 1.97526e8i | 0.474011 | + | 0.671677i | ||||
\(666\) | 1.61505e8 | − | 1.90160e8i | 0.546717 | − | 0.643720i | ||||
\(667\) | − | 1.28362e8i | − | 0.432574i | ||||||
\(668\) | 2.96695e8 | 0.995361 | ||||||||
\(669\) | 2.93031e8 | + | 1.07645e8i | 0.978669 | + | 0.359513i | ||||
\(670\) | 1.40070e8 | + | 1.98480e8i | 0.465716 | + | 0.659923i | ||||
\(671\) | 2.47574e8i | 0.819478i | ||||||||
\(672\) | 6.52711e8 | + | 2.39773e8i | 2.15087 | + | 0.790119i | ||||
\(673\) | 3.63557e8i | 1.19269i | 0.802728 | + | 0.596345i | \(0.203381\pi\) | ||||
−0.802728 | + | 0.596345i | \(0.796619\pi\) | |||||||
\(674\) | − | 2.52385e8i | − | 0.824296i | ||||||
\(675\) | 5.29287e7 | + | 3.02958e8i | 0.172100 | + | 0.985080i | ||||
\(676\) | 2.76853e8 | 0.896208 | ||||||||
\(677\) | −4.99793e8 | −1.61074 | −0.805368 | − | 0.592775i | \(-0.798032\pi\) | ||||
−0.805368 | + | 0.592775i | \(0.798032\pi\) | |||||||
\(678\) | 8.99003e7 | − | 2.44727e8i | 0.288451 | − | 0.785223i | ||||
\(679\) | −8.62356e8 | −2.75472 | ||||||||
\(680\) | −4.22502e7 | + | 2.98165e7i | −0.134370 | + | 0.0948265i | ||||
\(681\) | −1.27956e8 | + | 3.48321e8i | −0.405152 | + | 1.10291i | ||||
\(682\) | 1.13485e8i | 0.357754i | ||||||||
\(683\) | −262982. | −0.000825399 | −0.000412700 | − | 1.00000i | \(-0.500131\pi\) | ||||
−0.000412700 | 1.00000i | \(0.500131\pi\) | ||||||||
\(684\) | 1.50522e8 | + | 1.27840e8i | 0.470363 | + | 0.399483i | ||||
\(685\) | −2.79128e8 | + | 1.96984e8i | −0.868425 | + | 0.612858i | ||||
\(686\) | 4.64969e8i | 1.44030i | ||||||||
\(687\) | −4.35373e7 | + | 1.18518e8i | −0.134274 | + | 0.365521i | ||||
\(688\) | − | 1.17507e8i | − | 0.360827i | ||||||
\(689\) | − | 1.61053e8i | − | 0.492393i | ||||||
\(690\) | 5.26145e7 | + | 1.95808e8i | 0.160161 | + | 0.596052i | ||||
\(691\) | −4.32873e8 | −1.31198 | −0.655989 | − | 0.754770i | \(-0.727748\pi\) | ||||
−0.655989 | + | 0.754770i | \(0.727748\pi\) | |||||||
\(692\) | −2.35362e8 | −0.710260 | ||||||||
\(693\) | 2.45782e8 | + | 2.08745e8i | 0.738500 | + | 0.627214i | ||||
\(694\) | −4.82361e8 | −1.44309 | ||||||||
\(695\) | 2.92897e8 | − | 2.06702e8i | 0.872492 | − | 0.615729i | ||||
\(696\) | −1.03246e8 | − | 3.79272e7i | −0.306227 | − | 0.112492i | ||||
\(697\) | − | 1.43558e8i | − | 0.423965i | ||||||
\(698\) | −5.97395e8 | −1.75669 | ||||||||
\(699\) | 1.77809e8 | − | 4.84033e8i | 0.520622 | − | 1.41724i | ||||
\(700\) | 6.30907e8 | + | 2.24380e8i | 1.83938 | + | 0.654169i | ||||
\(701\) | 3.96250e8i | 1.15031i | 0.818044 | + | 0.575155i | \(0.195058\pi\) | ||||
−0.818044 | + | 0.575155i | \(0.804942\pi\) | |||||||
\(702\) | 1.29020e8 | + | 2.28156e8i | 0.372945 | + | 0.659508i | ||||
\(703\) | 1.00605e8i | 0.289569i | ||||||||
\(704\) | − | 2.86661e8i | − | 0.821583i | ||||||
\(705\) | 1.32902e8 | + | 4.94602e8i | 0.379283 | + | 1.41153i | ||||
\(706\) | 4.19393e8 | 1.19181 | ||||||||
\(707\) | −5.31846e7 | −0.150497 | ||||||||
\(708\) | −7.87635e8 | − | 2.89337e8i | −2.21935 | − | 0.815276i | ||||
\(709\) | −4.09941e7 | −0.115022 | −0.0575112 | − | 0.998345i | \(-0.518316\pi\) | ||||
−0.0575112 | + | 0.998345i | \(0.518316\pi\) | |||||||
