Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [112,4,Mod(31,112)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(112, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("112.31");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 112 = 2^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 112.p (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: | \(6.60821392064\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 47.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 112.47 |
Dual form | 112.4.p.b.31.1 |
$q$-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 \(\left(\mathbb{Z}/112\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(17\) | \(85\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.500000 | − | 0.866025i | −0.0962250 | − | 0.166667i | 0.813894 | − | 0.581013i | \(-0.197344\pi\) |
−0.910119 | + | 0.414346i | \(0.864010\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.50000 | − | 2.59808i | −0.402492 | − | 0.232379i | 0.285067 | − | 0.958508i | \(-0.407984\pi\) |
−0.687559 | + | 0.726129i | \(0.741318\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 14.0000 | + | 12.1244i | 0.755929 | + | 0.654654i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 13.0000 | − | 22.5167i | 0.481481 | − | 0.833950i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 22.5000 | − | 12.9904i | 0.616728 | − | 0.356068i | −0.158866 | − | 0.987300i | \(-0.550784\pi\) |
0.775594 | + | 0.631232i | \(0.217451\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 69.2820i | − | 1.47811i | −0.673647 | − | 0.739053i | \(-0.735273\pi\) | ||
0.673647 | − | 0.739053i | \(-0.264727\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.19615i | 0.0894427i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 31.5000 | − | 18.1865i | 0.449404 | − | 0.259464i | −0.258174 | − | 0.966098i | \(-0.583121\pi\) |
0.707579 | + | 0.706635i | \(0.249788\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.50000 | − | 14.7224i | 0.102633 | − | 0.177766i | −0.810135 | − | 0.586243i | \(-0.800606\pi\) |
0.912769 | + | 0.408477i | \(0.133940\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.50000 | − | 18.1865i | 0.0363696 | − | 0.188982i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 121.500 | + | 70.1481i | 1.10150 | + | 0.635951i | 0.936615 | − | 0.350361i | \(-0.113941\pi\) |
0.164885 | + | 0.986313i | \(0.447275\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −49.0000 | − | 84.8705i | −0.392000 | − | 0.678964i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −53.0000 | −0.377772 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 90.0000 | 0.576296 | 0.288148 | − | 0.957586i | \(-0.406961\pi\) | ||||
0.288148 | + | 0.957586i | \(0.406961\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.50000 | − | 14.7224i | −0.0492466 | − | 0.0852976i | 0.840351 | − | 0.542042i | \(-0.182349\pi\) |
−0.889598 | + | 0.456745i | \(0.849015\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −22.5000 | − | 12.9904i | −0.118689 | − | 0.0685253i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −31.5000 | − | 90.9327i | −0.152128 | − | 0.439155i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −99.5000 | + | 172.339i | −0.442100 | + | 0.765740i | −0.997845 | − | 0.0656131i | \(-0.979100\pi\) |
0.555745 | + | 0.831353i | \(0.312433\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −60.0000 | + | 34.6410i | −0.246351 | + | 0.142231i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 187.061i | 0.712539i | 0.934383 | + | 0.356269i | \(0.115951\pi\) | ||||
−0.934383 | + | 0.356269i | \(0.884049\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 252.879i | − | 0.896831i | −0.893825 | − | 0.448416i | \(-0.851988\pi\) | ||
0.893825 | − | 0.448416i | \(-0.148012\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −117.000 | + | 67.5500i | −0.387585 | + | 0.223772i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −283.500 | + | 491.036i | −0.879845 | + | 1.52394i | −0.0283351 | + | 0.999598i | \(0.509021\pi\) |
−0.851510 | + | 0.524338i | \(0.824313\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | + | 339.482i | 0.142857 | + | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −31.5000 | − | 18.1865i | −0.0864879 | − | 0.0499338i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 166.500 | + | 288.386i | 0.431520 | + | 0.747414i | 0.997004 | − | 0.0773449i | \(-0.0246443\pi\) |
−0.565485 | + | 0.824759i | \(0.691311\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −135.000 | −0.330971 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −17.0000 | −0.0395036 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −400.500 | − | 693.686i | −0.883740 | − | 1.53068i | −0.847151 | − | 0.531352i | \(-0.821684\pi\) |
−0.0365889 | − | 0.999330i | \(-0.511649\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −310.500 | − | 179.267i | −0.651729 | − | 0.376276i | 0.137390 | − | 0.990517i | \(-0.456129\pi\) |
−0.789118 | + | 0.614241i | \(0.789462\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 455.000 | − | 157.617i | 0.909914 | − | 0.315204i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −180.000 | + | 311.769i | −0.343481 | + | 0.594926i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −187.500 | + | 108.253i | −0.341892 | + | 0.197391i | −0.661108 | − | 0.750290i | \(-0.729914\pi\) |
0.319216 | + | 0.947682i | \(0.396580\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 140.296i | − | 0.244778i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 488.438i | 0.816436i | 0.912884 | + | 0.408218i | \(0.133850\pi\) | ||||
−0.912884 | + | 0.408218i | \(0.866150\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 349.500 | − | 201.784i | 0.560355 | − | 0.323521i | −0.192933 | − | 0.981212i | \(-0.561800\pi\) |
0.753288 | + | 0.657691i | \(0.228467\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −49.0000 | + | 84.8705i | −0.0754404 | + | 0.130667i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 472.500 | + | 90.9327i | 0.699304 | + | 0.134581i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1033.50 | + | 596.692i | 1.47187 | + | 0.849785i | 0.999500 | − | 0.0316144i | \(-0.0100649\pi\) |
0.472371 | + | 0.881400i | \(0.343398\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −324.500 | − | 562.050i | −0.445130 | − | 0.770988i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −468.000 | −0.618912 | −0.309456 | − | 0.950914i | \(-0.600147\pi\) | ||||
−0.309456 | + | 0.950914i | \(0.600147\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −189.000 | −0.241176 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −45.0000 | − | 77.9423i | −0.0554541 | − | 0.0960493i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −166.500 | − | 96.1288i | −0.198303 | − | 0.114490i | 0.397561 | − | 0.917576i | \(-0.369857\pi\) |
−0.595864 | + | 0.803086i | \(0.703190\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 840.000 | − | 969.948i | 0.967648 | − | 1.11734i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.50000 | + | 14.7224i | −0.00947752 | + | 0.0164155i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −76.5000 | + | 44.1673i | −0.0826183 | + | 0.0476997i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1392.57i | − | 1.45767i | −0.684690 | − | 0.728835i | \(-0.740062\pi\) | ||
0.684690 | − | 0.728835i | \(-0.259938\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 675.500i | − | 0.685760i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1453.50 | − | 839.179i | 1.43197 | − | 0.826746i | 0.434696 | − | 0.900577i | \(-0.356856\pi\) |
0.997271 | + | 0.0738307i | \(0.0235225\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −665.500 | + | 1152.68i | −0.636638 | + | 1.10269i | 0.349528 | + | 0.936926i | \(0.386342\pi\) |
−0.986166 | + | 0.165763i | \(0.946991\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −63.0000 | + | 72.7461i | −0.0585540 | + | 0.0676123i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1435.50 | + | 828.786i | 1.29696 | + | 0.748802i | 0.979878 | − | 0.199595i | \(-0.0639628\pi\) |
