Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(99,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.99");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.u (of order \(18\), degree \(6\), 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: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 190) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 499.3 | ||
Character | \(\chi\) | \(=\) | 950.499 |
Dual form | 950.2.u.e.99.3 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{8}{9}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.342020 | + | 0.939693i | 0.241845 | + | 0.664463i | ||||
\(3\) | −1.31143 | − | 0.231240i | −0.757154 | − | 0.133507i | −0.218272 | − | 0.975888i | \(-0.570042\pi\) |
−0.538882 | + | 0.842381i | \(0.681153\pi\) | |||||||
\(4\) | −0.766044 | + | 0.642788i | −0.383022 | + | 0.321394i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.231240 | − | 1.31143i | −0.0944035 | − | 0.535389i | ||||
\(7\) | 2.05411 | − | 1.18594i | 0.776380 | − | 0.448243i | −0.0587655 | − | 0.998272i | \(-0.518716\pi\) |
0.835146 | + | 0.550028i | \(0.185383\pi\) | |||||||
\(8\) | −0.866025 | − | 0.500000i | −0.306186 | − | 0.176777i | ||||
\(9\) | −1.15270 | − | 0.419550i | −0.384235 | − | 0.139850i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.33676 | + | 2.31534i | −0.403049 | + | 0.698102i | −0.994092 | − | 0.108538i | \(-0.965383\pi\) |
0.591043 | + | 0.806640i | \(0.298716\pi\) | |||||||
\(12\) | 1.15325 | − | 0.665830i | 0.332915 | − | 0.192209i | ||||
\(13\) | 0.955868 | − | 0.168545i | 0.265110 | − | 0.0467460i | −0.0395130 | − | 0.999219i | \(-0.512581\pi\) |
0.304623 | + | 0.952473i | \(0.401470\pi\) | |||||||
\(14\) | 1.81697 | + | 1.52462i | 0.485605 | + | 0.407471i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.173648 | − | 0.984808i | 0.0434120 | − | 0.246202i | ||||
\(17\) | 1.93170 | + | 5.30729i | 0.468505 | + | 1.28721i | 0.918940 | + | 0.394398i | \(0.129047\pi\) |
−0.450435 | + | 0.892809i | \(0.648731\pi\) | |||||||
\(18\) | − | 1.22668i | − | 0.289132i | ||||||
\(19\) | −2.94212 | − | 3.21620i | −0.674968 | − | 0.737847i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.96806 | + | 1.08028i | −0.647683 | + | 0.235737i | ||||
\(22\) | −2.63291 | − | 0.464253i | −0.561338 | − | 0.0989791i | ||||
\(23\) | 5.49663 | + | 6.55063i | 1.14613 | + | 1.36590i | 0.920054 | + | 0.391791i | \(0.128144\pi\) |
0.226073 | + | 0.974110i | \(0.427411\pi\) | |||||||
\(24\) | 1.02011 | + | 0.855975i | 0.208229 | + | 0.174725i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.485307 | + | 0.840576i | 0.0951765 | + | 0.164850i | ||||
\(27\) | 4.87443 | + | 2.81425i | 0.938084 | + | 0.541603i | ||||
\(28\) | −0.811231 | + | 2.22884i | −0.153308 | + | 0.421211i | ||||
\(29\) | 0.0701275 | + | 0.0255243i | 0.0130224 | + | 0.00473975i | 0.348523 | − | 0.937300i | \(-0.386683\pi\) |
−0.335501 | + | 0.942040i | \(0.608906\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.00986693 | + | 0.0170900i | 0.00177215 | + | 0.00306946i | 0.866910 | − | 0.498464i | \(-0.166103\pi\) |
−0.865138 | + | 0.501534i | \(0.832769\pi\) | |||||||
\(32\) | 0.984808 | − | 0.173648i | 0.174091 | − | 0.0306970i | ||||
\(33\) | 2.28847 | − | 2.72729i | 0.398372 | − | 0.474761i | ||||
\(34\) | −4.32654 | + | 3.63040i | −0.741996 | + | 0.622609i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.15270 | − | 0.419550i | 0.192117 | − | 0.0699250i | ||||
\(37\) | 1.17396i | 0.192997i | 0.995333 | + | 0.0964987i | \(0.0307644\pi\) | ||||
−0.995333 | + | 0.0964987i | \(0.969236\pi\) | |||||||
\(38\) | 2.01598 | − | 3.86469i | 0.327034 | − | 0.626936i | ||||
\(39\) | −1.29253 | −0.206970 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.90311 | + | 10.7931i | −0.297216 | + | 1.68560i | 0.360840 | + | 0.932628i | \(0.382490\pi\) |
−0.658056 | + | 0.752969i | \(0.728621\pi\) | |||||||
\(42\) | −2.03027 | − | 2.41958i | −0.313278 | − | 0.373350i | ||||
\(43\) | −3.69269 | + | 4.40077i | −0.563130 | + | 0.671112i | −0.970206 | − | 0.242283i | \(-0.922104\pi\) |
0.407076 | + | 0.913394i | \(0.366548\pi\) | |||||||
\(44\) | −0.464253 | − | 2.63291i | −0.0699888 | − | 0.396926i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.27562 | + | 7.40559i | −0.630406 | + | 1.09190i | ||||
\(47\) | −1.79973 | + | 4.94471i | −0.262517 | + | 0.721260i | 0.736479 | + | 0.676461i | \(0.236487\pi\) |
−0.998996 | + | 0.0447996i | \(0.985735\pi\) | |||||||
\(48\) | −0.455455 | + | 1.25135i | −0.0657392 | + | 0.180617i | ||||
\(49\) | −0.687089 | + | 1.19007i | −0.0981556 | + | 0.170010i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.30602 | − | 7.40682i | −0.182880 | − | 1.03716i | ||||
\(52\) | −0.623898 | + | 0.743533i | −0.0865191 | + | 0.103109i | ||||
\(53\) | 0.0572129 | + | 0.0681837i | 0.00785879 | + | 0.00936575i | 0.769960 | − | 0.638093i | \(-0.220276\pi\) |
−0.762101 | + | 0.647458i | \(0.775832\pi\) | |||||||
\(54\) | −0.977379 | + | 5.54299i | −0.133004 | + | 0.754306i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.37188 | −0.316956 | ||||||||
\(57\) | 3.11466 | + | 4.89815i | 0.412547 | + | 0.648776i | ||||
\(58\) | 0.0746282i | 0.00979916i | ||||||||
\(59\) | 10.0952 | − | 3.67436i | 1.31429 | − | 0.478361i | 0.412663 | − | 0.910884i | \(-0.364599\pi\) |
0.901623 | + | 0.432523i | \(0.142377\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.12774 | + | 5.14179i | −0.784577 | + | 0.658339i | −0.944397 | − | 0.328808i | \(-0.893353\pi\) |
0.159820 | + | 0.987146i | \(0.448909\pi\) | |||||||
\(62\) | −0.0126847 | + | 0.0151170i | −0.00161096 | + | 0.00191986i | ||||
\(63\) | −2.86534 | + | 0.505237i | −0.360999 | + | 0.0636539i | ||||
\(64\) | 0.500000 | + | 0.866025i | 0.0625000 | + | 0.108253i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.34552 | + | 1.21767i | 0.411805 | + | 0.149885i | ||||
\(67\) | 1.74678 | − | 4.79924i | 0.213403 | − | 0.586321i | −0.786091 | − | 0.618111i | \(-0.787898\pi\) |
0.999495 | + | 0.0317896i | \(0.0101206\pi\) | |||||||
\(68\) | −4.89123 | − | 2.82395i | −0.593148 | − | 0.342454i | ||||
\(69\) | −5.69367 | − | 9.86173i | −0.685438 | − | 1.18721i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.95955 | − | 6.67886i | −0.944625 | − | 0.792635i | 0.0337592 | − | 0.999430i | \(-0.489252\pi\) |
−0.978384 | + | 0.206795i | \(0.933697\pi\) | |||||||
\(72\) | 0.788496 | + | 0.939693i | 0.0929251 | + | 0.110744i | ||||
\(73\) | −8.38420 | − | 1.47836i | −0.981296 | − | 0.173029i | −0.340086 | − | 0.940394i | \(-0.610456\pi\) |
−0.641210 | + | 0.767365i | \(0.721567\pi\) | |||||||
\(74\) | −1.10316 | + | 0.401517i | −0.128240 | + | 0.0466754i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.32113 | + | 0.572595i | 0.495667 | + | 0.0656811i | ||||
\(77\) | 6.34129i | 0.722657i | ||||||||
\(78\) | −0.442070 | − | 1.21458i | −0.0500546 | − | 0.137524i | ||||
\(79\) | −2.75957 | + | 15.6503i | −0.310476 | + | 1.76079i | 0.286063 | + | 0.958211i | \(0.407653\pi\) |
−0.596539 | + | 0.802584i | \(0.703458\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.92262 | − | 2.45237i | −0.324735 | − | 0.272485i | ||||
\(82\) | −10.7931 | + | 1.90311i | −1.19190 | + | 0.210164i | ||||
\(83\) | 5.08485 | − | 2.93574i | 0.558134 | − | 0.322239i | −0.194262 | − | 0.980950i | \(-0.562231\pi\) |
0.752396 | + | 0.658711i | \(0.228898\pi\) | |||||||
\(84\) | 1.57927 | − | 2.73538i | 0.172312 | − | 0.298454i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.39835 | − | 1.96484i | −0.582119 | − | 0.211874i | ||||
\(87\) | −0.0860650 | − | 0.0496897i | −0.00922714 | − | 0.00532729i | ||||
\(88\) | 2.31534 | − | 1.33676i | 0.246816 | − | 0.142499i | ||||
\(89\) | 0.149473 | + | 0.847706i | 0.0158442 | + | 0.0898567i | 0.991704 | − | 0.128539i | \(-0.0410288\pi\) |
−0.975860 | + | 0.218396i | \(0.929918\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.76357 | − | 1.47981i | 0.184873 | − | 0.155127i | ||||
\(92\) | −8.42133 | − | 1.48491i | −0.877984 | − | 0.154812i | ||||
\(93\) | −0.00898788 | − | 0.0246940i | −0.000932000 | − | 0.00256065i | ||||
\(94\) | −5.26205 | −0.542739 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.33166 | −0.135912 | ||||||||
\(97\) | 3.79863 | + | 10.4367i | 0.385692 | + | 1.05968i | 0.968920 | + | 0.247373i | \(0.0795672\pi\) |
−0.583228 | + | 0.812309i | \(0.698211\pi\) | |||||||
\(98\) | −1.35330 | − | 0.238624i | −0.136704 | − | 0.0241046i | ||||
\(99\) | 2.51229 | − | 2.10806i | 0.252495 | − | 0.211868i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.748963 | + | 4.24758i | 0.0745246 | + | 0.422650i | 0.999129 | + | 0.0417220i | \(0.0132844\pi\) |
−0.924605 | + | 0.380928i | \(0.875604\pi\) | |||||||
\(102\) | 6.51345 | − | 3.76054i | 0.644928 | − | 0.372349i | ||||
\(103\) | 0.0151012 | + | 0.00871870i | 0.00148797 | + | 0.000859079i | 0.500744 | − | 0.865596i | \(-0.333060\pi\) |
−0.499256 | + | 0.866455i | \(0.666393\pi\) | |||||||
\(104\) | −0.912078 | − | 0.331969i | −0.0894366 | − | 0.0325523i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.0445037 | + | 0.0770827i | −0.00432258 | + | 0.00748693i | ||||
\(107\) | 9.97826 | − | 5.76095i | 0.964635 | − | 0.556932i | 0.0670387 | − | 0.997750i | \(-0.478645\pi\) |
0.897597 | + | 0.440818i | \(0.145312\pi\) | |||||||
\(108\) | −5.54299 | + | 0.977379i | −0.533375 | + | 0.0940484i | ||||
\(109\) | 7.16924 | + | 6.01570i | 0.686688 | + | 0.576200i | 0.917952 | − | 0.396691i | \(-0.129842\pi\) |
−0.231264 | + | 0.972891i | \(0.574286\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.271466 | − | 1.53956i | 0.0257664 | − | 0.146129i | ||||
