Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [385,2,Mod(221,385)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(385, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("385.221");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 385 = 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 385.i (of order \(3\), 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: | \(3.07424047782\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} + 13 x^{10} - 12 x^{9} + 49 x^{8} - 38 x^{7} + 136 x^{6} - 34 x^{5} + 113 x^{4} - 72 x^{3} + 58 x^{2} - 16 x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 221.3 | ||
Root | \(0.271923 + 0.470985i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 385.221 |
Dual form | 385.2.i.b.331.3 |
$q$-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 \(\left(\mathbb{Z}/385\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(276\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.228077 | + | 0.395041i | 0.161275 | + | 0.279336i | 0.935326 | − | 0.353787i | \(-0.115106\pi\) |
−0.774051 | + | 0.633123i | \(0.781773\pi\) | |||||||
\(3\) | 0.0572064 | − | 0.0990845i | 0.0330282 | − | 0.0572064i | −0.849039 | − | 0.528330i | \(-0.822818\pi\) |
0.882067 | + | 0.471124i | \(0.156152\pi\) | |||||||
\(4\) | 0.895962 | − | 1.55185i | 0.447981 | − | 0.775926i | ||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0.0521899 | 0.0213064 | ||||||||
\(7\) | −1.96234 | − | 1.77460i | −0.741696 | − | 0.670736i | ||||
\(8\) | 1.72970 | 0.611542 | ||||||||
\(9\) | 1.49345 | + | 2.58674i | 0.497818 | + | 0.862247i | ||||
\(10\) | −0.228077 | + | 0.395041i | −0.0721243 | + | 0.124923i | ||||
\(11\) | 0.500000 | − | 0.866025i | 0.150756 | − | 0.261116i | ||||
\(12\) | −0.102510 | − | 0.177552i | −0.0295920 | − | 0.0512548i | ||||
\(13\) | 4.50529 | 1.24954 | 0.624771 | − | 0.780808i | \(-0.285192\pi\) | ||||
0.624771 | + | 0.780808i | \(0.285192\pi\) | |||||||
\(14\) | 0.253475 | − | 1.17995i | 0.0677439 | − | 0.315355i | ||||
\(15\) | 0.114413 | 0.0295413 | ||||||||
\(16\) | −1.39742 | − | 2.42040i | −0.349355 | − | 0.605100i | ||||
\(17\) | 2.20225 | − | 3.81441i | 0.534125 | − | 0.925131i | −0.465081 | − | 0.885268i | \(-0.653975\pi\) |
0.999205 | − | 0.0398625i | \(-0.0126920\pi\) | |||||||
\(18\) | −0.681245 | + | 1.17995i | −0.160571 | + | 0.278117i | ||||
\(19\) | 1.37904 | + | 2.38857i | 0.316374 | + | 0.547976i | 0.979729 | − | 0.200329i | \(-0.0642012\pi\) |
−0.663355 | + | 0.748305i | \(0.730868\pi\) | |||||||
\(20\) | 1.79192 | 0.400686 | ||||||||
\(21\) | −0.288094 | + | 0.0929191i | −0.0628673 | + | 0.0202766i | ||||
\(22\) | 0.456154 | 0.0972523 | ||||||||
\(23\) | −4.31975 | − | 7.48202i | −0.900729 | − | 1.56011i | −0.826550 | − | 0.562864i | \(-0.809700\pi\) |
−0.0741796 | − | 0.997245i | \(-0.523634\pi\) | |||||||
\(24\) | 0.0989500 | − | 0.171386i | 0.0201981 | − | 0.0349841i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 1.02755 | + | 1.77977i | 0.201520 | + | 0.349042i | ||||
\(27\) | 0.684980 | 0.131824 | ||||||||
\(28\) | −4.51210 | + | 1.45529i | −0.852707 | + | 0.275024i | ||||
\(29\) | 4.71355 | 0.875285 | 0.437642 | − | 0.899149i | \(-0.355814\pi\) | ||||
0.437642 | + | 0.899149i | \(0.355814\pi\) | |||||||
\(30\) | 0.0260949 | + | 0.0451978i | 0.00476426 | + | 0.00825195i | ||||
\(31\) | −5.12634 | + | 8.87908i | −0.920718 | + | 1.59473i | −0.122411 | + | 0.992480i | \(0.539062\pi\) |
−0.798307 | + | 0.602250i | \(0.794271\pi\) | |||||||
\(32\) | 2.36714 | − | 4.10000i | 0.418455 | − | 0.724785i | ||||
\(33\) | −0.0572064 | − | 0.0990845i | −0.00995836 | − | 0.0172484i | ||||
\(34\) | 2.00913 | 0.344563 | ||||||||
\(35\) | 0.555678 | − | 2.58674i | 0.0939267 | − | 0.437239i | ||||
\(36\) | 5.35231 | 0.892052 | ||||||||
\(37\) | 1.13479 | + | 1.96552i | 0.186559 | + | 0.323130i | 0.944101 | − | 0.329657i | \(-0.106933\pi\) |
−0.757542 | + | 0.652787i | \(0.773600\pi\) | |||||||
\(38\) | −0.629055 | + | 1.08956i | −0.102046 | + | 0.176749i | ||||
\(39\) | 0.257731 | − | 0.446404i | 0.0412701 | − | 0.0714818i | ||||
\(40\) | 0.864850 | + | 1.49796i | 0.136745 | + | 0.236849i | ||||
\(41\) | −1.26433 | −0.197455 | −0.0987274 | − | 0.995115i | \(-0.531477\pi\) | ||||
−0.0987274 | + | 0.995115i | \(0.531477\pi\) | |||||||
\(42\) | −0.102414 | − | 0.0926162i | −0.0158029 | − | 0.0142910i | ||||
\(43\) | −10.4536 | −1.59416 | −0.797082 | − | 0.603871i | \(-0.793624\pi\) | ||||
−0.797082 | + | 0.603871i | \(0.793624\pi\) | |||||||
\(44\) | −0.895962 | − | 1.55185i | −0.135071 | − | 0.233950i | ||||
\(45\) | −1.49345 | + | 2.58674i | −0.222631 | + | 0.385608i | ||||
\(46\) | 1.97047 | − | 3.41295i | 0.290530 | − | 0.503212i | ||||
\(47\) | 5.76655 | + | 9.98796i | 0.841138 | + | 1.45689i | 0.888934 | + | 0.458036i | \(0.151447\pi\) |
−0.0477959 | + | 0.998857i | \(0.515220\pi\) | |||||||
\(48\) | −0.319765 | −0.0461542 | ||||||||
\(49\) | 0.701583 | + | 6.96475i | 0.100226 | + | 0.994965i | ||||
\(50\) | −0.456154 | −0.0645099 | ||||||||
\(51\) | −0.251966 | − | 0.436418i | −0.0352823 | − | 0.0611107i | ||||
\(52\) | 4.03656 | − | 6.99154i | 0.559771 | − | 0.969551i | ||||
\(53\) | 2.86987 | − | 4.97076i | 0.394207 | − | 0.682786i | −0.598793 | − | 0.800904i | \(-0.704353\pi\) |
0.993000 | + | 0.118118i | \(0.0376861\pi\) | |||||||
\(54\) | 0.156228 | + | 0.270595i | 0.0212599 | + | 0.0368233i | ||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | −3.39427 | − | 3.06953i | −0.453578 | − | 0.410183i | ||||
\(57\) | 0.315560 | 0.0417970 | ||||||||
\(58\) | 1.07505 | + | 1.86205i | 0.141161 | + | 0.244499i | ||||
\(59\) | −4.43080 | + | 7.67438i | −0.576842 | + | 0.999119i | 0.418997 | + | 0.907988i | \(0.362382\pi\) |
−0.995839 | + | 0.0911315i | \(0.970952\pi\) | |||||||
\(60\) | 0.102510 | − | 0.177552i | 0.0132339 | − | 0.0229218i | ||||
\(61\) | −2.35391 | − | 4.07710i | −0.301388 | − | 0.522019i | 0.675063 | − | 0.737760i | \(-0.264117\pi\) |
−0.976451 | + | 0.215741i | \(0.930783\pi\) | |||||||
\(62\) | −4.67680 | −0.593954 | ||||||||
\(63\) | 1.65976 | − | 7.72636i | 0.209110 | − | 0.973430i | ||||
\(64\) | −3.43012 | −0.428765 | ||||||||
\(65\) | 2.25264 | + | 3.90169i | 0.279406 | + | 0.483945i | ||||
\(66\) | 0.0260949 | − | 0.0451978i | 0.00321207 | − | 0.00556346i | ||||
\(67\) | −0.542943 | + | 0.940405i | −0.0663311 | + | 0.114889i | −0.897284 | − | 0.441454i | \(-0.854463\pi\) |
0.830953 | + | 0.556343i | \(0.187796\pi\) | |||||||
\(68\) | −3.94627 | − | 6.83514i | −0.478555 | − | 0.828882i | ||||
\(69\) | −0.988469 | −0.118998 | ||||||||
\(70\) | 1.14861 | − | 0.370460i | 0.137285 | − | 0.0442785i | ||||
\(71\) | −12.8021 | −1.51933 | −0.759667 | − | 0.650312i | \(-0.774638\pi\) | ||||
−0.759667 | + | 0.650312i | \(0.774638\pi\) | |||||||
\(72\) | 2.58323 | + | 4.47429i | 0.304437 | + | 0.527300i | ||||
\(73\) | −5.32506 | + | 9.22327i | −0.623251 | + | 1.07950i | 0.365625 | + | 0.930762i | \(0.380855\pi\) |
−0.988876 | + | 0.148740i | \(0.952478\pi\) | |||||||
\(74\) | −0.517641 | + | 0.896580i | −0.0601745 | + | 0.104225i | ||||
\(75\) | 0.0572064 | + | 0.0990845i | 0.00660563 | + | 0.0114413i | ||||
\(76\) | 4.94228 | 0.566918 | ||||||||
\(77\) | −2.51802 | + | 0.812139i | −0.286955 | + | 0.0925518i | ||||
\(78\) | 0.235130 | 0.0266233 | ||||||||
\(79\) | 4.62203 | + | 8.00559i | 0.520019 | + | 0.900700i | 0.999729 | + | 0.0232725i | \(0.00740853\pi\) |
−0.479710 | + | 0.877427i | \(0.659258\pi\) | |||||||
\(80\) | 1.39742 | − | 2.42040i | 0.156236 | − | 0.270609i | ||||
\(81\) | −4.44118 | + | 7.69235i | −0.493464 | + | 0.854705i | ||||
\(82\) | −0.288364 | − | 0.499461i | −0.0318445 | − | 0.0551563i | ||||
\(83\) | −2.60431 | −0.285860 | −0.142930 | − | 0.989733i | \(-0.545652\pi\) | ||||
−0.142930 | + | 0.989733i | \(0.545652\pi\) | |||||||
\(84\) | −0.113925 | + | 0.530331i | −0.0124302 | + | 0.0578639i | ||||
\(85\) | 4.40450 | 0.477736 | ||||||||
\(86\) | −2.38423 | − | 4.12961i | −0.257099 | − | 0.445308i | ||||
\(87\) | 0.269646 | − | 0.467040i | 0.0289090 | − | 0.0500719i | ||||
\(88\) | 0.864850 | − | 1.49796i | 0.0921934 | − | 0.159684i | ||||
\(89\) | −2.00155 | − | 3.46679i | −0.212164 | − | 0.367479i | 0.740227 | − | 0.672357i | \(-0.234718\pi\) |
−0.952392 | + | 0.304878i | \(0.901384\pi\) | |||||||
\(90\) | −1.36249 | −0.143619 | ||||||||
\(91\) | −8.84092 | − | 7.99509i | −0.926780 | − | 0.838113i | ||||
\(92\) | −15.4813 | −1.61404 | ||||||||
\(93\) | 0.586519 | + | 1.01588i | 0.0608192 | + | 0.105342i | ||||
\(94\) | −2.63043 | + | 4.55605i | −0.271309 | + | 0.469920i | ||||
\(95\) | −1.37904 | + | 2.38857i | −0.141487 | + | 0.245062i | ||||
\(96\) | −0.270831 | − | 0.469093i | −0.0276416 | − | 0.0478766i | ||||
\(97\) | −5.03725 | −0.511455 | −0.255728 | − | 0.966749i | \(-0.582315\pi\) | ||||
−0.255728 | + | 0.966749i | \(0.582315\pi\) | |||||||
\(98\) | −2.59135 | + | 1.86565i | −0.261766 | + | 0.188459i | ||||
\(99\) | 2.98691 | 0.300196 | ||||||||
\(100\) | 0.895962 | + | 1.55185i | 0.0895962 | + | 0.155185i | ||||
\(101\) | 6.72616 | − | 11.6501i | 0.669278 | − | 1.15922i | −0.308828 | − | 0.951118i | \(-0.599937\pi\) |
0.978106 | − | 0.208106i | \(-0.0667300\pi\) | |||||||
\(102\) | 0.114935 | − | 0.199074i | 0.0113803 | − | 0.0197112i | ||||
\(103\) | 0.291429 | + | 0.504770i | 0.0287154 | + | 0.0497365i | 0.880026 | − | 0.474926i | \(-0.157525\pi\) |
−0.851311 | + | 0.524662i | \(0.824192\pi\) | |||||||
\(104\) | 7.79280 | 0.764147 | ||||||||
\(105\) | −0.224517 | − | 0.203037i | −0.0219107 | − | 0.0198144i | ||||
\(106\) | 2.61820 | 0.254302 | ||||||||
\(107\) | −7.07851 | − | 12.2603i | −0.684305 | − | 1.18525i | −0.973655 | − | 0.228028i | \(-0.926772\pi\) |
0.289350 | − | 0.957223i | \(-0.406561\pi\) | |||||||
\(108\) | 0.613716 | − | 1.06299i | 0.0590548 | − | 0.102286i | ||||