0.317084 | + | 0.948397i | \(0.397296\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −395.500 | − | 685.026i | −0.347542 | − | 0.601960i | 0.638271 | − | 0.769812i | \(-0.279650\pi\) |
−0.985812 | + | 0.167852i | \(0.946317\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 199.000 | 0.170164 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 990.000 | 0.824171 | 0.412086 | − | 0.911145i | \(-0.364800\pi\) | ||||
0.412086 | + | 0.911145i | \(0.364800\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −364.500 | − | 631.333i | −0.295563 | − | 0.511931i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1560.00 | − | 900.666i | −1.23267 | − | 0.711681i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 661.500 | + | 127.306i | 0.509577 | + | 0.0980680i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −328.000 | + | 568.113i | −0.246431 | + | 0.426831i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 162.000 | − | 93.5307i | 0.118756 | − | 0.0685641i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1158.74i | 0.829128i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1784.01i | − | 1.24650i | −0.782023 | − | 0.623250i | \(-0.785812\pi\) | ||
0.782023 | − | 0.623250i | \(-0.214188\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −219.000 | + | 126.440i | −0.149472 | + | 0.0862976i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1309.50 | + | 2268.12i | −0.873371 | + | 1.51272i | −0.0148822 | + | 0.999889i | \(0.504737\pi\) |
−0.858488 | + | 0.512833i | \(0.828596\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 297.500 | − | 103.057i | 0.193959 | − | 0.0671893i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 238.500 | + | 137.698i | 0.152050 | + | 0.0877864i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1030.50 | + | 1784.88i | 0.642639 | + | 1.11308i | 0.984841 | + | 0.173457i | \(0.0554939\pi\) |
−0.342202 | + | 0.939626i | \(0.611173\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1108.00 | −0.676110 | −0.338055 | − | 0.941126i | \(-0.609769\pi\) | ||||
−0.338055 | + | 0.941126i | \(0.609769\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 567.000 | 0.338653 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −900.000 | − | 1558.85i | −0.526306 | − | 0.911589i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −405.000 | − | 233.827i | −0.231955 | − | 0.133919i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 269.500 | − | 212.176i | 0.151211 | − | 0.119048i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1381.50 | + | 2392.83i | −0.759576 | + | 1.31562i | 0.183490 | + | 0.983022i | \(0.441260\pi\) |
−0.943067 | + | 0.332603i | \(0.892073\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −715.500 | + | 413.094i | −0.385606 | + | 0.222630i | −0.680255 | − | 0.732976i | \(-0.738131\pi\) |
0.294648 | + | 0.955606i | \(0.404797\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 945.700i | − | 0.499708i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 88.3346i | 0.0457755i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −760.500 | + | 439.075i | −0.386589 | + | 0.223197i | −0.680681 | − | 0.732580i | \(-0.738316\pi\) |
0.294092 | + | 0.955777i | \(0.404983\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 166.500 | − | 288.386i | 0.0830460 | − | 0.143840i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 850.500 | + | 2455.18i | 0.416328 | + | 1.20184i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2101.50 | + | 1213.30i | 1.00983 | + | 0.583025i | 0.911142 | − | 0.412093i | \(-0.135202\pi\) |
0.0986877 | + | 0.995118i | \(0.468536\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 67.5000 | + | 116.913i | 0.0318477 | + | 0.0551618i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2700.00 | −1.25109 | −0.625546 | − | 0.780188i | \(-0.715124\pi\) | ||||
−0.625546 | + | 0.780188i | \(0.715124\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2603.00 | −1.18480 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −221.000 | − | 382.783i | −0.0988321 | − | 0.171182i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1201.50 | + | 693.686i | 0.528025 | + | 0.304855i | 0.740212 | − | 0.672374i | \(-0.234725\pi\) |
−0.212187 | + | 0.977229i | \(0.568059\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 343.000 | − | 1782.28i | 0.148162 | − | 0.769873i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −400.500 | + | 693.686i | −0.170076 | + | 0.294580i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2209.50 | + | 1275.66i | −0.922602 | + | 0.532665i | −0.884464 | − | 0.466608i | \(-0.845476\pi\) |
−0.0381379 | + | 0.999272i | \(0.512143\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 879.882i | 0.361332i | 0.983545 | + | 0.180666i | \(0.0578253\pi\) | ||||
−0.983545 | + | 0.180666i | \(0.942175\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 358.535i | 0.144829i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 895.500 | − | 517.017i | 0.355884 | − | 0.205470i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 472.500 | − | 818.394i | 0.184773 | − | 0.320037i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −742.000 | − | 642.591i | −0.285569 | − | 0.247310i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −976.500 | − | 563.783i | −0.369932 | − | 0.213580i | 0.303497 | − | 0.952833i | \(-0.401846\pi\) |
−0.673429 | + | 0.739252i | \(0.735179\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −657.500 | − | 1138.82i | −0.245222 | − | 0.424737i | 0.716972 | − | 0.697102i | \(-0.245528\pi\) |
−0.962194 | + | 0.272365i | \(0.912194\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 360.000 | 0.132206 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3258.00 | 1.17829 | 0.589144 | − | 0.808028i | \(-0.299465\pi\) | ||||
0.589144 | + | 0.808028i | \(0.299465\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −876.500 | − | 1518.14i | −0.312228 | − | 0.540795i | 0.666616 | − | 0.745401i | \(-0.267742\pi\) |
−0.978844 | + | 0.204606i | \(0.934409\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 187.500 | + | 108.253i | 0.0657972 | + | 0.0379880i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1260.00 | + | 1091.19i | 0.435639 | + | 0.377274i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 486.000 | − | 841.777i | 0.165579 | − | 0.286791i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3159.00 | − | 1823.85i | 1.06070 | − | 0.612398i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 441.673i | − | 0.146178i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3543.78i | 1.15623i | 0.815957 | + | 0.578113i | \(0.196211\pi\) | ||||
−0.815957 | + | 0.578113i | \(0.803789\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 423.000 | − | 244.219i | 0.136073 | − | 0.0785616i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −657.000 | + | 1137.96i | −0.208405 | + | 0.360968i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 59.5000 | − | 309.171i | 0.0186135 | − | 0.0967184i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −349.500 | − | 201.784i | −0.107840 | − | 0.0622616i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1260.00 | − | 2182.38i | −0.383515 | − | 0.664267i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2896.00 | 0.869644 | 0.434822 | − | 0.900517i | \(-0.356811\pi\) | ||||
0.434822 | + | 0.900517i | \(0.356811\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2548.00 | −0.754963 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1849.50 | + | 3203.43i | 0.540774 | + | 0.936647i | 0.998860 | + | 0.0477397i | \(0.0152018\pi\) |
−0.458086 | + | 0.888908i | \(0.651465\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3304.50 | − | 1907.85i | −0.953570 | − | 0.550544i | −0.0593818 | − | 0.998235i | \(-0.518913\pi\) |
−0.894188 | + | 0.447692i | \(0.852246\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −157.500 | − | 454.663i | −0.0448603 | − | 0.129501i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2830.50 | − | 4902.57i | 0.795846 | − | 1.37845i | −0.126454 | − | 0.991972i | \(-0.540360\pi\) |
