Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [98,5,Mod(19,98)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(98, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("98.19");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 98 = 2 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 98.d (of order \(6\), degree \(2\), not 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: | \(10.1302563822\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.339738624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.1 | ||
Root | \(-1.60021 - 0.923880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 98.31 |
Dual form | 98.5.d.c.19.1 |
$q$-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 \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | − | 2.44949i | −0.353553 | − | 0.612372i | ||||
\(3\) | −1.76104 | − | 1.01673i | −0.195671 | − | 0.112970i | 0.398964 | − | 0.916967i | \(-0.369370\pi\) |
−0.594634 | + | 0.803996i | \(0.702703\pi\) | |||||||
\(4\) | −4.00000 | + | 6.92820i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0.615721 | − | 0.355487i | 0.0246289 | − | 0.0142195i | −0.487635 | − | 0.873048i | \(-0.662140\pi\) |
0.512264 | + | 0.858828i | \(0.328807\pi\) | |||||||
\(6\) | 5.75152i | 0.159764i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 22.6274 | 0.353553 | ||||||||
\(9\) | −38.4325 | − | 66.5670i | −0.474475 | − | 0.821815i | ||||
\(10\) | −1.74152 | − | 1.00547i | −0.0174152 | − | 0.0100547i | ||||
\(11\) | −75.8320 | + | 131.345i | −0.626711 | + | 1.08549i | 0.361497 | + | 0.932373i | \(0.382266\pi\) |
−0.988207 | + | 0.153121i | \(0.951067\pi\) | |||||||
\(12\) | 14.0883 | − | 8.13387i | 0.0978353 | − | 0.0564852i | ||||
\(13\) | 260.864i | 1.54358i | 0.635880 | + | 0.771788i | \(0.280637\pi\) | ||||
−0.635880 | + | 0.771788i | \(0.719363\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.44574 | −0.00642552 | ||||||||
\(16\) | −32.0000 | − | 55.4256i | −0.125000 | − | 0.216506i | ||||
\(17\) | 333.938 | + | 192.799i | 1.15549 | + | 0.667125i | 0.950220 | − | 0.311580i | \(-0.100858\pi\) |
0.205274 | + | 0.978705i | \(0.434191\pi\) | |||||||
\(18\) | −108.704 | + | 188.280i | −0.335505 | + | 0.581111i | ||||
\(19\) | 337.871 | − | 195.070i | 0.935931 | − | 0.540360i | 0.0472483 | − | 0.998883i | \(-0.484955\pi\) |
0.888682 | + | 0.458523i | \(0.151621\pi\) | |||||||
\(20\) | 5.68779i | 0.0142195i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 428.971 | 0.886303 | ||||||||
\(23\) | 88.8234 | + | 153.847i | 0.167908 | + | 0.290825i | 0.937684 | − | 0.347489i | \(-0.112965\pi\) |
−0.769776 | + | 0.638314i | \(0.779632\pi\) | |||||||
\(24\) | −39.8477 | − | 23.0061i | −0.0691800 | − | 0.0399411i | ||||
\(25\) | −312.247 | + | 540.828i | −0.499596 | + | 0.865325i | ||||
\(26\) | 638.984 | − | 368.918i | 0.945243 | − | 0.545736i | ||||
\(27\) | 321.013i | 0.440348i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −320.887 | −0.381554 | −0.190777 | − | 0.981633i | \(-0.561101\pi\) | ||||
−0.190777 | + | 0.981633i | \(0.561101\pi\) | |||||||
\(30\) | 2.04459 | + | 3.54133i | 0.00227177 | + | 0.00393481i | ||||
\(31\) | 1165.99 | + | 673.186i | 1.21331 | + | 0.700506i | 0.963479 | − | 0.267783i | \(-0.0862909\pi\) |
0.249833 | + | 0.968289i | \(0.419624\pi\) | |||||||
\(32\) | −90.5097 | + | 156.767i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 267.086 | − | 154.202i | 0.245258 | − | 0.141600i | ||||
\(34\) | − | 1090.64i | − | 0.943457i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 614.920 | 0.474475 | ||||||||
\(37\) | 398.544 | + | 690.299i | 0.291121 | + | 0.504236i | 0.974075 | − | 0.226225i | \(-0.0726386\pi\) |
−0.682954 | + | 0.730461i | \(0.739305\pi\) | |||||||
\(38\) | −955.643 | − | 551.741i | −0.661803 | − | 0.382092i | ||||
\(39\) | 265.230 | − | 459.391i | 0.174378 | − | 0.302032i | ||||
\(40\) | 13.9322 | − | 8.04375i | 0.00870762 | − | 0.00502734i | ||||
\(41\) | 815.856i | 0.485340i | 0.970109 | + | 0.242670i | \(0.0780232\pi\) | ||||
−0.970109 | + | 0.242670i | \(0.921977\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2167.70 | −1.17236 | −0.586182 | − | 0.810179i | \(-0.699370\pi\) | ||||
−0.586182 | + | 0.810179i | \(0.699370\pi\) | |||||||
\(44\) | −606.656 | − | 1050.76i | −0.313355 | − | 0.542747i | ||||
\(45\) | −47.3274 | − | 27.3245i | −0.0233716 | − | 0.0134936i | ||||
\(46\) | 251.230 | − | 435.144i | 0.118729 | − | 0.205645i | ||||
\(47\) | −3711.45 | + | 2142.80i | −1.68015 | + | 0.970034i | −0.718589 | + | 0.695435i | \(0.755212\pi\) |
−0.961559 | + | 0.274598i | \(0.911455\pi\) | |||||||
\(48\) | 130.142i | 0.0564852i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1766.34 | 0.706535 | ||||||||
\(51\) | −392.051 | − | 679.052i | −0.150731 | − | 0.261073i | ||||
\(52\) | −1807.32 | − | 1043.46i | −0.668388 | − | 0.385894i | ||||
\(53\) | 1585.78 | − | 2746.66i | 0.564536 | − | 0.977806i | −0.432556 | − | 0.901607i | \(-0.642388\pi\) |
0.997093 | − | 0.0761987i | \(-0.0242783\pi\) | |||||||
\(54\) | 786.319 | − | 453.982i | 0.269657 | − | 0.155686i | ||||
\(55\) | 107.829i | 0.0356460i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −793.337 | −0.244179 | ||||||||
\(58\) | 453.803 | + | 786.010i | 0.134900 | + | 0.233653i | ||||
\(59\) | −4075.86 | − | 2353.20i | −1.17089 | − | 0.676012i | −0.216998 | − | 0.976172i | \(-0.569627\pi\) |
−0.953889 | + | 0.300160i | \(0.902960\pi\) | |||||||
\(60\) | 5.78297 | − | 10.0164i | 0.00160638 | − | 0.00278233i | ||||
\(61\) | −2195.18 | + | 1267.39i | −0.589944 | + | 0.340604i | −0.765075 | − | 0.643941i | \(-0.777298\pi\) |
0.175131 | + | 0.984545i | \(0.443965\pi\) | |||||||
\(62\) | − | 3808.12i | − | 0.990665i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 512.000 | 0.125000 | ||||||||
\(65\) | 92.7338 | + | 160.620i | 0.0219488 | + | 0.0380165i | ||||
\(66\) | −755.432 | − | 436.149i | −0.173423 | − | 0.100126i | ||||
\(67\) | 2046.21 | − | 3544.15i | 0.455828 | − | 0.789518i | −0.542907 | − | 0.839793i | \(-0.682676\pi\) |
0.998735 | + | 0.0502748i | \(0.0160097\pi\) | |||||||
\(68\) | −2671.50 | + | 1542.39i | −0.577747 | + | 0.333562i | ||||
\(69\) | − | 361.239i | − | 0.0758746i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2255.28 | −0.447388 | −0.223694 | − | 0.974659i | \(-0.571812\pi\) | ||||
−0.223694 | + | 0.974659i | \(0.571812\pi\) | |||||||
\(72\) | −869.628 | − | 1506.24i | −0.167752 | − | 0.290556i | ||||
\(73\) | 4029.78 | + | 2326.60i | 0.756198 | + | 0.436591i | 0.827929 | − | 0.560833i | \(-0.189519\pi\) |
−0.0717308 | + | 0.997424i | \(0.522852\pi\) | |||||||
\(74\) | 1127.25 | − | 1952.46i | 0.205853 | − | 0.356549i | ||||
\(75\) | 1099.76 | − | 634.945i | 0.195512 | − | 0.112879i | ||||
\(76\) | 3121.12i | 0.540360i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1500.37 | −0.246608 | ||||||||
\(79\) | 2096.87 | + | 3631.88i | 0.335983 | + | 0.581939i | 0.983673 | − | 0.179965i | \(-0.0575983\pi\) |
−0.647690 | + | 0.761904i | \(0.724265\pi\) | |||||||
\(80\) | −39.4062 | − | 22.7512i | −0.00615721 | − | 0.00355487i | ||||
\(81\) | −2786.65 | + | 4826.61i | −0.424729 | + | 0.735652i | ||||
\(82\) | 1998.43 | − | 1153.80i | 0.297209 | − | 0.171594i | ||||
\(83\) | − | 7799.12i | − | 1.13211i | −0.824367 | − | 0.566056i | \(-0.808468\pi\) | ||
0.824367 | − | 0.566056i | \(-0.191532\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 274.150 | 0.0379447 | ||||||||
\(86\) | 3065.59 | + | 5309.76i | 0.414493 | + | 0.717923i | ||||
\(87\) | 565.094 | + | 326.257i | 0.0746590 | + | 0.0431044i | ||||
\(88\) | −1715.88 | + | 2972.00i | −0.221576 | + | 0.383780i | ||||
\(89\) | 8200.49 | − | 4734.55i | 1.03528 | − | 0.597722i | 0.116790 | − | 0.993157i | \(-0.462739\pi\) |
0.918494 | + | 0.395435i | \(0.129406\pi\) | |||||||
\(90\) | 154.571i | 0.0190828i | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1421.17 | −0.167908 | ||||||||
\(93\) | −1368.90 | − | 2371.01i | −0.158273 | − | 0.274137i | ||||
\(94\) | 10497.6 | + | 6060.77i | 1.18804 | + | 0.685917i | ||||
\(95\) | 138.690 | − | 240.217i | 0.0153673 | − | 0.0266169i | ||||
\(96\) | 318.781 | − | 184.049i | 0.0345900 | − | 0.0199705i | ||||
\(97\) | 9945.39i | 1.05701i | 0.848931 | + | 0.528504i | \(0.177247\pi\) | ||||
−0.848931 | + | 0.528504i | \(0.822753\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11657.7 | 1.18944 | ||||||||
\(100\) | −2497.98 | − | 4326.62i | −0.249798 | − | 0.432662i | ||||
\(101\) | −1791.21 | − | 1034.16i | −0.175592 | − | 0.101378i | 0.409628 | − | 0.912253i | \(-0.365659\pi\) |
−0.585220 | + | 0.810875i | \(0.698992\pi\) | |||||||
\(102\) | −1108.89 | + | 1920.65i | −0.106583 | + | 0.184607i | ||||
\(103\) | 2169.19 | − | 1252.38i | 0.204467 | − | 0.118049i | −0.394271 | − | 0.918994i | \(-0.629003\pi\) |
0.598737 | + | 0.800946i | \(0.295669\pi\) | |||||||
\(104\) | 5902.68i | 0.545736i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8970.54 | −0.798375 | ||||||||
\(107\) | −3221.70 | − | 5580.14i | −0.281395 | − | 0.487391i | 0.690333 | − | 0.723491i | \(-0.257464\pi\) |
−0.971729 | + | 0.236100i | \(0.924131\pi\) | |||||||
\(108\) | −2224.05 | − | 1284.05i | −0.190676 | − | 0.110087i | ||||