\(109\) | 2.69792 | − | 4.67293i | 0.258414 | − | 0.447586i | −0.707403 | − | 0.706810i | \(-0.750134\pi\) |
0.965817 | + | 0.259224i | \(0.0834669\pi\) | |||||||
\(110\) | 0.228077 | + | 0.395041i | 0.0217463 | + | 0.0376657i | ||||
\(111\) | 0.259670 | 0.0246468 | ||||||||
\(112\) | −1.55303 | + | 7.22952i | −0.146747 | + | 0.683125i | ||||
\(113\) | −14.2416 | −1.33974 | −0.669869 | − | 0.742479i | \(-0.733650\pi\) | ||||
−0.669869 | + | 0.742479i | \(0.733650\pi\) | |||||||
\(114\) | 0.0719720 | + | 0.124659i | 0.00674080 | + | 0.0116754i | ||||
\(115\) | 4.31975 | − | 7.48202i | 0.402818 | − | 0.697702i | ||||
\(116\) | 4.22316 | − | 7.31473i | 0.392111 | − | 0.679156i | ||||
\(117\) | 6.72844 | + | 11.6540i | 0.622045 | + | 1.07741i | ||||
\(118\) | −4.04226 | −0.372120 | ||||||||
\(119\) | −11.0906 | + | 3.57707i | −1.01668 | + | 0.327909i | ||||
\(120\) | 0.197900 | 0.0180657 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | 1.07375 | − | 1.85978i | 0.0972125 | − | 0.168377i | ||||
\(123\) | −0.0723277 | + | 0.125275i | −0.00652157 | + | 0.0112957i | ||||
\(124\) | 9.18601 | + | 15.9106i | 0.824928 | + | 1.42882i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 3.43078 | − | 1.10653i | 0.305638 | − | 0.0985776i | ||||
\(127\) | −1.61303 | −0.143133 | −0.0715666 | − | 0.997436i | \(-0.522800\pi\) | ||||
−0.0715666 | + | 0.997436i | \(0.522800\pi\) | |||||||
\(128\) | −5.51661 | − | 9.55504i | −0.487604 | − | 0.844555i | ||||
\(129\) | −0.598015 | + | 1.03579i | −0.0526523 | + | 0.0911965i | ||||
\(130\) | −1.02755 | + | 1.77977i | −0.0901223 | + | 0.156096i | ||||
\(131\) | 7.15742 | + | 12.3970i | 0.625347 | + | 1.08313i | 0.988474 | + | 0.151393i | \(0.0483759\pi\) |
−0.363127 | + | 0.931740i | \(0.618291\pi\) | |||||||
\(132\) | −0.205019 | −0.0178446 | ||||||||
\(133\) | 1.53261 | − | 7.13445i | 0.132894 | − | 0.618635i | ||||
\(134\) | −0.495331 | −0.0427901 | ||||||||
\(135\) | 0.342490 | + | 0.593210i | 0.0294768 | + | 0.0510554i | ||||
\(136\) | 3.80924 | − | 6.59779i | 0.326639 | − | 0.565756i | ||||
\(137\) | 4.05676 | − | 7.02651i | 0.346592 | − | 0.600315i | −0.639050 | − | 0.769165i | \(-0.720672\pi\) |
0.985642 | + | 0.168850i | \(0.0540055\pi\) | |||||||
\(138\) | −0.225447 | − | 0.390486i | −0.0191913 | − | 0.0332403i | ||||
\(139\) | 16.3917 | 1.39033 | 0.695163 | − | 0.718852i | \(-0.255332\pi\) | ||||
0.695163 | + | 0.718852i | \(0.255332\pi\) | |||||||
\(140\) | −3.51637 | − | 3.17995i | −0.297187 | − | 0.268755i | ||||
\(141\) | 1.31954 | 0.111125 | ||||||||
\(142\) | −2.91987 | − | 5.05737i | −0.245030 | − | 0.424405i | ||||
\(143\) | 2.25264 | − | 3.90169i | 0.188375 | − | 0.326276i | ||||
\(144\) | 4.17396 | − | 7.22952i | 0.347830 | − | 0.602460i | ||||
\(145\) | 2.35678 | + | 4.08206i | 0.195720 | + | 0.338996i | ||||
\(146\) | −4.85809 | −0.402059 | ||||||||
\(147\) | 0.730234 | + | 0.328913i | 0.0602287 | + | 0.0271283i | ||||
\(148\) | 4.06693 | 0.334299 | ||||||||
\(149\) | 7.45484 | + | 12.9122i | 0.610725 | + | 1.05781i | 0.991119 | + | 0.132981i | \(0.0424551\pi\) |
−0.380394 | + | 0.924825i | \(0.624212\pi\) | |||||||
\(150\) | −0.0260949 | + | 0.0451978i | −0.00213064 | + | 0.00369038i | ||||
\(151\) | 11.4730 | − | 19.8719i | 0.933663 | − | 1.61715i | 0.156661 | − | 0.987652i | \(-0.449927\pi\) |
0.777001 | − | 0.629499i | \(-0.216740\pi\) | |||||||
\(152\) | 2.38533 | + | 4.13151i | 0.193476 | + | 0.335110i | ||||
\(153\) | 13.1559 | 1.06359 | ||||||||
\(154\) | −0.895131 | − | 0.809491i | −0.0721317 | − | 0.0652307i | ||||
\(155\) | −10.2527 | −0.823515 | ||||||||
\(156\) | −0.461835 | − | 0.799922i | −0.0369764 | − | 0.0640450i | ||||
\(157\) | −8.91886 | + | 15.4479i | −0.711803 | + | 1.23288i | 0.252377 | + | 0.967629i | \(0.418788\pi\) |
−0.964180 | + | 0.265249i | \(0.914546\pi\) | |||||||
\(158\) | −2.10836 | + | 3.65178i | −0.167732 | + | 0.290520i | ||||
\(159\) | −0.328350 | − | 0.568718i | −0.0260398 | − | 0.0451023i | ||||
\(160\) | 4.73428 | 0.374277 | ||||||||
\(161\) | −4.80077 | + | 22.3481i | −0.378354 | + | 1.76128i | ||||
\(162\) | −4.05172 | −0.318333 | ||||||||
\(163\) | 10.8525 | + | 18.7970i | 0.850030 | + | 1.47229i | 0.881181 | + | 0.472780i | \(0.156749\pi\) |
−0.0311508 | + | 0.999515i | \(0.509917\pi\) | |||||||
\(164\) | −1.13279 | + | 1.96205i | −0.0884560 | + | 0.153210i | ||||
\(165\) | 0.0572064 | − | 0.0990845i | 0.00445352 | − | 0.00771372i | ||||
\(166\) | −0.593984 | − | 1.02881i | −0.0461021 | − | 0.0798511i | ||||
\(167\) | 2.53749 | 0.196357 | 0.0981784 | − | 0.995169i | \(-0.468698\pi\) | ||||
0.0981784 | + | 0.995169i | \(0.468698\pi\) | |||||||
\(168\) | −0.498317 | + | 0.160722i | −0.0384460 | + | 0.0124000i | ||||
\(169\) | 7.29761 | 0.561354 | ||||||||
\(170\) | 1.00457 | + | 1.73996i | 0.0770467 | + | 0.133449i | ||||
\(171\) | −4.11907 | + | 7.13445i | −0.314993 | + | 0.545585i | ||||
\(172\) | −9.36606 | + | 16.2225i | −0.714155 | + | 1.23695i | ||||
\(173\) | −4.96057 | − | 8.59196i | −0.377145 | − | 0.653234i | 0.613501 | − | 0.789694i | \(-0.289761\pi\) |
−0.990646 | + | 0.136460i | \(0.956428\pi\) | |||||||
\(174\) | 0.246000 | 0.0186492 | ||||||||
\(175\) | 2.51802 | − | 0.812139i | 0.190345 | − | 0.0613919i | ||||
\(176\) | −2.79484 | −0.210669 | ||||||||
\(177\) | 0.506941 | + | 0.878048i | 0.0381040 | + | 0.0659981i | ||||
\(178\) | 0.913016 | − | 1.58139i | 0.0684334 | − | 0.118530i | ||||
\(179\) | 2.93234 | − | 5.07896i | 0.219173 | − | 0.379619i | −0.735382 | − | 0.677653i | \(-0.762997\pi\) |
0.954555 | + | 0.298033i | \(0.0963307\pi\) | |||||||
\(180\) | 2.67616 | + | 4.63524i | 0.199469 | + | 0.345490i | ||||
\(181\) | −17.1905 | −1.27776 | −0.638880 | − | 0.769307i | \(-0.720602\pi\) | ||||
−0.638880 | + | 0.769307i | \(0.720602\pi\) | |||||||
\(182\) | 1.14198 | − | 5.31602i | 0.0846489 | − | 0.394050i | ||||
\(183\) | −0.538636 | −0.0398171 | ||||||||
\(184\) | −7.47187 | − | 12.9417i | −0.550833 | − | 0.954071i | ||||
\(185\) | −1.13479 | + | 1.96552i | −0.0834317 | + | 0.144508i | ||||
\(186\) | −0.267543 | + | 0.463398i | −0.0196172 | + | 0.0339780i | ||||
\(187\) | −2.20225 | − | 3.81441i | −0.161045 | − | 0.278937i | ||||
\(188\) | 20.6664 | 1.50725 | ||||||||
\(189\) | −1.34417 | − | 1.21557i | −0.0977736 | − | 0.0884194i | ||||
\(190\) | −1.25811 | −0.0912729 | ||||||||
\(191\) | 6.47512 | + | 11.2152i | 0.468523 | + | 0.811506i | 0.999353 | − | 0.0359724i | \(-0.0114528\pi\) |
−0.530829 | + | 0.847479i | \(0.678119\pi\) | |||||||
\(192\) | −0.196225 | + | 0.339871i | −0.0141613 | + | 0.0245281i | ||||
\(193\) | 1.41535 | − | 2.45146i | 0.101879 | − | 0.176460i | −0.810580 | − | 0.585628i | \(-0.800848\pi\) |
0.912459 | + | 0.409168i | \(0.134181\pi\) | |||||||
\(194\) | −1.14888 | − | 1.98992i | −0.0824848 | − | 0.142868i | ||||
\(195\) | 0.515463 | 0.0369131 | ||||||||
\(196\) | 11.4369 | + | 5.15140i | 0.816918 | + | 0.367957i | ||||
\(197\) | 1.57926 | 0.112517 | 0.0562586 | − | 0.998416i | \(-0.482083\pi\) | ||||
0.0562586 | + | 0.998416i | \(0.482083\pi\) | |||||||
\(198\) | 0.681245 | + | 1.17995i | 0.0484140 | + | 0.0838555i | ||||
\(199\) | 10.2009 | − | 17.6684i | 0.723120 | − | 1.25248i | −0.236624 | − | 0.971601i | \(-0.576041\pi\) |
0.959743 | − | 0.280878i | \(-0.0906258\pi\) | |||||||
\(200\) | −0.864850 | + | 1.49796i | −0.0611542 | + | 0.105922i | ||||
\(201\) | 0.0621197 | + | 0.107594i | 0.00438159 | + | 0.00758913i | ||||
\(202\) | 6.13633 | 0.431751 | ||||||||
\(203\) | −9.24961 | − | 8.36468i | −0.649195 | − | 0.587085i | ||||
\(204\) | −0.903008 | −0.0632232 | ||||||||
\(205\) | −0.632164 | − | 1.09494i | −0.0441523 | − | 0.0764739i | ||||
\(206\) | −0.132937 | + | 0.230253i | −0.00926213 | + | 0.0160425i | ||||
\(207\) | 12.9027 | − | 22.3481i | 0.896799 | − | 1.55330i | ||||
\(208\) | −6.29577 | − | 10.9046i | −0.436533 | − | 0.756098i | ||||
\(209\) | 2.75808 | 0.190781 | ||||||||
\(210\) | 0.0290008 | − | 0.135002i | 0.00200124 | − | 0.00931600i | ||||
\(211\) | −16.3729 | −1.12716 | −0.563580 | − | 0.826061i | \(-0.690576\pi\) | ||||
−0.563580 | + | 0.826061i | \(0.690576\pi\) | |||||||
\(212\) | −5.14258 | − | 8.90721i | −0.353194 | − | 0.611750i | ||||
\(213\) | −0.732365 | + | 1.26849i | −0.0501808 | + | 0.0869157i | ||||
\(214\) | 3.22889 | − | 5.59260i | 0.220722 | − | 0.382302i | ||||
\(215\) | −5.22682 | − | 9.05311i | −0.356466 | − | 0.617417i | ||||
\(216\) | 1.18481 | 0.0806161 | ||||||||
\(217\) | 25.8165 | − | 8.32660i | 1.75254 | − | 0.565246i | ||||
\(218\) | 2.46133 | 0.166702 | ||||||||
\(219\) | 0.609256 | + | 1.05526i | 0.0411697 | + | 0.0713080i | ||||
\(220\) | 0.895962 | − | 1.55185i | 0.0604057 | − | 0.104626i | ||||
\(221\) | 9.92178 | − | 17.1850i | 0.667411 | − | 1.15599i | ||||
\(222\) | 0.0592248 | + | 0.102580i | 0.00397491 | + | 0.00688474i | ||||
\(223\) | 12.9854 | 0.869569 | 0.434785 | − | 0.900534i | \(-0.356825\pi\) | ||||
0.434785 | + | 0.900534i | \(0.356825\pi\) | |||||||
\(224\) | −11.9210 | + | 3.84489i | −0.796506 | + | 0.256898i | ||||
\(225\) | −2.98691 | −0.199127 | ||||||||
\(226\) | −3.24818 | − | 5.62602i | −0.216066 | − | 0.374237i | ||||
\(227\) | 7.48569 | − | 12.9656i | 0.496843 | − | 0.860557i | −0.503150 | − | 0.864199i | \(-0.667826\pi\) |
0.999993 | + | 0.00364156i | \(0.00115915\pi\) | |||||||
\(228\) | 0.282730 | − | 0.489703i | 0.0187243 | − | 0.0324314i | ||||
\(229\) | 5.60355 | + | 9.70564i | 0.370293 | + | 0.641367i | 0.989611 | − | 0.143774i | \(-0.0459239\pi\) |
−0.619317 | + | 0.785141i | \(0.712591\pi\) | |||||||
\(230\) | 3.94094 | 0.259858 | ||||||||
\(231\) | −0.0635767 | + | 0.295956i | −0.00418304 | + | 0.0194725i | ||||
\(232\) | 8.15304 | 0.535273 | ||||||||
\(233\) | 3.93590 | + | 6.81718i | 0.257849 | + | 0.446608i | 0.965666 | − | 0.259788i | \(-0.0836528\pi\) |