\(112\) | −0.811231 | − | 2.22884i | −0.0766541 | − | 0.210606i | ||||
\(113\) | − | 9.03320i | − | 0.849772i | −0.905247 | − | 0.424886i | \(-0.860314\pi\) | ||
0.905247 | − | 0.424886i | \(-0.139686\pi\) | |||||||
\(114\) | −3.53748 | + | 4.60209i | −0.331315 | + | 0.431026i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.0701275 | + | 0.0255243i | −0.00651118 | + | 0.00236987i | ||||
\(117\) | −1.17255 | − | 0.206751i | −0.108402 | − | 0.0191142i | ||||
\(118\) | 6.90554 | + | 8.22970i | 0.635706 | + | 0.757605i | ||||
\(119\) | 10.2620 | + | 8.61088i | 0.940721 | + | 0.789358i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.92613 | + | 3.33615i | 0.175103 | + | 0.303287i | ||||
\(122\) | −6.92751 | − | 3.99960i | −0.627188 | − | 0.362107i | ||||
\(123\) | 4.99159 | − | 13.7143i | 0.450077 | − | 1.23658i | ||||
\(124\) | −0.0185438 | − | 0.00674938i | −0.00166528 | − | 0.000606112i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.45477 | − | 2.51974i | −0.129601 | − | 0.224476i | ||||
\(127\) | 9.23057 | − | 1.62760i | 0.819081 | − | 0.144426i | 0.251620 | − | 0.967826i | \(-0.419037\pi\) |
0.567461 | + | 0.823400i | \(0.307926\pi\) | |||||||
\(128\) | −0.642788 | + | 0.766044i | −0.0568149 | + | 0.0677094i | ||||
\(129\) | 5.86033 | − | 4.91740i | 0.515974 | − | 0.432953i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.87062 | − | 2.13673i | 0.512919 | − | 0.186687i | −0.0725767 | − | 0.997363i | \(-0.523122\pi\) |
0.585496 | + | 0.810676i | \(0.300900\pi\) | |||||||
\(132\) | 3.56023i | 0.309878i | ||||||||
\(133\) | −9.85766 | − | 3.11725i | −0.854767 | − | 0.270300i | ||||
\(134\) | 5.10725 | 0.441199 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.980748 | − | 5.56210i | 0.0840984 | − | 0.476946i | ||||
\(137\) | −9.56600 | − | 11.4003i | −0.817279 | − | 0.973995i | 0.182679 | − | 0.983173i | \(-0.441523\pi\) |
−0.999958 | + | 0.00917780i | \(0.997079\pi\) | |||||||
\(138\) | 7.31965 | − | 8.72322i | 0.623090 | − | 0.742569i | ||||
\(139\) | −1.87014 | − | 10.6061i | −0.158624 | − | 0.899599i | −0.955398 | − | 0.295322i | \(-0.904573\pi\) |
0.796774 | − | 0.604277i | \(-0.206538\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.50363 | − | 6.06847i | 0.295059 | − | 0.511057i | ||||
\(142\) | 3.55375 | − | 9.76384i | 0.298224 | − | 0.819363i | ||||
\(143\) | −0.887529 | + | 2.43846i | −0.0742189 | + | 0.203915i | ||||
\(144\) | −0.613341 | + | 1.06234i | −0.0511117 | + | 0.0885281i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.47836 | − | 8.38420i | −0.122350 | − | 0.693881i | ||||
\(147\) | 1.17626 | − | 1.40181i | 0.0970164 | − | 0.115620i | ||||
\(148\) | −0.754605 | − | 0.899304i | −0.0620282 | − | 0.0739223i | ||||
\(149\) | 2.81132 | − | 15.9438i | 0.230313 | − | 1.30617i | −0.621951 | − | 0.783056i | \(-0.713660\pi\) |
0.852264 | − | 0.523112i | \(-0.175229\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.11979 | 0.498022 | 0.249011 | − | 0.968501i | \(-0.419895\pi\) | ||||
0.249011 | + | 0.968501i | \(0.419895\pi\) | |||||||
\(152\) | 0.939849 | + | 4.25637i | 0.0762318 | + | 0.345237i | ||||
\(153\) | − | 6.92818i | − | 0.560110i | ||||||
\(154\) | −5.95886 | + | 2.16885i | −0.480179 | + | 0.174771i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.990133 | − | 0.830820i | 0.0792741 | − | 0.0665189i | ||||
\(157\) | 13.5539 | − | 16.1529i | 1.08172 | − | 1.28914i | 0.126910 | − | 0.991914i | \(-0.459494\pi\) |
0.954807 | − | 0.297226i | \(-0.0960615\pi\) | |||||||
\(158\) | −15.6503 | + | 2.75957i | −1.24507 | + | 0.219539i | ||||
\(159\) | −0.0592638 | − | 0.102648i | −0.00469993 | − | 0.00814051i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 19.0594 | + | 6.93704i | 1.50209 | + | 0.546715i | ||||
\(162\) | 1.30488 | − | 3.58512i | 0.102521 | − | 0.281674i | ||||
\(163\) | 14.0402 | + | 8.10611i | 1.09971 | + | 0.634920i | 0.936146 | − | 0.351612i | \(-0.114367\pi\) |
0.163567 | + | 0.986532i | \(0.447700\pi\) | |||||||
\(164\) | −5.47979 | − | 9.49128i | −0.427900 | − | 0.741144i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.49781 | + | 3.77411i | 0.349098 | + | 0.292928i | ||||
\(167\) | 0.300481 | + | 0.358099i | 0.0232519 | + | 0.0277106i | 0.777545 | − | 0.628827i | \(-0.216465\pi\) |
−0.754293 | + | 0.656538i | \(0.772020\pi\) | |||||||
\(168\) | 3.11055 | + | 0.548475i | 0.239984 | + | 0.0423157i | ||||
\(169\) | −11.3307 | + | 4.12405i | −0.871595 | + | 0.317234i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.04203 | + | 4.94169i | 0.156158 | + | 0.377900i | ||||
\(172\) | − | 5.74480i | − | 0.438037i | ||||||
\(173\) | 8.79654 | + | 24.1683i | 0.668788 | + | 1.83748i | 0.531721 | + | 0.846919i | \(0.321545\pi\) |
0.137067 | + | 0.990562i | \(0.456232\pi\) | |||||||
\(174\) | 0.0172570 | − | 0.0978695i | 0.00130825 | − | 0.00741947i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.04804 | + | 1.71851i | 0.154377 | + | 0.129538i | ||||
\(177\) | −14.0888 | + | 2.48424i | −1.05898 | + | 0.186727i | ||||
\(178\) | −0.745460 | + | 0.430392i | −0.0558746 | + | 0.0322592i | ||||
\(179\) | 7.08189 | − | 12.2662i | 0.529325 | − | 0.916818i | −0.470090 | − | 0.882619i | \(-0.655779\pi\) |
0.999415 | − | 0.0341995i | \(-0.0108882\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.32396 | − | 2.66570i | −0.544386 | − | 0.198140i | 0.0551645 | − | 0.998477i | \(-0.482432\pi\) |
−0.599550 | + | 0.800337i | \(0.704654\pi\) | |||||||
\(182\) | 1.99375 | + | 1.15109i | 0.147786 | + | 0.0853245i | ||||
\(183\) | 9.22509 | − | 5.32611i | 0.681938 | − | 0.393717i | ||||
\(184\) | −1.48491 | − | 8.42133i | −0.109469 | − | 0.620829i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.0201307 | − | 0.0168917i | 0.00147606 | − | 0.00123856i | ||||
\(187\) | −14.8704 | − | 2.62205i | −1.08743 | − | 0.191744i | ||||
\(188\) | −1.79973 | − | 4.94471i | −0.131259 | − | 0.360630i | ||||
\(189\) | 13.3501 | 0.971080 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.264057 | −0.0191065 | −0.00955326 | − | 0.999954i | \(-0.503041\pi\) | ||||
−0.00955326 | + | 0.999954i | \(0.503041\pi\) | |||||||
\(192\) | −0.455455 | − | 1.25135i | −0.0328696 | − | 0.0903085i | ||||
\(193\) | 3.07060 | + | 0.541429i | 0.221027 | + | 0.0389729i | 0.283065 | − | 0.959101i | \(-0.408649\pi\) |
−0.0620381 | + | 0.998074i | \(0.519760\pi\) | |||||||
\(194\) | −8.50804 | + | 7.13909i | −0.610841 | + | 0.512557i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.238624 | − | 1.35330i | −0.0170445 | − | 0.0966644i | ||||
\(197\) | −18.1672 | + | 10.4888i | −1.29436 | + | 0.747298i | −0.979424 | − | 0.201816i | \(-0.935316\pi\) |
−0.314934 | + | 0.949113i | \(0.601982\pi\) | |||||||
\(198\) | 2.84019 | + | 1.63978i | 0.201843 | + | 0.116534i | ||||
\(199\) | −20.6330 | − | 7.50979i | −1.46263 | − | 0.532355i | −0.516544 | − | 0.856260i | \(-0.672782\pi\) |
−0.946090 | + | 0.323905i | \(0.895004\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.40056 | + | 5.88994i | −0.239857 | + | 0.415444i | ||||
\(202\) | −3.73526 | + | 2.15655i | −0.262812 | + | 0.151735i | ||||
\(203\) | 0.174320 | − | 0.0307373i | 0.0122349 | − | 0.00215734i | ||||
\(204\) | 5.76149 | + | 4.83446i | 0.403385 | + | 0.338480i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.00302797 | + | 0.0171725i | −0.000210969 | + | 0.00119646i | ||||
\(207\) | −3.58767 | − | 9.85705i | −0.249360 | − | 0.685112i | ||||
\(208\) | − | 0.970613i | − | 0.0672999i | ||||||
\(209\) | 11.3795 | − | 2.51271i | 0.787137 | − | 0.173808i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.1676 | − | 4.79262i | 0.906497 | − | 0.329938i | 0.153644 | − | 0.988126i | \(-0.450899\pi\) |
0.752853 | + | 0.658189i | \(0.228677\pi\) | |||||||
\(212\) | −0.0876552 | − | 0.0154560i | −0.00602019 | − | 0.00106152i | ||||
\(213\) | 8.89397 | + | 10.5994i | 0.609405 | + | 0.726260i | ||||
\(214\) | 8.82629 | + | 7.40614i | 0.603353 | + | 0.506273i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.81425 | − | 4.87443i | −0.191486 | − | 0.331663i | ||||
\(217\) | 0.0405355 | + | 0.0234032i | 0.00275173 | + | 0.00158871i | ||||
\(218\) | −3.20089 | + | 8.79437i | −0.216792 | + | 0.595630i | ||||
\(219\) | 10.6534 | + | 3.87753i | 0.719892 | + | 0.262019i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.74096 | + | 4.74749i | 0.184377 | + | 0.319351i | ||||
\(222\) | 1.53956 | − | 0.271466i | 0.103329 | − | 0.0182196i | ||||
\(223\) | 10.1108 | − | 12.0495i | 0.677067 | − | 0.806897i | −0.312661 | − | 0.949865i | \(-0.601220\pi\) |
0.989727 | + | 0.142968i | \(0.0456647\pi\) | |||||||
\(224\) | 1.81697 | − | 1.52462i | 0.121401 | − | 0.101868i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.48843 | − | 3.08954i | 0.564642 | − | 0.205513i | ||||
\(227\) | − | 8.01180i | − | 0.531762i | −0.964006 | − | 0.265881i | \(-0.914337\pi\) | ||
0.964006 | − | 0.265881i | \(-0.0856628\pi\) | |||||||
\(228\) | −5.53444 | − | 1.75014i | −0.366528 | − | 0.115906i | ||||
\(229\) | −19.8826 | −1.31388 | −0.656939 | − | 0.753944i | \(-0.728149\pi\) | ||||
−0.656939 | + | 0.753944i | \(0.728149\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.46636 | − | 8.31615i | 0.0964795 | − | 0.547162i | ||||
\(232\) | −0.0479701 | − | 0.0571685i | −0.00314939 | − | 0.00375330i | ||||
\(233\) | −16.0364 | + | 19.1114i | −1.05058 | + | 1.25203i | −0.0837839 | + | 0.996484i | \(0.526701\pi\) |
−0.966796 | + | 0.255549i | \(0.917744\pi\) | |||||||
\(234\) | −0.206751 | − | 1.17255i | −0.0135158 | − | 0.0766517i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −5.37155 | + | 9.30380i | −0.349658 | + | 0.605626i | ||||
\(237\) | 7.23796 | − | 19.8861i | 0.470156 | − | 1.29174i | ||||
