Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [403,2,Mod(311,403)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(403, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("403.311");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 403 = 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 403.c (of order \(2\), degree \(1\), 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: | \(3.21797120146\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 311.17 | ||
Character | \(\chi\) | \(=\) | 403.311 |
Dual form | 403.2.c.b.311.16 |
$q$-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 \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).
\(n\) | \(249\) | \(313\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.327248i | 0.231399i | 0.993284 | + | 0.115700i | \(0.0369110\pi\) | ||||
−0.993284 | + | 0.115700i | \(0.963089\pi\) | |||||||
\(3\) | −1.21221 | −0.699869 | −0.349934 | − | 0.936774i | \(-0.613796\pi\) | ||||
−0.349934 | + | 0.936774i | \(0.613796\pi\) | |||||||
\(4\) | 1.89291 | 0.946454 | ||||||||
\(5\) | 2.01769i | 0.902337i | 0.892439 | + | 0.451168i | \(0.148993\pi\) | ||||
−0.892439 | + | 0.451168i | \(0.851007\pi\) | |||||||
\(6\) | − | 0.396693i | − | 0.161949i | ||||||
\(7\) | − | 0.699230i | − | 0.264284i | −0.991231 | − | 0.132142i | \(-0.957814\pi\) | ||
0.991231 | − | 0.132142i | \(-0.0421855\pi\) | |||||||
\(8\) | 1.27395i | 0.450408i | ||||||||
\(9\) | −1.53055 | −0.510184 | ||||||||
\(10\) | −0.660284 | −0.208800 | ||||||||
\(11\) | 4.61697i | 1.39207i | 0.718009 | + | 0.696034i | \(0.245054\pi\) | ||||
−0.718009 | + | 0.696034i | \(0.754946\pi\) | |||||||
\(12\) | −2.29460 | −0.662394 | ||||||||
\(13\) | 3.60514 | − | 0.0546339i | 0.999885 | − | 0.0151527i | ||||
\(14\) | 0.228822 | 0.0611552 | ||||||||
\(15\) | − | 2.44585i | − | 0.631517i | ||||||
\(16\) | 3.36892 | 0.842230 | ||||||||
\(17\) | −4.66988 | −1.13261 | −0.566306 | − | 0.824195i | \(-0.691628\pi\) | ||||
−0.566306 | + | 0.824195i | \(0.691628\pi\) | |||||||
\(18\) | − | 0.500871i | − | 0.118056i | ||||||
\(19\) | 2.12056i | 0.486490i | 0.969965 | + | 0.243245i | \(0.0782119\pi\) | ||||
−0.969965 | + | 0.243245i | \(0.921788\pi\) | |||||||
\(20\) | 3.81929i | 0.854020i | ||||||||
\(21\) | 0.847613i | 0.184964i | ||||||||
\(22\) | −1.51089 | −0.322124 | ||||||||
\(23\) | −0.894850 | −0.186589 | −0.0932945 | − | 0.995639i | \(-0.529740\pi\) | ||||
−0.0932945 | + | 0.995639i | \(0.529740\pi\) | |||||||
\(24\) | − | 1.54429i | − | 0.315227i | ||||||
\(25\) | 0.928944 | 0.185789 | ||||||||
\(26\) | 0.0178789 | + | 1.17977i | 0.00350633 | + | 0.231373i | ||||
\(27\) | 5.49197 | 1.05693 | ||||||||
\(28\) | − | 1.32358i | − | 0.250133i | ||||||
\(29\) | −3.00018 | −0.557120 | −0.278560 | − | 0.960419i | \(-0.589857\pi\) | ||||
−0.278560 | + | 0.960419i | \(0.589857\pi\) | |||||||
\(30\) | 0.800402 | 0.146133 | ||||||||
\(31\) | 1.00000i | 0.179605i | ||||||||
\(32\) | 3.65037i | 0.645300i | ||||||||
\(33\) | − | 5.59672i | − | 0.974264i | ||||||
\(34\) | − | 1.52821i | − | 0.262086i | ||||||
\(35\) | 1.41083 | 0.238473 | ||||||||
\(36\) | −2.89720 | −0.482866 | ||||||||
\(37\) | 9.14616i | 1.50362i | 0.659380 | + | 0.751810i | \(0.270819\pi\) | ||||
−0.659380 | + | 0.751810i | \(0.729181\pi\) | |||||||
\(38\) | −0.693950 | −0.112574 | ||||||||
\(39\) | −4.37018 | + | 0.0662277i | −0.699788 | + | 0.0106049i | ||||
\(40\) | −2.57043 | −0.406420 | ||||||||
\(41\) | 8.88294i | 1.38728i | 0.720321 | + | 0.693641i | \(0.243995\pi\) | ||||
−0.720321 | + | 0.693641i | \(0.756005\pi\) | |||||||
\(42\) | −0.277380 | −0.0428006 | ||||||||
\(43\) | −0.0731027 | −0.0111481 | −0.00557403 | − | 0.999984i | \(-0.501774\pi\) | ||||
−0.00557403 | + | 0.999984i | \(0.501774\pi\) | |||||||
\(44\) | 8.73949i | 1.31753i | ||||||||
\(45\) | − | 3.08817i | − | 0.460358i | ||||||
\(46\) | − | 0.292838i | − | 0.0431766i | ||||||
\(47\) | − | 10.2247i | − | 1.49142i | −0.666270 | − | 0.745711i | \(-0.732110\pi\) | ||
0.666270 | − | 0.745711i | \(-0.267890\pi\) | |||||||
\(48\) | −4.08383 | −0.589450 | ||||||||
\(49\) | 6.51108 | 0.930154 | ||||||||
\(50\) | 0.303995i | 0.0429914i | ||||||||
\(51\) | 5.66086 | 0.792680 | ||||||||
\(52\) | 6.82420 | − | 0.103417i | 0.946346 | − | 0.0143414i | ||||
\(53\) | 6.80879 | 0.935259 | 0.467630 | − | 0.883924i | \(-0.345108\pi\) | ||||
0.467630 | + | 0.883924i | \(0.345108\pi\) | |||||||
\(54\) | 1.79724i | 0.244573i | ||||||||
\(55\) | −9.31559 | −1.25611 | ||||||||
\(56\) | 0.890783 | 0.119036 | ||||||||
\(57\) | − | 2.57056i | − | 0.340479i | ||||||
\(58\) | − | 0.981804i | − | 0.128917i | ||||||
\(59\) | − | 10.8578i | − | 1.41357i | −0.707429 | − | 0.706785i | \(-0.750145\pi\) | ||
0.707429 | − | 0.706785i | \(-0.249855\pi\) | |||||||
\(60\) | − | 4.62978i | − | 0.597702i | ||||||
\(61\) | −1.63534 | −0.209384 | −0.104692 | − | 0.994505i | \(-0.533386\pi\) | ||||
−0.104692 | + | 0.994505i | \(0.533386\pi\) | |||||||
\(62\) | −0.327248 | −0.0415606 | ||||||||
\(63\) | 1.07021i | 0.134834i | ||||||||
\(64\) | 5.54326 | 0.692908 | ||||||||
\(65\) | 0.110234 | + | 7.27403i | 0.0136729 | + | 0.902233i | ||||
\(66\) | 1.83152 | 0.225444 | ||||||||
\(67\) | − | 12.8524i | − | 1.57016i | −0.619391 | − | 0.785082i | \(-0.712621\pi\) | ||
0.619391 | − | 0.785082i | \(-0.287379\pi\) | |||||||
\(68\) | −8.83965 | −1.07197 | ||||||||
\(69\) | 1.08474 | 0.130588 | ||||||||
\(70\) | 0.461691i | 0.0551826i | ||||||||
\(71\) | − | 7.88186i | − | 0.935405i | −0.883886 | − | 0.467703i | \(-0.845082\pi\) | ||
0.883886 | − | 0.467703i | \(-0.154918\pi\) | |||||||
\(72\) | − | 1.94984i | − | 0.229791i | ||||||
\(73\) | − | 12.0989i | − | 1.41606i | −0.706180 | − | 0.708032i | \(-0.749583\pi\) | ||
0.706180 | − | 0.708032i | \(-0.250417\pi\) | |||||||
\(74\) | −2.99307 | −0.347937 | ||||||||
\(75\) | −1.12607 | −0.130028 | ||||||||
\(76\) | 4.01403i | 0.460441i | ||||||||
\(77\) | 3.22832 | 0.367902 | ||||||||
\(78\) | −0.0216729 | − | 1.43013i | −0.00245397 | − | 0.161931i | ||||
\(79\) | −13.7040 | −1.54182 | −0.770912 | − | 0.636942i | \(-0.780199\pi\) | ||||
−0.770912 | + | 0.636942i | \(0.780199\pi\) | |||||||
\(80\) | 6.79742i | 0.759975i | ||||||||
\(81\) | −2.06575 | −0.229528 | ||||||||
\(82\) | −2.90693 | −0.321016 | ||||||||
\(83\) | − | 4.48027i | − | 0.491774i | −0.969298 | − | 0.245887i | \(-0.920921\pi\) | ||
0.969298 | − | 0.245887i | \(-0.0790792\pi\) | |||||||
\(84\) | 1.60445i | 0.175060i | ||||||||
\(85\) | − | 9.42235i | − | 1.02200i | ||||||
\(86\) | − | 0.0239227i | − | 0.00257965i | ||||||
\(87\) | 3.63684 | 0.389911 | ||||||||
\(88\) | −5.88177 | −0.626999 | ||||||||
\(89\) | 5.02369i | 0.532510i | 0.963903 | + | 0.266255i | \(0.0857863\pi\) | ||||
−0.963903 | + | 0.266255i | \(0.914214\pi\) | |||||||
\(90\) | 1.01060 | 0.106527 | ||||||||
\(91\) | −0.0382017 | − | 2.52082i | −0.00400463 | − | 0.264254i | ||||
\(92\) | −1.69387 | −0.176598 | ||||||||
\(93\) | − | 1.21221i | − | 0.125700i | ||||||
\(94\) | 3.34601 | 0.345114 | ||||||||
\(95\) | −4.27863 | −0.438978 | ||||||||
\(96\) | − | 4.42501i | − | 0.451625i | ||||||
\(97\) | − | 17.0411i | − | 1.73026i | −0.501547 | − | 0.865131i | \(-0.667235\pi\) | ||
0.501547 | − | 0.865131i | \(-0.332765\pi\) | |||||||
\(98\) | 2.13074i | 0.215237i | ||||||||
\(99\) | − | 7.06651i | − | 0.710211i | ||||||
\(100\) | 1.75841 | 0.175841 | ||||||||
\(101\) | 18.1294 | 1.80394 | 0.901970 | − | 0.431799i | \(-0.142121\pi\) | ||||
0.901970 | + | 0.431799i | \(0.142121\pi\) | |||||||
\(102\) | 1.85251i | 0.183426i | ||||||||
\(103\) | 2.39529 | 0.236015 | 0.118007 | − | 0.993013i | \(-0.462349\pi\) | ||||
0.118007 | + | 0.993013i | \(0.462349\pi\) | |||||||
\(104\) | 0.0696008 | + | 4.59276i | 0.00682492 | + | 0.450357i | ||||
\(105\) | −1.71022 | −0.166900 | ||||||||