\(710\) | 1.29947e8 | + | 1.84136e8i | 0.363071 | + | 0.514474i | ||||
\(711\) | −2.42856e8 | − | 2.06260e8i | −0.675678 | − | 0.573859i | ||||
\(712\) | − | 1.01176e8i | − | 0.280308i | ||||||
\(713\) | 6.02608e7 | 0.166252 | ||||||||
\(714\) | 4.30352e8 | + | 1.58090e8i | 1.18231 | + | 0.434319i | ||||
\(715\) | 9.14352e7 | − | 6.45270e7i | 0.250147 | − | 0.176532i | ||||
\(716\) | 1.60217e8i | 0.436486i | ||||||||
\(717\) | −1.93685e8 | − | 7.11501e7i | −0.525459 | − | 0.193027i | ||||
\(718\) | − | 2.01004e8i | − | 0.543039i | ||||||
\(719\) | 4.41110e8i | 1.18675i | 0.804925 | + | 0.593377i | \(0.202206\pi\) | ||||
−0.804925 | + | 0.593377i | \(0.797794\pi\) | |||||||
\(720\) | −2.76991e8 | − | 2.48691e7i | −0.742110 | − | 0.0666288i | ||||
\(721\) | 2.01520e8 | 0.537665 | ||||||||
\(722\) | 4.14165e8 | 1.10043 | ||||||||
\(723\) | 2.27335e7 | − | 6.18854e7i | 0.0601523 | − | 0.163747i | ||||
\(724\) | −2.23398e8 | −0.588658 | ||||||||
\(725\) | 3.74146e8 | + | 1.33064e8i | 0.981809 | + | 0.349178i | ||||
\(726\) | −1.25364e8 | + | 3.41267e8i | −0.327615 | + | 0.891834i | ||||
\(727\) | − | 2.20449e8i | − | 0.573726i | −0.957972 | − | 0.286863i | \(-0.907388\pi\) | ||
0.957972 | − | 0.286863i | \(-0.0926124\pi\) | |||||||
\(728\) | 9.92657e7 | 0.257279 | ||||||||
\(729\) | 1.99679e8 | − | 3.31998e8i | 0.515406 | − | 0.856946i | ||||
\(730\) | −6.01580e7 | − | 8.52442e7i | −0.154641 | − | 0.219127i | ||||
\(731\) | − | 9.93712e7i | − | 0.254395i | ||||||
\(732\) | 2.23313e8 | − | 6.07903e8i | 0.569352 | − | 1.54989i | ||||
\(733\) | − | 5.85539e8i | − | 1.48677i | −0.668863 | − | 0.743385i | \(-0.733219\pi\) | ||
0.668863 | − | 0.743385i | \(-0.266781\pi\) | |||||||
\(734\) | − | 4.02927e8i | − | 1.01891i | ||||||
\(735\) | −1.64933e8 | − | 6.13808e8i | −0.415379 | − | 1.54586i | ||||
\(736\) | −2.35158e8 | −0.589829 | ||||||||
\(737\) | −1.30659e8 | −0.326391 | ||||||||
\(738\) | −3.12223e8 | + | 3.67620e8i | −0.776776 | + | 0.914598i | ||||
\(739\) | 2.72485e6 | 0.00675164 | 0.00337582 | − | 0.999994i | \(-0.498925\pi\) | ||||
0.00337582 | + | 0.999994i | \(0.498925\pi\) | |||||||
\(740\) | 1.60668e8 | + | 2.27667e8i | 0.396491 | + | 0.561830i | ||||
\(741\) | −9.92114e7 | − | 3.64452e7i | −0.243841 | − | 0.0895748i | ||||
\(742\) | 9.46459e8i | 2.31681i | ||||||||
\(743\) | 6.73301e8 | 1.64151 | 0.820753 | − | 0.571283i | \(-0.193554\pi\) | ||||
0.820753 | + | 0.571283i | \(0.193554\pi\) | |||||||
\(744\) | 1.78052e7 | − | 4.84695e7i | 0.0432344 | − | 0.117693i | ||||
\(745\) | −2.68101e8 | − | 3.79900e8i | −0.648379 | − | 0.918758i | ||||
\(746\) | − | 5.83563e8i | − | 1.40563i | ||||||
\(747\) | 1.90550e8 | + | 1.61836e8i | 0.457137 | + | 0.388251i | ||||
\(748\) | − | 1.59901e8i | − | 0.382073i | ||||||
\(749\) | 2.41987e7i | 0.0575899i | ||||||||
\(750\) | −6.25277e8 | − | 4.96214e7i | −1.48214 | − | 0.117621i | ||||
\(751\) | 8.01454e8 | 1.89216 | 0.946082 | − | 0.323927i | \(-0.105003\pi\) | ||||
0.946082 | + | 0.323927i | \(0.105003\pi\) | |||||||
\(752\) | −4.63119e8 | −1.08903 | ||||||||
\(753\) | 6.40272e7 | + | 2.35203e7i | 0.149961 | + | 0.0550882i | ||||