\(238\) | −4.58175 | + | 12.5883i | −0.296991 | + | 0.815976i | ||||
\(239\) | 5.32201 | − | 9.21799i | 0.344252 | − | 0.596262i | −0.640965 | − | 0.767570i | \(-0.721466\pi\) |
0.985218 | + | 0.171307i | \(0.0547991\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.91741 | − | 16.5454i | −0.187927 | − | 1.06579i | −0.922137 | − | 0.386863i | \(-0.873559\pi\) |
0.734210 | − | 0.678922i | \(-0.237553\pi\) | |||||||
\(242\) | −2.47618 | + | 2.95100i | −0.159175 | + | 0.189698i | ||||
\(243\) | −7.58808 | − | 9.04312i | −0.486775 | − | 0.580116i | ||||
\(244\) | 1.38905 | − | 7.87768i | 0.0889246 | − | 0.504317i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 14.5944 | 0.930507 | ||||||||
\(247\) | −3.35435 | − | 2.57838i | −0.213432 | − | 0.164058i | ||||
\(248\) | − | 0.0197339i | − | 0.00125310i | ||||||
\(249\) | −7.34728 | + | 2.67419i | −0.465615 | + | 0.169470i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.3801 | − | 14.5836i | 1.09702 | − | 0.920508i | 0.0997980 | − | 0.995008i | \(-0.468180\pi\) |
0.997221 | + | 0.0744994i | \(0.0237359\pi\) | |||||||
\(252\) | 1.87022 | − | 2.22884i | 0.117813 | − | 0.140404i | ||||
\(253\) | −22.5146 | + | 3.96994i | −1.41548 | + | 0.249588i | ||||
\(254\) | 4.68648 | + | 8.11723i | 0.294056 | + | 0.509320i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.939693 | − | 0.342020i | −0.0587308 | − | 0.0213763i | ||||
\(257\) | −7.71712 | + | 21.2026i | −0.481380 | + | 1.32258i | 0.426930 | + | 0.904285i | \(0.359595\pi\) |
−0.908310 | + | 0.418297i | \(0.862627\pi\) | |||||||
\(258\) | 6.62520 | + | 3.82506i | 0.412467 | + | 0.238138i | ||||
\(259\) | 1.39224 | + | 2.41144i | 0.0865099 | + | 0.149839i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.0701275 | − | 0.0588440i | −0.00434079 | − | 0.00364235i | ||||
\(262\) | 4.01574 | + | 4.78578i | 0.248093 | + | 0.295666i | ||||
\(263\) | 8.31518 | + | 1.46619i | 0.512736 | + | 0.0904091i | 0.424029 | − | 0.905649i | \(-0.360615\pi\) |
0.0887068 | + | 0.996058i | \(0.471727\pi\) | |||||||
\(264\) | −3.34552 | + | 1.21767i | −0.205902 | + | 0.0749424i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.442261 | − | 10.3293i | −0.0271168 | − | 0.633332i | ||||
\(267\) | − | 1.14627i | − | 0.0701506i | ||||||
\(268\) | 1.74678 | + | 4.79924i | 0.106702 | + | 0.293160i | ||||
\(269\) | −4.57571 | + | 25.9501i | −0.278986 | + | 1.58221i | 0.447024 | + | 0.894522i | \(0.352484\pi\) |
−0.726010 | + | 0.687684i | \(0.758627\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.465903 | − | 0.390939i | −0.0283016 | − | 0.0237479i | 0.628527 | − | 0.777788i | \(-0.283658\pi\) |
−0.656829 | + | 0.754040i | \(0.728103\pi\) | |||||||
\(272\) | 5.56210 | − | 0.980748i | 0.337252 | − | 0.0594666i | ||||
\(273\) | −2.65499 | + | 1.53286i | −0.160687 | + | 0.0927729i | ||||
\(274\) | 7.44103 | − | 12.8882i | 0.449529 | − | 0.778607i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 10.7006 | + | 3.89470i | 0.644101 | + | 0.234434i | ||||
\(277\) | −5.89679 | − | 3.40451i | −0.354304 | − | 0.204557i | 0.312275 | − | 0.949992i | \(-0.398909\pi\) |
−0.666579 | + | 0.745434i | \(0.732242\pi\) | |||||||
\(278\) | 9.32686 | − | 5.38487i | 0.559388 | − | 0.322963i | ||||
\(279\) | −0.00420353 | − | 0.0238394i | −0.000251659 | − | 0.00142723i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.7616 | − | 15.7429i | 1.11922 | − | 0.939141i | 0.120659 | − | 0.992694i | \(-0.461499\pi\) |
0.998565 | + | 0.0535531i | \(0.0170546\pi\) | |||||||
\(282\) | 6.90081 | + | 1.21680i | 0.410937 | + | 0.0724593i | ||||
\(283\) | 11.0599 | + | 30.3868i | 0.657443 | + | 1.80631i | 0.588208 | + | 0.808710i | \(0.299834\pi\) |
0.0692348 | + | 0.997600i | \(0.477944\pi\) | |||||||
\(284\) | 10.3905 | 0.616560 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.59496 | −0.153443 | ||||||||
\(287\) | 8.89076 | + | 24.4272i | 0.524805 | + | 1.44189i | ||||
\(288\) | −1.20805 | − | 0.213011i | −0.0711848 | − | 0.0125518i | ||||
\(289\) | −11.4131 | + | 9.57676i | −0.671361 | + | 0.563339i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.56826 | − | 14.5653i | −0.150554 | − | 0.853834i | ||||
\(292\) | 7.37294 | − | 4.25677i | 0.431469 | − | 0.249109i | ||||
\(293\) | −23.1715 | − | 13.3781i | −1.35369 | − | 0.781556i | −0.364930 | − | 0.931035i | \(-0.618907\pi\) |
−0.988765 | + | 0.149479i | \(0.952240\pi\) | |||||||
\(294\) | 1.71958 | + | 0.625876i | 0.100288 | + | 0.0365018i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.586979 | − | 1.01668i | 0.0341175 | − | 0.0590932i | ||||
\(297\) | −13.0319 | + | 7.52397i | −0.756188 | + | 0.436585i | ||||
\(298\) | 15.9438 | − | 2.81132i | 0.923600 | − | 0.162856i | ||||
\(299\) | 6.35813 | + | 5.33511i | 0.367700 | + | 0.308537i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.36613 | + | 13.4190i | −0.136381 | + | 0.773457i | ||||
\(302\) | 2.09309 | + | 5.75072i | 0.120444 | + | 0.330917i | ||||
\(303\) | − | 5.74359i | − | 0.329961i | ||||||
\(304\) | −3.67823 | + | 2.33893i | −0.210961 | + | 0.134147i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.51036 | − | 2.36958i | 0.372172 | − | 0.135460i | ||||
\(307\) | −11.5754 | − | 2.04105i | −0.660640 | − | 0.116489i | −0.166731 | − | 0.986002i | \(-0.553321\pi\) |
−0.493909 | + | 0.869514i | \(0.664432\pi\) | |||||||
\(308\) | −4.07610 | − | 4.85771i | −0.232257 | − | 0.276794i | ||||
\(309\) | −0.0177881 | − | 0.0149260i | −0.00101193 | − | 0.000849109i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.95715 | − | 8.58603i | −0.281094 | − | 0.486869i | 0.690560 | − | 0.723275i | \(-0.257364\pi\) |
−0.971654 | + | 0.236406i | \(0.924031\pi\) | |||||||
\(312\) | 1.11936 | + | 0.646263i | 0.0633713 | + | 0.0365875i | ||||
\(313\) | 0.122823 | − | 0.337454i | 0.00694238 | − | 0.0190740i | −0.936173 | − | 0.351540i | \(-0.885658\pi\) |
0.943115 | + | 0.332466i | \(0.107881\pi\) | |||||||
\(314\) | 19.8144 | + | 7.21187i | 1.11819 | + | 0.406989i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.94586 | − | 13.7626i | −0.446990 | − | 0.774209i | ||||
\(317\) | 25.5519 | − | 4.50550i | 1.43514 | − | 0.253054i | 0.598639 | − | 0.801019i | \(-0.295708\pi\) |
0.836501 | + | 0.547965i | \(0.184597\pi\) | |||||||
\(318\) | 0.0761881 | − | 0.0907975i | 0.00427242 | − | 0.00509167i | ||||
\(319\) | −0.152841 | + | 0.128249i | −0.00855748 | + | 0.00718058i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.4180 | + | 5.24770i | −0.804732 | + | 0.292898i | ||||
\(322\) | 20.2825i | 1.13030i | ||||||||
\(323\) | 11.3860 | − | 21.8274i | 0.633536 | − | 1.21451i | ||||
\(324\) | 3.81521 | 0.211956 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.81522 | + | 15.9659i | −0.155921 | + | 0.884271i | ||||
\(327\) | −8.01087 | − | 9.54699i | −0.443002 | − | 0.527950i | ||||
\(328\) | 7.04468 | − | 8.39553i | 0.388978 | − | 0.463565i | ||||
\(329\) | 2.16730 | + | 12.2913i | 0.119487 | + | 0.677644i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.72198 | − | 11.6428i | 0.369474 | − | 0.639947i | −0.620010 | − | 0.784594i | \(-0.712871\pi\) |
0.989483 | + | 0.144647i | \(0.0462047\pi\) | |||||||
\(332\) | −2.00816 | + | 5.51738i | −0.110212 | + | 0.302806i | ||||
\(333\) | 0.492534 | − | 1.35323i | 0.0269907 | − | 0.0741563i | ||||
\(334\) | −0.233733 | + | 0.404837i | −0.0127893 | + | 0.0221517i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.548475 | + | 3.11055i | 0.0299217 | + | 0.169695i | ||||
\(337\) | 10.5517 | − | 12.5750i | 0.574786 | − | 0.685004i | −0.397820 | − | 0.917464i | \(-0.630233\pi\) |
0.972606 | + | 0.232460i | \(0.0746775\pi\) | |||||||
\(338\) | −7.75068 | − | 9.23689i | −0.421581 | − | 0.502421i | ||||
\(339\) | −2.08884 | + | 11.8464i | −0.113450 | + | 0.643408i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.0527590 | −0.00285706 | ||||||||
\(342\) | −3.94525 | + | 3.60904i | −0.213335 | + | 0.195155i | ||||
\(343\) | 19.8626i | 1.07248i | ||||||||
\(344\) | 5.39835 | − | 1.96484i | 0.291059 | − | 0.105937i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −19.7022 | + | 16.5321i | −1.05920 | + | 0.888770i | ||||
\(347\) | −4.32095 | + | 5.14951i | −0.231961 | + | 0.276440i | −0.869452 | − | 0.494018i | \(-0.835528\pi\) |
0.637491 | + | 0.770458i | \(0.279972\pi\) | |||||||
\(348\) | 0.0978695 | − | 0.0172570i | 0.00524636 | − | 0.000925075i | ||||
\(349\) | −9.98033 | − | 17.2864i | −0.534235 | − | 0.925322i | −0.999200 | − | 0.0399930i | \(-0.987266\pi\) |
0.464965 | − | 0.885329i | \(-0.346067\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.13363 | + | 1.86849i | 0.274013 | + | 0.0997326i | ||||
\(352\) | −0.914400 | + | 2.51229i | −0.0487377 | + | 0.133906i | ||||
\(353\) | −21.9749 | − | 12.6872i | −1.16961 | − | 0.675273i | −0.216020 | − | 0.976389i | \(-0.569308\pi\) |
−0.953588 | + | 0.301116i | \(0.902641\pi\) | |||||||
\(354\) | −7.15308 | − | 12.3895i | −0.380182 | − | 0.658495i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.659398 | − | 0.553301i | −0.0349480 | − | 0.0293249i | ||||
\(357\) | −11.4668 | − | 13.6656i | −0.606886 | − | 0.723258i | ||||
\(358\) | 13.9486 | + | 2.45951i | 0.737206 | + | 0.129989i | ||||
\(359\) | −13.6119 | + | 4.95433i | −0.718409 | + | 0.261480i | −0.675250 | − | 0.737589i | \(-0.735964\pi\) |
−0.0431590 | + | 0.999068i | \(0.513742\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.68788 | + | 18.9249i | −0.0888358 | + | 0.996046i | ||||
\(362\) | − | 7.79400i | − | 0.409643i | ||||||
\(363\) | −1.75453 | − | 4.82053i | −0.0920889 | − | 0.253012i | ||||
\(364\) | −0.399769 | + | 2.26720i | −0.0209536 | + | 0.118834i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 8.16007 | + | 6.84711i | 0.426534 | + | 0.357904i | ||||