\(106\) | 2.22817i | 0.216419i | ||||||||
\(107\) | 15.3468 | 1.48363 | 0.741814 | − | 0.670605i | \(-0.233966\pi\) | ||||
0.741814 | + | 0.670605i | \(0.233966\pi\) | |||||||
\(108\) | 10.3958 | 1.00034 | ||||||||
\(109\) | 11.2306i | 1.07569i | 0.843043 | + | 0.537846i | \(0.180762\pi\) | ||||
−0.843043 | + | 0.537846i | \(0.819238\pi\) | |||||||
\(110\) | − | 3.04851i | − | 0.290664i | ||||||
\(111\) | − | 11.0870i | − | 1.05234i | ||||||
\(112\) | − | 2.35565i | − | 0.222588i | ||||||
\(113\) | −3.45258 | −0.324791 | −0.162396 | − | 0.986726i | \(-0.551922\pi\) | ||||
−0.162396 | + | 0.986726i | \(0.551922\pi\) | |||||||
\(114\) | 0.841212 | 0.0787867 | ||||||||
\(115\) | − | 1.80553i | − | 0.168366i | ||||||
\(116\) | −5.67907 | −0.527288 | ||||||||
\(117\) | −5.51785 | + | 0.0836201i | −0.510125 | + | 0.00773068i | ||||
\(118\) | 3.55321 | 0.327099 | ||||||||
\(119\) | 3.26532i | 0.299332i | ||||||||
\(120\) | 3.11589 | 0.284441 | ||||||||
\(121\) | −10.3164 | −0.937852 | ||||||||
\(122\) | − | 0.535162i | − | 0.0484513i | ||||||
\(123\) | − | 10.7680i | − | 0.970915i | ||||||
\(124\) | 1.89291i | 0.169988i | ||||||||
\(125\) | 11.9627i | 1.06998i | ||||||||
\(126\) | −0.350224 | −0.0312004 | ||||||||
\(127\) | 2.00484 | 0.177901 | 0.0889503 | − | 0.996036i | \(-0.471649\pi\) | ||||
0.0889503 | + | 0.996036i | \(0.471649\pi\) | |||||||
\(128\) | 9.11476i | 0.805639i | ||||||||
\(129\) | 0.0886157 | 0.00780218 | ||||||||
\(130\) | −2.38042 | + | 0.0360739i | −0.208776 | + | 0.00316389i | ||||
\(131\) | −10.2051 | −0.891620 | −0.445810 | − | 0.895128i | \(-0.647084\pi\) | ||||
−0.445810 | + | 0.895128i | \(0.647084\pi\) | |||||||
\(132\) | − | 10.5941i | − | 0.922097i | ||||||
\(133\) | 1.48276 | 0.128572 | ||||||||
\(134\) | 4.20591 | 0.363335 | ||||||||
\(135\) | 11.0811i | 0.953707i | ||||||||
\(136\) | − | 5.94918i | − | 0.510138i | ||||||
\(137\) | 2.21909i | 0.189589i | 0.995497 | + | 0.0947947i | \(0.0302195\pi\) | ||||
−0.995497 | + | 0.0947947i | \(0.969781\pi\) | |||||||
\(138\) | 0.354981i | 0.0302180i | ||||||||
\(139\) | 16.0205 | 1.35884 | 0.679422 | − | 0.733747i | \(-0.262230\pi\) | ||||
0.679422 | + | 0.733747i | \(0.262230\pi\) | |||||||
\(140\) | 2.67057 | 0.225704 | ||||||||
\(141\) | 12.3944i | 1.04380i | ||||||||
\(142\) | 2.57933 | 0.216452 | ||||||||
\(143\) | 0.252243 | + | 16.6448i | 0.0210936 | + | 1.39191i | ||||
\(144\) | −5.15631 | −0.429692 | ||||||||
\(145\) | − | 6.05342i | − | 0.502710i | ||||||
\(146\) | 3.95933 | 0.327677 | ||||||||
\(147\) | −7.89278 | −0.650985 | ||||||||
\(148\) | 17.3128i | 1.42311i | ||||||||
\(149\) | 1.88611i | 0.154516i | 0.997011 | + | 0.0772579i | \(0.0246165\pi\) | ||||
−0.997011 | + | 0.0772579i | \(0.975384\pi\) | |||||||
\(150\) | − | 0.368505i | − | 0.0300883i | ||||||
\(151\) | − | 1.17038i | − | 0.0952439i | −0.998865 | − | 0.0476220i | \(-0.984836\pi\) | ||
0.998865 | − | 0.0476220i | \(-0.0151643\pi\) | |||||||
\(152\) | −2.70148 | −0.219119 | ||||||||
\(153\) | 7.14749 | 0.577841 | ||||||||
\(154\) | 1.05646i | 0.0851322i | ||||||||
\(155\) | −2.01769 | −0.162064 | ||||||||
\(156\) | −8.27234 | + | 0.125363i | −0.662318 | + | 0.0100371i | ||||
\(157\) | −11.3089 | −0.902546 | −0.451273 | − | 0.892386i | \(-0.649030\pi\) | ||||
−0.451273 | + | 0.892386i | \(0.649030\pi\) | |||||||
\(158\) | − | 4.48462i | − | 0.356777i | ||||||
\(159\) | −8.25367 | −0.654559 | ||||||||
\(160\) | −7.36530 | −0.582278 | ||||||||
\(161\) | 0.625706i | 0.0493126i | ||||||||
\(162\) | − | 0.676015i | − | 0.0531127i | ||||||
\(163\) | 13.5178i | 1.05880i | 0.848373 | + | 0.529400i | \(0.177583\pi\) | ||||
−0.848373 | + | 0.529400i | \(0.822417\pi\) | |||||||
\(164\) | 16.8146i | 1.31300i | ||||||||
\(165\) | 11.2924 | 0.879114 | ||||||||
\(166\) | 1.46616 | 0.113796 | ||||||||
\(167\) | − | 16.8398i | − | 1.30310i | −0.758604 | − | 0.651552i | \(-0.774118\pi\) | ||
0.758604 | − | 0.651552i | \(-0.225882\pi\) | |||||||
\(168\) | −1.07981 | −0.0833095 | ||||||||
\(169\) | 12.9940 | − | 0.393926i | 0.999541 | − | 0.0303020i | ||||
\(170\) | 3.08345 | 0.236490 | ||||||||
\(171\) | − | 3.24563i | − | 0.248199i | ||||||
\(172\) | −0.138377 | −0.0105511 | ||||||||
\(173\) | 15.0900 | 1.14727 | 0.573636 | − | 0.819110i | \(-0.305532\pi\) | ||||
0.573636 | + | 0.819110i | \(0.305532\pi\) | |||||||
\(174\) | 1.19015i | 0.0902251i | ||||||||
\(175\) | − | 0.649546i | − | 0.0491010i | ||||||
\(176\) | 15.5542i | 1.17244i | ||||||||
\(177\) | 13.1619i | 0.989313i | ||||||||
\(178\) | −1.64399 | −0.123223 | ||||||||
\(179\) | −15.7065 | −1.17396 | −0.586979 | − | 0.809602i | \(-0.699683\pi\) | ||||
−0.586979 | + | 0.809602i | \(0.699683\pi\) | |||||||
\(180\) | − | 5.84563i | − | 0.435708i | ||||||
\(181\) | −22.0513 | −1.63906 | −0.819531 | − | 0.573034i | \(-0.805766\pi\) | ||||
−0.819531 | + | 0.573034i | \(0.805766\pi\) | |||||||
\(182\) | 0.824935 | − | 0.0125014i | 0.0611482 | − | 0.000926669i | ||||
\(183\) | 1.98237 | 0.146541 | ||||||||
\(184\) | − | 1.13999i | − | 0.0840413i | ||||||
\(185\) | −18.4541 | −1.35677 | ||||||||
\(186\) | 0.396693 | 0.0290869 | ||||||||
\(187\) | − | 21.5607i | − | 1.57667i | ||||||
\(188\) | − | 19.3544i | − | 1.41156i | ||||||
\(189\) | − | 3.84015i | − | 0.279330i | ||||||
\(190\) | − | 1.40017i | − | 0.101579i | ||||||
\(191\) | −4.94588 | −0.357871 | −0.178936 | − | 0.983861i | \(-0.557265\pi\) | ||||
−0.178936 | + | 0.983861i | \(0.557265\pi\) | |||||||
\(192\) | −6.71959 | −0.484944 | ||||||||
\(193\) | 19.2814i | 1.38791i | 0.720020 | + | 0.693954i | \(0.244133\pi\) | ||||
−0.720020 | + | 0.693954i | \(0.755867\pi\) | |||||||
\(194\) | 5.57667 | 0.400382 | ||||||||
\(195\) | −0.133627 | − | 8.81764i | −0.00956921 | − | 0.631444i | ||||
\(196\) | 12.3249 | 0.880348 | ||||||||
\(197\) | − | 4.28606i | − | 0.305369i | −0.988275 | − | 0.152685i | \(-0.951208\pi\) | ||
0.988275 | − | 0.152685i | \(-0.0487919\pi\) | |||||||
\(198\) | 2.31250 | 0.164342 | ||||||||
\(199\) | 4.86238 | 0.344685 | 0.172343 | − | 0.985037i | \(-0.444866\pi\) | ||||
0.172343 | + | 0.985037i | \(0.444866\pi\) | |||||||
\(200\) | 1.18343i | 0.0836808i | ||||||||
\(201\) | 15.5797i | 1.09891i | ||||||||
\(202\) | 5.93280i | 0.417431i | ||||||||
\(203\) | 2.09782i | 0.147238i | ||||||||
\(204\) | 10.7155 | 0.750235 | ||||||||
\(205\) | −17.9230 | −1.25180 | ||||||||
\(206\) | 0.783854i | 0.0546137i | ||||||||
\(207\) | 1.36961 | 0.0951948 | ||||||||
\(208\) | 12.1454 | − | 0.184057i | 0.842133 | − | 0.0127621i | ||||
\(209\) | −9.79056 | −0.677227 | ||||||||
\(210\) | − | 0.559665i | − | 0.0386206i | ||||||
\(211\) | 4.12075 | 0.283684 | 0.141842 | − | 0.989889i | \(-0.454698\pi\) | ||||
0.141842 | + | 0.989889i | \(0.454698\pi\) | |||||||
\(212\) | 12.8884 | 0.885180 | ||||||||
\(213\) | 9.55446i | 0.654661i | ||||||||
\(214\) | 5.02221i | 0.343311i | ||||||||
\(215\) | − | 0.147498i | − | 0.0100593i | ||||||
\(216\) | 6.99648i | 0.476050i | ||||||||
\(217\) | 0.699230 | 0.0474669 | ||||||||
\(218\) | −3.67518 | −0.248915 | ||||||||
\(219\) | 14.6663i | 0.991059i | ||||||||
\(220\) | −17.6336 | −1.18885 | ||||||||
\(221\) | −16.8356 | + | 0.255134i | −1.13248 | + | 0.0171622i | ||||
\(222\) | 3.62822 | 0.243510 | ||||||||
\(223\) | − | 8.03216i | − | 0.537873i | −0.963158 | − | 0.268936i | \(-0.913328\pi\) | ||
0.963158 | − | 0.268936i | \(-0.0866722\pi\) | |||||||
\(224\) | 2.55245 | 0.170543 | ||||||||
\(225\) | −1.42180 | −0.0947864 | ||||||||
\(226\) | − | 1.12985i | − | 0.0751565i | ||||||
\(227\) | − | 19.5451i | − | 1.29725i | −0.761108 | − | 0.648626i | \(-0.775344\pi\) | ||
0.761108 | − | 0.648626i | \(-0.224656\pi\) | |||||||
\(228\) | − | 4.86584i | − | 0.322248i | ||||||
\(229\) | 2.50838i | 0.165758i | 0.996560 | + | 0.0828791i | \(0.0264115\pi\) | ||||
−0.996560 | + | 0.0828791i | \(0.973588\pi\) | |||||||
