Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,7,Mod(58,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
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("177.58");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.c (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: | \(40.7195728007\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.17 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.7.c.a.58.44 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 8.09269i | − | 1.01159i | −0.862655 | − | 0.505793i | \(-0.831200\pi\) | ||
0.862655 | − | 0.505793i | \(-0.168800\pi\) | |||||||
\(3\) | −15.5885 | −0.577350 | ||||||||
\(4\) | −1.49168 | −0.0233076 | ||||||||
\(5\) | −181.057 | −1.44846 | −0.724229 | − | 0.689559i | \(-0.757804\pi\) | ||||
−0.724229 | + | 0.689559i | \(0.757804\pi\) | |||||||
\(6\) | 126.153i | 0.584040i | ||||||||
\(7\) | 502.973 | 1.46639 | 0.733196 | − | 0.680017i | \(-0.238028\pi\) | ||||
0.733196 | + | 0.680017i | \(0.238028\pi\) | |||||||
\(8\) | − | 505.861i | − | 0.988009i | ||||||
\(9\) | 243.000 | 0.333333 | ||||||||
\(10\) | 1465.24i | 1.46524i | ||||||||
\(11\) | 1074.07i | 0.806965i | 0.914987 | + | 0.403482i | \(0.132200\pi\) | ||||
−0.914987 | + | 0.403482i | \(0.867800\pi\) | |||||||
\(12\) | 23.2531 | 0.0134566 | ||||||||
\(13\) | − | 3240.18i | − | 1.47482i | −0.675445 | − | 0.737411i | \(-0.736048\pi\) | ||
0.675445 | − | 0.737411i | \(-0.263952\pi\) | |||||||
\(14\) | − | 4070.40i | − | 1.48338i | ||||||
\(15\) | 2822.40 | 0.836268 | ||||||||
\(16\) | −4189.24 | −1.02276 | ||||||||
\(17\) | −8984.93 | −1.82881 | −0.914404 | − | 0.404804i | \(-0.867340\pi\) | ||||
−0.914404 | + | 0.404804i | \(0.867340\pi\) | |||||||
\(18\) | − | 1966.52i | − | 0.337196i | ||||||
\(19\) | −3953.23 | −0.576356 | −0.288178 | − | 0.957577i | \(-0.593050\pi\) | ||||
−0.288178 | + | 0.957577i | \(0.593050\pi\) | |||||||
\(20\) | 270.080 | 0.0337600 | ||||||||
\(21\) | −7840.57 | −0.846622 | ||||||||
\(22\) | 8692.12 | 0.816315 | ||||||||
\(23\) | − | 8371.32i | − | 0.688035i | −0.938963 | − | 0.344017i | \(-0.888212\pi\) | ||
0.938963 | − | 0.344017i | \(-0.111788\pi\) | |||||||
\(24\) | 7885.59i | 0.570427i | ||||||||
\(25\) | 17156.7 | 1.09803 | ||||||||
\(26\) | −26221.8 | −1.49191 | ||||||||
\(27\) | −3788.00 | −0.192450 | ||||||||
\(28\) | −750.276 | −0.0341780 | ||||||||
\(29\) | 24362.4 | 0.998909 | 0.499454 | − | 0.866340i | \(-0.333534\pi\) | ||||
0.499454 | + | 0.866340i | \(0.333534\pi\) | |||||||
\(30\) | − | 22840.8i | − | 0.845957i | ||||||
\(31\) | 32425.1i | 1.08842i | 0.838950 | + | 0.544209i | \(0.183170\pi\) | ||||
−0.838950 | + | 0.544209i | \(0.816830\pi\) | |||||||
\(32\) | 1527.18i | 0.0466057i | ||||||||
\(33\) | − | 16743.1i | − | 0.465901i | ||||||
\(34\) | 72712.3i | 1.85000i | ||||||||
\(35\) | −91066.9 | −2.12401 | ||||||||
\(36\) | −362.479 | −0.00776919 | ||||||||
\(37\) | 6561.95i | 0.129547i | 0.997900 | + | 0.0647735i | \(0.0206325\pi\) | ||||
−0.997900 | + | 0.0647735i | \(0.979368\pi\) | |||||||
\(38\) | 31992.2i | 0.583034i | ||||||||
\(39\) | 50509.5i | 0.851489i | ||||||||
\(40\) | 91589.8i | 1.43109i | ||||||||
\(41\) | −33681.4 | −0.488696 | −0.244348 | − | 0.969688i | \(-0.578574\pi\) | ||||
−0.244348 | + | 0.969688i | \(0.578574\pi\) | |||||||
\(42\) | 63451.3i | 0.856432i | ||||||||
\(43\) | 29921.5i | 0.376338i | 0.982137 | + | 0.188169i | \(0.0602552\pi\) | ||||
−0.982137 | + | 0.188169i | \(0.939745\pi\) | |||||||
\(44\) | − | 1602.17i | − | 0.0188084i | ||||||
\(45\) | −43996.9 | −0.482819 | ||||||||
\(46\) | −67746.5 | −0.696007 | ||||||||
\(47\) | 43669.3i | 0.420612i | 0.977636 | + | 0.210306i | \(0.0674461\pi\) | ||||
−0.977636 | + | 0.210306i | \(0.932554\pi\) | |||||||
\(48\) | 65303.8 | 0.590493 | ||||||||
\(49\) | 135332. | 1.15031 | ||||||||
\(50\) | − | 138844.i | − | 1.11075i | ||||||
\(51\) | 140061. | 1.05586 | ||||||||
\(52\) | 4833.33i | 0.0343745i | ||||||||
\(53\) | 44950.7 | 0.301932 | 0.150966 | − | 0.988539i | \(-0.451762\pi\) | ||||
0.150966 | + | 0.988539i | \(0.451762\pi\) | |||||||
\(54\) | 30655.1i | 0.194680i | ||||||||
\(55\) | − | 194468.i | − | 1.16886i | ||||||
\(56\) | − | 254434.i | − | 1.44881i | ||||||
\(57\) | 61624.7 | 0.332759 | ||||||||
\(58\) | − | 197157.i | − | 1.01048i | ||||||
\(59\) | −74835.6 | + | 191259.i | −0.364378 | + | 0.931251i | ||||
\(60\) | −4210.14 | −0.0194914 | ||||||||
\(61\) | 414592.i | 1.82655i | 0.407346 | + | 0.913274i | \(0.366454\pi\) | ||||
−0.407346 | + | 0.913274i | \(0.633546\pi\) | |||||||
\(62\) | 262406. | 1.10103 | ||||||||
\(63\) | 122222. | 0.488797 | ||||||||
\(64\) | −255753. | −0.975619 | ||||||||
\(65\) | 586659.i | 2.13622i | ||||||||
\(66\) | −135497. | −0.471300 | ||||||||
\(67\) | 53813.1i | 0.178922i | 0.995990 | + | 0.0894610i | \(0.0285145\pi\) | ||||
−0.995990 | + | 0.0894610i | \(0.971486\pi\) | |||||||
\(68\) | 13402.7 | 0.0426251 | ||||||||
\(69\) | 130496.i | 0.397237i | ||||||||
\(70\) | 736976.i | 2.14862i | ||||||||
\(71\) | −495039. | −1.38313 | −0.691567 | − | 0.722313i | \(-0.743079\pi\) | ||||
−0.691567 | + | 0.722313i | \(0.743079\pi\) | |||||||
\(72\) | − | 122924.i | − | 0.329336i | ||||||
\(73\) | − | 388925.i | − | 0.999764i | −0.866093 | − | 0.499882i | \(-0.833377\pi\) | ||
0.866093 | − | 0.499882i | \(-0.166623\pi\) | |||||||
\(74\) | 53103.8 | 0.131048 | ||||||||
\(75\) | −267447. | −0.633949 | ||||||||
\(76\) | 5896.97 | 0.0134335 | ||||||||
\(77\) | 540228.i | 1.18333i | ||||||||
\(78\) | 408757. | 0.861354 | ||||||||
\(79\) | 490758. | 0.995374 | 0.497687 | − | 0.867357i | \(-0.334183\pi\) | ||||
0.497687 | + | 0.867357i | \(0.334183\pi\) | |||||||
\(80\) | 758493. | 1.48143 | ||||||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | 272573.i | 0.494359i | ||||||||
\(83\) | 150512.i | 0.263230i | 0.991301 | + | 0.131615i | \(0.0420163\pi\) | ||||
−0.991301 | + | 0.131615i | \(0.957984\pi\) | |||||||
\(84\) | 11695.7 | 0.0197327 | ||||||||
\(85\) | 1.62679e6 | 2.64895 | ||||||||
\(86\) | 242145. | 0.380698 | ||||||||
\(87\) | −379772. | −0.576720 | ||||||||
\(88\) | 543330. | 0.797289 | ||||||||
\(89\) | 1.05548e6i | 1.49720i | 0.663021 | + | 0.748601i | \(0.269274\pi\) | ||||
−0.663021 | + | 0.748601i | \(0.730726\pi\) | |||||||
\(90\) | 356054.i | 0.488414i | ||||||||
\(91\) | − | 1.62972e6i | − | 2.16267i | ||||||
\(92\) | 12487.4i | 0.0160364i | ||||||||
\(93\) | − | 505457.i | − | 0.628398i | ||||||
\(94\) | 353402. | 0.425486 | ||||||||
\(95\) | 715760. | 0.834828 | ||||||||
\(96\) | − | 23806.3i | − | 0.0269078i | ||||||
\(97\) | 358889.i | 0.393229i | 0.980481 | + | 0.196614i | \(0.0629947\pi\) | ||||
−0.980481 | + | 0.196614i | \(0.937005\pi\) | |||||||
\(98\) | − | 1.09520e6i | − | 1.16364i | ||||||
\(99\) | 260999.i | 0.268988i | ||||||||
\(100\) | −25592.4 | −0.0255924 | ||||||||
\(101\) | 1.61640e6i | 1.56886i | 0.620217 | + | 0.784430i | \(0.287045\pi\) | ||||
−0.620217 | + | 0.784430i | \(0.712955\pi\) | |||||||
\(102\) | − | 1.13347e6i | − | 1.06810i | ||||||
\(103\) | − | 142003.i | − | 0.129953i | −0.997887 | − | 0.0649766i | \(-0.979303\pi\) | ||
0.997887 | − | 0.0649766i | \(-0.0206973\pi\) | |||||||
\(104\) | −1.63908e6 | −1.45714 | ||||||||
\(105\) | 1.41959e6 | 1.22630 | ||||||||
\(106\) | − | 363772.i | − | 0.305430i | ||||||
\(107\) | −2.21316e6 | −1.80660 | −0.903299 | − | 0.429012i | \(-0.858862\pi\) | ||||
−0.903299 | + | 0.429012i | \(0.858862\pi\) | |||||||
\(108\) | 5650.49 | 0.00448554 | ||||||||
\(109\) | 1.19205e6i | 0.920483i | 0.887794 | + | 0.460241i | \(0.152237\pi\) | ||||
−0.887794 | + | 0.460241i | \(0.847763\pi\) | |||||||
\(110\) | −1.57377e6 | −1.18240 | ||||||||
\(111\) | − | 102291.i | − | 0.0747940i | ||||||