\(367\) | −2.09575 | + | 0.369537i | −0.109397 | + | 0.0192897i | −0.228079 | − | 0.973643i | \(-0.573244\pi\) |
0.118682 | + | 0.992932i | \(0.462133\pi\) | |||||||
\(368\) | 7.40559 | − | 4.27562i | 0.386043 | − | 0.222882i | ||||
\(369\) | 6.72196 | − | 11.6428i | 0.349931 | − | 0.606099i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.198383 | + | 0.0722056i | 0.0102995 | + | 0.00374873i | ||||
\(372\) | 0.0227581 | + | 0.0131394i | 0.00117995 | + | 0.000681246i | ||||
\(373\) | −23.8796 | + | 13.7869i | −1.23644 | + | 0.713859i | −0.968365 | − | 0.249539i | \(-0.919721\pi\) |
−0.268075 | + | 0.963398i | \(0.586387\pi\) | |||||||
\(374\) | −2.62205 | − | 14.8704i | −0.135583 | − | 0.768931i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.03097 | − | 3.38238i | 0.207881 | − | 0.174433i | ||||
\(377\) | 0.0713346 | + | 0.0125782i | 0.00367392 | + | 0.000647811i | ||||
\(378\) | 4.56602 | + | 12.5450i | 0.234851 | + | 0.645247i | ||||
\(379\) | 2.88506 | 0.148195 | 0.0740977 | − | 0.997251i | \(-0.476392\pi\) | ||||
0.0740977 | + | 0.997251i | \(0.476392\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.4816 | −0.639452 | ||||||||
\(382\) | −0.0903130 | − | 0.248133i | −0.00462081 | − | 0.0126956i | ||||
\(383\) | 12.2562 | + | 2.16110i | 0.626262 | + | 0.110427i | 0.477767 | − | 0.878486i | \(-0.341446\pi\) |
0.148494 | + | 0.988913i | \(0.452557\pi\) | |||||||
\(384\) | 1.02011 | − | 0.855975i | 0.0520573 | − | 0.0436813i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.541429 | + | 3.07060i | 0.0275580 | + | 0.156289i | ||||
\(387\) | 6.10292 | − | 3.52352i | 0.310229 | − | 0.179111i | ||||
\(388\) | −9.61847 | − | 5.55323i | −0.488304 | − | 0.281922i | ||||
\(389\) | 29.1597 | + | 10.6132i | 1.47845 | + | 0.538113i | 0.950381 | − | 0.311087i | \(-0.100693\pi\) |
0.528072 | + | 0.849200i | \(0.322915\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.1483 | + | 41.8261i | −1.22123 | + | 2.11524i | ||||
\(392\) | 1.19007 | − | 0.687089i | 0.0601078 | − | 0.0347032i | ||||
\(393\) | −8.19301 | + | 1.44465i | −0.413282 | + | 0.0728729i | ||||
\(394\) | −16.0698 | − | 13.4842i | −0.809585 | − | 0.679323i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.569490 | + | 3.22974i | −0.0286180 | + | 0.162301i | ||||
\(397\) | −2.69088 | − | 7.39313i | −0.135051 | − | 0.371050i | 0.853671 | − | 0.520813i | \(-0.174371\pi\) |
−0.988722 | + | 0.149763i | \(0.952149\pi\) | |||||||
\(398\) | − | 21.9572i | − | 1.10061i | ||||||
\(399\) | 12.2068 | + | 6.36754i | 0.611104 | + | 0.318776i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.4546 | + | 9.99266i | −1.37102 | + | 0.499010i | −0.919443 | − | 0.393224i | \(-0.871360\pi\) |
−0.451575 | + | 0.892233i | \(0.649138\pi\) | |||||||
\(402\) | −6.69779 | − | 1.18100i | −0.334056 | − | 0.0589030i | ||||
\(403\) | 0.0123119 | + | 0.0146728i | 0.000613301 | + | 0.000730903i | ||||
\(404\) | −3.30403 | − | 2.77241i | −0.164382 | − | 0.137933i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.0885046 | + | 0.153294i | 0.00439241 | + | 0.00760787i | ||||
\(407\) | −2.71811 | − | 1.56930i | −0.134732 | − | 0.0777875i | ||||
\(408\) | −2.57236 | + | 7.06751i | −0.127351 | + | 0.349894i | ||||
\(409\) | 13.3081 | + | 4.84375i | 0.658043 | + | 0.239508i | 0.649391 | − | 0.760455i | \(-0.275024\pi\) |
0.00865164 | + | 0.999963i | \(0.497246\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.90892 | + | 17.1628i | 0.488771 | + | 0.846576i | ||||
\(412\) | −0.0171725 | + | 0.00302797i | −0.000846028 | + | 0.000149177i | ||||
\(413\) | 16.3791 | − | 19.5199i | 0.805964 | − | 0.960510i | ||||
\(414\) | 8.03554 | − | 6.74262i | 0.394925 | − | 0.331382i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.912078 | − | 0.331969i | 0.0447183 | − | 0.0162761i | ||||
\(417\) | 14.3416i | 0.702312i | ||||||||
\(418\) | 6.25320 | + | 9.83385i | 0.305854 | + | 0.480989i | ||||
\(419\) | −30.0769 | −1.46935 | −0.734677 | − | 0.678417i | \(-0.762666\pi\) | ||||
−0.734677 | + | 0.678417i | \(0.762666\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.36476 | + | 13.4112i | −0.115251 | + | 0.653623i | 0.871374 | + | 0.490619i | \(0.163229\pi\) |
−0.986625 | + | 0.163004i | \(0.947882\pi\) | |||||||
\(422\) | 9.00719 | + | 10.7343i | 0.438463 | + | 0.522540i | ||||
\(423\) | 4.14911 | − | 4.94471i | 0.201736 | − | 0.240420i | ||||
\(424\) | −0.0154560 | − | 0.0876552i | −0.000750609 | − | 0.00425691i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −6.91828 | + | 11.9828i | −0.335192 | + | 0.580569i | ||||
\(427\) | −6.48920 | + | 17.8289i | −0.314035 | + | 0.862803i | ||||
\(428\) | −3.94072 | + | 10.8271i | −0.190482 | + | 0.523345i | ||||
\(429\) | 1.72780 | − | 2.99264i | 0.0834191 | − | 0.144486i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.13794 | − | 29.1387i | −0.247486 | − | 1.40356i | −0.814648 | − | 0.579956i | \(-0.803070\pi\) |
0.567162 | − | 0.823606i | \(-0.308041\pi\) | |||||||
\(432\) | 3.61793 | − | 4.31168i | 0.174068 | − | 0.207446i | ||||
\(433\) | 0.621064 | + | 0.740155i | 0.0298464 | + | 0.0355696i | 0.780761 | − | 0.624830i | \(-0.214832\pi\) |
−0.750915 | + | 0.660399i | \(0.770387\pi\) | |||||||
\(434\) | −0.00812785 | + | 0.0460953i | −0.000390149 | + | 0.00221265i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.35877 | −0.448204 | ||||||||
\(437\) | 4.89640 | − | 36.9510i | 0.234226 | − | 1.76761i | ||||
\(438\) | 11.3371i | 0.541709i | ||||||||
\(439\) | −22.1502 | + | 8.06200i | −1.05717 | + | 0.384778i | −0.811364 | − | 0.584541i | \(-0.801275\pi\) |
−0.245805 | + | 0.969319i | \(0.579052\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.29130 | − | 1.08353i | 0.0614907 | − | 0.0515968i | ||||
\(442\) | −3.52372 | + | 4.19940i | −0.167606 | + | 0.199745i | ||||
\(443\) | −0.670532 | + | 0.118233i | −0.0318579 | + | 0.00561741i | −0.189554 | − | 0.981870i | \(-0.560704\pi\) |
0.157696 | + | 0.987488i | \(0.449593\pi\) | |||||||
\(444\) | 0.781656 | + | 1.35387i | 0.0370958 | + | 0.0642518i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 14.7809 | + | 5.37982i | 0.699898 | + | 0.254742i | ||||
\(447\) | −7.37370 | + | 20.2591i | −0.348764 | + | 0.958222i | ||||
\(448\) | 2.05411 | + | 1.18594i | 0.0970476 | + | 0.0560304i | ||||
\(449\) | −14.8474 | − | 25.7165i | −0.700693 | − | 1.21364i | −0.968223 | − | 0.250087i | \(-0.919541\pi\) |
0.267530 | − | 0.963549i | \(-0.413792\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.4457 | − | 18.8341i | −1.05692 | − | 0.886865i | ||||
\(452\) | 5.80643 | + | 6.91983i | 0.273111 | + | 0.325482i | ||||
\(453\) | −8.02567 | − | 1.41514i | −0.377079 | − | 0.0664892i | ||||
\(454\) | 7.52863 | − | 2.74020i | 0.353336 | − | 0.128604i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.248301 | − | 5.79926i | −0.0116278 | − | 0.271575i | ||||
\(457\) | − | 2.71312i | − | 0.126914i | −0.997985 | − | 0.0634572i | \(-0.979787\pi\) | ||
0.997985 | − | 0.0634572i | \(-0.0202126\pi\) | |||||||
\(458\) | −6.80024 | − | 18.6835i | −0.317754 | − | 0.873023i | ||||
\(459\) | −5.52014 | + | 31.3063i | −0.257658 | + | 1.46125i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.5554 | + | 18.9262i | 1.05051 | + | 0.881482i | 0.993147 | − | 0.116872i | \(-0.0372867\pi\) |
0.0573618 | + | 0.998353i | \(0.481731\pi\) | |||||||
\(462\) | 8.31615 | − | 1.46636i | 0.386902 | − | 0.0682213i | ||||
\(463\) | 27.6008 | − | 15.9354i | 1.28272 | − | 0.740579i | 0.305375 | − | 0.952232i | \(-0.401218\pi\) |
0.977345 | + | 0.211653i | \(0.0678848\pi\) | |||||||
\(464\) | 0.0373141 | − | 0.0646299i | 0.00173226 | − | 0.00300037i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −23.4437 | − | 8.53279i | −1.08601 | − | 0.395274i | ||||
\(467\) | 33.0631 | + | 19.0890i | 1.52998 | + | 0.883333i | 0.999362 | + | 0.0357205i | \(0.0113726\pi\) |
0.530616 | + | 0.847612i | \(0.321961\pi\) | |||||||
\(468\) | 1.03112 | − | 0.595317i | 0.0476635 | − | 0.0275185i | ||||
\(469\) | −2.10354 | − | 11.9298i | −0.0971323 | − | 0.550865i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −21.5101 | + | 18.0492i | −0.991135 | + | 0.831661i | ||||
\(472\) | −10.5799 | − | 1.86552i | −0.486979 | − | 0.0858676i | ||||
\(473\) | −5.25305 | − | 14.4326i | −0.241535 | − | 0.663613i | ||||
\(474\) | 21.1624 | 0.972020 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −13.3962 | −0.614012 | ||||||||
\(477\) | −0.0373431 | − | 0.102599i | −0.00170982 | − | 0.00469769i | ||||
\(478\) | 10.4823 | + | 1.84832i | 0.479450 | + | 0.0845400i | ||||
\(479\) | −22.4094 | + | 18.8037i | −1.02391 | + | 0.859163i | −0.990114 | − | 0.140266i | \(-0.955204\pi\) |
−0.0337965 | + | 0.999429i | \(0.510760\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.197865 | + | 1.12215i | 0.00902187 | + | 0.0511655i | ||||
\(482\) | 14.5498 | − | 8.40034i | 0.662726 | − | 0.382625i | ||||
\(483\) | −23.3909 | − | 13.5047i | −1.06432 | − | 0.614486i | ||||
\(484\) | −3.61994 | − | 1.31755i | −0.164543 | − | 0.0598886i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 5.90247 | − | 10.2234i | 0.267742 | − | 0.463742i | ||||
\(487\) | 12.6228 | − | 7.28777i | 0.571993 | − | 0.330240i | −0.185952 | − | 0.982559i | \(-0.559537\pi\) |
0.757945 | + | 0.652318i | \(0.226203\pi\) | |||||||
\(488\) | 7.87768 | − | 1.38905i | 0.356606 | − | 0.0628792i | ||||
\(489\) | −16.5383 | − | 13.8773i | −0.747886 | − | 0.627551i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.15669 | + | 6.55990i | −0.0522006 | + | 0.296044i | −0.999720 | − | 0.0236533i | \(-0.992470\pi\) |
