Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [117,4,Mod(10,117)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(117, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("117.10");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 117 = 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 117.q (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.90322347067\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 32x^{10} + 823x^{8} - 5964x^{6} + 32913x^{4} - 47034x^{2} + 54756 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 82.1 | ||
Root | \(-4.24667 + 2.45182i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 117.82 |
Dual form | 117.4.q.f.10.1 |
$q$-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 \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(92\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.24667 | − | 2.45182i | −1.50142 | − | 0.866848i | −0.999999 | − | 0.00164665i | \(-0.999476\pi\) |
−0.501425 | − | 0.865201i | \(-0.667191\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 8.02279 | + | 13.8959i | 1.00285 | + | 1.73699i | ||||
\(5\) | − | 5.61325i | − | 0.502065i | −0.967979 | − | 0.251032i | \(-0.919230\pi\) | ||
0.967979 | − | 0.251032i | \(-0.0807701\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.78293 | − | 1.60672i | 0.150264 | − | 0.0867550i | −0.422983 | − | 0.906138i | \(-0.639017\pi\) |
0.573247 | + | 0.819383i | \(0.305684\pi\) | |||||||
\(8\) | − | 39.4526i | − | 1.74357i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −13.7627 | + | 23.8376i | −0.435214 | + | 0.753812i | ||||
\(11\) | −37.7991 | − | 21.8233i | −1.03608 | − | 0.598179i | −0.117357 | − | 0.993090i | \(-0.537442\pi\) |
−0.918720 | + | 0.394910i | \(0.870776\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −46.8108 | + | 2.39816i | −0.998690 | + | 0.0511639i | ||||
\(14\) | −15.7576 | −0.300813 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −32.5481 | + | 56.3750i | −0.508564 | + | 0.880859i | ||||
\(17\) | 32.9378 | + | 57.0500i | 0.469918 | + | 0.813921i | 0.999408 | − | 0.0343944i | \(-0.0109502\pi\) |
−0.529491 | + | 0.848316i | \(0.677617\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.65374 | + | 1.53214i | −0.0320426 | + | 0.0184998i | −0.515936 | − | 0.856627i | \(-0.672556\pi\) |
0.483893 | + | 0.875127i | \(0.339222\pi\) | |||||||
\(20\) | 78.0011 | − | 45.0340i | 0.872079 | − | 0.503495i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 107.013 | + | 185.353i | 1.03706 | + | 1.79624i | ||||
\(23\) | −81.8821 | + | 141.824i | −0.742330 | + | 1.28575i | 0.209102 | + | 0.977894i | \(0.432946\pi\) |
−0.951432 | + | 0.307859i | \(0.900387\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 93.4914 | 0.747931 | ||||||||
\(26\) | 204.670 | + | 104.587i | 1.54381 | + | 0.788894i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 44.6537 | + | 25.7808i | 0.301384 | + | 0.174004i | ||||
\(29\) | −77.7243 | + | 134.622i | −0.497691 | + | 0.862027i | −0.999996 | − | 0.00266388i | \(-0.999152\pi\) |
0.502305 | + | 0.864690i | \(0.332485\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 240.463i | 1.39318i | 0.717471 | + | 0.696588i | \(0.245299\pi\) | ||||
−0.717471 | + | 0.696588i | \(0.754701\pi\) | |||||||
\(32\) | 3.10650 | − | 1.79354i | 0.0171611 | − | 0.00990799i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 323.030i | − | 1.62939i | ||||||
\(35\) | −9.01895 | − | 15.6213i | −0.0435566 | − | 0.0754423i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −275.104 | − | 158.831i | −1.22234 | − | 0.705721i | −0.256927 | − | 0.966431i | \(-0.582710\pi\) |
−0.965417 | + | 0.260710i | \(0.916043\pi\) | |||||||
\(38\) | 15.0261 | 0.0641460 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −221.457 | −0.875387 | ||||||||
\(41\) | 110.773 | + | 63.9551i | 0.421949 | + | 0.243612i | 0.695911 | − | 0.718128i | \(-0.255001\pi\) |
−0.273962 | + | 0.961741i | \(0.588334\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −189.501 | − | 328.225i | −0.672060 | − | 1.16404i | −0.977319 | − | 0.211773i | \(-0.932076\pi\) |
0.305259 | − | 0.952269i | \(-0.401257\pi\) | |||||||
\(44\) | − | 700.336i | − | 2.39954i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 695.452 | − | 401.519i | 2.22910 | − | 1.28697i | ||||
\(47\) | 79.4626i | 0.246613i | 0.992369 | + | 0.123306i | \(0.0393498\pi\) | ||||
−0.992369 | + | 0.123306i | \(0.960650\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −166.337 | + | 288.104i | −0.484947 | + | 0.839953i | ||||
\(50\) | −397.027 | − | 229.224i | −1.12296 | − | 0.648342i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −408.878 | − | 631.237i | −1.09041 | − | 1.68340i | ||||
\(53\) | −571.746 | −1.48180 | −0.740899 | − | 0.671616i | \(-0.765600\pi\) | ||||
−0.740899 | + | 0.671616i | \(0.765600\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −122.500 | + | 212.176i | −0.300325 | + | 0.520178i | ||||
\(56\) | −63.3895 | − | 109.794i | −0.151264 | − | 0.261997i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 660.139 | − | 381.131i | 1.49449 | − | 0.862845i | ||||
\(59\) | −91.3986 | + | 52.7690i | −0.201679 | + | 0.116440i | −0.597439 | − | 0.801915i | \(-0.703815\pi\) |
0.395759 | + | 0.918354i | \(0.370482\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 362.319 | + | 627.555i | 0.760495 | + | 1.31722i | 0.942596 | + | 0.333936i | \(0.108377\pi\) |
−0.182101 | + | 0.983280i | \(0.558290\pi\) | |||||||
\(62\) | 589.571 | − | 1021.17i | 1.20767 | − | 2.09175i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 503.180 | 0.982774 | ||||||||
\(65\) | 13.4615 | + | 262.761i | 0.0256876 | + | 0.501407i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −261.732 | − | 151.111i | −0.477248 | − | 0.275539i | 0.242021 | − | 0.970271i | \(-0.422190\pi\) |
−0.719269 | + | 0.694732i | \(0.755523\pi\) | |||||||
\(68\) | −528.507 | + | 915.401i | −0.942513 | + | 1.63248i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 88.4512i | 0.151028i | ||||||||
\(71\) | 868.960 | − | 501.694i | 1.45249 | − | 0.838594i | 0.453865 | − | 0.891071i | \(-0.350045\pi\) |
0.998622 | + | 0.0524770i | \(0.0167116\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 277.988i | − | 0.445699i | −0.974853 | − | 0.222850i | \(-0.928464\pi\) | ||
0.974853 | − | 0.222850i | \(-0.0715359\pi\) | |||||||
\(74\) | 778.849 | + | 1349.01i | 1.22350 | + | 2.11917i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −42.5808 | − | 24.5840i | −0.0642678 | − | 0.0371050i | ||||
\(77\) | −140.256 | −0.207580 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −959.137 | −1.36597 | −0.682983 | − | 0.730434i | \(-0.739318\pi\) | ||||
−0.682983 | + | 0.730434i | \(0.739318\pi\) | |||||||
\(80\) | 316.447 | + | 182.701i | 0.442248 | + | 0.255332i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −313.612 | − | 543.192i | −0.422349 | − | 0.731531i | ||||
\(83\) | − | 410.957i | − | 0.543475i | −0.962371 | − | 0.271737i | \(-0.912402\pi\) | ||
0.962371 | − | 0.271737i | \(-0.0875982\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 320.236 | − | 184.888i | 0.408641 | − | 0.235929i | ||||
\(86\) | 1858.48i | 2.33029i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −860.986 | + | 1491.27i | −1.04297 | + | 1.80648i | ||||
\(89\) | 195.894 | + | 113.100i | 0.233312 | + | 0.134703i | 0.612099 | − | 0.790781i | \(-0.290325\pi\) |
−0.378787 | + | 0.925484i | \(0.623659\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −126.418 | + | 81.8860i | −0.145629 | + | 0.0943295i | ||||
\(92\) | −2627.69 | −2.97778 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 194.828 | − | 337.451i | 0.213776 | − | 0.370271i | ||||
\(95\) | 8.60027 | + | 14.8961i | 0.00928810 | + | 0.0160875i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −769.427 | + | 444.229i | −0.805397 | + | 0.464996i | −0.845355 | − | 0.534205i | \(-0.820611\pi\) |
0.0399579 | + | 0.999201i | \(0.487278\pi\) | |||||||
\(98\) | 1412.76 | − | 815.655i | 1.45622 | − | 0.840750i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 750.062 | + | 1299.15i | 0.750062 | + | 1.29915i | ||||
\(101\) | 930.180 | − | 1611.12i | 0.916400 | − | 1.58725i | 0.111561 | − | 0.993758i | \(-0.464415\pi\) |
0.804839 | − | 0.593494i | \(-0.202252\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −328.512 | −0.314265 | −0.157132 | − | 0.987578i | \(-0.550225\pi\) | ||||
−0.157132 | + | 0.987578i | \(0.550225\pi\) | |||||||
\(104\) | 94.6137 | + | 1846.81i | 0.0892081 | + | 1.74129i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2428.01 | + | 1401.81i | 2.22481 | + | 1.28449i | ||||
