Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,7,Mod(13,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.13");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.j (of order \(18\), degree \(6\), 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: | \(60\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 29.1 | ||
Character | \(\chi\) | \(=\) | 76.29 |
Dual form | 76.7.j.a.21.1 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{17}{18}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −31.3285 | − | 37.3358i | −1.16031 | − | 1.38281i | −0.909982 | − | 0.414647i | \(-0.863905\pi\) |
−0.250331 | − | 0.968160i | \(-0.580540\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 37.0498 | + | 13.4850i | 0.296398 | + | 0.107880i | 0.485939 | − | 0.873993i | \(-0.338478\pi\) |
−0.189541 | + | 0.981873i | \(0.560700\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −148.463 | + | 257.146i | −0.432837 | + | 0.749695i | −0.997116 | − | 0.0758885i | \(-0.975821\pi\) |
0.564279 | + | 0.825584i | \(0.309154\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −285.900 | + | 1621.42i | −0.392182 | + | 2.22417i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −242.144 | − | 419.405i | −0.181926 | − | 0.315105i | 0.760610 | − | 0.649209i | \(-0.224900\pi\) |
−0.942536 | + | 0.334103i | \(0.891567\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −423.045 | + | 504.165i | −0.192556 | + | 0.229479i | −0.853681 | − | 0.520797i | \(-0.825635\pi\) |
0.661125 | + | 0.750276i | \(0.270079\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −657.238 | − | 1805.75i | −0.194737 | − | 0.535036i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 332.340 | + | 1884.79i | 0.0676450 | + | 0.383634i | 0.999769 | + | 0.0214946i | \(0.00684248\pi\) |
−0.932124 | + | 0.362139i | \(0.882046\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6811.05 | − | 809.605i | 0.993009 | − | 0.118035i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 14251.9 | − | 2512.99i | 1.53891 | − | 0.271352i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 13274.6 | − | 4831.54i | 1.09103 | − | 0.397102i | 0.267028 | − | 0.963689i | \(-0.413959\pi\) |
0.824002 | + | 0.566587i | \(0.191736\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −10778.6 | − | 9044.32i | −0.689831 | − | 0.578837i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 38723.8 | − | 22357.2i | 1.96737 | − | 1.13586i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 18843.2 | + | 3322.57i | 0.772611 | + | 0.136232i | 0.546036 | − | 0.837762i | \(-0.316136\pi\) |
0.226575 | + | 0.973994i | \(0.427247\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2078.65 | + | 1200.11i | 0.0697745 | + | 0.0402843i | 0.534481 | − | 0.845180i | \(-0.320507\pi\) |
−0.464707 | + | 0.885465i | \(0.653840\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8072.85 | + | 22180.0i | −0.224639 | + | 0.617190i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8968.13 | + | 7525.15i | −0.209169 | + | 0.175514i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 78184.4i | 1.54353i | 0.635908 | + | 0.771765i | \(0.280626\pi\) | ||||
−0.635908 | + | 0.771765i | \(0.719374\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 32076.7 | 0.540750 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7742.49 | + | 9227.15i | 0.112339 | + | 0.133880i | 0.819283 | − | 0.573389i | \(-0.194372\pi\) |
−0.706945 | + | 0.707269i | \(0.749927\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −17391.5 | − | 6329.98i | −0.218742 | − | 0.0796154i | 0.230325 | − | 0.973114i | \(-0.426021\pi\) |
−0.449066 | + | 0.893498i | \(0.648243\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −32457.4 | + | 56217.9i | −0.356186 | + | 0.616932i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 31825.7 | − | 180493.i | 0.306538 | − | 1.73847i | −0.309635 | − | 0.950856i | \(-0.600207\pi\) |
0.616173 | − | 0.787611i | \(-0.288682\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14742.0 | + | 25533.8i | 0.125305 | + | 0.217034i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 59958.6 | − | 71455.9i | 0.452003 | − | 0.538676i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 91075.1 | + | 250227.i | 0.611748 | + | 1.68076i | 0.726328 | + | 0.687349i | \(0.241226\pi\) |
−0.114580 | + | 0.993414i | \(0.536552\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3315.68 | − | 18804.2i | −0.0199290 | − | 0.113023i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −243607. | − | 228932.i | −1.31542 | − | 1.23618i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 18413.6 | − | 3246.82i | 0.0896567 | − | 0.0158089i | −0.128640 | − | 0.991691i | \(-0.541061\pi\) |
0.218297 | + | 0.975882i | \(0.429950\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 210217. | − | 76512.6i | 0.926142 | − | 0.337088i | 0.165462 | − | 0.986216i | \(-0.447088\pi\) |
0.760679 | + | 0.649128i | \(0.224866\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −374496. | − | 314239.i | −1.49770 | − | 1.25672i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −22472.4 | + | 12974.4i | −0.0818293 | + | 0.0472442i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 320356. | + | 56487.3i | 1.06514 | + | 0.187813i | 0.678637 | − | 0.734474i | \(-0.262571\pi\) |
0.386506 | + | 0.922287i | \(0.373682\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −596261. | − | 344252.i | −1.81505 | − | 1.04792i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −91899.1 | + | 252491.i | −0.256765 | + | 0.705456i | 0.742597 | + | 0.669739i | \(0.233594\pi\) |
−0.999362 | + | 0.0357177i | \(0.988628\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −532504. | + | 446824.i | −1.36885 | + | 1.14860i | −0.395706 | + | 0.918377i | \(0.629500\pi\) |
−0.973139 | + | 0.230220i | \(0.926055\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 685773.i | 1.62554i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 143798. | 0.314977 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 329216. | + | 392344.i | 0.667728 | + | 0.795767i | 0.988473 | − | 0.151399i | \(-0.0483778\pi\) |
−0.320745 | + | 0.947166i | \(0.603933\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −920012. | − | 334857.i | −1.73117 | − | 0.630093i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −337004. | + | 583709.i | −0.589388 | + | 1.02085i | 0.404925 | + | 0.914350i | \(0.367298\pi\) |
−0.994313 | + | 0.106500i | \(0.966036\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13103.3 | + | 74312.8i | −0.0213366 | + | 0.121006i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −466278. | − | 807617.i | −0.708088 | − | 1.22644i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 254809. | − | 303669.i | 0.361447 | − | 0.430756i | −0.554420 | − | 0.832237i | \(-0.687060\pi\) |
0.915867 | + | 0.401481i | \(0.131504\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −66837.3 | − | 183634.i | −0.0886941 | − | 0.243685i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −20313.9 | − | 115206.i | −0.0252548 | − | 0.143227i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 263265. | + | 61851.4i | 0.307060 | + | 0.0721404i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 925946. | − | 163269.i | 1.01454 | − | 0.178891i | 0.358432 | − | 0.933556i | \(-0.383311\pi\) |
0.656111 | + | 0.754665i | \(0.272200\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 749262. | − | 272709.i | 0.772197 | − | 0.281057i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 91299.9 | + | 76609.7i | 0.0886148 | + | 0.0743566i | 0.686019 | − | 0.727584i | \(-0.259357\pi\) |
−0.597404 | + | 0.801940i | \(0.703801\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −188214. | + | 108666.i | −0.172243 | + | 0.0994443i | −0.583643 | − | 0.812010i | \(-0.698373\pi\) |
0.411400 | + | 0.911455i | \(0.365040\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 561915. | + | 99080.8i | 0.485404 | + | 0.0855898i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 877446. | + | 506594.i | 0.716258 | + | 0.413532i | 0.813374 | − | 0.581742i | \(-0.197628\pi\) |
−0.0971161 | + | 0.995273i | \(0.530962\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 281569. | − | 773604.i | 0.217423 | − | 0.597364i | −0.782249 | − | 0.622965i | \(-0.785928\pi\) |