0.922300 | − | 0.386474i | \(-0.126307\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2551.50 | − | 1473.11i | 0.708262 | − | 0.408915i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 1193.38i | − | 0.327083i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 3481.42i | − | 0.942236i | −0.882070 | − | 0.471118i | \(-0.843851\pi\) | ||
0.882070 | − | 0.471118i | \(-0.156149\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2101.50 | − | 1213.30i | 0.561699 | − | 0.324297i | −0.192128 | − | 0.981370i | \(-0.561539\pi\) |
0.753827 | + | 0.657073i | \(0.228206\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1040.00 | + | 1801.33i | −0.274552 | + | 0.475537i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 661.500 | − | 1654.97i | 0.172497 | − | 0.431561i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1020.00 | − | 588.897i | −0.262757 | − | 0.151703i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 234.000 | + | 405.300i | 0.0595548 | + | 0.103152i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6120.00 | 1.53901 | 0.769504 | − | 0.638642i | \(-0.220504\pi\) | ||||
0.769504 | + | 0.638642i | \(0.220504\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3645.00 | 0.905768 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 94.5000 | + | 163.679i | 0.0232071 | + | 0.0401959i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3091.50 | + | 1784.88i | 0.750360 | + | 0.433220i | 0.825824 | − | 0.563928i | \(-0.190710\pi\) |
−0.0754641 | + | 0.997149i | \(0.524044\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3482.50 | + | 1206.37i | −0.835490 | + | 0.289422i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1170.00 | − | 2026.50i | 0.277476 | − | 0.480602i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3433.50 | + | 1982.33i | −0.805014 | + | 0.464775i | −0.845221 | − | 0.534416i | \(-0.820531\pi\) |
0.0402074 | + | 0.999191i | \(0.487198\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1730.32i | − | 0.401104i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 192.258i | 0.0440673i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5332.50 | + | 3078.72i | −1.20866 | + | 0.697817i | −0.962465 | − | 0.271404i | \(-0.912512\pi\) |
−0.246190 | + | 0.969222i | \(0.579179\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2874.50 | − | 4978.78i | 0.644330 | − | 1.11601i | −0.340126 | − | 0.940380i | \(-0.610470\pi\) |
0.984456 | − | 0.175632i | \(-0.0561970\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1260.00 | − | 242.487i | −0.279336 | − | 0.0537582i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2205.00 | − | 1273.06i | −0.483515 | − | 0.279157i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 98.5000 | + | 170.607i | 0.0213657 | + | 0.0370064i | 0.876511 | − | 0.481383i | \(-0.159865\pi\) |
−0.855145 | + | 0.518389i | \(0.826532\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −442.000 | −0.0948453 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3618.00 | −0.768085 | −0.384042 | − | 0.923315i | \(-0.625468\pi\) | ||||
−0.384042 | + | 0.923315i | \(0.625468\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1781.50 | + | 3085.65i | 0.374202 | + | 0.648137i | 0.990207 | − | 0.139605i | \(-0.0445833\pi\) |
−0.616005 | + | 0.787742i | \(0.711250\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 76.5000 | + | 44.1673i | 0.0158999 | + | 0.00917981i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2268.00 | + | 2618.86i | −0.466466 | + | 0.538629i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1795.00 | + | 3109.03i | −0.365357 | + | 0.632817i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1206.00 | + | 696.284i | −0.242945 | + | 0.140264i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6048.32i | 1.20596i | 0.797756 | + | 0.602981i | \(0.206020\pi\) | ||||
−0.797756 | + | 0.602981i | \(0.793980\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4162.12i | 0.821450i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1192.50 | + | 688.490i | −0.232983 | + | 0.134513i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4860.00 | − | 8417.77i | 0.940004 | − | 1.62813i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3066.00 | − | 3540.31i | 0.587114 | − | 0.677941i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1453.50 | − | 839.179i | −0.275582 | − | 0.159107i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 931.500 | + | 1613.41i | 0.174877 | + | 0.302896i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7316.00 | −1.36009 | −0.680043 | − | 0.733173i | \(-0.738039\pi\) | ||||
−0.680043 | + | 0.733173i | \(0.738039\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1331.00 | 0.245042 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1273.50 | + | 2205.77i | 0.232198 | + | 0.402179i | 0.958455 | − | 0.285245i | \(-0.0920750\pi\) |
−0.726257 | + | 0.687424i | \(0.758742\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7957.50 | + | 4594.26i | 1.43701 | + | 0.829659i | 0.997641 | − | 0.0686473i | \(-0.0218683\pi\) |
0.439370 | + | 0.898306i | \(0.355202\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2457.00 | − | 472.850i | −0.439480 | − | 0.0845780i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −247.500 | + | 428.683i | −0.0438517 | + | 0.0759534i | −0.887118 | − | 0.461542i | \(-0.847296\pi\) |
0.843266 | + | 0.537496i | \(0.180630\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2025.00 | − | 1169.13i | 0.355418 | − | 0.205200i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 1657.57i | − | 0.288214i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 618.342i | − | 0.106519i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5880.00 | + | 3394.82i | −1.00358 | + | 0.579418i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −395.500 | + | 685.026i | −0.0668844 | + | 0.115847i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9922.50 | + | 3437.25i | −1.66275 | + | 0.575994i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7954.50 | − | 4592.53i | −1.32090 | − | 0.762624i | −0.337030 | − | 0.941494i | \(-0.609422\pi\) |
−0.983873 | + | 0.178870i | \(0.942756\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2587.00 | + | 4480.82i | 0.425726 | + | 0.737379i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1125.00 | 0.183479 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5194.00 | −0.839570 | −0.419785 | − | 0.907623i | \(-0.637895\pi\) | ||||
−0.419785 | + | 0.907623i | \(0.637895\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −495.000 | − | 857.365i | −0.0793059 | − | 0.137362i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −382.500 | − | 220.836i | −0.0607435 | − | 0.0350703i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3430.00 | + | 5346.84i | −0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −364.500 | + | 631.333i | −0.0568812 | + | 0.0985212i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3892.50 | − | 2247.34i | 0.602191 | − | 0.347675i | −0.167712 | − | 0.985836i | \(-0.553638\pi\) |
0.769903 | + | 0.638161i | \(0.220305\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9436.21i | 1.44730i | 0.690165 | + | 0.723652i | \(0.257538\pi\) | ||||
−0.690165 | + | 0.723652i | \(0.742462\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3671.95i | 0.558388i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5395.50 | − | 3115.09i | 0.813523 | − | 0.469688i | −0.0346551 | − | 0.999399i | \(-0.511033\pi\) |
0.848178 | + | 0.529712i | \(0.177700\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1269.00 | − | 2197.97i | 0.189723 | − | 0.328609i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −220.500 | − | 636.529i | −0.0326893 | − | 0.0943660i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5836.50 | − | 3369.70i | −0.858046 | − | 0.495393i | 0.00531114 | − | 0.999986i | \(-0.498309\pi\) |
