Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,5,Mod(47,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("230.47");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.f (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(23.7750915093\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 47.7 | ||
Character | \(\chi\) | \(=\) | 230.47 |
Dual form | 230.5.f.b.93.7 |
$q$-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 \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | + | 2.00000i | 0.500000 | + | 0.500000i | ||||
\(3\) | −4.66373 | + | 4.66373i | −0.518192 | + | 0.518192i | −0.917024 | − | 0.398832i | \(-0.869416\pi\) |
0.398832 | + | 0.917024i | \(0.369416\pi\) | |||||||
\(4\) | 8.00000i | 0.500000i | ||||||||
\(5\) | −12.4209 | + | 21.6961i | −0.496837 | + | 0.867844i | ||||
\(6\) | −18.6549 | −0.518192 | ||||||||
\(7\) | −24.9944 | − | 24.9944i | −0.510089 | − | 0.510089i | 0.404464 | − | 0.914554i | \(-0.367458\pi\) |
−0.914554 | + | 0.404464i | \(0.867458\pi\) | |||||||
\(8\) | −16.0000 | + | 16.0000i | −0.250000 | + | 0.250000i | ||||
\(9\) | 37.4993i | 0.462954i | ||||||||
\(10\) | −68.2341 | + | 18.5503i | −0.682341 | + | 0.185503i | ||||
\(11\) | 42.7740 | 0.353504 | 0.176752 | − | 0.984255i | \(-0.443441\pi\) | ||||
0.176752 | + | 0.984255i | \(0.443441\pi\) | |||||||
\(12\) | −37.3098 | − | 37.3098i | −0.259096 | − | 0.259096i | ||||
\(13\) | −124.381 | + | 124.381i | −0.735981 | + | 0.735981i | −0.971798 | − | 0.235816i | \(-0.924224\pi\) |
0.235816 | + | 0.971798i | \(0.424224\pi\) | |||||||
\(14\) | − | 99.9775i | − | 0.510089i | ||||||
\(15\) | −43.2568 | − | 159.113i | −0.192252 | − | 0.707167i | ||||
\(16\) | −64.0000 | −0.250000 | ||||||||
\(17\) | −82.2327 | − | 82.2327i | −0.284542 | − | 0.284542i | 0.550375 | − | 0.834917i | \(-0.314485\pi\) |
−0.834917 | + | 0.550375i | \(0.814485\pi\) | |||||||
\(18\) | −74.9986 | + | 74.9986i | −0.231477 | + | 0.231477i | ||||
\(19\) | − | 142.138i | − | 0.393735i | −0.980430 | − | 0.196867i | \(-0.936923\pi\) | ||
0.980430 | − | 0.196867i | \(-0.0630769\pi\) | |||||||
\(20\) | −173.569 | − | 99.3675i | −0.433922 | − | 0.248419i | ||||
\(21\) | 233.134 | 0.528648 | ||||||||
\(22\) | 85.5480 | + | 85.5480i | 0.176752 | + | 0.176752i | ||||
\(23\) | 77.9968 | − | 77.9968i | 0.147442 | − | 0.147442i | ||||
\(24\) | − | 149.239i | − | 0.259096i | ||||||
\(25\) | −316.441 | − | 538.971i | −0.506305 | − | 0.862354i | ||||
\(26\) | −497.523 | −0.735981 | ||||||||
\(27\) | −552.648 | − | 552.648i | −0.758091 | − | 0.758091i | ||||
\(28\) | 199.955 | − | 199.955i | 0.255045 | − | 0.255045i | ||||
\(29\) | − | 448.952i | − | 0.533831i | −0.963720 | − | 0.266915i | \(-0.913996\pi\) | ||
0.963720 | − | 0.266915i | \(-0.0860044\pi\) | |||||||
\(30\) | 231.711 | − | 404.739i | 0.257457 | − | 0.449710i | ||||
\(31\) | 1207.80 | 1.25681 | 0.628407 | − | 0.777885i | \(-0.283707\pi\) | ||||
0.628407 | + | 0.777885i | \(0.283707\pi\) | |||||||
\(32\) | −128.000 | − | 128.000i | −0.125000 | − | 0.125000i | ||||
\(33\) | −199.486 | + | 199.486i | −0.183183 | + | 0.183183i | ||||
\(34\) | − | 328.931i | − | 0.284542i | ||||||
\(35\) | 852.734 | − | 231.827i | 0.696109 | − | 0.189246i | ||||
\(36\) | −299.994 | −0.231477 | ||||||||
\(37\) | 1166.74 | + | 1166.74i | 0.852260 | + | 0.852260i | 0.990411 | − | 0.138151i | \(-0.0441159\pi\) |
−0.138151 | + | 0.990411i | \(0.544116\pi\) | |||||||
\(38\) | 284.277 | − | 284.277i | 0.196867 | − | 0.196867i | ||||
\(39\) | − | 1160.16i | − | 0.762759i | ||||||
\(40\) | −148.403 | − | 545.872i | −0.0927516 | − | 0.341170i | ||||
\(41\) | −983.682 | −0.585177 | −0.292588 | − | 0.956239i | \(-0.594517\pi\) | ||||
−0.292588 | + | 0.956239i | \(0.594517\pi\) | |||||||
\(42\) | 466.268 | + | 466.268i | 0.264324 | + | 0.264324i | ||||
\(43\) | 1264.77 | − | 1264.77i | 0.684031 | − | 0.684031i | −0.276875 | − | 0.960906i | \(-0.589299\pi\) |
0.960906 | + | 0.276875i | \(0.0892989\pi\) | |||||||
\(44\) | 342.192i | 0.176752i | ||||||||
\(45\) | −813.588 | − | 465.776i | −0.401772 | − | 0.230013i | ||||
\(46\) | 311.987 | 0.147442 | ||||||||
\(47\) | −1747.20 | − | 1747.20i | −0.790946 | − | 0.790946i | 0.190702 | − | 0.981648i | \(-0.438924\pi\) |
−0.981648 | + | 0.190702i | \(0.938924\pi\) | |||||||
\(48\) | 298.479 | − | 298.479i | 0.129548 | − | 0.129548i | ||||
\(49\) | − | 1151.56i | − | 0.479618i | ||||||
\(50\) | 445.061 | − | 1710.82i | 0.178025 | − | 0.684330i | ||||
\(51\) | 767.022 | 0.294895 | ||||||||
\(52\) | −995.047 | − | 995.047i | −0.367991 | − | 0.367991i | ||||
\(53\) | −2008.22 | + | 2008.22i | −0.714922 | + | 0.714922i | −0.967561 | − | 0.252639i | \(-0.918702\pi\) |
0.252639 | + | 0.967561i | \(0.418702\pi\) | |||||||
\(54\) | − | 2210.59i | − | 0.758091i | ||||||
\(55\) | −531.293 | + | 928.029i | −0.175634 | + | 0.306786i | ||||
\(56\) | 799.820 | 0.255045 | ||||||||
\(57\) | 662.894 | + | 662.894i | 0.204030 | + | 0.204030i | ||||
\(58\) | 897.903 | − | 897.903i | 0.266915 | − | 0.266915i | ||||
\(59\) | 957.449i | 0.275050i | 0.990498 | + | 0.137525i | \(0.0439148\pi\) | ||||
−0.990498 | + | 0.137525i | \(0.956085\pi\) | |||||||
\(60\) | 1272.90 | − | 346.054i | 0.353583 | − | 0.0961262i | ||||
\(61\) | −3399.49 | −0.913595 | −0.456797 | − | 0.889571i | \(-0.651004\pi\) | ||||
−0.456797 | + | 0.889571i | \(0.651004\pi\) | |||||||
\(62\) | 2415.60 | + | 2415.60i | 0.628407 | + | 0.628407i | ||||
\(63\) | 937.271 | − | 937.271i | 0.236148 | − | 0.236148i | ||||
\(64\) | − | 512.000i | − | 0.125000i | ||||||
\(65\) | −1153.65 | − | 4243.50i | −0.273054 | − | 1.00438i | ||||
\(66\) | −797.945 | −0.183183 | ||||||||
\(67\) | −3861.25 | − | 3861.25i | −0.860159 | − | 0.860159i | 0.131198 | − | 0.991356i | \(-0.458118\pi\) |
−0.991356 | + | 0.131198i | \(0.958118\pi\) | |||||||
\(68\) | 657.862 | − | 657.862i | 0.142271 | − | 0.142271i | ||||
\(69\) | 727.512i | 0.152806i | ||||||||
\(70\) | 2169.12 | + | 1241.81i | 0.442678 | + | 0.253431i | ||||
\(71\) | 535.782 | 0.106285 | 0.0531424 | − | 0.998587i | \(-0.483076\pi\) | ||||
0.0531424 | + | 0.998587i | \(0.483076\pi\) | |||||||
\(72\) | −599.989 | − | 599.989i | −0.115739 | − | 0.115739i | ||||
\(73\) | 2478.94 | − | 2478.94i | 0.465179 | − | 0.465179i | −0.435170 | − | 0.900348i | \(-0.643312\pi\) |
0.900348 | + | 0.435170i | \(0.143312\pi\) | |||||||
\(74\) | 4666.98i | 0.852260i | ||||||||
\(75\) | 3989.41 | + | 1037.82i | 0.709228 | + | 0.184502i | ||||
\(76\) | 1137.11 | 0.196867 | ||||||||
\(77\) | −1069.11 | − | 1069.11i | −0.180319 | − | 0.180319i | ||||
\(78\) | 2320.31 | − | 2320.31i | 0.381380 | − | 0.381380i | ||||
\(79\) | 4130.99i | 0.661912i | 0.943646 | + | 0.330956i | \(0.107371\pi\) | ||||
−0.943646 | + | 0.330956i | \(0.892629\pi\) | |||||||
\(80\) | 794.940 | − | 1388.55i | 0.124209 | − | 0.216961i | ||||
\(81\) | 2117.36 | 0.322719 | ||||||||
\(82\) | −1967.36 | − | 1967.36i | −0.292588 | − | 0.292588i | ||||
\(83\) | −7578.13 | + | 7578.13i | −1.10003 | + | 1.10003i | −0.105628 | + | 0.994406i | \(0.533685\pi\) |
−0.994406 | + | 0.105628i | \(0.966315\pi\) | |||||||
\(84\) | 1865.07i | 0.264324i | ||||||||
\(85\) | 2805.54 | − | 762.722i | 0.388310 | − | 0.105567i | ||||
\(86\) | 5059.09 | 0.684031 | ||||||||
\(87\) | 2093.79 | + | 2093.79i | 0.276627 | + | 0.276627i | ||||
\(88\) | −684.384 | + | 684.384i | −0.0883761 | + | 0.0883761i | ||||
\(89\) | 8592.11i | 1.08473i | 0.840145 | + | 0.542363i | \(0.182470\pi\) | ||||
−0.840145 | + | 0.542363i | \(0.817530\pi\) | |||||||
\(90\) | −695.624 | − | 2558.73i | −0.0858795 | − | 0.315892i | ||||
\(91\) | 6217.64 | 0.750832 | ||||||||
\(92\) | 623.974 | + | 623.974i | 0.0737210 | + | 0.0737210i | ||||
\(93\) | −5632.84 | + | 5632.84i | −0.651271 | + | 0.651271i | ||||
\(94\) | − | 6988.80i | − | 0.790946i | ||||||
\(95\) | 3083.85 | + | 1765.49i | 0.341700 | + | 0.195622i | ||||
\(96\) | 1193.91 | 0.129548 | ||||||||
\(97\) | −12600.5 | − | 12600.5i | −1.33920 | − | 1.33920i | −0.896836 | − | 0.442363i | \(-0.854140\pi\) |
−0.442363 | − | 0.896836i | \(-0.645860\pi\) | |||||||
\(98\) | 2303.13 | − | 2303.13i | 0.239809 | − | 0.239809i | ||||
\(99\) | 1603.99i | 0.163656i | ||||||||
\(100\) | 4311.77 | − | 2531.53i | 0.431177 | − | 0.253153i | ||||
\(101\) | 5054.13 | 0.495455 | 0.247727 | − | 0.968830i | \(-0.420316\pi\) | ||||
0.247727 | + | 0.968830i | \(0.420316\pi\) | |||||||
\(102\) | 1534.04 | + | 1534.04i | 0.147448 | + | 0.147448i | ||||
\(103\) | −9510.99 | + | 9510.99i | −0.896502 | + | 0.896502i | −0.995125 | − | 0.0986228i | \(-0.968556\pi\) |
0.0986228 | + | 0.995125i | \(0.468556\pi\) | |||||||
\(104\) | − | 3980.19i | − | 0.367991i | ||||||
\(105\) | −2895.74 | + | 5058.09i | −0.262652 | + | 0.458784i | ||||
\(106\) | −8032.86 | −0.714922 | ||||||||
\(107\) | 6390.68 | + | 6390.68i | 0.558186 | + | 0.558186i | 0.928791 | − | 0.370604i | \(-0.120849\pi\) |
−0.370604 | + | 0.928791i | \(0.620849\pi\) | |||||||
\(108\) | 4421.19 | − | 4421.19i | 0.379046 | − | 0.379046i | ||||
\(109\) | − | 145.625i | − | 0.0122569i | −0.999981 | − | 0.00612847i | \(-0.998049\pi\) | ||
0.999981 | − | 0.00612847i | \(-0.00195076\pi\) | |||||||
\(110\) | −2918.64 | + | 793.471i | −0.241210 | + | 0.0655761i | ||||
\(111\) | −10882.8 | −0.883269 | ||||||||
\(112\) | 1599.64 | + | 1599.64i | 0.127522 | + | 0.127522i | ||||
