Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [693,2,Mod(64,693)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(693, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("693.64");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 693 = 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 693.m (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.53363286007\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.159390625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 64.2 | ||
Root | \(-0.628998 - 0.456994i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 693.64 |
Dual form | 693.2.m.g.379.2 |
$q$-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 \(\left(\mathbb{Z}/693\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(442\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.240256 | − | 0.739431i | 0.169887 | − | 0.522857i | −0.829477 | − | 0.558542i | \(-0.811361\pi\) |
0.999363 | + | 0.0356845i | \(0.0113611\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.12900 | + | 0.820265i | 0.564499 | + | 0.410133i | ||||
\(5\) | 0.0687611 | + | 0.211625i | 0.0307509 | + | 0.0946416i | 0.965254 | − | 0.261313i | \(-0.0841556\pi\) |
−0.934503 | + | 0.355955i | \(0.884156\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.809017 | + | 0.587785i | 0.305780 | + | 0.222162i | ||||
\(8\) | 2.13577 | − | 1.55173i | 0.755110 | − | 0.548620i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.173002 | 0.0547082 | ||||||||
\(11\) | −0.660531 | + | 3.25018i | −0.199158 | + | 0.979967i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.01774 | − | 6.20997i | 0.559620 | − | 1.72233i | −0.123798 | − | 0.992307i | \(-0.539507\pi\) |
0.683418 | − | 0.730027i | \(-0.260493\pi\) | |||||||
\(14\) | 0.628998 | − | 0.456994i | 0.168107 | − | 0.122137i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.228211 | + | 0.702362i | 0.0570529 | + | 0.175591i | ||||
\(17\) | 1.33947 | + | 4.12246i | 0.324869 | + | 0.999844i | 0.971500 | + | 0.237041i | \(0.0761775\pi\) |
−0.646631 | + | 0.762803i | \(0.723822\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.35829 | + | 1.71340i | −0.541029 | + | 0.393080i | −0.824467 | − | 0.565910i | \(-0.808525\pi\) |
0.283438 | + | 0.958991i | \(0.408525\pi\) | |||||||
\(20\) | −0.0959574 | + | 0.295327i | −0.0214567 | + | 0.0660370i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.24459 | + | 1.26929i | 0.478549 | + | 0.270614i | ||||
\(23\) | 3.89796 | 0.812780 | 0.406390 | − | 0.913700i | \(-0.366787\pi\) | ||||
0.406390 | + | 0.913700i | \(0.366787\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.00503 | − | 2.90982i | 0.801006 | − | 0.581965i | ||||
\(26\) | −4.10707 | − | 2.98396i | −0.805463 | − | 0.585203i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.431239 | + | 1.32722i | 0.0814965 | + | 0.250820i | ||||
\(29\) | −3.05322 | − | 2.21829i | −0.566969 | − | 0.411927i | 0.267034 | − | 0.963687i | \(-0.413956\pi\) |
−0.834003 | + | 0.551760i | \(0.813956\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.12900 | + | 6.55238i | −0.382379 | + | 1.17684i | 0.555984 | + | 0.831193i | \(0.312341\pi\) |
−0.938364 | + | 0.345650i | \(0.887659\pi\) | |||||||
\(32\) | 5.85410 | 1.03487 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.37009 | 0.577966 | ||||||||
\(35\) | −0.0687611 | + | 0.211625i | −0.0116228 | + | 0.0357712i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.57379 | + | 3.32305i | 0.751926 | + | 0.546306i | 0.896423 | − | 0.443199i | \(-0.146156\pi\) |
−0.144497 | + | 0.989505i | \(0.546156\pi\) | |||||||
\(38\) | 0.700347 | + | 2.15545i | 0.113611 | + | 0.349660i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.475243 | + | 0.345285i | 0.0751426 | + | 0.0545943i | ||||
\(41\) | 1.08255 | − | 0.786521i | 0.169066 | − | 0.122834i | −0.500035 | − | 0.866005i | \(-0.666679\pi\) |
0.669101 | + | 0.743171i | \(0.266679\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.70820 | −0.717994 | −0.358997 | − | 0.933339i | \(-0.616881\pi\) | ||||
−0.358997 | + | 0.933339i | \(0.616881\pi\) | |||||||
\(44\) | −3.41175 | + | 3.12764i | −0.514341 | + | 0.471510i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.936507 | − | 2.88227i | 0.138080 | − | 0.424968i | ||||
\(47\) | 4.89094 | − | 3.55348i | 0.713417 | − | 0.518328i | −0.170857 | − | 0.985296i | \(-0.554654\pi\) |
0.884274 | + | 0.466968i | \(0.154654\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.309017 | + | 0.951057i | 0.0441453 | + | 0.135865i | ||||
\(50\) | −1.18938 | − | 3.66055i | −0.168204 | − | 0.517679i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.37184 | − | 5.35596i | 1.02229 | − | 0.742738i | ||||
\(53\) | 0.530865 | − | 1.63383i | 0.0729199 | − | 0.224424i | −0.907954 | − | 0.419071i | \(-0.862356\pi\) |
0.980873 | + | 0.194646i | \(0.0623559\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.733239 | + | 0.0837016i | −0.0988700 | + | 0.0112863i | ||||
\(56\) | 2.63996 | 0.352780 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.37383 | + | 1.72469i | −0.311699 | + | 0.226463i | ||||
\(59\) | −7.71239 | − | 5.60338i | −1.00407 | − | 0.729498i | −0.0411113 | − | 0.999155i | \(-0.513090\pi\) |
−0.962957 | + | 0.269657i | \(0.913090\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.97566 | − | 9.15813i | −0.380994 | − | 1.17258i | −0.939345 | − | 0.342974i | \(-0.888566\pi\) |
0.558351 | − | 0.829605i | \(-0.311434\pi\) | |||||||
\(62\) | 4.33353 | + | 3.14850i | 0.550359 | + | 0.399859i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.950059 | − | 2.92398i | 0.118757 | − | 0.365498i | ||||
\(65\) | 1.45293 | 0.180213 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.27155 | 0.155344 | 0.0776722 | − | 0.996979i | \(-0.475251\pi\) | ||||
0.0776722 | + | 0.996979i | \(0.475251\pi\) | |||||||
\(68\) | −1.86925 | + | 5.75297i | −0.226680 | + | 0.697650i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.139962 | + | 0.101688i | 0.0167287 | + | 0.0121541i | ||||
\(71\) | 2.87670 | + | 8.85357i | 0.341401 | + | 1.05072i | 0.963482 | + | 0.267772i | \(0.0862874\pi\) |
−0.622081 | + | 0.782953i | \(0.713713\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.52169 | − | 3.28520i | −0.529223 | − | 0.384503i | 0.290844 | − | 0.956771i | \(-0.406064\pi\) |
−0.820067 | + | 0.572267i | \(0.806064\pi\) | |||||||
\(74\) | 3.55605 | − | 2.58362i | 0.413382 | − | 0.300340i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.06794 | −0.466625 | ||||||||
\(77\) | −2.44479 | + | 2.24120i | −0.278610 | + | 0.255409i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.39971 | + | 4.30785i | −0.157479 | + | 0.484671i | −0.998404 | − | 0.0564813i | \(-0.982012\pi\) |
0.840924 | + | 0.541153i | \(0.182012\pi\) | |||||||
\(80\) | −0.132945 | + | 0.0965905i | −0.0148638 | + | 0.0107991i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.321489 | − | 0.989441i | −0.0355025 | − | 0.109265i | ||||
\(83\) | −3.48688 | − | 10.7315i | −0.382734 | − | 1.17793i | −0.938111 | − | 0.346336i | \(-0.887426\pi\) |
0.555376 | − | 0.831599i | \(-0.312574\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.780313 | + | 0.566931i | −0.0846368 | + | 0.0614922i | ||||
\(86\) | −1.13117 | + | 3.48139i | −0.121978 | + | 0.375408i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.63267 | + | 7.96663i | 0.387244 | + | 0.849245i | ||||
\(89\) | −7.92157 | −0.839684 | −0.419842 | − | 0.907597i | \(-0.637915\pi\) | ||||
−0.419842 | + | 0.907597i | \(0.637915\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.28251 | − | 3.83797i | 0.553758 | − | 0.402329i | ||||
\(92\) | 4.40079 | + | 3.19736i | 0.458814 | + | 0.333348i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.45248 | − | 4.47026i | −0.149811 | − | 0.461072i | ||||
\(95\) | −0.524757 | − | 0.381258i | −0.0538389 | − | 0.0391162i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.79781 | + | 8.61078i | −0.284075 | + | 0.874292i | 0.702600 | + | 0.711585i | \(0.252023\pi\) |
−0.986674 | + | 0.162707i | \(0.947977\pi\) | |||||||
\(98\) | 0.777484 | 0.0785378 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.90849 | 0.690849 | ||||||||
\(101\) | 5.93627 | − | 18.2700i | 0.590681 | − | 1.81793i | 0.0155316 | − | 0.999879i | \(-0.495056\pi\) |
0.575149 | − | 0.818049i | \(-0.304944\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.1371 | − | 9.54464i | −1.29443 | − | 0.940461i | −0.294549 | − | 0.955636i | \(-0.595169\pi\) |
−0.999885 | + | 0.0151755i | \(0.995169\pi\) | |||||||
\(104\) | −5.32676 | − | 16.3941i | −0.522332 | − | 1.60757i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.08057 | − | 0.785077i | −0.104954 | − | 0.0762534i | ||||
\(107\) | −4.36332 | + | 3.17014i | −0.421818 | + | 0.306469i | −0.778369 | − | 0.627807i | \(-0.783953\pi\) |
0.356551 | + | 0.934276i | \(0.383953\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.39901 | 0.517132 | 0.258566 | − | 0.965994i | \(-0.416750\pi\) | ||||
0.258566 | + | 0.965994i | \(0.416750\pi\) | |||||||