0.947520 | + | 0.319698i | \(0.103581\pi\) | |||||||
\(492\) | 4.99159 | + | 13.7143i | 0.225038 | + | 0.618288i | ||||
\(493\) | 0.421493i | 0.0189831i | ||||||||
\(494\) | 1.27563 | − | 4.03392i | 0.0573933 | − | 0.181494i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.0185438 | − | 0.00674938i | 0.000832640 | − | 0.000303056i | ||||
\(497\) | −24.2705 | − | 4.27955i | −1.08868 | − | 0.191964i | ||||
\(498\) | −5.02583 | − | 5.98956i | −0.225213 | − | 0.268398i | ||||
\(499\) | −3.72597 | − | 3.12646i | −0.166797 | − | 0.139960i | 0.555568 | − | 0.831471i | \(-0.312501\pi\) |
−0.722366 | + | 0.691511i | \(0.756945\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.311253 | − | 0.539105i | −0.0139057 | − | 0.0240854i | ||||
\(502\) | 19.6484 | + | 11.3440i | 0.876952 | + | 0.506309i | ||||
\(503\) | −2.23778 | + | 6.14824i | −0.0997775 | + | 0.274137i | −0.979531 | − | 0.201294i | \(-0.935485\pi\) |
0.879753 | + | 0.475430i | \(0.157708\pi\) | |||||||
\(504\) | 2.73408 | + | 0.995122i | 0.121785 | + | 0.0443263i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −11.4310 | − | 19.7990i | −0.508169 | − | 0.880175i | ||||
\(507\) | 15.8131 | − | 2.78828i | 0.702284 | − | 0.123832i | ||||
\(508\) | −6.02483 | + | 7.18011i | −0.267309 | + | 0.318566i | ||||
\(509\) | −6.45683 | + | 5.41792i | −0.286194 | + | 0.240145i | −0.774570 | − | 0.632488i | \(-0.782034\pi\) |
0.488376 | + | 0.872633i | \(0.337589\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.9753 | + | 6.90645i | −0.839418 | + | 0.305523i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −5.28994 | − | 23.9570i | −0.233557 | − | 1.05773i | ||||
\(514\) | −22.5633 | −0.995226 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.32843 | + | 7.53390i | −0.0584809 | + | 0.331661i | ||||
\(517\) | −9.04289 | − | 10.7769i | −0.397706 | − | 0.473967i | ||||
\(518\) | −1.78983 | + | 2.13304i | −0.0786408 | + | 0.0937205i | ||||
\(519\) | −5.94735 | − | 33.7291i | −0.261060 | − | 1.48054i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.5648 | − | 25.2269i | 0.638094 | − | 1.10521i | −0.347757 | − | 0.937585i | \(-0.613056\pi\) |
0.985851 | − | 0.167626i | \(-0.0536102\pi\) | |||||||
\(522\) | 0.0313102 | − | 0.0860242i | 0.00137041 | − | 0.00376517i | ||||
\(523\) | 9.32362 | − | 25.6164i | 0.407693 | − | 1.12013i | −0.550706 | − | 0.834699i | \(-0.685642\pi\) |
0.958400 | − | 0.285429i | \(-0.0921362\pi\) | |||||||
\(524\) | −3.12369 | + | 5.41040i | −0.136459 | + | 0.236354i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.46619 | + | 8.31518i | 0.0639289 | + | 0.362559i | ||||
\(527\) | −0.0716419 | + | 0.0853794i | −0.00312077 | + | 0.00371919i | ||||
\(528\) | −2.28847 | − | 2.72729i | −0.0995929 | − | 0.118690i | ||||
\(529\) | −8.70390 | + | 49.3623i | −0.378430 | + | 2.14619i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.1784 | −0.571893 | ||||||||
\(532\) | 9.55513 | − | 3.94843i | 0.414267 | − | 0.171186i | ||||
\(533\) | 10.6375i | 0.460762i | ||||||||
\(534\) | 1.07714 | − | 0.392048i | 0.0466125 | − | 0.0169656i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.91238 | + | 3.28288i | −0.168989 | + | 0.141799i | ||||
\(537\) | −12.1238 | + | 14.4486i | −0.523182 | + | 0.623504i | ||||
\(538\) | −25.9501 | + | 4.57571i | −1.11879 | + | 0.197273i | ||||
\(539\) | −1.83695 | − | 3.18169i | −0.0791230 | − | 0.137045i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.0683 | − | 9.12412i | −1.07777 | − | 0.392277i | −0.258694 | − | 0.965959i | \(-0.583292\pi\) |
−0.819077 | + | 0.573683i | \(0.805514\pi\) | |||||||
\(542\) | 0.208014 | − | 0.571515i | 0.00893498 | − | 0.0245487i | ||||
\(543\) | 8.98844 | + | 5.18948i | 0.385731 | + | 0.222702i | ||||
\(544\) | 2.82395 | + | 4.89123i | 0.121076 | + | 0.209710i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.34848 | − | 1.97061i | −0.100506 | − | 0.0843342i | ||||
\(547\) | 2.90170 | + | 3.45811i | 0.124068 | + | 0.147858i | 0.824503 | − | 0.565858i | \(-0.191455\pi\) |
−0.700435 | + | 0.713716i | \(0.747011\pi\) | |||||||
\(548\) | 14.6560 | + | 2.58424i | 0.626072 | + | 0.110393i | ||||
\(549\) | 9.22071 | − | 3.35606i | 0.393530 | − | 0.143233i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.124232 | − | 0.300640i | −0.00529247 | − | 0.0128077i | ||||
\(552\) | 11.3873i | 0.484678i | ||||||||
\(553\) | 12.8919 | + | 35.4201i | 0.548218 | + | 1.50622i | ||||
\(554\) | 1.18238 | − | 6.70558i | 0.0502343 | − | 0.284893i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.25009 | + | 6.92265i | 0.349882 | + | 0.293586i | ||||
\(557\) | 20.8264 | − | 3.67225i | 0.882442 | − | 0.155598i | 0.285976 | − | 0.958237i | \(-0.407682\pi\) |
0.596466 | + | 0.802639i | \(0.296571\pi\) | |||||||
\(558\) | 0.0209640 | − | 0.0121036i | 0.000887478 | − | 0.000512386i | ||||
\(559\) | −2.78799 | + | 4.82894i | −0.117919 | + | 0.204242i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18.8952 | + | 6.87728i | 0.797755 | + | 0.290359i | ||||
\(562\) | 21.2103 | + | 12.2458i | 0.894703 | + | 0.516557i | ||||
\(563\) | −16.2119 | + | 9.35993i | −0.683249 | + | 0.394474i | −0.801078 | − | 0.598560i | \(-0.795740\pi\) |
0.117829 | + | 0.993034i | \(0.462406\pi\) | |||||||
\(564\) | 1.21680 | + | 6.90081i | 0.0512365 | + | 0.290576i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −24.7716 | + | 20.7858i | −1.04123 | + | 0.873693i | ||||
\(567\) | −8.91174 | − | 1.57138i | −0.374258 | − | 0.0659918i | ||||
\(568\) | 3.55375 | + | 9.76384i | 0.149112 | + | 0.409681i | ||||
\(569\) | 41.7205 | 1.74902 | 0.874508 | − | 0.485011i | \(-0.161184\pi\) | ||||
0.874508 | + | 0.485011i | \(0.161184\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.6363 | −1.40763 | −0.703817 | − | 0.710381i | \(-0.748522\pi\) | ||||
−0.703817 | + | 0.710381i | \(0.748522\pi\) | |||||||
\(572\) | −0.887529 | − | 2.43846i | −0.0371094 | − | 0.101957i | ||||
\(573\) | 0.346293 | + | 0.0610607i | 0.0144666 | + | 0.00255085i | ||||
\(574\) | −19.9132 | + | 16.7092i | −0.831161 | + | 0.697427i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.213011 | − | 1.20805i | −0.00887546 | − | 0.0503352i | ||||
\(577\) | −14.4179 | + | 8.32416i | −0.600223 | + | 0.346539i | −0.769129 | − | 0.639093i | \(-0.779310\pi\) |
0.168906 | + | 0.985632i | \(0.445977\pi\) | |||||||
\(578\) | −12.9027 | − | 7.44940i | −0.536683 | − | 0.309854i | ||||
\(579\) | −3.90167 | − | 1.42009i | −0.162148 | − | 0.0590170i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.96322 | − | 12.0607i | 0.288883 | − | 0.500360i | ||||
\(582\) | 12.8085 | − | 7.39501i | 0.530931 | − | 0.306533i | ||||
\(583\) | −0.234349 | + | 0.0413220i | −0.00970572 | + | 0.00171138i | ||||
\(584\) | 6.52175 | + | 5.47240i | 0.269872 | + | 0.226449i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.64616 | − | 26.3497i | 0.191931 | − | 1.08850i | ||||
\(587\) | −2.50704 | − | 6.88805i | −0.103477 | − | 0.284300i | 0.877140 | − | 0.480234i | \(-0.159448\pi\) |
−0.980617 | + | 0.195934i | \(0.937226\pi\) | |||||||
\(588\) | 1.82994i | 0.0754654i | ||||||||
\(589\) | 0.0259353 | − | 0.0820149i | 0.00106864 | − | 0.00337937i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 26.2504 | − | 9.55437i | 1.07980 | − | 0.393014i | ||||
\(592\) | 1.15612 | + | 0.203856i | 0.0475163 | + | 0.00837841i | ||||
\(593\) | 13.7873 | + | 16.4311i | 0.566177 | + | 0.674744i | 0.970842 | − | 0.239722i | \(-0.0770561\pi\) |
−0.404665 | + | 0.914465i | \(0.632612\pi\) | |||||||
\(594\) | −11.5274 | − | 9.67263i | −0.472975 | − | 0.396873i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.09488 | + | 14.0208i | 0.331579 | + | 0.574312i | ||||
\(597\) | 25.3221 | + | 14.6197i | 1.03637 | + | 0.598346i | ||||
\(598\) | −2.83875 | + | 7.79940i | −0.116085 | + | 0.318941i | ||||
\(599\) | 8.88650 | + | 3.23442i | 0.363093 | + | 0.132155i | 0.517123 | − | 0.855911i | \(-0.327003\pi\) |
−0.154030 | + | 0.988066i | \(0.549225\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.88906 | − | 6.73606i | −0.158638 | − | 0.274769i | 0.775740 | − | 0.631053i | \(-0.217377\pi\) |
−0.934378 | + | 0.356284i | \(0.884044\pi\) | |||||||
\(602\) | −13.4190 | + | 2.36613i | −0.546917 | + | 0.0964362i | ||||
\(603\) | −4.02704 | + | 4.79924i | −0.163994 | + | 0.195440i | ||||
\(604\) | −4.68803 | + | 3.93373i | −0.190753 | + | 0.160061i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.39721 | − | 1.96442i | 0.219247 | − | 0.0797993i | ||||
\(607\) | − | 1.12754i | − | 0.0457656i | −0.999738 | − | 0.0228828i | \(-0.992716\pi\) | ||
0.999738 | − | 0.0228828i | \(-0.00728446\pi\) | |||||||
\(608\) | −3.45591 | − | 2.65644i | −0.140156 | − | 0.107733i | ||||
\(609\) | −0.235716 | −0.00955170 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.886894 | + | 5.02982i | −0.0358799 | + | 0.203485i | ||||
\(612\) | 4.45335 | + | 5.30729i | 0.180016 | + | 0.214535i | ||||
\(613\) | 26.3081 | − | 31.3528i | 1.06258 | − | 1.26633i | 0.100095 | − | 0.994978i | \(-0.468085\pi\) |
0.962481 | − | 0.271351i | \(-0.0874703\pi\) | |||||||
\(614\) | −2.04105 | − | 11.5754i | −0.0823699 | − | 0.467143i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.17064 | − | 5.49172i | 0.127749 | − | 0.221268i | ||||
\(617\) | −8.46227 | + | 23.2499i | −0.340678 | + | 0.936005i | 0.644520 | + | 0.764587i | \(0.277057\pi\) |
−0.985198 | + | 0.171418i | \(0.945165\pi\) | |||||||
\(618\) | 0.00794194 | − | 0.0218203i | 0.000319472 | − | 0.000877741i | ||||
\(619\) | 17.1323 | − | 29.6741i | 0.688607 | − | 1.19270i | −0.283682 | − | 0.958918i | \(-0.591556\pi\) |