\(113\) | −10026.1 | + | 10026.1i | −0.785191 | + | 0.785191i | −0.980702 | − | 0.195511i | \(-0.937364\pi\) |
0.195511 | + | 0.980702i | \(0.437364\pi\) | |||||||
\(114\) | 2651.58i | 0.204030i | ||||||||
\(115\) | 723.433 | + | 2661.02i | 0.0547019 | + | 0.201211i | ||||
\(116\) | 3591.61 | 0.266915 | ||||||||
\(117\) | −4664.19 | − | 4664.19i | −0.340726 | − | 0.340726i | ||||
\(118\) | −1914.90 | + | 1914.90i | −0.137525 | + | 0.137525i | ||||
\(119\) | 4110.71i | 0.290284i | ||||||||
\(120\) | 3237.91 | + | 1853.69i | 0.224855 | + | 0.128729i | ||||
\(121\) | −12811.4 | −0.875035 | ||||||||
\(122\) | −6798.97 | − | 6798.97i | −0.456797 | − | 0.456797i | ||||
\(123\) | 4587.62 | − | 4587.62i | 0.303234 | − | 0.303234i | ||||
\(124\) | 9662.39i | 0.628407i | ||||||||
\(125\) | 15624.1 | − | 171.000i | 0.999940 | − | 0.0109440i | ||||
\(126\) | 3749.08 | 0.236148 | ||||||||
\(127\) | −12405.3 | − | 12405.3i | −0.769127 | − | 0.769127i | 0.208825 | − | 0.977953i | \(-0.433036\pi\) |
−0.977953 | + | 0.208825i | \(0.933036\pi\) | |||||||
\(128\) | 1024.00 | − | 1024.00i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 11797.1i | 0.708918i | ||||||||
\(130\) | 6179.70 | − | 10794.3i | 0.365663 | − | 0.638717i | ||||
\(131\) | −15991.0 | −0.931821 | −0.465910 | − | 0.884832i | \(-0.654273\pi\) | ||||
−0.465910 | + | 0.884832i | \(0.654273\pi\) | |||||||
\(132\) | −1595.89 | − | 1595.89i | −0.0915915 | − | 0.0915915i | ||||
\(133\) | −3552.66 | + | 3552.66i | −0.200840 | + | 0.200840i | ||||
\(134\) | − | 15445.0i | − | 0.860159i | ||||||
\(135\) | 18854.7 | − | 5125.90i | 1.03455 | − | 0.281257i | ||||
\(136\) | 2631.45 | 0.142271 | ||||||||
\(137\) | −7572.59 | − | 7572.59i | −0.403463 | − | 0.403463i | 0.475989 | − | 0.879451i | \(-0.342090\pi\) |
−0.879451 | + | 0.475989i | \(0.842090\pi\) | |||||||
\(138\) | −1455.02 | + | 1455.02i | −0.0764032 | + | 0.0764032i | ||||
\(139\) | 20076.9i | 1.03912i | 0.854433 | + | 0.519561i | \(0.173905\pi\) | ||||
−0.854433 | + | 0.519561i | \(0.826095\pi\) | |||||||
\(140\) | 1854.61 | + | 6821.87i | 0.0946232 | + | 0.348055i | ||||
\(141\) | 16296.9 | 0.819724 | ||||||||
\(142\) | 1071.56 | + | 1071.56i | 0.0531424 | + | 0.0531424i | ||||
\(143\) | −5320.27 | + | 5320.27i | −0.260172 | + | 0.260172i | ||||
\(144\) | − | 2399.95i | − | 0.115739i | ||||||
\(145\) | 9740.49 | + | 5576.40i | 0.463282 | + | 0.265227i | ||||
\(146\) | 9915.75 | 0.465179 | ||||||||
\(147\) | 5370.57 | + | 5370.57i | 0.248534 | + | 0.248534i | ||||
\(148\) | −9333.95 | + | 9333.95i | −0.426130 | + | 0.426130i | ||||
\(149\) | − | 5570.13i | − | 0.250896i | −0.992100 | − | 0.125448i | \(-0.959963\pi\) | ||
0.992100 | − | 0.125448i | \(-0.0400368\pi\) | |||||||
\(150\) | 5903.17 | + | 10054.5i | 0.262363 | + | 0.446865i | ||||
\(151\) | 25453.1 | 1.11631 | 0.558156 | − | 0.829736i | \(-0.311509\pi\) | ||||
0.558156 | + | 0.829736i | \(0.311509\pi\) | |||||||
\(152\) | 2274.21 | + | 2274.21i | 0.0984337 | + | 0.0984337i | ||||
\(153\) | 3083.67 | − | 3083.67i | 0.131730 | − | 0.131730i | ||||
\(154\) | − | 4276.44i | − | 0.180319i | ||||||
\(155\) | −15002.0 | + | 26204.5i | −0.624432 | + | 1.09072i | ||||
\(156\) | 9281.25 | 0.381380 | ||||||||
\(157\) | 4542.67 | + | 4542.67i | 0.184294 | + | 0.184294i | 0.793224 | − | 0.608930i | \(-0.208401\pi\) |
−0.608930 | + | 0.793224i | \(0.708401\pi\) | |||||||
\(158\) | −8261.98 | + | 8261.98i | −0.330956 | + | 0.330956i | ||||
\(159\) | − | 18731.5i | − | 0.740934i | ||||||
\(160\) | 4366.98 | − | 1187.22i | 0.170585 | − | 0.0463758i | ||||
\(161\) | −3898.96 | −0.150417 | ||||||||
\(162\) | 4234.72 | + | 4234.72i | 0.161360 | + | 0.161360i | ||||
\(163\) | −27110.2 | + | 27110.2i | −1.02037 | + | 1.02037i | −0.0205802 | + | 0.999788i | \(0.506551\pi\) |
−0.999788 | + | 0.0205802i | \(0.993449\pi\) | |||||||
\(164\) | − | 7869.46i | − | 0.292588i | ||||||
\(165\) | −1850.27 | − | 6805.88i | −0.0679621 | − | 0.249986i | ||||
\(166\) | −30312.5 | −1.10003 | ||||||||
\(167\) | −12748.7 | − | 12748.7i | −0.457125 | − | 0.457125i | 0.440586 | − | 0.897710i | \(-0.354771\pi\) |
−0.897710 | + | 0.440586i | \(0.854771\pi\) | |||||||
\(168\) | −3730.14 | + | 3730.14i | −0.132162 | + | 0.132162i | ||||
\(169\) | − | 2380.18i | − | 0.0833366i | ||||||
\(170\) | 7136.52 | + | 4085.63i | 0.246938 | + | 0.141371i | ||||
\(171\) | 5330.09 | 0.182281 | ||||||||
\(172\) | 10118.2 | + | 10118.2i | 0.342015 | + | 0.342015i | ||||
\(173\) | 18097.1 | − | 18097.1i | 0.604668 | − | 0.604668i | −0.336880 | − | 0.941548i | \(-0.609372\pi\) |
0.941548 | + | 0.336880i | \(0.109372\pi\) | |||||||
\(174\) | 8375.15i | 0.276627i | ||||||||
\(175\) | −5562.01 | + | 21380.5i | −0.181617 | + | 0.698139i | ||||
\(176\) | −2737.54 | −0.0883761 | ||||||||
\(177\) | −4465.28 | − | 4465.28i | −0.142529 | − | 0.142529i | ||||
\(178\) | −17184.2 | + | 17184.2i | −0.542363 | + | 0.542363i | ||||
\(179\) | 45446.0i | 1.41837i | 0.705023 | + | 0.709185i | \(0.250937\pi\) | ||||
−0.705023 | + | 0.709185i | \(0.749063\pi\) | |||||||
\(180\) | 3726.21 | − | 6508.70i | 0.115006 | − | 0.200886i | ||||
\(181\) | −3679.25 | −0.112306 | −0.0561529 | − | 0.998422i | \(-0.517883\pi\) | ||||
−0.0561529 | + | 0.998422i | \(0.517883\pi\) | |||||||
\(182\) | 12435.3 | + | 12435.3i | 0.375416 | + | 0.375416i | ||||
\(183\) | 15854.3 | − | 15854.3i | 0.473418 | − | 0.473418i | ||||
\(184\) | 2495.90i | 0.0737210i | ||||||||
\(185\) | −39805.8 | + | 10821.7i | −1.16306 | + | 0.316194i | ||||
\(186\) | −22531.4 | −0.651271 | ||||||||
\(187\) | −3517.42 | − | 3517.42i | −0.100587 | − | 0.100587i | ||||
\(188\) | 13977.6 | − | 13977.6i | 0.395473 | − | 0.395473i | ||||
\(189\) | 27626.2i | 0.773388i | ||||||||
\(190\) | 2636.71 | + | 9698.67i | 0.0730391 | + | 0.268661i | ||||
\(191\) | 5569.88 | 0.152679 | 0.0763395 | − | 0.997082i | \(-0.475677\pi\) | ||||
0.0763395 | + | 0.997082i | \(0.475677\pi\) | |||||||
\(192\) | 2387.83 | + | 2387.83i | 0.0647740 | + | 0.0647740i | ||||
\(193\) | 14063.7 | − | 14063.7i | 0.377560 | − | 0.377560i | −0.492661 | − | 0.870221i | \(-0.663976\pi\) |
0.870221 | + | 0.492661i | \(0.163976\pi\) | |||||||
\(194\) | − | 50402.1i | − | 1.33920i | ||||||
\(195\) | 25170.9 | + | 14410.2i | 0.661956 | + | 0.378967i | ||||
\(196\) | 9212.50 | 0.239809 | ||||||||
\(197\) | −15522.4 | − | 15522.4i | −0.399968 | − | 0.399968i | 0.478253 | − | 0.878222i | \(-0.341270\pi\) |
−0.878222 | + | 0.478253i | \(0.841270\pi\) | |||||||
\(198\) | −3207.99 | + | 3207.99i | −0.0818281 | + | 0.0818281i | ||||
\(199\) | − | 23916.6i | − | 0.603940i | −0.953317 | − | 0.301970i | \(-0.902356\pi\) | ||
0.953317 | − | 0.301970i | \(-0.0976442\pi\) | |||||||
\(200\) | 13686.6 | + | 3560.49i | 0.342165 | + | 0.0890123i | ||||
\(201\) | 36015.7 | 0.891455 | ||||||||
\(202\) | 10108.3 | + | 10108.3i | 0.247727 | + | 0.247727i | ||||
\(203\) | −11221.3 | + | 11221.3i | −0.272301 | + | 0.272301i | ||||
\(204\) | 6136.18i | 0.147448i | ||||||||
\(205\) | 12218.2 | − | 21342.1i | 0.290738 | − | 0.507842i | ||||
\(206\) | −38044.0 | −0.896502 | ||||||||
\(207\) | 2924.82 | + | 2924.82i | 0.0682589 | + | 0.0682589i | ||||
\(208\) | 7960.37 | − | 7960.37i | 0.183995 | − | 0.183995i | ||||
\(209\) | − | 6079.83i | − | 0.139187i | ||||||
\(210\) | −15907.7 | + | 4324.71i | −0.360718 | + | 0.0980659i | ||||
\(211\) | 52595.9 | 1.18137 | 0.590686 | − | 0.806902i | \(-0.298857\pi\) | ||||
0.590686 | + | 0.806902i | \(0.298857\pi\) | |||||||
\(212\) | −16065.7 | − | 16065.7i | −0.357461 | − | 0.357461i | ||||
\(213\) | −2498.74 | + | 2498.74i | −0.0550759 | + | 0.0550759i | ||||
\(214\) | 25562.7i | 0.558186i | ||||||||
\(215\) | 11731.0 | + | 43150.3i | 0.253780 | + | 0.933484i | ||||
\(216\) | 17684.7 | 0.379046 | ||||||||
\(217\) | −30188.2 | − | 30188.2i | −0.641088 | − | 0.641088i | ||||
\(218\) | 291.249 | − | 291.249i | 0.00612847 | − | 0.00612847i | ||||
\(219\) | 23122.2i | 0.482104i | ||||||||
\(220\) | −7424.23 | − | 4250.35i | −0.153393 | − | 0.0878171i | ||||
\(221\) | 20456.4 | 0.418836 | ||||||||
\(222\) | −21765.5 | − | 21765.5i | −0.441634 | − | 0.441634i | ||||
\(223\) | −29029.2 | + | 29029.2i | −0.583748 | + | 0.583748i | −0.935931 | − | 0.352183i | \(-0.885439\pi\) |
0.352183 | + | 0.935931i | \(0.385439\pi\) | |||||||
\(224\) | 6398.56i | 0.127522i | ||||||||
\(225\) | 20211.0 | − | 11866.3i | 0.399231 | − | 0.234396i | ||||
\(226\) | −40104.4 | −0.785191 | ||||||||
\(227\) | −3673.75 | − | 3673.75i | −0.0712948 | − | 0.0712948i | 0.670560 | − | 0.741855i | \(-0.266054\pi\) |
−0.741855 | + | 0.670560i | \(0.766054\pi\) | |||||||
\(228\) | −5303.16 | + | 5303.16i | −0.102015 | + | 0.102015i | ||||
\(229\) | − | 101280.i | − | 1.93131i | −0.259820 | − | 0.965657i | \(-0.583663\pi\) | ||
0.259820 | − | 0.965657i | \(-0.416337\pi\) | |||||||
\(230\) | −3875.17 | + | 6768.90i | −0.0732547 | + | 0.127957i | ||||
\(231\) | 9972.07 | 0.186879 | ||||||||
\(232\) | 7183.22 | + | 7183.22i | 0.133458 | + | 0.133458i | ||||
\(233\) | −1199.03 | + | 1199.03i | −0.0220860 | + | 0.0220860i | −0.718064 | − | 0.695978i | \(-0.754971\pi\) |
0.695978 | + | 0.718064i | \(0.254971\pi\) | |||||||
\(234\) | − | 18656.8i | − | 0.340726i | ||||||
\(235\) | 59609.3 | − | 16205.6i | 1.07939 | − | 0.293446i | ||||
\(236\) | −7659.60 | −0.137525 | ||||||||