\(230\) | 0.590855 | 0.0389598 | ||||||||
\(231\) | −3.91340 | −0.257483 | ||||||||
\(232\) | − | 3.82207i | − | 0.250931i | ||||||
\(233\) | 14.3889 | 0.942646 | 0.471323 | − | 0.881961i | \(-0.343777\pi\) | ||||
0.471323 | + | 0.881961i | \(0.343777\pi\) | |||||||
\(234\) | −0.0273645 | − | 1.80571i | −0.00178888 | − | 0.118043i | ||||
\(235\) | 20.6302 | 1.34576 | ||||||||
\(236\) | − | 20.5529i | − | 1.33788i | ||||||
\(237\) | 16.6121 | 1.07907 | ||||||||
\(238\) | −1.06857 | −0.0692652 | ||||||||
\(239\) | 6.28434i | 0.406500i | 0.979127 | + | 0.203250i | \(0.0651504\pi\) | ||||
−0.979127 | + | 0.203250i | \(0.934850\pi\) | |||||||
\(240\) | − | 8.23989i | − | 0.531883i | ||||||
\(241\) | 4.56420i | 0.294006i | 0.989136 | + | 0.147003i | \(0.0469626\pi\) | ||||
−0.989136 | + | 0.147003i | \(0.953037\pi\) | |||||||
\(242\) | − | 3.37602i | − | 0.217018i | ||||||
\(243\) | −13.9718 | −0.896291 | ||||||||
\(244\) | −3.09555 | −0.198172 | ||||||||
\(245\) | 13.1373i | 0.839312i | ||||||||
\(246\) | 3.52380 | 0.224669 | ||||||||
\(247\) | 0.115855 | + | 7.64491i | 0.00737165 | + | 0.486434i | ||||
\(248\) | −1.27395 | −0.0808958 | ||||||||
\(249\) | 5.43102i | 0.344177i | ||||||||
\(250\) | −3.91479 | −0.247593 | ||||||||
\(251\) | 11.3881 | 0.718809 | 0.359404 | − | 0.933182i | \(-0.382980\pi\) | ||||
0.359404 | + | 0.933182i | \(0.382980\pi\) | |||||||
\(252\) | 2.02581i | 0.127614i | ||||||||
\(253\) | − | 4.13149i | − | 0.259745i | ||||||
\(254\) | 0.656080i | 0.0411661i | ||||||||
\(255\) | 11.4218i | 0.715264i | ||||||||
\(256\) | 8.10374 | 0.506484 | ||||||||
\(257\) | −3.40809 | −0.212591 | −0.106295 | − | 0.994335i | \(-0.533899\pi\) | ||||
−0.106295 | + | 0.994335i | \(0.533899\pi\) | |||||||
\(258\) | 0.0289993i | 0.00180542i | ||||||||
\(259\) | 6.39527 | 0.397383 | ||||||||
\(260\) | 0.208663 | + | 13.7691i | 0.0129407 | + | 0.853922i | ||||
\(261\) | 4.59193 | 0.284234 | ||||||||
\(262\) | − | 3.33959i | − | 0.206320i | ||||||
\(263\) | 9.90035 | 0.610482 | 0.305241 | − | 0.952275i | \(-0.401263\pi\) | ||||
0.305241 | + | 0.952275i | \(0.401263\pi\) | |||||||
\(264\) | 7.12993 | 0.438817 | ||||||||
\(265\) | 13.7380i | 0.843919i | ||||||||
\(266\) | 0.485231i | 0.0297514i | ||||||||
\(267\) | − | 6.08976i | − | 0.372687i | ||||||
\(268\) | − | 24.3283i | − | 1.48609i | ||||||
\(269\) | −5.96941 | −0.363961 | −0.181981 | − | 0.983302i | \(-0.558251\pi\) | ||||
−0.181981 | + | 0.983302i | \(0.558251\pi\) | |||||||
\(270\) | −3.62626 | −0.220687 | ||||||||
\(271\) | 26.2814i | 1.59648i | 0.602338 | + | 0.798241i | \(0.294236\pi\) | ||||
−0.602338 | + | 0.798241i | \(0.705764\pi\) | |||||||
\(272\) | −15.7324 | −0.953920 | ||||||||
\(273\) | 0.0463084 | + | 3.05576i | 0.00280271 | + | 0.184943i | ||||
\(274\) | −0.726192 | −0.0438709 | ||||||||
\(275\) | 4.28890i | 0.258630i | ||||||||
\(276\) | 2.05332 | 0.123595 | ||||||||
\(277\) | 14.3088 | 0.859735 | 0.429867 | − | 0.902892i | \(-0.358560\pi\) | ||||
0.429867 | + | 0.902892i | \(0.358560\pi\) | |||||||
\(278\) | 5.24270i | 0.314436i | ||||||||
\(279\) | − | 1.53055i | − | 0.0916318i | ||||||
\(280\) | 1.79732i | 0.107410i | ||||||||
\(281\) | 31.8409i | 1.89947i | 0.313054 | + | 0.949735i | \(0.398648\pi\) | ||||
−0.313054 | + | 0.949735i | \(0.601352\pi\) | |||||||
\(282\) | −4.05605 | −0.241535 | ||||||||
\(283\) | −10.4060 | −0.618573 | −0.309287 | − | 0.950969i | \(-0.600090\pi\) | ||||
−0.309287 | + | 0.950969i | \(0.600090\pi\) | |||||||
\(284\) | − | 14.9196i | − | 0.885318i | ||||||
\(285\) | 5.18658 | 0.307227 | ||||||||
\(286\) | −5.44698 | + | 0.0825461i | −0.322087 | + | 0.00488105i | ||||
\(287\) | 6.21122 | 0.366637 | ||||||||
\(288\) | − | 5.58708i | − | 0.329222i | ||||||
\(289\) | 4.80777 | 0.282810 | ||||||||
\(290\) | 1.98097 | 0.116327 | ||||||||
\(291\) | 20.6574i | 1.21096i | ||||||||
\(292\) | − | 22.9020i | − | 1.34024i | ||||||
\(293\) | − | 6.03440i | − | 0.352533i | −0.984342 | − | 0.176267i | \(-0.943598\pi\) | ||
0.984342 | − | 0.176267i | \(-0.0564021\pi\) | |||||||
\(294\) | − | 2.58290i | − | 0.150638i | ||||||
\(295\) | 21.9077 | 1.27552 | ||||||||
\(296\) | −11.6517 | −0.677243 | ||||||||
\(297\) | 25.3562i | 1.47132i | ||||||||
\(298\) | −0.617225 | −0.0357549 | ||||||||
\(299\) | −3.22606 | + | 0.0488892i | −0.186568 | + | 0.00282733i | ||||
\(300\) | −2.13155 | −0.123065 | ||||||||
\(301\) | 0.0511156i | 0.00294626i | ||||||||
\(302\) | 0.383004 | 0.0220394 | ||||||||
\(303\) | −21.9766 | −1.26252 | ||||||||
\(304\) | 7.14400i | 0.409737i | ||||||||
\(305\) | − | 3.29960i | − | 0.188935i | ||||||
\(306\) | 2.33900i | 0.133712i | ||||||||
\(307\) | 3.95437i | 0.225688i | 0.993613 | + | 0.112844i | \(0.0359960\pi\) | ||||
−0.993613 | + | 0.112844i | \(0.964004\pi\) | |||||||
\(308\) | 6.11092 | 0.348202 | ||||||||
\(309\) | −2.90359 | −0.165179 | ||||||||
\(310\) | − | 0.660284i | − | 0.0375016i | ||||||
\(311\) | 22.0723 | 1.25161 | 0.625803 | − | 0.779981i | \(-0.284771\pi\) | ||||
0.625803 | + | 0.779981i | \(0.284771\pi\) | |||||||
\(312\) | −0.0843706 | − | 5.56738i | −0.00477655 | − | 0.315191i | ||||
\(313\) | −30.6318 | −1.73141 | −0.865706 | − | 0.500552i | \(-0.833130\pi\) | ||||
−0.865706 | + | 0.500552i | \(0.833130\pi\) | |||||||
\(314\) | − | 3.70081i | − | 0.208849i | ||||||
\(315\) | −2.15934 | −0.121665 | ||||||||
\(316\) | −25.9405 | −1.45927 | ||||||||
\(317\) | − | 7.53657i | − | 0.423296i | −0.977346 | − | 0.211648i | \(-0.932117\pi\) | ||
0.977346 | − | 0.211648i | \(-0.0678830\pi\) | |||||||
\(318\) | − | 2.70100i | − | 0.151465i | ||||||
\(319\) | − | 13.8517i | − | 0.775548i | ||||||
\(320\) | 11.1846i | 0.625236i | ||||||||
\(321\) | −18.6035 | −1.03835 | ||||||||
\(322\) | −0.204761 | −0.0114109 | ||||||||
\(323\) | − | 9.90276i | − | 0.551005i | ||||||
\(324\) | −3.91028 | −0.217238 | ||||||||
\(325\) | 3.34897 | − | 0.0507518i | 0.185767 | − | 0.00281521i | ||||
\(326\) | −4.42369 | −0.245006 | ||||||||
\(327\) | − | 13.6138i | − | 0.752843i | ||||||
\(328\) | −11.3164 | −0.624843 | ||||||||
\(329\) | −7.14940 | −0.394159 | ||||||||
\(330\) | 3.69543i | 0.203427i | ||||||||
\(331\) | 10.6709i | 0.586525i | 0.956032 | + | 0.293263i | \(0.0947410\pi\) | ||||
−0.956032 | + | 0.293263i | \(0.905259\pi\) | |||||||
\(332\) | − | 8.48075i | − | 0.465442i | ||||||
\(333\) | − | 13.9987i | − | 0.767123i | ||||||
\(334\) | 5.51080 | 0.301538 | ||||||||
\(335\) | 25.9320 | 1.41682 | ||||||||
\(336\) | 2.85554i | 0.155782i | ||||||||
\(337\) | −7.59648 | −0.413806 | −0.206903 | − | 0.978361i | \(-0.566339\pi\) | ||||
−0.206903 | + | 0.978361i | \(0.566339\pi\) | |||||||
\(338\) | 0.128912 | + | 4.25227i | 0.00701186 | + | 0.231293i | ||||
\(339\) | 4.18524 | 0.227311 | ||||||||
\(340\) | − | 17.8356i | − | 0.967274i | ||||||
\(341\) | −4.61697 | −0.250023 | ||||||||
\(342\) | 1.06213 | 0.0574332 | ||||||||
\(343\) | − | 9.44736i | − | 0.510109i | ||||||
\(344\) | − | 0.0931290i | − | 0.00502118i | ||||||
\(345\) | 2.18867i | 0.117834i | ||||||||
\(346\) | 4.93818i | 0.265478i | ||||||||
\(347\) | −2.98264 | −0.160116 | −0.0800582 | − | 0.996790i | \(-0.525511\pi\) | ||||
−0.0800582 | + | 0.996790i | \(0.525511\pi\) | |||||||
\(348\) | 6.88421 | 0.369033 | ||||||||
\(349\) | − | 22.5564i | − | 1.20742i | −0.797204 | − | 0.603709i | \(-0.793689\pi\) | ||
0.797204 | − | 0.603709i | \(-0.206311\pi\) | |||||||
\(350\) | 0.212563 | 0.0113620 | ||||||||
\(351\) | 19.7993 | − | 0.300048i | 1.05681 | − | 0.0160154i | ||||
\(352\) | −16.8536 | −0.898301 | ||||||||
\(353\) | − | 3.59914i | − | 0.191563i | −0.995402 | − | 0.0957815i | \(-0.969465\pi\) | ||
0.995402 | − | 0.0957815i | \(-0.0305350\pi\) | |||||||
\(354\) | −4.30723 | −0.228926 | ||||||||
\(355\) | 15.9031 | 0.844050 | ||||||||
\(356\) | 9.50939i | 0.503996i | ||||||||