\(107\) | 164.387 | − | 284.727i | 0.148522 | − | 0.257248i | −0.782159 | − | 0.623079i | \(-0.785882\pi\) |
0.930682 | + | 0.365830i | \(0.119215\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 201.673i | 0.177218i | 0.996066 | + | 0.0886092i | \(0.0282422\pi\) | ||||
−0.996066 | + | 0.0886092i | \(0.971758\pi\) | |||||||
\(110\) | 1040.43 | − | 600.693i | 0.901830 | − | 0.520672i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 209.183i | 0.176482i | ||||||||
\(113\) | 144.992 | + | 251.134i | 0.120705 | + | 0.209068i | 0.920046 | − | 0.391810i | \(-0.128151\pi\) |
−0.799341 | + | 0.600878i | \(0.794818\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 796.094 | + | 459.625i | 0.645531 | + | 0.372698i | ||||
\(116\) | −2494.27 | −1.99644 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 517.520 | 0.403742 | ||||||||
\(119\) | 183.327 | + | 105.844i | 0.141223 | + | 0.0815354i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 287.013 | + | 497.121i | 0.215637 | + | 0.373494i | ||||
\(122\) | − | 3553.36i | − | 2.63693i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3341.45 | + | 1929.19i | −2.41993 | + | 1.39715i | ||||
\(125\) | − | 1226.45i | − | 0.877574i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 376.283 | − | 651.742i | 0.262911 | − | 0.455376i | −0.704103 | − | 0.710098i | \(-0.748651\pi\) |
0.967014 | + | 0.254722i | \(0.0819840\pi\) | |||||||
\(128\) | −2161.69 | − | 1248.05i | −1.49272 | − | 0.861823i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 587.074 | − | 1148.86i | 0.396076 | − | 0.775092i | ||||
\(131\) | −2200.41 | −1.46756 | −0.733782 | − | 0.679385i | \(-0.762247\pi\) | ||||
−0.733782 | + | 0.679385i | \(0.762247\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.92345 | + | 8.52766i | −0.00320990 | + | 0.00555971i | ||||
\(134\) | 740.992 | + | 1283.44i | 0.477701 | + | 0.827402i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2250.77 | − | 1299.48i | 1.41913 | − | 0.819337i | ||||
\(137\) | 315.299 | − | 182.038i | 0.196626 | − | 0.113522i | −0.398455 | − | 0.917188i | \(-0.630453\pi\) |
0.595081 | + | 0.803666i | \(0.297120\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1226.79 | − | 2124.87i | −0.748600 | − | 1.29661i | −0.948494 | − | 0.316795i | \(-0.897393\pi\) |
0.199894 | − | 0.979817i | \(-0.435940\pi\) | |||||||
\(140\) | 144.714 | − | 250.653i | 0.0873614 | − | 0.151314i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4920.25 | −2.90773 | ||||||||
\(143\) | 1821.74 | + | 930.917i | 1.06533 | + | 0.544386i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 755.670 | + | 436.286i | 0.432793 | + | 0.249873i | ||||
\(146\) | −681.575 | + | 1180.52i | −0.386353 | + | 0.669183i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 5097.08i | − | 2.83093i | ||||||
\(149\) | 56.4171 | − | 32.5724i | 0.0310192 | − | 0.0179090i | −0.484410 | − | 0.874841i | \(-0.660966\pi\) |
0.515429 | + | 0.856932i | \(0.327632\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 250.204i | 0.134843i | 0.997725 | + | 0.0674216i | \(0.0214773\pi\) | ||||
−0.997725 | + | 0.0674216i | \(0.978523\pi\) | |||||||
\(152\) | 60.4468 | + | 104.697i | 0.0322558 | + | 0.0558687i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 595.621 | + | 343.882i | 0.311666 | + | 0.179940i | ||||
\(155\) | 1349.78 | 0.699464 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1768.99 | 0.899242 | 0.449621 | − | 0.893219i | \(-0.351559\pi\) | ||||
0.449621 | + | 0.893219i | \(0.351559\pi\) | |||||||
\(158\) | 4073.13 | + | 2351.63i | 2.05089 | + | 1.18408i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −10.0676 | − | 17.4376i | −0.00497445 | − | 0.00861600i | ||||
\(161\) | 526.248i | 0.257603i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2344.60 | + | 1353.66i | −1.12665 | + | 0.650470i | −0.943090 | − | 0.332538i | \(-0.892095\pi\) |
−0.183558 | + | 0.983009i | \(0.558762\pi\) | |||||||
\(164\) | 2052.39i | 0.977226i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1007.59 | + | 1745.20i | −0.471110 | + | 0.815986i | ||||
\(167\) | −3024.42 | − | 1746.15i | −1.40142 | − | 0.809107i | −0.406877 | − | 0.913483i | \(-0.633382\pi\) |
−0.994538 | + | 0.104375i | \(0.966716\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2185.50 | − | 224.520i | 0.994765 | − | 0.102194i | ||||
\(170\) | −1813.25 | −0.818058 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3040.65 | − | 5266.56i | 1.34795 | − | 2.33472i | ||||
\(173\) | 1990.98 | + | 3448.48i | 0.874979 | + | 1.51551i | 0.856785 | + | 0.515674i | \(0.172458\pi\) |
0.0181944 | + | 0.999834i | \(0.494208\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 260.180 | − | 150.215i | 0.112387 | − | 0.0648868i | ||||
\(176\) | 2460.58 | − | 1420.61i | 1.05382 | − | 0.608425i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −554.598 | − | 960.593i | −0.233533 | − | 0.404491i | ||||
\(179\) | −1127.53 | + | 1952.93i | −0.470812 | + | 0.815470i | −0.999443 | − | 0.0333818i | \(-0.989372\pi\) |
0.528631 | + | 0.848852i | \(0.322706\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 890.108 | 0.365532 | 0.182766 | − | 0.983156i | \(-0.441495\pi\) | ||||
0.182766 | + | 0.983156i | \(0.441495\pi\) | |||||||
\(182\) | 737.624 | − | 37.7892i | 0.300419 | − | 0.0153908i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5595.32 | + | 3230.46i | 2.24181 | + | 1.29431i | ||||
\(185\) | −891.559 | + | 1544.23i | −0.354318 | + | 0.613696i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 2875.25i | − | 1.12438i | ||||||
\(188\) | −1104.20 | + | 637.512i | −0.428363 | + | 0.247316i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 84.3451i | − | 0.0322055i | ||||||
\(191\) | 399.887 | + | 692.624i | 0.151491 | + | 0.262390i | 0.931776 | − | 0.363034i | \(-0.118259\pi\) |
−0.780285 | + | 0.625424i | \(0.784926\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2332.56 | + | 1346.70i | 0.869954 | + | 0.502268i | 0.867333 | − | 0.497729i | \(-0.165832\pi\) |
0.00262073 | + | 0.999997i | \(0.499166\pi\) | |||||||
\(194\) | 4356.67 | 1.61232 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5337.95 | −1.94532 | ||||||||
\(197\) | −2369.19 | − | 1367.85i | −0.856842 | − | 0.494698i | 0.00611178 | − | 0.999981i | \(-0.498055\pi\) |
−0.862953 | + | 0.505284i | \(0.831388\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −588.218 | − | 1018.82i | −0.209536 | − | 0.362927i | 0.742033 | − | 0.670364i | \(-0.233862\pi\) |
−0.951568 | + | 0.307437i | \(0.900529\pi\) | |||||||
\(200\) | − | 3688.48i | − | 1.30407i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7900.33 | + | 4561.26i | −2.75181 | + | 1.58876i | ||||
\(203\) | 499.526i | 0.172709i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 358.996 | − | 621.799i | 0.122309 | − | 0.211846i | ||||
\(206\) | 1395.08 | + | 805.451i | 0.471845 | + | 0.272420i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1388.41 | − | 2717.01i | 0.462830 | − | 0.905726i | ||||
\(209\) | 133.745 | 0.0442648 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1457.33 | − | 2524.16i | 0.475481 | − | 0.823556i | −0.524125 | − | 0.851641i | \(-0.675608\pi\) |
0.999606 | + | 0.0280849i | \(0.00894088\pi\) | |||||||
\(212\) | −4587.00 | − | 7944.91i | −1.48602 | − | 2.57386i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1396.19 | + | 806.093i | −0.445990 | + | 0.257492i | ||||
\(215\) | −1842.41 | + | 1063.72i | −0.584425 | + | 0.337418i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 386.358 | + | 669.192i | 0.120865 | + | 0.209344i | ||||
\(218\) | 494.466 | − | 856.440i | 0.153621 | − | 0.266080i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3931.16 | −1.20472 | ||||||||
\(221\) | −1678.66 | − | 2591.57i | −0.510946 | − | 0.788813i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1282.92 | − | 740.694i | −0.385250 | − | 0.222424i | 0.294850 | − | 0.955543i | \(-0.404730\pi\) |
−0.680100 | + | 0.733120i | \(0.738064\pi\) | |||||||
\(224\) | 5.76344 | − | 9.98258i | 0.00171914 | − | 0.00297763i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 1421.98i | − | 0.418533i | ||||||
\(227\) | 3.79613 | − | 2.19169i | 0.00110995 | − | 0.000640828i | −0.499445 | − | 0.866346i | \(-0.666463\pi\) |
0.500555 | + | 0.865705i | \(0.333129\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4689.58i | 1.35326i | 0.736324 | + | 0.676629i | \(0.236560\pi\) | ||||
−0.736324 | + | 0.676629i | \(0.763440\pi\) | |||||||
\(230\) | −2253.83 | − | 3903.75i | −0.646144 | − | 1.11915i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5311.21 | + | 3066.43i | 1.50301 | + | 0.867762i | ||||
