Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [539,2,Mod(148,539)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(539, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("539.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 539 = 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 539.f (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: | \(4.30393666895\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 295.1 | ||
Root | \(-0.628998 - 0.456994i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 539.295 |
Dual form | 539.2.f.d.148.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/539\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(442\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
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 | −0.999363 | − | 0.0356845i | \(-0.988639\pi\) |
0.829477 | + | 0.558542i | \(0.188639\pi\) | |||||||
\(3\) | 0.500000 | − | 0.363271i | 0.288675 | − | 0.209735i | −0.434017 | − | 0.900905i | \(-0.642904\pi\) |
0.722692 | + | 0.691170i | \(0.242904\pi\) | |||||||
\(4\) | 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 | \(0.884156\pi\) | |||||||
\(6\) | 0.148486 | + | 0.456994i | 0.0606193 | + | 0.186567i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.13577 | + | 1.55173i | −0.755110 | + | 0.548620i | ||||
\(9\) | −0.809017 | + | 2.48990i | −0.269672 | + | 0.829966i | ||||
\(10\) | −0.173002 | −0.0547082 | ||||||||
\(11\) | 0.660531 | − | 3.25018i | 0.199158 | − | 0.979967i | ||||
\(12\) | 0.862478 | 0.248976 | ||||||||
\(13\) | −2.01774 | + | 6.20997i | −0.559620 | + | 1.72233i | 0.123798 | + | 0.992307i | \(0.460493\pi\) |
−0.683418 | + | 0.730027i | \(0.739507\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.111258 | + | 0.0808336i | 0.0287267 | + | 0.0208711i | ||||
\(16\) | 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 | \(0.723822\pi\) | |||||||
\(18\) | −1.64674 | − | 1.19643i | −0.388140 | − | 0.282000i | ||||
\(19\) | 2.35829 | − | 1.71340i | 0.541029 | − | 0.393080i | −0.283438 | − | 0.958991i | \(-0.591475\pi\) |
0.824467 | + | 0.565910i | \(0.191475\pi\) | |||||||
\(20\) | −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 | \(-0.633213\pi\) | ||||
−0.406390 | + | 0.913700i | \(0.633213\pi\) | |||||||
\(24\) | −0.504188 | + | 1.55173i | −0.102917 | + | 0.316746i | ||||
\(25\) | 4.00503 | − | 2.90982i | 0.801006 | − | 0.581965i | ||||
\(26\) | −4.10707 | − | 2.98396i | −0.805463 | − | 0.585203i | ||||
\(27\) | 1.07295 | + | 3.30220i | 0.206489 | + | 0.635508i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.05322 | + | 2.21829i | 0.566969 | + | 0.411927i | 0.834003 | − | 0.551760i | \(-0.186044\pi\) |
−0.267034 | + | 0.963687i | \(0.586044\pi\) | |||||||
\(30\) | −0.0865012 | + | 0.0628468i | −0.0157929 | + | 0.0114742i | ||||
\(31\) | 2.12900 | − | 6.55238i | 0.382379 | − | 1.17684i | −0.555984 | − | 0.831193i | \(-0.687659\pi\) |
0.938364 | − | 0.345650i | \(-0.112341\pi\) | |||||||
\(32\) | −5.85410 | −1.03487 | ||||||||
\(33\) | −0.850433 | − | 1.86504i | −0.148041 | − | 0.324662i | ||||
\(34\) | −3.37009 | −0.577966 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.95576 | + | 2.14748i | −0.492626 | + | 0.357914i | ||||
\(37\) | 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 | ||||
\(39\) | 1.24703 | + | 3.83797i | 0.199685 | + | 0.614567i | ||||
\(40\) | −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 | ||||
\(45\) | −0.582554 | −0.0868420 | ||||||||
\(46\) | 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 | \(0.154654\pi\) | |||||||
\(48\) | 0.369254 | + | 0.268279i | 0.0532972 | + | 0.0387227i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.18938 | + | 3.66055i | 0.168204 | + | 0.517679i | ||||
\(51\) | 2.16731 | + | 1.57464i | 0.303484 | + | 0.220494i | ||||
\(52\) | −7.37184 | + | 5.35596i | −1.02229 | + | 0.742738i | ||||
\(53\) | −0.530865 | + | 1.63383i | −0.0729199 | + | 0.224424i | −0.980873 | − | 0.194646i | \(-0.937644\pi\) |
0.907954 | + | 0.419071i | \(0.137644\pi\) | |||||||
\(54\) | −2.69953 | −0.367360 | ||||||||
\(55\) | 0.733239 | − | 0.0837016i | 0.0988700 | − | 0.0112863i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.556717 | − | 1.71340i | 0.0737389 | − | 0.226945i | ||||
\(58\) | −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 | \(0.913090\pi\) | |||||||
\(60\) | 0.0593050 | + | 0.182522i | 0.00765624 | + | 0.0235635i | ||||
\(61\) | 2.97566 | + | 9.15813i | 0.380994 | + | 1.17258i | 0.939345 | + | 0.342974i | \(0.111434\pi\) |
−0.558351 | + | 0.829605i | \(0.688566\pi\) | |||||||
\(62\) | 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 | ||||||||
\(66\) | 1.58339 | − | 0.180749i | 0.194902 | − | 0.0222487i | ||||
\(67\) | 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 | ||||
\(69\) | −1.94898 | + | 1.41602i | −0.234629 | + | 0.170468i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.87670 | − | 8.85357i | −0.341401 | − | 1.05072i | −0.963482 | − | 0.267772i | \(-0.913713\pi\) |
0.622081 | − | 0.782953i | \(-0.286287\pi\) | |||||||
\(72\) | −2.13577 | − | 6.57324i | −0.251703 | − | 0.774663i | ||||
\(73\) | 4.52169 | + | 3.28520i | 0.529223 | + | 0.384503i | 0.820067 | − | 0.572267i | \(-0.193936\pi\) |
−0.290844 | + | 0.956771i | \(0.593936\pi\) | |||||||
\(74\) | −3.55605 | + | 2.58362i | −0.413382 | + | 0.300340i | ||||
\(75\) | 0.945459 | − | 2.90982i | 0.109172 | − | 0.335997i | ||||
\(76\) | 4.06794 | 0.466625 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.13752 | −0.355254 | ||||||||
\(79\) | −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 | ||||
\(81\) | −4.61803 | − | 3.35520i | −0.513115 | − | 0.372800i | ||||
\(82\) | 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 | ||||
\(87\) | 2.33245 | 0.250065 | ||||||||
\(88\) | 3.63267 | + | 7.96663i | 0.387244 | + | 0.849245i | ||||
\(89\) | −7.92157 | −0.839684 | −0.419842 | − | 0.907597i | \(-0.637915\pi\) | ||||
−0.419842 | + | 0.907597i | \(0.637915\pi\) | |||||||
\(90\) | 0.139962 | − | 0.430759i | 0.0147533 | − | 0.0454059i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.40079 | − | 3.19736i | −0.458814 | − | 0.333348i | ||||
\(93\) | −1.31579 | − | 4.04959i | −0.136441 | − | 0.419923i | ||||
\(94\) | 1.45248 | + | 4.47026i | 0.149811 | + | 0.461072i | ||||
\(95\) | 0.524757 | + | 0.381258i | 0.0538389 | + | 0.0391162i | ||||
\(96\) | −2.92705 | + | 2.12663i | −0.298741 | + | 0.217048i | ||||
\(97\) | 2.79781 | − | 8.61078i | 0.284075 | − | 0.874292i | −0.702600 | − | 0.711585i | \(-0.747977\pi\) |
0.986674 | − | 0.162707i | \(-0.0520225\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.55825 | + | 4.27411i | 0.759633 | + | 0.429564i | ||||
\(100\) | 6.90849 | 0.690849 | ||||||||
\(101\) | 5.93627 | − | 18.2700i | 0.590681 | − | 1.81793i | 0.0155316 | − | 0.999879i | \(-0.495056\pi\) |
0.575149 | − | 0.818049i | \(-0.304944\pi\) | |||||||
\(102\) | −1.68505 | + | 1.22426i | −0.166845 | + | 0.121220i | ||||
\(103\) | 13.1371 | + | 9.54464i | 1.29443 | + | 0.940461i | 0.999885 | − | 0.0151755i | \(-0.00483070\pi\) |
0.294549 | + | 0.955636i | \(0.404831\pi\) | |||||||
\(104\) | −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 | −0.356551 | − | 0.934276i | \(-0.616047\pi\) |
0.778369 | + | 0.627807i | \(0.216047\pi\) | |||||||
\(108\) | −1.49732 | + | 4.60828i | −0.144080 | + | 0.443432i | ||||
\(109\) | 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 | ||||
