Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [250,2,Mod(49,250)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(250, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("250.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 250 = 2 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 250.e (of order \(10\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.99626005053\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\Q(\zeta_{20})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 50) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 149.1 | ||
Root | \(-0.951057 - 0.309017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 250.149 |
Dual form | 250.2.e.b.99.1 |
$q$-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 \(\left(\mathbb{Z}/250\mathbb{Z}\right)^\times\).
\(n\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{10}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.951057 | − | 0.309017i | −0.672499 | − | 0.218508i | ||||
\(3\) | 0.224514 | − | 0.309017i | 0.129623 | − | 0.178411i | −0.739272 | − | 0.673407i | \(-0.764830\pi\) |
0.868895 | + | 0.494996i | \(0.164830\pi\) | |||||||
\(4\) | 0.809017 | + | 0.587785i | 0.404508 | + | 0.293893i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.309017 | + | 0.224514i | −0.126156 | + | 0.0916575i | ||||
\(7\) | − | 3.00000i | − | 1.13389i | −0.823754 | − | 0.566947i | \(-0.808125\pi\) | ||
0.823754 | − | 0.566947i | \(-0.191875\pi\) | |||||||
\(8\) | −0.587785 | − | 0.809017i | −0.207813 | − | 0.286031i | ||||
\(9\) | 0.881966 | + | 2.71441i | 0.293989 | + | 0.904804i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.30902 | − | 4.02874i | 0.394683 | − | 1.21471i | −0.534524 | − | 0.845153i | \(-0.679509\pi\) |
0.929208 | − | 0.369558i | \(-0.120491\pi\) | |||||||
\(12\) | 0.363271 | − | 0.118034i | 0.104867 | − | 0.0340735i | ||||
\(13\) | 0.951057 | − | 0.309017i | 0.263776 | − | 0.0857059i | −0.174143 | − | 0.984720i | \(-0.555716\pi\) |
0.437919 | + | 0.899014i | \(0.355716\pi\) | |||||||
\(14\) | −0.927051 | + | 2.85317i | −0.247765 | + | 0.762542i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.309017 | + | 0.951057i | 0.0772542 | + | 0.237764i | ||||
\(17\) | −0.673542 | − | 0.927051i | −0.163358 | − | 0.224843i | 0.719489 | − | 0.694504i | \(-0.244376\pi\) |
−0.882847 | + | 0.469661i | \(0.844376\pi\) | |||||||
\(18\) | − | 2.85410i | − | 0.672718i | ||||||
\(19\) | 4.73607 | − | 3.44095i | 1.08653 | − | 0.789409i | 0.107719 | − | 0.994181i | \(-0.465645\pi\) |
0.978810 | + | 0.204772i | \(0.0656454\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.927051 | − | 0.673542i | −0.202299 | − | 0.146979i | ||||
\(22\) | −2.48990 | + | 3.42705i | −0.530848 | + | 0.730650i | ||||
\(23\) | 1.67760 | + | 0.545085i | 0.349804 | + | 0.113658i | 0.478648 | − | 0.878007i | \(-0.341127\pi\) |
−0.128845 | + | 0.991665i | \(0.541127\pi\) | |||||||
\(24\) | −0.381966 | −0.0779685 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 2.12663 | + | 0.690983i | 0.409270 | + | 0.132980i | ||||
\(28\) | 1.76336 | − | 2.42705i | 0.333243 | − | 0.458670i | ||||
\(29\) | −7.66312 | − | 5.56758i | −1.42301 | − | 1.03387i | −0.991266 | − | 0.131875i | \(-0.957900\pi\) |
−0.431739 | − | 0.901998i | \(-0.642100\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.190983 | − | 0.138757i | 0.0343016 | − | 0.0249215i | −0.570502 | − | 0.821296i | \(-0.693251\pi\) |
0.604804 | + | 0.796374i | \(0.293251\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | −0.951057 | − | 1.30902i | −0.165558 | − | 0.227871i | ||||
\(34\) | 0.354102 | + | 1.08981i | 0.0607280 | + | 0.186902i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.881966 | + | 2.71441i | −0.146994 | + | 0.452402i | ||||
\(37\) | 7.91872 | − | 2.57295i | 1.30183 | − | 0.422990i | 0.425612 | − | 0.904906i | \(-0.360059\pi\) |
0.876218 | + | 0.481915i | \(0.160059\pi\) | |||||||
\(38\) | −5.56758 | + | 1.80902i | −0.903181 | + | 0.293461i | ||||
\(39\) | 0.118034 | − | 0.363271i | 0.0189006 | − | 0.0581700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.454915 | + | 1.40008i | 0.0710458 | + | 0.218656i | 0.980275 | − | 0.197640i | \(-0.0633278\pi\) |
−0.909229 | + | 0.416297i | \(0.863328\pi\) | |||||||
\(42\) | 0.673542 | + | 0.927051i | 0.103930 | + | 0.143047i | ||||
\(43\) | 6.23607i | 0.950991i | 0.879718 | + | 0.475496i | \(0.157731\pi\) | ||||
−0.879718 | + | 0.475496i | \(0.842269\pi\) | |||||||
\(44\) | 3.42705 | − | 2.48990i | 0.516647 | − | 0.375366i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.42705 | − | 1.03681i | −0.210407 | − | 0.152870i | ||||
\(47\) | −7.02067 | + | 9.66312i | −1.02407 | + | 1.40951i | −0.114759 | + | 0.993393i | \(0.536609\pi\) |
−0.909311 | + | 0.416117i | \(0.863391\pi\) | |||||||
\(48\) | 0.363271 | + | 0.118034i | 0.0524337 | + | 0.0170367i | ||||
\(49\) | −2.00000 | −0.285714 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.437694 | −0.0612894 | ||||||||
\(52\) | 0.951057 | + | 0.309017i | 0.131888 | + | 0.0428529i | ||||
\(53\) | −6.15537 | + | 8.47214i | −0.845505 | + | 1.16374i | 0.139331 | + | 0.990246i | \(0.455505\pi\) |
−0.984835 | + | 0.173491i | \(0.944495\pi\) | |||||||
\(54\) | −1.80902 | − | 1.31433i | −0.246176 | − | 0.178857i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.42705 | + | 1.76336i | −0.324328 | + | 0.235638i | ||||
\(57\) | − | 2.23607i | − | 0.296174i | ||||||
\(58\) | 5.56758 | + | 7.66312i | 0.731059 | + | 1.00622i | ||||
\(59\) | 1.38197 | + | 4.25325i | 0.179917 | + | 0.553727i | 0.999824 | − | 0.0187700i | \(-0.00597502\pi\) |
−0.819907 | + | 0.572496i | \(0.805975\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.73607 | + | 8.42075i | −0.350318 | + | 1.07817i | 0.608357 | + | 0.793663i | \(0.291829\pi\) |
−0.958675 | + | 0.284504i | \(0.908171\pi\) | |||||||
\(62\) | −0.224514 | + | 0.0729490i | −0.0285133 | + | 0.00926453i | ||||
\(63\) | 8.14324 | − | 2.64590i | 1.02595 | − | 0.333352i | ||||
\(64\) | −0.309017 | + | 0.951057i | −0.0386271 | + | 0.118882i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.500000 | + | 1.53884i | 0.0615457 | + | 0.189418i | ||||
\(67\) | 6.01661 | + | 8.28115i | 0.735046 | + | 1.01170i | 0.998888 | + | 0.0471381i | \(0.0150101\pi\) |
−0.263843 | + | 0.964566i | \(0.584990\pi\) | |||||||
\(68\) | − | 1.14590i | − | 0.138961i | ||||||
\(69\) | 0.545085 | − | 0.396027i | 0.0656205 | − | 0.0476761i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.42705 | + | 1.76336i | 0.288038 | + | 0.209272i | 0.722416 | − | 0.691459i | \(-0.243032\pi\) |
−0.434378 | + | 0.900731i | \(0.643032\pi\) | |||||||
\(72\) | 1.67760 | − | 2.30902i | 0.197707 | − | 0.272120i | ||||
\(73\) | −7.33094 | − | 2.38197i | −0.858021 | − | 0.278788i | −0.153219 | − | 0.988192i | \(-0.548964\pi\) |
−0.704802 | + | 0.709404i | \(0.748964\pi\) | |||||||
\(74\) | −8.32624 | −0.967905 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.85410 | 0.671512 | ||||||||
\(77\) | −12.0862 | − | 3.92705i | −1.37735 | − | 0.447529i | ||||
\(78\) | −0.224514 | + | 0.309017i | −0.0254212 | + | 0.0349893i | ||||
\(79\) | −5.85410 | − | 4.25325i | −0.658638 | − | 0.478528i | 0.207565 | − | 0.978221i | \(-0.433446\pi\) |
−0.866203 | + | 0.499693i | \(0.833446\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.23607 | + | 4.53077i | −0.692896 | + | 0.503419i | ||||
\(82\) | − | 1.47214i | − | 0.162570i | ||||||
\(83\) | −2.66141 | − | 3.66312i | −0.292128 | − | 0.402080i | 0.637576 | − | 0.770387i | \(-0.279937\pi\) |
−0.929704 | + | 0.368308i | \(0.879937\pi\) | |||||||
\(84\) | −0.354102 | − | 1.08981i | −0.0386357 | − | 0.118908i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.92705 | − | 5.93085i | 0.207799 | − | 0.639540i | ||||
\(87\) | −3.44095 | + | 1.11803i | −0.368909 | + | 0.119866i | ||||
\(88\) | −4.02874 | + | 1.30902i | −0.429465 | + | 0.139542i | ||||
\(89\) | −1.38197 | + | 4.25325i | −0.146488 | + | 0.450844i | −0.997199 | − | 0.0747893i | \(-0.976172\pi\) |
0.850711 | + | 0.525633i | \(0.176172\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.927051 | − | 2.85317i | −0.0971813 | − | 0.299093i | ||||
\(92\) | 1.03681 | + | 1.42705i | 0.108095 | + | 0.148780i | ||||
\(93\) | − | 0.0901699i | − | 0.00935019i | ||||||
\(94\) | 9.66312 | − | 7.02067i | 0.996675 | − | 0.724126i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.309017 | − | 0.224514i | −0.0315389 | − | 0.0229144i | ||||
\(97\) | 5.62058 | − | 7.73607i | 0.570684 | − | 0.785479i | −0.421952 | − | 0.906618i | \(-0.638655\pi\) |
0.992635 | + | 0.121140i | \(0.0386549\pi\) | |||||||
\(98\) | 1.90211 | + | 0.618034i | 0.192142 | + | 0.0624309i | ||||
\(99\) | 12.0902 | 1.21511 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.618034 | 0.0614967 | 0.0307483 | − | 0.999527i | \(-0.490211\pi\) | ||||
0.0307483 | + | 0.999527i | \(0.490211\pi\) | |||||||
\(102\) | 0.416272 | + | 0.135255i | 0.0412171 | + | 0.0133922i | ||||
\(103\) | 7.72696 | − | 10.6353i | 0.761360 | − | 1.04792i | −0.235739 | − | 0.971816i | \(-0.575751\pi\) |
0.997100 | − | 0.0761065i | \(-0.0242489\pi\) | |||||||
\(104\) | −0.809017 | − | 0.587785i | −0.0793306 | − | 0.0576371i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.47214 | − | 6.15537i | 0.822887 | − | 0.597862i | ||||
\(107\) | − | 1.09017i | − | 0.105391i | −0.998611 | − | 0.0526954i | \(-0.983219\pi\) | ||
0.998611 | − | 0.0526954i | \(-0.0167812\pi\) | |||||||
\(108\) | 1.31433 | + | 1.80902i | 0.126471 | + | 0.174073i | ||||