0.999672 | + | 0.0256010i | \(0.00814993\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.91908e6 | − | 2.44940e6i | 2.13441 | − | 1.79098i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.54223e6i | 1.76189i | 0.473216 | + | 0.880947i | \(0.343093\pi\) | ||||
−0.473216 | + | 0.880947i | \(0.656907\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 556973. | 0.366219 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −696516. | − | 830075.i | −0.434884 | − | 0.518274i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −534007. | − | 194363.i | −0.316888 | − | 0.115338i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 768513. | − | 1.33110e6i | 0.433806 | − | 0.751373i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 101942. | − | 578145.i | 0.0547823 | − | 0.310686i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −585409. | − | 1.01396e6i | −0.299730 | − | 0.519147i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −543606. | + | 647845.i | −0.265383 | + | 0.316271i | −0.882236 | − | 0.470807i | \(-0.843963\pi\) |
0.616853 | + | 0.787078i | \(0.288407\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 308513. | + | 847634.i | 0.143716 | + | 0.394856i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 615006. | + | 3.48787e6i | 0.273568 | + | 1.55148i | 0.743474 | + | 0.668765i | \(0.233177\pi\) |
−0.469906 | + | 0.882717i | \(0.655712\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −803003. | + | 1.87163e6i | −0.341320 | + | 0.795545i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.73619e6 | − | 306138.i | 0.705662 | − | 0.124427i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −288469. | + | 104994.i | −0.112186 | + | 0.0408322i | −0.397503 | − | 0.917601i | \(-0.630123\pi\) |
0.285317 | + | 0.958433i | \(0.407901\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.55077e6 | + | 2.14035e6i | 0.949788 | + | 0.796966i | 0.979262 | − | 0.202599i | \(-0.0649388\pi\) |
−0.0294742 | + | 0.999566i | \(0.509383\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.73589e6 | + | 4.46632e6i | −2.75965 | + | 1.59328i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 313887. | + | 55346.8i | 0.107341 | + | 0.0189271i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 653332. | + | 377201.i | 0.214304 | + | 0.123728i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 491483. | − | 1.35034e6i | 0.154724 | − | 0.425099i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.43614e6 | − | 2.88327e6i | 1.03875 | − | 0.871617i | 0.0468864 | − | 0.998900i | \(-0.485070\pi\) |
0.991866 | + | 0.127283i | \(0.0406257\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2.00834e6i | − | 0.583320i | −0.956522 | − | 0.291660i | \(-0.905792\pi\) | ||
0.956522 | − | 0.291660i | \(-0.0942076\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.15106e6 | −0.879798 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 60830.0 | + | 72494.4i | 0.0163351 | + | 0.0194675i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.47202e6 | − | 1.99165e6i | −1.41400 | − | 0.514653i | −0.481697 | − | 0.876338i | \(-0.659979\pi\) |
−0.932300 | + | 0.361685i | \(0.882201\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.48918e6 | − | 1.12396e7i | 1.61435 | − | 2.79614i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −728371. | + | 4.13080e6i | −0.174532 | + | 0.989821i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.02772e6 | − | 6.97621e6i | −0.930028 | − | 1.61086i | −0.783269 | − | 0.621683i | \(-0.786449\pi\) |
−0.146759 | − | 0.989172i | \(-0.546884\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −598194. | + | 712900.i | −0.133165 | + | 0.158700i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.69694e6 | − | 4.66229e6i | −0.364348 | − | 1.00104i | −0.977475 | − | 0.211053i | \(-0.932311\pi\) |
0.613127 | − | 0.789984i | \(-0.289911\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 762951. | + | 4.32691e6i | 0.158065 | + | 0.896433i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −634571. | + | 1.12751e7i | −0.126909 | + | 2.25492i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.05633e6 | − | 891567.i | 0.976555 | − | 0.172193i | 0.337476 | − | 0.941334i | \(-0.390427\pi\) |
0.639079 | + | 0.769141i | \(0.279316\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.92593e6 | − | 1.42892e6i | 0.732535 | − | 0.266621i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −698092. | − | 585769.i | −0.125891 | − | 0.105635i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.76948e6 | + | 3.90836e6i | −1.18031 | + | 0.681453i | −0.956086 | − | 0.293085i | \(-0.905318\pi\) |
−0.224224 | + | 0.974538i | \(0.571985\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 347793. | + | 61325.3i | 0.0586523 | + | 0.0103420i | 0.202897 | − | 0.979200i | \(-0.434964\pi\) |
−0.144245 | + | 0.989542i | \(0.546075\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.44242e6 | − | 5.45158e6i | −1.54074 | − | 0.889548i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.05432e6 | + | 2.89671e6i | −0.166516 | + | 0.457499i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 710019. | − | 595776.i | 0.108579 | − | 0.0911084i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.32769e7i | 1.96657i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.98900e6 | −0.428968 | −0.214484 | − | 0.976727i | \(-0.568807\pi\) | ||||
−0.214484 | + | 0.976727i | \(0.568807\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.61399e6 | − | 6.69050e6i | −0.780908 | − | 0.930650i | 0.218066 | − | 0.975934i | \(-0.430025\pi\) |
−0.998974 | + | 0.0452839i | \(0.985581\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.18844e6 | + | 432555.i | 0.160277 | + | 0.0583361i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.00190e6 | + | 8.66355e6i | −0.654239 | + | 1.13318i | 0.327845 | + | 0.944732i | \(0.393678\pi\) |
−0.982084 | + | 0.188444i | \(0.939656\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.67114e6 | − | 9.47750e6i | 0.212057 | − | 1.20264i | −0.673883 | − | 0.738838i | \(-0.735375\pi\) |
0.885940 | − | 0.463799i | \(-0.153514\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.92725e6 | − | 1.37304e7i | −0.976190 | − | 1.69081i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.65190e6 | + | 4.35217e6i | −0.436547 | + | 0.520257i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 162429. | + | 446271.i | 0.0188540 | + | 0.0518009i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.03877e6 | + | 2.29050e7i | 0.455342 | + | 2.58238i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.98881e6 | − | 2.66055e6i | −0.217848 | − | 0.291429i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.13327e7 | + | 1.99826e6i | −1.20639 | + | 0.212719i | −0.740458 | − | 0.672103i | \(-0.765391\pi\) |
−0.465930 | + | 0.884822i | \(0.654280\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.23060e7 | − | 4.47902e6i | 1.27344 | − | 0.463494i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −558990. | − | 469049.i | −0.0562456 | − | 0.0471957i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −617206. | + | 356344.i | −0.0604019 | + | 0.0348731i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.33651e7 | + | 5.88316e6i | 3.17658 | + | 0.560117i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.09084e6 | − | 629798.i | −0.101061 | − | 0.0583478i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.09700e6 | + | 3.01399e6i | −0.0989220 | + | 0.271786i | −0.979276 | − | 0.202532i | \(-0.935083\pi\) |
0.880354 | + | 0.474318i | \(0.157305\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.77463e7 | − | 1.48909e7i | 1.55797 | − | 1.30729i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.41155e7i | 1.20675i | 0.797456 | + | 0.603377i | \(0.206179\pi\) | ||||
−0.797456 | + | 0.603377i | \(0.793821\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.53287e7 | 1.27644 | 0.638219 | − | 0.769855i | \(-0.279671\pi\) | ||||
0.638219 | + | 0.769855i | \(0.279671\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.50496e6 | − | 5.36880e6i | −0.365473 | − | 0.435553i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.16397e7 | − | 4.23650e6i | −0.920181 | − | 0.334918i | −0.161870 | − | 0.986812i | \(-0.551753\pi\) |