−0.863358 | + | 0.504593i | \(0.831643\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3285.00 | + | 5689.79i | 0.478933 | + | 0.829536i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 656.000 | 0.0948514 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2097.00 | −0.300718 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6245.50 | + | 10817.5i | 0.888317 | + | 1.53861i | 0.841864 | + | 0.539690i | \(0.181459\pi\) |
0.0464536 | + | 0.998920i | \(0.485208\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4212.00 | + | 2431.80i | 0.594222 | + | 0.343074i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1165.50 | + | 6056.12i | −0.163099 | + | 0.847487i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3888.50 | − | 6735.08i | 0.539783 | − | 0.934931i | −0.459133 | − | 0.888368i | \(-0.651840\pi\) |
0.998915 | − | 0.0465632i | \(-0.0148269\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1003.50 | − | 579.371i | 0.138188 | − | 0.0797829i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 6235.38i | − | 0.851826i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 6231.92i | − | 0.844623i | −0.906451 | − | 0.422312i | \(-0.861219\pi\) | ||
0.906451 | − | 0.422312i | \(-0.138781\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1545.00 | + | 892.006i | −0.207750 | + | 0.119945i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3640.50 | − | 6305.53i | 0.485694 | − | 0.841247i | −0.514171 | − | 0.857688i | \(-0.671900\pi\) |
0.999865 | + | 0.0164409i | \(0.00523355\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1890.00 | − | 1636.79i | −0.250190 | − | 0.216671i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5694.00 | − | 3287.43i | −0.747913 | − | 0.431808i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5791.50 | − | 10031.2i | −0.754860 | − | 1.30746i | −0.945444 | − | 0.325786i | \(-0.894371\pi\) |
0.190583 | − | 0.981671i | \(-0.438962\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5103.00 | 0.660025 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2619.00 | 0.336160 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3100.50 | − | 5370.22i | −0.394945 | − | 0.684064i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2260.50 | − | 1305.10i | −0.285771 | − | 0.164990i | 0.350262 | − | 0.936652i | \(-0.386093\pi\) |
−0.636033 | + | 0.771662i | \(0.719426\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −238.000 | − | 206.114i | −0.0298619 | − | 0.0258612i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3802.50 | − | 6586.12i | 0.473536 | − | 0.820188i | −0.526005 | − | 0.850481i | \(-0.676311\pi\) |
0.999541 | + | 0.0302934i | \(0.00964418\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1020.00 | + | 588.897i | −0.126079 | + | 0.0727917i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3372.30i | 0.413756i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5170.17i | 0.629671i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4228.50 | + | 2441.33i | −0.511212 | + | 0.295149i | −0.733332 | − | 0.679871i | \(-0.762036\pi\) |
0.222119 | + | 0.975019i | \(0.428702\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1030.50 | − | 1784.88i | 0.123676 | − | 0.214213i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2803.50 | − | 14567.4i | 0.334022 | − | 1.73563i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2106.00 | + | 1215.90i | 0.249107 | + | 0.143822i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 554.000 | + | 959.556i | 0.0650587 | + | 0.112685i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12780.0 | 1.49008 | 0.745040 | − | 0.667019i | \(-0.232430\pi\) | ||||
0.745040 | + | 0.667019i | \(0.232430\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9802.00 | 1.13473 | 0.567364 | − | 0.823467i | \(-0.307963\pi\) | ||||
0.567364 | + | 0.823467i | \(0.307963\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7371.00 | + | 12766.9i | 0.847258 | + | 1.46749i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3087.00 | − | 1782.28i | −0.352333 | − | 0.203420i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2173.50 | − | 6274.35i | −0.246330 | − | 0.711094i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −900.000 | + | 1558.85i | −0.101288 | + | 0.175435i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2083.50 | + | 1202.91i | −0.232851 | + | 0.134436i | −0.611886 | − | 0.790946i | \(-0.709589\pi\) |
0.379036 | + | 0.925382i | \(0.376256\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 8390.05i | − | 0.931178i | −0.885001 | − | 0.465589i | \(-0.845842\pi\) | ||
0.885001 | − | 0.465589i | \(-0.154158\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 467.654i | 0.0515455i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2065.50 | − | 1192.52i | 0.226101 | − | 0.130540i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 752.500 | − | 1303.37i | 0.0818106 | − | 0.141700i | −0.822217 | − | 0.569174i | \(-0.807263\pi\) |
0.904028 | + | 0.427474i | \(0.140596\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8281.00 | + | 3309.95i | 0.894180 | + | 0.357407i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5611.50 | + | 3239.80i | 0.601829 | + | 0.347466i | 0.769761 | − | 0.638332i | \(-0.220375\pi\) |
−0.167932 | + | 0.985799i | \(0.553709\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 499.500 | + | 865.159i | 0.0532103 | + | 0.0921629i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2763.00 | 0.292361 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18090.0 | −1.90138 | −0.950690 | − | 0.310142i | \(-0.899623\pi\) | ||||
−0.950690 | + | 0.310142i | \(0.899623\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2430.00 | + | 4208.88i | 0.253712 | + | 0.439443i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 715.500 | + | 413.094i | 0.0742100 | + | 0.0428452i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6300.00 | + | 2182.38i | −0.649118 | + | 0.224861i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5868.50 | − | 10164.5i | 0.600693 | − | 1.04043i | −0.392023 | − | 0.919955i | \(-0.628225\pi\) |
0.992716 | − | 0.120476i | \(-0.0384421\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1669.50 | + | 963.886i | −0.169773 | + | 0.0980182i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 956.092i | 0.0965936i | 0.998833 | + | 0.0482968i | \(0.0153793\pi\) | ||||
−0.998833 | + | 0.0482968i | \(0.984621\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4922.49i | 0.494098i | 0.969003 | + | 0.247049i | \(0.0794609\pi\) | ||||
−0.969003 | + | 0.247049i | \(0.920539\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 76.5000 | − | 44.1673i | 0.00762925 | − | 0.00440475i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4198.50 | − | 7272.02i | 0.416024 | − | 0.720575i | −0.579511 | − | 0.814964i | \(-0.696756\pi\) |
0.995535 | + | 0.0943890i | \(0.0300897\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3937.50 | − | 757.772i | −0.387669 | − | 0.0746070i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 760.500 | + | 439.075i | 0.0743991 | + | 0.0429544i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3285.00 | − | 5689.79i | −0.319333 | − | 0.553101i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1666.00 | −0.160929 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8658.00 | 0.831075 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7870.50 | − | 13632.1i | −0.750756 | − | 1.30035i | −0.947457 | − | 0.319885i | \(-0.896356\pi\) |
0.196700 | − | 0.980464i | \(-0.436977\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11940.0 | + | 6893.56i | 1.13184 | + | 0.653471i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1701.00 | − | 1964.15i | 0.160245 | − | 0.185035i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3618.00 | + | 6266.56i | −0.338732 | + | 0.586701i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 934.500 | − | 539.534i | 0.0869533 | − | 0.0502025i | −0.455893 | − | 0.890035i | \(-0.650680\pi\) |
0.542846 | + | 0.839832i | \(0.317347\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 2426.60i | − | 0.224407i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1278.25i | 0.117488i | 0.998273 | + | 0.0587442i | \(0.0187096\pi\) | ||||