−0.707816 | + | 0.706397i | \(0.750319\pi\) | |||||||
\(234\) | −3.06920 | + | 5.31602i | −0.200640 | + | 0.347519i | ||||
\(235\) | −5.76655 | + | 9.98796i | −0.376168 | + | 0.651542i | ||||
\(236\) | 7.93966 | + | 13.7519i | 0.516828 | + | 0.895172i | ||||
\(237\) | 1.05764 | 0.0687011 | ||||||||
\(238\) | −3.94261 | − | 3.56541i | −0.255561 | − | 0.231111i | ||||
\(239\) | 14.8640 | 0.961472 | 0.480736 | − | 0.876865i | \(-0.340370\pi\) | ||||
0.480736 | + | 0.876865i | \(0.340370\pi\) | |||||||
\(240\) | −0.159883 | − | 0.276925i | −0.0103204 | − | 0.0178754i | ||||
\(241\) | −4.49062 | + | 7.77799i | −0.289266 | + | 0.501024i | −0.973635 | − | 0.228112i | \(-0.926745\pi\) |
0.684368 | + | 0.729136i | \(0.260078\pi\) | |||||||
\(242\) | 0.228077 | − | 0.395041i | 0.0146613 | − | 0.0253942i | ||||
\(243\) | 1.53560 | + | 2.65973i | 0.0985086 | + | 0.170622i | ||||
\(244\) | −8.43607 | −0.540064 | ||||||||
\(245\) | −5.68086 | + | 4.08996i | −0.362937 | + | 0.261298i | ||||
\(246\) | −0.0659851 | −0.00420706 | ||||||||
\(247\) | 6.21298 | + | 10.7612i | 0.395322 | + | 0.684718i | ||||
\(248\) | −8.86703 | + | 15.3582i | −0.563057 | + | 0.975244i | ||||
\(249\) | −0.148983 | + | 0.258047i | −0.00944145 | + | 0.0163531i | ||||
\(250\) | −0.228077 | − | 0.395041i | −0.0144249 | − | 0.0249846i | ||||
\(251\) | 0.937051 | 0.0591461 | 0.0295731 | − | 0.999563i | \(-0.490585\pi\) | ||||
0.0295731 | + | 0.999563i | \(0.490585\pi\) | |||||||
\(252\) | −10.5031 | − | 9.49822i | −0.661632 | − | 0.598332i | ||||
\(253\) | −8.63949 | −0.543160 | ||||||||
\(254\) | −0.367895 | − | 0.637212i | −0.0230838 | − | 0.0399823i | ||||
\(255\) | 0.251966 | − | 0.436418i | 0.0157787 | − | 0.0273296i | ||||
\(256\) | −0.913694 | + | 1.58257i | −0.0571059 | + | 0.0989103i | ||||
\(257\) | −0.184203 | − | 0.319049i | −0.0114903 | − | 0.0199017i | 0.860223 | − | 0.509918i | \(-0.170324\pi\) |
−0.871713 | + | 0.490016i | \(0.836991\pi\) | |||||||
\(258\) | −0.545574 | −0.0339660 | ||||||||
\(259\) | 1.26116 | − | 5.87083i | 0.0783647 | − | 0.364796i | ||||
\(260\) | 8.07313 | 0.500674 | ||||||||
\(261\) | 7.03948 | + | 12.1927i | 0.435733 | + | 0.754711i | ||||
\(262\) | −3.26489 | + | 5.65495i | −0.201705 | + | 0.349364i | ||||
\(263\) | 2.89322 | − | 5.01120i | 0.178403 | − | 0.309004i | −0.762930 | − | 0.646481i | \(-0.776240\pi\) |
0.941334 | + | 0.337477i | \(0.109573\pi\) | |||||||
\(264\) | −0.0989500 | − | 0.171386i | −0.00608995 | − | 0.0105481i | ||||
\(265\) | 5.73973 | 0.352589 | ||||||||
\(266\) | 3.16795 | − | 1.02176i | 0.194239 | − | 0.0626481i | ||||
\(267\) | −0.458007 | −0.0280296 | ||||||||
\(268\) | 0.972913 | + | 1.68513i | 0.0594301 | + | 0.102936i | ||||
\(269\) | 5.08076 | − | 8.80014i | 0.309779 | − | 0.536554i | −0.668535 | − | 0.743681i | \(-0.733078\pi\) |
0.978314 | + | 0.207127i | \(0.0664114\pi\) | |||||||
\(270\) | −0.156228 | + | 0.270595i | −0.00950774 | + | 0.0164679i | ||||
\(271\) | −10.7032 | − | 18.5385i | −0.650174 | − | 1.12613i | −0.983080 | − | 0.183175i | \(-0.941363\pi\) |
0.332906 | − | 0.942960i | \(-0.391971\pi\) | |||||||
\(272\) | −12.3099 | −0.746396 | ||||||||
\(273\) | −1.29795 | + | 0.418627i | −0.0785553 | + | 0.0253365i | ||||
\(274\) | 3.70101 | 0.223586 | ||||||||
\(275\) | 0.500000 | + | 0.866025i | 0.0301511 | + | 0.0522233i | ||||
\(276\) | −0.885631 | + | 1.53396i | −0.0533087 | + | 0.0923334i | ||||
\(277\) | 0.555299 | − | 0.961805i | 0.0333647 | − | 0.0577893i | −0.848861 | − | 0.528616i | \(-0.822711\pi\) |
0.882226 | + | 0.470827i | \(0.156044\pi\) | |||||||
\(278\) | 3.73857 | + | 6.47539i | 0.224225 | + | 0.388368i | ||||
\(279\) | −30.6238 | −1.83340 | ||||||||
\(280\) | 0.961156 | − | 4.47429i | 0.0574401 | − | 0.267390i | ||||
\(281\) | 1.63227 | 0.0973730 | 0.0486865 | − | 0.998814i | \(-0.484496\pi\) | ||||
0.0486865 | + | 0.998814i | \(0.484496\pi\) | |||||||
\(282\) | 0.300956 | + | 0.521270i | 0.0179216 | + | 0.0310412i | ||||
\(283\) | −5.64650 | + | 9.78002i | −0.335649 | + | 0.581362i | −0.983609 | − | 0.180313i | \(-0.942289\pi\) |
0.647960 | + | 0.761674i | \(0.275622\pi\) | |||||||
\(284\) | −11.4702 | + | 19.8670i | −0.680633 | + | 1.17889i | ||||
\(285\) | 0.157780 | + | 0.273283i | 0.00934609 | + | 0.0161879i | ||||
\(286\) | 2.05510 | 0.121521 | ||||||||
\(287\) | 2.48105 | + | 2.24368i | 0.146452 | + | 0.132440i | ||||
\(288\) | 14.1409 | 0.833258 | ||||||||
\(289\) | −1.19983 | − | 2.07816i | −0.0705781 | − | 0.122245i | ||||
\(290\) | −1.07505 | + | 1.86205i | −0.0631293 | + | 0.109343i | ||||
\(291\) | −0.288163 | + | 0.499113i | −0.0168924 | + | 0.0292585i | ||||
\(292\) | 9.54210 | + | 16.5274i | 0.558409 | + | 0.967193i | ||||
\(293\) | −1.08939 | −0.0636429 | −0.0318214 | − | 0.999494i | \(-0.510131\pi\) | ||||
−0.0318214 | + | 0.999494i | \(0.510131\pi\) | |||||||
\(294\) | 0.0366155 | + | 0.363490i | 0.00213546 | + | 0.0211991i | ||||
\(295\) | −8.86161 | −0.515943 | ||||||||
\(296\) | 1.96285 | + | 3.39976i | 0.114089 | + | 0.197607i | ||||
\(297\) | 0.342490 | − | 0.593210i | 0.0198733 | − | 0.0344215i | ||||
\(298\) | −3.40056 | + | 5.88994i | −0.196989 | + | 0.341195i | ||||
\(299\) | −19.4617 | − | 33.7086i | −1.12550 | − | 1.94942i | ||||
\(300\) | 0.205019 | 0.0118368 | ||||||||
\(301\) | 20.5136 | + | 18.5510i | 1.18239 | + | 1.06926i | ||||
\(302\) | 10.4669 | 0.602305 | ||||||||
\(303\) | −0.769560 | − | 1.33292i | −0.0442101 | − | 0.0765741i | ||||
\(304\) | 3.85420 | − | 6.67567i | 0.221053 | − | 0.382876i | ||||
\(305\) | 2.35391 | − | 4.07710i | 0.134785 | − | 0.233454i | ||||
\(306\) | 3.00055 | + | 5.19710i | 0.171530 | + | 0.297098i | ||||
\(307\) | −18.5398 | −1.05812 | −0.529060 | − | 0.848585i | \(-0.677455\pi\) | ||||
−0.529060 | + | 0.848585i | \(0.677455\pi\) | |||||||
\(308\) | −0.995732 | + | 4.63524i | −0.0567371 | + | 0.264117i | ||||
\(309\) | 0.0666865 | 0.00379366 | ||||||||
\(310\) | −2.33840 | − | 4.05023i | −0.132812 | − | 0.230037i | ||||
\(311\) | −4.27772 | + | 7.40923i | −0.242567 | + | 0.420139i | −0.961445 | − | 0.274998i | \(-0.911323\pi\) |
0.718878 | + | 0.695137i | \(0.244656\pi\) | |||||||
\(312\) | 0.445798 | − | 0.772145i | 0.0252384 | − | 0.0437141i | ||||
\(313\) | −5.21356 | − | 9.03015i | −0.294688 | − | 0.510414i | 0.680224 | − | 0.733004i | \(-0.261882\pi\) |
−0.974912 | + | 0.222590i | \(0.928549\pi\) | |||||||
\(314\) | −8.13675 | −0.459183 | ||||||||
\(315\) | 7.52110 | − | 2.42578i | 0.423766 | − | 0.136677i | ||||
\(316\) | 16.5647 | 0.931835 | ||||||||
\(317\) | 0.661522 | + | 1.14579i | 0.0371548 | + | 0.0643540i | 0.884005 | − | 0.467478i | \(-0.154837\pi\) |
−0.846850 | + | 0.531832i | \(0.821504\pi\) | |||||||
\(318\) | 0.149778 | − | 0.259423i | 0.00839913 | − | 0.0145477i | ||||
\(319\) | 2.35678 | − | 4.08206i | 0.131954 | − | 0.228551i | ||||
\(320\) | −1.71506 | − | 2.97057i | −0.0958747 | − | 0.166060i | ||||
\(321\) | −1.61974 | −0.0904053 | ||||||||
\(322\) | −9.92336 | + | 3.20059i | −0.553007 | + | 0.178362i | ||||
\(323\) | 12.1480 | 0.675932 | ||||||||
\(324\) | 7.95825 | + | 13.7841i | 0.442125 | + | 0.765783i | ||||
\(325\) | −2.25264 | + | 3.90169i | −0.124954 | + | 0.216427i | ||||
\(326\) | −4.95039 | + | 8.57432i | −0.274177 | + | 0.474888i | ||||
\(327\) | −0.308677 | − | 0.534644i | −0.0170699 | − | 0.0295659i | ||||
\(328\) | −2.18691 | −0.120752 | ||||||||
\(329\) | 6.40869 | − | 29.8331i | 0.353322 | − | 1.64475i | ||||
\(330\) | 0.0521899 | 0.00287296 | ||||||||
\(331\) | −11.4434 | − | 19.8206i | −0.628987 | − | 1.08944i | −0.987755 | − | 0.156010i | \(-0.950137\pi\) |
0.358769 | − | 0.933426i | \(-0.383197\pi\) | |||||||
\(332\) | −2.33337 | + | 4.04151i | −0.128060 | + | 0.221807i | ||||
\(333\) | −3.38953 | + | 5.87083i | −0.185745 | + | 0.321720i | ||||
\(334\) | 0.578742 | + | 1.00241i | 0.0316674 | + | 0.0548495i | ||||
\(335\) | −1.08589 | −0.0593283 | ||||||||
\(336\) | 0.627490 | + | 0.567456i | 0.0342324 | + | 0.0309573i | ||||
\(337\) | −18.4079 | −1.00274 | −0.501372 | − | 0.865232i | \(-0.667171\pi\) | ||||
−0.501372 | + | 0.865232i | \(0.667171\pi\) | |||||||
\(338\) | 1.66442 | + | 2.88285i | 0.0905323 | + | 0.156807i | ||||
\(339\) | −0.814712 | + | 1.41112i | −0.0442491 | + | 0.0766417i | ||||
\(340\) | 3.94627 | − | 6.83514i | 0.214016 | − | 0.370687i | ||||
\(341\) | 5.12634 | + | 8.87908i | 0.277607 | + | 0.480829i | ||||
\(342\) | −3.75786 | −0.203202 | ||||||||
\(343\) | 10.9829 | − | 14.9123i | 0.593021 | − | 0.805187i | ||||
\(344\) | −18.0817 | −0.974898 | ||||||||
\(345\) | −0.494235 | − | 0.856039i | −0.0266087 | − | 0.0460876i | ||||
\(346\) | 2.26278 | − | 3.91925i | 0.121648 | − | 0.210700i | ||||
\(347\) | −4.99277 | + | 8.64773i | −0.268026 | + | 0.464234i | −0.968352 | − | 0.249589i | \(-0.919705\pi\) |
0.700326 | + | 0.713823i | \(0.253038\pi\) | |||||||
\(348\) | −0.483184 | − | 0.836900i | −0.0259014 | − | 0.0448625i | ||||
\(349\) | −24.0504 | −1.28739 | −0.643694 | − | 0.765283i | \(-0.722599\pi\) | ||||
−0.643694 | + | 0.765283i | \(0.722599\pi\) | |||||||
\(350\) | 0.895131 | + | 0.809491i | 0.0478467 | + | 0.0432691i | ||||
\(351\) | 3.08603 | 0.164720 | ||||||||
\(352\) | −2.36714 | − | 4.10000i | −0.126169 | − | 0.218531i | ||||
\(353\) | 11.8135 | − | 20.4616i | 0.628770 | − | 1.08906i | −0.359028 | − | 0.933327i | \(-0.616892\pi\) |
0.987799 | − | 0.155736i | \(-0.0497748\pi\) | |||||||
\(354\) | −0.231243 | + | 0.400525i | −0.0122904 | + | 0.0212877i | ||||
\(355\) | −6.40107 | − | 11.0870i | −0.339733 | − | 0.588435i | ||||
\(356\) | −7.17326 | −0.380182 | ||||||||
\(357\) | −0.280024 | + | 1.30354i | −0.0148204 | + | 0.0689907i | ||||
\(358\) | 2.67520 | 0.141388 | ||||||||
\(359\) | −1.83335 | − | 3.17545i | −0.0967603 | − | 0.167594i | 0.813582 | − | 0.581451i | \(-0.197515\pi\) |
−0.910342 | + | 0.413857i | \(0.864181\pi\) | |||||||
