Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [33,5,Mod(5,33)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 4]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("33.5");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.h (of order \(10\), degree \(4\), 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: | \(3.41120878177\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 5.10 | ||
Character | \(\chi\) | \(=\) | 33.5 |
Dual form | 33.5.h.a.20.10 |
$q$-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 \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).
\(n\) | \(13\) | \(23\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.36002 | − | 0.766817i | 0.590005 | − | 0.191704i | 0.00122714 | − | 0.999999i | \(-0.499609\pi\) |
0.588778 | + | 0.808295i | \(0.299609\pi\) | |||||||
\(3\) | −7.49818 | − | 4.97767i | −0.833132 | − | 0.553075i | ||||
\(4\) | −7.96259 | + | 5.78516i | −0.497662 | + | 0.361573i | ||||
\(5\) | −40.2655 | − | 13.0831i | −1.61062 | − | 0.523323i | −0.640918 | − | 0.767609i | \(-0.721446\pi\) |
−0.969703 | + | 0.244287i | \(0.921446\pi\) | |||||||
\(6\) | −21.5128 | − | 5.99767i | −0.597578 | − | 0.166602i | ||||
\(7\) | 50.3841 | − | 36.6062i | 1.02825 | − | 0.747065i | 0.0602898 | − | 0.998181i | \(-0.480798\pi\) |
0.967957 | + | 0.251116i | \(0.0807975\pi\) | |||||||
\(8\) | −37.6929 | + | 51.8798i | −0.588951 | + | 0.810621i | ||||
\(9\) | 31.4455 | + | 74.6470i | 0.388216 | + | 0.921568i | ||||
\(10\) | −105.060 | −1.05060 | ||||||||
\(11\) | −31.4973 | − | 116.829i | −0.260308 | − | 0.965526i | ||||
\(12\) | 88.5016 | − | 3.74302i | 0.614595 | − | 0.0259932i | ||||
\(13\) | −16.7307 | − | 51.4918i | −0.0989982 | − | 0.304685i | 0.889277 | − | 0.457369i | \(-0.151208\pi\) |
−0.988275 | + | 0.152684i | \(0.951208\pi\) | |||||||
\(14\) | 90.8372 | − | 125.027i | 0.463455 | − | 0.637891i | ||||
\(15\) | 236.795 | + | 298.528i | 1.05242 | + | 1.32679i | ||||
\(16\) | −0.510564 | + | 1.57135i | −0.00199439 | + | 0.00613810i | ||||
\(17\) | −286.232 | − | 93.0025i | −0.990423 | − | 0.321808i | −0.231391 | − | 0.972861i | \(-0.574328\pi\) |
−0.759032 | + | 0.651053i | \(0.774328\pi\) | |||||||
\(18\) | 131.453 | + | 152.055i | 0.405718 | + | 0.469307i | ||||
\(19\) | 26.2484 | + | 19.0705i | 0.0727101 | + | 0.0528270i | 0.623547 | − | 0.781786i | \(-0.285691\pi\) |
−0.550836 | + | 0.834613i | \(0.685691\pi\) | |||||||
\(20\) | 396.306 | − | 128.767i | 0.990764 | − | 0.321919i | ||||
\(21\) | −560.003 | + | 23.6843i | −1.26985 | + | 0.0537060i | ||||
\(22\) | −163.920 | − | 251.565i | −0.338678 | − | 0.519762i | ||||
\(23\) | 422.615i | 0.798894i | 0.916756 | + | 0.399447i | \(0.130798\pi\) | ||||
−0.916756 | + | 0.399447i | \(0.869202\pi\) | |||||||
\(24\) | 540.869 | − | 201.381i | 0.939008 | − | 0.349620i | ||||
\(25\) | 944.511 | + | 686.227i | 1.51122 | + | 1.09796i | ||||
\(26\) | −78.9695 | − | 108.692i | −0.116819 | − | 0.160787i | ||||
\(27\) | 135.784 | − | 716.243i | 0.186261 | − | 0.982500i | ||||
\(28\) | −189.415 | + | 582.960i | −0.241601 | + | 0.743572i | ||||
\(29\) | −350.116 | − | 481.893i | −0.416309 | − | 0.573000i | 0.548434 | − | 0.836194i | \(-0.315224\pi\) |
−0.964743 | + | 0.263194i | \(0.915224\pi\) | |||||||
\(30\) | 787.757 | + | 522.953i | 0.875286 | + | 0.581059i | ||||
\(31\) | −281.574 | − | 866.597i | −0.293001 | − | 0.901766i | −0.983885 | − | 0.178800i | \(-0.942778\pi\) |
0.690884 | − | 0.722966i | \(-0.257222\pi\) | |||||||
\(32\) | − | 1021.93i | − | 0.997979i | ||||||
\(33\) | −345.362 | + | 1032.79i | −0.317137 | + | 0.948380i | ||||
\(34\) | −746.830 | −0.646046 | ||||||||
\(35\) | −2507.66 | + | 814.789i | −2.04707 | + | 0.665134i | ||||
\(36\) | −682.233 | − | 412.466i | −0.526414 | − | 0.318261i | ||||
\(37\) | −1047.11 | + | 760.770i | −0.764872 | + | 0.555712i | −0.900401 | − | 0.435061i | \(-0.856727\pi\) |
0.135529 | + | 0.990773i | \(0.456727\pi\) | |||||||
\(38\) | 76.5702 | + | 24.8792i | 0.0530265 | + | 0.0172293i | ||||
\(39\) | −130.859 | + | 469.375i | −0.0860351 | + | 0.308596i | ||||
\(40\) | 2196.47 | − | 1595.83i | 1.37279 | − | 0.997393i | ||||
\(41\) | 825.931 | − | 1136.80i | 0.491333 | − | 0.676262i | −0.489300 | − | 0.872116i | \(-0.662748\pi\) |
0.980633 | + | 0.195853i | \(0.0627477\pi\) | |||||||
\(42\) | −1303.46 | + | 485.315i | −0.738921 | + | 0.275122i | ||||
\(43\) | −883.407 | −0.477776 | −0.238888 | − | 0.971047i | \(-0.576783\pi\) | ||||
−0.238888 | + | 0.971047i | \(0.576783\pi\) | |||||||
\(44\) | 926.672 | + | 748.041i | 0.478653 | + | 0.386385i | ||||
\(45\) | −289.559 | − | 3417.11i | −0.142992 | − | 1.68746i | ||||
\(46\) | 324.068 | + | 997.380i | 0.153151 | + | 0.471351i | ||||
\(47\) | −848.681 | + | 1168.11i | −0.384192 | + | 0.528795i | −0.956689 | − | 0.291112i | \(-0.905975\pi\) |
0.572497 | + | 0.819907i | \(0.305975\pi\) | |||||||
\(48\) | 11.6500 | − | 9.24087i | 0.00505642 | − | 0.00401080i | ||||
\(49\) | 456.594 | − | 1405.25i | 0.190168 | − | 0.585278i | ||||
\(50\) | 2755.27 | + | 895.243i | 1.10211 | + | 0.358097i | ||||
\(51\) | 1683.29 | + | 2122.12i | 0.647169 | + | 0.815887i | ||||
\(52\) | 431.108 | + | 313.218i | 0.159433 | + | 0.115835i | ||||
\(53\) | 3520.73 | − | 1143.96i | 1.25338 | − | 0.407247i | 0.394247 | − | 0.919005i | \(-0.371006\pi\) |
0.859130 | + | 0.511758i | \(0.171006\pi\) | |||||||
\(54\) | −228.774 | − | 1794.47i | −0.0784546 | − | 0.615387i | ||||
\(55\) | −260.220 | + | 5116.25i | −0.0860231 | + | 1.69132i | ||||
\(56\) | 3993.71i | 1.27350i | ||||||||
\(57\) | −101.888 | − | 273.650i | −0.0313598 | − | 0.0842260i | ||||
\(58\) | −1195.80 | − | 868.802i | −0.355471 | − | 0.258264i | ||||
\(59\) | 948.882 | + | 1306.02i | 0.272589 | + | 0.375186i | 0.923262 | − | 0.384172i | \(-0.125513\pi\) |
−0.650673 | + | 0.759358i | \(0.725513\pi\) | |||||||
\(60\) | −3612.53 | − | 1007.16i | −1.00348 | − | 0.279766i | ||||
\(61\) | 2098.97 | − | 6459.97i | 0.564088 | − | 1.73608i | −0.106559 | − | 0.994306i | \(-0.533983\pi\) |
0.670647 | − | 0.741777i | \(-0.266017\pi\) | |||||||
\(62\) | −1329.04 | − | 1829.27i | −0.345744 | − | 0.475876i | ||||
\(63\) | 4316.90 | + | 2609.92i | 1.08765 | + | 0.657577i | ||||
\(64\) | −791.803 | − | 2436.92i | −0.193311 | − | 0.594951i | ||||
\(65\) | 2292.23i | 0.542540i | ||||||||
\(66\) | −23.1035 | + | 2702.22i | −0.00530384 | + | 0.620345i | ||||
\(67\) | −1694.79 | −0.377542 | −0.188771 | − | 0.982021i | \(-0.560450\pi\) | ||||
−0.188771 | + | 0.982021i | \(0.560450\pi\) | |||||||
\(68\) | 2817.19 | − | 915.359i | 0.609253 | − | 0.197958i | ||||
\(69\) | 2103.64 | − | 3168.85i | 0.441848 | − | 0.665584i | ||||
\(70\) | −5293.34 | + | 3845.84i | −1.08027 | + | 0.784865i | ||||
\(71\) | 3613.35 | + | 1174.05i | 0.716793 | + | 0.232900i | 0.644632 | − | 0.764493i | \(-0.277010\pi\) |
0.0721610 | + | 0.997393i | \(0.477010\pi\) | |||||||
\(72\) | −5057.94 | − | 1182.27i | −0.975683 | − | 0.228062i | ||||
\(73\) | 1040.84 | − | 756.211i | 0.195315 | − | 0.141905i | −0.485830 | − | 0.874054i | \(-0.661482\pi\) |
0.681145 | + | 0.732149i | \(0.261482\pi\) | |||||||
\(74\) | −1887.83 | + | 2598.37i | −0.344746 | + | 0.474502i | ||||
\(75\) | −3666.30 | − | 9846.93i | −0.651787 | − | 1.75056i | ||||
\(76\) | −319.331 | −0.0552858 | ||||||||
\(77\) | −5863.61 | − | 4733.31i | −0.988972 | − | 0.798331i | ||||
\(78\) | 51.0936 | + | 1208.08i | 0.00839802 | + | 0.198566i | ||||
\(79\) | 1496.64 | + | 4606.20i | 0.239808 | + | 0.738054i | 0.996447 | + | 0.0842210i | \(0.0268402\pi\) |
−0.756639 | + | 0.653833i | \(0.773160\pi\) | |||||||
\(80\) | 41.1162 | − | 56.5916i | 0.00642441 | − | 0.00884244i | ||||
\(81\) | −4583.36 | + | 4694.63i | −0.698576 | + | 0.715536i | ||||
\(82\) | 1077.50 | − | 3316.20i | 0.160247 | − | 0.493188i | ||||
\(83\) | −8647.58 | − | 2809.77i | −1.25527 | − | 0.407863i | −0.395466 | − | 0.918481i | \(-0.629417\pi\) |
−0.859808 | + | 0.510617i | \(0.829417\pi\) | |||||||
\(84\) | 4322.06 | − | 3428.30i | 0.612536 | − | 0.485870i | ||||
\(85\) | 10308.5 | + | 7489.59i | 1.42679 | + | 1.03662i | ||||
\(86\) | −2084.86 | + | 677.411i | −0.281890 | + | 0.0915916i | ||||
\(87\) | 226.526 | + | 5356.08i | 0.0299281 | + | 0.707634i | ||||
\(88\) | 7248.26 | + | 2769.53i | 0.935984 | + | 0.357636i | ||||
\(89\) | − | 42.1422i | − | 0.00532031i | −0.999996 | − | 0.00266016i | \(-0.999153\pi\) | ||
0.999996 | − | 0.00266016i | \(-0.000846755\pi\) | |||||||
\(90\) | −3303.66 | − | 7842.40i | −0.407859 | − | 0.968197i | ||||
\(91\) | −2727.88 | − | 1981.92i | −0.329414 | − | 0.239333i | ||||
\(92\) | −2444.90 | − | 3365.11i | −0.288858 | − | 0.397579i | ||||
\(93\) | −2202.34 | + | 7899.49i | −0.254635 | + | 0.913341i | ||||
\(94\) | −1107.18 | + | 3407.54i | −0.125303 | + | 0.385643i | ||||
\(95\) | −807.403 | − | 1111.29i | −0.0894629 | − | 0.123135i | ||||
\(96\) | −5086.84 | + | 7662.62i | −0.551957 | + | 0.831448i | ||||
\(97\) | −3031.59 | − | 9330.26i | −0.322201 | − | 0.991631i | −0.972688 | − | 0.232115i | \(-0.925436\pi\) |
0.650488 | − | 0.759517i | \(-0.274564\pi\) | |||||||
\(98\) | − | 3666.55i | − | 0.381773i | ||||||
\(99\) | 7730.46 | − | 6024.92i | 0.788742 | − | 0.614725i | ||||
\(100\) | −11490.7 | −1.14907 | ||||||||
\(101\) | 9769.71 | − | 3174.37i | 0.957720 | − | 0.311182i | 0.211872 | − | 0.977298i | \(-0.432044\pi\) |
0.745849 | + | 0.666115i | \(0.232044\pi\) | |||||||
\(102\) | 5599.87 | + | 3717.47i | 0.538242 | + | 0.357312i | ||||
\(103\) | −4920.14 | + | 3574.69i | −0.463771 | + | 0.336949i | −0.795009 | − | 0.606598i | \(-0.792534\pi\) |
0.331238 | + | 0.943547i | \(0.392534\pi\) | |||||||
\(104\) | 3302.01 | + | 1072.89i | 0.305289 | + | 0.0991945i | ||||
\(105\) | 22858.7 | + | 6372.89i | 2.07335 | + | 0.578040i | ||||
\(106\) | 7431.79 | − | 5399.51i | 0.661427 | − | 0.480555i | ||||
\(107\) | 2945.41 | − | 4054.01i | 0.257264 | − | 0.354093i | −0.660775 | − | 0.750584i | \(-0.729772\pi\) |
0.918039 | + | 0.396491i | \(0.129772\pi\) | |||||||
\(108\) | 3062.39 | + | 6488.68i | 0.262550 | + | 0.556300i | ||||
\(109\) | −8684.63 | −0.730968 | −0.365484 | − | 0.930818i | \(-0.619096\pi\) | ||||
−0.365484 | + | 0.930818i | \(0.619096\pi\) | |||||||
\(110\) | 3309.10 | + | 12274.0i | 0.273479 | + | 1.01438i | ||||
