Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [216,2,Mod(37,216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(216, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("216.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 216 = 2^{3} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 216.n (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.72476868366\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} + x^{14} + 2 x^{12} - 4 x^{11} - 8 x^{9} + 4 x^{8} - 16 x^{7} - 32 x^{5} + 32 x^{4} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 72) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 37.3 | ||
Root | \(0.587625 + 1.28635i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 216.37 |
Dual form | 216.2.n.b.181.3 |
$q$-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 \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).
\(n\) | \(55\) | \(109\) | \(137\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.820200 | − | 1.15207i | −0.579969 | − | 0.814639i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.654545 | + | 1.88986i | −0.327272 | + | 0.944930i | ||||
\(5\) | −1.97542 | − | 1.14051i | −0.883437 | − | 0.510052i | −0.0116467 | − | 0.999932i | \(-0.503707\pi\) |
−0.871790 | + | 0.489880i | \(0.837041\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.907824 | − | 1.57240i | −0.343125 | − | 0.594311i | 0.641886 | − | 0.766800i | \(-0.278152\pi\) |
−0.985011 | + | 0.172490i | \(0.944819\pi\) | |||||||
\(8\) | 2.71411 | − | 0.795980i | 0.959584 | − | 0.281421i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.306290 | + | 3.21128i | 0.0968573 | + | 1.01550i | ||||
\(11\) | −4.24153 | + | 2.44885i | −1.27887 | + | 0.738355i | −0.976640 | − | 0.214880i | \(-0.931064\pi\) |
−0.302228 | + | 0.953236i | \(0.597730\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.00895 | − | 2.31457i | −1.11188 | − | 0.641946i | −0.172567 | − | 0.984998i | \(-0.555206\pi\) |
−0.939317 | + | 0.343052i | \(0.888539\pi\) | |||||||
\(14\) | −1.06692 | + | 2.33556i | −0.285146 | + | 0.624205i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.14314 | − | 2.47400i | −0.785786 | − | 0.618499i | ||||
\(17\) | −1.92788 | −0.467579 | −0.233790 | − | 0.972287i | \(-0.575113\pi\) | ||||
−0.233790 | + | 0.972287i | \(0.575113\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.12907i | 0.488442i | 0.969720 | + | 0.244221i | \(0.0785322\pi\) | ||||
−0.969720 | + | 0.244221i | \(0.921468\pi\) | |||||||
\(20\) | 3.44841 | − | 2.98676i | 0.771088 | − | 0.667860i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.30015 | + | 2.87801i | 1.34320 | + | 0.613593i | ||||
\(23\) | 1.15765 | − | 2.00511i | 0.241387 | − | 0.418094i | −0.719723 | − | 0.694261i | \(-0.755731\pi\) |
0.961109 | + | 0.276168i | \(0.0890645\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.101535 | + | 0.175863i | 0.0203069 | + | 0.0351726i | ||||
\(26\) | 0.621589 | + | 6.51702i | 0.121904 | + | 1.27809i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.56582 | − | 0.686457i | 0.673877 | − | 0.129728i | ||||
\(29\) | 3.16440 | − | 1.82697i | 0.587615 | − | 0.339260i | −0.176539 | − | 0.984294i | \(-0.556490\pi\) |
0.764154 | + | 0.645034i | \(0.223157\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.65800 | + | 4.60379i | −0.477391 | + | 0.826865i | −0.999664 | − | 0.0259130i | \(-0.991751\pi\) |
0.522273 | + | 0.852778i | \(0.325084\pi\) | |||||||
\(32\) | −0.272218 | + | 5.65030i | −0.0481218 | + | 0.998841i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.58125 | + | 2.22106i | 0.271181 | + | 0.380908i | ||||
\(35\) | 4.14154i | 0.700048i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 7.98438i | − | 1.31262i | −0.754489 | − | 0.656312i | \(-0.772115\pi\) | ||
0.754489 | − | 0.656312i | \(-0.227885\pi\) | |||||||
\(38\) | 2.45284 | − | 1.74626i | 0.397904 | − | 0.283281i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.26935 | − | 1.52308i | −0.991272 | − | 0.240820i | ||||
\(41\) | 2.36240 | − | 4.09180i | 0.368946 | − | 0.639033i | −0.620455 | − | 0.784242i | \(-0.713052\pi\) |
0.989401 | + | 0.145209i | \(0.0463855\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.20800 | − | 1.27479i | 0.336717 | − | 0.194404i | −0.322102 | − | 0.946705i | \(-0.604390\pi\) |
0.658819 | + | 0.752301i | \(0.271056\pi\) | |||||||
\(44\) | −1.85171 | − | 9.61877i | −0.279156 | − | 1.45008i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.25953 | + | 0.310892i | −0.480592 | + | 0.0458386i | ||||
\(47\) | 2.02005 | + | 3.49884i | 0.294655 | + | 0.510358i | 0.974905 | − | 0.222623i | \(-0.0714619\pi\) |
−0.680249 | + | 0.732981i | \(0.738129\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.85171 | − | 3.20726i | 0.264530 | − | 0.458179i | ||||
\(50\) | 0.119328 | − | 0.261218i | 0.0168756 | − | 0.0369418i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.99825 | − | 6.06137i | 0.970483 | − | 0.840561i | ||||
\(53\) | − | 8.95958i | − | 1.23069i | −0.788257 | − | 0.615347i | \(-0.789016\pi\) | ||
0.788257 | − | 0.615347i | \(-0.210984\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.1718 | 1.50640 | ||||||||
\(56\) | −3.71554 | − | 3.54506i | −0.496509 | − | 0.473728i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.70024 | − | 2.14714i | −0.617172 | − | 0.281934i | ||||
\(59\) | 3.05255 | + | 1.76239i | 0.397408 | + | 0.229444i | 0.685365 | − | 0.728200i | \(-0.259643\pi\) |
−0.287957 | + | 0.957643i | \(0.592976\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.71675 | + | 0.991165i | −0.219807 | + | 0.126906i | −0.605861 | − | 0.795571i | \(-0.707171\pi\) |
0.386054 | + | 0.922476i | \(0.373838\pi\) | |||||||
\(62\) | 7.48399 | − | 0.713818i | 0.950468 | − | 0.0906550i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.73283 | − | 4.32076i | 0.841604 | − | 0.540095i | ||||
\(65\) | 5.27959 | + | 9.14451i | 0.654852 | + | 1.13424i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.72723 | + | 4.46132i | 0.944031 | + | 0.545036i | 0.891222 | − | 0.453568i | \(-0.149849\pi\) |
0.0528093 | + | 0.998605i | \(0.483182\pi\) | |||||||
\(68\) | 1.26188 | − | 3.64342i | 0.153026 | − | 0.441830i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.77135 | − | 3.39689i | 0.570286 | − | 0.406006i | ||||
\(71\) | −13.3561 | −1.58508 | −0.792539 | − | 0.609821i | \(-0.791241\pi\) | ||||
−0.792539 | + | 0.609821i | \(0.791241\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.5592 | −1.35290 | −0.676450 | − | 0.736489i | \(-0.736482\pi\) | ||||
−0.676450 | + | 0.736489i | \(0.736482\pi\) | |||||||
\(74\) | −9.19859 | + | 6.54879i | −1.06931 | + | 0.761281i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.02364 | − | 1.39357i | −0.461543 | − | 0.159854i | ||||
\(77\) | 7.70112 | + | 4.44625i | 0.877625 | + | 0.506697i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.97330 | − | 8.61401i | −0.559540 | − | 0.969151i | −0.997535 | − | 0.0701739i | \(-0.977645\pi\) |
0.437995 | − | 0.898977i | \(-0.355689\pi\) | |||||||
\(80\) | 3.38742 | + | 8.47198i | 0.378725 | + | 0.947196i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.65170 | + | 0.634435i | −0.734558 | + | 0.0700616i | ||||
\(83\) | 3.12153 | − | 1.80221i | 0.342632 | − | 0.197819i | −0.318803 | − | 0.947821i | \(-0.603281\pi\) |
0.661435 | + | 0.750002i | \(0.269948\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.80838 | + | 2.19877i | 0.413077 | + | 0.238490i | ||||
\(86\) | −3.27965 | − | 1.49820i | −0.353654 | − | 0.161555i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −9.56276 | + | 10.0226i | −1.01939 | + | 1.06841i | ||||
\(89\) | −2.49965 | −0.264962 | −0.132481 | − | 0.991186i | \(-0.542294\pi\) | ||||
−0.132481 | + | 0.991186i | \(0.542294\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.40489i | 0.881072i | ||||||||
\(92\) | 3.03164 | + | 3.50023i | 0.316070 | + | 0.364924i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.37407 | − | 5.19699i | 0.244866 | − | 0.536029i | ||||
\(95\) | 2.42823 | − | 4.20582i | 0.249131 | − | 0.431508i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.99370 | + | 12.1134i | 0.710103 | + | 1.22993i | 0.964818 | + | 0.262918i | \(0.0846849\pi\) |
−0.254715 | + | 0.967016i | \(0.581982\pi\) | |||||||
\(98\) | −5.21376 | + | 0.497285i | −0.526670 | + | 0.0502334i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.398816 | + | 0.0767760i | −0.0398816 | + | 0.00767760i | ||||
\(101\) | −1.13087 | + | 0.652911i | −0.112526 | + | 0.0649671i | −0.555207 | − | 0.831712i | \(-0.687361\pi\) |
0.442681 | + | 0.896679i | \(0.354028\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.22312 | + | 5.58261i | −0.317584 | + | 0.550071i | −0.979983 | − | 0.199080i | \(-0.936205\pi\) |
0.662400 | + | 0.749151i | \(0.269538\pi\) | |||||||
\(104\) | −12.7231 | − | 3.09096i | −1.24760 | − | 0.303094i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.3221 | + | 7.34865i | −1.00257 | + | 0.713764i | ||||
\(107\) | − | 3.10427i | − | 0.300101i | −0.988678 | − | 0.150051i | \(-0.952056\pi\) | ||