\(754\) | 3.38434e8 | 0.789515 | ||||||||
\(755\) | 4.35311e8 | − | 3.07205e8i | 1.01148 | − | 0.713817i | ||||
\(756\) | −4.15215e8 | − | 7.34258e8i | −0.960965 | − | 1.69935i | ||||
\(757\) | 5.24719e8i | 1.20959i | 0.796380 | + | 0.604797i | \(0.206746\pi\) | ||||
−0.796380 | + | 0.604797i | \(0.793254\pi\) | |||||||
\(758\) | 5.18861e8 | 1.19136 | ||||||||
\(759\) | −1.02363e8 | − | 3.76031e7i | −0.234110 | − | 0.0860001i | ||||
\(760\) | −5.72398e7 | + | 4.03948e7i | −0.130394 | + | 0.0920206i | ||||
\(761\) | 1.32891e8i | 0.301538i | 0.988569 | + | 0.150769i | \(0.0481750\pi\) | ||||
−0.988569 | + | 0.150769i | \(0.951825\pi\) | |||||||
\(762\) | 2.12698e8 | + | 7.81346e7i | 0.480728 | + | 0.176595i | ||||
\(763\) | − | 8.72657e7i | − | 0.196458i | ||||||
\(764\) | 8.93988e8i | 2.00471i | ||||||||
\(765\) | −2.34240e8 | − | 2.10308e7i | −0.523211 | − | 0.0469754i | ||||
\(766\) | −5.58589e8 | −1.24281 | ||||||||
\(767\) | 4.49085e8 | 0.995274 | ||||||||
\(768\) | 7.14064e7 | − | 1.94383e8i | 0.157635 | − | 0.429116i | ||||
\(769\) | −2.57071e8 | −0.565294 | −0.282647 | − | 0.959224i | \(-0.591212\pi\) | ||||
−0.282647 | + | 0.959224i | \(0.591212\pi\) | |||||||
\(770\) | −5.37335e8 | + | 3.79204e8i | −1.17699 | + | 0.830618i | ||||
\(771\) | −9.03737e7 | + | 2.46016e8i | −0.197187 | + | 0.536784i | ||||
\(772\) | 4.27740e8i | 0.929668i | ||||||||
\(773\) | −7.62255e8 | −1.65029 | −0.825147 | − | 0.564917i | \(-0.808908\pi\) | ||||
−0.825147 | + | 0.564917i | \(0.808908\pi\) | |||||||
\(774\) | −2.16121e8 | + | 2.54467e8i | −0.466094 | + | 0.548792i | ||||
\(775\) | −6.24680e7 | + | 1.75646e8i | −0.134200 | + | 0.377340i | ||||
\(776\) | − | 2.49896e8i | − | 0.534779i | ||||||
\(777\) | 1.48175e8 | − | 4.03364e8i | 0.315873 | − | 0.859872i | ||||
\(778\) | 1.00698e9i | 2.13836i | ||||||||
\(779\) | − | 1.94490e8i | − | 0.411420i | ||||||
\(780\) | −2.82718e8 | + | 7.59674e7i | −0.595757 | + | 0.160082i | ||||
\(781\) | −1.21217e8 | −0.254454 | ||||||||
\(782\) | −1.55047e8 | −0.324222 | ||||||||
\(783\) | −2.46235e8 | − | 4.35436e8i | −0.512937 | − | 0.907067i | ||||
\(784\) | 5.74737e8 | 1.19267 | ||||||||
\(785\) | −3.76768e8 | − | 5.33883e8i | −0.778871 | − | 1.10367i | ||||
\(786\) | 7.11192e8 | + | 2.61256e8i | 1.46460 | + | 0.538020i | ||||
\(787\) | − | 6.33980e8i | − | 1.30062i | −0.759667 | − | 0.650312i | \(-0.774638\pi\) | ||
0.759667 | − | 0.650312i | \(-0.225362\pi\) | |||||||
\(788\) | 7.70160e8 | 1.57399 | ||||||||
\(789\) | −2.33230e8 | + | 6.34900e8i | −0.474847 | + | 1.29263i | ||||
\(790\) | 5.30938e8 | − | 3.74690e8i | 1.07687 | − | 0.759960i | ||||
\(791\) | − | 4.49058e8i | − | 0.907347i | ||||||
\(792\) | −6.04907e7 | + | 7.12234e7i | −0.121762 | + | 0.143366i | ||||
\(793\) | 3.46608e8i | 0.695054i | ||||||||
\(794\) | 8.05706e8i | 1.60959i | ||||||||
\(795\) | −1.25988e8 | − | 4.68874e8i | −0.250743 | − | 0.933157i | ||||
\(796\) | 6.40824e8 | 1.27057 | ||||||||
\(797\) | −1.28919e8 | −0.254649 | −0.127325 | − | 0.991861i | \(-0.540639\pi\) | ||||
−0.127325 | + | 0.991861i | \(0.540639\pi\) | |||||||