\(360\) | −2.58323 | + | 4.47429i | −0.136148 | + | 0.235816i | ||||
\(361\) | 5.69649 | − | 9.86660i | 0.299815 | − | 0.519295i | ||||
\(362\) | −3.92076 | − | 6.79095i | −0.206070 | − | 0.356924i | ||||
\(363\) | −0.114413 | −0.00600512 | ||||||||
\(364\) | −20.3283 | + | 6.55650i | −1.06549 | + | 0.343654i | ||||
\(365\) | −10.6501 | −0.557453 | ||||||||
\(366\) | −0.122851 | − | 0.212783i | −0.00642150 | − | 0.0111224i | ||||
\(367\) | −9.64824 | + | 16.7112i | −0.503634 | + | 0.872320i | 0.496357 | + | 0.868118i | \(0.334671\pi\) |
−0.999991 | + | 0.00420139i | \(0.998663\pi\) | |||||||
\(368\) | −12.0730 | + | 20.9110i | −0.629348 | + | 1.09006i | ||||
\(369\) | −1.88822 | − | 3.27049i | −0.0982967 | − | 0.170255i | ||||
\(370\) | −1.03528 | −0.0538217 | ||||||||
\(371\) | −14.4528 | + | 4.66146i | −0.750350 | + | 0.242011i | ||||
\(372\) | 2.10200 | 0.108983 | ||||||||
\(373\) | 9.95630 | + | 17.2448i | 0.515518 | + | 0.892903i | 0.999838 | + | 0.0180120i | \(0.00573370\pi\) |
−0.484320 | + | 0.874891i | \(0.660933\pi\) | |||||||
\(374\) | 1.00457 | − | 1.73996i | 0.0519449 | − | 0.0899711i | ||||
\(375\) | −0.0572064 | + | 0.0990845i | −0.00295413 | + | 0.00511670i | ||||
\(376\) | 9.97440 | + | 17.2762i | 0.514391 | + | 0.890951i | ||||
\(377\) | 21.2359 | 1.09370 | ||||||||
\(378\) | 0.173625 | − | 0.808243i | 0.00893030 | − | 0.0415715i | ||||
\(379\) | 15.7649 | 0.809789 | 0.404894 | − | 0.914363i | \(-0.367308\pi\) | ||||
0.404894 | + | 0.914363i | \(0.367308\pi\) | |||||||
\(380\) | 2.47114 | + | 4.28014i | 0.126767 | + | 0.219566i | ||||
\(381\) | −0.0922757 | + | 0.159826i | −0.00472743 | + | 0.00818814i | ||||
\(382\) | −2.95365 | + | 5.11588i | −0.151122 | + | 0.261751i | ||||
\(383\) | 2.35543 | + | 4.07972i | 0.120357 | + | 0.208464i | 0.919908 | − | 0.392133i | \(-0.128263\pi\) |
−0.799552 | + | 0.600597i | \(0.794930\pi\) | |||||||
\(384\) | −1.26234 | −0.0644186 | ||||||||
\(385\) | −1.96234 | − | 1.77460i | −0.100010 | − | 0.0904420i | ||||
\(386\) | 1.29124 | 0.0657222 | ||||||||
\(387\) | −15.6120 | − | 27.0408i | −0.793604 | − | 1.37456i | ||||
\(388\) | −4.51319 | + | 7.81707i | −0.229122 | + | 0.396851i | ||||
\(389\) | −3.54729 | + | 6.14409i | −0.179855 | + | 0.311517i | −0.941831 | − | 0.336088i | \(-0.890896\pi\) |
0.761976 | + | 0.647605i | \(0.224229\pi\) | |||||||
\(390\) | 0.117565 | + | 0.203629i | 0.00595314 | + | 0.0103111i | ||||
\(391\) | −38.0527 | −1.92441 | ||||||||
\(392\) | 1.21353 | + | 12.0469i | 0.0612924 | + | 0.608462i | ||||
\(393\) | 1.63780 | 0.0826162 | ||||||||
\(394\) | 0.360192 | + | 0.623870i | 0.0181462 | + | 0.0314301i | ||||
\(395\) | −4.62203 | + | 8.00559i | −0.232560 | + | 0.402805i | ||||
\(396\) | 2.67616 | − | 4.63524i | 0.134482 | − | 0.232930i | ||||
\(397\) | 0.362935 | + | 0.628622i | 0.0182152 | + | 0.0315497i | 0.874989 | − | 0.484142i | \(-0.160868\pi\) |
−0.856774 | + | 0.515692i | \(0.827535\pi\) | |||||||
\(398\) | 9.30632 | 0.466484 | ||||||||
\(399\) | −0.619238 | − | 0.559994i | −0.0310007 | − | 0.0280348i | ||||
\(400\) | 2.79484 | 0.139742 | ||||||||
\(401\) | −15.8456 | − | 27.4454i | −0.791292 | − | 1.37056i | −0.925167 | − | 0.379560i | \(-0.876075\pi\) |
0.133875 | − | 0.990998i | \(-0.457258\pi\) | |||||||
\(402\) | −0.0283361 | + | 0.0490796i | −0.00141328 | + | 0.00244787i | ||||
\(403\) | −23.0956 | + | 40.0028i | −1.15048 | + | 1.99268i | ||||
\(404\) | −12.0528 | − | 20.8760i | −0.599648 | − | 1.03862i | ||||
\(405\) | −8.88236 | −0.441368 | ||||||||
\(406\) | 1.19477 | − | 5.56176i | 0.0592952 | − | 0.276026i | ||||
\(407\) | 2.26959 | 0.112499 | ||||||||
\(408\) | −0.435826 | − | 0.754872i | −0.0215766 | − | 0.0373718i | ||||
\(409\) | −9.41335 | + | 16.3044i | −0.465460 | + | 0.806201i | −0.999222 | − | 0.0394338i | \(-0.987445\pi\) |
0.533762 | + | 0.845635i | \(0.320778\pi\) | |||||||
\(410\) | 0.288364 | − | 0.499461i | 0.0142413 | − | 0.0246666i | ||||
\(411\) | −0.464145 | − | 0.803923i | −0.0228946 | − | 0.0396546i | ||||
\(412\) | 1.04444 | 0.0514558 | ||||||||
\(413\) | 22.3137 | − | 7.19686i | 1.09799 | − | 0.354134i | ||||
\(414\) | 11.7712 | 0.578524 | ||||||||
\(415\) | −1.30216 | − | 2.25540i | −0.0639203 | − | 0.110713i | ||||
\(416\) | 10.6646 | − | 18.4717i | 0.522877 | − | 0.905649i | ||||
\(417\) | 0.937711 | − | 1.62416i | 0.0459199 | − | 0.0795356i | ||||
\(418\) | 0.629055 | + | 1.08956i | 0.0307681 | + | 0.0532919i | ||||
\(419\) | −9.64442 | −0.471161 | −0.235580 | − | 0.971855i | \(-0.575699\pi\) | ||||
−0.235580 | + | 0.971855i | \(0.575699\pi\) | |||||||
\(420\) | −0.516243 | + | 0.166504i | −0.0251901 | + | 0.00812456i | ||||
\(421\) | 33.7268 | 1.64374 | 0.821872 | − | 0.569672i | \(-0.192930\pi\) | ||||
0.821872 | + | 0.569672i | \(0.192930\pi\) | |||||||
\(422\) | −3.73429 | − | 6.46798i | −0.181782 | − | 0.314856i | ||||
\(423\) | −17.2242 | + | 29.8331i | −0.837467 | + | 1.45054i | ||||
\(424\) | 4.96401 | − | 8.59792i | 0.241074 | − | 0.417552i | ||||
\(425\) | 2.20225 | + | 3.81441i | 0.106825 | + | 0.185026i | ||||
\(426\) | −0.668142 | −0.0323716 | ||||||||
\(427\) | −2.61604 | + | 12.1779i | −0.126599 | + | 0.589331i | ||||
\(428\) | −25.3683 | −1.22622 | ||||||||
\(429\) | −0.257731 | − | 0.446404i | −0.0124434 | − | 0.0215526i | ||||
\(430\) | 2.38423 | − | 4.12961i | 0.114978 | − | 0.199148i | ||||
\(431\) | −2.02474 | + | 3.50696i | −0.0975285 | + | 0.168924i | −0.910661 | − | 0.413154i | \(-0.864427\pi\) |
0.813133 | + | 0.582079i | \(0.197760\pi\) | |||||||
\(432\) | −0.957203 | − | 1.65793i | −0.0460535 | − | 0.0797670i | ||||
\(433\) | 28.2700 | 1.35857 | 0.679284 | − | 0.733876i | \(-0.262290\pi\) | ||||
0.679284 | + | 0.733876i | \(0.262290\pi\) | |||||||
\(434\) | 9.17749 | + | 8.29945i | 0.440533 | + | 0.398386i | ||||
\(435\) | 0.539291 | 0.0258570 | ||||||||
\(436\) | −4.83446 | − | 8.37354i | −0.231529 | − | 0.401020i | ||||
\(437\) | 11.9142 | − | 20.6360i | 0.569934 | − | 0.987155i | ||||
\(438\) | −0.277914 | + | 0.481362i | −0.0132793 | + | 0.0230003i | ||||
\(439\) | 7.88172 | + | 13.6515i | 0.376174 | + | 0.651552i | 0.990502 | − | 0.137499i | \(-0.0439062\pi\) |
−0.614328 | + | 0.789051i | \(0.710573\pi\) | |||||||
\(440\) | 1.72970 | 0.0824602 | ||||||||
\(441\) | −16.9682 | + | 12.2164i | −0.808010 | + | 0.581731i | ||||
\(442\) | 9.05171 | 0.430546 | ||||||||
\(443\) | 0.745210 | + | 1.29074i | 0.0354060 | + | 0.0613250i | 0.883185 | − | 0.469024i | \(-0.155394\pi\) |
−0.847779 | + | 0.530349i | \(0.822061\pi\) | |||||||
\(444\) | 0.232655 | − | 0.402969i | 0.0110413 | − | 0.0191241i | ||||
\(445\) | 2.00155 | − | 3.46679i | 0.0948827 | − | 0.164342i | ||||
\(446\) | 2.96168 | + | 5.12978i | 0.140240 | + | 0.242902i | ||||
\(447\) | 1.70586 | 0.0806844 | ||||||||
\(448\) | 6.73107 | + | 6.08709i | 0.318013 | + | 0.287588i | ||||
\(449\) | −39.0741 | −1.84402 | −0.922011 | − | 0.387163i | \(-0.873455\pi\) | ||||
−0.922011 | + | 0.387163i | \(0.873455\pi\) | |||||||
\(450\) | −0.681245 | − | 1.17995i | −0.0321142 | − | 0.0556234i | ||||
\(451\) | −0.632164 | + | 1.09494i | −0.0297674 | + | 0.0515587i | ||||
\(452\) | −12.7599 | + | 22.1009i | −0.600177 | + | 1.03954i | ||||
\(453\) | −1.31266 | − | 2.27360i | −0.0616743 | − | 0.106823i | ||||
\(454\) | 6.82926 | 0.320513 | ||||||||
\(455\) | 2.50349 | − | 11.6540i | 0.117365 | − | 0.546348i | ||||
\(456\) | 0.545825 | 0.0255606 | ||||||||
\(457\) | 5.33822 | + | 9.24607i | 0.249711 | + | 0.432513i | 0.963446 | − | 0.267904i | \(-0.0863309\pi\) |
−0.713734 | + | 0.700417i | \(0.752998\pi\) | |||||||
\(458\) | −2.55608 | + | 4.42726i | −0.119438 | + | 0.206872i | ||||
\(459\) | 1.50850 | − | 2.61279i | 0.0704106 | − | 0.121955i | ||||
\(460\) | −7.74065 | − | 13.4072i | −0.360910 | − | 0.625114i | ||||
\(461\) | −15.6778 | −0.730190 | −0.365095 | − | 0.930970i | \(-0.618963\pi\) | ||||
−0.365095 | + | 0.930970i | \(0.618963\pi\) | |||||||
\(462\) | −0.131415 | + | 0.0423854i | −0.00611399 | + | 0.00197195i | ||||
\(463\) | 11.0374 | 0.512953 | 0.256476 | − | 0.966551i | \(-0.417438\pi\) | ||||
0.256476 | + | 0.966551i | \(0.417438\pi\) | |||||||
\(464\) | −6.58681 | − | 11.4087i | −0.305785 | − | 0.529635i | ||||
\(465\) | −0.586519 | + | 1.01588i | −0.0271992 | + | 0.0471104i | ||||
\(466\) | −1.79538 | + | 3.10968i | −0.0831692 | + | 0.144053i | ||||
\(467\) | −5.86901 | − | 10.1654i | −0.271585 | − | 0.470399i | 0.697683 | − | 0.716407i | \(-0.254215\pi\) |
−0.969268 | + | 0.246007i | \(0.920881\pi\) | |||||||
\(468\) | 24.1137 | 1.11466 | ||||||||
\(469\) | 2.73429 | − | 0.881890i | 0.126258 | − | 0.0407219i | ||||
\(470\) | −5.26087 | −0.242666 | ||||||||
\(471\) | 1.02043 | + | 1.76744i | 0.0470191 | + | 0.0814394i | ||||
\(472\) | −7.66397 | + | 13.2744i | −0.352763 | + | 0.611003i | ||||
\(473\) | −5.22682 | + | 9.05311i | −0.240329 | + | 0.416263i | ||||
\(474\) | 0.241223 | + | 0.417811i | 0.0110798 | + | 0.0191907i | ||||
\(475\) | −2.75808 | −0.126550 | ||||||||
\(476\) | −4.38571 | + | 20.4159i | −0.201019 | + | 0.935763i | ||||
\(477\) | 17.1441 | 0.784973 | ||||||||
\(478\) | 3.39013 | + | 5.87188i | 0.155061 | + | 0.268574i | ||||
\(479\) | 18.2677 | − | 31.6406i | 0.834674 | − | 1.44570i | −0.0596215 | − | 0.998221i | \(-0.518989\pi\) |
0.894296 | − | 0.447477i | \(-0.147677\pi\) | |||||||
\(480\) | 0.270831 | − | 0.469093i | 0.0123617 | − | 0.0214111i | ||||
\(481\) | 5.11257 | + | 8.85523i | 0.233113 | + | 0.403764i | ||||
\(482\) | −4.09683 | −0.186605 | ||||||||
\(483\) | 1.93972 | + | 1.75414i | 0.0882601 | + | 0.0798161i | ||||
\(484\) | −1.79192 | −0.0814511 | ||||||||
\(485\) | −2.51863 | − | 4.36239i | −0.114365 | − | 0.198086i | ||||
\(486\) | −0.700469 | + | 1.21325i | −0.0317739 | + | 0.0550340i | ||||
