Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [390,2,Mod(49,390)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(390, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("390.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 390.x (of order \(6\), 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: | \(3.11416567883\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} - 8 x^{10} + 34 x^{9} + 8 x^{8} - 134 x^{7} + 98 x^{6} + 154 x^{5} + 104 x^{4} + \cdots + 2197 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 199.6 | ||
Root | \(-2.39378 - 0.0429626i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 390.199 |
Dual form | 390.2.x.b.49.6 |
$q$-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 \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).
\(n\) | \(131\) | \(157\) | \(301\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0.866025 | + | 0.500000i | 0.500000 | + | 0.288675i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 2.10012 | + | 0.767774i | 0.939204 | + | 0.343359i | ||||
\(6\) | 0.866025 | − | 0.500000i | 0.353553 | − | 0.204124i | ||||
\(7\) | 0.823063 | + | 1.42559i | 0.311088 | + | 0.538821i | 0.978598 | − | 0.205780i | \(-0.0659731\pi\) |
−0.667510 | + | 0.744601i | \(0.732640\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 1.71497 | − | 1.43487i | 0.542322 | − | 0.453747i | ||||
\(11\) | 2.08305 | + | 1.20265i | 0.628063 | + | 0.362612i | 0.780001 | − | 0.625778i | \(-0.215218\pi\) |
−0.151939 | + | 0.988390i | \(0.548552\pi\) | |||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | −3.59643 | + | 0.256262i | −0.997471 | + | 0.0710744i | ||||
\(14\) | 1.64613 | 0.439946 | ||||||||
\(15\) | 1.43487 | + | 1.71497i | 0.370483 | + | 0.442804i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0.210702 | − | 0.121649i | 0.0511027 | − | 0.0295041i | −0.474231 | − | 0.880400i | \(-0.657274\pi\) |
0.525334 | + | 0.850896i | \(0.323941\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 3.82681 | − | 2.20941i | 0.877930 | − | 0.506873i | 0.00795483 | − | 0.999968i | \(-0.497468\pi\) |
0.869975 | + | 0.493095i | \(0.164135\pi\) | |||||||
\(20\) | −0.385150 | − | 2.20265i | −0.0861222 | − | 0.492527i | ||||
\(21\) | 1.64613i | 0.359214i | ||||||||
\(22\) | 2.08305 | − | 1.20265i | 0.444107 | − | 0.256405i | ||||
\(23\) | −7.46758 | − | 4.31141i | −1.55710 | − | 0.898991i | −0.997533 | − | 0.0702038i | \(-0.977635\pi\) |
−0.559565 | − | 0.828787i | \(-0.689032\pi\) | |||||||
\(24\) | −0.866025 | − | 0.500000i | −0.176777 | − | 0.102062i | ||||
\(25\) | 3.82105 | + | 3.22484i | 0.764209 | + | 0.644969i | ||||
\(26\) | −1.57629 | + | 3.24273i | −0.309135 | + | 0.635952i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0.823063 | − | 1.42559i | 0.155544 | − | 0.269411i | ||||
\(29\) | 0.0221633 | − | 0.0383880i | 0.00411562 | − | 0.00712846i | −0.863960 | − | 0.503560i | \(-0.832023\pi\) |
0.868076 | + | 0.496432i | \(0.165357\pi\) | |||||||
\(30\) | 2.20265 | − | 0.385150i | 0.402147 | − | 0.0703185i | ||||
\(31\) | − | 4.24458i | − | 0.762348i | −0.924503 | − | 0.381174i | \(-0.875520\pi\) | ||
0.924503 | − | 0.381174i | \(-0.124480\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 1.20265 | + | 2.08305i | 0.209354 | + | 0.362612i | ||||
\(34\) | − | 0.243297i | − | 0.0417251i | ||||||
\(35\) | 0.634006 | + | 3.62584i | 0.107167 | + | 0.612878i | ||||
\(36\) | 0.500000 | − | 0.866025i | 0.0833333 | − | 0.144338i | ||||
\(37\) | 4.47415 | − | 7.74945i | 0.735545 | − | 1.27400i | −0.218939 | − | 0.975739i | \(-0.570260\pi\) |
0.954484 | − | 0.298263i | \(-0.0964071\pi\) | |||||||
\(38\) | − | 4.41882i | − | 0.716827i | ||||||
\(39\) | −3.24273 | − | 1.57629i | −0.519253 | − | 0.252408i | ||||
\(40\) | −2.10012 | − | 0.767774i | −0.332059 | − | 0.121396i | ||||
\(41\) | 0.210702 | + | 0.121649i | 0.0329061 | + | 0.0189983i | 0.516363 | − | 0.856370i | \(-0.327286\pi\) |
−0.483457 | + | 0.875368i | \(0.660619\pi\) | |||||||
\(42\) | 1.42559 | + | 0.823063i | 0.219973 | + | 0.127001i | ||||
\(43\) | −5.82728 | + | 3.36438i | −0.888652 | + | 0.513063i | −0.873501 | − | 0.486822i | \(-0.838156\pi\) |
−0.0151507 | + | 0.999885i | \(0.504823\pi\) | |||||||
\(44\) | − | 2.40530i | − | 0.362612i | ||||||
\(45\) | 0.385150 | + | 2.20265i | 0.0574148 | + | 0.328351i | ||||
\(46\) | −7.46758 | + | 4.31141i | −1.10103 | + | 0.635682i | ||||
\(47\) | −7.29560 | −1.06417 | −0.532086 | − | 0.846690i | \(-0.678592\pi\) | ||||
−0.532086 | + | 0.846690i | \(0.678592\pi\) | |||||||
\(48\) | −0.866025 | + | 0.500000i | −0.125000 | + | 0.0721688i | ||||
\(49\) | 2.14514 | − | 3.71548i | 0.306448 | − | 0.530783i | ||||
\(50\) | 4.70332 | − | 1.69670i | 0.665150 | − | 0.239950i | ||||
\(51\) | 0.243297 | 0.0340684 | ||||||||
\(52\) | 2.02015 | + | 2.98647i | 0.280144 | + | 0.414149i | ||||
\(53\) | 2.44613i | 0.336002i | 0.985787 | + | 0.168001i | \(0.0537312\pi\) | ||||
−0.985787 | + | 0.168001i | \(0.946269\pi\) | |||||||
\(54\) | 0.866025 | + | 0.500000i | 0.117851 | + | 0.0680414i | ||||
\(55\) | 3.45130 | + | 4.12502i | 0.465373 | + | 0.556218i | ||||
\(56\) | −0.823063 | − | 1.42559i | −0.109986 | − | 0.190502i | ||||
\(57\) | 4.41882 | 0.585287 | ||||||||
\(58\) | −0.0221633 | − | 0.0383880i | −0.00291018 | − | 0.00504059i | ||||
\(59\) | −8.35669 | + | 4.82474i | −1.08795 | + | 0.628127i | −0.933029 | − | 0.359800i | \(-0.882845\pi\) |
−0.154919 | + | 0.987927i | \(0.549512\pi\) | |||||||
\(60\) | 0.767774 | − | 2.10012i | 0.0991192 | − | 0.271125i | ||||
\(61\) | 1.31630 | + | 2.27990i | 0.168535 | + | 0.291911i | 0.937905 | − | 0.346892i | \(-0.112763\pi\) |
−0.769370 | + | 0.638804i | \(0.779430\pi\) | |||||||
\(62\) | −3.67591 | − | 2.12229i | −0.466841 | − | 0.269531i | ||||
\(63\) | −0.823063 | + | 1.42559i | −0.103696 | + | 0.179607i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −7.74971 | − | 2.22307i | −0.961233 | − | 0.275737i | ||||
\(66\) | 2.40530 | 0.296072 | ||||||||
\(67\) | 0.937098 | − | 1.62310i | 0.114485 | − | 0.198293i | −0.803089 | − | 0.595859i | \(-0.796812\pi\) |
0.917574 | + | 0.397566i | \(0.130145\pi\) | |||||||
\(68\) | −0.210702 | − | 0.121649i | −0.0255513 | − | 0.0147521i | ||||
\(69\) | −4.31141 | − | 7.46758i | −0.519032 | − | 0.898991i | ||||
\(70\) | 3.45707 | + | 1.26385i | 0.413199 | + | 0.151059i | ||||
\(71\) | −6.53035 | + | 3.77030i | −0.775010 | + | 0.447452i | −0.834659 | − | 0.550767i | \(-0.814335\pi\) |
0.0596488 | + | 0.998219i | \(0.481002\pi\) | |||||||
\(72\) | −0.500000 | − | 0.866025i | −0.0589256 | − | 0.102062i | ||||
\(73\) | 1.70370 | 0.199403 | 0.0997015 | − | 0.995017i | \(-0.468211\pi\) | ||||
0.0997015 | + | 0.995017i | \(0.468211\pi\) | |||||||
\(74\) | −4.47415 | − | 7.74945i | −0.520109 | − | 0.900855i | ||||
\(75\) | 1.69670 | + | 4.70332i | 0.195918 | + | 0.543092i | ||||
\(76\) | −3.82681 | − | 2.20941i | −0.438965 | − | 0.253437i | ||||
\(77\) | 3.95942i | 0.451218i | ||||||||
\(78\) | −2.98647 | + | 2.02015i | −0.338151 | + | 0.228737i | ||||
\(79\) | 6.79707 | 0.764730 | 0.382365 | − | 0.924011i | \(-0.375110\pi\) | ||||
0.382365 | + | 0.924011i | \(0.375110\pi\) | |||||||
\(80\) | −1.71497 | + | 1.43487i | −0.191740 | + | 0.160424i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0.210702 | − | 0.121649i | 0.0232681 | − | 0.0134338i | ||||
\(83\) | −17.4986 | −1.92073 | −0.960363 | − | 0.278754i | \(-0.910079\pi\) | ||||
−0.960363 | + | 0.278754i | \(0.910079\pi\) | |||||||
\(84\) | 1.42559 | − | 0.823063i | 0.155544 | − | 0.0898035i | ||||
\(85\) | 0.535898 | − | 0.0937060i | 0.0581263 | − | 0.0101638i | ||||
\(86\) | 6.72876i | 0.725581i | ||||||||
\(87\) | 0.0383880 | − | 0.0221633i | 0.00411562 | − | 0.00237615i | ||||
\(88\) | −2.08305 | − | 1.20265i | −0.222054 | − | 0.128203i | ||||
\(89\) | −8.69772 | − | 5.02163i | −0.921956 | − | 0.532292i | −0.0376977 | − | 0.999289i | \(-0.512002\pi\) |
−0.884259 | + | 0.466997i | \(0.845336\pi\) | |||||||
\(90\) | 2.10012 | + | 0.767774i | 0.221373 | + | 0.0809305i | ||||
\(91\) | −3.32541 | − | 4.91611i | −0.348598 | − | 0.515348i | ||||
\(92\) | 8.62281i | 0.898991i | ||||||||
\(93\) | 2.12229 | − | 3.67591i | 0.220071 | − | 0.381174i | ||||
\(94\) | −3.64780 | + | 6.31817i | −0.376242 | + | 0.651670i | ||||
\(95\) | 9.73310 | − | 1.70191i | 0.998595 | − | 0.174612i | ||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | 8.25647 | + | 14.3006i | 0.838317 | + | 1.45201i | 0.891301 | + | 0.453413i | \(0.149794\pi\) |
−0.0529831 | + | 0.998595i | \(0.516873\pi\) | |||||||
\(98\) | −2.14514 | − | 3.71548i | −0.216691 | − | 0.375321i | ||||
\(99\) | 2.40530i | 0.241741i | ||||||||
\(100\) | 0.882273 | − | 4.92154i | 0.0882273 | − | 0.492154i | ||||
\(101\) | 5.66777 | − | 9.81687i | 0.563964 | − | 0.976815i | −0.433181 | − | 0.901307i | \(-0.642609\pi\) |
0.997145 | − | 0.0755077i | \(-0.0240577\pi\) | |||||||
\(102\) | 0.121649 | − | 0.210702i | 0.0120450 | − | 0.0208626i | ||||
\(103\) | 5.98168i | 0.589392i | 0.955591 | + | 0.294696i | \(0.0952184\pi\) | ||||
−0.955591 | + | 0.294696i | \(0.904782\pi\) | |||||||
\(104\) | 3.59643 | − | 0.256262i | 0.352659 | − | 0.0251286i | ||||
\(105\) | −1.26385 | + | 3.45707i | −0.123339 | + | 0.337375i | ||||
\(106\) | 2.11841 | + | 1.22307i | 0.205758 | + | 0.118795i | ||||
\(107\) | 9.24559 | + | 5.33795i | 0.893805 | + | 0.516039i | 0.875185 | − | 0.483788i | \(-0.160739\pi\) |
0.0186200 | + | 0.999827i | \(0.494073\pi\) | |||||||
\(108\) | 0.866025 | − | 0.500000i | 0.0833333 | − | 0.0481125i | ||||
\(109\) | 9.50683i | 0.910589i | 0.890341 | + | 0.455295i | \(0.150466\pi\) | ||||
−0.890341 | + | 0.455295i | \(0.849534\pi\) | |||||||
\(110\) | 5.29802 | − | 0.926401i | 0.505147 | − | 0.0883288i | ||||
\(111\) | 7.74945 | − | 4.47415i | 0.735545 | − | 0.424667i | ||||
\(112\) | −1.64613 | −0.155544 | ||||||||
\(113\) | −3.11433 | + | 1.79806i | −0.292972 | + | 0.169147i | −0.639281 | − | 0.768973i | \(-0.720768\pi\) |
0.346310 | + | 0.938120i | \(0.387435\pi\) | |||||||