\(109\) | −11773.0 | + | 20391.5i | −0.990912 | + | 1.71631i | −0.378962 | + | 0.925412i | \(0.623719\pi\) |
−0.611949 | + | 0.790897i | \(0.709614\pi\) | |||||||
\(110\) | 264.126 | − | 152.493i | 0.0218286 | − | 0.0126028i | ||||
\(111\) | − | 1620.85i | − | 0.131552i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 19692.2 | 1.54219 | 0.771096 | − | 0.636719i | \(-0.219709\pi\) | ||||
0.771096 | + | 0.636719i | \(0.219709\pi\) | |||||||
\(114\) | 1121.95 | + | 1943.27i | 0.0863302 | + | 0.149528i | ||||
\(115\) | 109.381 | + | 63.1511i | 0.00827077 | + | 0.00477513i | ||||
\(116\) | 1283.55 | − | 2223.17i | 0.0953886 | − | 0.165218i | ||||
\(117\) | 17365.0 | − | 10025.7i | 1.26853 | − | 0.732389i | ||||
\(118\) | 13311.7i | 0.956025i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −32.7134 | −0.00227177 | ||||||||
\(121\) | −4180.48 | − | 7240.81i | −0.285533 | − | 0.494557i | ||||
\(122\) | 6208.91 | + | 3584.72i | 0.417154 | + | 0.240844i | ||||
\(123\) | 829.509 | − | 1436.75i | 0.0548291 | − | 0.0949667i | ||||
\(124\) | −9327.95 | + | 5385.49i | −0.606656 | + | 0.350253i | ||||
\(125\) | 888.358i | 0.0568549i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12550.5 | −0.778135 | −0.389067 | − | 0.921209i | \(-0.627203\pi\) | ||||
−0.389067 | + | 0.921209i | \(0.627203\pi\) | |||||||
\(128\) | −724.077 | − | 1254.14i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 3817.40 | + | 2203.98i | 0.229397 | + | 0.132442i | ||||
\(130\) | 262.291 | − | 454.301i | 0.0155202 | − | 0.0268817i | ||||
\(131\) | −16734.4 | + | 9661.63i | −0.975143 | + | 0.562999i | −0.900800 | − | 0.434234i | \(-0.857019\pi\) |
−0.0743429 | + | 0.997233i | \(0.523686\pi\) | |||||||
\(132\) | 2467.23i | 0.141600i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −11575.1 | −0.644639 | ||||||||
\(135\) | 114.116 | + | 197.655i | 0.00626151 | + | 0.0108453i | ||||
\(136\) | 7556.15 | + | 4362.54i | 0.408529 | + | 0.235864i | ||||
\(137\) | −1854.29 | + | 3211.73i | −0.0987955 | + | 0.171119i | −0.911186 | − | 0.411994i | \(-0.864832\pi\) |
0.812391 | + | 0.583113i | \(0.198166\pi\) | |||||||
\(138\) | −884.851 | + | 510.869i | −0.0464635 | + | 0.0268257i | ||||
\(139\) | 1096.09i | 0.0567307i | 0.999598 | + | 0.0283653i | \(0.00903018\pi\) | ||||
−0.999598 | + | 0.0283653i | \(0.990970\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8714.65 | 0.438341 | ||||||||
\(142\) | 3189.45 | + | 5524.29i | 0.158175 | + | 0.273968i | ||||
\(143\) | −34263.2 | − | 19781.9i | −1.67554 | − | 0.967375i | ||||
\(144\) | −2459.68 | + | 4260.29i | −0.118619 | + | 0.205454i | ||||
\(145\) | −197.577 | + | 114.071i | −0.00939725 | + | 0.00542551i | ||||
\(146\) | − | 13161.2i | − | 0.617433i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6376.71 | −0.291121 | ||||||||
\(149\) | 616.908 | + | 1068.52i | 0.0277874 | + | 0.0481291i | 0.879585 | − | 0.475742i | \(-0.157821\pi\) |
−0.851797 | + | 0.523872i | \(0.824487\pi\) | |||||||
\(150\) | −3110.58 | − | 1795.90i | −0.138248 | − | 0.0798176i | ||||
\(151\) | 21336.4 | − | 36955.7i | 0.935766 | − | 1.62079i | 0.162503 | − | 0.986708i | \(-0.448043\pi\) |
0.773262 | − | 0.634086i | \(-0.218624\pi\) | |||||||
\(152\) | 7645.15 | − | 4413.93i | 0.330901 | − | 0.191046i | ||||
\(153\) | − | 29639.0i | − | 1.26614i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 957.236 | 0.0398433 | ||||||||
\(156\) | 2121.84 | + | 3675.13i | 0.0871892 | + | 0.151016i | ||||
\(157\) | 25881.1 | + | 14942.5i | 1.04999 | + | 0.606209i | 0.922645 | − | 0.385650i | \(-0.126023\pi\) |
0.127340 | + | 0.991859i | \(0.459356\pi\) | |||||||
\(158\) | 5930.84 | − | 10272.5i | 0.237576 | − | 0.411493i | ||||
\(159\) | −5585.24 | + | 3224.64i | −0.220926 | + | 0.127552i | ||||
\(160\) | 128.700i | 0.00502734i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 15763.7 | 0.600658 | ||||||||
\(163\) | 13102.6 | + | 22694.4i | 0.493154 | + | 0.854168i | 0.999969 | − | 0.00788711i | \(-0.00251057\pi\) |
−0.506815 | + | 0.862055i | \(0.669177\pi\) | |||||||
\(164\) | −5652.42 | − | 3263.43i | −0.210158 | − | 0.121335i | ||||
\(165\) | 109.634 | − | 189.891i | 0.00402694 | − | 0.00697487i | ||||
\(166\) | −19103.9 | + | 11029.6i | −0.693275 | + | 0.400262i | ||||
\(167\) | − | 35887.5i | − | 1.28680i | −0.765532 | − | 0.643398i | \(-0.777524\pi\) | ||
0.765532 | − | 0.643398i | \(-0.222476\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −39489.2 | −1.38263 | ||||||||
\(170\) | −387.707 | − | 671.528i | −0.0134155 | − | 0.0232363i | ||||
\(171\) | −25970.5 | − | 14994.0i | −0.888152 | − | 0.512775i | ||||
\(172\) | 8670.80 | − | 15018.3i | 0.293091 | − | 0.507648i | ||||
\(173\) | 9502.65 | − | 5486.36i | 0.317506 | − | 0.183312i | −0.332774 | − | 0.943007i | \(-0.607985\pi\) |
0.650281 | + | 0.759694i | \(0.274651\pi\) | |||||||
\(174\) | − | 1845.59i | − | 0.0609588i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 9706.50 | 0.313355 | ||||||||
\(177\) | 4785.15 | + | 8288.13i | 0.152739 | + | 0.264551i | ||||
\(178\) | −23194.5 | − | 13391.3i | −0.732057 | − | 0.422653i | ||||
\(179\) | 16922.1 | − | 29309.9i | 0.528138 | − | 0.914761i | −0.471324 | − | 0.881960i | \(-0.656224\pi\) |
0.999462 | − | 0.0328012i | \(-0.0104428\pi\) | |||||||
\(180\) | 378.619 | − | 218.596i | 0.0116858 | − | 0.00674679i | ||||
\(181\) | 50094.5i | 1.52909i | 0.644571 | + | 0.764545i | \(0.277036\pi\) | ||||
−0.644571 | + | 0.764545i | \(0.722964\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5154.39 | 0.153913 | ||||||||
\(184\) | 2009.84 | + | 3481.15i | 0.0593645 | + | 0.102822i | ||||
\(185\) | 490.784 | + | 283.354i | 0.0143399 | + | 0.00827917i | ||||
\(186\) | −3871.84 | + | 6706.23i | −0.111916 | + | 0.193844i | ||||
\(187\) | −50646.3 | + | 29240.7i | −1.44832 | + | 0.836189i | ||||
\(188\) | − | 34284.9i | − | 0.970034i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −784.547 | −0.0217326 | ||||||||
\(191\) | −8806.47 | − | 15253.3i | −0.241399 | − | 0.418115i | 0.719714 | − | 0.694271i | \(-0.244273\pi\) |
−0.961113 | + | 0.276155i | \(0.910940\pi\) | |||||||
\(192\) | −901.650 | − | 520.568i | −0.0244588 | − | 0.0141213i | ||||
\(193\) | −6632.12 | + | 11487.2i | −0.178048 | + | 0.308389i | −0.941212 | − | 0.337817i | \(-0.890312\pi\) |
0.763164 | + | 0.646205i | \(0.223645\pi\) | |||||||
\(194\) | 24361.1 | − | 14064.9i | 0.647282 | − | 0.373709i | ||||
\(195\) | − | 377.143i | − | 0.00991828i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5362.20 | 0.138169 | 0.0690844 | − | 0.997611i | \(-0.477992\pi\) | ||||
0.0690844 | + | 0.997611i | \(0.477992\pi\) | |||||||
\(198\) | −16486.4 | − | 28555.3i | −0.420529 | − | 0.728377i | ||||
\(199\) | 36572.8 | + | 21115.3i | 0.923532 | + | 0.533202i | 0.884760 | − | 0.466047i | \(-0.154322\pi\) |
0.0387720 | + | 0.999248i | \(0.487655\pi\) | |||||||
\(200\) | −7065.35 | + | 12237.5i | −0.176634 | + | 0.305939i | ||||
\(201\) | −7206.91 | + | 4160.91i | −0.178384 | + | 0.102990i | ||||
\(202\) | 5850.08i | 0.143370i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 6272.81 | 0.150731 | ||||||||
\(205\) | 290.026 | + | 502.340i | 0.00690128 | + | 0.0119534i | ||||
\(206\) | −6135.38 | − | 3542.27i | −0.144580 | − | 0.0834731i | ||||
\(207\) | 6827.41 | − | 11825.4i | 0.159336 | − | 0.275979i | ||||
\(208\) | 14458.6 | − | 8347.66i | 0.334194 | − | 0.192947i | ||||
\(209\) | 59170.2i | 1.35460i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −77049.0 | −1.73062 | −0.865311 | − | 0.501236i | \(-0.832879\pi\) | ||||
−0.865311 | + | 0.501236i | \(0.832879\pi\) | |||||||
\(212\) | 12686.3 | + | 21973.2i | 0.282268 | + | 0.488903i | ||||
\(213\) | 3971.63 | + | 2293.02i | 0.0875406 | + | 0.0505416i | ||||
\(214\) | −9112.33 | + | 15783.0i | −0.198977 | + | 0.344638i | ||||
\(215\) | −1334.70 | + | 770.589i | −0.0288740 | + | 0.0166704i | ||||
\(216\) | 7263.71i | 0.155686i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 66598.3 | 1.40136 | ||||||||
\(219\) | −4731.06 | − | 8194.43i | −0.0986438 | − | 0.170856i | ||||
\(220\) | −747.062 | − | 431.317i | −0.0154352 | − | 0.00891150i | ||||
\(221\) | −50294.4 | + | 87112.4i | −1.02976 | + | 1.78359i | ||||
\(222\) | −3970.26 | + | 2292.23i | −0.0805589 | + | 0.0465107i | ||||
\(223\) | 3702.60i | 0.0744555i | 0.999307 | + | 0.0372278i | \(0.0118527\pi\) | ||||
−0.999307 | + | 0.0372278i | \(0.988147\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 48001.8 | 0.948183 | ||||||||
\(226\) | −27849.0 | − | 48235.9i | −0.545247 | − | 0.944396i | ||||
\(227\) | 10408.5 | + | 6009.38i | 0.201994 | + | 0.116621i | 0.597585 | − | 0.801805i | \(-0.296127\pi\) |
−0.395591 | + | 0.918427i | \(0.629460\pi\) | |||||||
\(228\) | 3173.35 | − | 5496.40i | 0.0610447 | − | 0.105733i | ||||
\(229\) | 28891.0 | − | 16680.2i | 0.550924 | − | 0.318076i | −0.198570 | − | 0.980087i | \(-0.563630\pi\) |
0.749495 | + | 0.662010i | \(0.230297\pi\) | |||||||
\(230\) | − | 357.237i | − | 0.00675305i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7260.85 | −0.134900 | ||||||||
\(233\) | −27069.4 | − | 46885.7i | −0.498618 | − | 0.863631i | 0.501381 | − | 0.865226i | \(-0.332825\pi\) |
−0.999999 | + | 0.00159563i | \(0.999492\pi\) | |||||||
\(234\) | −49115.5 | − | 28356.9i | −0.896989 | − | 0.517877i | ||||