\(111\) | 11638.3 | − | 492.221i | 0.944589 | − | 0.0399498i | ||||
\(112\) | 31.7970 | + | 97.8610i | 0.00253483 | + | 0.00780142i | ||||
\(113\) | −61.0132 | + | 83.9774i | −0.00477823 | + | 0.00657666i | −0.811399 | − | 0.584492i | \(-0.801294\pi\) |
0.806621 | + | 0.591069i | \(0.201294\pi\) | |||||||
\(114\) | −450.297 | − | 567.690i | −0.0346489 | − | 0.0436819i | ||||
\(115\) | 5529.10 | − | 17016.8i | 0.418079 | − | 1.28672i | ||||
\(116\) | 5575.66 | + | 1811.64i | 0.414362 | + | 0.134634i | ||||
\(117\) | 3317.60 | − | 2868.08i | 0.242355 | − | 0.209517i | ||||
\(118\) | 3240.86 | + | 2354.62i | 0.232754 | + | 0.169105i | ||||
\(119\) | −17826.0 | + | 5792.03i | −1.25881 | + | 0.409013i | ||||
\(120\) | −24413.0 | + | 1032.51i | −1.69535 | + | 0.0717019i | ||||
\(121\) | −12656.8 | + | 7359.57i | −0.864479 | + | 0.502669i | ||||
\(122\) | − | 16855.2i | − | 1.13244i | ||||||
\(123\) | −11851.6 | + | 4412.69i | −0.783369 | + | 0.291671i | ||||
\(124\) | 7255.46 | + | 5271.40i | 0.471869 | + | 0.342833i | ||||
\(125\) | −13499.9 | − | 18581.0i | −0.863991 | − | 1.18918i | ||||
\(126\) | 12189.3 | + | 2849.20i | 0.767781 | + | 0.179466i | ||||
\(127\) | −746.647 | + | 2297.94i | −0.0462922 | + | 0.142473i | −0.971531 | − | 0.236913i | \(-0.923865\pi\) |
0.925239 | + | 0.379385i | \(0.123865\pi\) | |||||||
\(128\) | 5873.48 | + | 8084.15i | 0.358488 | + | 0.493417i | ||||
\(129\) | 6623.95 | + | 4397.31i | 0.398050 | + | 0.264246i | ||||
\(130\) | 1757.72 | + | 5409.71i | 0.104007 | + | 0.320101i | ||||
\(131\) | 10439.5i | 0.608327i | 0.952620 | + | 0.304164i | \(0.0983770\pi\) | ||||
−0.952620 | + | 0.304164i | \(0.901623\pi\) | |||||||
\(132\) | −3224.85 | − | 10221.6i | −0.185081 | − | 0.586640i | ||||
\(133\) | 2020.60 | 0.114229 | ||||||||
\(134\) | −3999.73 | + | 1299.59i | −0.222752 | + | 0.0723764i | ||||
\(135\) | −14838.1 | + | 27063.4i | −0.814160 | + | 1.48496i | ||||
\(136\) | 15613.9 | − | 11344.1i | 0.844175 | − | 0.613329i | ||||
\(137\) | −7320.35 | − | 2378.53i | −0.390023 | − | 0.126726i | 0.107439 | − | 0.994212i | \(-0.465735\pi\) |
−0.497463 | + | 0.867485i | \(0.665735\pi\) | |||||||
\(138\) | 2534.71 | − | 9091.64i | 0.133097 | − | 0.477402i | ||||
\(139\) | 1033.29 | − | 750.730i | 0.0534802 | − | 0.0388556i | −0.560724 | − | 0.828003i | \(-0.689477\pi\) |
0.614204 | + | 0.789147i | \(0.289477\pi\) | |||||||
\(140\) | 15253.8 | − | 20995.1i | 0.778256 | − | 1.07118i | ||||
\(141\) | 12178.0 | − | 4534.24i | 0.612546 | − | 0.228069i | ||||
\(142\) | 9427.87 | 0.467559 | ||||||||
\(143\) | −5488.74 | + | 3576.48i | −0.268411 | + | 0.174897i | ||||
\(144\) | −133.352 | + | 11.3000i | −0.00643093 | + | 0.000544945i | ||||
\(145\) | 7792.96 | + | 23984.3i | 0.370652 | + | 1.14075i | ||||
\(146\) | 1876.52 | − | 2582.80i | 0.0880332 | − | 0.121167i | ||||
\(147\) | −10418.5 | + | 8264.06i | −0.482138 | + | 0.382436i | ||||
\(148\) | 3936.53 | − | 12115.4i | 0.179717 | − | 0.553113i | ||||
\(149\) | −25630.3 | − | 8327.78i | −1.15447 | − | 0.375108i | −0.331642 | − | 0.943405i | \(-0.607602\pi\) |
−0.822823 | + | 0.568297i | \(0.807602\pi\) | |||||||
\(150\) | −16203.3 | − | 20427.6i | −0.720148 | − | 0.907891i | ||||
\(151\) | −28175.4 | − | 20470.6i | −1.23571 | − | 0.897794i | −0.238403 | − | 0.971166i | \(-0.576624\pi\) |
−0.997305 | + | 0.0733722i | \(0.976624\pi\) | |||||||
\(152\) | −1978.75 | + | 642.935i | −0.0856454 | + | 0.0278279i | ||||
\(153\) | −2058.36 | − | 24290.9i | −0.0879305 | − | 1.03767i | ||||
\(154\) | −17467.8 | − | 6674.38i | −0.736541 | − | 0.281429i | ||||
\(155\) | 38577.8i | 1.60574i | ||||||||
\(156\) | −1673.43 | − | 4494.48i | −0.0687635 | − | 0.184684i | ||||
\(157\) | −10727.2 | − | 7793.75i | −0.435197 | − | 0.316189i | 0.348527 | − | 0.937299i | \(-0.386682\pi\) |
−0.783724 | + | 0.621110i | \(0.786682\pi\) | |||||||
\(158\) | 7064.22 | + | 9723.06i | 0.282976 | + | 0.389483i | ||||
\(159\) | −32093.3 | − | 8947.47i | −1.26947 | − | 0.353921i | ||||
\(160\) | −13370.0 | + | 41148.6i | −0.522265 | + | 1.60737i | ||||
\(161\) | 15470.3 | + | 21293.1i | 0.596826 | + | 0.821461i | ||||
\(162\) | −7216.89 | + | 14594.0i | −0.274992 | + | 0.556089i | ||||
\(163\) | 2198.17 | + | 6765.27i | 0.0827343 | + | 0.254630i | 0.983864 | − | 0.178921i | \(-0.0572605\pi\) |
−0.901129 | + | 0.433551i | \(0.857261\pi\) | |||||||
\(164\) | 13830.0i | 0.514202i | ||||||||
\(165\) | 27418.2 | − | 37067.3i | 1.00710 | − | 1.36152i | ||||
\(166\) | −22563.0 | −0.818807 | ||||||||
\(167\) | 36019.7 | − | 11703.5i | 1.29154 | − | 0.419646i | 0.418908 | − | 0.908029i | \(-0.362413\pi\) |
0.872630 | + | 0.488382i | \(0.162413\pi\) | |||||||
\(168\) | 19879.4 | − | 29945.5i | 0.704343 | − | 1.06100i | ||||
\(169\) | 20734.8 | − | 15064.7i | 0.725985 | − | 0.527459i | ||||
\(170\) | 30071.5 | + | 9770.82i | 1.04054 | + | 0.338091i | ||||
\(171\) | −598.166 | + | 2559.04i | −0.0204564 | + | 0.0875156i | ||||
\(172\) | 7034.21 | − | 5110.65i | 0.237771 | − | 0.172751i | ||||
\(173\) | −16959.3 | + | 23342.5i | −0.566651 | + | 0.779928i | −0.992153 | − | 0.125030i | \(-0.960097\pi\) |
0.425502 | + | 0.904957i | \(0.360097\pi\) | |||||||
\(174\) | 4641.74 | + | 12466.8i | 0.153314 | + | 0.411770i | ||||
\(175\) | 72708.5 | 2.37416 | ||||||||
\(176\) | 199.660 | + | 10.1550i | 0.00644565 | + | 0.000327835i | ||||
\(177\) | −613.930 | − | 14516.0i | −0.0195962 | − | 0.463342i | ||||
\(178\) | −32.3153 | − | 99.4564i | −0.00101993 | − | 0.00313901i | ||||
\(179\) | 17155.7 | − | 23612.9i | 0.535431 | − | 0.736958i | −0.452515 | − | 0.891757i | \(-0.649473\pi\) |
0.987946 | + | 0.154799i | \(0.0494731\pi\) | |||||||
\(180\) | 22074.1 | + | 25533.9i | 0.681301 | + | 0.788082i | ||||
\(181\) | −10840.4 | + | 33363.3i | −0.330893 | + | 1.01838i | 0.637817 | + | 0.770188i | \(0.279838\pi\) |
−0.968710 | + | 0.248195i | \(0.920162\pi\) | |||||||
\(182\) | −7957.61 | − | 2585.58i | −0.240237 | − | 0.0780577i | ||||
\(183\) | −47894.1 | + | 37990.0i | −1.43014 | + | 1.13440i | ||||
\(184\) | −21925.2 | − | 15929.6i | −0.647601 | − | 0.470510i | ||||
\(185\) | 52115.6 | − | 16933.4i | 1.52274 | − | 0.494767i | ||||
\(186\) | 859.895 | + | 20331.7i | 0.0248553 | + | 0.587690i | ||||
\(187\) | −1849.80 | + | 36369.5i | −0.0528984 | + | 1.04005i | ||||
\(188\) | − | 14210.9i | − | 0.402075i | ||||||
\(189\) | −19377.6 | − | 41057.8i | −0.542469 | − | 1.14940i | ||||
\(190\) | −2757.64 | − | 2003.55i | −0.0763891 | − | 0.0554999i | ||||
\(191\) | 38245.3 | + | 52640.1i | 1.04836 | + | 1.44295i | 0.890221 | + | 0.455529i | \(0.150550\pi\) |
0.158141 | + | 0.987417i | \(0.449450\pi\) | |||||||
\(192\) | −6193.10 | + | 22213.8i | −0.167999 | + | 0.602588i | ||||
\(193\) | 18552.1 | − | 57097.4i | 0.498056 | − | 1.53286i | −0.314084 | − | 0.949395i | \(-0.601697\pi\) |
0.812140 | − | 0.583463i | \(-0.198303\pi\) | |||||||
\(194\) | −14309.2 | − | 19694.9i | −0.380200 | − | 0.523300i | ||||
\(195\) | 11410.0 | − | 17187.6i | 0.300065 | − | 0.452007i | ||||
\(196\) | 4493.94 | + | 13830.9i | 0.116981 | + | 0.360030i | ||||
\(197\) | − | 41792.9i | − | 1.07689i | −0.842661 | − | 0.538444i | \(-0.819012\pi\) | ||
0.842661 | − | 0.538444i | \(-0.180988\pi\) | |||||||
\(198\) | 13624.0 | − | 20146.8i | 0.347516 | − | 0.513896i | ||||
\(199\) | 9442.99 | 0.238453 | 0.119227 | − | 0.992867i | \(-0.461958\pi\) | ||||
0.119227 | + | 0.992867i | \(0.461958\pi\) | |||||||
\(200\) | −71202.6 | + | 23135.1i | −1.78007 | + | 0.578378i | ||||
\(201\) | 12707.8 | + | 8436.10i | 0.314542 | + | 0.208809i | ||||
\(202\) | 20622.5 | − | 14983.1i | 0.505405 | − | 0.367198i | ||||
\(203\) | −35280.5 | − | 11463.3i | −0.856136 | − | 0.278176i | ||||
\(204\) | −25680.1 | − | 7159.50i | −0.617074 | − | 0.172037i | ||||
\(205\) | −48129.3 | + | 34968.0i | −1.14525 | + | 0.832076i | ||||
\(206\) | −8870.50 | + | 12209.2i | −0.209032 | + | 0.287708i | ||||
\(207\) | −31547.0 | + | 13289.4i | −0.736236 | + | 0.310144i | ||||
\(208\) | 89.4538 | 0.00206763 | ||||||||
\(209\) | 1401.23 | − | 3667.23i | 0.0320788 | − | 0.0839548i | ||||
\(210\) | 58833.7 | − | 2488.27i | 1.33410 | − | 0.0564234i | ||||
\(211\) | 1547.67 | + | 4763.25i | 0.0347628 | + | 0.106989i | 0.966932 | − | 0.255033i | \(-0.0820865\pi\) |
−0.932169 | + | 0.362022i | \(0.882086\pi\) | |||||||
\(212\) | −21416.2 | + | 29476.9i | −0.476508 | + | 0.655858i | ||||
\(213\) | −21249.6 | − | 26789.3i | −0.468372 | − | 0.590477i | ||||
\(214\) | 3842.54 | − | 11826.1i | 0.0839057 | − | 0.258235i | ||||
\(215\) | 35570.9 | + | 11557.7i | 0.769516 | + | 0.250031i | ||||
\(216\) | 32040.4 | + | 34041.7i | 0.686737 | + | 0.729632i | ||||
\(217\) | −45909.7 | − | 33355.3i | −0.974956 | − | 0.708347i | ||||
\(218\) | −20495.9 | + | 6659.52i | −0.431274 | + | 0.140130i | ||||
\(219\) | −11568.5 | + | 489.271i | −0.241207 | + | 0.0102014i | ||||
\(220\) | −27526.3 | − | 42244.0i | −0.568725 | − | 0.872810i | ||||
\(221\) | 16294.6i | 0.333626i | ||||||||
\(222\) | 27089.1 | − | 10086.1i | 0.549654 | − | 0.204652i | ||||
\(223\) | −72342.8 | − | 52560.1i | −1.45474 | − | 1.05693i | −0.984694 | − | 0.174290i | \(-0.944237\pi\) |
−0.470047 | − | 0.882642i | \(-0.655763\pi\) | |||||||
\(224\) | −37409.0 | − | 51489.1i | −0.745555 | − | 1.02617i | ||||
\(225\) | −21524.2 | + | 92083.7i | −0.425169 | + | 1.81894i | ||||
\(226\) | −79.5970 | + | 244.974i | −0.00155840 | + | 0.00479627i | ||||
\(227\) | −48550.4 | − | 66823.9i | −0.942195 | − | 1.29682i | −0.954908 | − | 0.296901i | \(-0.904047\pi\) |
0.0127131 | − | 0.999919i | \(-0.495953\pi\) | |||||||
\(228\) | 2394.40 | + | 1589.53i | 0.0460604 | + | 0.0305772i | ||||
\(229\) | 21492.8 | + | 66148.2i | 0.409848 | + | 1.26138i | 0.916779 | + | 0.399396i | \(0.130780\pi\) |
−0.506931 | + | 0.861987i | \(0.669220\pi\) | |||||||
\(230\) | − | 44399.8i | − | 0.839316i | ||||||
\(231\) | 20405.6 | + | 64678.4i | 0.382407 | + | 1.21209i | ||||
\(232\) | 38197.3 | 0.709671 | ||||||||
\(233\) | −16153.8 | + | 5248.67i | −0.297551 | + | 0.0966803i | −0.453988 | − | 0.891008i | \(-0.649999\pi\) |
0.156437 | + | 0.987688i | \(0.449999\pi\) | |||||||
\(234\) | 5630.31 | − | 9312.72i | 0.102825 | − | 0.170077i | ||||
\(235\) | 49455.0 | − | 35931.2i | 0.895519 | − | 0.650633i | ||||