\(357\) | − | 3.95825i | − | 0.209493i | ||||||
\(358\) | − | 5.13992i | − | 0.271653i | ||||||
\(359\) | 9.02624i | 0.476387i | 0.971218 | + | 0.238193i | \(0.0765552\pi\) | ||||
−0.971218 | + | 0.238193i | \(0.923445\pi\) | |||||||
\(360\) | 3.93417 | 0.207349 | ||||||||
\(361\) | 14.5032 | 0.763327 | ||||||||
\(362\) | − | 7.21626i | − | 0.379278i | ||||||
\(363\) | 12.5056 | 0.656373 | ||||||||
\(364\) | −0.0723124 | − | 4.77169i | −0.00379020 | − | 0.250104i | ||||
\(365\) | 24.4117 | 1.27777 | ||||||||
\(366\) | 0.648727i | 0.0339095i | ||||||||
\(367\) | −5.62283 | −0.293509 | −0.146755 | − | 0.989173i | \(-0.546883\pi\) | ||||
−0.146755 | + | 0.989173i | \(0.546883\pi\) | |||||||
\(368\) | −3.01468 | −0.157151 | ||||||||
\(369\) | − | 13.5958i | − | 0.707769i | ||||||
\(370\) | − | 6.03907i | − | 0.313956i | ||||||
\(371\) | − | 4.76091i | − | 0.247174i | ||||||
\(372\) | − | 2.29460i | − | 0.118969i | ||||||
\(373\) | 18.2843 | 0.946723 | 0.473362 | − | 0.880868i | \(-0.343040\pi\) | ||||
0.473362 | + | 0.880868i | \(0.343040\pi\) | |||||||
\(374\) | 7.05569 | 0.364841 | ||||||||
\(375\) | − | 14.5013i | − | 0.748846i | ||||||
\(376\) | 13.0257 | 0.671749 | ||||||||
\(377\) | −10.8161 | + | 0.163912i | −0.557056 | + | 0.00844188i | ||||
\(378\) | 1.25668 | 0.0646368 | ||||||||
\(379\) | − | 29.7452i | − | 1.52791i | −0.645271 | − | 0.763953i | \(-0.723256\pi\) | ||
0.645271 | − | 0.763953i | \(-0.276744\pi\) | |||||||
\(380\) | −8.09905 | −0.415472 | ||||||||
\(381\) | −2.43028 | −0.124507 | ||||||||
\(382\) | − | 1.61853i | − | 0.0828112i | ||||||
\(383\) | − | 0.0171338i | − | 0.000875497i | −1.00000 | 0.000437748i | \(-0.999861\pi\) | |||
1.00000 | 0.000437748i | \(-0.000139340\pi\) | ||||||||
\(384\) | − | 11.0490i | − | 0.563841i | ||||||
\(385\) | 6.51374i | 0.331971i | ||||||||
\(386\) | −6.30981 | −0.321161 | ||||||||
\(387\) | 0.111888 | 0.00568756 | ||||||||
\(388\) | − | 32.2572i | − | 1.63761i | ||||||
\(389\) | −30.7615 | −1.55967 | −0.779836 | − | 0.625984i | \(-0.784698\pi\) | ||||
−0.779836 | + | 0.625984i | \(0.784698\pi\) | |||||||
\(390\) | 2.88556 | − | 0.0437291i | 0.146116 | − | 0.00221431i | ||||
\(391\) | 4.17884 | 0.211333 | ||||||||
\(392\) | 8.29477i | 0.418949i | ||||||||
\(393\) | 12.3707 | 0.624017 | ||||||||
\(394\) | 1.40261 | 0.0706623 | ||||||||
\(395\) | − | 27.6504i | − | 1.39124i | ||||||
\(396\) | − | 13.3763i | − | 0.672182i | ||||||
\(397\) | − | 3.19453i | − | 0.160329i | −0.996782 | − | 0.0801644i | \(-0.974455\pi\) | ||
0.996782 | − | 0.0801644i | \(-0.0255445\pi\) | |||||||
\(398\) | 1.59121i | 0.0797600i | ||||||||
\(399\) | −1.79741 | −0.0899833 | ||||||||
\(400\) | 3.12954 | 0.156477 | ||||||||
\(401\) | 25.9036i | 1.29357i | 0.762674 | + | 0.646783i | \(0.223886\pi\) | ||||
−0.762674 | + | 0.646783i | \(0.776114\pi\) | |||||||
\(402\) | −5.09844 | −0.254287 | ||||||||
\(403\) | 0.0546339 | + | 3.60514i | 0.00272151 | + | 0.179585i | ||||
\(404\) | 34.3172 | 1.70735 | ||||||||
\(405\) | − | 4.16804i | − | 0.207112i | ||||||
\(406\) | −0.686507 | −0.0340708 | ||||||||
\(407\) | −42.2275 | −2.09314 | ||||||||
\(408\) | 7.21164i | 0.357030i | ||||||||
\(409\) | − | 16.1309i | − | 0.797624i | −0.917033 | − | 0.398812i | \(-0.869423\pi\) | ||
0.917033 | − | 0.398812i | \(-0.130577\pi\) | |||||||
\(410\) | − | 5.86526i | − | 0.289665i | ||||||
\(411\) | − | 2.68999i | − | 0.132688i | ||||||
\(412\) | 4.53406 | 0.223377 | ||||||||
\(413\) | −7.59213 | −0.373584 | ||||||||
\(414\) | 0.448204i | 0.0220280i | ||||||||
\(415\) | 9.03979 | 0.443746 | ||||||||
\(416\) | 0.199434 | + | 13.1601i | 0.00977806 | + | 0.645226i | ||||
\(417\) | −19.4202 | −0.951013 | ||||||||
\(418\) | − | 3.20394i | − | 0.156710i | ||||||
\(419\) | 23.6032 | 1.15309 | 0.576545 | − | 0.817065i | \(-0.304400\pi\) | ||||
0.576545 | + | 0.817065i | \(0.304400\pi\) | |||||||
\(420\) | −3.23728 | −0.157963 | ||||||||
\(421\) | − | 25.8384i | − | 1.25928i | −0.776885 | − | 0.629642i | \(-0.783202\pi\) | ||
0.776885 | − | 0.629642i | \(-0.216798\pi\) | |||||||
\(422\) | 1.34851i | 0.0656443i | ||||||||
\(423\) | 15.6494i | 0.760899i | ||||||||
\(424\) | 8.67404i | 0.421249i | ||||||||
\(425\) | −4.33805 | −0.210427 | ||||||||
\(426\) | −3.12668 | −0.151488 | ||||||||
\(427\) | 1.14348i | 0.0553368i | ||||||||
\(428\) | 29.0500 | 1.40419 | ||||||||
\(429\) | −0.305771 | − | 20.1770i | −0.0147628 | − | 0.974152i | ||||
\(430\) | 0.0482686 | 0.00232772 | ||||||||
\(431\) | − | 7.48330i | − | 0.360458i | −0.983625 | − | 0.180229i | \(-0.942316\pi\) | ||
0.983625 | − | 0.180229i | \(-0.0576839\pi\) | |||||||
\(432\) | 18.5020 | 0.890178 | ||||||||
\(433\) | 31.5403 | 1.51573 | 0.757865 | − | 0.652412i | \(-0.226243\pi\) | ||||
0.757865 | + | 0.652412i | \(0.226243\pi\) | |||||||
\(434\) | 0.228822i | 0.0109838i | ||||||||
\(435\) | 7.33801i | 0.351831i | ||||||||
\(436\) | 21.2584i | 1.01809i | ||||||||
\(437\) | − | 1.89758i | − | 0.0907737i | ||||||
\(438\) | −4.79953 | −0.229331 | ||||||||
\(439\) | −15.0348 | −0.717571 | −0.358786 | − | 0.933420i | \(-0.616809\pi\) | ||||
−0.358786 | + | 0.933420i | \(0.616809\pi\) | |||||||
\(440\) | − | 11.8676i | − | 0.565764i | ||||||
\(441\) | −9.96554 | −0.474550 | ||||||||
\(442\) | −0.0834921 | − | 5.50941i | −0.00397132 | − | 0.262056i | ||||
\(443\) | −39.0334 | −1.85453 | −0.927267 | − | 0.374402i | \(-0.877848\pi\) | ||||
−0.927267 | + | 0.374402i | \(0.877848\pi\) | |||||||
\(444\) | − | 20.9868i | − | 0.995988i | ||||||
\(445\) | −10.1362 | −0.480503 | ||||||||
\(446\) | 2.62851 | 0.124464 | ||||||||
\(447\) | − | 2.28635i | − | 0.108141i | ||||||
\(448\) | − | 3.87602i | − | 0.183125i | ||||||
\(449\) | − | 12.3994i | − | 0.585162i | −0.956241 | − | 0.292581i | \(-0.905486\pi\) | ||
0.956241 | − | 0.292581i | \(-0.0945141\pi\) | |||||||
\(450\) | − | 0.465280i | − | 0.0219335i | ||||||
\(451\) | −41.0122 | −1.93119 | ||||||||
\(452\) | −6.53542 | −0.307400 | ||||||||
\(453\) | 1.41874i | 0.0666582i | ||||||||
\(454\) | 6.39609 | 0.300183 | ||||||||
\(455\) | 5.08623 | − | 0.0770791i | 0.238446 | − | 0.00361352i | ||||
\(456\) | 3.27476 | 0.153355 | ||||||||
\(457\) | 34.8908i | 1.63212i | 0.577964 | + | 0.816062i | \(0.303847\pi\) | ||||
−0.577964 | + | 0.816062i | \(0.696153\pi\) | |||||||
\(458\) | −0.820862 | −0.0383564 | ||||||||
\(459\) | −25.6468 | −1.19709 | ||||||||
\(460\) | − | 3.41769i | − | 0.159351i | ||||||
\(461\) | − | 14.2242i | − | 0.662489i | −0.943545 | − | 0.331244i | \(-0.892532\pi\) | ||
0.943545 | − | 0.331244i | \(-0.107468\pi\) | |||||||
\(462\) | − | 1.28065i | − | 0.0595814i | ||||||
\(463\) | 37.6491i | 1.74970i | 0.484394 | + | 0.874850i | \(0.339040\pi\) | ||||
−0.484394 | + | 0.874850i | \(0.660960\pi\) | |||||||
\(464\) | −10.1074 | −0.469223 | ||||||||
\(465\) | 2.44585 | 0.113424 | ||||||||
\(466\) | 4.70873i | 0.218128i | ||||||||
\(467\) | −15.2210 | −0.704342 | −0.352171 | − | 0.935936i | \(-0.614556\pi\) | ||||
−0.352171 | + | 0.935936i | \(0.614556\pi\) | |||||||
\(468\) | −10.4448 | + | 0.158285i | −0.482810 | + | 0.00731674i | ||||
\(469\) | −8.98676 | −0.414970 | ||||||||
\(470\) | 6.75119i | 0.311409i | ||||||||
\(471\) | 13.7087 | 0.631664 | ||||||||
\(472\) | 13.8323 | 0.636684 | ||||||||
\(473\) | − | 0.337513i | − | 0.0155189i | ||||||
\(474\) | 5.43629i | 0.249697i | ||||||||
\(475\) | 1.96988i | 0.0903844i | ||||||||
\(476\) | 6.18096i | 0.283304i | ||||||||
\(477\) | −10.4212 | −0.477154 | ||||||||
\(478\) | −2.05654 | −0.0940639 | ||||||||
\(479\) | − | 4.97318i | − | 0.227230i | −0.993525 | − | 0.113615i | \(-0.963757\pi\) | ||
0.993525 | − | 0.113615i | \(-0.0362431\pi\) | |||||||
\(480\) | 8.92827 | 0.407518 | ||||||||
\(481\) | 0.499691 | + | 32.9732i | 0.0227839 | + | 1.50345i | ||||
\(482\) | −1.49363 | −0.0680328 | ||||||||