\(233\) | −4124.52 | −1.15968 | −0.579842 | − | 0.814729i | \(-0.696886\pi\) | ||||
−0.579842 | + | 0.814729i | \(0.696886\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 446.044 | 0.123816 | ||||||||
\(236\) | −1466.54 | − | 846.710i | −0.404508 | − | 0.233543i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −519.020 | − | 898.970i | −0.141358 | − | 0.244838i | ||||
\(239\) | 3455.41i | 0.935196i | 0.883941 | + | 0.467598i | \(0.154880\pi\) | ||||
−0.883941 | + | 0.467598i | \(0.845120\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3559.08 | − | 2054.83i | 0.951288 | − | 0.549226i | 0.0578069 | − | 0.998328i | \(-0.481589\pi\) |
0.893481 | + | 0.449102i | \(0.148256\pi\) | |||||||
\(242\) | − | 2814.81i | − | 0.747698i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5813.62 | + | 10069.5i | −1.52532 | + | 2.64194i | ||||
\(245\) | 1617.20 | + | 933.691i | 0.421711 | + | 0.243475i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 120.549 | − | 78.0846i | 0.0310541 | − | 0.0201150i | ||||
\(248\) | 9486.89 | 2.42911 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3007.02 | + | 5208.32i | −0.760723 | + | 1.31761i | ||||
\(251\) | 2516.11 | + | 4358.03i | 0.632730 | + | 1.09592i | 0.986991 | + | 0.160774i | \(0.0513991\pi\) |
−0.354261 | + | 0.935147i | \(0.615268\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6190.13 | − | 3573.87i | 1.53822 | − | 0.888093i | ||||
\(254\) | −3195.90 | + | 1845.15i | −0.789483 | + | 0.455808i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4107.27 | + | 7114.00i | 1.00275 | + | 1.73682i | ||||
\(257\) | 2816.99 | − | 4879.16i | 0.683731 | − | 1.18426i | −0.290103 | − | 0.956995i | \(-0.593690\pi\) |
0.973834 | − | 0.227261i | \(-0.0729770\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1020.79 | −0.244899 | ||||||||
\(260\) | −3543.30 | + | 2295.14i | −0.845176 | + | 0.547455i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9344.42 | + | 5395.00i | 2.20344 | + | 1.27215i | ||||
\(263\) | 2556.31 | − | 4427.66i | 0.599350 | − | 1.03810i | −0.393568 | − | 0.919296i | \(-0.628759\pi\) |
0.992917 | − | 0.118808i | \(-0.0379074\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3209.35i | 0.743959i | ||||||||
\(266\) | 41.8165 | − | 24.1428i | 0.00963884 | − | 0.00556499i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 4849.32i | − | 1.10530i | ||||||
\(269\) | 3281.24 | + | 5683.28i | 0.743721 | + | 1.28816i | 0.950790 | + | 0.309836i | \(0.100274\pi\) |
−0.207069 | + | 0.978326i | \(0.566392\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7067.90 | − | 4080.66i | −1.58430 | − | 0.914694i | −0.994222 | − | 0.107346i | \(-0.965765\pi\) |
−0.590075 | − | 0.807348i | \(-0.700902\pi\) | |||||||
\(272\) | −4288.26 | −0.955934 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1785.29 | −0.393626 | ||||||||
\(275\) | −3533.89 | − | 2040.29i | −0.774914 | − | 0.447397i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1363.28 | + | 2361.28i | 0.295710 | + | 0.512185i | 0.975150 | − | 0.221546i | \(-0.0711104\pi\) |
−0.679440 | + | 0.733731i | \(0.737777\pi\) | |||||||
\(278\) | 12031.5i | 2.59569i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −616.300 | + | 355.821i | −0.131539 | + | 0.0759442i | ||||
\(281\) | − | 1216.67i | − | 0.258294i | −0.991625 | − | 0.129147i | \(-0.958776\pi\) | ||
0.991625 | − | 0.129147i | \(-0.0412238\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1624.16 | + | 2813.13i | −0.341153 | + | 0.590895i | −0.984647 | − | 0.174557i | \(-0.944151\pi\) |
0.643494 | + | 0.765451i | \(0.277484\pi\) | |||||||
\(284\) | 13943.0 | + | 8049.98i | 2.91325 | + | 1.68197i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5453.89 | − | 8419.87i | −1.12761 | − | 1.74083i | ||||
\(287\) | 411.033 | 0.0845383 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 286.696 | − | 496.573i | 0.0583547 | − | 0.101073i | ||||
\(290\) | −2139.39 | − | 3705.53i | −0.433204 | − | 0.750331i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3862.89 | − | 2230.24i | 0.774173 | − | 0.446969i | ||||
\(293\) | −7986.99 | + | 4611.29i | −1.59251 | + | 0.919435i | −0.599634 | + | 0.800274i | \(0.704687\pi\) |
−0.992875 | + | 0.119161i | \(0.961980\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 296.206 | + | 513.044i | 0.0584602 | + | 0.101256i | ||||
\(296\) | −6266.30 | + | 10853.5i | −1.23048 | + | 2.13125i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −319.446 | −0.0620974 | ||||||||
\(299\) | 3492.85 | − | 6835.25i | 0.675574 | − | 1.32205i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1054.73 | − | 608.951i | −0.201973 | − | 0.116609i | ||||
\(302\) | 613.455 | − | 1062.53i | 0.116889 | − | 0.202457i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 199.473i | − | 0.0376334i | ||||||
\(305\) | 3522.62 | − | 2033.79i | 0.661327 | − | 0.381818i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2993.33i | − | 0.556477i | −0.960512 | − | 0.278238i | \(-0.910249\pi\) | ||
0.960512 | − | 0.278238i | \(-0.0897505\pi\) | |||||||
\(308\) | −1125.25 | − | 1948.98i | −0.208172 | − | 0.360564i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5732.07 | − | 3309.41i | −1.05019 | − | 0.606329i | ||||
\(311\) | 7261.04 | 1.32391 | 0.661955 | − | 0.749544i | \(-0.269727\pi\) | ||||
0.661955 | + | 0.749544i | \(0.269727\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3903.02 | −0.704829 | −0.352415 | − | 0.935844i | \(-0.614639\pi\) | ||||
−0.352415 | + | 0.935844i | \(0.614639\pi\) | |||||||
\(314\) | −7512.33 | − | 4337.25i | −1.35014 | − | 0.779506i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7694.96 | − | 13328.1i | −1.36986 | − | 2.37266i | ||||
\(317\) | 4592.24i | 0.813646i | 0.913507 | + | 0.406823i | \(0.133363\pi\) | ||||
−0.913507 | + | 0.406823i | \(0.866637\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5875.81 | − | 3392.40i | 1.03129 | − | 0.595417i | ||||
\(320\) | − | 2824.48i | − | 0.493416i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1290.26 | − | 2234.80i | 0.223303 | − | 0.386772i | ||||
\(323\) | −174.817 | − | 100.931i | −0.0301148 | − | 0.0173868i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4376.40 | + | 224.208i | −0.746951 | + | 0.0382671i | ||||
\(326\) | 13275.7 | 2.25543 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2523.19 | − | 4370.30i | 0.424756 | − | 0.735699i | ||||
\(329\) | 127.674 | + | 221.139i | 0.0213949 | + | 0.0370571i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4430.30 | + | 2557.84i | −0.735684 | + | 0.424747i | −0.820498 | − | 0.571649i | \(-0.806304\pi\) |
0.0848138 | + | 0.996397i | \(0.472970\pi\) | |||||||
\(332\) | 5710.62 | − | 3297.03i | 0.944008 | − | 0.545023i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8562.46 | + | 14830.6i | 1.40275 | + | 2.42963i | ||||
\(335\) | −848.223 | + | 1469.17i | −0.138339 | + | 0.239609i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6808.37 | 1.10052 | 0.550260 | − | 0.834993i | \(-0.314529\pi\) | ||||
0.550260 | + | 0.834993i | \(0.314529\pi\) | |||||||
\(338\) | −9831.56 | − | 4404.98i | −1.58215 | − | 0.708873i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5138.38 | + | 2966.64i | 0.819611 | + | 0.473203i | ||||
\(341\) | 5247.70 | − | 9089.28i | 0.833369 | − | 1.44344i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2171.24i | 0.341796i | ||||||||
\(344\) | −12949.3 | + | 7476.30i | −2.02960 | + | 1.17179i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 19526.1i | − | 3.03389i | ||||||
\(347\) | −5459.09 | − | 9455.42i | −0.844551 | − | 1.46281i | −0.886010 | − | 0.463665i | \(-0.846534\pi\) |
0.0414594 | − | 0.999140i | \(-0.486799\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8867.43 | + | 5119.62i | 1.36007 | + | 0.785234i | 0.989632 | − | 0.143625i | \(-0.0458759\pi\) |
0.370433 | + | 0.928859i | \(0.379209\pi\) | |||||||
\(350\) | −1473.20 | −0.224988 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −156.564 | −0.0237070 | ||||||||
\(353\) | −748.273 | − | 432.015i | −0.112823 | − | 0.0651384i | 0.442527 | − | 0.896755i | \(-0.354082\pi\) |
−0.555350 | + | 0.831617i | \(0.687416\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2816.14 | − | 4877.69i | −0.421028 | − | 0.729242i | ||||
\(356\) | 3629.50i | 0.540346i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9576.47 | − | 5528.98i | 1.41378 | − | 0.816244i | ||||
\(359\) | − | 11430.0i | − | 1.68036i | −0.542305 | − | 0.840182i | \(-0.682448\pi\) | ||