\(236\) | −15111.1 | − | 4909.90i | −0.271314 | − | 0.0881553i | ||||
\(237\) | 11706.0 | − | 41987.9i | 0.208407 | − | 0.747528i | ||||
\(238\) | −37628.3 | + | 27338.6i | −0.664295 | + | 0.482639i | ||||
\(239\) | 49253.2 | − | 67791.2i | 0.862260 | − | 1.18680i | −0.118766 | − | 0.992922i | \(-0.537894\pi\) |
0.981026 | − | 0.193877i | \(-0.0621063\pi\) | |||||||
\(240\) | −589.992 | + | 219.671i | −0.0102429 | + | 0.00381374i | ||||
\(241\) | 99776.0 | 1.71788 | 0.858939 | − | 0.512079i | \(-0.171124\pi\) | ||||
0.858939 | + | 0.512079i | \(0.171124\pi\) | |||||||
\(242\) | −24226.9 | + | 27074.2i | −0.413683 | + | 0.462301i | ||||
\(243\) | 57735.2 | − | 12386.7i | 0.977751 | − | 0.209771i | ||||
\(244\) | 20658.7 | + | 63580.9i | 0.346995 | + | 1.06794i | ||||
\(245\) | −36770.0 | + | 50609.6i | −0.612578 | + | 0.843142i | ||||
\(246\) | −24586.2 | + | 19502.0i | −0.406277 | + | 0.322262i | ||||
\(247\) | 542.823 | − | 1670.64i | 0.00889742 | − | 0.0273835i | ||||
\(248\) | 55572.2 | + | 18056.5i | 0.903554 | + | 0.293583i | ||||
\(249\) | 50855.0 | + | 64113.0i | 0.820229 | + | 1.03406i | ||||
\(250\) | −46108.1 | − | 33499.5i | −0.737730 | − | 0.535992i | ||||
\(251\) | 37301.0 | − | 12119.8i | 0.592070 | − | 0.192375i | 0.00236919 | − | 0.999997i | \(-0.499246\pi\) |
0.589700 | + | 0.807622i | \(0.299246\pi\) | |||||||
\(252\) | −49472.5 | + | 4192.20i | −0.779045 | + | 0.0660148i | ||||
\(253\) | 49373.5 | − | 13311.2i | 0.771353 | − | 0.207959i | ||||
\(254\) | 5995.73i | 0.0929340i | ||||||||
\(255\) | −40014.6 | − | 107471.i | −0.615372 | − | 1.65276i | ||||
\(256\) | 53228.0 | + | 38672.4i | 0.812195 | + | 0.590094i | ||||
\(257\) | −11240.3 | − | 15471.0i | −0.170182 | − | 0.234235i | 0.715404 | − | 0.698711i | \(-0.246243\pi\) |
−0.885586 | + | 0.464476i | \(0.846243\pi\) | |||||||
\(258\) | 19004.6 | + | 5298.39i | 0.285508 | + | 0.0795984i | ||||
\(259\) | −24908.8 | + | 76661.4i | −0.371324 | + | 1.14282i | ||||
\(260\) | −13260.9 | − | 18252.1i | −0.196168 | − | 0.270002i | ||||
\(261\) | 24962.3 | − | 41288.5i | 0.366441 | − | 0.606105i | ||||
\(262\) | 8005.19 | + | 24637.4i | 0.116619 | + | 0.358916i | ||||
\(263\) | 113300.i | 1.63802i | 0.573779 | + | 0.819010i | \(0.305477\pi\) | ||||
−0.573779 | + | 0.819010i | \(0.694523\pi\) | |||||||
\(264\) | −40563.0 | − | 56845.9i | −0.581999 | − | 0.815627i | ||||
\(265\) | −156731. | −2.23184 | ||||||||
\(266\) | 4768.65 | − | 1549.43i | 0.0673957 | − | 0.0218982i | ||||
\(267\) | −209.770 | + | 315.990i | −0.00294253 | + | 0.00443252i | ||||
\(268\) | 13494.9 | − | 9804.61i | 0.187888 | − | 0.136509i | ||||
\(269\) | 56479.3 | + | 18351.2i | 0.780521 | + | 0.253607i | 0.672063 | − | 0.740494i | \(-0.265409\pi\) |
0.108458 | + | 0.994101i | \(0.465409\pi\) | |||||||
\(270\) | −14265.5 | + | 75248.3i | −0.195685 | + | 1.03221i | ||||
\(271\) | 15889.7 | − | 11544.5i | 0.216360 | − | 0.157195i | −0.474327 | − | 0.880349i | \(-0.657308\pi\) |
0.690687 | + | 0.723154i | \(0.257308\pi\) | |||||||
\(272\) | 292.280 | − | 402.288i | 0.00395058 | − | 0.00543751i | ||||
\(273\) | 10588.8 | + | 28439.3i | 0.142076 | + | 0.381587i | ||||
\(274\) | −19100.1 | −0.254410 | ||||||||
\(275\) | 50421.4 | − | 131960.i | 0.666730 | − | 1.74493i | ||||
\(276\) | 1581.86 | + | 37402.1i | 0.0207658 | + | 0.490996i | ||||
\(277\) | 14794.2 | + | 45532.0i | 0.192812 | + | 0.593413i | 0.999995 | + | 0.00311241i | \(0.000990713\pi\) |
−0.807184 | + | 0.590300i | \(0.799009\pi\) | |||||||
\(278\) | 1862.91 | − | 2564.08i | 0.0241048 | − | 0.0331774i | ||||
\(279\) | 55834.6 | − | 48269.3i | 0.717291 | − | 0.620101i | ||||
\(280\) | 52249.9 | − | 160809.i | 0.666453 | − | 2.05113i | ||||
\(281\) | −17718.2 | − | 5757.00i | −0.224392 | − | 0.0729094i | 0.194663 | − | 0.980870i | \(-0.437639\pi\) |
−0.419055 | + | 0.907961i | \(0.637639\pi\) | |||||||
\(282\) | 25263.5 | − | 20039.2i | 0.317683 | − | 0.251989i | ||||
\(283\) | 24583.0 | + | 17860.6i | 0.306947 | + | 0.223010i | 0.730585 | − | 0.682822i | \(-0.239247\pi\) |
−0.423639 | + | 0.905831i | \(0.639247\pi\) | |||||||
\(284\) | −35563.7 | + | 11555.4i | −0.440931 | + | 0.143267i | ||||
\(285\) | 522.393 | + | 12351.7i | 0.00643143 | + | 0.152067i | ||||
\(286\) | −10211.0 | + | 12649.4i | −0.124835 | + | 0.154646i | ||||
\(287\) | − | 87510.7i | − | 1.06242i | ||||||
\(288\) | 76284.1 | − | 32135.2i | 0.919706 | − | 0.387432i | ||||
\(289\) | 5709.60 | + | 4148.26i | 0.0683612 | + | 0.0496673i | ||||
\(290\) | 36783.1 | + | 50627.5i | 0.437373 | + | 0.601992i | ||||
\(291\) | −23711.6 | + | 85050.2i | −0.280011 | + | 1.00436i | ||||
\(292\) | −3912.94 | + | 12042.8i | −0.0458921 | + | 0.141241i | ||||
\(293\) | 52963.8 | + | 72898.4i | 0.616941 | + | 0.849147i | 0.997126 | − | 0.0757640i | \(-0.0241395\pi\) |
−0.380185 | + | 0.924911i | \(0.624140\pi\) | |||||||
\(294\) | −18250.9 | + | 27492.4i | −0.211149 | + | 0.318067i | ||||
\(295\) | −21120.4 | − | 65002.0i | −0.242694 | − | 0.746935i | ||||
\(296\) | − | 82999.4i | − | 0.947309i | ||||||
\(297\) | −87954.5 | + | 6696.24i | −0.997114 | + | 0.0759134i | ||||
\(298\) | −66873.8 | −0.753050 | ||||||||
\(299\) | 21761.2 | − | 7070.64i | 0.243411 | − | 0.0790891i | ||||
\(300\) | 86159.3 | + | 57196.9i | 0.957326 | + | 0.635521i | ||||
\(301\) | −44509.7 | + | 32338.2i | −0.491271 | + | 0.356930i | ||||
\(302\) | −82191.6 | − | 26705.7i | −0.901184 | − | 0.292812i | ||||
\(303\) | −89056.0 | − | 24828.4i | −0.970014 | − | 0.270435i | ||||
\(304\) | −43.3680 | + | 31.5087i | −0.000469269 | + | 0.000340944i | ||||
\(305\) | −169032. | + | 232653.i | −1.81706 | + | 2.50097i | ||||
\(306\) | −23484.5 | − | 55748.6i | −0.250806 | − | 0.595376i | ||||
\(307\) | 21209.5 | 0.225037 | 0.112518 | − | 0.993650i | \(-0.464108\pi\) | ||||
0.112518 | + | 0.993650i | \(0.464108\pi\) | |||||||
\(308\) | 74072.5 | + | 3767.44i | 0.780828 | + | 0.0397141i | ||||
\(309\) | 54685.8 | − | 2312.84i | 0.572740 | − | 0.0242230i | ||||
\(310\) | 29582.1 | + | 91044.4i | 0.307827 | + | 0.947393i | ||||
\(311\) | 69175.3 | − | 95211.7i | 0.715205 | − | 0.984395i | −0.284465 | − | 0.958687i | \(-0.591816\pi\) |
0.999669 | − | 0.0257084i | \(-0.00818415\pi\) | |||||||
\(312\) | −19418.6 | − | 24481.0i | −0.199484 | − | 0.251490i | ||||
\(313\) | 29878.3 | − | 91956.0i | 0.304977 | − | 0.938623i | −0.674709 | − | 0.738084i | \(-0.735731\pi\) |
0.979686 | − | 0.200539i | \(-0.0642693\pi\) | |||||||
\(314\) | −31292.7 | − | 10167.6i | −0.317383 | − | 0.103124i | ||||
\(315\) | −139676. | − | 161568.i | −1.40767 | − | 1.62830i | ||||
\(316\) | −38564.7 | − | 28018.9i | −0.386204 | − | 0.280593i | ||||
\(317\) | −119767. | + | 38914.8i | −1.19184 | + | 0.387254i | −0.836755 | − | 0.547578i | \(-0.815550\pi\) |
−0.355090 | + | 0.934832i | \(0.615550\pi\) | |||||||
\(318\) | −82602.0 | + | 3493.51i | −0.816838 | + | 0.0345468i | ||||
\(319\) | −45271.2 | + | 56081.9i | −0.444877 | + | 0.551113i | ||||
\(320\) | 108483.i | 1.05940i | ||||||||
\(321\) | −42264.8 | + | 15736.4i | −0.410175 | + | 0.152720i | ||||
\(322\) | 52838.2 | + | 38389.2i | 0.509608 | + | 0.370252i | ||||
\(323\) | −5739.52 | − | 7899.77i | −0.0550137 | − | 0.0757198i | ||||
\(324\) | 9336.21 | − | 63896.9i | 0.0889366 | − | 0.608681i | ||||
\(325\) | 19532.7 | − | 60115.6i | 0.184925 | − | 0.569142i | ||||
\(326\) | 10375.4 | + | 14280.6i | 0.0976273 | + | 0.134372i | ||||
\(327\) | 65118.9 | + | 43229.2i | 0.608992 | + | 0.404280i | ||||
\(328\) | 27845.0 | + | 85698.2i | 0.258821 | + | 0.796570i | ||||
\(329\) | 89921.1i | 0.830749i | ||||||||
\(330\) | 36283.6 | − | 108504.i | 0.333183 | − | 0.996365i | ||||
\(331\) | 58328.1 | 0.532380 | 0.266190 | − | 0.963921i | \(-0.414235\pi\) | ||||
0.266190 | + | 0.963921i | \(0.414235\pi\) | |||||||
\(332\) | 85112.1 | − | 27654.6i | 0.772174 | − | 0.250895i | ||||
\(333\) | −89716.1 | − | 54240.8i | −0.809062 | − | 0.489145i | ||||
\(334\) | 76032.7 | − | 55241.0i | 0.681566 | − | 0.495186i | ||||
\(335\) | 68241.5 | + | 22173.0i | 0.608078 | + | 0.197576i | ||||
\(336\) | 248.701 | − | 892.054i | 0.00220292 | − | 0.00790156i | ||||
\(337\) | 134151. | − | 97466.6i | 1.18123 | − | 0.858215i | 0.188922 | − | 0.981992i | \(-0.439501\pi\) |
0.992310 | + | 0.123777i | \(0.0395008\pi\) | |||||||
\(338\) | 37382.7 | − | 51452.9i | 0.327218 | − | 0.450377i | ||||
\(339\) | 875.500 | − | 325.975i | 0.00761828 | − | 0.00283651i | ||||
\(340\) | −125411. | −1.08487 | ||||||||
\(341\) | −92374.5 | + | 60191.4i | −0.794407 | + | 0.517638i | ||||
\(342\) | 550.635 | + | 6498.08i | 0.00470773 | + | 0.0555562i | ||||
\(343\) | 17771.4 | + | 54694.8i | 0.151055 | + | 0.464898i | ||||
\(344\) | 33298.1 | − | 45831.0i | 0.281386 | − | 0.387295i | ||||
\(345\) | −126162. | + | 100073.i | −1.05997 | + | 0.840775i | ||||
\(346\) | −22124.9 | + | 68093.3i | −0.184811 | + | 0.568790i | ||||
\(347\) | 25571.7 | + | 8308.75i | 0.212374 | + | 0.0690044i | 0.413272 | − | 0.910608i | \(-0.364386\pi\) |
−0.200898 | + | 0.979612i | \(0.564386\pi\) | |||||||
\(348\) | −32789.5 | − | 41337.8i | −0.270755 | − | 0.341341i | ||||
\(349\) | −42027.2 | − | 30534.6i | −0.345048 | − | 0.250692i | 0.401740 | − | 0.915754i | \(-0.368405\pi\) |
−0.746789 | + | 0.665061i | \(0.768405\pi\) | |||||||
\(350\) | 171593. | − | 55754.1i | 1.40076 | − | 0.455135i | ||||
\(351\) | −39152.4 | + | 4991.47i | −0.317793 | + | 0.0405148i | ||||
\(352\) | −119391. | + | 32188.1i | −0.963574 | + | 0.259782i | ||||
\(353\) | − | 126542.i | − | 1.01551i | −0.861500 | − | 0.507757i | \(-0.830475\pi\) | ||
0.861500 | − | 0.507757i | \(-0.169525\pi\) | |||||||
\(354\) | −12580.0 | − | 33787.3i | −0.100386 | − | 0.269617i | ||||
\(355\) | −130133. | − | 94547.5i | −1.03260 | − | 0.750228i | ||||
\(356\) | 243.799 | + | 335.561i | 0.00192368 | + | 0.00264772i | ||||
\(357\) | 162494. | + | 45302.5i | 1.27497 | + | 0.355456i | ||||
\(358\) | 22381.2 | − | 68882.1i | 0.174629 | − | 0.537453i | ||||
\(359\) | 110663. | + | 152315.i | 0.858647 | + | 1.18183i | 0.981890 | + | 0.189450i | \(0.0606704\pi\) |
−0.123243 | + | 0.992376i | \(0.539330\pi\) | |||||||
\(360\) | 188193. | + | 113778.i | 1.45211 | + | 0.877919i | ||||
\(361\) | −39946.1 | − | 122941.i | −0.306521 | − | 0.943374i | ||||
\(362\) | 87050.5i | 0.664284i | ||||||||