−0.998273 | + | 0.0587442i | \(0.981290\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2835.00 | − | 1636.79i | 0.258990 | − | 0.149528i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1755.00 | + | 3039.75i | −0.159356 | + | 0.276013i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5922.00 | + | 6838.14i | −0.534483 | + | 0.617168i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10450.5 | − | 6033.60i | −0.937532 | − | 0.541285i | −0.0483464 | − | 0.998831i | \(-0.515395\pi\) |
−0.889186 | + | 0.457546i | \(0.848728\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1350.00 | + | 2338.27i | 0.120386 | + | 0.208515i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2808.00 | 0.248912 | 0.124456 | − | 0.992225i | \(-0.460282\pi\) | ||||
0.124456 | + | 0.992225i | \(0.460282\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8721.00 | −0.768474 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1301.50 | + | 2254.26i | 0.114007 | + | 0.197466i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11236.5 | − | 6487.40i | −0.978485 | − | 0.564929i | −0.0766729 | − | 0.997056i | \(-0.524430\pi\) |
−0.901813 | + | 0.432127i | \(0.857763\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7339.50 | + | 1412.49i | 0.635382 | + | 0.122279i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −450.500 | + | 780.289i | −0.0387720 | + | 0.0671552i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5989.50 | − | 3458.04i | 0.512483 | − | 0.295882i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14731.1i | 1.25314i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 1387.37i | − | 0.117339i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 373.500 | − | 215.640i | 0.0314075 | − | 0.0181332i | −0.484214 | − | 0.874950i | \(-0.660894\pi\) |
0.515622 | + | 0.856816i | \(0.327561\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9395.50 | + | 16273.5i | −0.785538 | + | 1.36059i | 0.143139 | + | 0.989703i | \(0.454281\pi\) |
−0.928677 | + | 0.370890i | \(0.879053\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1715.00 | + | 594.093i | −0.142569 | + | 0.0493874i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −535.500 | − | 309.171i | −0.0442633 | − | 0.0255554i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3758.00 | + | 6509.05i | 0.308868 | + | 0.534976i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −20826.0 | −1.70202 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12960.0 | 1.05321 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4306.50 | − | 7459.08i | −0.348012 | − | 0.602774i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2209.50 | + | 1275.66i | 0.177555 | + | 0.102511i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5512.50 | + | 7001.82i | 0.440520 | + | 0.559535i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6273.50 | + | 10866.0i | −0.498556 | + | 0.863524i | −0.999999 | − | 0.00166651i | \(-0.999470\pi\) |
0.501443 | + | 0.865191i | \(0.332803\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 762.000 | − | 439.941i | 0.0602220 | − | 0.0347692i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4110.16i | 0.323045i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2151.21i | 0.168152i | 0.996459 | + | 0.0840758i | \(0.0267938\pi\) | ||||
−0.996459 | + | 0.0840758i | \(0.973206\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8073.00 | + | 4660.95i | −0.627591 | + | 0.362340i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 765.000 | − | 1325.02i | 0.0591472 | − | 0.102446i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7234.50 | + | 20884.2i | 0.556315 | + | 1.60594i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −895.500 | − | 517.017i | −0.0684898 | − | 0.0395426i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1759.50 | − | 3047.54i | −0.133846 | − | 0.231829i | 0.791310 | − | 0.611415i | \(-0.209400\pi\) |
−0.925156 | + | 0.379587i | \(0.876066\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17520.0 | −1.32561 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −945.000 | −0.0711193 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4288.50 | − | 7427.90i | −0.321028 | − | 0.556037i | 0.659672 | − | 0.751553i | \(-0.270695\pi\) |
−0.980700 | + | 0.195517i | \(0.937362\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4455.00 | − | 2572.10i | −0.331723 | − | 0.191520i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2271.50 | − | 11803.1i | 0.168243 | − | 0.874219i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5431.50 | + | 9407.63i | −0.400176 | + | 0.693126i | −0.993747 | − | 0.111656i | \(-0.964384\pi\) |
0.593571 | + | 0.804782i | \(0.297718\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1261.50 | + | 728.327i | −0.0924556 | + | 0.0533792i | −0.545515 | − | 0.838101i | \(-0.683666\pi\) |
0.453059 | + | 0.891480i | \(0.350333\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1127.57i | 0.0822072i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 13749.0i | − | 0.997172i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 565.500 | − | 326.492i | 0.0408008 | − | 0.0235564i | −0.479461 | − | 0.877563i | \(-0.659168\pi\) |
0.520262 | + | 0.854007i | \(0.325834\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −657.500 | + | 1138.82i | −0.0471930 | + | 0.0817407i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6552.00 | − | 5674.20i | −0.467853 | − | 0.405173i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7492.50 | + | 4325.80i | 0.532260 | + | 0.307301i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4680.00 | + | 8106.00i | 0.330759 | + | 0.572892i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9684.00 | 0.680922 | 0.340461 | − | 0.940259i | \(-0.389417\pi\) | ||||
0.340461 | + | 0.940259i | \(0.389417\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −289.000 | −0.0202174 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1629.00 | − | 2821.51i | −0.113381 | − | 0.196381i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6187.50 | + | 3572.35i | 0.428483 | + | 0.247385i | 0.698700 | − | 0.715415i | \(-0.253762\pi\) |
−0.270217 | + | 0.962799i | \(0.587096\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2646.00 | − | 2291.50i | −0.182312 | − | 0.157887i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −876.500 | + | 1518.14i | −0.0600884 | + | 0.104076i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14773.5 | + | 8529.48i | −1.00773 | + | 0.581812i | −0.910526 | − | 0.413453i | \(-0.864323\pi\) |
−0.0972021 | + | 0.995265i | \(0.530989\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 26070.8i | − | 1.76947i | −0.466095 | − | 0.884735i | \(-0.654339\pi\) | ||
0.466095 | − | 0.884735i | \(-0.345661\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5629.17i | 0.380161i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2952.00 | − | 1704.34i | 0.198373 | − | 0.114531i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6147.50 | + | 10647.8i | −0.411070 | + | 0.711994i | −0.995007 | − | 0.0998051i | \(-0.968178\pi\) |
0.583937 | + | 0.811799i | \(0.301511\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 315.000 | − | 1636.79i | 0.0209597 | − | 0.108910i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 34020.0 | + | 19641.5i | 2.25254 | + | 1.30050i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −527.500 | − | 913.657i | −0.0347562 | − | 0.0601994i | 0.848124 | − | 0.529798i | \(-0.177732\pi\) |
−0.882880 | + | 0.469598i | \(0.844399\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −972.000 | −0.0637314 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1494.00 | 0.0974816 | 0.0487408 | − | 0.998811i | \(-0.484479\pi\) | ||||
0.0487408 | + | 0.998811i | \(0.484479\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2799.50 | + | 4848.88i | 0.181779 | + | 0.314851i | 0.942487 | − | 0.334244i | \(-0.108481\pi\) |