\(111\) | 3.49406 | 0.331642 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.3457 | − | 9.69624i | 1.25546 | − | 0.912145i | 0.256935 | − | 0.966429i | \(-0.417287\pi\) |
0.998526 | + | 0.0542834i | \(0.0172875\pi\) | |||||||
\(114\) | 1.13319 | + | 0.823308i | 0.106133 | + | 0.0771098i | ||||
\(115\) | −0.268028 | − | 0.824906i | −0.0249937 | − | 0.0769228i | ||||
\(116\) | 1.62749 | + | 5.00890i | 0.151109 | + | 0.465065i | ||||
\(117\) | −13.8298 | − | 10.0479i | −1.27857 | − | 0.928932i | ||||
\(118\) | 5.99626 | − | 4.35654i | 0.552001 | − | 0.401052i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.363054 | −0.0331421 | ||||||||
\(121\) | −10.1274 | − | 4.29369i | −0.920673 | − | 0.390336i | ||||
\(122\) | −7.48673 | −0.677816 | ||||||||
\(123\) | 0.255556 | − | 0.786521i | 0.0230427 | − | 0.0709182i | ||||
\(124\) | 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 | ||||
\(129\) | −2.35410 | + | 1.71036i | −0.207267 | + | 0.150588i | ||||
\(130\) | 0.349074 | − | 1.07434i | 0.0306158 | − | 0.0942258i | ||||
\(131\) | −1.37009 | −0.119706 | −0.0598528 | − | 0.998207i | \(-0.519063\pi\) | ||||
−0.0598528 | + | 0.998207i | \(0.519063\pi\) | |||||||
\(132\) | 0.569693 | − | 2.80321i | 0.0495854 | − | 0.243988i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.305497 | + | 0.940223i | −0.0263909 | + | 0.0812229i | ||||
\(135\) | −0.625051 | + | 0.454126i | −0.0537958 | + | 0.0390849i | ||||
\(136\) | −9.25776 | − | 6.72615i | −0.793846 | − | 0.576763i | ||||
\(137\) | 0.772308 | + | 2.37692i | 0.0659827 | + | 0.203074i | 0.978612 | − | 0.205714i | \(-0.0659516\pi\) |
−0.912629 | + | 0.408788i | \(0.865952\pi\) | |||||||
\(138\) | −0.578793 | − | 1.78134i | −0.0492702 | − | 0.151638i | ||||
\(139\) | −3.85302 | − | 2.79938i | −0.326809 | − | 0.237441i | 0.412266 | − | 0.911063i | \(-0.364737\pi\) |
−0.739075 | + | 0.673623i | \(0.764737\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.15459 | − | 3.55348i | 0.0972344 | − | 0.299257i | ||||
\(142\) | 7.23775 | 0.607378 | ||||||||
\(143\) | 18.8508 | + | 10.6599i | 1.57638 | + | 0.891426i | ||||
\(144\) | −1.93344 | −0.161120 | ||||||||
\(145\) | −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 | 0.816880 | − | 0.576807i | \(-0.195702\pi\) |
−0.999909 | + | 0.0135034i | \(0.995702\pi\) | |||||||
\(150\) | 1.92446 | + | 1.39820i | 0.157132 | + | 0.114163i | ||||
\(151\) | −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 | ||||
\(153\) | −11.3482 | −0.917445 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.53304 | 0.123137 | ||||||||
\(156\) | −1.74026 | + | 5.35596i | −0.139332 | + | 0.428820i | ||||
\(157\) | 16.3028 | − | 11.8447i | 1.30111 | − | 0.945311i | 0.301143 | − | 0.953579i | \(-0.402632\pi\) |
0.999966 | + | 0.00826862i | \(0.00263201\pi\) | |||||||
\(158\) | −2.84907 | − | 2.06997i | −0.226660 | − | 0.164678i | ||||
\(159\) | 0.328093 | + | 1.00977i | 0.0260194 | + | 0.0800796i | ||||
\(160\) | −0.402535 | − | 1.23887i | −0.0318232 | − | 0.0979416i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 3.59045 | − | 2.60861i | 0.282092 | − | 0.204952i | ||||
\(163\) | 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 | ||||||||
\(165\) | 0.336213 | − | 0.308216i | 0.0261742 | − | 0.0239945i | ||||
\(166\) | 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 | ||||
\(171\) | 2.35829 | + | 7.25807i | 0.180343 | + | 0.555038i | ||||
\(172\) | −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 | \(0.428878\pi\) | |||||||
\(174\) | −0.560385 | + | 1.72469i | −0.0424827 | + | 0.130748i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.43355 | − | 0.277797i | 0.183436 | − | 0.0209398i | ||||
\(177\) | −5.89174 | −0.442851 | ||||||||
\(178\) | 1.90320 | − | 5.85746i | 0.142651 | − | 0.439035i | ||||
\(179\) | 18.9386 | − | 13.7597i | 1.41554 | − | 1.02845i | 0.423051 | − | 0.906106i | \(-0.360959\pi\) |
0.992488 | − | 0.122343i | \(-0.0390408\pi\) | |||||||
\(180\) | −0.657702 | − | 0.477849i | −0.0490222 | − | 0.0356167i | ||||
\(181\) | 4.23851 | + | 13.0448i | 0.315046 | + | 0.969611i | 0.975736 | + | 0.218952i | \(0.0702639\pi\) |
−0.660690 | + | 0.750659i | \(0.729736\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.81471 | + | 3.49809i | 0.355914 | + | 0.258587i | ||||
\(184\) | 8.32516 | − | 6.04858i | 0.613739 | − | 0.445907i | ||||
\(185\) | −0.388742 | + | 1.19643i | −0.0285809 | + | 0.0879629i | ||||
\(186\) | 3.31052 | 0.242739 | ||||||||
\(187\) | 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 | 0.881207 | − | 0.472731i | \(-0.156732\pi\) |
−0.177286 | + | 0.984159i | \(0.556732\pi\) | |||||||
\(192\) | −0.587169 | − | 1.80712i | −0.0423753 | − | 0.130418i | ||||
\(193\) | 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 | ||||
\(195\) | −0.726463 | + | 0.527806i | −0.0520231 | + | 0.0377970i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.3035 | 0.876590 | 0.438295 | − | 0.898831i | \(-0.355582\pi\) | ||||
0.438295 | + | 0.898831i | \(0.355582\pi\) | |||||||
\(198\) | −4.97632 | + | 4.56193i | −0.353652 | + | 0.324202i | ||||
\(199\) | −15.2615 | −1.08186 | −0.540929 | − | 0.841068i | \(-0.681927\pi\) | ||||
−0.540929 | + | 0.841068i | \(0.681927\pi\) | |||||||
\(200\) | −4.03857 | + | 12.4294i | −0.285570 | + | 0.878895i | ||||
\(201\) | 0.635774 | − | 0.461917i | 0.0448440 | − | 0.0325811i | ||||
\(202\) | 12.0832 | + | 8.77892i | 0.850168 | + | 0.617683i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.15526 | + | 3.55553i | 0.0808845 | + | 0.248937i | ||||
\(205\) | 0.240885 | + | 0.175013i | 0.0168242 | + | 0.0122235i | ||||
\(206\) | −10.2139 | + | 7.42080i | −0.711633 | + | 0.517032i | ||||
\(207\) | 3.15351 | − | 9.70552i | 0.219184 | − | 0.674580i | ||||
\(208\) | −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 | ||||
\(213\) | −4.65459 | − | 3.38176i | −0.318928 | − | 0.231714i | ||||
\(214\) | 1.29579 | + | 3.98802i | 0.0885781 | + | 0.272615i | ||||
\(215\) | −0.323742 | − | 0.996374i | −0.0220790 | − | 0.0679521i | ||||
\(216\) | −7.41570 | − | 5.38782i | −0.504574 | − | 0.366595i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.29714 | + | 3.99220i | −0.0878537 | + | 0.270386i | ||||
\(219\) | 3.45426 | 0.233417 | ||||||||
\(220\) | 0.896483 | + | 0.506952i | 0.0604409 | + | 0.0341787i | ||||
\(221\) | −28.3031 | −1.90387 | ||||||||
\(222\) | −0.839469 | + | 2.58362i | −0.0563415 | + | 0.173401i | ||||
\(223\) | 0.578645 | − | 0.420410i | 0.0387489 | − | 0.0281527i | −0.568242 | − | 0.822861i | \(-0.692376\pi\) |
0.606991 | + | 0.794709i | \(0.292376\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.00503 | + | 12.3262i | 0.267002 | + | 0.821747i | ||||
\(226\) | 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 | \(0.756511\pi\) | |||||||
\(228\) | 2.03397 | − | 1.47777i | 0.134703 | − | 0.0978675i | ||||
\(229\) | 2.04208 | − | 6.28489i | 0.134945 | − | 0.415317i | −0.860637 | − | 0.509219i | \(-0.829934\pi\) |
0.995581 | + | 0.0939024i | \(0.0299341\pi\) | |||||||
\(230\) | 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 | \(0.201352\pi\) |
−0.999991 | + | 0.00424788i | \(0.998648\pi\) | |||||||
\(234\) | 10.7524 | − | 7.81211i | 0.702910 | − | 0.510694i | ||||
\(235\) | 1.08831 | + | 0.790705i | 0.0709936 | + | 0.0515799i | ||||
\(236\) | −4.11102 | − | 12.6524i | −0.267604 | − | 0.823602i | ||||
\(237\) | 0.865066 | + | 2.66240i | 0.0561921 | + | 0.172941i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.7194 | + | 15.7801i | −1.40491 | + | 1.02073i | −0.410872 | + | 0.911693i | \(0.634776\pi\) |
