Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [11,5,Mod(2,11)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(11, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("11.2");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 11 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 11.d (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: | \(1.13706959392\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 115x^{10} + 5030x^{8} + 102975x^{6} + 953170x^{4} + 2910655x^{2} + 73205 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 7.1 | ||
Root | \(6.10049i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 11.7 |
Dual form | 11.5.d.a.8.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/11\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{7}{10}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.46775 | + | 3.39656i | −0.616936 | + | 0.849140i | −0.997125 | − | 0.0757688i | \(-0.975859\pi\) |
0.380189 | + | 0.924909i | \(0.375859\pi\) | |||||||
\(3\) | −2.26281 | + | 6.96422i | −0.251424 | + | 0.773803i | 0.743090 | + | 0.669192i | \(0.233360\pi\) |
−0.994513 | + | 0.104611i | \(0.966640\pi\) | |||||||
\(4\) | −0.502581 | − | 1.54679i | −0.0314113 | − | 0.0966741i | ||||
\(5\) | 14.7329 | − | 10.7041i | 0.589315 | − | 0.428163i | −0.252755 | − | 0.967530i | \(-0.581337\pi\) |
0.842070 | + | 0.539368i | \(0.181337\pi\) | |||||||
\(6\) | −18.0704 | − | 24.8717i | −0.501954 | − | 0.690881i | ||||
\(7\) | 47.9990 | − | 15.5958i | 0.979571 | − | 0.318282i | 0.224898 | − | 0.974382i | \(-0.427795\pi\) |
0.754674 | + | 0.656100i | \(0.227795\pi\) | |||||||
\(8\) | −57.3923 | − | 18.6479i | −0.896755 | − | 0.291373i | ||||
\(9\) | 22.1503 | + | 16.0931i | 0.273460 | + | 0.198681i | ||||
\(10\) | 76.4560i | 0.764560i | ||||||||
\(11\) | −82.9397 | + | 88.1022i | −0.685452 | + | 0.728118i | ||||
\(12\) | 11.9094 | 0.0827042 | ||||||||
\(13\) | 125.766 | − | 173.103i | 0.744180 | − | 1.02428i | −0.254188 | − | 0.967155i | \(-0.581808\pi\) |
0.998367 | − | 0.0571206i | \(-0.0181919\pi\) | |||||||
\(14\) | −65.4772 | + | 201.518i | −0.334067 | + | 1.02815i | ||||
\(15\) | 41.2077 | + | 126.824i | 0.183146 | + | 0.563664i | ||||
\(16\) | 226.021 | − | 164.214i | 0.882894 | − | 0.641460i | ||||
\(17\) | −255.614 | − | 351.822i | −0.884477 | − | 1.21738i | −0.975161 | − | 0.221498i | \(-0.928905\pi\) |
0.0906838 | − | 0.995880i | \(-0.471095\pi\) | |||||||
\(18\) | −109.323 | + | 35.5210i | −0.337415 | + | 0.109633i | ||||
\(19\) | −61.3806 | − | 19.9438i | −0.170029 | − | 0.0552459i | 0.222765 | − | 0.974872i | \(-0.428492\pi\) |
−0.392795 | + | 0.919626i | \(0.628492\pi\) | |||||||
\(20\) | −23.9614 | − | 17.4089i | −0.0599034 | − | 0.0435224i | ||||
\(21\) | 369.566i | 0.838019i | ||||||||
\(22\) | −94.5704 | − | 499.124i | −0.195393 | − | 1.03125i | ||||
\(23\) | 536.875 | 1.01489 | 0.507443 | − | 0.861685i | \(-0.330591\pi\) | ||||
0.507443 | + | 0.861685i | \(0.330591\pi\) | |||||||
\(24\) | 259.736 | − | 357.496i | 0.450931 | − | 0.620653i | ||||
\(25\) | −90.6549 | + | 279.007i | −0.145048 | + | 0.446411i | ||||
\(26\) | 277.594 | + | 854.346i | 0.410642 | + | 1.26383i | ||||
\(27\) | −642.052 | + | 466.478i | −0.880730 | + | 0.639888i | ||||
\(28\) | −48.2468 | − | 66.4060i | −0.0615393 | − | 0.0847015i | ||||
\(29\) | −481.802 | + | 156.547i | −0.572892 | + | 0.186144i | −0.581114 | − | 0.813822i | \(-0.697383\pi\) |
0.00822167 | + | 0.999966i | \(0.497383\pi\) | |||||||
\(30\) | −532.457 | − | 173.006i | −0.591619 | − | 0.192229i | ||||
\(31\) | 192.037 | + | 139.523i | 0.199830 | + | 0.145185i | 0.683200 | − | 0.730231i | \(-0.260588\pi\) |
−0.483370 | + | 0.875416i | \(0.660588\pi\) | |||||||
\(32\) | 207.397i | 0.202536i | ||||||||
\(33\) | −425.887 | − | 776.970i | −0.391080 | − | 0.713471i | ||||
\(34\) | 1825.78 | 1.57939 | ||||||||
\(35\) | 540.225 | − | 743.556i | 0.441000 | − | 0.606984i | ||||
\(36\) | 13.7603 | − | 42.3498i | 0.0106175 | − | 0.0326773i | ||||
\(37\) | −718.836 | − | 2212.35i | −0.525081 | − | 1.61603i | −0.764156 | − | 0.645032i | \(-0.776844\pi\) |
0.239075 | − | 0.971001i | \(-0.423156\pi\) | |||||||
\(38\) | 219.212 | − | 159.267i | 0.151809 | − | 0.110296i | ||||
\(39\) | 920.939 | + | 1267.56i | 0.605483 | + | 0.833375i | ||||
\(40\) | −1045.16 | + | 339.594i | −0.653227 | + | 0.212246i | ||||
\(41\) | −100.981 | − | 32.8108i | −0.0600721 | − | 0.0195186i | 0.278827 | − | 0.960341i | \(-0.410054\pi\) |
−0.338899 | + | 0.940823i | \(0.610054\pi\) | |||||||
\(42\) | −1255.25 | − | 911.995i | −0.711595 | − | 0.517004i | ||||
\(43\) | 2058.95i | 1.11355i | 0.830664 | + | 0.556773i | \(0.187961\pi\) | ||||
−0.830664 | + | 0.556773i | \(0.812039\pi\) | |||||||
\(44\) | 177.959 | + | 84.0114i | 0.0919211 | + | 0.0433943i | ||||
\(45\) | 498.599 | 0.246222 | ||||||||
\(46\) | −1324.87 | + | 1823.53i | −0.626120 | + | 0.861780i | ||||
\(47\) | 17.8846 | − | 55.0431i | 0.00809624 | − | 0.0249177i | −0.946927 | − | 0.321449i | \(-0.895830\pi\) |
0.955023 | + | 0.296532i | \(0.0958300\pi\) | |||||||
\(48\) | 632.178 | + | 1945.64i | 0.274383 | + | 0.844464i | ||||
\(49\) | 118.225 | − | 85.8952i | 0.0492397 | − | 0.0357748i | ||||
\(50\) | −723.951 | − | 996.433i | −0.289580 | − | 0.398573i | ||||
\(51\) | 3028.58 | − | 984.044i | 1.16439 | − | 0.378333i | ||||
\(52\) | −330.960 | − | 107.536i | −0.122397 | − | 0.0397691i | ||||
\(53\) | 926.358 | + | 673.039i | 0.329782 | + | 0.239601i | 0.740338 | − | 0.672235i | \(-0.234665\pi\) |
−0.410556 | + | 0.911835i | \(0.634665\pi\) | |||||||
\(54\) | − | 3331.92i | − | 1.14263i | ||||||
\(55\) | −278.889 | + | 2185.79i | −0.0921948 | + | 0.722576i | ||||
\(56\) | −3045.60 | −0.971175 | ||||||||
\(57\) | 277.786 | − | 382.340i | 0.0854989 | − | 0.117679i | ||||
\(58\) | 657.244 | − | 2022.79i | 0.195376 | − | 0.601305i | ||||
\(59\) | −596.473 | − | 1835.75i | −0.171351 | − | 0.527364i | 0.828097 | − | 0.560585i | \(-0.189424\pi\) |
−0.999448 | + | 0.0332206i | \(0.989424\pi\) | |||||||
\(60\) | 175.460 | − | 127.479i | 0.0487389 | − | 0.0354108i | ||||
\(61\) | −375.548 | − | 516.897i | −0.100927 | − | 0.138913i | 0.755567 | − | 0.655072i | \(-0.227362\pi\) |
−0.856493 | + | 0.516158i | \(0.827362\pi\) | |||||||
\(62\) | −947.795 | + | 307.957i | −0.246565 | + | 0.0801138i | ||||
\(63\) | 1314.18 | + | 427.002i | 0.331110 | + | 0.107584i | ||||
\(64\) | 2911.90 | + | 2115.62i | 0.710912 | + | 0.516508i | ||||
\(65\) | − | 3896.51i | − | 0.922251i | ||||||
\(66\) | 3690.00 | + | 470.814i | 0.847108 | + | 0.108084i | ||||
\(67\) | −8692.22 | −1.93634 | −0.968169 | − | 0.250298i | \(-0.919471\pi\) | ||||
−0.968169 | + | 0.250298i | \(0.919471\pi\) | |||||||
\(68\) | −415.727 | + | 572.199i | −0.0899063 | + | 0.123745i | ||||
\(69\) | −1214.85 | + | 3738.92i | −0.255166 | + | 0.785322i | ||||
\(70\) | 1192.39 | + | 3669.81i | 0.243346 | + | 0.748941i | ||||
\(71\) | 1518.36 | − | 1103.16i | 0.301203 | − | 0.218837i | −0.426910 | − | 0.904294i | \(-0.640398\pi\) |
0.728113 | + | 0.685457i | \(0.240398\pi\) | |||||||
\(72\) | −971.154 | − | 1336.68i | −0.187337 | − | 0.257847i | ||||
\(73\) | 2334.33 | − | 758.471i | 0.438043 | − | 0.142329i | −0.0816893 | − | 0.996658i | \(-0.526032\pi\) |
0.519733 | + | 0.854329i | \(0.326032\pi\) | |||||||
\(74\) | 9288.28 | + | 3017.94i | 1.69618 | + | 0.551122i | ||||
\(75\) | −1737.93 | − | 1262.68i | −0.308966 | − | 0.224477i | ||||
\(76\) | 104.966i | 0.0181728i | ||||||||
\(77\) | −2607.00 | + | 5522.33i | −0.439703 | + | 0.931410i | ||||
\(78\) | −6578.00 | −1.08120 | ||||||||
\(79\) | −2255.51 | + | 3104.44i | −0.361401 | + | 0.497426i | −0.950539 | − | 0.310607i | \(-0.899468\pi\) |
0.589137 | + | 0.808033i | \(0.299468\pi\) | |||||||
\(80\) | 1572.18 | − | 4838.68i | 0.245654 | − | 0.756044i | ||||
\(81\) | −1110.50 | − | 3417.77i | −0.169258 | − | 0.520922i | ||||
\(82\) | 360.640 | − | 262.020i | 0.0536347 | − | 0.0389679i | ||||
\(83\) | 4351.57 | + | 5989.42i | 0.631669 | + | 0.869418i | 0.998137 | − | 0.0610127i | \(-0.0194330\pi\) |
−0.366468 | + | 0.930431i | \(0.619433\pi\) | |||||||
\(84\) | 571.640 | − | 185.737i | 0.0810147 | − | 0.0263233i | ||||
\(85\) | −7531.86 | − | 2447.25i | −1.04247 | − | 0.338720i | ||||
\(86\) | −6993.34 | − | 5080.96i | −0.945557 | − | 0.686987i | ||||
\(87\) | − | 3709.62i | − | 0.490107i | ||||||
\(88\) | 6403.03 | − | 3509.74i | 0.826837 | − | 0.453221i | ||||
\(89\) | 11104.2 | 1.40187 | 0.700937 | − | 0.713223i | \(-0.252765\pi\) | ||||
0.700937 | + | 0.713223i | \(0.252765\pi\) | |||||||
\(90\) | −1230.42 | + | 1693.52i | −0.151903 | + | 0.209077i | ||||
\(91\) | 3336.98 | − | 10270.2i | 0.402969 | − | 1.24021i | ||||
\(92\) | −269.823 | − | 830.430i | −0.0318789 | − | 0.0981132i | ||||
\(93\) | −1406.21 | + | 1021.67i | −0.162587 | + | 0.118126i | ||||
\(94\) | 142.823 | + | 196.578i | 0.0161637 | + | 0.0222475i | ||||
\(95\) | −1117.79 | + | 363.193i | −0.123855 | + | 0.0402430i | ||||
\(96\) | −1444.36 | − | 469.300i | −0.156723 | − | 0.0509223i | ||||
\(97\) | 9943.57 | + | 7224.43i | 1.05682 | + | 0.767821i | 0.973497 | − | 0.228702i | \(-0.0734481\pi\) |
0.0833186 | + | 0.996523i | \(0.473448\pi\) | |||||||
\(98\) | 613.524i | 0.0638822i | ||||||||
\(99\) | −3254.98 | + | 616.730i | −0.332107 | + | 0.0629252i | ||||
\(100\) | 477.125 | 0.0477125 | ||||||||
\(101\) | −4980.55 | + | 6855.14i | −0.488241 | + | 0.672006i | −0.980062 | − | 0.198690i | \(-0.936331\pi\) |
0.491821 | + | 0.870696i | \(0.336331\pi\) | |||||||
\(102\) | −4131.39 | + | 12715.1i | −0.397096 | + | 1.22214i | ||||
\(103\) | −3982.66 | − | 12257.4i | −0.375404 | − | 1.15537i | −0.943206 | − | 0.332209i | \(-0.892206\pi\) |
0.567802 | − | 0.823165i | \(-0.307794\pi\) | |||||||
\(104\) | −10446.0 | + | 7589.48i | −0.965794 | + | 0.701690i | ||||
\(105\) | 3955.86 | + | 5444.77i | 0.358808 | + | 0.493857i | ||||
\(106\) | −4572.03 | + | 1485.54i | −0.406909 | + | 0.132213i | ||||
\(107\) | −3063.72 | − | 995.464i | −0.267597 | − | 0.0869477i | 0.172145 | − | 0.985072i | \(-0.444930\pi\) |
−0.439742 | + | 0.898124i | \(0.644930\pi\) | |||||||
\(108\) | 1044.22 | + | 758.674i | 0.0895254 | + | 0.0650440i | ||||
\(109\) | 14090.5i | 1.18597i | 0.805215 | + | 0.592983i | \(0.202050\pi\) | ||||