\(237\) | −19265.8 | − | 19265.8i | −0.342997 | − | 0.342997i | ||||
\(238\) | −8221.42 | + | 8221.42i | −0.145142 | + | 0.145142i | ||||
\(239\) | − | 54134.6i | − | 0.947717i | −0.880601 | − | 0.473859i | \(-0.842861\pi\) | ||
0.880601 | − | 0.473859i | \(-0.157139\pi\) | |||||||
\(240\) | 2768.44 | + | 10183.2i | 0.0480631 | + | 0.176792i | ||||
\(241\) | −7291.94 | −0.125548 | −0.0627739 | − | 0.998028i | \(-0.519995\pi\) | ||||
−0.0627739 | + | 0.998028i | \(0.519995\pi\) | |||||||
\(242\) | −25622.8 | − | 25622.8i | −0.437517 | − | 0.437517i | ||||
\(243\) | 34889.7 | − | 34889.7i | 0.590861 | − | 0.590861i | ||||
\(244\) | − | 27195.9i | − | 0.456797i | ||||||
\(245\) | 24984.4 | + | 14303.5i | 0.416233 | + | 0.238292i | ||||
\(246\) | 18350.5 | 0.303234 | ||||||||
\(247\) | 17679.3 | + | 17679.3i | 0.289781 | + | 0.289781i | ||||
\(248\) | −19324.8 | + | 19324.8i | −0.314204 | + | 0.314204i | ||||
\(249\) | − | 70684.7i | − | 1.14006i | ||||||
\(250\) | 31590.1 | + | 30906.1i | 0.505442 | + | 0.494498i | ||||
\(251\) | 10648.0 | 0.169013 | 0.0845066 | − | 0.996423i | \(-0.473069\pi\) | ||||
0.0845066 | + | 0.996423i | \(0.473069\pi\) | |||||||
\(252\) | 7498.17 | + | 7498.17i | 0.118074 | + | 0.118074i | ||||
\(253\) | 3336.24 | − | 3336.24i | 0.0521214 | − | 0.0521214i | ||||
\(254\) | − | 49621.0i | − | 0.769127i | ||||||
\(255\) | −9527.13 | + | 16641.4i | −0.146515 | + | 0.255923i | ||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | −8601.08 | − | 8601.08i | −0.130223 | − | 0.130223i | 0.638991 | − | 0.769214i | \(-0.279352\pi\) |
−0.769214 | + | 0.638991i | \(0.779352\pi\) | |||||||
\(258\) | −23594.2 | + | 23594.2i | −0.354459 | + | 0.354459i | ||||
\(259\) | − | 58324.1i | − | 0.869458i | ||||||
\(260\) | 33948.0 | − | 9229.21i | 0.502190 | − | 0.136527i | ||||
\(261\) | 16835.4 | 0.247139 | ||||||||
\(262\) | −31982.0 | − | 31982.0i | −0.465910 | − | 0.465910i | ||||
\(263\) | 60665.1 | − | 60665.1i | 0.877057 | − | 0.877057i | −0.116172 | − | 0.993229i | \(-0.537063\pi\) |
0.993229 | + | 0.116172i | \(0.0370625\pi\) | |||||||
\(264\) | − | 6383.56i | − | 0.0915915i | ||||||
\(265\) | −18626.5 | − | 68514.3i | −0.265241 | − | 0.975640i | ||||
\(266\) | −14210.6 | −0.200840 | ||||||||
\(267\) | −40071.3 | − | 40071.3i | −0.562096 | − | 0.562096i | ||||
\(268\) | 30890.0 | − | 30890.0i | 0.430079 | − | 0.430079i | ||||
\(269\) | − | 100241.i | − | 1.38528i | −0.721281 | − | 0.692642i | \(-0.756447\pi\) | ||
0.721281 | − | 0.692642i | \(-0.243553\pi\) | |||||||
\(270\) | 47961.2 | + | 27457.6i | 0.657905 | + | 0.376648i | ||||
\(271\) | −73657.3 | −1.00294 | −0.501472 | − | 0.865174i | \(-0.667208\pi\) | ||||
−0.501472 | + | 0.865174i | \(0.667208\pi\) | |||||||
\(272\) | 5262.90 | + | 5262.90i | 0.0711356 | + | 0.0711356i | ||||
\(273\) | −28997.4 | + | 28997.4i | −0.389075 | + | 0.389075i | ||||
\(274\) | − | 30290.4i | − | 0.403463i | ||||||
\(275\) | −13535.4 | − | 23054.0i | −0.178981 | − | 0.304846i | ||||
\(276\) | −5820.09 | −0.0764032 | ||||||||
\(277\) | −60519.8 | − | 60519.8i | −0.788747 | − | 0.788747i | 0.192541 | − | 0.981289i | \(-0.438327\pi\) |
−0.981289 | + | 0.192541i | \(0.938327\pi\) | |||||||
\(278\) | −40153.8 | + | 40153.8i | −0.519561 | + | 0.519561i | ||||
\(279\) | 45291.6i | 0.581847i | ||||||||
\(280\) | −9934.51 | + | 17353.0i | −0.126716 | + | 0.221339i | ||||
\(281\) | −17421.0 | −0.220628 | −0.110314 | − | 0.993897i | \(-0.535186\pi\) | ||||
−0.110314 | + | 0.993897i | \(0.535186\pi\) | |||||||
\(282\) | 32593.9 | + | 32593.9i | 0.409862 | + | 0.409862i | ||||
\(283\) | 5222.91 | − | 5222.91i | 0.0652139 | − | 0.0652139i | −0.673748 | − | 0.738962i | \(-0.735317\pi\) |
0.738962 | + | 0.673748i | \(0.235317\pi\) | |||||||
\(284\) | 4286.25i | 0.0531424i | ||||||||
\(285\) | −22616.0 | + | 6148.45i | −0.278436 | + | 0.0756965i | ||||
\(286\) | −21281.1 | −0.260172 | ||||||||
\(287\) | 24586.5 | + | 24586.5i | 0.298492 | + | 0.298492i | ||||
\(288\) | 4799.91 | − | 4799.91i | 0.0578693 | − | 0.0578693i | ||||
\(289\) | − | 69996.6i | − | 0.838071i | ||||||
\(290\) | 8328.19 | + | 30633.8i | 0.0990273 | + | 0.364254i | ||||
\(291\) | 117531. | 1.38792 | ||||||||
\(292\) | 19831.5 | + | 19831.5i | 0.232589 | + | 0.232589i | ||||
\(293\) | −61084.0 | + | 61084.0i | −0.711529 | + | 0.711529i | −0.966855 | − | 0.255326i | \(-0.917817\pi\) |
0.255326 | + | 0.966855i | \(0.417817\pi\) | |||||||
\(294\) | 21482.3i | 0.248534i | ||||||||
\(295\) | −20772.9 | − | 11892.4i | −0.238700 | − | 0.136655i | ||||
\(296\) | −37335.8 | −0.426130 | ||||||||
\(297\) | −23639.0 | − | 23639.0i | −0.267988 | − | 0.267988i | ||||
\(298\) | 11140.3 | − | 11140.3i | 0.125448 | − | 0.125448i | ||||
\(299\) | 19402.6i | 0.217029i | ||||||||
\(300\) | −8302.58 | + | 31915.3i | −0.0922509 | + | 0.354614i | ||||
\(301\) | −63224.4 | −0.697833 | ||||||||
\(302\) | 50906.1 | + | 50906.1i | 0.558156 | + | 0.558156i | ||||
\(303\) | −23571.1 | + | 23571.1i | −0.256741 | + | 0.256741i | ||||
\(304\) | 9096.85i | 0.0984337i | ||||||||
\(305\) | 42224.8 | − | 73755.6i | 0.453908 | − | 0.792858i | ||||
\(306\) | 12334.7 | 0.131730 | ||||||||
\(307\) | −43241.8 | − | 43241.8i | −0.458804 | − | 0.458804i | 0.439459 | − | 0.898263i | \(-0.355170\pi\) |
−0.898263 | + | 0.439459i | \(0.855170\pi\) | |||||||
\(308\) | 8552.88 | − | 8552.88i | 0.0901594 | − | 0.0901594i | ||||
\(309\) | − | 88713.3i | − | 0.929120i | ||||||
\(310\) | −82413.0 | + | 22405.0i | −0.857575 | + | 0.233143i | ||||
\(311\) | 13366.9 | 0.138201 | 0.0691005 | − | 0.997610i | \(-0.477987\pi\) | ||||
0.0691005 | + | 0.997610i | \(0.477987\pi\) | |||||||
\(312\) | 18562.5 | + | 18562.5i | 0.190690 | + | 0.190690i | ||||
\(313\) | −120302. | + | 120302.i | −1.22796 | + | 1.22796i | −0.263224 | + | 0.964735i | \(0.584786\pi\) |
−0.964735 | + | 0.263224i | \(0.915214\pi\) | |||||||
\(314\) | 18170.7i | 0.184294i | ||||||||
\(315\) | 8693.34 | + | 31976.9i | 0.0876124 | + | 0.322267i | ||||
\(316\) | −33047.9 | −0.330956 | ||||||||
\(317\) | 106460. | + | 106460.i | 1.05942 | + | 1.05942i | 0.998119 | + | 0.0613025i | \(0.0195254\pi\) |
0.0613025 | + | 0.998119i | \(0.480475\pi\) | |||||||
\(318\) | 37463.1 | − | 37463.1i | 0.370467 | − | 0.370467i | ||||
\(319\) | − | 19203.5i | − | 0.188711i | ||||||
\(320\) | 11108.4 | + | 6359.52i | 0.108480 | + | 0.0621047i | ||||
\(321\) | −59608.7 | −0.578495 | ||||||||
\(322\) | −7797.92 | − | 7797.92i | −0.0752086 | − | 0.0752086i | ||||
\(323\) | −11688.4 | + | 11688.4i | −0.112034 | + | 0.112034i | ||||
\(324\) | 16938.9i | 0.161360i | ||||||||
\(325\) | 106397. | + | 27678.5i | 1.00731 | + | 0.262045i | ||||
\(326\) | −108441. | −1.02037 | ||||||||
\(327\) | 679.153 | + | 679.153i | 0.00635144 | + | 0.00635144i | ||||
\(328\) | 15738.9 | − | 15738.9i | 0.146294 | − | 0.146294i | ||||
\(329\) | 87340.3i | 0.806906i | ||||||||
\(330\) | 9911.23 | − | 17312.3i | 0.0910122 | − | 0.158974i | ||||
\(331\) | 134180. | 1.22471 | 0.612355 | − | 0.790583i | \(-0.290222\pi\) | ||||
0.612355 | + | 0.790583i | \(0.290222\pi\) | |||||||
\(332\) | −60625.1 | − | 60625.1i | −0.550017 | − | 0.550017i | ||||
\(333\) | −43752.1 | + | 43752.1i | −0.394557 | + | 0.394557i | ||||
\(334\) | − | 50995.0i | − | 0.457125i | ||||||
\(335\) | 131734. | − | 35813.7i | 1.17384 | − | 0.319124i | ||||
\(336\) | −14920.6 | −0.132162 | ||||||||
\(337\) | −35691.1 | − | 35691.1i | −0.314268 | − | 0.314268i | 0.532293 | − | 0.846560i | \(-0.321331\pi\) |
−0.846560 | + | 0.532293i | \(0.821331\pi\) | |||||||
\(338\) | 4760.35 | − | 4760.35i | 0.0416683 | − | 0.0416683i | ||||
\(339\) | − | 93518.0i | − | 0.813759i | ||||||
\(340\) | 6101.77 | + | 22444.3i | 0.0527835 | + | 0.194155i | ||||
\(341\) | 51662.4 | 0.444289 | ||||||||
\(342\) | 10660.2 | + | 10660.2i | 0.0911406 | + | 0.0911406i | ||||
\(343\) | −88794.1 | + | 88794.1i | −0.754737 | + | 0.754737i | ||||
\(344\) | 40472.7i | 0.342015i | ||||||||
\(345\) | −15784.2 | − | 9036.37i | −0.132612 | − | 0.0759200i | ||||
\(346\) | 72388.4 | 0.604668 | ||||||||
\(347\) | 82239.1 | + | 82239.1i | 0.682998 | + | 0.682998i | 0.960675 | − | 0.277677i | \(-0.0895644\pi\) |
−0.277677 | + | 0.960675i | \(0.589564\pi\) | |||||||
\(348\) | −16750.3 | + | 16750.3i | −0.138313 | + | 0.138313i | ||||
\(349\) | − | 63602.5i | − | 0.522184i | −0.965314 | − | 0.261092i | \(-0.915917\pi\) | ||
0.965314 | − | 0.261092i | \(-0.0840825\pi\) | |||||||
\(350\) | −53885.0 | + | 31637.0i | −0.439878 | + | 0.258261i | ||||
\(351\) | 137478. | 1.11588 | ||||||||
\(352\) | −5475.07 | − | 5475.07i | −0.0441880 | − | 0.0441880i | ||||
\(353\) | −126451. | + | 126451.i | −1.01478 | + | 1.01478i | −0.0148933 | + | 0.999889i | \(0.504741\pi\) |
−0.999889 | + | 0.0148933i | \(0.995259\pi\) | |||||||
\(354\) | − | 17861.1i | − | 0.142529i | ||||||
\(355\) | −6654.91 | + | 11624.4i | −0.0528063 | + | 0.0922386i | ||||
\(356\) | −68736.9 | −0.542363 | ||||||||
\(357\) | −19171.2 | − | 19171.2i | −0.150423 | − | 0.150423i | ||||
\(358\) | −90891.9 | + | 90891.9i | −0.709185 | + | 0.709185i | ||||
\(359\) | 93543.3i | 0.725812i | 0.931826 | + | 0.362906i | \(0.118215\pi\) | ||||
−0.931826 | + | 0.362906i | \(0.881785\pi\) | |||||||
\(360\) | 20469.8 | − | 5564.99i | 0.157946 | − | 0.0429397i | ||||
\(361\) | 110118. | 0.844973 | ||||||||
\(362\) | −7358.50 | − | 7358.50i | −0.0561529 | − | 0.0561529i | ||||