\(114\) | 2.20941 | − | 3.82681i | 0.206930 | − | 0.358414i | ||||
\(115\) | −12.3727 | − | 14.7879i | −1.15376 | − | 1.37898i | ||||
\(116\) | −0.0443266 | −0.00411562 | ||||||||
\(117\) | −2.02015 | − | 2.98647i | −0.186763 | − | 0.276099i | ||||
\(118\) | 9.64947i | 0.888306i | ||||||||
\(119\) | 0.346841 | + | 0.200249i | 0.0317949 | + | 0.0183568i | ||||
\(120\) | −1.43487 | − | 1.71497i | −0.130985 | − | 0.156555i | ||||
\(121\) | −2.60727 | − | 4.51593i | −0.237025 | − | 0.410539i | ||||
\(122\) | 2.63260 | 0.238345 | ||||||||
\(123\) | 0.121649 | + | 0.210702i | 0.0109687 | + | 0.0189983i | ||||
\(124\) | −3.67591 | + | 2.12229i | −0.330106 | + | 0.190587i | ||||
\(125\) | 5.54872 | + | 9.70627i | 0.496293 | + | 0.868155i | ||||
\(126\) | 0.823063 | + | 1.42559i | 0.0733243 | + | 0.127001i | ||||
\(127\) | −15.0230 | − | 8.67351i | −1.33307 | − | 0.769650i | −0.347303 | − | 0.937753i | \(-0.612902\pi\) |
−0.985769 | + | 0.168103i | \(0.946236\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −6.72876 | −0.592435 | ||||||||
\(130\) | −5.80009 | + | 5.59991i | −0.508701 | + | 0.491145i | ||||
\(131\) | 14.1654 | 1.23764 | 0.618818 | − | 0.785534i | \(-0.287612\pi\) | ||||
0.618818 | + | 0.785534i | \(0.287612\pi\) | |||||||
\(132\) | 1.20265 | − | 2.08305i | 0.104677 | − | 0.181306i | ||||
\(133\) | 6.29941 | + | 3.63697i | 0.546228 | + | 0.315365i | ||||
\(134\) | −0.937098 | − | 1.62310i | −0.0809530 | − | 0.140215i | ||||
\(135\) | −0.767774 | + | 2.10012i | −0.0660795 | + | 0.180750i | ||||
\(136\) | −0.210702 | + | 0.121649i | −0.0180675 | + | 0.0104313i | ||||
\(137\) | 3.66709 | + | 6.35158i | 0.313300 | + | 0.542652i | 0.979075 | − | 0.203501i | \(-0.0652320\pi\) |
−0.665774 | + | 0.746153i | \(0.731899\pi\) | |||||||
\(138\) | −8.62281 | −0.734023 | ||||||||
\(139\) | 7.10185 | + | 12.3008i | 0.602371 | + | 1.04334i | 0.992461 | + | 0.122561i | \(0.0391107\pi\) |
−0.390090 | + | 0.920777i | \(0.627556\pi\) | |||||||
\(140\) | 2.82306 | − | 2.36198i | 0.238592 | − | 0.199624i | ||||
\(141\) | −6.31817 | − | 3.64780i | −0.532086 | − | 0.307200i | ||||
\(142\) | 7.54060i | 0.632793i | ||||||||
\(143\) | −7.79974 | − | 3.79144i | −0.652247 | − | 0.317056i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0.0760190 | − | 0.0636031i | 0.00631303 | − | 0.00528195i | ||||
\(146\) | 0.851850 | − | 1.47545i | 0.0704996 | − | 0.122109i | ||||
\(147\) | 3.71548 | − | 2.14514i | 0.306448 | − | 0.176928i | ||||
\(148\) | −8.94829 | −0.735545 | ||||||||
\(149\) | −9.61623 | + | 5.55193i | −0.787792 | + | 0.454832i | −0.839185 | − | 0.543847i | \(-0.816967\pi\) |
0.0513926 | + | 0.998679i | \(0.483634\pi\) | |||||||
\(150\) | 4.92154 | + | 0.882273i | 0.401842 | + | 0.0720373i | ||||
\(151\) | 0.874663i | 0.0711791i | 0.999366 | + | 0.0355895i | \(0.0113309\pi\) | ||||
−0.999366 | + | 0.0355895i | \(0.988669\pi\) | |||||||
\(152\) | −3.82681 | + | 2.20941i | −0.310395 | + | 0.179207i | ||||
\(153\) | 0.210702 | + | 0.121649i | 0.0170342 | + | 0.00983471i | ||||
\(154\) | 3.42896 | + | 1.97971i | 0.276313 | + | 0.159530i | ||||
\(155\) | 3.25888 | − | 8.91414i | 0.261759 | − | 0.716001i | ||||
\(156\) | 0.256262 | + | 3.59643i | 0.0205174 | + | 0.287945i | ||||
\(157\) | − | 15.5085i | − | 1.23771i | −0.785504 | − | 0.618856i | \(-0.787596\pi\) | ||
0.785504 | − | 0.618856i | \(-0.212404\pi\) | |||||||
\(158\) | 3.39854 | − | 5.88644i | 0.270373 | − | 0.468300i | ||||
\(159\) | −1.22307 | + | 2.11841i | −0.0969954 | + | 0.168001i | ||||
\(160\) | 0.385150 | + | 2.20265i | 0.0304488 | + | 0.174135i | ||||
\(161\) | − | 14.1942i | − | 1.11866i | ||||||
\(162\) | 0.500000 | + | 0.866025i | 0.0392837 | + | 0.0680414i | ||||
\(163\) | −10.9464 | − | 18.9597i | −0.857388 | − | 1.48504i | −0.874411 | − | 0.485185i | \(-0.838752\pi\) |
0.0170229 | − | 0.999855i | \(-0.494581\pi\) | |||||||
\(164\) | − | 0.243297i | − | 0.0189983i | ||||||
\(165\) | 0.926401 | + | 5.29802i | 0.0721202 | + | 0.412450i | ||||
\(166\) | −8.74932 | + | 15.1543i | −0.679079 | + | 1.17620i | ||||
\(167\) | 2.64815 | − | 4.58673i | 0.204920 | − | 0.354932i | −0.745187 | − | 0.666855i | \(-0.767640\pi\) |
0.950107 | + | 0.311923i | \(0.100973\pi\) | |||||||
\(168\) | − | 1.64613i | − | 0.127001i | ||||||
\(169\) | 12.8687 | − | 1.84326i | 0.989897 | − | 0.141789i | ||||
\(170\) | 0.186797 | − | 0.510955i | 0.0143267 | − | 0.0391884i | ||||
\(171\) | 3.82681 | + | 2.20941i | 0.292643 | + | 0.168958i | ||||
\(172\) | 5.82728 | + | 3.36438i | 0.444326 | + | 0.256532i | ||||
\(173\) | 14.9469 | − | 8.62958i | 1.13639 | − | 0.656095i | 0.190856 | − | 0.981618i | \(-0.438874\pi\) |
0.945534 | + | 0.325523i | \(0.105540\pi\) | |||||||
\(174\) | − | 0.0443266i | − | 0.00336039i | ||||||
\(175\) | −1.45233 | + | 8.10148i | −0.109786 | + | 0.612414i | ||||
\(176\) | −2.08305 | + | 1.20265i | −0.157016 | + | 0.0906530i | ||||
\(177\) | −9.64947 | −0.725299 | ||||||||
\(178\) | −8.69772 | + | 5.02163i | −0.651922 | + | 0.376387i | ||||
\(179\) | −4.17781 | + | 7.23617i | −0.312264 | + | 0.540857i | −0.978852 | − | 0.204569i | \(-0.934421\pi\) |
0.666588 | + | 0.745426i | \(0.267754\pi\) | |||||||
\(180\) | 1.71497 | − | 1.43487i | 0.127827 | − | 0.106949i | ||||
\(181\) | 12.7335 | 0.946476 | 0.473238 | − | 0.880935i | \(-0.343085\pi\) | ||||
0.473238 | + | 0.880935i | \(0.343085\pi\) | |||||||
\(182\) | −5.92018 | + | 0.421840i | −0.438833 | + | 0.0312689i | ||||
\(183\) | 2.63260i | 0.194608i | ||||||||
\(184\) | 7.46758 | + | 4.31141i | 0.550517 | + | 0.317841i | ||||
\(185\) | 15.3461 | − | 12.8397i | 1.12827 | − | 0.943991i | ||||
\(186\) | −2.12229 | − | 3.67591i | −0.155614 | − | 0.269531i | ||||
\(187\) | 0.585202 | 0.0427942 | ||||||||
\(188\) | 3.64780 | + | 6.31817i | 0.266043 | + | 0.460800i | ||||
\(189\) | −1.42559 | + | 0.823063i | −0.103696 | + | 0.0598690i | ||||
\(190\) | 3.39265 | − | 9.28007i | 0.246129 | − | 0.673247i | ||||
\(191\) | −0.207632 | − | 0.359629i | −0.0150237 | − | 0.0260219i | 0.858416 | − | 0.512955i | \(-0.171449\pi\) |
−0.873440 | + | 0.486933i | \(0.838116\pi\) | |||||||
\(192\) | 0.866025 | + | 0.500000i | 0.0625000 | + | 0.0360844i | ||||
\(193\) | 12.9918 | − | 22.5025i | 0.935173 | − | 1.61977i | 0.160849 | − | 0.986979i | \(-0.448577\pi\) |
0.774324 | − | 0.632789i | \(-0.218090\pi\) | |||||||
\(194\) | 16.5129 | 1.18556 | ||||||||
\(195\) | −5.59991 | − | 5.80009i | −0.401018 | − | 0.415353i | ||||
\(196\) | −4.29027 | −0.306448 | ||||||||
\(197\) | 7.72121 | − | 13.3735i | 0.550113 | − | 0.952824i | −0.448152 | − | 0.893957i | \(-0.647918\pi\) |
0.998266 | − | 0.0588672i | \(-0.0187488\pi\) | |||||||
\(198\) | 2.08305 | + | 1.20265i | 0.148036 | + | 0.0854685i | ||||
\(199\) | 6.85286 | + | 11.8695i | 0.485787 | + | 0.841407i | 0.999867 | − | 0.0163352i | \(-0.00519988\pi\) |
−0.514080 | + | 0.857742i | \(0.671867\pi\) | |||||||
\(200\) | −3.82105 | − | 3.22484i | −0.270189 | − | 0.228031i | ||||
\(201\) | 1.62310 | − | 0.937098i | 0.114485 | − | 0.0660978i | ||||
\(202\) | −5.66777 | − | 9.81687i | −0.398783 | − | 0.690712i | ||||
\(203\) | 0.0729671 | 0.00512129 | ||||||||
\(204\) | −0.121649 | − | 0.210702i | −0.00851711 | − | 0.0147521i | ||||
\(205\) | 0.349101 | + | 0.417249i | 0.0243823 | + | 0.0291419i | ||||
\(206\) | 5.18029 | + | 2.99084i | 0.360928 | + | 0.208382i | ||||
\(207\) | − | 8.62281i | − | 0.599327i | ||||||
\(208\) | 1.57629 | − | 3.24273i | 0.109296 | − | 0.224843i | ||||
\(209\) | 10.6286 | 0.735193 | ||||||||
\(210\) | 2.36198 | + | 2.82306i | 0.162992 | + | 0.194810i | ||||
\(211\) | 8.05616 | − | 13.9537i | 0.554609 | − | 0.960611i | −0.443325 | − | 0.896361i | \(-0.646201\pi\) |
0.997934 | − | 0.0642497i | \(-0.0204654\pi\) | |||||||
\(212\) | 2.11841 | − | 1.22307i | 0.145493 | − | 0.0840005i | ||||
\(213\) | −7.54060 | −0.516673 | ||||||||
\(214\) | 9.24559 | − | 5.33795i | 0.632016 | − | 0.364894i | ||||
\(215\) | −14.8211 | + | 2.59159i | −1.01079 | + | 0.176745i | ||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | 6.05101 | − | 3.49355i | 0.410769 | − | 0.237158i | ||||
\(218\) | 8.23316 | + | 4.75342i | 0.557620 | + | 0.321942i | ||||
\(219\) | 1.47545 | + | 0.851850i | 0.0997015 | + | 0.0575627i | ||||
\(220\) | 1.84672 | − | 5.05142i | 0.124506 | − | 0.340567i | ||||
\(221\) | −0.726600 | + | 0.491496i | −0.0488764 | + | 0.0330616i | ||||
\(222\) | − | 8.94829i | − | 0.600570i | ||||||
\(223\) | −5.55886 | + | 9.62823i | −0.372249 | + | 0.644754i | −0.989911 | − | 0.141690i | \(-0.954747\pi\) |
0.617662 | + | 0.786443i | \(0.288080\pi\) | |||||||
\(224\) | −0.823063 | + | 1.42559i | −0.0549932 | + | 0.0952510i | ||||
\(225\) | −0.882273 | + | 4.92154i | −0.0588182 | + | 0.328103i | ||||
\(226\) | 3.59612i | 0.239210i | ||||||||
\(227\) | 11.0399 | + | 19.1217i | 0.732747 | + | 1.26915i | 0.955705 | + | 0.294327i | \(0.0950953\pi\) |
−0.222958 | + | 0.974828i | \(0.571571\pi\) | |||||||
\(228\) | −2.20941 | − | 3.82681i | −0.146322 | − | 0.253437i | ||||
\(229\) | 10.3397i | 0.683266i | 0.939834 | + | 0.341633i | \(0.110980\pi\) | ||||
−0.939834 | + | 0.341633i | \(0.889020\pi\) | |||||||
\(230\) | −18.9930 | + | 3.32108i | −1.25236 | + | 0.218985i | ||||
\(231\) | −1.97971 | + | 3.42896i | −0.130255 | + | 0.225609i | ||||
\(232\) | −0.0221633 | + | 0.0383880i | −0.00145509 | + | 0.00252029i | ||||
\(233\) | 21.8928i | 1.43425i | 0.696947 | + | 0.717123i | \(0.254541\pi\) | ||||
−0.696947 | + | 0.717123i | \(0.745459\pi\) | |||||||
\(234\) | −3.59643 | + | 0.256262i | −0.235106 | + | 0.0167524i | ||||
\(235\) | −15.3217 | − | 5.60137i | −0.999475 | − | 0.365393i | ||||
\(236\) | 8.35669 | + | 4.82474i | 0.543974 | + | 0.314064i | ||||
\(237\) | 5.88644 | + | 3.39854i | 0.382365 | + | 0.220759i | ||||
\(238\) | 0.346841 | − | 0.200249i | 0.0224824 | − | 0.0129802i | ||||
\(239\) | − | 26.2510i | − | 1.69804i | −0.528362 | − | 0.849019i | \(-0.677194\pi\) | ||
0.528362 | − | 0.849019i | \(-0.322806\pi\) | |||||||
\(240\) | −2.20265 | + | 0.385150i | −0.142180 | + | 0.0248613i | ||||