0.972289 | − | 0.233784i | \(-0.0751107\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.35781 | + | 47.3995i | 0.335387 | + | 1.90208i | ||||
\(622\) | 6.37278 | − | 7.59479i | 0.255525 | − | 0.304523i | ||||
\(623\) | 1.31236 | + | 1.56402i | 0.0525788 | + | 0.0626609i | ||||
\(624\) | −0.224445 | + | 1.27289i | −0.00898499 | + | 0.0509564i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0.359111 | 0.0143530 | ||||||||
\(627\) | −15.5045 | + | 0.663840i | −0.619189 | + | 0.0265112i | ||||
\(628\) | 21.0861i | 0.841427i | ||||||||
\(629\) | −6.23054 | + | 2.26773i | −0.248428 | + | 0.0904203i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.99216 | + | 3.34982i | −0.158925 | + | 0.133354i | −0.718783 | − | 0.695235i | \(-0.755300\pi\) |
0.559857 | + | 0.828589i | \(0.310856\pi\) | |||||||
\(632\) | 10.2150 | − | 12.1738i | 0.406331 | − | 0.484246i | ||||
\(633\) | −18.3767 | + | 3.24030i | −0.730406 | + | 0.128790i | ||||
\(634\) | 12.9731 | + | 22.4700i | 0.515226 | + | 0.892398i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.111380 | + | 0.0405388i | 0.00441649 | + | 0.00160747i | ||||
\(637\) | −0.456185 | + | 1.25336i | −0.0180747 | + | 0.0496598i | ||||
\(638\) | −0.172790 | − | 0.0997602i | −0.00684081 | − | 0.00394954i | ||||
\(639\) | 6.37289 | + | 11.0382i | 0.252108 | + | 0.436663i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.1012 | + | 25.2579i | 1.18893 | + | 0.997627i | 0.999877 | + | 0.0156594i | \(0.00498475\pi\) |
0.189048 | + | 0.981968i | \(0.439460\pi\) | |||||||
\(642\) | −9.86246 | − | 11.7536i | −0.389240 | − | 0.463878i | ||||
\(643\) | −40.1349 | − | 7.07687i | −1.58277 | − | 0.279085i | −0.688031 | − | 0.725681i | \(-0.741525\pi\) |
−0.894736 | + | 0.446596i | \(0.852636\pi\) | |||||||
\(644\) | −19.0594 | + | 6.93704i | −0.751044 | + | 0.273358i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 24.4053 | + | 3.23396i | 0.960214 | + | 0.127238i | ||||
\(647\) | − | 18.7570i | − | 0.737414i | −0.929546 | − | 0.368707i | \(-0.879800\pi\) | ||
0.929546 | − | 0.368707i | \(-0.120200\pi\) | |||||||
\(648\) | 1.30488 | + | 3.58512i | 0.0512604 | + | 0.140837i | ||||
\(649\) | −4.98752 | + | 28.2856i | −0.195777 | + | 1.11031i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.0477477 | − | 0.0400651i | −0.00187138 | − | 0.00157027i | ||||
\(652\) | −15.9659 | + | 2.81522i | −0.625274 | + | 0.110253i | ||||
\(653\) | 14.6095 | − | 8.43478i | 0.571713 | − | 0.330078i | −0.186120 | − | 0.982527i | \(-0.559591\pi\) |
0.757833 | + | 0.652449i | \(0.226258\pi\) | |||||||
\(654\) | 6.23135 | − | 10.7930i | 0.243665 | − | 0.422040i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 10.2986 | + | 3.74840i | 0.402094 | + | 0.146350i | ||||
\(657\) | 9.04425 | + | 5.22170i | 0.352850 | + | 0.203718i | ||||
\(658\) | −10.8088 | + | 6.24048i | −0.421372 | + | 0.243279i | ||||
\(659\) | −1.19202 | − | 6.76028i | −0.0464345 | − | 0.263343i | 0.952748 | − | 0.303761i | \(-0.0982423\pi\) |
−0.999183 | + | 0.0404175i | \(0.987131\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.5608 | − | 10.5398i | 0.488558 | − | 0.409949i | −0.364951 | − | 0.931027i | \(-0.618914\pi\) |
0.853509 | + | 0.521078i | \(0.174470\pi\) | |||||||
\(662\) | 13.2397 | + | 2.33452i | 0.514577 | + | 0.0907337i | ||||
\(663\) | −2.49677 | − | 6.85982i | −0.0969665 | − | 0.266413i | ||||
\(664\) | −5.87148 | −0.227857 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.44007 | 0.0558017 | ||||||||
\(667\) | 0.218265 | + | 0.599678i | 0.00845125 | + | 0.0232196i | ||||
\(668\) | −0.460364 | − | 0.0811745i | −0.0178120 | − | 0.00314074i | ||||
\(669\) | −16.0459 | + | 13.4641i | −0.620370 | + | 0.520552i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.71365 | − | 21.0612i | −0.143364 | − | 0.813058i | ||||
\(672\) | −2.73538 | + | 1.57927i | −0.105519 | + | 0.0609217i | ||||
\(673\) | 4.26530 | + | 2.46257i | 0.164415 | + | 0.0949251i | 0.579950 | − | 0.814652i | \(-0.303072\pi\) |
−0.415535 | + | 0.909577i | \(0.636406\pi\) | |||||||
\(674\) | 15.4255 | + | 5.61443i | 0.594169 | + | 0.216260i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.02895 | − | 10.4425i | 0.231883 | − | 0.401633i | ||||
\(677\) | −4.67017 | + | 2.69632i | −0.179489 | + | 0.103628i | −0.587053 | − | 0.809549i | \(-0.699712\pi\) |
0.407563 | + | 0.913177i | \(0.366379\pi\) | |||||||
\(678\) | −11.8464 | + | 2.08884i | −0.454958 | + | 0.0802214i | ||||
\(679\) | 20.1801 | + | 16.9331i | 0.774439 | + | 0.649832i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.85265 | + | 10.5069i | −0.0709937 | + | 0.402625i | ||||
\(682\) | −0.0180446 | − | 0.0495773i | −0.000690965 | − | 0.00189841i | ||||
\(683\) | 17.4871i | 0.669126i | 0.942373 | + | 0.334563i | \(0.108589\pi\) | ||||
−0.942373 | + | 0.334563i | \(0.891411\pi\) | |||||||
\(684\) | −4.74075 | − | 2.47296i | −0.181267 | − | 0.0945560i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −18.6647 | + | 6.79339i | −0.712622 | + | 0.259373i | ||||
\(687\) | 26.0746 | + | 4.59765i | 0.994807 | + | 0.175411i | ||||
\(688\) | 3.69269 | + | 4.40077i | 0.140782 | + | 0.167778i | ||||
\(689\) | 0.0661800 | + | 0.0555316i | 0.00252126 | + | 0.00211558i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.39377 | + | 12.8064i | 0.281272 | + | 0.487178i | 0.971698 | − | 0.236225i | \(-0.0759102\pi\) |
−0.690426 | + | 0.723403i | \(0.742577\pi\) | |||||||
\(692\) | −22.2736 | − | 12.8597i | −0.846716 | − | 0.488852i | ||||
\(693\) | 2.66049 | − | 7.30962i | 0.101063 | − | 0.277670i | ||||
\(694\) | −6.31681 | − | 2.29913i | −0.239783 | − | 0.0872738i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.0496897 | + | 0.0860650i | 0.00188348 | + | 0.00326229i | ||||
\(697\) | −60.9583 | + | 10.7486i | −2.30896 | + | 0.407132i | ||||
\(698\) | 12.8305 | − | 15.2908i | 0.485640 | − | 0.578764i | ||||
\(699\) | 25.4500 | − | 21.3550i | 0.962606 | − | 0.807722i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.07843 | + | 2.57634i | −0.267349 | + | 0.0973069i | −0.472216 | − | 0.881483i | \(-0.656546\pi\) |
0.204868 | + | 0.978790i | \(0.434324\pi\) | |||||||
\(702\) | 5.46310i | 0.206191i | ||||||||
\(703\) | 3.77568 | − | 3.45392i | 0.142403 | − | 0.130267i | ||||
\(704\) | −2.67353 | −0.100762 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.40623 | − | 24.9890i | 0.165831 | − | 0.940472i | ||||
\(707\) | 6.57583 | + | 7.83677i | 0.247310 | + | 0.294732i | ||||
\(708\) | 9.19583 | − | 10.9592i | 0.345600 | − | 0.411870i | ||||
\(709\) | −6.22196 | − | 35.2865i | −0.233671 | − | 1.32521i | −0.845395 | − | 0.534141i | \(-0.820635\pi\) |
0.611725 | − | 0.791071i | \(-0.290476\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.74704 | − | 16.8824i | 0.365543 | − | 0.633138i | ||||
\(712\) | 0.294405 | − | 0.808872i | 0.0110333 | − | 0.0303138i | ||||
\(713\) | −0.0577156 | + | 0.158572i | −0.00216147 | + | 0.00593858i | ||||
\(714\) | 8.91956 | − | 15.4491i | 0.333806 | − | 0.578169i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.45951 | + | 13.9486i | 0.0919163 | + | 0.521284i | ||||
\(717\) | −9.11101 | + | 10.8581i | −0.340257 | + | 0.405503i | ||||
\(718\) | −9.31110 | − | 11.0965i | −0.347487 | − | 0.414119i | ||||
\(719\) | −1.50797 | + | 8.55210i | −0.0562376 | + | 0.318940i | −0.999929 | − | 0.0118866i | \(-0.996216\pi\) |
0.943692 | + | 0.330826i | \(0.107327\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.0413594 | 0.00154031 | ||||||||
\(722\) | −18.3609 | + | 4.88660i | −0.683320 | + | 0.181860i | ||||
\(723\) | 22.3728i | 0.832053i | ||||||||
\(724\) | 7.32396 | − | 2.66570i | 0.272193 | − | 0.0990701i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.92973 | − | 3.29744i | 0.145846 | − | 0.122379i | ||||
\(727\) | −19.1997 | + | 22.8813i | −0.712078 | + | 0.848622i | −0.993836 | − | 0.110864i | \(-0.964638\pi\) |
0.281758 | + | 0.959486i | \(0.409083\pi\) | |||||||
\(728\) | −2.26720 | + | 0.399769i | −0.0840282 | + | 0.0148164i | ||||
\(729\) | 13.5829 | + | 23.5263i | 0.503070 | + | 0.871343i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −30.4893 | − | 11.0972i | −1.12769 | − | 0.410445i | ||||
\(732\) | −3.64327 | + | 10.0098i | −0.134659 | + | 0.369973i | ||||
\(733\) | 11.1709 | + | 6.44955i | 0.412608 | + | 0.238220i | 0.691910 | − | 0.721984i | \(-0.256770\pi\) |
−0.279301 | + | 0.960203i | \(0.590103\pi\) | |||||||
\(734\) | −1.06404 | − | 1.84297i | −0.0392744 | − | 0.0680253i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.55063 | + | 5.49663i | 0.241460 | + | 0.202609i | ||||
\(737\) | 8.77685 | + | 10.4598i | 0.323300 | + | 0.385293i | ||||
\(738\) | 13.2397 | + | 2.33451i | 0.487359 | + | 0.0859346i | ||||
\(739\) | −27.5586 | + | 10.0305i | −1.01376 | + | 0.368978i | −0.794875 | − | 0.606773i | \(-0.792464\pi\) |
−0.218883 | + | 0.975751i | \(0.570241\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.80277 | + | 4.15702i | 0.139698 | + | 0.152712i | ||||
\(742\) | 0.211115i | 0.00775028i | ||||||||
\(743\) | 16.3402 | + | 44.8942i | 0.599462 | + | 1.64701i | 0.752349 | + | 0.658765i | \(0.228921\pi\) |
−0.152886 | + | 0.988244i | \(0.548857\pi\) | |||||||
\(744\) | −0.00456327 | + | 0.0258796i | −0.000167297 | + | 0.000948791i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −21.1228 | − | 17.7241i | −0.773359 | − | 0.648925i | ||||
\(747\) | −7.09301 | + | 1.25069i | −0.259520 | + | 0.0457603i | ||||
\(748\) | 13.0768 | − | 7.54991i | 0.478136 | − | 0.276052i | ||||
\(749\) | 13.6643 | − | 23.6673i | 0.499283 | − | 0.864783i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 39.1332 | + | 14.2433i | 1.42799 | + | 0.519745i | 0.936354 | − | 0.351056i | \(-0.114177\pi\) |