\(363\) | 59748.8 | − | 59748.8i | 0.453436 | − | 0.453436i | ||||
\(364\) | 49741.1i | 0.375416i | ||||||||
\(365\) | 22992.5 | + | 84574.0i | 0.172584 | + | 0.634821i | ||||
\(366\) | 63417.1 | 0.473418 | ||||||||
\(367\) | −62615.3 | − | 62615.3i | −0.464888 | − | 0.464888i | 0.435366 | − | 0.900254i | \(-0.356619\pi\) |
−0.900254 | + | 0.435366i | \(0.856619\pi\) | |||||||
\(368\) | −4991.79 | + | 4991.79i | −0.0368605 | + | 0.0368605i | ||||
\(369\) | − | 36887.4i | − | 0.270910i | ||||||
\(370\) | −101255. | − | 57968.2i | −0.739629 | − | 0.423435i | ||||
\(371\) | 100388. | 0.729348 | ||||||||
\(372\) | −45062.8 | − | 45062.8i | −0.325636 | − | 0.325636i | ||||
\(373\) | −184074. | + | 184074.i | −1.32305 | + | 1.32305i | −0.411753 | + | 0.911295i | \(0.635083\pi\) |
−0.911295 | + | 0.411753i | \(0.864917\pi\) | |||||||
\(374\) | − | 14069.7i | − | 0.100587i | ||||||
\(375\) | −72068.9 | + | 73663.9i | −0.512490 | + | 0.523832i | ||||
\(376\) | 55910.4 | 0.395473 | ||||||||
\(377\) | 55841.0 | + | 55841.0i | 0.392889 | + | 0.392889i | ||||
\(378\) | −55252.4 | + | 55252.4i | −0.386694 | + | 0.386694i | ||||
\(379\) | 227889.i | 1.58651i | 0.608886 | + | 0.793257i | \(0.291617\pi\) | ||||
−0.608886 | + | 0.793257i | \(0.708383\pi\) | |||||||
\(380\) | −14123.9 | + | 24670.8i | −0.0978111 | + | 0.170850i | ||||
\(381\) | 115709. | 0.797111 | ||||||||
\(382\) | 11139.8 | + | 11139.8i | 0.0763395 | + | 0.0763395i | ||||
\(383\) | −18342.5 | + | 18342.5i | −0.125044 | + | 0.125044i | −0.766859 | − | 0.641815i | \(-0.778182\pi\) |
0.641815 | + | 0.766859i | \(0.278182\pi\) | |||||||
\(384\) | 9551.31i | 0.0647740i | ||||||||
\(385\) | 36474.8 | − | 9916.16i | 0.246078 | − | 0.0668994i | ||||
\(386\) | 56254.9 | 0.377560 | ||||||||
\(387\) | 47428.1 | + | 47428.1i | 0.316675 | + | 0.316675i | ||||
\(388\) | 100804. | − | 100804.i | 0.669599 | − | 0.669599i | ||||
\(389\) | 1991.67i | 0.0131619i | 0.999978 | + | 0.00658096i | \(0.00209480\pi\) | ||||
−0.999978 | + | 0.00658096i | \(0.997905\pi\) | |||||||
\(390\) | 21521.3 | + | 79162.2i | 0.141494 | + | 0.520461i | ||||
\(391\) | −12827.8 | −0.0839070 | ||||||||
\(392\) | 18425.0 | + | 18425.0i | 0.119904 | + | 0.119904i | ||||
\(393\) | 74577.6 | − | 74577.6i | 0.482862 | − | 0.482862i | ||||
\(394\) | − | 62089.5i | − | 0.399968i | ||||||
\(395\) | −89626.4 | − | 51310.8i | −0.574436 | − | 0.328863i | ||||
\(396\) | −12832.0 | −0.0818281 | ||||||||
\(397\) | 98644.9 | + | 98644.9i | 0.625884 | + | 0.625884i | 0.947030 | − | 0.321146i | \(-0.104068\pi\) |
−0.321146 | + | 0.947030i | \(0.604068\pi\) | |||||||
\(398\) | 47833.3 | − | 47833.3i | 0.301970 | − | 0.301970i | ||||
\(399\) | − | 33137.3i | − | 0.208147i | ||||||
\(400\) | 20252.2 | + | 34494.2i | 0.126576 | + | 0.215589i | ||||
\(401\) | −15128.5 | −0.0940820 | −0.0470410 | − | 0.998893i | \(-0.514979\pi\) | ||||
−0.0470410 | + | 0.998893i | \(0.514979\pi\) | |||||||
\(402\) | 72031.3 | + | 72031.3i | 0.445727 | + | 0.445727i | ||||
\(403\) | −150227. | + | 150227.i | −0.924992 | + | 0.924992i | ||||
\(404\) | 40433.1i | 0.247727i | ||||||||
\(405\) | −26299.6 | + | 45938.5i | −0.160339 | + | 0.280070i | ||||
\(406\) | −44885.1 | −0.272301 | ||||||||
\(407\) | 49906.3 | + | 49906.3i | 0.301278 | + | 0.301278i | ||||
\(408\) | −12272.4 | + | 12272.4i | −0.0737238 | + | 0.0737238i | ||||
\(409\) | 207979.i | 1.24329i | 0.783298 | + | 0.621646i | \(0.213536\pi\) | ||||
−0.783298 | + | 0.621646i | \(0.786464\pi\) | |||||||
\(410\) | 67120.6 | − | 18247.6i | 0.399290 | − | 0.108552i | ||||
\(411\) | 70633.0 | 0.418142 | ||||||||
\(412\) | −76087.9 | − | 76087.9i | −0.448251 | − | 0.448251i | ||||
\(413\) | 23930.8 | − | 23930.8i | 0.140300 | − | 0.140300i | ||||
\(414\) | 11699.3i | 0.0682589i | ||||||||
\(415\) | −70288.4 | − | 258543.i | −0.408119 | − | 1.50120i | ||||
\(416\) | 31841.5 | 0.183995 | ||||||||
\(417\) | −93633.1 | − | 93633.1i | −0.538465 | − | 0.538465i | ||||
\(418\) | 12159.7 | − | 12159.7i | 0.0695935 | − | 0.0695935i | ||||
\(419\) | − | 108509.i | − | 0.618071i | −0.951050 | − | 0.309036i | \(-0.899994\pi\) | ||
0.951050 | − | 0.309036i | \(-0.100006\pi\) | |||||||
\(420\) | −40464.8 | − | 23165.9i | −0.229392 | − | 0.131326i | ||||
\(421\) | 152462. | 0.860194 | 0.430097 | − | 0.902783i | \(-0.358479\pi\) | ||||
0.430097 | + | 0.902783i | \(0.358479\pi\) | |||||||
\(422\) | 105192. | + | 105192.i | 0.590686 | + | 0.590686i | ||||
\(423\) | 65518.7 | − | 65518.7i | 0.366172 | − | 0.366172i | ||||
\(424\) | − | 64262.9i | − | 0.357461i | ||||||
\(425\) | −18299.3 | + | 70342.9i | −0.101311 | + | 0.389442i | ||||
\(426\) | −9994.96 | −0.0550759 | ||||||||
\(427\) | 84968.0 | + | 84968.0i | 0.466015 | + | 0.466015i | ||||
\(428\) | −51125.4 | + | 51125.4i | −0.279093 | + | 0.279093i | ||||
\(429\) | − | 49624.5i | − | 0.269639i | ||||||
\(430\) | −62838.6 | + | 109762.i | −0.339852 | + | 0.593632i | ||||
\(431\) | 235938. | 1.27012 | 0.635059 | − | 0.772464i | \(-0.280976\pi\) | ||||
0.635059 | + | 0.772464i | \(0.280976\pi\) | |||||||
\(432\) | 35369.5 | + | 35369.5i | 0.189523 | + | 0.189523i | ||||
\(433\) | −37855.5 | + | 37855.5i | −0.201908 | + | 0.201908i | −0.800817 | − | 0.598909i | \(-0.795601\pi\) |
0.598909 | + | 0.800817i | \(0.295601\pi\) | |||||||
\(434\) | − | 120753.i | − | 0.641088i | ||||||
\(435\) | −71433.8 | + | 19420.2i | −0.377507 | + | 0.102630i | ||||
\(436\) | 1165.00 | 0.00612847 | ||||||||
\(437\) | −11086.3 | − | 11086.3i | −0.0580530 | − | 0.0580530i | ||||
\(438\) | −46244.4 | + | 46244.4i | −0.241052 | + | 0.241052i | ||||
\(439\) | 37764.4i | 0.195954i | 0.995189 | + | 0.0979768i | \(0.0312371\pi\) | ||||
−0.995189 | + | 0.0979768i | \(0.968763\pi\) | |||||||
\(440\) | −6347.77 | − | 23349.2i | −0.0327881 | − | 0.120605i | ||||
\(441\) | 43182.8 | 0.222041 | ||||||||
\(442\) | 40912.7 | + | 40912.7i | 0.209418 | + | 0.209418i | ||||
\(443\) | 80557.2 | − | 80557.2i | 0.410485 | − | 0.410485i | −0.471423 | − | 0.881907i | \(-0.656259\pi\) |
0.881907 | + | 0.471423i | \(0.156259\pi\) | |||||||
\(444\) | − | 87062.0i | − | 0.441634i | ||||||
\(445\) | −186415. | − | 106722.i | −0.941372 | − | 0.538932i | ||||
\(446\) | −116117. | −0.583748 | ||||||||
\(447\) | 25977.6 | + | 25977.6i | 0.130012 | + | 0.130012i | ||||
\(448\) | −12797.1 | + | 12797.1i | −0.0637612 | + | 0.0637612i | ||||
\(449\) | 97935.5i | 0.485789i | 0.970053 | + | 0.242894i | \(0.0780968\pi\) | ||||
−0.970053 | + | 0.242894i | \(0.921903\pi\) | |||||||
\(450\) | 64154.7 | + | 16689.5i | 0.316813 | + | 0.0824172i | ||||
\(451\) | −42076.0 | −0.206862 | ||||||||
\(452\) | −80208.8 | − | 80208.8i | −0.392595 | − | 0.392595i | ||||
\(453\) | −118706. | + | 118706.i | −0.578464 | + | 0.578464i | ||||
\(454\) | − | 14695.0i | − | 0.0712948i | ||||||
\(455\) | −77228.9 | + | 134899.i | −0.373041 | + | 0.651605i | ||||
\(456\) | −21212.6 | −0.102015 | ||||||||
\(457\) | −278458. | − | 278458.i | −1.33330 | − | 1.33330i | −0.902402 | − | 0.430895i | \(-0.858198\pi\) |
−0.430895 | − | 0.902402i | \(-0.641802\pi\) | |||||||
\(458\) | 202560. | − | 202560.i | 0.965657 | − | 0.965657i | ||||
\(459\) | 90891.6i | 0.431418i | ||||||||
\(460\) | −21288.1 | + | 5787.46i | −0.100606 | + | 0.0273509i | ||||
\(461\) | −220655. | −1.03828 | −0.519138 | − | 0.854691i | \(-0.673747\pi\) | ||||
−0.519138 | + | 0.854691i | \(0.673747\pi\) | |||||||
\(462\) | 19944.1 | + | 19944.1i | 0.0934397 | + | 0.0934397i | ||||
\(463\) | −170047. | + | 170047.i | −0.793245 | + | 0.793245i | −0.982020 | − | 0.188775i | \(-0.939548\pi\) |
0.188775 | + | 0.982020i | \(0.439548\pi\) | |||||||
\(464\) | 28732.9i | 0.133458i | ||||||||
\(465\) | −52245.5 | − | 192176.i | −0.241626 | − | 0.888777i | ||||
\(466\) | −4796.11 | −0.0220860 | ||||||||
\(467\) | 232244. | + | 232244.i | 1.06491 | + | 1.06491i | 0.997742 | + | 0.0671643i | \(0.0213952\pi\) |
0.0671643 | + | 0.997742i | \(0.478605\pi\) | |||||||
\(468\) | 37313.5 | − | 37313.5i | 0.170363 | − | 0.170363i | ||||
\(469\) | 193019.i | 0.877515i | ||||||||
\(470\) | 151630. | + | 86807.4i | 0.686417 | + | 0.392972i | ||||
\(471\) | −42371.6 | −0.191000 | ||||||||
\(472\) | −15319.2 | − | 15319.2i | −0.0687625 | − | 0.0687625i | ||||
\(473\) | 54099.4 | − | 54099.4i | 0.241808 | − | 0.241808i | ||||
\(474\) | − | 77063.3i | − | 0.342997i | ||||||
\(475\) | −76608.5 | + | 44978.4i | −0.339539 | + | 0.199350i | ||||
\(476\) | −32885.7 | −0.145142 | ||||||||
\(477\) | −75306.7 | − | 75306.7i | −0.330976 | − | 0.330976i | ||||
\(478\) | 108269. | − | 108269.i | 0.473859 | − | 0.473859i | ||||
\(479\) | 215924.i | 0.941086i | 0.882377 | + | 0.470543i | \(0.155942\pi\) | ||||
−0.882377 | + | 0.470543i | \(0.844058\pi\) | |||||||
\(480\) | −14829.5 | + | 25903.3i | −0.0643643 | + | 0.112427i | ||||
\(481\) | −290241. | −1.25450 | ||||||||
\(482\) | −14583.9 | − | 14583.9i | −0.0627739 | − | 0.0627739i | ||||
\(483\) | 18183.7 | − | 18183.7i | 0.0779449 | − | 0.0779449i | ||||
\(484\) | − | 102491.i | − | 0.437517i | ||||||
\(485\) | 429892. | − | 116872.i | 1.82758 | − | 0.496851i | ||||
\(486\) | 139559. | 0.590861 | ||||||||
\(487\) | −244390. | − | 244390.i | −1.03045 | − | 1.03045i | −0.999522 | − | 0.0309271i | \(-0.990154\pi\) |
−0.0309271 | − | 0.999522i | \(-0.509846\pi\) | |||||||