\(363\) | 131537. | + | 7818.18i | 0.998238 | + | 0.0593324i | ||||
\(364\) | 33186.7 | 0.250473 | ||||||||
\(365\) | −51803.3 | + | 16831.9i | −0.388841 | + | 0.126342i | ||||
\(366\) | −83899.5 | + | 126383.i | −0.626322 | + | 0.943468i | ||||
\(367\) | −203373. | + | 147759.i | −1.50995 | + | 1.09704i | −0.543745 | + | 0.839251i | \(0.682994\pi\) |
−0.966201 | + | 0.257789i | \(0.917006\pi\) | |||||||
\(368\) | −664.078 | − | 215.772i | −0.00490369 | − | 0.00159331i | ||||
\(369\) | 110830. | + | 25906.1i | 0.813965 | + | 0.190261i | ||||
\(370\) | 110009. | − | 79926.3i | 0.803572 | − | 0.583830i | ||||
\(371\) | 135513. | − | 186518.i | 0.984540 | − | 1.35510i | ||||
\(372\) | −28163.5 | − | 75641.3i | −0.203517 | − | 0.546604i | ||||
\(373\) | 104933. | 0.754216 | 0.377108 | − | 0.926169i | \(-0.376919\pi\) | ||||
0.377108 | + | 0.926169i | \(0.376919\pi\) | |||||||
\(374\) | 23523.1 | + | 87251.1i | 0.168171 | + | 0.623774i | ||||
\(375\) | 8734.46 | + | 206521.i | 0.0621117 | + | 1.46860i | ||||
\(376\) | −28612.0 | − | 88058.7i | −0.202382 | − | 0.622869i | ||||
\(377\) | −18955.8 | + | 26090.5i | −0.133371 | + | 0.183569i | ||||
\(378\) | −77215.2 | − | 82038.1i | −0.540405 | − | 0.574159i | ||||
\(379\) | −45491.5 | + | 140008.i | −0.316703 | + | 0.974711i | 0.658345 | + | 0.752716i | \(0.271257\pi\) |
−0.975048 | + | 0.221995i | \(0.928743\pi\) | |||||||
\(380\) | 12858.0 | + | 4177.83i | 0.0890446 | + | 0.0289323i | ||||
\(381\) | 17036.9 | − | 13513.8i | 0.117366 | − | 0.0930955i | ||||
\(382\) | 130625. | + | 94904.5i | 0.895157 | + | 0.650370i | ||||
\(383\) | −214444. | + | 69677.1i | −1.46190 | + | 0.474999i | −0.928649 | − | 0.370960i | \(-0.879029\pi\) |
−0.533247 | + | 0.845959i | \(0.679029\pi\) | |||||||
\(384\) | −3800.16 | − | 89852.7i | −0.0257715 | − | 0.609352i | ||||
\(385\) | 174175. | + | 267303.i | 1.17507 | + | 1.80336i | ||||
\(386\) | − | 148977.i | − | 0.999873i | ||||||
\(387\) | −27779.2 | − | 65943.7i | −0.185480 | − | 0.440303i | ||||
\(388\) | 78116.3 | + | 56754.8i | 0.518894 | + | 0.376998i | ||||
\(389\) | −41285.2 | − | 56824.3i | −0.272832 | − | 0.375521i | 0.650511 | − | 0.759497i | \(-0.274555\pi\) |
−0.923343 | + | 0.383975i | \(0.874555\pi\) | |||||||
\(390\) | 13748.1 | − | 49312.4i | 0.0903883 | − | 0.324210i | ||||
\(391\) | 39304.3 | − | 120966.i | 0.257091 | − | 0.791244i | ||||
\(392\) | 55693.8 | + | 76656.0i | 0.362439 | + | 0.498854i | ||||
\(393\) | 51964.5 | − | 78277.4i | 0.336451 | − | 0.506817i | ||||
\(394\) | −32047.5 | − | 98632.1i | −0.206444 | − | 0.635369i | ||||
\(395\) | − | 205052.i | − | 1.31422i | ||||||
\(396\) | −26699.4 | + | 92695.9i | −0.170259 | + | 0.591112i | ||||
\(397\) | −170477. | −1.08165 | −0.540824 | − | 0.841136i | \(-0.681887\pi\) | ||||
−0.540824 | + | 0.841136i | \(0.681887\pi\) | |||||||
\(398\) | 22285.6 | − | 7241.04i | 0.140689 | − | 0.0457125i | ||||
\(399\) | −15150.8 | − | 10057.9i | −0.0951679 | − | 0.0631773i | ||||
\(400\) | −1560.54 | + | 1133.80i | −0.00975336 | + | 0.00708623i | ||||
\(401\) | −219706. | − | 71386.8i | −1.36632 | − | 0.443945i | −0.468174 | − | 0.883637i | \(-0.655088\pi\) |
−0.898149 | + | 0.439691i | \(0.855088\pi\) | |||||||
\(402\) | 36459.6 | + | 10164.8i | 0.225611 | + | 0.0628993i | ||||
\(403\) | −39911.7 | + | 28997.5i | −0.245748 | + | 0.178546i | ||||
\(404\) | −59427.9 | + | 81795.5i | −0.364106 | + | 0.501149i | ||||
\(405\) | 245971. | − | 129067.i | 1.49960 | − | 0.786877i | ||||
\(406\) | −92053.0 | −0.558452 | ||||||||
\(407\) | 121861. | + | 98370.1i | 0.735657 | + | 0.593847i | ||||
\(408\) | −173543. | + | 7339.70i | −1.04253 | + | 0.0440918i | ||||
\(409\) | −35411.7 | − | 108986.i | −0.211690 | − | 0.651514i | −0.999372 | − | 0.0354325i | \(-0.988719\pi\) |
0.787682 | − | 0.616082i | \(-0.211281\pi\) | |||||||
\(410\) | −86772.1 | + | 119432.i | −0.516193 | + | 0.710479i | ||||
\(411\) | 43049.8 | + | 54272.9i | 0.254852 | + | 0.321292i | ||||
\(412\) | 18496.9 | − | 56927.6i | 0.108969 | − | 0.335374i | ||||
\(413\) | 95617.1 | + | 31067.9i | 0.560577 | + | 0.182143i | ||||
\(414\) | −64260.9 | + | 55553.9i | −0.374927 | + | 0.324126i | ||||
\(415\) | 311439. | + | 226274.i | 1.80833 | + | 1.31383i | ||||
\(416\) | −52621.0 | + | 17097.6i | −0.304069 | + | 0.0987981i | ||||
\(417\) | −11484.7 | + | 485.725i | −0.0660461 | + | 0.00279331i | ||||
\(418\) | 494.842 | − | 9729.22i | 0.00283214 | − | 0.0556833i | ||||
\(419\) | − | 101705.i | − | 0.579313i | −0.957131 | − | 0.289656i | \(-0.906459\pi\) | ||
0.957131 | − | 0.289656i | \(-0.0935410\pi\) | |||||||
\(420\) | −218882. | + | 81496.4i | −1.24083 | + | 0.461998i | ||||
\(421\) | 64516.7 | + | 46874.1i | 0.364006 | + | 0.264466i | 0.754721 | − | 0.656046i | \(-0.227772\pi\) |
−0.390715 | + | 0.920512i | \(0.627772\pi\) | |||||||
\(422\) | 7305.07 | + | 10054.6i | 0.0410204 | + | 0.0564597i | ||||
\(423\) | −113883. | − | 26619.7i | −0.636471 | − | 0.148772i | ||||
\(424\) | −73358.4 | + | 225774.i | −0.408054 | + | 1.25586i | ||||
\(425\) | −206529. | − | 284262.i | −1.14341 | − | 1.57377i | ||||
\(426\) | −70691.9 | − | 46928.8i | −0.389538 | − | 0.258595i | ||||
\(427\) | −130720. | − | 402315.i | −0.716946 | − | 2.20653i | ||||
\(428\) | 49320.1i | 0.269238i | ||||||||
\(429\) | 58958.1 | + | 504.082i | 0.320353 | + | 0.00273896i | ||||
\(430\) | 92810.5 | 0.501950 | ||||||||
\(431\) | −83407.5 | + | 27100.7i | −0.449004 | + | 0.145890i | −0.524786 | − | 0.851234i | \(-0.675855\pi\) |
0.0757818 | + | 0.997124i | \(0.475855\pi\) | |||||||
\(432\) | 1056.14 | + | 579.052i | 0.00565921 | + | 0.00310278i | ||||
\(433\) | −124523. | + | 90471.2i | −0.664161 | + | 0.482541i | −0.868066 | − | 0.496449i | \(-0.834637\pi\) |
0.203904 | + | 0.978991i | \(0.434637\pi\) | |||||||
\(434\) | −133925. | − | 43514.9i | −0.711021 | − | 0.231025i | ||||
\(435\) | 60952.8 | − | 218629.i | 0.322118 | − | 1.15539i | ||||
\(436\) | 69152.1 | − | 50242.0i | 0.363775 | − | 0.264298i | ||||
\(437\) | −8059.50 | + | 11093.0i | −0.0422032 | + | 0.0580877i | ||||
\(438\) | −26926.8 | + | 10025.6i | −0.140358 | + | 0.0522594i | ||||
\(439\) | 151417. | 0.785678 | 0.392839 | − | 0.919607i | \(-0.371493\pi\) | ||||
0.392839 | + | 0.919607i | \(0.371493\pi\) | |||||||
\(440\) | −255621. | − | 206346.i | −1.32036 | − | 1.06584i | ||||
\(441\) | 119256. | − | 10105.5i | 0.613200 | − | 0.0519614i | ||||
\(442\) | 12495.0 | + | 38455.6i | 0.0639574 | + | 0.196841i | ||||
\(443\) | 17596.8 | − | 24220.0i | 0.0896659 | − | 0.123415i | −0.761827 | − | 0.647780i | \(-0.775698\pi\) |
0.851493 | + | 0.524366i | \(0.175698\pi\) | |||||||
\(444\) | −89823.3 | + | 71248.7i | −0.455641 | + | 0.361419i | ||||
\(445\) | −551.349 | + | 1696.88i | −0.00278424 | + | 0.00856901i | ||||
\(446\) | −211034. | − | 68569.2i | −1.06092 | − | 0.344715i | ||||
\(447\) | 150728. | + | 190022.i | 0.754358 | + | 0.951020i | ||||
\(448\) | −129101. | − | 93797.0i | −0.643238 | − | 0.467340i | ||||
\(449\) | 91659.2 | − | 29781.9i | 0.454657 | − | 0.147727i | −0.0727312 | − | 0.997352i | \(-0.523172\pi\) |
0.527388 | + | 0.849625i | \(0.323172\pi\) | |||||||
\(450\) | 19813.8 | + | 233824.i | 0.0978461 | + | 1.15469i | ||||
\(451\) | −158825. | − | 60686.3i | −0.780846 | − | 0.298358i | ||||
\(452\) | − | 1021.65i | − | 0.00500063i | ||||||
\(453\) | 109368. | + | 293740.i | 0.532960 | + | 1.43142i | ||||
\(454\) | −165821. | − | 120476.i | −0.804505 | − | 0.584507i | ||||
\(455\) | 83909.9 | + | 115492.i | 0.405313 | + | 0.557865i | ||||
\(456\) | 18037.4 | + | 5028.73i | 0.0867448 | + | 0.0241840i | ||||
\(457\) | 33940.0 | − | 104457.i | 0.162510 | − | 0.500153i | −0.836334 | − | 0.548220i | \(-0.815306\pi\) |
0.998844 | + | 0.0480661i | \(0.0153058\pi\) | |||||||
\(458\) | 101447. | + | 139630.i | 0.483624 | + | 0.665652i | ||||
\(459\) | −105478. | + | 192384.i | −0.500654 | + | 0.913151i | ||||
\(460\) | 54419.1 | + | 167485.i | 0.257179 | + | 0.791516i | ||||
\(461\) | − | 202036.i | − | 0.950663i | −0.879807 | − | 0.475331i | \(-0.842328\pi\) | ||
0.879807 | − | 0.475331i | \(-0.157672\pi\) | |||||||
\(462\) | 97754.0 | + | 136995.i | 0.457984 | + | 0.641830i | ||||
\(463\) | 32028.7 | 0.149409 | 0.0747046 | − | 0.997206i | \(-0.476199\pi\) | ||||
0.0747046 | + | 0.997206i | \(0.476199\pi\) | |||||||
\(464\) | 935.980 | − | 304.118i | 0.00434741 | − | 0.00141256i | ||||
\(465\) | 192028. | − | 289264.i | 0.888093 | − | 1.33779i | ||||
\(466\) | −34098.4 | + | 24773.9i | −0.157023 | + | 0.114084i | ||||
\(467\) | 249117. | + | 80942.9i | 1.14227 | + | 0.371146i | 0.818226 | − | 0.574896i | \(-0.194958\pi\) |
0.324044 | + | 0.946042i | \(0.394958\pi\) | |||||||
\(468\) | −9824.39 | + | 42030.2i | −0.0448553 | + | 0.191898i | ||||
\(469\) | −85390.3 | + | 62039.7i | −0.388207 | + | 0.282049i | ||||
\(470\) | 89162.2 | − | 122721.i | 0.403632 | − | 0.555551i | ||||
\(471\) | 41639.6 | + | 111835.i | 0.187700 | + | 0.504124i | ||||
\(472\) | −103522. | −0.464676 | ||||||||
\(473\) | 27825.0 | + | 103207.i | 0.124369 | + | 0.461305i | ||||
\(474\) | −4570.57 | − | 108069.i | −0.0203430 | − | 0.480998i | ||||
\(475\) | 11705.1 | + | 36024.7i | 0.0518787 | + | 0.159666i | ||||
\(476\) | 108434. | − | 149246.i | 0.478575 | − | 0.658702i | ||||
\(477\) | 196104. | + | 226840.i | 0.861887 | + | 0.996972i | ||||
\(478\) | 64255.0 | − | 197757.i | 0.281223 | − | 0.865516i | ||||
\(479\) | −67738.2 | − | 22009.5i | −0.295231 | − | 0.0959264i | 0.157656 | − | 0.987494i | \(-0.449606\pi\) |
−0.452888 | + | 0.891568i | \(0.649606\pi\) | |||||||
\(480\) | 305075. | − | 241988.i | 1.32411 | − | 1.05030i | ||||
\(481\) | 56692.2 | + | 41189.3i | 0.245038 | + | 0.178031i | ||||
\(482\) | 235473. | − | 76509.9i | 1.01356 | − | 0.329324i | ||||
\(483\) | −10009.4 | − | 236666.i | −0.0429054 | − | 1.01447i | ||||
\(484\) | 58204.9 | − | 131823.i | 0.248467 | − | 0.562731i | ||||
\(485\) | 415350.i | 1.76576i | ||||||||
\(486\) | 126758. | − | 73505.3i | 0.536664 | − | 0.311204i | ||||
\(487\) | 77046.1 | + | 55977.3i | 0.324857 | + | 0.236023i | 0.738245 | − | 0.674532i | \(-0.235655\pi\) |
−0.413388 | + | 0.910555i | \(0.635655\pi\) | |||||||
\(488\) | 256025. | + | 352389.i | 1.07509 | + | 1.47973i | ||||