\(235\) | −1523.48 | + | 2638.74i | −0.0275867 | + | 0.0477816i | ||||
\(236\) | 32606.9 | − | 18825.6i | 0.585443 | − | 0.338006i | ||||
\(237\) | − | 8527.83i | − | 0.151824i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 29165.4 | 0.510590 | 0.255295 | − | 0.966863i | \(-0.417827\pi\) | ||||
0.255295 | + | 0.966863i | \(0.417827\pi\) | |||||||
\(240\) | 46.2638 | + | 80.1312i | 0.000803190 | + | 0.00139117i | ||||
\(241\) | 86715.3 | + | 50065.1i | 1.49301 | + | 0.861988i | 0.999968 | − | 0.00801977i | \(-0.00255280\pi\) |
0.493039 | + | 0.870007i | \(0.335886\pi\) | |||||||
\(242\) | −11824.2 | + | 20480.1i | −0.201902 | + | 0.349705i | ||||
\(243\) | 32333.2 | − | 18667.6i | 0.547566 | − | 0.316138i | ||||
\(244\) | − | 20278.2i | − | 0.340604i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4692.41 | −0.0775400 | ||||||||
\(247\) | 50886.8 | + | 88138.5i | 0.834086 | + | 1.44468i | ||||
\(248\) | 26383.4 | + | 15232.5i | 0.428971 | + | 0.247666i | ||||
\(249\) | −7929.64 | + | 13734.5i | −0.127895 | + | 0.221521i | ||||
\(250\) | 2176.02 | − | 1256.33i | 0.0348164 | − | 0.0201012i | ||||
\(251\) | 81988.2i | 1.30138i | 0.759344 | + | 0.650690i | \(0.225520\pi\) | ||||
−0.759344 | + | 0.650690i | \(0.774480\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −26942.6 | −0.420919 | ||||||||
\(254\) | 17749.1 | + | 30742.4i | 0.275112 | + | 0.476508i | ||||
\(255\) | −482.788 | − | 278.738i | −0.00742465 | − | 0.00428663i | ||||
\(256\) | −2048.00 | + | 3547.24i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 63890.8 | − | 36887.4i | 0.967324 | − | 0.558485i | 0.0689050 | − | 0.997623i | \(-0.478049\pi\) |
0.898420 | + | 0.439138i | \(0.144716\pi\) | |||||||
\(258\) | − | 12467.6i | − | 0.187302i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1483.74 | −0.0219488 | ||||||||
\(261\) | 12332.5 | + | 21360.5i | 0.181038 | + | 0.313567i | ||||
\(262\) | 47332.1 | + | 27327.2i | 0.689530 | + | 0.398101i | ||||
\(263\) | −19621.8 | + | 33985.9i | −0.283679 | + | 0.491346i | −0.972288 | − | 0.233787i | \(-0.924888\pi\) |
0.688609 | + | 0.725133i | \(0.258222\pi\) | |||||||
\(264\) | 6043.46 | − | 3489.19i | 0.0867117 | − | 0.0500630i | ||||
\(265\) | − | 2254.90i | − | 0.0321096i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −19255.1 | −0.270100 | ||||||||
\(268\) | 16369.7 | + | 28353.2i | 0.227914 | + | 0.394759i | ||||
\(269\) | 8930.08 | + | 5155.78i | 0.123410 | + | 0.0712509i | 0.560434 | − | 0.828199i | \(-0.310634\pi\) |
−0.437024 | + | 0.899450i | \(0.643968\pi\) | |||||||
\(270\) | 322.769 | − | 559.052i | 0.00442756 | − | 0.00766876i | ||||
\(271\) | −32016.3 | + | 18484.6i | −0.435946 | + | 0.251694i | −0.701877 | − | 0.712299i | \(-0.747654\pi\) |
0.265930 | + | 0.963992i | \(0.414321\pi\) | |||||||
\(272\) | − | 24678.3i | − | 0.333562i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10489.5 | 0.139718 | ||||||||
\(275\) | −47356.7 | − | 82024.2i | −0.626204 | − | 1.08462i | ||||
\(276\) | 2502.74 | + | 1444.96i | 0.0328547 | + | 0.0189687i | ||||
\(277\) | 46202.9 | − | 80025.8i | 0.602157 | − | 1.04297i | −0.390337 | − | 0.920672i | \(-0.627641\pi\) |
0.992494 | − | 0.122294i | \(-0.0390252\pi\) | |||||||
\(278\) | 2684.87 | − | 1550.11i | 0.0347403 | − | 0.0200573i | ||||
\(279\) | − | 103489.i | − | 1.32949i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21171.6 | 0.268128 | 0.134064 | − | 0.990973i | \(-0.457197\pi\) | ||||
0.134064 | + | 0.990973i | \(0.457197\pi\) | |||||||
\(282\) | −12324.4 | − | 21346.4i | −0.154977 | − | 0.268428i | ||||
\(283\) | −41625.7 | − | 24032.6i | −0.519743 | − | 0.300074i | 0.217087 | − | 0.976152i | \(-0.430345\pi\) |
−0.736829 | + | 0.676079i | \(0.763678\pi\) | |||||||
\(284\) | 9021.13 | − | 15625.0i | 0.111847 | − | 0.193725i | ||||
\(285\) | −488.475 | + | 282.021i | −0.00601384 | + | 0.00347209i | ||||
\(286\) | 111903.i | 1.36808i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 13914.1 | 0.167752 | ||||||||
\(289\) | 32582.5 | + | 56434.5i | 0.390111 | + | 0.675692i | ||||
\(290\) | 558.833 | + | 322.642i | 0.00664486 | + | 0.00383641i | ||||
\(291\) | 10111.8 | − | 17514.2i | 0.119411 | − | 0.206825i | ||||
\(292\) | −32238.2 | + | 18612.8i | −0.378099 | + | 0.218296i | ||||
\(293\) | − | 26781.1i | − | 0.311956i | −0.987761 | − | 0.155978i | \(-0.950147\pi\) | ||
0.987761 | − | 0.155978i | \(-0.0498528\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3346.12 | −0.0384501 | ||||||||
\(296\) | 9018.02 | + | 15619.7i | 0.102927 | + | 0.178274i | ||||
\(297\) | −42163.5 | − | 24343.1i | −0.477995 | − | 0.275971i | ||||
\(298\) | 1744.88 | − | 3022.22i | 0.0196486 | − | 0.0340324i | ||||
\(299\) | −40133.1 | + | 23170.8i | −0.448911 | + | 0.259179i | ||||
\(300\) | 10159.1i | 0.112879i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −120697. | −1.32337 | ||||||||
\(303\) | 2102.93 | + | 3642.38i | 0.0229055 | + | 0.0396734i | ||||
\(304\) | −21623.7 | − | 12484.5i | −0.233983 | − | 0.135090i | ||||
\(305\) | −901.081 | + | 1560.72i | −0.00968643 | + | 0.0167774i | ||||
\(306\) | −72600.4 | + | 41915.9i | −0.775347 | + | 0.447647i | ||||
\(307\) | − | 69996.0i | − | 0.742671i | −0.928499 | − | 0.371336i | \(-0.878900\pi\) | ||
0.928499 | − | 0.371336i | \(-0.121100\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5093.35 | −0.0533441 | ||||||||
\(310\) | −1353.74 | − | 2344.74i | −0.0140867 | − | 0.0243990i | ||||
\(311\) | −75310.9 | − | 43480.8i | −0.778641 | − | 0.449549i | 0.0573075 | − | 0.998357i | \(-0.481748\pi\) |
−0.835948 | + | 0.548808i | \(0.815082\pi\) | |||||||
\(312\) | 6001.46 | − | 10394.8i | 0.0616521 | − | 0.106785i | ||||
\(313\) | −28720.2 | + | 16581.6i | −0.293156 | + | 0.169253i | −0.639364 | − | 0.768904i | \(-0.720802\pi\) |
0.346208 | + | 0.938158i | \(0.387469\pi\) | |||||||
\(314\) | − | 84527.3i | − | 0.857310i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −33549.9 | −0.335983 | ||||||||
\(317\) | −14603.0 | − | 25293.1i | −0.145319 | − | 0.251700i | 0.784173 | − | 0.620543i | \(-0.213088\pi\) |
−0.929492 | + | 0.368842i | \(0.879754\pi\) | |||||||
\(318\) | 15797.4 | + | 9120.66i | 0.156218 | + | 0.0901928i | ||||
\(319\) | 24333.5 | − | 42146.9i | 0.239124 | − | 0.414175i | ||||
\(320\) | 315.249 | − | 182.009i | 0.00307861 | − | 0.00177743i | ||||
\(321\) | 13102.4i | 0.127157i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 150437. | 1.44195 | ||||||||
\(324\) | −22293.2 | − | 38612.9i | −0.212365 | − | 0.367826i | ||||
\(325\) | −141083. | − | 81454.1i | −1.33569 | − | 0.771164i | ||||
\(326\) | 37059.8 | − | 64189.4i | 0.348713 | − | 0.603988i | ||||
\(327\) | 41465.4 | − | 23940.1i | 0.387784 | − | 0.223887i | ||||
\(328\) | 18460.7i | 0.171594i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −620.181 | −0.00569496 | ||||||||
\(331\) | −83496.6 | − | 144620.i | −0.762102 | − | 1.32000i | −0.941765 | − | 0.336271i | \(-0.890834\pi\) |
0.179664 | − | 0.983728i | \(-0.442499\pi\) | |||||||
\(332\) | 54033.9 | + | 31196.5i | 0.490219 | + | 0.283028i | ||||
\(333\) | 30634.1 | − | 53059.8i | 0.276259 | − | 0.478495i | ||||
\(334\) | −87906.0 | + | 50752.5i | −0.787999 | + | 0.454951i | ||||
\(335\) | − | 2909.61i | − | 0.0259266i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16126.0 | 0.141993 | 0.0709964 | − | 0.997477i | \(-0.477382\pi\) | ||||
0.0709964 | + | 0.997477i | \(0.477382\pi\) | |||||||
\(338\) | 55846.1 | + | 96728.3i | 0.488832 | + | 0.846682i | ||||
\(339\) | −34678.7 | − | 20021.8i | −0.301761 | − | 0.174222i | ||||
\(340\) | −1096.60 | + | 1899.37i | −0.00948617 | + | 0.0164305i | ||||
\(341\) | −176839. | + | 102098.i | −1.52079 | + | 0.878030i | ||||
\(342\) | 84819.2i | 0.725173i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −49049.5 | −0.414493 | ||||||||
\(345\) | −128.416 | − | 222.423i | −0.00107890 | − | 0.00186871i | ||||
\(346\) | −26877.5 | − | 15517.8i | −0.224511 | − | 0.129621i | ||||
\(347\) | −5035.67 | + | 8722.04i | −0.0418214 | + | 0.0724368i | −0.886178 | − | 0.463344i | \(-0.846649\pi\) |
0.844357 | + | 0.535781i | \(0.179983\pi\) | |||||||
\(348\) | −4520.75 | + | 2610.06i | −0.0373295 | + | 0.0215522i | ||||
\(349\) | − | 97674.1i | − | 0.801915i | −0.916097 | − | 0.400958i | \(-0.868677\pi\) | ||
0.916097 | − | 0.400958i | \(-0.131323\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −83740.9 | −0.679710 | ||||||||
\(352\) | −13727.1 | − | 23776.0i | −0.110788 | − | 0.191890i | ||||
\(353\) | −73833.2 | − | 42627.6i | −0.592519 | − | 0.342091i | 0.173574 | − | 0.984821i | \(-0.444468\pi\) |
−0.766093 | + | 0.642730i | \(0.777802\pi\) | |||||||
\(354\) | 13534.5 | − | 23442.4i | 0.108003 | − | 0.187066i | ||||
\(355\) | −1388.63 | + | 801.723i | −0.0110186 | + | 0.00636162i | ||||
\(356\) | 75752.9i | 0.597722i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −95725.6 | −0.746899 | ||||||||
\(359\) | 71119.9 | + | 123183.i | 0.551826 | + | 0.955791i | 0.998143 | + | 0.0609162i | \(0.0194022\pi\) |
−0.446316 | + | 0.894875i | \(0.647264\pi\) | |||||||
\(360\) | −1070.90 | − | 618.283i | −0.00826310 | − | 0.00477070i | ||||
\(361\) | 10944.0 | − | 18955.6i | 0.0839775 | − | 0.145453i | ||||