\(483\) | − | 0.758486i | − | 0.0345123i | ||||||
\(484\) | −19.5279 | −0.887634 | ||||||||
\(485\) | 34.3836 | 1.56128 | ||||||||
\(486\) | − | 4.57224i | − | 0.207401i | ||||||
\(487\) | − | 12.7955i | − | 0.579817i | −0.957054 | − | 0.289909i | \(-0.906375\pi\) | ||
0.957054 | − | 0.289909i | \(-0.0936249\pi\) | |||||||
\(488\) | − | 2.08334i | − | 0.0943082i | ||||||
\(489\) | − | 16.3864i | − | 0.741020i | ||||||
\(490\) | −4.29916 | −0.194216 | ||||||||
\(491\) | 17.6587 | 0.796925 | 0.398462 | − | 0.917185i | \(-0.369544\pi\) | ||||
0.398462 | + | 0.917185i | \(0.369544\pi\) | |||||||
\(492\) | − | 20.3828i | − | 0.918927i | ||||||
\(493\) | 14.0105 | 0.631001 | ||||||||
\(494\) | −2.50178 | + | 0.0379132i | −0.112561 | + | 0.00170580i | ||||
\(495\) | 14.2580 | 0.640849 | ||||||||
\(496\) | 3.36892i | 0.151269i | ||||||||
\(497\) | −5.51124 | −0.247213 | ||||||||
\(498\) | −1.77729 | −0.0796424 | ||||||||
\(499\) | 19.2207i | 0.860435i | 0.902725 | + | 0.430217i | \(0.141563\pi\) | ||||
−0.902725 | + | 0.430217i | \(0.858437\pi\) | |||||||
\(500\) | 22.6444i | 1.01269i | ||||||||
\(501\) | 20.4134i | 0.912002i | ||||||||
\(502\) | 3.72673i | 0.166332i | ||||||||
\(503\) | 8.98709 | 0.400714 | 0.200357 | − | 0.979723i | \(-0.435790\pi\) | ||||
0.200357 | + | 0.979723i | \(0.435790\pi\) | |||||||
\(504\) | −1.36339 | −0.0607302 | ||||||||
\(505\) | 36.5794i | 1.62776i | ||||||||
\(506\) | 1.35202 | 0.0601048 | ||||||||
\(507\) | −15.7515 | + | 0.477520i | −0.699547 | + | 0.0212074i | ||||
\(508\) | 3.79498 | 0.168375 | ||||||||
\(509\) | − | 43.5846i | − | 1.93186i | −0.258813 | − | 0.965928i | \(-0.583331\pi\) | ||
0.258813 | − | 0.965928i | \(-0.416669\pi\) | |||||||
\(510\) | −3.73778 | −0.165512 | ||||||||
\(511\) | −8.45989 | −0.374244 | ||||||||
\(512\) | 20.8815i | 0.922839i | ||||||||
\(513\) | 11.6461i | 0.514186i | ||||||||
\(514\) | − | 1.11529i | − | 0.0491934i | ||||||
\(515\) | 4.83294i | 0.212965i | ||||||||
\(516\) | 0.167741 | 0.00738440 | ||||||||
\(517\) | 47.2070 | 2.07616 | ||||||||
\(518\) | 2.09284i | 0.0919542i | ||||||||
\(519\) | −18.2922 | −0.802940 | ||||||||
\(520\) | −9.26674 | + | 0.140433i | −0.406373 | + | 0.00615837i | ||||
\(521\) | 20.4202 | 0.894626 | 0.447313 | − | 0.894378i | \(-0.352381\pi\) | ||||
0.447313 | + | 0.894378i | \(0.352381\pi\) | |||||||
\(522\) | 1.50270i | 0.0657715i | ||||||||
\(523\) | −13.3544 | −0.583949 | −0.291974 | − | 0.956426i | \(-0.594312\pi\) | ||||
−0.291974 | + | 0.956426i | \(0.594312\pi\) | |||||||
\(524\) | −19.3172 | −0.843878 | ||||||||
\(525\) | 0.787384i | 0.0343643i | ||||||||
\(526\) | 3.23987i | 0.141265i | ||||||||
\(527\) | − | 4.66988i | − | 0.203423i | ||||||
\(528\) | − | 18.8549i | − | 0.820555i | ||||||
\(529\) | −22.1992 | −0.965185 | ||||||||
\(530\) | −4.49574 | −0.195282 | ||||||||
\(531\) | 16.6185i | 0.721180i | ||||||||
\(532\) | 2.80673 | 0.121687 | ||||||||
\(533\) | 0.485310 | + | 32.0242i | 0.0210211 | + | 1.38712i | ||||
\(534\) | 1.99286 | 0.0862396 | ||||||||
\(535\) | 30.9650i | 1.33873i | ||||||||
\(536\) | 16.3732 | 0.707216 | ||||||||
\(537\) | 19.0395 | 0.821617 | ||||||||
\(538\) | − | 1.95348i | − | 0.0842205i | ||||||
\(539\) | 30.0614i | 1.29484i | ||||||||
\(540\) | 20.9755i | 0.902640i | ||||||||
\(541\) | − | 12.8644i | − | 0.553086i | −0.961002 | − | 0.276543i | \(-0.910811\pi\) | ||
0.961002 | − | 0.276543i | \(-0.0891888\pi\) | |||||||
\(542\) | −8.60054 | −0.369425 | ||||||||
\(543\) | 26.7308 | 1.14713 | ||||||||
\(544\) | − | 17.0468i | − | 0.730875i | ||||||
\(545\) | −22.6597 | −0.970637 | ||||||||
\(546\) | −0.999992 | + | 0.0151544i | −0.0427957 | + | 0.000648546i | ||||
\(547\) | 8.34081 | 0.356627 | 0.178314 | − | 0.983974i | \(-0.442936\pi\) | ||||
0.178314 | + | 0.983974i | \(0.442936\pi\) | |||||||
\(548\) | 4.20053i | 0.179438i | ||||||||
\(549\) | 2.50297 | 0.106824 | ||||||||
\(550\) | −1.40354 | −0.0598469 | ||||||||
\(551\) | − | 6.36207i | − | 0.271033i | ||||||
\(552\) | 1.38191i | 0.0588179i | ||||||||
\(553\) | 9.58227i | 0.407480i | ||||||||
\(554\) | 4.68254i | 0.198942i | ||||||||
\(555\) | 22.3702 | 0.949561 | ||||||||
\(556\) | 30.3254 | 1.28608 | ||||||||
\(557\) | − | 4.36612i | − | 0.184999i | −0.995713 | − | 0.0924993i | \(-0.970514\pi\) | ||
0.995713 | − | 0.0924993i | \(-0.0294856\pi\) | |||||||
\(558\) | 0.500871 | 0.0212035 | ||||||||
\(559\) | −0.263545 | + | 0.00399389i | −0.0111468 | + | 0.000168924i | ||||
\(560\) | 4.75296 | 0.200849 | ||||||||
\(561\) | 26.1360i | 1.10346i | ||||||||
\(562\) | −10.4199 | −0.439536 | ||||||||
\(563\) | −41.3744 | −1.74372 | −0.871862 | − | 0.489751i | \(-0.837088\pi\) | ||||
−0.871862 | + | 0.489751i | \(0.837088\pi\) | |||||||
\(564\) | 23.4615i | 0.987908i | ||||||||
\(565\) | − | 6.96622i | − | 0.293071i | ||||||
\(566\) | − | 3.40535i | − | 0.143138i | ||||||
\(567\) | 1.44444i | 0.0606607i | ||||||||
\(568\) | 10.0411 | 0.421314 | ||||||||
\(569\) | 12.2313 | 0.512761 | 0.256380 | − | 0.966576i | \(-0.417470\pi\) | ||||
0.256380 | + | 0.966576i | \(0.417470\pi\) | |||||||
\(570\) | 1.69730i | 0.0710921i | ||||||||
\(571\) | −16.7386 | −0.700488 | −0.350244 | − | 0.936659i | \(-0.613901\pi\) | ||||
−0.350244 | + | 0.936659i | \(0.613901\pi\) | |||||||
\(572\) | 0.477473 | + | 31.5071i | 0.0199641 | + | 1.31738i | ||||
\(573\) | 5.99543 | 0.250463 | ||||||||
\(574\) | 2.03261i | 0.0848395i | ||||||||
\(575\) | −0.831265 | −0.0346661 | ||||||||
\(576\) | −8.48425 | −0.353511 | ||||||||
\(577\) | − | 22.9801i | − | 0.956675i | −0.878176 | − | 0.478338i | \(-0.841240\pi\) | ||
0.878176 | − | 0.478338i | \(-0.158760\pi\) | |||||||
\(578\) | 1.57333i | 0.0654421i | ||||||||
\(579\) | − | 23.3731i | − | 0.971353i | ||||||
\(580\) | − | 11.4586i | − | 0.475792i | ||||||
\(581\) | −3.13274 | −0.129968 | ||||||||
\(582\) | −6.76008 | −0.280214 | ||||||||
\(583\) | 31.4360i | 1.30194i | ||||||||
\(584\) | 15.4133 | 0.637808 | ||||||||
\(585\) | −0.168719 | − | 11.1333i | −0.00697568 | − | 0.460305i | ||||
\(586\) | 1.97475 | 0.0815760 | ||||||||
\(587\) | − | 19.9101i | − | 0.821778i | −0.911685 | − | 0.410889i | \(-0.865218\pi\) | ||
0.911685 | − | 0.410889i | \(-0.134782\pi\) | |||||||
\(588\) | −14.9403 | −0.616128 | ||||||||
\(589\) | −2.12056 | −0.0873762 | ||||||||
\(590\) | 7.16926i | 0.295154i | ||||||||
\(591\) | 5.19560i | 0.213718i | ||||||||
\(592\) | 30.8127i | 1.26639i | ||||||||
\(593\) | 23.6656i | 0.971828i | 0.874007 | + | 0.485914i | \(0.161513\pi\) | ||||
−0.874007 | + | 0.485914i | \(0.838487\pi\) | |||||||
\(594\) | −8.29779 | −0.340462 | ||||||||
\(595\) | −6.58839 | −0.270098 | ||||||||
\(596\) | 3.57022i | 0.146242i | ||||||||
\(597\) | −5.89422 | −0.241234 | ||||||||
\(598\) | −0.0159989 | − | 1.05572i | −0.000654243 | − | 0.0431717i | ||||
\(599\) | 30.9359 | 1.26401 | 0.632004 | − | 0.774965i | \(-0.282233\pi\) | ||||
0.632004 | + | 0.774965i | \(0.282233\pi\) | |||||||
\(600\) | − | 1.43456i | − | 0.0585656i | ||||||
\(601\) | 7.06072 | 0.288013 | 0.144006 | − | 0.989577i | \(-0.454001\pi\) | ||||
0.144006 | + | 0.989577i | \(0.454001\pi\) | |||||||
\(602\) | −0.0167275 | −0.000681762 | ||||||||
\(603\) | 19.6712i | 0.801073i | ||||||||
\(604\) | − | 2.21542i | − | 0.0901440i | ||||||
\(605\) | − | 20.8152i | − | 0.846258i | ||||||
\(606\) | − | 7.19179i | − | 0.292147i | ||||||
\(607\) | −6.08348 | −0.246921 | −0.123460 | − | 0.992350i | \(-0.539399\pi\) | ||||
−0.123460 | + | 0.992350i | \(0.539399\pi\) | |||||||
\(608\) | −7.74083 | −0.313932 | ||||||||
\(609\) | − | 2.54299i | − | 0.103047i | ||||||
\(610\) | 1.07979 | 0.0437193 | ||||||||
\(611\) | −0.558614 | − | 36.8613i | −0.0225991 | − | 1.49125i | ||||
\(612\) | 13.5296 | 0.546900 | ||||||||
\(613\) | − | 8.79807i | − | 0.355351i | −0.984089 | − | 0.177675i | \(-0.943142\pi\) | ||