0.542305 | − | 0.840182i | \(-0.317552\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3424.81 | + | 5931.94i | −0.499316 | + | 0.864840i | ||||
\(362\) | −3779.99 | − | 2182.38i | −0.548818 | − | 0.316860i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2152.10 | − | 1099.73i | −0.309892 | − | 0.158356i | ||||
\(365\) | −1560.42 | −0.223770 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4606.01 | + | 7977.85i | −0.655128 | + | 1.13471i | 0.326734 | + | 0.945116i | \(0.394052\pi\) |
−0.981862 | + | 0.189598i | \(0.939281\pi\) | |||||||
\(368\) | −5330.21 | − | 9232.20i | −0.755045 | − | 1.30778i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7572.31 | − | 4371.88i | 1.06396 | − | 0.614279i | ||||
\(371\) | −1591.13 | + | 918.638i | −0.222661 | + | 0.128553i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 559.064 | + | 968.327i | 0.0776065 | + | 0.134418i | 0.902217 | − | 0.431283i | \(-0.141939\pi\) |
−0.824610 | + | 0.565701i | \(0.808606\pi\) | |||||||
\(374\) | −7049.58 | + | 12210.2i | −0.974666 | + | 1.68817i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3135.00 | 0.429988 | ||||||||
\(377\) | 3315.49 | − | 6488.18i | 0.452935 | − | 0.886361i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6987.09 | − | 4034.00i | −0.946973 | − | 0.546735i | −0.0548334 | − | 0.998496i | \(-0.517463\pi\) |
−0.892139 | + | 0.451761i | \(0.850796\pi\) | |||||||
\(380\) | −137.996 | + | 239.017i | −0.0186291 | + | 0.0322666i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 3921.79i | − | 0.525279i | ||||||
\(383\) | −1752.61 | + | 1011.87i | −0.233822 | + | 0.134997i | −0.612334 | − | 0.790599i | \(-0.709769\pi\) |
0.378512 | + | 0.925596i | \(0.376436\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 787.293i | 0.104219i | ||||||||
\(386\) | −6603.73 | − | 11438.0i | −0.870779 | − | 1.50823i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −12345.9 | − | 7127.92i | −1.61538 | − | 0.932642i | ||||
\(389\) | 9697.21 | 1.26393 | 0.631964 | − | 0.774998i | \(-0.282249\pi\) | ||||
0.631964 | + | 0.774998i | \(0.282249\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10788.1 | −1.39534 | ||||||||
\(392\) | 11366.4 | + | 6562.42i | 1.46452 | + | 0.845542i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6707.44 | + | 11617.6i | 0.857655 | + | 1.48550i | ||||
\(395\) | 5383.88i | 0.685803i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2941.24 | + | 1698.13i | −0.371830 | + | 0.214676i | −0.674258 | − | 0.738496i | \(-0.735536\pi\) |
0.302427 | + | 0.953172i | \(0.402203\pi\) | |||||||
\(398\) | 5768.80i | 0.726543i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3042.97 | + | 5270.58i | −0.380371 | + | 0.658822i | ||||
\(401\) | −5758.99 | − | 3324.95i | −0.717183 | − | 0.414066i | 0.0965322 | − | 0.995330i | \(-0.469225\pi\) |
−0.813715 | + | 0.581264i | \(0.802558\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −576.670 | − | 11256.3i | −0.0712803 | − | 1.39135i | ||||
\(404\) | 29850.6 | 3.67604 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1224.75 | − | 2121.32i | 0.149712 | − | 0.259309i | ||||
\(407\) | 6932.44 | + | 12007.3i | 0.844295 | + | 1.46236i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2178.44 | + | 1257.72i | −0.263366 | + | 0.152055i | −0.625869 | − | 0.779928i | \(-0.715256\pi\) |
0.362503 | + | 0.931983i | \(0.381922\pi\) | |||||||
\(410\) | −3049.07 | + | 1760.38i | −0.367276 | + | 0.212047i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2635.59 | − | 4564.97i | −0.315160 | − | 0.545873i | ||||
\(413\) | −169.571 | + | 293.705i | −0.0202034 | + | 0.0349934i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2306.81 | −0.272860 | ||||||||
\(416\) | −141.116 | + | 91.4068i | −0.0166317 | + | 0.0107730i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −567.971 | − | 327.918i | −0.0664602 | − | 0.0383708i | ||||
\(419\) | −5953.72 | + | 10312.2i | −0.694173 | + | 1.20234i | 0.276286 | + | 0.961076i | \(0.410896\pi\) |
−0.970459 | + | 0.241267i | \(0.922437\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2382.88i | 0.275854i | 0.990442 | + | 0.137927i | \(0.0440440\pi\) | ||||
−0.990442 | + | 0.137927i | \(0.955956\pi\) | |||||||
\(422\) | −12377.6 | + | 7146.18i | −1.42780 | + | 0.824338i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 22556.9i | 2.58363i | ||||||||
\(425\) | 3079.40 | + | 5333.69i | 0.351466 | + | 0.608757i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2016.62 | + | 1164.29i | 0.228550 | + | 0.131953i | ||||
\(428\) | 5275.37 | 0.595782 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10432.1 | 1.16996 | ||||||||
\(431\) | 248.155 | + | 143.273i | 0.0277337 | + | 0.0160121i | 0.513803 | − | 0.857908i | \(-0.328236\pi\) |
−0.486069 | + | 0.873920i | \(0.661570\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −424.177 | − | 734.696i | −0.0470777 | − | 0.0815410i | 0.841526 | − | 0.540216i | \(-0.181658\pi\) |
−0.888604 | + | 0.458675i | \(0.848324\pi\) | |||||||
\(434\) | − | 3789.11i | − | 0.419086i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2802.43 | + | 1617.98i | −0.307826 | + | 0.177723i | ||||
\(437\) | − | 501.818i | − | 0.0549318i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 34.8466 | − | 60.3561i | 0.00378847 | − | 0.00656182i | −0.864125 | − | 0.503277i | \(-0.832127\pi\) |
0.867913 | + | 0.496716i | \(0.165461\pi\) | |||||||
\(440\) | 8370.88 | + | 4832.93i | 0.906969 | + | 0.523639i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 774.678 | + | 15121.3i | 0.0833658 | + | 1.62725i | ||||
\(443\) | −7331.02 | −0.786247 | −0.393123 | − | 0.919486i | \(-0.628605\pi\) | ||||
−0.393123 | + | 0.919486i | \(0.628605\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 634.856 | − | 1099.60i | 0.0676294 | − | 0.117138i | ||||
\(446\) | 3632.09 | + | 6290.96i | 0.385615 | + | 0.667905i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1400.31 | − | 808.472i | 0.147676 | − | 0.0852605i | ||||
\(449\) | −12309.0 | + | 7106.59i | −1.29376 | + | 0.746950i | −0.979318 | − | 0.202328i | \(-0.935149\pi\) |
−0.314438 | + | 0.949278i | \(0.601816\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2791.42 | − | 4834.88i | −0.291448 | − | 0.504802i | ||||
\(452\) | −2326.48 | + | 4029.59i | −0.242099 | + | 0.419327i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −21.4945 | −0.00222200 | ||||||||
\(455\) | 459.647 | + | 709.616i | 0.0473595 | + | 0.0731149i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5112.33 | + | 2951.60i | 0.523292 | + | 0.302123i | 0.738281 | − | 0.674494i | \(-0.235638\pi\) |
−0.214988 | + | 0.976617i | \(0.568971\pi\) | |||||||
\(458\) | 11498.0 | − | 19915.1i | 1.17307 | − | 2.03181i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 14749.9i | 1.49504i | ||||||||
\(461\) | −488.270 | + | 281.903i | −0.0493297 | + | 0.0284805i | −0.524462 | − | 0.851434i | \(-0.675734\pi\) |
0.475132 | + | 0.879914i | \(0.342400\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17543.8i | 1.76097i | 0.474070 | + | 0.880487i | \(0.342784\pi\) | ||||
−0.474070 | + | 0.880487i | \(0.657216\pi\) | |||||||
\(464\) | −5059.56 | − | 8763.42i | −0.506216 | − | 0.876792i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 17515.5 | + | 10112.6i | 1.74118 | + | 1.00527i | ||||
\(467\) | 9125.81 | 0.904266 | 0.452133 | − | 0.891951i | \(-0.350663\pi\) | ||||
0.452133 | + | 0.891951i | \(0.350663\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −971.174 | −0.0956176 | ||||||||
\(470\) | −1894.20 | − | 1093.62i | −0.185900 | − | 0.107329i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2081.87 | + | 3605.91i | 0.203021 | + | 0.351643i | ||||
\(473\) | 16542.1i | 1.60805i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −248.102 | + | 143.242i | −0.0239657 | + | 0.0138366i | ||||
\(476\) | 3396.66i | 0.327071i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8472.02 | − | 14674.0i | 0.810672 | − | 1.40413i | ||||
\(479\) | −4304.28 | − | 2485.08i | −0.410579 | − | 0.237048i | 0.280459 | − | 0.959866i | \(-0.409513\pi\) |
−0.691039 | + | 0.722818i | \(0.742847\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13258.7 | + | 6775.26i | 1.25685 | + | 0.642257i | ||||
\(482\) | −20152.3 | −1.90438 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4605.29 | + | 7976.60i | −0.432503 | + | 0.749117i | ||||
\(485\) | 2493.57 | + | 4318.99i | 0.233458 | + | 0.404361i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4950.89 | + | 2858.40i | −0.460670 | + | 0.265968i | −0.712326 | − | 0.701849i | \(-0.752358\pi\) |