\(488\) | 54391.8 | − | 54391.8i | 0.228399 | − | 0.228399i | ||||
\(489\) | − | 252869.i | − | 1.05749i | ||||||
\(490\) | 21361.8 | + | 78575.8i | 0.0889706 | + | 0.327263i | ||||
\(491\) | −76961.6 | −0.319235 | −0.159618 | − | 0.987179i | \(-0.551026\pi\) | ||||
−0.159618 | + | 0.987179i | \(0.551026\pi\) | |||||||
\(492\) | 36701.0 | + | 36701.0i | 0.151617 | + | 0.151617i | ||||
\(493\) | −36918.5 | + | 36918.5i | −0.151897 | + | 0.151897i | ||||
\(494\) | 70717.1i | 0.289781i | ||||||||
\(495\) | −34800.4 | − | 19923.1i | −0.142028 | − | 0.0813105i | ||||
\(496\) | −77299.1 | −0.314204 | ||||||||
\(497\) | −13391.5 | − | 13391.5i | −0.0542147 | − | 0.0542147i | ||||
\(498\) | 141369. | − | 141369.i | 0.570029 | − | 0.570029i | ||||
\(499\) | − | 14490.0i | − | 0.0581926i | −0.999577 | − | 0.0290963i | \(-0.990737\pi\) | ||
0.999577 | − | 0.0290963i | \(-0.00926294\pi\) | |||||||
\(500\) | 1368.00 | + | 124993.i | 0.00547199 | + | 0.499970i | ||||
\(501\) | 118913. | 0.473757 | ||||||||
\(502\) | 21296.0 | + | 21296.0i | 0.0845066 | + | 0.0845066i | ||||
\(503\) | 82880.3 | − | 82880.3i | 0.327578 | − | 0.327578i | −0.524087 | − | 0.851665i | \(-0.675593\pi\) |
0.851665 | + | 0.524087i | \(0.175593\pi\) | |||||||
\(504\) | 29992.7i | 0.118074i | ||||||||
\(505\) | −62777.0 | + | 109655.i | −0.246160 | + | 0.429977i | ||||
\(506\) | 13344.9 | 0.0521214 | ||||||||
\(507\) | 11100.5 | + | 11100.5i | 0.0431844 | + | 0.0431844i | ||||
\(508\) | 99242.1 | − | 99242.1i | 0.384564 | − | 0.384564i | ||||
\(509\) | 179121.i | 0.691370i | 0.938351 | + | 0.345685i | \(0.112353\pi\) | ||||
−0.938351 | + | 0.345685i | \(0.887647\pi\) | |||||||
\(510\) | −52337.0 | + | 14228.5i | −0.201219 | + | 0.0547040i | ||||
\(511\) | −123919. | −0.474566 | ||||||||
\(512\) | 8192.00 | + | 8192.00i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −78552.5 | + | 78552.5i | −0.298487 | + | 0.298487i | ||||
\(514\) | − | 34404.3i | − | 0.130223i | ||||||
\(515\) | −88215.9 | − | 324487.i | −0.332608 | − | 1.22344i | ||||
\(516\) | −94376.9 | −0.354459 | ||||||||
\(517\) | −74734.7 | − | 74734.7i | −0.279603 | − | 0.279603i | ||||
\(518\) | 116648. | − | 116648.i | 0.434729 | − | 0.434729i | ||||
\(519\) | 168800.i | 0.626668i | ||||||||
\(520\) | 86354.5 | + | 49437.6i | 0.319358 | + | 0.182831i | ||||
\(521\) | −277840. | −1.02358 | −0.511788 | − | 0.859112i | \(-0.671017\pi\) | ||||
−0.511788 | + | 0.859112i | \(0.671017\pi\) | |||||||
\(522\) | 33670.7 | + | 33670.7i | 0.123570 | + | 0.123570i | ||||
\(523\) | 4303.41 | − | 4303.41i | 0.0157329 | − | 0.0157329i | −0.699197 | − | 0.714929i | \(-0.746459\pi\) |
0.714929 | + | 0.699197i | \(0.246459\pi\) | |||||||
\(524\) | − | 127928.i | − | 0.465910i | ||||||
\(525\) | −73773.1 | − | 125653.i | −0.267657 | − | 0.455882i | ||||
\(526\) | 242661. | 0.877057 | ||||||||
\(527\) | −99320.6 | − | 99320.6i | −0.357617 | − | 0.357617i | ||||
\(528\) | 12767.1 | − | 12767.1i | 0.0457958 | − | 0.0457958i | ||||
\(529\) | − | 12167.0i | − | 0.0434783i | ||||||
\(530\) | 99775.7 | − | 174282.i | 0.355200 | − | 0.620440i | ||||
\(531\) | −35903.7 | −0.127336 | ||||||||
\(532\) | −28421.3 | − | 28421.3i | −0.100420 | − | 0.100420i | ||||
\(533\) | 122351. | − | 122351.i | 0.430679 | − | 0.430679i | ||||
\(534\) | − | 160285.i | − | 0.562096i | ||||||
\(535\) | −218031. | + | 59274.5i | −0.761746 | + | 0.207091i | ||||
\(536\) | 123560. | 0.430079 | ||||||||
\(537\) | −211948. | − | 211948.i | −0.734988 | − | 0.734988i | ||||
\(538\) | 200481. | − | 200481.i | 0.692642 | − | 0.692642i | ||||
\(539\) | − | 49256.9i | − | 0.169547i | ||||||
\(540\) | 41007.2 | + | 150838.i | 0.140628 | + | 0.517276i | ||||
\(541\) | −287938. | −0.983794 | −0.491897 | − | 0.870653i | \(-0.663696\pi\) | ||||
−0.491897 | + | 0.870653i | \(0.663696\pi\) | |||||||
\(542\) | −147315. | − | 147315.i | −0.501472 | − | 0.501472i | ||||
\(543\) | 17159.0 | − | 17159.0i | 0.0581959 | − | 0.0581959i | ||||
\(544\) | 21051.6i | 0.0711356i | ||||||||
\(545\) | 3159.48 | + | 1808.79i | 0.0106371 | + | 0.00608970i | ||||
\(546\) | −115990. | −0.389075 | ||||||||
\(547\) | 313350. | + | 313350.i | 1.04726 | + | 1.04726i | 0.998826 | + | 0.0484353i | \(0.0154235\pi\) |
0.0484353 | + | 0.998826i | \(0.484577\pi\) | |||||||
\(548\) | 60580.7 | − | 60580.7i | 0.201731 | − | 0.201731i | ||||
\(549\) | − | 127478.i | − | 0.422953i | ||||||
\(550\) | 19037.1 | − | 73178.8i | 0.0629324 | − | 0.241913i | ||||
\(551\) | −63813.2 | −0.210188 | ||||||||
\(552\) | −11640.2 | − | 11640.2i | −0.0382016 | − | 0.0382016i | ||||
\(553\) | 103252. | − | 103252.i | 0.337634 | − | 0.337634i | ||||
\(554\) | − | 242079.i | − | 0.788747i | ||||||
\(555\) | 135174. | − | 236113.i | 0.438841 | − | 0.766539i | ||||
\(556\) | −160615. | −0.519561 | ||||||||
\(557\) | −159935. | − | 159935.i | −0.515505 | − | 0.515505i | 0.400703 | − | 0.916208i | \(-0.368766\pi\) |
−0.916208 | + | 0.400703i | \(0.868766\pi\) | |||||||
\(558\) | −90583.2 | + | 90583.2i | −0.290924 | + | 0.290924i | ||||
\(559\) | 314627.i | 1.00687i | ||||||||
\(560\) | −54575.0 | + | 14836.9i | −0.174027 | + | 0.0473116i | ||||
\(561\) | 32808.6 | 0.104247 | ||||||||
\(562\) | −34842.0 | − | 34842.0i | −0.110314 | − | 0.110314i | ||||
\(563\) | 243163. | − | 243163.i | 0.767149 | − | 0.767149i | −0.210454 | − | 0.977604i | \(-0.567494\pi\) |
0.977604 | + | 0.210454i | \(0.0674943\pi\) | |||||||
\(564\) | 130375.i | 0.409862i | ||||||||
\(565\) | −92993.7 | − | 342061.i | −0.291311 | − | 1.07153i | ||||
\(566\) | 20891.6 | 0.0652139 | ||||||||
\(567\) | −52922.1 | − | 52922.1i | −0.164616 | − | 0.164616i | ||||
\(568\) | −8572.51 | + | 8572.51i | −0.0265712 | + | 0.0265712i | ||||
\(569\) | 576729.i | 1.78134i | 0.454647 | + | 0.890672i | \(0.349765\pi\) | ||||
−0.454647 | + | 0.890672i | \(0.650235\pi\) | |||||||
\(570\) | −57528.9 | − | 32935.1i | −0.177066 | − | 0.101370i | ||||
\(571\) | −287622. | −0.882164 | −0.441082 | − | 0.897467i | \(-0.645405\pi\) | ||||
−0.441082 | + | 0.897467i | \(0.645405\pi\) | |||||||
\(572\) | −42562.1 | − | 42562.1i | −0.130086 | − | 0.130086i | ||||
\(573\) | −25976.4 | + | 25976.4i | −0.0791170 | + | 0.0791170i | ||||
\(574\) | 98346.1i | 0.298492i | ||||||||
\(575\) | −66719.4 | − | 17356.7i | −0.201798 | − | 0.0524966i | ||||
\(576\) | 19199.6 | 0.0578693 | ||||||||
\(577\) | −223235. | − | 223235.i | −0.670517 | − | 0.670517i | 0.287318 | − | 0.957835i | \(-0.407236\pi\) |
−0.957835 | + | 0.287318i | \(0.907236\pi\) | |||||||
\(578\) | 139993. | − | 139993.i | 0.419036 | − | 0.419036i | ||||
\(579\) | 131179.i | 0.391297i | ||||||||
\(580\) | −44611.2 | + | 77924.0i | −0.132613 | + | 0.231641i | ||||
\(581\) | 378821. | 1.12223 | ||||||||
\(582\) | 235062. | + | 235062.i | 0.693962 | + | 0.693962i | ||||
\(583\) | −85899.4 | + | 85899.4i | −0.252728 | + | 0.252728i | ||||
\(584\) | 79326.0i | 0.232589i | ||||||||
\(585\) | 159128. | − | 43261.1i | 0.464982 | − | 0.126411i | ||||
\(586\) | −244336. | −0.711529 | ||||||||
\(587\) | 396735. | + | 396735.i | 1.15139 | + | 1.15139i | 0.986273 | + | 0.165120i | \(0.0528012\pi\) |
0.165120 | + | 0.986273i | \(0.447199\pi\) | |||||||
\(588\) | −42964.6 | + | 42964.6i | −0.124267 | + | 0.124267i | ||||
\(589\) | − | 171674.i | − | 0.494852i | ||||||
\(590\) | −17761.0 | − | 65330.7i | −0.0510227 | − | 0.187678i | ||||
\(591\) | 144784. | 0.414521 | ||||||||
\(592\) | −74671.6 | − | 74671.6i | −0.213065 | − | 0.213065i | ||||
\(593\) | −31678.1 | + | 31678.1i | −0.0900843 | + | 0.0900843i | −0.750713 | − | 0.660629i | \(-0.770290\pi\) |
0.660629 | + | 0.750713i | \(0.270290\pi\) | |||||||
\(594\) | − | 94556.0i | − | 0.267988i | ||||||
\(595\) | −89186.4 | − | 51058.9i | −0.251921 | − | 0.144224i | ||||
\(596\) | 44561.1 | 0.125448 | ||||||||
\(597\) | 111541. | + | 111541.i | 0.312957 | + | 0.312957i | ||||
\(598\) | −38805.2 | + | 38805.2i | −0.108515 | + | 0.108515i | ||||
\(599\) | 25172.7i | 0.0701578i | 0.999385 | + | 0.0350789i | \(0.0111683\pi\) | ||||
−0.999385 | + | 0.0350789i | \(0.988832\pi\) | |||||||
\(600\) | −80435.7 | + | 47225.4i | −0.223433 | + | 0.131182i | ||||
\(601\) | 146403. | 0.405324 | 0.202662 | − | 0.979249i | \(-0.435041\pi\) | ||||
0.202662 | + | 0.979249i | \(0.435041\pi\) | |||||||
\(602\) | −126449. | − | 126449.i | −0.348917 | − | 0.348917i | ||||
\(603\) | 144794. | − | 144794.i | 0.398214 | − | 0.398214i | ||||
\(604\) | 203624.i | 0.558156i | ||||||||
\(605\) | 159129. | − | 277957.i | 0.434750 | − | 0.759393i | ||||
\(606\) | −94284.4 | −0.256741 | ||||||||
\(607\) | 94409.0 | + | 94409.0i | 0.256234 | + | 0.256234i | 0.823520 | − | 0.567287i | \(-0.192007\pi\) |
−0.567287 | + | 0.823520i | \(0.692007\pi\) | |||||||
\(608\) | −18193.7 | + | 18193.7i | −0.0492169 | + | 0.0492169i | ||||
\(609\) | − | 104666.i | − | 0.282209i | ||||||
\(610\) | 231961. | − | 63061.6i | 0.623383 | − | 0.169475i | ||||
\(611\) | 434636. | 1.16424 | ||||||||
\(612\) | 24669.4 | + | 24669.4i | 0.0658650 | + | 0.0658650i | ||||
\(613\) | 377419. | − | 377419.i | 1.00439 | − | 1.00439i | 0.00440021 | − | 0.999990i | \(-0.498599\pi\) |
0.999990 | − | 0.00440021i | \(-0.00140064\pi\) | |||||||
\(614\) | − | 172967.i | − | 0.458804i | ||||||
\(615\) | 42550.9 | + | 156516.i | 0.112502 | + | 0.413817i | ||||
\(616\) | 34211.5 | 0.0901594 | ||||||||