\(110\) | −0.114273 | + | 0.562290i | −0.0108955 | + | 0.0536122i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.228211 | + | 0.702362i | −0.0215640 | + | 0.0663670i | ||||
\(113\) | −13.3457 | + | 9.69624i | −1.25546 | + | 0.912145i | −0.998526 | − | 0.0542834i | \(-0.982713\pi\) |
−0.256935 | + | 0.966429i | \(0.582713\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.268028 | + | 0.824906i | 0.0249937 | + | 0.0769228i | ||||
\(116\) | −1.62749 | − | 5.00890i | −0.151109 | − | 0.465065i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.99626 | + | 4.35654i | −0.552001 | + | 0.401052i | ||||
\(119\) | −1.33947 | + | 4.12246i | −0.122789 | + | 0.377906i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.1274 | − | 4.29369i | −0.920673 | − | 0.390336i | ||||
\(122\) | −7.48673 | −0.677816 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.77832 | + | 5.65128i | −0.698514 | + | 0.507500i | ||||
\(125\) | 1.79128 | + | 1.30144i | 0.160217 | + | 0.116404i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.617194 | + | 1.89953i | 0.0547671 | + | 0.168556i | 0.974699 | − | 0.223523i | \(-0.0717559\pi\) |
−0.919931 | + | 0.392079i | \(0.871756\pi\) | |||||||
\(128\) | 7.53831 | + | 5.47690i | 0.666299 | + | 0.484094i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.349074 | − | 1.07434i | 0.0306158 | − | 0.0942258i | ||||
\(131\) | −1.37009 | −0.119706 | −0.0598528 | − | 0.998207i | \(-0.519063\pi\) | ||||
−0.0598528 | + | 0.998207i | \(0.519063\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.91501 | −0.252763 | ||||||||
\(134\) | 0.305497 | − | 0.940223i | 0.0263909 | − | 0.0812229i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.25776 | + | 6.72615i | 0.793846 | + | 0.576763i | ||||
\(137\) | −0.772308 | − | 2.37692i | −0.0659827 | − | 0.203074i | 0.912629 | − | 0.408788i | \(-0.134048\pi\) |
−0.978612 | + | 0.205714i | \(0.934048\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.85302 | + | 2.79938i | 0.326809 | + | 0.237441i | 0.739075 | − | 0.673623i | \(-0.235263\pi\) |
−0.412266 | + | 0.911063i | \(0.635263\pi\) | |||||||
\(140\) | −0.251220 | + | 0.182522i | −0.0212320 | + | 0.0154259i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.23775 | 0.607378 | ||||||||
\(143\) | 18.8508 | + | 10.6599i | 1.57638 | + | 0.891426i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.259504 | − | 0.798670i | 0.0215506 | − | 0.0663260i | ||||
\(146\) | −3.51554 | + | 2.55419i | −0.290948 | + | 0.211386i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.43801 | + | 7.50344i | 0.200404 | + | 0.616779i | ||||
\(149\) | 2.23415 | + | 6.87600i | 0.183028 | + | 0.563304i | 0.999909 | − | 0.0135034i | \(-0.00429840\pi\) |
−0.816880 | + | 0.576807i | \(0.804298\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.58514 | + | 4.78439i | −0.535891 | + | 0.389348i | −0.822557 | − | 0.568683i | \(-0.807453\pi\) |
0.286666 | + | 0.958031i | \(0.407453\pi\) | |||||||
\(152\) | −2.37804 | + | 7.31886i | −0.192885 | + | 0.593638i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.06984 | + | 2.34622i | 0.0862103 | + | 0.189064i | ||||
\(155\) | −1.53304 | −0.123137 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.3028 | + | 11.8447i | −1.30111 | + | 0.945311i | −0.999966 | − | 0.00826862i | \(-0.997368\pi\) |
−0.301143 | + | 0.953579i | \(0.597368\pi\) | |||||||
\(158\) | 2.84907 | + | 2.06997i | 0.226660 | + | 0.164678i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.402535 | + | 1.23887i | 0.0318232 | + | 0.0979416i | ||||
\(161\) | 3.15351 | + | 2.29116i | 0.248532 | + | 0.180569i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.29739 | − | 7.07062i | 0.179945 | − | 0.553814i | −0.819880 | − | 0.572536i | \(-0.805960\pi\) |
0.999825 | + | 0.0187219i | \(0.00595970\pi\) | |||||||
\(164\) | 1.86736 | 0.145816 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.77295 | −0.680913 | ||||||||
\(167\) | 0.683275 | − | 2.10290i | 0.0528734 | − | 0.162728i | −0.921133 | − | 0.389248i | \(-0.872735\pi\) |
0.974006 | + | 0.226520i | \(0.0727350\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23.9752 | − | 17.4190i | −1.84424 | − | 1.33992i | ||||
\(170\) | 0.231732 | + | 0.713196i | 0.0177730 | + | 0.0546997i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.31555 | − | 3.86198i | −0.405307 | − | 0.294473i | ||||
\(173\) | −8.38320 | + | 6.09075i | −0.637363 | + | 0.463071i | −0.858943 | − | 0.512071i | \(-0.828878\pi\) |
0.221581 | + | 0.975142i | \(0.428878\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.95049 | 0.374222 | ||||||||
\(176\) | −2.43355 | + | 0.277797i | −0.183436 | + | 0.0209398i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.90320 | + | 5.85746i | −0.142651 | + | 0.439035i | ||||
\(179\) | −18.9386 | + | 13.7597i | −1.41554 | + | 1.02845i | −0.423051 | + | 0.906106i | \(0.639041\pi\) |
−0.992488 | + | 0.122343i | \(0.960959\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.23851 | − | 13.0448i | −0.315046 | − | 0.969611i | −0.975736 | − | 0.218952i | \(-0.929736\pi\) |
0.660690 | − | 0.750659i | \(-0.270264\pi\) | |||||||
\(182\) | −1.56876 | − | 4.82815i | −0.116284 | − | 0.357886i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.32516 | − | 6.04858i | 0.613739 | − | 0.445907i | ||||
\(185\) | −0.388742 | + | 1.19643i | −0.0285809 | + | 0.0879629i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.2835 | + | 1.63051i | −1.04451 | + | 0.119235i | ||||
\(188\) | 8.43666 | 0.615306 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.407990 | + | 0.296422i | −0.0295987 | + | 0.0215047i | ||||
\(191\) | −9.72838 | − | 7.06808i | −0.703921 | − | 0.511429i | 0.177286 | − | 0.984159i | \(-0.443268\pi\) |
−0.881207 | + | 0.472731i | \(0.843268\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.90840 | + | 15.1065i | 0.353315 | + | 1.08739i | 0.956980 | + | 0.290153i | \(0.0937062\pi\) |
−0.603666 | + | 0.797238i | \(0.706294\pi\) | |||||||
\(194\) | 5.69489 | + | 4.13758i | 0.408869 | + | 0.297061i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.431239 | + | 1.32722i | −0.0308028 | + | 0.0948012i | ||||
\(197\) | −12.3035 | −0.876590 | −0.438295 | − | 0.898831i | \(-0.644418\pi\) | ||||
−0.438295 | + | 0.898831i | \(0.644418\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.2615 | 1.08186 | 0.540929 | − | 0.841068i | \(-0.318073\pi\) | ||||
0.540929 | + | 0.841068i | \(0.318073\pi\) | |||||||
\(200\) | 4.03857 | − | 12.4294i | 0.285570 | − | 0.878895i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −12.0832 | − | 8.77892i | −0.850168 | − | 0.617683i | ||||
\(203\) | −1.16623 | − | 3.58928i | −0.0818530 | − | 0.251918i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.240885 | + | 0.175013i | 0.0168242 | + | 0.0122235i | ||||
\(206\) | −10.2139 | + | 7.42080i | −0.711633 | + | 0.517032i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.82212 | 0.334354 | ||||||||
\(209\) | −4.01114 | − | 8.79663i | −0.277456 | − | 0.608476i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.76058 | − | 8.49620i | 0.190046 | − | 0.584903i | −0.809952 | − | 0.586496i | \(-0.800507\pi\) |
0.999999 | + | 0.00159295i | \(0.000507051\pi\) | |||||||
\(212\) | 1.93952 | − | 1.40915i | 0.133207 | − | 0.0967805i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.29579 | + | 3.98802i | 0.0885781 | + | 0.272615i | ||||
\(215\) | −0.323742 | − | 0.996374i | −0.0220790 | − | 0.0679521i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.57379 | + | 4.04959i | −0.378373 | + | 0.274904i | ||||
\(218\) | 1.29714 | − | 3.99220i | 0.0878537 | − | 0.270386i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.896483 | − | 0.506952i | −0.0604409 | − | 0.0341787i | ||||
\(221\) | 28.3031 | 1.90387 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.578645 | + | 0.420410i | −0.0387489 | + | 0.0281527i | −0.606991 | − | 0.794709i | \(-0.707624\pi\) |
0.568242 | + | 0.822861i | \(0.307624\pi\) | |||||||
\(224\) | 4.73607 | + | 3.44095i | 0.316442 | + | 0.229908i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.96331 | + | 12.1978i | 0.263636 | + | 0.811387i | ||||
\(227\) | −4.30528 | − | 3.12797i | −0.285751 | − | 0.207611i | 0.435671 | − | 0.900106i | \(-0.356511\pi\) |
−0.721422 | + | 0.692496i | \(0.756511\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.04208 | + | 6.28489i | −0.134945 | + | 0.415317i | −0.995581 | − | 0.0939024i | \(-0.970066\pi\) |
0.860637 | + | 0.509219i | \(0.170066\pi\) | |||||||
\(230\) | 0.674356 | 0.0444657 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.96318 | −0.654115 | ||||||||
\(233\) | 2.95332 | − | 9.08937i | 0.193478 | − | 0.595464i | −0.806513 | − | 0.591217i | \(-0.798648\pi\) |
0.999991 | − | 0.00424788i | \(-0.00135215\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.08831 | + | 0.790705i | 0.0709936 | + | 0.0515799i | ||||
\(236\) | −4.11102 | − | 12.6524i | −0.267604 | − | 0.823602i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.72646 | + | 1.98089i | 0.176730 | + | 0.128402i | ||||