0.251656 | + | 0.967817i | \(0.419025\pi\) | |||||||
\(488\) | 24758.7 | − | 14294.4i | 2.29666 | − | 1.32598i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4578.48 | − | 7930.15i | −0.422111 | − | 0.731118i | ||||
\(491\) | 3022.11 | − | 5234.44i | 0.277771 | − | 0.481114i | −0.693059 | − | 0.720881i | \(-0.743738\pi\) |
0.970831 | + | 0.239767i | \(0.0770709\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10240.3 | −0.935496 | ||||||||
\(494\) | −703.382 | + | 36.0349i | −0.0640620 | + | 0.00328196i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −13556.1 | − | 7826.62i | −1.22719 | − | 0.708520i | ||||
\(497\) | 1612.17 | − | 2792.36i | 0.145504 | − | 0.252021i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1101.16i | 0.0987870i | 0.998779 | + | 0.0493935i | \(0.0157288\pi\) | ||||
−0.998779 | + | 0.0493935i | \(0.984271\pi\) | |||||||
\(500\) | 17042.6 | − | 9839.54i | 1.52433 | − | 0.880075i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 24676.1i | − | 2.19392i | ||||||
\(503\) | −670.986 | − | 1162.18i | −0.0594787 | − | 0.103020i | 0.834753 | − | 0.550625i | \(-0.185611\pi\) |
−0.894232 | + | 0.447605i | \(0.852277\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9043.62 | − | 5221.34i | −0.796903 | − | 0.460092i | ||||
\(506\) | −35049.9 | −3.07937 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 12075.4 | 1.05464 | ||||||||
\(509\) | −11668.5 | − | 6736.80i | −1.01610 | − | 0.586647i | −0.103130 | − | 0.994668i | \(-0.532886\pi\) |
−0.912973 | + | 0.408021i | \(0.866219\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −446.650 | − | 773.621i | −0.0386666 | − | 0.0669725i | ||||
\(512\) | − | 20312.2i | − | 1.75328i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −23925.6 | + | 13813.5i | −2.05314 | + | 1.18538i | ||||
\(515\) | 1844.02i | 0.157781i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1734.14 | − | 3003.61i | 0.147519 | − | 0.255510i | ||||
\(518\) | 4334.96 | + | 2502.79i | 0.367698 | + | 0.212290i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 10366.6 | − | 531.091i | 0.874241 | − | 0.0447882i | ||||
\(521\) | −10374.9 | −0.872423 | −0.436211 | − | 0.899844i | \(-0.643680\pi\) | ||||
−0.436211 | + | 0.899844i | \(0.643680\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11147.7 | − | 19308.4i | 0.932037 | − | 1.61433i | 0.152202 | − | 0.988349i | \(-0.451364\pi\) |
0.779835 | − | 0.625985i | \(-0.215303\pi\) | |||||||
\(524\) | −17653.4 | − | 30576.7i | −1.47175 | − | 2.54914i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −21711.6 | + | 12535.2i | −1.79976 | + | 1.03909i | ||||
\(527\) | −13718.4 | + | 7920.34i | −1.13394 | + | 0.654678i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7325.85 | − | 12688.7i | −0.602108 | − | 1.04288i | ||||
\(530\) | 7868.74 | − | 13629.1i | 0.644899 | − | 1.11700i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −157.999 | −0.0128762 | ||||||||
\(533\) | −5338.76 | − | 2728.13i | −0.433860 | − | 0.221705i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1598.24 | − | 922.746i | −0.129155 | − | 0.0745678i | ||||
\(536\) | −5961.71 | + | 10326.0i | −0.480423 | + | 0.832117i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 32180.0i | − | 2.57877i | ||||||
\(539\) | 12574.8 | − | 7260.04i | 1.00489 | − | 0.580171i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10201.9i | 0.810747i | 0.914151 | + | 0.405373i | \(0.132859\pi\) | ||||
−0.914151 | + | 0.405373i | \(0.867141\pi\) | |||||||
\(542\) | 20010.0 | + | 34658.4i | 1.58580 | + | 2.74669i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 204.643 | + | 118.151i | 0.0161287 | + | 0.00931188i | ||||
\(545\) | 1132.04 | 0.0889751 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9312.12 | −0.727893 | −0.363947 | − | 0.931420i | \(-0.618571\pi\) | ||||
−0.363947 | + | 0.931420i | \(0.618571\pi\) | |||||||
\(548\) | 5059.15 | + | 2920.90i | 0.394373 | + | 0.227691i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 10004.8 | + | 17328.9i | 0.775650 | + | 1.34346i | ||||
\(551\) | − | 476.337i | − | 0.0368288i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2669.21 | + | 1541.07i | −0.205256 | + | 0.118504i | ||||
\(554\) | − | 13370.1i | − | 1.02534i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 19684.6 | − | 34094.8i | 1.50147 | − | 2.60061i | ||||
\(557\) | 124.988 | + | 72.1618i | 0.00950791 | + | 0.00548940i | 0.504746 | − | 0.863268i | \(-0.331586\pi\) |
−0.495239 | + | 0.868757i | \(0.664919\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9657.81 | + | 14910.0i | 0.730737 | + | 1.12813i | ||||
\(560\) | 1174.20 | 0.0886054 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2983.05 | + | 5166.80i | −0.223901 | + | 0.387808i | ||||
\(563\) | 7333.48 | + | 12702.0i | 0.548968 | + | 0.950841i | 0.998346 | + | 0.0574990i | \(0.0183126\pi\) |
−0.449377 | + | 0.893342i | \(0.648354\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1409.68 | − | 813.877i | 0.104966 | − | 0.0606019i | ||||
\(566\) | 13794.5 | − | 7964.28i | 1.02443 | − | 0.591456i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −19793.1 | − | 34282.7i | −1.46215 | − | 2.53252i | ||||
\(569\) | 9377.03 | − | 16241.5i | 0.690871 | − | 1.19662i | −0.280682 | − | 0.959801i | \(-0.590561\pi\) |
0.971553 | − | 0.236822i | \(-0.0761059\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13886.4 | 1.01773 | 0.508867 | − | 0.860845i | \(-0.330065\pi\) | ||||
0.508867 | + | 0.860845i | \(0.330065\pi\) | |||||||
\(572\) | 1679.52 | + | 32783.2i | 0.122770 | + | 2.39639i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1745.52 | − | 1007.78i | −0.126928 | − | 0.0732818i | ||||
\(575\) | −7655.27 | + | 13259.3i | −0.555212 | + | 0.961655i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 9338.81i | − | 0.673795i | −0.941541 | − | 0.336898i | \(-0.890622\pi\) | ||
0.941541 | − | 0.336898i | \(-0.109378\pi\) | |||||||
\(578\) | −2435.01 | + | 1405.85i | −0.175230 | + | 0.101169i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 14000.9i | 1.00234i | ||||||||
\(581\) | −660.295 | − | 1143.66i | −0.0471492 | − | 0.0816647i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21611.5 | + | 12477.4i | 1.53526 | + | 0.886381i | ||||
\(584\) | −10967.3 | −0.777110 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 45224.1 | 3.18804 | ||||||||
\(587\) | 3225.20 | + | 1862.07i | 0.226777 | + | 0.130930i | 0.609084 | − | 0.793105i | \(-0.291537\pi\) |
−0.382307 | + | 0.924035i | \(0.624870\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −368.422 | − | 638.126i | −0.0257735 | − | 0.0446410i | ||||
\(590\) | − | 2904.97i | − | 0.202704i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 17908.2 | − | 10339.3i | 1.24328 | − | 0.717809i | ||||
\(593\) | 19910.2i | 1.37877i | 0.724393 | + | 0.689387i | \(0.242120\pi\) | ||||
−0.724393 | + | 0.689387i | \(0.757880\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 594.130 | − | 1029.06i | 0.0409361 | − | 0.0709033i | ||||
\(596\) | 905.245 | + | 522.644i | 0.0622153 | + | 0.0359200i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −31591.7 | + | 20463.2i | −2.16034 | + | 1.39934i | ||||
\(599\) | −14756.0 | −1.00653 | −0.503265 | − | 0.864132i | \(-0.667868\pi\) | ||||
−0.503265 | + | 0.864132i | \(0.667868\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3969.53 | − | 6875.42i | 0.269418 | − | 0.466646i | −0.699293 | − | 0.714835i | \(-0.746502\pi\) |
0.968712 | + | 0.248189i | \(0.0798352\pi\) | |||||||
\(602\) | 2986.07 | + | 5172.03i | 0.202165 | + | 0.350160i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3476.81 | + | 2007.34i | −0.234221 | + | 0.135227i | ||||
\(605\) | 2790.47 | − | 1611.08i | 0.187518 | − | 0.108264i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1281.94 | + | 2220.39i | 0.0857205 | + | 0.148472i | 0.905698 | − | 0.423923i | \(-0.139347\pi\) |
−0.819977 | + | 0.572396i | \(0.806014\pi\) | |||||||
\(608\) | −5.49589 | + | 9.51916i | −0.000366592 | + | 0.000634956i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −19945.9 | −1.32391 | ||||||||
\(611\) | −190.564 | − | 3719.70i | −0.0126177 | − | 0.246290i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15236.4 | − | 8796.72i | −1.00390 | − | 0.579602i | −0.0945004 | − | 0.995525i | \(-0.530125\pi\) |
−0.909400 | + | 0.415923i | \(0.863459\pi\) | |||||||
\(614\) | −7339.09 | + | 12711.7i | −0.482381 | + | 0.835508i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5533.47i | 0.361932i | ||||||||
\(617\) | 21200.0 | − | 12239.8i | 1.38328 | − | 0.798635i | 0.390730 | − | 0.920506i | \(-0.372223\pi\) |
