Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [250,2,Mod(51,250)]
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([8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("250.51");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 250 = 2 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 250.d (of order \(5\), 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: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 50) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 151.1 | ||
Root | \(-0.309017 + 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 250.151 |
Dual form | 250.2.d.a.101.1 |
$q$-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 \(\left(\mathbb{Z}/250\mathbb{Z}\right)^\times\).
\(n\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.309017 | + | 0.951057i | 0.218508 | + | 0.672499i | ||||
\(3\) | −0.309017 | + | 0.224514i | −0.178411 | + | 0.129623i | −0.673407 | − | 0.739272i | \(-0.735170\pi\) |
0.494996 | + | 0.868895i | \(0.335170\pi\) | |||||||
\(4\) | −0.809017 | + | 0.587785i | −0.404508 | + | 0.293893i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.309017 | − | 0.224514i | −0.126156 | − | 0.0916575i | ||||
\(7\) | 3.00000 | 1.13389 | 0.566947 | − | 0.823754i | \(-0.308125\pi\) | ||||
0.566947 | + | 0.823754i | \(0.308125\pi\) | |||||||
\(8\) | −0.809017 | − | 0.587785i | −0.286031 | − | 0.207813i | ||||
\(9\) | −0.881966 | + | 2.71441i | −0.293989 | + | 0.904804i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.30902 | + | 4.02874i | 0.394683 | + | 1.21471i | 0.929208 | + | 0.369558i | \(0.120491\pi\) |
−0.534524 | + | 0.845153i | \(0.679509\pi\) | |||||||
\(12\) | 0.118034 | − | 0.363271i | 0.0340735 | − | 0.104867i | ||||
\(13\) | −0.309017 | + | 0.951057i | −0.0857059 | + | 0.263776i | −0.984720 | − | 0.174143i | \(-0.944284\pi\) |
0.899014 | + | 0.437919i | \(0.144284\pi\) | |||||||
\(14\) | 0.927051 | + | 2.85317i | 0.247765 | + | 0.762542i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.309017 | − | 0.951057i | 0.0772542 | − | 0.237764i | ||||
\(17\) | 0.927051 | + | 0.673542i | 0.224843 | + | 0.163358i | 0.694504 | − | 0.719489i | \(-0.255624\pi\) |
−0.469661 | + | 0.882847i | \(0.655624\pi\) | |||||||
\(18\) | −2.85410 | −0.672718 | ||||||||
\(19\) | −4.73607 | − | 3.44095i | −1.08653 | − | 0.789409i | −0.107719 | − | 0.994181i | \(-0.534355\pi\) |
−0.978810 | + | 0.204772i | \(0.934355\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.927051 | + | 0.673542i | −0.202299 | + | 0.146979i | ||||
\(22\) | −3.42705 | + | 2.48990i | −0.730650 | + | 0.530848i | ||||
\(23\) | 0.545085 | + | 1.67760i | 0.113658 | + | 0.349804i | 0.991665 | − | 0.128845i | \(-0.0411269\pi\) |
−0.878007 | + | 0.478648i | \(0.841127\pi\) | |||||||
\(24\) | 0.381966 | 0.0779685 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −0.690983 | − | 2.12663i | −0.132980 | − | 0.409270i | ||||
\(28\) | −2.42705 | + | 1.76336i | −0.458670 | + | 0.333243i | ||||
\(29\) | 7.66312 | − | 5.56758i | 1.42301 | − | 1.03387i | 0.431739 | − | 0.901998i | \(-0.357900\pi\) |
0.991266 | − | 0.131875i | \(-0.0420999\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.190983 | + | 0.138757i | 0.0343016 | + | 0.0249215i | 0.604804 | − | 0.796374i | \(-0.293251\pi\) |
−0.570502 | + | 0.821296i | \(0.693251\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.30902 | − | 0.951057i | −0.227871 | − | 0.165558i | ||||
\(34\) | −0.354102 | + | 1.08981i | −0.0607280 | + | 0.186902i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.881966 | − | 2.71441i | −0.146994 | − | 0.452402i | ||||
\(37\) | 2.57295 | − | 7.91872i | 0.422990 | − | 1.30183i | −0.481915 | − | 0.876218i | \(-0.660059\pi\) |
0.904906 | − | 0.425612i | \(-0.139941\pi\) | |||||||
\(38\) | 1.80902 | − | 5.56758i | 0.293461 | − | 0.903181i | ||||
\(39\) | −0.118034 | − | 0.363271i | −0.0189006 | − | 0.0581700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.454915 | − | 1.40008i | 0.0710458 | − | 0.218656i | −0.909229 | − | 0.416297i | \(-0.863328\pi\) |
0.980275 | + | 0.197640i | \(0.0633278\pi\) | |||||||
\(42\) | −0.927051 | − | 0.673542i | −0.143047 | − | 0.103930i | ||||
\(43\) | 6.23607 | 0.950991 | 0.475496 | − | 0.879718i | \(-0.342269\pi\) | ||||
0.475496 | + | 0.879718i | \(0.342269\pi\) | |||||||
\(44\) | −3.42705 | − | 2.48990i | −0.516647 | − | 0.375366i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.42705 | + | 1.03681i | −0.210407 | + | 0.152870i | ||||
\(47\) | −9.66312 | + | 7.02067i | −1.40951 | + | 1.02407i | −0.416117 | + | 0.909311i | \(0.636609\pi\) |
−0.993393 | + | 0.114759i | \(0.963391\pi\) | |||||||
\(48\) | 0.118034 | + | 0.363271i | 0.0170367 | + | 0.0524337i | ||||
\(49\) | 2.00000 | 0.285714 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.437694 | −0.0612894 | ||||||||
\(52\) | −0.309017 | − | 0.951057i | −0.0428529 | − | 0.131888i | ||||
\(53\) | 8.47214 | − | 6.15537i | 1.16374 | − | 0.845505i | 0.173491 | − | 0.984835i | \(-0.444495\pi\) |
0.990246 | + | 0.139331i | \(0.0444951\pi\) | |||||||
\(54\) | 1.80902 | − | 1.31433i | 0.246176 | − | 0.178857i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.42705 | − | 1.76336i | −0.324328 | − | 0.235638i | ||||
\(57\) | 2.23607 | 0.296174 | ||||||||
\(58\) | 7.66312 | + | 5.56758i | 1.00622 | + | 0.731059i | ||||
\(59\) | −1.38197 | + | 4.25325i | −0.179917 | + | 0.553727i | −0.999824 | − | 0.0187700i | \(-0.994025\pi\) |
0.819907 | + | 0.572496i | \(0.194025\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.73607 | − | 8.42075i | −0.350318 | − | 1.07817i | −0.958675 | − | 0.284504i | \(-0.908171\pi\) |
0.608357 | − | 0.793663i | \(-0.291829\pi\) | |||||||
\(62\) | −0.0729490 | + | 0.224514i | −0.00926453 | + | 0.0285133i | ||||
\(63\) | −2.64590 | + | 8.14324i | −0.333352 | + | 1.02595i | ||||
\(64\) | 0.309017 | + | 0.951057i | 0.0386271 | + | 0.118882i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.500000 | − | 1.53884i | 0.0615457 | − | 0.189418i | ||||
\(67\) | −8.28115 | − | 6.01661i | −1.01170 | − | 0.735046i | −0.0471381 | − | 0.998888i | \(-0.515010\pi\) |
−0.964566 | + | 0.263843i | \(0.915010\pi\) | |||||||
\(68\) | −1.14590 | −0.138961 | ||||||||
\(69\) | −0.545085 | − | 0.396027i | −0.0656205 | − | 0.0476761i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.42705 | − | 1.76336i | 0.288038 | − | 0.209272i | −0.434378 | − | 0.900731i | \(-0.643032\pi\) |
0.722416 | + | 0.691459i | \(0.243032\pi\) | |||||||
\(72\) | 2.30902 | − | 1.67760i | 0.272120 | − | 0.197707i | ||||
\(73\) | −2.38197 | − | 7.33094i | −0.278788 | − | 0.858021i | −0.988192 | − | 0.153219i | \(-0.951036\pi\) |
0.709404 | − | 0.704802i | \(-0.248964\pi\) | |||||||
\(74\) | 8.32624 | 0.967905 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.85410 | 0.671512 | ||||||||
\(77\) | 3.92705 | + | 12.0862i | 0.447529 | + | 1.37735i | ||||
\(78\) | 0.309017 | − | 0.224514i | 0.0349893 | − | 0.0254212i | ||||
\(79\) | 5.85410 | − | 4.25325i | 0.658638 | − | 0.478528i | −0.207565 | − | 0.978221i | \(-0.566554\pi\) |
0.866203 | + | 0.499693i | \(0.166554\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.23607 | − | 4.53077i | −0.692896 | − | 0.503419i | ||||
\(82\) | 1.47214 | 0.162570 | ||||||||
\(83\) | −3.66312 | − | 2.66141i | −0.402080 | − | 0.292128i | 0.368308 | − | 0.929704i | \(-0.379937\pi\) |
−0.770387 | + | 0.637576i | \(0.779937\pi\) | |||||||
\(84\) | 0.354102 | − | 1.08981i | 0.0386357 | − | 0.118908i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.92705 | + | 5.93085i | 0.207799 | + | 0.639540i | ||||
\(87\) | −1.11803 | + | 3.44095i | −0.119866 | + | 0.368909i | ||||
\(88\) | 1.30902 | − | 4.02874i | 0.139542 | − | 0.429465i | ||||
\(89\) | 1.38197 | + | 4.25325i | 0.146488 | + | 0.450844i | 0.997199 | − | 0.0747893i | \(-0.0238284\pi\) |
−0.850711 | + | 0.525633i | \(0.823828\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.927051 | + | 2.85317i | −0.0971813 | + | 0.299093i | ||||
\(92\) | −1.42705 | − | 1.03681i | −0.148780 | − | 0.108095i | ||||
\(93\) | −0.0901699 | −0.00935019 | ||||||||
\(94\) | −9.66312 | − | 7.02067i | −0.996675 | − | 0.724126i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.309017 | + | 0.224514i | −0.0315389 | + | 0.0229144i | ||||
\(97\) | 7.73607 | − | 5.62058i | 0.785479 | − | 0.570684i | −0.121140 | − | 0.992635i | \(-0.538655\pi\) |
0.906618 | + | 0.421952i | \(0.138655\pi\) | |||||||
\(98\) | 0.618034 | + | 1.90211i | 0.0624309 | + | 0.192142i | ||||
\(99\) | −12.0902 | −1.21511 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.618034 | 0.0614967 | 0.0307483 | − | 0.999527i | \(-0.490211\pi\) | ||||
0.0307483 | + | 0.999527i | \(0.490211\pi\) | |||||||
\(102\) | −0.135255 | − | 0.416272i | −0.0133922 | − | 0.0412171i | ||||
\(103\) | −10.6353 | + | 7.72696i | −1.04792 | + | 0.761360i | −0.971816 | − | 0.235739i | \(-0.924249\pi\) |
−0.0761065 | + | 0.997100i | \(0.524249\pi\) | |||||||
\(104\) | 0.809017 | − | 0.587785i | 0.0793306 | − | 0.0576371i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.47214 | + | 6.15537i | 0.822887 | + | 0.597862i | ||||
\(107\) | 1.09017 | 0.105391 | 0.0526954 | − | 0.998611i | \(-0.483219\pi\) | ||||
0.0526954 | + | 0.998611i | \(0.483219\pi\) | |||||||
\(108\) | 1.80902 | + | 1.31433i | 0.174073 | + | 0.126471i | ||||
\(109\) | −4.63525 | + | 14.2658i | −0.443977 | + | 1.36642i | 0.439625 | + | 0.898181i | \(0.355111\pi\) |