0.491635 | + | 0.870802i | \(0.336400\pi\) | |||||||
\(752\) | 4.55707 | + | 2.63103i | 0.166179 | + | 0.0959436i | ||||
\(753\) | −26.1650 | + | 15.1064i | −0.953506 | + | 0.550507i | ||||
\(754\) | 0.0125782 | + | 0.0713346i | 0.000458072 | + | 0.00259785i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −10.2268 | + | 8.58131i | −0.371945 | + | 0.312099i | ||||
\(757\) | 25.7489 | + | 4.54023i | 0.935861 | + | 0.165017i | 0.620724 | − | 0.784029i | \(-0.286839\pi\) |
0.315136 | + | 0.949046i | \(0.397950\pi\) | |||||||
\(758\) | 0.986748 | + | 2.71107i | 0.0358403 | + | 0.0984704i | ||||
\(759\) | 30.4444 | 1.10506 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.26023 | 0.190683 | 0.0953415 | − | 0.995445i | \(-0.469606\pi\) | ||||
0.0953415 | + | 0.995445i | \(0.469606\pi\) | |||||||
\(762\) | −4.26896 | − | 11.7289i | −0.154648 | − | 0.424892i | ||||
\(763\) | 21.8607 | + | 3.85463i | 0.791409 | + | 0.139547i | ||||
\(764\) | 0.202280 | − | 0.169733i | 0.00731822 | − | 0.00614072i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.16110 | + | 12.2562i | 0.0780835 | + | 0.442834i | ||||
\(767\) | 9.03040 | − | 5.21370i | 0.326069 | − | 0.188256i | ||||
\(768\) | 1.15325 | + | 0.665830i | 0.0416144 | + | 0.0240261i | ||||
\(769\) | 42.2718 | + | 15.3857i | 1.52436 | + | 0.554822i | 0.962233 | − | 0.272227i | \(-0.0877603\pi\) |
0.562129 | + | 0.827050i | \(0.309982\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.0233 | − | 26.0212i | 0.541053 | − | 0.937131i | ||||
\(772\) | −2.70024 | + | 1.55898i | −0.0971837 | + | 0.0561091i | ||||
\(773\) | 3.05491 | − | 0.538663i | 0.109877 | − | 0.0193744i | −0.118439 | − | 0.992961i | \(-0.537789\pi\) |
0.228316 | + | 0.973587i | \(0.426678\pi\) | |||||||
\(774\) | 5.39835 | + | 4.52975i | 0.194040 | + | 0.162819i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.92862 | − | 10.9377i | 0.0692332 | − | 0.392641i | ||||
\(777\) | −1.26821 | − | 3.48437i | −0.0454967 | − | 0.125001i | ||||
\(778\) | 31.0311i | 1.11252i | ||||||||
\(779\) | 40.3119 | − | 25.6337i | 1.44432 | − | 0.918424i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 26.1039 | − | 9.50103i | 0.934070 | − | 0.339974i | ||||
\(782\) | −47.5629 | − | 8.38661i | −1.70084 | − | 0.299905i | ||||
\(783\) | 0.270000 | + | 0.321773i | 0.00964900 | + | 0.0114992i | ||||
\(784\) | 1.05268 | + | 0.883305i | 0.0375958 | + | 0.0315466i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.15970 | − | 7.20481i | −0.148372 | − | 0.256987i | ||||
\(787\) | −23.9244 | − | 13.8128i | −0.852813 | − | 0.492372i | 0.00878567 | − | 0.999961i | \(-0.497203\pi\) |
−0.861599 | + | 0.507589i | \(0.830537\pi\) | |||||||
\(788\) | 7.17478 | − | 19.7125i | 0.255591 | − | 0.702230i | ||||
\(789\) | −10.5657 | − | 3.84561i | −0.376150 | − | 0.136907i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.7128 | − | 18.5552i | −0.380905 | − | 0.659746i | ||||
\(792\) | −3.22974 | + | 0.569490i | −0.114764 | + | 0.0202360i | ||||
\(793\) | −4.99069 | + | 5.94767i | −0.177225 | + | 0.211208i | ||||
\(794\) | 6.02693 | − | 5.05720i | 0.213888 | − | 0.179473i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 20.6330 | − | 7.50979i | 0.731317 | − | 0.266178i | ||||
\(797\) | − | 25.2302i | − | 0.893700i | −0.894609 | − | 0.446850i | \(-0.852546\pi\) | ||
0.894609 | − | 0.446850i | \(-0.147454\pi\) | |||||||
\(798\) | −1.80856 | + | 13.6485i | −0.0640224 | + | 0.483150i | ||||
\(799\) | −29.7196 | −1.05140 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.183356 | − | 1.03987i | 0.00647858 | − | 0.0367418i | ||||
\(802\) | −18.7801 | − | 22.3812i | −0.663147 | − | 0.790308i | ||||
\(803\) | 14.6306 | − | 17.4361i | 0.516302 | − | 0.615305i | ||||
\(804\) | −1.18100 | − | 6.69779i | −0.0416507 | − | 0.236213i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.00957698 | + | 0.0165878i | −0.000337335 | + | 0.000584281i | ||||
\(807\) | 12.0014 | − | 32.9736i | 0.422470 | − | 1.16073i | ||||
\(808\) | 1.47517 | − | 4.05300i | 0.0518963 | − | 0.142584i | ||||
\(809\) | −15.2498 | + | 26.4134i | −0.536154 | + | 0.928646i | 0.462952 | + | 0.886383i | \(0.346790\pi\) |
−0.999107 | + | 0.0422629i | \(0.986543\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.35482 | − | 7.68358i | −0.0475742 | − | 0.269807i | 0.951737 | − | 0.306915i | \(-0.0992966\pi\) |
−0.999311 | + | 0.0371078i | \(0.988186\pi\) | |||||||
\(812\) | −0.113779 | + | 0.135597i | −0.00399287 | + | 0.00475852i | ||||
\(813\) | 0.520598 | + | 0.620425i | 0.0182582 | + | 0.0217592i | ||||
\(814\) | 0.545013 | − | 3.09092i | 0.0191027 | − | 0.108337i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −7.52109 | −0.263291 | ||||||||
\(817\) | 25.0181 | − | 1.07118i | 0.875272 | − | 0.0374757i | ||||
\(818\) | 14.1622i | 0.495169i | ||||||||
\(819\) | −2.65373 | + | 0.965879i | −0.0927289 | + | 0.0337505i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 35.2031 | − | 29.5389i | 1.22860 | − | 1.03092i | 0.230269 | − | 0.973127i | \(-0.426040\pi\) |
0.998329 | − | 0.0577885i | \(-0.0184049\pi\) | |||||||
\(822\) | −12.7387 | + | 15.1813i | −0.444312 | + | 0.529510i | ||||
\(823\) | 14.9529 | − | 2.63661i | 0.521227 | − | 0.0919063i | 0.0931558 | − | 0.995652i | \(-0.470305\pi\) |
0.428071 | + | 0.903745i | \(0.359193\pi\) | |||||||
\(824\) | −0.00871870 | − | 0.0151012i | −0.000303730 | − | 0.000526076i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 23.9447 | + | 8.71515i | 0.833141 | + | 0.303239i | ||||
\(827\) | 0.215224 | − | 0.591323i | 0.00748408 | − | 0.0205623i | −0.935894 | − | 0.352281i | \(-0.885406\pi\) |
0.943378 | + | 0.331719i | \(0.107628\pi\) | |||||||
\(828\) | 9.08431 | + | 5.24483i | 0.315701 | + | 0.182270i | ||||
\(829\) | −20.5684 | − | 35.6256i | −0.714372 | − | 1.23733i | −0.963201 | − | 0.268781i | \(-0.913379\pi\) |
0.248830 | − | 0.968547i | \(-0.419954\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.94596 | + | 5.82836i | 0.240953 | + | 0.202183i | ||||
\(832\) | 0.623898 | + | 0.743533i | 0.0216298 | + | 0.0257774i | ||||
\(833\) | −7.64331 | − | 1.34772i | −0.264825 | − | 0.0466958i | ||||
\(834\) | −13.4767 | + | 4.90512i | −0.466660 | + | 0.169851i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −7.10207 | + | 9.23946i | −0.245630 | + | 0.319553i | ||||
\(837\) | 0.111072i | 0.00383921i | ||||||||
\(838\) | −10.2869 | − | 28.2631i | −0.355355 | − | 0.976331i | ||||
\(839\) | 5.04229 | − | 28.5962i | 0.174079 | − | 0.987252i | −0.765122 | − | 0.643885i | \(-0.777321\pi\) |
0.939201 | − | 0.343367i | \(-0.111567\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.2110 | − | 18.6373i | −0.765897 | − | 0.642664i | ||||
\(842\) | −13.4112 | + | 2.36476i | −0.462181 | + | 0.0814950i | ||||
\(843\) | −28.2449 | + | 16.3072i | −0.972807 | + | 0.561650i | ||||
\(844\) | −7.00635 | + | 12.1353i | −0.241168 | + | 0.417716i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.06559 | + | 2.20769i | 0.208539 | + | 0.0759020i | ||||
\(847\) | 7.91296 | + | 4.56855i | 0.271893 | + | 0.156977i | ||||
\(848\) | 0.0770827 | − | 0.0445037i | 0.00264703 | − | 0.00152826i | ||||
\(849\) | −7.47762 | − | 42.4077i | −0.256631 | − | 1.45543i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.69017 | + | 6.45282i | −0.263615 | + | 0.221200i | ||||
\(852\) | −13.6263 | − | 2.40269i | −0.466831 | − | 0.0823149i | ||||
\(853\) | −3.30684 | − | 9.08547i | −0.113224 | − | 0.311081i | 0.870118 | − | 0.492843i | \(-0.164042\pi\) |
−0.983343 | + | 0.181762i | \(0.941820\pi\) | |||||||
\(854\) | −18.9732 | −0.649248 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11.5219 | −0.393811 | ||||||||
\(857\) | −10.1083 | − | 27.7722i | −0.345292 | − | 0.948681i | −0.983832 | − | 0.179093i | \(-0.942684\pi\) |
0.638540 | − | 0.769588i | \(-0.279539\pi\) | |||||||
\(858\) | 3.40311 | + | 0.600059i | 0.116180 | + | 0.0204857i | ||||
\(859\) | −26.3636 | + | 22.1217i | −0.899513 | + | 0.754781i | −0.970095 | − | 0.242725i | \(-0.921959\pi\) |
0.0705819 | + | 0.997506i | \(0.477514\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.01105 | − | 34.0904i | −0.204856 | − | 1.16180i | ||||
\(862\) | 25.6241 | − | 14.7941i | 0.872762 | − | 0.503889i | ||||
\(863\) | 17.3598 | + | 10.0227i | 0.590934 | + | 0.341176i | 0.765467 | − | 0.643475i | \(-0.222508\pi\) |
−0.174533 | + | 0.984651i | \(0.555841\pi\) | |||||||
\(864\) | 5.28906 | + | 1.92506i | 0.179938 | + | 0.0654919i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −0.483102 | + | 0.836757i | −0.0164165 | + | 0.0284342i | ||||
\(867\) | 17.1821 | − | 9.92007i | 0.583533 | − | 0.336903i | ||||
\(868\) | −0.0460953 | + | 0.00812785i | −0.00156458 | + | 0.000275877i | ||||
\(869\) | −32.5469 | − | 27.3101i | −1.10408 | − | 0.926431i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.860802 | − | 4.88185i | 0.0291672 | − | 0.165415i | ||||
\(872\) | −3.20089 | − | 8.79437i | −0.108396 | − | 0.297815i | ||||
\(873\) | − | 13.6241i | − | 0.461105i | ||||||
\(874\) | 36.3973 | − | 8.03688i | 1.23116 | − | 0.271852i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10.6534 | + | 3.87753i | −0.359946 | + | 0.131010i | ||||
\(877\) | 12.1084 | + | 2.13503i | 0.408871 | + | 0.0720949i | 0.374301 | − | 0.927307i | \(-0.377883\pi\) |
0.0345699 | + | 0.999402i | \(0.488994\pi\) | |||||||
\(878\) | −15.1516 | − | 18.0570i | −0.511342 | − | 0.609393i | ||||
\(879\) | 27.2942 | + | 22.9026i | 0.920612 | + | 0.772485i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.3853 | + | 26.6481i | 0.518344 | + | 0.897799i | 0.999773 | + | 0.0213134i | \(0.00678479\pi\) |
−0.481428 | + | 0.876485i | \(0.659882\pi\) | |||||||