−0.994038 | + | 0.109034i | \(0.965224\pi\) | |||||||
\(240\) | −0.0313842 | + | 0.0965905i | −0.00202584 | + | 0.00623489i | ||||
\(241\) | −18.8663 | −1.21529 | −0.607643 | − | 0.794210i | \(-0.707885\pi\) | ||||
−0.607643 | + | 0.794210i | \(0.707885\pi\) | |||||||
\(242\) | 5.60806 | − | 6.45693i | 0.360500 | − | 0.415067i | ||||
\(243\) | −13.9443 | −0.894525 | ||||||||
\(244\) | −4.15258 | + | 12.7803i | −0.265842 | + | 0.818177i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.520180 | + | 0.377933i | 0.0331654 | + | 0.0240961i | ||||
\(247\) | 5.88173 | + | 18.1021i | 0.374245 | + | 1.15181i | ||||
\(248\) | 5.62047 | + | 17.2980i | 0.356900 | + | 1.09843i | ||||
\(249\) | −5.64188 | − | 4.09907i | −0.357540 | − | 0.259768i | ||||
\(250\) | −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 | ||||||||
\(255\) | −0.184207 | + | 0.566931i | −0.0115355 | + | 0.0355026i | ||||
\(256\) | 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 | \(0.876911\pi\) | |||||||
\(258\) | −0.699104 | − | 2.15162i | −0.0435243 | − | 0.133954i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.64035 | − | 1.19178i | −0.101730 | − | 0.0739114i | ||||
\(261\) | −7.99343 | + | 5.80757i | −0.494781 | + | 0.359480i | ||||
\(262\) | 0.329173 | − | 1.01309i | 0.0203364 | − | 0.0625889i | ||||
\(263\) | −8.18034 | −0.504421 | −0.252211 | − | 0.967672i | \(-0.581158\pi\) | ||||
−0.252211 | + | 0.967672i | \(0.581158\pi\) | |||||||
\(264\) | 4.71038 | + | 2.66367i | 0.289904 | + | 0.163938i | ||||
\(265\) | −0.382263 | −0.0234822 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.96078 | + | 2.87768i | −0.242396 | + | 0.176111i | ||||
\(268\) | 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 | \(0.839006\pi\) | |||||||
\(270\) | −0.185623 | − | 0.571288i | −0.0112966 | − | 0.0347675i | ||||
\(271\) | 6.36444 | + | 4.62403i | 0.386612 | + | 0.280890i | 0.764066 | − | 0.645138i | \(-0.223200\pi\) |
−0.377454 | + | 0.926028i | \(0.623200\pi\) | |||||||
\(272\) | −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 | ||||
\(276\) | −3.36190 | −0.202363 | ||||||||
\(277\) | 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 | ||||
\(279\) | 14.5924 | + | 10.6020i | 0.873622 | + | 0.634724i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.53723 | + | 20.1195i | 0.389978 | + | 1.20023i | 0.932804 | + | 0.360384i | \(0.117354\pi\) |
−0.542826 | + | 0.839846i | \(0.682646\pi\) | |||||||
\(282\) | 2.35015 | + | 1.70749i | 0.139950 | + | 0.101679i | ||||
\(283\) | −20.2281 | + | 14.6966i | −1.20244 | + | 0.873623i | −0.994522 | − | 0.104524i | \(-0.966668\pi\) |
−0.207916 | + | 0.978147i | \(0.566668\pi\) | |||||||
\(284\) | 4.01448 | − | 12.3553i | 0.238216 | − | 0.733153i | ||||
\(285\) | 0.400878 | 0.0237460 | ||||||||
\(286\) | −12.4113 | + | 11.3777i | −0.733894 | + | 0.672780i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 4.73607 | − | 14.5761i | 0.279075 | − | 0.858906i | ||||
\(289\) | −1.44723 | + | 1.05147i | −0.0851312 | + | 0.0618515i | ||||
\(290\) | −0.528215 | − | 0.383770i | −0.0310178 | − | 0.0225358i | ||||
\(291\) | −1.72914 | − | 5.32176i | −0.101364 | − | 0.311967i | ||||
\(292\) | 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 | ||||||||
\(297\) | 11.4415 | − | 1.30608i | 0.663901 | − | 0.0757864i | ||||
\(298\) | 5.62110 | 0.325621 | ||||||||
\(299\) | 7.86507 | − | 24.2062i | 0.454849 | − | 1.39988i | ||||
\(300\) | 3.45425 | − | 2.50966i | 0.199431 | − | 0.144895i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.95561 | − | 6.01874i | −0.112533 | − | 0.346339i | ||||
\(303\) | −3.66881 | − | 11.2915i | −0.210768 | − | 0.648677i | ||||
\(304\) | 1.74162 | + | 1.26536i | 0.0998885 | + | 0.0725732i | ||||
\(305\) | −1.73348 | + | 1.25945i | −0.0992588 | + | 0.0721157i | ||||
\(306\) | 2.72646 | − | 8.39119i | 0.155862 | − | 0.479692i | ||||
\(307\) | 8.03578 | 0.458626 | 0.229313 | − | 0.973353i | \(-0.426352\pi\) | ||||
0.229313 | + | 0.973353i | \(0.426352\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.0358 | 0.570918 | ||||||||
\(310\) | −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 | \(0.298764\pi\) | |||||||
\(312\) | −8.61887 | − | 6.26198i | −0.487948 | − | 0.354515i | ||||
\(313\) | 4.72485 | + | 14.5416i | 0.267064 | + | 0.821939i | 0.991211 | + | 0.132293i | \(0.0422340\pi\) |
−0.724146 | + | 0.689646i | \(0.757766\pi\) | |||||||
\(314\) | 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 | \(0.477217\pi\) |
−0.644136 | + | 0.764911i | \(0.722783\pi\) | |||||||
\(318\) | −0.825478 | −0.0462905 | ||||||||
\(319\) | 9.22661 | − | 8.45828i | 0.516591 | − | 0.473573i | ||||
\(320\) | 0.684115 | 0.0382432 | ||||||||
\(321\) | 1.03004 | − | 3.17014i | 0.0574912 | − | 0.176940i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.2223 | + | 7.42692i | 0.568783 | + | 0.413245i | ||||
\(324\) | −2.46160 | − | 7.57602i | −0.136756 | − | 0.420890i | ||||
\(325\) | 9.98880 | + | 30.7424i | 0.554079 | + | 1.70528i | ||||
\(326\) | 4.67628 | + | 3.39752i | 0.258995 | + | 0.188171i | ||||
\(327\) | 2.69951 | − | 1.96131i | 0.149283 | − | 0.108461i | ||||
\(328\) | −1.09162 | + | 3.35966i | −0.0602747 | + | 0.185506i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.147127 | + | 0.322657i | 0.00809908 | + | 0.0177617i | ||||
\(331\) | 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 | ||||
\(333\) | −11.9743 | + | 8.69986i | −0.656190 | + | 0.476750i | ||||
\(334\) | 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 | ||||
\(339\) | 3.15050 | − | 9.69624i | 0.171112 | − | 0.526627i | ||||
\(340\) | −1.34600 | −0.0729974 | ||||||||
\(341\) | −19.8902 | − | 11.2477i | −1.07711 | − | 0.609096i | ||||
\(342\) | −5.93344 | −0.320844 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 10.0557 | − | 7.30586i | 0.542165 | − | 0.393906i | ||||
\(345\) | −0.433679 | − | 0.315086i | −0.0233485 | − | 0.0169637i | ||||
\(346\) | −2.48958 | − | 7.66214i | −0.133841 | − | 0.411919i | ||||
\(347\) | 2.69791 | + | 8.30331i | 0.144831 | + | 0.445745i | 0.996989 | − | 0.0775398i | \(-0.0247065\pi\) |
−0.852158 | + | 0.523285i | \(0.824706\pi\) | |||||||
\(348\) | 2.63333 | + | 1.91323i | 0.141162 | + | 0.102560i | ||||
\(349\) | 14.9401 | − | 10.8546i | 0.799724 | − | 0.581034i | −0.111109 | − | 0.993808i | \(-0.535440\pi\) |
0.910833 | + | 0.412774i | \(0.135440\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −22.6715 | −1.21011 | ||||||||
\(352\) | −3.86681 | + | 19.0269i | −0.206102 | + | 1.01414i | ||||
\(353\) | 23.4857 | 1.25002 | 0.625009 | − | 0.780618i | \(-0.285095\pi\) | ||||
0.625009 | + | 0.780618i | \(0.285095\pi\) | |||||||
\(354\) | 1.41553 | − | 4.35654i | 0.0752343 | − | 0.231547i | ||||
\(355\) | 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 | 0.222865 | − | 0.974849i | \(-0.428459\pi\) |
−0.858267 | + | 0.513203i | \(0.828459\pi\) | |||||||
\(360\) | 1.24420 | − | 0.903967i | 0.0655753 | − | 0.0476432i | ||||
\(361\) | −3.24552 | + | 9.98870i | −0.170817 | + | 0.525721i | ||||
\(362\) | −10.6641 | −0.560490 | ||||||||
\(363\) | −6.62347 | + | 1.53215i | −0.347642 | + | 0.0804168i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.384314 | + | 1.18280i | −0.0201159 | + | 0.0619104i | ||||
\(366\) | −3.74336 | + | 2.71971i | −0.195669 | + | 0.142162i | ||||
\(367\) | −27.6894 | − | 20.1175i | −1.44537 | − | 1.05012i | −0.986885 | − | 0.161424i | \(-0.948391\pi\) |
−0.458487 | − | 0.888701i | \(-0.651609\pi\) | |||||||