−0.758310 | + | 0.651894i | \(0.773975\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.61308e6 | − | 6.25804e6i | 0.278403 | − | 0.482209i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.33466e6 | − | 2.45831e7i | 0.325619 | − | 1.84668i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.15357e6 | − | 8.92625e6i | −0.377498 | − | 0.653846i | 0.613200 | − | 0.789928i | \(-0.289882\pi\) |
−0.990698 | + | 0.136082i | \(0.956549\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.50153e7 | − | 1.78946e7i | 1.07271 | − | 1.27841i | 0.114170 | − | 0.993461i | \(-0.463579\pi\) |
0.958543 | − | 0.284949i | \(-0.0919765\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.17166e6 | + | 1.42090e7i | 0.360422 | + | 0.990251i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 201862. | + | 1.14482e6i | 0.0137264 | + | 0.0778463i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.47320e6 | + | 3.77639e6i | −0.164123 | + | 0.250603i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.23511e7 | − | 5.70437e6i | 2.09551 | − | 0.369496i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.58690e6 | − | 1.30552e6i | 0.226828 | − | 0.0825588i | −0.226106 | − | 0.974103i | \(-0.572599\pi\) |
0.452934 | + | 0.891544i | \(0.350377\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.24073e6 | − | 4.39749e6i | −0.323616 | − | 0.271546i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.18504e6 | − | 1.83888e6i | 0.192085 | − | 0.110900i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.73607e7 | + | 3.06117e6i | 1.02275 | + | 0.180338i | 0.659776 | − | 0.751462i | \(-0.270651\pi\) |
0.362972 | + | 0.931800i | \(0.381762\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.01048e7 | − | 1.16075e7i | −1.15718 | − | 0.668097i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.07746e7 | + | 2.96029e7i | −0.606008 | + | 1.66499i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.79371e7 | + | 1.50510e7i | −0.986018 | + | 0.827367i | −0.984986 | − | 0.172633i | \(-0.944773\pi\) |
−0.00103122 | + | 0.999999i | \(0.500328\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.04990e7i | 0.564170i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.93205e7 | −1.01504 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.92310e7 | + | 2.29186e7i | 0.987973 | + | 1.17742i | 0.984134 | + | 0.177428i | \(0.0567777\pi\) |
0.00383938 | + | 0.999993i | \(0.498778\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.83558e6 | + | 2.48795e6i | 0.343453 | + | 0.125007i | 0.507987 | − | 0.861365i | \(-0.330390\pi\) |
−0.164534 | + | 0.986371i | \(0.552612\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.76221e6 | + | 8.24839e6i | −0.234056 | + | 0.405398i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.18327e6 | + | 6.71063e6i | −0.0568963 | + | 0.322675i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.49464e7 | − | 2.58879e7i | −0.703229 | − | 1.21803i | −0.967327 | − | 0.253532i | \(-0.918408\pi\) |
0.264098 | − | 0.964496i | \(-0.414926\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.54017e6 | + | 3.02726e6i | −0.116964 | + | 0.139392i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.82841e6 | + | 2.15084e7i | 0.352821 | + | 0.969368i | 0.981459 | + | 0.191670i | \(0.0613904\pi\) |
−0.628638 | + | 0.777698i | \(0.716387\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.08510e6 | + | 6.15389e6i | 0.0478750 | + | 0.271513i | 0.999343 | − | 0.0362340i | \(-0.0115362\pi\) |
−0.951468 | + | 0.307747i | \(0.900425\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.93843e6 | − | 1.17669e7i | −0.256529 | − | 0.508310i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.52219e6 | + | 621058.i | −0.148994 | + | 0.0262716i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.92399e7 | − | 7.00275e6i | 0.797093 | − | 0.290118i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.51043e7 | − | 2.94560e7i | −1.42456 | − | 1.19535i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.61623e7 | + | 2.08783e7i | −1.43765 | + | 0.830028i | −0.997686 | − | 0.0679867i | \(-0.978342\pi\) |
−0.439965 | + | 0.898015i | \(0.645009\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 726003. | + | 128014.i | 0.0282795 | + | 0.00498645i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.87534e7 | − | 1.08273e7i | −0.715833 | − | 0.413286i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.17984e6 | + | 8.73653e6i | −0.118957 | + | 0.326833i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.20972e6 | − | 3.53237e6i | 0.154367 | − | 0.129529i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 5.80882e6i | − | 0.208814i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.82024e6 | 0.310872 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.89427e6 | − | 1.05998e7i | −0.307394 | − | 0.366338i | 0.590126 | − | 0.807311i | \(-0.299078\pi\) |
−0.897520 | + | 0.440973i | \(0.854633\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.95358e6 | + | 3.62281e6i | 0.337368 | + | 0.122792i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −199423. | + | 345411.i | −0.00662971 | + | 0.0114830i | −0.869321 | − | 0.494248i | \(-0.835444\pi\) |
0.862692 | + | 0.505731i | \(0.168777\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.99701e6 | + | 3.40107e7i | −0.195570 | + | 1.10913i | 0.716035 | + | 0.698064i | \(0.245955\pi\) |
−0.911605 | + | 0.411067i | \(0.865156\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.63746e6 | − | 1.66926e7i | −0.308341 | − | 0.534062i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.08407e7 | − | 1.29195e7i | 0.340314 | − | 0.405571i | −0.568559 | − | 0.822642i | \(-0.692499\pi\) |
0.908874 | + | 0.417071i | \(0.136943\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.16927e6 | − | 8.70748e6i | −0.0976307 | − | 0.268238i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.57495e6 | − | 4.86310e7i | −0.259249 | − | 1.47027i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.78953e6 | + | 1.25684e7i | 0.112455 | + | 0.372968i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.11966e6 | − | 1.60804e6i | 0.265662 | − | 0.0468433i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.77043e7 | + | 1.37232e7i | −1.07832 | + | 0.392476i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.16880e7 | + | 3.49803e7i | 1.17064 | + | 0.982283i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.65634e7 | − | 1.53364e7i | 0.732487 | − | 0.422902i | −0.0868442 | − | 0.996222i | \(-0.527678\pi\) |
0.819331 | + | 0.573320i | \(0.194345\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.26770e8 | − | 2.23530e7i | −3.43308 | − | 0.605344i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.11074e7 | + | 6.41284e6i | 0.295445 | + | 0.170575i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.72206e6 | − | 1.57212e7i | 0.149507 | − | 0.410768i | −0.842219 | − | 0.539135i | \(-0.818751\pi\) |
0.991727 | + | 0.128367i | \(0.0409735\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.49162e7 | − | 7.96442e7i | 2.43636 | − | 2.04435i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 1.16240e6i | − | 0.0293151i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.36876e7 | −1.08262 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.74491e7 | − | 2.07950e7i | −0.424928 | − | 0.506410i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.45510e7 | + | 8.93584e6i | 0.587599 | + | 0.213869i | 0.618673 | − | 0.785648i | \(-0.287670\pi\) |
−0.0310739 | + | 0.999517i | \(0.509893\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.62613e7 | + | 2.81654e7i | −0.382541 | + | 0.662581i | −0.991425 | − | 0.130679i | \(-0.958284\pi\) |
0.608883 | + | 0.793260i | \(0.291618\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.11018e6 | + | 2.89813e7i | −0.118172 | + | 0.670187i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.53382e7 | + | 4.38871e7i | 0.576039 | + | 0.997729i | 0.995928 | + | 0.0901536i | \(0.0287358\pi\) |
−0.419889 | + | 0.907576i | \(0.637931\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.80968e6 | + | 8.11546e6i | −0.152209 | + | 0.181396i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.47292e6 | + | 2.60266e7i | 0.208199 | + | 0.572023i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.37275e6 | + | 3.61417e7i | 0.137735 | + | 0.781133i | 0.972916 | + | 0.231158i | \(0.0742515\pi\) |