−0.883602 | + | 0.468239i | \(0.844889\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.982779 | + | 3.02468i | 0.0932813 | + | 0.287090i | ||||
\(112\) | 0.927051 | − | 2.85317i | 0.0875981 | − | 0.269599i | ||||
\(113\) | −1.16312 | + | 3.57971i | −0.109417 | + | 0.336751i | −0.990742 | − | 0.135760i | \(-0.956652\pi\) |
0.881325 | + | 0.472511i | \(0.156652\pi\) | |||||||
\(114\) | 0.690983 | + | 2.12663i | 0.0647165 | + | 0.199177i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.92705 | + | 9.00854i | −0.271770 | + | 0.836422i | ||||
\(117\) | −2.30902 | − | 1.67760i | −0.213469 | − | 0.155094i | ||||
\(118\) | −4.47214 | −0.411693 | ||||||||
\(119\) | 2.78115 | + | 2.02063i | 0.254948 | + | 0.185230i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.61803 | + | 4.08174i | −0.510730 | + | 0.371067i | ||||
\(122\) | 7.16312 | − | 5.20431i | 0.648518 | − | 0.471176i | ||||
\(123\) | 0.173762 | + | 0.534785i | 0.0156676 | + | 0.0482199i | ||||
\(124\) | −0.236068 | −0.0211995 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −8.56231 | −0.762791 | ||||||||
\(127\) | 1.09017 | + | 3.35520i | 0.0967369 | + | 0.297726i | 0.987702 | − | 0.156345i | \(-0.0499713\pi\) |
−0.890966 | + | 0.454071i | \(0.849971\pi\) | |||||||
\(128\) | −0.809017 | + | 0.587785i | −0.0715077 | + | 0.0519534i | ||||
\(129\) | −1.92705 | + | 1.40008i | −0.169667 | + | 0.123271i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.2812 | + | 9.64932i | 1.16038 | + | 0.843065i | 0.989826 | − | 0.142283i | \(-0.0454444\pi\) |
0.170554 | + | 0.985348i | \(0.445444\pi\) | |||||||
\(132\) | 1.61803 | 0.140832 | ||||||||
\(133\) | −14.2082 | − | 10.3229i | −1.23201 | − | 0.895106i | ||||
\(134\) | 3.16312 | − | 9.73508i | 0.273252 | − | 0.840983i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.354102 | − | 1.08981i | −0.0303640 | − | 0.0934508i | ||||
\(137\) | −1.57295 | + | 4.84104i | −0.134386 | + | 0.413598i | −0.995494 | − | 0.0948243i | \(-0.969771\pi\) |
0.861108 | + | 0.508422i | \(0.169771\pi\) | |||||||
\(138\) | 0.208204 | − | 0.640786i | 0.0177235 | − | 0.0545473i | ||||
\(139\) | −1.64590 | − | 5.06555i | −0.139603 | − | 0.429655i | 0.856674 | − | 0.515858i | \(-0.172527\pi\) |
−0.996278 | + | 0.0862030i | \(0.972527\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.40983 | − | 4.33901i | 0.118729 | − | 0.365411i | ||||
\(142\) | 2.42705 | + | 1.76336i | 0.203674 | + | 0.147978i | ||||
\(143\) | −4.23607 | −0.354238 | ||||||||
\(144\) | 2.30902 | + | 1.67760i | 0.192418 | + | 0.139800i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.23607 | − | 4.53077i | 0.516101 | − | 0.374969i | ||||
\(147\) | −0.618034 | + | 0.449028i | −0.0509746 | + | 0.0370352i | ||||
\(148\) | 2.57295 | + | 7.91872i | 0.211495 | + | 0.650915i | ||||
\(149\) | 2.23607 | 0.183186 | 0.0915929 | − | 0.995797i | \(-0.470804\pi\) | ||||
0.0915929 | + | 0.995797i | \(0.470804\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.70820 | −0.790042 | −0.395021 | − | 0.918672i | \(-0.629263\pi\) | ||||
−0.395021 | + | 0.918672i | \(0.629263\pi\) | |||||||
\(152\) | 1.80902 | + | 5.56758i | 0.146731 | + | 0.451591i | ||||
\(153\) | −2.64590 | + | 1.92236i | −0.213908 | + | 0.155413i | ||||
\(154\) | −10.2812 | + | 7.46969i | −0.828479 | + | 0.601925i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.309017 | + | 0.224514i | 0.0247412 | + | 0.0179755i | ||||
\(157\) | −4.56231 | −0.364112 | −0.182056 | − | 0.983288i | \(-0.558275\pi\) | ||||
−0.182056 | + | 0.983288i | \(0.558275\pi\) | |||||||
\(158\) | 5.85410 | + | 4.25325i | 0.465727 | + | 0.338371i | ||||
\(159\) | −1.23607 | + | 3.80423i | −0.0980266 | + | 0.301695i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.63525 | + | 5.03280i | 0.128876 | + | 0.396640i | ||||
\(162\) | 2.38197 | − | 7.33094i | 0.187145 | − | 0.575973i | ||||
\(163\) | −0.572949 | + | 1.76336i | −0.0448768 | + | 0.138117i | −0.970984 | − | 0.239143i | \(-0.923134\pi\) |
0.926108 | + | 0.377260i | \(0.123134\pi\) | |||||||
\(164\) | 0.454915 | + | 1.40008i | 0.0355229 | + | 0.109328i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.39919 | − | 4.30625i | 0.108598 | − | 0.334230i | ||||
\(167\) | 10.8262 | + | 7.86572i | 0.837759 | + | 0.608668i | 0.921744 | − | 0.387799i | \(-0.126765\pi\) |
−0.0839844 | + | 0.996467i | \(0.526765\pi\) | |||||||
\(168\) | 1.14590 | 0.0884080 | ||||||||
\(169\) | 9.70820 | + | 7.05342i | 0.746785 | + | 0.542571i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 13.5172 | − | 9.82084i | 1.03369 | − | 0.751018i | ||||
\(172\) | −5.04508 | + | 3.66547i | −0.384684 | + | 0.279489i | ||||
\(173\) | 0.381966 | + | 1.17557i | 0.0290403 | + | 0.0893770i | 0.964526 | − | 0.263987i | \(-0.0850377\pi\) |
−0.935486 | + | 0.353364i | \(0.885038\pi\) | |||||||
\(174\) | −3.61803 | −0.274282 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.23607 | 0.319306 | ||||||||
\(177\) | −0.527864 | − | 1.62460i | −0.0396767 | − | 0.122112i | ||||
\(178\) | −3.61803 | + | 2.62866i | −0.271183 | + | 0.197026i | ||||
\(179\) | −9.04508 | + | 6.57164i | −0.676061 | + | 0.491187i | −0.872049 | − | 0.489419i | \(-0.837209\pi\) |
0.195987 | + | 0.980606i | \(0.437209\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.38197 | − | 3.18368i | −0.325709 | − | 0.236641i | 0.412899 | − | 0.910777i | \(-0.364516\pi\) |
−0.738608 | + | 0.674136i | \(0.764516\pi\) | |||||||
\(182\) | −3.00000 | −0.222375 | ||||||||
\(183\) | 2.73607 | + | 1.98787i | 0.202256 | + | 0.146948i | ||||
\(184\) | 0.545085 | − | 1.67760i | 0.0401842 | − | 0.123674i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.0278640 | − | 0.0857567i | −0.00204309 | − | 0.00628799i | ||||
\(187\) | −1.50000 | + | 4.61653i | −0.109691 | + | 0.337594i | ||||
\(188\) | 3.69098 | − | 11.3597i | 0.269193 | − | 0.828490i | ||||
\(189\) | −2.07295 | − | 6.37988i | −0.150785 | − | 0.464068i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.21885 | + | 12.9843i | −0.305265 | + | 0.939509i | 0.674313 | + | 0.738446i | \(0.264440\pi\) |
−0.979578 | + | 0.201064i | \(0.935560\pi\) | |||||||
\(192\) | −0.309017 | − | 0.224514i | −0.0223014 | − | 0.0162029i | ||||
\(193\) | 14.6525 | 1.05471 | 0.527354 | − | 0.849646i | \(-0.323184\pi\) | ||||
0.527354 | + | 0.849646i | \(0.323184\pi\) | |||||||
\(194\) | 7.73607 | + | 5.62058i | 0.555417 | + | 0.403534i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.61803 | + | 1.17557i | −0.115574 | + | 0.0839693i | ||||
\(197\) | 9.70820 | − | 7.05342i | 0.691681 | − | 0.502536i | −0.185531 | − | 0.982638i | \(-0.559401\pi\) |
0.877212 | + | 0.480103i | \(0.159401\pi\) | |||||||
\(198\) | −3.73607 | − | 11.4984i | −0.265511 | − | 0.817158i | ||||
\(199\) | 2.56231 | 0.181637 | 0.0908185 | − | 0.995867i | \(-0.471052\pi\) | ||||
0.0908185 | + | 0.995867i | \(0.471052\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.90983 | 0.275778 | ||||||||
\(202\) | 0.190983 | + | 0.587785i | 0.0134375 | + | 0.0413564i | ||||
\(203\) | 22.9894 | − | 16.7027i | 1.61354 | − | 1.17230i | ||||
\(204\) | 0.354102 | − | 0.257270i | 0.0247921 | − | 0.0180125i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −10.6353 | − | 7.72696i | −0.740993 | − | 0.538363i | ||||
\(207\) | −5.03444 | −0.349918 | ||||||||
\(208\) | 0.809017 | + | 0.587785i | 0.0560952 | + | 0.0407556i | ||||
\(209\) | 7.66312 | − | 23.5847i | 0.530069 | − | 1.63138i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.88197 | − | 21.1805i | −0.473774 | − | 1.45813i | −0.847604 | − | 0.530629i | \(-0.821956\pi\) |
0.373830 | − | 0.927497i | \(-0.378044\pi\) | |||||||
\(212\) | −3.23607 | + | 9.95959i | −0.222254 | + | 0.684028i | ||||
\(213\) | −0.354102 | + | 1.08981i | −0.0242627 | + | 0.0746728i | ||||
\(214\) | 0.336881 | + | 1.03681i | 0.0230287 | + | 0.0708751i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.690983 | + | 2.12663i | −0.0470154 | + | 0.144699i | ||||
\(217\) | 0.572949 | + | 0.416272i | 0.0388943 | + | 0.0282584i | ||||
\(218\) | −15.0000 | −1.01593 | ||||||||
\(219\) | 2.38197 | + | 1.73060i | 0.160958 | + | 0.116943i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.927051 | + | 0.673542i | −0.0623602 | + | 0.0453073i | ||||
\(222\) | −2.57295 | + | 1.86936i | −0.172685 | + | 0.125463i | ||||
\(223\) | 2.78115 | + | 8.55951i | 0.186240 | + | 0.573187i | 0.999968 | − | 0.00805911i | \(-0.00256532\pi\) |
−0.813728 | + | 0.581246i | \(0.802565\pi\) | |||||||
\(224\) | 3.00000 | 0.200446 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.76393 | −0.250373 | ||||||||
\(227\) | −9.07295 | − | 27.9237i | −0.602193 | − | 1.85336i | −0.515044 | − | 0.857163i | \(-0.672225\pi\) |
−0.0871483 | − | 0.996195i | \(-0.527775\pi\) | |||||||
\(228\) | −1.80902 | + | 1.31433i | −0.119805 | + | 0.0870435i | ||||
\(229\) | 2.07295 | − | 1.50609i | 0.136984 | − | 0.0995249i | −0.517183 | − | 0.855875i | \(-0.673019\pi\) |
0.654167 | + | 0.756350i | \(0.273019\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.92705 | − | 2.85317i | −0.258381 | − | 0.187725i | ||||
\(232\) | −9.47214 | −0.621876 | ||||||||
\(233\) | 11.5623 | + | 8.40051i | 0.757472 | + | 0.550336i | 0.898134 | − | 0.439722i | \(-0.144923\pi\) |
−0.140662 | + | 0.990058i | \(0.544923\pi\) | |||||||
\(234\) | 0.881966 | − | 2.71441i | 0.0576559 | − | 0.177447i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.38197 | − | 4.25325i | −0.0899583 | − | 0.276863i | ||||