\(241\) | 22.5952 | − | 13.0454i | 1.45549 | − | 0.840326i | 0.456703 | − | 0.889619i | \(-0.349030\pi\) |
0.998784 | + | 0.0492931i | \(0.0156968\pi\) | |||||||
\(242\) | −5.21455 | −0.335204 | ||||||||
\(243\) | −0.866025 | + | 0.500000i | −0.0555556 | + | 0.0320750i | ||||
\(244\) | 1.31630 | − | 2.27990i | 0.0842676 | − | 0.145956i | ||||
\(245\) | 7.35770 | − | 6.15600i | 0.470066 | − | 0.393292i | ||||
\(246\) | 0.243297 | 0.0155121 | ||||||||
\(247\) | −13.1967 | + | 8.92666i | −0.839684 | + | 0.567990i | ||||
\(248\) | 4.24458i | 0.269531i | ||||||||
\(249\) | −15.1543 | − | 8.74932i | −0.960363 | − | 0.554466i | ||||
\(250\) | 11.1802 | + | 0.0478026i | 0.707100 | + | 0.00302330i | ||||
\(251\) | −0.312397 | − | 0.541088i | −0.0197183 | − | 0.0341532i | 0.855998 | − | 0.516979i | \(-0.172944\pi\) |
−0.875716 | + | 0.482826i | \(0.839610\pi\) | |||||||
\(252\) | 1.64613 | 0.103696 | ||||||||
\(253\) | −10.3702 | − | 17.9617i | −0.651970 | − | 1.12924i | ||||
\(254\) | −15.0230 | + | 8.67351i | −0.942624 | + | 0.544224i | ||||
\(255\) | 0.510955 | + | 0.186797i | 0.0319972 | + | 0.0116977i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 12.0758 | + | 6.97195i | 0.753266 | + | 0.434898i | 0.826873 | − | 0.562389i | \(-0.190118\pi\) |
−0.0736066 | + | 0.997287i | \(0.523451\pi\) | |||||||
\(258\) | −3.36438 | + | 5.82728i | −0.209457 | + | 0.362791i | ||||
\(259\) | 14.7300 | 0.915278 | ||||||||
\(260\) | 1.94962 | + | 7.82298i | 0.120910 | + | 0.485160i | ||||
\(261\) | 0.0443266 | 0.00274375 | ||||||||
\(262\) | 7.08270 | − | 12.2676i | 0.437571 | − | 0.757894i | ||||
\(263\) | 16.8325 | + | 9.71828i | 1.03794 | + | 0.599255i | 0.919249 | − | 0.393677i | \(-0.128797\pi\) |
0.118690 | + | 0.992931i | \(0.462130\pi\) | |||||||
\(264\) | −1.20265 | − | 2.08305i | −0.0740179 | − | 0.128203i | ||||
\(265\) | −1.87808 | + | 5.13718i | −0.115369 | + | 0.315574i | ||||
\(266\) | 6.29941 | − | 3.63697i | 0.386242 | − | 0.222997i | ||||
\(267\) | −5.02163 | − | 8.69772i | −0.307319 | − | 0.532292i | ||||
\(268\) | −1.87420 | −0.114485 | ||||||||
\(269\) | −1.50069 | − | 2.59928i | −0.0914989 | − | 0.158481i | 0.816643 | − | 0.577143i | \(-0.195832\pi\) |
−0.908142 | + | 0.418662i | \(0.862499\pi\) | |||||||
\(270\) | 1.43487 | + | 1.71497i | 0.0873237 | + | 0.104370i | ||||
\(271\) | −24.6538 | − | 14.2339i | −1.49761 | − | 0.864645i | −0.497613 | − | 0.867399i | \(-0.665790\pi\) |
−0.999996 | + | 0.00275396i | \(0.999123\pi\) | |||||||
\(272\) | 0.243297i | 0.0147521i | ||||||||
\(273\) | −0.421840 | − | 5.92018i | −0.0255309 | − | 0.358306i | ||||
\(274\) | 7.33417 | 0.443074 | ||||||||
\(275\) | 4.08107 | + | 11.3129i | 0.246098 | + | 0.682192i | ||||
\(276\) | −4.31141 | + | 7.46758i | −0.259516 | + | 0.449495i | ||||
\(277\) | 0.738423 | − | 0.426329i | 0.0443676 | − | 0.0256156i | −0.477652 | − | 0.878549i | \(-0.658512\pi\) |
0.522020 | + | 0.852933i | \(0.325179\pi\) | |||||||
\(278\) | 14.2037 | 0.851882 | ||||||||
\(279\) | 3.67591 | − | 2.12229i | 0.220071 | − | 0.127058i | ||||
\(280\) | −0.634006 | − | 3.62584i | −0.0378891 | − | 0.216685i | ||||
\(281\) | 15.6851i | 0.935697i | 0.883809 | + | 0.467848i | \(0.154971\pi\) | ||||
−0.883809 | + | 0.467848i | \(0.845029\pi\) | |||||||
\(282\) | −6.31817 | + | 3.64780i | −0.376242 | + | 0.217223i | ||||
\(283\) | 7.00390 | + | 4.04370i | 0.416339 | + | 0.240373i | 0.693510 | − | 0.720447i | \(-0.256063\pi\) |
−0.277171 | + | 0.960821i | \(0.589397\pi\) | |||||||
\(284\) | 6.53035 | + | 3.77030i | 0.387505 | + | 0.223726i | ||||
\(285\) | 9.28007 | + | 3.39265i | 0.549704 | + | 0.200964i | ||||
\(286\) | −7.18335 | + | 4.85905i | −0.424760 | + | 0.287322i | ||||
\(287\) | 0.400498i | 0.0236406i | ||||||||
\(288\) | −0.500000 | + | 0.866025i | −0.0294628 | + | 0.0510310i | ||||
\(289\) | −8.47040 | + | 14.6712i | −0.498259 | + | 0.863010i | ||||
\(290\) | −0.0170724 | − | 0.0976359i | −0.00100253 | − | 0.00573338i | ||||
\(291\) | 16.5129i | 0.968006i | ||||||||
\(292\) | −0.851850 | − | 1.47545i | −0.0498508 | − | 0.0863440i | ||||
\(293\) | −0.967192 | − | 1.67523i | −0.0565040 | − | 0.0978677i | 0.836390 | − | 0.548135i | \(-0.184662\pi\) |
−0.892894 | + | 0.450267i | \(0.851329\pi\) | |||||||
\(294\) | − | 4.29027i | − | 0.250214i | ||||||
\(295\) | −21.2544 | + | 3.71650i | −1.23748 | + | 0.216383i | ||||
\(296\) | −4.47415 | + | 7.74945i | −0.260054 | + | 0.450427i | ||||
\(297\) | −1.20265 | + | 2.08305i | −0.0697847 | + | 0.120871i | ||||
\(298\) | 11.1039i | 0.643229i | ||||||||
\(299\) | 27.9615 | + | 13.5920i | 1.61705 | + | 0.786047i | ||||
\(300\) | 3.22484 | − | 3.82105i | 0.186186 | − | 0.220608i | ||||
\(301\) | −9.59244 | − | 5.53820i | −0.552899 | − | 0.319216i | ||||
\(302\) | 0.757480 | + | 0.437332i | 0.0435881 | + | 0.0251656i | ||||
\(303\) | 9.81687 | − | 5.66777i | 0.563964 | − | 0.325605i | ||||
\(304\) | 4.41882i | 0.253437i | ||||||||
\(305\) | 1.01395 | + | 5.79870i | 0.0580585 | + | 0.332033i | ||||
\(306\) | 0.210702 | − | 0.121649i | 0.0120450 | − | 0.00695419i | ||||
\(307\) | −12.4384 | −0.709894 | −0.354947 | − | 0.934886i | \(-0.615501\pi\) | ||||
−0.354947 | + | 0.934886i | \(0.615501\pi\) | |||||||
\(308\) | 3.42896 | − | 1.97971i | 0.195383 | − | 0.112804i | ||||
\(309\) | −2.99084 | + | 5.18029i | −0.170143 | + | 0.294696i | ||||
\(310\) | −6.09043 | − | 7.27934i | −0.345913 | − | 0.413439i | ||||
\(311\) | −18.3700 | −1.04167 | −0.520835 | − | 0.853657i | \(-0.674379\pi\) | ||||
−0.520835 | + | 0.853657i | \(0.674379\pi\) | |||||||
\(312\) | 3.24273 | + | 1.57629i | 0.183584 | + | 0.0892397i | ||||
\(313\) | 31.9445i | 1.80561i | 0.430051 | + | 0.902804i | \(0.358496\pi\) | ||||
−0.430051 | + | 0.902804i | \(0.641504\pi\) | |||||||
\(314\) | −13.4307 | − | 7.75425i | −0.757941 | − | 0.437597i | ||||
\(315\) | −2.82306 | + | 2.36198i | −0.159062 | + | 0.133083i | ||||
\(316\) | −3.39854 | − | 5.88644i | −0.191183 | − | 0.331138i | ||||
\(317\) | −23.3625 | −1.31217 | −0.656083 | − | 0.754689i | \(-0.727788\pi\) | ||||
−0.656083 | + | 0.754689i | \(0.727788\pi\) | |||||||
\(318\) | 1.22307 | + | 2.11841i | 0.0685861 | + | 0.118795i | ||||
\(319\) | 0.0923344 | − | 0.0533093i | 0.00516973 | − | 0.00298475i | ||||
\(320\) | 2.10012 | + | 0.767774i | 0.117401 | + | 0.0429199i | ||||
\(321\) | 5.33795 | + | 9.24559i | 0.297935 | + | 0.516039i | ||||
\(322\) | −12.2926 | − | 7.09712i | −0.685038 | − | 0.395507i | ||||
\(323\) | 0.537543 | − | 0.931052i | 0.0299097 | − | 0.0518051i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −14.5685 | − | 10.6187i | −0.808117 | − | 0.589022i | ||||
\(326\) | −21.8928 | −1.21253 | ||||||||
\(327\) | −4.75342 | + | 8.23316i | −0.262865 | + | 0.455295i | ||||
\(328\) | −0.210702 | − | 0.121649i | −0.0116341 | − | 0.00671692i | ||||
\(329\) | −6.00474 | − | 10.4005i | −0.331052 | − | 0.573399i | ||||
\(330\) | 5.05142 | + | 1.84672i | 0.278072 | + | 0.101659i | ||||
\(331\) | −18.5879 | + | 10.7317i | −1.02168 | + | 0.589868i | −0.914590 | − | 0.404382i | \(-0.867487\pi\) |
−0.107090 | + | 0.994249i | \(0.534153\pi\) | |||||||
\(332\) | 8.74932 | + | 15.1543i | 0.480181 | + | 0.831698i | ||||
\(333\) | 8.94829 | 0.490363 | ||||||||
\(334\) | −2.64815 | − | 4.58673i | −0.144900 | − | 0.250975i | ||||
\(335\) | 3.21420 | − | 2.68924i | 0.175610 | − | 0.146929i | ||||
\(336\) | −1.42559 | − | 0.823063i | −0.0777721 | − | 0.0449018i | ||||
\(337\) | 14.3561i | 0.782026i | 0.920385 | + | 0.391013i | \(0.127875\pi\) | ||||
−0.920385 | + | 0.391013i | \(0.872125\pi\) | |||||||
\(338\) | 4.83802 | − | 12.0662i | 0.263154 | − | 0.656316i | ||||
\(339\) | −3.59612 | −0.195314 | ||||||||
\(340\) | −0.349101 | − | 0.417249i | −0.0189327 | − | 0.0226285i | ||||
\(341\) | 5.10473 | − | 8.84165i | 0.276437 | − | 0.478802i | ||||
\(342\) | 3.82681 | − | 2.20941i | 0.206930 | − | 0.119471i | ||||
\(343\) | 18.5852 | 1.00351 | ||||||||
\(344\) | 5.82728 | − | 3.36438i | 0.314186 | − | 0.181395i | ||||
\(345\) | −3.32108 | − | 18.9930i | −0.178801 | − | 1.02255i | ||||
\(346\) | − | 17.2592i | − | 0.927858i | ||||||
\(347\) | −0.576005 | + | 0.332557i | −0.0309216 | + | 0.0178526i | −0.515381 | − | 0.856961i | \(-0.672350\pi\) |
0.484460 | + | 0.874814i | \(0.339016\pi\) | |||||||
\(348\) | −0.0383880 | − | 0.0221633i | −0.00205781 | − | 0.00118808i | ||||
\(349\) | 3.25007 | + | 1.87643i | 0.173972 | + | 0.100443i | 0.584458 | − | 0.811424i | \(-0.301307\pi\) |
−0.410485 | + | 0.911867i | \(0.634641\pi\) | |||||||
\(350\) | 6.28992 | + | 5.30850i | 0.336210 | + | 0.283751i | ||||
\(351\) | −0.256262 | − | 3.59643i | −0.0136783 | − | 0.191963i | ||||
\(352\) | 2.40530i | 0.128203i | ||||||||
\(353\) | −2.28180 | + | 3.95219i | −0.121448 | + | 0.210354i | −0.920339 | − | 0.391122i | \(-0.872087\pi\) |
0.798891 | + | 0.601476i | \(0.205420\pi\) | |||||||
\(354\) | −4.82474 | + | 8.35669i | −0.256432 | + | 0.444153i | ||||
\(355\) | −16.6093 | + | 2.90426i | −0.881530 | + | 0.154142i | ||||
\(356\) | 10.0433i | 0.532292i | ||||||||
\(357\) | 0.200249 | + | 0.346841i | 0.0105983 | + | 0.0183568i | ||||
\(358\) | 4.17781 | + | 7.23617i | 0.220804 | + | 0.382444i | ||||
\(359\) | − | 4.75785i | − | 0.251110i | −0.992087 | − | 0.125555i | \(-0.959929\pi\) | ||
0.992087 | − | 0.125555i | \(-0.0400711\pi\) | |||||||
\(360\) | −0.385150 | − | 2.20265i | −0.0202992 | − | 0.116090i | ||||
\(361\) | 0.262979 | − | 0.455494i | 0.0138410 | − | 0.0239733i | ||||
\(362\) | 6.36677 | − | 11.0276i | 0.334630 | − | 0.579596i | ||||
\(363\) | − | 5.21455i | − | 0.273693i | ||||||
\(364\) | −2.59477 | + | 5.33795i | −0.136003 | + | 0.279784i | ||||
\(365\) | 3.57798 | + | 1.30806i | 0.187280 | + | 0.0684668i | ||||
\(366\) | 2.27990 | + | 1.31630i | 0.119172 | + | 0.0688042i | ||||
\(367\) | 1.29432 | + | 0.747277i | 0.0675630 | + | 0.0390075i | 0.533401 | − | 0.845863i | \(-0.320914\pi\) |
−0.465838 | + | 0.884870i | \(0.654247\pi\) | |||||||
\(368\) | 7.46758 | − | 4.31141i | 0.389274 | − | 0.224748i | ||||