\(487\) | 12.7359 | − | 22.0592i | 0.577119 | − | 0.999599i | −0.418689 | − | 0.908130i | \(-0.637510\pi\) |
0.995808 | − | 0.0914697i | \(-0.0291565\pi\) | |||||||
\(488\) | −4.07157 | − | 7.05216i | −0.184311 | − | 0.319236i | ||||
\(489\) | 2.48332 | 0.112300 | ||||||||
\(490\) | −2.91138 | − | 1.31135i | −0.131523 | − | 0.0592406i | ||||
\(491\) | 16.7966 | 0.758018 | 0.379009 | − | 0.925393i | \(-0.376265\pi\) | ||||
0.379009 | + | 0.925393i | \(0.376265\pi\) | |||||||
\(492\) | 0.129606 | + | 0.224484i | 0.00584308 | + | 0.0101205i | ||||
\(493\) | 10.3804 | − | 17.9794i | 0.467511 | − | 0.809753i | ||||
\(494\) | −2.83407 | + | 4.90876i | −0.127511 | + | 0.220856i | ||||
\(495\) | 1.49345 | + | 2.58674i | 0.0671258 | + | 0.116265i | ||||
\(496\) | 28.6546 | 1.28663 | ||||||||
\(497\) | 25.1222 | + | 22.7187i | 1.12688 | + | 1.01907i | ||||
\(498\) | −0.135919 | −0.00609067 | ||||||||
\(499\) | −7.10185 | − | 12.3008i | −0.317922 | − | 0.550658i | 0.662132 | − | 0.749387i | \(-0.269652\pi\) |
−0.980054 | + | 0.198730i | \(0.936318\pi\) | |||||||
\(500\) | −0.895962 | + | 1.55185i | −0.0400686 | + | 0.0694009i | ||||
\(501\) | 0.145161 | − | 0.251426i | 0.00648530 | − | 0.0112329i | ||||
\(502\) | 0.213720 | + | 0.370173i | 0.00953878 | + | 0.0165217i | ||||
\(503\) | 26.3324 | 1.17410 | 0.587051 | − | 0.809550i | \(-0.300289\pi\) | ||||
0.587051 | + | 0.809550i | \(0.300289\pi\) | |||||||
\(504\) | 2.87089 | − | 13.3643i | 0.127879 | − | 0.595293i | ||||
\(505\) | 13.4523 | 0.598621 | ||||||||
\(506\) | −1.97047 | − | 3.41295i | −0.0875980 | − | 0.151724i | ||||
\(507\) | 0.417470 | − | 0.723080i | 0.0185405 | − | 0.0321131i | ||||
\(508\) | −1.44521 | + | 2.50318i | −0.0641209 | + | 0.111061i | ||||
\(509\) | 3.56023 | + | 6.16650i | 0.157804 | + | 0.273325i | 0.934077 | − | 0.357073i | \(-0.116225\pi\) |
−0.776272 | + | 0.630398i | \(0.782892\pi\) | |||||||
\(510\) | 0.229871 | 0.0101788 | ||||||||
\(511\) | 26.8172 | − | 8.64937i | 1.18632 | − | 0.382626i | ||||
\(512\) | −22.9000 | −1.01205 | ||||||||
\(513\) | 0.944616 | + | 1.63612i | 0.0417058 | + | 0.0722366i | ||||
\(514\) | 0.0840248 | − | 0.145535i | 0.00370617 | − | 0.00641928i | ||||
\(515\) | −0.291429 | + | 0.504770i | −0.0128419 | + | 0.0222428i | ||||
\(516\) | 1.07160 | + | 1.85606i | 0.0471745 | + | 0.0817086i | ||||
\(517\) | 11.5331 | 0.507225 | ||||||||
\(518\) | 2.60686 | − | 0.840792i | 0.114539 | − | 0.0369423i | ||||
\(519\) | −1.13511 | −0.0498256 | ||||||||
\(520\) | 3.89640 | + | 6.74876i | 0.170868 | + | 0.295953i | ||||
\(521\) | 1.07498 | − | 1.86192i | 0.0470957 | − | 0.0815721i | −0.841517 | − | 0.540231i | \(-0.818337\pi\) |
0.888612 | + | 0.458659i | \(0.151670\pi\) | |||||||
\(522\) | −3.21109 | + | 5.56176i | −0.140545 | + | 0.243432i | ||||
\(523\) | −8.45938 | − | 14.6521i | −0.369903 | − | 0.640691i | 0.619647 | − | 0.784881i | \(-0.287276\pi\) |
−0.989550 | + | 0.144190i | \(0.953942\pi\) | |||||||
\(524\) | 25.6511 | 1.12057 | ||||||||
\(525\) | 0.0635767 | − | 0.295956i | 0.00277472 | − | 0.0129166i | ||||
\(526\) | 2.63950 | 0.115088 | ||||||||
\(527\) | 22.5790 | + | 39.1079i | 0.983556 | + | 1.70357i | ||||
\(528\) | −0.159883 | + | 0.276925i | −0.00695800 | + | 0.0120516i | ||||
\(529\) | −25.8204 | + | 44.7223i | −1.12263 | + | 1.94445i | ||||
\(530\) | 1.30910 | + | 2.26743i | 0.0568637 | + | 0.0984908i | ||||
\(531\) | −26.4688 | −1.14865 | ||||||||
\(532\) | −9.69844 | − | 8.77057i | −0.420481 | − | 0.380252i | ||||
\(533\) | −5.69616 | −0.246728 | ||||||||
\(534\) | −0.104461 | − | 0.180931i | −0.00452046 | − | 0.00782967i | ||||
\(535\) | 7.07851 | − | 12.2603i | 0.306031 | − | 0.530060i | ||||
\(536\) | −0.939129 | + | 1.62662i | −0.0405642 | + | 0.0702593i | ||||
\(537\) | −0.335497 | − | 0.581099i | −0.0144778 | − | 0.0250763i | ||||
\(538\) | 4.63522 | 0.199838 | ||||||||
\(539\) | 6.38244 | + | 2.87479i | 0.274911 | + | 0.123826i | ||||
\(540\) | 1.22743 | 0.0528202 | ||||||||
\(541\) | −0.217764 | − | 0.377178i | −0.00936239 | − | 0.0162161i | 0.861306 | − | 0.508086i | \(-0.169647\pi\) |
−0.870669 | + | 0.491870i | \(0.836314\pi\) | |||||||
\(542\) | 4.88231 | − | 8.45641i | 0.209713 | − | 0.363234i | ||||
\(543\) | −0.983407 | + | 1.70331i | −0.0422020 | + | 0.0730961i | ||||
\(544\) | −10.4261 | − | 18.0585i | −0.447014 | − | 0.774251i | ||||
\(545\) | 5.39584 | 0.231132 | ||||||||
\(546\) | −0.461407 | − | 0.417263i | −0.0197464 | − | 0.0178572i | ||||
\(547\) | 2.04321 | 0.0873612 | 0.0436806 | − | 0.999046i | \(-0.486092\pi\) | ||||
0.0436806 | + | 0.999046i | \(0.486092\pi\) | |||||||
\(548\) | −7.26940 | − | 12.5910i | −0.310533 | − | 0.537859i | ||||
\(549\) | 7.03093 | − | 12.1779i | 0.300073 | − | 0.519741i | ||||
\(550\) | −0.228077 | + | 0.395041i | −0.00972523 | + | 0.0168446i | ||||
\(551\) | 6.50019 | + | 11.2587i | 0.276917 | + | 0.479635i | ||||
\(552\) | −1.70976 | −0.0727720 | ||||||||
\(553\) | 5.13672 | − | 23.9120i | 0.218436 | − | 1.01684i | ||||
\(554\) | 0.506603 | 0.0215235 | ||||||||
\(555\) | 0.129835 | + | 0.224881i | 0.00551119 | + | 0.00954566i | ||||
\(556\) | 14.6863 | − | 25.4375i | 0.622840 | − | 1.07879i | ||||
\(557\) | 13.6958 | − | 23.7219i | 0.580311 | − | 1.00513i | −0.415131 | − | 0.909762i | \(-0.636264\pi\) |
0.995442 | − | 0.0953669i | \(-0.0304024\pi\) | |||||||
\(558\) | −6.98459 | − | 12.0977i | −0.295681 | − | 0.512135i | ||||
\(559\) | −47.0966 | −1.99198 | ||||||||
\(560\) | −7.03746 | + | 2.26980i | −0.297387 | + | 0.0959164i | ||||
\(561\) | −0.503932 | −0.0212760 | ||||||||
\(562\) | 0.372283 | + | 0.644813i | 0.0157038 | + | 0.0271998i | ||||
\(563\) | 1.57601 | − | 2.72973i | 0.0664209 | − | 0.115044i | −0.830902 | − | 0.556418i | \(-0.812175\pi\) |
0.897323 | + | 0.441374i | \(0.145509\pi\) | |||||||
\(564\) | 1.18225 | − | 2.04772i | 0.0497818 | − | 0.0862247i | ||||
\(565\) | −7.12081 | − | 12.3336i | −0.299575 | − | 0.518878i | ||||
\(566\) | −5.15134 | −0.216527 | ||||||||
\(567\) | 22.3660 | − | 7.21371i | 0.939282 | − | 0.302947i | ||||
\(568\) | −22.1439 | −0.929136 | ||||||||
\(569\) | 21.0547 | + | 36.4678i | 0.882659 | + | 1.52881i | 0.848373 | + | 0.529398i | \(0.177582\pi\) |
0.0342855 | + | 0.999412i | \(0.489084\pi\) | |||||||
\(570\) | −0.0719720 | + | 0.124659i | −0.00301458 | + | 0.00522140i | ||||
\(571\) | 12.8882 | − | 22.3230i | 0.539353 | − | 0.934186i | −0.459586 | − | 0.888133i | \(-0.652002\pi\) |
0.998939 | − | 0.0460533i | \(-0.0146644\pi\) | |||||||
\(572\) | −4.03656 | − | 6.99154i | −0.168777 | − | 0.292331i | ||||
\(573\) | 1.48167 | 0.0618979 | ||||||||
\(574\) | −0.320475 | + | 1.49185i | −0.0133764 | + | 0.0622684i | ||||
\(575\) | 8.63949 | 0.360292 | ||||||||
\(576\) | −5.12272 | − | 8.87282i | −0.213447 | − | 0.369701i | ||||
\(577\) | −8.31003 | + | 14.3934i | −0.345951 | + | 0.599205i | −0.985526 | − | 0.169524i | \(-0.945777\pi\) |
0.639575 | + | 0.768729i | \(0.279110\pi\) | |||||||
\(578\) | 0.547306 | − | 0.947962i | 0.0227649 | − | 0.0394300i | ||||
\(579\) | −0.161934 | − | 0.280479i | −0.00672976 | − | 0.0116563i | ||||
\(580\) | 8.44633 | 0.350715 | ||||||||
\(581\) | 5.11056 | + | 4.62162i | 0.212022 | + | 0.191737i | ||||
\(582\) | −0.262894 | −0.0108973 | ||||||||
\(583\) | −2.86987 | − | 4.97076i | −0.118858 | − | 0.205868i | ||||
\(584\) | −9.21076 | + | 15.9535i | −0.381144 | + | 0.660161i | ||||
\(585\) | −6.72844 | + | 11.6540i | −0.278187 | + | 0.481834i | ||||
\(586\) | −0.248465 | − | 0.430354i | −0.0102640 | − | 0.0177777i | ||||
\(587\) | 12.5734 | 0.518958 | 0.259479 | − | 0.965749i | \(-0.416449\pi\) | ||||
0.259479 | + | 0.965749i | \(0.416449\pi\) | |||||||
\(588\) | 1.16469 | − | 0.838521i | 0.0480308 | − | 0.0345800i | ||||
\(589\) | −28.2778 | −1.16516 | ||||||||
\(590\) | −2.02113 | − | 3.50070i | −0.0832085 | − | 0.144121i | ||||
\(591\) | 0.0903436 | − | 0.156480i | 0.00371624 | − | 0.00643671i | ||||
\(592\) | 3.17157 | − | 5.49331i | 0.130351 | − | 0.225774i | ||||
\(593\) | −6.12297 | − | 10.6053i | −0.251440 | − | 0.435507i | 0.712482 | − | 0.701690i | \(-0.247571\pi\) |
−0.963923 | + | 0.266183i | \(0.914237\pi\) | |||||||
\(594\) | 0.312456 | 0.0128202 | ||||||||
\(595\) | −8.64315 | − | 7.81624i | −0.354335 | − | 0.320434i | ||||
\(596\) | 26.7170 | 1.09437 | ||||||||
\(597\) | −1.16711 | − | 2.02149i | −0.0477666 | − | 0.0827342i | ||||
\(598\) | 8.87753 | − | 15.3763i | 0.363029 | − | 0.628785i | ||||
\(599\) | 15.4057 | − | 26.6834i | 0.629460 | − | 1.09026i | −0.358201 | − | 0.933645i | \(-0.616610\pi\) |
0.987660 | − | 0.156611i | \(-0.0500570\pi\) | |||||||
\(600\) | 0.0989500 | + | 0.171386i | 0.00403962 | + | 0.00699682i | ||||
\(601\) | −35.2612 | −1.43833 | −0.719166 | − | 0.694838i | \(-0.755476\pi\) | ||||
−0.719166 | + | 0.694838i | \(0.755476\pi\) | |||||||
\(602\) | −2.64973 | + | 12.3348i | −0.107995 | + | 0.502728i | ||||
\(603\) | −3.24344 | −0.132083 | ||||||||
\(604\) | −20.5588 | − | 35.6089i | −0.836526 | − | 1.44891i | ||||
\(605\) | 0.500000 | − | 0.866025i | 0.0203279 | − | 0.0352089i | ||||
\(606\) | 0.351038 | − | 0.608015i | 0.0142599 | − | 0.0246989i | ||||
\(607\) | −1.43290 | − | 2.48185i | −0.0581595 | − | 0.100735i | 0.835480 | − | 0.549521i | \(-0.185190\pi\) |
−0.893639 | + | 0.448786i | \(0.851857\pi\) | |||||||
\(608\) | 13.0575 | 0.529553 | ||||||||
\(609\) | −1.35795 | + | 0.437979i | −0.0550268 | + | 0.0177478i | ||||
\(610\) | 2.14749 | 0.0869495 | ||||||||
\(611\) | 25.9800 | + | 44.9986i | 1.05104 | + | 1.82045i | ||||
\(612\) | 11.7871 | − | 20.4159i | 0.476467 | − | 0.825265i | ||||
\(613\) | −2.28952 | + | 3.96556i | −0.0924728 | + | 0.160168i | −0.908551 | − | 0.417774i | \(-0.862810\pi\) |
0.816078 | + | 0.577941i | \(0.196144\pi\) | |||||||
\(614\) | −4.22849 | − | 7.32396i | −0.170648 | − | 0.295571i | ||||
\(615\) | −0.144655 | −0.00583307 | ||||||||
