Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,7,Mod(65,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.65");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.h (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.4841103551\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 9460 x^{18} + 36670708 x^{16} + 75655761912 x^{14} + 90488614064544 x^{12} + \cdots + 10\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{22}\cdot 3^{8}\cdot 19^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 65.8 | ||
Root | \(21.3475i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.65 |
Dual form | 76.7.h.a.69.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 16.9875 | + | 9.80775i | 0.629167 | + | 0.363250i | 0.780430 | − | 0.625244i | \(-0.215000\pi\) |
−0.151262 | + | 0.988494i | \(0.548334\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 72.3330 | − | 125.284i | 0.578664 | − | 1.00228i | −0.416969 | − | 0.908921i | \(-0.636908\pi\) |
0.995633 | − | 0.0933549i | \(-0.0297591\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 479.542 | 1.39808 | 0.699042 | − | 0.715081i | \(-0.253610\pi\) | ||||
0.699042 | + | 0.715081i | \(0.253610\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −172.116 | − | 298.114i | −0.236099 | − | 0.408935i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1675.76 | −1.25903 | −0.629513 | − | 0.776990i | \(-0.716745\pi\) | ||||
−0.629513 | + | 0.776990i | \(0.716745\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 653.454 | − | 377.272i | 0.297430 | − | 0.171721i | −0.343858 | − | 0.939022i | \(-0.611734\pi\) |
0.641288 | + | 0.767300i | \(0.278400\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2457.52 | − | 1418.85i | 0.728153 | − | 0.420399i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3910.26 | − | 6772.78i | 0.795901 | − | 1.37854i | −0.126364 | − | 0.991984i | \(-0.540331\pi\) |
0.922265 | − | 0.386558i | \(-0.126336\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6399.56 | − | 2468.11i | −0.933016 | − | 0.359835i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8146.24 | + | 4703.23i | 0.879628 | + | 0.507854i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 10038.9 | + | 17387.9i | 0.825092 | + | 1.42910i | 0.901849 | + | 0.432052i | \(0.142210\pi\) |
−0.0767564 | + | 0.997050i | \(0.524456\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2651.63 | − | 4592.76i | −0.169704 | − | 0.293937i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 21052.0i | − | 1.06955i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 39064.1 | − | 22553.7i | 1.60171 | − | 0.924749i | 0.610567 | − | 0.791965i | \(-0.290942\pi\) |
0.991145 | − | 0.132784i | \(-0.0423917\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 20987.2i | 0.704482i | 0.935909 | + | 0.352241i | \(0.114580\pi\) | ||||
−0.935909 | + | 0.352241i | \(0.885420\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −28467.1 | − | 16435.5i | −0.792138 | − | 0.457341i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 34686.8 | − | 60079.2i | 0.809021 | − | 1.40126i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 64541.3i | − | 1.27418i | −0.770787 | − | 0.637092i | \(-0.780137\pi\) | ||
0.770787 | − | 0.637092i | \(-0.219863\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 14800.8 | 0.249511 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 38429.1 | + | 22187.0i | 0.557581 | + | 0.321920i | 0.752174 | − | 0.658964i | \(-0.229005\pi\) |
−0.194593 | + | 0.980884i | \(0.562339\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −384.826 | + | 666.538i | −0.00484015 | + | 0.00838338i | −0.868435 | − | 0.495802i | \(-0.834874\pi\) |
0.863595 | + | 0.504186i | \(0.168207\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −49798.7 | −0.546488 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 24326.1 | + | 42134.0i | 0.234303 | + | 0.405825i | 0.959070 | − | 0.283169i | \(-0.0913857\pi\) |
−0.724767 | + | 0.688994i | \(0.758052\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 112312. | 0.954636 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 132851. | − | 76701.8i | 1.00151 | − | 0.578222i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −154862. | + | 89409.9i | −1.04020 | + | 0.600562i | −0.919891 | − | 0.392174i | \(-0.871723\pi\) |
−0.120313 | + | 0.992736i | \(0.538390\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −121213. | + | 209947.i | −0.728553 | + | 1.26189i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −84506.0 | − | 104692.i | −0.456313 | − | 0.565315i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −182560. | − | 105401.i | −0.888895 | − | 0.513204i | −0.0153141 | − | 0.999883i | \(-0.504875\pi\) |
−0.873581 | + | 0.486679i | \(0.838208\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 200137. | + | 346647.i | 0.881734 | + | 1.52721i | 0.849411 | + | 0.527731i | \(0.176957\pi\) |
0.0323229 | + | 0.999477i | \(0.489710\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −82537.0 | − | 142958.i | −0.330086 | − | 0.571726i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 109157.i | − | 0.397476i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −516018. | + | 297923.i | −1.71570 | + | 0.990558i | −0.789303 | + | 0.614004i | \(0.789558\pi\) |
−0.926395 | + | 0.376554i | \(0.877109\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 393836.i | 1.19886i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −20990.7 | − | 12119.0i | −0.0586479 | − | 0.0338604i | 0.470389 | − | 0.882459i | \(-0.344113\pi\) |
−0.529037 | + | 0.848599i | \(0.677447\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −62525.1 | + | 108297.i | −0.160726 | + | 0.278385i | −0.935129 | − | 0.354307i | \(-0.884717\pi\) |
0.774403 | + | 0.632692i | \(0.218050\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 104026.i | − | 0.246580i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −803599. | −1.76022 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 569365. | + | 328723.i | 1.15481 | + | 0.666729i | 0.950054 | − | 0.312085i | \(-0.101027\pi\) |
0.204754 | + | 0.978814i | \(0.434361\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 80999.9 | − | 140296.i | 0.152416 | − | 0.263992i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 992838. | 1.73638 | 0.868189 | − | 0.496234i | \(-0.165284\pi\) | ||||
0.868189 | + | 0.496234i | \(0.165284\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −565682. | − | 979791.i | −0.921119 | − | 1.59543i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 884804. | 1.34366 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −462997. | + | 267312.i | −0.656763 | + | 0.379182i | −0.791042 | − | 0.611761i | \(-0.790461\pi\) |
0.134280 | + | 0.990943i | \(0.457128\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 313359. | − | 180918.i | 0.415832 | − | 0.240081i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −205838. | + | 356521.i | −0.255903 | + | 0.443237i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −772115. | + | 623239.i | −0.900557 | + | 0.726915i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.42085e6 | − | 820331.i | −1.55681 | − | 0.898822i | −0.997560 | − | 0.0698204i | \(-0.977757\pi\) |
−0.559246 | − | 0.829002i | \(-0.688909\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 288426. | + | 499568.i | 0.297255 | + | 0.514860i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 146191. | + | 253210.i | 0.141891 | + | 0.245763i | 0.928209 | − | 0.372060i | \(-0.121348\pi\) |
−0.786318 | + | 0.617822i | \(0.788015\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 637190.i | 0.583119i | 0.956553 | + | 0.291560i | \(0.0941742\pi\) | ||||
−0.956553 | + | 0.291560i | \(0.905826\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.17848e6 | − | 680398.i | 1.01802 | − | 0.587753i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 391710.i | 0.319752i | 0.987137 | + | 0.159876i | \(0.0511095\pi\) | ||||