\(239\) | 21.7194 | − | 15.7801i | 1.40491 | − | 1.02073i | 0.410872 | − | 0.911693i | \(-0.365224\pi\) |
0.994038 | − | 0.109034i | \(-0.0347756\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.8663 | 1.21529 | 0.607643 | − | 0.794210i | \(-0.292115\pi\) | ||||
0.607643 | + | 0.794210i | \(0.292115\pi\) | |||||||
\(242\) | −5.60806 | + | 6.45693i | −0.360500 | + | 0.415067i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.15258 | − | 12.7803i | 0.265842 | − | 0.818177i | ||||
\(245\) | −0.180019 | + | 0.130791i | −0.0115010 | + | 0.00835596i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.88173 | + | 18.1021i | 0.374245 | + | 1.15181i | ||||
\(248\) | 5.62047 | + | 17.2980i | 0.356900 | + | 1.09843i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.39269 | − | 1.01185i | 0.0880814 | − | 0.0639949i | ||||
\(251\) | −9.07680 | + | 27.9355i | −0.572923 | + | 1.76328i | 0.0702229 | + | 0.997531i | \(0.477629\pi\) |
−0.643146 | + | 0.765744i | \(0.722371\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.57472 | + | 12.6691i | −0.161871 | + | 0.796498i | ||||
\(254\) | 1.55285 | 0.0974348 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 10.8355 | − | 7.87245i | 0.677218 | − | 0.492028i | ||||
\(257\) | −13.6856 | − | 9.94320i | −0.853687 | − | 0.620240i | 0.0724730 | − | 0.997370i | \(-0.476911\pi\) |
−0.926160 | + | 0.377130i | \(0.876911\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.74703 | + | 5.37681i | 0.108555 | + | 0.334099i | ||||
\(260\) | 1.64035 | + | 1.19178i | 0.101730 | + | 0.0739114i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.329173 | + | 1.01309i | −0.0203364 | + | 0.0625889i | ||||
\(263\) | 8.18034 | 0.504421 | 0.252211 | − | 0.967672i | \(-0.418842\pi\) | ||||
0.252211 | + | 0.967672i | \(0.418842\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.382263 | 0.0234822 | ||||||||
\(266\) | −0.700347 | + | 2.15545i | −0.0429411 | + | 0.132159i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.43558 | + | 1.04301i | 0.0876917 | + | 0.0637118i | ||||
\(269\) | 1.93048 | + | 5.94140i | 0.117703 | + | 0.362254i | 0.992501 | − | 0.122234i | \(-0.0390059\pi\) |
−0.874798 | + | 0.484488i | \(0.839006\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.36444 | − | 4.62403i | −0.386612 | − | 0.280890i | 0.377454 | − | 0.926028i | \(-0.376800\pi\) |
−0.764066 | + | 0.645138i | \(0.776800\pi\) | |||||||
\(272\) | −2.58978 | + | 1.88159i | −0.157029 | + | 0.114088i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.94312 | −0.117388 | ||||||||
\(275\) | 6.81202 | + | 14.9391i | 0.410780 | + | 0.900862i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.72293 | − | 11.4580i | 0.223689 | − | 0.688444i | −0.774733 | − | 0.632289i | \(-0.782116\pi\) |
0.998422 | − | 0.0561556i | \(-0.0178843\pi\) | |||||||
\(278\) | 2.99566 | − | 2.17648i | 0.179668 | − | 0.130536i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.181527 | + | 0.558682i | 0.0108483 | + | 0.0333876i | ||||
\(281\) | −6.53723 | − | 20.1195i | −0.389978 | − | 1.20023i | −0.932804 | − | 0.360384i | \(-0.882646\pi\) |
0.542826 | − | 0.839846i | \(-0.317354\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.2281 | − | 14.6966i | 1.20244 | − | 0.873623i | 0.207916 | − | 0.978147i | \(-0.433332\pi\) |
0.994522 | + | 0.104524i | \(0.0333319\pi\) | |||||||
\(284\) | −4.01448 | + | 12.3553i | −0.238216 | + | 0.733153i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 12.4113 | − | 11.3777i | 0.733894 | − | 0.672780i | ||||
\(287\) | 1.33811 | 0.0789861 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.44723 | + | 1.05147i | −0.0851312 | + | 0.0618515i | ||||
\(290\) | −0.528215 | − | 0.383770i | −0.0310178 | − | 0.0225358i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.41024 | − | 7.41796i | −0.141049 | − | 0.434104i | ||||
\(293\) | −0.368173 | − | 0.267494i | −0.0215089 | − | 0.0156271i | 0.576979 | − | 0.816759i | \(-0.304231\pi\) |
−0.598488 | + | 0.801132i | \(0.704231\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.655503 | − | 2.01743i | 0.0381648 | − | 0.117459i | ||||
\(296\) | 14.9251 | 0.867502 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.62110 | 0.325621 | ||||||||
\(299\) | 7.86507 | − | 24.2062i | 0.454849 | − | 1.39988i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.80902 | − | 2.76741i | −0.219548 | − | 0.159511i | ||||
\(302\) | 1.95561 | + | 6.01874i | 0.112533 | + | 0.346339i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.74162 | − | 1.26536i | −0.0998885 | − | 0.0725732i | ||||
\(305\) | 1.73348 | − | 1.25945i | 0.0992588 | − | 0.0721157i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.03578 | −0.458626 | −0.229313 | − | 0.973353i | \(-0.573648\pi\) | ||||
−0.229313 | + | 0.973353i | \(0.573648\pi\) | |||||||
\(308\) | −4.59855 | + | 0.524938i | −0.262026 | + | 0.0299111i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.368322 | + | 1.13358i | −0.0209193 | + | 0.0643829i | ||||
\(311\) | 0.110807 | − | 0.0805059i | 0.00628328 | − | 0.00456507i | −0.584639 | − | 0.811293i | \(-0.698764\pi\) |
0.590922 | + | 0.806728i | \(0.298764\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.72485 | − | 14.5416i | −0.267064 | − | 0.821939i | −0.991211 | − | 0.132293i | \(-0.957766\pi\) |
0.724146 | − | 0.689646i | \(-0.242234\pi\) | |||||||
\(314\) | 4.84150 | + | 14.9006i | 0.273221 | + | 0.840889i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.11385 | + | 3.71543i | −0.287676 | + | 0.209009i | ||||
\(317\) | 10.1953 | − | 31.3778i | 0.572622 | − | 1.76235i | −0.0715138 | − | 0.997440i | \(-0.522783\pi\) |
0.644136 | − | 0.764911i | \(-0.277217\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.22661 | − | 8.45828i | 0.516591 | − | 0.473573i | ||||
\(320\) | 0.684115 | 0.0382432 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.45181 | − | 1.78134i | 0.136634 | − | 0.0992703i | ||||
\(323\) | −10.2223 | − | 7.42692i | −0.568783 | − | 0.413245i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.98880 | − | 30.7424i | −0.554079 | − | 1.70528i | ||||
\(326\) | −4.67628 | − | 3.39752i | −0.258995 | − | 0.188171i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.09162 | − | 3.35966i | 0.0602747 | − | 0.185506i | ||||
\(329\) | 6.04554 | 0.333301 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.5335 | 1.62331 | 0.811653 | − | 0.584140i | \(-0.198568\pi\) | ||||
0.811653 | + | 0.584140i | \(0.198568\pi\) | |||||||
\(332\) | 4.86600 | − | 14.9760i | 0.267056 | − | 0.821915i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.39079 | − | 1.01047i | −0.0761008 | − | 0.0552905i | ||||
\(335\) | 0.0874331 | + | 0.269091i | 0.00477698 | + | 0.0147020i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.55497 | − | 3.30938i | −0.248125 | − | 0.180273i | 0.456770 | − | 0.889585i | \(-0.349006\pi\) |
−0.704895 | + | 0.709311i | \(0.749006\pi\) | |||||||
\(338\) | −18.6403 | + | 13.5430i | −1.01390 | + | 0.736641i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.34600 | −0.0729974 | ||||||||
\(341\) | −19.8902 | − | 11.2477i | −1.07711 | − | 0.609096i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.309017 | + | 0.951057i | −0.0166853 | + | 0.0513522i | ||||
\(344\) | −10.0557 | + | 7.30586i | −0.542165 | + | 0.393906i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.48958 | + | 7.66214i | 0.133841 | + | 0.411919i | ||||
\(347\) | −2.69791 | − | 8.30331i | −0.144831 | − | 0.445745i | 0.852158 | − | 0.523285i | \(-0.175294\pi\) |
−0.996989 | + | 0.0775398i | \(0.975294\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.9401 | + | 10.8546i | −0.799724 | + | 0.581034i | −0.910833 | − | 0.412774i | \(-0.864560\pi\) |
0.111109 | + | 0.993808i | \(0.464560\pi\) | |||||||
\(350\) | 1.18938 | − | 3.66055i | 0.0635752 | − | 0.195664i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.86681 | + | 19.0269i | −0.206102 | + | 1.01414i | ||||
\(353\) | 23.4857 | 1.25002 | 0.625009 | − | 0.780618i | \(-0.285095\pi\) | ||||
0.625009 | + | 0.780618i | \(0.285095\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.67583 | + | 1.21756i | −0.0889439 | + | 0.0646215i | ||||
\(356\) | −8.94343 | − | 6.49778i | −0.474001 | − | 0.344382i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.62425 | + | 17.3097i | 0.297251 | + | 0.914844i | ||||
\(359\) | 12.0391 | + | 8.74695i | 0.635402 | + | 0.461647i | 0.858267 | − | 0.513203i | \(-0.171541\pi\) |
−0.222865 | + | 0.974849i | \(0.571541\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.24552 | + | 9.98870i | −0.170817 | + | 0.525721i | ||||
\(362\) | −10.6641 | −0.560490 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.11210 | 0.477604 | ||||||||
\(365\) | 0.384314 | − | 1.18280i | 0.0201159 | − | 0.0619104i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.6894 | + | 20.1175i | 1.44537 | + | 1.05012i | 0.986885 | + | 0.161424i | \(0.0516085\pi\) |
0.458487 | + | 0.888701i | \(0.348391\pi\) | |||||||
\(368\) | 0.889558 | + | 2.73778i | 0.0463714 | + | 0.142717i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.791277 | + | 0.574896i | 0.0411365 | + | 0.0298874i | ||||