−0.805215 | + | 0.592983i | \(0.797950\pi\) | |||||||
\(110\) | −6735.94 | − | 6341.24i | −0.556690 | − | 0.524069i | ||||
\(111\) | 17033.9 | 1.38251 | ||||||||
\(112\) | 8287.72 | − | 11407.1i | 0.660692 | − | 0.909365i | ||||
\(113\) | 461.161 | − | 1419.31i | 0.0361157 | − | 0.111153i | −0.931373 | − | 0.364065i | \(-0.881389\pi\) |
0.967489 | + | 0.252913i | \(0.0813885\pi\) | |||||||
\(114\) | 613.134 | + | 1887.03i | 0.0471787 | + | 0.145201i | ||||
\(115\) | 7909.71 | − | 5746.74i | 0.598088 | − | 0.434536i | ||||
\(116\) | 484.289 | + | 666.567i | 0.0359906 | + | 0.0495368i | ||||
\(117\) | 5571.52 | − | 1810.30i | 0.407007 | − | 0.132245i | ||||
\(118\) | 7707.19 | + | 2504.22i | 0.553519 | + | 0.179849i | ||||
\(119\) | −17756.2 | − | 12900.6i | −1.25388 | − | 0.910996i | ||||
\(120\) | − | 8047.19i | − | 0.558832i | ||||||
\(121\) | −883.004 | − | 14614.3i | −0.0603104 | − | 0.998180i | ||||
\(122\) | 2682.43 | 0.180222 | ||||||||
\(123\) | 457.003 | − | 629.011i | 0.0302071 | − | 0.0415765i | ||||
\(124\) | 119.298 | − | 367.161i | 0.00775871 | − | 0.0238788i | ||||
\(125\) | 5168.06 | + | 15905.7i | 0.330756 | + | 1.01796i | ||||
\(126\) | −4693.39 | + | 3409.95i | −0.295628 | + | 0.214786i | ||||
\(127\) | −10211.8 | − | 14055.4i | −0.633134 | − | 0.871435i | 0.365092 | − | 0.930972i | \(-0.381038\pi\) |
−0.998226 | + | 0.0595368i | \(0.981038\pi\) | |||||||
\(128\) | −17527.6 | + | 5695.05i | −1.06980 | + | 0.347599i | ||||
\(129\) | −14339.0 | − | 4659.02i | −0.861665 | − | 0.279972i | ||||
\(130\) | 13234.7 | + | 9615.60i | 0.783120 | + | 0.568970i | ||||
\(131\) | 18372.1i | 1.07057i | 0.844671 | + | 0.535285i | \(0.179796\pi\) | ||||
−0.844671 | + | 0.535285i | \(0.820204\pi\) | |||||||
\(132\) | −987.763 | + | 1049.25i | −0.0566898 | + | 0.0602184i | ||||
\(133\) | −3257.25 | −0.184140 | ||||||||
\(134\) | 21450.2 | − | 29523.6i | 1.19460 | − | 1.64422i | ||||
\(135\) | −4466.06 | + | 13745.1i | −0.245052 | + | 0.754191i | ||||
\(136\) | 8109.53 | + | 24958.6i | 0.438448 | + | 1.34940i | ||||
\(137\) | 17181.8 | − | 12483.3i | 0.915434 | − | 0.665102i | −0.0269489 | − | 0.999637i | \(-0.508579\pi\) |
0.942383 | + | 0.334535i | \(0.108579\pi\) | |||||||
\(138\) | −9701.52 | − | 13353.0i | −0.509427 | − | 0.701165i | ||||
\(139\) | −3870.52 | + | 1257.61i | −0.200327 | + | 0.0650901i | −0.407462 | − | 0.913222i | \(-0.633586\pi\) |
0.207135 | + | 0.978312i | \(0.433586\pi\) | |||||||
\(140\) | −1421.63 | − | 461.915i | −0.0725320 | − | 0.0235671i | ||||
\(141\) | 342.863 | + | 249.105i | 0.0172458 | + | 0.0125298i | ||||
\(142\) | 7879.53i | 0.390772i | ||||||||
\(143\) | 4819.69 | + | 25437.4i | 0.235693 | + | 1.24394i | ||||
\(144\) | 7649.14 | 0.368882 | ||||||||
\(145\) | −5422.65 | + | 7463.63i | −0.257914 | + | 0.354988i | ||||
\(146\) | −3184.35 | + | 9800.42i | −0.149388 | + | 0.459768i | ||||
\(147\) | 330.673 | + | 1017.71i | 0.0153026 | + | 0.0470965i | ||||
\(148\) | −3060.76 | + | 2223.77i | −0.139735 | + | 0.101523i | ||||
\(149\) | −10578.8 | − | 14560.5i | −0.476503 | − | 0.655850i | 0.501325 | − | 0.865259i | \(-0.332846\pi\) |
−0.977828 | + | 0.209409i | \(0.932846\pi\) | |||||||
\(150\) | 8577.55 | − | 2787.01i | 0.381224 | − | 0.123867i | ||||
\(151\) | −8398.18 | − | 2728.73i | −0.368325 | − | 0.119676i | 0.119006 | − | 0.992894i | \(-0.462029\pi\) |
−0.487331 | + | 0.873218i | \(0.662029\pi\) | |||||||
\(152\) | 3150.87 | + | 2289.24i | 0.136378 | + | 0.0990842i | ||||
\(153\) | − | 11906.6i | − | 0.508633i | ||||||
\(154\) | −12323.5 | − | 22482.5i | −0.519629 | − | 0.947990i | ||||
\(155\) | 4322.71 | 0.179926 | ||||||||
\(156\) | 1497.80 | − | 2061.55i | 0.0615468 | − | 0.0847119i | ||||
\(157\) | −5990.27 | + | 18436.1i | −0.243023 | + | 0.747947i | 0.752933 | + | 0.658098i | \(0.228639\pi\) |
−0.995955 | + | 0.0898493i | \(0.971361\pi\) | |||||||
\(158\) | −4978.39 | − | 15321.9i | −0.199423 | − | 0.613761i | ||||
\(159\) | −6783.37 | + | 4928.40i | −0.268319 | + | 0.194945i | ||||
\(160\) | 2219.99 | + | 3055.55i | 0.0867183 | + | 0.119357i | ||||
\(161\) | 25769.5 | − | 8373.00i | 0.994153 | − | 0.323020i | ||||
\(162\) | 14349.1 | + | 4662.30i | 0.546757 | + | 0.177652i | ||||
\(163\) | 3687.37 | + | 2679.03i | 0.138785 | + | 0.100833i | 0.655011 | − | 0.755619i | \(-0.272664\pi\) |
−0.516227 | + | 0.856452i | \(0.672664\pi\) | |||||||
\(164\) | 172.686i | 0.00642052i | ||||||||
\(165\) | −14591.3 | − | 6888.29i | −0.535951 | − | 0.253013i | ||||
\(166\) | −31082.0 | −1.12796 | ||||||||
\(167\) | 7251.30 | − | 9980.56i | 0.260006 | − | 0.357867i | −0.658978 | − | 0.752162i | \(-0.729011\pi\) |
0.918984 | + | 0.394295i | \(0.129011\pi\) | |||||||
\(168\) | 6891.63 | − | 21210.3i | 0.244176 | − | 0.751498i | ||||
\(169\) | −5321.48 | − | 16377.8i | −0.186320 | − | 0.573434i | ||||
\(170\) | 26898.9 | − | 19543.2i | 0.930759 | − | 0.676236i | ||||
\(171\) | −1038.64 | − | 1429.57i | −0.0355200 | − | 0.0488891i | ||||
\(172\) | 3184.75 | − | 1034.79i | 0.107651 | − | 0.0349780i | ||||
\(173\) | 653.072 | + | 212.196i | 0.0218207 | + | 0.00708998i | 0.319907 | − | 0.947449i | \(-0.396348\pi\) |
−0.298086 | + | 0.954539i | \(0.596348\pi\) | |||||||
\(174\) | 12599.9 | + | 9154.39i | 0.416169 | + | 0.302365i | ||||
\(175\) | 14805.9i | 0.483458i | ||||||||
\(176\) | −4278.51 | + | 33532.8i | −0.138123 | + | 1.08254i | ||||
\(177\) | 14134.3 | 0.451158 | ||||||||
\(178\) | −27402.4 | + | 37716.2i | −0.864867 | + | 1.19039i | ||||
\(179\) | 4275.10 | − | 13157.4i | 0.133426 | − | 0.410643i | −0.861916 | − | 0.507051i | \(-0.830736\pi\) |
0.995342 | + | 0.0964086i | \(0.0307355\pi\) | |||||||
\(180\) | −250.587 | − | 771.226i | −0.00773415 | − | 0.0238033i | ||||
\(181\) | −16520.5 | + | 12002.8i | −0.504272 | + | 0.366375i | −0.810647 | − | 0.585536i | \(-0.800884\pi\) |
0.306374 | + | 0.951911i | \(0.400884\pi\) | |||||||
\(182\) | 26648.5 | + | 36678.5i | 0.804506 | + | 1.10731i | ||||
\(183\) | 4449.58 | − | 1445.76i | 0.132867 | − | 0.0431711i | ||||
\(184\) | −30812.5 | − | 10011.6i | −0.910105 | − | 0.295711i | ||||
\(185\) | −34271.6 | − | 24899.8i | −1.00136 | − | 0.727533i | ||||
\(186\) | − | 7297.51i | − | 0.210935i | ||||||
\(187\) | 52196.9 | + | 6659.89i | 1.49266 | + | 0.190451i | ||||
\(188\) | −94.1283 | −0.00266321 | ||||||||
\(189\) | −23542.7 | + | 32403.8i | −0.659073 | + | 0.907136i | ||||
\(190\) | 1524.82 | − | 4692.92i | 0.0422388 | − | 0.129998i | ||||
\(191\) | −2265.94 | − | 6973.85i | −0.0621130 | − | 0.191164i | 0.915185 | − | 0.403034i | \(-0.132045\pi\) |
−0.977298 | + | 0.211870i | \(0.932045\pi\) | |||||||
\(192\) | −21322.7 | + | 15491.9i | −0.578416 | + | 0.420244i | ||||
\(193\) | 21150.0 | + | 29110.5i | 0.567801 | + | 0.781511i | 0.992292 | − | 0.123921i | \(-0.0395470\pi\) |
−0.424491 | + | 0.905432i | \(0.639547\pi\) | |||||||
\(194\) | −49076.4 | + | 15945.9i | −1.30398 | + | 0.423687i | ||||
\(195\) | 27136.2 | + | 8817.08i | 0.713640 | + | 0.231876i | ||||
\(196\) | −192.279 | − | 139.699i | −0.00500518 | − | 0.00363647i | ||||
\(197\) | − | 39661.5i | − | 1.02197i | −0.859591 | − | 0.510983i | \(-0.829282\pi\) | ||
0.859591 | − | 0.510983i | \(-0.170718\pi\) | |||||||
\(198\) | 5937.70 | − | 12577.7i | 0.151456 | − | 0.320826i | ||||
\(199\) | 8985.83 | 0.226909 | 0.113455 | − | 0.993543i | \(-0.463808\pi\) | ||||
0.113455 | + | 0.993543i | \(0.463808\pi\) | |||||||
\(200\) | 10405.8 | − | 14322.3i | 0.260145 | − | 0.358058i | ||||
\(201\) | 19668.9 | − | 60534.6i | 0.486841 | − | 1.49834i | ||||
\(202\) | −10993.2 | − | 33833.5i | −0.269414 | − | 0.829170i | ||||
\(203\) | −20684.6 | + | 15028.2i | −0.501943 | + | 0.364683i | ||||
\(204\) | −3044.21 | − | 4189.99i | −0.0731500 | − | 0.100682i | ||||
\(205\) | −1838.95 | + | 597.512i | −0.0437586 | + | 0.0142180i | ||||
\(206\) | 51461.1 | + | 16720.7i | 1.21267 | + | 0.394022i | ||||
\(207\) | 11891.9 | + | 8639.99i | 0.277531 | + | 0.201638i | ||||
\(208\) | − | 59777.3i | − | 1.38169i | ||||||
\(209\) | 6847.99 | − | 3753.64i | 0.156773 | − | 0.0859330i | ||||
\(210\) | −28255.6 | −0.640716 | ||||||||
\(211\) | 4141.35 | − | 5700.08i | 0.0930202 | − | 0.128031i | −0.759970 | − | 0.649958i | \(-0.774787\pi\) |
0.852990 | + | 0.521927i | \(0.174787\pi\) | |||||||
\(212\) | 575.476 | − | 1771.13i | 0.0128043 | − | 0.0394076i | ||||
\(213\) | 4246.85 | + | 13070.5i | 0.0936069 | + | 0.288093i | ||||
\(214\) | 10941.6 | − | 7949.57i | 0.238921 | − | 0.173586i | ||||
\(215\) | 22039.1 | + | 30334.2i | 0.476779 | + | 0.656230i | ||||
\(216\) | 45547.7 | − | 14799.3i | 0.976245 | − | 0.317201i | ||||
\(217\) | 11393.5 | + | 3701.99i | 0.241958 | + | 0.0786168i | ||||
\(218\) | −47859.1 | − | 34771.7i | −1.00705 | − | 0.731665i | ||||
\(219\) | 17973.1i | 0.374744i | ||||||||
\(220\) | 3521.11 | − | 667.156i | 0.0727503 | − | 0.0137842i | ||||
\(221\) | −93049.0 | −1.90514 | ||||||||
\(222\) | −42035.3 | + | 57856.6i | −0.852920 | + | 1.17394i | ||||
\(223\) | −3954.30 | + | 12170.1i | −0.0795170 | + | 0.244728i | −0.982910 | − | 0.184085i | \(-0.941068\pi\) |
0.903393 | + | 0.428813i | \(0.141068\pi\) | |||||||
\(224\) | 3234.52 | + | 9954.83i | 0.0644635 | + | 0.198398i | ||||
\(225\) | −6498.12 | + | 4721.16i | −0.128358 | + | 0.0932575i | ||||
\(226\) | 3682.74 | + | 5068.85i | 0.0721031 | + | 0.0992414i | ||||
\(227\) | −53534.9 | + | 17394.5i | −1.03893 | + | 0.337568i | −0.778314 | − | 0.627876i | \(-0.783925\pi\) |
−0.260613 | + | 0.965443i | \(0.583925\pi\) | |||||||
\(228\) | −731.007 | − | 237.519i | −0.0140622 | − | 0.00456907i | ||||
\(229\) | 72710.1 | + | 52827.0i | 1.38651 | + | 1.00736i | 0.996238 | + | 0.0866626i | \(0.0276202\pi\) |
0.390275 | + | 0.920698i | \(0.372380\pi\) | |||||||
\(230\) | 41047.3i | 0.775941i | ||||||||
\(231\) | −32559.6 | − | 30651.7i | −0.610176 | − | 0.574422i | ||||
\(232\) | 30571.0 | 0.567982 | ||||||||
\(233\) | 14585.7 | − | 20075.5i | 0.268668 | − | 0.369790i | −0.653272 | − | 0.757124i | \(-0.726604\pi\) |
0.921939 | + | 0.387334i | \(0.126604\pi\) | |||||||
\(234\) | −7600.31 | + | 23391.4i | −0.138803 | + | 0.427193i | ||||
\(235\) | −325.693 | − | 1002.38i | −0.00589757 | − | 0.0181509i | ||||
\(236\) | −2539.74 | + | 1845.23i | −0.0456001 | + | 0.0331304i | ||||