0.992546 | + | 0.121871i | \(0.0388894\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 2927.43i | − | 0.190086i | −0.995473 | − | 0.0950431i | \(-0.969701\pi\) | ||
0.995473 | − | 0.0950431i | \(-0.0302989\pi\) | |||||||
\(620\) | 10829.0 | + | 18756.4i | 0.701457 | + | 1.21496i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −30835.2 | − | 17802.7i | −1.98775 | − | 1.14763i | ||||
\(623\) | 726.879 | 0.0467445 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4802.06 | 0.307332 | ||||||||
\(626\) | 16574.8 | + | 9569.47i | 1.05825 | + | 0.610979i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14192.3 | + | 24581.7i | 0.901805 | + | 1.56197i | ||||
\(629\) | − | 20926.2i | − | 1.32652i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8818.74 | + | 5091.50i | −0.556369 | + | 0.321220i | −0.751687 | − | 0.659520i | \(-0.770759\pi\) |
0.195318 | + | 0.980740i | \(0.437426\pi\) | |||||||
\(632\) | 37840.4i | 2.38166i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 11259.3 | − | 19501.7i | 0.705307 | − | 1.22163i | ||||
\(635\) | −3658.39 | − | 2112.17i | −0.228628 | − | 0.131999i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7095.44 | − | 13885.3i | 0.441337 | − | 0.863665i | ||||
\(638\) | −33270.2 | −2.06454 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −7005.64 | + | 12134.1i | −0.432691 | + | 0.749443i | ||||
\(641\) | 8551.71 | + | 14812.0i | 0.526946 | + | 0.912697i | 0.999507 | + | 0.0313988i | \(0.00999620\pi\) |
−0.472561 | + | 0.881298i | \(0.656670\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18822.1 | − | 10866.9i | 1.15439 | − | 0.666485i | 0.204434 | − | 0.978880i | \(-0.434465\pi\) |
0.949952 | + | 0.312395i | \(0.101131\pi\) | |||||||
\(644\) | −7312.68 | + | 4221.98i | −0.447453 | + | 0.258337i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 494.926 | + | 857.237i | 0.0301434 | + | 0.0522098i | ||||
\(647\) | 11151.1 | − | 19314.3i | 0.677584 | − | 1.17361i | −0.298123 | − | 0.954528i | \(-0.596360\pi\) |
0.975706 | − | 0.219082i | \(-0.0703062\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4606.38 | 0.278607 | ||||||||
\(650\) | 19134.9 | + | 9778.00i | 1.15466 | + | 0.590038i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −37620.6 | − | 21720.2i | −2.25972 | − | 1.30465i | ||||
\(653\) | 3488.57 | − | 6042.39i | 0.209063 | − | 0.362109i | −0.742356 | − | 0.670005i | \(-0.766292\pi\) |
0.951420 | + | 0.307897i | \(0.0996251\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12351.5i | 0.736812i | ||||||||
\(656\) | −7210.93 | + | 4163.23i | −0.429176 | + | 0.247785i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 1252.14i | − | 0.0741845i | ||||||
\(659\) | 5013.09 | + | 8682.92i | 0.296331 | + | 0.513260i | 0.975294 | − | 0.220913i | \(-0.0709035\pi\) |
−0.678963 | + | 0.734173i | \(0.737570\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4079.54 | + | 2355.32i | 0.240054 | + | 0.138595i | 0.615202 | − | 0.788370i | \(-0.289075\pi\) |
−0.375148 | + | 0.926965i | \(0.622408\pi\) | |||||||
\(662\) | 25085.4 | 1.47277 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −16213.3 | −0.947589 | ||||||||
\(665\) | 47.8679 | + | 27.6365i | 0.00279133 | + | 0.00161158i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12728.5 | − | 22046.3i | −0.738902 | − | 1.27982i | ||||
\(668\) | − | 56035.9i | − | 3.24565i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7204.25 | − | 4159.37i | 0.415409 | − | 0.239837i | ||||
\(671\) | − | 31628.0i | − | 1.81965i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7363.59 | + | 12754.1i | −0.421762 | + | 0.730512i | −0.996112 | − | 0.0880972i | \(-0.971921\pi\) |
0.574350 | + | 0.818610i | \(0.305255\pi\) | |||||||
\(674\) | −28912.9 | − | 16692.9i | −1.65235 | − | 0.953983i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 20653.7 | + | 28568.2i | 1.17511 | + | 1.62541i | ||||
\(677\) | −2118.31 | −0.120256 | −0.0601279 | − | 0.998191i | \(-0.519151\pi\) | ||||
−0.0601279 | + | 0.998191i | \(0.519151\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1427.51 | + | 2472.52i | −0.0806815 | + | 0.139744i | ||||
\(680\) | −7294.33 | − | 12634.2i | −0.411360 | − | 0.712497i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −44570.5 | + | 25732.8i | −2.50248 | + | 1.44481i | ||||
\(683\) | −6123.42 | + | 3535.36i | −0.343054 | + | 0.198063i | −0.661622 | − | 0.749838i | \(-0.730132\pi\) |
0.318568 | + | 0.947900i | \(0.396798\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1021.82 | − | 1769.85i | −0.0569955 | − | 0.0987191i | ||||
\(686\) | 5323.49 | − | 9220.55i | 0.296285 | − | 0.513181i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 24671.6 | 1.36714 | ||||||||
\(689\) | 26763.9 | − | 1371.14i | 1.47986 | − | 0.0758146i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13496.1 | + | 7791.98i | 0.743004 | + | 0.428974i | 0.823160 | − | 0.567809i | \(-0.192209\pi\) |
−0.0801566 | + | 0.996782i | \(0.525542\pi\) | |||||||
\(692\) | −31946.4 | + | 55332.9i | −1.75494 | + | 3.03965i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 53538.7i | 2.92839i | ||||||||
\(695\) | −11927.4 | + | 6886.31i | −0.650983 | + | 0.375845i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8426.17i | 0.457911i | ||||||||
\(698\) | −25104.7 | − | 43482.6i | −1.36136 | − | 2.35794i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4174.74 | + | 2410.29i | 0.225415 | + | 0.130143i | ||||
\(701\) | 13190.6 | 0.710703 | 0.355352 | − | 0.934733i | \(-0.384361\pi\) | ||||
0.355352 | + | 0.934733i | \(0.384361\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 973.404 | 0.0522228 | ||||||||
\(704\) | −19019.7 | − | 10981.1i | −1.01823 | − | 0.587875i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2118.44 | + | 3669.25i | 0.112930 | + | 0.195601i | ||||
\(707\) | − | 5978.17i | − | 0.318009i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27336.9 | − | 15783.0i | 1.44804 | − | 0.836025i | 0.449673 | − | 0.893193i | \(-0.351541\pi\) |
0.998365 | + | 0.0571687i | \(0.0182073\pi\) | |||||||
\(710\) | 27618.6i | 1.45987i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4462.07 | − | 7728.53i | 0.234864 | − | 0.406796i | ||||
\(713\) | −34103.4 | − | 19689.6i | −1.79128 | − | 1.03420i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5225.48 | − | 10225.9i | 0.273317 | − | 0.534862i | ||||
\(716\) | −36183.7 | −1.88861 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −28024.2 | + | 48539.3i | −1.45662 | + | 2.52294i | ||||
\(719\) | −7767.67 | − | 13454.0i | −0.402900 | − | 0.697844i | 0.591174 | − | 0.806544i | \(-0.298665\pi\) |
−0.994075 | + | 0.108700i | \(0.965331\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −914.226 | + | 527.829i | −0.0472227 | + | 0.0272640i | ||||
\(722\) | 29088.0 | − | 16794.0i | 1.49937 | − | 0.865661i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7141.16 | + | 12368.8i | 0.366573 | + | 0.634923i | ||||
\(725\) | −7266.56 | + | 12586.0i | −0.372239 | + | 0.644736i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27639.6 | 1.41004 | 0.705018 | − | 0.709189i | \(-0.250939\pi\) | ||||
0.705018 | + | 0.709189i | \(0.250939\pi\) | |||||||
\(728\) | 3230.61 | + | 4987.51i | 0.164470 | + | 0.253914i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6626.57 | + | 3825.85i | 0.335973 | + | 0.193974i | ||||
\(731\) | 12483.5 | − | 21622.0i | 0.631626 | − | 1.09401i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1318.97i | 0.0664629i | 0.999448 | + | 0.0332314i | \(0.0105798\pi\) | ||||
−0.999448 | + | 0.0332314i | \(0.989420\pi\) | |||||||
\(734\) | 39120.4 | − | 22586.2i | 1.96725 | − | 1.13579i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 587.434i | 0.0294200i | ||||||||
\(737\) | 6595.47 | + | 11423.7i | 0.329644 | + | 0.570960i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2572.74 | + | 1485.37i | 0.128065 | + | 0.0739382i | 0.562664 | − | 0.826686i | \(-0.309777\pi\) |
−0.434599 | + | 0.900624i | \(0.643110\pi\) | |||||||
\(740\) | −28611.2 | −1.42131 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9009.32 | 0.445745 | ||||||||
\(743\) | 24935.1 | + | 14396.3i | 1.23120 | + | 0.710833i | 0.967280 | − | 0.253712i | \(-0.0816515\pi\) |
0.263919 | + | 0.964545i | \(0.414985\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −182.837 | − | 316.683i | −0.00899146 | − | 0.0155737i | ||||
\(746\) | − | 5482.88i | − | 0.269092i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 39954.2 | − | 23067.5i | 1.95303 | − | 1.12758i | ||||