−0.987137 | + | 0.159876i | \(0.948891\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.00949e6 | − | 582827.i | −0.779509 | − | 0.450050i | 0.0567474 | − | 0.998389i | \(-0.481927\pi\) |
−0.836256 | + | 0.548339i | \(0.815260\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 633005. | − | 1.09640e6i | 0.462848 | − | 0.801676i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 65307.7i | 0.0452615i | 0.999744 | + | 0.0226308i | \(0.00720421\pi\) | ||||
−0.999744 | + | 0.0226308i | \(0.992796\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.90458e6 | 1.90981 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −224940. | − | 129869.i | −0.140446 | − | 0.0810865i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.87514e6 | − | 3.24783e6i | 1.11274 | − | 1.92732i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.03662e6 | 0.585145 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 435210. | + | 753805.i | 0.233875 | + | 0.405083i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.49320e6 | 0.764521 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −116431. | + | 67221.6i | −0.0568406 | + | 0.0328169i | −0.528151 | − | 0.849150i | \(-0.677114\pi\) |
0.471310 | + | 0.881967i | \(0.343781\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −13074.5 | + | 7548.55i | −0.00609053 | + | 0.00351637i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 279525. | − | 484151.i | 0.124339 | − | 0.215361i | −0.797135 | − | 0.603800i | \(-0.793652\pi\) |
0.921474 | + | 0.388439i | \(0.126986\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.06886e6 | − | 1.18356e6i | −1.30443 | − | 0.503080i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.63749e6 | − | 1.52275e6i | −1.07199 | − | 0.618911i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 922559. | + | 1.59792e6i | 0.358783 | + | 0.621431i | 0.987758 | − | 0.155995i | \(-0.0498584\pi\) |
−0.628975 | + | 0.777426i | \(0.716525\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 37752.2 | + | 65388.7i | 0.0140572 | + | 0.0243477i | 0.872968 | − | 0.487777i | \(-0.162192\pi\) |
−0.858911 | + | 0.512124i | \(0.828859\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 954337.i | 0.340443i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.09503e6 | + | 632219.i | −0.374472 | + | 0.216202i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 6.52551e6i | − | 2.14048i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.90790e6 | + | 1.10153e6i | 0.600626 | + | 0.346772i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −582135. | + | 1.00829e6i | −0.175981 | + | 0.304807i | −0.940500 | − | 0.339793i | \(-0.889643\pi\) |
0.764520 | + | 0.644600i | \(0.222976\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.85186e6i | 0.537869i | 0.963158 | + | 0.268935i | \(0.0866716\pi\) | ||||
−0.963158 | + | 0.268935i | \(0.913328\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.69208e6 | −0.751646 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.62937e6 | + | 1.51807e6i | 0.706086 | + | 0.407659i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −671911. | + | 1.16378e6i | −0.173625 | + | 0.300728i | −0.939685 | − | 0.342042i | \(-0.888881\pi\) |
0.766059 | + | 0.642770i | \(0.222215\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.50764e6 | −0.872616 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.81408e6 | + | 8.33823e6i | 1.15355 | + | 1.99800i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.35438e6 | −1.00546 | −0.502728 | − | 0.864444i | \(-0.667670\pi\) | ||||
−0.502728 | + | 0.864444i | \(0.667670\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.11822e6 | + | 2.37765e6i | −0.916763 | + | 0.529294i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.38284e6 | − | 3.68513e6i | 1.37045 | − | 0.791232i | 0.379469 | − | 0.925204i | \(-0.376107\pi\) |
0.990985 | + | 0.133972i | \(0.0427733\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.12874e6 | + | 3.68708e6i | −0.441023 | + | 0.763875i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 365689. | + | 2.33260e6i | 0.0731347 | + | 0.466500i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −243263. | − | 140448.i | −0.0469827 | − | 0.0271255i | 0.476325 | − | 0.879269i | \(-0.341969\pi\) |
−0.523307 | + | 0.852144i | \(0.675302\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.27157e6 | − | 2.20242e6i | −0.237261 | − | 0.410948i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.06750e6 | − | 3.58101e6i | −0.372842 | − | 0.645782i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.17348e6i | 1.25075i | 0.780324 | + | 0.625376i | \(0.215054\pi\) | ||||
−0.780324 | + | 0.625376i | \(0.784946\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.28844e6 | − | 743883.i | 0.217285 | − | 0.125450i | −0.387407 | − | 0.921909i | \(-0.626629\pi\) |
0.604693 | + | 0.796459i | \(0.293296\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.85157e6i | 1.28116i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.08602e6 | − | 4.66847e6i | −1.27708 | − | 0.737325i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.55268e6 | + | 1.13496e7i | −1.00206 | + | 1.73562i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 1.00953e7i | − | 1.49532i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.64832e6 | −0.810623 | −0.405312 | − | 0.914179i | \(-0.632837\pi\) | ||||
−0.405312 | + | 0.914179i | \(0.632837\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 458436. | + | 264678.i | 0.0637686 | + | 0.0368168i | 0.531545 | − | 0.847030i | \(-0.321612\pi\) |
−0.467777 | + | 0.883847i | \(0.654945\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.07058e6 | − | 1.85431e6i | 0.144383 | − | 0.250079i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 870815. | 0.113901 | 0.0569505 | − | 0.998377i | \(-0.481862\pi\) | ||||
0.0569505 | + | 0.998377i | \(0.481862\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −750692. | − | 1.30024e6i | −0.0952582 | − | 0.164992i | 0.814458 | − | 0.580222i | \(-0.197034\pi\) |
−0.909716 | + | 0.415230i | \(0.863701\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.16878e7 | −1.43928 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.87329e7 | − | 1.08155e7i | 2.23933 | − | 1.29288i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.55938e6 | − | 3.20971e6i | 0.645305 | − | 0.372567i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.45571e6 | − | 5.98547e6i | 0.389607 | − | 0.674819i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.07241e7 | + | 4.13597e6i | 1.17469 | + | 0.453042i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.22064e6 | − | 1.85944e6i | −0.342843 | − | 0.197941i | 0.318686 | − | 0.947861i | \(-0.396759\pi\) |
−0.661529 | + | 0.749920i | \(0.730092\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −237720. | − | 411744.i | −0.0245996 | − | 0.0426077i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 55671.2 | + | 96425.4i | 0.00560164 | + | 0.00970233i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.00643e7i | 0.984925i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.12429e6 | + | 1.22646e6i | −0.202247 | + | 0.116767i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 5.90093e6i | − | 0.546694i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.07682e6 | + | 1.19905e6i | 0.187277 | + | 0.108124i | 0.590707 | − | 0.806886i | \(-0.298849\pi\) |
−0.403430 | + | 0.915010i | \(0.632182\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −912777. | + | 1.58098e6i | −0.0801340 | + | 0.138796i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 1.02844e7i | − | 0.879231i | −0.898186 | − | 0.439615i | \(-0.855115\pi\) | ||
0.898186 | − | 0.439615i | \(-0.144885\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.02771e7 | 1.68849 | 0.844245 | − | 0.535957i | \(-0.180049\pi\) | ||||
0.844245 | + | 0.535957i | \(0.180049\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.36512e7 | − | 7.88150e6i | −1.10747 | − | 0.639401i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.84113e6 | + | 1.18492e7i | −0.540829 | + | 0.936744i | 0.458027 | + | 0.888938i | \(0.348556\pi\) |