\(112\) | −2.10707e6 | −1.49977 | ||||||||
\(113\) | − | 2.60820e6i | − | 1.80761i | −0.427944 | − | 0.903805i | \(-0.640762\pi\) | ||
0.427944 | − | 0.903805i | \(-0.359238\pi\) | |||||||
\(114\) | − | 498710.i | − | 0.336615i | ||||||
\(115\) | 1.51569e6i | 0.996590i | ||||||||
\(116\) | −36341.0 | −0.0232821 | ||||||||
\(117\) | − | 787364.i | − | 0.491607i | ||||||
\(118\) | 1.54780e6 | + | 605621.i | 0.942041 | + | 0.368600i | ||||
\(119\) | −4.51917e6 | −2.68175 | ||||||||
\(120\) | − | 1.42774e6i | − | 0.826240i | ||||||
\(121\) | 617934. | 0.348808 | ||||||||
\(122\) | 3.35516e6 | 1.84771 | ||||||||
\(123\) | 525041. | 0.282149 | ||||||||
\(124\) | − | 48368.0i | − | 0.0253684i | ||||||
\(125\) | −277333. | −0.141995 | ||||||||
\(126\) | − | 989108.i | − | 0.494461i | ||||||
\(127\) | −3.24582e6 | −1.58458 | −0.792289 | − | 0.610146i | \(-0.791111\pi\) | ||||
−0.792289 | + | 0.610146i | \(0.791111\pi\) | |||||||
\(128\) | 2.16747e6i | 1.03353i | ||||||||
\(129\) | − | 466430.i | − | 0.217279i | ||||||
\(130\) | 4.74765e6 | 2.16097 | ||||||||
\(131\) | 2.05977e6i | 0.916231i | 0.888893 | + | 0.458116i | \(0.151475\pi\) | ||||
−0.888893 | + | 0.458116i | \(0.848525\pi\) | |||||||
\(132\) | 24975.4i | 0.0108590i | ||||||||
\(133\) | −1.98836e6 | −0.845164 | ||||||||
\(134\) | 435493. | 0.180995 | ||||||||
\(135\) | 685844. | 0.278756 | ||||||||
\(136\) | 4.54512e6i | 1.80688i | ||||||||
\(137\) | −732623. | −0.284917 | −0.142459 | − | 0.989801i | \(-0.545501\pi\) | ||||
−0.142459 | + | 0.989801i | \(0.545501\pi\) | |||||||
\(138\) | 1.05606e6 | 0.401840 | ||||||||
\(139\) | 296030. | 0.110228 | 0.0551140 | − | 0.998480i | \(-0.482448\pi\) | ||||
0.0551140 | + | 0.998480i | \(0.482448\pi\) | |||||||
\(140\) | 135843. | 0.0495055 | ||||||||
\(141\) | − | 680736.i | − | 0.242841i | ||||||
\(142\) | 4.00620e6i | 1.39916i | ||||||||
\(143\) | 3.48018e6 | 1.19013 | ||||||||
\(144\) | −1.01799e6 | −0.340921 | ||||||||
\(145\) | −4.41099e6 | −1.44688 | ||||||||
\(146\) | −3.14745e6 | −1.01135 | ||||||||
\(147\) | −2.10962e6 | −0.664130 | ||||||||
\(148\) | − | 9788.35i | − | 0.00301943i | ||||||
\(149\) | − | 3.23510e6i | − | 0.977977i | −0.872290 | − | 0.488988i | \(-0.837366\pi\) | ||
0.872290 | − | 0.488988i | \(-0.162634\pi\) | |||||||
\(150\) | 2.16437e6i | 0.641294i | ||||||||
\(151\) | − | 5.90713e6i | − | 1.71572i | −0.513887 | − | 0.857858i | \(-0.671795\pi\) | ||
0.513887 | − | 0.857858i | \(-0.328205\pi\) | |||||||
\(152\) | 1.99978e6i | 0.569445i | ||||||||
\(153\) | −2.18334e6 | −0.609602 | ||||||||
\(154\) | 4.37190e6 | 1.19704 | ||||||||
\(155\) | − | 5.87079e6i | − | 1.57653i | ||||||
\(156\) | − | 75344.2i | − | 0.0198461i | ||||||
\(157\) | 1.48706e6i | 0.384265i | 0.981369 | + | 0.192132i | \(0.0615403\pi\) | ||||
−0.981369 | + | 0.192132i | \(0.938460\pi\) | |||||||
\(158\) | − | 3.97156e6i | − | 1.00691i | ||||||
\(159\) | −700712. | −0.174320 | ||||||||
\(160\) | − | 276506.i | − | 0.0675064i | ||||||
\(161\) | − | 4.21055e6i | − | 1.00893i | ||||||
\(162\) | − | 477865.i | − | 0.112399i | ||||||
\(163\) | −1.88948e6 | −0.436293 | −0.218147 | − | 0.975916i | \(-0.570001\pi\) | ||||
−0.218147 | + | 0.975916i | \(0.570001\pi\) | |||||||
\(164\) | 50242.1 | 0.0113903 | ||||||||
\(165\) | 3.03146e6i | 0.674839i | ||||||||
\(166\) | 1.21804e6 | 0.266280 | ||||||||
\(167\) | −5.60531e6 | −1.20351 | −0.601755 | − | 0.798680i | \(-0.705532\pi\) | ||||
−0.601755 | + | 0.798680i | \(0.705532\pi\) | |||||||
\(168\) | 3.96623e6i | 0.836470i | ||||||||
\(169\) | −5.67198e6 | −1.17510 | ||||||||
\(170\) | − | 1.31651e7i | − | 2.67964i | ||||||
\(171\) | −960634. | −0.192119 | ||||||||
\(172\) | − | 44633.4i | − | 0.00877152i | ||||||
\(173\) | 1.42134e6i | 0.274511i | 0.990536 | + | 0.137256i | \(0.0438282\pi\) | ||||
−0.990536 | + | 0.137256i | \(0.956172\pi\) | |||||||
\(174\) | 3.07338e6i | 0.583402i | ||||||||
\(175\) | 8.62937e6 | 1.61015 | ||||||||
\(176\) | − | 4.49954e6i | − | 0.825335i | ||||||
\(177\) | 1.16657e6 | − | 2.98144e6i | 0.210374 | − | 0.537658i | ||||
\(178\) | 8.54168e6 | 1.51455 | ||||||||
\(179\) | 2.41255e6i | 0.420647i | 0.977632 | + | 0.210323i | \(0.0674517\pi\) | ||||
−0.977632 | + | 0.210323i | \(0.932548\pi\) | |||||||
\(180\) | 65629.5 | 0.0112533 | ||||||||
\(181\) | 3.67987e6 | 0.620579 | 0.310290 | − | 0.950642i | \(-0.399574\pi\) | ||||
0.310290 | + | 0.950642i | \(0.399574\pi\) | |||||||
\(182\) | −1.31889e7 | −2.18773 | ||||||||
\(183\) | − | 6.46285e6i | − | 1.05456i | ||||||
\(184\) | −4.23472e6 | −0.679785 | ||||||||
\(185\) | − | 1.18809e6i | − | 0.187644i | ||||||
\(186\) | −4.09051e6 | −0.635679 | ||||||||
\(187\) | − | 9.65045e6i | − | 1.47578i | ||||||
\(188\) | − | 65140.7i | − | 0.00980346i | ||||||
\(189\) | −1.90526e6 | −0.282207 | ||||||||
\(190\) | − | 5.79243e6i | − | 0.844501i | ||||||
\(191\) | 1.06137e7i | 1.52323i | 0.648030 | + | 0.761614i | \(0.275593\pi\) | ||||
−0.648030 | + | 0.761614i | \(0.724407\pi\) | |||||||
\(192\) | 3.98679e6 | 0.563274 | ||||||||
\(193\) | −7.19890e6 | −1.00137 | −0.500684 | − | 0.865630i | \(-0.666918\pi\) | ||||
−0.500684 | + | 0.865630i | \(0.666918\pi\) | |||||||
\(194\) | 2.90438e6 | 0.397785 | ||||||||
\(195\) | − | 9.14510e6i | − | 1.23335i | ||||||
\(196\) | −201873. | −0.0268109 | ||||||||
\(197\) | 3.15905e6 | 0.413197 | 0.206598 | − | 0.978426i | \(-0.433761\pi\) | ||||
0.206598 | + | 0.978426i | \(0.433761\pi\) | |||||||
\(198\) | 2.11219e6 | 0.272105 | ||||||||
\(199\) | −1.07904e7 | −1.36923 | −0.684615 | − | 0.728905i | \(-0.740030\pi\) | ||||
−0.684615 | + | 0.728905i | \(0.740030\pi\) | |||||||
\(200\) | − | 8.67892e6i | − | 1.08487i | ||||||
\(201\) | − | 838864.i | − | 0.103301i | ||||||
\(202\) | 1.30810e7 | 1.58704 | ||||||||
\(203\) | 1.22536e7 | 1.46479 | ||||||||
\(204\) | −208927. | −0.0246096 | ||||||||
\(205\) | 6.09827e6 | 0.707856 | ||||||||
\(206\) | −1.14919e6 | −0.131459 | ||||||||
\(207\) | − | 2.03423e6i | − | 0.229345i | ||||||
\(208\) | 1.35739e7i | 1.50839i | ||||||||
\(209\) | − | 4.24604e6i | − | 0.465099i | ||||||
\(210\) | − | 1.14883e7i | − | 1.24051i | ||||||
\(211\) | − | 7.52245e6i | − | 0.800778i | −0.916345 | − | 0.400389i | \(-0.868875\pi\) | ||
0.916345 | − | 0.400389i | \(-0.131125\pi\) | |||||||
\(212\) | −67052.3 | −0.00703730 | ||||||||
\(213\) | 7.71689e6 | 0.798552 | ||||||||
\(214\) | 1.79104e7i | 1.82753i | ||||||||
\(215\) | − | 5.41750e6i | − | 0.545110i | ||||||
\(216\) | 1.91620e6i | 0.190142i | ||||||||
\(217\) | 1.63089e7i | 1.59605i | ||||||||
\(218\) | 9.64691e6 | 0.931148 | ||||||||
\(219\) | 6.06275e6i | 0.577214i | ||||||||
\(220\) | 290085.i | 0.0272432i | ||||||||
\(221\) | 2.91128e7i | 2.69716i | ||||||||
\(222\) | −827807. | −0.0756606 | ||||||||
\(223\) | 1.15483e7 | 1.04136 | 0.520682 | − | 0.853751i | \(-0.325678\pi\) | ||||
0.520682 | + | 0.853751i | \(0.325678\pi\) | |||||||
\(224\) | 768128.i | 0.0683423i | ||||||||
\(225\) | 4.16909e6 | 0.366011 | ||||||||
\(226\) | −2.11073e7 | −1.82855 | ||||||||
\(227\) | − | 2.29119e7i | − | 1.95877i | −0.202008 | − | 0.979384i | \(-0.564747\pi\) | ||
0.202008 | − | 0.979384i | \(-0.435253\pi\) | |||||||
\(228\) | −91924.6 | −0.00775581 | ||||||||
\(229\) | 2.08143e7i | 1.73323i | 0.498981 | + | 0.866613i | \(0.333708\pi\) | ||||
−0.498981 | + | 0.866613i | \(0.666292\pi\) | |||||||
\(230\) | 1.22660e7 | 1.00814 | ||||||||
\(231\) | − | 8.42132e6i | − | 0.683194i | ||||||
\(232\) | − | 1.23240e7i | − | 0.986931i | ||||||
\(233\) | − | 1.12126e7i | − | 0.886417i | −0.896419 | − | 0.443208i | \(-0.853840\pi\) | ||
0.896419 | − | 0.443208i | \(-0.146160\pi\) | |||||||
\(234\) | −6.37190e6 | −0.497303 | ||||||||
\(235\) | − | 7.90664e6i | − | 0.609240i | ||||||