\(882\) | 1.45984 | + | 0.842839i | 0.0491554 | + | 0.0283799i | ||||
\(883\) | 13.1283 | − | 36.0696i | 0.441801 | − | 1.21384i | −0.496505 | − | 0.868034i | \(-0.665384\pi\) |
0.938306 | − | 0.345805i | \(-0.112394\pi\) | |||||||
\(884\) | −5.15133 | − | 1.87493i | −0.173258 | − | 0.0630607i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.340438 | − | 0.589656i | −0.0114372 | − | 0.0198099i | ||||
\(887\) | 16.3575 | − | 2.88427i | 0.549232 | − | 0.0968444i | 0.107856 | − | 0.994167i | \(-0.465602\pi\) |
0.441376 | + | 0.897322i | \(0.354490\pi\) | |||||||
\(888\) | −1.00488 | + | 1.19757i | −0.0337215 | + | 0.0401877i | ||||
\(889\) | 17.0304 | − | 14.2902i | 0.571180 | − | 0.479277i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.58492 | − | 3.48862i | 0.321107 | − | 0.116873i | ||||
\(892\) | 15.7296i | 0.526664i | ||||||||
\(893\) | 21.1982 | − | 8.75964i | 0.709370 | − | 0.293130i | ||||
\(894\) | −21.5593 | −0.721050 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.411873 | + | 2.33585i | −0.0137597 | + | 0.0780352i | ||||
\(897\) | −7.10455 | − | 8.46687i | −0.237214 | − | 0.282701i | ||||
\(898\) | 19.0875 | − | 22.7476i | 0.636957 | − | 0.759096i | ||||
\(899\) | 0.000255732 | 0.00145033i | 8.52914e−6 | 4.83712e-5i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.251353 | + | 0.435356i | −0.00837377 | + | 0.0145038i | ||||
\(902\) | 10.0214 | − | 27.5337i | 0.333677 | − | 0.916771i | ||||
\(903\) | 6.20602 | − | 17.0509i | 0.206523 | − | 0.567418i | ||||
\(904\) | −4.51660 | + | 7.82298i | −0.150220 | + | 0.260188i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.41514 | − | 8.02567i | −0.0470150 | − | 0.266635i | ||||
\(907\) | 10.2694 | − | 12.2386i | 0.340989 | − | 0.406375i | −0.568111 | − | 0.822952i | \(-0.692326\pi\) |
0.909101 | + | 0.416576i | \(0.136770\pi\) | |||||||
\(908\) | 5.14988 | + | 6.13739i | 0.170905 | + | 0.203677i | ||||
\(909\) | 0.918740 | − | 5.21043i | 0.0304727 | − | 0.172819i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 55.7482 | 1.84702 | 0.923510 | − | 0.383573i | \(-0.125307\pi\) | ||||
0.923510 | + | 0.383573i | \(0.125307\pi\) | |||||||
\(912\) | 5.36460 | − | 2.21679i | 0.177640 | − | 0.0734053i | ||||
\(913\) | 15.6975i | 0.519513i | ||||||||
\(914\) | 2.54950 | − | 0.927941i | 0.0843299 | − | 0.0306936i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15.2309 | − | 12.7803i | 0.503244 | − | 0.422272i | ||||
\(917\) | 9.52487 | − | 11.3513i | 0.314539 | − | 0.374853i | ||||
\(918\) | −31.3063 | + | 5.52014i | −1.03326 | + | 0.182192i | ||||
\(919\) | 20.2845 | + | 35.1339i | 0.669126 | + | 1.15896i | 0.978149 | + | 0.207905i | \(0.0666645\pi\) |
−0.309023 | + | 0.951054i | \(0.600002\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.7083 | + | 5.35338i | 0.484654 | + | 0.176400i | ||||
\(922\) | −10.0704 | + | 27.6683i | −0.331652 | + | 0.911206i | ||||
\(923\) | −8.73397 | − | 5.04256i | −0.287482 | − | 0.165978i | ||||
\(924\) | 4.22222 | + | 7.31310i | 0.138901 | + | 0.240583i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 24.4144 | + | 20.4861i | 0.802306 | + | 0.673215i | ||||
\(927\) | −0.0137493 | − | 0.0163858i | −0.000451587 | − | 0.000538180i | ||||
\(928\) | 0.0734944 | + | 0.0129590i | 0.00241257 | + | 0.000425401i | ||||
\(929\) | 22.3308 | − | 8.12775i | 0.732650 | − | 0.266663i | 0.0513639 | − | 0.998680i | \(-0.483643\pi\) |
0.681286 | + | 0.732017i | \(0.261421\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.84901 | − | 1.29152i | 0.191694 | − | 0.0423279i | ||||
\(932\) | − | 24.9482i | − | 0.817206i | ||||||
\(933\) | 4.51551 | + | 12.4063i | 0.147831 | + | 0.406163i | ||||
\(934\) | −6.62954 | + | 37.5980i | −0.216925 | + | 1.23024i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.912078 | + | 0.765324i | 0.0298122 | + | 0.0250154i | ||||
\(937\) | 29.2148 | − | 5.15136i | 0.954406 | − | 0.168288i | 0.325303 | − | 0.945610i | \(-0.394534\pi\) |
0.629103 | + | 0.777322i | \(0.283423\pi\) | |||||||
\(938\) | 10.4908 | − | 6.05689i | 0.342538 | − | 0.197765i | ||||
\(939\) | −0.239107 | + | 0.414145i | −0.00780296 | + | 0.0135151i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −47.7023 | − | 17.3622i | −1.55505 | − | 0.565993i | −0.585456 | − | 0.810704i | \(-0.699084\pi\) |
−0.969596 | + | 0.244712i | \(0.921307\pi\) | |||||||
\(942\) | −24.3176 | − | 14.0398i | −0.792309 | − | 0.457440i | ||||
\(943\) | −81.1622 | + | 46.8590i | −2.64301 | + | 1.52594i | ||||
\(944\) | −1.86552 | − | 10.5799i | −0.0607175 | − | 0.344346i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11.7656 | − | 9.87250i | 0.382532 | − | 0.320983i | ||||
\(947\) | 23.2192 | + | 4.09416i | 0.754521 | + | 0.133042i | 0.537662 | − | 0.843160i | \(-0.319308\pi\) |
0.216859 | + | 0.976203i | \(0.430419\pi\) | |||||||
\(948\) | 7.23796 | + | 19.8861i | 0.235078 | + | 0.645871i | ||||
\(949\) | −8.26335 | −0.268240 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −34.5514 | −1.12041 | ||||||||
\(952\) | −4.58175 | − | 12.5883i | −0.148496 | − | 0.407988i | ||||
\(953\) | 28.9205 | + | 5.09946i | 0.936825 | + | 0.165188i | 0.621161 | − | 0.783683i | \(-0.286661\pi\) |
0.315665 | + | 0.948871i | \(0.397773\pi\) | |||||||
\(954\) | 0.0836396 | − | 0.0701820i | 0.00270793 | − | 0.00227223i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.84832 | + | 10.4823i | 0.0597788 | + | 0.339022i | ||||
\(957\) | 0.230097 | − | 0.132847i | 0.00743798 | − | 0.00429432i | ||||
\(958\) | −25.3342 | − | 14.6267i | −0.818509 | − | 0.472567i | ||||
\(959\) | −33.1697 | − | 12.0728i | −1.07111 | − | 0.389851i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.4998 | − | 26.8465i | 0.499994 | − | 0.866015i | ||||
\(962\) | −0.986800 | + | 0.569729i | −0.0318157 | + | 0.0183688i | ||||
\(963\) | −13.9190 | + | 2.45429i | −0.448533 | + | 0.0790885i | ||||
\(964\) | 12.8701 | + | 10.7993i | 0.414517 | + | 0.347821i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 4.69014 | − | 26.5991i | 0.150903 | − | 0.855812i | ||||
\(967\) | −8.41119 | − | 23.1096i | −0.270486 | − | 0.743153i | −0.998349 | − | 0.0574316i | \(-0.981709\pi\) |
0.727864 | − | 0.685722i | \(-0.240513\pi\) | |||||||
\(968\) | − | 3.85226i | − | 0.123816i | ||||||
\(969\) | −19.9793 | + | 25.9922i | −0.641829 | + | 0.834989i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.8954 | + | 6.14944i | −0.542200 | + | 0.197345i | −0.598578 | − | 0.801065i | \(-0.704267\pi\) |
0.0563774 | + | 0.998410i | \(0.482045\pi\) | |||||||
\(972\) | 11.6256 | + | 2.04991i | 0.372891 | + | 0.0657508i | ||||
\(973\) | −16.4197 | − | 19.5682i | −0.526392 | − | 0.627329i | ||||
\(974\) | 11.1655 | + | 9.36898i | 0.357766 | + | 0.300201i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.99960 | + | 6.92751i | 0.128024 | + | 0.221744i | ||||
\(977\) | 3.40407 | + | 1.96534i | 0.108906 | + | 0.0628768i | 0.553464 | − | 0.832873i | \(-0.313306\pi\) |
−0.444558 | + | 0.895750i | \(0.646639\pi\) | |||||||
\(978\) | 7.38393 | − | 20.2872i | 0.236112 | − | 0.648713i | ||||
\(979\) | −2.16254 | − | 0.787100i | −0.0691151 | − | 0.0251558i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.74012 | − | 9.94218i | −0.183268 | − | 0.317429i | ||||
\(982\) | −6.55990 | + | 1.15669i | −0.209335 | + | 0.0369114i | ||||
\(983\) | −1.17464 | + | 1.39988i | −0.0374651 | + | 0.0446492i | −0.784452 | − | 0.620190i | \(-0.787055\pi\) |
0.746987 | + | 0.664839i | \(0.231500\pi\) | |||||||
\(984\) | −11.1800 | + | 9.38112i | −0.356405 | + | 0.299059i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.396073 | + | 0.144159i | −0.0126135 | + | 0.00459096i | ||||
\(987\) | − | 16.6204i | − | 0.529033i | ||||||
\(988\) | 4.22693 | − | 0.180981i | 0.134477 | − | 0.00575776i | ||||
\(989\) | −49.1252 | −1.56209 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.21061 | + | 6.86571i | −0.0384563 | + | 0.218096i | −0.997980 | − | 0.0635322i | \(-0.979763\pi\) |
0.959524 | + | 0.281628i | \(0.0908746\pi\) | |||||||
\(992\) | 0.0126847 | + | 0.0151170i | 0.000402739 | + | 0.000479966i | ||||
\(993\) | −11.5077 | + | 13.7143i | −0.365186 | + | 0.435211i | ||||
\(994\) | −4.27955 | − | 24.2705i | −0.135739 | − | 0.769814i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3.90940 | − | 6.77129i | 0.123874 | − | 0.214556i | ||||
\(997\) | −1.80015 | + | 4.94588i | −0.0570115 | + | 0.156638i | −0.964929 | − | 0.262511i | \(-0.915449\pi\) |
0.907917 | + | 0.419149i | \(0.137672\pi\) | |||||||
\(998\) | 1.66356 | − | 4.57058i | 0.0526589 | − | 0.144679i | ||||
\(999\) | −3.30381 | + | 5.72237i | −0.104528 | + | 0.181048i |
(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 | 950.2.u.e.499.3 | 24 | ||
5.2 | odd | 4 | 950.2.l.h.651.1 | 12 | |||
5.3 | odd | 4 | 190.2.k.b.81.2 | yes | 12 | ||
5.4 | even | 2 | inner | 950.2.u.e.499.2 | 24 | ||
19.4 | even | 9 | inner | 950.2.u.e.99.2 | 24 | ||
95.4 | even | 18 | inner | 950.2.u.e.99.3 | 24 | ||
95.23 | odd | 36 | 190.2.k.b.61.2 | ✓ | 12 | ||
95.42 | odd | 36 | 950.2.l.h.251.1 | 12 | |||
95.78 | even | 36 | 3610.2.a.be.1.3 | 6 | |||
95.93 | odd | 36 | 3610.2.a.bc.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
190.2.k.b.61.2 | ✓ | 12 | 95.23 | odd | 36 | ||
190.2.k.b.81.2 | yes | 12 | 5.3 | odd | 4 | ||
950.2.l.h.251.1 | 12 | 95.42 | odd | 36 | |||
950.2.l.h.651.1 | 12 | 5.2 | odd | 4 | |||
950.2.u.e.99.2 | 24 | 19.4 | even | 9 | inner | ||
950.2.u.e.99.3 | 24 | 95.4 | even | 18 | inner | ||
950.2.u.e.499.2 | 24 | 5.4 | even | 2 | inner | ||
950.2.u.e.499.3 | 24 | 1.1 | even | 1 | trivial | ||
3610.2.a.bc.1.4 | 6 | 95.93 | odd | 36 | |||
3610.2.a.be.1.3 | 6 | 95.78 | even | 36 |