−0.998857 | + | 0.0478058i | \(0.984777\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.03832e6 | 0.542332 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.44807e6 | + | 1.11684e7i | 0.484378 | + | 0.838968i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.65777e6 | 0.634180 | 0.317090 | − | 0.948396i | \(-0.397294\pi\) | ||||
0.317090 | + | 0.948396i | \(0.397294\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −292332. | + | 168778.i | −0.0208846 | + | 0.0120577i | −0.510406 | − | 0.859934i | \(-0.670505\pi\) |
0.489521 | + | 0.871991i | \(0.337172\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.05388e7 | + | 6.08459e6i | −0.734469 | + | 0.424046i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.12386e6 | − | 1.40709e7i | 0.552414 | − | 0.956809i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.11297e6 | + | 801576.i | −0.339299 | + | 0.0531929i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.68659e7 | + | 9.73750e6i | 1.09247 | + | 0.630739i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.69434e6 | + | 2.93468e6i | 0.107147 | + | 0.185584i | 0.914613 | − | 0.404330i | \(-0.132495\pi\) |
−0.807467 | + | 0.589913i | \(0.799162\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.68228e7 | − | 2.91380e7i | −1.03881 | − | 1.79928i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 2.21923e7i | − | 1.33839i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.86463e7 | − | 1.07654e7i | 1.09848 | − | 0.634209i | 0.162660 | − | 0.986682i | \(-0.447993\pi\) |
0.935822 | + | 0.352474i | \(0.114659\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 3.09503e7i | − | 1.78142i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.34471e7 | − | 7.76371e6i | −0.756325 | − | 0.436664i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.11051e6 | + | 8.85167e6i | −0.280930 | + | 0.486584i | −0.971614 | − | 0.236572i | \(-0.923976\pi\) |
0.690684 | + | 0.723156i | \(0.257309\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.58691e7i | 1.39009i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.04869e7 | −0.550952 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.12047e7 | + | 1.22425e7i | 1.08937 | + | 0.628948i | 0.933409 | − | 0.358815i | \(-0.116819\pi\) |
0.155962 | + | 0.987763i | \(0.450152\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.65278e6 | + | 8.05885e6i | −0.233778 | + | 0.404916i | −0.958917 | − | 0.283687i | \(-0.908442\pi\) |
0.725139 | + | 0.688603i | \(0.241776\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.09759e6 | 0.348838 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.44350e6 | + | 7.69638e6i | 0.213662 | + | 0.370074i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.23186e7 | 1.05009 | 0.525047 | − | 0.851073i | \(-0.324048\pi\) | ||||
0.525047 | + | 0.851073i | \(0.324048\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.25659e6 | − | 3.61224e6i | 0.288088 | − | 0.166328i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.23215e7 | + | 7.11380e6i | −0.555320 | + | 0.320614i | −0.751265 | − | 0.660001i | \(-0.770556\pi\) |
0.195945 | + | 0.980615i | \(0.437223\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.32695e6 | + | 1.44227e7i | −0.367390 | + | 0.636337i | −0.989157 | − | 0.146865i | \(-0.953082\pi\) |
0.621767 | + | 0.783202i | \(0.286415\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.92289e7 | + | 3.01458e6i | −0.830653 | + | 0.130224i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.84284e7 | + | 1.06396e7i | 0.779545 | + | 0.450071i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.85115e7 | − | 3.20629e7i | −0.766918 | − | 1.32834i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.60912e7 | − | 2.78708e7i | −0.652994 | − | 1.13102i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.25894e6i | 0.248827i | 0.992230 | + | 0.124414i | \(0.0397050\pi\) | ||||
−0.992230 | + | 0.124414i | \(0.960295\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.64103e7 | + | 1.52480e7i | −1.02874 | + | 0.593945i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.52781e7i | 1.34659i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.31199e7 | + | 7.57479e6i | 0.490815 | + | 0.283372i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −184540. | + | 319633.i | −0.00676693 | + | 0.0117207i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.73520e6i | 0.206168i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.79060e7 | 2.04091 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.54271e7 | − | 1.46803e7i | −0.878783 | − | 0.507366i | −0.00852607 | − | 0.999964i | \(-0.502714\pi\) |
−0.870257 | + | 0.492598i | \(0.836047\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.24940e6 | + | 1.08243e7i | −0.211818 | + | 0.366880i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.57357e7 | 1.18801 | 0.594006 | − | 0.804460i | \(-0.297545\pi\) | ||||
0.594006 | + | 0.804460i | \(0.297545\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.78953e7 | − | 3.09956e7i | −0.583587 | − | 1.01080i | −0.995050 | − | 0.0993761i | \(-0.968315\pi\) |
0.411463 | − | 0.911427i | \(-0.365018\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.38806e7 | −0.764036 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.12209e7 | + | 1.22519e7i | −0.666171 | + | 0.384614i | −0.794624 | − | 0.607102i | \(-0.792332\pi\) |
0.128453 | + | 0.991716i | \(0.458999\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.54623e7 | + | 3.77946e7i | −2.01660 | + | 1.16428i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.84180e6 | + | 6.65419e6i | −0.116150 | + | 0.201178i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.17399e7 | + | 3.36918e7i | −1.23864 | + | 0.999808i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.46544e6 | − | 2.00077e6i | −0.100950 | − | 0.0582838i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.14324e7 | − | 1.98016e7i | −0.326961 | − | 0.566313i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.16654e7 | + | 2.02051e7i | 0.327576 | + | 0.567378i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.39323e6i | 0.148718i | 0.997232 | + | 0.0743592i | \(0.0236911\pi\) | ||||
−0.997232 | + | 0.0743592i | \(0.976309\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.92407e7 | + | 1.11086e7i | −0.521059 | + | 0.300834i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.61988e7i | 2.29280i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.11633e6 | + | 1.22186e6i | 0.0552960 | + | 0.0319251i | 0.527393 | − | 0.849621i | \(-0.323170\pi\) |
−0.472097 | + | 0.881547i | \(0.656503\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −640522. | + | 1.10942e6i | −0.0164412 | + | 0.0284771i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 3.51696e7i | − | 0.886961i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.55933e6 | −0.0634225 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.93415e7 | + | 2.84873e7i | 1.20159 | + | 0.693737i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.44727e7 | − | 4.23879e7i | 0.585724 | − | 1.01450i | −0.409061 | − | 0.912507i | \(-0.634144\pi\) |
0.994785 | − | 0.101996i | \(-0.0325230\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.31844e7 | −0.780652 | −0.390326 | − | 0.920677i | \(-0.627638\pi\) | ||||
−0.390326 | + | 0.920677i | \(0.627638\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.94233e6 | − | 1.37565e7i | −0.183665 | − | 0.318117i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.56483e7 | 0.583089 | 0.291544 | − | 0.956557i | \(-0.405831\pi\) | ||||
0.291544 | + | 0.956557i | \(0.405831\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.03665e6 | + | 1.75321e6i | −0.0678749 | + | 0.0391876i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.37079e7 | − | 3.67818e7i | 1.40019 | − | 0.808403i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.70037e7 | − | 6.40922e7i | 0.799763 | − | 1.38523i | −0.120007 | − | 0.992773i | \(-0.538292\pi\) |