\(371\) | 1.38982 | − | 1.00977i | 0.0721560 | − | 0.0524244i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.01739 | 0.156235 | 0.0781173 | − | 0.996944i | \(-0.475109\pi\) | ||||
0.0781173 | + | 0.996944i | \(0.475109\pi\) | |||||||
\(374\) | −2.22605 | + | 10.9534i | −0.115106 | + | 0.566388i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.93191 | − | 15.1788i | 0.254344 | − | 0.782789i | ||||
\(377\) | −19.9361 | + | 14.4845i | −1.02676 | + | 0.745987i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.89252 | − | 5.82457i | −0.0972121 | − | 0.299188i | 0.890612 | − | 0.454764i | \(-0.150277\pi\) |
−0.987824 | + | 0.155576i | \(0.950277\pi\) | |||||||
\(380\) | −0.279717 | − | 0.860879i | −0.0143492 | − | 0.0441622i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7.56367 | + | 5.49532i | −0.386991 | + | 0.281165i | ||||
\(383\) | −1.35689 | + | 4.17607i | −0.0693338 | + | 0.213387i | −0.979720 | − | 0.200373i | \(-0.935785\pi\) |
0.910386 | + | 0.413760i | \(0.135785\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.642402 | − | 0.363271i | −0.0327398 | − | 0.0185140i | ||||
\(386\) | 12.3495 | 0.628573 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −10.2218 | + | 7.42661i | −0.518936 | + | 0.377029i | ||||
\(389\) | 8.49145 | + | 6.16940i | 0.430533 | + | 0.312801i | 0.781862 | − | 0.623451i | \(-0.214270\pi\) |
−0.351329 | + | 0.936252i | \(0.614270\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.22119 | + | 16.0692i | 0.264047 | + | 0.812654i | ||||
\(392\) | 2.13577 | + | 1.55173i | 0.107873 | + | 0.0783742i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.95600 | + | 9.09762i | −0.148921 | + | 0.458331i | ||||
\(395\) | −1.00789 | −0.0507127 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.3888 | 0.571589 | 0.285794 | − | 0.958291i | \(-0.407743\pi\) | ||||
0.285794 | + | 0.958291i | \(0.407743\pi\) | |||||||
\(398\) | 3.66666 | − | 11.2848i | 0.183793 | − | 0.565657i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.95774 | + | 2.14893i | 0.147887 | + | 0.107446i | ||||
\(401\) | 1.46009 | + | 4.49370i | 0.0729135 | + | 0.224405i | 0.980871 | − | 0.194657i | \(-0.0623592\pi\) |
−0.907958 | + | 0.419061i | \(0.862359\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 36.3943 | + | 26.4420i | 1.81293 | + | 1.31717i | ||||
\(404\) | 21.6882 | − | 15.7574i | 1.07903 | − | 0.783961i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.93422 | −0.145623 | ||||||||
\(407\) | −13.8217 | + | 12.6707i | −0.685114 | + | 0.628062i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.761863 | − | 2.34477i | 0.0376717 | − | 0.115942i | −0.930452 | − | 0.366413i | \(-0.880586\pi\) |
0.968124 | + | 0.250472i | \(0.0805857\pi\) | |||||||
\(410\) | 0.187285 | − | 0.136070i | 0.00924932 | − | 0.00672003i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7.00259 | − | 21.5518i | −0.344993 | − | 1.06178i | ||||
\(413\) | −2.94587 | − | 9.06646i | −0.144957 | − | 0.446131i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.03129 | − | 1.47582i | 0.0997122 | − | 0.0724452i | ||||
\(416\) | 11.8121 | − | 36.3538i | 0.579134 | − | 1.78239i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7.46820 | + | 0.852519i | −0.365282 | + | 0.0416981i | ||||
\(419\) | 14.3399 | 0.700548 | 0.350274 | − | 0.936647i | \(-0.386088\pi\) | ||||
0.350274 | + | 0.936647i | \(0.386088\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.0087 | − | 10.1779i | 0.682744 | − | 0.496043i | −0.191523 | − | 0.981488i | \(-0.561343\pi\) |
0.874267 | + | 0.485446i | \(0.161343\pi\) | |||||||
\(422\) | −5.61911 | − | 4.08253i | −0.273534 | − | 0.198734i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.40146 | − | 4.31326i | −0.0680611 | − | 0.209470i | ||||
\(425\) | 17.3602 | + | 12.6130i | 0.842096 | + | 0.611818i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.97566 | − | 9.15813i | 0.144002 | − | 0.443193i | ||||
\(428\) | −7.52653 | −0.363808 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.814531 | −0.0392802 | ||||||||
\(431\) | −8.61919 | + | 26.5272i | −0.415172 | + | 1.27777i | 0.496925 | + | 0.867794i | \(0.334462\pi\) |
−0.912097 | + | 0.409975i | \(0.865538\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.9040 | + | 17.3673i | 1.14875 | + | 0.834619i | 0.988315 | − | 0.152426i | \(-0.0487087\pi\) |
0.160440 | + | 0.987046i | \(0.448709\pi\) | |||||||
\(434\) | 1.65526 | + | 5.09437i | 0.0794551 | + | 0.244538i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.09548 | + | 4.42862i | 0.291920 | + | 0.212093i | ||||
\(437\) | −9.19251 | + | 6.67875i | −0.439738 | + | 0.319488i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −33.6655 | −1.60677 | −0.803384 | − | 0.595461i | \(-0.796970\pi\) | ||||
−0.803384 | + | 0.595461i | \(0.796970\pi\) | |||||||
\(440\) | −1.43615 | + | 1.31656i | −0.0684658 | + | 0.0627644i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.79997 | − | 20.9282i | 0.323442 | − | 0.995451i | ||||
\(443\) | 8.35449 | − | 6.06989i | 0.396934 | − | 0.288389i | −0.371357 | − | 0.928490i | \(-0.621107\pi\) |
0.768291 | + | 0.640101i | \(0.221107\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.544696 | − | 1.67640i | −0.0258211 | − | 0.0794691i | ||||
\(446\) | 0.171842 | + | 0.528874i | 0.00813694 | + | 0.0250429i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.48729 | − | 1.80712i | 0.117513 | − | 0.0853784i | ||||
\(449\) | 0.852224 | − | 2.62287i | 0.0402189 | − | 0.123781i | −0.928931 | − | 0.370253i | \(-0.879271\pi\) |
0.969150 | + | 0.246471i | \(0.0792712\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.84128 | + | 4.03802i | 0.0867025 | + | 0.190143i | ||||
\(452\) | −23.0208 | −1.08281 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.34729 | + | 2.43195i | −0.157096 | + | 0.114137i | ||||
\(455\) | 1.17544 | + | 0.854009i | 0.0551056 | + | 0.0400365i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.4628 | − | 38.3566i | −0.582986 | − | 1.79425i | −0.607213 | − | 0.794539i | \(-0.707713\pi\) |
0.0242276 | − | 0.999706i | \(-0.492287\pi\) | |||||||
\(458\) | 4.15662 | + | 3.01996i | 0.194226 | + | 0.141114i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.374038 | + | 1.15117i | −0.0174396 | + | 0.0536736i | ||||
\(461\) | 34.2251 | 1.59402 | 0.797011 | − | 0.603965i | \(-0.206413\pi\) | ||||
0.797011 | + | 0.603965i | \(0.206413\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.707349 | 0.0328733 | 0.0164367 | − | 0.999865i | \(-0.494768\pi\) | ||||
0.0164367 | + | 0.999865i | \(0.494768\pi\) | |||||||
\(464\) | 0.861267 | − | 2.65071i | 0.0399833 | − | 0.123056i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.01142 | − | 4.36755i | −0.278473 | − | 0.202323i | ||||
\(467\) | 8.83555 | + | 27.1930i | 0.408860 | + | 1.25834i | 0.917629 | + | 0.397439i | \(0.130101\pi\) |
−0.508768 | + | 0.860904i | \(0.669899\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.02870 | + | 0.747397i | 0.0475011 | + | 0.0345116i | ||||
\(470\) | 0.846145 | − | 0.614760i | 0.0390298 | − | 0.0283568i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −25.1669 | −1.15840 | ||||||||
\(473\) | 3.10991 | − | 15.3025i | 0.142994 | − | 0.703611i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.45933 | + | 13.7244i | −0.204608 | + | 0.629719i | ||||
\(476\) | −4.89377 | + | 3.55553i | −0.224306 | + | 0.162968i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.45006 | − | 19.8512i | −0.295019 | − | 0.907975i | ||||
\(479\) | 1.57511 | + | 4.84769i | 0.0719686 | + | 0.221497i | 0.980571 | − | 0.196166i | \(-0.0628493\pi\) |
−0.908602 | + | 0.417663i | \(0.862849\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 29.8648 | − | 21.6980i | 1.36172 | − | 0.989344i | ||||
\(482\) | 4.53274 | − | 13.9503i | 0.206461 | − | 0.635421i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.91185 | − | 13.1547i | −0.359629 | − | 0.597942i | ||||
\(485\) | −2.01464 | −0.0914800 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.6138 | + | 17.1564i | −1.07004 | + | 0.777433i | −0.975920 | − | 0.218128i | \(-0.930005\pi\) |
−0.0941240 | + | 0.995560i | \(0.530005\pi\) | |||||||
\(488\) | −20.5663 | − | 14.9423i | −0.930992 | − | 0.676405i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.0534607 | + | 0.164535i | 0.00241511 | + | 0.00743294i | ||||
\(491\) | 24.3870 | + | 17.7182i | 1.10057 | + | 0.799610i | 0.981153 | − | 0.193235i | \(-0.0618979\pi\) |
0.119416 | + | 0.992844i | \(0.461898\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.05514 | − | 15.5581i | 0.227672 | − | 0.700703i | ||||
\(494\) | 14.7984 | 0.665810 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.08801 | −0.228458 | ||||||||
\(497\) | −2.87670 | + | 8.85357i | −0.129038 | + | 0.397137i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.81450 | − | 3.49794i | −0.215526 | − | 0.156589i | 0.474784 | − | 0.880102i | \(-0.342526\pi\) |
−0.690311 | + | 0.723513i | \(0.742526\pi\) | |||||||