\(109\) | 4.63525 | + | 14.2658i | 0.443977 | + | 1.36642i | 0.883602 | + | 0.468239i | \(0.155111\pi\) |
−0.439625 | + | 0.898181i | \(0.644889\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.982779 | − | 3.02468i | 0.0932813 | − | 0.287090i | ||||
\(112\) | 2.85317 | − | 0.927051i | 0.269599 | − | 0.0875981i | ||||
\(113\) | 3.57971 | − | 1.16312i | 0.336751 | − | 0.109417i | −0.135760 | − | 0.990742i | \(-0.543348\pi\) |
0.472511 | + | 0.881325i | \(0.343348\pi\) | |||||||
\(114\) | −0.690983 | + | 2.12663i | −0.0647165 | + | 0.199177i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.92705 | − | 9.00854i | −0.271770 | − | 0.836422i | ||||
\(117\) | 1.67760 | + | 2.30902i | 0.155094 | + | 0.213469i | ||||
\(118\) | − | 4.47214i | − | 0.411693i | ||||||
\(119\) | −2.78115 | + | 2.02063i | −0.254948 | + | 0.185230i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.61803 | − | 4.08174i | −0.510730 | − | 0.371067i | ||||
\(122\) | 5.20431 | − | 7.16312i | 0.471176 | − | 0.648518i | ||||
\(123\) | 0.534785 | + | 0.173762i | 0.0482199 | + | 0.0156676i | ||||
\(124\) | 0.236068 | 0.0211995 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −8.56231 | −0.762791 | ||||||||
\(127\) | −3.35520 | − | 1.09017i | −0.297726 | − | 0.0967369i | 0.156345 | − | 0.987702i | \(-0.450029\pi\) |
−0.454071 | + | 0.890966i | \(0.650029\pi\) | |||||||
\(128\) | 0.587785 | − | 0.809017i | 0.0519534 | − | 0.0715077i | ||||
\(129\) | 1.92705 | + | 1.40008i | 0.169667 | + | 0.123271i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.2812 | − | 9.64932i | 1.16038 | − | 0.843065i | 0.170554 | − | 0.985348i | \(-0.445444\pi\) |
0.989826 | + | 0.142283i | \(0.0454444\pi\) | |||||||
\(132\) | − | 1.61803i | − | 0.140832i | ||||||
\(133\) | −10.3229 | − | 14.2082i | −0.895106 | − | 1.23201i | ||||
\(134\) | −3.16312 | − | 9.73508i | −0.273252 | − | 0.840983i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.354102 | + | 1.08981i | −0.0303640 | + | 0.0934508i | ||||
\(137\) | −4.84104 | + | 1.57295i | −0.413598 | + | 0.134386i | −0.508422 | − | 0.861108i | \(-0.669771\pi\) |
0.0948243 | + | 0.995494i | \(0.469771\pi\) | |||||||
\(138\) | −0.640786 | + | 0.208204i | −0.0545473 | + | 0.0177235i | ||||
\(139\) | 1.64590 | − | 5.06555i | 0.139603 | − | 0.429655i | −0.856674 | − | 0.515858i | \(-0.827473\pi\) |
0.996278 | + | 0.0862030i | \(0.0274734\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.40983 | + | 4.33901i | 0.118729 | + | 0.365411i | ||||
\(142\) | −1.76336 | − | 2.42705i | −0.147978 | − | 0.203674i | ||||
\(143\) | − | 4.23607i | − | 0.354238i | ||||||
\(144\) | −2.30902 | + | 1.67760i | −0.192418 | + | 0.139800i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.23607 | + | 4.53077i | 0.516101 | + | 0.374969i | ||||
\(147\) | −0.449028 | + | 0.618034i | −0.0370352 | + | 0.0509746i | ||||
\(148\) | 7.91872 | + | 2.57295i | 0.650915 | + | 0.211495i | ||||
\(149\) | −2.23607 | −0.183186 | −0.0915929 | − | 0.995797i | \(-0.529196\pi\) | ||||
−0.0915929 | + | 0.995797i | \(0.529196\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.70820 | −0.790042 | −0.395021 | − | 0.918672i | \(-0.629263\pi\) | ||||
−0.395021 | + | 0.918672i | \(0.629263\pi\) | |||||||
\(152\) | −5.56758 | − | 1.80902i | −0.451591 | − | 0.146731i | ||||
\(153\) | 1.92236 | − | 2.64590i | 0.155413 | − | 0.213908i | ||||
\(154\) | 10.2812 | + | 7.46969i | 0.828479 | + | 0.601925i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.309017 | − | 0.224514i | 0.0247412 | − | 0.0179755i | ||||
\(157\) | 4.56231i | 0.364112i | 0.983288 | + | 0.182056i | \(0.0582752\pi\) | ||||
−0.983288 | + | 0.182056i | \(0.941725\pi\) | |||||||
\(158\) | 4.25325 | + | 5.85410i | 0.338371 | + | 0.465727i | ||||
\(159\) | 1.23607 | + | 3.80423i | 0.0980266 | + | 0.301695i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.63525 | − | 5.03280i | 0.128876 | − | 0.396640i | ||||
\(162\) | 7.33094 | − | 2.38197i | 0.575973 | − | 0.187145i | ||||
\(163\) | 1.76336 | − | 0.572949i | 0.138117 | − | 0.0448768i | −0.239143 | − | 0.970984i | \(-0.576866\pi\) |
0.377260 | + | 0.926108i | \(0.376866\pi\) | |||||||
\(164\) | −0.454915 | + | 1.40008i | −0.0355229 | + | 0.109328i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.39919 | + | 4.30625i | 0.108598 | + | 0.334230i | ||||
\(167\) | −7.86572 | − | 10.8262i | −0.608668 | − | 0.837759i | 0.387799 | − | 0.921744i | \(-0.373235\pi\) |
−0.996467 | + | 0.0839844i | \(0.973235\pi\) | |||||||
\(168\) | 1.14590i | 0.0884080i | ||||||||
\(169\) | −9.70820 | + | 7.05342i | −0.746785 | + | 0.542571i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 13.5172 | + | 9.82084i | 1.03369 | + | 0.751018i | ||||
\(172\) | −3.66547 | + | 5.04508i | −0.279489 | + | 0.384684i | ||||
\(173\) | 1.17557 | + | 0.381966i | 0.0893770 | + | 0.0290403i | 0.353364 | − | 0.935486i | \(-0.385038\pi\) |
−0.263987 | + | 0.964526i | \(0.585038\pi\) | |||||||
\(174\) | 3.61803 | 0.274282 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.23607 | 0.319306 | ||||||||
\(177\) | 1.62460 | + | 0.527864i | 0.122112 | + | 0.0396767i | ||||
\(178\) | 2.62866 | − | 3.61803i | 0.197026 | − | 0.271183i | ||||
\(179\) | 9.04508 | + | 6.57164i | 0.676061 | + | 0.491187i | 0.872049 | − | 0.489419i | \(-0.162791\pi\) |
−0.195987 | + | 0.980606i | \(0.562791\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.38197 | + | 3.18368i | −0.325709 | + | 0.236641i | −0.738608 | − | 0.674136i | \(-0.764516\pi\) |
0.412899 | + | 0.910777i | \(0.364516\pi\) | |||||||
\(182\) | 3.00000i | 0.222375i | ||||||||
\(183\) | 1.98787 | + | 2.73607i | 0.146948 | + | 0.202256i | ||||
\(184\) | −0.545085 | − | 1.67760i | −0.0401842 | − | 0.123674i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.0278640 | + | 0.0857567i | −0.00204309 | + | 0.00628799i | ||||
\(187\) | −4.61653 | + | 1.50000i | −0.337594 | + | 0.109691i | ||||
\(188\) | −11.3597 | + | 3.69098i | −0.828490 | + | 0.269193i | ||||
\(189\) | 2.07295 | − | 6.37988i | 0.150785 | − | 0.464068i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.21885 | − | 12.9843i | −0.305265 | − | 0.939509i | −0.979578 | − | 0.201064i | \(-0.935560\pi\) |
0.674313 | − | 0.738446i | \(-0.264440\pi\) | |||||||
\(192\) | 0.224514 | + | 0.309017i | 0.0162029 | + | 0.0223014i | ||||
\(193\) | 14.6525i | 1.05471i | 0.849646 | + | 0.527354i | \(0.176816\pi\) | ||||
−0.849646 | + | 0.527354i | \(0.823184\pi\) | |||||||
\(194\) | −7.73607 | + | 5.62058i | −0.555417 | + | 0.403534i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.61803 | − | 1.17557i | −0.115574 | − | 0.0839693i | ||||
\(197\) | 7.05342 | − | 9.70820i | 0.502536 | − | 0.691681i | −0.480103 | − | 0.877212i | \(-0.659401\pi\) |
0.982638 | + | 0.185531i | \(0.0594006\pi\) | |||||||
\(198\) | −11.4984 | − | 3.73607i | −0.817158 | − | 0.265511i | ||||
\(199\) | −2.56231 | −0.181637 | −0.0908185 | − | 0.995867i | \(-0.528948\pi\) | ||||
−0.0908185 | + | 0.995867i | \(0.528948\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.90983 | 0.275778 | ||||||||
\(202\) | −0.587785 | − | 0.190983i | −0.0413564 | − | 0.0134375i | ||||
\(203\) | −16.7027 | + | 22.9894i | −1.17230 | + | 1.61354i | ||||
\(204\) | −0.354102 | − | 0.257270i | −0.0247921 | − | 0.0180125i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −10.6353 | + | 7.72696i | −0.740993 | + | 0.538363i | ||||
\(207\) | 5.03444i | 0.349918i | ||||||||
\(208\) | 0.587785 | + | 0.809017i | 0.0407556 | + | 0.0560952i | ||||
\(209\) | −7.66312 | − | 23.5847i | −0.530069 | − | 1.63138i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.88197 | + | 21.1805i | −0.473774 | + | 1.45813i | 0.373830 | + | 0.927497i | \(0.378044\pi\) |
−0.847604 | + | 0.530629i | \(0.821956\pi\) | |||||||
\(212\) | −9.95959 | + | 3.23607i | −0.684028 | + | 0.222254i | ||||
\(213\) | 1.08981 | − | 0.354102i | 0.0746728 | − | 0.0242627i | ||||
\(214\) | −0.336881 | + | 1.03681i | −0.0230287 | + | 0.0708751i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.690983 | − | 2.12663i | −0.0470154 | − | 0.144699i | ||||
\(217\) | −0.416272 | − | 0.572949i | −0.0282584 | − | 0.0388943i | ||||
\(218\) | − | 15.0000i | − | 1.01593i | ||||||
\(219\) | −2.38197 | + | 1.73060i | −0.160958 | + | 0.116943i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.927051 | − | 0.673542i | −0.0623602 | − | 0.0453073i | ||||
\(222\) | −1.86936 | + | 2.57295i | −0.125463 | + | 0.172685i | ||||
\(223\) | 8.55951 | + | 2.78115i | 0.573187 | + | 0.186240i | 0.581246 | − | 0.813728i | \(-0.302565\pi\) |
−0.00805911 | + | 0.999968i | \(0.502565\pi\) | |||||||
\(224\) | −3.00000 | −0.200446 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.76393 | −0.250373 | ||||||||
\(227\) | 27.9237 | + | 9.07295i | 1.85336 | + | 0.602193i | 0.996195 | + | 0.0871483i | \(0.0277754\pi\) |
0.857163 | + | 0.515044i | \(0.172225\pi\) | |||||||
\(228\) | 1.31433 | − | 1.80902i | 0.0870435 | − | 0.119805i | ||||
\(229\) | −2.07295 | − | 1.50609i | −0.136984 | − | 0.0995249i | 0.517183 | − | 0.855875i | \(-0.326981\pi\) |
−0.654167 | + | 0.756350i | \(0.726981\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.92705 | + | 2.85317i | −0.258381 | + | 0.187725i | ||||
\(232\) | 9.47214i | 0.621876i | ||||||||
\(233\) | 8.40051 | + | 11.5623i | 0.550336 | + | 0.757472i | 0.990058 | − | 0.140662i | \(-0.0449231\pi\) |
−0.439722 | + | 0.898134i | \(0.644923\pi\) | |||||||
\(234\) | −0.881966 | − | 2.71441i | −0.0576559 | − | 0.177447i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.38197 | + | 4.25325i | −0.0899583 | + | 0.276863i | ||||