\(236\) | 111631. | − | 285299.i | 0.00849276 | − | 0.0217052i | ||||
\(237\) | −7.65016e6 | −0.574679 | ||||||||
\(238\) | 3.65723e7i | 2.71282i | ||||||||
\(239\) | 1.48994e7 | 1.09138 | 0.545690 | − | 0.837987i | \(-0.316267\pi\) | ||||
0.545690 | + | 0.837987i | \(0.316267\pi\) | |||||||
\(240\) | −1.18237e7 | −0.855305 | ||||||||
\(241\) | 6.30441e6 | 0.450395 | 0.225197 | − | 0.974313i | \(-0.427697\pi\) | ||||
0.225197 | + | 0.974313i | \(0.427697\pi\) | |||||||
\(242\) | − | 5.00075e6i | − | 0.352849i | ||||||
\(243\) | −920483. | −0.0641500 | ||||||||
\(244\) | − | 618440.i | − | 0.0425724i | ||||||
\(245\) | −2.45029e7 | −1.66617 | ||||||||
\(246\) | − | 4.24900e6i | − | 0.285418i | ||||||
\(247\) | 1.28092e7i | 0.850022i | ||||||||
\(248\) | 1.64026e7 | 1.07537 | ||||||||
\(249\) | − | 2.34624e6i | − | 0.151976i | ||||||
\(250\) | 2.24437e6i | 0.143640i | ||||||||
\(251\) | 4.31335e6 | 0.272768 | 0.136384 | − | 0.990656i | \(-0.456452\pi\) | ||||
0.136384 | + | 0.990656i | \(0.456452\pi\) | |||||||
\(252\) | −182317. | −0.0113927 | ||||||||
\(253\) | 8.99139e6 | 0.555220 | ||||||||
\(254\) | 2.62674e7i | 1.60294i | ||||||||
\(255\) | −2.53591e7 | −1.52937 | ||||||||
\(256\) | 1.17248e6 | 0.0698850 | ||||||||
\(257\) | 509644. | 0.0300239 | 0.0150120 | − | 0.999887i | \(-0.495221\pi\) | ||||
0.0150120 | + | 0.999887i | \(0.495221\pi\) | |||||||
\(258\) | −3.77467e6 | −0.219796 | ||||||||
\(259\) | 3.30048e6i | 0.189967i | ||||||||
\(260\) | − | 875110.i | − | 0.0497900i | ||||||
\(261\) | 5.92006e6 | 0.332970 | ||||||||
\(262\) | 1.66691e7 | 0.926847 | ||||||||
\(263\) | 1.62201e6 | 0.0891631 | 0.0445815 | − | 0.999006i | \(-0.485805\pi\) | ||||
0.0445815 | + | 0.999006i | \(0.485805\pi\) | |||||||
\(264\) | −8.46967e6 | −0.460315 | ||||||||
\(265\) | −8.13865e6 | −0.437336 | ||||||||
\(266\) | 1.60912e7i | 0.854957i | ||||||||
\(267\) | − | 1.64533e7i | − | 0.864410i | ||||||
\(268\) | − | 80272.2i | − | 0.00417024i | ||||||
\(269\) | − | 1.49664e7i | − | 0.768881i | −0.923150 | − | 0.384440i | \(-0.874394\pi\) | ||
0.923150 | − | 0.384440i | \(-0.125606\pi\) | |||||||
\(270\) | − | 5.55033e6i | − | 0.281986i | ||||||
\(271\) | −2.85453e7 | −1.43426 | −0.717129 | − | 0.696940i | \(-0.754544\pi\) | ||||
−0.717129 | + | 0.696940i | \(0.754544\pi\) | |||||||
\(272\) | 3.76400e7 | 1.87044 | ||||||||
\(273\) | 2.54049e7i | 1.24862i | ||||||||
\(274\) | 5.92890e6i | 0.288219i | ||||||||
\(275\) | 1.84275e7i | 0.886073i | ||||||||
\(276\) | − | 194659.i | − | 0.00925863i | ||||||
\(277\) | −1.84671e7 | −0.868880 | −0.434440 | − | 0.900701i | \(-0.643054\pi\) | ||||
−0.434440 | + | 0.900701i | \(0.643054\pi\) | |||||||
\(278\) | − | 2.39568e6i | − | 0.111505i | ||||||
\(279\) | 7.87929e6i | 0.362806i | ||||||||
\(280\) | 4.60671e7i | 2.09854i | ||||||||
\(281\) | 1.41891e7 | 0.639494 | 0.319747 | − | 0.947503i | \(-0.396402\pi\) | ||||
0.319747 | + | 0.947503i | \(0.396402\pi\) | |||||||
\(282\) | −5.50899e6 | −0.245654 | ||||||||
\(283\) | 1.59920e7i | 0.705576i | 0.935703 | + | 0.352788i | \(0.114766\pi\) | ||||
−0.935703 | + | 0.352788i | \(0.885234\pi\) | |||||||
\(284\) | 738441. | 0.0322375 | ||||||||
\(285\) | −1.11576e7 | −0.481988 | ||||||||
\(286\) | − | 2.81641e7i | − | 1.20392i | ||||||
\(287\) | −1.69408e7 | −0.716620 | ||||||||
\(288\) | 371104.i | 0.0155352i | ||||||||
\(289\) | 5.65914e7 | 2.34454 | ||||||||
\(290\) | 3.56968e7i | 1.46364i | ||||||||
\(291\) | − | 5.59453e6i | − | 0.227031i | ||||||
\(292\) | 580154.i | 0.0233021i | ||||||||
\(293\) | −2.92252e7 | −1.16186 | −0.580932 | − | 0.813952i | \(-0.697312\pi\) | ||||
−0.580932 | + | 0.813952i | \(0.697312\pi\) | |||||||
\(294\) | 1.70725e7i | 0.671825i | ||||||||
\(295\) | 1.35495e7 | − | 3.46289e7i | 0.527786 | − | 1.34888i | ||||
\(296\) | 3.31943e6 | 0.127994 | ||||||||
\(297\) | − | 4.06857e6i | − | 0.155300i | ||||||
\(298\) | −2.61807e7 | −0.989308 | ||||||||
\(299\) | −2.71246e7 | −1.01473 | ||||||||
\(300\) | 398947. | 0.0147758 | ||||||||
\(301\) | 1.50497e7i | 0.551859i | ||||||||
\(302\) | −4.78046e7 | −1.73560 | ||||||||
\(303\) | − | 2.51972e7i | − | 0.905782i | ||||||
\(304\) | 1.65610e7 | 0.589476 | ||||||||
\(305\) | − | 7.50649e7i | − | 2.64568i | ||||||
\(306\) | 1.76691e7i | 0.616666i | ||||||||
\(307\) | 1.48404e7 | 0.512898 | 0.256449 | − | 0.966558i | \(-0.417447\pi\) | ||||
0.256449 | + | 0.966558i | \(0.417447\pi\) | |||||||
\(308\) | − | 805850.i | − | 0.0275805i | ||||||
\(309\) | 2.21361e6i | 0.0750285i | ||||||||
\(310\) | −4.75105e7 | −1.59479 | ||||||||
\(311\) | −2.14470e7 | −0.712994 | −0.356497 | − | 0.934296i | \(-0.616029\pi\) | ||||
−0.356497 | + | 0.934296i | \(0.616029\pi\) | |||||||
\(312\) | 2.55507e7 | 0.841278 | ||||||||
\(313\) | 9.09563e6i | 0.296620i | 0.988941 | + | 0.148310i | \(0.0473833\pi\) | ||||
−0.988941 | + | 0.148310i | \(0.952617\pi\) | |||||||
\(314\) | 1.20344e7 | 0.388717 | ||||||||
\(315\) | −2.21292e7 | −0.708003 | ||||||||
\(316\) | −732056. | −0.0231997 | ||||||||
\(317\) | 8.24643e6 | 0.258874 | 0.129437 | − | 0.991588i | \(-0.458683\pi\) | ||||
0.129437 | + | 0.991588i | \(0.458683\pi\) | |||||||
\(318\) | 5.67065e6i | 0.176340i | ||||||||
\(319\) | 2.61669e7i | 0.806084i | ||||||||
\(320\) | 4.63059e7 | 1.41314 | ||||||||
\(321\) | 3.44997e7 | 1.04304 | ||||||||
\(322\) | −3.40747e7 | −1.02062 | ||||||||
\(323\) | 3.55195e7 | 1.05404 | ||||||||
\(324\) | −88082.5 | −0.00258973 | ||||||||
\(325\) | − | 5.55910e7i | − | 1.61940i | ||||||
\(326\) | 1.52909e7i | 0.441348i | ||||||||
\(327\) | − | 1.85822e7i | − | 0.531441i | ||||||
\(328\) | 1.70381e7i | 0.482836i | ||||||||
\(329\) | 2.19644e7i | 0.616783i | ||||||||
\(330\) | 2.45327e7 | 0.682658 | ||||||||
\(331\) | 1.87982e6 | 0.0518360 | 0.0259180 | − | 0.999664i | \(-0.491749\pi\) | ||||
0.0259180 | + | 0.999664i | \(0.491749\pi\) | |||||||
\(332\) | − | 224516.i | − | 0.00613525i | ||||||
\(333\) | 1.59455e6i | 0.0431823i | ||||||||
\(334\) | 4.53620e7i | 1.21746i | ||||||||
\(335\) | − | 9.74326e6i | − | 0.259161i | ||||||
\(336\) | 3.28460e7 | 0.865895 | ||||||||
\(337\) | 1.28467e7i | 0.335661i | 0.985816 | + | 0.167831i | \(0.0536762\pi\) | ||||
−0.985816 | + | 0.167831i | \(0.946324\pi\) | |||||||
\(338\) | 4.59016e7i | 1.18871i | ||||||||
\(339\) | 4.06577e7i | 1.04362i | ||||||||
\(340\) | −2.42665e6 | −0.0617406 | ||||||||
\(341\) | −3.48268e7 | −0.878315 | ||||||||
\(342\) | 7.77412e6i | 0.194345i | ||||||||
\(343\) | 8.89429e6 | 0.220409 | ||||||||
\(344\) | 1.51361e7 | 0.371825 | ||||||||
\(345\) | − | 2.36273e7i | − | 0.575382i | ||||||
\(346\) | 1.15025e7 | 0.277692 | ||||||||
\(347\) | − | 3.81906e7i | − | 0.914047i | −0.889455 | − | 0.457023i | \(-0.848916\pi\) | ||
0.889455 | − | 0.457023i | \(-0.151084\pi\) | |||||||
\(348\) | 566500. | 0.0134419 | ||||||||
\(349\) | − | 5.47515e7i | − | 1.28801i | −0.765021 | − | 0.644006i | \(-0.777271\pi\) | ||
0.765021 | − | 0.644006i | \(-0.222729\pi\) | |||||||
\(350\) | − | 6.98349e7i | − | 1.62880i | ||||||
\(351\) | 1.22738e7i | 0.283830i | ||||||||
\(352\) | −1.64029e6 | −0.0376092 | ||||||||
\(353\) | − | 6.62688e7i | − | 1.50656i | −0.657703 | − | 0.753278i | \(-0.728472\pi\) | ||
0.657703 | − | 0.753278i | \(-0.271528\pi\) | |||||||
\(354\) | −2.41279e7 | − | 9.44070e6i | −0.543888 | − | 0.212811i | ||||
\(355\) | 8.96304e7 | 2.00341 | ||||||||
\(356\) | − | 1.57444e6i | − | 0.0348961i | ||||||
\(357\) | 7.04469e7 | 1.54831 | ||||||||
\(358\) | 1.95240e7 | 0.425520 | ||||||||
\(359\) | −2.03844e7 | −0.440570 | −0.220285 | − | 0.975436i | \(-0.570699\pi\) | ||||
−0.220285 | + | 0.975436i | \(0.570699\pi\) | |||||||
\(360\) | 2.22563e7i | 0.477030i | ||||||||
\(361\) | −3.14179e7 | −0.667814 | ||||||||