−0.835181 | + | 0.549975i | \(0.814637\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.57350e7 | − | 1.10285e7i | 0.972135 | − | 0.234421i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.37742e7 | + | 1.30084e7i | −1.54236 | + | 0.271959i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.57546e7 | + | 9.37390e6i | −0.529634 | + | 0.192771i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.12674e7 | + | 9.45447e6i | 0.227942 | + | 0.191266i | 0.749605 | − | 0.661886i | \(-0.230244\pi\) |
−0.521662 | + | 0.853152i | \(0.674688\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.71747e7 | + | 9.91581e6i | −0.341830 | + | 0.197355i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.78660e7 | − | 1.37299e7i | −1.52485 | − | 0.268872i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.79023e7 | + | 4.49769e7i | 1.50115 | + | 0.866689i | 0.999999 | + | 0.00132863i | \(0.000422915\pi\) |
0.501150 | + | 0.865360i | \(0.332910\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.95170e7 | + | 5.36225e7i | −0.370100 | + | 1.01684i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.64664e6 | + | 8.09449e6i | −0.180033 | + | 0.151066i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 9.20053e7i | − | 1.69003i | −0.534741 | − | 0.845016i | \(-0.679591\pi\) | ||
0.534741 | − | 0.845016i | \(-0.320409\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.12182e7 | 0.745270 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.27927e7 | + | 2.71632e7i | 0.405694 | + | 0.483487i | 0.929747 | − | 0.368198i | \(-0.120025\pi\) |
−0.524053 | + | 0.851685i | \(0.675581\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.32767e6 | + | 1.93911e6i | 0.0933587 | + | 0.0339798i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.52358e7 | − | 2.63892e7i | 0.262865 | − | 0.455295i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.02493e7 | + | 5.81268e7i | −0.174119 | + | 0.987479i | 0.765036 | + | 0.643987i | \(0.222721\pi\) |
−0.939156 | + | 0.343492i | \(0.888390\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.35181e7 | + | 2.34141e7i | 0.226145 | + | 0.391694i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.10955e8 | − | 1.32231e8i | 1.82798 | − | 2.17850i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.90660e6 | + | 1.89757e7i | 0.112066 | + | 0.307898i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.77126e6 | − | 1.57166e7i | −0.0442901 | − | 0.251181i | 0.954622 | − | 0.297821i | \(-0.0962599\pi\) |
−0.998912 | + | 0.0466396i | \(0.985149\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.50356e7 | − | 2.86545e7i | 1.49612 | − | 0.451101i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.15766e7 | + | 7.33108e6i | −0.644787 | + | 0.113693i | −0.486473 | − | 0.873696i | \(-0.661717\pi\) |
−0.158314 | + | 0.987389i | \(0.550606\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.48442e6 | + | 540283.i | −0.0226799 | + | 0.00825479i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.95707e7 | − | 2.48127e7i | −0.445140 | − | 0.373516i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.27910e7 | − | 1.89319e7i | 0.486375 | − | 0.280809i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.29540e6 | − | 1.11005e6i | −0.0920140 | − | 0.0162245i | 0.127452 | − | 0.991845i | \(-0.459320\pi\) |
−0.219466 | + | 0.975620i | \(0.570431\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.29573e7 | + | 7.48091e6i | 0.186633 | + | 0.107753i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.89884e6 | + | 5.21701e6i | −0.0269549 | + | 0.0740579i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.03573e7 | + | 1.70818e7i | −0.284823 | + | 0.238995i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 1.62289e8i | − | 2.23810i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.69646e7 | 0.774396 | 0.387198 | − | 0.921997i | \(-0.373443\pi\) | ||||
0.387198 | + | 0.921997i | \(0.373443\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.76699e7 | + | 3.29757e7i | 0.370818 | + | 0.441924i | 0.918894 | − | 0.394505i | \(-0.129084\pi\) |
−0.548076 | + | 0.836429i | \(0.684639\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.83556e8 | + | 1.03206e8i | 3.74643 | + | 1.36359i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.34645e7 | − | 2.33212e7i | 0.175398 | − | 0.303798i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.15345e7 | + | 6.54155e7i | −0.148155 | + | 0.840228i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.76719e6 | − | 1.34532e7i | −0.0983766 | − | 0.170393i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.28026e7 | + | 2.71751e7i | −0.284809 | + | 0.339422i | −0.889413 | − | 0.457104i | \(-0.848887\pi\) |
0.604605 | + | 0.796526i | \(0.293331\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.18105e7 | − | 3.24490e7i | −0.145480 | − | 0.399703i | 0.845455 | − | 0.534047i | \(-0.179330\pi\) |
−0.990935 | + | 0.134344i | \(0.957107\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.38476e6 | − | 3.62098e7i | −0.0775670 | − | 0.439904i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.65021e7 | − | 4.36551e7i | 1.03653 | − | 0.523107i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.74048e7 | − | 4.83221e6i | 0.323917 | − | 0.0571153i | −0.00932544 | − | 0.999957i | \(-0.502968\pi\) |
0.333242 | + | 0.942841i | \(0.391857\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.56158e7 | + | 1.66028e7i | −0.531863 | + | 0.193582i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.19328e8 | − | 1.00128e8i | −1.37256 | − | 1.15172i | −0.971874 | − | 0.235501i | \(-0.924327\pi\) |
−0.400687 | − | 0.916215i | \(-0.631228\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.35356e7 | − | 7.81478e6i | 0.153602 | − | 0.0886822i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.15298e8 | − | 3.79629e7i | −2.41056 | − | 0.425046i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.30509e7 | − | 5.37229e7i | −1.02797 | − | 0.593500i | −0.111569 | − | 0.993757i | \(-0.535588\pi\) |
−0.916403 | + | 0.400257i | \(0.868921\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.99512e6 | − | 5.48154e6i | 0.0217490 | − | 0.0597548i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.49831e7 | + | 6.29183e7i | −0.806620 | + | 0.676834i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 7.70489e6i | − | 0.0817961i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.31597e7 | 0.347426 | 0.173713 | − | 0.984796i | \(-0.444423\pi\) | ||||
0.173713 | + | 0.984796i | \(0.444423\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.50081e7 | + | 6.55562e7i | 0.568838 | + | 0.677915i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.53129e7 | + | 2.37719e7i | 0.666647 | + | 0.242640i | 0.653104 | − | 0.757269i | \(-0.273467\pi\) |
0.0135436 | + | 0.999908i | \(0.495689\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.49634e6 | − | 4.32380e6i | 0.0251514 | − | 0.0435634i | −0.853176 | − | 0.521624i | \(-0.825327\pi\) |
0.878327 | + | 0.478060i | \(0.158660\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 800926. | − | 4.54228e6i | 0.00796587 | − | 0.0451767i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.73978e7 | + | 3.01338e7i | 0.170822 | + | 0.295872i | 0.938707 | − | 0.344715i | \(-0.112024\pi\) |
−0.767886 | + | 0.640587i | \(0.778691\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.20864e7 | + | 7.39917e7i | −0.601836 | + | 0.717240i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.70700e7 | + | 2.66698e8i | 0.929014 | + | 2.55244i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.55641e6 | + | 8.82685e6i | 0.0147076 | + | 0.0834108i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.07360e7 | − | 5.28749e7i | −0.753332 | − | 0.493366i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.31762e8 | + | 7.61313e7i | −3.97822 | + | 0.701468i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.88966e7 | + | 3.23557e7i | −0.808870 | + | 0.294405i | −0.713157 | − | 0.701004i | \(-0.752735\pi\) |
−0.0957129 | + | 0.995409i | \(0.530513\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.94179e7 | − | 3.30755e7i | −0.354208 | − | 0.297215i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.77045e8 | − | 1.02217e8i | 1.57124 | − | 0.907158i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.65078e7 | + | 6.43730e6i | 0.320007 | + | 0.0564259i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.27625e8 | − | 7.36844e7i | −1.10497 | − | 0.637953i | −0.167445 | − | 0.985881i | \(-0.553552\pi\) |