\(500\) | 0.954823 | + | 2.93864i | 0.0427010 | + | 0.131420i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 18.4757 | + | 13.4233i | 0.824609 | + | 0.599113i | ||||
\(503\) | −4.02773 | + | 2.92632i | −0.179588 | + | 0.130478i | −0.673947 | − | 0.738779i | \(-0.735403\pi\) |
0.494360 | + | 0.869257i | \(0.335403\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.27456 | 0.190216 | ||||||||
\(506\) | 8.74933 | + | 4.94765i | 0.388955 | + | 0.219950i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.861305 | + | 2.65083i | −0.0382142 | + | 0.117611i | ||||
\(509\) | −17.2551 | + | 12.5366i | −0.764821 | + | 0.555675i | −0.900385 | − | 0.435094i | \(-0.856715\pi\) |
0.135565 | + | 0.990769i | \(0.456715\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.72713 | − | 5.31556i | −0.0764038 | − | 0.235147i | ||||
\(512\) | 2.54091 | + | 7.82012i | 0.112293 | + | 0.345604i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10.6404 | + | 7.73068i | −0.469327 | + | 0.340986i | ||||
\(515\) | 1.11656 | − | 3.43643i | 0.0492017 | − | 0.151427i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.31884 | + | 18.2436i | 0.365862 | + | 0.802354i | ||||
\(518\) | 4.39552 | 0.193128 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.10312 | − | 2.25455i | 0.136081 | − | 0.0988686i | ||||
\(521\) | −17.9103 | − | 13.0126i | −0.784664 | − | 0.570092i | 0.121711 | − | 0.992566i | \(-0.461162\pi\) |
−0.906375 | + | 0.422473i | \(0.861162\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.51773 | + | 4.67108i | 0.0663655 | + | 0.204252i | 0.978740 | − | 0.205104i | \(-0.0657533\pi\) |
−0.912375 | + | 0.409356i | \(0.865753\pi\) | |||||||
\(524\) | −1.54683 | − | 1.12384i | −0.0675737 | − | 0.0490952i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.96537 | − | 6.04880i | 0.0856944 | − | 0.263740i | ||||
\(527\) | −29.8637 | −1.30088 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.80592 | −0.339388 | ||||||||
\(530\) | 0.0918410 | − | 0.282657i | 0.00398932 | − | 0.0122779i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.29104 | − | 2.39108i | −0.142685 | − | 0.103666i | ||||
\(533\) | −2.69996 | − | 8.30962i | −0.116948 | − | 0.359929i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.970907 | − | 0.705405i | −0.0419760 | − | 0.0304973i | ||||
\(536\) | 2.71574 | − | 1.97310i | 0.117302 | − | 0.0852250i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.85707 | 0.209403 | ||||||||
\(539\) | −3.29522 | + | 0.376160i | −0.141935 | + | 0.0162024i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.99013 | − | 18.4357i | 0.257536 | − | 0.792614i | −0.735784 | − | 0.677217i | \(-0.763186\pi\) |
0.993319 | − | 0.115397i | \(-0.0368141\pi\) | |||||||
\(542\) | −4.94825 | + | 3.59511i | −0.212546 | + | 0.154423i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.84139 | + | 24.1333i | 0.336197 | + | 1.03471i | ||||
\(545\) | 0.371242 | + | 1.14257i | 0.0159023 | + | 0.0489422i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.6904 | + | 8.49354i | −0.499843 | + | 0.363158i | −0.808957 | − | 0.587868i | \(-0.799968\pi\) |
0.309114 | + | 0.951025i | \(0.399968\pi\) | |||||||
\(548\) | 1.07777 | − | 3.31703i | 0.0460400 | − | 0.141697i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 12.6831 | − | 1.44781i | 0.540808 | − | 0.0617349i | ||||
\(551\) | 11.0012 | 0.468667 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.66448 | + | 2.66240i | −0.155829 | + | 0.113217i | ||||
\(554\) | −7.57795 | − | 5.50570i | −0.321956 | − | 0.233915i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.05382 | + | 6.32100i | 0.0871012 | + | 0.268070i | ||||
\(557\) | 14.9432 | + | 10.8569i | 0.633164 | + | 0.460021i | 0.857495 | − | 0.514492i | \(-0.172020\pi\) |
−0.224331 | + | 0.974513i | \(0.572020\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.49993 | + | 29.2378i | −0.401804 | + | 1.23663i | ||||
\(560\) | −0.164330 | −0.00694419 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −16.4476 | −0.693801 | ||||||||
\(563\) | −9.66724 | + | 29.7527i | −0.407426 | + | 1.25393i | 0.511427 | + | 0.859327i | \(0.329117\pi\) |
−0.918853 | + | 0.394600i | \(0.870883\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.96963 | − | 2.15757i | −0.124933 | − | 0.0907695i | ||||
\(566\) | −6.00720 | − | 18.4883i | −0.252502 | − | 0.777120i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 19.8823 | + | 14.4454i | 0.834244 | + | 0.606114i | ||||
\(569\) | 1.40449 | − | 1.02042i | 0.0588794 | − | 0.0427784i | −0.557956 | − | 0.829870i | \(-0.688414\pi\) |
0.616836 | + | 0.787092i | \(0.288414\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.5309 | 0.524403 | 0.262201 | − | 0.965013i | \(-0.415551\pi\) | ||||
0.262201 | + | 0.965013i | \(0.415551\pi\) | |||||||
\(572\) | 12.5385 | + | 27.4976i | 0.524262 | + | 1.14973i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.321489 | − | 0.989441i | 0.0134187 | − | 0.0412985i | ||||
\(575\) | 15.6114 | − | 11.3424i | 0.651042 | − | 0.473009i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.23893 | + | 19.2015i | 0.259730 | + | 0.799368i | 0.992861 | + | 0.119280i | \(0.0380585\pi\) |
−0.733130 | + | 0.680088i | \(0.761942\pi\) | |||||||
\(578\) | 0.429788 | + | 1.32275i | 0.0178768 | + | 0.0550192i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.948101 | − | 0.688835i | 0.0393677 | − | 0.0286023i | ||||
\(581\) | 3.48688 | − | 10.7315i | 0.144660 | − | 0.445218i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.95961 | + | 2.80461i | 0.205406 | + | 0.116155i | ||||
\(584\) | −14.7550 | −0.610568 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.286249 | + | 0.207972i | −0.0118248 | + | 0.00859125i | ||||
\(587\) | −0.00677611 | − | 0.00492314i | −0.000279680 | − | 0.000203200i | 0.587645 | − | 0.809119i | \(-0.300055\pi\) |
−0.587925 | + | 0.808915i | \(0.700055\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.20604 | − | 19.1002i | −0.255716 | − | 0.787012i | ||||
\(590\) | −1.33426 | − | 0.969399i | −0.0549307 | − | 0.0399095i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.29020 | + | 3.97082i | −0.0530267 | + | 0.163200i | ||||
\(593\) | 0.439298 | 0.0180398 | 0.00901989 | − | 0.999959i | \(-0.497129\pi\) | ||||
0.00901989 | + | 0.999959i | \(0.497129\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.964520 | −0.0395415 | ||||||||
\(596\) | −3.11779 | + | 9.59558i | −0.127710 | + | 0.393050i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −16.0092 | − | 11.6314i | −0.654664 | − | 0.475641i | ||||
\(599\) | −13.9572 | − | 42.9558i | −0.570275 | − | 1.75512i | −0.651734 | − | 0.758448i | \(-0.725958\pi\) |
0.0814591 | − | 0.996677i | \(-0.474042\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.01541 | − | 6.55008i | −0.367746 | − | 0.267183i | 0.388529 | − | 0.921436i | \(-0.372983\pi\) |
−0.756276 | + | 0.654253i | \(0.772983\pi\) | |||||||
\(602\) | −2.96145 | + | 2.15162i | −0.120700 | + | 0.0876935i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −11.3591 | −0.462194 | ||||||||
\(605\) | 0.212282 | − | 2.43845i | 0.00863047 | − | 0.0991371i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.0318 | + | 33.9525i | −0.447768 | + | 1.37809i | 0.431651 | + | 0.902041i | \(0.357931\pi\) |
−0.879419 | + | 0.476049i | \(0.842069\pi\) | |||||||
\(608\) | −13.8057 | + | 10.0304i | −0.559894 | + | 0.406787i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.514796 | − | 1.58438i | −0.0208435 | − | 0.0641496i | ||||
\(611\) | −12.1983 | − | 37.5426i | −0.493491 | − | 1.51881i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.9135 | + | 10.1087i | −0.561960 | + | 0.408288i | −0.832176 | − | 0.554512i | \(-0.812905\pi\) |
0.270216 | + | 0.962800i | \(0.412905\pi\) | |||||||
\(614\) | −1.93064 | + | 5.94191i | −0.0779144 | + | 0.239796i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.74378 | + | 8.58036i | −0.0702587 | + | 0.345713i | ||||
\(617\) | 16.8852 | 0.679774 | 0.339887 | − | 0.940466i | \(-0.389611\pi\) | ||||
0.339887 | + | 0.940466i | \(0.389611\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.1355 | + | 18.2620i | −1.01028 | + | 0.734013i | −0.964268 | − | 0.264928i | \(-0.914652\pi\) |
−0.0460139 | + | 0.998941i | \(0.514652\pi\) | |||||||
\(620\) | −1.73080 | − | 1.25750i | −0.0695106 | − | 0.0505024i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.0329066 | − | 0.101276i | −0.00131943 | − | 0.00406080i | ||||
\(623\) | −6.40868 | − | 4.65618i | −0.256758 | − | 0.186546i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.49668 | − | 23.0724i | 0.299867 | − | 0.922896i | ||||
\(626\) | −11.8877 | −0.475127 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −28.1217 | −1.12218 | ||||||||
\(629\) | −7.57271 | + | 23.3064i | −0.301944 | + | 0.929287i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.86832 | − | 4.26359i | −0.233614 | − | 0.169731i | 0.464819 | − | 0.885406i | \(-0.346119\pi\) |
−0.698434 | + | 0.715675i | \(0.746119\pi\) | |||||||