\(489\) | 17193.0 | − | 61669.0i | 0.0719009 | − | 0.257899i | ||||
\(490\) | −47969.7 | + | 147635.i | −0.199790 | + | 0.614891i | ||||
\(491\) | −156518. | − | 215429.i | −0.649234 | − | 0.893595i | 0.349831 | − | 0.936813i | \(-0.386239\pi\) |
−0.999066 | + | 0.0432182i | \(0.986239\pi\) | |||||||
\(492\) | 68841.2 | − | 103700.i | 0.284392 | − | 0.428398i | ||||
\(493\) | 55397.2 | + | 170495.i | 0.227926 | + | 0.701484i | ||||
\(494\) | − | 4358.98i | − | 0.0178620i | ||||||
\(495\) | −390095. | + | 141458.i | −1.59206 | + | 0.577322i | ||||
\(496\) | 1505.49 | 0.00611948 | ||||||||
\(497\) | 225033. | − | 73117.7i | 0.911032 | − | 0.296012i | ||||
\(498\) | 169182. | + | 112311.i | 0.682174 | + | 0.452861i | ||||
\(499\) | 305576. | − | 222014.i | 1.22721 | − | 0.891619i | 0.230530 | − | 0.973065i | \(-0.425954\pi\) |
0.996678 | + | 0.0814466i | \(0.0259540\pi\) | |||||||
\(500\) | 214988. | + | 69853.8i | 0.859951 | + | 0.279415i | ||||
\(501\) | −328339. | − | 91539.3i | −1.30812 | − | 0.364697i | ||||
\(502\) | 78737.3 | − | 57206.0i | 0.312445 | − | 0.227004i | ||||
\(503\) | −245604. | + | 338045.i | −0.970731 | + | 1.33610i | −0.0290545 | + | 0.999578i | \(0.509250\pi\) |
−0.941677 | + | 0.336519i | \(0.890750\pi\) | |||||||
\(504\) | −298118. | + | 125584.i | −1.17362 | + | 0.494395i | ||||
\(505\) | −434913. | −1.70537 | ||||||||
\(506\) | 106315. | − | 69275.2i | 0.415235 | − | 0.270568i | ||||
\(507\) | −230461. | + | 9746.95i | −0.896565 | + | 0.0379186i | ||||
\(508\) | −7348.73 | − | 22617.1i | −0.0284764 | − | 0.0876413i | ||||
\(509\) | −71723.5 | + | 98718.9i | −0.276838 | + | 0.381035i | −0.924683 | − | 0.380737i | \(-0.875670\pi\) |
0.647845 | + | 0.761772i | \(0.275670\pi\) | |||||||
\(510\) | −176846. | − | 222950.i | −0.679914 | − | 0.857168i | ||||
\(511\) | 24759.5 | − | 76202.0i | 0.0948202 | − | 0.291826i | ||||
\(512\) | 3218.07 | + | 1045.61i | 0.0122760 | + | 0.00398870i | ||||
\(513\) | 17223.3 | − | 16210.7i | 0.0654456 | − | 0.0615981i | ||||
\(514\) | −38390.8 | − | 27892.6i | −0.145312 | − | 0.105575i | ||||
\(515\) | 244880. | − | 79566.4i | 0.923292 | − | 0.299996i | ||||
\(516\) | −78183.0 | + | 3306.61i | −0.293638 | + | 0.0124189i | ||||
\(517\) | 163200. | + | 62357.9i | 0.610574 | + | 0.233298i | ||||
\(518\) | 200023.i | 0.745453i | ||||||||
\(519\) | 243355. | − | 90608.2i | 0.903453 | − | 0.336382i | ||||
\(520\) | −118920. | − | 86400.8i | −0.439795 | − | 0.319530i | ||||
\(521\) | −302718. | − | 416656.i | −1.11523 | − | 1.53498i | −0.813483 | − | 0.581588i | \(-0.802431\pi\) |
−0.301743 | − | 0.953389i | \(-0.597569\pi\) | |||||||
\(522\) | 27250.8 | − | 116583.i | 0.100009 | − | 0.427853i | ||||
\(523\) | −36028.9 | + | 110885.i | −0.131719 | + | 0.405388i | −0.995065 | − | 0.0992231i | \(-0.968364\pi\) |
0.863347 | + | 0.504611i | \(0.168364\pi\) | |||||||
\(524\) | −60394.2 | − | 83125.5i | −0.219955 | − | 0.302741i | ||||
\(525\) | −545182. | − | 361919.i | −1.97798 | − | 1.31309i | ||||
\(526\) | 86880.5 | + | 267391.i | 0.314015 | + | 0.966440i | ||||
\(527\) | 274235.i | 0.987420i | ||||||||
\(528\) | −1446.54 | − | 1069.99i | −0.00518875 | − | 0.00383805i | ||||
\(529\) | 101237. | 0.361768 | ||||||||
\(530\) | −369887. | + | 120184.i | −1.31679 | + | 0.427852i | ||||
\(531\) | −67652.7 | + | 111900.i | −0.239936 | + | 0.396863i | ||||
\(532\) | −16089.2 | + | 11689.5i | −0.0568475 | + | 0.0413021i | ||||
\(533\) | −72354.1 | − | 23509.3i | −0.254688 | − | 0.0827532i | ||||
\(534\) | −252.755 | + | 906.597i | −0.000886375 | + | 0.00317930i | ||||
\(535\) | −171638. | + | 124702.i | −0.599659 | + | 0.435678i | ||||
\(536\) | 63881.4 | − | 87925.2i | 0.222354 | − | 0.306044i | ||||
\(537\) | −246174. | + | 91657.8i | −0.853677 | + | 0.317849i | ||||
\(538\) | 147364. | 0.509129 | ||||||||
\(539\) | −178555. | − | 9081.58i | −0.614603 | − | 0.0312596i | ||||
\(540\) | −38416.7 | − | 301336.i | −0.131745 | − | 1.03339i | ||||
\(541\) | −82687.6 | − | 254486.i | −0.282518 | − | 0.869501i | −0.987132 | − | 0.159910i | \(-0.948880\pi\) |
0.704614 | − | 0.709591i | \(-0.251120\pi\) | |||||||
\(542\) | 28647.4 | − | 39429.8i | 0.0975185 | − | 0.134223i | ||||
\(543\) | 247355. | − | 196204.i | 0.838919 | − | 0.665439i | ||||
\(544\) | −95042.2 | + | 292510.i | −0.321158 | + | 0.988422i | ||||
\(545\) | 349691. | + | 113622.i | 1.17731 | + | 0.382532i | ||||
\(546\) | 46797.4 | + | 58997.6i | 0.156977 | + | 0.197901i | ||||
\(547\) | 251502. | + | 182727.i | 0.840557 | + | 0.610700i | 0.922526 | − | 0.385934i | \(-0.126121\pi\) |
−0.0819692 | + | 0.996635i | \(0.526121\pi\) | |||||||
\(548\) | 72049.1 | − | 23410.2i | 0.239920 | − | 0.0779549i | ||||
\(549\) | 548221. | − | 46455.1i | 1.81891 | − | 0.154131i | ||||
\(550\) | 17806.2 | − | 350093.i | 0.0588635 | − | 1.15733i | ||||
\(551\) | − | 19325.8i | − | 0.0636552i | ||||||
\(552\) | 85106.8 | + | 228579.i | 0.279310 | + | 0.750168i | ||||
\(553\) | 244022. | + | 177293.i | 0.797957 | + | 0.579749i | ||||
\(554\) | 69829.3 | + | 96111.8i | 0.227519 | + | 0.313154i | ||||
\(555\) | −475062. | − | 132445.i | −1.54228 | − | 0.429981i | ||||
\(556\) | −3884.58 | + | 11955.5i | −0.0125659 | + | 0.0386739i | ||||
\(557\) | 145059. | + | 199657.i | 0.467557 | + | 0.643538i | 0.976054 | − | 0.217526i | \(-0.0697987\pi\) |
−0.508497 | + | 0.861064i | \(0.669799\pi\) | |||||||
\(558\) | 94757.1 | − | 156731.i | 0.304329 | − | 0.503370i | ||||
\(559\) | 14780.0 | + | 45488.2i | 0.0472989 | + | 0.145571i | ||||
\(560\) | − | 4356.43i | − | 0.0138917i | ||||||
\(561\) | 194905. | − | 263497.i | 0.619296 | − | 0.837240i | ||||
\(562\) | −46229.9 | −0.146369 | ||||||||
\(563\) | −247637. | + | 80462.2i | −0.781266 | + | 0.253849i | −0.672381 | − | 0.740205i | \(-0.734728\pi\) |
−0.108886 | + | 0.994054i | \(0.534728\pi\) | |||||||
\(564\) | −70737.4 | + | 106556.i | −0.222377 | + | 0.334981i | ||||
\(565\) | 3555.41 | − | 2583.16i | 0.0111376 | − | 0.00809196i | ||||
\(566\) | 71712.3 | + | 23300.7i | 0.223852 | + | 0.0727339i | ||||
\(567\) | −59075.8 | + | 404314.i | −0.183757 | + | 1.25763i | ||||
\(568\) | −197107. | + | 143207.i | −0.610950 | + | 0.443881i | ||||
\(569\) | 333884. | − | 459551.i | 1.03127 | − | 1.41942i | 0.127273 | − | 0.991868i | \(-0.459378\pi\) |
0.903993 | − | 0.427548i | \(-0.140622\pi\) | |||||||
\(570\) | 10704.3 | + | 28749.6i | 0.0329465 | + | 0.0884876i | ||||
\(571\) | −317468. | −0.973707 | −0.486853 | − | 0.873484i | \(-0.661855\pi\) | ||||
−0.486853 | + | 0.873484i | \(0.661855\pi\) | |||||||
\(572\) | 23014.1 | − | 60231.2i | 0.0703399 | − | 0.184090i | ||||
\(573\) | −24744.8 | − | 585078.i | −0.0753660 | − | 1.78199i | ||||
\(574\) | −67104.6 | − | 206527.i | −0.203671 | − | 0.626834i | ||||
\(575\) | −290010. | + | 399165.i | −0.877157 | + | 1.20730i | ||||
\(576\) | 157010. | − | 135736.i | 0.473241 | − | 0.409119i | ||||
\(577\) | 714.336 | − | 2198.50i | 0.00214561 | − | 0.00660351i | −0.949978 | − | 0.312317i | \(-0.898895\pi\) |
0.952124 | + | 0.305713i | \(0.0988949\pi\) | |||||||
\(578\) | 16655.7 | + | 5411.77i | 0.0498549 | + | 0.0161988i | ||||
\(579\) | −423319. | + | 335781.i | −1.26273 | + | 1.00161i | ||||
\(580\) | −200805. | − | 145893.i | −0.596923 | − | 0.433690i | ||||
\(581\) | −538555. | + | 174987.i | −1.59543 | + | 0.518387i | ||||
\(582\) | 9258.10 | + | 218903.i | 0.0273323 | + | 0.646257i | ||||
\(583\) | −244540. | − | 375291.i | −0.719471 | − | 1.10416i | ||||
\(584\) | 82502.0i | 0.241902i | ||||||||
\(585\) | −171108. | + | 72080.4i | −0.499988 | + | 0.210623i | ||||
\(586\) | 180895. | + | 131428.i | 0.526783 | + | 0.382730i | ||||
\(587\) | −380539. | − | 523767.i | −1.10439 | − | 1.52006i | −0.829433 | − | 0.558606i | \(-0.811336\pi\) |
−0.274958 | − | 0.961456i | \(-0.588664\pi\) | |||||||
\(588\) | 35149.4 | − | 126076.i | 0.101663 | − | 0.364652i | ||||
\(589\) | 9135.61 | − | 28116.5i | 0.0263334 | − | 0.0810459i | ||||
\(590\) | −99689.3 | − | 137211.i | −0.286381 | − | 0.394170i | ||||
\(591\) | −208032. | + | 313371.i | −0.595599 | + | 0.897189i | ||||
\(592\) | −660.822 | − | 2033.80i | −0.00188556 | − | 0.00580316i | ||||
\(593\) | 163543.i | 0.465074i | 0.972587 | + | 0.232537i | \(0.0747027\pi\) | ||||
−0.972587 | + | 0.232537i | \(0.925297\pi\) | |||||||
\(594\) | −202439. | + | 83248.2i | −0.573749 | + | 0.235940i | ||||
\(595\) | 793552. | 2.24151 | ||||||||
\(596\) | 252261. | − | 81964.6i | 0.710162 | − | 0.230746i | ||||
\(597\) | −70805.2 | − | 47004.1i | −0.198663 | − | 0.131882i | ||||
\(598\) | 45935.0 | − | 33373.7i | 0.128452 | − | 0.0933259i | ||||
\(599\) | 441139. | + | 143335.i | 1.22948 | + | 0.399482i | 0.850526 | − | 0.525933i | \(-0.176284\pi\) |
0.378954 | + | 0.925415i | \(0.376284\pi\) | |||||||
\(600\) | 649050. | + | 180952.i | 1.80292 | + | 0.502644i | ||||
\(601\) | −164405. | + | 119448.i | −0.455163 | + | 0.330695i | −0.791631 | − | 0.611000i | \(-0.790768\pi\) |
0.336468 | + | 0.941695i | \(0.390768\pi\) | |||||||
\(602\) | −80246.2 | + | 110449.i | −0.221428 | + | 0.304769i | ||||
\(603\) | −53293.5 | − | 126511.i | −0.146568 | − | 0.347931i | ||||
\(604\) | 342775. | 0.939582 | ||||||||
\(605\) | 605920. | − | 130747.i | 1.65541 | − | 0.357208i | ||||
\(606\) | −229213. | + | 9694.15i | −0.624157 | + | 0.0263976i | ||||
\(607\) | 15539.4 | + | 47825.5i | 0.0421753 | + | 0.129802i | 0.969927 | − | 0.243396i | \(-0.0782613\pi\) |
−0.927752 | + | 0.373198i | \(0.878261\pi\) | |||||||
\(608\) | 19488.8 | − | 26824.0i | 0.0527202 | − | 0.0725632i | ||||
\(609\) | 207479. | + | 261569.i | 0.559422 | + | 0.705264i | ||||
\(610\) | −220517. | + | 678682.i | −0.592629 | + | 1.82392i | ||||
\(611\) | 74347.0 | + | 24156.8i | 0.199150 | + | 0.0647079i | ||||
\(612\) | 156917. | + | 181511.i | 0.418954 | + | 0.484618i | ||||
\(613\) | −423338. | − | 307573.i | −1.12659 | − | 0.818517i | −0.141397 | − | 0.989953i | \(-0.545159\pi\) |
−0.985195 | + | 0.171436i | \(0.945159\pi\) | |||||||
\(614\) | 50054.8 | − | 16263.8i | 0.132773 | − | 0.0431405i | ||||
\(615\) | 534942. | − | 22624.4i | 1.41435 | − | 0.0598174i | ||||
\(616\) | 466579. | − | 125791.i | 1.22960 | − | 0.331504i | ||||
\(617\) | 245951.i | 0.646067i | 0.946388 | + | 0.323033i | \(0.104703\pi\) | ||||