\(237\) | −16516.2 | − | 22732.6i | −0.294045 | − | 0.404718i | ||||
\(238\) | 87635.4 | − | 28474.5i | 1.54713 | − | 0.502692i | ||||
\(239\) | 31899.0 | + | 10364.6i | 0.558445 | + | 0.181450i | 0.574622 | − | 0.818419i | \(-0.305149\pi\) |
−0.0161762 | + | 0.999869i | \(0.505149\pi\) | |||||||
\(240\) | 30140.1 | + | 21898.1i | 0.523266 | + | 0.380175i | ||||
\(241\) | − | 71818.0i | − | 1.23651i | −0.785976 | − | 0.618257i | \(-0.787839\pi\) | ||
0.785976 | − | 0.618257i | \(-0.212161\pi\) | |||||||
\(242\) | 51817.5 | + | 33065.3i | 0.884802 | + | 0.564601i | ||||
\(243\) | −37968.2 | −0.642996 | ||||||||
\(244\) | −610.786 | + | 840.674i | −0.0102591 | + | 0.0141204i | ||||
\(245\) | 822.361 | − | 2530.97i | 0.0137003 | − | 0.0421652i | ||||
\(246\) | 1008.71 | + | 3104.48i | 0.0166684 | + | 0.0513001i | ||||
\(247\) | −11171.9 | + | 8116.89i | −0.183120 | + | 0.133044i | ||||
\(248\) | −8419.63 | − | 11588.6i | −0.136896 | − | 0.188421i | ||||
\(249\) | −51558.5 | + | 16752.4i | −0.831575 | + | 0.270195i | ||||
\(250\) | −66778.0 | − | 21697.5i | −1.06845 | − | 0.347160i | ||||
\(251\) | −38944.7 | − | 28295.0i | −0.618160 | − | 0.449120i | 0.234118 | − | 0.972208i | \(-0.424780\pi\) |
−0.852278 | + | 0.523089i | \(0.824780\pi\) | |||||||
\(252\) | − | 2247.35i | − | 0.0353892i | ||||||
\(253\) | −44528.2 | + | 47299.9i | −0.695656 | + | 0.738956i | ||||
\(254\) | 72940.1 | 1.13057 | ||||||||
\(255\) | 34086.4 | − | 46915.9i | 0.524204 | − | 0.721505i | ||||
\(256\) | 6114.07 | − | 18817.2i | 0.0932933 | − | 0.287127i | ||||
\(257\) | 7798.62 | + | 24001.7i | 0.118073 | + | 0.363392i | 0.992576 | − | 0.121629i | \(-0.0388119\pi\) |
−0.874502 | + | 0.485021i | \(0.838812\pi\) | |||||||
\(258\) | 51209.6 | − | 37205.9i | 0.769328 | − | 0.558950i | ||||
\(259\) | −69006.8 | − | 94979.7i | −1.02871 | − | 1.41590i | ||||
\(260\) | −6027.07 | + | 1958.31i | −0.0891578 | + | 0.0289691i | ||||
\(261\) | −13191.4 | − | 4286.14i | −0.193646 | − | 0.0629196i | ||||
\(262\) | −62401.8 | − | 45337.6i | −0.909064 | − | 0.660474i | ||||
\(263\) | 73780.1i | 1.06666i | 0.845906 | + | 0.533332i | \(0.179060\pi\) | ||||
−0.845906 | + | 0.533332i | \(0.820940\pi\) | |||||||
\(264\) | 9953.77 | + | 52534.0i | 0.142817 | + | 0.753759i | ||||
\(265\) | 20852.2 | 0.296934 | ||||||||
\(266\) | 8038.06 | − | 11063.4i | 0.113603 | − | 0.156360i | ||||
\(267\) | −25126.8 | + | 77332.4i | −0.352464 | + | 1.08477i | ||||
\(268\) | 4368.54 | + | 13445.0i | 0.0608229 | + | 0.187194i | ||||
\(269\) | 114414. | − | 83127.0i | 1.58116 | − | 1.14878i | 0.665813 | − | 0.746119i | \(-0.268085\pi\) |
0.915348 | − | 0.402663i | \(-0.131915\pi\) | |||||||
\(270\) | −35665.1 | − | 49088.7i | −0.489233 | − | 0.673371i | ||||
\(271\) | 96839.3 | − | 31465.0i | 1.31860 | − | 0.428439i | 0.436586 | − | 0.899663i | \(-0.356187\pi\) |
0.882014 | + | 0.471223i | \(0.156187\pi\) | |||||||
\(272\) | −115548. | − | 37543.8i | −1.56180 | − | 0.507459i | ||||
\(273\) | 63972.9 | + | 46479.0i | 0.858362 | + | 0.623636i | ||||
\(274\) | 89164.6i | 1.18766i | ||||||||
\(275\) | −17062.2 | − | 31127.7i | −0.225616 | − | 0.411605i | ||||
\(276\) | 6393.86 | 0.0839354 | ||||||||
\(277\) | 15920.1 | − | 21912.2i | 0.207485 | − | 0.285579i | −0.692574 | − | 0.721347i | \(-0.743523\pi\) |
0.900059 | + | 0.435768i | \(0.143523\pi\) | |||||||
\(278\) | 5279.91 | − | 16249.9i | 0.0683183 | − | 0.210262i | ||||
\(279\) | 2008.31 | + | 6180.94i | 0.0258001 | + | 0.0794047i | ||||
\(280\) | −44870.5 | + | 32600.3i | −0.572328 | + | 0.415821i | ||||
\(281\) | 77971.9 | + | 107319.i | 0.987474 | + | 1.35914i | 0.932704 | + | 0.360642i | \(0.117442\pi\) |
0.0547693 | + | 0.998499i | \(0.482558\pi\) | |||||||
\(282\) | −1692.20 | + | 549.828i | −0.0212791 | + | 0.00691399i | ||||
\(283\) | 80080.5 | + | 26019.7i | 0.999894 | + | 0.324885i | 0.762823 | − | 0.646607i | \(-0.223813\pi\) |
0.237071 | + | 0.971492i | \(0.423813\pi\) | |||||||
\(284\) | −2469.45 | − | 1794.16i | −0.0306170 | − | 0.0222446i | ||||
\(285\) | − | 8606.40i | − | 0.105958i | ||||||
\(286\) | −98293.3 | − | 46402.6i | −1.20169 | − | 0.567297i | ||||
\(287\) | −5358.71 | −0.0650574 | ||||||||
\(288\) | −3337.66 | + | 4593.90i | −0.0402399 | + | 0.0553855i | ||||
\(289\) | −32631.1 | + | 100428.i | −0.390693 | + | 1.20243i | ||||
\(290\) | −11969.0 | − | 36836.7i | −0.142318 | − | 0.438011i | ||||
\(291\) | −72813.0 | + | 52901.7i | −0.859850 | + | 0.624718i | ||||
\(292\) | −2346.38 | − | 3229.52i | −0.0275190 | − | 0.0378767i | ||||
\(293\) | −114757. | + | 37286.9i | −1.33673 | + | 0.434331i | −0.888209 | − | 0.459440i | \(-0.848050\pi\) |
−0.448524 | + | 0.893771i | \(0.648050\pi\) | |||||||
\(294\) | −4272.72 | − | 1388.29i | −0.0494322 | − | 0.0160615i | ||||
\(295\) | −28437.8 | − | 20661.3i | −0.326777 | − | 0.237418i | ||||
\(296\) | 140377.i | 1.60218i | ||||||||
\(297\) | 12153.9 | − | 95255.8i | 0.137785 | − | 1.07989i | ||||
\(298\) | 75561.6 | 0.850880 | ||||||||
\(299\) | 67520.8 | − | 92934.4i | 0.755258 | − | 1.03952i | ||||
\(300\) | −1079.65 | + | 3322.81i | −0.0119961 | + | 0.0369201i | ||||
\(301\) | 32111.0 | + | 98827.4i | 0.354422 | + | 1.09080i | ||||
\(302\) | 29992.9 | − | 21791.1i | 0.328855 | − | 0.238927i | ||||
\(303\) | −36470.7 | − | 50197.5i | −0.397245 | − | 0.546761i | ||||
\(304\) | −17148.3 | + | 5571.83i | −0.185556 | + | 0.0602908i | ||||
\(305\) | −11065.8 | − | 3595.50i | −0.118955 | − | 0.0386508i | ||||
\(306\) | 40441.4 | + | 29382.4i | 0.431901 | + | 0.313794i | ||||
\(307\) | − | 130584.i | − | 1.38553i | −0.721166 | − | 0.692763i | \(-0.756393\pi\) | ||
0.721166 | − | 0.692763i | \(-0.243607\pi\) | |||||||
\(308\) | 9852.09 | + | 1257.05i | 0.103855 | + | 0.0132510i | ||||
\(309\) | 94375.0 | 0.988417 | ||||||||
\(310\) | −10667.4 | + | 14682.4i | −0.111003 | + | 0.152782i | ||||
\(311\) | 30522.3 | − | 93937.9i | 0.315570 | − | 0.971225i | −0.659949 | − | 0.751311i | \(-0.729422\pi\) |
0.975519 | − | 0.219915i | \(-0.0705780\pi\) | |||||||
\(312\) | −29217.4 | − | 89922.0i | −0.300146 | − | 0.923755i | ||||
\(313\) | −50811.9 | + | 36917.0i | −0.518653 | + | 0.376823i | −0.816096 | − | 0.577916i | \(-0.803866\pi\) |
0.297443 | + | 0.954739i | \(0.403866\pi\) | |||||||
\(314\) | −47837.0 | − | 65842.0i | −0.485182 | − | 0.667796i | ||||
\(315\) | 23932.3 | − | 7776.07i | 0.241192 | − | 0.0783680i | ||||
\(316\) | 5935.47 | + | 1928.55i | 0.0594403 | + | 0.0193133i | ||||
\(317\) | −15918.3 | − | 11565.4i | −0.158409 | − | 0.115091i | 0.505757 | − | 0.862676i | \(-0.331213\pi\) |
−0.664166 | + | 0.747585i | \(0.731213\pi\) | |||||||
\(318\) | − | 35202.2i | − | 0.348109i | ||||||
\(319\) | 26168.4 | − | 55431.8i | 0.257156 | − | 0.544726i | ||||
\(320\) | 65546.3 | 0.640101 | ||||||||
\(321\) | 13865.3 | − | 19083.9i | 0.134561 | − | 0.185207i | ||||
\(322\) | −35153.0 | + | 108190.i | −0.339040 | + | 1.04346i | ||||
\(323\) | 8673.08 | + | 26693.0i | 0.0831320 | + | 0.255854i | ||||
\(324\) | −4728.44 | + | 3435.41i | −0.0450431 | + | 0.0327257i | ||||
\(325\) | 36895.5 | + | 50782.3i | 0.349306 | + | 0.480779i | ||||
\(326\) | −18199.0 | + | 5913.21i | −0.171243 | + | 0.0556401i | ||||
\(327\) | −98129.1 | − | 31884.1i | −0.917704 | − | 0.298180i | ||||
\(328\) | 5183.70 | + | 3766.18i | 0.0481828 | + | 0.0350068i | ||||
\(329\) | − | 2920.94i | − | 0.0269855i | ||||||
\(330\) | 59404.0 | − | 32561.6i | 0.545491 | − | 0.299004i | ||||
\(331\) | 28807.4 | 0.262935 | 0.131468 | − | 0.991320i | \(-0.458031\pi\) | ||||
0.131468 | + | 0.991320i | \(0.458031\pi\) | |||||||
\(332\) | 7077.33 | − | 9741.11i | 0.0642086 | − | 0.0883756i | ||||
\(333\) | 19681.2 | − | 60572.5i | 0.177485 | − | 0.546244i | ||||
\(334\) | 16005.2 | + | 49259.0i | 0.143472 | + | 0.441563i | ||||
\(335\) | −128061. | + | 93042.1i | −1.14111 | + | 0.829067i | ||||
\(336\) | 60687.8 | + | 83529.6i | 0.537555 | + | 0.739881i | ||||
\(337\) | −178804. | + | 58096.9i | −1.57441 | + | 0.511556i | −0.960608 | − | 0.277906i | \(-0.910360\pi\) |
−0.613800 | + | 0.789462i | \(0.710360\pi\) | |||||||
\(338\) | 68760.4 | + | 22341.6i | 0.601873 | + | 0.195560i | ||||
\(339\) | 8840.86 | + | 6423.26i | 0.0769299 | + | 0.0558928i | ||||
\(340\) | 12880.1i | 0.111420i | ||||||||
\(341\) | −28219.7 | + | 5346.88i | −0.242686 | + | 0.0459824i | ||||
\(342\) | 7418.71 | 0.0634273 | ||||||||
\(343\) | −66890.6 | + | 92067.1i | −0.568561 | + | 0.782557i | ||||
\(344\) | 38395.1 | − | 118168.i | 0.324458 | − | 0.998579i | ||||
\(345\) | 22123.4 | + | 68088.8i | 0.185872 | + | 0.572055i | ||||
\(346\) | −2332.35 | + | 1694.55i | −0.0194824 | + | 0.0141548i | ||||
\(347\) | 17060.3 | + | 23481.5i | 0.141687 | + | 0.195015i | 0.873963 | − | 0.485993i | \(-0.161542\pi\) |
−0.732276 | + | 0.681008i | \(0.761542\pi\) | |||||||
\(348\) | −5737.98 | + | 1864.38i | −0.0473806 | + | 0.0153949i | ||||
\(349\) | 90136.3 | + | 29287.0i | 0.740029 | + | 0.240450i | 0.654685 | − | 0.755902i | \(-0.272801\pi\) |
0.0853437 | + | 0.996352i | \(0.472801\pi\) | |||||||
\(350\) | −50289.1 | − | 36537.2i | −0.410523 | − | 0.298263i | ||||
\(351\) | 169808.i | 1.37830i | ||||||||
\(352\) | −18272.1 | − | 17201.4i | −0.147470 | − | 0.138829i | ||||
\(353\) | −107013. | −0.858793 | −0.429397 | − | 0.903116i | \(-0.641274\pi\) | ||||
−0.429397 | + | 0.903116i | \(0.641274\pi\) | |||||||
\(354\) | −34879.9 | + | 48008.0i | −0.278335 | + | 0.383096i | ||||
\(355\) | 10561.6 | − | 32505.3i | 0.0838058 | − | 0.257928i | ||||
\(356\) | −5580.78 | − | 17175.9i | −0.0440347 | − | 0.135525i | ||||
\(357\) | 130022. | − | 94466.2i | 1.02019 | − | 0.741208i | ||||
\(358\) | 34140.0 | + | 46989.7i | 0.266378 | + | 0.366638i | ||||
\(359\) | 64156.8 | − | 20845.8i | 0.497799 | − | 0.161745i | −0.0493475 | − | 0.998782i | \(-0.515714\pi\) |
0.547146 | + | 0.837037i | \(0.315714\pi\) | |||||||
\(360\) | −28615.8 | − | 9297.83i | −0.220801 | − | 0.0717425i | ||||
\(361\) | −102062. | − | 74152.4i | −0.783159 | − | 0.568998i | ||||
\(362\) | − | 85732.7i | − | 0.654228i | ||||||
\(363\) | 103776. | + | 26920.1i | 0.787558 | + | 0.204298i | ||||
\(364\) | −17562.9 | −0.132554 | ||||||||
\(365\) | 26272.7 | − | 36161.3i | 0.197206 | − | 0.271430i | ||||