−0.760707 | + | 0.649095i | \(0.775148\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6439.50 | − | 3717.85i | −0.416116 | − | 0.240245i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1165.50 | − | 3364.51i | −0.0749515 | − | 0.216366i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3114.50 | + | 5394.47i | −0.199328 | + | 0.345246i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −382.500 | + | 220.836i | −0.0243630 | + | 0.0140660i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7238.24i | 0.458836i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 19007.5i | − | 1.19917i | −0.800310 | − | 0.599586i | \(-0.795332\pi\) | ||
0.800310 | − | 0.599586i | \(-0.204668\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3069.00 | − | 1771.89i | 0.192704 | − | 0.111258i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4635.00 | + | 8028.06i | −0.289660 | + | 0.501707i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 23520.0 | − | 3394.82i | 1.46295 | − | 0.211158i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10998.0 | + | 6349.70i | 0.680867 | + | 0.393099i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11011.5 | − | 19072.5i | −0.678515 | − | 1.17522i | −0.975428 | − | 0.220318i | \(-0.929291\pi\) |
0.296913 | − | 0.954904i | \(-0.404043\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10036.0 | 0.615523 | 0.307761 | − | 0.951464i | \(-0.400420\pi\) | ||||
0.307761 | + | 0.951464i | \(0.400420\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1314.00 | 0.0802150 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13846.5 | − | 23982.8i | −0.841363 | − | 1.45728i | −0.888742 | − | 0.458407i | \(-0.848420\pi\) |
0.0473790 | − | 0.998877i | \(-0.484913\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −18022.5 | − | 10405.3i | −1.09005 | − | 0.629343i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −297.500 | + | 103.057i | −0.0179108 | + | 0.00620449i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −643.500 | + | 1114.57i | −0.0385637 | + | 0.0667943i | −0.884663 | − | 0.466231i | \(-0.845612\pi\) |
0.846099 | + | 0.533025i | \(0.178945\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11785.5 | − | 6804.36i | 0.703050 | − | 0.405906i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 10492.8i | − | 0.623077i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 5767.73i | − | 0.340939i | −0.985363 | − | 0.170470i | \(-0.945472\pi\) | ||
0.985363 | − | 0.170470i | \(-0.0545284\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9259.50 | − | 5345.97i | 0.544861 | − | 0.314575i | −0.202186 | − | 0.979347i | \(-0.564805\pi\) |
0.747047 | + | 0.664772i | \(0.231471\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1260.00 | + | 2182.38i | −0.0738075 | + | 0.127838i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1606.50 | − | 309.171i | −0.0936803 | − | 0.0180288i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10935.0 | + | 6313.33i | 0.634790 | + | 0.366496i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1448.00 | − | 2508.01i | −0.0836815 | − | 0.144941i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9315.00 | −0.535919 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14518.0 | 0.831542 | 0.415771 | − | 0.909469i | \(-0.363512\pi\) | ||||
0.415771 | + | 0.909469i | \(0.363512\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2597.00 | + | 4498.14i | 0.148087 | + | 0.256494i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7312.50 | − | 4221.87i | −0.415129 | − | 0.239675i | 0.277862 | − | 0.960621i | \(-0.410374\pi\) |
−0.692991 | + | 0.720946i | \(0.743707\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16884.0 | − | 19496.0i | 0.954269 | − | 1.10189i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1849.50 | − | 3203.43i | 0.104072 | − | 0.180258i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23557.5 | + | 13600.9i | −1.31977 | + | 0.761969i | −0.983691 | − | 0.179865i | \(-0.942434\pi\) |
−0.336078 | + | 0.941834i | \(0.609101\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 10709.3i | − | 0.597343i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3815.71i | 0.211904i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 19980.0 | − | 11535.5i | 1.10476 | − | 0.637832i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9953.50 | + | 17240.0i | −0.547972 | + | 0.949116i | 0.450441 | + | 0.892806i | \(0.351267\pi\) |
−0.998413 | + | 0.0563099i | \(0.982067\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8190.00 | − | 9457.00i | 0.448936 | − | 0.518386i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4986.00 | + | 2878.67i | 0.272129 | + | 0.157114i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3402.00 | + | 5892.44i | 0.184878 | + | 0.320218i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5661.00 | −0.306321 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12294.0 | 0.662394 | 0.331197 | − | 0.943562i | \(-0.392548\pi\) | ||||
0.331197 | + | 0.943562i | \(0.392548\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1691.50 | + | 2929.76i | 0.0907484 | + | 0.157181i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2551.50 | − | 1473.11i | −0.136305 | − | 0.0786957i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 30523.5 | + | 5874.25i | 1.62370 | + | 0.312481i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4080.50 | − | 7067.63i | 0.216144 | − | 0.374373i | −0.737482 | − | 0.675367i | \(-0.763985\pi\) |
0.953626 | + | 0.300994i | \(0.0973185\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 26871.0 | − | 15514.0i | 1.41736 | − | 0.818312i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 2385.03i | − | 0.125274i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9353.07i | 0.489210i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3015.00 | + | 1740.71i | −0.157039 | + | 0.0906667i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6997.50 | + | 12120.0i | −0.362952 | + | 0.628652i | −0.988445 | − | 0.151578i | \(-0.951565\pi\) |
0.625493 | + | 0.780230i | \(0.284898\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23292.5 | + | 8068.76i | −1.20313 | + | 0.416777i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2101.50 | − | 1213.30i | −0.108099 | − | 0.0624110i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4410.00 | − | 7638.34i | −0.225908 | − | 0.391284i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1232.00 | 0.0628506 | 0.0314253 | − | 0.999506i | \(-0.489995\pi\) | ||||
0.0314253 | + | 0.999506i | \(0.489995\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15443.0 | −0.784586 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4599.00 | − | 7965.70i | −0.232695 | − | 0.403040i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23902.5 | − | 13800.1i | −1.20445 | − | 0.695387i | −0.242905 | − | 0.970050i | \(-0.578100\pi\) |
−0.961541 | + | 0.274663i | \(0.911434\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1764.00 | + | 254.611i | −0.0885253 | + | 0.0127775i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2812.50 | + | 4871.39i | −0.140570 | + | 0.243474i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20554.5 | − | 11867.1i | 1.02315 | − | 0.590717i | 0.108137 | − | 0.994136i | \(-0.465512\pi\) |
0.915015 | + | 0.403419i | \(0.132178\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1177.79i | 0.0583905i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 11275.7i | − | 0.556748i | −0.960473 | − | 0.278374i | \(-0.910205\pi\) | ||
0.960473 | − | 0.278374i | \(-0.0897954\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12433.5 | − | 7178.48i | 0.611447 | − | 0.353019i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6084.00 | + | 10537.8i | −0.297995 | + | 0.516142i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10048.5 | + | 29007.5i | 0.490206 | + | 1.41510i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5392.50 | − | 3113.36i | −0.262017 | − | 0.151276i | 0.363237 | − | 0.931697i | \(-0.381672\pi\) |