−0.937521 | + | 0.347929i | \(0.886885\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.34280e8 | + | 3.68932e8i | −1.14838 | + | 3.15515i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.92074e6 | + | 8.32449e6i | −0.0838108 | + | 0.0703256i | −0.683731 | − | 0.729735i | \(-0.739644\pi\) |
0.599920 | + | 0.800060i | \(0.295199\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.66198e7i | 0.305615i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.14375e7 | 0.259198 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.12832e7 | − | 6.11170e7i | −0.417740 | − | 0.497843i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.82069e7 | + | 2.11856e7i | 0.468461 | + | 0.170506i | 0.565455 | − | 0.824779i | \(-0.308701\pi\) |
−0.0969943 | + | 0.995285i | \(0.530923\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.20908e8 | + | 2.09419e8i | −0.961484 | + | 1.66534i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.01352e7 | − | 2.27618e8i | 0.315371 | − | 1.78856i | −0.254759 | − | 0.967004i | \(-0.581996\pi\) |
0.570130 | − | 0.821554i | \(-0.306893\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.34956e6 | + | 4.06955e6i | 0.0182436 | + | 0.0315989i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.37647e8 | − | 1.64041e8i | 1.05619 | − | 1.25872i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.91735e7 | − | 8.01535e7i | −0.221225 | − | 0.607812i | 0.778580 | − | 0.627545i | \(-0.215940\pi\) |
−0.999805 | + | 0.0197338i | \(0.993718\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.58416e7 | − | 2.03268e8i | −0.268612 | − | 1.52337i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.45649e8 | − | 1.83627e8i | 1.81955 | − | 1.36014i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.43865e6 | + | 1.48796e6i | −0.0617805 | + | 0.0108936i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.34060e7 | + | 3.03573e7i | −0.603568 | + | 0.219681i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.91694e8 | − | 1.60851e8i | −1.37122 | − | 1.15059i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.89390e7 | − | 5.71225e7i | 0.699608 | − | 0.403919i | −0.107594 | − | 0.994195i | \(-0.534315\pi\) |
0.807201 | + | 0.590276i | \(0.200981\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.37047e6 | − | 1.47594e6i | −0.0585120 | − | 0.0103172i | 0.144316 | − | 0.989532i | \(-0.453902\pi\) |
−0.202828 | + | 0.979214i | \(0.565013\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.76343e8 | − | 1.01812e8i | −1.21866 | − | 0.703592i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.57114e6 | + | 4.31667e6i | −0.0107345 | + | 0.0294929i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.94681e7 | − | 3.31176e7i | 0.266611 | − | 0.223713i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.07845e7i | 0.205612i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.92742e6 | −0.0523541 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.56778e7 | + | 3.06016e7i | 0.167686 | + | 0.199840i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.57999e8 | + | 1.30301e8i | 2.31185 | + | 0.841444i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.13935e6 | − | 1.23657e7i | 0.0455924 | − | 0.0789683i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.78962e6 | − | 4.41771e7i | 0.0491954 | − | 0.279001i | −0.950280 | − | 0.311398i | \(-0.899203\pi\) |
0.999475 | + | 0.0323967i | \(0.0103140\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.60619e6 | − | 1.49064e7i | −0.0537541 | − | 0.0931048i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.08641e7 | − | 2.48649e7i | 0.128887 | − | 0.153602i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.27564e7 | + | 2.27371e8i | 0.505638 | + | 1.38923i | 0.885696 | + | 0.464266i | \(0.153682\pi\) |
−0.380058 | + | 0.924963i | \(0.624096\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.39582e7 | + | 3.62725e8i | 0.386526 | + | 2.19210i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.31032e8 | + | 7.37460e6i | 0.783290 | + | 0.0440843i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.49766e8 | + | 2.64078e7i | −0.885600 | + | 0.156155i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.41181e8 | − | 5.13858e7i | 0.825845 | − | 0.300583i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.59350e8 | − | 1.33711e8i | −0.922121 | − | 0.773751i | 0.0522654 | − | 0.998633i | \(-0.483356\pi\) |
−0.974386 | + | 0.224882i | \(0.927800\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.05487e7 | − | 6.09031e6i | 0.0603900 | − | 0.0348662i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.44876e7 | − | 7.84436e6i | −0.251971 | − | 0.0444293i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.15625e8 | + | 6.67559e7i | 0.647925 | + | 0.374080i | 0.787661 | − | 0.616109i | \(-0.211292\pi\) |
−0.139736 | + | 0.990189i | \(0.544625\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.42820e7 | + | 9.41890e7i | −0.190073 | + | 0.522222i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.22695e8 | − | 1.86863e8i | 1.22169 | − | 1.02512i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 1.51450e8i | − | 0.822117i | −0.911609 | − | 0.411058i | \(-0.865159\pi\) | ||
0.911609 | − | 0.411058i | \(-0.134841\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.68042e8 | −1.43977 | −0.719887 | − | 0.694091i | \(-0.755806\pi\) | ||||
−0.719887 | + | 0.694091i | \(0.755806\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.36406e7 | + | 1.11597e8i | 0.497738 | + | 0.593181i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.86779e8 | − | 6.79821e7i | −0.982483 | − | 0.357595i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.11743e6 | − | 1.93544e6i | 0.00581690 | − | 0.0100752i | −0.863102 | − | 0.505029i | \(-0.831482\pi\) |
0.868919 | + | 0.494954i | \(0.164815\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.39173e7 | + | 4.19206e8i | −0.380812 | + | 2.15969i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.00065e8 | − | 1.73318e8i | −0.510218 | − | 0.883723i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.28932e7 | − | 9.87883e7i | 0.418325 | − | 0.498540i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.46122e7 | − | 4.01466e7i | −0.0729872 | − | 0.200531i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.84878e7 | − | 1.04850e8i | −0.0914054 | − | 0.518386i | −0.995790 | − | 0.0916670i | \(-0.970780\pi\) |
0.904384 | − | 0.426719i | \(-0.140331\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.51294e7 | + | 6.49112e6i | 0.0740417 | + | 0.0317668i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.80162e8 | − | 8.46656e7i | 2.32609 | − | 0.410152i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.23843e8 | − | 8.14722e7i | 1.07344 | − | 0.390702i | 0.255980 | − | 0.966682i | \(-0.417602\pi\) |
0.817463 | + | 0.575981i | \(0.195380\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.71638e7 | − | 1.44022e7i | −0.0814823 | − | 0.0683718i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.06204e8 | + | 2.34522e8i | −1.90907 | + | 1.10220i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.22493e8 | − | 3.92316e7i | −1.03523 | − | 0.182539i | −0.369886 | − | 0.929077i | \(-0.620603\pi\) |
−0.665342 | + | 0.746538i | \(0.731714\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.43439e8 | + | 8.28145e7i | 0.660760 | + | 0.381490i | 0.792566 | − | 0.609786i | \(-0.208744\pi\) |
−0.131807 | + | 0.991275i | \(0.542078\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.83180e8 | + | 5.03282e8i | −0.835459 | + | 2.29541i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.64232e7 | − | 3.89537e7i | 0.209637 | − | 0.175907i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 7.62124e7i | − | 0.340768i | −0.985378 | − | 0.170384i | \(-0.945499\pi\) | ||
0.985378 | − | 0.170384i | \(-0.0545009\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.76900e8 | 1.22595 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.75344e7 | + | 9.24019e7i | 0.339915 | + | 0.405095i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.89383e8 | + | 1.05327e8i | 1.25629 | + | 0.457254i | 0.882524 | − | 0.470268i | \(-0.155843\pi\) |
0.373770 | + | 0.927521i | \(0.378065\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.15732e7 | − | 2.00454e7i | 0.0497541 | − | 0.0861767i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −983517. | + | 5.57780e6i | −0.00418723 | + | 0.0237469i | −0.986830 | − | 0.161762i | \(-0.948282\pi\) |