\(798\) | 5.83034e8 | + | 2.14177e8i | 1.14732 | + | 0.421467i | ||||
\(799\) | −3.91641e8 | −0.767799 | ||||||||
\(800\) | 2.43771e8 | − | 6.85430e8i | 0.476116 | − | 1.33873i | ||||
\(801\) | 2.97869e8 | − | 3.50720e8i | 0.579600 | − | 0.682437i | ||||
\(802\) | − | 1.48985e9i | − | 2.88814i | ||||||
\(803\) | 5.61162e7 | 0.108378 | ||||||||
\(804\) | 3.20827e8 | + | 1.17856e8i | 0.617309 | + | 0.226768i | ||||
\(805\) | 2.01359e8 | + | 2.85327e8i | 0.385996 | + | 0.546959i | ||||
\(806\) | 1.58881e8i | 0.303435i | ||||||||
\(807\) | −4.66331e8 | − | 1.71307e8i | −0.887307 | − | 0.325952i | ||||
\(808\) | − | 1.54120e7i | − | 0.0292163i | ||||||
\(809\) | − | 1.31019e7i | − | 0.0247451i | −0.999923 | − | 0.0123726i | \(-0.996062\pi\) | ||
0.999923 | − | 0.0123726i | \(-0.00393841\pi\) | |||||||
\(810\) | 5.54096e8 | + | 5.63300e8i | 1.04263 | + | 1.05995i | ||||
\(811\) | 6.44274e8 | 1.20784 | 0.603918 | − | 0.797047i | \(-0.293605\pi\) | ||||
0.603918 | + | 0.797047i | \(0.293605\pi\) | |||||||
\(812\) | −1.08916e9 | −2.03434 | ||||||||
\(813\) | −3.34423e8 | + | 9.10368e8i | −0.622335 | + | 1.69412i | ||||
\(814\) | −2.73677e8 | −0.507417 | ||||||||
\(815\) | 1.34475e8 | + | 1.90552e8i | 0.248410 | + | 0.351998i | ||||
\(816\) | 7.33321e7 | − | 1.99625e8i | 0.134966 | − | 0.367405i | ||||
\(817\) | − | 1.34626e8i | − | 0.246867i | ||||||
\(818\) | −1.39124e9 | −2.54180 | ||||||||
\(819\) | 3.44099e8 | + | 2.92246e8i | 0.626371 | + | 0.531983i | ||||
\(820\) | −3.10605e8 | − | 4.40129e8i | −0.563334 | − | 0.798249i | ||||
\(821\) | 9.84742e8i | 1.77948i | 0.456468 | + | 0.889740i | \(0.349114\pi\) | ||||
−0.456468 | + | 0.889740i | \(0.650886\pi\) | |||||||
\(822\) | −3.02657e8 | + | 8.23896e8i | −0.544924 | + | 1.48339i | ||||
\(823\) | 4.83684e8i | 0.867686i | 0.900989 | + | 0.433843i | \(0.142843\pi\) | ||||
−0.900989 | + | 0.433843i | \(0.857157\pi\) | |||||||
\(824\) | 5.83970e7i | 0.104378i | ||||||||
\(825\) | 2.15717e8 | − | 2.59385e8i | 0.384169 | − | 0.461937i | ||||
\(826\) | −2.63913e9 | −4.68296 | ||||||||
\(827\) | 3.06240e8 | 0.541434 | 0.270717 | − | 0.962659i | \(-0.412739\pi\) | ||||
0.270717 | + | 0.962659i | \(0.412739\pi\) | |||||||
\(828\) | 2.17430e8 | + | 1.84665e8i | 0.383025 | + | 0.325307i | ||||
\(829\) | 5.74507e8 | 1.00840 | 0.504199 | − | 0.863588i | \(-0.331788\pi\) | ||||
0.504199 | + | 0.863588i | \(0.331788\pi\) | |||||||
\(830\) | −4.16585e8 | + | 2.93989e8i | −0.728567 | + | 0.514159i | ||||
\(831\) | −2.50301e8 | − | 9.19480e7i | −0.436174 | − | 0.160228i | ||||
\(832\) | − | 4.01331e8i | − | 0.696840i | ||||||
\(833\) | 4.86032e8 | 0.840871 | ||||||||
\(834\) | 3.17587e8 | − | 8.64538e8i | 0.547476 | − | 1.49034i | ||||
\(835\) | −3.91103e8 | + | 2.76006e8i | −0.671787 | + | 0.474089i | ||||
\(836\) | − | 2.16631e8i | − | 0.370767i | ||||||
\(837\) | 2.04419e8 | − | 1.15597e8i | 0.348614 | − | 0.197138i | ||||
\(838\) | 1.00118e9i | 1.70129i | ||||||||
\(839\) | − | 4.06052e8i | − | 0.687537i | −0.939054 | − | 0.343768i | \(-0.888296\pi\) | ||
0.939054 | − | 0.343768i | \(-0.111704\pi\) | |||||||