\(366\) | −6069.83 | + | 18681.0i | −0.0453121 | + | 0.139456i | ||||
\(367\) | −50426.9 | − | 155198.i | −0.374395 | − | 1.15227i | −0.943886 | − | 0.330272i | \(-0.892859\pi\) |
0.569491 | − | 0.821998i | \(-0.307141\pi\) | |||||||
\(368\) | 121345. | − | 88162.2i | 0.896037 | − | 0.651009i | ||||
\(369\) | −1708.74 | − | 2351.87i | −0.0125494 | − | 0.0172727i | ||||
\(370\) | 169147. | − | 54959.3i | 1.23555 | − | 0.401456i | ||||
\(371\) | 54960.9 | + | 17857.9i | 0.399306 | + | 0.129742i | ||||
\(372\) | 2287.04 | + | 1661.63i | 0.0165268 | + | 0.0120074i | ||||
\(373\) | − | 125734.i | − | 0.903719i | −0.892089 | − | 0.451860i | \(-0.850761\pi\) | ||
0.892089 | − | 0.451860i | \(-0.149239\pi\) | |||||||
\(374\) | −151429. | + | 160855.i | −1.08260 | + | 1.14998i | ||||
\(375\) | −122465. | −0.870862 | ||||||||
\(376\) | −2052.88 | + | 2825.54i | −0.0145207 | + | 0.0199860i | ||||
\(377\) | −33495.8 | + | 103090.i | −0.235672 | + | 0.725324i | ||||
\(378\) | −51964.0 | − | 159929.i | −0.363680 | − | 1.11929i | ||||
\(379\) | −78050.7 | + | 56707.2i | −0.543373 | + | 0.394784i | −0.825336 | − | 0.564641i | \(-0.809014\pi\) |
0.281963 | + | 0.959425i | \(0.409014\pi\) | |||||||
\(380\) | 1123.56 | + | 1546.45i | 0.00778091 | + | 0.0107095i | ||||
\(381\) | 120992. | − | 39312.8i | 0.833504 | − | 0.270822i | ||||
\(382\) | 29278.9 | + | 9513.29i | 0.200645 | + | 0.0651934i | ||||
\(383\) | 123692. | + | 89867.7i | 0.843228 | + | 0.612641i | 0.923270 | − | 0.384151i | \(-0.125506\pi\) |
−0.0800426 | + | 0.996791i | \(0.525506\pi\) | |||||||
\(384\) | − | 134953.i | − | 0.915207i | ||||||
\(385\) | 20702.8 | + | 109265.i | 0.139672 | + | 0.737158i | ||||
\(386\) | −151068. | −1.01391 | ||||||||
\(387\) | −33134.9 | + | 45606.3i | −0.221240 | + | 0.304511i | ||||
\(388\) | 6177.19 | − | 19011.4i | 0.0410325 | − | 0.126285i | ||||
\(389\) | −10802.6 | − | 33246.9i | −0.0713884 | − | 0.219711i | 0.908996 | − | 0.416804i | \(-0.136850\pi\) |
−0.980385 | + | 0.197093i | \(0.936850\pi\) | |||||||
\(390\) | −96912.9 | + | 70411.3i | −0.637166 | + | 0.462928i | ||||
\(391\) | −137233. | − | 188884.i | −0.897643 | − | 1.23550i | ||||
\(392\) | −8386.95 | + | 2725.09i | −0.0545798 | + | 0.0177341i | ||||
\(393\) | −127947. | − | 41572.5i | −0.828410 | − | 0.269167i | ||||
\(394\) | 134713. | + | 97874.4i | 0.867792 | + | 0.630488i | ||||
\(395\) | 69880.4i | 0.447879i | ||||||||
\(396\) | 2589.84 | + | 4724.80i | 0.0165151 | + | 0.0301296i | ||||
\(397\) | 20457.2 | 0.129797 | 0.0648986 | − | 0.997892i | \(-0.479328\pi\) | ||||
0.0648986 | + | 0.997892i | \(0.479328\pi\) | |||||||
\(398\) | −22174.7 | + | 30520.9i | −0.139989 | + | 0.192678i | ||||
\(399\) | 7370.55 | − | 22684.2i | 0.0462971 | − | 0.142488i | ||||
\(400\) | 25326.9 | + | 77948.1i | 0.158293 | + | 0.487176i | ||||
\(401\) | 153780. | − | 111728.i | 0.956338 | − | 0.694820i | 0.00404091 | − | 0.999992i | \(-0.498714\pi\) |
0.952297 | + | 0.305171i | \(0.0987137\pi\) | |||||||
\(402\) | 157072. | + | 216190.i | 0.971953 | + | 1.33778i | ||||
\(403\) | 48303.5 | − | 15694.8i | 0.297419 | − | 0.0966373i | ||||
\(404\) | 13106.6 | + | 4258.58i | 0.0803019 | + | 0.0260917i | ||||
\(405\) | −52944.9 | − | 38466.7i | −0.322786 | − | 0.234517i | ||||
\(406\) | − | 107342.i | − | 0.651205i | ||||||
\(407\) | 254533. | + | 120161.i | 1.53658 | + | 0.725393i | ||||
\(408\) | −192167. | −1.15441 | ||||||||
\(409\) | −110780. | + | 152476.i | −0.662240 | + | 0.911495i | −0.999553 | − | 0.0298979i | \(-0.990482\pi\) |
0.337313 | + | 0.941392i | \(0.390482\pi\) | |||||||
\(410\) | 2508.58 | − | 7720.62i | 0.0149232 | − | 0.0459288i | ||||
\(411\) | 48057.3 | + | 147905.i | 0.284496 | + | 0.875588i | ||||
\(412\) | −16957.9 | + | 12320.6i | −0.0999028 | + | 0.0725836i | ||||
\(413\) | −57260.2 | − | 78811.9i | −0.335701 | − | 0.462053i | ||||
\(414\) | −58692.5 | + | 19070.3i | −0.342438 | + | 0.111265i | ||||
\(415\) | 128222. | + | 41661.9i | 0.744504 | + | 0.241904i | ||||
\(416\) | 35900.9 | + | 26083.5i | 0.207452 | + | 0.150723i | ||||
\(417\) | − | 29800.9i | − | 0.171379i | ||||||
\(418\) | −4149.62 | + | 32522.6i | −0.0237496 | + | 0.186137i | ||||
\(419\) | −34335.6 | −0.195577 | −0.0977883 | − | 0.995207i | \(-0.531177\pi\) | ||||
−0.0977883 | + | 0.995207i | \(0.531177\pi\) | |||||||
\(420\) | 6433.76 | − | 8855.31i | 0.0364725 | − | 0.0502002i | ||||
\(421\) | 81293.7 | − | 250196.i | 0.458662 | − | 1.41162i | −0.408119 | − | 0.912929i | \(-0.633815\pi\) |
0.866781 | − | 0.498688i | \(-0.166185\pi\) | |||||||
\(422\) | 9140.87 | + | 28132.7i | 0.0513290 | + | 0.157974i | ||||
\(423\) | 1281.96 | − | 931.402i | 0.00716465 | − | 0.00520543i | ||||
\(424\) | −40615.1 | − | 55901.9i | −0.225921 | − | 0.310953i | ||||
\(425\) | 121333. | − | 39423.6i | 0.671743 | − | 0.218262i | ||||
\(426\) | −54874.8 | − | 17829.9i | −0.302380 | − | 0.0982493i | ||||
\(427\) | −26087.3 | − | 18953.6i | −0.143078 | − | 0.103953i | ||||
\(428\) | 5239.22i | 0.0286009i | ||||||||
\(429\) | −188058. | − | 23994.6i | −1.02182 | − | 0.130376i | ||||
\(430\) | −157419. | −0.851373 | ||||||||
\(431\) | −128666. | + | 177094.i | −0.692643 | + | 0.953341i | 0.307355 | + | 0.951595i | \(0.400556\pi\) |
−0.999998 | + | 0.00174659i | \(0.999444\pi\) | |||||||
\(432\) | −68515.0 | + | 210867.i | −0.367129 | + | 1.12991i | ||||
\(433\) | 21470.6 | + | 66079.8i | 0.114517 | + | 0.352446i | 0.991846 | − | 0.127443i | \(-0.0406769\pi\) |
−0.877329 | + | 0.479889i | \(0.840677\pi\) | |||||||
\(434\) | −40690.4 | + | 29563.3i | −0.216029 | + | 0.156954i | ||||
\(435\) | −39708.0 | − | 54653.3i | −0.209845 | − | 0.288827i | ||||
\(436\) | 21794.9 | − | 7081.60i | 0.114652 | − | 0.0372527i | ||||
\(437\) | −32953.7 | − | 10707.3i | −0.172561 | − | 0.0560683i | ||||
\(438\) | −61046.7 | − | 44353.0i | −0.318210 | − | 0.231193i | ||||
\(439\) | − | 72005.3i | − | 0.373625i | −0.982396 | − | 0.186812i | \(-0.940184\pi\) | ||
0.982396 | − | 0.186812i | \(-0.0598156\pi\) | |||||||
\(440\) | 56766.5 | − | 120247.i | 0.293216 | − | 0.621111i | ||||
\(441\) | 4001.03 | 0.0205729 | ||||||||
\(442\) | 229621. | − | 316046.i | 1.17535 | − | 1.61773i | ||||
\(443\) | −13800.0 | + | 42472.2i | −0.0703190 | + | 0.216420i | −0.980040 | − | 0.198800i | \(-0.936295\pi\) |
0.909721 | + | 0.415220i | \(0.136295\pi\) | |||||||
\(444\) | −8560.91 | − | 26347.8i | −0.0434264 | − | 0.133653i | ||||
\(445\) | 163597. | − | 118861.i | 0.826146 | − | 0.600230i | ||||
\(446\) | −31578.2 | − | 43463.7i | −0.158752 | − | 0.218503i | ||||
\(447\) | 125341. | − | 40725.7i | 0.627303 | − | 0.203823i | ||||
\(448\) | 172763. | + | 56134.1i | 0.860785 | + | 0.279686i | ||||
\(449\) | −104641. | − | 76026.2i | −0.519050 | − | 0.377112i | 0.297196 | − | 0.954817i | \(-0.403949\pi\) |
−0.816246 | + | 0.577704i | \(0.803949\pi\) | |||||||
\(450\) | − | 33721.9i | − | 0.166528i | ||||||
\(451\) | 11266.1 | − | 6175.35i | 0.0553884 | − | 0.0303605i | ||||
\(452\) | −2427.14 | −0.0118800 | ||||||||
\(453\) | 38007.0 | − | 52312.2i | 0.185211 | − | 0.254922i | ||||
\(454\) | 73028.8 | − | 224760.i | 0.354309 | − | 1.09045i | ||||
\(455\) | −60769.3 | − | 187029.i | −0.293536 | − | 0.903411i | ||||
\(456\) | −23072.6 | + | 16763.2i | −0.110960 | + | 0.0806173i | ||||
\(457\) | 180382. | + | 248275.i | 0.863697 | + | 1.18878i | 0.980675 | + | 0.195642i | \(0.0626791\pi\) |
−0.116979 | + | 0.993134i | \(0.537321\pi\) | |||||||
\(458\) | −358860. | + | 116601.i | −1.71078 | + | 0.555866i | ||||
\(459\) | 328235. | + | 106650.i | 1.55797 | + | 0.506215i | ||||
\(460\) | −12864.2 | − | 9346.42i | −0.0607951 | − | 0.0441702i | ||||
\(461\) | 22814.7i | 0.107353i | 0.998558 | + | 0.0536764i | \(0.0170940\pi\) | ||||
−0.998558 | + | 0.0536764i | \(0.982906\pi\) | |||||||
\(462\) | 184459. | − | 34950.0i | 0.864204 | − | 0.163743i | ||||
\(463\) | 247942. | 1.15661 | 0.578307 | − | 0.815819i | \(-0.303713\pi\) | ||||
0.578307 | + | 0.815819i | \(0.303713\pi\) | |||||||
\(464\) | −83190.2 | + | 114501.i | −0.386399 | + | 0.531833i | ||||
\(465\) | −9781.50 | + | 30104.4i | −0.0452376 | + | 0.139227i | ||||
\(466\) | 32193.8 | + | 99082.5i | 0.148252 | + | 0.456273i | ||||
\(467\) | −261318. | + | 189859.i | −1.19822 | + | 0.870557i | −0.994108 | − | 0.108390i | \(-0.965430\pi\) |
−0.204111 | + | 0.978948i | \(0.565430\pi\) | |||||||
\(468\) | −5600.28 | − | 7708.13i | −0.0255693 | − | 0.0351931i | ||||
\(469\) | −417218. | + | 135562.i | −1.89678 | + | 0.616301i | ||||
\(470\) | 4208.38 | + | 1367.38i | 0.0190511 | + | 0.00619006i | ||||
\(471\) | −114839. | − | 83435.1i | −0.517662 | − | 0.376103i | ||||
\(472\) | 116481.i | 0.522844i | ||||||||
\(473\) | −181398. | − | 170769.i | −0.810793 | − | 0.763283i | ||||
\(474\) | 117970. | 0.525069 | ||||||||
\(475\) | 11128.9 | − | 15317.6i | 0.0493248 | − | 0.0678898i | ||||
\(476\) | −11030.6 | + | 33948.6i | −0.0486837 | + | 0.149833i | ||||
\(477\) | 9687.80 | + | 29816.0i | 0.0425783 | + | 0.131043i | ||||
\(478\) | −113922. | + | 82769.5i | −0.498602 | + | 0.362255i | ||||
\(479\) | 58964.1 | + | 81157.2i | 0.256990 | + | 0.353717i | 0.917944 | − | 0.396710i | \(-0.129848\pi\) |
−0.660954 | + | 0.750427i | \(0.729848\pi\) | |||||||
\(480\) | −26303.0 | + | 8546.35i | −0.114162 | + | 0.0370935i | ||||
\(481\) | −473369. | − | 153807.i | −2.04602 | − | 0.664791i | ||||
\(482\) | 243934. | + | 177229.i | 1.04997 | + | 0.762851i | ||||
\(483\) | 198411.i | 0.850493i | ||||||||
\(484\) | −22161.5 | + | 8710.71i | −0.0946037 | + | 0.0371846i | ||||
\(485\) | 223828. | 0.951549 | ||||||||
\(486\) | 93695.9 | − | 128961.i | 0.396687 | − | 0.545993i | ||||
\(487\) | −113517. | + | 349368.i | −0.478632 | + | 1.47308i | 0.362365 | + | 0.932036i | \(0.381969\pi\) |
−0.840997 | + | 0.541040i | \(0.818031\pi\) | |||||||
\(488\) | 11914.5 | + | 36669.1i | 0.0500307 | + | 0.153979i | ||||
\(489\) | −27001.2 | + | 19617.5i | −0.112919 | + | 0.0820402i | ||||
\(490\) | 6567.20 | + | 9038.98i | 0.0273520 | + | 0.0376467i | ||||
\(491\) | 212925. | − | 69183.6i | 0.883210 | − | 0.286972i | 0.167921 | − | 0.985801i | \(-0.446295\pi\) |
0.715290 | + | 0.698828i | \(0.246295\pi\) | |||||||