\(237\) | −0.854102 | + | 2.62866i | −0.0554799 | + | 0.170750i | ||||
\(238\) | −1.06231 | + | 3.26944i | −0.0688591 | + | 0.211926i | ||||
\(239\) | −2.13525 | − | 6.57164i | −0.138118 | − | 0.425084i | 0.857944 | − | 0.513743i | \(-0.171742\pi\) |
−0.996062 | + | 0.0886595i | \(0.971742\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.82624 | − | 14.8536i | 0.310885 | − | 0.956807i | −0.666530 | − | 0.745478i | \(-0.732221\pi\) |
0.977415 | − | 0.211328i | \(-0.0677789\pi\) | |||||||
\(242\) | −5.61803 | − | 4.08174i | −0.361141 | − | 0.262384i | ||||
\(243\) | 9.65248 | 0.619207 | ||||||||
\(244\) | 7.16312 | + | 5.20431i | 0.458572 | + | 0.333172i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.454915 | + | 0.330515i | −0.0290043 | + | 0.0210729i | ||||
\(247\) | 4.73607 | − | 3.44095i | 0.301349 | − | 0.218943i | ||||
\(248\) | −0.0729490 | − | 0.224514i | −0.00463227 | − | 0.0142567i | ||||
\(249\) | 1.72949 | 0.109602 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.819660 | 0.0517365 | 0.0258682 | − | 0.999665i | \(-0.491765\pi\) | ||||
0.0258682 | + | 0.999665i | \(0.491765\pi\) | |||||||
\(252\) | −2.64590 | − | 8.14324i | −0.166676 | − | 0.512976i | ||||
\(253\) | −6.04508 | + | 4.39201i | −0.380051 | + | 0.276123i | ||||
\(254\) | −2.85410 | + | 2.07363i | −0.179082 | + | 0.130111i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.809017 | − | 0.587785i | −0.0505636 | − | 0.0367366i | ||||
\(257\) | −25.7426 | −1.60578 | −0.802891 | − | 0.596126i | \(-0.796706\pi\) | ||||
−0.802891 | + | 0.596126i | \(0.796706\pi\) | |||||||
\(258\) | −1.92705 | − | 1.40008i | −0.119973 | − | 0.0871655i | ||||
\(259\) | 7.71885 | − | 23.7562i | 0.479626 | − | 1.47614i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.35410 | + | 25.7113i | 0.517106 | + | 1.59149i | ||||
\(262\) | −5.07295 | + | 15.6129i | −0.313408 | + | 0.964570i | ||||
\(263\) | −1.42705 | + | 4.39201i | −0.0879957 | + | 0.270823i | −0.985365 | − | 0.170457i | \(-0.945476\pi\) |
0.897369 | + | 0.441280i | \(0.145476\pi\) | |||||||
\(264\) | 0.500000 | + | 1.53884i | 0.0307729 | + | 0.0947092i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5.42705 | − | 16.7027i | 0.332754 | − | 1.02411i | ||||
\(267\) | −1.38197 | − | 1.00406i | −0.0845749 | − | 0.0614473i | ||||
\(268\) | 10.2361 | 0.625267 | ||||||||
\(269\) | −1.54508 | − | 1.12257i | −0.0942055 | − | 0.0684443i | 0.539685 | − | 0.841867i | \(-0.318543\pi\) |
−0.633891 | + | 0.773422i | \(0.718543\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.0623 | + | 16.7557i | −1.40094 | + | 1.01784i | −0.406372 | + | 0.913708i | \(0.633206\pi\) |
−0.994564 | + | 0.104131i | \(0.966794\pi\) | |||||||
\(272\) | 0.927051 | − | 0.673542i | 0.0562107 | − | 0.0408395i | ||||
\(273\) | −0.354102 | − | 1.08981i | −0.0214312 | − | 0.0659585i | ||||
\(274\) | −5.09017 | −0.307508 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.673762 | 0.0405557 | ||||||||
\(277\) | −0.0901699 | − | 0.277515i | −0.00541779 | − | 0.0166742i | 0.948311 | − | 0.317342i | \(-0.102790\pi\) |
−0.953729 | + | 0.300668i | \(0.902790\pi\) | |||||||
\(278\) | 4.30902 | − | 3.13068i | 0.258438 | − | 0.187766i | ||||
\(279\) | −0.545085 | + | 0.396027i | −0.0326334 | + | 0.0237095i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.57295 | − | 1.86936i | −0.153489 | − | 0.111516i | 0.508390 | − | 0.861127i | \(-0.330241\pi\) |
−0.661879 | + | 0.749610i | \(0.730241\pi\) | |||||||
\(282\) | 4.56231 | 0.271681 | ||||||||
\(283\) | −9.94427 | − | 7.22494i | −0.591126 | − | 0.429478i | 0.251592 | − | 0.967833i | \(-0.419046\pi\) |
−0.842718 | + | 0.538355i | \(0.819046\pi\) | |||||||
\(284\) | −0.927051 | + | 2.85317i | −0.0550104 | + | 0.169304i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.30902 | − | 4.02874i | −0.0774038 | − | 0.238224i | ||||
\(287\) | 1.36475 | − | 4.20025i | 0.0805584 | − | 0.247933i | ||||
\(288\) | −0.881966 | + | 2.71441i | −0.0519703 | + | 0.159948i | ||||
\(289\) | −4.84752 | − | 14.9191i | −0.285148 | − | 0.877597i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.12868 | + | 3.47371i | −0.0661642 | + | 0.203633i | ||||
\(292\) | 6.23607 | + | 4.53077i | 0.364938 | + | 0.265143i | ||||
\(293\) | −8.56231 | −0.500215 | −0.250108 | − | 0.968218i | \(-0.580466\pi\) | ||||
−0.250108 | + | 0.968218i | \(0.580466\pi\) | |||||||
\(294\) | −0.618034 | − | 0.449028i | −0.0360445 | − | 0.0261878i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.73607 | + | 4.89404i | −0.391526 | + | 0.284460i | ||||
\(297\) | 7.66312 | − | 5.56758i | 0.444659 | − | 0.323064i | ||||
\(298\) | 0.690983 | + | 2.12663i | 0.0400276 | + | 0.123192i | ||||
\(299\) | −1.76393 | −0.102011 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.7082 | 1.07832 | ||||||||
\(302\) | −3.00000 | − | 9.23305i | −0.172631 | − | 0.531302i | ||||
\(303\) | −0.190983 | + | 0.138757i | −0.0109717 | + | 0.00797140i | ||||
\(304\) | −4.73607 | + | 3.44095i | −0.271632 | + | 0.197352i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.64590 | − | 1.92236i | −0.151256 | − | 0.109894i | ||||
\(307\) | 23.1246 | 1.31979 | 0.659896 | − | 0.751357i | \(-0.270600\pi\) | ||||
0.659896 | + | 0.751357i | \(0.270600\pi\) | |||||||
\(308\) | −10.2812 | − | 7.46969i | −0.585823 | − | 0.425625i | ||||
\(309\) | 1.55166 | − | 4.77553i | 0.0882710 | − | 0.271670i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.06231 | − | 9.42481i | −0.173647 | − | 0.534432i | 0.825922 | − | 0.563785i | \(-0.190655\pi\) |
−0.999569 | + | 0.0293530i | \(0.990655\pi\) | |||||||
\(312\) | −0.118034 | + | 0.363271i | −0.00668236 | + | 0.0205662i | ||||
\(313\) | 5.11803 | − | 15.7517i | 0.289288 | − | 0.890338i | −0.695792 | − | 0.718243i | \(-0.744946\pi\) |
0.985080 | − | 0.172095i | \(-0.0550535\pi\) | |||||||
\(314\) | −1.40983 | − | 4.33901i | −0.0795613 | − | 0.244865i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.23607 | + | 6.88191i | −0.125789 | + | 0.387138i | ||||
\(317\) | 6.78115 | + | 4.92680i | 0.380867 | + | 0.276716i | 0.761703 | − | 0.647926i | \(-0.224364\pi\) |
−0.380835 | + | 0.924643i | \(0.624364\pi\) | |||||||
\(318\) | −4.00000 | −0.224309 | ||||||||
\(319\) | 32.4615 | + | 23.5847i | 1.81749 | + | 1.32049i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.336881 | + | 0.244758i | −0.0188029 | + | 0.0136611i | ||||
\(322\) | −4.28115 | + | 3.11044i | −0.238579 | + | 0.173338i | ||||
\(323\) | −2.07295 | − | 6.37988i | −0.115342 | − | 0.354986i | ||||
\(324\) | 7.70820 | 0.428234 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.85410 | −0.102689 | ||||||||
\(327\) | −1.77051 | − | 5.44907i | −0.0979094 | − | 0.301334i | ||||
\(328\) | −1.19098 | + | 0.865300i | −0.0657610 | + | 0.0477782i | ||||
\(329\) | −28.9894 | + | 21.0620i | −1.59823 | + | 1.16119i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.5902 | + | 9.14729i | 0.692018 | + | 0.502781i | 0.877323 | − | 0.479900i | \(-0.159327\pi\) |
−0.185305 | + | 0.982681i | \(0.559327\pi\) | |||||||
\(332\) | 4.52786 | 0.248499 | ||||||||
\(333\) | 19.2254 | + | 13.9681i | 1.05355 | + | 0.765447i | ||||
\(334\) | −4.13525 | + | 12.7270i | −0.226271 | + | 0.696391i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.354102 | + | 1.08981i | 0.0193178 | + | 0.0594542i | ||||
\(337\) | 1.41641 | − | 4.35926i | 0.0771567 | − | 0.237464i | −0.905038 | − | 0.425331i | \(-0.860158\pi\) |
0.982194 | + | 0.187868i | \(0.0601576\pi\) | |||||||
\(338\) | −3.70820 | + | 11.4127i | −0.201700 | + | 0.620768i | ||||
\(339\) | −0.444272 | − | 1.36733i | −0.0241295 | − | 0.0742631i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.309017 | + | 0.951057i | −0.0167342 | + | 0.0515026i | ||||
\(342\) | 13.5172 | + | 9.82084i | 0.730928 | + | 0.531050i | ||||
\(343\) | −15.0000 | −0.809924 | ||||||||
\(344\) | −5.04508 | − | 3.66547i | −0.272013 | − | 0.197629i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.00000 | + | 0.726543i | −0.0537603 | + | 0.0390592i | ||||
\(347\) | −17.0623 | + | 12.3965i | −0.915953 | + | 0.665478i | −0.942513 | − | 0.334169i | \(-0.891544\pi\) |
0.0265607 | + | 0.999647i | \(0.491544\pi\) | |||||||
\(348\) | −1.11803 | − | 3.44095i | −0.0599329 | − | 0.184455i | ||||
\(349\) | −17.7639 | −0.950881 | −0.475441 | − | 0.879748i | \(-0.657711\pi\) | ||||
−0.475441 | + | 0.879748i | \(0.657711\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.23607 | 0.119352 | ||||||||
\(352\) | 1.30902 | + | 4.02874i | 0.0697708 | + | 0.214733i | ||||
\(353\) | −17.1803 | + | 12.4822i | −0.914417 | + | 0.664363i | −0.942128 | − | 0.335253i | \(-0.891178\pi\) |
0.0277109 | + | 0.999616i | \(0.491178\pi\) | |||||||
\(354\) | 1.38197 | − | 1.00406i | 0.0734507 | − | 0.0533650i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3.61803 | − | 2.62866i | −0.191755 | − | 0.139318i | ||||
\(357\) | −1.31308 | −0.0694957 | ||||||||
\(358\) | −9.04508 | − | 6.57164i | −0.478048 | − | 0.347322i | ||||
\(359\) | −2.50000 | + | 7.69421i | −0.131945 | + | 0.406085i | −0.995102 | − | 0.0988502i | \(-0.968484\pi\) |
0.863157 | + | 0.504935i | \(0.168484\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.71885 | + | 14.5231i | 0.248360 | + | 0.764375i | ||||
\(362\) | 1.67376 | − | 5.15131i | 0.0879710 | − | 0.270747i | ||||
\(363\) | 0.819660 | − | 2.52265i | 0.0430210 | − | 0.132405i | ||||
\(364\) | −0.927051 | − | 2.85317i | −0.0485907 | − | 0.149547i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.04508 | + | 3.21644i | −0.0546275 | + | 0.168126i | ||||