\(749\) | − | 1056.50i | − | 0.0515402i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3919.72 | + | 6789.16i | −0.190456 | + | 0.329880i | −0.945402 | − | 0.325908i | \(-0.894330\pi\) |
0.754945 | + | 0.655788i | \(0.227663\pi\) | |||||||
\(752\) | −4479.70 | − | 2586.36i | −0.217231 | − | 0.125419i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −29987.6 | + | 19424.2i | −1.44839 | + | 0.938179i | ||||
\(755\) | 1404.46 | 0.0677000 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1596.21 | − | 2764.71i | 0.0766383 | − | 0.132741i | −0.825159 | − | 0.564900i | \(-0.808915\pi\) |
0.901798 | + | 0.432159i | \(0.142248\pi\) | |||||||
\(758\) | 19781.2 | + | 34262.1i | 0.947872 | + | 1.64176i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 587.690 | − | 339.303i | 0.0280497 | − | 0.0161945i | ||||
\(761\) | 22016.0 | − | 12710.9i | 1.04872 | − | 0.605481i | 0.126432 | − | 0.991975i | \(-0.459648\pi\) |
0.922292 | + | 0.386495i | \(0.126314\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 324.034 | + | 561.243i | 0.0153746 | + | 0.0266296i | ||||
\(764\) | −6416.42 | + | 11113.6i | −0.303845 | + | 0.526276i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9923.64 | 0.468089 | ||||||||
\(767\) | 4151.89 | − | 2689.35i | 0.195458 | − | 0.126606i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29384.8 | − | 16965.3i | −1.37795 | − | 0.795559i | −0.386036 | − | 0.922484i | \(-0.626156\pi\) |
−0.991912 | + | 0.126925i | \(0.959489\pi\) | |||||||
\(770\) | 1930.30 | − | 3343.37i | 0.0903417 | − | 0.156476i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 43217.2i | 2.01480i | ||||||||
\(773\) | −35158.0 | + | 20298.5i | −1.63589 | + | 0.944483i | −0.653666 | + | 0.756783i | \(0.726770\pi\) |
−0.982226 | + | 0.187700i | \(0.939897\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 22481.2i | 1.04200i | ||||||||
\(776\) | 17526.0 | + | 30355.9i | 0.810756 | + | 1.40427i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −41180.8 | − | 23775.8i | −1.89769 | − | 1.09563i | ||||
\(779\) | −391.952 | −0.0180271 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −43794.5 | −2.00652 | ||||||||
\(782\) | 45813.4 | + | 26450.4i | 2.09499 | + | 1.20954i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −10827.9 | − | 18754.5i | −0.493254 | − | 0.854340i | ||||
\(785\) | − | 9929.81i | − | 0.451478i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33815.0 | − | 19523.1i | 1.53161 | − | 0.884274i | 0.532319 | − | 0.846544i | \(-0.321321\pi\) |
0.999288 | − | 0.0377296i | \(-0.0120126\pi\) | |||||||
\(788\) | − | 43896.0i | − | 1.98443i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 13200.3 | − | 22863.5i | 0.594487 | − | 1.02968i | ||||
\(791\) | 807.005 | + | 465.925i | 0.0362754 | + | 0.0209436i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18465.4 | − | 28507.4i | −0.826893 | − | 1.27658i | ||||
\(794\) | 16654.0 | 0.744367 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9438.30 | − | 16347.6i | 0.420266 | − | 0.727922i | ||||
\(797\) | 4037.40 | + | 6992.98i | 0.179438 | + | 0.310795i | 0.941688 | − | 0.336487i | \(-0.109239\pi\) |
−0.762250 | + | 0.647282i | \(0.775905\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4533.34 | + | 2617.33i | −0.200724 | + | 0.115888i | ||||
\(800\) | 290.431 | − | 167.680i | 0.0128354 | − | 0.00741049i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 16304.3 | + | 28240.0i | 0.717863 | + | 1.24338i | ||||
\(803\) | −6066.62 | + | 10507.7i | −0.266608 | + | 0.461779i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2953.96 | 0.129334 | ||||||||
\(806\) | −25149.4 | + | 49215.5i | −1.09907 | + | 2.15080i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −63562.8 | − | 36698.0i | −2.76749 | − | 1.59781i | ||||
\(809\) | −15064.0 | + | 26091.6i | −0.654663 | + | 1.13391i | 0.327316 | + | 0.944915i | \(0.393856\pi\) |
−0.981978 | + | 0.188994i | \(0.939477\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 707.812i | 0.0306469i | 0.999883 | + | 0.0153235i | \(0.00487780\pi\) | ||||
−0.999883 | + | 0.0153235i | \(0.995122\pi\) | |||||||
\(812\) | −6941.36 | + | 4007.60i | −0.299993 | + | 0.173201i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 67988.2i | − | 2.92750i | ||||||
\(815\) | 7598.43 | + | 13160.9i | 0.326578 | + | 0.565650i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1005.77 | + | 580.682i | 0.0430691 | + | 0.0248660i | ||||
\(818\) | 12334.8 | 0.527233 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 11520.6 | 0.490630 | ||||||||
\(821\) | −13527.5 | − | 7810.13i | −0.575048 | − | 0.332004i | 0.184115 | − | 0.982905i | \(-0.441058\pi\) |
−0.759163 | + | 0.650900i | \(0.774392\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16355.0 | + | 28327.7i | 0.692710 | + | 1.19981i | 0.970947 | + | 0.239296i | \(0.0769168\pi\) |
−0.278236 | + | 0.960513i | \(0.589750\pi\) | |||||||
\(824\) | 12960.7i | 0.547944i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1440.22 | − | 831.511i | 0.0606679 | − | 0.0350266i | ||||
\(827\) | 28246.1i | 1.18768i | 0.804582 | + | 0.593842i | \(0.202389\pi\) | ||||
−0.804582 | + | 0.593842i | \(0.797611\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7049.60 | + | 12210.3i | −0.295347 | + | 0.511556i | −0.975066 | − | 0.221917i | \(-0.928769\pi\) |
0.679719 | + | 0.733473i | \(0.262102\pi\) | |||||||
\(830\) | 9796.24 | + | 5655.86i | 0.409678 | + | 0.236528i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −23554.3 | + | 1206.71i | −0.981487 | + | 0.0502825i | ||||
\(833\) | −21915.1 | −0.911541 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9801.57 | + | 16976.8i | −0.406224 | + | 0.703601i | ||||
\(836\) | 1073.01 | + | 1858.51i | 0.0443909 | + | 0.0768874i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 50567.0 | − | 29194.9i | 2.08450 | − | 1.20348i | ||||
\(839\) | −9946.53 | + | 5742.63i | −0.409288 | + | 0.236302i | −0.690484 | − | 0.723348i | \(-0.742602\pi\) |
0.281196 | + | 0.959650i | \(0.409269\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 112.357 | + | 194.608i | 0.00460687 | + | 0.00797933i | ||||
\(842\) | 5842.39 | − | 10119.3i | 0.239123 | − | 0.414174i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 46767.3 | 1.90734 | ||||||||
\(845\) | −1260.29 | − | 12267.8i | −0.0513079 | − | 0.499436i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1597.47 | + | 922.302i | 0.0648050 | + | 0.0374152i | ||||
\(848\) | 18609.2 | − | 32232.2i | 0.753590 | − | 1.30526i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 30200.5i | − | 1.21867i | ||||||
\(851\) | 45052.1 | − | 26010.8i | 1.81477 | − | 1.04776i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11836.8i | 0.475128i | 0.971372 | + | 0.237564i | \(0.0763489\pi\) | ||||
−0.971372 | + | 0.237564i | \(0.923651\pi\) | |||||||
\(854\) | −5709.26 | − | 9888.74i | −0.228767 | − | 0.396236i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11233.2 | − | 6485.49i | −0.448532 | − | 0.258960i | ||||
\(857\) | −31156.2 | −1.24186 | −0.620931 | − | 0.783865i | \(-0.713245\pi\) | ||||
−0.620931 | + | 0.783865i | \(0.713245\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1584.88 | −0.0629515 | −0.0314758 | − | 0.999505i | \(-0.510021\pi\) | ||||
−0.0314758 | + | 0.999505i | \(0.510021\pi\) | |||||||
\(860\) | −29562.5 | − | 17067.9i | −1.17218 | − | 0.676758i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −702.556 | − | 1216.86i | −0.0277600 | − | 0.0480818i | ||||
\(863\) | 19884.8i | 0.784340i | 0.919893 | + | 0.392170i | \(0.128276\pi\) | ||||
−0.919893 | + | 0.392170i | \(0.871724\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 19357.2 | − | 11175.9i | 0.760883 | − | 0.439296i | ||||
\(866\) | 4160.02i | 0.163237i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6199.34 | + | 10737.6i | −0.242419 | + | 0.419881i | ||||
\(869\) | 36254.5 | + | 20931.5i | 1.41525 | + | 0.817093i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12614.2 | + | 6445.94i | 0.490720 | + | 0.250760i | ||||
\(872\) | 7956.54 | 0.308994 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1230.37 | + | 2131.06i | −0.0476175 | + | 0.0824760i | ||||
\(875\) | −1970.56 | − | 3413.12i | −0.0761340 | − | 0.131868i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4748.79 | − | 2741.72i | 0.182845 | − | 0.105566i | −0.405784 | − | 0.913969i | \(-0.633001\pi\) |
0.588629 | + | 0.808403i | \(0.299668\pi\) | |||||||
\(878\) | −295.964 | + | 170.875i | −0.0113762 | + | 0.00656805i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −7974.27 | − | 13811.8i | −0.305469 | − | 0.529088i | ||||