0.988678 | − | 0.150051i | \(-0.0479437\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.0837i | 1.73210i | 0.499955 | + | 0.866051i | \(0.333350\pi\) | ||||
−0.499955 | + | 0.866051i | \(0.666650\pi\) | |||||||
\(110\) | −9.16307 | − | 12.8707i | −0.873665 | − | 1.22717i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.03668 | + | 7.18822i | −0.0979574 | + | 0.679223i | ||||
\(113\) | 1.41718 | − | 2.45463i | 0.133317 | − | 0.230913i | −0.791636 | − | 0.610993i | \(-0.790770\pi\) |
0.924953 | + | 0.380080i | \(0.124104\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.57370 | + | 2.64063i | −0.426500 | + | 0.246240i | ||||
\(116\) | 1.38147 | + | 7.17611i | 0.128267 | + | 0.666285i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.473298 | − | 4.96227i | −0.0435706 | − | 0.456814i | ||||
\(119\) | 1.75018 | + | 3.03139i | 0.160438 | + | 0.277887i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.49370 | − | 11.2474i | 0.590337 | − | 1.02249i | ||||
\(122\) | 2.54997 | + | 1.16487i | 0.230863 | + | 0.105462i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.96074 | − | 8.03663i | −0.625093 | − | 0.721711i | ||||
\(125\) | 10.9419i | 0.978674i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.44962 | −0.661047 | −0.330523 | − | 0.943798i | \(-0.607225\pi\) | ||||
−0.330523 | + | 0.943798i | \(0.607225\pi\) | |||||||
\(128\) | −10.5001 | − | 4.21283i | −0.928086 | − | 0.372365i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.20483 | − | 13.5828i | 0.544200 | − | 1.19129i | ||||
\(131\) | −3.12153 | − | 1.80221i | −0.272729 | − | 0.157460i | 0.357398 | − | 0.933952i | \(-0.383664\pi\) |
−0.630127 | + | 0.776492i | \(0.716997\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.34774 | − | 1.93282i | 0.290286 | − | 0.167597i | ||||
\(134\) | −1.19811 | − | 12.5615i | −0.103501 | − | 1.08515i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.23248 | + | 1.53455i | −0.448682 | + | 0.131587i | ||||
\(137\) | −5.88147 | − | 10.1870i | −0.502488 | − | 0.870335i | −0.999996 | − | 0.00287543i | \(-0.999085\pi\) |
0.497508 | − | 0.867460i | \(-0.334249\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.0400 | − | 6.37395i | −0.936400 | − | 0.540631i | −0.0475703 | − | 0.998868i | \(-0.515148\pi\) |
−0.888830 | + | 0.458237i | \(0.848481\pi\) | |||||||
\(140\) | −7.82693 | − | 2.71082i | −0.661496 | − | 0.229106i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.9547 | + | 15.3872i | 0.919296 | + | 1.29127i | ||||
\(143\) | 22.6721 | 1.89594 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.33472 | −0.692161 | ||||||||
\(146\) | 9.48083 | + | 13.3170i | 0.784639 | + | 1.10212i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 15.0894 | + | 5.22613i | 1.24034 | + | 0.429586i | ||||
\(149\) | −6.59790 | − | 3.80930i | −0.540521 | − | 0.312070i | 0.204769 | − | 0.978810i | \(-0.434356\pi\) |
−0.745290 | + | 0.666740i | \(0.767689\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.26988 | + | 3.93155i | 0.184720 | + | 0.319945i | 0.943482 | − | 0.331423i | \(-0.107529\pi\) |
−0.758762 | + | 0.651368i | \(0.774195\pi\) | |||||||
\(152\) | 1.69470 | + | 5.77854i | 0.137458 | + | 0.468701i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.19406 | − | 12.5191i | −0.0962201 | − | 1.00882i | ||||
\(155\) | 10.5014 | − | 6.06296i | 0.843489 | − | 0.486989i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.4105 | + | 6.58787i | 0.910659 | + | 0.525769i | 0.880643 | − | 0.473780i | \(-0.157111\pi\) |
0.0300161 | + | 0.999549i | \(0.490444\pi\) | |||||||
\(158\) | −5.84486 | + | 12.7948i | −0.464992 | + | 1.01790i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 6.98198 | − | 10.8513i | 0.551974 | − | 0.857869i | ||||
\(161\) | −4.20377 | −0.331303 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 20.5911i | − | 1.61282i | −0.591358 | − | 0.806409i | \(-0.701408\pi\) | ||
0.591358 | − | 0.806409i | \(-0.298592\pi\) | |||||||
\(164\) | 6.18664 | + | 7.14288i | 0.483095 | + | 0.557765i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.63656 | − | 2.11805i | −0.359867 | − | 0.164393i | ||||
\(167\) | −2.53912 | + | 4.39789i | −0.196483 | + | 0.340319i | −0.947386 | − | 0.320094i | \(-0.896285\pi\) |
0.750903 | + | 0.660413i | \(0.229619\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.21446 | + | 7.29967i | 0.324190 | + | 0.561513i | ||||
\(170\) | −0.590490 | − | 6.19096i | −0.0452885 | − | 0.474825i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.963939 | + | 5.00722i | 0.0734997 | + | 0.381797i | ||||
\(173\) | −11.0398 | + | 6.37385i | −0.839343 | + | 0.484595i | −0.857041 | − | 0.515248i | \(-0.827700\pi\) |
0.0176977 | + | 0.999843i | \(0.494366\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.184351 | − | 0.319306i | 0.0139356 | − | 0.0241372i | ||||
\(176\) | 19.3902 | + | 2.79644i | 1.46159 | + | 0.210790i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.05021 | + | 2.87978i | 0.153670 | + | 0.215849i | ||||
\(179\) | − | 8.82019i | − | 0.659252i | −0.944112 | − | 0.329626i | \(-0.893077\pi\) | ||
0.944112 | − | 0.329626i | \(-0.106923\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 15.4369i | − | 1.14741i | −0.819061 | − | 0.573707i | \(-0.805505\pi\) | ||
0.819061 | − | 0.573707i | \(-0.194495\pi\) | |||||||
\(182\) | 9.68305 | − | 6.89369i | 0.717755 | − | 0.510994i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.54597 | − | 6.36356i | 0.113970 | − | 0.469128i | ||||
\(185\) | −9.10628 | + | 15.7725i | −0.669507 | + | 1.15962i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.17715 | − | 4.72108i | 0.597972 | − | 0.345239i | ||||
\(188\) | −7.93453 | + | 1.52748i | −0.578685 | + | 0.111403i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.83704 | + | 0.652112i | −0.496011 | + | 0.0473092i | ||||
\(191\) | −4.81698 | − | 8.34326i | −0.348545 | − | 0.603697i | 0.637446 | − | 0.770495i | \(-0.279991\pi\) |
−0.985991 | + | 0.166797i | \(0.946657\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.49335 | − | 6.05066i | 0.251457 | − | 0.435536i | −0.712470 | − | 0.701702i | \(-0.752424\pi\) |
0.963927 | + | 0.266166i | \(0.0857570\pi\) | |||||||
\(194\) | 8.21934 | − | 17.9927i | 0.590114 | − | 1.29180i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.84924 | + | 5.59876i | 0.346374 | + | 0.399912i | ||||
\(197\) | 4.31842i | 0.307675i | 0.988096 | + | 0.153837i | \(0.0491632\pi\) | ||||
−0.988096 | + | 0.153837i | \(0.950837\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.90649 | 0.418700 | 0.209350 | − | 0.977841i | \(-0.432865\pi\) | ||||
0.209350 | + | 0.977841i | \(0.432865\pi\) | |||||||
\(200\) | 0.415560 | + | 0.396493i | 0.0293845 | + | 0.0280363i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.67974 | + | 0.767333i | 0.118186 | + | 0.0539894i | ||||
\(203\) | −5.74544 | − | 3.31713i | −0.403251 | − | 0.232817i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.33350 | + | 5.38870i | −0.651880 | + | 0.376363i | ||||
\(206\) | 9.07518 | − | 0.865585i | 0.632298 | − | 0.0603082i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.87447 | + | 17.1932i | 0.476659 | + | 1.19213i | ||||
\(209\) | −5.21376 | − | 9.03050i | −0.360644 | − | 0.624653i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.8781 | − | 9.16723i | −1.09309 | − | 0.631098i | −0.158696 | − | 0.987328i | \(-0.550729\pi\) |
−0.934399 | + | 0.356229i | \(0.884062\pi\) | |||||||
\(212\) | 16.9324 | + | 5.86445i | 1.16292 | + | 0.402772i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.57635 | + | 2.54612i | −0.244474 | + | 0.174049i | ||||
\(215\) | −5.81565 | −0.396624 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.65199 | 0.655220 | ||||||||
\(218\) | 20.8337 | − | 14.8322i | 1.41104 | − | 1.00457i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −7.31241 | + | 21.1131i | −0.493003 | + | 1.42344i | ||||
\(221\) | 7.72877 | + | 4.46221i | 0.519893 | + | 0.300161i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.63263 | − | 4.55986i | −0.176294 | − | 0.305350i | 0.764314 | − | 0.644844i | \(-0.223078\pi\) |
−0.940608 | + | 0.339494i | \(0.889744\pi\) | |||||||
\(224\) | 9.13165 | − | 4.70145i | 0.610134 | − | 0.314129i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.99029 | + | 0.380591i | −0.265430 | + | 0.0253166i | ||||
\(227\) | −1.53638 | + | 0.887027i | −0.101973 | + | 0.0588741i | −0.550119 | − | 0.835086i | \(-0.685418\pi\) |
0.448146 | + | 0.893960i | \(0.352084\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.30687 | − | 1.90922i | −0.218524 | − | 0.126165i | 0.386742 | − | 0.922188i | \(-0.373600\pi\) |
−0.605267 | + | 0.796023i | \(0.706934\pi\) | |||||||
\(230\) | 6.79354 | + | 3.10339i | 0.447953 | + | 0.204632i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.13432 | − | 7.47740i | 0.468391 | − | 0.490915i | ||||
\(233\) | 20.3207 | 1.33125 | 0.665627 | − | 0.746284i | \(-0.268164\pi\) | ||||
0.665627 | + | 0.746284i | \(0.268164\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 9.21558i | − | 0.601158i | ||||||