\(367\) | 28.7533 | + | 20.8905i | 1.50091 | + | 1.09047i | 0.970018 | + | 0.243035i | \(0.0781430\pi\) |
0.530892 | + | 0.847440i | \(0.321857\pi\) | |||||||
\(368\) | 1.76393 | 0.0919513 | ||||||||
\(369\) | 3.39919 | + | 2.46965i | 0.176955 | + | 0.128565i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 25.4164 | − | 18.4661i | 1.31955 | − | 0.958712i | ||||
\(372\) | 0.0729490 | − | 0.0530006i | 0.00378223 | − | 0.00274795i | ||||
\(373\) | 3.63525 | + | 11.1882i | 0.188226 | + | 0.579301i | 0.999989 | − | 0.00468631i | \(-0.00149170\pi\) |
−0.811763 | + | 0.583987i | \(0.801492\pi\) | |||||||
\(374\) | −4.85410 | −0.251000 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11.9443 | 0.615979 | ||||||||
\(377\) | 2.92705 | + | 9.00854i | 0.150751 | + | 0.463963i | ||||
\(378\) | 5.42705 | − | 3.94298i | 0.279137 | − | 0.202805i | ||||
\(379\) | −7.66312 | + | 5.56758i | −0.393628 | + | 0.285987i | −0.766941 | − | 0.641718i | \(-0.778222\pi\) |
0.373313 | + | 0.927706i | \(0.378222\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.09017 | − | 0.792055i | −0.0558511 | − | 0.0405782i | ||||
\(382\) | −13.6525 | −0.698521 | ||||||||
\(383\) | 9.16312 | + | 6.65740i | 0.468214 | + | 0.340177i | 0.796745 | − | 0.604316i | \(-0.206554\pi\) |
−0.328531 | + | 0.944493i | \(0.606554\pi\) | |||||||
\(384\) | 0.118034 | − | 0.363271i | 0.00602340 | − | 0.0185381i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.52786 | + | 13.9353i | 0.230462 | + | 0.709290i | ||||
\(387\) | −5.50000 | + | 16.9273i | −0.279581 | + | 0.860461i | ||||
\(388\) | −2.95492 | + | 9.09429i | −0.150013 | + | 0.461693i | ||||
\(389\) | 5.62868 | + | 17.3233i | 0.285385 | + | 0.878326i | 0.986283 | + | 0.165064i | \(0.0527830\pi\) |
−0.700898 | + | 0.713262i | \(0.747217\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.624612 | + | 1.92236i | −0.0315880 | + | 0.0972178i | ||||
\(392\) | −1.61803 | − | 1.17557i | −0.0817231 | − | 0.0593753i | ||||
\(393\) | −6.27051 | −0.316305 | ||||||||
\(394\) | 9.70820 | + | 7.05342i | 0.489092 | + | 0.355346i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 9.78115 | − | 7.10642i | 0.491521 | − | 0.357111i | ||||
\(397\) | −8.28115 | + | 6.01661i | −0.415619 | + | 0.301965i | −0.775873 | − | 0.630889i | \(-0.782690\pi\) |
0.360254 | + | 0.932854i | \(0.382690\pi\) | |||||||
\(398\) | 0.791796 | + | 2.43690i | 0.0396892 | + | 0.122151i | ||||
\(399\) | 6.70820 | 0.335830 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.1803 | −0.708132 | −0.354066 | − | 0.935220i | \(-0.615201\pi\) | ||||
−0.354066 | + | 0.935220i | \(0.615201\pi\) | |||||||
\(402\) | 1.20820 | + | 3.71847i | 0.0602597 | + | 0.185460i | ||||
\(403\) | −0.190983 | + | 0.138757i | −0.00951354 | + | 0.00691199i | ||||
\(404\) | −0.500000 | + | 0.363271i | −0.0248759 | + | 0.0180734i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 22.9894 | + | 16.7027i | 1.14094 | + | 0.828943i | ||||
\(407\) | 35.2705 | 1.74829 | ||||||||
\(408\) | 0.354102 | + | 0.257270i | 0.0175307 | + | 0.0127368i | ||||
\(409\) | −2.07295 | + | 6.37988i | −0.102501 | + | 0.315465i | −0.989136 | − | 0.147005i | \(-0.953037\pi\) |
0.886635 | + | 0.462470i | \(0.153037\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.600813 | − | 1.84911i | −0.0296359 | − | 0.0912100i | ||||
\(412\) | 4.06231 | − | 12.5025i | 0.200135 | − | 0.615954i | ||||
\(413\) | −4.14590 | + | 12.7598i | −0.204006 | + | 0.627867i | ||||
\(414\) | −1.55573 | − | 4.78804i | −0.0764599 | − | 0.235319i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.309017 | + | 0.951057i | −0.0151508 | + | 0.0466294i | ||||
\(417\) | 1.64590 | + | 1.19581i | 0.0806000 | + | 0.0585593i | ||||
\(418\) | 24.7984 | 1.21293 | ||||||||
\(419\) | −18.4164 | − | 13.3803i | −0.899700 | − | 0.653671i | 0.0386886 | − | 0.999251i | \(-0.487682\pi\) |
−0.938389 | + | 0.345581i | \(0.887682\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.2082 | + | 12.5025i | −0.838677 | + | 0.609334i | −0.922001 | − | 0.387188i | \(-0.873446\pi\) |
0.0833241 | + | 0.996522i | \(0.473446\pi\) | |||||||
\(422\) | 18.0172 | − | 13.0903i | 0.877065 | − | 0.637225i | ||||
\(423\) | −10.5344 | − | 32.4217i | −0.512202 | − | 1.57640i | ||||
\(424\) | −10.4721 | −0.508572 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.14590 | −0.0555189 | ||||||||
\(427\) | −8.20820 | − | 25.2623i | −0.397223 | − | 1.22253i | ||||
\(428\) | −0.881966 | + | 0.640786i | −0.0426314 | + | 0.0309736i | ||||
\(429\) | 1.30902 | − | 0.951057i | 0.0631999 | − | 0.0459174i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.0902 | − | 15.3229i | −1.01588 | − | 0.738078i | −0.0504440 | − | 0.998727i | \(-0.516064\pi\) |
−0.965434 | + | 0.260649i | \(0.916064\pi\) | |||||||
\(432\) | −2.23607 | −0.107583 | ||||||||
\(433\) | −17.2812 | − | 12.5555i | −0.830479 | − | 0.603378i | 0.0892157 | − | 0.996012i | \(-0.471564\pi\) |
−0.919695 | + | 0.392634i | \(0.871564\pi\) | |||||||
\(434\) | −0.218847 | + | 0.673542i | −0.0105050 | + | 0.0323310i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.63525 | − | 14.2658i | −0.221988 | − | 0.683210i | ||||
\(437\) | 3.19098 | − | 9.82084i | 0.152645 | − | 0.469794i | ||||
\(438\) | −0.909830 | + | 2.80017i | −0.0434734 | + | 0.133797i | ||||
\(439\) | 7.92705 | + | 24.3970i | 0.378338 | + | 1.16440i | 0.941199 | + | 0.337852i | \(0.109700\pi\) |
−0.562862 | + | 0.826551i | \(0.690300\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.76393 | + | 5.42882i | −0.0839968 | + | 0.258515i | ||||
\(442\) | −0.927051 | − | 0.673542i | −0.0440953 | − | 0.0320371i | ||||
\(443\) | −19.4164 | −0.922501 | −0.461251 | − | 0.887270i | \(-0.652599\pi\) | ||||
−0.461251 | + | 0.887270i | \(0.652599\pi\) | |||||||
\(444\) | −2.57295 | − | 1.86936i | −0.122107 | − | 0.0887158i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.28115 | + | 5.29007i | −0.344773 | + | 0.250492i | ||||
\(447\) | −0.690983 | + | 0.502029i | −0.0326824 | + | 0.0237451i | ||||
\(448\) | 0.927051 | + | 2.85317i | 0.0437990 | + | 0.134800i | ||||
\(449\) | −3.94427 | −0.186142 | −0.0930709 | − | 0.995659i | \(-0.529668\pi\) | ||||
−0.0930709 | + | 0.995659i | \(0.529668\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.23607 | 0.293645 | ||||||||
\(452\) | −1.16312 | − | 3.57971i | −0.0547085 | − | 0.168375i | ||||
\(453\) | 3.00000 | − | 2.17963i | 0.140952 | − | 0.102408i | ||||
\(454\) | 23.7533 | − | 17.2578i | 1.11480 | − | 0.809947i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.80902 | − | 1.31433i | −0.0847150 | − | 0.0615490i | ||||
\(457\) | −40.2148 | −1.88117 | −0.940584 | − | 0.339561i | \(-0.889722\pi\) | ||||
−0.940584 | + | 0.339561i | \(0.889722\pi\) | |||||||
\(458\) | 2.07295 | + | 1.50609i | 0.0968625 | + | 0.0703748i | ||||
\(459\) | 0.791796 | − | 2.43690i | 0.0369579 | − | 0.113745i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.79837 | + | 5.53483i | 0.0837586 | + | 0.257783i | 0.984161 | − | 0.177275i | \(-0.0567281\pi\) |
−0.900403 | + | 0.435057i | \(0.856728\pi\) | |||||||
\(462\) | 1.50000 | − | 4.61653i | 0.0697863 | − | 0.214780i | ||||
\(463\) | 10.8090 | − | 33.2667i | 0.502338 | − | 1.54604i | −0.302863 | − | 0.953034i | \(-0.597943\pi\) |
0.805201 | − | 0.593002i | \(-0.202057\pi\) | |||||||
\(464\) | −2.92705 | − | 9.00854i | −0.135885 | − | 0.418211i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.41641 | + | 13.5923i | −0.204586 | + | 0.629651i | ||||
\(467\) | −15.5172 | − | 11.2739i | −0.718051 | − | 0.521695i | 0.167710 | − | 0.985836i | \(-0.446363\pi\) |
−0.885761 | + | 0.464142i | \(0.846363\pi\) | |||||||
\(468\) | 2.85410 | 0.131931 | ||||||||
\(469\) | −24.8435 | − | 18.0498i | −1.14716 | − | 0.833464i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.40983 | − | 1.02430i | 0.0649615 | − | 0.0471973i | ||||
\(472\) | 3.61803 | − | 2.62866i | 0.166534 | − | 0.120994i | ||||
\(473\) | 8.16312 | + | 25.1235i | 0.375341 | + | 1.15518i | ||||
\(474\) | −2.76393 | −0.126952 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.43769 | −0.157566 | ||||||||
\(477\) | 9.23607 | + | 28.4257i | 0.422891 | + | 1.30152i | ||||
\(478\) | 5.59017 | − | 4.06150i | 0.255688 | − | 0.185769i | ||||
\(479\) | 12.2984 | − | 8.93529i | 0.561927 | − | 0.408264i | −0.270237 | − | 0.962794i | \(-0.587102\pi\) |
0.832164 | + | 0.554530i | \(0.187102\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.73607 | + | 4.89404i | 0.307138 | + | 0.223149i | ||||
\(482\) | 15.6180 | 0.711382 | ||||||||
\(483\) | −1.63525 | − | 1.18808i | −0.0744067 | − | 0.0540596i | ||||
\(484\) | 2.14590 | − | 6.60440i | 0.0975408 | − | 0.300200i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.98278 | + | 9.18005i | 0.135302 | + | 0.416416i | ||||
\(487\) | −6.83688 | + | 21.0418i | −0.309809 | + | 0.953493i | 0.668030 | + | 0.744134i | \(0.267138\pi\) |
−0.977839 | + | 0.209359i | \(0.932862\pi\) | |||||||
\(488\) | −2.73607 | + | 8.42075i | −0.123856 | + | 0.381190i | ||||
\(489\) | −0.218847 | − | 0.673542i | −0.00989661 | − | 0.0304586i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.94427 | − | 18.2946i | 0.268261 | − | 0.825623i | −0.722663 | − | 0.691201i | \(-0.757082\pi\) |
0.990924 | − | 0.134423i | \(-0.0429179\pi\) | |||||||
\(492\) | −0.454915 | − | 0.330515i | −0.0205092 | − | 0.0149008i | ||||
\(493\) | 10.8541 | 0.488844 | ||||||||