\(368\) | −0.889558 | − | 2.73778i | −0.0463714 | − | 0.142717i | ||||
\(369\) | 1.08255 | + | 3.33176i | 0.0563555 | + | 0.173444i | ||||
\(370\) | −0.791277 | − | 0.574896i | −0.0411365 | − | 0.0298874i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.83621 | − | 5.65128i | 0.0952032 | − | 0.293005i | ||||
\(373\) | 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 | ||||
\(375\) | 1.36841 | 0.0706646 | ||||||||
\(376\) | −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 | ||||
\(381\) | 0.998641 | + | 0.725555i | 0.0511619 | + | 0.0371713i | ||||
\(382\) | −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 | \(0.135785\pi\) | |||||||
\(384\) | −5.75876 | −0.293875 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12.3495 | −0.628573 | ||||||||
\(387\) | 3.80902 | − | 11.7229i | 0.193623 | − | 0.595911i | ||||
\(388\) | 10.2218 | − | 7.42661i | 0.518936 | − | 0.377029i | ||||
\(389\) | −8.49145 | − | 6.16940i | −0.430533 | − | 0.312801i | 0.351329 | − | 0.936252i | \(-0.385730\pi\) |
−0.781862 | + | 0.623451i | \(0.785730\pi\) | |||||||
\(390\) | −0.215740 | − | 0.663978i | −0.0109244 | − | 0.0336218i | ||||
\(391\) | −5.22119 | − | 16.0692i | −0.264047 | − | 0.812654i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.685047 | + | 0.497716i | −0.0345560 | + | 0.0251064i | ||||
\(394\) | −2.95600 | + | 9.09762i | −0.148921 | + | 0.458331i | ||||
\(395\) | −1.00789 | −0.0507127 | ||||||||
\(396\) | 5.02734 | + | 11.0252i | 0.252634 | + | 0.554038i | ||||
\(397\) | −11.3888 | −0.571589 | −0.285794 | − | 0.958291i | \(-0.592257\pi\) | ||||
−0.285794 | + | 0.958291i | \(0.592257\pi\) | |||||||
\(398\) | 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 | 0.907958 | − | 0.419061i | \(-0.137641\pi\) |
−0.980871 | + | 0.194657i | \(0.937641\pi\) | |||||||
\(402\) | 0.188807 | + | 0.581090i | 0.00941686 | + | 0.0289821i | ||||
\(403\) | 36.3943 | + | 26.4420i | 1.81293 | + | 1.31717i | ||||
\(404\) | 21.6882 | − | 15.7574i | 1.07903 | − | 0.783961i | ||||
\(405\) | 0.392503 | − | 1.20800i | 0.0195036 | − | 0.0600260i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.8217 | − | 12.6707i | 0.685114 | − | 0.628062i | ||||
\(408\) | −7.07230 | −0.350131 | ||||||||
\(409\) | −0.761863 | + | 2.34477i | −0.0376717 | + | 0.115942i | −0.968124 | − | 0.250472i | \(-0.919414\pi\) |
0.930452 | + | 0.366413i | \(0.119414\pi\) | |||||||
\(410\) | −0.187285 | + | 0.136070i | −0.00924932 | + | 0.00672003i | ||||
\(411\) | 1.24962 | + | 0.907902i | 0.0616392 | + | 0.0447835i | ||||
\(412\) | 7.00259 | + | 21.5518i | 0.344993 | + | 1.06178i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 6.41892 | + | 4.66362i | 0.315472 | + | 0.229204i | ||||
\(415\) | 2.03129 | − | 1.47582i | 0.0997122 | − | 0.0724452i | ||||
\(416\) | 11.8121 | − | 36.3538i | 0.579134 | − | 1.78239i | ||||
\(417\) | −2.94345 | −0.144141 | ||||||||
\(418\) | 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 | ||||
\(423\) | 4.89094 | + | 15.0528i | 0.237806 | + | 0.731891i | ||||
\(424\) | −1.40146 | − | 4.31326i | −0.0680611 | − | 0.209470i | ||||
\(425\) | 17.3602 | + | 12.6130i | 0.842096 | + | 0.611818i | ||||
\(426\) | 3.61887 | − | 2.62927i | 0.175335 | − | 0.127388i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 7.52653 | 0.363808 | ||||||||
\(429\) | 13.2978 | − | 1.51799i | 0.642024 | − | 0.0732891i | ||||
\(430\) | 0.814531 | 0.0392802 | ||||||||
\(431\) | 8.61919 | − | 26.5272i | 0.415172 | − | 1.27777i | −0.496925 | − | 0.867794i | \(-0.665538\pi\) |
0.912097 | − | 0.409975i | \(-0.134462\pi\) | |||||||
\(432\) | −2.07448 | + | 1.50720i | −0.0998085 | + | 0.0725151i | ||||
\(433\) | −23.9040 | − | 17.3673i | −1.14875 | − | 0.834619i | −0.160440 | − | 0.987046i | \(-0.551291\pi\) |
−0.988315 | + | 0.152426i | \(0.951291\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.160382 | + | 0.493605i | 0.00768973 | + | 0.0236666i | ||||
\(436\) | 6.09548 | + | 4.42862i | 0.291920 | + | 0.212093i | ||||
\(437\) | −9.19251 | + | 6.67875i | −0.439738 | + | 0.319488i | ||||
\(438\) | −0.829907 | + | 2.55419i | −0.0396545 | + | 0.122044i | ||||
\(439\) | 33.6655 | 1.60677 | 0.803384 | − | 0.595461i | \(-0.203030\pi\) | ||||
0.803384 | + | 0.595461i | \(0.203030\pi\) | |||||||
\(440\) | −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 | −0.768291 | − | 0.640101i | \(-0.778893\pi\) |
0.371357 | + | 0.928490i | \(0.378893\pi\) | |||||||
\(444\) | 3.94479 | + | 2.86606i | 0.187211 | + | 0.136017i | ||||
\(445\) | −0.544696 | − | 1.67640i | −0.0258211 | − | 0.0794691i | ||||
\(446\) | 0.171842 | + | 0.528874i | 0.00813694 | + | 0.0250429i | ||||
\(447\) | −3.61493 | − | 2.62640i | −0.170980 | − | 0.124224i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.852224 | + | 2.62287i | −0.0402189 | + | 0.123781i | −0.969150 | − | 0.246471i | \(-0.920729\pi\) |
0.928931 | + | 0.370253i | \(0.120729\pi\) | |||||||
\(450\) | −10.0766 | −0.475016 | ||||||||
\(451\) | −1.84128 | − | 4.03802i | −0.0867025 | − | 0.190143i | ||||
\(452\) | 23.0208 | 1.08281 | ||||||||
\(453\) | −1.55454 | + | 4.78439i | −0.0730387 | + | 0.224790i | ||||
\(454\) | 3.34729 | − | 2.43195i | 0.157096 | − | 0.114137i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.46971 | + | 4.52331i | 0.0688255 | + | 0.211823i | ||||
\(457\) | −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 | ||||
\(459\) | −12.1760 | + | 8.84638i | −0.568327 | + | 0.412914i | ||||
\(460\) | 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 | ||||
\(465\) | 0.766520 | − | 0.556910i | 0.0355465 | − | 0.0258261i | ||||
\(466\) | −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 | \(0.669899\pi\) | |||||||
\(468\) | −7.37184 | − | 22.6882i | −0.340764 | − | 1.04876i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.846145 | + | 0.614760i | −0.0390298 | + | 0.0283568i | ||||
\(471\) | 3.84858 | − | 11.8447i | 0.177333 | − | 0.545775i | ||||
\(472\) | 25.1669 | 1.15840 | ||||||||
\(473\) | −3.10991 | + | 15.3025i | −0.142994 | + | 0.703611i | ||||
\(474\) | −2.17650 | −0.0999699 | ||||||||
\(475\) | 4.45933 | − | 13.7244i | 0.204608 | − | 0.629719i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.63860 | − | 2.64360i | −0.166600 | − | 0.121042i | ||||
\(478\) | −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 | \(0.862849\pi\) | |||||||
\(480\) | −0.651315 | − | 0.473208i | −0.0297283 | − | 0.0215989i | ||||
\(481\) | −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 | ||||||||
\(486\) | 3.35019 | − | 10.3108i | 0.151968 | − | 0.467709i | ||||
\(487\) | −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 | ||||
\(489\) | −1.41986 | − | 4.36989i | −0.0642084 | − | 0.197613i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.3870 | − | 17.7182i | −1.10057 | − | 0.799610i | −0.119416 | − | 0.992844i | \(-0.538102\pi\) |
−0.981153 | + | 0.193235i | \(0.938102\pi\) | |||||||
\(492\) | 0.933679 | − | 0.678357i | 0.0420935 | − | 0.0305827i | ||||
\(493\) | −5.05514 | + | 15.5581i | −0.227672 | + | 0.700703i | ||||
\(494\) | −14.7984 | −0.665810 | ||||||||
\(495\) | −0.384795 | + | 1.89341i | −0.0172952 | + | 0.0851023i | ||||
\(496\) | 5.08801 | 0.228458 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 4.38647 | − | 3.18696i | 0.196563 | − | 0.142811i | ||||
\(499\) | −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 | ||||
\(501\) | −0.422287 | − | 1.29967i | −0.0188664 | − | 0.0580648i | ||||
\(502\) | −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 | ||||