\(840\) | 2.88992e8 | − | 7.76534e7i | 0.487583 | − | 0.131015i | ||||
\(841\) | −5.10802e7 | −0.0858746 | ||||||||
\(842\) | 1.26059e9 | 2.11173 | ||||||||
\(843\) | 5.87105e8 | + | 2.15673e8i | 0.980017 | + | 0.360008i | ||||
\(844\) | 4.89514e8 | 0.814212 | ||||||||
\(845\) | −3.64947e8 | + | 2.57548e8i | −0.604867 | + | 0.426862i | ||||
\(846\) | 1.00290e9 | + | 8.51774e8i | 1.65633 | + | 1.40674i | ||||
\(847\) | 6.26202e8i | 1.03054i | ||||||||
\(848\) | 4.39028e8 | 0.719954 | ||||||||
\(849\) | −8.14376e8 | − | 2.99161e8i | −1.33077 | − | 0.488856i | ||||
\(850\) | 1.60726e8 | − | 4.51925e8i | 0.261715 | − | 0.735884i | ||||
\(851\) | 1.45323e8i | 0.235802i | ||||||||
\(852\) | 2.97641e8 | + | 1.09338e8i | 0.481253 | + | 0.176788i | ||||
\(853\) | − | 7.67399e8i | − | 1.23644i | −0.786004 | − | 0.618221i | \(-0.787854\pi\) | ||
0.786004 | − | 0.618221i | \(-0.212146\pi\) | |||||||
\(854\) | − | 2.03690e9i | − | 3.27037i | ||||||
\(855\) | −3.17344e8 | − | 2.84921e7i | −0.507729 | − | 0.0455854i | ||||
\(856\) | −7.01236e6 | −0.0111800 | ||||||||
\(857\) | 2.99694e8 | 0.476141 | 0.238070 | − | 0.971248i | \(-0.423485\pi\) | ||||
0.238070 | + | 0.971248i | \(0.423485\pi\) | |||||||
\(858\) | 9.91427e7 | − | 2.69887e8i | 0.156964 | − | 0.427287i | ||||
\(859\) | −2.47498e8 | −0.390474 | −0.195237 | − | 0.980756i | \(-0.562548\pi\) | ||||
−0.195237 | + | 0.980756i | \(0.562548\pi\) | |||||||
\(860\) | −2.15001e8 | − | 3.04657e8i | −0.338021 | − | 0.478979i | ||||
\(861\) | −2.86455e8 | + | 7.79788e8i | −0.448793 | + | 1.22171i | ||||
\(862\) | − | 8.13459e8i | − | 1.27003i | ||||||
\(863\) | −5.04285e8 | −0.784592 | −0.392296 | − | 0.919839i | \(-0.628319\pi\) | ||||
−0.392296 | + | 0.919839i | \(0.628319\pi\) | |||||||
\(864\) | −7.97713e8 | + | 4.51098e8i | −1.23682 | + | 0.699407i | ||||
\(865\) | 3.10254e8 | − | 2.18950e8i | 0.479367 | − | 0.338296i | ||||
\(866\) | − | 1.20862e9i | − | 1.86095i | ||||||
\(867\) | −1.62710e8 | + | 4.42929e8i | −0.249664 | + | 0.679637i | ||||
\(868\) | − | 5.11315e8i | − | 0.781861i | ||||||
\(869\) | 3.49516e8i | 0.532608i | ||||||||
\(870\) | 9.85283e8 | − | 2.64750e8i | 1.49625 | − | 0.402048i | ||||
\(871\) | −1.82926e8 | −0.276834 | ||||||||
\(872\) | 2.52881e7 | 0.0381388 | ||||||||
\(873\) | 7.35715e8 | − | 8.66251e8i | 1.10577 | − | 1.30197i | ||||
\(874\) | −2.10055e8 | −0.314628 | ||||||||
\(875\) | −1.04039e9 | + | 2.91136e8i | −1.55301 | + | 0.434582i | ||||
\(876\) | −1.37790e8 | − | 5.06172e7i | −0.204978 | − | 0.0752983i | ||||
\(877\) | 1.25925e9i | 1.86686i | 0.358755 | + | 0.933432i | \(0.383201\pi\) | ||||
−0.358755 | + | 0.933432i | \(0.616799\pi\) | |||||||
\(878\) | 4.54795e8 | 0.671943 | ||||||||
\(879\) | 1.14864e8 | − | 3.12685e8i | 0.169129 | − | 0.460405i | ||||
\(880\) | 1.75899e8 | + | 2.49251e8i | 0.258117 | + | 0.365753i | ||||
\(881\) | − | 3.01970e7i | − | 0.0441608i | −0.999756 | − | 0.0220804i | \(-0.992971\pi\) | ||
0.999756 | − | 0.0220804i | \(-0.00702898\pi\) | |||||||
\(882\) | −1.24462e9 | − | 1.05706e9i | −1.81397 | − | 1.54062i | ||||
\(883\) | 2.99514e8i | 0.435045i | 0.976055 | + | 0.217523i | \(0.0697976\pi\) | ||||