\(237\) | −2.62866 | + | 0.854102i | −0.170750 | + | 0.0554799i | ||||
\(238\) | 3.26944 | − | 1.06231i | 0.211926 | − | 0.0688591i | ||||
\(239\) | 2.13525 | − | 6.57164i | 0.138118 | − | 0.425084i | −0.857944 | − | 0.513743i | \(-0.828258\pi\) |
0.996062 | + | 0.0886595i | \(0.0282583\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.82624 | + | 14.8536i | 0.310885 | + | 0.956807i | 0.977415 | + | 0.211328i | \(0.0677789\pi\) |
−0.666530 | + | 0.745478i | \(0.732221\pi\) | |||||||
\(242\) | 4.08174 | + | 5.61803i | 0.262384 | + | 0.361141i | ||||
\(243\) | 9.65248i | 0.619207i | ||||||||
\(244\) | −7.16312 | + | 5.20431i | −0.458572 | + | 0.333172i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.454915 | − | 0.330515i | −0.0290043 | − | 0.0210729i | ||||
\(247\) | 3.44095 | − | 4.73607i | 0.218943 | − | 0.301349i | ||||
\(248\) | −0.224514 | − | 0.0729490i | −0.0142567 | − | 0.00463227i | ||||
\(249\) | −1.72949 | −0.109602 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.819660 | 0.0517365 | 0.0258682 | − | 0.999665i | \(-0.491765\pi\) | ||||
0.0258682 | + | 0.999665i | \(0.491765\pi\) | |||||||
\(252\) | 8.14324 | + | 2.64590i | 0.512976 | + | 0.166676i | ||||
\(253\) | 4.39201 | − | 6.04508i | 0.276123 | − | 0.380051i | ||||
\(254\) | 2.85410 | + | 2.07363i | 0.179082 | + | 0.130111i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.809017 | + | 0.587785i | −0.0505636 | + | 0.0367366i | ||||
\(257\) | 25.7426i | 1.60578i | 0.596126 | + | 0.802891i | \(0.296706\pi\) | ||||
−0.596126 | + | 0.802891i | \(0.703294\pi\) | |||||||
\(258\) | −1.40008 | − | 1.92705i | −0.0871655 | − | 0.119973i | ||||
\(259\) | −7.71885 | − | 23.7562i | −0.479626 | − | 1.47614i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.35410 | − | 25.7113i | 0.517106 | − | 1.59149i | ||||
\(262\) | −15.6129 | + | 5.07295i | −0.964570 | + | 0.313408i | ||||
\(263\) | 4.39201 | − | 1.42705i | 0.270823 | − | 0.0879957i | −0.170457 | − | 0.985365i | \(-0.554524\pi\) |
0.441280 | + | 0.897369i | \(0.354524\pi\) | |||||||
\(264\) | −0.500000 | + | 1.53884i | −0.0307729 | + | 0.0947092i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5.42705 | + | 16.7027i | 0.332754 | + | 1.02411i | ||||
\(267\) | 1.00406 | + | 1.38197i | 0.0614473 | + | 0.0845749i | ||||
\(268\) | 10.2361i | 0.625267i | ||||||||
\(269\) | 1.54508 | − | 1.12257i | 0.0942055 | − | 0.0684443i | −0.539685 | − | 0.841867i | \(-0.681457\pi\) |
0.633891 | + | 0.773422i | \(0.281457\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.0623 | − | 16.7557i | −1.40094 | − | 1.01784i | −0.994564 | − | 0.104131i | \(-0.966794\pi\) |
−0.406372 | − | 0.913708i | \(-0.633206\pi\) | |||||||
\(272\) | 0.673542 | − | 0.927051i | 0.0408395 | − | 0.0562107i | ||||
\(273\) | −1.08981 | − | 0.354102i | −0.0659585 | − | 0.0214312i | ||||
\(274\) | 5.09017 | 0.307508 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.673762 | 0.0405557 | ||||||||
\(277\) | 0.277515 | + | 0.0901699i | 0.0166742 | + | 0.00541779i | 0.317342 | − | 0.948311i | \(-0.397210\pi\) |
−0.300668 | + | 0.953729i | \(0.597210\pi\) | |||||||
\(278\) | −3.13068 | + | 4.30902i | −0.187766 | + | 0.258438i | ||||
\(279\) | 0.545085 | + | 0.396027i | 0.0326334 | + | 0.0237095i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.57295 | + | 1.86936i | −0.153489 | + | 0.111516i | −0.661879 | − | 0.749610i | \(-0.730241\pi\) |
0.508390 | + | 0.861127i | \(0.330241\pi\) | |||||||
\(282\) | − | 4.56231i | − | 0.271681i | ||||||
\(283\) | −7.22494 | − | 9.94427i | −0.429478 | − | 0.591126i | 0.538355 | − | 0.842718i | \(-0.319046\pi\) |
−0.967833 | + | 0.251592i | \(0.919046\pi\) | |||||||
\(284\) | 0.927051 | + | 2.85317i | 0.0550104 | + | 0.169304i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.30902 | + | 4.02874i | −0.0774038 | + | 0.238224i | ||||
\(287\) | 4.20025 | − | 1.36475i | 0.247933 | − | 0.0805584i | ||||
\(288\) | 2.71441 | − | 0.881966i | 0.159948 | − | 0.0519703i | ||||
\(289\) | 4.84752 | − | 14.9191i | 0.285148 | − | 0.877597i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.12868 | − | 3.47371i | −0.0661642 | − | 0.203633i | ||||
\(292\) | −4.53077 | − | 6.23607i | −0.265143 | − | 0.364938i | ||||
\(293\) | − | 8.56231i | − | 0.500215i | −0.968218 | − | 0.250108i | \(-0.919534\pi\) | ||
0.968218 | − | 0.250108i | \(-0.0804660\pi\) | |||||||
\(294\) | 0.618034 | − | 0.449028i | 0.0360445 | − | 0.0261878i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.73607 | − | 4.89404i | −0.391526 | − | 0.284460i | ||||
\(297\) | 5.56758 | − | 7.66312i | 0.323064 | − | 0.444659i | ||||
\(298\) | 2.12663 | + | 0.690983i | 0.123192 | + | 0.0400276i | ||||
\(299\) | 1.76393 | 0.102011 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.7082 | 1.07832 | ||||||||
\(302\) | 9.23305 | + | 3.00000i | 0.531302 | + | 0.172631i | ||||
\(303\) | 0.138757 | − | 0.190983i | 0.00797140 | − | 0.0109717i | ||||
\(304\) | 4.73607 | + | 3.44095i | 0.271632 | + | 0.197352i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.64590 | + | 1.92236i | −0.151256 | + | 0.109894i | ||||
\(307\) | − | 23.1246i | − | 1.31979i | −0.751357 | − | 0.659896i | \(-0.770600\pi\) | ||
0.751357 | − | 0.659896i | \(-0.229400\pi\) | |||||||
\(308\) | −7.46969 | − | 10.2812i | −0.425625 | − | 0.585823i | ||||
\(309\) | −1.55166 | − | 4.77553i | −0.0882710 | − | 0.271670i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.06231 | + | 9.42481i | −0.173647 | + | 0.534432i | −0.999569 | − | 0.0293530i | \(-0.990655\pi\) |
0.825922 | + | 0.563785i | \(0.190655\pi\) | |||||||
\(312\) | −0.363271 | + | 0.118034i | −0.0205662 | + | 0.00668236i | ||||
\(313\) | −15.7517 | + | 5.11803i | −0.890338 | + | 0.289288i | −0.718243 | − | 0.695792i | \(-0.755054\pi\) |
−0.172095 | + | 0.985080i | \(0.555054\pi\) | |||||||
\(314\) | 1.40983 | − | 4.33901i | 0.0795613 | − | 0.244865i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.23607 | − | 6.88191i | −0.125789 | − | 0.387138i | ||||
\(317\) | −4.92680 | − | 6.78115i | −0.276716 | − | 0.380867i | 0.647926 | − | 0.761703i | \(-0.275636\pi\) |
−0.924643 | + | 0.380835i | \(0.875636\pi\) | |||||||
\(318\) | − | 4.00000i | − | 0.224309i | ||||||
\(319\) | −32.4615 | + | 23.5847i | −1.81749 | + | 1.32049i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.336881 | − | 0.244758i | −0.0188029 | − | 0.0136611i | ||||
\(322\) | −3.11044 | + | 4.28115i | −0.173338 | + | 0.238579i | ||||
\(323\) | −6.37988 | − | 2.07295i | −0.354986 | − | 0.115342i | ||||
\(324\) | −7.70820 | −0.428234 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.85410 | −0.102689 | ||||||||
\(327\) | 5.44907 | + | 1.77051i | 0.301334 | + | 0.0979094i | ||||
\(328\) | 0.865300 | − | 1.19098i | 0.0477782 | − | 0.0657610i | ||||
\(329\) | 28.9894 | + | 21.0620i | 1.59823 | + | 1.16119i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.5902 | − | 9.14729i | 0.692018 | − | 0.502781i | −0.185305 | − | 0.982681i | \(-0.559327\pi\) |
0.877323 | + | 0.479900i | \(0.159327\pi\) | |||||||
\(332\) | − | 4.52786i | − | 0.248499i | ||||||
\(333\) | 13.9681 | + | 19.2254i | 0.765447 | + | 1.05355i | ||||
\(334\) | 4.13525 | + | 12.7270i | 0.226271 | + | 0.696391i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.354102 | − | 1.08981i | 0.0193178 | − | 0.0594542i | ||||
\(337\) | 4.35926 | − | 1.41641i | 0.237464 | − | 0.0771567i | −0.187868 | − | 0.982194i | \(-0.560158\pi\) |
0.425331 | + | 0.905038i | \(0.360158\pi\) | |||||||
\(338\) | 11.4127 | − | 3.70820i | 0.620768 | − | 0.201700i | ||||
\(339\) | 0.444272 | − | 1.36733i | 0.0241295 | − | 0.0742631i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.309017 | − | 0.951057i | −0.0167342 | − | 0.0515026i | ||||
\(342\) | −9.82084 | − | 13.5172i | −0.531050 | − | 0.730928i | ||||
\(343\) | − | 15.0000i | − | 0.809924i | ||||||
\(344\) | 5.04508 | − | 3.66547i | 0.272013 | − | 0.197629i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.00000 | − | 0.726543i | −0.0537603 | − | 0.0390592i | ||||
\(347\) | −12.3965 | + | 17.0623i | −0.665478 | + | 0.915953i | −0.999647 | − | 0.0265607i | \(-0.991544\pi\) |
0.334169 | + | 0.942513i | \(0.391544\pi\) | |||||||
\(348\) | −3.44095 | − | 1.11803i | −0.184455 | − | 0.0599329i | ||||
\(349\) | 17.7639 | 0.950881 | 0.475441 | − | 0.879748i | \(-0.342289\pi\) | ||||
0.475441 | + | 0.879748i | \(0.342289\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.23607 | 0.119352 | ||||||||
\(352\) | −4.02874 | − | 1.30902i | −0.214733 | − | 0.0697708i | ||||
\(353\) | 12.4822 | − | 17.1803i | 0.664363 | − | 0.914417i | −0.335253 | − | 0.942128i | \(-0.608822\pi\) |
0.999616 | + | 0.0277109i | \(0.00882179\pi\) | |||||||
\(354\) | −1.38197 | − | 1.00406i | −0.0734507 | − | 0.0533650i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3.61803 | + | 2.62866i | −0.191755 | + | 0.139318i | ||||
\(357\) | 1.31308i | 0.0694957i | ||||||||
\(358\) | −6.57164 | − | 9.04508i | −0.347322 | − | 0.478048i | ||||
\(359\) | 2.50000 | + | 7.69421i | 0.131945 | + | 0.406085i | 0.995102 | − | 0.0988502i | \(-0.0315165\pi\) |
−0.863157 | + | 0.504935i | \(0.831516\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.71885 | − | 14.5231i | 0.248360 | − | 0.764375i | ||||
\(362\) | 5.15131 | − | 1.67376i | 0.270747 | − | 0.0879710i | ||||
\(363\) | −2.52265 | + | 0.819660i | −0.132405 | + | 0.0430210i | ||||