\(632\) | 3.69517 | + | 11.3726i | 0.146986 | + | 0.452376i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −20.7522 | − | 15.0774i | −0.824176 | − | 0.598799i | ||||
\(635\) | −0.359549 | + | 0.261227i | −0.0142683 | + | 0.0103665i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.52954 | 0.258710 | ||||||||
\(638\) | −4.03757 | − | 8.85460i | −0.159849 | − | 0.350557i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.640707 | + | 1.97189i | −0.0253262 | + | 0.0779459i | ||||
\(641\) | −16.7870 | + | 12.1965i | −0.663047 | + | 0.481732i | −0.867691 | − | 0.497104i | \(-0.834397\pi\) |
0.204643 | + | 0.978837i | \(0.434397\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.19750 | + | 6.76322i | 0.0866611 | + | 0.266715i | 0.984991 | − | 0.172606i | \(-0.0552188\pi\) |
−0.898330 | + | 0.439322i | \(0.855219\pi\) | |||||||
\(644\) | 1.68095 | + | 5.17343i | 0.0662387 | + | 0.203862i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.94766 | + | 5.77431i | −0.312696 | + | 0.227187i | ||||
\(647\) | −8.52234 | + | 26.2291i | −0.335048 | + | 1.03117i | 0.631651 | + | 0.775253i | \(0.282378\pi\) |
−0.966699 | + | 0.255918i | \(0.917622\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 23.3063 | − | 21.3655i | 0.914852 | − | 0.838669i | ||||
\(650\) | −25.1317 | −0.985748 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.39353 | − | 6.09826i | 0.328716 | − | 0.238826i | ||||
\(653\) | 13.0690 | + | 9.49516i | 0.511428 | + | 0.371574i | 0.813365 | − | 0.581753i | \(-0.197633\pi\) |
−0.301937 | + | 0.953328i | \(0.597633\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.0942092 | − | 0.289946i | −0.00368106 | − | 0.0113291i | ||||
\(656\) | 0.799474 | + | 0.580852i | 0.0312142 | + | 0.0226785i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.45248 | − | 4.47026i | 0.0566234 | − | 0.174269i | ||||
\(659\) | 13.2085 | 0.514531 | 0.257266 | − | 0.966341i | \(-0.417178\pi\) | ||||
0.257266 | + | 0.966341i | \(0.417178\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.90660 | −0.190845 | −0.0954223 | − | 0.995437i | \(-0.530420\pi\) | ||||
−0.0954223 | + | 0.995437i | \(0.530420\pi\) | |||||||
\(662\) | 7.09559 | − | 21.8380i | 0.275778 | − | 0.848757i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −24.0996 | − | 17.5094i | −0.935245 | − | 0.679495i | ||||
\(665\) | −0.200439 | − | 0.616888i | −0.00777270 | − | 0.0239219i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.9013 | − | 8.64682i | −0.460821 | − | 0.334806i | ||||
\(668\) | 2.49635 | − | 1.81371i | 0.0965869 | − | 0.0701745i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.219981 | 0.00849861 | ||||||||
\(671\) | 31.7311 | − | 3.62221i | 1.22497 | − | 0.139834i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.26654 | + | 28.5195i | −0.357199 | + | 1.09935i | 0.597524 | + | 0.801851i | \(0.296151\pi\) |
−0.954723 | + | 0.297495i | \(0.903849\pi\) | |||||||
\(674\) | −3.54142 | + | 2.57299i | −0.136410 | + | 0.0991079i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.7797 | − | 39.3320i | −0.491528 | − | 1.51277i | ||||
\(677\) | −3.89019 | − | 11.9728i | −0.149512 | − | 0.460151i | 0.848051 | − | 0.529914i | \(-0.177776\pi\) |
−0.997564 | + | 0.0697626i | \(0.977776\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.32477 | + | 5.32176i | −0.281099 | + | 0.204230i | ||||
\(680\) | −0.786849 | + | 2.42167i | −0.0301743 | + | 0.0928668i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −13.0956 | + | 12.0051i | −0.501457 | + | 0.459699i | ||||
\(683\) | 28.5342 | 1.09183 | 0.545916 | − | 0.837840i | \(-0.316182\pi\) | ||||
0.545916 | + | 0.837840i | \(0.316182\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.449911 | − | 0.326879i | 0.0171902 | − | 0.0124894i | ||||
\(686\) | 0.628998 | + | 0.456994i | 0.0240153 | + | 0.0174481i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.07447 | − | 3.30687i | −0.0409636 | − | 0.126073i | ||||
\(689\) | −9.07491 | − | 6.59331i | −0.345726 | − | 0.251185i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.84107 | − | 24.1323i | 0.298288 | − | 0.918037i | −0.683809 | − | 0.729661i | \(-0.739678\pi\) |
0.982097 | − | 0.188376i | \(-0.0603223\pi\) | |||||||
\(692\) | −14.4606 | −0.549711 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.78791 | −0.257666 | ||||||||
\(695\) | −0.327482 | + | 1.00788i | −0.0124221 | + | 0.0382312i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.69245 | + | 3.40927i | 0.177739 | + | 0.129135i | ||||
\(698\) | 4.43679 | + | 13.6551i | 0.167935 | + | 0.516851i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.58909 | + | 4.06071i | 0.211248 | + | 0.153480i | ||||
\(701\) | −36.9738 | + | 26.8630i | −1.39648 | + | 1.01460i | −0.401363 | + | 0.915919i | \(0.631463\pi\) |
−0.995119 | + | 0.0986843i | \(0.968537\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.4800 | −0.621556 | ||||||||
\(704\) | 8.87594 | + | 5.01925i | 0.334525 | + | 0.189170i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.64257 | − | 17.3661i | 0.212361 | − | 0.653580i | ||||
\(707\) | 15.5413 | − | 11.2915i | 0.584493 | − | 0.424659i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.9065 | + | 36.6446i | 0.447160 | + | 1.37622i | 0.880098 | + | 0.474793i | \(0.157477\pi\) |
−0.432938 | + | 0.901424i | \(0.642523\pi\) | |||||||
\(710\) | 0.497676 | + | 1.53169i | 0.0186774 | + | 0.0574833i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −16.9187 | + | 12.2921i | −0.634054 | + | 0.460667i | ||||
\(713\) | −8.29874 | + | 25.5409i | −0.310790 | + | 0.956515i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.959703 | + | 4.72228i | −0.0358908 | + | 0.176603i | ||||
\(716\) | −32.6683 | −1.22087 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.36025 | − | 6.80062i | 0.349321 | − | 0.253797i | ||||
\(719\) | 4.61312 | + | 3.35163i | 0.172040 | + | 0.124995i | 0.670473 | − | 0.741934i | \(-0.266091\pi\) |
−0.498433 | + | 0.866928i | \(0.666091\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.01791 | − | 15.4435i | −0.186877 | − | 0.575148i | ||||
\(722\) | 6.60620 | + | 4.79969i | 0.245857 | + | 0.178626i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.91491 | − | 18.2042i | 0.219826 | − | 0.676555i | ||||
\(725\) | −18.6831 | −0.693872 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.8221 | 0.438458 | 0.219229 | − | 0.975673i | \(-0.429646\pi\) | ||||
0.219229 | + | 0.975673i | \(0.429646\pi\) | |||||||
\(728\) | 5.32676 | − | 16.3941i | 0.197423 | − | 0.607605i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.782263 | − | 0.568347i | −0.0289529 | − | 0.0210355i | ||||
\(731\) | −6.30649 | − | 19.4094i | −0.233254 | − | 0.717882i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.12900 | − | 5.17952i | −0.263316 | − | 0.191310i | 0.448292 | − | 0.893887i | \(-0.352033\pi\) |
−0.711607 | + | 0.702577i | \(0.752033\pi\) | |||||||
\(734\) | 21.5280 | − | 15.6410i | 0.794614 | − | 0.577321i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 22.8190 | 0.841121 | ||||||||
\(737\) | −0.839897 | + | 4.13277i | −0.0309380 | + | 0.152232i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.148578 | − | 0.457276i | 0.00546553 | − | 0.0168212i | −0.948287 | − | 0.317416i | \(-0.897185\pi\) |
0.953752 | + | 0.300594i | \(0.0971850\pi\) | |||||||
\(740\) | −1.42027 | + | 1.03189i | −0.0522103 | + | 0.0379330i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.412739 | − | 1.27028i | −0.0151521 | − | 0.0466335i | ||||
\(743\) | −10.2730 | − | 31.6172i | −0.376881 | − | 1.15992i | −0.942201 | − | 0.335049i | \(-0.891247\pi\) |
0.565319 | − | 0.824872i | \(-0.308753\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.30151 | + | 0.945603i | −0.0476837 | + | 0.0346442i | ||||
\(746\) | 0.724946 | − | 2.23116i | 0.0265422 | − | 0.0816884i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −17.4635 | − | 9.87543i | −0.638530 | − | 0.361082i | ||||
\(749\) | −5.39336 | −0.197069 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.6578 | + | 16.4619i | −0.826796 | + | 0.600703i | −0.918651 | − | 0.395070i | \(-0.870720\pi\) |
0.0918547 | + | 0.995772i | \(0.470720\pi\) | |||||||
\(752\) | 3.61200 | + | 2.62427i | 0.131716 | + | 0.0956973i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.92049 | + | 18.2214i | 0.215611 | + | 0.663584i | ||||
\(755\) | −1.46530 | − | 1.06460i | −0.0533276 | − | 0.0387448i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.87465 | + | 21.1580i | −0.249863 | + | 0.769001i | 0.744935 | + | 0.667137i | \(0.232481\pi\) |
−0.994798 | + | 0.101864i | \(0.967519\pi\) | |||||||
\(758\) | −4.76156 | −0.172948 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.71237 | −0.0621142 | ||||||||
\(761\) | 14.9025 | − | 45.8651i | 0.540214 | − | 1.66261i | −0.191891 | − | 0.981416i | \(-0.561462\pi\) |
0.732105 | − | 0.681192i | \(-0.238538\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.36789 | + | 3.17346i | 0.158128 | + | 0.114887i | ||||
\(764\) | −5.18562 | − | 15.9597i | −0.187609 | − | 0.577402i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.76192 | + | 2.00665i | 0.0997922 | + | 0.0725033i | ||||