\(616\) | −4.35542 | + | 1.40476i | −0.175485 | + | 0.0565993i | ||||
\(617\) | 24.5005 | 0.986353 | 0.493176 | − | 0.869929i | \(-0.335836\pi\) | ||||
0.493176 | + | 0.869929i | \(0.335836\pi\) | |||||||
\(618\) | 0.0152097 | + | 0.0263439i | 0.000611822 | + | 0.00105971i | ||||
\(619\) | 17.2517 | − | 29.8809i | 0.693405 | − | 1.20101i | −0.277310 | − | 0.960780i | \(-0.589443\pi\) |
0.970715 | − | 0.240232i | \(-0.0772237\pi\) | |||||||
\(620\) | −9.18601 | + | 15.9106i | −0.368919 | + | 0.638986i | ||||
\(621\) | −2.95894 | − | 5.12503i | −0.118738 | − | 0.205660i | ||||
\(622\) | −3.90260 | −0.156480 | ||||||||
\(623\) | −2.22444 | + | 10.3550i | −0.0891202 | + | 0.414864i | ||||
\(624\) | −1.44064 | −0.0576716 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 2.37819 | − | 4.11914i | 0.0950514 | − | 0.164634i | ||||
\(627\) | 0.157780 | − | 0.273283i | 0.00630113 | − | 0.0109139i | ||||
\(628\) | 15.9819 | + | 27.6815i | 0.637748 | + | 1.10461i | ||||
\(629\) | 9.99641 | 0.398583 | ||||||||
\(630\) | 2.67367 | + | 2.41788i | 0.106522 | + | 0.0963305i | ||||
\(631\) | 41.4967 | 1.65196 | 0.825979 | − | 0.563702i | \(-0.190623\pi\) | ||||
0.825979 | + | 0.563702i | \(0.190623\pi\) | |||||||
\(632\) | 7.99473 | + | 13.8473i | 0.318013 | + | 0.550815i | ||||
\(633\) | −0.936638 | + | 1.62230i | −0.0372280 | + | 0.0644808i | ||||
\(634\) | −0.301756 | + | 0.522656i | −0.0119843 | + | 0.0207573i | ||||
\(635\) | −0.806515 | − | 1.39692i | −0.0320056 | − | 0.0554352i | ||||
\(636\) | −1.17676 | −0.0466614 | ||||||||
\(637\) | 3.16083 | + | 31.3782i | 0.125237 | + | 1.24325i | ||||
\(638\) | 2.15011 | 0.0851235 | ||||||||
\(639\) | −19.1194 | − | 33.1158i | −0.756352 | − | 1.31004i | ||||
\(640\) | 5.51661 | − | 9.55504i | 0.218063 | − | 0.377696i | ||||
\(641\) | −2.77652 | + | 4.80907i | −0.109666 | + | 0.189947i | −0.915635 | − | 0.402011i | \(-0.868311\pi\) |
0.805969 | + | 0.591958i | \(0.201645\pi\) | |||||||
\(642\) | −0.369426 | − | 0.639865i | −0.0145801 | − | 0.0252535i | ||||
\(643\) | −47.5230 | −1.87412 | −0.937061 | − | 0.349164i | \(-0.886465\pi\) | ||||
−0.937061 | + | 0.349164i | \(0.886465\pi\) | |||||||
\(644\) | 30.3796 | + | 27.4731i | 1.19713 | + | 1.08259i | ||||
\(645\) | −1.19603 | −0.0470937 | ||||||||
\(646\) | 2.77068 | + | 4.79895i | 0.109011 | + | 0.188812i | ||||
\(647\) | 11.9333 | − | 20.6691i | 0.469147 | − | 0.812587i | −0.530231 | − | 0.847853i | \(-0.677895\pi\) |
0.999378 | + | 0.0352665i | \(0.0112280\pi\) | |||||||
\(648\) | −7.68191 | + | 13.3055i | −0.301774 | + | 0.522688i | ||||
\(649\) | 4.43080 | + | 7.67438i | 0.173924 | + | 0.301246i | ||||
\(650\) | −2.05510 | −0.0806078 | ||||||||
\(651\) | 0.651832 | − | 3.03435i | 0.0255473 | − | 0.118925i | ||||
\(652\) | 38.8935 | 1.52319 | ||||||||
\(653\) | 8.46747 | + | 14.6661i | 0.331358 | + | 0.573928i | 0.982778 | − | 0.184788i | \(-0.0591600\pi\) |
−0.651421 | + | 0.758717i | \(0.725827\pi\) | |||||||
\(654\) | 0.140804 | − | 0.243880i | 0.00550587 | − | 0.00953645i | ||||
\(655\) | −7.15742 | + | 12.3970i | −0.279664 | + | 0.484392i | ||||
\(656\) | 1.76680 | + | 3.06018i | 0.0689818 | + | 0.119480i | ||||
\(657\) | −31.8109 | −1.24106 | ||||||||
\(658\) | 13.2470 | − | 4.27255i | 0.516421 | − | 0.166562i | ||||
\(659\) | 12.5122 | 0.487407 | 0.243703 | − | 0.969850i | \(-0.421638\pi\) | ||||
0.243703 | + | 0.969850i | \(0.421638\pi\) | |||||||
\(660\) | −0.102510 | − | 0.177552i | −0.00399018 | − | 0.00691119i | ||||
\(661\) | −5.00645 | + | 8.67142i | −0.194728 | + | 0.337279i | −0.946811 | − | 0.321789i | \(-0.895716\pi\) |
0.752083 | + | 0.659068i | \(0.229049\pi\) | |||||||
\(662\) | 5.21995 | − | 9.04123i | 0.202879 | − | 0.351397i | ||||
\(663\) | −1.13518 | − | 1.96619i | −0.0440867 | − | 0.0763604i | ||||
\(664\) | −4.50468 | −0.174816 | ||||||||
\(665\) | 6.94491 | − | 2.23995i | 0.269312 | − | 0.0868614i | ||||
\(666\) | −3.09229 | −0.119824 | ||||||||
\(667\) | −20.3614 | − | 35.2669i | −0.788395 | − | 1.36554i | ||||
\(668\) | 2.27349 | − | 3.93780i | 0.0879641 | − | 0.152358i | ||||
\(669\) | 0.742851 | − | 1.28666i | 0.0287203 | − | 0.0497450i | ||||
\(670\) | −0.247666 | − | 0.428969i | −0.00956816 | − | 0.0165725i | ||||
\(671\) | −4.70783 | −0.181744 | ||||||||
\(672\) | −0.300990 | + | 1.40114i | −0.0116109 | + | 0.0540501i | ||||
\(673\) | 14.6357 | 0.564163 | 0.282082 | − | 0.959390i | \(-0.408975\pi\) | ||||
0.282082 | + | 0.959390i | \(0.408975\pi\) | |||||||
\(674\) | −4.19843 | − | 7.27189i | −0.161717 | − | 0.280103i | ||||
\(675\) | −0.342490 | + | 0.593210i | −0.0131824 | + | 0.0228327i | ||||
\(676\) | 6.53838 | − | 11.3248i | 0.251476 | − | 0.435569i | ||||
\(677\) | −18.8759 | − | 32.6939i | −0.725458 | − | 1.25653i | −0.958785 | − | 0.284132i | \(-0.908295\pi\) |
0.233327 | − | 0.972398i | \(-0.425039\pi\) | |||||||
\(678\) | −0.743268 | −0.0285450 | ||||||||
\(679\) | 9.88482 | + | 8.93911i | 0.379345 | + | 0.343052i | ||||
\(680\) | 7.61847 | 0.292155 | ||||||||
\(681\) | −0.856460 | − | 1.48343i | −0.0328196 | − | 0.0568452i | ||||
\(682\) | −2.33840 | + | 4.05023i | −0.0895420 | + | 0.155091i | ||||
\(683\) | −14.7844 | + | 25.6073i | −0.565709 | + | 0.979837i | 0.431274 | + | 0.902221i | \(0.358064\pi\) |
−0.996983 | + | 0.0776158i | \(0.975269\pi\) | |||||||
\(684\) | 7.38107 | + | 12.7844i | 0.282222 | + | 0.488823i | ||||
\(685\) | 8.11351 | 0.310001 | ||||||||
\(686\) | 8.39590 | + | 0.937554i | 0.320557 | + | 0.0357960i | ||||
\(687\) | 1.28224 | 0.0489204 | ||||||||
\(688\) | 14.6081 | + | 25.3020i | 0.556929 | + | 0.964629i | ||||
\(689\) | 12.9296 | − | 22.3947i | 0.492577 | − | 0.853169i | ||||
\(690\) | 0.225447 | − | 0.390486i | 0.00858262 | − | 0.0148655i | ||||
\(691\) | −1.34742 | − | 2.33380i | −0.0512583 | − | 0.0887819i | 0.839258 | − | 0.543734i | \(-0.182990\pi\) |
−0.890516 | + | 0.454952i | \(0.849657\pi\) | |||||||
\(692\) | −17.7779 | −0.675815 | ||||||||
\(693\) | −5.86134 | − | 5.30057i | −0.222654 | − | 0.201352i | ||||
\(694\) | −4.55494 | −0.172903 | ||||||||
\(695\) | 8.19585 | + | 14.1956i | 0.310886 | + | 0.538471i | ||||
\(696\) | 0.466406 | − | 0.807839i | 0.0176791 | − | 0.0306211i | ||||
\(697\) | −2.78437 | + | 4.82267i | −0.105466 | + | 0.182672i | ||||
\(698\) | −5.48534 | − | 9.50089i | −0.207623 | − | 0.359614i | ||||
\(699\) | 0.900635 | 0.0340652 | ||||||||
\(700\) | 0.995732 | − | 4.63524i | 0.0376351 | − | 0.175196i | ||||
\(701\) | −36.6363 | −1.38373 | −0.691867 | − | 0.722025i | \(-0.743211\pi\) | ||||
−0.691867 | + | 0.722025i | \(0.743211\pi\) | |||||||
\(702\) | 0.703852 | + | 1.21911i | 0.0265652 | + | 0.0460123i | ||||
\(703\) | −3.12986 | + | 5.42107i | −0.118045 | + | 0.204460i | ||||
\(704\) | −1.71506 | + | 2.97057i | −0.0646387 | + | 0.111957i | ||||
\(705\) | 0.659768 | + | 1.14275i | 0.0248483 | + | 0.0430385i | ||||
\(706\) | 10.7776 | 0.405619 | ||||||||
\(707\) | −33.8733 | + | 10.9252i | −1.27393 | + | 0.410883i | ||||
\(708\) | 1.81680 | 0.0682795 | ||||||||
\(709\) | 8.77583 | + | 15.2002i | 0.329583 | + | 0.570855i | 0.982429 | − | 0.186636i | \(-0.0597584\pi\) |
−0.652846 | + | 0.757491i | \(0.726425\pi\) | |||||||
\(710\) | 2.91987 | − | 5.05737i | 0.109581 | − | 0.189800i | ||||
\(711\) | −13.8056 | + | 23.9120i | −0.517750 | + | 0.896769i | ||||
\(712\) | −3.46209 | − | 5.99651i | −0.129747 | − | 0.224729i | ||||
\(713\) | 88.5779 | 3.31727 | ||||||||
\(714\) | −0.578819 | + | 0.186687i | −0.0216618 | + | 0.00698658i | ||||
\(715\) | 4.50529 | 0.168488 | ||||||||
\(716\) | −5.25453 | − | 9.10111i | −0.196371 | − | 0.340124i | ||||
\(717\) | 0.850316 | − | 1.47279i | 0.0317556 | − | 0.0550024i | ||||
\(718\) | 0.836288 | − | 1.44849i | 0.0312100 | − | 0.0540573i | ||||
\(719\) | 8.10580 | + | 14.0397i | 0.302295 | + | 0.523591i | 0.976655 | − | 0.214812i | \(-0.0689138\pi\) |
−0.674360 | + | 0.738403i | \(0.735580\pi\) | |||||||
\(720\) | 8.34793 | 0.311109 | ||||||||
\(721\) | 0.323882 | − | 1.50770i | 0.0120620 | − | 0.0561498i | ||||
\(722\) | 5.19695 | 0.193410 | ||||||||
\(723\) | 0.513785 | + | 0.889902i | 0.0191079 | + | 0.0330958i | ||||
\(724\) | −15.4020 | + | 26.6771i | −0.572412 | + | 0.991447i | ||||
\(725\) | −2.35678 | + | 4.08206i | −0.0875285 | + | 0.151604i | ||||
\(726\) | −0.0260949 | − | 0.0451978i | −0.000968474 | − | 0.00167745i | ||||
\(727\) | 14.4655 | 0.536497 | 0.268248 | − | 0.963350i | \(-0.413555\pi\) | ||||
0.268248 | + | 0.963350i | \(0.413555\pi\) | |||||||
\(728\) | −15.2921 | − | 13.8291i | −0.566765 | − | 0.512541i | ||||
\(729\) | −26.2957 | −0.973914 | ||||||||
\(730\) | −2.42905 | − | 4.20723i | −0.0899031 | − | 0.155717i | ||||
\(731\) | −23.0215 | + | 39.8745i | −0.851482 | + | 1.47481i | ||||
\(732\) | −0.482598 | + | 0.835883i | −0.0178373 | + | 0.0308951i | ||||
\(733\) | −18.3024 | − | 31.7007i | −0.676014 | − | 1.17089i | −0.976171 | − | 0.217001i | \(-0.930372\pi\) |
0.300157 | − | 0.953890i | \(-0.402961\pi\) | |||||||
\(734\) | −8.80217 | −0.324894 | ||||||||
\(735\) | 0.0802701 | + | 0.796858i | 0.00296081 | + | 0.0293925i | ||||
\(736\) | −40.9017 | −1.50766 | ||||||||
\(737\) | 0.542943 | + | 0.940405i | 0.0199996 | + | 0.0346403i | ||||
\(738\) | 0.861317 | − | 1.49185i | 0.0317055 | − | 0.0549156i | ||||
\(739\) | −18.8352 | + | 32.6235i | −0.692863 | + | 1.20007i | 0.278032 | + | 0.960572i | \(0.410318\pi\) |
−0.970896 | + | 0.239503i | \(0.923016\pi\) | |||||||
\(740\) | 2.03346 | + | 3.52206i | 0.0747516 | + | 0.129474i | ||||
\(741\) | 1.42169 | 0.0522271 | ||||||||
\(742\) | −5.13781 | − | 4.64626i | −0.188615 | − | 0.170570i | ||||
\(743\) | −21.1779 | −0.776943 | −0.388471 | − | 0.921461i | \(-0.626997\pi\) | ||||
−0.388471 | + | 0.921461i | \(0.626997\pi\) | |||||||
\(744\) | 1.01450 | + | 1.75717i | 0.0371935 | + | 0.0644210i | ||||