\(492\) | −1202.63 | − | 390.757i | −0.00496822 | − | 0.00161427i | ||||
\(493\) | 178232. | + | 129493.i | 0.733318 | + | 0.532786i | ||||
\(494\) | − | 57976.6i | − | 0.237574i | ||||||
\(495\) | −41353.7 | + | 43927.7i | −0.168773 | + | 0.179278i | ||||
\(496\) | 66315.8 | 0.269559 | ||||||||
\(497\) | 55675.4 | − | 76630.5i | 0.225398 | − | 0.310234i | ||||
\(498\) | 70332.8 | − | 216462.i | 0.283595 | − | 0.872816i | ||||
\(499\) | −128358. | − | 395046.i | −0.515492 | − | 1.58652i | −0.782384 | − | 0.622796i | \(-0.785997\pi\) |
0.266892 | − | 0.963726i | \(-0.414003\pi\) | |||||||
\(500\) | 22005.3 | − | 15987.8i | 0.0880211 | − | 0.0639511i | ||||
\(501\) | 53098.5 | + | 73083.9i | 0.211547 | + | 0.291170i | ||||
\(502\) | 192211. | − | 62453.2i | 0.762731 | − | 0.247826i | ||||
\(503\) | −319477. | − | 103805.i | −1.26271 | − | 0.410280i | −0.400252 | − | 0.916405i | \(-0.631077\pi\) |
−0.862460 | + | 0.506125i | \(0.831077\pi\) | |||||||
\(504\) | −67461.0 | − | 49013.3i | −0.265578 | − | 0.192954i | ||||
\(505\) | 154308.i | 0.605070i | ||||||||
\(506\) | −50772.4 | − | 267967.i | −0.198302 | − | 1.04660i | ||||
\(507\) | 126100. | 0.490570 | ||||||||
\(508\) | −16608.4 | + | 22859.5i | −0.0643576 | + | 0.0885806i | ||||
\(509\) | 69443.4 | − | 213725.i | 0.268038 | − | 0.824935i | −0.722940 | − | 0.690910i | \(-0.757210\pi\) |
0.990978 | − | 0.134024i | \(-0.0427901\pi\) | |||||||
\(510\) | 75236.1 | + | 231553.i | 0.289258 | + | 0.890245i | ||||
\(511\) | 100217. | − | 72811.7i | 0.383794 | − | 0.278843i | ||||
\(512\) | −124497. | − | 171355.i | −0.474917 | − | 0.653667i | ||||
\(513\) | 48712.9 | − | 15827.8i | 0.185101 | − | 0.0601430i | ||||
\(514\) | −100768. | − | 32741.5i | −0.381414 | − | 0.123929i | ||||
\(515\) | −189880. | − | 137956.i | −0.715919 | − | 0.520146i | ||||
\(516\) | 24520.8i | 0.0920950i | ||||||||
\(517\) | 3366.08 | + | 6140.93i | 0.0125934 | + | 0.0229749i | ||||
\(518\) | 492895. | 1.83694 | ||||||||
\(519\) | −2955.56 | + | 4067.98i | −0.0109725 | + | 0.0151023i | ||||
\(520\) | −72661.7 | + | 223630.i | −0.268719 | + | 0.827033i | ||||
\(521\) | 65350.4 | + | 201128.i | 0.240754 | + | 0.740964i | 0.996306 | + | 0.0858752i | \(0.0273686\pi\) |
−0.755552 | + | 0.655088i | \(0.772631\pi\) | |||||||
\(522\) | 47111.1 | − | 34228.2i | 0.172895 | − | 0.125616i | ||||
\(523\) | −79321.4 | − | 109177.i | −0.289993 | − | 0.399141i | 0.639019 | − | 0.769191i | \(-0.279340\pi\) |
−0.929012 | + | 0.370050i | \(0.879340\pi\) | |||||||
\(524\) | 28417.6 | − | 9233.45i | 0.103496 | − | 0.0336280i | ||||
\(525\) | −103112. | − | 33503.0i | −0.374101 | − | 0.121553i | ||||
\(526\) | −250599. | − | 182071.i | −0.905748 | − | 0.658064i | ||||
\(527\) | − | 103227.i | − | 0.371682i | ||||||
\(528\) | −223848. | − | 105675.i | −0.802945 | − | 0.379057i | ||||
\(529\) | 8393.49 | 0.0299938 | ||||||||
\(530\) | −51457.8 | + | 70825.7i | −0.183189 | + | 0.252138i | ||||
\(531\) | 16331.0 | − | 50261.6i | 0.0579193 | − | 0.178257i | ||||
\(532\) | 1637.03 | + | 5038.27i | 0.00578407 | + | 0.0178015i | ||||
\(533\) | −18379.7 | + | 13353.6i | −0.0646969 | + | 0.0470050i | ||||
\(534\) | −200658. | − | 276182.i | −0.703677 | − | 0.968528i | ||||
\(535\) | −55793.0 | + | 18128.2i | −0.194927 | + | 0.0633356i | ||||
\(536\) | 498867. | + | 162092.i | 1.73642 | + | 0.564197i | ||||
\(537\) | 81957.3 | + | 59545.5i | 0.284210 | + | 0.206491i | ||||
\(538\) | 593752.i | 2.05135i | ||||||||
\(539\) | −2237.96 | + | 17540.0i | −0.00770325 | + | 0.0603742i | ||||
\(540\) | 23505.3 | 0.0806081 | ||||||||
\(541\) | −36527.6 | + | 50275.9i | −0.124803 | + | 0.171777i | −0.866847 | − | 0.498575i | \(-0.833857\pi\) |
0.742043 | + | 0.670352i | \(0.233857\pi\) | |||||||
\(542\) | −132102. | + | 406568.i | −0.449687 | + | 1.38400i | ||||
\(543\) | −46207.6 | − | 142212.i | −0.156716 | − | 0.482323i | ||||
\(544\) | 72966.8 | − | 53013.5i | 0.246563 | − | 0.179138i | ||||
\(545\) | 150825. | + | 207593.i | 0.507786 | + | 0.698908i | ||||
\(546\) | −315737. | + | 102589.i | −1.05911 | + | 0.344125i | ||||
\(547\) | −338850. | − | 110099.i | −1.13249 | − | 0.367967i | −0.317966 | − | 0.948102i | \(-0.603000\pi\) |
−0.814520 | + | 0.580135i | \(0.803000\pi\) | |||||||
\(548\) | −27944.2 | − | 20302.7i | −0.0930531 | − | 0.0676071i | ||||
\(549\) | − | 17493.1i | − | 0.0580395i | ||||||
\(550\) | 147832. | + | 18862.2i | 0.488702 | + | 0.0623543i | ||||
\(551\) | 32695.5 | 0.107692 | ||||||||
\(552\) | 139446. | − | 191931.i | 0.457644 | − | 0.629893i | ||||
\(553\) | −59845.8 | + | 184186.i | −0.195697 | + | 0.602292i | ||||
\(554\) | 35139.2 | + | 108147.i | 0.114491 | + | 0.352368i | ||||
\(555\) | 250958. | − | 182332.i | 0.814733 | − | 0.591938i | ||||
\(556\) | 3890.50 | + | 5354.81i | 0.0125851 | + | 0.0173218i | ||||
\(557\) | 376433. | − | 122311.i | 1.21333 | − | 0.394234i | 0.368679 | − | 0.929557i | \(-0.379810\pi\) |
0.844647 | + | 0.535323i | \(0.179810\pi\) | |||||||
\(558\) | −25949.9 | − | 8431.64i | −0.0833427 | − | 0.0270797i | ||||
\(559\) | 356409. | + | 258946.i | 1.14058 | + | 0.828679i | ||||
\(560\) | − | 256771.i | − | 0.818786i | ||||||
\(561\) | −164493. | + | 348441.i | −0.522662 | + | 1.10714i | ||||
\(562\) | −556931. | −1.76331 | ||||||||
\(563\) | 254804. | − | 350707.i | 0.803876 | − | 1.10644i | −0.188363 | − | 0.982099i | \(-0.560318\pi\) |
0.992240 | − | 0.124341i | \(-0.0396817\pi\) | |||||||
\(564\) | 212.995 | − | 655.531i | 0.000669593 | − | 0.00206080i | ||||
\(565\) | −8398.14 | − | 25846.8i | −0.0263079 | − | 0.0809674i | ||||
\(566\) | −285996. | + | 207788.i | −0.892744 | + | 0.648617i | ||||
\(567\) | −106606. | − | 146730.i | −0.331600 | − | 0.456409i | ||||
\(568\) | −107714. | + | 34998.4i | −0.333869 | + | 0.108481i | ||||
\(569\) | 81414.7 | + | 26453.2i | 0.251466 | + | 0.0817061i | 0.432037 | − | 0.901856i | \(-0.357795\pi\) |
−0.180572 | + | 0.983562i | \(0.557795\pi\) | |||||||
\(570\) | 29232.2 | + | 21238.4i | 0.0899728 | + | 0.0653691i | ||||
\(571\) | 474437.i | 1.45514i | 0.686031 | + | 0.727572i | \(0.259351\pi\) | ||||
−0.686031 | + | 0.727572i | \(0.740649\pi\) | |||||||
\(572\) | 36923.9 | − | 20239.4i | 0.112854 | − | 0.0618593i | ||||
\(573\) | 53694.9 | 0.163540 | ||||||||
\(574\) | 13223.9 | − | 18201.2i | 0.0401362 | − | 0.0552428i | ||||
\(575\) | −48670.3 | + | 149792.i | −0.147207 | + | 0.453056i | ||||
\(576\) | 30452.5 | + | 93723.0i | 0.0917862 | + | 0.282489i | ||||
\(577\) | 499816. | − | 363138.i | 1.50127 | − | 1.09074i | 0.531396 | − | 0.847123i | \(-0.321668\pi\) |
0.969873 | − | 0.243612i | \(-0.0783325\pi\) | |||||||
\(578\) | −260585. | − | 358664.i | −0.779998 | − | 1.07358i | ||||
\(579\) | −250591. | + | 81421.8i | −0.747494 | + | 0.242875i | ||||
\(580\) | 14270.0 | + | 4636.59i | 0.0424196 | + | 0.0137830i | ||||
\(581\) | 302281. | + | 219620.i | 0.895485 | + | 0.650608i | ||||
\(582\) | − | 377862.i | − | 1.11554i | ||||||
\(583\) | −136128. | + | 25792.6i | −0.400507 | + | 0.0758853i | ||||
\(584\) | −148117. | −0.434289 | ||||||||
\(585\) | 62707.0 | − | 86308.8i | 0.183233 | − | 0.252199i | ||||
\(586\) | 156544. | − | 481794.i | 0.455871 | − | 1.40303i | ||||
\(587\) | 52321.6 | + | 161029.i | 0.151846 | + | 0.467335i | 0.997828 | − | 0.0658772i | \(-0.0209846\pi\) |
−0.845981 | + | 0.533213i | \(0.820985\pi\) | |||||||
\(588\) | 1407.98 | − | 1022.96i | 0.00407233 | − | 0.00295872i | ||||
\(589\) | −9004.72 | − | 12393.9i | −0.0259561 | − | 0.0357255i | ||||
\(590\) | 140354. | − | 45603.9i | 0.403202 | − | 0.131008i | ||||
\(591\) | 276211. | + | 89746.5i | 0.790800 | + | 0.256946i | ||||
\(592\) | −525770. | − | 381994.i | −1.50021 | − | 1.08997i | ||||
\(593\) | − | 519770.i | − | 1.47809i | −0.673654 | − | 0.739047i | \(-0.735276\pi\) | ||
0.673654 | − | 0.739047i | \(-0.264724\pi\) | |||||||
\(594\) | 293549. | + | 276348.i | 0.831971 | + | 0.783220i | ||||
\(595\) | −399688. | −1.12898 | ||||||||
\(596\) | −17205.3 | + | 23681.0i | −0.0484361 | + | 0.0666666i | ||||
\(597\) | −20333.3 | + | 62579.4i | −0.0570504 | + | 0.175583i | ||||
\(598\) | 149033. | + | 458677.i | 0.416755 | + | 1.28264i | ||||
\(599\) | −364603. | + | 264899.i | −1.01617 | + | 0.738291i | −0.965494 | − | 0.260425i | \(-0.916137\pi\) |
−0.0506757 | + | 0.998715i | \(0.516137\pi\) | |||||||
\(600\) | 76197.6 | + | 104877.i | 0.211660 | + | 0.291325i | ||||
\(601\) | 18199.0 | − | 5913.22i | 0.0503848 | − | 0.0163710i | −0.283716 | − | 0.958908i | \(-0.591567\pi\) |
0.334101 | + | 0.942537i | \(0.391567\pi\) | |||||||
\(602\) | −414915. | − | 134814.i | −1.14490 | − | 0.371999i | ||||
\(603\) | −192535. | − | 139885.i | −0.529511 | − | 0.384713i | ||||
\(604\) | 14361.6i | 0.0393667i | ||||||||
\(605\) | −169442. | − | 205860.i | −0.462925 | − | 0.562420i | ||||
\(606\) | 260499. | 0.709351 | ||||||||
\(607\) | 179595. | − | 247192.i | 0.487436 | − | 0.670898i | −0.492477 | − | 0.870326i | \(-0.663908\pi\) |
0.979913 | + | 0.199428i | \(0.0639083\pi\) | |||||||
\(608\) | 4136.27 | − | 12730.1i | 0.0111893 | − | 0.0344371i | ||||
\(609\) | −57854.5 | − | 178058.i | −0.155992 | − | 0.480094i | ||||
\(610\) | 39519.9 | − | 28712.9i | 0.106208 | − | 0.0771644i | ||||
\(611\) | −7278.82 | − | 10018.4i | −0.0194975 | − | 0.0268360i | ||||
\(612\) | −18416.9 | + | 5984.03i | −0.0491716 | + | 0.0159768i | ||||
\(613\) | 471453. | + | 153184.i | 1.25463 | + | 0.407656i | 0.859580 | − | 0.511002i | \(-0.170725\pi\) |
0.395055 | + | 0.918657i | \(0.370725\pi\) | |||||||
\(614\) | 443538. | + | 322249.i | 1.17650 | + | 0.854781i | ||||
\(615\) | − | 14158.9i | − | 0.0374352i | ||||||
\(616\) | 252602. | − | 268325.i | 0.665694 | − | 0.707129i | ||||
\(617\) | −481904. | −1.26587 | −0.632937 | − | 0.774203i | \(-0.718151\pi\) | ||||
−0.632937 | + | 0.774203i | \(0.718151\pi\) | |||||||
\(618\) | −232894. | + | 320550.i | −0.609790 | + | 0.839304i | ||||
\(619\) | 172028. | − | 529448.i | 0.448971 | − | 1.38179i | −0.429099 | − | 0.903257i | \(-0.641169\pi\) |
0.878070 | − | 0.478532i | \(-0.158831\pi\) | |||||||
\(620\) | −2172.51 | − | 6686.31i | −0.00565170 | − | 0.0173942i | ||||
\(621\) | −344702. | + | 250440.i | −0.893840 | + | 0.649413i | ||||
\(622\) | 243745. | + | 335486.i | 0.630020 | + | 0.867148i | ||||