−0.976055 | + | 0.217523i | \(0.930202\pi\) | |||||||
\(884\) | − | 2.23864e8i | − | 0.324062i | ||||||
\(885\) | 1.30742e9 | − | 3.51309e8i | 1.88619 | − | 0.506827i | ||||
\(886\) | 1.42953e9 | 2.05538 | ||||||||
\(887\) | −5.62808e8 | −0.806472 | −0.403236 | − | 0.915096i | \(-0.632115\pi\) | ||||
−0.403236 | + | 0.915096i | \(0.632115\pi\) | |||||||
\(888\) | 1.16888e8 | + | 4.29387e7i | 0.166929 | + | 0.0613211i | ||||
\(889\) | 3.90288e8 | 0.555495 | ||||||||
\(890\) | 5.41107e8 | + | 7.66753e8i | 0.767562 | + | 1.08764i | ||||
\(891\) | −4.19375e8 | + | 6.88025e7i | −0.592884 | + | 0.0972683i | ||||
\(892\) | 8.95791e8i | 1.26215i | ||||||||
\(893\) | −5.30588e8 | −0.745080 | ||||||||
\(894\) | −1.12134e9 | − | 4.11924e8i | −1.56937 | − | 0.576507i | ||||
\(895\) | −1.49045e8 | − | 2.11198e8i | −0.207897 | − | 0.294592i | ||||
\(896\) | 7.10239e8i | 0.987371i | ||||||||
\(897\) | −1.43311e8 | − | 5.26451e7i | −0.198564 | − | 0.0729425i | ||||
\(898\) | − | 7.62593e8i | − | 1.05309i | ||||||
\(899\) | − | 3.03225e8i | − | 0.417336i | ||||||
\(900\) | −7.63648e8 | + | 4.42327e8i | −1.04753 | + | 0.606759i | ||||
\(901\) | 3.71268e8 | 0.507591 | ||||||||
\(902\) | 5.29076e8 | 0.720939 | ||||||||
\(903\) | −1.98284e8 | + | 5.39770e8i | −0.269293 | + | 0.733069i | ||||
\(904\) | 1.30129e8 | 0.176145 | ||||||||
\(905\) | 2.94483e8 | − | 2.07820e8i | 0.397296 | − | 0.280377i | ||||
\(906\) | 4.72006e8 | − | 1.28490e9i | 0.634692 | − | 1.72776i | ||||
\(907\) | − | 3.12764e8i | − | 0.419175i | −0.977790 | − | 0.209588i | \(-0.932788\pi\) | ||
0.977790 | − | 0.209588i | \(-0.0672121\pi\) | |||||||
\(908\) | −1.06481e9 | −1.42238 | ||||||||
\(909\) | 4.53742e7 | − | 5.34249e7i | 0.0604112 | − | 0.0711298i | ||||
\(910\) | −7.52279e8 | + | 5.30893e8i | −0.998286 | + | 0.704503i | ||||
\(911\) | 2.78730e8i | 0.368663i | 0.982864 | + | 0.184331i | \(0.0590120\pi\) | ||||
−0.982864 | + | 0.184331i | \(0.940988\pi\) | |||||||
\(912\) | 9.93490e7 | − | 2.70448e8i | 0.130972 | − | 0.356533i | ||||
\(913\) | − | 2.74238e8i | − | 0.360342i | ||||||
\(914\) | 1.27908e9i | 1.67517i | ||||||||
\(915\) | 2.71144e8 | + | 1.00908e9i | 0.353945 | + | 1.31723i | ||||
\(916\) | −3.62306e8 | −0.471399 | ||||||||
\(917\) | 1.30499e9 | 1.69239 | ||||||||
\(918\) | −5.25957e8 | + | 2.97423e8i | −0.679864 | + | 0.384456i | ||||
\(919\) | 5.75417e8 | 0.741372 | 0.370686 | − | 0.928758i | \(-0.379123\pi\) | ||||
0.370686 | + | 0.928758i | \(0.379123\pi\) | |||||||
\(920\) | −8.26828e7 | + | 5.83503e7i | −0.106182 | + | 0.0749341i | ||||
\(921\) | −8.30411e8 | − | 3.05051e8i | −1.06295 | − | 0.390475i | ||||
\(922\) | 3.26727e8i | 0.416862i | ||||||||
\(923\) | −1.69705e8 | −0.215820 | ||||||||
\(924\) | −3.19064e8 | + | 8.68558e8i | −0.404448 | + | 1.10099i | ||||
\(925\) | −4.23584e8 | − | 1.50646e8i | −0.535197 | − | 0.190341i | ||||
\(926\) | 1.93198e9i | 2.43315i | ||||||||
\(927\) | −1.71926e8 | + | 2.02430e8i | −0.215825 | + | 0.254118i | ||||
\(928\) | 1.18329e9i | 1.48063i | ||||||||
\(929\) | − | 4.36852e8i | − | 0.544863i | −0.962175 | − | 0.272431i | \(-0.912172\pi\) | ||