\(362\) | − | 2.97801e7i | − | 0.627770i | ||||||
\(363\) | −9.63264e6 | −0.201384 | ||||||||
\(364\) | 2.43103e6i | 0.0504065i | ||||||||
\(365\) | 7.04178e7i | 1.44812i | ||||||||
\(366\) | −5.23018e7 | −1.06678 | ||||||||
\(367\) | 3.15331e7i | 0.637924i | 0.947768 | + | 0.318962i | \(0.103334\pi\) | ||||
−0.947768 | + | 0.318962i | \(0.896666\pi\) | |||||||
\(368\) | 3.50695e7i | 0.703698i | ||||||||
\(369\) | −8.18459e6 | −0.162899 | ||||||||
\(370\) | −9.61483e6 | −0.189818 | ||||||||
\(371\) | 2.26090e7 | 0.442751 | ||||||||
\(372\) | 753982.i | 0.0146464i | ||||||||
\(373\) | −8.34425e7 | −1.60791 | −0.803953 | − | 0.594692i | \(-0.797274\pi\) | ||||
−0.803953 | + | 0.594692i | \(0.797274\pi\) | |||||||
\(374\) | −7.80981e7 | −1.49288 | ||||||||
\(375\) | 4.32320e6 | 0.0819807 | ||||||||
\(376\) | 2.20906e7 | 0.415569 | ||||||||
\(377\) | − | 7.89386e7i | − | 1.47321i | ||||||
\(378\) | 1.54187e7i | 0.285477i | ||||||||
\(379\) | 2.24835e7 | 0.412997 | 0.206499 | − | 0.978447i | \(-0.433793\pi\) | ||||
0.206499 | + | 0.978447i | \(0.433793\pi\) | |||||||
\(380\) | −1.06769e6 | −0.0194578 | ||||||||
\(381\) | 5.05973e7 | 0.914856 | ||||||||
\(382\) | 8.58931e7 | 1.54088 | ||||||||
\(383\) | −4.67001e6 | −0.0831231 | −0.0415615 | − | 0.999136i | \(-0.513233\pi\) | ||||
−0.0415615 | + | 0.999136i | \(0.513233\pi\) | |||||||
\(384\) | − | 3.37875e7i | − | 0.596708i | ||||||
\(385\) | − | 9.78122e7i | − | 1.71400i | ||||||
\(386\) | 5.82585e7i | 1.01297i | ||||||||
\(387\) | 7.27092e6i | 0.125446i | ||||||||
\(388\) | − | 535349.i | − | 0.00916520i | ||||||
\(389\) | 1.10798e8 | 1.88228 | 0.941141 | − | 0.338015i | \(-0.109755\pi\) | ||||
0.941141 | + | 0.338015i | \(0.109755\pi\) | |||||||
\(390\) | −7.40085e7 | −1.24764 | ||||||||
\(391\) | 7.52157e7i | 1.25828i | ||||||||
\(392\) | − | 6.84594e7i | − | 1.13651i | ||||||
\(393\) | − | 3.21087e7i | − | 0.528986i | ||||||
\(394\) | − | 2.55652e7i | − | 0.417985i | ||||||
\(395\) | −8.88553e7 | −1.44176 | ||||||||
\(396\) | − | 389328.i | − | 0.00626946i | ||||||
\(397\) | − | 8.45514e7i | − | 1.35129i | −0.737226 | − | 0.675646i | \(-0.763865\pi\) | ||
0.737226 | − | 0.675646i | \(-0.236135\pi\) | |||||||
\(398\) | 8.73230e7i | 1.38509i | ||||||||
\(399\) | 3.09955e7 | 0.487956 | ||||||||
\(400\) | −7.18738e7 | −1.12303 | ||||||||
\(401\) | 1.95146e7i | 0.302640i | 0.988485 | + | 0.151320i | \(0.0483524\pi\) | ||||
−0.988485 | + | 0.151320i | \(0.951648\pi\) | |||||||
\(402\) | −6.78867e6 | −0.104498 | ||||||||
\(403\) | 1.05063e8 | 1.60522 | ||||||||
\(404\) | − | 2.41116e6i | − | 0.0365663i | ||||||
\(405\) | −1.06913e7 | −0.160940 | ||||||||
\(406\) | − | 9.91647e7i | − | 1.48176i | ||||||
\(407\) | −7.04799e6 | −0.104540 | ||||||||
\(408\) | − | 7.08514e7i | − | 1.04320i | ||||||
\(409\) | − | 1.29898e8i | − | 1.89860i | −0.314369 | − | 0.949301i | \(-0.601793\pi\) | ||
0.314369 | − | 0.949301i | \(-0.398207\pi\) | |||||||
\(410\) | − | 4.93514e7i | − | 0.716058i | ||||||
\(411\) | 1.14205e7 | 0.164497 | ||||||||
\(412\) | 211824.i | 0.00302889i | ||||||||
\(413\) | −3.76402e7 | + | 9.61983e7i | −0.534321 | + | 1.36558i | ||||
\(414\) | −1.64624e7 | −0.232002 | ||||||||
\(415\) | − | 2.72512e7i | − | 0.381278i | ||||||
\(416\) | 4.94833e6 | 0.0687351 | ||||||||
\(417\) | −4.61466e6 | −0.0636401 | ||||||||
\(418\) | −3.43619e7 | −0.470488 | ||||||||
\(419\) | − | 8.50090e7i | − | 1.15564i | −0.816164 | − | 0.577820i | \(-0.803903\pi\) | ||
0.816164 | − | 0.577820i | \(-0.196097\pi\) | |||||||
\(420\) | −2.11758e6 | −0.0285820 | ||||||||
\(421\) | − | 6.79876e7i | − | 0.911137i | −0.890201 | − | 0.455568i | \(-0.849436\pi\) | ||
0.890201 | − | 0.455568i | \(-0.150564\pi\) | |||||||
\(422\) | −6.08769e7 | −0.810056 | ||||||||
\(423\) | 1.06116e7i | 0.140204i | ||||||||
\(424\) | − | 2.27388e7i | − | 0.298311i | ||||||
\(425\) | −1.54152e8 | −2.00809 | ||||||||
\(426\) | − | 6.24504e7i | − | 0.807805i | ||||||
\(427\) | 2.08528e8i | 2.67844i | ||||||||
\(428\) | 3.30134e6 | 0.0421074 | ||||||||
\(429\) | −5.42507e7 | −0.687121 | ||||||||
\(430\) | −4.38422e7 | −0.551426 | ||||||||
\(431\) | 1.14061e8i | 1.42464i | 0.701855 | + | 0.712320i | \(0.252355\pi\) | ||||
−0.701855 | + | 0.712320i | \(0.747645\pi\) | |||||||
\(432\) | 1.58688e7 | 0.196831 | ||||||||
\(433\) | 4.10358e6 | 0.0505474 | 0.0252737 | − | 0.999681i | \(-0.491954\pi\) | ||||
0.0252737 | + | 0.999681i | \(0.491954\pi\) | |||||||
\(434\) | 1.31983e8 | 1.61454 | ||||||||
\(435\) | 6.87605e7 | 0.835355 | ||||||||
\(436\) | − | 1.77817e6i | − | 0.0214542i | ||||||
\(437\) | 3.30937e7i | 0.396553i | ||||||||
\(438\) | 4.90639e7 | 0.583902 | ||||||||
\(439\) | −7.48938e7 | −0.885223 | −0.442611 | − | 0.896714i | \(-0.645948\pi\) | ||||
−0.442611 | + | 0.896714i | \(0.645948\pi\) | |||||||
\(440\) | −9.83738e7 | −1.15484 | ||||||||
\(441\) | 3.28858e7 | 0.383436 | ||||||||
\(442\) | 2.35601e8 | 2.72842 | ||||||||
\(443\) | − | 1.15108e8i | − | 1.32402i | −0.749495 | − | 0.662011i | \(-0.769703\pi\) | ||
0.749495 | − | 0.662011i | \(-0.230297\pi\) | |||||||
\(444\) | 152585.i | 0.00174327i | ||||||||
\(445\) | − | 1.91103e8i | − | 2.16863i | ||||||
\(446\) | − | 9.34566e7i | − | 1.05343i | ||||||
\(447\) | 5.04302e7i | 0.564635i | ||||||||
\(448\) | −1.28637e8 | −1.43064 | ||||||||
\(449\) | −4.15193e7 | −0.458681 | −0.229341 | − | 0.973346i | \(-0.573657\pi\) | ||||
−0.229341 | + | 0.973346i | \(0.573657\pi\) | |||||||
\(450\) | − | 3.37392e7i | − | 0.370251i | ||||||
\(451\) | − | 3.61762e7i | − | 0.394361i | ||||||
\(452\) | 3.89061e6i | 0.0421310i | ||||||||
\(453\) | 9.20830e7i | 0.990569i | ||||||||
\(454\) | −1.85419e8 | −1.98146 | ||||||||
\(455\) | 2.95073e8i | 3.13253i | ||||||||
\(456\) | − | 3.11735e7i | − | 0.328769i | ||||||
\(457\) | 6.26855e7i | 0.656778i | 0.944543 | + | 0.328389i | \(0.106506\pi\) | ||||
−0.944543 | + | 0.328389i | \(0.893494\pi\) | |||||||
\(458\) | 1.68444e8 | 1.75331 | ||||||||
\(459\) | 3.40349e7 | 0.351954 | ||||||||
\(460\) | − | 2.26093e6i | − | 0.0232281i | ||||||
\(461\) | 7.66005e7 | 0.781860 | 0.390930 | − | 0.920420i | \(-0.372153\pi\) | ||||
0.390930 | + | 0.920420i | \(0.372153\pi\) | |||||||
\(462\) | −6.81512e7 | −0.691110 | ||||||||
\(463\) | − | 5.27702e7i | − | 0.531674i | −0.964018 | − | 0.265837i | \(-0.914352\pi\) | ||
0.964018 | − | 0.265837i | \(-0.0856483\pi\) | |||||||
\(464\) | −1.02060e8 | −1.02165 | ||||||||
\(465\) | 9.15166e7i | 0.910209i | ||||||||
\(466\) | −9.07400e7 | −0.896688 | ||||||||
\(467\) | 1.77663e8i | 1.74440i | 0.489150 | + | 0.872200i | \(0.337307\pi\) | ||||
−0.489150 | + | 0.872200i | \(0.662693\pi\) | |||||||
\(468\) | 1.17450e6i | 0.0114582i | ||||||||
\(469\) | 2.70665e7i | 0.262370i | ||||||||
\(470\) | −6.39860e7 | −0.616299 | ||||||||
\(471\) | − | 2.31810e7i | − | 0.221855i | ||||||
\(472\) | 9.67506e7 | + | 3.78564e7i | 0.920085 | + | 0.360009i | ||||
\(473\) | −3.21378e7 | −0.303691 | ||||||||
\(474\) | 6.19104e7i | 0.581338i | ||||||||
\(475\) | −6.78245e7 | −0.632857 | ||||||||
\(476\) | 6.74118e6 | 0.0625051 | ||||||||
\(477\) | 1.09230e7 | 0.100644 | ||||||||
\(478\) | − | 1.20577e8i | − | 1.10403i | ||||||
\(479\) | −6.15345e7 | −0.559902 | −0.279951 | − | 0.960014i | \(-0.590318\pi\) | ||||
−0.279951 | + | 0.960014i | \(0.590318\pi\) | |||||||
\(480\) | 4.31031e6i | 0.0389749i | ||||||||
\(481\) | 2.12619e7 | 0.191059 | ||||||||
\(482\) | − | 5.10197e7i | − | 0.455613i | ||||||
\(483\) | 6.56359e7i | 0.582506i | ||||||||
\(484\) | −921763. | −0.00812986 | ||||||||
\(485\) | − | 6.49795e7i | − | 0.569575i | ||||||
\(486\) | 7.44919e6i | 0.0648933i | ||||||||
\(487\) | −2.91174e7 | −0.252096 | −0.126048 | − | 0.992024i | \(-0.540229\pi\) | ||||