\(507\) | −18.3154 | −0.813416 | ||||||||
\(508\) | −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 | \(0.456715\pi\) | |||||||
\(510\) | −0.374949 | − | 0.272417i | −0.0166030 | − | 0.0120628i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −2.54091 | − | 7.82012i | −0.112293 | − | 0.345604i | ||||
\(513\) | 8.18830 | + | 5.94915i | 0.361522 | + | 0.262661i | ||||
\(514\) | 10.6404 | − | 7.73068i | 0.469327 | − | 0.340986i | ||||
\(515\) | −1.11656 | + | 3.43643i | −0.0492017 | + | 0.151427i | ||||
\(516\) | −4.06072 | −0.178763 | ||||||||
\(517\) | −8.31884 | − | 18.2436i | −0.365862 | − | 0.802354i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.97900 | + | 6.09075i | −0.0868686 | + | 0.267354i | ||||
\(520\) | 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 | \(0.861162\pi\) | |||||||
\(522\) | −2.37383 | − | 7.30590i | −0.103900 | − | 0.319771i | ||||
\(523\) | −1.51773 | − | 4.67108i | −0.0663655 | − | 0.204252i | 0.912375 | − | 0.409356i | \(-0.134247\pi\) |
−0.978740 | + | 0.205104i | \(0.934247\pi\) | |||||||
\(524\) | −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 | ||||||||
\(528\) | 1.11586 | − | 1.02294i | 0.0485615 | − | 0.0445176i | ||||
\(529\) | −7.80592 | −0.339388 | ||||||||
\(530\) | 0.0918410 | − | 0.282657i | 0.00398932 | − | 0.0122779i | ||||
\(531\) | 20.1913 | − | 14.6698i | 0.876228 | − | 0.636617i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.69996 | + | 8.30962i | 0.116948 | + | 0.359929i | ||||
\(534\) | −1.17624 | − | 3.62011i | −0.0509010 | − | 0.156657i | ||||
\(535\) | 0.970907 | + | 0.705405i | 0.0419760 | + | 0.0304973i | ||||
\(536\) | −2.71574 | + | 1.97310i | −0.117302 | + | 0.0852250i | ||||
\(537\) | 4.47080 | − | 13.7597i | 0.192929 | − | 0.593775i | ||||
\(538\) | −4.85707 | −0.209403 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.07818 | −0.0463977 | ||||||||
\(541\) | 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 | ||||
\(543\) | 6.85805 | + | 4.98266i | 0.294307 | + | 0.213827i | ||||
\(544\) | −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 | ||||
\(549\) | −25.2102 | −1.07594 | ||||||||
\(550\) | 12.6831 | − | 1.44781i | 0.540808 | − | 0.0617349i | ||||
\(551\) | 11.0012 | 0.468667 | ||||||||
\(552\) | 1.96530 | − | 6.04858i | 0.0836489 | − | 0.257445i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 7.57795 | + | 5.50570i | 0.321956 | + | 0.233915i | ||||
\(555\) | 0.240256 | + | 0.739431i | 0.0101983 | + | 0.0313871i | ||||
\(556\) | −2.05382 | − | 6.32100i | −0.0871012 | − | 0.268070i | ||||
\(557\) | −14.9432 | − | 10.8569i | −0.633164 | − | 0.460021i | 0.224331 | − | 0.974513i | \(-0.427980\pi\) |
−0.857495 | + | 0.514492i | \(0.827980\pi\) | |||||||
\(558\) | −11.3453 | + | 8.24287i | −0.480286 | + | 0.348949i | ||||
\(559\) | 9.49993 | − | 29.2378i | 0.401804 | − | 1.23663i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.54945 | − | 6.00405i | 0.276518 | − | 0.253491i | ||||
\(562\) | −16.4476 | −0.693801 | ||||||||
\(563\) | −9.66724 | + | 29.7527i | −0.407426 | + | 1.25393i | 0.511427 | + | 0.859327i | \(0.329117\pi\) |
−0.918853 | + | 0.394600i | \(0.870883\pi\) | |||||||
\(564\) | 4.21833 | − | 3.06479i | 0.177624 | − | 0.129051i | ||||
\(565\) | 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 | −0.616836 | − | 0.787092i | \(-0.711586\pi\) |
0.557956 | + | 0.829870i | \(0.311586\pi\) | |||||||
\(570\) | −0.0963134 | + | 0.296422i | −0.00403412 | + | 0.0124158i | ||||
\(571\) | 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 | ||||
\(573\) | 7.43182 | 0.310469 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −15.6114 | + | 11.3424i | −0.651042 | + | 0.473009i | ||||
\(576\) | 6.51180 | + | 4.73110i | 0.271325 | + | 0.197129i | ||||
\(577\) | −6.23893 | − | 19.2015i | −0.259730 | − | 0.799368i | −0.992861 | − | 0.119280i | \(-0.961942\pi\) |
0.733130 | − | 0.680088i | \(-0.238058\pi\) | |||||||
\(578\) | −0.429788 | − | 1.32275i | −0.0178768 | − | 0.0550192i | ||||
\(579\) | 7.94196 | + | 5.77017i | 0.330057 | + | 0.239800i | ||||
\(580\) | −0.948101 | + | 0.688835i | −0.0393677 | + | 0.0286023i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 4.35051 | 0.180334 | ||||||||
\(583\) | 4.95961 | + | 2.80461i | 0.205406 | + | 0.116155i | ||||
\(584\) | −14.7550 | −0.610568 | ||||||||
\(585\) | 1.17544 | − | 3.61764i | 0.0485986 | − | 0.149571i | ||||
\(586\) | 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 | ||||
\(591\) | 6.15177 | − | 4.46952i | 0.253050 | − | 0.183851i | ||||
\(592\) | −1.29020 | + | 3.97082i | −0.0530267 | + | 0.163200i | ||||
\(593\) | 0.439298 | 0.0180398 | 0.00901989 | − | 0.999959i | \(-0.497129\pi\) | ||||
0.00901989 | + | 0.999959i | \(0.497129\pi\) | |||||||
\(594\) | −1.78312 | + | 8.77397i | −0.0731624 | + | 0.360001i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.11779 | − | 9.59558i | 0.127710 | − | 0.393050i | ||||
\(597\) | −7.63075 | + | 5.54406i | −0.312306 | + | 0.226903i | ||||
\(598\) | 16.0092 | + | 11.6314i | 0.654664 | + | 0.475641i | ||||
\(599\) | 13.9572 | + | 42.9558i | 0.570275 | + | 1.75512i | 0.651734 | + | 0.758448i | \(0.274042\pi\) |
−0.0814591 | + | 0.996677i | \(0.525958\pi\) | |||||||
\(600\) | 2.49598 | + | 7.68182i | 0.101898 | + | 0.313609i | ||||
\(601\) | 9.01541 | + | 6.55008i | 0.367746 | + | 0.267183i | 0.756276 | − | 0.654253i | \(-0.227017\pi\) |
−0.388529 | + | 0.921436i | \(0.627017\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.02870 | + | 3.16603i | −0.0418921 | + | 0.128931i | ||||
\(604\) | −11.3591 | −0.462194 | ||||||||
\(605\) | 0.212282 | − | 2.43845i | 0.00863047 | − | 0.0991371i | ||||
\(606\) | 9.23071 | 0.374972 | ||||||||
\(607\) | 11.0318 | − | 33.9525i | 0.447768 | − | 1.37809i | −0.431651 | − | 0.902041i | \(-0.642069\pi\) |
0.879419 | − | 0.476049i | \(-0.157931\pi\) | |||||||
\(608\) | −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 | ||||
\(612\) | −12.8121 | − | 9.30850i | −0.517897 | − | 0.376274i | ||||
\(613\) | −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 | ||||
\(615\) | 0.184020 | 0.00742040 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.8852 | −0.679774 | −0.339887 | − | 0.940466i | \(-0.610389\pi\) | ||||
−0.339887 | + | 0.940466i | \(0.610389\pi\) | |||||||
\(618\) | −2.41117 | + | 7.42080i | −0.0969913 | + | 0.298509i | ||||
\(619\) | 25.1355 | − | 18.2620i | 1.01028 | − | 0.734013i | 0.0460139 | − | 0.998941i | \(-0.485348\pi\) |
0.964268 | + | 0.264928i | \(0.0853481\pi\) | |||||||
\(620\) | 1.73080 | + | 1.25750i | 0.0695106 | + | 0.0505024i | ||||
\(621\) | −4.18231 | − | 12.8718i | −0.167830 | − | 0.516529i | ||||
\(622\) | 0.0329066 | + | 0.101276i | 0.00131943 | + | 0.00406080i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2.41106 | + | 1.75174i | −0.0965196 | + | 0.0701256i | ||||
\(625\) | 7.49668 | − | 23.0724i | 0.299867 | − | 0.922896i | ||||
\(626\) | −11.8877 | −0.475127 | ||||||||
\(627\) | −5.20113 | − | 2.94118i | −0.207713 | − | 0.117460i | ||||
\(628\) | 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 | ||||
\(633\) | −1.70613 | − | 5.25094i | −0.0678128 | − | 0.208706i | ||||
\(634\) | −20.7522 | − | 15.0774i | −0.824176 | − | 0.598799i | ||||
\(635\) | −0.359549 | + | 0.261227i | −0.0142683 | + | 0.0103665i | ||||
\(636\) | −0.457859 | + | 1.40915i | −0.0181553 | + | 0.0558763i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.03757 | + | 8.85460i | 0.159849 | + | 0.350557i | ||||
\(639\) | 24.3718 | 0.964132 | ||||||||