0.919770 | − | 0.392457i | \(-0.128375\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.48627e7 | + | 3.15896e7i | 0.741037 | + | 0.671464i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.76096e7 | + | 1.01669e7i | 0.368154 | + | 0.212554i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.04525e6 | + | 1.56668e7i | 0.186013 | + | 0.322183i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.76966e7 | − | 4.79719e7i | −0.560310 | − | 0.970485i | −0.997469 | − | 0.0711009i | \(-0.977349\pi\) |
0.437159 | − | 0.899384i | \(-0.355985\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 1.52750e7i | − | 0.304020i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.42631e7 | + | 4.28758e7i | −1.45429 | + | 0.839635i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 7.16019e7i | − | 1.37974i | −0.723932 | − | 0.689871i | \(-0.757667\pi\) | ||
0.723932 | − | 0.689871i | \(-0.242333\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.53658e7 | + | 1.46450e7i | 0.481012 | + | 0.277712i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.70178e7 | − | 2.94756e7i | 0.317598 | − | 0.550097i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 9.27549e7i | − | 1.70380i | −0.523702 | − | 0.851901i | \(-0.675449\pi\) | ||
0.523702 | − | 0.851901i | \(-0.324551\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.63717e6 | −0.0476830 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.75745e7 | − | 1.01467e7i | −0.312815 | − | 0.180604i | 0.335370 | − | 0.942086i | \(-0.391139\pi\) |
−0.648185 | + | 0.761482i | \(0.724472\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.81268e7 | + | 1.00679e8i | −1.01858 | + | 1.76423i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 264939. | 0.00457102 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.31042e7 | − | 4.00176e7i | −0.392502 | − | 0.679833i | 0.600277 | − | 0.799792i | \(-0.295057\pi\) |
−0.992779 | + | 0.119959i | \(0.961724\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.57019e8 | 2.62677 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.49687e6 | − | 5.48302e6i | 0.156460 | − | 0.0903321i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.23678e7 | − | 4.75551e7i | 1.33649 | − | 0.771624i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.30268e7 | + | 2.25631e7i | −0.208193 | + | 0.360602i | −0.951145 | − | 0.308743i | \(-0.900092\pi\) |
0.742952 | + | 0.669345i | \(0.233425\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.05242e7 | − | 5.02044e7i | −0.637963 | − | 0.790357i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.66330e7 | − | 9.60308e6i | −0.257951 | − | 0.148928i | 0.365448 | − | 0.930832i | \(-0.380916\pi\) |
−0.623400 | + | 0.781903i | \(0.714249\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.91790e6 | + | 1.37142e7i | 0.120975 | + | 0.209534i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.17179e7 | − | 2.02961e7i | −0.176395 | − | 0.305525i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.08156e8i | 1.60423i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.57833e7 | + | 4.37535e7i | −1.10765 | + | 0.639504i | −0.938220 | − | 0.346038i | \(-0.887527\pi\) |
−0.169433 | + | 0.985542i | \(0.554193\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.61929e7i | 0.521312i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.75454e7 | − | 5.05444e7i | −1.24275 | − | 0.717501i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.18150e7 | − | 1.24387e8i | 1.00478 | − | 1.74033i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.48105e6i | 0.0204250i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.07404e7 | 0.689782 | 0.344891 | − | 0.938643i | \(-0.387916\pi\) | ||||
0.344891 | + | 0.938643i | \(0.387916\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.66586e7 | + | 2.69383e7i | 0.625295 | + | 0.361014i | 0.778928 | − | 0.627114i | \(-0.215764\pi\) |
−0.153633 | + | 0.988128i | \(0.549097\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.37382e6 | − | 1.45039e7i | 0.110638 | − | 0.191630i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.14743e7 | −0.540272 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.59742e7 | + | 1.66232e8i | 1.23274 | + | 2.13516i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.48026e7 | −0.314141 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.19013e7 | + | 1.26447e7i | −0.273551 | + | 0.157935i | −0.630500 | − | 0.776189i | \(-0.717150\pi\) |
0.356949 | + | 0.934124i | \(0.383817\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.16881e7 | − | 4.13891e7i | 0.883046 | − | 0.509827i | 0.0113843 | − | 0.999935i | \(-0.496376\pi\) |
0.871661 | + | 0.490108i | \(0.163043\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.40005e7 | − | 1.10852e8i | 0.777528 | − | 1.34672i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.13293e7 | − | 1.36052e8i | −0.255583 | − | 1.63027i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.04607e8 | + | 6.03947e7i | 1.23642 | + | 0.713847i | 0.968360 | − | 0.249556i | \(-0.0802847\pi\) |
0.268058 | + | 0.963403i | \(0.413618\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.93307e7 | − | 3.34818e7i | −0.225389 | − | 0.390384i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.44943e7 | + | 5.97459e7i | 0.396768 | + | 0.687222i | 0.993325 | − | 0.115348i | \(-0.0367984\pi\) |
−0.596557 | + | 0.802571i | \(0.703465\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.73418e7i | 0.877676i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.97780e7 | + | 1.14189e7i | −0.221442 | + | 0.127850i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.48148e7i | 0.826511i | 0.910615 | + | 0.413256i | \(0.135608\pi\) | ||||
−0.910615 | + | 0.413256i | \(0.864392\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.43980e7 | − | 3.71802e7i | −0.702009 | − | 0.405305i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.81626e7 | + | 3.14585e7i | −0.195381 | + | 0.338410i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 5.23454e7i | − | 0.555705i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.28041e7 | 0.553247 | 0.276623 | − | 0.960978i | \(-0.410785\pi\) | ||||
0.276623 | + | 0.960978i | \(0.410785\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.42580e8 | − | 8.23188e7i | −1.47442 | − | 0.851258i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.25780e7 | − | 1.08388e8i | 0.638733 | − | 1.10632i | −0.346979 | − | 0.937873i | \(-0.612792\pi\) |
0.985711 | − | 0.168444i | \(-0.0538743\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.70244e8 | −1.71526 | −0.857630 | − | 0.514267i | \(-0.828064\pi\) | ||||
−0.857630 | + | 0.514267i | \(0.828064\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.97777e7 | + | 5.15765e7i | 0.296164 | + | 0.512971i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.00664e7 | 0.295210 | 0.147605 | − | 0.989046i | \(-0.452844\pi\) | ||||
0.147605 | + | 0.989046i | \(0.452844\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.47453e8 | + | 1.42867e8i | −2.39869 | + | 1.38488i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.28282e7 | + | 1.31799e7i | −0.218479 | + | 0.126139i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 644877. | − | 1.11696e6i | 0.00609387 | − | 0.0105549i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.63382e6 | + | 3.59361e7i | 0.0525681 | + | 0.335313i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.33086e7 | + | 3.07778e7i | 0.491182 | + | 0.283584i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.25052e6 | + | 7.36212e6i | 0.0386755 | + | 0.0669879i | 0.884715 | − | 0.466132i | \(-0.154353\pi\) |
−0.846040 | + | 0.533120i | \(0.821019\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.43496e7 | − | 4.21748e7i | −0.218805 | − | 0.378981i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.88861e8i | 1.67610i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.05549e8 | + | 1.18674e8i | −1.80174 | + | 1.04023i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.86160e7i | 0.507492i | 0.967271 | + | 0.253746i | \(0.0816627\pi\) | ||||