−0.946388 | + | 0.323033i | \(0.895297\pi\) | |||||||
\(618\) | 127286. | − | 47392.3i | 0.333276 | − | 0.124088i | ||||
\(619\) | −315525. | − | 229242.i | −0.823479 | − | 0.598293i | 0.0942276 | − | 0.995551i | \(-0.469962\pi\) |
−0.917707 | + | 0.397258i | \(0.869962\pi\) | |||||||
\(620\) | −223179. | − | 307180.i | −0.580591 | − | 0.799114i | ||||
\(621\) | 302695. | + | 57384.5i | 0.784914 | + | 0.148803i | ||||
\(622\) | 90245.2 | − | 277746.i | 0.233262 | − | 0.717905i | ||||
\(623\) | −1542.67 | − | 2123.30i | −0.00397462 | − | 0.00547059i | ||||
\(624\) | −670.741 | − | 445.272i | −0.00172261 | − | 0.00114355i | ||||
\(625\) | 75001.3 | + | 230830.i | 0.192003 | + | 0.590925i | ||||
\(626\) | − | 239929.i | − | 0.612258i | ||||||
\(627\) | −28761.0 | + | 20522.7i | −0.0731591 | + | 0.0522034i | ||||
\(628\) | 130504. | 0.330906 | ||||||||
\(629\) | 370470. | − | 120373.i | 0.936380 | − | 0.304248i | ||||
\(630\) | −453532. | − | 274198.i | −1.14269 | − | 0.690848i | ||||
\(631\) | −235710. | + | 171253.i | −0.591995 | + | 0.430110i | −0.843029 | − | 0.537869i | \(-0.819230\pi\) |
0.251033 | + | 0.967978i | \(0.419230\pi\) | |||||||
\(632\) | −295381. | − | 95975.2i | −0.739518 | − | 0.240284i | ||||
\(633\) | 12105.2 | − | 43419.5i | 0.0302108 | − | 0.108362i | ||||
\(634\) | −252813. | + | 183679.i | −0.628956 | + | 0.456963i | ||||
\(635\) | 60128.3 | − | 82759.5i | 0.149118 | − | 0.205244i | ||||
\(636\) | 307309. | − | 114420.i | 0.759732 | − | 0.282871i | ||||
\(637\) | −79998.1 | −0.197152 | ||||||||
\(638\) | −63836.3 | + | 167069.i | −0.156829 | + | 0.410444i | ||||
\(639\) | 25984.5 | + | 306645.i | 0.0636374 | + | 0.750990i | ||||
\(640\) | −130733. | − | 402355.i | −0.319173 | − | 0.982313i | ||||
\(641\) | 133364. | − | 183559.i | 0.324580 | − | 0.446746i | −0.615279 | − | 0.788310i | \(-0.710956\pi\) |
0.939859 | + | 0.341564i | \(0.110956\pi\) | |||||||
\(642\) | −87678.8 | + | 69547.6i | −0.212728 | + | 0.168738i | ||||
\(643\) | −187062. | + | 575718.i | −0.452443 | + | 1.39248i | 0.421668 | + | 0.906750i | \(0.361445\pi\) |
−0.874111 | + | 0.485727i | \(0.838555\pi\) | |||||||
\(644\) | −246368. | − | 80049.7i | −0.594035 | − | 0.193014i | ||||
\(645\) | −209187. | − | 263722.i | −0.502822 | − | 0.633908i | ||||
\(646\) | −19603.0 | − | 14242.4i | −0.0469741 | − | 0.0341287i | ||||
\(647\) | 195188. | − | 63420.3i | 0.466277 | − | 0.151502i | −0.0664502 | − | 0.997790i | \(-0.521167\pi\) |
0.532727 | + | 0.846287i | \(0.321167\pi\) | |||||||
\(648\) | −70796.5 | − | 414738.i | −0.168602 | − | 0.987696i | ||||
\(649\) | 122694. | − | 151993.i | 0.291295 | − | 0.360856i | ||||
\(650\) | − | 156852.i | − | 0.371247i | ||||||
\(651\) | 178207. | + | 478628.i | 0.420497 | + | 1.12937i | ||||
\(652\) | −56641.3 | − | 41152.3i | −0.133241 | − | 0.0968053i | ||||
\(653\) | 235646. | + | 324339.i | 0.552629 | + | 0.760629i | 0.990366 | − | 0.138474i | \(-0.0442198\pi\) |
−0.437737 | + | 0.899103i | \(0.644220\pi\) | |||||||
\(654\) | 186831. | + | 52087.5i | 0.436810 | + | 0.121781i | ||||
\(655\) | 136581. | − | 420352.i | 0.318352 | − | 0.979785i | ||||
\(656\) | 1364.62 | + | 1878.24i | 0.00317105 | + | 0.00436458i | ||||
\(657\) | 89178.5 | + | 53915.8i | 0.206600 | + | 0.124907i | ||||
\(658\) | 68953.0 | + | 212215.i | 0.159258 | + | 0.490146i | ||||
\(659\) | 591347.i | 1.36167i | 0.732438 | + | 0.680834i | \(0.238383\pi\) | ||||
−0.732438 | + | 0.680834i | \(0.761617\pi\) | |||||||
\(660\) | −3879.66 | + | 453770.i | −0.00890647 | + | 1.04171i | ||||
\(661\) | 177064. | 0.405255 | 0.202627 | − | 0.979256i | \(-0.435052\pi\) | ||||
0.202627 | + | 0.979256i | \(0.435052\pi\) | |||||||
\(662\) | 137655. | − | 44726.9i | 0.314107 | − | 0.102059i | ||||
\(663\) | 81109.2 | − | 122180.i | 0.184520 | − | 0.277954i | ||||
\(664\) | 471722. | − | 342726.i | 1.06992 | − | 0.777340i | ||||
\(665\) | −81360.5 | − | 26435.6i | −0.183980 | − | 0.0597787i | ||||
\(666\) | −253324. | − | 59213.6i | −0.571122 | − | 0.133497i | ||||
\(667\) | 203655. | − | 147964.i | 0.457766 | − | 0.332587i | ||||
\(668\) | −219103. | + | 301570.i | −0.491017 | + | 0.675827i | ||||
\(669\) | 280813. | + | 754205.i | 0.627429 | + | 1.68514i | ||||
\(670\) | 178054. | 0.396645 | ||||||||
\(671\) | −820821. | − | 41748.1i | −1.82307 | − | 0.0927240i | ||||
\(672\) | 24203.8 | + | 572284.i | 0.0535975 | + | 1.26728i | ||||
\(673\) | −134472. | − | 413863.i | −0.296895 | − | 0.913749i | −0.982578 | − | 0.185849i | \(-0.940497\pi\) |
0.685683 | − | 0.727900i | \(-0.259503\pi\) | |||||||
\(674\) | 241861. | − | 332893.i | 0.532409 | − | 0.732798i | ||||
\(675\) | 619755. | − | 583320.i | 1.36023 | − | 1.28026i | ||||
\(676\) | −77951.1 | + | 239909.i | −0.170580 | + | 0.524992i | ||||
\(677\) | −827565. | − | 268892.i | −1.80561 | − | 0.586679i | −0.805630 | − | 0.592419i | \(-0.798173\pi\) |
−0.999984 | + | 0.00573954i | \(0.998173\pi\) | |||||||
\(678\) | 1816.23 | − | 1440.65i | 0.00395105 | − | 0.00313401i | ||||
\(679\) | −494289. | − | 359122.i | −1.07211 | − | 0.778937i | ||||
\(680\) | −777117. | + | 252501.i | −1.68062 | + | 0.546065i | ||||
\(681\) | 31412.3 | + | 742725.i | 0.0677338 | + | 1.60153i | ||||
\(682\) | −171850. | + | 212887.i | −0.369471 | + | 0.457700i | ||||
\(683\) | − | 518249.i | − | 1.11096i | −0.831531 | − | 0.555479i | \(-0.812535\pi\) | ||
0.831531 | − | 0.555479i | \(-0.187465\pi\) | |||||||
\(684\) | −10041.5 | − | 23837.1i | −0.0214629 | − | 0.0509497i | ||||
\(685\) | 263639. | + | 191545.i | 0.561861 | + | 0.408216i | ||||
\(686\) | 83881.8 | + | 115453.i | 0.178246 | + | 0.245334i | ||||
\(687\) | 168107. | − | 602975.i | 0.356182 | − | 1.27757i | ||||
\(688\) | 451.036 | − | 1388.14i | 0.000952871 | − | 0.00293263i | ||||
\(689\) | −117809. | − | 162150.i | −0.248164 | − | 0.341568i | ||||
\(690\) | −221008. | + | 332918.i | −0.464205 | + | 0.699261i | ||||
\(691\) | −19772.5 | − | 60853.4i | −0.0414099 | − | 0.127447i | 0.928214 | − | 0.372046i | \(-0.121344\pi\) |
−0.969624 | + | 0.244599i | \(0.921344\pi\) | |||||||
\(692\) | − | 283979.i | − | 0.593026i | ||||||
\(693\) | 168943. | − | 586543.i | 0.351782 | − | 1.22133i | ||||
\(694\) | 66721.0 | 0.138530 | ||||||||
\(695\) | −51427.9 | + | 16709.9i | −0.106470 | + | 0.0345943i | ||||
\(696\) | −286411. | − | 190134.i | −0.591250 | − | 0.392501i | ||||
\(697\) | −342133. | + | 248574.i | −0.704255 | + | 0.511671i | ||||
\(698\) | −122600. | − | 39835.0i | −0.251639 | − | 0.0817625i | ||||
\(699\) | 147250. | + | 41052.6i | 0.301371 | + | 0.0840207i | ||||
\(700\) | −578948. | + | 420630.i | −1.18153 | + | 0.858429i | ||||
\(701\) | 276626. | − | 380744.i | 0.562934 | − | 0.774812i | −0.428762 | − | 0.903418i | \(-0.641050\pi\) |
0.991696 | + | 0.128605i | \(0.0410500\pi\) | |||||||
\(702\) | −88572.8 | + | 41802.6i | −0.179732 | + | 0.0848261i | ||||
\(703\) | −41993.2 | −0.0849705 | ||||||||
\(704\) | −259762. | + | 169262.i | −0.524119 | + | 0.341517i | ||||
\(705\) | −549677. | + | 23247.6i | −1.10593 | + | 0.0467735i | ||||
\(706\) | −97034.7 | − | 298642.i | −0.194678 | − | 0.599159i | ||||
\(707\) | 376036. | − | 517569.i | 0.752300 | − | 1.03545i | ||||
\(708\) | 88866.1 | + | 112034.i | 0.177284 | + | 0.223502i | ||||
\(709\) | −135622. | + | 417402.i | −0.269797 | + | 0.830351i | 0.720752 | + | 0.693193i | \(0.243797\pi\) |
−0.990549 | + | 0.137158i | \(0.956203\pi\) | |||||||
\(710\) | −379618. | − | 123345.i | −0.753061 | − | 0.244684i | ||||
\(711\) | −296776. | + | 256564.i | −0.587070 | + | 0.507524i | ||||
\(712\) | 2186.33 | + | 1588.46i | 0.00431276 | + | 0.00313340i | ||||
\(713\) | 366237. | − | 118998.i | 0.720416 | − | 0.234077i | ||||
\(714\) | 418227. | − | 17688.2i | 0.820381 | − | 0.0346966i | ||||
\(715\) | 267798. | − | 72199.2i | 0.523836 | − | 0.141228i | ||||
\(716\) | 287268.i | 0.560353i | ||||||||
\(717\) | −706752. | + | 263144.i | −1.37477 | + | 0.511866i | ||||
\(718\) | 377965. | + | 274608.i | 0.733167 | + | 0.532677i | ||||
\(719\) | 323463. | + | 445209.i | 0.625701 | + | 0.861204i | 0.997752 | − | 0.0670082i | \(-0.0213454\pi\) |
−0.372051 | + | 0.928212i | \(0.621345\pi\) | |||||||
\(720\) | 5517.32 | + | 1289.65i | 0.0106430 | + | 0.00248775i | ||||
\(721\) | −117041. | + | 360215.i | −0.225148 | + | 0.692934i | ||||
\(722\) | −188547. | − | 259513.i | −0.361698 | − | 0.497834i | ||||
\(723\) | −748139. | − | 496652.i | −1.43122 | − | 0.950115i | ||||
\(724\) | −106694. | − | 328371.i | −0.203547 | − | 0.626452i | ||||
\(725\) | − | 695412.i | − | 1.32302i | ||||||
\(726\) | 316425. | − | 82413.6i | 0.600340 | − | 0.156360i | ||||
\(727\) | −307836. | −0.582440 | −0.291220 | − | 0.956656i | \(-0.594061\pi\) | ||||
−0.291220 | + | 0.956656i | \(0.594061\pi\) | |||||||
\(728\) | 205643. | − | 66817.5i | 0.388017 | − | 0.126074i | ||||
\(729\) | −494566. | − | 194509.i | −0.930614 | − | 0.366003i | ||||
\(730\) | −109350. | + | 79447.3i | −0.205198 | + | 0.149085i | ||||
\(731\) | 252860. | + | 82159.1i | 0.473200 | + | 0.153752i | ||||
\(732\) | 161582. | − | 579574.i | 0.301559 | − | 1.08165i | ||||
\(733\) | 798862. | − | 580407.i | 1.48684 | − | 1.08025i | 0.511565 | − | 0.859244i | \(-0.329066\pi\) |
0.975272 | − | 0.221006i | \(-0.0709342\pi\) | |||||||
\(734\) | −366660. | + | 504664.i | −0.680568 | + | 0.936722i | ||||
\(735\) | 527626. | − | 196451.i | 0.976679 | − | 0.363646i | ||||
\(736\) | 431883. | 0.797280 | ||||||||
\(737\) | 53381.2 | + | 198000.i | 0.0982774 | + | 0.364527i | ||||
\(738\) | 281427. | − | 23847.6i | 0.516717 | − | 0.0437856i | ||||
\(739\) | 202258. | + | 622485.i | 0.370353 | + | 1.13983i | 0.946561 | + | 0.322526i | \(0.104532\pi\) |
−0.576207 | + | 0.817303i | \(0.695468\pi\) | |||||||
\(740\) | −317013. | + | 436331.i | −0.578913 | + | 0.796806i | ||||
\(741\) | −12386.1 | + | 9824.75i | −0.0225578 | + | 0.0178931i | ||||
\(742\) | 176789. | − | 544099.i | 0.321104 | − | 0.988258i | ||||
\(743\) | 470010. | + | 152716.i | 0.851392 | + | 0.276634i | 0.702029 | − | 0.712148i | \(-0.252278\pi\) |
0.149363 | + | 0.988782i | \(0.452278\pi\) | |||||||
\(744\) | −326811. | − | 412011.i | −0.590406 | − | 0.744326i | ||||
\(745\) | 923064. | + | 670645.i | 1.66310 | + | 1.20832i | ||||
\(746\) | 247645. | − | 80464.6i | 0.444991 | − | 0.144586i | ||||