0.962175 | − | 0.272431i | \(-0.0878278\pi\) | |||||||
\(930\) | 1.24289e8 | + | 4.62549e8i | 0.154520 | + | 0.575055i | ||||
\(931\) | 6.58467e8 | 0.815990 | ||||||||
\(932\) | 1.47968e9 | 1.82776 | ||||||||
\(933\) | −1.34071e9 | − | 4.92509e8i | −1.65078 | − | 0.606414i | ||||
\(934\) | 7.97049e8 | 0.978238 | ||||||||
\(935\) | 1.48751e8 | + | 2.10781e8i | 0.181981 | + | 0.257868i | ||||
\(936\) | −8.46880e7 | + | 9.97140e7i | −0.103275 | + | 0.121599i | ||||
\(937\) | − | 1.21122e8i | − | 0.147233i | −0.997287 | − | 0.0736165i | \(-0.976546\pi\) | ||
0.997287 | − | 0.0736165i | \(-0.0234541\pi\) | |||||||
\(938\) | 1.07500e9 | 1.30256 | ||||||||
\(939\) | 1.07801e9 | + | 3.96005e8i | 1.30204 | + | 0.478304i | ||||
\(940\) | −1.20071e9 | + | 8.47358e8i | −1.44562 | + | 1.02020i | ||||
\(941\) | − | 1.48647e9i | − | 1.78396i | −0.452071 | − | 0.891982i | \(-0.649314\pi\) | ||
0.452071 | − | 0.891982i | \(-0.350686\pi\) | |||||||
\(942\) | −1.57585e9 | − | 5.78887e8i | −1.88522 | − | 0.692534i | ||||
\(943\) | − | 2.80941e8i | − | 0.335027i | ||||||
\(944\) | 1.22420e9i | 1.45524i | ||||||||
\(945\) | 1.23039e9 | + | 5.81636e8i | 1.45797 | + | 0.689217i | ||||
\(946\) | 3.66227e8 | 0.432590 | ||||||||
\(947\) | −1.38450e9 | −1.63021 | −0.815105 | − | 0.579313i | \(-0.803321\pi\) | ||||
−0.815105 | + | 0.579313i | \(0.803321\pi\) | |||||||
\(948\) | 3.15266e8 | − | 8.58217e8i | 0.370042 | − | 1.00733i | ||||
\(949\) | 7.85638e7 | 0.0919229 | ||||||||
\(950\) | 2.17748e8 | − | 6.12260e8i | 0.253971 | − | 0.714110i | ||||
\(951\) | 1.80783e8 | − | 4.92129e8i | 0.210192 | − | 0.572186i | ||||
\(952\) | 2.28833e8i | 0.265220i | ||||||||
\(953\) | 5.27582e7 | 0.0609553 | 0.0304777 | − | 0.999535i | \(-0.490297\pi\) | ||||
0.0304777 | + | 0.999535i | \(0.490297\pi\) | |||||||
\(954\) | −9.50733e8 | − | 8.07466e8i | −1.09500 | − | 0.929992i | ||||
\(955\) | −8.31651e8 | − | 1.17845e9i | −0.954840 | − | 1.35302i | ||||
\(956\) | − | 5.92091e8i | − | 0.677665i | ||||||
\(957\) | −1.89214e8 | + | 5.15080e8i | −0.215883 | + | 0.587678i | ||||
\(958\) | − | 1.65600e9i | − | 1.88349i | ||||||
\(959\) | 1.51180e9i | 1.71410i | ||||||||
\(960\) | −3.13952e8 | − | 1.16840e9i | −0.354854 | − | 1.32061i | ||||
\(961\) | −7.45152e8 | −0.839605 | ||||||||
\(962\) | −3.83153e8 | −0.430375 | ||||||||
\(963\) | −2.43080e7 | − | 2.06450e7i | −0.0272189 | − | 0.0231172i | ||||
\(964\) | 1.89182e8 | 0.211178 | ||||||||
\(965\) | −3.97914e8 | − | 5.63846e8i | −0.442799 | − | 0.627450i | ||||
\(966\) | 8.42191e8 | + | 3.09378e8i | 0.934285 | + | 0.343209i | ||||
\(967\) | − | 3.67686e8i | − | 0.406628i | −0.979114 | − | 0.203314i | \(-0.934829\pi\) | ||
0.979114 | − | 0.203314i | \(-0.0651712\pi\) | |||||||
\(968\) | −1.81463e8 | −0.200060 | ||||||||
\(969\) | 8.40154e7 | − | 2.28707e8i | 0.0923396 | − | 0.251367i | ||||
\(970\) | 1.33649e9 | + | 1.89382e9i | 1.46437 | + | 2.07503i | ||||
\(971\) | − | 1.31090e9i | − | 1.43189i | −0.698156 | − | 0.715946i | \(-0.745996\pi\) | ||
0.698156 | − | 0.715946i | \(-0.254004\pi\) | |||||||
\(972\) | 1.09181e9 | + | 2.09338e8i | 1.18891 | + | 0.227955i | ||||