\(623\) | 532993. | − | 173180.i | 1.37324 | − | 0.446191i | ||||
\(624\) | 416303. | + | 135265.i | 1.06915 | + | 0.347389i | ||||
\(625\) | 98059.8 | + | 71244.6i | 0.251033 | + | 0.182386i | ||||
\(626\) | − | 263687.i | − | 0.672885i | ||||||
\(627\) | 10645.5 | + | 56184.7i | 0.0270788 | + | 0.142917i | ||||
\(628\) | 31527.3 | 0.0799407 | ||||||||
\(629\) | −594609. | + | 818409.i | −1.50290 | + | 2.06857i | ||||
\(630\) | −32646.9 | + | 100477.i | −0.0822546 | + | 0.253154i | ||||
\(631\) | −122608. | − | 377349.i | −0.307936 | − | 0.947730i | −0.978565 | − | 0.205937i | \(-0.933976\pi\) |
0.670629 | − | 0.741793i | \(-0.266024\pi\) | |||||||
\(632\) | 187340. | − | 136110.i | 0.469025 | − | 0.340767i | ||||
\(633\) | 30325.5 | + | 41739.5i | 0.0756835 | + | 0.104169i | ||||
\(634\) | 78564.8 | − | 25527.3i | 0.195456 | − | 0.0635076i | ||||
\(635\) | −300899. | − | 97768.1i | −0.746232 | − | 0.242465i | ||||
\(636\) | 11032.4 | + | 8015.49i | 0.0272744 | + | 0.0198160i | ||||
\(637\) | − | 31267.7i | − | 0.0770579i | ||||||
\(638\) | 123701. | + | 225674.i | 0.303900 | + | 0.554422i | ||||
\(639\) | 51385.4 | 0.125846 | ||||||||
\(640\) | −197271. | + | 271521.i | −0.481620 | + | 0.662893i | ||||
\(641\) | −220138. | + | 677516.i | −0.535771 | + | 1.64893i | 0.206205 | + | 0.978509i | \(0.433889\pi\) |
−0.741976 | + | 0.670426i | \(0.766111\pi\) | |||||||
\(642\) | 30603.7 | + | 94188.4i | 0.0742512 | + | 0.228522i | ||||
\(643\) | −93657.4 | + | 68046.1i | −0.226527 | + | 0.164582i | −0.695260 | − | 0.718758i | \(-0.744711\pi\) |
0.468733 | + | 0.883340i | \(0.344711\pi\) | |||||||
\(644\) | −25902.5 | − | 35651.7i | −0.0624553 | − | 0.0859624i | ||||
\(645\) | −261125. | + | 84844.6i | −0.627666 | + | 0.203941i | ||||
\(646\) | −112067. | − | 36412.9i | −0.268543 | − | 0.0872549i | ||||
\(647\) | −453337. | − | 329369.i | −1.08296 | − | 0.786817i | −0.104764 | − | 0.994497i | \(-0.533409\pi\) |
−0.978197 | + | 0.207680i | \(0.933409\pi\) | |||||||
\(648\) | 216862.i | 0.516457i | ||||||||
\(649\) | 211205. | + | 99706.4i | 0.501436 | + | 0.236719i | ||||
\(650\) | −263534. | −0.623748 | ||||||||
\(651\) | −51562.9 | + | 70970.3i | −0.121668 | + | 0.167461i | ||||
\(652\) | 2290.69 | − | 7050.01i | 0.00538853 | − | 0.0165842i | ||||
\(653\) | −125501. | − | 386251.i | −0.294320 | − | 0.905823i | −0.983449 | − | 0.181184i | \(-0.942007\pi\) |
0.689129 | − | 0.724638i | \(-0.257993\pi\) | |||||||
\(654\) | 350454. | − | 254620.i | 0.819361 | − | 0.595301i | ||||
\(655\) | 196656. | + | 270673.i | 0.458378 | + | 0.630903i | ||||
\(656\) | −28211.8 | + | 9166.58i | −0.0655577 | + | 0.0213010i | ||||
\(657\) | 63912.3 | + | 20766.4i | 0.148065 | + | 0.0481094i | ||||
\(658\) | 9921.15 | + | 7208.13i | 0.0229145 | + | 0.0166483i | ||||
\(659\) | 237251.i | 0.546307i | 0.961970 | + | 0.273154i | \(0.0880667\pi\) | ||||
−0.961970 | + | 0.273154i | \(0.911933\pi\) | |||||||
\(660\) | −3321.40 | + | 26031.5i | −0.00762490 | + | 0.0597601i | ||||
\(661\) | 202580. | 0.463655 | 0.231827 | − | 0.972757i | \(-0.425530\pi\) | ||||
0.231827 | + | 0.972757i | \(0.425530\pi\) | |||||||
\(662\) | −71089.4 | + | 97846.2i | −0.162214 | + | 0.223269i | ||||
\(663\) | 210552. | − | 648014.i | 0.478998 | − | 1.47420i | ||||
\(664\) | −138057. | − | 424895.i | −0.313127 | − | 0.963707i | ||||
\(665\) | −47988.7 | + | 34865.8i | −0.108516 | + | 0.0788418i | ||||
\(666\) | 157170. | + | 216326.i | 0.354341 | + | 0.487708i | ||||
\(667\) | −258668. | + | 84046.2i | −0.581420 | + | 0.188915i | ||||
\(668\) | −19082.2 | − | 6200.17i | −0.0427636 | − | 0.0138947i | ||||
\(669\) | −75807.4 | − | 55077.3i | −0.169379 | − | 0.123061i | ||||
\(670\) | − | 664572.i | − | 1.48045i | ||||||
\(671\) | 76687.6 | + | 9784.71i | 0.170326 | + | 0.0217322i | ||||
\(672\) | −76646.8 | −0.169729 | ||||||||
\(673\) | 122108. | − | 168067.i | 0.269596 | − | 0.371066i | −0.652658 | − | 0.757653i | \(-0.726346\pi\) |
0.922253 | + | 0.386587i | \(0.126346\pi\) | |||||||
\(674\) | 243913. | − | 750687.i | 0.536927 | − | 1.65249i | ||||
\(675\) | −71945.5 | − | 221425.i | −0.157905 | − | 0.485982i | ||||
\(676\) | −22658.5 | + | 16462.4i | −0.0495836 | + | 0.0360246i | ||||
\(677\) | 212149. | + | 291998.i | 0.462875 | + | 0.637093i | 0.975102 | − | 0.221758i | \(-0.0711794\pi\) |
−0.512227 | + | 0.858850i | \(0.671179\pi\) | |||||||
\(678\) | −43634.0 | + | 14177.5i | −0.0949217 | + | 0.0308419i | ||||
\(679\) | 589952. | + | 191687.i | 1.27961 | + | 0.415770i | ||||
\(680\) | 386635. | + | 280907.i | 0.836148 | + | 0.607497i | ||||
\(681\) | − | 412189.i | − | 0.888797i | ||||||
\(682\) | 51478.2 | − | 109045.i | 0.110676 | − | 0.234442i | ||||
\(683\) | 310133. | 0.664824 | 0.332412 | − | 0.943134i | \(-0.392138\pi\) | ||||
0.332412 | + | 0.943134i | \(0.392138\pi\) | |||||||
\(684\) | −1689.23 | + | 2325.03i | −0.00361058 | + | 0.00496954i | ||||
\(685\) | 119515. | − | 367830.i | 0.254708 | − | 0.783910i | ||||
\(686\) | −147642. | − | 454396.i | −0.313735 | − | 0.965576i | ||||
\(687\) | −532429. | + | 386832.i | −1.12810 | + | 0.819613i | ||||
\(688\) | 338107. | + | 465365.i | 0.714295 | + | 0.983143i | ||||
\(689\) | 233009. | − | 75709.3i | 0.490834 | − | 0.159482i | ||||
\(690\) | −285863. | − | 92882.4i | −0.600426 | − | 0.195090i | ||||
\(691\) | 27576.4 | + | 20035.5i | 0.0577540 | + | 0.0419607i | 0.616288 | − | 0.787521i | \(-0.288636\pi\) |
−0.558534 | + | 0.829482i | \(0.688636\pi\) | |||||||
\(692\) | − | 1116.81i | − | 0.00233220i | ||||||
\(693\) | −146617. | + | 80366.5i | −0.305294 | + | 0.167343i | ||||
\(694\) | −121857. | −0.253006 | ||||||||
\(695\) | −43562.3 | + | 59958.4i | −0.0901865 | + | 0.124131i | ||||
\(696\) | −69176.6 | + | 212904.i | −0.142804 | + | 0.439506i | ||||
\(697\) | 14268.6 | + | 43914.3i | 0.0293709 | + | 0.0903943i | ||||
\(698\) | −321909. | + | 233880.i | −0.660726 | + | 0.480046i | ||||
\(699\) | 106806. | + | 147005.i | 0.218595 | + | 0.300870i | ||||
\(700\) | 22901.5 | − | 7441.16i | 0.0467378 | − | 0.0151860i | ||||
\(701\) | −154914. | − | 50334.5i | −0.315249 | − | 0.102431i | 0.147119 | − | 0.989119i | \(-0.453000\pi\) |
−0.462368 | + | 0.886688i | \(0.653000\pi\) | |||||||
\(702\) | −576763. | − | 419043.i | −1.17037 | − | 0.850324i | ||||
\(703\) | 150132.i | 0.303782i | ||||||||
\(704\) | −427903. | + | 81075.9i | −0.863375 | + | 0.163586i | ||||
\(705\) | 7717.79 | 0.0155280 | ||||||||
\(706\) | 264082. | − | 363477.i | 0.529821 | − | 0.729236i | ||||
\(707\) | −132150. | + | 406715.i | −0.264380 | + | 0.813677i | ||||
\(708\) | −7103.64 | − | 21862.8i | −0.0141715 | − | 0.0436152i | ||||
\(709\) | −42019.7 | + | 30529.1i | −0.0835912 | + | 0.0607326i | −0.628796 | − | 0.777570i | \(-0.716452\pi\) |
0.545205 | + | 0.838303i | \(0.316452\pi\) | |||||||
\(710\) | 84342.9 | + | 116088.i | 0.167314 | + | 0.230288i | ||||
\(711\) | −99920.2 | + | 32466.0i | −0.197658 | + | 0.0642229i | ||||
\(712\) | −637299. | − | 207071.i | −1.25714 | − | 0.408469i | ||||
\(713\) | 103100. | + | 74906.3i | 0.202805 | + | 0.147346i | ||||
\(714\) | 674745.i | 1.32356i | ||||||||
\(715\) | 343291. | + | 323176.i | 0.671507 | + | 0.632159i | ||||
\(716\) | −22500.3 | −0.0438896 | ||||||||
\(717\) | −144363. | + | 198698.i | −0.280813 | + | 0.386506i | ||||
\(718\) | −87518.6 | + | 269354.i | −0.169766 | + | 0.522487i | ||||
\(719\) | 298239. | + | 917885.i | 0.576908 | + | 1.77554i | 0.629589 | + | 0.776929i | \(0.283223\pi\) |
−0.0526809 | + | 0.998611i | \(0.516777\pi\) | |||||||
\(720\) | 112694. | − | 81876.8i | 0.217388 | − | 0.157941i | ||||
\(721\) | −382327. | − | 526228.i | −0.735470 | − | 1.01229i | ||||
\(722\) | 503726. | − | 163671.i | 0.966319 | − | 0.313976i | ||||
\(723\) | 500157. | + | 162511.i | 0.956818 | + | 0.310889i | ||||
\(724\) | 26868.7 | + | 19521.2i | 0.0512589 | + | 0.0372417i | ||||
\(725\) | − | 148618.i | − | 0.282745i | ||||||
\(726\) | −347528. | + | 286048.i | −0.659350 | + | 0.542708i | ||||
\(727\) | −138074. | −0.261241 | −0.130621 | − | 0.991432i | \(-0.541697\pi\) | ||||
−0.130621 | + | 0.991432i | \(0.541697\pi\) | |||||||
\(728\) | −383035. | + | 527202.i | −0.722729 | + | 0.994751i | ||||
\(729\) | 175866. | − | 541259.i | 0.330922 | − | 1.01847i | ||||
\(730\) | 57989.7 | + | 178474.i | 0.108819 | + | 0.334911i | ||||
\(731\) | 724384. | − | 526296.i | 1.35561 | − | 0.984906i | ||||
\(732\) | −4472.55 | − | 6155.94i | −0.00834705 | − | 0.0114887i | ||||
\(733\) | −512975. | + | 166676.i | −0.954746 | + | 0.310216i | −0.744643 | − | 0.667463i | \(-0.767380\pi\) |
−0.210104 | + | 0.977679i | \(0.567380\pi\) | |||||||
\(734\) | 651580. | + | 211711.i | 1.20942 | + | 0.392963i | ||||
\(735\) | 15765.4 | + | 11454.2i | 0.0291830 | + | 0.0212027i | ||||
\(736\) | 111346.i | 0.205551i | ||||||||
\(737\) | 720930. | − | 765804.i | 1.32727 | − | 1.40988i | ||||
\(738\) | 12205.0 | 0.0224091 | ||||||||
\(739\) | 115460. | − | 158917.i | 0.211419 | − | 0.290993i | −0.690117 | − | 0.723698i | \(-0.742441\pi\) |
0.901536 | + | 0.432705i | \(0.142441\pi\) | |||||||
\(740\) | −21290.4 | + | 65525.0i | −0.0388794 | + | 0.119659i | ||||
\(741\) | −31247.8 | − | 96170.9i | −0.0569093 | − | 0.175149i | ||||
\(742\) | −196285. | + | 142609.i | −0.356516 | + | 0.259024i | ||||
\(743\) | −510591. | − | 702769.i | −0.924902 | − | 1.27302i | −0.961815 | − | 0.273700i | \(-0.911752\pi\) |
0.0369131 | − | 0.999318i | \(-0.488248\pi\) | |||||||
\(744\) | 99757.8 | − | 32413.3i | 0.180219 | − | 0.0585568i | ||||
\(745\) | −311714. | − | 101282.i | −0.561621 | − | 0.182482i | ||||
\(746\) | 427062. | + | 310278.i | 0.767384 | + | 0.557537i | ||||
\(747\) | 202698.i | 0.363252i | ||||||||
\(748\) | −15931.7 | − | 84084.5i | −0.0284747 | − | 0.150284i | ||||
\(749\) | −162581. | −0.289805 | ||||||||
\(750\) | 302212. | − | 415960.i | 0.537266 | − | 0.739484i | ||||
\(751\) | −213891. | + | 658290.i | −0.379239 | + | 1.16718i | 0.561335 | + | 0.827589i | \(0.310288\pi\) |
−0.940574 | + | 0.339589i | \(0.889712\pi\) | |||||||
\(752\) | −4996.54 | − | 15377.8i | −0.00883556 | − | 0.0271931i | ||||
\(753\) | 285177. | − | 207193.i | 0.502950 | − | 0.365415i | ||||
\(754\) | −267491. | − | 368169.i | −0.470507 | − | 0.647597i | ||||