\(747\) | −62186.8 | − | 733871.i | −0.111444 | − | 1.31516i | ||||
\(748\) | −195674. | − | 300296.i | −0.349727 | − | 0.536719i | ||||
\(749\) | − | 312078.i | − | 0.556288i | ||||||
\(750\) | 178978. | + | 480697.i | 0.318182 | + | 0.854572i | ||||
\(751\) | 142450. | + | 103496.i | 0.252571 | + | 0.183504i | 0.706866 | − | 0.707348i | \(-0.250109\pi\) |
−0.454294 | + | 0.890852i | \(0.650109\pi\) | |||||||
\(752\) | −1402.21 | − | 1929.97i | −0.00247957 | − | 0.00341283i | ||||
\(753\) | −340018. | − | 94795.4i | −0.599670 | − | 0.167185i | ||||
\(754\) | −24729.5 | + | 76109.7i | −0.0434984 | + | 0.133874i | ||||
\(755\) | 866678. | + | 1.19288e6i | 1.52042 | + | 2.09268i | ||||
\(756\) | 391821. | + | 214824.i | 0.685559 | + | 0.375871i | ||||
\(757\) | −46810.8 | − | 144069.i | −0.0816873 | − | 0.251408i | 0.901869 | − | 0.432010i | \(-0.142195\pi\) |
−0.983556 | + | 0.180602i | \(0.942195\pi\) | |||||||
\(758\) | 365306.i | 0.635797i | ||||||||
\(759\) | −436471. | − | 145955.i | −0.757655 | − | 0.253359i | ||||
\(760\) | 88087.0 | 0.152505 | ||||||||
\(761\) | 436830. | − | 141935.i | 0.754298 | − | 0.245086i | 0.0934685 | − | 0.995622i | \(-0.470205\pi\) |
0.660830 | + | 0.750536i | \(0.270205\pi\) | |||||||
\(762\) | 29844.8 | − | 44957.1i | 0.0513995 | − | 0.0774263i | ||||
\(763\) | −437567. | + | 317911.i | −0.751615 | + | 0.546080i | ||||
\(764\) | −609063. | − | 197897.i | −1.04346 | − | 0.339040i | ||||
\(765\) | −234918. | + | 1.00502e6i | −0.401416 | + | 1.71732i | ||||
\(766\) | −452663. | + | 328879.i | −0.771466 | + | 0.560503i | ||||
\(767\) | 51374.0 | − | 70710.3i | 0.0873279 | − | 0.120197i | ||||
\(768\) | −206615. | − | 554925.i | −0.350299 | − | 0.940831i | ||||
\(769\) | −686932. | −1.16161 | −0.580806 | − | 0.814042i | \(-0.697263\pi\) | ||||
−0.580806 | + | 0.814042i | \(0.697263\pi\) | |||||||
\(770\) | 616030. | + | 497280.i | 1.03901 | + | 0.838725i | ||||
\(771\) | 7272.54 | + | 171955.i | 0.0122343 | + | 0.289272i | ||||
\(772\) | 182595. | + | 561970.i | 0.306376 | + | 0.942929i | ||||
\(773\) | −399325. | + | 549624.i | −0.668294 | + | 0.919828i | −0.999720 | − | 0.0236528i | \(-0.992470\pi\) |
0.331426 | + | 0.943481i | \(0.392470\pi\) | |||||||
\(774\) | −116126. | − | 134327.i | −0.193842 | − | 0.224223i | ||||
\(775\) | 328732. | − | 1.01173e6i | 0.547317 | − | 1.68447i | ||||
\(776\) | 598321. | + | 194406.i | 0.993598 | + | 0.322840i | ||||
\(777\) | 568366. | − | 450833.i | 0.941426 | − | 0.746748i | ||||
\(778\) | −141008. | − | 102448.i | −0.232961 | − | 0.169256i | ||||
\(779\) | 43358.7 | − | 14088.1i | 0.0714498 | − | 0.0232154i | ||||
\(780\) | 8579.87 | + | 202866.i | 0.0141024 | + | 0.333442i | ||||
\(781\) | 23351.7 | − | 459123.i | 0.0382838 | − | 0.752708i | ||||
\(782\) | − | 315622.i | − | 0.516123i | ||||||
\(783\) | −392692. | + | 185334.i | −0.640515 | + | 0.302296i | ||||
\(784\) | 1975.03 | + | 1434.94i | 0.00321322 | + | 0.00233454i | ||||
\(785\) | 329969. | + | 454164.i | 0.535469 | + | 0.737009i | ||||
\(786\) | 62612.7 | − | 224583.i | 0.101349 | − | 0.363523i | ||||
\(787\) | −217386. | + | 669047.i | −0.350980 | + | 1.08021i | 0.607323 | + | 0.794455i | \(0.292243\pi\) |
−0.958304 | + | 0.285752i | \(0.907757\pi\) | |||||||
\(788\) | 241779. | + | 332780.i | 0.389373 | + | 0.535926i | ||||
\(789\) | 563972. | − | 849546.i | 0.905948 | − | 1.36469i | ||||
\(790\) | −157237. | − | 483926.i | −0.251942 | − | 0.775398i | ||||
\(791\) | 6464.59i | 0.0103321i | ||||||||
\(792\) | 21188.3 | + | 628151.i | 0.0337789 | + | 1.00141i | ||||
\(793\) | −367752. | −0.584802 | ||||||||
\(794\) | −402330. | + | 130725.i | −0.638177 | + | 0.207356i | ||||
\(795\) | 1.17520e6 | + | 780154.i | 1.85941 | + | 1.23437i | ||||
\(796\) | −75190.6 | + | 54629.2i | −0.118669 | + | 0.0862181i | ||||
\(797\) | −224589. | − | 72973.5i | −0.353568 | − | 0.114881i | 0.126848 | − | 0.991922i | \(-0.459514\pi\) |
−0.480415 | + | 0.877041i | \(0.659514\pi\) | |||||||
\(798\) | −43468.8 | − | 12118.9i | −0.0682609 | − | 0.0190308i | ||||
\(799\) | 351557. | − | 255421.i | 0.550684 | − | 0.400095i | ||||
\(800\) | 701277. | − | 965225.i | 1.09575 | − | 1.50816i | ||||
\(801\) | 3145.79 | − | 1325.18i | 0.00490303 | − | 0.00206543i | ||||
\(802\) | −573251. | −0.891243 | ||||||||
\(803\) | −121131. | − | 97780.7i | −0.187855 | − | 0.151643i | ||||
\(804\) | −149991. | + | 6343.62i | −0.232035 | + | 0.00981353i | ||||
\(805\) | −344342. | − | 1.05978e6i | −0.531372 | − | 1.63539i | ||||
\(806\) | −71956.5 | + | 99039.6i | −0.110764 | + | 0.152454i | ||||
\(807\) | −332146. | − | 418736.i | −0.510013 | − | 0.642974i | ||||
\(808\) | −203563. | + | 626501.i | −0.311799 | + | 0.959620i | ||||
\(809\) | 544292. | + | 176851.i | 0.831639 | + | 0.270216i | 0.693735 | − | 0.720230i | \(-0.255964\pi\) |
0.137903 | + | 0.990446i | \(0.455964\pi\) | |||||||
\(810\) | 481526. | − | 493217.i | 0.733922 | − | 0.751740i | ||||
\(811\) | 725780. | + | 527310.i | 1.10348 | + | 0.801723i | 0.981624 | − | 0.190825i | \(-0.0611163\pi\) |
0.121853 | + | 0.992548i | \(0.461116\pi\) | |||||||
\(812\) | 347242. | − | 112826.i | 0.526647 | − | 0.171118i | ||||
\(813\) | −176609. | + | 7469.36i | −0.267197 | + | 0.0113006i | ||||
\(814\) | 363026. | + | 138711.i | 0.547884 | + | 0.209344i | ||||
\(815\) | − | 301166.i | − | 0.453409i | ||||||
\(816\) | −4194.03 | + | 1561.56i | −0.00629870 | + | 0.00234519i | ||||
\(817\) | −23188.0 | − | 16847.1i | −0.0347391 | − | 0.0252395i | ||||
\(818\) | −167144. | − | 230055.i | −0.249796 | − | 0.343815i | ||||
\(819\) | 62164.8 | − | 265950.i | 0.0926781 | − | 0.396491i | ||||
\(820\) | 180939. | − | 556872.i | 0.269094 | − | 0.828185i | ||||
\(821\) | −32582.8 | − | 44846.4i | −0.0483396 | − | 0.0665337i | 0.784163 | − | 0.620555i | \(-0.213093\pi\) |
−0.832503 | + | 0.554021i | \(0.813093\pi\) | |||||||
\(822\) | 143216. | + | 95073.8i | 0.211957 | + | 0.140708i | ||||
\(823\) | 116561. | + | 358738.i | 0.172089 | + | 0.529636i | 0.999489 | − | 0.0319778i | \(-0.0101806\pi\) |
−0.827399 | + | 0.561614i | \(0.810181\pi\) | |||||||
\(824\) | − | 389996.i | − | 0.574389i | ||||||
\(825\) | −1.03492e6 | + | 738481.i | −1.52055 | + | 1.08500i | ||||
\(826\) | 249482. | 0.365661 | ||||||||
\(827\) | −643847. | + | 209199.i | −0.941395 | + | 0.305878i | −0.739214 | − | 0.673470i | \(-0.764803\pi\) |
−0.202181 | + | 0.979348i | \(0.564803\pi\) | |||||||
\(828\) | 174314. | − | 288322.i | 0.254257 | − | 0.420549i | ||||
\(829\) | 656852. | − | 477231.i | 0.955781 | − | 0.694416i | 0.00361429 | − | 0.999993i | \(-0.498850\pi\) |
0.952167 | + | 0.305578i | \(0.0988495\pi\) | |||||||
\(830\) | 908513. | + | 295194.i | 1.31879 | + | 0.428500i | ||||
\(831\) | 115713. | − | 415048.i | 0.167564 | − | 0.601030i | ||||
\(832\) | −112234. | + | 81542.6i | −0.162135 | + | 0.117798i | ||||
\(833\) | −261384. | + | 359764.i | −0.376694 | + | 0.518475i | ||||
\(834\) | −26731.6 | + | 9952.98i | −0.0384320 | + | 0.0143094i | ||||
\(835\) | −1.60347e6 | −2.29979 | ||||||||
\(836\) | 10058.1 | + | 37307.0i | 0.0143914 | + | 0.0533799i | ||||
\(837\) | −658927. | + | 84005.4i | −0.940560 | + | 0.119910i | ||||
\(838\) | −77988.8 | − | 240025.i | −0.111057 | − | 0.341797i | ||||
\(839\) | −240483. | + | 330997.i | −0.341634 | + | 0.470218i | −0.944918 | − | 0.327308i | \(-0.893859\pi\) |
0.603284 | + | 0.797526i | \(0.293859\pi\) | |||||||
\(840\) | −1.19223e6 | + | 945690.i | −1.68967 | + | 1.34026i | ||||
\(841\) | 108922. | − | 335228.i | 0.154001 | − | 0.473967i | ||||
\(842\) | 188205. | + | 61151.4i | 0.265464 | + | 0.0862545i | ||||
\(843\) | 104198. | + | 131363.i | 0.146624 | + | 0.184849i | ||||
\(844\) | −39879.6 | − | 28974.2i | −0.0559843 | − | 0.0406750i | ||||
\(845\) | −1.03199e6 | + | 335315.i | −1.44532 | + | 0.469612i | ||||
\(846\) | −289179. | + | 24504.4i | −0.404041 | + | 0.0342377i | ||||
\(847\) | −368297. | + | 834124.i | −0.513372 | + | 1.16269i | ||||
\(848\) | 6116.38i | 0.00850555i | ||||||||
\(849\) | −95423.8 | − | 256289.i | −0.132386 | − | 0.355561i | ||||
\(850\) | −705389. | − | 512495.i | −0.976317 | − | 0.709336i | ||||
\(851\) | −321513. | − | 442524.i | −0.443955 | − | 0.611052i | ||||
\(852\) | 324182. | + | 90380.5i | 0.446591 | + | 0.124507i | ||||
\(853\) | 61041.9 | − | 187868.i | 0.0838938 | − | 0.258199i | −0.900307 | − | 0.435256i | \(-0.856658\pi\) |
0.984201 | + | 0.177057i | \(0.0566578\pi\) | |||||||
\(854\) | −617003. | − | 849232.i | −0.846003 | − | 1.16442i | ||||
\(855\) | 57565.6 | − | 95215.5i | 0.0787465 | − | 0.130249i | ||||
\(856\) | 99300.2 | + | 305615.i | 0.135520 | + | 0.417087i | ||||
\(857\) | 298001.i | 0.405747i | 0.979205 | + | 0.202874i | \(0.0650281\pi\) | ||||
−0.979205 | + | 0.202874i | \(0.934972\pi\) | |||||||
\(858\) | 139529. | − | 44020.4i | 0.189535 | − | 0.0597970i | ||||
\(859\) | 322700. | 0.437333 | 0.218667 | − | 0.975800i | \(-0.429829\pi\) | ||||
0.218667 | + | 0.975800i | \(0.429829\pi\) | |||||||
\(860\) | −350099. | + | 113754.i | −0.473363 | + | 0.153805i | ||||
\(861\) | −435599. | + | 656171.i | −0.587599 | + | 0.885137i | ||||
\(862\) | −176062. | + | 127917.i | −0.236947 | + | 0.172152i | ||||
\(863\) | −610114. | − | 198238.i | −0.819200 | − | 0.266174i | −0.130710 | − | 0.991421i | \(-0.541726\pi\) |
−0.688489 | + | 0.725247i | \(0.741726\pi\) | |||||||
\(864\) | −731950. | − | 138762.i | −0.980515 | − | 0.185885i | ||||
\(865\) | 988265. | − | 718017.i | 1.32081 | − | 0.959627i | ||||
\(866\) | −224502. | + | 309000.i | −0.299353 | + | 0.412024i | ||||
\(867\) | −22162.9 | − | 59524.9i | −0.0294841 | − | 0.0791883i | ||||
\(868\) | 558526. | 0.741317 | ||||||||
\(869\) | 490995. | − | 319934.i | 0.650186 | − | 0.423663i | ||||
\(870\) | −23798.8 | − | 562709.i | −0.0314424 | − | 0.743439i | ||||
\(871\) | 28355.0 | + | 87267.6i | 0.0373760 | + | 0.115031i | ||||
\(872\) | 327348. | − | 450556.i | 0.430504 | − | 0.592538i | ||||
\(873\) | 601146. | − | 519694.i | 0.788772 | − | 0.681897i | ||||
\(874\) | −10514.3 | + | 32359.7i | −0.0137644 | + | 0.0423625i | ||||
\(875\) | −1.36036e6 | − | 442007.i | −1.77679 | − | 0.577315i | ||||
\(876\) | 89285.1 | − | 70821.8i | 0.116351 | − | 0.0922908i | ||||