−0.967271 | + | 0.253746i | \(0.918337\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.39701e7 | − | 4.27066e7i | −0.632601 | − | 0.365232i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.73857e7 | − | 3.01129e7i | 0.146875 | − | 0.254395i | −0.783196 | − | 0.621775i | \(-0.786412\pi\) |
0.930071 | + | 0.367380i | \(0.119745\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 3.52764e8i | − | 2.94404i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.34508e7 | 0.688042 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.00660e7 | − | 5.81158e6i | −0.0819947 | − | 0.0473396i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.06825e7 | + | 1.85026e7i | −0.0859749 | + | 0.148913i | −0.905806 | − | 0.423692i | \(-0.860734\pi\) |
0.819831 | + | 0.572605i | \(0.194067\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.44571e8 | 1.14966 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.00789e7 | + | 6.94186e7i | 0.314928 | + | 0.545472i | 0.979422 | − | 0.201822i | \(-0.0646862\pi\) |
−0.664494 | + | 0.747294i | \(0.731353\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.22976e7 | 0.328429 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.23239e7 | + | 4.17562e7i | −0.554955 | + | 0.320404i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.04620e7 | − | 4.06812e7i | 0.534320 | − | 0.308490i | −0.208454 | − | 0.978032i | \(-0.566843\pi\) |
0.742774 | + | 0.669542i | \(0.233510\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.99834e7 | + | 5.19328e7i | −0.224708 | + | 0.389206i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.19586e7 | + | 1.34723e8i | −0.384862 | + | 0.997909i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.98300e7 | + | 4.60899e7i | 0.584446 | + | 0.337430i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.07648e7 | − | 7.06066e7i | −0.294994 | − | 0.510945i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.75496e6 | − | 4.77172e6i | −0.0197066 | − | 0.0341329i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.41254e8i | 0.998821i | 0.866366 | + | 0.499410i | \(0.166450\pi\) | ||||
−0.866366 | + | 0.499410i | \(0.833550\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.14406e7 | − | 2.39258e7i | 0.289682 | − | 0.167248i | −0.348117 | − | 0.937451i | \(-0.613179\pi\) |
0.637798 | + | 0.770203i | \(0.279845\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 4.98849e7i | − | 0.344740i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.42142e8 | + | 8.20656e7i | 0.971158 | + | 0.560699i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.27541e8 | + | 2.20908e8i | −0.861555 | + | 1.49226i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.25650e7i | 0.484667i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.34822e7 | 0.221122 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.90752e7 | + | 2.83336e7i | 0.320480 | + | 0.185029i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.03557e7 | + | 1.21860e8i | −0.454335 | + | 0.786932i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.88208e8 | −1.20191 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.33126e8 | − | 2.30580e8i | −0.840755 | − | 1.45623i | −0.889257 | − | 0.457407i | \(-0.848778\pi\) |
0.0485022 | − | 0.998823i | \(-0.484555\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.91833e7 | 0.182278 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.46038e8 | + | 8.43153e7i | −0.902148 | + | 0.520855i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.90348e8 | − | 1.09898e8i | 1.16302 | − | 0.671470i | 0.210994 | − | 0.977487i | \(-0.432330\pi\) |
0.952026 | + | 0.306017i | \(0.0989965\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.88936e7 | − | 1.19327e8i | 0.416353 | − | 0.721145i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.05658e8 | + | 4.79190e7i | −1.82718 | + | 0.286453i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.73035e8 | + | 1.57637e8i | 1.61452 | + | 0.932142i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.15743e7 | − | 1.58611e8i | −0.535667 | − | 0.927802i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.05811e7 | − | 8.76091e7i | −0.292700 | − | 0.506972i | 0.681747 | − | 0.731588i | \(-0.261220\pi\) |
−0.974447 | + | 0.224616i | \(0.927887\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 580736.i | 0.00332463i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.22627e8 | + | 1.28534e8i | −1.26093 | + | 0.727997i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 1.75466e8i | − | 0.983260i | −0.870804 | − | 0.491630i | \(-0.836401\pi\) | ||
0.870804 | − | 0.491630i | \(-0.163599\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.18204e6 | + | 4.72390e6i | 0.0453645 | + | 0.0261912i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.88429e7 | − | 6.72779e7i | 0.213090 | − | 0.369082i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 1.29570e8i | − | 0.703342i | −0.936124 | − | 0.351671i | \(-0.885614\pi\) | ||
0.936124 | − | 0.351671i | \(-0.114386\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.78253e8 | 0.957475 | 0.478737 | − | 0.877958i | \(-0.341095\pi\) | ||||
0.478737 | + | 0.877958i | \(0.341095\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.59509e7 | − | 5.53973e7i | −0.510018 | − | 0.294459i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.32389e7 | − | 9.22125e7i | 0.280044 | − | 0.485050i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.66437e8 | 1.90753 | 0.953766 | − | 0.300550i | \(-0.0971704\pi\) | ||||
0.953766 | + | 0.300550i | \(0.0971704\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.19180e6 | + | 8.99246e6i | 0.0267474 | + | 0.0463279i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.76108e8 | 2.42760 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.59513e8 | − | 1.49830e8i | 1.30964 | − | 0.756123i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.25412e7 | + | 1.87877e7i | −0.162542 | + | 0.0938437i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.95703e7 | − | 6.85377e7i | 0.195639 | − | 0.338856i | −0.751471 | − | 0.659766i | \(-0.770655\pi\) |
0.947110 | + | 0.320910i | \(0.103989\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.17988e7 | − | 1.34309e8i | 0.253498 | − | 0.657293i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.47930e7 | + | 8.54074e6i | 0.0716628 | + | 0.0413745i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.76464e8 | − | 3.05645e8i | −0.846239 | − | 1.46573i | −0.884541 | − | 0.466463i | \(-0.845528\pi\) |
0.0383017 | − | 0.999266i | \(-0.487805\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.71269e8 | − | 4.69851e8i | −1.28780 | − | 2.23054i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 2.94504e7i | − | 0.138410i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.62481e8 | + | 1.51544e8i | −1.22129 | + | 0.705110i | −0.965192 | − | 0.261541i | \(-0.915769\pi\) |
−0.256095 | + | 0.966652i | \(0.582436\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.56371e8i | 1.64164i | 0.571184 | + | 0.820822i | \(0.306484\pi\) | ||||
−0.571184 | + | 0.820822i | \(0.693516\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.77630e8 | + | 1.02555e8i | 0.810149 | + | 0.467740i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.49819e7 | − | 1.29872e8i | 0.338603 | − | 0.586477i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 7.93413e7i | − | 0.354759i | −0.984143 | − | 0.177379i | \(-0.943238\pi\) | ||
0.984143 | − | 0.177379i | \(-0.0567620\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.24301e8 | 1.87855 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.17920e7 | + | 1.83551e7i | 0.139378 | + | 0.0804699i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.83104e8 | + | 3.17145e8i | −0.794907 | + | 1.37682i | 0.127991 | + | 0.991775i | \(0.459147\pi\) |