\(364\) | 0.927051 | − | 2.85317i | 0.0485907 | − | 0.149547i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.04508 | − | 3.21644i | −0.0546275 | − | 0.168126i | ||||
\(367\) | −20.8905 | − | 28.7533i | −1.09047 | − | 1.50091i | −0.847440 | − | 0.530892i | \(-0.821857\pi\) |
−0.243035 | − | 0.970018i | \(-0.578143\pi\) | |||||||
\(368\) | 1.76393i | 0.0919513i | ||||||||
\(369\) | −3.39919 | + | 2.46965i | −0.176955 | + | 0.128565i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 25.4164 | + | 18.4661i | 1.31955 | + | 0.958712i | ||||
\(372\) | 0.0530006 | − | 0.0729490i | 0.00274795 | − | 0.00378223i | ||||
\(373\) | 11.1882 | + | 3.63525i | 0.579301 | + | 0.188226i | 0.583987 | − | 0.811763i | \(-0.301492\pi\) |
−0.00468631 | + | 0.999989i | \(0.501492\pi\) | |||||||
\(374\) | 4.85410 | 0.251000 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11.9443 | 0.615979 | ||||||||
\(377\) | −9.00854 | − | 2.92705i | −0.463963 | − | 0.150751i | ||||
\(378\) | −3.94298 | + | 5.42705i | −0.202805 | + | 0.279137i | ||||
\(379\) | 7.66312 | + | 5.56758i | 0.393628 | + | 0.285987i | 0.766941 | − | 0.641718i | \(-0.221778\pi\) |
−0.373313 | + | 0.927706i | \(0.621778\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.09017 | + | 0.792055i | −0.0558511 | + | 0.0405782i | ||||
\(382\) | 13.6525i | 0.698521i | ||||||||
\(383\) | 6.65740 | + | 9.16312i | 0.340177 | + | 0.468214i | 0.944493 | − | 0.328531i | \(-0.106554\pi\) |
−0.604316 | + | 0.796745i | \(0.706554\pi\) | |||||||
\(384\) | −0.118034 | − | 0.363271i | −0.00602340 | − | 0.0185381i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.52786 | − | 13.9353i | 0.230462 | − | 0.709290i | ||||
\(387\) | −16.9273 | + | 5.50000i | −0.860461 | + | 0.279581i | ||||
\(388\) | 9.09429 | − | 2.95492i | 0.461693 | − | 0.150013i | ||||
\(389\) | −5.62868 | + | 17.3233i | −0.285385 | + | 0.878326i | 0.700898 | + | 0.713262i | \(0.252783\pi\) |
−0.986283 | + | 0.165064i | \(0.947217\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.624612 | − | 1.92236i | −0.0315880 | − | 0.0972178i | ||||
\(392\) | 1.17557 | + | 1.61803i | 0.0593753 | + | 0.0817231i | ||||
\(393\) | − | 6.27051i | − | 0.316305i | ||||||
\(394\) | −9.70820 | + | 7.05342i | −0.489092 | + | 0.355346i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 9.78115 | + | 7.10642i | 0.491521 | + | 0.357111i | ||||
\(397\) | −6.01661 | + | 8.28115i | −0.301965 | + | 0.415619i | −0.932854 | − | 0.360254i | \(-0.882690\pi\) |
0.630889 | + | 0.775873i | \(0.282690\pi\) | |||||||
\(398\) | 2.43690 | + | 0.791796i | 0.122151 | + | 0.0396892i | ||||
\(399\) | −6.70820 | −0.335830 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.1803 | −0.708132 | −0.354066 | − | 0.935220i | \(-0.615201\pi\) | ||||
−0.354066 | + | 0.935220i | \(0.615201\pi\) | |||||||
\(402\) | −3.71847 | − | 1.20820i | −0.185460 | − | 0.0602597i | ||||
\(403\) | 0.138757 | − | 0.190983i | 0.00691199 | − | 0.00951354i | ||||
\(404\) | 0.500000 | + | 0.363271i | 0.0248759 | + | 0.0180734i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 22.9894 | − | 16.7027i | 1.14094 | − | 0.828943i | ||||
\(407\) | − | 35.2705i | − | 1.74829i | ||||||
\(408\) | 0.257270 | + | 0.354102i | 0.0127368 | + | 0.0175307i | ||||
\(409\) | 2.07295 | + | 6.37988i | 0.102501 | + | 0.315465i | 0.989136 | − | 0.147005i | \(-0.0469634\pi\) |
−0.886635 | + | 0.462470i | \(0.846963\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.600813 | + | 1.84911i | −0.0296359 | + | 0.0912100i | ||||
\(412\) | 12.5025 | − | 4.06231i | 0.615954 | − | 0.200135i | ||||
\(413\) | 12.7598 | − | 4.14590i | 0.627867 | − | 0.204006i | ||||
\(414\) | 1.55573 | − | 4.78804i | 0.0764599 | − | 0.235319i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.309017 | − | 0.951057i | −0.0151508 | − | 0.0466294i | ||||
\(417\) | −1.19581 | − | 1.64590i | −0.0585593 | − | 0.0806000i | ||||
\(418\) | 24.7984i | 1.21293i | ||||||||
\(419\) | 18.4164 | − | 13.3803i | 0.899700 | − | 0.653671i | −0.0386886 | − | 0.999251i | \(-0.512318\pi\) |
0.938389 | + | 0.345581i | \(0.112318\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.2082 | − | 12.5025i | −0.838677 | − | 0.609334i | 0.0833241 | − | 0.996522i | \(-0.473446\pi\) |
−0.922001 | + | 0.387188i | \(0.873446\pi\) | |||||||
\(422\) | 13.0903 | − | 18.0172i | 0.637225 | − | 0.877065i | ||||
\(423\) | −32.4217 | − | 10.5344i | −1.57640 | − | 0.512202i | ||||
\(424\) | 10.4721 | 0.508572 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.14590 | −0.0555189 | ||||||||
\(427\) | 25.2623 | + | 8.20820i | 1.22253 | + | 0.397223i | ||||
\(428\) | 0.640786 | − | 0.881966i | 0.0309736 | − | 0.0426314i | ||||
\(429\) | −1.30902 | − | 0.951057i | −0.0631999 | − | 0.0459174i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.0902 | + | 15.3229i | −1.01588 | + | 0.738078i | −0.965434 | − | 0.260649i | \(-0.916064\pi\) |
−0.0504440 | + | 0.998727i | \(0.516064\pi\) | |||||||
\(432\) | 2.23607i | 0.107583i | ||||||||
\(433\) | −12.5555 | − | 17.2812i | −0.603378 | − | 0.830479i | 0.392634 | − | 0.919695i | \(-0.371564\pi\) |
−0.996012 | + | 0.0892157i | \(0.971564\pi\) | |||||||
\(434\) | 0.218847 | + | 0.673542i | 0.0105050 | + | 0.0323310i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.63525 | + | 14.2658i | −0.221988 | + | 0.683210i | ||||
\(437\) | 9.82084 | − | 3.19098i | 0.469794 | − | 0.152645i | ||||
\(438\) | 2.80017 | − | 0.909830i | 0.133797 | − | 0.0434734i | ||||
\(439\) | −7.92705 | + | 24.3970i | −0.378338 | + | 1.16440i | 0.562862 | + | 0.826551i | \(0.309700\pi\) |
−0.941199 | + | 0.337852i | \(0.890300\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.76393 | − | 5.42882i | −0.0839968 | − | 0.258515i | ||||
\(442\) | 0.673542 | + | 0.927051i | 0.0320371 | + | 0.0440953i | ||||
\(443\) | − | 19.4164i | − | 0.922501i | −0.887270 | − | 0.461251i | \(-0.847401\pi\) | ||
0.887270 | − | 0.461251i | \(-0.152599\pi\) | |||||||
\(444\) | 2.57295 | − | 1.86936i | 0.122107 | − | 0.0887158i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.28115 | − | 5.29007i | −0.344773 | − | 0.250492i | ||||
\(447\) | −0.502029 | + | 0.690983i | −0.0237451 | + | 0.0326824i | ||||
\(448\) | 2.85317 | + | 0.927051i | 0.134800 | + | 0.0437990i | ||||
\(449\) | 3.94427 | 0.186142 | 0.0930709 | − | 0.995659i | \(-0.470332\pi\) | ||||
0.0930709 | + | 0.995659i | \(0.470332\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.23607 | 0.293645 | ||||||||
\(452\) | 3.57971 | + | 1.16312i | 0.168375 | + | 0.0547085i | ||||
\(453\) | −2.17963 | + | 3.00000i | −0.102408 | + | 0.140952i | ||||
\(454\) | −23.7533 | − | 17.2578i | −1.11480 | − | 0.809947i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.80902 | + | 1.31433i | −0.0847150 | + | 0.0615490i | ||||
\(457\) | 40.2148i | 1.88117i | 0.339561 | + | 0.940584i | \(0.389722\pi\) | ||||
−0.339561 | + | 0.940584i | \(0.610278\pi\) | |||||||
\(458\) | 1.50609 | + | 2.07295i | 0.0703748 | + | 0.0968625i | ||||
\(459\) | −0.791796 | − | 2.43690i | −0.0369579 | − | 0.113745i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.79837 | − | 5.53483i | 0.0837586 | − | 0.257783i | −0.900403 | − | 0.435057i | \(-0.856728\pi\) |
0.984161 | + | 0.177275i | \(0.0567281\pi\) | |||||||
\(462\) | 4.61653 | − | 1.50000i | 0.214780 | − | 0.0697863i | ||||
\(463\) | −33.2667 | + | 10.8090i | −1.54604 | + | 0.502338i | −0.953034 | − | 0.302863i | \(-0.902057\pi\) |
−0.593002 | + | 0.805201i | \(0.702057\pi\) | |||||||
\(464\) | 2.92705 | − | 9.00854i | 0.135885 | − | 0.418211i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.41641 | − | 13.5923i | −0.204586 | − | 0.629651i | ||||
\(467\) | 11.2739 | + | 15.5172i | 0.521695 | + | 0.718051i | 0.985836 | − | 0.167710i | \(-0.0536371\pi\) |
−0.464142 | + | 0.885761i | \(0.653637\pi\) | |||||||
\(468\) | 2.85410i | 0.131931i | ||||||||
\(469\) | 24.8435 | − | 18.0498i | 1.14716 | − | 0.833464i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.40983 | + | 1.02430i | 0.0649615 | + | 0.0471973i | ||||
\(472\) | 2.62866 | − | 3.61803i | 0.120994 | − | 0.166534i | ||||
\(473\) | 25.1235 | + | 8.16312i | 1.15518 | + | 0.375341i | ||||
\(474\) | 2.76393 | 0.126952 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.43769 | −0.157566 | ||||||||
\(477\) | −28.4257 | − | 9.23607i | −1.30152 | − | 0.422891i | ||||
\(478\) | −4.06150 | + | 5.59017i | −0.185769 | + | 0.255688i | ||||
\(479\) | −12.2984 | − | 8.93529i | −0.561927 | − | 0.408264i | 0.270237 | − | 0.962794i | \(-0.412898\pi\) |
−0.832164 | + | 0.554530i | \(0.812898\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.73607 | − | 4.89404i | 0.307138 | − | 0.223149i | ||||
\(482\) | − | 15.6180i | − | 0.711382i | ||||||
\(483\) | −1.18808 | − | 1.63525i | −0.0540596 | − | 0.0744067i | ||||
\(484\) | −2.14590 | − | 6.60440i | −0.0975408 | − | 0.300200i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.98278 | − | 9.18005i | 0.135302 | − | 0.416416i | ||||
\(487\) | −21.0418 | + | 6.83688i | −0.953493 | + | 0.309809i | −0.744134 | − | 0.668030i | \(-0.767138\pi\) |
−0.209359 | + | 0.977839i | \(0.567138\pi\) | |||||||
\(488\) | 8.42075 | − | 2.73607i | 0.381190 | − | 0.123856i | ||||
\(489\) | 0.218847 | − | 0.673542i | 0.00989661 | − | 0.0304586i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.94427 | + | 18.2946i | 0.268261 | + | 0.825623i | 0.990924 | + | 0.134423i | \(0.0429179\pi\) |
−0.722663 | + | 0.691201i | \(0.757082\pi\) | |||||||
\(492\) | 0.330515 | + | 0.454915i | 0.0149008 | + | 0.0205092i | ||||
\(493\) | 10.8541i | 0.488844i | ||||||||