\(494\) | 4.73607 | + | 3.44095i | 0.213086 | + | 0.154816i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.190983 | − | 0.138757i | 0.00857539 | − | 0.00623039i | ||||
\(497\) | 7.28115 | − | 5.29007i | 0.326604 | − | 0.237292i | ||||
\(498\) | 0.534442 | + | 1.64484i | 0.0239489 | + | 0.0737072i | ||||
\(499\) | 34.1459 | 1.52858 | 0.764290 | − | 0.644873i | \(-0.223090\pi\) | ||||
0.764290 | + | 0.644873i | \(0.223090\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.11146 | −0.228363 | ||||||||
\(502\) | 0.253289 | + | 0.779543i | 0.0113048 | + | 0.0347927i | ||||
\(503\) | −24.6803 | + | 17.9313i | −1.10044 | + | 0.799518i | −0.981132 | − | 0.193339i | \(-0.938068\pi\) |
−0.119310 | + | 0.992857i | \(0.538068\pi\) | |||||||
\(504\) | 6.92705 | − | 5.03280i | 0.308555 | − | 0.224179i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −6.04508 | − | 4.39201i | −0.268737 | − | 0.195249i | ||||
\(507\) | −4.58359 | −0.203564 | ||||||||
\(508\) | −2.85410 | − | 2.07363i | −0.126630 | − | 0.0920023i | ||||
\(509\) | −0.590170 | + | 1.81636i | −0.0261588 | + | 0.0805086i | −0.963284 | − | 0.268486i | \(-0.913477\pi\) |
0.937125 | + | 0.348994i | \(0.113477\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.14590 | − | 21.9928i | −0.316116 | − | 0.972905i | ||||
\(512\) | 0.309017 | − | 0.951057i | 0.0136568 | − | 0.0420312i | ||||
\(513\) | −4.04508 | + | 12.4495i | −0.178595 | + | 0.549658i | ||||
\(514\) | −7.95492 | − | 24.4827i | −0.350876 | − | 1.07989i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.736068 | − | 2.26538i | 0.0324036 | − | 0.0997280i | ||||
\(517\) | −40.9336 | − | 29.7400i | −1.80026 | − | 1.30796i | ||||
\(518\) | 24.9787 | 1.09750 | ||||||||
\(519\) | −0.381966 | − | 0.277515i | −0.0167664 | − | 0.0121815i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.9721 | − | 13.7841i | 0.831184 | − | 0.603891i | −0.0887098 | − | 0.996058i | \(-0.528274\pi\) |
0.919894 | + | 0.392167i | \(0.128274\pi\) | |||||||
\(522\) | −21.8713 | + | 15.8904i | −0.957282 | + | 0.695506i | ||||
\(523\) | 1.43769 | + | 4.42477i | 0.0628660 | + | 0.193482i | 0.977557 | − | 0.210673i | \(-0.0675657\pi\) |
−0.914691 | + | 0.404155i | \(0.867566\pi\) | |||||||
\(524\) | −16.4164 | −0.717154 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.61803 | −0.201356 | ||||||||
\(527\) | 0.0835921 | + | 0.257270i | 0.00364133 | + | 0.0112069i | ||||
\(528\) | −1.30902 | + | 0.951057i | −0.0569677 | + | 0.0413894i | ||||
\(529\) | 16.0902 | − | 11.6902i | 0.699573 | − | 0.508269i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.3262 | − | 7.50245i | −0.448121 | − | 0.325579i | ||||
\(532\) | 17.5623 | 0.761423 | ||||||||
\(533\) | 1.19098 | + | 0.865300i | 0.0515872 | + | 0.0374803i | ||||
\(534\) | 0.527864 | − | 1.62460i | 0.0228429 | − | 0.0703033i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.16312 | + | 9.73508i | 0.136626 | + | 0.420491i | ||||
\(537\) | 1.31966 | − | 4.06150i | 0.0569475 | − | 0.175266i | ||||
\(538\) | 0.590170 | − | 1.81636i | 0.0254440 | − | 0.0783087i | ||||
\(539\) | 2.61803 | + | 8.05748i | 0.112767 | + | 0.347060i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.72542 | − | 14.5434i | 0.203162 | − | 0.625268i | −0.796622 | − | 0.604478i | \(-0.793382\pi\) |
0.999784 | − | 0.0207902i | \(-0.00661819\pi\) | |||||||
\(542\) | −23.0623 | − | 16.7557i | −0.990611 | − | 0.719721i | ||||
\(543\) | 2.06888 | 0.0887843 | ||||||||
\(544\) | 0.927051 | + | 0.673542i | 0.0397470 | + | 0.0288779i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.927051 | − | 0.673542i | 0.0396741 | − | 0.0288249i | ||||
\(547\) | 6.78115 | − | 4.92680i | 0.289941 | − | 0.210655i | −0.433301 | − | 0.901249i | \(-0.642651\pi\) |
0.723242 | + | 0.690595i | \(0.242651\pi\) | |||||||
\(548\) | −1.57295 | − | 4.84104i | −0.0671931 | − | 0.206799i | ||||
\(549\) | 25.2705 | 1.07852 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −55.4508 | −2.36229 | ||||||||
\(552\) | 0.208204 | + | 0.640786i | 0.00886175 | + | 0.0272737i | ||||
\(553\) | 17.5623 | − | 12.7598i | 0.746825 | − | 0.542600i | ||||
\(554\) | 0.236068 | − | 0.171513i | 0.0100296 | − | 0.00728691i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.30902 | + | 3.13068i | 0.182743 | + | 0.132771i | ||||
\(557\) | −24.8885 | −1.05456 | −0.527281 | − | 0.849691i | \(-0.676788\pi\) | ||||
−0.527281 | + | 0.849691i | \(0.676788\pi\) | |||||||
\(558\) | −0.545085 | − | 0.396027i | −0.0230753 | − | 0.0167652i | ||||
\(559\) | −1.92705 | + | 5.93085i | −0.0815056 | + | 0.250848i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.572949 | − | 1.76336i | −0.0241899 | − | 0.0744489i | ||||
\(562\) | 0.982779 | − | 3.02468i | 0.0414560 | − | 0.127589i | ||||
\(563\) | 8.69756 | − | 26.7683i | 0.366558 | − | 1.12815i | −0.582441 | − | 0.812873i | \(-0.697902\pi\) |
0.948999 | − | 0.315278i | \(-0.102098\pi\) | |||||||
\(564\) | 1.40983 | + | 4.33901i | 0.0593646 | + | 0.182705i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3.79837 | − | 11.6902i | 0.159658 | − | 0.491375i | ||||
\(567\) | −18.7082 | − | 13.5923i | −0.785671 | − | 0.570823i | ||||
\(568\) | −3.00000 | −0.125877 | ||||||||
\(569\) | −14.3713 | − | 10.4414i | −0.602477 | − | 0.437725i | 0.244280 | − | 0.969705i | \(-0.421448\pi\) |
−0.846757 | + | 0.531979i | \(0.821448\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.0172 | + | 10.1841i | −0.586602 | + | 0.426192i | −0.841098 | − | 0.540882i | \(-0.818090\pi\) |
0.254496 | + | 0.967074i | \(0.418090\pi\) | |||||||
\(572\) | 3.42705 | − | 2.48990i | 0.143292 | − | 0.104108i | ||||
\(573\) | −1.61146 | − | 4.95955i | −0.0673195 | − | 0.207188i | ||||
\(574\) | 4.41641 | 0.184337 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.85410 | −0.118921 | ||||||||
\(577\) | 13.2877 | + | 40.8954i | 0.553175 | + | 1.70250i | 0.700714 | + | 0.713443i | \(0.252865\pi\) |
−0.147538 | + | 0.989056i | \(0.547135\pi\) | |||||||
\(578\) | 12.6910 | − | 9.22054i | 0.527875 | − | 0.383524i | ||||
\(579\) | −4.52786 | + | 3.28969i | −0.188172 | + | 0.136715i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.9894 | − | 7.98424i | −0.455915 | − | 0.331242i | ||||
\(582\) | −3.65248 | −0.151400 | ||||||||
\(583\) | 35.8885 | + | 26.0746i | 1.48635 | + | 1.07990i | ||||
\(584\) | −2.38197 | + | 7.33094i | −0.0985665 | + | 0.303356i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.64590 | − | 8.14324i | −0.109301 | − | 0.336394i | ||||
\(587\) | 10.5623 | − | 32.5074i | 0.435953 | − | 1.34173i | −0.456154 | − | 0.889901i | \(-0.650773\pi\) |
0.892107 | − | 0.451824i | \(-0.149227\pi\) | |||||||
\(588\) | 0.236068 | − | 0.726543i | 0.00973528 | − | 0.0299621i | ||||
\(589\) | −0.427051 | − | 1.31433i | −0.0175963 | − | 0.0541559i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.41641 | + | 4.35926i | −0.0582632 | + | 0.179316i | ||||
\(592\) | −6.73607 | − | 4.89404i | −0.276851 | − | 0.201144i | ||||
\(593\) | −29.0132 | −1.19143 | −0.595714 | − | 0.803197i | \(-0.703131\pi\) | ||||
−0.595714 | + | 0.803197i | \(0.703131\pi\) | |||||||
\(594\) | 7.66312 | + | 5.56758i | 0.314422 | + | 0.228441i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.80902 | + | 1.31433i | −0.0741002 | + | 0.0538370i | ||||
\(597\) | −0.791796 | + | 0.575274i | −0.0324061 | + | 0.0235444i | ||||
\(598\) | −0.545085 | − | 1.67760i | −0.0222902 | − | 0.0686021i | ||||
\(599\) | 8.94427 | 0.365453 | 0.182727 | − | 0.983164i | \(-0.441508\pi\) | ||||
0.182727 | + | 0.983164i | \(0.441508\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.8328 | 1.58402 | 0.792012 | − | 0.610506i | \(-0.209034\pi\) | ||||
0.792012 | + | 0.610506i | \(0.209034\pi\) | |||||||
\(602\) | 5.78115 | + | 17.7926i | 0.235622 | + | 0.725171i | ||||
\(603\) | 23.6353 | − | 17.1720i | 0.962502 | − | 0.699299i | ||||
\(604\) | 7.85410 | − | 5.70634i | 0.319579 | − | 0.232188i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.190983 | − | 0.138757i | −0.00775815 | − | 0.00563663i | ||||
\(607\) | 33.8541 | 1.37410 | 0.687048 | − | 0.726612i | \(-0.258906\pi\) | ||||
0.687048 | + | 0.726612i | \(0.258906\pi\) | |||||||
\(608\) | −4.73607 | − | 3.44095i | −0.192073 | − | 0.139549i | ||||
\(609\) | −3.35410 | + | 10.3229i | −0.135915 | + | 0.418304i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.69098 | − | 11.3597i | −0.149321 | − | 0.459563i | ||||
\(612\) | 1.01064 | − | 3.11044i | 0.0408528 | − | 0.125732i | ||||
\(613\) | 6.62461 | − | 20.3885i | 0.267566 | − | 0.823482i | −0.723526 | − | 0.690297i | \(-0.757480\pi\) |
0.991091 | − | 0.133185i | \(-0.0425203\pi\) | |||||||
\(614\) | 7.14590 | + | 21.9928i | 0.288385 | + | 0.887558i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.92705 | − | 12.0862i | 0.158225 | − | 0.486968i | ||||
\(617\) | 11.6180 | + | 8.44100i | 0.467724 | + | 0.339822i | 0.796554 | − | 0.604568i | \(-0.206654\pi\) |
−0.328829 | + | 0.944389i | \(0.606654\pi\) | |||||||
\(618\) | 5.02129 | 0.201986 | ||||||||
\(619\) | −37.9894 | − | 27.6009i | −1.52692 | − | 1.10937i | −0.957920 | − | 0.287037i | \(-0.907330\pi\) |
−0.569002 | − | 0.822336i | \(-0.692670\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.19098 | − | 2.31838i | 0.128050 | − | 0.0930336i | ||||
\(622\) | 8.01722 | − | 5.82485i | 0.321461 | − | 0.233555i | ||||
\(623\) | 4.14590 | + | 12.7598i | 0.166102 | + | 0.511209i | ||||