\(236\) | −5.32870 | + | 4.61533i | −0.346869 | + | 0.300432i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.05689 | − | 4.50268i | 0.133328 | − | 0.291865i | ||||
\(239\) | −8.69811 | + | 15.0656i | −0.562634 | + | 0.974510i | 0.434632 | + | 0.900608i | \(0.356879\pi\) |
−0.997266 | + | 0.0739020i | \(0.976455\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.85611 | − | 11.8751i | −0.441641 | − | 0.764944i | 0.556171 | − | 0.831068i | \(-0.312270\pi\) |
−0.997811 | + | 0.0661240i | \(0.978937\pi\) | |||||||
\(242\) | −18.2840 | + | 1.74391i | −1.17534 | + | 0.112103i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.749475 | − | 3.89317i | −0.0479802 | − | 0.249235i | ||||
\(245\) | −7.31583 | + | 4.22379i | −0.467391 | + | 0.269848i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.92788 | − | 8.53534i | 0.313553 | − | 0.543090i | ||||
\(248\) | −3.54959 | + | 14.6109i | −0.225399 | + | 0.927795i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 12.6059 | − | 8.97455i | 0.797266 | − | 0.567601i | ||||
\(251\) | − | 4.50751i | − | 0.284512i | −0.989830 | − | 0.142256i | \(-0.954564\pi\) | ||
0.989830 | − | 0.142256i | \(-0.0454356\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.3396i | 0.712916i | ||||||||
\(254\) | 6.11018 | + | 8.58250i | 0.383387 | + | 0.538514i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.75869 | + | 15.5522i | 0.234918 | + | 0.972015i | ||||
\(257\) | 4.11258 | − | 7.12320i | 0.256536 | − | 0.444333i | −0.708776 | − | 0.705434i | \(-0.750752\pi\) |
0.965311 | + | 0.261101i | \(0.0840856\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.5546 | + | 7.24842i | −0.780106 | + | 0.450395i | ||||
\(260\) | −20.7376 | + | 3.99219i | −1.28609 | + | 0.247585i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.483993 | + | 5.07440i | 0.0299012 | + | 0.313498i | ||||
\(263\) | −2.51376 | − | 4.35395i | −0.155005 | − | 0.268476i | 0.778056 | − | 0.628195i | \(-0.216206\pi\) |
−0.933061 | + | 0.359719i | \(0.882873\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.2185 | + | 17.6990i | −0.627718 | + | 1.08724i | ||||
\(266\) | −4.97257 | − | 2.27155i | −0.304888 | − | 0.139277i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −13.4891 | + | 11.6832i | −0.823977 | + | 0.713668i | ||||
\(269\) | 23.1577i | 1.41195i | 0.708236 | + | 0.705976i | \(0.249491\pi\) | ||||
−0.708236 | + | 0.705976i | \(0.750509\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.9367 | 1.27181 | 0.635906 | − | 0.771766i | \(-0.280627\pi\) | ||||
0.635906 | + | 0.771766i | \(0.280627\pi\) | |||||||
\(272\) | 6.05960 | + | 4.76956i | 0.367417 | + | 0.289197i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.91220 | + | 15.1313i | −0.417581 | + | 0.914113i | ||||
\(275\) | −0.861323 | − | 0.497285i | −0.0519398 | − | 0.0299874i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.2687 | − | 11.1248i | 1.15775 | − | 0.668425i | 0.206983 | − | 0.978345i | \(-0.433636\pi\) |
0.950763 | + | 0.309920i | \(0.100302\pi\) | |||||||
\(278\) | 1.71175 | + | 17.9468i | 0.102664 | + | 1.07638i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.29658 | + | 11.2406i | 0.197008 | + | 0.671755i | ||||
\(281\) | 9.28029 | + | 16.0739i | 0.553616 | + | 0.958890i | 0.998010 | + | 0.0630590i | \(0.0200856\pi\) |
−0.444394 | + | 0.895831i | \(0.646581\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.75962 | + | 1.01592i | 0.104599 | + | 0.0603901i | 0.551387 | − | 0.834250i | \(-0.314099\pi\) |
−0.446788 | + | 0.894640i | \(0.647432\pi\) | |||||||
\(284\) | 8.74217 | − | 25.2412i | 0.518752 | − | 1.49779i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −18.5957 | − | 26.1199i | −1.09958 | − | 1.54450i | ||||
\(287\) | −8.57859 | −0.506378 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.2833 | −0.781370 | ||||||||
\(290\) | 6.83613 | + | 9.60220i | 0.401432 | + | 0.563861i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.56600 | − | 21.8452i | 0.442766 | − | 1.27840i | ||||
\(293\) | −29.5484 | − | 17.0598i | −1.72623 | − | 0.996642i | −0.904057 | − | 0.427411i | \(-0.859426\pi\) |
−0.822178 | − | 0.569231i | \(-0.807241\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.02005 | − | 6.96294i | −0.234057 | − | 0.405398i | ||||
\(296\) | −6.35541 | − | 21.6705i | −0.369401 | − | 1.25957i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.02300 | + | 10.7256i | 0.0592611 | + | 0.621320i | ||||
\(299\) | −9.28192 | + | 5.35892i | −0.536787 | + | 0.309914i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.00895 | − | 2.31457i | −0.231072 | − | 0.133410i | ||||
\(302\) | 2.66767 | − | 5.83972i | 0.153507 | − | 0.336038i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.26731 | − | 6.69197i | 0.302101 | − | 0.383811i | ||||
\(305\) | 4.52174 | 0.258914 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.77588i | 0.272574i | 0.990669 | + | 0.136287i | \(0.0435169\pi\) | ||||
−0.990669 | + | 0.136287i | \(0.956483\pi\) | |||||||
\(308\) | −13.4435 | + | 11.6438i | −0.766015 | + | 0.663466i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −15.5982 | − | 7.12549i | −0.885917 | − | 0.404701i | ||||
\(311\) | 11.1771 | − | 19.3592i | 0.633793 | − | 1.09776i | −0.352976 | − | 0.935632i | \(-0.614830\pi\) |
0.986769 | − | 0.162130i | \(-0.0518364\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.22411 | + | 2.12022i | 0.0691907 | + | 0.119842i | 0.898545 | − | 0.438881i | \(-0.144625\pi\) |
−0.829355 | + | 0.558723i | \(0.811292\pi\) | |||||||
\(314\) | −1.76920 | − | 18.5491i | −0.0998420 | − | 1.04679i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 19.5345 | − | 3.76059i | 1.09890 | − | 0.211550i | ||||
\(317\) | 14.2886 | − | 8.24953i | 0.802528 | − | 0.463340i | −0.0418263 | − | 0.999125i | \(-0.513318\pi\) |
0.844354 | + | 0.535785i | \(0.179984\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.94793 | + | 15.4983i | −0.500988 | + | 0.867737i | ||||
\(320\) | −18.2281 | + | 0.856461i | −1.01898 | + | 0.0478776i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.44793 | + | 4.84305i | 0.192146 | + | 0.269893i | ||||
\(323\) | − | 4.10459i | − | 0.228385i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 0.940035i | − | 0.0521438i | ||||||
\(326\) | −23.7224 | + | 16.8888i | −1.31386 | + | 0.935385i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.15484 | − | 12.9861i | 0.174197 | − | 0.717035i | ||||
\(329\) | 3.66771 | − | 6.35266i | 0.202207 | − | 0.350233i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.329200 | + | 0.190064i | −0.0180945 | + | 0.0104469i | −0.509020 | − | 0.860755i | \(-0.669992\pi\) |
0.490925 | + | 0.871202i | \(0.336659\pi\) | |||||||
\(332\) | 1.36275 | + | 7.07888i | 0.0747909 | + | 0.388504i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.14928 | − | 0.681893i | 0.391191 | − | 0.0373115i | ||||
\(335\) | −10.1764 | − | 17.6260i | −0.555994 | − | 0.963010i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.51872 | + | 4.36255i | −0.137203 | + | 0.237643i | −0.926437 | − | 0.376450i | \(-0.877145\pi\) |
0.789234 | + | 0.614093i | \(0.210478\pi\) | |||||||
\(338\) | 4.95305 | − | 10.8426i | 0.269410 | − | 0.589757i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.64812 | + | 5.75811i | −0.360545 | + | 0.312277i | ||||
\(341\) | − | 26.0361i | − | 1.40994i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.4337 | −1.04932 | ||||||||
\(344\) | 4.97806 | − | 5.21745i | 0.268399 | − | 0.281306i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 16.3980 | + | 7.49086i | 0.881563 | + | 0.402711i | ||||
\(347\) | 8.40337 | + | 4.85169i | 0.451116 | + | 0.260452i | 0.708302 | − | 0.705910i | \(-0.249462\pi\) |
−0.257185 | + | 0.966362i | \(0.582795\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.1239 | + | 15.0827i | −1.39838 | + | 0.807356i | −0.994223 | − | 0.107333i | \(-0.965769\pi\) |
−0.404158 | + | 0.914689i | \(0.632436\pi\) | |||||||
\(350\) | −0.519068 | + | 0.0495084i | −0.0277454 | + | 0.00264633i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −12.6821 | − | 24.6325i | −0.675958 | − | 1.31292i | ||||
\(353\) | −13.2376 | − | 22.9282i | −0.704565 | − | 1.22034i | −0.966848 | − | 0.255352i | \(-0.917809\pi\) |
0.262283 | − | 0.964991i | \(-0.415525\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 26.3840 | + | 15.2328i | 1.40032 | + | 0.808473i | ||||
\(356\) | 1.63613 | − | 4.72399i | 0.0867148 | − | 0.250371i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.1615 | + | 7.23431i | −0.537052 | + | 0.382345i | ||||
\(359\) | 23.4619 | 1.23827 | 0.619135 | − | 0.785285i | \(-0.287483\pi\) | ||||
0.619135 | + | 0.785285i | \(0.287483\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.4671 | 0.761424 | ||||||||
\(362\) | −17.7844 | + | 12.6613i | −0.934727 | + | 0.665464i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −15.8841 | − | 5.50138i | −0.832551 | − | 0.288350i | ||||
\(365\) | 22.8343 | + | 13.1834i | 1.19520 | + | 0.690050i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.62599 | + | 16.6727i | 0.502472 | + | 0.870308i | 0.999996 | + | 0.00285720i | \(0.000909476\pi\) |