\(755\) | −152938. | + | 49692.5i | −0.268300 | + | 0.0871761i | ||||
\(756\) | 61953.9 | + | 20130.0i | 0.108399 | + | 0.0352209i | ||||
\(757\) | −61422.9 | − | 44626.4i | −0.107186 | − | 0.0778753i | 0.532901 | − | 0.846178i | \(-0.321102\pi\) |
−0.640087 | + | 0.768302i | \(0.721102\pi\) | |||||||
\(758\) | − | 405043.i | − | 0.704957i | ||||||
\(759\) | −228648. | − | 417135.i | −0.396902 | − | 0.724092i | ||||
\(760\) | 70925.6 | 0.122794 | ||||||||
\(761\) | 327846. | − | 451241.i | 0.566109 | − | 0.779182i | −0.425978 | − | 0.904733i | \(-0.640070\pi\) |
0.992087 | + | 0.125551i | \(0.0400700\pi\) | |||||||
\(762\) | −165050. | + | 507971.i | −0.284253 | + | 0.874841i | ||||
\(763\) | 219752. | + | 676328.i | 0.377472 | + | 1.16174i | ||||
\(764\) | −9648.24 | + | 7009.85i | −0.0165296 | + | 0.0120094i | ||||
\(765\) | −127449. | − | 175418.i | −0.217778 | − | 0.299745i | ||||
\(766\) | −610482. | + | 198358.i | −1.04044 | + | 0.338058i | ||||
\(767\) | −392790. | − | 127625.i | −0.667682 | − | 0.216943i | ||||
\(768\) | 117212. | + | 85159.5i | 0.198724 | + | 0.144381i | ||||
\(769\) | − | 113451.i | − | 0.191848i | −0.995389 | − | 0.0959239i | \(-0.969419\pi\) | ||
0.995389 | − | 0.0959239i | \(-0.0305805\pi\) | |||||||
\(770\) | −422215. | − | 199321.i | −0.712119 | − | 0.336179i | ||||
\(771\) | −184800. | −0.310880 | ||||||||
\(772\) | 34398.1 | − | 47344.9i | 0.0577165 | − | 0.0794399i | ||||
\(773\) | −120125. | + | 369706.i | −0.201036 | + | 0.618724i | 0.798817 | + | 0.601574i | \(0.205459\pi\) |
−0.999853 | + | 0.0171505i | \(0.994541\pi\) | |||||||
\(774\) | −73136.0 | − | 225089.i | −0.122081 | − | 0.375728i | ||||
\(775\) | −56336.9 | + | 40931.2i | −0.0937971 | + | 0.0681476i | ||||
\(776\) | −435965. | − | 600054.i | −0.723982 | − | 0.996476i | ||||
\(777\) | 817609. | − | 265657.i | 1.35427 | − | 0.440028i | ||||
\(778\) | 139583. | + | 45353.2i | 0.230607 | + | 0.0749289i | ||||
\(779\) | 5543.92 | + | 4027.90i | 0.00913571 | + | 0.00663748i | ||||
\(780\) | − | 46405.1i | − | 0.0762740i | ||||||
\(781\) | −28742.2 | + | 225267.i | −0.0471214 | + | 0.369313i | ||||
\(782\) | 980213. | 1.60290 | ||||||||
\(783\) | 236316. | − | 325262.i | 0.385452 | − | 0.530529i | ||||
\(784\) | 12616.0 | − | 38828.2i | 0.0205254 | − | 0.0631706i | ||||
\(785\) | 109088. | + | 335738.i | 0.177026 | + | 0.544830i | ||||
\(786\) | 456945. | − | 331990.i | 0.739637 | − | 0.537377i | ||||
\(787\) | 190393. | + | 262053.i | 0.307398 | + | 0.423097i | 0.934568 | − | 0.355786i | \(-0.115787\pi\) |
−0.627169 | + | 0.778883i | \(0.715787\pi\) | |||||||
\(788\) | −61347.8 | + | 19933.1i | −0.0987976 | + | 0.0321013i | ||||
\(789\) | −513821. | − | 166951.i | −0.825388 | − | 0.268185i | ||||
\(790\) | −237353. | − | 172447.i | −0.380312 | − | 0.276313i | ||||
\(791\) | − | 75317.6i | − | 0.120377i | ||||||
\(792\) | 198312. | + | 25302.9i | 0.316153 | + | 0.0403386i | ||||
\(793\) | −136707. | −0.217393 | ||||||||
\(794\) | −50483.2 | + | 69484.2i | −0.0800767 | + | 0.110216i | ||||
\(795\) | −47184.6 | + | 145219.i | −0.0746562 | + | 0.229768i | ||||
\(796\) | −4516.11 | − | 13899.2i | −0.00712752 | − | 0.0219362i | ||||
\(797\) | −561981. | + | 408303.i | −0.884718 | + | 0.642785i | −0.934495 | − | 0.355975i | \(-0.884149\pi\) |
0.0497774 | + | 0.998760i | \(0.484149\pi\) | |||||||
\(798\) | 58859.7 | + | 81013.4i | 0.0924298 | + | 0.127219i | ||||
\(799\) | −23936.9 | + | 7777.58i | −0.0374952 | + | 0.0121829i | ||||
\(800\) | −57865.1 | − | 18801.5i | −0.0904142 | − | 0.0293774i | ||||
\(801\) | 245962. | + | 178702.i | 0.383357 | + | 0.278525i | ||||
\(802\) | 798039.i | 1.24073i | ||||||||
\(803\) | −126786. | + | 268567.i | −0.196626 | + | 0.416507i | ||||
\(804\) | −103519. | −0.160143 | ||||||||
\(805\) | 290033. | − | 399196.i | 0.447565 | − | 0.616020i | ||||
\(806\) | −65892.6 | + | 202796.i | −0.101430 | + | 0.312169i | ||||
\(807\) | 320016. | + | 984909.i | 0.491388 | + | 1.51234i | ||||
\(808\) | 413679. | − | 300556.i | 0.633638 | − | 0.460365i | ||||
\(809\) | −334920. | − | 460978.i | −0.511734 | − | 0.704341i | 0.472477 | − | 0.881343i | \(-0.343360\pi\) |
−0.984211 | + | 0.177002i | \(0.943360\pi\) | |||||||
\(810\) | 261309. | − | 84904.5i | 0.398276 | − | 0.129408i | ||||
\(811\) | 115629. | + | 37570.0i | 0.175802 | + | 0.0571215i | 0.395595 | − | 0.918425i | \(-0.370538\pi\) |
−0.219793 | + | 0.975546i | \(0.570538\pi\) | |||||||
\(812\) | 33641.1 | + | 24441.7i | 0.0510220 | + | 0.0370697i | ||||
\(813\) | 745610.i | 1.12806i | ||||||||
\(814\) | −1.03625e6 | + | 568011.i | −1.56393 | + | 0.857250i | ||||
\(815\) | 83002.2 | 0.124961 | ||||||||
\(816\) | 522928. | − | 719748.i | 0.785346 | − | 1.08094i | ||||
\(817\) | 41063.2 | − | 126380.i | 0.0615189 | − | 0.189336i | ||||
\(818\) | −244516. | − | 752542.i | −0.365427 | − | 1.12467i | ||||
\(819\) | 239194. | − | 173785.i | 0.356602 | − | 0.259086i | ||||
\(820\) | 1848.45 | + | 2544.17i | 0.00274903 | + | 0.00378371i | ||||
\(821\) | −603167. | + | 195981.i | −0.894853 | + | 0.290755i | −0.720111 | − | 0.693859i | \(-0.755909\pi\) |
−0.174742 | + | 0.984614i | \(0.555909\pi\) | |||||||
\(822\) | −620962. | − | 201763.i | −0.919013 | − | 0.298605i | ||||
\(823\) | −87568.3 | − | 63622.1i | −0.129285 | − | 0.0939309i | 0.521264 | − | 0.853396i | \(-0.325461\pi\) |
−0.650548 | + | 0.759465i | \(0.725461\pi\) | |||||||
\(824\) | 777747.i | 1.14547i | ||||||||
\(825\) | 255389. | − | 48389.2i | 0.375227 | − | 0.0710953i | ||||
\(826\) | 408993. | 0.599454 | ||||||||
\(827\) | 186226. | − | 256318.i | 0.272288 | − | 0.374773i | −0.650872 | − | 0.759187i | \(-0.725597\pi\) |
0.923161 | + | 0.384414i | \(0.125597\pi\) | |||||||
\(828\) | 7387.55 | − | 22736.6i | 0.0107756 | − | 0.0331638i | ||||
\(829\) | 251882. | + | 775214.i | 0.366512 | + | 1.12801i | 0.949029 | + | 0.315190i | \(0.102068\pi\) |
−0.582516 | + | 0.812819i | \(0.697932\pi\) | |||||||
\(830\) | −457927. | + | 332704.i | −0.664722 | + | 0.482949i | ||||
\(831\) | 116577. | + | 160454.i | 0.168815 | + | 0.232354i | ||||
\(832\) | 732437. | − | 237983.i | 1.05809 | − | 0.343795i | ||||
\(833\) | −60439.7 | − | 19638.0i | −0.0871028 | − | 0.0283014i | ||||
\(834\) | 101220. | + | 73540.9i | 0.145524 | + | 0.105730i | ||||
\(835\) | − | 224661.i | − | 0.322222i | ||||||
\(836\) | −9247.74 | − | 8705.86i | −0.0132319 | − | 0.0124566i | ||||
\(837\) | −188382. | −0.268898 | ||||||||
\(838\) | 84731.6 | − | 116623.i | 0.120658 | − | 0.166072i | ||||
\(839\) | 80718.2 | − | 248425.i | 0.114669 | − | 0.352916i | −0.877208 | − | 0.480110i | \(-0.840597\pi\) |
0.991878 | + | 0.127193i | \(0.0405969\pi\) | |||||||
\(840\) | −125502. | − | 386257.i | −0.177866 | − | 0.547416i | ||||
\(841\) | −364576. | + | 264880.i | −0.515461 | + | 0.374504i | ||||
\(842\) | 649195. | + | 893540.i | 0.915695 | + | 1.26035i | ||||
\(843\) | −923830. | + | 300171.i | −1.29998 | + | 0.422389i | ||||
\(844\) | −10898.2 | − | 3541.03i | −0.0152992 | − | 0.00497101i | ||||
\(845\) | −253710. | − | 184331.i | −0.355324 | − | 0.258158i | ||||
\(846\) | 6652.73i | 0.00929521i | ||||||||
\(847\) | −270306. | − | 687703.i | −0.376781 | − | 0.958593i | ||||
\(848\) | 319898. | 0.444857 | ||||||||
\(849\) | −362415. | + | 498821.i | −0.502794 | + | 0.692037i | ||||
\(850\) | −165515. | + | 509404.i | −0.229087 | + | 0.705057i | ||||
\(851\) | −385925. | − | 1.18775e6i | −0.532897 | − | 1.64009i | ||||
\(852\) | 18082.8 | − | 13137.9i | 0.0249108 | − | 0.0180987i | ||||
\(853\) | −494677. | − | 680864.i | −0.679866 | − | 0.935756i | 0.320066 | − | 0.947395i | \(-0.396295\pi\) |
−0.999932 | + | 0.0116396i | \(0.996295\pi\) | |||||||
\(854\) | 128754. | − | 41834.7i | 0.176541 | − | 0.0573615i | ||||
\(855\) | −30604.3 | − | 9943.96i | −0.0418650 | − | 0.0136028i | ||||
\(856\) | 157271. | + | 114264.i | 0.214635 | + | 0.155942i | ||||
\(857\) | − | 93389.0i | − | 0.127155i | −0.997977 | − | 0.0635776i | \(-0.979749\pi\) | ||
0.997977 | − | 0.0635776i | \(-0.0202510\pi\) | |||||||
\(858\) | 545578. | − | 579536.i | 0.741109 | − | 0.787238i | ||||
\(859\) | 1.16761e6 | 1.58238 | 0.791190 | − | 0.611571i | \(-0.209462\pi\) | ||||
0.791190 | + | 0.611571i | \(0.209462\pi\) | |||||||
\(860\) | 35844.1 | − | 49335.2i | 0.0484642 | − | 0.0667052i | ||||
\(861\) | 12125.8 | − | 37319.3i | 0.0163570 | − | 0.0503416i | ||||
\(862\) | −283994. | − | 874044.i | −0.382204 | − | 1.17630i | ||||
\(863\) | 763401. | − | 554643.i | 1.02502 | − | 0.744718i | 0.0577115 | − | 0.998333i | \(-0.481620\pi\) |
0.967305 | + | 0.253615i | \(0.0816197\pi\) | |||||||
\(864\) | −96746.0 | − | 133159.i | −0.129600 | − | 0.178379i | ||||
\(865\) | 11893.0 | − | 3864.27i | 0.0158949 | − | 0.00516458i | ||||
\(866\) | −277428. | − | 90141.8i | −0.369926 | − | 0.120196i | ||||
\(867\) | −625566. | − | 454500.i | −0.832214 | − | 0.604639i | ||||
\(868\) | − | 19483.9i | − | 0.0258605i | ||||||
\(869\) | −86436.8 | − | 456196.i | −0.114461 | − | 0.604105i | ||||
\(870\) | 283622. | 0.374716 | ||||||||
\(871\) | −1.09319e6 | + | 1.50465e6i | −1.44098 | + | 1.98334i | ||||
\(872\) | 262758. | − | 808684.i | 0.345559 | − | 1.06352i | ||||
\(873\) | 103989. | + | 320046.i | 0.136446 | + | 0.419937i | ||||
\(874\) | 117689. | − | 85506.4i | 0.154069 | − | 0.111937i | ||||
\(875\) | 496124. | + | 682856.i | 0.647998 | + | 0.891893i | ||||
\(876\) | 27800.5 | − | 9032.94i | 0.0362280 | − | 0.0117712i | ||||
\(877\) | 982991. | + | 319393.i | 1.27806 | + | 0.415266i | 0.867895 | − | 0.496747i | \(-0.165472\pi\) |
0.410162 | + | 0.912013i | \(0.365472\pi\) | |||||||
\(878\) | 244570. | + | 177691.i | 0.317260 | + | 0.230503i | ||||
\(879\) | − | 883568.i | − | 1.14357i | ||||||
\(880\) | 295902. | + | 539832.i | 0.382105 | + | 0.697097i | ||||
\(881\) | 609739. | 0.785584 | 0.392792 | − | 0.919627i | \(-0.371509\pi\) | ||||
0.392792 | + | 0.919627i | \(0.371509\pi\) | |||||||
\(882\) | −9873.52 | + | 13589.7i | −0.0126921 | + | 0.0174692i | ||||
\(883\) | 96058.9 | − | 295639.i | 0.123202 | − | 0.379175i | −0.870368 | − | 0.492403i | \(-0.836119\pi\) |
0.993569 | + | 0.113227i | \(0.0361188\pi\) | |||||||
\(884\) | 46764.6 | + | 143927.i | 0.0598430 | + | 0.184178i | ||||