\(369\) | 0.243297i | 0.0126656i | ||||||||
\(370\) | −3.44644 | − | 19.7099i | −0.179172 | − | 1.02467i | ||||
\(371\) | −3.48717 | + | 2.01332i | −0.181045 | + | 0.104526i | ||||
\(372\) | −4.24458 | −0.220071 | ||||||||
\(373\) | 17.8323 | − | 10.2955i | 0.923323 | − | 0.533081i | 0.0386291 | − | 0.999254i | \(-0.487701\pi\) |
0.884694 | + | 0.466173i | \(0.154368\pi\) | |||||||
\(374\) | 0.292601 | − | 0.506800i | 0.0151300 | − | 0.0262060i | ||||
\(375\) | −0.0478026 | + | 11.1802i | −0.00246852 | + | 0.577345i | ||||
\(376\) | 7.29560 | 0.376242 | ||||||||
\(377\) | −0.0698714 | + | 0.143739i | −0.00359856 | + | 0.00740295i | ||||
\(378\) | 1.64613i | 0.0846676i | ||||||||
\(379\) | −18.4173 | − | 10.6332i | −0.946032 | − | 0.546192i | −0.0541858 | − | 0.998531i | \(-0.517256\pi\) |
−0.891846 | + | 0.452339i | \(0.850590\pi\) | |||||||
\(380\) | −6.34045 | − | 7.57816i | −0.325258 | − | 0.388751i | ||||
\(381\) | −8.67351 | − | 15.0230i | −0.444357 | − | 0.769650i | ||||
\(382\) | −0.415264 | −0.0212468 | ||||||||
\(383\) | 5.31095 | + | 9.19884i | 0.271377 | + | 0.470039i | 0.969215 | − | 0.246217i | \(-0.0791877\pi\) |
−0.697838 | + | 0.716256i | \(0.745854\pi\) | |||||||
\(384\) | 0.866025 | − | 0.500000i | 0.0441942 | − | 0.0255155i | ||||
\(385\) | −3.03994 | + | 8.31527i | −0.154930 | + | 0.423786i | ||||
\(386\) | −12.9918 | − | 22.5025i | −0.661267 | − | 1.14535i | ||||
\(387\) | −5.82728 | − | 3.36438i | −0.296217 | − | 0.171021i | ||||
\(388\) | 8.25647 | − | 14.3006i | 0.419159 | − | 0.726004i | ||||
\(389\) | −37.0443 | −1.87822 | −0.939111 | − | 0.343613i | \(-0.888349\pi\) | ||||
−0.939111 | + | 0.343613i | \(0.888349\pi\) | |||||||
\(390\) | −7.82298 | + | 1.94962i | −0.396132 | + | 0.0987230i | ||||
\(391\) | −2.09791 | −0.106096 | ||||||||
\(392\) | −2.14514 | + | 3.71548i | −0.108346 | + | 0.187660i | ||||
\(393\) | 12.2676 | + | 7.08270i | 0.618818 | + | 0.357275i | ||||
\(394\) | −7.72121 | − | 13.3735i | −0.388989 | − | 0.673749i | ||||
\(395\) | 14.2747 | + | 5.21862i | 0.718238 | + | 0.262577i | ||||
\(396\) | 2.08305 | − | 1.20265i | 0.104677 | − | 0.0604353i | ||||
\(397\) | −0.843593 | − | 1.46115i | −0.0423387 | − | 0.0733328i | 0.844079 | − | 0.536218i | \(-0.180148\pi\) |
−0.886418 | + | 0.462885i | \(0.846814\pi\) | |||||||
\(398\) | 13.7057 | 0.687006 | ||||||||
\(399\) | 3.63697 | + | 6.29941i | 0.182076 | + | 0.315365i | ||||
\(400\) | −4.70332 | + | 1.69670i | −0.235166 | + | 0.0848351i | ||||
\(401\) | 17.2949 | + | 9.98524i | 0.863668 | + | 0.498639i | 0.865239 | − | 0.501360i | \(-0.167167\pi\) |
−0.00157101 | + | 0.999999i | \(0.500500\pi\) | |||||||
\(402\) | − | 1.87420i | − | 0.0934764i | ||||||
\(403\) | 1.08772 | + | 15.2653i | 0.0541834 | + | 0.760420i | ||||
\(404\) | −11.3355 | −0.563964 | ||||||||
\(405\) | −1.71497 | + | 1.43487i | −0.0852178 | + | 0.0712995i | ||||
\(406\) | 0.0364836 | − | 0.0631914i | 0.00181065 | − | 0.00313614i | ||||
\(407\) | 18.6397 | − | 10.7616i | 0.923936 | − | 0.533435i | ||||
\(408\) | −0.243297 | −0.0120450 | ||||||||
\(409\) | 10.6603 | − | 6.15471i | 0.527117 | − | 0.304331i | −0.212725 | − | 0.977112i | \(-0.568234\pi\) |
0.739842 | + | 0.672781i | \(0.234900\pi\) | |||||||
\(410\) | 0.535898 | − | 0.0937060i | 0.0264661 | − | 0.00462781i | ||||
\(411\) | 7.33417i | 0.361768i | ||||||||
\(412\) | 5.18029 | − | 2.99084i | 0.255214 | − | 0.147348i | ||||
\(413\) | −13.7562 | − | 7.94212i | −0.676896 | − | 0.390806i | ||||
\(414\) | −7.46758 | − | 4.31141i | −0.367011 | − | 0.211894i | ||||
\(415\) | −36.7493 | − | 13.4350i | −1.80395 | − | 0.659498i | ||||
\(416\) | −2.02015 | − | 2.98647i | −0.0990458 | − | 0.146424i | ||||
\(417\) | 14.2037i | 0.695559i | ||||||||
\(418\) | 5.31428 | − | 9.20461i | 0.259930 | − | 0.450212i | ||||
\(419\) | 11.0411 | − | 19.1238i | 0.539393 | − | 0.934256i | −0.459544 | − | 0.888155i | \(-0.651987\pi\) |
0.998937 | − | 0.0461011i | \(-0.0146796\pi\) | |||||||
\(420\) | 3.62584 | − | 0.634006i | 0.176923 | − | 0.0309363i | ||||
\(421\) | 8.98036i | 0.437676i | 0.975761 | + | 0.218838i | \(0.0702266\pi\) | ||||
−0.975761 | + | 0.218838i | \(0.929773\pi\) | |||||||
\(422\) | −8.05616 | − | 13.9537i | −0.392168 | − | 0.679254i | ||||
\(423\) | −3.64780 | − | 6.31817i | −0.177362 | − | 0.307200i | ||||
\(424\) | − | 2.44613i | − | 0.118795i | ||||||
\(425\) | 1.19740 | + | 0.214655i | 0.0580824 | + | 0.0104123i | ||||
\(426\) | −3.77030 | + | 6.53035i | −0.182672 | + | 0.316397i | ||||
\(427\) | −2.16680 | + | 3.75300i | −0.104859 | + | 0.181621i | ||||
\(428\) | − | 10.6759i | − | 0.516039i | ||||||
\(429\) | −4.85905 | − | 7.18335i | −0.234597 | − | 0.346815i | ||||
\(430\) | −5.16617 | + | 14.1312i | −0.249135 | + | 0.681469i | ||||
\(431\) | 7.16090 | + | 4.13435i | 0.344928 | + | 0.199145i | 0.662449 | − | 0.749107i | \(-0.269517\pi\) |
−0.317521 | + | 0.948251i | \(0.602850\pi\) | |||||||
\(432\) | −0.866025 | − | 0.500000i | −0.0416667 | − | 0.0240563i | ||||
\(433\) | 17.1825 | − | 9.92035i | 0.825740 | − | 0.476741i | −0.0266515 | − | 0.999645i | \(-0.508484\pi\) |
0.852392 | + | 0.522903i | \(0.175151\pi\) | |||||||
\(434\) | − | 6.98710i | − | 0.335392i | ||||||
\(435\) | 0.0976359 | − | 0.0170724i | 0.00468128 | − | 0.000818559i | ||||
\(436\) | 8.23316 | − | 4.75342i | 0.394297 | − | 0.227647i | ||||
\(437\) | −38.1027 | −1.82270 | ||||||||
\(438\) | 1.47545 | − | 0.851850i | 0.0704996 | − | 0.0407030i | ||||
\(439\) | −14.4415 | + | 25.0134i | −0.689255 | + | 1.19382i | 0.282824 | + | 0.959172i | \(0.408729\pi\) |
−0.972079 | + | 0.234653i | \(0.924605\pi\) | |||||||
\(440\) | −3.45130 | − | 4.12502i | −0.164534 | − | 0.196653i | ||||
\(441\) | 4.29027 | 0.204299 | ||||||||
\(442\) | 0.0623479 | + | 0.875002i | 0.00296559 | + | 0.0416196i | ||||
\(443\) | 5.76986i | 0.274134i | 0.990562 | + | 0.137067i | \(0.0437676\pi\) | ||||
−0.990562 | + | 0.137067i | \(0.956232\pi\) | |||||||
\(444\) | −7.74945 | − | 4.47415i | −0.367772 | − | 0.212334i | ||||
\(445\) | −14.4108 | − | 17.2239i | −0.683138 | − | 0.816493i | ||||
\(446\) | 5.55886 | + | 9.62823i | 0.263220 | + | 0.455910i | ||||
\(447\) | −11.1039 | −0.525195 | ||||||||
\(448\) | 0.823063 | + | 1.42559i | 0.0388861 | + | 0.0673526i | ||||
\(449\) | −33.9034 | + | 19.5741i | −1.60000 | + | 0.923760i | −0.608514 | + | 0.793543i | \(0.708234\pi\) |
−0.991486 | + | 0.130217i | \(0.958433\pi\) | |||||||
\(450\) | 3.82105 | + | 3.22484i | 0.180126 | + | 0.152021i | ||||
\(451\) | 0.292601 | + | 0.506800i | 0.0137780 | + | 0.0238643i | ||||
\(452\) | 3.11433 | + | 1.79806i | 0.146486 | + | 0.0845736i | ||||
\(453\) | −0.437332 | + | 0.757480i | −0.0205476 | + | 0.0355895i | ||||
\(454\) | 22.0799 | 1.03626 | ||||||||
\(455\) | −3.20932 | − | 12.8776i | −0.150455 | − | 0.603711i | ||||
\(456\) | −4.41882 | −0.206930 | ||||||||
\(457\) | −12.2403 | + | 21.2008i | −0.572575 | + | 0.991730i | 0.423725 | + | 0.905791i | \(0.360722\pi\) |
−0.996300 | + | 0.0859387i | \(0.972611\pi\) | |||||||
\(458\) | 8.95443 | + | 5.16984i | 0.418413 | + | 0.241571i | ||||
\(459\) | 0.121649 | + | 0.210702i | 0.00567807 | + | 0.00983471i | ||||
\(460\) | −6.62037 | + | 18.1090i | −0.308677 | + | 0.844336i | ||||
\(461\) | 3.02923 | − | 1.74893i | 0.141085 | − | 0.0814557i | −0.427796 | − | 0.903875i | \(-0.640710\pi\) |
0.568881 | + | 0.822420i | \(0.307376\pi\) | |||||||
\(462\) | 1.97971 | + | 3.42896i | 0.0921044 | + | 0.159530i | ||||
\(463\) | 18.3063 | 0.850767 | 0.425384 | − | 0.905013i | \(-0.360139\pi\) | ||||
0.425384 | + | 0.905013i | \(0.360139\pi\) | |||||||
\(464\) | 0.0221633 | + | 0.0383880i | 0.00102891 | + | 0.00178212i | ||||
\(465\) | 7.27934 | − | 6.09043i | 0.337571 | − | 0.282437i | ||||
\(466\) | 18.9597 | + | 10.9464i | 0.878292 | + | 0.507082i | ||||
\(467\) | 6.46019i | 0.298942i | 0.988766 | + | 0.149471i | \(0.0477571\pi\) | ||||
−0.988766 | + | 0.149471i | \(0.952243\pi\) | |||||||
\(468\) | −1.57629 | + | 3.24273i | −0.0728639 | + | 0.149895i | ||||
\(469\) | 3.08516 | 0.142460 | ||||||||
\(470\) | −12.5118 | + | 10.4683i | −0.577125 | + | 0.482865i | ||||
\(471\) | 7.75425 | − | 13.4307i | 0.357297 | − | 0.618856i | ||||
\(472\) | 8.35669 | − | 4.82474i | 0.384648 | − | 0.222077i | ||||
\(473\) | −16.1847 | −0.744172 | ||||||||
\(474\) | 5.88644 | − | 3.39854i | 0.270373 | − | 0.156100i | ||||
\(475\) | 21.7474 | + | 3.89860i | 0.997840 | + | 0.178880i | ||||
\(476\) | − | 0.400498i | − | 0.0183568i | ||||||
\(477\) | −2.11841 | + | 1.22307i | −0.0969954 | + | 0.0560003i | ||||
\(478\) | −22.7341 | − | 13.1255i | −1.03983 | − | 0.600347i | ||||
\(479\) | 26.5980 | + | 15.3564i | 1.21529 | + | 0.701651i | 0.963908 | − | 0.266236i | \(-0.0857800\pi\) |
0.251387 | + | 0.967887i | \(0.419113\pi\) | |||||||
\(480\) | −0.767774 | + | 2.10012i | −0.0350439 | + | 0.0958571i | ||||
\(481\) | −14.1051 | + | 29.0169i | −0.643136 | + | 1.32306i | ||||
\(482\) | − | 26.0907i | − | 1.18840i | ||||||
\(483\) | 7.09712 | − | 12.2926i | 0.322930 | − | 0.559331i | ||||
\(484\) | −2.60727 | + | 4.51593i | −0.118512 | + | 0.205270i | ||||
\(485\) | 6.35996 | + | 36.3722i | 0.288791 | + | 1.65158i | ||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | 6.23335 | + | 10.7965i | 0.282460 | + | 0.489235i | 0.971990 | − | 0.235022i | \(-0.0755162\pi\) |
−0.689530 | + | 0.724257i | \(0.742183\pi\) | |||||||
\(488\) | −1.31630 | − | 2.27990i | −0.0595862 | − | 0.103206i | ||||
\(489\) | − | 21.8928i | − | 0.990027i | ||||||
\(490\) | −1.65240 | − | 9.44996i | −0.0746478 | − | 0.426906i | ||||
\(491\) | 1.29120 | − | 2.23642i | 0.0582710 | − | 0.100928i | −0.835418 | − | 0.549615i | \(-0.814775\pi\) |
0.893689 | + | 0.448686i | \(0.148108\pi\) | |||||||
\(492\) | 0.121649 | − | 0.210702i | 0.00548434 | − | 0.00949916i | ||||
\(493\) | − | 0.0107845i | − | 0.000485711i | ||||||
\(494\) | 1.13238 | + | 15.8920i | 0.0509480 | + | 0.715014i | ||||
\(495\) | −1.84672 | + | 5.05142i | −0.0830041 | + | 0.227045i | ||||