\(362\) | 122706. | − | 70844.3i | 0.936372 | − | 0.540615i | ||||
\(363\) | 17001.8i | 0.129027i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3308.30 | 0.0248324 | ||||||||
\(366\) | −7289.41 | − | 12625.6i | −0.0544164 | − | 0.0942520i | ||||
\(367\) | 154015. | + | 88920.4i | 1.14348 | + | 0.660191i | 0.947291 | − | 0.320375i | \(-0.103809\pi\) |
0.196193 | + | 0.980565i | \(0.437142\pi\) | |||||||
\(368\) | 5684.70 | − | 9846.18i | 0.0419770 | − | 0.0727063i | ||||
\(369\) | 54309.1 | − | 31355.4i | 0.398860 | − | 0.230282i | ||||
\(370\) | − | 1602.90i | − | 0.0117085i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 21902.5 | 0.158273 | ||||||||
\(373\) | 10835.4 | + | 18767.5i | 0.0778803 | + | 0.134893i | 0.902335 | − | 0.431035i | \(-0.141851\pi\) |
−0.824455 | + | 0.565928i | \(0.808518\pi\) | |||||||
\(374\) | 143249. | + | 82705.1i | 1.02412 | + | 0.591275i | ||||
\(375\) | 903.224 | − | 1564.43i | 0.00642293 | − | 0.0111248i | ||||
\(376\) | −83980.4 | + | 48486.1i | −0.594022 | + | 0.342959i | ||||
\(377\) | − | 83708.0i | − | 0.588958i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 125199. | 0.871608 | 0.435804 | − | 0.900042i | \(-0.356464\pi\) | ||||
0.435804 | + | 0.900042i | \(0.356464\pi\) | |||||||
\(380\) | 1109.52 | + | 1921.74i | 0.00768363 | + | 0.0133084i | ||||
\(381\) | 22101.9 | + | 12760.6i | 0.152258 | + | 0.0879062i | ||||
\(382\) | −24908.5 | + | 43142.7i | −0.170695 | + | 0.295652i | ||||
\(383\) | 183086. | − | 105705.i | 1.24813 | − | 0.720605i | 0.277390 | − | 0.960757i | \(-0.410531\pi\) |
0.970735 | + | 0.240152i | \(0.0771973\pi\) | |||||||
\(384\) | 2944.78i | 0.0199705i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 37516.9 | 0.251798 | ||||||||
\(387\) | 83310.2 | + | 144297.i | 0.556258 | + | 0.963467i | ||||
\(388\) | −68903.7 | − | 39781.5i | −0.457698 | − | 0.264252i | ||||
\(389\) | 19580.4 | − | 33914.2i | 0.129396 | − | 0.224121i | −0.794047 | − | 0.607857i | \(-0.792029\pi\) |
0.923443 | + | 0.383736i | \(0.125363\pi\) | |||||||
\(390\) | −923.807 | + | 533.360i | −0.00607368 | + | 0.00350664i | ||||
\(391\) | 68500.3i | 0.448063i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 39293.2 | 0.254409 | ||||||||
\(394\) | −7583.29 | − | 13134.6i | −0.0488501 | − | 0.0846108i | ||||
\(395\) | 2582.17 | + | 1490.82i | 0.0165497 | + | 0.00955500i | ||||
\(396\) | −46630.6 | + | 80766.6i | −0.297359 | + | 0.515041i | ||||
\(397\) | 170195. | − | 98262.3i | 1.07986 | − | 0.623456i | 0.149000 | − | 0.988837i | \(-0.452395\pi\) |
0.930858 | + | 0.365381i | \(0.119061\pi\) | |||||||
\(398\) | − | 119446.i | − | 0.754061i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 39967.6 | 0.249798 | ||||||||
\(401\) | −106825. | − | 185026.i | −0.664330 | − | 1.15065i | −0.979466 | − | 0.201608i | \(-0.935383\pi\) |
0.315136 | − | 0.949047i | \(-0.397950\pi\) | |||||||
\(402\) | 20384.2 | + | 11768.8i | 0.126137 | + | 0.0728251i | ||||
\(403\) | −175610. | + | 304166.i | −1.08128 | + | 1.87284i | ||||
\(404\) | 14329.7 | − | 8273.26i | 0.0877960 | − | 0.0506890i | ||||
\(405\) | 3962.47i | 0.0241577i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −120890. | −0.729794 | ||||||||
\(408\) | −8871.10 | − | 15365.2i | −0.0532914 | − | 0.0923034i | ||||
\(409\) | 30834.0 | + | 17802.0i | 0.184325 | + | 0.106420i | 0.589323 | − | 0.807898i | \(-0.299395\pi\) |
−0.404998 | + | 0.914317i | \(0.632728\pi\) | |||||||
\(410\) | 820.318 | − | 1420.83i | 0.00487994 | − | 0.00845231i | ||||
\(411\) | 6530.95 | − | 3770.65i | 0.0386628 | − | 0.0223220i | ||||
\(412\) | 20038.1i | 0.118049i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −38621.7 | −0.225336 | ||||||||
\(415\) | −2772.49 | − | 4802.09i | −0.0160981 | − | 0.0278826i | ||||
\(416\) | −40895.0 | − | 23610.7i | −0.236311 | − | 0.136434i | ||||
\(417\) | 1114.44 | − | 1930.26i | 0.00640889 | − | 0.0111005i | ||||
\(418\) | 144937. | − | 83679.2i | 0.829518 | − | 0.478922i | ||||
\(419\) | 254947.i | 1.45219i | 0.687597 | + | 0.726093i | \(0.258666\pi\) | ||||
−0.687597 | + | 0.726093i | \(0.741334\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 107186. | 0.604748 | 0.302374 | − | 0.953189i | \(-0.402221\pi\) | ||||
0.302374 | + | 0.953189i | \(0.402221\pi\) | |||||||
\(422\) | 108964. | + | 188731.i | 0.611867 | + | 1.05978i | ||||
\(423\) | 285280. | + | 164707.i | 1.59438 | + | 0.920514i | ||||
\(424\) | 35882.2 | − | 62149.7i | 0.199594 | − | 0.345707i | ||||
\(425\) | −208542. | + | 120402.i | −1.15456 | + | 0.666585i | ||||
\(426\) | − | 12971.3i | − | 0.0714766i | ||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 51547.1 | 0.281395 | ||||||||
\(429\) | 40225.8 | + | 69673.1i | 0.218570 | + | 0.378574i | ||||
\(430\) | 3775.10 | + | 2179.56i | 0.0204170 | + | 0.0117878i | ||||
\(431\) | −59979.2 | + | 103887.i | −0.322884 | + | 0.559251i | −0.981082 | − | 0.193594i | \(-0.937986\pi\) |
0.658198 | + | 0.752845i | \(0.271319\pi\) | |||||||
\(432\) | 17792.4 | − | 10272.4i | 0.0953381 | − | 0.0550435i | ||||
\(433\) | − | 110159.i | − | 0.587547i | −0.955875 | − | 0.293773i | \(-0.905089\pi\) | ||
0.955875 | − | 0.293773i | \(-0.0949111\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 463.921 | 0.00245169 | ||||||||
\(436\) | −94184.2 | − | 163132.i | −0.495456 | − | 0.858155i | ||||
\(437\) | 60021.7 | + | 34653.5i | 0.314301 | + | 0.181462i | ||||
\(438\) | −13381.4 | + | 23177.4i | −0.0697517 | + | 0.120814i | ||||
\(439\) | 305096. | − | 176148.i | 1.58310 | − | 0.914003i | 0.588696 | − | 0.808355i | \(-0.299642\pi\) |
0.994404 | − | 0.105648i | \(-0.0336917\pi\) | |||||||
\(440\) | 2439.90i | 0.0126028i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 284508. | 1.45630 | ||||||||
\(443\) | −142866. | − | 247452.i | −0.727984 | − | 1.26091i | −0.957734 | − | 0.287656i | \(-0.907124\pi\) |
0.229749 | − | 0.973250i | \(-0.426209\pi\) | |||||||
\(444\) | 11229.6 | + | 6483.41i | 0.0569637 | + | 0.0328880i | ||||
\(445\) | 3366.14 | − | 5830.33i | 0.0169986 | − | 0.0294424i | ||||
\(446\) | 9069.48 | − | 5236.27i | 0.0455945 | − | 0.0263240i | ||||
\(447\) | − | 2508.92i | − | 0.0125566i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −342184. | −1.69733 | −0.848667 | − | 0.528927i | \(-0.822594\pi\) | ||||
−0.848667 | + | 0.528927i | \(0.822594\pi\) | |||||||
\(450\) | −67884.8 | − | 117580.i | −0.335233 | − | 0.580641i | ||||
\(451\) | −107159. | − | 61868.0i | −0.526834 | − | 0.304168i | ||||
\(452\) | −78769.0 | + | 136432.i | −0.385548 | + | 0.667788i | ||||
\(453\) | −75148.3 | + | 43386.9i | −0.366204 | + | 0.211428i | ||||
\(454\) | − | 33994.2i | − | 0.164927i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −17951.2 | −0.0863302 | ||||||||
\(457\) | 138812. | + | 240430.i | 0.664653 | + | 1.15121i | 0.979379 | + | 0.202030i | \(0.0647540\pi\) |
−0.314726 | + | 0.949183i | \(0.601913\pi\) | |||||||
\(458\) | −81716.2 | − | 47178.8i | −0.389562 | − | 0.224914i | ||||
\(459\) | −61891.1 | + | 107199.i | −0.293767 | + | 0.508819i | ||||
\(460\) | −875.047 | + | 505.209i | −0.00413538 | + | 0.00238757i | ||||
\(461\) | 361934.i | 1.70305i | 0.524315 | + | 0.851524i | \(0.324322\pi\) | ||||
−0.524315 | + | 0.851524i | \(0.675678\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 146876. | 0.685153 | 0.342577 | − | 0.939490i | \(-0.388700\pi\) | ||||
0.342577 | + | 0.939490i | \(0.388700\pi\) | |||||||
\(464\) | 10268.4 | + | 17785.4i | 0.0476943 | + | 0.0826090i | ||||
\(465\) | −1685.73 | − | 973.255i | −0.00779617 | − | 0.00450112i | ||||
\(466\) | −76564.0 | + | 132613.i | −0.352576 | + | 0.610679i | ||||
\(467\) | −232450. | + | 134205.i | −1.06585 | + | 0.615367i | −0.927044 | − | 0.374953i | \(-0.877659\pi\) |
−0.138803 | + | 0.990320i | \(0.544326\pi\) | |||||||
\(468\) | 160411.i | 0.732389i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 8618.09 | 0.0390136 | ||||||||
\(471\) | −30385.0 | − | 52628.4i | −0.136968 | − | 0.237235i | ||||
\(472\) | −92226.1 | − | 53246.8i | −0.413971 | − | 0.239006i | ||||
\(473\) | 164381. | − | 284716.i | 0.734733 | − | 1.27259i | ||||
\(474\) | −20888.8 | + | 12060.2i | −0.0929731 | + | 0.0536780i | ||||
\(475\) | 243640.i | 1.07985i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −243782. | −1.07143 | ||||||||
\(478\) | −41246.1 | − | 71440.4i | −0.180521 | − | 0.312671i | ||||
\(479\) | 134481. | + | 77642.5i | 0.586124 | + | 0.338399i | 0.763563 | − | 0.645733i | \(-0.223448\pi\) |
−0.177440 | + | 0.984132i | \(0.556781\pi\) | |||||||
\(480\) | 130.854 | − | 226.645i | 0.000567941 | − | 0.000983703i | ||||
\(481\) | −180074. | + | 103966.i | −0.778326 | + | 0.449367i | ||||
\(482\) | − | 283211.i | − | 1.21903i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 66887.7 | 0.285533 | ||||||||
\(485\) | 3535.46 | + | 6123.59i | 0.0150301 | + | 0.0260329i | ||||
\(486\) | −91452.2 | − | 52800.0i | −0.387188 | − | 0.223543i | ||||
\(487\) | 77813.9 | − | 134778.i | 0.328095 | − | 0.568277i | −0.654039 | − | 0.756461i | \(-0.726927\pi\) |
0.982134 | + | 0.188184i | \(0.0602601\pi\) | |||||||
\(488\) | −49671.3 | + | 28677.7i | −0.208577 | + | 0.120422i | ||||
\(489\) | − | 53287.5i | − | 0.222847i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 37550.7 | 0.155760 | 0.0778798 | − | 0.996963i | \(-0.475185\pi\) | ||||