−0.497524 | + | 0.867450i | \(0.665757\pi\) | |||||||
\(368\) | −8.59928 | + | 3.43832i | −0.448269 | + | 0.179235i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 25.6401 | − | 2.44553i | 1.33296 | − | 0.127137i | ||||
\(371\) | −14.0880 | + | 8.13373i | −0.731414 | + | 0.422282i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.09206 | − | 5.24930i | −0.470769 | − | 0.271799i | 0.245793 | − | 0.969322i | \(-0.420952\pi\) |
−0.716562 | + | 0.697524i | \(0.754285\pi\) | |||||||
\(374\) | −12.1459 | − | 5.54844i | −0.628051 | − | 0.286903i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.26766 | + | 7.88832i | 0.426372 | + | 0.406809i | ||||
\(377\) | −16.9146 | −0.871145 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 35.5203i | 1.82455i | 0.409574 | + | 0.912277i | \(0.365677\pi\) | ||||
−0.409574 | + | 0.912277i | \(0.634323\pi\) | |||||||
\(380\) | 6.35902 | + | 7.34191i | 0.326211 | + | 0.376632i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5.66116 | + | 12.3927i | −0.289650 | + | 0.634064i | ||||
\(383\) | −18.0395 | + | 31.2453i | −0.921774 | + | 1.59656i | −0.125105 | + | 0.992144i | \(0.539927\pi\) |
−0.796669 | + | 0.604416i | \(0.793407\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.1420 | − | 17.5664i | −0.516884 | − | 0.895269i | ||||
\(386\) | −9.83605 | + | 0.938156i | −0.500642 | + | 0.0477509i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −27.4704 | + | 5.28833i | −1.39460 | + | 0.268474i | ||||
\(389\) | 17.5243 | − | 10.1177i | 0.888519 | − | 0.512987i | 0.0150612 | − | 0.999887i | \(-0.495206\pi\) |
0.873458 | + | 0.486900i | \(0.161872\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.23181 | + | 3.86560i | −0.112867 | + | 0.195492i | ||||
\(392\) | 2.47284 | − | 10.1788i | 0.124897 | − | 0.514106i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.97513 | − | 3.54197i | 0.250644 | − | 0.178442i | ||||
\(395\) | 22.6884i | 1.14158i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.99499i | 0.200503i | 0.994962 | + | 0.100251i | \(0.0319647\pi\) | ||||
−0.994962 | + | 0.100251i | \(0.968035\pi\) | |||||||
\(398\) | −4.84450 | − | 6.80471i | −0.242833 | − | 0.341089i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.115947 | − | 0.803959i | 0.00579733 | − | 0.0401979i | ||||
\(401\) | −14.0124 | + | 24.2702i | −0.699747 | + | 1.21200i | 0.268807 | + | 0.963194i | \(0.413371\pi\) |
−0.968554 | + | 0.248803i | \(0.919963\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21.3116 | − | 12.3042i | 1.06161 | − | 0.612918i | ||||
\(404\) | −0.493702 | − | 2.56455i | −0.0245626 | − | 0.127591i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.890832 | + | 9.33988i | 0.0442112 | + | 0.463531i | ||||
\(407\) | 19.5525 | + | 33.8660i | 0.969183 | + | 1.67867i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.22481 | − | 14.2458i | 0.406691 | − | 0.704409i | −0.587826 | − | 0.808987i | \(-0.700016\pi\) |
0.994517 | + | 0.104579i | \(0.0333494\pi\) | |||||||
\(410\) | 13.8635 | + | 6.33307i | 0.684670 | + | 0.312768i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8.44068 | − | 9.74532i | −0.415842 | − | 0.480118i | ||||
\(413\) | − | 6.39976i | − | 0.314912i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.22179 | −0.403592 | ||||||||
\(416\) | 14.1693 | − | 22.0217i | 0.694708 | − | 1.07970i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.12747 | + | 13.4135i | −0.299704 | + | 0.656074i | ||||
\(419\) | 20.5573 | + | 11.8688i | 1.00429 | + | 0.579827i | 0.909515 | − | 0.415672i | \(-0.136453\pi\) |
0.0947752 | + | 0.995499i | \(0.469787\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.9420 | − | 14.9776i | 1.26433 | − | 0.729963i | 0.290424 | − | 0.956898i | \(-0.406204\pi\) |
0.973910 | + | 0.226935i | \(0.0728704\pi\) | |||||||
\(422\) | 2.46190 | + | 25.8117i | 0.119844 | + | 1.25649i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −7.13165 | − | 24.3173i | −0.346343 | − | 1.18095i | ||||
\(425\) | −0.195746 | − | 0.339043i | −0.00949509 | − | 0.0164460i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.11701 | + | 1.79961i | 0.150843 | + | 0.0870891i | ||||
\(428\) | 5.86664 | + | 2.03188i | 0.283575 | + | 0.0982148i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.76999 | + | 6.70005i | 0.230030 | + | 0.323105i | ||||
\(431\) | 11.0367 | 0.531621 | 0.265810 | − | 0.964025i | \(-0.414360\pi\) | ||||
0.265810 | + | 0.964025i | \(0.414360\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.9394 | 1.67908 | 0.839541 | − | 0.543297i | \(-0.182824\pi\) | ||||
0.839541 | + | 0.543297i | \(0.182824\pi\) | |||||||
\(434\) | −7.91656 | − | 11.1198i | −0.380007 | − | 0.533767i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −34.1756 | − | 11.8366i | −1.63672 | − | 0.566869i | ||||
\(437\) | 4.26901 | + | 2.46472i | 0.204215 | + | 0.117903i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.58518 | − | 11.4059i | −0.314293 | − | 0.544372i | 0.664994 | − | 0.746849i | \(-0.268434\pi\) |
−0.979287 | + | 0.202477i | \(0.935101\pi\) | |||||||
\(440\) | 30.3214 | − | 8.89249i | 1.44552 | − | 0.423933i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.19835 | − | 12.5640i | −0.0569996 | − | 0.597609i | ||||
\(443\) | 23.6849 | − | 13.6745i | 1.12530 | − | 0.649694i | 0.182554 | − | 0.983196i | \(-0.441564\pi\) |
0.942749 | + | 0.333502i | \(0.108230\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.93787 | + | 2.85088i | 0.234077 | + | 0.135145i | ||||
\(446\) | −3.09400 | + | 6.77298i | −0.146505 | + | 0.320710i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −12.9062 | − | 6.66420i | −0.609760 | − | 0.314854i | ||||
\(449\) | 13.8225 | 0.652323 | 0.326161 | − | 0.945314i | \(-0.394245\pi\) | ||||
0.326161 | + | 0.945314i | \(0.394245\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.1407i | 1.08965i | ||||||||
\(452\) | 3.71130 | + | 4.28495i | 0.174565 | + | 0.201547i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.28206 | + | 1.04248i | 0.107102 | + | 0.0489259i | ||||
\(455\) | 9.58588 | − | 16.6032i | 0.449393 | − | 0.778371i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.86205 | − | 4.95722i | −0.133881 | − | 0.231889i | 0.791288 | − | 0.611443i | \(-0.209411\pi\) |
−0.925170 | + | 0.379554i | \(0.876077\pi\) | |||||||
\(458\) | 0.512731 | + | 5.37570i | 0.0239584 | + | 0.251190i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.99672 | − | 10.3721i | −0.0930977 | − | 0.483600i | ||||
\(461\) | 19.3717 | − | 11.1843i | 0.902231 | − | 0.520903i | 0.0243074 | − | 0.999705i | \(-0.492262\pi\) |
0.877923 | + | 0.478801i | \(0.158929\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.5733 | − | 32.1699i | 0.863174 | − | 1.49506i | −0.00567564 | − | 0.999984i | \(-0.501807\pi\) |
0.868849 | − | 0.495077i | \(-0.164860\pi\) | |||||||
\(464\) | −14.4661 | − | 2.08629i | −0.671571 | − | 0.0968537i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16.6671 | − | 23.4110i | −0.772086 | − | 1.08449i | ||||
\(467\) | 22.6850i | 1.04974i | 0.851184 | + | 0.524868i | \(0.175885\pi\) | ||||
−0.851184 | + | 0.524868i | \(0.824115\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 16.2004i | − | 0.748063i | ||||||
\(470\) | −10.6170 | + | 7.55862i | −0.489727 | + | 0.348653i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 9.68780 | + | 2.35356i | 0.445917 | + | 0.108331i | ||||
\(473\) | −6.24353 | + | 10.8141i | −0.287078 | + | 0.497233i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.374425 | + | 0.216174i | −0.0171798 | + | 0.00991875i | ||||
\(476\) | −6.87447 | + | 1.32340i | −0.315091 | + | 0.0606582i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 24.4908 | − | 2.33592i | 1.12018 | − | 0.106842i | ||||
\(479\) | −13.1576 | − | 22.7897i | −0.601188 | − | 1.04129i | −0.992641 | − | 0.121091i | \(-0.961361\pi\) |
0.391453 | − | 0.920198i | \(-0.371973\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.4804 | + | 32.0090i | −0.842634 | + | 1.45948i | ||||
\(482\) | −8.05763 | + | 17.6387i | −0.367015 | + | 0.803421i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 17.0056 | + | 19.6341i | 0.772984 | + | 0.892460i | ||||
\(485\) | − | 31.9056i | − | 1.44876i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.0388 | −1.08930 | −0.544652 | − | 0.838662i | \(-0.683338\pi\) | ||||
−0.544652 | + | 0.838662i | \(0.683338\pi\) | |||||||
\(488\) | −3.87050 | + | 4.05663i | −0.175209 | + | 0.183635i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 10.8666 | + | 4.96401i | 0.490901 | + | 0.224251i | ||||
\(491\) | −27.2256 | − | 15.7187i | −1.22867 | − | 0.709374i | −0.261920 | − | 0.965090i | \(-0.584356\pi\) |
−0.966752 | + | 0.255715i | \(0.917689\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.10058 | + | 3.52217i | −0.274756 | + | 0.158631i | ||||
\(494\) | −13.8752 | + | 1.32340i | −0.624274 | + | 0.0595428i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 19.7442 | − | 7.89449i | 0.886542 | − | 0.354473i | ||||