\(640\) | 0.640707 | − | 1.97189i | 0.0253262 | − | 0.0779459i | ||||
\(641\) | 16.7870 | − | 12.1965i | 0.663047 | − | 0.481732i | −0.204643 | − | 0.978837i | \(-0.565603\pi\) |
0.867691 | + | 0.497104i | \(0.165603\pi\) | |||||||
\(642\) | 2.09663 | + | 1.52329i | 0.0827472 | + | 0.0601194i | ||||
\(643\) | −2.19750 | − | 6.76322i | −0.0866611 | − | 0.266715i | 0.898330 | − | 0.439322i | \(-0.144781\pi\) |
−0.984991 | + | 0.172606i | \(0.944781\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.523825 | − | 0.380581i | −0.0206256 | − | 0.0149854i | ||||
\(646\) | −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 | \(0.917622\pi\) | |||||||
\(648\) | 15.0694 | 0.591984 | ||||||||
\(649\) | −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 | 0.301937 | − | 0.953328i | \(-0.402367\pi\) |
−0.813365 | + | 0.581753i | \(0.802367\pi\) | |||||||
\(654\) | 0.801680 | + | 2.46732i | 0.0313482 | + | 0.0964797i | ||||
\(655\) | −0.0942092 | − | 0.289946i | −0.00368106 | − | 0.0113291i | ||||
\(656\) | 0.799474 | + | 0.580852i | 0.0312142 | + | 0.0226785i | ||||
\(657\) | −11.8379 | + | 8.60076i | −0.461842 | + | 0.335548i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.2085 | −0.514531 | −0.257266 | − | 0.966341i | \(-0.582822\pi\) | ||||
−0.257266 | + | 0.966341i | \(0.582822\pi\) | |||||||
\(660\) | 0.632403 | − | 0.0721907i | 0.0246162 | − | 0.00281002i | ||||
\(661\) | 4.90660 | 0.190845 | 0.0954223 | − | 0.995437i | \(-0.469580\pi\) | ||||
0.0954223 | + | 0.995437i | \(0.469580\pi\) | |||||||
\(662\) | −7.09559 | + | 21.8380i | −0.275778 | + | 0.848757i | ||||
\(663\) | −14.1515 | + | 10.2817i | −0.549600 | + | 0.399308i | ||||
\(664\) | 24.0996 | + | 17.5094i | 0.935245 | + | 0.679495i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.55605 | − | 10.9444i | −0.137794 | − | 0.424087i | ||||
\(667\) | −11.9013 | − | 8.64682i | −0.460821 | − | 0.334806i | ||||
\(668\) | 2.49635 | − | 1.81371i | 0.0965869 | − | 0.0701745i | ||||
\(669\) | 0.136599 | − | 0.420410i | 0.00528124 | − | 0.0162540i | ||||
\(670\) | −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 | ||||
\(675\) | 13.9060 | + | 10.1033i | 0.535242 | + | 0.388876i | ||||
\(676\) | −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 | \(0.977776\pi\) | |||||||
\(678\) | 6.41278 | + | 4.65916i | 0.246281 | + | 0.178934i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.786849 | − | 2.42167i | 0.0301743 | − | 0.0928668i | ||||
\(681\) | −3.28894 | −0.126033 | ||||||||
\(682\) | 13.0956 | − | 12.0051i | 0.501457 | − | 0.459699i | ||||
\(683\) | −28.5342 | −1.09183 | −0.545916 | − | 0.837840i | \(-0.683818\pi\) | ||||
−0.545916 | + | 0.837840i | \(0.683818\pi\) | |||||||
\(684\) | −3.29104 | + | 10.1288i | −0.125836 | + | 0.387283i | ||||
\(685\) | −0.449911 | + | 0.326879i | −0.0171902 | + | 0.0124894i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.26208 | − | 3.88427i | −0.0481513 | − | 0.148194i | ||||
\(688\) | −1.07447 | − | 3.30687i | −0.0409636 | − | 0.126073i | ||||
\(689\) | −9.07491 | − | 6.59331i | −0.345726 | − | 0.251185i | ||||
\(690\) | 0.337178 | − | 0.244974i | 0.0128362 | − | 0.00932601i | ||||
\(691\) | −7.84107 | + | 24.1323i | −0.298288 | + | 0.918037i | 0.683809 | + | 0.729661i | \(0.260322\pi\) |
−0.982097 | + | 0.188376i | \(0.939678\pi\) | |||||||
\(692\) | −14.4606 | −0.549711 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.78791 | −0.257666 | ||||||||
\(695\) | 0.327482 | − | 1.00788i | 0.0124221 | − | 0.0382312i | ||||
\(696\) | −4.98159 | + | 3.61934i | −0.188827 | + | 0.137191i | ||||
\(697\) | 4.69245 | + | 3.40927i | 0.177739 | + | 0.129135i | ||||
\(698\) | 4.43679 | + | 13.6551i | 0.167935 | + | 0.516851i | ||||
\(699\) | 1.82525 | + | 5.61754i | 0.0690373 | + | 0.212475i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.9738 | − | 26.8630i | 1.39648 | − | 1.01460i | 0.401363 | − | 0.915919i | \(-0.368537\pi\) |
0.995119 | − | 0.0986843i | \(-0.0314634\pi\) | |||||||
\(702\) | 5.44695 | − | 16.7640i | 0.205582 | − | 0.632716i | ||||
\(703\) | 16.4800 | 0.621556 | ||||||||
\(704\) | −8.87594 | − | 5.01925i | −0.334525 | − | 0.189170i | ||||
\(705\) | 0.831396 | 0.0313122 | ||||||||
\(706\) | −5.64257 | + | 17.3661i | −0.212361 | + | 0.653580i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −6.65177 | − | 4.83279i | −0.249989 | − | 0.181627i | ||||
\(709\) | 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 | ||||
\(711\) | −9.59373 | − | 6.97025i | −0.359793 | − | 0.261405i | ||||
\(712\) | 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 | ||||||||
\(717\) | −5.12725 | + | 15.7801i | −0.191481 | + | 0.589317i | ||||
\(718\) | 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 | \(0.666091\pi\) | |||||||
\(720\) | −0.132945 | − | 0.409164i | −0.00495458 | − | 0.0152486i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −6.60620 | − | 4.79969i | −0.245857 | − | 0.178626i | ||||
\(723\) | −9.43316 | + | 6.85359i | −0.350823 | + | 0.254888i | ||||
\(724\) | −5.91491 | + | 18.2042i | −0.219826 | + | 0.676555i | ||||
\(725\) | 18.6831 | 0.693872 | ||||||||
\(726\) | 0.458411 | − | 5.26571i | 0.0170132 | − | 0.195429i | ||||
\(727\) | −11.8221 | −0.438458 | −0.219229 | − | 0.975673i | \(-0.570354\pi\) | ||||
−0.219229 | + | 0.975673i | \(0.570354\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 6.88197 | − | 5.00004i | 0.254888 | − | 0.185187i | ||||
\(730\) | −0.782263 | − | 0.568347i | −0.0289529 | − | 0.0210355i | ||||
\(731\) | −6.30649 | − | 19.4094i | −0.233254 | − | 0.717882i | ||||
\(732\) | 2.56644 | + | 7.89868i | 0.0948582 | + | 0.291944i | ||||
\(733\) | 7.12900 | + | 5.17952i | 0.263316 | + | 0.191310i | 0.711607 | − | 0.702577i | \(-0.247967\pi\) |
−0.448292 | + | 0.893887i | \(0.647967\pi\) | |||||||
\(734\) | 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 | ||||
\(738\) | −2.72370 | −0.100261 | ||||||||
\(739\) | 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 | ||||
\(741\) | 9.51683 | + | 6.91438i | 0.349610 | + | 0.254006i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.2730 | + | 31.6172i | 0.376881 | + | 1.15992i | 0.942201 | + | 0.335049i | \(0.108753\pi\) |
−0.565319 | + | 0.824872i | \(0.691247\pi\) | |||||||
\(744\) | 9.09412 | + | 6.60726i | 0.333407 | + | 0.242234i | ||||
\(745\) | 1.30151 | − | 0.945603i | 0.0476837 | − | 0.0346442i | ||||
\(746\) | −0.724946 | + | 2.23116i | −0.0265422 | + | 0.0816884i | ||||
\(747\) | 29.5413 | 1.08086 | ||||||||
\(748\) | 17.4635 | + | 9.87543i | 0.638530 | + | 0.361082i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −0.328769 | + | 1.01185i | −0.0120050 | + | 0.0369475i | ||||
\(751\) | −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 | ||||
\(753\) | 5.60977 | + | 17.2651i | 0.204432 | + | 0.629176i | ||||
\(754\) | −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 | ||||||||
\(759\) | 3.31495 | + | 7.26986i | 0.120325 | + | 0.263879i | ||||
\(760\) | −1.71237 | −0.0621142 | ||||||||
\(761\) | 14.9025 | − | 45.8651i | 0.540214 | − | 1.66261i | −0.191891 | − | 0.981416i | \(-0.561462\pi\) |
0.732105 | − | 0.681192i | \(-0.238538\pi\) | |||||||
\(762\) | −0.776427 | + | 0.564108i | −0.0281270 | + | 0.0204355i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 5.18562 | + | 15.9597i | 0.187609 | + | 0.577402i | ||||
\(765\) | −0.780313 | − | 2.40156i | −0.0282123 | − | 0.0868284i | ||||
\(766\) | −2.76192 | − | 2.00665i | −0.0997922 | − | 0.0725033i | ||||
\(767\) | 50.3584 | − | 36.5875i | 1.81834 | − | 1.32110i | ||||