−0.625255 | + | 0.780421i | \(0.715005\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3060.00 | − | 5300.08i | −0.148091 | − | 0.256501i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4293.00 | 0.206938 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17062.0 | −0.819193 | −0.409596 | − | 0.912267i | \(-0.634330\pi\) | ||||
−0.409596 | + | 0.912267i | \(0.634330\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1822.50 | − | 3156.66i | −0.0871575 | − | 0.150961i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23251.5 | + | 13424.3i | 1.10758 | + | 0.639460i | 0.938201 | − | 0.346091i | \(-0.112491\pi\) |
0.169376 | + | 0.985551i | \(0.445825\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2768.50 | − | 14385.5i | 0.131358 | − | 0.682558i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2457.00 | + | 4255.65i | −0.116122 | + | 0.201129i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −48060.0 | + | 27747.5i | −2.26251 | + | 1.30626i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4330.13i | 0.203054i | 0.994833 | + | 0.101527i | \(0.0323728\pi\) | ||||
−0.994833 | + | 0.101527i | \(0.967627\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 3569.76i | − | 0.166747i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14593.5 | − | 8425.56i | 0.679032 | − | 0.392039i | −0.120458 | − | 0.992718i | \(-0.538436\pi\) |
0.799490 | + | 0.600679i | \(0.205103\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −833.000 | + | 1442.80i | −0.0386093 | + | 0.0668733i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2786.00 | + | 2412.75i | 0.128632 | + | 0.111399i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2754.00 | + | 1590.02i | 0.126665 | + | 0.0731303i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6345.00 | + | 10989.9i | 0.290707 | + | 0.503519i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4770.00 | −0.217709 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4563.00 | 0.207466 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13532.5 | − | 23439.0i | −0.612937 | − | 1.06164i | −0.990743 | − | 0.135753i | \(-0.956655\pi\) |
0.377806 | − | 0.925885i | \(-0.376679\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3433.50 | + | 1982.33i | 0.154925 | + | 0.0894460i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13860.0 | + | 12003.1i | 0.623015 | + | 0.539547i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12420.0 | + | 21512.1i | −0.556175 | + | 0.963324i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1498.50 | + | 865.159i | −0.0668507 | + | 0.0385963i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13717.8i | 0.609675i | 0.952404 | + | 0.304837i | \(0.0986021\pi\) | ||||
−0.952404 | + | 0.304837i | \(0.901398\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20623.5i | 0.913151i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4329.00 | + | 2499.35i | −0.190958 | + | 0.110250i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5242.50 | − | 9080.28i | 0.230391 | − | 0.399049i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2551.50 | − | 13258.0i | 0.111712 | − | 0.580475i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5332.50 | + | 3078.72i | 0.232606 | + | 0.134295i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11164.5 | + | 19337.5i | 0.485195 | + | 0.840383i | 0.999855 | − | 0.0170116i | \(-0.00541521\pi\) |
−0.514660 | + | 0.857394i | \(0.672082\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −43252.0 | −1.87273 | −0.936364 | − | 0.351029i | \(-0.885832\pi\) | ||||
−0.936364 | + | 0.351029i | \(0.885832\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5749.00 | −0.248003 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6304.50 | − | 10919.7i | −0.270966 | − | 0.469326i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3723.00 | − | 2149.48i | −0.159426 | − | 0.0920448i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −10920.0 | − | 31523.3i | −0.465904 | − | 1.34495i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14845.5 | + | 25713.2i | −0.631074 | + | 1.09305i | 0.356259 | + | 0.934387i | \(0.384052\pi\) |
−0.987333 | + | 0.158664i | \(0.949281\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10858.5 | − | 6269.16i | 0.459907 | − | 0.265527i | −0.252098 | − | 0.967702i | \(-0.581121\pi\) |
0.712005 | + | 0.702174i | \(0.247787\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2546.11i | 0.107448i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6910.88i | 0.290586i | 0.989389 | + | 0.145293i | \(0.0464125\pi\) | ||||
−0.989389 | + | 0.145293i | \(0.953587\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −37546.5 | + | 21677.5i | −1.57303 | + | 0.908191i | −0.577238 | + | 0.816576i | \(0.695869\pi\) |
−0.995795 | + | 0.0916146i | \(0.970797\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 98.5000 | − | 170.607i | 0.00411183 | − | 0.00712189i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7717.50 | + | 9802.54i | 0.321003 | + | 0.407729i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12150.0 | + | 7014.81i | 0.503555 | + | 0.290727i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 450.500 | + | 780.289i | 0.0186040 | + | 0.0322231i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9648.00 | 0.397004 | 0.198502 | − | 0.980101i | \(-0.436392\pi\) | ||||
0.198502 | + | 0.980101i | \(0.436392\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16289.0 | −0.667883 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1809.00 | + | 3133.28i | 0.0739090 | + | 0.128014i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11713.5 | + | 6762.79i | 0.476872 | + | 0.275322i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11480.0 | + | 3976.79i | −0.465711 | + | 0.161327i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1781.50 | − | 3085.65i | 0.0720152 | − | 0.124734i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −24178.5 | + | 13959.5i | −0.973946 | + | 0.562308i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8119.85i | 0.325930i | 0.986632 | + | 0.162965i | \(0.0521058\pi\) | ||||
−0.986632 | + | 0.162965i | \(0.947894\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2296.70i | 0.0918660i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1201.50 | − | 693.686i | 0.0478908 | − | 0.0276498i | −0.475863 | − | 0.879519i | \(-0.657864\pi\) |
0.523754 | + | 0.851869i | \(0.324531\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −507.500 | + | 879.016i | −0.0201579 | + | 0.0349146i | −0.875928 | − | 0.482441i | \(-0.839750\pi\) |
0.855770 | + | 0.517356i | \(0.173084\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3402.00 | + | 654.715i | 0.134657 | + | 0.0259148i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2794.50 | − | 1613.41i | −0.110227 | − | 0.0636396i | 0.443873 | − | 0.896090i | \(-0.353604\pi\) |
−0.554100 | + | 0.832450i | \(0.686937\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3604.50 | − | 6243.18i | −0.141684 | − | 0.245404i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3590.00 | 0.140626 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 31005.0 | 1.21033 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7500.00 | + | 12990.4i | 0.291766 | + | 0.505353i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −31356.0 | − | 18103.4i | −1.21562 | − | 0.701841i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −14049.0 | + | 16222.4i | −0.542792 | + | 0.626762i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7770.50 | − | 13458.9i | 0.299192 | − | 0.518215i | −0.676760 | − | 0.736204i | \(-0.736616\pi\) |
0.975951 | + | 0.217989i | \(0.0699497\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5238.00 | − | 3024.16i | 0.200994 | − | 0.116044i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28724.3i | 1.09846i | 0.835670 | + | 0.549232i | \(0.185080\pi\) | ||||
−0.835670 | + | 0.549232i | \(0.814920\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 45826.6i | − | 1.74653i | −0.487244 | − | 0.873266i | \(-0.661998\pi\) | ||