\(497\) | 12.1250 | + | 21.0011i | 0.543881 | + | 0.942029i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.08156 | + | 2.93384i | 0.227482 | + | 0.131337i | 0.609410 | − | 0.792855i | \(-0.291406\pi\) |
−0.381928 | + | 0.924192i | \(0.624740\pi\) | |||||||
\(500\) | −20.6787 | − | 7.16197i | −0.924779 | − | 0.320293i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5.19298 | + | 3.69706i | −0.231774 | + | 0.165008i | ||||
\(503\) | −32.4317 | −1.44606 | −0.723029 | − | 0.690818i | \(-0.757251\pi\) | ||||
−0.723029 | + | 0.690818i | \(0.757251\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.97861 | 0.132546 | ||||||||
\(506\) | 13.0641 | − | 9.30076i | 0.580769 | − | 0.413469i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.87611 | − | 14.0787i | 0.216342 | − | 0.624643i | ||||
\(509\) | 13.6855 | + | 7.90133i | 0.606599 | + | 0.350220i | 0.771633 | − | 0.636068i | \(-0.219440\pi\) |
−0.165034 | + | 0.986288i | \(0.552773\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.4937 | + | 18.1756i | 0.464214 | + | 0.804042i | ||||
\(512\) | 14.8344 | − | 17.0862i | 0.655596 | − | 0.755112i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −11.5796 | + | 1.10445i | −0.510753 | + | 0.0487153i | ||||
\(515\) | 12.7341 | − | 7.35202i | 0.561130 | − | 0.323969i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17.1362 | − | 9.89361i | −0.753650 | − | 0.435120i | ||||
\(518\) | 18.6480 | + | 8.51870i | 0.819346 | + | 0.374290i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 21.6083 | + | 20.6168i | 0.947585 | + | 0.904107i | ||||
\(521\) | −5.50310 | −0.241095 | −0.120548 | − | 0.992708i | \(-0.538465\pi\) | ||||
−0.120548 | + | 0.992708i | \(0.538465\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 38.5894i | − | 1.68740i | −0.536818 | − | 0.843698i | \(-0.680374\pi\) | ||
0.536818 | − | 0.843698i | \(-0.319626\pi\) | |||||||
\(524\) | 5.44911 | − | 4.71962i | 0.238046 | − | 0.206178i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.95429 | + | 6.46714i | −0.128813 | + | 0.281981i | ||||
\(527\) | 5.12430 | − | 8.87555i | 0.223218 | − | 0.386625i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.81970 | + | 15.2762i | 0.383465 | + | 0.664181i | ||||
\(530\) | 28.7717 | − | 2.74423i | 1.24976 | − | 0.119202i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.46151 | + | 7.59189i | 0.0633647 | + | 0.329150i | ||||
\(533\) | −18.9415 | + | 10.9359i | −0.820449 | + | 0.473686i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.54046 | + | 6.13225i | −0.153067 | + | 0.265120i | ||||
\(536\) | 24.5237 | + | 5.95781i | 1.05926 | + | 0.257338i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 26.6794 | − | 18.9940i | 1.15023 | − | 0.818888i | ||||
\(539\) | 18.1382i | 0.781268i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 22.5666i | − | 0.970214i | −0.874455 | − | 0.485107i | \(-0.838781\pi\) | ||
0.874455 | − | 0.485107i | \(-0.161219\pi\) | |||||||
\(542\) | −17.1723 | − | 24.1206i | −0.737612 | − | 1.03607i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.524803 | − | 10.8931i | 0.0225008 | − | 0.467037i | ||||
\(545\) | 20.6246 | − | 35.7229i | 0.883463 | − | 1.53020i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.2679 | + | 6.50552i | −0.481780 | + | 0.278156i | −0.721158 | − | 0.692770i | \(-0.756390\pi\) |
0.239378 | + | 0.970927i | \(0.423057\pi\) | |||||||
\(548\) | 23.1017 | − | 4.44731i | 0.986856 | − | 0.189980i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.133548 | + | 1.40018i | 0.00569452 | + | 0.0597039i | ||||
\(551\) | 3.88974 | + | 6.73723i | 0.165709 | + | 0.287016i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.02976 | + | 15.6400i | −0.383985 | + | 0.665081i | ||||
\(554\) | −28.6208 | − | 13.0744i | −1.21598 | − | 0.555479i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 19.2720 | − | 16.6920i | 0.817316 | − | 0.707899i | ||||
\(557\) | − | 5.73693i | − | 0.243081i | −0.992586 | − | 0.121541i | \(-0.961217\pi\) | ||
0.992586 | − | 0.121541i | \(-0.0387835\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.8024 | −0.499186 | ||||||||
\(560\) | 10.2461 | − | 13.0174i | 0.432979 | − | 0.550087i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10.9067 | − | 23.8754i | 0.460069 | − | 1.00712i | ||||
\(563\) | −13.2510 | − | 7.65045i | −0.558462 | − | 0.322428i | 0.194066 | − | 0.980988i | \(-0.437832\pi\) |
−0.752528 | + | 0.658560i | \(0.771166\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.59908 | + | 3.23263i | −0.235555 | + | 0.135998i | ||||
\(566\) | −0.272830 | − | 2.86047i | −0.0114679 | − | 0.120235i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −36.2500 | + | 10.6312i | −1.52102 | + | 0.446075i | ||||
\(569\) | −6.63095 | − | 11.4851i | −0.277984 | − | 0.481482i | 0.692900 | − | 0.721034i | \(-0.256333\pi\) |
−0.970884 | + | 0.239552i | \(0.922999\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.4262 | + | 13.5251i | 0.980357 | + | 0.566009i | 0.902378 | − | 0.430946i | \(-0.141820\pi\) |
0.0779788 | + | 0.996955i | \(0.475153\pi\) | |||||||
\(572\) | −14.8399 | + | 42.8471i | −0.620488 | + | 1.79153i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.03616 | + | 9.88317i | 0.293684 | + | 0.412515i | ||||
\(575\) | 0.470166 | 0.0196073 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.78434 | −0.199174 | −0.0995872 | − | 0.995029i | \(-0.531752\pi\) | ||||
−0.0995872 | + | 0.995029i | \(0.531752\pi\) | |||||||
\(578\) | 10.8949 | + | 15.3033i | 0.453170 | + | 0.636534i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.45544 | − | 15.7514i | 0.226525 | − | 0.654043i | ||||
\(581\) | −5.66760 | − | 3.27219i | −0.235132 | − | 0.135753i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21.9406 | + | 38.0023i | 0.908689 | + | 1.57390i | ||||
\(584\) | −31.3729 | + | 9.20087i | −1.29822 | + | 0.380735i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.58148 | + | 48.0343i | 0.189259 | + | 1.98428i | ||||
\(587\) | −37.0796 | + | 21.4079i | −1.53044 | + | 0.883598i | −0.531095 | + | 0.847312i | \(0.678219\pi\) |
−0.999341 | + | 0.0362861i | \(0.988447\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.80179 | − | 5.65906i | −0.403876 | − | 0.233178i | ||||
\(590\) | −4.72457 | + | 10.3424i | −0.194507 | + | 0.425790i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −19.7533 | + | 25.0961i | −0.811857 | + | 1.03144i | ||||
\(593\) | 0.825572 | 0.0339022 | 0.0169511 | − | 0.999856i | \(-0.494604\pi\) | ||||
0.0169511 | + | 0.999856i | \(0.494604\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 7.98438i | − | 0.327328i | ||||||
\(596\) | 11.5177 | − | 9.97575i | 0.471782 | − | 0.408623i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 13.7869 | + | 6.29807i | 0.563788 | + | 0.257547i | ||||
\(599\) | 0.961228 | − | 1.66490i | 0.0392747 | − | 0.0680258i | −0.845720 | − | 0.533627i | \(-0.820829\pi\) |
0.884995 | + | 0.465601i | \(0.154162\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.5937 | − | 37.4014i | −0.880825 | − | 1.52563i | −0.850425 | − | 0.526096i | \(-0.823655\pi\) |
−0.0303994 | − | 0.999538i | \(-0.509678\pi\) | |||||||
\(602\) | 0.621589 | + | 6.51702i | 0.0253341 | + | 0.265614i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.91581 | + | 1.71638i | −0.362779 | + | 0.0698386i | ||||
\(605\) | −25.6556 | + | 14.8123i | −1.04305 | + | 0.602205i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.5078 | − | 35.5206i | 0.832386 | − | 1.44174i | −0.0637546 | − | 0.997966i | \(-0.520307\pi\) |
0.896141 | − | 0.443770i | \(-0.146359\pi\) | |||||||
\(608\) | −12.0299 | − | 0.579571i | −0.487876 | − | 0.0235047i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.70873 | − | 5.20937i | −0.150162 | − | 0.210921i | ||||
\(611\) | − | 18.7022i | − | 0.756611i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.05878i | 0.204322i | 0.994768 | + | 0.102161i | \(0.0325757\pi\) | ||||
−0.994768 | + | 0.102161i | \(0.967424\pi\) | |||||||
\(614\) | 5.50216 | − | 3.91717i | 0.222049 | − | 0.158084i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 24.4409 | + | 5.93768i | 0.984750 | + | 0.239236i | ||||
\(617\) | 16.0739 | − | 27.8408i | 0.647112 | − | 1.12083i | −0.336698 | − | 0.941613i | \(-0.609310\pi\) |
0.983809 | − | 0.179217i | \(-0.0573566\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.3562 | + | 15.7941i | −1.09954 | + | 0.634820i | −0.936100 | − | 0.351734i | \(-0.885592\pi\) |
−0.163440 | + | 0.986553i | \(0.552259\pi\) | |||||||
\(620\) | 4.58454 | + | 23.8146i | 0.184120 | + | 0.956416i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −31.4707 | + | 3.00165i | −1.26186 | + | 0.120355i | ||||
\(623\) | 2.26924 | + | 3.93044i | 0.0909153 | + | 0.157470i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.9871 | − | 22.4942i | 0.519482 | − | 0.899770i | ||||
\(626\) | 1.43863 | − | 3.14927i | 0.0574993 | − | 0.125870i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −19.9189 | + | 17.2522i | −0.794849 | + | 0.688440i | ||||
\(629\) | 15.3929i | 0.613756i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.4885 | −0.616586 | −0.308293 | − | 0.951292i | \(-0.599758\pi\) | ||||