\(624\) | −0.381966 | −0.0152909 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 16.5623 | 0.661963 | ||||||||
\(627\) | 2.92705 | + | 9.00854i | 0.116895 | + | 0.359766i | ||||
\(628\) | 3.69098 | − | 2.68166i | 0.147286 | − | 0.107010i | ||||
\(629\) | 7.71885 | − | 5.60807i | 0.307771 | − | 0.223608i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.2705 | + | 26.3521i | 1.44391 | + | 1.04906i | 0.987208 | + | 0.159438i | \(0.0509681\pi\) |
0.456698 | + | 0.889622i | \(0.349032\pi\) | |||||||
\(632\) | −7.23607 | −0.287835 | ||||||||
\(633\) | 6.88197 | + | 5.00004i | 0.273534 | + | 0.198734i | ||||
\(634\) | −2.59017 | + | 7.97172i | −0.102869 | + | 0.316598i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.23607 | − | 3.80423i | −0.0490133 | − | 0.150847i | ||||
\(637\) | −0.618034 | + | 1.90211i | −0.0244874 | + | 0.0753645i | ||||
\(638\) | −12.3992 | + | 38.1608i | −0.490889 | + | 1.51080i | ||||
\(639\) | 2.64590 | + | 8.14324i | 0.104670 | + | 0.322141i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.38197 | + | 28.8747i | −0.370565 | + | 1.14048i | 0.575857 | + | 0.817551i | \(0.304669\pi\) |
−0.946422 | + | 0.322932i | \(0.895331\pi\) | |||||||
\(642\) | −0.336881 | − | 0.244758i | −0.0132956 | − | 0.00965984i | ||||
\(643\) | 31.7639 | 1.25265 | 0.626324 | − | 0.779563i | \(-0.284559\pi\) | ||||
0.626324 | + | 0.779563i | \(0.284559\pi\) | |||||||
\(644\) | −4.28115 | − | 3.11044i | −0.168701 | − | 0.122568i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.42705 | − | 3.94298i | 0.213524 | − | 0.155135i | ||||
\(647\) | −19.1353 | + | 13.9026i | −0.752284 | + | 0.546567i | −0.896534 | − | 0.442975i | \(-0.853923\pi\) |
0.144250 | + | 0.989541i | \(0.453923\pi\) | |||||||
\(648\) | 2.38197 | + | 7.33094i | 0.0935725 | + | 0.287986i | ||||
\(649\) | −18.9443 | −0.743628 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.270510 | −0.0106021 | ||||||||
\(652\) | −0.572949 | − | 1.76336i | −0.0224384 | − | 0.0690583i | ||||
\(653\) | −6.95492 | + | 5.05304i | −0.272167 | + | 0.197741i | −0.715494 | − | 0.698619i | \(-0.753798\pi\) |
0.443327 | + | 0.896360i | \(0.353798\pi\) | |||||||
\(654\) | 4.63525 | − | 3.36771i | 0.181253 | − | 0.131688i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.19098 | − | 0.865300i | −0.0465001 | − | 0.0337843i | ||||
\(657\) | 22.0000 | 0.858302 | ||||||||
\(658\) | −28.9894 | − | 21.0620i | −1.13012 | − | 0.821082i | ||||
\(659\) | −7.92705 | + | 24.3970i | −0.308794 | + | 0.950370i | 0.669440 | + | 0.742866i | \(0.266534\pi\) |
−0.978234 | + | 0.207504i | \(0.933466\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.42705 | − | 25.9358i | −0.327774 | − | 1.00879i | −0.970173 | − | 0.242415i | \(-0.922061\pi\) |
0.642398 | − | 0.766371i | \(-0.277939\pi\) | |||||||
\(662\) | −4.80902 | + | 14.8006i | −0.186908 | + | 0.575243i | ||||
\(663\) | 0.135255 | − | 0.416272i | 0.00525287 | − | 0.0161667i | ||||
\(664\) | 1.39919 | + | 4.30625i | 0.0542990 | + | 0.167115i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.34346 | + | 22.6008i | −0.284553 | + | 0.875765i | ||||
\(667\) | 13.5172 | + | 9.82084i | 0.523389 | + | 0.380264i | ||||
\(668\) | −13.3820 | −0.517764 | ||||||||
\(669\) | −2.78115 | − | 2.02063i | −0.107526 | − | 0.0781219i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 30.3435 | − | 22.0458i | 1.17140 | − | 0.851069i | ||||
\(672\) | −0.927051 | + | 0.673542i | −0.0357618 | + | 0.0259824i | ||||
\(673\) | −1.00000 | − | 3.07768i | −0.0385472 | − | 0.118636i | 0.929931 | − | 0.367733i | \(-0.119866\pi\) |
−0.968478 | + | 0.249097i | \(0.919866\pi\) | |||||||
\(674\) | 4.58359 | 0.176553 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.0000 | −0.461538 | ||||||||
\(677\) | −2.59017 | − | 7.97172i | −0.0995483 | − | 0.306378i | 0.888864 | − | 0.458171i | \(-0.151495\pi\) |
−0.988412 | + | 0.151793i | \(0.951495\pi\) | |||||||
\(678\) | 1.16312 | − | 0.845055i | 0.0446693 | − | 0.0324542i | ||||
\(679\) | 23.2082 | − | 16.8617i | 0.890649 | − | 0.647094i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.07295 | + | 6.59188i | 0.347676 | + | 0.252602i | ||||
\(682\) | −1.00000 | −0.0382920 | ||||||||
\(683\) | −9.19098 | − | 6.67764i | −0.351683 | − | 0.255513i | 0.397892 | − | 0.917432i | \(-0.369742\pi\) |
−0.749575 | + | 0.661920i | \(0.769742\pi\) | |||||||
\(684\) | −5.16312 | + | 15.8904i | −0.197417 | + | 0.607586i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −4.63525 | − | 14.2658i | −0.176975 | − | 0.544673i | ||||
\(687\) | −0.302439 | + | 0.930812i | −0.0115388 | + | 0.0355127i | ||||
\(688\) | 1.92705 | − | 5.93085i | 0.0734681 | − | 0.226112i | ||||
\(689\) | 3.23607 | + | 9.95959i | 0.123284 | + | 0.379430i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.97214 | + | 30.6911i | −0.379358 | + | 1.16754i | 0.561133 | + | 0.827725i | \(0.310366\pi\) |
−0.940491 | + | 0.339818i | \(0.889634\pi\) | |||||||
\(692\) | −1.00000 | − | 0.726543i | −0.0380143 | − | 0.0276190i | ||||
\(693\) | −36.2705 | −1.37780 | ||||||||
\(694\) | −17.0623 | − | 12.3965i | −0.647676 | − | 0.470564i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.92705 | − | 2.12663i | 0.110950 | − | 0.0806096i | ||||
\(697\) | 1.36475 | − | 0.991545i | 0.0516934 | − | 0.0375575i | ||||
\(698\) | −5.48936 | − | 16.8945i | −0.207775 | − | 0.639466i | ||||
\(699\) | −5.45898 | −0.206478 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.1803 | 0.686662 | 0.343331 | − | 0.939214i | \(-0.388445\pi\) | ||||
0.343331 | + | 0.939214i | \(0.388445\pi\) | |||||||
\(702\) | 0.690983 | + | 2.12663i | 0.0260795 | + | 0.0802644i | ||||
\(703\) | −39.4336 | + | 28.6502i | −1.48727 | + | 1.08056i | ||||
\(704\) | −3.42705 | + | 2.48990i | −0.129162 | + | 0.0938416i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −17.1803 | − | 12.4822i | −0.646591 | − | 0.469776i | ||||
\(707\) | 1.85410 | 0.0697307 | ||||||||
\(708\) | 1.38197 | + | 1.00406i | 0.0519375 | + | 0.0377348i | ||||
\(709\) | 3.78115 | − | 11.6372i | 0.142004 | − | 0.437044i | −0.854609 | − | 0.519271i | \(-0.826203\pi\) |
0.996614 | + | 0.0822274i | \(0.0262034\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.38197 | + | 19.6417i | 0.239342 | + | 0.736620i | ||||
\(712\) | 1.38197 | − | 4.25325i | 0.0517914 | − | 0.159397i | ||||
\(713\) | −0.128677 | + | 0.396027i | −0.00481900 | + | 0.0148313i | ||||
\(714\) | −0.405765 | − | 1.24882i | −0.0151854 | − | 0.0467357i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.45492 | − | 10.6331i | 0.129116 | − | 0.397379i | ||||
\(717\) | 2.13525 | + | 1.55135i | 0.0797426 | + | 0.0579364i | ||||
\(718\) | −8.09017 | −0.301922 | ||||||||
\(719\) | −9.30902 | − | 6.76340i | −0.347168 | − | 0.252232i | 0.400512 | − | 0.916291i | \(-0.368832\pi\) |
−0.747680 | + | 0.664059i | \(0.768832\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −31.9058 | + | 23.1809i | −1.18823 | + | 0.863302i | ||||
\(722\) | −12.3541 | + | 8.97578i | −0.459772 | + | 0.334044i | ||||
\(723\) | 1.84346 | + | 5.67358i | 0.0685590 | + | 0.211003i | ||||
\(724\) | 5.41641 | 0.201299 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.65248 | 0.0984426 | ||||||||
\(727\) | −0.819660 | − | 2.52265i | −0.0303995 | − | 0.0935601i | 0.934706 | − | 0.355423i | \(-0.115663\pi\) |
−0.965105 | + | 0.261863i | \(0.915663\pi\) | |||||||
\(728\) | 2.42705 | − | 1.76336i | 0.0899525 | − | 0.0653543i | ||||
\(729\) | 15.7254 | − | 11.4252i | 0.582423 | − | 0.423155i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.78115 | + | 4.20025i | 0.213824 | + | 0.155352i | ||||
\(732\) | −3.38197 | −0.125001 | ||||||||
\(733\) | 25.7082 | + | 18.6781i | 0.949554 | + | 0.689891i | 0.950701 | − | 0.310108i | \(-0.100365\pi\) |
−0.00114721 | + | 0.999999i | \(0.500365\pi\) | |||||||
\(734\) | −10.9828 | + | 33.8015i | −0.405382 | + | 1.24764i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.545085 | + | 1.67760i | 0.0200921 | + | 0.0618371i | ||||
\(737\) | 13.3992 | − | 41.2385i | 0.493565 | − | 1.51904i | ||||
\(738\) | −1.29837 | + | 3.99598i | −0.0477938 | + | 0.147094i | ||||
\(739\) | 9.27051 | + | 28.5317i | 0.341021 | + | 1.04956i | 0.963679 | + | 0.267062i | \(0.0860527\pi\) |
−0.622658 | + | 0.782494i | \(0.713947\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.690983 | + | 2.12663i | −0.0253839 | + | 0.0781236i | ||||
\(742\) | 25.4164 | + | 18.4661i | 0.933066 | + | 0.677912i | ||||
\(743\) | −15.2705 | −0.560221 | −0.280110 | − | 0.959968i | \(-0.590371\pi\) | ||||
−0.280110 | + | 0.959968i | \(0.590371\pi\) | |||||||
\(744\) | 0.0729490 | + | 0.0530006i | 0.00267444 | + | 0.00194309i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −9.51722 | + | 6.91467i | −0.348450 | + | 0.253164i | ||||
\(747\) | 10.4549 | − | 7.59594i | 0.382525 | − | 0.277921i | ||||
\(748\) | −1.50000 | − | 4.61653i | −0.0548454 | − | 0.168797i | ||||
\(749\) | 3.27051 | 0.119502 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.85410 | 0.286600 | 0.143300 | − | 0.989679i | \(-0.454229\pi\) | ||||
0.143300 | + | 0.989679i | \(0.454229\pi\) | |||||||
\(752\) | 3.69098 | + | 11.3597i | 0.134596 | + | 0.414245i | ||||
\(753\) | −0.253289 | + | 0.184025i | −0.00923036 | + | 0.00670625i | ||||
\(754\) | −7.66312 | + | 5.56758i | −0.279074 | + | 0.202759i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.42705 | + | 3.94298i | 0.197380 | + | 0.143405i | ||||
\(757\) | 16.4164 | 0.596664 | 0.298332 | − | 0.954462i | \(-0.403570\pi\) | ||||