\(767\) | −50.3584 | + | 36.5875i | −1.81834 | + | 1.32110i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 43.6883 | 1.57544 | 0.787721 | − | 0.616032i | \(-0.211261\pi\) | ||||
0.787721 | + | 0.616032i | \(0.211261\pi\) | |||||||
\(770\) | −0.422955 | + | 0.387734i | −0.0152422 | + | 0.0139730i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.84977 | + | 21.0814i | −0.246528 | + | 0.758737i | ||||
\(773\) | −0.473736 | + | 0.344189i | −0.0170391 | + | 0.0123796i | −0.596272 | − | 0.802782i | \(-0.703352\pi\) |
0.579233 | + | 0.815162i | \(0.303352\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.5396 | + | 32.4375i | 0.378593 | + | 1.16519i | ||||
\(776\) | 7.38612 | + | 22.7321i | 0.265146 | + | 0.816036i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.60197 | − | 4.79661i | 0.236692 | − | 0.171967i | ||||
\(779\) | −1.20535 | + | 3.70969i | −0.0431862 | + | 0.132913i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.6759 | + | 3.50175i | −1.09767 | + | 0.125302i | ||||
\(782\) | 13.1365 | 0.469760 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.597465 | + | 0.434084i | −0.0213380 | + | 0.0155030i | ||||
\(785\) | −3.62764 | − | 2.63563i | −0.129476 | − | 0.0940698i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.49195 | + | 29.2132i | 0.338351 | + | 1.04134i | 0.965048 | + | 0.262075i | \(0.0844067\pi\) |
−0.626696 | + | 0.779264i | \(0.715593\pi\) | |||||||
\(788\) | −13.8907 | − | 10.0922i | −0.494834 | − | 0.359518i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.242153 | + | 0.745269i | −0.00861540 | + | 0.0265155i | ||||
\(791\) | −16.4962 | −0.586538 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −62.8758 | −2.23278 | ||||||||
\(794\) | 2.73623 | − | 8.42125i | 0.0971052 | − | 0.298859i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17.2302 | + | 12.5185i | 0.610708 | + | 0.443705i | ||||
\(797\) | 3.34767 | + | 10.3031i | 0.118581 | + | 0.364953i | 0.992677 | − | 0.120799i | \(-0.0385456\pi\) |
−0.874096 | + | 0.485752i | \(0.838546\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.2003 | + | 15.4029i | 0.750014 | + | 0.544917i | ||||
\(800\) | 23.4458 | − | 17.0344i | 0.828936 | − | 0.602257i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.67358 | 0.129719 | ||||||||
\(803\) | 13.6642 | − | 12.5263i | 0.482200 | − | 0.442045i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.268028 | + | 0.824906i | −0.00944675 | + | 0.0290741i | ||||
\(806\) | 28.2960 | − | 20.5582i | 0.996684 | − | 0.724133i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −15.6715 | − | 48.2320i | −0.551322 | − | 1.69679i | ||||
\(809\) | 11.9250 | + | 36.7013i | 0.419260 | + | 1.29035i | 0.908385 | + | 0.418136i | \(0.137316\pi\) |
−0.489125 | + | 0.872214i | \(0.662684\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.1737 | − | 29.9144i | 1.44580 | − | 1.05044i | 0.459015 | − | 0.888428i | \(-0.348202\pi\) |
0.986789 | − | 0.162010i | \(-0.0517977\pi\) | |||||||
\(812\) | 1.62749 | − | 5.00890i | 0.0571137 | − | 0.175778i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.04836 | + | 13.2644i | 0.211995 | + | 0.464916i | ||||
\(815\) | 1.65429 | 0.0579473 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.1033 | − | 8.06703i | 0.388456 | − | 0.282230i | ||||
\(818\) | −1.55076 | − | 1.12669i | −0.0542209 | − | 0.0393938i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.128402 | + | 0.395180i | 0.00448398 | + | 0.0138003i | ||||
\(821\) | −32.6110 | − | 23.6933i | −1.13813 | − | 0.826901i | −0.151274 | − | 0.988492i | \(-0.548338\pi\) |
−0.986858 | + | 0.161590i | \(0.948338\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.93609 | − | 24.4248i | 0.276635 | − | 0.851395i | −0.712147 | − | 0.702030i | \(-0.752277\pi\) |
0.988782 | − | 0.149365i | \(-0.0477228\pi\) | |||||||
\(824\) | −42.8685 | −1.49340 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.41179 | −0.257889 | ||||||||
\(827\) | 9.87486 | − | 30.3917i | 0.343382 | − | 1.05682i | −0.619062 | − | 0.785342i | \(-0.712487\pi\) |
0.962444 | − | 0.271480i | \(-0.0875131\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −39.1566 | − | 28.4489i | −1.35996 | − | 0.988072i | −0.998447 | − | 0.0557070i | \(-0.982259\pi\) |
−0.361518 | − | 0.932365i | \(-0.617741\pi\) | |||||||
\(830\) | −0.603238 | − | 1.85658i | −0.0209387 | − | 0.0644427i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −16.2409 | − | 11.7997i | −0.563050 | − | 0.409080i | ||||
\(833\) | −3.50678 | + | 2.54782i | −0.121503 | + | 0.0882768i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.492010 | 0.0170267 | ||||||||
\(836\) | 2.68700 | − | 13.2216i | 0.0929319 | − | 0.457278i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.44524 | − | 10.6033i | 0.119014 | − | 0.366287i | ||||
\(839\) | −30.5133 | + | 22.1692i | −1.05344 | + | 0.765366i | −0.972863 | − | 0.231382i | \(-0.925675\pi\) |
−0.0805734 | + | 0.996749i | \(0.525675\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.56017 | − | 14.0348i | −0.157247 | − | 0.483957i | ||||
\(842\) | −4.16021 | − | 12.8038i | −0.143370 | − | 0.441248i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 10.0858 | − | 7.32779i | 0.347169 | − | 0.252233i | ||||
\(845\) | 2.03773 | − | 6.27150i | 0.0701001 | − | 0.215746i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.66947 | − | 9.42641i | −0.194805 | − | 0.323895i | ||||
\(848\) | 1.26869 | 0.0435671 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 13.4973 | − | 9.80638i | 0.462954 | − | 0.336356i | ||||
\(851\) | 17.8284 | + | 12.9531i | 0.611151 | + | 0.444027i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.87035 | + | 8.83403i | 0.0982789 | + | 0.302471i | 0.988094 | − | 0.153849i | \(-0.0491670\pi\) |
−0.889815 | + | 0.456321i | \(0.849167\pi\) | |||||||
\(854\) | −6.05689 | − | 4.40059i | −0.207262 | − | 0.150585i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.39986 | + | 13.5414i | −0.150384 | + | 0.462835i | ||||
\(857\) | 29.7644 | 1.01673 | 0.508365 | − | 0.861141i | \(-0.330250\pi\) | ||||
0.508365 | + | 0.861141i | \(0.330250\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.2611 | 1.13485 | 0.567427 | − | 0.823424i | \(-0.307939\pi\) | ||||
0.567427 | + | 0.823424i | \(0.307939\pi\) | |||||||
\(860\) | 0.451787 | − | 1.39046i | 0.0154058 | − | 0.0474142i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 17.5442 | + | 12.7466i | 0.597558 | + | 0.434151i | ||||
\(863\) | 5.73772 | + | 17.6589i | 0.195314 | + | 0.601116i | 0.999973 | + | 0.00737787i | \(0.00234847\pi\) |
−0.804658 | + | 0.593738i | \(0.797652\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.86539 | − | 1.35529i | −0.0634253 | − | 0.0460812i | ||||
\(866\) | 18.5850 | − | 13.5028i | 0.631544 | − | 0.458844i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −9.61454 | −0.326339 | ||||||||
\(869\) | −13.0768 | − | 7.39477i | −0.443599 | − | 0.250850i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.56565 | − | 7.89627i | 0.0869339 | − | 0.267555i | ||||
\(872\) | 11.5311 | − | 8.37782i | 0.390491 | − | 0.283709i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.72992 | + | 8.40184i | 0.0923411 | + | 0.284197i | ||||
\(875\) | 0.684207 | + | 2.10577i | 0.0231304 | + | 0.0711881i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.1965 | − | 13.2205i | 0.614452 | − | 0.446426i | −0.236527 | − | 0.971625i | \(-0.576009\pi\) |
0.850979 | + | 0.525199i | \(0.176009\pi\) | |||||||
\(878\) | −8.08834 | + | 24.8934i | −0.272968 | + | 0.840110i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.226122 | − | 0.495898i | −0.00762259 | − | 0.0167167i | ||||
\(881\) | −7.06565 | −0.238048 | −0.119024 | − | 0.992891i | \(-0.537977\pi\) | ||||
−0.119024 | + | 0.992891i | \(0.537977\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.1304 | − | 11.7194i | 0.542830 | − | 0.394389i | −0.282305 | − | 0.959325i | \(-0.591099\pi\) |
0.825135 | + | 0.564936i | \(0.191099\pi\) | |||||||
\(884\) | 31.9541 | + | 23.2160i | 1.07473 | + | 0.780839i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.48105 | − | 7.63590i | −0.0833527 | − | 0.256533i | ||||
\(887\) | 5.62656 | + | 4.08793i | 0.188921 | + | 0.137259i | 0.678226 | − | 0.734854i | \(-0.262749\pi\) |
−0.489304 | + | 0.872113i | \(0.662749\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.617194 | + | 1.89953i | −0.0207000 | + | 0.0637081i | ||||
\(890\) | −1.37045 | −0.0459376 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.998136 | −0.0334201 | ||||||||
\(893\) | −5.44574 | + | 16.7603i | −0.182235 | + | 0.560861i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.21414 | − | 3.06175i | −0.140863 | − | 0.102343i | ||||
\(896\) | 2.87938 | + | 8.86181i | 0.0961933 | + | 0.296052i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.73468 | − | 1.26032i | −0.0578872 | − | 0.0420575i | ||||
\(899\) | 21.0354 | − | 15.2831i | 0.701570 | − | 0.509721i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.44650 | 0.248079 | ||||||||