−0.308293 | + | 0.951292i | \(0.599758\pi\) | |||||||
\(632\) | −20.3547 | − | 19.4207i | −0.809665 | − | 0.772516i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −21.2236 | − | 9.69525i | −0.842896 | − | 0.385048i | ||||
\(635\) | 14.7162 | + | 8.49638i | 0.583993 | + | 0.337168i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.8468 | + | 8.57182i | −0.588253 | + | 0.339628i | ||||
\(638\) | 25.1942 | − | 2.40301i | 0.997449 | − | 0.0951361i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 15.9374 | + | 20.2976i | 0.629980 | + | 0.802334i | ||||
\(641\) | 15.2248 | + | 26.3701i | 0.601344 | + | 1.04156i | 0.992618 | + | 0.121284i | \(0.0387011\pi\) |
−0.391274 | + | 0.920274i | \(0.627966\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.5911 | − | 8.42419i | −0.575418 | − | 0.332218i | 0.183893 | − | 0.982946i | \(-0.441130\pi\) |
−0.759310 | + | 0.650729i | \(0.774463\pi\) | |||||||
\(644\) | 2.75155 | − | 7.94454i | 0.108426 | − | 0.313059i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.72878 | + | 3.36658i | −0.186051 | + | 0.132456i | ||||
\(647\) | −18.6734 | −0.734126 | −0.367063 | − | 0.930196i | \(-0.619637\pi\) | ||||
−0.367063 | + | 0.930196i | \(0.619637\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.2633 | −0.677644 | ||||||||
\(650\) | −1.08299 | + | 0.771017i | −0.0424783 | + | 0.0302418i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 38.9143 | + | 13.4778i | 1.52400 | + | 0.527831i | ||||
\(653\) | −31.4276 | − | 18.1448i | −1.22986 | − | 0.710059i | −0.262858 | − | 0.964834i | \(-0.584665\pi\) |
−0.967000 | + | 0.254775i | \(0.917999\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.11089 | + | 7.12028i | 0.160626 | + | 0.278212i | ||||
\(656\) | −17.5485 | + | 7.01655i | −0.685153 | + | 0.273950i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −10.3270 | + | 0.984980i | −0.402588 | + | 0.0383985i | ||||
\(659\) | −19.3088 | + | 11.1480i | −0.752166 | + | 0.434263i | −0.826476 | − | 0.562972i | \(-0.809658\pi\) |
0.0743103 | + | 0.997235i | \(0.476324\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.19793 | + | 3.00103i | 0.202176 | + | 0.116726i | 0.597670 | − | 0.801742i | \(-0.296093\pi\) |
−0.395494 | + | 0.918469i | \(0.629427\pi\) | |||||||
\(662\) | 0.488978 | + | 0.223373i | 0.0190047 | + | 0.00868162i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7.03765 | − | 7.37609i | 0.273114 | − | 0.286248i | ||||
\(665\) | −8.81762 | −0.341933 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 8.45996i | − | 0.327571i | ||||||
\(668\) | −6.64943 | − | 7.67720i | −0.257274 | − | 0.297040i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −11.9598 | + | 26.1807i | −0.462046 | + | 1.01145i | ||||
\(671\) | 4.85442 | − | 8.40810i | 0.187403 | − | 0.324591i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.70444 | − | 6.41629i | −0.142796 | − | 0.247330i | 0.785753 | − | 0.618541i | \(-0.212276\pi\) |
−0.928548 | + | 0.371211i | \(0.878943\pi\) | |||||||
\(674\) | 7.09183 | − | 0.676414i | 0.273167 | − | 0.0260545i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −16.5539 | + | 3.18679i | −0.636689 | + | 0.122569i | ||||
\(677\) | −8.57613 | + | 4.95143i | −0.329607 | + | 0.190299i | −0.655667 | − | 0.755050i | \(-0.727612\pi\) |
0.326059 | + | 0.945349i | \(0.394279\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.6981 | − | 21.9938i | 0.487309 | − | 0.844043i | ||||
\(680\) | 12.0865 | + | 2.93632i | 0.463498 | + | 0.112603i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −29.9955 | + | 21.3548i | −1.14859 | + | 0.817719i | ||||
\(683\) | − | 39.0736i | − | 1.49511i | −0.664200 | − | 0.747555i | \(-0.731228\pi\) | ||
0.664200 | − | 0.747555i | \(-0.268772\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 26.8316i | 1.02518i | ||||||||
\(686\) | 15.9395 | + | 22.3890i | 0.608572 | + | 0.854815i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −10.0939 | − | 1.45574i | −0.384826 | − | 0.0554994i | ||||
\(689\) | −20.7376 | + | 35.9185i | −0.790039 | + | 1.36839i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.07502 | − | 1.19801i | 0.0789375 | − | 0.0455746i | −0.460012 | − | 0.887913i | \(-0.652155\pi\) |
0.538949 | + | 0.842338i | \(0.318821\pi\) | |||||||
\(692\) | −4.81962 | − | 25.0357i | −0.183215 | − | 0.951715i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.30294 | − | 13.6606i | −0.0494590 | − | 0.518551i | ||||
\(695\) | 14.5391 | + | 25.1825i | 0.551500 | + | 0.955227i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.55443 | + | 7.88850i | −0.172511 | + | 0.298798i | ||||
\(698\) | 38.8032 | + | 17.7259i | 1.46872 | + | 0.670934i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.482777 | + | 0.557398i | 0.0182472 | + | 0.0210677i | ||||
\(701\) | 30.9184i | 1.16777i | 0.811836 | + | 0.583885i | \(0.198468\pi\) | ||||
−0.811836 | + | 0.583885i | \(0.801532\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.9993 | 0.641141 | ||||||||
\(704\) | −17.9766 | + | 34.8143i | −0.677519 | + | 1.31211i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −15.5575 | + | 34.0563i | −0.585513 | + | 1.28173i | ||||
\(707\) | 2.05327 | + | 1.18546i | 0.0772212 | + | 0.0445837i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.46959 | + | 2.58052i | −0.167859 | + | 0.0969133i | −0.581576 | − | 0.813492i | \(-0.697564\pi\) |
0.413717 | + | 0.910406i | \(0.364230\pi\) | |||||||
\(710\) | −4.09084 | − | 42.8902i | −0.153526 | − | 1.60964i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.78434 | + | 1.98967i | −0.254254 | + | 0.0745661i | ||||
\(713\) | 6.15406 | + | 10.6591i | 0.230471 | + | 0.399188i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −44.7870 | − | 25.8578i | −1.67494 | − | 0.967027i | ||||
\(716\) | 16.6689 | + | 5.77320i | 0.622947 | + | 0.215755i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −19.2434 | − | 27.0298i | −0.718158 | − | 1.00874i | ||||
\(719\) | −14.7871 | −0.551465 | −0.275733 | − | 0.961234i | \(-0.588920\pi\) | ||||
−0.275733 | + | 0.961234i | \(0.588920\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.7041 | 0.435884 | ||||||||
\(722\) | −11.8659 | − | 16.6671i | −0.441602 | − | 0.620286i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 29.1735 | + | 10.1041i | 1.08423 | + | 0.375517i | ||||
\(725\) | 0.642593 | + | 0.371001i | 0.0238653 | + | 0.0137786i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.06681 | − | 1.84777i | −0.0395658 | − | 0.0685299i | 0.845564 | − | 0.533873i | \(-0.179264\pi\) |
−0.885130 | + | 0.465344i | \(0.845931\pi\) | |||||||
\(728\) | 6.69012 | + | 22.8118i | 0.247952 | + | 0.845463i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.54046 | − | 37.1198i | −0.131038 | − | 1.37386i | ||||
\(731\) | −4.25675 | + | 2.45764i | −0.157442 | + | 0.0908990i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.2298 | + | 12.8344i | 0.821076 | + | 0.474048i | 0.850787 | − | 0.525510i | \(-0.176125\pi\) |
−0.0297113 | + | 0.999559i | \(0.509459\pi\) | |||||||
\(734\) | 11.3129 | − | 24.7648i | 0.417568 | − | 0.914085i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 11.0143 | + | 7.08689i | 0.405993 | + | 0.261226i | ||||
\(737\) | −43.7003 | −1.60972 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.46282i | 0.200953i | 0.994939 | + | 0.100476i | \(0.0320367\pi\) | ||||
−0.994939 | + | 0.100476i | \(0.967963\pi\) | |||||||
\(740\) | −23.8474 | − | 27.5334i | −0.876649 | − | 1.01215i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 20.9257 | + | 9.55916i | 0.768205 | + | 0.350928i | ||||
\(743\) | 16.8170 | − | 29.1279i | 0.616955 | − | 1.06860i | −0.373083 | − | 0.927798i | \(-0.621699\pi\) |
0.990038 | − | 0.140800i | \(-0.0449674\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.68910 | + | 15.0500i | 0.318344 | + | 0.551388i | ||||
\(746\) | 1.40972 | + | 14.7802i | 0.0516137 | + | 0.541141i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.56987 | + | 18.5438i | 0.130527 | + | 0.678029i | ||||
\(749\) | −4.88115 | + | 2.81813i | −0.178353 | + | 0.102972i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.6727 | + | 21.9498i | −0.462435 | + | 0.800961i | −0.999082 | − | 0.0428462i | \(-0.986357\pi\) |
0.536647 | + | 0.843807i | \(0.319691\pi\) | |||||||
\(752\) | 2.30679 | − | 15.9949i | 0.0841198 | − | 0.583276i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 13.8733 | + | 19.4868i | 0.505237 | + | 0.709669i | ||||
\(755\) | − | 10.3553i | − | 0.376868i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 3.95103i | − | 0.143603i | −0.997419 | − | 0.0718014i | \(-0.977125\pi\) | ||
0.997419 | − | 0.0718014i | \(-0.0228748\pi\) | |||||||
\(758\) | 40.9219 | − | 29.1337i | 1.48635 | − | 1.05818i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.24275 | − | 13.3479i | 0.117627 | − | 0.484179i | ||||
\(761\) | 23.3979 | − | 40.5264i | 0.848175 | − | 1.46908i | −0.0346607 | − | 0.999399i | \(-0.511035\pi\) |
0.882835 | − | 0.469682i | \(-0.155632\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.4347 | − | 16.4168i | 1.02941 | − | 0.594328i | ||||