−0.126048 | + | 0.992024i | \(0.540229\pi\) | |||||||
\(488\) | 2.09726e8 | 1.80465 | ||||||||
\(489\) | 2.94540e7 | 0.251894 | ||||||||
\(490\) | 1.98295e8i | 1.68548i | ||||||||
\(491\) | 1.87066e8 | 1.58034 | 0.790168 | − | 0.612891i | \(-0.209993\pi\) | ||||
0.790168 | + | 0.612891i | \(0.209993\pi\) | |||||||
\(492\) | −783196. | −0.00657620 | ||||||||
\(493\) | −2.18894e8 | −1.82681 | ||||||||
\(494\) | 1.03661e8 | 0.859871 | ||||||||
\(495\) | − | 4.72558e7i | − | 0.389618i | ||||||
\(496\) | − | 1.35836e8i | − | 1.11320i | ||||||
\(497\) | −2.48991e8 | −2.02822 | ||||||||
\(498\) | −1.89874e7 | −0.153737 | ||||||||
\(499\) | −1.67013e8 | −1.34415 | −0.672077 | − | 0.740481i | \(-0.734598\pi\) | ||||
−0.672077 | + | 0.740481i | \(0.734598\pi\) | |||||||
\(500\) | 413694. | 0.00330955 | ||||||||
\(501\) | 8.73781e7 | 0.694847 | ||||||||
\(502\) | − | 3.49066e7i | − | 0.275928i | ||||||
\(503\) | 8.91849e7i | 0.700789i | 0.936602 | + | 0.350395i | \(0.113953\pi\) | ||||
−0.936602 | + | 0.350395i | \(0.886047\pi\) | |||||||
\(504\) | − | 6.18275e7i | − | 0.482936i | ||||||
\(505\) | − | 2.92661e8i | − | 2.27243i | ||||||
\(506\) | − | 7.27645e7i | − | 0.561653i | ||||||
\(507\) | 8.84174e7 | 0.678443 | ||||||||
\(508\) | 4.84174e6 | 0.0369326 | ||||||||
\(509\) | 9.46235e7i | 0.717539i | 0.933426 | + | 0.358770i | \(0.116804\pi\) | ||||
−0.933426 | + | 0.358770i | \(0.883196\pi\) | |||||||
\(510\) | 2.05223e8i | 1.54709i | ||||||||
\(511\) | − | 1.95619e8i | − | 1.46605i | ||||||
\(512\) | 1.29229e8i | 0.962834i | ||||||||
\(513\) | 1.49748e7 | 0.110920 | ||||||||
\(514\) | − | 4.12439e6i | − | 0.0303718i | ||||||
\(515\) | 2.57107e7i | 0.188232i | ||||||||
\(516\) | 695766.i | 0.00506424i | ||||||||
\(517\) | −4.69038e7 | −0.339420 | ||||||||
\(518\) | 2.67098e7 | 0.192168 | ||||||||
\(519\) | − | 2.21565e7i | − | 0.158489i | ||||||
\(520\) | 2.96768e8 | 2.11060 | ||||||||
\(521\) | −2.18083e8 | −1.54209 | −0.771044 | − | 0.636782i | \(-0.780265\pi\) | ||||
−0.771044 | + | 0.636782i | \(0.780265\pi\) | |||||||
\(522\) | − | 4.79092e7i | − | 0.336828i | ||||||
\(523\) | −2.69917e8 | −1.88680 | −0.943399 | − | 0.331660i | \(-0.892391\pi\) | ||||
−0.943399 | + | 0.331660i | \(0.892391\pi\) | |||||||
\(524\) | − | 3.07253e6i | − | 0.0213551i | ||||||
\(525\) | −1.34519e8 | −0.929618 | ||||||||
\(526\) | − | 1.31264e7i | − | 0.0901962i | ||||||
\(527\) | − | 2.91337e8i | − | 1.99051i | ||||||
\(528\) | 7.01409e7i | 0.476507i | ||||||||
\(529\) | 7.79569e7 | 0.526608 | ||||||||
\(530\) | 6.58636e7i | 0.442403i | ||||||||
\(531\) | −1.81850e7 | + | 4.64760e7i | −0.121459 | + | 0.310417i | ||||
\(532\) | 2.96601e6 | 0.0196987 | ||||||||
\(533\) | 1.09134e8i | 0.720740i | ||||||||
\(534\) | −1.33152e8 | −0.874425 | ||||||||
\(535\) | 4.00709e8 | 2.61678 | ||||||||
\(536\) | 2.72219e7 | 0.176777 | ||||||||
\(537\) | − | 3.76079e7i | − | 0.242860i | ||||||
\(538\) | −1.21118e8 | −0.777790 | ||||||||
\(539\) | 1.45357e8i | 0.928257i | ||||||||
\(540\) | −1.02306e6 | −0.00649712 | ||||||||
\(541\) | 4.97524e7i | 0.314211i | 0.987582 | + | 0.157106i | \(0.0502163\pi\) | ||||
−0.987582 | + | 0.157106i | \(0.949784\pi\) | |||||||
\(542\) | 2.31009e8i | 1.45088i | ||||||||
\(543\) | −5.73636e7 | −0.358292 | ||||||||
\(544\) | − | 1.37216e7i | − | 0.0852329i | ||||||
\(545\) | − | 2.15830e8i | − | 1.33328i | ||||||
\(546\) | 2.05594e8 | 1.26308 | ||||||||
\(547\) | −1.70686e8 | −1.04289 | −0.521443 | − | 0.853286i | \(-0.674606\pi\) | ||||
−0.521443 | + | 0.853286i | \(0.674606\pi\) | |||||||
\(548\) | 1.09284e6 | 0.00664073 | ||||||||
\(549\) | 1.00746e8i | 0.608849i | ||||||||
\(550\) | 1.49128e8 | 0.896340 | ||||||||
\(551\) | −9.63100e7 | −0.575727 | ||||||||
\(552\) | 6.60128e7 | 0.392474 | ||||||||
\(553\) | 2.46838e8 | 1.45961 | ||||||||
\(554\) | 1.49449e8i | 0.878947i | ||||||||
\(555\) | 1.85205e7i | 0.108336i | ||||||||
\(556\) | −441584. | −0.00256915 | ||||||||
\(557\) | 2.82753e8 | 1.63622 | 0.818109 | − | 0.575063i | \(-0.195023\pi\) | ||||
0.818109 | + | 0.575063i | \(0.195023\pi\) | |||||||
\(558\) | 6.37647e7 | 0.367010 | ||||||||
\(559\) | 9.69511e7 | 0.555031 | ||||||||
\(560\) | 3.81501e8 | 2.17236 | ||||||||
\(561\) | 1.50436e8i | 0.852044i | ||||||||
\(562\) | − | 1.14828e8i | − | 0.646904i | ||||||
\(563\) | 9.96556e7i | 0.558440i | 0.960227 | + | 0.279220i | \(0.0900759\pi\) | ||||
−0.960227 | + | 0.279220i | \(0.909924\pi\) | |||||||
\(564\) | 1.01544e6i | 0.00566003i | ||||||||
\(565\) | 4.72233e8i | 2.61825i | ||||||||
\(566\) | 1.29418e8 | 0.713751 | ||||||||
\(567\) | 2.97000e7 | 0.162932 | ||||||||
\(568\) | 2.50421e8i | 1.36655i | ||||||||
\(569\) | − | 2.02184e8i | − | 1.09751i | −0.835982 | − | 0.548757i | \(-0.815101\pi\) | ||
0.835982 | − | 0.548757i | \(-0.184899\pi\) | |||||||
\(570\) | 9.02950e7i | 0.487573i | ||||||||
\(571\) | 1.98397e8i | 1.06568i | 0.846216 | + | 0.532840i | \(0.178875\pi\) | ||||
−0.846216 | + | 0.532840i | \(0.821125\pi\) | |||||||
\(572\) | −5.19134e6 | −0.0277390 | ||||||||
\(573\) | − | 1.65451e8i | − | 0.879437i | ||||||
\(574\) | 1.37097e8i | 0.724924i | ||||||||
\(575\) | − | 1.43625e8i | − | 0.755484i | ||||||
\(576\) | −6.21479e7 | −0.325206 | ||||||||
\(577\) | −8.58467e7 | −0.446885 | −0.223443 | − | 0.974717i | \(-0.571730\pi\) | ||||
−0.223443 | + | 0.974717i | \(0.571730\pi\) | |||||||
\(578\) | − | 4.57977e8i | − | 2.37170i | ||||||
\(579\) | 1.12220e8 | 0.578140 | ||||||||
\(580\) | 6.57980e6 | 0.0337232 | ||||||||
\(581\) | 7.57032e7i | 0.385999i | ||||||||
\(582\) | −4.52748e7 | −0.229661 | ||||||||
\(583\) | 4.82802e7i | 0.243648i | ||||||||
\(584\) | −1.96742e8 | −0.987776 | ||||||||
\(585\) | 1.42558e8i | 0.712072i | ||||||||
\(586\) | 2.36511e8i | 1.17533i | ||||||||
\(587\) | 1.87040e8i | 0.924744i | 0.886686 | + | 0.462372i | \(0.153001\pi\) | ||||
−0.886686 | + | 0.462372i | \(0.846999\pi\) | |||||||
\(588\) | 3.14689e6 | 0.0154793 | ||||||||
\(589\) | − | 1.28184e8i | − | 0.627316i | ||||||
\(590\) | −2.80241e8 | − | 1.09652e8i | −1.36451 | − | 0.533901i | ||||
\(591\) | −4.92446e7 | −0.238559 | ||||||||
\(592\) | − | 2.74896e7i | − | 0.132496i | ||||||
\(593\) | 1.21559e8 | 0.582941 | 0.291470 | − | 0.956580i | \(-0.405856\pi\) | ||||
0.291470 | + | 0.956580i | \(0.405856\pi\) | |||||||
\(594\) | −3.29257e7 | −0.157100 | ||||||||
\(595\) | 8.18229e8 | 3.88440 | ||||||||
\(596\) | 4.82575e6i | 0.0227943i | ||||||||
\(597\) | 1.68205e8 | 0.790525 | ||||||||
\(598\) | 2.19511e8i | 1.02649i | ||||||||
\(599\) | 3.22698e8 | 1.50147 | 0.750733 | − | 0.660606i | \(-0.229701\pi\) | ||||
0.750733 | + | 0.660606i | \(0.229701\pi\) | |||||||
\(600\) | 1.35291e8i | 0.626347i | ||||||||
\(601\) | − | 2.44614e8i | − | 1.12683i | −0.826175 | − | 0.563413i | \(-0.809488\pi\) | ||
0.826175 | − | 0.563413i | \(-0.190512\pi\) | |||||||
\(602\) | 1.21793e8 | 0.558253 | ||||||||
\(603\) | 1.30766e7i | 0.0596407i | ||||||||
\(604\) | 8.81157e6i | 0.0399892i | ||||||||
\(605\) | −1.11881e8 | −0.505233 | ||||||||
\(606\) | −2.03913e8 | −0.916277 | ||||||||
\(607\) | −1.85485e7 | −0.0829358 | −0.0414679 | − | 0.999140i | \(-0.513203\pi\) | ||||
−0.0414679 | + | 0.999140i | \(0.513203\pi\) | |||||||
\(608\) | − | 6.03727e6i | − | 0.0268615i | ||||||
\(609\) | −1.91015e8 | −0.845698 | ||||||||
\(610\) | −6.07477e8 | −2.67633 | ||||||||
\(611\) | 1.41496e8 | 0.620328 | ||||||||
\(612\) | 3.25685e6 | 0.0142084 | ||||||||
\(613\) | 2.82096e8i | 1.22466i | 0.790602 | + | 0.612330i | \(0.209768\pi\) | ||||
−0.790602 | + | 0.612330i | \(0.790232\pi\) | |||||||
\(614\) | − | 1.20099e8i | − | 0.518841i | ||||||
\(615\) | −9.50626e7 | −0.408681 | ||||||||
\(616\) | 2.73280e8 | 1.16914 | ||||||||