0.298332 | + | 0.954462i | \(0.403570\pi\) | |||||||
\(758\) | −7.66312 | − | 5.56758i | −0.278337 | − | 0.202224i | ||||
\(759\) | 0.881966 | − | 2.71441i | 0.0320133 | − | 0.0985269i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.31966 | + | 25.6053i | 0.301587 | + | 0.928191i | 0.980929 | + | 0.194368i | \(0.0622656\pi\) |
−0.679341 | + | 0.733823i | \(0.737734\pi\) | |||||||
\(762\) | 0.416408 | − | 1.28157i | 0.0150849 | − | 0.0464264i | ||||
\(763\) | −13.9058 | + | 42.7975i | −0.503422 | + | 1.54938i | ||||
\(764\) | −4.21885 | − | 12.9843i | −0.152633 | − | 0.469755i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.50000 | + | 10.7719i | −0.126460 | + | 0.389204i | ||||
\(767\) | −3.61803 | − | 2.62866i | −0.130640 | − | 0.0949153i | ||||
\(768\) | 0.381966 | 0.0137830 | ||||||||
\(769\) | −2.76393 | − | 2.00811i | −0.0996699 | − | 0.0724144i | 0.536834 | − | 0.843688i | \(-0.319620\pi\) |
−0.636504 | + | 0.771273i | \(0.719620\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.95492 | − | 5.77958i | 0.286489 | − | 0.208147i | ||||
\(772\) | −11.8541 | + | 8.61251i | −0.426638 | + | 0.309971i | ||||
\(773\) | −9.51722 | − | 29.2910i | −0.342311 | − | 1.05352i | −0.963008 | − | 0.269473i | \(-0.913150\pi\) |
0.620697 | − | 0.784050i | \(-0.286850\pi\) | |||||||
\(774\) | −17.7984 | −0.639749 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −9.56231 | −0.343267 | ||||||||
\(777\) | 2.94834 | + | 9.07405i | 0.105771 | + | 0.325530i | ||||
\(778\) | −14.7361 | + | 10.7064i | −0.528314 | + | 0.383842i | ||||
\(779\) | −6.97214 | + | 5.06555i | −0.249803 | + | 0.181492i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.2812 | + | 7.46969i | 0.367889 | + | 0.267287i | ||||
\(782\) | −2.02129 | −0.0722810 | ||||||||
\(783\) | −17.1353 | − | 12.4495i | −0.612364 | − | 0.444909i | ||||
\(784\) | 0.618034 | − | 1.90211i | 0.0220726 | − | 0.0679326i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.93769 | − | 5.96361i | −0.0691153 | − | 0.212715i | ||||
\(787\) | 3.52786 | − | 10.8576i | 0.125755 | − | 0.387033i | −0.868283 | − | 0.496069i | \(-0.834776\pi\) |
0.994038 | + | 0.109036i | \(0.0347763\pi\) | |||||||
\(788\) | −3.70820 | + | 11.4127i | −0.132099 | + | 0.406560i | ||||
\(789\) | −0.545085 | − | 1.67760i | −0.0194055 | − | 0.0597241i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.48936 | + | 10.7391i | −0.124067 | + | 0.381840i | ||||
\(792\) | 9.78115 | + | 7.10642i | 0.347558 | + | 0.252516i | ||||
\(793\) | 8.85410 | 0.314418 | ||||||||
\(794\) | −8.28115 | − | 6.01661i | −0.293887 | − | 0.213521i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.07295 | + | 1.50609i | −0.0734737 | + | 0.0533818i | ||||
\(797\) | 4.54508 | − | 3.30220i | 0.160995 | − | 0.116970i | −0.504371 | − | 0.863487i | \(-0.668276\pi\) |
0.665366 | + | 0.746517i | \(0.268276\pi\) | |||||||
\(798\) | 2.07295 | + | 6.37988i | 0.0733816 | + | 0.225845i | ||||
\(799\) | −13.6869 | −0.484208 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.7639 | −0.450991 | ||||||||
\(802\) | −4.38197 | − | 13.4863i | −0.154733 | − | 0.476218i | ||||
\(803\) | 26.4164 | − | 19.1926i | 0.932215 | − | 0.677294i | ||||
\(804\) | −3.16312 | + | 2.29814i | −0.111555 | + | 0.0810492i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.190983 | − | 0.138757i | −0.00672709 | − | 0.00488752i | ||||
\(807\) | 0.729490 | 0.0256793 | ||||||||
\(808\) | −0.500000 | − | 0.363271i | −0.0175899 | − | 0.0127798i | ||||
\(809\) | −0.690983 | + | 2.12663i | −0.0242937 | + | 0.0747682i | −0.962468 | − | 0.271394i | \(-0.912515\pi\) |
0.938175 | + | 0.346162i | \(0.112515\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.6525 | + | 38.9403i | 0.444289 | + | 1.36738i | 0.883262 | + | 0.468880i | \(0.155342\pi\) |
−0.438974 | + | 0.898500i | \(0.644658\pi\) | |||||||
\(812\) | −8.78115 | + | 27.0256i | −0.308158 | + | 0.948413i | ||||
\(813\) | 3.36475 | − | 10.3556i | 0.118007 | − | 0.363187i | ||||
\(814\) | 10.8992 | + | 33.5442i | 0.382016 | + | 1.17573i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.135255 | + | 0.416272i | −0.00473487 | + | 0.0145724i | ||||
\(817\) | −29.5344 | − | 21.4580i | −1.03328 | − | 0.750721i | ||||
\(818\) | −6.70820 | −0.234547 | ||||||||
\(819\) | −6.92705 | − | 5.03280i | −0.242051 | − | 0.175860i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −31.6803 | + | 23.0171i | −1.10565 | + | 0.803303i | −0.981973 | − | 0.189020i | \(-0.939469\pi\) |
−0.123678 | + | 0.992322i | \(0.539469\pi\) | |||||||
\(822\) | 1.57295 | − | 1.14281i | 0.0548629 | − | 0.0398602i | ||||
\(823\) | 6.43769 | + | 19.8132i | 0.224404 | + | 0.690644i | 0.998352 | + | 0.0573946i | \(0.0182793\pi\) |
−0.773948 | + | 0.633250i | \(0.781721\pi\) | |||||||
\(824\) | 13.1459 | 0.457959 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13.4164 | −0.466817 | ||||||||
\(827\) | 1.55573 | + | 4.78804i | 0.0540980 | + | 0.166496i | 0.974455 | − | 0.224583i | \(-0.0721019\pi\) |
−0.920357 | + | 0.391079i | \(0.872102\pi\) | |||||||
\(828\) | 4.07295 | − | 2.95917i | 0.141545 | − | 0.102838i | ||||
\(829\) | −43.2148 | + | 31.3974i | −1.50091 | + | 1.09048i | −0.530895 | + | 0.847438i | \(0.678144\pi\) |
−0.970017 | + | 0.243038i | \(0.921856\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.0901699 | + | 0.0655123i | 0.00312796 | + | 0.00227260i | ||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 1.85410 | + | 1.34708i | 0.0642408 | + | 0.0466737i | ||||
\(834\) | −0.628677 | + | 1.93487i | −0.0217693 | + | 0.0669990i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7.66312 | + | 23.5847i | 0.265035 | + | 0.815692i | ||||
\(837\) | 0.163119 | − | 0.502029i | 0.00563822 | − | 0.0173526i | ||||
\(838\) | 7.03444 | − | 21.6498i | 0.243001 | − | 0.747879i | ||||
\(839\) | −17.0729 | − | 52.5451i | −0.589424 | − | 1.81406i | −0.580729 | − | 0.814097i | \(-0.697232\pi\) |
−0.00869515 | − | 0.999962i | \(-0.502768\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.7639 | − | 57.7494i | 0.647032 | − | 1.99136i | ||||
\(842\) | −17.2082 | − | 12.5025i | −0.593034 | − | 0.430864i | ||||
\(843\) | 1.21478 | 0.0418393 | ||||||||
\(844\) | 18.0172 | + | 13.0903i | 0.620178 | + | 0.450586i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 27.5795 | − | 20.0377i | 0.948204 | − | 0.688910i | ||||
\(847\) | −16.8541 | + | 12.2452i | −0.579114 | + | 0.420751i | ||||
\(848\) | −3.23607 | − | 9.95959i | −0.111127 | − | 0.342014i | ||||
\(849\) | 4.69505 | 0.161134 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.6869 | 0.503461 | ||||||||
\(852\) | −0.354102 | − | 1.08981i | −0.0121313 | − | 0.0373364i | ||||
\(853\) | −14.6803 | + | 10.6659i | −0.502645 | + | 0.365193i | −0.810026 | − | 0.586393i | \(-0.800547\pi\) |
0.307381 | + | 0.951586i | \(0.400547\pi\) | |||||||
\(854\) | 21.4894 | − | 15.6129i | 0.735351 | − | 0.534264i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.881966 | − | 0.640786i | −0.0301450 | − | 0.0219016i | ||||
\(857\) | 56.3394 | 1.92452 | 0.962259 | − | 0.272137i | \(-0.0877304\pi\) | ||||
0.962259 | + | 0.272137i | \(0.0877304\pi\) | |||||||
\(858\) | 1.30902 | + | 0.951057i | 0.0446891 | + | 0.0324685i | ||||
\(859\) | 10.6287 | − | 32.7117i | 0.362646 | − | 1.11611i | −0.588796 | − | 0.808281i | \(-0.700398\pi\) |
0.951442 | − | 0.307828i | \(-0.0996020\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.521286 | + | 1.60435i | 0.0177654 | + | 0.0546762i | ||||
\(862\) | 8.05573 | − | 24.7930i | 0.274379 | − | 0.844452i | ||||
\(863\) | 3.47214 | − | 10.6861i | 0.118193 | − | 0.363760i | −0.874407 | − | 0.485194i | \(-0.838749\pi\) |
0.992600 | + | 0.121433i | \(0.0387491\pi\) | |||||||
\(864\) | −0.690983 | − | 2.12663i | −0.0235077 | − | 0.0723493i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 6.60081 | − | 20.3152i | 0.224305 | − | 0.690339i | ||||
\(867\) | 4.84752 | + | 3.52193i | 0.164631 | + | 0.119611i | ||||
\(868\) | −0.708204 | −0.0240380 | ||||||||
\(869\) | 24.7984 | + | 18.0171i | 0.841227 | + | 0.611187i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.28115 | − | 6.01661i | 0.280596 | − | 0.203865i | ||||
\(872\) | 12.1353 | − | 8.81678i | 0.410952 | − | 0.298574i | ||||
\(873\) | 8.43363 | + | 25.9560i | 0.285435 | + | 0.878479i | ||||
\(874\) | 10.3262 | 0.349290 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.94427 | −0.0994777 | ||||||||
\(877\) | −1.37132 | − | 4.22050i | −0.0463063 | − | 0.142516i | 0.925230 | − | 0.379406i | \(-0.123872\pi\) |
−0.971536 | + | 0.236890i | \(0.923872\pi\) | |||||||
\(878\) | −20.7533 | + | 15.0781i | −0.700390 | + | 0.508863i | ||||
\(879\) | 2.64590 | − | 1.92236i | 0.0892439 | − | 0.0648395i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.8885 | − | 22.4418i | −1.04066 | − | 0.756085i | −0.0702469 | − | 0.997530i | \(-0.522379\pi\) |
−0.970415 | + | 0.241445i | \(0.922379\pi\) | |||||||
\(882\) | −5.70820 | −0.192205 | ||||||||
\(883\) | −33.7254 | − | 24.5030i | −1.13495 | − | 0.824590i | −0.148543 | − | 0.988906i | \(-0.547458\pi\) |
−0.986408 | + | 0.164316i | \(0.947458\pi\) | |||||||
\(884\) | 0.354102 | − | 1.08981i | 0.0119097 | − | 0.0366544i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.00000 | − | 18.4661i | −0.201574 | − | 0.620381i | ||||
\(887\) | −10.2533 | + | 31.5564i | −0.344272 | + | 1.05956i | 0.617701 | + | 0.786413i | \(0.288064\pi\) |
−0.961973 | + | 0.273146i | \(0.911936\pi\) | |||||||