\(768\) | 2.55791 | − | 7.87245i | 0.0923007 | − | 0.284072i | ||||
\(769\) | −43.6883 | −1.57544 | −0.787721 | − | 0.616032i | \(-0.788739\pi\) | ||||
−0.787721 | + | 0.616032i | \(0.788739\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.4549 | −0.376524 | ||||||||
\(772\) | −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 | \(0.303352\pi\) | |||||||
\(774\) | 7.75318 | + | 5.63301i | 0.278682 | + | 0.202475i | ||||
\(775\) | −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 | ||||
\(780\) | −1.25312 | −0.0448688 | ||||||||
\(781\) | −30.6759 | + | 3.50175i | −1.09767 | + | 0.125302i | ||||
\(782\) | 13.1365 | 0.469760 | ||||||||
\(783\) | −4.04930 | + | 12.4625i | −0.144710 | + | 0.445372i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.62764 | + | 2.63563i | 0.129476 | + | 0.0940698i | ||||
\(786\) | −0.203440 | − | 0.626124i | −0.00725647 | − | 0.0223331i | ||||
\(787\) | −9.49195 | − | 29.2132i | −0.338351 | − | 1.04134i | −0.965048 | − | 0.262075i | \(-0.915593\pi\) |
0.626696 | − | 0.779264i | \(-0.284407\pi\) | |||||||
\(788\) | 13.8907 | + | 10.0922i | 0.494834 | + | 0.359518i | ||||
\(789\) | −4.09017 | + | 2.97168i | −0.145614 | + | 0.105795i | ||||
\(790\) | 0.242153 | − | 0.745269i | 0.00861540 | − | 0.0265155i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −22.7750 | + | 2.59984i | −0.809274 | + | 0.0923811i | ||||
\(793\) | −62.8758 | −2.23278 | ||||||||
\(794\) | 2.73623 | − | 8.42125i | 0.0971052 | − | 0.298859i | ||||
\(795\) | −0.191132 | + | 0.138865i | −0.00677874 | + | 0.00492504i | ||||
\(796\) | −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 | ||||
\(801\) | 6.40868 | − | 19.7239i | 0.226440 | − | 0.696910i | ||||
\(802\) | 3.67358 | 0.129719 | ||||||||
\(803\) | 13.6642 | − | 12.5263i | 0.482200 | − | 0.442045i | ||||
\(804\) | 1.09668 | 0.0386770 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −28.2960 | + | 20.5582i | −0.996684 | + | 0.724133i | ||||
\(807\) | 3.12358 | + | 2.26941i | 0.109955 | + | 0.0798872i | ||||
\(808\) | 15.6715 | + | 48.2320i | 0.551322 | + | 1.69679i | ||||
\(809\) | −11.9250 | − | 36.7013i | −0.419260 | − | 1.29035i | −0.908385 | − | 0.418136i | \(-0.862684\pi\) |
0.489125 | − | 0.872214i | \(-0.337316\pi\) | |||||||
\(810\) | 0.798931 | + | 0.580458i | 0.0280716 | + | 0.0203952i | ||||
\(811\) | −41.1737 | + | 29.9144i | −1.44580 | + | 1.05044i | −0.459015 | + | 0.888428i | \(0.651798\pi\) |
−0.986789 | + | 0.162010i | \(0.948202\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.86200 | 0.170518 | ||||||||
\(814\) | 6.04836 | + | 13.2644i | 0.211995 | + | 0.464916i | ||||
\(815\) | 1.65429 | 0.0579473 | ||||||||
\(816\) | −0.611364 | + | 1.88159i | −0.0214020 | + | 0.0658687i | ||||
\(817\) | −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 | 0.986858 | − | 0.161590i | \(-0.0516623\pi\) |
0.151274 | + | 0.988492i | \(0.451662\pi\) | |||||||
\(822\) | −0.971560 | + | 0.705880i | −0.0338870 | + | 0.0246204i | ||||
\(823\) | 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 | ||||||||
\(825\) | −8.83296 | − | 4.99494i | −0.307524 | − | 0.173902i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.87486 | + | 30.3917i | −0.343382 | + | 1.05682i | 0.619062 | + | 0.785342i | \(0.287513\pi\) |
−0.962444 | + | 0.271480i | \(0.912487\pi\) | |||||||
\(828\) | 11.5214 | − | 8.37079i | 0.400397 | − | 0.290905i | ||||
\(829\) | 39.1566 | + | 28.4489i | 1.35996 | + | 0.988072i | 0.998447 | + | 0.0557070i | \(0.0177413\pi\) |
0.361518 | + | 0.932365i | \(0.382259\pi\) | |||||||
\(830\) | 0.603238 | + | 1.85658i | 0.0209387 | + | 0.0644427i | ||||
\(831\) | −2.30090 | − | 7.08143i | −0.0798172 | − | 0.245652i | ||||
\(832\) | 16.2409 | + | 11.7997i | 0.563050 | + | 0.409080i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0.707180 | − | 2.17648i | 0.0244876 | − | 0.0753652i | ||||
\(835\) | 0.492010 | 0.0170267 | ||||||||
\(836\) | 2.68700 | − | 13.2216i | 0.0929319 | − | 0.457278i | ||||
\(837\) | 23.9216 | 0.826850 | ||||||||
\(838\) | −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 | ||||
\(843\) | 10.5775 | + | 7.68497i | 0.364307 | + | 0.264685i | ||||
\(844\) | 10.0858 | − | 7.32779i | 0.347169 | − | 0.252233i | ||||
\(845\) | 2.03773 | − | 6.27150i | 0.0701001 | − | 0.215746i | ||||
\(846\) | −12.3056 | −0.423074 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.26869 | −0.0435671 | ||||||||
\(849\) | −4.77522 | + | 14.6966i | −0.163885 | + | 0.504386i | ||||
\(850\) | −13.4973 | + | 9.80638i | −0.462954 | + | 0.336356i | ||||
\(851\) | −17.8284 | − | 12.9531i | −0.611151 | − | 0.444027i | ||||
\(852\) | −2.48109 | − | 7.63600i | −0.0850007 | − | 0.261605i | ||||
\(853\) | −2.87035 | − | 8.83403i | −0.0982789 | − | 0.302471i | 0.889815 | − | 0.456321i | \(-0.150833\pi\) |
−0.988094 | + | 0.153849i | \(0.950833\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.37383 | + | 0.998146i | −0.0469840 | + | 0.0341359i | ||||
\(856\) | −4.39986 | + | 13.5414i | −0.150384 | + | 0.462835i | ||||
\(857\) | 29.7644 | 1.01673 | 0.508365 | − | 0.861141i | \(-0.330250\pi\) | ||||
0.508365 | + | 0.861141i | \(0.330250\pi\) | |||||||
\(858\) | −2.07243 | + | 10.1975i | −0.0707516 | + | 0.348138i | ||||
\(859\) | −33.2611 | −1.13485 | −0.567427 | − | 0.823424i | \(-0.692061\pi\) | ||||
−0.567427 | + | 0.823424i | \(0.692061\pi\) | |||||||
\(860\) | 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 | \(-0.997652\pi\) |
0.804658 | − | 0.593738i | \(-0.202348\pi\) | |||||||
\(864\) | −6.28115 | − | 19.3314i | −0.213689 | − | 0.657668i | ||||
\(865\) | −1.86539 | − | 1.35529i | −0.0634253 | − | 0.0460812i | ||||
\(866\) | 18.5850 | − | 13.5028i | 0.631544 | − | 0.458844i | ||||
\(867\) | −0.341645 | + | 1.05147i | −0.0116029 | + | 0.0357100i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.0768 | + | 7.39477i | 0.443599 | + | 0.250850i | ||||
\(870\) | −0.403520 | −0.0136806 | ||||||||
\(871\) | −2.56565 | + | 7.89627i | −0.0869339 | + | 0.267555i | ||||
\(872\) | −11.5311 | + | 8.37782i | −0.390491 | + | 0.283709i | ||||
\(873\) | 19.1765 | + | 13.9325i | 0.649026 | + | 0.471545i | ||||
\(874\) | −2.72992 | − | 8.40184i | −0.0923411 | − | 0.284197i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.89985 | + | 2.83341i | 0.131764 | + | 0.0957321i | ||||
\(877\) | 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 | ||||
\(879\) | −0.281259 | −0.00948664 | ||||||||
\(880\) | 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 | ||||
\(885\) | −0.405123 | − | 1.24684i | −0.0136181 | − | 0.0419121i | ||||
\(886\) | −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 | \(0.662749\pi\) | |||||||
\(888\) | −7.46253 | + | 5.42185i | −0.250426 | + | 0.181945i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.37045 | 0.0459376 | ||||||||
\(891\) | −13.9554 | + | 12.7933i | −0.467522 | + | 0.428590i | ||||
\(892\) | 0.998136 | 0.0334201 | ||||||||
\(893\) | 5.44574 | − | 16.7603i | 0.182235 | − | 0.560861i | ||||
\(894\) | 2.81055 | − | 2.04198i | 0.0939988 | − | 0.0682941i | ||||
\(895\) | 4.21414 | + | 3.06175i | 0.140863 | + | 0.102343i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.86088 | − | 14.9602i | −0.162300 | − | 0.499508i | ||||
\(898\) | −1.73468 | − | 1.26032i | −0.0578872 | − | 0.0420575i | ||||
\(899\) | 21.0354 | − | 15.2831i | 0.701570 | − | 0.509721i | ||||
\(900\) | −5.58909 | + | 17.2014i | −0.186303 | + | 0.573382i | ||||
\(901\) | −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 | ||||