0.984089 | − | 0.177675i | \(-0.0568577\pi\) | |||||||
\(614\) | −1.29406 | −0.0522240 | ||||||||
\(615\) | 21.7264 | 0.876092 | ||||||||
\(616\) | 4.11271i | 0.165706i | ||||||||
\(617\) | − | 18.8381i | − | 0.758394i | −0.925316 | − | 0.379197i | \(-0.876200\pi\) | ||
0.925316 | − | 0.379197i | \(-0.123800\pi\) | |||||||
\(618\) | − | 0.950195i | − | 0.0382224i | ||||||
\(619\) | − | 35.9128i | − | 1.44346i | −0.692177 | − | 0.721728i | \(-0.743348\pi\) | ||
0.692177 | − | 0.721728i | \(-0.256652\pi\) | |||||||
\(620\) | −3.81929 | −0.153387 | ||||||||
\(621\) | −4.91449 | −0.197212 | ||||||||
\(622\) | 7.22313i | 0.289621i | ||||||||
\(623\) | 3.51272 | 0.140734 | ||||||||
\(624\) | −14.7228 | + | 0.223116i | −0.589383 | + | 0.00893178i | ||||
\(625\) | −19.4923 | −0.779694 | ||||||||
\(626\) | − | 10.0242i | − | 0.400648i | ||||||
\(627\) | 11.8682 | 0.473970 | ||||||||
\(628\) | −21.4067 | −0.854219 | ||||||||
\(629\) | − | 42.7115i | − | 1.70302i | ||||||
\(630\) | − | 0.706642i | − | 0.0281533i | ||||||
\(631\) | − | 32.0555i | − | 1.27611i | −0.769990 | − | 0.638056i | \(-0.779739\pi\) | ||
0.769990 | − | 0.638056i | \(-0.220261\pi\) | |||||||
\(632\) | − | 17.4582i | − | 0.694450i | ||||||
\(633\) | −4.99520 | −0.198542 | ||||||||
\(634\) | 2.46633 | 0.0979505 | ||||||||
\(635\) | 4.04513i | 0.160526i | ||||||||
\(636\) | −15.6234 | −0.619510 | ||||||||
\(637\) | 23.4733 | − | 0.355726i | 0.930047 | − | 0.0140944i | ||||
\(638\) | 4.53296 | 0.179461 | ||||||||
\(639\) | 12.0636i | 0.477229i | ||||||||
\(640\) | −18.3907 | −0.726957 | ||||||||
\(641\) | 41.4629 | 1.63769 | 0.818843 | − | 0.574018i | \(-0.194616\pi\) | ||||
0.818843 | + | 0.574018i | \(0.194616\pi\) | |||||||
\(642\) | − | 6.08796i | − | 0.240272i | ||||||
\(643\) | 39.4717i | 1.55661i | 0.627884 | + | 0.778307i | \(0.283921\pi\) | ||||
−0.627884 | + | 0.778307i | \(0.716079\pi\) | |||||||
\(644\) | 1.18440i | 0.0466721i | ||||||||
\(645\) | 0.178799i | 0.00704019i | ||||||||
\(646\) | 3.24066 | 0.127502 | ||||||||
\(647\) | −23.3211 | −0.916847 | −0.458423 | − | 0.888734i | \(-0.651586\pi\) | ||||
−0.458423 | + | 0.888734i | \(0.651586\pi\) | |||||||
\(648\) | − | 2.63166i | − | 0.103381i | ||||||
\(649\) | 50.1302 | 1.96778 | ||||||||
\(650\) | 0.0166085 | + | 1.09594i | 0.000651437 | + | 0.0429865i | ||||
\(651\) | −0.847613 | −0.0332206 | ||||||||
\(652\) | 25.5880i | 1.00210i | ||||||||
\(653\) | −24.5064 | −0.959011 | −0.479506 | − | 0.877539i | \(-0.659184\pi\) | ||||
−0.479506 | + | 0.877539i | \(0.659184\pi\) | |||||||
\(654\) | 4.45508 | 0.174208 | ||||||||
\(655\) | − | 20.5906i | − | 0.804542i | ||||||
\(656\) | 29.9259i | 1.16841i | ||||||||
\(657\) | 18.5179i | 0.722454i | ||||||||
\(658\) | − | 2.33963i | − | 0.0912082i | ||||||
\(659\) | 11.9514 | 0.465560 | 0.232780 | − | 0.972529i | \(-0.425218\pi\) | ||||
0.232780 | + | 0.972529i | \(0.425218\pi\) | |||||||
\(660\) | 21.3755 | 0.832041 | ||||||||
\(661\) | 38.7978i | 1.50906i | 0.656266 | + | 0.754529i | \(0.272135\pi\) | ||||
−0.656266 | + | 0.754529i | \(0.727865\pi\) | |||||||
\(662\) | −3.49203 | −0.135722 | ||||||||
\(663\) | 20.4082 | − | 0.309275i | 0.792589 | − | 0.0120113i | ||||
\(664\) | 5.70764 | 0.221499 | ||||||||
\(665\) | 2.99175i | 0.116015i | ||||||||
\(666\) | 4.58104 | 0.177512 | ||||||||
\(667\) | 2.68471 | 0.103952 | ||||||||
\(668\) | − | 31.8762i | − | 1.23333i | ||||||
\(669\) | 9.73664i | 0.376440i | ||||||||
\(670\) | 8.48621i | 0.327851i | ||||||||
\(671\) | − | 7.55030i | − | 0.291476i | ||||||
\(672\) | −3.09410 | −0.119357 | ||||||||
\(673\) | −40.0398 | −1.54342 | −0.771711 | − | 0.635974i | \(-0.780599\pi\) | ||||
−0.771711 | + | 0.635974i | \(0.780599\pi\) | |||||||
\(674\) | − | 2.48593i | − | 0.0957546i | ||||||
\(675\) | 5.10173 | 0.196366 | ||||||||
\(676\) | 24.5965 | − | 0.745665i | 0.946020 | − | 0.0286794i | ||||
\(677\) | 7.21788 | 0.277406 | 0.138703 | − | 0.990334i | \(-0.455707\pi\) | ||||
0.138703 | + | 0.990334i | \(0.455707\pi\) | |||||||
\(678\) | 1.36961i | 0.0525997i | ||||||||
\(679\) | −11.9157 | −0.457281 | ||||||||
\(680\) | 12.0036 | 0.460316 | ||||||||
\(681\) | 23.6927i | 0.907905i | ||||||||
\(682\) | − | 1.51089i | − | 0.0578551i | ||||||
\(683\) | − | 14.1103i | − | 0.539916i | −0.962872 | − | 0.269958i | \(-0.912990\pi\) | ||
0.962872 | − | 0.269958i | \(-0.0870099\pi\) | |||||||
\(684\) | − | 6.14368i | − | 0.234909i | ||||||
\(685\) | −4.47742 | −0.171073 | ||||||||
\(686\) | 3.09163 | 0.118039 | ||||||||
\(687\) | − | 3.04068i | − | 0.116009i | ||||||
\(688\) | −0.246277 | −0.00938923 | ||||||||
\(689\) | 24.5466 | − | 0.371991i | 0.935152 | − | 0.0141717i | ||||
\(690\) | −0.716239 | −0.0272668 | ||||||||
\(691\) | 37.5902i | 1.43000i | 0.699126 | + | 0.714998i | \(0.253573\pi\) | ||||
−0.699126 | + | 0.714998i | \(0.746427\pi\) | |||||||
\(692\) | 28.5640 | 1.08584 | ||||||||
\(693\) | −4.94112 | −0.187697 | ||||||||
\(694\) | − | 0.976063i | − | 0.0370508i | ||||||
\(695\) | 32.3244i | 1.22614i | ||||||||
\(696\) | 4.63315i | 0.175619i | ||||||||
\(697\) | − | 41.4822i | − | 1.57125i | ||||||
\(698\) | 7.38156 | 0.279396 | ||||||||
\(699\) | −17.4423 | −0.659729 | ||||||||
\(700\) | − | 1.22953i | − | 0.0464719i | ||||||
\(701\) | −46.6987 | −1.76378 | −0.881892 | − | 0.471451i | \(-0.843730\pi\) | ||||
−0.881892 | + | 0.471451i | \(0.843730\pi\) | |||||||
\(702\) | 0.0981902 | + | 6.47929i | 0.00370595 | + | 0.244545i | ||||
\(703\) | −19.3950 | −0.731496 | ||||||||
\(704\) | 25.5931i | 0.964575i | ||||||||
\(705\) | −25.0081 | −0.941858 | ||||||||
\(706\) | 1.17781 | 0.0443276 | ||||||||
\(707\) | − | 12.6766i | − | 0.476753i | ||||||
\(708\) | 24.9144i | 0.936339i | ||||||||
\(709\) | 1.41589i | 0.0531749i | 0.999646 | + | 0.0265874i | \(0.00846404\pi\) | ||||
−0.999646 | + | 0.0265874i | \(0.991536\pi\) | |||||||
\(710\) | 5.20427i | 0.195313i | ||||||||
\(711\) | 20.9747 | 0.786614 | ||||||||
\(712\) | −6.39992 | −0.239847 | ||||||||
\(713\) | − | 0.894850i | − | 0.0335124i | ||||||
\(714\) | 1.29533 | 0.0484765 | ||||||||
\(715\) | −33.5840 | + | 0.508947i | −1.25597 | + | 0.0190335i | ||||
\(716\) | −29.7310 | −1.11110 | ||||||||
\(717\) | − | 7.61793i | − | 0.284497i | ||||||
\(718\) | −2.95382 | −0.110236 | ||||||||
\(719\) | −23.6465 | −0.881864 | −0.440932 | − | 0.897541i | \(-0.645352\pi\) | ||||
−0.440932 | + | 0.897541i | \(0.645352\pi\) | |||||||
\(720\) | − | 10.4038i | − | 0.387727i | ||||||
\(721\) | − | 1.67486i | − | 0.0623750i | ||||||
\(722\) | 4.74615i | 0.176634i | ||||||||
\(723\) | − | 5.53275i | − | 0.205765i | ||||||
\(724\) | −41.7412 | −1.55130 | ||||||||
\(725\) | −2.78700 | −0.103507 | ||||||||
\(726\) | 4.09243i | 0.151884i | ||||||||
\(727\) | −9.85004 | −0.365318 | −0.182659 | − | 0.983176i | \(-0.558470\pi\) | ||||
−0.182659 | + | 0.983176i | \(0.558470\pi\) | |||||||
\(728\) | 3.21139 | − | 0.0486670i | 0.119022 | − | 0.00180372i | ||||
\(729\) | 23.1340 | 0.856814 | ||||||||
\(730\) | 7.98869i | 0.295675i | ||||||||
\(731\) | 0.341381 | 0.0126264 | ||||||||
\(732\) | 3.75245 | 0.138694 | ||||||||
\(733\) | 39.7533i | 1.46832i | 0.678977 | + | 0.734160i | \(0.262424\pi\) | ||||
−0.678977 | + | 0.734160i | \(0.737576\pi\) | |||||||
\(734\) | − | 1.84006i | − | 0.0679179i | ||||||
\(735\) | − | 15.9251i | − | 0.587408i | ||||||
\(736\) | − | 3.26653i | − | 0.120406i | ||||||
\(737\) | 59.3389 | 2.18578 | ||||||||
\(738\) | 4.44920 | 0.163777 | ||||||||
\(739\) | − | 20.1976i | − | 0.742979i | −0.928437 | − | 0.371490i | \(-0.878847\pi\) | ||
0.928437 | − | 0.371490i | \(-0.121153\pi\) | |||||||
\(740\) | −34.9319 | −1.28412 | ||||||||
\(741\) | −0.140440 | − | 9.26723i | −0.00515919 | − | 0.340440i | ||||
\(742\) | 1.55800 | 0.0571960 | ||||||||
\(743\) | 11.4479i | 0.419984i | 0.977703 | + | 0.209992i | \(0.0673438\pi\) | ||||