\(496\) | 3.67591 | + | 2.12229i | 0.165053 | + | 0.0952935i | ||||
\(497\) | −10.7498 | − | 6.20639i | −0.482194 | − | 0.278395i | ||||
\(498\) | −15.1543 | + | 8.74932i | −0.679079 | + | 0.392066i | ||||
\(499\) | − | 20.2443i | − | 0.906261i | −0.891444 | − | 0.453130i | \(-0.850307\pi\) | ||
0.891444 | − | 0.453130i | \(-0.149693\pi\) | |||||||
\(500\) | 5.63152 | − | 9.65847i | 0.251849 | − | 0.431940i | ||||
\(501\) | 4.58673 | − | 2.64815i | 0.204920 | − | 0.118311i | ||||
\(502\) | −0.624794 | −0.0278859 | ||||||||
\(503\) | −7.33148 | + | 4.23283i | −0.326894 | + | 0.188733i | −0.654461 | − | 0.756095i | \(-0.727105\pi\) |
0.327567 | + | 0.944828i | \(0.393771\pi\) | |||||||
\(504\) | 0.823063 | − | 1.42559i | 0.0366621 | − | 0.0635007i | ||||
\(505\) | 19.4402 | − | 16.2651i | 0.865076 | − | 0.723786i | ||||
\(506\) | −20.7404 | −0.922024 | ||||||||
\(507\) | 12.0662 | + | 4.83802i | 0.535879 | + | 0.214864i | ||||
\(508\) | 17.3470i | 0.769650i | ||||||||
\(509\) | −33.4172 | − | 19.2935i | −1.48119 | − | 0.855167i | −0.481421 | − | 0.876490i | \(-0.659879\pi\) |
−0.999773 | + | 0.0213225i | \(0.993212\pi\) | |||||||
\(510\) | 0.417249 | − | 0.349101i | 0.0184761 | − | 0.0154585i | ||||
\(511\) | 1.40225 | + | 2.42877i | 0.0620320 | + | 0.107443i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.20941 | + | 3.82681i | 0.0975478 | + | 0.168958i | ||||
\(514\) | 12.0758 | − | 6.97195i | 0.532640 | − | 0.307520i | ||||
\(515\) | −4.59258 | + | 12.5623i | −0.202373 | + | 0.553560i | ||||
\(516\) | 3.36438 | + | 5.82728i | 0.148109 | + | 0.256532i | ||||
\(517\) | −15.1971 | − | 8.77404i | −0.668367 | − | 0.385882i | ||||
\(518\) | 7.36500 | − | 12.7566i | 0.323600 | − | 0.560491i | ||||
\(519\) | 17.2592 | 0.757593 | ||||||||
\(520\) | 7.74971 | + | 2.22307i | 0.339847 | + | 0.0974879i | ||||
\(521\) | 12.5345 | 0.549148 | 0.274574 | − | 0.961566i | \(-0.411463\pi\) | ||||
0.274574 | + | 0.961566i | \(0.411463\pi\) | |||||||
\(522\) | 0.0221633 | − | 0.0383880i | 0.000970061 | − | 0.00168020i | ||||
\(523\) | 11.0846 | + | 6.39970i | 0.484696 | + | 0.279839i | 0.722371 | − | 0.691505i | \(-0.243052\pi\) |
−0.237676 | + | 0.971345i | \(0.576386\pi\) | |||||||
\(524\) | −7.08270 | − | 12.2676i | −0.309409 | − | 0.535912i | ||||
\(525\) | −5.30850 | + | 6.28992i | −0.231682 | + | 0.274515i | ||||
\(526\) | 16.8325 | − | 9.71828i | 0.733934 | − | 0.423737i | ||||
\(527\) | −0.516347 | − | 0.894339i | −0.0224924 | − | 0.0389580i | ||||
\(528\) | −2.40530 | −0.104677 | ||||||||
\(529\) | 25.6765 | + | 44.4729i | 1.11637 | + | 1.93361i | ||||
\(530\) | 3.50989 | + | 4.19505i | 0.152460 | + | 0.182221i | ||||
\(531\) | −8.35669 | − | 4.82474i | −0.362649 | − | 0.209376i | ||||
\(532\) | − | 7.27393i | − | 0.315365i | ||||||
\(533\) | −0.788948 | − | 0.383506i | −0.0341731 | − | 0.0166115i | ||||
\(534\) | −10.0433 | −0.434614 | ||||||||
\(535\) | 15.3186 | + | 18.3089i | 0.662279 | + | 0.791562i | ||||
\(536\) | −0.937098 | + | 1.62310i | −0.0404765 | + | 0.0701073i | ||||
\(537\) | −7.23617 | + | 4.17781i | −0.312264 | + | 0.180286i | ||||
\(538\) | −3.00139 | −0.129399 | ||||||||
\(539\) | 8.93684 | − | 5.15969i | 0.384937 | − | 0.222243i | ||||
\(540\) | 2.20265 | − | 0.385150i | 0.0947869 | − | 0.0165742i | ||||
\(541\) | 24.9605i | 1.07314i | 0.843857 | + | 0.536568i | \(0.180280\pi\) | ||||
−0.843857 | + | 0.536568i | \(0.819720\pi\) | |||||||
\(542\) | −24.6538 | + | 14.2339i | −1.05897 | + | 0.611396i | ||||
\(543\) | 11.0276 | + | 6.36677i | 0.473238 | + | 0.273224i | ||||
\(544\) | 0.210702 | + | 0.121649i | 0.00903376 | + | 0.00521564i | ||||
\(545\) | −7.29910 | + | 19.9655i | −0.312659 | + | 0.855229i | ||||
\(546\) | −5.33795 | − | 2.59477i | −0.228443 | − | 0.111046i | ||||
\(547\) | − | 10.4152i | − | 0.445321i | −0.974896 | − | 0.222660i | \(-0.928526\pi\) | ||
0.974896 | − | 0.222660i | \(-0.0714741\pi\) | |||||||
\(548\) | 3.66709 | − | 6.35158i | 0.156650 | − | 0.271326i | ||||
\(549\) | −1.31630 | + | 2.27990i | −0.0561784 | + | 0.0973038i | ||||
\(550\) | 11.8378 | + | 2.12213i | 0.504764 | + | 0.0904878i | ||||
\(551\) | − | 0.195871i | − | 0.00834439i | ||||||
\(552\) | 4.31141 | + | 7.46758i | 0.183506 | + | 0.317841i | ||||
\(553\) | 5.59442 | + | 9.68981i | 0.237899 | + | 0.412053i | ||||
\(554\) | − | 0.852658i | − | 0.0362260i | ||||||
\(555\) | 19.7099 | − | 3.44644i | 0.836640 | − | 0.146293i | ||||
\(556\) | 7.10185 | − | 12.3008i | 0.301186 | − | 0.521669i | ||||
\(557\) | 0.697392 | − | 1.20792i | 0.0295495 | − | 0.0511812i | −0.850872 | − | 0.525372i | \(-0.823926\pi\) |
0.880422 | + | 0.474191i | \(0.157259\pi\) | |||||||
\(558\) | − | 4.24458i | − | 0.179687i | ||||||
\(559\) | 20.0953 | − | 13.5931i | 0.849939 | − | 0.574926i | ||||
\(560\) | −3.45707 | − | 1.26385i | −0.146088 | − | 0.0534075i | ||||
\(561\) | 0.506800 | + | 0.292601i | 0.0213971 | + | 0.0123536i | ||||
\(562\) | 13.5837 | + | 7.84257i | 0.572995 | + | 0.330819i | ||||
\(563\) | −14.0404 | + | 8.10624i | −0.591733 | + | 0.341637i | −0.765782 | − | 0.643100i | \(-0.777648\pi\) |
0.174049 | + | 0.984737i | \(0.444315\pi\) | |||||||
\(564\) | 7.29560i | 0.307200i | ||||||||
\(565\) | −7.92099 | + | 1.38505i | −0.333238 | + | 0.0582693i | ||||
\(566\) | 7.00390 | − | 4.04370i | 0.294396 | − | 0.169970i | ||||
\(567\) | −1.64613 | −0.0691308 | ||||||||
\(568\) | 6.53035 | − | 3.77030i | 0.274007 | − | 0.158198i | ||||
\(569\) | 19.6198 | − | 33.9825i | 0.822505 | − | 1.42462i | −0.0813055 | − | 0.996689i | \(-0.525909\pi\) |
0.903811 | − | 0.427932i | \(-0.140758\pi\) | |||||||
\(570\) | 7.57816 | − | 6.34045i | 0.317414 | − | 0.265572i | ||||
\(571\) | −16.0498 | −0.671662 | −0.335831 | − | 0.941922i | \(-0.609017\pi\) | ||||
−0.335831 | + | 0.941922i | \(0.609017\pi\) | |||||||
\(572\) | 0.616387 | + | 8.65049i | 0.0257724 | + | 0.361695i | ||||
\(573\) | − | 0.415264i | − | 0.0173479i | ||||||
\(574\) | 0.346841 | + | 0.200249i | 0.0144769 | + | 0.00835823i | ||||
\(575\) | −14.6303 | − | 40.5558i | −0.610127 | − | 1.69130i | ||||
\(576\) | 0.500000 | + | 0.866025i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | 28.5363 | 1.18798 | 0.593992 | − | 0.804471i | \(-0.297551\pi\) | ||||
0.593992 | + | 0.804471i | \(0.297551\pi\) | |||||||
\(578\) | 8.47040 | + | 14.6712i | 0.352322 | + | 0.610240i | ||||
\(579\) | 22.5025 | − | 12.9918i | 0.935173 | − | 0.539923i | ||||
\(580\) | −0.0930914 | − | 0.0340328i | −0.00386541 | − | 0.00141314i | ||||
\(581\) | −14.4025 | − | 24.9458i | −0.597515 | − | 1.03493i | ||||
\(582\) | 14.3006 | + | 8.25647i | 0.592780 | + | 0.342242i | ||||
\(583\) | −2.94183 | + | 5.09541i | −0.121838 | + | 0.211030i | ||||
\(584\) | −1.70370 | −0.0704996 | ||||||||
\(585\) | −1.94962 | − | 7.82298i | −0.0806070 | − | 0.323440i | ||||
\(586\) | −1.93438 | −0.0799087 | ||||||||
\(587\) | 22.5265 | − | 39.0171i | 0.929770 | − | 1.61041i | 0.146066 | − | 0.989275i | \(-0.453339\pi\) |
0.783704 | − | 0.621134i | \(-0.213328\pi\) | |||||||
\(588\) | −3.71548 | − | 2.14514i | −0.153224 | − | 0.0884639i | ||||
\(589\) | −9.37800 | − | 16.2432i | −0.386414 | − | 0.669289i | ||||
\(590\) | −7.40862 | + | 20.2651i | −0.305008 | + | 0.834301i | ||||
\(591\) | 13.3735 | − | 7.72121i | 0.550113 | − | 0.317608i | ||||
\(592\) | 4.47415 | + | 7.74945i | 0.183886 | + | 0.318500i | ||||
\(593\) | 37.0634 | 1.52201 | 0.761005 | − | 0.648746i | \(-0.224706\pi\) | ||||
0.761005 | + | 0.648746i | \(0.224706\pi\) | |||||||
\(594\) | 1.20265 | + | 2.08305i | 0.0493453 | + | 0.0854685i | ||||
\(595\) | 0.574664 | + | 0.686844i | 0.0235589 | + | 0.0281578i | ||||
\(596\) | 9.61623 | + | 5.55193i | 0.393896 | + | 0.227416i | ||||
\(597\) | 13.7057i | 0.560938i | ||||||||
\(598\) | 25.7518 | − | 17.4193i | 1.05307 | − | 0.712330i | ||||
\(599\) | 18.6309 | 0.761238 | 0.380619 | − | 0.924732i | \(-0.375711\pi\) | ||||
0.380619 | + | 0.924732i | \(0.375711\pi\) | |||||||
\(600\) | −1.69670 | − | 4.70332i | −0.0692675 | − | 0.192012i | ||||
\(601\) | 9.69008 | − | 16.7837i | 0.395266 | − | 0.684622i | −0.597869 | − | 0.801594i | \(-0.703986\pi\) |
0.993135 | + | 0.116972i | \(0.0373189\pi\) | |||||||
\(602\) | −9.59244 | + | 5.53820i | −0.390958 | + | 0.225720i | ||||
\(603\) | 1.87420 | 0.0763232 | ||||||||
\(604\) | 0.757480 | − | 0.437332i | 0.0308214 | − | 0.0177948i | ||||
\(605\) | −2.00839 | − | 11.4858i | −0.0816525 | − | 0.466965i | ||||
\(606\) | − | 11.3355i | − | 0.460475i | ||||||
\(607\) | 30.2066 | − | 17.4398i | 1.22605 | − | 0.707858i | 0.259846 | − | 0.965650i | \(-0.416328\pi\) |
0.966200 | + | 0.257792i | \(0.0829949\pi\) | |||||||
\(608\) | 3.82681 | + | 2.20941i | 0.155198 | + | 0.0896034i | ||||
\(609\) | 0.0631914 | + | 0.0364836i | 0.00256064 | + | 0.00147839i | ||||
\(610\) | 5.52879 | + | 2.02124i | 0.223854 | + | 0.0818378i | ||||
\(611\) | 26.2381 | − | 1.86959i | 1.06148 | − | 0.0756354i | ||||
\(612\) | − | 0.243297i | − | 0.00983471i | ||||||
\(613\) | −4.07179 | + | 7.05254i | −0.164458 | + | 0.284849i | −0.936463 | − | 0.350767i | \(-0.885921\pi\) |
0.772005 | + | 0.635617i | \(0.219254\pi\) | |||||||
\(614\) | −6.21918 | + | 10.7719i | −0.250986 | + | 0.434720i | ||||
\(615\) | 0.0937060 | + | 0.535898i | 0.00377859 | + | 0.0216095i | ||||
\(616\) | − | 3.95942i | − | 0.159530i | ||||||
\(617\) | −16.7288 | − | 28.9752i | −0.673477 | − | 1.16650i | −0.976912 | − | 0.213644i | \(-0.931467\pi\) |
0.303435 | − | 0.952852i | \(-0.401867\pi\) | |||||||
\(618\) | 2.99084 | + | 5.18029i | 0.120309 | + | 0.208382i | ||||
\(619\) | − | 41.1780i | − | 1.65508i | −0.561404 | − | 0.827542i | \(-0.689739\pi\) | ||
0.561404 | − | 0.827542i | \(-0.310261\pi\) | |||||||
\(620\) | −9.34931 | + | 1.63480i | −0.375477 | + | 0.0656551i | ||||
\(621\) | 4.31141 | − | 7.46758i | 0.173011 | − | 0.299664i | ||||
\(622\) | −9.18502 | + | 15.9089i | −0.368286 | + | 0.637890i | ||||
\(623\) | − | 16.5325i | − | 0.662359i | ||||||
\(624\) | 2.98647 | − | 2.02015i | 0.119555 | − | 0.0808706i | ||||