\(617\) | 3.38596e8 | 1.44154 | 0.720770 | − | 0.693174i | \(-0.243788\pi\) | ||||
0.720770 | + | 0.693174i | \(0.243788\pi\) | |||||||
\(618\) | 1.79141e7 | 0.0758978 | ||||||||
\(619\) | −1.86438e8 | −0.786071 | −0.393036 | − | 0.919523i | \(-0.628575\pi\) | ||||
−0.393036 | + | 0.919523i | \(0.628575\pi\) | |||||||
\(620\) | 8.75737e6i | 0.0367450i | ||||||||
\(621\) | 3.17105e7i | 0.132412i | ||||||||
\(622\) | 1.73564e8i | 0.721256i | ||||||||
\(623\) | 5.30878e8i | 2.19549i | ||||||||
\(624\) | − | 2.11596e8i | − | 0.870872i | ||||||
\(625\) | −2.17861e8 | −0.892358 | ||||||||
\(626\) | 7.36082e7 | 0.300057 | ||||||||
\(627\) | 6.61893e7i | 0.268525i | ||||||||
\(628\) | − | 2.21823e6i | − | 0.00895628i | ||||||
\(629\) | − | 5.89586e7i | − | 0.236917i | ||||||
\(630\) | 1.79085e8i | 0.716206i | ||||||||
\(631\) | −3.44905e8 | −1.37281 | −0.686407 | − | 0.727218i | \(-0.740813\pi\) | ||||
−0.686407 | + | 0.727218i | \(0.740813\pi\) | |||||||
\(632\) | − | 2.48255e8i | − | 0.983438i | ||||||
\(633\) | 1.17263e8i | 0.462329i | ||||||||
\(634\) | − | 6.67358e7i | − | 0.261873i | ||||||
\(635\) | 5.87680e8 | 2.29519 | ||||||||
\(636\) | 1.04524e6 | 0.00406299 | ||||||||
\(637\) | − | 4.38502e8i | − | 1.69650i | ||||||
\(638\) | 2.11761e8 | 0.815424 | ||||||||
\(639\) | −1.20294e8 | −0.461044 | ||||||||
\(640\) | − | 3.92436e8i | − | 1.49702i | ||||||
\(641\) | −4.28085e8 | −1.62538 | −0.812691 | − | 0.582694i | \(-0.801999\pi\) | ||||
−0.812691 | + | 0.582694i | \(0.801999\pi\) | |||||||
\(642\) | − | 2.79196e8i | − | 1.05512i | ||||||
\(643\) | −4.70703e8 | −1.77057 | −0.885286 | − | 0.465047i | \(-0.846038\pi\) | ||||
−0.885286 | + | 0.465047i | \(0.846038\pi\) | |||||||
\(644\) | 6.28081e6i | 0.0235157i | ||||||||
\(645\) | 8.44505e7i | 0.314719i | ||||||||
\(646\) | − | 2.87448e8i | − | 1.06626i | ||||||
\(647\) | −1.81727e8 | −0.670975 | −0.335487 | − | 0.942045i | \(-0.608901\pi\) | ||||
−0.335487 | + | 0.942045i | \(0.608901\pi\) | |||||||
\(648\) | − | 2.98706e7i | − | 0.109779i | ||||||
\(649\) | −2.05426e8 | − | 8.03787e7i | −0.751487 | − | 0.294040i | ||||
\(650\) | −4.49881e8 | −1.63816 | ||||||||
\(651\) | − | 2.54231e8i | − | 0.921479i | ||||||
\(652\) | 2.81850e6 | 0.0101689 | ||||||||
\(653\) | −1.64342e8 | −0.590213 | −0.295106 | − | 0.955464i | \(-0.595355\pi\) | ||||
−0.295106 | + | 0.955464i | \(0.595355\pi\) | |||||||
\(654\) | −1.50380e8 | −0.537599 | ||||||||
\(655\) | − | 3.72937e8i | − | 1.32712i | ||||||
\(656\) | 1.41100e8 | 0.499821 | ||||||||
\(657\) | − | 9.45089e7i | − | 0.333255i | ||||||
\(658\) | 1.77751e8 | 0.623929 | ||||||||
\(659\) | 1.34126e8i | 0.468659i | 0.972157 | + | 0.234329i | \(0.0752894\pi\) | ||||
−0.972157 | + | 0.234329i | \(0.924711\pi\) | |||||||
\(660\) | − | 4.52198e6i | − | 0.0157289i | ||||||
\(661\) | −3.06053e8 | −1.05972 | −0.529862 | − | 0.848084i | \(-0.677756\pi\) | ||||
−0.529862 | + | 0.848084i | \(0.677756\pi\) | |||||||
\(662\) | − | 1.52128e7i | − | 0.0524366i | ||||||
\(663\) | − | 4.53824e8i | − | 1.55721i | ||||||
\(664\) | 7.61379e7 | 0.260074 | ||||||||
\(665\) | 3.60008e8 | 1.22419 | ||||||||
\(666\) | 1.29042e7 | 0.0436827 | ||||||||
\(667\) | − | 2.03945e8i | − | 0.687284i | ||||||
\(668\) | 8.36135e6 | 0.0280509 | ||||||||
\(669\) | −1.80020e8 | −0.601231 | ||||||||
\(670\) | −7.88492e7 | −0.262164 | ||||||||
\(671\) | −4.45301e8 | −1.47396 | ||||||||
\(672\) | − | 1.19739e7i | − | 0.0394574i | ||||||
\(673\) | 6.88272e7i | 0.225795i | 0.993607 | + | 0.112898i | \(0.0360132\pi\) | ||||
−0.993607 | + | 0.112898i | \(0.963987\pi\) | |||||||
\(674\) | 1.03964e8 | 0.339550 | ||||||||
\(675\) | −6.49897e7 | −0.211316 | ||||||||
\(676\) | 8.46080e6 | 0.0273887 | ||||||||
\(677\) | 2.16960e8 | 0.699221 | 0.349611 | − | 0.936895i | \(-0.386314\pi\) | ||||
0.349611 | + | 0.936895i | \(0.386314\pi\) | |||||||
\(678\) | 3.29031e8 | 1.05572 | ||||||||
\(679\) | 1.80511e8i | 0.576627i | ||||||||
\(680\) | − | 8.22927e8i | − | 2.61719i | ||||||
\(681\) | 3.57161e8i | 1.13090i | ||||||||
\(682\) | 2.81843e8i | 0.888492i | ||||||||
\(683\) | 4.96754e8i | 1.55912i | 0.626328 | + | 0.779560i | \(0.284557\pi\) | ||||
−0.626328 | + | 0.779560i | \(0.715443\pi\) | |||||||
\(684\) | 1.43296e6 | 0.00447782 | ||||||||
\(685\) | 1.32647e8 | 0.412691 | ||||||||
\(686\) | − | 7.19788e7i | − | 0.222963i | ||||||
\(687\) | − | 3.24463e8i | − | 1.00068i | ||||||
\(688\) | − | 1.25348e8i | − | 0.384905i | ||||||
\(689\) | − | 1.45649e8i | − | 0.445296i | ||||||
\(690\) | −1.91208e8 | −0.582048 | ||||||||
\(691\) | 2.16699e8i | 0.656785i | 0.944541 | + | 0.328392i | \(0.106507\pi\) | ||||
−0.944541 | + | 0.328392i | \(0.893493\pi\) | |||||||
\(692\) | − | 2.12020e6i | − | 0.00639820i | ||||||
\(693\) | 1.31275e8i | 0.394442i | ||||||||
\(694\) | −3.09065e8 | −0.924637 | ||||||||
\(695\) | −5.35985e7 | −0.159661 | ||||||||
\(696\) | 1.92112e8i | 0.569805i | ||||||||
\(697\) | 3.02625e8 | 0.893731 | ||||||||
\(698\) | −4.43087e8 | −1.30293 | ||||||||
\(699\) | 1.74787e8i | 0.511773i | ||||||||
\(700\) | −1.28723e7 | −0.0375286 | ||||||||
\(701\) | 3.80877e8i | 1.10568i | 0.833286 | + | 0.552842i | \(0.186457\pi\) | ||||
−0.833286 | + | 0.552842i | \(0.813543\pi\) | |||||||
\(702\) | 9.93281e7 | 0.287118 | ||||||||
\(703\) | − | 2.59409e7i | − | 0.0746652i | ||||||
\(704\) | − | 2.74696e8i | − | 0.787290i | ||||||
\(705\) | 1.23252e8i | 0.351745i | ||||||||
\(706\) | −5.36293e8 | −1.52401 | ||||||||
\(707\) | 8.13004e8i | 2.30057i | ||||||||
\(708\) | −1.74016e6 | + | 4.44737e6i | −0.00490330 | + | 0.0125315i | ||||
\(709\) | 6.14643e8 | 1.72458 | 0.862292 | − | 0.506412i | \(-0.169028\pi\) | ||||
0.862292 | + | 0.506412i | \(0.169028\pi\) | |||||||
\(710\) | − | 7.25351e8i | − | 2.02662i | ||||||
\(711\) | 1.19254e8 | 0.331791 | ||||||||
\(712\) | 5.33926e8 | 1.47925 | ||||||||
\(713\) | 2.71441e8 | 0.748870 | ||||||||
\(714\) | − | 5.70105e8i | − | 1.56625i | ||||||
\(715\) | −6.30113e8 | −1.72385 | ||||||||
\(716\) | − | 3.59876e6i | − | 0.00980425i | ||||||
\(717\) | −2.32259e8 | −0.630109 | ||||||||
\(718\) | 1.64965e8i | 0.445675i | ||||||||
\(719\) | − | 2.89336e8i | − | 0.778423i | −0.921148 | − | 0.389211i | \(-0.872748\pi\) | ||
0.921148 | − | 0.389211i | \(-0.127252\pi\) | |||||||
\(720\) | 1.84314e8 | 0.493811 | ||||||||
\(721\) | − | 7.14238e7i | − | 0.190562i | ||||||
\(722\) | 2.54255e8i | 0.675551i | ||||||||
\(723\) | −9.82761e7 | −0.260036 | ||||||||
\(724\) | −5.48921e6 | −0.0144642 | ||||||||
\(725\) | 4.17979e8 | 1.09683 | ||||||||
\(726\) | 7.79540e7i | 0.203718i | ||||||||
\(727\) | 1.60533e8 | 0.417793 | 0.208896 | − | 0.977938i | \(-0.433013\pi\) | ||||
0.208896 | + | 0.977938i | \(0.433013\pi\) | |||||||
\(728\) | −8.24413e8 | −2.13673 | ||||||||
\(729\) | 1.43489e7 | 0.0370370 | ||||||||
\(730\) | 5.69869e8 | 1.46490 | ||||||||
\(731\) | − | 2.68842e8i | − | 0.688249i | ||||||
\(732\) | 9.64053e6i | 0.0245792i | ||||||||
\(733\) | 1.67584e8 | 0.425519 | 0.212760 | − | 0.977105i | \(-0.431755\pi\) | ||||
0.212760 | + | 0.977105i | \(0.431755\pi\) | |||||||
\(734\) | 2.55188e8 | 0.645315 | ||||||||
\(735\) | 3.81963e8 | 0.961965 | ||||||||
\(736\) | 1.27845e7 | 0.0320664 | ||||||||
\(737\) | −5.77991e7 | −0.144384 | ||||||||
\(738\) | 6.62354e7i | 0.164786i | ||||||||
\(739\) | 1.50914e8i | 0.373934i | 0.982366 | + | 0.186967i | \(0.0598658\pi\) | ||||
−0.982366 | + | 0.186967i | \(0.940134\pi\) | |||||||
\(740\) | 1.77225e6i | 0.00437351i | ||||||||
\(741\) | − | 1.99675e8i | − | 0.490761i | ||||||
\(742\) | − | 1.82967e8i | − | 0.447881i | ||||||
\(743\) | −5.60788e8 | −1.36720 | −0.683601 | − | 0.729856i | \(-0.739587\pi\) | ||||
−0.683601 | + | 0.729856i | \(0.739587\pi\) | |||||||