−0.977703 | + | 0.209992i | \(0.932656\pi\) | |||||||
\(744\) | 1.54429 | 0.0566164 | ||||||||
\(745\) | −3.80557 | −0.139425 | ||||||||
\(746\) | 5.98349i | 0.219071i | ||||||||
\(747\) | 6.85729i | 0.250895i | ||||||||
\(748\) | − | 40.8124i | − | 1.49225i | ||||||
\(749\) | − | 10.7309i | − | 0.392100i | ||||||
\(750\) | 4.74554 | 0.173283 | ||||||||
\(751\) | −47.6401 | −1.73841 | −0.869206 | − | 0.494451i | \(-0.835369\pi\) | ||||
−0.869206 | + | 0.494451i | \(0.835369\pi\) | |||||||
\(752\) | − | 34.4461i | − | 1.25612i | ||||||
\(753\) | −13.8047 | −0.503072 | ||||||||
\(754\) | −0.0536398 | − | 3.53954i | −0.00195345 | − | 0.128902i | ||||
\(755\) | 2.36145 | 0.0859421 | ||||||||
\(756\) | − | 7.26906i | − | 0.264373i | ||||||
\(757\) | 7.16086 | 0.260266 | 0.130133 | − | 0.991497i | \(-0.458460\pi\) | ||||
0.130133 | + | 0.991497i | \(0.458460\pi\) | |||||||
\(758\) | 9.73406 | 0.353557 | ||||||||
\(759\) | 5.00822i | 0.181787i | ||||||||
\(760\) | − | 5.45075i | − | 0.197719i | ||||||
\(761\) | 20.6576i | 0.748839i | 0.927259 | + | 0.374420i | \(0.122158\pi\) | ||||
−0.927259 | + | 0.374420i | \(0.877842\pi\) | |||||||
\(762\) | − | 0.795305i | − | 0.0288109i | ||||||
\(763\) | 7.85275 | 0.284289 | ||||||||
\(764\) | −9.36209 | −0.338709 | ||||||||
\(765\) | 14.4214i | 0.521407i | ||||||||
\(766\) | 0.00560701 | 0.000202589 | ||||||||
\(767\) | −0.593206 | − | 39.1440i | −0.0214194 | − | 1.41341i | ||||
\(768\) | −9.82341 | −0.354472 | ||||||||
\(769\) | 7.53702i | 0.271792i | 0.990723 | + | 0.135896i | \(0.0433913\pi\) | ||||
−0.990723 | + | 0.135896i | \(0.956609\pi\) | |||||||
\(770\) | −2.13161 | −0.0768179 | ||||||||
\(771\) | 4.13131 | 0.148786 | ||||||||
\(772\) | 36.4980i | 1.31359i | ||||||||
\(773\) | − | 43.9283i | − | 1.57999i | −0.613113 | − | 0.789995i | \(-0.710083\pi\) | ||
0.613113 | − | 0.789995i | \(-0.289917\pi\) | |||||||
\(774\) | 0.0366150i | 0.00131610i | ||||||||
\(775\) | 0.928944i | 0.0333686i | ||||||||
\(776\) | 21.7095 | 0.779324 | ||||||||
\(777\) | −7.75240 | −0.278116 | ||||||||
\(778\) | − | 10.0667i | − | 0.360907i | ||||||
\(779\) | −18.8368 | −0.674899 | ||||||||
\(780\) | −0.252943 | − | 16.6910i | −0.00905682 | − | 0.597633i | ||||
\(781\) | 36.3903 | 1.30215 | ||||||||
\(782\) | 1.36752i | 0.0489023i | ||||||||
\(783\) | −16.4769 | −0.588837 | ||||||||
\(784\) | 21.9353 | 0.783403 | ||||||||
\(785\) | − | 22.8177i | − | 0.814400i | ||||||
\(786\) | 4.04828i | 0.144397i | ||||||||
\(787\) | 32.9223i | 1.17355i | 0.809748 | + | 0.586777i | \(0.199604\pi\) | ||||
−0.809748 | + | 0.586777i | \(0.800396\pi\) | |||||||
\(788\) | − | 8.11313i | − | 0.289018i | ||||||
\(789\) | −12.0013 | −0.427257 | ||||||||
\(790\) | 9.04855 | 0.321933 | ||||||||
\(791\) | 2.41415i | 0.0858372i | ||||||||
\(792\) | 9.00236 | 0.319885 | ||||||||
\(793\) | −5.89562 | + | 0.0893450i | −0.209360 | + | 0.00317273i | ||||
\(794\) | 1.04540 | 0.0371000 | ||||||||
\(795\) | − | 16.6533i | − | 0.590632i | ||||||
\(796\) | 9.20405 | 0.326229 | ||||||||
\(797\) | −17.6438 | −0.624976 | −0.312488 | − | 0.949922i | \(-0.601162\pi\) | ||||
−0.312488 | + | 0.949922i | \(0.601162\pi\) | |||||||
\(798\) | − | 0.588201i | − | 0.0208221i | ||||||
\(799\) | 47.7480i | 1.68920i | ||||||||
\(800\) | 3.39099i | 0.119889i | ||||||||
\(801\) | − | 7.68902i | − | 0.271678i | ||||||
\(802\) | −8.47692 | −0.299331 | ||||||||
\(803\) | 55.8600 | 1.97126 | ||||||||
\(804\) | 29.4910i | 1.04007i | ||||||||
\(805\) | −1.26248 | −0.0444965 | ||||||||
\(806\) | −1.17977 | + | 0.0178789i | −0.0415558 | + | 0.000629756i | ||||
\(807\) | 7.23616 | 0.254725 | ||||||||
\(808\) | 23.0959i | 0.812510i | ||||||||
\(809\) | 29.2140 | 1.02711 | 0.513554 | − | 0.858057i | \(-0.328329\pi\) | ||||
0.513554 | + | 0.858057i | \(0.328329\pi\) | |||||||
\(810\) | 1.36399 | 0.0479255 | ||||||||
\(811\) | − | 29.2664i | − | 1.02768i | −0.857885 | − | 0.513841i | \(-0.828222\pi\) | ||
0.857885 | − | 0.513841i | \(-0.171778\pi\) | |||||||
\(812\) | 3.97098i | 0.139354i | ||||||||
\(813\) | − | 31.8585i | − | 1.11733i | ||||||
\(814\) | − | 13.8189i | − | 0.484351i | ||||||
\(815\) | −27.2748 | −0.955393 | ||||||||
\(816\) | 19.0710 | 0.667619 | ||||||||
\(817\) | − | 0.155019i | − | 0.00542342i | ||||||
\(818\) | 5.27883 | 0.184570 | ||||||||
\(819\) | 0.0584697 | + | 3.85825i | 0.00204310 | + | 0.134818i | ||||
\(820\) | −33.9266 | −1.18477 | ||||||||
\(821\) | 21.8487i | 0.762526i | 0.924467 | + | 0.381263i | \(0.124511\pi\) | ||||
−0.924467 | + | 0.381263i | \(0.875489\pi\) | |||||||
\(822\) | 0.880296 | 0.0307038 | ||||||||
\(823\) | 29.8070 | 1.03901 | 0.519504 | − | 0.854468i | \(-0.326117\pi\) | ||||
0.519504 | + | 0.854468i | \(0.326117\pi\) | |||||||
\(824\) | 3.05147i | 0.106303i | ||||||||
\(825\) | − | 5.19904i | − | 0.181007i | ||||||
\(826\) | − | 2.48451i | − | 0.0864472i | ||||||
\(827\) | − | 4.26809i | − | 0.148416i | −0.997243 | − | 0.0742080i | \(-0.976357\pi\) | ||
0.997243 | − | 0.0742080i | \(-0.0236429\pi\) | |||||||
\(828\) | 2.59255 | 0.0900975 | ||||||||
\(829\) | −5.79713 | −0.201343 | −0.100671 | − | 0.994920i | \(-0.532099\pi\) | ||||
−0.100671 | + | 0.994920i | \(0.532099\pi\) | |||||||
\(830\) | 2.95825i | 0.102683i | ||||||||
\(831\) | −17.3453 | −0.601701 | ||||||||
\(832\) | 19.9842 | − | 0.302850i | 0.692828 | − | 0.0104994i | ||||
\(833\) | −30.4059 | −1.05350 | ||||||||
\(834\) | − | 6.35524i | − | 0.220064i | ||||||
\(835\) | 33.9775 | 1.17584 | ||||||||
\(836\) | −18.5326 | −0.640964 | ||||||||
\(837\) | 5.49197i | 0.189830i | ||||||||
\(838\) | 7.72410i | 0.266825i | ||||||||
\(839\) | − | 50.9502i | − | 1.75900i | −0.475901 | − | 0.879499i | \(-0.657878\pi\) | ||
0.475901 | − | 0.879499i | \(-0.342122\pi\) | |||||||
\(840\) | − | 2.17873i | − | 0.0751732i | ||||||
\(841\) | −19.9989 | −0.689618 | ||||||||
\(842\) | 8.45556 | 0.291398 | ||||||||
\(843\) | − | 38.5978i | − | 1.32938i | ||||||
\(844\) | 7.80020 | 0.268494 | ||||||||
\(845\) | 0.794818 | + | 26.2179i | 0.0273426 | + | 0.901922i | ||||
\(846\) | −5.12124 | −0.176072 | ||||||||
\(847\) | 7.21352i | 0.247860i | ||||||||
\(848\) | 22.9383 | 0.787704 | ||||||||
\(849\) | 12.6143 | 0.432920 | ||||||||
\(850\) | − | 1.41962i | − | 0.0486926i | ||||||
\(851\) | − | 8.18444i | − | 0.280559i | ||||||
\(852\) | 18.0857i | 0.619606i | ||||||||
\(853\) | 26.7856i | 0.917120i | 0.888663 | + | 0.458560i | \(0.151635\pi\) | ||||
−0.888663 | + | 0.458560i | \(0.848365\pi\) | |||||||
\(854\) | −0.374201 | −0.0128049 | ||||||||
\(855\) | 6.54866 | 0.223959 | ||||||||
\(856\) | 19.5510i | 0.668239i | ||||||||
\(857\) | 26.6005 | 0.908655 | 0.454327 | − | 0.890835i | \(-0.349880\pi\) | ||||
0.454327 | + | 0.890835i | \(0.349880\pi\) | |||||||
\(858\) | 6.60287 | − | 0.100063i | 0.225418 | − | 0.00341610i | ||||
\(859\) | 38.5399 | 1.31496 | 0.657482 | − | 0.753470i | \(-0.271622\pi\) | ||||
0.657482 | + | 0.753470i | \(0.271622\pi\) | |||||||
\(860\) | − | 0.279201i | − | 0.00952067i | ||||||
\(861\) | −7.52929 | −0.256598 | ||||||||
\(862\) | 2.44890 | 0.0834097 | ||||||||
\(863\) | − | 41.5784i | − | 1.41534i | −0.706541 | − | 0.707672i | \(-0.749746\pi\) | ||
0.706541 | − | 0.707672i | \(-0.250254\pi\) | |||||||
\(864\) | 20.0477i | 0.682037i | ||||||||
\(865\) | 30.4469i | 1.03523i | ||||||||
\(866\) | 10.3215i | 0.350739i | ||||||||
\(867\) | −5.82802 | −0.197930 | ||||||||
\(868\) | 1.32358 | 0.0449252 | ||||||||
\(869\) | − | 63.2710i | − | 2.14632i | ||||||
\(870\) | −2.40135 | −0.0814134 | ||||||||
\(871\) | −0.702175 | − | 46.3345i | −0.0237923 | − | 1.56998i | ||||
\(872\) | −14.3071 | −0.484501 | ||||||||
\(873\) | 26.0823i | 0.882752i | ||||||||
\(874\) | 0.620981 | 0.0210050 | ||||||||
\(875\) | 8.36472 | 0.282779 | ||||||||
\(876\) | 27.7620i | 0.937992i | ||||||||