−0.922898 | + | 0.385044i | \(0.874186\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.25920e8 | 0.541340 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.57432e8 | + | 2.72680e8i | 0.670250 | + | 1.16091i | 0.977833 | + | 0.209386i | \(0.0671464\pi\) |
−0.307583 | + | 0.951521i | \(0.599520\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.06434e8 | −0.448754 | −0.224377 | − | 0.974502i | \(-0.572035\pi\) | ||||
−0.224377 | + | 0.974502i | \(0.572035\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.66049e8 | − | 2.11339e8i | 1.52850 | − | 0.882479i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.22027e8 | + | 1.28187e8i | −0.918209 | + | 0.530128i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.49440e8 | − | 2.58837e8i | 0.612105 | − | 1.06020i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.41612e8 | + | 1.75439e8i | 0.574510 | + | 0.711745i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.37124e8 | − | 2.52373e8i | −1.75652 | − | 1.01413i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.96465e7 | + | 5.13493e7i | 0.118001 | + | 0.204384i | 0.918975 | − | 0.394315i | \(-0.129018\pi\) |
−0.800974 | + | 0.598699i | \(0.795685\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.64738e7 | − | 6.31745e7i | −0.143804 | − | 0.249075i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.94494e7i | 0.0759599i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.33908e7 | − | 4.23722e7i | 0.283938 | − | 0.163932i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.34351e6i | 0.0319776i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.29264e8 | − | 2.47836e8i | −1.62986 | − | 0.941000i | −0.984133 | − | 0.177431i | \(-0.943221\pi\) |
−0.645727 | − | 0.763569i | \(-0.723445\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.39583e6 | − | 5.88176e6i | 0.0127736 | − | 0.0221245i | −0.859568 | − | 0.511021i | \(-0.829267\pi\) |
0.872342 | + | 0.488897i | \(0.162601\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.18404e6i | 0.00813918i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.56052e7 | 0.0576179 | 0.0288090 | − | 0.999585i | \(-0.490829\pi\) | ||||
0.0288090 | + | 0.999585i | \(0.490829\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.05928e8 | + | 1.76628e8i | 1.11914 | + | 0.646137i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.87078e7 | + | 1.70967e8i | −0.357774 | + | 0.619683i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.38685e8 | 0.498069 | 0.249034 | − | 0.968495i | \(-0.419887\pi\) | ||||
0.249034 | + | 0.968495i | \(0.419887\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.04378e7 | − | 7.00403e7i | −0.143901 | − | 0.249244i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.30463e7 | 0.151789 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.26135e8 | + | 1.88294e8i | −1.13957 | + | 0.657932i | −0.946324 | − | 0.323218i | \(-0.895235\pi\) |
−0.193247 | + | 0.981150i | \(0.561902\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.70005e8 | + | 2.71358e8i | −1.62741 | + | 0.939588i | −0.642554 | + | 0.766240i | \(0.722125\pi\) |
−0.984861 | + | 0.173348i | \(0.944541\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.78749e7 | − | 1.00242e8i | 0.198586 | − | 0.343962i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.70262e8 | + | 2.98870e8i | −1.25905 | + | 1.01629i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.84322e8 | + | 4.52829e8i | 2.64312 | + | 1.52601i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.35200e7 | + | 4.07379e7i | 0.0785524 | + | 0.136057i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.35382e8 | − | 5.80899e8i | −1.11013 | − | 1.92279i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.85863e7i | 0.323423i | 0.986838 | + | 0.161712i | \(0.0517014\pi\) | ||||
−0.986838 | + | 0.161712i | \(0.948299\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9.66867e7 | + | 5.58221e7i | −0.314380 | + | 0.181508i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.46094e8i | 0.793112i | 0.918010 | + | 0.396556i | \(0.129795\pi\) | ||||
−0.918010 | + | 0.396556i | \(0.870205\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.81360e8 | − | 3.93383e8i | −2.17654 | − | 1.25663i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.00867e8 | − | 1.74707e8i | 0.319380 | − | 0.553183i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 1.80543e8i | − | 0.566654i | −0.959023 | − | 0.283327i | \(-0.908562\pi\) | ||
0.959023 | − | 0.283327i | \(-0.0914382\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.66926e8 | 0.830460 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.44457e8 | + | 1.98872e8i | 1.06234 | + | 0.613344i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.74637e7 | + | 1.16851e8i | −0.206259 | + | 0.357251i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.85003e8 | −0.560720 | −0.280360 | − | 0.959895i | \(-0.590454\pi\) | ||||
−0.280360 | + | 0.959895i | \(0.590454\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.38312e8 | + | 2.39564e8i | 0.415587 | + | 0.719817i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.09229e7 | 0.0325375 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.00536e8 | − | 1.73514e8i | 0.887560 | − | 0.512433i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.32428e8 | + | 1.34192e8i | −0.680544 | + | 0.392912i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.09718e8 | − | 1.90037e8i | 0.318510 | − | 0.551675i | −0.661667 | − | 0.749797i | \(-0.730151\pi\) |
0.980177 | + | 0.198122i | \(0.0634842\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.59295e8 | + | 4.13036e8i | −0.458497 | + | 1.18883i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.19564e8 | + | 6.90300e7i | 0.341218 | + | 0.197002i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.01046e7 | + | 1.21425e8i | 0.198376 | + | 0.343597i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.15984e8 | − | 3.74096e8i | −0.606016 | − | 1.04965i | −0.991890 | − | 0.127098i | \(-0.959434\pi\) |
0.385875 | − | 0.922551i | \(-0.373900\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 2.26314e8i | − | 0.629656i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.64924e8 | + | 2.10689e8i | −1.00678 | + | 0.581263i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.82921e8i | 0.500433i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.47074e8 | + | 8.49132e7i | 0.399005 | + | 0.230366i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.60987e8 | + | 4.52043e8i | −0.702153 | + | 1.21617i | 0.265556 | + | 0.964096i | \(0.414445\pi\) |
−0.967709 | + | 0.252070i | \(0.918889\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.05560e8i | 0.815249i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.62133e6 | −0.0175198 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.07167e8 | − | 1.19608e8i | −0.543635 | − | 0.313868i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.32657e6 | + | 4.02973e6i | −0.00605498 | + | 0.0104875i | −0.869037 | − | 0.494747i | \(-0.835261\pi\) |
0.862982 | + | 0.505235i | \(0.168594\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.56803e8 | −0.920970 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.00954e6 | + | 5.21268e6i | 0.00770456 | + | 0.0133447i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.07531e7 | −0.179653 | −0.0898263 | − | 0.995957i | \(-0.528631\pi\) | ||||
−0.0898263 | + | 0.995957i | \(0.528631\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.76009e8 | − | 1.59354e8i | 0.695121 | − | 0.401328i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.64724e8 | − | 4.99249e8i | 2.16011 | − | 1.24714i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.88312e8 | + | 3.26166e8i | −0.466600 | + | 0.808175i | −0.999272 | − | 0.0381465i | \(-0.987855\pi\) |
0.532672 | + | 0.846322i | \(0.321188\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.47183e7 | − | 3.65299e7i | −0.232798 | − | 0.0897830i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.78200e8 | − | 1.60619e8i | −0.678252 | − | 0.391589i | 0.120944 | − | 0.992659i | \(-0.461408\pi\) |