\(973\) | − | 1.58637e9i | − | 1.72213i | ||||||
\(974\) | − | 4.44672e8i | − | 0.481241i | ||||||
\(975\) | 3.02008e8 | − | 3.63144e8i | 0.325840 | − | 0.391800i | ||||
\(976\) | −9.44846e8 | −1.01628 | ||||||||
\(977\) | −7.72338e7 | −0.0828178 | −0.0414089 | − | 0.999142i | \(-0.513185\pi\) | ||||
−0.0414089 | + | 0.999142i | \(0.513185\pi\) | |||||||
\(978\) | 5.62447e8 | + | 2.06615e8i | 0.601264 | + | 0.220874i | ||||
\(979\) | −5.04753e8 | −0.537936 | ||||||||
\(980\) | 1.49010e9 | − | 1.05158e9i | 1.58321 | − | 1.11729i | ||||
\(981\) | 8.76598e7 | + | 7.44502e7i | 0.0928525 | + | 0.0788604i | ||||
\(982\) | − | 1.64527e9i | − | 1.73741i | ||||||
\(983\) | 1.49397e9 | 1.57283 | 0.786417 | − | 0.617696i | \(-0.211934\pi\) | ||||
0.786417 | + | 0.617696i | \(0.211934\pi\) | |||||||
\(984\) | −2.25969e8 | − | 8.30096e7i | −0.237172 | − | 0.0871251i | ||||
\(985\) | −1.01522e9 | + | 7.16457e8i | −1.06231 | + | 0.749689i | ||||
\(986\) | 7.80177e8i | 0.813883i | ||||||||
\(987\) | 2.12734e9 | + | 7.81475e8i | 2.21251 | + | 0.812762i | ||||
\(988\) | − | 3.03287e8i | − | 0.314473i | ||||||
\(989\) | − | 1.94467e8i | − | 0.201029i | ||||||
\(990\) | 7.75077e7 | − | 8.63279e8i | 0.0798802 | − | 0.889704i | ||||
\(991\) | −4.50465e8 | −0.462849 | −0.231425 | − | 0.972853i | \(-0.574339\pi\) | ||||
−0.231425 | + | 0.972853i | \(0.574339\pi\) | |||||||
\(992\) | −5.55503e8 | −0.569052 | ||||||||
\(993\) | 2.21288e8 | − | 6.02391e8i | 0.226001 | − | 0.615220i | ||||
\(994\) | 9.97305e8 | 1.01547 | ||||||||
\(995\) | −8.44734e8 | + | 5.96140e8i | −0.857533 | + | 0.605172i | ||||
\(996\) | −2.47364e8 | + | 6.73375e8i | −0.250356 | + | 0.681521i | ||||
\(997\) | 1.44711e9i | 1.46021i | 0.683332 | + | 0.730107i | \(0.260530\pi\) | ||||
−0.683332 | + | 0.730107i | \(0.739470\pi\) | |||||||
\(998\) | −2.08866e9 | −2.10124 | ||||||||
\(999\) | 2.78771e8 | + | 4.92972e8i | 0.279609 | + | 0.494454i |
(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 | 15.7.d.c.14.1 | ✓ | 8 | |
3.2 | odd | 2 | inner | 15.7.d.c.14.7 | yes | 8 | |
4.3 | odd | 2 | 240.7.c.c.209.4 | 8 | |||
5.2 | odd | 4 | 75.7.c.e.26.1 | 8 | |||
5.3 | odd | 4 | 75.7.c.e.26.8 | 8 | |||
5.4 | even | 2 | inner | 15.7.d.c.14.8 | yes | 8 | |
12.11 | even | 2 | 240.7.c.c.209.6 | 8 | |||
15.2 | even | 4 | 75.7.c.e.26.7 | 8 | |||
15.8 | even | 4 | 75.7.c.e.26.2 | 8 | |||
15.14 | odd | 2 | inner | 15.7.d.c.14.2 | yes | 8 | |
20.19 | odd | 2 | 240.7.c.c.209.5 | 8 | |||
60.59 | even | 2 | 240.7.c.c.209.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.7.d.c.14.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
15.7.d.c.14.2 | yes | 8 | 15.14 | odd | 2 | inner | |
15.7.d.c.14.7 | yes | 8 | 3.2 | odd | 2 | inner | |
15.7.d.c.14.8 | yes | 8 | 5.4 | even | 2 | inner | |
75.7.c.e.26.1 | 8 | 5.2 | odd | 4 | |||
75.7.c.e.26.2 | 8 | 15.8 | even | 4 | |||
75.7.c.e.26.7 | 8 | 15.2 | even | 4 | |||
75.7.c.e.26.8 | 8 | 5.3 | odd | 4 | |||
240.7.c.c.209.3 | 8 | 60.59 | even | 2 | |||
240.7.c.c.209.4 | 8 | 4.3 | odd | 2 | |||
240.7.c.c.209.5 | 8 | 20.19 | odd | 2 | |||
240.7.c.c.209.6 | 8 | 12.11 | even | 2 |