\(617\) | −258016. | − | 258016.i | −0.677759 | − | 0.677759i | 0.281733 | − | 0.959493i | \(-0.409091\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(618\) | 177427. | − | 177427.i | 0.464560 | − | 0.464560i | ||||
\(619\) | − | 142371.i | − | 0.371569i | −0.982591 | − | 0.185784i | \(-0.940517\pi\) | ||
0.982591 | − | 0.185784i | \(-0.0594826\pi\) | |||||||
\(620\) | −209636. | − | 120016.i | −0.545359 | − | 0.312216i | ||||
\(621\) | −86209.6 | −0.223549 | ||||||||
\(622\) | 26733.9 | + | 26733.9i | 0.0691005 | + | 0.0691005i | ||||
\(623\) | 214754. | − | 214754.i | 0.553307 | − | 0.553307i | ||||
\(624\) | 74250.0i | 0.190690i | ||||||||
\(625\) | −190355. | + | 341105.i | −0.487310 | + | 0.873229i | ||||
\(626\) | −481208. | −1.22796 | ||||||||
\(627\) | 28354.7 | + | 28354.7i | 0.0721256 | + | 0.0721256i | ||||
\(628\) | −36341.4 | + | 36341.4i | −0.0921472 | + | 0.0921472i | ||||
\(629\) | − | 191889.i | − | 0.485008i | ||||||
\(630\) | −46567.1 | + | 81340.5i | −0.117327 | + | 0.204939i | ||||
\(631\) | −164037. | −0.411988 | −0.205994 | − | 0.978553i | \(-0.566043\pi\) | ||||
−0.205994 | + | 0.978553i | \(0.566043\pi\) | |||||||
\(632\) | −66095.9 | − | 66095.9i | −0.165478 | − | 0.165478i | ||||
\(633\) | −245293. | + | 245293.i | −0.612177 | + | 0.612177i | ||||
\(634\) | 425841.i | 1.05942i | ||||||||
\(635\) | 423230. | − | 115061.i | 1.04961 | − | 0.285351i | ||||
\(636\) | 149852. | 0.370467 | ||||||||
\(637\) | 143232. | + | 143232.i | 0.352990 | + | 0.352990i | ||||
\(638\) | 38406.9 | − | 38406.9i | 0.0943557 | − | 0.0943557i | ||||
\(639\) | 20091.4i | 0.0492050i | ||||||||
\(640\) | 9497.76 | + | 34935.8i | 0.0231879 | + | 0.0852926i | ||||
\(641\) | 1611.31 | 0.00392160 | 0.00196080 | − | 0.999998i | \(-0.499376\pi\) | ||||
0.00196080 | + | 0.999998i | \(0.499376\pi\) | |||||||
\(642\) | −119217. | − | 119217.i | −0.289248 | − | 0.289248i | ||||
\(643\) | −340836. | + | 340836.i | −0.824372 | + | 0.824372i | −0.986732 | − | 0.162360i | \(-0.948090\pi\) |
0.162360 | + | 0.986732i | \(0.448090\pi\) | |||||||
\(644\) | − | 31191.7i | − | 0.0752086i | ||||||
\(645\) | −255951. | − | 146531.i | −0.615230 | − | 0.352217i | ||||
\(646\) | −46753.7 | −0.112034 | ||||||||
\(647\) | 427266. | + | 427266.i | 1.02068 | + | 1.02068i | 0.999782 | + | 0.0208983i | \(0.00665262\pi\) |
0.0208983 | + | 0.999782i | \(0.493347\pi\) | |||||||
\(648\) | −33877.8 | + | 33877.8i | −0.0806798 | + | 0.0806798i | ||||
\(649\) | 40954.0i | 0.0972314i | ||||||||
\(650\) | 157437. | + | 268151.i | 0.372631 | + | 0.634677i | ||||
\(651\) | 281579. | 0.664413 | ||||||||
\(652\) | −216881. | − | 216881.i | −0.510184 | − | 0.510184i | ||||
\(653\) | 404699. | − | 404699.i | 0.949086 | − | 0.949086i | −0.0496792 | − | 0.998765i | \(-0.515820\pi\) |
0.998765 | + | 0.0496792i | \(0.0158199\pi\) | |||||||
\(654\) | 2716.61i | 0.00635144i | ||||||||
\(655\) | 198623. | − | 346942.i | 0.462963 | − | 0.808675i | ||||
\(656\) | 62955.6 | 0.146294 | ||||||||
\(657\) | 92958.4 | + | 92958.4i | 0.215356 | + | 0.215356i | ||||
\(658\) | −174681. | + | 174681.i | −0.403453 | + | 0.403453i | ||||
\(659\) | 158812.i | 0.365690i | 0.983142 | + | 0.182845i | \(0.0585306\pi\) | ||||
−0.983142 | + | 0.182845i | \(0.941469\pi\) | |||||||
\(660\) | 54447.0 | − | 14802.1i | 0.124993 | − | 0.0339810i | ||||
\(661\) | −245185. | −0.561164 | −0.280582 | − | 0.959830i | \(-0.590528\pi\) | ||||
−0.280582 | + | 0.959830i | \(0.590528\pi\) | |||||||
\(662\) | 268361. | + | 268361.i | 0.612355 | + | 0.612355i | ||||
\(663\) | −95402.9 | + | 95402.9i | −0.217037 | + | 0.217037i | ||||
\(664\) | − | 242500.i | − | 0.550017i | ||||||
\(665\) | −32951.5 | − | 121206.i | −0.0745129 | − | 0.274082i | ||||
\(666\) | −175008. | −0.394557 | ||||||||
\(667\) | −35016.8 | − | 35016.8i | −0.0787090 | − | 0.0787090i | ||||
\(668\) | 101990. | − | 101990.i | 0.228562 | − | 0.228562i | ||||
\(669\) | − | 270768.i | − | 0.604987i | ||||||
\(670\) | 335096. | + | 191841.i | 0.746483 | + | 0.427359i | ||||
\(671\) | −145410. | −0.322960 | ||||||||
\(672\) | −29841.1 | − | 29841.1i | −0.0660810 | − | 0.0660810i | ||||
\(673\) | 370502. | − | 370502.i | 0.818013 | − | 0.818013i | −0.167807 | − | 0.985820i | \(-0.553669\pi\) |
0.985820 | + | 0.167807i | \(0.0536686\pi\) | |||||||
\(674\) | − | 142764.i | − | 0.314268i | ||||||
\(675\) | −122981. | + | 472742.i | −0.269918 | + | 1.03757i | ||||
\(676\) | 19041.4 | 0.0416683 | ||||||||
\(677\) | 101209. | + | 101209.i | 0.220821 | + | 0.220821i | 0.808844 | − | 0.588023i | \(-0.200094\pi\) |
−0.588023 | + | 0.808844i | \(0.700094\pi\) | |||||||
\(678\) | 187036. | − | 187036.i | 0.406880 | − | 0.406880i | ||||
\(679\) | 629884.i | 1.36622i | ||||||||
\(680\) | −32685.0 | + | 57092.1i | −0.0706856 | + | 0.123469i | ||||
\(681\) | 34266.8 | 0.0738888 | ||||||||
\(682\) | 103325. | + | 103325.i | 0.222145 | + | 0.222145i | ||||
\(683\) | 116405. | − | 116405.i | 0.249534 | − | 0.249534i | −0.571245 | − | 0.820779i | \(-0.693539\pi\) |
0.820779 | + | 0.571245i | \(0.193539\pi\) | |||||||
\(684\) | 42640.7i | 0.0911406i | ||||||||
\(685\) | 258354. | − | 70237.0i | 0.550598 | − | 0.149687i | ||||
\(686\) | −355176. | −0.754737 | ||||||||
\(687\) | 472343. | + | 472343.i | 1.00079 | + | 1.00079i | ||||
\(688\) | −80945.5 | + | 80945.5i | −0.171008 | + | 0.171008i | ||||
\(689\) | − | 499567.i | − | 1.05234i | ||||||
\(690\) | −13495.6 | − | 49641.1i | −0.0283461 | − | 0.104266i | ||||
\(691\) | −323661. | −0.677852 | −0.338926 | − | 0.940813i | \(-0.610064\pi\) | ||||
−0.338926 | + | 0.940813i | \(0.610064\pi\) | |||||||
\(692\) | 144777. | + | 144777.i | 0.302334 | + | 0.302334i | ||||
\(693\) | 40090.8 | − | 40090.8i | 0.0834793 | − | 0.0834793i | ||||
\(694\) | 328956.i | 0.682998i | ||||||||
\(695\) | −435590. | − | 249374.i | −0.901796 | − | 0.516275i | ||||
\(696\) | −67001.2 | −0.138313 | ||||||||
\(697\) | 80890.9 | + | 80890.9i | 0.166508 | + | 0.166508i | ||||
\(698\) | 127205. | − | 127205.i | 0.261092 | − | 0.261092i | ||||
\(699\) | − | 11183.9i | − | 0.0228896i | ||||||
\(700\) | −171044. | − | 44496.1i | −0.349069 | − | 0.0908084i | ||||
\(701\) | 233087. | 0.474332 | 0.237166 | − | 0.971469i | \(-0.423782\pi\) | ||||
0.237166 | + | 0.971469i | \(0.423782\pi\) | |||||||
\(702\) | 274955. | + | 274955.i | 0.557941 | + | 0.557941i | ||||
\(703\) | 165839. | − | 165839.i | 0.335565 | − | 0.335565i | ||||
\(704\) | − | 21900.3i | − | 0.0441880i | ||||||
\(705\) | −202423. | + | 353580.i | −0.407269 | + | 0.711392i | ||||
\(706\) | −505804. | −1.01478 | ||||||||
\(707\) | −126325. | − | 126325.i | −0.252726 | − | 0.252726i | ||||
\(708\) | 35722.3 | − | 35722.3i | 0.0712644 | − | 0.0712644i | ||||
\(709\) | 557827.i | 1.10970i | 0.831949 | + | 0.554852i | \(0.187225\pi\) | ||||
−0.831949 | + | 0.554852i | \(0.812775\pi\) | |||||||
\(710\) | −36558.6 | + | 9938.92i | −0.0725224 | + | 0.0197162i | ||||
\(711\) | −154909. | −0.306435 | ||||||||
\(712\) | −137474. | − | 137474.i | −0.271181 | − | 0.271181i | ||||
\(713\) | 94204.4 | − | 94204.4i | 0.185307 | − | 0.185307i | ||||
\(714\) | − | 76685.0i | − | 0.150423i | ||||||
\(715\) | −49346.3 | − | 181512.i | −0.0965256 | − | 0.355052i | ||||
\(716\) | −363568. | −0.709185 | ||||||||
\(717\) | 252469. | + | 252469.i | 0.491099 | + | 0.491099i | ||||
\(718\) | −187087. | + | 187087.i | −0.362906 | + | 0.362906i | ||||
\(719\) | 509896.i | 0.986333i | 0.869935 | + | 0.493166i | \(0.164161\pi\) | ||||
−0.869935 | + | 0.493166i | \(0.835839\pi\) | |||||||
\(720\) | 52069.6 | + | 29809.7i | 0.100443 | + | 0.0575032i | ||||
\(721\) | 475443. | 0.914592 | ||||||||
\(722\) | 220235. | + | 220235.i | 0.422486 | + | 0.422486i | ||||
\(723\) | 34007.6 | − | 34007.6i | 0.0650578 | − | 0.0650578i | ||||
\(724\) | − | 29434.0i | − | 0.0561529i | ||||||
\(725\) | −241972. | + | 142067.i | −0.460351 | + | 0.270281i | ||||
\(726\) | 238995. | 0.453436 | ||||||||
\(727\) | −230319. | − | 230319.i | −0.435774 | − | 0.435774i | 0.454813 | − | 0.890587i | \(-0.349706\pi\) |
−0.890587 | + | 0.454813i | \(0.849706\pi\) | |||||||
\(728\) | −99482.3 | + | 99482.3i | −0.187708 | + | 0.187708i | ||||
\(729\) | 496939.i | 0.935078i | ||||||||
\(730\) | −123163. | + | 215133.i | −0.231118 | + | 0.403703i | ||||
\(731\) | −208011. | −0.389271 | ||||||||
\(732\) | 126834. | + | 126834.i | 0.236709 | + | 0.236709i | ||||
\(733\) | −220700. | + | 220700.i | −0.410766 | + | 0.410766i | −0.882005 | − | 0.471240i | \(-0.843807\pi\) |
0.471240 | + | 0.882005i | \(0.343807\pi\) | |||||||
\(734\) | − | 250461.i | − | 0.464888i | ||||||
\(735\) | −183228. | + | 49812.9i | −0.339170 | + | 0.0922077i | ||||
\(736\) | −19967.2 | −0.0368605 | ||||||||
\(737\) | −165161. | − | 165161.i | −0.304070 | − | 0.304070i | ||||
\(738\) | 73774.7 | − | 73774.7i | 0.135455 | − | 0.135455i | ||||
\(739\) | − | 118916.i | − | 0.217746i | −0.994056 | − | 0.108873i | \(-0.965276\pi\) | ||
0.994056 | − | 0.108873i | \(-0.0347242\pi\) | |||||||
\(740\) | −86573.9 | − | 318447.i | −0.158097 | − | 0.581532i | ||||
\(741\) | −164903. | −0.300325 | ||||||||
\(742\) | 200776. | + | 200776.i | 0.364674 | + | 0.364674i | ||||
\(743\) | −246622. | + | 246622.i | −0.446739 | + | 0.446739i | −0.894269 | − | 0.447530i | \(-0.852304\pi\) |
0.447530 | + | 0.894269i | \(0.352304\pi\) | |||||||