−0.799196 | + | 0.601070i | \(0.794741\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.42151e7 | + | 1.45865e8i | 0.203667 | + | 0.352762i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.70883e8 | − | 2.95979e8i | −0.409957 | − | 0.710066i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.87842e8i | 0.447040i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.54561e7 | − | 4.35646e7i | 0.178145 | − | 0.102852i | −0.408276 | − | 0.912859i | \(-0.633870\pi\) |
0.586421 | + | 0.810006i | \(0.300536\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.64706e7i | 0.155684i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.32009e8 | + | 1.33950e8i | 0.539093 | + | 0.311246i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.40754e8 | + | 5.90202e8i | −0.785512 | + | 1.36055i | 0.143181 | + | 0.989697i | \(0.454267\pi\) |
−0.928693 | + | 0.370850i | \(0.879066\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 6.59976e8i | − | 1.50939i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.29867e7 | −0.165611 | −0.0828057 | − | 0.996566i | \(-0.526388\pi\) | ||||
−0.0828057 | + | 0.996566i | \(0.526388\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.84092e8 | − | 2.79490e8i | −1.08982 | − | 0.629207i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.94726e8 | + | 3.37276e8i | −0.434951 | + | 0.753356i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.59060e8 | −0.352512 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.82080e7 | + | 1.70101e8i | 0.215957 | + | 0.374049i | 0.953568 | − | 0.301177i | \(-0.0973795\pi\) |
−0.737611 | + | 0.675226i | \(0.764046\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.22339e8 | 0.921505 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.72911e8 | − | 9.98303e7i | 0.374356 | − | 0.216134i | −0.301004 | − | 0.953623i | \(-0.597322\pi\) |
0.675360 | + | 0.737488i | \(0.263988\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.63893e7 | − | 5.56504e7i | 0.207073 | − | 0.119554i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.03553e8 | − | 5.25769e8i | 0.647099 | − | 1.12081i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.91169e8 | − | 2.36834e8i | −0.404394 | − | 0.500994i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.51755e7 | + | 2.03086e7i | 0.0738392 | + | 0.0426311i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.74800e8 | − | 8.22378e8i | −0.989067 | − | 1.71311i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.72027e7 | + | 1.68360e8i | 0.200941 | + | 0.348041i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.06372e8i | 1.44914i | 0.689203 | + | 0.724568i | \(0.257961\pi\) | ||||
−0.689203 | + | 0.724568i | \(0.742039\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.73630e8 | + | 1.00245e8i | −0.353503 | + | 0.204095i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.13178e7i | 0.0632794i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.61561e8 | + | 1.51012e8i | 0.524509 | + | 0.302825i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.53718e8 | + | 4.39452e8i | −0.504952 | + | 0.874602i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 2.45124e8i | − | 0.484185i | −0.970253 | − | 0.242092i | \(-0.922166\pi\) | ||
0.970253 | − | 0.242092i | \(-0.0778337\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.80486e8 | 0.745930 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.59379e8 | + | 9.20173e7i | 0.310122 | + | 0.179049i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.04777e8 | − | 1.81479e8i | 0.202358 | − | 0.350494i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.39287e9 | 2.67007 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.40144e8 | + | 4.15941e8i | 0.456931 | + | 0.791428i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.06400e8 | −0.578686 | −0.289343 | − | 0.957225i | \(-0.593437\pi\) | ||||
−0.289343 | + | 0.957225i | \(0.593437\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.16295e8 | + | 2.98083e8i | −0.967911 | + | 0.558823i | −0.898599 | − | 0.438772i | \(-0.855414\pi\) |
−0.0693120 | + | 0.997595i | \(0.522080\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.58078e8 | + | 9.12666e7i | −0.294172 | + | 0.169840i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.14965e8 | + | 5.45536e8i | −0.581822 | + | 1.00774i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.10780e6 | − | 3.31575e6i | 0.00753257 | − | 0.00608017i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.07868e8 | − | 6.22778e7i | −0.196355 | − | 0.113366i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.07421e8 | + | 3.59264e8i | 0.374821 | + | 0.649209i | 0.990300 | − | 0.138944i | \(-0.0443709\pi\) |
−0.615479 | + | 0.788153i | \(0.711038\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.93877e8 | − | 5.09009e8i | −0.527188 | − | 0.913116i | −0.999498 | − | 0.0316837i | \(-0.989913\pi\) |
0.472310 | − | 0.881432i | \(-0.343420\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.74323e8i | 0.310451i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.14159e8 | − | 1.23645e8i | 0.378635 | − | 0.218605i | −0.298589 | − | 0.954382i | \(-0.596516\pi\) |
0.677224 | + | 0.735777i | \(0.263183\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1.10394e9i | − | 1.93768i | −0.247694 | − | 0.968838i | \(-0.579673\pi\) | ||
0.247694 | − | 0.968838i | \(-0.420327\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.79138e8 | + | 2.18895e8i | 0.660684 | + | 0.381446i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.39169e8 | − | 7.60664e8i | 0.759796 | − | 1.31601i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 1.06623e9i | − | 1.83143i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.41823e8 | 0.753480 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.45140e8 | + | 2.57002e8i | 0.753721 | + | 0.435161i | 0.827037 | − | 0.562148i | \(-0.190025\pi\) |
−0.0733159 | + | 0.997309i | \(0.523358\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.19927e8 | − | 1.24695e9i | 1.21032 | − | 2.09634i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.79082e8 | −0.465853 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.07956e8 | + | 5.33395e8i | 0.510409 | + | 0.884054i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.97103e8 | 0.818082 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.82909e8 | + | 1.63337e8i | −0.462299 | + | 0.266908i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.12224e9 | − | 6.47923e8i | 1.82094 | − | 1.05132i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.98430e7 | − | 1.03651e8i | 0.0964198 | − | 0.167004i | −0.813780 | − | 0.581172i | \(-0.802594\pi\) |
0.910200 | + | 0.414168i | \(0.135928\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.18690e8 | + | 1.22909e8i | 0.509882 | + | 0.196646i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.76218e8 | − | 3.90415e8i | −1.07435 | − | 0.620274i | −0.144981 | − | 0.989434i | \(-0.546312\pi\) |
−0.929366 | + | 0.369160i | \(0.879645\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.99149e8 | − | 8.64552e8i | −0.787501 | − | 1.36399i | −0.927494 | − | 0.373838i | \(-0.878041\pi\) |
0.139993 | − | 0.990152i | \(-0.455292\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.08702e8 | + | 3.61482e8i | 0.326976 | + | 0.566339i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.85694e8i | 0.911251i | 0.890171 | + | 0.455626i | \(0.150584\pi\) | ||||
−0.890171 | + | 0.455626i | \(0.849416\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.51919e7 | + | 2.03180e7i | −0.0543744 | + | 0.0313931i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 7.26226e8i | − | 1.11433i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.54121e8 | − | 5.50862e8i | −1.45393 | − | 0.839428i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.24796e8 | + | 3.89359e8i | −0.340200 | + | 0.589244i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.64769e8i | 0.848844i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.16055e8 | 1.06886 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.05820e9 | − | 6.10949e8i | −1.56880 | − | 0.905746i | −0.996309 | − | 0.0858337i | \(-0.972645\pi\) |