0.0778798 | + | 0.996963i | \(0.475185\pi\) | |||||||
\(492\) | 6636.07 | + | 11494.0i | 0.0274145 | + | 0.0474834i | ||||
\(493\) | −107156. | − | 61866.8i | −0.440884 | − | 0.254544i | ||||
\(494\) | 143930. | − | 249293.i | 0.589788 | − | 1.02154i | ||||
\(495\) | 7177.87 | − | 4144.14i | 0.0292944 | − | 0.0169131i | ||||
\(496\) | − | 86167.9i | − | 0.350253i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 44856.8 | 0.180871 | ||||||||
\(499\) | −83910.2 | − | 145337.i | −0.336987 | − | 0.583679i | 0.646877 | − | 0.762594i | \(-0.276075\pi\) |
−0.983865 | + | 0.178915i | \(0.942741\pi\) | |||||||
\(500\) | −6154.72 | − | 3553.43i | −0.0246189 | − | 0.0142137i | ||||
\(501\) | −36488.0 | + | 63199.1i | −0.145370 | + | 0.251788i | ||||
\(502\) | 200829. | − | 115949.i | 0.796929 | − | 0.460107i | ||||
\(503\) | − | 133035.i | − | 0.525810i | −0.964822 | − | 0.262905i | \(-0.915319\pi\) | ||
0.964822 | − | 0.262905i | \(-0.0846806\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1470.52 | −0.00576617 | ||||||||
\(506\) | 38102.6 | + | 65995.7i | 0.148817 | + | 0.257759i | ||||
\(507\) | 69541.8 | + | 40150.0i | 0.270539 | + | 0.156196i | ||||
\(508\) | 50202.1 | − | 86952.7i | 0.194534 | − | 0.336942i | ||||
\(509\) | −197449. | + | 113997.i | −0.762112 | + | 0.440005i | −0.830053 | − | 0.557684i | \(-0.811690\pi\) |
0.0679416 | + | 0.997689i | \(0.478357\pi\) | |||||||
\(510\) | 1576.78i | 0.00606220i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 11585.2 | 0.0441942 | ||||||||
\(513\) | 62620.1 | + | 108461.i | 0.237946 | + | 0.412135i | ||||
\(514\) | −180711. | − | 104333.i | −0.684002 | − | 0.394909i | ||||
\(515\) | 890.410 | − | 1542.23i | 0.00335719 | − | 0.00581482i | ||||
\(516\) | −30539.2 | + | 17631.8i | −0.114699 | + | 0.0662212i | ||||
\(517\) | − | 649973.i | − | 2.43172i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −22312.7 | −0.0828355 | ||||||||
\(520\) | 2098.33 | + | 3634.41i | 0.00776009 | + | 0.0134409i | ||||
\(521\) | −295670. | − | 170705.i | −1.08926 | − | 0.628885i | −0.155882 | − | 0.987776i | \(-0.549822\pi\) |
−0.933380 | + | 0.358890i | \(0.883155\pi\) | |||||||
\(522\) | 34881.6 | − | 60416.7i | 0.128013 | − | 0.221726i | ||||
\(523\) | 54483.4 | − | 31456.0i | 0.199187 | − | 0.115001i | −0.397089 | − | 0.917780i | \(-0.629980\pi\) |
0.596276 | + | 0.802779i | \(0.296646\pi\) | |||||||
\(524\) | − | 154586.i | − | 0.562999i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 110998. | 0.401182 | ||||||||
\(527\) | 259579. | + | 449605.i | 0.934650 | + | 1.61886i | ||||
\(528\) | −17093.5 | − | 9868.93i | −0.0613144 | − | 0.0353999i | ||||
\(529\) | 124141. | − | 215019.i | 0.443614 | − | 0.768362i | ||||
\(530\) | −5523.35 | + | 3188.91i | −0.0196631 | + | 0.0113525i | ||||
\(531\) | 361757.i | 1.28300i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −212828. | −0.749159 | ||||||||
\(534\) | 27230.9 | + | 47165.2i | 0.0954946 | + | 0.165402i | ||||
\(535\) | −3967.33 | − | 2290.54i | −0.0138609 | − | 0.00800259i | ||||
\(536\) | 46300.5 | − | 80194.9i | 0.161160 | − | 0.279137i | ||||
\(537\) | −59600.7 | + | 34410.5i | −0.206682 | + | 0.119328i | ||||
\(538\) | − | 29165.5i | − | 0.100764i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1825.86 | −0.00626151 | ||||||||
\(541\) | −125601. | − | 217548.i | −0.429141 | − | 0.743294i | 0.567656 | − | 0.823266i | \(-0.307850\pi\) |
−0.996797 | + | 0.0799715i | \(0.974517\pi\) | |||||||
\(542\) | 90555.9 | + | 52282.5i | 0.308261 | + | 0.177974i | ||||
\(543\) | 50932.8 | − | 88218.2i | 0.172742 | − | 0.299198i | ||||
\(544\) | −60449.2 | + | 34900.4i | −0.204264 | + | 0.117932i | ||||
\(545\) | 16740.6i | 0.0563610i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −153431. | −0.512789 | −0.256395 | − | 0.966572i | \(-0.582535\pi\) | ||||
−0.256395 | + | 0.966572i | \(0.582535\pi\) | |||||||
\(548\) | −14834.3 | − | 25693.8i | −0.0493978 | − | 0.0855594i | ||||
\(549\) | 168733. | + | 97417.9i | 0.559828 | + | 0.323217i | ||||
\(550\) | −133945. | + | 231999.i | −0.442793 | + | 0.766940i | ||||
\(551\) | −108419. | + | 62595.5i | −0.357109 | + | 0.206177i | ||||
\(552\) | − | 8173.91i | − | 0.0268257i | ||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −261363. | −0.851579 | ||||||||
\(555\) | −576.192 | − | 997.994i | −0.00187060 | − | 0.00323998i | ||||
\(556\) | −7593.96 | − | 4384.37i | −0.0245651 | − | 0.0141827i | ||||
\(557\) | 237576. | − | 411493.i | 0.765758 | − | 1.32633i | −0.174087 | − | 0.984730i | \(-0.555697\pi\) |
0.939845 | − | 0.341601i | \(-0.110969\pi\) | |||||||
\(558\) | −253495. | + | 146356.i | −0.814144 | + | 0.470046i | ||||
\(559\) | − | 565476.i | − | 1.80963i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 118920. | 0.377858 | ||||||||
\(562\) | −29941.2 | − | 51859.7i | −0.0947975 | − | 0.164194i | ||||
\(563\) | 34196.7 | + | 19743.5i | 0.107887 | + | 0.0622884i | 0.552972 | − | 0.833200i | \(-0.313493\pi\) |
−0.445086 | + | 0.895488i | \(0.646827\pi\) | |||||||
\(564\) | −34858.6 | + | 60376.9i | −0.109585 | + | 0.189807i | ||||
\(565\) | 12124.9 | − | 7000.34i | 0.0379824 | − | 0.0219292i | ||||
\(566\) | 135949.i | 0.424368i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −51031.2 | −0.158175 | ||||||||
\(569\) | 42653.8 | + | 73878.6i | 0.131745 | + | 0.228189i | 0.924349 | − | 0.381547i | \(-0.124609\pi\) |
−0.792604 | + | 0.609736i | \(0.791275\pi\) | |||||||
\(570\) | 1381.61 | + | 797.676i | 0.00425243 | + | 0.00245514i | ||||
\(571\) | −44549.5 | + | 77162.0i | −0.136638 | + | 0.236664i | −0.926222 | − | 0.376979i | \(-0.876963\pi\) |
0.789584 | + | 0.613642i | \(0.210296\pi\) | |||||||
\(572\) | 274105. | − | 158255.i | 0.837772 | − | 0.483688i | ||||
\(573\) | 35815.4i | 0.109084i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −110939. | −0.335545 | ||||||||
\(576\) | −19677.4 | − | 34082.3i | −0.0593094 | − | 0.102727i | ||||
\(577\) | −269400. | − | 155538.i | −0.809181 | − | 0.467181i | 0.0374905 | − | 0.999297i | \(-0.488064\pi\) |
−0.846671 | + | 0.532116i | \(0.821397\pi\) | |||||||
\(578\) | 92157.1 | − | 159621.i | 0.275850 | − | 0.477786i | ||||
\(579\) | 23358.8 | − | 13486.2i | 0.0696776 | − | 0.0402284i | ||||
\(580\) | − | 1825.14i | − | 0.00542551i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −57201.1 | −0.168872 | ||||||||
\(583\) | 240506. | + | 416569.i | 0.707602 | + | 1.22560i | ||||
\(584\) | 91183.5 | + | 52644.8i | 0.267356 | + | 0.154358i | ||||
\(585\) | 7127.99 | − | 12346.0i | 0.0208284 | − | 0.0360758i | ||||
\(586\) | −65600.0 | + | 37874.2i | −0.191033 | + | 0.110293i | ||||
\(587\) | 62466.3i | 0.181288i | 0.995883 | + | 0.0906440i | \(0.0288926\pi\) | ||||
−0.995883 | + | 0.0906440i | \(0.971107\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 525274. | 1.51410 | ||||||||
\(590\) | 4732.13 | + | 8196.30i | 0.0135942 | + | 0.0235458i | ||||
\(591\) | −9443.01 | − | 5451.93i | −0.0270356 | − | 0.0156090i | ||||
\(592\) | 25506.8 | − | 44179.1i | 0.0727802 | − | 0.126059i | ||||
\(593\) | −41194.5 | + | 23783.7i | −0.117147 | + | 0.0676346i | −0.557428 | − | 0.830225i | \(-0.688212\pi\) |
0.440282 | + | 0.897860i | \(0.354879\pi\) | |||||||
\(594\) | 137705.i | 0.390281i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9870.52 | −0.0277874 | ||||||||
\(597\) | −42937.3 | − | 74369.6i | −0.120472 | − | 0.208664i | ||||
\(598\) | 113513. | + | 65537.0i | 0.317428 | + | 0.183267i | ||||
\(599\) | −282017. | + | 488468.i | −0.785999 | + | 1.36139i | 0.142401 | + | 0.989809i | \(0.454518\pi\) |
−0.928400 | + | 0.371582i | \(0.878815\pi\) | |||||||
\(600\) | 24884.7 | − | 14367.2i | 0.0691240 | − | 0.0399088i | ||||
\(601\) | 255637.i | 0.707740i | 0.935295 | + | 0.353870i | \(0.115135\pi\) | ||||
−0.935295 | + | 0.353870i | \(0.884865\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −314565. | −0.865118 | ||||||||
\(604\) | 170691. | + | 295646.i | 0.467883 | + | 0.810397i | ||||
\(605\) | −5148.03 | − | 2972.22i | −0.0140647 | − | 0.00812025i | ||||
\(606\) | 5947.98 | − | 10302.2i | 0.0161966 | − | 0.0280533i | ||||
\(607\) | 495972. | − | 286350.i | 1.34611 | − | 0.777176i | 0.358412 | − | 0.933564i | \(-0.383318\pi\) |
0.987696 | + | 0.156388i | \(0.0499850\pi\) | |||||||
\(608\) | 70622.8i | 0.191046i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5097.28 | 0.0136987 | ||||||||
\(611\) | −558981. | − | 968184.i | −1.49732 | − | 2.59343i | ||||
\(612\) | 205345. | + | 118556.i | 0.548253 | + | 0.316534i | ||||
\(613\) | −141501. | + | 245087.i | −0.376563 | + | 0.652227i | −0.990560 | − | 0.137082i | \(-0.956228\pi\) |
0.613996 | + | 0.789309i | \(0.289561\pi\) | |||||||
\(614\) | −171455. | + | 98989.3i | −0.454791 | + | 0.262574i | ||||
\(615\) | − | 1179.52i | − | 0.00311856i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 248170. | 0.651896 | 0.325948 | − | 0.945388i | \(-0.394317\pi\) | ||||
0.325948 | + | 0.945388i | \(0.394317\pi\) | |||||||
\(618\) | 7203.09 | + | 12476.1i | 0.0188600 | + | 0.0326665i | ||||
\(619\) | −49006.8 | − | 28294.1i | −0.127901 | − | 0.0738438i | 0.434684 | − | 0.900583i | \(-0.356860\pi\) |