\(744\) | −2.55691e8 | −0.620863 | ||||||||
\(745\) | 5.85738e8i | 1.41656i | ||||||||
\(746\) | 6.75275e8i | 1.62654i | ||||||||
\(747\) | 3.65743e7i | 0.0877434i | ||||||||
\(748\) | 1.43954e7i | 0.0343969i | ||||||||
\(749\) | −1.11316e9 | −2.64918 | ||||||||
\(750\) | − | 3.49863e7i | − | 0.0829305i | ||||||
\(751\) | − | 4.66632e8i | − | 1.10168i | −0.834612 | − | 0.550839i | \(-0.814308\pi\) | ||
0.834612 | − | 0.550839i | \(-0.185692\pi\) | |||||||
\(752\) | − | 1.82941e8i | − | 0.430187i | ||||||
\(753\) | −6.72384e7 | −0.157483 | ||||||||
\(754\) | −6.38826e8 | −1.49028 | ||||||||
\(755\) | 1.06953e9i | 2.48514i | ||||||||
\(756\) | 2.84204e6 | 0.00657757 | ||||||||
\(757\) | −5.19434e8 | −1.19741 | −0.598705 | − | 0.800969i | \(-0.704318\pi\) | ||||
−0.598705 | + | 0.800969i | \(0.704318\pi\) | |||||||
\(758\) | − | 1.81952e8i | − | 0.417783i | ||||||
\(759\) | −1.40162e8 | −0.320556 | ||||||||
\(760\) | − | 3.62075e8i | − | 0.824817i | ||||||
\(761\) | 3.22688e8 | 0.732198 | 0.366099 | − | 0.930576i | \(-0.380693\pi\) | ||||
0.366099 | + | 0.930576i | \(0.380693\pi\) | |||||||
\(762\) | − | 4.09469e8i | − | 0.925456i | ||||||
\(763\) | 5.99569e8i | 1.34979i | ||||||||
\(764\) | − | 1.58322e7i | − | 0.0355028i | ||||||
\(765\) | 3.95309e8 | 0.882984 | ||||||||
\(766\) | 3.77930e7i | 0.0840862i | ||||||||
\(767\) | 6.19716e8 | + | 2.42481e8i | 1.37343 | + | 0.537392i | ||||
\(768\) | −1.82771e7 | −0.0403481 | ||||||||
\(769\) | 7.22488e7i | 0.158874i | 0.996840 | + | 0.0794368i | \(0.0253122\pi\) | ||||
−0.996840 | + | 0.0794368i | \(0.974688\pi\) | |||||||
\(770\) | −7.91564e8 | −1.73386 | ||||||||
\(771\) | −7.94456e6 | −0.0173343 | ||||||||
\(772\) | 1.07385e7 | 0.0233395 | ||||||||
\(773\) | 6.92238e7i | 0.149871i | 0.997188 | + | 0.0749354i | \(0.0238751\pi\) | ||||
−0.997188 | + | 0.0749354i | \(0.976125\pi\) | |||||||
\(774\) | 5.88413e7 | 0.126899 | ||||||||
\(775\) | 5.56308e8i | 1.19512i | ||||||||
\(776\) | 1.81548e8 | 0.388513 | ||||||||
\(777\) | − | 5.14494e7i | − | 0.109677i | ||||||
\(778\) | − | 8.96657e8i | − | 1.90409i | ||||||
\(779\) | 1.33150e8 | 0.281663 | ||||||||
\(780\) | 1.36416e7i | 0.0287463i | ||||||||
\(781\) | − | 5.31706e8i | − | 1.11614i | ||||||
\(782\) | 6.08698e8 | 1.27286 | ||||||||
\(783\) | −9.22846e7 | −0.192240 | ||||||||
\(784\) | −5.66940e8 | −1.17649 | ||||||||
\(785\) | − | 2.69244e8i | − | 0.556592i | ||||||
\(786\) | −2.59845e8 | −0.535115 | ||||||||
\(787\) | 1.41470e7 | 0.0290229 | 0.0145115 | − | 0.999895i | \(-0.495381\pi\) | ||||
0.0145115 | + | 0.999895i | \(0.495381\pi\) | |||||||
\(788\) | −4.71230e6 | −0.00963062 | ||||||||
\(789\) | −2.52846e7 | −0.0514783 | ||||||||
\(790\) | 7.19079e8i | 1.45846i | ||||||||
\(791\) | − | 1.31185e9i | − | 2.65067i | ||||||
\(792\) | 1.32029e8 | 0.265763 | ||||||||
\(793\) | 1.34335e9 | 2.69383 | ||||||||
\(794\) | −6.84248e8 | −1.36695 | ||||||||
\(795\) | 1.26869e8 | 0.252496 | ||||||||
\(796\) | 1.60958e7 | 0.0319134 | ||||||||
\(797\) | − | 9.86007e8i | − | 1.94762i | −0.227356 | − | 0.973812i | \(-0.573008\pi\) | ||
0.227356 | − | 0.973812i | \(-0.426992\pi\) | |||||||
\(798\) | − | 2.50837e8i | − | 0.493610i | ||||||
\(799\) | − | 3.92365e8i | − | 0.769219i | ||||||
\(800\) | 2.62014e7i | 0.0511746i | ||||||||
\(801\) | 2.56482e8i | 0.499067i | ||||||||
\(802\) | 1.57926e8 | 0.306147 | ||||||||
\(803\) | 4.17733e8 | 0.806775 | ||||||||
\(804\) | 1.25132e6i | 0.00240769i | ||||||||
\(805\) | 7.62350e8i | 1.46139i | ||||||||
\(806\) | − | 8.50244e8i | − | 1.62382i | ||||||
\(807\) | 2.33302e8i | 0.443914i | ||||||||
\(808\) | 8.17673e8 | 1.55005 | ||||||||
\(809\) | − | 5.99861e8i | − | 1.13293i | −0.824084 | − | 0.566467i | \(-0.808310\pi\) | ||
0.824084 | − | 0.566467i | \(-0.191690\pi\) | |||||||
\(810\) | 8.65210e7i | 0.162805i | ||||||||
\(811\) | − | 7.16951e8i | − | 1.34409i | −0.740512 | − | 0.672043i | \(-0.765417\pi\) | ||
0.740512 | − | 0.672043i | \(-0.234583\pi\) | |||||||
\(812\) | −1.82785e7 | −0.0341407 | ||||||||
\(813\) | 4.44978e8 | 0.828070 | ||||||||
\(814\) | 5.70372e7i | 0.105751i | ||||||||
\(815\) | 3.42103e8 | 0.631953 | ||||||||
\(816\) | −5.86750e8 | −1.07990 | ||||||||
\(817\) | − | 1.18286e8i | − | 0.216905i | ||||||
\(818\) | −1.05123e9 | −1.92060 | ||||||||
\(819\) | − | 3.96023e8i | − | 0.720889i | ||||||
\(820\) | −9.09669e6 | −0.0164984 | ||||||||
\(821\) | 2.94146e8i | 0.531537i | 0.964037 | + | 0.265768i | \(0.0856256\pi\) | ||||
−0.964037 | + | 0.265768i | \(0.914374\pi\) | |||||||
\(822\) | − | 9.24223e7i | − | 0.166403i | ||||||
\(823\) | − | 3.32995e8i | − | 0.597362i | −0.954353 | − | 0.298681i | \(-0.903453\pi\) | ||
0.954353 | − | 0.298681i | \(-0.0965467\pi\) | |||||||
\(824\) | −7.18339e7 | −0.128395 | ||||||||
\(825\) | − | 2.87257e8i | − | 0.511574i | ||||||
\(826\) | 7.78503e8 | + | 3.04611e8i | 1.38140 | + | 0.540512i | ||||
\(827\) | −9.20117e7 | −0.162677 | −0.0813386 | − | 0.996687i | \(-0.525920\pi\) | ||||
−0.0813386 | + | 0.996687i | \(0.525920\pi\) | |||||||
\(828\) | 3.03443e6i | 0.00534547i | ||||||||
\(829\) | 8.36926e8 | 1.46901 | 0.734503 | − | 0.678605i | \(-0.237415\pi\) | ||||
0.734503 | + | 0.678605i | \(0.237415\pi\) | |||||||
\(830\) | −2.20536e8 | −0.385696 | ||||||||
\(831\) | 2.87874e8 | 0.501648 | ||||||||
\(832\) | 8.28685e8i | 1.43886i | ||||||||
\(833\) | −1.21595e9 | −2.10369 | ||||||||
\(834\) | 3.73450e7i | 0.0643775i | ||||||||
\(835\) | 1.01488e9 | 1.74324 | ||||||||
\(836\) | 6.33376e6i | 0.0108403i | ||||||||
\(837\) | − | 1.22826e8i | − | 0.209466i | ||||||
\(838\) | −6.87952e8 | −1.16903 | ||||||||
\(839\) | − | 6.10917e8i | − | 1.03442i | −0.855859 | − | 0.517209i | \(-0.826971\pi\) | ||
0.855859 | − | 0.517209i | \(-0.173029\pi\) | |||||||
\(840\) | − | 7.18116e8i | − | 1.21159i | ||||||
\(841\) | −1.29750e6 | −0.00218132 | ||||||||
\(842\) | −5.50203e8 | −0.921694 | ||||||||
\(843\) | −2.21186e8 | −0.369212 | ||||||||
\(844\) | 1.12211e7i | 0.0186642i | ||||||||
\(845\) | 1.02695e9 | 1.70208 | ||||||||
\(846\) | 8.58767e7 | 0.141829 | ||||||||
\(847\) | 3.10804e8 | 0.511489 | ||||||||
\(848\) | −1.88309e8 | −0.308805 | ||||||||
\(849\) | − | 2.49291e8i | − | 0.407364i | ||||||
\(850\) | 1.24751e9i | 2.03135i | ||||||||
\(851\) | 5.49322e7 | 0.0891329 | ||||||||
\(852\) | −1.15112e7 | −0.0186123 | ||||||||
\(853\) | 1.57273e8 | 0.253400 | 0.126700 | − | 0.991941i | \(-0.459562\pi\) | ||||
0.126700 | + | 0.991941i | \(0.459562\pi\) | |||||||
\(854\) | 1.68756e9 | 2.70947 | ||||||||
\(855\) | 1.73930e8 | 0.278276 | ||||||||
\(856\) | 1.11955e9i | 1.78493i | ||||||||
\(857\) | − | 2.92371e8i | − | 0.464506i | −0.972655 | − | 0.232253i | \(-0.925390\pi\) | ||
0.972655 | − | 0.232253i | \(-0.0746097\pi\) | |||||||
\(858\) | 4.39034e8i | 0.695083i | ||||||||
\(859\) | 1.03265e9i | 1.62920i | 0.580021 | + | 0.814601i | \(0.303044\pi\) | ||||
−0.580021 | + | 0.814601i | \(0.696956\pi\) | |||||||
\(860\) | 8.08121e6i | 0.0127052i | ||||||||
\(861\) | 2.64081e8 | 0.413741 | ||||||||
\(862\) | 9.23060e8 | 1.44115 | ||||||||
\(863\) | − | 3.56626e8i | − | 0.554856i | −0.960746 | − | 0.277428i | \(-0.910518\pi\) | ||
0.960746 | − | 0.277428i | \(-0.0894819\pi\) | |||||||
\(864\) | − | 5.78494e6i | − | 0.00896927i | ||||||
\(865\) | − | 2.57344e8i | − | 0.397618i | ||||||
\(866\) | − | 3.32090e7i | − | 0.0511331i | ||||||
\(867\) | −8.82172e8 | −1.35362 | ||||||||
\(868\) | − | 2.43278e7i | − | 0.0372000i | ||||||
\(869\) | 5.27109e8i | 0.803232i | ||||||||
\(870\) | − | 5.56458e8i | − | 0.845034i | ||||||
\(871\) | 1.74364e8 | 0.263878 | ||||||||
\(872\) | 6.03012e8 | 0.909445 | ||||||||
\(873\) | 8.72101e7i | 0.131076i | ||||||||
\(874\) | 2.67817e8 | 0.401148 | ||||||||