\(744\) | − | 180251.i | − | 0.325636i | ||||||
\(745\) | 120850. | + | 69186.3i | 0.217738 | + | 0.124654i | ||||
\(746\) | −736298. | −1.32305 | ||||||||
\(747\) | −284175. | − | 284175.i | −0.509265 | − | 0.509265i | ||||
\(748\) | 28139.4 | − | 28139.4i | 0.0502935 | − | 0.0502935i | ||||
\(749\) | − | 319462.i | − | 0.569450i | ||||||
\(750\) | −291466. | + | 3189.99i | −0.518161 | + | 0.00567109i | ||||
\(751\) | −785884. | −1.39341 | −0.696704 | − | 0.717358i | \(-0.745351\pi\) | ||||
−0.696704 | + | 0.717358i | \(0.745351\pi\) | |||||||
\(752\) | 111821. | + | 111821.i | 0.197736 | + | 0.197736i | ||||
\(753\) | −49659.4 | + | 49659.4i | −0.0875813 | + | 0.0875813i | ||||
\(754\) | 223364.i | 0.392889i | ||||||||
\(755\) | −316151. | + | 552232.i | −0.554626 | + | 0.968785i | ||||
\(756\) | −221010. | −0.386694 | ||||||||
\(757\) | 10653.9 | + | 10653.9i | 0.0185916 | + | 0.0185916i | 0.716341 | − | 0.697750i | \(-0.245815\pi\) |
−0.697750 | + | 0.716341i | \(0.745815\pi\) | |||||||
\(758\) | −455777. | + | 455777.i | −0.793257 | + | 0.793257i | ||||
\(759\) | 31118.6i | 0.0540177i | ||||||||
\(760\) | −77589.4 | + | 21093.7i | −0.134331 | + | 0.0365195i | ||||
\(761\) | −394139. | −0.680581 | −0.340290 | − | 0.940320i | \(-0.610525\pi\) | ||||
−0.340290 | + | 0.940320i | \(0.610525\pi\) | |||||||
\(762\) | 231419. | + | 231419.i | 0.398556 | + | 0.398556i | ||||
\(763\) | −3639.80 | + | 3639.80i | −0.00625213 | + | 0.00625213i | ||||
\(764\) | 44559.0i | 0.0763395i | ||||||||
\(765\) | 28601.5 | + | 105206.i | 0.0488727 | + | 0.179770i | ||||
\(766\) | −73370.1 | −0.125044 | ||||||||
\(767\) | −119088. | − | 119088.i | −0.202432 | − | 0.202432i | ||||
\(768\) | −19102.6 | + | 19102.6i | −0.0323870 | + | 0.0323870i | ||||
\(769\) | − | 119699.i | − | 0.202412i | −0.994865 | − | 0.101206i | \(-0.967730\pi\) | ||
0.994865 | − | 0.101206i | \(-0.0322701\pi\) | |||||||
\(770\) | 92782.0 | + | 53117.4i | 0.156488 | + | 0.0895891i | ||||
\(771\) | 80226.2 | 0.134961 | ||||||||
\(772\) | 112510. | + | 112510.i | 0.188780 | + | 0.188780i | ||||
\(773\) | 229621. | − | 229621.i | 0.384285 | − | 0.384285i | −0.488358 | − | 0.872643i | \(-0.662404\pi\) |
0.872643 | + | 0.488358i | \(0.162404\pi\) | |||||||
\(774\) | 189712.i | 0.316675i | ||||||||
\(775\) | −382197. | − | 650969.i | −0.636332 | − | 1.08382i | ||||
\(776\) | 403217. | 0.669599 | ||||||||
\(777\) | 272008. | + | 272008.i | 0.450546 | + | 0.450546i | ||||
\(778\) | −3983.35 | + | 3983.35i | −0.00658096 | + | 0.00658096i | ||||
\(779\) | 139819.i | 0.230404i | ||||||||
\(780\) | −115282. | + | 201367.i | −0.189484 | + | 0.330978i | ||||
\(781\) | 22917.5 | 0.0375721 | ||||||||
\(782\) | −25655.6 | − | 25655.6i | −0.0419535 | − | 0.0419535i | ||||
\(783\) | −248112. | + | 248112.i | −0.404692 | + | 0.404692i | ||||
\(784\) | 73700.0i | 0.119904i | ||||||||
\(785\) | −154982. | + | 42134.0i | −0.251503 | + | 0.0683744i | ||||
\(786\) | 298310. | 0.482862 | ||||||||
\(787\) | −855733. | − | 855733.i | −1.38162 | − | 1.38162i | −0.841745 | − | 0.539875i | \(-0.818471\pi\) |
−0.539875 | − | 0.841745i | \(-0.681529\pi\) | |||||||
\(788\) | 124179. | − | 124179.i | 0.199984 | − | 0.199984i | ||||
\(789\) | 565851.i | 0.908967i | ||||||||
\(790\) | −76631.2 | − | 281874.i | −0.122787 | − | 0.451649i | ||||
\(791\) | 501192. | 0.801035 | ||||||||
\(792\) | −25663.9 | − | 25663.9i | −0.0409141 | − | 0.0409141i | ||||
\(793\) | 422831. | − | 422831.i | 0.672389 | − | 0.672389i | ||||
\(794\) | 394580.i | 0.625884i | ||||||||
\(795\) | 406401. | + | 232663.i | 0.643015 | + | 0.368123i | ||||
\(796\) | 191333. | 0.301970 | ||||||||
\(797\) | −553344. | − | 553344.i | −0.871122 | − | 0.871122i | 0.121473 | − | 0.992595i | \(-0.461238\pi\) |
−0.992595 | + | 0.121473i | \(0.961238\pi\) | |||||||
\(798\) | 66274.5 | − | 66274.5i | 0.104074 | − | 0.104074i | ||||
\(799\) | 287354.i | 0.450115i | ||||||||
\(800\) | −28483.9 | + | 109493.i | −0.0445061 | + | 0.171082i | ||||
\(801\) | −322198. | −0.502178 | ||||||||
\(802\) | −30257.0 | − | 30257.0i | −0.0470410 | − | 0.0470410i | ||||
\(803\) | 106034. | − | 106034.i | 0.164443 | − | 0.164443i | ||||
\(804\) | 288125.i | 0.445727i | ||||||||
\(805\) | 48428.8 | − | 84592.2i | 0.0747328 | − | 0.130539i | ||||
\(806\) | −600908. | −0.924992 | ||||||||
\(807\) | 467495. | + | 467495.i | 0.717843 | + | 0.717843i | ||||
\(808\) | −80866.1 | + | 80866.1i | −0.123864 | + | 0.123864i | ||||
\(809\) | 872153.i | 1.33259i | 0.745690 | + | 0.666293i | \(0.232120\pi\) | ||||
−0.745690 | + | 0.666293i | \(0.767880\pi\) | |||||||
\(810\) | −144476. | + | 39277.7i | −0.220204 | + | 0.0598655i | ||||
\(811\) | 471012. | 0.716128 | 0.358064 | − | 0.933697i | \(-0.383437\pi\) | ||||
0.358064 | + | 0.933697i | \(0.383437\pi\) | |||||||
\(812\) | −89770.1 | − | 89770.1i | −0.136151 | − | 0.136151i | ||||
\(813\) | 343517. | − | 343517.i | 0.519718 | − | 0.519718i | ||||
\(814\) | 199625.i | 0.301278i | ||||||||
\(815\) | −251451. | − | 924918.i | −0.378563 | − | 1.39248i | ||||
\(816\) | −49089.4 | −0.0737238 | ||||||||
\(817\) | −179773. | − | 179773.i | −0.269327 | − | 0.269327i | ||||
\(818\) | −415958. | + | 415958.i | −0.621646 | + | 0.621646i | ||||
\(819\) | 233157.i | 0.347601i | ||||||||
\(820\) | 170736. | + | 97746.0i | 0.253921 | + | 0.145369i | ||||
\(821\) | −382604. | −0.567628 | −0.283814 | − | 0.958879i | \(-0.591600\pi\) | ||||
−0.283814 | + | 0.958879i | \(0.591600\pi\) | |||||||
\(822\) | 141266. | + | 141266.i | 0.209071 | + | 0.209071i | ||||
\(823\) | 372527. | − | 372527.i | 0.549994 | − | 0.549994i | −0.376445 | − | 0.926439i | \(-0.622854\pi\) |
0.926439 | + | 0.376445i | \(0.122854\pi\) | |||||||
\(824\) | − | 304352.i | − | 0.448251i | ||||||
\(825\) | 170643. | + | 44391.8i | 0.250715 | + | 0.0652222i | ||||
\(826\) | 95723.4 | 0.140300 | ||||||||
\(827\) | 807954. | + | 807954.i | 1.18134 | + | 1.18134i | 0.979397 | + | 0.201945i | \(0.0647263\pi\) |
0.201945 | + | 0.979397i | \(0.435274\pi\) | |||||||
\(828\) | −23398.6 | + | 23398.6i | −0.0341294 | + | 0.0341294i | ||||
\(829\) | − | 634241.i | − | 0.922880i | −0.887172 | − | 0.461440i | \(-0.847333\pi\) | ||
0.887172 | − | 0.461440i | \(-0.152667\pi\) | |||||||
\(830\) | 376510. | − | 657663.i | 0.546538 | − | 0.954657i | ||||
\(831\) | 564496. | 0.817445 | ||||||||
\(832\) | 63683.0 | + | 63683.0i | 0.0919976 | + | 0.0919976i | ||||
\(833\) | −94696.1 | + | 94696.1i | −0.136472 | + | 0.136472i | ||||
\(834\) | − | 374532.i | − | 0.538465i | ||||||
\(835\) | 434949. | − | 118247.i | 0.623829 | − | 0.169596i | ||||
\(836\) | 48638.6 | 0.0695935 | ||||||||
\(837\) | −667488. | − | 667488.i | −0.952780 | − | 0.952780i | ||||
\(838\) | 217018. | − | 217018.i | 0.309036 | − | 0.309036i | ||||
\(839\) | 454249.i | 0.645313i | 0.946516 | + | 0.322656i | \(0.104576\pi\) | ||||
−0.946516 | + | 0.322656i | \(0.895424\pi\) | |||||||
\(840\) | −34597.7 | − | 127261.i | −0.0490330 | − | 0.180359i | ||||
\(841\) | 505724. | 0.715025 | ||||||||
\(842\) | 304923. | + | 304923.i | 0.430097 | + | 0.430097i | ||||
\(843\) | 81246.7 | − | 81246.7i | 0.114327 | − | 0.114327i | ||||
\(844\) | 420767.i | 0.590686i | ||||||||
\(845\) | 51640.5 | + | 29564.0i | 0.0723231 | + | 0.0414047i | ||||
\(846\) | 262075. | 0.366172 | ||||||||
\(847\) | 320213. | + | 320213.i | 0.446346 | + | 0.446346i | ||||
\(848\) | 128526. | − | 128526.i | 0.178730 | − | 0.178730i | ||||
\(849\) | 48716.5i | 0.0675866i | ||||||||
\(850\) | −177284. | + | 104087.i | −0.245376 | + | 0.144065i | ||||
\(851\) | 182005. | 0.251318 | ||||||||
\(852\) | −19989.9 | − | 19989.9i | −0.0275380 | − | 0.0275380i | ||||
\(853\) | −468758. | + | 468758.i | −0.644244 | + | 0.644244i | −0.951596 | − | 0.307352i | \(-0.900557\pi\) |
0.307352 | + | 0.951596i | \(0.400557\pi\) | |||||||
\(854\) | 339872.i | 0.466015i | ||||||||
\(855\) | −66204.6 | + | 115642.i | −0.0905641 | + | 0.158192i | ||||
\(856\) | −204502. | −0.279093 | ||||||||
\(857\) | 749030. | + | 749030.i | 1.01985 | + | 1.01985i | 0.999799 | + | 0.0200546i | \(0.00638402\pi\) |
0.0200546 | + | 0.999799i | \(0.493616\pi\) | |||||||
\(858\) | 99249.1 | − | 99249.1i | 0.134819 | − | 0.134819i | ||||
\(859\) | − | 1.01362e6i | − | 1.37370i | −0.726801 | − | 0.686848i | \(-0.758994\pi\) | ||
0.726801 | − | 0.686848i | \(-0.241006\pi\) | |||||||
\(860\) | −345202. | + | 93847.7i | −0.466742 | + | 0.126890i | ||||
\(861\) | −229330. | −0.309353 | ||||||||
\(862\) | 471877. | + | 471877.i | 0.635059 | + | 0.635059i | ||||
\(863\) | 504686. | − | 504686.i | 0.677641 | − | 0.677641i | −0.281825 | − | 0.959466i | \(-0.590940\pi\) |
0.959466 | + | 0.281825i | \(0.0909398\pi\) | |||||||
\(864\) | 141478.i | 0.189523i | ||||||||
\(865\) | 167853. | + | 617419.i | 0.224336 | + | 0.825179i | ||||
\(866\) | −151422. | −0.201908 | ||||||||
\(867\) | 326445. | + | 326445.i | 0.434282 | + | 0.434282i | ||||
\(868\) | 241505. | − | 241505.i | 0.320544 | − | 0.320544i | ||||
\(869\) | 176699.i | 0.233989i | ||||||||
\(870\) | −181708. | − | 104027.i | −0.240069 | − | 0.137439i | ||||
\(871\) | 960531. | 1.26612 | ||||||||
\(872\) | 2329.99 | + | 2329.99i | 0.00306423 | + | 0.00306423i | ||||
\(873\) | 472511. | − | 472511.i | 0.619988 | − | 0.619988i | ||||
\(874\) | − | 44345.3i | − | 0.0580530i | ||||||