\(494\) | −4.73607 | + | 3.44095i | −0.213086 | + | 0.154816i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.190983 | + | 0.138757i | 0.00857539 | + | 0.00623039i | ||||
\(497\) | 5.29007 | − | 7.28115i | 0.237292 | − | 0.326604i | ||||
\(498\) | 1.64484 | + | 0.534442i | 0.0737072 | + | 0.0239489i | ||||
\(499\) | −34.1459 | −1.52858 | −0.764290 | − | 0.644873i | \(-0.776910\pi\) | ||||
−0.764290 | + | 0.644873i | \(0.776910\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.11146 | −0.228363 | ||||||||
\(502\) | −0.779543 | − | 0.253289i | −0.0347927 | − | 0.0113048i | ||||
\(503\) | 17.9313 | − | 24.6803i | 0.799518 | − | 1.10044i | −0.193339 | − | 0.981132i | \(-0.561932\pi\) |
0.992857 | − | 0.119310i | \(-0.0380682\pi\) | |||||||
\(504\) | −6.92705 | − | 5.03280i | −0.308555 | − | 0.224179i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −6.04508 | + | 4.39201i | −0.268737 | + | 0.195249i | ||||
\(507\) | 4.58359i | 0.203564i | ||||||||
\(508\) | −2.07363 | − | 2.85410i | −0.0920023 | − | 0.126630i | ||||
\(509\) | 0.590170 | + | 1.81636i | 0.0261588 | + | 0.0805086i | 0.963284 | − | 0.268486i | \(-0.0865232\pi\) |
−0.937125 | + | 0.348994i | \(0.886523\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.14590 | + | 21.9928i | −0.316116 | + | 0.972905i | ||||
\(512\) | 0.951057 | − | 0.309017i | 0.0420312 | − | 0.0136568i | ||||
\(513\) | 12.4495 | − | 4.04508i | 0.549658 | − | 0.178595i | ||||
\(514\) | 7.95492 | − | 24.4827i | 0.350876 | − | 1.07989i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.736068 | + | 2.26538i | 0.0324036 | + | 0.0997280i | ||||
\(517\) | 29.7400 | + | 40.9336i | 1.30796 | + | 1.80026i | ||||
\(518\) | 24.9787i | 1.09750i | ||||||||
\(519\) | 0.381966 | − | 0.277515i | 0.0167664 | − | 0.0121815i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.9721 | + | 13.7841i | 0.831184 | + | 0.603891i | 0.919894 | − | 0.392167i | \(-0.128274\pi\) |
−0.0887098 | + | 0.996058i | \(0.528274\pi\) | |||||||
\(522\) | −15.8904 | + | 21.8713i | −0.695506 | + | 0.957282i | ||||
\(523\) | 4.42477 | + | 1.43769i | 0.193482 | + | 0.0628660i | 0.404155 | − | 0.914691i | \(-0.367566\pi\) |
−0.210673 | + | 0.977557i | \(0.567566\pi\) | |||||||
\(524\) | 16.4164 | 0.717154 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.61803 | −0.201356 | ||||||||
\(527\) | −0.257270 | − | 0.0835921i | −0.0112069 | − | 0.00364133i | ||||
\(528\) | 0.951057 | − | 1.30902i | 0.0413894 | − | 0.0569677i | ||||
\(529\) | −16.0902 | − | 11.6902i | −0.699573 | − | 0.508269i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.3262 | + | 7.50245i | −0.448121 | + | 0.325579i | ||||
\(532\) | − | 17.5623i | − | 0.761423i | ||||||
\(533\) | 0.865300 | + | 1.19098i | 0.0374803 | + | 0.0515872i | ||||
\(534\) | −0.527864 | − | 1.62460i | −0.0228429 | − | 0.0703033i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.16312 | − | 9.73508i | 0.136626 | − | 0.420491i | ||||
\(537\) | 4.06150 | − | 1.31966i | 0.175266 | − | 0.0569475i | ||||
\(538\) | −1.81636 | + | 0.590170i | −0.0783087 | + | 0.0254440i | ||||
\(539\) | −2.61803 | + | 8.05748i | −0.112767 | + | 0.347060i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.72542 | + | 14.5434i | 0.203162 | + | 0.625268i | 0.999784 | + | 0.0207902i | \(0.00661819\pi\) |
−0.796622 | + | 0.604478i | \(0.793382\pi\) | |||||||
\(542\) | 16.7557 | + | 23.0623i | 0.719721 | + | 0.990611i | ||||
\(543\) | 2.06888i | 0.0887843i | ||||||||
\(544\) | −0.927051 | + | 0.673542i | −0.0397470 | + | 0.0288779i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.927051 | + | 0.673542i | 0.0396741 | + | 0.0288249i | ||||
\(547\) | 4.92680 | − | 6.78115i | 0.210655 | − | 0.289941i | −0.690595 | − | 0.723242i | \(-0.742651\pi\) |
0.901249 | + | 0.433301i | \(0.142651\pi\) | |||||||
\(548\) | −4.84104 | − | 1.57295i | −0.206799 | − | 0.0671931i | ||||
\(549\) | −25.2705 | −1.07852 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −55.4508 | −2.36229 | ||||||||
\(552\) | −0.640786 | − | 0.208204i | −0.0272737 | − | 0.00886175i | ||||
\(553\) | −12.7598 | + | 17.5623i | −0.542600 | + | 0.746825i | ||||
\(554\) | −0.236068 | − | 0.171513i | −0.0100296 | − | 0.00728691i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.30902 | − | 3.13068i | 0.182743 | − | 0.132771i | ||||
\(557\) | 24.8885i | 1.05456i | 0.849691 | + | 0.527281i | \(0.176788\pi\) | ||||
−0.849691 | + | 0.527281i | \(0.823212\pi\) | |||||||
\(558\) | −0.396027 | − | 0.545085i | −0.0167652 | − | 0.0230753i | ||||
\(559\) | 1.92705 | + | 5.93085i | 0.0815056 | + | 0.250848i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.572949 | + | 1.76336i | −0.0241899 | + | 0.0744489i | ||||
\(562\) | 3.02468 | − | 0.982779i | 0.127589 | − | 0.0414560i | ||||
\(563\) | −26.7683 | + | 8.69756i | −1.12815 | + | 0.366558i | −0.812873 | − | 0.582441i | \(-0.802098\pi\) |
−0.315278 | + | 0.948999i | \(0.602098\pi\) | |||||||
\(564\) | −1.40983 | + | 4.33901i | −0.0593646 | + | 0.182705i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3.79837 | + | 11.6902i | 0.159658 | + | 0.491375i | ||||
\(567\) | 13.5923 | + | 18.7082i | 0.570823 | + | 0.785671i | ||||
\(568\) | − | 3.00000i | − | 0.125877i | ||||||
\(569\) | 14.3713 | − | 10.4414i | 0.602477 | − | 0.437725i | −0.244280 | − | 0.969705i | \(-0.578552\pi\) |
0.846757 | + | 0.531979i | \(0.178552\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.0172 | − | 10.1841i | −0.586602 | − | 0.426192i | 0.254496 | − | 0.967074i | \(-0.418090\pi\) |
−0.841098 | + | 0.540882i | \(0.818090\pi\) | |||||||
\(572\) | 2.48990 | − | 3.42705i | 0.104108 | − | 0.143292i | ||||
\(573\) | −4.95955 | − | 1.61146i | −0.207188 | − | 0.0673195i | ||||
\(574\) | −4.41641 | −0.184337 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.85410 | −0.118921 | ||||||||
\(577\) | −40.8954 | − | 13.2877i | −1.70250 | − | 0.553175i | −0.713443 | − | 0.700714i | \(-0.752865\pi\) |
−0.989056 | + | 0.147538i | \(0.952865\pi\) | |||||||
\(578\) | −9.22054 | + | 12.6910i | −0.383524 | + | 0.527875i | ||||
\(579\) | 4.52786 | + | 3.28969i | 0.188172 | + | 0.136715i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.9894 | + | 7.98424i | −0.455915 | + | 0.331242i | ||||
\(582\) | 3.65248i | 0.151400i | ||||||||
\(583\) | 26.0746 | + | 35.8885i | 1.07990 | + | 1.48635i | ||||
\(584\) | 2.38197 | + | 7.33094i | 0.0985665 | + | 0.303356i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.64590 | + | 8.14324i | −0.109301 | + | 0.336394i | ||||
\(587\) | 32.5074 | − | 10.5623i | 1.34173 | − | 0.435953i | 0.451824 | − | 0.892107i | \(-0.350773\pi\) |
0.889901 | + | 0.456154i | \(0.150773\pi\) | |||||||
\(588\) | −0.726543 | + | 0.236068i | −0.0299621 | + | 0.00973528i | ||||
\(589\) | 0.427051 | − | 1.31433i | 0.0175963 | − | 0.0541559i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.41641 | − | 4.35926i | −0.0582632 | − | 0.179316i | ||||
\(592\) | 4.89404 | + | 6.73607i | 0.201144 | + | 0.276851i | ||||
\(593\) | − | 29.0132i | − | 1.19143i | −0.803197 | − | 0.595714i | \(-0.796869\pi\) | ||
0.803197 | − | 0.595714i | \(-0.203131\pi\) | |||||||
\(594\) | −7.66312 | + | 5.56758i | −0.314422 | + | 0.228441i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.80902 | − | 1.31433i | −0.0741002 | − | 0.0538370i | ||||
\(597\) | −0.575274 | + | 0.791796i | −0.0235444 | + | 0.0324061i | ||||
\(598\) | −1.67760 | − | 0.545085i | −0.0686021 | − | 0.0222902i | ||||
\(599\) | −8.94427 | −0.365453 | −0.182727 | − | 0.983164i | \(-0.558492\pi\) | ||||
−0.182727 | + | 0.983164i | \(0.558492\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.8328 | 1.58402 | 0.792012 | − | 0.610506i | \(-0.209034\pi\) | ||||
0.792012 | + | 0.610506i | \(0.209034\pi\) | |||||||
\(602\) | −17.7926 | − | 5.78115i | −0.725171 | − | 0.235622i | ||||
\(603\) | −17.1720 | + | 23.6353i | −0.699299 | + | 0.962502i | ||||
\(604\) | −7.85410 | − | 5.70634i | −0.319579 | − | 0.232188i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.190983 | + | 0.138757i | −0.00775815 | + | 0.00563663i | ||||
\(607\) | − | 33.8541i | − | 1.37410i | −0.726612 | − | 0.687048i | \(-0.758906\pi\) | ||
0.726612 | − | 0.687048i | \(-0.241094\pi\) | |||||||
\(608\) | −3.44095 | − | 4.73607i | −0.139549 | − | 0.192073i | ||||
\(609\) | 3.35410 | + | 10.3229i | 0.135915 | + | 0.418304i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.69098 | + | 11.3597i | −0.149321 | + | 0.459563i | ||||
\(612\) | 3.11044 | − | 1.01064i | 0.125732 | − | 0.0408528i | ||||
\(613\) | −20.3885 | + | 6.62461i | −0.823482 | + | 0.267566i | −0.690297 | − | 0.723526i | \(-0.742520\pi\) |
−0.133185 | + | 0.991091i | \(0.542520\pi\) | |||||||
\(614\) | −7.14590 | + | 21.9928i | −0.288385 | + | 0.887558i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.92705 | + | 12.0862i | 0.158225 | + | 0.486968i | ||||
\(617\) | −8.44100 | − | 11.6180i | −0.339822 | − | 0.467724i | 0.604568 | − | 0.796554i | \(-0.293346\pi\) |
−0.944389 | + | 0.328829i | \(0.893346\pi\) | |||||||
\(618\) | 5.02129i | 0.201986i | ||||||||
\(619\) | 37.9894 | − | 27.6009i | 1.52692 | − | 1.10937i | 0.569002 | − | 0.822336i | \(-0.307330\pi\) |
0.957920 | − | 0.287037i | \(-0.0926702\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.19098 | + | 2.31838i | 0.128050 | + | 0.0930336i | ||||
\(622\) | 5.82485 | − | 8.01722i | 0.233555 | − | 0.321461i | ||||
\(623\) | 12.7598 | + | 4.14590i | 0.511209 | + | 0.166102i | ||||