\(902\) | 3.42822 | − | 0.391342i | 0.114147 | − | 0.0130303i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13.4575 | + | 41.4179i | −0.447590 | + | 1.37754i | ||||
\(905\) | 2.46916 | − | 1.79395i | 0.0820776 | − | 0.0596329i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.24340 | − | 22.2929i | −0.240513 | − | 0.740224i | −0.996342 | − | 0.0854543i | \(-0.972766\pi\) |
0.755829 | − | 0.654769i | \(-0.227234\pi\) | |||||||
\(908\) | −2.29489 | − | 7.06294i | −0.0761586 | − | 0.234392i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.913888 | − | 0.663978i | 0.0302951 | − | 0.0220107i | ||||
\(911\) | −14.4650 | + | 44.5186i | −0.479246 | + | 1.47497i | 0.360899 | + | 0.932605i | \(0.382470\pi\) |
−0.840145 | + | 0.542362i | \(0.817530\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 37.1825 | − | 4.24450i | 1.23056 | − | 0.140473i | ||||
\(914\) | −31.3563 | −1.03718 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.46078 | + | 5.42058i | −0.246511 | + | 0.179101i | ||||
\(917\) | −1.10843 | − | 0.805321i | −0.0366036 | − | 0.0265940i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.28402 | + | 10.1072i | 0.108330 | + | 0.333405i | 0.990498 | − | 0.137530i | \(-0.0439165\pi\) |
−0.882168 | + | 0.470935i | \(0.843916\pi\) | |||||||
\(920\) | 1.85248 | + | 1.34590i | 0.0610744 | + | 0.0443732i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8.22278 | − | 25.3071i | 0.270803 | − | 0.833445i | ||||
\(923\) | 60.7848 | 2.00075 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 27.9876 | 0.920228 | ||||||||
\(926\) | 0.169945 | − | 0.523036i | 0.00558473 | − | 0.0171880i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −17.8739 | − | 12.9861i | −0.586738 | − | 0.426290i | ||||
\(929\) | 11.3319 | + | 34.8762i | 0.371789 | + | 1.14425i | 0.945619 | + | 0.325275i | \(0.105457\pi\) |
−0.573830 | + | 0.818974i | \(0.694543\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.35829 | − | 1.71340i | −0.0772898 | − | 0.0561543i | ||||
\(932\) | 10.7900 | − | 7.83938i | 0.353438 | − | 0.256787i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 22.2302 | 0.727393 | ||||||||
\(935\) | −1.32721 | − | 2.91064i | −0.0434043 | − | 0.0951880i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.4278 | + | 38.2490i | −0.406000 | + | 1.24954i | 0.514057 | + | 0.857756i | \(0.328142\pi\) |
−0.920057 | + | 0.391784i | \(0.871858\pi\) | |||||||
\(938\) | 0.799801 | − | 0.581090i | 0.0261144 | − | 0.0189732i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.580114 | + | 1.78541i | 0.0189212 | + | 0.0582336i | ||||
\(941\) | −7.69751 | − | 23.6905i | −0.250932 | − | 0.772288i | −0.994604 | − | 0.103744i | \(-0.966918\pi\) |
0.743672 | − | 0.668544i | \(-0.233082\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.21975 | − | 3.06583i | 0.137414 | − | 0.0998371i | ||||
\(944\) | 2.17555 | − | 6.69565i | 0.0708081 | − | 0.217925i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.5680 | − | 5.97609i | −0.343595 | − | 0.194299i | ||||
\(947\) | 32.2061 | 1.04656 | 0.523279 | − | 0.852161i | \(-0.324708\pi\) | ||||
0.523279 | + | 0.852161i | \(0.324708\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −29.5246 | + | 21.4508i | −0.958408 | + | 0.696324i | ||||
\(950\) | 9.07688 | + | 6.59474i | 0.294493 | + | 0.213962i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.53615 | + | 10.8831i | 0.114607 | + | 0.352725i | ||||
\(953\) | 36.4552 | + | 26.4863i | 1.18090 | + | 0.857975i | 0.992273 | − | 0.124074i | \(-0.0395960\pi\) |
0.188628 | + | 0.982049i | \(0.439596\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.826849 | − | 2.54478i | 0.0267562 | − | 0.0823471i | ||||
\(956\) | 37.4650 | 1.21170 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.96296 | 0.128038 | ||||||||
\(959\) | 0.772308 | − | 2.37692i | 0.0249391 | − | 0.0767547i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.3216 | − | 9.67867i | −0.429727 | − | 0.312215i | ||||
\(962\) | −8.86901 | − | 27.2960i | −0.285948 | − | 0.880059i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 21.3000 | + | 15.4754i | 0.686028 | + | 0.498428i | ||||
\(965\) | −2.85941 | + | 2.07748i | −0.0920476 | + | 0.0668765i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.81387 | 0.0583300 | 0.0291650 | − | 0.999575i | \(-0.490715\pi\) | ||||
0.0291650 | + | 0.999575i | \(0.490715\pi\) | |||||||
\(968\) | −28.2925 | + | 6.54464i | −0.909355 | + | 0.210353i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.484029 | + | 1.48969i | −0.0155412 | + | 0.0478310i | ||||
\(971\) | 18.6510 | − | 13.5507i | 0.598539 | − | 0.434864i | −0.246821 | − | 0.969061i | \(-0.579386\pi\) |
0.845360 | + | 0.534197i | \(0.179386\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.47172 | + | 4.52950i | 0.0471813 | + | 0.145209i | ||||
\(974\) | 7.01266 | + | 21.5827i | 0.224700 | + | 0.691555i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.75325 | − | 4.17998i | 0.184157 | − | 0.133798i | ||||
\(977\) | 2.19232 | − | 6.74726i | 0.0701385 | − | 0.215864i | −0.909843 | − | 0.414953i | \(-0.863798\pi\) |
0.979981 | + | 0.199089i | \(0.0637981\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.23244 | − | 25.7466i | 0.167229 | − | 0.822863i | ||||
\(980\) | −0.310525 | −0.00991935 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 18.9605 | − | 13.7756i | 0.605053 | − | 0.439597i | ||||
\(983\) | 31.0260 | + | 22.5417i | 0.989576 | + | 0.718969i | 0.959828 | − | 0.280589i | \(-0.0905297\pi\) |
0.0297474 | + | 0.999557i | \(0.490530\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.846005 | − | 2.60374i | −0.0269560 | − | 0.0829619i | ||||
\(986\) | −10.2896 | − | 7.47586i | −0.327689 | − | 0.238080i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.20806 | + | 25.2618i | −0.261133 | + | 0.803685i | ||||
\(989\) | −18.3524 | −0.583572 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.2722 | 0.643967 | 0.321984 | − | 0.946745i | \(-0.395650\pi\) | ||||
0.321984 | + | 0.946745i | \(0.395650\pi\) | |||||||
\(992\) | −12.4634 | + | 38.3583i | −0.395712 | + | 1.21788i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.85546 | + | 4.25424i | 0.185724 | + | 0.134936i | ||||
\(995\) | 1.04940 | + | 3.22971i | 0.0332681 | + | 0.102389i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.4675 | − | 9.05819i | −0.394851 | − | 0.286876i | 0.372590 | − | 0.927996i | \(-0.378470\pi\) |
−0.767440 | + | 0.641120i | \(0.778470\pi\) | |||||||
\(998\) | −3.74319 | + | 2.71959i | −0.118489 | + | 0.0860871i | ||||
\(999\) | 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 | 693.2.m.g.64.2 | 8 | ||
3.2 | odd | 2 | 77.2.f.a.64.1 | ✓ | 8 | ||
11.4 | even | 5 | 7623.2.a.ch.1.3 | 4 | |||
11.5 | even | 5 | inner | 693.2.m.g.379.2 | 8 | ||
11.7 | odd | 10 | 7623.2.a.co.1.2 | 4 | |||
21.2 | odd | 6 | 539.2.q.c.361.2 | 16 | |||
21.5 | even | 6 | 539.2.q.b.361.2 | 16 | |||
21.11 | odd | 6 | 539.2.q.c.471.1 | 16 | |||
21.17 | even | 6 | 539.2.q.b.471.1 | 16 | |||
21.20 | even | 2 | 539.2.f.d.295.1 | 8 | |||
33.2 | even | 10 | 847.2.f.s.729.1 | 8 | |||
33.5 | odd | 10 | 77.2.f.a.71.1 | yes | 8 | ||
33.8 | even | 10 | 847.2.f.s.323.1 | 8 | |||
33.14 | odd | 10 | 847.2.f.p.323.2 | 8 | |||
33.17 | even | 10 | 847.2.f.q.148.2 | 8 | |||
33.20 | odd | 10 | 847.2.f.p.729.2 | 8 | |||
33.26 | odd | 10 | 847.2.a.l.1.2 | 4 | |||
33.29 | even | 10 | 847.2.a.k.1.3 | 4 | |||
33.32 | even | 2 | 847.2.f.q.372.2 | 8 | |||
231.5 | even | 30 | 539.2.q.b.214.1 | 16 | |||
231.38 | even | 30 | 539.2.q.b.324.2 | 16 | |||
231.62 | odd | 10 | 5929.2.a.bb.1.3 | 4 | |||
231.104 | even | 10 | 539.2.f.d.148.1 | 8 | |||
231.125 | even | 10 | 5929.2.a.bi.1.2 | 4 | |||
231.137 | odd | 30 | 539.2.q.c.324.2 | 16 | |||
231.170 | odd | 30 | 539.2.q.c.214.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.a.64.1 | ✓ | 8 | 3.2 | odd | 2 | ||
77.2.f.a.71.1 | yes | 8 | 33.5 | odd | 10 | ||
539.2.f.d.148.1 | 8 | 231.104 | even | 10 | |||
539.2.f.d.295.1 | 8 | 21.20 | even | 2 | |||
539.2.q.b.214.1 | 16 | 231.5 | even | 30 | |||
539.2.q.b.324.2 | 16 | 231.38 | even | 30 | |||
539.2.q.b.361.2 | 16 | 21.5 | even | 6 | |||
539.2.q.b.471.1 | 16 | 21.17 | even | 6 | |||
539.2.q.c.214.1 | 16 | 231.170 | odd | 30 | |||
539.2.q.c.324.2 | 16 | 231.137 | odd | 30 | |||
539.2.q.c.361.2 | 16 | 21.2 | odd | 6 | |||
539.2.q.c.471.1 | 16 | 21.11 | odd | 6 | |||
693.2.m.g.64.2 | 8 | 1.1 | even | 1 | trivial | ||
693.2.m.g.379.2 | 8 | 11.5 | even | 5 | inner | ||
847.2.a.k.1.3 | 4 | 33.29 | even | 10 | |||
847.2.a.l.1.2 | 4 | 33.26 | odd | 10 | |||
847.2.f.p.323.2 | 8 | 33.14 | odd | 10 | |||
847.2.f.p.729.2 | 8 | 33.20 | odd | 10 | |||
847.2.f.q.148.2 | 8 | 33.17 | even | 10 | |||
847.2.f.q.372.2 | 8 | 33.32 | even | 2 | |||
847.2.f.s.323.1 | 8 | 33.8 | even | 10 | |||
847.2.f.s.729.1 | 8 | 33.2 | even | 10 | |||
5929.2.a.bb.1.3 | 4 | 231.62 | odd | 10 | |||
5929.2.a.bi.1.2 | 4 | 231.125 | even | 10 | |||
7623.2.a.ch.1.3 | 4 | 11.4 | even | 5 | |||
7623.2.a.co.1.2 | 4 | 11.7 | odd | 10 |