0.982643 | + | 0.185509i | \(0.0593934\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.24041e7 | − | 7.34461e7i | −0.178787 | − | 0.309668i | 0.762678 | − | 0.646778i | \(-0.223884\pi\) |
−0.941465 | + | 0.337110i | \(0.890551\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.06021e8 | − | 4.83877e8i | 1.69541 | − | 2.02051i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.02575e7 | + | 1.10607e8i | 0.166488 | + | 0.457422i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.01607e7 | + | 1.71050e8i | 0.123538 | + | 0.700620i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.70275e7 | + | 1.57605e8i | −0.150218 | + | 0.639391i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.47362e8 | + | 2.59838e7i | −0.592151 | + | 0.104412i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.30870e8 | + | 8.40299e7i | −0.918924 | + | 0.334461i | −0.757810 | − | 0.652475i | \(-0.773731\pi\) |
−0.161114 | + | 0.986936i | \(0.551509\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.29644e8 | + | 3.60514e8i | 1.69394 | + | 1.42138i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.88767e7 | + | 1.66720e7i | −0.112778 | + | 0.0651126i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.91098e7 | − | 3.36957e6i | −0.0739328 | − | 0.0130363i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.83120e8 | − | 2.21194e8i | −1.46836 | − | 0.847757i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.58495e8 | − | 4.35463e8i | 0.601787 | − | 1.65340i | −0.145864 | − | 0.989305i | \(-0.546596\pi\) |
0.747651 | − | 0.664091i | \(-0.231181\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.05342e8 | − | 3.40122e8i | 1.52471 | − | 1.27939i | 0.699360 | − | 0.714770i | \(-0.253469\pi\) |
0.825353 | − | 0.564616i | \(-0.190976\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.55649e7i | 0.132539i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.61848e8 | 0.597576 | 0.298788 | − | 0.954319i | \(-0.403418\pi\) | ||||
0.298788 | + | 0.954319i | \(0.403418\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.82047e6 | − | 6.93657e6i | −0.0212924 | − | 0.0253753i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.26405e7 | + | 1.18802e7i | 0.118308 | + | 0.0430605i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.90607e8 | − | 3.30142e8i | 0.684542 | − | 1.18566i | −0.289039 | − | 0.957317i | \(-0.593336\pi\) |
0.973581 | − | 0.228344i | \(-0.0733310\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.42482e7 | + | 1.37518e8i | −0.0862889 | + | 0.489369i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.72247e8 | − | 9.91161e8i | −2.01784 | − | 3.49501i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.27563e7 | + | 9.86251e7i | −0.289164 | + | 0.344613i | −0.890997 | − | 0.454010i | \(-0.849993\pi\) |
0.601832 | + | 0.798622i | \(0.294438\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.16305e7 | + | 1.69328e8i | 0.213398 | + | 0.586308i | 0.999494 | − | 0.0317971i | \(-0.0101230\pi\) |
−0.786096 | + | 0.618105i | \(0.787901\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.06604e7 | + | 6.04581e7i | 0.0365791 | + | 0.207450i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.49900e7 | + | 5.85149e7i | −0.186990 | + | 0.198976i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.66188e8 | − | 4.69362e7i | 0.897040 | − | 0.158172i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.46897e8 | − | 5.34662e7i | 0.490608 | − | 0.178567i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.29924e7 | − | 6.96389e7i | −0.274708 | − | 0.230507i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.90836e8 | + | 2.25649e8i | −1.28218 | + | 0.740267i | −0.977247 | − | 0.212106i | \(-0.931968\pi\) |
−0.304934 | + | 0.952373i | \(0.598634\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.19594e8 | − | 1.09251e8i | −2.01463 | − | 0.355234i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.75557e7 | − | 1.01358e7i | −0.0565787 | − | 0.0326658i | 0.471444 | − | 0.881896i | \(-0.343733\pi\) |
−0.528023 | + | 0.849230i | \(0.677066\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.54848e7 | + | 2.62342e8i | −0.305018 | + | 0.838029i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.27014e8 | − | 4.42217e8i | 1.66871 | − | 1.40021i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.87646e8i | 1.53053i | 0.643713 | + | 0.765267i | \(0.277393\pi\) | ||||
−0.643713 | + | 0.765267i | \(0.722607\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.21035e7 | −0.0376566 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.80225e8 | − | 5.72310e8i | −1.48107 | − | 1.76507i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.64684e8 | − | 5.99403e7i | −0.503495 | − | 0.183257i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.46020e7 | + | 9.45734e7i | −0.165491 | + | 0.286639i | −0.936830 | − | 0.349786i | \(-0.886254\pi\) |
0.771339 | + | 0.636425i | \(0.219588\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.11118e7 | + | 2.33157e8i | −0.123528 | + | 0.700564i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.56427e7 | + | 1.13697e8i | 0.195538 | + | 0.338682i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.48181e7 | + | 1.76596e7i | −0.0437618 | + | 0.0521533i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.06480e8 | + | 5.67300e8i | 0.604570 | + | 1.66104i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.65171e7 | + | 1.50386e8i | 0.0769789 | + | 0.436569i | 0.998801 | + | 0.0489557i | \(0.0155893\pi\) |
−0.921822 | + | 0.387613i | \(0.873300\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.32986e7 | + | 5.32518e8i | 0.182191 | + | 1.53274i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.46841e8 | + | 6.11575e7i | −0.989837 | + | 0.174535i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.32545e7 | + | 1.21036e7i | −0.0941005 | + | 0.0342498i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.99162e8 | + | 2.51027e8i | 0.839399 | + | 0.704339i | 0.957428 | − | 0.288671i | \(-0.0932133\pi\) |
−0.118030 | + | 0.993010i | \(0.537658\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.30278e8 | + | 4.21626e8i | −2.03179 | + | 1.17306i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.33916e7 | + | 5.88783e6i | 0.0921230 | + | 0.0162438i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.08831e7 | + | 6.28336e6i | 0.0297738 | + | 0.0171899i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.71815e8 | + | 4.72058e8i | −0.466127 | + | 1.28067i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.83850e8 | − | 4.05998e8i | 1.30174 | − | 1.09229i | 0.311897 | − | 0.950116i | \(-0.399035\pi\) |
0.989842 | − | 0.142173i | \(-0.0454090\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 6.45313e7i | − | 0.172173i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.13852e9 | −3.01248 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.73053e8 | − | 2.06237e8i | −0.454115 | − | 0.541193i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.10281e8 | − | 1.49330e8i | −1.06777 | − | 0.388637i | −0.252428 | − | 0.967616i | \(-0.581229\pi\) |
−0.815342 | + | 0.578979i | \(0.803451\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.16189e7 | − | 2.01245e7i | 0.0299904 | − | 0.0519450i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.15083e6 | − | 3.48831e7i | 0.0157464 | − | 0.0893023i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.46781e8 | − | 4.27437e8i | −0.626613 | − | 1.08533i | −0.988227 | − | 0.152997i | \(-0.951107\pi\) |
0.361614 | − | 0.932328i | \(-0.382226\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.64186e7 | − | 4.34020e7i | 0.0917195 | − | 0.109307i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.38810e7 | − | 1.48037e8i | −0.134596 | − | 0.369801i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.98200e7 | + | 4.52682e8i | 0.197778 | + | 1.12166i | 0.908407 | + | 0.418088i | \(0.137300\pi\) |
−0.710628 | + | 0.703568i | \(0.751589\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.18476e8 | − | 2.59695e7i | 0.536970 | − | 0.0638277i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.93848e8 | − | 1.04711e8i | 1.44780 | − | 0.255286i | 0.606168 | − | 0.795337i | \(-0.292706\pi\) |