\(745\) | −7.45484 | + | 12.9122i | −0.273124 | + | 0.473065i | ||||
\(746\) | −4.54161 | + | 7.86629i | −0.166280 | + | 0.288005i | ||||
\(747\) | −3.88942 | − | 6.73668i | −0.142307 | − | 0.246482i | ||||
\(748\) | −7.89253 | −0.288580 | ||||||||
\(749\) | −7.86674 | + | 36.6205i | −0.287444 | + | 1.33808i | ||||
\(750\) | −0.0521899 | −0.00190571 | ||||||||
\(751\) | −11.9923 | − | 20.7712i | −0.437605 | − | 0.757954i | 0.559900 | − | 0.828560i | \(-0.310840\pi\) |
−0.997504 | + | 0.0706070i | \(0.977506\pi\) | |||||||
\(752\) | 16.1166 | − | 27.9147i | 0.587711 | − | 1.01795i | ||||
\(753\) | 0.0536054 | − | 0.0928472i | 0.00195349 | − | 0.00338354i | ||||
\(754\) | 4.84342 | + | 8.38905i | 0.176387 | + | 0.305511i | ||||
\(755\) | 22.9461 | 0.835093 | ||||||||
\(756\) | −3.09070 | + | 0.996844i | −0.112408 | + | 0.0362549i | ||||
\(757\) | 9.27258 | 0.337018 | 0.168509 | − | 0.985700i | \(-0.446105\pi\) | ||||
0.168509 | + | 0.985700i | \(0.446105\pi\) | |||||||
\(758\) | 3.59561 | + | 6.22778i | 0.130598 | + | 0.226203i | ||||
\(759\) | −0.494235 | + | 0.856039i | −0.0179396 | + | 0.0310723i | ||||
\(760\) | −2.38533 | + | 4.13151i | −0.0865250 | + | 0.149866i | ||||
\(761\) | −1.77411 | − | 3.07284i | −0.0643113 | − | 0.111390i | 0.832077 | − | 0.554660i | \(-0.187152\pi\) |
−0.896388 | + | 0.443270i | \(0.853818\pi\) | |||||||
\(762\) | −0.0841838 | −0.00304966 | ||||||||
\(763\) | −13.5868 | + | 4.38217i | −0.491876 | + | 0.158645i | ||||
\(764\) | 23.2058 | 0.839558 | ||||||||
\(765\) | 6.57793 | + | 11.3933i | 0.237825 | + | 0.411926i | ||||
\(766\) | −1.07444 | + | 1.86098i | −0.0388210 | + | 0.0672399i | ||||
\(767\) | −19.9620 | + | 34.5753i | −0.720788 | + | 1.24844i | ||||
\(768\) | 0.104538 | + | 0.181066i | 0.00377221 | + | 0.00653365i | ||||
\(769\) | 27.6695 | 0.997787 | 0.498893 | − | 0.866663i | \(-0.333740\pi\) | ||||
0.498893 | + | 0.866663i | \(0.333740\pi\) | |||||||
\(770\) | 0.253475 | − | 1.17995i | 0.00913459 | − | 0.0425225i | ||||
\(771\) | −0.0421503 | −0.00151801 | ||||||||
\(772\) | −2.53620 | − | 4.39283i | −0.0912799 | − | 0.158101i | ||||
\(773\) | −7.04182 | + | 12.1968i | −0.253277 | + | 0.438688i | −0.964426 | − | 0.264353i | \(-0.914842\pi\) |
0.711149 | + | 0.703041i | \(0.248175\pi\) | |||||||
\(774\) | 7.12149 | − | 12.3348i | 0.255977 | − | 0.443365i | ||||
\(775\) | −5.12634 | − | 8.87908i | −0.184144 | − | 0.318946i | ||||
\(776\) | −8.71294 | −0.312776 | ||||||||
\(777\) | −0.509562 | − | 0.460811i | −0.0182804 | − | 0.0165315i | ||||
\(778\) | −3.23622 | −0.116024 | ||||||||
\(779\) | −1.74356 | − | 3.01994i | −0.0624696 | − | 0.108200i | ||||
\(780\) | 0.461835 | − | 0.799922i | 0.0165363 | − | 0.0286418i | ||||
\(781\) | −6.40107 | + | 11.0870i | −0.229048 | + | 0.396723i | ||||
\(782\) | −8.67894 | − | 15.0324i | −0.310358 | − | 0.537556i | ||||
\(783\) | 3.22869 | 0.115384 | ||||||||
\(784\) | 15.8771 | − | 11.4308i | 0.567039 | − | 0.408242i | ||||
\(785\) | −17.8377 | −0.636656 | ||||||||
\(786\) | 0.373545 | + | 0.646999i | 0.0133239 | + | 0.0230777i | ||||
\(787\) | −21.4169 | + | 37.0952i | −0.763431 | + | 1.32230i | 0.177641 | + | 0.984095i | \(0.443153\pi\) |
−0.941072 | + | 0.338206i | \(0.890180\pi\) | |||||||
\(788\) | 1.41495 | − | 2.45077i | 0.0504056 | − | 0.0873050i | ||||
\(789\) | −0.331021 | − | 0.573345i | −0.0117847 | − | 0.0204116i | ||||
\(790\) | −4.21671 | −0.150024 | ||||||||
\(791\) | 27.9469 | + | 25.2732i | 0.993679 | + | 0.898611i | ||||
\(792\) | 5.16646 | 0.183582 | ||||||||
\(793\) | −10.6051 | − | 18.3685i | −0.376597 | − | 0.652285i | ||||
\(794\) | −0.165554 | + | 0.286749i | −0.00587530 | + | 0.0101763i | ||||
\(795\) | 0.328350 | − | 0.568718i | 0.0116454 | − | 0.0201704i | ||||
\(796\) | −18.2792 | − | 31.6604i | −0.647887 | − | 1.12217i | ||||
\(797\) | −47.6777 | −1.68883 | −0.844415 | − | 0.535689i | \(-0.820052\pi\) | ||||
−0.844415 | + | 0.535689i | \(0.820052\pi\) | |||||||
\(798\) | 0.0799865 | − | 0.372346i | 0.00283149 | − | 0.0131809i | ||||
\(799\) | 50.7976 | 1.79709 | ||||||||
\(800\) | 2.36714 | + | 4.10000i | 0.0836910 | + | 0.144957i | ||||
\(801\) | 5.97846 | − | 10.3550i | 0.211238 | − | 0.365876i | ||||
\(802\) | 7.22804 | − | 12.5193i | 0.255231 | − | 0.442073i | ||||
\(803\) | 5.32506 | + | 9.22327i | 0.187917 | + | 0.325482i | ||||
\(804\) | 0.222628 | 0.00785147 | ||||||||
\(805\) | −21.7544 | + | 7.01647i | −0.766743 | + | 0.247298i | ||||
\(806\) | −21.0703 | −0.742170 | ||||||||
\(807\) | −0.581305 | − | 1.00685i | −0.0204629 | − | 0.0354428i | ||||
\(808\) | 11.6343 | − | 20.1511i | 0.409292 | − | 0.708914i | ||||
\(809\) | 26.4555 | − | 45.8223i | 0.930127 | − | 1.61103i | 0.147027 | − | 0.989132i | \(-0.453030\pi\) |
0.783100 | − | 0.621895i | \(-0.213637\pi\) | |||||||
\(810\) | −2.02586 | − | 3.50889i | −0.0711815 | − | 0.123290i | ||||
\(811\) | −9.70911 | −0.340933 | −0.170466 | − | 0.985363i | \(-0.554527\pi\) | ||||
−0.170466 | + | 0.985363i | \(0.554527\pi\) | |||||||
\(812\) | −21.2680 | + | 6.85959i | −0.746362 | + | 0.240724i | ||||
\(813\) | −2.44917 | −0.0858962 | ||||||||
\(814\) | 0.517641 | + | 0.896580i | 0.0181433 | + | 0.0314251i | ||||
\(815\) | −10.8525 | + | 18.7970i | −0.380145 | + | 0.658430i | ||||
\(816\) | −0.704204 | + | 1.21972i | −0.0246521 | + | 0.0426986i | ||||
\(817\) | −14.4160 | − | 24.9693i | −0.504352 | − | 0.873564i | ||||
\(818\) | −8.58788 | −0.300268 | ||||||||
\(819\) | 7.47769 | − | 34.8095i | 0.261292 | − | 1.21634i | ||||
\(820\) | −2.26558 | −0.0791175 | ||||||||
\(821\) | −9.41313 | − | 16.3040i | −0.328521 | − | 0.569014i | 0.653698 | − | 0.756756i | \(-0.273217\pi\) |
−0.982219 | + | 0.187741i | \(0.939883\pi\) | |||||||
\(822\) | 0.211722 | − | 0.366713i | 0.00738464 | − | 0.0127906i | ||||
\(823\) | −9.43420 | + | 16.3405i | −0.328855 | + | 0.569594i | −0.982285 | − | 0.187393i | \(-0.939996\pi\) |
0.653430 | + | 0.756987i | \(0.273330\pi\) | |||||||
\(824\) | 0.504085 | + | 0.873102i | 0.0175606 | + | 0.0304159i | ||||
\(825\) | 0.114413 | 0.00398335 | ||||||||
\(826\) | 7.93230 | + | 7.17339i | 0.276000 | + | 0.249594i | ||||
\(827\) | 4.27820 | 0.148768 | 0.0743838 | − | 0.997230i | \(-0.476301\pi\) | ||||
0.0743838 | + | 0.997230i | \(0.476301\pi\) | |||||||
\(828\) | −23.1206 | − | 40.0461i | −0.803498 | − | 1.39170i | ||||
\(829\) | −8.60101 | + | 14.8974i | −0.298725 | + | 0.517407i | −0.975845 | − | 0.218466i | \(-0.929895\pi\) |
0.677119 | + | 0.735873i | \(0.263228\pi\) | |||||||
\(830\) | 0.593984 | − | 1.02881i | 0.0206175 | − | 0.0357105i | ||||
\(831\) | −0.0635333 | − | 0.110043i | −0.00220395 | − | 0.00381735i | ||||
\(832\) | −15.4537 | −0.535759 | ||||||||
\(833\) | 28.1115 | + | 12.6620i | 0.974006 | + | 0.438713i | ||||
\(834\) | 0.855481 | 0.0296229 | ||||||||
\(835\) | 1.26874 | + | 2.19753i | 0.0439067 | + | 0.0760486i | ||||
\(836\) | 2.47114 | − | 4.28014i | 0.0854661 | − | 0.148032i | ||||
\(837\) | −3.51144 | + | 6.08199i | −0.121373 | + | 0.210224i | ||||
\(838\) | −2.19967 | − | 3.80994i | −0.0759863 | − | 0.131612i | ||||
\(839\) | 1.07278 | 0.0370363 | 0.0185182 | − | 0.999829i | \(-0.494105\pi\) | ||||
0.0185182 | + | 0.999829i | \(0.494105\pi\) | |||||||
\(840\) | −0.388348 | − | 0.351194i | −0.0133993 | − | 0.0121173i | ||||
\(841\) | −6.78242 | −0.233876 | ||||||||
\(842\) | 7.69231 | + | 13.3235i | 0.265094 | + | 0.459157i | ||||
\(843\) | 0.0933763 | − | 0.161732i | 0.00321605 | − | 0.00557036i | ||||
\(844\) | −14.6695 | + | 25.4084i | −0.504946 | + | 0.874592i | ||||
\(845\) | 3.64880 | + | 6.31991i | 0.125523 | + | 0.217412i | ||||
\(846\) | −15.7137 | −0.540249 | ||||||||
\(847\) | −0.555678 | + | 2.58674i | −0.0190933 | + | 0.0888814i | ||||
\(848\) | −16.0416 | −0.550872 | ||||||||
\(849\) | 0.646032 | + | 1.11896i | 0.0221718 | + | 0.0384026i | ||||
\(850\) | −1.00457 | + | 1.73996i | −0.0344563 | + | 0.0596801i | ||||
\(851\) | 9.80404 | − | 16.9811i | 0.336078 | − | 0.582105i | ||||
\(852\) | 1.31234 | + | 2.27304i | 0.0449601 | + | 0.0778731i | ||||
\(853\) | −57.2538 | −1.96033 | −0.980167 | − | 0.198173i | \(-0.936499\pi\) | ||||
−0.980167 | + | 0.198173i | \(0.936499\pi\) | |||||||
\(854\) | −5.40744 | + | 1.74406i | −0.185039 | + | 0.0596806i | ||||
\(855\) | −8.23815 | −0.281739 | ||||||||
\(856\) | −12.2437 | − | 21.2067i | −0.418481 | − | 0.724830i | ||||
\(857\) | −7.35987 | + | 12.7477i | −0.251408 | + | 0.435452i | −0.963914 | − | 0.266214i | \(-0.914227\pi\) |
0.712505 | + | 0.701667i | \(0.247560\pi\) | |||||||
\(858\) | 0.117565 | − | 0.203629i | 0.00401361 | − | 0.00695178i | ||||
\(859\) | 8.84371 | + | 15.3177i | 0.301743 | + | 0.522635i | 0.976531 | − | 0.215377i | \(-0.0690981\pi\) |
−0.674788 | + | 0.738012i | \(0.735765\pi\) | |||||||
\(860\) | −18.7321 | −0.638760 | ||||||||
\(861\) | 0.364245 | − | 0.117480i | 0.0124135 | − | 0.00400372i | ||||
\(862\) | −1.84719 | −0.0629155 | ||||||||
\(863\) | 9.83005 | + | 17.0261i | 0.334619 | + | 0.579577i | 0.983412 | − | 0.181388i | \(-0.0580591\pi\) |
−0.648793 | + | 0.760965i | \(0.724726\pi\) | |||||||
\(864\) | 1.62144 | − | 2.80842i | 0.0551626 | − | 0.0955444i | ||||
\(865\) | 4.96057 | − | 8.59196i | 0.168664 | − | 0.292135i | ||||
\(866\) | 6.44773 | + | 11.1678i | 0.219103 | + | 0.379497i | ||||
\(867\) | −0.274552 | −0.00932426 | ||||||||
\(868\) | 10.2089 | − | 47.5236i | 0.346513 | − | 1.61306i | ||||
\(869\) | 9.24406 | 0.313583 | ||||||||
\(870\) | 0.123000 | + | 0.213042i | 0.00417009 | + | 0.00722280i | ||||
\(871\) | −2.44611 | + | 4.23680i | −0.0828834 | + | 0.143558i | ||||
\(872\) | 4.66659 | − | 8.08277i | 0.158031 | − | 0.273717i | ||||
\(873\) | −7.52291 | − | 13.0301i | −0.254612 | − | 0.441001i | ||||
\(874\) | 10.8694 | 0.367664 | ||||||||
\(875\) | 1.96234 | + | 1.77460i | 0.0663393 | + | 0.0599925i | ||||