−0.562586 | + | 0.826739i | \(0.690193\pi\) | |||||||
\(620\) | −3828.94 | + | 6631.93i | −0.00996083 | + | 0.0172527i | ||||
\(621\) | −49386.8 | + | 28513.5i | −0.128064 | + | 0.0739379i | ||||
\(622\) | 245964.i | 0.635758i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −33949.4 | −0.0871892 | ||||||||
\(625\) | −194839. | − | 337471.i | −0.498787 | − | 0.863925i | ||||
\(626\) | 81232.9 | + | 46899.8i | 0.207292 | + | 0.119680i | ||||
\(627\) | 60160.3 | − | 104201.i | 0.153029 | − | 0.265055i | ||||
\(628\) | −207049. | + | 119540.i | −0.524993 | + | 0.303105i | ||||
\(629\) | 307356.i | 0.776855i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 681448. | 1.71149 | 0.855744 | − | 0.517399i | \(-0.173100\pi\) | ||||
0.855744 | + | 0.517399i | \(0.173100\pi\) | |||||||
\(632\) | 47446.7 | + | 82180.1i | 0.118788 | + | 0.205747i | ||||
\(633\) | 135686. | + | 78338.3i | 0.338632 | + | 0.195509i | ||||
\(634\) | −41303.5 | + | 71539.8i | −0.102756 | + | 0.177979i | ||||
\(635\) | −7727.63 | + | 4461.55i | −0.0191646 | + | 0.0110647i | ||||
\(636\) | − | 51594.2i | − | 0.127552i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −137651. | −0.338173 | ||||||||
\(639\) | 86676.1 | + | 150127.i | 0.212274 | + | 0.367670i | ||||
\(640\) | −891.660 | − | 514.800i | −0.00217690 | − | 0.00125684i | ||||
\(641\) | −339057. | + | 587264.i | −0.825195 | + | 1.42928i | 0.0765754 | + | 0.997064i | \(0.475601\pi\) |
−0.901770 | + | 0.432216i | \(0.857732\pi\) | |||||||
\(642\) | 32094.3 | − | 18529.6i | 0.0778677 | − | 0.0449569i | ||||
\(643\) | 345520.i | 0.835701i | 0.908516 | + | 0.417851i | \(0.137216\pi\) | ||||
−0.908516 | + | 0.417851i | \(0.862784\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3133.94 | 0.00753305 | ||||||||
\(646\) | −212750. | − | 368494.i | −0.509806 | − | 0.883010i | ||||
\(647\) | 6718.19 | + | 3878.75i | 0.0160489 | + | 0.00926581i | 0.508003 | − | 0.861355i | \(-0.330384\pi\) |
−0.491954 | + | 0.870621i | \(0.663717\pi\) | |||||||
\(648\) | −63054.6 | + | 109214.i | −0.150164 | + | 0.260092i | ||||
\(649\) | 618161. | − | 356895.i | 1.46761 | − | 0.847328i | ||||
\(650\) | 460774.i | 1.09059i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −209642. | −0.493154 | ||||||||
\(653\) | 224236. | + | 388389.i | 0.525872 | + | 0.910836i | 0.999546 | + | 0.0301362i | \(0.00959410\pi\) |
−0.473674 | + | 0.880700i | \(0.657073\pi\) | |||||||
\(654\) | −117282. | − | 67712.7i | −0.274205 | − | 0.158312i | ||||
\(655\) | −6869.17 | + | 11897.7i | −0.0160111 | + | 0.0277321i | ||||
\(656\) | 45219.3 | − | 26107.4i | 0.105079 | − | 0.0606675i | ||||
\(657\) | − | 357667.i | − | 0.828607i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 583660. | 1.34397 | 0.671984 | − | 0.740565i | \(-0.265442\pi\) | ||||
0.671984 | + | 0.740565i | \(0.265442\pi\) | |||||||
\(660\) | 877.069 | + | 1519.13i | 0.00201347 | + | 0.00348744i | ||||
\(661\) | −331589. | − | 191443.i | −0.758922 | − | 0.438164i | 0.0699869 | − | 0.997548i | \(-0.477704\pi\) |
−0.828908 | + | 0.559384i | \(0.811038\pi\) | |||||||
\(662\) | −236164. | + | 409048.i | −0.538887 | + | 0.933380i | ||||
\(663\) | 177140. | − | 102272.i | 0.402986 | − | 0.232664i | ||||
\(664\) | − | 176474.i | − | 0.400262i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −173293. | −0.390689 | ||||||||
\(667\) | −28502.3 | − | 49367.4i | −0.0640661 | − | 0.110966i | ||||
\(668\) | 248636. | + | 143550.i | 0.557199 | + | 0.321699i | ||||
\(669\) | 3764.56 | − | 6520.41i | 0.00841128 | − | 0.0145688i | ||||
\(670\) | −7127.06 | + | 4114.81i | −0.0158767 | + | 0.00916643i | ||||
\(671\) | − | 384435.i | − | 0.853842i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −323802. | −0.714907 | −0.357453 | − | 0.933931i | \(-0.616355\pi\) | ||||
−0.357453 | + | 0.933931i | \(0.616355\pi\) | |||||||
\(674\) | −22805.6 | − | 39500.4i | −0.0502021 | − | 0.0869525i | ||||
\(675\) | −173613. | − | 100236.i | −0.381044 | − | 0.219996i | ||||
\(676\) | 157957. | − | 273589.i | 0.345656 | − | 0.598694i | ||||
\(677\) | 324589. | − | 187402.i | 0.708201 | − | 0.408880i | −0.102194 | − | 0.994765i | \(-0.532586\pi\) |
0.810395 | + | 0.585884i | \(0.199253\pi\) | |||||||
\(678\) | 113260.i | 0.246387i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 6203.31 | 0.0134155 | ||||||||
\(681\) | −12219.9 | − | 21165.5i | −0.0263495 | − | 0.0456387i | ||||
\(682\) | 500177. | + | 288777.i | 1.07536 | + | 0.620861i | ||||
\(683\) | −48682.3 | + | 84320.1i | −0.104359 | + | 0.180755i | −0.913476 | − | 0.406892i | \(-0.866612\pi\) |
0.809117 | + | 0.587647i | \(0.199946\pi\) | |||||||
\(684\) | 207764. | − | 119952.i | 0.444076 | − | 0.256387i | ||||
\(685\) | 2636.71i | 0.00561928i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −67837.5 | −0.143733 | ||||||||
\(688\) | 69366.4 | + | 120146.i | 0.146545 | + | 0.253824i | ||||
\(689\) | 716504. | + | 413674.i | 1.50932 | + | 0.871404i | ||||
\(690\) | −363.215 | + | 629.106i | −0.000762896 | + | 0.00132137i | ||||
\(691\) | −681662. | + | 393558.i | −1.42762 | + | 0.824238i | −0.996933 | − | 0.0782630i | \(-0.975063\pi\) |
−0.430689 | + | 0.902501i | \(0.641729\pi\) | |||||||
\(692\) | 87781.7i | 0.183312i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 28486.1 | 0.0591444 | ||||||||
\(695\) | 389.647 | + | 674.888i | 0.000806681 | + | 0.00139721i | ||||
\(696\) | 12786.6 | + | 7382.35i | 0.0263959 | + | 0.0152397i | ||||
\(697\) | −157296. | + | 272445.i | −0.323782 | + | 0.560807i | ||||
\(698\) | −239252. | + | 138132.i | −0.491071 | + | 0.283520i | ||||
\(699\) | 110090.i | 0.225316i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −232522. | −0.473182 | −0.236591 | − | 0.971609i | \(-0.576030\pi\) | ||||
−0.236591 | + | 0.971609i | \(0.576030\pi\) | |||||||
\(702\) | 118428. | + | 205123.i | 0.240314 | + | 0.416236i | ||||
\(703\) | 269313. | + | 155488.i | 0.544937 | + | 0.314620i | ||||
\(704\) | −38826.0 | + | 67248.6i | −0.0783388 | + | 0.135687i | ||||
\(705\) | 5365.80 | − | 3097.94i | 0.0107958 | − | 0.00623297i | ||||
\(706\) | 241138.i | 0.483790i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −76562.4 | −0.152739 | ||||||||
\(709\) | −75524.5 | − | 130812.i | −0.150243 | − | 0.260229i | 0.781073 | − | 0.624439i | \(-0.214672\pi\) |
−0.931317 | + | 0.364210i | \(0.881339\pi\) | |||||||
\(710\) | 3927.63 | + | 2267.62i | 0.00779136 | + | 0.00449834i | ||||
\(711\) | 161176. | − | 279165.i | 0.318831 | − | 0.552231i | ||||
\(712\) | 185556. | − | 107131.i | 0.366028 | − | 0.211327i | ||||
\(713\) | 239179.i | 0.470483i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −28128.8 | −0.0550223 | ||||||||
\(716\) | 135376. | + | 234479.i | 0.264069 | + | 0.457381i | ||||
\(717\) | −51361.3 | − | 29653.5i | −0.0999074 | − | 0.0576816i | ||||
\(718\) | 201158. | − | 348415.i | 0.390200 | − | 0.675847i | ||||
\(719\) | 616705. | − | 356055.i | 1.19294 | − | 0.688746i | 0.233971 | − | 0.972244i | \(-0.424828\pi\) |
0.958973 | + | 0.283497i | \(0.0914947\pi\) | |||||||
\(720\) | 3497.54i | 0.00674679i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −61908.8 | −0.118762 | ||||||||
\(723\) | −101806. | − | 176333.i | −0.194758 | − | 0.337331i | ||||
\(724\) | −347065. | − | 200378.i | −0.662115 | − | 0.382272i | ||||
\(725\) | 100196. | − | 173545.i | 0.190623 | − | 0.330169i | ||||
\(726\) | 41645.6 | − | 24044.1i | 0.0790126 | − | 0.0456179i | ||||
\(727\) | − | 693160.i | − | 1.31149i | −0.754983 | − | 0.655744i | \(-0.772355\pi\) | ||
0.754983 | − | 0.655744i | \(-0.227645\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 375517. | 0.706601 | ||||||||
\(730\) | −4678.64 | − | 8103.64i | −0.00877958 | − | 0.0152067i | ||||
\(731\) | −723877. | − | 417931.i | −1.35466 | − | 0.782113i | ||||
\(732\) | −20617.6 | + | 35710.7i | −0.0384782 | + | 0.0666463i | ||||
\(733\) | −233054. | + | 134554.i | −0.433759 | + | 0.250431i | −0.700947 | − | 0.713214i | \(-0.747239\pi\) |
0.267188 | + | 0.963644i | \(0.413906\pi\) | |||||||
\(734\) | − | 503010.i | − | 0.933651i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −32157.5 | −0.0593645 | ||||||||
\(737\) | 310337. | + | 537519.i | 0.571345 | + | 0.989599i | ||||
\(738\) | −153609. | − | 88686.5i | −0.282036 | − | 0.162834i | ||||
\(739\) | −43092.6 | + | 74638.5i | −0.0789066 | + | 0.136670i | −0.902778 | − | 0.430106i | \(-0.858476\pi\) |
0.823872 | + | 0.566776i | \(0.191810\pi\) | |||||||
\(740\) | −3926.28 | + | 2266.84i | −0.00716997 | + | 0.00413958i | ||||
\(741\) | − | 206953.i | − | 0.376908i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −457439. | −0.828620 | −0.414310 | − | 0.910136i | \(-0.635977\pi\) | ||||
−0.414310 | + | 0.910136i | \(0.635977\pi\) | |||||||
\(744\) | −30974.7 | − | 53649.8i | −0.0559580 | − | 0.0969220i | ||||
\(745\) | 759.686 | + | 438.605i | 0.00136874 | + | 0.000790244i | ||||
\(746\) | 30647.2 | − | 53082.4i | 0.0550697 | − | 0.0953835i | ||||
\(747\) | −519165. | + | 299740.i | −0.930388 | + | 0.537160i | ||||
\(748\) | − | 467851.i | − | 0.836189i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −5109.41 | −0.00908339 | ||||||||
\(751\) | 290721. | + | 503543.i | 0.515462 | + | 0.892806i | 0.999839 | + | 0.0179464i | \(0.00571284\pi\) |