0.841633 | + | 0.540050i | \(0.181595\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.66189e8 | − | 6.04879e7i | 0.401914 | − | 0.146285i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.50089e8 | − | 7.13309e8i | −2.03940 | − | 1.71126i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.60537e8 | + | 1.50421e8i | −0.620045 | + | 0.357983i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.09537e8 | + | 5.45798e7i | 0.730791 | + | 0.128858i | 0.526649 | − | 0.850083i | \(-0.323448\pi\) |
0.204142 | + | 0.978941i | \(0.434559\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.61115e8 | − | 9.30196e7i | −0.377355 | − | 0.217866i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.70825e7 | − | 7.44086e7i | 0.0629286 | − | 0.172895i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.55469e8 | + | 2.14364e8i | −0.588911 | + | 0.494155i | −0.887860 | − | 0.460114i | \(-0.847809\pi\) |
0.298948 | + | 0.954269i | \(0.403364\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.33434e8i | 0.762577i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.39991e8 | 1.22527 | 0.612636 | − | 0.790365i | \(-0.290109\pi\) | ||||
0.612636 | + | 0.790365i | \(0.290109\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.57126e8 | + | 1.87256e8i | 0.353733 | + | 0.421562i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.16746e8 | − | 4.24921e7i | −0.260770 | − | 0.0949126i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.15285e6 | + | 1.06570e7i | −0.0136361 | + | 0.0236184i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.39665e6 | + | 4.19485e7i | −0.0162651 | + | 0.0922438i | −0.991860 | − | 0.127336i | \(-0.959357\pi\) |
0.975595 | + | 0.219580i | \(0.0704685\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.29594e8 | − | 7.44079e8i | −0.937335 | − | 1.62351i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.05370e8 | − | 3.63926e8i | 0.661133 | − | 0.787907i | −0.326415 | − | 0.945226i | \(-0.605841\pi\) |
0.987548 | + | 0.157319i | \(0.0502852\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.15508e7 | − | 3.17355e7i | −0.0248145 | − | 0.0681774i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.96476e8 | + | 1.11427e9i | 0.418839 | + | 2.37536i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.02049e7 | + | 5.65782e7i | 0.127356 | + | 0.119684i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.28149e8 | − | 2.25961e7i | 0.269006 | − | 0.0474329i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.03963e8 | − | 2.92619e8i | 1.67475 | − | 0.609561i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.75879e8 | − | 1.47580e8i | −0.363585 | − | 0.305084i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.31342e8 | − | 3.06770e8i | 1.09006 | − | 0.629346i | 0.156467 | − | 0.987683i | \(-0.449990\pi\) |
0.933592 | + | 0.358337i | \(0.116656\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.12388e9 | + | 1.98171e8i | 2.28818 | + | 0.403468i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.53723e8 | − | 3.77427e8i | −1.32088 | − | 0.762612i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.03560e7 | + | 1.38352e8i | −0.100979 | + | 0.277438i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.91988e8 | − | 3.28917e8i | 0.780139 | − | 0.654614i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.68440e8i | 0.727766i | 0.931445 | + | 0.363883i | \(0.118549\pi\) | ||||
−0.931445 | + | 0.363883i | \(0.881451\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.50769e8 | 0.687671 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.19526e8 | + | 4.99972e8i | 0.816322 | + | 0.972855i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.16343e8 | + | 1.15139e8i | 0.610958 | + | 0.222371i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.26898e7 | + | 1.43223e8i | −0.158513 | + | 0.274552i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.53207e8 | − | 1.43601e9i | 0.481788 | − | 2.73235i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.13340e8 | − | 3.69516e8i | −0.402928 | − | 0.697891i | 0.591150 | − | 0.806561i | \(-0.298674\pi\) |
−0.994078 | + | 0.108670i | \(0.965341\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.42491e8 | + | 1.69815e8i | −0.267132 | + | 0.318356i | −0.882890 | − | 0.469580i | \(-0.844406\pi\) |
0.615758 | + | 0.787935i | \(0.288850\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.21259e8 | − | 3.33155e8i | −0.225653 | − | 0.619976i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.51517e7 | − | 3.12781e8i | −0.101879 | − | 0.577786i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.23579e8 | − | 2.90336e7i | −0.226610 | − | 0.0532396i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.16857e8 | − | 5.58704e7i | 0.576782 | − | 0.101702i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.79901e7 | + | 2.83861e7i | −0.140932 | + | 0.0512951i | −0.411523 | − | 0.911399i | \(-0.635003\pi\) |
0.270591 | + | 0.962694i | \(0.412781\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.65109e8 | − | 2.22453e8i | −0.475581 | − | 0.399060i | 0.373244 | − | 0.927733i | \(-0.378245\pi\) |
−0.848826 | + | 0.528673i | \(0.822690\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.87617e8 | − | 1.66056e8i | 0.512215 | − | 0.295728i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.93359e8 | + | 1.22258e8i | 1.22586 | + | 0.216153i | 0.748847 | − | 0.662743i | \(-0.230608\pi\) |
0.477015 | + | 0.878895i | \(0.341719\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.61595e8 | − | 9.32966e7i | −0.283637 | − | 0.163758i | 0.351432 | − | 0.936214i | \(-0.385695\pi\) |
−0.635069 | + | 0.772456i | \(0.719028\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.98298e8 | + | 1.36906e9i | −0.868333 | + | 2.38572i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.32267e7 | + | 3.62715e7i | −0.0747854 | + | 0.0627524i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 1.95620e8i | − | 0.336011i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.07324e8 | 0.183030 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.78229e8 | + | 5.69931e8i | 0.809748 | + | 0.965020i | 0.999860 | − | 0.0167420i | \(-0.00532940\pi\) |
−0.190112 | + | 0.981763i | \(0.560885\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.14924e8 | − | 7.82259e7i | −0.361324 | − | 0.131511i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.57781e8 | − | 9.66104e8i | 0.931066 | − | 1.61265i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.00813e7 | + | 1.70599e8i | −0.0498570 | + | 0.282753i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.28192e8 | + | 3.95239e8i | 0.375534 | + | 0.650444i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.95766e8 | − | 2.33305e8i | 0.319900 | − | 0.381242i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.77752e8 | + | 1.03786e9i | 0.612940 | + | 1.68404i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.99579e7 | + | 2.26613e8i | 0.0643807 | + | 0.365121i | 0.999929 | + | 0.0119221i | \(0.00379502\pi\) |
−0.935548 | + | 0.353199i | \(0.885094\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.75555e8 | + | 4.09181e8i | −0.280876 | + | 0.654662i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.05743e9 | + | 1.86454e8i | −1.68000 | + | 0.296230i | −0.930642 | − | 0.365930i | \(-0.880751\pi\) |
−0.749362 | + | 0.662160i | \(0.769640\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.18363e8 | + | 4.30804e7i | −0.186739 | + | 0.0679674i | −0.433697 | − | 0.901059i | \(-0.642791\pi\) |
0.246958 | + | 0.969026i | \(0.420569\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.33533e8 | + | 1.12047e8i | 0.209208 | + | 0.175546i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.08595e8 | + | 4.09107e8i | −1.10247 | + | 0.636509i | −0.936868 | − | 0.349684i | \(-0.886289\pi\) |
−0.165599 | + | 0.986193i | \(0.552956\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.99359e8 | + | 3.51523e7i | 0.308025 | + | 0.0543132i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.64210e8 | − | 4.98952e8i | −1.32606 | − | 0.765599i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.48336e7 | − | 2.33079e8i | 0.129273 | − | 0.355175i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.64004e8 | + | 1.37615e8i | −0.248198 | + | 0.208263i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.54803e9i | 2.32668i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.47647e8 | 0.518936 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.71112e8 | − | 7.99801e8i | −0.994939 | − | 1.18572i | −0.982588 | − | 0.185798i | \(-0.940513\pi\) |