0.487244 | − | 0.873266i | \(-0.338002\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3604.50 | − | 2081.06i | 0.136908 | − | 0.0790441i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3064.50 | − | 5307.87i | 0.116004 | − | 0.200925i | −0.802176 | − | 0.597087i | \(-0.796325\pi\) |
0.918181 | + | 0.396162i | \(0.129658\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21630.0 | − | 24976.2i | 0.816026 | − | 0.942265i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −14602.5 | − | 8430.76i | −0.549048 | − | 0.316993i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4819.50 | + | 8347.62i | 0.180603 | + | 0.312813i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13257.0 | 0.495120 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9720.00 | −0.361808 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −765.000 | − | 1325.02i | −0.0283806 | − | 0.0491567i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10489.5 | + | 6056.12i | 0.387853 | + | 0.223927i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4599.00 | − | 885.078i | −0.169485 | − | 0.0326174i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2286.00 | − | 3959.47i | 0.0839660 | − | 0.145433i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6352.50 | − | 3667.62i | 0.232559 | − | 0.134268i | −0.379193 | − | 0.925318i | \(-0.623798\pi\) |
0.611752 | + | 0.791049i | \(0.290465\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 43637.3i | − | 1.59225i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2774.75i | 0.100913i | 0.998726 | + | 0.0504563i | \(0.0160676\pi\) | ||||
−0.998726 | + | 0.0504563i | \(0.983932\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10530.0 | + | 6079.50i | −0.381700 | + | 0.220375i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 931.500 | − | 1613.41i | 0.0336551 | − | 0.0582924i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −45832.5 | + | 15876.8i | −1.65052 | + | 0.571755i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1027.50 | + | 593.227i | 0.0368815 | + | 0.0212935i | 0.518327 | − | 0.855182i | \(-0.326555\pi\) |
−0.481446 | + | 0.876476i | \(0.659888\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3658.00 | + | 6335.84i | 0.130874 | + | 0.226681i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 33840.0 | 1.20678 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19502.0 | 0.693213 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 17303.0 | + | 29969.7i | 0.613058 | + | 1.06185i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22009.5 | + | 12707.2i | 0.777296 | + | 0.448772i | 0.835471 | − | 0.549534i | \(-0.185195\pi\) |
−0.0581749 | + | 0.998306i | \(0.518528\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5414.50 | + | 2164.20i | 0.190605 | + | 0.0761855i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1273.50 | − | 2205.77i | 0.0446865 | − | 0.0773993i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4252.50 | + | 2455.18i | −0.148740 | + | 0.0858749i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 13870.3i | − | 0.483588i | −0.970328 | − | 0.241794i | \(-0.922264\pi\) | ||
0.970328 | − | 0.241794i | \(-0.0777358\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 9188.53i | − | 0.319336i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8851.50 | − | 5110.42i | 0.306643 | − | 0.177040i | −0.338781 | − | 0.940865i | \(-0.610014\pi\) |
0.645423 | + | 0.763825i | \(0.276681\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13122.0 | + | 22728.0i | −0.453140 | + | 0.784862i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1669.50 | + | 4819.43i | 0.0574697 | + | 0.165901i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11686.5 | − | 6747.20i | −0.401014 | − | 0.231526i | 0.285907 | − | 0.958257i | \(-0.407705\pi\) |
−0.686921 | + | 0.726732i | \(0.741038\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13980.0 | − | 24214.1i | −0.478198 | − | 0.828263i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 495.000 | 0.0168785 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6966.00 | 0.236780 | 0.118390 | − | 0.992967i | \(-0.462227\pi\) | ||||
0.118390 | + | 0.992967i | \(0.462227\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2929.50 | + | 5074.04i | 0.0992632 | + | 0.171929i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2025.00 | − | 1169.13i | −0.0684002 | − | 0.0394909i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7213.50 | + | 37482.4i | −0.242895 | + | 1.26212i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14751.0 | − | 25549.5i | 0.495150 | − | 0.857624i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 37323.0 | − | 21548.4i | 1.24893 | − | 0.721068i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6832.94i | 0.227938i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15979.9i | 0.531416i | 0.964054 | + | 0.265708i | \(0.0856057\pi\) | ||||
−0.964054 | + | 0.265708i | \(0.914394\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −535.500 | + | 309.171i | −0.0177531 | + | 0.0102497i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11074.5 | − | 19181.6i | 0.366012 | − | 0.633951i | −0.622926 | − | 0.782281i | \(-0.714056\pi\) |
0.988938 | + | 0.148329i | \(0.0473896\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15512.0 | − | 13433.8i | −0.511091 | − | 0.442618i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5880.00 | + | 3394.82i | 0.193139 | + | 0.111509i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13369.5 | − | 23156.7i | −0.437798 | − | 0.758288i | 0.559722 | − | 0.828681i | \(-0.310908\pi\) |
−0.997519 | + | 0.0703930i | \(0.977575\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4995.00 | −0.163065 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −20566.0 | −0.669339 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2623.50 | + | 4544.04i | 0.0851238 | + | 0.147439i | 0.905444 | − | 0.424466i | \(-0.139538\pi\) |
−0.820320 | + | 0.571905i | \(0.806205\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14661.0 | − | 8464.53i | −0.474252 | − | 0.273810i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7938.00 | + | 6874.51i | 0.255997 | + | 0.221700i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 17739.0 | − | 30724.8i | 0.570341 | − | 0.987860i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30430.5 | − | 17569.1i | 0.975436 | − | 0.563168i | 0.0745466 | − | 0.997218i | \(-0.476249\pi\) |
0.900889 | + | 0.434050i | \(0.142916\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9185.07i | 0.293534i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9108.86i | 0.290221i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19279.5 | − | 11131.0i | 0.612425 | − | 0.353584i | −0.161489 | − | 0.986875i | \(-0.551630\pi\) |
0.773914 | + | 0.633291i | \(0.218296\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5273.50 | − | 9133.97i | 0.167013 | − | 0.289275i |
(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 | 112.4.p.b.47.1 | yes | 2 | |
4.3 | odd | 2 | 112.4.p.c.47.1 | yes | 2 | ||
7.2 | even | 3 | 784.4.f.c.783.2 | 2 | |||
7.3 | odd | 6 | 112.4.p.c.31.1 | yes | 2 | ||
7.5 | odd | 6 | 784.4.f.b.783.1 | 2 | |||
8.3 | odd | 2 | 448.4.p.b.383.1 | 2 | |||
8.5 | even | 2 | 448.4.p.c.383.1 | 2 | |||
28.3 | even | 6 | inner | 112.4.p.b.31.1 | ✓ | 2 | |
28.19 | even | 6 | 784.4.f.c.783.1 | 2 | |||
28.23 | odd | 6 | 784.4.f.b.783.2 | 2 | |||
56.3 | even | 6 | 448.4.p.c.255.1 | 2 | |||
56.45 | odd | 6 | 448.4.p.b.255.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.4.p.b.31.1 | ✓ | 2 | 28.3 | even | 6 | inner | |
112.4.p.b.47.1 | yes | 2 | 1.1 | even | 1 | trivial | |
112.4.p.c.31.1 | yes | 2 | 7.3 | odd | 6 | ||
112.4.p.c.47.1 | yes | 2 | 4.3 | odd | 2 | ||
448.4.p.b.255.1 | 2 | 56.45 | odd | 6 | |||
448.4.p.b.383.1 | 2 | 8.3 | odd | 2 | |||
448.4.p.c.255.1 | 2 | 56.3 | even | 6 | |||
448.4.p.c.383.1 | 2 | 8.5 | even | 2 | |||
784.4.f.b.783.1 | 2 | 7.5 | odd | 6 | |||
784.4.f.b.783.2 | 2 | 28.23 | odd | 6 | |||
784.4.f.c.783.1 | 2 | 28.19 | even | 6 | |||
784.4.f.c.783.2 | 2 | 7.2 | even | 3 |