\(624\) | 0.381966 | 0.0152909 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 16.5623 | 0.661963 | ||||||||
\(627\) | −9.00854 | − | 2.92705i | −0.359766 | − | 0.116895i | ||||
\(628\) | −2.68166 | + | 3.69098i | −0.107010 | + | 0.147286i | ||||
\(629\) | −7.71885 | − | 5.60807i | −0.307771 | − | 0.223608i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.2705 | − | 26.3521i | 1.44391 | − | 1.04906i | 0.456698 | − | 0.889622i | \(-0.349032\pi\) |
0.987208 | − | 0.159438i | \(-0.0509681\pi\) | |||||||
\(632\) | 7.23607i | 0.287835i | ||||||||
\(633\) | 5.00004 | + | 6.88197i | 0.198734 | + | 0.273534i | ||||
\(634\) | 2.59017 | + | 7.97172i | 0.102869 | + | 0.316598i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.23607 | + | 3.80423i | −0.0490133 | + | 0.150847i | ||||
\(637\) | −1.90211 | + | 0.618034i | −0.0753645 | + | 0.0244874i | ||||
\(638\) | 38.1608 | − | 12.3992i | 1.51080 | − | 0.490889i | ||||
\(639\) | −2.64590 | + | 8.14324i | −0.104670 | + | 0.322141i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.38197 | − | 28.8747i | −0.370565 | − | 1.14048i | −0.946422 | − | 0.322932i | \(-0.895331\pi\) |
0.575857 | − | 0.817551i | \(-0.304669\pi\) | |||||||
\(642\) | 0.244758 | + | 0.336881i | 0.00965984 | + | 0.0132956i | ||||
\(643\) | 31.7639i | 1.25265i | 0.779563 | + | 0.626324i | \(0.215441\pi\) | ||||
−0.779563 | + | 0.626324i | \(0.784559\pi\) | |||||||
\(644\) | 4.28115 | − | 3.11044i | 0.168701 | − | 0.122568i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.42705 | + | 3.94298i | 0.213524 | + | 0.155135i | ||||
\(647\) | −13.9026 | + | 19.1353i | −0.546567 | + | 0.752284i | −0.989541 | − | 0.144250i | \(-0.953923\pi\) |
0.442975 | + | 0.896534i | \(0.353923\pi\) | |||||||
\(648\) | 7.33094 | + | 2.38197i | 0.287986 | + | 0.0935725i | ||||
\(649\) | 18.9443 | 0.743628 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.270510 | −0.0106021 | ||||||||
\(652\) | 1.76336 | + | 0.572949i | 0.0690583 | + | 0.0224384i | ||||
\(653\) | 5.05304 | − | 6.95492i | 0.197741 | − | 0.272167i | −0.698619 | − | 0.715494i | \(-0.746202\pi\) |
0.896360 | + | 0.443327i | \(0.146202\pi\) | |||||||
\(654\) | −4.63525 | − | 3.36771i | −0.181253 | − | 0.131688i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.19098 | + | 0.865300i | −0.0465001 | + | 0.0337843i | ||||
\(657\) | − | 22.0000i | − | 0.858302i | ||||||
\(658\) | −21.0620 | − | 28.9894i | −0.821082 | − | 1.13012i | ||||
\(659\) | 7.92705 | + | 24.3970i | 0.308794 | + | 0.950370i | 0.978234 | + | 0.207504i | \(0.0665341\pi\) |
−0.669440 | + | 0.742866i | \(0.733466\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.42705 | + | 25.9358i | −0.327774 | + | 1.00879i | 0.642398 | + | 0.766371i | \(0.277939\pi\) |
−0.970173 | + | 0.242415i | \(0.922061\pi\) | |||||||
\(662\) | −14.8006 | + | 4.80902i | −0.575243 | + | 0.186908i | ||||
\(663\) | −0.416272 | + | 0.135255i | −0.0161667 | + | 0.00525287i | ||||
\(664\) | −1.39919 | + | 4.30625i | −0.0542990 | + | 0.167115i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.34346 | − | 22.6008i | −0.284553 | − | 0.875765i | ||||
\(667\) | −9.82084 | − | 13.5172i | −0.380264 | − | 0.523389i | ||||
\(668\) | − | 13.3820i | − | 0.517764i | ||||||
\(669\) | 2.78115 | − | 2.02063i | 0.107526 | − | 0.0781219i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 30.3435 | + | 22.0458i | 1.17140 | + | 0.851069i | ||||
\(672\) | −0.673542 | + | 0.927051i | −0.0259824 | + | 0.0357618i | ||||
\(673\) | −3.07768 | − | 1.00000i | −0.118636 | − | 0.0385472i | 0.249097 | − | 0.968478i | \(-0.419866\pi\) |
−0.367733 | + | 0.929931i | \(0.619866\pi\) | |||||||
\(674\) | −4.58359 | −0.176553 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.0000 | −0.461538 | ||||||||
\(677\) | 7.97172 | + | 2.59017i | 0.306378 | + | 0.0995483i | 0.458171 | − | 0.888864i | \(-0.348505\pi\) |
−0.151793 | + | 0.988412i | \(0.548505\pi\) | |||||||
\(678\) | −0.845055 | + | 1.16312i | −0.0324542 | + | 0.0446693i | ||||
\(679\) | −23.2082 | − | 16.8617i | −0.890649 | − | 0.647094i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.07295 | − | 6.59188i | 0.347676 | − | 0.252602i | ||||
\(682\) | 1.00000i | 0.0382920i | ||||||||
\(683\) | −6.67764 | − | 9.19098i | −0.255513 | − | 0.351683i | 0.661920 | − | 0.749575i | \(-0.269742\pi\) |
−0.917432 | + | 0.397892i | \(0.869742\pi\) | |||||||
\(684\) | 5.16312 | + | 15.8904i | 0.197417 | + | 0.607586i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −4.63525 | + | 14.2658i | −0.176975 | + | 0.544673i | ||||
\(687\) | −0.930812 | + | 0.302439i | −0.0355127 | + | 0.0115388i | ||||
\(688\) | −5.93085 | + | 1.92705i | −0.226112 | + | 0.0734681i | ||||
\(689\) | −3.23607 | + | 9.95959i | −0.123284 | + | 0.379430i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.97214 | − | 30.6911i | −0.379358 | − | 1.16754i | −0.940491 | − | 0.339818i | \(-0.889634\pi\) |
0.561133 | − | 0.827725i | \(-0.310366\pi\) | |||||||
\(692\) | 0.726543 | + | 1.00000i | 0.0276190 | + | 0.0380143i | ||||
\(693\) | − | 36.2705i | − | 1.37780i | ||||||
\(694\) | 17.0623 | − | 12.3965i | 0.647676 | − | 0.470564i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.92705 | + | 2.12663i | 0.110950 | + | 0.0806096i | ||||
\(697\) | 0.991545 | − | 1.36475i | 0.0375575 | − | 0.0516934i | ||||
\(698\) | −16.8945 | − | 5.48936i | −0.639466 | − | 0.207775i | ||||
\(699\) | 5.45898 | 0.206478 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.1803 | 0.686662 | 0.343331 | − | 0.939214i | \(-0.388445\pi\) | ||||
0.343331 | + | 0.939214i | \(0.388445\pi\) | |||||||
\(702\) | −2.12663 | − | 0.690983i | −0.0802644 | − | 0.0260795i | ||||
\(703\) | 28.6502 | − | 39.4336i | 1.08056 | − | 1.48727i | ||||
\(704\) | 3.42705 | + | 2.48990i | 0.129162 | + | 0.0938416i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −17.1803 | + | 12.4822i | −0.646591 | + | 0.469776i | ||||
\(707\) | − | 1.85410i | − | 0.0697307i | ||||||
\(708\) | 1.00406 | + | 1.38197i | 0.0377348 | + | 0.0519375i | ||||
\(709\) | −3.78115 | − | 11.6372i | −0.142004 | − | 0.437044i | 0.854609 | − | 0.519271i | \(-0.173797\pi\) |
−0.996614 | + | 0.0822274i | \(0.973797\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.38197 | − | 19.6417i | 0.239342 | − | 0.736620i | ||||
\(712\) | 4.25325 | − | 1.38197i | 0.159397 | − | 0.0517914i | ||||
\(713\) | 0.396027 | − | 0.128677i | 0.0148313 | − | 0.00481900i | ||||
\(714\) | 0.405765 | − | 1.24882i | 0.0151854 | − | 0.0467357i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.45492 | + | 10.6331i | 0.129116 | + | 0.397379i | ||||
\(717\) | −1.55135 | − | 2.13525i | −0.0579364 | − | 0.0797426i | ||||
\(718\) | − | 8.09017i | − | 0.301922i | ||||||
\(719\) | 9.30902 | − | 6.76340i | 0.347168 | − | 0.252232i | −0.400512 | − | 0.916291i | \(-0.631168\pi\) |
0.747680 | + | 0.664059i | \(0.231168\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −31.9058 | − | 23.1809i | −1.18823 | − | 0.863302i | ||||
\(722\) | −8.97578 | + | 12.3541i | −0.334044 | + | 0.459772i | ||||
\(723\) | 5.67358 | + | 1.84346i | 0.211003 | + | 0.0685590i | ||||
\(724\) | −5.41641 | −0.201299 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.65248 | 0.0984426 | ||||||||
\(727\) | 2.52265 | + | 0.819660i | 0.0935601 | + | 0.0303995i | 0.355423 | − | 0.934706i | \(-0.384337\pi\) |
−0.261863 | + | 0.965105i | \(0.584337\pi\) | |||||||
\(728\) | −1.76336 | + | 2.42705i | −0.0653543 | + | 0.0899525i | ||||
\(729\) | −15.7254 | − | 11.4252i | −0.582423 | − | 0.423155i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.78115 | − | 4.20025i | 0.213824 | − | 0.155352i | ||||
\(732\) | 3.38197i | 0.125001i | ||||||||
\(733\) | 18.6781 | + | 25.7082i | 0.689891 | + | 0.949554i | 0.999999 | − | 0.00114721i | \(-0.000365167\pi\) |
−0.310108 | + | 0.950701i | \(0.600365\pi\) | |||||||
\(734\) | 10.9828 | + | 33.8015i | 0.405382 | + | 1.24764i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.545085 | − | 1.67760i | 0.0200921 | − | 0.0618371i | ||||
\(737\) | 41.2385 | − | 13.3992i | 1.51904 | − | 0.493565i | ||||
\(738\) | 3.99598 | − | 1.29837i | 0.147094 | − | 0.0477938i | ||||
\(739\) | −9.27051 | + | 28.5317i | −0.341021 | + | 1.04956i | 0.622658 | + | 0.782494i | \(0.286053\pi\) |
−0.963679 | + | 0.267062i | \(0.913947\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.690983 | − | 2.12663i | −0.0253839 | − | 0.0781236i | ||||
\(742\) | −18.4661 | − | 25.4164i | −0.677912 | − | 0.933066i | ||||
\(743\) | − | 15.2705i | − | 0.560221i | −0.959968 | − | 0.280110i | \(-0.909629\pi\) | ||
0.959968 | − | 0.280110i | \(-0.0903711\pi\) | |||||||
\(744\) | −0.0729490 | + | 0.0530006i | −0.00267444 | + | 0.00194309i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −9.51722 | − | 6.91467i | −0.348450 | − | 0.253164i | ||||
\(747\) | 7.59594 | − | 10.4549i | 0.277921 | − | 0.382525i | ||||
\(748\) | −4.61653 | − | 1.50000i | −0.168797 | − | 0.0548454i | ||||
\(749\) | −3.27051 | −0.119502 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.85410 | 0.286600 | 0.143300 | − | 0.989679i | \(-0.454229\pi\) | ||||
0.143300 | + | 0.989679i | \(0.454229\pi\) | |||||||
\(752\) | −11.3597 | − | 3.69098i | −0.414245 | − | 0.134596i | ||||
\(753\) | 0.184025 | − | 0.253289i | 0.00670625 | − | 0.00923036i | ||||
\(754\) | 7.66312 | + | 5.56758i | 0.279074 | + | 0.202759i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.42705 | − | 3.94298i | 0.197380 | − | 0.143405i | ||||
\(757\) | − | 16.4164i | − | 0.596664i | −0.954462 | − | 0.298332i | \(-0.903570\pi\) | ||