−0.484377 | + | 0.874859i | \(0.660954\pi\) | |||||||
\(752\) | 237533. | + | 137139.i | 0.420037 | + | 0.242508i | ||||
\(753\) | 83360.2 | − | 144384.i | 0.147017 | − | 0.254642i | ||||
\(754\) | −205042. | + | 118381.i | −0.360662 | + | 0.208228i | ||||
\(755\) | − | 30339.2i | − | 0.0532244i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 398071. | 0.694655 | 0.347327 | − | 0.937744i | \(-0.387089\pi\) | ||||
0.347327 | + | 0.937744i | \(0.387089\pi\) | |||||||
\(758\) | −177058. | − | 306673.i | −0.308160 | − | 0.533749i | ||||
\(759\) | 47446.9 | + | 27393.5i | 0.0823615 | + | 0.0475514i | ||||
\(760\) | 3138.19 | − | 5435.50i | 0.00543315 | − | 0.00941049i | ||||
\(761\) | 280562. | − | 161982.i | 0.484462 | − | 0.279704i | −0.237812 | − | 0.971311i | \(-0.576430\pi\) |
0.722274 | + | 0.691607i | \(0.243097\pi\) | |||||||
\(762\) | − | 72184.6i | − | 0.124318i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 140904. | 0.241399 | ||||||||
\(765\) | −10536.3 | − | 18249.4i | −0.0180038 | − | 0.0311835i | ||||
\(766\) | −517846. | − | 298979.i | −0.882558 | − | 0.509545i | ||||
\(767\) | 613865. | − | 1.06325e6i | 1.04348 | − | 1.80735i | ||||
\(768\) | 7213.20 | − | 4164.54i | 0.0122294 | − | 0.00706065i | ||||
\(769\) | 318602.i | 0.538760i | 0.963034 | + | 0.269380i | \(0.0868187\pi\) | ||||
−0.963034 | + | 0.269380i | \(0.913181\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −150019. | −0.252369 | ||||||||
\(772\) | −53057.0 | − | 91897.4i | −0.0890242 | − | 0.154194i | ||||
\(773\) | 443418. | + | 256007.i | 0.742086 | + | 0.428443i | 0.822827 | − | 0.568292i | \(-0.192395\pi\) |
−0.0807415 | + | 0.996735i | \(0.525729\pi\) | |||||||
\(774\) | 235637. | − | 408135.i | 0.393334 | − | 0.681274i | ||||
\(775\) | −728156. | + | 420401.i | −1.21233 | + | 0.699940i | ||||
\(776\) | 225038.i | 0.373709i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −110763. | −0.182994 | ||||||||
\(779\) | 159149. | + | 275654.i | 0.262258 | + | 0.454244i | ||||
\(780\) | 2612.92 | + | 1508.57i | 0.00429474 | + | 0.00247957i | ||||
\(781\) | 171023. | − | 296220.i | 0.280383 | − | 0.485637i | ||||
\(782\) | 167791. | − | 96874.0i | 0.274381 | − | 0.158414i | ||||
\(783\) | − | 103009.i | − | 0.168017i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 21247.4 | 0.0344799 | ||||||||
\(786\) | −55569.0 | − | 96248.4i | −0.0899472 | − | 0.155793i | ||||
\(787\) | −558516. | − | 322460.i | −0.901751 | − | 0.520626i | −0.0239830 | − | 0.999712i | \(-0.507635\pi\) |
−0.877768 | + | 0.479086i | \(0.840968\pi\) | |||||||
\(788\) | −21448.8 | + | 37150.4i | −0.0345422 | + | 0.0598289i | ||||
\(789\) | 69109.3 | − | 39900.3i | 0.111015 | − | 0.0640946i | ||||
\(790\) | − | 8433.34i | − | 0.0135128i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 263783. | 0.420529 | ||||||||
\(793\) | −330617. | − | 572645.i | −0.525749 | − | 0.910623i | ||||
\(794\) | −481385. | − | 277928.i | −0.763575 | − | 0.440850i | ||||
\(795\) | −2292.63 | + | 3970.96i | −0.00362744 | + | 0.00628291i | ||||
\(796\) | −292582. | + | 168923.i | −0.461766 | + | 0.266601i | ||||
\(797\) | − | 278844.i | − | 0.438980i | −0.975615 | − | 0.219490i | \(-0.929561\pi\) | ||
0.975615 | − | 0.219490i | \(-0.0704393\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.65252e6 | −2.58853 | ||||||||
\(800\) | −56522.8 | − | 97900.3i | −0.0883169 | − | 0.152969i | ||||
\(801\) | −630331. | − | 363922.i | −0.982434 | − | 0.567208i | ||||
\(802\) | −302147. | + | 523333.i | −0.469753 | + | 0.813635i | ||||
\(803\) | −611173. | + | 352861.i | −0.947835 | + | 0.547233i | ||||
\(804\) | − | 66574.6i | − | 0.102990i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 993402. | 1.52917 | ||||||||
\(807\) | −10484.1 | − | 18159.0i | −0.0160985 | − | 0.0278834i | ||||
\(808\) | −40530.5 | − | 23400.3i | −0.0620811 | − | 0.0358426i | ||||
\(809\) | −331260. | + | 573759.i | −0.506142 | + | 0.876663i | 0.493833 | + | 0.869557i | \(0.335595\pi\) |
−0.999975 | + | 0.00710632i | \(0.997738\pi\) | |||||||
\(810\) | 9706.02 | − | 5603.77i | 0.0147935 | − | 0.00854104i | ||||
\(811\) | 586078.i | 0.891073i | 0.895264 | + | 0.445537i | \(0.146987\pi\) | ||||
−0.895264 | + | 0.445537i | \(0.853013\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 75175.9 | 0.113736 | ||||||||
\(814\) | 170964. | + | 296118.i | 0.258021 | + | 0.446906i | ||||
\(815\) | 16135.1 | + | 9315.61i | 0.0242916 | + | 0.0140248i | ||||
\(816\) | −25091.2 | + | 43459.3i | −0.0376827 | + | 0.0652683i | ||||
\(817\) | −732403. | + | 422853.i | −1.09725 | + | 0.633498i | ||||
\(818\) | − | 100704.i | − | 0.150501i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4640.42 | −0.00690128 | ||||||||
\(821\) | −395267. | − | 684623.i | −0.586414 | − | 1.01570i | −0.994698 | − | 0.102844i | \(-0.967206\pi\) |
0.408284 | − | 0.912855i | \(-0.366127\pi\) | |||||||
\(822\) | −18472.3 | − | 10665.0i | −0.0273387 | − | 0.0157840i | ||||
\(823\) | 578225. | − | 1.00151e6i | 0.853684 | − | 1.47862i | −0.0241766 | − | 0.999708i | \(-0.507696\pi\) |
0.877861 | − | 0.478916i | \(-0.158970\pi\) | |||||||
\(824\) | 49083.1 | − | 28338.1i | 0.0722899 | − | 0.0417366i | ||||
\(825\) | 192597.i | 0.282970i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 390408. | 0.570832 | 0.285416 | − | 0.958404i | \(-0.407868\pi\) | ||||
0.285416 | + | 0.958404i | \(0.407868\pi\) | |||||||
\(828\) | 54619.3 | + | 94603.4i | 0.0796682 | + | 0.137989i | ||||
\(829\) | 460055. | + | 265613.i | 0.669423 | + | 0.386492i | 0.795858 | − | 0.605483i | \(-0.207020\pi\) |
−0.126435 | + | 0.991975i | \(0.540353\pi\) | |||||||
\(830\) | −7841.78 | + | 13582.4i | −0.0113830 | + | 0.0197160i | ||||
\(831\) | −162730. | + | 93952.1i | −0.235649 | + | 0.136052i | ||||
\(832\) | 133562.i | 0.192947i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −6304.20 | −0.00906354 | ||||||||
\(835\) | −12757.5 | − | 22096.7i | −0.0182976 | − | 0.0316923i | ||||
\(836\) | −409943. | − | 236681.i | −0.586558 | − | 0.338649i | ||||
\(837\) | −216102. | + | 374300.i | −0.308466 | + | 0.534279i | ||||
\(838\) | 624490. | − | 360550.i | 0.889278 | − | 0.513425i | ||||
\(839\) | − | 263842.i | − | 0.374817i | −0.982282 | − | 0.187409i | \(-0.939991\pi\) | ||
0.982282 | − | 0.187409i | \(-0.0600089\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −604312. | −0.854416 | ||||||||
\(842\) | −151584. | − | 262552.i | −0.213811 | − | 0.370331i | ||||
\(843\) | −37284.0 | − | 21525.9i | −0.0524647 | − | 0.0302905i | ||||
\(844\) | 308196. | − | 533811.i | 0.432655 | − | 0.749381i | ||||
\(845\) | −24314.3 | + | 14037.9i | −0.0340525 | + | 0.0196602i | ||||
\(846\) | − | 931722.i | − | 1.30180i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −202980. | −0.282268 | ||||||||
\(849\) | 48869.5 | + | 84644.5i | 0.0677989 | + | 0.117431i | ||||
\(850\) | 589847. | + | 340548.i | 0.816397 | + | 0.471347i | ||||
\(851\) | −70800.1 | + | 122629.i | −0.0977630 | + | 0.169331i | ||||
\(852\) | −31773.0 | + | 18344.2i | −0.0437703 | + | 0.0252708i | ||||
\(853\) | 1.17089e6i | 1.60923i | 0.593798 | + | 0.804614i | \(0.297628\pi\) | ||||
−0.593798 | + | 0.804614i | \(0.702372\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −21320.8 | −0.0291656 | ||||||||
\(856\) | −72898.6 | − | 126264.i | −0.0994883 | − | 0.172319i | ||||
\(857\) | 367922. | + | 212420.i | 0.500950 | + | 0.289223i | 0.729106 | − | 0.684401i | \(-0.239936\pi\) |
−0.228156 | + | 0.973625i | \(0.573270\pi\) | |||||||
\(858\) | 113776. | − | 197065.i | 0.154552 | − | 0.267692i | ||||
\(859\) | −353490. | + | 204087.i | −0.479061 | + | 0.276586i | −0.720025 | − | 0.693948i | \(-0.755870\pi\) |
0.240964 | + | 0.970534i | \(0.422536\pi\) | |||||||
\(860\) | − | 12329.4i | − | 0.0166704i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 339294. | 0.456627 | ||||||||
\(863\) | 441370. | + | 764476.i | 0.592627 | + | 1.02646i | 0.993877 | + | 0.110492i | \(0.0352425\pi\) |
−0.401250 | + | 0.915969i | \(0.631424\pi\) | |||||||
\(864\) | −50324.4 | − | 29054.8i | −0.0674142 | − | 0.0389216i | ||||
\(865\) | 3900.66 | − | 6756.13i | 0.00521321 | − | 0.00902955i | ||||
\(866\) | −269832. | + | 155788.i | −0.359797 | + | 0.207729i | ||||
\(867\) | − | 132511.i | − | 0.176284i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −636039. | −0.842256 | ||||||||
\(870\) | −656.083 | − | 1136.37i | −0.000866802 | − | 0.00150135i | ||||
\(871\) | 924541. | + | 533784.i | 1.21868 | + | 0.703606i | ||||
\(872\) | −266393. | + | 461406.i | −0.350340 | + | 0.606807i | ||||
\(873\) | 662035. | − | 382226.i | 0.868665 | − | 0.501524i | ||||
\(874\) | − | 196030.i | − | 0.256625i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 75696.9 | 0.0986438 | ||||||||
\(877\) | 297696. | + | 515624.i | 0.387056 | + | 0.670400i | 0.992052 | − | 0.125828i | \(-0.0401588\pi\) |
−0.604996 | + | 0.796228i | \(0.706825\pi\) | |||||||
\(878\) | −862943. | − | 498220.i | −1.11942 | − | 0.646298i | ||||
\(879\) | −27229.2 | + | 47162.4i | −0.0352418 | + | 0.0610405i | ||||
\(880\) | 5976.50 | − | 3450.53i | 0.00771759 | − | 0.00445575i | ||||
\(881\) | 238444.i | 0.307209i | 0.988132 | + | 0.153605i | \(0.0490882\pi\) | ||||