\(875\) | −1.39491e8 | −0.208220 | ||||||||
\(876\) | − | 9.04370e6i | − | 0.0134535i | ||||||
\(877\) | −8.95563e8 | −1.32769 | −0.663846 | − | 0.747869i | \(-0.731077\pi\) | ||||
−0.663846 | + | 0.747869i | \(0.731077\pi\) | |||||||
\(878\) | 6.06093e8i | 0.895479i | ||||||||
\(879\) | 4.55576e8 | 0.670802 | ||||||||
\(880\) | 8.14675e8i | 1.19546i | ||||||||
\(881\) | − | 1.04441e9i | − | 1.52736i | −0.645593 | − | 0.763682i | \(-0.723390\pi\) | ||
0.645593 | − | 0.763682i | \(-0.276610\pi\) | |||||||
\(882\) | − | 2.66135e8i | − | 0.387878i | ||||||
\(883\) | −1.51595e8 | −0.220193 | −0.110096 | − | 0.993921i | \(-0.535116\pi\) | ||||
−0.110096 | + | 0.993921i | \(0.535116\pi\) | |||||||
\(884\) | − | 4.34271e7i | − | 0.0628643i | ||||||
\(885\) | −2.11216e8 | + | 5.39811e8i | −0.304718 | + | 0.778775i | ||||
\(886\) | −9.31535e8 | −1.33936 | ||||||||
\(887\) | − | 5.27508e8i | − | 0.755889i | −0.925828 | − | 0.377944i | \(-0.876631\pi\) | ||
0.925828 | − | 0.377944i | \(-0.123369\pi\) | |||||||
\(888\) | −5.17448e7 | −0.0738972 | ||||||||
\(889\) | −1.63256e9 | −2.32361 | ||||||||
\(890\) | −1.54653e9 | −2.19376 | ||||||||
\(891\) | 6.34228e7i | 0.0896628i | ||||||||
\(892\) | −1.72264e7 | −0.0242716 | ||||||||
\(893\) | − | 1.72634e8i | − | 0.242423i | ||||||
\(894\) | 4.08116e8 | 0.571178 | ||||||||
\(895\) | − | 4.36810e8i | − | 0.609289i | ||||||
\(896\) | 1.09018e9i | 1.51556i | ||||||||
\(897\) | 4.22831e8 | 0.585854 | ||||||||
\(898\) | 3.36003e8i | 0.463996i | ||||||||
\(899\) | 7.89952e8i | 1.08723i | ||||||||
\(900\) | −6.21897e6 | −0.00853082 | ||||||||
\(901\) | −4.03879e8 | −0.552175 | ||||||||
\(902\) | −2.92763e8 | −0.398930 | ||||||||
\(903\) | − | 2.34601e8i | − | 0.318616i | ||||||
\(904\) | −1.31938e9 | −1.78594 | ||||||||
\(905\) | −6.66268e8 | −0.898883 | ||||||||
\(906\) | 7.45199e8 | 1.00205 | ||||||||
\(907\) | 1.24612e9 | 1.67008 | 0.835038 | − | 0.550192i | \(-0.185445\pi\) | ||||
0.835038 | + | 0.550192i | \(0.185445\pi\) | |||||||
\(908\) | 3.41773e7i | 0.0456541i | ||||||||
\(909\) | 3.92785e8i | 0.522954i | ||||||||
\(910\) | 2.38794e9 | 3.16883 | ||||||||
\(911\) | −1.15443e9 | −1.52691 | −0.763455 | − | 0.645862i | \(-0.776498\pi\) | ||||
−0.763455 | + | 0.645862i | \(0.776498\pi\) | |||||||
\(912\) | −2.58161e8 | −0.340334 | ||||||||
\(913\) | −1.61660e8 | −0.212417 | ||||||||
\(914\) | 5.07295e8 | 0.664388 | ||||||||
\(915\) | 1.17015e9i | 1.52748i | ||||||||
\(916\) | − | 3.10484e7i | − | 0.0403973i | ||||||
\(917\) | 1.03601e9i | 1.34355i | ||||||||
\(918\) | − | 2.75434e8i | − | 0.356032i | ||||||
\(919\) | 5.88107e8i | 0.757722i | 0.925454 | + | 0.378861i | \(0.123684\pi\) | ||||
−0.925454 | + | 0.378861i | \(0.876316\pi\) | |||||||
\(920\) | 7.66727e8 | 0.984640 | ||||||||
\(921\) | −2.31339e8 | −0.296122 | ||||||||
\(922\) | − | 6.19905e8i | − | 0.790919i | ||||||
\(923\) | 1.60402e9i | 2.03987i | ||||||||
\(924\) | 1.25620e7i | 0.0159236i | ||||||||
\(925\) | 1.12582e8i | 0.142247i | ||||||||
\(926\) | −4.27053e8 | −0.537834 | ||||||||
\(927\) | − | 3.45068e7i | − | 0.0433177i | ||||||
\(928\) | 3.72057e7i | 0.0465549i | ||||||||
\(929\) | − | 1.33958e9i | − | 1.67078i | −0.549655 | − | 0.835392i | \(-0.685241\pi\) | ||
0.549655 | − | 0.835392i | \(-0.314759\pi\) | |||||||
\(930\) | 7.40616e8 | 0.920755 | ||||||||
\(931\) | −5.35000e8 | −0.662986 | ||||||||
\(932\) | 1.67256e7i | 0.0206602i | ||||||||
\(933\) | 3.34326e8 | 0.411647 | ||||||||
\(934\) | 1.43777e9 | 1.76461 | ||||||||
\(935\) | 1.74728e9i | 2.13761i | ||||||||
\(936\) | −3.98297e8 | −0.485712 | ||||||||
\(937\) | − | 2.41475e7i | − | 0.0293530i | −0.999892 | − | 0.0146765i | \(-0.995328\pi\) | ||
0.999892 | − | 0.0146765i | \(-0.00467185\pi\) | |||||||
\(938\) | 2.19041e8 | 0.265410 | ||||||||
\(939\) | − | 1.41787e8i | − | 0.171253i | ||||||
\(940\) | 1.17942e7i | 0.0141999i | ||||||||
\(941\) | 2.86628e8i | 0.343994i | 0.985098 | + | 0.171997i | \(0.0550219\pi\) | ||||
−0.985098 | + | 0.171997i | \(0.944978\pi\) | |||||||
\(942\) | −1.87597e8 | −0.224426 | ||||||||
\(943\) | 2.81958e8i | 0.336240i | ||||||||
\(944\) | 3.13504e8 | − | 8.01232e8i | 0.372673 | − | 0.952450i | ||||
\(945\) | 3.44961e8 | 0.408766 | ||||||||
\(946\) | 2.60081e8i | 0.307210i | ||||||||
\(947\) | 1.13493e9 | 1.33635 | 0.668173 | − | 0.744006i | \(-0.267077\pi\) | ||||
0.668173 | + | 0.744006i | \(0.267077\pi\) | |||||||
\(948\) | 1.14116e7 | 0.0133944 | ||||||||
\(949\) | −1.26019e9 | −1.47447 | ||||||||
\(950\) | 5.48883e8i | 0.640190i | ||||||||
\(951\) | −1.28549e8 | −0.149461 | ||||||||
\(952\) | 2.28607e9i | 2.64959i | ||||||||
\(953\) | −6.66635e8 | −0.770210 | −0.385105 | − | 0.922873i | \(-0.625835\pi\) | ||||
−0.385105 | + | 0.922873i | \(0.625835\pi\) | |||||||
\(954\) | − | 8.83967e7i | − | 0.101810i | ||||||
\(955\) | − | 1.92168e9i | − | 2.20633i | ||||||
\(956\) | −2.22253e7 | −0.0254374 | ||||||||
\(957\) | − | 4.07902e8i | − | 0.465393i | ||||||
\(958\) | 4.97980e8i | 0.566389i | ||||||||
\(959\) | −3.68489e8 | −0.417801 | ||||||||
\(960\) | −7.21837e8 | −0.815878 | ||||||||
\(961\) | −1.63881e8 | −0.184654 | ||||||||
\(962\) | − | 1.72066e8i | − | 0.193273i | ||||||
\(963\) | −5.37798e8 | −0.602199 | ||||||||
\(964\) | −9.40419e6 | −0.0104976 | ||||||||
\(965\) | 1.30341e9 | 1.45044 | ||||||||
\(966\) | 5.31171e8 | 0.589255 | ||||||||
\(967\) | − | 3.95435e8i | − | 0.437317i | −0.975801 | − | 0.218658i | \(-0.929832\pi\) | ||
0.975801 | − | 0.218658i | \(-0.0701680\pi\) | |||||||
\(968\) | − | 3.12589e8i | − | 0.344625i | ||||||
\(969\) | −5.53694e8 | −0.608553 | ||||||||
\(970\) | −5.25859e8 | −0.576175 | ||||||||
\(971\) | −3.39952e8 | −0.371330 | −0.185665 | − | 0.982613i | \(-0.559444\pi\) | ||||
−0.185665 | + | 0.982613i | \(0.559444\pi\) | |||||||
\(972\) | 1.37307e6 | 0.00149518 | ||||||||
\(973\) | 1.48895e8 | 0.161637 | ||||||||
\(974\) | 2.35638e8i | 0.255017i | ||||||||
\(975\) | 8.66578e8i | 0.934961i | ||||||||
\(976\) | − | 1.73683e9i | − | 1.86813i | ||||||
\(977\) | 2.08637e8i | 0.223722i | 0.993724 | + | 0.111861i | \(0.0356811\pi\) | ||||
−0.993724 | + | 0.111861i | \(0.964319\pi\) | |||||||
\(978\) | − | 2.38362e8i | − | 0.254813i | ||||||
\(979\) | −1.13366e9 | −1.20819 | ||||||||
\(980\) | 3.65506e7 | 0.0388344 | ||||||||
\(981\) | 2.89669e8i | 0.306828i | ||||||||
\(982\) | − | 1.51386e9i | − | 1.59865i | ||||||
\(983\) | − | 2.55966e7i | − | 0.0269477i | −0.999909 | − | 0.0134739i | \(-0.995711\pi\) | ||
0.999909 | − | 0.0134739i | \(-0.00428900\pi\) | |||||||
\(984\) | − | 2.65598e8i | − | 0.278766i | ||||||
\(985\) | −5.71968e8 | −0.598499 | ||||||||
\(986\) | 1.77144e9i | 1.84798i | ||||||||
\(987\) | − | 3.42392e8i | − | 0.356100i | ||||||
\(988\) | − | 1.91073e7i | − | 0.0198120i | ||||||
\(989\) | 2.50482e8 | 0.258934 | ||||||||
\(990\) | −3.82427e8 | −0.394133 | ||||||||
\(991\) | − | 8.95181e8i | − | 0.919793i | −0.887973 | − | 0.459896i | \(-0.847887\pi\) | ||
0.887973 | − | 0.459896i | \(-0.152113\pi\) | |||||||
\(992\) | −4.95188e7 | −0.0507265 | ||||||||
\(993\) | −2.93035e7 | −0.0299275 | ||||||||
\(994\) | 2.01501e9i | 2.05172i | ||||||||
\(995\) | 1.95367e9 | 1.98327 | ||||||||
\(996\) | 3.49985e6i | 0.00354219i | ||||||||
\(997\) | 4.67903e8 | 0.472139 | 0.236070 | − | 0.971736i | \(-0.424141\pi\) | ||||
0.236070 | + | 0.971736i | \(0.424141\pi\) | |||||||
\(998\) | 1.35159e9i | 1.35973i | ||||||||
\(999\) | − | 2.48566e7i | − | 0.0249313i |
(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 | 177.7.c.a.58.17 | ✓ | 60 | |
59.58 | odd | 2 | inner | 177.7.c.a.58.44 | yes | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.7.c.a.58.17 | ✓ | 60 | 1.1 | even | 1 | trivial | |
177.7.c.a.58.44 | yes | 60 | 59.58 | odd | 2 | inner |