\(877\) | − | 15.5114i | − | 0.523782i | −0.965097 | − | 0.261891i | \(-0.915654\pi\) | ||
0.965097 | − | 0.261891i | \(-0.0843461\pi\) | |||||||
\(878\) | − | 4.92011i | − | 0.166046i | ||||||
\(879\) | 7.31495i | 0.246727i | ||||||||
\(880\) | −31.3835 | −1.05794 | ||||||||
\(881\) | −32.1828 | −1.08427 | −0.542133 | − | 0.840293i | \(-0.682383\pi\) | ||||
−0.542133 | + | 0.840293i | \(0.682383\pi\) | |||||||
\(882\) | − | 3.26121i | − | 0.109811i | ||||||
\(883\) | 24.1305 | 0.812056 | 0.406028 | − | 0.913861i | \(-0.366914\pi\) | ||||
0.406028 | + | 0.913861i | \(0.366914\pi\) | |||||||
\(884\) | −31.8682 | + | 0.482945i | −1.07184 | + | 0.0162432i | ||||
\(885\) | −26.5567 | −0.892693 | ||||||||
\(886\) | − | 12.7736i | − | 0.429138i | ||||||
\(887\) | −34.0446 | −1.14311 | −0.571553 | − | 0.820565i | \(-0.693659\pi\) | ||||
−0.571553 | + | 0.820565i | \(0.693659\pi\) | |||||||
\(888\) | 14.1243 | 0.473981 | ||||||||
\(889\) | − | 1.40184i | − | 0.0470163i | ||||||
\(890\) | − | 3.31706i | − | 0.111188i | ||||||
\(891\) | − | 9.53752i | − | 0.319519i | ||||||
\(892\) | − | 15.2041i | − | 0.509072i | ||||||
\(893\) | 21.6820 | 0.725562 | ||||||||
\(894\) | 0.748205 | 0.0250237 | ||||||||
\(895\) | − | 31.6908i | − | 1.05931i | ||||||
\(896\) | 6.37332 | 0.212918 | ||||||||
\(897\) | 3.91065 | − | 0.0592638i | 0.130573 | − | 0.00197876i | ||||
\(898\) | 4.05767 | 0.135406 | ||||||||
\(899\) | − | 3.00018i | − | 0.100062i | ||||||
\(900\) | −2.69133 | −0.0897110 | ||||||||
\(901\) | −31.7962 | −1.05929 | ||||||||
\(902\) | − | 13.4212i | − | 0.446876i | ||||||
\(903\) | − | 0.0619628i | − | 0.00206199i | ||||||
\(904\) | − | 4.39840i | − | 0.146289i | ||||||
\(905\) | − | 44.4927i | − | 1.47899i | ||||||
\(906\) | −0.464280 | −0.0154247 | ||||||||
\(907\) | 0.0424329 | 0.00140896 | 0.000704481 | − | 1.00000i | \(-0.499776\pi\) | ||||
0.000704481 | 1.00000i | \(0.499776\pi\) | ||||||||
\(908\) | − | 36.9970i | − | 1.22779i | ||||||
\(909\) | −27.7479 | −0.920341 | ||||||||
\(910\) | 0.0252240 | + | 1.66446i | 0.000836167 | + | 0.0551763i | ||||
\(911\) | −22.2458 | −0.737035 | −0.368517 | − | 0.929621i | \(-0.620134\pi\) | ||||
−0.368517 | + | 0.929621i | \(0.620134\pi\) | |||||||
\(912\) | − | 8.66001i | − | 0.286762i | ||||||
\(913\) | 20.6853 | 0.684583 | ||||||||
\(914\) | −11.4180 | −0.377673 | ||||||||
\(915\) | 3.99980i | 0.132229i | ||||||||
\(916\) | 4.74813i | 0.156883i | ||||||||
\(917\) | 7.13569i | 0.235641i | ||||||||
\(918\) | − | 8.39288i | − | 0.277006i | ||||||
\(919\) | 34.7094 | 1.14496 | 0.572478 | − | 0.819920i | \(-0.305982\pi\) | ||||
0.572478 | + | 0.819920i | \(0.305982\pi\) | |||||||
\(920\) | 2.30014 | 0.0758335 | ||||||||
\(921\) | − | 4.79352i | − | 0.157952i | ||||||
\(922\) | 4.65486 | 0.153300 | ||||||||
\(923\) | −0.430617 | − | 28.4152i | −0.0141739 | − | 0.935298i | ||||
\(924\) | −7.40771 | −0.243696 | ||||||||
\(925\) | 8.49627i | 0.279356i | ||||||||
\(926\) | −12.3206 | −0.404880 | ||||||||
\(927\) | −3.66612 | −0.120411 | ||||||||
\(928\) | − | 10.9518i | − | 0.359509i | ||||||
\(929\) | − | 7.00242i | − | 0.229742i | −0.993380 | − | 0.114871i | \(-0.963355\pi\) | ||
0.993380 | − | 0.114871i | \(-0.0366455\pi\) | |||||||
\(930\) | 0.800402i | 0.0262462i | ||||||||
\(931\) | 13.8071i | 0.452511i | ||||||||
\(932\) | 27.2368 | 0.892172 | ||||||||
\(933\) | −26.7562 | −0.875960 | ||||||||
\(934\) | − | 4.98103i | − | 0.162984i | ||||||
\(935\) | 43.5027 | 1.42269 | ||||||||
\(936\) | −0.106528 | − | 7.02945i | −0.00348196 | − | 0.229765i | ||||
\(937\) | 9.69248 | 0.316640 | 0.158320 | − | 0.987388i | \(-0.449392\pi\) | ||||
0.158320 | + | 0.987388i | \(0.449392\pi\) | |||||||
\(938\) | − | 2.94090i | − | 0.0960238i | ||||||
\(939\) | 37.1321 | 1.21176 | ||||||||
\(940\) | 39.0510 | 1.27370 | ||||||||
\(941\) | − | 17.1945i | − | 0.560526i | −0.959923 | − | 0.280263i | \(-0.909578\pi\) | ||
0.959923 | − | 0.280263i | \(-0.0904217\pi\) | |||||||
\(942\) | 4.48615i | 0.146167i | ||||||||
\(943\) | − | 7.94889i | − | 0.258852i | ||||||
\(944\) | − | 36.5792i | − | 1.19055i | ||||||
\(945\) | 7.74822 | 0.252050 | ||||||||
\(946\) | 0.110450 | 0.00359105 | ||||||||
\(947\) | − | 23.8643i | − | 0.775486i | −0.921767 | − | 0.387743i | \(-0.873255\pi\) | ||
0.921767 | − | 0.387743i | \(-0.126745\pi\) | |||||||
\(948\) | 31.4452 | 1.02129 | ||||||||
\(949\) | −0.661009 | − | 43.6181i | −0.0214572 | − | 1.41590i | ||||
\(950\) | −0.644640 | −0.0209149 | ||||||||
\(951\) | 9.13589i | 0.296252i | ||||||||
\(952\) | −4.15985 | −0.134821 | ||||||||
\(953\) | −46.8342 | −1.51711 | −0.758554 | − | 0.651610i | \(-0.774094\pi\) | ||||
−0.758554 | + | 0.651610i | \(0.774094\pi\) | |||||||
\(954\) | − | 3.41032i | − | 0.110413i | ||||||
\(955\) | − | 9.97922i | − | 0.322920i | ||||||
\(956\) | 11.8957i | 0.384734i | ||||||||
\(957\) | 16.7912i | 0.542782i | ||||||||
\(958\) | 1.62746 | 0.0525810 | ||||||||
\(959\) | 1.55165 | 0.0501055 | ||||||||
\(960\) | − | 13.5580i | − | 0.437583i | ||||||
\(961\) | −1.00000 | −0.0322581 | ||||||||
\(962\) | −10.7904 | + | 0.163523i | −0.347897 | + | 0.00527219i | ||||
\(963\) | −23.4890 | −0.756924 | ||||||||
\(964\) | 8.63960i | 0.278263i | ||||||||
\(965\) | −38.9039 | −1.25236 | ||||||||
\(966\) | 0.248213 | 0.00798613 | ||||||||
\(967\) | 27.3105i | 0.878247i | 0.898427 | + | 0.439123i | \(0.144711\pi\) | ||||
−0.898427 | + | 0.439123i | \(0.855289\pi\) | |||||||
\(968\) | − | 13.1425i | − | 0.422417i | ||||||
\(969\) | 12.0042i | 0.385631i | ||||||||
\(970\) | 11.2520i | 0.361279i | ||||||||
\(971\) | −9.70031 | −0.311298 | −0.155649 | − | 0.987812i | \(-0.549747\pi\) | ||||
−0.155649 | + | 0.987812i | \(0.549747\pi\) | |||||||
\(972\) | −26.4473 | −0.848298 | ||||||||
\(973\) | − | 11.2021i | − | 0.359121i | ||||||
\(974\) | 4.18729 | 0.134169 | ||||||||
\(975\) | −4.05965 | + | 0.0615218i | −0.130013 | + | 0.00197027i | ||||
\(976\) | −5.50932 | −0.176349 | ||||||||
\(977\) | − | 28.0246i | − | 0.896586i | −0.893887 | − | 0.448293i | \(-0.852032\pi\) | ||
0.893887 | − | 0.448293i | \(-0.147968\pi\) | |||||||
\(978\) | 5.36243 | 0.171472 | ||||||||
\(979\) | −23.1942 | −0.741290 | ||||||||
\(980\) | 24.8677i | 0.794370i | ||||||||
\(981\) | − | 17.1890i | − | 0.548801i | ||||||
\(982\) | 5.77877i | 0.184408i | ||||||||
\(983\) | 53.8397i | 1.71722i | 0.512629 | + | 0.858611i | \(0.328672\pi\) | ||||
−0.512629 | + | 0.858611i | \(0.671328\pi\) | |||||||
\(984\) | 13.7178 | 0.437308 | ||||||||
\(985\) | 8.64793 | 0.275546 | ||||||||
\(986\) | 4.58491i | 0.146013i | ||||||||
\(987\) | 8.66656 | 0.275860 | ||||||||
\(988\) | 0.219302 | + | 14.4711i | 0.00697693 | + | 0.460388i | ||||
\(989\) | 0.0654159 | 0.00208011 | ||||||||
\(990\) | 4.66590i | 0.148292i | ||||||||
\(991\) | 18.9399 | 0.601644 | 0.300822 | − | 0.953680i | \(-0.402739\pi\) | ||||
0.300822 | + | 0.953680i | \(0.402739\pi\) | |||||||
\(992\) | −3.65037 | −0.115899 | ||||||||
\(993\) | − | 12.9353i | − | 0.410491i | ||||||
\(994\) | − | 1.80354i | − | 0.0572049i | ||||||
\(995\) | 9.81076i | 0.311022i | ||||||||
\(996\) | 10.2804i | 0.325748i | ||||||||
\(997\) | 21.3281 | 0.675468 | 0.337734 | − | 0.941242i | \(-0.390340\pi\) | ||||
0.337734 | + | 0.941242i | \(0.390340\pi\) | |||||||
\(998\) | −6.28993 | −0.199104 | ||||||||
\(999\) | 50.2304i | 1.58922i |
(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 | 403.2.c.b.311.17 | yes | 32 | |
13.5 | odd | 4 | 5239.2.a.k.1.10 | 16 | |||
13.8 | odd | 4 | 5239.2.a.l.1.7 | 16 | |||
13.12 | even | 2 | inner | 403.2.c.b.311.16 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
403.2.c.b.311.16 | ✓ | 32 | 13.12 | even | 2 | inner | |
403.2.c.b.311.17 | yes | 32 | 1.1 | even | 1 | trivial | |
5239.2.a.k.1.10 | 16 | 13.5 | odd | 4 | |||
5239.2.a.l.1.7 | 16 | 13.8 | odd | 4 |