\(888\) | 0.982779 | − | 3.02468i | 0.0329799 | − | 0.101502i | ||||
\(889\) | 3.27051 | + | 10.0656i | 0.109689 | + | 0.337589i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.0902 | − | 31.0543i | 0.338033 | − | 1.04036i | ||||
\(892\) | −7.28115 | − | 5.29007i | −0.243791 | − | 0.177125i | ||||
\(893\) | 69.9230 | 2.33988 | ||||||||
\(894\) | −0.690983 | − | 0.502029i | −0.0231099 | − | 0.0167903i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.42705 | + | 1.76336i | −0.0810821 | + | 0.0589096i | ||||
\(897\) | 0.545085 | − | 0.396027i | 0.0181999 | − | 0.0132230i | ||||
\(898\) | −1.21885 | − | 3.75123i | −0.0406735 | − | 0.125180i | ||||
\(899\) | 2.23607 | 0.0745770 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.0000 | 0.399778 | ||||||||
\(902\) | 1.92705 | + | 5.93085i | 0.0641638 | + | 0.197476i | ||||
\(903\) | −5.78115 | + | 4.20025i | −0.192385 | + | 0.139776i | ||||
\(904\) | 3.04508 | − | 2.21238i | 0.101278 | − | 0.0735828i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.00000 | + | 2.17963i | 0.0996683 | + | 0.0724133i | ||||
\(907\) | −25.6180 | −0.850633 | −0.425316 | − | 0.905045i | \(-0.639837\pi\) | ||||
−0.425316 | + | 0.905045i | \(0.639837\pi\) | |||||||
\(908\) | 23.7533 | + | 17.2578i | 0.788281 | + | 0.572719i | ||||
\(909\) | −0.545085 | + | 1.67760i | −0.0180793 | + | 0.0556424i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.07295 | − | 15.6129i | −0.168074 | − | 0.517280i | 0.831175 | − | 0.556010i | \(-0.187669\pi\) |
−0.999250 | + | 0.0387308i | \(0.987669\pi\) | |||||||
\(912\) | 0.690983 | − | 2.12663i | 0.0228807 | − | 0.0704197i | ||||
\(913\) | 5.92705 | − | 18.2416i | 0.196157 | − | 0.603708i | ||||
\(914\) | −12.4271 | − | 38.2465i | −0.411050 | − | 1.26508i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.791796 | + | 2.43690i | −0.0261617 | + | 0.0805174i | ||||
\(917\) | 39.8435 | + | 28.9480i | 1.31575 | + | 0.955946i | ||||
\(918\) | 2.56231 | 0.0845687 | ||||||||
\(919\) | 4.57295 | + | 3.32244i | 0.150848 | + | 0.109597i | 0.660649 | − | 0.750695i | \(-0.270281\pi\) |
−0.509801 | + | 0.860292i | \(0.670281\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.14590 | + | 5.19180i | −0.235465 | + | 0.171076i | ||||
\(922\) | −4.70820 | + | 3.42071i | −0.155056 | + | 0.112655i | ||||
\(923\) | 0.927051 | + | 2.85317i | 0.0305143 | + | 0.0939132i | ||||
\(924\) | 4.85410 | 0.159688 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 34.9787 | 1.14947 | ||||||||
\(927\) | −11.5942 | − | 35.6834i | −0.380805 | − | 1.17200i | ||||
\(928\) | 7.66312 | − | 5.56758i | 0.251554 | − | 0.182765i | ||||
\(929\) | 42.7877 | − | 31.0871i | 1.40382 | − | 1.01993i | 0.409635 | − | 0.912250i | \(-0.365656\pi\) |
0.994185 | − | 0.107685i | \(-0.0343439\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.47214 | − | 6.88191i | −0.310437 | − | 0.225545i | ||||
\(932\) | −14.2918 | −0.468143 | ||||||||
\(933\) | 3.06231 | + | 2.22490i | 0.100255 | + | 0.0728398i | ||||
\(934\) | 5.92705 | − | 18.2416i | 0.193939 | − | 0.596883i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.881966 | + | 2.71441i | 0.0288280 | + | 0.0887233i | ||||
\(937\) | −12.9549 | + | 39.8711i | −0.423219 | + | 1.30253i | 0.481471 | + | 0.876462i | \(0.340103\pi\) |
−0.904690 | + | 0.426071i | \(0.859897\pi\) | |||||||
\(938\) | 9.48936 | − | 29.2052i | 0.309838 | − | 0.953585i | ||||
\(939\) | 1.95492 | + | 6.01661i | 0.0637962 | + | 0.196345i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.89919 | + | 8.92278i | −0.0945108 | + | 0.290874i | −0.987126 | − | 0.159945i | \(-0.948868\pi\) |
0.892615 | + | 0.450820i | \(0.148868\pi\) | |||||||
\(942\) | 1.40983 | + | 1.02430i | 0.0459347 | + | 0.0333735i | ||||
\(943\) | 2.59675 | 0.0845617 | ||||||||
\(944\) | 3.61803 | + | 2.62866i | 0.117757 | + | 0.0855555i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −21.3713 | + | 15.5272i | −0.694842 | + | 0.504832i | ||||
\(947\) | −31.8607 | + | 23.1481i | −1.03533 | + | 0.752213i | −0.969369 | − | 0.245609i | \(-0.921012\pi\) |
−0.0659639 | + | 0.997822i | \(0.521012\pi\) | |||||||
\(948\) | −0.854102 | − | 2.62866i | −0.0277399 | − | 0.0853748i | ||||
\(949\) | 7.70820 | 0.250219 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.20163 | −0.103820 | ||||||||
\(952\) | −1.06231 | − | 3.26944i | −0.0344295 | − | 0.105963i | ||||
\(953\) | 36.0967 | − | 26.2258i | 1.16929 | − | 0.849538i | 0.178365 | − | 0.983964i | \(-0.442919\pi\) |
0.990924 | + | 0.134427i | \(0.0429193\pi\) | |||||||
\(954\) | −24.1803 | + | 17.5680i | −0.782867 | + | 0.568786i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.59017 | + | 4.06150i | 0.180799 | + | 0.131358i | ||||
\(957\) | −15.3262 | −0.495427 | ||||||||
\(958\) | 12.2984 | + | 8.93529i | 0.397342 | + | 0.288686i | ||||
\(959\) | −4.71885 | + | 14.5231i | −0.152380 | + | 0.468976i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.56231 | − | 29.4298i | −0.308461 | − | 0.949347i | ||||
\(962\) | −2.57295 | + | 7.91872i | −0.0829552 | + | 0.255310i | ||||
\(963\) | −0.961493 | + | 2.95917i | −0.0309837 | + | 0.0953579i | ||||
\(964\) | 4.82624 | + | 14.8536i | 0.155443 | + | 0.478403i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.624612 | − | 1.92236i | 0.0200966 | − | 0.0618508i | ||||
\(967\) | −10.6180 | − | 7.71445i | −0.341453 | − | 0.248080i | 0.403822 | − | 0.914838i | \(-0.367682\pi\) |
−0.745275 | + | 0.666758i | \(0.767682\pi\) | |||||||
\(968\) | 6.94427 | 0.223197 | ||||||||
\(969\) | 2.07295 | + | 1.50609i | 0.0665927 | + | 0.0483824i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.90983 | + | 3.56720i | −0.157564 | + | 0.114477i | −0.663774 | − | 0.747934i | \(-0.731046\pi\) |
0.506210 | + | 0.862410i | \(0.331046\pi\) | |||||||
\(972\) | −7.80902 | + | 5.67358i | −0.250474 | + | 0.181980i | ||||
\(973\) | −4.93769 | − | 15.1967i | −0.158295 | − | 0.487183i | ||||
\(974\) | −22.1246 | −0.708918 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.85410 | −0.283413 | ||||||||
\(977\) | −15.4549 | − | 47.5653i | −0.494447 | − | 1.52175i | −0.817817 | − | 0.575478i | \(-0.804816\pi\) |
0.323371 | − | 0.946272i | \(-0.395184\pi\) | |||||||
\(978\) | 0.572949 | − | 0.416272i | 0.0183209 | − | 0.0133109i | ||||
\(979\) | −15.3262 | + | 11.1352i | −0.489829 | + | 0.355881i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −34.6353 | − | 25.1640i | −1.10582 | − | 0.803424i | ||||
\(982\) | 19.2361 | 0.613848 | ||||||||
\(983\) | 31.1353 | + | 22.6211i | 0.993060 | + | 0.721501i | 0.960589 | − | 0.277972i | \(-0.0896623\pi\) |
0.0324712 | + | 0.999473i | \(0.489662\pi\) | |||||||
\(984\) | 0.173762 | − | 0.534785i | 0.00553933 | − | 0.0170483i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.35410 | + | 10.3229i | 0.106816 | + | 0.328747i | ||||
\(987\) | 4.22949 | − | 13.0170i | 0.134626 | − | 0.414337i | ||||
\(988\) | −1.80902 | + | 5.56758i | −0.0575525 | + | 0.177128i | ||||
\(989\) | 3.39919 | + | 10.4616i | 0.108088 | + | 0.332660i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.06637 | + | 3.28195i | −0.0338744 | + | 0.104255i | −0.966564 | − | 0.256425i | \(-0.917455\pi\) |
0.932690 | + | 0.360680i | \(0.117455\pi\) | |||||||
\(992\) | 0.190983 | + | 0.138757i | 0.00606372 | + | 0.00440555i | ||||
\(993\) | −5.94427 | −0.188636 | ||||||||
\(994\) | 7.28115 | + | 5.29007i | 0.230944 | + | 0.167791i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.39919 | + | 1.01657i | −0.0443349 | + | 0.0322112i | ||||
\(997\) | 22.0451 | − | 16.0167i | 0.698175 | − | 0.507254i | −0.181162 | − | 0.983453i | \(-0.557986\pi\) |
0.879337 | + | 0.476199i | \(0.157986\pi\) | |||||||
\(998\) | 10.5517 | + | 32.4747i | 0.334007 | + | 1.02797i | ||||
\(999\) | −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.d.a.151.1 | 4 | ||
5.2 | odd | 4 | 250.2.e.b.99.1 | 8 | |||
5.3 | odd | 4 | 250.2.e.b.99.2 | 8 | |||
5.4 | even | 2 | 50.2.d.a.31.1 | yes | 4 | ||
15.14 | odd | 2 | 450.2.h.a.181.1 | 4 | |||
20.19 | odd | 2 | 400.2.u.c.81.1 | 4 | |||
25.2 | odd | 20 | 1250.2.b.b.1249.4 | 4 | |||
25.3 | odd | 20 | 250.2.e.b.149.1 | 8 | |||
25.4 | even | 10 | 50.2.d.a.21.1 | ✓ | 4 | ||
25.11 | even | 5 | 1250.2.a.d.1.1 | 2 | |||
25.14 | even | 10 | 1250.2.a.a.1.2 | 2 | |||
25.21 | even | 5 | inner | 250.2.d.a.101.1 | 4 | ||
25.22 | odd | 20 | 250.2.e.b.149.2 | 8 | |||
25.23 | odd | 20 | 1250.2.b.b.1249.1 | 4 | |||
75.29 | odd | 10 | 450.2.h.a.271.1 | 4 | |||
100.11 | odd | 10 | 10000.2.a.a.1.2 | 2 | |||
100.39 | odd | 10 | 10000.2.a.n.1.1 | 2 | |||
100.79 | odd | 10 | 400.2.u.c.321.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
50.2.d.a.21.1 | ✓ | 4 | 25.4 | even | 10 | ||
50.2.d.a.31.1 | yes | 4 | 5.4 | even | 2 | ||
250.2.d.a.101.1 | 4 | 25.21 | even | 5 | inner | ||
250.2.d.a.151.1 | 4 | 1.1 | even | 1 | trivial | ||
250.2.e.b.99.1 | 8 | 5.2 | odd | 4 | |||
250.2.e.b.99.2 | 8 | 5.3 | odd | 4 | |||
250.2.e.b.149.1 | 8 | 25.3 | odd | 20 | |||
250.2.e.b.149.2 | 8 | 25.22 | odd | 20 | |||
400.2.u.c.81.1 | 4 | 20.19 | odd | 2 | |||
400.2.u.c.321.1 | 4 | 100.79 | odd | 10 | |||
450.2.h.a.181.1 | 4 | 15.14 | odd | 2 | |||
450.2.h.a.271.1 | 4 | 75.29 | odd | 10 | |||
1250.2.a.a.1.2 | 2 | 25.14 | even | 10 | |||
1250.2.a.d.1.1 | 2 | 25.11 | even | 5 | |||
1250.2.b.b.1249.1 | 4 | 25.23 | odd | 20 | |||
1250.2.b.b.1249.4 | 4 | 25.2 | odd | 20 | |||
10000.2.a.a.1.2 | 2 | 100.11 | odd | 10 | |||
10000.2.a.n.1.1 | 2 | 100.39 | odd | 10 |