\(764\) | 18.9205 | − | 3.64239i | 0.684521 | − | 0.131777i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 50.7928 | − | 4.84459i | 1.83522 | − | 0.175042i | ||||
\(767\) | −8.15835 | − | 14.1307i | −0.294581 | − | 0.510229i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.60083 | − | 4.50478i | 0.0937885 | − | 0.162446i | −0.815314 | − | 0.579019i | \(-0.803436\pi\) |
0.909102 | + | 0.416573i | \(0.136769\pi\) | |||||||
\(770\) | −11.9194 | + | 26.0923i | −0.429544 | + | 0.940302i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9.14835 | + | 10.5624i | 0.329256 | + | 0.380148i | ||||
\(773\) | 38.8477i | 1.39725i | 0.715486 | + | 0.698627i | \(0.246205\pi\) | ||||
−0.715486 | + | 0.698627i | \(0.753795\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.07952 | −0.0387773 | ||||||||
\(776\) | 28.6238 | + | 27.3104i | 1.02753 | + | 0.980387i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −26.0298 | − | 11.8908i | −0.933212 | − | 0.426306i | ||||
\(779\) | 8.71173 | + | 5.02972i | 0.312130 | + | 0.180209i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 56.6503 | − | 32.7071i | 2.02711 | − | 1.17035i | ||||
\(782\) | 6.28399 | − | 0.599362i | 0.224715 | − | 0.0214332i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −13.7549 | + | 5.49974i | −0.491247 | + | 0.196419i | ||||
\(785\) | −15.0271 | − | 26.0277i | −0.536340 | − | 0.928968i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −40.8579 | − | 23.5893i | −1.45643 | − | 0.840869i | −0.457595 | − | 0.889161i | \(-0.651289\pi\) |
−0.998833 | + | 0.0482918i | \(0.984622\pi\) | |||||||
\(788\) | −8.16121 | − | 2.82660i | −0.290731 | − | 0.100693i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 26.1387 | − | 18.6090i | 0.929974 | − | 0.662080i | ||||
\(791\) | −5.14621 | −0.182978 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.17648 | 0.325866 | ||||||||
\(794\) | 4.60252 | − | 3.27669i | 0.163337 | − | 0.116285i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.86606 | + | 11.1624i | −0.137029 | + | 0.395642i | ||||
\(797\) | −6.35645 | − | 3.66990i | −0.225157 | − | 0.129995i | 0.383179 | − | 0.923674i | \(-0.374829\pi\) |
−0.608336 | + | 0.793680i | \(0.708163\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.89442 | − | 6.74533i | −0.137775 | − | 0.238633i | ||||
\(800\) | −1.02132 | + | 0.525828i | −0.0361091 | + | 0.0185908i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 39.4541 | − | 3.76310i | 1.39317 | − | 0.132880i | ||||
\(803\) | 49.0286 | − | 28.3067i | 1.73018 | − | 0.998920i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.30423 | + | 4.79445i | 0.292686 | + | 0.168982i | ||||
\(806\) | −31.6552 | − | 14.4606i | −1.11501 | − | 0.509351i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.54962 | + | 2.67223i | −0.0896953 | + | 0.0940087i | ||||
\(809\) | −2.25520 | −0.0792887 | −0.0396443 | − | 0.999214i | \(-0.512622\pi\) | ||||
−0.0396443 | + | 0.999214i | \(0.512622\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 15.9986i | − | 0.561785i | −0.959739 | − | 0.280893i | \(-0.909369\pi\) | ||
0.959739 | − | 0.280893i | \(-0.0906305\pi\) | |||||||
\(812\) | 10.0296 | − | 8.68687i | 0.351969 | − | 0.304849i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 22.9791 | − | 50.3028i | 0.805417 | − | 1.76311i | ||||
\(815\) | −23.4844 | + | 40.6761i | −0.822622 | + | 1.42482i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.71411 | + | 4.70098i | 0.0949548 | + | 0.164467i | ||||
\(818\) | −23.1582 | + | 2.20881i | −0.809707 | + | 0.0772293i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.07470 | − | 21.1662i | −0.142295 | − | 0.739154i | ||||
\(821\) | 25.2413 | − | 14.5731i | 0.880928 | − | 0.508604i | 0.00996351 | − | 0.999950i | \(-0.496828\pi\) |
0.870964 | + | 0.491347i | \(0.163495\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.15695 | + | 7.20005i | −0.144902 | + | 0.250978i | −0.929336 | − | 0.369234i | \(-0.879620\pi\) |
0.784434 | + | 0.620212i | \(0.212953\pi\) | |||||||
\(824\) | −4.30428 | + | 17.7174i | −0.149947 | + | 0.617215i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.37300 | + | 5.24908i | −0.256539 | + | 0.182639i | ||||
\(827\) | − | 43.5035i | − | 1.51277i | −0.654129 | − | 0.756383i | \(-0.726965\pi\) | ||
0.654129 | − | 0.756383i | \(-0.273035\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.9248i | 0.553092i | 0.961001 | + | 0.276546i | \(0.0891897\pi\) | ||||
−0.961001 | + | 0.276546i | \(0.910810\pi\) | |||||||
\(830\) | 6.74351 | + | 9.47210i | 0.234071 | + | 0.328781i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −36.9923 | + | 1.73811i | −1.28248 | + | 0.0602582i | ||||
\(833\) | −3.56987 | + | 6.18320i | −0.123689 | + | 0.214235i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.0317 | − | 5.79180i | 0.347161 | − | 0.200433i | ||||
\(836\) | 20.4790 | − | 3.94242i | 0.708282 | − | 0.136351i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3.18741 | − | 33.4183i | −0.110107 | − | 1.15442i | ||||
\(839\) | 21.0582 | + | 36.4739i | 0.727009 | + | 1.25922i | 0.958142 | + | 0.286295i | \(0.0924237\pi\) |
−0.231132 | + | 0.972922i | \(0.574243\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.82437 | + | 13.5522i | −0.269806 | + | 0.467318i | ||||
\(842\) | −38.5329 | − | 17.6024i | −1.32793 | − | 0.606619i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 27.7177 | − | 24.0070i | 0.954083 | − | 0.826357i | ||||
\(845\) | − | 19.2266i | − | 0.661415i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23.5806 | −0.810238 | ||||||||
\(848\) | −22.1660 | + | 28.1613i | −0.761182 | + | 0.967061i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.230051 | + | 0.503597i | −0.00789068 | + | 0.0172732i | ||||
\(851\) | −16.0095 | − | 9.24311i | −0.548800 | − | 0.316850i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34.2013 | + | 19.7461i | −1.17103 | + | 0.676095i | −0.953923 | − | 0.300053i | \(-0.902996\pi\) |
−0.217108 | + | 0.976148i | \(0.569662\pi\) | |||||||
\(854\) | −0.483293 | − | 5.06706i | −0.0165379 | − | 0.173391i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.47094 | − | 8.42535i | −0.0844549 | − | 0.287972i | ||||
\(857\) | 12.6170 | + | 21.8532i | 0.430988 | + | 0.746493i | 0.996959 | − | 0.0779326i | \(-0.0248319\pi\) |
−0.565971 | + | 0.824425i | \(0.691499\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 47.5539 | + | 27.4552i | 1.62252 | + | 0.936761i | 0.986244 | + | 0.165297i | \(0.0528584\pi\) |
0.636274 | + | 0.771463i | \(0.280475\pi\) | |||||||
\(860\) | 3.80660 | − | 10.9908i | 0.129804 | − | 0.374782i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9.05233 | − | 12.7151i | −0.308324 | − | 0.433079i | ||||
\(863\) | 54.3877 | 1.85138 | 0.925689 | − | 0.378285i | \(-0.123486\pi\) | ||||
0.925689 | + | 0.378285i | \(0.123486\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 29.0778 | 0.988675 | ||||||||
\(866\) | −28.6573 | − | 40.2528i | −0.973815 | − | 1.36784i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.31766 | + | 18.2409i | −0.214435 | + | 0.619137i | ||||
\(869\) | 42.1888 | + | 24.3577i | 1.43116 | + | 0.826278i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.6521 | − | 35.7704i | −0.699768 | − | 1.21203i | ||||
\(872\) | 14.3942 | + | 49.0812i | 0.487451 | + | 1.66210i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.661911 | − | 6.93977i | −0.0223895 | − | 0.234741i | ||||
\(875\) | 17.2050 | − | 9.93334i | 0.581637 | − | 0.335808i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.90001 | + | 3.40637i | 0.199229 | + | 0.115025i | 0.596296 | − | 0.802765i | \(-0.296639\pi\) |
−0.397067 | + | 0.917790i | \(0.629972\pi\) | |||||||
\(878\) | −7.73922 | + | 16.9417i | −0.261186 | + | 0.571754i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −35.1144 | − | 27.6389i | −1.18371 | − | 0.931706i | ||||
\(881\) | 43.2881 | 1.45841 | 0.729207 | − | 0.684293i | \(-0.239889\pi\) | ||||
0.729207 | + | 0.684293i | \(0.239889\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 31.1510i | − | 1.04832i | −0.851621 | − | 0.524158i | \(-0.824380\pi\) | ||
0.851621 | − | 0.524158i | \(-0.175620\pi\) | |||||||
\(884\) | −13.4918 | + | 11.6856i | −0.453778 | + | 0.393029i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −35.1803 | − | 16.0709i | −1.18191 | − | 0.539913i | ||||
\(887\) | 24.8886 | − | 43.1083i | 0.835677 | − | 1.44743i | −0.0578015 | − | 0.998328i | \(-0.518409\pi\) |
0.893478 | − | 0.449107i | \(-0.148258\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.76295 | + | 11.7138i | 0.226822 | + | 0.392867i | ||||
\(890\) | −0.765617 | − | 8.02708i | −0.0256636 | − | 0.269068i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10.3407 | − | 1.99068i | 0.346231 | − | 0.0666529i | ||||
\(893\) | −7.44926 | + | 4.30083i | −0.249280 | + | 0.143922i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.0595 | + | 17.4236i | −0.336253 | + | 0.582407i | ||||
\(896\) | 2.90800 | + | 20.3348i | 0.0971496 | + | 0.679339i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11.3372 | − | 15.9245i | −0.378327 | − | 0.531407i | ||||