\(877\) | 974345. | + | 707903.i | 1.26682 | + | 0.920396i | 0.999071 | − | 0.0430934i | \(-0.0137213\pi\) |
0.267746 | + | 0.963490i | \(0.413721\pi\) | |||||||
\(878\) | 357346. | − | 116109.i | 0.463554 | − | 0.150618i | ||||
\(879\) | −34267.8 | − | 810242.i | −0.0443515 | − | 1.04867i | ||||
\(880\) | −7906.57 | − | 3021.07i | −0.0102099 | − | 0.00390117i | ||||
\(881\) | 1.48732e6i | 1.91625i | 0.286353 | + | 0.958124i | \(0.407557\pi\) | ||||
−0.286353 | + | 0.958124i | \(0.592443\pi\) | |||||||
\(882\) | 273697. | − | 115296.i | 0.351830 | − | 0.148210i | ||||
\(883\) | 404328. | + | 293762.i | 0.518576 | + | 0.376768i | 0.816067 | − | 0.577957i | \(-0.196150\pi\) |
−0.297491 | + | 0.954725i | \(0.596150\pi\) | |||||||
\(884\) | −94266.9 | − | 129747.i | −0.120630 | − | 0.166033i | ||||
\(885\) | −165194. | + | 592528.i | −0.210915 | + | 0.756523i | ||||
\(886\) | 22956.6 | − | 70653.2i | 0.0292442 | − | 0.0900045i | ||||
\(887\) | −521536. | − | 717832.i | −0.662883 | − | 0.912380i | 0.336690 | − | 0.941616i | \(-0.390693\pi\) |
−0.999573 | + | 0.0292356i | \(0.990693\pi\) | |||||||
\(888\) | −413144. | + | 622345.i | −0.523933 | + | 0.789233i | ||||
\(889\) | 46499.8 | + | 143112.i | 0.0588366 | + | 0.181080i | ||||
\(890\) | 4427.45i | 0.00558951i | ||||||||
\(891\) | 692830. | + | 387599.i | 0.872713 | + | 0.488233i | ||||
\(892\) | 880105. | 1.10613 | ||||||||
\(893\) | −44553.0 | + | 14476.1i | −0.0558694 | + | 0.0181531i | ||||
\(894\) | 501432. | + | 332876.i | 0.627389 | + | 0.416493i | ||||
\(895\) | −999714. | + | 726335.i | −1.24804 | + | 0.906756i | ||||
\(896\) | 591859. | + | 192307.i | 0.737229 | + | 0.239540i | ||||
\(897\) | −198365. | − | 55303.2i | −0.246536 | − | 0.0687330i | ||||
\(898\) | 193480. | − | 140572.i | 0.239930 | − | 0.174319i | ||||
\(899\) | −319023. | + | 439098.i | −0.394733 | + | 0.543303i | ||||
\(900\) | −361331. | − | 857746.i | −0.446087 | − | 1.05895i | ||||
\(901\) | −1.11414e6 | −1.37243 | ||||||||
\(902\) | −421365. | − | 21431.3i | −0.517900 | − | 0.0263411i | ||||
\(903\) | 494711. | − | 20922.9i | 0.606702 | − | 0.0256594i | ||||
\(904\) | −2056.97 | − | 6330.70i | −0.00251704 | − | 0.00774666i | ||||
\(905\) | 872987. | − | 1.20156e6i | 1.06589 | − | 1.46707i | ||||
\(906\) | 483356. | + | 609367.i | 0.588858 | + | 0.742374i | ||||
\(907\) | 379037. | − | 1.16656e6i | 0.460751 | − | 1.41805i | −0.403496 | − | 0.914981i | \(-0.632205\pi\) |
0.864248 | − | 0.503066i | \(-0.167795\pi\) | |||||||
\(908\) | 773173. | + | 251219.i | 0.937789 | + | 0.304706i | ||||
\(909\) | 544171. | + | 629460.i | 0.658578 | + | 0.761799i | ||||
\(910\) | 286590. | + | 208220.i | 0.346082 | + | 0.251443i | ||||
\(911\) | 675515. | − | 219488.i | 0.813951 | − | 0.264469i | 0.127681 | − | 0.991815i | \(-0.459247\pi\) |
0.686270 | + | 0.727347i | \(0.259247\pi\) | |||||||
\(912\) | 482.021 | − | 20.3862i | 0.000579531 | − | 2.45102e-5i | ||||
\(913\) | −55885.8 | + | 1.09878e6i | −0.0670440 | + | 1.31817i | ||||
\(914\) | − | 272545.i | − | 0.326247i | ||||||
\(915\) | 2.42551e6 | − | 903087.i | 2.89708 | − | 1.07867i | ||||
\(916\) | −553816. | − | 402371.i | −0.660047 | − | 0.479552i | ||||
\(917\) | 382151. | + | 525985.i | 0.454460 | + | 0.625511i | ||||
\(918\) | −101408. | + | 534911.i | −0.120333 | + | 0.634741i | ||||
\(919\) | −35490.4 | + | 109228.i | −0.0420223 | + | 0.129331i | −0.969867 | − | 0.243636i | \(-0.921660\pi\) |
0.927844 | + | 0.372967i | \(0.121660\pi\) | |||||||
\(920\) | 674421. | + | 928261.i | 0.796811 | + | 1.09672i | ||||
\(921\) | −159033. | − | 105574.i | −0.187485 | − | 0.124462i | ||||
\(922\) | −154924. | − | 476808.i | −0.182246 | − | 0.560896i | ||||
\(923\) | − | 205701.i | − | 0.241453i | ||||||
\(924\) | −536656. | − | 396958.i | −0.628568 | − | 0.464943i | ||||
\(925\) | −1.51107e6 | −1.76604 | ||||||||
\(926\) | 75588.4 | − | 24560.2i | 0.0881522 | − | 0.0286424i | ||||
\(927\) | −421557. | − | 254866.i | −0.490565 | − | 0.296587i | ||||
\(928\) | −492461. | + | 357794.i | −0.571842 | + | 0.415468i | ||||
\(929\) | −1.10210e6 | − | 358093.i | −1.27699 | − | 0.414921i | −0.409474 | − | 0.912322i | \(-0.634288\pi\) |
−0.867520 | + | 0.497401i | \(0.834288\pi\) | |||||||
\(930\) | 231377. | − | 829918.i | 0.267519 | − | 0.959554i | ||||
\(931\) | 38783.8 | − | 28178.1i | 0.0447456 | − | 0.0325096i | ||||
\(932\) | 98261.3 | − | 135245.i | 0.113123 | − | 0.155700i | ||||
\(933\) | −992622. | + | 369582.i | −1.14030 | + | 0.424569i | ||||
\(934\) | 649988. | 0.745095 | ||||||||
\(935\) | 550307. | − | 1.44023e6i | 0.629480 | − | 1.64744i | ||||
\(936\) | 23745.5 | + | 280223.i | 0.0271038 | + | 0.319854i | ||||
\(937\) | 221814. | + | 682673.i | 0.252644 | + | 0.777559i | 0.994285 | + | 0.106762i | \(0.0340481\pi\) |
−0.741640 | + | 0.670798i | \(0.765952\pi\) | |||||||
\(938\) | −153950. | + | 211894.i | −0.174974 | + | 0.240831i | ||||
\(939\) | −681760. | + | 540778.i | −0.773215 | + | 0.613321i | ||||
\(940\) | −185923. | + | 572211.i | −0.210415 | + | 0.647590i | ||||
\(941\) | 338288. | + | 109916.i | 0.382038 | + | 0.124132i | 0.493739 | − | 0.869610i | \(-0.335630\pi\) |
−0.111701 | + | 0.993742i | \(0.535630\pi\) | |||||||
\(942\) | 184027. | + | 232003.i | 0.207387 | + | 0.261452i | ||||
\(943\) | 480427. | + | 349051.i | 0.540262 | + | 0.392523i | ||||
\(944\) | −2536.69 | + | 824.220i | −0.00284658 | + | 0.000924910i | ||||
\(945\) | 243086. | + | 1.90673e6i | 0.272205 | + | 2.13514i | ||||
\(946\) | 144808. | + | 222234.i | 0.161812 | + | 0.248330i | ||||
\(947\) | − | 333162.i | − | 0.371497i | −0.982597 | − | 0.185748i | \(-0.940529\pi\) | ||
0.982597 | − | 0.185748i | \(-0.0594709\pi\) | |||||||
\(948\) | 149696. | + | 402054.i | 0.166569 | + | 0.447371i | ||||
\(949\) | −56352.5 | − | 40942.5i | −0.0625721 | − | 0.0454613i | ||||
\(950\) | 55248.6 | + | 76043.2i | 0.0612173 | + | 0.0842584i | ||||
\(951\) | 1.09174e6 | + | 304373.i | 1.20714 | + | 0.336546i | ||||
\(952\) | 371425. | − | 1.14313e6i | 0.409824 | − | 1.26131i | ||||
\(953\) | −827584. | − | 1.13907e6i | −0.911226 | − | 1.25419i | −0.966746 | − | 0.255737i | \(-0.917682\pi\) |
0.0555203 | − | 0.998458i | \(-0.482318\pi\) | |||||||
\(954\) | 636754. | + | 384971.i | 0.699641 | + | 0.422991i | ||||
\(955\) | −851273. | − | 2.61995e6i | −0.933387 | − | 2.87267i | ||||
\(956\) | 824731.i | 0.902394i | ||||||||
\(957\) | 618609. | − | 195167.i | 0.675448 | − | 0.213099i | ||||
\(958\) | −176741. | −0.192577 | ||||||||
\(959\) | −455898. | + | 148130.i | −0.495713 | + | 0.161067i | ||||
\(960\) | 539993. | − | 813425.i | 0.585930 | − | 0.882623i | ||||
\(961\) | 75438.1 | − | 54809.0i | 0.0816853 | − | 0.0593479i | ||||
\(962\) | 165379. | + | 53735.0i | 0.178703 | + | 0.0580641i | ||||
\(963\) | 395240. | + | 92385.7i | 0.426195 | + | 0.0996213i | ||||
\(964\) | −794476. | + | 577220.i | −0.854922 | + | 0.621137i | ||||
\(965\) | −1.49402e6 | + | 2.05634e6i | −1.60436 | + | 2.20821i | ||||
\(966\) | −205101. | − | 550860.i | −0.219793 | − | 0.590319i | ||||
\(967\) | 1.49664e6 | 1.60053 | 0.800265 | − | 0.599646i | \(-0.204692\pi\) | ||||
0.800265 | + | 0.599646i | \(0.204692\pi\) | |||||||
\(968\) | 95259.4 | − | 934037.i | 0.101662 | − | 0.996812i | ||||
\(969\) | 3713.49 | + | 87803.4i | 0.00395489 | + | 0.0935112i | ||||
\(970\) | 318498. | + | 980235.i | 0.338503 | + | 1.04181i | ||||
\(971\) | −47056.7 | + | 64768.0i | −0.0499095 | + | 0.0686945i | −0.833242 | − | 0.552908i | \(-0.813518\pi\) |
0.783333 | + | 0.621603i | \(0.213518\pi\) | |||||||
\(972\) | −388062. | + | 432638.i | −0.410742 | + | 0.457923i | ||||
\(973\) | 24580.1 | − | 75649.7i | 0.0259632 | − | 0.0799064i | ||||
\(974\) | 224755. | + | 73027.2i | 0.236914 | + | 0.0769780i | ||||
\(975\) | −445696. | + | 353530.i | −0.468845 | + | 0.371892i | ||||
\(976\) | 9079.23 | + | 6596.45i | 0.00953124 | + | 0.00692485i | ||||
\(977\) | 1.38860e6 | − | 451183.i | 1.45475 | − | 0.472676i | 0.528286 | − | 0.849067i | \(-0.322835\pi\) |
0.926461 | + | 0.376391i | \(0.122835\pi\) | |||||||
\(978\) | −6712.95 | − | 158724.i | −0.00701836 | − | 0.165945i | ||||
\(979\) | −4923.41 | + | 1327.37i | −0.00513690 | + | 0.00138492i | ||||
\(980\) | − | 615704.i | − | 0.641091i | ||||||
\(981\) | −273093. | − | 648282.i | −0.283774 | − | 0.673637i | ||||
\(982\) | −534580. | − | 388395.i | −0.554357 | − | 0.402764i | ||||
\(983\) | −262361. | − | 361109.i | −0.271514 | − | 0.373707i | 0.651386 | − | 0.758746i | \(-0.274188\pi\) |
−0.922900 | + | 0.385040i | \(0.874188\pi\) | |||||||
\(984\) | 217791. | − | 781185.i | 0.224931 | − | 0.806795i | ||||
\(985\) | −546780. | + | 1.68281e6i | −0.563560 | + | 1.73446i | ||||
\(986\) | 261477. | + | 359892.i | 0.268955 | + | 0.370185i | ||||
\(987\) | 447598. | − | 674245.i | 0.459466 | − | 0.692123i | ||||
\(988\) | 5342.63 | + | 16442.9i | 0.00547320 | + | 0.0168448i | ||||
\(989\) | − | 373341.i | − | 0.381692i | ||||||
\(990\) | −812160. | + | 632976.i | −0.828650 | + | 0.645828i | ||||
\(991\) | 448310. | 0.456490 | 0.228245 | − | 0.973604i | \(-0.426701\pi\) | ||||
0.228245 | + | 0.973604i | \(0.426701\pi\) | |||||||
\(992\) | −885602. | + | 287750.i | −0.899944 | + | 0.292409i | ||||
\(993\) | −437355. | − | 290338.i | −0.443543 | − | 0.294446i | ||||
\(994\) | 475015. | − | 345118.i | 0.480766 | − | 0.349297i | ||||
\(995\) | −380227. | − | 123543.i | −0.384058 | − | 0.124788i | ||||
\(996\) | −775842. | − | 216301.i | −0.782086 | − | 0.218042i | ||||
\(997\) | 649687. | − | 472025.i | 0.653602 | − | 0.474870i | −0.210894 | − | 0.977509i | \(-0.567637\pi\) |
0.864496 | + | 0.502639i | \(0.167637\pi\) | |||||||
\(998\) | 550921. | − | 758278.i | 0.553131 | − | 0.761320i | ||||
\(999\) | 402715. | + | 853285.i | 0.403521 | + | 0.854994i |
(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 | 33.5.h.a.5.10 | yes | 56 | |
3.2 | odd | 2 | inner | 33.5.h.a.5.5 | ✓ | 56 | |
11.9 | even | 5 | inner | 33.5.h.a.20.5 | yes | 56 | |
33.20 | odd | 10 | inner | 33.5.h.a.20.10 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.5.h.a.5.5 | ✓ | 56 | 3.2 | odd | 2 | inner | |
33.5.h.a.5.10 | yes | 56 | 1.1 | even | 1 | trivial | |
33.5.h.a.20.5 | yes | 56 | 11.9 | even | 5 | inner | |
33.5.h.a.20.10 | yes | 56 | 33.20 | odd | 10 | inner |