0.954462 | − | 0.298332i | \(-0.0964303\pi\) | |||||||
\(758\) | −5.56758 | − | 7.66312i | −0.202224 | − | 0.278337i | ||||
\(759\) | −0.881966 | − | 2.71441i | −0.0320133 | − | 0.0985269i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.31966 | − | 25.6053i | 0.301587 | − | 0.928191i | −0.679341 | − | 0.733823i | \(-0.737734\pi\) |
0.980929 | − | 0.194368i | \(-0.0622656\pi\) | |||||||
\(762\) | 1.28157 | − | 0.416408i | 0.0464264 | − | 0.0150849i | ||||
\(763\) | 42.7975 | − | 13.9058i | 1.54938 | − | 0.503422i | ||||
\(764\) | 4.21885 | − | 12.9843i | 0.152633 | − | 0.469755i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.50000 | − | 10.7719i | −0.126460 | − | 0.389204i | ||||
\(767\) | 2.62866 | + | 3.61803i | 0.0949153 | + | 0.130640i | ||||
\(768\) | 0.381966i | 0.0137830i | ||||||||
\(769\) | 2.76393 | − | 2.00811i | 0.0996699 | − | 0.0724144i | −0.536834 | − | 0.843688i | \(-0.680380\pi\) |
0.636504 | + | 0.771273i | \(0.280380\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.95492 | + | 5.77958i | 0.286489 | + | 0.208147i | ||||
\(772\) | −8.61251 | + | 11.8541i | −0.309971 | + | 0.426638i | ||||
\(773\) | −29.2910 | − | 9.51722i | −1.05352 | − | 0.342311i | −0.269473 | − | 0.963008i | \(-0.586850\pi\) |
−0.784050 | + | 0.620697i | \(0.786850\pi\) | |||||||
\(774\) | 17.7984 | 0.639749 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −9.56231 | −0.343267 | ||||||||
\(777\) | −9.07405 | − | 2.94834i | −0.325530 | − | 0.105771i | ||||
\(778\) | 10.7064 | − | 14.7361i | 0.383842 | − | 0.528314i | ||||
\(779\) | 6.97214 | + | 5.06555i | 0.249803 | + | 0.181492i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.2812 | − | 7.46969i | 0.367889 | − | 0.267287i | ||||
\(782\) | 2.02129i | 0.0722810i | ||||||||
\(783\) | −12.4495 | − | 17.1353i | −0.444909 | − | 0.612364i | ||||
\(784\) | −0.618034 | − | 1.90211i | −0.0220726 | − | 0.0679326i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.93769 | + | 5.96361i | −0.0691153 | + | 0.212715i | ||||
\(787\) | 10.8576 | − | 3.52786i | 0.387033 | − | 0.125755i | −0.109036 | − | 0.994038i | \(-0.534776\pi\) |
0.496069 | + | 0.868283i | \(0.334776\pi\) | |||||||
\(788\) | 11.4127 | − | 3.70820i | 0.406560 | − | 0.132099i | ||||
\(789\) | 0.545085 | − | 1.67760i | 0.0194055 | − | 0.0597241i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.48936 | − | 10.7391i | −0.124067 | − | 0.381840i | ||||
\(792\) | −7.10642 | − | 9.78115i | −0.252516 | − | 0.347558i | ||||
\(793\) | 8.85410i | 0.314418i | ||||||||
\(794\) | 8.28115 | − | 6.01661i | 0.293887 | − | 0.213521i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.07295 | − | 1.50609i | −0.0734737 | − | 0.0533818i | ||||
\(797\) | 3.30220 | − | 4.54508i | 0.116970 | − | 0.160995i | −0.746517 | − | 0.665366i | \(-0.768276\pi\) |
0.863487 | + | 0.504371i | \(0.168276\pi\) | |||||||
\(798\) | 6.37988 | + | 2.07295i | 0.225845 | + | 0.0733816i | ||||
\(799\) | 13.6869 | 0.484208 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.7639 | −0.450991 | ||||||||
\(802\) | 13.4863 | + | 4.38197i | 0.476218 | + | 0.154733i | ||||
\(803\) | −19.1926 | + | 26.4164i | −0.677294 | + | 0.932215i | ||||
\(804\) | 3.16312 | + | 2.29814i | 0.111555 | + | 0.0810492i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.190983 | + | 0.138757i | −0.00672709 | + | 0.00488752i | ||||
\(807\) | − | 0.729490i | − | 0.0256793i | ||||||
\(808\) | −0.363271 | − | 0.500000i | −0.0127798 | − | 0.0175899i | ||||
\(809\) | 0.690983 | + | 2.12663i | 0.0242937 | + | 0.0747682i | 0.962468 | − | 0.271394i | \(-0.0874847\pi\) |
−0.938175 | + | 0.346162i | \(0.887485\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.6525 | − | 38.9403i | 0.444289 | − | 1.36738i | −0.438974 | − | 0.898500i | \(-0.644658\pi\) |
0.883262 | − | 0.468880i | \(-0.155342\pi\) | |||||||
\(812\) | −27.0256 | + | 8.78115i | −0.948413 | + | 0.308158i | ||||
\(813\) | −10.3556 | + | 3.36475i | −0.363187 | + | 0.118007i | ||||
\(814\) | −10.8992 | + | 33.5442i | −0.382016 | + | 1.17573i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.135255 | − | 0.416272i | −0.00473487 | − | 0.0145724i | ||||
\(817\) | 21.4580 | + | 29.5344i | 0.750721 | + | 1.03328i | ||||
\(818\) | − | 6.70820i | − | 0.234547i | ||||||
\(819\) | 6.92705 | − | 5.03280i | 0.242051 | − | 0.175860i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −31.6803 | − | 23.0171i | −1.10565 | − | 0.803303i | −0.123678 | − | 0.992322i | \(-0.539469\pi\) |
−0.981973 | + | 0.189020i | \(0.939469\pi\) | |||||||
\(822\) | 1.14281 | − | 1.57295i | 0.0398602 | − | 0.0548629i | ||||
\(823\) | 19.8132 | + | 6.43769i | 0.690644 | + | 0.224404i | 0.633250 | − | 0.773948i | \(-0.281721\pi\) |
0.0573946 | + | 0.998352i | \(0.481721\pi\) | |||||||
\(824\) | −13.1459 | −0.457959 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13.4164 | −0.466817 | ||||||||
\(827\) | −4.78804 | − | 1.55573i | −0.166496 | − | 0.0540980i | 0.224583 | − | 0.974455i | \(-0.427898\pi\) |
−0.391079 | + | 0.920357i | \(0.627898\pi\) | |||||||
\(828\) | −2.95917 | + | 4.07295i | −0.102838 | + | 0.141545i | ||||
\(829\) | 43.2148 | + | 31.3974i | 1.50091 | + | 1.09048i | 0.970017 | + | 0.243038i | \(0.0781440\pi\) |
0.530895 | + | 0.847438i | \(0.321856\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.0901699 | − | 0.0655123i | 0.00312796 | − | 0.00227260i | ||||
\(832\) | 1.00000i | 0.0346688i | ||||||||
\(833\) | 1.34708 | + | 1.85410i | 0.0466737 | + | 0.0642408i | ||||
\(834\) | 0.628677 | + | 1.93487i | 0.0217693 | + | 0.0669990i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7.66312 | − | 23.5847i | 0.265035 | − | 0.815692i | ||||
\(837\) | 0.502029 | − | 0.163119i | 0.0173526 | − | 0.00563822i | ||||
\(838\) | −21.6498 | + | 7.03444i | −0.747879 | + | 0.243001i | ||||
\(839\) | 17.0729 | − | 52.5451i | 0.589424 | − | 1.81406i | 0.00869515 | − | 0.999962i | \(-0.497232\pi\) |
0.580729 | − | 0.814097i | \(-0.302768\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.7639 | + | 57.7494i | 0.647032 | + | 1.99136i | ||||
\(842\) | 12.5025 | + | 17.2082i | 0.430864 | + | 0.593034i | ||||
\(843\) | 1.21478i | 0.0418393i | ||||||||
\(844\) | −18.0172 | + | 13.0903i | −0.620178 | + | 0.450586i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 27.5795 | + | 20.0377i | 0.948204 | + | 0.688910i | ||||
\(847\) | −12.2452 | + | 16.8541i | −0.420751 | + | 0.579114i | ||||
\(848\) | −9.95959 | − | 3.23607i | −0.342014 | − | 0.111127i | ||||
\(849\) | −4.69505 | −0.161134 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.6869 | 0.503461 | ||||||||
\(852\) | 1.08981 | + | 0.354102i | 0.0373364 | + | 0.0121313i | ||||
\(853\) | 10.6659 | − | 14.6803i | 0.365193 | − | 0.502645i | −0.586393 | − | 0.810026i | \(-0.699453\pi\) |
0.951586 | + | 0.307381i | \(0.0994527\pi\) | |||||||
\(854\) | −21.4894 | − | 15.6129i | −0.735351 | − | 0.534264i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.881966 | + | 0.640786i | −0.0301450 | + | 0.0219016i | ||||
\(857\) | − | 56.3394i | − | 1.92452i | −0.272137 | − | 0.962259i | \(-0.587730\pi\) | ||
0.272137 | − | 0.962259i | \(-0.412270\pi\) | |||||||
\(858\) | 0.951057 | + | 1.30902i | 0.0324685 | + | 0.0446891i | ||||
\(859\) | −10.6287 | − | 32.7117i | −0.362646 | − | 1.11611i | −0.951442 | − | 0.307828i | \(-0.900398\pi\) |
0.588796 | − | 0.808281i | \(-0.299602\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.521286 | − | 1.60435i | 0.0177654 | − | 0.0546762i | ||||
\(862\) | 24.7930 | − | 8.05573i | 0.844452 | − | 0.274379i | ||||
\(863\) | −10.6861 | + | 3.47214i | −0.363760 | + | 0.118193i | −0.485194 | − | 0.874407i | \(-0.661251\pi\) |
0.121433 | + | 0.992600i | \(0.461251\pi\) | |||||||
\(864\) | 0.690983 | − | 2.12663i | 0.0235077 | − | 0.0723493i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 6.60081 | + | 20.3152i | 0.224305 | + | 0.690339i | ||||
\(867\) | −3.52193 | − | 4.84752i | −0.119611 | − | 0.164631i | ||||
\(868\) | − | 0.708204i | − | 0.0240380i | ||||||
\(869\) | −24.7984 | + | 18.0171i | −0.841227 | + | 0.611187i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.28115 | + | 6.01661i | 0.280596 | + | 0.203865i | ||||
\(872\) | 8.81678 | − | 12.1353i | 0.298574 | − | 0.410952i | ||||
\(873\) | 25.9560 | + | 8.43363i | 0.878479 | + | 0.285435i | ||||
\(874\) | −10.3262 | −0.349290 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.94427 | −0.0994777 | ||||||||
\(877\) | 4.22050 | + | 1.37132i | 0.142516 | + | 0.0463063i | 0.379406 | − | 0.925230i | \(-0.376128\pi\) |
−0.236890 | + | 0.971536i | \(0.576128\pi\) | |||||||
\(878\) | 15.0781 | − | 20.7533i | 0.508863 | − | 0.700390i | ||||
\(879\) | −2.64590 | − | 1.92236i | −0.0892439 | − | 0.0648395i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.8885 | + | 22.4418i | −1.04066 | + | 0.756085i | −0.970415 | − | 0.241445i | \(-0.922379\pi\) |
−0.0702469 | + | 0.997530i | \(0.522379\pi\) | |||||||
\(882\) | 5.70820i | 0.192205i | ||||||||
\(883\) | −24.5030 | − | 33.7254i | −0.824590 | − | 1.13495i | −0.988906 | − | 0.148543i | \(-0.952542\pi\) |
0.164316 | − | 0.986408i | \(-0.447458\pi\) | |||||||
\(884\) | −0.354102 | − | 1.08981i | −0.0119097 | − | 0.0366544i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.00000 | + | 18.4661i | −0.201574 | + | 0.620381i | ||||
\(887\) | −31.5564 | + | 10.2533i | −1.05956 | + | 0.344272i | −0.786413 | − | 0.617701i | \(-0.788064\pi\) |
−0.273146 | + | 0.961973i | \(0.588064\pi\) | |||||||