\(625\) | 4.20078 | + | 24.6445i | 0.168031 | + | 0.985782i | ||||
\(626\) | 27.6647 | + | 15.9722i | 1.10571 | + | 0.638379i | ||||
\(627\) | 9.20461 | + | 5.31428i | 0.367597 | + | 0.212232i | ||||
\(628\) | −13.4307 | + | 7.75425i | −0.535945 | + | 0.309428i | ||||
\(629\) | − | 2.17709i | − | 0.0868065i | ||||||
\(630\) | 0.634006 | + | 3.62584i | 0.0252594 | + | 0.144457i | ||||
\(631\) | 12.6839 | − | 7.32307i | 0.504939 | − | 0.291527i | −0.225812 | − | 0.974171i | \(-0.572503\pi\) |
0.730751 | + | 0.682644i | \(0.239170\pi\) | |||||||
\(632\) | −6.79707 | −0.270373 | ||||||||
\(633\) | 13.9537 | − | 8.05616i | 0.554609 | − | 0.320204i | ||||
\(634\) | −11.6812 | + | 20.2325i | −0.463921 | + | 0.803535i | ||||
\(635\) | −24.8908 | − | 29.7497i | −0.987761 | − | 1.18058i | ||||
\(636\) | 2.44613 | 0.0969954 | ||||||||
\(637\) | −6.76270 | + | 13.9122i | −0.267948 | + | 0.551222i | ||||
\(638\) | − | 0.106619i | − | 0.00422107i | ||||||
\(639\) | −6.53035 | − | 3.77030i | −0.258337 | − | 0.149151i | ||||
\(640\) | 1.71497 | − | 1.43487i | 0.0677903 | − | 0.0567184i | ||||
\(641\) | 23.9793 | + | 41.5334i | 0.947125 | + | 1.64047i | 0.751439 | + | 0.659803i | \(0.229360\pi\) |
0.195686 | + | 0.980667i | \(0.437307\pi\) | |||||||
\(642\) | 10.6759 | 0.421344 | ||||||||
\(643\) | −1.99884 | − | 3.46209i | −0.0788265 | − | 0.136531i | 0.823917 | − | 0.566710i | \(-0.191784\pi\) |
−0.902744 | + | 0.430178i | \(0.858451\pi\) | |||||||
\(644\) | −12.2926 | + | 7.09712i | −0.484395 | + | 0.279666i | ||||
\(645\) | −14.1312 | − | 5.16617i | −0.556417 | − | 0.203418i | ||||
\(646\) | −0.537543 | − | 0.931052i | −0.0211494 | − | 0.0366318i | ||||
\(647\) | −20.4521 | − | 11.8080i | −0.804053 | − | 0.464220i | 0.0408333 | − | 0.999166i | \(-0.486999\pi\) |
−0.844886 | + | 0.534946i | \(0.820332\pi\) | |||||||
\(648\) | 0.500000 | − | 0.866025i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | −23.2098 | −0.911066 | ||||||||
\(650\) | −16.4804 | + | 7.30736i | −0.646413 | + | 0.286618i | ||||
\(651\) | 6.98710 | 0.273846 | ||||||||
\(652\) | −10.9464 | + | 18.9597i | −0.428694 | + | 0.742520i | ||||
\(653\) | −30.5411 | − | 17.6329i | −1.19516 | − | 0.690029i | −0.235692 | − | 0.971828i | \(-0.575735\pi\) |
−0.959473 | + | 0.281799i | \(0.909069\pi\) | |||||||
\(654\) | 4.75342 | + | 8.23316i | 0.185873 | + | 0.321942i | ||||
\(655\) | 29.7491 | + | 10.8758i | 1.16239 | + | 0.424954i | ||||
\(656\) | −0.210702 | + | 0.121649i | −0.00822652 | + | 0.00474958i | ||||
\(657\) | 0.851850 | + | 1.47545i | 0.0332338 | + | 0.0575627i | ||||
\(658\) | −12.0095 | −0.468178 | ||||||||
\(659\) | 12.6686 | + | 21.9427i | 0.493499 | + | 0.854765i | 0.999972 | − | 0.00749088i | \(-0.00238444\pi\) |
−0.506473 | + | 0.862256i | \(0.669051\pi\) | |||||||
\(660\) | 4.12502 | − | 3.45130i | 0.160566 | − | 0.134342i | ||||
\(661\) | 4.21373 | + | 2.43280i | 0.163895 | + | 0.0946248i | 0.579704 | − | 0.814827i | \(-0.303168\pi\) |
−0.415809 | + | 0.909452i | \(0.636502\pi\) | |||||||
\(662\) | 21.4634i | 0.834199i | ||||||||
\(663\) | −0.875002 | + | 0.0623479i | −0.0339823 | + | 0.00242139i | ||||
\(664\) | 17.4986 | 0.679079 | ||||||||
\(665\) | 10.4372 | + | 12.4746i | 0.404736 | + | 0.483744i | ||||
\(666\) | 4.47415 | − | 7.74945i | 0.173370 | − | 0.300285i | ||||
\(667\) | −0.331012 | + | 0.191110i | −0.0128168 | + | 0.00739981i | ||||
\(668\) | −5.29630 | −0.204920 | ||||||||
\(669\) | −9.62823 | + | 5.55886i | −0.372249 | + | 0.214918i | ||||
\(670\) | −0.721847 | − | 4.12820i | −0.0278874 | − | 0.159486i | ||||
\(671\) | 6.33219i | 0.244452i | ||||||||
\(672\) | −1.42559 | + | 0.823063i | −0.0549932 | + | 0.0317503i | ||||
\(673\) | 6.48493 | + | 3.74408i | 0.249976 | + | 0.144324i | 0.619753 | − | 0.784797i | \(-0.287233\pi\) |
−0.369777 | + | 0.929120i | \(0.620566\pi\) | |||||||
\(674\) | 12.4327 | + | 7.17805i | 0.478891 | + | 0.276488i | ||||
\(675\) | −3.22484 | + | 3.82105i | −0.124124 | + | 0.147072i | ||||
\(676\) | −8.03064 | − | 10.2230i | −0.308871 | − | 0.393191i | ||||
\(677\) | − | 37.4181i | − | 1.43810i | −0.694961 | − | 0.719048i | \(-0.744578\pi\) | ||
0.694961 | − | 0.719048i | \(-0.255422\pi\) | |||||||
\(678\) | −1.79806 | + | 3.11433i | −0.0690541 | + | 0.119605i | ||||
\(679\) | −13.5912 | + | 23.5406i | −0.521582 | + | 0.903406i | ||||
\(680\) | −0.535898 | + | 0.0937060i | −0.0205508 | + | 0.00359346i | ||||
\(681\) | 22.0799i | 0.846103i | ||||||||
\(682\) | −5.10473 | − | 8.84165i | −0.195470 | − | 0.338564i | ||||
\(683\) | −3.13940 | − | 5.43761i | −0.120126 | − | 0.208064i | 0.799691 | − | 0.600411i | \(-0.204997\pi\) |
−0.919817 | + | 0.392347i | \(0.871663\pi\) | |||||||
\(684\) | − | 4.41882i | − | 0.168958i | ||||||
\(685\) | 2.82476 | + | 16.1546i | 0.107928 | + | 0.617236i | ||||
\(686\) | 9.29260 | − | 16.0953i | 0.354793 | − | 0.614520i | ||||
\(687\) | −5.16984 | + | 8.95443i | −0.197242 | + | 0.341633i | ||||
\(688\) | − | 6.72876i | − | 0.256532i | ||||||
\(689\) | −0.626851 | − | 8.79735i | −0.0238811 | − | 0.335152i | ||||
\(690\) | −18.1090 | − | 6.62037i | −0.689397 | − | 0.252033i | ||||
\(691\) | −9.17461 | − | 5.29696i | −0.349019 | − | 0.201506i | 0.315234 | − | 0.949014i | \(-0.397917\pi\) |
−0.664253 | + | 0.747508i | \(0.731250\pi\) | |||||||
\(692\) | −14.9469 | − | 8.62958i | −0.568195 | − | 0.328047i | ||||
\(693\) | −3.42896 | + | 1.97971i | −0.130255 | + | 0.0752030i | ||||
\(694\) | 0.665114i | 0.0252474i | ||||||||
\(695\) | 5.47056 | + | 31.2858i | 0.207510 | + | 1.18674i | ||||
\(696\) | −0.0383880 | + | 0.0221633i | −0.00145509 | + | 0.000840098i | ||||
\(697\) | 0.0591936 | 0.00224212 | ||||||||
\(698\) | 3.25007 | − | 1.87643i | 0.123017 | − | 0.0710239i | ||||
\(699\) | −10.9464 | + | 18.9597i | −0.414031 | + | 0.717123i | ||||
\(700\) | 7.74225 | − | 2.79298i | 0.292630 | − | 0.105565i | ||||
\(701\) | −29.6773 | −1.12090 | −0.560449 | − | 0.828189i | \(-0.689371\pi\) | ||||
−0.560449 | + | 0.828189i | \(0.689371\pi\) | |||||||
\(702\) | −3.24273 | − | 1.57629i | −0.122389 | − | 0.0594931i | ||||
\(703\) | − | 39.5409i | − | 1.49131i | ||||||
\(704\) | 2.08305 | + | 1.20265i | 0.0785078 | + | 0.0453265i | ||||
\(705\) | −10.4683 | − | 12.5118i | −0.394258 | − | 0.471220i | ||||
\(706\) | 2.28180 | + | 3.95219i | 0.0858766 | + | 0.148743i | ||||
\(707\) | 18.6597 | 0.701771 | ||||||||
\(708\) | 4.82474 | + | 8.35669i | 0.181325 | + | 0.314064i | ||||
\(709\) | 0.563901 | − | 0.325568i | 0.0211777 | − | 0.0122270i | −0.489374 | − | 0.872074i | \(-0.662775\pi\) |
0.510551 | + | 0.859847i | \(0.329441\pi\) | |||||||
\(710\) | −5.78948 | + | 15.8362i | −0.217275 | + | 0.594322i | ||||
\(711\) | 3.39854 | + | 5.88644i | 0.127455 | + | 0.220759i | ||||
\(712\) | 8.69772 | + | 5.02163i | 0.325961 | + | 0.188194i | ||||
\(713\) | −18.3001 | + | 31.6967i | −0.685344 | + | 1.18705i | ||||
\(714\) | 0.400498 | 0.0149883 | ||||||||
\(715\) | −13.4694 | − | 13.9509i | −0.503729 | − | 0.521735i | ||||
\(716\) | 8.35561 | 0.312264 | ||||||||
\(717\) | 13.1255 | − | 22.7341i | 0.490181 | − | 0.849019i | ||||
\(718\) | −4.12042 | − | 2.37892i | −0.153773 | − | 0.0887807i | ||||
\(719\) | −3.21203 | − | 5.56340i | −0.119789 | − | 0.207480i | 0.799895 | − | 0.600140i | \(-0.204888\pi\) |
−0.919684 | + | 0.392660i | \(0.871555\pi\) | |||||||
\(720\) | −2.10012 | − | 0.767774i | −0.0782670 | − | 0.0286133i | ||||
\(721\) | −8.52740 | + | 4.92330i | −0.317577 | + | 0.183353i | ||||
\(722\) | −0.262979 | − | 0.455494i | −0.00978708 | − | 0.0169517i | ||||
\(723\) | 26.0907 | 0.970325 | ||||||||
\(724\) | −6.36677 | − | 11.0276i | −0.236619 | − | 0.409836i | ||||
\(725\) | 0.208482 | − | 0.0752090i | 0.00774283 | − | 0.00279319i | ||||
\(726\) | −4.51593 | − | 2.60727i | −0.167602 | − | 0.0967650i | ||||
\(727\) | 16.3170i | 0.605165i | 0.953123 | + | 0.302583i | \(0.0978488\pi\) | ||||
−0.953123 | + | 0.302583i | \(0.902151\pi\) | |||||||
\(728\) | 3.32541 | + | 4.91611i | 0.123248 | + | 0.182203i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 2.92180 | − | 2.44459i | 0.108141 | − | 0.0904785i | ||||
\(731\) | −0.818545 | + | 1.41776i | −0.0302750 | + | 0.0524378i | ||||
\(732\) | 2.27990 | − | 1.31630i | 0.0842676 | − | 0.0486519i | ||||
\(733\) | 24.4136 | 0.901735 | 0.450868 | − | 0.892591i | \(-0.351115\pi\) | ||||
0.450868 | + | 0.892591i | \(0.351115\pi\) | |||||||
\(734\) | 1.29432 | − | 0.747277i | 0.0477743 | − | 0.0275825i | ||||
\(735\) | 9.44996 | − | 1.65240i | 0.348567 | − | 0.0609497i | ||||
\(736\) | − | 8.62281i | − | 0.317841i | ||||||
\(737\) | 3.90404 | − | 2.25400i | 0.143807 | − | 0.0830271i | ||||
\(738\) | 0.210702 | + | 0.121649i | 0.00775603 | + | 0.00447795i | ||||
\(739\) | 4.75775 | + | 2.74689i | 0.175017 | + | 0.101046i | 0.584949 | − | 0.811070i | \(-0.301114\pi\) |
−0.409932 | + | 0.912116i | \(0.634448\pi\) | |||||||
\(740\) | −18.7925 | − | 6.87027i | −0.690827 | − | 0.252556i | ||||
\(741\) | −15.8920 | + | 1.13238i | −0.583807 | + | 0.0415989i | ||||
\(742\) | 4.02664i | 0.147823i | ||||||||
\(743\) | −10.6512 | + | 18.4484i | −0.390753 | + | 0.676804i | −0.992549 | − | 0.121845i | \(-0.961119\pi\) |
0.601796 | + | 0.798650i | \(0.294452\pi\) | |||||||
\(744\) | −2.12229 | + | 3.67591i | −0.0778068 | + | 0.134765i | ||||
\(745\) | −24.4579 | + | 4.27666i | −0.896068 | + | 0.156685i | ||||
\(746\) | − | 20.5910i | − | 0.753890i | ||||||
\(747\) | −8.74932 | − | 15.1543i | −0.320121 | − | 0.554466i | ||||
\(748\) | −0.292601 | − | 0.506800i | −0.0106986 | − | 0.0185304i | ||||
\(749\) | 17.5739i | 0.642135i | ||||||||
\(750\) | 9.65847 | + | 5.63152i | 0.352677 | + | 0.205634i | ||||
\(751\) | −15.4023 | + | 26.6776i | −0.562040 | + | 0.973481i | 0.435279 | + | 0.900296i | \(0.356650\pi\) |
−0.997318 | + | 0.0731853i | \(0.976684\pi\) | |||||||
\(752\) | 3.64780 | − | 6.31817i | 0.133022 | − | 0.230400i | ||||
\(753\) | − | 0.624794i | − | 0.0227688i | ||||||
\(754\) | 0.0895462 | + | 0.132380i | 0.00326108 | + | 0.00482100i | ||||