−0.572489 | − | 0.819912i | \(-0.694022\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.13861e7 | + | 1.06324e8i | −0.0903865 | + | 0.156554i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.76883e8 | −0.551162 | −0.275581 | − | 0.961278i | \(-0.588870\pi\) | ||||
−0.275581 | + | 0.961278i | \(0.588870\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.66348e8 | − | 2.88123e8i | −0.241621 | − | 0.418500i | 0.719555 | − | 0.694435i | \(-0.244346\pi\) |
−0.961176 | + | 0.275935i | \(0.911012\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.98194e8 | −0.863002 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.36249e8 | + | 3.09604e8i | −0.768415 | + | 0.443645i | −0.832309 | − | 0.554312i | \(-0.812981\pi\) |
0.0638937 | + | 0.997957i | \(0.479648\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.58337e7 | + | 3.22356e7i | −0.0794678 | + | 0.0458808i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.35737e8 | + | 2.35103e8i | −0.191895 | + | 0.332372i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.16848e7 | − | 3.29678e8i | −0.0725785 | − | 0.462952i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.98726e8 | + | 5.18880e8i | 1.25360 | + | 0.723765i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.48583e8 | + | 2.57354e8i | 0.205870 | + | 0.356577i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.73340e8 | + | 8.19848e8i | 0.651469 | + | 1.12838i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.39846e9i | 1.91195i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.26976e6 | + | 3.61985e6i | −0.00851506 | + | 0.00491617i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 2.15229e8i | − | 0.290373i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.44639e8 | − | 1.98977e8i | −0.461894 | − | 0.266675i | 0.250946 | − | 0.968001i | \(-0.419258\pi\) |
−0.712840 | + | 0.701326i | \(0.752592\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.03235e7 | − | 8.71629e7i | 0.0670007 | − | 0.116049i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.15131e8i | 0.284543i | 0.989828 | + | 0.142271i | \(0.0454406\pi\) | ||||
−0.989828 | + | 0.142271i | \(0.954559\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.66376e9 | −2.18614 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.83680e8 | + | 5.67928e8i | 1.28408 | + | 0.741361i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.34044e8 | − | 2.32171e8i | 0.173836 | − | 0.301093i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.50647e8 | 1.09598 | 0.547990 | − | 0.836485i | \(-0.315393\pi\) | ||||
0.547990 | + | 0.836485i | \(0.315393\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.87962e8 | − | 4.98765e8i | −0.368601 | − | 0.638436i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.82887e7 | −0.0232582 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.96423e8 | + | 1.71140e8i | −0.374530 | + | 0.216235i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.89955e8 | − | 1.09671e8i | 0.238458 | − | 0.137674i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.39242e8 | − | 9.33995e8i | 0.672569 | − | 1.16492i | −0.304605 | − | 0.952479i | \(-0.598524\pi\) |
0.977173 | − | 0.212444i | \(-0.0681423\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.18747e8 | − | 2.77198e8i | −0.890691 | − | 0.343512i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.07061e8 | + | 3.50487e8i | 0.747459 | + | 0.431546i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.47950e8 | + | 1.64190e9i | 1.15971 | + | 2.00868i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.24661e8 | + | 1.08194e9i | 0.759321 | + | 1.31518i | 0.943197 | + | 0.332233i | \(0.107802\pi\) |
−0.183877 | + | 0.982949i | \(0.558865\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 7.02050e8i | − | 0.847952i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.01517e8 | + | 4.05021e8i | −0.841917 | + | 0.486081i | −0.857916 | − | 0.513791i | \(-0.828241\pi\) |
0.0159981 | + | 0.999872i | \(0.494907\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.90933e8i | 1.06245i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.26479e9 | − | 7.30225e8i | −1.49872 | − | 0.865289i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.63881e8 | − | 6.30261e8i | 0.428460 | − | 0.742114i | −0.568277 | − | 0.822837i | \(-0.692390\pi\) |
0.996737 | + | 0.0807237i | \(0.0257231\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.43559e7i | 0.110400i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.80654e8 | −0.558844 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.12803e7 | + | 1.80597e7i | 0.0361403 | + | 0.0208656i | 0.517961 | − | 0.855404i | \(-0.326691\pi\) |
−0.481821 | + | 0.876270i | \(0.660024\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.08560e8 | + | 7.07646e8i | −0.469079 | + | 0.812468i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.48272e9 | −1.69170 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.42406e8 | + | 7.66270e8i | 0.501609 | + | 0.868812i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.47040e8 | 0.503705 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.16774e8 | − | 6.74196e7i | 0.130758 | − | 0.0754932i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.63202e7 | − | 3.82900e7i | 0.0738012 | − | 0.0426092i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.78062e8 | − | 3.08412e8i | 0.196920 | − | 0.341076i | −0.750608 | − | 0.660748i | \(-0.770239\pi\) |
0.947528 | + | 0.319672i | \(0.103573\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.03950e9 | + | 1.62965e8i | −1.14249 | + | 0.179112i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.15308e9 | − | 6.65730e8i | −1.25951 | − | 0.727177i | −0.286529 | − | 0.958072i | \(-0.592501\pi\) |
−0.972979 | + | 0.230895i | \(0.925835\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.81038e7 | + | 3.13566e7i | 0.0196531 | + | 0.0340401i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.92462e7 | − | 6.79763e7i | −0.0423432 | − | 0.0733405i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.13278e9i | 1.21468i | 0.794442 | + | 0.607339i | \(0.207763\pi\) | ||||
−0.794442 | + | 0.607339i | \(0.792237\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.75874e8 | − | 4.47951e8i | 0.826881 | − | 0.477400i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.01256e8i | 0.425025i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.03981e9 | + | 6.00334e8i | 1.09469 | + | 0.632022i | 0.934822 | − | 0.355116i | \(-0.115559\pi\) |
0.159872 | + | 0.987138i | \(0.448892\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.29887e7 | − | 1.09100e8i | 0.0659104 | − | 0.114160i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.57645e8i | 0.475967i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.54529e7 | −0.0159743 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.08820e9 | − | 6.28275e8i | −1.11812 | − | 0.645548i | −0.177201 | − | 0.984175i | \(-0.556704\pi\) |
−0.940921 | + | 0.338626i | \(0.890038\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.28954e7 | + | 9.16176e7i | −0.0540220 | + | 0.0935688i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.17199e8 | −0.220490 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.66824e8 | + | 2.88947e8i | 0.168334 | + | 0.291564i | 0.937834 | − | 0.347083i | \(-0.112828\pi\) |
−0.769500 | + | 0.638647i | \(0.779495\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.35872e9 | −1.36281 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 76.7.h.a.65.8 | ✓ | 20 | |
3.2 | odd | 2 | 684.7.y.c.217.2 | 20 | |||
19.12 | odd | 6 | inner | 76.7.h.a.69.8 | yes | 20 | |
57.50 | even | 6 | 684.7.y.c.145.2 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.7.h.a.65.8 | ✓ | 20 | 1.1 | even | 1 | trivial | |
76.7.h.a.69.8 | yes | 20 | 19.12 | odd | 6 | inner | |
684.7.y.c.145.2 | 20 | 57.50 | even | 6 | |||
684.7.y.c.217.2 | 20 | 3.2 | odd | 2 |