\(899\) | 19.4243i | 0.647838i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.2730i | 0.575447i | ||||||||
\(902\) | 26.6597 | − | 18.9800i | 0.887672 | − | 0.631964i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.89256 | − | 7.79021i | 0.0629456 | − | 0.259098i | ||||
\(905\) | −17.6059 | + | 30.4944i | −0.585241 | + | 1.01367i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.6712 | + | 9.62515i | −0.553559 | + | 0.319598i | −0.750556 | − | 0.660806i | \(-0.770214\pi\) |
0.196997 | + | 0.980404i | \(0.436881\pi\) | |||||||
\(908\) | −0.670731 | − | 3.48413i | −0.0222590 | − | 0.115625i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −26.9905 | + | 2.57433i | −0.894725 | + | 0.0853383i | ||||
\(911\) | −11.1396 | − | 19.2944i | −0.369072 | − | 0.639252i | 0.620348 | − | 0.784326i | \(-0.286991\pi\) |
−0.989421 | + | 0.145074i | \(0.953658\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.82669 | + | 15.2883i | −0.292121 | + | 0.505968i | ||||
\(914\) | −3.36363 | + | 7.36321i | −0.111259 | + | 0.243553i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.77266 | − | 4.99986i | 0.190734 | − | 0.165200i | ||||
\(917\) | 6.54438i | 0.216114i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.0122 | 0.924039 | 0.462019 | − | 0.886870i | \(-0.347125\pi\) | ||||
0.462019 | + | 0.886870i | \(0.347125\pi\) | |||||||
\(920\) | −10.3117 | + | 10.8075i | −0.339965 | + | 0.356314i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −28.7738 | − | 13.1443i | −0.947613 | − | 0.432884i | ||||
\(923\) | 53.5440 | + | 30.9136i | 1.76242 | + | 1.01753i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.40416 | − | 0.810691i | 0.0461684 | − | 0.0266554i | ||||
\(926\) | −52.2958 | + | 4.98794i | −1.71855 | + | 0.163914i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9.46151 | + | 18.3772i | 0.310589 | + | 0.603260i | ||||
\(929\) | 3.94220 | + | 6.82809i | 0.129339 | + | 0.224022i | 0.923421 | − | 0.383789i | \(-0.125381\pi\) |
−0.794081 | + | 0.607811i | \(0.792048\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.82847 | + | 3.94242i | 0.223794 | + | 0.129208i | ||||
\(932\) | −13.3008 | + | 38.4033i | −0.435683 | + | 1.25794i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 26.1348 | − | 18.6062i | 0.855156 | − | 0.608814i | ||||
\(935\) | −21.5378 | −0.704361 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.98600 | −0.293560 | −0.146780 | − | 0.989169i | \(-0.546891\pi\) | ||||
−0.146780 | + | 0.989169i | \(0.546891\pi\) | |||||||
\(938\) | −18.6640 | + | 13.2875i | −0.609401 | + | 0.433853i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 17.4162 | + | 6.03201i | 0.568053 | + | 0.196742i | ||||
\(941\) | 21.0227 | + | 12.1375i | 0.685322 | + | 0.395671i | 0.801857 | − | 0.597516i | \(-0.203845\pi\) |
−0.116535 | + | 0.993187i | \(0.537179\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.46967 | − | 9.47375i | −0.178117 | − | 0.308508i | ||||
\(944\) | −5.23445 | − | 13.0914i | −0.170367 | − | 0.426090i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 17.5796 | − | 1.67673i | 0.571561 | − | 0.0545151i | ||||
\(947\) | 1.71382 | − | 0.989473i | 0.0556916 | − | 0.0321536i | −0.471896 | − | 0.881654i | \(-0.656430\pi\) |
0.527587 | + | 0.849501i | \(0.323097\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 46.3402 | + | 26.7545i | 1.50427 | + | 0.868488i | ||||
\(950\) | 0.556151 | + | 0.254059i | 0.0180439 | + | 0.00824275i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.16310 | + | 6.83444i | 0.232157 | + | 0.221505i | ||||
\(953\) | −28.9674 | −0.938347 | −0.469173 | − | 0.883106i | \(-0.655448\pi\) | ||||
−0.469173 | + | 0.883106i | \(0.655448\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.9753i | 0.711104i | ||||||||
\(956\) | −22.7785 | − | 26.2993i | −0.736710 | − | 0.850580i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −15.4635 | + | 33.8507i | −0.499604 | + | 1.09367i | ||||
\(959\) | −10.6787 | + | 18.4960i | −0.344833 | + | 0.597268i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.37008 | + | 2.37304i | 0.0441961 | + | 0.0765498i | ||||
\(962\) | 52.0343 | − | 4.96300i | 1.67765 | − | 0.160014i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 26.9300 | − | 5.18428i | 0.867355 | − | 0.166975i | ||||
\(965\) | −13.8017 | + | 7.96842i | −0.444293 | + | 0.256512i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.00531192 | − | 0.00920052i | 0.000170820 | − | 0.000295869i | −0.865940 | − | 0.500148i | \(-0.833279\pi\) |
0.866111 | + | 0.499852i | \(0.166612\pi\) | |||||||
\(968\) | 8.67193 | − | 35.6956i | 0.278726 | − | 1.14730i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −36.7576 | + | 26.1690i | −1.18021 | + | 0.840235i | ||||
\(971\) | 17.0984i | 0.548715i | 0.961628 | + | 0.274357i | \(0.0884651\pi\) | ||||
−0.961628 | + | 0.274357i | \(0.911535\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 23.1457i | 0.742017i | ||||||||
\(974\) | 19.7166 | + | 27.6945i | 0.631762 | + | 0.887389i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.84812 | + | 1.13185i | 0.251212 | + | 0.0362297i | ||||
\(977\) | 5.50612 | − | 9.53688i | 0.176156 | − | 0.305112i | −0.764404 | − | 0.644737i | \(-0.776967\pi\) |
0.940561 | + | 0.339625i | \(0.110300\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.6023 | − | 6.12126i | 0.338852 | − | 0.195636i | ||||
\(980\) | −3.19385 | − | 16.5905i | −0.102024 | − | 0.529966i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.22133 | + | 44.2583i | 0.134708 | + | 1.41234i | ||||
\(983\) | −22.7443 | − | 39.3943i | −0.725432 | − | 1.25648i | −0.958796 | − | 0.284095i | \(-0.908307\pi\) |
0.233364 | − | 0.972389i | \(-0.425027\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.92521 | − | 8.53071i | 0.156930 | − | 0.271811i | ||||
\(986\) | 9.06150 | + | 4.13943i | 0.288577 | + | 0.131826i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 12.9051 | + | 14.8998i | 0.410565 | + | 0.474024i | ||||
\(989\) | − | 5.90304i | − | 0.187706i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.93737 | 0.125075 | 0.0625374 | − | 0.998043i | \(-0.480081\pi\) | ||||
0.0625374 | + | 0.998043i | \(0.480081\pi\) | |||||||
\(992\) | −25.2892 | − | 16.2717i | −0.802934 | − | 0.516628i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 14.2499 | − | 31.1940i | 0.451979 | − | 0.989413i | ||||
\(995\) | −11.6678 | − | 6.73642i | −0.369895 | − | 0.213559i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.16558 | − | 1.25030i | 0.0685847 | − | 0.0395974i | −0.465316 | − | 0.885145i | \(-0.654059\pi\) |
0.533900 | + | 0.845547i | \(0.320726\pi\) | |||||||
\(998\) | −0.787897 | − | 8.26066i | −0.0249404 | − | 0.261487i | ||||
\(999\) | 0 | 0 |
(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 | 216.2.n.b.37.3 | 16 | ||
3.2 | odd | 2 | 72.2.n.b.13.6 | yes | 16 | ||
4.3 | odd | 2 | 864.2.r.b.145.2 | 16 | |||
8.3 | odd | 2 | 864.2.r.b.145.7 | 16 | |||
8.5 | even | 2 | inner | 216.2.n.b.37.4 | 16 | ||
9.2 | odd | 6 | 72.2.n.b.61.5 | yes | 16 | ||
9.4 | even | 3 | 648.2.d.k.325.7 | 8 | |||
9.5 | odd | 6 | 648.2.d.j.325.2 | 8 | |||
9.7 | even | 3 | inner | 216.2.n.b.181.4 | 16 | ||
12.11 | even | 2 | 288.2.r.b.49.8 | 16 | |||
24.5 | odd | 2 | 72.2.n.b.13.5 | ✓ | 16 | ||
24.11 | even | 2 | 288.2.r.b.49.1 | 16 | |||
36.7 | odd | 6 | 864.2.r.b.721.7 | 16 | |||
36.11 | even | 6 | 288.2.r.b.241.1 | 16 | |||
36.23 | even | 6 | 2592.2.d.j.1297.2 | 8 | |||
36.31 | odd | 6 | 2592.2.d.k.1297.7 | 8 | |||
72.5 | odd | 6 | 648.2.d.j.325.1 | 8 | |||
72.11 | even | 6 | 288.2.r.b.241.8 | 16 | |||
72.13 | even | 6 | 648.2.d.k.325.8 | 8 | |||
72.29 | odd | 6 | 72.2.n.b.61.6 | yes | 16 | ||
72.43 | odd | 6 | 864.2.r.b.721.2 | 16 | |||
72.59 | even | 6 | 2592.2.d.j.1297.7 | 8 | |||
72.61 | even | 6 | inner | 216.2.n.b.181.3 | 16 | ||
72.67 | odd | 6 | 2592.2.d.k.1297.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.2.n.b.13.5 | ✓ | 16 | 24.5 | odd | 2 | ||
72.2.n.b.13.6 | yes | 16 | 3.2 | odd | 2 | ||
72.2.n.b.61.5 | yes | 16 | 9.2 | odd | 6 | ||
72.2.n.b.61.6 | yes | 16 | 72.29 | odd | 6 | ||
216.2.n.b.37.3 | 16 | 1.1 | even | 1 | trivial | ||
216.2.n.b.37.4 | 16 | 8.5 | even | 2 | inner | ||
216.2.n.b.181.3 | 16 | 72.61 | even | 6 | inner | ||
216.2.n.b.181.4 | 16 | 9.7 | even | 3 | inner | ||
288.2.r.b.49.1 | 16 | 24.11 | even | 2 | |||
288.2.r.b.49.8 | 16 | 12.11 | even | 2 | |||
288.2.r.b.241.1 | 16 | 36.11 | even | 6 | |||
288.2.r.b.241.8 | 16 | 72.11 | even | 6 | |||
648.2.d.j.325.1 | 8 | 72.5 | odd | 6 | |||
648.2.d.j.325.2 | 8 | 9.5 | odd | 6 | |||
648.2.d.k.325.7 | 8 | 9.4 | even | 3 | |||
648.2.d.k.325.8 | 8 | 72.13 | even | 6 | |||
864.2.r.b.145.2 | 16 | 4.3 | odd | 2 | |||
864.2.r.b.145.7 | 16 | 8.3 | odd | 2 | |||
864.2.r.b.721.2 | 16 | 72.43 | odd | 6 | |||
864.2.r.b.721.7 | 16 | 36.7 | odd | 6 | |||
2592.2.d.j.1297.2 | 8 | 36.23 | even | 6 | |||
2592.2.d.j.1297.7 | 8 | 72.59 | even | 6 | |||
2592.2.d.k.1297.2 | 8 | 72.67 | odd | 6 | |||
2592.2.d.k.1297.7 | 8 | 36.31 | odd | 6 |