\(755\) | −0.671544 | + | 1.83690i | −0.0244400 | + | 0.0668517i | ||||
\(756\) | 1.42559 | + | 0.823063i | 0.0518481 | + | 0.0299345i | ||||
\(757\) | −30.4180 | − | 17.5618i | −1.10556 | − | 0.638296i | −0.167885 | − | 0.985807i | \(-0.553694\pi\) |
−0.937676 | + | 0.347511i | \(0.887027\pi\) | |||||||
\(758\) | −18.4173 | + | 10.6332i | −0.668946 | + | 0.386216i | ||||
\(759\) | − | 20.7404i | − | 0.752830i | ||||||
\(760\) | −9.73310 | + | 1.70191i | −0.353057 | + | 0.0617347i | ||||
\(761\) | −25.0686 | + | 14.4734i | −0.908737 | + | 0.524659i | −0.880024 | − | 0.474928i | \(-0.842474\pi\) |
−0.0287122 | + | 0.999588i | \(0.509141\pi\) | |||||||
\(762\) | −17.3470 | −0.628416 | ||||||||
\(763\) | −13.5528 | + | 7.82472i | −0.490645 | + | 0.283274i | ||||
\(764\) | −0.207632 | + | 0.359629i | −0.00751187 | + | 0.0130109i | ||||
\(765\) | 0.349101 | + | 0.417249i | 0.0126218 | + | 0.0150857i | ||||
\(766\) | 10.6219 | 0.383785 | ||||||||
\(767\) | 28.8179 | − | 19.4933i | 1.04055 | − | 0.703864i | ||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | −34.3740 | − | 19.8459i | −1.23956 | − | 0.715660i | −0.270555 | − | 0.962704i | \(-0.587207\pi\) |
−0.969004 | + | 0.247045i | \(0.920541\pi\) | |||||||
\(770\) | 5.68127 | + | 6.79030i | 0.204739 | + | 0.244706i | ||||
\(771\) | 6.97195 | + | 12.0758i | 0.251089 | + | 0.434898i | ||||
\(772\) | −25.9837 | −0.935173 | ||||||||
\(773\) | −7.16938 | − | 12.4177i | −0.257865 | − | 0.446635i | 0.707805 | − | 0.706408i | \(-0.249686\pi\) |
−0.965670 | + | 0.259773i | \(0.916352\pi\) | |||||||
\(774\) | −5.82728 | + | 3.36438i | −0.209457 | + | 0.120930i | ||||
\(775\) | 13.6881 | − | 16.2187i | 0.491691 | − | 0.582594i | ||||
\(776\) | −8.25647 | − | 14.3006i | −0.296390 | − | 0.513363i | ||||
\(777\) | 12.7566 | + | 7.36500i | 0.457639 | + | 0.264218i | ||||
\(778\) | −18.5222 | + | 32.0813i | −0.664052 | + | 1.15017i | ||||
\(779\) | 1.07509 | 0.0385190 | ||||||||
\(780\) | −2.22307 | + | 7.74971i | −0.0795985 | + | 0.277484i | ||||
\(781\) | −18.1374 | −0.649007 | ||||||||
\(782\) | −1.04895 | + | 1.81684i | −0.0375105 | + | 0.0649701i | ||||
\(783\) | 0.0383880 | + | 0.0221633i | 0.00137187 | + | 0.000792052i | ||||
\(784\) | 2.14514 | + | 3.71548i | 0.0766120 | + | 0.132696i | ||||
\(785\) | 11.9070 | − | 32.5698i | 0.424980 | − | 1.16246i | ||||
\(786\) | 12.2676 | − | 7.08270i | 0.437571 | − | 0.252631i | ||||
\(787\) | 5.52776 | + | 9.57437i | 0.197043 | + | 0.341289i | 0.947568 | − | 0.319553i | \(-0.103533\pi\) |
−0.750525 | + | 0.660842i | \(0.770199\pi\) | |||||||
\(788\) | −15.4424 | −0.550113 | ||||||||
\(789\) | 9.71828 | + | 16.8325i | 0.345980 | + | 0.599255i | ||||
\(790\) | 11.6568 | − | 9.75294i | 0.414730 | − | 0.346994i | ||||
\(791\) | −5.12658 | − | 2.95983i | −0.182280 | − | 0.105240i | ||||
\(792\) | − | 2.40530i | − | 0.0854685i | ||||||
\(793\) | −5.31824 | − | 7.86219i | −0.188856 | − | 0.279195i | ||||
\(794\) | −1.68719 | −0.0598760 | ||||||||
\(795\) | −4.19505 | + | 3.50989i | −0.148783 | + | 0.124483i | ||||
\(796\) | 6.85286 | − | 11.8695i | 0.242893 | − | 0.420704i | ||||
\(797\) | 0.453218 | − | 0.261666i | 0.0160538 | − | 0.00926867i | −0.491952 | − | 0.870623i | \(-0.663716\pi\) |
0.508005 | + | 0.861354i | \(0.330383\pi\) | |||||||
\(798\) | 7.27393 | 0.257494 | ||||||||
\(799\) | −1.53719 | + | 0.887500i | −0.0543820 | + | 0.0313975i | ||||
\(800\) | −0.882273 | + | 4.92154i | −0.0311931 | + | 0.174003i | ||||
\(801\) | − | 10.0433i | − | 0.354861i | ||||||
\(802\) | 17.2949 | − | 9.98524i | 0.610705 | − | 0.352591i | ||||
\(803\) | 3.54889 | + | 2.04895i | 0.125238 | + | 0.0723059i | ||||
\(804\) | −1.62310 | − | 0.937098i | −0.0572424 | − | 0.0330489i | ||||
\(805\) | 10.8980 | − | 29.8097i | 0.384103 | − | 1.05065i | ||||
\(806\) | 13.7640 | + | 6.69067i | 0.484817 | + | 0.235669i | ||||
\(807\) | − | 3.00139i | − | 0.105654i | ||||||
\(808\) | −5.66777 | + | 9.81687i | −0.199391 | + | 0.345356i | ||||
\(809\) | −24.5608 | + | 42.5405i | −0.863511 | + | 1.49564i | 0.00500771 | + | 0.999987i | \(0.498406\pi\) |
−0.868518 | + | 0.495657i | \(0.834927\pi\) | |||||||
\(810\) | 0.385150 | + | 2.20265i | 0.0135328 | + | 0.0773932i | ||||
\(811\) | − | 31.5157i | − | 1.10667i | −0.832960 | − | 0.553333i | \(-0.813356\pi\) | ||
0.832960 | − | 0.553333i | \(-0.186644\pi\) | |||||||
\(812\) | −0.0364836 | − | 0.0631914i | −0.00128032 | − | 0.00221758i | ||||
\(813\) | −14.2339 | − | 24.6538i | −0.499203 | − | 0.864645i | ||||
\(814\) | − | 21.5233i | − | 0.754391i | ||||||
\(815\) | −8.43202 | − | 48.2222i | −0.295361 | − | 1.68915i | ||||
\(816\) | −0.121649 | + | 0.210702i | −0.00425855 | + | 0.00737603i | ||||
\(817\) | −14.8666 | + | 25.7497i | −0.520116 | + | 0.900868i | ||||
\(818\) | − | 12.3094i | − | 0.430389i | ||||||
\(819\) | 2.59477 | − | 5.33795i | 0.0906685 | − | 0.186523i | ||||
\(820\) | 0.186797 | − | 0.510955i | 0.00652325 | − | 0.0178433i | ||||
\(821\) | −13.8449 | − | 7.99335i | −0.483190 | − | 0.278970i | 0.238555 | − | 0.971129i | \(-0.423326\pi\) |
−0.721745 | + | 0.692159i | \(0.756660\pi\) | |||||||
\(822\) | 6.35158 | + | 3.66709i | 0.221537 | + | 0.127904i | ||||
\(823\) | 21.8287 | − | 12.6028i | 0.760900 | − | 0.439306i | −0.0687187 | − | 0.997636i | \(-0.521891\pi\) |
0.829619 | + | 0.558330i | \(0.188558\pi\) | |||||||
\(824\) | − | 5.98168i | − | 0.208382i | ||||||
\(825\) | −2.12213 | + | 11.8378i | −0.0738830 | + | 0.412138i | ||||
\(826\) | −13.7562 | + | 7.94212i | −0.478638 | + | 0.276342i | ||||
\(827\) | 22.0889 | 0.768106 | 0.384053 | − | 0.923311i | \(-0.374528\pi\) | ||||
0.384053 | + | 0.923311i | \(0.374528\pi\) | |||||||
\(828\) | −7.46758 | + | 4.31141i | −0.259516 | + | 0.149832i | ||||
\(829\) | −4.72499 | + | 8.18393i | −0.164106 | + | 0.284240i | −0.936337 | − | 0.351102i | \(-0.885807\pi\) |
0.772232 | + | 0.635341i | \(0.219141\pi\) | |||||||
\(830\) | −30.0097 | + | 25.1083i | −1.04165 | + | 0.871523i | ||||
\(831\) | 0.852658 | 0.0295784 | ||||||||
\(832\) | −3.59643 | + | 0.256262i | −0.124684 | + | 0.00888430i | ||||
\(833\) | − | 1.04381i | − | 0.0361659i | ||||||
\(834\) | 12.3008 | + | 7.10185i | 0.425941 | + | 0.245917i | ||||
\(835\) | 9.08302 | − | 7.59952i | 0.314331 | − | 0.262992i | ||||
\(836\) | −5.31428 | − | 9.20461i | −0.183798 | − | 0.318348i | ||||
\(837\) | 4.24458 | 0.146714 | ||||||||
\(838\) | −11.0411 | − | 19.1238i | −0.381409 | − | 0.660619i | ||||
\(839\) | −10.8542 | + | 6.26667i | −0.374728 | + | 0.216350i | −0.675522 | − | 0.737340i | \(-0.736082\pi\) |
0.300794 | + | 0.953689i | \(0.402748\pi\) | |||||||
\(840\) | 1.26385 | − | 3.45707i | 0.0436071 | − | 0.119280i | ||||
\(841\) | 14.4990 | + | 25.1130i | 0.499966 | + | 0.865967i | ||||
\(842\) | 7.77722 | + | 4.49018i | 0.268021 | + | 0.154742i | ||||
\(843\) | −7.84257 | + | 13.5837i | −0.270112 | + | 0.467848i | ||||
\(844\) | −16.1123 | −0.554609 | ||||||||
\(845\) | 28.4410 | + | 6.00915i | 0.978400 | + | 0.206721i | ||||
\(846\) | −7.29560 | −0.250828 | ||||||||
\(847\) | 4.29190 | − | 7.43379i | 0.147471 | − | 0.255428i | ||||
\(848\) | −2.11841 | − | 1.22307i | −0.0727465 | − | 0.0420002i | ||||
\(849\) | 4.04370 | + | 7.00390i | 0.138780 | + | 0.240373i | ||||
\(850\) | 0.784596 | − | 0.929650i | 0.0269114 | − | 0.0318867i | ||||
\(851\) | −66.8220 | + | 38.5797i | −2.29063 | + | 1.32250i | ||||
\(852\) | 3.77030 | + | 6.53035i | 0.129168 | + | 0.223726i | ||||
\(853\) | −54.5472 | −1.86766 | −0.933830 | − | 0.357718i | \(-0.883555\pi\) | ||||
−0.933830 | + | 0.357718i | \(0.883555\pi\) | |||||||
\(854\) | 2.16680 | + | 3.75300i | 0.0741463 | + | 0.128425i | ||||
\(855\) | 6.34045 | + | 7.57816i | 0.216839 | + | 0.259168i | ||||
\(856\) | −9.24559 | − | 5.33795i | −0.316008 | − | 0.182447i | ||||
\(857\) | − | 16.1596i | − | 0.552000i | −0.961158 | − | 0.276000i | \(-0.910991\pi\) | ||
0.961158 | − | 0.276000i | \(-0.0890091\pi\) | |||||||
\(858\) | −8.65049 | + | 0.616387i | −0.295323 | + | 0.0210431i | ||||
\(859\) | 8.02338 | 0.273754 | 0.136877 | − | 0.990588i | \(-0.456293\pi\) | ||||
0.136877 | + | 0.990588i | \(0.456293\pi\) | |||||||
\(860\) | 9.65493 | + | 11.5397i | 0.329230 | + | 0.393499i | ||||
\(861\) | −0.200249 | + | 0.346841i | −0.00682447 | + | 0.0118203i | ||||
\(862\) | 7.16090 | − | 4.13435i | 0.243901 | − | 0.140816i | ||||
\(863\) | −28.2909 | −0.963033 | −0.481517 | − | 0.876437i | \(-0.659914\pi\) | ||||
−0.481517 | + | 0.876437i | \(0.659914\pi\) | |||||||
\(864\) | −0.866025 | + | 0.500000i | −0.0294628 | + | 0.0170103i | ||||
\(865\) | 38.0159 | − | 6.64737i | 1.29258 | − | 0.226017i | ||||
\(866\) | − | 19.8407i | − | 0.674214i | ||||||
\(867\) | −14.6712 | + | 8.47040i | −0.498259 | + | 0.287670i | ||||
\(868\) | −6.05101 | − | 3.49355i | −0.205385 | − | 0.118579i | ||||
\(869\) | 14.1586 | + | 8.17449i | 0.480298 | + | 0.277300i | ||||
\(870\) | 0.0340328 | − | 0.0930914i | 0.00115382 | − | 0.00315609i | ||||
\(871\) | −2.95427 | + | 6.07752i | −0.100102 | + | 0.205929i | ||||
\(872\) | − | 9.50683i | − | 0.321942i | ||||||
\(873\) | −8.25647 | + | 14.3006i | −0.279439 | + | 0.484003i | ||||
\(874\) | −19.0513 | + | 32.9979i | −0.644421 | + | 1.11617i | ||||
\(875\) | −9.27018 | + | 15.8991i | −0.313389 | + | 0.537486i | ||||
\(876\) | − | 1.70370i | − | 0.0575627i | ||||||
\(877\) | 11.3031 | + | 19.5775i | 0.381678 | + | 0.661085i | 0.991302 | − | 0.131605i | \(-0.0420131\pi\) |
−0.609625 | + | 0.792690i | \(0.708680\pi\) | |||||||
\(878\) | 14.4415 | + | 25.0134i | 0.487377 | + | 0.844161i | ||||
\(879\) | − | 1.93438i | − | 0.0652451i | ||||||
\(880\) | −5.29802 | + | 0.926401i | −0.178596 | + | 0.0312290i | ||||
\(881\) | 22.1679 | − | 38.3959i | 0.746854 | − | 1.29359i | −0.202470 | − | 0.979289i | \(-0.564897\pi\) |
0.949324 | − | 0.314301i | \(-0.101770\pi\) | |||||||
\(882\) | 2.14514 | − | 3.71548i | 0.0722305 | − | 0.125107i | ||||
\(883\) | 3.93200i | 0.132322i | 0.997809 | + | 0.0661612i | \(0.0210752\pi\) | ||||