−0.0123511 | − | 0.999924i | \(-0.503932\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.91242e9 | + | 6.96064e8i | 2.81590 | + | 1.02490i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.07303e8 | + | 3.59059e8i | −0.303164 | + | 0.525095i | −0.976851 | − | 0.213922i | \(-0.931376\pi\) |
0.673687 | + | 0.739017i | \(0.264710\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.23567e8 | − | 7.00781e8i | 0.179481 | − | 1.01789i | −0.753362 | − | 0.657606i | \(-0.771569\pi\) |
0.932843 | − | 0.360283i | \(-0.117320\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.79651e7 | − | 3.11164e7i | −0.0259178 | − | 0.0448910i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.28434e8 | + | 5.10588e8i | −0.613922 | + | 0.731644i | −0.980013 | − | 0.198935i | \(-0.936252\pi\) |
0.366090 | + | 0.930579i | \(0.380696\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.58849e7 | − | 2.35967e8i | −0.122240 | − | 0.335850i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.23344e7 | + | 4.66942e8i | 0.116399 | + | 0.660130i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.06388e7 | − | 1.25511e9i | 0.0991949 | − | 1.76250i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.03512e8 | + | 5.35173e7i | −0.423357 | + | 0.0746492i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.25805e8 | − | 1.54980e8i | 0.589974 | − | 0.214733i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.51810e7 | + | 2.95204e7i | 0.0484205 | + | 0.0406296i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.41358e8 | + | 2.54818e8i | −0.603416 | + | 0.348382i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.63768e8 | − | 4.65094e7i | −0.358227 | − | 0.0631652i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.20587e7 | + | 6.96208e6i | 0.0162687 | + | 0.00939276i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.84740e8 | − | 1.33181e9i | 0.649661 | − | 1.78493i | 0.0306727 | − | 0.999529i | \(-0.490235\pi\) |
0.618989 | − | 0.785400i | \(-0.287543\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.50319e8 | + | 1.26133e8i | −0.200135 | + | 0.167933i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.65924e7i | 0.101305i | 0.998716 | + | 0.0506525i | \(0.0161301\pi\) | ||||
−0.998716 | + | 0.0506525i | \(0.983870\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.26414e8 | 0.428901 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.76325e8 | − | 3.29311e8i | −0.360709 | − | 0.429876i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.88196e8 | − | 3.59674e8i | −1.28155 | − | 0.466446i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.04560e7 | − | 1.81104e7i | 0.0134717 | − | 0.0233336i | −0.859211 | − | 0.511621i | \(-0.829045\pi\) |
0.872683 | + | 0.488288i | \(0.162378\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.17107e8 | + | 6.64150e8i | −0.149901 | + | 0.850133i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.84195e7 | − | 1.53147e8i | −0.112446 | − | 0.194762i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.07125e8 | − | 8.42719e8i | 0.893452 | − | 1.06477i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.22382e8 | − | 3.36242e8i | −0.153631 | − | 0.422098i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.56266e8 | − | 8.86227e8i | −0.194902 | − | 1.10535i | −0.912558 | − | 0.408947i | \(-0.865896\pi\) |
0.717656 | − | 0.696398i | \(-0.245215\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.21081e8 | + | 1.61977e8i | 0.150046 | + | 0.200726i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.91438e7 | − | 3.37557e6i | 0.0235713 | − | 0.00415626i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.43401e7 | − | 1.24988e7i | 0.0420113 | − | 0.0152909i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.12276e8 | + | 2.62030e8i | 0.379594 | + | 0.318517i | 0.812543 | − | 0.582901i | \(-0.198083\pi\) |
−0.432949 | + | 0.901418i | \(0.642527\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.45770e9 | − | 8.41601e8i | 1.76064 | − | 1.01650i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.62158e7 | − | 1.52022e7i | −0.103471 | − | 0.0182447i | 0.121673 | − | 0.992570i | \(-0.461174\pi\) |
−0.225144 | + | 0.974326i | \(0.572285\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.47360e8 | + | 8.50781e7i | 0.175729 | + | 0.101457i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.79039e8 | + | 4.91904e8i | −0.212154 | + | 0.582888i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.83606e8 | + | 4.89704e8i | −0.687179 | + | 0.576612i | −0.918094 | − | 0.396362i | \(-0.870272\pi\) |
0.230915 | + | 0.972974i | \(0.425828\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 4.57496e8i | − | 0.535290i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.21982e8 | −0.955698 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.75248e8 | + | 6.85554e8i | 0.664625 | + | 0.792069i | 0.988042 | − | 0.154187i | \(-0.0492760\pi\) |
−0.323417 | + | 0.946257i | \(0.604832\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.10742e8 | − | 4.03066e7i | −0.127145 | − | 0.0462771i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.25813e8 | + | 3.91119e8i | −0.257640 | + | 0.446245i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.58282e7 | − | 8.97661e7i | 0.0179463 | − | 0.101779i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.40871e8 | − | 7.63612e8i | −0.496754 | − | 0.860404i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.07227e9 | + | 1.27788e9i | −1.20067 | + | 1.43090i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.17776e8 | − | 3.23586e8i | −0.131061 | − | 0.360087i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.89459e7 | − | 4.47724e8i | −0.0873072 | − | 0.495144i | −0.996835 | − | 0.0795002i | \(-0.974668\pi\) |
0.909528 | − | 0.415643i | \(-0.136444\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.50530e8 | − | 5.35233e8i | 0.385260 | − | 0.588263i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.39767e8 | + | 1.65706e8i | −1.02651 | + | 0.181001i | −0.661455 | − | 0.749985i | \(-0.730061\pi\) |
−0.365054 | + | 0.930986i | \(0.618950\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.29076e8 | + | 3.38156e8i | −1.00859 | + | 0.367095i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.45743e8 | − | 2.90112e8i | −0.373026 | − | 0.313006i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.37948e8 | + | 1.95114e8i | −0.362382 | + | 0.209221i | −0.670125 | − | 0.742248i | \(-0.733760\pi\) |
0.307743 | + | 0.951469i | \(0.400426\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.89061e8 | − | 3.33365e7i | −0.201490 | − | 0.0355281i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.17384e9 | + | 6.77716e8i | 1.24337 | + | 0.717862i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.97563e8 | + | 8.17549e8i | −0.313270 | + | 0.860702i | 0.678721 | + | 0.734396i | \(0.262534\pi\) |
−0.991991 | + | 0.126306i | \(0.959688\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.02147e8 | + | 2.53532e8i | −0.316162 | + | 0.265292i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 2.65233e9i | − | 2.75852i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.61448e8 | −0.270269 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.96383e8 | − | 1.06827e9i | −0.921027 | − | 1.09764i | −0.994950 | − | 0.100374i | \(-0.967996\pi\) |
0.0739223 | − | 0.997264i | \(-0.476448\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.40479e9 | − | 5.11301e8i | −1.43471 | − | 0.522190i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.89720e8 | − | 3.28604e8i | 0.192594 | − | 0.333583i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.27026e8 | + | 1.28753e9i | −0.229081 | + | 1.29918i | 0.625646 | + | 0.780107i | \(0.284835\pi\) |
−0.854727 | + | 0.519077i | \(0.826276\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.74798e9 | + | 3.02760e9i | 1.75324 | + | 3.03670i |
(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.j.a.29.1 | yes | 60 | |
19.2 | odd | 18 | inner | 76.7.j.a.21.1 | ✓ | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.7.j.a.21.1 | ✓ | 60 | 19.2 | odd | 18 | inner | |
76.7.j.a.29.1 | yes | 60 | 1.1 | even | 1 | trivial |