\(881\) | 3290.56 | − | 5699.41i | 0.125836 | − | 0.217955i | −0.796223 | − | 0.605003i | \(-0.793172\pi\) |
0.922060 | + | 0.387048i | \(0.126505\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6942.60 | −0.264595 | −0.132297 | − | 0.991210i | \(-0.542235\pi\) | ||||
−0.132297 | + | 0.991210i | \(0.542235\pi\) | |||||||
\(884\) | 22544.6 | − | 44118.1i | 0.857755 | − | 1.67857i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 31132.4 | + | 17974.3i | 1.18049 | + | 0.681556i | ||||
\(887\) | 3281.34 | − | 5683.45i | 0.124213 | − | 0.215143i | −0.797212 | − | 0.603699i | \(-0.793693\pi\) |
0.921425 | + | 0.388557i | \(0.127026\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 2418.34i | − | 0.0912355i | ||||||
\(890\) | −5392.05 | + | 3113.10i | −0.203081 | + | 0.117249i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 23769.7i | − | 0.892231i | ||||||
\(893\) | −121.748 | − | 210.873i | −0.00456229 | − | 0.00790212i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10962.3 | + | 6329.09i | 0.409419 | + | 0.236378i | ||||
\(896\) | −8021.11 | −0.299070 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 69696.2 | 2.58997 | ||||||||
\(899\) | −32371.7 | − | 18689.8i | −1.20095 | − | 0.693371i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18832.1 | − | 32618.1i | −0.696323 | − | 1.20607i | ||||
\(902\) | 27376.2i | 1.01056i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9907.88 | − | 5720.31i | 0.364526 | − | 0.210459i | ||||
\(905\) | − | 4996.40i | − | 0.183521i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −826.163 | + | 1430.96i | −0.0302451 | + | 0.0523860i | −0.880752 | − | 0.473578i | \(-0.842962\pi\) |
0.850507 | + | 0.525964i | \(0.176295\pi\) | |||||||
\(908\) | 60.9111 | + | 35.1670i | 0.00222622 | + | 0.00128531i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −212.120 | − | 4140.47i | −0.00772717 | − | 0.150830i | ||||
\(911\) | 506.240 | 0.0184110 | 0.00920552 | − | 0.999958i | \(-0.497070\pi\) | ||||
0.00920552 | + | 0.999958i | \(0.497070\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8968.44 | + | 15533.8i | −0.325095 | + | 0.563082i | ||||
\(914\) | −14473.6 | − | 25069.0i | −0.523789 | − | 0.907229i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −65165.9 | + | 37623.5i | −2.35059 | + | 1.35711i | ||||
\(917\) | −6123.59 | + | 3535.46i | −0.220522 | + | 0.127318i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1234.64 | + | 2138.47i | 0.0443168 | + | 0.0767590i | 0.887333 | − | 0.461129i | \(-0.152556\pi\) |
−0.843016 | + | 0.537888i | \(0.819222\pi\) | |||||||
\(920\) | 18133.4 | − | 31408.0i | 0.649826 | − | 1.12553i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2764.69 | 0.0987531 | ||||||||
\(923\) | −39473.5 | + | 25568.6i | −1.40768 | + | 0.911810i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25719.8 | − | 14849.3i | −0.914229 | − | 0.527831i | ||||
\(926\) | 43014.2 | − | 74502.8i | 1.52650 | − | 2.64397i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 557.606i | 0.0197245i | ||||||||
\(929\) | −36066.2 | + | 20822.9i | −1.27373 | + | 0.735388i | −0.975688 | − | 0.219164i | \(-0.929667\pi\) |
−0.298042 | + | 0.954553i | \(0.596334\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 1019.40i | − | 0.0358857i | ||||||
\(932\) | −33090.2 | − | 57313.8i | −1.16299 | − | 2.01435i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −38754.3 | − | 22374.8i | −1.35769 | − | 0.783860i | ||||
\(935\) | −16139.5 | −0.564512 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33891.2 | −1.18162 | −0.590810 | − | 0.806811i | \(-0.701192\pi\) | ||||
−0.590810 | + | 0.806811i | \(0.701192\pi\) | |||||||
\(938\) | 4124.25 | + | 2381.14i | 0.143563 | + | 0.0828859i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3578.52 | + | 6198.17i | 0.124168 | + | 0.215066i | ||||
\(941\) | 28351.3i | 0.982173i | 0.871111 | + | 0.491087i | \(0.163400\pi\) | ||||
−0.871111 | + | 0.491087i | \(0.836600\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18140.7 | + | 10473.5i | −0.626451 | + | 0.361681i | ||||
\(944\) | − | 6870.13i | − | 0.236868i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 40558.2 | − | 70248.9i | 1.39393 | − | 2.41437i | ||||
\(947\) | 3232.62 | + | 1866.36i | 0.110925 | + | 0.0640427i | 0.554436 | − | 0.832226i | \(-0.312934\pi\) |
−0.443511 | + | 0.896269i | \(0.646267\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 666.660 | + | 13012.8i | 0.0228037 | + | 0.445115i | ||||
\(950\) | 1404.81 | 0.0479768 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4175.83 | − | 7232.74i | 0.142163 | − | 0.246234i | ||||
\(953\) | −4826.05 | − | 8358.96i | −0.164041 | − | 0.284127i | 0.772273 | − | 0.635290i | \(-0.219120\pi\) |
−0.936314 | + | 0.351163i | \(0.885786\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3887.88 | − | 2244.67i | 0.131737 | − | 0.0760583i | ||||
\(956\) | −48016.0 | + | 27722.0i | −1.62442 | + | 0.937860i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12185.9 | + | 21106.6i | 0.410969 | + | 0.711819i | ||||
\(959\) | 584.969 | − | 1013.20i | 0.0196972 | − | 0.0341166i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28031.5 | −0.940939 | ||||||||
\(962\) | −39693.7 | − | 61280.2i | −1.33033 | − | 2.05380i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 57107.5 | + | 32971.0i | 1.90800 | + | 1.10158i | ||||
\(965\) | 7559.38 | − | 13093.2i | 0.252171 | − | 0.436773i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36196.6i | 1.20373i | 0.798598 | + | 0.601864i | \(0.205575\pi\) | ||||
−0.798598 | + | 0.601864i | \(0.794425\pi\) | |||||||
\(968\) | 19612.7 | − | 11323.4i | 0.651216 | − | 0.375979i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | − | 24455.1i | − | 0.809490i | ||||||
\(971\) | −2625.49 | − | 4547.48i | −0.0867723 | − | 0.150294i | 0.819373 | − | 0.573261i | \(-0.194322\pi\) |
−0.906145 | + | 0.422967i | \(0.860989\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6828.16 | − | 3942.24i | −0.224975 | − | 0.129890i | ||||
\(974\) | 28033.1 | 0.922215 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −47171.2 | −1.54704 | ||||||||
\(977\) | 20069.9 | + | 11587.4i | 0.657210 | + | 0.379440i | 0.791213 | − | 0.611541i | \(-0.209450\pi\) |
−0.134003 | + | 0.990981i | \(0.542783\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4936.41 | − | 8550.12i | −0.161153 | − | 0.279124i | ||||
\(980\) | 29963.2i | 0.976674i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −25667.8 | + | 14819.3i | −0.834105 | + | 0.481571i | ||||
\(983\) | 33285.5i | 1.08000i | 0.841664 | + | 0.540001i | \(0.181576\pi\) | ||||
−0.841664 | + | 0.540001i | \(0.818424\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7678.10 | + | 13298.9i | −0.248370 | + | 0.430190i | ||||
\(986\) | 43487.1 | + | 25107.3i | 1.40458 | + | 0.810932i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2052.20 | + | 1048.68i | 0.0660821 | + | 0.0337682i | ||||
\(989\) | 62066.8 | 1.99556 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7767.68 | − | 13454.0i | 0.248990 | − | 0.431262i | −0.714256 | − | 0.699884i | \(-0.753235\pi\) |
0.963246 | + | 0.268622i | \(0.0865682\pi\) | |||||||
\(992\) | 431.280 | + | 746.998i | 0.0138036 | + | 0.0239085i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −13692.7 | + | 7905.48i | −0.436927 | + | 0.252260i | ||||
\(995\) | −5718.91 | + | 3301.81i | −0.182213 | + | 0.105201i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13151.2 | − | 22778.5i | −0.417756 | − | 0.723574i | 0.577958 | − | 0.816067i | \(-0.303850\pi\) |
−0.995713 | + | 0.0924929i | \(0.970516\pi\) | |||||||
\(998\) | 2699.84 | − | 4676.27i | 0.0856333 | − | 0.148321i | ||||
\(999\) | 0 | 0 |
(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 | 117.4.q.f.82.1 | yes | 12 | |
3.2 | odd | 2 | inner | 117.4.q.f.82.6 | yes | 12 | |
13.6 | odd | 12 | 1521.4.a.bl.1.11 | 12 | |||
13.7 | odd | 12 | 1521.4.a.bl.1.2 | 12 | |||
13.10 | even | 6 | inner | 117.4.q.f.10.1 | ✓ | 12 | |
39.20 | even | 12 | 1521.4.a.bl.1.12 | 12 | |||
39.23 | odd | 6 | inner | 117.4.q.f.10.6 | yes | 12 | |
39.32 | even | 12 | 1521.4.a.bl.1.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
117.4.q.f.10.1 | ✓ | 12 | 13.10 | even | 6 | inner | |
117.4.q.f.10.6 | yes | 12 | 39.23 | odd | 6 | inner | |
117.4.q.f.82.1 | yes | 12 | 1.1 | even | 1 | trivial | |
117.4.q.f.82.6 | yes | 12 | 3.2 | odd | 2 | inner | |
1521.4.a.bl.1.1 | 12 | 39.32 | even | 12 | |||
1521.4.a.bl.1.2 | 12 | 13.7 | odd | 12 | |||
1521.4.a.bl.1.11 | 12 | 13.6 | odd | 12 | |||
1521.4.a.bl.1.12 | 12 | 39.20 | even | 12 |