\(906\) | −3.16424 | − | 2.29895i | −0.105125 | − | 0.0763776i | ||||
\(907\) | −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 | ||||
\(909\) | 40.6878 | + | 29.5614i | 1.34953 | + | 0.980490i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.4650 | − | 44.5186i | 0.479246 | − | 1.47497i | −0.360899 | − | 0.932605i | \(-0.617530\pi\) |
0.840145 | − | 0.542362i | \(-0.182470\pi\) | |||||||
\(912\) | 1.33048 | 0.0440564 | ||||||||
\(913\) | −37.1825 | + | 4.24450i | −1.23056 | + | 0.140473i | ||||
\(914\) | 31.3563 | 1.03718 | ||||||||
\(915\) | −0.409219 | + | 1.25945i | −0.0135284 | + | 0.0416360i | ||||
\(916\) | 7.46078 | − | 5.42058i | 0.246511 | − | 0.179101i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −3.61594 | − | 11.1287i | −0.119344 | − | 0.367302i | ||||
\(919\) | 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 | ||||
\(921\) | 4.01789 | − | 2.91917i | 0.132394 | − | 0.0961898i | ||||
\(922\) | −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 | ||||
\(927\) | −34.3933 | + | 24.9882i | −1.12962 | + | 0.820720i | ||||
\(928\) | −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 | \(0.694543\pi\) | |||||||
\(930\) | 0.227635 | + | 0.700590i | 0.00746446 | + | 0.0229733i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −10.7900 | + | 7.83938i | −0.353438 | + | 0.256787i | ||||
\(933\) | 0.0261579 | − | 0.0805059i | 0.000856373 | − | 0.00263564i | ||||
\(934\) | −22.2302 | −0.727393 | ||||||||
\(935\) | 1.32721 | + | 2.91064i | 0.0434043 | + | 0.0951880i | ||||
\(936\) | 45.1290 | 1.47509 | ||||||||
\(937\) | 12.4278 | − | 38.2490i | 0.406000 | − | 1.24954i | −0.514057 | − | 0.857756i | \(-0.671858\pi\) |
0.920057 | − | 0.391784i | \(-0.128142\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.64497 | + | 5.55439i | 0.249484 | + | 0.181261i | ||||
\(940\) | 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 | \(-0.233082\pi\) | |||||||
\(942\) | 7.83371 | + | 5.69152i | 0.255236 | + | 0.185440i | ||||
\(943\) | −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 | \(-0.675292\pi\) | ||||
−0.523279 | + | 0.852161i | \(0.675292\pi\) | |||||||
\(948\) | −1.20722 | + | 3.71543i | −0.0392085 | + | 0.120671i | ||||
\(949\) | −29.5246 | + | 21.4508i | −0.958408 | + | 0.696324i | ||||
\(950\) | 9.07688 | + | 6.59474i | 0.294493 | + | 0.213962i | ||||
\(951\) | 6.30101 | + | 19.3925i | 0.204324 | + | 0.628846i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −36.4552 | − | 26.4863i | −1.18090 | − | 0.857975i | −0.188628 | − | 0.982049i | \(-0.560404\pi\) |
−0.992273 | + | 0.124074i | \(0.960404\pi\) | |||||||
\(954\) | 2.82896 | − | 2.05536i | 0.0915908 | − | 0.0665446i | ||||
\(955\) | −0.826849 | + | 2.54478i | −0.0267562 | + | 0.0823471i | ||||
\(956\) | −37.4650 | −1.21170 | ||||||||
\(957\) | 1.54066 | − | 7.58090i | 0.0498024 | − | 0.245056i | ||||
\(958\) | −3.96296 | −0.128038 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.342058 | − | 0.248519i | 0.0110399 | − | 0.00802093i | ||||
\(961\) | −13.3216 | − | 9.67867i | −0.429727 | − | 0.312215i | ||||
\(962\) | −8.86901 | − | 27.2960i | −0.285948 | − | 0.880059i | ||||
\(963\) | 4.36332 | + | 13.4289i | 0.140606 | + | 0.432741i | ||||
\(964\) | −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 | ||||
\(969\) | 7.80912 | 0.250865 | ||||||||
\(970\) | −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 | \(0.179386\pi\) | |||||||
\(972\) | −15.7431 | − | 11.4380i | −0.504959 | − | 0.366874i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −7.01266 | − | 21.5827i | −0.224700 | − | 0.691555i | ||||
\(975\) | 16.1622 | + | 11.7425i | 0.517605 | + | 0.376062i | ||||
\(976\) | −5.75325 | + | 4.17998i | −0.184157 | + | 0.133798i | ||||
\(977\) | −2.19232 | + | 6.74726i | −0.0701385 | + | 0.215864i | −0.979981 | − | 0.199089i | \(-0.936202\pi\) |
0.909843 | + | 0.414953i | \(0.136202\pi\) | |||||||
\(978\) | 3.57236 | 0.114232 | ||||||||
\(979\) | −5.23244 | + | 25.7466i | −0.167229 | + | 0.822863i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.36789 | + | 13.4430i | −0.139456 | + | 0.429202i | ||||
\(982\) | 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 | \(0.490530\pi\) | |||||||
\(984\) | 0.674659 | + | 2.07639i | 0.0215073 | + | 0.0661928i | ||||
\(985\) | 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 | ||||||||
\(990\) | −1.30760 | − | 0.739431i | −0.0415581 | − | 0.0235007i | ||||
\(991\) | 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 | ||||
\(993\) | 14.7667 | − | 10.7287i | 0.468608 | − | 0.340464i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.04940 | − | 3.22971i | −0.0332681 | − | 0.102389i | ||||
\(996\) | −3.00735 | − | 9.25568i | −0.0952916 | − | 0.293277i | ||||
\(997\) | 12.4675 | + | 9.05819i | 0.394851 | + | 0.286876i | 0.767440 | − | 0.641120i | \(-0.221530\pi\) |
−0.372590 | + | 0.927996i | \(0.621530\pi\) | |||||||
\(998\) | 3.74319 | − | 2.71959i | 0.118489 | − | 0.0860871i | ||||
\(999\) | −6.06593 | + | 18.6690i | −0.191918 | + | 0.590662i |
(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 | 539.2.f.d.295.1 | 8 | ||
7.2 | even | 3 | 539.2.q.b.361.2 | 16 | |||
7.3 | odd | 6 | 539.2.q.c.471.1 | 16 | |||
7.4 | even | 3 | 539.2.q.b.471.1 | 16 | |||
7.5 | odd | 6 | 539.2.q.c.361.2 | 16 | |||
7.6 | odd | 2 | 77.2.f.a.64.1 | ✓ | 8 | ||
11.4 | even | 5 | 5929.2.a.bi.1.2 | 4 | |||
11.5 | even | 5 | inner | 539.2.f.d.148.1 | 8 | ||
11.7 | odd | 10 | 5929.2.a.bb.1.3 | 4 | |||
21.20 | even | 2 | 693.2.m.g.64.2 | 8 | |||
77.5 | odd | 30 | 539.2.q.c.214.1 | 16 | |||
77.6 | even | 10 | 847.2.f.q.148.2 | 8 | |||
77.13 | even | 10 | 847.2.f.s.729.1 | 8 | |||
77.16 | even | 15 | 539.2.q.b.214.1 | 16 | |||
77.20 | odd | 10 | 847.2.f.p.729.2 | 8 | |||
77.27 | odd | 10 | 77.2.f.a.71.1 | yes | 8 | ||
77.38 | odd | 30 | 539.2.q.c.324.2 | 16 | |||
77.41 | even | 10 | 847.2.f.s.323.1 | 8 | |||
77.48 | odd | 10 | 847.2.a.l.1.2 | 4 | |||
77.60 | even | 15 | 539.2.q.b.324.2 | 16 | |||
77.62 | even | 10 | 847.2.a.k.1.3 | 4 | |||
77.69 | odd | 10 | 847.2.f.p.323.2 | 8 | |||
77.76 | even | 2 | 847.2.f.q.372.2 | 8 | |||
231.62 | odd | 10 | 7623.2.a.co.1.2 | 4 | |||
231.104 | even | 10 | 693.2.m.g.379.2 | 8 | |||
231.125 | even | 10 | 7623.2.a.ch.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.a.64.1 | ✓ | 8 | 7.6 | odd | 2 | ||
77.2.f.a.71.1 | yes | 8 | 77.27 | odd | 10 | ||
539.2.f.d.148.1 | 8 | 11.5 | even | 5 | inner | ||
539.2.f.d.295.1 | 8 | 1.1 | even | 1 | trivial | ||
539.2.q.b.214.1 | 16 | 77.16 | even | 15 | |||
539.2.q.b.324.2 | 16 | 77.60 | even | 15 | |||
539.2.q.b.361.2 | 16 | 7.2 | even | 3 | |||
539.2.q.b.471.1 | 16 | 7.4 | even | 3 | |||
539.2.q.c.214.1 | 16 | 77.5 | odd | 30 | |||
539.2.q.c.324.2 | 16 | 77.38 | odd | 30 | |||
539.2.q.c.361.2 | 16 | 7.5 | odd | 6 | |||
539.2.q.c.471.1 | 16 | 7.3 | odd | 6 | |||
693.2.m.g.64.2 | 8 | 21.20 | even | 2 | |||
693.2.m.g.379.2 | 8 | 231.104 | even | 10 | |||
847.2.a.k.1.3 | 4 | 77.62 | even | 10 | |||
847.2.a.l.1.2 | 4 | 77.48 | odd | 10 | |||
847.2.f.p.323.2 | 8 | 77.69 | odd | 10 | |||
847.2.f.p.729.2 | 8 | 77.20 | odd | 10 | |||
847.2.f.q.148.2 | 8 | 77.6 | even | 10 | |||
847.2.f.q.372.2 | 8 | 77.76 | even | 2 | |||
847.2.f.s.323.1 | 8 | 77.41 | even | 10 | |||
847.2.f.s.729.1 | 8 | 77.13 | even | 10 | |||
5929.2.a.bb.1.3 | 4 | 11.7 | odd | 10 | |||
5929.2.a.bi.1.2 | 4 | 11.4 | even | 5 | |||
7623.2.a.ch.1.3 | 4 | 231.125 | even | 10 | |||
7623.2.a.co.1.2 | 4 | 231.62 | odd | 10 |