\(888\) | −3.02468 | + | 0.982779i | −0.101502 | + | 0.0329799i | ||||
\(889\) | −3.27051 | + | 10.0656i | −0.109689 | + | 0.337589i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.0902 | + | 31.0543i | 0.338033 | + | 1.04036i | ||||
\(892\) | 5.29007 | + | 7.28115i | 0.177125 | + | 0.243791i | ||||
\(893\) | 69.9230i | 2.33988i | ||||||||
\(894\) | 0.690983 | − | 0.502029i | 0.0231099 | − | 0.0167903i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.42705 | − | 1.76336i | −0.0810821 | − | 0.0589096i | ||||
\(897\) | 0.396027 | − | 0.545085i | 0.0132230 | − | 0.0181999i | ||||
\(898\) | −3.75123 | − | 1.21885i | −0.125180 | − | 0.0406735i | ||||
\(899\) | −2.23607 | −0.0745770 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.0000 | 0.399778 | ||||||||
\(902\) | −5.93085 | − | 1.92705i | −0.197476 | − | 0.0641638i | ||||
\(903\) | 4.20025 | − | 5.78115i | 0.139776 | − | 0.192385i | ||||
\(904\) | −3.04508 | − | 2.21238i | −0.101278 | − | 0.0735828i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.00000 | − | 2.17963i | 0.0996683 | − | 0.0724133i | ||||
\(907\) | 25.6180i | 0.850633i | 0.905045 | + | 0.425316i | \(0.139837\pi\) | ||||
−0.905045 | + | 0.425316i | \(0.860163\pi\) | |||||||
\(908\) | 17.2578 | + | 23.7533i | 0.572719 | + | 0.788281i | ||||
\(909\) | 0.545085 | + | 1.67760i | 0.0180793 | + | 0.0556424i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.07295 | + | 15.6129i | −0.168074 | + | 0.517280i | −0.999250 | − | 0.0387308i | \(-0.987669\pi\) |
0.831175 | + | 0.556010i | \(0.187669\pi\) | |||||||
\(912\) | 2.12663 | − | 0.690983i | 0.0704197 | − | 0.0228807i | ||||
\(913\) | −18.2416 | + | 5.92705i | −0.603708 | + | 0.196157i | ||||
\(914\) | 12.4271 | − | 38.2465i | 0.411050 | − | 1.26508i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.791796 | − | 2.43690i | −0.0261617 | − | 0.0805174i | ||||
\(917\) | −28.9480 | − | 39.8435i | −0.955946 | − | 1.31575i | ||||
\(918\) | 2.56231i | 0.0845687i | ||||||||
\(919\) | −4.57295 | + | 3.32244i | −0.150848 | + | 0.109597i | −0.660649 | − | 0.750695i | \(-0.729719\pi\) |
0.509801 | + | 0.860292i | \(0.329719\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.14590 | − | 5.19180i | −0.235465 | − | 0.171076i | ||||
\(922\) | −3.42071 | + | 4.70820i | −0.112655 | + | 0.155056i | ||||
\(923\) | 2.85317 | + | 0.927051i | 0.0939132 | + | 0.0305143i | ||||
\(924\) | −4.85410 | −0.159688 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 34.9787 | 1.14947 | ||||||||
\(927\) | 35.6834 | + | 11.5942i | 1.17200 | + | 0.380805i | ||||
\(928\) | −5.56758 | + | 7.66312i | −0.182765 | + | 0.251554i | ||||
\(929\) | −42.7877 | − | 31.0871i | −1.40382 | − | 1.01993i | −0.994185 | − | 0.107685i | \(-0.965656\pi\) |
−0.409635 | − | 0.912250i | \(-0.634344\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.47214 | + | 6.88191i | −0.310437 | + | 0.225545i | ||||
\(932\) | 14.2918i | 0.468143i | ||||||||
\(933\) | 2.22490 | + | 3.06231i | 0.0728398 | + | 0.100255i | ||||
\(934\) | −5.92705 | − | 18.2416i | −0.193939 | − | 0.596883i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.881966 | − | 2.71441i | 0.0288280 | − | 0.0887233i | ||||
\(937\) | −39.8711 | + | 12.9549i | −1.30253 | + | 0.423219i | −0.876462 | − | 0.481471i | \(-0.840103\pi\) |
−0.426071 | + | 0.904690i | \(0.640103\pi\) | |||||||
\(938\) | −29.2052 | + | 9.48936i | −0.953585 | + | 0.309838i | ||||
\(939\) | −1.95492 | + | 6.01661i | −0.0637962 | + | 0.196345i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.89919 | − | 8.92278i | −0.0945108 | − | 0.290874i | 0.892615 | − | 0.450820i | \(-0.148868\pi\) |
−0.987126 | + | 0.159945i | \(0.948868\pi\) | |||||||
\(942\) | −1.02430 | − | 1.40983i | −0.0333735 | − | 0.0459347i | ||||
\(943\) | 2.59675i | 0.0845617i | ||||||||
\(944\) | −3.61803 | + | 2.62866i | −0.117757 | + | 0.0855555i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −21.3713 | − | 15.5272i | −0.694842 | − | 0.504832i | ||||
\(947\) | −23.1481 | + | 31.8607i | −0.752213 | + | 1.03533i | 0.245609 | + | 0.969369i | \(0.421012\pi\) |
−0.997822 | + | 0.0659639i | \(0.978988\pi\) | |||||||
\(948\) | −2.62866 | − | 0.854102i | −0.0853748 | − | 0.0277399i | ||||
\(949\) | −7.70820 | −0.250219 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.20163 | −0.103820 | ||||||||
\(952\) | 3.26944 | + | 1.06231i | 0.105963 | + | 0.0344295i | ||||
\(953\) | −26.2258 | + | 36.0967i | −0.849538 | + | 1.16929i | 0.134427 | + | 0.990924i | \(0.457081\pi\) |
−0.983964 | + | 0.178365i | \(0.942919\pi\) | |||||||
\(954\) | 24.1803 | + | 17.5680i | 0.782867 | + | 0.568786i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.59017 | − | 4.06150i | 0.180799 | − | 0.131358i | ||||
\(957\) | 15.3262i | 0.495427i | ||||||||
\(958\) | 8.93529 | + | 12.2984i | 0.288686 | + | 0.397342i | ||||
\(959\) | 4.71885 | + | 14.5231i | 0.152380 | + | 0.468976i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.56231 | + | 29.4298i | −0.308461 | + | 0.949347i | ||||
\(962\) | −7.91872 | + | 2.57295i | −0.255310 | + | 0.0829552i | ||||
\(963\) | 2.95917 | − | 0.961493i | 0.0953579 | − | 0.0309837i | ||||
\(964\) | −4.82624 | + | 14.8536i | −0.155443 | + | 0.478403i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.624612 | + | 1.92236i | 0.0200966 | + | 0.0618508i | ||||
\(967\) | 7.71445 | + | 10.6180i | 0.248080 | + | 0.341453i | 0.914838 | − | 0.403822i | \(-0.132318\pi\) |
−0.666758 | + | 0.745275i | \(0.732318\pi\) | |||||||
\(968\) | 6.94427i | 0.223197i | ||||||||
\(969\) | −2.07295 | + | 1.50609i | −0.0665927 | + | 0.0483824i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.90983 | − | 3.56720i | −0.157564 | − | 0.114477i | 0.506210 | − | 0.862410i | \(-0.331046\pi\) |
−0.663774 | + | 0.747934i | \(0.731046\pi\) | |||||||
\(972\) | −5.67358 | + | 7.80902i | −0.181980 | + | 0.250474i | ||||
\(973\) | −15.1967 | − | 4.93769i | −0.487183 | − | 0.158295i | ||||
\(974\) | 22.1246 | 0.708918 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.85410 | −0.283413 | ||||||||
\(977\) | 47.5653 | + | 15.4549i | 1.52175 | + | 0.494447i | 0.946272 | − | 0.323371i | \(-0.104816\pi\) |
0.575478 | + | 0.817817i | \(0.304816\pi\) | |||||||
\(978\) | −0.416272 | + | 0.572949i | −0.0133109 | + | 0.0183209i | ||||
\(979\) | 15.3262 | + | 11.1352i | 0.489829 | + | 0.355881i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −34.6353 | + | 25.1640i | −1.10582 | + | 0.803424i | ||||
\(982\) | − | 19.2361i | − | 0.613848i | ||||||
\(983\) | 22.6211 | + | 31.1353i | 0.721501 | + | 0.993060i | 0.999473 | + | 0.0324712i | \(0.0103377\pi\) |
−0.277972 | + | 0.960589i | \(0.589662\pi\) | |||||||
\(984\) | −0.173762 | − | 0.534785i | −0.00553933 | − | 0.0170483i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.35410 | − | 10.3229i | 0.106816 | − | 0.328747i | ||||
\(987\) | 13.0170 | − | 4.22949i | 0.414337 | − | 0.134626i | ||||
\(988\) | 5.56758 | − | 1.80902i | 0.177128 | − | 0.0575525i | ||||
\(989\) | −3.39919 | + | 10.4616i | −0.108088 | + | 0.332660i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.06637 | − | 3.28195i | −0.0338744 | − | 0.104255i | 0.932690 | − | 0.360680i | \(-0.117455\pi\) |
−0.966564 | + | 0.256425i | \(0.917455\pi\) | |||||||
\(992\) | −0.138757 | − | 0.190983i | −0.00440555 | − | 0.00606372i | ||||
\(993\) | − | 5.94427i | − | 0.188636i | ||||||
\(994\) | −7.28115 | + | 5.29007i | −0.230944 | + | 0.167791i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.39919 | − | 1.01657i | −0.0443349 | − | 0.0322112i | ||||
\(997\) | 16.0167 | − | 22.0451i | 0.507254 | − | 0.698175i | −0.476199 | − | 0.879337i | \(-0.657986\pi\) |
0.983453 | + | 0.181162i | \(0.0579860\pi\) | |||||||
\(998\) | 32.4747 | + | 10.5517i | 1.02797 | + | 0.334007i | ||||
\(999\) | 18.6180 | 0.589049 |
(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 | 250.2.e.b.149.1 | 8 | ||
5.2 | odd | 4 | 250.2.d.a.101.1 | 4 | |||
5.3 | odd | 4 | 50.2.d.a.21.1 | ✓ | 4 | ||
5.4 | even | 2 | inner | 250.2.e.b.149.2 | 8 | ||
15.8 | even | 4 | 450.2.h.a.271.1 | 4 | |||
20.3 | even | 4 | 400.2.u.c.321.1 | 4 | |||
25.6 | even | 5 | inner | 250.2.e.b.99.2 | 8 | ||
25.8 | odd | 20 | 50.2.d.a.31.1 | yes | 4 | ||
25.9 | even | 10 | 1250.2.b.b.1249.4 | 4 | |||
25.12 | odd | 20 | 1250.2.a.d.1.1 | 2 | |||
25.13 | odd | 20 | 1250.2.a.a.1.2 | 2 | |||
25.16 | even | 5 | 1250.2.b.b.1249.1 | 4 | |||
25.17 | odd | 20 | 250.2.d.a.151.1 | 4 | |||
25.19 | even | 10 | inner | 250.2.e.b.99.1 | 8 | ||
75.8 | even | 20 | 450.2.h.a.181.1 | 4 | |||
100.63 | even | 20 | 10000.2.a.n.1.1 | 2 | |||
100.83 | even | 20 | 400.2.u.c.81.1 | 4 | |||
100.87 | even | 20 | 10000.2.a.a.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
50.2.d.a.21.1 | ✓ | 4 | 5.3 | odd | 4 | ||
50.2.d.a.31.1 | yes | 4 | 25.8 | odd | 20 | ||
250.2.d.a.101.1 | 4 | 5.2 | odd | 4 | |||
250.2.d.a.151.1 | 4 | 25.17 | odd | 20 | |||
250.2.e.b.99.1 | 8 | 25.19 | even | 10 | inner | ||
250.2.e.b.99.2 | 8 | 25.6 | even | 5 | inner | ||
250.2.e.b.149.1 | 8 | 1.1 | even | 1 | trivial | ||
250.2.e.b.149.2 | 8 | 5.4 | even | 2 | inner | ||
400.2.u.c.81.1 | 4 | 100.83 | even | 20 | |||
400.2.u.c.321.1 | 4 | 20.3 | even | 4 | |||
450.2.h.a.181.1 | 4 | 75.8 | even | 20 | |||
450.2.h.a.271.1 | 4 | 15.8 | even | 4 | |||
1250.2.a.a.1.2 | 2 | 25.13 | odd | 20 | |||
1250.2.a.d.1.1 | 2 | 25.12 | odd | 20 | |||
1250.2.b.b.1249.1 | 4 | 25.16 | even | 5 | |||
1250.2.b.b.1249.4 | 4 | 25.9 | even | 10 | |||
10000.2.a.a.1.2 | 2 | 100.87 | even | 20 | |||
10000.2.a.n.1.1 | 2 | 100.63 | even | 20 |