\(875\) | −394788. | − | 386240.i | −0.515641 | − | 0.504476i | ||||
\(876\) | −184977. | −0.241052 | ||||||||
\(877\) | 744464. | + | 744464.i | 0.967932 | + | 0.967932i | 0.999502 | − | 0.0315697i | \(-0.0100506\pi\) |
−0.0315697 | + | 0.999502i | \(0.510051\pi\) | |||||||
\(878\) | −75528.8 | + | 75528.8i | −0.0979768 | + | 0.0979768i | ||||
\(879\) | − | 569758.i | − | 0.737417i | ||||||
\(880\) | 34002.8 | − | 59393.8i | 0.0439085 | − | 0.0766966i | ||||
\(881\) | 702725. | 0.905386 | 0.452693 | − | 0.891666i | \(-0.350463\pi\) | ||||
0.452693 | + | 0.891666i | \(0.350463\pi\) | |||||||
\(882\) | 86365.5 | + | 86365.5i | 0.111021 | + | 0.111021i | ||||
\(883\) | −166088. | + | 166088.i | −0.213018 | + | 0.213018i | −0.805548 | − | 0.592530i | \(-0.798129\pi\) |
0.592530 | + | 0.805548i | \(0.298129\pi\) | |||||||
\(884\) | 163651.i | 0.209418i | ||||||||
\(885\) | 152342. | − | 41416.2i | 0.194506 | − | 0.0528791i | ||||
\(886\) | 322229. | 0.410485 | ||||||||
\(887\) | −576103. | − | 576103.i | −0.732238 | − | 0.732238i | 0.238824 | − | 0.971063i | \(-0.423238\pi\) |
−0.971063 | + | 0.238824i | \(0.923238\pi\) | |||||||
\(888\) | 174124. | − | 174124.i | 0.220817 | − | 0.220817i | ||||
\(889\) | 620123.i | 0.784647i | ||||||||
\(890\) | −159386. | − | 586274.i | −0.201220 | − | 0.740152i | ||||
\(891\) | 90568.0 | 0.114083 | ||||||||
\(892\) | −232234. | − | 232234.i | −0.291874 | − | 0.291874i | ||||
\(893\) | −248344. | + | 248344.i | −0.311423 | + | 0.311423i | ||||
\(894\) | 103910.i | 0.130012i | ||||||||
\(895\) | −986000. | − | 564481.i | −1.23092 | − | 0.704699i | ||||
\(896\) | −51188.5 | −0.0637612 | ||||||||
\(897\) | −90488.5 | − | 90488.5i | −0.112463 | − | 0.112463i | ||||
\(898\) | −195871. | + | 195871.i | −0.242894 | + | 0.242894i | ||||
\(899\) | − | 542243.i | − | 0.670926i | ||||||
\(900\) | 94930.4 | + | 161688.i | 0.117198 | + | 0.199615i | ||||
\(901\) | 330282. | 0.406851 | ||||||||
\(902\) | −84152.0 | − | 84152.0i | −0.103431 | − | 0.103431i | ||||
\(903\) | 294861. | − | 294861.i | 0.361612 | − | 0.361612i | ||||
\(904\) | − | 320835.i | − | 0.392595i | ||||||
\(905\) | 45699.7 | − | 79825.3i | 0.0557977 | − | 0.0974638i | ||||
\(906\) | −474824. | −0.578464 | ||||||||
\(907\) | −947695. | − | 947695.i | −1.15200 | − | 1.15200i | −0.986150 | − | 0.165853i | \(-0.946962\pi\) |
−0.165853 | − | 0.986150i | \(-0.553038\pi\) | |||||||
\(908\) | 29390.0 | − | 29390.0i | 0.0356474 | − | 0.0356474i | ||||
\(909\) | 189526.i | 0.229373i | ||||||||
\(910\) | −424255. | + | 115339.i | −0.512323 | + | 0.139282i | ||||
\(911\) | 774755. | 0.933529 | 0.466764 | − | 0.884382i | \(-0.345420\pi\) | ||||
0.466764 | + | 0.884382i | \(0.345420\pi\) | |||||||
\(912\) | −42425.2 | − | 42425.2i | −0.0510076 | − | 0.0510076i | ||||
\(913\) | −324147. | + | 324147.i | −0.388867 | + | 0.388867i | ||||
\(914\) | − | 1.11383e6i | − | 1.33330i | ||||||
\(915\) | 147051. | + | 540901.i | 0.175641 | + | 0.646064i | ||||
\(916\) | 810240. | 0.965657 | ||||||||
\(917\) | 399685. | + | 399685.i | 0.475312 | + | 0.475312i | ||||
\(918\) | −181783. | + | 181783.i | −0.215709 | + | 0.215709i | ||||
\(919\) | − | 1.02993e6i | − | 1.21949i | −0.792598 | − | 0.609745i | \(-0.791272\pi\) | ||
0.792598 | − | 0.609745i | \(-0.208728\pi\) | |||||||
\(920\) | −54151.2 | − | 31001.4i | −0.0639783 | − | 0.0366273i | ||||
\(921\) | 403336. | 0.475497 | ||||||||
\(922\) | −441311. | − | 441311.i | −0.519138 | − | 0.519138i | ||||
\(923\) | −66641.0 | + | 66641.0i | −0.0782236 | + | 0.0782236i | ||||
\(924\) | 79776.6i | 0.0934397i | ||||||||
\(925\) | 259636. | − | 998047.i | 0.303446 | − | 1.16645i | ||||
\(926\) | −680189. | −0.793245 | ||||||||
\(927\) | −356655. | − | 356655.i | −0.415039 | − | 0.415039i | ||||
\(928\) | −57465.8 | + | 57465.8i | −0.0667288 | + | 0.0667288i | ||||
\(929\) | 534769.i | 0.619634i | 0.950796 | + | 0.309817i | \(0.100268\pi\) | ||||
−0.950796 | + | 0.309817i | \(0.899732\pi\) | |||||||
\(930\) | 279861. | − | 488843.i | 0.323576 | − | 0.565202i | ||||
\(931\) | −163681. | −0.188842 | ||||||||
\(932\) | −9592.22 | − | 9592.22i | −0.0110430 | − | 0.0110430i | ||||
\(933\) | −62339.8 | + | 62339.8i | −0.0716147 | + | 0.0716147i | ||||
\(934\) | 928977.i | 1.06491i | ||||||||
\(935\) | 120004. | − | 32624.7i | 0.137269 | − | 0.0373184i | ||||
\(936\) | 149254. | 0.170363 | ||||||||
\(937\) | 175076. | + | 175076.i | 0.199410 | + | 0.199410i | 0.799747 | − | 0.600337i | \(-0.204967\pi\) |
−0.600337 | + | 0.799747i | \(0.704967\pi\) | |||||||
\(938\) | −386038. | + | 386038.i | −0.438758 | + | 0.438758i | ||||
\(939\) | − | 1.12211e6i | − | 1.27264i | ||||||
\(940\) | 129644. | + | 476874.i | 0.146723 | + | 0.539694i | ||||
\(941\) | 197693. | 0.223261 | 0.111630 | − | 0.993750i | \(-0.464393\pi\) | ||||
0.111630 | + | 0.993750i | \(0.464393\pi\) | |||||||
\(942\) | −84743.1 | − | 84743.1i | −0.0954999 | − | 0.0954999i | ||||
\(943\) | −76724.0 | + | 76724.0i | −0.0862796 | + | 0.0862796i | ||||
\(944\) | − | 61276.8i | − | 0.0687625i | ||||||
\(945\) | −599381. | − | 343143.i | −0.671180 | − | 0.384248i | ||||
\(946\) | 216398. | 0.241808 | ||||||||
\(947\) | −185844. | − | 185844.i | −0.207228 | − | 0.207228i | 0.595860 | − | 0.803088i | \(-0.296811\pi\) |
−0.803088 | + | 0.595860i | \(0.796811\pi\) | |||||||
\(948\) | 154127. | − | 154127.i | 0.171499 | − | 0.171499i | ||||
\(949\) | 616665.i | 0.684726i | ||||||||
\(950\) | −243174. | − | 63260.3i | −0.269445 | − | 0.0700945i | ||||
\(951\) | −993003. | −1.09797 | ||||||||
\(952\) | −65771.4 | − | 65771.4i | −0.0725710 | − | 0.0725710i | ||||
\(953\) | −938606. | + | 938606.i | −1.03347 | + | 1.03347i | −0.0340494 | + | 0.999420i | \(0.510840\pi\) |
−0.999420 | + | 0.0340494i | \(0.989160\pi\) | |||||||
\(954\) | − | 301227.i | − | 0.330976i | ||||||
\(955\) | −69183.1 | + | 120845.i | −0.0758566 | + | 0.132501i | ||||
\(956\) | 433076. | 0.473859 | ||||||||
\(957\) | 89559.7 | + | 89559.7i | 0.0977887 | + | 0.0977887i | ||||
\(958\) | −431847. | + | 431847.i | −0.470543 | + | 0.470543i | ||||
\(959\) | 378544.i | 0.411604i | ||||||||
\(960\) | −81465.6 | + | 22147.5i | −0.0883958 | + | 0.0240316i | ||||
\(961\) | 535256. | 0.579582 | ||||||||
\(962\) | −580482. | − | 580482.i | −0.627248 | − | 0.627248i | ||||
\(963\) | −239646. | + | 239646.i | −0.258415 | + | 0.258415i | ||||
\(964\) | − | 58335.5i | − | 0.0627739i | ||||||
\(965\) | 130443. | + | 479812.i | 0.140077 | + | 0.515249i | ||||
\(966\) | 72734.8 | 0.0779449 | ||||||||
\(967\) | −109058. | − | 109058.i | −0.116629 | − | 0.116629i | 0.646384 | − | 0.763012i | \(-0.276281\pi\) |
−0.763012 | + | 0.646384i | \(0.776281\pi\) | |||||||
\(968\) | 204982. | − | 204982.i | 0.218759 | − | 0.218759i | ||||
\(969\) | − | 109023.i | − | 0.116111i | ||||||
\(970\) | 1.09353e6 | + | 626041.i | 1.16222 | + | 0.665364i | ||||
\(971\) | −1.67376e6 | −1.77523 | −0.887613 | − | 0.460590i | \(-0.847638\pi\) | ||||
−0.887613 | + | 0.460590i | \(0.847638\pi\) | |||||||
\(972\) | 279118. | + | 279118.i | 0.295430 | + | 0.295430i | ||||
\(973\) | 501809. | − | 501809.i | 0.530045 | − | 0.530045i | ||||
\(974\) | − | 977562.i | − | 1.03045i | ||||||
\(975\) | −625291. | + | 367121.i | −0.657769 | + | 0.386189i | ||||
\(976\) | 217567. | 0.228399 | ||||||||
\(977\) | 761307. | + | 761307.i | 0.797573 | + | 0.797573i | 0.982712 | − | 0.185139i | \(-0.0592736\pi\) |
−0.185139 | + | 0.982712i | \(0.559274\pi\) | |||||||
\(978\) | 505738. | − | 505738.i | 0.528747 | − | 0.528747i | ||||
\(979\) | 367519.i | 0.383455i | ||||||||
\(980\) | −114428. | + | 199875.i | −0.119146 | + | 0.208117i | ||||
\(981\) | 5460.82 | 0.00567440 | ||||||||
\(982\) | −153923. | − | 153923.i | −0.159618 | − | 0.159618i | ||||
\(983\) | 549265. | − | 549265.i | 0.568427 | − | 0.568427i | −0.363260 | − | 0.931688i | \(-0.618336\pi\) |
0.931688 | + | 0.363260i | \(0.118336\pi\) | |||||||
\(984\) | 146804.i | 0.151617i | ||||||||
\(985\) | 529577. | − | 143972.i | 0.545829 | − | 0.148391i | ||||
\(986\) | −147674. | −0.151897 | ||||||||
\(987\) | −407332. | − | 407332.i | −0.418132 | − | 0.418132i | ||||
\(988\) | −141434. | + | 141434.i | −0.144891 | + | 0.144891i | ||||
\(989\) | − | 197296.i | − | 0.201710i | ||||||
\(990\) | −29754.6 | − | 109447.i | −0.0303588 | − | 0.111669i | ||||
\(991\) | −1.39416e6 | −1.41960 | −0.709800 | − | 0.704403i | \(-0.751215\pi\) | ||||
−0.709800 | + | 0.704403i | \(0.751215\pi\) | |||||||
\(992\) | −154598. | − | 154598.i | −0.157102 | − | 0.157102i | ||||
\(993\) | −625781. | + | 625781.i | −0.634635 | + | 0.634635i | ||||
\(994\) | − | 53566.1i | − | 0.0542147i | ||||||
\(995\) | 518897. | + | 297067.i | 0.524125 | + | 0.300060i | ||||
\(996\) | 565478. | 0.570029 | ||||||||
\(997\) | −1.38856e6 | − | 1.38856e6i | −1.39692 | − | 1.39692i | −0.808691 | − | 0.588234i | \(-0.799823\pi\) |
−0.588234 | − | 0.808691i | \(-0.700177\pi\) | |||||||
\(998\) | 28980.0 | − | 28980.0i | 0.0290963 | − | 0.0290963i | ||||
\(999\) | − | 1.28960e6i | − | 1.29218i |
(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 | 230.5.f.b.47.7 | ✓ | 44 | |
5.3 | odd | 4 | inner | 230.5.f.b.93.7 | yes | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.5.f.b.47.7 | ✓ | 44 | 1.1 | even | 1 | trivial | |
230.5.f.b.93.7 | yes | 44 | 5.3 | odd | 4 | inner |