−0.997809 | + | 0.0661612i | \(0.978925\pi\) | |||||||
\(884\) | 0.788948 | + | 0.383506i | 0.0265352 | + | 0.0128987i | ||||
\(885\) | −20.2651 | − | 7.40862i | −0.681204 | − | 0.249038i | ||||
\(886\) | 4.99684 | + | 2.88493i | 0.167872 | + | 0.0969211i | ||||
\(887\) | 25.2382 | + | 14.5713i | 0.847416 | + | 0.489256i | 0.859778 | − | 0.510668i | \(-0.170602\pi\) |
−0.0123622 | + | 0.999924i | \(0.503935\pi\) | |||||||
\(888\) | −7.74945 | + | 4.47415i | −0.260054 | + | 0.150142i | ||||
\(889\) | − | 28.5554i | − | 0.957717i | ||||||
\(890\) | −22.1218 | + | 3.86817i | −0.741523 | + | 0.129661i | ||||
\(891\) | −2.08305 | + | 1.20265i | −0.0697847 | + | 0.0402902i | ||||
\(892\) | 11.1177 | 0.372249 | ||||||||
\(893\) | −27.9189 | + | 16.1190i | −0.934269 | + | 0.539401i | ||||
\(894\) | −5.55193 | + | 9.61623i | −0.185684 | + | 0.321615i | ||||
\(895\) | −14.3297 | + | 11.9893i | −0.478988 | + | 0.400756i | ||||
\(896\) | 1.64613 | 0.0549932 | ||||||||
\(897\) | 17.4193 | + | 25.7518i | 0.581615 | + | 0.859827i | ||||
\(898\) | 39.1483i | 1.30639i | ||||||||
\(899\) | −0.162941 | − | 0.0940738i | −0.00543437 | − | 0.00313754i | ||||
\(900\) | 4.70332 | − | 1.69670i | 0.156777 | − | 0.0565567i | ||||
\(901\) | 0.297569 | + | 0.515404i | 0.00991344 | + | 0.0171706i | ||||
\(902\) | 0.585202 | 0.0194851 | ||||||||
\(903\) | −5.53820 | − | 9.59244i | −0.184300 | − | 0.319216i | ||||
\(904\) | 3.11433 | − | 1.79806i | 0.103581 | − | 0.0598026i | ||||
\(905\) | 26.7420 | + | 9.77648i | 0.888934 | + | 0.324981i | ||||
\(906\) | 0.437332 | + | 0.757480i | 0.0145294 | + | 0.0251656i | ||||
\(907\) | 31.2795 | + | 18.0592i | 1.03862 | + | 0.599647i | 0.919442 | − | 0.393226i | \(-0.128641\pi\) |
0.119177 | + | 0.992873i | \(0.461974\pi\) | |||||||
\(908\) | 11.0399 | − | 19.1217i | 0.366373 | − | 0.634577i | ||||
\(909\) | 11.3355 | 0.375976 | ||||||||
\(910\) | −12.7570 | − | 3.65944i | −0.422890 | − | 0.121309i | ||||
\(911\) | −16.1738 | −0.535863 | −0.267931 | − | 0.963438i | \(-0.586340\pi\) | ||||
−0.267931 | + | 0.963438i | \(0.586340\pi\) | |||||||
\(912\) | −2.20941 | + | 3.82681i | −0.0731609 | + | 0.126718i | ||||
\(913\) | −36.4505 | − | 21.0447i | −1.20634 | − | 0.696478i | ||||
\(914\) | 12.2403 | + | 21.2008i | 0.404872 | + | 0.701259i | ||||
\(915\) | −2.02124 | + | 5.52879i | −0.0668203 | + | 0.182776i | ||||
\(916\) | 8.95443 | − | 5.16984i | 0.295863 | − | 0.170816i | ||||
\(917\) | 11.6590 | + | 20.1940i | 0.385014 | + | 0.666865i | ||||
\(918\) | 0.243297 | 0.00803001 | ||||||||
\(919\) | −1.12534 | − | 1.94914i | −0.0371214 | − | 0.0642962i | 0.846868 | − | 0.531803i | \(-0.178486\pi\) |
−0.883989 | + | 0.467507i | \(0.845152\pi\) | |||||||
\(920\) | 12.3727 | + | 14.7879i | 0.407914 | + | 0.487543i | ||||
\(921\) | −10.7719 | − | 6.21918i | −0.354947 | − | 0.204929i | ||||
\(922\) | − | 3.49785i | − | 0.115196i | ||||||
\(923\) | 22.5198 | − | 15.2331i | 0.741248 | − | 0.501404i | ||||
\(924\) | 3.95942 | 0.130255 | ||||||||
\(925\) | 42.0867 | − | 15.1826i | 1.38380 | − | 0.499200i | ||||
\(926\) | 9.15317 | − | 15.8537i | 0.300792 | − | 0.520987i | ||||
\(927\) | −5.18029 | + | 2.99084i | −0.170143 | + | 0.0982321i | ||||
\(928\) | 0.0443266 | 0.00145509 | ||||||||
\(929\) | 23.2193 | − | 13.4057i | 0.761801 | − | 0.439826i | −0.0681412 | − | 0.997676i | \(-0.521707\pi\) |
0.829942 | + | 0.557850i | \(0.188374\pi\) | |||||||
\(930\) | −1.63480 | − | 9.34931i | −0.0536072 | − | 0.306576i | ||||
\(931\) | − | 18.9579i | − | 0.621321i | ||||||
\(932\) | 18.9597 | − | 10.9464i | 0.621046 | − | 0.358561i | ||||
\(933\) | −15.9089 | − | 9.18502i | −0.520835 | − | 0.300704i | ||||
\(934\) | 5.59469 | + | 3.23010i | 0.183064 | + | 0.105692i | ||||
\(935\) | 1.22900 | + | 0.449303i | 0.0401925 | + | 0.0146938i | ||||
\(936\) | 2.02015 | + | 2.98647i | 0.0660305 | + | 0.0976159i | ||||
\(937\) | − | 44.1333i | − | 1.44177i | −0.693053 | − | 0.720887i | \(-0.743735\pi\) | ||
0.693053 | − | 0.720887i | \(-0.256265\pi\) | |||||||
\(938\) | 1.54258 | − | 2.67183i | 0.0503671 | − | 0.0872383i | ||||
\(939\) | −15.9722 | + | 27.6647i | −0.521234 | + | 0.902804i | ||||
\(940\) | 2.80990 | + | 16.0696i | 0.0916489 | + | 0.524134i | ||||
\(941\) | 28.3857i | 0.925348i | 0.886528 | + | 0.462674i | \(0.153110\pi\) | ||||
−0.886528 | + | 0.462674i | \(0.846890\pi\) | |||||||
\(942\) | −7.75425 | − | 13.4307i | −0.252647 | − | 0.437597i | ||||
\(943\) | −1.04895 | − | 1.81684i | −0.0341586 | − | 0.0591645i | ||||
\(944\) | − | 9.64947i | − | 0.314064i | ||||||
\(945\) | −3.62584 | + | 0.634006i | −0.117948 | + | 0.0206242i | ||||
\(946\) | −8.09234 | + | 14.0163i | −0.263105 | + | 0.455710i | ||||
\(947\) | −24.6676 | + | 42.7256i | −0.801590 | + | 1.38839i | 0.116979 | + | 0.993134i | \(0.462679\pi\) |
−0.918569 | + | 0.395260i | \(0.870654\pi\) | |||||||
\(948\) | − | 6.79707i | − | 0.220759i | ||||||
\(949\) | −6.12724 | + | 0.436594i | −0.198899 | + | 0.0141724i | ||||
\(950\) | 14.2500 | − | 16.8845i | 0.462331 | − | 0.547806i | ||||
\(951\) | −20.2325 | − | 11.6812i | −0.656083 | − | 0.378790i | ||||
\(952\) | −0.346841 | − | 0.200249i | −0.0112412 | − | 0.00649011i | ||||
\(953\) | −9.62904 | + | 5.55933i | −0.311915 | + | 0.180084i | −0.647783 | − | 0.761825i | \(-0.724304\pi\) |
0.335868 | + | 0.941909i | \(0.390970\pi\) | |||||||
\(954\) | 2.44613i | 0.0791964i | ||||||||
\(955\) | −0.159939 | − | 0.914681i | −0.00517551 | − | 0.0295984i | ||||
\(956\) | −22.7341 | + | 13.1255i | −0.735272 | + | 0.424510i | ||||
\(957\) | 0.106619 | 0.00344649 | ||||||||
\(958\) | 26.5980 | − | 15.3564i | 0.859343 | − | 0.496142i | ||||
\(959\) | −6.03648 | + | 10.4555i | −0.194928 | + | 0.337626i | ||||
\(960\) | 1.43487 | + | 1.71497i | 0.0463104 | + | 0.0553506i | ||||
\(961\) | 12.9836 | 0.418825 | ||||||||
\(962\) | 18.0769 | + | 26.7238i | 0.582821 | + | 0.861610i | ||||
\(963\) | 10.6759i | 0.344026i | ||||||||
\(964\) | −22.5952 | − | 13.0454i | −0.727744 | − | 0.420163i | ||||
\(965\) | 44.5614 | − | 37.2833i | 1.43448 | − | 1.20019i | ||||
\(966\) | −7.09712 | − | 12.2926i | −0.228346 | − | 0.395507i | ||||
\(967\) | −55.3514 | −1.77998 | −0.889990 | − | 0.455980i | \(-0.849289\pi\) | ||||
−0.889990 | + | 0.455980i | \(0.849289\pi\) | |||||||
\(968\) | 2.60727 | + | 4.51593i | 0.0838010 | + | 0.145148i | ||||
\(969\) | 0.931052 | − | 0.537543i | 0.0299097 | − | 0.0172684i | ||||
\(970\) | 34.6792 | + | 12.6782i | 1.11348 | + | 0.407073i | ||||
\(971\) | −26.8248 | − | 46.4619i | −0.860848 | − | 1.49103i | −0.871112 | − | 0.491085i | \(-0.836601\pi\) |
0.0102641 | − | 0.999947i | \(-0.496733\pi\) | |||||||
\(972\) | 0.866025 | + | 0.500000i | 0.0277778 | + | 0.0160375i | ||||
\(973\) | −11.6905 | + | 20.2486i | −0.374782 | + | 0.649141i | ||||
\(974\) | 12.4667 | 0.399459 | ||||||||
\(975\) | −7.30736 | − | 16.4804i | −0.234023 | − | 0.527794i | ||||
\(976\) | −2.63260 | −0.0842676 | ||||||||
\(977\) | −6.23411 | + | 10.7978i | −0.199447 | + | 0.345452i | −0.948349 | − | 0.317228i | \(-0.897248\pi\) |
0.748902 | + | 0.662680i | \(0.230581\pi\) | |||||||
\(978\) | −18.9597 | − | 10.9464i | −0.606265 | − | 0.350027i | ||||
\(979\) | −12.0785 | − | 20.9206i | −0.386031 | − | 0.668625i | ||||
\(980\) | −9.01010 | − | 3.29396i | −0.287817 | − | 0.105222i | ||||
\(981\) | −8.23316 | + | 4.75342i | −0.262865 | + | 0.151765i | ||||
\(982\) | −1.29120 | − | 2.23642i | −0.0412038 | − | 0.0713671i | ||||
\(983\) | 19.1972 | 0.612296 | 0.306148 | − | 0.951984i | \(-0.400960\pi\) | ||||
0.306148 | + | 0.951984i | \(0.400960\pi\) | |||||||
\(984\) | −0.121649 | − | 0.210702i | −0.00387802 | − | 0.00671692i | ||||
\(985\) | 26.4833 | − | 22.1579i | 0.843830 | − | 0.706010i | ||||
\(986\) | −0.00933969 | − | 0.00539227i | −0.000297436 | − | 0.000171725i | ||||
\(987\) | − | 12.0095i | − | 0.382266i | ||||||
\(988\) | 14.3291 | + | 6.96533i | 0.455868 | + | 0.221597i | ||||
\(989\) | 58.0209 | 1.84496 | ||||||||
\(990\) | 3.45130 | + | 4.12502i | 0.109689 | + | 0.131102i | ||||
\(991\) | −27.4152 | + | 47.4845i | −0.870872 | + | 1.50840i | −0.00977694 | + | 0.999952i | \(0.503112\pi\) |
−0.861096 | + | 0.508443i | \(0.830221\pi\) | |||||||
\(992\) | 3.67591 | − | 2.12229i | 0.116710 | − | 0.0673827i | ||||
\(993\) | −21.4634 | −0.681120 | ||||||||
\(994\) | −10.7498 | + | 6.20639i | −0.340962 | + | 0.196855i | ||||
\(995\) | 5.27876 | + | 30.1889i | 0.167348 | + | 0.957052i | ||||
\(996\) | 17.4986i | 0.554466i | ||||||||
\(997\) | 35.4227 | − | 20.4513i | 1.12185 | − | 0.647700i | 0.179977 | − | 0.983671i | \(-0.442398\pi\) |
0.941872 | + | 0.335971i | \(0.109064\pi\) | |||||||
\(998\) | −17.5321 | − | 10.1222i | −0.554969 | − | 0.320412i | ||||
\(999\) | 7.74945 | + | 4.47415i | 0.245182 | + | 0.141556i |
(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 | 390.2.x.b.199.6 | yes | 12 | |
3.2 | odd | 2 | 1170.2.bj.c.199.1 | 12 | |||
5.2 | odd | 4 | 1950.2.bc.j.901.5 | 12 | |||
5.3 | odd | 4 | 1950.2.bc.i.901.2 | 12 | |||
5.4 | even | 2 | 390.2.x.a.199.1 | yes | 12 | ||
13.10 | even | 6 | 390.2.x.a.49.1 | ✓ | 12 | ||
15.14 | odd | 2 | 1170.2.bj.d.199.6 | 12 | |||
39.23 | odd | 6 | 1170.2.bj.d.829.6 | 12 | |||
65.23 | odd | 12 | 1950.2.bc.i.751.2 | 12 | |||
65.49 | even | 6 | inner | 390.2.x.b.49.6 | yes | 12 | |
65.62 | odd | 12 | 1950.2.bc.j.751.5 | 12 | |||
195.179 | odd | 6 | 1170.2.bj.c.829.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.x.a.49.1 | ✓ | 12 | 13.10 | even | 6 | ||
390.2.x.a.199.1 | yes | 12 | 5.4 | even | 2 | ||
390.2.x.b.49.6 | yes | 12 | 65.49 | even | 6 | inner | |
390.2.x.b.199.6 | yes | 12 | 1.1 | even | 1 | trivial | |
1170.2.bj.c.199.1 | 12 | 3.2 | odd | 2 | |||
1170.2.bj.c.829.1 | 12 | 195.179 | odd | 6 | |||
1170.2.bj.d.199.6 | 12 | 15.14 | odd | 2 | |||
1170.2.bj.d.829.6 | 12 | 39.23 | odd | 6 | |||
1950.2.bc.i.751.2 | 12 | 65.23 | odd | 12 | |||
1950.2.bc.i.901.2 | 12 | 5.3 | odd | 4 | |||
1950.2.bc.j.751.5 | 12 | 65.62 | odd | 12 | |||
1950.2.bc.j.901.5 | 12 | 5.2 | odd | 4 |