\(885\) | 208239. | − | 151295.i | 0.265874 | − | 0.193169i | ||||
\(886\) | −110204. | − | 151683.i | −0.140388 | − | 0.193228i | ||||
\(887\) | −249889. | + | 81194.0i | −0.317615 | + | 0.103199i | −0.463486 | − | 0.886104i | \(-0.653402\pi\) |
0.145871 | + | 0.989304i | \(0.453402\pi\) | |||||||
\(888\) | −977614. | − | 317646.i | −1.23977 | − | 0.402826i | ||||
\(889\) | −709362. | − | 515382.i | −0.897562 | − | 0.652117i | ||||
\(890\) | 848986.i | 1.07182i | ||||||||
\(891\) | 393218. | + | 185631.i | 0.495311 | + | 0.233828i | ||||
\(892\) | 20811.9 | 0.0261566 | ||||||||
\(893\) | −2195.54 | + | 3021.90i | −0.00275320 | + | 0.00378945i | ||||
\(894\) | −170982. | + | 526228.i | −0.213932 | + | 0.658413i | ||||
\(895\) | −77853.1 | − | 239607.i | −0.0971919 | − | 0.299126i | ||||
\(896\) | −752487. | + | 546714.i | −0.937310 | + | 0.680995i | ||||
\(897\) | 494429. | + | 680523.i | 0.614496 | + | 0.845781i | ||||
\(898\) | 516455. | − | 167806.i | 0.640442 | − | 0.208092i | ||||
\(899\) | −114366. | − | 37159.6i | −0.141506 | − | 0.0459782i | ||||
\(900\) | 10568.5 | + | 7678.44i | 0.0130475 | + | 0.00947955i | ||||
\(901\) | − | 497951.i | − | 0.613391i | ||||||
\(902\) | −6826.81 | + | 53505.1i | −0.00839082 | + | 0.0657630i | ||||
\(903\) | −760918. | −0.933173 | ||||||||
\(904\) | −52934.3 | + | 72857.8i | −0.0647739 | + | 0.0891536i | ||||
\(905\) | −114915. | + | 353672.i | −0.140307 | + | 0.431821i | ||||
\(906\) | 83889.8 | + | 258186.i | 0.102200 | + | 0.314541i | ||||
\(907\) | −228786. | + | 166222.i | −0.278108 | + | 0.202058i | −0.718092 | − | 0.695948i | \(-0.754984\pi\) |
0.439984 | + | 0.898006i | \(0.354984\pi\) | |||||||
\(908\) | 53811.2 | + | 74064.8i | 0.0652681 | + | 0.0898338i | ||||
\(909\) | −220641. | + | 71690.6i | −0.267029 | + | 0.0867630i | ||||
\(910\) | 785217. | + | 255132.i | 0.948215 | + | 0.308094i | ||||
\(911\) | 1.12857e6 | + | 819956.i | 1.35985 | + | 0.987992i | 0.998454 | + | 0.0555816i | \(0.0177013\pi\) |
0.361401 | + | 0.932411i | \(0.382299\pi\) | |||||||
\(912\) | − | 132033.i | − | 0.158742i | ||||||
\(913\) | −888599. | − | 113378.i | −1.06602 | − | 0.136015i | ||||
\(914\) | −1.28842e6 | −1.54228 | ||||||||
\(915\) | 50079.7 | − | 68928.7i | 0.0598163 | − | 0.0823300i | ||||
\(916\) | 45169.3 | − | 139017.i | 0.0538335 | − | 0.165682i | ||||
\(917\) | 286527. | + | 881840.i | 0.340743 | + | 1.04870i | ||||
\(918\) | −1.17224e6 | + | 851684.i | −1.39102 | + | 1.01063i | ||||
\(919\) | −85147.5 | − | 117196.i | −0.100819 | − | 0.138765i | 0.755627 | − | 0.655002i | \(-0.227332\pi\) |
−0.856446 | + | 0.516237i | \(0.827332\pi\) | |||||||
\(920\) | −561122. | + | 182319.i | −0.662951 | + | 0.215406i | ||||
\(921\) | 909419. | + | 295488.i | 1.07212 | + | 0.348354i | ||||
\(922\) | −77491.6 | − | 56301.0i | −0.0911576 | − | 0.0662299i | ||||
\(923\) | − | 401573.i | − | 0.471369i | ||||||
\(924\) | −31047.8 | + | 65767.7i | −0.0363653 | + | 0.0770316i | ||||
\(925\) | 682427. | 0.797577 | ||||||||
\(926\) | −611859. | + | 842151.i | −0.713558 | + | 0.982128i | ||||
\(927\) | 109042. | − | 335597.i | 0.126892 | − | 0.390534i | ||||
\(928\) | −32467.3 | − | 99924.2i | −0.0377008 | − | 0.116031i | ||||
\(929\) | −562289. | + | 408527.i | −0.651521 | + | 0.473358i | −0.863789 | − | 0.503854i | \(-0.831915\pi\) |
0.212268 | + | 0.977211i | \(0.431915\pi\) | |||||||
\(930\) | −78113.0 | − | 107513.i | −0.0903145 | − | 0.124307i | ||||
\(931\) | −8969.78 | + | 2914.46i | −0.0103486 | + | 0.00336247i | ||||
\(932\) | −38383.0 | − | 12471.4i | −0.0441883 | − | 0.0143576i | ||||
\(933\) | 585138. | + | 425128.i | 0.672195 | + | 0.488378i | ||||
\(934\) | − | 1.35611e6i | − | 1.55453i | ||||||
\(935\) | 840298. | − | 460599.i | 0.961192 | − | 0.526866i | ||||
\(936\) | −353521. | −0.403518 | ||||||||
\(937\) | 647243. | − | 890854.i | 0.737205 | − | 1.01468i | −0.261569 | − | 0.965185i | \(-0.584240\pi\) |
0.998775 | − | 0.0494911i | \(-0.0157599\pi\) | |||||||
\(938\) | 569142. | − | 1.75164e6i | 0.646867 | − | 1.99085i | ||||
\(939\) | −142120. | − | 437402.i | −0.161185 | − | 0.496077i | ||||
\(940\) | −1386.78 | + | 1007.56i | −0.00156947 | + | 0.00114028i | ||||
\(941\) | 497946. | + | 685364.i | 0.562345 | + | 0.774002i | 0.991622 | − | 0.129171i | \(-0.0412316\pi\) |
−0.429277 | + | 0.903173i | \(0.641232\pi\) | |||||||
\(942\) | 566785. | − | 184160.i | 0.638728 | − | 0.207535i | ||||
\(943\) | −54214.3 | − | 17615.3i | −0.0609664 | − | 0.0198092i | ||||
\(944\) | −436271. | − | 316970.i | −0.489568 | − | 0.355692i | ||||
\(945\) | 729405.i | 0.816780i | ||||||||
\(946\) | 1.02767e6 | − | 194715.i | 1.14834 | − | 0.217580i | ||||
\(947\) | −1.75534e6 | −1.95732 | −0.978660 | − | 0.205486i | \(-0.934122\pi\) | ||||
−0.978660 | + | 0.205486i | \(0.934122\pi\) | |||||||
\(948\) | −26861.7 | + | 36972.0i | −0.0298894 | + | 0.0411393i | ||||
\(949\) | 162287. | − | 499469.i | 0.180199 | − | 0.554595i | ||||
\(950\) | 24563.9 | + | 75600.0i | 0.0272177 | + | 0.0837673i | ||||
\(951\) | 116564. | − | 84688.7i | 0.128885 | − | 0.0936406i | ||||
\(952\) | 778499. | + | 1.07151e6i | 0.858982 | + | 1.18229i | ||||
\(953\) | 363486. | − | 118104.i | 0.400222 | − | 0.130040i | −0.101988 | − | 0.994786i | \(-0.532520\pi\) |
0.502210 | + | 0.864746i | \(0.332520\pi\) | |||||||
\(954\) | −125179. | − | 40673.1i | −0.137542 | − | 0.0446900i | ||||
\(955\) | −108032. | − | 78490.2i | −0.118453 | − | 0.0860614i | ||||
\(956\) | − | 54549.9i | − | 0.0596868i | ||||||
\(957\) | 326825. | + | 307675.i | 0.356855 | + | 0.335945i | ||||
\(958\) | −421164. | −0.458902 | ||||||||
\(959\) | 630021. | − | 867150.i | 0.685043 | − | 0.942881i | ||||
\(960\) | −148319. | + | 456479.i | −0.160937 | + | 0.495312i | ||||
\(961\) | −267972. | − | 824734.i | −0.290164 | − | 0.893032i | ||||
\(962\) | 1.69057e6 | − | 1.22827e6i | 1.82676 | − | 1.32722i | ||||
\(963\) | −51842.2 | − | 71354.7i | −0.0559024 | − | 0.0769431i | ||||
\(964\) | −111087. | + | 36094.4i | −0.119539 | + | 0.0388405i | ||||
\(965\) | 623201. | + | 202490.i | 0.669227 | + | 0.217445i | ||||
\(966\) | −673914. | − | 489627.i | −0.722188 | − | 0.524700i | ||||
\(967\) | − | 1.17380e6i | − | 1.25528i | −0.778505 | − | 0.627639i | \(-0.784021\pi\) | ||
0.778505 | − | 0.627639i | \(-0.215979\pi\) | |||||||
\(968\) | −221849. | + | 855218.i | −0.236759 | + | 0.912696i | ||||
\(969\) | −205521. | −0.218882 | ||||||||
\(970\) | −552351. | + | 760246.i | −0.587045 | + | 0.807999i | ||||
\(971\) | 38552.4 | − | 118652.i | 0.0408897 | − | 0.125845i | −0.928528 | − | 0.371263i | \(-0.878925\pi\) |
0.969418 | + | 0.245417i | \(0.0789250\pi\) | |||||||
\(972\) | 19082.1 | + | 58728.7i | 0.0201973 | + | 0.0621610i | ||||
\(973\) | −166167. | + | 120728.i | −0.175517 | + | 0.127521i | ||||
\(974\) | −906520. | − | 1.24772e6i | −0.955563 | − | 1.31522i | ||||
\(975\) | −437147. | + | 142038.i | −0.459852 | + | 0.149415i | ||||
\(976\) | −169763. | − | 55159.4i | −0.178215 | − | 0.0579055i | ||||
\(977\) | −326932. | − | 237530.i | −0.342506 | − | 0.248845i | 0.403213 | − | 0.915106i | \(-0.367894\pi\) |
−0.745718 | + | 0.666261i | \(0.767894\pi\) | |||||||
\(978\) | − | 140122.i | − | 0.146497i | ||||||
\(979\) | −920983. | + | 978309.i | −0.960918 | + | 1.02073i | ||||
\(980\) | −4328.17 | −0.00450663 | ||||||||
\(981\) | −226760. | + | 312108.i | −0.235628 | + | 0.324315i | ||||
\(982\) | −290459. | + | 893941.i | −0.301205 | + | 0.927013i | ||||
\(983\) | 136988. | + | 421605.i | 0.141767 | + | 0.436314i | 0.996581 | − | 0.0826204i | \(-0.0263289\pi\) |
−0.854814 | + | 0.518934i | \(0.826329\pi\) | |||||||
\(984\) | −37958.2 | + | 27578.3i | −0.0392027 | + | 0.0284824i | ||||
\(985\) | −424539. | − | 584328.i | −0.437567 | − | 0.602260i | ||||
\(986\) | −879663. | + | 285820.i | −0.904821 | + | 0.293994i | ||||
\(987\) | 20342.1 | + | 6609.54i | 0.0208815 | + | 0.00678480i | ||||
\(988\) | 18169.9 | + | 13201.2i | 0.0186139 | + | 0.0135238i | ||||
\(989\) | 1.10540e6i | 1.13012i | ||||||||
\(990\) | −47152.7 | − | 248863.i | −0.0481101 | − | 0.253916i | ||||
\(991\) | −790967. | −0.805399 | −0.402699 | − | 0.915332i | \(-0.631928\pi\) | ||||
−0.402699 | + | 0.915332i | \(0.631928\pi\) | |||||||
\(992\) | −28936.6 | + | 39827.8i | −0.0294052 | + | 0.0404728i | ||||
\(993\) | −65185.9 | + | 200621.i | −0.0661081 | + | 0.203460i | ||||
\(994\) | 122888. | + | 378209.i | 0.124376 | + | 0.382789i | ||||
\(995\) | 132387. | − | 96184.9i | 0.133721 | − | 0.0971541i | ||||
\(996\) | 51824.6 | + | 71330.4i | 0.0522417 | + | 0.0719045i | ||||
\(997\) | 1.29408e6 | − | 420473.i | 1.30188 | − | 0.423007i | 0.425646 | − | 0.904890i | \(-0.360047\pi\) |
0.876236 | + | 0.481883i | \(0.160047\pi\) | |||||||
\(998\) | 1.65855e6 | + | 538896.i | 1.66521 | + | 0.541058i | ||||
\(999\) | 1.49354e6 | + | 1.08512e6i | 1.49653 | + | 1.08730i |
(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 | 11.5.d.a.7.1 | ✓ | 12 | |
3.2 | odd | 2 | 99.5.k.a.73.3 | 12 | |||
4.3 | odd | 2 | 176.5.n.a.161.2 | 12 | |||
11.2 | odd | 10 | 121.5.d.e.94.1 | 12 | |||
11.3 | even | 5 | 121.5.d.d.118.3 | 12 | |||
11.4 | even | 5 | 121.5.d.e.112.1 | 12 | |||
11.5 | even | 5 | 121.5.b.b.120.3 | 12 | |||
11.6 | odd | 10 | 121.5.b.b.120.10 | 12 | |||
11.7 | odd | 10 | 121.5.d.c.112.3 | 12 | |||
11.8 | odd | 10 | inner | 11.5.d.a.8.1 | yes | 12 | |
11.9 | even | 5 | 121.5.d.c.94.3 | 12 | |||
11.10 | odd | 2 | 121.5.d.d.40.3 | 12 | |||
33.8 | even | 10 | 99.5.k.a.19.3 | 12 | |||
44.19 | even | 10 | 176.5.n.a.129.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
11.5.d.a.7.1 | ✓ | 12 | 1.1 | even | 1 | trivial | |
11.5.d.a.8.1 | yes | 12 | 11.8 | odd | 10 | inner | |
99.5.k.a.19.3 | 12 | 33.8 | even | 10 | |||
99.5.k.a.73.3 | 12 | 3.2 | odd | 2 | |||
121.5.b.b.120.3 | 12 | 11.5 | even | 5 | |||
121.5.b.b.120.10 | 12 | 11.6 | odd | 10 | |||
121.5.d.c.94.3 | 12 | 11.9 | even | 5 | |||
121.5.d.c.112.3 | 12 | 11.7 | odd | 10 | |||
121.5.d.d.40.3 | 12 | 11.10 | odd | 2 | |||
121.5.d.d.118.3 | 12 | 11.3 | even | 5 | |||
121.5.d.e.94.1 | 12 | 11.2 | odd | 10 | |||
121.5.d.e.112.1 | 12 | 11.4 | even | 5 | |||
176.5.n.a.129.2 | 12 | 44.19 | even | 10 | |||
176.5.n.a.161.2 | 12 | 4.3 | odd | 2 |