−0.988132 | + | 0.153605i | \(0.950912\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 189523. | 0.243076 | 0.121538 | − | 0.992587i | \(-0.461217\pi\) | ||||
0.121538 | + | 0.992587i | \(0.461217\pi\) | |||||||
\(884\) | −402355. | − | 696899.i | −0.514879 | − | 0.891796i | ||||
\(885\) | 5892.64 | + | 3402.12i | 0.00752356 | + | 0.00434373i | ||||
\(886\) | −404087. | + | 699899.i | −0.514763 | + | 0.891595i | ||||
\(887\) | 709753. | − | 409776.i | 0.902111 | − | 0.520834i | 0.0242268 | − | 0.999706i | \(-0.492288\pi\) |
0.877885 | + | 0.478872i | \(0.158954\pi\) | |||||||
\(888\) | − | 36675.7i | − | 0.0465107i | ||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −19041.8 | −0.0240396 | ||||||||
\(891\) | −422634. | − | 732024.i | −0.532365 | − | 0.922082i | ||||
\(892\) | −25652.4 | − | 14810.4i | −0.0322402 | − | 0.0186139i | ||||
\(893\) | −835993. | + | 1.44798e6i | −1.04833 | + | 1.81577i | ||||
\(894\) | −6145.58 | + | 3548.15i | −0.00768932 | + | 0.00443943i | ||||
\(895\) | − | 24062.3i | − | 0.0300394i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 94234.3 | 0.117118 | ||||||||
\(898\) | 483922. | + | 838177.i | 0.600098 | + | 1.03940i | ||||
\(899\) | −374152. | − | 216017.i | −0.462945 | − | 0.267281i | ||||
\(900\) | −192007. | + | 332566.i | −0.237046 | + | 0.410575i | ||||
\(901\) | 1.05911e6 | − | 611475.i | 1.30464 | − | 0.753232i | ||||
\(902\) | 349978.i | 0.430158i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 445585. | 0.545247 | ||||||||
\(905\) | 17807.9 | + | 30844.3i | 0.0217429 | + | 0.0376597i | ||||
\(906\) | 212551. | + | 122717.i | 0.258945 | + | 0.149502i | ||||
\(907\) | 328809. | − | 569515.i | 0.399696 | − | 0.692294i | −0.593992 | − | 0.804471i | \(-0.702449\pi\) |
0.993688 | + | 0.112177i | \(0.0357824\pi\) | |||||||
\(908\) | −83268.4 | + | 48075.0i | −0.100997 | + | 0.0583106i | ||||
\(909\) | 158981.i | 0.192406i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.32632e6 | 1.59812 | 0.799061 | − | 0.601250i | \(-0.205330\pi\) | ||||
0.799061 | + | 0.601250i | \(0.205330\pi\) | |||||||
\(912\) | 25386.8 | + | 43971.2i | 0.0305223 | + | 0.0528663i | ||||
\(913\) | 1.02437e6 | + | 591423.i | 1.22890 | + | 0.709507i | ||||
\(914\) | 392620. | − | 680038.i | 0.469981 | − | 0.814031i | ||||
\(915\) | 3173.67 | − | 1832.32i | 0.00379070 | − | 0.00218856i | ||||
\(916\) | 266884.i | 0.318076i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 350109. | 0.415449 | ||||||||
\(919\) | 118155. | + | 204651.i | 0.139901 | + | 0.242316i | 0.927459 | − | 0.373925i | \(-0.121988\pi\) |
−0.787558 | + | 0.616241i | \(0.788655\pi\) | |||||||
\(920\) | 2475.01 | + | 1428.95i | 0.00292416 | + | 0.00168826i | ||||
\(921\) | −71167.3 | + | 123265.i | −0.0838999 | + | 0.145319i | ||||
\(922\) | 886553. | − | 511852.i | 1.04290 | − | 0.602119i | ||||
\(923\) | − | 588322.i | − | 0.690577i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −497777. | −0.581770 | ||||||||
\(926\) | −207713. | − | 359770.i | −0.242238 | − | 0.419569i | ||||
\(927\) | −166735. | − | 96264.2i | −0.194029 | − | 0.112023i | ||||
\(928\) | 29043.4 | − | 50304.6i | 0.0337250 | − | 0.0584134i | ||||
\(929\) | 305501. | − | 176381.i | 0.353982 | − | 0.204372i | −0.312456 | − | 0.949932i | \(-0.601152\pi\) |
0.666438 | + | 0.745561i | \(0.267818\pi\) | |||||||
\(930\) | 5505.56i | 0.00636554i | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 433111. | 0.498618 | ||||||||
\(933\) | 88416.8 | + | 153142.i | 0.101571 | + | 0.175927i | ||||
\(934\) | 657467. | + | 379589.i | 0.753668 | + | 0.435130i | ||||
\(935\) | −20789.4 | + | 36008.2i | −0.0237803 | + | 0.0411887i | ||||
\(936\) | 392924. | − | 226855.i | 0.448495 | − | 0.258938i | ||||
\(937\) | − | 113445.i | − | 0.129213i | −0.997911 | − | 0.0646066i | \(-0.979421\pi\) | ||
0.997911 | − | 0.0646066i | \(-0.0205793\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 67436.3 | 0.0764826 | ||||||||
\(940\) | −12187.8 | − | 21109.9i | −0.0137934 | − | 0.0238908i | ||||
\(941\) | 1.01629e6 | + | 586757.i | 1.14773 | + | 0.662642i | 0.948333 | − | 0.317277i | \(-0.102769\pi\) |
0.199396 | + | 0.979919i | \(0.436102\pi\) | |||||||
\(942\) | −85941.8 | + | 148856.i | −0.0968507 | + | 0.167750i | ||||
\(943\) | −125517. | + | 72467.1i | −0.141149 | + | 0.0814925i | ||||
\(944\) | 301209.i | 0.338006i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −929880. | −1.03907 | ||||||||
\(947\) | −135979. | − | 235522.i | −0.151625 | − | 0.262622i | 0.780200 | − | 0.625530i | \(-0.215117\pi\) |
−0.931825 | + | 0.362908i | \(0.881784\pi\) | |||||||
\(948\) | 59082.5 | + | 34111.3i | 0.0657419 | + | 0.0379561i | ||||
\(949\) | −606925. | + | 1.05123e6i | −0.673912 | + | 1.16725i | ||||
\(950\) | 596794. | − | 344559.i | 0.661268 | − | 0.381783i | ||||
\(951\) | 59389.5i | 0.0656672i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 465476. | 0.512520 | 0.256260 | − | 0.966608i | \(-0.417510\pi\) | ||||
0.256260 | + | 0.966608i | \(0.417510\pi\) | |||||||
\(954\) | 344760. | + | 597142.i | 0.378809 | + | 0.656117i | ||||
\(955\) | −10844.7 | − | 6261.17i | −0.0118908 | − | 0.00686513i | ||||
\(956\) | −116662. | + | 202064.i | −0.127647 | + | 0.221092i | ||||
\(957\) | −85704.4 | + | 49481.5i | −0.0935792 | + | 0.0540280i | ||||
\(958\) | − | 439212.i | − | 0.478568i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −740.220 | −0.000803190 | ||||||||
\(961\) | 444600. | + | 770069.i | 0.481418 | + | 0.833840i | ||||
\(962\) | 509327. | + | 294060.i | 0.550360 | + | 0.317750i | ||||
\(963\) | −247636. | + | 428918.i | −0.267030 | + | 0.462510i | ||||
\(964\) | −693722. | + | 400521.i | −0.746503 | + | 0.430994i | ||||
\(965\) | 9430.53i | 0.0101270i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.49573e6 | −1.59956 | −0.799782 | − | 0.600291i | \(-0.795051\pi\) | ||||
−0.799782 | + | 0.600291i | \(0.795051\pi\) | |||||||
\(968\) | −94593.6 | − | 163841.i | −0.100951 | − | 0.174852i | ||||
\(969\) | −264925. | − | 152955.i | −0.282147 | − | 0.162898i | ||||
\(970\) | 9999.78 | − | 17320.1i | 0.0106279 | − | 0.0184080i | ||||
\(971\) | 350328. | − | 202262.i | 0.371567 | − | 0.214524i | −0.302576 | − | 0.953125i | \(-0.597847\pi\) |
0.674143 | + | 0.738601i | \(0.264513\pi\) | |||||||
\(972\) | 298682.i | 0.316138i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −440182. | −0.463996 | ||||||||
\(975\) | 165634. | + | 286887.i | 0.174237 | + | 0.301788i | ||||
\(976\) | 140492. | + | 81112.9i | 0.147486 | + | 0.0851511i | ||||
\(977\) | 825968. | − | 1.43062e6i | 0.865315 | − | 1.49877i | −0.00141922 | − | 0.999999i | \(-0.500452\pi\) |
0.866734 | − | 0.498770i | \(-0.166215\pi\) | |||||||
\(978\) | −130527. | + | 75359.9i | −0.136466 | + | 0.0787884i | ||||
\(979\) | 1.43612e6i | 1.49839i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.80987e6 | 1.88065 | ||||||||
\(982\) | −53104.7 | − | 91980.0i | −0.0550693 | − | 0.0953829i | ||||
\(983\) | −847459. | − | 489281.i | −0.877025 | − | 0.506350i | −0.00734850 | − | 0.999973i | \(-0.502339\pi\) |
−0.869676 | + | 0.493623i | \(0.835672\pi\) | |||||||
\(984\) | 18769.6 | − | 32510.0i | 0.0193850 | − | 0.0335758i | ||||
\(985\) | 3301.62 | − | 1906.19i | 0.00340294 | − | 0.00196469i | ||||
\(986\) | 349971.i | 0.359980i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −814188. | −0.834086 | ||||||||
\(989\) | −192543. | − | 333493.i | −0.196849 | − | 0.340953i | ||||
\(990\) | −20302.1 | − | 11721.4i | −0.0207143 | − | 0.0119594i | ||||
\(991\) | −634268. | + | 1.09859e6i | −0.645841 | + | 1.11863i | 0.338265 | + | 0.941051i | \(0.390160\pi\) |
−0.984107 | + | 0.177579i | \(0.943173\pi\) | |||||||
\(992\) | −211067. | + | 121860.i | −0.214485 | + | 0.123833i | ||||
\(993\) | 339575.i | 0.344380i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 30024.9 | 0.0303274 | ||||||||
\(996\) | −63437.1 | − | 109876.i | −0.0639476 | − | 0.110761i | ||||
\(997\) | −1793.83 | − | 1035.67i | −0.00180464 | − | 0.00104191i | 0.499097 | − | 0.866546i | \(-0.333665\pi\) |
−0.500902 | + | 0.865504i | \(0.666998\pi\) | |||||||
\(998\) | −237334. | + | 411074.i | −0.238286 | + | 0.412724i | ||||
\(999\) | −221595. | + | 127938.i | −0.222039 | + | 0.128194i |
(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 | 98.5.d.c.31.1 | 8 | ||
7.2 | even | 3 | inner | 98.5.d.c.19.2 | 8 | ||
7.3 | odd | 6 | 98.5.b.a.97.3 | ✓ | 4 | ||
7.4 | even | 3 | 98.5.b.a.97.4 | yes | 4 | ||
7.5 | odd | 6 | inner | 98.5.d.c.19.1 | 8 | ||
7.6 | odd | 2 | inner | 98.5.d.c.31.2 | 8 | ||
21.11 | odd | 6 | 882.5.c.c.685.1 | 4 | |||
21.17 | even | 6 | 882.5.c.c.685.2 | 4 | |||
28.3 | even | 6 | 784.5.c.a.97.3 | 4 | |||
28.11 | odd | 6 | 784.5.c.a.97.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
98.5.b.a.97.3 | ✓ | 4 | 7.3 | odd | 6 | ||
98.5.b.a.97.4 | yes | 4 | 7.4 | even | 3 | ||
98.5.d.c.19.1 | 8 | 7.5 | odd | 6 | inner | ||
98.5.d.c.19.2 | 8 | 7.2 | even | 3 | inner | ||
98.5.d.c.31.1 | 8 | 1.1 | even | 1 | trivial | ||
98.5.d.c.31.2 | 8 | 7.6 | odd | 2 | inner | ||
784.5.c.a.97.2 | 4 | 28.11 | odd | 6 | |||
784.5.c.a.97.3 | 4 | 28.3 | even | 6 | |||
882.5.c.c.685.1 | 4 | 21.11 | odd | 6 | |||
882.5.c.c.685.2 | 4 | 21.17 | even | 6 |