\(876\) | 2.18348 | 0.0737729 | ||||||||
\(877\) | 18.3218 | + | 31.7344i | 0.618685 | + | 1.07159i | 0.989726 | + | 0.142977i | \(0.0456674\pi\) |
−0.371041 | + | 0.928616i | \(0.620999\pi\) | |||||||
\(878\) | −3.59527 | + | 6.22720i | −0.121335 | + | 0.210158i | ||||
\(879\) | −0.0623201 | + | 0.107942i | −0.00210201 | + | 0.00364078i | ||||
\(880\) | −1.39742 | − | 2.42040i | −0.0471070 | − | 0.0815917i | ||||
\(881\) | 20.9238 | 0.704940 | 0.352470 | − | 0.935823i | \(-0.385342\pi\) | ||||
0.352470 | + | 0.935823i | \(0.385342\pi\) | |||||||
\(882\) | −8.69602 | − | 3.91687i | −0.292810 | − | 0.131888i | ||||
\(883\) | 16.4768 | 0.554488 | 0.277244 | − | 0.960800i | \(-0.410579\pi\) | ||||
0.277244 | + | 0.960800i | \(0.410579\pi\) | |||||||
\(884\) | −17.7791 | − | 30.7942i | −0.597975 | − | 1.03572i | ||||
\(885\) | −0.506941 | + | 0.878048i | −0.0170406 | + | 0.0295153i | ||||
\(886\) | −0.339931 | + | 0.588777i | −0.0114202 | + | 0.0197804i | ||||
\(887\) | 22.1403 | + | 38.3481i | 0.743398 | + | 1.28760i | 0.950939 | + | 0.309377i | \(0.100121\pi\) |
−0.207541 | + | 0.978226i | \(0.566546\pi\) | |||||||
\(888\) | 0.449152 | 0.0150725 | ||||||||
\(889\) | 3.16532 | + | 2.86248i | 0.106161 | + | 0.0960046i | ||||
\(890\) | 1.82603 | 0.0612087 | ||||||||
\(891\) | 4.44118 | + | 7.69235i | 0.148785 | + | 0.257703i | ||||
\(892\) | 11.6345 | − | 20.1515i | 0.389550 | − | 0.674721i | ||||
\(893\) | −15.9046 | + | 27.5476i | −0.532228 | + | 0.921846i | ||||
\(894\) | 0.389067 | + | 0.673885i | 0.0130124 | + | 0.0225381i | ||||
\(895\) | 5.86468 | 0.196035 | ||||||||
\(896\) | −6.13091 | + | 28.5401i | −0.204819 | + | 0.953456i | ||||
\(897\) | −4.45334 | −0.148693 | ||||||||
\(898\) | −8.91191 | − | 15.4359i | −0.297394 | − | 0.515102i | ||||
\(899\) | −24.1633 | + | 41.8520i | −0.805890 | + | 1.39584i | ||||
\(900\) | −2.67616 | + | 4.63524i | −0.0892052 | + | 0.154508i | ||||
\(901\) | −12.6403 | − | 21.8937i | −0.421111 | − | 0.729385i | ||||
\(902\) | −0.576728 | −0.0192029 | ||||||||
\(903\) | 3.01163 | − | 0.971343i | 0.100221 | − | 0.0323243i | ||||
\(904\) | −24.6337 | −0.819306 | ||||||||
\(905\) | −8.59525 | − | 14.8874i | −0.285716 | − | 0.494874i | ||||
\(906\) | 0.598777 | − | 1.03711i | 0.0198930 | − | 0.0344557i | ||||
\(907\) | −1.04587 | + | 1.81150i | −0.0347276 | + | 0.0601499i | −0.882867 | − | 0.469623i | \(-0.844390\pi\) |
0.848139 | + | 0.529773i | \(0.177723\pi\) | |||||||
\(908\) | −13.4138 | − | 23.2334i | −0.445152 | − | 0.771027i | ||||
\(909\) | 40.1809 | 1.33272 | ||||||||
\(910\) | 5.17480 | − | 1.66903i | 0.171543 | − | 0.0553278i | ||||
\(911\) | 13.4632 | 0.446054 | 0.223027 | − | 0.974812i | \(-0.428406\pi\) | ||||
0.223027 | + | 0.974812i | \(0.428406\pi\) | |||||||
\(912\) | −0.440970 | − | 0.763782i | −0.0146020 | − | 0.0252914i | ||||
\(913\) | −1.30216 | + | 2.25540i | −0.0430951 | + | 0.0746429i | ||||
\(914\) | −2.43505 | + | 4.21763i | −0.0805443 | + | 0.139507i | ||||
\(915\) | −0.269318 | − | 0.466473i | −0.00890338 | − | 0.0154211i | ||||
\(916\) | 20.0823 | 0.663537 | ||||||||
\(917\) | 7.95444 | − | 37.0288i | 0.262679 | − | 1.22280i | ||||
\(918\) | 1.37621 | 0.0454218 | ||||||||
\(919\) | −9.45339 | − | 16.3737i | −0.311838 | − | 0.540120i | 0.666922 | − | 0.745128i | \(-0.267611\pi\) |
−0.978760 | + | 0.205008i | \(0.934278\pi\) | |||||||
\(920\) | 7.47187 | − | 12.9417i | 0.246340 | − | 0.426674i | ||||
\(921\) | −1.06059 | + | 1.83700i | −0.0349477 | + | 0.0605313i | ||||
\(922\) | −3.57575 | − | 6.19339i | −0.117761 | − | 0.203968i | ||||
\(923\) | −57.6773 | −1.89847 | ||||||||
\(924\) | 0.402318 | + | 0.363827i | 0.0132353 | + | 0.0119690i | ||||
\(925\) | −2.26959 | −0.0746236 | ||||||||
\(926\) | 2.51738 | + | 4.36023i | 0.0827263 | + | 0.143286i | ||||
\(927\) | −0.870473 | + | 1.50770i | −0.0285901 | + | 0.0495195i | ||||
\(928\) | 11.1576 | − | 19.3256i | 0.366267 | − | 0.634394i | ||||
\(929\) | 25.8686 | + | 44.8057i | 0.848721 | + | 1.47003i | 0.882350 | + | 0.470594i | \(0.155960\pi\) |
−0.0336285 | + | 0.999434i | \(0.510706\pi\) | |||||||
\(930\) | −0.535086 | −0.0175462 | ||||||||
\(931\) | −15.6683 | + | 11.2805i | −0.513508 | + | 0.369702i | ||||
\(932\) | 14.1057 | 0.462046 | ||||||||
\(933\) | 0.489426 | + | 0.847711i | 0.0160231 | + | 0.0277528i | ||||
\(934\) | 2.67717 | − | 4.63700i | 0.0875997 | − | 0.151727i | ||||
\(935\) | 2.20225 | − | 3.81441i | 0.0720213 | − | 0.124745i | ||||
\(936\) | 11.6382 | + | 20.1579i | 0.380406 | + | 0.658883i | ||||
\(937\) | −43.2317 | −1.41232 | −0.706159 | − | 0.708053i | \(-0.749574\pi\) | ||||
−0.706159 | + | 0.708053i | \(0.749574\pi\) | |||||||
\(938\) | 0.972010 | + | 0.879015i | 0.0317373 | + | 0.0287009i | ||||
\(939\) | −1.19300 | −0.0389320 | ||||||||
\(940\) | 10.3332 | + | 17.8977i | 0.337032 | + | 0.583757i | ||||
\(941\) | 7.73776 | − | 13.4022i | 0.252244 | − | 0.436899i | −0.711899 | − | 0.702281i | \(-0.752165\pi\) |
0.964143 | + | 0.265382i | \(0.0854982\pi\) | |||||||
\(942\) | −0.465474 | + | 0.806225i | −0.0151660 | + | 0.0262682i | ||||
\(943\) | 5.46158 | + | 9.45973i | 0.177853 | + | 0.308051i | ||||
\(944\) | 24.7668 | 0.806089 | ||||||||
\(945\) | 0.380628 | − | 1.77186i | 0.0123818 | − | 0.0576387i | ||||
\(946\) | −4.76847 | −0.155036 | ||||||||
\(947\) | −9.83635 | − | 17.0371i | −0.319639 | − | 0.553630i | 0.660774 | − | 0.750585i | \(-0.270228\pi\) |
−0.980413 | + | 0.196955i | \(0.936895\pi\) | |||||||
\(948\) | 0.947605 | − | 1.64130i | 0.0307768 | − | 0.0533069i | ||||
\(949\) | −23.9909 | + | 41.5535i | −0.778778 | + | 1.34888i | ||||
\(950\) | −0.629055 | − | 1.08956i | −0.0204092 | − | 0.0353499i | ||||
\(951\) | 0.151373 | 0.00490862 | ||||||||
\(952\) | −19.1835 | + | 6.18726i | −0.621740 | + | 0.200530i | ||||
\(953\) | −60.1478 | −1.94838 | −0.974188 | − | 0.225736i | \(-0.927521\pi\) | ||||
−0.974188 | + | 0.225736i | \(0.927521\pi\) | |||||||
\(954\) | 3.91017 | + | 6.77261i | 0.126596 | + | 0.219271i | ||||
\(955\) | −6.47512 | + | 11.2152i | −0.209530 | + | 0.362917i | ||||
\(956\) | 13.3176 | − | 23.0667i | 0.430721 | − | 0.746031i | ||||
\(957\) | −0.269646 | − | 0.467040i | −0.00871641 | − | 0.0150973i | ||||
\(958\) | 16.6658 | 0.538447 | ||||||||
\(959\) | −20.4300 | + | 6.58930i | −0.659719 | + | 0.212779i | ||||
\(960\) | −0.392450 | −0.0126663 | ||||||||
\(961\) | −37.0587 | − | 64.1876i | −1.19544 | − | 2.07057i | ||||
\(962\) | −2.33212 | + | 4.03935i | −0.0751906 | + | 0.130234i | ||||
\(963\) | 21.1429 | − | 36.6205i | 0.681319 | − | 1.18008i | ||||
\(964\) | 8.04685 | + | 13.9376i | 0.259172 | + | 0.448898i | ||||
\(965\) | 2.83070 | 0.0911235 | ||||||||
\(966\) | −0.250552 | + | 1.16635i | −0.00806137 | + | 0.0375266i | ||||
\(967\) | 31.9509 | 1.02747 | 0.513735 | − | 0.857949i | \(-0.328261\pi\) | ||||
0.513735 | + | 0.857949i | \(0.328261\pi\) | |||||||
\(968\) | −0.864850 | − | 1.49796i | −0.0277973 | − | 0.0481464i | ||||
\(969\) | 0.694943 | − | 1.20368i | 0.0223248 | − | 0.0386677i | ||||
\(970\) | 1.14888 | − | 1.98992i | 0.0368883 | − | 0.0638925i | ||||
\(971\) | 6.73204 | + | 11.6602i | 0.216041 | + | 0.374195i | 0.953594 | − | 0.301095i | \(-0.0973520\pi\) |
−0.737553 | + | 0.675289i | \(0.764019\pi\) | |||||||
\(972\) | 5.50335 | 0.176520 | ||||||||
\(973\) | −32.1662 | − | 29.0887i | −1.03120 | − | 0.932542i | ||||
\(974\) | 11.6191 | 0.372299 | ||||||||
\(975\) | 0.257731 | + | 0.446404i | 0.00825401 | + | 0.0142964i | ||||
\(976\) | −6.57881 | + | 11.3948i | −0.210583 | + | 0.364740i | ||||
\(977\) | 17.9353 | − | 31.0649i | 0.573801 | − | 0.993853i | −0.422370 | − | 0.906424i | \(-0.638802\pi\) |
0.996171 | − | 0.0874290i | \(-0.0278651\pi\) | |||||||
\(978\) | 0.566388 | + | 0.981013i | 0.0181111 | + | 0.0313693i | ||||
\(979\) | −4.00310 | −0.127940 | ||||||||
\(980\) | 1.25718 | + | 12.4803i | 0.0401592 | + | 0.398669i | ||||
\(981\) | 16.1169 | 0.514572 | ||||||||
\(982\) | 3.83091 | + | 6.63533i | 0.122249 | + | 0.211742i | ||||
\(983\) | 19.1739 | − | 33.2102i | 0.611552 | − | 1.05924i | −0.379427 | − | 0.925222i | \(-0.623879\pi\) |
0.990979 | − | 0.134018i | \(-0.0427879\pi\) | |||||||
\(984\) | −0.125105 | + | 0.216689i | −0.00398821 | + | 0.00690778i | ||||
\(985\) | 0.789628 | + | 1.36767i | 0.0251596 | + | 0.0435777i | ||||
\(986\) | 9.47015 | 0.301591 | ||||||||
\(987\) | −2.58938 | − | 2.34165i | −0.0824209 | − | 0.0745355i | ||||
\(988\) | 22.2664 | 0.708388 | ||||||||
\(989\) | 45.1571 | + | 78.2143i | 1.43591 | + | 2.48707i | ||||
\(990\) | −0.681245 | + | 1.17995i | −0.0216514 | + | 0.0375013i | ||||
\(991\) | 2.48430 | − | 4.30293i | 0.0789164 | − | 0.136687i | −0.823866 | − | 0.566784i | \(-0.808187\pi\) |
0.902783 | + | 0.430097i | \(0.141521\pi\) | |||||||
\(992\) | 24.2695 | + | 42.0360i | 0.770558 | + | 1.33465i | ||||
\(993\) | −2.61855 | −0.0830971 | ||||||||
\(994\) | −3.24502 | + | 15.1059i | −0.102926 | + | 0.479130i | ||||
\(995\) | 20.4017 | 0.646778 | ||||||||
\(996\) | 0.266967 | + | 0.462400i | 0.00845917 | + | 0.0146517i | ||||
\(997\) | −9.65030 | + | 16.7148i | −0.305628 | + | 0.529364i | −0.977401 | − | 0.211394i | \(-0.932200\pi\) |
0.671773 | + | 0.740757i | \(0.265533\pi\) | |||||||
\(998\) | 3.23954 | − | 5.61104i | 0.102546 | − | 0.177614i | ||||
\(999\) | 0.777311 | + | 1.34634i | 0.0245930 | + | 0.0425964i |
(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 | 385.2.i.b.221.3 | ✓ | 12 | |
7.2 | even | 3 | inner | 385.2.i.b.331.3 | yes | 12 | |
7.3 | odd | 6 | 2695.2.a.q.1.4 | 6 | |||
7.4 | even | 3 | 2695.2.a.r.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
385.2.i.b.221.3 | ✓ | 12 | 1.1 | even | 1 | trivial | |
385.2.i.b.331.3 | yes | 12 | 7.2 | even | 3 | inner | |
2695.2.a.q.1.4 | 6 | 7.3 | odd | 6 | |||
2695.2.a.r.1.4 | 6 | 7.4 | even | 3 |